Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,2,Mod(5,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 16]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.i (of order \(9\), 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: | \(0.606863055362\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} - 3 x^{10} + 70 x^{9} - 15 x^{8} - 426 x^{7} + 64 x^{6} + 1659 x^{5} + 267 x^{4} + \cdots + 4161 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 9.1 | ||
Root | \(2.26253 - 0.984808i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.9 |
Dual form | 76.2.i.a.17.1 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{4}{9}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.834130 | + | 0.699919i | −0.481585 | + | 0.404098i | −0.850999 | − | 0.525167i | \(-0.824003\pi\) |
0.369414 | + | 0.929265i | \(0.379558\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.00735 | + | 1.09458i | 1.34493 | + | 0.489513i | 0.911360 | − | 0.411609i | \(-0.135033\pi\) |
0.433565 | + | 0.901122i | \(0.357255\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.278396 | − | 0.482195i | 0.105224 | − | 0.182253i | −0.808606 | − | 0.588351i | \(-0.799777\pi\) |
0.913830 | + | 0.406098i | \(0.133111\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.315057 | + | 1.78678i | −0.105019 | + | 0.595592i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.96291 | − | 3.39985i | −0.591838 | − | 1.02509i | −0.993985 | − | 0.109518i | \(-0.965069\pi\) |
0.402147 | − | 0.915575i | \(-0.368264\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.19334 | − | 2.67953i | −0.885674 | − | 0.743169i | 0.0816634 | − | 0.996660i | \(-0.473977\pi\) |
−0.967338 | + | 0.253491i | \(0.918421\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.27464 | + | 1.19187i | −0.845508 | + | 0.307740i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.660076 | − | 3.74348i | −0.160092 | − | 0.907926i | −0.953982 | − | 0.299865i | \(-0.903058\pi\) |
0.793890 | − | 0.608062i | \(-0.208053\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.84488 | + | 3.94923i | −0.423244 | + | 0.906016i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.105279 | + | 0.597068i | 0.0229738 | + | 0.130291i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.67290 | − | 1.70080i | 0.974368 | − | 0.354641i | 0.194720 | − | 0.980859i | \(-0.437620\pi\) |
0.779648 | + | 0.626218i | \(0.215398\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.01579 | + | 3.36965i | 0.803158 | + | 0.673929i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.62112 | − | 4.53991i | −0.504435 | − | 0.873706i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.0201569 | − | 0.114315i | 0.00374304 | − | 0.0212278i | −0.982879 | − | 0.184252i | \(-0.941014\pi\) |
0.986622 | + | 0.163024i | \(0.0521249\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.54372 | + | 6.13791i | −0.636472 | + | 1.10240i | 0.349730 | + | 0.936851i | \(0.386273\pi\) |
−0.986201 | + | 0.165550i | \(0.947060\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.01694 | + | 1.46205i | 0.699259 | + | 0.254510i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.36503 | − | 1.14540i | 0.230733 | − | 0.193608i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.67687 | −0.933271 | −0.466636 | − | 0.884450i | \(-0.654534\pi\) | ||||
−0.466636 | + | 0.884450i | \(0.654534\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.53912 | 0.726841 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.20379 | − | 7.72289i | 1.43739 | − | 1.20611i | 0.496212 | − | 0.868201i | \(-0.334724\pi\) |
0.941178 | − | 0.337912i | \(-0.109721\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.74642 | + | 2.45550i | 1.02882 | + | 0.374460i | 0.800631 | − | 0.599157i | \(-0.204498\pi\) |
0.228188 | + | 0.973617i | \(0.426720\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.90326 | + | 5.02860i | −0.432793 | + | 0.749619i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.00419623 | + | 0.0237980i | −0.000612084 | + | 0.00347130i | −0.985112 | − | 0.171912i | \(-0.945005\pi\) |
0.984500 | + | 0.175384i | \(0.0561166\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.34499 | + | 5.79370i | 0.477856 | + | 0.827671i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.17072 | + | 2.66055i | 0.443989 | + | 0.372551i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.18260 | + | 2.97822i | −1.12397 | + | 0.409090i | −0.836098 | − | 0.548580i | \(-0.815169\pi\) |
−0.287868 | + | 0.957670i | \(0.592946\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.18171 | − | 12.3731i | −0.294182 | − | 1.66839i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.22527 | − | 4.58544i | −0.162291 | − | 0.607356i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.88690 | + | 10.7011i | 0.245653 | + | 1.39317i | 0.818972 | + | 0.573834i | \(0.194545\pi\) |
−0.573319 | + | 0.819332i | \(0.694344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.7981 | + | 4.29417i | −1.51060 | + | 0.549812i | −0.958779 | − | 0.284154i | \(-0.908287\pi\) |
−0.551817 | + | 0.833966i | \(0.686065\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.773865 | + | 0.649350i | 0.0974978 | + | 0.0818104i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.67051 | − | 11.5537i | −0.827375 | − | 1.43306i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.27074 | − | 12.8780i | 0.277415 | − | 1.57330i | −0.453769 | − | 0.891119i | \(-0.649921\pi\) |
0.731184 | − | 0.682180i | \(-0.238968\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.70739 | + | 4.68934i | −0.325932 | + | 0.564530i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.17872 | + | 1.15696i | 0.377244 | + | 0.137306i | 0.523681 | − | 0.851914i | \(-0.324558\pi\) |
−0.146437 | + | 0.989220i | \(0.546781\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.338853 | − | 0.284332i | 0.0396598 | − | 0.0332785i | −0.622742 | − | 0.782427i | \(-0.713982\pi\) |
0.662402 | + | 0.749148i | \(0.269537\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.70817 | −0.659123 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.18586 | −0.249101 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.31335 | − | 1.10203i | 0.147764 | − | 0.123988i | −0.565909 | − | 0.824467i | \(-0.691475\pi\) |
0.713673 | + | 0.700479i | \(0.247030\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.249157 | + | 0.0906859i | 0.0276842 | + | 0.0100762i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.90300 | + | 5.02815i | −0.318646 | + | 0.551911i | −0.980206 | − | 0.197981i | \(-0.936561\pi\) |
0.661560 | + | 0.749892i | \(0.269895\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.11247 | − | 11.9804i | 0.229130 | − | 1.29946i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.0631980 | + | 0.109462i | 0.00677553 | + | 0.0117356i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.83132 | + | 1.53666i | 0.194120 | + | 0.162886i | 0.734667 | − | 0.678428i | \(-0.237338\pi\) |
−0.540547 | + | 0.841314i | \(0.681783\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.18107 | + | 0.793845i | −0.228638 | + | 0.0832176i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.34011 | − | 7.60013i | −0.138963 | − | 0.788097i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.87095 | + | 9.85733i | −1.01274 | + | 1.01134i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.86728 | + | 10.5899i | 0.189594 | + | 1.07524i | 0.919909 | + | 0.392131i | \(0.128262\pi\) |
−0.730315 | + | 0.683110i | \(0.760627\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.69320 | − | 2.43613i | 0.672692 | − | 0.244840i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.12586 | + | 4.30110i | 0.510042 | + | 0.427976i | 0.861144 | − | 0.508361i | \(-0.169749\pi\) |
−0.351102 | + | 0.936337i | \(0.614193\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.52153 | + | 11.2956i | 0.642586 | + | 1.11299i | 0.984854 | + | 0.173388i | \(0.0554716\pi\) |
−0.342268 | + | 0.939602i | \(0.611195\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.336930 | + | 1.91083i | −0.0328810 | + | 0.186478i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.76100 | − | 8.24629i | 0.460263 | − | 0.797199i | −0.538711 | − | 0.842491i | \(-0.681088\pi\) |
0.998974 | + | 0.0452919i | \(0.0144218\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.76788 | + | 2.82728i | 0.744028 | + | 0.270804i | 0.686090 | − | 0.727516i | \(-0.259325\pi\) |
0.0579374 | + | 0.998320i | \(0.481548\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.73525 | − | 3.97335i | 0.449450 | − | 0.377133i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.08270 | 0.195924 | 0.0979618 | − | 0.995190i | \(-0.468768\pi\) | ||||
0.0979618 | + | 0.995190i | \(0.468768\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.9147 | 1.48405 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.79381 | − | 4.86159i | 0.535638 | − | 0.449454i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.98885 | − | 0.723882i | −0.182317 | − | 0.0663581i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.20599 | + | 3.82089i | −0.200545 | + | 0.347354i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.27176 | + | 12.8838i | −0.204838 | + | 1.16169i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.387625 | + | 0.671385i | 0.0346702 | + | 0.0600505i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.9449 | − | 10.8621i | −1.14867 | − | 0.963853i | −0.148987 | − | 0.988839i | \(-0.547601\pi\) |
−0.999688 | + | 0.0249866i | \(0.992046\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.34604 | + | 2.67374i | −0.646783 | + | 0.235410i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.287814 | + | 1.63227i | 0.0251464 | + | 0.142612i | 0.994796 | − | 0.101886i | \(-0.0324877\pi\) |
−0.969650 | + | 0.244499i | \(0.921377\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.39069 | + | 1.98904i | 0.120589 | + | 0.172472i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.91330 | − | 16.5221i | −0.250737 | − | 1.42200i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.84678 | − | 1.40012i | 0.328653 | − | 0.119620i | −0.172423 | − | 0.985023i | \(-0.555160\pi\) |
0.501076 | + | 0.865403i | \(0.332938\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.46307 | − | 4.58406i | −0.463372 | − | 0.388815i | 0.380998 | − | 0.924576i | \(-0.375580\pi\) |
−0.844370 | + | 0.535761i | \(0.820025\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.0131565 | − | 0.0227877i | −0.00110797 | − | 0.00191907i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.84179 | + | 16.1166i | −0.237642 | + | 1.34774i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.185746 | − | 0.321722i | 0.0154254 | − | 0.0267176i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.84527 | − | 2.49148i | −0.564589 | − | 0.205493i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.50092 | − | 3.77672i | 0.368729 | − | 0.309401i | −0.439529 | − | 0.898228i | \(-0.644855\pi\) |
0.808259 | + | 0.588828i | \(0.200410\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.47180 | 0.526667 | 0.263334 | − | 0.964705i | \(-0.415178\pi\) | ||||
0.263334 | + | 0.964705i | \(0.415178\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.89672 | 0.557567 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.3757 | + | 14.5799i | −1.39565 | + | 1.17109i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.579693 | + | 0.210991i | 0.0462646 | + | 0.0168389i | 0.365049 | − | 0.930988i | \(-0.381052\pi\) |
−0.318784 | + | 0.947827i | \(0.603275\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.74084 | − | 8.21138i | 0.375973 | − | 0.651204i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.480799 | − | 2.72675i | 0.0378923 | − | 0.214898i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.7455 | − | 20.3438i | −0.919979 | − | 1.59345i | −0.799443 | − | 0.600742i | \(-0.794872\pi\) |
−0.120537 | − | 0.992709i | \(-0.538462\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.4800 | + | 8.79375i | 0.815866 | + | 0.684593i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.2110 | + | 5.17239i | −1.09968 | + | 0.400252i | −0.827199 | − | 0.561909i | \(-0.810067\pi\) |
−0.272483 | + | 0.962160i | \(0.587845\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.760119 | + | 4.31085i | 0.0584707 | + | 0.331604i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.47515 | − | 4.54062i | −0.495167 | − | 0.347230i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.583180 | + | 3.30738i | 0.0443384 | + | 0.251455i | 0.998918 | − | 0.0464995i | \(-0.0148066\pi\) |
−0.954580 | + | 0.297955i | \(0.903695\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.74280 | − | 0.998299i | 0.207337 | − | 0.0754643i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.06383 | − | 7.60545i | −0.681279 | − | 0.571661i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.0510390 | + | 0.0884022i | 0.00381484 | + | 0.00660749i | 0.867927 | − | 0.496693i | \(-0.165452\pi\) |
−0.864112 | + | 0.503300i | \(0.832119\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.33951 | − | 7.59673i | 0.0995649 | − | 0.564660i | −0.893688 | − | 0.448689i | \(-0.851891\pi\) |
0.993253 | − | 0.115971i | \(-0.0369980\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.83561 | − | 11.8396i | 0.505303 | − | 0.875210i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −17.0723 | − | 6.21381i | −1.25518 | − | 0.456848i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.4316 | + | 9.59225i | −0.835961 | + | 0.701455i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.91883 | −0.212314 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.0096 | −1.08606 | −0.543028 | − | 0.839715i | \(-0.682722\pi\) | ||||
−0.543028 | + | 0.839715i | \(0.682722\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.98477 | + | 1.66542i | −0.142867 | + | 0.119880i | −0.711420 | − | 0.702767i | \(-0.751948\pi\) |
0.568553 | + | 0.822646i | \(0.307503\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.6507 | + | 4.96845i | 0.977547 | + | 0.355798i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.21799 | − | 5.57372i | 0.229272 | − | 0.397111i | −0.728320 | − | 0.685237i | \(-0.759699\pi\) |
0.957593 | + | 0.288126i | \(0.0930321\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.957517 | + | 5.43035i | −0.0678765 | + | 0.384947i | 0.931878 | + | 0.362773i | \(0.118170\pi\) |
−0.999754 | + | 0.0221741i | \(0.992941\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.11946 | + | 12.3313i | 0.502168 | + | 0.869781i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.0495107 | − | 0.0415444i | −0.00347497 | − | 0.00291585i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 36.1323 | − | 13.1511i | 2.52359 | − | 0.918512i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.56672 | + | 8.88528i | 0.108894 | + | 0.617570i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.0481 | − | 1.47966i | 1.17924 | − | 0.102350i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.30065 | − | 7.37636i | −0.0895405 | − | 0.507809i | −0.996284 | − | 0.0861271i | \(-0.972551\pi\) |
0.906744 | − | 0.421682i | \(-0.138560\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.46124 | + | 1.25979i | −0.237160 | + | 0.0863193i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.6011 | + | 14.7690i | 1.20038 | + | 1.00724i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.97311 | + | 3.41753i | 0.133944 | + | 0.231997i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.0836389 | + | 0.474340i | −0.00565179 | + | 0.0320529i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.92292 | + | 13.7229i | −0.532953 | + | 0.923102i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.2194 | + | 4.81148i | 0.885238 | + | 0.322200i | 0.744322 | − | 0.667821i | \(-0.232773\pi\) |
0.140916 | + | 0.990022i | \(0.454995\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.28601 | + | 6.11369i | −0.485734 | + | 0.407579i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.3417 | 1.68199 | 0.840994 | − | 0.541044i | \(-0.181971\pi\) | ||||
0.840994 | + | 0.541044i | \(0.181971\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.8311 | −1.31047 | −0.655237 | − | 0.755423i | \(-0.727431\pi\) | ||||
−0.655237 | + | 0.755423i | \(0.727431\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.82329 | − | 1.52992i | 0.119964 | − | 0.100661i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.8061 | − | 7.57279i | −1.36305 | − | 0.496110i | −0.446055 | − | 0.895006i | \(-0.647171\pi\) |
−0.916996 | + | 0.398895i | \(0.869394\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.0386685 | + | 0.0669757i | −0.00252245 | + | 0.00436901i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.324173 | + | 1.83848i | −0.0210573 | + | 0.119422i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.02364 | − | 1.77299i | −0.0662135 | − | 0.114685i | 0.831018 | − | 0.556245i | \(-0.187758\pi\) |
−0.897232 | + | 0.441560i | \(0.854425\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.941858 | + | 0.790313i | 0.0606704 | + | 0.0509085i | 0.672619 | − | 0.739989i | \(-0.265169\pi\) |
−0.611948 | + | 0.790898i | \(0.709614\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.5070 | − | 5.28011i | 0.930623 | − | 0.338719i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.71786 | + | 21.0850i | 0.237525 | + | 1.34707i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.4734 | − | 7.66784i | 1.04818 | − | 0.487893i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.09781 | − | 6.22600i | −0.0695710 | − | 0.394557i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.52471 | + | 2.37480i | −0.411836 | + | 0.149896i | −0.539625 | − | 0.841905i | \(-0.681434\pi\) |
0.127789 | + | 0.991801i | \(0.459212\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.9549 | − | 12.5487i | −0.940208 | − | 0.788928i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.62325 | + | 11.4718i | 0.414764 | + | 0.718392i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.71799 | − | 9.74318i | 0.107165 | − | 0.607763i | −0.883168 | − | 0.469056i | \(-0.844594\pi\) |
0.990333 | − | 0.138707i | \(-0.0442946\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.58041 | + | 2.73736i | −0.0982022 | + | 0.170091i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.197905 | + | 0.0720317i | 0.0122500 | + | 0.00445865i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.64566 | − | 1.38087i | 0.101476 | − | 0.0851483i | −0.590638 | − | 0.806936i | \(-0.701124\pi\) |
0.692114 | + | 0.721788i | \(0.256680\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −27.8678 | −1.71191 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.60310 | −0.159307 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.58263 | − | 6.36258i | 0.462321 | − | 0.387933i | −0.381663 | − | 0.924301i | \(-0.624649\pi\) |
0.843984 | + | 0.536368i | \(0.180204\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.4238 | − | 6.34176i | −1.05842 | − | 0.385234i | −0.246587 | − | 0.969121i | \(-0.579309\pi\) |
−0.811836 | + | 0.583886i | \(0.801531\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.26367 | − | 2.18874i | 0.0764809 | − | 0.132469i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.57369 | − | 20.2674i | 0.215501 | − | 1.22217i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.1235 | + | 22.7305i | 0.788514 | + | 1.36575i | 0.926877 | + | 0.375364i | \(0.122482\pi\) |
−0.138364 | + | 0.990381i | \(0.544184\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.85060 | − | 8.26563i | −0.589740 | − | 0.494850i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.0065 | − | 7.28179i | 1.19349 | − | 0.434395i | 0.332543 | − | 0.943088i | \(-0.392093\pi\) |
0.860948 | + | 0.508693i | \(0.169871\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.89350 | + | 16.4099i | 0.172001 | + | 0.975465i | 0.941549 | + | 0.336876i | \(0.109370\pi\) |
−0.769548 | + | 0.638589i | \(0.779518\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.33433 | − | 15.1312i | 0.0790391 | − | 0.896292i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.16165 | − | 6.58804i | −0.0685700 | − | 0.388880i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.39686 | − | 0.872386i | 0.140992 | − | 0.0513168i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.96963 | − | 7.52641i | −0.525809 | − | 0.441206i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.8152 | − | 18.7324i | −0.631828 | − | 1.09436i | −0.987178 | − | 0.159625i | \(-0.948971\pi\) |
0.355349 | − | 0.934734i | \(-0.384362\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.03873 | + | 34.2473i | −0.351588 | + | 1.99396i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.2900 | + | 17.8228i | −0.597087 | + | 1.03419i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −19.4795 | − | 7.08997i | −1.12653 | − | 0.410024i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.06220 | − | 2.56949i | 0.176502 | − | 0.148103i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.28606 | −0.418573 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −40.1814 | −2.30078 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.14077 | + | 5.99182i | −0.407545 | + | 0.341971i | −0.823401 | − | 0.567459i | \(-0.807926\pi\) |
0.415856 | + | 0.909430i | \(0.363482\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.3458 | − | 4.85748i | −0.759217 | − | 0.276333i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.5503 | − | 28.6659i | 0.938481 | − | 1.62550i | 0.170175 | − | 0.985414i | \(-0.445567\pi\) |
0.768306 | − | 0.640083i | \(-0.221100\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.53367 | + | 8.69786i | −0.0866880 | + | 0.491632i | 0.910292 | + | 0.413968i | \(0.135857\pi\) |
−0.996980 | + | 0.0776645i | \(0.975254\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.61651 | + | 2.79988i | 0.0910800 | + | 0.157755i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.3790 | + | 18.7782i | 1.25693 | + | 1.05469i | 0.996002 | + | 0.0893315i | \(0.0284730\pi\) |
0.260928 | + | 0.965358i | \(0.415971\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.428221 | + | 0.155860i | −0.0239758 | + | 0.00872647i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.80044 | + | 10.2108i | 0.100491 | + | 0.569911i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.0016 | + | 4.29946i | 0.890354 | + | 0.239229i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.79471 | − | 21.5209i | −0.210493 | − | 1.19376i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.45829 | + | 3.07856i | −0.467744 | + | 0.170245i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.0103071 | + | 0.00864867i | 0.000568248 | + | 0.000476816i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.83418 | + | 10.1051i | 0.320676 | + | 0.555426i | 0.980628 | − | 0.195881i | \(-0.0627567\pi\) |
−0.659952 | + | 0.751308i | \(0.729423\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.78854 | − | 10.1433i | 0.0980112 | − | 0.555849i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20.9250 | − | 36.2431i | 1.14325 | − | 1.98017i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.01893 | − | 0.734831i | −0.109978 | − | 0.0400288i | 0.286445 | − | 0.958097i | \(-0.407526\pi\) |
−0.396423 | + | 0.918068i | \(0.629749\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.73724 | + | 1.45772i | −0.0943539 | + | 0.0791723i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.8240 | 1.50675 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.62246 | 0.411574 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.2749 | + | 11.1390i | −0.714699 | + | 0.599703i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.81918 | + | 2.11801i | 0.312390 | + | 0.113701i | 0.493457 | − | 0.869770i | \(-0.335733\pi\) |
−0.181067 | + | 0.983471i | \(0.557955\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.71083 | + | 9.89145i | −0.305694 | + | 0.529477i | −0.977416 | − | 0.211326i | \(-0.932222\pi\) |
0.671722 | + | 0.740803i | \(0.265555\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.79471 | + | 21.5209i | −0.202547 | + | 1.14870i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.61637 | − | 2.79963i | −0.0860305 | − | 0.149009i | 0.819799 | − | 0.572651i | \(-0.194085\pi\) |
−0.905830 | + | 0.423642i | \(0.860752\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.29311 | + | 6.95874i | 0.440152 | + | 0.369332i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.16562 | − | 0.788220i | 0.114617 | − | 0.0417170i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.981506 | + | 5.56640i | 0.0518019 | + | 0.293783i | 0.999692 | − | 0.0248140i | \(-0.00789935\pi\) |
−0.947890 | + | 0.318597i | \(0.896788\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.1929 | − | 14.5717i | −0.641729 | − | 0.766931i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.834227 | − | 4.73114i | −0.0437856 | − | 0.248320i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.33027 | − | 0.484180i | 0.0696298 | − | 0.0253432i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.742863 | − | 0.623336i | −0.0387771 | − | 0.0325379i | 0.623193 | − | 0.782068i | \(-0.285835\pi\) |
−0.661970 | + | 0.749530i | \(0.730279\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.8994 | + | 18.8783i | 0.567398 | + | 0.982763i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.841914 | + | 4.77473i | −0.0437100 | + | 0.247892i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.27654 | − | 14.3354i | 0.428543 | − | 0.742258i | −0.568201 | − | 0.822890i | \(-0.692360\pi\) |
0.996744 | + | 0.0806318i | \(0.0256938\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.793245 | − | 0.288717i | −0.0409630 | − | 0.0149093i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.370680 | + | 0.311037i | −0.0190910 | + | 0.0160192i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.9306 | 1.17787 | 0.588934 | − | 0.808181i | \(-0.299548\pi\) | ||||
0.588934 | + | 0.808181i | \(0.299548\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.4003 | 0.942676 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.8570 | + | 10.7883i | −0.656963 | + | 0.551257i | −0.909175 | − | 0.416415i | \(-0.863286\pi\) |
0.252212 | + | 0.967672i | \(0.418842\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.57362 | − | 2.39260i | −0.335023 | − | 0.121938i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.51293 | + | 11.2807i | −0.331071 | + | 0.573431i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.18972 | − | 12.4185i | 0.111023 | − | 0.629643i | −0.877620 | − | 0.479358i | \(-0.840870\pi\) |
0.988643 | − | 0.150285i | \(-0.0480192\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.45137 | − | 16.3703i | −0.477976 | − | 0.827879i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.38253 | − | 1.16008i | −0.0697396 | − | 0.0585185i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.15597 | − | 1.87662i | 0.259425 | − | 0.0944229i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.86953 | + | 21.9452i | 0.194206 | + | 1.10140i | 0.913545 | + | 0.406738i | \(0.133334\pi\) |
−0.719339 | + | 0.694659i | \(0.755555\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.55219 | − | 0.685746i | −0.127769 | − | 0.0343302i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.54626 | + | 31.4544i | 0.276967 | + | 1.57076i | 0.732644 | + | 0.680612i | \(0.238286\pi\) |
−0.455677 | + | 0.890145i | \(0.650603\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 27.7631 | − | 10.1049i | 1.38298 | − | 0.503362i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.650039 | + | 0.545448i | 0.0323007 | + | 0.0271035i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.1432 | + | 19.3005i | 0.552346 | + | 0.956691i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.86728 | − | 10.5899i | 0.0923313 | − | 0.523637i | −0.903201 | − | 0.429217i | \(-0.858789\pi\) |
0.995533 | − | 0.0944194i | \(-0.0300995\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.22875 | + | 3.86031i | −0.109936 | + | 0.190415i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.68533 | + | 2.06929i | 0.279757 | + | 0.101823i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.2341 | + | 11.9438i | −0.698723 | + | 0.586298i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.76538 | 0.380272 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.43928 | 0.265726 | 0.132863 | − | 0.991134i | \(-0.457583\pi\) | ||||
0.132863 | + | 0.991134i | \(0.457583\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.90505 | + | 1.59852i | −0.0928463 | + | 0.0779073i | −0.688029 | − | 0.725683i | \(-0.741524\pi\) |
0.595183 | + | 0.803590i | \(0.297080\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.0411997 | − | 0.0149955i | −0.00200320 | − | 0.000729104i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.96347 | − | 17.2572i | 0.483299 | − | 0.837099i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.21392 | + | 6.88448i | −0.0587457 | + | 0.333163i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.90986 | − | 15.4323i | −0.430172 | − | 0.745080i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.2174 | − | 16.9644i | −0.973840 | − | 0.817149i | 0.00930869 | − | 0.999957i | \(-0.497037\pi\) |
−0.983149 | + | 0.182808i | \(0.941481\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.03750 | − | 1.46953i | 0.194030 | − | 0.0706211i | −0.243178 | − | 0.969982i | \(-0.578190\pi\) |
0.437207 | + | 0.899361i | \(0.355968\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.0702426 | + | 0.398366i | 0.00336788 | + | 0.0191002i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.90409 | + | 21.5921i | −0.0910851 | + | 1.03289i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.68530 | − | 32.2429i | −0.271345 | − | 1.53887i | −0.750339 | − | 0.661054i | \(-0.770110\pi\) |
0.478994 | − | 0.877818i | \(-0.341002\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.4059 | + | 4.15141i | −0.543138 | + | 0.197686i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.9985 | − | 25.1718i | −1.42527 | − | 1.19595i | −0.948441 | − | 0.316953i | \(-0.897340\pi\) |
−0.476833 | − | 0.878994i | \(-0.658215\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.82541 | + | 6.62580i | 0.181342 | + | 0.314093i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.11096 | + | 6.30055i | −0.0525465 | + | 0.298006i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.6553 | − | 23.6517i | 0.644435 | − | 1.11619i | −0.339997 | − | 0.940427i | \(-0.610426\pi\) |
0.984432 | − | 0.175768i | \(-0.0562408\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −44.3229 | − | 16.1322i | −2.08708 | − | 0.759636i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.39832 | + | 4.52973i | −0.253635 | + | 0.212825i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.42816 | −0.348238 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.2138 | 0.711670 | 0.355835 | − | 0.934549i | \(-0.384196\pi\) | ||||
0.355835 | + | 0.934549i | \(0.384196\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15.2649 | + | 12.8088i | −0.712505 | + | 0.597863i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.80157 | − | 2.83954i | −0.363356 | − | 0.132251i | 0.153889 | − | 0.988088i | \(-0.450820\pi\) |
−0.517245 | + | 0.855838i | \(0.673042\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.3022 | + | 31.7003i | −0.850574 | + | 1.47324i | 0.0301179 | + | 0.999546i | \(0.490412\pi\) |
−0.880691 | + | 0.473690i | \(0.842922\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.28882 | − | 24.3231i | 0.198889 | − | 1.12796i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.06233 | − | 5.30410i | −0.141708 | − | 0.245445i | 0.786432 | − | 0.617677i | \(-0.211926\pi\) |
−0.928140 | + | 0.372232i | \(0.878593\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.57755 | − | 4.68012i | −0.257547 | − | 0.216108i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.631217 | + | 0.229744i | −0.0290849 | + | 0.0105860i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.89426 | − | 27.7567i | −0.225038 | − | 1.27626i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.7161 | + | 9.64269i | −0.950522 | + | 0.442437i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.74343 | − | 15.5588i | −0.125613 | − | 0.712388i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.2232 | + | 7.72462i | −0.969713 | + | 0.352947i | −0.777833 | − | 0.628471i | \(-0.783681\pi\) |
−0.191881 | + | 0.981418i | \(0.561459\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.1282 | + | 15.2114i | 0.826575 | + | 0.693578i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.50745 | + | 2.61098i | 0.0685914 | + | 0.118804i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.97597 | + | 33.8914i | −0.271355 | + | 1.53893i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.27441 | − | 3.93940i | 0.103063 | − | 0.178511i | −0.809882 | − | 0.586593i | \(-0.800469\pi\) |
0.912945 | + | 0.408082i | \(0.133802\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.0363 | + | 8.74850i | 1.08696 | + | 0.395621i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.2170 | − | 26.1941i | 1.40880 | − | 1.18213i | 0.451773 | − | 0.892133i | \(-0.350792\pi\) |
0.957029 | − | 0.289993i | \(-0.0936528\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.441242 | −0.0198725 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 22.7953 | 1.02457 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.44282 | − | 1.21067i | 0.0647193 | − | 0.0543060i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.41383 | − | 2.69841i | −0.331889 | − | 0.120798i | 0.170701 | − | 0.985323i | \(-0.445397\pi\) |
−0.502589 | + | 0.864525i | \(0.667619\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.23360 | − | 14.2610i | 0.367850 | − | 0.637135i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.85027 | − | 16.1647i | 0.127087 | − | 0.720748i | −0.852959 | − | 0.521978i | \(-0.825194\pi\) |
0.980046 | − | 0.198770i | \(-0.0636946\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.7073 | + | 18.5456i | 0.476469 | + | 0.825268i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.65128 | − | 3.06379i | −0.162159 | − | 0.136068i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −35.7499 | + | 13.0119i | −1.58459 | + | 0.576743i | −0.976195 | − | 0.216894i | \(-0.930407\pi\) |
−0.608392 | + | 0.793637i | \(0.708185\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0427682 | − | 0.242550i | −0.00189195 | − | 0.0107298i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22.7648 | − | 1.97582i | 1.00509 | − | 0.0872347i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.24848 | + | 41.1082i | 0.319406 | + | 1.81144i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.0891465 | − | 0.0324467i | 0.00392066 | − | 0.00142700i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.80134 | − | 2.35061i | −0.122965 | − | 0.103180i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.73838 | + | 8.20711i | 0.207592 | + | 0.359560i | 0.950955 | − | 0.309328i | \(-0.100104\pi\) |
−0.743363 | + | 0.668888i | \(0.766771\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.07903 | − | 11.7907i | 0.0909095 | − | 0.515573i | −0.905015 | − | 0.425380i | \(-0.860140\pi\) |
0.995924 | − | 0.0901932i | \(-0.0287484\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.58913 | + | 2.75245i | −0.0693553 | + | 0.120127i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.3162 | + | 9.21436i | 1.10279 | + | 0.401384i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.32430 | − | 1.11122i | 0.0575783 | − | 0.0483139i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −19.7150 | −0.855557 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −50.0846 | −2.16941 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.3442 | − | 19.5881i | 1.00926 | − | 0.846868i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.104448 | − | 0.0380158i | −0.00450724 | − | 0.00164050i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.1318 | − | 22.7450i | 0.565627 | − | 0.979694i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.84939 | + | 33.1736i | −0.251485 | + | 1.42624i | 0.553452 | + | 0.832881i | \(0.313310\pi\) |
−0.804937 | + | 0.593361i | \(0.797801\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.19977 | + | 7.27421i | 0.180229 | + | 0.312166i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.2660 | + | 17.0052i | 0.868100 | + | 0.728422i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.2090 | + | 5.17166i | −0.607534 | + | 0.221124i | −0.627424 | − | 0.778678i | \(-0.715891\pi\) |
0.0198899 | + | 0.999802i | \(0.493668\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.95564 | − | 22.4335i | −0.168822 | − | 0.957439i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.414271 | + | 0.290502i | 0.0176485 | + | 0.0123758i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.165764 | − | 0.940092i | −0.00704899 | − | 0.0399768i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18.5897 | − | 6.76609i | 0.789088 | − | 0.287205i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.7963 | + | 12.4155i | 0.626937 | + | 0.526063i | 0.899976 | − | 0.435940i | \(-0.143584\pi\) |
−0.273038 | + | 0.962003i | \(0.588029\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.9641 | − | 25.9185i | −0.632912 | − | 1.09624i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.82165 | − | 16.0024i | 0.119130 | − | 0.675621i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.1965 | + | 33.2493i | −0.809037 | + | 1.40129i | 0.104495 | + | 0.994525i | \(0.466677\pi\) |
−0.913532 | + | 0.406767i | \(0.866656\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.26338 | + | 2.27969i | 0.263503 | + | 0.0959071i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.113093 | − | 0.0948960i | 0.00474944 | − | 0.00398526i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.84346 | −0.203048 | −0.101524 | − | 0.994833i | \(-0.532372\pi\) | ||||
−0.101524 | + | 0.994833i | \(0.532372\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.5129 | 1.56987 | 0.784934 | − | 0.619580i | \(-0.212697\pi\) | ||||
0.784934 | + | 0.619580i | \(0.212697\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.5200 | − | 10.5055i | 0.523029 | − | 0.438873i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.4965 | + | 8.91599i | 1.02157 | + | 0.371822i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.22241 | + | 2.11728i | −0.0508896 | + | 0.0881433i | −0.890348 | − | 0.455280i | \(-0.849539\pi\) |
0.839458 | + | 0.543424i | \(0.182872\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.489900 | − | 2.77836i | 0.0203596 | − | 0.115465i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.61637 | + | 2.79963i | 0.0670582 | + | 0.116148i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26.1872 | + | 21.9736i | 1.08456 | + | 0.910055i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 22.7454 | − | 8.27865i | 0.940407 | − | 0.342280i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.79011 | + | 10.1522i | 0.0738856 | + | 0.419026i | 0.999206 | + | 0.0398401i | \(0.0126849\pi\) |
−0.925320 | + | 0.379186i | \(0.876204\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.7023 | − | 25.3187i | −0.729410 | − | 1.04324i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.21693 | + | 6.90154i | 0.0500577 | + | 0.283891i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.02362 | + | 3.28433i | −0.370556 | + | 0.134871i | −0.520584 | − | 0.853810i | \(-0.674286\pi\) |
0.150028 | + | 0.988682i | \(0.452064\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.18880 | − | 4.35392i | −0.212720 | − | 0.178493i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.00211 | − | 5.19980i | −0.122868 | − | 0.212814i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.30188 | − | 18.7259i | 0.134911 | − | 0.765118i | −0.840011 | − | 0.542570i | \(-0.817451\pi\) |
0.974922 | − | 0.222548i | \(-0.0714375\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.65441 | + | 13.2578i | −0.312230 | + | 0.540798i | −0.978845 | − | 0.204604i | \(-0.934409\pi\) |
0.666615 | + | 0.745402i | \(0.267743\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 22.2947 | + | 8.11461i | 0.907911 | + | 0.330452i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.8165 | + | 9.07610i | −0.439752 | + | 0.368996i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.95975 | 0.160721 | 0.0803607 | − | 0.996766i | \(-0.474393\pi\) | ||||
0.0803607 | + | 0.996766i | \(0.474393\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.0703761 | 0.00285178 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.0771676 | − | 0.0647513i | 0.00312187 | − | 0.00261956i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.0409 | + | 3.65457i | 0.405547 | + | 0.147607i | 0.536736 | − | 0.843751i | \(-0.319657\pi\) |
−0.131189 | + | 0.991357i | \(0.541879\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −20.9344 | + | 36.2594i | −0.844156 | + | 1.46212i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.954966 | − | 5.41588i | 0.0384455 | − | 0.218035i | −0.959532 | − | 0.281599i | \(-0.909135\pi\) |
0.997978 | + | 0.0635633i | \(0.0202465\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.8634 | + | 24.0122i | 0.557219 | + | 0.965131i | 0.997727 | + | 0.0673827i | \(0.0214648\pi\) |
−0.440508 | + | 0.897748i | \(0.645202\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −19.9697 | − | 16.7566i | −0.801357 | − | 0.672418i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.25080 | − | 0.455254i | 0.0501123 | − | 0.0182394i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.12069 | − | 23.3696i | −0.164828 | − | 0.934784i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.1847 | + | 13.1665i | −0.526547 | + | 0.525820i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.74716 | + | 21.2512i | 0.149409 | + | 0.847342i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.0204469 | + | 0.00744206i | −0.000813978 | + | 0.000296264i | −0.342427 | − | 0.939544i | \(-0.611249\pi\) |
0.341613 | + | 0.939841i | \(0.389027\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.24776 | + | 5.24249i | 0.248326 | + | 0.208370i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −27.0404 | − | 46.8353i | −1.07306 | − | 1.85860i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.84269 | − | 27.4643i | 0.191875 | − | 1.08817i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.06870 | + | 5.31515i | −0.121396 | + | 0.210264i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.9085 | − | 10.1579i | −1.10232 | − | 0.401211i | −0.274148 | − | 0.961687i | \(-0.588396\pi\) |
−0.828170 | + | 0.560476i | \(0.810618\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.1147 | − | 10.1655i | 0.477758 | − | 0.400887i | −0.371857 | − | 0.928290i | \(-0.621279\pi\) |
0.849615 | + | 0.527404i | \(0.176834\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −25.0187 | −0.985111 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.3133 | −1.38831 | −0.694154 | − | 0.719826i | \(-0.744221\pi\) | ||||
−0.694154 | + | 0.719826i | \(0.744221\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.6784 | − | 27.4204i | 1.28274 | − | 1.07635i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.03783 | − | 1.46965i | −0.158255 | − | 0.0576001i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.0337 | + | 41.6275i | −0.940510 | + | 1.62901i | −0.176010 | + | 0.984388i | \(0.556319\pi\) |
−0.764500 | + | 0.644623i | \(0.777014\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.921106 | + | 5.22385i | −0.0359906 | + | 0.204113i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.401279 | + | 0.695036i | 0.0156554 | + | 0.0271159i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.45303 | + | 3.73654i | 0.173466 | + | 0.145555i | 0.725387 | − | 0.688341i | \(-0.241661\pi\) |
−0.551922 | + | 0.833896i | \(0.686105\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.1778 | + | 9.52794i | −1.01820 | + | 0.370594i | −0.796576 | − | 0.604539i | \(-0.793357\pi\) |
−0.221623 | + | 0.975133i | \(0.571135\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.99616 | − | 16.9921i | −0.116361 | − | 0.659918i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.00513 | + | 7.50396i | 0.0777555 | + | 0.290991i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.100236 | − | 0.568468i | −0.00388116 | − | 0.0220112i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.3944 | + | 5.23912i | −0.556518 | + | 0.202556i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37.7581 | + | 31.6828i | 1.45764 | + | 1.22310i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.5701 | − | 39.0926i | −0.870015 | − | 1.50691i | −0.861980 | − | 0.506943i | \(-0.830775\pi\) |
−0.00803563 | − | 0.999968i | \(-0.502558\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.77204 | − | 27.0636i | 0.183676 | − | 1.04168i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.71076 | + | 4.69517i | −0.104183 | + | 0.180450i | −0.913404 | − | 0.407054i | \(-0.866556\pi\) |
0.809221 | + | 0.587504i | \(0.199889\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.62624 | + | 2.04778i | 0.215915 | + | 0.0785868i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.1383 | + | 17.7371i | −0.810021 | + | 0.679689i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.9254 | −1.29812 | −0.649060 | − | 0.760738i | \(-0.724837\pi\) | ||||
−0.649060 | + | 0.760738i | \(0.724837\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.1012 | 0.500569 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.5417 | − | 13.8801i | 0.631105 | − | 0.529560i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34.1101 | + | 12.4151i | 1.29949 | + | 0.472976i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.2022 | − | 24.5990i | 0.540278 | − | 0.935788i | −0.458610 | − | 0.888638i | \(-0.651653\pi\) |
0.998888 | − | 0.0471508i | \(-0.0150141\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.688669 | − | 3.90564i | 0.0261604 | − | 0.148363i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.4117 | − | 19.7656i | −0.432870 | − | 0.749753i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −34.9857 | − | 29.3565i | −1.32518 | − | 1.11196i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.6553 | − | 8.24586i | 0.856903 | − | 0.311887i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.72496 | − | 21.1253i | −0.140690 | − | 0.797891i | −0.970727 | − | 0.240184i | \(-0.922792\pi\) |
0.830038 | − | 0.557707i | \(-0.188319\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.4731 | − | 22.4193i | 0.395002 | − | 0.845559i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.0146230 | − | 0.0829313i | −0.000550735 | − | 0.00312337i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.50099 | − | 1.27426i | 0.131668 | − | 0.0479233i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.40631 | + | 3.69734i | 0.165483 | + | 0.138856i | 0.721768 | − | 0.692135i | \(-0.243330\pi\) |
−0.556286 | + | 0.830991i | \(0.687774\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.55531 | + | 2.69387i | 0.0583285 | + | 0.101028i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.12014 | + | 34.7090i | −0.229201 | + | 1.29986i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26.1872 | + | 45.3575i | −0.979345 | + | 1.69627i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.09479 | + | 0.762442i | 0.0782315 | + | 0.0284739i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.67624 | + | 8.11933i | −0.360863 | + | 0.302800i | −0.805135 | − | 0.593092i | \(-0.797907\pi\) |
0.444272 | + | 0.895892i | \(0.353463\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.26226 | 0.270461 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.33879 | −0.0497900 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.466148 | − | 0.391145i | 0.0173123 | − | 0.0145267i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.6845 | + | 7.16458i | 0.730058 | + | 0.265719i | 0.680189 | − | 0.733036i | \(-0.261897\pi\) |
0.0498687 | + | 0.998756i | \(0.484120\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.80279 | + | 15.2469i | −0.326029 | + | 0.564699i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.73894 | − | 26.8759i | 0.175276 | − | 0.994040i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.8459 | − | 23.9818i | −0.511410 | − | 0.885788i | −0.999913 | − | 0.0132253i | \(-0.995790\pi\) |
0.488503 | − | 0.872562i | \(-0.337543\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −17.8590 | − | 14.9855i | −0.658738 | − | 0.552747i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −48.2406 | + | 17.5581i | −1.77696 | + | 0.646762i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.13266 | + | 6.42366i | 0.0416658 | + | 0.236298i | 0.998528 | − | 0.0542449i | \(-0.0172752\pi\) |
−0.956862 | + | 0.290543i | \(0.906164\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.37412 | + | 17.9260i | −0.307631 | + | 0.658530i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.37272 | + | 47.4840i | 0.307165 | + | 1.74202i | 0.613134 | + | 0.789979i | \(0.289909\pi\) |
−0.305969 | + | 0.952042i | \(0.598980\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.6697 | − | 6.43126i | 0.647369 | − | 0.235623i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.06957 | − | 6.77117i | −0.295250 | − | 0.247744i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.65088 | − | 4.59146i | −0.0968611 | − | 0.167768i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.08778 | + | 6.16908i | −0.0396935 | + | 0.225113i | −0.998201 | − | 0.0599538i | \(-0.980905\pi\) |
0.958508 | + | 0.285067i | \(0.0920158\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.78029 | − | 6.54766i | 0.137762 | − | 0.238610i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.4629 | + | 7.08392i | 0.708328 | + | 0.257810i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.5477 | − | 20.5979i | 0.892200 | − | 0.748645i | −0.0764503 | − | 0.997073i | \(-0.524359\pi\) |
0.968650 | + | 0.248429i | \(0.0799142\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 21.2574 | 0.771595 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.1308 | 1.56349 | 0.781745 | − | 0.623598i | \(-0.214330\pi\) | ||||
0.781745 | + | 0.623598i | \(0.214330\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.52584 | − | 2.95853i | 0.127644 | − | 0.107106i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 20.7408 | + | 7.54904i | 0.749885 | + | 0.272936i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.6485 | − | 39.2283i | 0.817790 | − | 1.41645i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.88829 | + | 33.3942i | −0.212337 | + | 1.20422i | 0.673131 | + | 0.739524i | \(0.264949\pi\) |
−0.885468 | + | 0.464701i | \(0.846162\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.38641 | + | 9.32954i | 0.193987 | + | 0.335995i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.2612 | + | 11.9666i | 0.512939 | + | 0.430407i | 0.862162 | − | 0.506633i | \(-0.169110\pi\) |
−0.349223 | + | 0.937040i | \(0.613554\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34.9134 | + | 12.7074i | −1.25413 | + | 0.456465i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.597656 | − | 3.38948i | −0.0214408 | − | 0.121597i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.5196 | + | 50.5957i | 0.484391 | + | 1.81278i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.30603 | − | 13.0782i | −0.0825163 | − | 0.467973i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.571815 | + | 0.208124i | −0.0204350 | + | 0.00743774i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.51239 | + | 1.26905i | 0.0539795 | + | 0.0452942i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.59309 | + | 13.1516i | 0.270664 | + | 0.468804i | 0.969032 | − | 0.246935i | \(-0.0794233\pi\) |
−0.698368 | + | 0.715739i | \(0.746090\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.406197 | + | 2.30366i | −0.0144610 | + | 0.0820123i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.579813 | − | 1.00427i | 0.0206158 | − | 0.0357076i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.1818 | + | 17.9007i | 1.74650 | + | 0.635673i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.2454 | − | 19.5052i | 0.824429 | − | 0.691778i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.44693 | 0.0866746 | 0.0433373 | − | 0.999060i | \(-0.486201\pi\) | ||||
0.0433373 | + | 0.999060i | \(0.486201\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.0918572 | 0.00324967 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.32264 | + | 2.78802i | −0.117400 | + | 0.0985100i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.63182 | − | 0.593935i | −0.0575858 | − | 0.0209595i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.43058 | − | 7.67399i | 0.156158 | − | 0.270473i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.87161 | + | 10.6144i | −0.0658839 | + | 0.373646i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.50615 | − | 11.2690i | −0.228744 | − | 0.396197i | 0.728692 | − | 0.684842i | \(-0.240129\pi\) |
−0.957436 | + | 0.288645i | \(0.906795\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.08728 | + | 7.62513i | 0.319098 | + | 0.267755i | 0.788240 | − | 0.615368i | \(-0.210993\pi\) |
−0.469143 | + | 0.883122i | \(0.655437\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.9725 | − | 6.90542i | 0.665394 | − | 0.242183i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.0548 | − | 74.0373i | −0.457289 | − | 2.59341i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.1436 | + | 22.1131i | −0.774708 | + | 0.773639i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.731262 | − | 4.14719i | −0.0255524 | − | 0.144915i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.1000 | − | 4.04006i | 0.387392 | − | 0.140999i | −0.140979 | − | 0.990013i | \(-0.545025\pi\) |
0.528371 | + | 0.849013i | \(0.322803\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.2113 | + | 9.40736i | 0.390800 | + | 0.327920i | 0.816925 | − | 0.576744i | \(-0.195677\pi\) |
−0.426125 | + | 0.904664i | \(0.640122\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.2046 | + | 19.4069i | 0.390094 | + | 0.675662i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.07253 | − | 11.7539i | 0.0720691 | − | 0.408724i | −0.927336 | − | 0.374230i | \(-0.877907\pi\) |
0.999405 | − | 0.0344938i | \(-0.0109819\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.39076 | + | 16.2653i | −0.326154 | + | 0.564916i | −0.981745 | − | 0.190200i | \(-0.939086\pi\) |
0.655591 | + | 0.755116i | \(0.272420\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.8562 | − | 9.77487i | −0.931632 | − | 0.339086i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.4806 | − | 16.3462i | 0.674963 | − | 0.566361i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −48.3991 | −1.67492 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 37.1541 | 1.28423 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.4639 | + | 20.5276i | −0.844587 | + | 0.708693i | −0.958591 | − | 0.284788i | \(-0.908077\pi\) |
0.114004 | + | 0.993480i | \(0.463632\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.2384 | + | 9.91398i | 0.939256 | + | 0.341861i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.5914 | + | 20.0769i | −0.399229 | + | 0.691486i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.43265 | + | 13.7962i | −0.0836856 | + | 0.474605i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.22828 | + | 2.12744i | 0.0422041 | + | 0.0730997i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.8991 | − | 11.6628i | −0.477017 | − | 0.400265i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.5275 | + | 9.65521i | −0.909350 | + | 0.330976i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.31018 | − | 18.7730i | −0.113338 | − | 0.642775i | −0.987559 | − | 0.157246i | \(-0.949738\pi\) |
0.874221 | − | 0.485528i | \(-0.161373\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.5029 | − | 20.7428i | −0.495990 | − | 0.709389i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.69018 | − | 43.6132i | −0.262691 | − | 1.48980i | −0.775529 | − | 0.631312i | \(-0.782517\pi\) |
0.512838 | − | 0.858486i | \(-0.328594\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.9800 | − | 7.27211i | 0.681707 | − | 0.248121i | 0.0221269 | − | 0.999755i | \(-0.492956\pi\) |
0.659580 | + | 0.751634i | \(0.270734\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.58006 | + | 4.68223i | 0.190168 | + | 0.159570i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.32952 | − | 14.4272i | −0.283540 | − | 0.491106i | 0.688714 | − | 0.725033i | \(-0.258176\pi\) |
−0.972254 | + | 0.233927i | \(0.924842\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.86638 | + | 10.5848i | −0.0634588 | + | 0.359893i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.38869 | + | 2.40529i | −0.0471625 | + | 0.0816879i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.32473 | − | 2.30201i | −0.214552 | − | 0.0780904i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.7583 | + | 35.0394i | −1.41493 | + | 1.18726i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19.5101 | −0.660316 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.431652 | 0.0145925 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.5025 | + | 16.3646i | −0.658554 | + | 0.552592i | −0.909653 | − | 0.415369i | \(-0.863652\pi\) |
0.251099 | + | 0.967961i | \(0.419208\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.1324 | + | 8.05554i | 0.746508 | + | 0.271707i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.5261 | − | 23.4279i | 0.455707 | − | 0.789307i | −0.543022 | − | 0.839719i | \(-0.682720\pi\) |
0.998729 | + | 0.0504114i | \(0.0160532\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.60183 | + | 9.08441i | −0.0539057 | + | 0.305715i | −0.999825 | − | 0.0186864i | \(-0.994052\pi\) |
0.945920 | + | 0.324401i | \(0.105163\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.9332 | − | 32.7933i | −0.636434 | − | 1.10234i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.8042 | − | 10.7440i | −0.429922 | − | 0.360748i | 0.402000 | − | 0.915640i | \(-0.368315\pi\) |
−0.831922 | + | 0.554892i | \(0.812760\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.84144 | + | 3.21802i | −0.296532 | + | 0.107929i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.180754 | − | 1.02511i | −0.00605548 | − | 0.0343423i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.0862423 | − | 0.0604763i | −0.00288599 | − | 0.00202376i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.0567283 | + | 0.321722i | 0.00189622 | + | 0.0107540i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 21.2109 | − | 7.72013i | 0.708211 | − | 0.257768i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.630227 | + | 0.528823i | 0.0210192 | + | 0.0176372i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.5500 | + | 28.6655i | 0.551362 | + | 0.954986i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.755840 | + | 4.28658i | −0.0251528 | + | 0.142649i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.3436 | − | 21.3798i | 0.410316 | − | 0.710688i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.49613 | − | 2.36440i | −0.215700 | − | 0.0785085i | 0.231910 | − | 0.972737i | \(-0.425503\pi\) |
−0.447610 | + | 0.894229i | \(0.647725\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.30005 | + | 7.80367i | −0.308463 | + | 0.258831i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53.3065 | 1.76612 | 0.883062 | − | 0.469256i | \(-0.155478\pi\) | ||||
0.883062 | + | 0.469256i | \(0.155478\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.7933 | 0.754348 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 33.5165 | − | 28.1237i | 1.10802 | − | 0.929740i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.867201 | + | 0.315635i | 0.0286375 | + | 0.0104232i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.0547 | + | 43.3960i | −0.826477 | + | 1.43150i | 0.0743077 | + | 0.997235i | \(0.476325\pi\) |
−0.900785 | + | 0.434265i | \(0.857008\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.76255 | − | 9.99592i | 0.0580780 | − | 0.329377i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.05063 | − | 12.2120i | −0.232074 | − | 0.401964i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.7971 | − | 19.1290i | −0.749564 | − | 0.628959i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22.2374 | + | 8.09375i | −0.730372 | + | 0.265834i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.50614 | + | 36.8982i | 0.213460 | + | 1.21059i | 0.883559 | + | 0.468319i | \(0.155140\pi\) |
−0.670100 | + | 0.742271i | \(0.733749\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29.0517 | + | 2.52148i | −0.952132 | + | 0.0826383i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.25872 | + | 35.4950i | 0.204901 | + | 1.16205i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −44.8783 | + | 16.3344i | −1.46768 | + | 0.534191i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.3267 | − | 22.0907i | −0.860057 | − | 0.721673i | 0.101924 | − | 0.994792i | \(-0.467500\pi\) |
−0.961980 | + | 0.273119i | \(0.911945\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.80852 | − | 8.32860i | −0.156920 | − | 0.271793i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.30597 | − | 13.0778i | 0.0751724 | − | 0.426324i | −0.923875 | − | 0.382694i | \(-0.874996\pi\) |
0.999048 | − | 0.0436304i | \(-0.0138924\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.8733 | − | 51.7421i | 0.972810 | − | 1.68496i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.77793 | − | 3.19491i | −0.285546 | − | 0.103930i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.1563 | − | 8.52215i | 0.330035 | − | 0.276933i | −0.462679 | − | 0.886526i | \(-0.653112\pi\) |
0.792714 | + | 0.609593i | \(0.208667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.84395 | −0.0598572 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31.8102 | −1.03152 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.3329 | + | 19.5786i | −0.755826 | + | 0.634213i | −0.937037 | − | 0.349231i | \(-0.886443\pi\) |
0.181211 | + | 0.983444i | \(0.441998\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −45.1390 | − | 16.4293i | −1.46066 | − | 0.531638i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.248103 | − | 0.429727i | 0.00802004 | − | 0.0138911i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.395799 | − | 2.24469i | 0.0127810 | − | 0.0724847i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.61595 | − | 16.6553i | −0.310192 | − | 0.537268i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.2343 | + | 11.1049i | 0.426469 | + | 0.357850i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.79185 | + | 2.83600i | −0.250828 | + | 0.0912941i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.19804 | − | 12.4657i | −0.0706843 | − | 0.400871i | −0.999537 | − | 0.0304218i | \(-0.990315\pi\) |
0.928853 | − | 0.370449i | \(-0.120796\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.3567 | + | 7.61351i | −0.525453 | + | 0.244581i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.716843 | + | 4.06542i | 0.0230046 | + | 0.130465i | 0.994147 | − | 0.108034i | \(-0.0344556\pi\) |
−0.971143 | + | 0.238500i | \(0.923344\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.73131 | + | 1.35808i | −0.119620 | + | 0.0435382i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.2281 | + | 15.2952i | 0.583768 | + | 0.489839i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.6929 | − | 37.5732i | −0.694017 | − | 1.20207i | −0.970511 | − | 0.241058i | \(-0.922506\pi\) |
0.276493 | − | 0.961016i | \(-0.410828\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.62971 | − | 9.24253i | 0.0520857 | − | 0.295393i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.49904 | + | 12.9887i | −0.239426 | + | 0.414698i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.4272 | + | 5.61506i | 0.492053 | + | 0.179093i | 0.576116 | − | 0.817368i | \(-0.304568\pi\) |
−0.0840634 | + | 0.996460i | \(0.526790\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.7785 | − | 13.2397i | 0.502745 | − | 0.421853i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.0146508 | −0.000466340 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 35.7017 | 1.13525 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.6095 | − | 21.4889i | 0.813512 | − | 0.682618i | −0.137931 | − | 0.990442i | \(-0.544045\pi\) |
0.951443 | + | 0.307824i | \(0.0996009\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.9392 | − | 4.34552i | −0.378880 | − | 0.137901i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.82355 | + | 15.2828i | −0.279725 | + | 0.484499i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.22589 | − | 52.3226i | 0.292187 | − | 1.65707i | −0.386235 | − | 0.922401i | \(-0.626225\pi\) |
0.678421 | − | 0.734673i | \(-0.262664\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.8798 | + | 25.7725i | 0.470774 | + | 0.815405i |
(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 | 76.2.i.a.9.1 | ✓ | 12 | |
3.2 | odd | 2 | 684.2.bo.c.541.1 | 12 | |||
4.3 | odd | 2 | 304.2.u.e.161.2 | 12 | |||
19.4 | even | 9 | 1444.2.e.g.429.5 | 12 | |||
19.6 | even | 9 | 1444.2.a.h.1.2 | 6 | |||
19.9 | even | 9 | 1444.2.e.g.653.5 | 12 | |||
19.10 | odd | 18 | 1444.2.e.h.653.2 | 12 | |||
19.13 | odd | 18 | 1444.2.a.g.1.5 | 6 | |||
19.15 | odd | 18 | 1444.2.e.h.429.2 | 12 | |||
19.17 | even | 9 | inner | 76.2.i.a.17.1 | yes | 12 | |
57.17 | odd | 18 | 684.2.bo.c.397.1 | 12 | |||
76.51 | even | 18 | 5776.2.a.by.1.2 | 6 | |||
76.55 | odd | 18 | 304.2.u.e.17.2 | 12 | |||
76.63 | odd | 18 | 5776.2.a.bw.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.2.i.a.9.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
76.2.i.a.17.1 | yes | 12 | 19.17 | even | 9 | inner | |
304.2.u.e.17.2 | 12 | 76.55 | odd | 18 | |||
304.2.u.e.161.2 | 12 | 4.3 | odd | 2 | |||
684.2.bo.c.397.1 | 12 | 57.17 | odd | 18 | |||
684.2.bo.c.541.1 | 12 | 3.2 | odd | 2 | |||
1444.2.a.g.1.5 | 6 | 19.13 | odd | 18 | |||
1444.2.a.h.1.2 | 6 | 19.6 | even | 9 | |||
1444.2.e.g.429.5 | 12 | 19.4 | even | 9 | |||
1444.2.e.g.653.5 | 12 | 19.9 | even | 9 | |||
1444.2.e.h.429.2 | 12 | 19.15 | odd | 18 | |||
1444.2.e.h.653.2 | 12 | 19.10 | odd | 18 | |||
5776.2.a.bw.1.5 | 6 | 76.63 | odd | 18 | |||
5776.2.a.by.1.2 | 6 | 76.51 | even | 18 |