Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,2,Mod(37,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.14984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 109.3 | ||
Root | \(0.500000 - 1.44392i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.109 |
Dual form | 144.2.k.b.37.3 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.167452 | + | 1.40426i | 0.118406 | + | 0.992965i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.94392 | + | 0.470294i | −0.971960 | + | 0.235147i | ||||
\(5\) | −1.74912 | + | 1.74912i | −0.782229 | + | 0.782229i | −0.980207 | − | 0.197977i | \(-0.936563\pi\) |
0.197977 | + | 0.980207i | \(0.436563\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.55765i | 0.966700i | 0.875427 | + | 0.483350i | \(0.160580\pi\) | ||||
−0.875427 | + | 0.483350i | \(0.839420\pi\) | |||||||
\(8\) | −0.985930 | − | 2.65103i | −0.348579 | − | 0.937279i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.74912 | − | 2.16333i | −0.869347 | − | 0.684105i | ||||
\(11\) | −0.473626 | + | 0.473626i | −0.142804 | + | 0.142804i | −0.774894 | − | 0.632091i | \(-0.782197\pi\) |
0.632091 | + | 0.774894i | \(0.282197\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.88784 | + | 2.88784i | 0.800943 | + | 0.800943i | 0.983243 | − | 0.182300i | \(-0.0583543\pi\) |
−0.182300 | + | 0.983243i | \(0.558354\pi\) | |||||||
\(14\) | −3.59161 | + | 0.428283i | −0.959899 | + | 0.114463i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.55765 | − | 1.82843i | 0.889412 | − | 0.457107i | ||||
\(17\) | 6.44549 | 1.56326 | 0.781630 | − | 0.623742i | \(-0.214389\pi\) | ||||
0.781630 | + | 0.623742i | \(0.214389\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.55765 | − | 4.55765i | −1.04560 | − | 1.04560i | −0.998910 | − | 0.0466864i | \(-0.985134\pi\) |
−0.0466864 | − | 0.998910i | \(-0.514866\pi\) | |||||||
\(20\) | 2.57754 | − | 4.22274i | 0.576357 | − | 0.944234i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.744406 | − | 0.585786i | −0.158708 | − | 0.124890i | ||||
\(23\) | − | 2.82843i | − | 0.589768i | −0.955533 | − | 0.294884i | \(-0.904719\pi\) | ||
0.955533 | − | 0.294884i | \(-0.0952810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.11882i | − | 0.223765i | ||||||
\(26\) | −3.57172 | + | 4.53887i | −0.700471 | + | 0.890145i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.20285 | − | 4.97186i | −0.227317 | − | 0.939593i | ||||
\(29\) | 3.07931 | + | 3.07931i | 0.571813 | + | 0.571813i | 0.932635 | − | 0.360821i | \(-0.117504\pi\) |
−0.360821 | + | 0.932635i | \(0.617504\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.55765 | 1.17779 | 0.588894 | − | 0.808210i | \(-0.299563\pi\) | ||||
0.588894 | + | 0.808210i | \(0.299563\pi\) | |||||||
\(32\) | 3.16333 | + | 4.68971i | 0.559203 | + | 0.829031i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.07931 | + | 9.05117i | 0.185100 | + | 1.55226i | ||||
\(35\) | −4.47363 | − | 4.47363i | −0.756181 | − | 0.756181i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.72922 | + | 2.72922i | −0.448681 | + | 0.448681i | −0.894916 | − | 0.446235i | \(-0.852765\pi\) |
0.446235 | + | 0.894916i | \(0.352765\pi\) | |||||||
\(38\) | 5.63696 | − | 7.16333i | 0.914435 | − | 1.16205i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.36147 | + | 2.91245i | 1.00584 | + | 0.460499i | ||||
\(41\) | − | 0.788632i | − | 0.123164i | −0.998102 | − | 0.0615818i | \(-0.980385\pi\) | ||
0.998102 | − | 0.0615818i | \(-0.0196145\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.389604 | + | 0.389604i | −0.0594141 | + | 0.0594141i | −0.736190 | − | 0.676775i | \(-0.763377\pi\) |
0.676775 | + | 0.736190i | \(0.263377\pi\) | |||||||
\(44\) | 0.697947 | − | 1.14343i | 0.105219 | − | 0.172379i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.97186 | − | 0.473626i | 0.585619 | − | 0.0698323i | ||||
\(47\) | −2.82843 | −0.412568 | −0.206284 | − | 0.978492i | \(-0.566137\pi\) | ||||
−0.206284 | + | 0.978492i | \(0.566137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.458440 | 0.0654915 | ||||||||
\(50\) | 1.57113 | − | 0.187349i | 0.222191 | − | 0.0264952i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.97186 | − | 4.25559i | −0.966823 | − | 0.590145i | ||||
\(53\) | 2.57754 | − | 2.57754i | 0.354053 | − | 0.354053i | −0.507562 | − | 0.861615i | \(-0.669453\pi\) |
0.861615 | + | 0.507562i | \(0.169453\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.65685i | − | 0.223410i | ||||||
\(56\) | 6.78039 | − | 2.52166i | 0.906068 | − | 0.336971i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.80853 | + | 4.83980i | −0.500084 | + | 0.635497i | ||||
\(59\) | −4.00000 | + | 4.00000i | −0.520756 | + | 0.520756i | −0.917800 | − | 0.397044i | \(-0.870036\pi\) |
0.397044 | + | 0.917800i | \(0.370036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.38607 | − | 4.38607i | −0.561579 | − | 0.561579i | 0.368177 | − | 0.929756i | \(-0.379982\pi\) |
−0.929756 | + | 0.368177i | \(0.879982\pi\) | |||||||
\(62\) | 1.09809 | + | 9.20867i | 0.139458 | + | 1.16950i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.05588 | + | 5.22746i | −0.756985 | + | 0.653432i | ||||
\(65\) | −10.1023 | −1.25304 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.11882 | − | 2.11882i | −0.258856 | − | 0.258856i | 0.565733 | − | 0.824589i | \(-0.308593\pi\) |
−0.824589 | + | 0.565733i | \(0.808593\pi\) | |||||||
\(68\) | −12.5295 | + | 3.03127i | −1.51943 | + | 0.367596i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.53304 | − | 7.03127i | 0.661325 | − | 0.840398i | ||||
\(71\) | 5.11529i | 0.607074i | 0.952820 | + | 0.303537i | \(0.0981676\pi\) | ||||
−0.952820 | + | 0.303537i | \(0.901832\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 14.7721i | − | 1.72895i | −0.502676 | − | 0.864475i | \(-0.667651\pi\) | ||
0.502676 | − | 0.864475i | \(-0.332349\pi\) | |||||||
\(74\) | −4.28956 | − | 3.37553i | −0.498651 | − | 0.392398i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.0031 | + | 6.71627i | 1.26215 | + | 0.770409i | ||||
\(77\) | −1.21137 | − | 1.21137i | −0.138048 | − | 0.138048i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.32000 | −0.711055 | −0.355528 | − | 0.934666i | \(-0.615699\pi\) | ||||
−0.355528 | + | 0.934666i | \(0.615699\pi\) | |||||||
\(80\) | −3.02461 | + | 9.42088i | −0.338162 | + | 1.05329i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.10745 | − | 0.132058i | 0.122297 | − | 0.0145834i | ||||
\(83\) | −0.641669 | − | 0.641669i | −0.0704323 | − | 0.0704323i | 0.671013 | − | 0.741445i | \(-0.265859\pi\) |
−0.741445 | + | 0.671013i | \(0.765859\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.2739 | + | 11.2739i | −1.22283 | + | 1.22283i | ||||
\(86\) | −0.612348 | − | 0.481868i | −0.0660311 | − | 0.0519611i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.72256 | + | 0.788632i | 0.183625 | + | 0.0840685i | ||||
\(89\) | − | 6.31724i | − | 0.669626i | −0.942285 | − | 0.334813i | \(-0.891327\pi\) | ||
0.942285 | − | 0.334813i | \(-0.108673\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.38607 | + | 7.38607i | −0.774271 | + | 0.774271i | ||||
\(92\) | 1.33019 | + | 5.49824i | 0.138682 | + | 0.573231i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.473626 | − | 3.97186i | −0.0488508 | − | 0.409666i | ||||
\(95\) | 15.9437 | 1.63579 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.6533 | 1.28475 | 0.642375 | − | 0.766390i | \(-0.277949\pi\) | ||||
0.642375 | + | 0.766390i | \(0.277949\pi\) | |||||||
\(98\) | 0.0767667 | + | 0.643772i | 0.00775461 | + | 0.0650308i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.526176 | + | 2.17490i | 0.0526176 | + | 0.217490i | ||||
\(101\) | −7.52480 | + | 7.52480i | −0.748745 | + | 0.748745i | −0.974244 | − | 0.225498i | \(-0.927599\pi\) |
0.225498 | + | 0.974244i | \(0.427599\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 3.33686i | − | 0.328790i | −0.986395 | − | 0.164395i | \(-0.947433\pi\) | ||
0.986395 | − | 0.164395i | \(-0.0525672\pi\) | |||||||
\(104\) | 4.80853 | − | 10.5029i | 0.471515 | − | 1.02990i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.05117 | + | 3.18794i | 0.393484 | + | 0.309640i | ||||
\(107\) | 14.0625 | − | 14.0625i | 1.35948 | − | 1.35948i | 0.484918 | − | 0.874560i | \(-0.338849\pi\) |
0.874560 | − | 0.484918i | \(-0.161151\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.76901 | + | 2.76901i | 0.265224 | + | 0.265224i | 0.827172 | − | 0.561949i | \(-0.189948\pi\) |
−0.561949 | + | 0.827172i | \(0.689948\pi\) | |||||||
\(110\) | 2.32666 | − | 0.277444i | 0.221839 | − | 0.0264532i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.67647 | + | 9.09921i | 0.441885 | + | 0.859794i | ||||
\(113\) | −2.23765 | −0.210500 | −0.105250 | − | 0.994446i | \(-0.533564\pi\) | ||||
−0.105250 | + | 0.994446i | \(0.533564\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.94725 | + | 4.94725i | 0.461334 | + | 0.461334i | ||||
\(116\) | −7.43411 | − | 4.53775i | −0.690240 | − | 0.421320i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.28687 | − | 4.94725i | −0.578753 | − | 0.455431i | ||||
\(119\) | 16.4853i | 1.51120i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5514i | 0.959214i | ||||||||
\(122\) | 5.42475 | − | 6.89367i | 0.491134 | − | 0.624123i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −12.7475 | + | 3.08402i | −1.14476 | + | 0.276953i | ||||
\(125\) | −6.78863 | − | 6.78863i | −0.607194 | − | 0.607194i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.2145 | 1.08386 | 0.541931 | − | 0.840423i | \(-0.317693\pi\) | ||||
0.541931 | + | 0.840423i | \(0.317693\pi\) | |||||||
\(128\) | −8.35480 | − | 7.62872i | −0.738467 | − | 0.674290i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.69166 | − | 14.1864i | −0.148368 | − | 1.24423i | ||||
\(131\) | 3.77568 | + | 3.77568i | 0.329883 | + | 0.329883i | 0.852542 | − | 0.522659i | \(-0.175060\pi\) |
−0.522659 | + | 0.852542i | \(0.675060\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.6569 | − | 11.6569i | 1.01078 | − | 1.01078i | ||||
\(134\) | 2.62059 | − | 3.33019i | 0.226384 | − | 0.287685i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.35480 | − | 17.0872i | −0.544920 | − | 1.46521i | ||||
\(137\) | 5.10587i | 0.436224i | 0.975924 | + | 0.218112i | \(0.0699898\pi\) | ||||
−0.975924 | + | 0.218112i | \(0.930010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.7757 | − | 11.7757i | 0.998800 | − | 0.998800i | −0.00119925 | − | 0.999999i | \(-0.500382\pi\) |
0.999999 | + | 0.00119925i | \(0.000381735\pi\) | |||||||
\(140\) | 10.8003 | + | 6.59245i | 0.912791 | + | 0.557164i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.18323 | + | 0.856566i | −0.602803 | + | 0.0718814i | ||||
\(143\) | −2.73551 | −0.228755 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.7721 | −0.894578 | ||||||||
\(146\) | 20.7440 | − | 2.47363i | 1.71679 | − | 0.204719i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.02185 | − | 6.58892i | 0.330594 | − | 0.541606i | ||||
\(149\) | 7.90774 | − | 7.90774i | 0.647827 | − | 0.647827i | −0.304640 | − | 0.952467i | \(-0.598536\pi\) |
0.952467 | + | 0.304640i | \(0.0985363\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.6506i | 1.19225i | 0.802893 | + | 0.596123i | \(0.203293\pi\) | ||||
−0.802893 | + | 0.596123i | \(0.796707\pi\) | |||||||
\(152\) | −7.58892 | + | 16.5760i | −0.615543 | + | 1.34449i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.49824 | − | 1.90393i | 0.120731 | − | 0.153423i | ||||
\(155\) | −11.4701 | + | 11.4701i | −0.921300 | + | 0.921300i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.15196 | − | 3.15196i | −0.251553 | − | 0.251553i | 0.570054 | − | 0.821607i | \(-0.306922\pi\) |
−0.821607 | + | 0.570054i | \(0.806922\pi\) | |||||||
\(158\) | −1.05830 | − | 8.87495i | −0.0841935 | − | 0.706053i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −13.7359 | − | 2.66981i | −1.08592 | − | 0.211067i | ||||
\(161\) | 7.23412 | 0.570128 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.50490 | + | 5.50490i | 0.431177 | + | 0.431177i | 0.889029 | − | 0.457852i | \(-0.151381\pi\) |
−0.457852 | + | 0.889029i | \(0.651381\pi\) | |||||||
\(164\) | 0.370889 | + | 1.53304i | 0.0289616 | + | 0.119710i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.793624 | − | 1.00852i | 0.0615972 | − | 0.0782765i | ||||
\(167\) | − | 20.1814i | − | 1.56168i | −0.624730 | − | 0.780841i | \(-0.714791\pi\) | ||
0.624730 | − | 0.780841i | \(-0.285209\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.67923i | 0.283018i | ||||||||
\(170\) | −17.7194 | − | 13.9437i | −1.35902 | − | 1.06943i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.574131 | − | 0.940588i | 0.0437771 | − | 0.0717191i | ||||
\(173\) | −4.35322 | − | 4.35322i | −0.330969 | − | 0.330969i | 0.521985 | − | 0.852955i | \(-0.325192\pi\) |
−0.852955 | + | 0.521985i | \(0.825192\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.86156 | 0.216313 | ||||||||
\(176\) | −0.819003 | + | 2.55098i | −0.0617347 | + | 0.192288i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.87108 | − | 1.05783i | 0.664915 | − | 0.0792880i | ||||
\(179\) | 13.2833 | + | 13.2833i | 0.992843 | + | 0.992843i | 0.999975 | − | 0.00713130i | \(-0.00226998\pi\) |
−0.00713130 | + | 0.999975i | \(0.502270\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.34628 | − | 6.34628i | 0.471715 | − | 0.471715i | −0.430754 | − | 0.902469i | \(-0.641752\pi\) |
0.902469 | + | 0.430754i | \(0.141752\pi\) | |||||||
\(182\) | −11.6088 | − | 9.13519i | −0.860503 | − | 0.677145i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.49824 | + | 2.78863i | −0.552777 | + | 0.205581i | ||||
\(185\) | − | 9.54745i | − | 0.701943i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.05275 | + | 3.05275i | −0.223239 | + | 0.223239i | ||||
\(188\) | 5.49824 | − | 1.33019i | 0.401000 | − | 0.0970142i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.66981 | + | 22.3892i | 0.193688 | + | 1.62428i | ||||
\(191\) | −5.60058 | −0.405243 | −0.202622 | − | 0.979257i | \(-0.564946\pi\) | ||||
−0.202622 | + | 0.979257i | \(0.564946\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.4514 | −1.40014 | −0.700071 | − | 0.714074i | \(-0.746848\pi\) | ||||
−0.700071 | + | 0.714074i | \(0.746848\pi\) | |||||||
\(194\) | 2.11882 | + | 17.7686i | 0.152123 | + | 1.27571i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.891171 | + | 0.215602i | −0.0636551 | + | 0.0154001i | ||||
\(197\) | −1.23793 | + | 1.23793i | −0.0881988 | + | 0.0881988i | −0.749830 | − | 0.661631i | \(-0.769865\pi\) |
0.661631 | + | 0.749830i | \(0.269865\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.993710i | 0.0704422i | 0.999380 | + | 0.0352211i | \(0.0112135\pi\) | ||||
−0.999380 | + | 0.0352211i | \(0.988786\pi\) | |||||||
\(200\) | −2.96603 | + | 1.10308i | −0.209730 | + | 0.0779997i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.8268 | − | 9.30676i | −0.832134 | − | 0.654822i | ||||
\(203\) | −7.87579 | + | 7.87579i | −0.552772 | + | 0.552772i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.37941 | + | 1.37941i | 0.0963422 | + | 0.0963422i | ||||
\(206\) | 4.68583 | − | 0.558763i | 0.326477 | − | 0.0389309i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 15.5541 | + | 4.99371i | 1.07848 | + | 0.346251i | ||||
\(209\) | 4.31724 | 0.298630 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.22432 | + | 4.22432i | 0.290814 | + | 0.290814i | 0.837402 | − | 0.546588i | \(-0.184073\pi\) |
−0.546588 | + | 0.837402i | \(0.684073\pi\) | |||||||
\(212\) | −3.79834 | + | 6.22274i | −0.260871 | + | 0.427380i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 22.1023 | + | 17.3927i | 1.51088 | + | 1.18894i | ||||
\(215\) | − | 1.36293i | − | 0.0929509i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.7721i | 1.13857i | ||||||||
\(218\) | −3.42475 | + | 4.35211i | −0.231954 | + | 0.294762i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.779208 | + | 3.22079i | 0.0525342 | + | 0.217146i | ||||
\(221\) | 18.6135 | + | 18.6135i | 1.25208 | + | 1.25208i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.7659 | −1.59148 | −0.795740 | − | 0.605639i | \(-0.792918\pi\) | ||||
−0.795740 | + | 0.605639i | \(0.792918\pi\) | |||||||
\(224\) | −11.9946 | + | 8.09069i | −0.801424 | + | 0.540582i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.374699 | − | 3.14225i | −0.0249246 | − | 0.209019i | ||||
\(227\) | 0.641669 | + | 0.641669i | 0.0425891 | + | 0.0425891i | 0.728081 | − | 0.685492i | \(-0.240413\pi\) |
−0.685492 | + | 0.728081i | \(0.740413\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.34275 | − | 5.34275i | 0.353059 | − | 0.353059i | −0.508188 | − | 0.861246i | \(-0.669684\pi\) |
0.861246 | + | 0.508188i | \(0.169684\pi\) | |||||||
\(230\) | −6.11882 | + | 7.77568i | −0.403463 | + | 0.512713i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.12735 | − | 11.1993i | 0.336627 | − | 0.735271i | ||||
\(233\) | 23.2271i | 1.52166i | 0.648954 | + | 0.760828i | \(0.275207\pi\) | ||||
−0.648954 | + | 0.760828i | \(0.724793\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.94725 | − | 4.94725i | 0.322723 | − | 0.322723i | ||||
\(236\) | 5.89450 | − | 9.65685i | 0.383699 | − | 0.628608i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −23.1497 | + | 2.76049i | −1.50057 | + | 0.178936i | ||||
\(239\) | −26.9213 | −1.74140 | −0.870698 | − | 0.491817i | \(-0.836333\pi\) | ||||
−0.870698 | + | 0.491817i | \(0.836333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.3494 | −0.666664 | −0.333332 | − | 0.942809i | \(-0.608173\pi\) | ||||
−0.333332 | + | 0.942809i | \(0.608173\pi\) | |||||||
\(242\) | −14.8169 | + | 1.76685i | −0.952466 | + | 0.113577i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.5889 | + | 6.46343i | 0.677886 | + | 0.413779i | ||||
\(245\) | −0.801866 | + | 0.801866i | −0.0512293 | + | 0.0512293i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 26.3235i | − | 1.67492i | ||||||
\(248\) | −6.46538 | − | 17.3845i | −0.410552 | − | 1.10392i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.39627 | − | 10.6698i | 0.531027 | − | 0.674818i | ||||
\(251\) | 9.75696 | − | 9.75696i | 0.615854 | − | 0.615854i | −0.328611 | − | 0.944465i | \(-0.606581\pi\) |
0.944465 | + | 0.328611i | \(0.106581\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.33962 | + | 1.33962i | 0.0842209 | + | 0.0842209i | ||||
\(254\) | 2.04534 | + | 17.1524i | 0.128336 | + | 1.07624i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.31371 | − | 13.0098i | 0.582107 | − | 0.813112i | ||||
\(257\) | −16.9965 | −1.06021 | −0.530105 | − | 0.847932i | \(-0.677848\pi\) | ||||
−0.530105 | + | 0.847932i | \(0.677848\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.98038 | − | 6.98038i | −0.433740 | − | 0.433740i | ||||
\(260\) | 19.6381 | − | 4.75107i | 1.21791 | − | 0.294649i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.66981 | + | 5.93430i | −0.288502 | + | 0.366622i | ||||
\(263\) | − | 29.9929i | − | 1.84944i | −0.380643 | − | 0.924722i | \(-0.624297\pi\) | ||
0.380643 | − | 0.924722i | \(-0.375703\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.01686i | 0.553901i | ||||||||
\(266\) | 18.3213 | + | 14.4173i | 1.12335 | + | 0.883984i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.11529 | + | 3.12235i | 0.312466 | + | 0.190728i | ||||
\(269\) | −20.6003 | − | 20.6003i | −1.25602 | − | 1.25602i | −0.952976 | − | 0.303046i | \(-0.901996\pi\) |
−0.303046 | − | 0.952976i | \(-0.598004\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.6506 | −1.61891 | −0.809453 | − | 0.587184i | \(-0.800236\pi\) | ||||
−0.809453 | + | 0.587184i | \(0.800236\pi\) | |||||||
\(272\) | 22.9308 | − | 11.7851i | 1.39038 | − | 0.714577i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.16999 | + | 0.854988i | −0.433155 | + | 0.0516517i | ||||
\(275\) | 0.529904 | + | 0.529904i | 0.0319544 | + | 0.0319544i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.1220 | − | 12.1220i | 0.728338 | − | 0.728338i | −0.241951 | − | 0.970289i | \(-0.577787\pi\) |
0.970289 | + | 0.241951i | \(0.0777872\pi\) | |||||||
\(278\) | 18.5080 | + | 14.5643i | 1.11004 | + | 0.873509i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.44902 | + | 16.2704i | −0.445164 | + | 0.972341i | ||||
\(281\) | 2.76588i | 0.164999i | 0.996591 | + | 0.0824993i | \(0.0262902\pi\) | ||||
−0.996591 | + | 0.0824993i | \(0.973710\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.48528 | − | 4.48528i | 0.266622 | − | 0.266622i | −0.561115 | − | 0.827738i | \(-0.689628\pi\) |
0.827738 | + | 0.561115i | \(0.189628\pi\) | |||||||
\(284\) | −2.40569 | − | 9.94372i | −0.142752 | − | 0.590051i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.458067 | − | 3.84138i | −0.0270860 | − | 0.227146i | ||||
\(287\) | 2.01704 | 0.119062 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.5443 | 1.44378 | ||||||||
\(290\) | −1.80382 | − | 15.1270i | −0.105924 | − | 0.888285i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.94725 | + | 28.7159i | 0.406557 | + | 1.68047i | ||||
\(293\) | 8.20793 | − | 8.20793i | 0.479512 | − | 0.479512i | −0.425463 | − | 0.904976i | \(-0.639889\pi\) |
0.904976 | + | 0.425463i | \(0.139889\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 13.9929i | − | 0.814700i | ||||||
\(296\) | 9.92606 | + | 4.54441i | 0.576940 | + | 0.264139i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.4287 | + | 9.78039i | 0.719977 | + | 0.566563i | ||||
\(299\) | 8.16804 | − | 8.16804i | 0.472370 | − | 0.472370i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.996470 | − | 0.996470i | −0.0574356 | − | 0.0574356i | ||||
\(302\) | −20.5733 | + | 2.45327i | −1.18386 | + | 0.141170i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −24.5478 | − | 7.88118i | −1.40791 | − | 0.452016i | ||||
\(305\) | 15.3435 | 0.878567 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.4549 | + | 10.4549i | 0.596693 | + | 0.596693i | 0.939431 | − | 0.342738i | \(-0.111354\pi\) |
−0.342738 | + | 0.939431i | \(0.611354\pi\) | |||||||
\(308\) | 2.92450 | + | 1.78510i | 0.166639 | + | 0.101716i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −18.0277 | − | 14.1864i | −1.02391 | − | 0.805731i | ||||
\(311\) | 15.0761i | 0.854885i | 0.904043 | + | 0.427442i | \(0.140585\pi\) | ||||
−0.904043 | + | 0.427442i | \(0.859415\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 23.0027i | − | 1.30019i | −0.759852 | − | 0.650096i | \(-0.774729\pi\) | ||
0.759852 | − | 0.650096i | \(-0.225271\pi\) | |||||||
\(314\) | 3.89838 | − | 4.95398i | 0.219998 | − | 0.279569i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.2856 | − | 2.97226i | 0.691117 | − | 0.167203i | ||||
\(317\) | 6.75892 | + | 6.75892i | 0.379618 | + | 0.379618i | 0.870964 | − | 0.491346i | \(-0.163495\pi\) |
−0.491346 | + | 0.870964i | \(0.663495\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.91688 | −0.163314 | ||||||||
\(320\) | 1.44902 | − | 19.7359i | 0.0810025 | − | 1.10327i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.21137 | + | 10.1586i | 0.0675069 | + | 0.566118i | ||||
\(323\) | −29.3763 | − | 29.3763i | −1.63454 | − | 1.63454i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.23099 | − | 3.23099i | 0.179223 | − | 0.179223i | ||||
\(326\) | −6.80853 | + | 8.65214i | −0.377090 | + | 0.479198i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.09069 | + | 0.777537i | −0.115439 | + | 0.0429323i | ||||
\(329\) | − | 7.23412i | − | 0.398830i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.6631 | + | 19.6631i | −1.08078 | + | 1.08078i | −0.0843464 | + | 0.996436i | \(0.526880\pi\) |
−0.996436 | + | 0.0843464i | \(0.973120\pi\) | |||||||
\(332\) | 1.54913 | + | 0.945580i | 0.0850193 | + | 0.0518954i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 28.3400 | − | 3.37941i | 1.55070 | − | 0.184913i | ||||
\(335\) | 7.41215 | 0.404969 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.00980 | 0.163954 | 0.0819771 | − | 0.996634i | \(-0.473877\pi\) | ||||
0.0819771 | + | 0.996634i | \(0.473877\pi\) | |||||||
\(338\) | −5.16662 | + | 0.616095i | −0.281027 | + | 0.0335111i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 16.6135 | − | 27.2176i | 0.900995 | − | 1.47608i | ||||
\(341\) | −3.10587 | + | 3.10587i | −0.168192 | + | 0.168192i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.0761i | 1.03001i | ||||||||
\(344\) | 1.41697 | + | 0.648728i | 0.0763981 | + | 0.0349771i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.38412 | − | 6.84203i | 0.289452 | − | 0.367830i | ||||
\(347\) | −6.27521 | + | 6.27521i | −0.336871 | + | 0.336871i | −0.855188 | − | 0.518317i | \(-0.826559\pi\) |
0.518317 | + | 0.855188i | \(0.326559\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.74255 | − | 4.74255i | −0.253863 | − | 0.253863i | 0.568690 | − | 0.822552i | \(-0.307451\pi\) |
−0.822552 | + | 0.568690i | \(0.807451\pi\) | |||||||
\(350\) | 0.479174 | + | 4.01839i | 0.0256129 | + | 0.214792i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.71940 | − | 0.722930i | −0.198245 | − | 0.0385323i | ||||
\(353\) | 8.75882 | 0.466185 | 0.233093 | − | 0.972455i | \(-0.425116\pi\) | ||||
0.233093 | + | 0.972455i | \(0.425116\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.94725 | − | 8.94725i | −0.474871 | − | 0.474871i | ||||
\(356\) | 2.97096 | + | 12.2802i | 0.157460 | + | 0.650849i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.4290 | + | 20.8776i | −0.868300 | + | 1.10342i | ||||
\(359\) | 32.7917i | 1.73068i | 0.501184 | + | 0.865341i | \(0.332898\pi\) | ||||
−0.501184 | + | 0.865341i | \(0.667102\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.5443i | 1.18654i | ||||||||
\(362\) | 9.97455 | + | 7.84916i | 0.524251 | + | 0.412543i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.8843 | − | 17.8316i | 0.570493 | − | 0.934628i | ||||
\(365\) | 25.8382 | + | 25.8382i | 1.35243 | + | 1.35243i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.6435 | 1.07758 | 0.538791 | − | 0.842439i | \(-0.318881\pi\) | ||||
0.538791 | + | 0.842439i | \(0.318881\pi\) | |||||||
\(368\) | −5.17157 | − | 10.0625i | −0.269587 | − | 0.524546i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 13.4072 | − | 1.59874i | 0.697005 | − | 0.0831145i | ||||
\(371\) | 6.59245 | + | 6.59245i | 0.342263 | + | 0.342263i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.6167 | + | 16.6167i | −0.860378 | + | 0.860378i | −0.991382 | − | 0.131004i | \(-0.958180\pi\) |
0.131004 | + | 0.991382i | \(0.458180\pi\) | |||||||
\(374\) | −4.79806 | − | 3.77568i | −0.248102 | − | 0.195236i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.78863 | + | 7.49824i | 0.143813 | + | 0.386692i | ||||
\(377\) | 17.7851i | 0.915979i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.77844 | − | 7.77844i | 0.399552 | − | 0.399552i | −0.478523 | − | 0.878075i | \(-0.658828\pi\) |
0.878075 | + | 0.478523i | \(0.158828\pi\) | |||||||
\(380\) | −30.9933 | + | 7.49824i | −1.58992 | + | 0.384651i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.937828 | − | 7.86469i | −0.0479834 | − | 0.402393i | ||||
\(383\) | 17.2037 | 0.879070 | 0.439535 | − | 0.898225i | \(-0.355143\pi\) | ||||
0.439535 | + | 0.898225i | \(0.355143\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.23765 | 0.215971 | ||||||||
\(386\) | −3.25717 | − | 27.3149i | −0.165786 | − | 1.39029i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −24.5970 | + | 5.95078i | −1.24873 | + | 0.302105i | ||||
\(389\) | 23.8515 | − | 23.8515i | 1.20932 | − | 1.20932i | 0.238069 | − | 0.971248i | \(-0.423486\pi\) |
0.971248 | − | 0.238069i | \(-0.0765143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 18.2306i | − | 0.921961i | ||||||
\(392\) | −0.451990 | − | 1.21534i | −0.0228290 | − | 0.0613838i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.94567 | − | 1.53109i | −0.0980216 | − | 0.0771350i | ||||
\(395\) | 11.0544 | − | 11.0544i | 0.556208 | − | 0.556208i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.2673 | − | 10.2673i | −0.515299 | − | 0.515299i | 0.400847 | − | 0.916145i | \(-0.368716\pi\) |
−0.916145 | + | 0.400847i | \(0.868716\pi\) | |||||||
\(398\) | −1.39543 | + | 0.166399i | −0.0699467 | + | 0.00834081i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.04569 | − | 3.98038i | −0.102284 | − | 0.199019i | ||||
\(401\) | −32.2274 | −1.60936 | −0.804681 | − | 0.593708i | \(-0.797663\pi\) | ||||
−0.804681 | + | 0.593708i | \(0.797663\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.9374 | + | 18.9374i | 0.943341 | + | 0.943341i | ||||
\(404\) | 11.0887 | − | 18.1665i | 0.551685 | − | 0.903815i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.3785 | − | 9.74088i | −0.614335 | − | 0.483432i | ||||
\(407\) | − | 2.58526i | − | 0.128146i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.5702i | 0.572110i | 0.958213 | + | 0.286055i | \(0.0923440\pi\) | ||||
−0.958213 | + | 0.286055i | \(0.907656\pi\) | |||||||
\(410\) | −1.70607 | + | 2.16804i | −0.0842569 | + | 0.107072i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.56930 | + | 6.48658i | 0.0773140 | + | 0.319571i | ||||
\(413\) | −10.2306 | − | 10.2306i | −0.503414 | − | 0.503414i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.24471 | 0.110188 | ||||||||
\(416\) | −4.40792 | + | 22.6783i | −0.216116 | + | 1.11190i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.722930 | + | 6.06255i | 0.0353597 | + | 0.296529i | ||||
\(419\) | −6.74717 | − | 6.74717i | −0.329621 | − | 0.329621i | 0.522822 | − | 0.852442i | \(-0.324879\pi\) |
−0.852442 | + | 0.522822i | \(0.824879\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.2239 | + | 17.2239i | −0.839443 | + | 0.839443i | −0.988785 | − | 0.149343i | \(-0.952284\pi\) |
0.149343 | + | 0.988785i | \(0.452284\pi\) | |||||||
\(422\) | −5.22470 | + | 6.63944i | −0.254334 | + | 0.323203i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.37442 | − | 4.29186i | −0.455262 | − | 0.208431i | ||||
\(425\) | − | 7.21137i | − | 0.349803i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.2180 | − | 11.2180i | 0.542879 | − | 0.542879i | ||||
\(428\) | −20.7229 | + | 33.9500i | −1.00168 | + | 1.64103i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.91391 | − | 0.228225i | 0.0922970 | − | 0.0110060i | ||||
\(431\) | −40.7088 | −1.96087 | −0.980437 | − | 0.196832i | \(-0.936935\pi\) | ||||
−0.980437 | + | 0.196832i | \(0.936935\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.31371 | 0.351474 | 0.175737 | − | 0.984437i | \(-0.443769\pi\) | ||||
0.175737 | + | 0.984437i | \(0.443769\pi\) | |||||||
\(434\) | −23.5525 | + | 2.80853i | −1.13056 | + | 0.134814i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.68499 | − | 4.08049i | −0.320153 | − | 0.195420i | ||||
\(437\) | −12.8910 | + | 12.8910i | −0.616659 | + | 0.616659i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.7122i | 0.845356i | 0.906280 | + | 0.422678i | \(0.138910\pi\) | ||||
−0.906280 | + | 0.422678i | \(0.861090\pi\) | |||||||
\(440\) | −4.39236 | + | 1.63354i | −0.209398 | + | 0.0778761i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −23.0215 | + | 29.2552i | −1.09502 | + | 1.39153i | ||||
\(443\) | −15.6944 | + | 15.6944i | −0.745664 | + | 0.745664i | −0.973662 | − | 0.227997i | \(-0.926782\pi\) |
0.227997 | + | 0.973662i | \(0.426782\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.0496 | + | 11.0496i | 0.523801 | + | 0.523801i | ||||
\(446\) | −3.97964 | − | 33.3736i | −0.188441 | − | 1.58028i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −13.3700 | − | 15.4888i | −0.631673 | − | 0.731778i | ||||
\(449\) | 28.3400 | 1.33745 | 0.668723 | − | 0.743511i | \(-0.266841\pi\) | ||||
0.668723 | + | 0.743511i | \(0.266841\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.373517 | + | 0.373517i | 0.0175882 | + | 0.0175882i | ||||
\(452\) | 4.34981 | − | 1.05235i | 0.204598 | − | 0.0494985i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.793624 | + | 1.00852i | −0.0372466 | + | 0.0473323i | ||||
\(455\) | − | 25.8382i | − | 1.21131i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 17.3396i | − | 0.811113i | −0.914070 | − | 0.405557i | \(-0.867078\pi\) | ||
0.914070 | − | 0.405557i | \(-0.132922\pi\) | |||||||
\(458\) | 8.39729 | + | 6.60798i | 0.392380 | + | 0.308771i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −11.9437 | − | 7.29040i | −0.556879 | − | 0.339917i | ||||
\(461\) | 1.69284 | + | 1.69284i | 0.0788434 | + | 0.0788434i | 0.745429 | − | 0.666585i | \(-0.232245\pi\) |
−0.666585 | + | 0.745429i | \(0.732245\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.70238 | 0.125590 | 0.0627951 | − | 0.998026i | \(-0.479999\pi\) | ||||
0.0627951 | + | 0.998026i | \(0.479999\pi\) | |||||||
\(464\) | 16.5854 | + | 5.32480i | 0.769957 | + | 0.247198i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −32.6169 | + | 3.88942i | −1.51095 | + | 0.180174i | ||||
\(467\) | 17.1136 | + | 17.1136i | 0.791924 | + | 0.791924i | 0.981807 | − | 0.189883i | \(-0.0608108\pi\) |
−0.189883 | + | 0.981807i | \(0.560811\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.41921 | − | 5.41921i | 0.250236 | − | 0.250236i | ||||
\(470\) | 7.77568 | + | 6.11882i | 0.358665 | + | 0.282240i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 14.5478 | + | 6.66038i | 0.669618 | + | 0.306569i | ||||
\(473\) | − | 0.369053i | − | 0.0169691i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.09921 | + | 5.09921i | −0.233968 | + | 0.233968i | ||||
\(476\) | −7.75293 | − | 32.0461i | −0.355355 | − | 1.46883i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.50803 | − | 37.8047i | −0.206193 | − | 1.72915i | ||||
\(479\) | 22.2251 | 1.01549 | 0.507745 | − | 0.861508i | \(-0.330479\pi\) | ||||
0.507745 | + | 0.861508i | \(0.330479\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.7631 | −0.718735 | ||||||||
\(482\) | −1.73303 | − | 14.5333i | −0.0789373 | − | 0.661974i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.96224 | − | 20.5110i | −0.225556 | − | 0.932318i | ||||
\(485\) | −22.1322 | + | 22.1322i | −1.00497 | + | 1.00497i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 13.9839i | − | 0.633672i | −0.948480 | − | 0.316836i | \(-0.897380\pi\) | ||
0.948480 | − | 0.316836i | \(-0.102620\pi\) | |||||||
\(488\) | −7.30324 | + | 15.9520i | −0.330602 | + | 0.722111i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.26031 | − | 0.991758i | −0.0569348 | − | 0.0448031i | ||||
\(491\) | −7.23412 | + | 7.23412i | −0.326471 | + | 0.326471i | −0.851243 | − | 0.524772i | \(-0.824151\pi\) |
0.524772 | + | 0.851243i | \(0.324151\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.8476 | + | 19.8476i | 0.893893 | + | 0.893893i | ||||
\(494\) | 36.9652 | − | 4.40792i | 1.66314 | − | 0.198322i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.3298 | − | 11.9902i | 1.04754 | − | 0.538375i | ||||
\(497\) | −13.0831 | −0.586858 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.59078 | + | 2.59078i | 0.115979 | + | 0.115979i | 0.762715 | − | 0.646735i | \(-0.223866\pi\) |
−0.646735 | + | 0.762715i | \(0.723866\pi\) | |||||||
\(500\) | 16.3892 | + | 10.0039i | 0.732948 | + | 0.447388i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.3352 | + | 12.0675i | 0.684443 | + | 0.538601i | ||||
\(503\) | 39.6443i | 1.76765i | 0.467817 | + | 0.883825i | \(0.345041\pi\) | ||||
−0.467817 | + | 0.883825i | \(0.654959\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 26.3235i | − | 1.17138i | ||||||
\(506\) | −1.65685 | + | 2.10550i | −0.0736562 | + | 0.0936008i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −23.7440 | + | 5.74441i | −1.05347 | + | 0.254867i | ||||
\(509\) | −20.2875 | − | 20.2875i | −0.899229 | − | 0.899229i | 0.0961393 | − | 0.995368i | \(-0.469351\pi\) |
−0.995368 | + | 0.0961393i | \(0.969351\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 37.7819 | 1.67137 | ||||||||
\(512\) | 19.8288 | + | 10.9004i | 0.876317 | + | 0.481734i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.84609 | − | 23.8675i | −0.125536 | − | 1.05275i | ||||
\(515\) | 5.83655 | + | 5.83655i | 0.257189 | + | 0.257189i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.33962 | − | 1.33962i | 0.0589162 | − | 0.0589162i | ||||
\(518\) | 8.63343 | − | 10.9712i | 0.379331 | − | 0.482046i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.96021 | + | 26.7816i | 0.436784 | + | 1.17445i | ||||
\(521\) | − | 23.1784i | − | 1.01546i | −0.861515 | − | 0.507732i | \(-0.830484\pi\) | ||
0.861515 | − | 0.507732i | \(-0.169516\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.78550 | + | 5.78550i | −0.252982 | + | 0.252982i | −0.822192 | − | 0.569210i | \(-0.807249\pi\) |
0.569210 | + | 0.822192i | \(0.307249\pi\) | |||||||
\(524\) | −9.11529 | − | 5.56394i | −0.398203 | − | 0.243062i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 42.1180 | − | 5.02238i | 1.83643 | − | 0.218986i | ||||
\(527\) | 42.2672 | 1.84119 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000 | 0.652174 | ||||||||
\(530\) | −12.6621 | + | 1.50989i | −0.550005 | + | 0.0655855i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −17.1778 | + | 28.1421i | −0.744754 | + | 1.22012i | ||||
\(533\) | 2.27744 | − | 2.27744i | 0.0986470 | − | 0.0986470i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 49.1941i | 2.12685i | ||||||||
\(536\) | −3.52805 | + | 7.70607i | −0.152388 | + | 0.332852i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 25.4787 | − | 32.3778i | 1.09847 | − | 1.39591i | ||||
\(539\) | −0.217129 | + | 0.217129i | −0.00935241 | + | 0.00935241i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.55175 | + | 4.55175i | 0.195695 | + | 0.195695i | 0.798152 | − | 0.602457i | \(-0.205811\pi\) |
−0.602457 | + | 0.798152i | \(0.705811\pi\) | |||||||
\(542\) | −4.46269 | − | 37.4245i | −0.191689 | − | 1.60752i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 20.3892 | + | 30.2274i | 0.874180 | + | 1.29599i | ||||
\(545\) | −9.68667 | −0.414931 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.7355 | − | 27.7355i | −1.18588 | − | 1.18588i | −0.978195 | − | 0.207689i | \(-0.933406\pi\) |
−0.207689 | − | 0.978195i | \(-0.566594\pi\) | |||||||
\(548\) | −2.40126 | − | 9.92540i | −0.102577 | − | 0.423992i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.655392 | + | 0.832859i | −0.0279460 | + | 0.0355132i | ||||
\(551\) | − | 28.0688i | − | 1.19577i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 16.1643i | − | 0.687377i | ||||||
\(554\) | 19.0523 | + | 14.9926i | 0.809454 | + | 0.636974i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.3529 | + | 28.4290i | −0.735929 | + | 1.20566i | ||||
\(557\) | 1.17538 | + | 1.17538i | 0.0498026 | + | 0.0498026i | 0.731569 | − | 0.681767i | \(-0.238788\pi\) |
−0.681767 | + | 0.731569i | \(0.738788\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.25023 | −0.0951745 | ||||||||
\(560\) | −24.0953 | − | 7.73588i | −1.01821 | − | 0.326901i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.88403 | + | 0.463152i | −0.163838 | + | 0.0195369i | ||||
\(563\) | 28.7346 | + | 28.7346i | 1.21102 | + | 1.21102i | 0.970692 | + | 0.240326i | \(0.0772544\pi\) |
0.240326 | + | 0.970692i | \(0.422746\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.91391 | − | 3.91391i | 0.164659 | − | 0.164659i | ||||
\(566\) | 7.04959 | + | 5.54745i | 0.296316 | + | 0.233177i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.5608 | − | 5.04332i | 0.568998 | − | 0.211613i | ||||
\(569\) | − | 27.0004i | − | 1.13191i | −0.824435 | − | 0.565957i | \(-0.808507\pi\) | ||
0.824435 | − | 0.565957i | \(-0.191493\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.8284 | + | 14.8284i | −0.620550 | + | 0.620550i | −0.945672 | − | 0.325122i | \(-0.894595\pi\) |
0.325122 | + | 0.945672i | \(0.394595\pi\) | |||||||
\(572\) | 5.31761 | − | 1.28649i | 0.222341 | − | 0.0537910i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.337758 | + | 2.83246i | 0.0140977 | + | 0.118225i | ||||
\(575\) | −3.16451 | −0.131969 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.6372 | −1.56686 | −0.783429 | − | 0.621481i | \(-0.786531\pi\) | ||||
−0.783429 | + | 0.621481i | \(0.786531\pi\) | |||||||
\(578\) | 4.10999 | + | 34.4667i | 0.170953 | + | 1.43363i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 20.9402 | − | 5.06608i | 0.869494 | − | 0.210357i | ||||
\(581\) | 1.64116 | − | 1.64116i | 0.0680869 | − | 0.0680869i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.44158i | 0.101120i | ||||||||
\(584\) | −39.1614 | + | 14.5643i | −1.62051 | + | 0.602675i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.9005 | + | 10.1517i | 0.532917 | + | 0.419362i | ||||
\(587\) | 31.2574 | − | 31.2574i | 1.29013 | − | 1.29013i | 0.355429 | − | 0.934703i | \(-0.384335\pi\) |
0.934703 | − | 0.355429i | \(-0.115665\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.8874 | − | 29.8874i | −1.23149 | − | 1.23149i | ||||
\(590\) | 19.6498 | − | 2.34315i | 0.808969 | − | 0.0964658i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.71942 | + | 14.6998i | −0.193967 | + | 0.604157i | ||||
\(593\) | 3.59611 | 0.147675 | 0.0738373 | − | 0.997270i | \(-0.476475\pi\) | ||||
0.0738373 | + | 0.997270i | \(0.476475\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28.8347 | − | 28.8347i | −1.18211 | − | 1.18211i | ||||
\(596\) | −11.6530 | + | 19.0910i | −0.477327 | + | 0.781996i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.8379 | + | 10.1023i | 0.524979 | + | 0.413115i | ||||
\(599\) | − | 22.0296i | − | 0.900104i | −0.893002 | − | 0.450052i | \(-0.851405\pi\) | ||
0.893002 | − | 0.450052i | \(-0.148595\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 10.7721i | − | 0.439405i | −0.975567 | − | 0.219703i | \(-0.929491\pi\) | ||
0.975567 | − | 0.219703i | \(-0.0705087\pi\) | |||||||
\(602\) | 1.23245 | − | 1.56617i | 0.0502308 | − | 0.0638323i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.89007 | − | 28.4795i | −0.280353 | − | 1.15882i | ||||
\(605\) | −18.4556 | − | 18.4556i | −0.750325 | − | 0.750325i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.47453 | 0.222204 | 0.111102 | − | 0.993809i | \(-0.464562\pi\) | ||||
0.111102 | + | 0.993809i | \(0.464562\pi\) | |||||||
\(608\) | 6.95668 | − | 35.7914i | 0.282130 | − | 1.45153i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.56930 | + | 21.5464i | 0.104028 | + | 0.872387i | ||||
\(611\) | −8.16804 | − | 8.16804i | −0.330444 | − | 0.330444i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.5049 | + | 10.5049i | −0.424289 | + | 0.424289i | −0.886677 | − | 0.462389i | \(-0.846993\pi\) |
0.462389 | + | 0.886677i | \(0.346993\pi\) | |||||||
\(614\) | −12.9308 | + | 16.4322i | −0.521843 | + | 0.663148i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.01704 | + | 4.40569i | −0.0812690 | + | 0.177510i | ||||
\(617\) | − | 22.2235i | − | 0.894686i | −0.894363 | − | 0.447343i | \(-0.852370\pi\) | ||
0.894363 | − | 0.447343i | \(-0.147630\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.6398 | − | 11.6398i | 0.467843 | − | 0.467843i | −0.433372 | − | 0.901215i | \(-0.642676\pi\) |
0.901215 | + | 0.433372i | \(0.142676\pi\) | |||||||
\(620\) | 16.9026 | − | 27.6913i | 0.678826 | − | 1.11211i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21.1708 | + | 2.52452i | −0.848871 | + | 0.101224i | ||||
\(623\) | 16.1573 | 0.647327 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 29.3424 | 1.17369 | ||||||||
\(626\) | 32.3019 | − | 3.85185i | 1.29105 | − | 0.153951i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.60949 | + | 4.64480i | 0.303652 | + | 0.185348i | ||||
\(629\) | −17.5912 | + | 17.5912i | −0.701405 | + | 0.701405i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 4.06977i | − | 0.162015i | −0.996713 | − | 0.0810075i | \(-0.974186\pi\) | ||
0.996713 | − | 0.0810075i | \(-0.0258138\pi\) | |||||||
\(632\) | 6.23108 | + | 16.7545i | 0.247859 | + | 0.666458i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.35951 | + | 10.6231i | −0.331999 | + | 0.421897i | ||||
\(635\) | −21.3646 | + | 21.3646i | −0.847828 | + | 0.847828i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.32390 | + | 1.32390i | 0.0524549 | + | 0.0524549i | ||||
\(638\) | −0.488437 | − | 4.09607i | −0.0193374 | − | 0.162165i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 27.9570 | − | 1.27001i | 1.10510 | − | 0.0502016i | ||||
\(641\) | 8.41958 | 0.332553 | 0.166277 | − | 0.986079i | \(-0.446826\pi\) | ||||
0.166277 | + | 0.986079i | \(0.446826\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.37275 | − | 7.37275i | −0.290753 | − | 0.290753i | 0.546625 | − | 0.837378i | \(-0.315912\pi\) |
−0.837378 | + | 0.546625i | \(0.815912\pi\) | |||||||
\(644\) | −14.0625 | + | 3.40216i | −0.554142 | + | 0.134064i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 36.3329 | − | 46.1712i | 1.42950 | − | 1.81658i | ||||
\(647\) | 11.6132i | 0.456560i | 0.973595 | + | 0.228280i | \(0.0733102\pi\) | ||||
−0.973595 | + | 0.228280i | \(0.926690\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 3.78901i | − | 0.148731i | ||||||
\(650\) | 5.07819 | + | 3.99612i | 0.199183 | + | 0.156741i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.2900 | − | 8.11216i | −0.520477 | − | 0.317697i | ||||
\(653\) | 1.93049 | + | 1.93049i | 0.0755458 | + | 0.0755458i | 0.743870 | − | 0.668324i | \(-0.232988\pi\) |
−0.668324 | + | 0.743870i | \(0.732988\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.2082 | −0.516088 | ||||||||
\(656\) | −1.44196 | − | 2.80568i | −0.0562990 | − | 0.109543i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 10.1586 | − | 1.21137i | 0.396024 | − | 0.0472240i | ||||
\(659\) | −22.3102 | − | 22.3102i | −0.869081 | − | 0.869081i | 0.123290 | − | 0.992371i | \(-0.460656\pi\) |
−0.992371 | + | 0.123290i | \(0.960656\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.7033 | − | 10.7033i | 0.416311 | − | 0.416311i | −0.467619 | − | 0.883930i | \(-0.654888\pi\) |
0.883930 | + | 0.467619i | \(0.154888\pi\) | |||||||
\(662\) | −30.9049 | − | 24.3196i | −1.20115 | − | 0.945208i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.06844 | + | 2.33372i | −0.0414635 | + | 0.0905660i | ||||
\(665\) | 40.7784i | 1.58132i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.70960 | − | 8.70960i | 0.337237 | − | 0.337237i | ||||
\(668\) | 9.49118 | + | 39.2310i | 0.367225 | + | 1.51789i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.24118 | + | 10.4086i | 0.0479509 | + | 0.402120i | ||||
\(671\) | 4.15472 | 0.160391 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.6345 | −0.795401 | −0.397700 | − | 0.917515i | \(-0.630192\pi\) | ||||
−0.397700 | + | 0.917515i | \(0.630192\pi\) | |||||||
\(674\) | 0.503997 | + | 4.22655i | 0.0194132 | + | 0.162801i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.73032 | − | 7.15213i | −0.0665508 | − | 0.275082i | ||||
\(677\) | −26.8246 | + | 26.8246i | −1.03095 | + | 1.03095i | −0.0314484 | + | 0.999505i | \(0.510012\pi\) |
−0.999505 | + | 0.0314484i | \(0.989988\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.3627i | 1.24197i | ||||||||
\(680\) | 41.0027 | + | 18.7721i | 1.57238 | + | 0.719879i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.88155 | − | 3.84138i | −0.186924 | − | 0.147094i | ||||
\(683\) | −12.9026 | + | 12.9026i | −0.493705 | + | 0.493705i | −0.909472 | − | 0.415766i | \(-0.863513\pi\) |
0.415766 | + | 0.909472i | \(0.363513\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.93077 | − | 8.93077i | −0.341227 | − | 0.341227i | ||||
\(686\) | −26.7878 | + | 3.19432i | −1.02276 | + | 0.121960i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.673711 | + | 2.09844i | −0.0256850 | + | 0.0800022i | ||||
\(689\) | 14.8871 | 0.567152 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.3923 | − | 21.3923i | −0.813803 | − | 0.813803i | 0.171399 | − | 0.985202i | \(-0.445171\pi\) |
−0.985202 | + | 0.171399i | \(0.945171\pi\) | |||||||
\(692\) | 10.5096 | + | 6.41502i | 0.399515 | + | 0.243863i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.86286 | − | 7.76126i | −0.374389 | − | 0.294614i | ||||
\(695\) | 41.1941i | 1.56258i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 5.08312i | − | 0.192537i | ||||||
\(698\) | 5.86564 | − | 7.45394i | 0.222018 | − | 0.282136i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.56264 | + | 1.34577i | −0.210248 | + | 0.0508655i | ||||
\(701\) | −14.2040 | − | 14.2040i | −0.536479 | − | 0.536479i | 0.386014 | − | 0.922493i | \(-0.373852\pi\) |
−0.922493 | + | 0.386014i | \(0.873852\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.8776 | 0.938278 | ||||||||
\(704\) | 0.392364 | − | 5.34408i | 0.0147878 | − | 0.201413i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.46668 | + | 12.2997i | 0.0551993 | + | 0.462906i | ||||
\(707\) | −19.2458 | − | 19.2458i | −0.723812 | − | 0.723812i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.5474 | + | 29.5474i | −1.10968 | + | 1.10968i | −0.116485 | + | 0.993192i | \(0.537163\pi\) |
−0.993192 | + | 0.116485i | \(0.962837\pi\) | |||||||
\(710\) | 11.0661 | − | 14.0625i | 0.415302 | − | 0.527758i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −16.7472 | + | 6.22836i | −0.627627 | + | 0.233418i | ||||
\(713\) | − | 18.5478i | − | 0.694622i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.78473 | − | 4.78473i | 0.178939 | − | 0.178939i | ||||
\(716\) | −32.0688 | − | 19.5747i | −1.19847 | − | 0.731540i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −46.0483 | + | 5.49104i | −1.71851 | + | 0.204924i | ||||
\(719\) | −28.3683 | −1.05796 | −0.528979 | − | 0.848635i | \(-0.677425\pi\) | ||||
−0.528979 | + | 0.848635i | \(0.677425\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.53450 | 0.317841 | ||||||||
\(722\) | −31.6582 | + | 3.77509i | −1.17819 | + | 0.140494i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.35204 | + | 15.3213i | −0.347566 | + | 0.569411i | ||||
\(725\) | 3.44521 | − | 3.44521i | 0.127952 | − | 0.127952i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 20.4843i | − | 0.759722i | −0.925044 | − | 0.379861i | \(-0.875972\pi\) | ||
0.925044 | − | 0.379861i | \(-0.124028\pi\) | |||||||
\(728\) | 26.8628 | + | 12.2985i | 0.995603 | + | 0.455814i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −31.9570 | + | 40.6104i | −1.18278 | + | 1.50306i | ||||
\(731\) | −2.51119 | + | 2.51119i | −0.0928797 | + | 0.0928797i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.9961 | + | 33.9961i | 1.25567 | + | 1.25567i | 0.953138 | + | 0.302536i | \(0.0978331\pi\) |
0.302536 | + | 0.953138i | \(0.402167\pi\) | |||||||
\(734\) | 3.45680 | + | 28.9889i | 0.127593 | + | 1.07000i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.2645 | − | 8.94725i | 0.488936 | − | 0.329800i | ||||
\(737\) | 2.00706 | 0.0739310 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.1645 | + | 15.1645i | 0.557836 | + | 0.557836i | 0.928691 | − | 0.370855i | \(-0.120935\pi\) |
−0.370855 | + | 0.928691i | \(0.620935\pi\) | |||||||
\(740\) | 4.49011 | + | 18.5595i | 0.165060 | + | 0.682260i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.15363 | + | 10.3615i | −0.299329 | + | 0.380381i | ||||
\(743\) | 2.17431i | 0.0797677i | 0.999204 | + | 0.0398839i | \(0.0126988\pi\) | ||||
−0.999204 | + | 0.0398839i | \(0.987301\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.6631i | 1.01350i | ||||||||
\(746\) | −26.1167 | − | 20.5517i | −0.956200 | − | 0.752451i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.49861 | − | 7.36999i | 0.164485 | − | 0.269473i | ||||
\(749\) | 35.9670 | + | 35.9670i | 1.31421 | + | 1.31421i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.8980 | 1.09099 | 0.545497 | − | 0.838113i | \(-0.316341\pi\) | ||||
0.545497 | + | 0.838113i | \(0.316341\pi\) | |||||||
\(752\) | −10.0625 | + | 5.17157i | −0.366943 | + | 0.188588i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −24.9750 | + | 2.97815i | −0.909536 | + | 0.108458i | ||||
\(755\) | −25.6256 | − | 25.6256i | −0.932610 | − | 0.932610i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.3294 | + | 15.3294i | −0.557157 | + | 0.557157i | −0.928497 | − | 0.371340i | \(-0.878899\pi\) |
0.371340 | + | 0.928497i | \(0.378899\pi\) | |||||||
\(758\) | 12.2255 | + | 9.62047i | 0.444050 | + | 0.349431i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −15.7194 | − | 42.2672i | −0.570203 | − | 1.53319i | ||||
\(761\) | 4.29449i | 0.155675i | 0.996966 | + | 0.0778375i | \(0.0248015\pi\) | ||||
−0.996966 | + | 0.0778375i | \(0.975198\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.08216 | + | 7.08216i | −0.256392 | + | 0.256392i | ||||
\(764\) | 10.8871 | − | 2.63392i | 0.393880 | − | 0.0952918i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.88080 | + | 24.1586i | 0.104088 | + | 0.872886i | ||||
\(767\) | −23.1027 | −0.834191 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.8819 | 1.22181 | 0.610907 | − | 0.791703i | \(-0.290805\pi\) | ||||
0.610907 | + | 0.791703i | \(0.290805\pi\) | |||||||
\(770\) | 0.709603 | + | 5.95078i | 0.0255723 | + | 0.214451i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 37.8119 | − | 9.14787i | 1.36088 | − | 0.329239i | ||||
\(773\) | 35.0230 | − | 35.0230i | 1.25969 | − | 1.25969i | 0.308450 | − | 0.951240i | \(-0.400190\pi\) |
0.951240 | − | 0.308450i | \(-0.0998104\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 7.33686i | − | 0.263548i | ||||||
\(776\) | −12.4753 | − | 33.5443i | −0.447837 | − | 1.20417i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 37.4877 | + | 29.4998i | 1.34400 | + | 1.05762i | ||||
\(779\) | −3.59431 | + | 3.59431i | −0.128779 | + | 0.128779i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.42274 | − | 2.42274i | −0.0866923 | − | 0.0866923i | ||||
\(782\) | 25.6006 | − | 3.05275i | 0.915475 | − | 0.109166i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.63097 | − | 0.838225i | 0.0582489 | − | 0.0299366i | ||||
\(785\) | 11.0263 | 0.393545 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.1090 | + | 24.1090i | 0.859393 | + | 0.859393i | 0.991267 | − | 0.131873i | \(-0.0420992\pi\) |
−0.131873 | + | 0.991267i | \(0.542099\pi\) | |||||||
\(788\) | 1.82424 | − | 2.98862i | 0.0649860 | − | 0.106465i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 17.3744 | + | 13.6722i | 0.618154 | + | 0.486437i | ||||
\(791\) | − | 5.72312i | − | 0.203491i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 25.3326i | − | 0.899585i | ||||||
\(794\) | 12.6987 | − | 16.1372i | 0.450659 | − | 0.572688i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.467336 | − | 1.93169i | −0.0165643 | − | 0.0684670i | ||||
\(797\) | 28.7722 | + | 28.7722i | 1.01917 | + | 1.01917i | 0.999813 | + | 0.0193524i | \(0.00616044\pi\) |
0.0193524 | + | 0.999813i | \(0.493840\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.2306 | −0.644952 | ||||||||
\(800\) | 5.24696 | − | 3.53921i | 0.185508 | − | 0.125130i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.39655 | − | 45.2559i | −0.190559 | − | 1.59804i | ||||
\(803\) | 6.99647 | + | 6.99647i | 0.246900 | + | 0.246900i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.6533 | + | 12.6533i | −0.445971 | + | 0.445971i | ||||
\(806\) | −23.4221 | + | 29.7643i | −0.825007 | + | 1.04840i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 27.3674 | + | 12.5295i | 0.962780 | + | 0.440787i | ||||
\(809\) | 10.9926i | 0.386478i | 0.981152 | + | 0.193239i | \(0.0618993\pi\) | ||||
−0.981152 | + | 0.193239i | \(0.938101\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.0259 | + | 15.0259i | −0.527630 | + | 0.527630i | −0.919865 | − | 0.392235i | \(-0.871702\pi\) |
0.392235 | + | 0.919865i | \(0.371702\pi\) | |||||||
\(812\) | 11.6060 | − | 19.0138i | 0.407289 | − | 0.667255i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.63039 | − | 0.432907i | 0.127245 | − | 0.0151734i | ||||
\(815\) | −19.2574 | −0.674558 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.55136 | 0.124246 | ||||||||
\(818\) | −16.2476 | + | 1.93745i | −0.568085 | + | 0.0677415i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.33019 | − | 2.03274i | −0.116295 | − | 0.0709862i | ||||
\(821\) | 21.2536 | − | 21.2536i | 0.741756 | − | 0.741756i | −0.231159 | − | 0.972916i | \(-0.574252\pi\) |
0.972916 | + | 0.231159i | \(0.0742519\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 55.0851i | − | 1.92015i | −0.279751 | − | 0.960073i | \(-0.590252\pi\) | ||
0.279751 | − | 0.960073i | \(-0.409748\pi\) | |||||||
\(824\) | −8.84609 | + | 3.28991i | −0.308168 | + | 0.114609i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.6533 | − | 16.0796i | 0.440265 | − | 0.559480i | ||||
\(827\) | 24.4290 | − | 24.4290i | 0.849480 | − | 0.849480i | −0.140588 | − | 0.990068i | \(-0.544899\pi\) |
0.990068 | + | 0.140588i | \(0.0448994\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.9235 | − | 21.9235i | −0.761436 | − | 0.761436i | 0.215146 | − | 0.976582i | \(-0.430977\pi\) |
−0.976582 | + | 0.215146i | \(0.930977\pi\) | |||||||
\(830\) | 0.375881 | + | 3.15217i | 0.0130470 | + | 0.109413i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −32.5845 | − | 2.39236i | −1.12966 | − | 0.0829403i | ||||
\(833\) | 2.95487 | 0.102380 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.2996 | + | 35.2996i | 1.22159 | + | 1.22159i | ||||
\(836\) | −8.39236 | + | 2.03037i | −0.290256 | + | 0.0702218i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.34498 | − | 10.6046i | 0.288273 | − | 0.366331i | ||||
\(839\) | 5.14195i | 0.177520i | 0.996053 | + | 0.0887599i | \(0.0282904\pi\) | ||||
−0.996053 | + | 0.0887599i | \(0.971710\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 10.0357i | − | 0.346059i | ||||||
\(842\) | −27.0711 | − | 21.3028i | −0.932933 | − | 0.734142i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.1984 | − | 6.22507i | −0.351044 | − | 0.214276i | ||||
\(845\) | −6.43541 | − | 6.43541i | −0.221385 | − | 0.221385i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.9867 | −0.927272 | ||||||||
\(848\) | 4.45714 | − | 13.8828i | 0.153059 | − | 0.476739i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.1267 | − | 1.20756i | 0.347342 | − | 0.0414189i | ||||
\(851\) | 7.71940 | + | 7.71940i | 0.264618 | + | 0.264618i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.0857 | − | 13.0857i | 0.448046 | − | 0.448046i | −0.446659 | − | 0.894704i | \(-0.647386\pi\) |
0.894704 | + | 0.446659i | \(0.147386\pi\) | |||||||
\(854\) | 17.6316 | + | 13.8746i | 0.603340 | + | 0.474779i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −51.1449 | − | 23.4155i | −1.74810 | − | 0.800325i | ||||
\(857\) | 22.8878i | 0.781833i | 0.920426 | + | 0.390916i | \(0.127842\pi\) | ||||
−0.920426 | + | 0.390916i | \(0.872158\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.1225 | + | 25.1225i | −0.857169 | + | 0.857169i | −0.991004 | − | 0.133834i | \(-0.957271\pi\) |
0.133834 | + | 0.991004i | \(0.457271\pi\) | |||||||
\(860\) | 0.640976 | + | 2.64942i | 0.0218571 | + | 0.0903445i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.81677 | − | 57.1660i | −0.232180 | − | 1.94708i | ||||
\(863\) | 43.9296 | 1.49538 | 0.747691 | − | 0.664047i | \(-0.231163\pi\) | ||||
0.747691 | + | 0.664047i | \(0.231163\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.2286 | 0.517788 | ||||||||
\(866\) | 1.22470 | + | 10.2704i | 0.0416168 | + | 0.349002i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.88784 | − | 32.6037i | −0.267731 | − | 1.10664i | ||||
\(869\) | 2.99331 | − | 2.99331i | 0.101541 | − | 0.101541i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 12.2376i | − | 0.414657i | ||||||
\(872\) | 4.61068 | − | 10.0708i | 0.156137 | − | 0.341040i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −20.2610 | − | 15.9437i | −0.685337 | − | 0.539304i | ||||
\(875\) | 17.3629 | − | 17.3629i | 0.586974 | − | 0.586974i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.2575 | + | 15.2575i | 0.515208 | + | 0.515208i | 0.916117 | − | 0.400910i | \(-0.131306\pi\) |
−0.400910 | + | 0.916117i | \(0.631306\pi\) | |||||||
\(878\) | −24.8726 | + | 2.96594i | −0.839409 | + | 0.100096i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.02944 | − | 5.89450i | −0.102122 | − | 0.198704i | ||||
\(881\) | −21.6686 | −0.730035 | −0.365018 | − | 0.931001i | \(-0.618937\pi\) | ||||
−0.365018 | + | 0.931001i | \(0.618937\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.0590385 | − | 0.0590385i | −0.00198680 | − | 0.00198680i | 0.706113 | − | 0.708099i | \(-0.250447\pi\) |
−0.708099 | + | 0.706113i | \(0.750447\pi\) | |||||||
\(884\) | −44.9370 | − | 27.4294i | −1.51140 | − | 0.922550i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.6672 | − | 19.4111i | −0.828710 | − | 0.652127i | ||||
\(887\) | − | 30.8043i | − | 1.03431i | −0.855892 | − | 0.517154i | \(-0.826991\pi\) | ||
0.855892 | − | 0.517154i | \(-0.173009\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.2404i | 1.04777i | ||||||||
\(890\) | −13.6663 | + | 17.3668i | −0.458095 | + | 0.582137i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 46.1989 | − | 11.1769i | 1.54685 | − | 0.374232i | ||||
\(893\) | 12.8910 | + | 12.8910i | 0.431380 | + | 0.431380i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −46.4682 | −1.55326 | ||||||||
\(896\) | 19.5116 | − | 21.3686i | 0.651836 | − | 0.713876i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.74559 | + | 39.7969i | 0.158362 | + | 1.32804i | ||||
\(899\) | 20.1930 | + | 20.1930i | 0.673475 | + | 0.673475i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.6135 | − | 16.6135i | 0.553477 | − | 0.553477i | ||||
\(902\) | −0.461970 | + | 0.587062i | −0.0153819 | + | 0.0195470i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.20617 | + | 5.93207i | 0.0733760 | + | 0.197298i | ||||
\(905\) | 22.2008i | 0.737979i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.0170 | − | 35.0170i | 1.16272 | − | 1.16272i | 0.178844 | − | 0.983878i | \(-0.442764\pi\) |
0.983878 | − | 0.178844i | \(-0.0572356\pi\) | |||||||
\(908\) | −1.54913 | − | 0.945580i | −0.0514095 | − | 0.0313802i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 36.2837 | − | 4.32666i | 1.20279 | − | 0.143427i | ||||
\(911\) | −0.0829331 | −0.00274770 | −0.00137385 | − | 0.999999i | \(-0.500437\pi\) | ||||
−0.00137385 | + | 0.999999i | \(0.500437\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.607822 | 0.0201160 | ||||||||
\(914\) | 24.3494 | − | 2.90355i | 0.805407 | − | 0.0960410i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.87321 | + | 12.8985i | −0.260138 | + | 0.426180i | ||||
\(917\) | −9.65685 | + | 9.65685i | −0.318897 | + | 0.318897i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.1161i | 0.663568i | 0.943355 | + | 0.331784i | \(0.107650\pi\) | ||||
−0.943355 | + | 0.331784i | \(0.892350\pi\) | |||||||
\(920\) | 8.23765 | − | 17.9929i | 0.271587 | − | 0.593210i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.09373 | + | 2.66066i | −0.0689532 | + | 0.0876243i | ||||
\(923\) | −14.7721 | + | 14.7721i | −0.486231 | + | 0.486231i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.05352 | + | 3.05352i | 0.100399 | + | 0.100399i | ||||
\(926\) | 0.452519 | + | 3.79486i | 0.0148707 | + | 0.124707i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.70018 | + | 24.1819i | −0.154291 | + | 0.793811i | ||||
\(929\) | −8.55098 | −0.280549 | −0.140274 | − | 0.990113i | \(-0.544798\pi\) | ||||
−0.140274 | + | 0.990113i | \(0.544798\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.08941 | − | 2.08941i | −0.0684776 | − | 0.0684776i | ||||
\(932\) | −10.9235 | − | 45.1515i | −0.357813 | − | 1.47899i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −21.1663 | + | 26.8978i | −0.692584 | + | 0.880122i | ||||
\(935\) | − | 10.6792i | − | 0.349248i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.5780i | 1.09695i | 0.836168 | + | 0.548473i | \(0.184791\pi\) | ||||
−0.836168 | + | 0.548473i | \(0.815209\pi\) | |||||||
\(938\) | 8.51746 | + | 6.70254i | 0.278105 | + | 0.218846i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.29040 | + | 11.9437i | −0.237787 | + | 0.389561i | ||||
\(941\) | 8.48463 | + | 8.48463i | 0.276591 | + | 0.276591i | 0.831747 | − | 0.555156i | \(-0.187341\pi\) |
−0.555156 | + | 0.831747i | \(0.687341\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.23059 | −0.0726380 | ||||||||
\(944\) | −6.91688 | + | 21.5443i | −0.225125 | + | 0.701207i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.518248 | − | 0.0617987i | 0.0168497 | − | 0.00200925i | ||||
\(947\) | −17.8571 | − | 17.8571i | −0.580277 | − | 0.580277i | 0.354702 | − | 0.934979i | \(-0.384582\pi\) |
−0.934979 | + | 0.354702i | \(0.884582\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.6596 | − | 42.6596i | 1.38479 | − | 1.38479i | ||||
\(950\) | −8.01451 | − | 6.30676i | −0.260025 | − | 0.204618i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 43.7029 | − | 16.2533i | 1.41642 | − | 0.526774i | ||||
\(953\) | 3.86469i | 0.125190i | 0.998039 | + | 0.0625948i | \(0.0199376\pi\) | ||||
−0.998039 | + | 0.0625948i | \(0.980062\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.79607 | − | 9.79607i | 0.316993 | − | 0.316993i | ||||
\(956\) | 52.3329 | − | 12.6609i | 1.69257 | − | 0.409484i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.72163 | + | 31.2099i | 0.120240 | + | 1.00835i | ||||
\(959\) | −13.0590 | −0.421698 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.0027 | 0.387185 | ||||||||
\(962\) | −2.63956 | − | 22.1356i | −0.0851029 | − | 0.713679i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20.1184 | − | 4.86727i | 0.647971 | − | 0.156764i | ||||
\(965\) | 34.0228 | − | 34.0228i | 1.09523 | − | 1.09523i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.8714i | 1.21786i | 0.793224 | + | 0.608930i | \(0.208401\pi\) | ||||
−0.793224 | + | 0.608930i | \(0.791599\pi\) | |||||||
\(968\) | 27.9719 | − | 10.4029i | 0.899052 | − | 0.334362i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −34.7855 | − | 27.3733i | −1.11689 | − | 0.878905i | ||||
\(971\) | −2.64873 | + | 2.64873i | −0.0850017 | + | 0.0850017i | −0.748329 | − | 0.663327i | \(-0.769144\pi\) |
0.663327 | + | 0.748329i | \(0.269144\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.1180 | + | 30.1180i | 0.965540 | + | 0.965540i | ||||
\(974\) | 19.6371 | − | 2.34163i | 0.629214 | − | 0.0750308i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −23.6237 | − | 7.58449i | −0.756177 | − | 0.242774i | ||||
\(977\) | −17.6530 | −0.564768 | −0.282384 | − | 0.959301i | \(-0.591125\pi\) | ||||
−0.282384 | + | 0.959301i | \(0.591125\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.99201 | + | 2.99201i | 0.0956250 | + | 0.0956250i | ||||
\(980\) | 1.18165 | − | 1.93588i | 0.0377464 | − | 0.0618393i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −11.3700 | − | 8.94725i | −0.362831 | − | 0.285518i | ||||
\(983\) | − | 22.3557i | − | 0.713035i | −0.934289 | − | 0.356518i | \(-0.883964\pi\) | ||
0.934289 | − | 0.356518i | \(-0.116036\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 4.33057i | − | 0.137983i | ||||||
\(986\) | −24.5478 | + | 31.1949i | −0.781762 | + | 0.993447i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.3798 | + | 51.1708i | 0.393853 | + | 1.62796i | ||||
\(989\) | 1.10197 | + | 1.10197i | 0.0350405 | + | 0.0350405i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.8769 | 0.567878 | 0.283939 | − | 0.958842i | \(-0.408359\pi\) | ||||
0.283939 | + | 0.958842i | \(0.408359\pi\) | |||||||
\(992\) | 20.7440 | + | 30.7534i | 0.658623 | + | 0.976422i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.19079 | − | 18.3722i | −0.0694878 | − | 0.582730i | ||||
\(995\) | −1.73812 | − | 1.73812i | −0.0551020 | − | 0.0551020i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.28610 | − | 4.28610i | 0.135742 | − | 0.135742i | −0.635971 | − | 0.771713i | \(-0.719400\pi\) |
0.771713 | + | 0.635971i | \(0.219400\pi\) | |||||||
\(998\) | −3.20431 | + | 4.07197i | −0.101431 | + | 0.128896i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 144.2.k.b.109.3 | 8 | ||
3.2 | odd | 2 | 48.2.j.a.13.2 | ✓ | 8 | ||
4.3 | odd | 2 | 576.2.k.b.145.1 | 8 | |||
8.3 | odd | 2 | 1152.2.k.f.289.4 | 8 | |||
8.5 | even | 2 | 1152.2.k.c.289.4 | 8 | |||
12.11 | even | 2 | 192.2.j.a.145.4 | 8 | |||
16.3 | odd | 4 | 1152.2.k.f.865.4 | 8 | |||
16.5 | even | 4 | inner | 144.2.k.b.37.3 | 8 | ||
16.11 | odd | 4 | 576.2.k.b.433.1 | 8 | |||
16.13 | even | 4 | 1152.2.k.c.865.4 | 8 | |||
24.5 | odd | 2 | 384.2.j.b.289.3 | 8 | |||
24.11 | even | 2 | 384.2.j.a.289.1 | 8 | |||
32.5 | even | 8 | 9216.2.a.y.1.2 | 4 | |||
32.11 | odd | 8 | 9216.2.a.bn.1.3 | 4 | |||
32.21 | even | 8 | 9216.2.a.bo.1.3 | 4 | |||
32.27 | odd | 8 | 9216.2.a.x.1.2 | 4 | |||
48.5 | odd | 4 | 48.2.j.a.37.2 | yes | 8 | ||
48.11 | even | 4 | 192.2.j.a.49.4 | 8 | |||
48.29 | odd | 4 | 384.2.j.b.97.3 | 8 | |||
48.35 | even | 4 | 384.2.j.a.97.1 | 8 | |||
96.5 | odd | 8 | 3072.2.a.t.1.3 | 4 | |||
96.11 | even | 8 | 3072.2.a.o.1.2 | 4 | |||
96.29 | odd | 8 | 3072.2.d.f.1537.3 | 8 | |||
96.35 | even | 8 | 3072.2.d.i.1537.7 | 8 | |||
96.53 | odd | 8 | 3072.2.a.i.1.2 | 4 | |||
96.59 | even | 8 | 3072.2.a.n.1.3 | 4 | |||
96.77 | odd | 8 | 3072.2.d.f.1537.6 | 8 | |||
96.83 | even | 8 | 3072.2.d.i.1537.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.j.a.13.2 | ✓ | 8 | 3.2 | odd | 2 | ||
48.2.j.a.37.2 | yes | 8 | 48.5 | odd | 4 | ||
144.2.k.b.37.3 | 8 | 16.5 | even | 4 | inner | ||
144.2.k.b.109.3 | 8 | 1.1 | even | 1 | trivial | ||
192.2.j.a.49.4 | 8 | 48.11 | even | 4 | |||
192.2.j.a.145.4 | 8 | 12.11 | even | 2 | |||
384.2.j.a.97.1 | 8 | 48.35 | even | 4 | |||
384.2.j.a.289.1 | 8 | 24.11 | even | 2 | |||
384.2.j.b.97.3 | 8 | 48.29 | odd | 4 | |||
384.2.j.b.289.3 | 8 | 24.5 | odd | 2 | |||
576.2.k.b.145.1 | 8 | 4.3 | odd | 2 | |||
576.2.k.b.433.1 | 8 | 16.11 | odd | 4 | |||
1152.2.k.c.289.4 | 8 | 8.5 | even | 2 | |||
1152.2.k.c.865.4 | 8 | 16.13 | even | 4 | |||
1152.2.k.f.289.4 | 8 | 8.3 | odd | 2 | |||
1152.2.k.f.865.4 | 8 | 16.3 | odd | 4 | |||
3072.2.a.i.1.2 | 4 | 96.53 | odd | 8 | |||
3072.2.a.n.1.3 | 4 | 96.59 | even | 8 | |||
3072.2.a.o.1.2 | 4 | 96.11 | even | 8 | |||
3072.2.a.t.1.3 | 4 | 96.5 | odd | 8 | |||
3072.2.d.f.1537.3 | 8 | 96.29 | odd | 8 | |||
3072.2.d.f.1537.6 | 8 | 96.77 | odd | 8 | |||
3072.2.d.i.1537.2 | 8 | 96.83 | even | 8 | |||
3072.2.d.i.1537.7 | 8 | 96.35 | even | 8 | |||
9216.2.a.x.1.2 | 4 | 32.27 | odd | 8 | |||
9216.2.a.y.1.2 | 4 | 32.5 | even | 8 | |||
9216.2.a.bn.1.3 | 4 | 32.11 | odd | 8 | |||
9216.2.a.bo.1.3 | 4 | 32.21 | even | 8 |