Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(214,441)]
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([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.214");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.h (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 | 214.6 | ||
Character | \(\chi\) | \(=\) | 441.214 |
Dual form | 441.2.h.h.373.6 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.10281 | −0.779807 | −0.389903 | − | 0.920856i | \(-0.627492\pi\) | ||||
−0.389903 | + | 0.920856i | \(0.627492\pi\) | |||||||
\(3\) | 1.22001 | − | 1.22947i | 0.704371 | − | 0.709832i | ||||
\(4\) | −0.783802 | −0.391901 | ||||||||
\(5\) | 0.0527330 | − | 0.0913363i | 0.0235829 | − | 0.0408468i | −0.853993 | − | 0.520284i | \(-0.825826\pi\) |
0.877576 | + | 0.479438i | \(0.159159\pi\) | |||||||
\(6\) | −1.34544 | + | 1.35587i | −0.549273 | + | 0.553532i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.07001 | 1.08541 | ||||||||
\(9\) | −0.0231690 | − | 2.99991i | −0.00772300 | − | 0.999970i | ||||
\(10\) | −0.0581547 | + | 0.100727i | −0.0183901 | + | 0.0318527i | ||||
\(11\) | −1.66866 | − | 2.89020i | −0.503119 | − | 0.871428i | −0.999994 | − | 0.00360543i | \(-0.998852\pi\) |
0.496874 | − | 0.867822i | \(-0.334481\pi\) | |||||||
\(12\) | −0.956244 | + | 0.963657i | −0.276044 | + | 0.278184i | ||||
\(13\) | 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 | ||||
\(16\) | −1.81805 | −0.454512 | ||||||||
\(17\) | 0.806594 | − | 1.39706i | 0.195628 | − | 0.338837i | −0.751478 | − | 0.659758i | \(-0.770659\pi\) |
0.947106 | + | 0.320921i | \(0.103992\pi\) | |||||||
\(18\) | 0.0255511 | + | 3.30834i | 0.00602245 | + | 0.779784i | ||||
\(19\) | −3.84133 | − | 6.65338i | −0.881262 | − | 1.52639i | −0.849939 | − | 0.526880i | \(-0.823362\pi\) |
−0.0313221 | − | 0.999509i | \(-0.509972\pi\) | |||||||
\(20\) | −0.0413323 | + | 0.0715896i | −0.00924218 | + | 0.0160079i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.84022 | + | 3.18735i | 0.392336 | + | 0.679546i | ||||
\(23\) | 0.948593 | − | 1.64301i | 0.197795 | − | 0.342592i | −0.750018 | − | 0.661417i | \(-0.769955\pi\) |
0.947813 | + | 0.318826i | \(0.103289\pi\) | |||||||
\(24\) | 3.74544 | − | 3.77448i | 0.764534 | − | 0.770462i | ||||
\(25\) | 2.49444 | + | 4.32049i | 0.498888 | + | 0.864099i | ||||
\(26\) | −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 | \(-0.164495\pi\) | |||||||
\(30\) | 0.0528911 | + | 0.194387i | 0.00965655 | + | 0.0354900i | ||||
\(31\) | −9.26162 | −1.66344 | −0.831718 | − | 0.555199i | \(-0.812642\pi\) | ||||
−0.831718 | + | 0.555199i | \(0.812642\pi\) | |||||||
\(32\) | −4.13506 | −0.730982 | ||||||||
\(33\) | −5.58917 | − | 1.47451i | −0.972950 | − | 0.256678i | ||||
\(34\) | −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 | 0.935930 | − | 0.352186i | \(-0.114561\pi\) |
−0.772967 | + | 0.634447i | \(0.781228\pi\) | |||||||
\(38\) | 4.23627 | + | 7.33744i | 0.687214 | + | 1.19029i | ||||
\(39\) | 4.15329 | + | 1.09570i | 0.665059 | + | 0.175452i | ||||
\(40\) | 0.161891 | − | 0.280404i | 0.0255973 | − | 0.0443357i | ||||
\(41\) | −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 | ||||
\(45\) | −0.275223 | − | 0.156078i | −0.0410278 | − | 0.0232668i | ||||
\(46\) | −1.04612 | + | 1.81194i | −0.154242 | + | 0.267155i | ||||
\(47\) | 3.19560 | 0.466127 | 0.233063 | − | 0.972462i | \(-0.425125\pi\) | ||||
0.233063 | + | 0.972462i | \(0.425125\pi\) | |||||||
\(48\) | −2.21803 | + | 2.23523i | −0.320145 | + | 0.322627i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.75090 | − | 4.76470i | −0.389036 | − | 0.673830i | ||||
\(51\) | −0.733589 | − | 2.69610i | −0.102723 | − | 0.377530i | ||||
\(52\) | −0.971894 | − | 1.68337i | −0.134777 | − | 0.233441i | ||||
\(53\) | 4.98839 | − | 8.64015i | 0.685209 | − | 1.18682i | −0.288163 | − | 0.957581i | \(-0.593044\pi\) |
0.973371 | − | 0.229234i | \(-0.0736223\pi\) | |||||||
\(54\) | 4.09866 | + | 4.00478i | 0.557757 | + | 0.544982i | ||||
\(55\) | −0.351974 | −0.0474601 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.8665 | − | 3.39438i | −1.70422 | − | 0.449597i | ||||
\(58\) | −5.12280 | + | 8.87296i | −0.672657 | + | 1.16508i | ||||
\(59\) | −4.45986 | −0.580625 | −0.290312 | − | 0.956932i | \(-0.593759\pi\) | ||||
−0.290312 | + | 0.956932i | \(0.593759\pi\) | |||||||
\(60\) | 0.0375913 | + | 0.138156i | 0.00485301 | + | 0.0178359i | ||||
\(61\) | 5.67100 | 0.726097 | 0.363048 | − | 0.931770i | \(-0.381736\pi\) | ||||
0.363048 | + | 0.931770i | \(0.381736\pi\) | |||||||
\(62\) | 10.2138 | 1.29716 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.19630 | 1.02454 | ||||||||
\(65\) | 0.261550 | 0.0324413 | ||||||||
\(66\) | 6.16381 | + | 1.62610i | 0.758713 | + | 0.200160i | ||||
\(67\) | 9.97141 | 1.21820 | 0.609101 | − | 0.793093i | \(-0.291530\pi\) | ||||
0.609101 | + | 0.793093i | \(0.291530\pi\) | |||||||
\(68\) | −0.632210 | + | 1.09502i | −0.0766667 | + | 0.132791i | ||||
\(69\) | −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 | \(0.437448\pi\) | |||||||
\(72\) | −0.0711292 | − | 9.20977i | −0.00838265 | − | 1.08538i | ||||
\(73\) | −2.36189 | + | 4.09091i | −0.276438 | + | 0.478805i | −0.970497 | − | 0.241113i | \(-0.922488\pi\) |
0.694059 | + | 0.719919i | \(0.255821\pi\) | |||||||
\(74\) | −1.09318 | − | 1.89345i | −0.127080 | − | 0.220109i | ||||
\(75\) | 8.35513 | + | 2.20421i | 0.964767 | + | 0.254520i | ||||
\(76\) | 3.01084 | + | 5.21493i | 0.345367 | + | 0.598194i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.58031 | − | 1.20835i | −0.518618 | − | 0.136819i | ||||
\(79\) | 7.69409 | 0.865653 | 0.432827 | − | 0.901477i | \(-0.357516\pi\) | ||||
0.432827 | + | 0.901477i | \(0.357516\pi\) | |||||||
\(80\) | −0.0958713 | + | 0.166054i | −0.0107187 | + | 0.0185654i | ||||
\(81\) | −8.99893 | + | 0.139010i | −0.999881 | + | 0.0154455i | ||||
\(82\) | 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 | ||||
\(86\) | 4.16189 | − | 7.20860i | 0.448788 | − | 0.777323i | ||||
\(87\) | −4.22477 | − | 15.5270i | −0.452943 | − | 1.66467i | ||||
\(88\) | −5.12280 | − | 8.87296i | −0.546093 | − | 0.945860i | ||||
\(89\) | 3.01477 | + | 5.22173i | 0.319565 | + | 0.553503i | 0.980397 | − | 0.197031i | \(-0.0631299\pi\) |
−0.660832 | + | 0.750534i | \(0.729797\pi\) | |||||||
\(90\) | 0.303519 | + | 0.172125i | 0.0319937 | + | 0.0181436i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.743509 | + | 1.28780i | −0.0775162 | + | 0.134262i | ||||
\(93\) | −11.2992 | + | 11.3868i | −1.17168 | + | 1.18076i | ||||
\(94\) | −3.52415 | −0.363489 | ||||||||
\(95\) | −0.810260 | −0.0831309 | ||||||||
\(96\) | −5.04480 | + | 5.08391i | −0.514883 | + | 0.518875i | ||||
\(97\) | 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 | ||||
\(101\) | 8.73512 | + | 15.1297i | 0.869177 | + | 1.50546i | 0.862839 | + | 0.505479i | \(0.168684\pi\) |
0.00633771 | + | 0.999980i | \(0.497983\pi\) | |||||||
\(102\) | 0.809012 | + | 2.97330i | 0.0801041 | + | 0.294400i | ||||
\(103\) | −4.36602 | + | 7.56217i | −0.430197 | + | 0.745123i | −0.996890 | − | 0.0788062i | \(-0.974889\pi\) |
0.566693 | + | 0.823929i | \(0.308223\pi\) | |||||||
\(104\) | 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 | 0.854471 | + | 0.519500i | \(0.173882\pi\) |
0.0226645 | + | 0.999743i | \(0.492785\pi\) | |||||||
\(108\) | 2.91304 | + | 2.84632i | 0.280308 | + | 0.273887i | ||||
\(109\) | 2.11124 | − | 3.65678i | 0.202220 | − | 0.350256i | −0.747023 | − | 0.664798i | \(-0.768518\pi\) |
0.949243 | + | 0.314542i | \(0.101851\pi\) | |||||||
\(110\) | 0.388161 | 0.0370097 | ||||||||
\(111\) | 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 | \(0.802495\pi\) | |||||||
\(114\) | 14.1894 | + | 3.74337i | 1.32896 | + | 0.350599i | ||||
\(115\) | −0.100044 | − | 0.173282i | −0.00932919 | − | 0.0161586i | ||||
\(116\) | −3.64093 | + | 6.30627i | −0.338052 | + | 0.585523i | ||||
\(117\) | 6.41417 | − | 3.76957i | 0.592990 | − | 0.348497i | ||||
\(118\) | 4.91840 | 0.452775 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.147238 | − | 0.541134i | −0.0134410 | − | 0.0493986i | ||||
\(121\) | −0.0688352 | + | 0.119226i | −0.00625774 | + | 0.0108387i | ||||
\(122\) | −6.25405 | −0.566215 | ||||||||
\(123\) | −12.5361 | − | 3.30721i | −1.13034 | − | 0.298201i | ||||
\(124\) | 7.25928 | 0.651902 | ||||||||
\(125\) | 1.05349 | 0.0942268 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.317159 | 0.0281433 | 0.0140717 | − | 0.999901i | \(-0.495521\pi\) | ||||
0.0140717 | + | 0.999901i | \(0.495521\pi\) | |||||||
\(128\) | −0.768871 | −0.0679592 | ||||||||
\(129\) | 3.43231 | + | 12.6145i | 0.302198 | + | 1.11064i | ||||
\(130\) | −0.288441 | −0.0252980 | ||||||||
\(131\) | −7.47816 | + | 12.9525i | −0.653370 | + | 1.13167i | 0.328930 | + | 0.944354i | \(0.393312\pi\) |
−0.982300 | + | 0.187315i | \(0.940021\pi\) | |||||||
\(132\) | 4.38081 | + | 1.15572i | 0.381300 | + | 0.100593i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −10.9966 | −0.949962 | ||||||||
\(135\) | −0.527666 | + | 0.147960i | −0.0454143 | + | 0.0127344i | ||||
\(136\) | 2.47625 | − | 4.28900i | 0.212337 | − | 0.367779i | ||||
\(137\) | 7.62367 | + | 13.2046i | 0.651334 | + | 1.12814i | 0.982799 | + | 0.184676i | \(0.0591235\pi\) |
−0.331466 | + | 0.943467i | \(0.607543\pi\) | |||||||
\(138\) | 0.951437 | + | 3.49674i | 0.0809917 | + | 0.297663i | ||||
\(139\) | 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 | ||||
\(142\) | −3.62872 | −0.304516 | ||||||||
\(143\) | 4.13818 | − | 7.16754i | 0.346052 | − | 0.599380i | ||||
\(144\) | 0.0421224 | + | 5.45399i | 0.00351020 | + | 0.454499i | ||||
\(145\) | −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 | ||||
\(149\) | 5.57430 | − | 9.65497i | 0.456664 | − | 0.790966i | −0.542118 | − | 0.840303i | \(-0.682377\pi\) |
0.998782 | + | 0.0493365i | \(0.0157107\pi\) | |||||||
\(150\) | −9.21415 | − | 2.43083i | −0.752332 | − | 0.198476i | ||||
\(151\) | 5.63676 | + | 9.76315i | 0.458713 | + | 0.794514i | 0.998893 | − | 0.0470354i | \(-0.0149774\pi\) |
−0.540180 | + | 0.841549i | \(0.681644\pi\) | |||||||
\(152\) | −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 | ||||
\(156\) | −3.25536 | − | 0.858812i | −0.260637 | − | 0.0687600i | ||||
\(157\) | 12.2064 | 0.974173 | 0.487087 | − | 0.873354i | \(-0.338060\pi\) | ||||
0.487087 | + | 0.873354i | \(0.338060\pi\) | |||||||
\(158\) | −8.48515 | −0.675042 | ||||||||
\(159\) | −4.53689 | − | 16.6741i | −0.359799 | − | 1.32234i | ||||
\(160\) | −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 | 0.635422 | − | 0.772165i | \(-0.280826\pi\) |
−0.986426 | + | 0.164209i | \(0.947493\pi\) | |||||||
\(164\) | 2.93352 | + | 5.08101i | 0.229070 | + | 0.396760i | ||||
\(165\) | −0.429410 | + | 0.432739i | −0.0334295 | + | 0.0336887i | ||||
\(166\) | −0.644515 | + | 1.11633i | −0.0500240 | + | 0.0866442i | ||||
\(167\) | −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 | ||||
\(171\) | −19.8705 | + | 11.6778i | −1.51954 | + | 0.893024i | ||||
\(172\) | 2.95798 | − | 5.12337i | 0.225544 | − | 0.390653i | ||||
\(173\) | 2.82933 | 0.215110 | 0.107555 | − | 0.994199i | \(-0.465698\pi\) | ||||
0.107555 | + | 0.994199i | \(0.465698\pi\) | |||||||
\(174\) | 4.65914 | + | 17.1234i | 0.353208 | + | 1.29812i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.03370 | + | 5.25453i | 0.228674 | + | 0.396075i | ||||
\(177\) | −5.44106 | + | 5.48325i | −0.408975 | + | 0.412146i | ||||
\(178\) | −3.32473 | − | 5.75860i | −0.249199 | − | 0.431625i | ||||
\(179\) | 5.08135 | − | 8.80115i | 0.379798 | − | 0.657829i | −0.611235 | − | 0.791449i | \(-0.709327\pi\) |
0.991033 | + | 0.133620i | \(0.0426603\pi\) | |||||||
\(180\) | 0.215720 | + | 0.122334i | 0.0160788 | + | 0.00911827i | ||||
\(181\) | −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 | ||||
\(184\) | 2.91220 | − | 5.04407i | 0.214690 | − | 0.371854i | ||||
\(185\) | 0.209090 | 0.0153726 | ||||||||
\(186\) | 12.4609 | − | 12.5576i | 0.913681 | − | 0.920765i | ||||
\(187\) | −5.38371 | −0.393696 | ||||||||
\(188\) | −2.50472 | −0.182676 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.893566 | 0.0648261 | ||||||||
\(191\) | −22.4000 | −1.62081 | −0.810404 | − | 0.585872i | \(-0.800752\pi\) | ||||
−0.810404 | + | 0.585872i | \(0.800752\pi\) | |||||||
\(192\) | 9.99954 | − | 10.0771i | 0.721654 | − | 0.727249i | ||||
\(193\) | −0.256786 | −0.0184839 | −0.00924194 | − | 0.999957i | \(-0.502942\pi\) | ||||
−0.00924194 | + | 0.999957i | \(0.502942\pi\) | |||||||
\(194\) | −2.09675 | + | 3.63168i | −0.150538 | + | 0.260739i | ||||
\(195\) | 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 | \(0.508657\pi\) | |||||||
\(198\) | 9.51913 | − | 5.59434i | 0.676495 | − | 0.397572i | ||||
\(199\) | 2.51561 | − | 4.35716i | 0.178327 | − | 0.308871i | −0.762981 | − | 0.646421i | \(-0.776265\pi\) |
0.941307 | + | 0.337550i | \(0.109598\pi\) | |||||||
\(200\) | 7.65796 | + | 13.2640i | 0.541500 | + | 0.937905i | ||||
\(201\) | 12.1652 | − | 12.2595i | 0.858066 | − | 0.864719i | ||||
\(202\) | −9.63321 | − | 16.6852i | −0.677790 | − | 1.17397i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.574988 | + | 2.11321i | 0.0402572 | + | 0.147954i | ||||
\(205\) | −0.789452 | −0.0551377 | ||||||||
\(206\) | 4.81491 | − | 8.33966i | 0.335470 | − | 0.581052i | ||||
\(207\) | −4.95087 | − | 2.80763i | −0.344109 | − | 0.195144i | ||||
\(208\) | −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 | \(0.913174\pi\) | |||||||
\(212\) | −3.90991 | + | 6.77217i | −0.268534 | + | 0.465114i | ||||
\(213\) | 4.01434 | − | 4.04546i | 0.275058 | − | 0.277190i | ||||
\(214\) | −10.0060 | − | 17.3309i | −0.683996 | − | 1.18472i | ||||
\(215\) | 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 | ||||
\(219\) | 2.14812 | + | 7.89480i | 0.145156 | + | 0.533481i | ||||
\(220\) | 0.275878 | 0.0185997 | ||||||||
\(221\) | 4.00062 | 0.269111 | ||||||||
\(222\) | −3.66162 | − | 0.965990i | −0.245752 | − | 0.0648330i | ||||
\(223\) | 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 | ||||
\(227\) | −11.8853 | − | 20.5860i | −0.788857 | − | 1.36634i | −0.926668 | − | 0.375881i | \(-0.877340\pi\) |
0.137811 | − | 0.990459i | \(-0.455993\pi\) | |||||||
\(228\) | 10.0848 | + | 2.66052i | 0.667884 | + | 0.176198i | ||||
\(229\) | 0.952737 | − | 1.65019i | 0.0629586 | − | 0.109048i | −0.832828 | − | 0.553532i | \(-0.813280\pi\) |
0.895787 | + | 0.444484i | \(0.146613\pi\) | |||||||
\(230\) | 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 | 0.738766 | − | 0.673962i | \(-0.235409\pi\) |
−0.953051 | + | 0.302809i | \(0.902075\pi\) | |||||||
\(234\) | −7.07363 | + | 4.15713i | −0.462418 | + | 0.271760i | ||||
\(235\) | 0.168514 | − | 0.291875i | 0.0109926 | − | 0.0190398i | ||||
\(236\) | 3.49565 | 0.227547 | ||||||||
\(237\) | 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 | \(0.590764\pi\) | |||||||
\(240\) | 0.0871940 | + | 0.320457i | 0.00562835 | + | 0.0206854i | ||||
\(241\) | 10.0331 | + | 17.3778i | 0.646288 | + | 1.11940i | 0.984003 | + | 0.178155i | \(0.0570127\pi\) |
−0.337715 | + | 0.941248i | \(0.609654\pi\) | |||||||
\(242\) | 0.0759124 | − | 0.131484i | 0.00487983 | − | 0.00845212i | ||||
\(243\) | −10.8078 | + | 11.2335i | −0.693323 | + | 0.720627i | ||||
\(244\) | −4.44494 | −0.284558 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 13.8250 | + | 3.64724i | 0.881451 | + | 0.232540i | ||||
\(247\) | 9.52629 | − | 16.5000i | 0.606144 | − | 1.04987i | ||||
\(248\) | −28.4333 | −1.80552 | ||||||||
\(249\) | −0.531531 | − | 1.95349i | −0.0336844 | − | 0.123798i | ||||
\(250\) | −1.16180 | −0.0734787 | ||||||||
\(251\) | −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 | ||||||||
\(254\) | −0.349767 | −0.0219464 | ||||||||
\(255\) | −0.284936 | − | 0.0751704i | −0.0178434 | − | 0.00470735i | ||||
\(256\) | −15.5447 | −0.971542 | ||||||||
\(257\) | 7.19415 | − | 12.4606i | 0.448759 | − | 0.777273i | −0.549546 | − | 0.835463i | \(-0.685199\pi\) |
0.998306 | + | 0.0581897i | \(0.0185328\pi\) | |||||||
\(258\) | −3.78519 | − | 13.9114i | −0.235656 | − | 0.866088i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.205004 | −0.0127138 | ||||||||
\(261\) | −24.2441 | − | 13.7488i | −1.50067 | − | 0.851030i | ||||
\(262\) | 8.24701 | − | 14.2842i | 0.509502 | − | 0.882484i | ||||
\(263\) | 0.769503 | + | 1.33282i | 0.0474496 | + | 0.0821851i | 0.888775 | − | 0.458344i | \(-0.151557\pi\) |
−0.841325 | + | 0.540529i | \(0.818224\pi\) | |||||||
\(264\) | −17.1588 | − | 4.52675i | −1.05605 | − | 0.278602i | ||||
\(265\) | −0.526106 | − | 0.911243i | −0.0323185 | − | 0.0559772i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.0980 | + | 2.66399i | 0.617986 | + | 0.163034i | ||||
\(268\) | −7.81562 | −0.477415 | ||||||||
\(269\) | 13.1285 | − | 22.7393i | 0.800461 | − | 1.38644i | −0.118852 | − | 0.992912i | \(-0.537921\pi\) |
0.919313 | − | 0.393527i | \(-0.128745\pi\) | |||||||
\(270\) | 0.581917 | − | 0.163172i | 0.0354144 | − | 0.00993035i | ||||
\(271\) | −8.96673 | − | 15.5308i | −0.544690 | − | 0.943431i | −0.998626 | − | 0.0523969i | \(-0.983314\pi\) |
0.453936 | − | 0.891034i | \(-0.350019\pi\) | |||||||
\(272\) | −1.46643 | + | 2.53993i | −0.0889152 | + | 0.154006i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.40748 | − | 14.5622i | −0.507915 | − | 0.879734i | ||||
\(275\) | 8.32473 | − | 14.4188i | 0.502000 | − | 0.869489i | ||||
\(276\) | 0.676214 | + | 2.48524i | 0.0407033 | + | 0.149594i | ||||
\(277\) | 9.43563 | + | 16.3430i | 0.566932 | + | 0.981955i | 0.996867 | + | 0.0790954i | \(0.0252032\pi\) |
−0.429935 | + | 0.902860i | \(0.641463\pi\) | |||||||
\(278\) | −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 | \(0.214235\pi\) | |||||||
\(282\) | −4.29949 | + | 4.33282i | −0.256031 | + | 0.258016i | ||||
\(283\) | 15.3927 | 0.915000 | 0.457500 | − | 0.889210i | \(-0.348745\pi\) | ||||
0.457500 | + | 0.889210i | \(0.348745\pi\) | |||||||
\(284\) | −2.57904 | −0.153038 | ||||||||
\(285\) | −0.988522 | + | 0.996187i | −0.0585550 | + | 0.0590090i | ||||
\(286\) | −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 | ||||
\(290\) | 0.540282 | + | 0.935796i | 0.0317265 | + | 0.0549518i | ||||
\(291\) | −1.72919 | − | 6.35516i | −0.101367 | − | 0.372546i | ||||
\(292\) | 1.85126 | − | 3.20647i | 0.108337 | − | 0.187644i | ||||
\(293\) | 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 | ||||
\(297\) | −4.29389 | + | 16.8012i | −0.249157 | + | 0.974903i | ||||
\(298\) | −6.14741 | + | 10.6476i | −0.356110 | + | 0.616801i | ||||
\(299\) | 4.70492 | 0.272093 | ||||||||
\(300\) | −6.54877 | − | 1.72766i | −0.378093 | − | 0.0997465i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.21629 | − | 10.7669i | −0.357707 | − | 0.619567i | ||||
\(303\) | 29.2583 | + | 7.71877i | 1.68085 | + | 0.443432i | ||||
\(304\) | 6.98373 | + | 12.0962i | 0.400544 | + | 0.693763i | ||||
\(305\) | 0.299049 | − | 0.517968i | 0.0171235 | − | 0.0296588i | ||||
\(306\) | 4.64257 | + | 2.63279i | 0.265398 | + | 0.150507i | ||||
\(307\) | 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 | ||||
\(310\) | 0.538607 | − | 0.932894i | 0.0305908 | − | 0.0529848i | ||||
\(311\) | 1.30986 | 0.0742755 | 0.0371377 | − | 0.999310i | \(-0.488176\pi\) | ||||
0.0371377 | + | 0.999310i | \(0.488176\pi\) | |||||||
\(312\) | 12.7507 | + | 3.36382i | 0.721865 | + | 0.190439i | ||||
\(313\) | −21.5770 | −1.21960 | −0.609802 | − | 0.792554i | \(-0.708751\pi\) | ||||
−0.609802 | + | 0.792554i | \(0.708751\pi\) | |||||||
\(314\) | −13.4613 | −0.759667 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.03065 | −0.339250 | ||||||||
\(317\) | −24.7819 | −1.39189 | −0.695946 | − | 0.718094i | \(-0.745015\pi\) | ||||
−0.695946 | + | 0.718094i | \(0.745015\pi\) | |||||||
\(318\) | 5.00335 | + | 18.3884i | 0.280574 | + | 1.03117i | ||||
\(319\) | −31.0051 | −1.73595 | ||||||||
\(320\) | 0.432216 | − | 0.748620i | 0.0241616 | − | 0.0418491i | ||||
\(321\) | 30.3906 | + | 8.01748i | 1.69624 | + | 0.447492i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.3936 | −0.689597 | ||||||||
\(324\) | 7.05338 | − | 0.108956i | 0.391854 | − | 0.00605312i | ||||
\(325\) | −6.18608 | + | 10.7146i | −0.343142 | + | 0.594339i | ||||
\(326\) | 4.94206 | + | 8.55990i | 0.273715 | + | 0.474089i | ||||
\(327\) | −1.92015 | − | 7.05699i | −0.106185 | − | 0.390252i | ||||
\(328\) | −11.4901 | − | 19.9014i | −0.634434 | − | 1.09887i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.473559 | − | 0.477231i | 0.0260686 | − | 0.0262707i | ||||
\(331\) | 13.8451 | 0.760996 | 0.380498 | − | 0.924782i | \(-0.375753\pi\) | ||||
0.380498 | + | 0.924782i | \(0.375753\pi\) | |||||||
\(332\) | −0.458076 | + | 0.793410i | −0.0251402 | + | 0.0435440i | ||||
\(333\) | 5.12766 | − | 3.01349i | 0.280994 | − | 0.165139i | ||||
\(334\) | 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 | \(0.803911\pi\) | |||||||
\(338\) | −3.77706 | + | 6.54206i | −0.205445 | + | 0.355841i | ||||
\(339\) | 3.44408 | + | 0.908600i | 0.187057 | + | 0.0493484i | ||||
\(340\) | 0.0666767 | + | 0.115487i | 0.00361605 | + | 0.00626319i | ||||
\(341\) | 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 | ||||
\(345\) | −0.335099 | − | 0.0884040i | −0.0180411 | − | 0.00475951i | ||||
\(346\) | −3.12022 | −0.167744 | ||||||||
\(347\) | −14.5148 | −0.779195 | −0.389597 | − | 0.920985i | \(-0.627386\pi\) | ||||
−0.389597 | + | 0.920985i | \(0.627386\pi\) | |||||||
\(348\) | 3.31139 | + | 12.1701i | 0.177509 | + | 0.652385i | ||||
\(349\) | −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 | ||||
\(353\) | −2.07211 | − | 3.58900i | −0.110287 | − | 0.191023i | 0.805599 | − | 0.592462i | \(-0.201844\pi\) |
−0.915886 | + | 0.401438i | \(0.868510\pi\) | |||||||
\(354\) | 6.00048 | − | 6.04700i | 0.318922 | − | 0.321394i | ||||
\(355\) | 0.173514 | − | 0.300535i | 0.00920917 | − | 0.0159508i | ||||
\(356\) | −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 | 0.742040 | − | 0.670356i | \(-0.233859\pi\) |
−0.951565 | + | 0.307447i | \(0.900525\pi\) | |||||||
\(360\) | −0.844937 | − | 0.479163i | −0.0445321 | − | 0.0252541i | ||||
\(361\) | −20.0116 | + | 34.6612i | −1.05324 | + | 1.82427i | ||||
\(362\) | 18.8437 | 0.990405 | ||||||||
\(363\) | 0.0626049 | + | 0.230087i | 0.00328590 | + | 0.0120764i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.249099 | + | 0.431453i | 0.0130385 | + | 0.0225833i | ||||
\(366\) | −7.62998 | + | 7.68914i | −0.398826 | + | 0.401918i | ||||
\(367\) | −6.57455 | − | 11.3875i | −0.343189 | − | 0.594420i | 0.641834 | − | 0.766843i | \(-0.278174\pi\) |
−0.985023 | + | 0.172423i | \(0.944840\pi\) | |||||||
\(368\) | −1.72459 | + | 2.98708i | −0.0899004 | + | 0.155712i | ||||
\(369\) | −19.3603 | + | 11.3779i | −1.00785 | + | 0.592310i | ||||
\(370\) | −0.230588 | −0.0119877 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8.85636 | − | 8.92503i | 0.459181 | − | 0.462741i | ||||
\(373\) | −3.90543 | + | 6.76441i | −0.202216 | + | 0.350248i | −0.949242 | − | 0.314547i | \(-0.898147\pi\) |
0.747026 | + | 0.664794i | \(0.231481\pi\) | |||||||
\(374\) | 5.93723 | 0.307007 | ||||||||
\(375\) | 1.28526 | − | 1.29523i | 0.0663706 | − | 0.0668852i | ||||
\(376\) | 9.81055 | 0.505940 | ||||||||
\(377\) | 23.0398 | 1.18661 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.6147 | −1.62394 | −0.811968 | − | 0.583702i | \(-0.801604\pi\) | ||||
−0.811968 | + | 0.583702i | \(0.801604\pi\) | |||||||
\(380\) | 0.635084 | 0.0325791 | ||||||||
\(381\) | 0.386936 | − | 0.389936i | 0.0198233 | − | 0.0199770i | ||||
\(382\) | 24.7030 | 1.26392 | ||||||||
\(383\) | −5.36593 | + | 9.29407i | −0.274186 | + | 0.474905i | −0.969930 | − | 0.243386i | \(-0.921742\pi\) |
0.695743 | + | 0.718291i | \(0.255075\pi\) | |||||||
\(384\) | −0.938027 | + | 0.945300i | −0.0478685 | + | 0.0482396i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.283187 | 0.0144139 | ||||||||
\(387\) | 19.6965 | + | 11.1699i | 1.00123 | + | 0.567796i | ||||
\(388\) | −1.49022 | + | 2.58114i | −0.0756546 | + | 0.131038i | ||||
\(389\) | −12.0734 | − | 20.9118i | −0.612147 | − | 1.06027i | −0.990878 | − | 0.134763i | \(-0.956973\pi\) |
0.378731 | − | 0.925507i | \(-0.376361\pi\) | |||||||
\(390\) | −0.351900 | + | 0.354628i | −0.0178192 | + | 0.0179573i | ||||
\(391\) | −1.53026 | − | 2.65049i | −0.0773885 | − | 0.134041i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.80131 | + | 24.9963i | 0.343081 | + | 1.26090i | ||||
\(394\) | 0.841854 | 0.0424120 | ||||||||
\(395\) | 0.405733 | − | 0.702750i | 0.0204146 | − | 0.0353592i | ||||
\(396\) | 6.76553 | − | 3.97606i | 0.339981 | − | 0.199805i | ||||
\(397\) | 12.0285 | + | 20.8339i | 0.603691 | + | 1.04562i | 0.992257 | + | 0.124203i | \(0.0396373\pi\) |
−0.388566 | + | 0.921421i | \(0.627029\pi\) | |||||||
\(398\) | −2.77424 | + | 4.80513i | −0.139060 | + | 0.240860i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.53501 | − | 7.85487i | −0.226751 | − | 0.392744i | ||||
\(401\) | 0.781158 | − | 1.35301i | 0.0390092 | − | 0.0675659i | −0.845862 | − | 0.533402i | \(-0.820913\pi\) |
0.884871 | + | 0.465836i | \(0.154247\pi\) | |||||||
\(402\) | −13.4159 | + | 13.5199i | −0.669126 | + | 0.674314i | ||||
\(403\) | −11.4842 | − | 19.8911i | −0.572067 | − | 0.990849i | ||||
\(404\) | −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 | ||||
\(408\) | −2.25213 | − | 8.27708i | −0.111497 | − | 0.409776i | ||||
\(409\) | 22.3456 | 1.10492 | 0.552460 | − | 0.833539i | \(-0.313689\pi\) | ||||
0.552460 | + | 0.833539i | \(0.313689\pi\) | |||||||
\(410\) | 0.870619 | 0.0429968 | ||||||||
\(411\) | 25.5355 | + | 6.73664i | 1.25957 | + | 0.332294i | ||||
\(412\) | 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 | ||||
\(416\) | −5.12736 | − | 8.88086i | −0.251390 | − | 0.435420i | ||||
\(417\) | 13.5971 | + | 3.58711i | 0.665852 | + | 0.175661i | ||||
\(418\) | 14.1378 | − | 24.4873i | 0.691501 | − | 1.19771i | ||||
\(419\) | −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 | ||||
\(423\) | −0.0740389 | − | 9.58652i | −0.00359989 | − | 0.466113i | ||||
\(424\) | 15.3144 | − | 26.5254i | 0.743735 | − | 1.28819i | ||||
\(425\) | 8.04799 | 0.390385 | ||||||||
\(426\) | −4.42707 | + | 4.46139i | −0.214492 | + | 0.216155i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.11156 | − | 12.3176i | −0.343750 | − | 0.595393i | ||||
\(429\) | −3.76363 | − | 13.8322i | −0.181710 | − | 0.667825i | ||||
\(430\) | −0.438938 | − | 0.760263i | −0.0211675 | − | 0.0366631i | ||||
\(431\) | 9.70169 | − | 16.8038i | 0.467314 | − | 0.809411i | −0.531989 | − | 0.846751i | \(-0.678555\pi\) |
0.999303 | + | 0.0373401i | \(0.0118885\pi\) | |||||||
\(432\) | 6.75688 | + | 6.60211i | 0.325090 | + | 0.317644i | ||||
\(433\) | −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 | ||||
\(436\) | −1.65480 | + | 2.86619i | −0.0792503 | + | 0.137266i | ||||
\(437\) | −14.5754 | −0.697238 | ||||||||
\(438\) | −2.36897 | − | 8.70650i | −0.113194 | − | 0.416013i | ||||
\(439\) | −17.3412 | −0.827650 | −0.413825 | − | 0.910356i | \(-0.635807\pi\) | ||||
−0.413825 | + | 0.910356i | \(0.635807\pi\) | |||||||
\(440\) | −1.08056 | −0.0515139 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.41194 | −0.209854 | ||||||||
\(443\) | 19.6100 | 0.931698 | 0.465849 | − | 0.884864i | \(-0.345749\pi\) | ||||
0.465849 | + | 0.884864i | \(0.345749\pi\) | |||||||
\(444\) | −2.60242 | − | 0.686557i | −0.123506 | − | 0.0325826i | ||||
\(445\) | 0.635912 | 0.0301451 | ||||||||
\(446\) | −6.16590 | + | 10.6796i | −0.291964 | + | 0.505696i | ||||
\(447\) | −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 | \(0.637434\pi\) | |||||||
\(450\) | −14.2299 | + | 8.36285i | −0.670806 | + | 0.394228i | ||||
\(451\) | −12.4905 | + | 21.6342i | −0.588155 | + | 1.01871i | ||||
\(452\) | −0.805935 | − | 1.39592i | −0.0379080 | − | 0.0656586i | ||||
\(453\) | 18.8803 | + | 4.98091i | 0.887075 | + | 0.234023i | ||||
\(454\) | 13.1073 | + | 22.7025i | 0.615156 | + | 1.06548i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −39.5005 | − | 10.4208i | −1.84978 | − | 0.487999i | ||||
\(457\) | 0.485451 | 0.0227084 | 0.0113542 | − | 0.999936i | \(-0.496386\pi\) | ||||
0.0113542 | + | 0.999936i | \(0.496386\pi\) | |||||||
\(458\) | −1.05069 | + | 1.81985i | −0.0490956 | + | 0.0850361i | ||||
\(459\) | −8.07107 | + | 2.26317i | −0.376725 | + | 0.105636i | ||||
\(460\) | 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 | \(0.754987\pi\) | |||||||
\(464\) | −8.44523 | + | 14.6276i | −0.392060 | + | 0.679068i | ||||
\(465\) | 0.444189 | + | 1.63249i | 0.0205988 | + | 0.0757050i | ||||
\(466\) | 3.60721 | + | 6.24788i | 0.167101 | + | 0.289427i | ||||
\(467\) | 10.9489 | + | 18.9640i | 0.506653 | + | 0.877549i | 0.999970 | + | 0.00769944i | \(0.00245083\pi\) |
−0.493317 | + | 0.869849i | \(0.664216\pi\) | |||||||
\(468\) | −5.02744 | + | 2.95460i | −0.232394 | + | 0.136576i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.185839 | + | 0.321883i | −0.00857213 | + | 0.0148474i | ||||
\(471\) | 14.8918 | − | 15.0073i | 0.686179 | − | 0.691499i | ||||
\(472\) | −13.6918 | −0.630218 | ||||||||
\(473\) | 25.1893 | 1.15820 | ||||||||
\(474\) | −10.3519 | + | 10.4322i | −0.475480 | + | 0.479167i | ||||
\(475\) | 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 | ||||
\(479\) | 2.00085 | + | 3.46557i | 0.0914210 | + | 0.158346i | 0.908109 | − | 0.418733i | \(-0.137526\pi\) |
−0.816688 | + | 0.577079i | \(0.804192\pi\) | |||||||
\(480\) | 0.198318 | + | 0.728864i | 0.00905194 | + | 0.0332679i | ||||
\(481\) | −2.45829 | + | 4.25789i | −0.112088 | + | 0.194143i | ||||
\(482\) | −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 | ||||
\(486\) | 11.9190 | − | 12.3884i | 0.540658 | − | 0.561950i | ||||
\(487\) | 13.2377 | − | 22.9284i | 0.599859 | − | 1.03899i | −0.392982 | − | 0.919546i | \(-0.628557\pi\) |
0.992841 | − | 0.119440i | \(-0.0381100\pi\) | |||||||
\(488\) | 17.4100 | 0.788116 | ||||||||
\(489\) | −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 | \(0.611641\pi\) | |||||||
\(492\) | 9.82584 | + | 2.59220i | 0.442983 | + | 0.116865i | ||||
\(493\) | −7.49360 | − | 12.9793i | −0.337495 | − | 0.584558i | ||||
\(494\) | −10.5057 | + | 18.1965i | −0.472675 | + | 0.818697i | ||||
\(495\) | 0.00815487 | + | 1.05589i | 0.000366534 | + | 0.0474587i | ||||
\(496\) | 16.8381 | 0.756052 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.586179 | + | 2.15434i | 0.0262673 | + | 0.0965383i | ||||
\(499\) | 3.71559 | − | 6.43559i | 0.166333 | − | 0.288097i | −0.770795 | − | 0.637083i | \(-0.780141\pi\) |
0.937128 | + | 0.348986i | \(0.113474\pi\) | |||||||
\(500\) | −0.825726 | −0.0369276 | ||||||||
\(501\) | −29.1686 | − | 7.69510i | −1.30316 | − | 0.343792i | ||||
\(502\) | 7.51531 | 0.335425 | ||||||||
\(503\) | 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 | ||||||||
\(506\) | 6.98247 | 0.310409 | ||||||||
\(507\) | −3.11494 | − | 11.4481i | −0.138339 | − | 0.508428i | ||||
\(508\) | −0.248590 | −0.0110294 | ||||||||
\(509\) | 14.4532 | − | 25.0336i | 0.640625 | − | 1.10960i | −0.344668 | − | 0.938725i | \(-0.612009\pi\) |
0.985293 | − | 0.170871i | \(-0.0546581\pi\) | |||||||
\(510\) | 0.314232 | + | 0.0828990i | 0.0139144 | + | 0.00367083i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 18.6806 | 0.825575 | ||||||||
\(513\) | −9.88474 | + | 38.6771i | −0.436422 | + | 1.70764i | ||||
\(514\) | −7.93381 | + | 13.7418i | −0.349945 | + | 0.606123i | ||||
\(515\) | 0.460467 | + | 0.797553i | 0.0202906 | + | 0.0351444i | ||||
\(516\) | −2.69025 | − | 9.88727i | −0.118432 | − | 0.435263i | ||||
\(517\) | −5.33237 | − | 9.23593i | −0.234517 | − | 0.406196i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.45180 | − | 3.47856i | 0.151517 | − | 0.152692i | ||||
\(520\) | 0.802963 | 0.0352123 | ||||||||
\(521\) | −16.8995 | + | 29.2708i | −0.740381 | + | 1.28238i | 0.211941 | + | 0.977283i | \(0.432022\pi\) |
−0.952322 | + | 0.305095i | \(0.901312\pi\) | |||||||
\(522\) | 26.7368 | + | 15.1624i | 1.17024 | + | 0.663639i | ||||
\(523\) | 7.18895 | + | 12.4516i | 0.314351 | + | 0.544471i | 0.979299 | − | 0.202418i | \(-0.0648799\pi\) |
−0.664949 | + | 0.746889i | \(0.731547\pi\) | |||||||
\(524\) | 5.86140 | − | 10.1522i | 0.256056 | − | 0.443502i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.848618 | − | 1.46985i | −0.0370015 | − | 0.0640885i | ||||
\(527\) | −7.47036 | + | 12.9390i | −0.325414 | + | 0.563634i | ||||
\(528\) | 10.1614 | + | 2.68072i | 0.442218 | + | 0.116664i | ||||
\(529\) | 9.70034 | + | 16.8015i | 0.421754 | + | 0.730499i | ||||
\(530\) | 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 | ||||
\(534\) | −11.1362 | − | 2.93789i | −0.481910 | − | 0.127135i | ||||
\(535\) | 1.91382 | 0.0827417 | ||||||||
\(536\) | 30.6124 | 1.32225 | ||||||||
\(537\) | −4.62143 | − | 16.9848i | −0.199429 | − | 0.732948i | ||||
\(538\) | −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 | 0.998835 | + | 0.0482577i | \(0.0153669\pi\) |
−0.457625 | + | 0.889145i | \(0.651300\pi\) | |||||||
\(542\) | 9.88863 | + | 17.1276i | 0.424753 | + | 0.735694i | ||||
\(543\) | −20.8462 | + | 21.0078i | −0.894596 | + | 0.901532i | ||||
\(544\) | −3.33531 | + | 5.77693i | −0.143000 | + | 0.247684i | ||||
\(545\) | −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 | ||||
\(549\) | −0.131391 | − | 17.0125i | −0.00560764 | − | 0.726075i | ||||
\(550\) | −9.18062 | + | 15.9013i | −0.391463 | + | 0.678034i | ||||
\(551\) | −71.3752 | −3.04068 | ||||||||
\(552\) | −2.64861 | − | 9.73424i | −0.112732 | − | 0.414317i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −10.4057 | − | 18.0233i | −0.442098 | − | 0.765736i | ||||
\(555\) | 0.255092 | − | 0.257069i | 0.0108280 | − | 0.0109120i | ||||
\(556\) | −3.18179 | − | 5.51102i | −0.134938 | − | 0.233719i | ||||
\(557\) | −10.0229 | + | 17.3602i | −0.424686 | + | 0.735577i | −0.996391 | − | 0.0848820i | \(-0.972949\pi\) |
0.571705 | + | 0.820459i | \(0.306282\pi\) | |||||||
\(558\) | −0.236644 | − | 30.6406i | −0.0100180 | − | 1.29712i | ||||
\(559\) | −18.7181 | −0.791689 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.56817 | + | 6.61909i | −0.277308 | + | 0.279458i | ||||
\(562\) | 2.75238 | − | 4.76727i | 0.116102 | − | 0.201095i | ||||
\(563\) | 39.8013 | 1.67743 | 0.838713 | − | 0.544574i | \(-0.183309\pi\) | ||||
0.838713 | + | 0.544574i | \(0.183309\pi\) | |||||||
\(564\) | −3.05578 | + | 3.07947i | −0.128671 | + | 0.129669i | ||||
\(565\) | 0.216888 | 0.00912457 | ||||||||
\(566\) | −16.9753 | −0.713523 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.1017 | 0.423856 | ||||||||
\(569\) | 13.8159 | 0.579194 | 0.289597 | − | 0.957149i | \(-0.406479\pi\) | ||||
0.289597 | + | 0.957149i | \(0.406479\pi\) | |||||||
\(570\) | 1.09016 | − | 1.09861i | 0.0456616 | − | 0.0460156i | ||||
\(571\) | 10.4387 | 0.436846 | 0.218423 | − | 0.975854i | \(-0.429909\pi\) | ||||
0.218423 | + | 0.975854i | \(0.429909\pi\) | |||||||
\(572\) | −3.24352 | + | 5.61793i | −0.135618 | + | 0.234898i | ||||
\(573\) | −27.3281 | + | 27.5400i | −1.14165 | + | 1.15050i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.46483 | 0.394711 | ||||||||
\(576\) | −0.189900 | − | 24.5882i | −0.00791250 | − | 1.02451i | ||||
\(577\) | 12.7461 | − | 22.0769i | 0.530628 | − | 0.919075i | −0.468733 | − | 0.883340i | \(-0.655289\pi\) |
0.999361 | − | 0.0357353i | \(-0.0113773\pi\) | |||||||
\(578\) | −7.93895 | − | 13.7507i | −0.330217 | − | 0.571952i | ||||
\(579\) | −0.313281 | + | 0.315710i | −0.0130195 | + | 0.0131204i | ||||
\(580\) | 0.383994 | + | 0.665098i | 0.0159445 | + | 0.0276167i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.90697 | + | 7.00855i | 0.0790466 | + | 0.290514i | ||||
\(583\) | −33.2957 | −1.37897 | ||||||||
\(584\) | −7.25104 | + | 12.5592i | −0.300050 | + | 0.519702i | ||||
\(585\) | −0.00605986 | − | 0.784628i | −0.000250544 | − | 0.0324404i | ||||
\(586\) | −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 | ||||
\(590\) | 0.259362 | − | 0.449228i | 0.0106778 | − | 0.0184944i | ||||
\(591\) | −0.931316 | + | 0.938536i | −0.0383092 | + | 0.0386062i | ||||
\(592\) | −1.80217 | − | 3.12146i | −0.0740689 | − | 0.128291i | ||||
\(593\) | −18.0646 | − | 31.2888i | −0.741824 | − | 1.28488i | −0.951664 | − | 0.307141i | \(-0.900628\pi\) |
0.209840 | − | 0.977736i | \(-0.432706\pi\) | |||||||
\(594\) | 4.73536 | − | 18.5286i | 0.194294 | − | 0.760236i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.36915 | + | 7.56759i | −0.178967 | + | 0.309980i | ||||
\(597\) | −2.28792 | − | 8.40861i | −0.0936383 | − | 0.344142i | ||||
\(598\) | −5.18865 | −0.212180 | ||||||||
\(599\) | −40.9484 | −1.67310 | −0.836552 | − | 0.547887i | \(-0.815432\pi\) | ||||
−0.836552 | + | 0.547887i | \(0.815432\pi\) | |||||||
\(600\) | 25.6504 | + | 6.76694i | 1.04717 | + | 0.276259i | ||||
\(601\) | −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 | ||||
\(605\) | 0.00725978 | + | 0.0125743i | 0.000295152 | + | 0.000511218i | ||||
\(606\) | −32.2665 | − | 8.51236i | −1.31074 | − | 0.345791i | ||||
\(607\) | 3.42258 | − | 5.92808i | 0.138918 | − | 0.240613i | −0.788169 | − | 0.615459i | \(-0.788971\pi\) |
0.927087 | + | 0.374845i | \(0.122304\pi\) | |||||||
\(608\) | 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 | ||||
\(612\) | 3.29961 | + | 1.87120i | 0.133379 | + | 0.0756389i | ||||
\(613\) | 14.5648 | − | 25.2271i | 0.588269 | − | 1.01891i | −0.406191 | − | 0.913788i | \(-0.633143\pi\) |
0.994459 | − | 0.105123i | \(-0.0335235\pi\) | |||||||
\(614\) | −24.5833 | −0.992101 | ||||||||
\(615\) | −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 | \(0.969990\pi\) | |||||||
\(618\) | −4.37911 | − | 16.0942i | −0.176154 | − | 0.647404i | ||||
\(619\) | −4.43178 | − | 7.67606i | −0.178128 | − | 0.308527i | 0.763111 | − | 0.646267i | \(-0.223671\pi\) |
−0.941239 | + | 0.337740i | \(0.890337\pi\) | |||||||
\(620\) | 0.382804 | − | 0.663035i | 0.0153738 | − | 0.0266281i | ||||
\(621\) | −9.49197 | + | 2.66159i | −0.380900 | + | 0.106806i | ||||
\(622\) | −1.44453 | −0.0579205 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −7.55090 | − | 1.99204i | −0.302278 | − | 0.0797453i | ||||
\(625\) | −12.4166 | + | 21.5062i | −0.496666 | + | 0.860250i | ||||
\(626\) | 23.7954 | 0.951055 | ||||||||
\(627\) | 11.6594 | + | 42.8509i | 0.465632 | + | 1.71130i | ||||
\(628\) | −9.56737 | −0.381779 | ||||||||
\(629\) | 3.19820 | 0.127521 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.4661 | 1.05360 | 0.526799 | − | 0.849990i | \(-0.323392\pi\) | ||||
0.526799 | + | 0.849990i | \(0.323392\pi\) | |||||||
\(632\) | 23.6210 | 0.939592 | ||||||||
\(633\) | −12.0762 | − | 3.18588i | −0.479985 | − | 0.126627i | ||||
\(634\) | 27.3299 | 1.08541 | ||||||||
\(635\) | 0.0167248 | − | 0.0289681i | 0.000663702 | − | 0.00114957i | ||||
\(636\) | 3.55603 | + | 13.0692i | 0.141006 | + | 0.518227i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 34.1928 | 1.35371 | ||||||||
\(639\) | −0.0762358 | − | 9.87098i | −0.00301584 | − | 0.390490i | ||||
\(640\) | −0.0405449 | + | 0.0702258i | −0.00160268 | + | 0.00277592i | ||||
\(641\) | 8.26595 | + | 14.3171i | 0.326486 | + | 0.565489i | 0.981812 | − | 0.189856i | \(-0.0608022\pi\) |
−0.655326 | + | 0.755346i | \(0.727469\pi\) | |||||||
\(642\) | −33.5151 | − | 8.84178i | −1.32274 | − | 0.348957i | ||||
\(643\) | 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 | ||||
\(646\) | 13.6678 | 0.537752 | ||||||||
\(647\) | −0.649903 | + | 1.12567i | −0.0255503 | + | 0.0442545i | −0.878518 | − | 0.477710i | \(-0.841467\pi\) |
0.852968 | + | 0.521964i | \(0.174800\pi\) | |||||||
\(648\) | −27.6268 | + | 0.426762i | −1.08528 | + | 0.0167648i | ||||
\(649\) | 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 | ||||
\(653\) | 22.4435 | − | 38.8733i | 0.878281 | − | 1.52123i | 0.0250558 | − | 0.999686i | \(-0.492024\pi\) |
0.853226 | − | 0.521542i | \(-0.174643\pi\) | |||||||
\(654\) | 2.11757 | + | 7.78254i | 0.0828035 | + | 0.304321i | ||||
\(655\) | 0.788692 | + | 1.36605i | 0.0308167 | + | 0.0533762i | ||||
\(656\) | 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 | \(0.0531549\pi\) | |||||||
\(660\) | 0.336572 | − | 0.339182i | 0.0131011 | − | 0.0132026i | ||||
\(661\) | −33.0256 | −1.28455 | −0.642274 | − | 0.766475i | \(-0.722009\pi\) | ||||
−0.642274 | + | 0.766475i | \(0.722009\pi\) | |||||||
\(662\) | −15.2686 | −0.593430 | ||||||||
\(663\) | 4.88078 | − | 4.91862i | 0.189554 | − | 0.191023i | ||||
\(664\) | 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 | ||||
\(668\) | 6.82561 | + | 11.8223i | 0.264091 | + | 0.457419i | ||||
\(669\) | −5.08501 | − | 18.6885i | −0.196598 | − | 0.722541i | ||||
\(670\) | −0.579885 | + | 1.00439i | −0.0224029 | + | 0.0388030i | ||||
\(671\) | −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 | ||||
\(675\) | 6.41884 | − | 25.1157i | 0.247061 | − | 0.966704i | ||||
\(676\) | −2.68447 | + | 4.64964i | −0.103249 | + | 0.178832i | ||||
\(677\) | −8.30167 | −0.319059 | −0.159530 | − | 0.987193i | \(-0.550998\pi\) | ||||
−0.159530 | + | 0.987193i | \(0.550998\pi\) | |||||||
\(678\) | −3.79818 | − | 1.00202i | −0.145868 | − | 0.0384822i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.261161 | − | 0.452344i | −0.0100151 | − | 0.0173466i | ||||
\(681\) | −39.8099 | − | 10.5024i | −1.52552 | − | 0.402454i | ||||
\(682\) | −17.0434 | − | 29.5200i | −0.652625 | − | 1.13038i | ||||
\(683\) | −1.24728 | + | 2.16036i | −0.0477259 | + | 0.0826637i | −0.888902 | − | 0.458098i | \(-0.848531\pi\) |
0.841176 | + | 0.540762i | \(0.181864\pi\) | |||||||
\(684\) | 15.5746 | − | 9.15308i | 0.595509 | − | 0.349977i | ||||
\(685\) | 1.60808 | 0.0614414 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.866505 | − | 3.18460i | −0.0330592 | − | 0.121500i | ||||
\(688\) | 6.86110 | − | 11.8838i | 0.261577 | − | 0.453065i | ||||
\(689\) | 24.7419 | 0.942591 | ||||||||
\(690\) | 0.369552 | + | 0.0974932i | 0.0140686 | + | 0.00371150i | ||||
\(691\) | 16.8691 | 0.641731 | 0.320865 | − | 0.947125i | \(-0.396026\pi\) | ||||
0.320865 | + | 0.947125i | \(0.396026\pi\) | |||||||
\(692\) | −2.21763 | −0.0843017 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.0071 | 0.607621 | ||||||||
\(695\) | 0.856265 | 0.0324800 | ||||||||
\(696\) | −12.9701 | − | 47.6681i | −0.491631 | − | 1.80685i | ||||
\(697\) | −12.0753 | −0.457385 | ||||||||
\(698\) | 8.67266 | − | 15.0215i | 0.328265 | − | 0.568572i | ||||
\(699\) | −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 | \(0.399258\pi\) | |||||||
\(702\) | −3.51883 | + | 13.7685i | −0.132810 | + | 0.519659i | ||||
\(703\) | 7.61558 | − | 13.1906i | 0.287227 | − | 0.497492i | ||||
\(704\) | −13.6768 | − | 23.6889i | −0.515464 | − | 0.892811i | ||||
\(705\) | −0.153262 | − | 0.563271i | −0.00577217 | − | 0.0212140i | ||||
\(706\) | 2.28515 | + | 3.95800i | 0.0860029 | + | 0.148961i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.26472 | − | 4.29778i | 0.160278 | − | 0.161520i | ||||
\(709\) | −29.4925 | −1.10761 | −0.553807 | − | 0.832645i | \(-0.686825\pi\) | ||||
−0.553807 | + | 0.832645i | \(0.686825\pi\) | |||||||
\(710\) | −0.191354 | + | 0.331434i | −0.00718138 | + | 0.0124385i | ||||
\(711\) | −0.178264 | − | 23.0816i | −0.00668544 | − | 0.865627i | ||||
\(712\) | 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 | ||||
\(716\) | −3.98277 | + | 6.89836i | −0.148843 | + | 0.257804i | ||||
\(717\) | 35.7508 | + | 9.43158i | 1.33514 | + | 0.352229i | ||||
\(718\) | 4.37810 | + | 7.58310i | 0.163389 | + | 0.282999i | ||||
\(719\) | −0.217311 | − | 0.376394i | −0.00810433 | − | 0.0140371i | 0.861945 | − | 0.507002i | \(-0.169246\pi\) |
−0.870049 | + | 0.492965i | \(0.835913\pi\) | |||||||
\(720\) | 0.500368 | + | 0.283758i | 0.0186476 | + | 0.0105750i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 22.0691 | − | 38.2248i | 0.821327 | − | 1.42258i | ||||
\(723\) | 33.6058 | + | 8.86571i | 1.24981 | + | 0.329719i | ||||
\(724\) | 13.3928 | 0.497740 | ||||||||
\(725\) | 46.3488 | 1.72135 | ||||||||
\(726\) | −0.0690415 | − | 0.253743i | −0.00256237 | − | 0.00941729i | ||||
\(727\) | −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 | ||||
\(731\) | 6.08798 | + | 10.5447i | 0.225172 | + | 0.390009i | ||||
\(732\) | −5.42285 | + | 5.46490i | −0.200434 | + | 0.201988i | ||||
\(733\) | −2.83307 | + | 4.90702i | −0.104642 | + | 0.181245i | −0.913592 | − | 0.406632i | \(-0.866703\pi\) |
0.808950 | + | 0.587878i | \(0.200036\pi\) | |||||||
\(734\) | 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 | ||||
\(738\) | 21.3508 | − | 12.5477i | 0.785932 | − | 0.461888i | ||||
\(739\) | 6.80540 | − | 11.7873i | 0.250341 | − | 0.433603i | −0.713279 | − | 0.700880i | \(-0.752791\pi\) |
0.963620 | + | 0.267278i | \(0.0861241\pi\) | |||||||
\(740\) | −0.163885 | −0.00602455 | ||||||||
\(741\) | −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 | \(0.907985\pi\) | |||||||
\(744\) | −34.6888 | + | 34.9578i | −1.27175 | + | 1.28161i | ||||
\(745\) | −0.587900 | − | 1.01827i | −0.0215390 | − | 0.0373066i | ||||
\(746\) | 4.30696 | − | 7.45988i | 0.157689 | − | 0.273126i | ||||
\(747\) | −3.05022 | − | 1.72978i | −0.111602 | − | 0.0632892i | ||||
\(748\) | 4.21977 | 0.154290 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.41740 | + | 1.42839i | −0.0517563 | + | 0.0521576i | ||||
\(751\) | 3.57269 | − | 6.18808i | 0.130369 | − | 0.225806i | −0.793450 | − | 0.608636i | \(-0.791717\pi\) |
0.923819 | + | 0.382830i | \(0.125050\pi\) | |||||||
\(752\) | −5.80977 | −0.211860 | ||||||||
\(753\) | −8.31394 | + | 8.37840i | −0.302977 | + | 0.305326i | ||||
\(754\) | −25.4086 | −0.925325 | ||||||||
\(755\) | 1.18897 | 0.0432712 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.6446 | 1.36822 | 0.684108 | − | 0.729381i | \(-0.260192\pi\) | ||||
0.684108 | + | 0.729381i | \(0.260192\pi\) | |||||||
\(758\) | 34.8651 | 1.26636 | ||||||||
\(759\) | −7.72448 | + | 7.78437i | −0.280381 | + | 0.282555i | ||||
\(760\) | −2.48751 | −0.0902315 | ||||||||
\(761\) | 5.02358 | − | 8.70109i | 0.182104 | − | 0.315414i | −0.760493 | − | 0.649347i | \(-0.775042\pi\) |
0.942597 | + | 0.333933i | \(0.108376\pi\) | |||||||
\(762\) | −0.426718 | + | 0.430027i | −0.0154584 | + | 0.0155782i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 17.5572 | 0.635196 | ||||||||
\(765\) | −0.440044 | + | 0.258611i | −0.0159098 | + | 0.00935010i | ||||
\(766\) | 5.91762 | − | 10.2496i | 0.213812 | − | 0.370334i | ||||
\(767\) | −5.53011 | − | 9.57843i | −0.199681 | − | 0.345857i | ||||
\(768\) | −18.9646 | + | 19.1116i | −0.684326 | + | 0.689632i | ||||
\(769\) | −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 | ||||
\(772\) | 0.201270 | 0.00724385 | ||||||||
\(773\) | −24.2939 | + | 42.0783i | −0.873792 | + | 1.51345i | −0.0157473 | + | 0.999876i | \(0.505013\pi\) |
−0.858044 | + | 0.513576i | \(0.828321\pi\) | |||||||
\(774\) | −21.7216 | − | 12.3183i | −0.780766 | − | 0.442771i | ||||
\(775\) | −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 | ||||
\(779\) | −28.7538 | + | 49.8030i | −1.03021 | + | 1.78438i | ||||
\(780\) | −0.250106 | + | 0.252045i | −0.00895522 | + | 0.00902466i | ||||
\(781\) | −5.49059 | − | 9.50998i | −0.196469 | − | 0.340294i | ||||
\(782\) | 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 | ||||
\(786\) | −7.50057 | − | 27.5663i | −0.267537 | − | 0.983257i | ||||
\(787\) | −48.9551 | −1.74506 | −0.872531 | − | 0.488560i | \(-0.837522\pi\) | ||||
−0.872531 | + | 0.488560i | \(0.837522\pi\) | |||||||
\(788\) | 0.598331 | 0.0213147 | ||||||||
\(789\) | 2.57745 | + | 0.679970i | 0.0917597 | + | 0.0242076i | ||||
\(790\) | −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 | ||||
\(794\) | −13.2652 | − | 22.9759i | −0.470763 | − | 0.815385i | ||||
\(795\) | −1.76219 | − | 0.464893i | −0.0624986 | − | 0.0164880i | ||||
\(796\) | −1.97174 | + | 3.41515i | −0.0698864 | + | 0.121047i | ||||
\(797\) | −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 | ||||
\(801\) | 15.5949 | − | 9.16502i | 0.551018 | − | 0.323830i | ||||
\(802\) | −0.861472 | + | 1.49211i | −0.0304196 | + | 0.0526883i | ||||
\(803\) | 15.7647 | 0.556326 | ||||||||
\(804\) | −9.53510 | + | 9.60903i | −0.336277 | + | 0.338884i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.6649 | + | 21.9362i | 0.446102 | + | 0.772671i | ||||
\(807\) | −11.9403 | − | 43.8832i | −0.420317 | − | 1.54476i | ||||
\(808\) | 26.8169 | + | 46.4483i | 0.943417 | + | 1.63405i | ||||
\(809\) | −5.84869 | + | 10.1302i | −0.205629 | + | 0.356160i | −0.950333 | − | 0.311235i | \(-0.899257\pi\) |
0.744704 | + | 0.667395i | \(0.232591\pi\) | |||||||
\(810\) | 0.509328 | − | 0.914518i | 0.0178960 | − | 0.0321329i | ||||
\(811\) | 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 | ||||
\(814\) | −3.64830 | + | 6.31904i | −0.127873 | + | 0.221482i | ||||
\(815\) | −0.945254 | −0.0331108 | ||||||||
\(816\) | 1.33370 | + | 4.90165i | 0.0466889 | + | 0.171592i | ||||
\(817\) | 57.9869 | 2.02870 | ||||||||
\(818\) | −24.6431 | −0.861624 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.618775 | 0.0216085 | ||||||||
\(821\) | 34.0137 | 1.18709 | 0.593543 | − | 0.804803i | \(-0.297729\pi\) | ||||
0.593543 | + | 0.804803i | \(0.297729\pi\) | |||||||
\(822\) | −28.1609 | − | 7.42925i | −0.982224 | − | 0.259125i | ||||
\(823\) | 43.3780 | 1.51206 | 0.756031 | − | 0.654536i | \(-0.227136\pi\) | ||||
0.756031 | + | 0.654536i | \(0.227136\pi\) | |||||||
\(824\) | −13.4037 | + | 23.2160i | −0.466942 | + | 0.808767i | ||||
\(825\) | −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 | \(0.701949\pi\) | |||||||
\(828\) | 3.88050 | + | 2.20062i | 0.134857 | + | 0.0764770i | ||||
\(829\) | −8.45833 | + | 14.6503i | −0.293770 | + | 0.508824i | −0.974698 | − | 0.223526i | \(-0.928243\pi\) |
0.680928 | + | 0.732350i | \(0.261577\pi\) | |||||||
\(830\) | 0.0679744 | + | 0.117735i | 0.00235943 | + | 0.00408665i | ||||
\(831\) | 31.6047 | + | 8.33778i | 1.09635 | + | 0.289234i | ||||
\(832\) | 10.1632 | + | 17.6032i | 0.352345 | + | 0.610280i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −14.9950 | − | 3.95591i | −0.519236 | − | 0.136982i | ||||
\(835\) | −1.83687 | −0.0635674 | ||||||||
\(836\) | 10.0481 | − | 17.4039i | 0.347522 | − | 0.601926i | ||||
\(837\) | 34.4213 | + | 33.6329i | 1.18977 | + | 1.16252i | ||||
\(838\) | 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 | ||||
\(842\) | −8.06812 | + | 13.9744i | −0.278046 | + | 0.481589i | ||||
\(843\) | 2.26989 | + | 8.34235i | 0.0781792 | + | 0.287326i | ||||
\(844\) | 2.82590 | + | 4.89459i | 0.0972713 | + | 0.168479i | ||||
\(845\) | −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 | ||||
\(849\) | 18.7792 | − | 18.9248i | 0.644499 | − | 0.649496i | ||||
\(850\) | −8.87544 | −0.304425 | ||||||||
\(851\) | 3.76124 | 0.128934 | ||||||||
\(852\) | −3.14645 | + | 3.17084i | −0.107796 | + | 0.108631i | ||||
\(853\) | 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 | ||||
\(857\) | −14.5284 | − | 25.1639i | −0.496280 | − | 0.859582i | 0.503711 | − | 0.863872i | \(-0.331968\pi\) |
−0.999991 | + | 0.00429061i | \(0.998634\pi\) | |||||||
\(858\) | 4.15059 | + | 15.2543i | 0.141699 | + | 0.520774i | ||||
\(859\) | −6.29820 | + | 10.9088i | −0.214892 | + | 0.372203i | −0.953239 | − | 0.302217i | \(-0.902273\pi\) |
0.738347 | + | 0.674421i | \(0.235607\pi\) | |||||||
\(860\) | −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 | 0.963421 | − | 0.267993i | \(-0.0863605\pi\) |
−0.713799 | + | 0.700350i | \(0.753027\pi\) | |||||||
\(864\) | 15.3682 | + | 15.0162i | 0.522836 | + | 0.510860i | ||||
\(865\) | 0.149199 | − | 0.258420i | 0.00507292 | − | 0.00878655i | ||||
\(866\) | 1.49119 | 0.0506726 | ||||||||
\(867\) | 24.1124 | + | 6.36122i | 0.818901 | + | 0.216038i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.8388 | − | 22.2375i | −0.435527 | − | 0.754354i | ||||
\(870\) | 1.80968 | + | 0.477419i | 0.0613538 | + | 0.0161860i | ||||
\(871\) | 12.3643 | + | 21.4156i | 0.418948 | + | 0.725639i | ||||
\(872\) | 6.48154 | − | 11.2264i | 0.219493 | − | 0.380172i | ||||
\(873\) | −9.92307 | − | 5.62736i | −0.335845 | − | 0.190457i | ||||
\(874\) | 16.0740 | 0.543711 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.68370 | − | 6.18797i | −0.0568869 | − | 0.209072i | ||||
\(877\) | −16.5951 | + | 28.7435i | −0.560376 | + | 0.970600i | 0.437087 | + | 0.899419i | \(0.356010\pi\) |
−0.997463 | + | 0.0711811i | \(0.977323\pi\) | |||||||
\(878\) | 19.1241 | 0.645407 | ||||||||
\(879\) | 43.2128 | + | 11.4002i | 1.45753 | + | 0.384518i | ||||
\(880\) | 0.639905 | 0.0215712 | ||||||||
\(881\) | 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 | \(0.731581\pi\) | |||||||
\(884\) | −3.13569 | −0.105465 | ||||||||
\(885\) | 0.213896 | + | 0.786115i | 0.00719003 | + | 0.0264250i | ||||
\(886\) | −21.6262 | −0.726545 | ||||||||
\(887\) | 24.9513 | − | 43.2169i | 0.837782 | − | 1.45108i | −0.0539627 | − | 0.998543i | \(-0.517185\pi\) |
0.891745 | − | 0.452538i | \(-0.149481\pi\) | |||||||
\(888\) | 10.1932 | + | 2.68912i | 0.342062 | + | 0.0902411i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.701292 | −0.0235074 | ||||||||
\(891\) | 15.4179 | + | 25.7767i | 0.516519 | + | 0.863553i | ||||
\(892\) | −4.38228 | + | 7.59034i | −0.146730 | + | 0.254143i | ||||
\(893\) | −12.2754 | − | 21.2616i | −0.410779 | − | 0.711491i | ||||
\(894\) | 5.59101 | + | 20.5482i | 0.186991 | + | 0.687235i | ||||
\(895\) | −0.535910 | − | 0.928223i | −0.0179135 | − | 0.0310271i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.74003 | − | 5.78454i | 0.191654 | − | 0.193140i | ||||
\(898\) | 19.5578 | 0.652653 | ||||||||
\(899\) | −43.0222 | + | 74.5166i | −1.43487 | + | 2.48527i | ||||
\(900\) | −10.1136 | + | 5.94372i | −0.337121 | + | 0.198124i | ||||
\(901\) | −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 | ||||
\(905\) | −0.901048 | + | 1.56066i | −0.0299518 | + | 0.0518781i | ||||
\(906\) | −20.8215 | − | 5.49301i | −0.691747 | − | 0.182493i | ||||
\(907\) | 6.96080 | + | 12.0565i | 0.231129 | + | 0.400328i | 0.958141 | − | 0.286298i | \(-0.0924246\pi\) |
−0.727011 | + | 0.686625i | \(0.759091\pi\) | |||||||
\(908\) | 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 | \(0.138109\pi\) | |||||||
\(912\) | 23.3920 | + | 6.17116i | 0.774587 | + | 0.204347i | ||||
\(913\) | −3.90084 | −0.129099 | ||||||||
\(914\) | −0.535362 | −0.0177082 | ||||||||
\(915\) | −0.271982 | − | 0.999594i | −0.00899144 | − | 0.0330456i | ||||
\(916\) | −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 | −0.997388 | − | 0.0722280i | \(-0.976989\pi\) |
0.436143 | − | 0.899877i | \(-0.356344\pi\) | |||||||
\(920\) | −0.307138 | − | 0.531978i | −0.0101260 | − | 0.0175388i | ||||
\(921\) | 27.1957 | − | 27.4065i | 0.896129 | − | 0.903076i | ||||
\(922\) | 4.40781 | − | 7.63455i | 0.145163 | − | 0.251430i | ||||
\(923\) | 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 | ||||
\(927\) | 22.7870 | + | 12.9225i | 0.748423 | + | 0.424429i | ||||
\(928\) | −19.2082 | + | 33.2696i | −0.630541 | + | 1.09213i | ||||
\(929\) | −10.6329 | −0.348855 | −0.174427 | − | 0.984670i | \(-0.555807\pi\) | ||||
−0.174427 | + | 0.984670i | \(0.555807\pi\) | |||||||
\(930\) | −0.489857 | − | 1.80033i | −0.0160631 | − | 0.0590353i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.56375 | + | 4.44055i | 0.0839785 | + | 0.145455i | ||||
\(933\) | 1.59804 | − | 1.61043i | 0.0523175 | − | 0.0527231i | ||||
\(934\) | −12.0746 | − | 20.9137i | −0.395092 | − | 0.684319i | ||||
\(935\) | −0.283900 | + | 0.491729i | −0.00928451 | + | 0.0160812i | ||||
\(936\) | 19.6916 | − | 11.5726i | 0.643640 | − | 0.378263i | ||||
\(937\) | −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 | ||||
\(940\) | −0.132082 | + | 0.228772i | −0.00430802 | + | 0.00746172i | ||||
\(941\) | 34.3656 | 1.12029 | 0.560143 | − | 0.828396i | \(-0.310746\pi\) | ||||
0.560143 | + | 0.828396i | \(0.310746\pi\) | |||||||
\(942\) | −16.4229 | + | 16.5502i | −0.535087 | + | 0.539236i | ||||
\(943\) | −14.2011 | −0.462453 | ||||||||
\(944\) | 8.10825 | 0.263901 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.7791 | −0.903175 | ||||||||
\(947\) | −40.5840 | −1.31880 | −0.659401 | − | 0.751791i | \(-0.729190\pi\) | ||||
−0.659401 | + | 0.751791i | \(0.729190\pi\) | |||||||
\(948\) | −7.35743 | + | 7.41447i | −0.238958 | + | 0.240811i | ||||
\(949\) | −11.7147 | −0.380276 | ||||||||
\(950\) | −21.1342 | + | 36.6056i | −0.685685 | + | 1.18764i | ||||
\(951\) | −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 | \(0.619789\pi\) | |||||||
\(954\) | 28.7120 | + | 16.2825i | 0.929586 | + | 0.527167i | ||||
\(955\) | −1.18122 | + | 2.04593i | −0.0382234 | + | 0.0662049i | ||||
\(956\) | −8.36589 | − | 14.4901i | −0.270572 | − | 0.468645i | ||||
\(957\) | −37.8264 | + | 38.1197i | −1.22275 | + | 1.23223i | ||||
\(958\) | −2.20656 | − | 3.82187i | −0.0712907 | − | 0.123479i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.393096 | − | 1.44472i | −0.0126871 | − | 0.0466280i | ||||
\(961\) | 54.7775 | 1.76702 | ||||||||
\(962\) | 2.71104 | − | 4.69566i | 0.0874074 | − | 0.151394i | ||||
\(963\) | 46.9339 | − | 27.5828i | 1.51242 | − | 0.888842i | ||||
\(964\) | −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 | \(0.960982\pi\) | |||||||
\(968\) | −0.211325 | + | 0.366026i | −0.00679224 | + | 0.0117645i | ||||
\(969\) | −15.1202 | + | 15.2375i | −0.485732 | + | 0.489498i | ||||
\(970\) | 0.221136 | + | 0.383019i | 0.00710025 | + | 0.0122980i | ||||
\(971\) | 22.7886 | + | 39.4709i | 0.731319 | + | 1.26668i | 0.956319 | + | 0.292324i | \(0.0944285\pi\) |
−0.225000 | + | 0.974359i | \(0.572238\pi\) | |||||||
\(972\) | 8.47121 | − | 8.80481i | 0.271714 | − | 0.282414i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −14.5988 | + | 25.2858i | −0.467774 | + | 0.810209i | ||||
\(975\) | 5.62617 | + | 20.6774i | 0.180182 | + | 0.662208i | ||||
\(976\) | −10.3102 | −0.330020 | ||||||||
\(977\) | −14.6896 | −0.469963 | −0.234981 | − | 0.972000i | \(-0.575503\pi\) | ||||
−0.234981 | + | 0.972000i | \(0.575503\pi\) | |||||||
\(978\) | 16.5534 | + | 4.36704i | 0.529321 | + | 0.139643i | ||||
\(979\) | 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 | ||||
\(983\) | −22.2955 | − | 38.6169i | −0.711115 | − | 1.23169i | −0.964439 | − | 0.264305i | \(-0.914857\pi\) |
0.253324 | − | 0.967381i | \(-0.418476\pi\) | |||||||
\(984\) | −38.4861 | − | 10.1532i | −1.22689 | − | 0.323672i | ||||
\(985\) | −0.0402548 | + | 0.0697234i | −0.00128262 | + | 0.00222157i | ||||
\(986\) | 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 | ||||
\(990\) | −0.00899330 | − | 1.16445i | −0.000285826 | − | 0.0370086i | ||||
\(991\) | −12.0915 | + | 20.9430i | −0.384098 | + | 0.665277i | −0.991644 | − | 0.129007i | \(-0.958821\pi\) |
0.607546 | + | 0.794285i | \(0.292154\pi\) | |||||||
\(992\) | 38.2973 | 1.21594 | ||||||||
\(993\) | 16.8911 | − | 17.0221i | 0.536024 | − | 0.540179i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.265311 | − | 0.459532i | −0.00841093 | − | 0.0145682i | ||||
\(996\) | 0.416615 | + | 1.53115i | 0.0132010 | + | 0.0485165i | ||||
\(997\) | −5.43262 | − | 9.40957i | −0.172053 | − | 0.298004i | 0.767085 | − | 0.641546i | \(-0.221707\pi\) |
−0.939137 | + | 0.343542i | \(0.888373\pi\) | |||||||
\(998\) | −4.09760 | + | 7.09726i | −0.129707 | + | 0.224660i | ||||
\(999\) | 2.55079 | − | 9.98076i | 0.0807034 | − | 0.315777i |
(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.h.h.214.6 | 24 | ||
3.2 | odd | 2 | 1323.2.h.h.802.7 | 24 | |||
7.2 | even | 3 | 441.2.g.h.79.8 | 24 | |||
7.3 | odd | 6 | 441.2.f.h.295.8 | yes | 24 | ||
7.4 | even | 3 | 441.2.f.h.295.7 | yes | 24 | ||
7.5 | odd | 6 | 441.2.g.h.79.7 | 24 | |||
7.6 | odd | 2 | inner | 441.2.h.h.214.5 | 24 | ||
9.4 | even | 3 | 441.2.g.h.67.8 | 24 | |||
9.5 | odd | 6 | 1323.2.g.h.361.6 | 24 | |||
21.2 | odd | 6 | 1323.2.g.h.667.6 | 24 | |||
21.5 | even | 6 | 1323.2.g.h.667.5 | 24 | |||
21.11 | odd | 6 | 1323.2.f.h.883.6 | 24 | |||
21.17 | even | 6 | 1323.2.f.h.883.5 | 24 | |||
21.20 | even | 2 | 1323.2.h.h.802.8 | 24 | |||
63.4 | even | 3 | 441.2.f.h.148.7 | ✓ | 24 | ||
63.5 | even | 6 | 1323.2.h.h.226.8 | 24 | |||
63.11 | odd | 6 | 3969.2.a.bi.1.8 | 12 | |||
63.13 | odd | 6 | 441.2.g.h.67.7 | 24 | |||
63.23 | odd | 6 | 1323.2.h.h.226.7 | 24 | |||
63.25 | even | 3 | 3969.2.a.bh.1.5 | 12 | |||
63.31 | odd | 6 | 441.2.f.h.148.8 | yes | 24 | ||
63.32 | odd | 6 | 1323.2.f.h.442.6 | 24 | |||
63.38 | even | 6 | 3969.2.a.bi.1.7 | 12 | |||
63.40 | odd | 6 | inner | 441.2.h.h.373.5 | 24 | ||
63.41 | even | 6 | 1323.2.g.h.361.5 | 24 | |||
63.52 | odd | 6 | 3969.2.a.bh.1.6 | 12 | |||
63.58 | even | 3 | inner | 441.2.h.h.373.6 | 24 | ||
63.59 | even | 6 | 1323.2.f.h.442.5 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.7 | ✓ | 24 | 63.4 | even | 3 | ||
441.2.f.h.148.8 | yes | 24 | 63.31 | odd | 6 | ||
441.2.f.h.295.7 | yes | 24 | 7.4 | even | 3 | ||
441.2.f.h.295.8 | yes | 24 | 7.3 | odd | 6 | ||
441.2.g.h.67.7 | 24 | 63.13 | odd | 6 | |||
441.2.g.h.67.8 | 24 | 9.4 | even | 3 | |||
441.2.g.h.79.7 | 24 | 7.5 | odd | 6 | |||
441.2.g.h.79.8 | 24 | 7.2 | even | 3 | |||
441.2.h.h.214.5 | 24 | 7.6 | odd | 2 | inner | ||
441.2.h.h.214.6 | 24 | 1.1 | even | 1 | trivial | ||
441.2.h.h.373.5 | 24 | 63.40 | odd | 6 | inner | ||
441.2.h.h.373.6 | 24 | 63.58 | even | 3 | inner | ||
1323.2.f.h.442.5 | 24 | 63.59 | even | 6 | |||
1323.2.f.h.442.6 | 24 | 63.32 | odd | 6 | |||
1323.2.f.h.883.5 | 24 | 21.17 | even | 6 | |||
1323.2.f.h.883.6 | 24 | 21.11 | odd | 6 | |||
1323.2.g.h.361.5 | 24 | 63.41 | even | 6 | |||
1323.2.g.h.361.6 | 24 | 9.5 | odd | 6 | |||
1323.2.g.h.667.5 | 24 | 21.5 | even | 6 | |||
1323.2.g.h.667.6 | 24 | 21.2 | odd | 6 | |||
1323.2.h.h.226.7 | 24 | 63.23 | odd | 6 | |||
1323.2.h.h.226.8 | 24 | 63.5 | even | 6 | |||
1323.2.h.h.802.7 | 24 | 3.2 | odd | 2 | |||
1323.2.h.h.802.8 | 24 | 21.20 | even | 2 | |||
3969.2.a.bh.1.5 | 12 | 63.25 | even | 3 | |||
3969.2.a.bh.1.6 | 12 | 63.52 | odd | 6 | |||
3969.2.a.bi.1.7 | 12 | 63.38 | even | 6 | |||
3969.2.a.bi.1.8 | 12 | 63.11 | odd | 6 |