Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1156,2,Mod(733,1156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1156, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1156.733");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1156 = 2^{2} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1156.h (of order \(8\), degree \(4\), 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: | \(9.23070647366\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{8})\) |
Coefficient field: | 16.0.229607785695641627262976.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 799x^{8} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 68) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 733.4 | ||
Root | \(2.12749 + 0.881234i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1156.733 |
Dual form | 1156.2.h.e.757.4 |
$q$-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 \(\left(\mathbb{Z}/1156\mathbb{Z}\right)^\times\).
\(n\) | \(579\) | \(581\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{7}{8}\right)\) |
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 | 0 | ||||||||
\(3\) | 3.00872 | − | 1.24625i | 1.73709 | − | 0.719525i | 0.738091 | − | 0.674701i | \(-0.235727\pi\) |
0.998995 | − | 0.0448236i | \(-0.0142726\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.541196 | + | 1.30656i | 0.242030 | + | 0.584313i | 0.997484 | − | 0.0708890i | \(-0.0225836\pi\) |
−0.755454 | + | 0.655202i | \(0.772584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.24625 | + | 3.00872i | −0.471039 | + | 1.13719i | 0.492665 | + | 0.870219i | \(0.336023\pi\) |
−0.963705 | + | 0.266971i | \(0.913977\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.37794 | − | 5.37794i | 1.79265 | − | 1.79265i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.395595 | − | 0.163861i | −0.119277 | − | 0.0494059i | 0.322247 | − | 0.946656i | \(-0.395562\pi\) |
−0.441524 | + | 0.897250i | \(0.645562\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.60555i | 0.722650i | 0.932440 | + | 0.361325i | \(0.117675\pi\) | ||||
−0.932440 | + | 0.361325i | \(0.882325\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.25662 | + | 3.25662i | 0.840855 | + | 0.840855i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.428189 | + | 0.428189i | 0.0982334 | + | 0.0982334i | 0.754516 | − | 0.656282i | \(-0.227872\pi\) |
−0.656282 | + | 0.754516i | \(0.727872\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.6056i | 2.31432i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.62185 | + | 2.32865i | 1.17224 | + | 0.485556i | 0.881931 | − | 0.471378i | \(-0.156243\pi\) |
0.290305 | + | 0.956934i | \(0.406243\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.12132 | − | 2.12132i | 0.424264 | − | 0.424264i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.73968 | − | 13.8568i | 1.10460 | − | 2.66675i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.868918 | − | 2.09775i | −0.161354 | − | 0.389543i | 0.822438 | − | 0.568854i | \(-0.192613\pi\) |
−0.983792 | + | 0.179311i | \(0.942613\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.62185 | − | 2.32865i | 1.00971 | − | 0.418237i | 0.184363 | − | 0.982858i | \(-0.440978\pi\) |
0.825350 | + | 0.564621i | \(0.190978\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.39445 | −0.242742 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.60555 | −0.778480 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.91969 | + | 1.62359i | −0.644393 | + | 0.266916i | −0.680854 | − | 0.732419i | \(-0.738391\pi\) |
0.0364615 | + | 0.999335i | \(0.488391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.24718 | + | 7.83938i | 0.519964 | + | 1.25531i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.541196 | + | 1.30656i | −0.0845206 | + | 0.204051i | −0.960489 | − | 0.278317i | \(-0.910223\pi\) |
0.875969 | + | 0.482368i | \(0.160223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.40024 | − | 2.40024i | 0.366033 | − | 0.366033i | −0.499995 | − | 0.866028i | \(-0.666665\pi\) |
0.866028 | + | 0.499995i | \(0.166665\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.93713 | + | 4.11609i | 1.48134 | + | 0.613591i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.00000i | − | 0.583460i | −0.956501 | − | 0.291730i | \(-0.905769\pi\) | ||
0.956501 | − | 0.291730i | \(-0.0942309\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.54951 | − | 2.54951i | −0.364216 | − | 0.364216i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.68481 | − | 3.68481i | −0.506147 | − | 0.506147i | 0.407194 | − | 0.913341i | \(-0.366507\pi\) |
−0.913341 | + | 0.407194i | \(0.866507\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.605551i | − | 0.0816525i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.82194 | + | 0.754670i | 0.241321 | + | 0.0999585i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.08504 | + | 6.08504i | −0.792205 | + | 0.792205i | −0.981852 | − | 0.189647i | \(-0.939266\pi\) |
0.189647 | + | 0.981852i | \(0.439266\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.36142 | + | 8.11520i | −0.430386 | + | 1.03904i | 0.548777 | + | 0.835969i | \(0.315094\pi\) |
−0.979163 | + | 0.203076i | \(0.934906\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.47844 | + | 22.8830i | 1.19417 | + | 2.88299i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.40432 | + | 1.41011i | −0.422254 | + | 0.174903i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.21110 | −1.12532 | −0.562658 | − | 0.826690i | \(-0.690221\pi\) | ||||
−0.562658 | + | 0.826690i | \(0.690221\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 19.8167 | 2.38564 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.79991 | + | 1.57398i | −0.450967 | + | 0.186796i | −0.596594 | − | 0.802543i | \(-0.703480\pi\) |
0.145628 | + | 0.989339i | \(0.453480\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.78837 | + | 9.14594i | 0.443395 | + | 1.07045i | 0.974749 | + | 0.223301i | \(0.0716834\pi\) |
−0.531354 | + | 0.847150i | \(0.678317\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.73876 | − | 9.02616i | 0.431715 | − | 1.04225i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.986024 | − | 0.986024i | 0.112368 | − | 0.112368i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.395595 | − | 0.163861i | −0.0445080 | − | 0.0184358i | 0.360318 | − | 0.932829i | \(-0.382668\pi\) |
−0.404826 | + | 0.914394i | \(0.632668\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 26.0278i | − | 2.89197i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.5983 | − | 12.5983i | −1.38284 | − | 1.38284i | −0.839535 | − | 0.543305i | \(-0.817173\pi\) |
−0.543305 | − | 0.839535i | \(-0.682827\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.22866 | − | 5.22866i | −0.560572 | − | 0.560572i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 7.81665i | − | 0.828564i | −0.910149 | − | 0.414282i | \(-0.864033\pi\) | ||
0.910149 | − | 0.414282i | \(-0.135967\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.83938 | − | 3.24718i | −0.821790 | − | 0.340397i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.0125 | − | 14.0125i | 1.45303 | − | 1.45303i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.327722 | + | 0.791191i | −0.0336236 | + | 0.0811745i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.11609 | − | 9.93713i | −0.417926 | − | 1.00896i | −0.982947 | − | 0.183887i | \(-0.941132\pi\) |
0.565021 | − | 0.825076i | \(-0.308868\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.00872 | + | 1.24625i | −0.302388 | + | 0.125253i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.6056 | −1.05529 | −0.527646 | − | 0.849464i | \(-0.676925\pi\) | ||||
−0.527646 | + | 0.849464i | \(0.676925\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.2111 | −1.30173 | −0.650864 | − | 0.759194i | \(-0.725593\pi\) | ||||
−0.650864 | + | 0.759194i | \(0.725593\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13.8568 | + | 5.73968i | −1.35229 | + | 0.560136i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.08332 | − | 7.44378i | −0.298075 | − | 0.719618i | −0.999973 | − | 0.00733983i | \(-0.997664\pi\) |
0.701898 | − | 0.712278i | \(-0.252336\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.36142 | − | 8.11520i | 0.321966 | − | 0.777295i | −0.677174 | − | 0.735823i | \(-0.736795\pi\) |
0.999140 | − | 0.0414716i | \(-0.0132046\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.76985 | + | 9.76985i | −0.927313 | + | 0.927313i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.5503 | + | 5.19849i | 1.18063 | + | 0.489033i | 0.884692 | − | 0.466175i | \(-0.154368\pi\) |
0.295936 | + | 0.955208i | \(0.404368\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.60555i | 0.802472i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.0125 | + | 14.0125i | 1.29546 | + | 1.29546i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.64853 | − | 7.64853i | −0.695321 | − | 0.695321i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.60555i | 0.415269i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.4525 | + | 4.32957i | 0.934900 | + | 0.387248i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.428189 | + | 0.428189i | −0.0379957 | + | 0.0379957i | −0.725849 | − | 0.687854i | \(-0.758553\pi\) |
0.687854 | + | 0.725849i | \(0.258553\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.23034 | − | 10.2130i | 0.372461 | − | 0.899200i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.41104 | − | 8.23497i | −0.298024 | − | 0.719493i | −0.999974 | − | 0.00726659i | \(-0.997687\pi\) |
0.701950 | − | 0.712226i | \(-0.252313\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.82194 | + | 0.754670i | −0.157982 | + | 0.0654382i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 21.2111 | 1.82556 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.60555 | −0.222607 | −0.111304 | − | 0.993786i | \(-0.535503\pi\) | ||||
−0.111304 | + | 0.993786i | \(0.535503\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.395595 | + | 0.163861i | −0.0335540 | + | 0.0138985i | −0.399397 | − | 0.916778i | \(-0.630781\pi\) |
0.365843 | + | 0.930676i | \(0.380781\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.98501 | − | 12.0349i | −0.419814 | − | 1.01352i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.426948 | − | 1.03074i | 0.0357032 | − | 0.0861952i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.27059 | − | 2.27059i | 0.188562 | − | 0.188562i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.8481 | − | 4.49343i | −0.894736 | − | 0.370612i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.42221i | 0.689974i | 0.938607 | + | 0.344987i | \(0.112117\pi\) | ||||
−0.938607 | + | 0.344987i | \(0.887883\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.25662 | − | 3.25662i | −0.265020 | − | 0.265020i | 0.562070 | − | 0.827090i | \(-0.310005\pi\) |
−0.827090 | + | 0.562070i | \(0.810005\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.08504 | + | 6.08504i | 0.488762 | + | 0.488762i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.42221i | 0.672165i | 0.941833 | + | 0.336083i | \(0.109102\pi\) | ||||
−0.941833 | + | 0.336083i | \(0.890898\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.6788 | − | 6.49435i | −1.24341 | − | 0.515036i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.0125 | + | 14.0125i | −1.10434 | + | 1.10434i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.32865 | + | 5.62185i | −0.182394 | + | 0.440337i | −0.988459 | − | 0.151490i | \(-0.951593\pi\) |
0.806065 | + | 0.591827i | \(0.201593\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.754670 | − | 1.82194i | −0.0587510 | − | 0.141837i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.4787 | − | 8.06833i | 1.50730 | − | 0.624346i | 0.532305 | − | 0.846553i | \(-0.321326\pi\) |
0.975000 | + | 0.222207i | \(0.0713260\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.21110 | 0.477777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.60555 | 0.352195 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.3589 | − | 8.01872i | 1.47183 | − | 0.609652i | 0.504554 | − | 0.863380i | \(-0.331657\pi\) |
0.967275 | + | 0.253729i | \(0.0816570\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.73876 | + | 9.02616i | 0.282624 | + | 0.682314i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.7247 | + | 25.8917i | −0.806117 | + | 1.94614i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.6262 | − | 10.6262i | 0.794242 | − | 0.794242i | −0.187939 | − | 0.982181i | \(-0.560181\pi\) |
0.982181 | + | 0.187939i | \(0.0601808\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.9853 | − | 7.03555i | −1.26251 | − | 0.522948i | −0.351830 | − | 0.936064i | \(-0.614441\pi\) |
−0.910679 | + | 0.413116i | \(0.864441\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28.6056i | 2.11458i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.24264 | − | 4.24264i | −0.311925 | − | 0.311925i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 34.5382 | + | 34.5382i | 2.51229 | + | 2.51229i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 6.78890i | − | 0.491227i | −0.969368 | − | 0.245614i | \(-0.921011\pi\) | ||
0.969368 | − | 0.245614i | \(-0.0789895\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.7283 | + | 4.44382i | 0.772242 | + | 0.319873i | 0.733780 | − | 0.679387i | \(-0.237754\pi\) |
0.0384615 | + | 0.999260i | \(0.487754\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.48528 | + | 8.48528i | −0.607644 | + | 0.607644i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.52806 | + | 23.0028i | −0.678846 | + | 1.63888i | 0.0872765 | + | 0.996184i | \(0.472184\pi\) |
−0.766122 | + | 0.642695i | \(0.777816\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.47660 | − | 13.2217i | −0.388226 | − | 0.937259i | −0.990316 | − | 0.138832i | \(-0.955665\pi\) |
0.602090 | − | 0.798428i | \(-0.294335\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −27.7136 | + | 11.4794i | −1.95477 | + | 0.809692i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.39445 | 0.518989 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.00000 | −0.139686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 42.7572 | − | 17.7106i | 2.97183 | − | 1.23097i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0992262 | − | 0.239553i | −0.00686362 | − | 0.0165702i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.39605 | + | 20.2699i | −0.578008 | + | 1.39543i | 0.316590 | + | 0.948563i | \(0.397462\pi\) |
−0.894598 | + | 0.446872i | \(0.852538\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.47131 | + | 9.47131i | −0.648963 | + | 0.648963i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.43506 | + | 1.83706i | 0.302469 | + | 0.125287i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.8167i | 1.34524i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.7963 | + | 22.7963i | 1.54043 | + | 1.54043i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.5983 | − | 12.5983i | −0.843643 | − | 0.843643i | 0.145688 | − | 0.989331i | \(-0.453461\pi\) |
−0.989331 | + | 0.145688i | \(0.953461\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | − | 22.8167i | − | 1.52111i | ||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.395595 | + | 0.163861i | 0.0262566 | + | 0.0108758i | 0.395773 | − | 0.918348i | \(-0.370477\pi\) |
−0.369516 | + | 0.929224i | \(0.620477\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.25662 | − | 3.25662i | 0.215203 | − | 0.215203i | −0.591270 | − | 0.806474i | \(-0.701373\pi\) |
0.806474 | + | 0.591270i | \(0.201373\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.73784 | − | 4.19551i | 0.114341 | − | 0.276044i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.03370 | + | 7.32401i | 0.198744 | + | 0.479812i | 0.991560 | − | 0.129650i | \(-0.0413855\pi\) |
−0.792815 | + | 0.609462i | \(0.791386\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.22625 | − | 2.16478i | 0.340923 | − | 0.141215i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.39445 | −0.0905792 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.7889 | −0.956614 | −0.478307 | − | 0.878193i | \(-0.658749\pi\) | ||||
−0.478307 | + | 0.878193i | \(0.658749\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.7591 | + | 4.87076i | −0.757468 | + | 0.313754i | −0.727785 | − | 0.685806i | \(-0.759450\pi\) |
−0.0296835 | + | 0.999559i | \(0.509450\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.2181 | − | 36.7398i | −0.976243 | − | 2.35686i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.95131 | − | 4.71088i | 0.124665 | − | 0.300967i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.11567 | + | 1.11567i | −0.0709883 | + | 0.0709883i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −53.6053 | − | 22.2041i | −3.39710 | − | 1.40713i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 12.0000i | − | 0.757433i | −0.925513 | − | 0.378717i | \(-0.876365\pi\) | ||
0.925513 | − | 0.378717i | \(-0.123635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.84240 | − | 1.84240i | −0.115831 | − | 0.115831i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.7139 | + | 13.7139i | 0.855452 | + | 0.855452i | 0.990798 | − | 0.135346i | \(-0.0432146\pi\) |
−0.135346 | + | 0.990798i | \(0.543215\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 13.8167i | − | 0.858525i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.9546 | − | 6.60860i | −0.987563 | − | 0.409062i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.2831 | − | 16.2831i | 1.00406 | − | 1.00406i | 0.00406616 | − | 0.999992i | \(-0.498706\pi\) |
0.999992 | − | 0.00406616i | \(-0.00129430\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.82023 | − | 6.80863i | 0.173245 | − | 0.418251i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.74153 | − | 23.5181i | −0.596172 | − | 1.43929i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.7632 | − | 9.42883i | 1.38790 | − | 0.574886i | 0.441316 | − | 0.897352i | \(-0.354512\pi\) |
0.946581 | + | 0.322466i | \(0.104512\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.21110 | −0.0735692 | −0.0367846 | − | 0.999323i | \(-0.511712\pi\) | ||||
−0.0367846 | + | 0.999323i | \(0.511712\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −27.6333 | −1.67244 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.18679 | + | 0.491583i | −0.0715659 | + | 0.0296436i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.95131 | − | 4.71088i | −0.117243 | − | 0.283049i | 0.854354 | − | 0.519691i | \(-0.173953\pi\) |
−0.971597 | + | 0.236642i | \(0.923953\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.7106 | − | 42.7572i | 1.06031 | − | 2.55981i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.0265 | + | 13.0265i | −0.777094 | + | 0.777094i | −0.979336 | − | 0.202242i | \(-0.935177\pi\) |
0.202242 | + | 0.979336i | \(0.435177\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.76917 | + | 1.14703i | 0.164610 | + | 0.0681837i | 0.463467 | − | 0.886114i | \(-0.346605\pi\) |
−0.298857 | + | 0.954298i | \(0.596605\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.78890i | 0.165200i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.25662 | − | 3.25662i | −0.192232 | − | 0.192232i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −24.7684 | − | 24.7684i | −1.45195 | − | 1.45195i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.6333i | 1.26383i | 0.775037 | + | 0.631916i | \(0.217731\pi\) | ||||
−0.775037 | + | 0.631916i | \(0.782269\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.2437 | − | 4.65729i | −0.654633 | − | 0.271158i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.54118 | + | 4.54118i | −0.263506 | + | 0.263506i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.06740 | + | 14.6480i | −0.350887 | + | 0.847116i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.23034 | + | 10.2130i | 0.243833 | + | 0.588665i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −31.9091 | + | 13.2172i | −1.83313 | + | 0.759308i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.4222 | −0.711293 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.2111 | 1.21058 | 0.605291 | − | 0.796004i | \(-0.293057\pi\) | ||||
0.605291 | + | 0.796004i | \(0.293057\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −39.7485 | + | 16.4644i | −2.26121 | + | 0.936626i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.2331 | − | 24.7049i | −0.580267 | − | 1.40089i | −0.892572 | − | 0.450906i | \(-0.851101\pi\) |
0.312305 | − | 0.949982i | \(-0.398899\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.36142 | + | 8.11520i | −0.189999 | + | 0.458698i | −0.989959 | − | 0.141355i | \(-0.954854\pi\) |
0.799960 | + | 0.600053i | \(0.204854\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −24.7684 | + | 24.7684i | −1.39554 | + | 1.39554i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.6159 | + | 10.6104i | 1.43873 | + | 0.595942i | 0.959490 | − | 0.281741i | \(-0.0909119\pi\) |
0.479241 | + | 0.877683i | \(0.340912\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.972244i | 0.0544352i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.5537 | − | 18.5537i | −1.03557 | − | 1.03557i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.52721 | + | 5.52721i | 0.306594 | + | 0.306594i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 28.6056i | − | 1.58189i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.0349 | + | 4.98501i | 0.663505 | + | 0.274833i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.40024 | + | 2.40024i | −0.131929 | + | 0.131929i | −0.769988 | − | 0.638059i | \(-0.779738\pi\) |
0.638059 | + | 0.769988i | \(0.279738\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.3483 | + | 29.8114i | −0.676682 | + | 1.63365i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.98501 | − | 12.0349i | −0.272360 | − | 0.657536i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.1808 | + | 8.77339i | −1.15379 | + | 0.477917i | −0.875804 | − | 0.482667i | \(-0.839668\pi\) |
−0.277989 | + | 0.960584i | \(0.589668\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 44.2389 | 2.40273 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.60555 | −0.141099 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.2130 | + | 4.23034i | −0.551447 | + | 0.228417i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.7247 | + | 25.8917i | 0.577398 | + | 1.39396i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.98409 | − | 7.20423i | 0.160194 | − | 0.386743i | −0.823319 | − | 0.567579i | \(-0.807880\pi\) |
0.983513 | + | 0.180836i | \(0.0578802\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.7113 | + | 16.7113i | −0.894534 | + | 0.894534i | −0.994946 | − | 0.100412i | \(-0.967984\pi\) |
0.100412 | + | 0.994946i | \(0.467984\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 36.1047 | + | 14.9550i | 1.92712 | + | 0.798241i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 31.2111i | − | 1.66120i | −0.556870 | − | 0.830600i | \(-0.687998\pi\) | ||
0.556870 | − | 0.830600i | \(-0.312002\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.11300 | − | 4.11300i | −0.218295 | − | 0.218295i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.7419 | + | 11.7419i | 0.619714 | + | 0.619714i | 0.945458 | − | 0.325744i | \(-0.105615\pi\) |
−0.325744 | + | 0.945458i | \(0.605615\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 18.6333i | − | 0.980700i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −32.5443 | − | 13.4803i | −1.70813 | − | 0.707532i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.89949 | + | 9.89949i | −0.518163 | + | 0.518163i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.73876 | + | 9.02616i | −0.195162 | + | 0.471162i | −0.990920 | − | 0.134452i | \(-0.957073\pi\) |
0.795758 | + | 0.605614i | \(0.207073\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.11609 | + | 9.93713i | 0.214275 | + | 0.517306i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.6788 | − | 6.49435i | 0.814000 | − | 0.337170i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.0278 | −1.08878 | −0.544388 | − | 0.838834i | \(-0.683238\pi\) | ||||
−0.544388 | + | 0.838834i | \(0.683238\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 36.8444 | 1.90264 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.46581 | − | 2.26401i | 0.281503 | − | 0.116602i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.2163 | + | 27.0785i | 0.576142 | + | 1.39093i | 0.896251 | + | 0.443548i | \(0.146280\pi\) |
−0.320109 | + | 0.947381i | \(0.603720\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.754670 | + | 1.82194i | −0.0386629 | + | 0.0933406i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.7139 | − | 13.7139i | 0.700750 | − | 0.700750i | −0.263822 | − | 0.964571i | \(-0.584983\pi\) |
0.964571 | + | 0.263822i | \(0.0849830\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.82194 | + | 0.754670i | 0.0928544 | + | 0.0384616i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 25.8167i | − | 1.31233i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.20071 | − | 7.20071i | −0.365091 | − | 0.365091i | 0.500592 | − | 0.865683i | \(-0.333116\pi\) |
−0.865683 | + | 0.500592i | \(0.833116\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.5257 | − | 20.5257i | −1.03539 | − | 1.03539i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 0.605551i | − | 0.0304686i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.7591 | + | 4.87076i | 0.590171 | + | 0.244457i | 0.657724 | − | 0.753259i | \(-0.271519\pi\) |
−0.0675534 | + | 0.997716i | \(0.521519\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.54118 | + | 4.54118i | −0.227344 | + | 0.227344i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.78837 | + | 9.14594i | −0.189182 | + | 0.456726i | −0.989803 | − | 0.142445i | \(-0.954503\pi\) |
0.800620 | + | 0.599172i | \(0.204503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.06740 | + | 14.6480i | 0.302239 | + | 0.729669i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 34.0069 | − | 14.0861i | 1.68982 | − | 0.699945i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.81665 | 0.0900482 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.2111 | 1.14772 | 0.573858 | − | 0.818955i | \(-0.305446\pi\) | ||||
0.573858 | + | 0.818955i | \(0.305446\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.83938 | + | 3.24718i | −0.386688 | + | 0.160171i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.7247 | − | 25.8917i | −0.527728 | − | 1.27405i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.64230 | − | 23.2786i | 0.473322 | − | 1.14270i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.986024 | + | 0.986024i | −0.0482858 | + | 0.0482858i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.00872 | + | 1.24625i | 0.146986 | + | 0.0608835i | 0.454964 | − | 0.890510i | \(-0.349652\pi\) |
−0.307978 | + | 0.951394i | \(0.599652\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.6056i | 0.906779i | 0.891312 | + | 0.453390i | \(0.149785\pi\) | ||||
−0.891312 | + | 0.453390i | \(0.850215\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21.5117 | − | 21.5117i | −1.04594 | − | 1.04594i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.2272 | − | 20.2272i | −0.978862 | − | 0.978862i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 3.63331i | − | 0.175418i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.45708 | + | 1.01776i | 0.118354 | + | 0.0490237i | 0.441074 | − | 0.897471i | \(-0.354597\pi\) |
−0.322721 | + | 0.946494i | \(0.604597\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.6262 | + | 10.6262i | −0.510664 | + | 0.510664i | −0.914730 | − | 0.404066i | \(-0.867597\pi\) |
0.404066 | + | 0.914730i | \(0.367597\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.00185 | − | 9.66131i | 0.191874 | − | 0.463224i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.41011 | + | 3.40432i | 0.0674549 | + | 0.162851i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.3662 | + | 14.2350i | −1.64021 | + | 0.679398i | −0.996319 | − | 0.0857193i | \(-0.972681\pi\) |
−0.643891 | + | 0.765117i | \(0.722681\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −27.4222 | −1.30582 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.2111 | −0.817724 | −0.408862 | − | 0.912596i | \(-0.634074\pi\) | ||||
−0.408862 | + | 0.912596i | \(0.634074\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.2130 | − | 4.23034i | 0.484140 | − | 0.200537i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.4962 | + | 25.3401i | 0.496453 | + | 1.19854i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.10111 | − | 21.9720i | 0.429508 | − | 1.03692i | −0.549936 | − | 0.835207i | \(-0.685348\pi\) |
0.979444 | − | 0.201717i | \(-0.0646521\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.428189 | − | 0.428189i | 0.0201627 | − | 0.0201627i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.8568 | − | 5.73968i | −0.651050 | − | 0.269674i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 12.0000i | − | 0.562569i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.8840 | + | 25.8840i | 1.21080 | + | 1.21080i | 0.970763 | + | 0.240041i | \(0.0771610\pi\) |
0.240041 | + | 0.970763i | \(0.422839\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.6554 | + | 20.6554i | 0.962016 | + | 0.962016i | 0.999305 | − | 0.0372881i | \(-0.0118719\pi\) |
−0.0372881 | + | 0.999305i | \(0.511872\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.6333i | 1.84192i | 0.389662 | + | 0.920958i | \(0.372592\pi\) | ||||
−0.389662 | + | 0.920958i | \(0.627408\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 25.8917 | + | 10.7247i | 1.20070 | + | 0.497346i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.4826 | − | 11.4826i | 0.531352 | − | 0.531352i | −0.389623 | − | 0.920975i | \(-0.627395\pi\) |
0.920975 | + | 0.389623i | \(0.127395\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.4794 | − | 27.7136i | 0.530068 | − | 1.27970i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.4962 | + | 25.3401i | 0.483639 | + | 1.16761i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.34283 | + | 0.556218i | −0.0617433 | + | 0.0255749i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.81665 | 0.0833538 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −39.6333 | −1.81468 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.0744 | + | 6.65821i | −0.734456 | + | 0.304222i | −0.718382 | − | 0.695649i | \(-0.755117\pi\) |
−0.0160742 | + | 0.999871i | \(0.505117\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.23034 | − | 10.2130i | −0.192887 | − | 0.465670i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −24.6966 | + | 59.6228i | −1.12373 | + | 2.71293i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.7559 | − | 10.7559i | 0.488399 | − | 0.488399i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.6434 | − | 9.37922i | −1.02607 | − | 0.425013i | −0.194779 | − | 0.980847i | \(-0.562399\pi\) |
−0.831293 | + | 0.555834i | \(0.812399\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.8167i | 0.896140i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.94142 | + | 6.94142i | 0.313262 | + | 0.313262i | 0.846172 | − | 0.532910i | \(-0.178902\pi\) |
−0.532910 | + | 0.846172i | \(0.678902\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.25662 | − | 3.25662i | −0.146374 | − | 0.146374i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 13.3944i | − | 0.600823i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.4612 | − | 5.57582i | −0.602607 | − | 0.249608i | 0.0604568 | − | 0.998171i | \(-0.480744\pi\) |
−0.663064 | + | 0.748563i | \(0.730744\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 48.5507 | − | 48.5507i | 2.16909 | − | 2.16909i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.8904 | − | 35.9486i | 0.663930 | − | 1.60287i | −0.127661 | − | 0.991818i | \(-0.540747\pi\) |
0.791591 | − | 0.611052i | \(-0.209253\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.73968 | − | 13.8568i | −0.255413 | − | 0.616620i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.6875 | − | 7.74061i | 0.829940 | − | 0.343772i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.21110 | 0.142330 | 0.0711648 | − | 0.997465i | \(-0.477328\pi\) | ||||
0.0711648 | + | 0.997465i | \(0.477328\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.2389 | −1.42616 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.39102 | − | 3.47567i | 0.370472 | − | 0.153455i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.14980 | − | 17.2611i | −0.315058 | − | 0.760617i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.655444 | + | 1.58238i | −0.0288264 | + | 0.0695931i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 48.2522 | − | 48.2522i | 2.11803 | − | 2.11803i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.9853 | + | 7.03555i | 0.744140 | + | 0.308233i | 0.722348 | − | 0.691530i | \(-0.243063\pi\) |
0.0217921 | + | 0.999763i | \(0.493063\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 12.0000i | − | 0.524723i | −0.964970 | − | 0.262362i | \(-0.915499\pi\) | ||
0.964970 | − | 0.262362i | \(-0.0845013\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 22.4978 | + | 22.4978i | 0.981883 | + | 0.981883i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.91912 | + | 9.91912i | 0.431266 | + | 0.431266i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 65.4500i | 2.84029i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.40432 | − | 1.41011i | −0.147457 | − | 0.0610788i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.05709 | − | 8.05709i | 0.348338 | − | 0.348338i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.7284 | − | 45.2143i | 0.808190 | − | 1.95114i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.590809 | + | 1.42634i | 0.0254480 | + | 0.0614368i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.91969 | − | 1.62359i | 0.168521 | − | 0.0698035i | −0.296828 | − | 0.954931i | \(-0.595929\pi\) |
0.465349 | + | 0.885127i | \(0.345929\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −59.8722 | −2.56936 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.4222 | 0.532109 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.0436 | − | 6.23127i | 0.643218 | − | 0.266430i | −0.0371393 | − | 0.999310i | \(-0.511825\pi\) |
0.680357 | + | 0.732880i | \(0.261825\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 25.5655 | + | 61.7205i | 1.09111 | + | 2.63417i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.526174 | − | 1.27030i | 0.0224158 | − | 0.0541165i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.986024 | − | 0.986024i | 0.0419300 | − | 0.0419300i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −18.0523 | − | 7.47752i | −0.766279 | − | 0.317403i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 21.3944i | − | 0.906512i | −0.891380 | − | 0.453256i | \(-0.850262\pi\) | ||
0.891380 | − | 0.453256i | \(-0.149738\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.25394 | + | 6.25394i | 0.264514 | + | 0.264514i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.5703 | + | 14.5703i | 0.614066 | + | 0.614066i | 0.944003 | − | 0.329937i | \(-0.107028\pi\) |
−0.329937 | + | 0.944003i | \(0.607028\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.2111i | 0.808217i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 78.3103 | + | 32.4372i | 3.28872 | + | 1.36223i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.5117 | + | 21.5117i | −0.901819 | + | 0.901819i | −0.995593 | − | 0.0937741i | \(-0.970107\pi\) |
0.0937741 | + | 0.995593i | \(0.470107\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.24625 | − | 3.00872i | 0.0521541 | − | 0.125911i | −0.895655 | − | 0.444749i | \(-0.853293\pi\) |
0.947809 | + | 0.318838i | \(0.103293\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.46069 | − | 20.4259i | −0.353450 | − | 0.853304i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.8655 | − | 6.98594i | 0.703342 | − | 0.291334i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.4500 | 1.30928 | 0.654640 | − | 0.755941i | \(-0.272820\pi\) | ||||
0.654640 | + | 0.755941i | \(0.272820\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 37.8167 | 1.57161 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 53.6053 | − | 22.2041i | 2.22392 | − | 0.921180i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.853896 | + | 2.06149i | 0.0353648 | + | 0.0853781i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.7247 | + | 25.8917i | −0.443412 | + | 1.07049i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.25662 | − | 3.25662i | 0.134415 | − | 0.134415i | −0.636698 | − | 0.771113i | \(-0.719700\pi\) |
0.771113 | + | 0.636698i | \(0.219700\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.40432 | + | 1.41011i | 0.140272 | + | 0.0581027i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 81.0833i | 3.33532i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.11567 | − | 1.11567i | −0.0458151 | − | 0.0458151i | 0.683828 | − | 0.729643i | \(-0.260314\pi\) |
−0.729643 | + | 0.683828i | \(0.760314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −32.9551 | − | 32.9551i | −1.34876 | − | 1.34876i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 26.0555i | − | 1.06460i | −0.846556 | − | 0.532300i | \(-0.821328\pi\) | ||
0.846556 | − | 0.532300i | \(-0.178672\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.50207 | + | 2.27903i | 0.224434 | + | 0.0929637i | 0.492067 | − | 0.870557i | \(-0.336241\pi\) |
−0.267633 | + | 0.963521i | \(0.586241\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −49.5367 | + | 49.5367i | −2.01729 | + | 2.01729i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.85393 | − | 14.1326i | 0.237996 | − | 0.574573i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.14887 | + | 12.4305i | 0.208986 | + | 0.504538i | 0.993264 | − | 0.115872i | \(-0.0369663\pi\) |
−0.784278 | + | 0.620410i | \(0.786966\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 22.2478 | − | 9.21536i | 0.901528 | − | 0.373425i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.4222 | 0.421637 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.4222 | 1.63264 | 0.816319 | − | 0.577602i | \(-0.196011\pi\) | ||||
0.816319 | + | 0.577602i | \(0.196011\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.01744 | + | 2.49251i | −0.242647 | + | 0.100508i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.868918 | − | 2.09775i | −0.0349813 | − | 0.0844524i | 0.905423 | − | 0.424510i | \(-0.139554\pi\) |
−0.940405 | + | 0.340057i | \(0.889554\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.83983 | + | 18.9270i | −0.315109 | + | 0.760742i | 0.684390 | + | 0.729116i | \(0.260068\pi\) |
−0.999500 | + | 0.0316257i | \(0.989932\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 64.5352 | − | 64.5352i | 2.58971 | − | 2.58971i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.5181 | + | 9.74153i | 0.942234 | + | 0.390286i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000i | 0.0400000i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.597088 | − | 0.597088i | −0.0238454 | − | 0.0238454i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.1395 | + | 17.1395i | 0.682311 | + | 0.682311i | 0.960520 | − | 0.278209i | \(-0.0897409\pi\) |
−0.278209 | + | 0.960520i | \(0.589741\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 71.4500i | 2.83988i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.791191 | − | 0.327722i | −0.0313975 | − | 0.0130053i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.64288 | − | 6.64288i | 0.263200 | − | 0.263200i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.9709 | + | 28.9004i | −0.473563 | + | 1.14328i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.6779 | + | 40.2639i | 0.658736 | + | 1.59033i | 0.799758 | + | 0.600322i | \(0.204961\pi\) |
−0.141023 | + | 0.990006i | \(0.545039\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.38229 | − | 2.22942i | 0.212257 | − | 0.0879197i | −0.274022 | − | 0.961724i | \(-0.588354\pi\) |
0.486279 | + | 0.873804i | \(0.338354\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.6333 | 0.615561 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.2111 | −0.676638 | −0.338319 | − | 0.941031i | \(-0.609858\pi\) | ||||
−0.338319 | + | 0.941031i | \(0.609858\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.40432 | − | 1.41011i | 0.133631 | − | 0.0553518i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.6966 | + | 59.6228i | 0.967935 | + | 2.33680i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.4307 | + | 32.4245i | −0.525583 | + | 1.26887i | 0.408808 | + | 0.912620i | \(0.365945\pi\) |
−0.934391 | + | 0.356249i | \(0.884055\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.91347 | − | 8.91347i | 0.348278 | − | 0.348278i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 69.5599 | + | 28.8127i | 2.71379 | + | 1.12409i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 32.0000i | − | 1.24654i | −0.782006 | − | 0.623272i | \(-0.785803\pi\) | ||
0.782006 | − | 0.623272i | \(-0.214197\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.856379 | + | 0.856379i | 0.0333093 | + | 0.0333093i | 0.723565 | − | 0.690256i | \(-0.242502\pi\) |
−0.690256 | + | 0.723565i | \(0.742502\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.97205 | − | 1.97205i | −0.0764728 | − | 0.0764728i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 13.8167i | − | 0.534983i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −53.6053 | − | 22.2041i | −2.07250 | − | 0.858459i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.65953 | − | 2.65953i | 0.102670 | − | 0.102670i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.03370 | − | 7.32401i | 0.116941 | − | 0.282320i | −0.854562 | − | 0.519350i | \(-0.826174\pi\) |
0.971502 | + | 0.237030i | \(0.0761741\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17.2190 | − | 41.5705i | −0.662762 | − | 1.60005i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.9413 | + | 8.67416i | −0.804838 | + | 0.333375i | −0.746893 | − | 0.664945i | \(-0.768455\pi\) |
−0.0579459 | + | 0.998320i | \(0.518455\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 35.0278 | 1.34424 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.39445 | 0.0534354 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.947233 | − | 0.392357i | 0.0362449 | − | 0.0150131i | −0.364487 | − | 0.931208i | \(-0.618756\pi\) |
0.400732 | + | 0.916195i | \(0.368756\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.41011 | − | 3.40432i | −0.0538777 | − | 0.130072i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.73968 | − | 13.8568i | 0.218983 | − | 0.528671i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.60095 | − | 9.60095i | 0.365767 | − | 0.365767i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.20423 | − | 2.98409i | −0.274062 | − | 0.113520i | 0.241420 | − | 0.970421i | \(-0.422387\pi\) |
−0.515482 | + | 0.856901i | \(0.672387\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 10.6056i | − | 0.402872i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.428189 | − | 0.428189i | −0.0162422 | − | 0.0162422i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.2551 | + | 18.2551i | 0.690472 | + | 0.690472i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.81665i | 0.295231i | 0.989045 | + | 0.147615i | \(0.0471598\pi\) | ||||
−0.989045 | + | 0.147615i | \(0.952840\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.37357 | − | 0.983166i | −0.0895210 | − | 0.0370808i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.0265 | − | 13.0265i | 0.490605 | − | 0.490605i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.2172 | − | 31.9091i | 0.497084 | − | 1.20007i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.79022 | + | 18.8073i | 0.292568 | + | 0.706321i | 1.00000 | 0.000460118i | \(-0.000146460\pi\) | |
−0.707432 | + | 0.706781i | \(0.750146\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.00872 | + | 1.24625i | −0.112836 | + | 0.0467381i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 37.0278 | 1.38670 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.57779 | 0.0590062 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −44.4957 | + | 18.4307i | −1.66172 | + | 0.688308i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.55714 | + | 6.17348i | 0.0953653 | + | 0.230232i | 0.964362 | − | 0.264585i | \(-0.0852350\pi\) |
−0.868997 | + | 0.494817i | \(0.835235\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.4644 | − | 39.7485i | 0.613166 | − | 1.48031i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −29.3095 | + | 29.3095i | −1.09003 | + | 1.09003i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.29326 | − | 2.60675i | −0.233726 | − | 0.0968124i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 6.42221i | − | 0.238186i | −0.992883 | − | 0.119093i | \(-0.962001\pi\) | ||
0.992883 | − | 0.119093i | \(-0.0379987\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −36.3610 | − | 36.3610i | −1.34670 | − | 1.34670i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.5662 | − | 32.5662i | −1.20286 | − | 1.20286i | −0.973293 | − | 0.229566i | \(-0.926269\pi\) |
−0.229566 | − | 0.973293i | \(-0.573731\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 16.6056i | − | 0.612505i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.64387 | + | 1.50934i | 0.134224 | + | 0.0555973i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.5091 | − | 24.5091i | 0.901581 | − | 0.901581i | −0.0939921 | − | 0.995573i | \(-0.529963\pi\) |
0.995573 | + | 0.0939921i | \(0.0299628\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.96633 | + | 4.74715i | −0.0722350 | + | 0.174391i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.96910 | + | 19.2391i | 0.292358 | + | 0.705815i | 1.00000 | 0.000756791i | \(-0.000240894\pi\) | |
−0.707642 | + | 0.706571i | \(0.750241\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.0041 | + | 4.55806i | −0.403161 | + | 0.166995i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −135.505 | −4.95789 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26.2389 | 0.958747 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.21753 | + | 0.918531i | −0.0809188 | + | 0.0335177i | −0.422776 | − | 0.906234i | \(-0.638944\pi\) |
0.341857 | + | 0.939752i | \(0.388944\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.9550 | − | 36.1047i | −0.544992 | − | 1.31573i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.49251 | − | 6.01744i | 0.0907116 | − | 0.218997i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.5968 | + | 27.5968i | −1.00302 | + | 1.00302i | −0.00302702 | + | 0.999995i | \(0.500964\pi\) |
−0.999995 | + | 0.00302702i | \(0.999036\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.83938 | − | 3.24718i | −0.284551 | − | 0.117865i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 31.4500i | − | 1.14006i | −0.821624 | − | 0.570030i | \(-0.806932\pi\) | ||
0.821624 | − | 0.570030i | \(-0.193068\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.2272 | + | 20.2272i | 0.732273 | + | 0.732273i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.8549 | − | 15.8549i | −0.572487 | − | 0.572487i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.6056i | 0.670933i | 0.942052 | + | 0.335467i | \(0.108894\pi\) | ||||
−0.942052 | + | 0.335467i | \(0.891106\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 58.3525 | + | 24.1704i | 2.10151 | + | 0.870475i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.2272 | + | 20.2272i | −0.727521 | + | 0.727521i | −0.970125 | − | 0.242604i | \(-0.921998\pi\) |
0.242604 | + | 0.970125i | \(0.421998\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.98594 | − | 16.8655i | 0.250942 | − | 0.605828i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.2190 | − | 41.5705i | −0.617730 | − | 1.49133i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.791191 | + | 0.327722i | −0.0283474 | + | 0.0117419i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.76114 | 0.0630186 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −34.0555 | −1.21704 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.0041 | + | 4.55806i | −0.392755 | + | 0.162684i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.96910 | − | 19.2391i | −0.284068 | − | 0.685800i | 0.715855 | − | 0.698249i | \(-0.246037\pi\) |
−0.999923 | + | 0.0124489i | \(0.996037\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28.6984 | − | 69.2841i | 1.02169 | − | 2.46658i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.2816 | + | 31.2816i | −1.11225 | + | 1.11225i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.1446 | − | 8.75836i | −0.750865 | − | 0.311019i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 24.0000i | − | 0.851192i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.56914 | − | 2.56914i | −0.0910035 | − | 0.0910035i | 0.660140 | − | 0.751143i | \(-0.270497\pi\) |
−0.751143 | + | 0.660140i | \(0.770497\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −42.0375 | − | 42.0375i | −1.48532 | − | 1.48532i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 4.23886i | − | 0.149586i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25.8917 | − | 10.7247i | −0.912563 | − | 0.377996i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 56.7374 | − | 56.7374i | 1.99725 | − | 1.99725i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.2659 | + | 27.1983i | −0.396088 | + | 0.956240i | 0.592497 | + | 0.805573i | \(0.298142\pi\) |
−0.988585 | + | 0.150667i | \(0.951858\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.80432 | + | 14.0129i | 0.203817 | + | 0.492058i | 0.992427 | − | 0.122836i | \(-0.0391988\pi\) |
−0.788610 | + | 0.614894i | \(0.789199\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.64387 | + | 1.50934i | −0.127796 | + | 0.0529349i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.60555 | −0.301439 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.05551 | 0.0719133 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −59.6228 | + | 24.6966i | −2.08339 | + | 0.862968i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.93632 | − | 16.7458i | −0.242079 | − | 0.584431i | 0.755410 | − | 0.655253i | \(-0.227438\pi\) |
−0.997489 | + | 0.0708216i | \(0.977438\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.98594 | + | 16.8655i | −0.243514 | + | 0.587896i | −0.997627 | − | 0.0688493i | \(-0.978067\pi\) |
0.754113 | + | 0.656745i | \(0.228067\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.95807 | + | 2.95807i | −0.102987 | + | 0.102987i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.23497 | + | 3.41104i | 0.286358 | + | 0.118613i | 0.521239 | − | 0.853411i | \(-0.325470\pi\) |
−0.234881 | + | 0.972024i | \(0.575470\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 18.8444i | − | 0.654493i | −0.944939 | − | 0.327247i | \(-0.893879\pi\) | ||
0.944939 | − | 0.327247i | \(-0.106121\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.7419 | − | 11.7419i | −0.407322 | − | 0.407322i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.0836 | + | 21.0836i | 0.729627 | + | 0.729627i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 91.2666i | − | 3.15464i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.4787 | + | 8.06833i | 0.672478 | + | 0.278550i | 0.692679 | − | 0.721246i | \(-0.256430\pi\) |
−0.0202004 | + | 0.999796i | \(0.506430\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.8605 | − | 16.8605i | 0.581398 | − | 0.581398i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22.9587 | + | 55.4273i | −0.790741 | + | 1.90902i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.36142 | + | 8.11520i | 0.115637 | + | 0.279171i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32.5443 | − | 13.4803i | 1.11824 | − | 0.463188i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.76114 | 0.335001 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.8167 | −0.884983 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.4420 | + | 15.9232i | −1.31623 | + | 0.545199i | −0.926695 | − | 0.375813i | \(-0.877363\pi\) |
−0.389532 | + | 0.921013i | \(0.627363\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.49251 | + | 6.01744i | 0.0852419 | + | 0.205792i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.0843 | − | 24.3456i | 0.344472 | − | 0.831630i | −0.652780 | − | 0.757548i | \(-0.726397\pi\) |
0.997252 | − | 0.0740819i | \(-0.0236026\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.28457 | + | 1.28457i | −0.0438289 | + | 0.0438289i | −0.728682 | − | 0.684853i | \(-0.759867\pi\) |
0.684853 | + | 0.728682i | \(0.259867\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.8568 | − | 5.73968i | −0.472239 | − | 0.195608i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 52.4777i | − | 1.78636i | −0.449697 | − | 0.893181i | \(-0.648468\pi\) | ||
0.449697 | − | 0.893181i | \(-0.351532\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.9539 | + | 20.9539i | 0.712454 | + | 0.712454i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.129645 | + | 0.129645i | 0.00439792 | + | 0.00439792i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 24.0000i | − | 0.813209i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −75.5774 | − | 31.3052i | −2.55791 | − | 1.05952i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −26.0529 | + | 26.0529i | −0.880750 | + | 0.880750i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.968144 | − | 2.33731i | 0.0326919 | − | 0.0789253i | −0.906690 | − | 0.421797i | \(-0.861400\pi\) |
0.939382 | + | 0.342872i | \(0.111400\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.9606 | + | 65.0886i | 0.909358 | + | 2.19538i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.6333 | + | 13.1030i | −1.06575 | + | 0.441450i | −0.845490 | − | 0.533991i | \(-0.820692\pi\) |
−0.220264 | + | 0.975440i | \(0.570692\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.5778 | −0.860761 | −0.430381 | − | 0.902647i | \(-0.641621\pi\) | ||||
−0.430381 | + | 0.902647i | \(0.641621\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −39.6333 | −1.33226 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.2832 | − | 6.33049i | 0.513158 | − | 0.212557i | −0.111050 | − | 0.993815i | \(-0.535421\pi\) |
0.624209 | + | 0.781258i | \(0.285421\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.754670 | − | 1.82194i | −0.0253108 | − | 0.0611057i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.26493 | + | 10.2965i | −0.142881 | + | 0.344944i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.71276 | − | 1.71276i | 0.0573152 | − | 0.0573152i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.6347 | + | 8.13296i | 0.656316 | + | 0.271855i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 51.6333i | 1.72399i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.76985 | − | 9.76985i | −0.325843 | − | 0.325843i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.4558 | + | 25.4558i | 0.847117 | + | 0.847117i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 26.0000i | − | 0.864269i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.0652 | − | 13.2818i | −1.06471 | − | 0.441016i | −0.219587 | − | 0.975593i | \(-0.570471\pi\) |
−0.845120 | + | 0.534577i | \(0.820471\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −57.0360 | + | 57.0360i | −1.89176 | + | 1.89176i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.55714 | − | 6.17348i | 0.0847219 | − | 0.204537i | −0.875841 | − | 0.482600i | \(-0.839693\pi\) |
0.960563 | + | 0.278063i | \(0.0896925\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.91945 | + | 7.04819i | 0.0966198 | + | 0.233261i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −37.3750 | + | 15.4812i | −1.23558 | + | 0.511793i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 29.0278 | 0.958581 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.8444 | 1.34733 | 0.673666 | − | 0.739036i | \(-0.264718\pi\) | ||||
0.673666 | + | 0.739036i | \(0.264718\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 63.8183 | − | 26.4344i | 2.10288 | − | 0.871043i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.10107 | − | 9.90087i | −0.134988 | − | 0.325891i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.87076 | + | 11.7591i | −0.160150 | + | 0.386636i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −71.0485 | + | 71.0485i | −2.33354 | + | 2.33354i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.30656 | + | 0.541196i | 0.0428669 | + | 0.0177561i | 0.404014 | − | 0.914753i | \(-0.367615\pi\) |
−0.361147 | + | 0.932509i | \(0.617615\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2.18335i | − | 0.0715563i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −61.5772 | − | 61.5772i | −2.01595 | − | 2.01595i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.54118 | + | 4.54118i | 0.148354 | + | 0.148354i | 0.777382 | − | 0.629028i | \(-0.216547\pi\) |
−0.629028 | + | 0.777382i | \(0.716547\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.6056i | 0.933507i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.9413 | + | 8.67416i | 0.682666 | + | 0.282770i | 0.696941 | − | 0.717129i | \(-0.254544\pi\) |
−0.0142749 | + | 0.999898i | \(0.504544\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.08504 | + | 6.08504i | −0.198156 | + | 0.198156i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −26.4344 | + | 63.8183i | −0.859911 | + | 2.07601i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.01960 | − | 12.1184i | −0.163115 | − | 0.393795i | 0.821097 | − | 0.570789i | \(-0.193363\pi\) |
−0.984212 | + | 0.176994i | \(0.943363\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.8302 | + | 9.87080i | −0.773562 | + | 0.320420i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 90.2944 | 2.92800 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 50.2389 | 1.62740 | 0.813698 | − | 0.581288i | \(-0.197451\pi\) | ||||
0.813698 | + | 0.581288i | \(0.197451\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.87012 | − | 3.67412i | 0.287030 | − | 0.118892i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.21166 | + | 2.92521i | 0.0391675 | + | 0.0945586i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.24718 | − | 7.83938i | 0.104857 | − | 0.253147i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.26227 | − | 4.26227i | 0.137492 | − | 0.137492i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −56.6141 | − | 23.4503i | −1.82436 | − | 0.755676i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.4222i | 0.528649i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.4267 | − | 15.4267i | −0.496089 | − | 0.496089i | 0.414129 | − | 0.910218i | \(-0.364086\pi\) |
−0.910218 | + | 0.414129i | \(0.864086\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.9105 | + | 38.9105i | 1.24870 | + | 1.24870i | 0.956296 | + | 0.292402i | \(0.0944545\pi\) |
0.292402 | + | 0.956296i | \(0.405546\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1.39445i | − | 0.0447040i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 23.5181 | + | 9.74153i | 0.753183 | + | 0.311979i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.9108 | − | 11.9108i | 0.381060 | − | 0.381060i | −0.490424 | − | 0.871484i | \(-0.663158\pi\) |
0.871484 | + | 0.490424i | \(0.163158\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.28084 | + | 3.09223i | −0.0409360 | + | 0.0988282i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.5655 | − | 61.7205i | −0.816243 | − | 1.97059i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.6085 | − | 4.39420i | 0.338360 | − | 0.140153i | −0.207033 | − | 0.978334i | \(-0.566381\pi\) |
0.545393 | + | 0.838181i | \(0.316381\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −35.2111 | −1.12192 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 42.4222 | 1.35031 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.0831 | − | 7.90447i | 0.606806 | − | 0.251347i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.7256 | + | 30.7224i | 0.404243 | + | 0.975928i | 0.986624 | + | 0.163012i | \(0.0521210\pi\) |
−0.582381 | + | 0.812916i | \(0.697879\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.23034 | + | 10.2130i | −0.134246 | + | 0.324098i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.3110 | − | 14.3110i | 0.453690 | − | 0.453690i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.2680 | + | 21.2359i | 1.62368 | + | 0.672548i | 0.994502 | − | 0.104717i | \(-0.0333937\pi\) |
0.629173 | + | 0.777265i | \(0.283394\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 63.6333i | 2.01327i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))