Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,2,Mod(38,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.38");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.f (of order \(6\), 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: | \(1.60499308063\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 38.3 | ||
Character | \(\chi\) | \(=\) | 201.38 |
Dual form | 201.2.f.b.164.3 |
$q$-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 \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22221 | + | 2.11693i | −0.864235 | + | 1.49690i | 0.00357031 | + | 0.999994i | \(0.498864\pi\) |
−0.867805 | + | 0.496905i | \(0.834470\pi\) | |||||||
\(3\) | 1.40479 | − | 1.01319i | 0.811056 | − | 0.584968i | ||||
\(4\) | −1.98761 | − | 3.44264i | −0.993803 | − | 1.72132i | ||||
\(5\) | 0.554650 | 0.248047 | 0.124024 | − | 0.992279i | \(-0.460420\pi\) | ||||
0.124024 | + | 0.992279i | \(0.460420\pi\) | |||||||
\(6\) | 0.427913 | + | 4.21219i | 0.174695 | + | 1.71962i | ||||
\(7\) | 0.273771 | − | 0.158062i | 0.103476 | − | 0.0597418i | −0.447369 | − | 0.894349i | \(-0.647639\pi\) |
0.550845 | + | 0.834608i | \(0.314306\pi\) | |||||||
\(8\) | 4.82826 | 1.70705 | ||||||||
\(9\) | 0.946874 | − | 2.84665i | 0.315625 | − | 0.948884i | ||||
\(10\) | −0.677901 | + | 1.17416i | −0.214371 | + | 0.371301i | ||||
\(11\) | 2.42671 | + | 4.20319i | 0.731681 | + | 1.26731i | 0.956164 | + | 0.292831i | \(0.0945974\pi\) |
−0.224483 | + | 0.974478i | \(0.572069\pi\) | |||||||
\(12\) | −6.28023 | − | 2.82235i | −1.81295 | − | 0.814742i | ||||
\(13\) | 4.34339 | + | 2.50766i | 1.20464 | + | 0.695499i | 0.961583 | − | 0.274513i | \(-0.0885168\pi\) |
0.243056 | + | 0.970012i | \(0.421850\pi\) | |||||||
\(14\) | 0.772741i | 0.206524i | ||||||||
\(15\) | 0.779168 | − | 0.561969i | 0.201180 | − | 0.145100i | ||||
\(16\) | −1.92595 | + | 3.33584i | −0.481487 | + | 0.833960i | ||||
\(17\) | 1.69341 | + | 0.977692i | 0.410713 | + | 0.237125i | 0.691096 | − | 0.722763i | \(-0.257128\pi\) |
−0.280383 | + | 0.959888i | \(0.590462\pi\) | |||||||
\(18\) | 4.86890 | + | 5.48368i | 1.14761 | + | 1.29252i | ||||
\(19\) | 1.70071 | − | 2.94571i | 0.390169 | − | 0.675792i | −0.602303 | − | 0.798268i | \(-0.705750\pi\) |
0.992471 | + | 0.122476i | \(0.0390834\pi\) | |||||||
\(20\) | −1.10243 | − | 1.90946i | −0.246510 | − | 0.426968i | ||||
\(21\) | 0.224444 | − | 0.499427i | 0.0489776 | − | 0.108984i | ||||
\(22\) | −11.8638 | −2.52938 | ||||||||
\(23\) | −4.07208 | − | 2.35102i | −0.849088 | − | 0.490221i | 0.0112553 | − | 0.999937i | \(-0.496417\pi\) |
−0.860343 | + | 0.509716i | \(0.829751\pi\) | |||||||
\(24\) | 6.78270 | − | 4.89197i | 1.38451 | − | 0.998569i | ||||
\(25\) | −4.69236 | −0.938473 | ||||||||
\(26\) | −10.6171 | + | 6.12978i | −2.08218 | + | 1.20215i | ||||
\(27\) | −1.55405 | − | 4.95832i | −0.299078 | − | 0.954229i | ||||
\(28\) | −1.08830 | − | 0.628330i | −0.205669 | − | 0.118743i | ||||
\(29\) | −4.07773 | + | 2.35428i | −0.757216 | + | 0.437179i | −0.828295 | − | 0.560292i | \(-0.810689\pi\) |
0.0710791 | + | 0.997471i | \(0.477356\pi\) | |||||||
\(30\) | 0.237342 | + | 2.33629i | 0.0433326 | + | 0.426547i | ||||
\(31\) | −0.0759515 | + | 0.0438506i | −0.0136413 | + | 0.00787580i | −0.506805 | − | 0.862061i | \(-0.669174\pi\) |
0.493164 | + | 0.869936i | \(0.335840\pi\) | |||||||
\(32\) | 0.120428 | + | 0.208587i | 0.0212888 | + | 0.0368732i | ||||
\(33\) | 7.66767 | + | 3.44587i | 1.33477 | + | 0.599849i | ||||
\(34\) | −4.13942 | + | 2.38989i | −0.709904 | + | 0.409863i | ||||
\(35\) | 0.151847 | − | 0.0876691i | 0.0256669 | − | 0.0148188i | ||||
\(36\) | −11.6820 | + | 2.39828i | −1.94700 | + | 0.399714i | ||||
\(37\) | 2.84485 | − | 4.92742i | 0.467690 | − | 0.810063i | −0.531628 | − | 0.846978i | \(-0.678420\pi\) |
0.999318 | + | 0.0369148i | \(0.0117530\pi\) | |||||||
\(38\) | 4.15725 | + | 7.20056i | 0.674394 | + | 1.16809i | ||||
\(39\) | 8.64230 | − | 0.877965i | 1.38388 | − | 0.140587i | ||||
\(40\) | 2.67800 | 0.423428 | ||||||||
\(41\) | −6.23388 | − | 10.7974i | −0.973569 | − | 1.68627i | −0.684580 | − | 0.728938i | \(-0.740014\pi\) |
−0.288989 | − | 0.957332i | \(-0.593319\pi\) | |||||||
\(42\) | 0.782937 | + | 1.08554i | 0.120810 | + | 0.167502i | ||||
\(43\) | 2.81401i | 0.429132i | 0.976710 | + | 0.214566i | \(0.0688337\pi\) | ||||
−0.976710 | + | 0.214566i | \(0.931166\pi\) | |||||||
\(44\) | 9.64670 | − | 16.7086i | 1.45429 | − | 2.51891i | ||||
\(45\) | 0.525184 | − | 1.57890i | 0.0782898 | − | 0.235368i | ||||
\(46\) | 9.95390 | − | 5.74688i | 1.46762 | − | 0.847332i | ||||
\(47\) | −4.42357 | + | 2.55395i | −0.645244 | + | 0.372532i | −0.786632 | − | 0.617422i | \(-0.788177\pi\) |
0.141388 | + | 0.989954i | \(0.454844\pi\) | |||||||
\(48\) | 0.674301 | + | 6.63751i | 0.0973269 | + | 0.958043i | ||||
\(49\) | −3.45003 | + | 5.97563i | −0.492862 | + | 0.853662i | ||||
\(50\) | 5.73506 | − | 9.93342i | 0.811061 | − | 1.40480i | ||||
\(51\) | 3.36948 | − | 0.342303i | 0.471822 | − | 0.0479321i | ||||
\(52\) | − | 19.9369i | − | 2.76476i | ||||||
\(53\) | 6.20981 | 0.852983 | 0.426492 | − | 0.904491i | \(-0.359749\pi\) | ||||
0.426492 | + | 0.904491i | \(0.359749\pi\) | |||||||
\(54\) | 12.3958 | + | 2.77029i | 1.68686 | + | 0.376989i | ||||
\(55\) | 1.34598 | + | 2.33130i | 0.181491 | + | 0.314352i | ||||
\(56\) | 1.32184 | − | 0.763164i | 0.176638 | − | 0.101982i | ||||
\(57\) | −0.595440 | − | 5.86125i | −0.0788680 | − | 0.776341i | ||||
\(58\) | − | 11.5097i | − | 1.51130i | ||||||
\(59\) | − | 5.28317i | − | 0.687810i | −0.939004 | − | 0.343905i | \(-0.888250\pi\) | ||
0.939004 | − | 0.343905i | \(-0.111750\pi\) | |||||||
\(60\) | −3.48333 | − | 1.56542i | −0.449696 | − | 0.202095i | ||||
\(61\) | 6.01339 | + | 3.47183i | 0.769936 | + | 0.444523i | 0.832852 | − | 0.553496i | \(-0.186707\pi\) |
−0.0629156 | + | 0.998019i | \(0.520040\pi\) | |||||||
\(62\) | − | 0.214379i | − | 0.0272262i | ||||||
\(63\) | −0.190720 | − | 0.928996i | −0.0240285 | − | 0.117042i | ||||
\(64\) | −8.29254 | −1.03657 | ||||||||
\(65\) | 2.40906 | + | 1.39087i | 0.298807 | + | 0.172517i | ||||
\(66\) | −16.6662 | + | 12.0204i | −2.05147 | + | 1.47961i | ||||
\(67\) | −1.06651 | + | 8.11558i | −0.130294 | + | 0.991475i | ||||
\(68\) | − | 7.77307i | − | 0.942623i | ||||||
\(69\) | −8.10246 | + | 0.823124i | −0.975421 | + | 0.0990924i | ||||
\(70\) | 0.428601i | 0.0512276i | ||||||||
\(71\) | −11.2691 | + | 6.50624i | −1.33740 | + | 0.772148i | −0.986421 | − | 0.164235i | \(-0.947484\pi\) |
−0.350978 | + | 0.936384i | \(0.614151\pi\) | |||||||
\(72\) | 4.57175 | − | 13.7444i | 0.538786 | − | 1.61979i | ||||
\(73\) | 4.56635 | − | 7.90915i | 0.534451 | − | 0.925697i | −0.464739 | − | 0.885448i | \(-0.653852\pi\) |
0.999190 | − | 0.0402486i | \(-0.0128150\pi\) | |||||||
\(74\) | 6.95402 | + | 12.0447i | 0.808388 | + | 1.40017i | ||||
\(75\) | −6.59179 | + | 4.75428i | −0.761154 | + | 0.548977i | ||||
\(76\) | −13.5213 | −1.55100 | ||||||||
\(77\) | 1.32873 | + | 0.767141i | 0.151423 | + | 0.0874239i | ||||
\(78\) | −8.70413 | + | 19.3682i | −0.985548 | + | 2.19302i | ||||
\(79\) | −11.7856 | + | 6.80443i | −1.32599 | + | 0.765559i | −0.984676 | − | 0.174392i | \(-0.944204\pi\) |
−0.341310 | + | 0.939951i | \(0.610871\pi\) | |||||||
\(80\) | −1.06823 | + | 1.85022i | −0.119431 | + | 0.206861i | ||||
\(81\) | −7.20686 | − | 5.39084i | −0.800762 | − | 0.598982i | ||||
\(82\) | 30.4765 | 3.36557 | ||||||||
\(83\) | −5.31447 | − | 3.06831i | −0.583339 | − | 0.336791i | 0.179120 | − | 0.983827i | \(-0.442675\pi\) |
−0.762459 | + | 0.647036i | \(0.776008\pi\) | |||||||
\(84\) | −2.16545 | + | 0.219987i | −0.236270 | + | 0.0240025i | ||||
\(85\) | 0.939251 | + | 0.542277i | 0.101876 | + | 0.0588182i | ||||
\(86\) | −5.95706 | − | 3.43931i | −0.642367 | − | 0.370871i | ||||
\(87\) | −3.34302 | + | 7.43881i | −0.358409 | + | 0.797524i | ||||
\(88\) | 11.7168 | + | 20.2941i | 1.24902 | + | 2.16336i | ||||
\(89\) | − | 10.6357i | − | 1.12738i | −0.825986 | − | 0.563691i | \(-0.809381\pi\) | ||
0.825986 | − | 0.563691i | \(-0.190619\pi\) | |||||||
\(90\) | 2.70053 | + | 3.04153i | 0.284661 | + | 0.320605i | ||||
\(91\) | 1.58546 | 0.166201 | ||||||||
\(92\) | 18.6916i | 1.94873i | ||||||||
\(93\) | −0.0622667 | + | 0.138555i | −0.00645676 | + | 0.0143674i | ||||
\(94\) | − | 12.4859i | − | 1.28782i | ||||||
\(95\) | 0.943297 | − | 1.63384i | 0.0967802 | − | 0.167628i | ||||
\(96\) | 0.380514 | + | 0.171004i | 0.0388361 | + | 0.0174530i | ||||
\(97\) | −4.02127 | − | 2.32168i | −0.408298 | − | 0.235731i | 0.281760 | − | 0.959485i | \(-0.409082\pi\) |
−0.690058 | + | 0.723754i | \(0.742415\pi\) | |||||||
\(98\) | −8.43335 | − | 14.6070i | −0.851897 | − | 1.47553i | ||||
\(99\) | 14.2628 | − | 2.92812i | 1.43347 | − | 0.294287i | ||||
\(100\) | 9.32657 | + | 16.1541i | 0.932657 | + | 1.61541i | ||||
\(101\) | −2.63337 | − | 4.56114i | −0.262031 | − | 0.453850i | 0.704751 | − | 0.709455i | \(-0.251059\pi\) |
−0.966781 | + | 0.255605i | \(0.917725\pi\) | |||||||
\(102\) | −3.39359 | + | 7.55134i | −0.336015 | + | 0.747694i | ||||
\(103\) | −0.965658 | − | 1.67257i | −0.0951491 | − | 0.164803i | 0.814522 | − | 0.580133i | \(-0.196999\pi\) |
−0.909671 | + | 0.415330i | \(0.863666\pi\) | |||||||
\(104\) | 20.9710 | + | 12.1076i | 2.05638 | + | 1.18725i | ||||
\(105\) | 0.124488 | − | 0.277007i | 0.0121488 | − | 0.0270332i | ||||
\(106\) | −7.58971 | + | 13.1458i | −0.737178 | + | 1.27683i | ||||
\(107\) | − | 5.69570i | − | 0.550624i | −0.961355 | − | 0.275312i | \(-0.911219\pi\) | ||
0.961355 | − | 0.275312i | \(-0.0887811\pi\) | |||||||
\(108\) | −13.9808 | + | 15.2052i | −1.34531 | + | 1.46312i | ||||
\(109\) | 18.1860i | 1.74191i | 0.491366 | + | 0.870953i | \(0.336498\pi\) | ||||
−0.491366 | + | 0.870953i | \(0.663502\pi\) | |||||||
\(110\) | −6.58028 | −0.627405 | ||||||||
\(111\) | −0.996020 | − | 9.80438i | −0.0945381 | − | 0.930590i | ||||
\(112\) | 1.21768i | 0.115059i | ||||||||
\(113\) | 7.22486 | + | 12.5138i | 0.679658 | + | 1.17720i | 0.975084 | + | 0.221836i | \(0.0712050\pi\) |
−0.295426 | + | 0.955366i | \(0.595462\pi\) | |||||||
\(114\) | 13.1356 | + | 5.90318i | 1.23026 | + | 0.552884i | ||||
\(115\) | −2.25858 | − | 1.30399i | −0.210614 | − | 0.121598i | ||||
\(116\) | 16.2099 | + | 9.35877i | 1.50505 | + | 0.868940i | ||||
\(117\) | 11.2511 | − | 9.98969i | 1.04016 | − | 0.923547i | ||||
\(118\) | 11.1841 | + | 6.45716i | 1.02958 | + | 0.594429i | ||||
\(119\) | 0.618143 | 0.0566651 | ||||||||
\(120\) | 3.76202 | − | 2.71333i | 0.343424 | − | 0.247692i | ||||
\(121\) | −6.27787 | + | 10.8736i | −0.570715 | + | 0.988508i | ||||
\(122\) | −14.6993 | + | 8.48664i | −1.33081 | + | 0.768344i | ||||
\(123\) | −19.6972 | − | 8.85195i | −1.77603 | − | 0.798154i | ||||
\(124\) | 0.301923 | + | 0.174316i | 0.0271135 | + | 0.0156540i | ||||
\(125\) | −5.37587 | −0.480833 | ||||||||
\(126\) | 2.19972 | + | 0.731688i | 0.195967 | + | 0.0651839i | ||||
\(127\) | −7.75428 | − | 13.4308i | −0.688081 | − | 1.19179i | −0.972458 | − | 0.233079i | \(-0.925120\pi\) |
0.284377 | − | 0.958713i | \(-0.408213\pi\) | |||||||
\(128\) | 9.89439 | − | 17.1376i | 0.874549 | − | 1.51476i | ||||
\(129\) | 2.85113 | + | 3.95309i | 0.251028 | + | 0.348050i | ||||
\(130\) | −5.88877 | + | 3.39988i | −0.516479 | + | 0.298190i | ||||
\(131\) | 12.9443i | 1.13095i | 0.824765 | + | 0.565475i | \(0.191307\pi\) | ||||
−0.824765 | + | 0.565475i | \(0.808693\pi\) | |||||||
\(132\) | −3.37744 | − | 33.2460i | −0.293969 | − | 2.89370i | ||||
\(133\) | − | 1.07527i | − | 0.0932374i | ||||||
\(134\) | −15.8766 | − | 12.1767i | −1.37153 | − | 1.05191i | ||||
\(135\) | −0.861956 | − | 2.75013i | −0.0741854 | − | 0.236694i | ||||
\(136\) | 8.17623 | + | 4.72055i | 0.701106 | + | 0.404784i | ||||
\(137\) | 17.2275 | 1.47184 | 0.735922 | − | 0.677066i | \(-0.236749\pi\) | ||||
0.735922 | + | 0.677066i | \(0.236749\pi\) | |||||||
\(138\) | 8.16043 | − | 18.1584i | 0.694662 | − | 1.54575i | ||||
\(139\) | − | 14.5260i | − | 1.23208i | −0.787716 | − | 0.616038i | \(-0.788737\pi\) | ||
0.787716 | − | 0.616038i | \(-0.211263\pi\) | |||||||
\(140\) | −0.603625 | − | 0.348503i | −0.0510156 | − | 0.0294539i | ||||
\(141\) | −3.62654 | + | 8.06970i | −0.305410 | + | 0.679592i | ||||
\(142\) | − | 31.8080i | − | 2.66927i | ||||||
\(143\) | 24.3414i | 2.03553i | ||||||||
\(144\) | 7.67234 | + | 8.64112i | 0.639362 | + | 0.720093i | ||||
\(145\) | −2.26172 | + | 1.30580i | −0.187825 | + | 0.108441i | ||||
\(146\) | 11.1621 | + | 19.3333i | 0.923783 | + | 1.60004i | ||||
\(147\) | 1.20790 | + | 11.8901i | 0.0996263 | + | 0.980676i | ||||
\(148\) | −22.6178 | −1.85917 | ||||||||
\(149\) | 4.68659i | 0.383941i | 0.981401 | + | 0.191970i | \(0.0614878\pi\) | ||||
−0.981401 | + | 0.191970i | \(0.938512\pi\) | |||||||
\(150\) | −2.00793 | − | 19.7651i | −0.163946 | − | 1.61381i | ||||
\(151\) | −1.94998 | + | 3.37747i | −0.158687 | + | 0.274855i | −0.934396 | − | 0.356237i | \(-0.884060\pi\) |
0.775708 | + | 0.631092i | \(0.217393\pi\) | |||||||
\(152\) | 8.21145 | − | 14.2226i | 0.666036 | − | 1.15361i | ||||
\(153\) | 4.38660 | − | 3.89480i | 0.354635 | − | 0.314876i | ||||
\(154\) | −3.24798 | + | 1.87522i | −0.261729 | + | 0.151109i | ||||
\(155\) | −0.0421265 | + | 0.0243218i | −0.00338368 | + | 0.00195357i | ||||
\(156\) | −20.2000 | − | 28.0072i | −1.61729 | − | 2.24237i | ||||
\(157\) | 5.17973 | − | 8.97156i | 0.413388 | − | 0.716008i | −0.581870 | − | 0.813282i | \(-0.697679\pi\) |
0.995258 | + | 0.0972734i | \(0.0310121\pi\) | |||||||
\(158\) | − | 33.2659i | − | 2.64649i | ||||||
\(159\) | 8.72349 | − | 6.29175i | 0.691817 | − | 0.498968i | ||||
\(160\) | 0.0667952 | + | 0.115693i | 0.00528062 | + | 0.00914630i | ||||
\(161\) | −1.48642 | −0.117147 | ||||||||
\(162\) | 20.2204 | − | 8.66770i | 1.58866 | − | 0.680999i | ||||
\(163\) | −7.09012 | − | 12.2804i | −0.555341 | − | 0.961878i | −0.997877 | − | 0.0651278i | \(-0.979254\pi\) |
0.442536 | − | 0.896751i | \(-0.354079\pi\) | |||||||
\(164\) | −24.7810 | + | 42.9220i | −1.93507 | + | 3.35164i | ||||
\(165\) | 4.25288 | + | 1.91125i | 0.331086 | + | 0.148791i | ||||
\(166\) | 12.9908 | − | 7.50026i | 1.00828 | − | 0.582133i | ||||
\(167\) | 15.6696 | − | 9.04683i | 1.21255 | − | 0.700065i | 0.249234 | − | 0.968443i | \(-0.419821\pi\) |
0.963314 | + | 0.268379i | \(0.0864878\pi\) | |||||||
\(168\) | 1.08367 | − | 2.41136i | 0.0836072 | − | 0.186041i | ||||
\(169\) | 6.07669 | + | 10.5251i | 0.467437 | + | 0.809625i | ||||
\(170\) | −2.29593 | + | 1.32556i | −0.176090 | + | 0.101665i | ||||
\(171\) | −6.77505 | − | 7.63053i | −0.518101 | − | 0.583521i | ||||
\(172\) | 9.68759 | − | 5.59314i | 0.738672 | − | 0.426473i | ||||
\(173\) | −3.31248 | − | 1.91246i | −0.251843 | − | 0.145402i | 0.368765 | − | 0.929523i | \(-0.379781\pi\) |
−0.620608 | + | 0.784121i | \(0.713114\pi\) | |||||||
\(174\) | −11.6616 | − | 16.1688i | −0.884063 | − | 1.22575i | ||||
\(175\) | −1.28463 | + | 0.741684i | −0.0971092 | + | 0.0560660i | ||||
\(176\) | −18.6949 | −1.40918 | ||||||||
\(177\) | −5.35288 | − | 7.42175i | −0.402347 | − | 0.557853i | ||||
\(178\) | 22.5151 | + | 12.9991i | 1.68758 | + | 0.974322i | ||||
\(179\) | −15.2614 | −1.14069 | −0.570344 | − | 0.821406i | \(-0.693190\pi\) | ||||
−0.570344 | + | 0.821406i | \(0.693190\pi\) | |||||||
\(180\) | −6.47942 | + | 1.33021i | −0.482948 | + | 0.0991480i | ||||
\(181\) | 11.7000 | + | 20.2649i | 0.869652 | + | 1.50628i | 0.862353 | + | 0.506308i | \(0.168990\pi\) |
0.00729935 | + | 0.999973i | \(0.497677\pi\) | |||||||
\(182\) | −1.93777 | + | 3.35631i | −0.143637 | + | 0.248786i | ||||
\(183\) | 11.9652 | − | 1.21554i | 0.884493 | − | 0.0898551i | ||||
\(184\) | −19.6611 | − | 11.3513i | −1.44943 | − | 0.836831i | ||||
\(185\) | 1.57790 | − | 2.73300i | 0.116009 | − | 0.200934i | ||||
\(186\) | −0.217208 | − | 0.301158i | −0.0159264 | − | 0.0220820i | ||||
\(187\) | 9.49031i | 0.694000i | ||||||||
\(188\) | 17.5846 | + | 10.1525i | 1.28249 | + | 0.740447i | ||||
\(189\) | −1.20918 | − | 1.11181i | −0.0879546 | − | 0.0808721i | ||||
\(190\) | 2.30582 | + | 3.99379i | 0.167282 | + | 0.289740i | ||||
\(191\) | −0.0929143 | + | 0.160932i | −0.00672304 | + | 0.0116447i | −0.869367 | − | 0.494166i | \(-0.835473\pi\) |
0.862644 | + | 0.505811i | \(0.168807\pi\) | |||||||
\(192\) | −11.6493 | + | 8.40196i | −0.840715 | + | 0.606359i | ||||
\(193\) | 9.21072 | 0.663002 | 0.331501 | − | 0.943455i | \(-0.392445\pi\) | ||||
0.331501 | + | 0.943455i | \(0.392445\pi\) | |||||||
\(194\) | 9.82969 | − | 5.67517i | 0.705730 | − | 0.407454i | ||||
\(195\) | 4.79345 | − | 0.486964i | 0.343266 | − | 0.0348722i | ||||
\(196\) | 27.4292 | 1.95923 | ||||||||
\(197\) | 2.07645 | + | 3.59652i | 0.147941 | + | 0.256241i | 0.930466 | − | 0.366377i | \(-0.119402\pi\) |
−0.782525 | + | 0.622619i | \(0.786069\pi\) | |||||||
\(198\) | −11.2335 | + | 33.7722i | −0.798334 | + | 2.40009i | ||||
\(199\) | −9.03504 | + | 15.6491i | −0.640477 | + | 1.10934i | 0.344849 | + | 0.938658i | \(0.387930\pi\) |
−0.985326 | + | 0.170681i | \(0.945403\pi\) | |||||||
\(200\) | −22.6560 | −1.60202 | ||||||||
\(201\) | 6.72444 | + | 12.4813i | 0.474305 | + | 0.880360i | ||||
\(202\) | 12.8742 | 0.905823 | ||||||||
\(203\) | −0.744244 | + | 1.28907i | −0.0522357 | + | 0.0904749i | ||||
\(204\) | −7.87563 | − | 10.9195i | −0.551404 | − | 0.764520i | ||||
\(205\) | −3.45762 | − | 5.98878i | −0.241491 | − | 0.418275i | ||||
\(206\) | 4.72096 | 0.328925 | ||||||||
\(207\) | −10.5483 | + | 9.36568i | −0.733156 | + | 0.650960i | ||||
\(208\) | −16.7303 | + | 9.65923i | −1.16004 | + | 0.669747i | ||||
\(209\) | 16.5085 | 1.14192 | ||||||||
\(210\) | 0.434256 | + | 0.602094i | 0.0299665 | + | 0.0415485i | ||||
\(211\) | 8.36031 | − | 14.4805i | 0.575547 | − | 0.996877i | −0.420435 | − | 0.907323i | \(-0.638122\pi\) |
0.995982 | − | 0.0895544i | \(-0.0285443\pi\) | |||||||
\(212\) | −12.3427 | − | 21.3781i | −0.847698 | − | 1.46826i | ||||
\(213\) | −9.23869 | + | 20.5577i | −0.633024 | + | 1.40859i | ||||
\(214\) | 12.0574 | + | 6.96135i | 0.824228 | + | 0.475868i | ||||
\(215\) | 1.56079i | 0.106445i | ||||||||
\(216\) | −7.50338 | − | 23.9401i | −0.510540 | − | 1.62891i | ||||
\(217\) | −0.0138622 | + | 0.0240101i | −0.000941029 | + | 0.00162991i | ||||
\(218\) | −38.4986 | − | 22.2272i | −2.60746 | − | 1.50542i | ||||
\(219\) | −1.59874 | − | 15.7373i | −0.108033 | − | 1.06343i | ||||
\(220\) | 5.35055 | − | 9.26742i | 0.360734 | − | 0.624809i | ||||
\(221\) | 4.90343 | + | 8.49299i | 0.329840 | + | 0.571300i | ||||
\(222\) | 21.9726 | + | 9.87452i | 1.47470 | + | 0.662735i | ||||
\(223\) | 0.125563 | 0.00840834 | 0.00420417 | − | 0.999991i | \(-0.498662\pi\) | ||||
0.00420417 | + | 0.999991i | \(0.498662\pi\) | |||||||
\(224\) | 0.0659392 | + | 0.0380700i | 0.00440574 | + | 0.00254366i | ||||
\(225\) | −4.44307 | + | 13.3575i | −0.296205 | + | 0.890502i | ||||
\(226\) | −35.3213 | −2.34954 | ||||||||
\(227\) | 4.67009 | − | 2.69628i | 0.309965 | − | 0.178958i | −0.336946 | − | 0.941524i | \(-0.609394\pi\) |
0.646911 | + | 0.762566i | \(0.276061\pi\) | |||||||
\(228\) | −18.9946 | + | 13.6997i | −1.25795 | + | 0.907287i | ||||
\(229\) | −18.4704 | − | 10.6639i | −1.22056 | − | 0.704689i | −0.255521 | − | 0.966804i | \(-0.582247\pi\) |
−0.965037 | + | 0.262114i | \(0.915580\pi\) | |||||||
\(230\) | 5.52093 | − | 3.18751i | 0.364039 | − | 0.210178i | ||||
\(231\) | 2.64385 | − | 0.268587i | 0.173952 | − | 0.0176717i | ||||
\(232\) | −19.6884 | + | 11.3671i | −1.29260 | + | 0.746286i | ||||
\(233\) | −4.37106 | − | 7.57090i | −0.286358 | − | 0.495986i | 0.686580 | − | 0.727054i | \(-0.259111\pi\) |
−0.972938 | + | 0.231068i | \(0.925778\pi\) | |||||||
\(234\) | 7.39631 | + | 36.0273i | 0.483512 | + | 2.35518i | ||||
\(235\) | −2.45354 | + | 1.41655i | −0.160051 | + | 0.0924055i | ||||
\(236\) | −18.1880 | + | 10.5009i | −1.18394 | + | 0.683548i | ||||
\(237\) | −9.66212 | + | 21.4999i | −0.627622 | + | 1.39657i | ||||
\(238\) | −0.755502 | + | 1.30857i | −0.0489719 | + | 0.0848219i | ||||
\(239\) | −1.63739 | − | 2.83604i | −0.105914 | − | 0.183448i | 0.808197 | − | 0.588912i | \(-0.200443\pi\) |
−0.914111 | + | 0.405463i | \(0.867110\pi\) | |||||||
\(240\) | 0.374001 | + | 3.68150i | 0.0241417 | + | 0.237640i | ||||
\(241\) | 22.2128 | 1.43085 | 0.715426 | − | 0.698689i | \(-0.246233\pi\) | ||||
0.715426 | + | 0.698689i | \(0.246233\pi\) | |||||||
\(242\) | −15.3458 | − | 26.5797i | −0.986464 | − | 1.70861i | ||||
\(243\) | −15.5861 | − | 0.271049i | −0.999849 | − | 0.0173878i | ||||
\(244\) | − | 27.6026i | − | 1.76707i | ||||||
\(245\) | −1.91356 | + | 3.31439i | −0.122253 | + | 0.211748i | ||||
\(246\) | 42.8131 | − | 30.8786i | 2.72966 | − | 1.96875i | ||||
\(247\) | 14.7736 | − | 8.52957i | 0.940025 | − | 0.542724i | ||||
\(248\) | −0.366714 | + | 0.211722i | −0.0232863 | + | 0.0134444i | ||||
\(249\) | −10.5745 | + | 1.07426i | −0.670133 | + | 0.0680784i | ||||
\(250\) | 6.57046 | − | 11.3804i | 0.415552 | − | 0.719758i | ||||
\(251\) | −5.06113 | + | 8.76613i | −0.319456 | + | 0.553313i | −0.980375 | − | 0.197144i | \(-0.936833\pi\) |
0.660919 | + | 0.750457i | \(0.270167\pi\) | |||||||
\(252\) | −2.81912 | + | 2.50306i | −0.177588 | + | 0.157678i | ||||
\(253\) | − | 22.8210i | − | 1.43474i | ||||||
\(254\) | 37.9095 | 2.37865 | ||||||||
\(255\) | 1.86888 | − | 0.189859i | 0.117034 | − | 0.0118894i | ||||
\(256\) | 15.8936 | + | 27.5284i | 0.993347 | + | 1.72053i | ||||
\(257\) | 2.18750 | − | 1.26296i | 0.136453 | − | 0.0787810i | −0.430220 | − | 0.902724i | \(-0.641564\pi\) |
0.566672 | + | 0.823943i | \(0.308231\pi\) | |||||||
\(258\) | −11.8531 | + | 1.20415i | −0.737943 | + | 0.0749672i | ||||
\(259\) | − | 1.79865i | − | 0.111763i | ||||||
\(260\) | − | 11.0580i | − | 0.685790i | ||||||
\(261\) | 2.84072 | + | 13.8371i | 0.175836 | + | 0.856495i | ||||
\(262\) | −27.4023 | − | 15.8207i | −1.69292 | − | 0.977406i | ||||
\(263\) | 19.7948i | 1.22060i | 0.792170 | + | 0.610301i | \(0.208951\pi\) | ||||
−0.792170 | + | 0.610301i | \(0.791049\pi\) | |||||||
\(264\) | 37.0215 | + | 16.6376i | 2.27852 | + | 1.02397i | ||||
\(265\) | 3.44427 | 0.211580 | ||||||||
\(266\) | 2.27627 | + | 1.31420i | 0.139567 | + | 0.0805790i | ||||
\(267\) | −10.7760 | − | 14.9409i | −0.659482 | − | 0.914370i | ||||
\(268\) | 30.0588 | − | 12.4590i | 1.83613 | − | 0.761053i | ||||
\(269\) | − | 4.19080i | − | 0.255517i | −0.991805 | − | 0.127759i | \(-0.959222\pi\) | ||
0.991805 | − | 0.127759i | \(-0.0407783\pi\) | |||||||
\(270\) | 6.87534 | + | 1.53654i | 0.418420 | + | 0.0935109i | ||||
\(271\) | 27.5947i | 1.67626i | 0.545474 | + | 0.838128i | \(0.316350\pi\) | ||||
−0.545474 | + | 0.838128i | \(0.683650\pi\) | |||||||
\(272\) | −6.52284 | + | 3.76597i | −0.395505 | + | 0.228345i | ||||
\(273\) | 2.22724 | − | 1.60638i | 0.134799 | − | 0.0972225i | ||||
\(274\) | −21.0557 | + | 36.4695i | −1.27202 | + | 2.20320i | ||||
\(275\) | −11.3870 | − | 19.7229i | −0.686663 | − | 1.18934i | ||||
\(276\) | 18.9382 | + | 26.2578i | 1.13995 | + | 1.58053i | ||||
\(277\) | 18.3013 | 1.09962 | 0.549809 | − | 0.835290i | \(-0.314700\pi\) | ||||
0.549809 | + | 0.835290i | \(0.314700\pi\) | |||||||
\(278\) | 30.7505 | + | 17.7538i | 1.84429 | + | 1.06480i | ||||
\(279\) | 0.0529110 | + | 0.257728i | 0.00316770 | + | 0.0154298i | ||||
\(280\) | 0.733158 | − | 0.423289i | 0.0438146 | − | 0.0252964i | ||||
\(281\) | 11.5843 | − | 20.0646i | 0.691063 | − | 1.19696i | −0.280427 | − | 0.959875i | \(-0.590476\pi\) |
0.971490 | − | 0.237081i | \(-0.0761906\pi\) | |||||||
\(282\) | −12.6506 | − | 17.5400i | −0.753334 | − | 1.04449i | ||||
\(283\) | 1.87184 | 0.111269 | 0.0556346 | − | 0.998451i | \(-0.482282\pi\) | ||||
0.0556346 | + | 0.998451i | \(0.482282\pi\) | |||||||
\(284\) | 44.7972 | + | 25.8637i | 2.65822 | + | 1.53473i | ||||
\(285\) | −0.330261 | − | 3.25094i | −0.0195630 | − | 0.192569i | ||||
\(286\) | −51.5292 | − | 29.7504i | −3.04699 | − | 1.75918i | ||||
\(287\) | −3.41331 | − | 1.97068i | −0.201482 | − | 0.116325i | ||||
\(288\) | 0.707803 | − | 0.145310i | 0.0417077 | − | 0.00856248i | ||||
\(289\) | −6.58824 | − | 11.4112i | −0.387543 | − | 0.671245i | ||||
\(290\) | − | 6.38387i | − | 0.374874i | ||||||
\(291\) | −8.00135 | + | 0.812852i | −0.469048 | + | 0.0476502i | ||||
\(292\) | −36.3045 | −2.12456 | ||||||||
\(293\) | 9.42262i | 0.550475i | 0.961376 | + | 0.275238i | \(0.0887565\pi\) | ||||
−0.961376 | + | 0.275238i | \(0.911244\pi\) | |||||||
\(294\) | −26.6468 | − | 11.9751i | −1.55407 | − | 0.698404i | ||||
\(295\) | − | 2.93031i | − | 0.170609i | ||||||
\(296\) | 13.7357 | − | 23.7909i | 0.798369 | − | 1.38282i | ||||
\(297\) | 17.0695 | − | 18.5644i | 0.990473 | − | 1.07722i | ||||
\(298\) | −9.92121 | − | 5.72801i | −0.574720 | − | 0.331815i | ||||
\(299\) | −11.7911 | − | 20.4228i | −0.681896 | − | 1.18108i | ||||
\(300\) | 29.4691 | + | 13.2435i | 1.70140 | + | 0.764613i | ||||
\(301\) | 0.444787 | + | 0.770393i | 0.0256371 | + | 0.0444047i | ||||
\(302\) | −4.76659 | − | 8.25597i | −0.274286 | − | 0.475078i | ||||
\(303\) | −8.32066 | − | 3.73932i | −0.478009 | − | 0.214819i | ||||
\(304\) | 6.55094 | + | 11.3466i | 0.375722 | + | 0.650770i | ||||
\(305\) | 3.33533 | + | 1.92565i | 0.190980 | + | 0.110263i | ||||
\(306\) | 2.88369 | + | 14.0464i | 0.164850 | + | 0.802980i | ||||
\(307\) | −15.5499 | + | 26.9332i | −0.887480 | + | 1.53716i | −0.0446359 | + | 0.999003i | \(0.514213\pi\) |
−0.842844 | + | 0.538158i | \(0.819121\pi\) | |||||||
\(308\) | − | 6.09910i | − | 0.347529i | ||||||
\(309\) | −3.05118 | − | 1.37121i | −0.173576 | − | 0.0780054i | ||||
\(310\) | − | 0.118905i | − | 0.00675337i | ||||||
\(311\) | 18.6474 | 1.05740 | 0.528698 | − | 0.848810i | \(-0.322680\pi\) | ||||
0.528698 | + | 0.848810i | \(0.322680\pi\) | |||||||
\(312\) | 41.7273 | − | 4.23905i | 2.36234 | − | 0.239989i | ||||
\(313\) | − | 10.5279i | − | 0.595073i | −0.954710 | − | 0.297537i | \(-0.903835\pi\) | ||
0.954710 | − | 0.297537i | \(-0.0961650\pi\) | |||||||
\(314\) | 12.6615 | + | 21.9303i | 0.714528 | + | 1.23760i | ||||
\(315\) | −0.105783 | − | 0.515268i | −0.00596021 | − | 0.0290321i | ||||
\(316\) | 46.8504 | + | 27.0491i | 2.63554 | + | 1.52163i | ||||
\(317\) | 20.9867 | + | 12.1167i | 1.17873 | + | 0.680541i | 0.955721 | − | 0.294275i | \(-0.0950782\pi\) |
0.223011 | + | 0.974816i | \(0.428412\pi\) | |||||||
\(318\) | 2.65726 | + | 26.1569i | 0.149012 | + | 1.46681i | ||||
\(319\) | −19.7910 | − | 11.4263i | −1.10808 | − | 0.639752i | ||||
\(320\) | −4.59946 | −0.257118 | ||||||||
\(321\) | −5.77085 | − | 8.00126i | −0.322097 | − | 0.446587i | ||||
\(322\) | 1.81673 | − | 3.14666i | 0.101242 | − | 0.175357i | ||||
\(323\) | 5.75999 | − | 3.32553i | 0.320494 | − | 0.185037i | ||||
\(324\) | −4.23429 | + | 35.5255i | −0.235238 | + | 1.97364i | ||||
\(325\) | −20.3808 | − | 11.7668i | −1.13052 | − | 0.652707i | ||||
\(326\) | 34.6625 | 1.91978 | ||||||||
\(327\) | 18.4260 | + | 25.5476i | 1.01896 | + | 1.41278i | ||||
\(328\) | −30.0988 | − | 52.1327i | −1.66193 | − | 2.87854i | ||||
\(329\) | −0.807364 | + | 1.39840i | −0.0445114 | + | 0.0770961i | ||||
\(330\) | −9.24391 | + | 6.66710i | −0.508861 | + | 0.367012i | ||||
\(331\) | −11.6099 | + | 6.70295i | −0.638135 | + | 0.368428i | −0.783896 | − | 0.620892i | \(-0.786770\pi\) |
0.145760 | + | 0.989320i | \(0.453437\pi\) | |||||||
\(332\) | 24.3944i | 1.33882i | ||||||||
\(333\) | −11.3329 | − | 12.7639i | −0.621041 | − | 0.699459i | ||||
\(334\) | 44.2286i | 2.42008i | ||||||||
\(335\) | −0.591538 | + | 4.50131i | −0.0323192 | + | 0.245933i | ||||
\(336\) | 1.23374 | + | 1.71058i | 0.0673061 | + | 0.0933197i | ||||
\(337\) | 7.18974 | + | 4.15100i | 0.391650 | + | 0.226119i | 0.682875 | − | 0.730535i | \(-0.260729\pi\) |
−0.291225 | + | 0.956655i | \(0.594063\pi\) | |||||||
\(338\) | −29.7080 | −1.61590 | ||||||||
\(339\) | 22.8284 | + | 10.2591i | 1.23987 | + | 0.557199i | ||||
\(340\) | − | 4.31133i | − | 0.233815i | ||||||
\(341\) | −0.368625 | − | 0.212826i | −0.0199622 | − | 0.0115252i | ||||
\(342\) | 24.4339 | − | 5.01621i | 1.32123 | − | 0.271246i | ||||
\(343\) | 4.39414i | 0.237261i | ||||||||
\(344\) | 13.5868i | 0.732549i | ||||||||
\(345\) | −4.49403 | + | 0.456546i | −0.241951 | + | 0.0245796i | ||||
\(346\) | 8.09712 | − | 4.67487i | 0.435304 | − | 0.251323i | ||||
\(347\) | −10.2571 | − | 17.7658i | −0.550629 | − | 0.953717i | −0.998229 | − | 0.0594833i | \(-0.981055\pi\) |
0.447601 | − | 0.894234i | \(-0.352279\pi\) | |||||||
\(348\) | 32.2537 | − | 3.27663i | 1.72898 | − | 0.175646i | ||||
\(349\) | 16.8339 | 0.901099 | 0.450549 | − | 0.892752i | \(-0.351228\pi\) | ||||
0.450549 | + | 0.892752i | \(0.351228\pi\) | |||||||
\(350\) | − | 3.62598i | − | 0.193817i | ||||||
\(351\) | 5.68390 | − | 25.4329i | 0.303384 | − | 1.35751i | ||||
\(352\) | −0.584486 | + | 1.01236i | −0.0311532 | + | 0.0539589i | ||||
\(353\) | 8.11194 | − | 14.0503i | 0.431755 | − | 0.747822i | −0.565269 | − | 0.824906i | \(-0.691228\pi\) |
0.997025 | + | 0.0770845i | \(0.0245611\pi\) | |||||||
\(354\) | 22.2537 | − | 2.26074i | 1.18277 | − | 0.120157i | ||||
\(355\) | −6.25043 | + | 3.60869i | −0.331738 | + | 0.191529i | ||||
\(356\) | −36.6148 | + | 21.1396i | −1.94058 | + | 1.12040i | ||||
\(357\) | 0.868362 | − | 0.626299i | 0.0459586 | − | 0.0331473i | ||||
\(358\) | 18.6526 | − | 32.3073i | 0.985822 | − | 1.70749i | ||||
\(359\) | − | 19.1819i | − | 1.01238i | −0.862421 | − | 0.506192i | \(-0.831053\pi\) | ||
0.862421 | − | 0.506192i | \(-0.168947\pi\) | |||||||
\(360\) | 2.53572 | − | 7.62333i | 0.133644 | − | 0.401785i | ||||
\(361\) | 3.71520 | + | 6.43492i | 0.195537 | + | 0.338680i | ||||
\(362\) | −57.1994 | −3.00633 | ||||||||
\(363\) | 2.19797 | + | 21.6358i | 0.115363 | + | 1.13559i | ||||
\(364\) | −3.15127 | − | 5.45816i | −0.165171 | − | 0.286085i | ||||
\(365\) | 2.53273 | − | 4.38682i | 0.132569 | − | 0.229616i | ||||
\(366\) | −12.0508 | + | 26.8152i | −0.629906 | + | 1.40165i | ||||
\(367\) | −10.0787 | + | 5.81895i | −0.526105 | + | 0.303747i | −0.739429 | − | 0.673235i | \(-0.764904\pi\) |
0.213324 | + | 0.976982i | \(0.431571\pi\) | |||||||
\(368\) | 15.6852 | − | 9.05587i | 0.817649 | − | 0.472070i | ||||
\(369\) | −36.6391 | + | 7.52192i | −1.90736 | + | 0.391576i | ||||
\(370\) | 3.85705 | + | 6.68060i | 0.200518 | + | 0.347308i | ||||
\(371\) | 1.70007 | − | 0.981534i | 0.0882631 | − | 0.0509587i | ||||
\(372\) | 0.600755 | − | 0.0610303i | 0.0311477 | − | 0.00316427i | ||||
\(373\) | −24.5353 | + | 14.1655i | −1.27039 | + | 0.733460i | −0.975061 | − | 0.221935i | \(-0.928763\pi\) |
−0.295329 | + | 0.955396i | \(0.595429\pi\) | |||||||
\(374\) | −20.0904 | − | 11.5992i | −1.03885 | − | 0.599779i | ||||
\(375\) | −7.55198 | + | 5.44680i | −0.389982 | + | 0.281272i | ||||
\(376\) | −21.3582 | + | 12.3311i | −1.10146 | + | 0.635930i | ||||
\(377\) | −23.6149 | −1.21623 | ||||||||
\(378\) | 3.83149 | − | 1.20088i | 0.197071 | − | 0.0617666i | ||||
\(379\) | −5.46399 | − | 3.15464i | −0.280667 | − | 0.162043i | 0.353059 | − | 0.935601i | \(-0.385142\pi\) |
−0.633725 | + | 0.773558i | \(0.718475\pi\) | |||||||
\(380\) | −7.49961 | −0.384722 | ||||||||
\(381\) | −24.5012 | − | 11.0109i | −1.25523 | − | 0.564104i | ||||
\(382\) | −0.227122 | − | 0.393387i | −0.0116206 | − | 0.0201274i | ||||
\(383\) | 8.10051 | − | 14.0305i | 0.413917 | − | 0.716925i | −0.581397 | − | 0.813620i | \(-0.697494\pi\) |
0.995314 | + | 0.0966951i | \(0.0308272\pi\) | |||||||
\(384\) | −3.46416 | − | 34.0997i | −0.176780 | − | 1.74014i | ||||
\(385\) | 0.736979 | + | 0.425495i | 0.0375599 | + | 0.0216852i | ||||
\(386\) | −11.2575 | + | 19.4985i | −0.572990 | + | 0.992447i | ||||
\(387\) | 8.01050 | + | 2.66451i | 0.407196 | + | 0.135445i | ||||
\(388\) | 18.4583i | 0.937080i | ||||||||
\(389\) | −2.73555 | − | 1.57937i | −0.138698 | − | 0.0800773i | 0.429045 | − | 0.903283i | \(-0.358850\pi\) |
−0.567743 | + | 0.823206i | \(0.692183\pi\) | |||||||
\(390\) | −4.82775 | + | 10.7426i | −0.244462 | + | 0.543973i | ||||
\(391\) | −4.59714 | − | 7.96248i | −0.232487 | − | 0.402680i | ||||
\(392\) | −16.6577 | + | 28.8519i | −0.841339 | + | 1.45724i | ||||
\(393\) | 13.1151 | + | 18.1841i | 0.661570 | + | 0.917264i | ||||
\(394\) | −10.1515 | −0.511423 | ||||||||
\(395\) | −6.53690 | + | 3.77408i | −0.328907 | + | 0.189895i | ||||
\(396\) | −38.4293 | − | 43.2817i | −1.93115 | − | 2.17499i | ||||
\(397\) | 24.6917 | 1.23924 | 0.619621 | − | 0.784901i | \(-0.287286\pi\) | ||||
0.619621 | + | 0.784901i | \(0.287286\pi\) | |||||||
\(398\) | −22.0855 | − | 38.2532i | −1.10704 | − | 1.91746i | ||||
\(399\) | −1.08945 | − | 1.51052i | −0.0545409 | − | 0.0756208i | ||||
\(400\) | 9.03724 | − | 15.6530i | 0.451862 | − | 0.782648i | ||||
\(401\) | 6.63572 | 0.331372 | 0.165686 | − | 0.986179i | \(-0.447016\pi\) | ||||
0.165686 | + | 0.986179i | \(0.447016\pi\) | |||||||
\(402\) | −34.6407 | − | 1.01956i | −1.72772 | − | 0.0508511i | ||||
\(403\) | −0.439849 | −0.0219104 | ||||||||
\(404\) | −10.4682 | + | 18.1315i | −0.520814 | + | 0.902076i | ||||
\(405\) | −3.99729 | − | 2.99003i | −0.198627 | − | 0.148576i | ||||
\(406\) | −1.81925 | − | 3.15103i | −0.0902878 | − | 0.156383i | ||||
\(407\) | 27.6145 | 1.36880 | ||||||||
\(408\) | 16.2687 | − | 1.65273i | 0.805422 | − | 0.0818223i | ||||
\(409\) | 22.1899 | − | 12.8113i | 1.09722 | − | 0.633480i | 0.161730 | − | 0.986835i | \(-0.448293\pi\) |
0.935489 | + | 0.353355i | \(0.114959\pi\) | |||||||
\(410\) | 16.9038 | 0.834819 | ||||||||
\(411\) | 24.2010 | − | 17.4548i | 1.19375 | − | 0.860982i | ||||
\(412\) | −3.83870 | + | 6.64882i | −0.189119 | + | 0.327564i | ||||
\(413\) | −0.835068 | − | 1.44638i | −0.0410910 | − | 0.0711717i | ||||
\(414\) | −6.93430 | − | 33.7769i | −0.340802 | − | 1.66004i | ||||
\(415\) | −2.94767 | − | 1.70184i | −0.144696 | − | 0.0835401i | ||||
\(416\) | 1.20796i | 0.0592253i | ||||||||
\(417\) | −14.7176 | − | 20.4059i | −0.720726 | − | 0.999283i | ||||
\(418\) | −20.1769 | + | 34.9474i | −0.986884 | + | 1.70933i | ||||
\(419\) | 8.79700 | + | 5.07895i | 0.429761 | + | 0.248123i | 0.699245 | − | 0.714882i | \(-0.253520\pi\) |
−0.269484 | + | 0.963005i | \(0.586853\pi\) | |||||||
\(420\) | −1.20107 | + | 0.122016i | −0.0586061 | + | 0.00595376i | ||||
\(421\) | −0.461960 | + | 0.800138i | −0.0225146 | + | 0.0389963i | −0.877063 | − | 0.480375i | \(-0.840501\pi\) |
0.854549 | + | 0.519371i | \(0.173834\pi\) | |||||||
\(422\) | 20.4361 | + | 35.3964i | 0.994816 | + | 1.72307i | ||||
\(423\) | 3.08165 | + | 15.0106i | 0.149835 | + | 0.729842i | ||||
\(424\) | 29.9826 | 1.45608 | ||||||||
\(425\) | −7.94610 | − | 4.58768i | −0.385443 | − | 0.222535i | ||||
\(426\) | −32.2277 | − | 44.6836i | −1.56144 | − | 2.16493i | ||||
\(427\) | 2.19506 | 0.106226 | ||||||||
\(428\) | −19.6082 | + | 11.3208i | −0.947799 | + | 0.547212i | ||||
\(429\) | 24.6626 | + | 34.1946i | 1.19072 | + | 1.65093i | ||||
\(430\) | −3.30409 | − | 1.90762i | −0.159337 | − | 0.0919934i | ||||
\(431\) | 2.96212 | − | 1.71018i | 0.142680 | − | 0.0823766i | −0.426960 | − | 0.904270i | \(-0.640416\pi\) |
0.569641 | + | 0.821894i | \(0.307082\pi\) | |||||||
\(432\) | 19.5332 | + | 4.36539i | 0.939790 | + | 0.210030i | ||||
\(433\) | 13.9947 | − | 8.07984i | 0.672542 | − | 0.388293i | −0.124497 | − | 0.992220i | \(-0.539732\pi\) |
0.797039 | + | 0.603927i | \(0.206398\pi\) | |||||||
\(434\) | −0.0338852 | − | 0.0586908i | −0.00162654 | − | 0.00281725i | ||||
\(435\) | −1.85421 | + | 4.12594i | −0.0889024 | + | 0.197824i | ||||
\(436\) | 62.6079 | − | 36.1467i | 2.99838 | − | 1.73111i | ||||
\(437\) | −13.8508 | + | 7.99677i | −0.662574 | + | 0.382538i | ||||
\(438\) | 35.2689 | + | 15.8499i | 1.68521 | + | 0.757338i | ||||
\(439\) | −9.74150 | + | 16.8728i | −0.464937 | + | 0.805294i | −0.999199 | − | 0.0400251i | \(-0.987256\pi\) |
0.534262 | + | 0.845319i | \(0.320590\pi\) | |||||||
\(440\) | 6.49873 | + | 11.2561i | 0.309815 | + | 0.536615i | ||||
\(441\) | 13.7438 | + | 15.4792i | 0.654467 | + | 0.737105i | ||||
\(442\) | −23.9721 | −1.14024 | ||||||||
\(443\) | 5.35484 | + | 9.27486i | 0.254416 | + | 0.440662i | 0.964737 | − | 0.263217i | \(-0.0847834\pi\) |
−0.710321 | + | 0.703878i | \(0.751450\pi\) | |||||||
\(444\) | −31.7732 | + | 22.9162i | −1.50789 | + | 1.08755i | ||||
\(445\) | − | 5.89909i | − | 0.279644i | ||||||
\(446\) | −0.153465 | + | 0.265809i | −0.00726678 | + | 0.0125864i | ||||
\(447\) | 4.74843 | + | 6.58368i | 0.224593 | + | 0.311398i | ||||
\(448\) | −2.27026 | + | 1.31073i | −0.107260 | + | 0.0619264i | ||||
\(449\) | −25.7361 | + | 14.8588i | −1.21456 | + | 0.701228i | −0.963750 | − | 0.266807i | \(-0.914031\pi\) |
−0.250813 | + | 0.968035i | \(0.580698\pi\) | |||||||
\(450\) | −22.8466 | − | 25.7314i | −1.07700 | − | 1.21299i | ||||
\(451\) | 30.2557 | − | 52.4044i | 1.42468 | − | 2.46763i | ||||
\(452\) | 28.7204 | − | 49.7451i | 1.35089 | − | 2.33981i | ||||
\(453\) | 0.682716 | + | 6.72035i | 0.0320768 | + | 0.315750i | ||||
\(454\) | 13.1817i | 0.618648i | ||||||||
\(455\) | 0.879376 | 0.0412258 | ||||||||
\(456\) | −2.87494 | − | 28.2996i | −0.134631 | − | 1.32525i | ||||
\(457\) | 2.03063 | + | 3.51716i | 0.0949889 | + | 0.164526i | 0.909604 | − | 0.415476i | \(-0.136385\pi\) |
−0.814615 | + | 0.580002i | \(0.803052\pi\) | |||||||
\(458\) | 45.1495 | − | 26.0671i | 2.10970 | − | 1.21803i | ||||
\(459\) | 2.21605 | − | 9.91586i | 0.103437 | − | 0.462833i | ||||
\(460\) | 10.3673i | 0.483378i | ||||||||
\(461\) | − | 6.54079i | − | 0.304635i | −0.988332 | − | 0.152318i | \(-0.951326\pi\) | ||
0.988332 | − | 0.152318i | \(-0.0486736\pi\) | |||||||
\(462\) | −2.66276 | + | 5.92512i | −0.123883 | + | 0.275662i | ||||
\(463\) | 16.6896 | + | 9.63572i | 0.775629 | + | 0.447810i | 0.834879 | − | 0.550433i | \(-0.185538\pi\) |
−0.0592498 | + | 0.998243i | \(0.518871\pi\) | |||||||
\(464\) | − | 18.1369i | − | 0.841984i | ||||||
\(465\) | −0.0345363 | + | 0.0768493i | −0.00160158 | + | 0.00356380i | ||||
\(466\) | 21.3695 | 0.989921 | ||||||||
\(467\) | 4.90194 | + | 2.83014i | 0.226835 | + | 0.130963i | 0.609111 | − | 0.793085i | \(-0.291526\pi\) |
−0.382276 | + | 0.924048i | \(0.624860\pi\) | |||||||
\(468\) | −56.7535 | − | 18.8778i | −2.62343 | − | 0.872625i | ||||
\(469\) | 0.990784 | + | 2.39038i | 0.0457502 | + | 0.110378i | ||||
\(470\) | − | 6.92530i | − | 0.319440i | ||||||
\(471\) | −1.81350 | − | 17.8512i | −0.0835615 | − | 0.822542i | ||||
\(472\) | − | 25.5085i | − | 1.17412i | ||||||
\(473\) | −11.8278 | + | 6.82878i | −0.543843 | + | 0.313988i | ||||
\(474\) | −33.7048 | − | 46.7316i | −1.54811 | − | 2.14645i | ||||
\(475\) | −7.98033 | + | 13.8223i | −0.366162 | + | 0.634212i | ||||
\(476\) | −1.22863 | − | 2.12804i | −0.0563139 | − | 0.0975386i | ||||
\(477\) | 5.87991 | − | 17.6772i | 0.269222 | − | 0.809382i | ||||
\(478\) | 8.00496 | 0.366138 | ||||||||
\(479\) | 3.26198 | + | 1.88330i | 0.149043 | + | 0.0860503i | 0.572667 | − | 0.819788i | \(-0.305909\pi\) |
−0.423624 | + | 0.905838i | \(0.639242\pi\) | |||||||
\(480\) | 0.211052 | + | 0.0948474i | 0.00963318 | + | 0.00432917i | ||||
\(481\) | 24.7126 | − | 14.2678i | 1.12680 | − | 0.650556i | ||||
\(482\) | −27.1487 | + | 47.0230i | −1.23659 | + | 2.14184i | ||||
\(483\) | −2.08812 | + | 1.50604i | −0.0950125 | + | 0.0685271i | ||||
\(484\) | 49.9117 | 2.26871 | ||||||||
\(485\) | −2.23040 | − | 1.28772i | −0.101277 | − | 0.0584724i | ||||
\(486\) | 19.6233 | − | 32.6635i | 0.890132 | − | 1.48165i | ||||
\(487\) | −7.53258 | − | 4.34894i | −0.341334 | − | 0.197069i | 0.319528 | − | 0.947577i | \(-0.396476\pi\) |
−0.660862 | + | 0.750508i | \(0.729809\pi\) | |||||||
\(488\) | 29.0342 | + | 16.7629i | 1.31432 | + | 0.758822i | ||||
\(489\) | −22.4026 | − | 10.0678i | −1.01308 | − | 0.455281i | ||||
\(490\) | −4.67756 | − | 8.10177i | −0.211311 | − | 0.366001i | ||||
\(491\) | − | 20.5724i | − | 0.928421i | −0.885725 | − | 0.464211i | \(-0.846338\pi\) | ||
0.885725 | − | 0.464211i | \(-0.153662\pi\) | |||||||
\(492\) | 8.67617 | + | 85.4044i | 0.391152 | + | 3.85033i | ||||
\(493\) | −9.20705 | −0.414664 | ||||||||
\(494\) | 41.6998i | 1.87616i | ||||||||
\(495\) | 7.91087 | − | 1.62408i | 0.355567 | − | 0.0729971i | ||||
\(496\) | − | 0.337816i | − | 0.0151684i | ||||||
\(497\) | −2.05678 | + | 3.56244i | −0.0922590 | + | 0.159797i | ||||
\(498\) | 10.6502 | − | 23.6985i | 0.477246 | − | 1.06196i | ||||
\(499\) | −19.4497 | − | 11.2293i | −0.870688 | − | 0.502692i | −0.00311098 | − | 0.999995i | \(-0.500990\pi\) |
−0.867577 | + | 0.497303i | \(0.834324\pi\) | |||||||
\(500\) | 10.6851 | + | 18.5072i | 0.477853 | + | 0.827666i | ||||
\(501\) | 12.8463 | − | 28.5852i | 0.573929 | − | 1.27709i | ||||
\(502\) | −12.3715 | − | 21.4282i | −0.552169 | − | 0.956385i | ||||
\(503\) | 6.78638 | + | 11.7543i | 0.302590 | + | 0.524100i | 0.976722 | − | 0.214510i | \(-0.0688155\pi\) |
−0.674132 | + | 0.738611i | \(0.735482\pi\) | |||||||
\(504\) | −0.920848 | − | 4.48543i | −0.0410178 | − | 0.199797i | ||||
\(505\) | −1.46060 | − | 2.52984i | −0.0649959 | − | 0.112576i | ||||
\(506\) | 48.3105 | + | 27.8921i | 2.14766 | + | 1.23995i | ||||
\(507\) | 19.2005 | + | 8.62874i | 0.852723 | + | 0.383216i | ||||
\(508\) | −30.8249 | + | 53.3903i | −1.36763 | + | 2.36881i | ||||
\(509\) | 23.8855i | 1.05871i | 0.848401 | + | 0.529354i | \(0.177566\pi\) | ||||
−0.848401 | + | 0.529354i | \(0.822434\pi\) | |||||||
\(510\) | −1.88225 | + | 4.18835i | −0.0833476 | + | 0.185463i | ||||
\(511\) | − | 2.88706i | − | 0.127716i | ||||||
\(512\) | −38.1236 | −1.68484 | ||||||||
\(513\) | −17.2487 | − | 3.85485i | −0.761551 | − | 0.170196i | ||||
\(514\) | 6.17440i | 0.272341i | ||||||||
\(515\) | −0.535602 | − | 0.927691i | −0.0236015 | − | 0.0408789i | ||||
\(516\) | 7.94211 | − | 17.6726i | 0.349632 | − | 0.777993i | ||||
\(517\) | −21.4695 | − | 12.3954i | −0.944226 | − | 0.545149i | ||||
\(518\) | 3.80762 | + | 2.19833i | 0.167297 | + | 0.0965890i | ||||
\(519\) | −6.59104 | + | 0.669580i | −0.289315 | + | 0.0293913i | ||||
\(520\) | 11.6316 | + | 6.71550i | 0.510079 | + | 0.294494i | ||||
\(521\) | −19.0625 | −0.835142 | −0.417571 | − | 0.908644i | \(-0.637118\pi\) | ||||
−0.417571 | + | 0.908644i | \(0.637118\pi\) | |||||||
\(522\) | −32.7642 | − | 10.8983i | −1.43405 | − | 0.477004i | ||||
\(523\) | 1.61705 | − | 2.80081i | 0.0707086 | − | 0.122471i | −0.828503 | − | 0.559984i | \(-0.810807\pi\) |
0.899212 | + | 0.437513i | \(0.144141\pi\) | |||||||
\(524\) | 44.5626 | − | 25.7282i | 1.94672 | − | 1.12394i | ||||
\(525\) | −1.05317 | + | 2.34349i | −0.0459642 | + | 0.102278i | ||||
\(526\) | −41.9044 | − | 24.1935i | −1.82712 | − | 1.05489i | ||||
\(527\) | −0.171490 | −0.00747020 | ||||||||
\(528\) | −26.2624 | + | 18.9416i | −1.14292 | + | 0.824325i | ||||
\(529\) | −0.445437 | − | 0.771520i | −0.0193668 | − | 0.0335443i | ||||
\(530\) | −4.20964 | + | 7.29130i | −0.182855 | + | 0.316714i | ||||
\(531\) | −15.0393 | − | 5.00249i | −0.652652 | − | 0.217090i | ||||
\(532\) | −3.70175 | + | 2.13721i | −0.160491 | + | 0.0926597i | ||||
\(533\) | − | 62.5297i | − | 2.70846i | ||||||
\(534\) | 44.7996 | − | 4.55116i | 1.93867 | − | 0.196948i | ||||
\(535\) | − | 3.15912i | − | 0.136581i | ||||||
\(536\) | −5.14937 | + | 39.1841i | −0.222419 | + | 1.69250i | ||||
\(537\) | −21.4390 | + | 15.4627i | −0.925162 | + | 0.667266i | ||||
\(538\) | 8.87164 | + | 5.12204i | 0.382484 | + | 0.220827i | ||||
\(539\) | −33.4890 | −1.44247 | ||||||||
\(540\) | −7.75447 | + | 8.43358i | −0.333699 | + | 0.362924i | ||||
\(541\) | − | 34.8913i | − | 1.50009i | −0.661384 | − | 0.750047i | \(-0.730031\pi\) | ||
0.661384 | − | 0.750047i | \(-0.269969\pi\) | |||||||
\(542\) | −58.4161 | − | 33.7265i | −2.50918 | − | 1.44868i | ||||
\(543\) | 36.9683 | + | 16.6137i | 1.58646 | + | 0.712960i | ||||
\(544\) | 0.470964i | 0.0201924i | ||||||||
\(545\) | 10.0869i | 0.432075i | ||||||||
\(546\) | 0.678439 | + | 6.67825i | 0.0290345 | + | 0.285803i | ||||
\(547\) | 34.5288 | − | 19.9352i | 1.47635 | − | 0.852368i | 0.476702 | − | 0.879065i | \(-0.341832\pi\) |
0.999644 | + | 0.0266968i | \(0.00849886\pi\) | |||||||
\(548\) | −34.2415 | − | 59.3080i | −1.46272 | − | 2.53351i | ||||
\(549\) | 15.5770 | − | 13.8307i | 0.664811 | − | 0.590278i | ||||
\(550\) | 55.6694 | 2.37375 | ||||||||
\(551\) | 16.0158i | 0.682294i | ||||||||
\(552\) | −39.1208 | + | 3.97426i | −1.66509 | + | 0.169156i | ||||
\(553\) | −2.15104 | + | 3.72572i | −0.0914716 | + | 0.158434i | ||||
\(554\) | −22.3681 | + | 38.7427i | −0.950329 | + | 1.64602i | ||||
\(555\) | −0.552443 | − | 5.43800i | −0.0234499 | − | 0.230830i | ||||
\(556\) | −50.0076 | + | 28.8719i | −2.12080 | + | 1.22444i | ||||
\(557\) | −11.2429 | + | 6.49112i | −0.476379 | + | 0.275038i | −0.718906 | − | 0.695107i | \(-0.755357\pi\) |
0.242527 | + | 0.970145i | \(0.422024\pi\) | |||||||
\(558\) | −0.610263 | − | 0.202990i | −0.0258345 | − | 0.00859325i | ||||
\(559\) | −7.05656 | + | 12.2223i | −0.298461 | + | 0.516949i | ||||
\(560\) | 0.675384i | 0.0285402i | ||||||||
\(561\) | 9.61553 | + | 13.3319i | 0.405968 | + | 0.562873i | ||||
\(562\) | 28.3170 | + | 49.0465i | 1.19448 | + | 2.06890i | ||||
\(563\) | 31.3358 | 1.32065 | 0.660324 | − | 0.750981i | \(-0.270419\pi\) | ||||
0.660324 | + | 0.750981i | \(0.270419\pi\) | |||||||
\(564\) | 34.9892 | − | 3.55453i | 1.47331 | − | 0.149673i | ||||
\(565\) | 4.00727 | + | 6.94080i | 0.168587 | + | 0.292002i | ||||
\(566\) | −2.28778 | + | 3.96256i | −0.0961627 | + | 0.166559i | ||||
\(567\) | −2.82512 | − | 0.336727i | −0.118644 | − | 0.0141412i | ||||
\(568\) | −54.4103 | + | 31.4138i | −2.28301 | + | 1.31809i | ||||
\(569\) | −34.4866 | + | 19.9109i | −1.44576 | + | 0.834707i | −0.998225 | − | 0.0595616i | \(-0.981030\pi\) |
−0.447531 | + | 0.894269i | \(0.647696\pi\) | |||||||
\(570\) | 7.28568 | + | 3.27420i | 0.305164 | + | 0.137141i | ||||
\(571\) | 7.90831 | + | 13.6976i | 0.330952 | + | 0.573226i | 0.982699 | − | 0.185211i | \(-0.0592967\pi\) |
−0.651747 | + | 0.758437i | \(0.725963\pi\) | |||||||
\(572\) | 83.7987 | − | 48.3812i | 3.50380 | − | 2.02292i | ||||
\(573\) | 0.0325306 | + | 0.320217i | 0.00135898 | + | 0.0133772i | ||||
\(574\) | 8.34359 | − | 4.81717i | 0.348255 | − | 0.201065i | ||||
\(575\) | 19.1077 | + | 11.0318i | 0.796845 | + | 0.460059i | ||||
\(576\) | −7.85199 | + | 23.6060i | −0.327166 | + | 0.983583i | ||||
\(577\) | −31.6191 | + | 18.2553i | −1.31632 | + | 0.759978i | −0.983135 | − | 0.182883i | \(-0.941457\pi\) |
−0.333186 | + | 0.942861i | \(0.608124\pi\) | |||||||
\(578\) | 32.2089 | 1.33971 | ||||||||
\(579\) | 12.9391 | − | 9.33225i | 0.537732 | − | 0.387835i | ||||
\(580\) | 8.99081 | + | 5.19085i | 0.373323 | + | 0.215538i | ||||
\(581\) | −1.93993 | −0.0804820 | ||||||||
\(582\) | 8.05860 | − | 17.9318i | 0.334040 | − | 0.743298i | ||||
\(583\) | 15.0694 | + | 26.1010i | 0.624112 | + | 1.08099i | ||||
\(584\) | 22.0475 | − | 38.1875i | 0.912334 | − | 1.58021i | ||||
\(585\) | 6.24041 | − | 5.54078i | 0.258009 | − | 0.229083i | ||||
\(586\) | −19.9471 | − | 11.5164i | −0.824005 | − | 0.475740i | ||||
\(587\) | 5.53643 | − | 9.58937i | 0.228513 | − | 0.395796i | −0.728855 | − | 0.684668i | \(-0.759947\pi\) |
0.957368 | + | 0.288873i | \(0.0932804\pi\) | |||||||
\(588\) | 38.5323 | − | 27.7912i | 1.58905 | − | 1.14609i | ||||
\(589\) | 0.298308i | 0.0122916i | ||||||||
\(590\) | 6.20328 | + | 3.58146i | 0.255385 | + | 0.147447i | ||||
\(591\) | 6.56096 | + | 2.94851i | 0.269882 | + | 0.121285i | ||||
\(592\) | 10.9581 | + | 18.9799i | 0.450373 | + | 0.780069i | ||||
\(593\) | −5.92238 | + | 10.2579i | −0.243203 | + | 0.421240i | −0.961625 | − | 0.274368i | \(-0.911531\pi\) |
0.718422 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(594\) | 18.4370 | + | 58.8247i | 0.756481 | + | 2.41360i | ||||
\(595\) | 0.342853 | 0.0140556 | ||||||||
\(596\) | 16.1342 | − | 9.31511i | 0.660884 | − | 0.381562i | ||||
\(597\) | 3.16329 | + | 31.1380i | 0.129465 | + | 1.27439i | ||||
\(598\) | 57.6449 | 2.35727 | ||||||||
\(599\) | 6.70993 | + | 11.6219i | 0.274160 | + | 0.474860i | 0.969923 | − | 0.243412i | \(-0.0782668\pi\) |
−0.695763 | + | 0.718272i | \(0.744933\pi\) | |||||||
\(600\) | −31.8269 | + | 22.9549i | −1.29933 | + | 0.937129i | ||||
\(601\) | −12.1980 | + | 21.1275i | −0.497566 | + | 0.861809i | −0.999996 | − | 0.00280871i | \(-0.999106\pi\) |
0.502430 | + | 0.864618i | \(0.332439\pi\) | |||||||
\(602\) | −2.17450 | −0.0886258 | ||||||||
\(603\) | 22.0924 | + | 10.7204i | 0.899671 | + | 0.436568i | ||||
\(604\) | 15.5032 | 0.630816 | ||||||||
\(605\) | −3.48202 | + | 6.03104i | −0.141564 | + | 0.245197i | ||||
\(606\) | 18.0855 | − | 13.0440i | 0.734674 | − | 0.529878i | ||||
\(607\) | 7.77840 | + | 13.4726i | 0.315715 | + | 0.546835i | 0.979589 | − | 0.201009i | \(-0.0644222\pi\) |
−0.663874 | + | 0.747845i | \(0.731089\pi\) | |||||||
\(608\) | 0.819247 | 0.0332248 | ||||||||
\(609\) | 0.260570 | + | 2.56494i | 0.0105588 | + | 0.103936i | ||||
\(610\) | −8.15297 | + | 4.70712i | −0.330104 | + | 0.190586i | ||||
\(611\) | −25.6177 | −1.03638 | ||||||||
\(612\) | −22.1272 | − | 7.36011i | −0.894440 | − | 0.297515i | ||||
\(613\) | 13.2263 | − | 22.9087i | 0.534206 | − | 0.925272i | −0.464995 | − | 0.885313i | \(-0.653944\pi\) |
0.999201 | − | 0.0399589i | \(-0.0127227\pi\) | |||||||
\(614\) | −38.0106 | − | 65.8363i | −1.53398 | − | 2.65694i | ||||
\(615\) | −10.9250 | − | 4.90974i | −0.440540 | − | 0.197980i | ||||
\(616\) | 6.41544 | + | 3.70396i | 0.258486 | + | 0.149237i | ||||
\(617\) | − | 23.6066i | − | 0.950364i | −0.879888 | − | 0.475182i | \(-0.842382\pi\) | ||
0.879888 | − | 0.475182i | \(-0.157618\pi\) | |||||||
\(618\) | 6.63195 | − | 4.78325i | 0.266776 | − | 0.192410i | ||||
\(619\) | −5.92015 | + | 10.2540i | −0.237951 | + | 0.412143i | −0.960126 | − | 0.279567i | \(-0.909809\pi\) |
0.722175 | + | 0.691710i | \(0.243142\pi\) | |||||||
\(620\) | 0.167462 | + | 0.0966842i | 0.00672543 | + | 0.00388293i | ||||
\(621\) | −5.32886 | + | 23.8443i | −0.213840 | + | 0.956838i | ||||
\(622\) | −22.7911 | + | 39.4753i | −0.913838 | + | 1.58281i | ||||
\(623\) | −1.68110 | − | 2.91175i | −0.0673518 | − | 0.116657i | ||||
\(624\) | −13.7159 | + | 30.5202i | −0.549074 | + | 1.22179i | ||||
\(625\) | 20.4801 | 0.819203 | ||||||||
\(626\) | 22.2869 | + | 12.8674i | 0.890764 | + | 0.514283i | ||||
\(627\) | 23.1910 | − | 16.7263i | 0.926158 | − | 0.667985i | ||||
\(628\) | −41.1811 | −1.64330 | ||||||||
\(629\) | 9.63500 | − | 5.56277i | 0.384172 | − | 0.221802i | ||||
\(630\) | 1.22008 | + | 0.405831i | 0.0486091 | + | 0.0161687i | ||||
\(631\) | 3.33223 | + | 1.92386i | 0.132654 | + | 0.0765878i | 0.564858 | − | 0.825188i | \(-0.308931\pi\) |
−0.432204 | + | 0.901776i | \(0.642264\pi\) | |||||||
\(632\) | −56.9041 | + | 32.8536i | −2.26352 | + | 1.30685i | ||||
\(633\) | −2.92706 | − | 28.8127i | −0.116340 | − | 1.14520i | ||||
\(634\) | −51.3005 | + | 29.6183i | −2.03740 | + | 1.17629i | ||||
\(635\) | −4.30091 | − | 7.44940i | −0.170677 | − | 0.295620i | ||||
\(636\) | −38.9991 | − | 17.5263i | −1.54641 | − | 0.694962i | ||||
\(637\) | −29.9697 | + | 17.3030i | −1.18744 | + | 0.685570i | ||||
\(638\) | 48.3776 | − | 27.9308i | 1.91529 | − | 1.10579i | ||||
\(639\) | 7.85055 | + | 38.2399i | 0.310563 | + | 1.51275i | ||||
\(640\) | 5.48793 | − | 9.50537i | 0.216929 | − | 0.375733i | ||||
\(641\) | 4.19692 | + | 7.26927i | 0.165768 | + | 0.287119i | 0.936928 | − | 0.349523i | \(-0.113656\pi\) |
−0.771160 | + | 0.636642i | \(0.780323\pi\) | |||||||
\(642\) | 23.9913 | − | 2.43727i | 0.946863 | − | 0.0961912i | ||||
\(643\) | 1.84759 | 0.0728618 | 0.0364309 | − | 0.999336i | \(-0.488401\pi\) | ||||
0.0364309 | + | 0.999336i | \(0.488401\pi\) | |||||||
\(644\) | 2.95443 | + | 5.11722i | 0.116421 | + | 0.201647i | ||||
\(645\) | 1.58138 | + | 2.19258i | 0.0622669 | + | 0.0863328i | ||||
\(646\) | 16.2580i | 0.639663i | ||||||||
\(647\) | −1.06831 | + | 1.85036i | −0.0419995 | + | 0.0727453i | −0.886261 | − | 0.463186i | \(-0.846706\pi\) |
0.844261 | + | 0.535931i | \(0.180039\pi\) | |||||||
\(648\) | −34.7966 | − | 26.0284i | −1.36694 | − | 1.02249i | ||||
\(649\) | 22.2062 | − | 12.8207i | 0.871668 | − | 0.503258i | ||||
\(650\) | 49.8192 | − | 28.7631i | 1.95407 | − | 1.12818i | ||||
\(651\) | 0.00485335 | + | 0.0477742i | 0.000190218 | + | 0.00187242i | ||||
\(652\) | −28.1847 | + | 48.8174i | −1.10380 | + | 1.91184i | ||||
\(653\) | −13.9839 | + | 24.2208i | −0.547232 | + | 0.947834i | 0.451230 | + | 0.892408i | \(0.350985\pi\) |
−0.998463 | + | 0.0554268i | \(0.982348\pi\) | |||||||
\(654\) | −76.6030 | + | 7.78205i | −2.99542 | + | 0.304302i | ||||
\(655\) | 7.17957i | 0.280529i | ||||||||
\(656\) | 48.0245 | 1.87504 | ||||||||
\(657\) | −18.1909 | − | 20.4878i | −0.709693 | − | 0.799305i | ||||
\(658\) | −1.97354 | − | 3.41827i | −0.0769366 | − | 0.133258i | ||||
\(659\) | 14.6289 | − | 8.44598i | 0.569860 | − | 0.329009i | −0.187234 | − | 0.982315i | \(-0.559952\pi\) |
0.757093 | + | 0.653307i | \(0.226619\pi\) | |||||||
\(660\) | −1.87330 | − | 18.4399i | −0.0729181 | − | 0.717773i | ||||
\(661\) | − | 24.6063i | − | 0.957073i | −0.878068 | − | 0.478537i | \(-0.841167\pi\) | ||
0.878068 | − | 0.478537i | \(-0.158833\pi\) | |||||||
\(662\) | − | 32.7697i | − | 1.27363i | ||||||
\(663\) | 15.4933 | + | 6.96275i | 0.601712 | + | 0.270411i | ||||
\(664\) | −25.6597 | − | 14.8146i | −0.995788 | − | 0.574919i | ||||
\(665\) | − | 0.596397i | − | 0.0231273i | ||||||
\(666\) | 40.8717 | − | 8.39085i | 1.58375 | − | 0.325139i | ||||
\(667\) | 22.1398 | 0.857257 | ||||||||
\(668\) | −62.2899 | − | 35.9631i | −2.41007 | − | 1.39145i | ||||
\(669\) | 0.176390 | − | 0.127220i | 0.00681963 | − | 0.00491861i | ||||
\(670\) | −8.80598 | − | 6.75380i | −0.340205 | − | 0.260922i | ||||
\(671\) | 33.7006i | 1.30100i | ||||||||
\(672\) | 0.131203 | − | 0.0133288i | 0.00506127 | − | 0.000514171i | ||||
\(673\) | − | 2.61136i | − | 0.100661i | −0.998733 | − | 0.0503303i | \(-0.983973\pi\) | ||
0.998733 | − | 0.0503303i | \(-0.0160274\pi\) | |||||||
\(674\) | −17.5748 | + | 10.1468i | −0.676955 | + | 0.390840i | ||||
\(675\) | 7.29218 | + | 23.2662i | 0.280676 | + | 0.895518i | ||||
\(676\) | 24.1561 | − | 41.8396i | 0.929082 | − | 1.60922i | ||||
\(677\) | 9.10514 | + | 15.7706i | 0.349939 | + | 0.606112i | 0.986238 | − | 0.165330i | \(-0.0528690\pi\) |
−0.636299 | + | 0.771442i | \(0.719536\pi\) | |||||||
\(678\) | −49.6190 | + | 35.7873i | −1.90561 | + | 1.37440i | ||||
\(679\) | −1.46788 | −0.0563319 | ||||||||
\(680\) | 4.53495 | + | 2.61825i | 0.173907 | + | 0.100405i | ||||
\(681\) | 3.82865 | − | 8.51942i | 0.146714 | − | 0.326465i | ||||
\(682\) | 0.901076 | − | 0.520236i | 0.0345040 | − | 0.0199209i | ||||
\(683\) | −21.2686 | + | 36.8382i | −0.813819 | + | 1.40958i | 0.0963545 | + | 0.995347i | \(0.469282\pi\) |
−0.910173 | + | 0.414228i | \(0.864052\pi\) | |||||||
\(684\) | −12.8030 | + | 38.4905i | −0.489535 | + | 1.47172i | ||||
\(685\) | 9.55524 | 0.365087 | ||||||||
\(686\) | −9.30210 | − | 5.37057i | −0.355156 | − | 0.205049i | ||||
\(687\) | −36.7516 | + | 3.73357i | −1.40216 | + | 0.142445i | ||||
\(688\) | −9.38707 | − | 5.41963i | −0.357879 | − | 0.206621i | ||||
\(689\) | 26.9716 | + | 15.5721i | 1.02754 | + | 0.593249i | ||||
\(690\) | 4.52618 | − | 10.0716i | 0.172309 | − | 0.383418i | ||||
\(691\) | −19.7288 | − | 34.1712i | −0.750517 | − | 1.29993i | −0.947572 | − | 0.319542i | \(-0.896471\pi\) |
0.197055 | − | 0.980392i | \(-0.436862\pi\) | |||||||
\(692\) | 15.2049i | 0.578003i | ||||||||
\(693\) | 3.44192 | − | 3.05604i | 0.130748 | − | 0.116089i | ||||
\(694\) | 50.1453 | 1.90349 | ||||||||
\(695\) | − | 8.05683i | − | 0.305613i | ||||||
\(696\) | −16.1410 | + | 35.9165i | −0.611822 | + | 1.36141i | ||||
\(697\) | − | 24.3793i | − | 0.923430i | ||||||
\(698\) | −20.5746 | + | 35.6363i | −0.778761 | + | 1.34885i | ||||
\(699\) | −13.8112 | − | 6.20679i | −0.522388 | − | 0.234763i | ||||
\(700\) | 5.10669 | + | 2.94835i | 0.193015 | + | 0.111437i | ||||
\(701\) | 1.93484 | + | 3.35124i | 0.0730778 | + | 0.126574i | 0.900249 | − | 0.435376i | \(-0.143385\pi\) |
−0.827171 | + | 0.561950i | \(0.810051\pi\) | |||||||
\(702\) | 46.8929 | + | 43.1169i | 1.76986 | + | 1.62734i | ||||
\(703\) | −9.67649 | − | 16.7602i | −0.364956 | − | 0.632122i | ||||
\(704\) | −20.1236 | − | 34.8551i | −0.758437 | − | 1.31365i | ||||
\(705\) | −2.01146 | + | 4.47586i | −0.0757561 | + | 0.168571i | ||||
\(706\) | 19.8290 | + | 34.3449i | 0.746276 | + | 1.29259i | ||||
\(707\) | −1.44188 | − | 0.832472i | −0.0542276 | − | 0.0313083i | ||||
\(708\) | −14.9110 | + | 33.1795i | −0.560388 | + | 1.24696i | ||||
\(709\) | 17.9371 | − | 31.0679i | 0.673641 | − | 1.16678i | −0.303223 | − | 0.952920i | \(-0.598063\pi\) |
0.976864 | − | 0.213861i | \(-0.0686041\pi\) | |||||||
\(710\) | − | 17.6423i | − | 0.662105i | ||||||
\(711\) | 8.21036 | + | 39.9925i | 0.307913 | + | 1.49984i | ||||
\(712\) | − | 51.3519i | − | 1.92449i | ||||||
\(713\) | 0.412374 | 0.0154435 | ||||||||
\(714\) | 0.264512 | + | 2.60373i | 0.00989910 | + | 0.0974423i | ||||
\(715\) | 13.5010i | 0.504909i | ||||||||
\(716\) | 30.3336 | + | 52.5393i | 1.13362 | + | 1.96349i | ||||
\(717\) | −5.17365 | − | 2.32505i | −0.193214 | − | 0.0868307i | ||||
\(718\) | 40.6069 | + | 23.4444i | 1.51544 | + | 0.874938i | ||||
\(719\) | −18.0990 | − | 10.4495i | −0.674980 | − | 0.389700i | 0.122981 | − | 0.992409i | \(-0.460755\pi\) |
−0.797961 | + | 0.602709i | \(0.794088\pi\) | |||||||
\(720\) | 4.25547 | + | 4.79280i | 0.158592 | + | 0.178617i | ||||
\(721\) | −0.528738 | − | 0.305267i | −0.0196912 | − | 0.0113687i | ||||
\(722\) | −18.1631 | −0.675960 | ||||||||
\(723\) | 31.2043 | − | 22.5059i | 1.16050 | − | 0.837002i | ||||
\(724\) | 46.5099 | − | 80.5575i | 1.72853 | − | 2.99390i | ||||
\(725\) | 19.1342 | − | 11.0471i | 0.710627 | − | 0.410281i | ||||
\(726\) | −48.4880 | − | 21.7906i | −1.79956 | − | 0.808725i | ||||
\(727\) | 0.668064 | + | 0.385707i | 0.0247771 | + | 0.0143051i | 0.512337 | − | 0.858784i | \(-0.328780\pi\) |
−0.487560 | + | 0.873089i | \(0.662113\pi\) | |||||||
\(728\) | 7.65501 | 0.283714 | ||||||||
\(729\) | −22.1698 | + | 15.4110i | −0.821105 | + | 0.570777i | ||||
\(730\) | 6.19107 | + | 10.7232i | 0.229142 | + | 0.396885i | ||||
\(731\) | −2.75123 | + | 4.76527i | −0.101758 | + | 0.176250i | ||||
\(732\) | −27.9668 | − | 38.7758i | −1.03368 | − | 1.43320i | ||||
\(733\) | −43.8173 | + | 25.2979i | −1.61843 | + | 0.934400i | −0.631101 | + | 0.775701i | \(0.717397\pi\) |
−0.987327 | + | 0.158699i | \(0.949270\pi\) | |||||||
\(734\) | − | 28.4480i | − | 1.05003i | ||||||
\(735\) | 0.669964 | + | 6.59483i | 0.0247120 | + | 0.243254i | ||||
\(736\) | − | 1.13251i | − | 0.0417448i | ||||||
\(737\) | −36.6994 | + | 15.2114i | −1.35184 | + | 0.560321i | ||||
\(738\) | 28.8574 | − | 86.7560i | 1.06226 | − | 3.19353i | ||||
\(739\) | −3.77677 | − | 2.18052i | −0.138931 | − | 0.0802117i | 0.428924 | − | 0.903341i | \(-0.358893\pi\) |
−0.567854 | + | 0.823129i | \(0.692226\pi\) | |||||||
\(740\) | −12.5449 | −0.461161 | ||||||||
\(741\) | 12.1118 | − | 26.9508i | 0.444937 | − | 0.990064i | ||||
\(742\) | 4.79857i | 0.176161i | ||||||||
\(743\) | 21.1968 | + | 12.2380i | 0.777637 | + | 0.448969i | 0.835592 | − | 0.549350i | \(-0.185125\pi\) |
−0.0579552 | + | 0.998319i | \(0.518458\pi\) | |||||||
\(744\) | −0.300640 | + | 0.668978i | −0.0110220 | + | 0.0245259i | ||||
\(745\) | 2.59942i | 0.0952354i | ||||||||
\(746\) | − | 69.2528i | − | 2.53553i | ||||||
\(747\) | −13.7666 | + | 12.2232i | −0.503692 | + | 0.447222i | ||||
\(748\) | 32.6717 | − | 18.8630i | 1.19459 | − | 0.689699i | ||||
\(749\) | −0.900272 | − | 1.55932i | −0.0328952 | − | 0.0569762i | ||||
\(750\) | −2.30041 | − | 22.6442i | −0.0839990 | − | 0.826849i | ||||
\(751\) | −22.8657 | −0.834382 | −0.417191 | − | 0.908819i | \(-0.636985\pi\) | ||||
−0.417191 | + | 0.908819i | \(0.636985\pi\) | |||||||
\(752\) | − | 19.6751i | − | 0.717477i | ||||||
\(753\) | 1.77197 | + | 17.4425i | 0.0645742 | + | 0.635640i | ||||
\(754\) | 28.8624 | − | 49.9912i | 1.05111 | − | 1.82057i | ||||
\(755\) | −1.08156 | + | 1.87331i | −0.0393620 | + | 0.0681769i | ||||
\(756\) | −1.42418 | + | 6.37259i | −0.0517970 | + | 0.231769i | ||||
\(757\) | 34.3592 | − | 19.8373i | 1.24881 | − | 0.720999i | 0.277936 | − | 0.960600i | \(-0.410350\pi\) |
0.970872 | + | 0.239600i | \(0.0770165\pi\) | |||||||
\(758\) | 13.3563 | − | 7.71128i | 0.485124 | − | 0.280086i | ||||
\(759\) | −23.1221 | − | 32.0587i | −0.839278 | − | 1.16366i | ||||
\(760\) | 4.55448 | − | 7.88859i | 0.165208 | − | 0.286149i | ||||
\(761\) | − | 12.2506i | − | 0.444084i | −0.975037 | − | 0.222042i | \(-0.928728\pi\) | ||
0.975037 | − | 0.222042i | \(-0.0712723\pi\) | |||||||
\(762\) | 53.2549 | − | 38.4097i | 1.92922 | − | 1.39144i | ||||
\(763\) | 2.87452 | + | 4.97881i | 0.104065 | + | 0.180245i | ||||
\(764\) | 0.738709 | 0.0267255 | ||||||||
\(765\) | 2.43303 | − | 2.16025i | 0.0879663 | − | 0.0781042i | ||||
\(766\) | 19.8011 | + | 34.2965i | 0.715442 | + | 1.23918i | ||||
\(767\) | 13.2484 | − | 22.9469i | 0.478371 | − | 0.828563i | ||||
\(768\) | 50.2188 | + | 22.5684i | 1.81211 | + | 0.814368i | ||||
\(769\) | −0.214768 | + | 0.123996i | −0.00774472 | + | 0.00447142i | −0.503867 | − | 0.863781i | \(-0.668090\pi\) |
0.496123 | + | 0.868252i | \(0.334757\pi\) | |||||||
\(770\) | −1.80149 | + | 1.04009i | −0.0649212 | + | 0.0374823i | ||||
\(771\) | 1.79336 | − | 3.99056i | 0.0645864 | − | 0.143716i | ||||
\(772\) | −18.3073 | − | 31.7092i | −0.658894 | − | 1.14124i | ||||
\(773\) | 5.31156 | − | 3.06663i | 0.191044 | − | 0.110299i | −0.401427 | − | 0.915891i | \(-0.631486\pi\) |
0.592471 | + | 0.805592i | \(0.298152\pi\) | |||||||
\(774\) | −15.4311 | + | 13.7011i | −0.554660 | + | 0.492476i | ||||
\(775\) | 0.356392 | − | 0.205763i | 0.0128020 | − | 0.00739123i | ||||
\(776\) | −19.4157 | − | 11.2097i | −0.696984 | − | 0.402404i | ||||
\(777\) | −1.82238 | − | 2.52672i | −0.0653775 | − | 0.0906457i | ||||
\(778\) | 6.68685 | − | 3.86065i | 0.239735 | − | 0.138411i | ||||
\(779\) | −42.4080 | −1.51942 | ||||||||
\(780\) | −11.2039 | − | 15.5342i | −0.401165 | − | 0.556214i | ||||
\(781\) | −54.6939 | − | 31.5775i | −1.95710 | − | 1.12993i | ||||
\(782\) | 22.4747 | 0.803695 | ||||||||
\(783\) | 18.0103 | + | 16.5600i | 0.643635 | + | 0.591807i | ||||
\(784\) | −13.2892 | − | 23.0175i | −0.474613 | − | 0.822054i | ||||
\(785\) | 2.87294 | − | 4.97608i | 0.102540 | − | 0.177604i | ||||
\(786\) | −54.5239 | + | 5.53905i | −1.94480 | + | 0.197571i | ||||
\(787\) | −3.20544 | − | 1.85066i | −0.114262 | − | 0.0659689i | 0.441780 | − | 0.897123i | \(-0.354347\pi\) |
−0.556042 | + | 0.831154i | \(0.687680\pi\) | |||||||
\(788\) | 8.25434 | − | 14.2969i | 0.294049 | − | 0.509307i | ||||
\(789\) | 20.0560 | + | 27.8076i | 0.714013 | + | 0.989977i | ||||
\(790\) | − | 18.4509i | − | 0.656454i | ||||||
\(791\) | 3.95592 | + | 2.28395i | 0.140656 | + | 0.0812079i | ||||
\(792\) | 68.8646 | − | 14.1377i | 2.44700 | − | 0.502362i | ||||
\(793\) | 17.4123 | + | 30.1591i | 0.618330 | + | 1.07098i | ||||
\(794\) | −30.1785 | + | 52.2707i | −1.07100 | + | 1.85502i | ||||
\(795\) | 4.83848 | − | 3.48972i | 0.171603 | − | 0.123768i | ||||
\(796\) | 71.8324 | 2.54603 | ||||||||
\(797\) | 0.352241 | − | 0.203367i | 0.0124770 | − | 0.00720362i | −0.493749 | − | 0.869605i | \(-0.664374\pi\) |
0.506226 | + | 0.862401i | \(0.331040\pi\) | |||||||
\(798\) | 4.52922 | − | 0.460121i | 0.160333 | − | 0.0162881i | ||||
\(799\) | −9.98790 | −0.353347 | ||||||||
\(800\) | −0.565090 | − | 0.978764i | −0.0199789 | − | 0.0346045i | ||||
\(801\) | −30.2761 | − | 10.0707i | −1.06975 | − | 0.355829i | ||||
\(802\) | −8.11026 | + | 14.0474i | −0.286383 | + | 0.496030i | ||||
\(803\) | 44.3249 | 1.56419 | ||||||||
\(804\) | 29.6029 | − | 47.9576i | 1.04401 | − | 1.69134i | ||||
\(805\) | −0.824446 | −0.0290579 | ||||||||
\(806\) | 0.537589 | − | 0.931132i | 0.0189358 | − | 0.0327977i | ||||
\(807\) | −4.24609 | − | 5.88719i | −0.149470 | − | 0.207239i | ||||
\(808\) | −12.7146 | − | 22.0224i | −0.447299 | − | 0.774744i | ||||
\(809\) | 22.3994 | 0.787519 | 0.393760 | − | 0.919213i | \(-0.371174\pi\) | ||||
0.393760 | + | 0.919213i | \(0.371174\pi\) | |||||||
\(810\) | 11.2152 | − | 4.80754i | 0.394063 | − | 0.168920i | ||||
\(811\) | 11.0833 | − | 6.39897i | 0.389189 | − | 0.224698i | −0.292620 | − | 0.956229i | \(-0.594527\pi\) |
0.681809 | + | 0.731531i | \(0.261194\pi\) | |||||||
\(812\) | 5.91706 | 0.207648 | ||||||||
\(813\) | 27.9588 | + | 38.7647i | 0.980556 | + | 1.35954i | ||||
\(814\) | −33.7508 | + | 58.4581i | −1.18296 | + | 2.04896i | ||||
\(815\) | −3.93254 | − | 6.81135i | −0.137751 | − | 0.238591i | ||||
\(816\) | −5.34757 | + | 11.8993i | −0.187203 | + | 0.416559i | ||||
\(817\) | 8.28924 | + | 4.78579i | 0.290004 | + | 0.167434i | ||||
\(818\) | 62.6327i | 2.18990i | ||||||||
\(819\) | 1.50123 | − | 4.51325i | 0.0524572 | − | 0.157706i | ||||
\(820\) | −13.7448 | + | 23.8067i | −0.479989 | + | 0.831365i | ||||
\(821\) | −39.3647 | − | 22.7272i | −1.37384 | − | 0.793186i | −0.382429 | − | 0.923985i | \(-0.624912\pi\) |
−0.991409 | + | 0.130799i | \(0.958246\pi\) | |||||||
\(822\) | 7.37188 | + | 72.5655i | 0.257124 | + | 2.53101i | ||||
\(823\) | 2.01983 | − | 3.49846i | 0.0704070 | − | 0.121949i | −0.828673 | − | 0.559733i | \(-0.810904\pi\) |
0.899080 | + | 0.437785i | \(0.144237\pi\) | |||||||
\(824\) | −4.66245 | − | 8.07560i | −0.162424 | − | 0.281327i | ||||
\(825\) | −35.9795 | − | 16.1693i | −1.25265 | − | 0.562942i | ||||
\(826\) | 4.08252 | 0.142049 | ||||||||
\(827\) | 29.4880 | + | 17.0249i | 1.02540 | + | 0.592015i | 0.915663 | − | 0.401946i | \(-0.131666\pi\) |
0.109736 | + | 0.993961i | \(0.464999\pi\) | |||||||
\(828\) | 53.2085 | + | 17.6986i | 1.84912 | + | 0.615068i | ||||
\(829\) | −28.6915 | −0.996498 | −0.498249 | − | 0.867034i | \(-0.666023\pi\) | ||||
−0.498249 | + | 0.867034i | \(0.666023\pi\) | |||||||
\(830\) | 7.20537 | − | 4.16002i | 0.250102 | − | 0.144396i | ||||
\(831\) | 25.7095 | − | 18.5428i | 0.891853 | − | 0.643242i | ||||
\(832\) | −36.0177 | − | 20.7948i | −1.24869 | − | 0.720932i | ||||
\(833\) | −11.6847 | + | 6.74614i | −0.404849 | + | 0.233740i | ||||
\(834\) | 61.1861 | − | 6.21586i | 2.11870 | − | 0.215238i | ||||
\(835\) | 8.69113 | − | 5.01783i | 0.300769 | − | 0.173649i | ||||
\(836\) | −32.8124 | − | 56.8327i | −1.13484 | − | 1.96560i | ||||
\(837\) | 0.335458 | + | 0.308445i | 0.0115951 | + | 0.0106614i | ||||
\(838\) | −21.5036 | + | 12.4151i | −0.742829 | + | 0.428873i | ||||
\(839\) | 23.4244 | − | 13.5241i | 0.808699 | − | 0.466903i | −0.0378049 | − | 0.999285i | \(-0.512037\pi\) |
0.846504 | + | 0.532383i | \(0.178703\pi\) | |||||||
\(840\) | 0.601060 | − | 1.33746i | 0.0207385 | − | 0.0461469i | ||||
\(841\) | −3.41472 | + | 5.91447i | −0.117749 | + | 0.203947i | ||||
\(842\) | −1.12923 | − | 1.95588i | −0.0389157 | − | 0.0674040i | ||||
\(843\) | −4.05583 | − | 39.9238i | −0.139690 | − | 1.37505i | ||||
\(844\) | −66.4680 | −2.28792 | ||||||||
\(845\) | 3.37044 | + | 5.83777i | 0.115947 | + | 0.200825i | ||||
\(846\) | −35.5430 | − | 11.8225i | −1.22199 | − | 0.406468i | ||||
\(847\) | 3.96917i | 0.136382i | ||||||||
\(848\) | −11.9598 | + | 20.7149i | −0.410700 | + | 0.711354i | ||||
\(849\) | 2.62954 | − | 1.89654i | 0.0902456 | − | 0.0650890i | ||||
\(850\) | 19.4237 | − | 11.2143i | 0.666226 | − | 0.384646i | ||||
\(851\) | −23.1689 | + | 13.3766i | −0.794220 | + | 0.458543i | ||||
\(852\) | 89.1356 | − | 9.05523i | 3.05374 | − | 0.310227i | ||||
\(853\) | −19.8568 | + | 34.3930i | −0.679883 | + | 1.17759i | 0.295133 | + | 0.955456i | \(0.404636\pi\) |
−0.975016 | + | 0.222136i | \(0.928697\pi\) | |||||||
\(854\) | −2.68283 | + | 4.64679i | −0.0918045 | + | 0.159010i | ||||
\(855\) | −3.75779 | − | 4.23228i | −0.128514 | − | 0.144741i | ||||
\(856\) | − | 27.5003i | − | 0.939941i | ||||||
\(857\) | −0.248334 | −0.00848293 | −0.00424147 | − | 0.999991i | \(-0.501350\pi\) | ||||
−0.00424147 | + | 0.999991i | \(0.501350\pi\) | |||||||
\(858\) | −102.531 | + | 10.4160i | −3.50034 | + | 0.355598i | ||||
\(859\) | 6.65866 | + | 11.5331i | 0.227191 | + | 0.393506i | 0.956974 | − | 0.290172i | \(-0.0937126\pi\) |
−0.729784 | + | 0.683678i | \(0.760379\pi\) | |||||||
\(860\) | 5.37323 | − | 3.10223i | 0.183226 | − | 0.105785i | ||||
\(861\) | −6.79167 | + | 0.689961i | −0.231460 | + | 0.0235138i | ||||
\(862\) | 8.36083i | 0.284771i | ||||||||
\(863\) | − | 2.72688i | − | 0.0928239i | −0.998922 | − | 0.0464120i | \(-0.985221\pi\) | ||
0.998922 | − | 0.0464120i | \(-0.0147787\pi\) | |||||||
\(864\) | 0.847088 | − | 0.921273i | 0.0288185 | − | 0.0313423i | ||||
\(865\) | −1.83727 | − | 1.06075i | −0.0624690 | − | 0.0360665i | ||||
\(866\) | 39.5011i | 1.34230i | ||||||||
\(867\) | −20.8168 | − | 9.35513i | −0.706976 | − | 0.317717i | ||||
\(868\) | 0.110211 | 0.00374079 | ||||||||
\(869\) | −57.2007 | − | 33.0248i | −1.94040 | − | 1.12029i | ||||
\(870\) | −6.46811 | − | 8.96801i | −0.219289 | − | 0.304044i | ||||
\(871\) | −24.9833 | + | 32.5747i | −0.846528 | + | 1.10375i | ||||
\(872\) | 87.8069i | 2.97352i | ||||||||
\(873\) | −10.4166 | + | 9.24881i | −0.352550 | + | 0.313025i | ||||
\(874\) | − | 39.0950i | − | 1.32241i | ||||||
\(875\) | −1.47176 | + | 0.849720i | −0.0497545 | + | 0.0287258i | ||||
\(876\) | −51.0002 | + | 36.7835i | −1.72314 | + | 1.24280i | ||||
\(877\) | 5.13963 | − | 8.90211i | 0.173553 | − | 0.300603i | −0.766106 | − | 0.642714i | \(-0.777809\pi\) |
0.939660 | + | 0.342111i | \(0.111142\pi\) | |||||||
\(878\) | −23.8124 | − | 41.2442i | −0.803629 | − | 1.39193i | ||||
\(879\) | 9.54694 | + | 13.2368i | 0.322010 | + | 0.446466i | ||||
\(880\) | −10.3691 | −0.349543 | ||||||||
\(881\) | −40.7153 | − | 23.5070i | −1.37173 | − | 0.791970i | −0.380586 | − | 0.924745i | \(-0.624278\pi\) |
−0.991146 | + | 0.132775i | \(0.957611\pi\) | |||||||
\(882\) | −49.5663 | + | 10.1758i | −1.66898 | + | 0.342638i | ||||
\(883\) | −22.5648 | + | 13.0278i | −0.759368 | + | 0.438421i | −0.829069 | − | 0.559147i | \(-0.811129\pi\) |
0.0697010 | + | 0.997568i | \(0.477795\pi\) | |||||||
\(884\) | 19.4922 | − | 33.7615i | 0.655593 | − | 1.13552i | ||||
\(885\) | −2.96898 | − | 4.11647i | −0.0998010 | − | 0.138374i | ||||
\(886\) | −26.1790 | −0.879501 | ||||||||
\(887\) | 29.3529 | + | 16.9469i | 0.985575 | + | 0.569022i | 0.903949 | − | 0.427641i | \(-0.140655\pi\) |
0.0816261 | + | 0.996663i | \(0.473989\pi\) | |||||||
\(888\) | −4.80905 | − | 47.3381i | −0.161381 | − | 1.58856i | ||||
\(889\) | −4.24580 | − | 2.45131i | −0.142399 | − | 0.0822143i | ||||
\(890\) | 12.4880 | + | 7.20994i | 0.418598 | + | 0.241678i | ||||
\(891\) | 5.16974 | − | 43.3738i | 0.173193 | − | 1.45308i | ||||
\(892\) | −0.249570 | − | 0.432268i | −0.00835623 | − | 0.0144734i | ||||
\(893\) | 17.3741i | 0.581401i | ||||||||
\(894\) | −19.7408 | + | 2.00546i | −0.660232 | + | 0.0670725i | ||||
\(895\) | −8.46472 | −0.282945 | ||||||||
\(896\) | − | 6.25570i | − | 0.208988i | ||||||
\(897\) | −37.2562 | − | 16.7430i | −1.24395 | − | 0.559034i | ||||
\(898\) | − | 72.6423i | − | 2.42410i | ||||||
\(899\) | 0.206473 | − | 0.357622i | 0.00688627 | − | 0.0119274i | ||||
\(900\) | 54.8162 | − | 11.2536i | 1.82721 | − | 0.375121i | ||||
\(901\) | 10.5158 | + | 6.07128i | 0.350331 | + | 0.202264i | ||||
\(902\) | 73.9577 | + | 128.099i | 2.46252 | + | 4.26522i | ||||
\(903\) | 1.40539 | + | 0.631586i | 0.0467685 | + | 0.0210179i | ||||
\(904\) | 34.8835 | + | 60.4200i | 1.16021 | + | 2.00954i | ||||
\(905\) | 6.48939 | + | 11.2400i | 0.215715 | + | 0.373629i | ||||
\(906\) | −15.0610 | − | 6.76843i | −0.500367 | − | 0.224866i | ||||
\(907\) | 6.04032 | + | 10.4621i | 0.200565 | + | 0.347390i | 0.948711 | − | 0.316145i | \(-0.102389\pi\) |
−0.748145 | + | 0.663535i | \(0.769055\pi\) | |||||||
\(908\) | −18.5646 | − | 10.7183i | −0.616088 | − | 0.355699i | ||||
\(909\) | −15.4774 | + | 3.17748i | −0.513354 | + | 0.105390i | ||||
\(910\) | −1.07478 | + | 1.86158i | −0.0356287 | + | 0.0617108i | ||||
\(911\) | 4.77638i | 0.158249i | 0.996865 | + | 0.0791243i | \(0.0252124\pi\) | ||||
−0.996865 | + | 0.0791243i | \(0.974788\pi\) | |||||||
\(912\) | 20.6990 | + | 9.30216i | 0.685411 | + | 0.308025i | ||||
\(913\) | − | 29.7837i | − | 0.985695i | ||||||
\(914\) | −9.92745 | −0.328371 | ||||||||
\(915\) | 6.63650 | − | 0.674198i | 0.219396 | − | 0.0222883i | ||||
\(916\) | 84.7824i | 2.80129i | ||||||||
\(917\) | 2.04600 | + | 3.54378i | 0.0675649 | + | 0.117026i | ||||
\(918\) | 18.2827 | + | 16.8105i | 0.603420 | + | 0.554830i | ||||
\(919\) | −29.6436 | − | 17.1148i | −0.977854 | − | 0.564564i | −0.0762322 | − | 0.997090i | \(-0.524289\pi\) |
−0.901621 | + | 0.432526i | \(0.857622\pi\) | |||||||
\(920\) | −10.9050 | − | 6.29602i | −0.359528 | − | 0.207573i | ||||
\(921\) | 5.44424 | + | 53.5906i | 0.179394 | + | 1.76587i | ||||
\(922\) | 13.8464 | + | 7.99424i | 0.456008 | + | 0.263276i | ||||
\(923\) | −65.2616 | −2.14811 | ||||||||
\(924\) | −6.17958 | − | 8.56796i | −0.203293 | − | 0.281865i | ||||
\(925\) | −13.3491 | + | 23.1212i | −0.438914 | + | 0.760222i | ||||
\(926\) | −40.7964 | + | 23.5538i | −1.34065 | + | 0.774026i | ||||
\(927\) | −5.67558 | + | 1.16518i | −0.186410 | + | 0.0382696i | ||||
\(928\) | −0.982143 | − | 0.567040i | −0.0322404 | − | 0.0186140i | ||||
\(929\) | 23.0215 | 0.755311 | 0.377656 | − | 0.925946i | \(-0.376730\pi\) | ||||
0.377656 | + | 0.925946i | \(0.376730\pi\) | |||||||
\(930\) | −0.120474 | − | 0.167037i | −0.00395051 | − | 0.00547737i | ||||
\(931\) | 11.7350 | + | 20.3256i | 0.384598 | + | 0.666144i | ||||
\(932\) | −17.3759 | + | 30.0959i | −0.569167 | + | 0.985825i | ||||
\(933\) | 26.1957 | − | 18.8934i | 0.857607 | − | 0.618543i | ||||
\(934\) | −11.9824 | + | 6.91806i | −0.392077 | + | 0.226366i | ||||
\(935\) | 5.26380i | 0.172145i | ||||||||
\(936\) | 54.3231 | − | 48.2328i | 1.77561 | − | 1.57654i | ||||
\(937\) | 0.449957i | 0.0146994i | 0.999973 | + | 0.00734972i | \(0.00233951\pi\) | ||||
−0.999973 | + | 0.00734972i | \(0.997660\pi\) | |||||||
\(938\) | −6.27123 | − | 0.824133i | −0.204763 | − | 0.0269089i | ||||
\(939\) | −10.6668 | − | 14.7895i | −0.348099 | − | 0.482638i | ||||
\(940\) | 9.75333 | + | 5.63109i | 0.318118 | + | 0.183666i | ||||
\(941\) | 59.5842 | 1.94239 | 0.971194 | − | 0.238289i | \(-0.0765865\pi\) | ||||
0.971194 | + | 0.238289i | \(0.0765865\pi\) | |||||||
\(942\) | 40.0064 | + | 17.9790i | 1.30348 | + | 0.585786i | ||||
\(943\) | 58.6238i | 1.90906i | ||||||||
\(944\) | 17.6238 | + | 10.1751i | 0.573606 | + | 0.331171i | ||||
\(945\) | −0.670670 | − | 0.616665i | −0.0218169 | − | 0.0200601i | ||||
\(946\) | − | 33.3849i | − | 1.08544i | ||||||
\(947\) | − | 29.1289i | − | 0.946562i | −0.880912 | − | 0.473281i | \(-0.843070\pi\) | ||
0.880912 | − | 0.473281i | \(-0.156930\pi\) | |||||||
\(948\) | 93.2210 | − | 9.47026i | 3.02768 | − | 0.307580i | ||||
\(949\) | 39.6669 | − | 22.9017i | 1.28764 | − | 0.743420i | ||||
\(950\) | −19.5073 | − | 33.7876i | −0.632901 | − | 1.09622i | ||||
\(951\) | 41.7585 | − | 4.24222i | 1.35411 | − | 0.137563i | ||||
\(952\) | 2.98456 | 0.0967300 | ||||||||
\(953\) | 52.6439i | 1.70530i | 0.522481 | + | 0.852651i | \(0.325007\pi\) | ||||
−0.522481 | + | 0.852651i | \(0.674993\pi\) | |||||||
\(954\) | 30.2349 | + | 34.0526i | 0.978892 | + | 1.10250i | ||||
\(955\) | −0.0515350 | + | 0.0892612i | −0.00166763 | + | 0.00288842i | ||||
\(956\) | −6.50898 | + | 11.2739i | −0.210515 | + | 0.364623i | ||||
\(957\) | −39.3793 | + | 4.00052i | −1.27295 | + | 0.129318i | ||||
\(958\) | −7.97366 | + | 4.60359i | −0.257617 | + | 0.148735i | ||||
\(959\) | 4.71639 | − | 2.72301i | 0.152300 | − | 0.0879306i | ||||
\(960\) | −6.46128 | + | 4.66015i | −0.208537 | + | 0.150406i | ||||
\(961\) | −15.4962 | + | 26.8401i | −0.499876 | + | 0.865811i | ||||
\(962\) | 69.7531i | 2.24893i | ||||||||
\(963\) | −16.2137 | − | 5.39310i | −0.522478 | − | 0.173790i | ||||
\(964\) | −44.1503 | − | 76.4705i | −1.42198 | − | 2.46295i | ||||
\(965\) | 5.10873 | 0.164456 | ||||||||
\(966\) | −0.636061 | − | 6.26110i | −0.0204649 | − | 0.201448i | ||||
\(967\) | −13.1261 | − | 22.7351i | −0.422108 | − | 0.731112i | 0.574038 | − | 0.818829i | \(-0.305376\pi\) |
−0.996145 | + | 0.0877169i | \(0.972043\pi\) | |||||||
\(968\) | −30.3112 | + | 52.5005i | −0.974238 | + | 1.68743i | ||||
\(969\) | 4.72217 | − | 10.5077i | 0.151698 | − | 0.337555i | ||||
\(970\) | 5.45204 | − | 3.14774i | 0.175054 | − | 0.101068i | ||||
\(971\) | 33.6646 | − | 19.4363i | 1.08035 | − | 0.623739i | 0.149357 | − | 0.988783i | \(-0.452279\pi\) |
0.930990 | + | 0.365044i | \(0.118946\pi\) | |||||||
\(972\) | 30.0459 | + | 54.1960i | 0.963723 | + | 1.73834i | ||||
\(973\) | −2.29600 | − | 3.97679i | −0.0736064 | − | 0.127490i | ||||
\(974\) | 18.4128 | − | 10.6306i | 0.589985 | − | 0.340628i | ||||
\(975\) | −40.5528 | + | 4.11973i | −1.29873 | + | 0.131937i | ||||
\(976\) | −23.1630 | + | 13.3731i | −0.741428 | + | 0.428064i | ||||
\(977\) | 11.7002 | + | 6.75513i | 0.374323 | + | 0.216116i | 0.675346 | − | 0.737501i | \(-0.263994\pi\) |
−0.301022 | + | 0.953617i | \(0.597328\pi\) | |||||||
\(978\) | 48.6936 | − | 35.1199i | 1.55705 | − | 1.12301i | ||||
\(979\) | 44.7038 | − | 25.8098i | 1.42874 | − | 0.824884i | ||||
\(980\) | 15.2136 | 0.485982 | ||||||||
\(981\) | 51.7693 | + | 17.2199i | 1.65287 | + | 0.549788i | ||||
\(982\) | 43.5505 | + | 25.1439i | 1.38975 | + | 0.802374i | ||||
\(983\) | −37.5622 | −1.19805 | −0.599024 | − | 0.800731i | \(-0.704445\pi\) | ||||
−0.599024 | + | 0.800731i | \(0.704445\pi\) | |||||||
\(984\) | −95.1030 | − | 42.7395i | −3.03177 | − | 1.36249i | ||||
\(985\) | 1.15170 | + | 1.99481i | 0.0366964 | + | 0.0635600i | ||||
\(986\) | 11.2530 | − | 19.4907i | 0.358367 | − | 0.620711i | ||||
\(987\) | 0.282669 | + | 2.78247i | 0.00899747 | + | 0.0885670i | ||||
\(988\) | −58.7284 | − | 33.9069i | −1.86840 | − | 1.07872i | ||||
\(989\) | 6.61577 | − | 11.4589i | 0.210369 | − | 0.364370i | ||||
\(990\) | −6.23069 | + | 18.7318i | −0.198024 | + | 0.595335i | ||||
\(991\) | 49.1587i | 1.56158i | 0.624795 | + | 0.780789i | \(0.285182\pi\) | ||||
−0.624795 | + | 0.780789i | \(0.714818\pi\) | |||||||
\(992\) | −0.0182933 | − | 0.0105616i | −0.000580813 | − | 0.000335332i | ||||
\(993\) | −9.51802 | + | 21.1793i | −0.302045 | + | 0.672105i | ||||
\(994\) | −5.02763 | − | 8.70811i | −0.159467 | − | 0.276205i | ||||
\(995\) | −5.01129 | + | 8.67980i | −0.158868 | + | 0.275168i | ||||
\(996\) | 24.7163 | + | 34.2690i | 0.783165 | + | 1.08586i | ||||
\(997\) | 3.15161 | 0.0998125 | 0.0499063 | − | 0.998754i | \(-0.484108\pi\) | ||||
0.0499063 | + | 0.998754i | \(0.484108\pi\) | |||||||
\(998\) | 47.5433 | − | 27.4491i | 1.50496 | − | 0.868887i | ||||
\(999\) | −28.8528 | − | 6.44818i | −0.912861 | − | 0.204011i |
(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 | 201.2.f.b.38.3 | ✓ | 40 | |
3.2 | odd | 2 | inner | 201.2.f.b.38.18 | yes | 40 | |
67.30 | odd | 6 | inner | 201.2.f.b.164.18 | yes | 40 | |
201.164 | even | 6 | inner | 201.2.f.b.164.3 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.2.f.b.38.3 | ✓ | 40 | 1.1 | even | 1 | trivial | |
201.2.f.b.38.18 | yes | 40 | 3.2 | odd | 2 | inner | |
201.2.f.b.164.3 | yes | 40 | 201.164 | even | 6 | inner | |
201.2.f.b.164.18 | yes | 40 | 67.30 | odd | 6 | inner |