Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(25,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 8, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.bb (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 25.11 | ||
Character | \(\chi\) | \(=\) | 429.25 |
Dual form | 429.2.bb.a.103.11 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.897576 | + | 1.23541i | 0.634682 | + | 0.873565i | 0.998318 | − | 0.0579763i | \(-0.0184648\pi\) |
−0.363636 | + | 0.931541i | \(0.618465\pi\) | |||||||
\(3\) | 0.309017 | + | 0.951057i | 0.178411 | + | 0.549093i | ||||
\(4\) | −0.102555 | + | 0.315631i | −0.0512773 | + | 0.157815i | ||||
\(5\) | −0.900087 | + | 1.23886i | −0.402531 | + | 0.554037i | −0.961377 | − | 0.275235i | \(-0.911244\pi\) |
0.558846 | + | 0.829272i | \(0.311244\pi\) | |||||||
\(6\) | −0.897576 | + | 1.23541i | −0.366434 | + | 0.504353i | ||||
\(7\) | 2.72966 | + | 0.886920i | 1.03171 | + | 0.335224i | 0.775468 | − | 0.631387i | \(-0.217514\pi\) |
0.256247 | + | 0.966611i | \(0.417514\pi\) | |||||||
\(8\) | 2.42263 | − | 0.787161i | 0.856530 | − | 0.278304i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | −2.33840 | −0.739466 | ||||||||
\(11\) | 2.52359 | − | 2.15209i | 0.760890 | − | 0.648881i | ||||
\(12\) | −0.331874 | −0.0958037 | ||||||||
\(13\) | 0.547996 | + | 3.56366i | 0.151987 | + | 0.988383i | ||||
\(14\) | 1.35437 | + | 4.16832i | 0.361970 | + | 1.11403i | ||||
\(15\) | −1.45637 | − | 0.473204i | −0.376034 | − | 0.122181i | ||||
\(16\) | 3.68395 | + | 2.67654i | 0.920986 | + | 0.669136i | ||||
\(17\) | −4.09764 | − | 2.97711i | −0.993825 | − | 0.722056i | −0.0330693 | − | 0.999453i | \(-0.510528\pi\) |
−0.960755 | + | 0.277397i | \(0.910528\pi\) | |||||||
\(18\) | −1.45231 | − | 0.471884i | −0.342312 | − | 0.111224i | ||||
\(19\) | −5.66469 | + | 1.84057i | −1.29957 | + | 0.422255i | −0.875431 | − | 0.483343i | \(-0.839423\pi\) |
−0.424137 | + | 0.905598i | \(0.639423\pi\) | |||||||
\(20\) | −0.298715 | − | 0.411146i | −0.0667948 | − | 0.0919351i | ||||
\(21\) | 2.87013i | 0.626315i | ||||||||
\(22\) | 4.92382 | + | 1.18599i | 1.04976 | + | 0.252854i | ||||
\(23\) | −7.08980 | −1.47833 | −0.739163 | − | 0.673527i | \(-0.764779\pi\) | ||||
−0.739163 | + | 0.673527i | \(0.764779\pi\) | |||||||
\(24\) | 1.49727 | + | 2.06082i | 0.305629 | + | 0.420662i | ||||
\(25\) | 0.820459 | + | 2.52511i | 0.164092 | + | 0.505022i | ||||
\(26\) | −3.91071 | + | 3.87566i | −0.766953 | + | 0.760079i | ||||
\(27\) | −0.809017 | − | 0.587785i | −0.155695 | − | 0.113119i | ||||
\(28\) | −0.559879 | + | 0.770607i | −0.105807 | + | 0.145631i | ||||
\(29\) | 2.11547 | − | 6.51076i | 0.392833 | − | 1.20902i | −0.537803 | − | 0.843071i | \(-0.680745\pi\) |
0.930636 | − | 0.365946i | \(-0.119255\pi\) | |||||||
\(30\) | −0.722605 | − | 2.22395i | −0.131929 | − | 0.406036i | ||||
\(31\) | −0.0788687 | − | 0.108553i | −0.0141652 | − | 0.0194968i | 0.801876 | − | 0.597491i | \(-0.203836\pi\) |
−0.816041 | + | 0.577994i | \(0.803836\pi\) | |||||||
\(32\) | 1.85896i | 0.328621i | ||||||||
\(33\) | 2.82659 | + | 1.73504i | 0.492047 | + | 0.302032i | ||||
\(34\) | − | 7.73444i | − | 1.32645i | ||||||
\(35\) | −3.55570 | + | 2.58337i | −0.601024 | + | 0.436669i | ||||
\(36\) | −0.102555 | − | 0.315631i | −0.0170924 | − | 0.0526051i | ||||
\(37\) | 2.68440 | + | 0.872214i | 0.441313 | + | 0.143391i | 0.521241 | − | 0.853409i | \(-0.325469\pi\) |
−0.0799285 | + | 0.996801i | \(0.525469\pi\) | |||||||
\(38\) | −7.35834 | − | 5.34615i | −1.19368 | − | 0.867260i | ||||
\(39\) | −3.21991 | + | 1.62241i | −0.515598 | + | 0.259793i | ||||
\(40\) | −1.20540 | + | 3.70983i | −0.190590 | + | 0.586575i | ||||
\(41\) | 8.76999 | − | 2.84954i | 1.36964 | − | 0.445024i | 0.470392 | − | 0.882458i | \(-0.344113\pi\) |
0.899250 | + | 0.437434i | \(0.144113\pi\) | |||||||
\(42\) | −3.54578 | + | 2.57616i | −0.547126 | + | 0.397511i | ||||
\(43\) | 5.67881 | 0.866011 | 0.433005 | − | 0.901391i | \(-0.357453\pi\) | ||||
0.433005 | + | 0.901391i | \(0.357453\pi\) | |||||||
\(44\) | 0.420462 | + | 1.01723i | 0.0633870 | + | 0.153353i | ||||
\(45\) | − | 1.53132i | − | 0.228276i | ||||||
\(46\) | −6.36364 | − | 8.75879i | −0.938267 | − | 1.29141i | ||||
\(47\) | 7.76525 | − | 2.52308i | 1.13268 | − | 0.368029i | 0.318085 | − | 0.948062i | \(-0.396960\pi\) |
0.814593 | + | 0.580033i | \(0.196960\pi\) | |||||||
\(48\) | −1.40714 | + | 4.33074i | −0.203103 | + | 0.625088i | ||||
\(49\) | 1.00129 | + | 0.727483i | 0.143042 | + | 0.103926i | ||||
\(50\) | −2.38312 | + | 3.28008i | −0.337024 | + | 0.463873i | ||||
\(51\) | 1.56516 | − | 4.81707i | 0.219166 | − | 0.674525i | ||||
\(52\) | −1.18100 | − | 0.192506i | −0.163775 | − | 0.0266958i | ||||
\(53\) | 5.50546 | − | 3.99995i | 0.756233 | − | 0.549435i | −0.141520 | − | 0.989935i | \(-0.545199\pi\) |
0.897753 | + | 0.440500i | \(0.145199\pi\) | |||||||
\(54\) | − | 1.52705i | − | 0.207805i | ||||||
\(55\) | 0.394704 | + | 5.06345i | 0.0532219 | + | 0.682756i | ||||
\(56\) | 7.31111 | 0.976989 | ||||||||
\(57\) | −3.50097 | − | 4.81867i | −0.463715 | − | 0.638249i | ||||
\(58\) | 9.94223 | − | 3.23043i | 1.30548 | − | 0.424176i | ||||
\(59\) | −12.8943 | − | 4.18961i | −1.67870 | − | 0.545441i | −0.694038 | − | 0.719938i | \(-0.744170\pi\) |
−0.984658 | + | 0.174497i | \(0.944170\pi\) | |||||||
\(60\) | 0.298715 | − | 0.411146i | 0.0385640 | − | 0.0530788i | ||||
\(61\) | −8.81938 | − | 6.40765i | −1.12921 | − | 0.820416i | −0.143627 | − | 0.989632i | \(-0.545876\pi\) |
−0.985579 | + | 0.169216i | \(0.945876\pi\) | |||||||
\(62\) | 0.0633171 | − | 0.194870i | 0.00804128 | − | 0.0247485i | ||||
\(63\) | −2.72966 | + | 0.886920i | −0.343905 | + | 0.111741i | ||||
\(64\) | 5.07132 | − | 3.68453i | 0.633915 | − | 0.460566i | ||||
\(65\) | −4.90814 | − | 2.52872i | −0.608780 | − | 0.313649i | ||||
\(66\) | 0.393603 | + | 5.04933i | 0.0484492 | + | 0.621529i | ||||
\(67\) | 1.96611i | 0.240199i | 0.992762 | + | 0.120099i | \(0.0383213\pi\) | ||||
−0.992762 | + | 0.120099i | \(0.961679\pi\) | |||||||
\(68\) | 1.35990 | − | 0.988026i | 0.164912 | − | 0.119816i | ||||
\(69\) | −2.19087 | − | 6.74280i | −0.263750 | − | 0.811738i | ||||
\(70\) | −6.38303 | − | 2.07397i | −0.762918 | − | 0.247887i | ||||
\(71\) | 1.56752 | − | 2.15751i | 0.186031 | − | 0.256050i | −0.705808 | − | 0.708404i | \(-0.749416\pi\) |
0.891838 | + | 0.452354i | \(0.149416\pi\) | |||||||
\(72\) | −1.49727 | + | 2.06082i | −0.176455 | + | 0.242869i | ||||
\(73\) | −4.32333 | − | 1.40473i | −0.506007 | − | 0.164412i | 0.0448783 | − | 0.998992i | \(-0.485710\pi\) |
−0.550886 | + | 0.834581i | \(0.685710\pi\) | |||||||
\(74\) | 1.33191 | + | 4.09921i | 0.154832 | + | 0.476523i | ||||
\(75\) | −2.14799 | + | 1.56061i | −0.248028 | + | 0.180203i | ||||
\(76\) | − | 1.97671i | − | 0.226744i | ||||||
\(77\) | 8.79727 | − | 3.63627i | 1.00254 | − | 0.414391i | ||||
\(78\) | −4.89444 | − | 2.52166i | −0.554187 | − | 0.285522i | ||||
\(79\) | 1.31096 | − | 0.952470i | 0.147495 | − | 0.107161i | −0.511591 | − | 0.859229i | \(-0.670944\pi\) |
0.659085 | + | 0.752068i | \(0.270944\pi\) | |||||||
\(80\) | −6.63174 | + | 2.15478i | −0.741452 | + | 0.240912i | ||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 11.3921 | + | 8.27683i | 1.25804 | + | 0.914023i | ||||
\(83\) | −2.15267 | + | 2.96290i | −0.236286 | + | 0.325220i | −0.910650 | − | 0.413180i | \(-0.864418\pi\) |
0.674363 | + | 0.738400i | \(0.264418\pi\) | |||||||
\(84\) | −0.905903 | − | 0.294346i | −0.0988421 | − | 0.0321157i | ||||
\(85\) | 7.37647 | − | 2.39676i | 0.800091 | − | 0.259965i | ||||
\(86\) | 5.09717 | + | 7.01565i | 0.549642 | + | 0.756517i | ||||
\(87\) | 6.84581 | 0.733948 | ||||||||
\(88\) | 4.41968 | − | 7.20021i | 0.471139 | − | 0.767545i | ||||
\(89\) | 12.8685i | 1.36406i | 0.731323 | + | 0.682031i | \(0.238903\pi\) | ||||
−0.731323 | + | 0.682031i | \(0.761097\pi\) | |||||||
\(90\) | 1.89180 | − | 1.37448i | 0.199414 | − | 0.144882i | ||||
\(91\) | −1.66484 | + | 10.2136i | −0.174523 | + | 1.07068i | ||||
\(92\) | 0.727092 | − | 2.23776i | 0.0758046 | − | 0.233303i | ||||
\(93\) | 0.0788687 | − | 0.108553i | 0.00817830 | − | 0.0112565i | ||||
\(94\) | 10.0869 | + | 7.32858i | 1.04039 | + | 0.755886i | ||||
\(95\) | 2.81850 | − | 8.67445i | 0.289172 | − | 0.889980i | ||||
\(96\) | −1.76797 | + | 0.574450i | −0.180443 | + | 0.0586295i | ||||
\(97\) | −2.14642 | − | 2.95430i | −0.217936 | − | 0.299964i | 0.686025 | − | 0.727578i | \(-0.259354\pi\) |
−0.903961 | + | 0.427614i | \(0.859354\pi\) | |||||||
\(98\) | 1.88998i | 0.190917i | ||||||||
\(99\) | −0.776655 | + | 3.22441i | −0.0780567 | + | 0.324065i | ||||
\(100\) | −0.881145 | −0.0881145 | ||||||||
\(101\) | −16.0155 | + | 11.6359i | −1.59360 | + | 1.15782i | −0.695034 | + | 0.718977i | \(0.744611\pi\) |
−0.898565 | + | 0.438840i | \(0.855389\pi\) | |||||||
\(102\) | 7.35589 | − | 2.39007i | 0.728342 | − | 0.236653i | ||||
\(103\) | 5.75706 | − | 17.7184i | 0.567260 | − | 1.74585i | −0.0938797 | − | 0.995584i | \(-0.529927\pi\) |
0.661140 | − | 0.750263i | \(-0.270073\pi\) | |||||||
\(104\) | 4.13277 | + | 8.20209i | 0.405252 | + | 0.804281i | ||||
\(105\) | −3.55570 | − | 2.58337i | −0.347001 | − | 0.252111i | ||||
\(106\) | 9.88313 | + | 3.21122i | 0.959935 | + | 0.311902i | ||||
\(107\) | −3.83803 | − | 11.8122i | −0.371036 | − | 1.14193i | −0.946114 | − | 0.323833i | \(-0.895028\pi\) |
0.575078 | − | 0.818098i | \(-0.304972\pi\) | |||||||
\(108\) | 0.268492 | − | 0.195071i | 0.0258356 | − | 0.0187707i | ||||
\(109\) | 6.88249i | 0.659223i | 0.944117 | + | 0.329611i | \(0.106918\pi\) | ||||
−0.944117 | + | 0.329611i | \(0.893082\pi\) | |||||||
\(110\) | −5.90115 | + | 5.03245i | −0.562652 | + | 0.479826i | ||||
\(111\) | 2.82255i | 0.267904i | ||||||||
\(112\) | 7.68204 | + | 10.5734i | 0.725884 | + | 0.999094i | ||||
\(113\) | −0.676498 | − | 2.08205i | −0.0636395 | − | 0.195862i | 0.914181 | − | 0.405306i | \(-0.132835\pi\) |
−0.977821 | + | 0.209443i | \(0.932835\pi\) | |||||||
\(114\) | 2.81064 | − | 8.65025i | 0.263240 | − | 0.810170i | ||||
\(115\) | 6.38144 | − | 8.78330i | 0.595072 | − | 0.819047i | ||||
\(116\) | 1.83804 | + | 1.33542i | 0.170658 | + | 0.123990i | ||||
\(117\) | −2.53801 | − | 2.56096i | −0.234639 | − | 0.236761i | ||||
\(118\) | −6.39774 | − | 19.6902i | −0.588960 | − | 1.81263i | ||||
\(119\) | −8.54471 | − | 11.7608i | −0.783292 | − | 1.07811i | ||||
\(120\) | −3.90074 | −0.356087 | ||||||||
\(121\) | 1.73698 | − | 10.8620i | 0.157907 | − | 0.987454i | ||||
\(122\) | − | 16.6469i | − | 1.50714i | ||||||
\(123\) | 5.42015 | + | 7.46020i | 0.488719 | + | 0.672663i | ||||
\(124\) | 0.0423512 | − | 0.0137607i | 0.00380325 | − | 0.00123575i | ||||
\(125\) | −11.1486 | − | 3.62240i | −0.997162 | − | 0.323998i | ||||
\(126\) | −3.54578 | − | 2.57616i | −0.315884 | − | 0.229503i | ||||
\(127\) | 12.4065 | + | 9.01387i | 1.10090 | + | 0.799851i | 0.981207 | − | 0.192959i | \(-0.0618086\pi\) |
0.119694 | + | 0.992811i | \(0.461809\pi\) | |||||||
\(128\) | 12.6397 | + | 4.10690i | 1.11721 | + | 0.363002i | ||||
\(129\) | 1.75485 | + | 5.40087i | 0.154506 | + | 0.475520i | ||||
\(130\) | −1.28143 | − | 8.33326i | −0.112389 | − | 0.730876i | ||||
\(131\) | 12.4277 | 1.08581 | 0.542905 | − | 0.839794i | \(-0.317324\pi\) | ||||
0.542905 | + | 0.839794i | \(0.317324\pi\) | |||||||
\(132\) | −0.837512 | + | 0.714224i | −0.0728961 | + | 0.0621652i | ||||
\(133\) | −17.0951 | −1.48233 | ||||||||
\(134\) | −2.42895 | + | 1.76474i | −0.209829 | + | 0.152450i | ||||
\(135\) | 1.45637 | − | 0.473204i | 0.125345 | − | 0.0407269i | ||||
\(136\) | −12.2706 | − | 3.98695i | −1.05219 | − | 0.341878i | ||||
\(137\) | −2.56231 | + | 3.52672i | −0.218913 | + | 0.301308i | −0.904323 | − | 0.426850i | \(-0.859623\pi\) |
0.685409 | + | 0.728158i | \(0.259623\pi\) | |||||||
\(138\) | 6.36364 | − | 8.75879i | 0.541709 | − | 0.745598i | ||||
\(139\) | −3.98164 | + | 12.2542i | −0.337718 | + | 1.03939i | 0.627650 | + | 0.778496i | \(0.284017\pi\) |
−0.965368 | + | 0.260893i | \(0.915983\pi\) | |||||||
\(140\) | −0.450737 | − | 1.38723i | −0.0380942 | − | 0.117242i | ||||
\(141\) | 4.79919 | + | 6.60551i | 0.404164 | + | 0.556285i | ||||
\(142\) | 4.07238 | 0.341746 | ||||||||
\(143\) | 9.05226 | + | 7.81388i | 0.756988 | + | 0.653429i | ||||
\(144\) | −4.55361 | −0.379467 | ||||||||
\(145\) | 6.16183 | + | 8.48103i | 0.511712 | + | 0.704311i | ||||
\(146\) | −2.14510 | − | 6.60193i | −0.177529 | − | 0.546379i | ||||
\(147\) | −0.382461 | + | 1.17709i | −0.0315448 | + | 0.0970850i | ||||
\(148\) | −0.550595 | + | 0.757830i | −0.0452587 | + | 0.0622932i | ||||
\(149\) | −6.95271 | + | 9.56958i | −0.569588 | + | 0.783971i | −0.992506 | − | 0.122197i | \(-0.961006\pi\) |
0.422918 | + | 0.906168i | \(0.361006\pi\) | |||||||
\(150\) | −3.85597 | − | 1.25288i | −0.314838 | − | 0.102297i | ||||
\(151\) | 14.3594 | − | 4.66565i | 1.16855 | − | 0.379685i | 0.340448 | − | 0.940263i | \(-0.389421\pi\) |
0.828101 | + | 0.560578i | \(0.189421\pi\) | |||||||
\(152\) | −12.2746 | + | 8.91805i | −0.995605 | + | 0.723349i | ||||
\(153\) | 5.06497 | 0.409478 | ||||||||
\(154\) | 12.3885 | + | 7.60438i | 0.998293 | + | 0.612779i | ||||
\(155\) | 0.205472 | 0.0165039 | ||||||||
\(156\) | −0.181865 | − | 1.18269i | −0.0145609 | − | 0.0946907i | ||||
\(157\) | −4.46800 | − | 13.7511i | −0.356585 | − | 1.09746i | −0.955085 | − | 0.296333i | \(-0.904236\pi\) |
0.598499 | − | 0.801123i | \(-0.295764\pi\) | |||||||
\(158\) | 2.35338 | + | 0.764659i | 0.187225 | + | 0.0608330i | ||||
\(159\) | 5.50546 | + | 3.99995i | 0.436611 | + | 0.317217i | ||||
\(160\) | −2.30300 | − | 1.67322i | −0.182068 | − | 0.132280i | ||||
\(161\) | −19.3527 | − | 6.28809i | −1.52521 | − | 0.495571i | ||||
\(162\) | 1.45231 | − | 0.471884i | 0.114104 | − | 0.0370747i | ||||
\(163\) | −4.57149 | − | 6.29211i | −0.358067 | − | 0.492836i | 0.591542 | − | 0.806274i | \(-0.298519\pi\) |
−0.949609 | + | 0.313438i | \(0.898519\pi\) | |||||||
\(164\) | 3.06031i | 0.238970i | ||||||||
\(165\) | −4.69366 | + | 1.94008i | −0.365401 | + | 0.151035i | ||||
\(166\) | −5.59257 | −0.434068 | ||||||||
\(167\) | −6.28511 | − | 8.65071i | −0.486356 | − | 0.669412i | 0.493354 | − | 0.869828i | \(-0.335771\pi\) |
−0.979711 | + | 0.200416i | \(0.935771\pi\) | |||||||
\(168\) | 2.25926 | + | 6.95328i | 0.174306 | + | 0.536457i | ||||
\(169\) | −12.3994 | + | 3.90575i | −0.953800 | + | 0.300442i | ||||
\(170\) | 9.58192 | + | 6.96167i | 0.734900 | + | 0.533936i | ||||
\(171\) | 3.50097 | − | 4.81867i | 0.267726 | − | 0.368493i | ||||
\(172\) | −0.582389 | + | 1.79241i | −0.0444067 | + | 0.136670i | ||||
\(173\) | 5.08024 | + | 15.6354i | 0.386244 | + | 1.18874i | 0.935574 | + | 0.353131i | \(0.114883\pi\) |
−0.549330 | + | 0.835605i | \(0.685117\pi\) | |||||||
\(174\) | 6.14464 | + | 8.45737i | 0.465824 | + | 0.641151i | ||||
\(175\) | 7.62038i | 0.576046i | ||||||||
\(176\) | 15.0569 | − | 1.17371i | 1.13496 | − | 0.0884719i | ||||
\(177\) | − | 13.5579i | − | 1.01907i | ||||||
\(178\) | −15.8979 | + | 11.5505i | −1.19160 | + | 0.865746i | ||||
\(179\) | −0.286173 | − | 0.880749i | −0.0213896 | − | 0.0658303i | 0.939792 | − | 0.341747i | \(-0.111019\pi\) |
−0.961182 | + | 0.275917i | \(0.911019\pi\) | |||||||
\(180\) | 0.483332 | + | 0.157044i | 0.0360254 | + | 0.0117054i | ||||
\(181\) | 3.71819 | + | 2.70142i | 0.276371 | + | 0.200795i | 0.717333 | − | 0.696731i | \(-0.245363\pi\) |
−0.440962 | + | 0.897526i | \(0.645363\pi\) | |||||||
\(182\) | −14.1123 | + | 7.11074i | −1.04607 | + | 0.527083i | ||||
\(183\) | 3.36870 | − | 10.3678i | 0.249022 | − | 0.766410i | ||||
\(184\) | −17.1760 | + | 5.58082i | −1.26623 | + | 0.411423i | ||||
\(185\) | −3.49675 | + | 2.54054i | −0.257086 | + | 0.186784i | ||||
\(186\) | 0.204898 | 0.0150239 | ||||||||
\(187\) | −16.7478 | + | 1.30552i | −1.22472 | + | 0.0954689i | ||||
\(188\) | 2.70970i | 0.197626i | ||||||||
\(189\) | −1.68702 | − | 2.32199i | −0.122713 | − | 0.168900i | ||||
\(190\) | 13.2463 | − | 4.30398i | 0.960987 | − | 0.312244i | ||||
\(191\) | −1.23007 | + | 3.78578i | −0.0890050 | + | 0.273929i | −0.985645 | − | 0.168831i | \(-0.946001\pi\) |
0.896640 | + | 0.442760i | \(0.146001\pi\) | |||||||
\(192\) | 5.07132 | + | 3.68453i | 0.365991 | + | 0.265908i | ||||
\(193\) | −1.01433 | + | 1.39611i | −0.0730132 | + | 0.100494i | −0.843962 | − | 0.536403i | \(-0.819783\pi\) |
0.770948 | + | 0.636897i | \(0.219783\pi\) | |||||||
\(194\) | 1.72318 | − | 5.30342i | 0.123717 | − | 0.380763i | ||||
\(195\) | 0.888254 | − | 5.44933i | 0.0636092 | − | 0.390235i | ||||
\(196\) | −0.332304 | + | 0.241433i | −0.0237360 | + | 0.0172452i | ||||
\(197\) | 6.15199i | 0.438311i | 0.975690 | + | 0.219156i | \(0.0703302\pi\) | ||||
−0.975690 | + | 0.219156i | \(0.929670\pi\) | |||||||
\(198\) | −4.68056 | + | 1.93467i | −0.332633 | + | 0.137491i | ||||
\(199\) | −20.1505 | −1.42843 | −0.714215 | − | 0.699926i | \(-0.753216\pi\) | ||||
−0.714215 | + | 0.699926i | \(0.753216\pi\) | |||||||
\(200\) | 3.97534 | + | 5.47159i | 0.281099 | + | 0.386900i | ||||
\(201\) | −1.86988 | + | 0.607562i | −0.131891 | + | 0.0428541i | ||||
\(202\) | −28.7502 | − | 9.34151i | −2.02286 | − | 0.657266i | ||||
\(203\) | 11.5490 | − | 15.8959i | 0.810584 | − | 1.11567i | ||||
\(204\) | 1.35990 | + | 0.988026i | 0.0952121 | + | 0.0691756i | ||||
\(205\) | −4.36356 | + | 13.4297i | −0.304764 | + | 0.937968i | ||||
\(206\) | 27.0568 | − | 8.79130i | 1.88514 | − | 0.612519i | ||||
\(207\) | 5.73577 | − | 4.16728i | 0.398664 | − | 0.289646i | ||||
\(208\) | −7.51951 | + | 14.5951i | −0.521385 | + | 1.01199i | ||||
\(209\) | −10.3343 | + | 16.8358i | −0.714835 | + | 1.16456i | ||||
\(210\) | − | 6.71151i | − | 0.463139i | ||||||
\(211\) | −9.08393 | + | 6.59986i | −0.625364 | + | 0.454353i | −0.854791 | − | 0.518973i | \(-0.826315\pi\) |
0.229427 | + | 0.973326i | \(0.426315\pi\) | |||||||
\(212\) | 0.697897 | + | 2.14791i | 0.0479317 | + | 0.147519i | ||||
\(213\) | 2.53631 | + | 0.824096i | 0.173785 | + | 0.0564661i | ||||
\(214\) | 11.1480 | − | 15.3439i | 0.762061 | − | 1.04889i | ||||
\(215\) | −5.11143 | + | 7.03528i | −0.348596 | + | 0.479802i | ||||
\(216\) | −2.42263 | − | 0.787161i | −0.164839 | − | 0.0535595i | ||||
\(217\) | −0.119006 | − | 0.366264i | −0.00807868 | − | 0.0248636i | ||||
\(218\) | −8.50268 | + | 6.17756i | −0.575874 | + | 0.418397i | ||||
\(219\) | − | 4.54582i | − | 0.307178i | ||||||
\(220\) | −1.63866 | − | 0.394700i | −0.110478 | − | 0.0266107i | ||||
\(221\) | 8.36394 | − | 16.2341i | 0.562619 | − | 1.09202i | ||||
\(222\) | −3.48699 | + | 2.53345i | −0.234032 | + | 0.170034i | ||||
\(223\) | 19.7805 | − | 6.42709i | 1.32460 | − | 0.430390i | 0.440530 | − | 0.897738i | \(-0.354791\pi\) |
0.884073 | + | 0.467348i | \(0.154791\pi\) | |||||||
\(224\) | −1.64875 | + | 5.07432i | −0.110162 | + | 0.339043i | ||||
\(225\) | −2.14799 | − | 1.56061i | −0.143199 | − | 0.104040i | ||||
\(226\) | 1.96497 | − | 2.70454i | 0.130708 | − | 0.179904i | ||||
\(227\) | 18.6188 | + | 6.04960i | 1.23577 | + | 0.401526i | 0.852802 | − | 0.522235i | \(-0.174902\pi\) |
0.382969 | + | 0.923761i | \(0.374902\pi\) | |||||||
\(228\) | 1.87996 | − | 0.610837i | 0.124504 | − | 0.0404536i | ||||
\(229\) | 12.6575 | + | 17.4215i | 0.836430 | + | 1.15125i | 0.986692 | + | 0.162601i | \(0.0519883\pi\) |
−0.150262 | + | 0.988646i | \(0.548012\pi\) | |||||||
\(230\) | 16.5788 | 1.09317 | ||||||||
\(231\) | 6.17680 | + | 7.24303i | 0.406404 | + | 0.476556i | ||||
\(232\) | − | 17.4384i | − | 1.14489i | ||||||
\(233\) | −3.00491 | + | 2.18319i | −0.196858 | + | 0.143026i | −0.681848 | − | 0.731494i | \(-0.738823\pi\) |
0.484990 | + | 0.874520i | \(0.338823\pi\) | |||||||
\(234\) | 0.885776 | − | 5.43413i | 0.0579050 | − | 0.355240i | ||||
\(235\) | −3.86364 | + | 11.8911i | −0.252036 | + | 0.775688i | ||||
\(236\) | 2.64474 | − | 3.64018i | 0.172158 | − | 0.236955i | ||||
\(237\) | 1.31096 | + | 0.952470i | 0.0851562 | + | 0.0618696i | ||||
\(238\) | 6.85983 | − | 21.1124i | 0.444657 | − | 1.36851i | ||||
\(239\) | −9.80947 | + | 3.18729i | −0.634522 | + | 0.206169i | −0.608577 | − | 0.793495i | \(-0.708259\pi\) |
−0.0259446 | + | 0.999663i | \(0.508259\pi\) | |||||||
\(240\) | −4.09864 | − | 5.64130i | −0.264566 | − | 0.364144i | ||||
\(241\) | − | 2.39783i | − | 0.154458i | −0.997013 | − | 0.0772289i | \(-0.975393\pi\) | ||
0.997013 | − | 0.0772289i | \(-0.0246072\pi\) | |||||||
\(242\) | 14.9781 | − | 7.60359i | 0.962826 | − | 0.488777i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.92692 | − | 2.12653i | 0.187377 | − | 0.136137i | ||||
\(245\) | −1.80251 | + | 0.585669i | −0.115158 | + | 0.0374171i | ||||
\(246\) | −4.35139 | + | 13.3922i | −0.277434 | + | 0.853855i | ||||
\(247\) | −9.66339 | − | 19.1784i | −0.614867 | − | 1.22029i | ||||
\(248\) | −0.276519 | − | 0.200903i | −0.0175590 | − | 0.0127573i | ||||
\(249\) | −3.48309 | − | 1.13173i | −0.220732 | − | 0.0717202i | ||||
\(250\) | −5.53158 | − | 17.0245i | −0.349848 | − | 1.07672i | ||||
\(251\) | 7.79775 | − | 5.66539i | 0.492189 | − | 0.357597i | −0.313836 | − | 0.949477i | \(-0.601614\pi\) |
0.806026 | + | 0.591881i | \(0.201614\pi\) | |||||||
\(252\) | − | 0.952522i | − | 0.0600033i | ||||||
\(253\) | −17.8917 | + | 15.2579i | −1.12484 | + | 0.959257i | ||||
\(254\) | 23.4177i | 1.46936i | ||||||||
\(255\) | 4.55891 | + | 6.27480i | 0.285490 | + | 0.392943i | ||||
\(256\) | 2.39729 | + | 7.37809i | 0.149830 | + | 0.461131i | ||||
\(257\) | −0.856504 | + | 2.63605i | −0.0534273 | + | 0.164432i | −0.974210 | − | 0.225644i | \(-0.927551\pi\) |
0.920783 | + | 0.390076i | \(0.127551\pi\) | |||||||
\(258\) | −5.09717 | + | 7.01565i | −0.317336 | + | 0.436775i | ||||
\(259\) | 6.55391 | + | 4.76170i | 0.407240 | + | 0.295877i | ||||
\(260\) | 1.30149 | − | 1.28983i | 0.0807152 | − | 0.0799917i | ||||
\(261\) | 2.11547 | + | 6.51076i | 0.130944 | + | 0.403006i | ||||
\(262\) | 11.1548 | + | 15.3532i | 0.689144 | + | 0.948526i | ||||
\(263\) | −23.4694 | −1.44719 | −0.723593 | − | 0.690226i | \(-0.757511\pi\) | ||||
−0.723593 | + | 0.690226i | \(0.757511\pi\) | |||||||
\(264\) | 8.21356 | + | 1.97838i | 0.505510 | + | 0.121761i | ||||
\(265\) | 10.4208i | 0.640145i | ||||||||
\(266\) | −15.3442 | − | 21.1194i | −0.940811 | − | 1.29491i | ||||
\(267\) | −12.2387 | + | 3.97660i | −0.748997 | + | 0.243364i | ||||
\(268\) | −0.620566 | − | 0.201634i | −0.0379071 | − | 0.0123168i | ||||
\(269\) | −12.3739 | − | 8.99019i | −0.754452 | − | 0.548141i | 0.142752 | − | 0.989759i | \(-0.454405\pi\) |
−0.897204 | + | 0.441617i | \(0.854405\pi\) | |||||||
\(270\) | 1.89180 | + | 1.37448i | 0.115131 | + | 0.0836479i | ||||
\(271\) | 9.19919 | + | 2.98900i | 0.558811 | + | 0.181569i | 0.574786 | − | 0.818304i | \(-0.305085\pi\) |
−0.0159751 | + | 0.999872i | \(0.505085\pi\) | |||||||
\(272\) | −7.12713 | − | 21.9350i | −0.432146 | − | 1.33001i | ||||
\(273\) | −10.2282 | + | 1.57282i | −0.619038 | + | 0.0951915i | ||||
\(274\) | −6.65681 | −0.402153 | ||||||||
\(275\) | 7.50478 | + | 4.60663i | 0.452555 | + | 0.277790i | ||||
\(276\) | 2.35292 | 0.141629 | ||||||||
\(277\) | −4.96048 | + | 3.60400i | −0.298046 | + | 0.216543i | −0.726750 | − | 0.686902i | \(-0.758970\pi\) |
0.428704 | + | 0.903445i | \(0.358970\pi\) | |||||||
\(278\) | −18.7128 | + | 6.08015i | −1.12232 | + | 0.364663i | ||||
\(279\) | 0.127612 | + | 0.0414637i | 0.00763994 | + | 0.00248237i | ||||
\(280\) | −6.58064 | + | 9.05747i | −0.393268 | + | 0.541288i | ||||
\(281\) | −7.18944 | + | 9.89542i | −0.428886 | + | 0.590311i | −0.967697 | − | 0.252115i | \(-0.918874\pi\) |
0.538811 | + | 0.842427i | \(0.318874\pi\) | |||||||
\(282\) | −3.85287 | + | 11.8579i | −0.229435 | + | 0.706128i | ||||
\(283\) | 9.57457 | + | 29.4675i | 0.569149 | + | 1.75166i | 0.655289 | + | 0.755378i | \(0.272547\pi\) |
−0.0861394 | + | 0.996283i | \(0.527453\pi\) | |||||||
\(284\) | 0.520220 | + | 0.716022i | 0.0308694 | + | 0.0424881i | ||||
\(285\) | 9.12085 | 0.540273 | ||||||||
\(286\) | −1.52823 | + | 18.1968i | −0.0903662 | + | 1.07600i | ||||
\(287\) | 26.4664 | 1.56226 | ||||||||
\(288\) | −1.09267 | − | 1.50393i | −0.0643861 | − | 0.0886199i | ||||
\(289\) | 2.67420 | + | 8.23033i | 0.157306 | + | 0.484137i | ||||
\(290\) | −4.94682 | + | 15.2247i | −0.290487 | + | 0.894027i | ||||
\(291\) | 2.14642 | − | 2.95430i | 0.125826 | − | 0.173184i | ||||
\(292\) | 0.886755 | − | 1.22051i | 0.0518934 | − | 0.0714251i | ||||
\(293\) | 4.94804 | + | 1.60772i | 0.289068 | + | 0.0939238i | 0.449962 | − | 0.893048i | \(-0.351438\pi\) |
−0.160894 | + | 0.986972i | \(0.551438\pi\) | |||||||
\(294\) | −1.79748 | + | 0.584036i | −0.104831 | + | 0.0340616i | ||||
\(295\) | 16.7964 | − | 12.2033i | 0.977922 | − | 0.710502i | ||||
\(296\) | 7.18989 | 0.417904 | ||||||||
\(297\) | −3.30659 | + | 0.257754i | −0.191868 | + | 0.0149564i | ||||
\(298\) | −18.0629 | −1.04636 | ||||||||
\(299\) | −3.88518 | − | 25.2657i | −0.224686 | − | 1.46115i | ||||
\(300\) | −0.272289 | − | 0.838019i | −0.0157206 | − | 0.0483830i | ||||
\(301\) | 15.5012 | + | 5.03665i | 0.893476 | + | 0.290308i | ||||
\(302\) | 18.6526 | + | 13.5519i | 1.07334 | + | 0.779825i | ||||
\(303\) | −16.0155 | − | 11.6359i | −0.920065 | − | 0.668466i | ||||
\(304\) | −25.7948 | − | 8.38123i | −1.47943 | − | 0.480696i | ||||
\(305\) | 15.8764 | − | 5.15856i | 0.909081 | − | 0.295378i | ||||
\(306\) | 4.54619 | + | 6.25730i | 0.259888 | + | 0.357706i | ||||
\(307\) | 34.4846i | 1.96814i | 0.177775 | + | 0.984071i | \(0.443110\pi\) | ||||
−0.177775 | + | 0.984071i | \(0.556890\pi\) | |||||||
\(308\) | 0.245517 | + | 3.14960i | 0.0139896 | + | 0.179465i | ||||
\(309\) | 18.6302 | 1.05984 | ||||||||
\(310\) | 0.184426 | + | 0.253841i | 0.0104747 | + | 0.0144172i | ||||
\(311\) | −3.65021 | − | 11.2342i | −0.206985 | − | 0.637033i | −0.999626 | − | 0.0273449i | \(-0.991295\pi\) |
0.792642 | − | 0.609688i | \(-0.208705\pi\) | |||||||
\(312\) | −6.52356 | + | 6.46508i | −0.369324 | + | 0.366013i | ||||
\(313\) | −23.2455 | − | 16.8888i | −1.31391 | − | 0.954613i | −0.999987 | − | 0.00516585i | \(-0.998356\pi\) |
−0.313926 | − | 0.949447i | \(-0.601644\pi\) | |||||||
\(314\) | 12.9778 | − | 17.8624i | 0.732381 | − | 1.00804i | ||||
\(315\) | 1.35816 | − | 4.17998i | 0.0765235 | − | 0.235515i | ||||
\(316\) | 0.166184 | + | 0.511461i | 0.00934856 | + | 0.0287719i | ||||
\(317\) | 2.17424 | + | 2.99259i | 0.122118 | + | 0.168080i | 0.865699 | − | 0.500565i | \(-0.166874\pi\) |
−0.743581 | + | 0.668645i | \(0.766874\pi\) | |||||||
\(318\) | 10.3917i | 0.582740i | ||||||||
\(319\) | −8.67319 | − | 20.9832i | −0.485605 | − | 1.17483i | ||||
\(320\) | 9.59907i | 0.536604i | ||||||||
\(321\) | 10.0481 | − | 7.30036i | 0.560829 | − | 0.407466i | ||||
\(322\) | −9.60221 | − | 29.5526i | −0.535110 | − | 1.64690i | ||||
\(323\) | 28.6915 | + | 9.32242i | 1.59644 | + | 0.518713i | ||||
\(324\) | 0.268492 | + | 0.195071i | 0.0149162 | + | 0.0108373i | ||||
\(325\) | −8.54904 | + | 4.30759i | −0.474216 | + | 0.238942i | ||||
\(326\) | 3.67006 | − | 11.2953i | 0.203266 | − | 0.625589i | ||||
\(327\) | −6.54564 | + | 2.12681i | −0.361974 | + | 0.117613i | ||||
\(328\) | 19.0034 | − | 13.8068i | 1.04929 | − | 0.762353i | ||||
\(329\) | 23.4343 | 1.29197 | ||||||||
\(330\) | −6.60970 | − | 4.05721i | −0.363852 | − | 0.223342i | ||||
\(331\) | − | 3.79120i | − | 0.208383i | −0.994557 | − | 0.104192i | \(-0.966774\pi\) | ||
0.994557 | − | 0.104192i | \(-0.0332255\pi\) | |||||||
\(332\) | −0.714415 | − | 0.983308i | −0.0392086 | − | 0.0539660i | ||||
\(333\) | −2.68440 | + | 0.872214i | −0.147104 | + | 0.0477971i | ||||
\(334\) | 5.04579 | − | 15.5293i | 0.276093 | − | 0.849728i | ||||
\(335\) | −2.43574 | − | 1.76967i | −0.133079 | − | 0.0966875i | ||||
\(336\) | −7.68204 | + | 10.5734i | −0.419090 | + | 0.576827i | ||||
\(337\) | −7.85315 | + | 24.1695i | −0.427788 | + | 1.31660i | 0.472511 | + | 0.881325i | \(0.343348\pi\) |
−0.900299 | + | 0.435272i | \(0.856652\pi\) | |||||||
\(338\) | −15.9546 | − | 11.8126i | −0.867815 | − | 0.642521i | ||||
\(339\) | 1.77109 | − | 1.28677i | 0.0961926 | − | 0.0698880i | ||||
\(340\) | 2.57404i | 0.139597i | ||||||||
\(341\) | −0.432649 | − | 0.104211i | −0.0234293 | − | 0.00564335i | ||||
\(342\) | 9.09541 | 0.491823 | ||||||||
\(343\) | −9.72118 | − | 13.3801i | −0.524894 | − | 0.722455i | ||||
\(344\) | 13.7577 | − | 4.47014i | 0.741765 | − | 0.241014i | ||||
\(345\) | 10.3254 | + | 3.35492i | 0.555900 | + | 0.180623i | ||||
\(346\) | −14.7562 | + | 20.3101i | −0.793296 | + | 1.09188i | ||||
\(347\) | 18.7051 | + | 13.5900i | 1.00414 | + | 0.729552i | 0.962972 | − | 0.269601i | \(-0.0868917\pi\) |
0.0411694 | + | 0.999152i | \(0.486892\pi\) | |||||||
\(348\) | −0.702070 | + | 2.16075i | −0.0376349 | + | 0.115828i | ||||
\(349\) | 11.6045 | − | 3.77054i | 0.621177 | − | 0.201833i | 0.0185140 | − | 0.999829i | \(-0.494106\pi\) |
0.602663 | + | 0.797996i | \(0.294106\pi\) | |||||||
\(350\) | −9.41427 | + | 6.83987i | −0.503214 | + | 0.365606i | ||||
\(351\) | 1.65133 | − | 3.20517i | 0.0881415 | − | 0.171079i | ||||
\(352\) | 4.00066 | + | 4.69124i | 0.213236 | + | 0.250044i | ||||
\(353\) | − | 2.01271i | − | 0.107126i | −0.998564 | − | 0.0535629i | \(-0.982942\pi\) | ||
0.998564 | − | 0.0535629i | \(-0.0170578\pi\) | |||||||
\(354\) | 16.7495 | − | 12.1692i | 0.890226 | − | 0.646787i | ||||
\(355\) | 1.26195 | + | 3.88390i | 0.0669776 | + | 0.206136i | ||||
\(356\) | −4.06171 | − | 1.31973i | −0.215270 | − | 0.0699455i | ||||
\(357\) | 8.54471 | − | 11.7608i | 0.452234 | − | 0.622447i | ||||
\(358\) | 0.831222 | − | 1.14408i | 0.0439315 | − | 0.0604665i | ||||
\(359\) | −13.4994 | − | 4.38622i | −0.712470 | − | 0.231496i | −0.0697148 | − | 0.997567i | \(-0.522209\pi\) |
−0.642756 | + | 0.766071i | \(0.722209\pi\) | |||||||
\(360\) | −1.20540 | − | 3.70983i | −0.0635299 | − | 0.195525i | ||||
\(361\) | 13.3297 | − | 9.68458i | 0.701562 | − | 0.509714i | ||||
\(362\) | 7.01821i | 0.368869i | ||||||||
\(363\) | 10.8671 | − | 1.70458i | 0.570376 | − | 0.0894671i | ||||
\(364\) | −3.05299 | − | 1.57293i | −0.160020 | − | 0.0824439i | ||||
\(365\) | 5.63165 | − | 4.09163i | 0.294774 | − | 0.214166i | ||||
\(366\) | 15.8321 | − | 5.14417i | 0.827558 | − | 0.268890i | ||||
\(367\) | 1.48685 | − | 4.57607i | 0.0776132 | − | 0.238869i | −0.904721 | − | 0.426005i | \(-0.859921\pi\) |
0.982334 | + | 0.187136i | \(0.0599206\pi\) | |||||||
\(368\) | −26.1184 | − | 18.9762i | −1.36152 | − | 0.989201i | ||||
\(369\) | −5.42015 | + | 7.46020i | −0.282162 | + | 0.388362i | ||||
\(370\) | −6.27719 | − | 2.03958i | −0.326336 | − | 0.106033i | ||||
\(371\) | 18.5757 | − | 6.03560i | 0.964400 | − | 0.313353i | ||||
\(372\) | 0.0261745 | + | 0.0360260i | 0.00135708 | + | 0.00186786i | ||||
\(373\) | −30.7445 | −1.59189 | −0.795944 | − | 0.605370i | \(-0.793025\pi\) | ||||
−0.795944 | + | 0.605370i | \(0.793025\pi\) | |||||||
\(374\) | −16.6453 | − | 19.5185i | −0.860706 | − | 1.00928i | ||||
\(375\) | − | 11.7223i | − | 0.605339i | ||||||
\(376\) | 16.8263 | − | 12.2250i | 0.867749 | − | 0.630456i | ||||
\(377\) | 24.3614 | + | 3.97097i | 1.25468 | + | 0.204515i | ||||
\(378\) | 1.35437 | − | 4.16832i | 0.0696612 | − | 0.214395i | ||||
\(379\) | −12.4263 | + | 17.1033i | −0.638296 | + | 0.878539i | −0.998523 | − | 0.0543255i | \(-0.982699\pi\) |
0.360227 | + | 0.932865i | \(0.382699\pi\) | |||||||
\(380\) | 2.44887 | + | 1.77921i | 0.125625 | + | 0.0912715i | ||||
\(381\) | −4.73887 | + | 14.5847i | −0.242780 | + | 0.747199i | ||||
\(382\) | −5.78106 | + | 1.87838i | −0.295785 | + | 0.0961063i | ||||
\(383\) | −12.6135 | − | 17.3610i | −0.644518 | − | 0.887104i | 0.354328 | − | 0.935121i | \(-0.384710\pi\) |
−0.998846 | + | 0.0480176i | \(0.984710\pi\) | |||||||
\(384\) | 13.2902i | 0.678213i | ||||||||
\(385\) | −3.41347 | + | 14.1716i | −0.173967 | + | 0.722250i | ||||
\(386\) | −2.63520 | −0.134128 | ||||||||
\(387\) | −4.59426 | + | 3.33792i | −0.233539 | + | 0.169676i | ||||
\(388\) | 1.15259 | − | 0.374500i | 0.0585141 | − | 0.0190124i | ||||
\(389\) | −4.38692 | + | 13.5016i | −0.222426 | + | 0.684557i | 0.776117 | + | 0.630589i | \(0.217187\pi\) |
−0.998543 | + | 0.0539674i | \(0.982813\pi\) | |||||||
\(390\) | 7.52942 | − | 3.79383i | 0.381267 | − | 0.192108i | ||||
\(391\) | 29.0515 | + | 21.1071i | 1.46920 | + | 1.06743i | ||||
\(392\) | 2.99842 | + | 0.974245i | 0.151443 | + | 0.0492068i | ||||
\(393\) | 3.84036 | + | 11.8194i | 0.193721 | + | 0.596211i | ||||
\(394\) | −7.60021 | + | 5.52188i | −0.382893 | + | 0.278188i | ||||
\(395\) | 2.48141i | 0.124853i | ||||||||
\(396\) | −0.938073 | − | 0.575814i | −0.0471399 | − | 0.0289358i | ||||
\(397\) | − | 18.6886i | − | 0.937953i | −0.883211 | − | 0.468976i | \(-0.844623\pi\) | ||
0.883211 | − | 0.468976i | \(-0.155377\pi\) | |||||||
\(398\) | −18.0866 | − | 24.8941i | −0.906599 | − | 1.24783i | ||||
\(399\) | −5.28268 | − | 16.2584i | −0.264465 | − | 0.813939i | ||||
\(400\) | −3.73605 | + | 11.4984i | −0.186802 | + | 0.574918i | ||||
\(401\) | 12.0311 | − | 16.5595i | 0.600807 | − | 0.826940i | −0.394975 | − | 0.918692i | \(-0.629247\pi\) |
0.995782 | + | 0.0917522i | \(0.0292468\pi\) | |||||||
\(402\) | −2.42895 | − | 1.76474i | −0.121145 | − | 0.0880170i | ||||
\(403\) | 0.343628 | − | 0.340548i | 0.0171173 | − | 0.0169639i | ||||
\(404\) | −2.03019 | − | 6.24829i | −0.101006 | − | 0.310864i | ||||
\(405\) | 0.900087 | + | 1.23886i | 0.0447257 | + | 0.0615596i | ||||
\(406\) | 30.0040 | 1.48908 | ||||||||
\(407\) | 8.65140 | − | 3.57597i | 0.428834 | − | 0.177254i | ||||
\(408\) | − | 12.9020i | − | 0.638746i | ||||||
\(409\) | 6.25713 | + | 8.61220i | 0.309395 | + | 0.425846i | 0.935192 | − | 0.354140i | \(-0.115226\pi\) |
−0.625797 | + | 0.779986i | \(0.715226\pi\) | |||||||
\(410\) | −20.5077 | + | 6.66336i | −1.01280 | + | 0.329080i | ||||
\(411\) | −4.14591 | − | 1.34709i | −0.204503 | − | 0.0664470i | ||||
\(412\) | 5.00206 | + | 3.63421i | 0.246434 | + | 0.179045i | ||||
\(413\) | −31.4812 | − | 22.8724i | −1.54909 | − | 1.12548i | ||||
\(414\) | 10.2966 | + | 3.34556i | 0.506049 | + | 0.164425i | ||||
\(415\) | −1.73303 | − | 5.33373i | −0.0850713 | − | 0.261822i | ||||
\(416\) | −6.62470 | + | 1.01870i | −0.324803 | + | 0.0499460i | ||||
\(417\) | −12.8848 | −0.630974 | ||||||||
\(418\) | −30.0748 | + | 2.34438i | −1.47101 | + | 0.114667i | ||||
\(419\) | 19.3647 | 0.946026 | 0.473013 | − | 0.881055i | \(-0.343166\pi\) | ||||
0.473013 | + | 0.881055i | \(0.343166\pi\) | |||||||
\(420\) | 1.18005 | − | 0.857353i | 0.0575803 | − | 0.0418345i | ||||
\(421\) | −7.84714 | + | 2.54969i | −0.382446 | + | 0.124264i | −0.493929 | − | 0.869502i | \(-0.664440\pi\) |
0.111483 | + | 0.993766i | \(0.464440\pi\) | |||||||
\(422\) | −16.3070 | − | 5.29848i | −0.793814 | − | 0.257926i | ||||
\(423\) | −4.79919 | + | 6.60551i | −0.233344 | + | 0.321171i | ||||
\(424\) | 10.1891 | − | 14.0241i | 0.494826 | − | 0.681070i | ||||
\(425\) | 4.15560 | − | 12.7896i | 0.201576 | − | 0.620387i | ||||
\(426\) | 1.25843 | + | 3.87306i | 0.0609713 | + | 0.187650i | ||||
\(427\) | −18.3908 | − | 25.3128i | −0.889994 | − | 1.22497i | ||||
\(428\) | 4.12191 | 0.199240 | ||||||||
\(429\) | −4.63414 | + | 11.0238i | −0.223738 | + | 0.532235i | ||||
\(430\) | −13.2793 | −0.640386 | ||||||||
\(431\) | 1.71894 | + | 2.36591i | 0.0827983 | + | 0.113962i | 0.848407 | − | 0.529345i | \(-0.177562\pi\) |
−0.765609 | + | 0.643307i | \(0.777562\pi\) | |||||||
\(432\) | −1.40714 | − | 4.33074i | −0.0677012 | − | 0.208363i | ||||
\(433\) | 2.70440 | − | 8.32330i | 0.129965 | − | 0.399992i | −0.864808 | − | 0.502103i | \(-0.832560\pi\) |
0.994773 | + | 0.102111i | \(0.0325597\pi\) | |||||||
\(434\) | 0.345668 | − | 0.475771i | 0.0165926 | − | 0.0228378i | ||||
\(435\) | −6.16183 | + | 8.48103i | −0.295437 | + | 0.406634i | ||||
\(436\) | −2.17233 | − | 0.705831i | −0.104036 | − | 0.0338032i | ||||
\(437\) | 40.1615 | − | 13.0493i | 1.92119 | − | 0.624231i | ||||
\(438\) | 5.61594 | − | 4.08022i | 0.268340 | − | 0.194960i | ||||
\(439\) | 8.15200 | 0.389074 | 0.194537 | − | 0.980895i | \(-0.437680\pi\) | ||||
0.194537 | + | 0.980895i | \(0.437680\pi\) | |||||||
\(440\) | 4.94198 | + | 11.9562i | 0.235600 | + | 0.569989i | ||||
\(441\) | −1.23767 | −0.0589366 | ||||||||
\(442\) | 27.5630 | − | 4.23844i | 1.31104 | − | 0.201602i | ||||
\(443\) | 1.95236 | + | 6.00874i | 0.0927593 | + | 0.285484i | 0.986663 | − | 0.162775i | \(-0.0520444\pi\) |
−0.893904 | + | 0.448259i | \(0.852044\pi\) | |||||||
\(444\) | −0.890882 | − | 0.289465i | −0.0422794 | − | 0.0137374i | ||||
\(445\) | −15.9424 | − | 11.5828i | −0.755741 | − | 0.549078i | ||||
\(446\) | 25.6946 | + | 18.6682i | 1.21668 | + | 0.883966i | ||||
\(447\) | −11.2497 | − | 3.65526i | −0.532094 | − | 0.172888i | ||||
\(448\) | 17.1109 | − | 5.55966i | 0.808412 | − | 0.262669i | ||||
\(449\) | −6.59978 | − | 9.08382i | −0.311463 | − | 0.428692i | 0.624374 | − | 0.781126i | \(-0.285354\pi\) |
−0.935837 | + | 0.352434i | \(0.885354\pi\) | |||||||
\(450\) | − | 4.05440i | − | 0.191126i | ||||||
\(451\) | 15.9993 | − | 26.0649i | 0.753379 | − | 1.22735i | ||||
\(452\) | 0.726536 | 0.0341734 | ||||||||
\(453\) | 8.87459 | + | 12.2148i | 0.416964 | + | 0.573902i | ||||
\(454\) | 9.23803 | + | 28.4317i | 0.433562 | + | 1.33437i | ||||
\(455\) | −11.1548 | − | 11.2557i | −0.522944 | − | 0.527673i | ||||
\(456\) | −12.2746 | − | 8.91805i | −0.574813 | − | 0.417626i | ||||
\(457\) | 14.2172 | − | 19.5683i | 0.665051 | − | 0.915364i | −0.334584 | − | 0.942366i | \(-0.608596\pi\) |
0.999635 | + | 0.0270016i | \(0.00859591\pi\) | |||||||
\(458\) | −10.1616 | + | 31.2743i | −0.474822 | + | 1.46135i | ||||
\(459\) | 1.56516 | + | 4.81707i | 0.0730554 | + | 0.224842i | ||||
\(460\) | 2.11783 | + | 2.91495i | 0.0987444 | + | 0.135910i | ||||
\(461\) | 21.1788i | 0.986395i | 0.869917 | + | 0.493197i | \(0.164172\pi\) | ||||
−0.869917 | + | 0.493197i | \(0.835828\pi\) | |||||||
\(462\) | −3.40395 | + | 14.1320i | −0.158366 | + | 0.657482i | ||||
\(463\) | − | 1.87180i | − | 0.0869899i | −0.999054 | − | 0.0434949i | \(-0.986151\pi\) | ||
0.999054 | − | 0.0434949i | \(-0.0138492\pi\) | |||||||
\(464\) | 25.2196 | − | 18.3231i | 1.17079 | − | 0.850629i | ||||
\(465\) | 0.0634942 | + | 0.195415i | 0.00294447 | + | 0.00906216i | ||||
\(466\) | −5.39427 | − | 1.75270i | −0.249885 | − | 0.0811925i | ||||
\(467\) | −8.40940 | − | 6.10979i | −0.389141 | − | 0.282727i | 0.375963 | − | 0.926635i | \(-0.377312\pi\) |
−0.765103 | + | 0.643908i | \(0.777312\pi\) | |||||||
\(468\) | 1.06860 | − | 0.538435i | 0.0493962 | − | 0.0248891i | ||||
\(469\) | −1.74378 | + | 5.36682i | −0.0805205 | + | 0.247817i | ||||
\(470\) | −18.1582 | + | 5.89997i | −0.837577 | + | 0.272145i | ||||
\(471\) | 11.6974 | − | 8.49864i | 0.538987 | − | 0.391597i | ||||
\(472\) | −34.5361 | −1.58965 | ||||||||
\(473\) | 14.3310 | − | 12.2213i | 0.658939 | − | 0.561938i | ||||
\(474\) | 2.47449i | 0.113657i | ||||||||
\(475\) | −9.29529 | − | 12.7939i | −0.426497 | − | 0.587023i | ||||
\(476\) | 4.58837 | − | 1.49085i | 0.210307 | − | 0.0683330i | ||||
\(477\) | −2.10290 | + | 6.47205i | −0.0962851 | + | 0.296335i | ||||
\(478\) | −12.7423 | − | 9.25785i | −0.582821 | − | 0.423444i | ||||
\(479\) | −11.1335 | + | 15.3240i | −0.508704 | + | 0.700171i | −0.983700 | − | 0.179817i | \(-0.942449\pi\) |
0.474996 | + | 0.879988i | \(0.342449\pi\) | |||||||
\(480\) | 0.879666 | − | 2.70733i | 0.0401511 | − | 0.123572i | ||||
\(481\) | −1.63724 | + | 10.0443i | −0.0746517 | + | 0.457979i | ||||
\(482\) | 2.96230 | − | 2.15223i | 0.134929 | − | 0.0980316i | ||||
\(483\) | − | 20.3487i | − | 0.925897i | ||||||
\(484\) | 3.25024 | + | 1.66219i | 0.147738 | + | 0.0755541i | ||||
\(485\) | 5.59194 | 0.253917 | ||||||||
\(486\) | 0.897576 | + | 1.23541i | 0.0407149 | + | 0.0560392i | ||||
\(487\) | 0.793330 | − | 0.257769i | 0.0359492 | − | 0.0116806i | −0.290987 | − | 0.956727i | \(-0.593984\pi\) |
0.326936 | + | 0.945046i | \(0.393984\pi\) | |||||||
\(488\) | −26.4100 | − | 8.58112i | −1.19552 | − | 0.388449i | ||||
\(489\) | 4.57149 | − | 6.29211i | 0.206730 | − | 0.284539i | ||||
\(490\) | −2.34143 | − | 1.70115i | −0.105775 | − | 0.0768499i | ||||
\(491\) | 3.47325 | − | 10.6896i | 0.156746 | − | 0.482414i | −0.841588 | − | 0.540120i | \(-0.818379\pi\) |
0.998334 | + | 0.0577065i | \(0.0183788\pi\) | |||||||
\(492\) | −2.91053 | + | 0.945688i | −0.131217 | + | 0.0426349i | ||||
\(493\) | −28.0517 | + | 20.3808i | −1.26339 | + | 0.917903i | ||||
\(494\) | 15.0195 | − | 29.1523i | 0.675761 | − | 1.31162i | ||||
\(495\) | −3.29554 | − | 3.86442i | −0.148124 | − | 0.173693i | ||||
\(496\) | − | 0.611000i | − | 0.0274347i | ||||||
\(497\) | 6.19235 | − | 4.49900i | 0.277765 | − | 0.201808i | ||||
\(498\) | −1.72820 | − | 5.31885i | −0.0774424 | − | 0.238343i | ||||
\(499\) | 41.4260 | + | 13.4601i | 1.85448 | + | 0.602558i | 0.995961 | + | 0.0897830i | \(0.0286174\pi\) |
0.858523 | + | 0.512775i | \(0.171383\pi\) | |||||||
\(500\) | 2.28668 | − | 3.14735i | 0.102264 | − | 0.140754i | ||||
\(501\) | 6.28511 | − | 8.65071i | 0.280798 | − | 0.386485i | ||||
\(502\) | 13.9981 | + | 4.54827i | 0.624767 | + | 0.202999i | ||||
\(503\) | −7.53416 | − | 23.1877i | −0.335931 | − | 1.03389i | −0.966261 | − | 0.257563i | \(-0.917080\pi\) |
0.630330 | − | 0.776327i | \(-0.282920\pi\) | |||||||
\(504\) | −5.91482 | + | 4.29737i | −0.263467 | + | 0.191420i | ||||
\(505\) | − | 30.3143i | − | 1.34897i | ||||||
\(506\) | −34.9089 | − | 8.40842i | −1.55189 | − | 0.373800i | ||||
\(507\) | −7.54621 | − | 10.5856i | −0.335139 | − | 0.470123i | ||||
\(508\) | −4.11740 | + | 2.99147i | −0.182680 | + | 0.132725i | ||||
\(509\) | −22.3297 | + | 7.25537i | −0.989747 | + | 0.321588i | −0.758761 | − | 0.651369i | \(-0.774195\pi\) |
−0.230986 | + | 0.972957i | \(0.574195\pi\) | |||||||
\(510\) | −3.65997 | + | 11.2642i | −0.162066 | + | 0.498788i | ||||
\(511\) | −10.5553 | − | 7.66889i | −0.466940 | − | 0.339252i | ||||
\(512\) | 8.66038 | − | 11.9200i | 0.382738 | − | 0.526794i | ||||
\(513\) | 5.66469 | + | 1.84057i | 0.250102 | + | 0.0812631i | ||||
\(514\) | −4.02537 | + | 1.30792i | −0.177552 | + | 0.0576900i | ||||
\(515\) | 16.7688 | + | 23.0803i | 0.738923 | + | 1.01704i | ||||
\(516\) | −1.88465 | −0.0829671 | ||||||||
\(517\) | 14.1664 | − | 23.0788i | 0.623036 | − | 1.01500i | ||||
\(518\) | 12.3707i | 0.543539i | ||||||||
\(519\) | −13.3003 | + | 9.66320i | −0.583816 | + | 0.424167i | ||||
\(520\) | −13.8811 | − | 2.26266i | −0.608728 | − | 0.0992240i | ||||
\(521\) | −11.0729 | + | 34.0788i | −0.485111 | + | 1.49302i | 0.346709 | + | 0.937973i | \(0.387299\pi\) |
−0.831820 | + | 0.555045i | \(0.812701\pi\) | |||||||
\(522\) | −6.14464 | + | 8.45737i | −0.268943 | + | 0.370169i | ||||
\(523\) | 12.1935 | + | 8.85909i | 0.533184 | + | 0.387381i | 0.821547 | − | 0.570140i | \(-0.193111\pi\) |
−0.288363 | + | 0.957521i | \(0.593111\pi\) | |||||||
\(524\) | −1.27452 | + | 3.92256i | −0.0556775 | + | 0.171358i | ||||
\(525\) | −7.24741 | + | 2.35483i | −0.316303 | + | 0.102773i | ||||
\(526\) | −21.0656 | − | 28.9943i | −0.918503 | − | 1.26421i | ||||
\(527\) | 0.679614i | 0.0296045i | ||||||||
\(528\) | 5.76911 | + | 13.9573i | 0.251068 | + | 0.607413i | ||||
\(529\) | 27.2653 | 1.18545 | ||||||||
\(530\) | −12.8739 | + | 9.35347i | −0.559209 | + | 0.406289i | ||||
\(531\) | 12.8943 | − | 4.18961i | 0.559565 | − | 0.181814i | ||||
\(532\) | 1.75318 | − | 5.39574i | 0.0760101 | − | 0.233935i | ||||
\(533\) | 14.9607 | + | 29.6918i | 0.648021 | + | 1.28609i | ||||
\(534\) | −15.8979 | − | 11.5505i | −0.687969 | − | 0.499839i | ||||
\(535\) | 18.0883 | + | 5.87724i | 0.782025 | + | 0.254095i | ||||
\(536\) | 1.54765 | + | 4.76317i | 0.0668482 | + | 0.205738i | ||||
\(537\) | 0.749210 | − | 0.544333i | 0.0323308 | − | 0.0234897i | ||||
\(538\) | − | 23.3562i | − | 1.00696i | ||||||
\(539\) | 4.09247 | − | 0.319014i | 0.176275 | − | 0.0137409i | ||||
\(540\) | 0.508205i | 0.0218697i | ||||||||
\(541\) | −13.4617 | − | 18.5285i | −0.578765 | − | 0.796601i | 0.414794 | − | 0.909915i | \(-0.363854\pi\) |
−0.993559 | + | 0.113314i | \(0.963854\pi\) | |||||||
\(542\) | 4.56434 | + | 14.0476i | 0.196055 | + | 0.603396i | ||||
\(543\) | −1.42022 | + | 4.37099i | −0.0609475 | + | 0.187577i | ||||
\(544\) | 5.53433 | − | 7.61735i | 0.237282 | − | 0.326591i | ||||
\(545\) | −8.52646 | − | 6.19484i | −0.365234 | − | 0.265358i | ||||
\(546\) | −11.1237 | − | 11.2243i | −0.476048 | − | 0.480354i | ||||
\(547\) | 9.71269 | + | 29.8926i | 0.415284 | + | 1.27811i | 0.911996 | + | 0.410199i | \(0.134541\pi\) |
−0.496712 | + | 0.867916i | \(0.665459\pi\) | |||||||
\(548\) | −0.850365 | − | 1.17043i | −0.0363258 | − | 0.0499982i | ||||
\(549\) | 10.9014 | 0.465258 | ||||||||
\(550\) | 1.04504 | + | 13.4063i | 0.0445607 | + | 0.571645i | ||||
\(551\) | 40.7751i | 1.73708i | ||||||||
\(552\) | −10.6153 | − | 14.6108i | −0.451819 | − | 0.621876i | ||||
\(553\) | 4.42325 | − | 1.43720i | 0.188096 | − | 0.0611160i | ||||
\(554\) | −8.90482 | − | 2.89335i | −0.378330 | − | 0.122927i | ||||
\(555\) | −3.49675 | − | 2.54054i | −0.148429 | − | 0.107840i | ||||
\(556\) | −3.45947 | − | 2.51345i | −0.146714 | − | 0.106594i | ||||
\(557\) | −10.1299 | − | 3.29141i | −0.429219 | − | 0.139462i | 0.0864372 | − | 0.996257i | \(-0.472452\pi\) |
−0.515656 | + | 0.856796i | \(0.672452\pi\) | |||||||
\(558\) | 0.0633171 | + | 0.194870i | 0.00268043 | + | 0.00824950i | ||||
\(559\) | 3.11197 | + | 20.2374i | 0.131622 | + | 0.855950i | ||||
\(560\) | −20.0135 | −0.845726 | ||||||||
\(561\) | −6.41697 | − | 15.5247i | −0.270925 | − | 0.655452i | ||||
\(562\) | −18.6779 | −0.787882 | ||||||||
\(563\) | −10.7909 | + | 7.84006i | −0.454783 | + | 0.330419i | −0.791481 | − | 0.611194i | \(-0.790690\pi\) |
0.336698 | + | 0.941613i | \(0.390690\pi\) | |||||||
\(564\) | −2.57708 | + | 0.837345i | −0.108515 | + | 0.0352586i | ||||
\(565\) | 3.18828 | + | 1.03593i | 0.134132 | + | 0.0435821i | ||||
\(566\) | −27.8105 | + | 38.2778i | −1.16896 | + | 1.60894i | ||||
\(567\) | 1.68702 | − | 2.32199i | 0.0708483 | − | 0.0975143i | ||||
\(568\) | 2.09923 | − | 6.46076i | 0.0880816 | − | 0.271087i | ||||
\(569\) | −5.16220 | − | 15.8876i | −0.216411 | − | 0.666043i | −0.999050 | − | 0.0435685i | \(-0.986127\pi\) |
0.782640 | − | 0.622475i | \(-0.213873\pi\) | |||||||
\(570\) | 8.18666 | + | 11.2680i | 0.342901 | + | 0.471963i | ||||
\(571\) | 24.4068 | 1.02139 | 0.510695 | − | 0.859762i | \(-0.329388\pi\) | ||||
0.510695 | + | 0.859762i | \(0.329388\pi\) | |||||||
\(572\) | −3.39465 | + | 2.05582i | −0.141937 | + | 0.0859582i | ||||
\(573\) | −3.98060 | −0.166292 | ||||||||
\(574\) | 23.7556 | + | 32.6968i | 0.991540 | + | 1.36474i | ||||
\(575\) | −5.81689 | − | 17.9025i | −0.242581 | − | 0.746588i | ||||
\(576\) | −1.93707 | + | 5.96169i | −0.0807113 | + | 0.248404i | ||||
\(577\) | −9.44955 | + | 13.0062i | −0.393390 | + | 0.541455i | −0.959070 | − | 0.283170i | \(-0.908614\pi\) |
0.565680 | + | 0.824625i | \(0.308614\pi\) | |||||||
\(578\) | −7.76752 | + | 10.6911i | −0.323086 | + | 0.444690i | ||||
\(579\) | −1.64122 | − | 0.533266i | −0.0682069 | − | 0.0221618i | ||||
\(580\) | −3.30880 | + | 1.07509i | −0.137390 | + | 0.0446408i | ||||
\(581\) | −8.50391 | + | 6.17845i | −0.352802 | + | 0.256325i | ||||
\(582\) | 5.57634 | 0.231147 | ||||||||
\(583\) | 5.28523 | − | 21.9425i | 0.218892 | − | 0.908765i | ||||
\(584\) | −11.5796 | −0.479167 | ||||||||
\(585\) | 5.45711 | − | 0.839157i | 0.225624 | − | 0.0346949i | ||||
\(586\) | 2.45506 | + | 7.55590i | 0.101418 | + | 0.312131i | ||||
\(587\) | 7.03344 | + | 2.28530i | 0.290301 | + | 0.0943245i | 0.450547 | − | 0.892753i | \(-0.351229\pi\) |
−0.160246 | + | 0.987077i | \(0.551229\pi\) | |||||||
\(588\) | −0.332304 | − | 0.241433i | −0.0137040 | − | 0.00995652i | ||||
\(589\) | 0.646567 | + | 0.469758i | 0.0266413 | + | 0.0193560i | ||||
\(590\) | 30.1520 | + | 9.79698i | 1.24134 | + | 0.403335i | ||||
\(591\) | −5.85089 | + | 1.90107i | −0.240673 | + | 0.0781995i | ||||
\(592\) | 7.55466 | + | 10.3981i | 0.310495 | + | 0.427359i | ||||
\(593\) | 40.2226i | 1.65175i | 0.563856 | + | 0.825873i | \(0.309317\pi\) | ||||
−0.563856 | + | 0.825873i | \(0.690683\pi\) | |||||||
\(594\) | −3.28635 | − | 3.85364i | −0.134841 | − | 0.158117i | ||||
\(595\) | 22.2610 | 0.912612 | ||||||||
\(596\) | −2.30742 | − | 3.17589i | −0.0945157 | − | 0.130090i | ||||
\(597\) | −6.22685 | − | 19.1643i | −0.254848 | − | 0.784341i | ||||
\(598\) | 27.7261 | − | 27.4776i | 1.13381 | − | 1.12364i | ||||
\(599\) | −1.65654 | − | 1.20354i | −0.0676842 | − | 0.0491754i | 0.553429 | − | 0.832897i | \(-0.313319\pi\) |
−0.621113 | + | 0.783721i | \(0.713319\pi\) | |||||||
\(600\) | −3.97534 | + | 5.47159i | −0.162293 | + | 0.223377i | ||||
\(601\) | 6.17163 | − | 18.9943i | 0.251746 | − | 0.774795i | −0.742707 | − | 0.669616i | \(-0.766459\pi\) |
0.994453 | − | 0.105178i | \(-0.0335414\pi\) | |||||||
\(602\) | 7.69121 | + | 23.6711i | 0.313470 | + | 0.964762i | ||||
\(603\) | −1.15565 | − | 1.59062i | −0.0470618 | − | 0.0647750i | ||||
\(604\) | 5.01075i | 0.203884i | ||||||||
\(605\) | 11.8931 | + | 11.9286i | 0.483523 | + | 0.484967i | ||||
\(606\) | − | 30.2298i | − | 1.22800i | ||||||
\(607\) | 20.0107 | − | 14.5386i | 0.812209 | − | 0.590104i | −0.102261 | − | 0.994758i | \(-0.532608\pi\) |
0.914470 | + | 0.404653i | \(0.132608\pi\) | |||||||
\(608\) | −3.42154 | − | 10.5304i | −0.138762 | − | 0.427065i | ||||
\(609\) | 18.6867 | + | 6.07169i | 0.757225 | + | 0.246037i | ||||
\(610\) | 20.6232 | + | 14.9836i | 0.835009 | + | 0.606670i | ||||
\(611\) | 13.2467 | + | 26.2901i | 0.535906 | + | 1.06358i | ||||
\(612\) | −0.519436 | + | 1.59866i | −0.0209969 | + | 0.0646220i | ||||
\(613\) | −25.2434 | + | 8.20208i | −1.01957 | + | 0.331279i | −0.770660 | − | 0.637247i | \(-0.780073\pi\) |
−0.248912 | + | 0.968526i | \(0.580073\pi\) | |||||||
\(614\) | −42.6026 | + | 30.9526i | −1.71930 | + | 1.24914i | ||||
\(615\) | −14.1208 | −0.569405 | ||||||||
\(616\) | 18.4502 | − | 15.7342i | 0.743381 | − | 0.633949i | ||||
\(617\) | 47.5811i | 1.91554i | 0.287531 | + | 0.957771i | \(0.407166\pi\) | ||||
−0.287531 | + | 0.957771i | \(0.592834\pi\) | |||||||
\(618\) | 16.7221 | + | 23.0159i | 0.672660 | + | 0.925836i | ||||
\(619\) | 21.5072 | − | 6.98811i | 0.864447 | − | 0.280876i | 0.156962 | − | 0.987605i | \(-0.449830\pi\) |
0.707485 | + | 0.706729i | \(0.249830\pi\) | |||||||
\(620\) | −0.0210721 | + | 0.0648532i | −0.000846275 | + | 0.00260457i | ||||
\(621\) | 5.73577 | + | 4.16728i | 0.230169 | + | 0.167227i | ||||
\(622\) | 10.6025 | − | 14.5930i | 0.425120 | − | 0.585128i | ||||
\(623\) | −11.4134 | + | 35.1267i | −0.457267 | + | 1.40732i | ||||
\(624\) | −16.2044 | − | 2.64136i | −0.648695 | − | 0.105739i | ||||
\(625\) | 3.78244 | − | 2.74810i | 0.151298 | − | 0.109924i | ||||
\(626\) | − | 43.8767i | − | 1.75366i | ||||||
\(627\) | −19.2052 | − | 4.62592i | −0.766983 | − | 0.184741i | ||||
\(628\) | 4.79848 | 0.191480 | ||||||||
\(629\) | −8.40303 | − | 11.5658i | −0.335051 | − | 0.461158i | ||||
\(630\) | 6.38303 | − | 2.07397i | 0.254306 | − | 0.0826290i | ||||
\(631\) | 9.97216 | + | 3.24015i | 0.396985 | + | 0.128988i | 0.500705 | − | 0.865618i | \(-0.333074\pi\) |
−0.103719 | + | 0.994607i | \(0.533074\pi\) | |||||||
\(632\) | 2.42624 | − | 3.33943i | 0.0965105 | − | 0.132835i | ||||
\(633\) | −9.08393 | − | 6.59986i | −0.361054 | − | 0.262321i | ||||
\(634\) | −1.74552 | + | 5.37215i | −0.0693233 | + | 0.213355i | ||||
\(635\) | −22.3339 | + | 7.25673i | −0.886294 | + | 0.287974i | ||||
\(636\) | −1.82712 | + | 1.32748i | −0.0724499 | + | 0.0526379i | ||||
\(637\) | −2.04380 | + | 3.96694i | −0.0809783 | + | 0.157176i | ||||
\(638\) | 18.1379 | − | 29.5489i | 0.718086 | − | 1.16985i | ||||
\(639\) | 2.66683i | 0.105498i | ||||||||
\(640\) | −16.4648 | + | 11.9623i | −0.650827 | + | 0.472853i | ||||
\(641\) | 6.78945 | + | 20.8958i | 0.268167 | + | 0.825334i | 0.990947 | + | 0.134255i | \(0.0428643\pi\) |
−0.722779 | + | 0.691079i | \(0.757136\pi\) | |||||||
\(642\) | 18.0378 | + | 5.86085i | 0.711897 | + | 0.231309i | ||||
\(643\) | 8.23217 | − | 11.3306i | 0.324645 | − | 0.446836i | −0.615233 | − | 0.788345i | \(-0.710938\pi\) |
0.939878 | + | 0.341510i | \(0.110938\pi\) | |||||||
\(644\) | 3.96943 | − | 5.46345i | 0.156417 | − | 0.215290i | ||||
\(645\) | −8.27046 | − | 2.68724i | −0.325649 | − | 0.105810i | ||||
\(646\) | 14.2358 | + | 43.8132i | 0.560099 | + | 1.72381i | ||||
\(647\) | 29.7896 | − | 21.6434i | 1.17115 | − | 0.850890i | 0.180004 | − | 0.983666i | \(-0.442389\pi\) |
0.991146 | + | 0.132776i | \(0.0423890\pi\) | |||||||
\(648\) | − | 2.54731i | − | 0.100068i | ||||||
\(649\) | −41.5563 | + | 17.1769i | −1.63123 | + | 0.674253i | ||||
\(650\) | −12.9950 | − | 6.69516i | −0.509708 | − | 0.262606i | ||||
\(651\) | 0.311563 | − | 0.226364i | 0.0122111 | − | 0.00887189i | ||||
\(652\) | 2.45481 | − | 0.797617i | 0.0961378 | − | 0.0312371i | ||||
\(653\) | 6.74434 | − | 20.7569i | 0.263926 | − | 0.812281i | −0.728013 | − | 0.685564i | \(-0.759556\pi\) |
0.991939 | − | 0.126718i | \(-0.0404442\pi\) | |||||||
\(654\) | −8.50268 | − | 6.17756i | −0.332481 | − | 0.241562i | ||||
\(655\) | −11.1860 | + | 15.3962i | −0.437073 | + | 0.601579i | ||||
\(656\) | 39.9351 | + | 12.9757i | 1.55920 | + | 0.506616i | ||||
\(657\) | 4.32333 | − | 1.40473i | 0.168669 | − | 0.0548039i | ||||
\(658\) | 21.0340 | + | 28.9508i | 0.819991 | + | 1.12862i | ||||
\(659\) | −20.5211 | −0.799387 | −0.399693 | − | 0.916649i | \(-0.630883\pi\) | ||||
−0.399693 | + | 0.916649i | \(0.630883\pi\) | |||||||
\(660\) | −0.130992 | − | 1.68043i | −0.00509886 | − | 0.0654105i | ||||
\(661\) | 24.6891i | 0.960294i | 0.877188 | + | 0.480147i | \(0.159417\pi\) | ||||
−0.877188 | + | 0.480147i | \(0.840583\pi\) | |||||||
\(662\) | 4.68368 | − | 3.40289i | 0.182036 | − | 0.132257i | ||||
\(663\) | 18.0241 | + | 2.93797i | 0.699999 | + | 0.114101i | ||||
\(664\) | −2.88285 | + | 8.87251i | −0.111876 | + | 0.344320i | ||||
\(665\) | 15.3871 | − | 21.1785i | 0.596686 | − | 0.821267i | ||||
\(666\) | −3.48699 | − | 2.53345i | −0.135118 | − | 0.0981691i | ||||
\(667\) | −14.9983 | + | 46.1600i | −0.580736 | + | 1.78732i | ||||
\(668\) | 3.37500 | − | 1.09660i | 0.130583 | − | 0.0424289i | ||||
\(669\) | 12.2251 | + | 16.8263i | 0.472648 | + | 0.650544i | ||||
\(670\) | − | 4.59755i | − | 0.177619i | ||||||
\(671\) | −36.0463 | + | 2.80987i | −1.39155 | + | 0.108474i | ||||
\(672\) | −5.33546 | −0.205820 | ||||||||
\(673\) | 3.32376 | − | 2.41485i | 0.128121 | − | 0.0930857i | −0.521879 | − | 0.853020i | \(-0.674769\pi\) |
0.650000 | + | 0.759934i | \(0.274769\pi\) | |||||||
\(674\) | −36.9080 | + | 11.9921i | −1.42164 | + | 0.461920i | ||||
\(675\) | 0.820459 | − | 2.52511i | 0.0315795 | − | 0.0971916i | ||||
\(676\) | 0.0388430 | − | 4.31418i | 0.00149396 | − | 0.165930i | ||||
\(677\) | 11.7393 | + | 8.52913i | 0.451180 | + | 0.327801i | 0.790061 | − | 0.613028i | \(-0.210049\pi\) |
−0.338882 | + | 0.940829i | \(0.610049\pi\) | |||||||
\(678\) | 3.17938 | + | 1.03304i | 0.122103 | + | 0.0396738i | ||||
\(679\) | −3.23878 | − | 9.96794i | −0.124293 | − | 0.382534i | ||||
\(680\) | 15.9839 | − | 11.6129i | 0.612953 | − | 0.445336i | ||||
\(681\) | 19.5769i | 0.750189i | ||||||||
\(682\) | −0.259592 | − | 0.628035i | −0.00994031 | − | 0.0240487i | ||||
\(683\) | − | 4.39105i | − | 0.168019i | −0.996465 | − | 0.0840094i | \(-0.973227\pi\) | ||
0.996465 | − | 0.0840094i | \(-0.0267726\pi\) | |||||||
\(684\) | 1.16188 | + | 1.59919i | 0.0444256 | + | 0.0611466i | ||||
\(685\) | −2.06282 | − | 6.34871i | −0.0788164 | − | 0.242572i | ||||
\(686\) | 7.80432 | − | 24.0192i | 0.297970 | − | 0.917059i | ||||
\(687\) | −12.6575 | + | 17.4215i | −0.482913 | + | 0.664673i | ||||
\(688\) | 20.9204 | + | 15.1996i | 0.797584 | + | 0.579479i | ||||
\(689\) | 17.2714 | + | 17.4276i | 0.657989 | + | 0.663940i | ||||
\(690\) | 5.12312 | + | 15.7674i | 0.195034 | + | 0.600253i | ||||
\(691\) | 8.29259 | + | 11.4138i | 0.315465 | + | 0.434200i | 0.937076 | − | 0.349126i | \(-0.113521\pi\) |
−0.621611 | + | 0.783326i | \(0.713521\pi\) | |||||||
\(692\) | −5.45601 | −0.207406 | ||||||||
\(693\) | −4.97980 | + | 8.11271i | −0.189167 | + | 0.308176i | ||||
\(694\) | 35.3065i | 1.34022i | ||||||||
\(695\) | −11.5975 | − | 15.9626i | −0.439918 | − | 0.605495i | ||||
\(696\) | 16.5849 | − | 5.38876i | 0.628649 | − | 0.204260i | ||||
\(697\) | −44.4197 | − | 14.4328i | −1.68252 | − | 0.546683i | ||||
\(698\) | 15.0741 | + | 10.9520i | 0.570564 | + | 0.414539i | ||||
\(699\) | −3.00491 | − | 2.18319i | −0.113656 | − | 0.0825760i | ||||
\(700\) | −2.40523 | − | 0.781505i | −0.0909090 | − | 0.0295381i | ||||
\(701\) | 5.62251 | + | 17.3043i | 0.212359 | + | 0.653574i | 0.999331 | + | 0.0365849i | \(0.0116479\pi\) |
−0.786971 | + | 0.616990i | \(0.788352\pi\) | |||||||
\(702\) | 5.44188 | − | 0.836815i | 0.205391 | − | 0.0315836i | ||||
\(703\) | −16.8117 | −0.634064 | ||||||||
\(704\) | 4.86846 | − | 20.2122i | 0.183487 | − | 0.761776i | ||||
\(705\) | −12.5030 | −0.470891 | ||||||||
\(706\) | 2.48652 | − | 1.80656i | 0.0935814 | − | 0.0679908i | ||||
\(707\) | −54.0369 | + | 17.5577i | −2.03227 | + | 0.660324i | ||||
\(708\) | 4.27928 | + | 1.39042i | 0.160825 | + | 0.0522553i | ||||
\(709\) | 13.0224 | − | 17.9238i | 0.489066 | − | 0.673142i | −0.491149 | − | 0.871075i | \(-0.663423\pi\) |
0.980215 | + | 0.197934i | \(0.0634230\pi\) | |||||||
\(710\) | −3.66549 | + | 5.04512i | −0.137564 | + | 0.189340i | ||||
\(711\) | −0.500743 | + | 1.54113i | −0.0187793 | + | 0.0577969i | ||||
\(712\) | 10.1296 | + | 31.1758i | 0.379623 | + | 1.16836i | ||||
\(713\) | 0.559163 | + | 0.769622i | 0.0209408 | + | 0.0288226i | ||||
\(714\) | 22.1989 | 0.830773 | ||||||||
\(715\) | −17.8281 | + | 4.18134i | −0.666735 | + | 0.156373i | ||||
\(716\) | 0.307340 | 0.0114858 | ||||||||
\(717\) | −6.06258 | − | 8.34443i | −0.226411 | − | 0.311628i | ||||
\(718\) | −6.69796 | − | 20.6142i | −0.249966 | − | 0.769315i | ||||
\(719\) | −4.95950 | + | 15.2638i | −0.184958 | + | 0.569243i | −0.999948 | − | 0.0102330i | \(-0.996743\pi\) |
0.814989 | + | 0.579476i | \(0.196743\pi\) | |||||||
\(720\) | 4.09864 | − | 5.64130i | 0.152747 | − | 0.210239i | ||||
\(721\) | 31.4296 | − | 43.2592i | 1.17050 | − | 1.61106i | ||||
\(722\) | 23.9288 | + | 7.77494i | 0.890537 | + | 0.289353i | ||||
\(723\) | 2.28047 | − | 0.740970i | 0.0848117 | − | 0.0275570i | ||||
\(724\) | −1.23397 | + | 0.896531i | −0.0458601 | + | 0.0333193i | ||||
\(725\) | 18.1760 | 0.675041 | ||||||||
\(726\) | 11.8599 | + | 11.8953i | 0.440163 | + | 0.441477i | ||||
\(727\) | 5.27678 | 0.195705 | 0.0978524 | − | 0.995201i | \(-0.468803\pi\) | ||||
0.0978524 | + | 0.995201i | \(0.468803\pi\) | |||||||
\(728\) | 4.00646 | + | 26.0544i | 0.148489 | + | 0.965639i | ||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | 10.1097 | + | 3.28483i | 0.374175 | + | 0.121577i | ||||
\(731\) | −23.2698 | − | 16.9065i | −0.860663 | − | 0.625308i | ||||
\(732\) | 2.92692 | + | 2.12653i | 0.108182 | + | 0.0785989i | ||||
\(733\) | −5.67056 | − | 1.84248i | −0.209447 | − | 0.0680535i | 0.202414 | − | 0.979300i | \(-0.435121\pi\) |
−0.411861 | + | 0.911247i | \(0.635121\pi\) | |||||||
\(734\) | 6.98787 | − | 2.27050i | 0.257927 | − | 0.0838056i | ||||
\(735\) | −1.11401 | − | 1.53330i | −0.0410909 | − | 0.0565567i | ||||
\(736\) | − | 13.1796i | − | 0.485808i | ||||||
\(737\) | 4.23126 | + | 4.96165i | 0.155860 | + | 0.182765i | ||||
\(738\) | −14.0814 | −0.518343 | ||||||||
\(739\) | −8.36340 | − | 11.5112i | −0.307653 | − | 0.423447i | 0.626995 | − | 0.779023i | \(-0.284285\pi\) |
−0.934647 | + | 0.355576i | \(0.884285\pi\) | |||||||
\(740\) | −0.443264 | − | 1.36423i | −0.0162947 | − | 0.0501499i | ||||
\(741\) | 15.2536 | − | 15.1169i | 0.560355 | − | 0.555333i | ||||
\(742\) | 24.1295 | + | 17.5311i | 0.885821 | + | 0.643587i | ||||
\(743\) | 14.5578 | − | 20.0371i | 0.534075 | − | 0.735091i | −0.453670 | − | 0.891170i | \(-0.649885\pi\) |
0.987745 | + | 0.156079i | \(0.0498855\pi\) | |||||||
\(744\) | 0.105621 | − | 0.325068i | 0.00387225 | − | 0.0119176i | ||||
\(745\) | −5.59737 | − | 17.2269i | −0.205072 | − | 0.631145i | ||||
\(746\) | −27.5955 | − | 37.9819i | −1.01034 | − | 1.39062i | ||||
\(747\) | − | 3.66234i | − | 0.133998i | ||||||
\(748\) | 1.30550 | − | 5.42000i | 0.0477339 | − | 0.198175i | ||||
\(749\) | − | 35.6474i | − | 1.30253i | ||||||
\(750\) | 14.4819 | − | 10.5217i | 0.528803 | − | 0.384198i | ||||
\(751\) | −0.350410 | − | 1.07845i | −0.0127866 | − | 0.0393532i | 0.944460 | − | 0.328627i | \(-0.106586\pi\) |
−0.957246 | + | 0.289274i | \(0.906586\pi\) | |||||||
\(752\) | 35.3599 | + | 11.4891i | 1.28944 | + | 0.418965i | ||||
\(753\) | 7.79775 | + | 5.66539i | 0.284166 | + | 0.206458i | ||||
\(754\) | 16.9605 | + | 33.6605i | 0.617663 | + | 1.22584i | ||||
\(755\) | −7.14460 | + | 21.9888i | −0.260018 | + | 0.800254i | ||||
\(756\) | 0.905903 | − | 0.294346i | 0.0329474 | − | 0.0107052i | ||||
\(757\) | −14.5536 | + | 10.5738i | −0.528958 | + | 0.384310i | −0.819968 | − | 0.572410i | \(-0.806009\pi\) |
0.291010 | + | 0.956720i | \(0.406009\pi\) | |||||||
\(758\) | −32.2831 | −1.17258 | ||||||||
\(759\) | −20.0400 | − | 12.3011i | −0.727406 | − | 0.446501i | ||||
\(760\) | − | 23.2336i | − | 0.842772i | ||||||
\(761\) | 8.00173 | + | 11.0134i | 0.290062 | + | 0.399237i | 0.929034 | − | 0.369993i | \(-0.120640\pi\) |
−0.638972 | + | 0.769230i | \(0.720640\pi\) | |||||||
\(762\) | −22.2716 | + | 7.23648i | −0.806815 | + | 0.262150i | ||||
\(763\) | −6.10422 | + | 18.7869i | −0.220988 | + | 0.680130i | ||||
\(764\) | −1.06876 | − | 0.776498i | −0.0386663 | − | 0.0280927i | ||||
\(765\) | −4.55891 | + | 6.27480i | −0.164828 | + | 0.226866i | ||||
\(766\) | 10.1263 | − | 31.1656i | 0.365878 | − | 1.12606i | ||||
\(767\) | 7.86435 | − | 48.2469i | 0.283965 | − | 1.74209i | ||||
\(768\) | −6.27618 | + | 4.55991i | −0.226472 | + | 0.164542i | ||||
\(769\) | 13.0178i | 0.469434i | 0.972064 | + | 0.234717i | \(0.0754164\pi\) | ||||
−0.972064 | + | 0.234717i | \(0.924584\pi\) | |||||||
\(770\) | −20.5715 | + | 8.50304i | −0.741346 | + | 0.306428i | ||||
\(771\) | −2.77171 | −0.0998205 | ||||||||
\(772\) | −0.336630 | − | 0.463332i | −0.0121156 | − | 0.0166757i | ||||
\(773\) | −18.3992 | + | 5.97827i | −0.661774 | + | 0.215024i | −0.620599 | − | 0.784128i | \(-0.713110\pi\) |
−0.0411757 | + | 0.999152i | \(0.513110\pi\) | |||||||
\(774\) | −8.24739 | − | 2.67974i | −0.296446 | − | 0.0963212i | ||||
\(775\) | 0.209401 | − | 0.288216i | 0.00752191 | − | 0.0103530i | ||||
\(776\) | −7.52551 | − | 5.46760i | −0.270150 | − | 0.196275i | ||||
\(777\) | −2.50337 | + | 7.70459i | −0.0898080 | + | 0.276401i | ||||
\(778\) | −20.6175 | + | 6.69904i | −0.739174 | + | 0.240172i | ||||
\(779\) | −44.4345 | + | 32.2835i | −1.59203 | + | 1.15668i | ||||
\(780\) | 1.62888 | + | 0.839215i | 0.0583233 | + | 0.0300487i | ||||
\(781\) | −0.687387 | − | 8.81813i | −0.0245967 | − | 0.315537i | ||||
\(782\) | 54.8357i | 1.96092i | ||||||||
\(783\) | −5.53838 | + | 4.02387i | −0.197926 | + | 0.143801i | ||||
\(784\) | 1.74158 | + | 5.36002i | 0.0621991 | + | 0.191429i | ||||
\(785\) | 21.0573 | + | 6.84194i | 0.751568 | + | 0.244199i | ||||
\(786\) | −11.1548 | + | 15.3532i | −0.397878 | + | 0.547632i | ||||
\(787\) | 31.9849 | − | 44.0234i | 1.14014 | − | 1.56927i | 0.372941 | − | 0.927855i | \(-0.378349\pi\) |
0.767198 | − | 0.641411i | \(-0.221651\pi\) | |||||||
\(788\) | −1.94176 | − | 0.630915i | −0.0691722 | − | 0.0224754i | ||||
\(789\) | −7.25245 | − | 22.3208i | −0.258194 | − | 0.794640i | ||||
\(790\) | −3.06555 | + | 2.22725i | −0.109067 | + | 0.0792422i | ||||
\(791\) | − | 6.28328i | − | 0.223408i | ||||||
\(792\) | 0.656580 | + | 8.42291i | 0.0233305 | + | 0.299295i | ||||
\(793\) | 18.0017 | − | 34.9407i | 0.639261 | − | 1.24078i | ||||
\(794\) | 23.0880 | − | 16.7744i | 0.819363 | − | 0.595302i | ||||
\(795\) | −9.91078 | + | 3.22021i | −0.351499 | + | 0.114209i | ||||
\(796\) | 2.06653 | − | 6.36012i | 0.0732461 | − | 0.225428i | ||||
\(797\) | −18.7720 | − | 13.6387i | −0.664940 | − | 0.483107i | 0.203388 | − | 0.979098i | \(-0.434805\pi\) |
−0.868327 | + | 0.495991i | \(0.834805\pi\) | |||||||
\(798\) | 15.3442 | − | 21.1194i | 0.543177 | − | 0.747619i | ||||
\(799\) | −39.3307 | − | 12.7793i | −1.39142 | − | 0.452100i | ||||
\(800\) | −4.69408 | + | 1.52520i | −0.165961 | + | 0.0539239i | ||||
\(801\) | −7.56394 | − | 10.4109i | −0.267259 | − | 0.367850i | ||||
\(802\) | 31.2565 | 1.10371 | ||||||||
\(803\) | −13.9334 | + | 5.75924i | −0.491700 | + | 0.203239i | ||||
\(804\) | − | 0.652501i | − | 0.0230119i | ||||||
\(805\) | 25.2092 | − | 18.3156i | 0.888509 | − | 0.645540i | ||||
\(806\) | 0.729148 | + | 0.118853i | 0.0256832 | + | 0.00418641i | ||||
\(807\) | 4.72642 | − | 14.5464i | 0.166378 | − | 0.512059i | ||||
\(808\) | −29.6403 | + | 40.7963i | −1.04274 | + | 1.43521i | ||||
\(809\) | −6.58345 | − | 4.78316i | −0.231462 | − | 0.168167i | 0.466009 | − | 0.884780i | \(-0.345691\pi\) |
−0.697471 | + | 0.716613i | \(0.745691\pi\) | |||||||
\(810\) | −0.722605 | + | 2.22395i | −0.0253897 | + | 0.0781416i | ||||
\(811\) | 21.4262 | − | 6.96181i | 0.752377 | − | 0.244462i | 0.0923732 | − | 0.995724i | \(-0.470555\pi\) |
0.660004 | + | 0.751262i | \(0.270555\pi\) | |||||||
\(812\) | 3.83282 | + | 5.27543i | 0.134506 | + | 0.185131i | ||||
\(813\) | 9.67260i | 0.339233i | ||||||||
\(814\) | 12.1831 | + | 7.47830i | 0.427017 | + | 0.262114i | ||||
\(815\) | 11.9098 | 0.417182 | ||||||||
\(816\) | 18.6591 | − | 13.5566i | 0.653198 | − | 0.474576i | ||||
\(817\) | −32.1687 | + | 10.4522i | −1.12544 | + | 0.365678i | ||||
\(818\) | −5.02332 | + | 15.4602i | −0.175636 | + | 0.540553i | ||||
\(819\) | −4.65653 | − | 9.24156i | −0.162712 | − | 0.322926i | ||||
\(820\) | −3.79131 | − | 2.75455i | −0.132398 | − | 0.0961930i | ||||
\(821\) | −27.3257 | − | 8.87865i | −0.953672 | − | 0.309867i | −0.209465 | − | 0.977816i | \(-0.567172\pi\) |
−0.744207 | + | 0.667949i | \(0.767172\pi\) | |||||||
\(822\) | −2.05707 | − | 6.33100i | −0.0717485 | − | 0.220819i | ||||
\(823\) | 40.9503 | − | 29.7521i | 1.42744 | − | 1.03709i | 0.436951 | − | 0.899485i | \(-0.356058\pi\) |
0.990487 | − | 0.137608i | \(-0.0439416\pi\) | |||||||
\(824\) | − | 47.4569i | − | 1.65324i | ||||||
\(825\) | −2.06207 | + | 8.56100i | −0.0717919 | + | 0.298056i | ||||
\(826\) | − | 59.4219i | − | 2.06755i | ||||||
\(827\) | −3.23075 | − | 4.44675i | −0.112344 | − | 0.154629i | 0.749142 | − | 0.662409i | \(-0.230466\pi\) |
−0.861486 | + | 0.507781i | \(0.830466\pi\) | |||||||
\(828\) | 0.727092 | + | 2.23776i | 0.0252682 | + | 0.0777675i | ||||
\(829\) | −4.46937 | + | 13.7553i | −0.155228 | + | 0.477741i | −0.998184 | − | 0.0602408i | \(-0.980813\pi\) |
0.842956 | + | 0.537982i | \(0.180813\pi\) | |||||||
\(830\) | 5.03380 | − | 6.92843i | 0.174726 | − | 0.240489i | ||||
\(831\) | −4.96048 | − | 3.60400i | −0.172077 | − | 0.125021i | ||||
\(832\) | 15.9095 | + | 16.0534i | 0.551562 | + | 0.556551i | ||||
\(833\) | −1.93715 | − | 5.96194i | −0.0671183 | − | 0.206569i | ||||
\(834\) | −11.5651 | − | 15.9180i | −0.400468 | − | 0.551196i | ||||
\(835\) | 16.3742 | 0.566652 | ||||||||
\(836\) | −4.25406 | − | 4.98840i | −0.147130 | − | 0.172527i | ||||
\(837\) | 0.134179i | 0.00463792i | ||||||||
\(838\) | 17.3813 | + | 23.9233i | 0.600426 | + | 0.826416i | ||||
\(839\) | 4.33203 | − | 1.40756i | 0.149558 | − | 0.0485945i | −0.233281 | − | 0.972409i | \(-0.574946\pi\) |
0.382839 | + | 0.923815i | \(0.374946\pi\) | |||||||
\(840\) | −10.6477 | − | 3.45965i | −0.367381 | − | 0.119369i | ||||
\(841\) | −14.4532 | − | 10.5009i | −0.498387 | − | 0.362099i | ||||
\(842\) | −10.1933 | − | 7.40587i | −0.351285 | − | 0.255223i | ||||
\(843\) | −11.6328 | − | 3.77971i | −0.400654 | − | 0.130180i | ||||
\(844\) | −1.15152 | − | 3.54401i | −0.0396370 | − | 0.121990i | ||||
\(845\) | 6.32186 | − | 18.8767i | 0.217478 | − | 0.649377i | ||||
\(846\) | −12.4681 | −0.428663 | ||||||||
\(847\) | 14.3751 | − | 28.1090i | 0.493933 | − | 0.965836i | ||||
\(848\) | 30.9878 | 1.06413 | ||||||||
\(849\) | −25.0666 | + | 18.2119i | −0.860282 | + | 0.625032i | ||||
\(850\) | 19.5303 | − | 6.34579i | 0.669885 | − | 0.217659i | ||||
\(851\) | −19.0319 | − | 6.18383i | −0.652404 | − | 0.211979i | ||||
\(852\) | −0.520220 | + | 0.716022i | −0.0178225 | + | 0.0245305i | ||||
\(853\) | −29.6938 | + | 40.8701i | −1.01670 | + | 1.39936i | −0.102205 | + | 0.994763i | \(0.532590\pi\) |
−0.914493 | + | 0.404601i | \(0.867410\pi\) | |||||||
\(854\) | 14.7645 | − | 45.4403i | 0.505229 | − | 1.55494i | ||||
\(855\) | 2.81850 | + | 8.67445i | 0.0963906 | + | 0.296660i | ||||
\(856\) | −18.5963 | − | 25.5956i | −0.635607 | − | 0.874838i | ||||
\(857\) | −7.84322 | −0.267919 | −0.133960 | − | 0.990987i | \(-0.542769\pi\) | ||||
−0.133960 | + | 0.990987i | \(0.542769\pi\) | |||||||
\(858\) | −17.7784 | + | 4.16968i | −0.606945 | + | 0.142350i | ||||
\(859\) | −22.9393 | −0.782678 | −0.391339 | − | 0.920247i | \(-0.627988\pi\) | ||||
−0.391339 | + | 0.920247i | \(0.627988\pi\) | |||||||
\(860\) | −1.69635 | − | 2.33482i | −0.0578450 | − | 0.0796168i | ||||
\(861\) | 8.17857 | + | 25.1710i | 0.278725 | + | 0.857827i | ||||
\(862\) | −1.37999 | + | 4.24717i | −0.0470027 | + | 0.144659i | ||||
\(863\) | −6.23551 | + | 8.58245i | −0.212259 | + | 0.292150i | −0.901850 | − | 0.432050i | \(-0.857791\pi\) |
0.689591 | + | 0.724200i | \(0.257791\pi\) | |||||||
\(864\) | 1.09267 | − | 1.50393i | 0.0371733 | − | 0.0511647i | ||||
\(865\) | −23.9428 | − | 7.77948i | −0.814079 | − | 0.264510i | ||||
\(866\) | 12.7101 | − | 4.12975i | 0.431906 | − | 0.140335i | ||||
\(867\) | −7.00114 | + | 5.08662i | −0.237771 | + | 0.172751i | ||||
\(868\) | 0.127809 | 0.00433812 | ||||||||
\(869\) | 1.25852 | − | 5.22496i | 0.0426924 | − | 0.177245i | ||||
\(870\) | −16.0082 | −0.542730 | ||||||||
\(871\) | −7.00656 | + | 1.07742i | −0.237408 | + | 0.0365070i | ||||
\(872\) | 5.41763 | + | 16.6737i | 0.183464 | + | 0.564644i | ||||
\(873\) | 3.47299 | + | 1.12844i | 0.117543 | + | 0.0381920i | ||||
\(874\) | 52.1692 | + | 37.9031i | 1.76465 | + | 1.28209i | ||||
\(875\) | −27.2191 | − | 19.7759i | −0.920175 | − | 0.668546i | ||||
\(876\) | 1.43480 | + | 0.466195i | 0.0484774 | + | 0.0157513i | ||||
\(877\) | −26.6255 | + | 8.65115i | −0.899080 | + | 0.292129i | −0.721857 | − | 0.692042i | \(-0.756711\pi\) |
−0.177222 | + | 0.984171i | \(0.556711\pi\) | |||||||
\(878\) | 7.31704 | + | 10.0710i | 0.246938 | + | 0.339881i | ||||
\(879\) | 5.20268i | 0.175482i | ||||||||
\(880\) | −12.0985 | + | 19.7099i | −0.407840 | + | 0.664421i | ||||
\(881\) | 28.7996 | 0.970285 | 0.485142 | − | 0.874435i | \(-0.338768\pi\) | ||||
0.485142 | + | 0.874435i | \(0.338768\pi\) | |||||||
\(882\) | −1.11090 | − | 1.52902i | −0.0374060 | − | 0.0514849i | ||||
\(883\) | −14.6511 | − | 45.0913i | −0.493048 | − | 1.51744i | −0.819978 | − | 0.572396i | \(-0.806014\pi\) |
0.326930 | − | 0.945049i | \(-0.393986\pi\) | |||||||
\(884\) | 4.26621 | + | 4.30480i | 0.143488 | + | 0.144786i | ||||
\(885\) | 16.7964 | + | 12.2033i | 0.564603 | + | 0.410208i | ||||
\(886\) | −5.67085 | + | 7.80525i | −0.190516 | + | 0.262223i | ||||
\(887\) | 14.1014 | − | 43.3996i | 0.473479 | − | 1.45722i | −0.374520 | − | 0.927219i | \(-0.622193\pi\) |
0.847999 | − | 0.529998i | \(-0.177807\pi\) | |||||||
\(888\) | 2.22180 | + | 6.83799i | 0.0745587 | + | 0.229468i | ||||
\(889\) | 25.8710 | + | 35.6084i | 0.867686 | + | 1.19427i | ||||
\(890\) | − | 30.0918i | − | 1.00868i | ||||||
\(891\) | −1.26693 | − | 3.06511i | −0.0424438 | − | 0.102685i | ||||
\(892\) | 6.90248i | 0.231112i | ||||||||
\(893\) | −39.3438 | + | 28.5849i | −1.31659 | + | 0.956559i | ||||
\(894\) | −5.58175 | − | 17.1789i | −0.186682 | − | 0.574547i | ||||
\(895\) | 1.34871 | + | 0.438222i | 0.0450824 | + | 0.0146481i | ||||
\(896\) | 30.8597 | + | 22.4209i | 1.03095 | + | 0.749029i | ||||
\(897\) | 22.8285 | − | 11.5025i | 0.762221 | − | 0.384059i | ||||
\(898\) | 5.29841 | − | 16.3068i | 0.176810 | − | 0.544166i | ||||
\(899\) | −0.873610 | + | 0.283853i | −0.0291365 | + | 0.00946703i | ||||
\(900\) | 0.712861 | − | 0.517924i | 0.0237620 | − | 0.0172641i | ||||
\(901\) | −34.4677 | −1.14829 | ||||||||
\(902\) | 46.5614 | − | 3.62954i | 1.55033 | − | 0.120850i | ||||
\(903\) | 16.2990i | 0.542395i | ||||||||
\(904\) | −3.27781 | − | 4.51152i | −0.109018 | − | 0.150051i | ||||
\(905\) | −6.69338 | + | 2.17481i | −0.222496 | + | 0.0722932i | ||||
\(906\) | −7.12466 | + | 21.9275i | −0.236701 | + | 0.728491i | ||||
\(907\) | −15.5894 | − | 11.3264i | −0.517638 | − | 0.376086i | 0.298076 | − | 0.954542i | \(-0.403655\pi\) |
−0.815713 | + | 0.578456i | \(0.803655\pi\) | |||||||
\(908\) | −3.81888 | + | 5.25624i | −0.126734 | + | 0.174434i | ||||
\(909\) | 6.11737 | − | 18.8273i | 0.202900 | − | 0.624463i | ||||
\(910\) | 3.89307 | − | 23.8835i | 0.129054 | − | 0.791730i | ||||
\(911\) | 9.72908 | − | 7.06859i | 0.322339 | − | 0.234193i | −0.414834 | − | 0.909897i | \(-0.636160\pi\) |
0.737173 | + | 0.675704i | \(0.236160\pi\) | |||||||
\(912\) | − | 27.1222i | − | 0.898106i | ||||||
\(913\) | 0.943984 | + | 12.1099i | 0.0312413 | + | 0.400778i | ||||
\(914\) | 36.9357 | 1.22173 | ||||||||
\(915\) | 9.81216 | + | 13.5053i | 0.324380 | + | 0.446471i | ||||
\(916\) | −6.79686 | + | 2.20843i | −0.224574 | + | 0.0729687i | ||||
\(917\) | 33.9233 | + | 11.0224i | 1.12025 | + | 0.363990i | ||||
\(918\) | −4.54619 | + | 6.25730i | −0.150047 | + | 0.206522i | ||||
\(919\) | −21.4070 | − | 15.5531i | −0.706151 | − | 0.513049i | 0.175779 | − | 0.984430i | \(-0.443756\pi\) |
−0.881930 | + | 0.471381i | \(0.843756\pi\) | |||||||
\(920\) | 8.54602 | − | 26.3019i | 0.281754 | − | 0.867149i | ||||
\(921\) | −32.7968 | + | 10.6563i | −1.08069 | + | 0.351138i | ||||
\(922\) | −26.1644 | + | 19.0096i | −0.861680 | + | 0.626047i | ||||
\(923\) | 8.54764 | + | 4.40382i | 0.281349 | + | 0.144954i | ||||
\(924\) | −2.91958 | + | 1.20678i | −0.0960472 | + | 0.0397002i | ||||
\(925\) | 7.49403i | 0.246402i | ||||||||
\(926\) | 2.31243 | − | 1.68008i | 0.0759913 | − | 0.0552109i | ||||
\(927\) | 5.75706 | + | 17.7184i | 0.189087 | + | 0.581949i | ||||
\(928\) | 12.1032 | + | 3.93258i | 0.397308 | + | 0.129093i | ||||
\(929\) | −4.02982 | + | 5.54658i | −0.132214 | + | 0.181977i | −0.869991 | − | 0.493067i | \(-0.835876\pi\) |
0.737777 | + | 0.675045i | \(0.235876\pi\) | |||||||
\(930\) | −0.184426 | + | 0.253841i | −0.00604758 | + | 0.00832378i | ||||
\(931\) | −7.01101 | − | 2.27801i | −0.229776 | − | 0.0746589i | ||||
\(932\) | −0.380916 | − | 1.17234i | −0.0124773 | − | 0.0384012i | ||||
\(933\) | 9.55638 | − | 6.94311i | 0.312862 | − | 0.227307i | ||||
\(934\) | − | 15.8730i | − | 0.519382i | ||||||
\(935\) | 13.4571 | − | 21.9233i | 0.440095 | − | 0.716969i | ||||
\(936\) | −8.16455 | − | 4.20645i | −0.266867 | − | 0.137492i | ||||
\(937\) | 28.8092 | − | 20.9311i | 0.941154 | − | 0.683789i | −0.00754400 | − | 0.999972i | \(-0.502401\pi\) |
0.948698 | + | 0.316183i | \(0.102401\pi\) | |||||||
\(938\) | −8.19538 | + | 2.66284i | −0.267589 | + | 0.0869449i | ||||
\(939\) | 8.87899 | − | 27.3267i | 0.289755 | − | 0.891773i | ||||
\(940\) | −3.35695 | − | 2.43897i | −0.109492 | − | 0.0795504i | ||||
\(941\) | 10.3332 | − | 14.2225i | 0.336854 | − | 0.463639i | −0.606666 | − | 0.794957i | \(-0.707493\pi\) |
0.943519 | + | 0.331318i | \(0.107493\pi\) | |||||||
\(942\) | 20.9986 | + | 6.82285i | 0.684170 | + | 0.222300i | ||||
\(943\) | −62.1775 | + | 20.2027i | −2.02478 | + | 0.657890i | ||||
\(944\) | −36.2882 | − | 49.9465i | −1.18108 | − | 1.62562i | ||||
\(945\) | 4.39509 | 0.142972 | ||||||||
\(946\) | 27.9615 | + | 6.73501i | 0.909106 | + | 0.218974i | ||||
\(947\) | 11.4919i | 0.373438i | 0.982413 | + | 0.186719i | \(0.0597854\pi\) | ||||
−0.982413 | + | 0.186719i | \(0.940215\pi\) | |||||||
\(948\) | −0.435074 | + | 0.316100i | −0.0141306 | + | 0.0102665i | ||||
\(949\) | 2.63684 | − | 16.1767i | 0.0855953 | − | 0.525117i | ||||
\(950\) | 7.46241 | − | 22.9669i | 0.242112 | − | 0.745145i | ||||
\(951\) | −2.17424 | + | 2.99259i | −0.0705046 | + | 0.0970413i | ||||
\(952\) | −29.9583 | − | 21.7660i | −0.970955 | − | 0.705440i | ||||
\(953\) | 17.7499 | − | 54.6286i | 0.574976 | − | 1.76959i | −0.0612839 | − | 0.998120i | \(-0.519520\pi\) |
0.636260 | − | 0.771475i | \(-0.280480\pi\) | |||||||
\(954\) | −9.88313 | + | 3.21122i | −0.319978 | + | 0.103967i | ||||
\(955\) | −3.58289 | − | 4.93142i | −0.115940 | − | 0.159577i | ||||
\(956\) | − | 3.42304i | − | 0.110709i | ||||||
\(957\) | 17.2760 | − | 14.7328i | 0.558454 | − | 0.476245i | ||||
\(958\) | −28.9246 | −0.934510 | ||||||||
\(959\) | −10.1222 | + | 7.35418i | −0.326862 | + | 0.237479i | ||||
\(960\) | −9.12926 | + | 2.96628i | −0.294646 | + | 0.0957362i | ||||
\(961\) | 9.57396 | − | 29.4656i | 0.308838 | − | 0.950504i | ||||
\(962\) | −13.8783 | + | 6.99284i | −0.447455 | + | 0.225458i | ||||
\(963\) | 10.0481 | + | 7.30036i | 0.323795 | + | 0.235251i | ||||
\(964\) | 0.756829 | + | 0.245909i | 0.0243758 | + | 0.00792018i | ||||
\(965\) | −0.816600 | − | 2.51324i | −0.0262873 | − | 0.0809040i | ||||
\(966\) | 25.1389 | − | 18.2645i | 0.808831 | − | 0.587650i | ||||
\(967\) | − | 43.6144i | − | 1.40254i | −0.712894 | − | 0.701271i | \(-0.752616\pi\) | ||
0.712894 | − | 0.701271i | \(-0.247384\pi\) | |||||||
\(968\) | −4.34208 | − | 27.6819i | −0.139560 | − | 0.889730i | ||||
\(969\) | 30.1680i | 0.969135i | ||||||||
\(970\) | 5.01919 | + | 6.90833i | 0.161157 | + | 0.221813i | ||||
\(971\) | −1.12494 | − | 3.46222i | −0.0361011 | − | 0.111108i | 0.931382 | − | 0.364043i | \(-0.118604\pi\) |
−0.967483 | + | 0.252935i | \(0.918604\pi\) | |||||||
\(972\) | −0.102555 | + | 0.315631i | −0.00328944 | + | 0.0101239i | ||||
\(973\) | −21.7370 | + | 29.9184i | −0.696857 | + | 0.959141i | ||||
\(974\) | 1.03052 | + | 0.748719i | 0.0330201 | + | 0.0239905i | ||||
\(975\) | −6.73856 | − | 6.79951i | −0.215807 | − | 0.217758i | ||||
\(976\) | −15.3397 | − | 47.2109i | −0.491013 | − | 1.51118i | ||||
\(977\) | −23.3251 | − | 32.1043i | −0.746236 | − | 1.02711i | −0.998236 | − | 0.0593788i | \(-0.981088\pi\) |
0.251999 | − | 0.967727i | \(-0.418912\pi\) | |||||||
\(978\) | 11.8766 | 0.379771 | ||||||||
\(979\) | 27.6943 | + | 32.4749i | 0.885114 | + | 1.03790i | ||||
\(980\) | − | 0.628989i | − | 0.0200923i | ||||||
\(981\) | −4.04543 | − | 5.56805i | −0.129160 | − | 0.177774i | ||||
\(982\) | 16.3235 | − | 5.30382i | 0.520903 | − | 0.169252i | ||||
\(983\) | 2.95644 | + | 0.960606i | 0.0942958 | + | 0.0306386i | 0.355785 | − | 0.934568i | \(-0.384214\pi\) |
−0.261489 | + | 0.965206i | \(0.584214\pi\) | |||||||
\(984\) | 19.0034 | + | 13.8068i | 0.605807 | + | 0.440144i | ||||
\(985\) | −7.62148 | − | 5.53733i | −0.242840 | − | 0.176434i | ||||
\(986\) | −50.3571 | − | 16.3620i | −1.60370 | − | 0.521072i | ||||
\(987\) | 7.24158 | + | 22.2873i | 0.230502 | + | 0.709412i | ||||
\(988\) | 7.04433 | − | 1.08323i | 0.224110 | − | 0.0344621i | ||||
\(989\) | −40.2617 | −1.28025 | ||||||||
\(990\) | 1.81613 | − | 7.53995i | 0.0577203 | − | 0.239635i | ||||
\(991\) | −1.32044 | −0.0419453 | −0.0209726 | − | 0.999780i | \(-0.506676\pi\) | ||||
−0.0209726 | + | 0.999780i | \(0.506676\pi\) | |||||||
\(992\) | 0.201796 | − | 0.146614i | 0.00640704 | − | 0.00465499i | ||||
\(993\) | 3.60565 | − | 1.17155i | 0.114422 | − | 0.0371779i | ||||
\(994\) | 11.1162 | + | 3.61187i | 0.352585 | + | 0.114562i | ||||
\(995\) | 18.1372 | − | 24.9637i | 0.574988 | − | 0.791403i | ||||
\(996\) | 0.714415 | − | 0.983308i | 0.0226371 | − | 0.0311573i | ||||
\(997\) | 2.23346 | − | 6.87389i | 0.0707345 | − | 0.217698i | −0.909440 | − | 0.415836i | \(-0.863489\pi\) |
0.980174 | + | 0.198137i | \(0.0634892\pi\) | |||||||
\(998\) | 20.5543 | + | 63.2595i | 0.650634 | + | 2.00245i | ||||
\(999\) | −1.65905 | − | 2.28349i | −0.0524900 | − | 0.0722463i |
(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 | 429.2.bb.a.25.11 | yes | 56 | |
11.4 | even | 5 | inner | 429.2.bb.a.103.4 | yes | 56 | |
13.12 | even | 2 | inner | 429.2.bb.a.25.4 | ✓ | 56 | |
143.103 | even | 10 | inner | 429.2.bb.a.103.11 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.bb.a.25.4 | ✓ | 56 | 13.12 | even | 2 | inner | |
429.2.bb.a.25.11 | yes | 56 | 1.1 | even | 1 | trivial | |
429.2.bb.a.103.4 | yes | 56 | 11.4 | even | 5 | inner | |
429.2.bb.a.103.11 | yes | 56 | 143.103 | even | 10 | inner |