Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,2,Mod(100,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.14186074890\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 9x^{10} - 2x^{9} + 59x^{8} - 13x^{7} + 175x^{6} - 50x^{5} + 380x^{4} - 64x^{3} + 280x^{2} + 48x + 144 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 100.3 | ||
Root | \(-0.903935 + 1.56566i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 143.100 |
Dual form | 143.2.e.c.133.3 |
$q$-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 \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.134198 | + | 0.232438i | −0.0948923 | + | 0.164358i | −0.909564 | − | 0.415565i | \(-0.863584\pi\) |
0.814671 | + | 0.579923i | \(0.196917\pi\) | |||||||
\(3\) | −1.17558 | + | 2.03617i | −0.678724 | + | 1.17558i | 0.296641 | + | 0.954989i | \(0.404133\pi\) |
−0.975365 | + | 0.220596i | \(0.929200\pi\) | |||||||
\(4\) | 0.963982 | + | 1.66967i | 0.481991 | + | 0.834833i | ||||
\(5\) | −2.80787 | −1.25572 | −0.627859 | − | 0.778327i | \(-0.716069\pi\) | ||||
−0.627859 | + | 0.778327i | \(0.716069\pi\) | |||||||
\(6\) | −0.315522 | − | 0.546500i | −0.128811 | − | 0.223108i | ||||
\(7\) | −1.19233 | − | 2.06518i | −0.450659 | − | 0.780565i | 0.547768 | − | 0.836630i | \(-0.315478\pi\) |
−0.998427 | + | 0.0560655i | \(0.982144\pi\) | |||||||
\(8\) | −1.05425 | −0.372733 | ||||||||
\(9\) | −1.26400 | − | 2.18931i | −0.421333 | − | 0.729769i | ||||
\(10\) | 0.376811 | − | 0.652655i | 0.119158 | − | 0.206388i | ||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | −4.53297 | −1.30856 | ||||||||
\(13\) | 1.15941 | + | 3.41405i | 0.321563 | + | 0.946888i | ||||
\(14\) | 0.640034 | 0.171056 | ||||||||
\(15\) | 3.30089 | − | 5.71731i | 0.852286 | − | 1.47620i | ||||
\(16\) | −1.78649 | + | 3.09428i | −0.446621 | + | 0.773571i | ||||
\(17\) | 0.918197 | + | 1.59036i | 0.222695 | + | 0.385720i | 0.955626 | − | 0.294584i | \(-0.0951811\pi\) |
−0.732930 | + | 0.680304i | \(0.761848\pi\) | |||||||
\(18\) | 0.678504 | 0.159925 | ||||||||
\(19\) | 4.00924 | + | 6.94420i | 0.919782 | + | 1.59311i | 0.799745 | + | 0.600340i | \(0.204968\pi\) |
0.120038 | + | 0.992769i | \(0.461698\pi\) | |||||||
\(20\) | −2.70674 | − | 4.68820i | −0.605245 | − | 1.04831i | ||||
\(21\) | 5.60675 | 1.22349 | ||||||||
\(22\) | 0.134198 | + | 0.232438i | 0.0286111 | + | 0.0495559i | ||||
\(23\) | −2.83500 | + | 4.91036i | −0.591137 | + | 1.02388i | 0.402942 | + | 0.915225i | \(0.367988\pi\) |
−0.994080 | + | 0.108655i | \(0.965346\pi\) | |||||||
\(24\) | 1.23936 | − | 2.14663i | 0.252983 | − | 0.438180i | ||||
\(25\) | 2.88414 | 0.576827 | ||||||||
\(26\) | −0.949146 | − | 0.188668i | −0.186143 | − | 0.0370009i | ||||
\(27\) | −1.10976 | −0.213574 | ||||||||
\(28\) | 2.29877 | − | 3.98159i | 0.434427 | − | 0.752450i | ||||
\(29\) | 2.35255 | − | 4.07474i | 0.436858 | − | 0.756660i | −0.560587 | − | 0.828095i | \(-0.689425\pi\) |
0.997445 | + | 0.0714351i | \(0.0227579\pi\) | |||||||
\(30\) | 0.885945 | + | 1.53450i | 0.161751 | + | 0.280160i | ||||
\(31\) | 2.36542 | 0.424841 | 0.212421 | − | 0.977178i | \(-0.431865\pi\) | ||||
0.212421 | + | 0.977178i | \(0.431865\pi\) | |||||||
\(32\) | −1.53373 | − | 2.65651i | −0.271129 | − | 0.469609i | ||||
\(33\) | 1.17558 | + | 2.03617i | 0.204643 | + | 0.354452i | ||||
\(34\) | −0.492881 | −0.0845283 | ||||||||
\(35\) | 3.34792 | + | 5.79876i | 0.565901 | + | 0.980169i | ||||
\(36\) | 2.43694 | − | 4.22091i | 0.406157 | − | 0.703484i | ||||
\(37\) | 4.85504 | − | 8.40917i | 0.798163 | − | 1.38246i | −0.122647 | − | 0.992450i | \(-0.539138\pi\) |
0.920811 | − | 0.390009i | \(-0.127528\pi\) | |||||||
\(38\) | −2.15213 | −0.349121 | ||||||||
\(39\) | −8.31459 | − | 1.65275i | −1.33140 | − | 0.264652i | ||||
\(40\) | 2.96020 | 0.468048 | ||||||||
\(41\) | 1.76127 | − | 3.05061i | 0.275065 | − | 0.476426i | −0.695087 | − | 0.718926i | \(-0.744634\pi\) |
0.970151 | + | 0.242500i | \(0.0779674\pi\) | |||||||
\(42\) | −0.752415 | + | 1.30322i | −0.116100 | + | 0.201091i | ||||
\(43\) | 0.709691 | + | 1.22922i | 0.108227 | + | 0.187454i | 0.915052 | − | 0.403336i | \(-0.132149\pi\) |
−0.806825 | + | 0.590790i | \(0.798816\pi\) | |||||||
\(44\) | 1.92796 | 0.290651 | ||||||||
\(45\) | 3.54914 | + | 6.14729i | 0.529075 | + | 0.916384i | ||||
\(46\) | −0.760901 | − | 1.31792i | −0.112189 | − | 0.194317i | ||||
\(47\) | −9.28956 | −1.35502 | −0.677510 | − | 0.735513i | \(-0.736941\pi\) | ||||
−0.677510 | + | 0.735513i | \(0.736941\pi\) | |||||||
\(48\) | −4.20033 | − | 7.27518i | −0.606265 | − | 1.05008i | ||||
\(49\) | 0.656686 | − | 1.13741i | 0.0938123 | − | 0.162488i | ||||
\(50\) | −0.387045 | + | 0.670382i | −0.0547365 | + | 0.0948064i | ||||
\(51\) | −4.31767 | −0.604595 | ||||||||
\(52\) | −4.58268 | + | 5.22691i | −0.635503 | + | 0.724843i | ||||
\(53\) | 11.3543 | 1.55963 | 0.779814 | − | 0.626012i | \(-0.215314\pi\) | ||||
0.779814 | + | 0.626012i | \(0.215314\pi\) | |||||||
\(54\) | 0.148928 | − | 0.257951i | 0.0202665 | − | 0.0351026i | ||||
\(55\) | −1.40394 | + | 2.43169i | −0.189307 | + | 0.327889i | ||||
\(56\) | 1.25702 | + | 2.17722i | 0.167976 | + | 0.290943i | ||||
\(57\) | −18.8528 | −2.49711 | ||||||||
\(58\) | 0.631416 | + | 1.09364i | 0.0829089 | + | 0.143602i | ||||
\(59\) | 4.36291 | + | 7.55678i | 0.568002 | + | 0.983809i | 0.996763 | + | 0.0803910i | \(0.0256169\pi\) |
−0.428761 | + | 0.903418i | \(0.641050\pi\) | |||||||
\(60\) | 12.7280 | 1.64318 | ||||||||
\(61\) | 3.96207 | + | 6.86251i | 0.507291 | + | 0.878654i | 0.999964 | + | 0.00843957i | \(0.00268643\pi\) |
−0.492673 | + | 0.870214i | \(0.663980\pi\) | |||||||
\(62\) | −0.317434 | + | 0.549812i | −0.0403142 | + | 0.0698262i | ||||
\(63\) | −3.01421 | + | 5.22077i | −0.379755 | + | 0.657755i | ||||
\(64\) | −6.32265 | −0.790331 | ||||||||
\(65\) | −3.25548 | − | 9.58622i | −0.403792 | − | 1.18902i | ||||
\(66\) | −0.631044 | −0.0776762 | ||||||||
\(67\) | 0.331554 | − | 0.574268i | 0.0405058 | − | 0.0701580i | −0.845062 | − | 0.534669i | \(-0.820436\pi\) |
0.885568 | + | 0.464511i | \(0.153770\pi\) | |||||||
\(68\) | −1.77025 | + | 3.06616i | −0.214674 | + | 0.371827i | ||||
\(69\) | −6.66555 | − | 11.5451i | −0.802438 | − | 1.38986i | ||||
\(70\) | −1.79713 | −0.214799 | ||||||||
\(71\) | −1.77031 | − | 3.06627i | −0.210097 | − | 0.363899i | 0.741647 | − | 0.670790i | \(-0.234045\pi\) |
−0.951745 | + | 0.306891i | \(0.900711\pi\) | |||||||
\(72\) | 1.33257 | + | 2.30808i | 0.157045 | + | 0.272009i | ||||
\(73\) | −2.81169 | −0.329084 | −0.164542 | − | 0.986370i | \(-0.552615\pi\) | ||||
−0.164542 | + | 0.986370i | \(0.552615\pi\) | |||||||
\(74\) | 1.30307 | + | 2.25699i | 0.151479 | + | 0.262370i | ||||
\(75\) | −3.39055 | + | 5.87260i | −0.391507 | + | 0.678109i | ||||
\(76\) | −7.72967 | + | 13.3882i | −0.886653 | + | 1.53573i | ||||
\(77\) | −2.38467 | −0.271758 | ||||||||
\(78\) | 1.49996 | − | 1.71083i | 0.169837 | − | 0.193713i | ||||
\(79\) | 9.63788 | 1.08435 | 0.542173 | − | 0.840267i | \(-0.317602\pi\) | ||||
0.542173 | + | 0.840267i | \(0.317602\pi\) | |||||||
\(80\) | 5.01622 | − | 8.68835i | 0.560830 | − | 0.971387i | ||||
\(81\) | 5.09661 | − | 8.82759i | 0.566290 | − | 0.980844i | ||||
\(82\) | 0.472718 | + | 0.818772i | 0.0522030 | + | 0.0904183i | ||||
\(83\) | 3.79517 | 0.416574 | 0.208287 | − | 0.978068i | \(-0.433211\pi\) | ||||
0.208287 | + | 0.978068i | \(0.433211\pi\) | |||||||
\(84\) | 5.40481 | + | 9.36140i | 0.589713 | + | 1.02141i | ||||
\(85\) | −2.57818 | − | 4.46554i | −0.279643 | − | 0.484355i | ||||
\(86\) | −0.380956 | −0.0410796 | ||||||||
\(87\) | 5.53125 | + | 9.58040i | 0.593012 | + | 1.02713i | ||||
\(88\) | −0.527125 | + | 0.913007i | −0.0561917 | + | 0.0973269i | ||||
\(89\) | −1.53569 | + | 2.65989i | −0.162783 | + | 0.281948i | −0.935866 | − | 0.352357i | \(-0.885380\pi\) |
0.773083 | + | 0.634305i | \(0.218714\pi\) | |||||||
\(90\) | −1.90515 | −0.200820 | ||||||||
\(91\) | 5.66824 | − | 6.46508i | 0.594193 | − | 0.677725i | ||||
\(92\) | −10.9315 | −1.13969 | ||||||||
\(93\) | −2.78075 | + | 4.81639i | −0.288350 | + | 0.499437i | ||||
\(94\) | 1.24664 | − | 2.15924i | 0.128581 | − | 0.222709i | ||||
\(95\) | −11.2574 | − | 19.4984i | −1.15499 | − | 2.00050i | ||||
\(96\) | 7.21214 | 0.736086 | ||||||||
\(97\) | 0.765158 | + | 1.32529i | 0.0776900 | + | 0.134563i | 0.902253 | − | 0.431207i | \(-0.141912\pi\) |
−0.824563 | + | 0.565770i | \(0.808579\pi\) | |||||||
\(98\) | 0.176252 | + | 0.305277i | 0.0178041 | + | 0.0308376i | ||||
\(99\) | −2.52800 | −0.254073 | ||||||||
\(100\) | 2.78026 | + | 4.81554i | 0.278026 | + | 0.481554i | ||||
\(101\) | 3.34904 | − | 5.80071i | 0.333242 | − | 0.577192i | −0.649904 | − | 0.760017i | \(-0.725191\pi\) |
0.983146 | + | 0.182825i | \(0.0585241\pi\) | |||||||
\(102\) | 0.579423 | − | 1.00359i | 0.0573714 | − | 0.0993702i | ||||
\(103\) | −14.6760 | −1.44607 | −0.723034 | − | 0.690812i | \(-0.757253\pi\) | ||||
−0.723034 | + | 0.690812i | \(0.757253\pi\) | |||||||
\(104\) | −1.22231 | − | 3.59926i | −0.119857 | − | 0.352937i | ||||
\(105\) | −15.7430 | −1.53636 | ||||||||
\(106\) | −1.52372 | + | 2.63916i | −0.147997 | + | 0.256338i | ||||
\(107\) | −8.64052 | + | 14.9658i | −0.835311 | + | 1.44680i | 0.0584665 | + | 0.998289i | \(0.481379\pi\) |
−0.893777 | + | 0.448511i | \(0.851954\pi\) | |||||||
\(108\) | −1.06979 | − | 1.85293i | −0.102941 | − | 0.178299i | ||||
\(109\) | −8.75670 | −0.838740 | −0.419370 | − | 0.907815i | \(-0.637749\pi\) | ||||
−0.419370 | + | 0.907815i | \(0.637749\pi\) | |||||||
\(110\) | −0.376811 | − | 0.652655i | −0.0359275 | − | 0.0622282i | ||||
\(111\) | 11.4150 | + | 19.7714i | 1.08347 | + | 1.87662i | ||||
\(112\) | 8.52034 | 0.805096 | ||||||||
\(113\) | 1.22190 | + | 2.11639i | 0.114946 | + | 0.199093i | 0.917758 | − | 0.397139i | \(-0.129997\pi\) |
−0.802812 | + | 0.596232i | \(0.796664\pi\) | |||||||
\(114\) | 2.53001 | − | 4.38210i | 0.236957 | − | 0.410421i | ||||
\(115\) | 7.96030 | − | 13.7876i | 0.742302 | − | 1.28570i | ||||
\(116\) | 9.07127 | 0.842246 | ||||||||
\(117\) | 6.00892 | − | 6.85366i | 0.555525 | − | 0.633621i | ||||
\(118\) | −2.34197 | −0.215596 | ||||||||
\(119\) | 2.18959 | − | 3.79249i | 0.200720 | − | 0.347657i | ||||
\(120\) | −3.47996 | + | 6.02747i | −0.317675 | + | 0.550230i | ||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −2.12681 | −0.192552 | ||||||||
\(123\) | 4.14105 | + | 7.17251i | 0.373386 | + | 0.646723i | ||||
\(124\) | 2.28022 | + | 3.94945i | 0.204770 | + | 0.354671i | ||||
\(125\) | 5.94107 | 0.531385 | ||||||||
\(126\) | −0.809002 | − | 1.40123i | −0.0720716 | − | 0.124832i | ||||
\(127\) | 8.75815 | − | 15.1696i | 0.777160 | − | 1.34608i | −0.156412 | − | 0.987692i | \(-0.549993\pi\) |
0.933572 | − | 0.358389i | \(-0.116674\pi\) | |||||||
\(128\) | 3.91596 | − | 6.78263i | 0.346125 | − | 0.599506i | ||||
\(129\) | −3.33721 | −0.293825 | ||||||||
\(130\) | 2.66508 | + | 0.529756i | 0.233743 | + | 0.0464627i | ||||
\(131\) | 1.60414 | 0.140154 | 0.0700771 | − | 0.997542i | \(-0.477675\pi\) | ||||
0.0700771 | + | 0.997542i | \(0.477675\pi\) | |||||||
\(132\) | −2.26648 | + | 3.92567i | −0.197272 | + | 0.341685i | ||||
\(133\) | 9.56069 | − | 16.5596i | 0.829017 | − | 1.43590i | ||||
\(134\) | 0.0889877 | + | 0.154131i | 0.00768737 | + | 0.0133149i | ||||
\(135\) | 3.11607 | 0.268189 | ||||||||
\(136\) | −0.968009 | − | 1.67664i | −0.0830061 | − | 0.143771i | ||||
\(137\) | 0.968908 | + | 1.67820i | 0.0827794 | + | 0.143378i | 0.904443 | − | 0.426595i | \(-0.140287\pi\) |
−0.821663 | + | 0.569973i | \(0.806954\pi\) | |||||||
\(138\) | 3.57801 | 0.304581 | ||||||||
\(139\) | 6.14479 | + | 10.6431i | 0.521195 | + | 0.902735i | 0.999696 | + | 0.0246487i | \(0.00784673\pi\) |
−0.478502 | + | 0.878087i | \(0.658820\pi\) | |||||||
\(140\) | −6.45466 | + | 11.1798i | −0.545518 | + | 0.944865i | ||||
\(141\) | 10.9207 | − | 18.9151i | 0.919685 | − | 1.59294i | ||||
\(142\) | 0.950289 | 0.0797465 | ||||||||
\(143\) | 3.53636 | + | 0.702948i | 0.295726 | + | 0.0587835i | ||||
\(144\) | 9.03245 | 0.752704 | ||||||||
\(145\) | −6.60566 | + | 11.4413i | −0.548570 | + | 0.950152i | ||||
\(146\) | 0.377324 | − | 0.653544i | 0.0312275 | − | 0.0540877i | ||||
\(147\) | 1.54398 | + | 2.67425i | 0.127345 | + | 0.220568i | ||||
\(148\) | 18.7207 | 1.53883 | ||||||||
\(149\) | −2.88372 | − | 4.99475i | −0.236243 | − | 0.409186i | 0.723390 | − | 0.690440i | \(-0.242583\pi\) |
−0.959633 | + | 0.281254i | \(0.909250\pi\) | |||||||
\(150\) | −0.910009 | − | 1.57618i | −0.0743019 | − | 0.128695i | ||||
\(151\) | 0.712761 | 0.0580036 | 0.0290018 | − | 0.999579i | \(-0.490767\pi\) | ||||
0.0290018 | + | 0.999579i | \(0.490767\pi\) | |||||||
\(152\) | −4.22674 | − | 7.32092i | −0.342834 | − | 0.593805i | ||||
\(153\) | 2.32120 | − | 4.02043i | 0.187658 | − | 0.325033i | ||||
\(154\) | 0.320017 | − | 0.554286i | 0.0257877 | − | 0.0446656i | ||||
\(155\) | −6.64178 | −0.533481 | ||||||||
\(156\) | −5.25557 | − | 15.4758i | −0.420783 | − | 1.23906i | ||||
\(157\) | 7.27705 | 0.580772 | 0.290386 | − | 0.956910i | \(-0.406216\pi\) | ||||
0.290386 | + | 0.956910i | \(0.406216\pi\) | |||||||
\(158\) | −1.29338 | + | 2.24021i | −0.102896 | + | 0.178221i | ||||
\(159\) | −13.3479 | + | 23.1192i | −1.05856 | + | 1.83347i | ||||
\(160\) | 4.30653 | + | 7.45913i | 0.340461 | + | 0.589696i | ||||
\(161\) | 13.5210 | 1.06561 | ||||||||
\(162\) | 1.36791 | + | 2.36929i | 0.107473 | + | 0.186149i | ||||
\(163\) | −7.70189 | − | 13.3401i | −0.603258 | − | 1.04487i | −0.992324 | − | 0.123664i | \(-0.960535\pi\) |
0.389066 | − | 0.921210i | \(-0.372798\pi\) | |||||||
\(164\) | 6.79134 | 0.530314 | ||||||||
\(165\) | −3.30089 | − | 5.71731i | −0.256974 | − | 0.445092i | ||||
\(166\) | −0.509304 | + | 0.882141i | −0.0395297 | + | 0.0684674i | ||||
\(167\) | −1.19185 | + | 2.06434i | −0.0922279 | + | 0.159743i | −0.908448 | − | 0.417997i | \(-0.862732\pi\) |
0.816220 | + | 0.577741i | \(0.196065\pi\) | |||||||
\(168\) | −5.91091 | −0.456037 | ||||||||
\(169\) | −10.3115 | + | 7.91658i | −0.793195 | + | 0.608968i | ||||
\(170\) | 1.38395 | 0.106144 | ||||||||
\(171\) | 10.1353 | − | 17.5549i | 0.775068 | − | 1.34246i | ||||
\(172\) | −1.36826 | + | 2.36989i | −0.104329 | + | 0.180703i | ||||
\(173\) | −2.55445 | − | 4.42443i | −0.194211 | − | 0.336384i | 0.752430 | − | 0.658672i | \(-0.228881\pi\) |
−0.946642 | + | 0.322288i | \(0.895548\pi\) | |||||||
\(174\) | −2.96913 | −0.225089 | ||||||||
\(175\) | −3.43885 | − | 5.95626i | −0.259953 | − | 0.450251i | ||||
\(176\) | 1.78649 | + | 3.09428i | 0.134661 | + | 0.233240i | ||||
\(177\) | −20.5159 | −1.54207 | ||||||||
\(178\) | −0.412173 | − | 0.713904i | −0.0308937 | − | 0.0535094i | ||||
\(179\) | −12.1531 | + | 21.0497i | −0.908364 | + | 1.57333i | −0.0920263 | + | 0.995757i | \(0.529334\pi\) |
−0.816337 | + | 0.577575i | \(0.803999\pi\) | |||||||
\(180\) | −6.84262 | + | 11.8518i | −0.510018 | + | 0.883378i | ||||
\(181\) | −2.00442 | −0.148988 | −0.0744938 | − | 0.997221i | \(-0.523734\pi\) | ||||
−0.0744938 | + | 0.997221i | \(0.523734\pi\) | |||||||
\(182\) | 0.742063 | + | 2.18511i | 0.0550054 | + | 0.161971i | ||||
\(183\) | −18.6310 | −1.37724 | ||||||||
\(184\) | 2.98879 | − | 5.17674i | 0.220337 | − | 0.381634i | ||||
\(185\) | −13.6323 | + | 23.6119i | −1.00227 | + | 1.73598i | ||||
\(186\) | −0.746341 | − | 1.29270i | −0.0547244 | − | 0.0947854i | ||||
\(187\) | 1.83639 | 0.134290 | ||||||||
\(188\) | −8.95496 | − | 15.5104i | −0.653108 | − | 1.13122i | ||||
\(189\) | 1.32321 | + | 2.29186i | 0.0962491 | + | 0.166708i | ||||
\(190\) | 6.04289 | 0.438398 | ||||||||
\(191\) | 1.58514 | + | 2.74554i | 0.114697 | + | 0.198660i | 0.917658 | − | 0.397370i | \(-0.130077\pi\) |
−0.802962 | + | 0.596030i | \(0.796744\pi\) | |||||||
\(192\) | 7.43280 | − | 12.8740i | 0.536416 | − | 0.929100i | ||||
\(193\) | −12.0376 | + | 20.8498i | −0.866488 | + | 1.50080i | −0.000926311 | 1.00000i | \(0.500295\pi\) | |
−0.865562 | + | 0.500802i | \(0.833038\pi\) | |||||||
\(194\) | −0.410730 | −0.0294887 | ||||||||
\(195\) | 23.3463 | + | 4.64071i | 1.67186 | + | 0.332328i | ||||
\(196\) | 2.53213 | 0.180867 | ||||||||
\(197\) | −1.30520 | + | 2.26067i | −0.0929917 | + | 0.161066i | −0.908769 | − | 0.417300i | \(-0.862976\pi\) |
0.815777 | + | 0.578367i | \(0.196310\pi\) | |||||||
\(198\) | 0.339252 | − | 0.587601i | 0.0241096 | − | 0.0417590i | ||||
\(199\) | −8.52647 | − | 14.7683i | −0.604425 | − | 1.04690i | −0.992142 | − | 0.125117i | \(-0.960069\pi\) |
0.387717 | − | 0.921779i | \(-0.373264\pi\) | |||||||
\(200\) | −3.04060 | −0.215003 | ||||||||
\(201\) | 0.779539 | + | 1.35020i | 0.0549845 | + | 0.0952359i | ||||
\(202\) | 0.898868 | + | 1.55689i | 0.0632442 | + | 0.109542i | ||||
\(203\) | −11.2201 | −0.787497 | ||||||||
\(204\) | −4.16216 | − | 7.20907i | −0.291409 | − | 0.504736i | ||||
\(205\) | −4.94543 | + | 8.56573i | −0.345403 | + | 0.598256i | ||||
\(206\) | 1.96949 | − | 3.41126i | 0.137221 | − | 0.237673i | ||||
\(207\) | 14.3337 | 0.996262 | ||||||||
\(208\) | −12.6353 | − | 2.51161i | −0.876102 | − | 0.174149i | ||||
\(209\) | 8.01848 | 0.554650 | ||||||||
\(210\) | 2.11268 | − | 3.65927i | 0.145789 | − | 0.252514i | ||||
\(211\) | 10.1890 | − | 17.6479i | 0.701442 | − | 1.21493i | −0.266519 | − | 0.963830i | \(-0.585873\pi\) |
0.967960 | − | 0.251103i | \(-0.0807933\pi\) | |||||||
\(212\) | 10.9453 | + | 18.9578i | 0.751726 | + | 1.30203i | ||||
\(213\) | 8.32460 | 0.570392 | ||||||||
\(214\) | −2.31908 | − | 4.01677i | −0.158529 | − | 0.274580i | ||||
\(215\) | −1.99272 | − | 3.45149i | −0.135902 | − | 0.235390i | ||||
\(216\) | 1.16997 | 0.0796062 | ||||||||
\(217\) | −2.82036 | − | 4.88501i | −0.191459 | − | 0.331616i | ||||
\(218\) | 1.17513 | − | 2.03539i | 0.0795900 | − | 0.137854i | ||||
\(219\) | 3.30538 | − | 5.72509i | 0.223357 | − | 0.386866i | ||||
\(220\) | −5.41347 | −0.364976 | ||||||||
\(221\) | −4.36502 | + | 4.97866i | −0.293623 | + | 0.334901i | ||||
\(222\) | −6.12749 | −0.411250 | ||||||||
\(223\) | −0.509039 | + | 0.881682i | −0.0340878 | + | 0.0590418i | −0.882566 | − | 0.470189i | \(-0.844186\pi\) |
0.848478 | + | 0.529230i | \(0.177519\pi\) | |||||||
\(224\) | −3.65744 | + | 6.33488i | −0.244373 | + | 0.423267i | ||||
\(225\) | −3.64554 | − | 6.31426i | −0.243036 | − | 0.420951i | ||||
\(226\) | −0.655905 | −0.0436301 | ||||||||
\(227\) | −0.0114153 | − | 0.0197719i | −0.000757660 | − | 0.00131231i | 0.865646 | − | 0.500656i | \(-0.166908\pi\) |
−0.866404 | + | 0.499344i | \(0.833575\pi\) | |||||||
\(228\) | −18.1737 | − | 31.4779i | −1.20359 | − | 2.08467i | ||||
\(229\) | −21.4247 | −1.41578 | −0.707891 | − | 0.706322i | \(-0.750353\pi\) | ||||
−0.707891 | + | 0.706322i | \(0.750353\pi\) | |||||||
\(230\) | 2.13651 | + | 3.70055i | 0.140877 | + | 0.244007i | ||||
\(231\) | 2.80338 | − | 4.85559i | 0.184449 | − | 0.319474i | ||||
\(232\) | −2.48018 | + | 4.29579i | −0.162832 | + | 0.282033i | ||||
\(233\) | 27.0674 | 1.77324 | 0.886621 | − | 0.462496i | \(-0.153046\pi\) | ||||
0.886621 | + | 0.462496i | \(0.153046\pi\) | |||||||
\(234\) | 0.786665 | + | 2.31645i | 0.0514259 | + | 0.151431i | ||||
\(235\) | 26.0839 | 1.70152 | ||||||||
\(236\) | −8.41153 | + | 14.5692i | −0.547544 | + | 0.948374i | ||||
\(237\) | −11.3301 | + | 19.6244i | −0.735972 | + | 1.27474i | ||||
\(238\) | 0.587678 | + | 1.01789i | 0.0380935 | + | 0.0659799i | ||||
\(239\) | 29.1026 | 1.88249 | 0.941245 | − | 0.337726i | \(-0.109658\pi\) | ||||
0.941245 | + | 0.337726i | \(0.109658\pi\) | |||||||
\(240\) | 11.7940 | + | 20.4278i | 0.761298 | + | 1.31861i | ||||
\(241\) | −5.90258 | − | 10.2236i | −0.380219 | − | 0.658558i | 0.610875 | − | 0.791727i | \(-0.290818\pi\) |
−0.991093 | + | 0.133169i | \(0.957485\pi\) | |||||||
\(242\) | 0.268396 | 0.0172531 | ||||||||
\(243\) | 10.3184 | + | 17.8719i | 0.661923 | + | 1.14648i | ||||
\(244\) | −7.63873 | + | 13.2307i | −0.489019 | + | 0.847006i | ||||
\(245\) | −1.84389 | + | 3.19371i | −0.117802 | + | 0.204039i | ||||
\(246\) | −2.22288 | −0.141726 | ||||||||
\(247\) | −19.0595 | + | 21.7389i | −1.21273 | + | 1.38322i | ||||
\(248\) | −2.49374 | −0.158353 | ||||||||
\(249\) | −4.46154 | + | 7.72762i | −0.282739 | + | 0.489718i | ||||
\(250\) | −0.797279 | + | 1.38093i | −0.0504244 | + | 0.0873376i | ||||
\(251\) | 7.47739 | + | 12.9512i | 0.471969 | + | 0.817474i | 0.999486 | − | 0.0320706i | \(-0.0102101\pi\) |
−0.527517 | + | 0.849545i | \(0.676877\pi\) | |||||||
\(252\) | −11.6226 | −0.732154 | ||||||||
\(253\) | 2.83500 | + | 4.91036i | 0.178235 | + | 0.308711i | ||||
\(254\) | 2.35065 | + | 4.07145i | 0.147493 | + | 0.255466i | ||||
\(255\) | 12.1235 | 0.759201 | ||||||||
\(256\) | −5.27162 | − | 9.13071i | −0.329476 | − | 0.570669i | ||||
\(257\) | 6.27337 | − | 10.8658i | 0.391322 | − | 0.677789i | −0.601302 | − | 0.799022i | \(-0.705351\pi\) |
0.992624 | + | 0.121232i | \(0.0386846\pi\) | |||||||
\(258\) | 0.447846 | − | 0.775692i | 0.0278817 | − | 0.0482925i | ||||
\(259\) | −23.1553 | −1.43880 | ||||||||
\(260\) | 12.8676 | − | 14.6765i | 0.798013 | − | 0.910198i | ||||
\(261\) | −11.8945 | −0.736250 | ||||||||
\(262\) | −0.215272 | + | 0.372862i | −0.0132996 | + | 0.0230355i | ||||
\(263\) | 13.1504 | − | 22.7771i | 0.810888 | − | 1.40450i | −0.101355 | − | 0.994850i | \(-0.532318\pi\) |
0.912243 | − | 0.409649i | \(-0.134349\pi\) | |||||||
\(264\) | −1.23936 | − | 2.14663i | −0.0762773 | − | 0.132116i | ||||
\(265\) | −31.8813 | −1.95845 | ||||||||
\(266\) | 2.56605 | + | 4.44453i | 0.157335 | + | 0.272512i | ||||
\(267\) | −3.61066 | − | 6.25385i | −0.220969 | − | 0.382730i | ||||
\(268\) | 1.27845 | 0.0780936 | ||||||||
\(269\) | −10.7170 | − | 18.5624i | −0.653429 | − | 1.13177i | −0.982285 | − | 0.187392i | \(-0.939996\pi\) |
0.328856 | − | 0.944380i | \(-0.393337\pi\) | |||||||
\(270\) | −0.418170 | + | 0.724292i | −0.0254490 | + | 0.0440790i | ||||
\(271\) | −1.21707 | + | 2.10802i | −0.0739316 | + | 0.128053i | −0.900621 | − | 0.434605i | \(-0.856888\pi\) |
0.826690 | + | 0.562658i | \(0.190221\pi\) | |||||||
\(272\) | −6.56138 | −0.397842 | ||||||||
\(273\) | 6.50053 | + | 19.1418i | 0.393430 | + | 1.15851i | ||||
\(274\) | −0.520102 | −0.0314205 | ||||||||
\(275\) | 1.44207 | − | 2.49774i | 0.0869600 | − | 0.150619i | ||||
\(276\) | 12.8509 | − | 22.2585i | 0.773536 | − | 1.33980i | ||||
\(277\) | 2.82864 | + | 4.89935i | 0.169956 | + | 0.294373i | 0.938404 | − | 0.345539i | \(-0.112304\pi\) |
−0.768448 | + | 0.639912i | \(0.778971\pi\) | |||||||
\(278\) | −3.29847 | −0.197829 | ||||||||
\(279\) | −2.98988 | − | 5.17862i | −0.178999 | − | 0.310036i | ||||
\(280\) | −3.52954 | − | 6.11334i | −0.210930 | − | 0.365342i | ||||
\(281\) | 17.9567 | 1.07121 | 0.535604 | − | 0.844469i | \(-0.320084\pi\) | ||||
0.535604 | + | 0.844469i | \(0.320084\pi\) | |||||||
\(282\) | 2.93106 | + | 5.07674i | 0.174542 | + | 0.302316i | ||||
\(283\) | 7.18650 | − | 12.4474i | 0.427193 | − | 0.739920i | −0.569430 | − | 0.822040i | \(-0.692836\pi\) |
0.996622 | + | 0.0821203i | \(0.0261692\pi\) | |||||||
\(284\) | 3.41310 | − | 5.91166i | 0.202530 | − | 0.350792i | ||||
\(285\) | 52.9362 | 3.13567 | ||||||||
\(286\) | −0.637964 | + | 0.727650i | −0.0377236 | + | 0.0430268i | ||||
\(287\) | −8.40009 | −0.495842 | ||||||||
\(288\) | −3.87727 | + | 6.71564i | −0.228471 | + | 0.395723i | ||||
\(289\) | 6.81383 | − | 11.8019i | 0.400813 | − | 0.694229i | ||||
\(290\) | −1.77293 | − | 3.07081i | −0.104110 | − | 0.180324i | ||||
\(291\) | −3.59803 | −0.210920 | ||||||||
\(292\) | −2.71042 | − | 4.69459i | −0.158615 | − | 0.274730i | ||||
\(293\) | 13.5653 | + | 23.4957i | 0.792491 | + | 1.37263i | 0.924420 | + | 0.381376i | \(0.124550\pi\) |
−0.131929 | + | 0.991259i | \(0.542117\pi\) | |||||||
\(294\) | −0.828796 | −0.0483363 | ||||||||
\(295\) | −12.2505 | − | 21.2185i | −0.713251 | − | 1.23539i | ||||
\(296\) | −5.11842 | + | 8.86537i | −0.297502 | + | 0.515289i | ||||
\(297\) | −0.554881 | + | 0.961083i | −0.0321975 | + | 0.0557677i | ||||
\(298\) | 1.54796 | 0.0896707 | ||||||||
\(299\) | −20.0511 | − | 3.98571i | −1.15959 | − | 0.230499i | ||||
\(300\) | −13.0737 | −0.754810 | ||||||||
\(301\) | 1.69237 | − | 2.93128i | 0.0975469 | − | 0.168956i | ||||
\(302\) | −0.0956510 | + | 0.165672i | −0.00550410 | + | 0.00953338i | ||||
\(303\) | 7.87416 | + | 13.6384i | 0.452358 | + | 0.783508i | ||||
\(304\) | −28.6498 | −1.64318 | ||||||||
\(305\) | −11.1250 | − | 19.2690i | −0.637014 | − | 1.10334i | ||||
\(306\) | 0.623000 | + | 1.07907i | 0.0356145 | + | 0.0616862i | ||||
\(307\) | 10.2326 | 0.584008 | 0.292004 | − | 0.956417i | \(-0.405678\pi\) | ||||
0.292004 | + | 0.956417i | \(0.405678\pi\) | |||||||
\(308\) | −2.29877 | − | 3.98159i | −0.130985 | − | 0.226872i | ||||
\(309\) | 17.2529 | − | 29.8829i | 0.981482 | − | 1.69998i | ||||
\(310\) | 0.891314 | − | 1.54380i | 0.0506232 | − | 0.0876820i | ||||
\(311\) | −8.44726 | −0.479000 | −0.239500 | − | 0.970896i | \(-0.576984\pi\) | ||||
−0.239500 | + | 0.970896i | \(0.576984\pi\) | |||||||
\(312\) | 8.76565 | + | 1.74241i | 0.496257 | + | 0.0986445i | ||||
\(313\) | 20.9335 | 1.18323 | 0.591617 | − | 0.806219i | \(-0.298490\pi\) | ||||
0.591617 | + | 0.806219i | \(0.298490\pi\) | |||||||
\(314\) | −0.976565 | + | 1.69146i | −0.0551108 | + | 0.0954547i | ||||
\(315\) | 8.46352 | − | 14.6592i | 0.476865 | − | 0.825954i | ||||
\(316\) | 9.29074 | + | 16.0920i | 0.522645 | + | 0.905248i | ||||
\(317\) | 23.0814 | 1.29638 | 0.648189 | − | 0.761480i | \(-0.275527\pi\) | ||||
0.648189 | + | 0.761480i | \(0.275527\pi\) | |||||||
\(318\) | −3.58252 | − | 6.20511i | −0.200898 | − | 0.347965i | ||||
\(319\) | −2.35255 | − | 4.07474i | −0.131718 | − | 0.228142i | ||||
\(320\) | 17.7532 | 0.992432 | ||||||||
\(321\) | −20.3153 | − | 35.1872i | −1.13389 | − | 1.96396i | ||||
\(322\) | −1.81449 | + | 3.14280i | −0.101118 | + | 0.175141i | ||||
\(323\) | −7.36254 | + | 12.7523i | −0.409663 | + | 0.709557i | ||||
\(324\) | 19.6522 | 1.09179 | ||||||||
\(325\) | 3.34390 | + | 9.84660i | 0.185486 | + | 0.546191i | ||||
\(326\) | 4.13431 | 0.228978 | ||||||||
\(327\) | 10.2942 | − | 17.8302i | 0.569273 | − | 0.986010i | ||||
\(328\) | −1.85682 | + | 3.21611i | −0.102526 | + | 0.177580i | ||||
\(329\) | 11.0762 | + | 19.1846i | 0.610653 | + | 1.05768i | ||||
\(330\) | 1.77189 | 0.0975394 | ||||||||
\(331\) | −1.65132 | − | 2.86017i | −0.0907648 | − | 0.157209i | 0.817068 | − | 0.576541i | \(-0.195598\pi\) |
−0.907833 | + | 0.419332i | \(0.862264\pi\) | |||||||
\(332\) | 3.65848 | + | 6.33667i | 0.200785 | + | 0.347770i | ||||
\(333\) | −24.5470 | −1.34517 | ||||||||
\(334\) | −0.319887 | − | 0.554060i | −0.0175034 | − | 0.0303168i | ||||
\(335\) | −0.930961 | + | 1.61247i | −0.0508638 | + | 0.0880987i | ||||
\(336\) | −10.0164 | + | 17.3489i | −0.546438 | + | 0.946459i | ||||
\(337\) | 22.5110 | 1.22625 | 0.613127 | − | 0.789985i | \(-0.289912\pi\) | ||||
0.613127 | + | 0.789985i | \(0.289912\pi\) | |||||||
\(338\) | −0.456326 | − | 3.45918i | −0.0248208 | − | 0.188155i | ||||
\(339\) | −5.74577 | −0.312068 | ||||||||
\(340\) | 4.97063 | − | 8.60939i | 0.269570 | − | 0.466910i | ||||
\(341\) | 1.18271 | − | 2.04851i | 0.0640472 | − | 0.110933i | ||||
\(342\) | 2.72028 | + | 4.71167i | 0.147096 | + | 0.254778i | ||||
\(343\) | −19.8246 | −1.07043 | ||||||||
\(344\) | −0.748191 | − | 1.29591i | −0.0403398 | − | 0.0698705i | ||||
\(345\) | 18.7160 | + | 32.4171i | 1.00764 | + | 1.74528i | ||||
\(346\) | 1.37121 | 0.0737166 | ||||||||
\(347\) | 15.3883 | + | 26.6533i | 0.826088 | + | 1.43083i | 0.901085 | + | 0.433642i | \(0.142772\pi\) |
−0.0749978 | + | 0.997184i | \(0.523895\pi\) | |||||||
\(348\) | −10.6640 | + | 18.4707i | −0.571653 | + | 0.990132i | ||||
\(349\) | 15.2402 | − | 26.3967i | 0.815787 | − | 1.41298i | −0.0929752 | − | 0.995668i | \(-0.529638\pi\) |
0.908762 | − | 0.417315i | \(-0.137029\pi\) | |||||||
\(350\) | 1.84595 | 0.0986700 | ||||||||
\(351\) | −1.28667 | − | 3.78879i | −0.0686774 | − | 0.202231i | ||||
\(352\) | −3.06747 | −0.163497 | ||||||||
\(353\) | 2.03503 | − | 3.52477i | 0.108313 | − | 0.187604i | −0.806774 | − | 0.590861i | \(-0.798788\pi\) |
0.915087 | + | 0.403256i | \(0.132122\pi\) | |||||||
\(354\) | 2.75319 | − | 4.76866i | 0.146330 | − | 0.253452i | ||||
\(355\) | 4.97081 | + | 8.60969i | 0.263823 | + | 0.456955i | ||||
\(356\) | −5.92151 | −0.313839 | ||||||||
\(357\) | 5.14810 | + | 8.91677i | 0.272466 | + | 0.471926i | ||||
\(358\) | −3.26184 | − | 5.64967i | −0.172393 | − | 0.298594i | ||||
\(359\) | −29.7361 | −1.56941 | −0.784705 | − | 0.619870i | \(-0.787185\pi\) | ||||
−0.784705 | + | 0.619870i | \(0.787185\pi\) | |||||||
\(360\) | −3.74168 | − | 6.48078i | −0.197204 | − | 0.341567i | ||||
\(361\) | −22.6480 | + | 39.2275i | −1.19200 | + | 2.06460i | ||||
\(362\) | 0.268990 | − | 0.465904i | 0.0141378 | − | 0.0244874i | ||||
\(363\) | 2.35117 | 0.123404 | ||||||||
\(364\) | 16.2586 | + | 3.23184i | 0.852182 | + | 0.169394i | ||||
\(365\) | 7.89487 | 0.413237 | ||||||||
\(366\) | 2.50024 | − | 4.33054i | 0.130690 | − | 0.226361i | ||||
\(367\) | 3.15018 | − | 5.45627i | 0.164438 | − | 0.284815i | −0.772018 | − | 0.635601i | \(-0.780752\pi\) |
0.936456 | + | 0.350786i | \(0.114086\pi\) | |||||||
\(368\) | −10.1294 | − | 17.5446i | −0.528029 | − | 0.914573i | ||||
\(369\) | −8.90498 | −0.463575 | ||||||||
\(370\) | −3.65886 | − | 6.33733i | −0.190215 | − | 0.329462i | ||||
\(371\) | −13.5381 | − | 23.4486i | −0.702861 | − | 1.21739i | ||||
\(372\) | −10.7224 | −0.555928 | ||||||||
\(373\) | 3.50044 | + | 6.06294i | 0.181246 | + | 0.313927i | 0.942305 | − | 0.334755i | \(-0.108654\pi\) |
−0.761059 | + | 0.648683i | \(0.775320\pi\) | |||||||
\(374\) | −0.246440 | + | 0.426847i | −0.0127431 | + | 0.0220717i | ||||
\(375\) | −6.98423 | + | 12.0970i | −0.360664 | + | 0.624688i | ||||
\(376\) | 9.79351 | 0.505062 | ||||||||
\(377\) | 16.6390 | + | 3.30744i | 0.856950 | + | 0.170342i | ||||
\(378\) | −0.710286 | −0.0365332 | ||||||||
\(379\) | −3.46628 | + | 6.00378i | −0.178051 | + | 0.308393i | −0.941213 | − | 0.337814i | \(-0.890313\pi\) |
0.763162 | + | 0.646207i | \(0.223646\pi\) | |||||||
\(380\) | 21.7039 | − | 37.5923i | 1.11339 | − | 1.92844i | ||||
\(381\) | 20.5919 | + | 35.6662i | 1.05495 | + | 1.82724i | ||||
\(382\) | −0.850889 | −0.0435353 | ||||||||
\(383\) | −2.95524 | − | 5.11862i | −0.151006 | − | 0.261549i | 0.780592 | − | 0.625041i | \(-0.214918\pi\) |
−0.931597 | + | 0.363492i | \(0.881584\pi\) | |||||||
\(384\) | 9.20707 | + | 15.9471i | 0.469847 | + | 0.813798i | ||||
\(385\) | 6.69583 | 0.341251 | ||||||||
\(386\) | −3.23085 | − | 5.59600i | −0.164446 | − | 0.284829i | ||||
\(387\) | 1.79409 | − | 3.10746i | 0.0911990 | − | 0.157961i | ||||
\(388\) | −1.47520 | + | 2.55512i | −0.0748917 | + | 0.129716i | ||||
\(389\) | −1.83318 | −0.0929457 | −0.0464728 | − | 0.998920i | \(-0.514798\pi\) | ||||
−0.0464728 | + | 0.998920i | \(0.514798\pi\) | |||||||
\(390\) | −4.21170 | + | 4.80378i | −0.213268 | + | 0.243249i | ||||
\(391\) | −10.4123 | −0.526575 | ||||||||
\(392\) | −0.692311 | + | 1.19912i | −0.0349670 | + | 0.0605646i | ||||
\(393\) | −1.88580 | + | 3.26630i | −0.0951261 | + | 0.164763i | ||||
\(394\) | −0.350310 | − | 0.606755i | −0.0176484 | − | 0.0305679i | ||||
\(395\) | −27.0619 | −1.36163 | ||||||||
\(396\) | −2.43694 | − | 4.22091i | −0.122461 | − | 0.212109i | ||||
\(397\) | −4.69260 | − | 8.12782i | −0.235515 | − | 0.407924i | 0.723907 | − | 0.689897i | \(-0.242344\pi\) |
−0.959422 | + | 0.281973i | \(0.909011\pi\) | |||||||
\(398\) | 4.57694 | 0.229421 | ||||||||
\(399\) | 22.4788 | + | 38.9344i | 1.12535 | + | 1.94916i | ||||
\(400\) | −5.15247 | + | 8.92434i | −0.257623 | + | 0.446217i | ||||
\(401\) | −5.76867 | + | 9.99163i | −0.288074 | + | 0.498958i | −0.973350 | − | 0.229325i | \(-0.926348\pi\) |
0.685276 | + | 0.728283i | \(0.259681\pi\) | |||||||
\(402\) | −0.418450 | −0.0208704 | ||||||||
\(403\) | 2.74249 | + | 8.07566i | 0.136613 | + | 0.402277i | ||||
\(404\) | 12.9136 | 0.642478 | ||||||||
\(405\) | −14.3106 | + | 24.7867i | −0.711101 | + | 1.23166i | ||||
\(406\) | 1.50571 | − | 2.60797i | 0.0747274 | − | 0.129432i | ||||
\(407\) | −4.85504 | − | 8.40917i | −0.240655 | − | 0.416827i | ||||
\(408\) | 4.55190 | 0.225353 | ||||||||
\(409\) | −17.3892 | − | 30.1191i | −0.859843 | − | 1.48929i | −0.872078 | − | 0.489366i | \(-0.837228\pi\) |
0.0122354 | − | 0.999925i | \(-0.496105\pi\) | |||||||
\(410\) | −1.32733 | − | 2.29901i | −0.0655523 | − | 0.113540i | ||||
\(411\) | −4.55613 | −0.224738 | ||||||||
\(412\) | −14.1474 | − | 24.5040i | −0.696992 | − | 1.20723i | ||||
\(413\) | 10.4041 | − | 18.0204i | 0.511951 | − | 0.886725i | ||||
\(414\) | −1.92355 | + | 3.33169i | −0.0945376 | + | 0.163744i | ||||
\(415\) | −10.6563 | −0.523100 | ||||||||
\(416\) | 7.29123 | − | 8.31624i | 0.357482 | − | 0.407737i | ||||
\(417\) | −28.8949 | −1.41499 | ||||||||
\(418\) | −1.07606 | + | 1.86380i | −0.0526320 | + | 0.0911613i | ||||
\(419\) | 6.17269 | − | 10.6914i | 0.301556 | − | 0.522310i | −0.674933 | − | 0.737879i | \(-0.735827\pi\) |
0.976489 | + | 0.215569i | \(0.0691607\pi\) | |||||||
\(420\) | −15.1760 | − | 26.2856i | −0.740513 | − | 1.28261i | ||||
\(421\) | 2.52324 | 0.122975 | 0.0614875 | − | 0.998108i | \(-0.480416\pi\) | ||||
0.0614875 | + | 0.998108i | \(0.480416\pi\) | |||||||
\(422\) | 2.73469 | + | 4.73663i | 0.133123 | + | 0.230576i | ||||
\(423\) | 11.7420 | + | 20.3377i | 0.570914 | + | 0.988853i | ||||
\(424\) | −11.9702 | −0.581325 | ||||||||
\(425\) | 2.64821 | + | 4.58683i | 0.128457 | + | 0.222494i | ||||
\(426\) | −1.11715 | + | 1.93495i | −0.0541259 | + | 0.0937487i | ||||
\(427\) | 9.44821 | − | 16.3648i | 0.457231 | − | 0.791947i | ||||
\(428\) | −33.3172 | −1.61045 | ||||||||
\(429\) | −5.58862 | + | 6.37427i | −0.269821 | + | 0.307753i | ||||
\(430\) | 1.06968 | 0.0515843 | ||||||||
\(431\) | −7.95709 | + | 13.7821i | −0.383280 | + | 0.663860i | −0.991529 | − | 0.129886i | \(-0.958539\pi\) |
0.608249 | + | 0.793746i | \(0.291872\pi\) | |||||||
\(432\) | 1.98258 | − | 3.43392i | 0.0953867 | − | 0.165215i | ||||
\(433\) | 1.05516 | + | 1.82759i | 0.0507077 | + | 0.0878283i | 0.890265 | − | 0.455443i | \(-0.150519\pi\) |
−0.839557 | + | 0.543271i | \(0.817186\pi\) | |||||||
\(434\) | 1.51395 | 0.0726718 | ||||||||
\(435\) | −15.5310 | − | 26.9005i | −0.744656 | − | 1.28978i | ||||
\(436\) | −8.44130 | − | 14.6208i | −0.404265 | − | 0.700208i | ||||
\(437\) | −45.4647 | −2.17487 | ||||||||
\(438\) | 0.887152 | + | 1.53659i | 0.0423897 | + | 0.0734212i | ||||
\(439\) | 8.78185 | − | 15.2106i | 0.419135 | − | 0.725963i | −0.576718 | − | 0.816943i | \(-0.695667\pi\) |
0.995853 | + | 0.0909808i | \(0.0290002\pi\) | |||||||
\(440\) | 1.48010 | − | 2.56361i | 0.0705609 | − | 0.122215i | ||||
\(441\) | −3.32020 | −0.158105 | ||||||||
\(442\) | −0.571451 | − | 1.68272i | −0.0271812 | − | 0.0800389i | ||||
\(443\) | −32.3904 | −1.53892 | −0.769458 | − | 0.638697i | \(-0.779474\pi\) | ||||
−0.769458 | + | 0.638697i | \(0.779474\pi\) | |||||||
\(444\) | −22.0077 | + | 38.1185i | −1.04444 | + | 1.80902i | ||||
\(445\) | 4.31202 | − | 7.46863i | 0.204409 | − | 0.354047i | ||||
\(446\) | −0.136624 | − | 0.236640i | −0.00646934 | − | 0.0112052i | ||||
\(447\) | 13.5602 | 0.641377 | ||||||||
\(448\) | 7.53870 | + | 13.0574i | 0.356170 | + | 0.616904i | ||||
\(449\) | −11.8301 | − | 20.4903i | −0.558297 | − | 0.966999i | −0.997639 | − | 0.0686787i | \(-0.978122\pi\) |
0.439342 | − | 0.898320i | \(-0.355212\pi\) | |||||||
\(450\) | 1.95690 | 0.0922490 | ||||||||
\(451\) | −1.76127 | − | 3.05061i | −0.0829351 | − | 0.143648i | ||||
\(452\) | −2.35577 | + | 4.08032i | −0.110806 | + | 0.191922i | ||||
\(453\) | −0.837910 | + | 1.45130i | −0.0393685 | + | 0.0681882i | ||||
\(454\) | 0.00612764 | 0.000287584 | ||||||||
\(455\) | −15.9157 | + | 18.1531i | −0.746138 | + | 0.851031i | ||||
\(456\) | 19.8755 | 0.930758 | ||||||||
\(457\) | −1.76225 | + | 3.05231i | −0.0824348 | + | 0.142781i | −0.904295 | − | 0.426908i | \(-0.859603\pi\) |
0.821860 | + | 0.569689i | \(0.192936\pi\) | |||||||
\(458\) | 2.87515 | − | 4.97990i | 0.134347 | − | 0.232695i | ||||
\(459\) | −1.01898 | − | 1.76493i | −0.0475620 | − | 0.0823797i | ||||
\(460\) | 30.6943 | 1.43113 | ||||||||
\(461\) | 7.07243 | + | 12.2498i | 0.329396 | + | 0.570530i | 0.982392 | − | 0.186831i | \(-0.0598216\pi\) |
−0.652996 | + | 0.757361i | \(0.726488\pi\) | |||||||
\(462\) | 0.752415 | + | 1.30322i | 0.0350055 | + | 0.0606313i | ||||
\(463\) | 8.79709 | 0.408836 | 0.204418 | − | 0.978884i | \(-0.434470\pi\) | ||||
0.204418 | + | 0.978884i | \(0.434470\pi\) | |||||||
\(464\) | 8.40560 | + | 14.5589i | 0.390220 | + | 0.675881i | ||||
\(465\) | 7.80797 | − | 13.5238i | 0.362086 | − | 0.627152i | ||||
\(466\) | −3.63239 | + | 6.29148i | −0.168267 | + | 0.291447i | ||||
\(467\) | 5.12967 | 0.237373 | 0.118686 | − | 0.992932i | \(-0.462132\pi\) | ||||
0.118686 | + | 0.992932i | \(0.462132\pi\) | |||||||
\(468\) | 17.2358 | + | 3.42609i | 0.796726 | + | 0.158371i | ||||
\(469\) | −1.58129 | −0.0730172 | ||||||||
\(470\) | −3.50040 | + | 6.06287i | −0.161462 | + | 0.279660i | ||||
\(471\) | −8.55479 | + | 14.8173i | −0.394184 | + | 0.682746i | ||||
\(472\) | −4.59959 | − | 7.96673i | −0.211713 | − | 0.366699i | ||||
\(473\) | 1.41938 | 0.0652632 | ||||||||
\(474\) | −3.04096 | − | 5.26710i | −0.139676 | − | 0.241926i | ||||
\(475\) | 11.5632 | + | 20.0280i | 0.530556 | + | 0.918949i | ||||
\(476\) | 8.44291 | 0.386980 | ||||||||
\(477\) | −14.3518 | − | 24.8580i | −0.657122 | − | 1.13817i | ||||
\(478\) | −3.90551 | + | 6.76454i | −0.178634 | + | 0.309403i | ||||
\(479\) | 11.9389 | − | 20.6788i | 0.545503 | − | 0.944839i | −0.453072 | − | 0.891474i | \(-0.649672\pi\) |
0.998575 | − | 0.0533648i | \(-0.0169946\pi\) | |||||||
\(480\) | −20.2508 | −0.924316 | ||||||||
\(481\) | 34.3384 | + | 6.82568i | 1.56569 | + | 0.311224i | ||||
\(482\) | 3.16846 | 0.144319 | ||||||||
\(483\) | −15.8951 | + | 27.5311i | −0.723253 | + | 1.25271i | ||||
\(484\) | 0.963982 | − | 1.66967i | 0.0438174 | − | 0.0758939i | ||||
\(485\) | −2.14846 | − | 3.72125i | −0.0975567 | − | 0.168973i | ||||
\(486\) | −5.53881 | −0.251245 | ||||||||
\(487\) | 6.66290 | + | 11.5405i | 0.301925 | + | 0.522949i | 0.976572 | − | 0.215191i | \(-0.0690375\pi\) |
−0.674647 | + | 0.738140i | \(0.735704\pi\) | |||||||
\(488\) | −4.17701 | − | 7.23479i | −0.189084 | − | 0.327504i | ||||
\(489\) | 36.2169 | 1.63778 | ||||||||
\(490\) | −0.494892 | − | 0.857179i | −0.0223570 | − | 0.0387234i | ||||
\(491\) | −1.99224 | + | 3.45067i | −0.0899088 | + | 0.155727i | −0.907472 | − | 0.420112i | \(-0.861991\pi\) |
0.817564 | + | 0.575838i | \(0.195324\pi\) | |||||||
\(492\) | −7.98379 | + | 13.8283i | −0.359937 | + | 0.623429i | ||||
\(493\) | 8.64043 | 0.389145 | ||||||||
\(494\) | −2.49520 | − | 7.34748i | −0.112264 | − | 0.330579i | ||||
\(495\) | 7.09828 | 0.319044 | ||||||||
\(496\) | −4.22578 | + | 7.31927i | −0.189743 | + | 0.328645i | ||||
\(497\) | −4.22160 | + | 7.31203i | −0.189365 | + | 0.327989i | ||||
\(498\) | −1.19746 | − | 2.07406i | −0.0536595 | − | 0.0929410i | ||||
\(499\) | 3.44227 | 0.154097 | 0.0770485 | − | 0.997027i | \(-0.475450\pi\) | ||||
0.0770485 | + | 0.997027i | \(0.475450\pi\) | |||||||
\(500\) | 5.72708 | + | 9.91960i | 0.256123 | + | 0.443618i | ||||
\(501\) | −2.80223 | − | 4.85361i | −0.125195 | − | 0.216843i | ||||
\(502\) | −4.01380 | −0.179145 | ||||||||
\(503\) | 14.1758 | + | 24.5531i | 0.632065 | + | 1.09477i | 0.987129 | + | 0.159927i | \(0.0511260\pi\) |
−0.355063 | + | 0.934842i | \(0.615541\pi\) | |||||||
\(504\) | 3.17773 | − | 5.50399i | 0.141547 | − | 0.245167i | ||||
\(505\) | −9.40367 | + | 16.2876i | −0.418458 | + | 0.724790i | ||||
\(506\) | −1.52180 | −0.0676524 | ||||||||
\(507\) | −3.99745 | − | 30.3027i | −0.177533 | − | 1.34579i | ||||
\(508\) | 33.7708 | 1.49834 | ||||||||
\(509\) | −17.2089 | + | 29.8067i | −0.762771 | + | 1.32116i | 0.178646 | + | 0.983913i | \(0.442828\pi\) |
−0.941417 | + | 0.337245i | \(0.890505\pi\) | |||||||
\(510\) | −1.62694 | + | 2.81795i | −0.0720423 | + | 0.124781i | ||||
\(511\) | 3.35247 | + | 5.80666i | 0.148305 | + | 0.256871i | ||||
\(512\) | 18.4936 | 0.817309 | ||||||||
\(513\) | −4.44930 | − | 7.70642i | −0.196442 | − | 0.340247i | ||||
\(514\) | 1.68375 | + | 2.91633i | 0.0742668 | + | 0.128634i | ||||
\(515\) | 41.2083 | 1.81585 | ||||||||
\(516\) | −3.21701 | − | 5.57202i | −0.141621 | − | 0.245294i | ||||
\(517\) | −4.64478 | + | 8.04499i | −0.204277 | + | 0.353818i | ||||
\(518\) | 3.10739 | − | 5.38216i | 0.136531 | − | 0.236479i | ||||
\(519\) | 12.0119 | 0.527263 | ||||||||
\(520\) | 3.43208 | + | 10.1063i | 0.150507 | + | 0.443189i | ||||
\(521\) | −28.8248 | −1.26284 | −0.631420 | − | 0.775441i | \(-0.717527\pi\) | ||||
−0.631420 | + | 0.775441i | \(0.717527\pi\) | |||||||
\(522\) | 1.59622 | − | 2.76473i | 0.0698645 | − | 0.121009i | ||||
\(523\) | 4.66882 | − | 8.08663i | 0.204153 | − | 0.353604i | −0.745709 | − | 0.666271i | \(-0.767889\pi\) |
0.949863 | + | 0.312668i | \(0.101223\pi\) | |||||||
\(524\) | 1.54636 | + | 2.67838i | 0.0675531 | + | 0.117005i | ||||
\(525\) | 16.1706 | 0.705744 | ||||||||
\(526\) | 3.52951 | + | 6.11329i | 0.153894 | + | 0.266552i | ||||
\(527\) | 2.17192 | + | 3.76187i | 0.0946102 | + | 0.163870i | ||||
\(528\) | −8.40066 | −0.365592 | ||||||||
\(529\) | −4.57440 | − | 7.92309i | −0.198887 | − | 0.344482i | ||||
\(530\) | 4.27840 | − | 7.41041i | 0.185842 | − | 0.321888i | ||||
\(531\) | 11.0294 | − | 19.1035i | 0.478636 | − | 0.829021i | ||||
\(532\) | 36.8653 | 1.59831 | ||||||||
\(533\) | 12.4570 | + | 2.47617i | 0.539573 | + | 0.107255i | ||||
\(534\) | 1.93818 | 0.0838731 | ||||||||
\(535\) | 24.2615 | − | 42.0221i | 1.04891 | − | 1.81677i | ||||
\(536\) | −0.349541 | + | 0.605422i | −0.0150979 | + | 0.0261502i | ||||
\(537\) | −28.5739 | − | 49.4915i | −1.23306 | − | 2.13572i | ||||
\(538\) | 5.75282 | 0.248022 | ||||||||
\(539\) | −0.656686 | − | 1.13741i | −0.0282855 | − | 0.0489919i | ||||
\(540\) | 3.00384 | + | 5.20280i | 0.129264 | + | 0.223893i | ||||
\(541\) | −10.7783 | −0.463395 | −0.231697 | − | 0.972788i | \(-0.574428\pi\) | ||||
−0.231697 | + | 0.972788i | \(0.574428\pi\) | |||||||
\(542\) | −0.326656 | − | 0.565785i | −0.0140311 | − | 0.0243025i | ||||
\(543\) | 2.35637 | − | 4.08135i | 0.101121 | − | 0.175148i | ||||
\(544\) | 2.81654 | − | 4.87839i | 0.120758 | − | 0.209159i | ||||
\(545\) | 24.5877 | 1.05322 | ||||||||
\(546\) | −5.32162 | − | 1.05782i | −0.227744 | − | 0.0452704i | ||||
\(547\) | −19.4925 | −0.833439 | −0.416719 | − | 0.909035i | \(-0.636820\pi\) | ||||
−0.416719 | + | 0.909035i | \(0.636820\pi\) | |||||||
\(548\) | −1.86802 | + | 3.23551i | −0.0797979 | + | 0.138214i | ||||
\(549\) | 10.0161 | − | 17.3484i | 0.427476 | − | 0.740411i | ||||
\(550\) | 0.387045 | + | 0.670382i | 0.0165037 | + | 0.0285852i | ||||
\(551\) | 37.7278 | 1.60726 | ||||||||
\(552\) | 7.02716 | + | 12.1714i | 0.299096 | + | 0.518049i | ||||
\(553\) | −11.4916 | − | 19.9040i | −0.488671 | − | 0.846402i | ||||
\(554\) | −1.51839 | −0.0645102 | ||||||||
\(555\) | −32.0519 | − | 55.5155i | −1.36053 | − | 2.35650i | ||||
\(556\) | −11.8469 | + | 20.5195i | −0.502422 | + | 0.870220i | ||||
\(557\) | −6.03230 | + | 10.4482i | −0.255597 | + | 0.442706i | −0.965057 | − | 0.262039i | \(-0.915605\pi\) |
0.709461 | + | 0.704745i | \(0.248939\pi\) | |||||||
\(558\) | 1.60494 | 0.0679427 | ||||||||
\(559\) | −3.37380 | + | 3.84809i | −0.142697 | + | 0.162757i | ||||
\(560\) | −23.9240 | −1.01097 | ||||||||
\(561\) | −2.15884 | + | 3.73921i | −0.0911461 | + | 0.157870i | ||||
\(562\) | −2.40976 | + | 4.17382i | −0.101649 | + | 0.176062i | ||||
\(563\) | −10.4590 | − | 18.1156i | −0.440796 | − | 0.763481i | 0.556953 | − | 0.830544i | \(-0.311970\pi\) |
−0.997749 | + | 0.0670633i | \(0.978637\pi\) | |||||||
\(564\) | 42.1093 | 1.77312 | ||||||||
\(565\) | −3.43093 | − | 5.94254i | −0.144340 | − | 0.250005i | ||||
\(566\) | 1.92883 | + | 3.34083i | 0.0810746 | + | 0.140425i | ||||
\(567\) | −24.3074 | −1.02082 | ||||||||
\(568\) | 1.86635 | + | 3.23261i | 0.0783103 | + | 0.135637i | ||||
\(569\) | −5.54414 | + | 9.60273i | −0.232422 | + | 0.402567i | −0.958520 | − | 0.285024i | \(-0.907998\pi\) |
0.726098 | + | 0.687591i | \(0.241332\pi\) | |||||||
\(570\) | −7.10393 | + | 12.3044i | −0.297551 | + | 0.515373i | ||||
\(571\) | −12.6344 | −0.528732 | −0.264366 | − | 0.964422i | \(-0.585163\pi\) | ||||
−0.264366 | + | 0.964422i | \(0.585163\pi\) | |||||||
\(572\) | 2.23530 | + | 6.58217i | 0.0934627 | + | 0.275214i | ||||
\(573\) | −7.45385 | −0.311389 | ||||||||
\(574\) | 1.12728 | − | 1.95250i | 0.0470516 | − | 0.0814957i | ||||
\(575\) | −8.17651 | + | 14.1621i | −0.340984 | + | 0.590602i | ||||
\(576\) | 7.99181 | + | 13.8422i | 0.332992 | + | 0.576759i | ||||
\(577\) | −21.3084 | −0.887082 | −0.443541 | − | 0.896254i | \(-0.646278\pi\) | ||||
−0.443541 | + | 0.896254i | \(0.646278\pi\) | |||||||
\(578\) | 1.82880 | + | 3.16758i | 0.0760682 | + | 0.131754i | ||||
\(579\) | −28.3025 | − | 49.0214i | −1.17621 | − | 2.03726i | ||||
\(580\) | −25.4710 | −1.05762 | ||||||||
\(581\) | −4.52511 | − | 7.83771i | −0.187733 | − | 0.325163i | ||||
\(582\) | 0.482848 | − | 0.836318i | 0.0200147 | − | 0.0346665i | ||||
\(583\) | 5.67713 | − | 9.83308i | 0.235123 | − | 0.407244i | ||||
\(584\) | 2.96423 | 0.122661 | ||||||||
\(585\) | −16.8723 | + | 19.2442i | −0.697583 | + | 0.795650i | ||||
\(586\) | −7.28172 | −0.300805 | ||||||||
\(587\) | 10.8380 | − | 18.7720i | 0.447334 | − | 0.774805i | −0.550878 | − | 0.834586i | \(-0.685707\pi\) |
0.998212 | + | 0.0597810i | \(0.0190402\pi\) | |||||||
\(588\) | −2.97674 | + | 5.15586i | −0.122759 | + | 0.212624i | ||||
\(589\) | 9.48352 | + | 16.4259i | 0.390761 | + | 0.676819i | ||||
\(590\) | 6.57596 | 0.270728 | ||||||||
\(591\) | −3.06875 | − | 5.31522i | −0.126231 | − | 0.218639i | ||||
\(592\) | 17.3469 | + | 30.0457i | 0.712954 | + | 1.23487i | ||||
\(593\) | 3.39934 | 0.139594 | 0.0697971 | − | 0.997561i | \(-0.477765\pi\) | ||||
0.0697971 | + | 0.997561i | \(0.477765\pi\) | |||||||
\(594\) | −0.148928 | − | 0.257951i | −0.00611059 | − | 0.0105838i | ||||
\(595\) | −6.14809 | + | 10.6488i | −0.252047 | + | 0.436559i | ||||
\(596\) | 5.55971 | − | 9.62969i | 0.227734 | − | 0.394448i | ||||
\(597\) | 40.0943 | 1.64095 | ||||||||
\(598\) | 3.61725 | − | 4.12577i | 0.147920 | − | 0.168715i | ||||
\(599\) | 12.5139 | 0.511305 | 0.255653 | − | 0.966769i | \(-0.417710\pi\) | ||||
0.255653 | + | 0.966769i | \(0.417710\pi\) | |||||||
\(600\) | 3.57448 | − | 6.19118i | 0.145928 | − | 0.252754i | ||||
\(601\) | −16.6554 | + | 28.8480i | −0.679387 | + | 1.17673i | 0.295779 | + | 0.955257i | \(0.404421\pi\) |
−0.975166 | + | 0.221477i | \(0.928912\pi\) | |||||||
\(602\) | 0.454227 | + | 0.786743i | 0.0185129 | + | 0.0320653i | ||||
\(603\) | −1.67633 | −0.0682656 | ||||||||
\(604\) | 0.687088 | + | 1.19007i | 0.0279572 | + | 0.0484233i | ||||
\(605\) | 1.40394 | + | 2.43169i | 0.0570781 | + | 0.0988621i | ||||
\(606\) | −4.22678 | −0.171701 | ||||||||
\(607\) | 12.8594 | + | 22.2731i | 0.521945 | + | 0.904036i | 0.999674 | + | 0.0255286i | \(0.00812690\pi\) |
−0.477729 | + | 0.878507i | \(0.658540\pi\) | |||||||
\(608\) | 12.2982 | − | 21.3011i | 0.498759 | − | 0.863875i | ||||
\(609\) | 13.1902 | − | 22.8461i | 0.534493 | − | 0.925769i | ||||
\(610\) | 5.97180 | 0.241791 | ||||||||
\(611\) | −10.7704 | − | 31.7150i | −0.435724 | − | 1.28305i | ||||
\(612\) | 8.95037 | 0.361797 | ||||||||
\(613\) | 18.5817 | − | 32.1844i | 0.750508 | − | 1.29992i | −0.197069 | − | 0.980390i | \(-0.563142\pi\) |
0.947577 | − | 0.319528i | \(-0.103524\pi\) | |||||||
\(614\) | −1.37320 | + | 2.37845i | −0.0554179 | + | 0.0959866i | ||||
\(615\) | −11.6275 | − | 20.1395i | −0.468867 | − | 0.812102i | ||||
\(616\) | 2.51403 | 0.101293 | ||||||||
\(617\) | 1.70556 | + | 2.95411i | 0.0686632 | + | 0.118928i | 0.898313 | − | 0.439356i | \(-0.144793\pi\) |
−0.829650 | + | 0.558284i | \(0.811460\pi\) | |||||||
\(618\) | 4.63060 | + | 8.02044i | 0.186270 | + | 0.322629i | ||||
\(619\) | 0.940405 | 0.0377981 | 0.0188990 | − | 0.999821i | \(-0.493984\pi\) | ||||
0.0188990 | + | 0.999821i | \(0.493984\pi\) | |||||||
\(620\) | −6.40256 | − | 11.0896i | −0.257133 | − | 0.445367i | ||||
\(621\) | 3.14617 | − | 5.44933i | 0.126252 | − | 0.218674i | ||||
\(622\) | 1.13361 | − | 1.96346i | 0.0454534 | − | 0.0787276i | ||||
\(623\) | 7.32421 | 0.293438 | ||||||||
\(624\) | 19.9680 | − | 22.7751i | 0.799358 | − | 0.911733i | ||||
\(625\) | −31.1024 | −1.24410 | ||||||||
\(626\) | −2.80924 | + | 4.86574i | −0.112280 | + | 0.194474i | ||||
\(627\) | −9.42640 | + | 16.3270i | −0.376454 | + | 0.652037i | ||||
\(628\) | 7.01494 | + | 12.1502i | 0.279927 | + | 0.484847i | ||||
\(629\) | 17.8315 | 0.710990 | ||||||||
\(630\) | 2.27157 | + | 3.93448i | 0.0905016 | + | 0.156753i | ||||
\(631\) | 8.41513 | + | 14.5754i | 0.335001 | + | 0.580239i | 0.983485 | − | 0.180989i | \(-0.0579299\pi\) |
−0.648484 | + | 0.761228i | \(0.724597\pi\) | |||||||
\(632\) | −10.1607 | −0.404172 | ||||||||
\(633\) | 23.9561 | + | 41.4932i | 0.952171 | + | 1.64921i | ||||
\(634\) | −3.09747 | + | 5.36498i | −0.123016 | + | 0.213070i | ||||
\(635\) | −24.5918 | + | 42.5942i | −0.975894 | + | 1.69030i | ||||
\(636\) | −51.4685 | −2.04086 | ||||||||
\(637\) | 4.64456 | + | 0.923232i | 0.184024 | + | 0.0365798i | ||||
\(638\) | 1.26283 | 0.0499960 | ||||||||
\(639\) | −4.47534 | + | 7.75152i | −0.177042 | + | 0.306645i | ||||
\(640\) | −10.9955 | + | 19.0448i | −0.434635 | + | 0.752810i | ||||
\(641\) | −10.8312 | − | 18.7603i | −0.427808 | − | 0.740986i | 0.568870 | − | 0.822428i | \(-0.307381\pi\) |
−0.996678 | + | 0.0814420i | \(0.974047\pi\) | |||||||
\(642\) | 10.9051 | 0.430390 | ||||||||
\(643\) | −1.71425 | − | 2.96916i | −0.0676033 | − | 0.117092i | 0.830243 | − | 0.557402i | \(-0.188202\pi\) |
−0.897846 | + | 0.440310i | \(0.854869\pi\) | |||||||
\(644\) | 13.0340 | + | 22.5756i | 0.513613 | + | 0.889603i | ||||
\(645\) | 9.37044 | 0.368961 | ||||||||
\(646\) | −1.97608 | − | 3.42266i | −0.0777477 | − | 0.134663i | ||||
\(647\) | 22.5782 | − | 39.1065i | 0.887639 | − | 1.53744i | 0.0449804 | − | 0.998988i | \(-0.485677\pi\) |
0.842659 | − | 0.538448i | \(-0.180989\pi\) | |||||||
\(648\) | −5.37310 | + | 9.30648i | −0.211075 | + | 0.365593i | ||||
\(649\) | 8.72582 | 0.342518 | ||||||||
\(650\) | −2.73747 | − | 0.544145i | −0.107372 | − | 0.0213431i | ||||
\(651\) | 13.2623 | 0.519790 | ||||||||
\(652\) | 14.8490 | − | 25.7192i | 0.581530 | − | 1.00724i | ||||
\(653\) | −14.3241 | + | 24.8101i | −0.560545 | + | 0.970893i | 0.436904 | + | 0.899508i | \(0.356075\pi\) |
−0.997449 | + | 0.0713844i | \(0.977258\pi\) | |||||||
\(654\) | 2.76293 | + | 4.78554i | 0.108039 | + | 0.187129i | ||||
\(655\) | −4.50421 | −0.175994 | ||||||||
\(656\) | 6.29298 | + | 10.8998i | 0.245699 | + | 0.425564i | ||||
\(657\) | 3.55397 | + | 6.15567i | 0.138654 | + | 0.240155i | ||||
\(658\) | −5.94564 | −0.231785 | ||||||||
\(659\) | 9.50013 | + | 16.4547i | 0.370072 | + | 0.640984i | 0.989576 | − | 0.144009i | \(-0.0459996\pi\) |
−0.619504 | + | 0.784994i | \(0.712666\pi\) | |||||||
\(660\) | 6.36399 | − | 11.0228i | 0.247718 | − | 0.429060i | ||||
\(661\) | −18.4711 | + | 31.9929i | −0.718442 | + | 1.24438i | 0.243175 | + | 0.969982i | \(0.421811\pi\) |
−0.961617 | + | 0.274395i | \(0.911522\pi\) | |||||||
\(662\) | 0.886415 | 0.0344515 | ||||||||
\(663\) | −5.00596 | − | 14.7408i | −0.194415 | − | 0.572484i | ||||
\(664\) | −4.00106 | −0.155271 | ||||||||
\(665\) | −26.8452 | + | 46.4972i | −1.04101 | + | 1.80308i | ||||
\(666\) | 3.29416 | − | 5.70566i | 0.127646 | − | 0.221090i | ||||
\(667\) | 13.3390 | + | 23.1037i | 0.516486 | + | 0.894580i | ||||
\(668\) | −4.59567 | −0.177812 | ||||||||
\(669\) | −1.19684 | − | 2.07298i | −0.0462724 | − | 0.0801462i | ||||
\(670\) | −0.249866 | − | 0.432781i | −0.00965317 | − | 0.0167198i | ||||
\(671\) | 7.92414 | 0.305908 | ||||||||
\(672\) | −8.59927 | − | 14.8944i | −0.331724 | − | 0.574563i | ||||
\(673\) | 17.3176 | − | 29.9949i | 0.667544 | − | 1.15622i | −0.311045 | − | 0.950395i | \(-0.600679\pi\) |
0.978589 | − | 0.205825i | \(-0.0659876\pi\) | |||||||
\(674\) | −3.02093 | + | 5.23241i | −0.116362 | + | 0.201545i | ||||
\(675\) | −3.20071 | −0.123195 | ||||||||
\(676\) | −23.1582 | − | 9.58537i | −0.890699 | − | 0.368668i | ||||
\(677\) | −29.3445 | −1.12780 | −0.563900 | − | 0.825843i | \(-0.690700\pi\) | ||||
−0.563900 | + | 0.825843i | \(0.690700\pi\) | |||||||
\(678\) | 0.771071 | − | 1.33553i | 0.0296128 | − | 0.0512909i | ||||
\(679\) | 1.82465 | − | 3.16038i | 0.0700235 | − | 0.121284i | ||||
\(680\) | 2.71804 | + | 4.70779i | 0.104232 | + | 0.180535i | ||||
\(681\) | 0.0536786 | 0.00205697 | ||||||||
\(682\) | 0.317434 | + | 0.549812i | 0.0121552 | + | 0.0210534i | ||||
\(683\) | −19.2890 | − | 33.4095i | −0.738073 | − | 1.27838i | −0.953362 | − | 0.301830i | \(-0.902402\pi\) |
0.215288 | − | 0.976551i | \(-0.430931\pi\) | |||||||
\(684\) | 39.0811 | 1.49430 | ||||||||
\(685\) | −2.72057 | − | 4.71216i | −0.103948 | − | 0.180043i | ||||
\(686\) | 2.66042 | − | 4.60799i | 0.101575 | − | 0.175934i | ||||
\(687\) | 25.1865 | − | 43.6243i | 0.960925 | − | 1.66437i | ||||
\(688\) | −5.07141 | −0.193346 | ||||||||
\(689\) | 13.1642 | + | 38.7641i | 0.501518 | + | 1.47679i | ||||
\(690\) | −10.0466 | −0.382468 | ||||||||
\(691\) | −4.79080 | + | 8.29791i | −0.182251 | + | 0.315667i | −0.942647 | − | 0.333792i | \(-0.891672\pi\) |
0.760396 | + | 0.649460i | \(0.225005\pi\) | |||||||
\(692\) | 4.92488 | − | 8.53015i | 0.187216 | − | 0.324268i | ||||
\(693\) | 3.01421 | + | 5.22077i | 0.114500 | + | 0.198321i | ||||
\(694\) | −8.26032 | −0.313557 | ||||||||
\(695\) | −17.2538 | − | 29.8844i | −0.654473 | − | 1.13358i | ||||
\(696\) | −5.83132 | − | 10.1001i | −0.221035 | − | 0.382845i | ||||
\(697\) | 6.46878 | 0.245023 | ||||||||
\(698\) | 4.09039 | + | 7.08477i | 0.154824 | + | 0.268163i | ||||
\(699\) | −31.8200 | + | 55.1138i | −1.20354 | + | 2.08460i | ||||
\(700\) | 6.62998 | − | 11.4835i | 0.250590 | − | 0.434034i | ||||
\(701\) | −15.9373 | −0.601943 | −0.300971 | − | 0.953633i | \(-0.597311\pi\) | ||||
−0.300971 | + | 0.953633i | \(0.597311\pi\) | |||||||
\(702\) | 1.05333 | + | 0.209377i | 0.0397552 | + | 0.00790243i | ||||
\(703\) | 77.8600 | 2.93655 | ||||||||
\(704\) | −3.16132 | + | 5.47557i | −0.119147 | + | 0.206368i | ||||
\(705\) | −30.6638 | + | 53.1112i | −1.15487 | + | 2.00029i | ||||
\(706\) | 0.546193 | + | 0.946033i | 0.0205562 | + | 0.0356044i | ||||
\(707\) | −15.9727 | −0.600714 | ||||||||
\(708\) | −19.7769 | − | 34.2546i | −0.743262 | − | 1.28737i | ||||
\(709\) | 15.3120 | + | 26.5212i | 0.575054 | + | 0.996023i | 0.996036 | + | 0.0889538i | \(0.0283523\pi\) |
−0.420982 | + | 0.907069i | \(0.638314\pi\) | |||||||
\(710\) | −2.66829 | −0.100139 | ||||||||
\(711\) | −12.1823 | − | 21.1003i | −0.456870 | − | 0.791323i | ||||
\(712\) | 1.61900 | − | 2.80419i | 0.0606746 | − | 0.105091i | ||||
\(713\) | −6.70594 | + | 11.6150i | −0.251140 | + | 0.434986i | ||||
\(714\) | −2.76346 | −0.103420 | ||||||||
\(715\) | −9.92965 | − | 1.97379i | −0.371348 | − | 0.0738154i | ||||
\(716\) | −46.8614 | −1.75129 | ||||||||
\(717\) | −34.2125 | + | 59.2578i | −1.27769 | + | 2.21302i | ||||
\(718\) | 3.99052 | − | 6.91178i | 0.148925 | − | 0.257945i | ||||
\(719\) | −17.8179 | − | 30.8616i | −0.664497 | − | 1.15094i | −0.979421 | − | 0.201826i | \(-0.935312\pi\) |
0.314924 | − | 0.949117i | \(-0.398021\pi\) | |||||||
\(720\) | −25.3620 | −0.945184 | ||||||||
\(721\) | 17.4987 | + | 30.3086i | 0.651685 | + | 1.12875i | ||||
\(722\) | −6.07863 | − | 10.5285i | −0.226223 | − | 0.391830i | ||||
\(723\) | 27.7559 | 1.03225 | ||||||||
\(724\) | −1.93223 | − | 3.34672i | −0.0718107 | − | 0.124380i | ||||
\(725\) | 6.78508 | − | 11.7521i | 0.251992 | − | 0.436462i | ||||
\(726\) | −0.315522 | + | 0.546500i | −0.0117101 | + | 0.0202825i | ||||
\(727\) | 23.1160 | 0.857325 | 0.428663 | − | 0.903465i | \(-0.358985\pi\) | ||||
0.428663 | + | 0.903465i | \(0.358985\pi\) | |||||||
\(728\) | −5.97573 | + | 6.81581i | −0.221475 | + | 0.252611i | ||||
\(729\) | −17.9407 | −0.664471 | ||||||||
\(730\) | −1.05948 | + | 1.83507i | −0.0392130 | + | 0.0679189i | ||||
\(731\) | −1.30327 | + | 2.25733i | −0.0482033 | + | 0.0834905i | ||||
\(732\) | −17.9599 | − | 31.1075i | −0.663818 | − | 1.14977i | ||||
\(733\) | −4.90763 | −0.181267 | −0.0906337 | − | 0.995884i | \(-0.528889\pi\) | ||||
−0.0906337 | + | 0.995884i | \(0.528889\pi\) | |||||||
\(734\) | 0.845495 | + | 1.46444i | 0.0312078 | + | 0.0540535i | ||||
\(735\) | −4.33529 | − | 7.50895i | −0.159910 | − | 0.276972i | ||||
\(736\) | 17.3925 | 0.641097 | ||||||||
\(737\) | −0.331554 | − | 0.574268i | −0.0122129 | − | 0.0211534i | ||||
\(738\) | 1.19503 | − | 2.06985i | 0.0439897 | − | 0.0761923i | ||||
\(739\) | −4.73066 | + | 8.19374i | −0.174020 | + | 0.301412i | −0.939822 | − | 0.341665i | \(-0.889009\pi\) |
0.765802 | + | 0.643077i | \(0.222342\pi\) | |||||||
\(740\) | −52.5652 | −1.93234 | ||||||||
\(741\) | −21.8581 | − | 64.3645i | −0.802979 | − | 2.36449i | ||||
\(742\) | 7.26712 | 0.266784 | ||||||||
\(743\) | 15.1360 | − | 26.2163i | 0.555285 | − | 0.961782i | −0.442596 | − | 0.896721i | \(-0.645942\pi\) |
0.997881 | − | 0.0650610i | \(-0.0207242\pi\) | |||||||
\(744\) | 2.93160 | − | 5.07768i | 0.107478 | − | 0.186157i | ||||
\(745\) | 8.09711 | + | 14.0246i | 0.296655 | + | 0.513822i | ||||
\(746\) | −1.87901 | −0.0687954 | ||||||||
\(747\) | −4.79709 | − | 8.30880i | −0.175516 | − | 0.304003i | ||||
\(748\) | 1.77025 | + | 3.06616i | 0.0647268 | + | 0.112110i | ||||
\(749\) | 41.2095 | 1.50576 | ||||||||
\(750\) | −1.87454 | − | 3.24680i | −0.0684485 | − | 0.118556i | ||||
\(751\) | −26.8774 | + | 46.5530i | −0.980771 | + | 1.69874i | −0.321368 | + | 0.946954i | \(0.604143\pi\) |
−0.659403 | + | 0.751790i | \(0.729191\pi\) | |||||||
\(752\) | 16.5957 | − | 28.7445i | 0.605181 | − | 1.04820i | ||||
\(753\) | −35.1612 | −1.28135 | ||||||||
\(754\) | −3.00169 | + | 3.42367i | −0.109315 | + | 0.124683i | ||||
\(755\) | −2.00134 | −0.0728362 | ||||||||
\(756\) | −2.55109 | + | 4.41862i | −0.0927824 | + | 0.160704i | ||||
\(757\) | 10.7975 | − | 18.7019i | 0.392443 | − | 0.679731i | −0.600328 | − | 0.799754i | \(-0.704963\pi\) |
0.992771 | + | 0.120023i | \(0.0382967\pi\) | |||||||
\(758\) | −0.930336 | − | 1.61139i | −0.0337913 | − | 0.0585283i | ||||
\(759\) | −13.3311 | −0.483888 | ||||||||
\(760\) | 11.8681 | + | 20.5562i | 0.430502 | + | 0.745652i | ||||
\(761\) | 4.27236 | + | 7.39994i | 0.154873 | + | 0.268248i | 0.933013 | − | 0.359843i | \(-0.117170\pi\) |
−0.778140 | + | 0.628091i | \(0.783837\pi\) | |||||||
\(762\) | −11.0536 | −0.400428 | ||||||||
\(763\) | 10.4409 | + | 18.0842i | 0.377986 | + | 0.654691i | ||||
\(764\) | −3.05609 | + | 5.29330i | −0.110565 | + | 0.191505i | ||||
\(765\) | −6.51762 | + | 11.2889i | −0.235645 | + | 0.408149i | ||||
\(766\) | 1.58635 | 0.0573170 | ||||||||
\(767\) | −20.7409 | + | 23.6566i | −0.748909 | + | 0.854191i | ||||
\(768\) | 24.7889 | 0.894494 | ||||||||
\(769\) | 12.2280 | − | 21.1795i | 0.440954 | − | 0.763754i | −0.556807 | − | 0.830642i | \(-0.687974\pi\) |
0.997760 | + | 0.0668880i | \(0.0213070\pi\) | |||||||
\(770\) | −0.898567 | + | 1.55636i | −0.0323821 | + | 0.0560875i | ||||
\(771\) | 14.7497 | + | 25.5473i | 0.531199 | + | 0.920064i | ||||
\(772\) | −46.4163 | −1.67056 | ||||||||
\(773\) | −0.752970 | − | 1.30418i | −0.0270824 | − | 0.0469082i | 0.852167 | − | 0.523271i | \(-0.175288\pi\) |
−0.879249 | + | 0.476363i | \(0.841955\pi\) | |||||||
\(774\) | 0.481528 | + | 0.834031i | 0.0173082 | + | 0.0299786i | ||||
\(775\) | 6.82218 | 0.245060 | ||||||||
\(776\) | −0.806667 | − | 1.39719i | −0.0289577 | − | 0.0501561i | ||||
\(777\) | 27.2210 | − | 47.1481i | 0.976548 | − | 1.69143i | ||||
\(778\) | 0.246008 | − | 0.426099i | 0.00881983 | − | 0.0152764i | ||||
\(779\) | 28.2454 | 1.01200 | ||||||||
\(780\) | 14.7570 | + | 43.4540i | 0.528384 | + | 1.55590i | ||||
\(781\) | −3.54062 | −0.126693 | ||||||||
\(782\) | 1.39731 | − | 2.42022i | 0.0499679 | − | 0.0865469i | ||||
\(783\) | −2.61078 | + | 4.52200i | −0.0933015 | + | 0.161603i | ||||
\(784\) | 2.34632 | + | 4.06394i | 0.0837971 | + | 0.145141i | ||||
\(785\) | −20.4330 | −0.729286 | ||||||||
\(786\) | −0.506141 | − | 0.876662i | −0.0180535 | − | 0.0312695i | ||||
\(787\) | −5.29788 | − | 9.17620i | −0.188849 | − | 0.327096i | 0.756018 | − | 0.654551i | \(-0.227142\pi\) |
−0.944867 | + | 0.327455i | \(0.893809\pi\) | |||||||
\(788\) | −5.03276 | −0.179285 | ||||||||
\(789\) | 30.9188 | + | 53.5529i | 1.10074 | + | 1.90653i | ||||
\(790\) | 3.63165 | − | 6.29021i | 0.129208 | − | 0.223796i | ||||
\(791\) | 2.91382 | − | 5.04688i | 0.103603 | − | 0.179446i | ||||
\(792\) | 2.66514 | 0.0947015 | ||||||||
\(793\) | −18.8353 | + | 21.4832i | −0.668861 | + | 0.762890i | ||||
\(794\) | 2.51895 | 0.0893942 | ||||||||
\(795\) | 37.4791 | − | 64.9158i | 1.32925 | − | 2.30233i | ||||
\(796\) | 16.4387 | − | 28.4727i | 0.582655 | − | 1.00919i | ||||
\(797\) | −1.87305 | − | 3.24422i | −0.0663470 | − | 0.114916i | 0.830944 | − | 0.556356i | \(-0.187801\pi\) |
−0.897291 | + | 0.441440i | \(0.854468\pi\) | |||||||
\(798\) | −12.0664 | −0.427147 | ||||||||
\(799\) | −8.52964 | − | 14.7738i | −0.301757 | − | 0.522659i | ||||
\(800\) | −4.42350 | − | 7.66173i | −0.156394 | − | 0.270883i | ||||
\(801\) | 7.76443 | 0.274343 | ||||||||
\(802\) | −1.54829 | − | 2.68171i | −0.0546719 | − | 0.0946945i | ||||
\(803\) | −1.40585 | + | 2.43500i | −0.0496113 | + | 0.0859292i | ||||
\(804\) | −1.50292 | + | 2.60314i | −0.0530040 | + | 0.0918057i | ||||
\(805\) | −37.9653 | −1.33810 | ||||||||
\(806\) | −2.24512 | − | 0.446279i | −0.0790811 | − | 0.0157195i | ||||
\(807\) | 50.3951 | 1.77399 | ||||||||
\(808\) | −3.53072 | + | 6.11539i | −0.124210 | + | 0.215139i | ||||
\(809\) | 13.1394 | − | 22.7581i | 0.461956 | − | 0.800131i | −0.537102 | − | 0.843517i | \(-0.680481\pi\) |
0.999058 | + | 0.0433858i | \(0.0138145\pi\) | |||||||
\(810\) | −3.84091 | − | 6.65266i | −0.134956 | − | 0.233751i | ||||
\(811\) | 8.17124 | 0.286931 | 0.143465 | − | 0.989655i | \(-0.454175\pi\) | ||||
0.143465 | + | 0.989655i | \(0.454175\pi\) | |||||||
\(812\) | −10.8160 | − | 18.7338i | −0.379566 | − | 0.657428i | ||||
\(813\) | −2.86153 | − | 4.95632i | −0.100358 | − | 0.173826i | ||||
\(814\) | 2.60615 | 0.0913454 | ||||||||
\(815\) | 21.6259 | + | 37.4572i | 0.757522 | + | 1.31207i | ||||
\(816\) | 7.71346 | − | 13.3601i | 0.270025 | − | 0.467697i | ||||
\(817\) | −5.69064 | + | 9.85648i | −0.199090 | + | 0.344834i | ||||
\(818\) | 9.33441 | 0.326370 | ||||||||
\(819\) | −21.3187 | − | 4.23767i | −0.744935 | − | 0.148076i | ||||
\(820\) | −19.0692 | −0.665925 | ||||||||
\(821\) | 27.9142 | − | 48.3489i | 0.974214 | − | 1.68739i | 0.291708 | − | 0.956507i | \(-0.405776\pi\) |
0.682505 | − | 0.730881i | \(-0.260890\pi\) | |||||||
\(822\) | 0.611424 | − | 1.05902i | 0.0213259 | − | 0.0369375i | ||||
\(823\) | 15.2445 | + | 26.4043i | 0.531391 | + | 0.920396i | 0.999329 | + | 0.0366346i | \(0.0116638\pi\) |
−0.467938 | + | 0.883761i | \(0.655003\pi\) | |||||||
\(824\) | 15.4722 | 0.538998 | ||||||||
\(825\) | 3.39055 | + | 5.87260i | 0.118044 | + | 0.204458i | ||||
\(826\) | 2.79241 | + | 4.83660i | 0.0971604 | + | 0.168287i | ||||
\(827\) | 3.15547 | 0.109726 | 0.0548631 | − | 0.998494i | \(-0.482528\pi\) | ||||
0.0548631 | + | 0.998494i | \(0.482528\pi\) | |||||||
\(828\) | 13.8174 | + | 23.9325i | 0.480189 | + | 0.831712i | ||||
\(829\) | 7.93696 | − | 13.7472i | 0.275662 | − | 0.477461i | −0.694640 | − | 0.719358i | \(-0.744436\pi\) |
0.970302 | + | 0.241897i | \(0.0777696\pi\) | |||||||
\(830\) | 1.43006 | − | 2.47694i | 0.0496381 | − | 0.0859758i | ||||
\(831\) | −13.3012 | −0.461414 | ||||||||
\(832\) | −7.33054 | − | 21.5859i | −0.254141 | − | 0.748355i | ||||
\(833\) | 2.41187 | 0.0835663 | ||||||||
\(834\) | 3.87764 | − | 6.71626i | 0.134272 | − | 0.232565i | ||||
\(835\) | 3.34655 | − | 5.79640i | 0.115812 | − | 0.200593i | ||||
\(836\) | 7.72967 | + | 13.3882i | 0.267336 | + | 0.463040i | ||||
\(837\) | −2.62505 | −0.0907350 | ||||||||
\(838\) | 1.65673 | + | 2.86953i | 0.0572306 | + | 0.0991264i | ||||
\(839\) | −15.2475 | − | 26.4094i | −0.526401 | − | 0.911753i | −0.999527 | − | 0.0307583i | \(-0.990208\pi\) |
0.473126 | − | 0.880995i | \(-0.343126\pi\) | |||||||
\(840\) | 16.5971 | 0.572654 | ||||||||
\(841\) | 3.43099 | + | 5.94265i | 0.118310 | + | 0.204919i | ||||
\(842\) | −0.338613 | + | 0.586495i | −0.0116694 | + | 0.0202120i | ||||
\(843\) | −21.1096 | + | 36.5630i | −0.727055 | + | 1.25930i | ||||
\(844\) | 39.2882 | 1.35235 | ||||||||
\(845\) | 28.9534 | − | 22.2287i | 0.996029 | − | 0.764692i | ||||
\(846\) | −6.30300 | −0.216702 | ||||||||
\(847\) | −1.19233 | + | 2.06518i | −0.0409690 | + | 0.0709604i | ||||
\(848\) | −20.2842 | + | 35.1333i | −0.696563 | + | 1.20648i | ||||
\(849\) | 16.8967 | + | 29.2659i | 0.579892 | + | 1.00440i | ||||
\(850\) | −1.42154 | −0.0487583 | ||||||||
\(851\) | 27.5280 | + | 47.6799i | 0.943649 | + | 1.63445i | ||||
\(852\) | 8.02477 | + | 13.8993i | 0.274924 | + | 0.476182i | ||||
\(853\) | −33.0339 | −1.13106 | −0.565530 | − | 0.824728i | \(-0.691328\pi\) | ||||
−0.565530 | + | 0.824728i | \(0.691328\pi\) | |||||||
\(854\) | 2.53586 | + | 4.39224i | 0.0867754 | + | 0.150299i | ||||
\(855\) | −28.4587 | + | 49.2919i | −0.973267 | + | 1.68575i | ||||
\(856\) | 9.10927 | − | 15.7777i | 0.311348 | − | 0.539271i | ||||
\(857\) | −2.25150 | −0.0769098 | −0.0384549 | − | 0.999260i | \(-0.512244\pi\) | ||||
−0.0384549 | + | 0.999260i | \(0.512244\pi\) | |||||||
\(858\) | −0.731639 | − | 2.15442i | −0.0249778 | − | 0.0735507i | ||||
\(859\) | 14.7807 | 0.504309 | 0.252155 | − | 0.967687i | \(-0.418861\pi\) | ||||
0.252155 | + | 0.967687i | \(0.418861\pi\) | |||||||
\(860\) | 3.84189 | − | 6.65435i | 0.131007 | − | 0.226911i | ||||
\(861\) | 9.87502 | − | 17.1040i | 0.336540 | − | 0.582904i | ||||
\(862\) | −2.13565 | − | 3.69906i | −0.0727406 | − | 0.125990i | ||||
\(863\) | −42.7490 | −1.45519 | −0.727597 | − | 0.686005i | \(-0.759363\pi\) | ||||
−0.727597 | + | 0.686005i | \(0.759363\pi\) | |||||||
\(864\) | 1.70208 | + | 2.94809i | 0.0579060 | + | 0.100296i | ||||
\(865\) | 7.17256 | + | 12.4232i | 0.243874 | + | 0.422403i | ||||
\(866\) | −0.566400 | −0.0192471 | ||||||||
\(867\) | 16.0205 | + | 27.7483i | 0.544083 | + | 0.942380i | ||||
\(868\) | 5.43756 | − | 9.41812i | 0.184563 | − | 0.319672i | ||||
\(869\) | 4.81894 | − | 8.34665i | 0.163471 | − | 0.283141i | ||||
\(870\) | 8.33693 | 0.282648 | ||||||||
\(871\) | 2.34499 | + | 0.466130i | 0.0794570 | + | 0.0157942i | ||||
\(872\) | 9.23175 | 0.312626 | ||||||||
\(873\) | 1.93432 | − | 3.35033i | 0.0654667 | − | 0.113392i | ||||
\(874\) | 6.10127 | − | 10.5677i | 0.206378 | − | 0.357458i | ||||
\(875\) | −7.08373 | − | 12.2694i | −0.239474 | − | 0.414781i | ||||
\(876\) | 12.7453 | 0.430624 | ||||||||
\(877\) | 16.7639 | + | 29.0360i | 0.566078 | + | 0.980475i | 0.996949 | + | 0.0780617i | \(0.0248731\pi\) |
−0.430871 | + | 0.902414i | \(0.641794\pi\) | |||||||
\(878\) | 2.35701 | + | 4.08246i | 0.0795453 | + | 0.137777i | ||||
\(879\) | −63.7884 | −2.15153 | ||||||||
\(880\) | −5.01622 | − | 8.68835i | −0.169097 | − | 0.292884i | ||||
\(881\) | −11.1873 | + | 19.3769i | −0.376909 | + | 0.652825i | −0.990611 | − | 0.136713i | \(-0.956346\pi\) |
0.613702 | + | 0.789538i | \(0.289680\pi\) | |||||||
\(882\) | 0.445564 | − | 0.771739i | 0.0150029 | − | 0.0259858i | ||||
\(883\) | 10.7284 | 0.361041 | 0.180520 | − | 0.983571i | \(-0.442222\pi\) | ||||
0.180520 | + | 0.983571i | \(0.442222\pi\) | |||||||
\(884\) | −12.5205 | − | 2.48879i | −0.421110 | − | 0.0837070i | ||||
\(885\) | 57.6059 | 1.93640 | ||||||||
\(886\) | 4.34673 | − | 7.52876i | 0.146031 | − | 0.252934i | ||||
\(887\) | 2.75829 | − | 4.77749i | 0.0926142 | − | 0.160412i | −0.815996 | − | 0.578057i | \(-0.803811\pi\) |
0.908610 | + | 0.417645i | \(0.137144\pi\) | |||||||
\(888\) | −12.0343 | − | 20.8440i | −0.403844 | − | 0.699478i | ||||
\(889\) | −41.7705 | −1.40094 | ||||||||
\(890\) | 1.15733 | + | 2.00455i | 0.0387937 | + | 0.0671927i | ||||
\(891\) | −5.09661 | − | 8.82759i | −0.170743 | − | 0.295735i | ||||
\(892\) | −1.96282 | −0.0657200 | ||||||||
\(893\) | −37.2440 | − | 64.5086i | −1.24632 | − | 2.15870i | ||||
\(894\) | −1.81975 | + | 3.15191i | −0.0608617 | + | 0.105416i | ||||
\(895\) | 34.1243 | − | 59.1050i | 1.14065 | − | 1.97566i | ||||
\(896\) | −18.6765 | −0.623938 | ||||||||
\(897\) | 31.6874 | − | 36.1420i | 1.05801 | − | 1.20675i | ||||
\(898\) | 6.35030 | 0.211912 | ||||||||
\(899\) | 5.56476 | − | 9.63845i | 0.185595 | − | 0.321460i | ||||
\(900\) | 7.02847 | − | 12.1737i | 0.234282 | − | 0.405789i | ||||
\(901\) | 10.4254 | + | 18.0574i | 0.347322 | + | 0.601579i | ||||
\(902\) | 0.945437 | 0.0314796 | ||||||||
\(903\) | 3.97906 | + | 6.89193i | 0.132415 | + | 0.229349i | ||||
\(904\) | −1.28818 | − | 2.23120i | −0.0428444 | − | 0.0742087i | ||||
\(905\) | 5.62816 | 0.187086 | ||||||||
\(906\) | −0.224892 | − | 0.389524i | −0.00747153 | − | 0.0129411i | ||||
\(907\) | 8.76282 | − | 15.1777i | 0.290965 | − | 0.503966i | −0.683073 | − | 0.730350i | \(-0.739357\pi\) |
0.974038 | + | 0.226384i | \(0.0726904\pi\) | |||||||
\(908\) | 0.0220083 | − | 0.0381195i | 0.000730370 | − | 0.00126504i | ||||
\(909\) | −16.9327 | −0.561622 | ||||||||
\(910\) | −2.08362 | − | 6.13551i | −0.0690712 | − | 0.203390i | ||||
\(911\) | 27.8447 | 0.922537 | 0.461268 | − | 0.887261i | \(-0.347394\pi\) | ||||
0.461268 | + | 0.887261i | \(0.347394\pi\) | |||||||
\(912\) | 33.6802 | − | 58.3359i | 1.11526 | − | 1.93169i | ||||
\(913\) | 1.89759 | − | 3.28671i | 0.0628009 | − | 0.108774i | ||||
\(914\) | −0.472982 | − | 0.819229i | −0.0156449 | − | 0.0270977i | ||||
\(915\) | 52.3134 | 1.72943 | ||||||||
\(916\) | −20.6530 | − | 35.7720i | −0.682394 | − | 1.18194i | ||||
\(917\) | −1.91267 | − | 3.31284i | −0.0631618 | − | 0.109400i | ||||
\(918\) | 0.546981 | 0.0180531 | ||||||||
\(919\) | −23.4408 | − | 40.6007i | −0.773241 | − | 1.33929i | −0.935778 | − | 0.352590i | \(-0.885301\pi\) |
0.162537 | − | 0.986702i | \(-0.448032\pi\) | |||||||
\(920\) | −8.39214 | + | 14.5356i | −0.276681 | + | 0.479225i | ||||
\(921\) | −12.0293 | + | 20.8354i | −0.396380 | + | 0.686551i | ||||
\(922\) | −3.79642 | −0.125028 | ||||||||
\(923\) | 8.41589 | − | 9.59901i | 0.277013 | − | 0.315955i | ||||
\(924\) | 10.8096 | 0.355610 | ||||||||
\(925\) | 14.0026 | − | 24.2532i | 0.460403 | − | 0.797441i | ||||
\(926\) | −1.18055 | + | 2.04478i | −0.0387954 | + | 0.0671955i | ||||
\(927\) | 18.5504 | + | 32.1303i | 0.609276 | + | 1.05530i | ||||
\(928\) | −14.4328 | −0.473779 | ||||||||
\(929\) | 1.73354 | + | 3.00258i | 0.0568756 | + | 0.0985114i | 0.893061 | − | 0.449935i | \(-0.148553\pi\) |
−0.836186 | + | 0.548446i | \(0.815220\pi\) | |||||||
\(930\) | 2.09563 | + | 3.62974i | 0.0687184 | + | 0.119024i | ||||
\(931\) | 10.5312 | 0.345147 | ||||||||
\(932\) | 26.0925 | + | 45.1935i | 0.854687 | + | 1.48036i | ||||
\(933\) | 9.93047 | − | 17.2001i | 0.325109 | − | 0.563105i | ||||
\(934\) | −0.688391 | + | 1.19233i | −0.0225249 | + | 0.0390142i | ||||
\(935\) | −5.15636 | −0.168631 | ||||||||
\(936\) | −6.33491 | + | 7.22547i | −0.207063 | + | 0.236172i | ||||
\(937\) | 13.4020 | 0.437825 | 0.218913 | − | 0.975744i | \(-0.429749\pi\) | ||||
0.218913 | + | 0.975744i | \(0.429749\pi\) | |||||||
\(938\) | 0.212206 | − | 0.367551i | 0.00692877 | − | 0.0120010i | ||||
\(939\) | −24.6091 | + | 42.6243i | −0.803089 | + | 1.39099i | ||||
\(940\) | 25.1444 | + | 43.5513i | 0.820119 | + | 1.42049i | ||||
\(941\) | −11.9245 | −0.388728 | −0.194364 | − | 0.980930i | \(-0.562264\pi\) | ||||
−0.194364 | + | 0.980930i | \(0.562264\pi\) | |||||||
\(942\) | −2.29607 | − | 3.97691i | −0.0748100 | − | 0.129575i | ||||
\(943\) | 9.98640 | + | 17.2970i | 0.325202 | + | 0.563266i | ||||
\(944\) | −31.1771 | −1.01473 | ||||||||
\(945\) | −3.71539 | − | 6.43525i | −0.120862 | − | 0.209339i | ||||
\(946\) | −0.190478 | + | 0.329918i | −0.00619298 | + | 0.0107266i | ||||
\(947\) | 21.0637 | − | 36.4833i | 0.684477 | − | 1.18555i | −0.289124 | − | 0.957292i | \(-0.593364\pi\) |
0.973601 | − | 0.228257i | \(-0.0733027\pi\) | |||||||
\(948\) | −43.6882 | −1.41893 | ||||||||
\(949\) | −3.25991 | − | 9.59928i | −0.105821 | − | 0.311606i | ||||
\(950\) | −6.20703 | −0.201383 | ||||||||
\(951\) | −27.1341 | + | 46.9976i | −0.879883 | + | 1.52400i | ||||
\(952\) | −2.30838 | + | 3.99823i | −0.0748149 | + | 0.129583i | ||||
\(953\) | −12.1110 | − | 20.9769i | −0.392314 | − | 0.679508i | 0.600440 | − | 0.799670i | \(-0.294992\pi\) |
−0.992754 | + | 0.120161i | \(0.961659\pi\) | |||||||
\(954\) | 7.70391 | 0.249423 | ||||||||
\(955\) | −4.45086 | − | 7.70912i | −0.144027 | − | 0.249461i | ||||
\(956\) | 28.0544 | + | 48.5916i | 0.907343 | + | 1.57156i | ||||
\(957\) | 11.0625 | 0.357600 | ||||||||
\(958\) | 3.20436 | + | 5.55011i | 0.103528 | + | 0.179316i | ||||
\(959\) | 2.31052 | − | 4.00194i | 0.0746106 | − | 0.129229i | ||||
\(960\) | −20.8704 | + | 36.1485i | −0.673588 | + | 1.16669i | ||||
\(961\) | −25.4048 | −0.819510 | ||||||||
\(962\) | −6.19468 | + | 7.06554i | −0.199725 | + | 0.227802i | ||||
\(963\) | 43.6864 | 1.40777 | ||||||||
\(964\) | 11.3800 | − | 19.7107i | 0.366524 | − | 0.634838i | ||||
\(965\) | 33.8001 | − | 58.5435i | 1.08806 | − | 1.88458i | ||||
\(966\) | −4.26618 | − | 7.38925i | −0.137262 | − | 0.237745i | ||||
\(967\) | −30.0551 | −0.966506 | −0.483253 | − | 0.875481i | \(-0.660545\pi\) | ||||
−0.483253 | + | 0.875481i | \(0.660545\pi\) | |||||||
\(968\) | 0.527125 | + | 0.913007i | 0.0169424 | + | 0.0293452i | ||||
\(969\) | −17.3106 | − | 29.9828i | −0.556096 | − | 0.963186i | ||||
\(970\) | 1.15328 | 0.0370295 | ||||||||
\(971\) | −12.1208 | − | 20.9939i | −0.388976 | − | 0.673726i | 0.603336 | − | 0.797487i | \(-0.293838\pi\) |
−0.992312 | + | 0.123761i | \(0.960504\pi\) | |||||||
\(972\) | −19.8934 | + | 34.4564i | −0.638081 | + | 1.10519i | ||||
\(973\) | 14.6533 | − | 25.3802i | 0.469762 | − | 0.813652i | ||||
\(974\) | −3.57659 | −0.114601 | ||||||||
\(975\) | −23.9804 | − | 4.76676i | −0.767988 | − | 0.152658i | ||||
\(976\) | −28.3127 | −0.906268 | ||||||||
\(977\) | 16.5682 | − | 28.6970i | 0.530064 | − | 0.918098i | −0.469321 | − | 0.883028i | \(-0.655501\pi\) |
0.999385 | − | 0.0350703i | \(-0.0111655\pi\) | |||||||
\(978\) | −4.86023 | + | 8.41817i | −0.155413 | + | 0.269183i | ||||
\(979\) | 1.53569 | + | 2.65989i | 0.0490808 | + | 0.0850105i | ||||
\(980\) | −7.10990 | −0.227117 | ||||||||
\(981\) | 11.0685 | + | 19.1711i | 0.353388 | + | 0.612087i | ||||
\(982\) | −0.534710 | − | 0.926146i | −0.0170633 | − | 0.0295545i | ||||
\(983\) | 13.2214 | 0.421696 | 0.210848 | − | 0.977519i | \(-0.432378\pi\) | ||||
0.210848 | + | 0.977519i | \(0.432378\pi\) | |||||||
\(984\) | −4.36570 | − | 7.56161i | −0.139173 | − | 0.241055i | ||||
\(985\) | 3.66483 | − | 6.34768i | 0.116771 | − | 0.202254i | ||||
\(986\) | −1.15953 | + | 2.00836i | −0.0369269 | + | 0.0639592i | ||||
\(987\) | −52.0842 | −1.65786 | ||||||||
\(988\) | −54.6698 | − | 10.8671i | −1.73928 | − | 0.345729i | ||||
\(989\) | −8.04788 | −0.255908 | ||||||||
\(990\) | −0.952575 | + | 1.64991i | −0.0302748 | + | 0.0524375i | ||||
\(991\) | −3.22583 | + | 5.58730i | −0.102472 | + | 0.177487i | −0.912703 | − | 0.408625i | \(-0.866009\pi\) |
0.810231 | + | 0.586111i | \(0.199342\pi\) | |||||||
\(992\) | −3.62792 | − | 6.28374i | −0.115187 | − | 0.199509i | ||||
\(993\) | 7.76507 | 0.246417 | ||||||||
\(994\) | −1.13306 | − | 1.96252i | −0.0359385 | − | 0.0622473i | ||||
\(995\) | 23.9412 | + | 41.4674i | 0.758988 | + | 1.31461i | ||||
\(996\) | −17.2034 | −0.545110 | ||||||||
\(997\) | 3.43607 | + | 5.95146i | 0.108822 | + | 0.188485i | 0.915293 | − | 0.402788i | \(-0.131959\pi\) |
−0.806472 | + | 0.591273i | \(0.798626\pi\) | |||||||
\(998\) | −0.461945 | + | 0.800113i | −0.0146226 | + | 0.0253271i | ||||
\(999\) | −5.38794 | + | 9.33219i | −0.170467 | + | 0.295257i |
(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 | 143.2.e.c.100.3 | ✓ | 12 | |
13.3 | even | 3 | inner | 143.2.e.c.133.3 | yes | 12 | |
13.4 | even | 6 | 1859.2.a.l.1.3 | 6 | |||
13.9 | even | 3 | 1859.2.a.k.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.2.e.c.100.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
143.2.e.c.133.3 | yes | 12 | 13.3 | even | 3 | inner | |
1859.2.a.k.1.4 | 6 | 13.9 | even | 3 | |||
1859.2.a.l.1.3 | 6 | 13.4 | even | 6 |