Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(67,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.g (of order \(3\), degree \(2\), not 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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.8 | ||
Character | \(\chi\) | \(=\) | 441.79 |
Dual form | 441.2.g.h.67.8 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.551407 | + | 0.955065i | 0.389903 | + | 0.675333i | 0.992436 | − | 0.122762i | \(-0.0391750\pi\) |
−0.602533 | + | 0.798094i | \(0.705842\pi\) | |||||||
\(3\) | 0.454745 | + | 1.67129i | 0.262547 | + | 0.964919i | ||||
\(4\) | 0.391901 | − | 0.678793i | 0.195951 | − | 0.339396i | ||||
\(5\) | −0.105466 | −0.0471659 | −0.0235829 | − | 0.999722i | \(-0.507507\pi\) | ||||
−0.0235829 | + | 0.999722i | \(0.507507\pi\) | |||||||
\(6\) | −1.34544 | + | 1.35587i | −0.549273 | + | 0.553532i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.07001 | 1.08541 | ||||||||
\(9\) | −2.58641 | + | 1.52002i | −0.862138 | + | 0.506673i | ||||
\(10\) | −0.0581547 | − | 0.100727i | −0.0183901 | − | 0.0318527i | ||||
\(11\) | 3.33731 | 1.00624 | 0.503119 | − | 0.864217i | \(-0.332186\pi\) | ||||
0.503119 | + | 0.864217i | \(0.332186\pi\) | |||||||
\(12\) | 1.31267 | + | 0.346303i | 0.378936 | + | 0.0999689i | ||||
\(13\) | 1.23997 | + | 2.14770i | 0.343907 | + | 0.595664i | 0.985155 | − | 0.171670i | \(-0.0549162\pi\) |
−0.641248 | + | 0.767334i | \(0.721583\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0479602 | − | 0.176264i | −0.0123833 | − | 0.0455113i | ||||
\(16\) | 0.909025 | + | 1.57448i | 0.227256 | + | 0.393619i | ||||
\(17\) | 0.806594 | + | 1.39706i | 0.195628 | + | 0.338837i | 0.947106 | − | 0.320921i | \(-0.103992\pi\) |
−0.751478 | + | 0.659758i | \(0.770659\pi\) | |||||||
\(18\) | −2.87788 | − | 1.63204i | −0.678324 | − | 0.384676i | ||||
\(19\) | −3.84133 | + | 6.65338i | −0.881262 | + | 1.52639i | −0.0313221 | + | 0.999509i | \(0.509972\pi\) |
−0.849939 | + | 0.526880i | \(0.823362\pi\) | |||||||
\(20\) | −0.0413323 | + | 0.0715896i | −0.00924218 | + | 0.0160079i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.84022 | + | 3.18735i | 0.392336 | + | 0.679546i | ||||
\(23\) | −1.89719 | −0.395591 | −0.197795 | − | 0.980243i | \(-0.563378\pi\) | ||||
−0.197795 | + | 0.980243i | \(0.563378\pi\) | |||||||
\(24\) | 1.39607 | + | 5.13088i | 0.284972 | + | 1.04734i | ||||
\(25\) | −4.98888 | −0.997775 | ||||||||
\(26\) | −1.36746 | + | 2.36851i | −0.268181 | + | 0.464503i | ||||
\(27\) | −3.71655 | − | 3.63142i | −0.715251 | − | 0.698868i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.64521 | − | 8.04574i | 0.862594 | − | 1.49406i | −0.00682200 | − | 0.999977i | \(-0.502172\pi\) |
0.869416 | − | 0.494080i | \(-0.164495\pi\) | |||||||
\(30\) | 0.141898 | − | 0.142998i | 0.0259070 | − | 0.0261078i | ||||
\(31\) | 4.63081 | − | 8.02080i | 0.831718 | − | 1.44058i | −0.0649574 | − | 0.997888i | \(-0.520691\pi\) |
0.896675 | − | 0.442689i | \(-0.145976\pi\) | |||||||
\(32\) | 2.06753 | − | 3.58107i | 0.365491 | − | 0.633049i | ||||
\(33\) | 1.51763 | + | 5.57762i | 0.264185 | + | 0.970939i | ||||
\(34\) | −0.889523 | + | 1.54070i | −0.152552 | + | 0.264228i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.0181599 | + | 2.35134i | 0.00302665 | + | 0.391889i | ||||
\(37\) | 0.991268 | − | 1.71693i | 0.162963 | − | 0.282261i | −0.772967 | − | 0.634447i | \(-0.781228\pi\) |
0.935930 | + | 0.352186i | \(0.114561\pi\) | |||||||
\(38\) | −8.47254 | −1.37443 | ||||||||
\(39\) | −3.02555 | + | 3.04901i | −0.484476 | + | 0.488232i | ||||
\(40\) | −0.323782 | −0.0511945 | ||||||||
\(41\) | −3.74268 | − | 6.48252i | −0.584509 | − | 1.01240i | −0.994936 | − | 0.100506i | \(-0.967954\pi\) |
0.410427 | − | 0.911893i | \(-0.365379\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.77388 | + | 6.53655i | −0.575512 | + | 0.996815i | 0.420474 | + | 0.907304i | \(0.361864\pi\) |
−0.995986 | + | 0.0895108i | \(0.971470\pi\) | |||||||
\(44\) | 1.30790 | − | 2.26534i | 0.197173 | − | 0.341514i | ||||
\(45\) | 0.272779 | − | 0.160311i | 0.0406635 | − | 0.0238977i | ||||
\(46\) | −1.04612 | − | 1.81194i | −0.154242 | − | 0.267155i | ||||
\(47\) | −1.59780 | − | 2.76747i | −0.233063 | − | 0.403677i | 0.725645 | − | 0.688070i | \(-0.241542\pi\) |
−0.958708 | + | 0.284392i | \(0.908208\pi\) | |||||||
\(48\) | −2.21803 | + | 2.23523i | −0.320145 | + | 0.322627i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.75090 | − | 4.76470i | −0.389036 | − | 0.673830i | ||||
\(51\) | −1.96810 | + | 1.98336i | −0.275589 | + | 0.277726i | ||||
\(52\) | 1.94379 | 0.269555 | ||||||||
\(53\) | 4.98839 | + | 8.64015i | 0.685209 | + | 1.18682i | 0.973371 | + | 0.229234i | \(0.0736223\pi\) |
−0.288163 | + | 0.957581i | \(0.593044\pi\) | |||||||
\(54\) | 1.41891 | − | 5.55194i | 0.193090 | − | 0.755523i | ||||
\(55\) | −0.351974 | −0.0474601 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.8665 | − | 3.39438i | −1.70422 | − | 0.449597i | ||||
\(58\) | 10.2456 | 1.34531 | ||||||||
\(59\) | 2.22993 | − | 3.86235i | 0.290312 | − | 0.502836i | −0.683571 | − | 0.729884i | \(-0.739574\pi\) |
0.973884 | + | 0.227048i | \(0.0729075\pi\) | |||||||
\(60\) | −0.138443 | − | 0.0365232i | −0.0178729 | − | 0.00471512i | ||||
\(61\) | −2.83550 | − | 4.91123i | −0.363048 | − | 0.628818i | 0.625413 | − | 0.780294i | \(-0.284931\pi\) |
−0.988461 | + | 0.151476i | \(0.951597\pi\) | |||||||
\(62\) | 10.2138 | 1.29716 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.19630 | 1.02454 | ||||||||
\(65\) | −0.130775 | − | 0.226509i | −0.0162207 | − | 0.0280950i | ||||
\(66\) | −4.49016 | + | 4.52497i | −0.552700 | + | 0.556985i | ||||
\(67\) | −4.98571 | + | 8.63550i | −0.609101 | + | 1.05499i | 0.382288 | + | 0.924043i | \(0.375136\pi\) |
−0.991389 | + | 0.130951i | \(0.958197\pi\) | |||||||
\(68\) | 1.26442 | 0.153333 | ||||||||
\(69\) | −0.862736 | − | 3.17075i | −0.103861 | − | 0.381713i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.29042 | 0.390502 | 0.195251 | − | 0.980753i | \(-0.437448\pi\) | ||||
0.195251 | + | 0.980753i | \(0.437448\pi\) | |||||||
\(72\) | −7.94033 | + | 4.66648i | −0.935777 | + | 0.549950i | ||||
\(73\) | −2.36189 | − | 4.09091i | −0.276438 | − | 0.478805i | 0.694059 | − | 0.719919i | \(-0.255821\pi\) |
−0.970497 | + | 0.241113i | \(0.922488\pi\) | |||||||
\(74\) | 2.18637 | 0.254160 | ||||||||
\(75\) | −2.26867 | − | 8.33786i | −0.261963 | − | 0.962773i | ||||
\(76\) | 3.01084 | + | 5.21493i | 0.345367 | + | 0.598194i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.58031 | − | 1.20835i | −0.518618 | − | 0.136819i | ||||
\(79\) | −3.84705 | − | 6.66328i | −0.432827 | − | 0.749678i | 0.564289 | − | 0.825577i | \(-0.309150\pi\) |
−0.997115 | + | 0.0758997i | \(0.975817\pi\) | |||||||
\(80\) | −0.0958713 | − | 0.166054i | −0.0107187 | − | 0.0185654i | ||||
\(81\) | 4.37908 | − | 7.86280i | 0.486564 | − | 0.873645i | ||||
\(82\) | 4.12748 | − | 7.14901i | 0.455804 | − | 0.789476i | ||||
\(83\) | 0.584428 | − | 1.01226i | 0.0641493 | − | 0.111110i | −0.832167 | − | 0.554525i | \(-0.812900\pi\) |
0.896316 | + | 0.443415i | \(0.146233\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0850683 | − | 0.147343i | −0.00922695 | − | 0.0159815i | ||||
\(86\) | −8.32378 | −0.897576 | ||||||||
\(87\) | 15.5591 | + | 4.10473i | 1.66812 | + | 0.440073i | ||||
\(88\) | 10.2456 | 1.09219 | ||||||||
\(89\) | 3.01477 | − | 5.22173i | 0.319565 | − | 0.553503i | −0.660832 | − | 0.750534i | \(-0.729797\pi\) |
0.980397 | + | 0.197031i | \(0.0631299\pi\) | |||||||
\(90\) | 0.303519 | + | 0.172125i | 0.0319937 | + | 0.0181436i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.743509 | + | 1.28780i | −0.0775162 | + | 0.134262i | ||||
\(93\) | 15.5109 | + | 4.09200i | 1.60841 | + | 0.424321i | ||||
\(94\) | 1.76208 | − | 3.05201i | 0.181744 | − | 0.314791i | ||||
\(95\) | 0.405130 | − | 0.701706i | 0.0415655 | − | 0.0719935i | ||||
\(96\) | 6.92520 | + | 1.82697i | 0.706800 | + | 0.186464i | ||||
\(97\) | 1.90127 | − | 3.29310i | 0.193045 | − | 0.334364i | −0.753213 | − | 0.657777i | \(-0.771497\pi\) |
0.946258 | + | 0.323413i | \(0.104830\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.63168 | + | 5.07279i | −0.867516 | + | 0.509834i | ||||
\(100\) | −1.95515 | + | 3.38641i | −0.195515 | + | 0.338641i | ||||
\(101\) | −17.4702 | −1.73835 | −0.869177 | − | 0.494501i | \(-0.835351\pi\) | ||||
−0.869177 | + | 0.494501i | \(0.835351\pi\) | |||||||
\(102\) | −2.97946 | − | 0.786025i | −0.295010 | − | 0.0778280i | ||||
\(103\) | 8.73204 | 0.860394 | 0.430197 | − | 0.902735i | \(-0.358444\pi\) | ||||
0.430197 | + | 0.902735i | \(0.358444\pi\) | |||||||
\(104\) | 3.80674 | + | 6.59346i | 0.373281 | + | 0.646542i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.50127 | + | 9.52848i | −0.534330 | + | 0.925487i | ||||
\(107\) | 9.07316 | − | 15.7152i | 0.877135 | − | 1.51924i | 0.0226645 | − | 0.999743i | \(-0.492785\pi\) |
0.854471 | − | 0.519500i | \(-0.173882\pi\) | |||||||
\(108\) | −3.92150 | + | 1.09961i | −0.377347 | + | 0.105810i | ||||
\(109\) | 2.11124 | + | 3.65678i | 0.202220 | + | 0.350256i | 0.949243 | − | 0.314542i | \(-0.101851\pi\) |
−0.747023 | + | 0.664798i | \(0.768518\pi\) | |||||||
\(110\) | −0.194081 | − | 0.336157i | −0.0185049 | − | 0.0320514i | ||||
\(111\) | 3.32025 | + | 0.875932i | 0.315145 | + | 0.0831398i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.02824 | + | 1.78096i | 0.0967285 | + | 0.167539i | 0.910329 | − | 0.413886i | \(-0.135829\pi\) |
−0.813600 | + | 0.581425i | \(0.802495\pi\) | |||||||
\(114\) | −3.85284 | − | 14.1601i | −0.360852 | − | 1.32621i | ||||
\(115\) | 0.200089 | 0.0186584 | ||||||||
\(116\) | −3.64093 | − | 6.30627i | −0.338052 | − | 0.585523i | ||||
\(117\) | −6.47163 | − | 3.67005i | −0.598302 | − | 0.339296i | ||||
\(118\) | 4.91840 | 0.452775 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.147238 | − | 0.541134i | −0.0134410 | − | 0.0493986i | ||||
\(121\) | 0.137670 | 0.0125155 | ||||||||
\(122\) | 3.12703 | − | 5.41617i | 0.283108 | − | 0.490357i | ||||
\(123\) | 9.13220 | − | 9.20300i | 0.823422 | − | 0.829806i | ||||
\(124\) | −3.62964 | − | 6.28672i | −0.325951 | − | 0.564564i | ||||
\(125\) | 1.05349 | 0.0942268 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.317159 | 0.0281433 | 0.0140717 | − | 0.999901i | \(-0.495521\pi\) | ||||
0.0140717 | + | 0.999901i | \(0.495521\pi\) | |||||||
\(128\) | 0.384435 | + | 0.665862i | 0.0339796 | + | 0.0588544i | ||||
\(129\) | −12.6406 | − | 3.33478i | −1.11294 | − | 0.293611i | ||||
\(130\) | 0.144221 | − | 0.249797i | 0.0126490 | − | 0.0219087i | ||||
\(131\) | 14.9563 | 1.30674 | 0.653370 | − | 0.757039i | \(-0.273355\pi\) | ||||
0.653370 | + | 0.757039i | \(0.273355\pi\) | |||||||
\(132\) | 4.38081 | + | 1.15572i | 0.381300 | + | 0.100593i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −10.9966 | −0.949962 | ||||||||
\(135\) | 0.391970 | + | 0.382992i | 0.0337354 | + | 0.0329627i | ||||
\(136\) | 2.47625 | + | 4.28900i | 0.212337 | + | 0.367779i | ||||
\(137\) | −15.2473 | −1.30267 | −0.651334 | − | 0.758791i | \(-0.725790\pi\) | ||||
−0.651334 | + | 0.758791i | \(0.725790\pi\) | |||||||
\(138\) | 2.55255 | − | 2.57234i | 0.217287 | − | 0.218972i | ||||
\(139\) | 4.05943 | + | 7.03114i | 0.344316 | + | 0.596374i | 0.985229 | − | 0.171240i | \(-0.0547774\pi\) |
−0.640913 | + | 0.767614i | \(0.721444\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.89866 | − | 3.92888i | 0.328326 | − | 0.330872i | ||||
\(142\) | 1.81436 | + | 3.14257i | 0.152258 | + | 0.263718i | ||||
\(143\) | 4.13818 | + | 7.16754i | 0.346052 | + | 0.599380i | ||||
\(144\) | −4.74435 | − | 2.69051i | −0.395363 | − | 0.224210i | ||||
\(145\) | −0.489912 | + | 0.848553i | −0.0406850 | + | 0.0704685i | ||||
\(146\) | 2.60473 | − | 4.51152i | 0.215569 | − | 0.373376i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.776958 | − | 1.34573i | −0.0638656 | − | 0.110618i | ||||
\(149\) | −11.1486 | −0.913329 | −0.456664 | − | 0.889639i | \(-0.650956\pi\) | ||||
−0.456664 | + | 0.889639i | \(0.650956\pi\) | |||||||
\(150\) | 6.71223 | − | 6.76427i | 0.548051 | − | 0.552301i | ||||
\(151\) | −11.2735 | −0.917425 | −0.458713 | − | 0.888585i | \(-0.651689\pi\) | ||||
−0.458713 | + | 0.888585i | \(0.651689\pi\) | |||||||
\(152\) | −11.7929 | + | 20.4260i | −0.956534 | + | 1.65677i | ||||
\(153\) | −4.20975 | − | 2.38734i | −0.340338 | − | 0.193005i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.488393 | + | 0.845922i | −0.0392287 | + | 0.0679461i | ||||
\(156\) | 0.883928 | + | 3.24863i | 0.0707708 | + | 0.260099i | ||||
\(157\) | −6.10318 | + | 10.5710i | −0.487087 | + | 0.843659i | −0.999890 | − | 0.0148476i | \(-0.995274\pi\) |
0.512803 | + | 0.858506i | \(0.328607\pi\) | |||||||
\(158\) | 4.24258 | − | 7.34836i | 0.337521 | − | 0.584604i | ||||
\(159\) | −12.1717 | + | 12.2661i | −0.965282 | + | 0.972766i | ||||
\(160\) | −0.218054 | + | 0.377681i | −0.0172387 | + | 0.0298583i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.92414 | − | 0.153302i | 0.779714 | − | 0.0120445i | ||||
\(163\) | −4.48132 | + | 7.76187i | −0.351004 | + | 0.607957i | −0.986426 | − | 0.164209i | \(-0.947493\pi\) |
0.635422 | + | 0.772165i | \(0.280826\pi\) | |||||||
\(164\) | −5.86705 | −0.458139 | ||||||||
\(165\) | −0.160058 | − | 0.588250i | −0.0124605 | − | 0.0457952i | ||||
\(166\) | 1.28903 | 0.100048 | ||||||||
\(167\) | −8.70833 | − | 15.0833i | −0.673871 | − | 1.16718i | −0.976798 | − | 0.214165i | \(-0.931297\pi\) |
0.302927 | − | 0.953014i | \(-0.402036\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.42493 | − | 5.93216i | 0.263456 | − | 0.456320i | ||||
\(170\) | 0.0938145 | − | 0.162491i | 0.00719524 | − | 0.0124625i | ||||
\(171\) | −0.177999 | − | 23.0473i | −0.0136120 | − | 1.76247i | ||||
\(172\) | 2.95798 | + | 5.12337i | 0.225544 | + | 0.390653i | ||||
\(173\) | −1.41466 | − | 2.45027i | −0.107555 | − | 0.186291i | 0.807224 | − | 0.590245i | \(-0.200969\pi\) |
−0.914779 | + | 0.403954i | \(0.867635\pi\) | |||||||
\(174\) | 4.65914 | + | 17.1234i | 0.353208 | + | 1.29812i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.03370 | + | 5.25453i | 0.228674 | + | 0.396075i | ||||
\(177\) | 7.46916 | + | 1.97047i | 0.561416 | + | 0.148110i | ||||
\(178\) | 6.64946 | 0.498398 | ||||||||
\(179\) | 5.08135 | + | 8.80115i | 0.379798 | + | 0.657829i | 0.991033 | − | 0.133620i | \(-0.0426603\pi\) |
−0.611235 | + | 0.791449i | \(0.709327\pi\) | |||||||
\(180\) | −0.00191525 | − | 0.247986i | −0.000142755 | − | 0.0184838i | ||||
\(181\) | −17.0870 | −1.27006 | −0.635032 | − | 0.772486i | \(-0.719013\pi\) | ||||
−0.635032 | + | 0.772486i | \(0.719013\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.91865 | − | 6.97229i | 0.511441 | − | 0.515407i | ||||
\(184\) | −5.82439 | −0.429380 | ||||||||
\(185\) | −0.104545 | + | 0.181078i | −0.00768631 | + | 0.0133131i | ||||
\(186\) | 4.64469 | + | 17.0703i | 0.340565 | + | 1.25165i | ||||
\(187\) | 2.69186 | + | 4.66243i | 0.196848 | + | 0.340951i | ||||
\(188\) | −2.50472 | −0.182676 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.893566 | 0.0648261 | ||||||||
\(191\) | 11.2000 | + | 19.3990i | 0.810404 | + | 1.40366i | 0.912582 | + | 0.408894i | \(0.134086\pi\) |
−0.102178 | + | 0.994766i | \(0.532581\pi\) | |||||||
\(192\) | 3.72723 | + | 13.6984i | 0.268989 | + | 0.988596i | ||||
\(193\) | 0.128393 | − | 0.222383i | 0.00924194 | − | 0.0160075i | −0.861367 | − | 0.507982i | \(-0.830391\pi\) |
0.870609 | + | 0.491975i | \(0.163725\pi\) | |||||||
\(194\) | 4.19350 | 0.301076 | ||||||||
\(195\) | 0.319093 | − | 0.321567i | 0.0228507 | − | 0.0230279i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.763370 | −0.0543878 | −0.0271939 | − | 0.999630i | \(-0.508657\pi\) | ||||
−0.0271939 | + | 0.999630i | \(0.508657\pi\) | |||||||
\(198\) | −9.60440 | − | 5.44664i | −0.682555 | − | 0.387076i | ||||
\(199\) | 2.51561 | + | 4.35716i | 0.178327 | + | 0.308871i | 0.941307 | − | 0.337550i | \(-0.109598\pi\) |
−0.762981 | + | 0.646421i | \(0.776265\pi\) | |||||||
\(200\) | −15.3159 | −1.08300 | ||||||||
\(201\) | −16.6996 | − | 4.40561i | −1.17790 | − | 0.310748i | ||||
\(202\) | −9.63321 | − | 16.6852i | −0.677790 | − | 1.17397i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.574988 | + | 2.11321i | 0.0402572 | + | 0.147954i | ||||
\(205\) | 0.394726 | + | 0.683686i | 0.0275689 | + | 0.0477507i | ||||
\(206\) | 4.81491 | + | 8.33966i | 0.335470 | + | 0.581052i | ||||
\(207\) | 4.90691 | − | 2.88376i | 0.341054 | − | 0.200435i | ||||
\(208\) | −2.25433 | + | 3.90462i | −0.156310 | + | 0.270737i | ||||
\(209\) | −12.8197 | + | 22.2044i | −0.886759 | + | 1.53591i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.60537 | − | 6.24468i | −0.248204 | − | 0.429901i | 0.714824 | − | 0.699305i | \(-0.246507\pi\) |
−0.963027 | + | 0.269403i | \(0.913174\pi\) | |||||||
\(212\) | 7.81983 | 0.537068 | ||||||||
\(213\) | 1.49630 | + | 5.49925i | 0.102525 | + | 0.376802i | ||||
\(214\) | 20.0120 | 1.36799 | ||||||||
\(215\) | 0.398017 | − | 0.689385i | 0.0271445 | − | 0.0470157i | ||||
\(216\) | −11.4099 | − | 11.1485i | −0.776343 | − | 0.758561i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.32831 | + | 4.03274i | −0.157693 | + | 0.273132i | ||||
\(219\) | 5.76304 | − | 5.80772i | 0.389430 | − | 0.392450i | ||||
\(220\) | −0.137939 | + | 0.238917i | −0.00929983 | + | 0.0161078i | ||||
\(221\) | −2.00031 | + | 3.46464i | −0.134555 | + | 0.233057i | ||||
\(222\) | 0.994239 | + | 3.65405i | 0.0667290 | + | 0.245244i | ||||
\(223\) | 5.59106 | − | 9.68400i | 0.374405 | − | 0.648488i | −0.615833 | − | 0.787877i | \(-0.711180\pi\) |
0.990238 | + | 0.139388i | \(0.0445137\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.9033 | − | 7.58319i | 0.860220 | − | 0.505546i | ||||
\(226\) | −1.13395 | + | 1.96407i | −0.0754295 | + | 0.130648i | ||||
\(227\) | 23.7706 | 1.57771 | 0.788857 | − | 0.614577i | \(-0.210673\pi\) | ||||
0.788857 | + | 0.614577i | \(0.210673\pi\) | |||||||
\(228\) | −7.34649 | + | 7.40345i | −0.486534 | + | 0.490306i | ||||
\(229\) | −1.90547 | −0.125917 | −0.0629586 | − | 0.998016i | \(-0.520054\pi\) | ||||
−0.0629586 | + | 0.998016i | \(0.520054\pi\) | |||||||
\(230\) | 0.110330 | + | 0.191098i | 0.00727497 | + | 0.0126006i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 14.2609 | − | 24.7006i | 0.936272 | − | 1.62167i | ||||
\(233\) | −3.27092 | + | 5.66540i | −0.214285 | + | 0.371153i | −0.953051 | − | 0.302809i | \(-0.902075\pi\) |
0.738766 | + | 0.673962i | \(0.235409\pi\) | |||||||
\(234\) | −0.0633653 | − | 8.20451i | −0.00414232 | − | 0.536346i | ||||
\(235\) | 0.168514 | + | 0.291875i | 0.0109926 | + | 0.0190398i | ||||
\(236\) | −1.74782 | − | 3.02732i | −0.113774 | − | 0.197062i | ||||
\(237\) | 9.38684 | − | 9.45962i | 0.609741 | − | 0.614468i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.6735 | + | 18.4870i | 0.690409 | + | 1.19582i | 0.971704 | + | 0.236202i | \(0.0759028\pi\) |
−0.281295 | + | 0.959621i | \(0.590764\pi\) | |||||||
\(240\) | 0.233927 | − | 0.235741i | 0.0150999 | − | 0.0152170i | ||||
\(241\) | −20.0662 | −1.29258 | −0.646288 | − | 0.763094i | \(-0.723679\pi\) | ||||
−0.646288 | + | 0.763094i | \(0.723679\pi\) | |||||||
\(242\) | 0.0759124 | + | 0.131484i | 0.00487983 | + | 0.00845212i | ||||
\(243\) | 15.1324 | + | 3.74313i | 0.970743 | + | 0.240122i | ||||
\(244\) | −4.44494 | −0.284558 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 13.8250 | + | 3.64724i | 0.881451 | + | 0.232540i | ||||
\(247\) | −19.0526 | −1.21229 | ||||||||
\(248\) | 14.2167 | − | 24.6240i | 0.902758 | − | 1.56362i | ||||
\(249\) | 1.95754 | + | 0.516428i | 0.124054 | + | 0.0327273i | ||||
\(250\) | 0.580900 | + | 1.00615i | 0.0367394 | + | 0.0636344i | ||||
\(251\) | −6.81467 | −0.430138 | −0.215069 | − | 0.976599i | \(-0.568998\pi\) | ||||
−0.215069 | + | 0.976599i | \(0.568998\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.33151 | −0.398059 | ||||||||
\(254\) | 0.174884 | + | 0.302907i | 0.0109732 | + | 0.0190061i | ||||
\(255\) | 0.207568 | − | 0.209177i | 0.0129984 | − | 0.0130992i | ||||
\(256\) | 7.77234 | − | 13.4621i | 0.485771 | − | 0.841380i | ||||
\(257\) | −14.3883 | −0.897518 | −0.448759 | − | 0.893653i | \(-0.648134\pi\) | ||||
−0.448759 | + | 0.893653i | \(0.648134\pi\) | |||||||
\(258\) | −3.78519 | − | 13.9114i | −0.235656 | − | 0.866088i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.205004 | −0.0127138 | ||||||||
\(261\) | 0.215250 | + | 27.8704i | 0.0133236 | + | 1.72514i | ||||
\(262\) | 8.24701 | + | 14.2842i | 0.509502 | + | 0.882484i | ||||
\(263\) | −1.53901 | −0.0948992 | −0.0474496 | − | 0.998874i | \(-0.515109\pi\) | ||||
−0.0474496 | + | 0.998874i | \(0.515109\pi\) | |||||||
\(264\) | 4.65914 | + | 17.1234i | 0.286750 | + | 1.05387i | ||||
\(265\) | −0.526106 | − | 0.911243i | −0.0323185 | − | 0.0559772i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.0980 | + | 2.66399i | 0.617986 | + | 0.163034i | ||||
\(268\) | 3.90781 | + | 6.76852i | 0.238707 | + | 0.413453i | ||||
\(269\) | 13.1285 | + | 22.7393i | 0.800461 | + | 1.38644i | 0.919313 | + | 0.393527i | \(0.128745\pi\) |
−0.118852 | + | 0.992912i | \(0.537921\pi\) | |||||||
\(270\) | −0.149647 | + | 0.585541i | −0.00910724 | + | 0.0356349i | ||||
\(271\) | −8.96673 | + | 15.5308i | −0.544690 | + | 0.943431i | 0.453936 | + | 0.891034i | \(0.350019\pi\) |
−0.998626 | + | 0.0523969i | \(0.983314\pi\) | |||||||
\(272\) | −1.46643 | + | 2.53993i | −0.0889152 | + | 0.154006i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.40748 | − | 14.5622i | −0.507915 | − | 0.879734i | ||||
\(275\) | −16.6495 | −1.00400 | ||||||||
\(276\) | −2.49039 | − | 0.657001i | −0.149904 | − | 0.0395468i | ||||
\(277\) | −18.8713 | −1.13386 | −0.566932 | − | 0.823764i | \(-0.691870\pi\) | ||||
−0.566932 | + | 0.823764i | \(0.691870\pi\) | |||||||
\(278\) | −4.47680 | + | 7.75404i | −0.268500 | + | 0.465056i | ||||
\(279\) | 0.214582 | + | 27.7840i | 0.0128467 | + | 1.66339i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.49578 | + | 4.32283i | −0.148886 | + | 0.257878i | −0.930816 | − | 0.365488i | \(-0.880902\pi\) |
0.781930 | + | 0.623366i | \(0.214235\pi\) | |||||||
\(282\) | 5.90208 | + | 1.55706i | 0.351464 | + | 0.0927213i | ||||
\(283\) | −7.69634 | + | 13.3304i | −0.457500 | + | 0.792413i | −0.998828 | − | 0.0483984i | \(-0.984588\pi\) |
0.541328 | + | 0.840811i | \(0.317922\pi\) | |||||||
\(284\) | 1.28952 | − | 2.23352i | 0.0765190 | − | 0.132535i | ||||
\(285\) | 1.35698 | + | 0.357992i | 0.0803808 | + | 0.0212056i | ||||
\(286\) | −4.56364 | + | 7.90446i | −0.269854 | + | 0.467401i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.0958052 | + | 12.4048i | 0.00564537 | + | 0.730960i | ||||
\(289\) | 7.19881 | − | 12.4687i | 0.423460 | − | 0.733454i | ||||
\(290\) | −1.08056 | −0.0634529 | ||||||||
\(291\) | 6.36832 | + | 1.68006i | 0.373318 | + | 0.0984867i | ||||
\(292\) | −3.70251 | −0.216673 | ||||||||
\(293\) | 12.9013 | + | 22.3456i | 0.753700 | + | 1.30545i | 0.946018 | + | 0.324114i | \(0.105066\pi\) |
−0.192318 | + | 0.981333i | \(0.561601\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.235182 | + | 0.407347i | −0.0136928 | + | 0.0237167i | ||||
\(296\) | 3.04321 | − | 5.27099i | 0.176883 | − | 0.306370i | ||||
\(297\) | −12.4033 | − | 12.1192i | −0.719713 | − | 0.703228i | ||||
\(298\) | −6.14741 | − | 10.6476i | −0.356110 | − | 0.616801i | ||||
\(299\) | −2.35246 | − | 4.07458i | −0.136046 | − | 0.235639i | ||||
\(300\) | −6.54877 | − | 1.72766i | −0.378093 | − | 0.0997465i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.21629 | − | 10.7669i | −0.357707 | − | 0.619567i | ||||
\(303\) | −7.94450 | − | 29.1978i | −0.456400 | − | 1.67737i | ||||
\(304\) | −13.9675 | −0.801089 | ||||||||
\(305\) | 0.299049 | + | 0.517968i | 0.0171235 | + | 0.0296588i | ||||
\(306\) | −0.0412187 | − | 5.33698i | −0.00235632 | − | 0.305095i | ||||
\(307\) | 22.2914 | 1.27224 | 0.636120 | − | 0.771590i | \(-0.280538\pi\) | ||||
0.636120 | + | 0.771590i | \(0.280538\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.97085 | + | 14.5938i | 0.225894 | + | 0.830210i | ||||
\(310\) | −1.07721 | −0.0611816 | ||||||||
\(311\) | −0.654931 | + | 1.13437i | −0.0371377 | + | 0.0643245i | −0.883997 | − | 0.467493i | \(-0.845157\pi\) |
0.846859 | + | 0.531817i | \(0.178491\pi\) | |||||||
\(312\) | −9.28849 | + | 9.36050i | −0.525857 | + | 0.529934i | ||||
\(313\) | 10.7885 | + | 18.6862i | 0.609802 | + | 1.05621i | 0.991273 | + | 0.131827i | \(0.0420843\pi\) |
−0.381471 | + | 0.924381i | \(0.624582\pi\) | |||||||
\(314\) | −13.4613 | −0.759667 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.03065 | −0.339250 | ||||||||
\(317\) | 12.3910 | + | 21.4618i | 0.695946 | + | 1.20541i | 0.969861 | + | 0.243660i | \(0.0783480\pi\) |
−0.273915 | + | 0.961754i | \(0.588319\pi\) | |||||||
\(318\) | −18.4265 | − | 4.86118i | −1.03331 | − | 0.272602i | ||||
\(319\) | 15.5025 | − | 26.8512i | 0.867975 | − | 1.50338i | ||||
\(320\) | −0.864432 | −0.0483232 | ||||||||
\(321\) | 30.3906 | + | 8.01748i | 1.69624 | + | 0.447492i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.3936 | −0.689597 | ||||||||
\(324\) | −3.62105 | − | 6.05393i | −0.201169 | − | 0.336329i | ||||
\(325\) | −6.18608 | − | 10.7146i | −0.343142 | − | 0.594339i | ||||
\(326\) | −9.88412 | −0.547431 | ||||||||
\(327\) | −5.15145 | + | 5.19139i | −0.284876 | + | 0.287085i | ||||
\(328\) | −11.4901 | − | 19.9014i | −0.634434 | − | 1.09887i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.473559 | − | 0.477231i | 0.0260686 | − | 0.0262707i | ||||
\(331\) | −6.92256 | − | 11.9902i | −0.380498 | − | 0.659042i | 0.610635 | − | 0.791912i | \(-0.290914\pi\) |
−0.991133 | + | 0.132870i | \(0.957581\pi\) | |||||||
\(332\) | −0.458076 | − | 0.793410i | −0.0251402 | − | 0.0435440i | ||||
\(333\) | 0.0459334 | + | 5.94743i | 0.00251713 | + | 0.325917i | ||||
\(334\) | 9.60367 | − | 16.6340i | 0.525489 | − | 0.910174i | ||||
\(335\) | 0.525823 | − | 0.910752i | 0.0287288 | − | 0.0497597i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.69444 | + | 2.93485i | 0.0923018 | + | 0.159871i | 0.908479 | − | 0.417930i | \(-0.137244\pi\) |
−0.816178 | + | 0.577801i | \(0.803911\pi\) | |||||||
\(338\) | 7.55412 | 0.410890 | ||||||||
\(339\) | −2.50891 | + | 2.52837i | −0.136265 | + | 0.137322i | ||||
\(340\) | −0.133353 | −0.00723210 | ||||||||
\(341\) | 15.4545 | − | 26.7679i | 0.836906 | − | 1.44956i | ||||
\(342\) | 21.9135 | − | 12.8784i | 1.18495 | − | 0.696386i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −11.5859 | + | 20.0673i | −0.624668 | + | 1.08196i | ||||
\(345\) | 0.0909894 | + | 0.334406i | 0.00489870 | + | 0.0180038i | ||||
\(346\) | 1.56011 | − | 2.70219i | 0.0838720 | − | 0.145271i | ||||
\(347\) | 7.25739 | − | 12.5702i | 0.389597 | − | 0.674802i | −0.602798 | − | 0.797894i | \(-0.705948\pi\) |
0.992395 | + | 0.123091i | \(0.0392809\pi\) | |||||||
\(348\) | 8.88391 | − | 8.95279i | 0.476228 | − | 0.479920i | ||||
\(349\) | −7.86412 | + | 13.6211i | −0.420957 | + | 0.729119i | −0.996033 | − | 0.0889810i | \(-0.971639\pi\) |
0.575076 | + | 0.818100i | \(0.304972\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.19077 | − | 12.4849i | 0.170311 | − | 0.666395i | ||||
\(352\) | 6.90000 | − | 11.9511i | 0.367771 | − | 0.636998i | ||||
\(353\) | 4.14423 | 0.220575 | 0.110287 | − | 0.993900i | \(-0.464823\pi\) | ||||
0.110287 | + | 0.993900i | \(0.464823\pi\) | |||||||
\(354\) | 2.23662 | + | 8.22006i | 0.118875 | + | 0.436891i | ||||
\(355\) | −0.347028 | −0.0184183 | ||||||||
\(356\) | −2.36298 | − | 4.09281i | −0.125238 | − | 0.216918i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.60378 | + | 9.70603i | −0.296169 | + | 0.512979i | ||||
\(359\) | −3.96994 | + | 6.87614i | −0.209525 | + | 0.362909i | −0.951565 | − | 0.307447i | \(-0.900525\pi\) |
0.742040 | + | 0.670356i | \(0.233859\pi\) | |||||||
\(360\) | 0.837436 | − | 0.492156i | 0.0441367 | − | 0.0259389i | ||||
\(361\) | −20.0116 | − | 34.6612i | −1.05324 | − | 1.82427i | ||||
\(362\) | −9.42187 | − | 16.3192i | −0.495202 | − | 0.857716i | ||||
\(363\) | 0.0626049 | + | 0.230087i | 0.00328590 | + | 0.0120764i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.249099 | + | 0.431453i | 0.0130385 | + | 0.0225833i | ||||
\(366\) | 10.4740 | + | 2.76319i | 0.547484 | + | 0.144434i | ||||
\(367\) | 13.1491 | 0.686377 | 0.343189 | − | 0.939266i | \(-0.388493\pi\) | ||||
0.343189 | + | 0.939266i | \(0.388493\pi\) | |||||||
\(368\) | −1.72459 | − | 2.98708i | −0.0899004 | − | 0.155712i | ||||
\(369\) | 19.5337 | + | 11.0775i | 1.01688 | + | 0.576673i | ||||
\(370\) | −0.230588 | −0.0119877 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8.85636 | − | 8.92503i | 0.459181 | − | 0.462741i | ||||
\(373\) | 7.81086 | 0.404431 | 0.202216 | − | 0.979341i | \(-0.435186\pi\) | ||||
0.202216 | + | 0.979341i | \(0.435186\pi\) | |||||||
\(374\) | −2.96862 | + | 5.14180i | −0.153504 | + | 0.265876i | ||||
\(375\) | 0.479068 | + | 1.76068i | 0.0247390 | + | 0.0909213i | ||||
\(376\) | −4.90527 | − | 8.49618i | −0.252970 | − | 0.438157i | ||||
\(377\) | 23.0398 | 1.18661 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.6147 | −1.62394 | −0.811968 | − | 0.583702i | \(-0.801604\pi\) | ||||
−0.811968 | + | 0.583702i | \(0.801604\pi\) | |||||||
\(380\) | −0.317542 | − | 0.549999i | −0.0162896 | − | 0.0282143i | ||||
\(381\) | 0.144226 | + | 0.530064i | 0.00738894 | + | 0.0271560i | ||||
\(382\) | −12.3515 | + | 21.3934i | −0.631958 | + | 1.09458i | ||||
\(383\) | 10.7319 | 0.548373 | 0.274186 | − | 0.961677i | \(-0.411592\pi\) | ||||
0.274186 | + | 0.961677i | \(0.411592\pi\) | |||||||
\(384\) | −0.938027 | + | 0.945300i | −0.0478685 | + | 0.0482396i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.283187 | 0.0144139 | ||||||||
\(387\) | −0.174874 | − | 22.6426i | −0.00888935 | − | 1.15099i | ||||
\(388\) | −1.49022 | − | 2.58114i | −0.0756546 | − | 0.131038i | ||||
\(389\) | 24.1468 | 1.22429 | 0.612147 | − | 0.790744i | \(-0.290306\pi\) | ||||
0.612147 | + | 0.790744i | \(0.290306\pi\) | |||||||
\(390\) | 0.483067 | + | 0.127440i | 0.0244611 | + | 0.00645319i | ||||
\(391\) | −1.53026 | − | 2.65049i | −0.0773885 | − | 0.134041i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.80131 | + | 24.9963i | 0.343081 | + | 1.26090i | ||||
\(394\) | −0.420927 | − | 0.729067i | −0.0212060 | − | 0.0367299i | ||||
\(395\) | 0.405733 | + | 0.702750i | 0.0204146 | + | 0.0353592i | ||||
\(396\) | 0.0606053 | + | 7.84715i | 0.00304553 | + | 0.394334i | ||||
\(397\) | 12.0285 | − | 20.8339i | 0.603691 | − | 1.04562i | −0.388566 | − | 0.921421i | \(-0.627029\pi\) |
0.992257 | − | 0.124203i | \(-0.0396373\pi\) | |||||||
\(398\) | −2.77424 | + | 4.80513i | −0.139060 | + | 0.240860i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.53501 | − | 7.85487i | −0.226751 | − | 0.392744i | ||||
\(401\) | −1.56232 | −0.0780183 | −0.0390092 | − | 0.999239i | \(-0.512420\pi\) | ||||
−0.0390092 | + | 0.999239i | \(0.512420\pi\) | |||||||
\(402\) | −5.00065 | − | 18.3785i | −0.249410 | − | 0.916637i | ||||
\(403\) | 22.9683 | 1.14413 | ||||||||
\(404\) | −6.84661 | + | 11.8587i | −0.340631 | + | 0.589991i | ||||
\(405\) | −0.461844 | + | 0.829259i | −0.0229492 | + | 0.0412062i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.30817 | − | 5.72992i | 0.163980 | − | 0.284022i | ||||
\(408\) | −6.04209 | + | 6.08894i | −0.299128 | + | 0.301447i | ||||
\(409\) | −11.1728 | + | 19.3519i | −0.552460 | + | 0.956889i | 0.445636 | + | 0.895214i | \(0.352977\pi\) |
−0.998096 | + | 0.0616748i | \(0.980356\pi\) | |||||||
\(410\) | −0.435309 | + | 0.753978i | −0.0214984 | + | 0.0372363i | ||||
\(411\) | −6.93365 | − | 25.4827i | −0.342012 | − | 1.25697i | ||||
\(412\) | 3.42210 | − | 5.92725i | 0.168595 | − | 0.292014i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.45988 | + | 3.09629i | 0.268339 | + | 0.152174i | ||||
\(415\) | −0.0616373 | + | 0.106759i | −0.00302566 | + | 0.00524059i | ||||
\(416\) | 10.2547 | 0.502779 | ||||||||
\(417\) | −9.90506 | + | 9.98186i | −0.485053 | + | 0.488814i | ||||
\(418\) | −28.2755 | −1.38300 | ||||||||
\(419\) | −2.98648 | − | 5.17273i | −0.145899 | − | 0.252704i | 0.783809 | − | 0.621002i | \(-0.213274\pi\) |
−0.929708 | + | 0.368298i | \(0.879941\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.31594 | − | 12.6716i | 0.356557 | − | 0.617575i | −0.630826 | − | 0.775924i | \(-0.717284\pi\) |
0.987383 | + | 0.158349i | \(0.0506172\pi\) | |||||||
\(422\) | 3.97605 | − | 6.88672i | 0.193551 | − | 0.335240i | ||||
\(423\) | 8.33919 | + | 4.72914i | 0.405465 | + | 0.229939i | ||||
\(424\) | 15.3144 | + | 26.5254i | 0.743735 | + | 1.28819i | ||||
\(425\) | −4.02400 | − | 6.96977i | −0.195193 | − | 0.338083i | ||||
\(426\) | −4.42707 | + | 4.46139i | −0.214492 | + | 0.216155i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.11156 | − | 12.3176i | −0.343750 | − | 0.595393i | ||||
\(429\) | −10.0972 | + | 10.1755i | −0.487498 | + | 0.491278i | ||||
\(430\) | 0.877876 | 0.0423349 | ||||||||
\(431\) | 9.70169 | + | 16.8038i | 0.467314 | + | 0.809411i | 0.999303 | − | 0.0373401i | \(-0.0118885\pi\) |
−0.531989 | + | 0.846751i | \(0.678555\pi\) | |||||||
\(432\) | 2.33916 | − | 9.15268i | 0.112543 | − | 0.440359i | ||||
\(433\) | −1.35217 | −0.0649810 | −0.0324905 | − | 0.999472i | \(-0.510344\pi\) | ||||
−0.0324905 | + | 0.999472i | \(0.510344\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.64096 | − | 0.432910i | −0.0786781 | − | 0.0207564i | ||||
\(436\) | 3.30959 | 0.158501 | ||||||||
\(437\) | 7.28772 | − | 12.6227i | 0.348619 | − | 0.603826i | ||||
\(438\) | 8.72453 | + | 2.30166i | 0.416874 | + | 0.109978i | ||||
\(439\) | 8.67059 | + | 15.0179i | 0.413825 | + | 0.716766i | 0.995304 | − | 0.0967954i | \(-0.0308592\pi\) |
−0.581479 | + | 0.813561i | \(0.697526\pi\) | |||||||
\(440\) | −1.08056 | −0.0515139 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.41194 | −0.209854 | ||||||||
\(443\) | −9.80499 | − | 16.9827i | −0.465849 | − | 0.806874i | 0.533390 | − | 0.845869i | \(-0.320918\pi\) |
−0.999239 | + | 0.0389949i | \(0.987584\pi\) | |||||||
\(444\) | 1.89579 | − | 1.91049i | 0.0899701 | − | 0.0906676i | ||||
\(445\) | −0.317956 | + | 0.550716i | −0.0150726 | + | 0.0261064i | ||||
\(446\) | 12.3318 | 0.583927 | ||||||||
\(447\) | −5.06977 | − | 18.6325i | −0.239792 | − | 0.881289i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.7345 | −0.836942 | −0.418471 | − | 0.908230i | \(-0.637434\pi\) | ||||
−0.418471 | + | 0.908230i | \(0.637434\pi\) | |||||||
\(450\) | 14.3574 | + | 8.14206i | 0.676815 | + | 0.383821i | ||||
\(451\) | −12.4905 | − | 21.6342i | −0.588155 | − | 1.01871i | ||||
\(452\) | 1.61187 | 0.0758160 | ||||||||
\(453\) | −5.12657 | − | 18.8413i | −0.240867 | − | 0.885241i | ||||
\(454\) | 13.1073 | + | 22.7025i | 0.615156 | + | 1.06548i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −39.5005 | − | 10.4208i | −1.84978 | − | 0.487999i | ||||
\(457\) | −0.242725 | − | 0.420413i | −0.0113542 | − | 0.0196661i | 0.860292 | − | 0.509801i | \(-0.170281\pi\) |
−0.871647 | + | 0.490135i | \(0.836948\pi\) | |||||||
\(458\) | −1.05069 | − | 1.81985i | −0.0490956 | − | 0.0850361i | ||||
\(459\) | 2.07558 | − | 8.12134i | 0.0968796 | − | 0.379071i | ||||
\(460\) | 0.0784150 | − | 0.135819i | 0.00365612 | − | 0.00633259i | ||||
\(461\) | −3.99687 | + | 6.92279i | −0.186153 | + | 0.322426i | −0.943964 | − | 0.330047i | \(-0.892935\pi\) |
0.757811 | + | 0.652474i | \(0.226269\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.24280 | + | 9.08080i | 0.243654 | + | 0.422021i | 0.961752 | − | 0.273921i | \(-0.0883206\pi\) |
−0.718098 | + | 0.695942i | \(0.754987\pi\) | |||||||
\(464\) | 16.8905 | 0.784120 | ||||||||
\(465\) | −1.63587 | − | 0.431568i | −0.0758619 | − | 0.0200135i | ||||
\(466\) | −7.21443 | −0.334202 | ||||||||
\(467\) | 10.9489 | − | 18.9640i | 0.506653 | − | 0.877549i | −0.493317 | − | 0.869849i | \(-0.664216\pi\) |
0.999970 | − | 0.00769944i | \(-0.00245083\pi\) | |||||||
\(468\) | −5.02744 | + | 2.95460i | −0.232394 | + | 0.136576i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.185839 | + | 0.321883i | −0.00857213 | + | 0.0148474i | ||||
\(471\) | −20.4426 | − | 5.39306i | −0.941945 | − | 0.248499i | ||||
\(472\) | 6.84592 | − | 11.8575i | 0.315109 | − | 0.545785i | ||||
\(473\) | −12.5946 | + | 21.8145i | −0.579102 | + | 1.00303i | ||||
\(474\) | 14.2105 | + | 3.74894i | 0.652711 | + | 0.172195i | ||||
\(475\) | 19.1639 | − | 33.1929i | 0.879301 | − | 1.52299i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −26.0353 | − | 14.7645i | −1.19207 | − | 0.676022i | ||||
\(478\) | −11.7708 | + | 20.3877i | −0.538386 | + | 0.932512i | ||||
\(479\) | −4.00169 | −0.182842 | −0.0914210 | − | 0.995812i | \(-0.529141\pi\) | ||||
−0.0914210 | + | 0.995812i | \(0.529141\pi\) | |||||||
\(480\) | −0.730373 | − | 0.192683i | −0.0333368 | − | 0.00879474i | ||||
\(481\) | 4.91658 | 0.224177 | ||||||||
\(482\) | −11.0646 | − | 19.1645i | −0.503980 | − | 0.872918i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.0539532 | − | 0.0934496i | 0.00245242 | − | 0.00424771i | ||||
\(485\) | −0.200520 | + | 0.347311i | −0.00910514 | + | 0.0157706i | ||||
\(486\) | 4.76916 | + | 16.5164i | 0.216334 | + | 0.749199i | ||||
\(487\) | 13.2377 | + | 22.9284i | 0.599859 | + | 1.03899i | 0.992841 | + | 0.119440i | \(0.0381100\pi\) |
−0.392982 | + | 0.919546i | \(0.628557\pi\) | |||||||
\(488\) | −8.70502 | − | 15.0775i | −0.394058 | − | 0.682528i | ||||
\(489\) | −15.0102 | − | 3.95991i | −0.678784 | − | 0.179073i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.2149 | + | 24.6210i | 0.641511 | + | 1.11113i | 0.985096 | + | 0.172008i | \(0.0550255\pi\) |
−0.343584 | + | 0.939122i | \(0.611641\pi\) | |||||||
\(492\) | −2.66801 | − | 9.80553i | −0.120283 | − | 0.442068i | ||||
\(493\) | 14.9872 | 0.674989 | ||||||||
\(494\) | −10.5057 | − | 18.1965i | −0.472675 | − | 0.818697i | ||||
\(495\) | 0.910349 | − | 0.535007i | 0.0409172 | − | 0.0240468i | ||||
\(496\) | 16.8381 | 0.756052 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.586179 | + | 2.15434i | 0.0262673 | + | 0.0965383i | ||||
\(499\) | −7.43118 | −0.332665 | −0.166333 | − | 0.986070i | \(-0.553193\pi\) | ||||
−0.166333 | + | 0.986070i | \(0.553193\pi\) | |||||||
\(500\) | 0.412863 | − | 0.715100i | 0.0184638 | − | 0.0319802i | ||||
\(501\) | 21.2484 | − | 21.4132i | 0.949310 | − | 0.956670i | ||||
\(502\) | −3.75765 | − | 6.50845i | −0.167712 | − | 0.290486i | ||||
\(503\) | 10.1610 | 0.453057 | 0.226529 | − | 0.974004i | \(-0.427262\pi\) | ||||
0.226529 | + | 0.974004i | \(0.427262\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.84252 | 0.0819910 | ||||||||
\(506\) | −3.49124 | − | 6.04700i | −0.155204 | − | 0.268822i | ||||
\(507\) | 11.4718 | + | 3.02643i | 0.509481 | + | 0.134409i | ||||
\(508\) | 0.124295 | − | 0.215285i | 0.00551470 | − | 0.00955174i | ||||
\(509\) | −28.9063 | −1.28125 | −0.640625 | − | 0.767854i | \(-0.721325\pi\) | ||||
−0.640625 | + | 0.767854i | \(0.721325\pi\) | |||||||
\(510\) | 0.314232 | + | 0.0828990i | 0.0139144 | + | 0.00367083i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 18.6806 | 0.825575 | ||||||||
\(513\) | 38.4377 | − | 10.7781i | 1.69707 | − | 0.475866i | ||||
\(514\) | −7.93381 | − | 13.7418i | −0.349945 | − | 0.606123i | ||||
\(515\) | −0.920934 | −0.0405812 | ||||||||
\(516\) | −7.21750 | + | 7.27346i | −0.317733 | + | 0.320196i | ||||
\(517\) | −5.33237 | − | 9.23593i | −0.234517 | − | 0.406196i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.45180 | − | 3.47856i | 0.151517 | − | 0.152692i | ||||
\(520\) | −0.401482 | − | 0.695387i | −0.0176061 | − | 0.0304947i | ||||
\(521\) | −16.8995 | − | 29.2708i | −0.740381 | − | 1.28238i | −0.952322 | − | 0.305095i | \(-0.901312\pi\) |
0.211941 | − | 0.977283i | \(-0.432022\pi\) | |||||||
\(522\) | −26.4994 | + | 15.5735i | −1.15985 | + | 0.681635i | ||||
\(523\) | 7.18895 | − | 12.4516i | 0.314351 | − | 0.544471i | −0.664949 | − | 0.746889i | \(-0.731547\pi\) |
0.979299 | + | 0.202418i | \(0.0648799\pi\) | |||||||
\(524\) | 5.86140 | − | 10.1522i | 0.256056 | − | 0.443502i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.848618 | − | 1.46985i | −0.0370015 | − | 0.0640885i | ||||
\(527\) | 14.9407 | 0.650828 | ||||||||
\(528\) | −7.40227 | + | 7.45966i | −0.322143 | + | 0.324640i | ||||
\(529\) | −19.4007 | −0.843508 | ||||||||
\(530\) | 0.580197 | − | 1.00493i | 0.0252022 | − | 0.0436514i | ||||
\(531\) | 0.103331 | + | 13.3792i | 0.00448416 | + | 0.580607i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.28166 | − | 16.0763i | 0.402033 | − | 0.696342i | ||||
\(534\) | 3.02381 | + | 11.1132i | 0.130853 | + | 0.480914i | ||||
\(535\) | −0.956910 | + | 1.65742i | −0.0413708 | + | 0.0716564i | ||||
\(536\) | −15.3062 | + | 26.5111i | −0.661127 | + | 1.14511i | ||||
\(537\) | −12.3985 | + | 12.4947i | −0.535037 | + | 0.539185i | ||||
\(538\) | −14.4783 | + | 25.0772i | −0.624205 | + | 1.08116i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.413586 | − | 0.115971i | 0.0177979 | − | 0.00499062i | ||||
\(541\) | 12.5882 | − | 21.8034i | 0.541210 | − | 0.937403i | −0.457625 | − | 0.889145i | \(-0.651300\pi\) |
0.998835 | − | 0.0482577i | \(-0.0153669\pi\) | |||||||
\(542\) | −19.7773 | −0.849506 | ||||||||
\(543\) | −7.77021 | − | 28.5573i | −0.333452 | − | 1.22551i | ||||
\(544\) | 6.67063 | 0.286001 | ||||||||
\(545\) | −0.222664 | − | 0.385666i | −0.00953789 | − | 0.0165201i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.59011 | − | 2.75416i | 0.0679883 | − | 0.117759i | −0.830027 | − | 0.557723i | \(-0.811675\pi\) |
0.898016 | + | 0.439963i | \(0.145009\pi\) | |||||||
\(548\) | −5.97545 | + | 10.3498i | −0.255258 | + | 0.442121i | ||||
\(549\) | 14.7989 | + | 8.39245i | 0.631603 | + | 0.358181i | ||||
\(550\) | −9.18062 | − | 15.9013i | −0.391463 | − | 0.678034i | ||||
\(551\) | 35.6876 | + | 61.8127i | 1.52034 | + | 2.63331i | ||||
\(552\) | −2.64861 | − | 9.73424i | −0.112732 | − | 0.414317i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −10.4057 | − | 18.0233i | −0.442098 | − | 0.765736i | ||||
\(555\) | −0.350174 | − | 0.0923811i | −0.0148641 | − | 0.00392136i | ||||
\(556\) | 6.36358 | 0.269876 | ||||||||
\(557\) | −10.0229 | − | 17.3602i | −0.424686 | − | 0.735577i | 0.571705 | − | 0.820459i | \(-0.306282\pi\) |
−0.996391 | + | 0.0848820i | \(0.972949\pi\) | |||||||
\(558\) | −26.4172 | + | 15.5252i | −1.11833 | + | 0.657236i | ||||
\(559\) | −18.7181 | −0.791689 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.56817 | + | 6.61909i | −0.277308 | + | 0.279458i | ||||
\(562\) | −5.50477 | −0.232205 | ||||||||
\(563\) | −19.9007 | + | 34.4690i | −0.838713 | + | 1.45269i | 0.0522584 | + | 0.998634i | \(0.483358\pi\) |
−0.890971 | + | 0.454060i | \(0.849975\pi\) | |||||||
\(564\) | −1.13901 | − | 4.18611i | −0.0479609 | − | 0.176267i | ||||
\(565\) | −0.108444 | − | 0.187831i | −0.00456228 | − | 0.00790211i | ||||
\(566\) | −16.9753 | −0.713523 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.1017 | 0.423856 | ||||||||
\(569\) | −6.90797 | − | 11.9649i | −0.289597 | − | 0.501597i | 0.684117 | − | 0.729373i | \(-0.260188\pi\) |
−0.973714 | + | 0.227776i | \(0.926855\pi\) | |||||||
\(570\) | 0.406344 | + | 1.49341i | 0.0170199 | + | 0.0625519i | ||||
\(571\) | −5.21935 | + | 9.04019i | −0.218423 | + | 0.378320i | −0.954326 | − | 0.298767i | \(-0.903425\pi\) |
0.735903 | + | 0.677087i | \(0.236758\pi\) | |||||||
\(572\) | 6.48703 | 0.271236 | ||||||||
\(573\) | −27.3281 | + | 27.5400i | −1.14165 | + | 1.15050i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.46483 | 0.394711 | ||||||||
\(576\) | −21.1990 | + | 12.4585i | −0.883293 | + | 0.519106i | ||||
\(577\) | 12.7461 | + | 22.0769i | 0.530628 | + | 0.919075i | 0.999361 | + | 0.0357353i | \(0.0113773\pi\) |
−0.468733 | + | 0.883340i | \(0.655289\pi\) | |||||||
\(578\) | 15.8779 | 0.660433 | ||||||||
\(579\) | 0.430053 | + | 0.113454i | 0.0178724 | + | 0.00471500i | ||||
\(580\) | 0.383994 | + | 0.665098i | 0.0159445 | + | 0.0276167i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.90697 | + | 7.00855i | 0.0790466 | + | 0.290514i | ||||
\(583\) | 16.6478 | + | 28.8349i | 0.689483 | + | 1.19422i | ||||
\(584\) | −7.25104 | − | 12.5592i | −0.300050 | − | 0.519702i | ||||
\(585\) | 0.682537 | + | 0.387066i | 0.0282194 | + | 0.0160032i | ||||
\(586\) | −14.2277 | + | 24.6431i | −0.587740 | + | 1.01800i | ||||
\(587\) | 17.5168 | − | 30.3401i | 0.722998 | − | 1.25227i | −0.236795 | − | 0.971560i | \(-0.576097\pi\) |
0.959793 | − | 0.280709i | \(-0.0905697\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.5769 | + | 61.6210i | 1.46592 | + | 2.53905i | ||||
\(590\) | −0.518724 | −0.0213555 | ||||||||
\(591\) | −0.347138 | − | 1.27581i | −0.0142794 | − | 0.0524799i | ||||
\(592\) | 3.60435 | 0.148138 | ||||||||
\(593\) | −18.0646 | + | 31.2888i | −0.741824 | + | 1.28488i | 0.209840 | + | 0.977736i | \(0.432706\pi\) |
−0.951664 | + | 0.307141i | \(0.900628\pi\) | |||||||
\(594\) | 4.73536 | − | 18.5286i | 0.194294 | − | 0.760236i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.36915 | + | 7.56759i | −0.178967 | + | 0.309980i | ||||
\(597\) | −6.13811 | + | 6.18570i | −0.251216 | + | 0.253164i | ||||
\(598\) | 2.59433 | − | 4.49350i | 0.106090 | − | 0.183753i | ||||
\(599\) | 20.4742 | − | 35.4623i | 0.836552 | − | 1.44895i | −0.0562080 | − | 0.998419i | \(-0.517901\pi\) |
0.892760 | − | 0.450532i | \(-0.148766\pi\) | |||||||
\(600\) | −6.96484 | − | 25.5973i | −0.284338 | − | 1.04501i | ||||
\(601\) | −12.8547 | + | 22.2650i | −0.524354 | + | 0.908207i | 0.475244 | + | 0.879854i | \(0.342360\pi\) |
−0.999598 | + | 0.0283533i | \(0.990974\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.231028 | − | 29.9133i | −0.00940817 | − | 1.21817i | ||||
\(604\) | −4.41810 | + | 7.65238i | −0.179770 | + | 0.311371i | ||||
\(605\) | −0.0145196 | −0.000590304 | ||||||||
\(606\) | 23.5052 | − | 23.6874i | 0.954831 | − | 0.962234i | ||||
\(607\) | −6.84516 | −0.277836 | −0.138918 | − | 0.990304i | \(-0.544362\pi\) | ||||
−0.138918 | + | 0.990304i | \(0.544362\pi\) | |||||||
\(608\) | 15.8841 | + | 27.5121i | 0.644187 | + | 1.11576i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.329795 | + | 0.571222i | −0.0133530 | + | 0.0231281i | ||||
\(611\) | 3.96246 | − | 6.86319i | 0.160304 | − | 0.277655i | ||||
\(612\) | −3.27031 | + | 1.92194i | −0.132195 | + | 0.0776900i | ||||
\(613\) | 14.5648 | + | 25.2271i | 0.588269 | + | 1.01891i | 0.994459 | + | 0.105123i | \(0.0335235\pi\) |
−0.406191 | + | 0.913788i | \(0.633143\pi\) | |||||||
\(614\) | 12.2917 | + | 21.2898i | 0.496051 | + | 0.859185i | ||||
\(615\) | −0.963137 | + | 0.970604i | −0.0388374 | + | 0.0391385i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.3395 | − | 17.9085i | −0.416252 | − | 0.720969i | 0.579307 | − | 0.815109i | \(-0.303323\pi\) |
−0.995559 | + | 0.0941404i | \(0.969990\pi\) | |||||||
\(618\) | −11.7484 | + | 11.8395i | −0.472591 | + | 0.476255i | ||||
\(619\) | 8.86355 | 0.356256 | 0.178128 | − | 0.984007i | \(-0.442996\pi\) | ||||
0.178128 | + | 0.984007i | \(0.442996\pi\) | |||||||
\(620\) | 0.382804 | + | 0.663035i | 0.0153738 | + | 0.0266281i | ||||
\(621\) | 7.05099 | + | 6.88949i | 0.282947 | + | 0.276466i | ||||
\(622\) | −1.44453 | −0.0579205 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −7.55090 | − | 1.99204i | −0.302278 | − | 0.0797453i | ||||
\(625\) | 24.8333 | 0.993331 | ||||||||
\(626\) | −11.8977 | + | 20.6074i | −0.475528 | + | 0.823638i | ||||
\(627\) | −42.9397 | − | 11.3281i | −1.71485 | − | 0.452402i | ||||
\(628\) | 4.78368 | + | 8.28558i | 0.190890 | + | 0.330631i | ||||
\(629\) | 3.19820 | 0.127521 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.4661 | 1.05360 | 0.526799 | − | 0.849990i | \(-0.323392\pi\) | ||||
0.526799 | + | 0.849990i | \(0.323392\pi\) | |||||||
\(632\) | −11.8105 | − | 20.4564i | −0.469796 | − | 0.813711i | ||||
\(633\) | 8.79714 | − | 8.86535i | 0.349655 | − | 0.352366i | ||||
\(634\) | −13.6649 | + | 23.6683i | −0.542704 | + | 0.939990i | ||||
\(635\) | −0.0334495 | −0.00132740 | ||||||||
\(636\) | 3.55603 | + | 13.0692i | 0.141006 | + | 0.518227i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 34.1928 | 1.35371 | ||||||||
\(639\) | −8.51040 | + | 5.00151i | −0.336666 | + | 0.197857i | ||||
\(640\) | −0.0405449 | − | 0.0702258i | −0.00160268 | − | 0.00277592i | ||||
\(641\) | −16.5319 | −0.652971 | −0.326486 | − | 0.945202i | \(-0.605864\pi\) | ||||
−0.326486 | + | 0.945202i | \(0.605864\pi\) | |||||||
\(642\) | 9.10035 | + | 33.4458i | 0.359162 | + | 1.32000i | ||||
\(643\) | 15.4460 | + | 26.7532i | 0.609130 | + | 1.05504i | 0.991384 | + | 0.130987i | \(0.0418147\pi\) |
−0.382254 | + | 0.924057i | \(0.624852\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.33316 | + | 0.351706i | 0.0524930 | + | 0.0138484i | ||||
\(646\) | −6.83390 | − | 11.8367i | −0.268876 | − | 0.465707i | ||||
\(647\) | −0.649903 | − | 1.12567i | −0.0255503 | − | 0.0442545i | 0.852968 | − | 0.521964i | \(-0.174800\pi\) |
−0.878518 | + | 0.477710i | \(0.841467\pi\) | |||||||
\(648\) | 13.4438 | − | 24.1389i | 0.528124 | − | 0.948267i | ||||
\(649\) | 7.44198 | − | 12.8899i | 0.292123 | − | 0.505972i | ||||
\(650\) | 6.82209 | − | 11.8162i | 0.267584 | − | 0.463470i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.51247 | + | 6.08377i | 0.137559 | + | 0.238259i | ||||
\(653\) | −44.8870 | −1.75656 | −0.878281 | − | 0.478144i | \(-0.841310\pi\) | ||||
−0.878281 | + | 0.478144i | \(0.841310\pi\) | |||||||
\(654\) | −7.79866 | − | 2.05740i | −0.304952 | − | 0.0804508i | ||||
\(655\) | −1.57738 | −0.0616335 | ||||||||
\(656\) | 6.80438 | − | 11.7855i | 0.265667 | − | 0.460148i | ||||
\(657\) | 12.3271 | + | 6.99068i | 0.480926 | + | 0.272732i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.96167 | − | 15.5221i | 0.349097 | − | 0.604654i | −0.636992 | − | 0.770870i | \(-0.719822\pi\) |
0.986089 | + | 0.166216i | \(0.0531549\pi\) | |||||||
\(660\) | −0.462026 | − | 0.121889i | −0.0179844 | − | 0.00474454i | ||||
\(661\) | 16.5128 | − | 28.6010i | 0.642274 | − | 1.11245i | −0.342649 | − | 0.939463i | \(-0.611324\pi\) |
0.984924 | − | 0.172989i | \(-0.0553424\pi\) | |||||||
\(662\) | 7.63429 | − | 13.2230i | 0.296715 | − | 0.513925i | ||||
\(663\) | −6.70004 | − | 1.76757i | −0.260208 | − | 0.0686467i | ||||
\(664\) | 1.79420 | − | 3.10765i | 0.0696285 | − | 0.120600i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.65485 | + | 3.32332i | −0.219121 | + | 0.128776i | ||||
\(667\) | −8.81283 | + | 15.2643i | −0.341234 | + | 0.591035i | ||||
\(668\) | −13.6512 | −0.528182 | ||||||||
\(669\) | 18.7273 | + | 4.94053i | 0.724038 | + | 0.191012i | ||||
\(670\) | 1.15977 | 0.0448058 | ||||||||
\(671\) | −9.46295 | − | 16.3903i | −0.365313 | − | 0.632741i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.6758 | + | 18.4909i | −0.411520 | + | 0.712774i | −0.995056 | − | 0.0993135i | \(-0.968335\pi\) |
0.583536 | + | 0.812087i | \(0.301669\pi\) | |||||||
\(674\) | −1.86865 | + | 3.23659i | −0.0719776 | + | 0.124669i | ||||
\(675\) | 18.5414 | + | 18.1167i | 0.713660 | + | 0.697313i | ||||
\(676\) | −2.68447 | − | 4.64964i | −0.103249 | − | 0.178832i | ||||
\(677\) | 4.15084 | + | 7.18946i | 0.159530 | + | 0.276313i | 0.934699 | − | 0.355440i | \(-0.115669\pi\) |
−0.775170 | + | 0.631753i | \(0.782336\pi\) | |||||||
\(678\) | −3.79818 | − | 1.00202i | −0.145868 | − | 0.0384822i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.261161 | − | 0.452344i | −0.0100151 | − | 0.0173466i | ||||
\(681\) | 10.8096 | + | 39.7276i | 0.414224 | + | 1.52237i | ||||
\(682\) | 34.0868 | 1.30525 | ||||||||
\(683\) | −1.24728 | − | 2.16036i | −0.0477259 | − | 0.0826637i | 0.841176 | − | 0.540762i | \(-0.181864\pi\) |
−0.888902 | + | 0.458098i | \(0.848531\pi\) | |||||||
\(684\) | −15.7141 | − | 8.91143i | −0.600843 | − | 0.340737i | ||||
\(685\) | 1.60808 | 0.0614414 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.866505 | − | 3.18460i | −0.0330592 | − | 0.121500i | ||||
\(688\) | −13.7222 | −0.523154 | ||||||||
\(689\) | −12.3710 | + | 21.4271i | −0.471296 | + | 0.816308i | ||||
\(690\) | −0.269207 | + | 0.271295i | −0.0102486 | + | 0.0103280i | ||||
\(691\) | −8.43455 | − | 14.6091i | −0.320865 | − | 0.555755i | 0.659801 | − | 0.751440i | \(-0.270640\pi\) |
−0.980667 | + | 0.195685i | \(0.937307\pi\) | |||||||
\(692\) | −2.21763 | −0.0843017 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.0071 | 0.607621 | ||||||||
\(695\) | −0.428132 | − | 0.741547i | −0.0162400 | − | 0.0281285i | ||||
\(696\) | 47.7668 | + | 12.6016i | 1.81060 | + | 0.477662i | ||||
\(697\) | 6.03765 | − | 10.4575i | 0.228692 | − | 0.396107i | ||||
\(698\) | −17.3453 | −0.656530 | ||||||||
\(699\) | −10.9559 | − | 2.89034i | −0.414392 | − | 0.109323i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.4806 | 0.622465 | 0.311232 | − | 0.950334i | \(-0.399258\pi\) | ||||
0.311232 | + | 0.950334i | \(0.399258\pi\) | |||||||
\(702\) | 13.6833 | − | 3.83686i | 0.516443 | − | 0.144813i | ||||
\(703\) | 7.61558 | + | 13.1906i | 0.287227 | + | 0.497492i | ||||
\(704\) | 27.3536 | 1.03093 | ||||||||
\(705\) | −0.411176 | + | 0.414364i | −0.0154858 | + | 0.0156058i | ||||
\(706\) | 2.28515 | + | 3.95800i | 0.0860029 | + | 0.148961i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.26472 | − | 4.29778i | 0.160278 | − | 0.161520i | ||||
\(709\) | 14.7462 | + | 25.5412i | 0.553807 | + | 0.959222i | 0.997995 | + | 0.0632882i | \(0.0201587\pi\) |
−0.444188 | + | 0.895933i | \(0.646508\pi\) | |||||||
\(710\) | −0.191354 | − | 0.331434i | −0.00718138 | − | 0.0124385i | ||||
\(711\) | 20.0784 | + | 11.3864i | 0.752998 | + | 0.427024i | ||||
\(712\) | 9.25539 | − | 16.0308i | 0.346860 | − | 0.600780i | ||||
\(713\) | −8.78551 | + | 15.2169i | −0.329020 | + | 0.569879i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.436438 | − | 0.755933i | −0.0163219 | − | 0.0282703i | ||||
\(716\) | 7.96554 | 0.297686 | ||||||||
\(717\) | −26.0434 | + | 26.2453i | −0.972608 | + | 0.980149i | ||||
\(718\) | −8.75620 | −0.326779 | ||||||||
\(719\) | −0.217311 | + | 0.376394i | −0.00810433 | + | 0.0140371i | −0.870049 | − | 0.492965i | \(-0.835913\pi\) |
0.861945 | + | 0.507002i | \(0.169246\pi\) | |||||||
\(720\) | 0.500368 | + | 0.283758i | 0.0186476 | + | 0.0105750i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 22.0691 | − | 38.2248i | 0.821327 | − | 1.42258i | ||||
\(723\) | −9.12499 | − | 33.5364i | −0.339362 | − | 1.24723i | ||||
\(724\) | −6.69640 | + | 11.5985i | −0.248870 | + | 0.431055i | ||||
\(725\) | −23.1744 | + | 40.1392i | −0.860675 | + | 1.49073i | ||||
\(726\) | −0.185227 | + | 0.186663i | −0.00687443 | + | 0.00692772i | ||||
\(727\) | −13.5839 | + | 23.5280i | −0.503799 | + | 0.872605i | 0.496192 | + | 0.868213i | \(0.334731\pi\) |
−0.999990 | + | 0.00439187i | \(0.998602\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.625513 | + | 26.9928i | 0.0231672 | + | 0.999732i | ||||
\(730\) | −0.274710 | + | 0.475812i | −0.0101675 | + | 0.0176106i | ||||
\(731\) | −12.1760 | −0.450344 | ||||||||
\(732\) | −2.02131 | − | 7.42878i | −0.0747099 | − | 0.274576i | ||||
\(733\) | 5.66614 | 0.209284 | 0.104642 | − | 0.994510i | \(-0.466630\pi\) | ||||
0.104642 | + | 0.994510i | \(0.466630\pi\) | |||||||
\(734\) | 7.25050 | + | 12.5582i | 0.267621 | + | 0.463533i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.92249 | + | 6.79395i | −0.144585 | + | 0.250428i | ||||
\(737\) | −16.6389 | + | 28.8194i | −0.612901 | + | 1.06158i | ||||
\(738\) | 0.191259 | + | 24.7642i | 0.00704035 | + | 0.911581i | ||||
\(739\) | 6.80540 | + | 11.7873i | 0.250341 | + | 0.433603i | 0.963620 | − | 0.267278i | \(-0.0861241\pi\) |
−0.713279 | + | 0.700880i | \(0.752791\pi\) | |||||||
\(740\) | 0.0819427 | + | 0.141929i | 0.00301227 | + | 0.00521741i | ||||
\(741\) | −8.66407 | − | 31.8424i | −0.318282 | − | 1.16976i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.33421 | − | 10.9712i | −0.232380 | − | 0.402493i | 0.726128 | − | 0.687559i | \(-0.241318\pi\) |
−0.958508 | + | 0.285066i | \(0.907985\pi\) | |||||||
\(744\) | 47.6187 | + | 12.5625i | 1.74579 | + | 0.460564i | ||||
\(745\) | 1.17580 | 0.0430779 | ||||||||
\(746\) | 4.30696 | + | 7.45988i | 0.157689 | + | 0.273126i | ||||
\(747\) | 0.0270812 | + | 3.50646i | 0.000990849 | + | 0.128295i | ||||
\(748\) | 4.21977 | 0.154290 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.41740 | + | 1.42839i | −0.0517563 | + | 0.0521576i | ||||
\(751\) | −7.14538 | −0.260739 | −0.130369 | − | 0.991465i | \(-0.541616\pi\) | ||||
−0.130369 | + | 0.991465i | \(0.541616\pi\) | |||||||
\(752\) | 2.90488 | − | 5.03140i | 0.105930 | − | 0.183476i | ||||
\(753\) | −3.09894 | − | 11.3893i | −0.112931 | − | 0.415048i | ||||
\(754\) | 12.7043 | + | 22.0045i | 0.462663 | + | 0.801355i | ||||
\(755\) | 1.18897 | 0.0432712 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.6446 | 1.36822 | 0.684108 | − | 0.729381i | \(-0.260192\pi\) | ||||
0.684108 | + | 0.729381i | \(0.260192\pi\) | |||||||
\(758\) | −17.4325 | − | 30.1940i | −0.633178 | − | 1.09670i | ||||
\(759\) | −2.87922 | − | 10.5818i | −0.104509 | − | 0.384094i | ||||
\(760\) | 1.24376 | − | 2.15425i | 0.0451157 | − | 0.0781428i | ||||
\(761\) | −10.0472 | −0.364209 | −0.182104 | − | 0.983279i | \(-0.558291\pi\) | ||||
−0.182104 | + | 0.983279i | \(0.558291\pi\) | |||||||
\(762\) | −0.426718 | + | 0.430027i | −0.0154584 | + | 0.0155782i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 17.5572 | 0.635196 | ||||||||
\(765\) | 0.443986 | + | 0.251783i | 0.0160523 | + | 0.00910325i | ||||
\(766\) | 5.91762 | + | 10.2496i | 0.213812 | + | 0.370334i | ||||
\(767\) | 11.0602 | 0.399361 | ||||||||
\(768\) | 26.0335 | + | 6.86801i | 0.939402 | + | 0.247828i | ||||
\(769\) | −16.1463 | − | 27.9663i | −0.582252 | − | 1.00849i | −0.995212 | − | 0.0977407i | \(-0.968838\pi\) |
0.412960 | − | 0.910749i | \(-0.364495\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.54301 | − | 24.0470i | −0.235641 | − | 0.866032i | ||||
\(772\) | −0.100635 | − | 0.174305i | −0.00362192 | − | 0.00627336i | ||||
\(773\) | −24.2939 | − | 42.0783i | −0.873792 | − | 1.51345i | −0.858044 | − | 0.513576i | \(-0.828321\pi\) |
−0.0157473 | − | 0.999876i | \(-0.505013\pi\) | |||||||
\(774\) | 21.5287 | − | 12.6523i | 0.773834 | − | 0.454778i | ||||
\(775\) | −23.1025 | + | 40.0148i | −0.829867 | + | 1.43737i | ||||
\(776\) | 5.83694 | − | 10.1099i | 0.209534 | − | 0.362923i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.3147 | + | 23.0618i | 0.477356 | + | 0.826806i | ||||
\(779\) | 57.5075 | 2.06042 | ||||||||
\(780\) | −0.0932244 | − | 0.342620i | −0.00333797 | − | 0.0122678i | ||||
\(781\) | 10.9812 | 0.392938 | ||||||||
\(782\) | 1.68759 | − | 2.92299i | 0.0603481 | − | 0.104526i | ||||
\(783\) | −46.4817 | + | 13.0337i | −1.66112 | + | 0.465786i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.643678 | − | 1.11488i | 0.0229739 | − | 0.0397919i | ||||
\(786\) | −20.1228 | + | 20.2788i | −0.717757 | + | 0.723322i | ||||
\(787\) | 24.4776 | − | 42.3964i | 0.872531 | − | 1.51127i | 0.0131602 | − | 0.999913i | \(-0.495811\pi\) |
0.859370 | − | 0.511354i | \(-0.170856\pi\) | |||||||
\(788\) | −0.299165 | + | 0.518170i | −0.0106573 | + | 0.0184590i | ||||
\(789\) | −0.699855 | − | 2.57212i | −0.0249155 | − | 0.0915700i | ||||
\(790\) | −0.447448 | + | 0.775003i | −0.0159195 | + | 0.0275734i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −26.4994 | + | 15.5735i | −0.941615 | + | 0.553381i | ||||
\(793\) | 7.03188 | − | 12.1796i | 0.249710 | − | 0.432510i | ||||
\(794\) | 26.5303 | 0.941525 | ||||||||
\(795\) | 1.28371 | − | 1.29366i | 0.0455284 | − | 0.0458813i | ||||
\(796\) | 3.94348 | 0.139773 | ||||||||
\(797\) | −1.44417 | − | 2.50137i | −0.0511550 | − | 0.0886030i | 0.839314 | − | 0.543647i | \(-0.182957\pi\) |
−0.890469 | + | 0.455044i | \(0.849624\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.57755 | − | 4.46445i | 0.0911873 | − | 0.157941i | ||||
\(800\) | −10.3147 | + | 17.8655i | −0.364678 | + | 0.631641i | ||||
\(801\) | 0.139698 | + | 18.0881i | 0.00493600 | + | 0.639111i | ||||
\(802\) | −0.861472 | − | 1.49211i | −0.0304196 | − | 0.0526883i | ||||
\(803\) | −7.88237 | − | 13.6527i | −0.278163 | − | 0.481792i | ||||
\(804\) | −9.53510 | + | 9.60903i | −0.336277 | + | 0.338884i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.6649 | + | 21.9362i | 0.446102 | + | 0.772671i | ||||
\(807\) | −32.0338 | + | 32.2822i | −1.12764 | + | 1.13639i | ||||
\(808\) | −53.6339 | −1.88683 | ||||||||
\(809\) | −5.84869 | − | 10.1302i | −0.205629 | − | 0.356160i | 0.744704 | − | 0.667395i | \(-0.232591\pi\) |
−0.950333 | + | 0.311235i | \(0.899257\pi\) | |||||||
\(810\) | −1.04666 | + | 0.0161682i | −0.0367759 | + | 0.000568091i | ||||
\(811\) | 17.1780 | 0.603199 | 0.301600 | − | 0.953435i | \(-0.402479\pi\) | ||||
0.301600 | + | 0.953435i | \(0.402479\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −30.0341 | − | 7.92343i | −1.05334 | − | 0.277887i | ||||
\(814\) | 7.29660 | 0.255746 | ||||||||
\(815\) | 0.472627 | − | 0.818614i | 0.0165554 | − | 0.0286748i | ||||
\(816\) | −4.91180 | − | 1.29581i | −0.171947 | − | 0.0453623i | ||||
\(817\) | −28.9934 | − | 50.2181i | −1.01435 | − | 1.75691i | ||||
\(818\) | −24.6431 | −0.861624 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.618775 | 0.0216085 | ||||||||
\(821\) | −17.0068 | − | 29.4567i | −0.593543 | − | 1.02805i | −0.993751 | − | 0.111622i | \(-0.964396\pi\) |
0.400208 | − | 0.916424i | \(-0.368938\pi\) | |||||||
\(822\) | 20.5144 | − | 20.6734i | 0.715521 | − | 0.721068i | ||||
\(823\) | −21.6890 | + | 37.5664i | −0.756031 | + | 1.30948i | 0.188829 | + | 0.982010i | \(0.439531\pi\) |
−0.944860 | + | 0.327474i | \(0.893803\pi\) | |||||||
\(824\) | 26.8075 | 0.933883 | ||||||||
\(825\) | −7.57125 | − | 27.8260i | −0.263597 | − | 0.968779i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.0909 | −1.18546 | −0.592728 | − | 0.805403i | \(-0.701949\pi\) | ||||
−0.592728 | + | 0.805403i | \(0.701949\pi\) | |||||||
\(828\) | −0.0344527 | − | 4.46092i | −0.00119732 | − | 0.155028i | ||||
\(829\) | −8.45833 | − | 14.6503i | −0.293770 | − | 0.508824i | 0.680928 | − | 0.732350i | \(-0.261577\pi\) |
−0.974698 | + | 0.223526i | \(0.928243\pi\) | |||||||
\(830\) | −0.135949 | −0.00471885 | ||||||||
\(831\) | −8.58161 | − | 31.5393i | −0.297693 | − | 1.09409i | ||||
\(832\) | 10.1632 | + | 17.6032i | 0.352345 | + | 0.610280i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −14.9950 | − | 3.95591i | −0.519236 | − | 0.136982i | ||||
\(835\) | 0.918434 | + | 1.59077i | 0.0317837 | + | 0.0550510i | ||||
\(836\) | 10.0481 | + | 17.4039i | 0.347522 | + | 0.601926i | ||||
\(837\) | −46.3375 | + | 12.9933i | −1.60166 | + | 0.449113i | ||||
\(838\) | 3.29353 | − | 5.70456i | 0.113773 | − | 0.197061i | ||||
\(839\) | 8.16244 | − | 14.1378i | 0.281799 | − | 0.488089i | −0.690029 | − | 0.723782i | \(-0.742402\pi\) |
0.971828 | + | 0.235692i | \(0.0757357\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6560 | − | 49.6336i | −0.988138 | − | 1.71150i | ||||
\(842\) | 16.1362 | 0.556092 | ||||||||
\(843\) | −8.35964 | − | 2.20539i | −0.287921 | − | 0.0759578i | ||||
\(844\) | −5.65179 | −0.194543 | ||||||||
\(845\) | −0.361214 | + | 0.625641i | −0.0124261 | + | 0.0215227i | ||||
\(846\) | 0.0816511 | + | 10.5721i | 0.00280722 | + | 0.363478i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.06915 | + | 15.7082i | −0.311436 | + | 0.539423i | ||||
\(849\) | −25.7789 | − | 6.80085i | −0.884730 | − | 0.233405i | ||||
\(850\) | 4.43772 | − | 7.68635i | 0.152212 | − | 0.263640i | ||||
\(851\) | −1.88062 | + | 3.25733i | −0.0644668 | + | 0.111660i | ||||
\(852\) | 4.31925 | + | 1.13948i | 0.147975 | + | 0.0390380i | ||||
\(853\) | 14.4524 | − | 25.0323i | 0.494841 | − | 0.857089i | −0.505142 | − | 0.863036i | \(-0.668560\pi\) |
0.999982 | + | 0.00594733i | \(0.00189311\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0187729 | + | 2.43071i | 0.000642020 | + | 0.0831285i | ||||
\(856\) | 27.8547 | − | 48.2458i | 0.952055 | − | 1.64901i | ||||
\(857\) | 29.0567 | 0.992559 | 0.496280 | − | 0.868163i | \(-0.334699\pi\) | ||||
0.496280 | + | 0.868163i | \(0.334699\pi\) | |||||||
\(858\) | −15.2859 | − | 4.03265i | −0.521853 | − | 0.137673i | ||||
\(859\) | 12.5964 | 0.429783 | 0.214892 | − | 0.976638i | \(-0.431060\pi\) | ||||
0.214892 | + | 0.976638i | \(0.431060\pi\) | |||||||
\(860\) | −0.311966 | − | 0.540341i | −0.0106380 | − | 0.0184255i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.6992 | + | 18.5315i | −0.364415 | + | 0.631185i | ||||
\(863\) | 7.33309 | − | 12.7013i | 0.249621 | − | 0.432357i | −0.713799 | − | 0.700350i | \(-0.753027\pi\) |
0.963421 | + | 0.267993i | \(0.0863605\pi\) | |||||||
\(864\) | −20.6885 | + | 5.80114i | −0.703836 | + | 0.197359i | ||||
\(865\) | 0.149199 | + | 0.258420i | 0.00507292 | + | 0.00878655i | ||||
\(866\) | −0.745594 | − | 1.29141i | −0.0253363 | − | 0.0438838i | ||||
\(867\) | 24.1124 | + | 6.36122i | 0.818901 | + | 0.216038i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.8388 | − | 22.2375i | −0.435527 | − | 0.754354i | ||||
\(870\) | −0.491381 | − | 1.80593i | −0.0166594 | − | 0.0612269i | ||||
\(871\) | −24.7286 | −0.837896 | ||||||||
\(872\) | 6.48154 | + | 11.2264i | 0.219493 | + | 0.380172i | ||||
\(873\) | 0.0881012 | + | 11.4073i | 0.00298177 | + | 0.386079i | ||||
\(874\) | 16.0740 | 0.543711 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.68370 | − | 6.18797i | −0.0568869 | − | 0.209072i | ||||
\(877\) | 33.1902 | 1.12075 | 0.560376 | − | 0.828238i | \(-0.310657\pi\) | ||||
0.560376 | + | 0.828238i | \(0.310657\pi\) | |||||||
\(878\) | −9.56205 | + | 16.5620i | −0.322704 | + | 0.558939i | ||||
\(879\) | −31.4792 | + | 31.7233i | −1.06177 | + | 1.07000i | ||||
\(880\) | −0.319953 | − | 0.554174i | −0.0107856 | − | 0.0186812i | ||||
\(881\) | 31.7179 | 1.06860 | 0.534301 | − | 0.845294i | \(-0.320575\pi\) | ||||
0.534301 | + | 0.845294i | \(0.320575\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.5231 | −1.33006 | −0.665029 | − | 0.746818i | \(-0.731581\pi\) | ||||
−0.665029 | + | 0.746818i | \(0.731581\pi\) | |||||||
\(884\) | 1.56785 | + | 2.71559i | 0.0527324 | + | 0.0913352i | ||||
\(885\) | −0.787743 | − | 0.207818i | −0.0264797 | − | 0.00698573i | ||||
\(886\) | 10.8131 | − | 18.7288i | 0.363272 | − | 0.629206i | ||||
\(887\) | −49.9026 | −1.67556 | −0.837782 | − | 0.546005i | \(-0.816148\pi\) | ||||
−0.837782 | + | 0.546005i | \(0.816148\pi\) | |||||||
\(888\) | 10.1932 | + | 2.68912i | 0.342062 | + | 0.0902411i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.701292 | −0.0235074 | ||||||||
\(891\) | 14.6144 | − | 26.2407i | 0.489599 | − | 0.879095i | ||||
\(892\) | −4.38228 | − | 7.59034i | −0.146730 | − | 0.254143i | ||||
\(893\) | 24.5507 | 0.821559 | ||||||||
\(894\) | 14.9998 | − | 15.1161i | 0.501667 | − | 0.505557i | ||||
\(895\) | −0.535910 | − | 0.928223i | −0.0179135 | − | 0.0310271i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.74003 | − | 5.78454i | 0.191654 | − | 0.193140i | ||||
\(898\) | −9.77891 | − | 16.9376i | −0.326326 | − | 0.565214i | ||||
\(899\) | −43.0222 | − | 74.5166i | −1.43487 | − | 2.48527i | ||||
\(900\) | −0.0905975 | − | 11.7305i | −0.00301992 | − | 0.391018i | ||||
\(901\) | −8.04721 | + | 13.9382i | −0.268092 | + | 0.464348i | ||||
\(902\) | 13.7747 | − | 23.8585i | 0.458648 | − | 0.794401i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.15671 | + | 5.46757i | 0.104990 | + | 0.181849i | ||||
\(905\) | 1.80210 | 0.0599037 | ||||||||
\(906\) | 15.1678 | − | 15.2854i | 0.503917 | − | 0.507824i | ||||
\(907\) | −13.9216 | −0.462259 | −0.231129 | − | 0.972923i | \(-0.574242\pi\) | ||||
−0.231129 | + | 0.972923i | \(0.574242\pi\) | |||||||
\(908\) | 9.31574 | − | 16.1353i | 0.309154 | − | 0.535470i | ||||
\(909\) | 45.1853 | − | 26.5551i | 1.49870 | − | 0.880778i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.70428 | − | 4.68394i | 0.0895967 | − | 0.155186i | −0.817744 | − | 0.575582i | \(-0.804776\pi\) |
0.907341 | + | 0.420396i | \(0.138109\pi\) | |||||||
\(912\) | −6.35163 | − | 23.3437i | −0.210323 | − | 0.772986i | ||||
\(913\) | 1.95042 | − | 3.37822i | 0.0645494 | − | 0.111803i | ||||
\(914\) | 0.267681 | − | 0.463637i | 0.00885409 | − | 0.0153357i | ||||
\(915\) | −0.729683 | + | 0.735340i | −0.0241226 | + | 0.0243096i | ||||
\(916\) | −0.746758 | + | 1.29342i | −0.0246736 | + | 0.0427359i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 8.90089 | − | 2.49585i | 0.293773 | − | 0.0823754i | ||||
\(919\) | −17.0142 | + | 29.4694i | −0.561245 | + | 0.972105i | 0.436143 | + | 0.899877i | \(0.356344\pi\) |
−0.997388 | + | 0.0722280i | \(0.976989\pi\) | |||||||
\(920\) | 0.614276 | 0.0202521 | ||||||||
\(921\) | 10.1369 | + | 37.2554i | 0.334023 | + | 1.22761i | ||||
\(922\) | −8.81561 | −0.290327 | ||||||||
\(923\) | 4.08004 | + | 7.06683i | 0.134296 | + | 0.232608i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.94531 | + | 8.56554i | −0.162601 | + | 0.281633i | ||||
\(926\) | −5.78184 | + | 10.0144i | −0.190003 | + | 0.329095i | ||||
\(927\) | −22.5847 | + | 13.2729i | −0.741778 | + | 0.435939i | ||||
\(928\) | −19.2082 | − | 33.2696i | −0.630541 | − | 1.09213i | ||||
\(929\) | 5.31646 | + | 9.20837i | 0.174427 | + | 0.302117i | 0.939963 | − | 0.341277i | \(-0.110859\pi\) |
−0.765536 | + | 0.643393i | \(0.777526\pi\) | |||||||
\(930\) | −0.489857 | − | 1.80033i | −0.0160631 | − | 0.0590353i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.56375 | + | 4.44055i | 0.0839785 | + | 0.145455i | ||||
\(933\) | −2.19369 | − | 0.578729i | −0.0718183 | − | 0.0189467i | ||||
\(934\) | 24.1491 | 0.790183 | ||||||||
\(935\) | −0.283900 | − | 0.491729i | −0.00928451 | − | 0.0160812i | ||||
\(936\) | −19.8680 | − | 11.2671i | −0.649406 | − | 0.368277i | ||||
\(937\) | −52.6692 | −1.72063 | −0.860314 | − | 0.509765i | \(-0.829732\pi\) | ||||
−0.860314 | + | 0.509765i | \(0.829732\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.3241 | + | 26.5282i | −0.859053 | + | 0.865714i | ||||
\(940\) | 0.264163 | 0.00861605 | ||||||||
\(941\) | −17.1828 | + | 29.7615i | −0.560143 | + | 0.970197i | 0.437340 | + | 0.899296i | \(0.355921\pi\) |
−0.997483 | + | 0.0709006i | \(0.977413\pi\) | |||||||
\(942\) | −6.12147 | − | 22.4978i | −0.199448 | − | 0.733017i | ||||
\(943\) | 7.10057 | + | 12.2985i | 0.231226 | + | 0.400496i | ||||
\(944\) | 8.10825 | 0.263901 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.7791 | −0.903175 | ||||||||
\(947\) | 20.2920 | + | 35.1468i | 0.659401 | + | 1.14212i | 0.980771 | + | 0.195162i | \(0.0625234\pi\) |
−0.321370 | + | 0.946954i | \(0.604143\pi\) | |||||||
\(948\) | −2.74241 | − | 10.0790i | −0.0890692 | − | 0.327349i | ||||
\(949\) | 5.85736 | − | 10.1453i | 0.190138 | − | 0.329329i | ||||
\(950\) | 42.2685 | 1.37137 | ||||||||
\(951\) | −30.2341 | + | 30.4685i | −0.980408 | + | 0.988009i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.6904 | −0.735013 | −0.367507 | − | 0.930021i | \(-0.619789\pi\) | ||||
−0.367507 | + | 0.930021i | \(0.619789\pi\) | |||||||
\(954\) | −0.254918 | − | 33.0066i | −0.00825326 | − | 1.06863i | ||||
\(955\) | −1.18122 | − | 2.04593i | −0.0382234 | − | 0.0662049i | ||||
\(956\) | 16.7318 | 0.541144 | ||||||||
\(957\) | 51.9258 | + | 13.6988i | 1.67852 | + | 0.442819i | ||||
\(958\) | −2.20656 | − | 3.82187i | −0.0712907 | − | 0.123479i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.393096 | − | 1.44472i | −0.0126871 | − | 0.0466280i | ||||
\(961\) | −27.3888 | − | 47.4387i | −0.883509 | − | 1.53028i | ||||
\(962\) | 2.71104 | + | 4.69566i | 0.0874074 | + | 0.151394i | ||||
\(963\) | 0.420432 | + | 54.4373i | 0.0135482 | + | 1.75422i | ||||
\(964\) | −7.86395 | + | 13.6208i | −0.253281 | + | 0.438695i | ||||
\(965\) | −0.0135411 | + | 0.0234539i | −0.000435904 | + | 0.000755008i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.1388 | − | 21.0250i | −0.390357 | − | 0.676118i | 0.602139 | − | 0.798391i | \(-0.294315\pi\) |
−0.992497 | + | 0.122273i | \(0.960982\pi\) | |||||||
\(968\) | 0.422650 | 0.0135845 | ||||||||
\(969\) | −5.63591 | − | 20.7132i | −0.181052 | − | 0.665405i | ||||
\(970\) | −0.442272 | −0.0142005 | ||||||||
\(971\) | 22.7886 | − | 39.4709i | 0.731319 | − | 1.26668i | −0.225000 | − | 0.974359i | \(-0.572238\pi\) |
0.956319 | − | 0.292324i | \(-0.0944285\pi\) | |||||||
\(972\) | 8.47121 | − | 8.80481i | 0.271714 | − | 0.282414i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −14.5988 | + | 25.2858i | −0.467774 | + | 0.810209i | ||||
\(975\) | 15.0941 | − | 15.2111i | 0.483398 | − | 0.487146i | ||||
\(976\) | 5.15508 | − | 8.92885i | 0.165010 | − | 0.285806i | ||||
\(977\) | 7.34481 | − | 12.7216i | 0.234981 | − | 0.407000i | −0.724286 | − | 0.689500i | \(-0.757830\pi\) |
0.959267 | + | 0.282500i | \(0.0911637\pi\) | |||||||
\(978\) | −4.49475 | − | 16.5192i | −0.143726 | − | 0.528226i | ||||
\(979\) | 10.0612 | − | 17.4266i | 0.321558 | − | 0.556956i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.0189 | − | 6.24881i | −0.351807 | − | 0.199509i | ||||
\(982\) | −15.6764 | + | 27.1524i | −0.500255 | + | 0.866467i | ||||
\(983\) | 44.5909 | 1.42223 | 0.711115 | − | 0.703076i | \(-0.248191\pi\) | ||||
0.711115 | + | 0.703076i | \(0.248191\pi\) | |||||||
\(984\) | 28.0360 | − | 28.2533i | 0.893754 | − | 0.900684i | ||||
\(985\) | 0.0805096 | 0.00256525 | ||||||||
\(986\) | 8.26404 | + | 14.3137i | 0.263181 | + | 0.455842i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.46673 | + | 12.9328i | −0.237548 | + | 0.411446i | ||||
\(989\) | 7.15976 | − | 12.4011i | 0.227667 | − | 0.394331i | ||||
\(990\) | 1.01294 | + | 0.574436i | 0.0321933 | + | 0.0182568i | ||||
\(991\) | −12.0915 | − | 20.9430i | −0.384098 | − | 0.665277i | 0.607546 | − | 0.794285i | \(-0.292154\pi\) |
−0.991644 | + | 0.129007i | \(0.958821\pi\) | |||||||
\(992\) | −19.1487 | − | 33.1665i | −0.607971 | − | 1.05304i | ||||
\(993\) | 16.8911 | − | 17.0221i | 0.536024 | − | 0.540179i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.265311 | − | 0.459532i | −0.00841093 | − | 0.0145682i | ||||
\(996\) | 1.11771 | − | 1.12638i | 0.0354160 | − | 0.0356906i | ||||
\(997\) | 10.8652 | 0.344105 | 0.172053 | − | 0.985088i | \(-0.444960\pi\) | ||||
0.172053 | + | 0.985088i | \(0.444960\pi\) | |||||||
\(998\) | −4.09760 | − | 7.09726i | −0.129707 | − | 0.224660i | ||||
\(999\) | −9.91899 | + | 2.78133i | −0.313823 | + | 0.0879974i |
(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 | 441.2.g.h.79.8 | 24 | ||
3.2 | odd | 2 | 1323.2.g.h.667.6 | 24 | |||
7.2 | even | 3 | 441.2.f.h.295.7 | yes | 24 | ||
7.3 | odd | 6 | 441.2.h.h.214.5 | 24 | |||
7.4 | even | 3 | 441.2.h.h.214.6 | 24 | |||
7.5 | odd | 6 | 441.2.f.h.295.8 | yes | 24 | ||
7.6 | odd | 2 | inner | 441.2.g.h.79.7 | 24 | ||
9.4 | even | 3 | 441.2.h.h.373.6 | 24 | |||
9.5 | odd | 6 | 1323.2.h.h.226.7 | 24 | |||
21.2 | odd | 6 | 1323.2.f.h.883.6 | 24 | |||
21.5 | even | 6 | 1323.2.f.h.883.5 | 24 | |||
21.11 | odd | 6 | 1323.2.h.h.802.7 | 24 | |||
21.17 | even | 6 | 1323.2.h.h.802.8 | 24 | |||
21.20 | even | 2 | 1323.2.g.h.667.5 | 24 | |||
63.2 | odd | 6 | 3969.2.a.bi.1.8 | 12 | |||
63.4 | even | 3 | inner | 441.2.g.h.67.8 | 24 | ||
63.5 | even | 6 | 1323.2.f.h.442.5 | 24 | |||
63.13 | odd | 6 | 441.2.h.h.373.5 | 24 | |||
63.16 | even | 3 | 3969.2.a.bh.1.5 | 12 | |||
63.23 | odd | 6 | 1323.2.f.h.442.6 | 24 | |||
63.31 | odd | 6 | inner | 441.2.g.h.67.7 | 24 | ||
63.32 | odd | 6 | 1323.2.g.h.361.6 | 24 | |||
63.40 | odd | 6 | 441.2.f.h.148.8 | yes | 24 | ||
63.41 | even | 6 | 1323.2.h.h.226.8 | 24 | |||
63.47 | even | 6 | 3969.2.a.bi.1.7 | 12 | |||
63.58 | even | 3 | 441.2.f.h.148.7 | ✓ | 24 | ||
63.59 | even | 6 | 1323.2.g.h.361.5 | 24 | |||
63.61 | odd | 6 | 3969.2.a.bh.1.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.7 | ✓ | 24 | 63.58 | even | 3 | ||
441.2.f.h.148.8 | yes | 24 | 63.40 | odd | 6 | ||
441.2.f.h.295.7 | yes | 24 | 7.2 | even | 3 | ||
441.2.f.h.295.8 | yes | 24 | 7.5 | odd | 6 | ||
441.2.g.h.67.7 | 24 | 63.31 | odd | 6 | inner | ||
441.2.g.h.67.8 | 24 | 63.4 | even | 3 | inner | ||
441.2.g.h.79.7 | 24 | 7.6 | odd | 2 | inner | ||
441.2.g.h.79.8 | 24 | 1.1 | even | 1 | trivial | ||
441.2.h.h.214.5 | 24 | 7.3 | odd | 6 | |||
441.2.h.h.214.6 | 24 | 7.4 | even | 3 | |||
441.2.h.h.373.5 | 24 | 63.13 | odd | 6 | |||
441.2.h.h.373.6 | 24 | 9.4 | even | 3 | |||
1323.2.f.h.442.5 | 24 | 63.5 | even | 6 | |||
1323.2.f.h.442.6 | 24 | 63.23 | odd | 6 | |||
1323.2.f.h.883.5 | 24 | 21.5 | even | 6 | |||
1323.2.f.h.883.6 | 24 | 21.2 | odd | 6 | |||
1323.2.g.h.361.5 | 24 | 63.59 | even | 6 | |||
1323.2.g.h.361.6 | 24 | 63.32 | odd | 6 | |||
1323.2.g.h.667.5 | 24 | 21.20 | even | 2 | |||
1323.2.g.h.667.6 | 24 | 3.2 | odd | 2 | |||
1323.2.h.h.226.7 | 24 | 9.5 | odd | 6 | |||
1323.2.h.h.226.8 | 24 | 63.41 | even | 6 | |||
1323.2.h.h.802.7 | 24 | 21.11 | odd | 6 | |||
1323.2.h.h.802.8 | 24 | 21.17 | even | 6 | |||
3969.2.a.bh.1.5 | 12 | 63.16 | even | 3 | |||
3969.2.a.bh.1.6 | 12 | 63.61 | odd | 6 | |||
3969.2.a.bi.1.7 | 12 | 63.47 | even | 6 | |||
3969.2.a.bi.1.8 | 12 | 63.2 | odd | 6 |