Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [99,2,Mod(34,99)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(99, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("99.34");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.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: | \(0.790518980011\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.508277025.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 15x^{5} + 21x^{4} + 3x^{3} - 22x^{2} + 3x + 19 \) |
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 | 67.2 | ||
Root | \(-0.577806 + 2.22188i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 99.67 |
Dual form | 99.2.e.e.34.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.07781 | − | 1.86682i | −0.762124 | − | 1.32004i | −0.941754 | − | 0.336303i | \(-0.890823\pi\) |
0.179629 | − | 0.983734i | \(-0.442510\pi\) | |||||||
\(3\) | −0.635299 | + | 1.61133i | −0.366790 | + | 0.930304i | ||||
\(4\) | −1.32333 | + | 2.29208i | −0.661667 | + | 1.14604i | ||||
\(5\) | −1.81197 | + | 3.13842i | −0.810336 | + | 1.40354i | 0.102294 | + | 0.994754i | \(0.467382\pi\) |
−0.912629 | + | 0.408788i | \(0.865951\pi\) | |||||||
\(6\) | 3.69279 | − | 0.550720i | 1.50758 | − | 0.224831i | ||||
\(7\) | 1.13530 | + | 1.96640i | 0.429103 | + | 0.743227i | 0.996794 | − | 0.0800141i | \(-0.0254965\pi\) |
−0.567691 | + | 0.823242i | \(0.692163\pi\) | |||||||
\(8\) | 1.39396 | 0.492840 | ||||||||
\(9\) | −2.19279 | − | 2.04736i | −0.730930 | − | 0.682452i | ||||
\(10\) | 7.81179 | 2.47031 | ||||||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | ||||
\(12\) | −2.85259 | − | 3.58849i | −0.823473 | − | 1.03591i | ||||
\(13\) | −0.619175 | + | 1.07244i | −0.171728 | + | 0.297442i | −0.939024 | − | 0.343851i | \(-0.888268\pi\) |
0.767296 | + | 0.641293i | \(0.221602\pi\) | |||||||
\(14\) | 2.44726 | − | 4.23879i | 0.654059 | − | 1.13286i | ||||
\(15\) | −3.90590 | − | 4.91351i | −1.00850 | − | 1.26866i | ||||
\(16\) | 1.14425 | + | 1.98189i | 0.286061 | + | 0.495473i | ||||
\(17\) | 5.69681 | 1.38168 | 0.690839 | − | 0.723008i | \(-0.257241\pi\) | ||||
0.690839 | + | 0.723008i | \(0.257241\pi\) | |||||||
\(18\) | −1.45863 | + | 6.30019i | −0.343803 | + | 1.48497i | ||||
\(19\) | −2.89453 | −0.664050 | −0.332025 | − | 0.943271i | \(-0.607732\pi\) | ||||
−0.332025 | + | 0.943271i | \(0.607732\pi\) | |||||||
\(20\) | −4.79567 | − | 8.30634i | −1.07234 | − | 1.85735i | ||||
\(21\) | −3.88977 | + | 0.580097i | −0.848818 | + | 0.126587i | ||||
\(22\) | −1.07781 | + | 1.86682i | −0.229789 | + | 0.398006i | ||||
\(23\) | −2.95863 | + | 5.12450i | −0.616917 | + | 1.06853i | 0.373127 | + | 0.927780i | \(0.378285\pi\) |
−0.990045 | + | 0.140752i | \(0.955048\pi\) | |||||||
\(24\) | −0.885582 | + | 2.24614i | −0.180769 | + | 0.458491i | ||||
\(25\) | −4.06644 | − | 7.04328i | −0.813288 | − | 1.40866i | ||||
\(26\) | 2.66940 | 0.523513 | ||||||||
\(27\) | 4.69205 | − | 2.23263i | 0.902986 | − | 0.429671i | ||||
\(28\) | −6.00951 | −1.13569 | ||||||||
\(29\) | 1.75447 | + | 3.03884i | 0.325798 | + | 0.564298i | 0.981673 | − | 0.190571i | \(-0.0610339\pi\) |
−0.655876 | + | 0.754869i | \(0.727701\pi\) | |||||||
\(30\) | −4.96282 | + | 12.5874i | −0.906083 | + | 2.29813i | ||||
\(31\) | 1.25447 | − | 2.17281i | 0.225310 | − | 0.390248i | −0.731102 | − | 0.682268i | \(-0.760994\pi\) |
0.956412 | + | 0.292019i | \(0.0943272\pi\) | |||||||
\(32\) | 3.86051 | − | 6.68660i | 0.682448 | − | 1.18204i | ||||
\(33\) | 1.71311 | − | 0.255482i | 0.298213 | − | 0.0444737i | ||||
\(34\) | −6.14006 | − | 10.6349i | −1.05301 | − | 1.82387i | ||||
\(35\) | −8.22849 | −1.39087 | ||||||||
\(36\) | 7.59450 | − | 2.31672i | 1.26575 | − | 0.386120i | ||||
\(37\) | −0.333960 | −0.0549027 | −0.0274514 | − | 0.999623i | \(-0.508739\pi\) | ||||
−0.0274514 | + | 0.999623i | \(0.508739\pi\) | |||||||
\(38\) | 3.11974 | + | 5.40355i | 0.506089 | + | 0.876572i | ||||
\(39\) | −1.33470 | − | 1.67902i | −0.213723 | − | 0.268858i | ||||
\(40\) | −2.52581 | + | 4.37483i | −0.399366 | + | 0.691722i | ||||
\(41\) | 4.98370 | − | 8.63203i | 0.778324 | − | 1.34810i | −0.154584 | − | 0.987980i | \(-0.549404\pi\) |
0.932907 | − | 0.360116i | \(-0.117263\pi\) | |||||||
\(42\) | 5.27535 | + | 6.63625i | 0.814005 | + | 1.02400i | ||||
\(43\) | 3.57781 | + | 6.19694i | 0.545610 | + | 0.945025i | 0.998568 | + | 0.0534929i | \(0.0170355\pi\) |
−0.452958 | + | 0.891532i | \(0.649631\pi\) | |||||||
\(44\) | 2.64667 | 0.399000 | ||||||||
\(45\) | 10.3987 | − | 3.17215i | 1.55015 | − | 0.472877i | ||||
\(46\) | 12.7553 | 1.88067 | ||||||||
\(47\) | 4.34840 | + | 7.53166i | 0.634280 | + | 1.09860i | 0.986667 | + | 0.162751i | \(0.0520366\pi\) |
−0.352387 | + | 0.935854i | \(0.614630\pi\) | |||||||
\(48\) | −3.92042 | + | 0.584668i | −0.565865 | + | 0.0843895i | ||||
\(49\) | 0.922194 | − | 1.59729i | 0.131742 | − | 0.228184i | ||||
\(50\) | −8.76567 | + | 15.1826i | −1.23965 | + | 2.14714i | ||||
\(51\) | −3.61917 | + | 9.17946i | −0.506786 | + | 1.28538i | ||||
\(52\) | −1.63875 | − | 2.83840i | −0.227254 | − | 0.393615i | ||||
\(53\) | 6.16513 | 0.846845 | 0.423423 | − | 0.905932i | \(-0.360829\pi\) | ||||
0.423423 | + | 0.905932i | \(0.360829\pi\) | |||||||
\(54\) | −9.22504 | − | 6.35284i | −1.25537 | − | 0.864513i | ||||
\(55\) | 3.62393 | 0.488651 | ||||||||
\(56\) | 1.58256 | + | 2.74108i | 0.211479 | + | 0.366292i | ||||
\(57\) | 1.83889 | − | 4.66405i | 0.243567 | − | 0.617769i | ||||
\(58\) | 3.78196 | − | 6.55056i | 0.496596 | − | 0.860130i | ||||
\(59\) | −1.45863 | + | 2.52642i | −0.189898 | + | 0.328912i | −0.945216 | − | 0.326446i | \(-0.894149\pi\) |
0.755318 | + | 0.655358i | \(0.227482\pi\) | |||||||
\(60\) | 16.4310 | − | 2.45041i | 2.12123 | − | 0.316347i | ||||
\(61\) | −3.13530 | − | 5.43050i | −0.401434 | − | 0.695304i | 0.592465 | − | 0.805596i | \(-0.298155\pi\) |
−0.993899 | + | 0.110292i | \(0.964821\pi\) | |||||||
\(62\) | −5.40832 | −0.686857 | ||||||||
\(63\) | 1.53644 | − | 6.63625i | 0.193573 | − | 0.836089i | ||||
\(64\) | −12.0666 | −1.50832 | ||||||||
\(65\) | −2.24385 | − | 3.88646i | −0.278315 | − | 0.482055i | ||||
\(66\) | −2.32333 | − | 2.92269i | −0.285983 | − | 0.359758i | ||||
\(67\) | −4.68142 | + | 8.10846i | −0.571927 | + | 0.990606i | 0.424441 | + | 0.905456i | \(0.360471\pi\) |
−0.996368 | + | 0.0851510i | \(0.972863\pi\) | |||||||
\(68\) | −7.53877 | + | 13.0575i | −0.914211 | + | 1.58346i | ||||
\(69\) | −6.37766 | − | 8.02293i | −0.767781 | − | 0.965847i | ||||
\(70\) | 8.86872 | + | 15.3611i | 1.06001 | + | 1.83600i | ||||
\(71\) | −12.1230 | −1.43874 | −0.719369 | − | 0.694628i | \(-0.755569\pi\) | ||||
−0.719369 | + | 0.694628i | \(0.755569\pi\) | |||||||
\(72\) | −3.05667 | − | 2.85394i | −0.360232 | − | 0.336340i | ||||
\(73\) | 4.31271 | 0.504764 | 0.252382 | − | 0.967628i | \(-0.418786\pi\) | ||||
0.252382 | + | 0.967628i | \(0.418786\pi\) | |||||||
\(74\) | 0.359945 | + | 0.623442i | 0.0418427 | + | 0.0724737i | ||||
\(75\) | 13.9325 | − | 2.07780i | 1.60878 | − | 0.239924i | ||||
\(76\) | 3.83043 | − | 6.63449i | 0.439380 | − | 0.761028i | ||||
\(77\) | 1.13530 | − | 1.96640i | 0.129379 | − | 0.224092i | ||||
\(78\) | −1.69587 | + | 4.30130i | −0.192019 | + | 0.487026i | ||||
\(79\) | −0.708348 | − | 1.22690i | −0.0796954 | − | 0.138037i | 0.823423 | − | 0.567428i | \(-0.192061\pi\) |
−0.903119 | + | 0.429391i | \(0.858728\pi\) | |||||||
\(80\) | −8.29333 | −0.927223 | ||||||||
\(81\) | 0.616665 | + | 8.97885i | 0.0685184 | + | 0.997650i | ||||
\(82\) | −21.4859 | −2.37272 | ||||||||
\(83\) | 1.37840 | + | 2.38747i | 0.151300 | + | 0.262059i | 0.931705 | − | 0.363215i | \(-0.118321\pi\) |
−0.780406 | + | 0.625273i | \(0.784988\pi\) | |||||||
\(84\) | 3.81784 | − | 9.68333i | 0.416560 | − | 1.05654i | ||||
\(85\) | −10.3224 | + | 17.8790i | −1.11962 | + | 1.93924i | ||||
\(86\) | 7.71236 | − | 13.3582i | 0.831646 | − | 1.44045i | ||||
\(87\) | −6.01119 | + | 0.896472i | −0.644468 | + | 0.0961119i | ||||
\(88\) | −0.696981 | − | 1.20721i | −0.0742984 | − | 0.128689i | ||||
\(89\) | 4.77116 | 0.505742 | 0.252871 | − | 0.967500i | \(-0.418625\pi\) | ||||
0.252871 | + | 0.967500i | \(0.418625\pi\) | |||||||
\(90\) | −17.1296 | − | 15.9935i | −1.80562 | − | 1.68587i | ||||
\(91\) | −2.81179 | −0.294756 | ||||||||
\(92\) | −7.83051 | − | 13.5628i | −0.816387 | − | 1.41402i | ||||
\(93\) | 2.70416 | + | 3.40176i | 0.280408 | + | 0.352746i | ||||
\(94\) | 9.37347 | − | 16.2353i | 0.966800 | − | 1.67455i | ||||
\(95\) | 5.24479 | − | 9.08424i | 0.538104 | − | 0.932023i | ||||
\(96\) | 8.32177 | + | 10.4686i | 0.849337 | + | 1.06844i | ||||
\(97\) | 1.27954 | + | 2.21624i | 0.129918 | + | 0.225025i | 0.923645 | − | 0.383250i | \(-0.125195\pi\) |
−0.793727 | + | 0.608275i | \(0.791862\pi\) | |||||||
\(98\) | −3.97578 | −0.401615 | ||||||||
\(99\) | −0.676667 | + | 2.92269i | −0.0680076 | + | 0.293741i | ||||
\(100\) | 21.5250 | 2.15250 | ||||||||
\(101\) | 9.16681 | + | 15.8774i | 0.912131 | + | 1.57986i | 0.811048 | + | 0.584980i | \(0.198898\pi\) |
0.101084 | + | 0.994878i | \(0.467769\pi\) | |||||||
\(102\) | 21.0371 | − | 3.13735i | 2.08299 | − | 0.310644i | ||||
\(103\) | 2.28122 | − | 3.95120i | 0.224776 | − | 0.389323i | −0.731476 | − | 0.681867i | \(-0.761168\pi\) |
0.956252 | + | 0.292544i | \(0.0945017\pi\) | |||||||
\(104\) | −0.863106 | + | 1.49494i | −0.0846345 | + | 0.146591i | ||||
\(105\) | 5.22755 | − | 13.2588i | 0.510156 | − | 1.29393i | ||||
\(106\) | −6.64481 | − | 11.5092i | −0.645401 | − | 1.11787i | ||||
\(107\) | −5.11014 | −0.494016 | −0.247008 | − | 0.969013i | \(-0.579447\pi\) | ||||
−0.247008 | + | 0.969013i | \(0.579447\pi\) | |||||||
\(108\) | −1.09177 | + | 13.7091i | −0.105055 | + | 1.31916i | ||||
\(109\) | 4.67891 | 0.448159 | 0.224079 | − | 0.974571i | \(-0.428063\pi\) | ||||
0.224079 | + | 0.974571i | \(0.428063\pi\) | |||||||
\(110\) | −3.90590 | − | 6.76521i | −0.372413 | − | 0.645038i | ||||
\(111\) | 0.212165 | − | 0.538121i | 0.0201378 | − | 0.0510762i | ||||
\(112\) | −2.59812 | + | 4.50008i | −0.245499 | + | 0.425217i | ||||
\(113\) | 0.765841 | − | 1.32648i | 0.0720442 | − | 0.124784i | −0.827753 | − | 0.561093i | \(-0.810381\pi\) |
0.899797 | + | 0.436309i | \(0.143714\pi\) | |||||||
\(114\) | −10.6889 | + | 1.59407i | −1.00111 | + | 0.149299i | ||||
\(115\) | −10.7219 | − | 18.5708i | −0.999820 | − | 1.73174i | ||||
\(116\) | −9.28701 | −0.862277 | ||||||||
\(117\) | 3.55339 | − | 1.08397i | 0.328511 | − | 0.100213i | ||||
\(118\) | 6.28849 | 0.578902 | ||||||||
\(119\) | 6.46758 | + | 11.2022i | 0.592882 | + | 1.02690i | ||||
\(120\) | −5.44467 | − | 6.84925i | −0.497028 | − | 0.625248i | ||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | −6.75849 | + | 11.7060i | −0.611885 | + | 1.05982i | ||||
\(123\) | 10.7429 | + | 13.5143i | 0.968658 | + | 1.21855i | ||||
\(124\) | 3.32017 | + | 5.75071i | 0.298160 | + | 0.516429i | ||||
\(125\) | 11.3533 | 1.01547 | ||||||||
\(126\) | −14.0446 | + | 4.28435i | −1.25120 | + | 0.381680i | ||||
\(127\) | 8.72758 | 0.774447 | 0.387224 | − | 0.921986i | \(-0.373434\pi\) | ||||
0.387224 | + | 0.921986i | \(0.373434\pi\) | |||||||
\(128\) | 5.28439 | + | 9.15282i | 0.467078 | + | 0.809003i | ||||
\(129\) | −12.2583 | + | 1.82813i | −1.07928 | + | 0.160958i | ||||
\(130\) | −4.83686 | + | 8.37769i | −0.424221 | + | 0.734772i | ||||
\(131\) | 1.84439 | − | 3.19457i | 0.161145 | − | 0.279111i | −0.774135 | − | 0.633021i | \(-0.781815\pi\) |
0.935280 | + | 0.353910i | \(0.115148\pi\) | |||||||
\(132\) | −1.68142 | + | 4.26466i | −0.146349 | + | 0.371191i | ||||
\(133\) | −3.28615 | − | 5.69179i | −0.284946 | − | 0.493541i | ||||
\(134\) | 20.1827 | 1.74352 | ||||||||
\(135\) | −1.49490 | + | 18.7711i | −0.128660 | + | 1.61556i | ||||
\(136\) | 7.94113 | 0.680946 | ||||||||
\(137\) | −10.9843 | − | 19.0253i | −0.938449 | − | 1.62544i | −0.768364 | − | 0.640013i | \(-0.778929\pi\) |
−0.170085 | − | 0.985429i | \(-0.554404\pi\) | |||||||
\(138\) | −8.10344 | + | 20.5531i | −0.689811 | + | 1.74960i | ||||
\(139\) | 0.644985 | − | 1.11715i | 0.0547070 | − | 0.0947552i | −0.837375 | − | 0.546629i | \(-0.815911\pi\) |
0.892082 | + | 0.451874i | \(0.149244\pi\) | |||||||
\(140\) | 10.8890 | − | 18.8604i | 0.920291 | − | 1.59399i | ||||
\(141\) | −14.8985 | + | 2.22188i | −1.25468 | + | 0.187116i | ||||
\(142\) | 13.0663 | + | 22.6314i | 1.09650 | + | 1.89919i | ||||
\(143\) | 1.23835 | 0.103556 | ||||||||
\(144\) | 1.54855 | − | 6.68855i | 0.129045 | − | 0.557379i | ||||
\(145\) | −12.7162 | −1.05602 | ||||||||
\(146\) | −4.64826 | − | 8.05103i | −0.384693 | − | 0.666308i | ||||
\(147\) | 1.98789 | + | 2.50072i | 0.163959 | + | 0.206256i | ||||
\(148\) | 0.441941 | − | 0.765464i | 0.0363273 | − | 0.0629207i | ||||
\(149\) | 5.47234 | − | 9.47836i | 0.448311 | − | 0.776498i | −0.549965 | − | 0.835188i | \(-0.685359\pi\) |
0.998276 | + | 0.0586899i | \(0.0186923\pi\) | |||||||
\(150\) | −18.8954 | − | 23.7699i | −1.54280 | − | 1.94080i | ||||
\(151\) | −1.06886 | − | 1.85132i | −0.0869826 | − | 0.150658i | 0.819252 | − | 0.573434i | \(-0.194389\pi\) |
−0.906234 | + | 0.422776i | \(0.861056\pi\) | |||||||
\(152\) | −4.03486 | −0.327271 | ||||||||
\(153\) | −12.4919 | − | 11.6634i | −1.00991 | − | 0.942930i | ||||
\(154\) | −4.89453 | −0.394412 | ||||||||
\(155\) | 4.54612 | + | 7.87412i | 0.365154 | + | 0.632464i | ||||
\(156\) | 5.61470 | − | 0.837341i | 0.449535 | − | 0.0670409i | ||||
\(157\) | −4.75028 | + | 8.22773i | −0.379114 | + | 0.656645i | −0.990934 | − | 0.134353i | \(-0.957104\pi\) |
0.611820 | + | 0.790997i | \(0.290438\pi\) | |||||||
\(158\) | −1.52692 | + | 2.64471i | −0.121476 | + | 0.210402i | ||||
\(159\) | −3.91670 | + | 9.93407i | −0.310614 | + | 0.787823i | ||||
\(160\) | 13.9902 | + | 24.2318i | 1.10602 | + | 1.91569i | ||||
\(161\) | −13.4357 | −1.05888 | ||||||||
\(162\) | 16.0972 | − | 10.8287i | 1.26472 | − | 0.850780i | ||||
\(163\) | −19.4713 | −1.52511 | −0.762556 | − | 0.646922i | \(-0.776056\pi\) | ||||
−0.762556 | + | 0.646922i | \(0.776056\pi\) | |||||||
\(164\) | 13.1902 | + | 22.8461i | 1.02998 | + | 1.78398i | ||||
\(165\) | −2.30228 | + | 5.83936i | −0.179232 | + | 0.454594i | ||||
\(166\) | 2.97131 | − | 5.14645i | 0.230618 | − | 0.399442i | ||||
\(167\) | 7.64900 | − | 13.2485i | 0.591898 | − | 1.02520i | −0.402079 | − | 0.915605i | \(-0.631712\pi\) |
0.993977 | − | 0.109592i | \(-0.0349543\pi\) | |||||||
\(168\) | −5.42219 | + | 0.808632i | −0.418331 | + | 0.0623873i | ||||
\(169\) | 5.73325 | + | 9.93027i | 0.441019 | + | 0.763867i | ||||
\(170\) | 44.5023 | 3.41317 | ||||||||
\(171\) | 6.34710 | + | 5.92613i | 0.485375 | + | 0.453183i | ||||
\(172\) | −18.9385 | −1.44405 | ||||||||
\(173\) | −7.01045 | − | 12.1425i | −0.532995 | − | 0.923174i | −0.999258 | − | 0.0385279i | \(-0.987733\pi\) |
0.466263 | − | 0.884646i | \(-0.345600\pi\) | |||||||
\(174\) | 8.15245 | + | 10.2556i | 0.618036 | + | 0.777472i | ||||
\(175\) | 9.23325 | − | 15.9925i | 0.697968 | − | 1.20892i | ||||
\(176\) | 1.14425 | − | 1.98189i | 0.0862507 | − | 0.149391i | ||||
\(177\) | −3.14425 | − | 3.95538i | −0.236336 | − | 0.297304i | ||||
\(178\) | −5.14239 | − | 8.90688i | −0.385439 | − | 0.667599i | ||||
\(179\) | 3.94951 | 0.295200 | 0.147600 | − | 0.989047i | \(-0.452845\pi\) | ||||
0.147600 | + | 0.989047i | \(0.452845\pi\) | |||||||
\(180\) | −6.49014 | + | 28.0325i | −0.483746 | + | 2.08942i | ||||
\(181\) | 13.3662 | 0.993502 | 0.496751 | − | 0.867893i | \(-0.334526\pi\) | ||||
0.496751 | + | 0.867893i | \(0.334526\pi\) | |||||||
\(182\) | 3.03057 | + | 5.24910i | 0.224641 | + | 0.389089i | ||||
\(183\) | 10.7422 | − | 1.60202i | 0.794086 | − | 0.118425i | ||||
\(184\) | −4.12422 | + | 7.14336i | −0.304042 | + | 0.526615i | ||||
\(185\) | 0.605125 | − | 1.04811i | 0.0444896 | − | 0.0770583i | ||||
\(186\) | 3.43590 | − | 8.71460i | 0.251932 | − | 0.638986i | ||||
\(187\) | −2.84840 | − | 4.93358i | −0.208296 | − | 0.360779i | ||||
\(188\) | −23.0175 | −1.67873 | ||||||||
\(189\) | 9.71712 | + | 6.69172i | 0.706817 | + | 0.486751i | ||||
\(190\) | −22.6115 | −1.64041 | ||||||||
\(191\) | −9.46023 | − | 16.3856i | −0.684518 | − | 1.18562i | −0.973588 | − | 0.228312i | \(-0.926679\pi\) |
0.289070 | − | 0.957308i | \(-0.406654\pi\) | |||||||
\(192\) | 7.66587 | − | 19.4432i | 0.553236 | − | 1.40320i | ||||
\(193\) | 1.03225 | − | 1.78791i | 0.0743029 | − | 0.128696i | −0.826480 | − | 0.562966i | \(-0.809660\pi\) |
0.900783 | + | 0.434270i | \(0.142994\pi\) | |||||||
\(194\) | 2.75820 | − | 4.77734i | 0.198027 | − | 0.342993i | ||||
\(195\) | 7.68789 | − | 1.14652i | 0.550541 | − | 0.0821043i | ||||
\(196\) | 2.44074 | + | 4.22748i | 0.174338 | + | 0.301963i | ||||
\(197\) | −6.00148 | −0.427588 | −0.213794 | − | 0.976879i | \(-0.568582\pi\) | ||||
−0.213794 | + | 0.976879i | \(0.568582\pi\) | |||||||
\(198\) | 6.18544 | − | 1.88688i | 0.439580 | − | 0.134095i | ||||
\(199\) | 19.7132 | 1.39743 | 0.698717 | − | 0.715399i | \(-0.253755\pi\) | ||||
0.698717 | + | 0.715399i | \(0.253755\pi\) | |||||||
\(200\) | −5.66846 | − | 9.81806i | −0.400821 | − | 0.694242i | ||||
\(201\) | −10.0913 | − | 12.6946i | −0.711788 | − | 0.895410i | ||||
\(202\) | 19.7601 | − | 34.2255i | 1.39031 | − | 2.40810i | ||||
\(203\) | −3.98370 | + | 6.89998i | −0.279601 | + | 0.484283i | ||||
\(204\) | −16.2507 | − | 20.4429i | −1.13777 | − | 1.43129i | ||||
\(205\) | 18.0606 | + | 31.2819i | 1.26141 | + | 2.18482i | ||||
\(206\) | −9.83487 | −0.685228 | ||||||||
\(207\) | 16.9793 | − | 5.17959i | 1.18015 | − | 0.360006i | ||||
\(208\) | −2.83395 | −0.196499 | ||||||||
\(209\) | 1.44726 | + | 2.50674i | 0.100109 | + | 0.173395i | ||||
\(210\) | −30.3861 | + | 4.53159i | −2.09684 | + | 0.312710i | ||||
\(211\) | 5.84123 | − | 10.1173i | 0.402127 | − | 0.696504i | −0.591856 | − | 0.806044i | \(-0.701605\pi\) |
0.993982 | + | 0.109540i | \(0.0349378\pi\) | |||||||
\(212\) | −8.15852 | + | 14.1310i | −0.560329 | + | 0.970519i | ||||
\(213\) | 7.70174 | − | 19.5342i | 0.527714 | − | 1.33846i | ||||
\(214\) | 5.50774 | + | 9.53969i | 0.376502 | + | 0.652120i | ||||
\(215\) | −25.9314 | −1.76851 | ||||||||
\(216\) | 6.54054 | − | 3.11221i | 0.445027 | − | 0.211759i | ||||
\(217\) | 5.69681 | 0.386724 | ||||||||
\(218\) | −5.04296 | − | 8.73467i | −0.341553 | − | 0.591586i | ||||
\(219\) | −2.73986 | + | 6.94921i | −0.185142 | + | 0.469584i | ||||
\(220\) | −4.79567 | + | 8.30634i | −0.323324 | + | 0.560013i | ||||
\(221\) | −3.52732 | + | 6.10949i | −0.237273 | + | 0.410969i | ||||
\(222\) | −1.23325 | + | 0.183919i | −0.0827700 | + | 0.0123438i | ||||
\(223\) | 9.06168 | + | 15.6953i | 0.606815 | + | 1.05103i | 0.991762 | + | 0.128096i | \(0.0408865\pi\) |
−0.384947 | + | 0.922939i | \(0.625780\pi\) | |||||||
\(224\) | 17.5313 | 1.17136 | ||||||||
\(225\) | −5.50325 | + | 23.7699i | −0.366883 | + | 1.58466i | ||||
\(226\) | −3.30171 | −0.219627 | ||||||||
\(227\) | −8.75373 | − | 15.1619i | −0.581006 | − | 1.00633i | −0.995360 | − | 0.0962159i | \(-0.969326\pi\) |
0.414355 | − | 0.910115i | \(-0.364007\pi\) | |||||||
\(228\) | 8.25691 | + | 10.3870i | 0.546827 | + | 0.687894i | ||||
\(229\) | −2.27134 | + | 3.93407i | −0.150094 | + | 0.259971i | −0.931262 | − | 0.364350i | \(-0.881291\pi\) |
0.781168 | + | 0.624321i | \(0.214624\pi\) | |||||||
\(230\) | −23.1122 | + | 40.0315i | −1.52397 | + | 2.63960i | ||||
\(231\) | 2.44726 | + | 3.07859i | 0.161018 | + | 0.202557i | ||||
\(232\) | 2.44567 | + | 4.23602i | 0.160566 | + | 0.278109i | ||||
\(233\) | −8.16962 | −0.535210 | −0.267605 | − | 0.963529i | \(-0.586232\pi\) | ||||
−0.267605 | + | 0.963529i | \(0.586232\pi\) | |||||||
\(234\) | −5.85344 | − | 5.46521i | −0.382651 | − | 0.357272i | ||||
\(235\) | −31.5166 | −2.05592 | ||||||||
\(236\) | −3.86051 | − | 6.68660i | −0.251298 | − | 0.435261i | ||||
\(237\) | 2.42695 | − | 0.361940i | 0.157647 | − | 0.0235106i | ||||
\(238\) | 13.9416 | − | 24.1475i | 0.903699 | − | 1.56525i | ||||
\(239\) | −9.30042 | + | 16.1088i | −0.601594 | + | 1.04199i | 0.390985 | + | 0.920397i | \(0.372134\pi\) |
−0.992580 | + | 0.121595i | \(0.961199\pi\) | |||||||
\(240\) | 5.26874 | − | 13.3633i | 0.340096 | − | 0.862599i | ||||
\(241\) | −14.1763 | − | 24.5541i | −0.913177 | − | 1.58167i | −0.809548 | − | 0.587053i | \(-0.800288\pi\) |
−0.103629 | − | 0.994616i | \(-0.533045\pi\) | |||||||
\(242\) | 2.15561 | 0.138568 | ||||||||
\(243\) | −14.8597 | − | 4.71060i | −0.953249 | − | 0.302185i | ||||
\(244\) | 16.5962 | 1.06246 | ||||||||
\(245\) | 3.34197 | + | 5.78846i | 0.213510 | + | 0.369811i | ||||
\(246\) | 13.6499 | − | 34.6209i | 0.870289 | − | 2.20735i | ||||
\(247\) | 1.79222 | − | 3.10421i | 0.114036 | − | 0.197516i | ||||
\(248\) | 1.74869 | − | 3.02882i | 0.111042 | − | 0.192330i | ||||
\(249\) | −4.72270 | + | 0.704315i | −0.299289 | + | 0.0446341i | ||||
\(250\) | −12.2367 | − | 21.1946i | −0.773917 | − | 1.34046i | ||||
\(251\) | 4.93812 | 0.311691 | 0.155846 | − | 0.987781i | \(-0.450190\pi\) | ||||
0.155846 | + | 0.987781i | \(0.450190\pi\) | |||||||
\(252\) | 13.1776 | + | 12.3036i | 0.830111 | + | 0.775055i | ||||
\(253\) | 5.91726 | 0.372015 | ||||||||
\(254\) | −9.40664 | − | 16.2928i | −0.590225 | − | 1.02230i | ||||
\(255\) | −22.2511 | − | 27.9913i | −1.39342 | − | 1.75289i | ||||
\(256\) | −0.675465 | + | 1.16994i | −0.0422166 | + | 0.0731212i | ||||
\(257\) | −8.55675 | + | 14.8207i | −0.533756 | + | 0.924492i | 0.465467 | + | 0.885065i | \(0.345886\pi\) |
−0.999222 | + | 0.0394264i | \(0.987447\pi\) | |||||||
\(258\) | 16.6249 | + | 20.9136i | 1.03502 | + | 1.30203i | ||||
\(259\) | −0.379145 | − | 0.656698i | −0.0235589 | − | 0.0408052i | ||||
\(260\) | 11.8774 | 0.736606 | ||||||||
\(261\) | 2.37439 | − | 10.2556i | 0.146971 | − | 0.634804i | ||||
\(262\) | −7.95157 | −0.491250 | ||||||||
\(263\) | 2.22279 | + | 3.84999i | 0.137063 | + | 0.237400i | 0.926384 | − | 0.376581i | \(-0.122900\pi\) |
−0.789321 | + | 0.613981i | \(0.789567\pi\) | |||||||
\(264\) | 2.38800 | − | 0.356132i | 0.146971 | − | 0.0219184i | ||||
\(265\) | −11.1710 | + | 19.3487i | −0.686229 | + | 1.18858i | ||||
\(266\) | −7.08368 | + | 12.2693i | −0.434328 | + | 0.752278i | ||||
\(267\) | −3.03111 | + | 7.68794i | −0.185501 | + | 0.470494i | ||||
\(268\) | −12.3902 | − | 21.4604i | −0.756850 | − | 1.31090i | ||||
\(269\) | 19.5899 | 1.19441 | 0.597207 | − | 0.802087i | \(-0.296277\pi\) | ||||
0.597207 | + | 0.802087i | \(0.296277\pi\) | |||||||
\(270\) | 36.6533 | − | 17.4409i | 2.23065 | − | 1.06142i | ||||
\(271\) | 6.77601 | 0.411613 | 0.205807 | − | 0.978593i | \(-0.434018\pi\) | ||||
0.205807 | + | 0.978593i | \(0.434018\pi\) | |||||||
\(272\) | 6.51855 | + | 11.2905i | 0.395245 | + | 0.684584i | ||||
\(273\) | 1.78633 | − | 4.53074i | 0.108113 | − | 0.274213i | ||||
\(274\) | −23.6778 | + | 41.0112i | −1.43043 | + | 2.47758i | ||||
\(275\) | −4.06644 | + | 7.04328i | −0.245215 | + | 0.424726i | ||||
\(276\) | 26.8290 | − | 4.00111i | 1.61491 | − | 0.240838i | ||||
\(277\) | −0.738261 | − | 1.27871i | −0.0443578 | − | 0.0768300i | 0.842994 | − | 0.537923i | \(-0.180791\pi\) |
−0.887352 | + | 0.461093i | \(0.847457\pi\) | |||||||
\(278\) | −2.78068 | −0.166774 | ||||||||
\(279\) | −7.19932 | + | 2.19617i | −0.431012 | + | 0.131481i | ||||
\(280\) | −11.4702 | −0.685476 | ||||||||
\(281\) | 3.67342 | + | 6.36255i | 0.219138 | + | 0.379558i | 0.954545 | − | 0.298068i | \(-0.0963423\pi\) |
−0.735407 | + | 0.677626i | \(0.763009\pi\) | |||||||
\(282\) | 20.2056 | + | 25.4181i | 1.20322 | + | 1.51362i | ||||
\(283\) | 7.35809 | − | 12.7446i | 0.437393 | − | 0.757587i | −0.560094 | − | 0.828429i | \(-0.689235\pi\) |
0.997488 | + | 0.0708417i | \(0.0225685\pi\) | |||||||
\(284\) | 16.0428 | − | 27.7869i | 0.951964 | − | 1.64885i | ||||
\(285\) | 11.3057 | + | 14.2223i | 0.669694 | + | 0.842457i | ||||
\(286\) | −1.33470 | − | 2.31177i | −0.0789225 | − | 0.136698i | ||||
\(287\) | 22.6320 | 1.33592 | ||||||||
\(288\) | −22.1552 | + | 6.75848i | −1.30550 | + | 0.398247i | ||||
\(289\) | 15.4536 | 0.909036 | ||||||||
\(290\) | 13.7056 | + | 23.7388i | 0.804819 | + | 1.39399i | ||||
\(291\) | −4.38399 | + | 0.653801i | −0.256994 | + | 0.0383265i | ||||
\(292\) | −5.70715 | + | 9.88507i | −0.333985 | + | 0.578480i | ||||
\(293\) | 0.988066 | − | 1.71138i | 0.0577234 | − | 0.0999799i | −0.835720 | − | 0.549156i | \(-0.814949\pi\) |
0.893443 | + | 0.449176i | \(0.148283\pi\) | |||||||
\(294\) | 2.52581 | − | 6.40631i | 0.147308 | − | 0.373624i | ||||
\(295\) | −5.28598 | − | 9.15559i | −0.307762 | − | 0.533059i | ||||
\(296\) | −0.465528 | −0.0270583 | ||||||||
\(297\) | −4.27954 | − | 2.94712i | −0.248324 | − | 0.171009i | ||||
\(298\) | −23.5925 | −1.36668 | ||||||||
\(299\) | −3.66382 | − | 6.34592i | −0.211884 | − | 0.366994i | ||||
\(300\) | −13.6748 | + | 34.6840i | −0.789516 | + | 2.00248i | ||||
\(301\) | −8.12376 | + | 14.0708i | −0.468246 | + | 0.811025i | ||||
\(302\) | −2.30405 | + | 3.99073i | −0.132583 | + | 0.229641i | ||||
\(303\) | −31.4074 | + | 4.68391i | −1.80431 | + | 0.269083i | ||||
\(304\) | −3.31205 | − | 5.73664i | −0.189959 | − | 0.329019i | ||||
\(305\) | 22.7242 | 1.30118 | ||||||||
\(306\) | −8.30954 | + | 35.8910i | −0.475025 | + | 2.05175i | ||||
\(307\) | 11.9708 | 0.683208 | 0.341604 | − | 0.939844i | \(-0.389030\pi\) | ||||
0.341604 | + | 0.939844i | \(0.389030\pi\) | |||||||
\(308\) | 3.00476 | + | 5.20439i | 0.171212 | + | 0.296548i | ||||
\(309\) | 4.91744 | + | 6.18600i | 0.279743 | + | 0.351909i | ||||
\(310\) | 9.79968 | − | 16.9736i | 0.556585 | − | 0.964033i | ||||
\(311\) | −1.69866 | + | 2.94217i | −0.0963223 | + | 0.166835i | −0.910160 | − | 0.414258i | \(-0.864041\pi\) |
0.813837 | + | 0.581093i | \(0.197375\pi\) | |||||||
\(312\) | −1.86052 | − | 2.34049i | −0.105331 | − | 0.132504i | ||||
\(313\) | 11.3482 | + | 19.6557i | 0.641440 | + | 1.11101i | 0.985112 | + | 0.171917i | \(0.0549960\pi\) |
−0.343672 | + | 0.939090i | \(0.611671\pi\) | |||||||
\(314\) | 20.4795 | 1.15573 | ||||||||
\(315\) | 18.0434 | + | 16.8466i | 1.01663 | + | 0.949201i | ||||
\(316\) | 3.74952 | 0.210927 | ||||||||
\(317\) | −7.42547 | − | 12.8613i | −0.417056 | − | 0.722362i | 0.578586 | − | 0.815621i | \(-0.303605\pi\) |
−0.995642 | + | 0.0932594i | \(0.970271\pi\) | |||||||
\(318\) | 22.7665 | − | 3.39526i | 1.27668 | − | 0.190397i | ||||
\(319\) | 1.75447 | − | 3.03884i | 0.0982316 | − | 0.170142i | ||||
\(320\) | 21.8642 | − | 37.8699i | 1.22224 | − | 2.11699i | ||||
\(321\) | 3.24647 | − | 8.23414i | 0.181200 | − | 0.459585i | ||||
\(322\) | 14.4811 | + | 25.0820i | 0.807001 | + | 1.39777i | ||||
\(323\) | −16.4896 | −0.917504 | ||||||||
\(324\) | −21.3963 | − | 10.4686i | −1.18868 | − | 0.581587i | ||||
\(325\) | 10.0713 | 0.558658 | ||||||||
\(326\) | 20.9863 | + | 36.3494i | 1.16233 | + | 2.01321i | ||||
\(327\) | −2.97251 | + | 7.53929i | −0.164380 | + | 0.416924i | ||||
\(328\) | 6.94709 | − | 12.0327i | 0.383589 | − | 0.664396i | ||||
\(329\) | −9.87347 | + | 17.1014i | −0.544342 | + | 0.942828i | ||||
\(330\) | 13.3824 | − | 1.99577i | 0.736678 | − | 0.109864i | ||||
\(331\) | −8.10140 | − | 14.0320i | −0.445293 | − | 0.771270i | 0.552780 | − | 0.833328i | \(-0.313567\pi\) |
−0.998073 | + | 0.0620574i | \(0.980234\pi\) | |||||||
\(332\) | −7.29635 | −0.400439 | ||||||||
\(333\) | 0.732305 | + | 0.683736i | 0.0401301 | + | 0.0374685i | ||||
\(334\) | −32.9766 | −1.80440 | ||||||||
\(335\) | −16.9652 | − | 29.3845i | −0.926906 | − | 1.60545i | ||||
\(336\) | −5.60054 | − | 7.04533i | −0.305535 | − | 0.384354i | ||||
\(337\) | 5.63111 | − | 9.75337i | 0.306746 | − | 0.531300i | −0.670903 | − | 0.741546i | \(-0.734093\pi\) |
0.977649 | + | 0.210246i | \(0.0674264\pi\) | |||||||
\(338\) | 12.3587 | − | 21.4058i | 0.672222 | − | 1.16432i | ||||
\(339\) | 1.65086 | + | 2.07673i | 0.0896622 | + | 0.112793i | ||||
\(340\) | −27.3200 | − | 47.3196i | −1.48163 | − | 2.56627i | ||||
\(341\) | −2.50895 | −0.135867 | ||||||||
\(342\) | 4.22205 | − | 18.2361i | 0.228302 | − | 0.986094i | ||||
\(343\) | 20.0820 | 1.08433 | ||||||||
\(344\) | 4.98733 | + | 8.63830i | 0.268899 | + | 0.465746i | ||||
\(345\) | 36.7354 | − | 5.47849i | 1.97777 | − | 0.294952i | ||||
\(346\) | −15.1118 | + | 26.1744i | −0.812417 | + | 1.40715i | ||||
\(347\) | 8.53718 | − | 14.7868i | 0.458300 | − | 0.793798i | −0.540572 | − | 0.841298i | \(-0.681792\pi\) |
0.998871 | + | 0.0474996i | \(0.0151253\pi\) | |||||||
\(348\) | 5.90003 | − | 14.9645i | 0.316275 | − | 0.802180i | ||||
\(349\) | −11.4862 | − | 19.8947i | −0.614843 | − | 1.06494i | −0.990412 | − | 0.138145i | \(-0.955886\pi\) |
0.375569 | − | 0.926794i | \(-0.377447\pi\) | |||||||
\(350\) | −39.8066 | −2.12775 | ||||||||
\(351\) | −0.510828 | + | 6.41434i | −0.0272660 | + | 0.342372i | ||||
\(352\) | −7.72102 | −0.411532 | ||||||||
\(353\) | 10.2567 | + | 17.7652i | 0.545910 | + | 0.945544i | 0.998549 | + | 0.0538502i | \(0.0171494\pi\) |
−0.452639 | + | 0.891694i | \(0.649517\pi\) | |||||||
\(354\) | −3.99507 | + | 10.1329i | −0.212336 | + | 0.538555i | ||||
\(355\) | 21.9665 | − | 38.0471i | 1.16586 | − | 2.01933i | ||||
\(356\) | −6.31384 | + | 10.9359i | −0.334633 | + | 0.579601i | ||||
\(357\) | −22.1593 | + | 3.30470i | −1.17279 | + | 0.174903i | ||||
\(358\) | −4.25681 | − | 7.37301i | −0.224979 | − | 0.389676i | ||||
\(359\) | −2.91840 | −0.154027 | −0.0770136 | − | 0.997030i | \(-0.524538\pi\) | ||||
−0.0770136 | + | 0.997030i | \(0.524538\pi\) | |||||||
\(360\) | 14.4954 | − | 4.42186i | 0.763976 | − | 0.233052i | ||||
\(361\) | −10.6217 | −0.559037 | ||||||||
\(362\) | −14.4062 | − | 24.9522i | −0.757172 | − | 1.31146i | ||||
\(363\) | −1.07781 | − | 1.35585i | −0.0565702 | − | 0.0711638i | ||||
\(364\) | 3.72094 | − | 6.44485i | 0.195030 | − | 0.337802i | ||||
\(365\) | −7.81447 | + | 13.5351i | −0.409028 | + | 0.708458i | ||||
\(366\) | −14.5687 | − | 18.3270i | −0.761517 | − | 0.957969i | ||||
\(367\) | −3.37570 | − | 5.84688i | −0.176210 | − | 0.305204i | 0.764369 | − | 0.644779i | \(-0.223050\pi\) |
−0.940579 | + | 0.339574i | \(0.889717\pi\) | |||||||
\(368\) | −13.5416 | −0.705905 | ||||||||
\(369\) | −28.6011 | + | 8.72482i | −1.48891 | + | 0.454196i | ||||
\(370\) | −2.60883 | −0.135627 | ||||||||
\(371\) | 6.99926 | + | 12.1231i | 0.363383 | + | 0.629399i | ||||
\(372\) | −11.3756 | + | 1.69649i | −0.589798 | + | 0.0879588i | ||||
\(373\) | 11.1887 | − | 19.3794i | 0.579330 | − | 1.00343i | −0.416227 | − | 0.909261i | \(-0.636648\pi\) |
0.995556 | − | 0.0941677i | \(-0.0300190\pi\) | |||||||
\(374\) | −6.14006 | + | 10.6349i | −0.317495 | + | 0.549917i | ||||
\(375\) | −7.21276 | + | 18.2940i | −0.372465 | + | 0.944698i | ||||
\(376\) | 6.06151 | + | 10.4988i | 0.312598 | + | 0.541436i | ||||
\(377\) | −4.34530 | −0.223794 | ||||||||
\(378\) | 2.01903 | − | 25.3524i | 0.103848 | − | 1.30399i | ||||
\(379\) | 33.0321 | 1.69674 | 0.848372 | − | 0.529401i | \(-0.177583\pi\) | ||||
0.848372 | + | 0.529401i | \(0.177583\pi\) | |||||||
\(380\) | 13.8812 | + | 24.0429i | 0.712090 | + | 1.23338i | ||||
\(381\) | −5.54462 | + | 14.0630i | −0.284059 | + | 0.720471i | ||||
\(382\) | −20.3926 | + | 35.3210i | −1.04338 | + | 1.80718i | ||||
\(383\) | −11.7421 | + | 20.3379i | −0.599993 | + | 1.03922i | 0.392828 | + | 0.919612i | \(0.371497\pi\) |
−0.992821 | + | 0.119607i | \(0.961836\pi\) | |||||||
\(384\) | −18.1054 | + | 2.70013i | −0.923938 | + | 0.137790i | ||||
\(385\) | 4.11424 | + | 7.12608i | 0.209681 | + | 0.363179i | ||||
\(386\) | −4.45026 | −0.226512 | ||||||||
\(387\) | 4.84197 | − | 20.9136i | 0.246131 | − | 1.06310i | ||||
\(388\) | −6.77305 | −0.343850 | ||||||||
\(389\) | 15.5207 | + | 26.8827i | 0.786931 | + | 1.36300i | 0.927839 | + | 0.372982i | \(0.121665\pi\) |
−0.140908 | + | 0.990023i | \(0.545002\pi\) | |||||||
\(390\) | −10.4264 | − | 13.1161i | −0.527961 | − | 0.664161i | ||||
\(391\) | −16.8548 | + | 29.1933i | −0.852382 | + | 1.47637i | ||||
\(392\) | 1.28550 | − | 2.22656i | 0.0649277 | − | 0.112458i | ||||
\(393\) | 3.97578 | + | 5.00143i | 0.200552 | + | 0.252289i | ||||
\(394\) | 6.46843 | + | 11.2037i | 0.325875 | + | 0.564432i | ||||
\(395\) | 5.13401 | 0.258320 | ||||||||
\(396\) | −5.80359 | − | 5.41867i | −0.291641 | − | 0.272298i | ||||
\(397\) | 17.3804 | 0.872297 | 0.436148 | − | 0.899875i | \(-0.356342\pi\) | ||||
0.436148 | + | 0.899875i | \(0.356342\pi\) | |||||||
\(398\) | −21.2470 | − | 36.8009i | −1.06502 | − | 1.84466i | ||||
\(399\) | 11.2591 | − | 1.67911i | 0.563658 | − | 0.0840604i | ||||
\(400\) | 9.30601 | − | 16.1185i | 0.465300 | − | 0.805924i | ||||
\(401\) | 5.77396 | − | 10.0008i | 0.288338 | − | 0.499416i | −0.685075 | − | 0.728472i | \(-0.740231\pi\) |
0.973413 | + | 0.229057i | \(0.0735641\pi\) | |||||||
\(402\) | −12.8220 | + | 32.5210i | −0.639505 | + | 1.62200i | ||||
\(403\) | 1.55348 | + | 2.69070i | 0.0773841 | + | 0.134033i | ||||
\(404\) | −48.5230 | −2.41411 | ||||||||
\(405\) | −29.2967 | − | 14.3340i | −1.45577 | − | 0.712263i | ||||
\(406\) | 17.1746 | 0.852363 | ||||||||
\(407\) | 0.166980 | + | 0.289218i | 0.00827690 | + | 0.0143360i | ||||
\(408\) | −5.04499 | + | 12.7958i | −0.249764 | + | 0.633487i | ||||
\(409\) | −17.3678 | + | 30.0819i | −0.858783 | + | 1.48746i | 0.0143082 | + | 0.999898i | \(0.495445\pi\) |
−0.873091 | + | 0.487558i | \(0.837888\pi\) | |||||||
\(410\) | 38.9316 | − | 67.4316i | 1.92270 | − | 3.33021i | ||||
\(411\) | 37.6344 | − | 5.61256i | 1.85637 | − | 0.276847i | ||||
\(412\) | 6.03764 | + | 10.4575i | 0.297453 | + | 0.515204i | ||||
\(413\) | −6.62393 | −0.325942 | ||||||||
\(414\) | −27.9698 | − | 26.1147i | −1.37464 | − | 1.28347i | ||||
\(415\) | −9.99049 | −0.490414 | ||||||||
\(416\) | 4.78066 | + | 8.28035i | 0.234391 | + | 0.405977i | ||||
\(417\) | 1.39034 | + | 1.74901i | 0.0680852 | + | 0.0856493i | ||||
\(418\) | 3.11974 | − | 5.40355i | 0.152592 | − | 0.264296i | ||||
\(419\) | 3.71535 | − | 6.43518i | 0.181507 | − | 0.314379i | −0.760887 | − | 0.648884i | \(-0.775236\pi\) |
0.942394 | + | 0.334505i | \(0.108569\pi\) | |||||||
\(420\) | 23.4725 | + | 29.5278i | 1.14534 | + | 1.44081i | ||||
\(421\) | −5.92789 | − | 10.2674i | −0.288908 | − | 0.500403i | 0.684642 | − | 0.728880i | \(-0.259959\pi\) |
−0.973549 | + | 0.228477i | \(0.926625\pi\) | |||||||
\(422\) | −25.1828 | −1.22588 | ||||||||
\(423\) | 5.88484 | − | 25.4181i | 0.286131 | − | 1.23587i | ||||
\(424\) | 8.59395 | 0.417359 | ||||||||
\(425\) | −23.1657 | − | 40.1242i | −1.12370 | − | 1.94631i | ||||
\(426\) | −44.7678 | + | 6.67639i | −2.16901 | + | 0.323472i | ||||
\(427\) | 7.11900 | − | 12.3305i | 0.344513 | − | 0.596713i | ||||
\(428\) | 6.76242 | − | 11.7129i | 0.326874 | − | 0.566162i | ||||
\(429\) | −0.786722 | + | 1.99539i | −0.0379833 | + | 0.0963385i | ||||
\(430\) | 27.9491 | + | 48.4092i | 1.34782 | + | 2.33450i | ||||
\(431\) | 24.7496 | 1.19214 | 0.596072 | − | 0.802931i | \(-0.296727\pi\) | ||||
0.596072 | + | 0.802931i | \(0.296727\pi\) | |||||||
\(432\) | 9.79370 | + | 6.74445i | 0.471199 | + | 0.324493i | ||||
\(433\) | 19.0608 | 0.916003 | 0.458002 | − | 0.888951i | \(-0.348565\pi\) | ||||
0.458002 | + | 0.888951i | \(0.348565\pi\) | |||||||
\(434\) | −6.14006 | − | 10.6349i | −0.294732 | − | 0.510491i | ||||
\(435\) | 8.07857 | − | 20.4900i | 0.387338 | − | 0.982421i | ||||
\(436\) | −6.19176 | + | 10.7244i | −0.296532 | + | 0.513608i | ||||
\(437\) | 8.56384 | − | 14.8330i | 0.409664 | − | 0.709559i | ||||
\(438\) | 15.9259 | − | 2.37509i | 0.760970 | − | 0.113486i | ||||
\(439\) | 17.3742 | + | 30.0931i | 0.829227 | + | 1.43626i | 0.898645 | + | 0.438676i | \(0.144552\pi\) |
−0.0694179 | + | 0.997588i | \(0.522114\pi\) | |||||||
\(440\) | 5.05162 | 0.240827 | ||||||||
\(441\) | −5.29239 | + | 1.61446i | −0.252019 | + | 0.0768789i | ||||
\(442\) | 15.2071 | 0.723326 | ||||||||
\(443\) | 0.679943 | + | 1.17770i | 0.0323051 | + | 0.0559540i | 0.881726 | − | 0.471762i | \(-0.156382\pi\) |
−0.849421 | + | 0.527716i | \(0.823049\pi\) | |||||||
\(444\) | 0.952653 | + | 1.19841i | 0.0452109 | + | 0.0568741i | ||||
\(445\) | −8.64519 | + | 14.9739i | −0.409821 | + | 0.709831i | ||||
\(446\) | 19.5335 | − | 33.8330i | 0.924937 | − | 1.60204i | ||||
\(447\) | 11.7962 | + | 14.8393i | 0.557943 | + | 0.701877i | ||||
\(448\) | −13.6991 | − | 23.7276i | −0.647224 | − | 1.12102i | ||||
\(449\) | 31.7261 | 1.49725 | 0.748623 | − | 0.662995i | \(-0.230715\pi\) | ||||
0.748623 | + | 0.662995i | \(0.230715\pi\) | |||||||
\(450\) | 50.3054 | − | 15.3458i | 2.37142 | − | 0.723407i | ||||
\(451\) | −9.96741 | −0.469347 | ||||||||
\(452\) | 2.02692 | + | 3.51074i | 0.0953385 | + | 0.165131i | ||||
\(453\) | 3.66214 | − | 0.546149i | 0.172062 | − | 0.0256603i | ||||
\(454\) | −18.8697 | + | 32.6832i | −0.885597 | + | 1.53390i | ||||
\(455\) | 5.09487 | − | 8.82458i | 0.238851 | − | 0.413702i | ||||
\(456\) | 2.56334 | − | 6.50151i | 0.120040 | − | 0.304461i | ||||
\(457\) | −17.6912 | − | 30.6421i | −0.827561 | − | 1.43338i | −0.899946 | − | 0.436000i | \(-0.856395\pi\) |
0.0723859 | − | 0.997377i | \(-0.476939\pi\) | |||||||
\(458\) | 9.79225 | 0.457562 | ||||||||
\(459\) | 26.7297 | − | 12.7189i | 1.24764 | − | 0.593667i | ||||
\(460\) | 56.7545 | 2.64619 | ||||||||
\(461\) | 15.6183 | + | 27.0518i | 0.727419 | + | 1.25993i | 0.957971 | + | 0.286867i | \(0.0926137\pi\) |
−0.230551 | + | 0.973060i | \(0.574053\pi\) | |||||||
\(462\) | 3.10949 | − | 7.88672i | 0.144666 | − | 0.366923i | ||||
\(463\) | 0.119348 | − | 0.206717i | 0.00554657 | − | 0.00960693i | −0.863239 | − | 0.504796i | \(-0.831568\pi\) |
0.868785 | + | 0.495189i | \(0.164901\pi\) | |||||||
\(464\) | −4.01510 | + | 6.95435i | −0.186396 | + | 0.322848i | ||||
\(465\) | −15.5760 | + | 2.32291i | −0.722319 | + | 0.107722i | ||||
\(466\) | 8.80527 | + | 15.2512i | 0.407896 | + | 0.706497i | ||||
\(467\) | 1.40269 | 0.0649087 | 0.0324543 | − | 0.999473i | \(-0.489668\pi\) | ||||
0.0324543 | + | 0.999473i | \(0.489668\pi\) | |||||||
\(468\) | −2.21777 | + | 9.57911i | −0.102517 | + | 0.442794i | ||||
\(469\) | −21.2593 | −0.981661 | ||||||||
\(470\) | 33.9688 | + | 58.8357i | 1.56687 | + | 2.71389i | ||||
\(471\) | −10.2398 | − | 12.8814i | −0.471824 | − | 0.593542i | ||||
\(472\) | −2.03328 | + | 3.52174i | −0.0935892 | + | 0.162101i | ||||
\(473\) | 3.57781 | − | 6.19694i | 0.164508 | − | 0.284936i | ||||
\(474\) | −3.29146 | − | 4.14057i | −0.151182 | − | 0.190183i | ||||
\(475\) | 11.7704 | + | 20.3870i | 0.540064 | + | 0.935418i | ||||
\(476\) | −34.2350 | −1.56916 | ||||||||
\(477\) | −13.5188 | − | 12.6222i | −0.618985 | − | 0.577931i | ||||
\(478\) | 40.0962 | 1.83396 | ||||||||
\(479\) | −12.4665 | − | 21.5926i | −0.569609 | − | 0.986591i | −0.996605 | − | 0.0823374i | \(-0.973761\pi\) |
0.426996 | − | 0.904254i | \(-0.359572\pi\) | |||||||
\(480\) | −47.9335 | + | 7.14850i | −2.18785 | + | 0.326283i | ||||
\(481\) | 0.206780 | − | 0.358153i | 0.00942834 | − | 0.0163304i | ||||
\(482\) | −30.5587 | + | 52.9291i | −1.39191 | + | 2.41086i | ||||
\(483\) | 8.53570 | − | 21.6494i | 0.388388 | − | 0.985083i | ||||
\(484\) | −1.32333 | − | 2.29208i | −0.0601515 | − | 0.104185i | ||||
\(485\) | −9.27396 | −0.421109 | ||||||||
\(486\) | 7.22205 | + | 32.8174i | 0.327599 | + | 1.48863i | ||||
\(487\) | −16.0432 | −0.726989 | −0.363494 | − | 0.931596i | \(-0.618416\pi\) | ||||
−0.363494 | + | 0.931596i | \(0.618416\pi\) | |||||||
\(488\) | −4.37049 | − | 7.56991i | −0.197843 | − | 0.342673i | ||||
\(489\) | 12.3701 | − | 31.3748i | 0.559396 | − | 1.41882i | ||||
\(490\) | 7.20399 | − | 12.4777i | 0.325443 | − | 0.563684i | ||||
\(491\) | −5.03989 | + | 8.72934i | −0.227447 | + | 0.393950i | −0.957051 | − | 0.289920i | \(-0.906371\pi\) |
0.729604 | + | 0.683870i | \(0.239704\pi\) | |||||||
\(492\) | −45.1924 | + | 6.73971i | −2.03743 | + | 0.303850i | ||||
\(493\) | 9.99490 | + | 17.3117i | 0.450148 | + | 0.779678i | ||||
\(494\) | −7.72666 | −0.347639 | ||||||||
\(495\) | −7.94652 | − | 7.41948i | −0.357170 | − | 0.333481i | ||||
\(496\) | 5.74170 | 0.257810 | ||||||||
\(497\) | −13.7632 | − | 23.8386i | −0.617366 | − | 1.06931i | ||||
\(498\) | 6.40499 | + | 8.05730i | 0.287014 | + | 0.361056i | ||||
\(499\) | −16.6268 | + | 28.7985i | −0.744319 | + | 1.28920i | 0.206193 | + | 0.978511i | \(0.433893\pi\) |
−0.950512 | + | 0.310687i | \(0.899441\pi\) | |||||||
\(500\) | −15.0242 | + | 26.0228i | −0.671905 | + | 1.16377i | ||||
\(501\) | 16.4883 | + | 20.7418i | 0.736642 | + | 0.926676i | ||||
\(502\) | −5.32233 | − | 9.21855i | −0.237547 | − | 0.411444i | ||||
\(503\) | −23.0498 | −1.02774 | −0.513870 | − | 0.857868i | \(-0.671789\pi\) | ||||
−0.513870 | + | 0.857868i | \(0.671789\pi\) | |||||||
\(504\) | 2.14174 | − | 9.25069i | 0.0954005 | − | 0.412058i | ||||
\(505\) | −66.4398 | −2.95653 | ||||||||
\(506\) | −6.37766 | − | 11.0464i | −0.283522 | − | 0.491074i | ||||
\(507\) | −19.6433 | + | 2.92948i | −0.872390 | + | 0.130103i | ||||
\(508\) | −11.5495 | + | 20.0043i | −0.512426 | + | 0.887547i | ||||
\(509\) | 7.94615 | − | 13.7631i | 0.352207 | − | 0.610040i | −0.634429 | − | 0.772981i | \(-0.718765\pi\) |
0.986636 | + | 0.162941i | \(0.0520980\pi\) | |||||||
\(510\) | −28.2722 | + | 71.7080i | −1.25192 | + | 3.17528i | ||||
\(511\) | 4.89621 | + | 8.48048i | 0.216596 | + | 0.375155i | ||||
\(512\) | 24.0496 | 1.06285 | ||||||||
\(513\) | −13.5813 | + | 6.46243i | −0.599628 | + | 0.285323i | ||||
\(514\) | 36.8901 | 1.62715 | ||||||||
\(515\) | 8.26700 | + | 14.3189i | 0.364288 | + | 0.630965i | ||||
\(516\) | 12.0316 | − | 30.5163i | 0.529662 | − | 1.34340i | ||||
\(517\) | 4.34840 | − | 7.53166i | 0.191243 | − | 0.331242i | ||||
\(518\) | −0.817289 | + | 1.41559i | −0.0359096 | + | 0.0621973i | ||||
\(519\) | 24.0193 | − | 3.58209i | 1.05433 | − | 0.157236i | ||||
\(520\) | −3.12784 | − | 5.41757i | −0.137165 | − | 0.237576i | ||||
\(521\) | −4.07140 | −0.178371 | −0.0891855 | − | 0.996015i | \(-0.528426\pi\) | ||||
−0.0891855 | + | 0.996015i | \(0.528426\pi\) | |||||||
\(522\) | −21.7044 | + | 6.62097i | −0.949975 | + | 0.289792i | ||||
\(523\) | 1.94690 | 0.0851319 | 0.0425659 | − | 0.999094i | \(-0.486447\pi\) | ||||
0.0425659 | + | 0.999094i | \(0.486447\pi\) | |||||||
\(524\) | 4.88148 | + | 8.45497i | 0.213248 | + | 0.369357i | ||||
\(525\) | 19.9033 | + | 25.0378i | 0.868651 | + | 1.09274i | ||||
\(526\) | 4.79148 | − | 8.29908i | 0.208918 | − | 0.361857i | ||||
\(527\) | 7.14649 | − | 12.3781i | 0.311306 | − | 0.539198i | ||||
\(528\) | 2.46655 | + | 3.10285i | 0.107343 | + | 0.135034i | ||||
\(529\) | −6.00700 | − | 10.4044i | −0.261174 | − | 0.452367i | ||||
\(530\) | 48.1607 | 2.09197 | ||||||||
\(531\) | 8.37097 | − | 2.55358i | 0.363269 | − | 0.110816i | ||||
\(532\) | 17.3947 | 0.754156 | ||||||||
\(533\) | 6.17156 | + | 10.6895i | 0.267320 | + | 0.463012i | ||||
\(534\) | 17.6189 | − | 2.62758i | 0.762445 | − | 0.113706i | ||||
\(535\) | 9.25940 | − | 16.0378i | 0.400319 | − | 0.693373i | ||||
\(536\) | −6.52573 | + | 11.3029i | −0.281868 | + | 0.488210i | ||||
\(537\) | −2.50912 | + | 6.36398i | −0.108277 | + | 0.274626i | ||||
\(538\) | −21.1141 | − | 36.5706i | −0.910292 | − | 1.57667i | ||||
\(539\) | −1.84439 | −0.0794434 | ||||||||
\(540\) | −41.0465 | − | 28.2668i | −1.76636 | − | 1.21641i | ||||
\(541\) | −39.4039 | −1.69411 | −0.847053 | − | 0.531508i | \(-0.821626\pi\) | ||||
−0.847053 | + | 0.531508i | \(0.821626\pi\) | |||||||
\(542\) | −7.30322 | − | 12.6496i | −0.313700 | − | 0.543345i | ||||
\(543\) | −8.49154 | + | 21.5374i | −0.364407 | + | 0.924259i | ||||
\(544\) | 21.9926 | − | 38.0923i | 0.942925 | − | 1.63319i | ||||
\(545\) | −8.47803 | + | 14.6844i | −0.363159 | + | 0.629010i | ||||
\(546\) | −10.3834 | + | 1.54851i | −0.444367 | + | 0.0662701i | ||||
\(547\) | 12.5777 | + | 21.7853i | 0.537785 | + | 0.931470i | 0.999023 | + | 0.0441939i | \(0.0140719\pi\) |
−0.461238 | + | 0.887276i | \(0.652595\pi\) | |||||||
\(548\) | 58.1434 | 2.48376 | ||||||||
\(549\) | −4.24311 | + | 18.3270i | −0.181091 | + | 0.782178i | ||||
\(550\) | 17.5313 | 0.747539 | ||||||||
\(551\) | −5.07837 | − | 8.79600i | −0.216346 | − | 0.374722i | ||||
\(552\) | −8.89022 | − | 11.1837i | −0.378393 | − | 0.476008i | ||||
\(553\) | 1.60837 | − | 2.78579i | 0.0683950 | − | 0.118464i | ||||
\(554\) | −1.59140 | + | 2.75639i | −0.0676123 | + | 0.117108i | ||||
\(555\) | 1.30441 | + | 1.64092i | 0.0553693 | + | 0.0696531i | ||||
\(556\) | 1.70706 | + | 2.95672i | 0.0723955 | + | 0.125393i | ||||
\(557\) | −30.0269 | −1.27228 | −0.636140 | − | 0.771574i | \(-0.719470\pi\) | ||||
−0.636140 | + | 0.771574i | \(0.719470\pi\) | |||||||
\(558\) | 11.8593 | + | 11.0728i | 0.502045 | + | 0.468747i | ||||
\(559\) | −8.86115 | −0.374787 | ||||||||
\(560\) | −9.41541 | − | 16.3080i | −0.397874 | − | 0.689137i | ||||
\(561\) | 9.75923 | − | 1.45543i | 0.412035 | − | 0.0614484i | ||||
\(562\) | 7.91847 | − | 13.7152i | 0.334020 | − | 0.578540i | ||||
\(563\) | −9.16988 | + | 15.8827i | −0.386464 | + | 0.669376i | −0.991971 | − | 0.126464i | \(-0.959637\pi\) |
0.605507 | + | 0.795840i | \(0.292970\pi\) | |||||||
\(564\) | 14.6230 | − | 37.0889i | 0.615740 | − | 1.56173i | ||||
\(565\) | 2.77535 | + | 4.80705i | 0.116760 | + | 0.202234i | ||||
\(566\) | −31.7224 | −1.33339 | ||||||||
\(567\) | −16.9559 | + | 11.4063i | −0.712079 | + | 0.479019i | ||||
\(568\) | −16.8990 | −0.709067 | ||||||||
\(569\) | −16.1135 | − | 27.9094i | −0.675513 | − | 1.17002i | −0.976319 | − | 0.216338i | \(-0.930589\pi\) |
0.300805 | − | 0.953686i | \(-0.402745\pi\) | |||||||
\(570\) | 14.3650 | − | 36.4346i | 0.601685 | − | 1.52608i | ||||
\(571\) | 18.6411 | − | 32.2873i | 0.780105 | − | 1.35118i | −0.151775 | − | 0.988415i | \(-0.548499\pi\) |
0.931880 | − | 0.362767i | \(-0.118168\pi\) | |||||||
\(572\) | −1.63875 | + | 2.83840i | −0.0685195 | + | 0.118679i | ||||
\(573\) | 32.4127 | − | 4.83383i | 1.35406 | − | 0.201936i | ||||
\(574\) | −24.3929 | − | 42.2497i | −1.01814 | − | 1.76347i | ||||
\(575\) | 48.1244 | 2.00693 | ||||||||
\(576\) | 26.4594 | + | 24.7045i | 1.10248 | + | 1.02936i | ||||
\(577\) | −2.91538 | −0.121369 | −0.0606845 | − | 0.998157i | \(-0.519328\pi\) | ||||
−0.0606845 | + | 0.998157i | \(0.519328\pi\) | |||||||
\(578\) | −16.6560 | − | 28.8490i | −0.692799 | − | 1.19996i | ||||
\(579\) | 2.22513 | + | 2.79915i | 0.0924731 | + | 0.116329i | ||||
\(580\) | 16.8277 | − | 29.1465i | 0.698734 | − | 1.21024i | ||||
\(581\) | −3.12980 | + | 5.42098i | −0.129846 | + | 0.224900i | ||||
\(582\) | 5.94561 | + | 7.47942i | 0.246454 | + | 0.310032i | ||||
\(583\) | −3.08256 | − | 5.33916i | −0.127667 | − | 0.221125i | ||||
\(584\) | 6.01175 | 0.248768 | ||||||||
\(585\) | −3.03667 | + | 13.1161i | −0.125551 | + | 0.542286i | ||||
\(586\) | −4.25977 | −0.175970 | ||||||||
\(587\) | 9.62094 | + | 16.6640i | 0.397099 | + | 0.687795i | 0.993367 | − | 0.114990i | \(-0.0366837\pi\) |
−0.596268 | + | 0.802786i | \(0.703350\pi\) | |||||||
\(588\) | −8.36248 | + | 1.24713i | −0.344863 | + | 0.0514307i | ||||
\(589\) | −3.63111 | + | 6.28927i | −0.149617 | + | 0.259145i | ||||
\(590\) | −11.3945 | + | 19.7359i | −0.469105 | + | 0.812514i | ||||
\(591\) | 3.81273 | − | 9.67039i | 0.156835 | − | 0.397787i | ||||
\(592\) | −0.382133 | − | 0.661873i | −0.0157056 | − | 0.0272028i | ||||
\(593\) | 14.7811 | 0.606986 | 0.303493 | − | 0.952834i | \(-0.401847\pi\) | ||||
0.303493 | + | 0.952834i | \(0.401847\pi\) | |||||||
\(594\) | −0.889205 | + | 11.1655i | −0.0364845 | + | 0.458128i | ||||
\(595\) | −46.8761 | −1.92173 | ||||||||
\(596\) | 14.4834 | + | 25.0861i | 0.593265 | + | 1.02757i | ||||
\(597\) | −12.5238 | + | 31.7646i | −0.512564 | + | 1.30004i | ||||
\(598\) | −7.89777 | + | 13.6793i | −0.322964 | + | 0.559390i | ||||
\(599\) | 8.74025 | − | 15.1386i | 0.357117 | − | 0.618545i | −0.630361 | − | 0.776302i | \(-0.717093\pi\) |
0.987478 | + | 0.157758i | \(0.0504264\pi\) | |||||||
\(600\) | 19.4213 | − | 2.89638i | 0.792873 | − | 0.118244i | ||||
\(601\) | −11.8922 | − | 20.5979i | −0.485093 | − | 0.840205i | 0.514761 | − | 0.857334i | \(-0.327881\pi\) |
−0.999853 | + | 0.0171288i | \(0.994547\pi\) | |||||||
\(602\) | 35.0234 | 1.42745 | ||||||||
\(603\) | 26.8663 | − | 8.19563i | 1.09408 | − | 0.333752i | ||||
\(604\) | 5.65783 | 0.230214 | ||||||||
\(605\) | −1.81197 | − | 3.13842i | −0.0736669 | − | 0.127595i | ||||
\(606\) | 42.5951 | + | 53.5835i | 1.73031 | + | 2.17668i | ||||
\(607\) | −19.5986 | + | 33.9458i | −0.795484 | + | 1.37782i | 0.127048 | + | 0.991897i | \(0.459450\pi\) |
−0.922532 | + | 0.385922i | \(0.873883\pi\) | |||||||
\(608\) | −11.1744 | + | 19.3546i | −0.453180 | + | 0.784931i | ||||
\(609\) | −8.58732 | − | 10.8026i | −0.347976 | − | 0.437744i | ||||
\(610\) | −24.4923 | − | 42.4219i | −0.991664 | − | 1.71761i | ||||
\(611\) | −10.7697 | −0.435695 | ||||||||
\(612\) | 43.2644 | − | 13.1979i | 1.74886 | − | 0.533494i | ||||
\(613\) | 9.34643 | 0.377499 | 0.188749 | − | 0.982025i | \(-0.439557\pi\) | ||||
0.188749 | + | 0.982025i | \(0.439557\pi\) | |||||||
\(614\) | −12.9022 | − | 22.3472i | −0.520689 | − | 0.901860i | ||||
\(615\) | −61.8794 | + | 9.22831i | −2.49522 | + | 0.372121i | ||||
\(616\) | 1.58256 | − | 2.74108i | 0.0637633 | − | 0.110441i | ||||
\(617\) | 1.85481 | − | 3.21263i | 0.0746720 | − | 0.129336i | −0.826272 | − | 0.563272i | \(-0.809542\pi\) |
0.900944 | + | 0.433936i | \(0.142876\pi\) | |||||||
\(618\) | 6.24808 | − | 15.8473i | 0.251335 | − | 0.637470i | ||||
\(619\) | −15.1420 | − | 26.2268i | −0.608609 | − | 1.05414i | −0.991470 | − | 0.130336i | \(-0.958394\pi\) |
0.382861 | − | 0.923806i | \(-0.374939\pi\) | |||||||
\(620\) | −24.0642 | −0.966440 | ||||||||
\(621\) | −2.44091 | + | 30.6500i | −0.0979504 | + | 1.22994i | ||||
\(622\) | 7.32331 | 0.293638 | ||||||||
\(623\) | 5.41670 | + | 9.38199i | 0.217015 | + | 0.375882i | ||||
\(624\) | 1.80040 | − | 4.56644i | 0.0720739 | − | 0.182804i | ||||
\(625\) | −0.239656 | + | 0.415097i | −0.00958625 | + | 0.0166039i | ||||
\(626\) | 24.4624 | − | 42.3701i | 0.977714 | − | 1.69345i | ||||
\(627\) | −4.95863 | + | 0.739500i | −0.198029 | + | 0.0295328i | ||||
\(628\) | −12.5724 | − | 21.7761i | −0.501694 | − | 0.868959i | ||||
\(629\) | −1.90251 | −0.0758580 | ||||||||
\(630\) | 12.0023 | − | 51.8410i | 0.478185 | − | 2.06540i | ||||
\(631\) | −10.7233 | −0.426886 | −0.213443 | − | 0.976956i | \(-0.568468\pi\) | ||||
−0.213443 | + | 0.976956i | \(0.568468\pi\) | |||||||
\(632\) | −0.987411 | − | 1.71025i | −0.0392771 | − | 0.0680299i | ||||
\(633\) | 12.5914 | + | 15.8397i | 0.500464 | + | 0.629570i | ||||
\(634\) | −16.0064 | + | 27.7240i | −0.635697 | + | 1.10106i | ||||
\(635\) | −15.8141 | + | 27.3908i | −0.627562 | + | 1.08697i | ||||
\(636\) | −17.5866 | − | 22.1235i | −0.697354 | − | 0.877253i | ||||
\(637\) | 1.14200 | + | 1.97800i | 0.0452476 | + | 0.0783711i | ||||
\(638\) | −7.56393 | −0.299459 | ||||||||
\(639\) | 26.5832 | + | 24.8201i | 1.05162 | + | 0.981869i | ||||
\(640\) | −38.3005 | −1.51396 | ||||||||
\(641\) | 21.9083 | + | 37.9462i | 0.865324 | + | 1.49879i | 0.866725 | + | 0.498786i | \(0.166221\pi\) |
−0.00140071 | + | 0.999999i | \(0.500446\pi\) | |||||||
\(642\) | −18.8707 | + | 2.81426i | −0.744767 | + | 0.111070i | ||||
\(643\) | −16.0895 | + | 27.8678i | −0.634507 | + | 1.09900i | 0.352112 | + | 0.935958i | \(0.385464\pi\) |
−0.986619 | + | 0.163041i | \(0.947870\pi\) | |||||||
\(644\) | 17.7799 | − | 30.7958i | 0.700628 | − | 1.21352i | ||||
\(645\) | 16.4742 | − | 41.7842i | 0.648672 | − | 1.64525i | ||||
\(646\) | 17.7726 | + | 30.7830i | 0.699252 | + | 1.21114i | ||||
\(647\) | 10.9108 | 0.428946 | 0.214473 | − | 0.976730i | \(-0.431197\pi\) | ||||
0.214473 | + | 0.976730i | \(0.431197\pi\) | |||||||
\(648\) | 0.859608 | + | 12.5162i | 0.0337686 | + | 0.491682i | ||||
\(649\) | 2.91726 | 0.114513 | ||||||||
\(650\) | −10.8550 | − | 18.8013i | −0.425766 | − | 0.737449i | ||||
\(651\) | −3.61917 | + | 9.17946i | −0.141847 | + | 0.359771i | ||||
\(652\) | 25.7671 | − | 44.6299i | 1.00912 | − | 1.74784i | ||||
\(653\) | 23.5331 | − | 40.7605i | 0.920922 | − | 1.59508i | 0.122929 | − | 0.992415i | \(-0.460771\pi\) |
0.797992 | − | 0.602667i | \(-0.205895\pi\) | |||||||
\(654\) | 17.2783 | − | 2.57677i | 0.675633 | − | 0.100760i | ||||
\(655\) | 6.68393 | + | 11.5769i | 0.261163 | + | 0.452347i | ||||
\(656\) | 22.8103 | 0.890593 | ||||||||
\(657\) | −9.45686 | − | 8.82964i | −0.368947 | − | 0.344477i | ||||
\(658\) | 42.5668 | 1.65943 | ||||||||
\(659\) | −13.4862 | − | 23.3588i | −0.525348 | − | 0.909930i | −0.999564 | − | 0.0295212i | \(-0.990602\pi\) |
0.474216 | − | 0.880409i | \(-0.342732\pi\) | |||||||
\(660\) | −10.3376 | − | 13.0044i | −0.402391 | − | 0.506197i | ||||
\(661\) | −4.53345 | + | 7.85217i | −0.176331 | + | 0.305414i | −0.940621 | − | 0.339459i | \(-0.889756\pi\) |
0.764290 | + | 0.644872i | \(0.223090\pi\) | |||||||
\(662\) | −17.4635 | + | 30.2476i | −0.678737 | + | 1.17561i | ||||
\(663\) | −7.60353 | − | 9.56504i | −0.295297 | − | 0.371475i | ||||
\(664\) | 1.92144 | + | 3.32804i | 0.0745665 | + | 0.129153i | ||||
\(665\) | 23.8176 | 0.923607 | ||||||||
\(666\) | 0.487125 | − | 2.10401i | 0.0188757 | − | 0.0815289i | ||||
\(667\) | −20.7634 | −0.803961 | ||||||||
\(668\) | 20.2444 | + | 35.0643i | 0.783278 | + | 1.35668i | ||||
\(669\) | −31.0472 | + | 4.63019i | −1.20036 | + | 0.179014i | ||||
\(670\) | −36.5703 | + | 63.3416i | −1.41283 | + | 2.44710i | ||||
\(671\) | −3.13530 | + | 5.43050i | −0.121037 | + | 0.209642i | ||||
\(672\) | −11.1376 | + | 28.2488i | −0.429644 | + | 1.08972i | ||||
\(673\) | 4.36695 | + | 7.56378i | 0.168334 | + | 0.291562i | 0.937834 | − | 0.347084i | \(-0.112828\pi\) |
−0.769501 | + | 0.638646i | \(0.779495\pi\) | |||||||
\(674\) | −24.2770 | −0.935114 | ||||||||
\(675\) | −34.8050 | − | 23.9685i | −1.33965 | − | 0.922550i | ||||
\(676\) | −30.3480 | −1.16723 | ||||||||
\(677\) | 17.8921 | + | 30.9900i | 0.687650 | + | 1.19104i | 0.972596 | + | 0.232501i | \(0.0746908\pi\) |
−0.284947 | + | 0.958543i | \(0.591976\pi\) | |||||||
\(678\) | 2.09757 | − | 5.32016i | 0.0805568 | − | 0.204319i | ||||
\(679\) | −2.90533 | + | 5.03218i | −0.111496 | + | 0.193117i | ||||
\(680\) | −14.3891 | + | 24.9226i | −0.551795 | + | 0.955737i | ||||
\(681\) | 29.9921 | − | 4.47284i | 1.14930 | − | 0.171400i | ||||
\(682\) | 2.70416 | + | 4.68374i | 0.103548 | + | 0.179350i | ||||
\(683\) | −40.9545 | −1.56708 | −0.783541 | − | 0.621340i | \(-0.786588\pi\) | ||||
−0.783541 | + | 0.621340i | \(0.786588\pi\) | |||||||
\(684\) | −21.9825 | + | 6.70581i | −0.840522 | + | 0.256403i | ||||
\(685\) | 79.6125 | 3.04184 | ||||||||
\(686\) | −21.6446 | − | 37.4895i | −0.826393 | − | 1.43135i | ||||
\(687\) | −4.89612 | − | 6.15919i | −0.186799 | − | 0.234988i | ||||
\(688\) | −8.18778 | + | 14.1816i | −0.312156 | + | 0.540670i | ||||
\(689\) | −3.81729 | + | 6.61174i | −0.145427 | + | 0.251887i | ||||
\(690\) | −49.8210 | − | 62.6735i | −1.89665 | − | 2.38594i | ||||
\(691\) | −19.9963 | − | 34.6346i | −0.760696 | − | 1.31756i | −0.942492 | − | 0.334228i | \(-0.891525\pi\) |
0.181797 | − | 0.983336i | \(-0.441809\pi\) | |||||||
\(692\) | 37.1087 | 1.41066 | ||||||||
\(693\) | −6.51538 | + | 1.98753i | −0.247499 | + | 0.0755001i | ||||
\(694\) | −36.8057 | −1.39713 | ||||||||
\(695\) | 2.33738 | + | 4.04847i | 0.0886620 | + | 0.153567i | ||||
\(696\) | −8.37938 | + | 1.24965i | −0.317619 | + | 0.0473678i | ||||
\(697\) | 28.3912 | − | 49.1750i | 1.07539 | − | 1.86264i | ||||
\(698\) | −24.7598 | + | 42.8853i | −0.937173 | + | 1.62323i | ||||
\(699\) | 5.19015 | − | 13.1640i | 0.196309 | − | 0.497908i | ||||
\(700\) | 24.4373 | + | 42.3267i | 0.923644 | + | 1.59980i | ||||
\(701\) | −28.4894 | −1.07603 | −0.538015 | − | 0.842935i | \(-0.680826\pi\) | ||||
−0.538015 | + | 0.842935i | \(0.680826\pi\) | |||||||
\(702\) | 12.5250 | − | 5.95980i | 0.472724 | − | 0.224938i | ||||
\(703\) | 0.966658 | 0.0364582 | ||||||||
\(704\) | 6.03328 | + | 10.4499i | 0.227388 | + | 0.393847i | ||||
\(705\) | 20.0225 | − | 50.7838i | 0.754090 | − | 1.91263i | ||||
\(706\) | 22.1095 | − | 38.2948i | 0.832103 | − | 1.44124i | ||||
\(707\) | −20.8141 | + | 36.0511i | −0.782796 | + | 1.35584i | ||||
\(708\) | 13.2269 | − | 1.97258i | 0.497098 | − | 0.0741342i | ||||
\(709\) | −19.2455 | − | 33.3341i | −0.722779 | − | 1.25189i | −0.959882 | − | 0.280405i | \(-0.909531\pi\) |
0.237103 | − | 0.971485i | \(-0.423802\pi\) | |||||||
\(710\) | −94.7025 | −3.55412 | ||||||||
\(711\) | −0.958632 | + | 4.14057i | −0.0359515 | + | 0.155283i | ||||
\(712\) | 6.65082 | 0.249250 | ||||||||
\(713\) | 7.42305 | + | 12.8571i | 0.277995 | + | 0.481502i | ||||
\(714\) | 30.0527 | + | 37.8055i | 1.12469 | + | 1.41483i | ||||
\(715\) | −2.24385 | + | 3.88646i | −0.0839151 | + | 0.145345i | ||||
\(716\) | −5.22652 | + | 9.05260i | −0.195324 | + | 0.338311i | ||||
\(717\) | −20.0481 | − | 25.2200i | −0.748711 | − | 0.941858i | ||||
\(718\) | 3.14547 | + | 5.44811i | 0.117388 | + | 0.203322i | ||||
\(719\) | 19.0764 | 0.711430 | 0.355715 | − | 0.934594i | \(-0.384237\pi\) | ||||
0.355715 | + | 0.934594i | \(0.384237\pi\) | |||||||
\(720\) | 18.1855 | + | 16.9794i | 0.677735 | + | 0.632785i | ||||
\(721\) | 10.3595 | 0.385807 | ||||||||
\(722\) | 11.4481 | + | 19.8288i | 0.426056 | + | 0.737950i | ||||
\(723\) | 48.5711 | − | 7.24359i | 1.80638 | − | 0.269392i | ||||
\(724\) | −17.6879 | + | 30.6364i | −0.657367 | + | 1.13859i | ||||
\(725\) | 14.2689 | − | 24.7145i | 0.529934 | − | 0.917873i | ||||
\(726\) | −1.36946 | + | 3.47341i | −0.0508254 | + | 0.128910i | ||||
\(727\) | 3.03168 | + | 5.25103i | 0.112439 | + | 0.194750i | 0.916753 | − | 0.399454i | \(-0.130800\pi\) |
−0.804314 | + | 0.594204i | \(0.797467\pi\) | |||||||
\(728\) | −3.91953 | −0.145267 | ||||||||
\(729\) | 17.0307 | − | 20.9513i | 0.630766 | − | 0.775973i | ||||
\(730\) | 33.6900 | 1.24692 | ||||||||
\(731\) | 20.3821 | + | 35.3028i | 0.753858 | + | 1.30572i | ||||
\(732\) | −10.5435 | + | 26.7420i | −0.389700 | + | 0.988412i | ||||
\(733\) | −18.8883 | + | 32.7155i | −0.697655 | + | 1.20837i | 0.271622 | + | 0.962404i | \(0.412440\pi\) |
−0.969277 | + | 0.245970i | \(0.920894\pi\) | |||||||
\(734\) | −7.27669 | + | 12.6036i | −0.268588 | + | 0.465207i | ||||
\(735\) | −11.4503 | + | 1.70762i | −0.422350 | + | 0.0629867i | ||||
\(736\) | 22.8437 | + | 39.5664i | 0.842029 | + | 1.45844i | ||||
\(737\) | 9.36285 | 0.344885 | ||||||||
\(738\) | 47.1140 | + | 43.9892i | 1.73429 | + | 1.61927i | ||||
\(739\) | −11.0030 | −0.404752 | −0.202376 | − | 0.979308i | \(-0.564866\pi\) | ||||
−0.202376 | + | 0.979308i | \(0.564866\pi\) | |||||||
\(740\) | 1.60156 | + | 2.77399i | 0.0588746 | + | 0.101974i | ||||
\(741\) | 3.86333 | + | 4.85996i | 0.141923 | + | 0.178535i | ||||
\(742\) | 15.0877 | − | 26.1327i | 0.553887 | − | 0.959360i | ||||
\(743\) | −8.83265 | + | 15.2986i | −0.324038 | + | 0.561251i | −0.981317 | − | 0.192397i | \(-0.938374\pi\) |
0.657279 | + | 0.753647i | \(0.271707\pi\) | |||||||
\(744\) | 3.76949 | + | 4.74192i | 0.138196 | + | 0.173847i | ||||
\(745\) | 19.8314 | + | 34.3489i | 0.726565 | + | 1.25845i | ||||
\(746\) | −48.2371 | −1.76608 | ||||||||
\(747\) | 1.86544 | − | 8.05730i | 0.0682529 | − | 0.294801i | ||||
\(748\) | 15.0775 | 0.551290 | ||||||||
\(749\) | −5.80154 | − | 10.0486i | −0.211984 | − | 0.367166i | ||||
\(750\) | 41.9255 | − | 6.25251i | 1.53090 | − | 0.228309i | ||||
\(751\) | 2.14256 | − | 3.71103i | 0.0781833 | − | 0.135417i | −0.824283 | − | 0.566178i | \(-0.808421\pi\) |
0.902466 | + | 0.430761i | \(0.141755\pi\) | |||||||
\(752\) | −9.95128 | + | 17.2361i | −0.362886 | + | 0.628537i | ||||
\(753\) | −3.13718 | + | 7.95695i | −0.114325 | + | 0.289968i | ||||
\(754\) | 4.68339 | + | 8.11187i | 0.170559 | + | 0.295417i | ||||
\(755\) | 7.74695 | 0.281940 | ||||||||
\(756\) | −28.1969 | + | 13.4170i | −1.02551 | + | 0.487973i | ||||
\(757\) | −8.95117 | −0.325336 | −0.162668 | − | 0.986681i | \(-0.552010\pi\) | ||||
−0.162668 | + | 0.986681i | \(0.552010\pi\) | |||||||
\(758\) | −35.6022 | − | 61.6648i | −1.29313 | − | 2.23977i | ||||
\(759\) | −3.75923 | + | 9.53468i | −0.136451 | + | 0.346087i | ||||
\(760\) | 7.31103 | − | 12.6631i | 0.265199 | − | 0.459338i | ||||
\(761\) | 2.69037 | − | 4.65986i | 0.0975258 | − | 0.168920i | −0.813134 | − | 0.582076i | \(-0.802240\pi\) |
0.910660 | + | 0.413157i | \(0.135574\pi\) | |||||||
\(762\) | 32.2291 | − | 4.80645i | 1.16754 | − | 0.174119i | ||||
\(763\) | 5.31197 | + | 9.20059i | 0.192306 | + | 0.333084i | ||||
\(764\) | 50.0761 | 1.81169 | ||||||||
\(765\) | 59.2395 | − | 18.0711i | 2.14181 | − | 0.653364i | ||||
\(766\) | 50.6229 | 1.82908 | ||||||||
\(767\) | −1.80630 | − | 3.12860i | −0.0652215 | − | 0.112967i | ||||
\(768\) | −1.45604 | − | 1.83166i | −0.0525403 | − | 0.0660943i | ||||
\(769\) | 7.72456 | − | 13.3793i | 0.278555 | − | 0.482471i | −0.692471 | − | 0.721446i | \(-0.743478\pi\) |
0.971026 | + | 0.238975i | \(0.0768113\pi\) | |||||||
\(770\) | 8.86872 | − | 15.3611i | 0.319606 | − | 0.553575i | ||||
\(771\) | −18.4450 | − | 23.2034i | −0.664282 | − | 0.835649i | ||||
\(772\) | 2.73202 | + | 4.73199i | 0.0983274 | + | 0.170308i | ||||
\(773\) | −32.7213 | −1.17690 | −0.588451 | − | 0.808533i | \(-0.700262\pi\) | ||||
−0.588451 | + | 0.808533i | \(0.700262\pi\) | |||||||
\(774\) | −44.2606 | + | 13.5018i | −1.59091 | + | 0.485312i | ||||
\(775\) | −20.4050 | −0.732968 | ||||||||
\(776\) | 1.78364 | + | 3.08935i | 0.0640288 | + | 0.110901i | ||||
\(777\) | 1.29903 | − | 0.193729i | 0.0466024 | − | 0.00695000i | ||||
\(778\) | 33.4566 | − | 57.9486i | 1.19948 | − | 2.07756i | ||||
\(779\) | −14.4255 | + | 24.9856i | −0.516846 | + | 0.895204i | ||||
\(780\) | −7.54571 | + | 19.1385i | −0.270180 | + | 0.685268i | ||||
\(781\) | 6.06151 | + | 10.4988i | 0.216898 | + | 0.375678i | ||||
\(782\) | 72.6647 | 2.59848 | ||||||||
\(783\) | 15.0167 | + | 10.3413i | 0.536653 | + | 0.369567i | ||||
\(784\) | 4.22086 | 0.150745 | ||||||||
\(785\) | −17.2147 | − | 29.8167i | −0.614419 | − | 1.06420i | ||||
\(786\) | 5.05162 | − | 12.8126i | 0.180185 | − | 0.457011i | ||||
\(787\) | 12.4575 | − | 21.5771i | 0.444063 | − | 0.769139i | −0.553924 | − | 0.832567i | \(-0.686870\pi\) |
0.997986 | + | 0.0634284i | \(0.0202035\pi\) | |||||||
\(788\) | 7.94196 | − | 13.7559i | 0.282921 | − | 0.490033i | ||||
\(789\) | −7.61575 | + | 1.13577i | −0.271128 | + | 0.0404343i | ||||
\(790\) | −5.53347 | − | 9.58425i | −0.196872 | − | 0.340992i | ||||
\(791\) | 3.47783 | 0.123657 | ||||||||
\(792\) | −0.943248 | + | 4.07412i | −0.0335169 | + | 0.144768i | ||||
\(793\) | 7.76519 | 0.275750 | ||||||||
\(794\) | −18.7327 | − | 32.4460i | −0.664799 | − | 1.15146i | ||||
\(795\) | −24.0803 | − | 30.2924i | −0.854042 | − | 1.07436i | ||||
\(796\) | −26.0872 | + | 45.1843i | −0.924635 | + | 1.60151i | ||||
\(797\) | −4.54547 | + | 7.87298i | −0.161009 | + | 0.278875i | −0.935231 | − | 0.354039i | \(-0.884808\pi\) |
0.774222 | + | 0.632914i | \(0.218141\pi\) | |||||||
\(798\) | −15.2697 | − | 19.2088i | −0.540540 | − | 0.679985i | ||||
\(799\) | 24.7720 | + | 42.9064i | 0.876371 | + | 1.51792i | ||||
\(800\) | −62.7941 | −2.22011 | ||||||||
\(801\) | −10.4622 | − | 9.76827i | −0.369662 | − | 0.345145i | ||||
\(802\) | −24.8928 | −0.878997 | ||||||||
\(803\) | −2.15635 | − | 3.73491i | −0.0760960 | − | 0.131802i | ||||
\(804\) | 42.4513 | − | 6.33093i | 1.49714 | − | 0.223275i | ||||
\(805\) | 24.3451 | − | 42.1669i | 0.858051 | − | 1.48619i | ||||
\(806\) | 3.34869 | − | 5.80011i | 0.117953 | − | 0.204300i | ||||
\(807\) | −12.4454 | + | 31.5658i | −0.438099 | + | 1.11117i | ||||
\(808\) | 12.7782 | + | 22.1325i | 0.449535 | + | 0.778617i | ||||
\(809\) | 10.0563 | 0.353560 | 0.176780 | − | 0.984250i | \(-0.443432\pi\) | ||||
0.176780 | + | 0.984250i | \(0.443432\pi\) | |||||||
\(810\) | 4.81726 | + | 70.1409i | 0.169261 | + | 2.46450i | ||||
\(811\) | −16.2533 | −0.570730 | −0.285365 | − | 0.958419i | \(-0.592115\pi\) | ||||
−0.285365 | + | 0.958419i | \(0.592115\pi\) | |||||||
\(812\) | −10.5435 | − | 18.2619i | −0.370005 | − | 0.640868i | ||||
\(813\) | −4.30479 | + | 10.9184i | −0.150976 | + | 0.382925i | ||||
\(814\) | 0.359945 | − | 0.623442i | 0.0126161 | − | 0.0218516i | ||||
\(815\) | 35.2814 | − | 61.1092i | 1.23585 | − | 2.14056i | ||||
\(816\) | −22.3339 | + | 3.33074i | −0.781843 | + | 0.116599i | ||||
\(817\) | −10.3561 | − | 17.9372i | −0.362313 | − | 0.627544i | ||||
\(818\) | 74.8765 | 2.61800 | ||||||||
\(819\) | 6.16567 | + | 5.75674i | 0.215446 | + | 0.201157i | ||||
\(820\) | −95.6007 | −3.33852 | ||||||||
\(821\) | 10.4445 | + | 18.0904i | 0.364515 | + | 0.631359i | 0.988698 | − | 0.149919i | \(-0.0479013\pi\) |
−0.624183 | + | 0.781278i | \(0.714568\pi\) | |||||||
\(822\) | −51.0402 | − | 64.2072i | −1.78023 | − | 2.23948i | ||||
\(823\) | 6.73966 | − | 11.6734i | 0.234930 | − | 0.406910i | −0.724323 | − | 0.689461i | \(-0.757847\pi\) |
0.959252 | + | 0.282551i | \(0.0911807\pi\) | |||||||
\(824\) | 3.17994 | − | 5.50782i | 0.110778 | − | 0.191874i | ||||
\(825\) | −8.76567 | − | 11.0270i | −0.305181 | − | 0.383910i | ||||
\(826\) | 7.13932 | + | 12.3657i | 0.248409 | + | 0.430256i | ||||
\(827\) | 54.8435 | 1.90710 | 0.953548 | − | 0.301241i | \(-0.0974008\pi\) | ||||
0.953548 | + | 0.301241i | \(0.0974008\pi\) | |||||||
\(828\) | −10.5973 | + | 45.7723i | −0.368281 | + | 1.59070i | ||||
\(829\) | 1.57675 | 0.0547628 | 0.0273814 | − | 0.999625i | \(-0.491283\pi\) | ||||
0.0273814 | + | 0.999625i | \(0.491283\pi\) | |||||||
\(830\) | 10.7678 | + | 18.6504i | 0.373756 | + | 0.647365i | ||||
\(831\) | 2.52944 | − | 0.377225i | 0.0877452 | − | 0.0130858i | ||||
\(832\) | 7.47130 | − | 12.9407i | 0.259021 | − | 0.448637i | ||||
\(833\) | 5.25356 | − | 9.09943i | 0.182025 | − | 0.315277i | ||||
\(834\) | 1.76656 | − | 4.48060i | 0.0611710 | − | 0.155150i | ||||
\(835\) | 27.7195 | + | 48.0115i | 0.959271 | + | 1.66151i | ||||
\(836\) | −7.66085 | −0.264956 | ||||||||
\(837\) | 1.03496 | − | 12.9957i | 0.0357734 | − | 0.449198i | ||||
\(838\) | −16.0177 | −0.553323 | ||||||||
\(839\) | −14.5469 | − | 25.1960i | −0.502214 | − | 0.869861i | −0.999997 | − | 0.00255896i | \(-0.999185\pi\) |
0.497782 | − | 0.867302i | \(-0.334148\pi\) | |||||||
\(840\) | 7.28700 | − | 18.4823i | 0.251425 | − | 0.637701i | ||||
\(841\) | 8.34365 | − | 14.4516i | 0.287712 | − | 0.498332i | ||||
\(842\) | −12.7782 | + | 22.1326i | −0.440367 | + | 0.762738i | ||||
\(843\) | −12.5859 | + | 1.87698i | −0.433481 | + | 0.0646467i | ||||
\(844\) | 15.4598 | + | 26.7771i | 0.532147 | + | 0.921706i | ||||
\(845\) | −41.5538 | −1.42949 | ||||||||
\(846\) | −53.7936 | + | 16.4099i | −1.84946 | + | 0.564182i | ||||
\(847\) | −2.27060 | −0.0780187 | ||||||||
\(848\) | 7.05442 | + | 12.2186i | 0.242250 | + | 0.419589i | ||||
\(849\) | 15.8612 | + | 19.9530i | 0.544355 | + | 0.684784i | ||||
\(850\) | −49.9363 | + | 86.4922i | −1.71280 | + | 2.96666i | ||||
\(851\) | 0.988066 | − | 1.71138i | 0.0338705 | − | 0.0586653i | ||||
\(852\) | 34.5820 | + | 43.5033i | 1.18476 | + | 1.49040i | ||||
\(853\) | −12.8625 | − | 22.2785i | −0.440403 | − | 0.762800i | 0.557316 | − | 0.830300i | \(-0.311831\pi\) |
−0.997719 | + | 0.0675000i | \(0.978498\pi\) | |||||||
\(854\) | −30.6916 | −1.05025 | ||||||||
\(855\) | −30.0994 | + | 9.18189i | −1.02938 | + | 0.314014i | ||||
\(856\) | −7.12334 | −0.243471 | ||||||||
\(857\) | 23.0057 | + | 39.8470i | 0.785860 | + | 1.36115i | 0.928484 | + | 0.371372i | \(0.121113\pi\) |
−0.142625 | + | 0.989777i | \(0.545554\pi\) | |||||||
\(858\) | 4.57296 | − | 0.681984i | 0.156118 | − | 0.0232825i | ||||
\(859\) | 22.0242 | − | 38.1470i | 0.751455 | − | 1.30156i | −0.195663 | − | 0.980671i | \(-0.562686\pi\) |
0.947118 | − | 0.320886i | \(-0.103981\pi\) | |||||||
\(860\) | 34.3159 | − | 59.4370i | 1.17016 | − | 2.02678i | ||||
\(861\) | −14.3781 | + | 36.4676i | −0.490003 | + | 1.24281i | ||||
\(862\) | −26.6752 | − | 46.2029i | −0.908562 | − | 1.57368i | ||||
\(863\) | −13.4065 | −0.456362 | −0.228181 | − | 0.973619i | \(-0.573278\pi\) | ||||
−0.228181 | + | 0.973619i | \(0.573278\pi\) | |||||||
\(864\) | 3.18498 | − | 39.9930i | 0.108355 | − | 1.36059i | ||||
\(865\) | 50.8108 | 1.72762 | ||||||||
\(866\) | −20.5438 | − | 35.5830i | −0.698108 | − | 1.20916i | ||||
\(867\) | −9.81766 | + | 24.9009i | −0.333425 | + | 0.845680i | ||||
\(868\) | −7.53877 | + | 13.0575i | −0.255883 | + | 0.443202i | ||||
\(869\) | −0.708348 | + | 1.22690i | −0.0240291 | + | 0.0416196i | ||||
\(870\) | −46.9582 | + | 7.00306i | −1.59203 | + | 0.237426i | ||||
\(871\) | −5.79724 | − | 10.0411i | −0.196432 | − | 0.340230i | ||||
\(872\) | 6.52223 | 0.220871 | ||||||||
\(873\) | 1.73165 | − | 7.47942i | 0.0586075 | − | 0.253140i | ||||
\(874\) | −36.9207 | −1.24886 | ||||||||
\(875\) | 12.8894 | + | 22.3251i | 0.435742 | + | 0.754727i | ||||
\(876\) | −12.3024 | − | 15.4761i | −0.415659 | − | 0.522889i | ||||
\(877\) | −6.18860 | + | 10.7190i | −0.208974 | + | 0.361954i | −0.951392 | − | 0.307984i | \(-0.900346\pi\) |
0.742417 | + | 0.669938i | \(0.233679\pi\) | |||||||
\(878\) | 37.4521 | − | 64.8690i | 1.26395 | − | 2.18922i | ||||
\(879\) | 2.12989 | + | 2.67934i | 0.0718393 | + | 0.0903719i | ||||
\(880\) | 4.14667 | + | 7.18224i | 0.139784 | + | 0.242113i | ||||
\(881\) | −31.1210 | −1.04849 | −0.524247 | − | 0.851566i | \(-0.675653\pi\) | ||||
−0.524247 | + | 0.851566i | \(0.675653\pi\) | |||||||
\(882\) | 8.71807 | + | 8.13985i | 0.293553 | + | 0.274083i | ||||
\(883\) | −49.1130 | −1.65278 | −0.826392 | − | 0.563096i | \(-0.809610\pi\) | ||||
−0.826392 | + | 0.563096i | \(0.809610\pi\) | |||||||
\(884\) | −9.33563 | − | 16.1698i | −0.313991 | − | 0.543849i | ||||
\(885\) | 18.1109 | − | 2.70095i | 0.608791 | − | 0.0907913i | ||||
\(886\) | 1.46569 | − | 2.53866i | 0.0492410 | − | 0.0852878i | ||||
\(887\) | 23.1958 | − | 40.1763i | 0.778839 | − | 1.34899i | −0.153772 | − | 0.988106i | \(-0.549142\pi\) |
0.932611 | − | 0.360882i | \(-0.117524\pi\) | |||||||
\(888\) | 0.295749 | − | 0.750121i | 0.00992470 | − | 0.0251724i | ||||
\(889\) | 9.90841 | + | 17.1619i | 0.332317 | + | 0.575590i | ||||
\(890\) | 37.2713 | 1.24934 | ||||||||
\(891\) | 7.46758 | − | 5.02347i | 0.250173 | − | 0.168293i | ||||
\(892\) | −47.9665 | −1.60604 | ||||||||
\(893\) | −12.5866 | − | 21.8006i | −0.421194 | − | 0.729529i | ||||
\(894\) | 14.9883 | − | 38.0153i | 0.501283 | − | 1.27142i | ||||
\(895\) | −7.15638 | + | 12.3952i | −0.239211 | + | 0.414326i | ||||
\(896\) | −11.9987 | + | 20.7824i | −0.400849 | + | 0.694291i | ||||
\(897\) | 12.5530 | − | 1.87208i | 0.419133 | − | 0.0625069i | ||||
\(898\) | −34.1946 | − | 59.2268i | −1.14109 | − | 1.97642i | ||||
\(899\) | 8.80376 | 0.293622 | ||||||||
\(900\) | −47.1999 | − | 44.0694i | −1.57333 | − | 1.46898i | ||||
\(901\) | 35.1215 | 1.17007 | ||||||||
\(902\) | 10.7429 | + | 18.6073i | 0.357701 | + | 0.619555i | ||||
\(903\) | −17.5117 | − | 22.0292i | −0.582752 | − | 0.733087i | ||||
\(904\) | 1.06755 | − | 1.84906i | 0.0355063 | − | 0.0614987i | ||||
\(905\) | −24.2191 | + | 41.9487i | −0.805070 | + | 1.39442i | ||||
\(906\) | −4.96663 | − | 6.24789i | −0.165005 | − | 0.207572i | ||||
\(907\) | 3.71116 | + | 6.42792i | 0.123227 | + | 0.213436i | 0.921039 | − | 0.389471i | \(-0.127342\pi\) |
−0.797811 | + | 0.602907i | \(0.794009\pi\) | |||||||
\(908\) | 46.3364 | 1.53773 | ||||||||
\(909\) | 12.4057 | − | 53.5835i | 0.411473 | − | 1.77725i | ||||
\(910\) | −21.9651 | −0.728137 | ||||||||
\(911\) | −4.63530 | − | 8.02857i | −0.153574 | − | 0.265998i | 0.778965 | − | 0.627068i | \(-0.215745\pi\) |
−0.932539 | + | 0.361069i | \(0.882412\pi\) | |||||||
\(912\) | 11.3478 | − | 1.69234i | 0.375763 | − | 0.0560389i | ||||
\(913\) | 1.37840 | − | 2.38747i | 0.0456185 | − | 0.0790136i | ||||
\(914\) | −38.1354 | + | 66.0525i | −1.26141 | + | 2.18482i | ||||
\(915\) | −14.4367 | + | 36.6163i | −0.477261 | + | 1.21050i | ||||
\(916\) | −6.01147 | − | 10.4122i | −0.198625 | − | 0.344028i | ||||
\(917\) | 8.37572 | 0.276591 | ||||||||
\(918\) | −52.5533 | − | 36.1909i | −1.73452 | − | 1.19448i | ||||
\(919\) | −8.03556 | −0.265069 | −0.132534 | − | 0.991178i | \(-0.542311\pi\) | ||||
−0.132534 | + | 0.991178i | \(0.542311\pi\) | |||||||
\(920\) | −14.9459 | − | 25.8870i | −0.492751 | − | 0.853470i | ||||
\(921\) | −7.60501 | + | 19.2889i | −0.250594 | + | 0.635591i | ||||
\(922\) | 33.6671 | − | 58.3131i | 1.10877 | − | 1.92044i | ||||
\(923\) | 7.50626 | − | 13.0012i | 0.247072 | − | 0.427941i | ||||
\(924\) | −10.2949 | + | 1.53532i | −0.338678 | + | 0.0505084i | ||||
\(925\) | 1.35803 | + | 2.35218i | 0.0446517 | + | 0.0773391i | ||||
\(926\) | −0.514536 | −0.0169087 | ||||||||
\(927\) | −13.0918 | + | 3.99367i | −0.429990 | + | 0.131169i | ||||
\(928\) | 27.0927 | 0.889360 | ||||||||
\(929\) | 4.76732 | + | 8.25724i | 0.156411 | + | 0.270911i | 0.933572 | − | 0.358390i | \(-0.116674\pi\) |
−0.777161 | + | 0.629302i | \(0.783341\pi\) | |||||||
\(930\) | 21.1243 | + | 26.5738i | 0.692694 | + | 0.871390i | ||||
\(931\) | −2.66932 | + | 4.62339i | −0.0874833 | + | 0.151526i | ||||
\(932\) | 10.8111 | − | 18.7254i | 0.354130 | − | 0.613372i | ||||
\(933\) | −3.66166 | − | 4.60627i | −0.119877 | − | 0.150802i | ||||
\(934\) | −1.51183 | − | 2.61856i | −0.0494685 | − | 0.0856819i | ||||
\(935\) | 20.6448 | 0.675158 | ||||||||
\(936\) | 4.95329 | − | 1.51101i | 0.161903 | − | 0.0493890i | ||||
\(937\) | −17.8647 | −0.583614 | −0.291807 | − | 0.956477i | \(-0.594256\pi\) | ||||
−0.291807 | + | 0.956477i | \(0.594256\pi\) | |||||||
\(938\) | 22.9134 | + | 39.6871i | 0.748148 | + | 1.29583i | ||||
\(939\) | −38.8814 | + | 5.79854i | −1.26885 | + | 0.189228i | ||||
\(940\) | 41.7070 | − | 72.2386i | 1.36033 | − | 2.35616i | ||||
\(941\) | 24.4390 | − | 42.3296i | 0.796689 | − | 1.37991i | −0.125073 | − | 0.992148i | \(-0.539916\pi\) |
0.921761 | − | 0.387758i | \(-0.126750\pi\) | |||||||
\(942\) | −13.0106 | + | 32.9994i | −0.423909 | + | 1.07518i | ||||
\(943\) | 29.4899 | + | 51.0780i | 0.960323 | + | 1.66333i | ||||
\(944\) | −6.67613 | −0.217290 | ||||||||
\(945\) | −38.6085 | + | 18.3712i | −1.25593 | + | 0.597616i | ||||
\(946\) | −15.4247 | −0.501501 | ||||||||
\(947\) | 23.0552 | + | 39.9328i | 0.749193 | + | 1.29764i | 0.948210 | + | 0.317644i | \(0.102892\pi\) |
−0.199017 | + | 0.979996i | \(0.563775\pi\) | |||||||
\(948\) | −2.38207 | + | 6.04173i | −0.0773660 | + | 0.196226i | ||||
\(949\) | −2.67032 | + | 4.62513i | −0.0866822 | + | 0.150138i | ||||
\(950\) | 25.3725 | − | 43.9464i | 0.823192 | − | 1.42581i | ||||
\(951\) | 25.4412 | − | 3.79415i | 0.824988 | − | 0.123034i | ||||
\(952\) | 9.01556 | + | 15.6154i | 0.292196 | + | 0.506098i | ||||
\(953\) | −44.3793 | −1.43759 | −0.718793 | − | 0.695224i | \(-0.755305\pi\) | ||||
−0.718793 | + | 0.695224i | \(0.755305\pi\) | |||||||
\(954\) | −8.99265 | + | 38.8415i | −0.291148 | + | 1.25754i | ||||
\(955\) | 68.5664 | 2.21876 | ||||||||
\(956\) | −24.6151 | − | 42.6346i | −0.796110 | − | 1.37890i | ||||
\(957\) | 3.78196 | + | 4.75761i | 0.122254 | + | 0.153792i | ||||
\(958\) | −26.8729 | + | 46.5453i | −0.868225 | + | 1.50381i | ||||
\(959\) | 24.9409 | − | 43.1988i | 0.805382 | − | 1.39496i | ||||
\(960\) | 47.1307 | + | 59.2892i | 1.52114 | + | 1.91355i | ||||
\(961\) | 12.3526 | + | 21.3953i | 0.398471 | + | 0.690172i | ||||
\(962\) | −0.891474 | −0.0287423 | ||||||||
\(963\) | 11.2055 | + | 10.4623i | 0.361091 | + | 0.337142i | ||||
\(964\) | 75.0400 | 2.41687 | ||||||||
\(965\) | 3.74080 | + | 6.47925i | 0.120421 | + | 0.208574i | ||||
\(966\) | −49.6153 | + | 7.39932i | −1.59635 | + | 0.238069i | ||||
\(967\) | −11.0831 | + | 19.1965i | −0.356409 | + | 0.617319i | −0.987358 | − | 0.158505i | \(-0.949332\pi\) |
0.630949 | + | 0.775825i | \(0.282666\pi\) | |||||||
\(968\) | −0.696981 | + | 1.20721i | −0.0224018 | + | 0.0388011i | ||||
\(969\) | 10.4758 | − | 26.5702i | 0.336531 | − | 0.853558i | ||||
\(970\) | 9.99553 | + | 17.3128i | 0.320937 | + | 0.555880i | ||||
\(971\) | 23.1985 | 0.744476 | 0.372238 | − | 0.928137i | \(-0.378591\pi\) | ||||
0.372238 | + | 0.928137i | \(0.378591\pi\) | |||||||
\(972\) | 30.4614 | − | 27.8259i | 0.977049 | − | 0.892516i | ||||
\(973\) | 2.92900 | 0.0938996 | ||||||||
\(974\) | 17.2915 | + | 29.9498i | 0.554056 | + | 0.959653i | ||||
\(975\) | −6.39831 | + | 16.2283i | −0.204910 | + | 0.519721i | ||||
\(976\) | 7.17510 | − | 12.4276i | 0.229669 | − | 0.397799i | ||||
\(977\) | −7.78410 | + | 13.4825i | −0.249035 | + | 0.431342i | −0.963258 | − | 0.268576i | \(-0.913447\pi\) |
0.714223 | + | 0.699918i | \(0.246780\pi\) | |||||||
\(978\) | −71.9036 | + | 10.7233i | −2.29922 | + | 0.342892i | ||||
\(979\) | −2.38558 | − | 4.13195i | −0.0762435 | − | 0.132058i | ||||
\(980\) | −17.6901 | −0.565091 | ||||||||
\(981\) | −10.2599 | − | 9.57940i | −0.327573 | − | 0.305847i | ||||
\(982\) | 21.7281 | 0.693371 | ||||||||
\(983\) | −14.7920 | − | 25.6206i | −0.471793 | − | 0.817169i | 0.527686 | − | 0.849439i | \(-0.323060\pi\) |
−0.999479 | + | 0.0322700i | \(0.989726\pi\) | |||||||
\(984\) | 14.9752 | + | 18.8384i | 0.477393 | + | 0.600548i | ||||
\(985\) | 10.8745 | − | 18.8351i | 0.346490 | − | 0.600138i | ||||
\(986\) | 21.5451 | − | 37.3173i | 0.686137 | − | 1.18842i | ||||
\(987\) | −21.2834 | − | 26.7739i | −0.677458 | − | 0.852224i | ||||
\(988\) | 4.74340 | + | 8.21582i | 0.150908 | + | 0.261380i | ||||
\(989\) | −42.3416 | −1.34639 | ||||||||
\(990\) | −5.28598 | + | 22.8315i | −0.168000 | + | 0.725631i | ||||
\(991\) | −7.97155 | −0.253225 | −0.126612 | − | 0.991952i | \(-0.540410\pi\) | ||||
−0.126612 | + | 0.991952i | \(0.540410\pi\) | |||||||
\(992\) | −9.68582 | − | 16.7763i | −0.307525 | − | 0.532649i | ||||
\(993\) | 27.7571 | − | 4.13952i | 0.880845 | − | 0.131364i | ||||
\(994\) | −29.6682 | + | 51.3869i | −0.941019 | + | 1.62989i | ||||
\(995\) | −35.7197 | + | 61.8683i | −1.13239 | + | 1.96136i | ||||
\(996\) | 4.63536 | − | 11.7569i | 0.146877 | − | 0.372530i | ||||
\(997\) | −23.9970 | − | 41.5641i | −0.759994 | − | 1.31635i | −0.942853 | − | 0.333209i | \(-0.891869\pi\) |
0.182860 | − | 0.983139i | \(-0.441465\pi\) | |||||||
\(998\) | 71.6820 | 2.26905 | ||||||||
\(999\) | −1.56696 | + | 0.745611i | −0.0495764 | + | 0.0235901i |
(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 | 99.2.e.e.67.2 | yes | 8 | |
3.2 | odd | 2 | 297.2.e.e.199.3 | 8 | |||
9.2 | odd | 6 | 297.2.e.e.100.3 | 8 | |||
9.4 | even | 3 | 891.2.a.q.1.3 | 4 | |||
9.5 | odd | 6 | 891.2.a.p.1.2 | 4 | |||
9.7 | even | 3 | inner | 99.2.e.e.34.2 | ✓ | 8 | |
11.10 | odd | 2 | 1089.2.e.i.364.3 | 8 | |||
99.32 | even | 6 | 9801.2.a.bl.1.3 | 4 | |||
99.43 | odd | 6 | 1089.2.e.i.727.3 | 8 | |||
99.76 | odd | 6 | 9801.2.a.bi.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.e.e.34.2 | ✓ | 8 | 9.7 | even | 3 | inner | |
99.2.e.e.67.2 | yes | 8 | 1.1 | even | 1 | trivial | |
297.2.e.e.100.3 | 8 | 9.2 | odd | 6 | |||
297.2.e.e.199.3 | 8 | 3.2 | odd | 2 | |||
891.2.a.p.1.2 | 4 | 9.5 | odd | 6 | |||
891.2.a.q.1.3 | 4 | 9.4 | even | 3 | |||
1089.2.e.i.364.3 | 8 | 11.10 | odd | 2 | |||
1089.2.e.i.727.3 | 8 | 99.43 | odd | 6 | |||
9801.2.a.bi.1.2 | 4 | 99.76 | odd | 6 | |||
9801.2.a.bl.1.3 | 4 | 99.32 | even | 6 |