Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(269,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.269");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.ch (of order \(6\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.11 | ||
Character | \(\chi\) | \(=\) | 504.269 |
Dual form | 504.2.ch.b.341.11 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.447766 | − | 1.34146i | −0.316619 | − | 0.948553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.59901 | + | 1.20132i | −0.799505 | + | 0.600659i | ||||
\(5\) | −0.331990 | + | 0.191675i | −0.148471 | + | 0.0857195i | −0.572395 | − | 0.819978i | \(-0.693986\pi\) |
0.423924 | + | 0.905698i | \(0.360652\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.03027 | + | 1.69647i | −0.767368 | + | 0.641206i | ||||
\(8\) | 2.32750 | + | 1.60709i | 0.822895 | + | 0.568193i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.405777 | + | 0.359525i | 0.128318 | + | 0.113692i | ||||
\(11\) | 2.28107 | − | 3.95093i | 0.687769 | − | 1.19125i | −0.284789 | − | 0.958590i | \(-0.591923\pi\) |
0.972558 | − | 0.232661i | \(-0.0747432\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.84195 | 0.788216 | 0.394108 | − | 0.919064i | \(-0.371054\pi\) | ||||
0.394108 | + | 0.919064i | \(0.371054\pi\) | |||||||
\(14\) | 3.18483 | + | 1.96389i | 0.851181 | + | 0.524872i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.11367 | − | 3.84184i | 0.278417 | − | 0.960460i | ||||
\(17\) | 2.46500 | − | 4.26950i | 0.597850 | − | 1.03551i | −0.395288 | − | 0.918557i | \(-0.629355\pi\) |
0.993138 | − | 0.116949i | \(-0.0373113\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.18535 | − | 7.24924i | −0.960185 | − | 1.66309i | −0.722030 | − | 0.691861i | \(-0.756791\pi\) |
−0.238154 | − | 0.971227i | \(-0.576542\pi\) | |||||||
\(20\) | 0.300594 | − | 0.705316i | 0.0672148 | − | 0.157713i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.32139 | − | 1.29086i | −1.34773 | − | 0.275213i | ||||
\(23\) | 5.41792 | − | 3.12804i | 1.12971 | − | 0.652241i | 0.185852 | − | 0.982578i | \(-0.440496\pi\) |
0.943863 | + | 0.330337i | \(0.107162\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.42652 | + | 4.20286i | −0.485304 | + | 0.840572i | ||||
\(26\) | −1.27253 | − | 3.81236i | −0.249564 | − | 0.747665i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.20841 | − | 5.15167i | 0.228369 | − | 0.973575i | ||||
\(29\) | −0.292746 | −0.0543616 | −0.0271808 | − | 0.999631i | \(-0.508653\pi\) | ||||
−0.0271808 | + | 0.999631i | \(0.508653\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.93966 | + | 2.85191i | 0.887188 | + | 0.512218i | 0.873022 | − | 0.487681i | \(-0.162157\pi\) |
0.0141665 | + | 0.999900i | \(0.495490\pi\) | |||||||
\(32\) | −5.65233 | + | 0.226308i | −0.999199 | + | 0.0400059i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.83109 | − | 1.39495i | −1.17152 | − | 0.239232i | ||||
\(35\) | 0.348858 | − | 0.952363i | 0.0589677 | − | 0.160979i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.12469 | − | 3.53609i | 1.00689 | − | 0.581330i | 0.0966129 | − | 0.995322i | \(-0.469199\pi\) |
0.910281 | + | 0.413992i | \(0.135866\pi\) | |||||||
\(38\) | −7.85048 | + | 8.86043i | −1.27352 | + | 1.43735i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.08075 | − | 0.0874167i | −0.170881 | − | 0.0138218i | ||||
\(41\) | 4.92280 | 0.768812 | 0.384406 | − | 0.923164i | \(-0.374406\pi\) | ||||
0.384406 | + | 0.923164i | \(0.374406\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.35631i | 0.664332i | 0.943221 | + | 0.332166i | \(0.107779\pi\) | ||||
−0.943221 | + | 0.332166i | \(0.892221\pi\) | |||||||
\(44\) | 1.09887 | + | 9.05788i | 0.165661 | + | 1.36553i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.62209 | − | 5.86728i | −0.976374 | − | 0.865083i | ||||
\(47\) | −4.73214 | − | 8.19631i | −0.690253 | − | 1.19555i | −0.971755 | − | 0.235993i | \(-0.924166\pi\) |
0.281501 | − | 0.959561i | \(-0.409168\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.24396 | − | 6.88858i | 0.177709 | − | 0.984083i | ||||
\(50\) | 6.72447 | + | 1.37317i | 0.950983 | + | 0.194196i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.54431 | + | 3.41409i | −0.630183 | + | 0.473449i | ||||
\(53\) | −2.33050 | + | 4.03655i | −0.320119 | + | 0.554462i | −0.980512 | − | 0.196458i | \(-0.937056\pi\) |
0.660393 | + | 0.750920i | \(0.270390\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.74890i | 0.235821i | ||||||||
\(56\) | −7.45183 | + | 0.685712i | −0.995793 | + | 0.0916321i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.131082 | + | 0.392706i | 0.0172119 | + | 0.0515649i | ||||
\(59\) | −5.72506 | − | 3.30537i | −0.745340 | − | 0.430322i | 0.0786677 | − | 0.996901i | \(-0.474933\pi\) |
−0.824008 | + | 0.566579i | \(0.808267\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.40098 | + | 2.42656i | 0.179376 | + | 0.310689i | 0.941667 | − | 0.336546i | \(-0.109259\pi\) |
−0.762291 | + | 0.647235i | \(0.775925\pi\) | |||||||
\(62\) | 1.61390 | − | 7.90332i | 0.204966 | − | 1.00372i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.83450 | + | 7.48102i | 0.354313 | + | 0.935127i | ||||
\(65\) | −0.943501 | + | 0.544730i | −0.117027 | + | 0.0675655i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.81560 | − | 4.51234i | −0.954827 | − | 0.551270i | −0.0602503 | − | 0.998183i | \(-0.519190\pi\) |
−0.894577 | + | 0.446913i | \(0.852523\pi\) | |||||||
\(68\) | 1.18747 | + | 9.78822i | 0.144002 | + | 1.18700i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.43376 | − | 0.0415413i | −0.171367 | − | 0.00496514i | ||||
\(71\) | 4.37059i | 0.518694i | 0.965784 | + | 0.259347i | \(0.0835073\pi\) | ||||
−0.965784 | + | 0.259347i | \(0.916493\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.9929 | + | 6.34673i | 1.28662 | + | 0.742829i | 0.978049 | − | 0.208374i | \(-0.0668171\pi\) |
0.308568 | + | 0.951202i | \(0.400150\pi\) | |||||||
\(74\) | −7.48595 | − | 6.63267i | −0.870224 | − | 0.771032i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 15.4011 | + | 6.56367i | 1.76662 | + | 0.752905i | ||||
\(77\) | 2.07147 | + | 11.8912i | 0.236066 | + | 1.35513i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.0352186 | − | 0.0610004i | −0.00396240 | − | 0.00686308i | 0.864037 | − | 0.503428i | \(-0.167928\pi\) |
−0.868000 | + | 0.496565i | \(0.834595\pi\) | |||||||
\(80\) | 0.366656 | + | 1.48892i | 0.0409934 | + | 0.166466i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.20426 | − | 6.60372i | −0.243420 | − | 0.729259i | ||||
\(83\) | − | 6.48166i | − | 0.711454i | −0.934590 | − | 0.355727i | \(-0.884233\pi\) | ||
0.934590 | − | 0.355727i | \(-0.115767\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.88991i | 0.204990i | ||||||||
\(86\) | 5.84380 | − | 1.95061i | 0.630154 | − | 0.210340i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 11.6587 | − | 5.52990i | 1.24282 | − | 0.589489i | ||||
\(89\) | −1.63404 | − | 2.83024i | −0.173208 | − | 0.300004i | 0.766332 | − | 0.642445i | \(-0.222080\pi\) |
−0.939540 | + | 0.342441i | \(0.888746\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.76992 | + | 4.82130i | −0.604852 | + | 0.505409i | ||||
\(92\) | −4.90555 | + | 11.5104i | −0.511438 | + | 1.20004i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.87609 | + | 10.0180i | −0.915499 | + | 1.03328i | ||||
\(95\) | 2.77899 | + | 1.60445i | 0.285118 | + | 0.164613i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.349243i | 0.0354602i | 0.999843 | + | 0.0177301i | \(0.00564396\pi\) | ||||
−0.999843 | + | 0.0177301i | \(0.994356\pi\) | |||||||
\(98\) | −9.79774 | + | 1.41576i | −0.989721 | + | 0.143013i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.16894 | − | 9.63544i | −0.116894 | − | 0.963544i | ||||
\(101\) | −13.3130 | − | 7.68628i | −1.32470 | − | 0.764814i | −0.340222 | − | 0.940345i | \(-0.610502\pi\) |
−0.984474 | + | 0.175531i | \(0.943836\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.06085 | − | 1.18983i | 0.203062 | − | 0.117238i | −0.395021 | − | 0.918672i | \(-0.629263\pi\) |
0.598083 | + | 0.801434i | \(0.295929\pi\) | |||||||
\(104\) | 6.61464 | + | 4.56728i | 0.648619 | + | 0.447859i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.45837 | + | 1.31884i | 0.627292 | + | 0.128097i | ||||
\(107\) | −0.412090 | − | 0.713762i | −0.0398383 | − | 0.0690019i | 0.845419 | − | 0.534104i | \(-0.179351\pi\) |
−0.885257 | + | 0.465102i | \(0.846018\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.1259 | + | 8.15558i | 1.35301 | + | 0.781163i | 0.988670 | − | 0.150102i | \(-0.0479603\pi\) |
0.364343 | + | 0.931265i | \(0.381294\pi\) | |||||||
\(110\) | 2.34607 | − | 0.783096i | 0.223689 | − | 0.0746653i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.25653 | + | 9.68927i | 0.402204 | + | 0.915550i | ||||
\(113\) | − | 3.02323i | − | 0.284401i | −0.989838 | − | 0.142201i | \(-0.954582\pi\) | ||
0.989838 | − | 0.142201i | \(-0.0454178\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.19913 | + | 2.07696i | −0.111820 | + | 0.193677i | ||||
\(116\) | 0.468104 | − | 0.351681i | 0.0434624 | − | 0.0326528i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.87052 | + | 9.15996i | −0.172195 | + | 0.843242i | ||||
\(119\) | 2.23849 | + | 12.8500i | 0.205202 | + | 1.17796i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.90658 | − | 8.49845i | −0.446053 | − | 0.772586i | ||||
\(122\) | 2.62782 | − | 2.96588i | 0.237911 | − | 0.268518i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −11.3246 | + | 1.37386i | −1.01698 | + | 0.123376i | ||||
\(125\) | − | 3.77716i | − | 0.337839i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.89959 | 0.257297 | 0.128649 | − | 0.991690i | \(-0.458936\pi\) | ||||
0.128649 | + | 0.991690i | \(0.458936\pi\) | |||||||
\(128\) | 8.76626 | − | 7.15211i | 0.774835 | − | 0.632163i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.15320 | + | 1.02175i | 0.101142 | + | 0.0896137i | ||||
\(131\) | 10.5535 | − | 6.09304i | 0.922059 | − | 0.532351i | 0.0377678 | − | 0.999287i | \(-0.487975\pi\) |
0.884291 | + | 0.466935i | \(0.154642\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.7955 | + | 7.61755i | 1.80320 | + | 0.660525i | ||||
\(134\) | −2.55354 | + | 12.5048i | −0.220593 | + | 1.08025i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.5988 | − | 5.97578i | 1.08034 | − | 0.512419i | ||||
\(137\) | 15.9155 | + | 9.18879i | 1.35975 | + | 0.785051i | 0.989590 | − | 0.143917i | \(-0.0459699\pi\) |
0.370159 | + | 0.928968i | \(0.379303\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.40327 | −0.543118 | −0.271559 | − | 0.962422i | \(-0.587539\pi\) | ||||
−0.271559 | + | 0.962422i | \(0.587539\pi\) | |||||||
\(140\) | 0.586264 | + | 1.94193i | 0.0495483 | + | 0.164123i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.86296 | − | 1.95700i | 0.492008 | − | 0.164228i | ||||
\(143\) | 6.48270 | − | 11.2284i | 0.542111 | − | 0.938963i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.0971889 | − | 0.0561120i | 0.00807110 | − | 0.00465985i | ||||
\(146\) | 3.59163 | − | 17.5883i | 0.297245 | − | 1.45562i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.54548 | + | 13.0120i | −0.455835 | + | 1.06958i | ||||
\(149\) | 9.21714 | + | 15.9646i | 0.755098 | + | 1.30787i | 0.945326 | + | 0.326128i | \(0.105744\pi\) |
−0.190228 | + | 0.981740i | \(0.560923\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.38424 | + | 12.7899i | −0.600921 | + | 1.04083i | 0.391761 | + | 0.920067i | \(0.371866\pi\) |
−0.992682 | + | 0.120758i | \(0.961467\pi\) | |||||||
\(152\) | 1.90880 | − | 23.5988i | 0.154824 | − | 1.91412i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 15.0240 | − | 8.10327i | 1.21067 | − | 0.652980i | ||||
\(155\) | −2.18656 | −0.175628 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.02939 | + | 5.24706i | −0.241772 | + | 0.418761i | −0.961219 | − | 0.275786i | \(-0.911062\pi\) |
0.719447 | + | 0.694547i | \(0.244395\pi\) | |||||||
\(158\) | −0.0660597 | + | 0.0745582i | −0.00525543 | + | 0.00593153i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.83314 | − | 1.15854i | 0.144922 | − | 0.0915906i | ||||
\(161\) | −5.69319 | + | 15.5421i | −0.448686 | + | 1.22489i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.88592 | − | 2.24354i | 0.304369 | − | 0.175727i | −0.340035 | − | 0.940413i | \(-0.610439\pi\) |
0.644404 | + | 0.764685i | \(0.277106\pi\) | |||||||
\(164\) | −7.87161 | + | 5.91385i | −0.614670 | + | 0.461794i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.69486 | + | 2.90227i | −0.674852 | + | 0.225260i | ||||
\(167\) | −15.9351 | −1.23309 | −0.616546 | − | 0.787319i | \(-0.711468\pi\) | ||||
−0.616546 | + | 0.787319i | \(0.711468\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.92330 | −0.378715 | ||||||||
\(170\) | 2.53523 | − | 0.846238i | 0.194443 | − | 0.0649035i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.23332 | − | 6.96579i | −0.399037 | − | 0.531137i | ||||
\(173\) | −16.5050 | + | 9.52916i | −1.25485 | + | 0.724488i | −0.972069 | − | 0.234696i | \(-0.924591\pi\) |
−0.282782 | + | 0.959184i | \(0.591257\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.20355 | − | 12.6494i | −0.166573 | − | 0.956208i | ||||
\(176\) | −12.6385 | − | 13.1636i | −0.952662 | − | 0.992240i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.06497 | + | 3.45927i | −0.229729 | + | 0.259284i | ||||
\(179\) | 1.74852 | − | 3.02853i | 0.130691 | − | 0.226363i | −0.793252 | − | 0.608893i | \(-0.791614\pi\) |
0.923943 | + | 0.382530i | \(0.124947\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.3086 | −1.58386 | −0.791929 | − | 0.610613i | \(-0.790923\pi\) | ||||
−0.791929 | + | 0.610613i | \(0.790923\pi\) | |||||||
\(182\) | 9.05114 | + | 5.58128i | 0.670915 | + | 0.413712i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 17.6373 | + | 1.42660i | 1.30024 | + | 0.105170i | ||||
\(185\) | −1.35556 | + | 2.34790i | −0.0996627 | + | 0.172621i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.2457 | − | 19.4781i | −0.822365 | − | 1.42438i | ||||
\(188\) | 17.4131 | + | 7.42118i | 1.26998 | + | 0.541245i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.907962 | − | 4.44631i | 0.0658705 | − | 0.322569i | ||||
\(191\) | −17.2191 | + | 9.94147i | −1.24593 | + | 0.719340i | −0.970296 | − | 0.241922i | \(-0.922222\pi\) |
−0.275637 | + | 0.961262i | \(0.588889\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.21260 | − | 9.02849i | 0.375211 | − | 0.649885i | −0.615147 | − | 0.788412i | \(-0.710903\pi\) |
0.990359 | + | 0.138527i | \(0.0442368\pi\) | |||||||
\(194\) | 0.468494 | − | 0.156379i | 0.0336359 | − | 0.0112274i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.28627 | + | 12.5093i | 0.449019 | + | 0.893522i | ||||
\(197\) | 16.0387 | 1.14271 | 0.571355 | − | 0.820703i | \(-0.306418\pi\) | ||||
0.571355 | + | 0.820703i | \(0.306418\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00128 | + | 1.15544i | 0.141867 | + | 0.0819069i | 0.569253 | − | 0.822162i | \(-0.307232\pi\) |
−0.427387 | + | 0.904069i | \(0.640566\pi\) | |||||||
\(200\) | −12.4021 | + | 5.88250i | −0.876962 | + | 0.415956i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.34969 | + | 21.3005i | −0.306043 | + | 1.49870i | ||||
\(203\) | 0.594353 | − | 0.496636i | 0.0417154 | − | 0.0348570i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.63432 | + | 0.943576i | −0.114146 | + | 0.0659022i | ||||
\(206\) | −2.51889 | − | 2.23178i | −0.175500 | − | 0.155495i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.16500 | − | 10.9183i | 0.219453 | − | 0.757050i | ||||
\(209\) | −38.1883 | −2.64154 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.7274i | 0.876193i | 0.898928 | + | 0.438096i | \(0.144347\pi\) | ||||
−0.898928 | + | 0.438096i | \(0.855653\pi\) | |||||||
\(212\) | −1.12268 | − | 9.25415i | −0.0771060 | − | 0.635578i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.772960 | + | 0.872400i | −0.0528384 | + | 0.0596360i | ||||
\(215\) | −0.834995 | − | 1.44625i | −0.0569462 | − | 0.0986337i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.8670 | + | 2.58985i | −1.00924 | + | 0.175811i | ||||
\(218\) | 4.61526 | − | 22.6010i | 0.312585 | − | 1.53074i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.10098 | − | 2.79650i | −0.141648 | − | 0.188540i | ||||
\(221\) | 7.00541 | − | 12.1337i | 0.471235 | − | 0.816202i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 11.4933i | − | 0.769649i | −0.922990 | − | 0.384824i | \(-0.874262\pi\) | ||
0.922990 | − | 0.384824i | \(-0.125738\pi\) | |||||||
\(224\) | 11.0918 | − | 10.0485i | 0.741102 | − | 0.671392i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.05553 | + | 1.35370i | −0.269770 | + | 0.0900468i | ||||
\(227\) | 1.51766 | + | 0.876221i | 0.100731 | + | 0.0581568i | 0.549519 | − | 0.835481i | \(-0.314811\pi\) |
−0.448788 | + | 0.893638i | \(0.648144\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.91170 | − | 5.04322i | −0.192411 | − | 0.333265i | 0.753638 | − | 0.657290i | \(-0.228297\pi\) |
−0.946049 | + | 0.324025i | \(0.894964\pi\) | |||||||
\(230\) | 3.32308 | + | 0.678591i | 0.219117 | + | 0.0447450i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.681367 | − | 0.470470i | −0.0447339 | − | 0.0308879i | ||||
\(233\) | 7.44335 | − | 4.29742i | 0.487630 | − | 0.281533i | −0.235961 | − | 0.971763i | \(-0.575824\pi\) |
0.723591 | + | 0.690229i | \(0.242490\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.14205 | + | 1.81406i | 0.204965 | + | 0.118336i | ||||
\(236\) | 13.1252 | − | 1.59231i | 0.854380 | − | 0.103650i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 16.2354 | − | 8.75664i | 1.05239 | − | 0.567609i | ||||
\(239\) | 2.17800i | 0.140883i | 0.997516 | + | 0.0704417i | \(0.0224409\pi\) | ||||
−0.997516 | + | 0.0704417i | \(0.977559\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.08185 | − | 2.93401i | −0.327351 | − | 0.188996i | 0.327314 | − | 0.944916i | \(-0.393857\pi\) |
−0.654664 | + | 0.755920i | \(0.727190\pi\) | |||||||
\(242\) | −9.20330 | + | 10.3873i | −0.591610 | + | 0.667720i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.15524 | − | 2.19708i | −0.330031 | − | 0.140654i | ||||
\(245\) | 0.907384 | + | 2.52538i | 0.0579706 | + | 0.161340i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.8946 | − | 20.6020i | −0.756833 | − | 1.31087i | ||||
\(248\) | 6.91376 | + | 14.5763i | 0.439024 | + | 0.925596i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.06689 | + | 1.69128i | −0.320458 | + | 0.106966i | ||||
\(251\) | 29.5645i | 1.86609i | 0.359755 | + | 0.933047i | \(0.382860\pi\) | ||||
−0.359755 | + | 0.933047i | \(0.617140\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 28.5411i | − | 1.79437i | ||||||
\(254\) | −1.29834 | − | 3.88967i | −0.0814650 | − | 0.244060i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.5195 | − | 8.55708i | −0.844967 | − | 0.534818i | ||||
\(257\) | −10.4608 | − | 18.1187i | −0.652530 | − | 1.13021i | −0.982507 | − | 0.186226i | \(-0.940374\pi\) |
0.329977 | − | 0.943989i | \(-0.392959\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.43587 | + | 17.5696i | −0.399906 | + | 1.09172i | ||||
\(260\) | 0.854273 | − | 2.00447i | 0.0529798 | − | 0.124312i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.8990 | − | 11.4287i | −0.796904 | − | 0.706070i | ||||
\(263\) | 10.3508 | + | 5.97604i | 0.638258 | + | 0.368498i | 0.783943 | − | 0.620833i | \(-0.213205\pi\) |
−0.145685 | + | 0.989331i | \(0.546539\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.78679i | − | 0.109762i | ||||||
\(266\) | 0.907084 | − | 31.3071i | 0.0556169 | − | 1.91956i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 17.9180 | − | 2.17374i | 1.09451 | − | 0.132783i | ||||
\(269\) | 14.0600 | + | 8.11753i | 0.857251 | + | 0.494934i | 0.863091 | − | 0.505049i | \(-0.168525\pi\) |
−0.00583949 | + | 0.999983i | \(0.501859\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.0735 | + | 12.7441i | −1.34087 | + | 0.774151i | −0.986935 | − | 0.161119i | \(-0.948490\pi\) |
−0.353934 | + | 0.935270i | \(0.615156\pi\) | |||||||
\(272\) | −13.6575 | − | 14.2249i | −0.828110 | − | 0.862514i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.19996 | − | 25.4643i | 0.314141 | − | 1.53836i | ||||
\(275\) | 11.0701 | + | 19.1741i | 0.667555 | + | 1.15624i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.51680 | − | 5.49453i | −0.571809 | − | 0.330134i | 0.186062 | − | 0.982538i | \(-0.440427\pi\) |
−0.757872 | + | 0.652404i | \(0.773761\pi\) | |||||||
\(278\) | 2.86717 | + | 8.58970i | 0.171961 | + | 0.515176i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.34250 | − | 1.65598i | 0.139991 | − | 0.0989635i | ||||
\(281\) | 6.71345i | 0.400491i | 0.979746 | + | 0.200245i | \(0.0641740\pi\) | ||||
−0.979746 | + | 0.200245i | \(0.935826\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.07673 | − | 12.2573i | 0.420668 | − | 0.728619i | −0.575337 | − | 0.817917i | \(-0.695129\pi\) |
0.996005 | + | 0.0892979i | \(0.0284623\pi\) | |||||||
\(284\) | −5.25047 | − | 6.98862i | −0.311558 | − | 0.414698i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −17.9651 | − | 3.66858i | −1.06230 | − | 0.216927i | ||||
\(287\) | −9.99460 | + | 8.35140i | −0.589962 | + | 0.492967i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.65242 | − | 6.32618i | −0.214848 | − | 0.372128i | ||||
\(290\) | −0.118790 | − | 0.105250i | −0.00697557 | − | 0.00618047i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −25.2021 | + | 3.05743i | −1.47484 | + | 0.178923i | ||||
\(293\) | − | 7.73971i | − | 0.452159i | −0.974109 | − | 0.226079i | \(-0.927409\pi\) | ||
0.974109 | − | 0.226079i | \(-0.0725909\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.53422 | 0.147548 | ||||||||
\(296\) | 19.9381 | + | 1.61270i | 1.15888 | + | 0.0937363i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 17.2886 | − | 19.5128i | 1.00150 | − | 1.13035i | ||||
\(299\) | 15.3975 | − | 8.88974i | 0.890459 | − | 0.514107i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.39037 | − | 8.84447i | −0.425974 | − | 0.509787i | ||||
\(302\) | 20.4635 | + | 4.17876i | 1.17754 | + | 0.240460i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −32.5115 | + | 8.00619i | −1.86466 | + | 0.459186i | ||||
\(305\) | −0.930220 | − | 0.537063i | −0.0532643 | − | 0.0307521i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.8919 | 1.42066 | 0.710329 | − | 0.703870i | \(-0.248546\pi\) | ||||
0.710329 | + | 0.703870i | \(0.248546\pi\) | |||||||
\(308\) | −17.5974 | − | 16.5257i | −1.00271 | − | 0.941639i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.979066 | + | 2.93317i | 0.0556072 | + | 0.166593i | ||||
\(311\) | 4.24421 | − | 7.35119i | 0.240667 | − | 0.416848i | −0.720237 | − | 0.693728i | \(-0.755967\pi\) |
0.960904 | + | 0.276880i | \(0.0893005\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.06343 | − | 3.50072i | 0.342725 | − | 0.197873i | −0.318751 | − | 0.947838i | \(-0.603263\pi\) |
0.661477 | + | 0.749966i | \(0.269930\pi\) | |||||||
\(314\) | 8.39517 | + | 1.71434i | 0.473767 | + | 0.0967458i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.129596 | + | 0.0552316i | 0.00729034 | + | 0.00310702i | ||||
\(317\) | −12.5953 | − | 21.8157i | −0.707422 | − | 1.22529i | −0.965810 | − | 0.259250i | \(-0.916525\pi\) |
0.258388 | − | 0.966041i | \(-0.416809\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.667775 | + | 1.15662i | −0.0373882 | + | 0.0647583i | ||||
\(320\) | −2.37495 | − | 1.94032i | −0.132764 | − | 0.108467i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 23.3983 | + | 0.677935i | 1.30394 | + | 0.0377798i | ||||
\(323\) | −41.2675 | −2.29618 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.89606 | + | 11.9443i | −0.382525 | + | 0.662552i | ||||
\(326\) | −4.74959 | − | 4.20821i | −0.263056 | − | 0.233071i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.4578 | + | 7.91140i | 0.632652 | + | 0.436834i | ||||
\(329\) | 23.5123 | + | 8.61274i | 1.29628 | + | 0.474836i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.8109 | − | 10.2831i | 0.978974 | − | 0.565211i | 0.0770138 | − | 0.997030i | \(-0.475461\pi\) |
0.901960 | + | 0.431819i | \(0.142128\pi\) | |||||||
\(332\) | 7.78653 | + | 10.3642i | 0.427341 | + | 0.568811i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.13518 | + | 21.3762i | 0.390420 | + | 1.16965i | ||||
\(335\) | 3.45960 | 0.189018 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.77045 | 0.532230 | 0.266115 | − | 0.963941i | \(-0.414260\pi\) | ||||
0.266115 | + | 0.963941i | \(0.414260\pi\) | |||||||
\(338\) | 2.20449 | + | 6.60439i | 0.119908 | + | 0.359232i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.27038 | − | 3.02199i | −0.123129 | − | 0.163890i | ||||
\(341\) | 22.5354 | − | 13.0108i | 1.22036 | − | 0.704576i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.16072 | + | 16.0960i | 0.494632 | + | 0.869102i | ||||
\(344\) | −7.00100 | + | 10.1393i | −0.377469 | + | 0.546675i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.1733 | + | 17.8739i | 1.08452 | + | 0.960906i | ||||
\(347\) | 9.63809 | − | 16.6937i | 0.517400 | − | 0.896163i | −0.482396 | − | 0.875953i | \(-0.660233\pi\) |
0.999796 | − | 0.0202097i | \(-0.00643338\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.5766 | −1.63673 | −0.818363 | − | 0.574702i | \(-0.805118\pi\) | ||||
−0.818363 | + | 0.574702i | \(0.805118\pi\) | |||||||
\(350\) | −15.9820 | + | 8.61996i | −0.854274 | + | 0.460757i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −11.9992 | + | 22.8482i | −0.639562 | + | 1.21781i | ||||
\(353\) | 4.59814 | − | 7.96421i | 0.244734 | − | 0.423892i | −0.717323 | − | 0.696741i | \(-0.754633\pi\) |
0.962057 | + | 0.272849i | \(0.0879659\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.837731 | − | 1.45099i | −0.0444622 | − | 0.0770107i | ||||
\(356\) | 6.01286 | + | 2.56258i | 0.318681 | + | 0.135816i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.84557 | − | 0.989492i | −0.256096 | − | 0.0522963i | ||||
\(359\) | −0.890104 | + | 0.513902i | −0.0469779 | + | 0.0271227i | −0.523305 | − | 0.852145i | \(-0.675301\pi\) |
0.476327 | + | 0.879268i | \(0.341968\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −25.5343 | + | 44.2267i | −1.34391 | + | 2.32772i | ||||
\(362\) | 9.54128 | + | 28.5846i | 0.501479 | + | 1.50237i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.43426 | − | 14.6408i | 0.180004 | − | 0.767387i | ||||
\(365\) | −4.86603 | −0.254700 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.9698 | + | 13.2616i | 1.19902 | + | 0.692252i | 0.960336 | − | 0.278846i | \(-0.0899520\pi\) |
0.238680 | + | 0.971098i | \(0.423285\pi\) | |||||||
\(368\) | −5.98365 | − | 24.2984i | −0.311919 | − | 1.26664i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.75658 | + | 0.767114i | 0.195295 | + | 0.0398804i | ||||
\(371\) | −2.11635 | − | 12.1489i | −0.109876 | − | 0.630739i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.48008 | + | 2.58657i | −0.231970 | + | 0.133928i | −0.611480 | − | 0.791260i | \(-0.709426\pi\) |
0.379511 | + | 0.925187i | \(0.376092\pi\) | |||||||
\(374\) | −21.0936 | + | 23.8072i | −1.09072 | + | 1.23104i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.15818 | − | 26.6819i | 0.111300 | − | 1.37601i | ||||
\(377\) | −0.831971 | −0.0428487 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.2132i | 1.44921i | 0.689163 | + | 0.724606i | \(0.257978\pi\) | ||||
−0.689163 | + | 0.724606i | \(0.742022\pi\) | |||||||
\(380\) | −6.37109 | + | 0.772917i | −0.326830 | + | 0.0396498i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.0462 | + | 18.6473i | 1.07682 | + | 0.954077i | ||||
\(383\) | 1.84904 | + | 3.20262i | 0.0944813 | + | 0.163646i | 0.909392 | − | 0.415940i | \(-0.136547\pi\) |
−0.814911 | + | 0.579587i | \(0.803214\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.96695 | − | 3.55072i | −0.151210 | − | 0.180962i | ||||
\(386\) | −14.4454 | − | 2.94982i | −0.735249 | − | 0.150142i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.419551 | − | 0.558442i | −0.0212995 | − | 0.0283506i | ||||
\(389\) | −3.23187 | + | 5.59776i | −0.163862 | + | 0.283818i | −0.936251 | − | 0.351333i | \(-0.885729\pi\) |
0.772388 | + | 0.635151i | \(0.219062\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 30.8424i | − | 1.55977i | ||||||
\(392\) | 13.9659 | − | 14.0340i | 0.705385 | − | 0.708824i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.18159 | − | 21.5152i | −0.361803 | − | 1.08392i | ||||
\(395\) | 0.0233845 | + | 0.0135010i | 0.00117660 | + | 0.000679311i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.7284 | + | 25.5104i | 0.739198 | + | 1.28033i | 0.952857 | + | 0.303421i | \(0.0981287\pi\) |
−0.213658 | + | 0.976908i | \(0.568538\pi\) | |||||||
\(398\) | 0.653865 | − | 3.20199i | 0.0327753 | − | 0.160501i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.4444 | + | 14.0029i | 0.672219 | + | 0.700145i | ||||
\(401\) | −17.7242 | + | 10.2331i | −0.885105 | + | 0.511016i | −0.872338 | − | 0.488903i | \(-0.837397\pi\) |
−0.0127669 | + | 0.999918i | \(0.504064\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.0383 | + | 8.10500i | 0.699296 | + | 0.403739i | ||||
\(404\) | 30.5214 | − | 3.70274i | 1.51849 | − | 0.184218i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.932347 | − | 0.574921i | −0.0462716 | − | 0.0285329i | ||||
\(407\) | − | 32.2643i | − | 1.59928i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.5317 | + | 6.65785i | 0.570207 | + | 0.329209i | 0.757232 | − | 0.653146i | \(-0.226551\pi\) |
−0.187025 | + | 0.982355i | \(0.559884\pi\) | |||||||
\(410\) | 1.99756 | + | 1.76987i | 0.0986525 | + | 0.0874076i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.86596 | + | 4.37830i | −0.0919291 | + | 0.215703i | ||||
\(413\) | 17.2309 | − | 3.00164i | 0.847876 | − | 0.147701i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.24237 | + | 2.15185i | 0.0609855 | + | 0.105630i | ||||
\(416\) | −16.0636 | + | 0.643155i | −0.787585 | + | 0.0315333i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 17.0994 | + | 51.2280i | 0.836361 | + | 2.50564i | ||||
\(419\) | 35.6073i | 1.73953i | 0.493467 | + | 0.869764i | \(0.335729\pi\) | ||||
−0.493467 | + | 0.869764i | \(0.664271\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 16.1350i | − | 0.786370i | −0.919459 | − | 0.393185i | \(-0.871373\pi\) | ||
0.919459 | − | 0.393185i | \(-0.128627\pi\) | |||||||
\(422\) | 17.0733 | − | 5.69892i | 0.831115 | − | 0.277419i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.9113 | + | 5.64973i | −0.578466 | + | 0.274375i | ||||
\(425\) | 11.9627 | + | 20.7201i | 0.580278 | + | 1.00507i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.96095 | − | 2.54985i | −0.336864 | − | 0.123396i | ||||
\(428\) | 1.51639 | + | 0.646261i | 0.0732976 | + | 0.0312382i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.56620 | + | 1.76769i | −0.0755290 | + | 0.0852457i | ||||
\(431\) | 27.7465 | + | 16.0194i | 1.33650 | + | 0.771629i | 0.986287 | − | 0.165041i | \(-0.0527758\pi\) |
0.350213 | + | 0.936670i | \(0.386109\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 25.4744i | − | 1.22422i | −0.790771 | − | 0.612112i | \(-0.790320\pi\) | ||
0.790771 | − | 0.612112i | \(-0.209680\pi\) | |||||||
\(434\) | 10.1311 | + | 18.7838i | 0.486309 | + | 0.901651i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −32.3849 | + | 3.92881i | −1.55095 | + | 0.188156i | ||||
\(437\) | −45.3518 | − | 26.1839i | −2.16947 | − | 1.25254i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.7443 | − | 10.8220i | 0.894615 | − | 0.516506i | 0.0191655 | − | 0.999816i | \(-0.493899\pi\) |
0.875449 | + | 0.483310i | \(0.160566\pi\) | |||||||
\(440\) | −2.81064 | + | 4.07055i | −0.133992 | + | 0.194056i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −19.4136 | − | 3.96438i | −0.923413 | − | 0.188566i | ||||
\(443\) | 7.35423 | + | 12.7379i | 0.349410 | + | 0.605196i | 0.986145 | − | 0.165887i | \(-0.0530487\pi\) |
−0.636735 | + | 0.771083i | \(0.719715\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.08497 | + | 0.626407i | 0.0514325 | + | 0.0296945i | ||||
\(446\) | −15.4178 | + | 5.14631i | −0.730052 | + | 0.243685i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −18.4461 | − | 10.3798i | −0.871498 | − | 0.490399i | ||||
\(449\) | − | 25.7754i | − | 1.21642i | −0.793778 | − | 0.608208i | \(-0.791889\pi\) | ||
0.793778 | − | 0.608208i | \(-0.208111\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.2293 | − | 19.4497i | 0.528765 | − | 0.915849i | ||||
\(452\) | 3.63186 | + | 4.83418i | 0.170828 | + | 0.227380i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.495855 | − | 2.42822i | 0.0232716 | − | 0.113962i | ||||
\(455\) | 0.991437 | − | 2.70657i | 0.0464793 | − | 0.126886i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.5498 | + | 28.6651i | 0.774168 | + | 1.34090i | 0.935261 | + | 0.353960i | \(0.115165\pi\) |
−0.161092 | + | 0.986939i | \(0.551502\pi\) | |||||||
\(458\) | −5.46149 | + | 6.16411i | −0.255199 | + | 0.288030i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.577662 | − | 4.76161i | −0.0269336 | − | 0.222011i | ||||
\(461\) | − | 8.24676i | − | 0.384090i | −0.981386 | − | 0.192045i | \(-0.938488\pi\) | ||
0.981386 | − | 0.192045i | \(-0.0615120\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.2797 | 0.756582 | 0.378291 | − | 0.925687i | \(-0.376512\pi\) | ||||
0.378291 | + | 0.925687i | \(0.376512\pi\) | |||||||
\(464\) | −0.326023 | + | 1.12468i | −0.0151352 | + | 0.0522122i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.09768 | − | 8.06068i | −0.421442 | − | 0.373404i | ||||
\(467\) | −24.2507 | + | 14.0011i | −1.12219 | + | 0.647895i | −0.941959 | − | 0.335729i | \(-0.891017\pi\) |
−0.180229 | + | 0.983625i | \(0.557684\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.5228 | − | 4.09770i | 1.08618 | − | 0.189214i | ||||
\(470\) | 1.02658 | − | 5.02720i | 0.0473527 | − | 0.231887i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.01305 | − | 16.8940i | −0.368830 | − | 0.777607i | ||||
\(473\) | 17.2115 | + | 9.93707i | 0.791386 | + | 0.456907i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 40.6233 | 1.86393 | ||||||||
\(476\) | −19.0163 | − | 17.8582i | −0.871612 | − | 0.818528i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.92170 | − | 0.975237i | 0.133635 | − | 0.0446063i | ||||
\(479\) | 5.42512 | − | 9.39658i | 0.247880 | − | 0.429341i | −0.715057 | − | 0.699066i | \(-0.753600\pi\) |
0.962937 | + | 0.269725i | \(0.0869328\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.4061 | − | 10.0494i | 0.793650 | − | 0.458214i | ||||
\(482\) | −1.66036 | + | 8.13083i | −0.0756274 | + | 0.370349i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.0550 | + | 7.69475i | 0.820683 | + | 0.349761i | ||||
\(485\) | −0.0669409 | − | 0.115945i | −0.00303963 | − | 0.00526480i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.75857 | + | 9.97414i | −0.260946 | + | 0.451971i | −0.966494 | − | 0.256691i | \(-0.917368\pi\) |
0.705548 | + | 0.708662i | \(0.250701\pi\) | |||||||
\(488\) | −0.638940 | + | 7.89931i | −0.0289235 | + | 0.357585i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.98139 | − | 2.34799i | 0.134685 | − | 0.106072i | ||||
\(491\) | −5.61613 | −0.253452 | −0.126726 | − | 0.991938i | \(-0.540447\pi\) | ||||
−0.126726 | + | 0.991938i | \(0.540447\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.721619 | + | 1.24988i | −0.0325001 | + | 0.0562918i | ||||
\(494\) | −22.3107 | + | 25.1809i | −1.00381 | + | 1.13294i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.4577 | − | 15.8013i | 0.738974 | − | 0.709498i | ||||
\(497\) | −7.41459 | − | 8.87346i | −0.332590 | − | 0.398029i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.5584 | + | 7.25061i | −0.562193 | + | 0.324582i | −0.754025 | − | 0.656846i | \(-0.771890\pi\) |
0.191832 | + | 0.981428i | \(0.438557\pi\) | |||||||
\(500\) | 4.53757 | + | 6.03971i | 0.202926 | + | 0.270104i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 39.6595 | − | 13.2380i | 1.77009 | − | 0.590840i | ||||
\(503\) | −10.8393 | −0.483301 | −0.241651 | − | 0.970363i | \(-0.577689\pi\) | ||||
−0.241651 | + | 0.970363i | \(0.577689\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.89306 | 0.262238 | ||||||||
\(506\) | −38.2867 | + | 12.7798i | −1.70205 | + | 0.568130i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.63648 | + | 3.48333i | −0.205710 | + | 0.154548i | ||||
\(509\) | −21.6861 | + | 12.5205i | −0.961218 | + | 0.554959i | −0.896548 | − | 0.442947i | \(-0.853933\pi\) |
−0.0646702 | + | 0.997907i | \(0.520600\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −33.0855 | + | 5.76353i | −1.46362 | + | 0.254964i | ||||
\(512\) | −5.42539 | + | 21.9674i | −0.239770 | + | 0.970830i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.6215 | + | 22.1457i | −0.865465 | + | 0.976806i | ||||
\(515\) | −0.456122 | + | 0.790027i | −0.0200992 | + | 0.0348127i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −43.1774 | −1.89894 | ||||||||
\(518\) | 26.4506 | + | 0.766372i | 1.16217 | + | 0.0336724i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.07143 | − | 0.248434i | −0.134691 | − | 0.0108946i | ||||
\(521\) | 16.8507 | − | 29.1862i | 0.738240 | − | 1.27867i | −0.215047 | − | 0.976604i | \(-0.568990\pi\) |
0.953287 | − | 0.302066i | \(-0.0976764\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.74207 | + | 16.8738i | 0.425991 | + | 0.737838i | 0.996512 | − | 0.0834448i | \(-0.0265922\pi\) |
−0.570522 | + | 0.821283i | \(0.693259\pi\) | |||||||
\(524\) | −9.55540 | + | 22.4209i | −0.417430 | + | 0.979461i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.38186 | − | 16.5610i | 0.147456 | − | 0.722095i | ||||
\(527\) | 24.3525 | − | 14.0599i | 1.06081 | − | 0.612459i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.06926 | − | 13.9764i | 0.350837 | − | 0.607668i | ||||
\(530\) | −2.39690 | + | 0.800065i | −0.104115 | + | 0.0347526i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −42.4033 | + | 12.8015i | −1.83842 | + | 0.555014i | ||||
\(533\) | 13.9904 | 0.605990 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.273620 | + | 0.157975i | 0.0118296 | + | 0.00682984i | ||||
\(536\) | −10.9391 | − | 23.0629i | −0.472495 | − | 0.996164i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.59373 | − | 22.4956i | 0.198050 | − | 0.969854i | ||||
\(539\) | −24.3788 | − | 20.6282i | −1.05007 | − | 0.888518i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.3111 | + | 19.2322i | −1.43216 | + | 0.826856i | −0.997285 | − | 0.0736362i | \(-0.976540\pi\) |
−0.434872 | + | 0.900492i | \(0.643206\pi\) | |||||||
\(542\) | 26.9795 | + | 23.9042i | 1.15887 | + | 1.02677i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −12.9667 | + | 24.6905i | −0.555945 | + | 1.05859i | ||||
\(545\) | −6.25287 | −0.267844 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.2961i | 0.482985i | 0.970403 | + | 0.241493i | \(0.0776370\pi\) | ||||
−0.970403 | + | 0.241493i | \(0.922363\pi\) | |||||||
\(548\) | −36.4876 | + | 4.42655i | −1.55867 | + | 0.189093i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 20.7643 | − | 23.4356i | 0.885393 | − | 0.999298i | ||||
\(551\) | 1.22524 | + | 2.12219i | 0.0521972 | + | 0.0904082i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.174989 | + | 0.0640997i | 0.00744128 | + | 0.00272580i | ||||
\(554\) | −3.10937 | + | 15.2266i | −0.132104 | + | 0.646918i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.2389 | − | 7.69236i | 0.434226 | − | 0.326229i | ||||
\(557\) | 10.9385 | − | 18.9460i | 0.463477 | − | 0.802766i | −0.535654 | − | 0.844438i | \(-0.679935\pi\) |
0.999131 | + | 0.0416711i | \(0.0132682\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.3804i | 0.523637i | ||||||||
\(560\) | −3.27031 | − | 2.40087i | −0.138196 | − | 0.101455i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.00580 | − | 3.00606i | 0.379887 | − | 0.126803i | ||||
\(563\) | 12.5783 | + | 7.26211i | 0.530114 | + | 0.306061i | 0.741063 | − | 0.671436i | \(-0.234322\pi\) |
−0.210949 | + | 0.977497i | \(0.567655\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.579476 | + | 1.00368i | 0.0243788 | + | 0.0422252i | ||||
\(566\) | −19.6113 | − | 4.00474i | −0.824325 | − | 0.168332i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.02395 | + | 10.1725i | −0.294718 | + | 0.426830i | ||||
\(569\) | 8.24719 | − | 4.76152i | 0.345740 | − | 0.199613i | −0.317067 | − | 0.948403i | \(-0.602698\pi\) |
0.662807 | + | 0.748790i | \(0.269365\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.63806 | + | 3.83248i | 0.277794 | + | 0.160384i | 0.632424 | − | 0.774622i | \(-0.282060\pi\) |
−0.354630 | + | 0.935007i | \(0.615393\pi\) | |||||||
\(572\) | 3.12293 | + | 25.7421i | 0.130576 | + | 1.07633i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 15.6783 | + | 9.66784i | 0.654399 | + | 0.403528i | ||||
\(575\) | 30.3610i | 1.26614i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.5704 | + | 15.3405i | 1.10614 | + | 0.638631i | 0.937827 | − | 0.347102i | \(-0.112834\pi\) |
0.168315 | + | 0.985733i | \(0.446168\pi\) | |||||||
\(578\) | −6.85086 | + | 7.73221i | −0.284958 | + | 0.321618i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.0879977 | + | 0.206478i | −0.00365390 | + | 0.00857355i | ||||
\(581\) | 10.9960 | + | 13.1595i | 0.456189 | + | 0.545947i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.6321 | + | 18.4153i | 0.440336 | + | 0.762684i | ||||
\(584\) | 15.3861 | + | 32.4386i | 0.636681 | + | 1.34232i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.3825 | + | 3.46558i | −0.428897 | + | 0.143162i | ||||
\(587\) | 12.2533i | 0.505748i | 0.967499 | + | 0.252874i | \(0.0813758\pi\) | ||||
−0.967499 | + | 0.252874i | \(0.918624\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 47.7450i | − | 1.96730i | ||||||
\(590\) | −1.13474 | − | 3.39955i | −0.0467165 | − | 0.139957i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.76422 | − | 27.4681i | −0.278008 | − | 1.12893i | ||||
\(593\) | −5.04004 | − | 8.72961i | −0.206970 | − | 0.358482i | 0.743789 | − | 0.668415i | \(-0.233027\pi\) |
−0.950759 | + | 0.309933i | \(0.899694\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.20618 | − | 3.83702i | −0.131441 | − | 0.157302i | ||||
\(596\) | −33.9168 | − | 14.4548i | −1.38929 | − | 0.592091i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −18.8197 | − | 16.6745i | −0.769594 | − | 0.681872i | ||||
\(599\) | −8.63004 | − | 4.98256i | −0.352614 | − | 0.203582i | 0.313222 | − | 0.949680i | \(-0.398592\pi\) |
−0.665836 | + | 0.746098i | \(0.731925\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.9998i | 1.50925i | 0.656154 | + | 0.754627i | \(0.272182\pi\) | ||||
−0.656154 | + | 0.754627i | \(0.727818\pi\) | |||||||
\(602\) | −8.55532 | + | 13.8741i | −0.348689 | + | 0.565467i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.55723 | − | 29.3220i | −0.144742 | − | 1.19309i | ||||
\(605\) | 3.25788 | + | 1.88094i | 0.132451 | + | 0.0764709i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.8906 | − | 16.6800i | 1.17263 | − | 0.677021i | 0.218335 | − | 0.975874i | \(-0.429937\pi\) |
0.954299 | + | 0.298853i | \(0.0966041\pi\) | |||||||
\(608\) | 25.2975 | + | 40.0279i | 1.02595 | + | 1.62334i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.303925 | + | 1.48833i | −0.0123056 | + | 0.0602607i | ||||
\(611\) | −13.4485 | − | 23.2935i | −0.544069 | − | 0.942355i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.37477 | + | 3.68047i | 0.257474 | + | 0.148653i | 0.623182 | − | 0.782077i | \(-0.285840\pi\) |
−0.365708 | + | 0.930730i | \(0.619173\pi\) | |||||||
\(614\) | −11.1458 | − | 33.3915i | −0.449807 | − | 1.34757i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.2890 | + | 31.0058i | −0.575719 | + | 1.24926i | ||||
\(617\) | − | 16.0597i | − | 0.646540i | −0.946307 | − | 0.323270i | \(-0.895218\pi\) | ||
0.946307 | − | 0.323270i | \(-0.104782\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.283019 | + | 0.490203i | −0.0113755 | + | 0.0197029i | −0.871657 | − | 0.490116i | \(-0.836954\pi\) |
0.860282 | + | 0.509819i | \(0.170288\pi\) | |||||||
\(620\) | 3.49633 | − | 2.62675i | 0.140416 | − | 0.105493i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.7617 | − | 2.40181i | −0.471602 | − | 0.0963038i | ||||
\(623\) | 8.11895 | + | 2.97403i | 0.325279 | + | 0.119152i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.4086 | − | 19.7603i | −0.456345 | − | 0.790413i | ||||
\(626\) | −7.41107 | − | 6.56632i | −0.296206 | − | 0.262443i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.45936 | − | 12.0294i | −0.0582348 | − | 0.480024i | ||||
\(629\) | − | 34.8658i | − | 1.39019i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.2928 | 1.28556 | 0.642779 | − | 0.766052i | \(-0.277781\pi\) | ||||
0.642779 | + | 0.766052i | \(0.277781\pi\) | |||||||
\(632\) | 0.0160621 | − | 0.198578i | 0.000638915 | − | 0.00789901i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −23.6251 | + | 26.6644i | −0.938271 | + | 1.05898i | ||||
\(635\) | −0.962636 | + | 0.555778i | −0.0382010 | + | 0.0220554i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.53528 | − | 19.5770i | 0.140073 | − | 0.775670i | ||||
\(638\) | 1.85056 | + | 0.377896i | 0.0732645 | + | 0.0149610i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.53944 | + | 4.05470i | −0.0608515 | + | 0.160276i | ||||
\(641\) | −7.35118 | − | 4.24421i | −0.290354 | − | 0.167636i | 0.347747 | − | 0.937588i | \(-0.386947\pi\) |
−0.638102 | + | 0.769952i | \(0.720280\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.1690 | 1.15031 | 0.575156 | − | 0.818044i | \(-0.304942\pi\) | ||||
0.575156 | + | 0.818044i | \(0.304942\pi\) | |||||||
\(644\) | −9.56754 | − | 31.6913i | −0.377014 | − | 1.24881i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 18.4782 | + | 55.3585i | 0.727015 | + | 2.17805i | ||||
\(647\) | 4.70856 | − | 8.15546i | 0.185113 | − | 0.320624i | −0.758502 | − | 0.651671i | \(-0.774068\pi\) |
0.943614 | + | 0.331046i | \(0.107402\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.1186 | + | 15.0796i | −1.02524 | + | 0.591925i | ||||
\(650\) | 19.1106 | + | 3.90250i | 0.749580 | + | 0.153069i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.51843 | + | 8.25567i | −0.137792 | + | 0.323317i | ||||
\(653\) | −6.88850 | − | 11.9312i | −0.269568 | − | 0.466905i | 0.699182 | − | 0.714943i | \(-0.253548\pi\) |
−0.968750 | + | 0.248038i | \(0.920214\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.33576 | + | 4.04566i | −0.0912658 | + | 0.158077i | ||||
\(656\) | 5.48237 | − | 18.9126i | 0.214051 | − | 0.738414i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.02559 | − | 35.3972i | 0.0399816 | − | 1.37993i | ||||
\(659\) | 3.86377 | 0.150511 | 0.0752555 | − | 0.997164i | \(-0.476023\pi\) | ||||
0.0752555 | + | 0.997164i | \(0.476023\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.46098 | − | 2.53049i | 0.0568255 | − | 0.0984247i | −0.836213 | − | 0.548404i | \(-0.815235\pi\) |
0.893039 | + | 0.449980i | \(0.148569\pi\) | |||||||
\(662\) | −21.7695 | − | 19.2881i | −0.846094 | − | 0.749652i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.4166 | − | 15.0860i | 0.404243 | − | 0.585452i | ||||
\(665\) | −8.36399 | + | 1.45702i | −0.324342 | + | 0.0565008i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.58608 | + | 0.915722i | −0.0614131 | + | 0.0354569i | ||||
\(668\) | 25.4803 | − | 19.1431i | 0.985863 | − | 0.740668i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.54909 | − | 4.64091i | −0.0598467 | − | 0.179294i | ||||
\(671\) | 12.7829 | 0.493479 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.7127 | −1.49227 | −0.746133 | − | 0.665797i | \(-0.768092\pi\) | ||||
−0.746133 | + | 0.665797i | \(0.768092\pi\) | |||||||
\(674\) | −4.37488 | − | 13.1066i | −0.168514 | − | 0.504848i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.87241 | − | 5.91445i | 0.302785 | − | 0.227479i | ||||
\(677\) | −39.7095 | + | 22.9263i | −1.52616 | + | 0.881130i | −0.526644 | + | 0.850086i | \(0.676550\pi\) |
−0.999518 | + | 0.0310437i | \(0.990117\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.592480 | − | 0.709055i | −0.0227373 | − | 0.0272110i | ||||
\(680\) | −3.03726 | + | 4.39876i | −0.116474 | + | 0.168685i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −27.5441 | − | 24.4045i | −1.05472 | − | 0.934496i | ||||
\(683\) | −19.9744 | + | 34.5968i | −0.764301 | + | 1.32381i | 0.176315 | + | 0.984334i | \(0.443582\pi\) |
−0.940615 | + | 0.339474i | \(0.889751\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.04503 | −0.269177 | ||||||||
\(686\) | 17.4902 | − | 19.4960i | 0.667780 | − | 0.744359i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 16.7363 | + | 4.85149i | 0.638064 | + | 0.184961i | ||||
\(689\) | −6.62318 | + | 11.4717i | −0.252323 | + | 0.437036i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.9816 | − | 24.2169i | −0.531886 | − | 0.921253i | −0.999307 | − | 0.0372183i | \(-0.988150\pi\) |
0.467422 | − | 0.884035i | \(-0.345183\pi\) | |||||||
\(692\) | 14.9441 | − | 35.0650i | 0.568089 | − | 1.33297i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −26.7094 | − | 5.45422i | −1.01388 | − | 0.207039i | ||||
\(695\) | 2.12582 | − | 1.22734i | 0.0806370 | − | 0.0465558i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.1347 | − | 21.0179i | 0.459634 | − | 0.796110i | ||||
\(698\) | 13.6912 | + | 41.0171i | 0.518218 | + | 1.55252i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 18.7195 | + | 17.5794i | 0.707531 | + | 0.664440i | ||||
\(701\) | 47.3436 | 1.78814 | 0.894072 | − | 0.447923i | \(-0.147836\pi\) | ||||
0.894072 | + | 0.447923i | \(0.147836\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −51.2680 | − | 29.5996i | −1.93361 | − | 1.11637i | ||||
\(704\) | 36.0227 | + | 5.86581i | 1.35766 | + | 0.221076i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.7425 | − | 2.60210i | −0.479572 | − | 0.0979313i | ||||
\(707\) | 40.0686 | − | 6.98000i | 1.50693 | − | 0.262510i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.16943 | − | 4.71662i | 0.306810 | − | 0.177137i | −0.338688 | − | 0.940899i | \(-0.609983\pi\) |
0.645498 | + | 0.763762i | \(0.276650\pi\) | |||||||
\(710\) | −1.57134 | + | 1.77349i | −0.0589712 | + | 0.0665577i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.745232 | − | 9.21342i | 0.0279288 | − | 0.345287i | ||||
\(713\) | 35.6836 | 1.33636 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.97028i | 0.185878i | ||||||||
\(716\) | 0.842321 | + | 6.94318i | 0.0314790 | + | 0.259479i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.08794 | + | 0.963928i | 0.0406014 | + | 0.0359735i | ||||
\(719\) | −22.0452 | − | 38.1835i | −0.822148 | − | 1.42400i | −0.904079 | − | 0.427364i | \(-0.859442\pi\) |
0.0819312 | − | 0.996638i | \(-0.473891\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.16556 | + | 5.91186i | −0.0806497 | + | 0.220169i | ||||
\(722\) | 70.7615 | + | 14.4499i | 2.63347 | + | 0.537770i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 34.0727 | − | 25.5984i | 1.26630 | − | 0.951358i | ||||
\(725\) | 0.710355 | − | 1.23037i | 0.0263819 | − | 0.0456948i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.998475i | 0.0370314i | 0.999829 | + | 0.0185157i | \(0.00589406\pi\) | ||||
−0.999829 | + | 0.0185157i | \(0.994106\pi\) | |||||||
\(728\) | −21.1778 | + | 1.94876i | −0.784900 | + | 0.0722259i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.17884 | + | 6.52757i | 0.0806426 | + | 0.241596i | ||||
\(731\) | 18.5993 | + | 10.7383i | 0.687919 | + | 0.397170i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.6087 | + | 37.4274i | 0.798136 | + | 1.38241i | 0.920829 | + | 0.389967i | \(0.127514\pi\) |
−0.122693 | + | 0.992445i | \(0.539153\pi\) | |||||||
\(734\) | 7.50479 | − | 36.7511i | 0.277007 | − | 1.35651i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29.9160 | + | 18.9068i | −1.10272 | + | 0.696914i | ||||
\(737\) | −35.6559 | + | 20.5859i | −1.31340 | + | 0.758293i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.3992 | − | 11.7775i | −0.750398 | − | 0.433243i | 0.0754395 | − | 0.997150i | \(-0.475964\pi\) |
−0.825838 | + | 0.563908i | \(0.809297\pi\) | |||||||
\(740\) | −0.653018 | − | 5.38277i | −0.0240054 | − | 0.197875i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.3496 | + | 8.27886i | −0.563501 | + | 0.303927i | ||||
\(743\) | 0.745461i | 0.0273483i | 0.999907 | + | 0.0136742i | \(0.00435275\pi\) | ||||
−0.999907 | + | 0.0136742i | \(0.995647\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.12000 | − | 3.53339i | −0.224220 | − | 0.129453i | ||||
\(746\) | 5.47580 | + | 4.85165i | 0.200483 | + | 0.177631i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 41.3813 | + | 17.6360i | 1.51305 | + | 0.644837i | ||||
\(749\) | 2.04753 | + | 0.750026i | 0.0748151 | + | 0.0274053i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.2168 | + | 17.6961i | 0.372817 | + | 0.645738i | 0.989998 | − | 0.141083i | \(-0.0450585\pi\) |
−0.617180 | + | 0.786822i | \(0.711725\pi\) | |||||||
\(752\) | −36.7589 | + | 9.05215i | −1.34046 | + | 0.330098i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.372529 | + | 1.11605i | 0.0135667 | + | 0.0406443i | ||||
\(755\) | − | 5.66148i | − | 0.206042i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 12.6416i | − | 0.459465i | −0.973254 | − | 0.229733i | \(-0.926215\pi\) | ||
0.973254 | − | 0.229733i | \(-0.0737852\pi\) | |||||||
\(758\) | 37.8467 | − | 12.6329i | 1.37465 | − | 0.458848i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.88959 | + | 8.20045i | 0.141090 | + | 0.297462i | ||||
\(761\) | 20.0783 | + | 34.7767i | 0.727839 | + | 1.26065i | 0.957795 | + | 0.287452i | \(0.0928083\pi\) |
−0.229956 | + | 0.973201i | \(0.573858\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −42.5150 | + | 7.40617i | −1.53915 | + | 0.268121i | ||||
\(764\) | 15.5907 | − | 36.5822i | 0.564052 | − | 1.32350i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.46824 | − | 3.91443i | 0.125313 | − | 0.141434i | ||||
\(767\) | −16.2704 | − | 9.39370i | −0.587489 | − | 0.339187i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 9.78731i | − | 0.352939i | −0.984306 | − | 0.176470i | \(-0.943532\pi\) | ||
0.984306 | − | 0.176470i | \(-0.0564678\pi\) | |||||||
\(770\) | −3.43464 | + | 5.56993i | −0.123776 | + | 0.200726i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.51109 | + | 20.6987i | 0.0903759 | + | 0.744961i | ||||
\(773\) | 36.3366 | + | 20.9789i | 1.30694 | + | 0.754560i | 0.981584 | − | 0.191033i | \(-0.0611839\pi\) |
0.325352 | + | 0.945593i | \(0.394517\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −23.9724 | + | 13.8404i | −0.861113 | + | 0.497164i | ||||
\(776\) | −0.561265 | + | 0.812862i | −0.0201482 | + | 0.0291800i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.95628 | + | 1.82892i | 0.321098 | + | 0.0655701i | ||||
\(779\) | −20.6036 | − | 35.6865i | −0.738202 | − | 1.27860i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.2679 | + | 9.96963i | 0.617894 | + | 0.356741i | ||||
\(782\) | −41.3738 | + | 13.8102i | −1.47952 | + | 0.493852i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −25.0795 | − | 12.4507i | −0.895695 | − | 0.444668i | ||||
\(785\) | − | 2.32263i | − | 0.0828983i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.7140 | − | 27.2175i | 0.560145 | − | 0.970200i | −0.437338 | − | 0.899297i | \(-0.644079\pi\) |
0.997483 | − | 0.0709026i | \(-0.0225879\pi\) | |||||||
\(788\) | −25.6460 | + | 19.2676i | −0.913603 | + | 0.686379i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.00764026 | − | 0.0374146i | 0.000271828 | − | 0.00133115i | ||||
\(791\) | 5.12883 | + | 6.13796i | 0.182360 | + | 0.218241i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.98151 | + | 6.89617i | 0.141387 | + | 0.244890i | ||||
\(794\) | 27.6262 | − | 31.1802i | 0.980416 | − | 1.10654i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.58811 | + | 0.556613i | −0.162621 | + | 0.0197286i | ||||
\(797\) | 1.25772i | 0.0445507i | 0.999752 | + | 0.0222754i | \(0.00709105\pi\) | ||||
−0.999752 | + | 0.0222754i | \(0.992909\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −46.6588 | −1.65067 | ||||||||
\(800\) | 12.7644 | − | 24.3051i | 0.451288 | − | 0.859314i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21.6635 | + | 19.1942i | 0.764966 | + | 0.677772i | ||||
\(803\) | 50.1510 | − | 28.9547i | 1.76979 | − | 1.02179i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.08894 | − | 6.25107i | −0.0383802 | − | 0.220321i | ||||
\(806\) | 4.58664 | − | 22.4609i | 0.161557 | − | 0.791151i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −18.6335 | − | 39.2851i | −0.655524 | − | 1.38204i | ||||
\(809\) | 24.5857 | + | 14.1945i | 0.864386 | + | 0.499053i | 0.865479 | − | 0.500946i | \(-0.167014\pi\) |
−0.00109260 | + | 0.999999i | \(0.500348\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.97465 | −0.174684 | −0.0873418 | − | 0.996178i | \(-0.527837\pi\) | ||||
−0.0873418 | + | 0.996178i | \(0.527837\pi\) | |||||||
\(812\) | −0.353759 | + | 1.50813i | −0.0124145 | + | 0.0529251i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −43.2812 | + | 14.4469i | −1.51701 | + | 0.506363i | ||||
\(815\) | −0.860059 | + | 1.48967i | −0.0301265 | + | 0.0521807i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.5799 | − | 18.2327i | 1.10484 | − | 0.637881i | ||||
\(818\) | 3.76769 | − | 18.4505i | 0.131734 | − | 0.645106i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.47976 | − | 3.47213i | 0.0516756 | − | 0.121252i | ||||
\(821\) | −5.02868 | − | 8.70993i | −0.175502 | − | 0.303979i | 0.764833 | − | 0.644229i | \(-0.222822\pi\) |
−0.940335 | + | 0.340250i | \(0.889488\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.27031 | − | 3.93230i | 0.0791382 | − | 0.137071i | −0.823740 | − | 0.566967i | \(-0.808117\pi\) |
0.902878 | + | 0.429896i | \(0.141450\pi\) | |||||||
\(824\) | 6.70881 | + | 0.542646i | 0.233713 | + | 0.0189040i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.7420 | − | 21.7704i | −0.408555 | − | 0.757490i | ||||
\(827\) | −19.2538 | −0.669520 | −0.334760 | − | 0.942303i | \(-0.608655\pi\) | ||||
−0.334760 | + | 0.942303i | \(0.608655\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.0503 | − | 29.5321i | 0.592183 | − | 1.02569i | −0.401755 | − | 0.915747i | \(-0.631600\pi\) |
0.993938 | − | 0.109943i | \(-0.0350670\pi\) | |||||||
\(830\) | 2.33032 | − | 2.63011i | 0.0808865 | − | 0.0912924i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.05553 | + | 21.2607i | 0.279275 | + | 0.737082i | ||||
\(833\) | −26.3444 | − | 22.2914i | −0.912781 | − | 0.772352i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.29028 | − | 3.05435i | 0.183078 | − | 0.105700i | ||||
\(836\) | 61.0635 | − | 45.8763i | 2.11193 | − | 1.58667i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 47.7656 | − | 15.9437i | 1.65003 | − | 0.550767i | ||||
\(839\) | −12.0599 | −0.416355 | −0.208178 | − | 0.978091i | \(-0.566753\pi\) | ||||
−0.208178 | + | 0.978091i | \(0.566753\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9143 | −0.997045 | ||||||||
\(842\) | −21.6443 | + | 7.22469i | −0.745913 | + | 0.248979i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −15.2897 | − | 20.3513i | −0.526293 | − | 0.700521i | ||||
\(845\) | 1.63449 | − | 0.943672i | 0.0562281 | − | 0.0324633i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.3791 | + | 8.93023i | 0.837674 | + | 0.306846i | ||||
\(848\) | 12.9124 | + | 13.4488i | 0.443412 | + | 0.461833i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 22.4386 | − | 25.3252i | 0.769636 | − | 0.868649i | ||||
\(851\) | 22.1221 | − | 38.3166i | 0.758335 | − | 1.31348i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.7232 | 0.983464 | 0.491732 | − | 0.870747i | \(-0.336364\pi\) | ||||
0.491732 | + | 0.870747i | \(0.336364\pi\) | |||||||
\(854\) | −0.303631 | + | 10.4795i | −0.0103900 | + | 0.358603i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.187941 | − | 2.32355i | 0.00642370 | − | 0.0794172i | ||||
\(857\) | 7.96109 | − | 13.7890i | 0.271946 | − | 0.471024i | −0.697414 | − | 0.716668i | \(-0.745666\pi\) |
0.969360 | + | 0.245644i | \(0.0789996\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.1568 | − | 31.4484i | −0.619501 | − | 1.07301i | −0.989577 | − | 0.144006i | \(-0.954002\pi\) |
0.370076 | − | 0.929002i | \(-0.379332\pi\) | |||||||
\(860\) | 3.07258 | + | 1.30948i | 0.104774 | + | 0.0446529i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.06543 | − | 44.3936i | 0.308770 | − | 1.51205i | ||||
\(863\) | −26.8218 | + | 15.4856i | −0.913025 | + | 0.527135i | −0.881403 | − | 0.472365i | \(-0.843401\pi\) |
−0.0316219 | + | 0.999500i | \(0.510067\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.65300 | − | 6.32717i | 0.124206 | − | 0.215130i | ||||
\(866\) | −34.1729 | + | 11.4066i | −1.16124 | + | 0.387612i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 20.6613 | − | 22.0012i | 0.701289 | − | 0.746769i | ||||
\(869\) | −0.321345 | −0.0109009 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.2116 | − | 12.8239i | −0.752610 | − | 0.434520i | ||||
\(872\) | 19.7712 | + | 41.6837i | 0.669537 | + | 1.41159i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −14.8175 | + | 72.5617i | −0.501210 | + | 2.45444i | ||||
\(875\) | 6.40784 | + | 7.66863i | 0.216625 | + | 0.259247i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.7909 | + | 18.9318i | −1.10727 | + | 0.639282i | −0.938121 | − | 0.346309i | \(-0.887435\pi\) |
−0.169148 | + | 0.985591i | \(0.554102\pi\) | |||||||
\(878\) | −22.9103 | − | 20.2989i | −0.773185 | − | 0.685054i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.71898 | + | 1.94769i | 0.226497 | + | 0.0656567i | ||||
\(881\) | −23.9503 | −0.806906 | −0.403453 | − | 0.915000i | \(-0.632190\pi\) | ||||
−0.403453 | + | 0.915000i | \(0.632190\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.2002i | 0.343263i | 0.985161 | + | 0.171631i | \(0.0549038\pi\) | ||||
−0.985161 | + | 0.171631i | \(0.945096\pi\) | |||||||
\(884\) | 3.37474 | + | 27.8177i | 0.113505 | + | 0.935609i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.7944 | − | 15.5690i | 0.463430 | − | 0.523050i | ||||
\(887\) | 13.8743 | + | 24.0310i | 0.465854 | + | 0.806883i | 0.999240 | − | 0.0389894i | \(-0.0124139\pi\) |
−0.533386 | + | 0.845872i | \(0.679081\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.88694 | + | 4.91908i | −0.197442 | + | 0.164981i | ||||
\(890\) | 0.354485 | − | 1.73592i | 0.0118824 | − | 0.0581882i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.8071 | + | 18.3779i | 0.462296 | + | 0.615338i | ||||
\(893\) | −39.6113 | + | 68.6088i | −1.32554 | + | 2.29591i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.34059i | 0.0448109i | ||||||||
\(896\) | −5.66448 | + | 29.3924i | −0.189237 | + | 0.981931i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −34.5766 | + | 11.5414i | −1.15383 | + | 0.385140i | ||||
\(899\) | −1.44607 | − | 0.834886i | −0.0482290 | − | 0.0278450i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.4894 | + | 19.9002i | 0.382766 | + | 0.662970i | ||||
\(902\) | −31.1190 | − | 6.35467i | −1.03615 | − | 0.211587i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.85861 | − | 7.03656i | 0.161595 | − | 0.234033i | ||||
\(905\) | 7.07426 | − | 4.08432i | 0.235156 | − | 0.135767i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.5836 | − | 12.4613i | −0.716673 | − | 0.413771i | 0.0968542 | − | 0.995299i | \(-0.469122\pi\) |
−0.813527 | + | 0.581527i | \(0.802455\pi\) | |||||||
\(908\) | −3.47937 | + | 0.422105i | −0.115467 | + | 0.0140080i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.07468 | − | 0.118059i | −0.135074 | − | 0.00391360i | ||||
\(911\) | 27.2411i | 0.902538i | 0.892388 | + | 0.451269i | \(0.149029\pi\) | ||||
−0.892388 | + | 0.451269i | \(0.850971\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.6086 | − | 14.7851i | −0.847521 | − | 0.489316i | ||||
\(914\) | 31.0426 | − | 35.0362i | 1.02680 | − | 1.15889i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.7144 | + | 4.56628i | 0.354012 | + | 0.150874i | ||||
\(917\) | −11.0896 | + | 30.2741i | −0.366212 | + | 0.999740i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.106387 | + | 0.184268i | 0.00350938 | + | 0.00607843i | 0.867775 | − | 0.496958i | \(-0.165550\pi\) |
−0.864265 | + | 0.503036i | \(0.832216\pi\) | |||||||
\(920\) | −6.12884 | + | 2.90700i | −0.202062 | + | 0.0958409i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11.0627 | + | 3.69262i | −0.364330 | + | 0.121610i | ||||
\(923\) | 12.4210i | 0.408843i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.3216i | 1.12849i | ||||||||
\(926\) | −7.28951 | − | 21.8385i | −0.239548 | − | 0.717658i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.65470 | − | 0.0662507i | 0.0543181 | − | 0.00217478i | ||||
\(929\) | −8.81604 | − | 15.2698i | −0.289245 | − | 0.500987i | 0.684385 | − | 0.729121i | \(-0.260071\pi\) |
−0.973630 | + | 0.228134i | \(0.926738\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −55.1434 | + | 19.8133i | −1.80725 | + | 0.649356i | ||||
\(932\) | −6.73942 | + | 15.8134i | −0.220757 | + | 0.517987i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 29.6406 | + | 26.2620i | 0.969869 | + | 0.859319i | ||||
\(935\) | 7.46691 | + | 4.31102i | 0.244194 | + | 0.140985i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 5.18135i | − | 0.169267i | −0.996412 | − | 0.0846337i | \(-0.973028\pi\) | ||
0.996412 | − | 0.0846337i | \(-0.0269720\pi\) | |||||||
\(938\) | −16.0296 | − | 29.7200i | −0.523385 | − | 0.970393i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.20343 | + | 0.873894i | −0.234950 | + | 0.0285033i | ||||
\(941\) | −17.0687 | − | 9.85464i | −0.556425 | − | 0.321252i | 0.195284 | − | 0.980747i | \(-0.437437\pi\) |
−0.751709 | + | 0.659495i | \(0.770770\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.6714 | − | 15.3987i | 0.868539 | − | 0.501451i | ||||
\(944\) | −19.0745 | + | 18.3137i | −0.620823 | + | 0.596060i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.62341 | − | 27.5380i | 0.182833 | − | 0.895336i | ||||
\(947\) | 18.8273 | + | 32.6098i | 0.611804 | + | 1.05968i | 0.990936 | + | 0.134333i | \(0.0428893\pi\) |
−0.379132 | + | 0.925343i | \(0.623777\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.2412 | + | 18.0371i | 1.01413 | + | 0.585509i | ||||
\(950\) | −18.1898 | − | 54.4945i | −0.590154 | − | 1.76803i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15.4411 | + | 33.5059i | −0.500449 | + | 1.08593i | ||||
\(953\) | 42.9398i | 1.39096i | 0.718547 | + | 0.695478i | \(0.244808\pi\) | ||||
−0.718547 | + | 0.695478i | \(0.755192\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.81106 | − | 6.60094i | 0.123323 | − | 0.213602i | ||||
\(956\) | −2.61648 | − | 3.48265i | −0.0846229 | − | 0.112637i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15.0343 | − | 3.07009i | −0.485736 | − | 0.0991900i | ||||
\(959\) | −47.9011 | + | 8.34444i | −1.54681 | + | 0.269456i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.766797 | + | 1.32813i | 0.0247354 | + | 0.0428430i | ||||
\(962\) | −21.2747 | − | 18.8497i | −0.685924 | − | 0.607740i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.6506 | − | 1.41341i | 0.375241 | − | 0.0455229i | ||||
\(965\) | 3.99650i | 0.128652i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.4334 | −0.721408 | −0.360704 | − | 0.932680i | \(-0.617464\pi\) | ||||
−0.360704 | + | 0.932680i | \(0.617464\pi\) | |||||||
\(968\) | 2.23774 | − | 27.6655i | 0.0719236 | − | 0.889202i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.125561 | + | 0.141715i | −0.00403153 | + | 0.00455018i | ||||
\(971\) | −7.50553 | + | 4.33332i | −0.240864 | + | 0.139063i | −0.615574 | − | 0.788079i | \(-0.711076\pi\) |
0.374710 | + | 0.927142i | \(0.377742\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.0003 | − | 10.8630i | 0.416772 | − | 0.348251i | ||||
\(974\) | 15.9584 | + | 3.25879i | 0.511339 | + | 0.104418i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.8827 | − | 2.67994i | 0.348346 | − | 0.0857827i | ||||
\(977\) | −48.7155 | − | 28.1259i | −1.55855 | − | 0.899828i | −0.997396 | − | 0.0721142i | \(-0.977025\pi\) |
−0.561151 | − | 0.827714i | \(-0.689641\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.9094 | −0.476507 | ||||||||
\(980\) | −4.48470 | − | 2.94805i | −0.143258 | − | 0.0941720i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.51471 | + | 7.53379i | 0.0802477 | + | 0.240413i | ||||
\(983\) | −10.2462 | + | 17.7469i | −0.326802 | + | 0.566038i | −0.981875 | − | 0.189527i | \(-0.939304\pi\) |
0.655073 | + | 0.755565i | \(0.272638\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.32469 | + | 3.07421i | −0.169659 | + | 0.0979525i | ||||
\(986\) | 1.99978 | + | 0.408366i | 0.0636858 | + | 0.0130050i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 43.7691 | + | 18.6536i | 1.39248 | + | 0.593451i | ||||
\(989\) | 13.6267 | + | 23.6022i | 0.433304 | + | 0.750505i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.1943 | − | 22.8533i | 0.419132 | − | 0.725958i | −0.576720 | − | 0.816942i | \(-0.695668\pi\) |
0.995852 | + | 0.0909835i | \(0.0290011\pi\) | |||||||
\(992\) | −28.5660 | − | 15.0021i | −0.906970 | − | 0.476316i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.58336 | + | 13.9196i | −0.272248 | + | 0.441502i | ||||
\(995\) | −0.885873 | −0.0280841 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.5633 | + | 33.8847i | −0.619577 | + | 1.07314i | 0.369986 | + | 0.929038i | \(0.379363\pi\) |
−0.989563 | + | 0.144102i | \(0.953971\pi\) | |||||||
\(998\) | 15.3496 | + | 13.6000i | 0.485884 | + | 0.430501i | ||||
\(999\) | 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 | 504.2.ch.b.269.11 | yes | 56 | |
3.2 | odd | 2 | inner | 504.2.ch.b.269.18 | yes | 56 | |
4.3 | odd | 2 | 2016.2.cp.b.17.14 | 56 | |||
7.5 | odd | 6 | inner | 504.2.ch.b.341.7 | yes | 56 | |
8.3 | odd | 2 | 2016.2.cp.b.17.15 | 56 | |||
8.5 | even | 2 | inner | 504.2.ch.b.269.22 | yes | 56 | |
12.11 | even | 2 | 2016.2.cp.b.17.16 | 56 | |||
21.5 | even | 6 | inner | 504.2.ch.b.341.22 | yes | 56 | |
24.5 | odd | 2 | inner | 504.2.ch.b.269.7 | ✓ | 56 | |
24.11 | even | 2 | 2016.2.cp.b.17.13 | 56 | |||
28.19 | even | 6 | 2016.2.cp.b.593.13 | 56 | |||
56.5 | odd | 6 | inner | 504.2.ch.b.341.18 | yes | 56 | |
56.19 | even | 6 | 2016.2.cp.b.593.16 | 56 | |||
84.47 | odd | 6 | 2016.2.cp.b.593.15 | 56 | |||
168.5 | even | 6 | inner | 504.2.ch.b.341.11 | yes | 56 | |
168.131 | odd | 6 | 2016.2.cp.b.593.14 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.ch.b.269.7 | ✓ | 56 | 24.5 | odd | 2 | inner | |
504.2.ch.b.269.11 | yes | 56 | 1.1 | even | 1 | trivial | |
504.2.ch.b.269.18 | yes | 56 | 3.2 | odd | 2 | inner | |
504.2.ch.b.269.22 | yes | 56 | 8.5 | even | 2 | inner | |
504.2.ch.b.341.7 | yes | 56 | 7.5 | odd | 6 | inner | |
504.2.ch.b.341.11 | yes | 56 | 168.5 | even | 6 | inner | |
504.2.ch.b.341.18 | yes | 56 | 56.5 | odd | 6 | inner | |
504.2.ch.b.341.22 | yes | 56 | 21.5 | even | 6 | inner | |
2016.2.cp.b.17.13 | 56 | 24.11 | even | 2 | |||
2016.2.cp.b.17.14 | 56 | 4.3 | odd | 2 | |||
2016.2.cp.b.17.15 | 56 | 8.3 | odd | 2 | |||
2016.2.cp.b.17.16 | 56 | 12.11 | even | 2 | |||
2016.2.cp.b.593.13 | 56 | 28.19 | even | 6 | |||
2016.2.cp.b.593.14 | 56 | 168.131 | odd | 6 | |||
2016.2.cp.b.593.15 | 56 | 84.47 | odd | 6 | |||
2016.2.cp.b.593.16 | 56 | 56.19 | even | 6 |