Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(478,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.478");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.bm (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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.2346760387617129.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 550.1 | ||
Root | \(1.21245 - 0.727987i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.550 |
Dual form | 819.2.bm.f.478.6 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.30327i | − | 1.62866i | −0.580405 | − | 0.814328i | \(-0.697106\pi\) | ||
0.580405 | − | 0.814328i | \(-0.302894\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.30504 | −1.65252 | ||||||||
\(5\) | −0.733776 | + | 0.423646i | −0.328155 | + | 0.189460i | −0.655022 | − | 0.755610i | \(-0.727340\pi\) |
0.326867 | + | 0.945070i | \(0.394007\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.357777 | − | 2.62145i | −0.135227 | − | 0.990815i | ||||
\(8\) | 3.00585i | 1.06273i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.975769 | + | 1.69008i | 0.308565 | + | 0.534451i | ||||
\(11\) | −1.30198 | + | 0.751701i | −0.392563 | + | 0.226646i | −0.683270 | − | 0.730166i | \(-0.739443\pi\) |
0.290707 | + | 0.956812i | \(0.406110\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.92329 | + | 2.11054i | −0.810774 | + | 0.585360i | ||||
\(14\) | −6.03790 | + | 0.824057i | −1.61370 | + | 0.220238i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.313194 | 0.0782985 | ||||||||
\(17\) | 2.07140 | 0.502389 | 0.251194 | − | 0.967937i | \(-0.419177\pi\) | ||||
0.251194 | + | 0.967937i | \(0.419177\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0410731 | + | 0.0237136i | 0.00942282 | + | 0.00544027i | 0.504704 | − | 0.863292i | \(-0.331602\pi\) |
−0.495281 | + | 0.868733i | \(0.664935\pi\) | |||||||
\(20\) | 2.42516 | − | 1.40016i | 0.542282 | − | 0.313086i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.73137 | + | 2.99882i | 0.369129 | + | 0.639350i | ||||
\(23\) | −7.81870 | −1.63031 | −0.815156 | − | 0.579241i | \(-0.803349\pi\) | ||||
−0.815156 | + | 0.579241i | \(0.803349\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.14105 | + | 3.70840i | −0.428210 | + | 0.741681i | ||||
\(26\) | 4.86115 | + | 6.73311i | 0.953349 | + | 1.32047i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.18247 | + | 8.66399i | 0.223465 | + | 1.63734i | ||||
\(29\) | 0.679854 | − | 1.17754i | 0.126246 | − | 0.218664i | −0.795973 | − | 0.605331i | \(-0.793041\pi\) |
0.922219 | + | 0.386668i | \(0.126374\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.80787 | − | 3.93052i | −1.22273 | − | 0.705943i | −0.257230 | − | 0.966350i | \(-0.582810\pi\) |
−0.965499 | + | 0.260407i | \(0.916143\pi\) | |||||||
\(32\) | 5.29033i | 0.935206i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 4.77099i | − | 0.818218i | ||||||
\(35\) | 1.37309 | + | 1.77199i | 0.232095 | + | 0.299520i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.70219i | − | 1.10183i | −0.834560 | − | 0.550917i | \(-0.814278\pi\) | ||
0.834560 | − | 0.550917i | \(-0.185722\pi\) | |||||||
\(38\) | 0.0546187 | − | 0.0946024i | 0.00886032 | − | 0.0153465i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.27341 | − | 2.20562i | −0.201345 | − | 0.348739i | ||||
\(41\) | 8.67622 | + | 5.00922i | 1.35500 | + | 0.782309i | 0.988945 | − | 0.148285i | \(-0.0473754\pi\) |
0.366054 | + | 0.930594i | \(0.380709\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.63283 | + | 8.02430i | 0.706500 | + | 1.22369i | 0.966147 | + | 0.257991i | \(0.0830604\pi\) |
−0.259647 | + | 0.965704i | \(0.583606\pi\) | |||||||
\(44\) | 4.30311 | − | 2.48440i | 0.648718 | − | 0.374537i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.0086i | 2.65522i | ||||||||
\(47\) | 0.311781 | − | 0.180007i | 0.0454779 | − | 0.0262567i | −0.477089 | − | 0.878855i | \(-0.658308\pi\) |
0.522567 | + | 0.852598i | \(0.324975\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.74399 | + | 1.87579i | −0.963427 | + | 0.267970i | ||||
\(50\) | 8.54144 | + | 4.93141i | 1.20794 | + | 0.697406i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.66157 | − | 6.97543i | 1.33982 | − | 0.967318i | ||||
\(53\) | 1.35591 | − | 2.34850i | 0.186248 | − | 0.322591i | −0.757748 | − | 0.652547i | \(-0.773701\pi\) |
0.943996 | + | 0.329956i | \(0.107034\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.636910 | − | 1.10316i | 0.0858809 | − | 0.148750i | ||||
\(56\) | 7.87968 | − | 1.07542i | 1.05297 | − | 0.143710i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.71219 | − | 1.56588i | −0.356128 | − | 0.205611i | ||||
\(59\) | 1.64120i | 0.213666i | 0.994277 | + | 0.106833i | \(0.0340709\pi\) | ||||
−0.994277 | + | 0.106833i | \(0.965929\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.26097 | + | 3.91612i | −0.289488 | + | 0.501407i | −0.973688 | − | 0.227887i | \(-0.926818\pi\) |
0.684200 | + | 0.729295i | \(0.260152\pi\) | |||||||
\(62\) | −9.05305 | + | 15.6803i | −1.14974 | + | 1.99140i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12.8114 | 1.60143 | ||||||||
\(65\) | 1.25091 | − | 2.78711i | 0.155157 | − | 0.345698i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.76900 | + | 1.02133i | −0.216117 | + | 0.124775i | −0.604151 | − | 0.796870i | \(-0.706488\pi\) |
0.388034 | + | 0.921645i | \(0.373154\pi\) | |||||||
\(68\) | −6.84606 | −0.830206 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.08136 | − | 3.16260i | 0.487815 | − | 0.378003i | ||||
\(71\) | −12.3096 | + | 7.10697i | −1.46088 | + | 0.843442i | −0.999052 | − | 0.0435255i | \(-0.986141\pi\) |
−0.461832 | + | 0.886967i | \(0.652808\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.85563 | + | 3.38075i | 0.685349 | + | 0.395687i | 0.801867 | − | 0.597502i | \(-0.203840\pi\) |
−0.116518 | + | 0.993189i | \(0.537173\pi\) | |||||||
\(74\) | −15.4369 | −1.79451 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.135748 | − | 0.0783743i | −0.0155714 | − | 0.00899015i | ||||
\(77\) | 2.43637 | + | 3.14414i | 0.277650 | + | 0.358308i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.82952 | − | 10.0970i | −0.655873 | − | 1.13600i | −0.981674 | − | 0.190567i | \(-0.938967\pi\) |
0.325801 | − | 0.945438i | \(-0.394366\pi\) | |||||||
\(80\) | −0.229814 | + | 0.132683i | −0.0256940 | + | 0.0148344i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11.5376 | − | 19.9837i | 1.27411 | − | 2.20683i | ||||
\(83\) | − | 11.5362i | − | 1.26627i | −0.774043 | − | 0.633133i | \(-0.781768\pi\) | ||
0.774043 | − | 0.633133i | \(-0.218232\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.51994 | + | 0.877541i | −0.164861 | + | 0.0951826i | ||||
\(86\) | 18.4821 | − | 10.6706i | 1.99298 | − | 1.15065i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.25950 | − | 3.91357i | −0.240863 | − | 0.417188i | ||||
\(89\) | − | 17.5112i | − | 1.85619i | −0.372350 | − | 0.928093i | \(-0.621448\pi\) | ||
0.372350 | − | 0.928093i | \(-0.378552\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.57857 | + | 6.90814i | 0.689622 | + | 0.724170i | ||||
\(92\) | 25.8411 | 2.69412 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.414604 | − | 0.718115i | −0.0427631 | − | 0.0740679i | ||||
\(95\) | −0.0401846 | −0.00412286 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.369125 | − | 0.213115i | 0.0374790 | − | 0.0216385i | −0.481143 | − | 0.876642i | \(-0.659778\pi\) |
0.518622 | + | 0.855003i | \(0.326445\pi\) | |||||||
\(98\) | 4.32044 | + | 15.5332i | 0.436431 | + | 1.56909i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.07624 | − | 12.2564i | 0.707624 | − | 1.22564i | ||||
\(101\) | −4.83499 | − | 8.37444i | −0.481099 | − | 0.833288i | 0.518666 | − | 0.854977i | \(-0.326429\pi\) |
−0.999765 | + | 0.0216891i | \(0.993096\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.98912 | − | 8.64140i | −0.491592 | − | 0.851463i | 0.508361 | − | 0.861144i | \(-0.330252\pi\) |
−0.999953 | + | 0.00968129i | \(0.996918\pi\) | |||||||
\(104\) | −6.34397 | − | 8.78695i | −0.622078 | − | 0.861631i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.40922 | − | 3.12301i | −0.525390 | − | 0.303334i | ||||
\(107\) | −9.86223 | −0.953417 | −0.476709 | − | 0.879061i | \(-0.658170\pi\) | ||||
−0.476709 | + | 0.879061i | \(0.658170\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0507 | − | 5.80275i | −0.962679 | − | 0.555803i | −0.0656822 | − | 0.997841i | \(-0.520922\pi\) |
−0.896996 | + | 0.442038i | \(0.854256\pi\) | |||||||
\(110\) | −2.54087 | − | 1.46697i | −0.242263 | − | 0.139870i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.112054 | − | 0.821022i | −0.0105881 | − | 0.0775793i | ||||
\(113\) | −1.73879 | − | 3.01167i | −0.163572 | − | 0.283314i | 0.772576 | − | 0.634923i | \(-0.218968\pi\) |
−0.936147 | + | 0.351609i | \(0.885635\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.73718 | − | 3.31236i | 0.534994 | − | 0.308879i | ||||
\(116\) | −2.24694 | + | 3.89182i | −0.208623 | + | 0.361346i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.78011 | 0.347987 | ||||||||
\(119\) | −0.741100 | − | 5.43007i | −0.0679366 | − | 0.497774i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.36989 | + | 7.56887i | −0.397263 | + | 0.688079i | ||||
\(122\) | 9.01986 | + | 5.20762i | 0.816620 | + | 0.471476i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 22.5003 | + | 12.9905i | 2.02058 | + | 1.16658i | ||||
\(125\) | − | 7.86464i | − | 0.703435i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.84992 | + | 13.5965i | −0.696567 | + | 1.20649i | 0.273082 | + | 0.961991i | \(0.411957\pi\) |
−0.969649 | + | 0.244499i | \(0.921376\pi\) | |||||||
\(128\) | − | 18.9275i | − | 1.67297i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.41945 | − | 2.88119i | −0.563023 | − | 0.252697i | ||||
\(131\) | −1.27259 | − | 2.20418i | −0.111186 | − | 0.192580i | 0.805063 | − | 0.593190i | \(-0.202132\pi\) |
−0.916249 | + | 0.400610i | \(0.868798\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0474689 | − | 0.116155i | 0.00411608 | − | 0.0100719i | ||||
\(134\) | 2.35240 | + | 4.07447i | 0.203216 | + | 0.351981i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.22632i | 0.533902i | ||||||||
\(137\) | − | 1.86472i | − | 0.159314i | −0.996822 | − | 0.0796571i | \(-0.974617\pi\) | ||
0.996822 | − | 0.0796571i | \(-0.0253825\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.80462 | − | 13.5180i | −0.661979 | − | 1.14658i | −0.980095 | − | 0.198530i | \(-0.936383\pi\) |
0.318116 | − | 0.948052i | \(-0.396950\pi\) | |||||||
\(140\) | −4.53813 | − | 5.85648i | −0.383542 | − | 0.494963i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 16.3692 | + | 28.3524i | 1.37368 | + | 2.37928i | ||||
\(143\) | 2.21957 | − | 4.94533i | 0.185610 | − | 0.413550i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.15207i | 0.0956741i | ||||||||
\(146\) | 7.78676 | − | 13.4871i | 0.644437 | − | 1.11620i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 22.1510i | 1.82080i | ||||||||
\(149\) | −5.51106 | − | 3.18181i | −0.451484 | − | 0.260664i | 0.256973 | − | 0.966419i | \(-0.417275\pi\) |
−0.708457 | + | 0.705754i | \(0.750608\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.575122 | + | 0.332047i | 0.0468028 | + | 0.0270216i | 0.523219 | − | 0.852198i | \(-0.324731\pi\) |
−0.476416 | + | 0.879220i | \(0.658064\pi\) | |||||||
\(152\) | −0.0712794 | + | 0.123460i | −0.00578152 | + | 0.0100139i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.24180 | − | 5.61160i | 0.583561 | − | 0.452196i | ||||
\(155\) | 6.66060 | 0.534992 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.28798 | − | 14.3552i | 0.661453 | − | 1.14567i | −0.318781 | − | 0.947828i | \(-0.603273\pi\) |
0.980234 | − | 0.197842i | \(-0.0633933\pi\) | |||||||
\(158\) | −23.2562 | + | 13.4269i | −1.85016 | + | 1.06819i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.24122 | − | 3.88191i | −0.177184 | − | 0.306892i | ||||
\(161\) | 2.79735 | + | 20.4963i | 0.220462 | + | 1.61534i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.83863 | + | 4.52563i | 0.613969 | + | 0.354475i | 0.774517 | − | 0.632553i | \(-0.217993\pi\) |
−0.160548 | + | 0.987028i | \(0.551326\pi\) | |||||||
\(164\) | −28.6752 | − | 16.5557i | −2.23916 | − | 1.29278i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −26.5710 | −2.06231 | ||||||||
\(167\) | 2.30156 | + | 1.32880i | 0.178100 | + | 0.102826i | 0.586400 | − | 0.810022i | \(-0.300545\pi\) |
−0.408300 | + | 0.912848i | \(0.633878\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.09120 | − | 12.3395i | 0.314708 | − | 0.949189i | ||||
\(170\) | 2.02121 | + | 3.50084i | 0.155020 | + | 0.268502i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −15.3117 | − | 26.5206i | −1.16750 | − | 2.02218i | ||||
\(173\) | −9.79352 | + | 16.9629i | −0.744588 | + | 1.28966i | 0.205799 | + | 0.978594i | \(0.434021\pi\) |
−0.950387 | + | 0.311070i | \(0.899313\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.4874 | + | 4.28587i | 0.792774 | + | 0.323981i | ||||
\(176\) | −0.407774 | + | 0.235428i | −0.0307371 | + | 0.0177461i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −40.3330 | −3.02309 | ||||||||
\(179\) | 1.44666 | + | 2.50569i | 0.108129 | + | 0.187284i | 0.915012 | − | 0.403426i | \(-0.132181\pi\) |
−0.806884 | + | 0.590711i | \(0.798848\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.36804 | −0.101686 | −0.0508429 | − | 0.998707i | \(-0.516191\pi\) | ||||
−0.0508429 | + | 0.998707i | \(0.516191\pi\) | |||||||
\(182\) | 15.9113 | − | 15.1522i | 1.17942 | − | 1.12316i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 23.5018i | − | 1.73258i | ||||||
\(185\) | 2.83936 | + | 4.91791i | 0.208754 | + | 0.361572i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.69693 | + | 1.55707i | −0.197219 | + | 0.113865i | ||||
\(188\) | −1.03045 | + | 0.594929i | −0.0751531 | + | 0.0433897i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.0925559i | 0.00671471i | ||||||||
\(191\) | −0.756625 | + | 1.31051i | −0.0547475 | + | 0.0948254i | −0.892100 | − | 0.451837i | \(-0.850769\pi\) |
0.837353 | + | 0.546663i | \(0.184102\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.02229 | + | 3.47697i | −0.433494 | + | 0.250278i | −0.700834 | − | 0.713324i | \(-0.747189\pi\) |
0.267340 | + | 0.963602i | \(0.413855\pi\) | |||||||
\(194\) | −0.490860 | − | 0.850194i | −0.0352417 | − | 0.0610404i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 22.2891 | − | 6.19955i | 1.59208 | − | 0.442825i | ||||
\(197\) | 13.4037 | + | 7.73860i | 0.954971 | + | 0.551353i | 0.894622 | − | 0.446825i | \(-0.147445\pi\) |
0.0603494 | + | 0.998177i | \(0.480779\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.61529 | −0.468945 | −0.234473 | − | 0.972123i | \(-0.575336\pi\) | ||||
−0.234473 | + | 0.972123i | \(0.575336\pi\) | |||||||
\(200\) | −11.1469 | − | 6.43566i | −0.788205 | − | 0.455070i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −19.2886 | + | 11.1363i | −1.35714 | + | 0.783545i | ||||
\(203\) | −3.33010 | − | 1.36090i | −0.233727 | − | 0.0955168i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.48854 | −0.592865 | ||||||||
\(206\) | −19.9035 | + | 11.4913i | −1.38674 | + | 0.800634i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.915555 | + | 0.661010i | −0.0634823 | + | 0.0458328i | ||||
\(209\) | −0.0713021 | −0.00493207 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.04714 | − | 7.00986i | 0.278617 | − | 0.482578i | −0.692424 | − | 0.721490i | \(-0.743457\pi\) |
0.971041 | + | 0.238912i | \(0.0767907\pi\) | |||||||
\(212\) | −4.48132 | + | 7.76187i | −0.307778 | + | 0.533088i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 22.7153i | 1.55279i | ||||||||
\(215\) | −6.79892 | − | 3.92536i | −0.463683 | − | 0.267707i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.86797 | + | 19.2527i | −0.534113 | + | 1.30696i | ||||
\(218\) | −13.3653 | + | 23.1493i | −0.905211 | + | 1.56787i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.10501 | + | 3.64599i | −0.141920 | + | 0.245812i | ||||
\(221\) | −6.05530 | + | 4.37178i | −0.407323 | + | 0.294078i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.9067 | + | 8.02903i | 0.931261 | + | 0.537664i | 0.887210 | − | 0.461366i | \(-0.152640\pi\) |
0.0440506 | + | 0.999029i | \(0.485974\pi\) | |||||||
\(224\) | 13.8683 | − | 1.89276i | 0.926616 | − | 0.126465i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.93668 | + | 4.00490i | −0.461421 | + | 0.266402i | ||||
\(227\) | − | 1.29581i | − | 0.0860057i | −0.999075 | − | 0.0430029i | \(-0.986308\pi\) | ||
0.999075 | − | 0.0430029i | \(-0.0136925\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.0285 | − | 10.4088i | 1.19136 | − | 0.687831i | 0.232743 | − | 0.972538i | \(-0.425230\pi\) |
0.958614 | + | 0.284707i | \(0.0918965\pi\) | |||||||
\(230\) | −7.62925 | − | 13.2142i | −0.503058 | − | 0.871322i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.53951 | + | 2.04354i | 0.232380 | + | 0.134165i | ||||
\(233\) | 6.65213 | + | 11.5218i | 0.435796 | + | 0.754820i | 0.997360 | − | 0.0726127i | \(-0.0231337\pi\) |
−0.561565 | + | 0.827433i | \(0.689800\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.152518 | + | 0.264169i | −0.00994920 | + | 0.0172325i | ||||
\(236\) | − | 5.42421i | − | 0.353086i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.5069 | + | 1.70695i | −0.810702 | + | 0.110645i | ||||
\(239\) | − | 13.3652i | − | 0.864525i | −0.901748 | − | 0.432263i | \(-0.857715\pi\) | ||
0.901748 | − | 0.432263i | \(-0.142285\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.834153i | 0.0537325i | 0.999639 | + | 0.0268663i | \(0.00855282\pi\) | ||||
−0.999639 | + | 0.0268663i | \(0.991447\pi\) | |||||||
\(242\) | 17.4331 | + | 10.0650i | 1.12064 | + | 0.647004i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.47259 | − | 12.9429i | 0.478384 | − | 0.828585i | ||||
\(245\) | 4.15391 | − | 4.23347i | 0.265383 | − | 0.270467i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.170117 | + | 0.0173651i | −0.0108243 | + | 0.00110491i | ||||
\(248\) | 11.8146 | − | 20.4634i | 0.750225 | − | 1.29943i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −18.1144 | −1.14565 | ||||||||
\(251\) | −13.6360 | − | 23.6183i | −0.860699 | − | 1.49078i | −0.871255 | − | 0.490831i | \(-0.836693\pi\) |
0.0105555 | − | 0.999944i | \(-0.496640\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.1798 | − | 5.87733i | 0.640000 | − | 0.369504i | ||||
\(254\) | 31.3163 | + | 18.0804i | 1.96496 | + | 1.13447i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.9721 | −1.12326 | ||||||||
\(257\) | 6.55188 | 0.408695 | 0.204348 | − | 0.978898i | \(-0.434493\pi\) | ||||
0.204348 | + | 0.978898i | \(0.434493\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.5695 | + | 2.39789i | −1.09171 | + | 0.148998i | ||||
\(260\) | −4.13432 | + | 9.21148i | −0.256399 | + | 0.571272i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.07682 | + | 2.93110i | −0.313647 | + | 0.181084i | ||||
\(263\) | −11.2945 | − | 19.5627i | −0.696450 | − | 1.20629i | −0.969689 | − | 0.244341i | \(-0.921428\pi\) |
0.273239 | − | 0.961946i | \(-0.411905\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.29770i | 0.141146i | ||||||||
\(266\) | −0.267537 | − | 0.109334i | −0.0164037 | − | 0.00670367i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.84660 | − | 3.37553i | 0.357138 | − | 0.206194i | ||||
\(269\) | −16.0013 | −0.975617 | −0.487808 | − | 0.872951i | \(-0.662203\pi\) | ||||
−0.487808 | + | 0.872951i | \(0.662203\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 8.75935i | − | 0.532093i | −0.963960 | − | 0.266046i | \(-0.914283\pi\) | ||
0.963960 | − | 0.266046i | \(-0.0857174\pi\) | |||||||
\(272\) | 0.648750 | 0.0393363 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.29496 | −0.259468 | ||||||||
\(275\) | − | 6.43771i | − | 0.388209i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.9183 | 1.19677 | 0.598387 | − | 0.801208i | \(-0.295809\pi\) | ||||
0.598387 | + | 0.801208i | \(0.295809\pi\) | |||||||
\(278\) | −31.1355 | + | 17.9761i | −1.86739 | + | 1.07814i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.32632 | + | 4.12731i | −0.318308 | + | 0.246654i | ||||
\(281\) | 14.0234i | 0.836566i | 0.908317 | + | 0.418283i | \(0.137368\pi\) | ||||
−0.908317 | + | 0.418283i | \(0.862632\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.506295 | + | 0.876929i | 0.0300961 | + | 0.0521280i | 0.880681 | − | 0.473710i | \(-0.157085\pi\) |
−0.850585 | + | 0.525838i | \(0.823752\pi\) | |||||||
\(284\) | 40.6838 | − | 23.4888i | 2.41414 | − | 1.39380i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.3904 | − | 5.11227i | −0.673530 | − | 0.302295i | ||||
\(287\) | 10.0273 | − | 24.5365i | 0.591890 | − | 1.44834i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.7093 | −0.747606 | ||||||||
\(290\) | 2.65352 | 0.155820 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −19.3531 | − | 11.1735i | −1.13255 | − | 0.653879i | ||||
\(293\) | 0.172543 | − | 0.0996176i | 0.0100801 | − | 0.00581972i | −0.494952 | − | 0.868921i | \(-0.664814\pi\) |
0.505032 | + | 0.863101i | \(0.331481\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.695286 | − | 1.20427i | −0.0404811 | − | 0.0701153i | ||||
\(296\) | 20.1458 | 1.17095 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.32857 | + | 12.6935i | −0.424532 | + | 0.735312i | ||||
\(299\) | 22.8563 | − | 16.5017i | 1.32181 | − | 0.954319i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.3778 | − | 15.0156i | 1.11692 | − | 0.865487i | ||||
\(302\) | 0.764792 | − | 1.32466i | 0.0440088 | − | 0.0762256i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.0128639 | + | 0.00742695i | 0.000737793 | + | 0.000425965i | ||||
\(305\) | − | 3.83140i | − | 0.219386i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 27.2004i | − | 1.55241i | −0.630482 | − | 0.776204i | \(-0.717143\pi\) | ||
0.630482 | − | 0.776204i | \(-0.282857\pi\) | |||||||
\(308\) | −8.05228 | − | 10.3915i | −0.458821 | − | 0.592111i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 15.3411i | − | 0.871318i | ||||||
\(311\) | −13.5505 | + | 23.4701i | −0.768376 | + | 1.33087i | 0.170067 | + | 0.985432i | \(0.445602\pi\) |
−0.938443 | + | 0.345434i | \(0.887732\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0392 | + | 19.1205i | 0.623975 | + | 1.08076i | 0.988738 | + | 0.149656i | \(0.0478165\pi\) |
−0.364763 | + | 0.931100i | \(0.618850\pi\) | |||||||
\(314\) | −33.0639 | − | 19.0894i | −1.86590 | − | 1.07728i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.2668 | + | 33.3711i | 1.08384 | + | 1.87727i | ||||
\(317\) | 6.12126 | − | 3.53411i | 0.343804 | − | 0.198496i | −0.318149 | − | 0.948041i | \(-0.603061\pi\) |
0.661953 | + | 0.749545i | \(0.269728\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.04419i | 0.114453i | ||||||||
\(320\) | −9.40071 | + | 5.42750i | −0.525516 | + | 0.303407i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 47.2085 | − | 6.44305i | 2.63083 | − | 0.359057i | ||||
\(323\) | 0.0850789 | + | 0.0491204i | 0.00473392 | + | 0.00273313i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.56786 | − | 15.3595i | −0.0869690 | − | 0.851992i | ||||
\(326\) | 10.4237 | − | 18.0544i | 0.577318 | − | 0.999943i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −15.0569 | + | 26.0794i | −0.831381 | + | 1.43999i | ||||
\(329\) | −0.583427 | − | 0.752916i | −0.0321654 | − | 0.0415096i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.70588 | + | 3.29429i | 0.313623 | + | 0.181071i | 0.648547 | − | 0.761175i | \(-0.275377\pi\) |
−0.334923 | + | 0.942245i | \(0.608710\pi\) | |||||||
\(332\) | 38.1277i | 2.09253i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.06059 | − | 5.30110i | 0.167468 | − | 0.290063i | ||||
\(335\) | 0.865365 | − | 1.49886i | 0.0472799 | − | 0.0818912i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.22290 | −0.230036 | −0.115018 | − | 0.993363i | \(-0.536693\pi\) | ||||
−0.115018 | + | 0.993363i | \(0.536693\pi\) | |||||||
\(338\) | −28.4210 | − | 9.42313i | −1.54590 | − | 0.512551i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.02347 | − | 2.90030i | 0.272436 | − | 0.157291i | ||||
\(341\) | 11.8183 | 0.639998 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.33014 | + | 17.0079i | 0.395790 | + | 0.918341i | ||||
\(344\) | −24.1198 | + | 13.9256i | −1.30045 | + | 0.750817i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 39.0700 | + | 22.5571i | 2.10042 | + | 1.21268i | ||||
\(347\) | 9.09478 | 0.488233 | 0.244117 | − | 0.969746i | \(-0.421502\pi\) | ||||
0.244117 | + | 0.969746i | \(0.421502\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.98521 | + | 4.61026i | 0.427439 | + | 0.246782i | 0.698255 | − | 0.715849i | \(-0.253960\pi\) |
−0.270816 | + | 0.962631i | \(0.587294\pi\) | |||||||
\(350\) | 9.87149 | − | 24.1553i | 0.527653 | − | 1.29116i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.97674 | − | 6.88792i | −0.211961 | − | 0.367127i | ||||
\(353\) | −1.86584 | + | 1.07724i | −0.0993087 | + | 0.0573359i | −0.548832 | − | 0.835933i | \(-0.684927\pi\) |
0.449523 | + | 0.893269i | \(0.351594\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.02167 | − | 10.4298i | 0.319597 | − | 0.553559i | ||||
\(356\) | 57.8752i | 3.06738i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.77128 | − | 3.33205i | 0.305021 | − | 0.176104i | ||||
\(359\) | 7.41107 | − | 4.27878i | 0.391141 | − | 0.225825i | −0.291513 | − | 0.956567i | \(-0.594159\pi\) |
0.682654 | + | 0.730741i | \(0.260825\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.49888 | − | 16.4525i | −0.499941 | − | 0.865923i | ||||
\(362\) | 3.15096i | 0.165611i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −21.7424 | − | 22.8317i | −1.13961 | − | 1.19670i | ||||
\(365\) | −5.72896 | −0.299867 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.14912 | − | 1.99033i | −0.0599833 | − | 0.103894i | 0.834474 | − | 0.551047i | \(-0.185771\pi\) |
−0.894458 | + | 0.447153i | \(0.852438\pi\) | |||||||
\(368\) | −2.44877 | −0.127651 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 11.3273 | − | 6.53979i | 0.588876 | − | 0.339988i | ||||
\(371\) | −6.64158 | − | 2.71420i | −0.344814 | − | 0.140914i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.88418 | + | 10.1917i | −0.304672 | + | 0.527707i | −0.977188 | − | 0.212375i | \(-0.931880\pi\) |
0.672517 | + | 0.740082i | \(0.265213\pi\) | |||||||
\(374\) | 3.58636 | + | 6.21175i | 0.185446 | + | 0.321202i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.541073 | + | 0.937166i | 0.0279037 | + | 0.0483307i | ||||
\(377\) | 0.497847 | + | 4.87715i | 0.0256404 | + | 0.251186i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.92034 | − | 3.99546i | −0.355474 | − | 0.205233i | 0.311619 | − | 0.950207i | \(-0.399129\pi\) |
−0.667094 | + | 0.744974i | \(0.732462\pi\) | |||||||
\(380\) | 0.132812 | 0.00681310 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.01846 | + | 1.74271i | 0.154438 | + | 0.0891647i | ||||
\(383\) | 24.4605 | + | 14.1223i | 1.24988 | + | 0.721616i | 0.971084 | − | 0.238736i | \(-0.0767331\pi\) |
0.278791 | + | 0.960352i | \(0.410066\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.11975 | − | 1.27494i | −0.158997 | − | 0.0649770i | ||||
\(386\) | 8.00839 | + | 13.8709i | 0.407616 | + | 0.706012i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.21997 | + | 0.704352i | −0.0619347 | + | 0.0357580i | ||||
\(389\) | −3.84043 | + | 6.65182i | −0.194717 | + | 0.337261i | −0.946808 | − | 0.321799i | \(-0.895712\pi\) |
0.752090 | + | 0.659060i | \(0.229046\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.1957 | −0.819050 | ||||||||
\(392\) | −5.63834 | − | 20.2714i | −0.284779 | − | 1.02386i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 17.8241 | − | 30.8722i | 0.897964 | − | 1.55532i | ||||
\(395\) | 8.55513 | + | 4.93931i | 0.430455 | + | 0.248524i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.45433 | + | 3.72641i | 0.323933 | + | 0.187023i | 0.653144 | − | 0.757233i | \(-0.273449\pi\) |
−0.329211 | + | 0.944256i | \(0.606783\pi\) | |||||||
\(398\) | 15.2368i | 0.763750i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.670563 | + | 1.16145i | −0.0335282 | + | 0.0580725i | ||||
\(401\) | 18.1982i | 0.908777i | 0.890804 | + | 0.454389i | \(0.150142\pi\) | ||||
−0.890804 | + | 0.454389i | \(0.849858\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.1969 | − | 2.87826i | 1.40459 | − | 0.143376i | ||||
\(404\) | 15.9798 | + | 27.6778i | 0.795025 | + | 1.37702i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.13453 | + | 7.67011i | −0.155564 | + | 0.380661i | ||||
\(407\) | 5.03804 | + | 8.72615i | 0.249727 | + | 0.432539i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.2825i | 1.44793i | 0.689838 | + | 0.723964i | \(0.257682\pi\) | ||||
−0.689838 | + | 0.723964i | \(0.742318\pi\) | |||||||
\(410\) | 19.5514i | 0.965573i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 16.4892 | + | 28.5602i | 0.812365 | + | 1.40706i | ||||
\(413\) | 4.30231 | − | 0.587183i | 0.211703 | − | 0.0288934i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.88728 | + | 8.46502i | 0.239907 | + | 0.415531i | ||||
\(416\) | −11.1655 | − | 15.4651i | −0.547432 | − | 0.758241i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.164228i | 0.00803264i | ||||||||
\(419\) | −10.3697 | + | 17.9608i | −0.506591 | + | 0.877441i | 0.493380 | + | 0.869814i | \(0.335761\pi\) |
−0.999971 | + | 0.00762733i | \(0.997572\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 24.8696i | − | 1.21207i | −0.795437 | − | 0.606036i | \(-0.792759\pi\) | ||
0.795437 | − | 0.606036i | \(-0.207241\pi\) | |||||||
\(422\) | −16.1456 | − | 9.32165i | −0.785954 | − | 0.453771i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.05923 | + | 4.07565i | 0.342826 | + | 0.197931i | ||||
\(425\) | −4.43497 | + | 7.68159i | −0.215128 | + | 0.372612i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.0748 | + | 4.52592i | 0.535948 | + | 0.219025i | ||||
\(428\) | 32.5950 | 1.57554 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.04115 | + | 15.6597i | −0.436003 | + | 0.755179i | ||||
\(431\) | 18.3327 | − | 10.5844i | 0.883055 | − | 0.509832i | 0.0113906 | − | 0.999935i | \(-0.496374\pi\) |
0.871665 | + | 0.490103i | \(0.163041\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.7148 | − | 20.2906i | −0.562977 | − | 0.975105i | −0.997235 | − | 0.0743163i | \(-0.976323\pi\) |
0.434258 | − | 0.900789i | \(-0.357011\pi\) | |||||||
\(434\) | 44.3442 | + | 18.1220i | 2.12859 | + | 0.869885i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 33.2178 | + | 19.1783i | 1.59084 | + | 0.918474i | ||||
\(437\) | −0.321139 | − | 0.185409i | −0.0153621 | − | 0.00886934i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.0384 | 0.574561 | 0.287280 | − | 0.957847i | \(-0.407249\pi\) | ||||
0.287280 | + | 0.957847i | \(0.407249\pi\) | |||||||
\(440\) | 3.31593 | + | 1.91445i | 0.158081 | + | 0.0912680i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.0694 | + | 13.9470i | 0.478952 | + | 0.663390i | ||||
\(443\) | 7.86656 | + | 13.6253i | 0.373752 | + | 0.647357i | 0.990139 | − | 0.140086i | \(-0.0447379\pi\) |
−0.616388 | + | 0.787443i | \(0.711405\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.41855 | + | 12.8493i | 0.351673 | + | 0.609116i | ||||
\(446\) | 18.4930 | − | 32.0308i | 0.875669 | − | 1.51670i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.58363 | − | 33.5845i | −0.216556 | − | 1.58672i | ||||
\(449\) | −22.5177 | + | 13.0006i | −1.06268 | + | 0.613536i | −0.926171 | − | 0.377104i | \(-0.876920\pi\) |
−0.136504 | + | 0.990640i | \(0.543587\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.0617 | −0.709230 | ||||||||
\(452\) | 5.74676 | + | 9.95369i | 0.270305 | + | 0.468182i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.98459 | −0.140074 | ||||||||
\(455\) | −7.75380 | − | 2.28204i | −0.363504 | − | 0.106984i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.7958i | 1.44057i | 0.693679 | + | 0.720284i | \(0.255989\pi\) | ||||
−0.693679 | + | 0.720284i | \(0.744011\pi\) | |||||||
\(458\) | −23.9742 | − | 41.5245i | −1.12024 | − | 1.94031i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −18.9616 | + | 10.9475i | −0.884088 | + | 0.510429i | ||||
\(461\) | 29.5278 | − | 17.0479i | 1.37525 | − | 0.794000i | 0.383665 | − | 0.923472i | \(-0.374662\pi\) |
0.991583 | + | 0.129472i | \(0.0413284\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.69184i | 0.0786263i | 0.999227 | + | 0.0393131i | \(0.0125170\pi\) | ||||
−0.999227 | + | 0.0393131i | \(0.987483\pi\) | |||||||
\(464\) | 0.212926 | − | 0.368799i | 0.00988485 | − | 0.0171211i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 26.5378 | − | 15.3216i | 1.22934 | − | 0.709761i | ||||
\(467\) | −14.1762 | − | 24.5539i | −0.655996 | − | 1.13622i | −0.981643 | − | 0.190727i | \(-0.938916\pi\) |
0.325647 | − | 0.945491i | \(-0.394418\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.31027 | + | 4.27192i | 0.152854 | + | 0.197259i | ||||
\(470\) | 0.608453 | + | 0.351290i | 0.0280658 | + | 0.0162038i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.93318 | −0.227068 | ||||||||
\(473\) | −12.0637 | − | 6.96501i | −0.554692 | − | 0.320251i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.175879 | + | 0.101544i | −0.00806989 | + | 0.00465915i | ||||
\(476\) | 2.44936 | + | 17.9466i | 0.112266 | + | 0.822581i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −30.7837 | −1.40801 | ||||||||
\(479\) | −5.44077 | + | 3.14123i | −0.248595 | + | 0.143526i | −0.619121 | − | 0.785296i | \(-0.712511\pi\) |
0.370526 | + | 0.928822i | \(0.379178\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.1453 | + | 19.5924i | 0.644969 | + | 0.893338i | ||||
\(482\) | 1.92128 | 0.0875117 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.4427 | − | 25.0154i | 0.656484 | − | 1.13706i | ||||
\(485\) | −0.180570 | + | 0.312757i | −0.00819927 | + | 0.0142016i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.0176i | 0.589883i | 0.955515 | + | 0.294942i | \(0.0953002\pi\) | ||||
−0.955515 | + | 0.294942i | \(0.904700\pi\) | |||||||
\(488\) | −11.7712 | − | 6.79613i | −0.532859 | − | 0.307647i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9.75082 | − | 9.56756i | −0.440497 | − | 0.432218i | ||||
\(491\) | 6.17616 | − | 10.6974i | 0.278726 | − | 0.482768i | −0.692342 | − | 0.721569i | \(-0.743421\pi\) |
0.971068 | + | 0.238801i | \(0.0767544\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.40825 | − | 2.43916i | 0.0634244 | − | 0.109854i | ||||
\(494\) | 0.0399964 | + | 0.391825i | 0.00179952 | + | 0.0176290i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.13218 | − | 1.23102i | −0.0957378 | − | 0.0552743i | ||||
\(497\) | 23.0347 | + | 29.7264i | 1.03325 | + | 1.33341i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.92708 | − | 4.57670i | 0.354865 | − | 0.204881i | −0.311961 | − | 0.950095i | \(-0.600986\pi\) |
0.666826 | + | 0.745214i | \(0.267652\pi\) | |||||||
\(500\) | 25.9929i | 1.16244i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −54.3993 | + | 31.4074i | −2.42796 | + | 1.40178i | ||||
\(503\) | 11.2519 | + | 19.4888i | 0.501696 | + | 0.868963i | 0.999998 | + | 0.00195935i | \(0.000623680\pi\) |
−0.498302 | + | 0.867003i | \(0.666043\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.09559 | + | 4.09664i | 0.315750 | + | 0.182298i | ||||
\(506\) | −13.5370 | − | 23.4469i | −0.601795 | − | 1.04234i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 25.9443 | − | 44.9368i | 1.15109 | − | 1.99375i | ||||
\(509\) | 38.6606i | 1.71360i | 0.515649 | + | 0.856800i | \(0.327551\pi\) | ||||
−0.515649 | + | 0.856800i | \(0.672449\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.76745 | − | 16.5598i | 0.299374 | − | 0.732562i | ||||
\(512\) | 3.53972i | 0.156435i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 15.0907i | − | 0.665623i | ||||||
\(515\) | 7.32179 | + | 4.22724i | 0.322637 | + | 0.186274i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.270623 | + | 0.468732i | −0.0119020 | + | 0.0206148i | ||||
\(518\) | 5.52298 | + | 40.4671i | 0.242666 | + | 1.77802i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.37761 | + | 3.76006i | 0.367383 | + | 0.164889i | ||||
\(521\) | 20.1176 | − | 34.8446i | 0.881366 | − | 1.52657i | 0.0315430 | − | 0.999502i | \(-0.489958\pi\) |
0.849823 | − | 0.527068i | \(-0.176709\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.732146 | −0.0320145 | −0.0160073 | − | 0.999872i | \(-0.505095\pi\) | ||||
−0.0160073 | + | 0.999872i | \(0.505095\pi\) | |||||||
\(524\) | 4.20594 | + | 7.28491i | 0.183737 | + | 0.318243i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −45.0581 | + | 26.0143i | −1.96463 | + | 1.13428i | ||||
\(527\) | −14.1018 | − | 8.14169i | −0.614285 | − | 0.354658i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 38.1321 | 1.65792 | ||||||||
\(530\) | 5.29221 | 0.229879 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.156887 | + | 0.383898i | −0.00680189 | + | 0.0166441i | ||||
\(533\) | −35.9353 | + | 3.66817i | −1.55653 | + | 0.158886i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.23667 | − | 4.17809i | 0.312868 | − | 0.180635i | ||||
\(536\) | −3.06996 | − | 5.31733i | −0.132602 | − | 0.229674i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 36.8553i | 1.58894i | ||||||||
\(539\) | 7.37054 | − | 7.51171i | 0.317472 | − | 0.323552i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.4847 | + | 11.8268i | −0.880705 | + | 0.508476i | −0.870891 | − | 0.491476i | \(-0.836457\pi\) |
−0.00981448 | + | 0.999952i | \(0.503124\pi\) | |||||||
\(542\) | −20.1751 | −0.866595 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.9584i | 0.469837i | ||||||||
\(545\) | 9.83325 | 0.421210 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.9472 | −0.553582 | −0.276791 | − | 0.960930i | \(-0.589271\pi\) | ||||
−0.276791 | + | 0.960930i | \(0.589271\pi\) | |||||||
\(548\) | 6.16298i | 0.263270i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −14.8278 | −0.632258 | ||||||||
\(551\) | 0.0558475 | − | 0.0322436i | 0.00237918 | − | 0.00137362i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.3832 | + | 18.8943i | −1.03688 | + | 0.803467i | ||||
\(554\) | − | 45.8771i | − | 1.94913i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 25.7946 | + | 44.6775i | 1.09393 | + | 1.89475i | ||||
\(557\) | −5.54845 | + | 3.20340i | −0.235096 | + | 0.135732i | −0.612921 | − | 0.790145i | \(-0.710005\pi\) |
0.377825 | + | 0.925877i | \(0.376672\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −30.4787 | − | 13.6795i | −1.28911 | − | 0.578582i | ||||
\(560\) | 0.430045 | + | 0.554975i | 0.0181727 | + | 0.0234520i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 32.2996 | 1.36248 | ||||||||
\(563\) | 7.32084 | 0.308537 | 0.154268 | − | 0.988029i | \(-0.450698\pi\) | ||||
0.154268 | + | 0.988029i | \(0.450698\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.55176 | + | 1.47326i | 0.107354 | + | 0.0619806i | ||||
\(566\) | 2.01980 | − | 1.16613i | 0.0848986 | − | 0.0490162i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21.3625 | − | 37.0009i | −0.896349 | − | 1.55252i | ||||
\(569\) | −4.31743 | −0.180996 | −0.0904981 | − | 0.995897i | \(-0.528846\pi\) | ||||
−0.0904981 | + | 0.995897i | \(0.528846\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.0847 | − | 29.5916i | 0.714974 | − | 1.23837i | −0.247996 | − | 0.968761i | \(-0.579772\pi\) |
0.962970 | − | 0.269610i | \(-0.0868946\pi\) | |||||||
\(572\) | −7.33577 | + | 16.3445i | −0.306724 | + | 0.683398i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −56.5140 | − | 23.0954i | −2.35885 | − | 0.963985i | ||||
\(575\) | 16.7402 | − | 28.9949i | 0.698115 | − | 1.20917i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.50494 | − | 3.17828i | −0.229174 | − | 0.132314i | 0.381017 | − | 0.924568i | \(-0.375574\pi\) |
−0.610191 | + | 0.792254i | \(0.708907\pi\) | |||||||
\(578\) | 29.2729i | 1.21759i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 3.80763i | − | 0.158103i | ||||||
\(581\) | −30.2417 | + | 4.12740i | −1.25464 | + | 0.171234i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.07695i | 0.168850i | ||||||||
\(584\) | −10.1620 | + | 17.6011i | −0.420507 | + | 0.728339i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.229446 | − | 0.397412i | −0.00947832 | − | 0.0164169i | ||||
\(587\) | −27.2036 | − | 15.7060i | −1.12281 | − | 0.648256i | −0.180695 | − | 0.983539i | \(-0.557835\pi\) |
−0.942118 | + | 0.335283i | \(0.891168\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.186414 | − | 0.322878i | −0.00768104 | − | 0.0133040i | ||||
\(590\) | −2.77376 | + | 1.60143i | −0.114194 | + | 0.0659298i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 2.09909i | − | 0.0862719i | ||||||
\(593\) | −0.409641 | + | 0.236506i | −0.0168219 | + | 0.00971215i | −0.508387 | − | 0.861128i | \(-0.669758\pi\) |
0.491565 | + | 0.870841i | \(0.336425\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.84423 | + | 3.67049i | 0.116602 | + | 0.150476i | ||||
\(596\) | 18.2143 | + | 10.5160i | 0.746086 | + | 0.430753i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −38.0079 | − | 52.6442i | −1.55426 | − | 2.15278i | ||||
\(599\) | −4.81348 | + | 8.33719i | −0.196673 | + | 0.340648i | −0.947448 | − | 0.319910i | \(-0.896347\pi\) |
0.750774 | + | 0.660559i | \(0.229680\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.5399 | − | 35.5762i | 0.837842 | − | 1.45118i | −0.0538542 | − | 0.998549i | \(-0.517151\pi\) |
0.891696 | − | 0.452635i | \(-0.149516\pi\) | |||||||
\(602\) | −34.5850 | − | 44.6322i | −1.40958 | − | 1.81907i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.90080 | − | 1.09743i | −0.0773424 | − | 0.0446537i | ||||
\(605\) | − | 7.40514i | − | 0.301062i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.54289 | + | 16.5288i | −0.387334 | + | 0.670882i | −0.992090 | − | 0.125529i | \(-0.959937\pi\) |
0.604756 | + | 0.796411i | \(0.293271\pi\) | |||||||
\(608\) | −0.125453 | + | 0.217290i | −0.00508777 | + | 0.00881228i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.82474 | −0.357303 | ||||||||
\(611\) | −0.531513 | + | 1.18424i | −0.0215027 | + | 0.0479092i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.9131 | + | 19.0024i | −1.32935 | + | 0.767500i | −0.985199 | − | 0.171415i | \(-0.945166\pi\) |
−0.344149 | + | 0.938915i | \(0.611833\pi\) | |||||||
\(614\) | −62.6498 | −2.52834 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.45082 | + | 7.32335i | −0.380784 | + | 0.295066i | ||||
\(617\) | −7.20117 | + | 4.15759i | −0.289908 | + | 0.167378i | −0.637900 | − | 0.770119i | \(-0.720197\pi\) |
0.347992 | + | 0.937497i | \(0.386864\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.5146 | − | 22.2364i | −1.54803 | − | 0.893756i | −0.998292 | − | 0.0584199i | \(-0.981394\pi\) |
−0.549739 | − | 0.835336i | \(-0.685273\pi\) | |||||||
\(620\) | −22.0135 | −0.884085 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 54.0579 | + | 31.2103i | 2.16752 | + | 1.25142i | ||||
\(623\) | −45.9048 | + | 6.26512i | −1.83914 | + | 0.251007i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.37342 | − | 12.7711i | −0.294937 | − | 0.510845i | ||||
\(626\) | 44.0397 | − | 25.4263i | 1.76018 | − | 1.01624i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −27.3921 | + | 47.4445i | −1.09306 | + | 1.89324i | ||||
\(629\) | − | 13.8829i | − | 0.553549i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.1779 | + | 5.87622i | −0.405177 | + | 0.233929i | −0.688715 | − | 0.725032i | \(-0.741825\pi\) |
0.283539 | + | 0.958961i | \(0.408492\pi\) | |||||||
\(632\) | 30.3501 | − | 17.5227i | 1.20726 | − | 0.697014i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.14001 | − | 14.0989i | −0.323281 | − | 0.559939i | ||||
\(635\) | − | 13.3023i | − | 0.527887i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.7557 | − | 19.7170i | 0.624263 | − | 0.781215i | ||||
\(638\) | 4.70831 | 0.186404 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.01854 | + | 13.8885i | 0.316961 | + | 0.548992i | ||||
\(641\) | 10.4868 | 0.414205 | 0.207102 | − | 0.978319i | \(-0.433597\pi\) | ||||
0.207102 | + | 0.978319i | \(0.433597\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.0912 | − | 15.6411i | 1.06837 | − | 0.616825i | 0.140635 | − | 0.990061i | \(-0.455085\pi\) |
0.927736 | + | 0.373237i | \(0.121752\pi\) | |||||||
\(644\) | −9.24536 | − | 67.7411i | −0.364318 | − | 2.66937i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.113137 | − | 0.195959i | 0.00445133 | − | 0.00770992i | ||||
\(647\) | 13.4337 | + | 23.2679i | 0.528135 | + | 0.914757i | 0.999462 | + | 0.0327983i | \(0.0104419\pi\) |
−0.471327 | + | 0.881959i | \(0.656225\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.23369 | − | 2.13681i | −0.0484265 | − | 0.0838772i | ||||
\(650\) | −35.3770 | + | 3.61119i | −1.38760 | + | 0.141643i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −25.9070 | − | 14.9574i | −1.01459 | − | 0.585776i | ||||
\(653\) | 4.14161 | 0.162074 | 0.0810369 | − | 0.996711i | \(-0.474177\pi\) | ||||
0.0810369 | + | 0.996711i | \(0.474177\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.86759 | + | 1.07825i | 0.0729726 | + | 0.0421308i | ||||
\(656\) | 2.71734 | + | 1.56886i | 0.106094 | + | 0.0612536i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.73417 | + | 1.34379i | −0.0676048 | + | 0.0523863i | ||||
\(659\) | 10.7276 | + | 18.5807i | 0.417887 | + | 0.723801i | 0.995727 | − | 0.0923492i | \(-0.0294376\pi\) |
−0.577840 | + | 0.816150i | \(0.696104\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.7084 | + | 21.1936i | −1.42779 | + | 0.824335i | −0.996946 | − | 0.0780909i | \(-0.975118\pi\) |
−0.430844 | + | 0.902426i | \(0.641784\pi\) | |||||||
\(662\) | 7.58763 | − | 13.1422i | 0.294902 | − | 0.510785i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 34.6762 | 1.34570 | ||||||||
\(665\) | 0.0143772 | + | 0.105342i | 0.000557522 | + | 0.00408499i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.31558 | + | 9.20685i | −0.205820 | + | 0.356491i | ||||
\(668\) | −7.60673 | − | 4.39175i | −0.294313 | − | 0.169922i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.45226 | − | 1.99317i | −0.133373 | − | 0.0770027i | ||||
\(671\) | − | 6.79830i | − | 0.262445i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.7928 | + | 25.6219i | −0.570220 | + | 0.987650i | 0.426323 | + | 0.904571i | \(0.359809\pi\) |
−0.996543 | + | 0.0830790i | \(0.973525\pi\) | |||||||
\(674\) | 9.72645i | 0.374649i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.5216 | + | 40.7823i | −0.520061 | + | 1.56855i | ||||
\(677\) | 16.0830 | + | 27.8565i | 0.618118 | + | 1.07061i | 0.989829 | + | 0.142263i | \(0.0454380\pi\) |
−0.371711 | + | 0.928349i | \(0.621229\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.690734 | − | 0.891396i | −0.0265079 | − | 0.0342086i | ||||
\(680\) | −2.63775 | − | 4.56872i | −0.101153 | − | 0.175202i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 27.2207i | − | 1.04234i | ||||||
\(683\) | − | 8.60236i | − | 0.329160i | −0.986364 | − | 0.164580i | \(-0.947373\pi\) | ||
0.986364 | − | 0.164580i | \(-0.0526269\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.789983 | + | 1.36829i | 0.0301837 | + | 0.0522797i | ||||
\(686\) | 39.1738 | − | 16.8833i | 1.49566 | − | 0.644606i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.45097 | + | 2.51316i | 0.0553179 | + | 0.0958134i | ||||
\(689\) | 0.992909 | + | 9.72704i | 0.0378268 | + | 0.370571i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.4420i | 0.777651i | 0.921311 | + | 0.388826i | \(0.127119\pi\) | ||||
−0.921311 | + | 0.388826i | \(0.872881\pi\) | |||||||
\(692\) | 32.3680 | − | 56.0629i | 1.23044 | − | 2.13119i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 20.9477i | − | 0.795164i | ||||||
\(695\) | 11.4537 | + | 6.61279i | 0.434463 | + | 0.250837i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.9719 | + | 10.3761i | 0.680736 | + | 0.393023i | ||||
\(698\) | 10.6187 | − | 18.3921i | 0.401922 | − | 0.696150i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −34.6613 | − | 14.1649i | −1.31007 | − | 0.535385i | ||||
\(701\) | 25.1373 | 0.949422 | 0.474711 | − | 0.880142i | \(-0.342553\pi\) | ||||
0.474711 | + | 0.880142i | \(0.342553\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.158933 | − | 0.275280i | 0.00599427 | − | 0.0103824i | ||||
\(704\) | −16.6803 | + | 9.63036i | −0.628661 | + | 0.362958i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.48118 | + | 4.29753i | 0.0933804 | + | 0.161740i | ||||
\(707\) | −20.2233 | + | 15.6709i | −0.760576 | + | 0.589363i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.5416 | − | 14.7464i | −0.959234 | − | 0.553814i | −0.0632970 | − | 0.997995i | \(-0.520162\pi\) |
−0.895937 | + | 0.444181i | \(0.853495\pi\) | |||||||
\(710\) | −24.0227 | − | 13.8695i | −0.901556 | − | 0.520514i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 52.6360 | 1.97262 | ||||||||
\(713\) | 53.2287 | + | 30.7316i | 1.99343 | + | 1.15091i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.466399 | + | 4.56908i | 0.0174423 | + | 0.170874i | ||||
\(716\) | −4.78127 | − | 8.28140i | −0.178684 | − | 0.309491i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.85518 | − | 17.0697i | −0.367792 | − | 0.637034i | ||||
\(719\) | 4.16576 | − | 7.21531i | 0.155357 | − | 0.269086i | −0.777832 | − | 0.628472i | \(-0.783681\pi\) |
0.933189 | + | 0.359386i | \(0.117014\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.8680 | + | 16.1704i | −0.777165 | + | 0.602218i | ||||
\(722\) | −37.8946 | + | 21.8784i | −1.41029 | + | 0.814231i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.52143 | 0.168038 | ||||||||
\(725\) | 2.91120 | + | 5.04235i | 0.108119 | + | 0.187268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.66141 | 0.358322 | 0.179161 | − | 0.983820i | \(-0.442662\pi\) | ||||
0.179161 | + | 0.983820i | \(0.442662\pi\) | |||||||
\(728\) | −20.7648 | + | 19.7742i | −0.769595 | + | 0.732880i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13.1953i | 0.488381i | ||||||||
\(731\) | 9.59645 | + | 16.6215i | 0.354938 | + | 0.614770i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.1398 | + | 7.00894i | −0.448395 | + | 0.258881i | −0.707152 | − | 0.707061i | \(-0.750020\pi\) |
0.258757 | + | 0.965942i | \(0.416687\pi\) | |||||||
\(734\) | −4.58425 | + | 2.64672i | −0.169208 | + | 0.0976921i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 41.3635i | − | 1.52468i | ||||||
\(737\) | 1.53547 | − | 2.65951i | 0.0565598 | − | 0.0979644i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.6145 | − | 19.4073i | 1.23653 | − | 0.713910i | 0.268146 | − | 0.963378i | \(-0.413589\pi\) |
0.968383 | + | 0.249468i | \(0.0802559\pi\) | |||||||
\(740\) | −9.38417 | − | 16.2539i | −0.344969 | − | 0.597504i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.25153 | + | 15.2973i | −0.229501 | + | 0.561583i | ||||
\(743\) | −29.7863 | − | 17.1971i | −1.09275 | − | 0.630901i | −0.158445 | − | 0.987368i | \(-0.550648\pi\) |
−0.934308 | + | 0.356467i | \(0.883981\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.39185 | 0.197542 | ||||||||
\(746\) | 23.4742 | + | 13.5528i | 0.859452 | + | 0.496205i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.91346 | − | 5.14619i | 0.325908 | − | 0.188163i | ||||
\(749\) | 3.52848 | + | 25.8533i | 0.128928 | + | 0.944660i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.1470 | −1.75691 | −0.878454 | − | 0.477827i | \(-0.841425\pi\) | ||||
−0.878454 | + | 0.477827i | \(0.841425\pi\) | |||||||
\(752\) | 0.0976479 | − | 0.0563770i | 0.00356085 | − | 0.00205586i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11.2334 | − | 1.14667i | 0.409096 | − | 0.0417594i | ||||
\(755\) | −0.562681 | −0.0204781 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.45319 | − | 5.98110i | 0.125508 | − | 0.217387i | −0.796423 | − | 0.604740i | \(-0.793277\pi\) |
0.921931 | + | 0.387353i | \(0.126611\pi\) | |||||||
\(758\) | −9.20262 | + | 15.9394i | −0.334254 | + | 0.578945i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 0.120789i | − | 0.00438147i | ||||||
\(761\) | 27.6895 | + | 15.9865i | 1.00374 | + | 0.579511i | 0.909353 | − | 0.416025i | \(-0.136577\pi\) |
0.0943888 | + | 0.995535i | \(0.469910\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.6157 | + | 28.4234i | −0.420517 | + | 1.02900i | ||||
\(764\) | 2.50067 | − | 4.33129i | 0.0904712 | − | 0.156701i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.5274 | − | 56.3391i | 1.17526 | − | 2.03562i | ||||
\(767\) | −3.46382 | − | 4.79769i | −0.125071 | − | 0.173234i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.4665 | + | 7.19752i | 0.449553 | + | 0.259549i | 0.707641 | − | 0.706572i | \(-0.249759\pi\) |
−0.258089 | + | 0.966121i | \(0.583093\pi\) | |||||||
\(770\) | −2.93653 | + | 7.18562i | −0.105825 | + | 0.258952i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 19.9039 | − | 11.4915i | 0.716357 | − | 0.413589i | ||||
\(773\) | − | 37.2771i | − | 1.34076i | −0.742016 | − | 0.670382i | \(-0.766130\pi\) | ||
0.742016 | − | 0.670382i | \(-0.233870\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.1520 | − | 16.8309i | 1.04717 | − | 0.604583i | ||||
\(776\) | 0.640590 | + | 1.10953i | 0.0229958 | + | 0.0398300i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.3209 | + | 8.84553i | 0.549281 | + | 0.317128i | ||||
\(779\) | 0.237573 | + | 0.411489i | 0.00851194 | + | 0.0147431i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.6846 | − | 18.5063i | 0.382326 | − | 0.662208i | ||||
\(782\) | 37.3029i | 1.33395i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.11218 | + | 0.587486i | −0.0754349 | + | 0.0209816i | ||||
\(785\) | 14.0447i | 0.501276i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.3486i | 0.511472i | 0.966747 | + | 0.255736i | \(0.0823178\pi\) | ||||
−0.966747 | + | 0.255736i | \(0.917682\pi\) | |||||||
\(788\) | −44.2996 | − | 25.5764i | −1.57811 | − | 0.911120i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.3765 | − | 19.7047i | 0.404759 | − | 0.701064i | ||||
\(791\) | −7.27285 | + | 5.63566i | −0.258593 | + | 0.200381i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.65567 | − | 16.2198i | −0.0587947 | − | 0.575982i | ||||
\(794\) | 8.58291 | − | 14.8660i | 0.304596 | − | 0.527576i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.8638 | 0.774940 | ||||||||
\(797\) | −5.54219 | − | 9.59935i | −0.196314 | − | 0.340026i | 0.751016 | − | 0.660284i | \(-0.229564\pi\) |
−0.947331 | + | 0.320257i | \(0.896231\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.645824 | − | 0.372866i | 0.0228476 | − | 0.0131911i | ||||
\(800\) | −19.6187 | − | 11.3268i | −0.693625 | − | 0.400464i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 41.9154 | 1.48008 | ||||||||
\(803\) | −10.1652 | −0.358724 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.7358 | − | 13.8546i | −0.378388 | − | 0.488312i | ||||
\(806\) | −6.62941 | − | 64.9450i | −0.233511 | − | 2.28759i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 25.1723 | − | 14.5332i | 0.885558 | − | 0.511277i | ||||
\(809\) | −21.2768 | − | 36.8525i | −0.748052 | − | 1.29566i | −0.948755 | − | 0.316013i | \(-0.897656\pi\) |
0.200703 | − | 0.979652i | \(-0.435677\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 16.3622i | − | 0.574554i | −0.957848 | − | 0.287277i | \(-0.907250\pi\) | ||
0.957848 | − | 0.287277i | \(-0.0927500\pi\) | |||||||
\(812\) | 11.0061 | + | 4.49784i | 0.386239 | + | 0.157843i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 20.0986 | − | 11.6040i | 0.704457 | − | 0.406719i | ||||
\(815\) | −7.66906 | −0.268636 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.439444i | 0.0153742i | ||||||||
\(818\) | 67.4455 | 2.35818 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 28.0549 | 0.979721 | ||||||||
\(821\) | − | 3.10550i | − | 0.108383i | −0.998531 | − | 0.0541913i | \(-0.982742\pi\) | ||
0.998531 | − | 0.0541913i | \(-0.0172581\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −49.0164 | −1.70860 | −0.854301 | − | 0.519778i | \(-0.826015\pi\) | ||||
−0.854301 | + | 0.519778i | \(0.826015\pi\) | |||||||
\(824\) | 25.9747 | − | 14.9965i | 0.904873 | − | 0.522429i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.35244 | − | 9.90937i | −0.0470573 | − | 0.344791i | ||||
\(827\) | − | 13.0887i | − | 0.455140i | −0.973762 | − | 0.227570i | \(-0.926922\pi\) | ||
0.973762 | − | 0.227570i | \(-0.0730780\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.6282 | + | 42.6574i | 0.855374 | + | 1.48155i | 0.876297 | + | 0.481771i | \(0.160006\pi\) |
−0.0209227 | + | 0.999781i | \(0.506660\pi\) | |||||||
\(830\) | 19.4972 | − | 11.2567i | 0.676757 | − | 0.390726i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −37.4514 | + | 27.0391i | −1.29839 | + | 0.937411i | ||||
\(833\) | −13.9695 | + | 3.88551i | −0.484015 | + | 0.134625i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.25177 | −0.0779257 | ||||||||
\(836\) | 0.235656 | 0.00815034 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 41.3684 | + | 23.8841i | 1.42905 | + | 0.825062i | ||||
\(839\) | −14.9508 | + | 8.63182i | −0.516157 | + | 0.298004i | −0.735361 | − | 0.677676i | \(-0.762987\pi\) |
0.219204 | + | 0.975679i | \(0.429654\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.5756 | + | 23.5136i | 0.468124 | + | 0.810815i | ||||
\(842\) | −57.2814 | −1.97405 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.3760 | + | 23.1678i | −0.460419 | + | 0.797470i | ||||
\(845\) | 2.22553 | + | 10.7876i | 0.0765606 | + | 0.371105i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.4049 | + | 8.74748i | 0.735480 | + | 0.300567i | ||||
\(848\) | 0.424662 | − | 0.735535i | 0.0145829 | − | 0.0252584i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 17.6928 | + | 10.2149i | 0.606857 | + | 0.350369i | ||||
\(851\) | 52.4024i | 1.79633i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 52.4163i | 1.79470i | 0.441319 | + | 0.897350i | \(0.354511\pi\) | ||||
−0.441319 | + | 0.897350i | \(0.645489\pi\) | |||||||
\(854\) | 10.4244 | − | 25.5083i | 0.356716 | − | 0.872875i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 29.6443i | − | 1.01322i | ||||||
\(857\) | −5.06355 | + | 8.77032i | −0.172967 | + | 0.299588i | −0.939456 | − | 0.342670i | \(-0.888669\pi\) |
0.766489 | + | 0.642258i | \(0.222002\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.255118 | + | 0.441878i | 0.00870452 | + | 0.0150767i | 0.870345 | − | 0.492443i | \(-0.163896\pi\) |
−0.861640 | + | 0.507519i | \(0.830563\pi\) | |||||||
\(860\) | 22.4707 | + | 12.9735i | 0.766244 | + | 0.442391i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.3787 | − | 42.2251i | −0.830341 | − | 1.43819i | ||||
\(863\) | 17.7527 | − | 10.2495i | 0.604310 | − | 0.348898i | −0.166426 | − | 0.986054i | \(-0.553223\pi\) |
0.770735 | + | 0.637156i | \(0.219889\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 16.5959i | − | 0.564279i | ||||||
\(866\) | −46.7347 | + | 26.9823i | −1.58811 | + | 0.916896i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 26.0039 | − | 63.6310i | 0.882631 | − | 2.15978i | ||||
\(869\) | 15.1799 | + | 8.76412i | 0.514943 | + | 0.297302i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.01572 | − | 6.71919i | 0.102184 | − | 0.227671i | ||||
\(872\) | 17.4422 | − | 30.2107i | 0.590667 | − | 1.02306i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.427047 | + | 0.739668i | −0.0144451 | + | 0.0250196i | ||||
\(875\) | −20.6168 | + | 2.81379i | −0.696974 | + | 0.0951235i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.77794 | − | 5.64530i | −0.330178 | − | 0.190628i | 0.325742 | − | 0.945459i | \(-0.394386\pi\) |
−0.655920 | + | 0.754830i | \(0.727719\pi\) | |||||||
\(878\) | − | 27.7276i | − | 0.935762i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.199476 | − | 0.345503i | 0.00672435 | − | 0.0116469i | ||||
\(881\) | −11.2634 | + | 19.5088i | −0.379474 | + | 0.657268i | −0.990986 | − | 0.133967i | \(-0.957228\pi\) |
0.611512 | + | 0.791235i | \(0.290562\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.0268 | −0.943178 | −0.471589 | − | 0.881819i | \(-0.656319\pi\) | ||||
−0.471589 | + | 0.881819i | \(0.656319\pi\) | |||||||
\(884\) | 20.0130 | − | 14.4489i | 0.673109 | − | 0.485969i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31.3827 | − | 18.1188i | 1.05432 | − | 0.608713i | ||||
\(887\) | 20.6235 | 0.692470 | 0.346235 | − | 0.938148i | \(-0.387460\pi\) | ||||
0.346235 | + | 0.938148i | \(0.387460\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 38.4509 | + | 15.7137i | 1.28960 | + | 0.527019i | ||||
\(890\) | 29.5954 | − | 17.0869i | 0.992040 | − | 0.572754i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −45.9621 | − | 26.5362i | −1.53893 | − | 0.888499i | ||||
\(893\) | 0.0170744 | 0.000571374 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.12305 | − | 1.22574i | −0.0709658 | − | 0.0409721i | ||||
\(896\) | −49.6174 | + | 6.77181i | −1.65760 | + | 0.226230i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29.9438 | + | 51.8642i | 0.999238 | + | 1.73073i | ||||
\(899\) | −9.25671 | + | 5.34437i | −0.308729 | + | 0.178245i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.80863 | − | 4.86468i | 0.0935689 | − | 0.162066i | ||||
\(902\) | 34.6912i | 1.15509i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.05263 | − | 5.22654i | 0.301086 | − | 0.173832i | ||||
\(905\) | 1.00384 | − | 0.579565i | 0.0333686 | − | 0.0192654i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.7315 | + | 35.9081i | 0.688379 | + | 1.19231i | 0.972362 | + | 0.233479i | \(0.0750109\pi\) |
−0.283982 | + | 0.958829i | \(0.591656\pi\) | |||||||
\(908\) | 4.28269i | 0.142126i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.25616 | + | 17.8591i | −0.174240 | + | 0.592023i | ||||
\(911\) | −40.8187 | −1.35239 | −0.676193 | − | 0.736725i | \(-0.736371\pi\) | ||||
−0.676193 | + | 0.736725i | \(0.736371\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.67180 | + | 15.0200i | 0.286995 | + | 0.497090i | ||||
\(914\) | 70.9310 | 2.34619 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −59.5849 | + | 34.4014i | −1.96874 | + | 1.13665i | ||||
\(917\) | −5.32285 | + | 4.12463i | −0.175776 | + | 0.136207i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.3839 | − | 42.2341i | 0.804350 | − | 1.39318i | −0.112379 | − | 0.993665i | \(-0.535847\pi\) |
0.916729 | − | 0.399510i | \(-0.130820\pi\) | |||||||
\(920\) | 9.95645 | + | 17.2451i | 0.328254 | + | 0.568553i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −39.2659 | − | 68.0105i | −1.29315 | − | 2.23981i | ||||
\(923\) | 20.9850 | − | 46.7557i | 0.690730 | − | 1.53898i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.8544 | + | 14.3497i | 0.817209 | + | 0.471816i | ||||
\(926\) | 3.89675 | 0.128055 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.22958 | + | 3.59665i | 0.204496 | + | 0.118066i | ||||
\(929\) | 25.4464 | + | 14.6915i | 0.834868 | + | 0.482012i | 0.855517 | − | 0.517775i | \(-0.173240\pi\) |
−0.0206482 | + | 0.999787i | \(0.506573\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.321479 | − | 0.0828796i | −0.0105360 | − | 0.00271627i | ||||
\(932\) | −21.9855 | − | 38.0801i | −0.720160 | − | 1.24735i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −56.5541 | + | 32.6515i | −1.85051 | + | 1.06839i | ||||
\(935\) | 1.31930 | − | 2.28509i | 0.0431456 | − | 0.0747304i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.0196 | −0.686681 | −0.343340 | − | 0.939211i | \(-0.611558\pi\) | ||||
−0.343340 | + | 0.939211i | \(0.611558\pi\) | |||||||
\(938\) | 9.83938 | − | 7.62444i | 0.321267 | − | 0.248947i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.504079 | − | 0.873090i | 0.0164412 | − | 0.0284770i | ||||
\(941\) | 20.8740 | + | 12.0516i | 0.680474 | + | 0.392872i | 0.800034 | − | 0.599955i | \(-0.204815\pi\) |
−0.119560 | + | 0.992827i | \(0.538148\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −67.8368 | − | 39.1656i | −2.20907 | − | 1.27541i | ||||
\(944\) | 0.514013i | 0.0167297i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.0423 | + | 27.7860i | −0.521579 | + | 0.903402i | ||||
\(947\) | 3.34046i | 0.108550i | 0.998526 | + | 0.0542751i | \(0.0172848\pi\) | ||||
−0.998526 | + | 0.0542751i | \(0.982715\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.2529 | + | 2.47567i | −0.787282 | + | 0.0803636i | ||||
\(950\) | 0.233883 | + | 0.405097i | 0.00758815 | + | 0.0131431i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 16.3220 | − | 2.22763i | 0.528998 | − | 0.0721980i | ||||
\(953\) | 2.48562 | + | 4.30522i | 0.0805171 | + | 0.139460i | 0.903472 | − | 0.428647i | \(-0.141009\pi\) |
−0.822955 | + | 0.568106i | \(0.807676\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1.28216i | − | 0.0414898i | ||||||
\(956\) | 44.1726i | 1.42864i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.23509 | + | 12.5315i | 0.233755 | + | 0.404876i | ||||
\(959\) | −4.88828 | + | 0.667156i | −0.157851 | + | 0.0215436i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3981 | + | 26.6702i | 0.496711 | + | 0.860329i | ||||
\(962\) | 45.1266 | − | 32.5803i | 1.45494 | − | 1.05043i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 2.75691i | − | 0.0887939i | ||||||
\(965\) | 2.94601 | − | 5.10264i | 0.0948354 | − | 0.164260i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 47.4943i | − | 1.52731i | −0.645623 | − | 0.763657i | \(-0.723402\pi\) | ||
0.645623 | − | 0.763657i | \(-0.276598\pi\) | |||||||
\(968\) | −22.7509 | − | 13.1352i | −0.731241 | − | 0.422182i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.720362 | + | 0.415901i | 0.0231294 | + | 0.0133538i | ||||
\(971\) | 17.2357 | − | 29.8532i | 0.553121 | − | 0.958033i | −0.444926 | − | 0.895567i | \(-0.646770\pi\) |
0.998047 | − | 0.0624662i | \(-0.0198966\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.6444 | + | 25.2958i | −1.04653 | + | 0.810948i | ||||
\(974\) | 29.9830 | 0.960717 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.708122 | + | 1.22650i | −0.0226664 | + | 0.0392594i | ||||
\(977\) | −11.5598 | + | 6.67406i | −0.369831 | + | 0.213522i | −0.673385 | − | 0.739292i | \(-0.735160\pi\) |
0.303553 | + | 0.952814i | \(0.401827\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.1632 | + | 22.7993i | 0.420698 | + | 0.728670i | ||||
\(980\) | −13.7288 | + | 13.9918i | −0.438551 | + | 0.446951i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −24.6390 | − | 14.2253i | −0.786263 | − | 0.453949i | ||||
\(983\) | 10.8551 | + | 6.26720i | 0.346224 | + | 0.199893i | 0.663021 | − | 0.748601i | \(-0.269274\pi\) |
−0.316797 | + | 0.948493i | \(0.602607\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.1137 | −0.417838 | ||||||||
\(986\) | −5.61804 | − | 3.24358i | −0.178915 | − | 0.103297i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.562243 | − | 0.0573923i | 0.0178873 | − | 0.00182589i | ||||
\(989\) | −36.2227 | − | 62.7396i | −1.15182 | − | 1.99500i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.20596 | + | 9.01698i | 0.165373 | + | 0.286434i | 0.936788 | − | 0.349899i | \(-0.113784\pi\) |
−0.771415 | + | 0.636332i | \(0.780451\pi\) | |||||||
\(992\) | 20.7938 | − | 36.0158i | 0.660202 | − | 1.14350i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 68.4677 | − | 53.0550i | 2.17166 | − | 1.68280i | ||||
\(995\) | 4.85414 | − | 2.80254i | 0.153887 | − | 0.0888464i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.75270 | 0.182190 | 0.0910949 | − | 0.995842i | \(-0.470963\pi\) | ||||
0.0910949 | + | 0.995842i | \(0.470963\pi\) | |||||||
\(998\) | −10.5414 | − | 18.2582i | −0.333681 | − | 0.577953i | ||||
\(999\) | 0 | 0 |
(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 | 819.2.bm.f.550.1 | 12 | ||
3.2 | odd | 2 | 91.2.k.b.4.6 | ✓ | 12 | ||
7.2 | even | 3 | 819.2.do.e.667.1 | 12 | |||
13.10 | even | 6 | 819.2.do.e.361.1 | 12 | |||
21.2 | odd | 6 | 91.2.u.b.30.6 | yes | 12 | ||
21.5 | even | 6 | 637.2.u.g.30.6 | 12 | |||
21.11 | odd | 6 | 637.2.q.g.589.1 | 12 | |||
21.17 | even | 6 | 637.2.q.i.589.1 | 12 | |||
21.20 | even | 2 | 637.2.k.i.459.6 | 12 | |||
39.20 | even | 12 | 1183.2.e.j.508.11 | 24 | |||
39.23 | odd | 6 | 91.2.u.b.88.6 | yes | 12 | ||
39.32 | even | 12 | 1183.2.e.j.508.2 | 24 | |||
91.23 | even | 6 | inner | 819.2.bm.f.478.6 | 12 | ||
273.23 | odd | 6 | 91.2.k.b.23.1 | yes | 12 | ||
273.32 | even | 12 | 8281.2.a.cp.1.11 | 12 | |||
273.59 | odd | 12 | 8281.2.a.co.1.2 | 12 | |||
273.62 | even | 6 | 637.2.u.g.361.6 | 12 | |||
273.101 | even | 6 | 637.2.q.i.491.1 | 12 | |||
273.137 | even | 12 | 8281.2.a.cp.1.2 | 12 | |||
273.149 | even | 12 | 1183.2.e.j.170.2 | 24 | |||
273.179 | odd | 6 | 637.2.q.g.491.1 | 12 | |||
273.227 | odd | 12 | 8281.2.a.co.1.11 | 12 | |||
273.254 | even | 12 | 1183.2.e.j.170.11 | 24 | |||
273.257 | even | 6 | 637.2.k.i.569.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.6 | ✓ | 12 | 3.2 | odd | 2 | ||
91.2.k.b.23.1 | yes | 12 | 273.23 | odd | 6 | ||
91.2.u.b.30.6 | yes | 12 | 21.2 | odd | 6 | ||
91.2.u.b.88.6 | yes | 12 | 39.23 | odd | 6 | ||
637.2.k.i.459.6 | 12 | 21.20 | even | 2 | |||
637.2.k.i.569.1 | 12 | 273.257 | even | 6 | |||
637.2.q.g.491.1 | 12 | 273.179 | odd | 6 | |||
637.2.q.g.589.1 | 12 | 21.11 | odd | 6 | |||
637.2.q.i.491.1 | 12 | 273.101 | even | 6 | |||
637.2.q.i.589.1 | 12 | 21.17 | even | 6 | |||
637.2.u.g.30.6 | 12 | 21.5 | even | 6 | |||
637.2.u.g.361.6 | 12 | 273.62 | even | 6 | |||
819.2.bm.f.478.6 | 12 | 91.23 | even | 6 | inner | ||
819.2.bm.f.550.1 | 12 | 1.1 | even | 1 | trivial | ||
819.2.do.e.361.1 | 12 | 13.10 | even | 6 | |||
819.2.do.e.667.1 | 12 | 7.2 | even | 3 | |||
1183.2.e.j.170.2 | 24 | 273.149 | even | 12 | |||
1183.2.e.j.170.11 | 24 | 273.254 | even | 12 | |||
1183.2.e.j.508.2 | 24 | 39.32 | even | 12 | |||
1183.2.e.j.508.11 | 24 | 39.20 | even | 12 | |||
8281.2.a.co.1.2 | 12 | 273.59 | odd | 12 | |||
8281.2.a.co.1.11 | 12 | 273.227 | odd | 12 | |||
8281.2.a.cp.1.2 | 12 | 273.137 | even | 12 | |||
8281.2.a.cp.1.11 | 12 | 273.32 | even | 12 |