Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,2,Mod(13,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.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: | \(0.862384341830\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} + 24 x^{16} - 66 x^{15} + 153 x^{14} - 315 x^{13} + 651 x^{12} - 1350 x^{11} + \cdots + 19683 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 61.1 | ||
Root | \(-1.29960 - 1.14501i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.61 |
Dual form | 108.2.i.a.85.1 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{8}{9}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.829611 | − | 1.52044i | −0.478976 | − | 0.877828i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.399598 | − | 2.26623i | −0.178706 | − | 1.01349i | −0.933779 | − | 0.357850i | \(-0.883510\pi\) |
0.755073 | − | 0.655640i | \(-0.227601\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.715176 | − | 0.600104i | −0.270311 | − | 0.226818i | 0.497548 | − | 0.867436i | \(-0.334234\pi\) |
−0.767859 | + | 0.640618i | \(0.778678\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.62349 | + | 2.52275i | −0.541164 | + | 0.840917i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.843075 | − | 4.78132i | 0.254197 | − | 1.44162i | −0.543929 | − | 0.839131i | \(-0.683064\pi\) |
0.798126 | − | 0.602490i | \(-0.205825\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.71397 | + | 2.07972i | 1.58477 | + | 0.576809i | 0.976235 | − | 0.216717i | \(-0.0695348\pi\) |
0.608536 | + | 0.793526i | \(0.291757\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.11417 | + | 2.48766i | −0.804074 | + | 0.642310i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.42887 | + | 2.47487i | 0.346551 | + | 0.600245i | 0.985634 | − | 0.168893i | \(-0.0540193\pi\) |
−0.639083 | + | 0.769138i | \(0.720686\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50656 | + | 4.34148i | −0.575043 | + | 0.996004i | 0.420994 | + | 0.907064i | \(0.361681\pi\) |
−0.996037 | + | 0.0889406i | \(0.971652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.319106 | + | 1.58524i | −0.0696346 | + | 0.345927i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.51851 | + | 1.27419i | −0.316632 | + | 0.265686i | −0.787227 | − | 0.616664i | \(-0.788484\pi\) |
0.470595 | + | 0.882350i | \(0.344039\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.277670 | + | 0.101064i | −0.0555341 | + | 0.0202127i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.18257 | + | 0.375523i | 0.997385 | + | 0.0722695i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.76640 | − | 0.642919i | 0.328013 | − | 0.119387i | −0.172764 | − | 0.984963i | \(-0.555270\pi\) |
0.500777 | + | 0.865576i | \(0.333048\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.02045 | − | 0.856259i | 0.183278 | − | 0.153789i | −0.546533 | − | 0.837438i | \(-0.684053\pi\) |
0.729811 | + | 0.683649i | \(0.239608\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.96914 | + | 2.68479i | −1.38725 | + | 0.467361i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.07419 | + | 1.86056i | −0.181572 | + | 0.314491i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00392 | + | 5.20294i | 0.493841 | + | 0.855358i | 0.999975 | − | 0.00709729i | \(-0.00225916\pi\) |
−0.506134 | + | 0.862455i | \(0.668926\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.57829 | − | 10.4131i | −0.252728 | − | 1.66743i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.5092 | − | 3.82502i | −1.64126 | − | 0.597368i | −0.653998 | − | 0.756496i | \(-0.726910\pi\) |
−0.987258 | + | 0.159128i | \(0.949132\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.31468 | − | 7.45591i | 0.200486 | − | 1.13702i | −0.703899 | − | 0.710300i | \(-0.748559\pi\) |
0.904386 | − | 0.426715i | \(-0.140329\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.36589 | + | 2.67112i | 0.948970 | + | 0.398188i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.37180 | + | 7.02478i | 1.22115 | + | 1.02467i | 0.998764 | + | 0.0497113i | \(0.0158301\pi\) |
0.222390 | + | 0.974958i | \(0.428614\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.06419 | − | 6.03530i | −0.152026 | − | 0.862185i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.57750 | − | 4.22569i | 0.360922 | − | 0.591715i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.60406 | 0.357696 | 0.178848 | − | 0.983877i | \(-0.442763\pi\) | ||||
0.178848 | + | 0.983877i | \(0.442763\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.1725 | −1.50650 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.68044 | + | 0.209333i | 1.14975 | + | 0.0277269i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.763808 | + | 4.33177i | 0.0994393 | + | 0.563949i | 0.993296 | + | 0.115596i | \(0.0368779\pi\) |
−0.893857 | + | 0.448352i | \(0.852011\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.46625 | − | 7.10403i | −1.08399 | − | 0.909577i | −0.0877461 | − | 0.996143i | \(-0.527966\pi\) |
−0.996246 | + | 0.0865654i | \(0.972411\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.67499 | − | 0.829947i | 0.337018 | − | 0.104564i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.42983 | − | 13.7802i | 0.301383 | − | 1.70923i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.726818 | + | 0.264540i | 0.0887949 | + | 0.0323187i | 0.386036 | − | 0.922484i | \(-0.373844\pi\) |
−0.297241 | + | 0.954803i | \(0.596066\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.19710 | + | 1.25174i | 0.384886 | + | 0.150691i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.62509 | + | 8.01090i | 0.548898 | + | 0.950719i | 0.998350 | + | 0.0574144i | \(0.0182856\pi\) |
−0.449453 | + | 0.893304i | \(0.648381\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.221676 | − | 0.383954i | 0.0259452 | − | 0.0449384i | −0.852761 | − | 0.522301i | \(-0.825074\pi\) |
0.878706 | + | 0.477362i | \(0.158407\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.384020 | + | 0.338338i | 0.0443428 | + | 0.0390679i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.47223 | + | 2.91355i | −0.395698 | + | 0.332030i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.92366 | + | 1.79207i | −0.553955 | + | 0.201623i | −0.603803 | − | 0.797134i | \(-0.706349\pi\) |
0.0498479 | + | 0.998757i | \(0.484126\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.72855 | − | 8.19133i | −0.414283 | − | 0.910148i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.8790 | + | 5.41550i | −1.63318 | + | 0.594429i | −0.985827 | − | 0.167763i | \(-0.946346\pi\) |
−0.647352 | + | 0.762191i | \(0.724124\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.03766 | − | 4.22710i | 0.546411 | − | 0.458494i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.44295 | − | 2.15234i | −0.261912 | − | 0.230756i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.58162 | + | 13.1318i | −0.803650 | + | 1.39196i | 0.113548 | + | 0.993532i | \(0.463778\pi\) |
−0.917199 | + | 0.398431i | \(0.869555\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.83845 | − | 4.91634i | −0.297550 | − | 0.515372i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.14847 | − | 0.841174i | −0.222786 | − | 0.0872257i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.8404 | + | 3.94559i | 1.11220 | + | 0.404809i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.21115 | + | 6.86875i | −0.122973 | + | 0.697416i | 0.859518 | + | 0.511106i | \(0.170764\pi\) |
−0.982491 | + | 0.186310i | \(0.940347\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.6933 | + | 9.88930i | 1.07472 | + | 0.993912i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.77428 | + | 7.36249i | 0.873073 | + | 0.732595i | 0.964743 | − | 0.263194i | \(-0.0847760\pi\) |
−0.0916699 | + | 0.995789i | \(0.529220\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.64756 | + | 15.0151i | 0.260872 | + | 1.47948i | 0.780537 | + | 0.625109i | \(0.214946\pi\) |
−0.519665 | + | 0.854370i | \(0.673943\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.72003 | + | 0.0897105i | 0.363038 | + | 0.00875484i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.13078 | −0.109316 | −0.0546582 | − | 0.998505i | \(-0.517407\pi\) | ||||
−0.0546582 | + | 0.998505i | \(0.517407\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.4627 | 1.09793 | 0.548963 | − | 0.835847i | \(-0.315023\pi\) | ||||
0.548963 | + | 0.835847i | \(0.315023\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.41869 | − | 8.88370i | 0.514319 | − | 0.843203i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.55104 | − | 8.79638i | −0.145909 | − | 0.827493i | −0.966632 | − | 0.256167i | \(-0.917540\pi\) |
0.820723 | − | 0.571326i | \(-0.193571\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.49440 | + | 2.93215i | 0.325854 | + | 0.273424i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −14.5232 | + | 11.0385i | −1.34267 | + | 1.02051i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.463288 | − | 2.62744i | 0.0424695 | − | 0.240857i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.8136 | − | 4.29980i | −1.07396 | − | 0.390891i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.90279 | + | 19.1519i | 0.261736 | + | 1.72687i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.41299 | − | 9.37558i | −0.484153 | − | 0.838577i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.0199485 | − | 0.0345518i | 0.00177014 | − | 0.00306598i | −0.865139 | − | 0.501532i | \(-0.832770\pi\) |
0.866909 | + | 0.498466i | \(0.166103\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.4269 | + | 4.18661i | −1.09413 | + | 0.368610i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.18854 | − | 1.83640i | 0.191214 | − | 0.160447i | −0.542155 | − | 0.840279i | \(-0.682391\pi\) |
0.733369 | + | 0.679831i | \(0.237947\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.39797 | − | 1.60073i | 0.381352 | − | 0.138801i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.21992 | − | 11.8950i | −0.104994 | − | 1.02376i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.55367 | + | 3.11328i | −0.730790 | + | 0.265986i | −0.680499 | − | 0.732749i | \(-0.738237\pi\) |
−0.0502906 | + | 0.998735i | \(0.516015\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.65849 | + | 1.39164i | −0.140671 | + | 0.118037i | −0.710408 | − | 0.703790i | \(-0.751490\pi\) |
0.569737 | + | 0.821827i | \(0.307045\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.73543 | − | 18.5567i | 0.314580 | − | 1.56275i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.7611 | − | 25.5670i | 1.23438 | − | 2.13802i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.16286 | − | 3.74618i | −0.179615 | − | 0.311103i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.29346 | + | 6.62498i | −0.684033 | + | 0.546419i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.24975 | + | 1.18281i | 0.266230 | + | 0.0968999i | 0.471686 | − | 0.881766i | \(-0.343646\pi\) |
−0.205456 | + | 0.978666i | \(0.565868\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.850331 | − | 4.82247i | 0.0691989 | − | 0.392447i | −0.930462 | − | 0.366390i | \(-0.880594\pi\) |
0.999660 | − | 0.0260571i | \(-0.00829516\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.56324 | − | 0.413255i | −0.692297 | − | 0.0334096i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.34825 | − | 1.97042i | −0.188616 | − | 0.158268i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.210558 | − | 1.19413i | −0.0168043 | − | 0.0953021i | 0.975252 | − | 0.221096i | \(-0.0709634\pi\) |
−0.992056 | + | 0.125794i | \(0.959852\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.16036 | − | 3.95933i | −0.171328 | − | 0.313995i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.85065 | 0.145852 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.21181 | 0.721525 | 0.360762 | − | 0.932658i | \(-0.382517\pi\) | ||||
0.360762 | + | 0.932658i | \(0.382517\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.26880 | + | 16.9871i | 0.721575 | + | 1.32244i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.507283 | + | 2.87695i | 0.0392548 | + | 0.222625i | 0.998124 | − | 0.0612230i | \(-0.0195001\pi\) |
−0.958869 | + | 0.283848i | \(0.908389\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.3657 | + | 15.4106i | 1.41274 | + | 1.18543i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.88311 | − | 13.3718i | −0.526364 | − | 1.02257i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.53836 | − | 14.3958i | 0.192988 | − | 1.09449i | −0.722266 | − | 0.691615i | \(-0.756900\pi\) |
0.915255 | − | 0.402876i | \(-0.131989\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.259232 | + | 0.0943527i | 0.0195961 | + | 0.00713239i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.95255 | − | 4.75501i | 0.447421 | − | 0.357409i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.1929 | − | 17.6546i | −0.761852 | − | 1.31957i | −0.941895 | − | 0.335907i | \(-0.890957\pi\) |
0.180043 | − | 0.983659i | \(-0.442376\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.95796 | − | 3.39129i | 0.145534 | − | 0.252072i | −0.784038 | − | 0.620713i | \(-0.786843\pi\) |
0.929572 | + | 0.368640i | \(0.120177\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.77757 | + | 18.7660i | −0.279246 | + | 1.38722i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.5907 | − | 8.88666i | 0.778644 | − | 0.653360i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.0378 | − | 4.74537i | 0.953418 | − | 0.347016i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.48109 | − | 3.37864i | −0.253212 | − | 0.245760i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.6790 | + | 5.70669i | −1.13449 | + | 0.412922i | −0.839922 | − | 0.542707i | \(-0.817399\pi\) |
−0.294572 | + | 0.955629i | \(0.595177\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.141992 | + | 0.119146i | −0.0102208 | + | 0.00857629i | −0.647884 | − | 0.761739i | \(-0.724346\pi\) |
0.637663 | + | 0.770316i | \(0.279901\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −22.9679 | + | 7.73782i | −1.64476 | + | 0.554117i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.971346 | + | 1.68242i | −0.0692055 | + | 0.119868i | −0.898552 | − | 0.438867i | \(-0.855380\pi\) |
0.829346 | + | 0.558735i | \(0.188713\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.601693 | + | 1.04216i | 0.0426529 | + | 0.0738770i | 0.886564 | − | 0.462606i | \(-0.153086\pi\) |
−0.843911 | + | 0.536483i | \(0.819752\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.200758 | − | 1.32455i | −0.0141604 | − | 0.0934265i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.64911 | − | 0.600226i | −0.115745 | − | 0.0421276i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.46895 | + | 25.3447i | −0.312125 | + | 1.77015i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.749157 | − | 5.89946i | −0.0520700 | − | 0.410041i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.6448 | + | 15.6448i | 1.28969 | + | 1.08218i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.00749 | − | 5.71378i | −0.0693587 | − | 0.393353i | −0.999648 | − | 0.0265264i | \(-0.991555\pi\) |
0.930289 | − | 0.366826i | \(-0.119556\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.34308 | − | 13.6781i | 0.571658 | − | 0.937209i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.4222 | −1.18818 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.24365 | −0.0844242 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.767685 | − | 0.0185131i | −0.0518754 | − | 0.00125100i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.01748 | + | 17.1130i | 0.202978 | + | 1.15114i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.82195 | + | 7.40250i | 0.590762 | + | 0.495708i | 0.888461 | − | 0.458952i | \(-0.151775\pi\) |
−0.297700 | + | 0.954660i | \(0.596219\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.195837 | − | 0.864569i | 0.0130558 | − | 0.0576380i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.31231 | + | 13.1138i | −0.153474 | + | 0.870392i | 0.806694 | + | 0.590969i | \(0.201254\pi\) |
−0.960168 | + | 0.279423i | \(0.909857\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.2916 | − | 6.65760i | −1.20874 | − | 0.439946i | −0.342475 | − | 0.939527i | \(-0.611265\pi\) |
−0.866268 | + | 0.499580i | \(0.833488\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.31049 | + | 2.86222i | 0.480995 | + | 0.188320i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.72784 | + | 2.99271i | 0.113195 | + | 0.196059i | 0.917057 | − | 0.398757i | \(-0.130558\pi\) |
−0.803862 | + | 0.594816i | \(0.797225\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.5744 | − | 21.7795i | 0.820265 | − | 1.42074i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.80945 | + | 5.99942i | 0.442322 | + | 0.389704i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.82780 | − | 7.40741i | 0.571023 | − | 0.479145i | −0.310962 | − | 0.950422i | \(-0.600651\pi\) |
0.881985 | + | 0.471277i | \(0.156207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.8530 | + | 4.67811i | −0.827935 | + | 0.301344i | −0.721011 | − | 0.692923i | \(-0.756322\pi\) |
−0.106924 | + | 0.994267i | \(0.534100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.36120 | + | 12.4647i | −0.600521 | + | 0.799609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.2521 | + | 4.82338i | −0.846648 | + | 0.308155i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.3514 | + | 19.5942i | −1.48582 | + | 1.24675i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20.5777 | + | 18.1299i | 1.30406 | + | 1.14893i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.32328 | − | 12.6843i | 0.462241 | − | 0.800626i | −0.536831 | − | 0.843690i | \(-0.680379\pi\) |
0.999072 | + | 0.0430642i | \(0.0137120\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.81206 | + | 8.33473i | 0.302532 | + | 0.524000i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.6064 | − | 4.15263i | −0.664196 | − | 0.260048i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.0321 | + | 3.65138i | 0.625784 | + | 0.227767i | 0.635395 | − | 0.772187i | \(-0.280837\pi\) |
−0.00961103 | + | 0.999954i | \(0.503059\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.973973 | − | 5.52368i | 0.0605197 | − | 0.343225i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.24582 | + | 5.49997i | −0.0771142 | + | 0.340440i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.92891 | − | 5.81404i | −0.427255 | − | 0.358509i | 0.403660 | − | 0.914909i | \(-0.367738\pi\) |
−0.830915 | + | 0.556400i | \(0.812182\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.04058 | − | 5.90142i | −0.0639222 | − | 0.362521i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.2559 | + | 0.633174i | 1.60683 | + | 0.0387496i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.9649 | 0.973394 | 0.486697 | − | 0.873571i | \(-0.338202\pi\) | ||||
0.486697 | + | 0.873571i | \(0.338202\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.6954 | −0.771193 | −0.385596 | − | 0.922668i | \(-0.626004\pi\) | ||||
−0.385596 | + | 0.922668i | \(0.626004\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.12020 | + | 8.39435i | −0.309889 | + | 0.508049i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.249121 | + | 1.41283i | 0.0150225 | + | 0.0851971i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.8013 | − | 17.4543i | −1.24983 | − | 1.04873i | −0.996690 | − | 0.0812992i | \(-0.974093\pi\) |
−0.253137 | − | 0.967430i | \(-0.581463\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.503438 | + | 3.96447i | 0.0301400 | + | 0.237347i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.44027 | + | 8.16819i | −0.0859194 | + | 0.487273i | 0.911235 | + | 0.411887i | \(0.135130\pi\) |
−0.997154 | + | 0.0753864i | \(0.975981\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.0353 | + | 7.29225i | 1.19097 | + | 0.433479i | 0.860066 | − | 0.510183i | \(-0.170422\pi\) |
0.330909 | + | 0.943663i | \(0.392645\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.99429 | − | 19.7555i | −0.177366 | − | 1.17022i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.22049 | + | 9.04215i | 0.308156 | + | 0.533741i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.41667 | − | 7.64990i | 0.259804 | − | 0.449994i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.4483 | − | 3.85691i | 0.671112 | − | 0.226096i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.4526 | + | 11.2881i | −0.785910 | + | 0.659456i | −0.944729 | − | 0.327851i | \(-0.893676\pi\) |
0.158820 | + | 0.987308i | \(0.449231\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.51159 | − | 3.46193i | 0.553786 | − | 0.201562i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.16479 | − | 24.4629i | 0.357717 | − | 1.41948i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.3267 | + | 4.12258i | −0.655040 | + | 0.238415i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.41454 | + | 4.54334i | −0.312089 | + | 0.261874i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.91501 | − | 19.4488i | 0.224911 | − | 1.11730i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.7163 | + | 22.0253i | −0.728132 | + | 1.26116i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.0261 | − | 26.0260i | −0.857587 | − | 1.48538i | −0.874224 | − | 0.485523i | \(-0.838629\pi\) |
0.0166369 | − | 0.999862i | \(-0.494704\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.6331 | − | 16.4821i | 1.17378 | − | 0.937636i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.3160 | + | 7.03045i | 1.09531 | + | 0.398660i | 0.825585 | − | 0.564277i | \(-0.190845\pi\) |
0.269725 | + | 0.962937i | \(0.413067\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.37426 | − | 13.4651i | 0.134201 | − | 0.761093i | −0.841211 | − | 0.540706i | \(-0.818157\pi\) |
0.975413 | − | 0.220386i | \(-0.0707319\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.94978 | − | 5.73051i | −0.166201 | − | 0.322878i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.82833 | − | 7.40785i | −0.495848 | − | 0.416066i | 0.360268 | − | 0.932849i | \(-0.382685\pi\) |
−0.856117 | + | 0.516783i | \(0.827130\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.58479 | − | 8.98777i | −0.0887310 | − | 0.503218i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.938105 | + | 1.71928i | 0.0523599 | + | 0.0959609i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.3261 | −0.797128 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.79678 | −0.0996677 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.50957 | − | 17.4284i | −0.525880 | − | 0.963790i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.77172 | − | 10.0479i | −0.0976779 | − | 0.553959i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.46721 | + | 1.23114i | 0.0806453 | + | 0.0676694i | 0.682219 | − | 0.731148i | \(-0.261015\pi\) |
−0.601574 | + | 0.798817i | \(0.705459\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −18.0026 | − | 0.868787i | −0.986534 | − | 0.0476093i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.309074 | − | 1.75285i | 0.0168865 | − | 0.0957683i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.981575 | − | 0.357264i | −0.0534698 | − | 0.0194614i | 0.315147 | − | 0.949043i | \(-0.397946\pi\) |
−0.368617 | + | 0.929582i | \(0.620168\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.0876 | + | 9.65583i | −0.656510 | + | 0.524433i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.23373 | − | 5.60099i | −0.175116 | − | 0.303310i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.12831 | + | 10.6145i | −0.330898 | + | 0.573131i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.55917 | − | 7.74557i | 0.0839430 | − | 0.417007i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.42603 | + | 2.03568i | −0.130236 | + | 0.109281i | −0.705579 | − | 0.708631i | \(-0.749313\pi\) |
0.575343 | + | 0.817912i | \(0.304869\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.1942 | + | 8.07804i | −1.18803 | + | 0.432408i | −0.859032 | − | 0.511923i | \(-0.828933\pi\) |
−0.328999 | + | 0.944330i | \(0.606711\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 28.8321 | + | 12.9240i | 1.53894 | + | 0.689832i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.0013 | − | 10.9196i | 1.59681 | − | 0.581190i | 0.618036 | − | 0.786150i | \(-0.287929\pi\) |
0.978770 | + | 0.204960i | \(0.0657064\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.3064 | − | 13.6827i | 0.865453 | − | 0.726201i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.37922 | + | 1.47535i | −0.231773 | + | 0.0780837i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.84279 | + | 4.92386i | −0.150037 | + | 0.259871i | −0.931241 | − | 0.364404i | \(-0.881273\pi\) |
0.781204 | + | 0.624276i | \(0.214606\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.06564 | − | 5.30985i | −0.161350 | − | 0.279466i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.26309 | + | 21.5291i | 0.171268 | + | 1.12998i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.958711 | − | 0.348942i | −0.0501812 | − | 0.0182645i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.96923 | + | 16.8393i | −0.154993 | + | 0.879006i | 0.803800 | + | 0.594900i | \(0.202808\pi\) |
−0.958793 | + | 0.284107i | \(0.908303\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 26.7111 | − | 20.3021i | 1.39053 | − | 1.05689i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.86236 | − | 1.56271i | −0.0966891 | − | 0.0811318i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.60503 | − | 14.7739i | −0.134884 | − | 0.764963i | −0.974941 | − | 0.222465i | \(-0.928590\pi\) |
0.840057 | − | 0.542498i | \(-0.182521\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.76435 | + | 16.0082i | −0.504229 | + | 0.826661i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.4303 | 0.588689 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.5520 | 0.542020 | 0.271010 | − | 0.962577i | \(-0.412642\pi\) | ||||
0.271010 | + | 0.962577i | \(0.412642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.0690835 | − | 0.00166599i | −0.00353926 | − | 8.53510e-5i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.695233 | − | 3.94286i | −0.0355248 | − | 0.201471i | 0.961880 | − | 0.273473i | \(-0.0881724\pi\) |
−0.997404 | + | 0.0720019i | \(0.977061\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.99028 | + | 6.70464i | 0.407222 | + | 0.341700i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.6750 | + | 15.4212i | 0.847640 | + | 0.783904i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.52315 | + | 25.6520i | −0.229333 | + | 1.30061i | 0.624894 | + | 0.780710i | \(0.285142\pi\) |
−0.854227 | + | 0.519901i | \(0.825969\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.32320 | − | 1.93749i | −0.269206 | − | 0.0979829i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.60778 | − | 1.80405i | −0.232432 | − | 0.0910022i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.02872 | + | 10.4421i | 0.303338 | + | 0.525397i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.1476 | + | 19.3083i | −0.559484 | + | 0.969055i | 0.438055 | + | 0.898948i | \(0.355667\pi\) |
−0.997539 | + | 0.0701069i | \(0.977666\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.08242 | − | 5.35887i | −0.304502 | − | 0.268279i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.60036 | + | 7.21656i | −0.429481 | + | 0.360378i | −0.831756 | − | 0.555141i | \(-0.812664\pi\) |
0.402275 | + | 0.915519i | \(0.368220\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.61160 | − | 2.77040i | 0.379161 | − | 0.138003i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.0735 | + | 11.7230i | −0.848391 | + | 0.582521i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 27.4094 | − | 9.97621i | 1.35863 | − | 0.494503i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.1375 | + | 11.8628i | −0.699056 | + | 0.586577i | −0.921505 | − | 0.388367i | \(-0.873039\pi\) |
0.222449 | + | 0.974944i | \(0.428595\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.8298 | + | 10.4226i | 0.583520 | + | 0.514107i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.05325 | − | 3.55634i | 0.101034 | − | 0.174996i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.2184 | + | 31.5552i | 0.894306 | + | 1.54898i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.49180 | + | 1.36712i | 0.170994 | + | 0.0669481i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −37.7300 | − | 13.7326i | −1.84323 | − | 0.670882i | −0.988378 | − | 0.152015i | \(-0.951424\pi\) |
−0.854855 | − | 0.518867i | \(-0.826354\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.75622 | − | 32.6452i | 0.280541 | − | 1.59103i | −0.440250 | − | 0.897875i | \(-0.645110\pi\) |
0.720791 | − | 0.693152i | \(-0.243779\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −31.3133 | + | 9.71532i | −1.52251 | + | 0.472375i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.646874 | − | 0.542792i | −0.0313780 | − | 0.0263293i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.79170 | + | 10.1613i | 0.0867066 | + | 0.491738i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −51.1190 | − | 1.23276i | −2.46805 | − | 0.0595184i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.90172 | 0.380613 | 0.190306 | − | 0.981725i | \(-0.439052\pi\) | ||||
0.190306 | + | 0.981725i | \(0.439052\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.54423 | 0.314496 | 0.157248 | − | 0.987559i | \(-0.449738\pi\) | ||||
0.157248 | + | 0.987559i | \(0.449738\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.90152 | + | 6.39637i | −0.187063 | + | 0.306682i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.72561 | − | 9.78642i | −0.0825471 | − | 0.468148i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.3384 | − | 12.8704i | −0.732060 | − | 0.614271i | 0.198632 | − | 0.980074i | \(-0.436350\pi\) |
−0.930692 | + | 0.365803i | \(0.880794\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.9532 | + | 7.11357i | 0.807297 | + | 0.338742i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.97235 | − | 28.1996i | 0.236243 | − | 1.33980i | −0.603736 | − | 0.797184i | \(-0.706322\pi\) |
0.839980 | − | 0.542618i | \(-0.182567\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 32.7892 | + | 11.9343i | 1.55436 | + | 0.565740i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.897631 | − | 5.92234i | −0.0424565 | − | 0.280117i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.55211 | − | 4.42039i | −0.120442 | − | 0.208611i | 0.799500 | − | 0.600666i | \(-0.205098\pi\) |
−0.919942 | + | 0.392055i | \(0.871764\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.1487 | + | 47.0229i | −1.27838 | + | 2.21422i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.03773 | + | 2.70789i | −0.377645 | + | 0.127228i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.0073 | + | 8.39715i | −0.469151 | + | 0.393664i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.3836 | − | 6.69109i | 0.859949 | − | 0.312996i | 0.125859 | − | 0.992048i | \(-0.459831\pi\) |
0.734090 | + | 0.679052i | \(0.237609\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.47583 | + | 13.3628i | 0.302266 | + | 0.623720i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.87191 | − | 2.86514i | 0.366632 | − | 0.133443i | −0.152133 | − | 0.988360i | \(-0.548614\pi\) |
0.518765 | + | 0.854917i | \(0.326392\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.2770 | − | 21.2099i | 1.17472 | − | 0.985709i | 0.174723 | − | 0.984618i | \(-0.444097\pi\) |
0.999999 | − | 0.00109105i | \(-0.000347291\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.04777 | + | 5.20506i | −0.0485892 | + | 0.241379i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.70848 | − | 6.42327i | 0.171608 | − | 0.297234i | −0.767374 | − | 0.641200i | \(-0.778437\pi\) |
0.938982 | + | 0.343966i | \(0.111770\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.361051 | − | 0.625358i | −0.0166718 | − | 0.0288764i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.64093 | + | 1.31081i | −0.0756099 | + | 0.0603987i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −34.5407 | − | 12.5718i | −1.58818 | − | 0.578051i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.257230 | − | 1.45882i | 0.0118025 | − | 0.0669354i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.22768 | + | 6.56941i | −0.193572 | + | 0.300792i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.34791 | + | 1.13103i | 0.0615878 | + | 0.0516783i | 0.673062 | − | 0.739586i | \(-0.264979\pi\) |
−0.611474 | + | 0.791264i | \(0.709423\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.34367 | + | 35.9767i | 0.289246 | + | 1.64040i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.53532 | − | 2.81380i | −0.0698594 | − | 0.128033i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.0502 | 0.728800 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.863405 | 0.0391246 | 0.0195623 | − | 0.999809i | \(-0.493773\pi\) | ||||
0.0195623 | + | 0.999809i | \(0.493773\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.64222 | − | 14.0060i | −0.345593 | − | 0.633374i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.14334 | + | 17.8268i | 0.141857 | + | 0.804510i | 0.969837 | + | 0.243753i | \(0.0783787\pi\) |
−0.827980 | + | 0.560757i | \(0.810510\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.11510 | + | 3.45298i | 0.185335 | + | 0.155514i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 18.1384 | − | 28.1854i | 0.815261 | − | 1.26684i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.49961 | − | 8.50473i | 0.0672669 | − | 0.381489i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.39454 | − | 1.59948i | −0.196727 | − | 0.0716027i | 0.241778 | − | 0.970332i | \(-0.422269\pi\) |
−0.438505 | + | 0.898729i | \(0.644492\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.95338 | − | 3.15804i | 0.176624 | − | 0.141091i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.1410 | + | 17.5648i | 0.452166 | + | 0.783174i | 0.998520 | − | 0.0543801i | \(-0.0173183\pi\) |
−0.546355 | + | 0.837554i | \(0.683985\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.1789 | − | 22.8266i | 0.586455 | − | 1.01577i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.19462 | − | 40.7088i | 0.363936 | − | 1.80794i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.4839 | − | 23.0618i | 1.21820 | − | 1.02219i | 0.219288 | − | 0.975660i | \(-0.429627\pi\) |
0.998917 | − | 0.0465347i | \(-0.0148178\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.388950 | + | 0.141566i | −0.0172061 | + | 0.00626251i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.6207 | + | 21.5587i | −0.645520 | + | 0.951842i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 32.9697 | − | 12.0000i | 1.45282 | − | 0.528783i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 40.6457 | − | 34.1058i | 1.78760 | − | 1.49997i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.9938 | + | 8.08346i | −1.05321 | + | 0.354824i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.97163 | + | 17.2714i | −0.436865 | + | 0.756672i | −0.997446 | − | 0.0714274i | \(-0.977245\pi\) |
0.560581 | + | 0.828100i | \(0.310578\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.7394 | + | 20.3332i | 0.513328 | + | 0.889111i | 0.999880 | + | 0.0154593i | \(0.00492105\pi\) |
−0.486552 | + | 0.873652i | \(0.661746\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.0716037 | − | 0.472423i | −0.00312504 | − | 0.0206182i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.57722 | + | 1.30200i | 0.155826 | + | 0.0567161i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.31157 | + | 18.7808i | −0.143981 | + | 0.816558i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.1680 | − | 5.10570i | −0.528047 | − | 0.221568i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −52.0941 | − | 43.7122i | −2.25645 | − | 1.89338i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.451856 | + | 2.56260i | 0.0195354 | + | 0.110791i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.3867 | + | 30.1441i | −0.793443 | + | 1.30082i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −29.7538 | −1.28159 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.3333 | −1.43311 | −0.716555 | − | 0.697531i | \(-0.754282\pi\) | ||||
−0.716555 | + | 0.697531i | \(0.754282\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.78060 | − | 0.163518i | −0.290984 | − | 0.00701722i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.58047 | − | 25.9771i | −0.196206 | − | 1.11274i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.0588 | − | 15.9922i | −0.814894 | − | 0.683777i | 0.136877 | − | 0.990588i | \(-0.456294\pi\) |
−0.951770 | + | 0.306811i | \(0.900738\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 31.6666 | − | 9.82492i | 1.35150 | − | 0.419317i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.63637 | + | 9.28032i | −0.0697118 | + | 0.395355i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.59671 | + | 1.67306i | 0.195472 | + | 0.0711459i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −22.2978 | − | 8.73010i | −0.946490 | − | 0.370572i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.0496 | − | 17.4063i | −0.425813 | − | 0.737530i | 0.570683 | − | 0.821171i | \(-0.306679\pi\) |
−0.996496 | + | 0.0836406i | \(0.973345\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.0182 | − | 39.8687i | 0.973566 | − | 1.68627i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.0314 | − | 15.8864i | −0.761284 | − | 0.670724i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.4481 | − | 9.60610i | 0.482480 | − | 0.404849i | −0.368842 | − | 0.929492i | \(-0.620246\pi\) |
0.851322 | + | 0.524643i | \(0.175801\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.3148 | + | 7.03003i | −0.812582 | + | 0.295756i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.24908 | + | 8.09576i | −0.0944524 | + | 0.339990i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 36.7616 | − | 13.3801i | 1.54112 | − | 0.560923i | 0.574810 | − | 0.818287i | \(-0.305076\pi\) |
0.966315 | + | 0.257363i | \(0.0828538\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.20038 | + | 1.00724i | −0.0502342 | + | 0.0421515i | −0.667559 | − | 0.744557i | \(-0.732661\pi\) |
0.617325 | + | 0.786708i | \(0.288216\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.6842 | + | 19.1047i | 0.905870 | + | 0.798111i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.292873 | − | 0.507270i | 0.0122136 | − | 0.0211546i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.44151 | + | 4.22883i | 0.101642 | + | 0.176048i | 0.912361 | − | 0.409386i | \(-0.134257\pi\) |
−0.810720 | + | 0.585435i | \(0.800924\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.298952 | + | 0.117046i | 0.0124240 | + | 0.00486428i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.8909 | + | 5.05589i | 0.576293 | + | 0.209754i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.19542 | − | 12.4509i | 0.0909251 | − | 0.515662i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 30.8193 | + | 28.5020i | 1.27422 | + | 1.17841i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.5044 | − | 10.4925i | −0.516114 | − | 0.433071i | 0.347161 | − | 0.937806i | \(-0.387146\pi\) |
−0.863274 | + | 0.504735i | \(0.831590\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.15962 | + | 6.57653i | 0.0477813 | + | 0.270981i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.36386 | + | 0.0811213i | 0.138371 | + | 0.00333689i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.5826 | 0.598835 | 0.299418 | − | 0.954122i | \(-0.403208\pi\) | ||||
0.299418 | + | 0.954122i | \(0.403208\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.13951 | −0.251696 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.08538 | − | 1.77943i | 0.0444216 | − | 0.0728272i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.49878 | − | 25.5139i | −0.183815 | − | 1.04247i | −0.927468 | − | 0.373902i | \(-0.878019\pi\) |
0.743653 | − | 0.668566i | \(-0.233092\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.51430 | − | 6.30525i | −0.306515 | − | 0.257197i | 0.476535 | − | 0.879156i | \(-0.341893\pi\) |
−0.783050 | + | 0.621959i | \(0.786337\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.84735 | + | 1.40410i | −0.0752299 | + | 0.0571794i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.02365 | + | 28.4906i | −0.204241 | + | 1.15831i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.69750 | − | 3.52960i | −0.393610 | − | 0.143262i | 0.137630 | − | 0.990484i | \(-0.456051\pi\) |
−0.531240 | + | 0.847222i | \(0.678274\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.455508 | + | 3.00533i | 0.0184581 | + | 0.121782i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33.2267 | + | 57.5504i | 1.34421 | + | 2.32824i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.0542 | + | 38.1990i | −0.890761 | + | 1.54284i | −0.0517966 | + | 0.998658i | \(0.516495\pi\) |
−0.838965 | + | 0.544186i | \(0.816839\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 42.2426 | − | 14.2314i | 1.70339 | − | 0.573867i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.5158 | + | 22.2494i | −1.06749 | + | 0.895727i | −0.994822 | − | 0.101630i | \(-0.967594\pi\) |
−0.0726635 | + | 0.997357i | \(0.523150\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.5907 | + | 6.76644i | −0.747221 | + | 0.271966i | −0.687436 | − | 0.726245i | \(-0.741264\pi\) |
−0.0597854 | + | 0.998211i | \(0.519042\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.34829 | + | 6.03331i | −0.335005 | + | 0.242108i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.3026 | − | 4.84175i | 0.532958 | − | 0.193981i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.2160 | + | 16.9633i | −0.808641 | + | 0.678530i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.31915 | − | 41.3274i | 0.332235 | − | 1.65046i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.58440 | + | 14.8686i | −0.342283 | + | 0.592851i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.91382 | − | 15.4392i | −0.354854 | − | 0.614624i | 0.632239 | − | 0.774773i | \(-0.282136\pi\) |
−0.987093 | + | 0.160149i | \(0.948803\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.85165 | + | 6.27205i | −0.312075 | + | 0.249292i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.0862738 | − | 0.0314011i | −0.00342367 | − | 0.00124611i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.47097 | − | 36.6987i | 0.256389 | − | 1.45406i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27.7183 | − | 1.33766i | −1.09652 | − | 0.0529170i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.60947 | + | 2.18961i | 0.103068 | + | 0.0864842i | 0.692865 | − | 0.721067i | \(-0.256348\pi\) |
−0.589798 | + | 0.807551i | \(0.700792\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.77990 | + | 15.7656i | 0.109629 | + | 0.621735i | 0.989270 | + | 0.146098i | \(0.0466714\pi\) |
−0.879641 | + | 0.475637i | \(0.842217\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.4536 | + | 26.4894i | 0.569111 | + | 1.04302i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.63857 | −0.260989 | −0.130495 | − | 0.991449i | \(-0.541656\pi\) | ||||
−0.130495 | + | 0.991449i | \(0.541656\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.3555 | 0.838277 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.03174 | + | 1.89089i | 0.0404372 | + | 0.0741099i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.75420 | + | 38.3050i | 0.264312 | + | 1.49899i | 0.770986 | + | 0.636852i | \(0.219764\pi\) |
−0.506674 | + | 0.862138i | \(0.669125\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.03625 | − | 4.22592i | −0.196783 | − | 0.165120i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.608732 | + | 1.18258i | 0.0237489 | + | 0.0461368i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.22075 | + | 46.6222i | −0.320235 | + | 1.81614i | 0.221002 | + | 0.975273i | \(0.429067\pi\) |
−0.541237 | + | 0.840870i | \(0.682044\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.7979 | + | 10.4816i | 1.12011 | + | 0.407686i | 0.834692 | − | 0.550717i | \(-0.185646\pi\) |
0.285417 | + | 0.958403i | \(0.407868\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.5160 | − | 18.7850i | 0.913285 | − | 0.729550i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.38504 | − | 9.32717i | −0.208823 | − | 0.361692i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.86311 | + | 3.22701i | −0.0721401 | + | 0.124950i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.93628 | − | 19.5545i | 0.152186 | − | 0.756019i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41.1043 | + | 34.4906i | −1.58681 | + | 1.33149i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.2071 | − | 9.53859i | 1.01021 | − | 0.367686i | 0.216696 | − | 0.976239i | \(-0.430472\pi\) |
0.793513 | + | 0.608553i | \(0.208250\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.47700 | + | 0.419498i | −0.0568496 | + | 0.0161465i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.6944 | + | 7.53215i | −0.795351 | + | 0.289484i | −0.707559 | − | 0.706655i | \(-0.750203\pi\) |
−0.0877924 | + | 0.996139i | \(0.527981\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.98814 | − | 4.18555i | 0.191427 | − | 0.160627i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.8571 | − | 7.36359i | 0.837565 | − | 0.282174i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.40049 | − | 7.62187i | 0.168380 | − | 0.291643i | −0.769470 | − | 0.638682i | \(-0.779480\pi\) |
0.937850 | + | 0.347040i | \(0.112813\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.4735 | + | 18.1406i | 0.400170 | + | 0.693115i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.05242 | + | 33.3345i | 0.192762 | + | 1.27179i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.8795 | + | 5.41571i | 0.566866 | + | 0.206322i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.18070 | + | 29.3812i | −0.197083 | + | 1.11771i | 0.712337 | + | 0.701837i | \(0.247637\pi\) |
−0.909421 | + | 0.415878i | \(0.863474\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.71302 | − | 13.4897i | −0.0650723 | − | 0.512431i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.81650 | + | 3.20243i | 0.144768 | + | 0.121475i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.54977 | − | 31.4743i | −0.210212 | − | 1.19217i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.11681 | − | 5.10987i | 0.117888 | − | 0.193273i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.5757 | 0.474978 | 0.237489 | − | 0.971390i | \(-0.423676\pi\) | ||||
0.237489 | + | 0.971390i | \(0.423676\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.1179 | −1.13592 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −43.5464 | − | 1.05015i | −1.64005 | − | 0.0395508i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.85689 | − | 10.5309i | −0.0698356 | − | 0.396057i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.0741 | + | 14.3268i | 0.641230 | + | 0.538056i | 0.904396 | − | 0.426695i | \(-0.140322\pi\) |
−0.263165 | + | 0.964751i | \(0.584767\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.47258 | − | 15.3306i | 0.130232 | − | 0.574941i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.458536 | + | 2.60049i | −0.0171723 | + | 0.0973889i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −63.8392 | − | 23.2356i | −2.38745 | − | 0.868961i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.5862 | − | 7.27690i | −0.694114 | − | 0.271761i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.65446 | − | 4.59766i | −0.0989947 | − | 0.171464i | 0.812274 | − | 0.583276i | \(-0.198229\pi\) |
−0.911269 | + | 0.411812i | \(0.864896\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.11713 | − | 12.3272i | 0.265056 | − | 0.459090i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.7758 | + | 15.6613i | 0.661089 | + | 0.582448i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.425502 | + | 0.357039i | −0.0158028 | + | 0.0132601i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.0033 | + | 13.8321i | −1.40946 | + | 0.513003i | −0.930973 | − | 0.365089i | \(-0.881039\pi\) |
−0.478492 | + | 0.878092i | \(0.658816\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.7180 | + | 3.89235i | 0.989554 | + | 0.144161i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.3309 | − | 7.39985i | 0.751966 | − | 0.273693i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.28038 | + | 2.75257i | −0.121164 | + | 0.101668i | −0.701356 | − | 0.712811i | \(-0.747422\pi\) |
0.580193 | + | 0.814479i | \(0.302977\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 18.3278 | + | 16.1476i | 0.676031 | + | 0.595613i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.87761 | − | 3.25212i | 0.0691627 | − | 0.119793i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.8456 | − | 20.5172i | −0.435747 | − | 0.754736i | 0.561609 | − | 0.827402i | \(-0.310182\pi\) |
−0.997356 | + | 0.0726668i | \(0.976849\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 49.1644 | + | 19.2490i | 1.80610 | + | 0.707129i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.87858 | − | 2.13963i | −0.215664 | − | 0.0784953i | 0.231929 | − | 0.972733i | \(-0.425496\pi\) |
−0.447593 | + | 0.894237i | \(0.647719\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.38194 | − | 7.83735i | 0.0506302 | − | 0.287138i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.4939 | − | 46.3280i | 0.383952 | − | 1.69505i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.808704 | + | 0.678583i | 0.0295494 | + | 0.0247949i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.77619 | − | 27.0871i | −0.174286 | − | 0.988423i | −0.938965 | − | 0.344012i | \(-0.888214\pi\) |
0.764680 | − | 0.644411i | \(-0.222897\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −25.3612 | − | 0.611599i | −0.924214 | − | 0.0222879i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.2686 | −0.410107 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.48533 | 0.272059 | 0.136029 | − | 0.990705i | \(-0.456566\pi\) | ||||
0.136029 | + | 0.990705i | \(0.456566\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.68035 | − | 14.2310i | 0.315077 | − | 0.516554i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.78599 | + | 27.1427i | 0.173492 | + | 0.983921i | 0.939870 | + | 0.341532i | \(0.110946\pi\) |
−0.766378 | + | 0.642389i | \(0.777943\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.19783 | − | 6.87880i | −0.296781 | − | 0.249029i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.48532 | + | 19.5714i | 0.0898571 | + | 0.707607i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.64447 | + | 26.3401i | −0.167702 | + | 0.951087i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.9685 | − | 9.81572i | −0.972508 | − | 0.353964i | −0.193585 | − | 0.981084i | \(-0.562011\pi\) |
−0.778923 | + | 0.627120i | \(0.784234\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.77101 | − | 18.2824i | −0.0997956 | − | 0.658426i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.3371 | − | 43.8851i | −0.911311 | − | 1.57844i | −0.812215 | − | 0.583359i | \(-0.801738\pi\) |
−0.0990962 | − | 0.995078i | \(-0.531595\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.196812 | + | 0.340888i | −0.00706969 | + | 0.0122451i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.20645 | + | 3.10163i | −0.330280 | + | 0.111270i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 42.9481 | − | 36.0377i | 1.53877 | − | 1.29119i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 42.2019 | − | 15.3602i | 1.51010 | − | 0.549633i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.39594 | − | 2.66864i | 0.335783 | − | 0.0953695i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.62204 | + | 0.954345i | −0.0935847 | + | 0.0340620i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.4304 | + | 13.7868i | −0.585682 | + | 0.491445i | −0.886807 | − | 0.462139i | \(-0.847082\pi\) |
0.301126 | + | 0.953584i | \(0.402638\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.09162 | + | 15.3584i | −0.110065 | + | 0.546774i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.16947 | + | 7.22174i | −0.148249 | + | 0.256775i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.6016 | − | 58.1996i | −1.19323 | − | 2.06673i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.10949 | + | 6.47802i | −0.287614 | + | 0.229752i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.1545 | + | 12.0672i | 1.17439 | + | 0.427444i | 0.854218 | − | 0.519915i | \(-0.174036\pi\) |
0.320174 | + | 0.947359i | \(0.396259\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.42322 | + | 30.7566i | −0.191860 | + | 1.08809i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.8195 | − | 40.4458i | −0.735619 | − | 1.42908i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.64892 | − | 1.38361i | −0.0581890 | − | 0.0488264i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.739515 | − | 4.19400i | −0.0260645 | − | 0.147819i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.2446 | − | 24.2736i | −0.466233 | − | 0.854473i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.2973 | −1.24099 | −0.620493 | − | 0.784212i | \(-0.713068\pi\) | ||||
−0.620493 | + | 0.784212i | \(0.713068\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.0319 | 1.82709 | 0.913544 | − | 0.406741i | \(-0.133335\pi\) | ||||
0.913544 | + | 0.406741i | \(0.133335\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.5323 | + | 19.3027i | 0.369383 | + | 0.676975i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.68102 | − | 20.8761i | −0.128941 | − | 0.731258i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.0744 | + | 24.3963i | 1.01718 | + | 0.853518i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 17.0109 | + | 0.820931i | 0.594409 | + | 0.0286857i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.07166 | + | 6.07770i | −0.0374013 | + | 0.212113i | −0.997781 | − | 0.0665818i | \(-0.978791\pi\) |
0.960380 | + | 0.278695i | \(0.0899018\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 49.4317 | + | 17.9917i | 1.72308 | + | 0.627150i | 0.998100 | − | 0.0616193i | \(-0.0196265\pi\) |
0.724981 | + | 0.688769i | \(0.241849\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.94146 | − | 1.55088i | 0.0675930 | − | 0.0539946i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.02687 | + | 13.9029i | 0.279121 | + | 0.483453i | 0.971167 | − | 0.238402i | \(-0.0766235\pi\) |
−0.692045 | + | 0.721854i | \(0.743290\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.85932 | + | 8.41658i | −0.168771 | + | 0.292320i | −0.937988 | − | 0.346668i | \(-0.887313\pi\) |
0.769217 | + | 0.638988i | \(0.220647\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.28136 | + | 46.1074i | −0.321967 | + | 1.59945i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.4160 | − | 11.2574i | 0.464837 | − | 0.390044i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.31712 | − | 2.29924i | 0.218613 | − | 0.0795686i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.61010 | − | 4.05442i | 0.193913 | − | 0.140141i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.50811 | − | 1.27685i | 0.121114 | − | 0.0440817i | −0.280752 | − | 0.959780i | \(-0.590584\pi\) |
0.401866 | + | 0.915698i | \(0.368362\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.5084 | + | 16.3695i | −0.672705 | + | 0.564467i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.6141 | − | 4.58657i | 0.468896 | − | 0.157970i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 27.5852 | − | 47.7790i | 0.948960 | − | 1.64365i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.86847 | + | 10.1645i | 0.201643 | + | 0.349256i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.53405 | − | 36.5123i | −0.189928 | − | 1.25310i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.1910 | − | 4.07319i | −0.383623 | − | 0.139627i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.25348 | − | 7.10882i | 0.0429182 | − | 0.243401i | −0.955800 | − | 0.294018i | \(-0.905008\pi\) |
0.998718 | + | 0.0506165i | \(0.0161186\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −27.5531 | + | 20.9421i | −0.942296 | + | 0.716203i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.6370 | − | 13.9601i | −0.568309 | − | 0.476868i | 0.312775 | − | 0.949827i | \(-0.398741\pi\) |
−0.881084 | + | 0.472959i | \(0.843186\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.73108 | − | 49.5164i | −0.297901 | − | 1.68948i | −0.655173 | − | 0.755479i | \(-0.727404\pi\) |
0.357273 | − | 0.934000i | \(-0.383707\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.41710 | − | 15.4389i | 0.320934 | − | 0.526157i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.5856 | 1.38155 | 0.690776 | − | 0.723069i | \(-0.257269\pi\) | ||||
0.690776 | + | 0.723069i | \(0.257269\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33.6385 | −1.14374 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.2954 | − | 0.368856i | −0.519458 | − | 0.0125270i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.41742 | + | 25.0524i | 0.149851 | + | 0.849845i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.60285 | + | 3.02315i | 0.122078 | + | 0.102435i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15.3619 | − | 14.2068i | −0.519920 | − | 0.480826i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.75508 | + | 9.95354i | −0.0593325 | + | 0.336491i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.95738 | − | 2.89625i | −0.268701 | − | 0.0977993i | 0.204156 | − | 0.978938i | \(-0.434555\pi\) |
−0.472857 | + | 0.881139i | \(0.656777\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.3233 | + | 11.0892i | 0.955321 | + | 0.374030i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.5635 | − | 37.3491i | −0.726493 | − | 1.25832i | −0.958356 | − | 0.285575i | \(-0.907815\pi\) |
0.231863 | − | 0.972748i | \(-0.425518\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.9872 | − | 22.4945i | 0.437054 | − | 0.757000i | −0.560407 | − | 0.828218i | \(-0.689355\pi\) |
0.997461 | + | 0.0712176i | \(0.0226885\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.1546 | − | 11.5898i | −0.442187 | − | 0.389586i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.00642 | + | 6.71819i | −0.268829 | + | 0.225575i | −0.767230 | − | 0.641372i | \(-0.778365\pi\) |
0.498400 | + | 0.866947i | \(0.333921\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.0350013 | + | 0.0127394i | −0.00117391 | + | 0.000427267i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −42.3088 | + | 10.9215i | −1.41740 | + | 0.365883i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −51.4823 | + | 18.7380i | −1.72279 | + | 0.627045i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −35.9364 | + | 30.1542i | −1.20122 | + | 1.00794i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.6649 | + | 13.8015i | 0.523036 | + | 0.460817i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.25202 | − | 2.16857i | 0.0417573 | − | 0.0723258i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.72086 | + | 6.44472i | 0.123960 | + | 0.214705i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.3999 | + | 4.46330i | 0.379363 | + | 0.148529i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.46785 | − | 3.08204i | −0.281481 | − | 0.102451i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.72906 | + | 15.4772i | −0.0906168 | + | 0.513914i | 0.905386 | + | 0.424590i | \(0.139582\pi\) |
−0.996003 | + | 0.0893238i | \(0.971529\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −32.8187 | + | 10.1824i | −1.08853 | + | 0.337728i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.8864 | − | 26.7558i | −1.05644 | − | 0.886460i | −0.0626861 | − | 0.998033i | \(-0.519967\pi\) |
−0.993756 | + | 0.111573i | \(0.964411\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.3491 | + | 75.7068i | 0.441792 | + | 2.50553i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 44.0377 | + | 1.06199i | 1.45584 | + | 0.0351084i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.66722 | −0.0880794 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 59.0705 | 1.94856 | 0.974278 | − | 0.225348i | \(-0.0723520\pi\) | ||||
0.974278 | + | 0.225348i | \(0.0723520\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.1052 | + | 44.4379i | −0.893148 | + | 1.46428i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.76727 | + | 55.3929i | 0.321493 | + | 1.82328i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.35993 | − | 1.14111i | −0.0447141 | − | 0.0375196i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −42.1776 | − | 17.6977i | −1.38529 | − | 0.581269i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.03698 | + | 22.8948i | −0.132449 | + | 0.751155i | 0.844153 | + | 0.536102i | \(0.180104\pi\) |
−0.976602 | + | 0.215053i | \(0.931007\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.8696 | + | 10.5077i | 0.946162 | + | 0.344375i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.33537 | − | 35.2014i | −0.174672 | − | 1.15244i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.9640 | − | 27.6504i | −0.522078 | − | 0.904266i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.3639 | − | 28.3431i | 0.534586 | − | 0.925930i | −0.464597 | − | 0.885522i | \(-0.653801\pi\) |
0.999183 | − | 0.0404081i | \(-0.0128658\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.4426 | + | 7.56087i | −0.732388 | + | 0.246740i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.4606 | − | 33.9505i | 1.31898 | − | 1.10675i | 0.332457 | − | 0.943118i | \(-0.392122\pi\) |
0.986521 | − | 0.163636i | \(-0.0523222\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.8321 | − | 7.58227i | 0.678387 | − | 0.246913i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.26575 | + | 9.23906i | −0.203825 | + | 0.300547i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.8614 | − | 11.2326i | 1.00286 | − | 0.365012i | 0.212174 | − | 0.977232i | \(-0.431946\pi\) |
0.790687 | + | 0.612220i | \(0.209723\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.06517 | − | 1.73288i | 0.0670381 | − | 0.0562517i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.93913 | + | 19.5686i | −0.127735 | + | 0.634555i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.92754 | + | 3.33860i | −0.0624391 | + | 0.108148i | −0.895555 | − | 0.444951i | \(-0.853221\pi\) |
0.833116 | + | 0.553098i | \(0.186555\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.1980 | + | 33.2519i | 0.621233 | + | 1.07601i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.3506 | + | 9.86593i | −0.399239 | + | 0.318920i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.98567 | + | 2.90655i | 0.257871 | + | 0.0938573i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.07496 | + | 28.7815i | −0.163708 | + | 0.928435i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.83581 | − | 2.85267i | 0.0591580 | − | 0.0919260i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.326751 | + | 0.274177i | 0.0105185 | + | 0.00882607i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.438417 | − | 2.48638i | −0.0140985 | − | 0.0799567i | 0.976947 | − | 0.213483i | \(-0.0684809\pi\) |
−0.991045 | + | 0.133527i | \(0.957370\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.8851 | + | 21.7821i | 0.381805 | + | 0.699741i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.91263 | 0.286020 | 0.143010 | − | 0.989721i | \(-0.454322\pi\) | ||||
0.143010 | + | 0.989721i | \(0.454322\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.02124 | 0.0647979 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.49063 | + | 2.73191i | 0.0477384 | + | 0.0874911i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.20448 | − | 46.5299i | −0.262485 | − | 1.48862i | −0.776104 | − | 0.630605i | \(-0.782807\pi\) |
0.513619 | − | 0.858018i | \(-0.328304\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 56.3952 | + | 47.3212i | 1.80240 | + | 1.51239i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.6096 | + | 28.9175i | −0.594158 | + | 0.923265i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.324382 | + | 1.83966i | −0.0103462 | + | 0.0586761i | −0.989544 | − | 0.144233i | \(-0.953929\pi\) |
0.979198 | + | 0.202909i | \(0.0650396\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.20091 | + | 1.52900i | 0.133852 | + | 0.0487181i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.8074 | + | 11.0296i | −0.439495 | + | 0.351077i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.50385 | + | 12.9970i | 0.238609 | + | 0.413282i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.11469 | − | 14.0551i | 0.257772 | − | 0.446473i | −0.707873 | − | 0.706340i | \(-0.750345\pi\) |
0.965645 | + | 0.259866i | \(0.0836785\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.654658 | − | 3.25218i | 0.0207749 | − | 0.103205i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.12135 | − | 1.78002i | 0.0672513 | − | 0.0564305i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.6043 | + | 4.58759i | −0.399182 | + | 0.145290i | −0.533807 | − | 0.845606i | \(-0.679239\pi\) |
0.134625 | + | 0.990897i | \(0.457017\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.6142 | + | 28.0926i | 0.430733 | + | 0.888811i |
(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 | 108.2.i.a.61.1 | ✓ | 18 | |
3.2 | odd | 2 | 324.2.i.a.181.3 | 18 | |||
4.3 | odd | 2 | 432.2.u.d.385.3 | 18 | |||
9.2 | odd | 6 | 972.2.i.b.865.1 | 18 | |||
9.4 | even | 3 | 972.2.i.a.217.1 | 18 | |||
9.5 | odd | 6 | 972.2.i.d.217.3 | 18 | |||
9.7 | even | 3 | 972.2.i.c.865.3 | 18 | |||
27.2 | odd | 18 | 2916.2.a.c.1.8 | 9 | |||
27.4 | even | 9 | inner | 108.2.i.a.85.1 | yes | 18 | |
27.5 | odd | 18 | 972.2.i.d.757.3 | 18 | |||
27.7 | even | 9 | 2916.2.e.c.1945.8 | 18 | |||
27.11 | odd | 18 | 2916.2.e.d.973.2 | 18 | |||
27.13 | even | 9 | 972.2.i.c.109.3 | 18 | |||
27.14 | odd | 18 | 972.2.i.b.109.1 | 18 | |||
27.16 | even | 9 | 2916.2.e.c.973.8 | 18 | |||
27.20 | odd | 18 | 2916.2.e.d.1945.2 | 18 | |||
27.22 | even | 9 | 972.2.i.a.757.1 | 18 | |||
27.23 | odd | 18 | 324.2.i.a.145.3 | 18 | |||
27.25 | even | 9 | 2916.2.a.d.1.2 | 9 | |||
108.31 | odd | 18 | 432.2.u.d.193.3 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.2.i.a.61.1 | ✓ | 18 | 1.1 | even | 1 | trivial | |
108.2.i.a.85.1 | yes | 18 | 27.4 | even | 9 | inner | |
324.2.i.a.145.3 | 18 | 27.23 | odd | 18 | |||
324.2.i.a.181.3 | 18 | 3.2 | odd | 2 | |||
432.2.u.d.193.3 | 18 | 108.31 | odd | 18 | |||
432.2.u.d.385.3 | 18 | 4.3 | odd | 2 | |||
972.2.i.a.217.1 | 18 | 9.4 | even | 3 | |||
972.2.i.a.757.1 | 18 | 27.22 | even | 9 | |||
972.2.i.b.109.1 | 18 | 27.14 | odd | 18 | |||
972.2.i.b.865.1 | 18 | 9.2 | odd | 6 | |||
972.2.i.c.109.3 | 18 | 27.13 | even | 9 | |||
972.2.i.c.865.3 | 18 | 9.7 | even | 3 | |||
972.2.i.d.217.3 | 18 | 9.5 | odd | 6 | |||
972.2.i.d.757.3 | 18 | 27.5 | odd | 18 | |||
2916.2.a.c.1.8 | 9 | 27.2 | odd | 18 | |||
2916.2.a.d.1.2 | 9 | 27.25 | even | 9 | |||
2916.2.e.c.973.8 | 18 | 27.16 | even | 9 | |||
2916.2.e.c.1945.8 | 18 | 27.7 | even | 9 | |||
2916.2.e.d.973.2 | 18 | 27.11 | odd | 18 | |||
2916.2.e.d.1945.2 | 18 | 27.20 | odd | 18 |