Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,2,Mod(11,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.e (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: | \(0.295446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 27.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 37.27 |
Dual form | 37.2.e.a.11.1 |
$q$-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 \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | 0.161521 | − | 0.986869i | \(-0.448360\pi\) |
−0.773893 | + | 0.633316i | \(0.781693\pi\) | |||||||
\(3\) | 1.36603 | + | 2.36603i | 0.788675 | + | 1.36603i | 0.926779 | + | 0.375608i | \(0.122566\pi\) |
−0.138104 | + | 0.990418i | \(0.544101\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.232051 | − | 0.133975i | 0.103776 | − | 0.0599153i | −0.447214 | − | 0.894427i | \(-0.647584\pi\) |
0.550990 | + | 0.834512i | \(0.314250\pi\) | |||||||
\(6\) | − | 2.73205i | − | 1.11536i | ||||||
\(7\) | −1.73205 | − | 3.00000i | −0.654654 | − | 1.13389i | −0.981981 | − | 0.188982i | \(-0.939481\pi\) |
0.327327 | − | 0.944911i | \(-0.393852\pi\) | |||||||
\(8\) | 3.00000i | 1.06066i | ||||||||
\(9\) | −2.23205 | + | 3.86603i | −0.744017 | + | 1.28868i | ||||
\(10\) | −0.267949 | −0.0847330 | ||||||||
\(11\) | −4.73205 | −1.42677 | −0.713384 | − | 0.700774i | \(-0.752838\pi\) | ||||
−0.713384 | + | 0.700774i | \(0.752838\pi\) | |||||||
\(12\) | 1.36603 | − | 2.36603i | 0.394338 | − | 0.683013i | ||||
\(13\) | 3.00000 | − | 1.73205i | 0.832050 | − | 0.480384i | −0.0225039 | − | 0.999747i | \(-0.507164\pi\) |
0.854554 | + | 0.519362i | \(0.173830\pi\) | |||||||
\(14\) | 3.46410i | 0.925820i | ||||||||
\(15\) | 0.633975 | + | 0.366025i | 0.163692 | + | 0.0945074i | ||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 3.23205 | + | 1.86603i | 0.783887 | + | 0.452578i | 0.837806 | − | 0.545968i | \(-0.183838\pi\) |
−0.0539188 | + | 0.998545i | \(0.517171\pi\) | |||||||
\(18\) | 3.86603 | − | 2.23205i | 0.911231 | − | 0.526099i | ||||
\(19\) | 1.09808 | − | 0.633975i | 0.251916 | − | 0.145444i | −0.368725 | − | 0.929538i | \(-0.620206\pi\) |
0.620641 | + | 0.784095i | \(0.286872\pi\) | |||||||
\(20\) | −0.232051 | − | 0.133975i | −0.0518881 | − | 0.0299576i | ||||
\(21\) | 4.73205 | − | 8.19615i | 1.03262 | − | 1.78855i | ||||
\(22\) | 4.09808 | + | 2.36603i | 0.873713 | + | 0.504438i | ||||
\(23\) | 0.732051i | 0.152643i | 0.997083 | + | 0.0763216i | \(0.0243176\pi\) | ||||
−0.997083 | + | 0.0763216i | \(0.975682\pi\) | |||||||
\(24\) | −7.09808 | + | 4.09808i | −1.44889 | + | 0.836516i | ||||
\(25\) | −2.46410 | + | 4.26795i | −0.492820 | + | 0.853590i | ||||
\(26\) | −3.46410 | −0.679366 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | −1.73205 | + | 3.00000i | −0.327327 | + | 0.566947i | ||||
\(29\) | − | 0.267949i | − | 0.0497569i | −0.999690 | − | 0.0248785i | \(-0.992080\pi\) | ||
0.999690 | − | 0.0248785i | \(-0.00791988\pi\) | |||||||
\(30\) | −0.366025 | − | 0.633975i | −0.0668268 | − | 0.115747i | ||||
\(31\) | 8.19615i | 1.47207i | 0.676942 | + | 0.736036i | \(0.263305\pi\) | ||||
−0.676942 | + | 0.736036i | \(0.736695\pi\) | |||||||
\(32\) | 4.33013 | − | 2.50000i | 0.765466 | − | 0.441942i | ||||
\(33\) | −6.46410 | − | 11.1962i | −1.12526 | − | 1.94900i | ||||
\(34\) | −1.86603 | − | 3.23205i | −0.320021 | − | 0.554292i | ||||
\(35\) | −0.803848 | − | 0.464102i | −0.135875 | − | 0.0784475i | ||||
\(36\) | 4.46410 | 0.744017 | ||||||||
\(37\) | 0.500000 | − | 6.06218i | 0.0821995 | − | 0.996616i | ||||
\(38\) | −1.26795 | −0.205689 | ||||||||
\(39\) | 8.19615 | + | 4.73205i | 1.31243 | + | 0.757735i | ||||
\(40\) | 0.401924 | + | 0.696152i | 0.0635497 | + | 0.110071i | ||||
\(41\) | −1.50000 | − | 2.59808i | −0.234261 | − | 0.405751i | 0.724797 | − | 0.688963i | \(-0.241934\pi\) |
−0.959058 | + | 0.283211i | \(0.908600\pi\) | |||||||
\(42\) | −8.19615 | + | 4.73205i | −1.26469 | + | 0.730171i | ||||
\(43\) | − | 3.46410i | − | 0.528271i | −0.964486 | − | 0.264135i | \(-0.914913\pi\) | ||
0.964486 | − | 0.264135i | \(-0.0850865\pi\) | |||||||
\(44\) | 2.36603 | + | 4.09808i | 0.356692 | + | 0.617808i | ||||
\(45\) | 1.19615i | 0.178312i | ||||||||
\(46\) | 0.366025 | − | 0.633975i | 0.0539675 | − | 0.0934745i | ||||
\(47\) | −2.19615 | −0.320342 | −0.160171 | − | 0.987089i | \(-0.551205\pi\) | ||||
−0.160171 | + | 0.987089i | \(0.551205\pi\) | |||||||
\(48\) | 2.73205 | 0.394338 | ||||||||
\(49\) | −2.50000 | + | 4.33013i | −0.357143 | + | 0.618590i | ||||
\(50\) | 4.26795 | − | 2.46410i | 0.603579 | − | 0.348477i | ||||
\(51\) | 10.1962i | 1.42775i | ||||||||
\(52\) | −3.00000 | − | 1.73205i | −0.416025 | − | 0.240192i | ||||
\(53\) | 1.26795 | − | 2.19615i | 0.174166 | − | 0.301665i | −0.765706 | − | 0.643191i | \(-0.777610\pi\) |
0.939872 | + | 0.341526i | \(0.110944\pi\) | |||||||
\(54\) | 3.46410 | + | 2.00000i | 0.471405 | + | 0.272166i | ||||
\(55\) | −1.09808 | + | 0.633975i | −0.148065 | + | 0.0854851i | ||||
\(56\) | 9.00000 | − | 5.19615i | 1.20268 | − | 0.694365i | ||||
\(57\) | 3.00000 | + | 1.73205i | 0.397360 | + | 0.229416i | ||||
\(58\) | −0.133975 | + | 0.232051i | −0.0175917 | + | 0.0304698i | ||||
\(59\) | −11.6603 | − | 6.73205i | −1.51804 | − | 0.876438i | −0.999775 | − | 0.0212158i | \(-0.993246\pi\) |
−0.518261 | − | 0.855223i | \(-0.673420\pi\) | |||||||
\(60\) | − | 0.732051i | − | 0.0945074i | ||||||
\(61\) | 3.69615 | − | 2.13397i | 0.473244 | − | 0.273227i | −0.244353 | − | 0.969686i | \(-0.578576\pi\) |
0.717597 | + | 0.696459i | \(0.245242\pi\) | |||||||
\(62\) | 4.09808 | − | 7.09808i | 0.520456 | − | 0.901457i | ||||
\(63\) | 15.4641 | 1.94829 | ||||||||
\(64\) | −7.00000 | −0.875000 | ||||||||
\(65\) | 0.464102 | − | 0.803848i | 0.0575647 | − | 0.0997050i | ||||
\(66\) | 12.9282i | 1.59135i | ||||||||
\(67\) | 3.63397 | + | 6.29423i | 0.443961 | + | 0.768962i | 0.997979 | − | 0.0635419i | \(-0.0202397\pi\) |
−0.554019 | + | 0.832504i | \(0.686906\pi\) | |||||||
\(68\) | − | 3.73205i | − | 0.452578i | ||||||
\(69\) | −1.73205 | + | 1.00000i | −0.208514 | + | 0.120386i | ||||
\(70\) | 0.464102 | + | 0.803848i | 0.0554708 | + | 0.0960782i | ||||
\(71\) | −3.00000 | − | 5.19615i | −0.356034 | − | 0.616670i | 0.631260 | − | 0.775571i | \(-0.282538\pi\) |
−0.987294 | + | 0.158901i | \(0.949205\pi\) | |||||||
\(72\) | −11.5981 | − | 6.69615i | −1.36685 | − | 0.789149i | ||||
\(73\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(74\) | −3.46410 | + | 5.00000i | −0.402694 | + | 0.581238i | ||||
\(75\) | −13.4641 | −1.55470 | ||||||||
\(76\) | −1.09808 | − | 0.633975i | −0.125958 | − | 0.0727219i | ||||
\(77\) | 8.19615 | + | 14.1962i | 0.934038 | + | 1.61780i | ||||
\(78\) | −4.73205 | − | 8.19615i | −0.535799 | − | 0.928032i | ||||
\(79\) | 3.29423 | − | 1.90192i | 0.370630 | − | 0.213983i | −0.303104 | − | 0.952958i | \(-0.598023\pi\) |
0.673734 | + | 0.738974i | \(0.264690\pi\) | |||||||
\(80\) | − | 0.267949i | − | 0.0299576i | ||||||
\(81\) | 1.23205 | + | 2.13397i | 0.136895 | + | 0.237108i | ||||
\(82\) | 3.00000i | 0.331295i | ||||||||
\(83\) | 4.09808 | − | 7.09808i | 0.449822 | − | 0.779115i | −0.548552 | − | 0.836117i | \(-0.684821\pi\) |
0.998374 | + | 0.0570015i | \(0.0181540\pi\) | |||||||
\(84\) | −9.46410 | −1.03262 | ||||||||
\(85\) | 1.00000 | 0.108465 | ||||||||
\(86\) | −1.73205 | + | 3.00000i | −0.186772 | + | 0.323498i | ||||
\(87\) | 0.633975 | − | 0.366025i | 0.0679692 | − | 0.0392420i | ||||
\(88\) | − | 14.1962i | − | 1.51331i | ||||||
\(89\) | 7.96410 | + | 4.59808i | 0.844193 | + | 0.487395i | 0.858687 | − | 0.512500i | \(-0.171280\pi\) |
−0.0144942 | + | 0.999895i | \(0.504614\pi\) | |||||||
\(90\) | 0.598076 | − | 1.03590i | 0.0630428 | − | 0.109193i | ||||
\(91\) | −10.3923 | − | 6.00000i | −1.08941 | − | 0.628971i | ||||
\(92\) | 0.633975 | − | 0.366025i | 0.0660964 | − | 0.0381608i | ||||
\(93\) | −19.3923 | + | 11.1962i | −2.01089 | + | 1.16099i | ||||
\(94\) | 1.90192 | + | 1.09808i | 0.196168 | + | 0.113258i | ||||
\(95\) | 0.169873 | − | 0.294229i | 0.0174286 | − | 0.0301872i | ||||
\(96\) | 11.8301 | + | 6.83013i | 1.20741 | + | 0.697097i | ||||
\(97\) | 4.26795i | 0.433345i | 0.976244 | + | 0.216672i | \(0.0695203\pi\) | ||||
−0.976244 | + | 0.216672i | \(0.930480\pi\) | |||||||
\(98\) | 4.33013 | − | 2.50000i | 0.437409 | − | 0.252538i | ||||
\(99\) | 10.5622 | − | 18.2942i | 1.06154 | − | 1.83864i | ||||
\(100\) | 4.92820 | 0.492820 | ||||||||
\(101\) | −9.00000 | −0.895533 | −0.447767 | − | 0.894150i | \(-0.647781\pi\) | ||||
−0.447767 | + | 0.894150i | \(0.647781\pi\) | |||||||
\(102\) | 5.09808 | − | 8.83013i | 0.504785 | − | 0.874313i | ||||
\(103\) | 12.9282i | 1.27385i | 0.770924 | + | 0.636927i | \(0.219795\pi\) | ||||
−0.770924 | + | 0.636927i | \(0.780205\pi\) | |||||||
\(104\) | 5.19615 | + | 9.00000i | 0.509525 | + | 0.882523i | ||||
\(105\) | − | 2.53590i | − | 0.247478i | ||||||
\(106\) | −2.19615 | + | 1.26795i | −0.213309 | + | 0.123154i | ||||
\(107\) | 6.46410 | + | 11.1962i | 0.624908 | + | 1.08237i | 0.988559 | + | 0.150837i | \(0.0481970\pi\) |
−0.363650 | + | 0.931536i | \(0.618470\pi\) | |||||||
\(108\) | 2.00000 | + | 3.46410i | 0.192450 | + | 0.333333i | ||||
\(109\) | −5.89230 | − | 3.40192i | −0.564380 | − | 0.325845i | 0.190521 | − | 0.981683i | \(-0.438982\pi\) |
−0.754902 | + | 0.655838i | \(0.772315\pi\) | |||||||
\(110\) | 1.26795 | 0.120894 | ||||||||
\(111\) | 15.0263 | − | 7.09808i | 1.42623 | − | 0.673720i | ||||
\(112\) | −3.46410 | −0.327327 | ||||||||
\(113\) | −3.92820 | − | 2.26795i | −0.369534 | − | 0.213351i | 0.303721 | − | 0.952761i | \(-0.401771\pi\) |
−0.673255 | + | 0.739410i | \(0.735104\pi\) | |||||||
\(114\) | −1.73205 | − | 3.00000i | −0.162221 | − | 0.280976i | ||||
\(115\) | 0.0980762 | + | 0.169873i | 0.00914565 | + | 0.0158407i | ||||
\(116\) | −0.232051 | + | 0.133975i | −0.0215454 | + | 0.0124392i | ||||
\(117\) | 15.4641i | 1.42966i | ||||||||
\(118\) | 6.73205 | + | 11.6603i | 0.619736 | + | 1.07341i | ||||
\(119\) | − | 12.9282i | − | 1.18513i | ||||||
\(120\) | −1.09808 | + | 1.90192i | −0.100240 | + | 0.173621i | ||||
\(121\) | 11.3923 | 1.03566 | ||||||||
\(122\) | −4.26795 | −0.386402 | ||||||||
\(123\) | 4.09808 | − | 7.09808i | 0.369511 | − | 0.640012i | ||||
\(124\) | 7.09808 | − | 4.09808i | 0.637426 | − | 0.368018i | ||||
\(125\) | 2.66025i | 0.237940i | ||||||||
\(126\) | −13.3923 | − | 7.73205i | −1.19308 | − | 0.688826i | ||||
\(127\) | 6.09808 | − | 10.5622i | 0.541117 | − | 0.937242i | −0.457723 | − | 0.889095i | \(-0.651335\pi\) |
0.998840 | − | 0.0481471i | \(-0.0153316\pi\) | |||||||
\(128\) | −2.59808 | − | 1.50000i | −0.229640 | − | 0.132583i | ||||
\(129\) | 8.19615 | − | 4.73205i | 0.721631 | − | 0.416634i | ||||
\(130\) | −0.803848 | + | 0.464102i | −0.0705021 | + | 0.0407044i | ||||
\(131\) | −9.16987 | − | 5.29423i | −0.801176 | − | 0.462559i | 0.0427065 | − | 0.999088i | \(-0.486402\pi\) |
−0.843882 | + | 0.536529i | \(0.819735\pi\) | |||||||
\(132\) | −6.46410 | + | 11.1962i | −0.562628 | + | 0.974500i | ||||
\(133\) | −3.80385 | − | 2.19615i | −0.329835 | − | 0.190431i | ||||
\(134\) | − | 7.26795i | − | 0.627855i | ||||||
\(135\) | −0.928203 | + | 0.535898i | −0.0798870 | + | 0.0461228i | ||||
\(136\) | −5.59808 | + | 9.69615i | −0.480031 | + | 0.831438i | ||||
\(137\) | −6.46410 | −0.552265 | −0.276133 | − | 0.961120i | \(-0.589053\pi\) | ||||
−0.276133 | + | 0.961120i | \(0.589053\pi\) | |||||||
\(138\) | 2.00000 | 0.170251 | ||||||||
\(139\) | −6.29423 | + | 10.9019i | −0.533870 | + | 0.924689i | 0.465348 | + | 0.885128i | \(0.345929\pi\) |
−0.999217 | + | 0.0395611i | \(0.987404\pi\) | |||||||
\(140\) | 0.928203i | 0.0784475i | ||||||||
\(141\) | −3.00000 | − | 5.19615i | −0.252646 | − | 0.437595i | ||||
\(142\) | 6.00000i | 0.503509i | ||||||||
\(143\) | −14.1962 | + | 8.19615i | −1.18714 | + | 0.685397i | ||||
\(144\) | 2.23205 | + | 3.86603i | 0.186004 | + | 0.322169i | ||||
\(145\) | −0.0358984 | − | 0.0621778i | −0.00298120 | − | 0.00516359i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.6603 | −1.12668 | ||||||||
\(148\) | −5.50000 | + | 2.59808i | −0.452097 | + | 0.213561i | ||||
\(149\) | 5.53590 | 0.453518 | 0.226759 | − | 0.973951i | \(-0.427187\pi\) | ||||
0.226759 | + | 0.973951i | \(0.427187\pi\) | |||||||
\(150\) | 11.6603 | + | 6.73205i | 0.952056 | + | 0.549670i | ||||
\(151\) | −8.29423 | − | 14.3660i | −0.674975 | − | 1.16909i | −0.976476 | − | 0.215625i | \(-0.930821\pi\) |
0.301502 | − | 0.953466i | \(-0.402512\pi\) | |||||||
\(152\) | 1.90192 | + | 3.29423i | 0.154266 | + | 0.267197i | ||||
\(153\) | −14.4282 | + | 8.33013i | −1.16645 | + | 0.673451i | ||||
\(154\) | − | 16.3923i | − | 1.32093i | ||||||
\(155\) | 1.09808 | + | 1.90192i | 0.0881996 | + | 0.152766i | ||||
\(156\) | − | 9.46410i | − | 0.757735i | ||||||
\(157\) | 7.16025 | − | 12.4019i | 0.571450 | − | 0.989781i | −0.424967 | − | 0.905209i | \(-0.639714\pi\) |
0.996417 | − | 0.0845724i | \(-0.0269524\pi\) | |||||||
\(158\) | −3.80385 | −0.302618 | ||||||||
\(159\) | 6.92820 | 0.549442 | ||||||||
\(160\) | 0.669873 | − | 1.16025i | 0.0529581 | − | 0.0917261i | ||||
\(161\) | 2.19615 | − | 1.26795i | 0.173081 | − | 0.0999284i | ||||
\(162\) | − | 2.46410i | − | 0.193598i | ||||||
\(163\) | 19.3923 | + | 11.1962i | 1.51892 | + | 0.876950i | 0.999752 | + | 0.0222798i | \(0.00709247\pi\) |
0.519171 | + | 0.854671i | \(0.326241\pi\) | |||||||
\(164\) | −1.50000 | + | 2.59808i | −0.117130 | + | 0.202876i | ||||
\(165\) | −3.00000 | − | 1.73205i | −0.233550 | − | 0.134840i | ||||
\(166\) | −7.09808 | + | 4.09808i | −0.550918 | + | 0.318072i | ||||
\(167\) | 9.46410 | − | 5.46410i | 0.732354 | − | 0.422825i | −0.0869286 | − | 0.996215i | \(-0.527705\pi\) |
0.819283 | + | 0.573390i | \(0.194372\pi\) | |||||||
\(168\) | 24.5885 | + | 14.1962i | 1.89704 | + | 1.09526i | ||||
\(169\) | −0.500000 | + | 0.866025i | −0.0384615 | + | 0.0666173i | ||||
\(170\) | −0.866025 | − | 0.500000i | −0.0664211 | − | 0.0383482i | ||||
\(171\) | 5.66025i | 0.432850i | ||||||||
\(172\) | −3.00000 | + | 1.73205i | −0.228748 | + | 0.132068i | ||||
\(173\) | −4.96410 | + | 8.59808i | −0.377414 | + | 0.653700i | −0.990685 | − | 0.136173i | \(-0.956520\pi\) |
0.613271 | + | 0.789872i | \(0.289853\pi\) | |||||||
\(174\) | −0.732051 | −0.0554966 | ||||||||
\(175\) | 17.0718 | 1.29051 | ||||||||
\(176\) | −2.36603 | + | 4.09808i | −0.178346 | + | 0.308904i | ||||
\(177\) | − | 36.7846i | − | 2.76490i | ||||||
\(178\) | −4.59808 | − | 7.96410i | −0.344640 | − | 0.596935i | ||||
\(179\) | − | 1.46410i | − | 0.109432i | −0.998502 | − | 0.0547160i | \(-0.982575\pi\) | ||
0.998502 | − | 0.0547160i | \(-0.0174254\pi\) | |||||||
\(180\) | 1.03590 | − | 0.598076i | 0.0772113 | − | 0.0445780i | ||||
\(181\) | −4.96410 | − | 8.59808i | −0.368979 | − | 0.639090i | 0.620427 | − | 0.784264i | \(-0.286959\pi\) |
−0.989406 | + | 0.145174i | \(0.953626\pi\) | |||||||
\(182\) | 6.00000 | + | 10.3923i | 0.444750 | + | 0.770329i | ||||
\(183\) | 10.0981 | + | 5.83013i | 0.746471 | + | 0.430975i | ||||
\(184\) | −2.19615 | −0.161903 | ||||||||
\(185\) | −0.696152 | − | 1.47372i | −0.0511821 | − | 0.108350i | ||||
\(186\) | 22.3923 | 1.64188 | ||||||||
\(187\) | −15.2942 | − | 8.83013i | −1.11842 | − | 0.645723i | ||||
\(188\) | 1.09808 | + | 1.90192i | 0.0800854 | + | 0.138712i | ||||
\(189\) | 6.92820 | + | 12.0000i | 0.503953 | + | 0.872872i | ||||
\(190\) | −0.294229 | + | 0.169873i | −0.0213456 | + | 0.0123239i | ||||
\(191\) | 6.19615i | 0.448338i | 0.974550 | + | 0.224169i | \(0.0719667\pi\) | ||||
−0.974550 | + | 0.224169i | \(0.928033\pi\) | |||||||
\(192\) | −9.56218 | − | 16.5622i | −0.690091 | − | 1.19527i | ||||
\(193\) | 14.6603i | 1.05527i | 0.849472 | + | 0.527634i | \(0.176921\pi\) | ||||
−0.849472 | + | 0.527634i | \(0.823079\pi\) | |||||||
\(194\) | 2.13397 | − | 3.69615i | 0.153210 | − | 0.265368i | ||||
\(195\) | 2.53590 | 0.181599 | ||||||||
\(196\) | 5.00000 | 0.357143 | ||||||||
\(197\) | −13.9641 | + | 24.1865i | −0.994901 | + | 1.72322i | −0.410107 | + | 0.912038i | \(0.634509\pi\) |
−0.584794 | + | 0.811182i | \(0.698825\pi\) | |||||||
\(198\) | −18.2942 | + | 10.5622i | −1.30011 | + | 0.750621i | ||||
\(199\) | 11.0718i | 0.784859i | 0.919782 | + | 0.392429i | \(0.128365\pi\) | ||||
−0.919782 | + | 0.392429i | \(0.871635\pi\) | |||||||
\(200\) | −12.8038 | − | 7.39230i | −0.905369 | − | 0.522715i | ||||
\(201\) | −9.92820 | + | 17.1962i | −0.700281 | + | 1.21292i | ||||
\(202\) | 7.79423 | + | 4.50000i | 0.548400 | + | 0.316619i | ||||
\(203\) | −0.803848 | + | 0.464102i | −0.0564190 | + | 0.0325735i | ||||
\(204\) | 8.83013 | − | 5.09808i | 0.618233 | − | 0.356937i | ||||
\(205\) | −0.696152 | − | 0.401924i | −0.0486214 | − | 0.0280716i | ||||
\(206\) | 6.46410 | − | 11.1962i | 0.450375 | − | 0.780073i | ||||
\(207\) | −2.83013 | − | 1.63397i | −0.196707 | − | 0.113569i | ||||
\(208\) | − | 3.46410i | − | 0.240192i | ||||||
\(209\) | −5.19615 | + | 3.00000i | −0.359425 | + | 0.207514i | ||||
\(210\) | −1.26795 | + | 2.19615i | −0.0874968 | + | 0.151549i | ||||
\(211\) | −10.0000 | −0.688428 | −0.344214 | − | 0.938891i | \(-0.611855\pi\) | ||||
−0.344214 | + | 0.938891i | \(0.611855\pi\) | |||||||
\(212\) | −2.53590 | −0.174166 | ||||||||
\(213\) | 8.19615 | − | 14.1962i | 0.561591 | − | 0.972704i | ||||
\(214\) | − | 12.9282i | − | 0.883754i | ||||||
\(215\) | −0.464102 | − | 0.803848i | −0.0316515 | − | 0.0548219i | ||||
\(216\) | − | 12.0000i | − | 0.816497i | ||||||
\(217\) | 24.5885 | − | 14.1962i | 1.66917 | − | 0.963698i | ||||
\(218\) | 3.40192 | + | 5.89230i | 0.230407 | + | 0.399077i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.09808 | + | 0.633975i | 0.0740323 | + | 0.0427426i | ||||
\(221\) | 12.9282 | 0.869645 | ||||||||
\(222\) | −16.5622 | − | 1.36603i | −1.11158 | − | 0.0916816i | ||||
\(223\) | 4.58846 | 0.307266 | 0.153633 | − | 0.988128i | \(-0.450903\pi\) | ||||
0.153633 | + | 0.988128i | \(0.450903\pi\) | |||||||
\(224\) | −15.0000 | − | 8.66025i | −1.00223 | − | 0.578638i | ||||
\(225\) | −11.0000 | − | 19.0526i | −0.733333 | − | 1.27017i | ||||
\(226\) | 2.26795 | + | 3.92820i | 0.150862 | + | 0.261300i | ||||
\(227\) | 20.0263 | − | 11.5622i | 1.32919 | − | 0.767409i | 0.344016 | − | 0.938964i | \(-0.388212\pi\) |
0.985175 | + | 0.171555i | \(0.0548791\pi\) | |||||||
\(228\) | − | 3.46410i | − | 0.229416i | ||||||
\(229\) | −3.50000 | − | 6.06218i | −0.231287 | − | 0.400600i | 0.726900 | − | 0.686743i | \(-0.240960\pi\) |
−0.958187 | + | 0.286143i | \(0.907627\pi\) | |||||||
\(230\) | − | 0.196152i | − | 0.0129339i | ||||||
\(231\) | −22.3923 | + | 38.7846i | −1.47331 | + | 2.55184i | ||||
\(232\) | 0.803848 | 0.0527752 | ||||||||
\(233\) | −10.8564 | −0.711227 | −0.355613 | − | 0.934633i | \(-0.615728\pi\) | ||||
−0.355613 | + | 0.934633i | \(0.615728\pi\) | |||||||
\(234\) | 7.73205 | − | 13.3923i | 0.505460 | − | 0.875482i | ||||
\(235\) | −0.509619 | + | 0.294229i | −0.0332439 | + | 0.0191934i | ||||
\(236\) | 13.4641i | 0.876438i | ||||||||
\(237\) | 9.00000 | + | 5.19615i | 0.584613 | + | 0.337526i | ||||
\(238\) | −6.46410 | + | 11.1962i | −0.419005 | + | 0.725739i | ||||
\(239\) | 14.6603 | + | 8.46410i | 0.948293 | + | 0.547497i | 0.892550 | − | 0.450948i | \(-0.148914\pi\) |
0.0557428 | + | 0.998445i | \(0.482247\pi\) | |||||||
\(240\) | 0.633975 | − | 0.366025i | 0.0409229 | − | 0.0236268i | ||||
\(241\) | −13.3923 | + | 7.73205i | −0.862674 | + | 0.498065i | −0.864907 | − | 0.501932i | \(-0.832623\pi\) |
0.00223270 | + | 0.999998i | \(0.499289\pi\) | |||||||
\(242\) | −9.86603 | − | 5.69615i | −0.634212 | − | 0.366163i | ||||
\(243\) | −9.36603 | + | 16.2224i | −0.600831 | + | 1.04067i | ||||
\(244\) | −3.69615 | − | 2.13397i | −0.236622 | − | 0.136614i | ||||
\(245\) | 1.33975i | 0.0855932i | ||||||||
\(246\) | −7.09808 | + | 4.09808i | −0.452557 | + | 0.261284i | ||||
\(247\) | 2.19615 | − | 3.80385i | 0.139738 | − | 0.242033i | ||||
\(248\) | −24.5885 | −1.56137 | ||||||||
\(249\) | 22.3923 | 1.41905 | ||||||||
\(250\) | 1.33013 | − | 2.30385i | 0.0841246 | − | 0.145708i | ||||
\(251\) | − | 25.7128i | − | 1.62298i | −0.584367 | − | 0.811489i | \(-0.698657\pi\) | ||
0.584367 | − | 0.811489i | \(-0.301343\pi\) | |||||||
\(252\) | −7.73205 | − | 13.3923i | −0.487073 | − | 0.843636i | ||||
\(253\) | − | 3.46410i | − | 0.217786i | ||||||
\(254\) | −10.5622 | + | 6.09808i | −0.662730 | + | 0.382627i | ||||
\(255\) | 1.36603 | + | 2.36603i | 0.0855438 | + | 0.148166i | ||||
\(256\) | 8.50000 | + | 14.7224i | 0.531250 | + | 0.920152i | ||||
\(257\) | 16.9641 | + | 9.79423i | 1.05819 | + | 0.610947i | 0.924931 | − | 0.380134i | \(-0.124122\pi\) |
0.133260 | + | 0.991081i | \(0.457455\pi\) | |||||||
\(258\) | −9.46410 | −0.589209 | ||||||||
\(259\) | −19.0526 | + | 9.00000i | −1.18387 | + | 0.559233i | ||||
\(260\) | −0.928203 | −0.0575647 | ||||||||
\(261\) | 1.03590 | + | 0.598076i | 0.0641205 | + | 0.0370200i | ||||
\(262\) | 5.29423 | + | 9.16987i | 0.327079 | + | 0.566517i | ||||
\(263\) | 3.80385 | + | 6.58846i | 0.234555 | + | 0.406262i | 0.959143 | − | 0.282921i | \(-0.0913033\pi\) |
−0.724588 | + | 0.689182i | \(0.757970\pi\) | |||||||
\(264\) | 33.5885 | − | 19.3923i | 2.06723 | − | 1.19351i | ||||
\(265\) | − | 0.679492i | − | 0.0417409i | ||||||
\(266\) | 2.19615 | + | 3.80385i | 0.134655 | + | 0.233229i | ||||
\(267\) | 25.1244i | 1.53759i | ||||||||
\(268\) | 3.63397 | − | 6.29423i | 0.221980 | − | 0.384481i | ||||
\(269\) | 14.5359 | 0.886269 | 0.443135 | − | 0.896455i | \(-0.353866\pi\) | ||||
0.443135 | + | 0.896455i | \(0.353866\pi\) | |||||||
\(270\) | 1.07180 | 0.0652275 | ||||||||
\(271\) | 5.83013 | − | 10.0981i | 0.354155 | − | 0.613414i | −0.632818 | − | 0.774301i | \(-0.718102\pi\) |
0.986973 | + | 0.160886i | \(0.0514352\pi\) | |||||||
\(272\) | 3.23205 | − | 1.86603i | 0.195972 | − | 0.113144i | ||||
\(273\) | − | 32.7846i | − | 1.98421i | ||||||
\(274\) | 5.59808 | + | 3.23205i | 0.338192 | + | 0.195255i | ||||
\(275\) | 11.6603 | − | 20.1962i | 0.703140 | − | 1.21787i | ||||
\(276\) | 1.73205 | + | 1.00000i | 0.104257 | + | 0.0601929i | ||||
\(277\) | −8.89230 | + | 5.13397i | −0.534287 | + | 0.308471i | −0.742760 | − | 0.669557i | \(-0.766484\pi\) |
0.208474 | + | 0.978028i | \(0.433150\pi\) | |||||||
\(278\) | 10.9019 | − | 6.29423i | 0.653854 | − | 0.377503i | ||||
\(279\) | −31.6865 | − | 18.2942i | −1.89702 | − | 1.09525i | ||||
\(280\) | 1.39230 | − | 2.41154i | 0.0832061 | − | 0.144117i | ||||
\(281\) | 28.7487 | + | 16.5981i | 1.71500 | + | 0.990158i | 0.927478 | + | 0.373877i | \(0.121972\pi\) |
0.787526 | + | 0.616282i | \(0.211362\pi\) | |||||||
\(282\) | 6.00000i | 0.357295i | ||||||||
\(283\) | 9.00000 | − | 5.19615i | 0.534994 | − | 0.308879i | −0.208053 | − | 0.978117i | \(-0.566713\pi\) |
0.743048 | + | 0.669238i | \(0.233379\pi\) | |||||||
\(284\) | −3.00000 | + | 5.19615i | −0.178017 | + | 0.308335i | ||||
\(285\) | 0.928203 | 0.0549820 | ||||||||
\(286\) | 16.3923 | 0.969297 | ||||||||
\(287\) | −5.19615 | + | 9.00000i | −0.306719 | + | 0.531253i | ||||
\(288\) | 22.3205i | 1.31525i | ||||||||
\(289\) | −1.53590 | − | 2.66025i | −0.0903470 | − | 0.156486i | ||||
\(290\) | 0.0717968i | 0.00421605i | ||||||||
\(291\) | −10.0981 | + | 5.83013i | −0.591960 | + | 0.341768i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.4282 | − | 24.9904i | −0.842905 | − | 1.45995i | −0.887429 | − | 0.460945i | \(-0.847510\pi\) |
0.0445239 | − | 0.999008i | \(-0.485823\pi\) | |||||||
\(294\) | 11.8301 | + | 6.83013i | 0.689947 | + | 0.398341i | ||||
\(295\) | −3.60770 | −0.210048 | ||||||||
\(296\) | 18.1865 | + | 1.50000i | 1.05707 | + | 0.0871857i | ||||
\(297\) | 18.9282 | 1.09833 | ||||||||
\(298\) | −4.79423 | − | 2.76795i | −0.277722 | − | 0.160343i | ||||
\(299\) | 1.26795 | + | 2.19615i | 0.0733274 | + | 0.127007i | ||||
\(300\) | 6.73205 | + | 11.6603i | 0.388675 | + | 0.673205i | ||||
\(301\) | −10.3923 | + | 6.00000i | −0.599002 | + | 0.345834i | ||||
\(302\) | 16.5885i | 0.954558i | ||||||||
\(303\) | −12.2942 | − | 21.2942i | −0.706285 | − | 1.22332i | ||||
\(304\) | − | 1.26795i | − | 0.0727219i | ||||||
\(305\) | 0.571797 | − | 0.990381i | 0.0327410 | − | 0.0567091i | ||||
\(306\) | 16.6603 | 0.952403 | ||||||||
\(307\) | −14.3923 | −0.821412 | −0.410706 | − | 0.911768i | \(-0.634718\pi\) | ||||
−0.410706 | + | 0.911768i | \(0.634718\pi\) | |||||||
\(308\) | 8.19615 | − | 14.1962i | 0.467019 | − | 0.808901i | ||||
\(309\) | −30.5885 | + | 17.6603i | −1.74012 | + | 1.00466i | ||||
\(310\) | − | 2.19615i | − | 0.124733i | ||||||
\(311\) | −26.3205 | − | 15.1962i | −1.49250 | − | 0.861695i | −0.492536 | − | 0.870292i | \(-0.663930\pi\) |
−0.999963 | + | 0.00859730i | \(0.997263\pi\) | |||||||
\(312\) | −14.1962 | + | 24.5885i | −0.803699 | + | 1.39205i | ||||
\(313\) | −13.5000 | − | 7.79423i | −0.763065 | − | 0.440556i | 0.0673300 | − | 0.997731i | \(-0.478552\pi\) |
−0.830395 | + | 0.557175i | \(0.811885\pi\) | |||||||
\(314\) | −12.4019 | + | 7.16025i | −0.699881 | + | 0.404077i | ||||
\(315\) | 3.58846 | − | 2.07180i | 0.202187 | − | 0.116733i | ||||
\(316\) | −3.29423 | − | 1.90192i | −0.185315 | − | 0.106992i | ||||
\(317\) | 7.96410 | − | 13.7942i | 0.447309 | − | 0.774761i | −0.550901 | − | 0.834570i | \(-0.685716\pi\) |
0.998210 | + | 0.0598093i | \(0.0190493\pi\) | |||||||
\(318\) | −6.00000 | − | 3.46410i | −0.336463 | − | 0.194257i | ||||
\(319\) | 1.26795i | 0.0709915i | ||||||||
\(320\) | −1.62436 | + | 0.937822i | −0.0908042 | + | 0.0524259i | ||||
\(321\) | −17.6603 | + | 30.5885i | −0.985699 | + | 1.70728i | ||||
\(322\) | −2.53590 | −0.141320 | ||||||||
\(323\) | 4.73205 | 0.263298 | ||||||||
\(324\) | 1.23205 | − | 2.13397i | 0.0684473 | − | 0.118554i | ||||
\(325\) | 17.0718i | 0.946973i | ||||||||
\(326\) | −11.1962 | − | 19.3923i | −0.620098 | − | 1.07404i | ||||
\(327\) | − | 18.5885i | − | 1.02794i | ||||||
\(328\) | 7.79423 | − | 4.50000i | 0.430364 | − | 0.248471i | ||||
\(329\) | 3.80385 | + | 6.58846i | 0.209713 | + | 0.363233i | ||||
\(330\) | 1.73205 | + | 3.00000i | 0.0953463 | + | 0.165145i | ||||
\(331\) | 28.3923 | + | 16.3923i | 1.56058 | + | 0.901003i | 0.997198 | + | 0.0748075i | \(0.0238342\pi\) |
0.563384 | + | 0.826195i | \(0.309499\pi\) | |||||||
\(332\) | −8.19615 | −0.449822 | ||||||||
\(333\) | 22.3205 | + | 15.4641i | 1.22316 | + | 0.847428i | ||||
\(334\) | −10.9282 | −0.597965 | ||||||||
\(335\) | 1.68653 | + | 0.973721i | 0.0921452 | + | 0.0532000i | ||||
\(336\) | −4.73205 | − | 8.19615i | −0.258155 | − | 0.447137i | ||||
\(337\) | −14.6962 | − | 25.4545i | −0.800550 | − | 1.38659i | −0.919254 | − | 0.393664i | \(-0.871207\pi\) |
0.118704 | − | 0.992930i | \(-0.462126\pi\) | |||||||
\(338\) | 0.866025 | − | 0.500000i | 0.0471056 | − | 0.0271964i | ||||
\(339\) | − | 12.3923i | − | 0.673058i | ||||||
\(340\) | −0.500000 | − | 0.866025i | −0.0271163 | − | 0.0469668i | ||||
\(341\) | − | 38.7846i | − | 2.10030i | ||||||
\(342\) | 2.83013 | − | 4.90192i | 0.153036 | − | 0.265066i | ||||
\(343\) | −6.92820 | −0.374088 | ||||||||
\(344\) | 10.3923 | 0.560316 | ||||||||
\(345\) | −0.267949 | + | 0.464102i | −0.0144259 | + | 0.0249864i | ||||
\(346\) | 8.59808 | − | 4.96410i | 0.462235 | − | 0.266872i | ||||
\(347\) | − | 12.7321i | − | 0.683492i | −0.939792 | − | 0.341746i | \(-0.888982\pi\) | ||
0.939792 | − | 0.341746i | \(-0.111018\pi\) | |||||||
\(348\) | −0.633975 | − | 0.366025i | −0.0339846 | − | 0.0196210i | ||||
\(349\) | −4.03590 | + | 6.99038i | −0.216037 | + | 0.374187i | −0.953593 | − | 0.301099i | \(-0.902646\pi\) |
0.737556 | + | 0.675286i | \(0.235980\pi\) | |||||||
\(350\) | −14.7846 | − | 8.53590i | −0.790271 | − | 0.456263i | ||||
\(351\) | −12.0000 | + | 6.92820i | −0.640513 | + | 0.369800i | ||||
\(352\) | −20.4904 | + | 11.8301i | −1.09214 | + | 0.630548i | ||||
\(353\) | 10.6244 | + | 6.13397i | 0.565477 | + | 0.326479i | 0.755341 | − | 0.655332i | \(-0.227471\pi\) |
−0.189864 | + | 0.981810i | \(0.560805\pi\) | |||||||
\(354\) | −18.3923 | + | 31.8564i | −0.977540 | + | 1.69315i | ||||
\(355\) | −1.39230 | − | 0.803848i | −0.0738959 | − | 0.0426638i | ||||
\(356\) | − | 9.19615i | − | 0.487395i | ||||||
\(357\) | 30.5885 | − | 17.6603i | 1.61891 | − | 0.934680i | ||||
\(358\) | −0.732051 | + | 1.26795i | −0.0386901 | + | 0.0670132i | ||||
\(359\) | 16.3923 | 0.865153 | 0.432576 | − | 0.901597i | \(-0.357605\pi\) | ||||
0.432576 | + | 0.901597i | \(0.357605\pi\) | |||||||
\(360\) | −3.58846 | −0.189128 | ||||||||
\(361\) | −8.69615 | + | 15.0622i | −0.457692 | + | 0.792746i | ||||
\(362\) | 9.92820i | 0.521815i | ||||||||
\(363\) | 15.5622 | + | 26.9545i | 0.816803 | + | 1.41474i | ||||
\(364\) | 12.0000i | 0.628971i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.83013 | − | 10.0981i | −0.304746 | − | 0.527835i | ||||
\(367\) | 10.1962 | + | 17.6603i | 0.532235 | + | 0.921858i | 0.999292 | + | 0.0376305i | \(0.0119810\pi\) |
−0.467057 | + | 0.884227i | \(0.654686\pi\) | |||||||
\(368\) | 0.633975 | + | 0.366025i | 0.0330482 | + | 0.0190804i | ||||
\(369\) | 13.3923 | 0.697176 | ||||||||
\(370\) | −0.133975 | + | 1.62436i | −0.00696501 | + | 0.0844462i | ||||
\(371\) | −8.78461 | −0.456074 | ||||||||
\(372\) | 19.3923 | + | 11.1962i | 1.00544 | + | 0.580493i | ||||
\(373\) | −8.76795 | − | 15.1865i | −0.453987 | − | 0.786329i | 0.544642 | − | 0.838669i | \(-0.316665\pi\) |
−0.998629 | + | 0.0523397i | \(0.983332\pi\) | |||||||
\(374\) | 8.83013 | + | 15.2942i | 0.456595 | + | 0.790846i | ||||
\(375\) | −6.29423 | + | 3.63397i | −0.325033 | + | 0.187658i | ||||
\(376\) | − | 6.58846i | − | 0.339774i | ||||||
\(377\) | −0.464102 | − | 0.803848i | −0.0239024 | − | 0.0414003i | ||||
\(378\) | − | 13.8564i | − | 0.712697i | ||||||
\(379\) | −4.26795 | + | 7.39230i | −0.219230 | + | 0.379717i | −0.954573 | − | 0.297978i | \(-0.903688\pi\) |
0.735343 | + | 0.677695i | \(0.237021\pi\) | |||||||
\(380\) | −0.339746 | −0.0174286 | ||||||||
\(381\) | 33.3205 | 1.70706 | ||||||||
\(382\) | 3.09808 | − | 5.36603i | 0.158511 | − | 0.274550i | ||||
\(383\) | −13.7321 | + | 7.92820i | −0.701675 | + | 0.405112i | −0.807971 | − | 0.589222i | \(-0.799434\pi\) |
0.106296 | + | 0.994335i | \(0.466101\pi\) | |||||||
\(384\) | − | 8.19615i | − | 0.418258i | ||||||
\(385\) | 3.80385 | + | 2.19615i | 0.193862 | + | 0.111926i | ||||
\(386\) | 7.33013 | − | 12.6962i | 0.373094 | − | 0.646217i | ||||
\(387\) | 13.3923 | + | 7.73205i | 0.680769 | + | 0.393042i | ||||
\(388\) | 3.69615 | − | 2.13397i | 0.187644 | − | 0.108336i | ||||
\(389\) | 27.0167 | − | 15.5981i | 1.36980 | − | 0.790854i | 0.378897 | − | 0.925439i | \(-0.376303\pi\) |
0.990902 | + | 0.134585i | \(0.0429701\pi\) | |||||||
\(390\) | −2.19615 | − | 1.26795i | −0.111207 | − | 0.0642051i | ||||
\(391\) | −1.36603 | + | 2.36603i | −0.0690829 | + | 0.119655i | ||||
\(392\) | −12.9904 | − | 7.50000i | −0.656113 | − | 0.378807i | ||||
\(393\) | − | 28.9282i | − | 1.45923i | ||||||
\(394\) | 24.1865 | − | 13.9641i | 1.21850 | − | 0.703501i | ||||
\(395\) | 0.509619 | − | 0.882686i | 0.0256417 | − | 0.0444127i | ||||
\(396\) | −21.1244 | −1.06154 | ||||||||
\(397\) | −21.2487 | −1.06644 | −0.533221 | − | 0.845976i | \(-0.679019\pi\) | ||||
−0.533221 | + | 0.845976i | \(0.679019\pi\) | |||||||
\(398\) | 5.53590 | − | 9.58846i | 0.277490 | − | 0.480626i | ||||
\(399\) | − | 12.0000i | − | 0.600751i | ||||||
\(400\) | 2.46410 | + | 4.26795i | 0.123205 | + | 0.213397i | ||||
\(401\) | 5.60770i | 0.280035i | 0.990149 | + | 0.140017i | \(0.0447159\pi\) | ||||
−0.990149 | + | 0.140017i | \(0.955284\pi\) | |||||||
\(402\) | 17.1962 | − | 9.92820i | 0.857666 | − | 0.495174i | ||||
\(403\) | 14.1962 | + | 24.5885i | 0.707161 | + | 1.22484i | ||||
\(404\) | 4.50000 | + | 7.79423i | 0.223883 | + | 0.387777i | ||||
\(405\) | 0.571797 | + | 0.330127i | 0.0284128 | + | 0.0164041i | ||||
\(406\) | 0.928203 | 0.0460660 | ||||||||
\(407\) | −2.36603 | + | 28.6865i | −0.117280 | + | 1.42194i | ||||
\(408\) | −30.5885 | −1.51435 | ||||||||
\(409\) | 7.50000 | + | 4.33013i | 0.370851 | + | 0.214111i | 0.673830 | − | 0.738886i | \(-0.264648\pi\) |
−0.302979 | + | 0.952997i | \(0.597981\pi\) | |||||||
\(410\) | 0.401924 | + | 0.696152i | 0.0198496 | + | 0.0343805i | ||||
\(411\) | −8.83013 | − | 15.2942i | −0.435558 | − | 0.754409i | ||||
\(412\) | 11.1962 | − | 6.46410i | 0.551595 | − | 0.318463i | ||||
\(413\) | 46.6410i | 2.29505i | ||||||||
\(414\) | 1.63397 | + | 2.83013i | 0.0803055 | + | 0.139093i | ||||
\(415\) | − | 2.19615i | − | 0.107805i | ||||||
\(416\) | 8.66025 | − | 15.0000i | 0.424604 | − | 0.735436i | ||||
\(417\) | −34.3923 | −1.68420 | ||||||||
\(418\) | 6.00000 | 0.293470 | ||||||||
\(419\) | −8.66025 | + | 15.0000i | −0.423081 | + | 0.732798i | −0.996239 | − | 0.0866469i | \(-0.972385\pi\) |
0.573158 | + | 0.819445i | \(0.305718\pi\) | |||||||
\(420\) | −2.19615 | + | 1.26795i | −0.107161 | + | 0.0618696i | ||||
\(421\) | − | 16.2679i | − | 0.792851i | −0.918067 | − | 0.396426i | \(-0.870250\pi\) | ||
0.918067 | − | 0.396426i | \(-0.129750\pi\) | |||||||
\(422\) | 8.66025 | + | 5.00000i | 0.421575 | + | 0.243396i | ||||
\(423\) | 4.90192 | − | 8.49038i | 0.238340 | − | 0.412816i | ||||
\(424\) | 6.58846 | + | 3.80385i | 0.319964 | + | 0.184731i | ||||
\(425\) | −15.9282 | + | 9.19615i | −0.772631 | + | 0.446079i | ||||
\(426\) | −14.1962 | + | 8.19615i | −0.687806 | + | 0.397105i | ||||
\(427\) | −12.8038 | − | 7.39230i | −0.619622 | − | 0.357739i | ||||
\(428\) | 6.46410 | − | 11.1962i | 0.312454 | − | 0.541186i | ||||
\(429\) | −38.7846 | − | 22.3923i | −1.87254 | − | 1.08111i | ||||
\(430\) | 0.928203i | 0.0447619i | ||||||||
\(431\) | −9.97372 | + | 5.75833i | −0.480417 | + | 0.277369i | −0.720590 | − | 0.693361i | \(-0.756129\pi\) |
0.240173 | + | 0.970730i | \(0.422796\pi\) | |||||||
\(432\) | −2.00000 | + | 3.46410i | −0.0962250 | + | 0.166667i | ||||
\(433\) | 27.0000 | 1.29754 | 0.648769 | − | 0.760986i | \(-0.275284\pi\) | ||||
0.648769 | + | 0.760986i | \(0.275284\pi\) | |||||||
\(434\) | −28.3923 | −1.36287 | ||||||||
\(435\) | 0.0980762 | − | 0.169873i | 0.00470239 | − | 0.00814479i | ||||
\(436\) | 6.80385i | 0.325845i | ||||||||
\(437\) | 0.464102 | + | 0.803848i | 0.0222010 | + | 0.0384532i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.5885 | − | 7.26795i | 0.600814 | − | 0.346880i | −0.168548 | − | 0.985694i | \(-0.553908\pi\) |
0.769362 | + | 0.638813i | \(0.220574\pi\) | |||||||
\(440\) | −1.90192 | − | 3.29423i | −0.0906707 | − | 0.157046i | ||||
\(441\) | −11.1603 | − | 19.3301i | −0.531441 | − | 0.920482i | ||||
\(442\) | −11.1962 | − | 6.46410i | −0.532547 | − | 0.307466i | ||||
\(443\) | 33.4641 | 1.58993 | 0.794964 | − | 0.606657i | \(-0.207490\pi\) | ||||
0.794964 | + | 0.606657i | \(0.207490\pi\) | |||||||
\(444\) | −13.6603 | − | 9.46410i | −0.648287 | − | 0.449146i | ||||
\(445\) | 2.46410 | 0.116810 | ||||||||
\(446\) | −3.97372 | − | 2.29423i | −0.188161 | − | 0.108635i | ||||
\(447\) | 7.56218 | + | 13.0981i | 0.357679 | + | 0.619518i | ||||
\(448\) | 12.1244 | + | 21.0000i | 0.572822 | + | 0.992157i | ||||
\(449\) | −27.9282 | + | 16.1244i | −1.31801 | + | 0.760955i | −0.983409 | − | 0.181403i | \(-0.941936\pi\) |
−0.334605 | + | 0.942359i | \(0.608603\pi\) | |||||||
\(450\) | 22.0000i | 1.03709i | ||||||||
\(451\) | 7.09808 | + | 12.2942i | 0.334235 | + | 0.578913i | ||||
\(452\) | 4.53590i | 0.213351i | ||||||||
\(453\) | 22.6603 | − | 39.2487i | 1.06467 | − | 1.84407i | ||||
\(454\) | −23.1244 | −1.08528 | ||||||||
\(455\) | −3.21539 | −0.150740 | ||||||||
\(456\) | −5.19615 | + | 9.00000i | −0.243332 | + | 0.421464i | ||||
\(457\) | −31.2846 | + | 18.0622i | −1.46343 | + | 0.844913i | −0.999168 | − | 0.0407837i | \(-0.987015\pi\) |
−0.464264 | + | 0.885697i | \(0.653681\pi\) | |||||||
\(458\) | 7.00000i | 0.327089i | ||||||||
\(459\) | −12.9282 | − | 7.46410i | −0.603437 | − | 0.348394i | ||||
\(460\) | 0.0980762 | − | 0.169873i | 0.00457283 | − | 0.00792037i | ||||
\(461\) | −14.3205 | − | 8.26795i | −0.666973 | − | 0.385077i | 0.127956 | − | 0.991780i | \(-0.459158\pi\) |
−0.794929 | + | 0.606703i | \(0.792492\pi\) | |||||||
\(462\) | 38.7846 | − | 22.3923i | 1.80442 | − | 1.04178i | ||||
\(463\) | −13.3923 | + | 7.73205i | −0.622393 | + | 0.359339i | −0.777800 | − | 0.628512i | \(-0.783664\pi\) |
0.155407 | + | 0.987851i | \(0.450331\pi\) | |||||||
\(464\) | −0.232051 | − | 0.133975i | −0.0107727 | − | 0.00621961i | ||||
\(465\) | −3.00000 | + | 5.19615i | −0.139122 | + | 0.240966i | ||||
\(466\) | 9.40192 | + | 5.42820i | 0.435536 | + | 0.251457i | ||||
\(467\) | 3.32051i | 0.153655i | 0.997044 | + | 0.0768274i | \(0.0244790\pi\) | ||||
−0.997044 | + | 0.0768274i | \(0.975521\pi\) | |||||||
\(468\) | 13.3923 | − | 7.73205i | 0.619060 | − | 0.357414i | ||||
\(469\) | 12.5885 | − | 21.8038i | 0.581281 | − | 1.00681i | ||||
\(470\) | 0.588457 | 0.0271435 | ||||||||
\(471\) | 39.1244 | 1.80276 | ||||||||
\(472\) | 20.1962 | − | 34.9808i | 0.929603 | − | 1.61012i | ||||
\(473\) | 16.3923i | 0.753719i | ||||||||
\(474\) | −5.19615 | − | 9.00000i | −0.238667 | − | 0.413384i | ||||
\(475\) | 6.24871i | 0.286711i | ||||||||
\(476\) | −11.1962 | + | 6.46410i | −0.513175 | + | 0.296282i | ||||
\(477\) | 5.66025 | + | 9.80385i | 0.259165 | + | 0.448887i | ||||
\(478\) | −8.46410 | − | 14.6603i | −0.387139 | − | 0.670544i | ||||
\(479\) | −34.0526 | − | 19.6603i | −1.55590 | − | 0.898300i | −0.997642 | − | 0.0686333i | \(-0.978136\pi\) |
−0.558259 | − | 0.829667i | \(-0.688531\pi\) | |||||||
\(480\) | 3.66025 | 0.167067 | ||||||||
\(481\) | −9.00000 | − | 19.0526i | −0.410365 | − | 0.868722i | ||||
\(482\) | 15.4641 | 0.704371 | ||||||||
\(483\) | 6.00000 | + | 3.46410i | 0.273009 | + | 0.157622i | ||||
\(484\) | −5.69615 | − | 9.86603i | −0.258916 | − | 0.448456i | ||||
\(485\) | 0.571797 | + | 0.990381i | 0.0259640 | + | 0.0449709i | ||||
\(486\) | 16.2224 | − | 9.36603i | 0.735864 | − | 0.424852i | ||||
\(487\) | − | 32.4449i | − | 1.47022i | −0.677949 | − | 0.735109i | \(-0.737131\pi\) | ||
0.677949 | − | 0.735109i | \(-0.262869\pi\) | |||||||
\(488\) | 6.40192 | + | 11.0885i | 0.289801 | + | 0.501951i | ||||
\(489\) | 61.1769i | 2.76652i | ||||||||
\(490\) | 0.669873 | − | 1.16025i | 0.0302618 | − | 0.0524149i | ||||
\(491\) | 31.2679 | 1.41110 | 0.705551 | − | 0.708659i | \(-0.250699\pi\) | ||||
0.705551 | + | 0.708659i | \(0.250699\pi\) | |||||||
\(492\) | −8.19615 | −0.369511 | ||||||||
\(493\) | 0.500000 | − | 0.866025i | 0.0225189 | − | 0.0390038i | ||||
\(494\) | −3.80385 | + | 2.19615i | −0.171143 | + | 0.0988096i | ||||
\(495\) | − | 5.66025i | − | 0.254409i | ||||||
\(496\) | 7.09808 | + | 4.09808i | 0.318713 | + | 0.184009i | ||||
\(497\) | −10.3923 | + | 18.0000i | −0.466159 | + | 0.807410i | ||||
\(498\) | −19.3923 | − | 11.1962i | −0.868990 | − | 0.501712i | ||||
\(499\) | 10.9019 | − | 6.29423i | 0.488037 | − | 0.281768i | −0.235723 | − | 0.971820i | \(-0.575746\pi\) |
0.723760 | + | 0.690052i | \(0.242412\pi\) | |||||||
\(500\) | 2.30385 | − | 1.33013i | 0.103031 | − | 0.0594851i | ||||
\(501\) | 25.8564 | + | 14.9282i | 1.15518 | + | 0.666943i | ||||
\(502\) | −12.8564 | + | 22.2679i | −0.573810 | + | 0.993867i | ||||
\(503\) | −7.77757 | − | 4.49038i | −0.346785 | − | 0.200216i | 0.316484 | − | 0.948598i | \(-0.397498\pi\) |
−0.663268 | + | 0.748382i | \(0.730831\pi\) | |||||||
\(504\) | 46.3923i | 2.06648i | ||||||||
\(505\) | −2.08846 | + | 1.20577i | −0.0929351 | + | 0.0536561i | ||||
\(506\) | −1.73205 | + | 3.00000i | −0.0769991 | + | 0.133366i | ||||
\(507\) | −2.73205 | −0.121335 | ||||||||
\(508\) | −12.1962 | −0.541117 | ||||||||
\(509\) | 2.89230 | − | 5.00962i | 0.128199 | − | 0.222047i | −0.794780 | − | 0.606898i | \(-0.792414\pi\) |
0.922979 | + | 0.384850i | \(0.125747\pi\) | |||||||
\(510\) | − | 2.73205i | − | 0.120977i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 11.0000i | − | 0.486136i | ||||||
\(513\) | −4.39230 | + | 2.53590i | −0.193925 | + | 0.111963i | ||||
\(514\) | −9.79423 | − | 16.9641i | −0.432005 | − | 0.748254i | ||||
\(515\) | 1.73205 | + | 3.00000i | 0.0763233 | + | 0.132196i | ||||
\(516\) | −8.19615 | − | 4.73205i | −0.360815 | − | 0.208317i | ||||
\(517\) | 10.3923 | 0.457053 | ||||||||
\(518\) | 21.0000 | + | 1.73205i | 0.922687 | + | 0.0761019i | ||||
\(519\) | −27.1244 | −1.19063 | ||||||||
\(520\) | 2.41154 | + | 1.39230i | 0.105753 | + | 0.0610566i | ||||
\(521\) | −3.46410 | − | 6.00000i | −0.151765 | − | 0.262865i | 0.780111 | − | 0.625641i | \(-0.215162\pi\) |
−0.931876 | + | 0.362776i | \(0.881829\pi\) | |||||||
\(522\) | −0.598076 | − | 1.03590i | −0.0261771 | − | 0.0453400i | ||||
\(523\) | 13.9019 | − | 8.02628i | 0.607889 | − | 0.350965i | −0.164250 | − | 0.986419i | \(-0.552520\pi\) |
0.772139 | + | 0.635454i | \(0.219187\pi\) | |||||||
\(524\) | 10.5885i | 0.462559i | ||||||||
\(525\) | 23.3205 | + | 40.3923i | 1.01779 | + | 1.76286i | ||||
\(526\) | − | 7.60770i | − | 0.331711i | ||||||
\(527\) | −15.2942 | + | 26.4904i | −0.666227 | + | 1.15394i | ||||
\(528\) | −12.9282 | −0.562628 | ||||||||
\(529\) | 22.4641 | 0.976700 | ||||||||
\(530\) | −0.339746 | + | 0.588457i | −0.0147576 | + | 0.0255610i | ||||
\(531\) | 52.0526 | − | 30.0526i | 2.25889 | − | 1.30417i | ||||
\(532\) | 4.39230i | 0.190431i | ||||||||
\(533\) | −9.00000 | − | 5.19615i | −0.389833 | − | 0.225070i | ||||
\(534\) | 12.5622 | − | 21.7583i | 0.543619 | − | 0.941575i | ||||
\(535\) | 3.00000 | + | 1.73205i | 0.129701 | + | 0.0748831i | ||||
\(536\) | −18.8827 | + | 10.9019i | −0.815608 | + | 0.470891i | ||||
\(537\) | 3.46410 | − | 2.00000i | 0.149487 | − | 0.0863064i | ||||
\(538\) | −12.5885 | − | 7.26795i | −0.542727 | − | 0.313344i | ||||
\(539\) | 11.8301 | − | 20.4904i | 0.509560 | − | 0.882583i | ||||
\(540\) | 0.928203 | + | 0.535898i | 0.0399435 | + | 0.0230614i | ||||
\(541\) | 4.26795i | 0.183493i | 0.995782 | + | 0.0917467i | \(0.0292450\pi\) | ||||
−0.995782 | + | 0.0917467i | \(0.970755\pi\) | |||||||
\(542\) | −10.0981 | + | 5.83013i | −0.433750 | + | 0.250425i | ||||
\(543\) | 13.5622 | − | 23.4904i | 0.582009 | − | 1.00807i | ||||
\(544\) | 18.6603 | 0.800052 | ||||||||
\(545\) | −1.82309 | −0.0780924 | ||||||||
\(546\) | −16.3923 | + | 28.3923i | −0.701526 | + | 1.21508i | ||||
\(547\) | − | 3.80385i | − | 0.162641i | −0.996688 | − | 0.0813204i | \(-0.974086\pi\) | ||
0.996688 | − | 0.0813204i | \(-0.0259137\pi\) | |||||||
\(548\) | 3.23205 | + | 5.59808i | 0.138066 | + | 0.239138i | ||||
\(549\) | 19.0526i | 0.813143i | ||||||||
\(550\) | −20.1962 | + | 11.6603i | −0.861167 | + | 0.497195i | ||||
\(551\) | −0.169873 | − | 0.294229i | −0.00723683 | − | 0.0125346i | ||||
\(552\) | −3.00000 | − | 5.19615i | −0.127688 | − | 0.221163i | ||||
\(553\) | −11.4115 | − | 6.58846i | −0.485268 | − | 0.280170i | ||||
\(554\) | 10.2679 | 0.436243 | ||||||||
\(555\) | 2.53590 | − | 3.66025i | 0.107643 | − | 0.155369i | ||||
\(556\) | 12.5885 | 0.533870 | ||||||||
\(557\) | −15.3564 | − | 8.86603i | −0.650672 | − | 0.375666i | 0.138042 | − | 0.990426i | \(-0.455919\pi\) |
−0.788714 | + | 0.614761i | \(0.789253\pi\) | |||||||
\(558\) | 18.2942 | + | 31.6865i | 0.774456 | + | 1.34140i | ||||
\(559\) | −6.00000 | − | 10.3923i | −0.253773 | − | 0.439548i | ||||
\(560\) | −0.803848 | + | 0.464102i | −0.0339688 | + | 0.0196119i | ||||
\(561\) | − | 48.2487i | − | 2.03706i | ||||||
\(562\) | −16.5981 | − | 28.7487i | −0.700148 | − | 1.21269i | ||||
\(563\) | − | 34.5885i | − | 1.45773i | −0.684658 | − | 0.728865i | \(-0.740048\pi\) | ||
0.684658 | − | 0.728865i | \(-0.259952\pi\) | |||||||
\(564\) | −3.00000 | + | 5.19615i | −0.126323 | + | 0.218797i | ||||
\(565\) | −1.21539 | −0.0511319 | ||||||||
\(566\) | −10.3923 | −0.436821 | ||||||||
\(567\) | 4.26795 | − | 7.39230i | 0.179237 | − | 0.310448i | ||||
\(568\) | 15.5885 | − | 9.00000i | 0.654077 | − | 0.377632i | ||||
\(569\) | 36.5167i | 1.53086i | 0.643520 | + | 0.765429i | \(0.277473\pi\) | ||||
−0.643520 | + | 0.765429i | \(0.722527\pi\) | |||||||
\(570\) | −0.803848 | − | 0.464102i | −0.0336695 | − | 0.0194391i | ||||
\(571\) | 15.7583 | − | 27.2942i | 0.659466 | − | 1.14223i | −0.321289 | − | 0.946981i | \(-0.604116\pi\) |
0.980754 | − | 0.195247i | \(-0.0625507\pi\) | |||||||
\(572\) | 14.1962 | + | 8.19615i | 0.593571 | + | 0.342698i | ||||
\(573\) | −14.6603 | + | 8.46410i | −0.612441 | + | 0.353593i | ||||
\(574\) | 9.00000 | − | 5.19615i | 0.375653 | − | 0.216883i | ||||
\(575\) | −3.12436 | − | 1.80385i | −0.130295 | − | 0.0752256i | ||||
\(576\) | 15.6244 | − | 27.0622i | 0.651015 | − | 1.12759i | ||||
\(577\) | 11.1962 | + | 6.46410i | 0.466102 | + | 0.269104i | 0.714607 | − | 0.699527i | \(-0.246606\pi\) |
−0.248505 | + | 0.968631i | \(0.579939\pi\) | |||||||
\(578\) | 3.07180i | 0.127770i | ||||||||
\(579\) | −34.6865 | + | 20.0263i | −1.44152 | + | 0.832264i | ||||
\(580\) | −0.0358984 | + | 0.0621778i | −0.00149060 | + | 0.00258179i | ||||
\(581\) | −28.3923 | −1.17791 | ||||||||
\(582\) | 11.6603 | 0.483333 | ||||||||
\(583\) | −6.00000 | + | 10.3923i | −0.248495 | + | 0.430405i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.07180 | + | 3.58846i | 0.0856583 | + | 0.148364i | ||||
\(586\) | 28.8564i | 1.19205i | ||||||||
\(587\) | −14.1506 | + | 8.16987i | −0.584059 | + | 0.337207i | −0.762745 | − | 0.646699i | \(-0.776149\pi\) |
0.178686 | + | 0.983906i | \(0.442815\pi\) | |||||||
\(588\) | 6.83013 | + | 11.8301i | 0.281670 | + | 0.487866i | ||||
\(589\) | 5.19615 | + | 9.00000i | 0.214104 | + | 0.370839i | ||||
\(590\) | 3.12436 | + | 1.80385i | 0.128628 | + | 0.0742632i | ||||
\(591\) | −76.3013 | −3.13861 | ||||||||
\(592\) | −5.00000 | − | 3.46410i | −0.205499 | − | 0.142374i | ||||
\(593\) | 17.7846 | 0.730326 | 0.365163 | − | 0.930944i | \(-0.381013\pi\) | ||||
0.365163 | + | 0.930944i | \(0.381013\pi\) | |||||||
\(594\) | −16.3923 | − | 9.46410i | −0.672584 | − | 0.388317i | ||||
\(595\) | −1.73205 | − | 3.00000i | −0.0710072 | − | 0.122988i | ||||
\(596\) | −2.76795 | − | 4.79423i | −0.113380 | − | 0.196379i | ||||
\(597\) | −26.1962 | + | 15.1244i | −1.07214 | + | 0.618999i | ||||
\(598\) | − | 2.53590i | − | 0.103701i | ||||||
\(599\) | −3.97372 | − | 6.88269i | −0.162362 | − | 0.281219i | 0.773353 | − | 0.633975i | \(-0.218578\pi\) |
−0.935715 | + | 0.352756i | \(0.885245\pi\) | |||||||
\(600\) | − | 40.3923i | − | 1.64901i | ||||||
\(601\) | −15.6962 | + | 27.1865i | −0.640259 | + | 1.10896i | 0.345115 | + | 0.938560i | \(0.387840\pi\) |
−0.985375 | + | 0.170402i | \(0.945494\pi\) | |||||||
\(602\) | 12.0000 | 0.489083 | ||||||||
\(603\) | −32.4449 | −1.32126 | ||||||||
\(604\) | −8.29423 | + | 14.3660i | −0.337487 | + | 0.584545i | ||||
\(605\) | 2.64359 | − | 1.52628i | 0.107477 | − | 0.0620521i | ||||
\(606\) | 24.5885i | 0.998838i | ||||||||
\(607\) | 4.90192 | + | 2.83013i | 0.198963 | + | 0.114871i | 0.596172 | − | 0.802857i | \(-0.296688\pi\) |
−0.397209 | + | 0.917728i | \(0.630021\pi\) | |||||||
\(608\) | 3.16987 | − | 5.49038i | 0.128555 | − | 0.222664i | ||||
\(609\) | −2.19615 | − | 1.26795i | −0.0889926 | − | 0.0513799i | ||||
\(610\) | −0.990381 | + | 0.571797i | −0.0400994 | + | 0.0231514i | ||||
\(611\) | −6.58846 | + | 3.80385i | −0.266540 | + | 0.153887i | ||||
\(612\) | 14.4282 | + | 8.33013i | 0.583226 | + | 0.336725i | ||||
\(613\) | −1.69615 | + | 2.93782i | −0.0685070 | + | 0.118658i | −0.898244 | − | 0.439497i | \(-0.855157\pi\) |
0.829737 | + | 0.558154i | \(0.188490\pi\) | |||||||
\(614\) | 12.4641 | + | 7.19615i | 0.503010 | + | 0.290413i | ||||
\(615\) | − | 2.19615i | − | 0.0885574i | ||||||
\(616\) | −42.5885 | + | 24.5885i | −1.71594 | + | 0.990697i | ||||
\(617\) | 12.5885 | − | 21.8038i | 0.506792 | − | 0.877790i | −0.493177 | − | 0.869929i | \(-0.664164\pi\) |
0.999969 | − | 0.00786080i | \(-0.00250220\pi\) | |||||||
\(618\) | 35.3205 | 1.42080 | ||||||||
\(619\) | 6.78461 | 0.272696 | 0.136348 | − | 0.990661i | \(-0.456463\pi\) | ||||
0.136348 | + | 0.990661i | \(0.456463\pi\) | |||||||
\(620\) | 1.09808 | − | 1.90192i | 0.0440998 | − | 0.0763831i | ||||
\(621\) | − | 2.92820i | − | 0.117505i | ||||||
\(622\) | 15.1962 | + | 26.3205i | 0.609310 | + | 1.05536i | ||||
\(623\) | − | 31.8564i | − | 1.27630i | ||||||
\(624\) | 8.19615 | − | 4.73205i | 0.328109 | − | 0.189434i | ||||
\(625\) | −11.9641 | − | 20.7224i | −0.478564 | − | 0.828897i | ||||
\(626\) | 7.79423 | + | 13.5000i | 0.311520 | + | 0.539569i | ||||
\(627\) | −14.1962 | − | 8.19615i | −0.566940 | − | 0.327323i | ||||
\(628\) | −14.3205 | −0.571450 | ||||||||
\(629\) | 12.9282 | − | 18.6603i | 0.515481 | − | 0.744033i | ||||
\(630\) | −4.14359 | −0.165085 | ||||||||
\(631\) | 16.6865 | + | 9.63397i | 0.664280 | + | 0.383522i | 0.793906 | − | 0.608041i | \(-0.208044\pi\) |
−0.129626 | + | 0.991563i | \(0.541378\pi\) | |||||||
\(632\) | 5.70577 | + | 9.88269i | 0.226963 | + | 0.393112i | ||||
\(633\) | −13.6603 | − | 23.6603i | −0.542946 | − | 0.940411i | ||||
\(634\) | −13.7942 | + | 7.96410i | −0.547839 | + | 0.316295i | ||||
\(635\) | − | 3.26795i | − | 0.129685i | ||||||
\(636\) | −3.46410 | − | 6.00000i | −0.137361 | − | 0.237915i | ||||
\(637\) | 17.3205i | 0.686264i | ||||||||
\(638\) | 0.633975 | − | 1.09808i | 0.0250993 | − | 0.0434733i | ||||
\(639\) | 26.7846 | 1.05958 | ||||||||
\(640\) | −0.803848 | −0.0317749 | ||||||||
\(641\) | 8.89230 | − | 15.4019i | 0.351225 | − | 0.608339i | −0.635239 | − | 0.772315i | \(-0.719099\pi\) |
0.986464 | + | 0.163976i | \(0.0524319\pi\) | |||||||
\(642\) | 30.5885 | − | 17.6603i | 1.20723 | − | 0.696995i | ||||
\(643\) | − | 5.66025i | − | 0.223219i | −0.993752 | − | 0.111609i | \(-0.964399\pi\) | ||
0.993752 | − | 0.111609i | \(-0.0356005\pi\) | |||||||
\(644\) | −2.19615 | − | 1.26795i | −0.0865405 | − | 0.0499642i | ||||
\(645\) | 1.26795 | − | 2.19615i | 0.0499255 | − | 0.0864734i | ||||
\(646\) | −4.09808 | − | 2.36603i | −0.161237 | − | 0.0930900i | ||||
\(647\) | 37.6410 | − | 21.7321i | 1.47982 | − | 0.854375i | 0.480082 | − | 0.877224i | \(-0.340607\pi\) |
0.999739 | + | 0.0228485i | \(0.00727353\pi\) | |||||||
\(648\) | −6.40192 | + | 3.69615i | −0.251491 | + | 0.145199i | ||||
\(649\) | 55.1769 | + | 31.8564i | 2.16588 | + | 1.25047i | ||||
\(650\) | 8.53590 | − | 14.7846i | 0.334805 | − | 0.579900i | ||||
\(651\) | 67.1769 | + | 38.7846i | 2.63287 | + | 1.52009i | ||||
\(652\) | − | 22.3923i | − | 0.876950i | ||||||
\(653\) | −2.42820 | + | 1.40192i | −0.0950229 | + | 0.0548615i | −0.546758 | − | 0.837290i | \(-0.684138\pi\) |
0.451736 | + | 0.892152i | \(0.350805\pi\) | |||||||
\(654\) | −9.29423 | + | 16.0981i | −0.363433 | + | 0.629485i | ||||
\(655\) | −2.83717 | −0.110857 | ||||||||
\(656\) | −3.00000 | −0.117130 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 7.60770i | − | 0.296579i | ||||||
\(659\) | −4.73205 | − | 8.19615i | −0.184335 | − | 0.319277i | 0.759018 | − | 0.651070i | \(-0.225680\pi\) |
−0.943352 | + | 0.331793i | \(0.892346\pi\) | |||||||
\(660\) | 3.46410i | 0.134840i | ||||||||
\(661\) | −11.0885 | + | 6.40192i | −0.431291 | + | 0.249006i | −0.699896 | − | 0.714244i | \(-0.746771\pi\) |
0.268605 | + | 0.963250i | \(0.413437\pi\) | |||||||
\(662\) | −16.3923 | − | 28.3923i | −0.637105 | − | 1.10350i | ||||
\(663\) | 17.6603 | + | 30.5885i | 0.685867 | + | 1.18796i | ||||
\(664\) | 21.2942 | + | 12.2942i | 0.826376 | + | 0.477109i | ||||
\(665\) | −1.17691 | −0.0456388 | ||||||||
\(666\) | −11.5981 | − | 24.5526i | −0.449416 | − | 0.951392i | ||||
\(667\) | 0.196152 | 0.00759505 | ||||||||
\(668\) | −9.46410 | − | 5.46410i | −0.366177 | − | 0.211412i | ||||
\(669\) | 6.26795 | + | 10.8564i | 0.242333 | + | 0.419733i | ||||
\(670\) | −0.973721 | − | 1.68653i | −0.0376181 | − | 0.0651565i | ||||
\(671\) | −17.4904 | + | 10.0981i | −0.675209 | + | 0.389832i | ||||
\(672\) | − | 47.3205i | − | 1.82543i | ||||||
\(673\) | −7.85641 | − | 13.6077i | −0.302842 | − | 0.524538i | 0.673936 | − | 0.738789i | \(-0.264602\pi\) |
−0.976779 | + | 0.214251i | \(0.931269\pi\) | |||||||
\(674\) | 29.3923i | 1.13215i | ||||||||
\(675\) | 9.85641 | − | 17.0718i | 0.379373 | − | 0.657094i | ||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −44.3205 | −1.70338 | −0.851688 | − | 0.524050i | \(-0.824421\pi\) | ||||
−0.851688 | + | 0.524050i | \(0.824421\pi\) | |||||||
\(678\) | −6.19615 | + | 10.7321i | −0.237962 | + | 0.412162i | ||||
\(679\) | 12.8038 | − | 7.39230i | 0.491367 | − | 0.283691i | ||||
\(680\) | 3.00000i | 0.115045i | ||||||||
\(681\) | 54.7128 | + | 31.5885i | 2.09660 | + | 1.21047i | ||||
\(682\) | −19.3923 | + | 33.5885i | −0.742570 | + | 1.28617i | ||||
\(683\) | 26.9090 | + | 15.5359i | 1.02964 | + | 0.594465i | 0.916882 | − | 0.399158i | \(-0.130697\pi\) |
0.112761 | + | 0.993622i | \(0.464031\pi\) | |||||||
\(684\) | 4.90192 | − | 2.83013i | 0.187430 | − | 0.108213i | ||||
\(685\) | −1.50000 | + | 0.866025i | −0.0573121 | + | 0.0330891i | ||||
\(686\) | 6.00000 | + | 3.46410i | 0.229081 | + | 0.132260i | ||||
\(687\) | 9.56218 | − | 16.5622i | 0.364820 | − | 0.631886i | ||||
\(688\) | −3.00000 | − | 1.73205i | −0.114374 | − | 0.0660338i | ||||
\(689\) | − | 8.78461i | − | 0.334667i | ||||||
\(690\) | 0.464102 | − | 0.267949i | 0.0176680 | − | 0.0102007i | ||||
\(691\) | −8.02628 | + | 13.9019i | −0.305334 | + | 0.528854i | −0.977336 | − | 0.211696i | \(-0.932101\pi\) |
0.672002 | + | 0.740550i | \(0.265435\pi\) | |||||||
\(692\) | 9.92820 | 0.377414 | ||||||||
\(693\) | −73.1769 | −2.77976 | ||||||||
\(694\) | −6.36603 | + | 11.0263i | −0.241651 | + | 0.418552i | ||||
\(695\) | 3.37307i | 0.127948i | ||||||||
\(696\) | 1.09808 | + | 1.90192i | 0.0416225 | + | 0.0720922i | ||||
\(697\) | − | 11.1962i | − | 0.424085i | ||||||
\(698\) | 6.99038 | − | 4.03590i | 0.264590 | − | 0.152761i | ||||
\(699\) | −14.8301 | − | 25.6865i | −0.560927 | − | 0.971554i | ||||
\(700\) | −8.53590 | − | 14.7846i | −0.322627 | − | 0.558806i | ||||
\(701\) | −5.07180 | − | 2.92820i | −0.191559 | − | 0.110597i | 0.401153 | − | 0.916011i | \(-0.368610\pi\) |
−0.592712 | + | 0.805414i | \(0.701943\pi\) | |||||||
\(702\) | 13.8564 | 0.522976 | ||||||||
\(703\) | −3.29423 | − | 6.97372i | −0.124244 | − | 0.263019i | ||||
\(704\) | 33.1244 | 1.24842 | ||||||||
\(705\) | −1.39230 | − | 0.803848i | −0.0524372 | − | 0.0302747i | ||||
\(706\) | −6.13397 | − | 10.6244i | −0.230855 | − | 0.399853i | ||||
\(707\) | 15.5885 | + | 27.0000i | 0.586264 | + | 1.01544i | ||||
\(708\) | −31.8564 | + | 18.3923i | −1.19724 | + | 0.691225i | ||||
\(709\) | 30.0000i | 1.12667i | 0.826227 | + | 0.563337i | \(0.190483\pi\) | ||||
−0.826227 | + | 0.563337i | \(0.809517\pi\) | |||||||
\(710\) | 0.803848 | + | 1.39230i | 0.0301679 | + | 0.0522523i | ||||
\(711\) | 16.9808i | 0.636828i | ||||||||
\(712\) | −13.7942 | + | 23.8923i | −0.516961 | + | 0.895402i | ||||
\(713\) | −6.00000 | −0.224702 | ||||||||
\(714\) | −35.3205 | −1.32184 | ||||||||
\(715\) | −2.19615 | + | 3.80385i | −0.0821314 | + | 0.142256i | ||||
\(716\) | −1.26795 | + | 0.732051i | −0.0473855 | + | 0.0273580i | ||||
\(717\) | 46.2487i | 1.72719i | ||||||||
\(718\) | −14.1962 | − | 8.19615i | −0.529796 | − | 0.305878i | ||||
\(719\) | −13.2224 | + | 22.9019i | −0.493114 | + | 0.854098i | −0.999969 | − | 0.00793367i | \(-0.997475\pi\) |
0.506855 | + | 0.862031i | \(0.330808\pi\) | |||||||
\(720\) | 1.03590 | + | 0.598076i | 0.0386057 | + | 0.0222890i | ||||
\(721\) | 38.7846 | − | 22.3923i | 1.44441 | − | 0.833933i | ||||
\(722\) | 15.0622 | − | 8.69615i | 0.560556 | − | 0.323637i | ||||
\(723\) | −36.5885 | − | 21.1244i | −1.36074 | − | 0.785623i | ||||
\(724\) | −4.96410 | + | 8.59808i | −0.184489 | + | 0.319545i | ||||
\(725\) | 1.14359 | + | 0.660254i | 0.0424720 | + | 0.0245212i | ||||
\(726\) | − | 31.1244i | − | 1.15513i | ||||||
\(727\) | −1.60770 | + | 0.928203i | −0.0596261 | + | 0.0344252i | −0.529517 | − | 0.848300i | \(-0.677627\pi\) |
0.469891 | + | 0.882725i | \(0.344293\pi\) | |||||||
\(728\) | 18.0000 | − | 31.1769i | 0.667124 | − | 1.15549i | ||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.46410 | − | 11.1962i | 0.239083 | − | 0.414105i | ||||
\(732\) | − | 11.6603i | − | 0.430975i | ||||||
\(733\) | −14.3923 | − | 24.9282i | −0.531592 | − | 0.920744i | −0.999320 | − | 0.0368718i | \(-0.988261\pi\) |
0.467728 | − | 0.883872i | \(-0.345073\pi\) | |||||||
\(734\) | − | 20.3923i | − | 0.752694i | ||||||
\(735\) | −3.16987 | + | 1.83013i | −0.116923 | + | 0.0675053i | ||||
\(736\) | 1.83013 | + | 3.16987i | 0.0674594 | + | 0.116843i | ||||
\(737\) | −17.1962 | − | 29.7846i | −0.633428 | − | 1.09713i | ||||
\(738\) | −11.5981 | − | 6.69615i | −0.426931 | − | 0.246489i | ||||
\(739\) | −23.8038 | −0.875639 | −0.437819 | − | 0.899063i | \(-0.644249\pi\) | ||||
−0.437819 | + | 0.899063i | \(0.644249\pi\) | |||||||
\(740\) | −0.928203 | + | 1.33975i | −0.0341214 | + | 0.0492500i | ||||
\(741\) | 12.0000 | 0.440831 | ||||||||
\(742\) | 7.60770 | + | 4.39230i | 0.279287 | + | 0.161247i | ||||
\(743\) | 21.6340 | + | 37.4711i | 0.793674 | + | 1.37468i | 0.923678 | + | 0.383170i | \(0.125167\pi\) |
−0.130004 | + | 0.991513i | \(0.541499\pi\) | |||||||
\(744\) | −33.5885 | − | 58.1769i | −1.23141 | − | 2.13287i | ||||
\(745\) | 1.28461 | − | 0.741670i | 0.0470645 | − | 0.0271727i | ||||
\(746\) | 17.5359i | 0.642035i | ||||||||
\(747\) | 18.2942 | + | 31.6865i | 0.669351 | + | 1.15935i | ||||
\(748\) | 17.6603i | 0.645723i | ||||||||
\(749\) | 22.3923 | − | 38.7846i | 0.818197 | − | 1.41716i | ||||
\(750\) | 7.26795 | 0.265388 | ||||||||
\(751\) | −9.21539 | −0.336274 | −0.168137 | − | 0.985764i | \(-0.553775\pi\) | ||||
−0.168137 | + | 0.985764i | \(0.553775\pi\) | |||||||
\(752\) | −1.09808 | + | 1.90192i | −0.0400427 | + | 0.0693560i | ||||
\(753\) | 60.8372 | − | 35.1244i | 2.21703 | − | 1.28000i | ||||
\(754\) | 0.928203i | 0.0338032i | ||||||||
\(755\) | −3.84936 | − | 2.22243i | −0.140093 | − | 0.0808826i | ||||
\(756\) | 6.92820 | − | 12.0000i | 0.251976 | − | 0.436436i | ||||
\(757\) | 36.6962 | + | 21.1865i | 1.33374 | + | 0.770038i | 0.985871 | − | 0.167504i | \(-0.0535707\pi\) |
0.347873 | + | 0.937542i | \(0.386904\pi\) | |||||||
\(758\) | 7.39230 | − | 4.26795i | 0.268501 | − | 0.155019i | ||||
\(759\) | 8.19615 | − | 4.73205i | 0.297501 | − | 0.171763i | ||||
\(760\) | 0.882686 | + | 0.509619i | 0.0320184 | + | 0.0184858i | ||||
\(761\) | 1.83975 | − | 3.18653i | 0.0666907 | − | 0.115512i | −0.830752 | − | 0.556643i | \(-0.812089\pi\) |
0.897443 | + | 0.441131i | \(0.145423\pi\) | |||||||
\(762\) | −28.8564 | − | 16.6603i | −1.04536 | − | 0.603537i | ||||
\(763\) | 23.5692i | 0.853263i | ||||||||
\(764\) | 5.36603 | − | 3.09808i | 0.194136 | − | 0.112084i | ||||
\(765\) | −2.23205 | + | 3.86603i | −0.0807000 | + | 0.139776i | ||||
\(766\) | 15.8564 | 0.572915 | ||||||||
\(767\) | −46.6410 | −1.68411 | ||||||||
\(768\) | −23.2224 | + | 40.2224i | −0.837967 | + | 1.45140i | ||||
\(769\) | − | 20.5359i | − | 0.740543i | −0.928923 | − | 0.370272i | \(-0.879265\pi\) | ||
0.928923 | − | 0.370272i | \(-0.120735\pi\) | |||||||
\(770\) | −2.19615 | − | 3.80385i | −0.0791438 | − | 0.137081i | ||||
\(771\) | 53.5167i | 1.92736i | ||||||||
\(772\) | 12.6962 | − | 7.33013i | 0.456945 | − | 0.263817i | ||||
\(773\) | 24.0167 | + | 41.5981i | 0.863819 | + | 1.49618i | 0.868215 | + | 0.496188i | \(0.165267\pi\) |
−0.00439560 | + | 0.999990i | \(0.501399\pi\) | |||||||
\(774\) | −7.73205 | − | 13.3923i | −0.277923 | − | 0.481376i | ||||
\(775\) | −34.9808 | − | 20.1962i | −1.25655 | − | 0.725467i | ||||
\(776\) | −12.8038 | −0.459631 | ||||||||
\(777\) | −47.3205 | − | 32.7846i | −1.69761 | − | 1.17614i | ||||
\(778\) | −31.1962 | −1.11844 | ||||||||
\(779\) | −3.29423 | − | 1.90192i | −0.118028 | − | 0.0681435i | ||||
\(780\) | −1.26795 | − | 2.19615i | −0.0453999 | − | 0.0786349i | ||||
\(781\) | 14.1962 | + | 24.5885i | 0.507978 | + | 0.879844i | ||||
\(782\) | 2.36603 | − | 1.36603i | 0.0846089 | − | 0.0488490i | ||||
\(783\) | 1.07180i | 0.0383029i | ||||||||
\(784\) | 2.50000 | + | 4.33013i | 0.0892857 | + | 0.154647i | ||||
\(785\) | − | 3.83717i | − | 0.136954i | ||||||
\(786\) | −14.4641 | + | 25.0526i | −0.515917 | + | 0.893595i | ||||
\(787\) | 0.392305 | 0.0139842 | 0.00699208 | − | 0.999976i | \(-0.497774\pi\) | ||||
0.00699208 | + | 0.999976i | \(0.497774\pi\) | |||||||
\(788\) | 27.9282 | 0.994901 | ||||||||
\(789\) | −10.3923 | + | 18.0000i | −0.369976 | + | 0.640817i | ||||
\(790\) | −0.882686 | + | 0.509619i | −0.0314046 | + | 0.0181314i | ||||
\(791\) | 15.7128i | 0.558683i | ||||||||
\(792\) | 54.8827 | + | 31.6865i | 1.95017 | + | 1.12593i | ||||
\(793\) | 7.39230 | − | 12.8038i | 0.262508 | − | 0.454678i | ||||
\(794\) | 18.4019 | + | 10.6244i | 0.653060 | + | 0.377044i | ||||
\(795\) | 1.60770 | − | 0.928203i | 0.0570191 | − | 0.0329200i | ||||
\(796\) | 9.58846 | − | 5.53590i | 0.339854 | − | 0.196215i | ||||
\(797\) | −6.92820 | − | 4.00000i | −0.245410 | − | 0.141687i | 0.372251 | − | 0.928132i | \(-0.378586\pi\) |
−0.617661 | + | 0.786445i | \(0.711919\pi\) | |||||||
\(798\) | −6.00000 | + | 10.3923i | −0.212398 | + | 0.367884i | ||||
\(799\) | −7.09808 | − | 4.09808i | −0.251112 | − | 0.144980i | ||||
\(800\) | 24.6410i | 0.871191i | ||||||||
\(801\) | −35.5526 | + | 20.5263i | −1.25619 | + | 0.725260i | ||||
\(802\) | 2.80385 | − | 4.85641i | 0.0990073 | − | 0.171486i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 19.8564 | 0.700281 | ||||||||
\(805\) | 0.339746 | − | 0.588457i | 0.0119745 | − | 0.0207404i | ||||
\(806\) | − | 28.3923i | − | 1.00008i | ||||||
\(807\) | 19.8564 | + | 34.3923i | 0.698979 | + | 1.21067i | ||||
\(808\) | − | 27.0000i | − | 0.949857i | ||||||
\(809\) | 29.3205 | − | 16.9282i | 1.03085 | − | 0.595164i | 0.113625 | − | 0.993524i | \(-0.463754\pi\) |
0.917229 | + | 0.398360i | \(0.130420\pi\) | |||||||
\(810\) | −0.330127 | − | 0.571797i | −0.0115995 | − | 0.0200909i | ||||
\(811\) | −9.12436 | − | 15.8038i | −0.320399 | − | 0.554948i | 0.660171 | − | 0.751115i | \(-0.270484\pi\) |
−0.980570 | + | 0.196167i | \(0.937150\pi\) | |||||||
\(812\) | 0.803848 | + | 0.464102i | 0.0282095 | + | 0.0162868i | ||||
\(813\) | 31.8564 | 1.11725 | ||||||||
\(814\) | 16.3923 | − | 23.6603i | 0.574550 | − | 0.829291i | ||||
\(815\) | 6.00000 | 0.210171 | ||||||||
\(816\) | 8.83013 | + | 5.09808i | 0.309116 | + | 0.178468i | ||||
\(817\) | −2.19615 | − | 3.80385i | −0.0768336 | − | 0.133080i | ||||
\(818\) | −4.33013 | − | 7.50000i | −0.151399 | − | 0.262231i | ||||
\(819\) | 46.3923 | − | 26.7846i | 1.62108 | − | 0.935930i | ||||
\(820\) | 0.803848i | 0.0280716i | ||||||||
\(821\) | −24.5885 | − | 42.5885i | −0.858143 | − | 1.48635i | −0.873698 | − | 0.486468i | \(-0.838285\pi\) |
0.0155551 | − | 0.999879i | \(-0.495048\pi\) | |||||||
\(822\) | 17.6603i | 0.615972i | ||||||||
\(823\) | 1.50962 | − | 2.61474i | 0.0526220 | − | 0.0911440i | −0.838515 | − | 0.544879i | \(-0.816575\pi\) |
0.891137 | + | 0.453735i | \(0.149909\pi\) | |||||||
\(824\) | −38.7846 | −1.35113 | ||||||||
\(825\) | 63.7128 | 2.21820 | ||||||||
\(826\) | 23.3205 | − | 40.3923i | 0.811424 | − | 1.40543i | ||||
\(827\) | −19.8564 | + | 11.4641i | −0.690475 | + | 0.398646i | −0.803790 | − | 0.594913i | \(-0.797186\pi\) |
0.113315 | + | 0.993559i | \(0.463853\pi\) | |||||||
\(828\) | 3.26795i | 0.113569i | ||||||||
\(829\) | −38.5692 | − | 22.2679i | −1.33956 | − | 0.773398i | −0.352822 | − | 0.935691i | \(-0.614778\pi\) |
−0.986743 | + | 0.162293i | \(0.948111\pi\) | |||||||
\(830\) | −1.09808 | + | 1.90192i | −0.0381148 | + | 0.0660167i | ||||
\(831\) | −24.2942 | − | 14.0263i | −0.842757 | − | 0.486566i | ||||
\(832\) | −21.0000 | + | 12.1244i | −0.728044 | + | 0.420336i | ||||
\(833\) | −16.1603 | + | 9.33013i | −0.559920 | + | 0.323270i | ||||
\(834\) | 29.7846 | + | 17.1962i | 1.03136 | + | 0.595454i | ||||
\(835\) | 1.46410 | − | 2.53590i | 0.0506673 | − | 0.0877584i | ||||
\(836\) | 5.19615 | + | 3.00000i | 0.179713 | + | 0.103757i | ||||
\(837\) | − | 32.7846i | − | 1.13320i | ||||||
\(838\) | 15.0000 | − | 8.66025i | 0.518166 | − | 0.299164i | ||||
\(839\) | 14.8301 | − | 25.6865i | 0.511993 | − | 0.886798i | −0.487910 | − | 0.872894i | \(-0.662241\pi\) |
0.999903 | − | 0.0139040i | \(-0.00442591\pi\) | |||||||
\(840\) | 7.60770 | 0.262490 | ||||||||
\(841\) | 28.9282 | 0.997524 | ||||||||
\(842\) | −8.13397 | + | 14.0885i | −0.280315 | + | 0.485520i | ||||
\(843\) | 90.6936i | 3.12365i | ||||||||
\(844\) | 5.00000 | + | 8.66025i | 0.172107 | + | 0.298098i | ||||
\(845\) | 0.267949i | 0.00921773i | ||||||||
\(846\) | −8.49038 | + | 4.90192i | −0.291905 | + | 0.168532i | ||||
\(847\) | −19.7321 | − | 34.1769i | −0.678001 | − | 1.17433i | ||||
\(848\) | −1.26795 | − | 2.19615i | −0.0435416 | − | 0.0754162i | ||||
\(849\) | 24.5885 | + | 14.1962i | 0.843874 | + | 0.487211i | ||||
\(850\) | 18.3923 | 0.630851 | ||||||||
\(851\) | 4.43782 | + | 0.366025i | 0.152127 | + | 0.0125472i | ||||
\(852\) | −16.3923 | −0.561591 | ||||||||
\(853\) | 36.4808 | + | 21.0622i | 1.24908 | + | 0.721155i | 0.970926 | − | 0.239382i | \(-0.0769448\pi\) |
0.278152 | + | 0.960537i | \(0.410278\pi\) | |||||||
\(854\) | 7.39230 | + | 12.8038i | 0.252959 | + | 0.438139i | ||||
\(855\) | 0.758330 | + | 1.31347i | 0.0259343 | + | 0.0449196i | ||||
\(856\) | −33.5885 | + | 19.3923i | −1.14803 | + | 0.662815i | ||||
\(857\) | − | 23.7321i | − | 0.810671i | −0.914168 | − | 0.405336i | \(-0.867155\pi\) | ||
0.914168 | − | 0.405336i | \(-0.132845\pi\) | |||||||
\(858\) | 22.3923 | + | 38.7846i | 0.764461 | + | 1.32408i | ||||
\(859\) | 8.53590i | 0.291241i | 0.989341 | + | 0.145621i | \(0.0465179\pi\) | ||||
−0.989341 | + | 0.145621i | \(0.953482\pi\) | |||||||
\(860\) | −0.464102 | + | 0.803848i | −0.0158257 | + | 0.0274110i | ||||
\(861\) | −28.3923 | −0.967607 | ||||||||
\(862\) | 11.5167 | 0.392259 | ||||||||
\(863\) | −19.2679 | + | 33.3731i | −0.655889 | + | 1.13603i | 0.325782 | + | 0.945445i | \(0.394373\pi\) |
−0.981670 | + | 0.190587i | \(0.938961\pi\) | |||||||
\(864\) | −17.3205 | + | 10.0000i | −0.589256 | + | 0.340207i | ||||
\(865\) | 2.66025i | 0.0904514i | ||||||||
\(866\) | −23.3827 | − | 13.5000i | −0.794576 | − | 0.458749i | ||||
\(867\) | 4.19615 | − | 7.26795i | 0.142509 | − | 0.246832i | ||||
\(868\) | −24.5885 | − | 14.1962i | −0.834587 | − | 0.481849i | ||||
\(869\) | −15.5885 | + | 9.00000i | −0.528802 | + | 0.305304i | ||||
\(870\) | −0.169873 | + | 0.0980762i | −0.00575923 | + | 0.00332509i | ||||
\(871\) | 21.8038 | + | 12.5885i | 0.738795 | + | 0.426544i | ||||
\(872\) | 10.2058 | − | 17.6769i | 0.345611 | − | 0.598616i | ||||
\(873\) | −16.5000 | − | 9.52628i | −0.558440 | − | 0.322416i | ||||
\(874\) | − | 0.928203i | − | 0.0313969i | ||||||
\(875\) | 7.98076 | − | 4.60770i | 0.269799 | − | 0.155769i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.78461 | 0.195332 | 0.0976662 | − | 0.995219i | \(-0.468862\pi\) | ||||
0.0976662 | + | 0.995219i | \(0.468862\pi\) | |||||||
\(878\) | −14.5359 | −0.490563 | ||||||||
\(879\) | 39.4186 | − | 68.2750i | 1.32956 | − | 2.30286i | ||||
\(880\) | 1.26795i | 0.0427426i | ||||||||
\(881\) | −16.1603 | − | 27.9904i | −0.544453 | − | 0.943020i | −0.998641 | − | 0.0521142i | \(-0.983404\pi\) |
0.454188 | − | 0.890906i | \(-0.349929\pi\) | |||||||
\(882\) | 22.3205i | 0.751571i | ||||||||
\(883\) | −30.8827 | + | 17.8301i | −1.03929 | + | 0.600032i | −0.919631 | − | 0.392784i | \(-0.871512\pi\) |
−0.119654 | + | 0.992816i | \(0.538179\pi\) | |||||||
\(884\) | −6.46410 | − | 11.1962i | −0.217411 | − | 0.376567i | ||||
\(885\) | −4.92820 | − | 8.53590i | −0.165660 | − | 0.286931i | ||||
\(886\) | −28.9808 | − | 16.7321i | −0.973628 | − | 0.562124i | ||||
\(887\) | 28.9808 | 0.973079 | 0.486539 | − | 0.873659i | \(-0.338259\pi\) | ||||
0.486539 | + | 0.873659i | \(0.338259\pi\) | |||||||
\(888\) | 21.2942 | + | 45.0788i | 0.714588 | + | 1.51275i | ||||
\(889\) | −42.2487 | −1.41698 | ||||||||
\(890\) | −2.13397 | − | 1.23205i | −0.0715310 | − | 0.0412984i | ||||
\(891\) | −5.83013 | − | 10.0981i | −0.195317 | − | 0.338298i | ||||
\(892\) | −2.29423 | − | 3.97372i | −0.0768165 | − | 0.133050i | ||||
\(893\) | −2.41154 | + | 1.39230i | −0.0806992 | + | 0.0465917i | ||||
\(894\) | − | 15.1244i | − | 0.505834i | ||||||
\(895\) | −0.196152 | − | 0.339746i | −0.00655665 | − | 0.0113565i | ||||
\(896\) | 10.3923i | 0.347183i | ||||||||
\(897\) | −3.46410 | + | 6.00000i | −0.115663 | + | 0.200334i | ||||
\(898\) | 32.2487 | 1.07615 | ||||||||
\(899\) | 2.19615 | 0.0732458 | ||||||||
\(900\) | −11.0000 | + | 19.0526i | −0.366667 | + | 0.635085i | ||||
\(901\) | 8.19615 | − | 4.73205i | 0.273053 | − | 0.157647i | ||||
\(902\) | − | 14.1962i | − | 0.472680i | ||||||
\(903\) | −28.3923 | − | 16.3923i | −0.944837 | − | 0.545502i | ||||
\(904\) | 6.80385 | − | 11.7846i | 0.226293 | − | 0.391950i | ||||
\(905\) | −2.30385 | − | 1.33013i | −0.0765825 | − | 0.0442149i | ||||
\(906\) | −39.2487 | + | 22.6603i | −1.30395 | + | 0.752837i | ||||
\(907\) | 1.09808 | − | 0.633975i | 0.0364610 | − | 0.0210508i | −0.481659 | − | 0.876359i | \(-0.659965\pi\) |
0.518120 | + | 0.855308i | \(0.326632\pi\) | |||||||
\(908\) | −20.0263 | − | 11.5622i | −0.664595 | − | 0.383704i | ||||
\(909\) | 20.0885 | − | 34.7942i | 0.666292 | − | 1.15405i | ||||
\(910\) | 2.78461 | + | 1.60770i | 0.0923089 | + | 0.0532946i | ||||
\(911\) | 53.5167i | 1.77309i | 0.462646 | + | 0.886543i | \(0.346900\pi\) | ||||
−0.462646 | + | 0.886543i | \(0.653100\pi\) | |||||||
\(912\) | 3.00000 | − | 1.73205i | 0.0993399 | − | 0.0573539i | ||||
\(913\) | −19.3923 | + | 33.5885i | −0.641792 | + | 1.11162i | ||||
\(914\) | 36.1244 | 1.19489 | ||||||||
\(915\) | 3.12436 | 0.103288 | ||||||||
\(916\) | −3.50000 | + | 6.06218i | −0.115643 | + | 0.200300i | ||||
\(917\) | 36.6795i | 1.21126i | ||||||||
\(918\) | 7.46410 | + | 12.9282i | 0.246352 | + | 0.426694i | ||||
\(919\) | − | 4.05256i | − | 0.133682i | −0.997764 | − | 0.0668408i | \(-0.978708\pi\) | ||
0.997764 | − | 0.0668408i | \(-0.0212920\pi\) | |||||||
\(920\) | −0.509619 | + | 0.294229i | −0.0168016 | + | 0.00970043i | ||||
\(921\) | −19.6603 | − | 34.0526i | −0.647827 | − | 1.12207i | ||||
\(922\) | 8.26795 | + | 14.3205i | 0.272290 | + | 0.471621i | ||||
\(923\) | −18.0000 | − | 10.3923i | −0.592477 | − | 0.342067i | ||||
\(924\) | 44.7846 | 1.47331 | ||||||||
\(925\) | 24.6410 | + | 17.0718i | 0.810192 | + | 0.561317i | ||||
\(926\) | 15.4641 | 0.508182 | ||||||||
\(927\) | −49.9808 | − | 28.8564i | −1.64158 | − | 0.947769i | ||||
\(928\) | −0.669873 | − | 1.16025i | −0.0219897 | − | 0.0380872i | ||||
\(929\) | 15.2321 | + | 26.3827i | 0.499747 | + | 0.865588i | 1.00000 | 0.000291680i | \(-9.28447e-5\pi\) | |
−0.500253 | + | 0.865880i | \(0.666760\pi\) | |||||||
\(930\) | 5.19615 | − | 3.00000i | 0.170389 | − | 0.0983739i | ||||
\(931\) | 6.33975i | 0.207777i | ||||||||
\(932\) | 5.42820 | + | 9.40192i | 0.177807 | + | 0.307970i | ||||
\(933\) | − | 83.0333i | − | 2.71839i | ||||||
\(934\) | 1.66025 | − | 2.87564i | 0.0543252 | − | 0.0940940i | ||||
\(935\) | −4.73205 | −0.154755 | ||||||||
\(936\) | −46.3923 | −1.51638 | ||||||||
\(937\) | 6.30385 | − | 10.9186i | 0.205938 | − | 0.356695i | −0.744493 | − | 0.667630i | \(-0.767309\pi\) |
0.950431 | + | 0.310935i | \(0.100642\pi\) | |||||||
\(938\) | −21.8038 | + | 12.5885i | −0.711921 | + | 0.411028i | ||||
\(939\) | − | 42.5885i | − | 1.38982i | ||||||
\(940\) | 0.509619 | + | 0.294229i | 0.0166219 | + | 0.00959668i | ||||
\(941\) | 2.08846 | − | 3.61731i | 0.0680818 | − | 0.117921i | −0.829975 | − | 0.557800i | \(-0.811645\pi\) |
0.898057 | + | 0.439879i | \(0.144979\pi\) | |||||||
\(942\) | −33.8827 | − | 19.5622i | −1.10396 | − | 0.637370i | ||||
\(943\) | 1.90192 | − | 1.09808i | 0.0619352 | − | 0.0357583i | ||||
\(944\) | −11.6603 | + | 6.73205i | −0.379509 | + | 0.219110i | ||||
\(945\) | 3.21539 | + | 1.85641i | 0.104597 | + | 0.0603889i | ||||
\(946\) | 8.19615 | − | 14.1962i | 0.266480 | − | 0.461557i | ||||
\(947\) | −23.9090 | − | 13.8038i | −0.776937 | − | 0.448565i | 0.0584067 | − | 0.998293i | \(-0.481398\pi\) |
−0.835344 | + | 0.549728i | \(0.814731\pi\) | |||||||
\(948\) | − | 10.3923i | − | 0.337526i | ||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 3.12436 | − | 5.41154i | 0.101367 | − | 0.175574i | ||||
\(951\) | 43.5167 | 1.41112 | ||||||||
\(952\) | 38.7846 | 1.25702 | ||||||||
\(953\) | 2.07180 | − | 3.58846i | 0.0671121 | − | 0.116242i | −0.830517 | − | 0.556993i | \(-0.811955\pi\) |
0.897629 | + | 0.440752i | \(0.145288\pi\) | |||||||
\(954\) | − | 11.3205i | − | 0.366515i | ||||||
\(955\) | 0.830127 | + | 1.43782i | 0.0268623 | + | 0.0465268i | ||||
\(956\) | − | 16.9282i | − | 0.547497i | ||||||
\(957\) | −3.00000 | + | 1.73205i | −0.0969762 | + | 0.0559893i | ||||
\(958\) | 19.6603 | + | 34.0526i | 0.635194 | + | 1.10019i | ||||
\(959\) | 11.1962 | + | 19.3923i | 0.361543 | + | 0.626210i | ||||
\(960\) | −4.43782 | − | 2.56218i | −0.143230 | − | 0.0826939i | ||||
\(961\) | −36.1769 | −1.16700 | ||||||||
\(962\) | −1.73205 | + | 21.0000i | −0.0558436 | + | 0.677067i | ||||
\(963\) | −57.7128 | −1.85977 | ||||||||
\(964\) | 13.3923 | + | 7.73205i | 0.431337 | + | 0.249033i | ||||
\(965\) | 1.96410 | + | 3.40192i | 0.0632267 | + | 0.109512i | ||||
\(966\) | −3.46410 | − | 6.00000i | −0.111456 | − | 0.193047i | ||||
\(967\) | 28.3923 | − | 16.3923i | 0.913035 | − | 0.527141i | 0.0316286 | − | 0.999500i | \(-0.489931\pi\) |
0.881406 | + | 0.472359i | \(0.156597\pi\) | |||||||
\(968\) | 34.1769i | 1.09849i | ||||||||
\(969\) | 6.46410 | + | 11.1962i | 0.207657 | + | 0.359672i | ||||
\(970\) | − | 1.14359i | − | 0.0367186i | ||||||
\(971\) | 4.09808 | − | 7.09808i | 0.131514 | − | 0.227788i | −0.792747 | − | 0.609551i | \(-0.791350\pi\) |
0.924260 | + | 0.381763i | \(0.124683\pi\) | |||||||
\(972\) | 18.7321 | 0.600831 | ||||||||
\(973\) | 43.6077 | 1.39800 | ||||||||
\(974\) | −16.2224 | + | 28.0981i | −0.519800 | + | 0.900320i | ||||
\(975\) | −40.3923 | + | 23.3205i | −1.29359 | + | 0.746854i | ||||
\(976\) | − | 4.26795i | − | 0.136614i | ||||||
\(977\) | −14.0718 | − | 8.12436i | −0.450197 | − | 0.259921i | 0.257717 | − | 0.966221i | \(-0.417030\pi\) |
−0.707913 | + | 0.706299i | \(0.750363\pi\) | |||||||
\(978\) | 30.5885 | − | 52.9808i | 0.978111 | − | 1.69414i | ||||
\(979\) | −37.6865 | − | 21.7583i | −1.20447 | − | 0.695399i | ||||
\(980\) | 1.16025 | − | 0.669873i | 0.0370630 | − | 0.0213983i | ||||
\(981\) | 26.3038 | − | 15.1865i | 0.839817 | − | 0.484869i | ||||
\(982\) | −27.0788 | − | 15.6340i | −0.864120 | − | 0.498900i | ||||
\(983\) | −28.5622 | + | 49.4711i | −0.910992 | + | 1.57788i | −0.0983263 | + | 0.995154i | \(0.531349\pi\) |
−0.812666 | + | 0.582730i | \(0.801984\pi\) | |||||||
\(984\) | 21.2942 | + | 12.2942i | 0.678835 | + | 0.391926i | ||||
\(985\) | 7.48334i | 0.238439i | ||||||||
\(986\) | −0.866025 | + | 0.500000i | −0.0275799 | + | 0.0159232i | ||||
\(987\) | −10.3923 | + | 18.0000i | −0.330791 | + | 0.572946i | ||||
\(988\) | −4.39230 | −0.139738 | ||||||||
\(989\) | 2.53590 | 0.0806369 | ||||||||
\(990\) | −2.83013 | + | 4.90192i | −0.0899473 | + | 0.155793i | ||||
\(991\) | 46.3923i | 1.47370i | 0.676056 | + | 0.736850i | \(0.263688\pi\) | ||||
−0.676056 | + | 0.736850i | \(0.736312\pi\) | |||||||
\(992\) | 20.4904 | + | 35.4904i | 0.650570 | + | 1.12682i | ||||
\(993\) | 89.5692i | 2.84239i | ||||||||
\(994\) | 18.0000 | − | 10.3923i | 0.570925 | − | 0.329624i | ||||
\(995\) | 1.48334 | + | 2.56922i | 0.0470250 | + | 0.0814497i | ||||
\(996\) | −11.1962 | − | 19.3923i | −0.354764 | − | 0.614469i | ||||
\(997\) | 17.7846 | + | 10.2679i | 0.563244 | + | 0.325189i | 0.754447 | − | 0.656361i | \(-0.227905\pi\) |
−0.191202 | + | 0.981551i | \(0.561239\pi\) | |||||||
\(998\) | −12.5885 | −0.398481 | ||||||||
\(999\) | −2.00000 | + | 24.2487i | −0.0632772 | + | 0.767195i |
(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 | 37.2.e.a.27.1 | yes | 4 | |
3.2 | odd | 2 | 333.2.s.b.64.2 | 4 | |||
4.3 | odd | 2 | 592.2.w.c.545.1 | 4 | |||
5.2 | odd | 4 | 925.2.m.b.249.2 | 4 | |||
5.3 | odd | 4 | 925.2.m.a.249.1 | 4 | |||
5.4 | even | 2 | 925.2.n.a.101.2 | 4 | |||
37.10 | even | 3 | 1369.2.b.d.1368.3 | 4 | |||
37.11 | even | 6 | inner | 37.2.e.a.11.1 | ✓ | 4 | |
37.14 | odd | 12 | 1369.2.a.g.1.2 | 2 | |||
37.23 | odd | 12 | 1369.2.a.h.1.2 | 2 | |||
37.27 | even | 6 | 1369.2.b.d.1368.1 | 4 | |||
111.11 | odd | 6 | 333.2.s.b.307.2 | 4 | |||
148.11 | odd | 6 | 592.2.w.c.529.1 | 4 | |||
185.48 | odd | 12 | 925.2.m.b.899.2 | 4 | |||
185.122 | odd | 12 | 925.2.m.a.899.1 | 4 | |||
185.159 | even | 6 | 925.2.n.a.751.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.2.e.a.11.1 | ✓ | 4 | 37.11 | even | 6 | inner | |
37.2.e.a.27.1 | yes | 4 | 1.1 | even | 1 | trivial | |
333.2.s.b.64.2 | 4 | 3.2 | odd | 2 | |||
333.2.s.b.307.2 | 4 | 111.11 | odd | 6 | |||
592.2.w.c.529.1 | 4 | 148.11 | odd | 6 | |||
592.2.w.c.545.1 | 4 | 4.3 | odd | 2 | |||
925.2.m.a.249.1 | 4 | 5.3 | odd | 4 | |||
925.2.m.a.899.1 | 4 | 185.122 | odd | 12 | |||
925.2.m.b.249.2 | 4 | 5.2 | odd | 4 | |||
925.2.m.b.899.2 | 4 | 185.48 | odd | 12 | |||
925.2.n.a.101.2 | 4 | 5.4 | even | 2 | |||
925.2.n.a.751.2 | 4 | 185.159 | even | 6 | |||
1369.2.a.g.1.2 | 2 | 37.14 | odd | 12 | |||
1369.2.a.h.1.2 | 2 | 37.23 | odd | 12 | |||
1369.2.b.d.1368.1 | 4 | 37.27 | even | 6 | |||
1369.2.b.d.1368.3 | 4 | 37.10 | even | 3 |