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 | 37.2 | ||
Root | \(0.500000 + 0.691860i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.37 |
Dual form | 144.2.k.b.109.2 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.635665 | − | 1.26330i | −0.449483 | − | 0.893289i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.19186 | + | 1.60607i | −0.595930 | + | 0.803037i | ||||
\(5\) | 2.68554 | + | 2.68554i | 1.20101 | + | 1.20101i | 0.973859 | + | 0.227153i | \(0.0729416\pi\) |
0.227153 | + | 0.973859i | \(0.427058\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.15894i | 0.816003i | 0.912981 | + | 0.408002i | \(0.133774\pi\) | ||||
−0.912981 | + | 0.408002i | \(0.866226\pi\) | |||||||
\(8\) | 2.78658 | + | 0.484753i | 0.985204 | + | 0.171386i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.68554 | − | 5.09976i | 0.533016 | − | 1.61268i | ||||
\(11\) | −1.79793 | − | 1.79793i | −0.542097 | − | 0.542097i | 0.382046 | − | 0.924143i | \(-0.375220\pi\) |
−0.924143 | + | 0.382046i | \(0.875220\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.38372 | − | 1.38372i | 0.383775 | − | 0.383775i | −0.488685 | − | 0.872460i | \(-0.662523\pi\) |
0.872460 | + | 0.488685i | \(0.162523\pi\) | |||||||
\(14\) | 2.72739 | − | 1.37236i | 0.728927 | − | 0.366780i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.15894 | − | 3.82843i | −0.289735 | − | 0.957107i | ||||
\(17\) | 0.224777 | 0.0545165 | 0.0272583 | − | 0.999628i | \(-0.491322\pi\) | ||||
0.0272583 | + | 0.999628i | \(0.491322\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.158942 | − | 0.158942i | 0.0364637 | − | 0.0364637i | −0.688640 | − | 0.725104i | \(-0.741792\pi\) |
0.725104 | + | 0.688640i | \(0.241792\pi\) | |||||||
\(20\) | −7.51397 | + | 1.11239i | −1.68018 | + | 0.248738i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.12845 | + | 3.41421i | −0.240586 | + | 0.727913i | ||||
\(23\) | − | 2.82843i | − | 0.589768i | −0.955533 | − | 0.294884i | \(-0.904719\pi\) | ||
0.955533 | − | 0.294884i | \(-0.0952810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.42429i | 1.88486i | ||||||||
\(26\) | −2.62764 | − | 0.868472i | −0.515322 | − | 0.170321i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.46742 | − | 2.57316i | −0.655280 | − | 0.486281i | ||||
\(29\) | 1.85712 | − | 1.85712i | 0.344858 | − | 0.344858i | −0.513332 | − | 0.858190i | \(-0.671589\pi\) |
0.858190 | + | 0.513332i | \(0.171589\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.84106 | 0.330664 | 0.165332 | − | 0.986238i | \(-0.447130\pi\) | ||||
0.165332 | + | 0.986238i | \(0.447130\pi\) | |||||||
\(32\) | −4.09976 | + | 3.89769i | −0.724742 | + | 0.689021i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.142883 | − | 0.283962i | −0.0245043 | − | 0.0486990i | ||||
\(35\) | −5.79793 | + | 5.79793i | −0.980029 | + | 0.980029i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.66949 | − | 3.66949i | −0.603260 | − | 0.603260i | 0.337916 | − | 0.941176i | \(-0.390278\pi\) |
−0.941176 | + | 0.337916i | \(0.890278\pi\) | |||||||
\(38\) | −0.301825 | − | 0.0997575i | −0.0489625 | − | 0.0161828i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.18165 | + | 8.78530i | 0.977405 | + | 1.38908i | ||||
\(41\) | 5.88163i | 0.918557i | 0.888292 | + | 0.459278i | \(0.151892\pi\) | ||||
−0.888292 | + | 0.459278i | \(0.848108\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.75481 | − | 7.75481i | −1.18260 | − | 1.18260i | −0.979069 | − | 0.203528i | \(-0.934759\pi\) |
−0.203528 | − | 0.979069i | \(-0.565241\pi\) | |||||||
\(44\) | 5.03049 | − | 0.744728i | 0.758376 | − | 0.112272i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.57316 | + | 1.79793i | −0.526833 | + | 0.265091i | ||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.33897 | 0.334139 | ||||||||
\(50\) | 11.9057 | − | 5.99069i | 1.68372 | − | 0.847212i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.573155 | + | 3.87155i | 0.0794823 | + | 0.536888i | ||||
\(53\) | −7.51397 | − | 7.51397i | −1.03212 | − | 1.03212i | −0.999467 | − | 0.0326567i | \(-0.989603\pi\) |
−0.0326567 | − | 0.999467i | \(-0.510397\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 9.65685i | − | 1.30213i | ||||||
\(56\) | −1.04655 | + | 6.01606i | −0.139852 | + | 0.803930i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.52660 | − | 1.16559i | −0.463066 | − | 0.153050i | ||||
\(59\) | −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 | ||||||||
\(61\) | 5.98737 | − | 5.98737i | 0.766604 | − | 0.766604i | −0.210903 | − | 0.977507i | \(-0.567640\pi\) |
0.977507 | + | 0.210903i | \(0.0676404\pi\) | |||||||
\(62\) | −1.17030 | − | 2.32581i | −0.148628 | − | 0.295378i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.53003 | + | 2.70160i | 0.941254 | + | 0.337700i | ||||
\(65\) | 7.43208 | 0.921836 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.4243 | + | 10.4243i | −1.27353 | + | 1.27353i | −0.329307 | + | 0.944223i | \(0.606815\pi\) |
−0.944223 | + | 0.329307i | \(0.893185\pi\) | |||||||
\(68\) | −0.267903 | + | 0.361009i | −0.0324880 | + | 0.0437788i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 11.0101 | + | 3.63899i | 1.31596 | + | 0.434943i | ||||
\(71\) | 4.31788i | 0.512438i | 0.966619 | + | 0.256219i | \(0.0824769\pi\) | ||||
−0.966619 | + | 0.256219i | \(0.917523\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.97474i | − | 0.699290i | −0.936882 | − | 0.349645i | \(-0.886302\pi\) | ||
0.936882 | − | 0.349645i | \(-0.113698\pi\) | |||||||
\(74\) | −2.30310 | + | 6.96823i | −0.267730 | + | 0.810040i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.0658358 | + | 0.444708i | 0.00755188 | + | 0.0510115i | ||||
\(77\) | 3.88163 | − | 3.88163i | 0.442353 | − | 0.442353i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.0075 | 1.68848 | 0.844239 | − | 0.535966i | \(-0.180053\pi\) | ||||
0.844239 | + | 0.535966i | \(0.180053\pi\) | |||||||
\(80\) | 7.16902 | − | 13.3938i | 0.801521 | − | 1.49747i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.43027 | − | 3.73875i | 0.820536 | − | 0.412876i | ||||
\(83\) | 10.1158 | − | 10.1158i | 1.11036 | − | 1.11036i | 0.117253 | − | 0.993102i | \(-0.462591\pi\) |
0.993102 | − | 0.117253i | \(-0.0374088\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.603650 | + | 0.603650i | 0.0654750 | + | 0.0654750i | ||||
\(86\) | −4.86720 | + | 14.7261i | −0.524843 | + | 1.58796i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.13853 | − | 5.88163i | −0.441168 | − | 0.626984i | ||||
\(89\) | 1.42847i | 0.151417i | 0.997130 | + | 0.0757086i | \(0.0241219\pi\) | ||||
−0.997130 | + | 0.0757086i | \(0.975878\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.98737 | + | 2.98737i | 0.313161 | + | 0.313161i | ||||
\(92\) | 4.54266 | + | 3.37109i | 0.473605 | + | 0.351460i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.79793 | − | 3.57316i | −0.185443 | − | 0.368543i | ||||
\(95\) | 0.853690 | 0.0875867 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.3990 | −1.66507 | −0.832535 | − | 0.553973i | \(-0.813111\pi\) | ||||
−0.832535 | + | 0.553973i | \(0.813111\pi\) | |||||||
\(98\) | −1.48680 | − | 2.95482i | −0.150190 | − | 0.298482i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −15.1361 | − | 11.2324i | −1.51361 | − | 1.12324i | ||||
\(101\) | −0.0818942 | − | 0.0818942i | −0.00814878 | − | 0.00814878i | 0.703021 | − | 0.711169i | \(-0.251834\pi\) |
−0.711169 | + | 0.703021i | \(0.751834\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.3507i | 1.31548i | 0.753245 | + | 0.657740i | \(0.228488\pi\) | ||||
−0.753245 | + | 0.657740i | \(0.771512\pi\) | |||||||
\(104\) | 4.52660 | − | 3.18508i | 0.443870 | − | 0.312323i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.71604 | + | 14.2688i | −0.458062 | + | 1.38591i | ||||
\(107\) | 7.27798 | + | 7.27798i | 0.703589 | + | 0.703589i | 0.965179 | − | 0.261590i | \(-0.0842468\pi\) |
−0.261590 | + | 0.965179i | \(0.584247\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.04057 | + | 7.04057i | −0.674365 | + | 0.674365i | −0.958719 | − | 0.284355i | \(-0.908221\pi\) |
0.284355 | + | 0.958719i | \(0.408221\pi\) | |||||||
\(110\) | −12.1995 | + | 6.13853i | −1.16318 | + | 0.585285i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.26535 | − | 2.50209i | 0.781002 | − | 0.236425i | ||||
\(113\) | −18.8486 | −1.77313 | −0.886563 | − | 0.462608i | \(-0.846914\pi\) | ||||
−0.886563 | + | 0.462608i | \(0.846914\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.59587 | − | 7.59587i | 0.708318 | − | 0.708318i | ||||
\(116\) | 0.769243 | + | 5.19609i | 0.0714224 | + | 0.482445i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.51054 | + | 7.59587i | −0.231114 | + | 0.699256i | ||||
\(119\) | 0.485281i | 0.0444857i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 4.53488i | − | 0.412261i | ||||||
\(122\) | −11.3698 | − | 3.75789i | −1.02937 | − | 0.340223i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.19428 | + | 2.95687i | −0.197052 | + | 0.265535i | ||||
\(125\) | −11.8816 | + | 11.8816i | −1.06273 | + | 1.06273i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.81580 | −0.338597 | −0.169299 | − | 0.985565i | \(-0.554150\pi\) | ||||
−0.169299 | + | 0.985565i | \(0.554150\pi\) | |||||||
\(128\) | −1.37364 | − | 11.2300i | −0.121414 | − | 0.992602i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.72431 | − | 9.38895i | −0.414350 | − | 0.823465i | ||||
\(131\) | 0.767438 | − | 0.767438i | 0.0670514 | − | 0.0670514i | −0.672786 | − | 0.739837i | \(-0.734902\pi\) |
0.739837 | + | 0.672786i | \(0.234902\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.343146 | + | 0.343146i | 0.0297545 | + | 0.0297545i | ||||
\(134\) | 19.7954 | + | 6.54266i | 1.71006 | + | 0.565200i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.626360 | + | 0.108961i | 0.0537099 | + | 0.00934337i | ||||
\(137\) | − | 5.31010i | − | 0.453672i | −0.973933 | − | 0.226836i | \(-0.927162\pi\) | ||
0.973933 | − | 0.226836i | \(-0.0728382\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.76744 | + | 8.76744i | 0.743644 | + | 0.743644i | 0.973277 | − | 0.229633i | \(-0.0737526\pi\) |
−0.229633 | + | 0.973277i | \(0.573753\pi\) | |||||||
\(140\) | −2.40158 | − | 16.2222i | −0.202971 | − | 1.37103i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.45479 | − | 2.74473i | 0.457756 | − | 0.230332i | ||||
\(143\) | −4.97567 | −0.416086 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.97474 | 0.828357 | ||||||||
\(146\) | −7.54789 | + | 3.79793i | −0.624668 | + | 0.314319i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.2670 | − | 1.51995i | 0.843940 | − | 0.124939i | ||||
\(149\) | 1.02869 | + | 1.02869i | 0.0842735 | + | 0.0842735i | 0.747987 | − | 0.663713i | \(-0.231021\pi\) |
−0.663713 | + | 0.747987i | \(0.731021\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.03696i | − | 0.165766i | −0.996559 | − | 0.0828829i | \(-0.973587\pi\) | ||
0.996559 | − | 0.0828829i | \(-0.0264127\pi\) | |||||||
\(152\) | 0.519951 | − | 0.365856i | 0.0421736 | − | 0.0296748i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.37109 | − | 2.43625i | −0.593979 | − | 0.196319i | ||||
\(155\) | 4.94424 | + | 4.94424i | 0.397131 | + | 0.397131i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.09378 | − | 6.09378i | 0.486336 | − | 0.486336i | −0.420812 | − | 0.907148i | \(-0.638255\pi\) |
0.907148 | + | 0.420812i | \(0.138255\pi\) | |||||||
\(158\) | −9.53976 | − | 18.9590i | −0.758943 | − | 1.50830i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −21.4775 | − | 0.542661i | −1.69795 | − | 0.0429011i | ||||
\(161\) | 6.10641 | 0.481252 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.43692 | − | 3.43692i | 0.269201 | − | 0.269201i | −0.559577 | − | 0.828778i | \(-0.689037\pi\) |
0.828778 | + | 0.559577i | \(0.189037\pi\) | |||||||
\(164\) | −9.44633 | − | 7.01008i | −0.737634 | − | 0.547395i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −19.2096 | − | 6.34905i | −1.49095 | − | 0.492782i | ||||
\(167\) | 21.7023i | 1.67937i | 0.543072 | + | 0.839686i | \(0.317261\pi\) | ||||
−0.543072 | + | 0.839686i | \(0.682739\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.17064i | 0.705434i | ||||||||
\(170\) | 0.378872 | − | 1.14631i | 0.0290582 | − | 0.0879180i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 21.6974 | − | 3.21215i | 1.65441 | − | 0.244924i | ||||
\(173\) | 8.74653 | − | 8.74653i | 0.664987 | − | 0.664987i | −0.291565 | − | 0.956551i | \(-0.594176\pi\) |
0.956551 | + | 0.291565i | \(0.0941758\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.3465 | −1.53805 | ||||||||
\(176\) | −4.79956 | + | 8.96695i | −0.361780 | + | 0.675910i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.80458 | − | 0.908027i | 0.135259 | − | 0.0680595i | ||||
\(179\) | −8.23163 | + | 8.23163i | −0.615261 | + | 0.615261i | −0.944312 | − | 0.329051i | \(-0.893271\pi\) |
0.329051 | + | 0.944312i | \(0.393271\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.72269 | + | 6.72269i | 0.499694 | + | 0.499694i | 0.911343 | − | 0.411649i | \(-0.135047\pi\) |
−0.411649 | + | 0.911343i | \(0.635047\pi\) | |||||||
\(182\) | 1.87498 | − | 5.67291i | 0.138983 | − | 0.420504i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.37109 | − | 7.88163i | 0.101078 | − | 0.581042i | ||||
\(185\) | − | 19.7091i | − | 1.44904i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.404135 | − | 0.404135i | −0.0295533 | − | 0.0295533i | ||||
\(188\) | −3.37109 | + | 4.54266i | −0.245862 | + | 0.331308i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.542661 | − | 1.07847i | −0.0393687 | − | 0.0782402i | ||||
\(191\) | 20.8032 | 1.50526 | 0.752632 | − | 0.658441i | \(-0.228784\pi\) | ||||
0.752632 | + | 0.658441i | \(0.228784\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.1454 | 1.01821 | 0.509103 | − | 0.860705i | \(-0.329977\pi\) | ||||
0.509103 | + | 0.860705i | \(0.329977\pi\) | |||||||
\(194\) | 10.4243 | + | 20.7169i | 0.748421 | + | 1.48739i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.78772 | + | 3.75656i | −0.199123 | + | 0.268326i | ||||
\(197\) | 2.42865 | + | 2.42865i | 0.173034 | + | 0.173034i | 0.788311 | − | 0.615277i | \(-0.210956\pi\) |
−0.615277 | + | 0.788311i | \(0.710956\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.306182i | 0.0217047i | 0.999941 | + | 0.0108523i | \(0.00345447\pi\) | ||||
−0.999941 | + | 0.0108523i | \(0.996546\pi\) | |||||||
\(200\) | −4.56845 | + | 26.2615i | −0.323038 | + | 1.85697i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.0513998 | + | 0.155514i | −0.00361648 | + | 0.0109420i | ||||
\(203\) | 4.00941 | + | 4.00941i | 0.281405 | + | 0.281405i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.7954 | + | 15.7954i | −1.10320 | + | 1.10320i | ||||
\(206\) | 16.8659 | − | 8.48656i | 1.17510 | − | 0.591286i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.90112 | − | 3.69382i | −0.478506 | − | 0.256120i | ||||
\(209\) | −0.571533 | −0.0395337 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.23256 | − | 7.23256i | 0.497910 | − | 0.497910i | −0.412877 | − | 0.910787i | \(-0.635476\pi\) |
0.910787 | + | 0.412877i | \(0.135476\pi\) | |||||||
\(212\) | 21.0236 | − | 3.11239i | 1.44391 | − | 0.213760i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.56792 | − | 13.8206i | 0.312257 | − | 0.944760i | ||||
\(215\) | − | 41.6517i | − | 2.84063i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.97474i | 0.269823i | ||||||||
\(218\) | 13.3698 | + | 4.41892i | 0.905518 | + | 0.299287i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 15.5096 | + | 11.5096i | 1.04566 | + | 0.775978i | ||||
\(221\) | 0.311029 | − | 0.311029i | 0.0209221 | − | 0.0209221i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.71908 | −0.115118 | −0.0575591 | − | 0.998342i | \(-0.518332\pi\) | ||||
−0.0575591 | + | 0.998342i | \(0.518332\pi\) | |||||||
\(224\) | −8.41489 | − | 8.85114i | −0.562243 | − | 0.591391i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.9814 | + | 23.8114i | 0.796990 | + | 1.58391i | ||||
\(227\) | −10.1158 | + | 10.1158i | −0.671410 | + | 0.671410i | −0.958041 | − | 0.286631i | \(-0.907465\pi\) |
0.286631 | + | 0.958041i | \(0.407465\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.0195 | − | 12.0195i | −0.794270 | − | 0.794270i | 0.187915 | − | 0.982185i | \(-0.439827\pi\) |
−0.982185 | + | 0.187915i | \(0.939827\pi\) | |||||||
\(230\) | −14.4243 | − | 4.76744i | −0.951110 | − | 0.314356i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.07524 | − | 4.27476i | 0.398859 | − | 0.280652i | ||||
\(233\) | 13.3779i | 0.876418i | 0.898873 | + | 0.438209i | \(0.144387\pi\) | ||||
−0.898873 | + | 0.438209i | \(0.855613\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.59587 | + | 7.59587i | 0.495500 | + | 0.495500i | ||||
\(236\) | 11.1917 | − | 1.65685i | 0.728520 | − | 0.107852i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.613057 | − | 0.308476i | 0.0397386 | − | 0.0199956i | ||||
\(239\) | −13.3675 | −0.864670 | −0.432335 | − | 0.901713i | \(-0.642310\pi\) | ||||
−0.432335 | + | 0.901713i | \(0.642310\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.211474 | 0.0136222 | 0.00681112 | − | 0.999977i | \(-0.497832\pi\) | ||||
0.00681112 | + | 0.999977i | \(0.497832\pi\) | |||||||
\(242\) | −5.72891 | + | 2.88266i | −0.368269 | + | 0.185305i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.48005 | + | 16.7523i | 0.158769 | + | 1.07245i | ||||
\(245\) | 6.28141 | + | 6.28141i | 0.401305 | + | 0.401305i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.439861i | − | 0.0279877i | ||||||
\(248\) | 5.13025 | + | 0.892458i | 0.325771 | + | 0.0566711i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 22.5628 | + | 7.45734i | 1.42700 | + | 0.471644i | ||||
\(251\) | −10.4337 | − | 10.4337i | −0.658569 | − | 0.658569i | 0.296472 | − | 0.955041i | \(-0.404190\pi\) |
−0.955041 | + | 0.296472i | \(0.904190\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.08532 | + | 5.08532i | −0.319711 | + | 0.319711i | ||||
\(254\) | 2.42557 | + | 4.82050i | 0.152194 | + | 0.302465i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.3137 | + | 8.87385i | −0.832107 | + | 0.554615i | ||||
\(257\) | 0.742176 | 0.0462957 | 0.0231478 | − | 0.999732i | \(-0.492631\pi\) | ||||
0.0231478 | + | 0.999732i | \(0.492631\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.92221 | − | 7.92221i | 0.492262 | − | 0.492262i | ||||
\(260\) | −8.85799 | + | 11.9365i | −0.549349 | + | 0.740268i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.45734 | − | 0.481672i | −0.0900347 | − | 0.0297578i | ||||
\(263\) | − | 5.48435i | − | 0.338180i | −0.985601 | − | 0.169090i | \(-0.945917\pi\) | ||
0.985601 | − | 0.169090i | \(-0.0540828\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 40.3582i | − | 2.47918i | ||||||
\(266\) | 0.215371 | − | 0.651622i | 0.0132052 | − | 0.0399535i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.31788 | − | 29.1665i | −0.263757 | − | 1.78163i | ||||
\(269\) | −14.4741 | + | 14.4741i | −0.882500 | + | 0.882500i | −0.993788 | − | 0.111289i | \(-0.964502\pi\) |
0.111289 | + | 0.993788i | \(0.464502\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.0370 | −0.852685 | −0.426342 | − | 0.904562i | \(-0.640198\pi\) | ||||
−0.426342 | + | 0.904562i | \(0.640198\pi\) | |||||||
\(272\) | −0.260504 | − | 0.860544i | −0.0157954 | − | 0.0521781i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.70825 | + | 3.37545i | −0.405260 | + | 0.203918i | ||||
\(275\) | 16.9442 | − | 16.9442i | 1.02178 | − | 1.02178i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.49013 | + | 9.49013i | 0.570207 | + | 0.570207i | 0.932186 | − | 0.361980i | \(-0.117899\pi\) |
−0.361980 | + | 0.932186i | \(0.617899\pi\) | |||||||
\(278\) | 5.50276 | − | 16.6491i | 0.330034 | − | 0.998545i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −18.9670 | + | 13.3458i | −1.13349 | + | 0.797566i | ||||
\(281\) | − | 3.89359i | − | 0.232272i | −0.993233 | − | 0.116136i | \(-0.962949\pi\) | ||
0.993233 | − | 0.116136i | \(-0.0370509\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.4853 | − | 12.4853i | −0.742173 | − | 0.742173i | 0.230823 | − | 0.972996i | \(-0.425858\pi\) |
−0.972996 | + | 0.230823i | \(0.925858\pi\) | |||||||
\(284\) | −6.93484 | − | 5.14631i | −0.411507 | − | 0.305377i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.16286 | + | 6.28577i | 0.187024 | + | 0.371685i | ||||
\(287\) | −12.6981 | −0.749545 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9495 | −0.997028 | ||||||||
\(290\) | −6.34059 | − | 12.6011i | −0.372332 | − | 0.739962i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.59587 | + | 7.12105i | 0.561556 | + | 0.416728i | ||||
\(293\) | 11.1553 | + | 11.1553i | 0.651697 | + | 0.651697i | 0.953402 | − | 0.301704i | \(-0.0975556\pi\) |
−0.301704 | + | 0.953402i | \(0.597556\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 21.4844i | − | 1.25087i | ||||||
\(296\) | −8.44651 | − | 12.0041i | −0.490944 | − | 0.697724i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.645643 | − | 1.95345i | 0.0374011 | − | 0.113160i | ||||
\(299\) | −3.91375 | − | 3.91375i | −0.226338 | − | 0.226338i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.7422 | − | 16.7422i | 0.965003 | − | 0.965003i | ||||
\(302\) | −2.57330 | + | 1.29483i | −0.148077 | + | 0.0745089i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.792701 | − | 0.424292i | −0.0454645 | − | 0.0243348i | ||||
\(305\) | 32.1587 | 1.84140 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.40320 | + | 5.40320i | −0.308377 | + | 0.308377i | −0.844280 | − | 0.535903i | \(-0.819971\pi\) |
0.535903 | + | 0.844280i | \(0.319971\pi\) | |||||||
\(308\) | 1.60782 | + | 10.8605i | 0.0916143 | + | 0.618837i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.10318 | − | 9.38895i | 0.176249 | − | 0.533257i | ||||
\(311\) | 24.1623i | 1.37012i | 0.728488 | + | 0.685059i | \(0.240224\pi\) | ||||
−0.728488 | + | 0.685059i | \(0.759776\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 16.6105i | − | 0.938881i | −0.882964 | − | 0.469441i | \(-0.844456\pi\) | ||
0.882964 | − | 0.469441i | \(-0.155544\pi\) | |||||||
\(314\) | −11.5719 | − | 3.82467i | −0.653039 | − | 0.215839i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.8869 | + | 24.1032i | −1.00621 | + | 1.35591i | ||||
\(317\) | −1.81170 | + | 1.81170i | −0.101755 | + | 0.101755i | −0.756152 | − | 0.654397i | \(-0.772923\pi\) |
0.654397 | + | 0.756152i | \(0.272923\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.67794 | −0.373893 | ||||||||
\(320\) | 12.9670 | + | 27.4775i | 0.724875 | + | 1.53604i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.88163 | − | 7.71423i | −0.216315 | − | 0.429897i | ||||
\(323\) | 0.0357265 | − | 0.0357265i | 0.00198788 | − | 0.00198788i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.0406 | + | 13.0406i | 0.723361 | + | 0.723361i | ||||
\(326\) | −6.52660 | − | 2.15714i | −0.361475 | − | 0.119473i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.85114 | + | 16.3896i | −0.157428 | + | 0.904966i | ||||
\(329\) | 6.10641i | 0.336657i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.5252 | + | 13.5252i | 0.743411 | + | 0.743411i | 0.973233 | − | 0.229822i | \(-0.0738142\pi\) |
−0.229822 | + | 0.973233i | \(0.573814\pi\) | |||||||
\(332\) | 4.19011 | + | 28.3034i | 0.229962 | + | 1.55335i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 27.4165 | − | 13.7954i | 1.50016 | − | 0.754850i | ||||
\(335\) | −55.9898 | −3.05905 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.12615 | −0.0613454 | −0.0306727 | − | 0.999529i | \(-0.509765\pi\) | ||||
−0.0306727 | + | 0.999529i | \(0.509765\pi\) | |||||||
\(338\) | 11.5853 | − | 5.82946i | 0.630156 | − | 0.317081i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.68897 | + | 0.250040i | −0.0915973 | + | 0.0135603i | ||||
\(341\) | −3.31010 | − | 3.31010i | −0.179252 | − | 0.179252i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1623i | 1.08866i | ||||||||
\(344\) | −17.8502 | − | 25.3685i | −0.962419 | − | 1.36778i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.6094 | − | 5.48964i | −0.892925 | − | 0.295125i | ||||
\(347\) | −20.7938 | − | 20.7938i | −1.11627 | − | 1.11627i | −0.992284 | − | 0.123983i | \(-0.960433\pi\) |
−0.123983 | − | 0.992284i | \(-0.539567\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.2855 | + | 19.2855i | −1.03233 | + | 1.03233i | −0.0328700 | + | 0.999460i | \(0.510465\pi\) |
−0.999460 | + | 0.0328700i | \(0.989535\pi\) | |||||||
\(350\) | 12.9336 | + | 25.7038i | 0.691328 | + | 1.37392i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 14.3789 | + | 0.363303i | 0.766396 | + | 0.0193641i | ||||
\(353\) | −25.5908 | −1.36206 | −0.681029 | − | 0.732256i | \(-0.738467\pi\) | ||||
−0.681029 | + | 0.732256i | \(0.738467\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.5959 | + | 11.5959i | −0.615445 | + | 0.615445i | ||||
\(356\) | −2.29422 | − | 1.70253i | −0.121594 | − | 0.0902340i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.6316 | + | 5.16647i | 0.826155 | + | 0.273056i | ||||
\(359\) | − | 3.77296i | − | 0.199129i | −0.995031 | − | 0.0995645i | \(-0.968255\pi\) | ||
0.995031 | − | 0.0995645i | \(-0.0317450\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9495i | 0.997341i | ||||||||
\(362\) | 4.21940 | − | 12.7662i | 0.221767 | − | 0.670975i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.35846 | + | 1.23741i | −0.438102 | + | 0.0648578i | ||||
\(365\) | 16.0454 | − | 16.0454i | 0.839856 | − | 0.839856i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.4474 | −1.43274 | −0.716371 | − | 0.697720i | \(-0.754198\pi\) | ||||
−0.716371 | + | 0.697720i | \(0.754198\pi\) | |||||||
\(368\) | −10.8284 | + | 3.27798i | −0.564471 | + | 0.170877i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −24.8986 | + | 12.5284i | −1.29441 | + | 0.651321i | ||||
\(371\) | 16.2222 | − | 16.2222i | 0.842216 | − | 0.842216i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.6231 | + | 12.6231i | 0.653601 | + | 0.653601i | 0.953858 | − | 0.300257i | \(-0.0970725\pi\) |
−0.300257 | + | 0.953858i | \(0.597072\pi\) | |||||||
\(374\) | −0.253649 | + | 0.767438i | −0.0131159 | + | 0.0396833i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.88163 | + | 1.37109i | 0.406464 | + | 0.0707085i | ||||
\(377\) | − | 5.13946i | − | 0.264695i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.6686 | − | 11.6686i | −0.599373 | − | 0.599373i | 0.340772 | − | 0.940146i | \(-0.389311\pi\) |
−0.940146 | + | 0.340772i | \(0.889311\pi\) | |||||||
\(380\) | −1.01748 | + | 1.37109i | −0.0521955 | + | 0.0703353i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −13.2238 | − | 26.2807i | −0.676591 | − | 1.34464i | ||||
\(383\) | 17.1885 | 0.878291 | 0.439145 | − | 0.898416i | \(-0.355281\pi\) | ||||
0.439145 | + | 0.898416i | \(0.355281\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.8486 | 1.06254 | ||||||||
\(386\) | −8.99173 | − | 17.8699i | −0.457667 | − | 0.909553i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 19.5453 | − | 26.3380i | 0.992264 | − | 1.33711i | ||||
\(389\) | 1.88238 | + | 1.88238i | 0.0954404 | + | 0.0954404i | 0.753215 | − | 0.657774i | \(-0.228502\pi\) |
−0.657774 | + | 0.753215i | \(0.728502\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.635767i | − | 0.0321521i | ||||||
\(392\) | 6.51772 | + | 1.13382i | 0.329195 | + | 0.0572667i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.52431 | − | 4.61192i | 0.0767935 | − | 0.232345i | ||||
\(395\) | 40.3034 | + | 40.3034i | 2.02788 | + | 2.02788i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.41166 | − | 8.41166i | 0.422169 | − | 0.422169i | −0.463781 | − | 0.885950i | \(-0.653507\pi\) |
0.885950 | + | 0.463781i | \(0.153507\pi\) | |||||||
\(398\) | 0.386800 | − | 0.194629i | 0.0193885 | − | 0.00975588i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 36.0802 | − | 10.9222i | 1.80401 | − | 0.546110i | ||||
\(401\) | −1.12389 | −0.0561242 | −0.0280621 | − | 0.999606i | \(-0.508934\pi\) | ||||
−0.0280621 | + | 0.999606i | \(0.508934\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.54751 | − | 2.54751i | 0.126900 | − | 0.126900i | ||||
\(404\) | 0.229135 | − | 0.0339217i | 0.0113999 | − | 0.00168767i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.51645 | − | 7.61373i | 0.124889 | − | 0.377863i | ||||
\(407\) | 13.1950i | 0.654051i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.7211i | 0.678464i | 0.940703 | + | 0.339232i | \(0.110167\pi\) | ||||
−0.940703 | + | 0.339232i | \(0.889833\pi\) | |||||||
\(410\) | 29.9949 | + | 9.91375i | 1.48134 | + | 0.489605i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −21.4422 | − | 15.9121i | −1.05638 | − | 0.783934i | ||||
\(413\) | 8.63577 | − | 8.63577i | 0.424938 | − | 0.424938i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 54.3329 | 2.66710 | ||||||||
\(416\) | −0.279604 | + | 11.0662i | −0.0137087 | + | 0.542566i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.363303 | + | 0.722018i | 0.0177698 | + | 0.0353151i | ||||
\(419\) | 9.30755 | − | 9.30755i | 0.454703 | − | 0.454703i | −0.442209 | − | 0.896912i | \(-0.645805\pi\) |
0.896912 | + | 0.442209i | \(0.145805\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.44378 | + | 8.44378i | 0.411525 | + | 0.411525i | 0.882269 | − | 0.470745i | \(-0.156015\pi\) |
−0.470745 | + | 0.882269i | \(0.656015\pi\) | |||||||
\(422\) | −13.7344 | − | 4.53942i | −0.668580 | − | 0.220975i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −17.2958 | − | 24.5807i | −0.839960 | − | 1.19374i | ||||
\(425\) | 2.11837i | 0.102756i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.9264 | + | 12.9264i | 0.625551 | + | 0.625551i | ||||
\(428\) | −20.3633 | + | 3.01464i | −0.984297 | + | 0.145718i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −52.6187 | + | 26.4766i | −2.53750 | + | 1.27681i | ||||
\(431\) | 30.6054 | 1.47421 | 0.737105 | − | 0.675778i | \(-0.236192\pi\) | ||||
0.737105 | + | 0.675778i | \(0.236192\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.3137 | −0.735930 | −0.367965 | − | 0.929840i | \(-0.619945\pi\) | ||||
−0.367965 | + | 0.929840i | \(0.619945\pi\) | |||||||
\(434\) | 5.02129 | − | 2.52660i | 0.241030 | − | 0.121281i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.91630 | − | 19.6991i | −0.139665 | − | 0.943413i | ||||
\(437\) | −0.449555 | − | 0.449555i | −0.0215051 | − | 0.0215051i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 33.3676i | − | 1.59255i | −0.604936 | − | 0.796274i | \(-0.706801\pi\) | ||
0.604936 | − | 0.796274i | \(-0.293199\pi\) | |||||||
\(440\) | 4.68119 | − | 26.9096i | 0.223167 | − | 1.28286i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.590633 | − | 0.195213i | −0.0280936 | − | 0.00928533i | ||||
\(443\) | −2.28832 | − | 2.28832i | −0.108721 | − | 0.108721i | 0.650653 | − | 0.759375i | \(-0.274495\pi\) |
−0.759375 | + | 0.650653i | \(0.774495\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.83621 | + | 3.83621i | −0.181854 | + | 0.181854i | ||||
\(446\) | 1.09276 | + | 2.17172i | 0.0517437 | + | 0.102834i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.83260 | + | 16.2569i | −0.275565 | + | 0.768066i | ||||
\(449\) | 27.4165 | 1.29387 | 0.646933 | − | 0.762547i | \(-0.276052\pi\) | ||||
0.646933 | + | 0.762547i | \(0.276052\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.5748 | − | 10.5748i | 0.497947 | − | 0.497947i | ||||
\(452\) | 22.4649 | − | 30.2722i | 1.05666 | − | 1.42388i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 19.2096 | + | 6.34905i | 0.901551 | + | 0.297976i | ||||
\(455\) | 16.0454i | 0.752221i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.9147i | 0.510567i | 0.966866 | + | 0.255284i | \(0.0821688\pi\) | ||||
−0.966866 | + | 0.255284i | \(0.917831\pi\) | |||||||
\(458\) | −7.54386 | + | 22.8246i | −0.352501 | + | 1.06652i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.14631 | + | 21.2527i | 0.146697 | + | 0.990913i | ||||
\(461\) | −17.8319 | + | 17.8319i | −0.830512 | + | 0.830512i | −0.987587 | − | 0.157075i | \(-0.949794\pi\) |
0.157075 | + | 0.987587i | \(0.449794\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.4937 | 1.04537 | 0.522686 | − | 0.852525i | \(-0.324930\pi\) | ||||
0.522686 | + | 0.852525i | \(0.324930\pi\) | |||||||
\(464\) | −9.26213 | − | 4.95755i | −0.429983 | − | 0.230148i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.9004 | − | 8.50389i | 0.782895 | − | 0.393935i | ||||
\(467\) | −24.2171 | + | 24.2171i | −1.12063 | + | 1.12063i | −0.128989 | + | 0.991646i | \(0.541173\pi\) |
−0.991646 | + | 0.128989i | \(0.958827\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.5054 | − | 22.5054i | −1.03920 | − | 1.03920i | ||||
\(470\) | 4.76744 | − | 14.4243i | 0.219906 | − | 0.665343i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.20730 | − | 13.0853i | −0.423800 | − | 0.602301i | ||||
\(473\) | 27.8852i | 1.28216i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.49791 | + | 1.49791i | 0.0687289 | + | 0.0687289i | ||||
\(476\) | −0.779397 | − | 0.578387i | −0.0357236 | − | 0.0265103i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.49724 | + | 16.8872i | 0.388655 | + | 0.772400i | ||||
\(479\) | 36.2362 | 1.65568 | 0.827838 | − | 0.560968i | \(-0.189571\pi\) | ||||
0.827838 | + | 0.560968i | \(0.189571\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.1551 | −0.463032 | ||||||||
\(482\) | −0.134427 | − | 0.267156i | −0.00612297 | − | 0.0121686i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.28334 | + | 5.40494i | 0.331061 | + | 0.245679i | ||||
\(485\) | −44.0403 | − | 44.0403i | −1.99977 | − | 1.99977i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.8200i | 0.762186i | 0.924537 | + | 0.381093i | \(0.124452\pi\) | ||||
−0.924537 | + | 0.381093i | \(0.875548\pi\) | |||||||
\(488\) | 19.5867 | − | 13.7819i | 0.886646 | − | 0.623876i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.94244 | − | 11.9282i | 0.178101 | − | 0.538860i | ||||
\(491\) | −6.10641 | − | 6.10641i | −0.275578 | − | 0.275578i | 0.555763 | − | 0.831341i | \(-0.312426\pi\) |
−0.831341 | + | 0.555763i | \(0.812426\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.417438 | − | 0.417438i | 0.0188005 | − | 0.0188005i | ||||
\(494\) | −0.555677 | + | 0.279604i | −0.0250011 | + | 0.0125800i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.13368 | − | 7.04836i | −0.0958050 | − | 0.316481i | ||||
\(497\) | −9.32206 | −0.418151 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.6770 | + | 19.6770i | −0.880864 | + | 0.880864i | −0.993622 | − | 0.112758i | \(-0.964031\pi\) |
0.112758 | + | 0.993622i | \(0.464031\pi\) | |||||||
\(500\) | −4.92153 | − | 33.2440i | −0.220098 | − | 1.48672i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.54856 | + | 19.8132i | −0.292277 | + | 0.884308i | ||||
\(503\) | − | 25.7308i | − | 1.14728i | −0.819108 | − | 0.573639i | \(-0.805531\pi\) | ||
0.819108 | − | 0.573639i | \(-0.194469\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.439861i | − | 0.0195736i | ||||||
\(506\) | 9.65685 | + | 3.19173i | 0.429300 | + | 0.141890i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.54789 | − | 6.12845i | 0.201780 | − | 0.271906i | ||||
\(509\) | −1.73514 | + | 1.73514i | −0.0769087 | + | 0.0769087i | −0.744515 | − | 0.667606i | \(-0.767319\pi\) |
0.667606 | + | 0.744515i | \(0.267319\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.8991 | 0.570623 | ||||||||
\(512\) | 19.6734 | + | 11.1784i | 0.869450 | + | 0.494021i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.471775 | − | 0.937591i | −0.0208091 | − | 0.0413554i | ||||
\(515\) | −35.8538 | + | 35.8538i | −1.57991 | + | 1.57991i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.08532 | − | 5.08532i | −0.223652 | − | 0.223652i | ||||
\(518\) | −15.0440 | − | 4.97226i | −0.660995 | − | 0.218469i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 20.7101 | + | 3.60272i | 0.908196 | + | 0.157990i | ||||
\(521\) | − | 33.5944i | − | 1.47180i | −0.677092 | − | 0.735898i | \(-0.736760\pi\) | ||
0.677092 | − | 0.735898i | \(-0.263240\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.8158 | − | 21.8158i | −0.953938 | − | 0.953938i | 0.0450467 | − | 0.998985i | \(-0.485656\pi\) |
−0.998985 | + | 0.0450467i | \(0.985656\pi\) | |||||||
\(524\) | 0.317883 | + | 2.14724i | 0.0138868 | + | 0.0938026i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.92839 | + | 3.48621i | −0.302092 | + | 0.152006i | ||||
\(527\) | 0.413828 | 0.0180266 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000 | 0.652174 | ||||||||
\(530\) | −50.9846 | + | 25.6543i | −2.21463 | + | 1.11435i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.960099 | + | 0.142136i | −0.0416256 | + | 0.00616236i | ||||
\(533\) | 8.13853 | + | 8.13853i | 0.352519 | + | 0.352519i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39.0907i | 1.69004i | ||||||||
\(536\) | −34.1013 | + | 23.9949i | −1.47295 | + | 1.03642i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 27.4858 | + | 9.08445i | 1.18500 | + | 0.391658i | ||||
\(539\) | −4.20531 | − | 4.20531i | −0.181136 | − | 0.181136i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.2112 | − | 27.2112i | 1.16990 | − | 1.16990i | 0.187669 | − | 0.982232i | \(-0.439907\pi\) |
0.982232 | − | 0.187669i | \(-0.0600933\pi\) | |||||||
\(542\) | 8.92281 | + | 17.7329i | 0.383267 | + | 0.761694i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.921533 | + | 0.876113i | −0.0395104 | + | 0.0375630i | ||||
\(545\) | −37.8155 | −1.61984 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.80116 | + | 6.80116i | −0.290796 | + | 0.290796i | −0.837395 | − | 0.546598i | \(-0.815922\pi\) |
0.546598 | + | 0.837395i | \(0.315922\pi\) | |||||||
\(548\) | 8.52841 | + | 6.32889i | 0.364315 | + | 0.270357i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −32.1765 | − | 10.6348i | −1.37201 | − | 0.453470i | ||||
\(551\) | − | 0.590346i | − | 0.0251496i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.4004i | 1.37780i | ||||||||
\(554\) | 5.95635 | − | 18.0214i | 0.253061 | − | 0.765657i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −24.5307 | + | 3.63159i | −1.04033 | + | 0.154014i | ||||
\(557\) | 4.29337 | − | 4.29337i | 0.181916 | − | 0.181916i | −0.610274 | − | 0.792190i | \(-0.708941\pi\) |
0.792190 | + | 0.610274i | \(0.208941\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.4609 | −0.907701 | ||||||||
\(560\) | 28.9164 | + | 15.4775i | 1.22194 | + | 0.654044i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.91878 | + | 2.47502i | −0.207486 | + | 0.104402i | ||||
\(563\) | 10.0801 | − | 10.0801i | 0.424825 | − | 0.424825i | −0.462036 | − | 0.886861i | \(-0.652881\pi\) |
0.886861 | + | 0.462036i | \(0.152881\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −50.6187 | − | 50.6187i | −2.12954 | − | 2.12954i | ||||
\(566\) | −7.83621 | + | 23.7091i | −0.329381 | + | 0.996569i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.09311 | + | 12.0321i | −0.0878248 | + | 0.504856i | ||||
\(569\) | 32.5018i | 1.36255i | 0.732029 | + | 0.681274i | \(0.238574\pi\) | ||||
−0.732029 | + | 0.681274i | \(0.761426\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.17157 | − | 9.17157i | −0.383818 | − | 0.383818i | 0.488657 | − | 0.872476i | \(-0.337487\pi\) |
−0.872476 | + | 0.488657i | \(0.837487\pi\) | |||||||
\(572\) | 5.93030 | − | 7.99129i | 0.247958 | − | 0.334132i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.07174 | + | 16.0415i | 0.336908 | + | 0.669560i | ||||
\(575\) | 26.6559 | 1.11163 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.7536 | 0.489308 | 0.244654 | − | 0.969611i | \(-0.421326\pi\) | ||||
0.244654 | + | 0.969611i | \(0.421326\pi\) | |||||||
\(578\) | 10.7742 | + | 21.4123i | 0.448147 | + | 0.890634i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11.8885 | + | 16.0202i | −0.493643 | + | 0.665201i | ||||
\(581\) | 21.8395 | + | 21.8395i | 0.906053 | + | 0.906053i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.0192i | 1.11902i | ||||||||
\(584\) | 2.89627 | − | 16.6491i | 0.119849 | − | 0.688943i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.00144 | − | 21.1835i | 0.289227 | − | 0.875081i | ||||
\(587\) | −6.46002 | − | 6.46002i | −0.266634 | − | 0.266634i | 0.561109 | − | 0.827742i | \(-0.310375\pi\) |
−0.827742 | + | 0.561109i | \(0.810375\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.292621 | − | 0.292621i | 0.0120572 | − | 0.0120572i | ||||
\(590\) | −27.1412 | + | 13.6569i | −1.11739 | + | 0.562244i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.79564 | + | 18.3011i | −0.402598 | + | 0.752170i | ||||
\(593\) | −5.49270 | −0.225558 | −0.112779 | − | 0.993620i | \(-0.535975\pi\) | ||||
−0.112779 | + | 0.993620i | \(0.535975\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.30324 | + | 1.30324i | −0.0534278 | + | 0.0534278i | ||||
\(596\) | −2.87820 | + | 0.426097i | −0.117896 | + | 0.0174536i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.45641 | + | 7.43208i | −0.100450 | + | 0.303920i | ||||
\(599\) | − | 36.4348i | − | 1.48868i | −0.667799 | − | 0.744342i | \(-0.732763\pi\) | ||
0.667799 | − | 0.744342i | \(-0.267237\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 9.97474i | − | 0.406878i | −0.979088 | − | 0.203439i | \(-0.934788\pi\) | ||
0.979088 | − | 0.203439i | \(-0.0652119\pi\) | |||||||
\(602\) | −31.7928 | − | 10.5080i | −1.29578 | − | 0.428274i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.27151 | + | 2.42777i | 0.133116 | + | 0.0987848i | ||||
\(605\) | 12.1786 | − | 12.1786i | 0.495131 | − | 0.495131i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.51900 | 0.183421 | 0.0917103 | − | 0.995786i | \(-0.470767\pi\) | ||||
0.0917103 | + | 0.995786i | \(0.470767\pi\) | |||||||
\(608\) | −0.0321169 | + | 1.27113i | −0.00130251 | + | 0.0515510i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.4422 | − | 40.6261i | −0.827679 | − | 1.64490i | ||||
\(611\) | 3.91375 | − | 3.91375i | 0.158333 | − | 0.158333i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.43692 | − | 8.43692i | −0.340764 | − | 0.340764i | 0.515890 | − | 0.856655i | \(-0.327461\pi\) |
−0.856655 | + | 0.515890i | \(0.827461\pi\) | |||||||
\(614\) | 10.2605 | + | 3.39125i | 0.414080 | + | 0.136860i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.6981 | − | 8.93484i | 0.511621 | − | 0.359995i | ||||
\(617\) | − | 32.1201i | − | 1.29311i | −0.762869 | − | 0.646554i | \(-0.776210\pi\) | ||
0.762869 | − | 0.646554i | \(-0.223790\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.0412 | + | 15.0412i | 0.604559 | + | 0.604559i | 0.941519 | − | 0.336960i | \(-0.109399\pi\) |
−0.336960 | + | 0.941519i | \(0.609399\pi\) | |||||||
\(620\) | −13.8337 | + | 2.04797i | −0.555573 | + | 0.0822486i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 30.5243 | − | 15.3591i | 1.22391 | − | 0.615845i | ||||
\(623\) | −3.08398 | −0.123557 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.6958 | −0.667833 | ||||||||
\(626\) | −20.9841 | + | 10.5587i | −0.838692 | + | 0.422011i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.52413 | + | 17.0500i | 0.100724 | + | 0.680368i | ||||
\(629\) | −0.824818 | − | 0.824818i | −0.0328876 | − | 0.0328876i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 36.4685i | − | 1.45179i | −0.687807 | − | 0.725894i | \(-0.741426\pi\) | ||
0.687807 | − | 0.725894i | \(-0.258574\pi\) | |||||||
\(632\) | 41.8196 | + | 7.27494i | 1.66350 | + | 0.289382i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.44035 | + | 1.13709i | 0.136634 | + | 0.0451595i | ||||
\(635\) | −10.2475 | − | 10.2475i | −0.406659 | − | 0.406659i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.23648 | − | 3.23648i | 0.128234 | − | 0.128234i | ||||
\(638\) | 4.24494 | + | 8.43625i | 0.168059 | + | 0.333994i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 26.4697 | − | 33.8477i | 1.04631 | − | 1.33795i | ||||
\(641\) | −14.0036 | −0.553109 | −0.276555 | − | 0.960998i | \(-0.589193\pi\) | ||||
−0.276555 | + | 0.960998i | \(0.589193\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.6034 | − | 16.6034i | 0.654774 | − | 0.654774i | −0.299365 | − | 0.954139i | \(-0.596775\pi\) |
0.954139 | + | 0.299365i | \(0.0967748\pi\) | |||||||
\(644\) | −7.27798 | + | 9.80734i | −0.286793 | + | 0.386463i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.0678434 | − | 0.0224232i | −0.00266926 | − | 0.000882230i | ||||
\(647\) | 12.1908i | 0.479270i | 0.970863 | + | 0.239635i | \(0.0770277\pi\) | ||||
−0.970863 | + | 0.239635i | \(0.922972\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.3835i | 0.564600i | ||||||||
\(650\) | 8.18473 | − | 24.7636i | 0.321032 | − | 0.971309i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.42362 | + | 9.61628i | 0.0557533 | + | 0.376603i | ||||
\(653\) | −0.983270 | + | 0.983270i | −0.0384783 | + | 0.0384783i | −0.726084 | − | 0.687606i | \(-0.758662\pi\) |
0.687606 | + | 0.726084i | \(0.258662\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.12198 | 0.161059 | ||||||||
\(656\) | 22.5174 | − | 6.81647i | 0.879157 | − | 0.266138i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.71423 | − | 3.88163i | 0.300732 | − | 0.151322i | ||||
\(659\) | 18.0559 | − | 18.0559i | 0.703357 | − | 0.703357i | −0.261772 | − | 0.965130i | \(-0.584307\pi\) |
0.965130 | + | 0.261772i | \(0.0843069\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.55890 | − | 4.55890i | −0.177321 | − | 0.177321i | 0.612866 | − | 0.790187i | \(-0.290017\pi\) |
−0.790187 | + | 0.612866i | \(0.790017\pi\) | |||||||
\(662\) | 8.48889 | − | 25.6839i | 0.329930 | − | 0.998232i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 33.0922 | − | 23.2848i | 1.28423 | − | 0.903627i | ||||
\(665\) | 1.84307i | 0.0714710i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.25272 | − | 5.25272i | −0.203386 | − | 0.203386i | ||||
\(668\) | −34.8554 | − | 25.8661i | −1.34860 | − | 1.00079i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 35.5908 | + | 70.7320i | 1.37499 | + | 2.73261i | ||||
\(671\) | −21.5298 | −0.831148 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.8569 | −0.418504 | −0.209252 | − | 0.977862i | \(-0.567103\pi\) | ||||
−0.209252 | + | 0.977862i | \(0.567103\pi\) | |||||||
\(674\) | 0.715856 | + | 1.42267i | 0.0275737 | + | 0.0547992i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −14.7287 | − | 10.9301i | −0.566489 | − | 0.420389i | ||||
\(677\) | −23.7066 | − | 23.7066i | −0.911120 | − | 0.911120i | 0.0852405 | − | 0.996360i | \(-0.472834\pi\) |
−0.996360 | + | 0.0852405i | \(0.972834\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 35.4045i | − | 1.35870i | ||||||
\(680\) | 1.38950 | + | 1.97474i | 0.0532847 | + | 0.0757277i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.07754 | + | 6.28577i | −0.0795530 | + | 0.240694i | ||||
\(683\) | 17.8337 | + | 17.8337i | 0.682386 | + | 0.682386i | 0.960537 | − | 0.278151i | \(-0.0897217\pi\) |
−0.278151 | + | 0.960537i | \(0.589722\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.2605 | − | 14.2605i | 0.544866 | − | 0.544866i | ||||
\(686\) | 25.4710 | − | 12.8165i | 0.972489 | − | 0.489335i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −20.7013 | + | 38.6761i | −0.789231 | + | 1.47451i | ||||
\(689\) | −20.7945 | −0.792205 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.8557 | − | 10.8557i | 0.412970 | − | 0.412970i | −0.469802 | − | 0.882772i | \(-0.655675\pi\) |
0.882772 | + | 0.469802i | \(0.155675\pi\) | |||||||
\(692\) | 3.62293 | + | 24.4722i | 0.137723 | + | 0.930294i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.0509 | + | 39.4866i | −0.495406 | + | 1.49889i | ||||
\(695\) | 47.0907i | 1.78625i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.32206i | 0.0500765i | ||||||||
\(698\) | 36.6225 | + | 12.1043i | 1.38618 | + | 0.458154i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 24.2502 | − | 32.6780i | 0.916570 | − | 1.23511i | ||||
\(701\) | 6.08875 | − | 6.08875i | 0.229969 | − | 0.229969i | −0.582711 | − | 0.812680i | \(-0.698008\pi\) |
0.812680 | + | 0.582711i | \(0.198008\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.16647 | −0.0439942 | ||||||||
\(704\) | −8.68119 | − | 18.3958i | −0.327185 | − | 0.693317i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.2672 | + | 32.3288i | 0.612222 | + | 1.21671i | ||||
\(707\) | 0.176805 | − | 0.176805i | 0.00664943 | − | 0.00664943i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.8836 | + | 22.8836i | 0.859413 | + | 0.859413i | 0.991269 | − | 0.131856i | \(-0.0420936\pi\) |
−0.131856 | + | 0.991269i | \(0.542094\pi\) | |||||||
\(710\) | 22.0202 | + | 7.27798i | 0.826402 | + | 0.273138i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.692453 | + | 3.98053i | −0.0259508 | + | 0.149177i | ||||
\(713\) | − | 5.20730i | − | 0.195015i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.3624 | − | 13.3624i | −0.499724 | − | 0.499724i | ||||
\(716\) | −3.40965 | − | 23.0316i | −0.127425 | − | 0.860729i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.76638 | + | 2.39834i | −0.177880 | + | 0.0895052i | ||||
\(719\) | 1.46744 | 0.0547262 | 0.0273631 | − | 0.999626i | \(-0.491289\pi\) | ||||
0.0273631 | + | 0.999626i | \(0.491289\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.8233 | −1.07344 | ||||||||
\(722\) | 23.9389 | − | 12.0455i | 0.890913 | − | 0.448288i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −18.8096 | + | 2.78463i | −0.699055 | + | 0.103490i | ||||
\(725\) | 17.5020 | + | 17.5020i | 0.650008 | + | 0.650008i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.3928i | 0.570889i | 0.958395 | + | 0.285445i | \(0.0921412\pi\) | ||||
−0.958395 | + | 0.285445i | \(0.907859\pi\) | |||||||
\(728\) | 6.87640 | + | 9.77267i | 0.254856 | + | 0.362199i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −30.4697 | − | 10.0707i | −1.12773 | − | 0.372733i | ||||
\(731\) | −1.74311 | − | 1.74311i | −0.0644711 | − | 0.0644711i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.4185 | + | 12.4185i | −0.458688 | + | 0.458688i | −0.898225 | − | 0.439536i | \(-0.855143\pi\) |
0.439536 | + | 0.898225i | \(0.355143\pi\) | |||||||
\(734\) | 17.4473 | + | 34.6743i | 0.643993 | + | 1.27985i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.0243 | + | 11.5959i | 0.406362 | + | 0.427429i | ||||
\(737\) | 37.4844 | 1.38075 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.6559 | + | 14.6559i | −0.539127 | + | 0.539127i | −0.923273 | − | 0.384146i | \(-0.874496\pi\) |
0.384146 | + | 0.923273i | \(0.374496\pi\) | |||||||
\(740\) | 31.6543 | + | 23.4905i | 1.16364 | + | 0.863528i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −30.8055 | − | 10.1817i | −1.13090 | − | 0.373780i | ||||
\(743\) | 31.7821i | 1.16597i | 0.812482 | + | 0.582986i | \(0.198116\pi\) | ||||
−0.812482 | + | 0.582986i | \(0.801884\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.52518i | 0.202427i | ||||||||
\(746\) | 7.92273 | − | 23.9709i | 0.290072 | − | 0.877637i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.13074 | − | 0.167398i | 0.0413440 | − | 0.00612068i | ||||
\(749\) | −15.7127 | + | 15.7127i | −0.574131 | + | 0.574131i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.7594 | 1.08594 | 0.542968 | − | 0.839753i | \(-0.317301\pi\) | ||||
0.542968 | + | 0.839753i | \(0.317301\pi\) | |||||||
\(752\) | −3.27798 | − | 10.8284i | −0.119536 | − | 0.394872i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.49268 | + | 3.26697i | −0.236449 | + | 0.118976i | ||||
\(755\) | 5.47036 | − | 5.47036i | 0.199087 | − | 0.199087i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.6355 | + | 15.6355i | 0.568282 | + | 0.568282i | 0.931647 | − | 0.363365i | \(-0.118372\pi\) |
−0.363365 | + | 0.931647i | \(0.618372\pi\) | |||||||
\(758\) | −7.32361 | + | 22.1582i | −0.266005 | + | 0.804822i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.37887 | + | 0.413828i | 0.0862908 | + | 0.0150111i | ||||
\(761\) | 4.55957i | 0.165284i | 0.996579 | + | 0.0826422i | \(0.0263359\pi\) | ||||
−0.996579 | + | 0.0826422i | \(0.973664\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.2002 | − | 15.2002i | −0.550284 | − | 0.550284i | ||||
\(764\) | −24.7945 | + | 33.4114i | −0.897032 | + | 1.20878i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.9261 | − | 21.7142i | −0.394777 | − | 0.784567i | ||||
\(767\) | −11.0698 | −0.399706 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.5794 | 1.31909 | 0.659543 | − | 0.751667i | \(-0.270750\pi\) | ||||
0.659543 | + | 0.751667i | \(0.270750\pi\) | |||||||
\(770\) | −13.2527 | − | 26.3380i | −0.477595 | − | 0.949157i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16.8593 | + | 22.7185i | −0.606780 | + | 0.817657i | ||||
\(773\) | 18.7108 | + | 18.7108i | 0.672981 | + | 0.672981i | 0.958402 | − | 0.285421i | \(-0.0921335\pi\) |
−0.285421 | + | 0.958402i | \(0.592133\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.3507i | 0.623255i | ||||||||
\(776\) | −45.6972 | − | 7.94948i | −1.64043 | − | 0.285370i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.18145 | − | 3.57457i | 0.0423570 | − | 0.128155i | ||||
\(779\) | 0.934836 | + | 0.934836i | 0.0334940 | + | 0.0334940i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.76326 | − | 7.76326i | 0.277791 | − | 0.277791i | ||||
\(782\) | −0.803165 | + | 0.404135i | −0.0287211 | + | 0.0144518i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.71073 | − | 8.95458i | −0.0968118 | − | 0.319806i | ||||
\(785\) | 32.7302 | 1.16819 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.3759 | − | 13.3759i | 0.476801 | − | 0.476801i | −0.427306 | − | 0.904107i | \(-0.640537\pi\) |
0.904107 | + | 0.427306i | \(0.140537\pi\) | |||||||
\(788\) | −6.79520 | + | 1.00598i | −0.242069 | + | 0.0358365i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 25.2958 | − | 76.5347i | 0.899986 | − | 2.72298i | ||||
\(791\) | − | 40.6930i | − | 1.44688i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 16.5697i | − | 0.588406i | ||||||
\(794\) | −15.9735 | − | 5.27946i | −0.566877 | − | 0.187361i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.491751 | − | 0.364926i | −0.0174296 | − | 0.0129345i | ||||
\(797\) | 33.8043 | − | 33.8043i | 1.19741 | − | 1.19741i | 0.222471 | − | 0.974939i | \(-0.428588\pi\) |
0.974939 | − | 0.222471i | \(-0.0714124\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.635767 | 0.0224918 | ||||||||
\(800\) | −36.7330 | − | 38.6373i | −1.29871 | − | 1.36604i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.714416 | + | 1.41981i | 0.0252269 | + | 0.0501352i | ||||
\(803\) | −10.7422 | + | 10.7422i | −0.379083 | + | 0.379083i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.3990 | + | 16.3990i | 0.577990 | + | 0.577990i | ||||
\(806\) | −4.83763 | − | 1.59891i | −0.170398 | − | 0.0563191i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.188506 | − | 0.267903i | −0.00663163 | − | 0.00942480i | ||||
\(809\) | 29.9862i | 1.05426i | 0.849785 | + | 0.527129i | \(0.176732\pi\) | ||||
−0.849785 | + | 0.527129i | \(0.823268\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.05388 | − | 8.05388i | −0.282810 | − | 0.282810i | 0.551419 | − | 0.834229i | \(-0.314087\pi\) |
−0.834229 | + | 0.551419i | \(0.814087\pi\) | |||||||
\(812\) | −11.2181 | + | 1.66075i | −0.393676 | + | 0.0582809i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 16.6692 | − | 8.38759i | 0.584256 | − | 0.293985i | ||||
\(815\) | 18.4600 | 0.646626 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.46512 | −0.0862438 | ||||||||
\(818\) | 17.3339 | − | 8.72202i | 0.606064 | − | 0.304958i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.54266 | − | 44.1944i | −0.228480 | − | 1.54334i | ||||
\(821\) | −13.9250 | − | 13.9250i | −0.485984 | − | 0.485984i | 0.421052 | − | 0.907036i | \(-0.361661\pi\) |
−0.907036 | + | 0.421052i | \(0.861661\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 22.4666i | − | 0.783137i | −0.920149 | − | 0.391568i | \(-0.871933\pi\) | ||
0.920149 | − | 0.391568i | \(-0.128067\pi\) | |||||||
\(824\) | −6.47178 | + | 37.2027i | −0.225455 | + | 1.29602i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.3990 | − | 5.42012i | −0.570595 | − | 0.188590i | ||||
\(827\) | −7.63159 | − | 7.63159i | −0.265376 | − | 0.265376i | 0.561858 | − | 0.827234i | \(-0.310087\pi\) |
−0.827234 | + | 0.561858i | \(0.810087\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.4860 | + | 32.4860i | −1.12828 | + | 1.12828i | −0.137828 | + | 0.990456i | \(0.544012\pi\) |
−0.990456 | + | 0.137828i | \(0.955988\pi\) | |||||||
\(830\) | −34.5376 | − | 68.6389i | −1.19882 | − | 2.38249i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 14.1577 | − | 6.68119i | 0.490830 | − | 0.231628i | ||||
\(833\) | 0.525748 | 0.0182161 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −58.2824 | + | 58.2824i | −2.01695 | + | 2.01695i | ||||
\(836\) | 0.681187 | − | 0.917923i | 0.0235593 | − | 0.0317470i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −17.6747 | − | 5.84175i | −0.610563 | − | 0.201800i | ||||
\(839\) | − | 22.9142i | − | 0.791085i | −0.918448 | − | 0.395542i | \(-0.870557\pi\) | ||
0.918448 | − | 0.395542i | \(-0.129443\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.1022i | 0.762146i | ||||||||
\(842\) | 5.29962 | − | 16.0345i | 0.182637 | − | 0.552584i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.99583 | + | 20.2362i | 0.103121 | + | 0.696559i | ||||
\(845\) | −24.6282 | + | 24.6282i | −0.847235 | + | 0.847235i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.79053 | 0.336407 | ||||||||
\(848\) | −20.0584 | + | 37.4749i | −0.688810 | + | 1.28689i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.67614 | − | 1.34657i | 0.0917907 | − | 0.0461871i | ||||
\(851\) | −10.3789 | + | 10.3789i | −0.355783 | + | 0.355783i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.9424 | + | 38.9424i | 1.33336 | + | 1.33336i | 0.902344 | + | 0.431018i | \(0.141845\pi\) |
0.431018 | + | 0.902344i | \(0.358155\pi\) | |||||||
\(854\) | 8.11306 | − | 24.5468i | 0.277623 | − | 0.839973i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.7526 | + | 23.8087i | 0.572593 | + | 0.813764i | ||||
\(857\) | 1.79079i | 0.0611723i | 0.999532 | + | 0.0305861i | \(0.00973739\pi\) | ||||
−0.999532 | + | 0.0305861i | \(0.990263\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.0643 | + | 18.0643i | 0.616347 | + | 0.616347i | 0.944593 | − | 0.328245i | \(-0.106457\pi\) |
−0.328245 | + | 0.944593i | \(0.606457\pi\) | |||||||
\(860\) | 66.8958 | + | 49.6430i | 2.28113 | + | 1.69281i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19.4548 | − | 38.6638i | −0.662633 | − | 1.31690i | ||||
\(863\) | −42.1150 | −1.43361 | −0.716806 | − | 0.697273i | \(-0.754397\pi\) | ||||
−0.716806 | + | 0.697273i | \(0.754397\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 46.9784 | 1.59731 | ||||||||
\(866\) | 9.73439 | + | 19.3458i | 0.330788 | + | 0.657398i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.38372 | − | 4.73733i | −0.216678 | − | 0.160795i | ||||
\(869\) | −26.9825 | − | 26.9825i | −0.915319 | − | 0.915319i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.8486i | 0.977497i | ||||||||
\(872\) | −23.0320 | + | 16.2062i | −0.779963 | + | 0.548810i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.282157 | + | 0.853690i | −0.00954410 | + | 0.0288765i | ||||
\(875\) | −25.6517 | − | 25.6517i | −0.867187 | − | 0.867187i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.714491 | − | 0.714491i | 0.0241267 | − | 0.0241267i | −0.694941 | − | 0.719067i | \(-0.744569\pi\) |
0.719067 | + | 0.694941i | \(0.244569\pi\) | |||||||
\(878\) | −42.1533 | + | 21.2106i | −1.42261 | + | 0.715823i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −36.9706 | + | 11.1917i | −1.24628 | + | 0.377273i | ||||
\(881\) | 44.3972 | 1.49578 | 0.747889 | − | 0.663823i | \(-0.231067\pi\) | ||||
0.747889 | + | 0.663823i | \(0.231067\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.28968 | − | 1.28968i | 0.0434013 | − | 0.0434013i | −0.685073 | − | 0.728474i | \(-0.740230\pi\) |
0.728474 | + | 0.685073i | \(0.240230\pi\) | |||||||
\(884\) | 0.128832 | + | 0.870238i | 0.00433310 | + | 0.0292693i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.43623 | + | 4.34544i | −0.0482511 | + | 0.145988i | ||||
\(887\) | 4.38532i | 0.147245i | 0.997286 | + | 0.0736223i | \(0.0234559\pi\) | ||||
−0.997286 | + | 0.0736223i | \(0.976544\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 8.23808i | − | 0.276296i | ||||||
\(890\) | 7.28484 | + | 2.40774i | 0.244188 | + | 0.0807078i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.04890 | − | 2.76097i | 0.0686023 | − | 0.0924441i | ||||
\(893\) | 0.449555 | − | 0.449555i | 0.0150438 | − | 0.0150438i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −44.2128 | −1.47787 | ||||||||
\(896\) | 24.2449 | − | 2.96561i | 0.809966 | − | 0.0990740i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.4277 | − | 34.6353i | −0.581571 | − | 1.15580i | ||||
\(899\) | 3.41906 | − | 3.41906i | 0.114032 | − | 0.114032i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.68897 | − | 1.68897i | −0.0562678 | − | 0.0562678i | ||||
\(902\) | −20.0811 | − | 6.63711i | −0.668629 | − | 0.220992i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −52.5230 | − | 9.13690i | −1.74689 | − | 0.303889i | ||||
\(905\) | 36.1082i | 1.20028i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.87261 | − | 2.87261i | −0.0953835 | − | 0.0953835i | 0.657805 | − | 0.753188i | \(-0.271485\pi\) |
−0.753188 | + | 0.657805i | \(0.771485\pi\) | |||||||
\(908\) | −4.19011 | − | 28.3034i | −0.139054 | − | 0.939280i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 20.2702 | − | 10.1995i | 0.671951 | − | 0.338111i | ||||
\(911\) | −42.3784 | −1.40406 | −0.702029 | − | 0.712149i | \(-0.747722\pi\) | ||||
−0.702029 | + | 0.712149i | \(0.747722\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.3751 | −1.20384 | ||||||||
\(914\) | 13.7885 | − | 6.93808i | 0.456084 | − | 0.229491i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 33.6297 | − | 4.97863i | 1.11116 | − | 0.164499i | ||||
\(917\) | 1.65685 | + | 1.65685i | 0.0547141 | + | 0.0547141i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 44.8603i | − | 1.47980i | −0.672715 | − | 0.739902i | \(-0.734872\pi\) | ||
0.672715 | − | 0.739902i | \(-0.265128\pi\) | |||||||
\(920\) | 24.8486 | − | 17.4844i | 0.819234 | − | 0.576442i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 33.8621 | + | 11.1919i | 1.11519 | + | 0.368586i | ||||
\(923\) | 5.97474 | + | 5.97474i | 0.196661 | + | 0.196661i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.5823 | − | 34.5823i | 1.13706 | − | 1.13706i | ||||
\(926\) | −14.2985 | − | 28.4164i | −0.469877 | − | 0.933820i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.375263 | + | 14.8522i | −0.0123186 | + | 0.487547i | ||||
\(929\) | 2.96695 | 0.0973426 | 0.0486713 | − | 0.998815i | \(-0.484501\pi\) | ||||
0.0486713 | + | 0.998815i | \(0.484501\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.371760 | − | 0.371760i | 0.0121839 | − | 0.0121839i | ||||
\(932\) | −21.4860 | − | 15.9446i | −0.703796 | − | 0.522284i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 45.9875 | + | 15.1995i | 1.50476 | + | 0.497344i | ||||
\(935\) | − | 2.17064i | − | 0.0709876i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 54.7669i | − | 1.78916i | −0.446910 | − | 0.894579i | \(-0.647476\pi\) | ||
0.446910 | − | 0.894579i | \(-0.352524\pi\) | |||||||
\(938\) | −14.1252 | + | 42.7371i | −0.461205 | + | 1.39541i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −21.2527 | + | 3.14631i | −0.693187 | + | 0.102621i | ||||
\(941\) | 6.29012 | − | 6.29012i | 0.205052 | − | 0.205052i | −0.597108 | − | 0.802161i | \(-0.703684\pi\) |
0.802161 | + | 0.597108i | \(0.203684\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.6358 | 0.541735 | ||||||||
\(944\) | −10.6779 | + | 19.9495i | −0.347537 | + | 0.649300i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35.2275 | − | 17.7257i | 1.14534 | − | 0.576311i | ||||
\(947\) | 11.2105 | − | 11.2105i | 0.364294 | − | 0.364294i | −0.501097 | − | 0.865391i | \(-0.667070\pi\) |
0.865391 | + | 0.501097i | \(0.167070\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.26736 | − | 8.26736i | −0.268370 | − | 0.268370i | ||||
\(950\) | 0.940144 | − | 2.84449i | 0.0305023 | − | 0.0922873i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.235241 | + | 1.35227i | −0.00762422 | + | 0.0438275i | ||||
\(953\) | 30.2807i | 0.980887i | 0.871473 | + | 0.490443i | \(0.163165\pi\) | ||||
−0.871473 | + | 0.490443i | \(0.836835\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 55.8678 | + | 55.8678i | 1.80784 | + | 1.80784i | ||||
\(956\) | 15.9322 | − | 21.4691i | 0.515283 | − | 0.694362i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −23.0341 | − | 45.7773i | −0.744198 | − | 1.47900i | ||||
\(959\) | 11.4642 | 0.370198 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.6105 | −0.890661 | ||||||||
\(962\) | 6.45523 | + | 12.8289i | 0.208125 | + | 0.413621i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.252048 | + | 0.339643i | −0.00811790 | + | 0.0109392i | ||||
\(965\) | 37.9880 | + | 37.9880i | 1.22288 | + | 1.22288i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 10.5273i | − | 0.338537i | −0.985570 | − | 0.169268i | \(-0.945860\pi\) | ||
0.985570 | − | 0.169268i | \(-0.0541405\pi\) | |||||||
\(968\) | 2.19829 | − | 12.6368i | 0.0706558 | − | 0.406162i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −27.6413 | + | 83.6311i | −0.887508 | + | 2.68523i | ||||
\(971\) | −27.3685 | − | 27.3685i | −0.878298 | − | 0.878298i | 0.115060 | − | 0.993358i | \(-0.463294\pi\) |
−0.993358 | + | 0.115060i | \(0.963294\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.9284 | + | 18.9284i | −0.606816 | + | 0.606816i | ||||
\(974\) | 21.2487 | − | 10.6919i | 0.680852 | − | 0.342590i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −29.8612 | − | 15.9832i | −0.955834 | − | 0.511610i | ||||
\(977\) | 16.9009 | 0.540706 | 0.270353 | − | 0.962761i | \(-0.412860\pi\) | ||||
0.270353 | + | 0.962761i | \(0.412860\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.56829 | − | 2.56829i | 0.0820828 | − | 0.0820828i | ||||
\(980\) | −17.5750 | + | 2.60184i | −0.561412 | + | 0.0831129i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.83260 | + | 11.5959i | −0.122303 | + | 0.370039i | ||||
\(983\) | − | 10.0798i | − | 0.321496i | −0.986995 | − | 0.160748i | \(-0.948609\pi\) | ||
0.986995 | − | 0.160748i | \(-0.0513906\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.0445i | 0.415632i | ||||||||
\(986\) | −0.792701 | − | 0.261999i | −0.0252447 | − | 0.00834375i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.706449 | + | 0.524253i | 0.0224751 | + | 0.0166787i | ||||
\(989\) | −21.9339 | + | 21.9339i | −0.697458 | + | 0.697458i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.3446 | −1.34512 | −0.672561 | − | 0.740042i | \(-0.734806\pi\) | ||||
−0.672561 | + | 0.740042i | \(0.734806\pi\) | |||||||
\(992\) | −7.54789 | + | 7.17587i | −0.239646 | + | 0.227834i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.92571 | + | 11.7766i | 0.187952 | + | 0.373530i | ||||
\(995\) | −0.822265 | + | 0.822265i | −0.0260676 | + | 0.0260676i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.6676 | − | 33.6676i | −1.06626 | − | 1.06626i | −0.997643 | − | 0.0686216i | \(-0.978140\pi\) |
−0.0686216 | − | 0.997643i | \(-0.521860\pi\) | |||||||
\(998\) | 37.3660 | + | 12.3500i | 1.18280 | + | 0.390932i | ||||
\(999\) | 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.37.2 | 8 | ||
3.2 | odd | 2 | 48.2.j.a.37.3 | yes | 8 | ||
4.3 | odd | 2 | 576.2.k.b.433.4 | 8 | |||
8.3 | odd | 2 | 1152.2.k.f.865.1 | 8 | |||
8.5 | even | 2 | 1152.2.k.c.865.1 | 8 | |||
12.11 | even | 2 | 192.2.j.a.49.1 | 8 | |||
16.3 | odd | 4 | 576.2.k.b.145.4 | 8 | |||
16.5 | even | 4 | 1152.2.k.c.289.1 | 8 | |||
16.11 | odd | 4 | 1152.2.k.f.289.1 | 8 | |||
16.13 | even | 4 | inner | 144.2.k.b.109.2 | 8 | ||
24.5 | odd | 2 | 384.2.j.b.97.2 | 8 | |||
24.11 | even | 2 | 384.2.j.a.97.4 | 8 | |||
32.3 | odd | 8 | 9216.2.a.x.1.1 | 4 | |||
32.13 | even | 8 | 9216.2.a.bo.1.4 | 4 | |||
32.19 | odd | 8 | 9216.2.a.bn.1.4 | 4 | |||
32.29 | even | 8 | 9216.2.a.y.1.1 | 4 | |||
48.5 | odd | 4 | 384.2.j.b.289.2 | 8 | |||
48.11 | even | 4 | 384.2.j.a.289.4 | 8 | |||
48.29 | odd | 4 | 48.2.j.a.13.3 | ✓ | 8 | ||
48.35 | even | 4 | 192.2.j.a.145.1 | 8 | |||
96.5 | odd | 8 | 3072.2.d.f.1537.5 | 8 | |||
96.11 | even | 8 | 3072.2.d.i.1537.8 | 8 | |||
96.29 | odd | 8 | 3072.2.a.t.1.4 | 4 | |||
96.35 | even | 8 | 3072.2.a.n.1.4 | 4 | |||
96.53 | odd | 8 | 3072.2.d.f.1537.4 | 8 | |||
96.59 | even | 8 | 3072.2.d.i.1537.1 | 8 | |||
96.77 | odd | 8 | 3072.2.a.i.1.1 | 4 | |||
96.83 | even | 8 | 3072.2.a.o.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.j.a.13.3 | ✓ | 8 | 48.29 | odd | 4 | ||
48.2.j.a.37.3 | yes | 8 | 3.2 | odd | 2 | ||
144.2.k.b.37.2 | 8 | 1.1 | even | 1 | trivial | ||
144.2.k.b.109.2 | 8 | 16.13 | even | 4 | inner | ||
192.2.j.a.49.1 | 8 | 12.11 | even | 2 | |||
192.2.j.a.145.1 | 8 | 48.35 | even | 4 | |||
384.2.j.a.97.4 | 8 | 24.11 | even | 2 | |||
384.2.j.a.289.4 | 8 | 48.11 | even | 4 | |||
384.2.j.b.97.2 | 8 | 24.5 | odd | 2 | |||
384.2.j.b.289.2 | 8 | 48.5 | odd | 4 | |||
576.2.k.b.145.4 | 8 | 16.3 | odd | 4 | |||
576.2.k.b.433.4 | 8 | 4.3 | odd | 2 | |||
1152.2.k.c.289.1 | 8 | 16.5 | even | 4 | |||
1152.2.k.c.865.1 | 8 | 8.5 | even | 2 | |||
1152.2.k.f.289.1 | 8 | 16.11 | odd | 4 | |||
1152.2.k.f.865.1 | 8 | 8.3 | odd | 2 | |||
3072.2.a.i.1.1 | 4 | 96.77 | odd | 8 | |||
3072.2.a.n.1.4 | 4 | 96.35 | even | 8 | |||
3072.2.a.o.1.1 | 4 | 96.83 | even | 8 | |||
3072.2.a.t.1.4 | 4 | 96.29 | odd | 8 | |||
3072.2.d.f.1537.4 | 8 | 96.53 | odd | 8 | |||
3072.2.d.f.1537.5 | 8 | 96.5 | odd | 8 | |||
3072.2.d.i.1537.1 | 8 | 96.59 | even | 8 | |||
3072.2.d.i.1537.8 | 8 | 96.11 | even | 8 | |||
9216.2.a.x.1.1 | 4 | 32.3 | odd | 8 | |||
9216.2.a.y.1.1 | 4 | 32.29 | even | 8 | |||
9216.2.a.bn.1.4 | 4 | 32.19 | odd | 8 | |||
9216.2.a.bo.1.4 | 4 | 32.13 | even | 8 |