Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(49,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.u (of order \(9\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
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: | \( x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} - 1584 x^{3} + 936 x^{2} - 342 x + 57 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 54) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 337.2 | ||
Root | \(0.500000 - 1.74095i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 432.337 |
Dual form | 432.2.u.b.241.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{4}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.140451 | + | 1.72635i | −0.0810896 | + | 0.996707i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.42692 | + | 2.03643i | 1.08535 | + | 0.910717i | 0.996354 | − | 0.0853149i | \(-0.0271896\pi\) |
0.0889963 | + | 0.996032i | \(0.471634\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.46344 | + | 1.26059i | 1.30906 | + | 0.476458i | 0.899936 | − | 0.436021i | \(-0.143613\pi\) |
0.409122 | + | 0.912480i | \(0.365835\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.96055 | − | 0.484935i | −0.986849 | − | 0.161645i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.75046 | − | 1.46881i | 0.527785 | − | 0.442864i | −0.339551 | − | 0.940588i | \(-0.610275\pi\) |
0.867336 | + | 0.497724i | \(0.165831\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.538357 | − | 3.05317i | 0.149313 | − | 0.846798i | −0.814489 | − | 0.580179i | \(-0.802982\pi\) |
0.963802 | − | 0.266619i | \(-0.0859065\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.85644 | + | 3.90368i | −0.995728 | + | 1.00793i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.862878 | + | 1.49455i | −0.209279 | + | 0.362481i | −0.951487 | − | 0.307687i | \(-0.900445\pi\) |
0.742209 | + | 0.670169i | \(0.233778\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.69740 | − | 2.93998i | −0.389410 | − | 0.674478i | 0.602960 | − | 0.797771i | \(-0.293988\pi\) |
−0.992370 | + | 0.123293i | \(0.960654\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.66266 | + | 5.80205i | −0.581040 | + | 1.26611i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.15087 | + | 1.14682i | −0.657002 | + | 0.239129i | −0.648942 | − | 0.760838i | \(-0.724788\pi\) |
−0.00806071 | + | 0.999968i | \(0.502566\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.874658 | + | 4.96043i | 0.174932 | + | 0.992086i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.25298 | − | 5.04282i | 0.241136 | − | 0.970491i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.101661 | − | 0.576550i | −0.0188780 | − | 0.107063i | 0.973913 | − | 0.226923i | \(-0.0728665\pi\) |
−0.992791 | + | 0.119860i | \(0.961755\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.35827 | + | 1.58628i | −0.782769 | + | 0.284904i | −0.702327 | − | 0.711855i | \(-0.747855\pi\) |
−0.0804420 | + | 0.996759i | \(0.525633\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.28983 | + | 3.22820i | 0.398608 | + | 0.561958i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.83839 | + | 10.1124i | 0.986868 | + | 1.70931i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.65360 | − | 6.32822i | 0.600648 | − | 1.04035i | −0.392075 | − | 0.919933i | \(-0.628243\pi\) |
0.992723 | − | 0.120420i | \(-0.0384240\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.19523 | + | 1.35821i | 0.831902 | + | 0.217488i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.22952 | + | 6.97295i | −0.192019 | + | 1.08899i | 0.724582 | + | 0.689188i | \(0.242033\pi\) |
−0.916601 | + | 0.399803i | \(0.869078\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.27004 | + | 1.06569i | −0.193679 | + | 0.162516i | −0.734470 | − | 0.678641i | \(-0.762569\pi\) |
0.540791 | + | 0.841157i | \(0.318125\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.19747 | − | 7.20583i | −0.923864 | − | 1.07418i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.61968 | − | 1.31746i | −0.527984 | − | 0.192171i | 0.0642537 | − | 0.997934i | \(-0.479533\pi\) |
−0.592238 | + | 0.805763i | \(0.701756\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.04404 | + | 4.23245i | 0.720577 | + | 0.604636i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.45892 | − | 1.69954i | −0.344317 | − | 0.237983i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.58267 | −0.354757 | −0.177379 | − | 0.984143i | \(-0.556762\pi\) | ||||
−0.177379 | + | 0.984143i | \(0.556762\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.23936 | 0.976155 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.31383 | − | 2.51737i | 0.703834 | − | 0.333434i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.40243 | + | 6.21138i | 0.963714 | + | 0.808652i | 0.981553 | − | 0.191188i | \(-0.0612342\pi\) |
−0.0178389 | + | 0.999841i | \(0.505679\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.3018 | − | 4.47750i | −1.57509 | − | 0.573285i | −0.600960 | − | 0.799279i | \(-0.705215\pi\) |
−0.974129 | + | 0.225994i | \(0.927437\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.64238 | − | 5.41158i | −1.21483 | − | 0.681795i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.52411 | − | 6.31348i | 0.933251 | − | 0.783091i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.49490 | − | 8.47798i | 0.182631 | − | 1.03575i | −0.746331 | − | 0.665574i | \(-0.768187\pi\) |
0.928962 | − | 0.370175i | \(-0.120702\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.53727 | − | 5.60057i | −0.185066 | − | 0.674230i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.993732 | − | 1.72119i | 0.117934 | − | 0.204268i | −0.801015 | − | 0.598645i | \(-0.795706\pi\) |
0.918949 | + | 0.394377i | \(0.129039\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.32371 | − | 9.22094i | −0.623094 | − | 1.07923i | −0.988906 | − | 0.148541i | \(-0.952542\pi\) |
0.365812 | − | 0.930689i | \(-0.380791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.68627 | + | 0.813264i | −1.00300 | + | 0.0939077i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.91420 | − | 2.88053i | 0.901907 | − | 0.328267i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.44726 | − | 13.8791i | −0.275338 | − | 1.56152i | −0.737886 | − | 0.674925i | \(-0.764176\pi\) |
0.462548 | − | 0.886594i | \(-0.346935\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.52968 | + | 2.87135i | 0.947742 | + | 0.319038i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.538035 | + | 3.05135i | 0.0590571 | + | 0.334929i | 0.999993 | − | 0.00365453i | \(-0.00116328\pi\) |
−0.940936 | + | 0.338584i | \(0.890052\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.13767 | + | 1.86996i | −0.557258 | + | 0.202825i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.00960 | − | 0.0945255i | 0.108241 | − | 0.0101342i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.67300 | + | 15.0221i | 0.919336 | + | 1.59234i | 0.800425 | + | 0.599432i | \(0.204607\pi\) |
0.118911 | + | 0.992905i | \(0.462060\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.71337 | − | 9.89585i | 0.598924 | − | 1.03737i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.12635 | − | 7.74668i | −0.220492 | − | 0.803294i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.86760 | − | 10.5917i | 0.191612 | − | 1.08669i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.04084 | − | 5.90797i | 0.714889 | − | 0.599863i | −0.211077 | − | 0.977469i | \(-0.567697\pi\) |
0.925966 | + | 0.377606i | \(0.123253\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.89461 | + | 3.49963i | −0.592430 | + | 0.351726i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.2389 | − | 4.09062i | −1.11831 | − | 0.407032i | −0.284276 | − | 0.958743i | \(-0.591753\pi\) |
−0.834036 | + | 0.551710i | \(0.813975\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.76437 | + | 8.19328i | 0.962112 | + | 0.807308i | 0.981295 | − | 0.192508i | \(-0.0616623\pi\) |
−0.0191837 | + | 0.999816i | \(0.506107\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −18.2775 | + | 8.65879i | −1.78370 | + | 0.845011i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.09894 | −0.589607 | −0.294803 | − | 0.955558i | \(-0.595254\pi\) | ||||
−0.294803 | + | 0.955558i | \(0.595254\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.2390 | 1.07650 | 0.538250 | − | 0.842785i | \(-0.319086\pi\) | ||||
0.538250 | + | 0.842785i | \(0.319086\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.4115 | + | 7.19618i | 0.988220 | + | 0.683032i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.39062 | − | 4.52327i | −0.507107 | − | 0.425513i | 0.353003 | − | 0.935622i | \(-0.385161\pi\) |
−0.860110 | + | 0.510109i | \(0.829605\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.98233 | − | 3.63327i | −0.930857 | − | 0.338804i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.07442 | + | 8.77800i | −0.284230 | + | 0.811526i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.87254 | + | 4.08855i | −0.446665 | + | 0.374796i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00342 | + | 5.69068i | −0.0912200 | + | 0.517334i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.8650 | − | 3.10193i | −1.06983 | − | 0.279692i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.0585380 | + | 0.101391i | −0.00523579 | + | 0.00906866i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.99250 | + | 5.18316i | 0.265541 | + | 0.459931i | 0.967705 | − | 0.252084i | \(-0.0811160\pi\) |
−0.702164 | + | 0.712015i | \(0.747783\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.66137 | − | 2.34220i | −0.146275 | − | 0.206219i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.4251 | − | 5.61427i | 1.34770 | − | 0.490521i | 0.435468 | − | 0.900204i | \(-0.356583\pi\) |
0.912228 | + | 0.409683i | \(0.134361\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.17273 | − | 12.3222i | −0.188400 | − | 1.06847i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.3102 | − | 9.68691i | 1.14556 | − | 0.833717i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.0366673 | − | 0.207951i | −0.00313270 | − | 0.0177664i | 0.983201 | − | 0.182524i | \(-0.0584268\pi\) |
−0.986334 | + | 0.164758i | \(0.947316\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.45009 | − | 1.25573i | 0.292633 | − | 0.106510i | −0.191532 | − | 0.981486i | \(-0.561346\pi\) |
0.484165 | + | 0.874977i | \(0.339123\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.78277 | − | 6.06378i | 0.234352 | − | 0.510663i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.54217 | − | 6.13522i | −0.296211 | − | 0.513053i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.927377 | − | 1.60626i | 0.0770145 | − | 0.133393i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.01512 | + | 8.11331i | −0.661076 | + | 0.669174i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.68710 | − | 15.2393i | 0.220136 | − | 1.24845i | −0.651633 | − | 0.758535i | \(-0.725916\pi\) |
0.871769 | − | 0.489918i | \(-0.162973\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.4325 | + | 12.9494i | −1.25588 | + | 1.05381i | −0.259772 | + | 0.965670i | \(0.583648\pi\) |
−0.996108 | + | 0.0881390i | \(0.971908\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.27935 | − | 4.00624i | 0.265120 | − | 0.323885i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.8075 | − | 5.02552i | −1.10905 | − | 0.403660i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.7868 | + | 11.5685i | 1.10031 | + | 0.923269i | 0.997446 | − | 0.0714264i | \(-0.0227551\pi\) |
0.102863 | + | 0.994695i | \(0.467200\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.362739 | − | 4.45859i | 0.0287671 | − | 0.353589i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.3585 | −0.973989 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.05289 | −0.239121 | −0.119560 | − | 0.992827i | \(-0.538149\pi\) | ||||
−0.119560 | + | 0.992827i | \(0.538149\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.01678 | + | 12.4976i | −0.0791559 | + | 0.972940i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.14170 | + | 2.63620i | 0.243112 | + | 0.203995i | 0.756199 | − | 0.654341i | \(-0.227054\pi\) |
−0.513088 | + | 0.858336i | \(0.671498\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.18396 | + | 1.15887i | 0.244920 | + | 0.0891435i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.59953 | + | 9.52708i | 0.275263 | + | 0.728554i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.0435 | + | 10.9448i | −0.991680 | + | 0.832118i | −0.985810 | − | 0.167864i | \(-0.946313\pi\) |
−0.00586990 | + | 0.999983i | \(0.501868\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.22374 | + | 18.2828i | −0.243692 | + | 1.38205i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.7627 | + | 11.9068i | −0.884137 | + | 0.894967i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.27802 | + | 12.6059i | −0.543985 | + | 0.942210i | 0.454685 | + | 0.890652i | \(0.349752\pi\) |
−0.998670 | + | 0.0515575i | \(0.983581\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.51190 | + | 11.2789i | 0.484026 | + | 0.838357i | 0.999832 | − | 0.0183482i | \(-0.00584075\pi\) |
−0.515806 | + | 0.856706i | \(0.672507\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.45753 | − | 20.6084i | 0.699121 | − | 1.52341i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.7539 | − | 7.91778i | 1.59938 | − | 0.582127i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.684776 | + | 3.88356i | 0.0500758 | + | 0.283994i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.6966 | − | 15.8860i | 0.778060 | − | 1.15554i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.625632 | − | 3.54814i | −0.0452692 | − | 0.256734i | 0.953771 | − | 0.300534i | \(-0.0971648\pi\) |
−0.999040 | + | 0.0437996i | \(0.986054\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.38592 | + | 0.504435i | −0.0997610 | + | 0.0363100i | −0.391418 | − | 0.920213i | \(-0.628015\pi\) |
0.291657 | + | 0.956523i | \(0.405793\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.84248 | + | 13.8760i | 0.704835 | + | 0.993678i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.26931 | − | 2.19851i | −0.0904346 | − | 0.156637i | 0.817259 | − | 0.576270i | \(-0.195492\pi\) |
−0.907694 | + | 0.419633i | \(0.862159\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.925891 | + | 1.60369i | −0.0656347 | + | 0.113683i | −0.896975 | − | 0.442081i | \(-0.854241\pi\) |
0.831341 | + | 0.555763i | \(0.187574\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.4260 | + | 3.77145i | 1.01753 | + | 0.266018i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.374695 | − | 2.12500i | 0.0262984 | − | 0.149146i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.1838 | + | 14.4189i | −1.20017 | + | 1.00706i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.88444 | − | 1.86726i | 0.687016 | − | 0.129783i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.28951 | − | 2.65317i | −0.504226 | − | 0.183523i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.5459 | + | 12.2054i | 1.00138 | + | 0.840257i | 0.987175 | − | 0.159642i | \(-0.0510340\pi\) |
0.0142043 | + | 0.999899i | \(0.495478\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.83181 | + | 1.95727i | 0.194032 | + | 0.134110i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.25247 | −0.358215 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.0943 | −1.16043 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.6663 | − | 7.89549i | 1.12620 | − | 0.533527i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.09858 | + | 3.43912i | 0.275700 | + | 0.231340i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.81687 | − | 2.48114i | −0.456491 | − | 0.166149i | 0.103532 | − | 0.994626i | \(-0.466986\pi\) |
−0.560023 | + | 0.828477i | \(0.689208\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.183979 | − | 15.1097i | −0.0122652 | − | 1.00732i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.8531 | − | 18.3369i | 1.45044 | − | 1.21706i | 0.518182 | − | 0.855271i | \(-0.326609\pi\) |
0.932258 | − | 0.361793i | \(-0.117835\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.322184 | − | 1.82720i | 0.0212905 | − | 0.120744i | −0.972310 | − | 0.233694i | \(-0.924919\pi\) |
0.993601 | + | 0.112949i | \(0.0360298\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.86124 | + | 14.0672i | 0.254051 | + | 0.925556i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.26735 | + | 7.39126i | −0.279563 | + | 0.484218i | −0.971276 | − | 0.237955i | \(-0.923523\pi\) |
0.691713 | + | 0.722172i | \(0.256856\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.10176 | − | 10.5686i | −0.398035 | − | 0.689417i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 24.3038 | − | 2.27548i | 1.57870 | − | 0.147808i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.84845 | + | 2.49263i | −0.442989 | + | 0.161235i | −0.553878 | − | 0.832598i | \(-0.686853\pi\) |
0.110889 | + | 0.993833i | \(0.464630\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.231806 | − | 1.31464i | −0.0149319 | − | 0.0846833i | 0.976431 | − | 0.215829i | \(-0.0692455\pi\) |
−0.991363 | + | 0.131146i | \(0.958134\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.15494 | + | 14.3219i | −0.394840 | + | 0.918750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.62239 | + | 20.5436i | 0.231426 | + | 1.31248i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.89008 | + | 3.59969i | −0.629291 | + | 0.229043i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.34326 | + | 0.500270i | −0.338615 | + | 0.0317033i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.43928 | − | 2.49291i | −0.0908466 | − | 0.157351i | 0.817021 | − | 0.576608i | \(-0.195624\pi\) |
−0.907868 | + | 0.419257i | \(0.862291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.83102 | + | 6.63552i | −0.240854 | + | 0.417171i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.50660 | − | 9.13203i | −0.156970 | − | 0.571870i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.47629 | + | 25.3863i | −0.279223 | + | 1.58355i | 0.445996 | + | 0.895035i | \(0.352850\pi\) |
−0.725219 | + | 0.688518i | \(0.758262\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.6313 | − | 17.3117i | 1.28197 | − | 1.07570i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0213838 | + | 1.75620i | 0.00132362 | + | 0.108706i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.1609 | − | 5.15414i | −0.873197 | − | 0.317818i | −0.133736 | − | 0.991017i | \(-0.542697\pi\) |
−0.739461 | + | 0.673199i | \(0.764920\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.26793 | − | 5.25942i | −0.385036 | − | 0.323083i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.1515 | + | 12.8627i | −1.66164 | + | 0.787187i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.0615 | 0.979286 | 0.489643 | − | 0.871923i | \(-0.337127\pi\) | ||||
0.489643 | + | 0.871923i | \(0.337127\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.41446 | −0.571888 | −0.285944 | − | 0.958246i | \(-0.592307\pi\) | ||||
−0.285944 | + | 0.958246i | \(0.592307\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.2812 | + | 11.2531i | 0.985384 | + | 0.681071i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.81700 | + | 7.39834i | 0.531685 | + | 0.446137i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.23856 | − | 1.90668i | −0.314755 | − | 0.114561i | 0.179812 | − | 0.983701i | \(-0.442451\pi\) |
−0.494567 | + | 0.869140i | \(0.664673\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.6721 | − | 2.58278i | 0.818528 | − | 0.154627i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.4529 | − | 18.0011i | 1.27977 | − | 1.07386i | 0.286499 | − | 0.958081i | \(-0.407509\pi\) |
0.993275 | − | 0.115777i | \(-0.0369359\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.06884 | + | 6.06171i | −0.0635361 | + | 0.360331i | 0.936419 | + | 0.350883i | \(0.114119\pi\) |
−0.999955 | + | 0.00944797i | \(0.996993\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 18.0227 | + | 4.71175i | 1.06757 | + | 0.279100i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.0484 | + | 22.6005i | −0.770222 | + | 1.33406i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.01088 | + | 12.1432i | 0.412405 | + | 0.714306i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.21031 | + | 12.9847i | 0.539918 | + | 0.761177i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.19428 | + | 0.798651i | −0.128191 | + | 0.0466577i | −0.405319 | − | 0.914175i | \(-0.632840\pi\) |
0.277128 | + | 0.960833i | \(0.410617\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.31608 | + | 30.1490i | 0.309514 | + | 1.75534i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.21367 | − | 10.6677i | −0.302528 | − | 0.619001i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.80516 | + | 10.2376i | 0.104395 | + | 0.592054i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.74209 | + | 2.08995i | −0.330969 | + | 0.120463i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.64035 | − | 18.8277i | 0.496375 | − | 1.08162i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −20.7374 | − | 35.9183i | −1.18742 | − | 2.05668i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.41265 | − | 5.91088i | 0.194770 | − | 0.337351i | −0.752055 | − | 0.659100i | \(-0.770937\pi\) |
0.946825 | + | 0.321749i | \(0.104271\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.5159 | + | 15.7059i | −0.882666 | + | 0.893479i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.49254 | + | 8.46464i | −0.0846344 | + | 0.479986i | 0.912800 | + | 0.408406i | \(0.133915\pi\) |
−0.997435 | + | 0.0715798i | \(0.977196\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.5993 | + | 13.9285i | −0.938250 | + | 0.787285i | −0.977280 | − | 0.211953i | \(-0.932018\pi\) |
0.0390299 | + | 0.999238i | \(0.487573\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.3810 | − | 32.7694i | −0.697589 | − | 1.84635i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −33.1899 | − | 12.0801i | −1.86413 | − | 0.678488i | −0.975554 | − | 0.219760i | \(-0.929473\pi\) |
−0.888577 | − | 0.458728i | \(-0.848305\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.02480 | − | 0.859908i | −0.0573777 | − | 0.0481456i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.856604 | − | 10.5289i | 0.0478110 | − | 0.587665i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.85859 | 0.325981 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.6159 | 0.866217 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.57853 | + | 19.4024i | −0.0872929 | + | 1.07296i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.8758 | − | 9.12586i | −0.599601 | − | 0.503125i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.2569 | − | 8.82879i | −1.33328 | − | 0.485274i | −0.425590 | − | 0.904916i | \(-0.639933\pi\) |
−0.907690 | + | 0.419642i | \(0.862156\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.8854 | + | 16.9632i | −0.760917 | + | 0.929579i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20.8928 | − | 17.5311i | 1.14149 | − | 0.957826i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.587727 | + | 3.33317i | −0.0320156 | + | 0.181569i | −0.996622 | − | 0.0821241i | \(-0.973830\pi\) |
0.964607 | + | 0.263693i | \(0.0849407\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.56585 | − | 8.67078i | 0.465233 | − | 0.470932i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.29904 | + | 9.17821i | −0.286959 | + | 0.497028i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.765664 | − | 1.32617i | −0.0413420 | − | 0.0716064i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.67431 | − | 16.7227i | 0.413171 | − | 0.900318i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.2230 | + | 5.54073i | −0.817216 | + | 0.297442i | −0.716601 | − | 0.697483i | \(-0.754303\pi\) |
−0.100615 | + | 0.994925i | \(0.532081\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.780120 | + | 4.42428i | 0.0417589 | + | 0.236826i | 0.998542 | − | 0.0539752i | \(-0.0171892\pi\) |
−0.956783 | + | 0.290801i | \(0.906078\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.7221 | − | 6.54040i | −0.785806 | − | 0.349101i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.03327 | − | 22.8738i | −0.214669 | − | 1.21745i | −0.881479 | − | 0.472222i | \(-0.843452\pi\) |
0.666810 | − | 0.745228i | \(-0.267659\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.91679 | − | 2.15353i | 0.314030 | − | 0.114298i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.37389 | − | 8.98593i | −0.337342 | − | 0.475586i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.77697 | − | 10.0060i | −0.304897 | − | 0.528097i | 0.672341 | − | 0.740241i | \(-0.265289\pi\) |
−0.977238 | + | 0.212144i | \(0.931955\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.73768 | − | 6.47385i | 0.196720 | − | 0.340729i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.68315 | − | 2.53151i | −0.508234 | − | 0.132870i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.85755 | − | 33.2198i | 0.306598 | − | 1.73880i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.9271 | + | 10.0080i | −0.622589 | + | 0.522414i | −0.898616 | − | 0.438735i | \(-0.855427\pi\) |
0.276027 | + | 0.961150i | \(0.410982\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.02147 | − | 20.0475i | 0.365523 | − | 1.04363i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.94493 | − | 3.25569i | −0.464398 | − | 0.169027i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.47450 | − | 6.27185i | −0.387015 | − | 0.324744i | 0.428434 | − | 0.903573i | \(-0.359065\pi\) |
−0.815449 | + | 0.578829i | \(0.803510\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.166814 | − | 0.115297i | −0.00861423 | − | 0.00595392i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.81504 | −0.0934792 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.7904 | 0.965197 | 0.482599 | − | 0.875842i | \(-0.339693\pi\) | ||||
0.482599 | + | 0.875842i | \(0.339693\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.36823 | + | 4.43811i | −0.479949 | + | 0.227371i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.5697 | − | 19.7773i | −1.20435 | − | 1.01057i | −0.999495 | − | 0.0317817i | \(-0.989882\pi\) |
−0.204859 | − | 0.978791i | \(-0.565674\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 25.0731 | + | 9.12586i | 1.27784 | + | 0.465097i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.27679 | − | 2.53913i | 0.217402 | − | 0.129071i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.6754 | − | 19.0269i | 1.14969 | − | 0.964704i | 0.149978 | − | 0.988689i | \(-0.452080\pi\) |
0.999712 | + | 0.0239850i | \(0.00763540\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.00483 | − | 5.69870i | 0.0508167 | − | 0.288196i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.52571 | + | 27.4176i | 0.379622 | + | 1.38303i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.3244 | − | 38.6670i | 1.12326 | − | 1.94555i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.07134 | − | 13.9800i | −0.405089 | − | 0.701635i | 0.589243 | − | 0.807956i | \(-0.299426\pi\) |
−0.994332 | + | 0.106321i | \(0.966093\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 21.5775 | − | 2.02022i | 1.08023 | − | 0.101138i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.8328 | + | 8.67444i | −1.19016 | + | 0.433181i | −0.859778 | − | 0.510668i | \(-0.829398\pi\) |
−0.330377 | + | 0.943849i | \(0.607176\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.49689 | + | 14.1605i | 0.124379 | + | 0.705387i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.8535 | + | 24.3386i | 0.738078 | + | 1.20939i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.89948 | − | 16.4438i | −0.143722 | − | 0.815087i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.3980 | − | 7.78825i | 1.05806 | − | 0.385104i | 0.246364 | − | 0.969177i | \(-0.420764\pi\) |
0.811701 | + | 0.584073i | \(0.198542\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.364145 | − | 0.0340936i | 0.0179619 | − | 0.00168171i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.8079 | + | 30.8442i | 0.876269 | + | 1.51774i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.90808 | + | 8.50104i | −0.240928 | + | 0.417300i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.68326 | + | 6.13242i | 0.0824294 | + | 0.300306i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.854828 | − | 4.84797i | 0.0417611 | − | 0.236839i | −0.956782 | − | 0.290808i | \(-0.906076\pi\) |
0.998543 | + | 0.0539688i | \(0.0171872\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.1046 | − | 12.6742i | 0.736151 | − | 0.617704i | −0.195650 | − | 0.980674i | \(-0.562682\pi\) |
0.931801 | + | 0.362970i | \(0.118237\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.0773 | + | 5.65570i | 0.489977 | + | 0.274989i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.16833 | − | 2.97303i | −0.396222 | − | 0.144213i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −36.9624 | − | 31.0151i | −1.78874 | − | 1.50093i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.0890 | − | 5.25331i | 0.535383 | − | 0.253632i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.16323 | 0.296873 | 0.148436 | − | 0.988922i | \(-0.452576\pi\) | ||||
0.148436 | + | 0.988922i | \(0.452576\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.7838 | −0.710466 | −0.355233 | − | 0.934778i | \(-0.615599\pi\) | ||||
−0.355233 | + | 0.934778i | \(0.615599\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.64272 | + | 1.82658i | 0.126709 | + | 0.0875776i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.71993 | + | 7.31689i | 0.417131 | + | 0.350014i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.9719 | + | 10.1809i | 1.33502 | + | 0.485909i | 0.908242 | − | 0.418445i | \(-0.137425\pi\) |
0.426782 | + | 0.904354i | \(0.359647\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.8806 | − | 14.9764i | −0.613364 | − | 0.713162i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.3447 | + | 19.5885i | −1.10914 | + | 0.930680i | −0.998006 | − | 0.0631253i | \(-0.979893\pi\) |
−0.111136 | + | 0.993805i | \(0.535449\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.54269 | + | 54.1193i | −0.452367 | + | 2.56550i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 25.9309 | + | 6.77925i | 1.22649 | + | 0.320647i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.92055 | + | 10.2547i | −0.279408 | + | 0.483949i | −0.971238 | − | 0.238112i | \(-0.923472\pi\) |
0.691830 | + | 0.722061i | \(0.256805\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.08973 | + | 14.0118i | 0.380930 | + | 0.659791i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.1877 | − | 28.4606i | −0.948500 | − | 1.33720i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 34.0180 | − | 12.3816i | 1.59479 | − | 0.580456i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.0323668 | − | 0.183561i | −0.00151406 | − | 0.00858664i | 0.984041 | − | 0.177940i | \(-0.0569432\pi\) |
−0.985555 | + | 0.169353i | \(0.945832\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.45557 | + | 6.22397i | 0.301320 | + | 0.290510i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.80687 | + | 10.2473i | 0.0841543 | + | 0.477263i | 0.997536 | + | 0.0701583i | \(0.0223505\pi\) |
−0.913382 | + | 0.407105i | \(0.866538\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.2332 | − | 8.82016i | 1.12621 | − | 0.409907i | 0.289296 | − | 0.957240i | \(-0.406579\pi\) |
0.836915 | + | 0.547332i | \(0.184357\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.6151 | − | 23.1307i | 0.492262 | − | 1.07266i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.8506 | + | 18.7937i | 0.502104 | + | 0.869670i | 0.999997 | + | 0.00243153i | \(0.000773982\pi\) |
−0.497893 | + | 0.867239i | \(0.665893\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.8647 | − | 27.4785i | 0.732566 | − | 1.26884i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.9077 | + | 22.1760i | −1.00945 | + | 1.02182i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.657857 | + | 3.73089i | −0.0302483 | + | 0.171547i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.0989 | − | 10.9913i | 0.601020 | − | 0.504316i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.64612 | + | 1.25243i | 0.350092 | + | 0.0573447i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −36.7619 | − | 13.3802i | −1.67970 | − | 0.611359i | −0.686427 | − | 0.727199i | \(-0.740822\pi\) |
−0.993268 | + | 0.115839i | \(0.963044\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.3542 | − | 14.5619i | −0.791284 | − | 0.663966i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.73577 | − | 21.3351i | 0.0789804 | − | 0.970782i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 29.1187 | 1.32221 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.4833 | 0.475043 | 0.237522 | − | 0.971382i | \(-0.423665\pi\) | ||||
0.237522 | + | 0.971382i | \(0.423665\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.428782 | − | 5.27035i | 0.0193902 | − | 0.238334i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.25278 | − | 4.40761i | −0.237055 | − | 0.198913i | 0.516519 | − | 0.856276i | \(-0.327227\pi\) |
−0.753574 | + | 0.657363i | \(0.771672\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.949403 | + | 0.345554i | 0.0427589 | + | 0.0155630i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −21.4325 | − | 3.51062i | −0.963317 | − | 0.157791i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.61145 | − | 4.70857i | 0.251708 | − | 0.211208i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.26002 | + | 18.4885i | −0.145939 | + | 0.827659i | 0.820670 | + | 0.571402i | \(0.193600\pi\) |
−0.966609 | + | 0.256257i | \(0.917511\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.99225 | + | 5.05340i | −0.223037 | + | 0.225769i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.21350 | + | 10.7621i | −0.277046 | + | 0.479858i | −0.970649 | − | 0.240499i | \(-0.922689\pi\) |
0.693603 | + | 0.720357i | \(0.256022\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.9456 | − | 32.8148i | −0.843069 | − | 1.46024i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.44779 | + | 5.33385i | −0.108710 | + | 0.236885i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.9889 | + | 11.2790i | −1.37356 | + | 0.499935i | −0.920219 | − | 0.391403i | \(-0.871990\pi\) |
−0.453340 | + | 0.891338i | \(0.649768\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.81455 | − | 38.6472i | −0.301458 | − | 1.70965i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16.9526 | + | 4.87594i | −0.748476 | + | 0.215278i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.01231 | + | 39.7688i | 0.308999 | + | 1.75242i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.27121 | + | 3.01047i | −0.363767 | + | 0.132400i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.0626 | − | 24.0548i | −0.748963 | − | 1.05589i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.16598 | − | 12.4118i | −0.313947 | − | 0.543773i | 0.665266 | − | 0.746607i | \(-0.268318\pi\) |
−0.979213 | + | 0.202834i | \(0.934985\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.85442 | + | 4.94400i | −0.124815 | + | 0.216186i | −0.921661 | − | 0.387997i | \(-0.873167\pi\) |
0.796846 | + | 0.604183i | \(0.206500\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −31.1096 | − | 8.13313i | −1.35773 | − | 0.354959i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.38988 | − | 7.88241i | 0.0605442 | − | 0.343363i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.00623 | + | 7.55712i | −0.391575 | + | 0.328571i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.9031 | − | 21.9788i | −0.820326 | − | 0.953797i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.6277 | + | 7.50787i | 0.893485 | + | 0.325202i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.8016 | − | 12.4200i | −0.639930 | − | 0.536965i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.7400 | − | 14.3349i | −0.894995 | − | 0.618597i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.0461 | 0.648081 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.0099 | 0.774305 | 0.387153 | − | 0.922016i | \(-0.373459\pi\) | ||||
0.387153 | + | 0.922016i | \(0.373459\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.3860 | + | 9.65766i | −0.874846 | + | 0.414450i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27.2761 | + | 22.8874i | 1.16838 | + | 0.980387i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.3837 | − | 7.05509i | −0.828788 | − | 0.301654i | −0.107426 | − | 0.994213i | \(-0.534261\pi\) |
−0.721361 | + | 0.692559i | \(0.756483\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 34.2489 | + | 19.2214i | 1.46171 | + | 0.820351i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.52249 | + | 1.27752i | −0.0648601 | + | 0.0544241i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.01990 | − | 51.1544i | 0.383565 | − | 2.17531i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.6135 | + | 38.6669i | 0.450517 | + | 1.64132i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.90209 | − | 3.29452i | 0.0805942 | − | 0.139593i | −0.822911 | − | 0.568170i | \(-0.807652\pi\) |
0.903505 | + | 0.428577i | \(0.140985\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.57000 | + | 4.45136i | 0.108699 | + | 0.188273i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.80054 | + | 0.636710i | −0.287119 | + | 0.0268819i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.4037 | + | 3.78663i | −0.438463 | + | 0.159587i | −0.551813 | − | 0.833968i | \(-0.686064\pi\) |
0.113351 | + | 0.993555i | \(0.463842\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.87129 | − | 21.9552i | −0.162866 | − | 0.923662i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 25.9225 | + | 20.6972i | 1.08864 | + | 0.869199i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.11202 | + | 46.0056i | 0.340074 | + | 1.92865i | 0.369836 | + | 0.929097i | \(0.379414\pi\) |
−0.0297623 | + | 0.999557i | \(0.509475\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.7753 | + | 10.8373i | −1.24606 | + | 0.453528i | −0.879068 | − | 0.476697i | \(-0.841834\pi\) |
−0.366990 | + | 0.930225i | \(0.619612\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.21319 | − | 0.581718i | 0.259560 | − | 0.0243016i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.44468 | − | 14.6266i | −0.352167 | − | 0.609972i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.1642 | + | 38.3895i | −0.922707 | + | 1.59818i | −0.127499 | + | 0.991839i | \(0.540695\pi\) |
−0.795208 | + | 0.606336i | \(0.792639\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.676175 | − | 2.46343i | −0.0281009 | − | 0.102377i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.98305 | + | 11.2464i | −0.0822707 | + | 0.466580i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.52087 | + | 3.79346i | −0.187235 | + | 0.157109i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −25.3371 | + | 15.0426i | −1.04756 | + | 0.621937i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 38.5694 | + | 14.0381i | 1.59193 | + | 0.579414i | 0.977754 | − | 0.209756i | \(-0.0672669\pi\) |
0.614174 | + | 0.789170i | \(0.289489\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.0614 | + | 10.1207i | 0.496980 | + | 0.417015i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.97367 | − | 1.88249i | 0.163455 | − | 0.0774351i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.69265 | −0.398029 | −0.199015 | − | 0.979996i | \(-0.563774\pi\) | ||||
−0.199015 | + | 0.979996i | \(0.563774\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.1513 | −0.826121 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.63848 | − | 1.82365i | −0.107986 | − | 0.0746370i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.8572 | + | 19.1794i | 0.933918 | + | 0.783651i | 0.976517 | − | 0.215442i | \(-0.0691191\pi\) |
−0.0425983 | + | 0.999092i | \(0.513564\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.7938 | − | 4.29259i | −0.481079 | − | 0.175098i | 0.0900856 | − | 0.995934i | \(-0.471286\pi\) |
−0.571165 | + | 0.820836i | \(0.693508\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.53698 | + | 24.3745i | −0.347653 | + | 0.992607i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.0239 | + | 11.7674i | −0.570151 | + | 0.478413i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.482765 | − | 2.73790i | 0.0195948 | − | 0.111128i | −0.973442 | − | 0.228935i | \(-0.926476\pi\) |
0.993036 | + | 0.117808i | \(0.0375866\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.61586 | + | 0.945312i | 0.146522 | + | 0.0383060i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.97110 | + | 10.3422i | −0.241565 | + | 0.418403i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.29646 | + | 7.44168i | 0.173532 | + | 0.300567i | 0.939652 | − | 0.342131i | \(-0.111149\pi\) |
−0.766120 | + | 0.642697i | \(0.777815\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −22.4786 | − | 31.6904i | −0.906425 | − | 1.27788i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.8681 | − | 6.86743i | 0.759602 | − | 0.276472i | 0.0669615 | − | 0.997756i | \(-0.478670\pi\) |
0.692640 | + | 0.721283i | \(0.256447\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.45723 | − | 8.26436i | −0.0585710 | − | 0.332173i | 0.941416 | − | 0.337247i | \(-0.109496\pi\) |
−0.999987 | + | 0.00507458i | \(0.998385\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.83525 | + | 17.3262i | 0.0736461 | + | 0.695278i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.1018 | + | 62.9612i | 0.444783 | + | 2.52249i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.3174 | − | 8.48684i | 0.932696 | − | 0.339474i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.60411 | − | 12.2116i | 0.223806 | − | 0.487684i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.30522 | + | 10.9210i | 0.251405 | + | 0.435447i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.78157 | − | 15.2101i | 0.349589 | − | 0.605506i | −0.636588 | − | 0.771204i | \(-0.719655\pi\) |
0.986176 | + | 0.165699i | \(0.0529879\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.1138 | + | 23.3970i | −0.918691 | + | 0.929946i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.29257 | + | 18.6731i | −0.130662 | + | 0.741019i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.6379 | − | 13.1218i | 0.619596 | − | 0.519903i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.77666 | + | 4.61378i | −0.149402 | + | 0.182518i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.6056 | + | 4.58808i | 0.497893 | + | 0.181218i | 0.578746 | − | 0.815508i | \(-0.303542\pi\) |
−0.0808532 | + | 0.996726i | \(0.525765\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.99375 | + | 6.70755i | 0.315243 | + | 0.264520i | 0.786655 | − | 0.617393i | \(-0.211811\pi\) |
−0.471412 | + | 0.881913i | \(0.656256\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.737715 | − | 9.06758i | 0.0290475 | − | 0.357035i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.9585 | 1.49230 | 0.746152 | − | 0.665775i | \(-0.231899\pi\) | ||||
0.746152 | + | 0.665775i | \(0.231899\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.0810 | 0.866756 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.40091 | − | 29.5106i | 0.0940991 | − | 1.15661i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.9178 | − | 17.5521i | −0.818578 | − | 0.686868i | 0.134061 | − | 0.990973i | \(-0.457198\pi\) |
−0.952639 | + | 0.304105i | \(0.901643\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 48.8684 | + | 17.7867i | 1.90945 | + | 0.694982i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.2895 | + | 29.8807i | 0.440447 | + | 1.16576i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.3174 | − | 22.0829i | 1.02518 | − | 0.860228i | 0.0349104 | − | 0.999390i | \(-0.488885\pi\) |
0.990270 | + | 0.139162i | \(0.0444410\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.26787 | + | 24.2043i | −0.166001 | + | 0.941439i | 0.782025 | + | 0.623247i | \(0.214187\pi\) |
−0.948026 | + | 0.318192i | \(0.896924\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.51276 | + | 6.59254i | −0.252935 | + | 0.256033i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.8202 | − | 34.3295i | 0.768593 | − | 1.33124i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.981523 | + | 1.70005i | 0.0380047 | + | 0.0658261i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.24074 | − | 11.4198i | 0.202619 | − | 0.441515i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.1105 | + | 10.2314i | −1.08519 | + | 0.394979i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.44524 | + | 42.2241i | 0.286993 | + | 1.62762i | 0.698078 | + | 0.716021i | \(0.254039\pi\) |
−0.411085 | + | 0.911597i | \(0.634850\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 26.1105 | + | 1.80457i | 1.00499 | + | 0.0694580i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.30018 | + | 7.37368i | 0.0499699 | + | 0.283393i | 0.999546 | − | 0.0301446i | \(-0.00959678\pi\) |
−0.949576 | + | 0.313538i | \(0.898486\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.8331 | − | 11.5863i | 1.22164 | − | 0.444641i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.5866 | + | 40.3014i | 1.09544 | + | 1.54435i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.37724 | + | 14.5098i | 0.320546 | + | 0.555202i | 0.980601 | − | 0.196015i | \(-0.0628002\pi\) |
−0.660055 | + | 0.751218i | \(0.729467\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.334487 | − | 0.579349i | 0.0127801 | − | 0.0221358i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.10912 | + | 0.812833i | 0.118620 | + | 0.0310115i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.39040 | + | 7.88535i | −0.0529700 | + | 0.300408i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.4550 | − | 9.61189i | 0.435769 | − | 0.365653i | −0.398354 | − | 0.917232i | \(-0.630419\pi\) |
0.834123 | + | 0.551578i | \(0.185974\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −24.8272 | + | 4.69008i | −0.943109 | + | 0.178161i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.9303 | + | 3.97830i | 0.414609 | + | 0.150905i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.36048 | − | 7.85437i | −0.354553 | − | 0.297506i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.1605 | − | 8.40503i | −0.459953 | − | 0.317908i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.1025 | −1.59019 | −0.795094 | − | 0.606486i | \(-0.792579\pi\) | ||||
−0.795094 | + | 0.606486i | \(0.792579\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.8065 | −0.935593 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 19.1020 | − | 9.04939i | 0.719423 | − | 0.340820i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −33.7687 | − | 28.3353i | −1.27000 | − | 1.06566i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.7677 | − | 9.74265i | −1.00528 | − | 0.365893i | −0.213663 | − | 0.976907i | \(-0.568539\pi\) |
−0.791619 | + | 0.611015i | \(0.790762\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.514765 | + | 42.2764i | 0.0193052 | + | 1.58549i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.9132 | − | 9.99634i | 0.446152 | − | 0.374366i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.89736 | − | 22.1030i | 0.145753 | − | 0.826606i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.34127 | − | 12.1729i | −0.124782 | − | 0.454605i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.26744 | − | 2.19526i | 0.0472674 | − | 0.0818695i | −0.841424 | − | 0.540376i | \(-0.818282\pi\) |
0.888691 | + | 0.458506i | \(0.151615\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.4900 | + | 40.6858i | 0.874812 | + | 1.51522i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.30208 | − | 0.215535i | 0.0856152 | − | 0.00801585i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.77102 | − | 1.00857i | 0.102913 | − | 0.0374573i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.45271 | − | 19.5813i | −0.128054 | − | 0.726231i | −0.979447 | − | 0.201702i | \(-0.935353\pi\) |
0.851393 | − | 0.524529i | \(-0.175758\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8601 | − | 12.6371i | −0.883707 | − | 0.468040i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.496834 | − | 2.81769i | −0.0183761 | − | 0.104216i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.40733 | − | 3.42399i | 0.347468 | − | 0.126468i | −0.162390 | − | 0.986727i | \(-0.551920\pi\) |
0.509858 | + | 0.860259i | \(0.329698\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −35.9742 | + | 3.36813i | −1.32693 | + | 0.124235i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.83580 | − | 17.0361i | −0.362306 | − | 0.627533i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.1957 | + | 34.9800i | −0.742911 | + | 1.28676i | 0.208253 | + | 0.978075i | \(0.433222\pi\) |
−0.951164 | + | 0.308685i | \(0.900111\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.82525 | − | 17.5793i | −0.177260 | − | 0.645791i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.19059 | + | 35.1086i | −0.227111 | + | 1.28801i | 0.631498 | + | 0.775377i | \(0.282440\pi\) |
−0.858609 | + | 0.512631i | \(0.828671\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 37.5551 | − | 31.5124i | 1.37591 | − | 1.15453i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.113172 | − | 9.29458i | −0.00414076 | − | 0.340071i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −21.1233 | − | 7.68826i | −0.771830 | − | 0.280923i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.25347 | + | 6.08638i | 0.264683 | + | 0.222095i | 0.765464 | − | 0.643479i | \(-0.222509\pi\) |
−0.500781 | + | 0.865574i | \(0.666954\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.50577 | − | 2.13457i | 0.164199 | − | 0.0777879i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −63.8240 | −2.32279 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.9651 | −1.37987 | −0.689933 | − | 0.723873i | \(-0.742360\pi\) | ||||
−0.689933 | + | 0.723873i | \(0.742360\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.9171 | − | 7.54563i | −0.396267 | − | 0.273889i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.3845 | + | 28.8520i | 1.24644 | + | 1.04588i | 0.996993 | + | 0.0774952i | \(0.0246922\pi\) |
0.249444 | + | 0.968389i | \(0.419752\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38.9256 | + | 14.1678i | 1.40920 | + | 0.512908i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.1171 | − | 3.04466i | 0.582715 | − | 0.110080i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.9496 | − | 19.2570i | 0.828661 | − | 0.695329i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.94212 | − | 45.0420i | 0.286400 | − | 1.62426i | −0.413841 | − | 0.910349i | \(-0.635813\pi\) |
0.700241 | − | 0.713906i | \(-0.253076\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −43.1968 | − | 11.2932i | −1.55570 | − | 0.406713i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.2853 | − | 17.8147i | 0.369938 | − | 0.640752i | −0.619617 | − | 0.784904i | \(-0.712712\pi\) |
0.989556 | + | 0.144152i | \(0.0460455\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.6806 | − | 20.2315i | −0.419581 | − | 0.726735i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 26.9884 | + | 38.0483i | 0.968202 | + | 1.36497i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.5873 | − | 8.22111i | 0.809274 | − | 0.294552i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.788621 | − | 4.47249i | −0.0282191 | − | 0.160038i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.03482 | − | 0.209745i | −0.108456 | − | 0.00749567i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.90106 | + | 56.1517i | 0.353384 | + | 2.00414i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.8760 | − | 15.2416i | 1.49272 | − | 0.543305i | 0.538555 | − | 0.842590i | \(-0.318970\pi\) |
0.954164 | + | 0.299285i | \(0.0967483\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.8867 | − | 23.7227i | 0.387578 | − | 0.844550i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.9681 | − | 22.4614i | −0.461093 | − | 0.798637i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.2934 | + | 35.1492i | −0.720639 | + | 1.24818i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.95992 | − | 10.0819i | 0.353242 | − | 0.357569i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.61623 | − | 43.1938i | 0.269781 | − | 1.53000i | −0.485287 | − | 0.874355i | \(-0.661285\pi\) |
0.755067 | − | 0.655647i | \(-0.227604\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.09234 | − | 4.27298i | 0.180154 | − | 0.151167i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.3921 | − | 48.6794i | −0.649853 | − | 1.72000i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.8628 | − | 8.32138i | −0.806811 | − | 0.293655i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −29.9932 | − | 25.1672i | −1.05712 | − | 0.887029i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.25585 | + | 27.7277i | −0.0794098 | + | 0.976061i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.5821 | −0.547836 | −0.273918 | − | 0.961753i | \(-0.588320\pi\) | ||||
−0.273918 | + | 0.961753i | \(0.588320\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.4691 | 1.06992 | 0.534958 | − | 0.844879i | \(-0.320327\pi\) | ||||
0.534958 | + | 0.844879i | \(0.320327\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.32227 | − | 16.2526i | 0.0463741 | − | 0.570004i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.40912 | − | 6.21699i | −0.259530 | − | 0.217772i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.28886 | + | 1.92499i | 0.185034 | + | 0.0673468i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −21.7135 | + | 26.5265i | −0.758733 | + | 0.926911i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.45626 | + | 1.22195i | −0.0508240 | + | 0.0426464i | −0.667846 | − | 0.744300i | \(-0.732783\pi\) |
0.617022 | + | 0.786946i | \(0.288339\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.82738 | − | 21.7062i | 0.133414 | − | 0.756629i | −0.842537 | − | 0.538639i | \(-0.818939\pi\) |
0.975951 | − | 0.217991i | \(-0.0699502\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14.0105 | + | 14.1821i | −0.487782 | + | 0.493757i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.2488 | − | 42.0001i | 0.843213 | − | 1.46049i | −0.0439508 | − | 0.999034i | \(-0.513994\pi\) |
0.887164 | − | 0.461454i | \(-0.152672\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.1593 | + | 17.5964i | 0.352846 | + | 0.611148i | 0.986747 | − | 0.162267i | \(-0.0518805\pi\) |
−0.633900 | + | 0.773415i | \(0.718547\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.02735 | − | 8.77578i | 0.139707 | − | 0.304428i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.6780 | + | 3.88647i | −0.369970 | + | 0.134658i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.25622 | + | 12.7957i | 0.0780797 | + | 0.442812i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.53851 | + | 23.9656i | 0.0877438 | + | 0.828371i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.879762 | + | 4.98938i | 0.0303728 | + | 0.172253i | 0.996221 | − | 0.0868566i | \(-0.0276822\pi\) |
−0.965848 | + | 0.259109i | \(0.916571\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.9290 | − | 9.80136i | 0.928587 | − | 0.337978i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.0631 | + | 39.5635i | 0.966545 | + | 1.36264i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.36726 | + | 9.29636i | 0.184639 | + | 0.319804i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.6489 | + | 18.4444i | −0.365901 | + | 0.633758i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.3145 | − | 2.69657i | −0.353992 | − | 0.0925459i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.25467 | + | 24.1294i | −0.145848 | + | 0.827147i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.2756 | − | 17.0132i | 0.694222 | − | 0.582521i | −0.225902 | − | 0.974150i | \(-0.572533\pi\) |
0.920123 | + | 0.391629i | \(0.128088\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.6654 | + | 30.4516i | −0.364750 | + | 1.04142i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.2073 | + | 6.26295i | 0.587790 | + | 0.213938i | 0.618757 | − | 0.785582i | \(-0.287636\pi\) |
−0.0309669 | + | 0.999520i | \(0.509859\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.23097 | + | 6.06751i | 0.246718 | + | 0.207021i | 0.757757 | − | 0.652536i | \(-0.226295\pi\) |
−0.511040 | + | 0.859557i | \(0.670740\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −37.1836 | − | 25.7003i | −1.26721 | − | 0.875865i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.2154 | 0.483898 | 0.241949 | − | 0.970289i | \(-0.422213\pi\) | ||||
0.241949 | + | 0.970289i | \(0.422213\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −53.9438 | −1.83414 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.9481 | + | 10.3977i | −0.745396 | + | 0.353124i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.6696 | − | 20.7003i | −0.836859 | − | 0.702208i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.0800 | − | 9.12836i | −0.849802 | − | 0.309303i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −23.7097 | + | 14.0765i | −0.802452 | + | 0.476416i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.330555 | + | 0.277369i | −0.0111748 | + | 0.00937677i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.79059 | − | 38.5113i | 0.229302 | − | 1.30044i | −0.624986 | − | 0.780636i | \(-0.714895\pi\) |
0.854288 | − | 0.519800i | \(-0.173993\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.07056 | − | 3.90025i | −0.0361091 | − | 0.131552i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.4469 | − | 19.8266i | 0.385657 | − | 0.667977i | −0.606203 | − | 0.795310i | \(-0.707308\pi\) |
0.991860 | + | 0.127333i | \(0.0406416\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.57546 | − | 14.8531i | −0.288587 | − | 0.499847i | 0.684886 | − | 0.728651i | \(-0.259852\pi\) |
−0.973473 | + | 0.228803i | \(0.926519\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −52.7943 | + | 4.94294i | −1.77466 | + | 0.166155i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.1560 | − | 6.24427i | 0.576042 | − | 0.209662i | −0.0375373 | − | 0.999295i | \(-0.511951\pi\) |
0.613579 | + | 0.789633i | \(0.289729\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.83051 | + | 21.7239i | 0.128471 | + | 0.728596i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.1484 | − | 7.50231i | 0.641494 | − | 0.251337i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.27074 | + | 12.8780i | 0.0759876 | + | 0.430947i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −43.3342 | + | 15.7723i | −1.44850 | + | 0.527211i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.9271 | + | 1.67845i | −0.598569 | + | 0.0560419i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.35764 | + | 2.35150i | 0.0452797 | + | 0.0784268i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.22853 | − | 3.85993i | 0.0742431 | − | 0.128593i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.80150 | − | 10.2064i | −0.0932280 | − | 0.339647i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.16488 | + | 40.6341i | −0.238169 | + | 1.35072i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.3621 | + | 18.7640i | −0.742521 | + | 0.623049i | −0.933513 | − | 0.358542i | \(-0.883274\pi\) |
0.190992 | + | 0.981592i | \(0.438829\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 31.2896 | + | 17.5606i | 1.03781 | + | 0.582449i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.3409 | + | 18.6866i | 1.70100 | + | 0.619114i | 0.995939 | − | 0.0900315i | \(-0.0286968\pi\) |
0.705062 | + | 0.709145i | \(0.250919\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.42367 | + | 4.55100i | 0.179497 | + | 0.150616i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 64.9200 | − | 30.7552i | 2.14619 | − | 1.01674i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 60.5012 | 1.99793 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.0995 | −1.35575 | −0.677873 | − | 0.735179i | \(-0.737098\pi\) | ||||
−0.677873 | + | 0.735179i | \(0.737098\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.72491 | + | 6.72160i | 0.320447 | + | 0.221484i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.72012 | − | 3.96065i | −0.155365 | − | 0.130367i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.5863 | + | 12.5884i | 1.13719 | + | 0.413904i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.9347 | − | 28.9917i | −0.818962 | − | 0.952211i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.1812 | − | 9.38218i | 0.366845 | − | 0.307819i | −0.440667 | − | 0.897671i | \(-0.645258\pi\) |
0.807512 | + | 0.589851i | \(0.200814\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.88158 | − | 22.0135i | 0.127214 | − | 0.721464i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.4033 | − | 3.76552i | −0.471542 | − | 0.123278i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.24668 | + | 10.8196i | −0.204288 | + | 0.353838i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.4641 | − | 21.5885i | −0.407185 | − | 0.705265i | 0.587388 | − | 0.809305i | \(-0.300156\pi\) |
−0.994573 | + | 0.104041i | \(0.966823\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.7140 | − | 30.6125i | −0.708610 | − | 0.999001i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.5873 | + | 7.12918i | −0.638526 | + | 0.232405i | −0.640938 | − | 0.767592i | \(-0.721455\pi\) |
0.00241179 | + | 0.999997i | \(0.499232\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.12268 | − | 23.3809i | −0.134253 | − | 0.761387i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 58.3104 | − | 16.7714i | 1.89684 | − | 0.545572i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.23623 | − | 35.3674i | −0.202650 | − | 1.14929i | −0.901095 | − | 0.433622i | \(-0.857235\pi\) |
0.698445 | − | 0.715664i | \(-0.253876\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31.0192 | + | 11.2901i | −1.00693 | + | 0.366491i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.5161 | − | 55.6006i | 0.827415 | − | 1.80297i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.90103 | − | 5.02474i | −0.0939737 | − | 0.162767i | 0.815206 | − | 0.579171i | \(-0.196624\pi\) |
−0.909180 | + | 0.416404i | \(0.863290\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.70716 | − | 9.88509i | 0.184679 | − | 0.319874i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.62843 | − | 1.64838i | 0.0526398 | − | 0.0532846i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.135145 | − | 0.766447i | 0.00436407 | − | 0.0247499i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.26914 | + | 6.09953i | −0.234488 | + | 0.196759i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.0562 | + | 2.95759i | 0.581853 | + | 0.0953070i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.39077 | − | 1.59811i | −0.141344 | − | 0.0514449i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.7200 | − | 19.0644i | −0.730627 | − | 0.613069i | 0.199675 | − | 0.979862i | \(-0.436011\pi\) |
−0.930303 | + | 0.366793i | \(0.880456\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.822846 | + | 10.1140i | −0.0264336 | + | 0.324907i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.1522 | −1.51318 | −0.756592 | − | 0.653887i | \(-0.773137\pi\) | ||||
−0.756592 | + | 0.653887i | \(0.773137\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.5322 | 0.433821 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.19328 | + | 26.9585i | −0.0702411 | + | 0.863364i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.2341 | − | 15.3002i | −0.583361 | − | 0.489498i | 0.302688 | − | 0.953090i | \(-0.402116\pi\) |
−0.886049 | + | 0.463592i | \(0.846560\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 37.2464 | + | 13.5566i | 1.19040 | + | 0.433270i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −33.2736 | − | 5.45018i | −1.06234 | − | 0.174011i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.48950 | + | 7.12353i | −0.270773 | + | 0.227205i | −0.768056 | − | 0.640383i | \(-0.778776\pi\) |
0.497283 | + | 0.867589i | \(0.334331\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.39659 | − | 7.92046i | 0.0444991 | − | 0.252367i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17.2819 | − | 17.4936i | 0.550090 | − | 0.556828i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.77957 | − | 4.81435i | 0.0883851 | − | 0.153087i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.71846 | + | 9.90466i | 0.181653 | + | 0.314632i | 0.942443 | − | 0.334365i | \(-0.108522\pi\) |
−0.760791 | + | 0.648997i | \(0.775189\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.6485 | − | 40.6358i | 0.591791 | − | 1.28954i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.51286 | + | 2.00652i | −0.174769 | + | 0.0636108i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.84383 | − | 27.4707i | −0.153406 | − | 0.870007i | −0.960229 | − | 0.279214i | \(-0.909926\pi\) |
0.806823 | − | 0.590793i | \(-0.201185\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −27.3342 | − | 26.3536i | −0.864816 | − | 0.833790i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 432.2.u.b.337.2 | 12 | ||
4.3 | odd | 2 | 54.2.e.b.13.1 | ✓ | 12 | ||
12.11 | even | 2 | 162.2.e.b.91.1 | 12 | |||
27.25 | even | 9 | inner | 432.2.u.b.241.2 | 12 | ||
36.7 | odd | 6 | 486.2.e.h.109.1 | 12 | |||
36.11 | even | 6 | 486.2.e.e.109.2 | 12 | |||
36.23 | even | 6 | 486.2.e.g.433.1 | 12 | |||
36.31 | odd | 6 | 486.2.e.f.433.2 | 12 | |||
108.7 | odd | 18 | 486.2.e.h.379.1 | 12 | |||
108.11 | even | 18 | 486.2.e.g.55.1 | 12 | |||
108.23 | even | 18 | 1458.2.c.g.487.5 | 12 | |||
108.31 | odd | 18 | 1458.2.c.f.487.2 | 12 | |||
108.43 | odd | 18 | 486.2.e.f.55.2 | 12 | |||
108.47 | even | 18 | 486.2.e.e.379.2 | 12 | |||
108.59 | even | 18 | 1458.2.a.f.1.2 | 6 | |||
108.67 | odd | 18 | 1458.2.c.f.973.2 | 12 | |||
108.79 | odd | 18 | 54.2.e.b.25.1 | yes | 12 | ||
108.83 | even | 18 | 162.2.e.b.73.1 | 12 | |||
108.95 | even | 18 | 1458.2.c.g.973.5 | 12 | |||
108.103 | odd | 18 | 1458.2.a.g.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
54.2.e.b.13.1 | ✓ | 12 | 4.3 | odd | 2 | ||
54.2.e.b.25.1 | yes | 12 | 108.79 | odd | 18 | ||
162.2.e.b.73.1 | 12 | 108.83 | even | 18 | |||
162.2.e.b.91.1 | 12 | 12.11 | even | 2 | |||
432.2.u.b.241.2 | 12 | 27.25 | even | 9 | inner | ||
432.2.u.b.337.2 | 12 | 1.1 | even | 1 | trivial | ||
486.2.e.e.109.2 | 12 | 36.11 | even | 6 | |||
486.2.e.e.379.2 | 12 | 108.47 | even | 18 | |||
486.2.e.f.55.2 | 12 | 108.43 | odd | 18 | |||
486.2.e.f.433.2 | 12 | 36.31 | odd | 6 | |||
486.2.e.g.55.1 | 12 | 108.11 | even | 18 | |||
486.2.e.g.433.1 | 12 | 36.23 | even | 6 | |||
486.2.e.h.109.1 | 12 | 36.7 | odd | 6 | |||
486.2.e.h.379.1 | 12 | 108.7 | odd | 18 | |||
1458.2.a.f.1.2 | 6 | 108.59 | even | 18 | |||
1458.2.a.g.1.5 | 6 | 108.103 | odd | 18 | |||
1458.2.c.f.487.2 | 12 | 108.31 | odd | 18 | |||
1458.2.c.f.973.2 | 12 | 108.67 | odd | 18 | |||
1458.2.c.g.487.5 | 12 | 108.23 | even | 18 | |||
1458.2.c.g.973.5 | 12 | 108.95 | even | 18 |