Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(599,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.599");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.b (of order \(2\), degree \(1\), 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: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 599.1 | ||
Character | \(\chi\) | \(=\) | 690.599 |
Dual form | 690.3.b.a.599.2 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | −2.99999 | − | 0.00596006i | −0.999998 | − | 0.00198669i | ||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 1.21044 | + | 4.85127i | 0.242089 | + | 0.970254i | ||||
\(6\) | 4.24263 | + | 0.00842880i | 0.707105 | + | 0.00140480i | ||||
\(7\) | − | 6.90074i | − | 0.985821i | −0.870080 | − | 0.492910i | \(-0.835933\pi\) | ||
0.870080 | − | 0.492910i | \(-0.164067\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 8.99993 | + | 0.0357603i | 0.999992 | + | 0.00397337i | ||||
\(10\) | −1.71182 | − | 6.86073i | −0.171182 | − | 0.686073i | ||||
\(11\) | 1.93119i | 0.175563i | 0.996140 | + | 0.0877814i | \(0.0279777\pi\) | ||||
−0.996140 | + | 0.0877814i | \(0.972022\pi\) | |||||||
\(12\) | −5.99999 | − | 0.0119201i | −0.499999 | − | 0.000993343i | ||||
\(13\) | − | 4.38117i | − | 0.337013i | −0.985701 | − | 0.168507i | \(-0.946106\pi\) | ||
0.985701 | − | 0.168507i | \(-0.0538945\pi\) | |||||||
\(14\) | 9.75913i | 0.697080i | ||||||||
\(15\) | −3.60241 | − | 14.5610i | −0.240161 | − | 0.970733i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 6.60993 | 0.388819 | 0.194410 | − | 0.980920i | \(-0.437721\pi\) | ||||
0.194410 | + | 0.980920i | \(0.437721\pi\) | |||||||
\(18\) | −12.7278 | − | 0.0505727i | −0.707101 | − | 0.00280959i | ||||
\(19\) | −16.9559 | −0.892417 | −0.446209 | − | 0.894929i | \(-0.647226\pi\) | ||||
−0.446209 | + | 0.894929i | \(0.647226\pi\) | |||||||
\(20\) | 2.42089 | + | 9.70254i | 0.121044 | + | 0.485127i | ||||
\(21\) | −0.0411289 | + | 20.7022i | −0.00195852 | + | 0.985819i | ||||
\(22\) | − | 2.73112i | − | 0.124142i | ||||||
\(23\) | −4.79583 | −0.208514 | ||||||||
\(24\) | 8.48526 | + | 0.0168576i | 0.353553 | + | 0.000702400i | ||||
\(25\) | −22.0697 | + | 11.7444i | −0.882786 | + | 0.469775i | ||||
\(26\) | 6.19592i | 0.238304i | ||||||||
\(27\) | −26.9995 | − | 0.160921i | −0.999982 | − | 0.00596003i | ||||
\(28\) | − | 13.8015i | − | 0.492910i | ||||||
\(29\) | − | 5.45358i | − | 0.188055i | −0.995570 | − | 0.0940273i | \(-0.970026\pi\) | ||
0.995570 | − | 0.0940273i | \(-0.0299741\pi\) | |||||||
\(30\) | 5.09457 | + | 20.5924i | 0.169819 | + | 0.686412i | ||||
\(31\) | 19.1195 | 0.616759 | 0.308380 | − | 0.951263i | \(-0.400213\pi\) | ||||
0.308380 | + | 0.951263i | \(0.400213\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 0.0115100 | − | 5.79356i | 0.000348788 | − | 0.175562i | ||||
\(34\) | −9.34785 | −0.274937 | ||||||||
\(35\) | 33.4774 | − | 8.35296i | 0.956497 | − | 0.238656i | ||||
\(36\) | 17.9999 | + | 0.0715206i | 0.499996 | + | 0.00198668i | ||||
\(37\) | 4.29657i | 0.116123i | 0.998313 | + | 0.0580617i | \(0.0184920\pi\) | ||||
−0.998313 | + | 0.0580617i | \(0.981508\pi\) | |||||||
\(38\) | 23.9793 | 0.631034 | ||||||||
\(39\) | −0.0261121 | + | 13.1435i | −0.000669540 | + | 0.337013i | ||||
\(40\) | −3.42365 | − | 13.7215i | −0.0855912 | − | 0.343037i | ||||
\(41\) | 32.7285i | 0.798256i | 0.916895 | + | 0.399128i | \(0.130687\pi\) | ||||
−0.916895 | + | 0.399128i | \(0.869313\pi\) | |||||||
\(42\) | 0.0581650 | − | 29.2773i | 0.00138488 | − | 0.697079i | ||||
\(43\) | − | 29.3732i | − | 0.683098i | −0.939864 | − | 0.341549i | \(-0.889049\pi\) | ||
0.939864 | − | 0.341549i | \(-0.110951\pi\) | |||||||
\(44\) | 3.86238i | 0.0877814i | ||||||||
\(45\) | 10.7204 | + | 43.7044i | 0.238231 | + | 0.971208i | ||||
\(46\) | 6.78233 | 0.147442 | ||||||||
\(47\) | −23.8924 | −0.508348 | −0.254174 | − | 0.967158i | \(-0.581804\pi\) | ||||
−0.254174 | + | 0.967158i | \(0.581804\pi\) | |||||||
\(48\) | −12.0000 | − | 0.0238402i | −0.250000 | − | 0.000496672i | ||||
\(49\) | 1.37973 | 0.0281577 | ||||||||
\(50\) | 31.2112 | − | 16.6091i | 0.624224 | − | 0.332181i | ||||
\(51\) | −19.8297 | − | 0.0393956i | −0.388818 | − | 0.000772462i | ||||
\(52\) | − | 8.76235i | − | 0.168507i | ||||||
\(53\) | −28.4218 | −0.536260 | −0.268130 | − | 0.963383i | \(-0.586406\pi\) | ||||
−0.268130 | + | 0.963383i | \(0.586406\pi\) | |||||||
\(54\) | 38.1831 | + | 0.227576i | 0.707094 | + | 0.00421438i | ||||
\(55\) | −9.36873 | + | 2.33760i | −0.170340 | + | 0.0425017i | ||||
\(56\) | 19.5183i | 0.348540i | ||||||||
\(57\) | 50.8677 | + | 0.101058i | 0.892416 | + | 0.00177295i | ||||
\(58\) | 7.71253i | 0.132975i | ||||||||
\(59\) | − | 82.3938i | − | 1.39650i | −0.715852 | − | 0.698252i | \(-0.753961\pi\) | ||
0.715852 | − | 0.698252i | \(-0.246039\pi\) | |||||||
\(60\) | −7.20482 | − | 29.1220i | −0.120080 | − | 0.485367i | ||||
\(61\) | 64.8349 | 1.06287 | 0.531433 | − | 0.847100i | \(-0.321654\pi\) | ||||
0.531433 | + | 0.847100i | \(0.321654\pi\) | |||||||
\(62\) | −27.0391 | −0.436115 | ||||||||
\(63\) | 0.246773 | − | 62.1062i | 0.00391703 | − | 0.985813i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 21.2543 | − | 5.30316i | 0.326989 | − | 0.0815871i | ||||
\(66\) | −0.0162776 | + | 8.19333i | −0.000246631 | + | 0.124141i | ||||
\(67\) | − | 62.3462i | − | 0.930540i | −0.885169 | − | 0.465270i | \(-0.845957\pi\) | ||
0.885169 | − | 0.465270i | \(-0.154043\pi\) | |||||||
\(68\) | 13.2199 | 0.194410 | ||||||||
\(69\) | 14.3875 | + | 0.0285834i | 0.208514 | + | 0.000414253i | ||||
\(70\) | −47.3442 | + | 11.8129i | −0.676345 | + | 0.168755i | ||||
\(71\) | − | 130.312i | − | 1.83538i | −0.397300 | − | 0.917689i | \(-0.630053\pi\) | ||
0.397300 | − | 0.917689i | \(-0.369947\pi\) | |||||||
\(72\) | −25.4556 | − | 0.101145i | −0.353551 | − | 0.00140480i | ||||
\(73\) | − | 10.5750i | − | 0.144863i | −0.997373 | − | 0.0724314i | \(-0.976924\pi\) | ||
0.997373 | − | 0.0724314i | \(-0.0230758\pi\) | |||||||
\(74\) | − | 6.07626i | − | 0.0821117i | ||||||
\(75\) | 66.2788 | − | 35.1015i | 0.883718 | − | 0.468020i | ||||
\(76\) | −33.9119 | −0.446209 | ||||||||
\(77\) | 13.3267 | 0.173073 | ||||||||
\(78\) | 0.0369280 | − | 18.5877i | 0.000473436 | − | 0.238304i | ||||
\(79\) | 72.0807 | 0.912414 | 0.456207 | − | 0.889874i | \(-0.349208\pi\) | ||||
0.456207 | + | 0.889874i | \(0.349208\pi\) | |||||||
\(80\) | 4.84177 | + | 19.4051i | 0.0605221 | + | 0.242564i | ||||
\(81\) | 80.9974 | + | 0.643680i | 0.999968 | + | 0.00794667i | ||||
\(82\) | − | 46.2851i | − | 0.564452i | ||||||
\(83\) | −93.0145 | −1.12066 | −0.560328 | − | 0.828271i | \(-0.689325\pi\) | ||||
−0.560328 | + | 0.828271i | \(0.689325\pi\) | |||||||
\(84\) | −0.0822577 | + | 41.4044i | −0.000979258 | + | 0.492909i | ||||
\(85\) | 8.00094 | + | 32.0665i | 0.0941287 | + | 0.377253i | ||||
\(86\) | 41.5400i | 0.483023i | ||||||||
\(87\) | −0.0325037 | + | 16.3607i | −0.000373606 | + | 0.188054i | ||||
\(88\) | − | 5.46223i | − | 0.0620708i | ||||||
\(89\) | − | 164.282i | − | 1.84587i | −0.384959 | − | 0.922934i | \(-0.625784\pi\) | ||
0.384959 | − | 0.922934i | \(-0.374216\pi\) | |||||||
\(90\) | −15.1610 | − | 61.8073i | −0.168455 | − | 0.686748i | ||||
\(91\) | −30.2334 | −0.332235 | ||||||||
\(92\) | −9.59166 | −0.104257 | ||||||||
\(93\) | −57.3585 | − | 0.113954i | −0.616758 | − | 0.00122531i | ||||
\(94\) | 33.7889 | 0.359456 | ||||||||
\(95\) | −20.5242 | − | 82.2578i | −0.216044 | − | 0.865872i | ||||
\(96\) | 16.9705 | + | 0.0337152i | 0.176776 | + | 0.000351200i | ||||
\(97\) | − | 69.5724i | − | 0.717242i | −0.933483 | − | 0.358621i | \(-0.883247\pi\) | ||
0.933483 | − | 0.358621i | \(-0.116753\pi\) | |||||||
\(98\) | −1.95123 | −0.0199105 | ||||||||
\(99\) | −0.0690599 | + | 17.3806i | −0.000697575 | + | 0.175561i | ||||
\(100\) | −44.1393 | + | 23.4887i | −0.441393 | + | 0.234887i | ||||
\(101\) | − | 131.778i | − | 1.30474i | −0.757903 | − | 0.652368i | \(-0.773776\pi\) | ||
0.757903 | − | 0.652368i | \(-0.226224\pi\) | |||||||
\(102\) | 28.0435 | + | 0.0557137i | 0.274936 | + | 0.000546213i | ||||
\(103\) | − | 36.5773i | − | 0.355120i | −0.984110 | − | 0.177560i | \(-0.943180\pi\) | ||
0.984110 | − | 0.177560i | \(-0.0568204\pi\) | |||||||
\(104\) | 12.3918i | 0.119152i | ||||||||
\(105\) | −100.482 | + | 24.8593i | −0.956969 | + | 0.236755i | ||||
\(106\) | 40.1944 | 0.379193 | ||||||||
\(107\) | 79.1711 | 0.739917 | 0.369958 | − | 0.929048i | \(-0.379372\pi\) | ||||
0.369958 | + | 0.929048i | \(0.379372\pi\) | |||||||
\(108\) | −53.9990 | − | 0.321842i | −0.499991 | − | 0.00298001i | ||||
\(109\) | −87.8564 | −0.806022 | −0.403011 | − | 0.915195i | \(-0.632036\pi\) | ||||
−0.403011 | + | 0.915195i | \(0.632036\pi\) | |||||||
\(110\) | 13.2494 | − | 3.30586i | 0.120449 | − | 0.0300533i | ||||
\(111\) | 0.0256078 | − | 12.8897i | 0.000230701 | − | 0.116123i | ||||
\(112\) | − | 27.6030i | − | 0.246455i | ||||||
\(113\) | 5.97436 | 0.0528704 | 0.0264352 | − | 0.999651i | \(-0.491584\pi\) | ||||
0.0264352 | + | 0.999651i | \(0.491584\pi\) | |||||||
\(114\) | −71.9378 | − | 0.142918i | −0.631033 | − | 0.00125367i | ||||
\(115\) | −5.80508 | − | 23.2659i | −0.0504790 | − | 0.202312i | ||||
\(116\) | − | 10.9072i | − | 0.0940273i | ||||||
\(117\) | 0.156672 | − | 39.4303i | 0.00133908 | − | 0.337011i | ||||
\(118\) | 116.522i | 0.987478i | ||||||||
\(119\) | − | 45.6134i | − | 0.383306i | ||||||
\(120\) | 10.1891 | + | 41.1847i | 0.0849096 | + | 0.343206i | ||||
\(121\) | 117.271 | 0.969178 | ||||||||
\(122\) | −91.6903 | −0.751560 | ||||||||
\(123\) | 0.195064 | − | 98.1853i | 0.00158589 | − | 0.798255i | ||||
\(124\) | 38.2391 | 0.308380 | ||||||||
\(125\) | −83.6892 | − | 92.8500i | −0.669514 | − | 0.742800i | ||||
\(126\) | −0.348989 | + | 87.8314i | −0.00276976 | + | 0.697075i | ||||
\(127\) | − | 23.9163i | − | 0.188317i | −0.995557 | − | 0.0941586i | \(-0.969984\pi\) | ||
0.995557 | − | 0.0941586i | \(-0.0300161\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | −0.175066 | + | 88.1194i | −0.00135710 | + | 0.683096i | ||||
\(130\) | −30.0581 | + | 7.49980i | −0.231216 | + | 0.0576908i | ||||
\(131\) | 4.82841i | 0.0368581i | 0.999830 | + | 0.0184291i | \(0.00586648\pi\) | ||||
−0.999830 | + | 0.0184291i | \(0.994134\pi\) | |||||||
\(132\) | 0.0230200 | − | 11.5871i | 0.000174394 | − | 0.0877812i | ||||
\(133\) | 117.009i | 0.879764i | ||||||||
\(134\) | 88.1709i | 0.657991i | ||||||||
\(135\) | −31.9007 | − | 131.177i | −0.236302 | − | 0.971680i | ||||
\(136\) | −18.6957 | −0.137468 | ||||||||
\(137\) | 260.934 | 1.90463 | 0.952314 | − | 0.305119i | \(-0.0986964\pi\) | ||||
0.952314 | + | 0.305119i | \(0.0986964\pi\) | |||||||
\(138\) | −20.3469 | − | 0.0404231i | −0.147442 | − | 0.000292921i | ||||
\(139\) | −10.8481 | −0.0780440 | −0.0390220 | − | 0.999238i | \(-0.512424\pi\) | ||||
−0.0390220 | + | 0.999238i | \(0.512424\pi\) | |||||||
\(140\) | 66.9548 | − | 16.7059i | 0.478248 | − | 0.119328i | ||||
\(141\) | 71.6769 | + | 0.142400i | 0.508347 | + | 0.00100993i | ||||
\(142\) | 184.289i | 1.29781i | ||||||||
\(143\) | 8.46088 | 0.0591670 | ||||||||
\(144\) | 35.9997 | + | 0.143041i | 0.249998 | + | 0.000993342i | ||||
\(145\) | 26.4568 | − | 6.60125i | 0.182461 | − | 0.0455259i | ||||
\(146\) | 14.9553i | 0.102434i | ||||||||
\(147\) | −4.13917 | − | 0.00822326i | −0.0281576 | − | 5.59405e-5i | ||||
\(148\) | 8.59314i | 0.0580617i | ||||||||
\(149\) | 88.4787i | 0.593817i | 0.954906 | + | 0.296908i | \(0.0959556\pi\) | ||||
−0.954906 | + | 0.296908i | \(0.904044\pi\) | |||||||
\(150\) | −93.7324 | + | 49.6410i | −0.624883 | + | 0.330940i | ||||
\(151\) | −74.3683 | −0.492505 | −0.246253 | − | 0.969206i | \(-0.579199\pi\) | ||||
−0.246253 | + | 0.969206i | \(0.579199\pi\) | |||||||
\(152\) | 47.9586 | 0.315517 | ||||||||
\(153\) | 59.4889 | + | 0.236373i | 0.388816 | + | 0.00154492i | ||||
\(154\) | −18.8467 | −0.122381 | ||||||||
\(155\) | 23.1431 | + | 92.7541i | 0.149310 | + | 0.598413i | ||||
\(156\) | −0.0522241 | + | 26.2870i | −0.000334770 | + | 0.168506i | ||||
\(157\) | 160.285i | 1.02093i | 0.859900 | + | 0.510463i | \(0.170526\pi\) | ||||
−0.859900 | + | 0.510463i | \(0.829474\pi\) | |||||||
\(158\) | −101.937 | −0.645174 | ||||||||
\(159\) | 85.2651 | + | 0.169395i | 0.536259 | + | 0.00106538i | ||||
\(160\) | −6.84730 | − | 27.4429i | −0.0427956 | − | 0.171518i | ||||
\(161\) | 33.0948i | 0.205558i | ||||||||
\(162\) | −114.548 | − | 0.910301i | −0.707084 | − | 0.00561914i | ||||
\(163\) | − | 147.791i | − | 0.906694i | −0.891334 | − | 0.453347i | \(-0.850230\pi\) | ||
0.891334 | − | 0.453347i | \(-0.149770\pi\) | |||||||
\(164\) | 65.4570i | 0.399128i | ||||||||
\(165\) | 28.1201 | − | 6.95693i | 0.170425 | − | 0.0421632i | ||||
\(166\) | 131.542 | 0.792424 | ||||||||
\(167\) | 253.815 | 1.51985 | 0.759926 | − | 0.650010i | \(-0.225235\pi\) | ||||
0.759926 | + | 0.650010i | \(0.225235\pi\) | |||||||
\(168\) | 0.116330 | − | 58.5546i | 0.000692440 | − | 0.348540i | ||||
\(169\) | 149.805 | 0.886422 | ||||||||
\(170\) | −11.3150 | − | 45.3489i | −0.0665590 | − | 0.266758i | ||||
\(171\) | −152.602 | − | 0.606349i | −0.892410 | − | 0.00354590i | ||||
\(172\) | − | 58.7464i | − | 0.341549i | ||||||
\(173\) | −141.013 | −0.815104 | −0.407552 | − | 0.913182i | \(-0.633617\pi\) | ||||
−0.407552 | + | 0.913182i | \(0.633617\pi\) | |||||||
\(174\) | 0.0459672 | − | 23.1375i | 0.000264179 | − | 0.132974i | ||||
\(175\) | 81.0449 | + | 152.297i | 0.463114 | + | 0.870269i | ||||
\(176\) | 7.72476i | 0.0438907i | ||||||||
\(177\) | −0.491072 | + | 247.181i | −0.00277442 | + | 1.39650i | ||||
\(178\) | 232.330i | 1.30523i | ||||||||
\(179\) | 125.991i | 0.703860i | 0.936026 | + | 0.351930i | \(0.114475\pi\) | ||||
−0.936026 | + | 0.351930i | \(0.885525\pi\) | |||||||
\(180\) | 21.4408 | + | 87.4088i | 0.119116 | + | 0.485604i | ||||
\(181\) | −226.332 | −1.25045 | −0.625227 | − | 0.780443i | \(-0.714994\pi\) | ||||
−0.625227 | + | 0.780443i | \(0.714994\pi\) | |||||||
\(182\) | 42.7564 | 0.234925 | ||||||||
\(183\) | −194.504 | − | 0.386420i | −1.06286 | − | 0.00211158i | ||||
\(184\) | 13.5647 | 0.0737210 | ||||||||
\(185\) | −20.8438 | + | 5.20075i | −0.112669 | + | 0.0281122i | ||||
\(186\) | 81.1172 | + | 0.161155i | 0.436114 | + | 0.000866424i | ||||
\(187\) | 12.7650i | 0.0682622i | ||||||||
\(188\) | −47.7847 | −0.254174 | ||||||||
\(189\) | −1.11047 | + | 186.317i | −0.00587552 | + | 0.985803i | ||||
\(190\) | 29.0256 | + | 116.330i | 0.152766 | + | 0.612264i | ||||
\(191\) | − | 161.079i | − | 0.843345i | −0.906748 | − | 0.421673i | \(-0.861443\pi\) | ||
0.906748 | − | 0.421673i | \(-0.138557\pi\) | |||||||
\(192\) | −24.0000 | − | 0.0476805i | −0.125000 | − | 0.000248336i | ||||
\(193\) | 23.7745i | 0.123184i | 0.998101 | + | 0.0615921i | \(0.0196178\pi\) | ||||
−0.998101 | + | 0.0615921i | \(0.980382\pi\) | |||||||
\(194\) | 98.3903i | 0.507166i | ||||||||
\(195\) | −63.7943 | + | 15.7828i | −0.327150 | + | 0.0809373i | ||||
\(196\) | 2.75945 | 0.0140788 | ||||||||
\(197\) | −132.922 | −0.674730 | −0.337365 | − | 0.941374i | \(-0.609536\pi\) | ||||
−0.337365 | + | 0.941374i | \(0.609536\pi\) | |||||||
\(198\) | 0.0976655 | − | 24.5798i | 0.000493260 | − | 0.124141i | ||||
\(199\) | 148.011 | 0.743775 | 0.371887 | − | 0.928278i | \(-0.378711\pi\) | ||||
0.371887 | + | 0.928278i | \(0.378711\pi\) | |||||||
\(200\) | 62.4224 | − | 33.2181i | 0.312112 | − | 0.166091i | ||||
\(201\) | −0.371587 | + | 187.038i | −0.00184869 | + | 0.930539i | ||||
\(202\) | 186.363i | 0.922587i | ||||||||
\(203\) | −37.6338 | −0.185388 | ||||||||
\(204\) | −39.6595 | − | 0.0787911i | −0.194409 | − | 0.000386231i | ||||
\(205\) | −158.775 | + | 39.6160i | −0.774512 | + | 0.193249i | ||||
\(206\) | 51.7282i | 0.251108i | ||||||||
\(207\) | −43.1621 | − | 0.171500i | −0.208513 | − | 0.000828504i | ||||
\(208\) | − | 17.5247i | − | 0.0842533i | ||||||
\(209\) | − | 32.7451i | − | 0.156675i | ||||||
\(210\) | 142.103 | − | 35.1564i | 0.676679 | − | 0.167411i | ||||
\(211\) | −193.048 | −0.914920 | −0.457460 | − | 0.889230i | \(-0.651241\pi\) | ||||
−0.457460 | + | 0.889230i | \(0.651241\pi\) | |||||||
\(212\) | −56.8435 | −0.268130 | ||||||||
\(213\) | −0.776666 | + | 390.935i | −0.00364632 | + | 1.83537i | ||||
\(214\) | −111.965 | −0.523200 | ||||||||
\(215\) | 142.497 | − | 35.5546i | 0.662778 | − | 0.165370i | ||||
\(216\) | 76.3662 | + | 0.455153i | 0.353547 | + | 0.00210719i | ||||
\(217\) | − | 131.939i | − | 0.608014i | ||||||
\(218\) | 124.248 | 0.569944 | ||||||||
\(219\) | −0.0630276 | + | 31.7249i | −0.000287797 | + | 0.144863i | ||||
\(220\) | −18.7375 | + | 4.67519i | −0.0851702 | + | 0.0212509i | ||||
\(221\) | − | 28.9592i | − | 0.131037i | ||||||
\(222\) | −0.0362149 | + | 18.2288i | −0.000163130 | + | 0.0821115i | ||||
\(223\) | 44.5616i | 0.199828i | 0.994996 | + | 0.0999140i | \(0.0318568\pi\) | ||||
−0.994996 | + | 0.0999140i | \(0.968143\pi\) | |||||||
\(224\) | 39.0365i | 0.174270i | ||||||||
\(225\) | −199.045 | + | 104.909i | −0.884646 | + | 0.466264i | ||||
\(226\) | −8.44901 | −0.0373850 | ||||||||
\(227\) | 186.388 | 0.821094 | 0.410547 | − | 0.911839i | \(-0.365338\pi\) | ||||
0.410547 | + | 0.911839i | \(0.365338\pi\) | |||||||
\(228\) | 101.735 | + | 0.202117i | 0.446208 | + | 0.000886477i | ||||
\(229\) | 127.546 | 0.556970 | 0.278485 | − | 0.960441i | \(-0.410168\pi\) | ||||
0.278485 | + | 0.960441i | \(0.410168\pi\) | |||||||
\(230\) | 8.20962 | + | 32.9029i | 0.0356940 | + | 0.143056i | ||||
\(231\) | −39.9799 | − | 0.0794277i | −0.173073 | − | 0.000343843i | ||||
\(232\) | 15.4251i | 0.0664873i | ||||||||
\(233\) | −119.516 | −0.512945 | −0.256473 | − | 0.966551i | \(-0.582560\pi\) | ||||
−0.256473 | + | 0.966551i | \(0.582560\pi\) | |||||||
\(234\) | −0.221568 | + | 55.7628i | −0.000946871 | + | 0.238303i | ||||
\(235\) | −28.9203 | − | 115.908i | −0.123065 | − | 0.493227i | ||||
\(236\) | − | 164.788i | − | 0.698252i | ||||||
\(237\) | −216.242 | − | 0.429605i | −0.912412 | − | 0.00181268i | ||||
\(238\) | 64.5071i | 0.271038i | ||||||||
\(239\) | − | 404.639i | − | 1.69305i | −0.532348 | − | 0.846526i | \(-0.678690\pi\) | ||
0.532348 | − | 0.846526i | \(-0.321310\pi\) | |||||||
\(240\) | −14.4096 | − | 58.2440i | −0.0600401 | − | 0.242683i | ||||
\(241\) | −156.085 | −0.647654 | −0.323827 | − | 0.946116i | \(-0.604970\pi\) | ||||
−0.323827 | + | 0.946116i | \(0.604970\pi\) | |||||||
\(242\) | −165.846 | −0.685312 | ||||||||
\(243\) | −242.988 | − | 2.41379i | −0.999951 | − | 0.00993328i | ||||
\(244\) | 129.670 | 0.531433 | ||||||||
\(245\) | 1.67008 | + | 6.69343i | 0.00681666 | + | 0.0273201i | ||||
\(246\) | −0.275862 | + | 138.855i | −0.00112139 | + | 0.564451i | ||||
\(247\) | 74.2869i | 0.300757i | ||||||||
\(248\) | −54.0782 | −0.218057 | ||||||||
\(249\) | 279.043 | + | 0.554372i | 1.12065 | + | 0.00222639i | ||||
\(250\) | 118.354 | + | 131.310i | 0.473418 | + | 0.525239i | ||||
\(251\) | − | 150.203i | − | 0.598416i | −0.954188 | − | 0.299208i | \(-0.903277\pi\) | ||
0.954188 | − | 0.299208i | \(-0.0967225\pi\) | |||||||
\(252\) | 0.493545 | − | 124.212i | 0.00195851 | − | 0.492906i | ||||
\(253\) | − | 9.26166i | − | 0.0366074i | ||||||
\(254\) | 33.8227i | 0.133160i | ||||||||
\(255\) | −23.8117 | − | 96.2471i | −0.0933790 | − | 0.377440i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −11.3432 | −0.0441368 | −0.0220684 | − | 0.999756i | \(-0.507025\pi\) | ||||
−0.0220684 | + | 0.999756i | \(0.507025\pi\) | |||||||
\(258\) | 0.247581 | − | 124.620i | 0.000959616 | − | 0.483022i | ||||
\(259\) | 29.6495 | 0.114477 | ||||||||
\(260\) | 42.5085 | − | 10.6063i | 0.163494 | − | 0.0407935i | ||||
\(261\) | 0.195022 | − | 49.0819i | 0.000747210 | − | 0.188053i | ||||
\(262\) | − | 6.82841i | − | 0.0260626i | ||||||
\(263\) | −147.415 | −0.560511 | −0.280256 | − | 0.959925i | \(-0.590419\pi\) | ||||
−0.280256 | + | 0.959925i | \(0.590419\pi\) | |||||||
\(264\) | −0.0325552 | + | 16.3867i | −0.000123315 | + | 0.0620707i | ||||
\(265\) | −34.4029 | − | 137.882i | −0.129822 | − | 0.520308i | ||||
\(266\) | − | 165.475i | − | 0.622087i | ||||||
\(267\) | −0.979132 | + | 492.846i | −0.00366716 | + | 1.84586i | ||||
\(268\) | − | 124.692i | − | 0.465270i | ||||||
\(269\) | − | 205.779i | − | 0.764976i | −0.923960 | − | 0.382488i | \(-0.875067\pi\) | ||
0.923960 | − | 0.382488i | \(-0.124933\pi\) | |||||||
\(270\) | 45.1144 | + | 185.512i | 0.167090 | + | 0.687081i | ||||
\(271\) | −239.892 | −0.885209 | −0.442605 | − | 0.896717i | \(-0.645945\pi\) | ||||
−0.442605 | + | 0.896717i | \(0.645945\pi\) | |||||||
\(272\) | 26.4397 | 0.0972048 | ||||||||
\(273\) | 90.6999 | + | 0.180193i | 0.332234 | + | 0.000660046i | ||||
\(274\) | −369.016 | −1.34678 | ||||||||
\(275\) | −22.6806 | − | 42.6207i | −0.0824750 | − | 0.154984i | ||||
\(276\) | 28.7749 | + | 0.0571669i | 0.104257 | + | 0.000207126i | ||||
\(277\) | − | 165.615i | − | 0.597890i | −0.954270 | − | 0.298945i | \(-0.903365\pi\) | ||
0.954270 | − | 0.298945i | \(-0.0966347\pi\) | |||||||
\(278\) | 15.3415 | 0.0551854 | ||||||||
\(279\) | 172.075 | + | 0.683721i | 0.616755 | + | 0.00245061i | ||||
\(280\) | −94.6883 | + | 23.6257i | −0.338173 | + | 0.0843776i | ||||
\(281\) | 215.556i | 0.767104i | 0.923519 | + | 0.383552i | \(0.125299\pi\) | ||||
−0.923519 | + | 0.383552i | \(0.874701\pi\) | |||||||
\(282\) | −101.366 | − | 0.201384i | −0.359456 | − | 0.000714127i | ||||
\(283\) | 261.575i | 0.924293i | 0.886804 | + | 0.462147i | \(0.152921\pi\) | ||||
−0.886804 | + | 0.462147i | \(0.847079\pi\) | |||||||
\(284\) | − | 260.624i | − | 0.917689i | ||||||
\(285\) | 61.0822 | + | 246.895i | 0.214323 | + | 0.866299i | ||||
\(286\) | −11.9655 | −0.0418374 | ||||||||
\(287\) | 225.851 | 0.786938 | ||||||||
\(288\) | −50.9113 | − | 0.202291i | −0.176775 | − | 0.000702399i | ||||
\(289\) | −245.309 | −0.848820 | ||||||||
\(290\) | −37.4156 | + | 9.33558i | −0.129019 | + | 0.0321917i | ||||
\(291\) | −0.414656 | + | 208.717i | −0.00142493 | + | 0.717240i | ||||
\(292\) | − | 21.1500i | − | 0.0724314i | ||||||
\(293\) | −529.882 | −1.80847 | −0.904235 | − | 0.427036i | \(-0.859558\pi\) | ||||
−0.904235 | + | 0.427036i | \(0.859558\pi\) | |||||||
\(294\) | 5.85367 | + | 0.0116294i | 0.0199105 | + | 3.95559e-5i | ||||
\(295\) | 399.715 | − | 99.7330i | 1.35496 | − | 0.338078i | ||||
\(296\) | − | 12.1525i | − | 0.0410558i | ||||||
\(297\) | 0.310769 | − | 52.1412i | 0.00104636 | − | 0.175560i | ||||
\(298\) | − | 125.128i | − | 0.419892i | ||||||
\(299\) | 21.0114i | 0.0702721i | ||||||||
\(300\) | 132.558 | − | 70.2030i | 0.441859 | − | 0.234010i | ||||
\(301\) | −202.697 | −0.673412 | ||||||||
\(302\) | 105.173 | 0.348254 | ||||||||
\(303\) | −0.785407 | + | 395.334i | −0.00259210 | + | 1.30473i | ||||
\(304\) | −67.8237 | −0.223104 | ||||||||
\(305\) | 78.4789 | + | 314.531i | 0.257308 | + | 1.03125i | ||||
\(306\) | −84.1300 | − | 0.334282i | −0.274935 | − | 0.00109242i | ||||
\(307\) | − | 122.092i | − | 0.397693i | −0.980031 | − | 0.198847i | \(-0.936280\pi\) | ||
0.980031 | − | 0.198847i | \(-0.0637195\pi\) | |||||||
\(308\) | 26.6533 | 0.0865367 | ||||||||
\(309\) | −0.218003 | + | 109.732i | −0.000705512 | + | 0.355119i | ||||
\(310\) | −32.7293 | − | 131.174i | −0.105578 | − | 0.423142i | ||||
\(311\) | − | 50.4037i | − | 0.162070i | −0.996711 | − | 0.0810348i | \(-0.974178\pi\) | ||
0.996711 | − | 0.0810348i | \(-0.0258225\pi\) | |||||||
\(312\) | 0.0738561 | − | 37.1754i | 0.000236718 | − | 0.119152i | ||||
\(313\) | 491.711i | 1.57096i | 0.618887 | + | 0.785480i | \(0.287584\pi\) | ||||
−0.618887 | + | 0.785480i | \(0.712416\pi\) | |||||||
\(314\) | − | 226.678i | − | 0.721904i | ||||||
\(315\) | 301.593 | − | 73.9789i | 0.957437 | − | 0.234854i | ||||
\(316\) | 144.161 | 0.456207 | ||||||||
\(317\) | 534.614 | 1.68648 | 0.843240 | − | 0.537538i | \(-0.180645\pi\) | ||||
0.843240 | + | 0.537538i | \(0.180645\pi\) | |||||||
\(318\) | −120.583 | − | 0.239561i | −0.379192 | − | 0.000753337i | ||||
\(319\) | 10.5319 | 0.0330154 | ||||||||
\(320\) | 9.68354 | + | 38.8102i | 0.0302611 | + | 0.121282i | ||||
\(321\) | −237.513 | − | 0.471865i | −0.739915 | − | 0.00146998i | ||||
\(322\) | − | 46.8031i | − | 0.145351i | ||||||
\(323\) | −112.077 | −0.346989 | ||||||||
\(324\) | 161.995 | + | 1.28736i | 0.499984 | + | 0.00397333i | ||||
\(325\) | 51.4541 | + | 96.6910i | 0.158320 | + | 0.297511i | ||||
\(326\) | 209.008i | 0.641129i | ||||||||
\(327\) | 263.569 | + | 0.523630i | 0.806021 | + | 0.00160131i | ||||
\(328\) | − | 92.5702i | − | 0.282226i | ||||||
\(329\) | 164.875i | 0.501140i | ||||||||
\(330\) | −39.7678 | + | 9.83859i | −0.120508 | + | 0.0298139i | ||||
\(331\) | 360.609 | 1.08945 | 0.544727 | − | 0.838614i | \(-0.316633\pi\) | ||||
0.544727 | + | 0.838614i | \(0.316633\pi\) | |||||||
\(332\) | −186.029 | −0.560328 | ||||||||
\(333\) | −0.153647 | + | 38.6688i | −0.000461401 | + | 0.116123i | ||||
\(334\) | −358.949 | −1.07470 | ||||||||
\(335\) | 302.458 | − | 75.4665i | 0.902861 | − | 0.225273i | ||||
\(336\) | −0.164515 | + | 82.8088i | −0.000489629 | + | 0.246455i | ||||
\(337\) | − | 518.017i | − | 1.53714i | −0.639765 | − | 0.768571i | \(-0.720968\pi\) | ||
0.639765 | − | 0.768571i | \(-0.279032\pi\) | |||||||
\(338\) | −211.857 | −0.626795 | ||||||||
\(339\) | −17.9230 | − | 0.0356075i | −0.0528703 | − | 0.000105037i | ||||
\(340\) | 16.0019 | + | 64.1331i | 0.0470643 | + | 0.188627i | ||||
\(341\) | 36.9235i | 0.108280i | ||||||||
\(342\) | 215.812 | + | 0.857507i | 0.631029 | + | 0.00250733i | ||||
\(343\) | − | 347.658i | − | 1.01358i | ||||||
\(344\) | 83.0800i | 0.241512i | ||||||||
\(345\) | 17.2765 | + | 69.8321i | 0.0500769 | + | 0.202412i | ||||
\(346\) | 199.422 | 0.576365 | ||||||||
\(347\) | 341.360 | 0.983746 | 0.491873 | − | 0.870667i | \(-0.336313\pi\) | ||||
0.491873 | + | 0.870667i | \(0.336313\pi\) | |||||||
\(348\) | −0.0650074 | + | 32.7214i | −0.000186803 | + | 0.0940271i | ||||
\(349\) | −0.400677 | −0.00114807 | −0.000574036 | − | 1.00000i | \(-0.500183\pi\) | ||||
−0.000574036 | 1.00000i | \(0.500183\pi\) | ||||||||
\(350\) | −114.615 | − | 215.381i | −0.327471 | − | 0.615373i | ||||
\(351\) | −0.705022 | + | 118.290i | −0.00200861 | + | 0.337007i | ||||
\(352\) | − | 10.9245i | − | 0.0310354i | ||||||
\(353\) | −271.119 | −0.768042 | −0.384021 | − | 0.923324i | \(-0.625461\pi\) | ||||
−0.384021 | + | 0.923324i | \(0.625461\pi\) | |||||||
\(354\) | 0.694481 | − | 349.567i | 0.00196181 | − | 0.987476i | ||||
\(355\) | 632.178 | − | 157.735i | 1.78078 | − | 0.444324i | ||||
\(356\) | − | 328.564i | − | 0.922934i | ||||||
\(357\) | −0.271859 | + | 136.840i | −0.000761509 | + | 0.383305i | ||||
\(358\) | − | 178.178i | − | 0.497704i | ||||||
\(359\) | − | 348.233i | − | 0.970008i | −0.874512 | − | 0.485004i | \(-0.838818\pi\) | ||
0.874512 | − | 0.485004i | \(-0.161182\pi\) | |||||||
\(360\) | −30.3219 | − | 123.615i | −0.0842276 | − | 0.343374i | ||||
\(361\) | −73.4964 | −0.203591 | ||||||||
\(362\) | 320.082 | 0.884205 | ||||||||
\(363\) | −351.811 | − | 0.698939i | −0.969176 | − | 0.00192545i | ||||
\(364\) | −60.4667 | −0.166117 | ||||||||
\(365\) | 51.3021 | − | 12.8004i | 0.140554 | − | 0.0350696i | ||||
\(366\) | 275.070 | + | 0.546480i | 0.751559 | + | 0.00149311i | ||||
\(367\) | 546.201i | 1.48828i | 0.668021 | + | 0.744142i | \(0.267142\pi\) | ||||
−0.668021 | + | 0.744142i | \(0.732858\pi\) | |||||||
\(368\) | −19.1833 | −0.0521286 | ||||||||
\(369\) | −1.17038 | + | 294.554i | −0.00317176 | + | 0.798250i | ||||
\(370\) | 29.4776 | − | 7.35497i | 0.0796692 | − | 0.0198783i | ||||
\(371\) | 196.131i | 0.528656i | ||||||||
\(372\) | −114.717 | − | 0.227907i | −0.308379 | − | 0.000612654i | ||||
\(373\) | − | 561.225i | − | 1.50463i | −0.658806 | − | 0.752313i | \(-0.728938\pi\) | ||
0.658806 | − | 0.752313i | \(-0.271062\pi\) | |||||||
\(374\) | − | 18.0525i | − | 0.0482686i | ||||||
\(375\) | 250.514 | + | 279.048i | 0.668036 | + | 0.744129i | ||||
\(376\) | 67.5778 | 0.179728 | ||||||||
\(377\) | −23.8931 | −0.0633769 | ||||||||
\(378\) | 1.57045 | − | 263.492i | 0.00415462 | − | 0.697068i | ||||
\(379\) | −64.2274 | −0.169465 | −0.0847327 | − | 0.996404i | \(-0.527004\pi\) | ||||
−0.0847327 | + | 0.996404i | \(0.527004\pi\) | |||||||
\(380\) | −41.0484 | − | 164.516i | −0.108022 | − | 0.432936i | ||||
\(381\) | −0.142542 | + | 71.7487i | −0.000374127 | + | 0.188317i | ||||
\(382\) | 227.800i | 0.596335i | ||||||||
\(383\) | 54.9496 | 0.143471 | 0.0717357 | − | 0.997424i | \(-0.477146\pi\) | ||||
0.0717357 | + | 0.997424i | \(0.477146\pi\) | |||||||
\(384\) | 33.9411 | + | 0.0674304i | 0.0883882 | + | 0.000175600i | ||||
\(385\) | 16.1311 | + | 64.6512i | 0.0418991 | + | 0.167925i | ||||
\(386\) | − | 33.6223i | − | 0.0871044i | ||||||
\(387\) | 1.05039 | − | 264.357i | 0.00271420 | − | 0.683092i | ||||
\(388\) | − | 139.145i | − | 0.358621i | ||||||
\(389\) | 333.955i | 0.858497i | 0.903186 | + | 0.429248i | \(0.141222\pi\) | ||||
−0.903186 | + | 0.429248i | \(0.858778\pi\) | |||||||
\(390\) | 90.2187 | − | 22.3202i | 0.231330 | − | 0.0572313i | ||||
\(391\) | −31.7001 | −0.0810744 | ||||||||
\(392\) | −3.90246 | −0.00995525 | ||||||||
\(393\) | 0.0287776 | − | 14.4852i | 7.32255e−5 | − | 0.0368580i | ||||
\(394\) | 187.980 | 0.477106 | ||||||||
\(395\) | 87.2495 | + | 349.683i | 0.220885 | + | 0.885273i | ||||
\(396\) | −0.138120 | + | 34.7612i | −0.000348788 | + | 0.0877807i | ||||
\(397\) | 188.644i | 0.475175i | 0.971366 | + | 0.237587i | \(0.0763566\pi\) | ||||
−0.971366 | + | 0.237587i | \(0.923643\pi\) | |||||||
\(398\) | −209.319 | −0.525928 | ||||||||
\(399\) | 0.697378 | − | 351.025i | 0.00174781 | − | 0.879762i | ||||
\(400\) | −88.2786 | + | 46.9775i | −0.220697 | + | 0.117444i | ||||
\(401\) | − | 200.819i | − | 0.500796i | −0.968143 | − | 0.250398i | \(-0.919438\pi\) | ||
0.968143 | − | 0.250398i | \(-0.0805616\pi\) | |||||||
\(402\) | 0.525504 | − | 264.512i | 0.00130722 | − | 0.657990i | ||||
\(403\) | − | 83.7660i | − | 0.207856i | ||||||
\(404\) | − | 263.557i | − | 0.652368i | ||||||
\(405\) | 94.9201 | + | 393.720i | 0.234371 | + | 0.972147i | ||||
\(406\) | 53.2222 | 0.131089 | ||||||||
\(407\) | −8.29749 | −0.0203870 | ||||||||
\(408\) | 56.0870 | + | 0.111427i | 0.137468 | + | 0.000273107i | ||||
\(409\) | 324.047 | 0.792292 | 0.396146 | − | 0.918188i | \(-0.370347\pi\) | ||||
0.396146 | + | 0.918188i | \(0.370347\pi\) | |||||||
\(410\) | 224.542 | − | 56.0255i | 0.547662 | − | 0.136647i | ||||
\(411\) | −782.801 | − | 1.55518i | −1.90462 | − | 0.00378390i | ||||
\(412\) | − | 73.1547i | − | 0.177560i | ||||||
\(413\) | −568.579 | −1.37670 | ||||||||
\(414\) | 61.0405 | + | 0.242538i | 0.147441 | + | 0.000585841i | ||||
\(415\) | −112.589 | − | 451.238i | −0.271298 | − | 1.08732i | ||||
\(416\) | 24.7837i | 0.0595761i | ||||||||
\(417\) | 32.5443 | + | 0.0646554i | 0.0780438 | + | 0.000155049i | ||||
\(418\) | 46.3086i | 0.110786i | ||||||||
\(419\) | 51.6049i | 0.123162i | 0.998102 | + | 0.0615811i | \(0.0196143\pi\) | ||||
−0.998102 | + | 0.0615811i | \(0.980386\pi\) | |||||||
\(420\) | −200.963 | + | 49.7186i | −0.478484 | + | 0.118378i | ||||
\(421\) | −444.406 | −1.05560 | −0.527798 | − | 0.849370i | \(-0.676982\pi\) | ||||
−0.527798 | + | 0.849370i | \(0.676982\pi\) | |||||||
\(422\) | 273.011 | 0.646946 | ||||||||
\(423\) | −215.030 | − | 0.854398i | −0.508344 | − | 0.00201985i | ||||
\(424\) | 80.3889 | 0.189596 | ||||||||
\(425\) | −145.879 | + | 77.6294i | −0.343244 | + | 0.182658i | ||||
\(426\) | 1.09837 | − | 552.865i | 0.00257834 | − | 1.29781i | ||||
\(427\) | − | 447.409i | − | 1.04780i | ||||||
\(428\) | 158.342 | 0.369958 | ||||||||
\(429\) | −25.3826 | − | 0.0504274i | −0.0591669 | − | 0.000117546i | ||||
\(430\) | −201.522 | + | 50.2818i | −0.468655 | + | 0.116934i | ||||
\(431\) | 175.252i | 0.406618i | 0.979115 | + | 0.203309i | \(0.0651695\pi\) | ||||
−0.979115 | + | 0.203309i | \(0.934830\pi\) | |||||||
\(432\) | −107.998 | − | 0.643683i | −0.249996 | − | 0.00149001i | ||||
\(433\) | − | 687.223i | − | 1.58712i | −0.608492 | − | 0.793560i | \(-0.708225\pi\) | ||
0.608492 | − | 0.793560i | \(-0.291775\pi\) | |||||||
\(434\) | 186.590i | 0.429931i | ||||||||
\(435\) | −79.4096 | + | 19.6460i | −0.182551 | + | 0.0451633i | ||||
\(436\) | −175.713 | −0.403011 | ||||||||
\(437\) | 81.3178 | 0.186082 | ||||||||
\(438\) | 0.0891344 | − | 44.8658i | 0.000203503 | − | 0.102433i | ||||
\(439\) | 63.9919 | 0.145767 | 0.0728837 | − | 0.997340i | \(-0.476780\pi\) | ||||
0.0728837 | + | 0.997340i | \(0.476780\pi\) | |||||||
\(440\) | 26.4988 | − | 6.61172i | 0.0602245 | − | 0.0150266i | ||||
\(441\) | 12.4174 | + | 0.0493394i | 0.0281575 | + | 0.000111881i | ||||
\(442\) | 40.9545i | 0.0926573i | ||||||||
\(443\) | −619.458 | −1.39833 | −0.699163 | − | 0.714962i | \(-0.746444\pi\) | ||||
−0.699163 | + | 0.714962i | \(0.746444\pi\) | |||||||
\(444\) | 0.0512156 | − | 25.7794i | 0.000115350 | − | 0.0580616i | ||||
\(445\) | 796.977 | − | 198.854i | 1.79096 | − | 0.446863i | ||||
\(446\) | − | 63.0197i | − | 0.141300i | ||||||
\(447\) | 0.527339 | − | 265.436i | 0.00117973 | − | 0.593816i | ||||
\(448\) | − | 55.2060i | − | 0.123228i | ||||||
\(449\) | 321.746i | 0.716583i | 0.933610 | + | 0.358291i | \(0.116641\pi\) | ||||
−0.933610 | + | 0.358291i | \(0.883359\pi\) | |||||||
\(450\) | 281.493 | − | 148.364i | 0.625539 | − | 0.329698i | ||||
\(451\) | −63.2050 | −0.140144 | ||||||||
\(452\) | 11.9487 | 0.0264352 | ||||||||
\(453\) | 223.104 | + | 0.443239i | 0.492504 | + | 0.000978453i | ||||
\(454\) | −263.593 | −0.580601 | ||||||||
\(455\) | −36.5958 | − | 146.670i | −0.0804302 | − | 0.322352i | ||||
\(456\) | −143.876 | − | 0.285836i | −0.315517 | − | 0.000626834i | ||||
\(457\) | − | 694.280i | − | 1.51921i | −0.650383 | − | 0.759607i | \(-0.725392\pi\) | ||
0.650383 | − | 0.759607i | \(-0.274608\pi\) | |||||||
\(458\) | −180.378 | −0.393837 | ||||||||
\(459\) | −178.465 | − | 1.06367i | −0.388812 | − | 0.00231737i | ||||
\(460\) | −11.6102 | − | 46.5318i | −0.0252395 | − | 0.101156i | ||||
\(461\) | 878.547i | 1.90574i | 0.303376 | + | 0.952871i | \(0.401886\pi\) | ||||
−0.303376 | + | 0.952871i | \(0.598114\pi\) | |||||||
\(462\) | 56.5401 | + | 0.112328i | 0.122381 | + | 0.000243133i | ||||
\(463\) | 266.191i | 0.574926i | 0.957792 | + | 0.287463i | \(0.0928119\pi\) | ||||
−0.957792 | + | 0.287463i | \(0.907188\pi\) | |||||||
\(464\) | − | 21.8143i | − | 0.0470136i | ||||||
\(465\) | −68.8764 | − | 278.400i | −0.148121 | − | 0.598709i | ||||
\(466\) | 169.022 | 0.362707 | ||||||||
\(467\) | 240.484 | 0.514956 | 0.257478 | − | 0.966284i | \(-0.417109\pi\) | ||||
0.257478 | + | 0.966284i | \(0.417109\pi\) | |||||||
\(468\) | 0.313344 | − | 78.8605i | 0.000669539 | − | 0.168505i | ||||
\(469\) | −430.235 | −0.917346 | ||||||||
\(470\) | 40.8995 | + | 163.919i | 0.0870203 | + | 0.348764i | ||||
\(471\) | 0.955311 | − | 480.855i | 0.00202826 | − | 1.02092i | ||||
\(472\) | 233.045i | 0.493739i | ||||||||
\(473\) | 56.7252 | 0.119927 | ||||||||
\(474\) | 305.812 | + | 0.607554i | 0.645173 | + | 0.00128176i | ||||
\(475\) | 374.212 | − | 199.137i | 0.787814 | − | 0.419235i | ||||
\(476\) | − | 91.2268i | − | 0.191653i | ||||||
\(477\) | −255.794 | − | 1.01637i | −0.536255 | − | 0.00213076i | ||||
\(478\) | 572.246i | 1.19717i | ||||||||
\(479\) | − | 477.380i | − | 0.996617i | −0.867000 | − | 0.498309i | \(-0.833955\pi\) | ||
0.867000 | − | 0.498309i | \(-0.166045\pi\) | |||||||
\(480\) | 20.3783 | + | 82.3694i | 0.0424548 | + | 0.171603i | ||||
\(481\) | 18.8240 | 0.0391352 | ||||||||
\(482\) | 220.737 | 0.457961 | ||||||||
\(483\) | 0.197247 | − | 99.2842i | 0.000408379 | − | 0.205557i | ||||
\(484\) | 234.541 | 0.484589 | ||||||||
\(485\) | 337.515 | − | 84.2135i | 0.695907 | − | 0.173636i | ||||
\(486\) | 343.637 | + | 3.41361i | 0.707072 | + | 0.00702389i | ||||
\(487\) | 521.050i | 1.06992i | 0.844878 | + | 0.534959i | \(0.179673\pi\) | ||||
−0.844878 | + | 0.534959i | \(0.820327\pi\) | |||||||
\(488\) | −183.381 | −0.375780 | ||||||||
\(489\) | −0.880844 | + | 443.372i | −0.00180132 | + | 0.906692i | ||||
\(490\) | −2.36185 | − | 9.46594i | −0.00482010 | − | 0.0193182i | ||||
\(491\) | − | 763.114i | − | 1.55420i | −0.629375 | − | 0.777102i | \(-0.716689\pi\) | ||
0.629375 | − | 0.777102i | \(-0.283311\pi\) | |||||||
\(492\) | 0.390128 | − | 196.371i | 0.000792943 | − | 0.399127i | ||||
\(493\) | − | 36.0478i | − | 0.0731192i | ||||||
\(494\) | − | 105.058i | − | 0.212667i | ||||||
\(495\) | −84.4015 | + | 20.7032i | −0.170508 | + | 0.0418246i | ||||
\(496\) | 76.4782 | 0.154190 | ||||||||
\(497\) | −899.249 | −1.80935 | ||||||||
\(498\) | −394.626 | − | 0.784000i | −0.792422 | − | 0.00157430i | ||||
\(499\) | −605.819 | −1.21407 | −0.607033 | − | 0.794677i | \(-0.707640\pi\) | ||||
−0.607033 | + | 0.794677i | \(0.707640\pi\) | |||||||
\(500\) | −167.378 | − | 185.700i | −0.334757 | − | 0.371400i | ||||
\(501\) | −761.444 | − | 1.51275i | −1.51985 | − | 0.00301947i | ||||
\(502\) | 212.418i | 0.423144i | ||||||||
\(503\) | −325.402 | −0.646923 | −0.323462 | − | 0.946241i | \(-0.604847\pi\) | ||||
−0.323462 | + | 0.946241i | \(0.604847\pi\) | |||||||
\(504\) | −0.697978 | + | 175.663i | −0.00138488 | + | 0.348537i | ||||
\(505\) | 639.292 | − | 159.510i | 1.26593 | − | 0.315862i | ||||
\(506\) | 13.0980i | 0.0258853i | ||||||||
\(507\) | −449.415 | − | 0.892849i | −0.886420 | − | 0.00176104i | ||||
\(508\) | − | 47.8326i | − | 0.0941586i | ||||||
\(509\) | 428.784i | 0.842404i | 0.906967 | + | 0.421202i | \(0.138392\pi\) | ||||
−0.906967 | + | 0.421202i | \(0.861608\pi\) | |||||||
\(510\) | 33.6748 | + | 136.114i | 0.0660289 | + | 0.266890i | ||||
\(511\) | −72.9753 | −0.142809 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 457.802 | + | 2.72856i | 0.892402 | + | 0.00531883i | ||||
\(514\) | 16.0416 | 0.0312094 | ||||||||
\(515\) | 177.447 | − | 44.2748i | 0.344557 | − | 0.0859705i | ||||
\(516\) | −0.350132 | + | 176.239i | −0.000678551 | + | 0.341548i | ||||
\(517\) | − | 46.1407i | − | 0.0892470i | ||||||
\(518\) | −41.9307 | −0.0809474 | ||||||||
\(519\) | 423.038 | + | 0.840446i | 0.815102 | + | 0.00161936i | ||||
\(520\) | −60.1161 | + | 14.9996i | −0.115608 | + | 0.0288454i | ||||
\(521\) | 700.778i | 1.34506i | 0.740069 | + | 0.672531i | \(0.234793\pi\) | ||||
−0.740069 | + | 0.672531i | \(0.765207\pi\) | |||||||
\(522\) | −0.275802 | + | 69.4122i | −0.000528357 | + | 0.132974i | ||||
\(523\) | − | 411.838i | − | 0.787454i | −0.919228 | − | 0.393727i | \(-0.871186\pi\) | ||
0.919228 | − | 0.393727i | \(-0.128814\pi\) | |||||||
\(524\) | 9.65682i | 0.0184291i | ||||||||
\(525\) | −242.227 | − | 457.373i | −0.461384 | − | 0.871187i | ||||
\(526\) | 208.476 | 0.396341 | ||||||||
\(527\) | 126.379 | 0.239808 | ||||||||
\(528\) | 0.0460400 | − | 23.1742i | 8.71971e−5 | − | 0.0438906i | ||||
\(529\) | 23.0000 | 0.0434783 | ||||||||
\(530\) | 48.6531 | + | 194.994i | 0.0917982 | + | 0.367913i | ||||
\(531\) | 2.94643 | − | 741.538i | 0.00554883 | − | 1.39649i | ||||
\(532\) | 234.017i | 0.439882i | ||||||||
\(533\) | 143.389 | 0.269023 | ||||||||
\(534\) | 1.38470 | − | 696.989i | 0.00259307 | − | 1.30522i | ||||
\(535\) | 95.8321 | + | 384.080i | 0.179125 | + | 0.717907i | ||||
\(536\) | 176.342i | 0.328996i | ||||||||
\(537\) | 0.750914 | − | 377.972i | 0.00139835 | − | 0.703859i | ||||
\(538\) | 291.015i | 0.540920i | ||||||||
\(539\) | 2.66452i | 0.00494344i | ||||||||
\(540\) | −63.8014 | − | 262.354i | −0.118151 | − | 0.485840i | ||||
\(541\) | 598.358 | 1.10602 | 0.553011 | − | 0.833174i | \(-0.313479\pi\) | ||||
0.553011 | + | 0.833174i | \(0.313479\pi\) | |||||||
\(542\) | 339.258 | 0.625937 | ||||||||
\(543\) | 678.995 | + | 1.34895i | 1.25045 | + | 0.00248426i | ||||
\(544\) | −37.3914 | −0.0687342 | ||||||||
\(545\) | −106.345 | − | 426.215i | −0.195129 | − | 0.782047i | ||||
\(546\) | −128.269 | − | 0.254831i | −0.234925 | − | 0.000466723i | ||||
\(547\) | 779.530i | 1.42510i | 0.701621 | + | 0.712550i | \(0.252460\pi\) | ||||
−0.701621 | + | 0.712550i | \(0.747540\pi\) | |||||||
\(548\) | 521.868 | 0.952314 | ||||||||
\(549\) | 583.509 | + | 2.31851i | 1.06286 | + | 0.00422316i | ||||
\(550\) | 32.0752 | + | 60.2748i | 0.0583186 | + | 0.109591i | ||||
\(551\) | 92.4706i | 0.167823i | ||||||||
\(552\) | −40.6939 | − | 0.0808462i | −0.0737208 | − | 0.000146461i | ||||
\(553\) | − | 497.410i | − | 0.899476i | ||||||
\(554\) | 234.216i | 0.422772i | ||||||||
\(555\) | 62.5623 | − | 15.4780i | 0.112725 | − | 0.0278883i | ||||
\(556\) | −21.6962 | −0.0390220 | ||||||||
\(557\) | 185.855 | 0.333672 | 0.166836 | − | 0.985985i | \(-0.446645\pi\) | ||||
0.166836 | + | 0.985985i | \(0.446645\pi\) | |||||||
\(558\) | −243.350 | − | 0.966927i | −0.436111 | − | 0.00173284i | ||||
\(559\) | −128.689 | −0.230213 | ||||||||
\(560\) | 133.910 | − | 33.4118i | 0.239124 | − | 0.0596640i | ||||
\(561\) | 0.0760803 | − | 38.2950i | 0.000135616 | − | 0.0682620i | ||||
\(562\) | − | 304.843i | − | 0.542425i | ||||||
\(563\) | −252.783 | −0.448994 | −0.224497 | − | 0.974475i | \(-0.572074\pi\) | ||||
−0.224497 | + | 0.974475i | \(0.572074\pi\) | |||||||
\(564\) | 143.354 | + | 0.284800i | 0.254174 | + | 0.000504964i | ||||
\(565\) | 7.23162 | + | 28.9832i | 0.0127993 | + | 0.0512977i | ||||
\(566\) | − | 369.923i | − | 0.653574i | ||||||
\(567\) | 4.44187 | − | 558.943i | 0.00783399 | − | 0.985789i | ||||
\(568\) | 368.577i | 0.648904i | ||||||||
\(569\) | 155.819i | 0.273848i | 0.990582 | + | 0.136924i | \(0.0437216\pi\) | ||||
−0.990582 | + | 0.136924i | \(0.956278\pi\) | |||||||
\(570\) | −86.3832 | − | 349.163i | −0.151550 | − | 0.612566i | ||||
\(571\) | 217.567 | 0.381029 | 0.190514 | − | 0.981684i | \(-0.438984\pi\) | ||||
0.190514 | + | 0.981684i | \(0.438984\pi\) | |||||||
\(572\) | 16.9218 | 0.0295835 | ||||||||
\(573\) | −0.960040 | + | 483.236i | −0.00167546 | + | 0.843344i | ||||
\(574\) | −319.402 | −0.556449 | ||||||||
\(575\) | 105.842 | − | 56.3240i | 0.184074 | − | 0.0979548i | ||||
\(576\) | 71.9994 | + | 0.286082i | 0.124999 | + | 0.000496671i | ||||
\(577\) | − | 824.725i | − | 1.42933i | −0.699466 | − | 0.714666i | \(-0.746579\pi\) | ||
0.699466 | − | 0.714666i | \(-0.253421\pi\) | |||||||
\(578\) | 346.919 | 0.600206 | ||||||||
\(579\) | 0.141698 | − | 71.3235i | 0.000244728 | − | 0.123184i | ||||
\(580\) | 52.9136 | − | 13.2025i | 0.0912304 | − | 0.0227629i | ||||
\(581\) | 641.869i | 1.10477i | ||||||||
\(582\) | 0.586412 | − | 295.170i | 0.00100758 | − | 0.507165i | ||||
\(583\) | − | 54.8878i | − | 0.0941472i | ||||||
\(584\) | 29.9106i | 0.0512168i | ||||||||
\(585\) | 191.476 | − | 46.9680i | 0.327310 | − | 0.0802872i | ||||
\(586\) | 749.366 | 1.27878 | ||||||||
\(587\) | 455.443 | 0.775883 | 0.387942 | − | 0.921684i | \(-0.373186\pi\) | ||||
0.387942 | + | 0.921684i | \(0.373186\pi\) | |||||||
\(588\) | −8.27834 | − | 0.0164465i | −0.0140788 | − | 2.79703e-5i | ||||
\(589\) | −324.190 | −0.550407 | ||||||||
\(590\) | −565.282 | + | 141.044i | −0.958105 | + | 0.239057i | ||||
\(591\) | 398.765 | + | 0.792223i | 0.674729 | + | 0.00134048i | ||||
\(592\) | 17.1863i | 0.0290309i | ||||||||
\(593\) | 264.393 | 0.445857 | 0.222928 | − | 0.974835i | \(-0.428438\pi\) | ||||
0.222928 | + | 0.974835i | \(0.428438\pi\) | |||||||
\(594\) | −0.439493 | + | 73.7388i | −0.000739888 | + | 0.124139i | ||||
\(595\) | 221.283 | − | 55.2124i | 0.371904 | − | 0.0927940i | ||||
\(596\) | 176.957i | 0.296908i | ||||||||
\(597\) | −444.033 | − | 0.882155i | −0.743773 | − | 0.00147765i | ||||
\(598\) | − | 29.7146i | − | 0.0496899i | ||||||
\(599\) | 1090.92i | 1.82124i | 0.413249 | + | 0.910618i | \(0.364394\pi\) | ||||
−0.413249 | + | 0.910618i | \(0.635606\pi\) | |||||||
\(600\) | −187.465 | + | 99.2821i | −0.312441 | + | 0.165470i | ||||
\(601\) | −73.3335 | −0.122019 | −0.0610096 | − | 0.998137i | \(-0.519432\pi\) | ||||
−0.0610096 | + | 0.998137i | \(0.519432\pi\) | |||||||
\(602\) | 286.657 | 0.476174 | ||||||||
\(603\) | 2.22952 | − | 561.111i | 0.00369738 | − | 0.930533i | ||||
\(604\) | −148.737 | −0.246253 | ||||||||
\(605\) | 141.949 | + | 568.911i | 0.234627 | + | 0.940349i | ||||
\(606\) | 1.11073 | − | 559.087i | 0.00183289 | − | 0.922585i | ||||
\(607\) | − | 486.978i | − | 0.802271i | −0.916019 | − | 0.401135i | \(-0.868616\pi\) | ||
0.916019 | − | 0.401135i | \(-0.131384\pi\) | |||||||
\(608\) | 95.9172 | 0.157759 | ||||||||
\(609\) | 112.901 | + | 0.224300i | 0.185388 | + | 0.000368308i | ||||
\(610\) | −110.986 | − | 444.815i | −0.181944 | − | 0.729204i | ||||
\(611\) | 104.677i | 0.171320i | ||||||||
\(612\) | 118.978 | + | 0.472746i | 0.194408 | + | 0.000772461i | ||||
\(613\) | − | 977.971i | − | 1.59538i | −0.603065 | − | 0.797692i | \(-0.706054\pi\) | ||
0.603065 | − | 0.797692i | \(-0.293946\pi\) | |||||||
\(614\) | 172.664i | 0.281211i | ||||||||
\(615\) | 476.560 | − | 117.901i | 0.774894 | − | 0.191710i | ||||
\(616\) | −37.6935 | −0.0611907 | ||||||||
\(617\) | 119.147 | 0.193107 | 0.0965534 | − | 0.995328i | \(-0.469218\pi\) | ||||
0.0965534 | + | 0.995328i | \(0.469218\pi\) | |||||||
\(618\) | 0.308303 | − | 155.184i | 0.000498872 | − | 0.251107i | ||||
\(619\) | −661.995 | −1.06946 | −0.534730 | − | 0.845023i | \(-0.679587\pi\) | ||||
−0.534730 | + | 0.845023i | \(0.679587\pi\) | |||||||
\(620\) | 46.2862 | + | 185.508i | 0.0746552 | + | 0.299207i | ||||
\(621\) | 129.485 | + | 0.771749i | 0.208511 | + | 0.00124275i | ||||
\(622\) | 71.2815i | 0.114601i | ||||||||
\(623\) | −1133.67 | −1.81969 | ||||||||
\(624\) | −0.104448 | + | 52.5740i | −0.000167385 | + | 0.0842532i | ||||
\(625\) | 349.139 | − | 518.389i | 0.558623 | − | 0.829422i | ||||
\(626\) | − | 695.384i | − | 1.11084i | ||||||
\(627\) | −0.195163 | + | 98.2352i | −0.000311265 | + | 0.156675i | ||||
\(628\) | 320.571i | 0.510463i | ||||||||
\(629\) | 28.4000i | 0.0451510i | ||||||||
\(630\) | −426.517 | + | 104.622i | −0.677010 | + | 0.166067i | ||||
\(631\) | −334.926 | −0.530786 | −0.265393 | − | 0.964140i | \(-0.585502\pi\) | ||||
−0.265393 | + | 0.964140i | \(0.585502\pi\) | |||||||
\(632\) | −203.875 | −0.322587 | ||||||||
\(633\) | 579.143 | + | 1.15058i | 0.914918 | + | 0.00181766i | ||||
\(634\) | −756.058 | −1.19252 | ||||||||
\(635\) | 116.024 | − | 28.9493i | 0.182715 | − | 0.0455894i | ||||
\(636\) | 170.530 | + | 0.338791i | 0.268129 | + | 0.000532690i | ||||
\(637\) | − | 6.04482i | − | 0.00948952i | ||||||
\(638\) | −14.8944 | −0.0233454 | ||||||||
\(639\) | 4.65999 | − | 1172.80i | 0.00729263 | − | 1.83536i | ||||
\(640\) | −13.6946 | − | 54.8859i | −0.0213978 | − | 0.0857592i | ||||
\(641\) | − | 21.9255i | − | 0.0342052i | −0.999854 | − | 0.0171026i | \(-0.994556\pi\) | ||
0.999854 | − | 0.0171026i | \(-0.00544419\pi\) | |||||||
\(642\) | 335.894 | + | 0.667317i | 0.523199 | + | 0.00103943i | ||||
\(643\) | 624.566i | 0.971332i | 0.874145 | + | 0.485666i | \(0.161423\pi\) | ||||
−0.874145 | + | 0.485666i | \(0.838577\pi\) | |||||||
\(644\) | 66.1896i | 0.102779i | ||||||||
\(645\) | −427.703 | + | 105.814i | −0.663106 | + | 0.164053i | ||||
\(646\) | 158.501 | 0.245358 | ||||||||
\(647\) | −548.096 | −0.847134 | −0.423567 | − | 0.905865i | \(-0.639222\pi\) | ||||
−0.423567 | + | 0.905865i | \(0.639222\pi\) | |||||||
\(648\) | −229.095 | − | 1.82060i | −0.353542 | − | 0.00280957i | ||||
\(649\) | 159.118 | 0.245174 | ||||||||
\(650\) | −72.7671 | − | 136.742i | −0.111949 | − | 0.210372i | ||||
\(651\) | −0.786365 | + | 395.816i | −0.00120793 | + | 0.608013i | ||||
\(652\) | − | 295.582i | − | 0.453347i | ||||||
\(653\) | 1074.01 | 1.64473 | 0.822366 | − | 0.568959i | \(-0.192654\pi\) | ||||
0.822366 | + | 0.568959i | \(0.192654\pi\) | |||||||
\(654\) | −372.743 | − | 0.740524i | −0.569943 | − | 0.00113230i | ||||
\(655\) | −23.4239 | + | 5.84452i | −0.0357617 | + | 0.00892293i | ||||
\(656\) | 130.914i | 0.199564i | ||||||||
\(657\) | 0.378165 | − | 95.1741i | 0.000575593 | − | 0.144862i | ||||
\(658\) | − | 233.169i | − | 0.354359i | ||||||
\(659\) | 624.157i | 0.947127i | 0.880760 | + | 0.473564i | \(0.157033\pi\) | ||||
−0.880760 | + | 0.473564i | \(0.842967\pi\) | |||||||
\(660\) | 56.2401 | − | 13.9139i | 0.0852123 | − | 0.0210816i | ||||
\(661\) | 497.027 | 0.751931 | 0.375966 | − | 0.926634i | \(-0.377311\pi\) | ||||
0.375966 | + | 0.926634i | \(0.377311\pi\) | |||||||
\(662\) | −509.978 | −0.770360 | ||||||||
\(663\) | −0.172599 | + | 86.8775i | −0.000260330 | + | 0.131037i | ||||
\(664\) | 263.085 | 0.396212 | ||||||||
\(665\) | −567.640 | + | 141.632i | −0.853594 | + | 0.212981i | ||||
\(666\) | 0.217289 | − | 54.6859i | 0.000326260 | − | 0.0821110i | ||||
\(667\) | 26.1545i | 0.0392121i | ||||||||
\(668\) | 507.631 | 0.759926 | ||||||||
\(669\) | 0.265590 | − | 133.685i | 0.000396996 | − | 0.199828i | ||||
\(670\) | −427.741 | + | 106.726i | −0.638419 | + | 0.159292i | ||||
\(671\) | 125.208i | 0.186600i | ||||||||
\(672\) | 0.232660 | − | 117.109i | 0.000346220 | − | 0.174270i | ||||
\(673\) | 599.940i | 0.891442i | 0.895172 | + | 0.445721i | \(0.147053\pi\) | ||||
−0.895172 | + | 0.445721i | \(0.852947\pi\) | |||||||
\(674\) | 732.586i | 1.08692i | ||||||||
\(675\) | 597.760 | − | 313.541i | 0.885570 | − | 0.464505i | ||||
\(676\) | 299.611 | 0.443211 | ||||||||
\(677\) | −302.950 | −0.447488 | −0.223744 | − | 0.974648i | \(-0.571828\pi\) | ||||
−0.223744 | + | 0.974648i | \(0.571828\pi\) | |||||||
\(678\) | 25.3470 | + | 0.0503566i | 0.0373849 | + | 7.42723e-5i | ||||
\(679\) | −480.102 | −0.707072 | ||||||||
\(680\) | −22.6301 | − | 90.6979i | −0.0332795 | − | 0.133379i | ||||
\(681\) | −559.164 | − | 1.11089i | −0.821093 | − | 0.00163126i | ||||
\(682\) | − | 52.2177i | − | 0.0765655i | ||||||
\(683\) | 287.077 | 0.420318 | 0.210159 | − | 0.977667i | \(-0.432602\pi\) | ||||
0.210159 | + | 0.977667i | \(0.432602\pi\) | |||||||
\(684\) | −305.204 | − | 1.21270i | −0.446205 | − | 0.00177295i | ||||
\(685\) | 315.846 | + | 1265.86i | 0.461089 | + | 1.84797i | ||||
\(686\) | 491.662i | 0.716709i | ||||||||
\(687\) | −382.638 | − | 0.760183i | −0.556969 | − | 0.00110653i | ||||
\(688\) | − | 117.493i | − | 0.170774i | ||||||
\(689\) | 124.521i | 0.180727i | ||||||||
\(690\) | −24.4327 | − | 98.7575i | −0.0354097 | − | 0.143127i | ||||
\(691\) | −364.267 | −0.527159 | −0.263580 | − | 0.964638i | \(-0.584903\pi\) | ||||
−0.263580 | + | 0.964638i | \(0.584903\pi\) | |||||||
\(692\) | −282.026 | −0.407552 | ||||||||
\(693\) | 119.939 | + | 0.476565i | 0.173072 | + | 0.000687684i | ||||
\(694\) | −482.756 | −0.695613 | ||||||||
\(695\) | −13.1310 | − | 52.6271i | −0.0188936 | − | 0.0757225i | ||||
\(696\) | 0.0919343 | − | 46.2751i | 0.000132090 | − | 0.0664872i | ||||
\(697\) | 216.333i | 0.310377i | ||||||||
\(698\) | 0.566643 | 0.000811810 | ||||||||
\(699\) | 358.548 | + | 0.712324i | 0.512944 | + | 0.00101906i | ||||
\(700\) | 162.090 | + | 304.594i | 0.231557 | + | 0.435134i | ||||
\(701\) | 281.045i | 0.400921i | 0.979702 | + | 0.200460i | \(0.0642438\pi\) | ||||
−0.979702 | + | 0.200460i | \(0.935756\pi\) | |||||||
\(702\) | 0.997052 | − | 167.287i | 0.00142030 | − | 0.238300i | ||||
\(703\) | − | 72.8523i | − | 0.103631i | ||||||
\(704\) | 15.4495i | 0.0219453i | ||||||||
\(705\) | 86.0700 | + | 347.897i | 0.122085 | + | 0.493470i | ||||
\(706\) | 383.420 | 0.543087 | ||||||||
\(707\) | −909.368 | −1.28624 | ||||||||
\(708\) | −0.982144 | + | 494.362i | −0.00138721 | + | 0.698251i | ||||
\(709\) | −734.625 | −1.03614 | −0.518071 | − | 0.855337i | \(-0.673350\pi\) | ||||
−0.518071 | + | 0.855337i | \(0.673350\pi\) | |||||||
\(710\) | −894.035 | + | 223.071i | −1.25920 | + | 0.314185i | ||||
\(711\) | 648.721 | + | 2.57763i | 0.912407 | + | 0.00362535i | ||||
\(712\) | 464.660i | 0.652613i | ||||||||
\(713\) | −91.6941 | −0.128603 | ||||||||
\(714\) | 0.384466 | − | 193.521i | 0.000538468 | − | 0.271038i | ||||
\(715\) | 10.2414 | + | 41.0460i | 0.0143237 | + | 0.0574070i | ||||
\(716\) | 251.982i | 0.351930i | ||||||||
\(717\) | −2.41167 | + | 1213.92i | −0.00336356 | + | 1.69305i | ||||
\(718\) | 492.476i | 0.685899i | ||||||||
\(719\) | 976.727i | 1.35845i | 0.733929 | + | 0.679226i | \(0.237684\pi\) | ||||
−0.733929 | + | 0.679226i | \(0.762316\pi\) | |||||||
\(720\) | 42.8817 | + | 174.818i | 0.0595579 | + | 0.242802i | ||||
\(721\) | −252.411 | −0.350085 | ||||||||
\(722\) | 103.940 | 0.143961 | ||||||||
\(723\) | 468.253 | + | 0.930274i | 0.647653 | + | 0.00128669i | ||||
\(724\) | −452.664 | −0.625227 | ||||||||
\(725\) | 64.0489 | + | 120.359i | 0.0883433 | + | 0.166012i | ||||
\(726\) | 497.536 | + | 0.988449i | 0.685311 | + | 0.00136150i | ||||
\(727\) | 1318.22i | 1.81323i | 0.421956 | + | 0.906616i | \(0.361344\pi\) | ||||
−0.421956 | + | 0.906616i | \(0.638656\pi\) | |||||||
\(728\) | 85.5129 | 0.117463 | ||||||||
\(729\) | 728.948 | + | 8.68957i | 0.999929 | + | 0.0119198i | ||||
\(730\) | −72.5522 | + | 18.1025i | −0.0993865 | + | 0.0247980i | ||||
\(731\) | − | 194.155i | − | 0.265602i | ||||||
\(732\) | −389.008 | − | 0.772839i | −0.531432 | − | 0.00105579i | ||||
\(733\) | 272.542i | 0.371817i | 0.982567 | + | 0.185908i | \(0.0595228\pi\) | ||||
−0.982567 | + | 0.185908i | \(0.940477\pi\) | |||||||
\(734\) | − | 772.444i | − | 1.05238i | ||||||
\(735\) | −4.97034 | − | 20.0902i | −0.00676237 | − | 0.0273336i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | 120.402 | 0.163368 | ||||||||
\(738\) | 1.65517 | − | 416.563i | 0.00224278 | − | 0.564448i | ||||
\(739\) | −1298.32 | −1.75685 | −0.878427 | − | 0.477876i | \(-0.841407\pi\) | ||||
−0.878427 | + | 0.477876i | \(0.841407\pi\) | |||||||
\(740\) | −41.6876 | + | 10.4015i | −0.0563346 | + | 0.0140561i | ||||
\(741\) | 0.442754 | − | 222.860i | 0.000597509 | − | 0.300756i | ||||
\(742\) | − | 277.372i | − | 0.373816i | ||||||
\(743\) | 302.960 | 0.407753 | 0.203876 | − | 0.978997i | \(-0.434646\pi\) | ||||
0.203876 | + | 0.978997i | \(0.434646\pi\) | |||||||
\(744\) | 162.234 | + | 0.322310i | 0.218057 | + | 0.000433212i | ||||
\(745\) | −429.234 | + | 107.098i | −0.576153 | + | 0.143756i | ||||
\(746\) | 793.692i | 1.06393i | ||||||||
\(747\) | −837.124 | − | 3.32622i | −1.12065 | − | 0.00445278i | ||||
\(748\) | 25.5301i | 0.0341311i | ||||||||
\(749\) | − | 546.340i | − | 0.729425i | ||||||
\(750\) | −354.280 | − | 394.634i | −0.472373 | − | 0.526178i | ||||
\(751\) | 708.772 | 0.943770 | 0.471885 | − | 0.881660i | \(-0.343574\pi\) | ||||
0.471885 | + | 0.881660i | \(0.343574\pi\) | |||||||
\(752\) | −95.5694 | −0.127087 | ||||||||
\(753\) | −0.895216 | + | 450.607i | −0.00118887 | + | 0.598415i | ||||
\(754\) | 33.7899 | 0.0448142 | ||||||||
\(755\) | −90.0185 | − | 360.781i | −0.119230 | − | 0.477855i | ||||
\(756\) | −2.22095 | + | 372.634i | −0.00293776 | + | 0.492902i | ||||
\(757\) | 916.947i | 1.21129i | 0.795735 | + | 0.605645i | \(0.207085\pi\) | ||||
−0.795735 | + | 0.605645i | \(0.792915\pi\) | |||||||
\(758\) | 90.8312 | 0.119830 | ||||||||
\(759\) | −0.0552001 | + | 27.7849i | −7.27274e−5 | + | 0.0366073i | ||||
\(760\) | 58.0512 | + | 232.660i | 0.0763831 | + | 0.306132i | ||||
\(761\) | − | 239.914i | − | 0.315261i | −0.987498 | − | 0.157631i | \(-0.949614\pi\) | ||
0.987498 | − | 0.157631i | \(-0.0503855\pi\) | |||||||
\(762\) | 0.201585 | − | 101.468i | 0.000264548 | − | 0.133160i | ||||
\(763\) | 606.275i | 0.794593i | ||||||||
\(764\) | − | 322.158i | − | 0.421673i | ||||||
\(765\) | 70.8612 | + | 288.883i | 0.0926290 | + | 0.377624i | ||||
\(766\) | −77.7104 | −0.101450 | ||||||||
\(767\) | −360.982 | −0.470641 | ||||||||
\(768\) | −47.9999 | − | 0.0953610i | −0.0624999 | − | 0.000124168i | ||||
\(769\) | 391.054 | 0.508522 | 0.254261 | − | 0.967136i | \(-0.418168\pi\) | ||||
0.254261 | + | 0.967136i | \(0.418168\pi\) | |||||||
\(770\) | −22.8129 | − | 91.4306i | −0.0296271 | − | 0.118741i | ||||
\(771\) | 34.0294 | + | 0.0676059i | 0.0441367 | + | 8.76860e-5i | ||||
\(772\) | 47.5491i | 0.0615921i | ||||||||
\(773\) | 319.039 | 0.412729 | 0.206364 | − | 0.978475i | \(-0.433837\pi\) | ||||
0.206364 | + | 0.978475i | \(0.433837\pi\) | |||||||
\(774\) | −1.48548 | + | 373.857i | −0.00191923 | + | 0.483019i | ||||
\(775\) | −421.962 | + | 224.547i | −0.544467 | + | 0.289738i | ||||
\(776\) | 196.781i | 0.253583i | ||||||||
\(777\) | −88.9484 | − | 0.176713i | −0.114477 | − | 0.000227430i | ||||
\(778\) | − | 472.284i | − | 0.607049i | ||||||
\(779\) | − | 554.942i | − | 0.712378i | ||||||
\(780\) | −127.589 | + | 31.5655i | −0.163575 | + | 0.0404687i | ||||
\(781\) | 251.657 | 0.322224 | ||||||||
\(782\) | 44.8307 | 0.0573283 | ||||||||
\(783\) | −0.877595 | + | 147.244i | −0.00112081 | + | 0.188051i | ||||
\(784\) | 5.51891 | 0.00703942 | ||||||||
\(785\) | −777.588 | + | 194.016i | −0.990558 | + | 0.247155i | ||||
\(786\) | −0.0406977 | + | 20.4852i | −5.17783e−5 | + | 0.0260626i | ||||
\(787\) | 978.321i | 1.24310i | 0.783374 | + | 0.621551i | \(0.213497\pi\) | ||||
−0.783374 | + | 0.621551i | \(0.786503\pi\) | |||||||
\(788\) | −265.844 | −0.337365 | ||||||||
\(789\) | 442.243 | + | 0.878599i | 0.560510 | + | 0.00111356i | ||||
\(790\) | −123.389 | − | 494.526i | −0.156189 | − | 0.625983i | ||||
\(791\) | − | 41.2275i | − | 0.0521207i | ||||||
\(792\) | 0.195331 | − | 49.1597i | 0.000246630 | − | 0.0620703i | ||||
\(793\) | − | 284.053i | − | 0.358200i | ||||||
\(794\) | − | 266.783i | − | 0.335999i | ||||||
\(795\) | 102.387 | + | 413.849i | 0.128788 | + | 0.520565i | ||||
\(796\) | 296.022 | 0.371887 | ||||||||
\(797\) | −1099.26 | −1.37925 | −0.689623 | − | 0.724169i | \(-0.742224\pi\) | ||||
−0.689623 | + | 0.724169i | \(0.742224\pi\) | |||||||
\(798\) | −0.986242 | + | 496.424i | −0.00123589 | + | 0.622086i | ||||
\(799\) | −157.927 | −0.197655 | ||||||||
\(800\) | 124.845 | − | 66.4362i | 0.156056 | − | 0.0830453i | ||||
\(801\) | 5.87478 | − | 1478.53i | 0.00733431 | − | 1.84585i | ||||
\(802\) | 284.002i | 0.354117i | ||||||||
\(803\) | 20.4223 | 0.0254325 | ||||||||
\(804\) | −0.743174 | + | 374.077i | −0.000924346 | + | 0.465269i | ||||
\(805\) | −160.552 | + | 40.0594i | −0.199443 | + | 0.0497632i | ||||
\(806\) | 118.463i | 0.146977i | ||||||||
\(807\) | −1.22645 | + | 617.334i | −0.00151977 | + | 0.764974i | ||||
\(808\) | 372.725i | 0.461294i | ||||||||
\(809\) | − | 198.336i | − | 0.245162i | −0.992459 | − | 0.122581i | \(-0.960883\pi\) | ||
0.992459 | − | 0.122581i | \(-0.0391171\pi\) | |||||||
\(810\) | −134.237 | − | 556.804i | −0.165725 | − | 0.687412i | ||||
\(811\) | −559.844 | −0.690314 | −0.345157 | − | 0.938545i | \(-0.612174\pi\) | ||||
−0.345157 | + | 0.938545i | \(0.612174\pi\) | |||||||
\(812\) | −75.2676 | −0.0926940 | ||||||||
\(813\) | 719.674 | + | 1.42977i | 0.885207 | + | 0.00175863i | ||||
\(814\) | 11.7344 | 0.0144158 | ||||||||
\(815\) | 716.975 | − | 178.893i | 0.879723 | − | 0.219500i | ||||
\(816\) | −79.3190 | − | 0.157582i | −0.0972046 | − | 0.000193116i | ||||
\(817\) | 498.050i | 0.609608i | ||||||||
\(818\) | −458.272 | −0.560235 | ||||||||
\(819\) | −272.098 | − | 1.08115i | −0.332232 | − | 0.00132009i | ||||
\(820\) | −317.550 | + | 79.2320i | −0.387256 | + | 0.0966244i | ||||
\(821\) | − | 549.784i | − | 0.669652i | −0.942280 | − | 0.334826i | \(-0.891323\pi\) | ||
0.942280 | − | 0.334826i | \(-0.108677\pi\) | |||||||
\(822\) | 1107.05 | + | 2.19936i | 1.34677 | + | 0.00267562i | ||||
\(823\) | 731.107i | 0.888344i | 0.895941 | + | 0.444172i | \(0.146502\pi\) | ||||
−0.895941 | + | 0.444172i | \(0.853498\pi\) | |||||||
\(824\) | 103.456i | 0.125554i | ||||||||
\(825\) | 67.7877 | + | 127.997i | 0.0821669 | + | 0.155148i | ||||
\(826\) | 804.091 | 0.973476 | ||||||||
\(827\) | 645.393 | 0.780403 | 0.390202 | − | 0.920729i | \(-0.372405\pi\) | ||||
0.390202 | + | 0.920729i | \(0.372405\pi\) | |||||||
\(828\) | −86.3243 | − | 0.343001i | −0.104256 | − | 0.000414252i | ||||
\(829\) | 798.364 | 0.963045 | 0.481523 | − | 0.876434i | \(-0.340084\pi\) | ||||
0.481523 | + | 0.876434i | \(0.340084\pi\) | |||||||
\(830\) | 159.224 | + | 638.147i | 0.191837 | + | 0.768852i | ||||
\(831\) | −0.987078 | + | 496.845i | −0.00118782 | + | 0.597889i | ||||
\(832\) | − | 35.0494i | − | 0.0421267i | ||||||
\(833\) | 9.11989 | 0.0109483 | ||||||||
\(834\) | −46.0246 | − | 0.0914366i | −0.0551853 | − | 0.000109636i | ||||
\(835\) | 307.229 | + | 1231.33i | 0.367939 | + | 1.47464i | ||||
\(836\) | − | 65.4903i | − | 0.0783376i | ||||||
\(837\) | −516.219 | − | 3.07673i | −0.616749 | − | 0.00367590i | ||||
\(838\) | − | 72.9804i | − | 0.0870888i | ||||||
\(839\) | − | 853.257i | − | 1.01699i | −0.861064 | − | 0.508497i | \(-0.830201\pi\) | ||
0.861064 | − | 0.508497i | \(-0.169799\pi\) | |||||||
\(840\) | 284.205 | − | 70.3127i | 0.338340 | − | 0.0837056i | ||||
\(841\) | 811.258 | 0.964635 | ||||||||
\(842\) | 628.485 | 0.746419 | ||||||||
\(843\) | 1.28473 | − | 646.668i | 0.00152400 | − | 0.767103i | ||||
\(844\) | −386.096 | −0.457460 | ||||||||
\(845\) | 181.331 | + | 726.746i | 0.214593 | + | 0.860055i | ||||
\(846\) | 304.098 | + | 1.20830i | 0.359454 | + | 0.00142825i | ||||
\(847\) | − | 809.254i | − | 0.955435i | ||||||
\(848\) | −113.687 | −0.134065 | ||||||||
\(849\) | 1.55900 | − | 784.723i | 0.00183628 | − | 0.924291i | ||||
\(850\) | 206.304 | − | 109.785i | 0.242710 | − | 0.129158i | ||||
\(851\) | − | 20.6056i | − | 0.0242134i | ||||||
\(852\) | −1.55333 | + | 781.869i | −0.00182316 | + | 0.917687i | ||||
\(853\) | 635.381i | 0.744878i | 0.928057 | + | 0.372439i | \(0.121478\pi\) | ||||
−0.928057 | + | 0.372439i | \(0.878522\pi\) | |||||||
\(854\) | 632.732i | 0.740903i | ||||||||
\(855\) | −181.775 | − | 741.048i | −0.212602 | − | 0.866723i | ||||
\(856\) | −223.930 | −0.261600 | ||||||||
\(857\) | −637.244 | −0.743576 | −0.371788 | − | 0.928318i | \(-0.621255\pi\) | ||||
−0.371788 | + | 0.928318i | \(0.621255\pi\) | |||||||
\(858\) | 35.8964 | + | 0.0713151i | 0.0418373 | + | 8.31178e-5i | ||||
\(859\) | −1214.27 | −1.41359 | −0.706793 | − | 0.707420i | \(-0.749859\pi\) | ||||
−0.706793 | + | 0.707420i | \(0.749859\pi\) | |||||||
\(860\) | 284.995 | − | 71.1092i | 0.331389 | − | 0.0826851i | ||||
\(861\) | −677.552 | − | 1.34609i | −0.786936 | − | 0.00156340i | ||||
\(862\) | − | 247.844i | − | 0.287522i | ||||||
\(863\) | 1135.11 | 1.31530 | 0.657652 | − | 0.753322i | \(-0.271550\pi\) | ||||
0.657652 | + | 0.753322i | \(0.271550\pi\) | |||||||
\(864\) | 152.732 | + | 0.910305i | 0.176774 | + | 0.00105359i | ||||
\(865\) | −170.688 | − | 684.092i | −0.197327 | − | 0.790858i | ||||
\(866\) | 971.880i | 1.12226i | ||||||||
\(867\) | 735.925 | + | 1.46206i | 0.848818 | + | 0.00168634i | ||||
\(868\) | − | 263.878i | − | 0.304007i | ||||||
\(869\) | 139.202i | 0.160186i | ||||||||
\(870\) | 112.302 | − | 27.7837i | 0.129083 | − | 0.0319353i | ||||
\(871\) | −273.150 | −0.313605 | ||||||||
\(872\) | 248.496 | 0.284972 | ||||||||
\(873\) | 2.48793 | − | 626.147i | 0.00284986 | − | 0.717236i | ||||
\(874\) | −115.001 | −0.131580 | ||||||||
\(875\) | −640.734 | + | 577.518i | −0.732267 | + | 0.660020i | ||||
\(876\) | −0.126055 | + | 63.4498i | −0.000143899 | + | 0.0724313i | ||||
\(877\) | − | 1020.55i | − | 1.16368i | −0.813303 | − | 0.581840i | \(-0.802333\pi\) | ||
0.813303 | − | 0.581840i | \(-0.197667\pi\) | |||||||
\(878\) | −90.4982 | −0.103073 | ||||||||
\(879\) | 1589.64 | + | 3.15813i | 1.80847 | + | 0.00359286i | ||||
\(880\) | −37.4749 | + | 9.35038i | −0.0425851 | + | 0.0106254i | ||||
\(881\) | 830.290i | 0.942440i | 0.882016 | + | 0.471220i | \(0.156186\pi\) | ||||
−0.882016 | + | 0.471220i | \(0.843814\pi\) | |||||||
\(882\) | −17.5609 | − | 0.0697765i | −0.0199103 | − | 7.91117e-5i | ||||
\(883\) | 1220.35i | 1.38205i | 0.722833 | + | 0.691023i | \(0.242840\pi\) | ||||
−0.722833 | + | 0.691023i | \(0.757160\pi\) | |||||||
\(884\) | − | 57.9185i | − | 0.0655186i | ||||||
\(885\) | −1199.74 | + | 296.816i | −1.35563 | + | 0.335385i | ||||
\(886\) | 876.046 | 0.988766 | ||||||||
\(887\) | 1103.94 | 1.24457 | 0.622286 | − | 0.782790i | \(-0.286204\pi\) | ||||
0.622286 | + | 0.782790i | \(0.286204\pi\) | |||||||
\(888\) | −0.0724298 | + | 36.4575i | −8.15651e−5 | + | 0.0410558i | ||||
\(889\) | −165.040 | −0.185647 | ||||||||
\(890\) | −1127.10 | + | 281.222i | −1.26640 | + | 0.315980i | ||||
\(891\) | −1.24307 | + | 156.421i | −0.00139514 | + | 0.175557i | ||||
\(892\) | 89.1233i | 0.0999140i | ||||||||
\(893\) | 405.117 | 0.453659 | ||||||||
\(894\) | −0.745769 | + | 375.383i | −0.000834194 | + | 0.419891i | ||||
\(895\) | −611.216 | + | 152.505i | −0.682923 | + | 0.170397i | ||||
\(896\) | 78.0730i | 0.0871351i | ||||||||
\(897\) | 0.125229 | − | 63.0340i | 0.000139609 | − | 0.0702720i | ||||
\(898\) | − | 455.017i | − | 0.506701i | ||||||
\(899\) | − | 104.270i | − | 0.115984i | ||||||
\(900\) | −398.091 | + | 209.819i | −0.442323 | + | 0.233132i | ||||
\(901\) | −187.866 | −0.208508 | ||||||||
\(902\) | 89.3853 | 0.0990968 | ||||||||
\(903\) | 608.090 | + | 1.20809i | 0.673411 | + | 0.00133786i | ||||
\(904\) | −16.8980 | −0.0186925 | ||||||||
\(905\) | −273.962 | − | 1098.00i | −0.302721 | − | 1.21326i | ||||
\(906\) | −315.517 | − | 0.626835i | −0.348253 | − | 0.000691871i | ||||
\(907\) | − | 532.131i | − | 0.586694i | −0.956006 | − | 0.293347i | \(-0.905231\pi\) | ||
0.956006 | − | 0.293347i | \(-0.0947691\pi\) | |||||||
\(908\) | 372.777 | 0.410547 | ||||||||
\(909\) | 4.71243 | − | 1186.00i | 0.00518419 | − | 1.30473i | ||||
\(910\) | 51.7542 | + | 207.423i | 0.0568728 | + | 0.227937i | ||||
\(911\) | − | 1476.40i | − | 1.62064i | −0.585987 | − | 0.810321i | \(-0.699293\pi\) | ||
0.585987 | − | 0.810321i | \(-0.300707\pi\) | |||||||
\(912\) | 203.471 | + | 0.404234i | 0.223104 | + | 0.000443239i | ||||
\(913\) | − | 179.629i | − | 0.196746i | ||||||
\(914\) | 981.861i | 1.07425i | ||||||||
\(915\) | −233.562 | − | 944.060i | −0.255259 | − | 1.03176i | ||||
\(916\) | 255.092 | 0.278485 | ||||||||
\(917\) | 33.3196 | 0.0363355 | ||||||||
\(918\) | 252.387 | + | 1.50426i | 0.274932 | + | 0.00163863i | ||||
\(919\) | −1064.72 | −1.15857 | −0.579283 | − | 0.815127i | \(-0.696667\pi\) | ||||
−0.579283 | + | 0.815127i | \(0.696667\pi\) | |||||||
\(920\) | 16.4192 | + | 65.8058i | 0.0178470 | + | 0.0715281i | ||||
\(921\) | −0.727674 | + | 366.275i | −0.000790092 | + | 0.397692i | ||||
\(922\) | − | 1242.45i | − | 1.34756i | ||||||
\(923\) | −570.919 | −0.618547 | ||||||||
\(924\) | −79.9597 | − | 0.158855i | −0.0865365 | − | 0.000171921i | ||||
\(925\) | −50.4605 | − | 94.8238i | −0.0545519 | − | 0.102512i | ||||
\(926\) | − | 376.451i | − | 0.406534i | ||||||
\(927\) | 1.30802 | − | 329.194i | 0.00141102 | − | 0.355117i | ||||
\(928\) | 30.8501i | 0.0332437i | ||||||||
\(929\) | 360.641i | 0.388204i | 0.980981 | + | 0.194102i | \(0.0621793\pi\) | ||||
−0.980981 | + | 0.194102i | \(0.937821\pi\) | |||||||
\(930\) | 97.4059 | + | 393.717i | 0.104738 | + | 0.423351i | ||||
\(931\) | −23.3946 | −0.0251284 | ||||||||
\(932\) | −239.033 | −0.256473 | ||||||||
\(933\) | −0.300409 | + | 151.211i | −0.000321982 | + | 0.162069i | ||||
\(934\) | −340.096 | −0.364129 | ||||||||
\(935\) | −61.9266 | + | 15.4513i | −0.0662317 | + | 0.0165255i | ||||
\(936\) | −0.443136 | + | 111.526i | −0.000473435 | + | 0.119151i | ||||
\(937\) | 966.466i | 1.03145i | 0.856755 | + | 0.515724i | \(0.172477\pi\) | ||||
−0.856755 | + | 0.515724i | \(0.827523\pi\) | |||||||
\(938\) | 608.445 | 0.648662 | ||||||||
\(939\) | 2.93062 | − | 1475.13i | 0.00312101 | − | 1.57096i | ||||
\(940\) | −57.8407 | − | 231.817i | −0.0615326 | − | 0.246613i | ||||
\(941\) | − | 1223.99i | − | 1.30074i | −0.759618 | − | 0.650369i | \(-0.774614\pi\) | ||
0.759618 | − | 0.650369i | \(-0.225386\pi\) | |||||||
\(942\) | −1.35101 | + | 680.032i | −0.00143420 | + | 0.721902i | ||||
\(943\) | − | 156.960i | − | 0.166448i | ||||||
\(944\) | − | 329.575i | − | 0.349126i | ||||||
\(945\) | −905.217 | + | 220.139i | −0.957902 | + | 0.232951i | ||||
\(946\) | −80.2216 | −0.0848009 | ||||||||
\(947\) | 459.809 | 0.485543 | 0.242771 | − | 0.970084i | \(-0.421944\pi\) | ||||
0.242771 | + | 0.970084i | \(0.421944\pi\) | |||||||
\(948\) | −432.483 | − | 0.859211i | −0.456206 | − | 0.000906340i | ||||
\(949\) | −46.3309 | −0.0488207 | ||||||||
\(950\) | −529.215 | + | 281.622i | −0.557069 | + | 0.296444i | ||||
\(951\) | −1603.84 | − | 3.18633i | −1.68648 | − | 0.00335051i | ||||
\(952\) | 129.014i | 0.135519i | ||||||||
\(953\) | −1.23371 | −0.00129455 | −0.000647277 | − | 1.00000i | \(-0.500206\pi\) | ||||
−0.000647277 | 1.00000i | \(0.500206\pi\) | ||||||||
\(954\) | 361.747 | + | 1.43736i | 0.379190 | + | 0.00150667i | ||||
\(955\) | 781.438 | − | 194.977i | 0.818259 | − | 0.204164i | ||||
\(956\) | − | 809.279i | − | 0.846526i | ||||||
\(957\) | −31.5957 | − | 0.0627708i | −0.0330153 | − | 6.55912e-5i | ||||
\(958\) | 675.117i | 0.704715i | ||||||||
\(959\) | − | 1800.64i | − | 1.87762i | ||||||
\(960\) | −28.8193 | − | 116.488i | −0.0300201 | − | 0.121342i | ||||
\(961\) | −595.443 | −0.619608 | ||||||||
\(962\) | −26.6212 | −0.0276727 | ||||||||
\(963\) | 712.534 | + | 2.83118i | 0.739911 | + | 0.00293996i | ||||
\(964\) | −312.169 | −0.323827 | ||||||||
\(965\) | −115.337 | + | 28.7777i | −0.119520 | + | 0.0298215i | ||||
\(966\) | −0.278949 | + | 140.409i | −0.000288768 | + | 0.145351i | ||||
\(967\) | − | 301.660i | − | 0.311955i | −0.987761 | − | 0.155977i | \(-0.950147\pi\) | ||
0.987761 | − | 0.155977i | \(-0.0498527\pi\) | |||||||
\(968\) | −331.691 | −0.342656 | ||||||||
\(969\) | 336.232 | + | 0.667989i | 0.346988 | + | 0.000689359i | ||||
\(970\) | −477.318 | + | 119.096i | −0.492080 | + | 0.122779i | ||||
\(971\) | − | 155.375i | − | 0.160016i | −0.996794 | − | 0.0800079i | \(-0.974505\pi\) | ||
0.996794 | − | 0.0800079i | \(-0.0254945\pi\) | |||||||
\(972\) | −485.976 | − | 4.82757i | −0.499975 | − | 0.00496664i | ||||
\(973\) | 74.8601i | 0.0769374i | ||||||||
\(974\) | − | 736.875i | − | 0.756546i | ||||||
\(975\) | −153.786 | − | 290.379i | −0.157729 | − | 0.297825i | ||||
\(976\) | 259.339 | 0.265717 | ||||||||
\(977\) | 1528.18 | 1.56416 | 0.782080 | − | 0.623178i | \(-0.214159\pi\) | ||||
0.782080 | + | 0.623178i | \(0.214159\pi\) | |||||||
\(978\) | 1.24570 | − | 627.023i | 0.00127372 | − | 0.641128i | ||||
\(979\) | 317.260 | 0.324066 | ||||||||
\(980\) | 3.34016 | + | 13.3869i | 0.00340833 | + | 0.0136601i | ||||
\(981\) | −790.702 | − | 3.14177i | −0.806016 | − | 0.00320262i | ||||
\(982\) | 1079.21i | 1.09899i | ||||||||
\(983\) | −220.273 | −0.224083 | −0.112041 | − | 0.993704i | \(-0.535739\pi\) | ||||
−0.112041 | + | 0.993704i | \(0.535739\pi\) | |||||||
\(984\) | −0.551724 | + | 277.710i | −0.000560695 | + | 0.282226i | ||||
\(985\) | −160.894 | − | 644.840i | −0.163345 | − | 0.654660i | ||||
\(986\) | 50.9793i | 0.0517031i | ||||||||
\(987\) | 0.982665 | − | 494.624i | 0.000995608 | − | 0.501139i | ||||
\(988\) | 148.574i | 0.150378i | ||||||||
\(989\) | 140.869i | 0.142436i | ||||||||
\(990\) | 119.362 | − | 29.2787i | 0.120567 | − | 0.0295744i | ||||
\(991\) | 990.561 | 0.999557 | 0.499779 | − | 0.866153i | \(-0.333415\pi\) | ||||
0.499779 | + | 0.866153i | \(0.333415\pi\) | |||||||
\(992\) | −108.156 | −0.109029 | ||||||||
\(993\) | −1081.83 | − | 2.14925i | −1.08945 | − | 0.00216440i | ||||
\(994\) | 1271.73 | 1.27941 | ||||||||
\(995\) | 179.159 | + | 718.042i | 0.180059 | + | 0.721650i | ||||
\(996\) | 558.086 | + | 1.10874i | 0.560327 | + | 0.00111320i | ||||
\(997\) | 73.9862i | 0.0742089i | 0.999311 | + | 0.0371044i | \(0.0118134\pi\) | ||||
−0.999311 | + | 0.0371044i | \(0.988187\pi\) | |||||||
\(998\) | 856.758 | 0.858474 | ||||||||
\(999\) | 0.691407 | − | 116.005i | 0.000692099 | − | 0.116121i |
(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 | 690.3.b.a.599.1 | ✓ | 88 | |
3.2 | odd | 2 | inner | 690.3.b.a.599.87 | yes | 88 | |
5.4 | even | 2 | inner | 690.3.b.a.599.88 | yes | 88 | |
15.14 | odd | 2 | inner | 690.3.b.a.599.2 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.b.a.599.1 | ✓ | 88 | 1.1 | even | 1 | trivial | |
690.3.b.a.599.2 | yes | 88 | 15.14 | odd | 2 | inner | |
690.3.b.a.599.87 | yes | 88 | 3.2 | odd | 2 | inner | |
690.3.b.a.599.88 | yes | 88 | 5.4 | even | 2 | inner |