Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(47,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.be (of order \(18\), degree \(6\), 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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 47.5 | ||
Character | \(\chi\) | \(=\) | 432.47 |
Dual form | 432.2.be.c.239.5 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{18}\right)\) |
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 | 0 | ||||||||
\(3\) | 1.59623 | + | 0.672336i | 0.921586 | + | 0.388173i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.18690 | − | 0.738263i | 1.87244 | − | 0.330161i | 0.882348 | − | 0.470597i | \(-0.155961\pi\) |
0.990090 | + | 0.140435i | \(0.0448502\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.26944 | + | 1.51285i | −0.479801 | + | 0.571805i | −0.950593 | − | 0.310439i | \(-0.899524\pi\) |
0.470792 | + | 0.882244i | \(0.343968\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.09593 | + | 2.14641i | 0.698643 | + | 0.715470i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.313474 | − | 1.77780i | 0.0945158 | − | 0.536026i | −0.900379 | − | 0.435107i | \(-0.856711\pi\) |
0.994895 | − | 0.100919i | \(-0.0321783\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.16732 | − | 1.15281i | −0.878456 | − | 0.319732i | −0.136870 | − | 0.990589i | \(-0.543704\pi\) |
−0.741587 | + | 0.670857i | \(0.765926\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.17963 | + | 1.63656i | 1.85377 | + | 0.422558i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.51308 | + | 0.873578i | −0.366976 | + | 0.211874i | −0.672137 | − | 0.740427i | \(-0.734623\pi\) |
0.305160 | + | 0.952301i | \(0.401290\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.62765 | − | 2.09442i | −0.832240 | − | 0.480494i | 0.0223793 | − | 0.999750i | \(-0.492876\pi\) |
−0.854619 | + | 0.519256i | \(0.826209\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.04346 | + | 1.56138i | −0.664138 | + | 0.340722i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.40902 | + | 4.53870i | −1.12786 | + | 0.946385i | −0.998975 | − | 0.0452747i | \(-0.985584\pi\) |
−0.128883 | + | 0.991660i | \(0.541139\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.2866 | − | 4.47197i | 2.45733 | − | 0.894393i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.90249 | + | 4.83534i | 0.366134 | + | 0.930562i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00752 | − | 8.26311i | −0.558483 | − | 1.53442i | −0.821838 | − | 0.569721i | \(-0.807051\pi\) |
0.263355 | − | 0.964699i | \(-0.415171\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.17218 | − | 3.78046i | −0.569741 | − | 0.678991i | 0.401837 | − | 0.915711i | \(-0.368372\pi\) |
−0.971578 | + | 0.236720i | \(0.923928\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.69565 | − | 2.62702i | 0.295175 | − | 0.457306i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.19811 | + | 7.27134i | −0.709611 | + | 1.22908i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.864428 | + | 1.49723i | 0.142111 | + | 0.246144i | 0.928291 | − | 0.371854i | \(-0.121278\pi\) |
−0.786180 | + | 0.617997i | \(0.787944\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.28071 | − | 3.96966i | −0.685462 | − | 0.635654i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.58140 | + | 4.34487i | −0.246974 | + | 0.678554i | 0.752820 | + | 0.658227i | \(0.228693\pi\) |
−0.999793 | + | 0.0203276i | \(0.993529\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.92458 | + | 1.74997i | 1.51348 | + | 0.266868i | 0.867869 | − | 0.496794i | \(-0.165490\pi\) |
0.645616 | + | 0.763662i | \(0.276601\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.3601 | + | 7.43946i | 1.54439 | + | 1.10901i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.63291 | + | 2.20928i | 0.384050 | + | 0.322256i | 0.814290 | − | 0.580458i | \(-0.197127\pi\) |
−0.430240 | + | 0.902715i | \(0.641571\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.538276 | + | 3.05271i | 0.0768965 | + | 0.436102i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.00257 | + | 0.377137i | −0.420444 | + | 0.0528097i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 0.511832i | − | 0.0703056i | −0.999382 | − | 0.0351528i | \(-0.988808\pi\) | ||
0.999382 | − | 0.0351528i | \(-0.0111918\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 7.67488i | − | 1.03488i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.38242 | − | 5.78219i | −0.580466 | − | 0.765870i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.75988 | + | 9.98076i | 0.229116 | + | 1.29938i | 0.854657 | + | 0.519193i | \(0.173767\pi\) |
−0.625541 | + | 0.780191i | \(0.715122\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.752671 | + | 0.631566i | 0.0963697 | + | 0.0808638i | 0.689700 | − | 0.724096i | \(-0.257743\pi\) |
−0.593330 | + | 0.804959i | \(0.702187\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.90785 | + | 0.446106i | −0.744320 | + | 0.0562041i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.1123 | − | 2.48838i | −1.75042 | − | 0.308646i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.10742 | − | 11.2851i | 0.501802 | − | 1.37869i | −0.387712 | − | 0.921780i | \(-0.626735\pi\) |
0.889514 | − | 0.456908i | \(-0.151043\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.6856 | + | 3.60816i | −1.40678 | + | 0.434372i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.03319 | − | 1.78955i | −0.122618 | − | 0.212380i | 0.798182 | − | 0.602417i | \(-0.205796\pi\) |
−0.920799 | + | 0.390037i | \(0.872462\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.31302 | − | 2.27422i | 0.153678 | − | 0.266178i | −0.778899 | − | 0.627149i | \(-0.784222\pi\) |
0.932577 | + | 0.360972i | \(0.117555\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 22.6190 | + | 1.12243i | 2.61182 | + | 0.129607i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.29161 | + | 2.73104i | 0.261154 | + | 0.311231i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.02177 | − | 16.5447i | −0.677502 | − | 1.86142i | −0.468369 | − | 0.883533i | \(-0.655158\pi\) |
−0.209133 | − | 0.977887i | \(-0.567064\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.214158 | + | 8.99745i | −0.0237953 | + | 0.999717i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.45879 | + | 1.25890i | −0.379652 | + | 0.138182i | −0.524795 | − | 0.851229i | \(-0.675858\pi\) |
0.145143 | + | 0.989411i | \(0.453636\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.69019 | + | 4.77464i | −0.617188 | + | 0.517882i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.754866 | − | 15.2119i | 0.0809301 | − | 1.63089i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.46750 | − | 3.73401i | −0.685554 | − | 0.395805i | 0.116390 | − | 0.993204i | \(-0.462868\pi\) |
−0.801944 | + | 0.597399i | \(0.796201\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.76474 | − | 3.32827i | 0.604309 | − | 0.348898i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.52181 | − | 8.16728i | −0.261500 | − | 0.846907i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.7348 | − | 6.09098i | −1.71696 | − | 0.624922i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.250759 | + | 1.42213i | −0.0254607 | + | 0.144395i | −0.994888 | − | 0.100983i | \(-0.967801\pi\) |
0.969427 | + | 0.245378i | \(0.0789122\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.47290 | − | 3.05329i | 0.449543 | − | 0.306868i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.74078 | + | 5.64984i | −0.471725 | + | 0.562180i | −0.948472 | − | 0.316860i | \(-0.897371\pi\) |
0.476747 | + | 0.879041i | \(0.341816\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.8583 | + | 2.26726i | −1.26696 | + | 0.223399i | −0.766435 | − | 0.642322i | \(-0.777971\pi\) |
−0.500526 | + | 0.865721i | \(0.666860\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.5900 | + | 8.78423i | −1.13106 | + | 0.857253i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.16482 | 0.885997 | 0.442998 | − | 0.896522i | \(-0.353915\pi\) | ||||
0.442998 | + | 0.896522i | \(0.353915\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.4898 | −1.19630 | −0.598151 | − | 0.801383i | \(-0.704098\pi\) | ||||
−0.598151 | + | 0.801383i | \(0.704098\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.373187 | + | 2.97112i | 0.0354213 | + | 0.282006i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.38278 | + | 1.12546i | −0.600441 | + | 0.105874i | −0.465603 | − | 0.884994i | \(-0.654163\pi\) |
−0.134838 | + | 0.990868i | \(0.543051\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −19.2962 | + | 22.9964i | −1.79938 | + | 2.14442i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.16407 | − | 9.21457i | −0.384969 | − | 0.851888i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.599163 | − | 3.39802i | 0.0549252 | − | 0.311496i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.27432 | + | 2.64764i | 0.661302 | + | 0.240694i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.44550 | + | 5.87219i | −0.491004 | + | 0.529478i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 29.7319 | − | 17.1657i | 2.65930 | − | 1.53535i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.67356 | + | 5.00768i | 0.769654 | + | 0.444360i | 0.832751 | − | 0.553647i | \(-0.186764\pi\) |
−0.0630972 | + | 0.998007i | \(0.520098\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.6654 | + | 9.46602i | 1.29122 | + | 0.833436i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.79708 | − | 7.38162i | 0.768604 | − | 0.644936i | −0.171747 | − | 0.985141i | \(-0.554941\pi\) |
0.940351 | + | 0.340206i | \(0.110497\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.77362 | − | 2.82937i | 0.674059 | − | 0.245337i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.5353 | + | 18.8406i | 0.992799 | + | 1.62154i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.13684 | + | 3.12344i | 0.0971268 | + | 0.266854i | 0.978735 | − | 0.205128i | \(-0.0657611\pi\) |
−0.881608 | + | 0.471982i | \(0.843539\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.27514 | − | 7.47842i | −0.532251 | − | 0.634311i | 0.431181 | − | 0.902265i | \(-0.358097\pi\) |
−0.963432 | + | 0.267954i | \(0.913653\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.71737 | + | 5.29673i | 0.228844 | + | 0.446065i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.04233 | + | 5.26947i | −0.254413 | + | 0.440656i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.6926 | − | 32.3764i | −1.55233 | − | 2.68872i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.19323 | + | 5.23475i | −0.0984163 | + | 0.431755i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.99419 | + | 19.2164i | −0.572986 | + | 1.57427i | 0.226774 | + | 0.973947i | \(0.427182\pi\) |
−0.799761 | + | 0.600319i | \(0.795040\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.4203 | + | 1.83738i | 0.847990 | + | 0.149524i | 0.580725 | − | 0.814100i | \(-0.302769\pi\) |
0.267265 | + | 0.963623i | \(0.413880\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.04637 | − | 1.41674i | −0.407975 | − | 0.114536i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.0726 | − | 13.4865i | −1.29098 | − | 1.08326i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.76938 | + | 21.3772i | 0.300829 | + | 1.70609i | 0.642515 | + | 0.766273i | \(0.277891\pi\) |
−0.341686 | + | 0.939814i | \(0.610998\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.344123 | − | 0.817005i | 0.0272907 | − | 0.0647927i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 13.9446i | − | 1.09899i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.10221i | 0.0863315i | 0.999068 | + | 0.0431658i | \(0.0137444\pi\) | ||||
−0.999068 | + | 0.0431658i | \(0.986256\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.16010 | − | 12.2509i | 0.401713 | − | 0.953732i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.82002 | − | 10.3218i | −0.140837 | − | 0.798727i | −0.970616 | − | 0.240634i | \(-0.922645\pi\) |
0.829779 | − | 0.558092i | \(-0.188467\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.25564 | − | 1.05361i | −0.0965879 | − | 0.0810468i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.10780 | − | 12.1762i | −0.237660 | − | 0.931136i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.239692 | − | 0.0422642i | −0.0182235 | − | 0.00321329i | 0.164529 | − | 0.986372i | \(-0.447390\pi\) |
−0.182752 | + | 0.983159i | \(0.558501\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.83165 | + | 24.2648i | −0.667610 | + | 1.83424i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.90124 | + | 17.1149i | −0.293235 | + | 1.28643i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.372275 | + | 0.644799i | 0.0278251 | + | 0.0481946i | 0.879603 | − | 0.475709i | \(-0.157809\pi\) |
−0.851778 | + | 0.523904i | \(0.824475\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.83351 | − | 15.3001i | 0.656590 | − | 1.13725i | −0.324903 | − | 0.945747i | \(-0.605332\pi\) |
0.981493 | − | 0.191500i | \(-0.0613351\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.776815 | + | 1.51418i | 0.0574239 | + | 0.111931i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.72463 | + | 5.63059i | 0.347361 | + | 0.413969i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.07873 | + | 2.96380i | 0.0788848 | + | 0.216734i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.73025 | − | 3.25997i | −0.707772 | − | 0.237128i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.20584 | − | 3.35065i | 0.666111 | − | 0.242445i | 0.0132384 | − | 0.999912i | \(-0.495786\pi\) |
0.652873 | + | 0.757468i | \(0.273564\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.56436 | + | 5.50815i | −0.472513 | + | 0.396486i | −0.847710 | − | 0.530459i | \(-0.822019\pi\) |
0.375197 | + | 0.926945i | \(0.377575\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −20.8535 | − | 13.4603i | −1.49335 | − | 0.963909i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.15257 | + | 0.665435i | 0.0821170 | + | 0.0474103i | 0.540496 | − | 0.841346i | \(-0.318237\pi\) |
−0.458379 | + | 0.888757i | \(0.651570\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.2785 | − | 8.24368i | 1.01217 | − | 0.584379i | 0.100347 | − | 0.994953i | \(-0.468005\pi\) |
0.911828 | + | 0.410573i | \(0.134671\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.1438 | − | 15.2520i | 0.997623 | − | 1.07579i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.3187 | + | 5.93953i | 1.14535 | + | 0.416873i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.41352 | + | 19.3590i | −0.238410 | + | 1.35209i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −21.0788 | − | 2.09717i | −1.46508 | − | 0.145763i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.86063 | + | 5.79268i | −0.336217 | + | 0.400688i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.8106 | − | 2.08253i | 0.813078 | − | 0.143368i | 0.248377 | − | 0.968663i | \(-0.420103\pi\) |
0.564701 | + | 0.825296i | \(0.308992\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.446046 | − | 3.55119i | −0.0305626 | − | 0.243323i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 42.8452 | 2.92202 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.74617 | 0.661613 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.62493 | − | 2.74740i | 0.244950 | − | 0.185652i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.79948 | − | 1.02260i | 0.390115 | − | 0.0687878i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.09692 | − | 7.26603i | 0.408280 | − | 0.486569i | −0.522246 | − | 0.852795i | \(-0.674906\pi\) |
0.930526 | + | 0.366226i | \(0.119350\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 35.3506 | + | 16.9992i | 2.35671 | + | 1.13328i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.39601 | + | 7.91718i | −0.0926565 | + | 0.525481i | 0.902784 | + | 0.430095i | \(0.141520\pi\) |
−0.995440 | + | 0.0953866i | \(0.969591\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.27154 | + | 3.37456i | 0.612680 | + | 0.222997i | 0.629676 | − | 0.776858i | \(-0.283188\pi\) |
−0.0169953 | + | 0.999856i | \(0.505410\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.82178 | + | 5.90011i | 0.119864 | + | 0.388199i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.5103 | − | 10.1096i | 1.14714 | − | 0.662302i | 0.198952 | − | 0.980009i | \(-0.436246\pi\) |
0.948189 | + | 0.317707i | \(0.102913\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.6548 | + | 7.30624i | 0.825507 | + | 0.476606i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.51142 | − | 30.4578i | 0.0981771 | − | 1.97845i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.0130 | + | 17.6320i | −1.35922 | + | 1.14052i | −0.382993 | + | 0.923751i | \(0.625107\pi\) |
−0.976224 | + | 0.216766i | \(0.930449\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.83906 | − | 2.85318i | 0.504958 | − | 0.183790i | −0.0769646 | − | 0.997034i | \(-0.524523\pi\) |
0.581923 | + | 0.813244i | \(0.302301\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.39115 | + | 14.2181i | −0.409993 | + | 0.912089i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.50741 | + | 12.3840i | 0.287968 | + | 0.791186i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.07545 | + | 10.8157i | 0.577457 | + | 0.688186i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.36744 | − | 0.315973i | −0.403520 | − | 0.0200240i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.0064 | + | 17.3316i | −0.631600 | + | 1.09396i | 0.355624 | + | 0.934629i | \(0.384268\pi\) |
−0.987225 | + | 0.159335i | \(0.949065\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.37331 | + | 11.0389i | 0.400687 | + | 0.694009i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.2930 | + | 3.79572i | −0.769820 | + | 0.237697i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.768135 | − | 2.11043i | 0.0479150 | − | 0.131645i | −0.913427 | − | 0.407003i | \(-0.866574\pi\) |
0.961342 | + | 0.275357i | \(0.0887962\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.36243 | − | 0.592887i | −0.208931 | − | 0.0368402i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.4325 | − | 23.7743i | 0.707651 | − | 1.47159i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.74693 | + | 8.17865i | 0.601022 | + | 0.504317i | 0.891774 | − | 0.452481i | \(-0.149461\pi\) |
−0.290752 | + | 0.956798i | \(0.593906\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.377867 | − | 2.14299i | −0.0232122 | − | 0.131643i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.81314 | − | 10.3087i | −0.478156 | − | 0.630882i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.9356i | 0.849668i | 0.905271 | + | 0.424834i | \(0.139668\pi\) | ||||
−0.905271 | + | 0.424834i | \(0.860332\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.32883i | 0.0807208i | 0.999185 | + | 0.0403604i | \(0.0128506\pi\) | ||||
−0.999185 | + | 0.0403604i | \(0.987149\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.4396 | − | 1.43687i | 0.692356 | − | 0.0869631i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.09872 | − | 23.2450i | −0.247162 | − | 1.40172i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.21107 | + | 4.37261i | 0.313103 | + | 0.262724i | 0.785773 | − | 0.618515i | \(-0.212265\pi\) |
−0.472670 | + | 0.881239i | \(0.656710\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.46575 | − | 14.7324i | 0.0877521 | − | 0.882005i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.97579 | − | 0.701039i | −0.237176 | − | 0.0418205i | 0.0537967 | − | 0.998552i | \(-0.482868\pi\) |
−0.290972 | + | 0.956731i | \(0.593979\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.187770 | + | 0.515894i | −0.0111618 | + | 0.0306667i | −0.945148 | − | 0.326641i | \(-0.894083\pi\) |
0.933987 | + | 0.357308i | \(0.116305\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −22.6175 | − | 20.9741i | −1.33975 | − | 1.24240i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.56566 | − | 7.90796i | −0.269502 | − | 0.466792i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.97372 | + | 12.0788i | −0.410219 | + | 0.710520i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.35642 | + | 2.10145i | −0.0795146 | + | 0.123189i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.7794 | + | 14.0382i | 0.688163 | + | 0.820121i | 0.991132 | − | 0.132880i | \(-0.0424224\pi\) |
−0.302969 | + | 0.953000i | \(0.597978\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.7369 | + | 40.4892i | 0.858013 | + | 2.35737i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.19264 | − | 1.86648i | 0.533411 | − | 0.108304i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 22.3643 | − | 8.13995i | 1.29336 | − | 0.470746i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.2461 | + | 12.7930i | −0.878769 | + | 0.737374i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.3660 | + | 5.83108i | −0.652959 | + | 0.334987i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.61762 | + | 2.08863i | 0.207144 | + | 0.119595i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.9994 | + | 6.92784i | −0.684841 | + | 0.395393i | −0.801676 | − | 0.597758i | \(-0.796058\pi\) |
0.116836 | + | 0.993151i | \(0.462725\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22.0491 | − | 5.02599i | −1.25433 | − | 0.285918i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.49020 | − | 1.27033i | −0.197911 | − | 0.0720338i | 0.241163 | − | 0.970485i | \(-0.422471\pi\) |
−0.439074 | + | 0.898451i | \(0.644693\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.96289 | − | 22.4747i | 0.223996 | − | 1.27034i | −0.640599 | − | 0.767875i | \(-0.721314\pi\) |
0.864595 | − | 0.502469i | \(-0.167575\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −24.4062 | + | 6.22935i | −1.37514 | + | 0.350984i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.1228 | − | 13.2557i | 0.624720 | − | 0.744512i | −0.357155 | − | 0.934045i | \(-0.616253\pi\) |
0.981874 | + | 0.189533i | \(0.0606975\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.6329 | + | 2.75650i | −0.875275 | + | 0.154335i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.6292 | + | 6.16184i | 0.816523 | + | 0.343920i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.31857 | 0.407216 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −44.0710 | −2.44462 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −19.9366 | − | 8.39731i | −1.10250 | − | 0.464372i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.68463 | + | 1.17868i | −0.368536 | + | 0.0649828i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.63111 | − | 5.51914i | 0.254549 | − | 0.303359i | −0.623603 | − | 0.781741i | \(-0.714332\pi\) |
0.878152 | + | 0.478382i | \(0.158776\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.40190 | + | 4.99351i | −0.0768235 | + | 0.273643i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.86603 | − | 50.2817i | 0.484403 | − | 2.74718i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.8554 | − | 8.68267i | −1.29949 | − | 0.472975i | −0.402659 | − | 0.915350i | \(-0.631914\pi\) |
−0.896830 | + | 0.442375i | \(0.854136\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.9451 | − | 2.49488i | −0.594456 | − | 0.135503i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.71529 | + | 4.45443i | −0.417806 | + | 0.241221i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.2738 | − | 9.97301i | −0.932695 | − | 0.538492i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −46.2626 | + | 23.7341i | −2.49070 | + | 1.27780i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.38189 | − | 6.19414i | 0.396281 | − | 0.332519i | −0.422773 | − | 0.906235i | \(-0.638943\pi\) |
0.819054 | + | 0.573717i | \(0.194499\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.04043 | + | 0.378686i | −0.0556930 | + | 0.0202706i | −0.369716 | − | 0.929145i | \(-0.620545\pi\) |
0.314023 | + | 0.949415i | \(0.398323\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.451552 | − | 17.5083i | −0.0241021 | − | 0.934523i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.9418 | − | 30.0625i | −0.582375 | − | 1.60006i | −0.784109 | − | 0.620623i | \(-0.786880\pi\) |
0.201734 | − | 0.979440i | \(-0.435342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.64704 | − | 6.72988i | −0.299714 | − | 0.357185i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.24102 | − | 5.02120i | 0.171533 | − | 0.265750i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.37501 | + | 14.5059i | −0.442016 | + | 0.765595i | −0.997839 | − | 0.0657061i | \(-0.979070\pi\) |
0.555823 | + | 0.831301i | \(0.312403\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.726778 | − | 1.25882i | −0.0382515 | − | 0.0662535i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.83142 | + | 9.11704i | 0.516016 | + | 0.478520i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.81852 | − | 10.4913i | 0.199870 | − | 0.549140i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.44634 | + | 0.784010i | 0.232097 | + | 0.0409250i | 0.288487 | − | 0.957484i | \(-0.406848\pi\) |
−0.0563897 | + | 0.998409i | \(0.517959\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.6404 | + | 5.71220i | −0.658032 | + | 0.297365i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.774328 | + | 0.649738i | 0.0402011 | + | 0.0337327i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.72449 | − | 15.4513i | −0.141069 | − | 0.800040i | −0.970440 | − | 0.241342i | \(-0.922412\pi\) |
0.829372 | − | 0.558698i | \(-0.188699\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 59.0002 | − | 7.41070i | 3.04676 | − | 0.382687i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 29.6390i | 1.52649i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.3891i | 0.790485i | 0.918577 | + | 0.395242i | \(0.129339\pi\) | ||||
−0.918577 | + | 0.395242i | \(0.870661\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.4782 | + | 13.8250i | 0.536814 | + | 0.708275i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.92194 | + | 22.2424i | 0.200402 | + | 1.13654i | 0.904513 | + | 0.426446i | \(0.140235\pi\) |
−0.704111 | + | 0.710090i | \(0.748654\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.6110 | + | 9.74277i | 0.591750 | + | 0.496537i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.0451 | + | 24.9700i | 0.866450 | + | 1.26930i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.2621 | − | 2.33846i | −0.672414 | − | 0.118565i | −0.172992 | − | 0.984923i | \(-0.555343\pi\) |
−0.499423 | + | 0.866358i | \(0.666455\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.21937 | − | 11.5926i | 0.213383 | − | 0.586264i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.0051 | − | 5.86822i | 0.958682 | − | 0.296012i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −37.4268 | − | 64.8252i | −1.88315 | − | 3.26171i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.61332 | + | 2.79436i | −0.0809704 | + | 0.140245i | −0.903667 | − | 0.428236i | \(-0.859135\pi\) |
0.822697 | + | 0.568481i | \(0.192469\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.3108 | + | 0.710149i | 0.716437 | + | 0.0355519i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.1787 | + | 21.6646i | 0.907803 | + | 1.08188i | 0.996312 | + | 0.0858023i | \(0.0273453\pi\) |
−0.0885090 | + | 0.996075i | \(0.528210\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.68917 | + | 15.6309i | 0.283398 | + | 0.778628i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.74583 | + | 37.8295i | 0.285513 | + | 1.87976i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.93275 | − | 1.06743i | 0.145371 | − | 0.0529108i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.48887 | + | 3.76661i | −0.221961 | + | 0.186247i | −0.746987 | − | 0.664839i | \(-0.768500\pi\) |
0.525026 | + | 0.851086i | \(0.324056\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.285338 | + | 5.75009i | −0.0140747 | + | 0.283631i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.3335 | − | 10.0075i | −0.852925 | − | 0.492436i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.5522 | + | 7.82437i | −0.665252 | + | 0.384083i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.98859 | − | 16.1563i | −0.244292 | − | 0.791178i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.0245 | − | 3.64864i | −0.489731 | − | 0.178248i | 0.0853386 | − | 0.996352i | \(-0.472803\pi\) |
−0.575070 | + | 0.818105i | \(0.695025\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.69487 | − | 20.9547i | 0.180077 | − | 1.02127i | −0.752042 | − | 0.659116i | \(-0.770931\pi\) |
0.932119 | − | 0.362153i | \(-0.117958\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.776387 | + | 10.2818i | 0.0377492 | + | 0.499919i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.6841 | + | 17.4998i | −0.712282 | + | 0.848864i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.91093 | + | 0.336949i | −0.0924766 | + | 0.0163061i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.39913 | + | 6.36585i | −0.405514 | + | 0.307346i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.3332 | 0.786744 | 0.393372 | − | 0.919379i | \(-0.371309\pi\) | ||||
0.393372 | + | 0.919379i | \(0.371309\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.2969 | 1.74432 | 0.872159 | − | 0.489222i | \(-0.162719\pi\) | ||||
0.872159 | + | 0.489222i | \(0.162719\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.06986 | − | 64.2481i | −0.386920 | − | 3.08046i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 29.1280 | − | 5.13605i | 1.39338 | − | 0.245691i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.7942 | − | 14.0558i | 0.562906 | − | 0.670845i | −0.407253 | − | 0.913315i | \(-0.633513\pi\) |
0.970159 | + | 0.242470i | \(0.0779577\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.42419 | + | 7.55363i | −0.258295 | + | 0.359697i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.71016 | + | 9.69879i | −0.0812521 | + | 0.460804i | 0.916850 | + | 0.399231i | \(0.130723\pi\) |
−0.998103 | + | 0.0615728i | \(0.980388\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −29.8355 | − | 10.8592i | −1.41434 | − | 0.514776i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.0842 | + | 25.9714i | −1.13914 | + | 1.22840i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.3593 | + | 7.71300i | −0.630465 | + | 0.363999i | −0.780932 | − | 0.624616i | \(-0.785255\pi\) |
0.150467 | + | 0.988615i | \(0.451922\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.22856 | + | 4.17341i | 0.340380 | + | 0.196518i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.3979 | + | 9.93881i | 0.723455 | + | 0.466966i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 21.6792 | − | 18.1910i | 1.01634 | − | 0.852809i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.6347 | + | 6.78248i | −0.871695 | + | 0.317271i | −0.738853 | − | 0.673866i | \(-0.764632\pi\) |
−0.132841 | + | 0.991137i | \(0.542410\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.10267 | − | 5.65430i | −0.331524 | − | 0.263920i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.17082 | + | 3.21680i | 0.0545306 | + | 0.149822i | 0.963967 | − | 0.266021i | \(-0.0857090\pi\) |
−0.909437 | + | 0.415842i | \(0.863487\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.06961 | + | 9.61699i | 0.375027 | + | 0.446939i | 0.920238 | − | 0.391359i | \(-0.127995\pi\) |
−0.545211 | + | 0.838299i | \(0.683551\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −16.5882 | − | 32.3338i | −0.769258 | − | 1.49944i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.1463 | − | 17.5739i | 0.469514 | − | 0.813221i | −0.529879 | − | 0.848073i | \(-0.677763\pi\) |
0.999392 | + | 0.0348520i | \(0.0110960\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.8585 | + | 20.5396i | 0.547576 | + | 0.948429i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.35585 | + | 36.6573i | −0.385017 | + | 1.68908i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.22219 | − | 17.0953i | 0.286097 | − | 0.786044i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −53.9378 | − | 9.51068i | −2.47483 | − | 0.436380i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.09860 | − | 1.07276i | 0.0503016 | − | 0.0491185i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.80006 | − | 1.51043i | −0.0822467 | − | 0.0690131i | 0.600737 | − | 0.799446i | \(-0.294874\pi\) |
−0.682984 | + | 0.730433i | \(0.739318\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.01189 | − | 5.73874i | −0.0461384 | − | 0.261664i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.37548 | − | 22.2589i | 0.426599 | − | 1.01282i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.13943i | 0.278777i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.67682i | − | 0.302555i | −0.988491 | − | 0.151278i | \(-0.951661\pi\) | ||
0.988491 | − | 0.151278i | \(-0.0483388\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.741053 | + | 1.75938i | −0.0335116 | + | 0.0795620i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.97852 | + | 28.2346i | 0.224677 | + | 1.27421i | 0.863301 | + | 0.504690i | \(0.168393\pi\) |
−0.638623 | + | 0.769520i | \(0.720496\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.7691 | + | 9.87545i | 0.530053 | + | 0.444768i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.4735 | − | 16.0860i | 0.740427 | − | 0.723013i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.01890 | + | 0.708640i | 0.180272 | + | 0.0317868i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.7802 | − | 29.6183i | 0.482587 | − | 1.32590i | −0.424680 | − | 0.905344i | \(-0.639613\pi\) |
0.907267 | − | 0.420554i | \(-0.138164\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.03456 | − | 17.6997i | 0.180251 | − | 0.790765i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.82536 | + | 15.2860i | 0.393504 | + | 0.681568i | 0.992909 | − | 0.118878i | \(-0.0379296\pi\) |
−0.599405 | + | 0.800446i | \(0.704596\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.6781 | + | 27.1553i | −0.697666 | + | 1.20839i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.29592 | − | 2.52602i | −0.0575539 | − | 0.112184i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.38432 | − | 11.1838i | −0.415953 | − | 0.495713i | 0.516863 | − | 0.856068i | \(-0.327100\pi\) |
−0.932815 | + | 0.360356i | \(0.882655\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.77377 | + | 4.87339i | 0.0784669 | + | 0.215586i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.22570 | − | 21.5255i | 0.142418 | − | 0.950376i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −52.1624 | + | 18.9856i | −2.29855 | + | 0.836603i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.75300 | − | 3.98824i | 0.209037 | − | 0.175402i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.354189 | − | 0.228617i | −0.0155472 | − | 0.0100352i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.1782 | − | 17.4234i | −1.32213 | − | 0.763334i | −0.338064 | − | 0.941123i | \(-0.609772\pi\) |
−0.984069 | + | 0.177790i | \(0.943105\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.2393 | − | 13.9946i | 1.05991 | − | 0.611940i | 0.134504 | − | 0.990913i | \(-0.457056\pi\) |
0.925408 | + | 0.378973i | \(0.123723\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −30.4114 | + | 32.7944i | −1.32726 | + | 1.43127i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.10230 | + | 2.94900i | 0.352942 | + | 0.128460i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.66372 | − | 26.4493i | 0.202770 | − | 1.14997i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.7342 | + | 24.6964i | −0.769600 | + | 1.07173i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.0176 | − | 11.9385i | 0.433911 | − | 0.517115i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 38.3722 | − | 6.76605i | 1.65897 | − | 0.292522i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.160717 | + | 1.27954i | 0.00693544 | + | 0.0552164i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.59584 | 0.241030 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.19075 | 0.352148 | 0.176074 | − | 0.984377i | \(-0.443660\pi\) | ||||
0.176074 | + | 0.984377i | \(0.443660\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.3872 | − | 18.4835i | 1.04655 | − | 0.793201i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −52.2934 | + | 9.22073i | −2.24000 | + | 0.394973i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.5634 | − | 14.9725i | 0.537174 | − | 0.640179i | −0.427378 | − | 0.904073i | \(-0.640563\pi\) |
0.964552 | + | 0.263894i | \(0.0850071\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.221946 | + | 2.93926i | 0.00947241 | + | 0.125445i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.39620 | + | 36.2747i | −0.272487 | + | 1.54535i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.6739 | + | 11.8923i | 1.38944 | + | 0.505713i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.75596 | + | 12.1643i | 0.159432 | + | 0.516345i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.6096 | − | 11.3216i | 0.830885 | − | 0.479712i | −0.0232707 | − | 0.999729i | \(-0.507408\pi\) |
0.854156 | + | 0.520018i | \(0.174075\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.4169 | − | 16.9839i | −1.24420 | − | 0.718341i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.270754 | + | 5.45618i | −0.0114312 | + | 0.230360i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.9805 | + | 23.4784i | −1.17924 | + | 0.989498i | −0.179254 | + | 0.983803i | \(0.557368\pi\) |
−0.999984 | + | 0.00569511i | \(0.998187\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25.8932 | + | 9.42434i | −1.08933 | + | 0.396485i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.3400 | − | 11.7457i | −0.560226 | − | 0.493272i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.87353 | − | 10.6424i | −0.162387 | − | 0.446155i | 0.831637 | − | 0.555320i | \(-0.187404\pi\) |
−0.994024 | + | 0.109166i | \(0.965182\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.9162 | − | 15.3929i | −0.540525 | − | 0.644172i | 0.424781 | − | 0.905296i | \(-0.360351\pi\) |
−0.965305 | + | 0.261124i | \(0.915907\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.9474 | + | 0.840987i | 0.707989 | + | 0.0351328i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −46.1616 | + | 79.9543i | −1.92507 | + | 3.33433i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.972478 | + | 1.68438i | 0.0404848 | + | 0.0701217i | 0.885558 | − | 0.464529i | \(-0.153776\pi\) |
−0.845073 | + | 0.534651i | \(0.820443\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.1816 | + | 4.37885i | −0.589367 | + | 0.181979i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.48618 | − | 6.83073i | 0.103144 | − | 0.283387i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.909934 | − | 0.160446i | −0.0376856 | − | 0.00664499i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −24.2373 | − | 35.5063i | −1.00209 | − | 1.46801i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.3602 | + | 26.3143i | 1.29437 | + | 1.08611i | 0.991088 | + | 0.133207i | \(0.0425276\pi\) |
0.303284 | + | 0.952900i | \(0.401917\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.58968 | + | 20.3581i | 0.147910 | + | 0.838840i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.39237 | + | 1.83710i | 0.0572745 | + | 0.0755683i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.8316i | 1.38930i | 0.719349 | + | 0.694649i | \(0.244440\pi\) | ||||
−0.719349 | + | 0.694649i | \(0.755560\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 14.6695i | − | 0.601392i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 28.3343 | − | 3.55892i | 1.15965 | − | 0.145657i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.18292 | − | 29.3938i | −0.211768 | − | 1.20100i | −0.886427 | − | 0.462868i | \(-0.846820\pi\) |
0.674659 | − | 0.738130i | \(-0.264291\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.6280 | + | 8.91796i | 0.433525 | + | 0.363771i | 0.833280 | − | 0.552851i | \(-0.186460\pi\) |
−0.399755 | + | 0.916622i | \(0.630905\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.8312 | − | 14.8365i | 1.33699 | − | 0.604187i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 32.4115 | + | 5.71502i | 1.31772 | + | 0.232349i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.30592 | + | 17.3254i | −0.255949 | + | 0.703215i | 0.743458 | + | 0.668783i | \(0.233185\pi\) |
−0.999407 | + | 0.0344323i | \(0.989038\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 22.0552 | + | 20.4526i | 0.893720 | + | 0.828779i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.79240 | − | 10.0327i | −0.234336 | − | 0.405881i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.0815 | − | 22.6579i | 0.528358 | − | 0.915143i | −0.471095 | − | 0.882082i | \(-0.656141\pi\) |
0.999453 | − | 0.0330609i | \(-0.0105255\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.4645 | + | 28.6065i | −0.744562 | + | 1.15353i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.3160 | − | 14.6776i | −0.495823 | − | 0.590898i | 0.458866 | − | 0.888506i | \(-0.348256\pi\) |
−0.954688 | + | 0.297607i | \(0.903811\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.02766 | − | 16.5608i | −0.242272 | − | 0.665637i | −0.999916 | − | 0.0129686i | \(-0.995872\pi\) |
0.757644 | − | 0.652668i | \(-0.226350\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −32.2368 | − | 17.5196i | −1.29362 | − | 0.703038i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.8591 | − | 5.04430i | 0.555253 | − | 0.202096i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 61.7309 | − | 51.7984i | 2.46924 | − | 2.07194i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.6533 | + | 5.97849i | −0.465389 | + | 0.238758i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.61590 | − | 1.51029i | −0.104303 | − | 0.0602192i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.9375 | + | 10.9336i | −0.753892 | + | 0.435260i | −0.827098 | − | 0.562057i | \(-0.810010\pi\) |
0.0732067 | + | 0.997317i | \(0.476677\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.2527 | + | 4.61650i | 0.804973 | + | 0.183489i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 40.0123 | + | 14.5633i | 1.58784 | + | 0.577926i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.81431 | − | 10.2894i | 0.0718855 | − | 0.407683i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.67560 | − | 5.96842i | 0.0662856 | − | 0.236107i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.37132 | − | 9.97655i | 0.330647 | − | 0.394050i | −0.574950 | − | 0.818188i | \(-0.694979\pi\) |
0.905597 | + | 0.424138i | \(0.139423\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.5512 | + | 3.62373i | −0.810461 | + | 0.142906i | −0.563497 | − | 0.826118i | \(-0.690544\pi\) |
−0.246964 | + | 0.969025i | \(0.579433\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 68.3909 | + | 28.8063i | 2.69289 | + | 1.13425i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.0883 | −0.789751 | −0.394875 | − | 0.918735i | \(-0.629212\pi\) | ||||
−0.394875 | + | 0.918735i | \(0.629212\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.2954 | 0.718159 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.5572 | + | 6.55270i | 0.609734 | + | 0.256820i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.40965 | − | 1.30652i | 0.289962 | − | 0.0511281i | −0.0267752 | − | 0.999641i | \(-0.508524\pi\) |
0.316737 | + | 0.948513i | \(0.397413\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.3829 | − | 37.4007i | 1.22623 | − | 1.46137i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.63342 | − | 1.94832i | 0.297808 | − | 0.0760113i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.07319 | + | 45.7853i | −0.314487 | + | 1.78354i | 0.260597 | + | 0.965448i | \(0.416081\pi\) |
−0.575083 | + | 0.818095i | \(0.695030\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.5470 | + | 13.6660i | 1.46041 | + | 0.531546i | 0.945478 | − | 0.325685i | \(-0.105595\pi\) |
0.514932 | + | 0.857231i | \(0.327817\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.94486 | + | 2.26688i | 0.386227 | + | 0.0880383i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 30.4586 | − | 17.5853i | 1.18113 | − | 0.681927i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 53.7715 | + | 31.0450i | 2.08204 | + | 1.20207i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.6173 | − | 7.49911i | 0.565138 | − | 0.289932i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.35874 | − | 1.14012i | 0.0524535 | − | 0.0440137i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.8306 | + | 8.67365i | −0.918604 | + | 0.334345i | −0.757683 | − | 0.652623i | \(-0.773669\pi\) |
−0.160921 | + | 0.986967i | \(0.551446\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 44.9987 | + | 50.9022i | 1.73200 | + | 1.95923i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.71041 | + | 15.6892i | 0.219469 | + | 0.602986i | 0.999748 | − | 0.0224457i | \(-0.00714528\pi\) |
−0.780279 | + | 0.625431i | \(0.784923\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.83315 | − | 2.18466i | −0.0703497 | − | 0.0838395i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.55136 | + | 11.6991i | −0.289369 | + | 0.448310i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.39233 | − | 4.14363i | 0.0915398 | − | 0.158552i | −0.816619 | − | 0.577176i | \(-0.804154\pi\) |
0.908159 | + | 0.418625i | \(0.137488\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.06576 | + | 12.2383i | 0.269969 | + | 0.467600i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.5307 | + | 11.6202i | 0.478076 | + | 0.443337i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.590045 | + | 1.62114i | −0.0224789 | + | 0.0617604i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −46.6062 | − | 8.21794i | −1.77298 | − | 0.312625i | −0.810861 | − | 0.585239i | \(-0.801001\pi\) |
−0.962123 | + | 0.272614i | \(0.912112\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.05887 | + | 10.6428i | −0.0402231 | + | 0.404287i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31.7944 | − | 26.6787i | −1.20603 | − | 1.01198i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.40279 | − | 7.95562i | −0.0531345 | − | 0.301340i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 34.7477 | − | 4.36447i | 1.31428 | − | 0.165079i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.98736i | 0.0750617i | 0.999295 | + | 0.0375308i | \(0.0119492\pi\) | ||||
−0.999295 | + | 0.0375308i | \(0.988051\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 7.24191i | − | 0.273134i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.2877 | + | 20.1707i | 0.575770 | + | 0.759674i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.52927 | − | 14.3442i | −0.0951231 | − | 0.539470i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.0486 | − | 26.8920i | −1.20361 | − | 1.00995i | −0.999519 | − | 0.0309977i | \(-0.990132\pi\) |
−0.204092 | − | 0.978952i | \(-0.565424\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22.8904 | − | 47.6016i | 0.858459 | − | 1.78520i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 34.3168 | + | 6.05098i | 1.28517 | + | 0.226611i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.84768 | + | 24.3088i | −0.330884 | + | 0.909097i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −45.3962 | + | 14.0170i | −1.69535 | + | 0.523475i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.7447 | − | 18.6104i | −0.400710 | − | 0.694049i | 0.593102 | − | 0.805127i | \(-0.297903\pi\) |
−0.993812 | + | 0.111078i | \(0.964570\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.8927 | − | 22.3308i | 0.480149 | − | 0.831642i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.4313 | + | 0.716127i | 0.536705 | + | 0.0266330i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −73.9047 | − | 88.0762i | −2.74475 | − | 3.27107i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.78558 | − | 7.65333i | −0.103312 | − | 0.283846i | 0.877258 | − | 0.480020i | \(-0.159371\pi\) |
−0.980569 | + | 0.196174i | \(0.937148\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.7611 | + | 18.3984i | −0.731892 | + | 0.681421i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.5454 | + | 6.02205i | −0.611955 | + | 0.222733i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.7728 | − | 26.6606i | 1.17356 | − | 0.984731i | 0.173556 | − | 0.984824i | \(-0.444474\pi\) |
1.00000 | 9.33087e-5i | \(2.97011e-5\pi\) | ||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.13133 | + | 22.7983i | −0.0417296 | + | 0.840928i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.7750 | − | 10.8397i | −0.691585 | − | 0.399287i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.6244 | + | 9.02075i | −0.574753 | + | 0.331834i | −0.759045 | − | 0.651038i | \(-0.774334\pi\) |
0.184293 | + | 0.982871i | \(0.441001\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.21476 | + | 23.3661i | 0.265041 | + | 0.858376i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.4353 | − | 10.3496i | −1.04319 | − | 0.379690i | −0.237101 | − | 0.971485i | \(-0.576197\pi\) |
−0.806088 | + | 0.591795i | \(0.798419\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.0972 | + | 85.6206i | −0.553119 | + | 3.13689i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.95149 | − | 4.78543i | −0.364106 | − | 0.175090i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.6341 | + | 13.8650i | −0.425102 | + | 0.506617i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.07225 | − | 1.42336i | 0.294561 | − | 0.0519390i | −0.0244149 | − | 0.999702i | \(-0.507772\pi\) |
0.318976 | + | 0.947763i | \(0.396661\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.6253 | + | 20.9377i | −1.00672 | + | 0.763012i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 44.9851 | 1.63718 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.4321 | 0.451852 | 0.225926 | − | 0.974144i | \(-0.427459\pi\) | ||||
0.225926 | + | 0.974144i | \(0.427459\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.75145 | + | 21.9057i | 0.0998715 | + | 0.795126i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.3875 | − | 5.71079i | 1.17405 | − | 0.207016i | 0.447596 | − | 0.894236i | \(-0.352280\pi\) |
0.726449 | + | 0.687220i | \(0.241169\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.8549 | − | 18.8952i | 0.573987 | − | 0.684051i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −22.1746 | − | 2.20618i | −0.801723 | − | 0.0797647i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.93182 | − | 33.6410i | 0.214186 | − | 1.21471i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.0019 | − | 5.46024i | −0.540981 | − | 0.196901i | 0.0570536 | − | 0.998371i | \(-0.481829\pi\) |
−0.598035 | + | 0.801470i | \(0.704052\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.64504 | − | 2.85230i | 0.0952590 | − | 0.102723i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.6586 | + | 18.2781i | −1.13868 | + | 0.657417i | −0.946103 | − | 0.323865i | \(-0.895018\pi\) |
−0.192576 | + | 0.981282i | \(0.561684\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −55.8816 | − | 32.2632i | −2.00733 | − | 1.15893i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.96861 | − | 3.20707i | −0.178248 | − | 0.115053i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.8368 | − | 12.4495i | 0.531582 | − | 0.446050i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.50533 | + | 1.27584i | −0.125431 | + | 0.0456530i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 34.2332 | − | 30.2629i | 1.22339 | − | 1.08151i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 31.5640 | + | 86.7215i | 1.12657 | + | 3.09522i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.2330 | + | 36.0303i | 1.07769 | + | 1.28434i | 0.956506 | + | 0.291712i | \(0.0942248\pi\) |
0.121184 | + | 0.992630i | \(0.461331\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.0596 | + | 19.6082i | 0.358131 | + | 0.698072i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.39987 | − | 11.0849i | 0.227553 | − | 0.394134i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.65587 | − | 2.86806i | −0.0588018 | − | 0.101848i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.837644 | − | 3.67477i | 0.0297082 | − | 0.130331i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.2658 | + | 28.2049i | −0.363632 | + | 0.999070i | 0.614103 | + | 0.789226i | \(0.289518\pi\) |
−0.977735 | + | 0.209844i | \(0.932704\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.91379 | − | 1.04276i | −0.209215 | − | 0.0368902i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.54070 | − | 21.7081i | −0.195771 | − | 0.767020i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.63151 | − | 3.04720i | −0.128153 | − | 0.107533i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.2948 | − | 58.3848i | −0.362845 | − | 2.05779i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.36939 | + | 22.2445i | −0.329818 | + | 0.783043i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 29.1407i | − | 1.02453i | −0.858827 | − | 0.512266i | \(-0.828806\pi\) | ||
0.858827 | − | 0.512266i | \(-0.171194\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.3787i | 0.996509i | 0.867031 | + | 0.498255i | \(0.166026\pi\) | ||||
−0.867031 | + | 0.498255i | \(0.833974\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.893422 | + | 2.12113i | −0.0313337 | + | 0.0743912i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.813719 | + | 4.61483i | 0.0285033 | + | 0.161650i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.3377 | − | 27.1346i | −1.13135 | − | 0.949318i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 19.2263 | + | 5.39767i | 0.671822 | + | 0.188610i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.65056 | + | 0.291038i | 0.0576049 | + | 0.0101573i | 0.202376 | − | 0.979308i | \(-0.435134\pi\) |
−0.144771 | + | 0.989465i | \(0.546245\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.27702 | − | 9.00355i | 0.114230 | − | 0.313844i | −0.869383 | − | 0.494140i | \(-0.835483\pi\) |
0.983612 | + | 0.180296i | \(0.0577054\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.08591 | − | 39.8601i | 0.316331 | − | 1.38775i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.3642 | − | 31.8078i | −0.638587 | − | 1.10607i | −0.985743 | − | 0.168258i | \(-0.946186\pi\) |
0.347156 | − | 0.937808i | \(-0.387148\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.1409 | − | 19.2966i | 0.386940 | − | 0.670199i | −0.605097 | − | 0.796152i | \(-0.706865\pi\) |
0.992036 | + | 0.125953i | \(0.0401988\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.37823 | + | 10.4833i | 0.186569 | + | 0.363661i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.48124 | − | 4.14878i | −0.120618 | − | 0.143747i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.2405 | − | 41.8728i | −0.527418 | − | 1.44907i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.2448 | − | 22.5309i | 0.423242 | − | 0.778781i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.0188 | + | 14.5656i | −1.38160 | + | 0.502862i | −0.922663 | − | 0.385607i | \(-0.873992\pi\) |
−0.458938 | + | 0.888468i | \(0.651770\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −37.0184 | + | 31.0621i | −1.27650 | + | 1.07111i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.87496 | − | 3.79209i | −0.202344 | − | 0.130606i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.03509 | − | 3.48436i | −0.207613 | − | 0.119866i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.2398 | + | 7.64398i | −0.454924 | + | 0.262650i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.646579 | + | 0.697243i | −0.0221905 | + | 0.0239293i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.4712 | − | 4.17518i | −0.393228 | − | 0.143123i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.115822 | − | 0.656862i | 0.00396568 | − | 0.0224905i | −0.982761 | − | 0.184882i | \(-0.940810\pi\) |
0.986726 | + | 0.162392i | \(0.0519208\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.0013 | − | 48.6861i | −0.752428 | − | 1.66503i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.4655 | − | 43.4579i | 1.24564 | − | 1.48449i | 0.433363 | − | 0.901219i | \(-0.357327\pi\) |
0.812275 | − | 0.583275i | \(-0.198229\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.0689 | + | 3.36237i | −0.650623 | + | 0.114722i | −0.489212 | − | 0.872165i | \(-0.662716\pi\) |
−0.161411 | + | 0.986887i | \(0.551605\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.97107 | − | 15.6926i | −0.0671737 | − | 0.534803i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.1335 | 0.617273 | 0.308636 | − | 0.951180i | \(-0.400127\pi\) | ||||
0.308636 | + | 0.951180i | \(0.400127\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.03477 | −0.0351832 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19.2527 | + | 14.5920i | −0.653857 | + | 0.495570i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.3007 | + | 5.51916i | −1.06180 | + | 0.187225i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.0190 | + | 31.0083i | −0.881621 | + | 1.05068i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.57804 | + | 2.44244i | −0.121098 | + | 0.0826642i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.7735 | + | 66.7708i | −0.398017 | + | 2.25727i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.6730 | + | 6.06847i | 0.563007 | + | 0.204918i | 0.607816 | − | 0.794078i | \(-0.292046\pi\) |
−0.0448094 | + | 0.998996i | \(0.514268\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.36438 | + | 30.3280i | 0.315853 | + | 1.02294i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.421306 | + | 0.243241i | −0.0141942 | + | 0.00819500i | −0.507080 | − | 0.861899i | \(-0.669275\pi\) |
0.492886 | + | 0.870094i | \(0.335942\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.45185 | − | 5.45703i | −0.318080 | − | 0.183644i | 0.332456 | − | 0.943119i | \(-0.392123\pi\) |
−0.650536 | + | 0.759475i | \(0.725456\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.69884 | + | 74.5383i | −0.124335 | + | 2.50558i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.28856 | + | 1.92033i | −0.0768422 | + | 0.0644783i | −0.680400 | − | 0.732841i | \(-0.738194\pi\) |
0.603558 | + | 0.797319i | \(0.293749\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.5864 | + | 6.76490i | −0.623368 | + | 0.226888i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.9285 | + | 3.20119i | 0.533625 | + | 0.107244i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.92412 | − | 13.5289i | −0.164780 | − | 0.452728i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.03471 | + | 2.42487i | 0.0680128 | + | 0.0810545i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 41.1715 | + | 2.04307i | 1.37468 | + | 0.0682160i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21.6979 | + | 37.5819i | −0.723667 | + | 1.25343i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.447126 | + | 0.774444i | 0.0148959 | + | 0.0258005i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −32.9375 | + | 10.1701i | −1.09609 | + | 0.338440i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.6895 | − | 70.5814i | 0.853949 | − | 2.34621i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.1122 | + | 6.72021i | 1.26549 | + | 0.223141i | 0.765810 | − | 0.643067i | \(-0.222338\pi\) |
0.499684 | + | 0.866208i | \(0.333449\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −22.0632 | + | 1.66601i | −0.731791 | + | 0.0552581i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.14166 | + | 6.83166i | 0.269745 | + | 0.226343i | 0.767619 | − | 0.640906i | \(-0.221441\pi\) |
−0.497874 | + | 0.867249i | \(0.665886\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.15382 | + | 6.54366i | 0.0381860 | + | 0.216563i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.37031 | + | 5.76621i | 0.144478 | + | 0.190625i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22.6792i | 0.748933i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 48.9343i | − | 1.61420i | −0.590418 | − | 0.807098i | \(-0.701037\pi\) | ||
0.590418 | − | 0.807098i | \(-0.298963\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23.8117 | + | 2.99086i | −0.784621 | + | 0.0985520i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.20945 | + | 6.85914i | 0.0398096 | + | 0.225771i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.3165 | + | 14.5303i | 0.569363 | + | 0.477752i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −31.8165 | − | 22.8471i | −1.04499 | − | 0.750397i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.15541 | − | 0.909037i | −0.169143 | − | 0.0298245i | 0.0884350 | − | 0.996082i | \(-0.471813\pi\) |
−0.257578 | + | 0.966257i | \(0.582925\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.44100 | − | 12.2015i | 0.145548 | − | 0.399890i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.71709 | − | 4.37433i | −0.154431 | − | 0.143209i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.70461 | + | 11.6127i | 0.219264 | + | 0.379777i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.7145 | + | 49.7349i | −0.938061 | + | 1.62477i | −0.168979 | + | 0.985620i | \(0.554047\pi\) |
−0.769082 | + | 0.639150i | \(0.779286\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.4362 | − | 33.2105i | 0.699545 | − | 1.08378i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.74647 | + | 6.84838i | 0.187330 | + | 0.223251i | 0.851533 | − | 0.524301i | \(-0.175673\pi\) |
−0.664203 | + | 0.747552i | \(0.731229\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.1662 | − | 30.6790i | −0.363623 | − | 0.999045i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −43.1463 | − | 6.46568i | −1.40355 | − | 0.210328i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.5054 | − | 18.3825i | 1.64121 | − | 0.597350i | 0.653957 | − | 0.756532i | \(-0.273108\pi\) |
0.987249 | + | 0.159182i | \(0.0508856\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.78051 | + | 5.68952i | −0.220105 | + | 0.184690i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.6669 | − | 13.6809i | 0.864733 | − | 0.443633i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.0235 | + | 6.36443i | 0.357087 | + | 0.206164i | 0.667802 | − | 0.744339i | \(-0.267235\pi\) |
−0.310715 | + | 0.950503i | \(0.600569\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36.0702 | − | 20.8252i | 1.16721 | − | 0.673887i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −26.8071 | − | 6.11053i | −0.866550 | − | 0.197525i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.16846 | − | 2.24514i | −0.199190 | − | 0.0724992i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.15395 | − | 6.54439i | 0.0372242 | − | 0.211109i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19.2088 | + | 19.6715i | 0.618996 | + | 0.633904i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.4179 | + | 27.9083i | −0.753847 | + | 0.898400i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.8749 | + | 3.85714i | −0.703450 | + | 0.124037i | −0.513921 | − | 0.857838i | \(-0.671807\pi\) |
−0.189530 | + | 0.981875i | \(0.560696\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.6822 | + | 4.92054i | 0.375285 | + | 0.158070i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.9474 | −1.08942 | −0.544712 | − | 0.838623i | \(-0.683361\pi\) | ||||
−0.544712 | + | 0.838623i | \(0.683361\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.2796 | 0.618077 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −70.3476 | − | 29.6305i | −2.25293 | − | 0.948935i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.7009 | + | 3.29747i | −0.598295 | + | 0.105496i | −0.464590 | − | 0.885526i | \(-0.653798\pi\) |
−0.133705 | + | 0.991021i | \(0.542687\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.66571 | + | 10.3274i | −0.276957 | + | 0.330065i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26.1777 | − | 26.8081i | −0.835788 | − | 0.855918i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.33476 | − | 18.9124i | 0.106362 | − | 0.603210i | −0.884305 | − | 0.466909i | \(-0.845367\pi\) |
0.990667 | − | 0.136301i | \(-0.0435215\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.31695 | + | 1.93521i | 0.169412 | + | 0.0616610i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.4627 | − | 2.61286i | −0.364862 | − | 0.0831684i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −61.6248 | + | 35.5791i | −1.95956 | + | 1.13135i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.3164 | + | 19.8126i | 1.09009 | + | 0.629367i | 0.933602 | − | 0.358312i | \(-0.116648\pi\) |
0.156493 | + | 0.987679i | \(0.449981\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.1030 | − | 5.69618i | 0.352345 | − | 0.180763i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 53.6965 | − | 45.0568i | 1.70230 | − | 1.42840i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.8784 | + | 5.05134i | −0.439534 | + | 0.159977i | −0.552302 | − | 0.833644i | \(-0.686251\pi\) |
0.112768 | + | 0.993621i | \(0.464028\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.59507 | + | 7.02827i | −0.177020 | + | 0.222365i |
(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 | 432.2.be.c.47.5 | yes | 36 | |
4.3 | odd | 2 | 432.2.be.b.47.2 | ✓ | 36 | ||
27.23 | odd | 18 | 432.2.be.b.239.2 | yes | 36 | ||
108.23 | even | 18 | inner | 432.2.be.c.239.5 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.be.b.47.2 | ✓ | 36 | 4.3 | odd | 2 | ||
432.2.be.b.239.2 | yes | 36 | 27.23 | odd | 18 | ||
432.2.be.c.47.5 | yes | 36 | 1.1 | even | 1 | trivial | |
432.2.be.c.239.5 | yes | 36 | 108.23 | even | 18 | inner |