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 | 37.3 | ||
Root | \(0.500000 + 1.44392i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.37 |
Dual form | 144.2.k.b.109.3 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 | 0.197977 | − | 0.980207i | \(-0.436563\pi\) |
−0.980207 | + | 0.197977i | \(0.936563\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.55765i | − | 0.966700i | −0.875427 | − | 0.483350i | \(-0.839420\pi\) | ||
0.875427 | − | 0.483350i | \(-0.160580\pi\) | |||||||
\(8\) | −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 | 0.632091 | − | 0.774894i | \(-0.282197\pi\) |
−0.774894 | + | 0.632091i | \(0.782197\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.88784 | − | 2.88784i | 0.800943 | − | 0.800943i | −0.182300 | − | 0.983243i | \(-0.558354\pi\) |
0.983243 | + | 0.182300i | \(0.0583543\pi\) | |||||||
\(14\) | −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 | −0.0466864 | + | 0.998910i | \(0.514866\pi\) |
−0.998910 | + | 0.0466864i | \(0.985134\pi\) | |||||||
\(20\) | 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 | \(0.0952810\pi\) | ||||
−0.955533 | + | 0.294884i | \(0.904719\pi\) | |||||||
\(24\) | 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 | −0.360821 | − | 0.932635i | \(-0.617504\pi\) |
0.932635 | + | 0.360821i | \(0.117504\pi\) | |||||||
\(30\) | 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 | 0.446235 | − | 0.894916i | \(-0.352765\pi\) |
−0.894916 | + | 0.446235i | \(0.852765\pi\) | |||||||
\(38\) | 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 | \(0.0196145\pi\) | ||||
−0.998102 | + | 0.0615818i | \(0.980385\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.389604 | − | 0.389604i | −0.0594141 | − | 0.0594141i | 0.676775 | − | 0.736190i | \(-0.263377\pi\) |
−0.736190 | + | 0.676775i | \(0.763377\pi\) | |||||||
\(44\) | 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 | 0.861615 | − | 0.507562i | \(-0.169453\pi\) |
−0.507562 | + | 0.861615i | \(0.669453\pi\) | |||||||
\(54\) | 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 | 0.397044 | − | 0.917800i | \(-0.370036\pi\) |
−0.917800 | + | 0.397044i | \(0.870036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.38607 | + | 4.38607i | −0.561579 | + | 0.561579i | −0.929756 | − | 0.368177i | \(-0.879982\pi\) |
0.368177 | + | 0.929756i | \(0.379982\pi\) | |||||||
\(62\) | 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 | −0.824589 | − | 0.565733i | \(-0.808593\pi\) |
0.565733 | + | 0.824589i | \(0.308593\pi\) | |||||||
\(68\) | −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 | \(-0.901832\pi\) | ||
0.952820 | − | 0.303537i | \(-0.0981676\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.7721i | 1.72895i | 0.502676 | + | 0.864475i | \(0.332349\pi\) | ||||
−0.502676 | + | 0.864475i | \(0.667651\pi\) | |||||||
\(74\) | −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 | −0.741445 | − | 0.671013i | \(-0.765859\pi\) |
0.671013 | + | 0.741445i | \(0.265859\pi\) | |||||||
\(84\) | 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 | \(0.108673\pi\) | ||||
−0.942285 | + | 0.334813i | \(0.891327\pi\) | |||||||
\(90\) | 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 | 0.225498 | − | 0.974244i | \(-0.427599\pi\) |
−0.974244 | + | 0.225498i | \(0.927599\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.33686i | 0.328790i | 0.986395 | + | 0.164395i | \(0.0525672\pi\) | ||||
−0.986395 | + | 0.164395i | \(0.947433\pi\) | |||||||
\(104\) | 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 | 0.874560 | + | 0.484918i | \(0.161151\pi\) |
0.484918 | + | 0.874560i | \(0.338849\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.76901 | − | 2.76901i | 0.265224 | − | 0.265224i | −0.561949 | − | 0.827172i | \(-0.689948\pi\) |
0.827172 | + | 0.561949i | \(0.189948\pi\) | |||||||
\(110\) | 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 | −0.522659 | − | 0.852542i | \(-0.675060\pi\) |
0.852542 | + | 0.522659i | \(0.175060\pi\) | |||||||
\(132\) | 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 | \(-0.930010\pi\) | ||
0.975924 | − | 0.218112i | \(-0.0699898\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.7757 | + | 11.7757i | 0.998800 | + | 0.998800i | 0.999999 | − | 0.00119925i | \(-0.000381735\pi\) |
−0.00119925 | + | 0.999999i | \(0.500382\pi\) | |||||||
\(140\) | 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 | 0.952467 | − | 0.304640i | \(-0.0985363\pi\) |
−0.304640 | + | 0.952467i | \(0.598536\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 14.6506i | − | 1.19225i | −0.802893 | − | 0.596123i | \(-0.796707\pi\) | ||
0.802893 | − | 0.596123i | \(-0.203293\pi\) | |||||||
\(152\) | −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 | −0.821607 | − | 0.570054i | \(-0.806922\pi\) |
0.570054 | + | 0.821607i | \(0.306922\pi\) | |||||||
\(158\) | −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 | −0.457852 | − | 0.889029i | \(-0.651381\pi\) |
0.889029 | + | 0.457852i | \(0.151381\pi\) | |||||||
\(164\) | 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 | \(0.285209\pi\) | ||||
−0.624730 | + | 0.780841i | \(0.714791\pi\) | |||||||
\(168\) | 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 | −0.852955 | − | 0.521985i | \(-0.825192\pi\) |
0.521985 | + | 0.852955i | \(0.325192\pi\) | |||||||
\(174\) | 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 | −0.00713130 | − | 0.999975i | \(-0.502270\pi\) |
0.999975 | + | 0.00713130i | \(0.00226998\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.34628 | + | 6.34628i | 0.471715 | + | 0.471715i | 0.902469 | − | 0.430754i | \(-0.141752\pi\) |
−0.430754 | + | 0.902469i | \(0.641752\pi\) | |||||||
\(182\) | −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 | 0.661631 | − | 0.749830i | \(-0.269865\pi\) |
−0.749830 | + | 0.661631i | \(0.769865\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 0.993710i | − | 0.0704422i | −0.999380 | − | 0.0352211i | \(-0.988786\pi\) | ||
0.999380 | − | 0.0352211i | \(-0.0112135\pi\) | |||||||
\(200\) | −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 | −0.546588 | − | 0.837402i | \(-0.684073\pi\) |
0.837402 | + | 0.546588i | \(0.184073\pi\) | |||||||
\(212\) | −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 | −0.685492 | − | 0.728081i | \(-0.740413\pi\) |
0.728081 | + | 0.685492i | \(0.240413\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.34275 | + | 5.34275i | 0.353059 | + | 0.353059i | 0.861246 | − | 0.508188i | \(-0.169684\pi\) |
−0.508188 | + | 0.861246i | \(0.669684\pi\) | |||||||
\(230\) | −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 | \(-0.724793\pi\) | ||
0.648954 | − | 0.760828i | \(-0.275207\pi\) | |||||||
\(234\) | 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 | 0.944465 | − | 0.328611i | \(-0.106581\pi\) |
−0.328611 | + | 0.944465i | \(0.606581\pi\) | |||||||
\(252\) | 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 | \(0.375703\pi\) | ||||
−0.380643 | + | 0.924722i | \(0.624297\pi\) | |||||||
\(264\) | 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 | −0.303046 | + | 0.952976i | \(0.598004\pi\) |
−0.952976 | + | 0.303046i | \(0.901996\pi\) | |||||||
\(270\) | 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 | 0.970289 | − | 0.241951i | \(-0.0777872\pi\) |
−0.241951 | + | 0.970289i | \(0.577787\pi\) | |||||||
\(278\) | 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 | \(-0.973710\pi\) | ||
0.996591 | − | 0.0824993i | \(-0.0262902\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.48528 | + | 4.48528i | 0.266622 | + | 0.266622i | 0.827738 | − | 0.561115i | \(-0.189628\pi\) |
−0.561115 | + | 0.827738i | \(0.689628\pi\) | |||||||
\(284\) | −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 | 0.904976 | − | 0.425463i | \(-0.139889\pi\) |
−0.425463 | + | 0.904976i | \(0.639889\pi\) | |||||||
\(294\) | 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 | −0.342738 | − | 0.939431i | \(-0.611354\pi\) |
0.939431 | + | 0.342738i | \(0.111354\pi\) | |||||||
\(308\) | 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 | \(-0.859415\pi\) | ||
0.904043 | − | 0.427442i | \(-0.140585\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.0027i | 1.30019i | 0.759852 | + | 0.650096i | \(0.225271\pi\) | ||||
−0.759852 | + | 0.650096i | \(0.774729\pi\) | |||||||
\(314\) | 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 | −0.491346 | − | 0.870964i | \(-0.663495\pi\) |
0.870964 | + | 0.491346i | \(0.163495\pi\) | |||||||
\(318\) | 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 | −0.996436 | − | 0.0843464i | \(-0.973120\pi\) |
−0.0843464 | − | 0.996436i | \(-0.526880\pi\) | |||||||
\(332\) | 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 | 0.518317 | − | 0.855188i | \(-0.326559\pi\) |
−0.855188 | + | 0.518317i | \(0.826559\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.74255 | + | 4.74255i | −0.253863 | + | 0.253863i | −0.822552 | − | 0.568690i | \(-0.807451\pi\) |
0.568690 | + | 0.822552i | \(0.307451\pi\) | |||||||
\(350\) | 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 | \(-0.667102\pi\) | ||
0.501184 | − | 0.865341i | \(-0.332898\pi\) | |||||||
\(360\) | 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 | 0.131004 | − | 0.991382i | \(-0.458180\pi\) |
−0.991382 | + | 0.131004i | \(0.958180\pi\) | |||||||
\(374\) | −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 | 0.878075 | − | 0.478523i | \(-0.158828\pi\) |
−0.478523 | + | 0.878075i | \(0.658828\pi\) | |||||||
\(380\) | −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 | 0.971248 | + | 0.238069i | \(0.0765143\pi\) |
0.238069 | + | 0.971248i | \(0.423486\pi\) | |||||||
\(390\) | 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 | −0.916145 | − | 0.400847i | \(-0.868716\pi\) |
0.400847 | + | 0.916145i | \(0.368716\pi\) | |||||||
\(398\) | −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 | \(-0.907656\pi\) | ||
0.958213 | − | 0.286055i | \(-0.0923440\pi\) | |||||||
\(410\) | −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 | −0.852442 | − | 0.522822i | \(-0.824879\pi\) |
0.522822 | + | 0.852442i | \(0.324879\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.2239 | − | 17.2239i | −0.839443 | − | 0.839443i | 0.149343 | − | 0.988785i | \(-0.452284\pi\) |
−0.988785 | + | 0.149343i | \(0.952284\pi\) | |||||||
\(422\) | −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 | \(-0.861090\pi\) | ||
0.906280 | − | 0.422678i | \(-0.138910\pi\) | |||||||
\(440\) | −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 | 0.227997 | − | 0.973662i | \(-0.426782\pi\) |
−0.973662 | + | 0.227997i | \(0.926782\pi\) | |||||||
\(444\) | 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 | \(0.132922\pi\) | ||||
−0.914070 | + | 0.405557i | \(0.867078\pi\) | |||||||
\(458\) | 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 | −0.666585 | − | 0.745429i | \(-0.732245\pi\) |
0.745429 | + | 0.666585i | \(0.232245\pi\) | |||||||
\(462\) | 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 | −0.189883 | − | 0.981807i | \(-0.560811\pi\) |
0.981807 | + | 0.189883i | \(0.0608108\pi\) | |||||||
\(468\) | 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 | \(0.102620\pi\) | ||||
−0.948480 | + | 0.316836i | \(0.897380\pi\) | |||||||
\(488\) | −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 | 0.524772 | − | 0.851243i | \(-0.324151\pi\) |
−0.851243 | + | 0.524772i | \(0.824151\pi\) | |||||||
\(492\) | 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 | −0.646735 | − | 0.762715i | \(-0.723866\pi\) |
0.762715 | + | 0.646735i | \(0.223866\pi\) | |||||||
\(500\) | 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 | \(-0.654959\pi\) | ||
0.467817 | − | 0.883825i | \(-0.345041\pi\) | |||||||
\(504\) | 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 | −0.995368 | − | 0.0961393i | \(-0.969351\pi\) |
0.0961393 | + | 0.995368i | \(0.469351\pi\) | |||||||
\(510\) | 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 | \(0.169516\pi\) | ||||
−0.861515 | + | 0.507732i | \(0.830484\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.78550 | − | 5.78550i | −0.252982 | − | 0.252982i | 0.569210 | − | 0.822192i | \(-0.307249\pi\) |
−0.822192 | + | 0.569210i | \(0.807249\pi\) | |||||||
\(524\) | −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 | −0.602457 | − | 0.798152i | \(-0.705811\pi\) |
0.798152 | + | 0.602457i | \(0.205811\pi\) | |||||||
\(542\) | −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 | −0.207689 | + | 0.978195i | \(0.566594\pi\) |
−0.978195 | + | 0.207689i | \(0.933406\pi\) | |||||||
\(548\) | −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 | −0.681767 | − | 0.731569i | \(-0.738788\pi\) |
0.731569 | + | 0.681767i | \(0.238788\pi\) | |||||||
\(558\) | 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 | 0.240326 | − | 0.970692i | \(-0.422746\pi\) |
0.970692 | − | 0.240326i | \(-0.0772544\pi\) | |||||||
\(564\) | 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 | \(0.191493\pi\) | ||||
−0.824435 | + | 0.565957i | \(0.808507\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.8284 | − | 14.8284i | −0.620550 | − | 0.620550i | 0.325122 | − | 0.945672i | \(-0.394595\pi\) |
−0.945672 | + | 0.325122i | \(0.894595\pi\) | |||||||
\(572\) | 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 | 0.934703 | + | 0.355429i | \(0.115665\pi\) |
0.355429 | + | 0.934703i | \(0.384335\pi\) | |||||||
\(588\) | 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 | \(0.148595\pi\) | ||||
−0.893002 | + | 0.450052i | \(0.851405\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.7721i | 0.439405i | 0.975567 | + | 0.219703i | \(0.0705087\pi\) | ||||
−0.975567 | + | 0.219703i | \(0.929491\pi\) | |||||||
\(602\) | 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 | 0.462389 | − | 0.886677i | \(-0.346993\pi\) |
−0.886677 | + | 0.462389i | \(0.846993\pi\) | |||||||
\(614\) | −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 | \(0.147630\pi\) | ||||
−0.894363 | + | 0.447343i | \(0.852370\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.6398 | + | 11.6398i | 0.467843 | + | 0.467843i | 0.901215 | − | 0.433372i | \(-0.142676\pi\) |
−0.433372 | + | 0.901215i | \(0.642676\pi\) | |||||||
\(620\) | 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 | \(0.0258138\pi\) | ||||
−0.996713 | + | 0.0810075i | \(0.974186\pi\) | |||||||
\(632\) | 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 | −0.837378 | − | 0.546625i | \(-0.815912\pi\) |
0.546625 | + | 0.837378i | \(0.315912\pi\) | |||||||
\(644\) | −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 | \(-0.926690\pi\) | ||
0.973595 | − | 0.228280i | \(-0.0733102\pi\) | |||||||
\(648\) | 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 | −0.668324 | − | 0.743870i | \(-0.732988\pi\) |
0.743870 | + | 0.668324i | \(0.232988\pi\) | |||||||
\(654\) | 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 | −0.992371 | − | 0.123290i | \(-0.960656\pi\) |
0.123290 | + | 0.992371i | \(0.460656\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.7033 | + | 10.7033i | 0.416311 | + | 0.416311i | 0.883930 | − | 0.467619i | \(-0.154888\pi\) |
−0.467619 | + | 0.883930i | \(0.654888\pi\) | |||||||
\(662\) | −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 | −0.999505 | − | 0.0314484i | \(-0.989988\pi\) |
−0.0314484 | − | 0.999505i | \(-0.510012\pi\) | |||||||
\(678\) | 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 | 0.415766 | − | 0.909472i | \(-0.363513\pi\) |
−0.909472 | + | 0.415766i | \(0.863513\pi\) | |||||||
\(684\) | 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 | −0.985202 | − | 0.171399i | \(-0.945171\pi\) |
0.171399 | + | 0.985202i | \(0.445171\pi\) | |||||||
\(692\) | 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 | −0.922493 | − | 0.386014i | \(-0.873852\pi\) |
0.386014 | + | 0.922493i | \(0.373852\pi\) | |||||||
\(702\) | 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 | −0.993192 | − | 0.116485i | \(-0.962837\pi\) |
−0.116485 | − | 0.993192i | \(-0.537163\pi\) | |||||||
\(710\) | 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 | \(0.124028\pi\) | ||||
−0.925044 | + | 0.379861i | \(0.875972\pi\) | |||||||
\(728\) | 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 | 0.302536 | − | 0.953138i | \(-0.402167\pi\) |
0.953138 | − | 0.302536i | \(-0.0978331\pi\) | |||||||
\(734\) | 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 | −0.370855 | − | 0.928691i | \(-0.620935\pi\) |
0.928691 | + | 0.370855i | \(0.120935\pi\) | |||||||
\(740\) | 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 | \(-0.987301\pi\) | ||
0.999204 | − | 0.0398839i | \(-0.0126988\pi\) | |||||||
\(744\) | 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 | 0.371340 | − | 0.928497i | \(-0.378899\pi\) |
−0.928497 | + | 0.371340i | \(0.878899\pi\) | |||||||
\(758\) | 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 | \(-0.975198\pi\) | ||
0.996966 | − | 0.0778375i | \(-0.0248015\pi\) | |||||||
\(762\) | 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 | 0.951240 | + | 0.308450i | \(0.0998104\pi\) |
0.308450 | + | 0.951240i | \(0.400190\pi\) | |||||||
\(774\) | 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 | −0.131873 | − | 0.991267i | \(-0.542099\pi\) |
0.991267 | + | 0.131873i | \(0.0420992\pi\) | |||||||
\(788\) | 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 | 0.0193524 | − | 0.999813i | \(-0.493840\pi\) |
0.999813 | − | 0.0193524i | \(-0.00616044\pi\) | |||||||
\(798\) | 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 | \(-0.938101\pi\) | ||
0.981152 | − | 0.193239i | \(-0.0618993\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.0259 | − | 15.0259i | −0.527630 | − | 0.527630i | 0.392235 | − | 0.919865i | \(-0.371702\pi\) |
−0.919865 | + | 0.392235i | \(0.871702\pi\) | |||||||
\(812\) | 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 | 0.972916 | − | 0.231159i | \(-0.0742519\pi\) |
−0.231159 | + | 0.972916i | \(0.574252\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 55.0851i | 1.92015i | 0.279751 | + | 0.960073i | \(0.409748\pi\) | ||||
−0.279751 | + | 0.960073i | \(0.590252\pi\) | |||||||
\(824\) | −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 | 0.990068 | − | 0.140588i | \(-0.0448994\pi\) |
−0.140588 | + | 0.990068i | \(0.544899\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.9235 | + | 21.9235i | −0.761436 | + | 0.761436i | −0.976582 | − | 0.215146i | \(-0.930977\pi\) |
0.215146 | + | 0.976582i | \(0.430977\pi\) | |||||||
\(830\) | 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 | \(-0.971710\pi\) | ||
0.996053 | − | 0.0887599i | \(-0.0282904\pi\) | |||||||
\(840\) | 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 | 0.894704 | − | 0.446659i | \(-0.147386\pi\) |
−0.446659 | + | 0.894704i | \(0.647386\pi\) | |||||||
\(854\) | 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 | \(-0.872158\pi\) | ||
0.920426 | − | 0.390916i | \(-0.127842\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.1225 | − | 25.1225i | −0.857169 | − | 0.857169i | 0.133834 | − | 0.991004i | \(-0.457271\pi\) |
−0.991004 | + | 0.133834i | \(0.957271\pi\) | |||||||
\(860\) | 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 | −0.400910 | − | 0.916117i | \(-0.631306\pi\) |
0.916117 | + | 0.400910i | \(0.131306\pi\) | |||||||
\(878\) | −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 | −0.708099 | − | 0.706113i | \(-0.750447\pi\) |
0.706113 | + | 0.708099i | \(0.250447\pi\) | |||||||
\(884\) | −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 | \(0.173009\pi\) | ||||
−0.855892 | + | 0.517154i | \(0.826991\pi\) | |||||||
\(888\) | 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 | 0.983878 | + | 0.178844i | \(0.0572356\pi\) |
0.178844 | + | 0.983878i | \(0.442764\pi\) | |||||||
\(908\) | −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 | \(-0.892350\pi\) | ||
0.943355 | − | 0.331784i | \(-0.107650\pi\) | |||||||
\(920\) | 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 | \(-0.815209\pi\) | ||
0.836168 | − | 0.548473i | \(-0.184791\pi\) | |||||||
\(938\) | 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 | −0.555156 | − | 0.831747i | \(-0.687341\pi\) |
0.831747 | + | 0.555156i | \(0.187341\pi\) | |||||||
\(942\) | 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 | −0.934979 | − | 0.354702i | \(-0.884582\pi\) |
0.354702 | + | 0.934979i | \(0.384582\pi\) | |||||||
\(948\) | 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 | \(-0.980062\pi\) | ||
0.998039 | − | 0.0625948i | \(-0.0199376\pi\) | |||||||
\(954\) | 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 | \(-0.791599\pi\) | ||
0.793224 | − | 0.608930i | \(-0.208401\pi\) | |||||||
\(968\) | 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 | 0.663327 | − | 0.748329i | \(-0.269144\pi\) |
−0.748329 | + | 0.663327i | \(0.769144\pi\) | |||||||
\(972\) | 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 | \(0.116036\pi\) | ||||
−0.934289 | + | 0.356518i | \(0.883964\pi\) | |||||||
\(984\) | 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 | 0.771713 | − | 0.635971i | \(-0.219400\pi\) |
−0.635971 | + | 0.771713i | \(0.719400\pi\) | |||||||
\(998\) | −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.37.3 | 8 | ||
3.2 | odd | 2 | 48.2.j.a.37.2 | yes | 8 | ||
4.3 | odd | 2 | 576.2.k.b.433.1 | 8 | |||
8.3 | odd | 2 | 1152.2.k.f.865.4 | 8 | |||
8.5 | even | 2 | 1152.2.k.c.865.4 | 8 | |||
12.11 | even | 2 | 192.2.j.a.49.4 | 8 | |||
16.3 | odd | 4 | 576.2.k.b.145.1 | 8 | |||
16.5 | even | 4 | 1152.2.k.c.289.4 | 8 | |||
16.11 | odd | 4 | 1152.2.k.f.289.4 | 8 | |||
16.13 | even | 4 | inner | 144.2.k.b.109.3 | 8 | ||
24.5 | odd | 2 | 384.2.j.b.97.3 | 8 | |||
24.11 | even | 2 | 384.2.j.a.97.1 | 8 | |||
32.3 | odd | 8 | 9216.2.a.bn.1.3 | 4 | |||
32.13 | even | 8 | 9216.2.a.y.1.2 | 4 | |||
32.19 | odd | 8 | 9216.2.a.x.1.2 | 4 | |||
32.29 | even | 8 | 9216.2.a.bo.1.3 | 4 | |||
48.5 | odd | 4 | 384.2.j.b.289.3 | 8 | |||
48.11 | even | 4 | 384.2.j.a.289.1 | 8 | |||
48.29 | odd | 4 | 48.2.j.a.13.2 | ✓ | 8 | ||
48.35 | even | 4 | 192.2.j.a.145.4 | 8 | |||
96.5 | odd | 8 | 3072.2.d.f.1537.3 | 8 | |||
96.11 | even | 8 | 3072.2.d.i.1537.2 | 8 | |||
96.29 | odd | 8 | 3072.2.a.i.1.2 | 4 | |||
96.35 | even | 8 | 3072.2.a.o.1.2 | 4 | |||
96.53 | odd | 8 | 3072.2.d.f.1537.6 | 8 | |||
96.59 | even | 8 | 3072.2.d.i.1537.7 | 8 | |||
96.77 | odd | 8 | 3072.2.a.t.1.3 | 4 | |||
96.83 | even | 8 | 3072.2.a.n.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.j.a.13.2 | ✓ | 8 | 48.29 | odd | 4 | ||
48.2.j.a.37.2 | yes | 8 | 3.2 | odd | 2 | ||
144.2.k.b.37.3 | 8 | 1.1 | even | 1 | trivial | ||
144.2.k.b.109.3 | 8 | 16.13 | even | 4 | inner | ||
192.2.j.a.49.4 | 8 | 12.11 | even | 2 | |||
192.2.j.a.145.4 | 8 | 48.35 | even | 4 | |||
384.2.j.a.97.1 | 8 | 24.11 | even | 2 | |||
384.2.j.a.289.1 | 8 | 48.11 | even | 4 | |||
384.2.j.b.97.3 | 8 | 24.5 | odd | 2 | |||
384.2.j.b.289.3 | 8 | 48.5 | odd | 4 | |||
576.2.k.b.145.1 | 8 | 16.3 | odd | 4 | |||
576.2.k.b.433.1 | 8 | 4.3 | odd | 2 | |||
1152.2.k.c.289.4 | 8 | 16.5 | even | 4 | |||
1152.2.k.c.865.4 | 8 | 8.5 | even | 2 | |||
1152.2.k.f.289.4 | 8 | 16.11 | odd | 4 | |||
1152.2.k.f.865.4 | 8 | 8.3 | odd | 2 | |||
3072.2.a.i.1.2 | 4 | 96.29 | odd | 8 | |||
3072.2.a.n.1.3 | 4 | 96.83 | even | 8 | |||
3072.2.a.o.1.2 | 4 | 96.35 | even | 8 | |||
3072.2.a.t.1.3 | 4 | 96.77 | odd | 8 | |||
3072.2.d.f.1537.3 | 8 | 96.5 | odd | 8 | |||
3072.2.d.f.1537.6 | 8 | 96.53 | odd | 8 | |||
3072.2.d.i.1537.2 | 8 | 96.11 | even | 8 | |||
3072.2.d.i.1537.7 | 8 | 96.59 | even | 8 | |||
9216.2.a.x.1.2 | 4 | 32.19 | odd | 8 | |||
9216.2.a.y.1.2 | 4 | 32.13 | even | 8 | |||
9216.2.a.bn.1.3 | 4 | 32.3 | odd | 8 | |||
9216.2.a.bo.1.3 | 4 | 32.29 | even | 8 |