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: | 12.0.1952986685049.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 337.2 | ||
Root | \(0.500000 - 1.68614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 432.337 |
Dual form | 432.2.u.c.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 | ||||||||
\(3\) | 1.72962 | + | 0.0916693i | 0.998598 | + | 0.0529253i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.33735 | − | 1.12217i | −0.598081 | − | 0.501850i | 0.292747 | − | 0.956190i | \(-0.405431\pi\) |
−0.890828 | + | 0.454340i | \(0.849875\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.31094 | + | 0.841112i | 0.873452 | + | 0.317910i | 0.739564 | − | 0.673086i | \(-0.235032\pi\) |
0.133888 | + | 0.990997i | \(0.457254\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.98319 | + | 0.317107i | 0.994398 | + | 0.105702i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.960783 | − | 0.806193i | 0.289687 | − | 0.243076i | −0.486349 | − | 0.873764i | \(-0.661672\pi\) |
0.776036 | + | 0.630688i | \(0.217227\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.789931 | + | 4.47992i | −0.219087 | + | 1.24251i | 0.654584 | + | 0.755989i | \(0.272844\pi\) |
−0.873671 | + | 0.486517i | \(0.838267\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.21024 | − | 2.06353i | −0.570683 | − | 0.532800i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.32358 | − | 5.75662i | 0.806088 | − | 1.39618i | −0.109467 | − | 0.993990i | \(-0.534914\pi\) |
0.915554 | − | 0.402194i | \(-0.131752\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.124578 | + | 0.215776i | 0.0285802 | + | 0.0495023i | 0.879962 | − | 0.475045i | \(-0.157568\pi\) |
−0.851382 | + | 0.524547i | \(0.824235\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.91994 | + | 1.66665i | 0.855402 | + | 0.363693i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.791222 | − | 0.287981i | 0.164981 | − | 0.0600483i | −0.258209 | − | 0.966089i | \(-0.583132\pi\) |
0.423190 | + | 0.906041i | \(0.360910\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.339001 | − | 1.92257i | −0.0678002 | − | 0.384514i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.13073 | + | 0.821942i | 0.987410 | + | 0.158183i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0889744 | − | 0.504599i | −0.0165221 | − | 0.0937016i | 0.975432 | − | 0.220302i | \(-0.0707044\pi\) |
−0.991954 | + | 0.126601i | \(0.959593\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.770551 | + | 0.280458i | −0.138395 | + | 0.0503717i | −0.410289 | − | 0.911956i | \(-0.634572\pi\) |
0.271894 | + | 0.962327i | \(0.412350\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.73570 | − | 1.30634i | 0.302146 | − | 0.227404i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.14666 | − | 3.71812i | −0.362852 | − | 0.628478i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.30403 | + | 2.25865i | −0.214381 | + | 0.371319i | −0.953081 | − | 0.302715i | \(-0.902107\pi\) |
0.738700 | + | 0.674035i | \(0.235440\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.77695 | + | 7.67616i | −0.284540 | + | 1.22917i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.41572 | + | 8.02895i | −0.221099 | + | 1.25391i | 0.648906 | + | 0.760869i | \(0.275227\pi\) |
−0.870005 | + | 0.493044i | \(0.835884\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.31478 | + | 2.78143i | −0.505500 | + | 0.424165i | −0.859542 | − | 0.511065i | \(-0.829251\pi\) |
0.354042 | + | 0.935229i | \(0.384807\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.63373 | − | 3.77173i | −0.541684 | − | 0.562257i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.98256 | − | 1.81351i | −0.726782 | − | 0.264527i | −0.0479798 | − | 0.998848i | \(-0.515278\pi\) |
−0.678802 | + | 0.734321i | \(0.737501\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.729356 | − | 0.612002i | −0.104194 | − | 0.0874289i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.27625 | − | 9.65211i | 0.878851 | − | 1.35157i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.4841 | −1.44010 | −0.720052 | − | 0.693920i | \(-0.755882\pi\) | ||||
−0.720052 | + | 0.693920i | \(0.755882\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.18959 | −0.295244 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.195693 | + | 0.384630i | 0.0259202 | + | 0.0509456i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.30289 | + | 1.93235i | 0.299810 | + | 0.251571i | 0.780265 | − | 0.625449i | \(-0.215084\pi\) |
−0.480455 | + | 0.877019i | \(0.659529\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.70930 | − | 0.986103i | −0.346890 | − | 0.126258i | 0.162699 | − | 0.986676i | \(-0.447980\pi\) |
−0.509589 | + | 0.860418i | \(0.670202\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.62725 | + | 3.24201i | 0.834955 | + | 0.408455i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.08365 | − | 5.10479i | 0.754584 | − | 0.633171i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.75146 | + | 9.93303i | −0.213975 | + | 1.21351i | 0.668701 | + | 0.743531i | \(0.266851\pi\) |
−0.882676 | + | 0.469982i | \(0.844261\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.39492 | − | 0.425568i | 0.167928 | − | 0.0512324i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.0447378 | − | 0.0774882i | 0.00530940 | − | 0.00919615i | −0.863358 | − | 0.504591i | \(-0.831643\pi\) |
0.868668 | + | 0.495395i | \(0.164977\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.66057 | + | 4.60824i | 0.311396 | + | 0.539354i | 0.978665 | − | 0.205463i | \(-0.0658701\pi\) |
−0.667269 | + | 0.744817i | \(0.732537\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.410103 | − | 3.35640i | −0.0473546 | − | 0.387563i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.89841 | − | 1.05493i | 0.330304 | − | 0.120221i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.829503 | − | 4.70435i | −0.0933264 | − | 0.529280i | −0.995247 | − | 0.0973792i | \(-0.968954\pi\) |
0.901921 | − | 0.431901i | \(-0.142157\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.79889 | + | 1.89198i | 0.977654 | + | 0.210220i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.39625 | − | 7.91851i | −0.153258 | − | 0.869169i | −0.960361 | − | 0.278759i | \(-0.910077\pi\) |
0.807103 | − | 0.590410i | \(-0.201034\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.9047 | + | 3.96899i | −1.18278 | + | 0.430497i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.107636 | − | 0.880922i | −0.0115398 | − | 0.0944448i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.35189 | − | 5.80564i | −0.355299 | − | 0.615396i | 0.631870 | − | 0.775074i | \(-0.282288\pi\) |
−0.987169 | + | 0.159678i | \(0.948954\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.59359 | + | 9.68839i | −0.586368 | + | 1.01562i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.35847 | + | 0.414450i | −0.140867 | + | 0.0429765i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0755324 | − | 0.428365i | 0.00774946 | − | 0.0439494i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.20603 | − | 3.52928i | 0.427057 | − | 0.358344i | −0.403783 | − | 0.914855i | \(-0.632305\pi\) |
0.830840 | + | 0.556511i | \(0.187860\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.12185 | − | 2.10036i | 0.313758 | − | 0.211094i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.70360 | − | 1.71197i | −0.468025 | − | 0.170347i | 0.0972322 | − | 0.995262i | \(-0.469001\pi\) |
−0.565258 | + | 0.824914i | \(0.691223\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.90079 | − | 7.46865i | −0.877021 | − | 0.735908i | 0.0885431 | − | 0.996072i | \(-0.471779\pi\) |
−0.965564 | + | 0.260164i | \(0.916223\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.37208 | − | 6.62774i | −0.329081 | − | 0.646801i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.4581 | −1.88109 | −0.940544 | − | 0.339673i | \(-0.889684\pi\) | ||||
−0.940544 | + | 0.339673i | \(0.889684\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.31515 | 0.604881 | 0.302441 | − | 0.953168i | \(-0.402199\pi\) | ||||
0.302441 | + | 0.953168i | \(0.402199\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.46253 | + | 3.78707i | −0.233733 | + | 0.359453i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.29775 | − | 4.44534i | −0.498371 | − | 0.418183i | 0.358644 | − | 0.933474i | \(-0.383239\pi\) |
−0.857015 | + | 0.515292i | \(0.827684\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.38131 | − | 0.502754i | −0.128807 | − | 0.0468821i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.77713 | + | 13.1140i | −0.349196 | + | 1.21239i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.5226 | − | 10.5077i | 1.14794 | − | 0.963236i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.63697 | + | 9.28373i | −0.148816 | + | 0.843976i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.18467 | + | 13.7573i | −0.287152 | + | 1.24045i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.06855 | + | 10.5110i | −0.542788 | + | 0.940136i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.01162 | + | 10.4124i | 0.533445 | + | 0.923954i | 0.999237 | + | 0.0390598i | \(0.0124363\pi\) |
−0.465792 | + | 0.884894i | \(0.654230\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.98830 | + | 4.50697i | −0.527240 | + | 0.396817i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.2354 | + | 4.81728i | −1.15638 | + | 0.420888i | −0.847803 | − | 0.530311i | \(-0.822075\pi\) |
−0.308577 | + | 0.951199i | \(0.599853\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.106401 | + | 0.603428i | 0.00922610 | + | 0.0523238i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.93923 | − | 6.85678i | −0.511167 | − | 0.590138i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.392122 | + | 2.22383i | 0.0335012 | + | 0.189995i | 0.996966 | − | 0.0778409i | \(-0.0248026\pi\) |
−0.963465 | + | 0.267836i | \(0.913692\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.49414 | + | 2.72764i | −0.635644 | + | 0.231356i | −0.639686 | − | 0.768636i | \(-0.720936\pi\) |
0.00404179 | + | 0.999992i | \(0.498713\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.45172 | − | 3.59343i | −0.711763 | − | 0.302621i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.85273 | + | 4.94107i | 0.238557 | + | 0.413193i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.447256 | + | 0.774670i | −0.0371426 | + | 0.0643328i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.20541 | − | 1.12539i | −0.0994204 | − | 0.0928208i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.0185697 | + | 0.105314i | −0.00152129 | + | 0.00862764i | −0.985559 | − | 0.169333i | \(-0.945839\pi\) |
0.984038 | + | 0.177960i | \(0.0569499\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.5196 | − | 13.0225i | 1.26297 | − | 1.05976i | 0.267609 | − | 0.963528i | \(-0.413767\pi\) |
0.995359 | − | 0.0962282i | \(-0.0306779\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.7404 | − | 16.1192i | 0.949152 | − | 1.30316i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.34522 | + | 0.489620i | 0.108051 | + | 0.0393272i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.8953 | − | 13.3377i | −1.26858 | − | 1.06447i | −0.994712 | − | 0.102701i | \(-0.967252\pi\) |
−0.273871 | − | 0.961767i | \(-0.588304\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.1336 | − | 0.961071i | −1.43809 | − | 0.0762179i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.07069 | 0.163193 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.1346 | 1.57706 | 0.788531 | − | 0.614995i | \(-0.210842\pi\) | ||||
0.788531 | + | 0.614995i | \(0.210842\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.78716 | − | 0.200718i | −0.294830 | − | 0.0156259i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.2156 | + | 12.7674i | 1.17742 | + | 0.987974i | 0.999993 | + | 0.00383999i | \(0.00122231\pi\) |
0.177429 | + | 0.984134i | \(0.443222\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.22968 | − | 2.63139i | −0.556130 | − | 0.202415i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.303217 | + | 0.683205i | 0.0231876 | + | 0.0522460i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.4975 | − | 12.1648i | 1.10222 | − | 0.924875i | 0.104650 | − | 0.994509i | \(-0.466628\pi\) |
0.997573 | + | 0.0696342i | \(0.0221832\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.833686 | − | 4.72807i | 0.0630208 | − | 0.357409i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.80599 | + | 3.55334i | 0.286075 | + | 0.267085i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.45683 | − | 9.45151i | 0.407863 | − | 0.706439i | −0.586787 | − | 0.809741i | \(-0.699608\pi\) |
0.994650 | + | 0.103302i | \(0.0329409\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.97393 | + | 15.5433i | 0.667027 | + | 1.15532i | 0.978731 | + | 0.205146i | \(0.0657668\pi\) |
−0.311704 | + | 0.950179i | \(0.600900\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.59567 | − | 1.95395i | −0.339721 | − | 0.144440i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.27853 | − | 1.55726i | 0.314564 | − | 0.114492i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.44770 | − | 8.21031i | −0.105866 | − | 0.600397i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.1654 | + | 6.21498i | 0.812167 | + | 0.452073i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.68261 | + | 26.5564i | 0.338822 | + | 1.92155i | 0.385641 | + | 0.922649i | \(0.373980\pi\) |
−0.0468192 | + | 0.998903i | \(0.514908\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.1202 | − | 5.86729i | 1.16036 | − | 0.422337i | 0.311135 | − | 0.950366i | \(-0.399291\pi\) |
0.849226 | + | 0.528029i | \(0.177069\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.9904 | − | 8.27167i | 0.787037 | − | 0.592347i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.25612 | − | 2.17567i | −0.0894951 | − | 0.155010i | 0.817803 | − | 0.575499i | \(-0.195192\pi\) |
−0.907298 | + | 0.420489i | \(0.861859\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.26942 | − | 16.0551i | 0.657092 | − | 1.13812i | −0.324273 | − | 0.945964i | \(-0.605120\pi\) |
0.981365 | − | 0.192153i | \(-0.0615470\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.93992 | + | 17.0198i | −0.277901 | + | 1.20049i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.218810 | − | 1.24093i | 0.0153574 | − | 0.0870964i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.9032 | − | 9.14885i | 0.761510 | − | 0.638983i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.45169 | − | 0.608202i | 0.170404 | − | 0.0422730i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.293649 | + | 0.106880i | 0.0203121 | + | 0.00739301i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.82761 | + | 2.37264i | 0.194661 | + | 0.163340i | 0.734908 | − | 0.678166i | \(-0.237225\pi\) |
−0.540248 | + | 0.841506i | \(0.681670\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.0844829 | − | 0.129924i | 0.00578867 | − | 0.00890226i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.55427 | 0.515197 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.01659 | −0.136895 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.17935 | + | 8.21441i | 0.282414 | + | 0.555079i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.1638 | + | 19.4367i | 1.55816 | + | 1.30746i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.9601 | − | 7.26487i | −1.33662 | − | 0.486491i | −0.427876 | − | 0.903837i | \(-0.640738\pi\) |
−0.908748 | + | 0.417346i | \(0.862960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.401646 | − | 5.84289i | −0.0267764 | − | 0.389526i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.9851 | − | 9.21761i | 0.729108 | − | 0.611794i | −0.200781 | − | 0.979636i | \(-0.564348\pi\) |
0.929888 | + | 0.367842i | \(0.119903\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.93219 | − | 16.6293i | 0.193765 | − | 1.09889i | −0.720403 | − | 0.693556i | \(-0.756043\pi\) |
0.914167 | − | 0.405337i | \(-0.132846\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.10985 | − | 1.55894i | 0.336204 | − | 0.102571i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.79972 | + | 4.84926i | −0.183416 | + | 0.317686i | −0.943042 | − | 0.332675i | \(-0.892049\pi\) |
0.759626 | + | 0.650361i | \(0.225382\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.62837 | + | 8.01658i | 0.301922 | + | 0.522944i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.00348 | − | 8.21279i | −0.0651833 | − | 0.533478i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.95620 | + | 1.80391i | −0.320590 | + | 0.116685i | −0.497302 | − | 0.867577i | \(-0.665676\pi\) |
0.176712 | + | 0.984263i | \(0.443454\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.54590 | − | 8.76723i | −0.0995801 | − | 0.564747i | −0.993247 | − | 0.116017i | \(-0.962987\pi\) |
0.893667 | − | 0.448730i | \(-0.148124\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.0453 | + | 4.07900i | 0.965158 | + | 0.261668i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.288634 | + | 1.63692i | 0.0184401 | + | 0.104579i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.06507 | + | 0.387652i | −0.0677685 | + | 0.0246657i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.68910 | − | 13.8240i | −0.107042 | − | 0.876062i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.89010 | − | 6.73786i | −0.245541 | − | 0.425290i | 0.716742 | − | 0.697338i | \(-0.245632\pi\) |
−0.962284 | + | 0.272048i | \(0.912299\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.528024 | − | 0.914565i | 0.0331966 | − | 0.0574982i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −19.2249 | + | 5.86523i | −1.20391 | + | 0.367295i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.54877 | + | 20.1261i | −0.221366 | + | 1.25543i | 0.648145 | + | 0.761517i | \(0.275545\pi\) |
−0.869511 | + | 0.493913i | \(0.835566\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.91331 | + | 4.12275i | −0.305298 | + | 0.256175i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.105416 | − | 1.53353i | −0.00652510 | − | 0.0949231i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.5996 | + | 3.85792i | 0.653596 | + | 0.237890i | 0.647469 | − | 0.762092i | \(-0.275827\pi\) |
0.00612723 | + | 0.999981i | \(0.498050\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.0209 | + | 11.7650i | 0.861299 | + | 0.722716i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.26530 | − | 10.3488i | −0.322231 | − | 0.633338i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.307761 | −0.0187645 | −0.00938226 | − | 0.999956i | \(-0.502987\pi\) | ||||
−0.00938226 | + | 0.999956i | \(0.502987\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.22251 | 0.135008 | 0.0675040 | − | 0.997719i | \(-0.478496\pi\) | ||||
0.0675040 | + | 0.997719i | \(0.478496\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.5629 | + | 16.2445i | −0.639298 | + | 0.983162i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.87567 | − | 1.57387i | −0.113107 | − | 0.0949080i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.9228 | + | 7.97924i | 1.31721 | + | 0.479426i | 0.902564 | − | 0.430556i | \(-0.141683\pi\) |
0.414648 | + | 0.909982i | \(0.363905\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.38764 | + | 0.592313i | −0.142944 | + | 0.0354608i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.53502 | − | 4.64443i | 0.330192 | − | 0.277064i | −0.462586 | − | 0.886574i | \(-0.653078\pi\) |
0.792778 | + | 0.609511i | \(0.208634\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.23643 | + | 7.01212i | −0.0734979 | + | 0.416827i | 0.925753 | + | 0.378129i | \(0.123432\pi\) |
−0.999251 | + | 0.0386985i | \(0.987679\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.169911 | − | 0.733987i | 0.0100646 | − | 0.0434776i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.0249 | + | 17.3636i | −0.591751 | + | 1.02494i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.5924 | − | 23.5428i | −0.799555 | − | 1.38487i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.59837 | − | 5.71875i | 0.445424 | − | 0.335239i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.519166 | + | 0.188961i | −0.0303300 | + | 0.0110392i | −0.357141 | − | 0.934051i | \(-0.616248\pi\) |
0.326811 | + | 0.945090i | \(0.394026\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.911339 | − | 5.16846i | −0.0530602 | − | 0.300919i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.59216 | − | 3.34665i | 0.324490 | − | 0.194192i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.665122 | + | 3.77210i | 0.0384650 | + | 0.218146i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.99975 | + | 3.63961i | −0.576376 | + | 0.209784i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.97852 | − | 3.39224i | −0.458354 | − | 0.194879i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.51670 | + | 4.35906i | 0.144106 | + | 0.249599i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.36438 | − | 5.82728i | 0.192015 | − | 0.332580i | −0.753903 | − | 0.656986i | \(-0.771831\pi\) |
0.945918 | + | 0.324406i | \(0.105164\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.7104 | − | 13.7339i | −0.836844 | − | 0.781293i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.67825 | + | 15.1891i | −0.151870 | + | 0.861297i | 0.809722 | + | 0.586814i | \(0.199618\pi\) |
−0.961592 | + | 0.274483i | \(0.911493\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.0487 | + | 15.1446i | −1.02017 | + | 0.856025i | −0.989649 | − | 0.143509i | \(-0.954162\pi\) |
−0.0305223 | + | 0.999534i | \(0.509717\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.22486 | − | 11.7726i | −0.294388 | − | 0.663311i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.81469 | − | 2.48034i | −0.382751 | − | 0.139310i | 0.143477 | − | 0.989654i | \(-0.454172\pi\) |
−0.526228 | + | 0.850344i | \(0.676394\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.492289 | − | 0.413079i | −0.0275629 | − | 0.0231280i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −33.6552 | − | 1.78371i | −1.87845 | − | 0.0995571i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.65618 | 0.0921525 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.88074 | 0.492615 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.9228 | + | 0.578905i | 0.604034 | + | 0.0320135i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.98903 | − | 8.38179i | −0.550713 | − | 0.462103i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.2835 | + | 9.93037i | 1.49964 | + | 0.545823i | 0.955966 | − | 0.293477i | \(-0.0948124\pi\) |
0.543669 | + | 0.839300i | \(0.317035\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.60641 | + | 6.32447i | −0.252430 | + | 0.346579i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.4889 | − | 11.3185i | 0.736976 | − | 0.618396i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.201275 | + | 1.14149i | −0.0109641 | + | 0.0621807i | −0.989799 | − | 0.142471i | \(-0.954495\pi\) |
0.978835 | + | 0.204652i | \(0.0656063\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.75561 | − | 8.17441i | −0.475540 | − | 0.443973i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.514230 | + | 0.890672i | −0.0278471 | + | 0.0482326i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.77810 | − | 16.9362i | −0.527968 | − | 0.914467i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.34305 | − | 0.996198i | −0.126146 | − | 0.0536335i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.53452 | − | 2.01440i | 0.297108 | − | 0.108139i | −0.189165 | − | 0.981945i | \(-0.560578\pi\) |
0.486273 | + | 0.873807i | \(0.338356\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.31237 | − | 30.1279i | −0.284364 | − | 1.61271i | −0.707547 | − | 0.706666i | \(-0.750198\pi\) |
0.423183 | − | 0.906044i | \(-0.360913\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.73516 | + | 22.3360i | −0.412872 | + | 1.19221i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.41826 | + | 36.3997i | 0.341609 | + | 1.93736i | 0.348294 | + | 0.937385i | \(0.386761\pi\) |
−0.00668455 | + | 0.999978i | \(0.502128\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.146785 | + | 0.0534254i | −0.00779054 | + | 0.00283553i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 22.6225 | − | 17.0264i | 1.19731 | − | 0.901131i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.1880 | − | 22.8423i | −0.696037 | − | 1.20557i | −0.969830 | − | 0.243783i | \(-0.921611\pi\) |
0.273792 | − | 0.961789i | \(-0.411722\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.46896 | − | 16.4007i | 0.498366 | − | 0.863196i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.68238 | + | 15.9073i | −0.193275 | + | 0.834917i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.61312 | − | 9.14845i | 0.0844345 | − | 0.478852i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.66636 | − | 7.27194i | 0.452380 | − | 0.379592i | −0.387938 | − | 0.921685i | \(-0.626813\pi\) |
0.840318 | + | 0.542093i | \(0.182368\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.76941 | + | 23.5030i | −0.352401 | + | 1.22352i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.2281 | − | 8.81831i | −1.25786 | − | 0.457824i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.47682 | + | 3.75650i | 0.231801 | + | 0.194504i | 0.751289 | − | 0.659974i | \(-0.229433\pi\) |
−0.519487 | + | 0.854478i | \(0.673877\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.4599 | + | 17.6238i | −0.591784 | + | 0.910092i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.33085 | 0.120045 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.3265 | −1.24957 | −0.624783 | − | 0.780798i | \(-0.714813\pi\) | ||||
−0.624783 | + | 0.780798i | \(0.714813\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.44334 | + | 18.5607i | 0.483797 | + | 0.950892i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.92326 | + | 2.45291i | 0.149372 | + | 0.125338i | 0.714411 | − | 0.699726i | \(-0.246695\pi\) |
−0.565039 | + | 0.825064i | \(0.691139\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.06000 | − | 1.84169i | −0.257881 | − | 0.0938612i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.7707 | + | 7.24642i | −0.547503 | + | 0.368356i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.30534 | − | 6.96901i | 0.421097 | − | 0.353343i | −0.407483 | − | 0.913213i | \(-0.633593\pi\) |
0.828580 | + | 0.559870i | \(0.189149\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.971896 | − | 5.51189i | 0.0491509 | − | 0.278748i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −23.3338 | + | 7.11881i | −1.17704 | + | 0.359096i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.16974 | + | 7.22221i | −0.209802 | + | 0.363389i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.25461 | + | 9.10124i | 0.263721 | + | 0.456778i | 0.967228 | − | 0.253910i | \(-0.0817168\pi\) |
−0.703507 | + | 0.710689i | \(0.748383\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.128717 | + | 1.05346i | 0.00644392 | + | 0.0527388i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.4992 | + | 4.91332i | −0.674119 | + | 0.245359i | −0.656320 | − | 0.754482i | \(-0.727888\pi\) |
−0.0177987 | + | 0.999842i | \(0.505666\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.647746 | − | 3.67355i | −0.0322665 | − | 0.182993i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.64407 | − | 12.4041i | −0.479218 | − | 0.616364i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.568014 | + | 3.22137i | 0.0281554 | + | 0.159677i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.6159 | + | 6.04769i | −0.821603 | + | 0.299039i | −0.718408 | − | 0.695622i | \(-0.755129\pi\) |
−0.103195 | + | 0.994661i | \(0.532907\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.474366 | + | 3.88234i | 0.0233988 | + | 0.191502i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.69650 | + | 6.40252i | 0.181893 | + | 0.315047i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.01864 | + | 12.1566i | −0.344532 | + | 0.596746i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.2121 | + | 4.03081i | −0.646998 | + | 0.197390i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.58606 | + | 8.99500i | −0.0774842 | + | 0.439435i | 0.921243 | + | 0.388988i | \(0.127175\pi\) |
−0.998727 | + | 0.0504461i | \(0.983936\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.5344 | − | 15.5522i | 0.903310 | − | 0.757967i | −0.0675243 | − | 0.997718i | \(-0.521510\pi\) |
0.970835 | + | 0.239750i | \(0.0770656\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.2889 | − | 6.99004i | −0.694749 | − | 0.339867i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.1942 | − | 4.43832i | −0.591505 | − | 0.215290i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.43159 | − | 4.55764i | −0.262853 | − | 0.220560i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.48120 | + | 8.80769i | 0.216354 | + | 0.425239i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.5332 | 1.42256 | 0.711282 | − | 0.702907i | \(-0.248115\pi\) | ||||
0.711282 | + | 0.702907i | \(0.248115\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.669754 | 0.0321863 | 0.0160932 | − | 0.999870i | \(-0.494877\pi\) | ||||
0.0160932 | + | 0.999870i | \(0.494877\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.844598 | + | 1.29889i | −0.0404954 | + | 0.0622769i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.160708 | + | 0.134850i | 0.00768772 | + | 0.00645076i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.96599 | − | 2.17144i | −0.284741 | − | 0.103637i | 0.195701 | − | 0.980664i | \(-0.437302\pi\) |
−0.480442 | + | 0.877026i | \(0.659524\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.98174 | − | 2.05700i | −0.0943685 | − | 0.0979526i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.7618 | + | 9.86931i | −0.558819 | + | 0.468905i | −0.877914 | − | 0.478818i | \(-0.841066\pi\) |
0.319095 | + | 0.947723i | \(0.396621\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.03227 | + | 11.5256i | −0.0963387 | + | 0.546364i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.0417726 | + | 0.180451i | −0.00197577 | + | 0.00853503i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.0199 | − | 27.7473i | 0.756027 | − | 1.30948i | −0.188836 | − | 0.982009i | \(-0.560471\pi\) |
0.944862 | − | 0.327468i | \(-0.106195\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.11268 | + | 8.85543i | 0.240747 | + | 0.416986i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 28.0368 | − | 21.1013i | 1.31729 | − | 0.991428i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 18.3526 | − | 6.67980i | 0.860384 | − | 0.313154i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.32849 | + | 18.8768i | 0.155700 | + | 0.883021i | 0.958143 | + | 0.286291i | \(0.0924225\pi\) |
−0.802442 | + | 0.596730i | \(0.796466\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 21.7840 | − | 26.8039i | 1.01679 | − | 1.25110i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.906494 | − | 5.14098i | −0.0422196 | − | 0.239440i | 0.956394 | − | 0.292080i | \(-0.0943474\pi\) |
−0.998614 | + | 0.0526405i | \(0.983236\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.59502 | − | 0.580541i | 0.0741271 | − | 0.0269800i | −0.304690 | − | 0.952451i | \(-0.598553\pi\) |
0.378818 | + | 0.925471i | \(0.376331\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.28184 | + | 0.970173i | 0.105818 | + | 0.0449907i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.84136 | + | 17.0457i | 0.455404 | + | 0.788783i | 0.998711 | − | 0.0507511i | \(-0.0161615\pi\) |
−0.543307 | + | 0.839534i | \(0.682828\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.4023 | + | 21.4814i | −0.572685 | + | 0.991920i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −26.2702 | − | 24.5264i | −1.21047 | − | 1.13012i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.942416 | + | 5.34471i | −0.0433324 | + | 0.245750i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.372611 | − | 0.312658i | 0.0170966 | − | 0.0143457i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −31.2761 | − | 3.32458i | −1.43204 | − | 0.152222i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.4892 | − | 10.0053i | −1.25601 | − | 0.457152i | −0.373585 | − | 0.927596i | \(-0.621872\pi\) |
−0.882430 | + | 0.470444i | \(0.844094\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.08847 | − | 7.62613i | −0.414398 | − | 0.347722i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.58151 | + | 0.189818i | 0.162964 | + | 0.00863704i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.58538 | −0.435250 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.5056 | 0.929199 | 0.464600 | − | 0.885521i | \(-0.346198\pi\) | ||||
0.464600 | + | 0.885521i | \(0.346198\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 34.8252 | + | 1.84572i | 1.57485 | + | 0.0834664i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.4265 | − | 11.2661i | −0.605927 | − | 0.508433i | 0.287417 | − | 0.957805i | \(-0.407203\pi\) |
−0.893345 | + | 0.449372i | \(0.851648\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.20050 | − | 1.16489i | −0.144143 | − | 0.0524638i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.53197 | − | 0.694333i | −0.293590 | − | 0.0312080i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.168562 | − | 0.141441i | 0.00756106 | − | 0.00634448i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.31772 | − | 18.8157i | 0.148522 | − | 0.842307i | −0.815950 | − | 0.578122i | \(-0.803786\pi\) |
0.964472 | − | 0.264185i | \(-0.0851031\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.1469 | + | 23.4777i | 1.12348 | + | 1.04890i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.48381 | + | 9.49824i | −0.244511 | + | 0.423506i | −0.961994 | − | 0.273070i | \(-0.911961\pi\) |
0.717483 | + | 0.696576i | \(0.245294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.36924 | + | 7.56774i | 0.194429 | + | 0.336760i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.2634 | − | 5.21405i | −0.544637 | − | 0.231564i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.6993 | − | 6.80598i | 0.828831 | − | 0.301670i | 0.107452 | − | 0.994210i | \(-0.465731\pi\) |
0.721379 | + | 0.692540i | \(0.243509\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.27236 | + | 12.8872i | 0.100523 | + | 0.570096i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.461822 | + | 1.20948i | 0.0203899 | + | 0.0534000i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.52238 | + | 19.9764i | 0.155215 | + | 0.880266i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.24920 | + | 2.27452i | −0.274839 | + | 0.100033i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 26.1903 | − | 19.7116i | 1.14963 | − | 0.865243i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.5583 | − | 30.4119i | −0.769244 | − | 1.33237i | −0.937973 | − | 0.346708i | \(-0.887300\pi\) |
0.168729 | − | 0.985662i | \(-0.446034\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.12269 | + | 12.3369i | −0.311453 | + | 0.539453i | −0.978677 | − | 0.205404i | \(-0.934149\pi\) |
0.667224 | + | 0.744857i | \(0.267482\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.87538 | − | 8.10136i | 0.0818484 | − | 0.353572i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.946505 | + | 5.36789i | −0.0412304 | + | 0.233829i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.0759 | + | 14.3284i | −0.742431 | + | 0.622974i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.25719 | + | 6.49483i | 0.271539 | + | 0.281852i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −34.8507 | − | 12.6846i | −1.50955 | − | 0.549433i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.0223 | + | 21.8353i | 1.12504 | + | 0.944023i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.3047 | − | 15.8473i | 0.444679 | − | 0.683862i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.19414 | −0.0514354 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.2368 | −0.569094 | −0.284547 | − | 0.958662i | \(-0.591843\pi\) | ||||
−0.284547 | + | 0.958662i | \(0.591843\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.0967 | + | 27.7067i | 0.604946 | + | 1.18901i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.44557 | − | 7.08667i | −0.361768 | − | 0.303560i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.3216 | − | 5.57661i | −0.655105 | − | 0.238439i | −0.00698326 | − | 0.999976i | \(-0.502223\pi\) |
−0.648121 | + | 0.761537i | \(0.724445\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.76965 | − | 3.80087i | −0.331601 | − | 0.162217i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0977958 | − | 0.0820605i | 0.00416624 | − | 0.00349589i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.03995 | − | 11.5692i | 0.0867476 | − | 0.491970i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.54300 | − | 2.30126i | 0.320183 | − | 0.0976831i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.4486 | + | 26.7577i | −0.654577 | + | 1.13376i | 0.327422 | + | 0.944878i | \(0.393820\pi\) |
−0.982000 | + | 0.188883i | \(0.939513\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.84215 | − | 17.0471i | −0.416279 | − | 0.721016i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.75134 | − | 14.3335i | −0.0739417 | − | 0.605159i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.1612 | − | 9.15791i | 1.06042 | − | 0.385960i | 0.247832 | − | 0.968803i | \(-0.420282\pi\) |
0.812585 | + | 0.582843i | \(0.198060\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.09652 | + | 11.8900i | 0.0882013 | + | 0.500214i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.7423 | + | 11.7731i | 0.787102 | + | 0.494423i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.30985 | + | 18.7711i | 0.138756 | + | 0.786924i | 0.972170 | + | 0.234275i | \(0.0752717\pi\) |
−0.833414 | + | 0.552649i | \(0.813617\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.6420 | + | 6.42116i | −0.738294 | + | 0.268717i | −0.683671 | − | 0.729790i | \(-0.739618\pi\) |
−0.0546227 | + | 0.998507i | \(0.517396\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.66474 | + | 46.3618i | 0.236648 | + | 1.93679i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.821889 | − | 1.42355i | −0.0342751 | − | 0.0593663i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.42981 | − | 4.20856i | 0.101154 | − | 0.175204i | −0.811006 | − | 0.585038i | \(-0.801080\pi\) |
0.912161 | + | 0.409833i | \(0.134413\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 28.4198 | − | 8.67047i | 1.18109 | − | 0.360332i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.43371 | − | 19.4736i | 0.142454 | − | 0.807899i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.0730 | + | 8.45221i | −0.417179 | + | 0.350055i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.7675 | − | 13.2994i | 0.817284 | − | 0.549862i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.8194 | − | 11.2174i | −1.27205 | − | 0.462990i | −0.384257 | − | 0.923226i | \(-0.625542\pi\) |
−0.887796 | + | 0.460236i | \(0.847765\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.156510 | − | 0.131327i | −0.00644887 | − | 0.00541125i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.97318 | − | 3.87824i | −0.0811657 | − | 0.159529i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.3446 | 0.712258 | 0.356129 | − | 0.934437i | \(-0.384096\pi\) | ||||
0.356129 | + | 0.934437i | \(0.384096\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28.5384 | −1.16996 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.5044 | − | 26.9196i | 0.716406 | − | 1.10174i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.6975 | − | 15.6891i | −0.763961 | − | 0.641039i | 0.175194 | − | 0.984534i | \(-0.443945\pi\) |
−0.939155 | + | 0.343495i | \(0.888389\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.39563 | − | 2.69179i | −0.301674 | − | 0.109800i | 0.186748 | − | 0.982408i | \(-0.440205\pi\) |
−0.488422 | + | 0.872607i | \(0.662427\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.37478 | + | 29.0768i | −0.341047 | + | 1.18410i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.6071 | − | 10.5786i | 0.512553 | − | 0.430083i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.77772 | − | 10.0819i | 0.0721553 | − | 0.409213i | −0.927241 | − | 0.374466i | \(-0.877826\pi\) |
0.999396 | − | 0.0347476i | \(-0.0110627\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.492214 | − | 2.12629i | 0.0199455 | − | 0.0861615i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.0602 | − | 20.8889i | 0.487905 | − | 0.845076i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.11753 | − | 1.93563i | −0.0451368 | − | 0.0781792i | 0.842574 | − | 0.538580i | \(-0.181039\pi\) |
−0.887711 | + | 0.460401i | \(0.847706\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 19.6970 | − | 14.8246i | 0.794262 | − | 0.597784i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.9267 | + | 11.6204i | −1.28532 | + | 0.467818i | −0.892188 | − | 0.451664i | \(-0.850831\pi\) |
−0.393132 | + | 0.919482i | \(0.628609\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.01079 | + | 28.4176i | 0.201401 | + | 1.14220i | 0.903004 | + | 0.429632i | \(0.141357\pi\) |
−0.701604 | + | 0.712567i | \(0.747532\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.29625 | − | 0.827216i | 0.172403 | − | 0.0331950i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.86280 | − | 16.2358i | −0.114696 | − | 0.650472i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.7385 | − | 3.90849i | 0.429540 | − | 0.156340i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.498105 | + | 0.211780i | 0.0198924 | + | 0.00845768i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.66811 | + | 15.0136i | 0.345620 | + | 0.598632i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.57039 | + | 2.71999i | −0.0625162 | + | 0.108281i | −0.895590 | − | 0.444881i | \(-0.853246\pi\) |
0.833073 | + | 0.553163i | \(0.186579\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.67320 | + | 4.36299i | 0.185743 | + | 0.173413i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.64488 | − | 20.6711i | 0.144643 | − | 0.820309i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.31786 | − | 2.78402i | 0.131458 | − | 0.110307i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.158034 | − | 0.216976i | 0.00625171 | − | 0.00858342i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.9034 | + | 10.8839i | 1.18111 | + | 0.429890i | 0.856595 | − | 0.515989i | \(-0.172576\pi\) |
0.324518 | + | 0.945879i | \(0.394798\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.84142 | + | 8.25794i | 0.388108 | + | 0.325661i | 0.815876 | − | 0.578228i | \(-0.196255\pi\) |
−0.427768 | + | 0.903889i | \(0.640700\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.0660 | + | 0.692495i | 0.514475 | + | 0.0272669i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.2444 | −1.11040 | −0.555200 | − | 0.831717i | \(-0.687358\pi\) | ||||
−0.555200 | + | 0.831717i | \(0.687358\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.77042 | 0.148002 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.48794 | − | 0.184859i | −0.136703 | − | 0.00724521i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.9099 | + | 16.7064i | 0.779134 | + | 0.653771i | 0.943030 | − | 0.332707i | \(-0.107962\pi\) |
−0.163897 | + | 0.986477i | \(0.552406\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.1062 | + | 8.40995i | 0.902832 | + | 0.328604i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.47569 | + | 14.5910i | 0.252641 | + | 0.569248i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.4774 | − | 30.6081i | 1.42096 | − | 1.19232i | 0.470131 | − | 0.882597i | \(-0.344207\pi\) |
0.950826 | − | 0.309727i | \(-0.100238\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.152204 | + | 0.863192i | −0.00592005 | + | 0.0335743i | −0.987625 | − | 0.156836i | \(-0.949871\pi\) |
0.981705 | + | 0.190410i | \(0.0609818\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 38.2829 | + | 35.7416i | 1.48678 | + | 1.38809i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.534854 | − | 0.926394i | 0.0207407 | − | 0.0359240i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.215714 | − | 0.373627i | −0.00835246 | − | 0.0144669i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −33.8574 | − | 14.3952i | −1.30900 | − | 0.556551i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.39803 | + | 1.23678i | −0.131180 | + | 0.0477455i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.48393 | + | 36.7722i | 0.249937 | + | 1.41746i | 0.808742 | + | 0.588164i | \(0.200149\pi\) |
−0.558805 | + | 0.829299i | \(0.688740\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.159082 | − | 10.1428i | −0.00612306 | − | 0.390397i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.38231 | − | 13.5107i | −0.0915596 | − | 0.519260i | −0.995747 | − | 0.0921251i | \(-0.970634\pi\) |
0.904188 | − | 0.427135i | \(-0.140477\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.6884 | − | 4.61819i | 0.486935 | − | 0.177230i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.8451 | − | 14.9360i | 0.760465 | − | 0.572348i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.9943 | + | 43.2914i | 0.956381 | + | 1.65650i | 0.731175 | + | 0.682190i | \(0.238972\pi\) |
0.225206 | + | 0.974311i | \(0.427694\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.97112 | − | 3.41407i | 0.0753125 | − | 0.130445i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.59598 | − | 28.4936i | 0.251652 | − | 1.08710i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.28172 | − | 46.9680i | 0.315509 | − | 1.78934i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.2434 | + | 15.3080i | −0.694011 | + | 0.582345i | −0.920063 | − | 0.391771i | \(-0.871863\pi\) |
0.226052 | + | 0.974115i | \(0.427418\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.98103 | − | 2.22797i | 0.341161 | − | 0.0846335i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.0832 | + | 4.76188i | 0.496273 | + | 0.180629i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 41.5144 | + | 34.8347i | 1.57247 | + | 1.31946i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.28700 | + | 8.13075i | −0.199973 | + | 0.307533i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.4493 | 1.30113 | 0.650565 | − | 0.759450i | \(-0.274532\pi\) | ||||
0.650565 | + | 0.759450i | \(0.274532\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.649815 | −0.0245082 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.27047 | + | 14.2899i | 0.273822 | + | 0.538190i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.42975 | − | 7.91250i | −0.354642 | − | 0.297580i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.5871 | − | 5.30927i | −0.547830 | − | 0.199394i | 0.0532520 | − | 0.998581i | \(-0.483041\pi\) |
−0.601082 | + | 0.799187i | \(0.705264\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.982789 | − | 14.2970i | −0.0368575 | − | 0.536180i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.528911 | + | 0.443809i | −0.0198079 | + | 0.0166208i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.72962 | − | 9.80918i | 0.0646842 | − | 0.366843i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.73772 | + | 2.66575i | −0.326316 | + | 0.0995543i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.02686 | − | 10.4388i | 0.224764 | − | 0.389303i | −0.731485 | − | 0.681858i | \(-0.761172\pi\) |
0.956249 | + | 0.292555i | \(0.0945056\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.2872 | − | 24.7461i | −0.532083 | − | 0.921594i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.87014 | − | 15.3057i | −0.0695512 | − | 0.569226i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.939963 | + | 0.342119i | −0.0349094 | + | 0.0127060i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.49253 | + | 31.1497i | 0.203707 | + | 1.15528i | 0.899462 | + | 0.437000i | \(0.143959\pi\) |
−0.695755 | + | 0.718279i | \(0.744930\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.6488 | + | 8.43433i | 0.949956 | + | 0.312383i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.99469 | + | 28.3263i | 0.184735 | + | 1.04769i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.8831 | − | 6.50891i | 0.660527 | − | 0.240412i | 0.0100630 | − | 0.999949i | \(-0.496797\pi\) |
0.650464 | + | 0.759537i | \(0.274575\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.349172 | + | 2.85772i | 0.0128794 | + | 0.105409i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.32516 | + | 10.9555i | 0.232990 | + | 0.403551i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.30036 | − | 14.3767i | 0.305334 | − | 0.528854i | −0.672002 | − | 0.740550i | \(-0.734565\pi\) |
0.977336 | + | 0.211696i | \(0.0678986\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.87770 | + | 0.572858i | −0.0689789 | + | 0.0210445i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.78310 | − | 32.7976i | 0.212161 | − | 1.20323i | −0.673604 | − | 0.739093i | \(-0.735255\pi\) |
0.885765 | − | 0.464134i | \(-0.153634\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.143014 | − | 0.120003i | 0.00523963 | − | 0.00439657i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.65426 | − | 24.0652i | −0.0605263 | − | 0.880499i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −44.9665 | − | 16.3665i | −1.64304 | − | 0.598017i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.2819 | − | 17.8577i | −0.776589 | − | 0.651636i | 0.165798 | − | 0.986160i | \(-0.446980\pi\) |
−0.942387 | + | 0.334524i | \(0.891424\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.11076 | − | 12.0106i | −0.222688 | − | 0.437689i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −35.3686 | −1.28720 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.12036 | −0.113411 | −0.0567057 | − | 0.998391i | \(-0.518060\pi\) | ||||
−0.0567057 | + | 0.998391i | \(0.518060\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.997121 | − | 1.53345i | 0.0361932 | − | 0.0556607i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.6747 | − | 28.2564i | −1.22071 | − | 1.02429i | −0.998787 | − | 0.0492297i | \(-0.984323\pi\) |
−0.221919 | − | 0.975065i | \(-0.571232\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.5939 | + | 5.31175i | 0.528335 | + | 0.192298i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −33.7894 | + | 8.38230i | −1.22166 | + | 0.303063i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.4759 | + | 8.79032i | −0.378263 | + | 0.317400i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.644731 | − | 3.65645i | 0.0232496 | − | 0.131855i | −0.970974 | − | 0.239186i | \(-0.923119\pi\) |
0.994223 | + | 0.107331i | \(0.0342305\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.98298 | + | 34.4852i | −0.287500 | + | 1.24195i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.48452 | − | 7.76741i | 0.161297 | − | 0.279374i | −0.774037 | − | 0.633140i | \(-0.781766\pi\) |
0.935334 | + | 0.353766i | \(0.115099\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.800417 | + | 1.38636i | 0.0287518 | + | 0.0497996i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.87610 | + | 6.68041i | −0.318428 | + | 0.239658i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.90882 | + | 0.694754i | −0.0683906 | + | 0.0248921i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0194871 | − | 0.110517i | −0.000697302 | − | 0.00395459i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.0417527 | − | 2.66209i | −0.00149212 | − | 0.0951354i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.29037 | + | 35.6745i | 0.224513 | + | 1.27328i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.2069 | − | 14.9981i | 1.46887 | − | 0.534624i | 0.521074 | − | 0.853512i | \(-0.325532\pi\) |
0.947792 | + | 0.318888i | \(0.103309\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.9796 | + | 7.64441i | 0.640090 | + | 0.272148i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.50374 | − | 14.7289i | −0.302358 | − | 0.523699i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.55782 | − | 11.3585i | 0.232875 | − | 0.403351i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.1724 | + | 21.6342i | 0.821842 | + | 0.767287i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.08656 | − | 11.8335i | 0.0739097 | − | 0.419163i | −0.925294 | − | 0.379252i | \(-0.876181\pi\) |
0.999203 | − | 0.0399111i | \(-0.0127075\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.9996 | + | 22.6554i | −0.955178 | + | 0.801490i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.15832 | − | 18.3822i | −0.288260 | − | 0.649504i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.27136 | + | 2.28259i | 0.221311 | + | 0.0805508i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.76924 | − | 2.32366i | −0.0976027 | − | 0.0818984i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.532311 | − | 0.0282122i | −0.0187382 | − | 0.000993117i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.02937 | −0.282298 | −0.141149 | − | 0.989988i | \(-0.545080\pi\) | ||||
−0.141149 | + | 0.989988i | \(0.545080\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.8345 | 0.450681 | 0.225341 | − | 0.974280i | \(-0.427651\pi\) | ||||
0.225341 | + | 0.974280i | \(0.427651\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.84411 | + | 0.203736i | 0.134819 | + | 0.00714534i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −26.9270 | − | 22.5944i | −0.943211 | − | 0.791448i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.01312 | − | 0.368744i | −0.0354444 | − | 0.0129007i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −19.7590 | + | 27.1286i | −0.690436 | + | 0.947949i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.7250 | + | 19.0685i | −0.793108 | + | 0.665497i | −0.946513 | − | 0.322667i | \(-0.895421\pi\) |
0.153404 | + | 0.988163i | \(0.450976\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.60266 | + | 48.7881i | −0.299870 | + | 1.70065i | 0.346852 | + | 0.937920i | \(0.387251\pi\) |
−0.646722 | + | 0.762726i | \(0.723861\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.09992 | − | 2.89415i | −0.107925 | − | 0.100761i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.4215 | − | 35.3711i | 0.710126 | − | 1.22997i | −0.254683 | − | 0.967025i | \(-0.581971\pi\) |
0.964809 | − | 0.262950i | \(-0.0846955\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.72638 | + | 8.18633i | 0.164154 | + | 0.284323i | 0.936355 | − | 0.351056i | \(-0.114177\pi\) |
−0.772201 | + | 0.635379i | \(0.780844\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 37.1867 | + | 15.8107i | 1.28999 | + | 0.548468i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.94714 | + | 2.16458i | −0.206056 | + | 0.0749983i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.02140 | − | 34.1491i | −0.208379 | − | 1.18178i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.18401 | + | 0.805605i | −0.144621 | + | 0.0278458i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.13360 | + | 12.1002i | 0.0736599 | + | 0.417746i | 0.999232 | + | 0.0391756i | \(0.0124732\pi\) |
−0.925572 | + | 0.378571i | \(0.876416\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0044 | − | 9.82879i | 0.931186 | − | 0.338924i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.99925 | − | 7.52573i | 0.344392 | − | 0.259200i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.71575 | + | 11.6320i | 0.231029 | + | 0.400154i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.5916 | + | 20.0772i | −0.398292 | + | 0.689862i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.78135 | + | 12.0150i | −0.0954556 | + | 0.412353i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.381330 | + | 2.16263i | −0.0130718 | + | 0.0741339i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.6446 | + | 19.8402i | −0.809576 | + | 0.679315i | −0.950507 | − | 0.310704i | \(-0.899435\pi\) |
0.140930 | + | 0.990020i | \(0.454991\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.361165 | − | 1.25395i | 0.0123516 | − | 0.0428840i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.4738 | − | 3.81217i | −0.357780 | − | 0.130221i | 0.156876 | − | 0.987618i | \(-0.449858\pi\) |
−0.514655 | + | 0.857397i | \(0.672080\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.17807 | − | 2.66672i | −0.108434 | − | 0.0909872i | 0.586958 | − | 0.809617i | \(-0.300325\pi\) |
−0.695393 | + | 0.718630i | \(0.744770\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.9310 | + | 29.1135i | −0.645167 | + | 0.992187i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47.2534 | 1.60852 | 0.804262 | − | 0.594275i | \(-0.202561\pi\) | ||||
0.804262 | + | 0.594275i | \(0.202561\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33.0392 | −1.12337 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.3516 | − | 41.9662i | −0.725140 | − | 1.42525i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.58958 | − | 3.85112i | −0.155691 | − | 0.130640i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −43.1156 | − | 15.6928i | −1.46092 | − | 0.531731i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.6665 | − | 9.19475i | 0.462543 | − | 0.311195i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −22.8650 | + | 19.1860i | −0.772978 | + | 0.648606i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.10381 | − | 34.6164i | 0.206111 | − | 1.16891i | −0.689571 | − | 0.724218i | \(-0.742201\pi\) |
0.895682 | − | 0.444695i | \(-0.146688\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.915284 | + | 0.279240i | −0.0308718 | + | 0.00941852i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.67981 | − | 16.7659i | 0.326121 | − | 0.564858i | −0.655618 | − | 0.755093i | \(-0.727592\pi\) |
0.981739 | + | 0.190235i | \(0.0609250\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.89302 | − | 11.9391i | −0.231969 | − | 0.401781i | 0.726419 | − | 0.687252i | \(-0.241183\pi\) |
−0.958387 | + | 0.285471i | \(0.907850\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.10248 | − | 9.02303i | −0.0370596 | − | 0.303306i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.0192 | + | 10.1982i | −0.940794 | + | 0.342421i | −0.766479 | − | 0.642269i | \(-0.777993\pi\) |
−0.174315 | + | 0.984690i | \(0.555771\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.13445 | + | 29.1189i | 0.172204 | + | 0.976617i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.97912 | − | 5.27581i | 0.334313 | − | 0.176746i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.229408 | − | 1.30104i | −0.00767685 | − | 0.0435376i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.9039 | + | 6.51649i | −0.598461 | + | 0.217822i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.804626 | + | 6.58528i | 0.0268657 | + | 0.219876i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.210078 | + | 0.363866i | 0.00700649 | + | 0.0121356i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.8448 | + | 60.3530i | −1.16085 | + | 2.01065i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17.6294 | + | 5.37849i | −0.586671 | + | 0.178985i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.44094 | − | 30.8571i | 0.180863 | − | 1.02573i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.77366 | − | 4.00558i | 0.158507 | − | 0.133003i | −0.560085 | − | 0.828435i | \(-0.689231\pi\) |
0.718592 | + | 0.695432i | \(0.244787\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.4889 | − | 6.59868i | −0.447397 | − | 0.218864i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.7314 | − | 10.8213i | −0.985044 | − | 0.358527i | −0.201245 | − | 0.979541i | \(-0.564499\pi\) |
−0.783799 | + | 0.621014i | \(0.786721\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.72533 | − | 6.48232i | −0.255671 | − | 0.214534i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.95336 | + | 7.77023i | 0.130694 | + | 0.256876i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −34.6380 | −1.14385 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.0031 | −1.18763 | −0.593816 | − | 0.804601i | \(-0.702379\pi\) | ||||
−0.593816 | + | 0.804601i | \(0.702379\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.35329 | − | 9.77058i | 0.209348 | − | 0.321952i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.311801 | + | 0.261632i | 0.0102631 | + | 0.00861173i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.78447 | + | 1.74141i | 0.157313 | + | 0.0572571i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.1844 | − | 25.1029i | −0.794321 | − | 0.824489i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.4941 | − | 16.3575i | 0.639580 | − | 0.536672i | −0.264309 | − | 0.964438i | \(-0.585144\pi\) |
0.903889 | + | 0.427767i | \(0.140699\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0411934 | − | 0.233619i | 0.00135006 | − | 0.00765656i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.02475 | + | 26.0260i | −0.197241 | + | 0.852052i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.27728 | + | 12.6046i | −0.237993 | + | 0.412215i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.1524 | − | 24.5127i | −0.462338 | − | 0.800794i | 0.536739 | − | 0.843749i | \(-0.319656\pi\) |
−0.999077 | + | 0.0429549i | \(0.986323\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.6057 | + | 24.5400i | −1.06405 | + | 0.800833i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.79422 | + | 2.83687i | −0.254084 | + | 0.0924792i | −0.465922 | − | 0.884826i | \(-0.654277\pi\) |
0.211838 | + | 0.977305i | \(0.432055\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.19204 | + | 6.76039i | 0.0388181 | + | 0.220149i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.95786 | − | 20.8411i | −0.258869 | − | 0.677962i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.71877 | + | 43.7753i | 0.250826 | + | 1.42251i | 0.806563 | + | 0.591148i | \(0.201325\pi\) |
−0.555737 | + | 0.831358i | \(0.687564\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.7462 | + | 8.27895i | −0.738373 | + | 0.268746i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.5595 | − | 4.91476i | −0.374842 | − | 0.159372i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.83574 | + | 8.37576i | 0.156645 | + | 0.271317i | 0.933657 | − | 0.358169i | \(-0.116599\pi\) |
−0.777012 | + | 0.629486i | \(0.783265\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.5385 | − | 40.7699i | 0.761688 | − | 1.31928i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.813608 | − | 0.759599i | −0.0263002 | − | 0.0245544i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.964325 | + | 5.46896i | −0.0311397 | + | 0.176602i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.2323 | + | 19.4942i | −0.749429 | + | 0.628845i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −58.0473 | − | 6.17030i | −1.87055 | − | 0.198835i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28.1425 | − | 10.2430i | −0.905940 | − | 0.329735i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.3676 | + | 21.2860i | 0.815768 | + | 0.684510i | 0.951977 | − | 0.306170i | \(-0.0990475\pi\) |
−0.136209 | + | 0.990680i | \(0.543492\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.86457 | + | 0.151821i | 0.0920234 | + | 0.00487720i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.4309 | 0.880298 | 0.440149 | − | 0.897925i | \(-0.354926\pi\) | ||||
0.440149 | + | 0.897925i | \(0.354926\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.6127 | −0.628755 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15.3603 | + | 0.814091i | 0.491924 | + | 0.0260718i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.8668 | + | 23.3831i | 0.891539 | + | 0.748090i | 0.968518 | − | 0.248943i | \(-0.0800830\pi\) |
−0.0769792 | + | 0.997033i | \(0.524527\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.90089 | − | 2.87569i | −0.252514 | − | 0.0919075i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.8393 | + | 2.00258i | 0.601493 | + | 0.0639373i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.2790 | + | 27.0853i | −1.02954 | + | 0.863886i | −0.990796 | − | 0.135363i | \(-0.956780\pi\) |
−0.0387434 | + | 0.999249i | \(0.512335\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.761595 | + | 4.31922i | −0.0242664 | + | 0.137622i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.5089 | − | 15.4130i | −0.525484 | − | 0.490602i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.82173 | + | 3.15533i | −0.0579276 | + | 0.100334i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.7705 | + | 22.1191i | 0.405667 | + | 0.702635i | 0.994399 | − | 0.105693i | \(-0.0337060\pi\) |
−0.588732 | + | 0.808328i | \(0.700373\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 46.2798 | + | 19.6769i | 1.46865 | + | 0.624426i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.4130 | + | 11.0694i | −0.964158 | + | 0.350925i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.08644 | + | 23.1754i | 0.129419 | + | 0.733971i | 0.978585 | + | 0.205845i | \(0.0659942\pi\) |
−0.849166 | + | 0.528126i | \(0.822895\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.54711 | + | 10.5167i | −0.270419 | + | 0.332733i |
(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.c.337.2 | 12 | ||
4.3 | odd | 2 | 27.2.e.a.13.2 | ✓ | 12 | ||
12.11 | even | 2 | 81.2.e.a.10.1 | 12 | |||
20.3 | even | 4 | 675.2.u.b.499.3 | 24 | |||
20.7 | even | 4 | 675.2.u.b.499.2 | 24 | |||
20.19 | odd | 2 | 675.2.l.c.526.1 | 12 | |||
27.25 | even | 9 | inner | 432.2.u.c.241.2 | 12 | ||
36.7 | odd | 6 | 243.2.e.c.109.2 | 12 | |||
36.11 | even | 6 | 243.2.e.b.109.1 | 12 | |||
36.23 | even | 6 | 243.2.e.a.190.2 | 12 | |||
36.31 | odd | 6 | 243.2.e.d.190.1 | 12 | |||
108.7 | odd | 18 | 243.2.e.c.136.2 | 12 | |||
108.11 | even | 18 | 243.2.e.a.55.2 | 12 | |||
108.23 | even | 18 | 729.2.c.b.487.5 | 12 | |||
108.31 | odd | 18 | 729.2.c.e.487.2 | 12 | |||
108.43 | odd | 18 | 243.2.e.d.55.1 | 12 | |||
108.47 | even | 18 | 243.2.e.b.136.1 | 12 | |||
108.59 | even | 18 | 729.2.a.d.1.2 | 6 | |||
108.67 | odd | 18 | 729.2.c.e.244.2 | 12 | |||
108.79 | odd | 18 | 27.2.e.a.25.2 | yes | 12 | ||
108.83 | even | 18 | 81.2.e.a.73.1 | 12 | |||
108.95 | even | 18 | 729.2.c.b.244.5 | 12 | |||
108.103 | odd | 18 | 729.2.a.a.1.5 | 6 | |||
540.79 | odd | 18 | 675.2.l.c.376.1 | 12 | |||
540.187 | even | 36 | 675.2.u.b.349.3 | 24 | |||
540.403 | even | 36 | 675.2.u.b.349.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.2.e.a.13.2 | ✓ | 12 | 4.3 | odd | 2 | ||
27.2.e.a.25.2 | yes | 12 | 108.79 | odd | 18 | ||
81.2.e.a.10.1 | 12 | 12.11 | even | 2 | |||
81.2.e.a.73.1 | 12 | 108.83 | even | 18 | |||
243.2.e.a.55.2 | 12 | 108.11 | even | 18 | |||
243.2.e.a.190.2 | 12 | 36.23 | even | 6 | |||
243.2.e.b.109.1 | 12 | 36.11 | even | 6 | |||
243.2.e.b.136.1 | 12 | 108.47 | even | 18 | |||
243.2.e.c.109.2 | 12 | 36.7 | odd | 6 | |||
243.2.e.c.136.2 | 12 | 108.7 | odd | 18 | |||
243.2.e.d.55.1 | 12 | 108.43 | odd | 18 | |||
243.2.e.d.190.1 | 12 | 36.31 | odd | 6 | |||
432.2.u.c.241.2 | 12 | 27.25 | even | 9 | inner | ||
432.2.u.c.337.2 | 12 | 1.1 | even | 1 | trivial | ||
675.2.l.c.376.1 | 12 | 540.79 | odd | 18 | |||
675.2.l.c.526.1 | 12 | 20.19 | odd | 2 | |||
675.2.u.b.349.2 | 24 | 540.403 | even | 36 | |||
675.2.u.b.349.3 | 24 | 540.187 | even | 36 | |||
675.2.u.b.499.2 | 24 | 20.7 | even | 4 | |||
675.2.u.b.499.3 | 24 | 20.3 | even | 4 | |||
729.2.a.a.1.5 | 6 | 108.103 | odd | 18 | |||
729.2.a.d.1.2 | 6 | 108.59 | even | 18 | |||
729.2.c.b.244.5 | 12 | 108.95 | even | 18 | |||
729.2.c.b.487.5 | 12 | 108.23 | even | 18 | |||
729.2.c.e.244.2 | 12 | 108.67 | odd | 18 | |||
729.2.c.e.487.2 | 12 | 108.31 | odd | 18 |