Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(263,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.263");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.g (of order \(3\), degree \(2\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 263.4 | ||
Root | \(0.756174 + 1.30973i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.263 |
Dual form | 637.2.g.l.373.4 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.425563 | − | 0.737096i | 0.300918 | − | 0.521206i | −0.675426 | − | 0.737428i | \(-0.736040\pi\) |
0.976344 | + | 0.216222i | \(0.0693735\pi\) | |||||||
\(3\) | −0.661223 | −0.381757 | −0.190879 | − | 0.981614i | \(-0.561134\pi\) | ||||
−0.190879 | + | 0.981614i | \(0.561134\pi\) | |||||||
\(4\) | 0.637793 | + | 1.10469i | 0.318896 | + | 0.552345i | ||||
\(5\) | 1.72074 | + | 2.98041i | 0.769538 | + | 1.33288i | 0.937814 | + | 0.347139i | \(0.112847\pi\) |
−0.168276 | + | 0.985740i | \(0.553820\pi\) | |||||||
\(6\) | −0.281392 | + | 0.487385i | −0.114878 | + | 0.198974i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.78793 | 0.985684 | ||||||||
\(9\) | −2.56278 | −0.854261 | ||||||||
\(10\) | 2.92913 | 0.926272 | ||||||||
\(11\) | −0.897986 | −0.270753 | −0.135377 | − | 0.990794i | \(-0.543224\pi\) | ||||
−0.135377 | + | 0.990794i | \(0.543224\pi\) | |||||||
\(12\) | −0.421723 | − | 0.730446i | −0.121741 | − | 0.210862i | ||||
\(13\) | 3.07517 | − | 1.88237i | 0.852900 | − | 0.522075i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.13779 | − | 1.97071i | −0.293777 | − | 0.508836i | ||||
\(16\) | −0.0891447 | + | 0.154403i | −0.0222862 | + | 0.0386008i | ||||
\(17\) | 0.968404 | + | 1.67733i | 0.234873 | + | 0.406811i | 0.959236 | − | 0.282607i | \(-0.0911994\pi\) |
−0.724363 | + | 0.689419i | \(0.757866\pi\) | |||||||
\(18\) | −1.09063 | + | 1.88902i | −0.257063 | + | 0.445246i | ||||
\(19\) | −1.03804 | −0.238142 | −0.119071 | − | 0.992886i | \(-0.537992\pi\) | ||||
−0.119071 | + | 0.992886i | \(0.537992\pi\) | |||||||
\(20\) | −2.19495 | + | 3.80177i | −0.490806 | + | 0.850101i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.382150 | + | 0.661902i | −0.0814745 | + | 0.141118i | ||||
\(23\) | −2.82506 | + | 4.89315i | −0.589067 | + | 1.02029i | 0.405288 | + | 0.914189i | \(0.367171\pi\) |
−0.994355 | + | 0.106104i | \(0.966162\pi\) | |||||||
\(24\) | −1.84345 | −0.376292 | ||||||||
\(25\) | −3.42189 | + | 5.92688i | −0.684378 | + | 1.18538i | ||||
\(26\) | −0.0788077 | − | 3.06776i | −0.0154555 | − | 0.601638i | ||||
\(27\) | 3.67824 | 0.707878 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.917969 | + | 1.58997i | 0.170463 | + | 0.295250i | 0.938582 | − | 0.345057i | \(-0.112140\pi\) |
−0.768119 | + | 0.640307i | \(0.778807\pi\) | |||||||
\(30\) | −1.93681 | −0.353611 | ||||||||
\(31\) | −4.56692 | + | 7.91014i | −0.820244 | + | 1.42070i | 0.0852573 | + | 0.996359i | \(0.472829\pi\) |
−0.905501 | + | 0.424345i | \(0.860505\pi\) | |||||||
\(32\) | 2.86381 | + | 4.96026i | 0.506254 | + | 0.876858i | ||||
\(33\) | 0.593769 | 0.103362 | ||||||||
\(34\) | 1.64847 | 0.282710 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.63452 | − | 2.83108i | −0.272421 | − | 0.471847i | ||||
\(37\) | 5.30001 | − | 9.17989i | 0.871316 | − | 1.50916i | 0.0106808 | − | 0.999943i | \(-0.496600\pi\) |
0.860636 | − | 0.509221i | \(-0.170067\pi\) | |||||||
\(38\) | −0.441751 | + | 0.765135i | −0.0716614 | + | 0.124121i | ||||
\(39\) | −2.03338 | + | 1.24467i | −0.325601 | + | 0.199306i | ||||
\(40\) | 4.79731 | + | 8.30918i | 0.758521 | + | 1.31380i | ||||
\(41\) | −2.66571 | − | 4.61715i | −0.416314 | − | 0.721078i | 0.579251 | − | 0.815149i | \(-0.303345\pi\) |
−0.995565 | + | 0.0940715i | \(0.970012\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.95732 | − | 3.39018i | 0.298489 | − | 0.516998i | −0.677302 | − | 0.735706i | \(-0.736851\pi\) |
0.975790 | + | 0.218708i | \(0.0701841\pi\) | |||||||
\(44\) | −0.572729 | − | 0.991996i | −0.0863422 | − | 0.149549i | ||||
\(45\) | −4.40988 | − | 7.63814i | −0.657387 | − | 1.13863i | ||||
\(46\) | 2.40448 | + | 4.16469i | 0.354522 | + | 0.614050i | ||||
\(47\) | 3.59565 | + | 6.22784i | 0.524479 | + | 0.908424i | 0.999594 | + | 0.0285004i | \(0.00907317\pi\) |
−0.475115 | + | 0.879924i | \(0.657593\pi\) | |||||||
\(48\) | 0.0589445 | − | 0.102095i | 0.00850791 | − | 0.0147361i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.91246 | + | 5.04452i | 0.411883 | + | 0.713403i | ||||
\(51\) | −0.640331 | − | 1.10909i | −0.0896643 | − | 0.155303i | ||||
\(52\) | 4.04076 | + | 2.19655i | 0.560352 | + | 0.304607i | ||||
\(53\) | 4.69324 | − | 8.12893i | 0.644666 | − | 1.11659i | −0.339712 | − | 0.940529i | \(-0.610330\pi\) |
0.984378 | − | 0.176065i | \(-0.0563370\pi\) | |||||||
\(54\) | 1.56532 | − | 2.71122i | 0.213013 | − | 0.368950i | ||||
\(55\) | −1.54520 | − | 2.67637i | −0.208355 | − | 0.360881i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.686375 | 0.0909127 | ||||||||
\(58\) | 1.56261 | 0.205181 | ||||||||
\(59\) | −0.255259 | − | 0.442121i | −0.0332318 | − | 0.0575592i | 0.848931 | − | 0.528503i | \(-0.177247\pi\) |
−0.882163 | + | 0.470944i | \(0.843913\pi\) | |||||||
\(60\) | 1.45135 | − | 2.51382i | 0.187369 | − | 0.324532i | ||||
\(61\) | −1.43619 | −0.183885 | −0.0919426 | − | 0.995764i | \(-0.529308\pi\) | ||||
−0.0919426 | + | 0.995764i | \(0.529308\pi\) | |||||||
\(62\) | 3.88702 | + | 6.73252i | 0.493653 | + | 0.855031i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.51834 | 0.564792 | ||||||||
\(65\) | 10.9018 | + | 5.92620i | 1.35220 | + | 0.735055i | ||||
\(66\) | 0.252686 | − | 0.437665i | 0.0311035 | − | 0.0538729i | ||||
\(67\) | −8.44932 | −1.03225 | −0.516124 | − | 0.856514i | \(-0.672626\pi\) | ||||
−0.516124 | + | 0.856514i | \(0.672626\pi\) | |||||||
\(68\) | −1.23528 | + | 2.13957i | −0.149800 | + | 0.259461i | ||||
\(69\) | 1.86800 | − | 3.23547i | 0.224881 | − | 0.389504i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.72419 | − | 2.98638i | 0.204623 | − | 0.354418i | −0.745389 | − | 0.666629i | \(-0.767736\pi\) |
0.950013 | + | 0.312211i | \(0.101070\pi\) | |||||||
\(72\) | −7.14487 | −0.842031 | ||||||||
\(73\) | 5.45026 | − | 9.44013i | 0.637905 | − | 1.10488i | −0.347987 | − | 0.937499i | \(-0.613135\pi\) |
0.985892 | − | 0.167384i | \(-0.0535320\pi\) | |||||||
\(74\) | −4.51097 | − | 7.81324i | −0.524390 | − | 0.908270i | ||||
\(75\) | 2.26263 | − | 3.91899i | 0.261266 | − | 0.452526i | ||||
\(76\) | −0.662054 | − | 1.14671i | −0.0759428 | − | 0.131537i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.0521095 | + | 2.02848i | 0.00590024 | + | 0.229680i | ||||
\(79\) | 6.04589 | + | 10.4718i | 0.680216 | + | 1.17817i | 0.974915 | + | 0.222578i | \(0.0714472\pi\) |
−0.294699 | + | 0.955590i | \(0.595219\pi\) | |||||||
\(80\) | −0.613579 | −0.0686002 | ||||||||
\(81\) | 5.25621 | 0.584024 | ||||||||
\(82\) | −4.53771 | −0.501107 | ||||||||
\(83\) | −1.51669 | −0.166479 | −0.0832393 | − | 0.996530i | \(-0.526527\pi\) | ||||
−0.0832393 | + | 0.996530i | \(0.526527\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.33274 | + | 5.77248i | −0.361487 | + | 0.626113i | ||||
\(86\) | −1.66593 | − | 2.88547i | −0.179642 | − | 0.311148i | ||||
\(87\) | −0.606982 | − | 1.05132i | −0.0650754 | − | 0.112714i | ||||
\(88\) | −2.50353 | −0.266877 | ||||||||
\(89\) | 6.80391 | − | 11.7847i | 0.721213 | − | 1.24918i | −0.239301 | − | 0.970945i | \(-0.576918\pi\) |
0.960514 | − | 0.278232i | \(-0.0897484\pi\) | |||||||
\(90\) | −7.50673 | −0.791279 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.20722 | −0.751405 | ||||||||
\(93\) | 3.01976 | − | 5.23037i | 0.313134 | − | 0.542364i | ||||
\(94\) | 6.12069 | 0.631301 | ||||||||
\(95\) | −1.78619 | − | 3.09378i | −0.183260 | − | 0.317415i | ||||
\(96\) | −1.89362 | − | 3.27984i | −0.193266 | − | 0.334747i | ||||
\(97\) | 0.253120 | − | 0.438417i | 0.0257005 | − | 0.0445145i | −0.852889 | − | 0.522092i | \(-0.825152\pi\) |
0.878590 | + | 0.477578i | \(0.158485\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.30134 | 0.231294 | ||||||||
\(100\) | −8.72982 | −0.872982 | ||||||||
\(101\) | 5.98654 | 0.595683 | 0.297842 | − | 0.954615i | \(-0.403733\pi\) | ||||
0.297842 | + | 0.954615i | \(0.403733\pi\) | |||||||
\(102\) | −1.09000 | −0.107927 | ||||||||
\(103\) | −2.06651 | − | 3.57930i | −0.203619 | − | 0.352679i | 0.746073 | − | 0.665865i | \(-0.231937\pi\) |
−0.949692 | + | 0.313186i | \(0.898604\pi\) | |||||||
\(104\) | 8.57338 | − | 5.24792i | 0.840689 | − | 0.514601i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.99454 | − | 6.91874i | −0.387984 | − | 0.672008i | ||||
\(107\) | 7.06169 | − | 12.2312i | 0.682679 | − | 1.18243i | −0.291481 | − | 0.956577i | \(-0.594148\pi\) |
0.974160 | − | 0.225858i | \(-0.0725186\pi\) | |||||||
\(108\) | 2.34596 | + | 4.06331i | 0.225740 | + | 0.390993i | ||||
\(109\) | 2.10119 | − | 3.63936i | 0.201257 | − | 0.348588i | −0.747677 | − | 0.664063i | \(-0.768831\pi\) |
0.948934 | + | 0.315475i | \(0.102164\pi\) | |||||||
\(110\) | −2.63032 | −0.250791 | ||||||||
\(111\) | −3.50449 | + | 6.06995i | −0.332631 | + | 0.576135i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.88472 | + | 11.9247i | −0.647660 | + | 1.12178i | 0.336020 | + | 0.941855i | \(0.390919\pi\) |
−0.983680 | + | 0.179926i | \(0.942414\pi\) | |||||||
\(114\) | 0.292096 | − | 0.505925i | 0.0273573 | − | 0.0473842i | ||||
\(115\) | −19.4448 | −1.81324 | ||||||||
\(116\) | −1.17095 | + | 2.02814i | −0.108720 | + | 0.188308i | ||||
\(117\) | −7.88100 | + | 4.82410i | −0.728599 | + | 0.445989i | ||||
\(118\) | −0.434514 | −0.0400003 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.17209 | − | 5.49422i | −0.289571 | − | 0.501552i | ||||
\(121\) | −10.1936 | −0.926693 | ||||||||
\(122\) | −0.611189 | + | 1.05861i | −0.0553344 | + | 0.0958420i | ||||
\(123\) | 1.76263 | + | 3.05297i | 0.158931 | + | 0.275277i | ||||
\(124\) | −11.6510 | −1.04629 | ||||||||
\(125\) | −6.34531 | −0.567542 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.972482 | − | 1.68439i | −0.0862938 | − | 0.149465i | 0.819648 | − | 0.572868i | \(-0.194169\pi\) |
−0.905942 | + | 0.423402i | \(0.860836\pi\) | |||||||
\(128\) | −3.80478 | + | 6.59007i | −0.336298 | + | 0.582485i | ||||
\(129\) | −1.29423 | + | 2.24167i | −0.113950 | + | 0.197368i | ||||
\(130\) | 9.00758 | − | 5.51370i | 0.790017 | − | 0.483584i | ||||
\(131\) | −6.01770 | − | 10.4230i | −0.525769 | − | 0.910659i | −0.999549 | − | 0.0300158i | \(-0.990444\pi\) |
0.473780 | − | 0.880643i | \(-0.342889\pi\) | |||||||
\(132\) | 0.378702 | + | 0.655931i | 0.0329618 | + | 0.0570914i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.59571 | + | 6.22796i | −0.310622 | + | 0.538014i | ||||
\(135\) | 6.32930 | + | 10.9627i | 0.544739 | + | 0.943516i | ||||
\(136\) | 2.69985 | + | 4.67627i | 0.231510 | + | 0.400987i | ||||
\(137\) | −4.35857 | − | 7.54927i | −0.372378 | − | 0.644978i | 0.617553 | − | 0.786529i | \(-0.288124\pi\) |
−0.989931 | + | 0.141552i | \(0.954791\pi\) | |||||||
\(138\) | −1.58990 | − | 2.75379i | −0.135341 | − | 0.234418i | ||||
\(139\) | 2.10625 | − | 3.64813i | 0.178650 | − | 0.309430i | −0.762769 | − | 0.646672i | \(-0.776160\pi\) |
0.941418 | + | 0.337241i | \(0.109494\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.37752 | − | 4.11799i | −0.200224 | − | 0.346798i | ||||
\(142\) | −1.46750 | − | 2.54178i | −0.123150 | − | 0.213302i | ||||
\(143\) | −2.76146 | + | 1.69034i | −0.230925 | + | 0.141353i | ||||
\(144\) | 0.228459 | − | 0.395702i | 0.0190382 | − | 0.0329751i | ||||
\(145\) | −3.15917 | + | 5.47184i | −0.262355 | + | 0.454412i | ||||
\(146\) | −4.63885 | − | 8.03473i | −0.383914 | − | 0.664959i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 13.5212 | 1.11144 | ||||||||
\(149\) | 5.86484 | 0.480466 | 0.240233 | − | 0.970715i | \(-0.422776\pi\) | ||||
0.240233 | + | 0.970715i | \(0.422776\pi\) | |||||||
\(150\) | −1.92578 | − | 3.33555i | −0.157240 | − | 0.272347i | ||||
\(151\) | 8.42840 | − | 14.5984i | 0.685893 | − | 1.18800i | −0.287262 | − | 0.957852i | \(-0.592745\pi\) |
0.973155 | − | 0.230150i | \(-0.0739216\pi\) | |||||||
\(152\) | −2.89398 | −0.234733 | ||||||||
\(153\) | −2.48181 | − | 4.29862i | −0.200643 | − | 0.347523i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −31.4339 | −2.52483 | ||||||||
\(156\) | −2.67184 | − | 1.45241i | −0.213919 | − | 0.116286i | ||||
\(157\) | −0.969500 | + | 1.67922i | −0.0773746 | + | 0.134017i | −0.902116 | − | 0.431493i | \(-0.857987\pi\) |
0.824742 | + | 0.565509i | \(0.191320\pi\) | |||||||
\(158\) | 10.2916 | 0.818757 | ||||||||
\(159\) | −3.10328 | + | 5.37504i | −0.246106 | + | 0.426268i | ||||
\(160\) | −9.85573 | + | 17.0706i | −0.779164 | + | 1.34955i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.23685 | − | 3.87433i | 0.175743 | − | 0.304396i | ||||
\(163\) | −11.8959 | −0.931762 | −0.465881 | − | 0.884847i | \(-0.654262\pi\) | ||||
−0.465881 | + | 0.884847i | \(0.654262\pi\) | |||||||
\(164\) | 3.40035 | − | 5.88957i | 0.265522 | − | 0.459898i | ||||
\(165\) | 1.02172 | + | 1.76968i | 0.0795410 | + | 0.137769i | ||||
\(166\) | −0.645448 | + | 1.11795i | −0.0500965 | + | 0.0867696i | ||||
\(167\) | 8.28801 | + | 14.3553i | 0.641346 | + | 1.11084i | 0.985133 | + | 0.171796i | \(0.0549569\pi\) |
−0.343787 | + | 0.939048i | \(0.611710\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.91338 | − | 11.5772i | 0.454875 | − | 0.890555i | ||||
\(170\) | 2.83658 | + | 4.91310i | 0.217556 | + | 0.376818i | ||||
\(171\) | 2.66027 | 0.203436 | ||||||||
\(172\) | 4.99346 | 0.380748 | ||||||||
\(173\) | 9.98656 | 0.759264 | 0.379632 | − | 0.925138i | \(-0.376051\pi\) | ||||
0.379632 | + | 0.925138i | \(0.376051\pi\) | |||||||
\(174\) | −1.03324 | −0.0783295 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.0800507 | − | 0.138652i | 0.00603405 | − | 0.0104513i | ||||
\(177\) | 0.168783 | + | 0.292341i | 0.0126865 | + | 0.0219737i | ||||
\(178\) | −5.79098 | − | 10.0303i | −0.434052 | − | 0.751801i | ||||
\(179\) | 9.17657 | 0.685889 | 0.342945 | − | 0.939356i | \(-0.388576\pi\) | ||||
0.342945 | + | 0.939356i | \(0.388576\pi\) | |||||||
\(180\) | 5.62518 | − | 9.74310i | 0.419276 | − | 0.726208i | ||||
\(181\) | −6.00489 | −0.446340 | −0.223170 | − | 0.974780i | \(-0.571640\pi\) | ||||
−0.223170 | + | 0.974780i | \(0.571640\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.949642 | 0.0701995 | ||||||||
\(184\) | −7.87609 | + | 13.6418i | −0.580633 | + | 1.00569i | ||||
\(185\) | 36.4797 | 2.68204 | ||||||||
\(186\) | −2.57019 | − | 4.45170i | −0.188456 | − | 0.326415i | ||||
\(187\) | −0.869614 | − | 1.50622i | −0.0635925 | − | 0.110145i | ||||
\(188\) | −4.58655 | + | 7.94415i | −0.334509 | + | 0.579386i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.04055 | −0.220585 | ||||||||
\(191\) | 1.31612 | 0.0952313 | 0.0476156 | − | 0.998866i | \(-0.484838\pi\) | ||||
0.0476156 | + | 0.998866i | \(0.484838\pi\) | |||||||
\(192\) | −2.98763 | −0.215614 | ||||||||
\(193\) | −16.4254 | −1.18233 | −0.591163 | − | 0.806552i | \(-0.701331\pi\) | ||||
−0.591163 | + | 0.806552i | \(0.701331\pi\) | |||||||
\(194\) | −0.215437 | − | 0.373148i | −0.0154675 | − | 0.0267905i | ||||
\(195\) | −7.20852 | − | 3.91854i | −0.516213 | − | 0.280613i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.7938 | + | 22.1594i | 0.911517 | + | 1.57879i | 0.811922 | + | 0.583766i | \(0.198421\pi\) |
0.0995951 | + | 0.995028i | \(0.468245\pi\) | |||||||
\(198\) | 0.979367 | − | 1.69631i | 0.0696006 | − | 0.120552i | ||||
\(199\) | −12.6894 | − | 21.9787i | −0.899528 | − | 1.55803i | −0.828099 | − | 0.560582i | \(-0.810578\pi\) |
−0.0714284 | − | 0.997446i | \(-0.522756\pi\) | |||||||
\(200\) | −9.54000 | + | 16.5238i | −0.674580 | + | 1.16841i | ||||
\(201\) | 5.58688 | 0.394068 | ||||||||
\(202\) | 2.54765 | − | 4.41266i | 0.179252 | − | 0.310473i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.816797 | − | 1.41473i | 0.0571873 | − | 0.0990512i | ||||
\(205\) | 9.17399 | − | 15.8898i | 0.640740 | − | 1.10979i | ||||
\(206\) | −3.51772 | −0.245091 | ||||||||
\(207\) | 7.24003 | − | 12.5401i | 0.503217 | − | 0.871597i | ||||
\(208\) | 0.0165082 | + | 0.642619i | 0.00114464 | + | 0.0445576i | ||||
\(209\) | 0.932145 | 0.0644778 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.84824 | + | 4.93330i | 0.196081 | + | 0.339622i | 0.947254 | − | 0.320483i | \(-0.103845\pi\) |
−0.751173 | + | 0.660105i | \(0.770512\pi\) | |||||||
\(212\) | 11.9733 | 0.822327 | ||||||||
\(213\) | −1.14007 | + | 1.97466i | −0.0781165 | + | 0.135302i | ||||
\(214\) | −6.01038 | − | 10.4103i | −0.410861 | − | 0.711633i | ||||
\(215\) | 13.4722 | 0.918794 | ||||||||
\(216\) | 10.2547 | 0.697744 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.78837 | − | 3.09755i | −0.121124 | − | 0.209793i | ||||
\(219\) | −3.60384 | + | 6.24203i | −0.243525 | + | 0.421797i | ||||
\(220\) | 1.97104 | − | 3.41393i | 0.132887 | − | 0.230167i | ||||
\(221\) | 6.13536 | + | 3.33517i | 0.412709 | + | 0.224348i | ||||
\(222\) | 2.98276 | + | 5.16629i | 0.200190 | + | 0.346739i | ||||
\(223\) | 1.17906 | + | 2.04219i | 0.0789558 | + | 0.136755i | 0.902800 | − | 0.430061i | \(-0.141508\pi\) |
−0.823844 | + | 0.566817i | \(0.808175\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.76956 | − | 15.1893i | 0.584637 | − | 1.01262i | ||||
\(226\) | 5.85976 | + | 10.1494i | 0.389786 | + | 0.675129i | ||||
\(227\) | 13.1463 | + | 22.7701i | 0.872551 | + | 1.51130i | 0.859349 | + | 0.511390i | \(0.170869\pi\) |
0.0132022 | + | 0.999913i | \(0.495797\pi\) | |||||||
\(228\) | 0.437765 | + | 0.758232i | 0.0289917 | + | 0.0502151i | ||||
\(229\) | 0.0342777 | + | 0.0593708i | 0.00226514 | + | 0.00392333i | 0.867156 | − | 0.498037i | \(-0.165946\pi\) |
−0.864891 | + | 0.501960i | \(0.832612\pi\) | |||||||
\(230\) | −8.27498 | + | 14.3327i | −0.545636 | + | 0.945069i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.55924 | + | 4.43273i | 0.168022 | + | 0.291023i | ||||
\(233\) | −7.33514 | − | 12.7048i | −0.480541 | − | 0.832322i | 0.519210 | − | 0.854647i | \(-0.326226\pi\) |
−0.999751 | + | 0.0223253i | \(0.992893\pi\) | |||||||
\(234\) | 0.201967 | + | 7.86202i | 0.0132030 | + | 0.513956i | ||||
\(235\) | −12.3743 | + | 21.4330i | −0.807213 | + | 1.39813i | ||||
\(236\) | 0.325604 | − | 0.563963i | 0.0211950 | − | 0.0367109i | ||||
\(237\) | −3.99768 | − | 6.92419i | −0.259677 | − | 0.449774i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.35434 | 0.216974 | 0.108487 | − | 0.994098i | \(-0.465399\pi\) | ||||
0.108487 | + | 0.994098i | \(0.465399\pi\) | |||||||
\(240\) | 0.405713 | 0.0261886 | ||||||||
\(241\) | −4.28989 | − | 7.43031i | −0.276336 | − | 0.478628i | 0.694135 | − | 0.719845i | \(-0.255787\pi\) |
−0.970471 | + | 0.241216i | \(0.922454\pi\) | |||||||
\(242\) | −4.33802 | + | 7.51368i | −0.278859 | + | 0.482998i | ||||
\(243\) | −14.5103 | −0.930833 | ||||||||
\(244\) | −0.915991 | − | 1.58654i | −0.0586403 | − | 0.101568i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.00044 | 0.191301 | ||||||||
\(247\) | −3.19215 | + | 1.95397i | −0.203112 | + | 0.124328i | ||||
\(248\) | −12.7323 | + | 22.0530i | −0.808501 | + | 1.40036i | ||||
\(249\) | 1.00287 | 0.0635544 | ||||||||
\(250\) | −2.70033 | + | 4.67711i | −0.170784 | + | 0.295806i | ||||
\(251\) | 10.7575 | − | 18.6326i | 0.679010 | − | 1.17608i | −0.296270 | − | 0.955104i | \(-0.595743\pi\) |
0.975280 | − | 0.220975i | \(-0.0709238\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.53687 | − | 4.39399i | 0.159492 | − | 0.276248i | ||||
\(254\) | −1.65541 | −0.103870 | ||||||||
\(255\) | 2.20369 | − | 3.81690i | 0.138000 | − | 0.239023i | ||||
\(256\) | 7.75668 | + | 13.4350i | 0.484793 | + | 0.839686i | ||||
\(257\) | 2.46896 | − | 4.27636i | 0.154010 | − | 0.266752i | −0.778688 | − | 0.627411i | \(-0.784115\pi\) |
0.932698 | + | 0.360659i | \(0.117448\pi\) | |||||||
\(258\) | 1.10155 | + | 1.90794i | 0.0685795 | + | 0.118783i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.406471 | + | 15.8228i | 0.0252083 | + | 0.981288i | ||||
\(261\) | −2.35256 | − | 4.07475i | −0.145620 | − | 0.252221i | ||||
\(262\) | −10.2436 | −0.632854 | ||||||||
\(263\) | −8.95439 | −0.552151 | −0.276076 | − | 0.961136i | \(-0.589034\pi\) | ||||
−0.276076 | + | 0.961136i | \(0.589034\pi\) | |||||||
\(264\) | 1.65539 | 0.101882 | ||||||||
\(265\) | 32.3034 | 1.98438 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.49890 | + | 7.79233i | −0.275328 | + | 0.476883i | ||||
\(268\) | −5.38891 | − | 9.33387i | −0.329180 | − | 0.570157i | ||||
\(269\) | −2.41172 | − | 4.17723i | −0.147045 | − | 0.254690i | 0.783089 | − | 0.621910i | \(-0.213643\pi\) |
−0.930134 | + | 0.367220i | \(0.880310\pi\) | |||||||
\(270\) | 10.7740 | 0.655688 | ||||||||
\(271\) | −3.71072 | + | 6.42715i | −0.225410 | + | 0.390422i | −0.956442 | − | 0.291921i | \(-0.905706\pi\) |
0.731032 | + | 0.682343i | \(0.239039\pi\) | |||||||
\(272\) | −0.345312 | −0.0209376 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.41938 | −0.448221 | ||||||||
\(275\) | 3.07281 | − | 5.32226i | 0.185297 | − | 0.320944i | ||||
\(276\) | 4.76558 | 0.286854 | ||||||||
\(277\) | −1.90816 | − | 3.30503i | −0.114650 | − | 0.198580i | 0.802990 | − | 0.595993i | \(-0.203241\pi\) |
−0.917640 | + | 0.397413i | \(0.869908\pi\) | |||||||
\(278\) | −1.79268 | − | 3.10502i | −0.107518 | − | 0.186226i | ||||
\(279\) | 11.7040 | − | 20.2720i | 0.700702 | − | 1.21365i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.54978 | 0.510037 | 0.255019 | − | 0.966936i | \(-0.417918\pi\) | ||||
0.255019 | + | 0.966936i | \(0.417918\pi\) | |||||||
\(282\) | −4.04714 | −0.241004 | ||||||||
\(283\) | −15.2643 | −0.907371 | −0.453686 | − | 0.891162i | \(-0.649891\pi\) | ||||
−0.453686 | + | 0.891162i | \(0.649891\pi\) | |||||||
\(284\) | 4.39870 | 0.261015 | ||||||||
\(285\) | 1.18107 | + | 2.04568i | 0.0699607 | + | 0.121176i | ||||
\(286\) | 0.0707683 | + | 2.75481i | 0.00418461 | + | 0.162895i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −7.33932 | − | 12.7121i | −0.432474 | − | 0.749066i | ||||
\(289\) | 6.62439 | − | 11.4738i | 0.389670 | − | 0.674928i | ||||
\(290\) | 2.68885 | + | 4.65723i | 0.157895 | + | 0.273482i | ||||
\(291\) | −0.167369 | + | 0.289892i | −0.00981135 | + | 0.0169938i | ||||
\(292\) | 13.9045 | 0.813702 | ||||||||
\(293\) | −2.96982 | + | 5.14388i | −0.173499 | + | 0.300509i | −0.939641 | − | 0.342163i | \(-0.888841\pi\) |
0.766142 | + | 0.642671i | \(0.222174\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.878467 | − | 1.52155i | 0.0511463 | − | 0.0885881i | ||||
\(296\) | 14.7761 | − | 25.5929i | 0.858842 | − | 1.48756i | ||||
\(297\) | −3.30301 | −0.191660 | ||||||||
\(298\) | 2.49586 | − | 4.32295i | 0.144581 | − | 0.250422i | ||||
\(299\) | 0.523159 | + | 20.3651i | 0.0302551 | + | 1.17774i | ||||
\(300\) | 5.77236 | 0.333267 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7.17362 | − | 12.4251i | −0.412796 | − | 0.714983i | ||||
\(303\) | −3.95844 | −0.227406 | ||||||||
\(304\) | 0.0925356 | − | 0.160276i | 0.00530728 | − | 0.00919248i | ||||
\(305\) | −2.47131 | − | 4.28043i | −0.141507 | − | 0.245097i | ||||
\(306\) | −4.22467 | −0.241508 | ||||||||
\(307\) | −22.2133 | −1.26778 | −0.633891 | − | 0.773422i | \(-0.718543\pi\) | ||||
−0.633891 | + | 0.773422i | \(0.718543\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.36642 | + | 2.36672i | 0.0777332 | + | 0.134638i | ||||
\(310\) | −13.3771 | + | 23.1698i | −0.759769 | + | 1.31596i | ||||
\(311\) | 4.92130 | − | 8.52394i | 0.279061 | − | 0.483348i | −0.692091 | − | 0.721811i | \(-0.743310\pi\) |
0.971152 | + | 0.238463i | \(0.0766435\pi\) | |||||||
\(312\) | −5.66892 | + | 3.47005i | −0.320939 | + | 0.196453i | ||||
\(313\) | −10.4563 | − | 18.1108i | −0.591023 | − | 1.02368i | −0.994095 | − | 0.108513i | \(-0.965391\pi\) |
0.403072 | − | 0.915168i | \(-0.367942\pi\) | |||||||
\(314\) | 0.825166 | + | 1.42923i | 0.0465668 | + | 0.0806561i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.71205 | + | 13.3577i | −0.433837 | + | 0.751427i | ||||
\(317\) | 12.6801 | + | 21.9626i | 0.712188 | + | 1.23355i | 0.964034 | + | 0.265778i | \(0.0856288\pi\) |
−0.251847 | + | 0.967767i | \(0.581038\pi\) | |||||||
\(318\) | 2.64128 | + | 4.57483i | 0.148116 | + | 0.256544i | ||||
\(319\) | −0.824324 | − | 1.42777i | −0.0461533 | − | 0.0799398i | ||||
\(320\) | 7.77489 | + | 13.4665i | 0.434629 | + | 0.752800i | ||||
\(321\) | −4.66935 | + | 8.08755i | −0.260618 | + | 0.451403i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.00524 | − | 1.74113i | −0.0559331 | − | 0.0968790i | ||||
\(324\) | 3.35237 | + | 5.80648i | 0.186243 | + | 0.322582i | ||||
\(325\) | 0.633681 | + | 24.6674i | 0.0351503 | + | 1.36830i | ||||
\(326\) | −5.06247 | + | 8.76845i | −0.280384 | + | 0.485640i | ||||
\(327\) | −1.38935 | + | 2.40643i | −0.0768314 | + | 0.133076i | ||||
\(328\) | −7.43183 | − | 12.8723i | −0.410354 | − | 0.710755i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.73923 | 0.0957413 | ||||||||
\(331\) | 1.78283 | 0.0979935 | 0.0489967 | − | 0.998799i | \(-0.484398\pi\) | ||||
0.0489967 | + | 0.998799i | \(0.484398\pi\) | |||||||
\(332\) | −0.967335 | − | 1.67547i | −0.0530894 | − | 0.0919536i | ||||
\(333\) | −13.5828 | + | 23.5261i | −0.744332 | + | 1.28922i | ||||
\(334\) | 14.1083 | 0.771971 | ||||||||
\(335\) | −14.5391 | − | 25.1824i | −0.794354 | − | 1.37586i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.56149 | 0.520848 | 0.260424 | − | 0.965494i | \(-0.416138\pi\) | ||||
0.260424 | + | 0.965494i | \(0.416138\pi\) | |||||||
\(338\) | −6.01701 | − | 9.28556i | −0.327282 | − | 0.505068i | ||||
\(339\) | 4.55234 | − | 7.88488i | 0.247249 | − | 0.428248i | ||||
\(340\) | −8.50240 | −0.461107 | ||||||||
\(341\) | 4.10103 | − | 7.10320i | 0.222083 | − | 0.384660i | ||||
\(342\) | 1.13211 | − | 1.96087i | 0.0612176 | − | 0.106032i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.45689 | − | 9.45160i | 0.294216 | − | 0.509596i | ||||
\(345\) | 12.8573 | 0.692216 | ||||||||
\(346\) | 4.24991 | − | 7.36106i | 0.228477 | − | 0.395733i | ||||
\(347\) | −0.316694 | − | 0.548531i | −0.0170010 | − | 0.0294467i | 0.857400 | − | 0.514651i | \(-0.172079\pi\) |
−0.874401 | + | 0.485204i | \(0.838745\pi\) | |||||||
\(348\) | 0.774258 | − | 1.34105i | 0.0415046 | − | 0.0718881i | ||||
\(349\) | 15.2994 | + | 26.4994i | 0.818960 | + | 1.41848i | 0.906449 | + | 0.422315i | \(0.138783\pi\) |
−0.0874885 | + | 0.996166i | \(0.527884\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.3112 | − | 6.92381i | 0.603749 | − | 0.369565i | ||||
\(352\) | −2.57166 | − | 4.45425i | −0.137070 | − | 0.237412i | ||||
\(353\) | 1.10035 | 0.0585655 | 0.0292828 | − | 0.999571i | \(-0.490678\pi\) | ||||
0.0292828 | + | 0.999571i | \(0.490678\pi\) | |||||||
\(354\) | 0.287311 | 0.0152704 | ||||||||
\(355\) | 11.8675 | 0.629862 | ||||||||
\(356\) | 17.3579 | 0.919969 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.90521 | − | 6.76402i | 0.206397 | − | 0.357489i | ||||
\(359\) | 4.88693 | + | 8.46441i | 0.257922 | + | 0.446734i | 0.965685 | − | 0.259716i | \(-0.0836288\pi\) |
−0.707763 | + | 0.706450i | \(0.750295\pi\) | |||||||
\(360\) | −12.2945 | − | 21.2946i | −0.647975 | − | 1.12233i | ||||
\(361\) | −17.9225 | −0.943288 | ||||||||
\(362\) | −2.55546 | + | 4.42618i | −0.134312 | + | 0.232635i | ||||
\(363\) | 6.74026 | 0.353772 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 37.5139 | 1.96357 | ||||||||
\(366\) | 0.404132 | − | 0.699977i | 0.0211243 | − | 0.0365884i | ||||
\(367\) | 11.1473 | 0.581882 | 0.290941 | − | 0.956741i | \(-0.406032\pi\) | ||||
0.290941 | + | 0.956741i | \(0.406032\pi\) | |||||||
\(368\) | −0.503679 | − | 0.872397i | −0.0262561 | − | 0.0454769i | ||||
\(369\) | 6.83165 | + | 11.8328i | 0.355641 | + | 0.615989i | ||||
\(370\) | 15.5244 | − | 26.8891i | 0.807076 | − | 1.39790i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 7.70391 | 0.399429 | ||||||||
\(373\) | −30.7301 | −1.59115 | −0.795573 | − | 0.605858i | \(-0.792830\pi\) | ||||
−0.795573 | + | 0.605858i | \(0.792830\pi\) | |||||||
\(374\) | −1.48030 | −0.0765445 | ||||||||
\(375\) | 4.19567 | 0.216663 | ||||||||
\(376\) | 10.0244 | + | 17.3628i | 0.516970 | + | 0.895419i | ||||
\(377\) | 5.81582 | + | 3.16147i | 0.299530 | + | 0.162824i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.3286 | − | 19.6217i | −0.581912 | − | 1.00790i | −0.995253 | − | 0.0973246i | \(-0.968972\pi\) |
0.413341 | − | 0.910576i | \(-0.364362\pi\) | |||||||
\(380\) | 2.27844 | − | 3.94638i | 0.116882 | − | 0.202445i | ||||
\(381\) | 0.643028 | + | 1.11376i | 0.0329433 | + | 0.0570595i | ||||
\(382\) | 0.560093 | − | 0.970109i | 0.0286568 | − | 0.0496351i | ||||
\(383\) | 0.589263 | 0.0301099 | 0.0150550 | − | 0.999887i | \(-0.495208\pi\) | ||||
0.0150550 | + | 0.999887i | \(0.495208\pi\) | |||||||
\(384\) | 2.51581 | − | 4.35751i | 0.128384 | − | 0.222368i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.99004 | + | 12.1071i | −0.355783 | + | 0.616235i | ||||
\(387\) | −5.01619 | + | 8.68830i | −0.254988 | + | 0.441651i | ||||
\(388\) | 0.645753 | 0.0327832 | ||||||||
\(389\) | −2.84973 | + | 4.93587i | −0.144487 | + | 0.250259i | −0.929181 | − | 0.369624i | \(-0.879486\pi\) |
0.784695 | + | 0.619883i | \(0.212820\pi\) | |||||||
\(390\) | −5.95602 | + | 3.64579i | −0.301595 | + | 0.184612i | ||||
\(391\) | −10.9432 | −0.553422 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.97904 | + | 6.89191i | 0.200716 | + | 0.347651i | ||||
\(394\) | 21.7782 | 1.09717 | ||||||||
\(395\) | −20.8068 | + | 36.0384i | −1.04690 | + | 1.81329i | ||||
\(396\) | 1.46778 | + | 2.54227i | 0.0737588 | + | 0.127754i | ||||
\(397\) | 25.5283 | 1.28123 | 0.640614 | − | 0.767863i | \(-0.278680\pi\) | ||||
0.640614 | + | 0.767863i | \(0.278680\pi\) | |||||||
\(398\) | −21.6005 | −1.08274 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.610086 | − | 1.05670i | −0.0305043 | − | 0.0528350i | ||||
\(401\) | −12.7506 | + | 22.0846i | −0.636733 | + | 1.10285i | 0.349413 | + | 0.936969i | \(0.386381\pi\) |
−0.986145 | + | 0.165884i | \(0.946952\pi\) | |||||||
\(402\) | 2.37757 | − | 4.11807i | 0.118582 | − | 0.205391i | ||||
\(403\) | 0.845724 | + | 32.9217i | 0.0421285 | + | 1.63995i | ||||
\(404\) | 3.81817 | + | 6.61327i | 0.189961 | + | 0.329022i | ||||
\(405\) | 9.04457 | + | 15.6657i | 0.449428 | + | 0.778433i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.75934 | + | 8.24341i | −0.235912 | + | 0.408611i | ||||
\(408\) | −1.78520 | − | 3.09206i | −0.0883807 | − | 0.153080i | ||||
\(409\) | 0.0734938 | + | 0.127295i | 0.00363403 | + | 0.00629433i | 0.867837 | − | 0.496850i | \(-0.165510\pi\) |
−0.864203 | + | 0.503144i | \(0.832177\pi\) | |||||||
\(410\) | −7.80822 | − | 13.5242i | −0.385621 | − | 0.667914i | ||||
\(411\) | 2.88199 | + | 4.99175i | 0.142158 | + | 0.246225i | ||||
\(412\) | 2.63601 | − | 4.56570i | 0.129867 | − | 0.224936i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.16217 | − | 10.6732i | −0.302854 | − | 0.524559i | ||||
\(415\) | −2.60983 | − | 4.52036i | −0.128112 | − | 0.221896i | ||||
\(416\) | 18.1437 | + | 9.86292i | 0.889570 | + | 0.483569i | ||||
\(417\) | −1.39270 | + | 2.41223i | −0.0682008 | + | 0.118127i | ||||
\(418\) | 0.396686 | − | 0.687080i | 0.0194026 | − | 0.0336062i | ||||
\(419\) | 6.84795 | + | 11.8610i | 0.334544 | + | 0.579447i | 0.983397 | − | 0.181466i | \(-0.0580844\pi\) |
−0.648853 | + | 0.760914i | \(0.724751\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.44169 | 0.167738 | 0.0838688 | − | 0.996477i | \(-0.473272\pi\) | ||||
0.0838688 | + | 0.996477i | \(0.473272\pi\) | |||||||
\(422\) | 4.84842 | 0.236017 | ||||||||
\(423\) | −9.21486 | − | 15.9606i | −0.448042 | − | 0.776032i | ||||
\(424\) | 13.0844 | − | 22.6629i | 0.635437 | − | 1.10061i | ||||
\(425\) | −13.2551 | −0.642966 | ||||||||
\(426\) | 0.970345 | + | 1.68069i | 0.0470134 | + | 0.0814295i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 18.0156 | 0.870816 | ||||||||
\(429\) | 1.82594 | − | 1.11769i | 0.0881574 | − | 0.0539627i | ||||
\(430\) | 5.73325 | − | 9.93028i | 0.276482 | − | 0.478881i | ||||
\(431\) | 22.2910 | 1.07372 | 0.536861 | − | 0.843671i | \(-0.319610\pi\) | ||||
0.536861 | + | 0.843671i | \(0.319610\pi\) | |||||||
\(432\) | −0.327896 | + | 0.567932i | −0.0157759 | + | 0.0273246i | ||||
\(433\) | −12.9481 | + | 22.4268i | −0.622247 | + | 1.07776i | 0.366819 | + | 0.930292i | \(0.380447\pi\) |
−0.989066 | + | 0.147472i | \(0.952886\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.08892 | − | 3.61811i | 0.100156 | − | 0.173475i | ||||
\(436\) | 5.36049 | 0.256721 | ||||||||
\(437\) | 2.93253 | − | 5.07929i | 0.140282 | − | 0.242975i | ||||
\(438\) | 3.06732 | + | 5.31275i | 0.146562 | + | 0.253853i | ||||
\(439\) | −13.9919 | + | 24.2347i | −0.667798 | + | 1.15666i | 0.310721 | + | 0.950501i | \(0.399430\pi\) |
−0.978519 | + | 0.206159i | \(0.933904\pi\) | |||||||
\(440\) | −4.30792 | − | 7.46153i | −0.205372 | − | 0.355715i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.06932 | − | 3.10302i | 0.241123 | − | 0.147596i | ||||
\(443\) | −16.6044 | − | 28.7597i | −0.788900 | − | 1.36642i | −0.926641 | − | 0.375947i | \(-0.877317\pi\) |
0.137741 | − | 0.990468i | \(-0.456016\pi\) | |||||||
\(444\) | −8.94055 | −0.424300 | ||||||||
\(445\) | 46.8310 | 2.22000 | ||||||||
\(446\) | 2.00706 | 0.0950370 | ||||||||
\(447\) | −3.87796 | −0.183421 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.84320 | + | 17.0489i | −0.464529 | + | 0.804589i | −0.999180 | − | 0.0404845i | \(-0.987110\pi\) |
0.534651 | + | 0.845073i | \(0.320443\pi\) | |||||||
\(450\) | −7.46399 | − | 12.9280i | −0.351856 | − | 0.609433i | ||||
\(451\) | 2.39377 | + | 4.14614i | 0.112718 | + | 0.195234i | ||||
\(452\) | −17.5641 | −0.826146 | ||||||||
\(453\) | −5.57305 | + | 9.65281i | −0.261845 | + | 0.453528i | ||||
\(454\) | 22.3783 | 1.05027 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.91357 | 0.0896111 | ||||||||
\(457\) | 0.373471 | − | 0.646871i | 0.0174702 | − | 0.0302593i | −0.857158 | − | 0.515053i | \(-0.827772\pi\) |
0.874628 | + | 0.484794i | \(0.161105\pi\) | |||||||
\(458\) | 0.0583493 | 0.00272648 | ||||||||
\(459\) | 3.56203 | + | 6.16961i | 0.166261 | + | 0.287973i | ||||
\(460\) | −12.4017 | − | 21.4805i | −0.578235 | − | 1.00153i | ||||
\(461\) | −16.5855 | + | 28.7269i | −0.772464 | + | 1.33795i | 0.163744 | + | 0.986503i | \(0.447643\pi\) |
−0.936209 | + | 0.351445i | \(0.885691\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.7521 | −1.42917 | −0.714586 | − | 0.699548i | \(-0.753385\pi\) | ||||
−0.714586 | + | 0.699548i | \(0.753385\pi\) | |||||||
\(464\) | −0.327328 | −0.0151958 | ||||||||
\(465\) | 20.7848 | 0.963874 | ||||||||
\(466\) | −12.4863 | −0.578414 | ||||||||
\(467\) | −14.8033 | − | 25.6400i | −0.685013 | − | 1.18648i | −0.973433 | − | 0.228973i | \(-0.926463\pi\) |
0.288420 | − | 0.957504i | \(-0.406870\pi\) | |||||||
\(468\) | −10.3556 | − | 5.62928i | −0.478687 | − | 0.260214i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 10.5321 | + | 18.2422i | 0.485810 | + | 0.841448i | ||||
\(471\) | 0.641056 | − | 1.11034i | 0.0295383 | − | 0.0511618i | ||||
\(472\) | −0.711644 | − | 1.23260i | −0.0327561 | − | 0.0567352i | ||||
\(473\) | −1.75765 | + | 3.04434i | −0.0808168 | + | 0.139979i | ||||
\(474\) | −6.80506 | −0.312567 | ||||||||
\(475\) | 3.55205 | − | 6.15234i | 0.162979 | − | 0.282289i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.0278 | + | 20.8327i | −0.550714 | + | 0.953864i | ||||
\(478\) | 1.42748 | − | 2.47247i | 0.0652915 | − | 0.113088i | ||||
\(479\) | −14.0905 | −0.643813 | −0.321907 | − | 0.946771i | \(-0.604324\pi\) | ||||
−0.321907 | + | 0.946771i | \(0.604324\pi\) | |||||||
\(480\) | 6.51684 | − | 11.2875i | 0.297452 | − | 0.515201i | ||||
\(481\) | −0.981481 | − | 38.2063i | −0.0447517 | − | 1.74206i | ||||
\(482\) | −7.30247 | −0.332618 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.50142 | − | 11.2608i | −0.295519 | − | 0.511854i | ||||
\(485\) | 1.74222 | 0.0791100 | ||||||||
\(486\) | −6.17502 | + | 10.6955i | −0.280105 | + | 0.485156i | ||||
\(487\) | 8.39773 | + | 14.5453i | 0.380537 | + | 0.659110i | 0.991139 | − | 0.132828i | \(-0.0424057\pi\) |
−0.610602 | + | 0.791938i | \(0.709072\pi\) | |||||||
\(488\) | −4.00400 | −0.181253 | ||||||||
\(489\) | 7.86587 | 0.355707 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.8345 | − | 18.7659i | −0.488954 | − | 0.846893i | 0.510965 | − | 0.859601i | \(-0.329288\pi\) |
−0.999919 | + | 0.0127081i | \(0.995955\pi\) | |||||||
\(492\) | −2.24839 | + | 3.89432i | −0.101365 | + | 0.175570i | ||||
\(493\) | −1.77793 | + | 3.07947i | −0.0800740 | + | 0.138692i | ||||
\(494\) | 0.0818055 | + | 3.18446i | 0.00368060 | + | 0.143276i | ||||
\(495\) | 3.96001 | + | 6.85895i | 0.177989 | + | 0.308287i | ||||
\(496\) | −0.814234 | − | 1.41029i | −0.0365602 | − | 0.0633241i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.426785 | − | 0.739213i | 0.0191247 | − | 0.0331249i | ||||
\(499\) | 11.6524 | + | 20.1825i | 0.521633 | + | 0.903495i | 0.999683 | + | 0.0251622i | \(0.00801023\pi\) |
−0.478051 | + | 0.878332i | \(0.658656\pi\) | |||||||
\(500\) | −4.04699 | − | 7.00960i | −0.180987 | − | 0.313479i | ||||
\(501\) | −5.48023 | − | 9.49203i | −0.244838 | − | 0.424073i | ||||
\(502\) | −9.15601 | − | 15.8587i | −0.408653 | − | 0.707807i | ||||
\(503\) | −21.9415 | + | 38.0037i | −0.978322 | + | 1.69450i | −0.309816 | + | 0.950796i | \(0.600268\pi\) |
−0.668506 | + | 0.743707i | \(0.733066\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.3013 | + | 17.8423i | 0.458401 | + | 0.793974i | ||||
\(506\) | −2.15919 | − | 3.73983i | −0.0959879 | − | 0.166256i | ||||
\(507\) | −3.91006 | + | 7.65512i | −0.173652 | + | 0.339976i | ||||
\(508\) | 1.24048 | − | 2.14858i | 0.0550376 | − | 0.0953279i | ||||
\(509\) | 9.96210 | − | 17.2549i | 0.441563 | − | 0.764809i | −0.556243 | − | 0.831020i | \(-0.687758\pi\) |
0.997806 | + | 0.0662109i | \(0.0210910\pi\) | |||||||
\(510\) | −1.87561 | − | 3.24866i | −0.0830536 | − | 0.143853i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −2.01529 | −0.0890641 | ||||||||
\(513\) | −3.81816 | −0.168576 | ||||||||
\(514\) | −2.10139 | − | 3.63972i | −0.0926886 | − | 0.160541i | ||||
\(515\) | 7.11185 | − | 12.3181i | 0.313386 | − | 0.542800i | ||||
\(516\) | −3.30179 | −0.145353 | ||||||||
\(517\) | −3.22884 | − | 5.59252i | −0.142004 | − | 0.245959i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.60335 | −0.289855 | ||||||||
\(520\) | 30.3935 | + | 16.5219i | 1.33284 | + | 0.724532i | ||||
\(521\) | −8.26204 | + | 14.3103i | −0.361967 | + | 0.626944i | −0.988284 | − | 0.152623i | \(-0.951228\pi\) |
0.626318 | + | 0.779568i | \(0.284561\pi\) | |||||||
\(522\) | −4.00464 | −0.175278 | ||||||||
\(523\) | −5.99809 | + | 10.3890i | −0.262278 | + | 0.454279i | −0.966847 | − | 0.255357i | \(-0.917807\pi\) |
0.704569 | + | 0.709636i | \(0.251140\pi\) | |||||||
\(524\) | 7.67609 | − | 13.2954i | 0.335332 | − | 0.580812i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.81065 | + | 6.60024i | −0.166152 | + | 0.287784i | ||||
\(527\) | −17.6905 | −0.770611 | ||||||||
\(528\) | −0.0529314 | + | 0.0916798i | −0.00230354 | + | 0.00398985i | ||||
\(529\) | −4.46197 | − | 7.72837i | −0.193999 | − | 0.336016i | ||||
\(530\) | 13.7471 | − | 23.8107i | 0.597137 | − | 1.03427i | ||||
\(531\) | 0.654173 | + | 1.13306i | 0.0283887 | + | 0.0491706i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.8887 | − | 9.18068i | −0.731531 | − | 0.397660i | ||||
\(534\) | 3.82913 | + | 6.63225i | 0.165703 | + | 0.287005i | ||||
\(535\) | 48.6053 | 2.10139 | ||||||||
\(536\) | −23.5561 | −1.01747 | ||||||||
\(537\) | −6.06776 | −0.261843 | ||||||||
\(538\) | −4.10536 | −0.176995 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −8.07356 | + | 13.9838i | −0.347431 | + | 0.601767i | ||||
\(541\) | −18.1158 | − | 31.3775i | −0.778860 | − | 1.34903i | −0.932599 | − | 0.360914i | \(-0.882465\pi\) |
0.153739 | − | 0.988112i | \(-0.450869\pi\) | |||||||
\(542\) | 3.15829 | + | 5.47031i | 0.135660 | + | 0.234970i | ||||
\(543\) | 3.97057 | 0.170394 | ||||||||
\(544\) | −5.54665 | + | 9.60707i | −0.237811 | + | 0.411900i | ||||
\(545\) | 14.4624 | 0.619500 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.34857 | −0.314202 | −0.157101 | − | 0.987583i | \(-0.550215\pi\) | ||||
−0.157101 | + | 0.987583i | \(0.550215\pi\) | |||||||
\(548\) | 5.55973 | − | 9.62974i | 0.237500 | − | 0.411362i | ||||
\(549\) | 3.68064 | 0.157086 | ||||||||
\(550\) | −2.61535 | − | 4.52991i | −0.111519 | − | 0.193156i | ||||
\(551\) | −0.952888 | − | 1.65045i | −0.0405944 | − | 0.0703115i | ||||
\(552\) | 5.20786 | − | 9.02027i | 0.221661 | − | 0.383928i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.24816 | −0.138001 | ||||||||
\(555\) | −24.1213 | −1.02389 | ||||||||
\(556\) | 5.37340 | 0.227883 | ||||||||
\(557\) | 10.8280 | 0.458796 | 0.229398 | − | 0.973333i | \(-0.426324\pi\) | ||||
0.229398 | + | 0.973333i | \(0.426324\pi\) | |||||||
\(558\) | −9.96160 | − | 17.2540i | −0.421708 | − | 0.730420i | ||||
\(559\) | −0.362466 | − | 14.1098i | −0.0153307 | − | 0.596781i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.575009 | + | 0.995945i | 0.0242769 | + | 0.0420488i | ||||
\(562\) | 3.63847 | − | 6.30201i | 0.153480 | − | 0.265834i | ||||
\(563\) | −6.92997 | − | 12.0031i | −0.292064 | − | 0.505869i | 0.682234 | − | 0.731134i | \(-0.261009\pi\) |
−0.974298 | + | 0.225265i | \(0.927675\pi\) | |||||||
\(564\) | 3.03274 | − | 5.25285i | 0.127701 | − | 0.221185i | ||||
\(565\) | −47.3873 | −1.99360 | ||||||||
\(566\) | −6.49594 | + | 11.2513i | −0.273045 | + | 0.472927i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.80692 | − | 8.32583i | 0.201694 | − | 0.349344i | ||||
\(569\) | −13.7060 | + | 23.7395i | −0.574586 | + | 0.995212i | 0.421500 | + | 0.906828i | \(0.361504\pi\) |
−0.996086 | + | 0.0883842i | \(0.971830\pi\) | |||||||
\(570\) | 2.01048 | 0.0842099 | ||||||||
\(571\) | 0.103879 | − | 0.179923i | 0.00434719 | − | 0.00752956i | −0.863844 | − | 0.503760i | \(-0.831950\pi\) |
0.868191 | + | 0.496230i | \(0.165283\pi\) | |||||||
\(572\) | −3.62854 | − | 1.97247i | −0.151717 | − | 0.0824732i | ||||
\(573\) | −0.870251 | −0.0363552 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.3341 | − | 33.4876i | −0.806288 | − | 1.39653i | ||||
\(576\) | −11.5795 | −0.482480 | ||||||||
\(577\) | −1.66328 | + | 2.88089i | −0.0692434 | + | 0.119933i | −0.898568 | − | 0.438833i | \(-0.855392\pi\) |
0.829325 | + | 0.558766i | \(0.188725\pi\) | |||||||
\(578\) | −5.63818 | − | 9.76562i | −0.234518 | − | 0.406196i | ||||
\(579\) | 10.8609 | 0.451362 | ||||||||
\(580\) | −8.05959 | −0.334656 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.142452 | + | 0.246734i | 0.00590483 | + | 0.0102275i | ||||
\(583\) | −4.21447 | + | 7.29967i | −0.174545 | + | 0.302321i | ||||
\(584\) | 15.1950 | − | 26.3185i | 0.628772 | − | 1.08907i | ||||
\(585\) | −27.9389 | − | 15.1876i | −1.15513 | − | 0.627929i | ||||
\(586\) | 2.52769 | + | 4.37809i | 0.104418 | + | 0.180857i | ||||
\(587\) | −7.54051 | − | 13.0606i | −0.311230 | − | 0.539067i | 0.667399 | − | 0.744701i | \(-0.267408\pi\) |
−0.978629 | + | 0.205634i | \(0.934074\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.74064 | − | 8.21104i | 0.195335 | − | 0.338330i | ||||
\(590\) | −0.747686 | − | 1.29503i | −0.0307817 | − | 0.0533155i | ||||
\(591\) | −8.45953 | − | 14.6523i | −0.347978 | − | 0.602716i | ||||
\(592\) | 0.944935 | + | 1.63668i | 0.0388366 | + | 0.0672670i | ||||
\(593\) | 12.9245 | + | 22.3859i | 0.530747 | + | 0.919281i | 0.999356 | + | 0.0358751i | \(0.0114218\pi\) |
−0.468609 | + | 0.883405i | \(0.655245\pi\) | |||||||
\(594\) | −1.40564 | + | 2.43464i | −0.0576740 | + | 0.0998944i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.74055 | + | 6.47882i | 0.153219 | + | 0.265383i | ||||
\(597\) | 8.39052 | + | 14.5328i | 0.343401 | + | 0.594788i | ||||
\(598\) | 15.2337 | + | 8.28101i | 0.622952 | + | 0.338636i | ||||
\(599\) | 17.7734 | − | 30.7845i | 0.726203 | − | 1.25782i | −0.232274 | − | 0.972650i | \(-0.574617\pi\) |
0.958477 | − | 0.285170i | \(-0.0920501\pi\) | |||||||
\(600\) | 6.30807 | − | 10.9259i | 0.257526 | − | 0.446048i | ||||
\(601\) | −13.6474 | − | 23.6379i | −0.556688 | − | 0.964212i | −0.997770 | − | 0.0667449i | \(-0.978739\pi\) |
0.441082 | − | 0.897467i | \(-0.354595\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.6538 | 0.881810 | ||||||||
\(604\) | 21.5023 | 0.874915 | ||||||||
\(605\) | −17.5406 | − | 30.3811i | −0.713125 | − | 1.23517i | ||||
\(606\) | −1.68456 | + | 2.91775i | −0.0684308 | + | 0.118526i | ||||
\(607\) | 38.9258 | 1.57995 | 0.789976 | − | 0.613138i | \(-0.210093\pi\) | ||||
0.789976 | + | 0.613138i | \(0.210093\pi\) | |||||||
\(608\) | −2.97274 | − | 5.14894i | −0.120561 | − | 0.208817i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.20679 | −0.170328 | ||||||||
\(611\) | 22.7803 | + | 12.3834i | 0.921593 | + | 0.500977i | ||||
\(612\) | 3.16576 | − | 5.48326i | 0.127968 | − | 0.221648i | ||||
\(613\) | 0.886645 | 0.0358113 | 0.0179056 | − | 0.999840i | \(-0.494300\pi\) | ||||
0.0179056 | + | 0.999840i | \(0.494300\pi\) | |||||||
\(614\) | −9.45317 | + | 16.3734i | −0.381499 | + | 0.660775i | ||||
\(615\) | −6.06606 | + | 10.5067i | −0.244607 | + | 0.423672i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.3944 | + | 30.1280i | −0.700272 | + | 1.21291i | 0.268099 | + | 0.963391i | \(0.413605\pi\) |
−0.968371 | + | 0.249515i | \(0.919729\pi\) | |||||||
\(618\) | 2.32600 | 0.0935653 | ||||||||
\(619\) | 1.02781 | − | 1.78021i | 0.0413111 | − | 0.0715529i | −0.844631 | − | 0.535350i | \(-0.820180\pi\) |
0.885942 | + | 0.463797i | \(0.153513\pi\) | |||||||
\(620\) | −20.0483 | − | 34.7247i | −0.805161 | − | 1.39458i | ||||
\(621\) | −10.3913 | + | 17.9982i | −0.416987 | + | 0.722243i | ||||
\(622\) | −4.18864 | − | 7.25494i | −0.167949 | − | 0.290897i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.0109156 | − | 0.424915i | −0.000436975 | − | 0.0170102i | ||||
\(625\) | 6.19081 | + | 10.7228i | 0.247632 | + | 0.428912i | ||||
\(626\) | −17.7992 | −0.711398 | ||||||||
\(627\) | −0.616356 | −0.0246149 | ||||||||
\(628\) | −2.47336 | −0.0986979 | ||||||||
\(629\) | 20.5302 | 0.818593 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.6169 | − | 39.1736i | 0.900363 | − | 1.55947i | 0.0733401 | − | 0.997307i | \(-0.476634\pi\) |
0.827023 | − | 0.562168i | \(-0.190033\pi\) | |||||||
\(632\) | 16.8555 | + | 29.1946i | 0.670477 | + | 1.16130i | ||||
\(633\) | −1.88332 | − | 3.26201i | −0.0748554 | − | 0.129653i | ||||
\(634\) | 21.5848 | 0.857241 | ||||||||
\(635\) | 3.34678 | − | 5.79679i | 0.132813 | − | 0.230038i | ||||
\(636\) | −7.91700 | −0.313929 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.40321 | −0.0555534 | ||||||||
\(639\) | −4.41872 | + | 7.65345i | −0.174802 | + | 0.302766i | ||||
\(640\) | −26.1881 | −1.03518 | ||||||||
\(641\) | 9.53097 | + | 16.5081i | 0.376451 | + | 0.652032i | 0.990543 | − | 0.137202i | \(-0.0438111\pi\) |
−0.614092 | + | 0.789234i | \(0.710478\pi\) | |||||||
\(642\) | 3.97420 | + | 6.88352i | 0.156849 | + | 0.271671i | ||||
\(643\) | −5.26755 | + | 9.12367i | −0.207732 | + | 0.359802i | −0.951000 | − | 0.309192i | \(-0.899942\pi\) |
0.743268 | + | 0.668994i | \(0.233275\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.90811 | −0.350756 | ||||||||
\(646\) | −1.71117 | −0.0673252 | ||||||||
\(647\) | 24.1608 | 0.949860 | 0.474930 | − | 0.880024i | \(-0.342473\pi\) | ||||
0.474930 | + | 0.880024i | \(0.342473\pi\) | |||||||
\(648\) | 14.6540 | 0.575663 | ||||||||
\(649\) | 0.229219 | + | 0.397019i | 0.00899762 | + | 0.0155843i | ||||
\(650\) | 18.4520 | + | 10.0305i | 0.723745 | + | 0.393427i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.58714 | − | 13.1413i | −0.297135 | − | 0.514654i | ||||
\(653\) | 16.8445 | − | 29.1755i | 0.659176 | − | 1.14173i | −0.321653 | − | 0.946858i | \(-0.604238\pi\) |
0.980829 | − | 0.194869i | \(-0.0624282\pi\) | |||||||
\(654\) | 1.18251 | + | 2.04817i | 0.0462400 | + | 0.0800900i | ||||
\(655\) | 20.7098 | − | 35.8704i | 0.809199 | − | 1.40157i | ||||
\(656\) | 0.950537 | 0.0371122 | ||||||||
\(657\) | −13.9678 | + | 24.1930i | −0.544937 | + | 0.943859i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.10030 | − | 3.63782i | 0.0818159 | − | 0.141709i | −0.822214 | − | 0.569178i | \(-0.807261\pi\) |
0.904030 | + | 0.427469i | \(0.140595\pi\) | |||||||
\(660\) | −1.30329 | + | 2.25737i | −0.0507307 | + | 0.0878681i | ||||
\(661\) | −17.6726 | −0.687385 | −0.343693 | − | 0.939082i | \(-0.611678\pi\) | ||||
−0.343693 | + | 0.939082i | \(0.611678\pi\) | |||||||
\(662\) | 0.758708 | − | 1.31412i | 0.0294880 | − | 0.0510748i | ||||
\(663\) | −4.05684 | − | 2.20529i | −0.157555 | − | 0.0856465i | ||||
\(664\) | −4.22844 | −0.164095 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.5607 | + | 20.0236i | 0.447966 | + | 0.775900i | ||||
\(667\) | −10.3733 | −0.401655 | ||||||||
\(668\) | −10.5721 | + | 18.3114i | −0.409046 | + | 0.708488i | ||||
\(669\) | −0.779623 | − | 1.35035i | −0.0301420 | − | 0.0522074i | ||||
\(670\) | −24.7491 | −0.956143 | ||||||||
\(671\) | 1.28968 | 0.0497875 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.3052 | + | 17.8491i | 0.397235 | + | 0.688031i | 0.993384 | − | 0.114843i | \(-0.0366366\pi\) |
−0.596149 | + | 0.802874i | \(0.703303\pi\) | |||||||
\(674\) | 4.06901 | − | 7.04774i | 0.156733 | − | 0.271469i | ||||
\(675\) | −12.5865 | + | 21.8005i | −0.484456 | + | 0.839102i | ||||
\(676\) | 16.5607 | − | 0.851419i | 0.636952 | − | 0.0327469i | ||||
\(677\) | −10.6537 | − | 18.4527i | −0.409455 | − | 0.709196i | 0.585374 | − | 0.810763i | \(-0.300948\pi\) |
−0.994829 | + | 0.101567i | \(0.967614\pi\) | |||||||
\(678\) | −3.87461 | − | 6.71102i | −0.148804 | − | 0.257735i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −9.29147 | + | 16.0933i | −0.356312 | + | 0.617150i | ||||
\(681\) | −8.69264 | − | 15.0561i | −0.333103 | − | 0.576951i | ||||
\(682\) | −3.49049 | − | 6.04571i | −0.133658 | − | 0.231502i | ||||
\(683\) | 3.34878 | + | 5.80026i | 0.128138 | + | 0.221941i | 0.922955 | − | 0.384908i | \(-0.125767\pi\) |
−0.794817 | + | 0.606849i | \(0.792433\pi\) | |||||||
\(684\) | 1.69670 | + | 2.93877i | 0.0648750 | + | 0.112367i | ||||
\(685\) | 14.9999 | − | 25.9806i | 0.573118 | − | 0.992670i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.0226652 | − | 0.0392573i | −0.000864732 | − | 0.00149776i | ||||
\(688\) | 0.348970 | + | 0.604433i | 0.0133043 | + | 0.0230438i | ||||
\(689\) | −0.869117 | − | 33.8323i | −0.0331107 | − | 1.28891i | ||||
\(690\) | 5.47161 | − | 9.47710i | 0.208301 | − | 0.360787i | ||||
\(691\) | −12.4632 | + | 21.5868i | −0.474121 | + | 0.821202i | −0.999561 | − | 0.0296291i | \(-0.990567\pi\) |
0.525440 | + | 0.850831i | \(0.323901\pi\) | |||||||
\(692\) | 6.36936 | + | 11.0321i | 0.242127 | + | 0.419376i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.539093 | −0.0204637 | ||||||||
\(695\) | 14.4972 | 0.549911 | ||||||||
\(696\) | −1.69223 | − | 2.93102i | −0.0641437 | − | 0.111100i | ||||
\(697\) | 5.16298 | − | 8.94254i | 0.195562 | − | 0.338723i | ||||
\(698\) | 26.0435 | 0.985761 | ||||||||
\(699\) | 4.85017 | + | 8.40073i | 0.183450 | + | 0.317745i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.94583 | −0.186801 | −0.0934007 | − | 0.995629i | \(-0.529774\pi\) | ||||
−0.0934007 | + | 0.995629i | \(0.529774\pi\) | |||||||
\(702\) | −0.289874 | − | 11.2840i | −0.0109406 | − | 0.425886i | ||||
\(703\) | −5.50162 | + | 9.52908i | −0.207497 | + | 0.359396i | ||||
\(704\) | −4.05741 | −0.152919 | ||||||||
\(705\) | 8.18220 | − | 14.1720i | 0.308160 | − | 0.533748i | ||||
\(706\) | 0.468266 | − | 0.811061i | 0.0176234 | − | 0.0305247i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.215297 | + | 0.372905i | −0.00809136 | + | 0.0140146i | ||||
\(709\) | −4.64497 | −0.174446 | −0.0872228 | − | 0.996189i | \(-0.527799\pi\) | ||||
−0.0872228 | + | 0.996189i | \(0.527799\pi\) | |||||||
\(710\) | 5.05037 | − | 8.74749i | 0.189537 | − | 0.328288i | ||||
\(711\) | −15.4943 | − | 26.8369i | −0.581082 | − | 1.00646i | ||||
\(712\) | 18.9688 | − | 32.8550i | 0.710888 | − | 1.23129i | ||||
\(713\) | −25.8037 | − | 44.6933i | −0.966356 | − | 1.67378i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.78966 | − | 5.32165i | −0.366113 | − | 0.199018i | ||||
\(716\) | 5.85275 | + | 10.1373i | 0.218728 | + | 0.378847i | ||||
\(717\) | −2.21797 | −0.0828315 | ||||||||
\(718\) | 8.31878 | 0.310454 | ||||||||
\(719\) | −31.7413 | −1.18375 | −0.591875 | − | 0.806030i | \(-0.701612\pi\) | ||||
−0.591875 | + | 0.806030i | \(0.701612\pi\) | |||||||
\(720\) | 1.57247 | 0.0586025 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7.62714 | + | 13.2106i | −0.283853 | + | 0.491647i | ||||
\(723\) | 2.83658 | + | 4.91309i | 0.105493 | + | 0.182720i | ||||
\(724\) | −3.82987 | − | 6.63354i | −0.142336 | − | 0.246533i | ||||
\(725\) | −12.5647 | −0.466643 | ||||||||
\(726\) | 2.86840 | − | 4.96822i | 0.106456 | − | 0.184388i | ||||
\(727\) | −47.8755 | −1.77560 | −0.887801 | − | 0.460227i | \(-0.847768\pi\) | ||||
−0.887801 | + | 0.460227i | \(0.847768\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.17412 | −0.228671 | ||||||||
\(730\) | 15.9645 | − | 27.6514i | 0.590873 | − | 1.02342i | ||||
\(731\) | 7.58192 | 0.280427 | ||||||||
\(732\) | 0.605675 | + | 1.04906i | 0.0223864 | + | 0.0387743i | ||||
\(733\) | −3.80104 | − | 6.58359i | −0.140395 | − | 0.243171i | 0.787251 | − | 0.616633i | \(-0.211504\pi\) |
−0.927645 | + | 0.373463i | \(0.878170\pi\) | |||||||
\(734\) | 4.74386 | − | 8.21660i | 0.175099 | − | 0.303280i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −32.3618 | −1.19287 | ||||||||
\(737\) | 7.58737 | 0.279484 | ||||||||
\(738\) | 11.6292 | 0.428076 | ||||||||
\(739\) | −33.4236 | −1.22951 | −0.614754 | − | 0.788719i | \(-0.710745\pi\) | ||||
−0.614754 | + | 0.788719i | \(0.710745\pi\) | |||||||
\(740\) | 23.2665 | + | 40.2988i | 0.855294 | + | 1.48141i | ||||
\(741\) | 2.11072 | − | 1.29201i | 0.0775394 | − | 0.0474632i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.46912 | + | 2.54458i | 0.0538966 | + | 0.0933517i | 0.891715 | − | 0.452597i | \(-0.149503\pi\) |
−0.837818 | + | 0.545949i | \(0.816169\pi\) | |||||||
\(744\) | 8.41888 | − | 14.5819i | 0.308651 | − | 0.534599i | ||||
\(745\) | 10.0919 | + | 17.4796i | 0.369737 | + | 0.640403i | ||||
\(746\) | −13.0776 | + | 22.6511i | −0.478805 | + | 0.829314i | ||||
\(747\) | 3.88695 | 0.142216 | ||||||||
\(748\) | 1.10927 | − | 1.92131i | 0.0405588 | − | 0.0702499i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.78552 | − | 3.09261i | 0.0651980 | − | 0.112926i | ||||
\(751\) | −0.598389 | + | 1.03644i | −0.0218355 | + | 0.0378202i | −0.876737 | − | 0.480971i | \(-0.840284\pi\) |
0.854901 | + | 0.518791i | \(0.173618\pi\) | |||||||
\(752\) | −1.28213 | −0.0467545 | ||||||||
\(753\) | −7.11313 | + | 12.3203i | −0.259217 | + | 0.448977i | ||||
\(754\) | 4.80531 | − | 2.94141i | 0.174999 | − | 0.107120i | ||||
\(755\) | 58.0123 | 2.11128 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.77321 | − | 9.99950i | −0.209831 | − | 0.363438i | 0.741830 | − | 0.670588i | \(-0.233958\pi\) |
−0.951661 | + | 0.307150i | \(0.900625\pi\) | |||||||
\(758\) | −19.2841 | −0.700432 | ||||||||
\(759\) | −1.67744 | + | 2.90541i | −0.0608871 | + | 0.105460i | ||||
\(760\) | −4.97979 | − | 8.62525i | −0.180636 | − | 0.312871i | ||||
\(761\) | −34.6497 | −1.25605 | −0.628026 | − | 0.778192i | \(-0.716137\pi\) | ||||
−0.628026 | + | 0.778192i | \(0.716137\pi\) | |||||||
\(762\) | 1.09459 | 0.0396530 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.839413 | + | 1.45391i | 0.0303689 | + | 0.0526005i | ||||
\(765\) | 8.54110 | − | 14.7936i | 0.308804 | − | 0.534864i | ||||
\(766\) | 0.250768 | − | 0.434344i | 0.00906063 | − | 0.0156935i | ||||
\(767\) | −1.61720 | − | 0.879108i | −0.0583937 | − | 0.0317427i | ||||
\(768\) | −5.12890 | − | 8.88351i | −0.185073 | − | 0.320556i | ||||
\(769\) | −3.27437 | − | 5.67138i | −0.118077 | − | 0.204515i | 0.800929 | − | 0.598760i | \(-0.204340\pi\) |
−0.919006 | + | 0.394245i | \(0.871006\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.63253 | + | 2.82763i | −0.0587943 | + | 0.101835i | ||||
\(772\) | −10.4760 | − | 18.1450i | −0.377039 | − | 0.653051i | ||||
\(773\) | 16.9637 | + | 29.3821i | 0.610143 | + | 1.05680i | 0.991216 | + | 0.132254i | \(0.0422214\pi\) |
−0.381073 | + | 0.924545i | \(0.624445\pi\) | |||||||
\(774\) | 4.26941 | + | 7.39484i | 0.153461 | + | 0.265802i | ||||
\(775\) | −31.2550 | − | 54.1352i | −1.12271 | − | 1.94459i | ||||
\(776\) | 0.705683 | − | 1.22228i | 0.0253325 | − | 0.0438772i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.42547 | + | 4.20104i | 0.0869575 | + | 0.150615i | ||||
\(779\) | 2.76711 | + | 4.79278i | 0.0991422 | + | 0.171719i | ||||
\(780\) | −0.268768 | − | 10.4624i | −0.00962345 | − | 0.374614i | ||||
\(781\) | −1.54830 | + | 2.68173i | −0.0554024 | + | 0.0959598i | ||||
\(782\) | −4.65703 | + | 8.06620i | −0.166535 | + | 0.288447i | ||||
\(783\) | 3.37651 | + | 5.84829i | 0.120667 | + | 0.209001i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.67303 | −0.238171 | ||||||||
\(786\) | 6.77333 | 0.241597 | ||||||||
\(787\) | 6.48717 | + | 11.2361i | 0.231243 | + | 0.400524i | 0.958174 | − | 0.286186i | \(-0.0923876\pi\) |
−0.726932 | + | 0.686710i | \(0.759054\pi\) | |||||||
\(788\) | −16.3195 | + | 28.2662i | −0.581359 | + | 1.00694i | ||||
\(789\) | 5.92085 | 0.210788 | ||||||||
\(790\) | 17.7092 | + | 30.6732i | 0.630065 | + | 1.09130i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.41600 | 0.227983 | ||||||||
\(793\) | −4.41653 | + | 2.70344i | −0.156836 | + | 0.0960019i | ||||
\(794\) | 10.8639 | − | 18.8168i | 0.385545 | − | 0.667784i | ||||
\(795\) | −21.3597 | −0.757552 | ||||||||
\(796\) | 16.1864 | − | 28.0357i | 0.573712 | − | 0.993699i | ||||
\(797\) | 2.20956 | − | 3.82707i | 0.0782667 | − | 0.135562i | −0.824235 | − | 0.566247i | \(-0.808395\pi\) |
0.902502 | + | 0.430685i | \(0.141728\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.96408 | + | 12.0621i | −0.246371 | + | 0.426728i | ||||
\(800\) | −39.1985 | −1.38588 | ||||||||
\(801\) | −17.4369 | + | 30.2017i | −0.616104 | + | 1.06712i | ||||
\(802\) | 10.8523 | + | 18.7968i | 0.383209 | + | 0.663737i | ||||
\(803\) | −4.89426 | + | 8.47711i | −0.172715 | + | 0.299151i | ||||
\(804\) | 3.56327 | + | 6.17177i | 0.125667 | + | 0.217662i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 24.6264 | + | 13.3869i | 0.867427 | + | 0.471532i | ||||
\(807\) | 1.59469 | + | 2.76208i | 0.0561356 | + | 0.0972298i | ||||
\(808\) | 16.6901 | 0.587155 | ||||||||
\(809\) | 11.4716 | 0.403320 | 0.201660 | − | 0.979456i | \(-0.435366\pi\) | ||||
0.201660 | + | 0.979456i | \(0.435366\pi\) | |||||||
\(810\) | 15.3961 | 0.540965 | ||||||||
\(811\) | −23.8664 | −0.838063 | −0.419032 | − | 0.907972i | \(-0.637630\pi\) | ||||
−0.419032 | + | 0.907972i | \(0.637630\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.45361 | − | 4.24978i | 0.0860520 | − | 0.149046i | ||||
\(814\) | 4.05079 | + | 7.01618i | 0.141980 | + | 0.245917i | ||||
\(815\) | −20.4698 | − | 35.4548i | −0.717026 | − | 1.24193i | ||||
\(816\) | 0.228329 | 0.00799310 | ||||||||
\(817\) | −2.03178 | + | 3.51914i | −0.0710829 | + | 0.123119i | ||||
\(818\) | 0.125105 | 0.00437419 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.4044 | 0.817318 | ||||||||
\(821\) | −15.4847 | + | 26.8203i | −0.540420 | + | 0.936035i | 0.458460 | + | 0.888715i | \(0.348401\pi\) |
−0.998880 | + | 0.0473197i | \(0.984932\pi\) | |||||||
\(822\) | 4.90587 | 0.171112 | ||||||||
\(823\) | 4.30678 | + | 7.45957i | 0.150125 | + | 0.260024i | 0.931273 | − | 0.364321i | \(-0.118699\pi\) |
−0.781148 | + | 0.624346i | \(0.785366\pi\) | |||||||
\(824\) | −5.76129 | − | 9.97885i | −0.200704 | − | 0.347630i | ||||
\(825\) | −2.03181 | + | 3.51920i | −0.0707386 | + | 0.122523i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.9128 | 0.796756 | 0.398378 | − | 0.917221i | \(-0.369573\pi\) | ||||
0.398378 | + | 0.917221i | \(0.369573\pi\) | |||||||
\(828\) | 18.4706 | 0.641896 | ||||||||
\(829\) | 42.5611 | 1.47821 | 0.739104 | − | 0.673591i | \(-0.235249\pi\) | ||||
0.739104 | + | 0.673591i | \(0.235249\pi\) | |||||||
\(830\) | −4.44259 | −0.154204 | ||||||||
\(831\) | 1.26172 | + | 2.18536i | 0.0437685 | + | 0.0758093i | ||||
\(832\) | 13.8947 | − | 8.50518i | 0.481711 | − | 0.294864i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.18536 | + | 2.05311i | 0.0410458 | + | 0.0710933i | ||||
\(835\) | −28.5230 | + | 49.4033i | −0.987080 | + | 1.70967i | ||||
\(836\) | 0.594515 | + | 1.02973i | 0.0205617 | + | 0.0356140i | ||||
\(837\) | −16.7982 | + | 29.0954i | −0.580632 | + | 1.00568i | ||||
\(838\) | 11.6569 | 0.402682 | ||||||||
\(839\) | 0.920524 | − | 1.59439i | 0.0317800 | − | 0.0550446i | −0.849698 | − | 0.527270i | \(-0.823216\pi\) |
0.881478 | + | 0.472225i | \(0.156549\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.8147 | − | 22.1957i | 0.441885 | − | 0.765367i | ||||
\(842\) | 1.46465 | − | 2.53686i | 0.0504753 | − | 0.0874258i | ||||
\(843\) | −5.65332 | −0.194711 | ||||||||
\(844\) | −3.63317 | + | 6.29284i | −0.125059 | + | 0.216609i | ||||
\(845\) | 44.6802 | − | 2.29709i | 1.53705 | − | 0.0790224i | ||||
\(846\) | −15.6860 | −0.539296 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.836755 | + | 1.44930i | 0.0287343 | + | 0.0497692i | ||||
\(849\) | 10.0931 | 0.346396 | ||||||||
\(850\) | −5.64087 | + | 9.77027i | −0.193480 | + | 0.335118i | ||||
\(851\) | 29.9457 | + | 51.8675i | 1.02653 | + | 1.77800i | ||||
\(852\) | −2.90852 | −0.0996442 | ||||||||
\(853\) | 27.0293 | 0.925466 | 0.462733 | − | 0.886498i | \(-0.346869\pi\) | ||||
0.462733 | + | 0.886498i | \(0.346869\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.57763 | + | 7.92869i | 0.156552 | + | 0.271155i | ||||
\(856\) | 19.6875 | − | 34.0998i | 0.672906 | − | 1.16551i | ||||
\(857\) | 8.39268 | − | 14.5365i | 0.286688 | − | 0.496559i | −0.686329 | − | 0.727291i | \(-0.740779\pi\) |
0.973017 | + | 0.230732i | \(0.0741122\pi\) | |||||||
\(858\) | −0.0467936 | − | 1.82154i | −0.00159751 | − | 0.0621865i | ||||
\(859\) | 25.8058 | + | 44.6969i | 0.880482 | + | 1.52504i | 0.850806 | + | 0.525481i | \(0.176114\pi\) |
0.0296769 | + | 0.999560i | \(0.490552\pi\) | |||||||
\(860\) | 8.59245 | + | 14.8826i | 0.293000 | + | 0.507491i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.48624 | − | 16.4306i | 0.323102 | − | 0.559630i | ||||
\(863\) | −10.9807 | − | 19.0191i | −0.373787 | − | 0.647417i | 0.616358 | − | 0.787466i | \(-0.288607\pi\) |
−0.990145 | + | 0.140049i | \(0.955274\pi\) | |||||||
\(864\) | 10.5338 | + | 18.2450i | 0.358366 | + | 0.620709i | ||||
\(865\) | 17.1843 | + | 29.7640i | 0.584283 | + | 1.01201i | ||||
\(866\) | 11.0205 | + | 19.0880i | 0.374491 | + | 0.648638i | ||||
\(867\) | −4.38020 | + | 7.58673i | −0.148759 | + | 0.257659i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.42913 | − | 9.40352i | −0.184170 | − | 0.318993i | ||||
\(870\) | −1.77793 | − | 3.07947i | −0.0602775 | − | 0.104404i | ||||
\(871\) | −25.9831 | + | 15.9047i | −0.880404 | + | 0.538911i | ||||
\(872\) | 5.85797 | − | 10.1463i | 0.198376 | − | 0.343597i | ||||
\(873\) | −0.648693 | + | 1.12357i | −0.0219549 | + | 0.0380270i | ||||
\(874\) | −2.49595 | − | 4.32311i | −0.0844267 | − | 0.146231i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.19401 | −0.310637 | ||||||||
\(877\) | −9.61745 | −0.324758 | −0.162379 | − | 0.986728i | \(-0.551917\pi\) | ||||
−0.162379 | + | 0.986728i | \(0.551917\pi\) | |||||||
\(878\) | 11.9089 | + | 20.6268i | 0.401905 | + | 0.696120i | ||||
\(879\) | 1.96371 | − | 3.40125i | 0.0662344 | − | 0.114721i | ||||
\(880\) | 0.550986 | 0.0185737 | ||||||||
\(881\) | 14.4863 | + | 25.0910i | 0.488055 | + | 0.845336i | 0.999906 | − | 0.0137383i | \(-0.00437318\pi\) |
−0.511851 | + | 0.859075i | \(0.671040\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.60727 | 0.222352 | 0.111176 | − | 0.993801i | \(-0.464538\pi\) | ||||
0.111176 | + | 0.993801i | \(0.464538\pi\) | |||||||
\(884\) | 0.228755 | + | 8.90481i | 0.00769388 | + | 0.299501i | ||||
\(885\) | −0.580863 | + | 1.00608i | −0.0195255 | + | 0.0338191i | ||||
\(886\) | −28.2649 | −0.949578 | ||||||||
\(887\) | −15.7072 | + | 27.2057i | −0.527397 | + | 0.913478i | 0.472094 | + | 0.881548i | \(0.343498\pi\) |
−0.999490 | + | 0.0319293i | \(0.989835\pi\) | |||||||
\(888\) | −9.77029 | + | 16.9226i | −0.327869 | + | 0.567886i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 19.9295 | − | 34.5190i | 0.668039 | − | 1.15708i | ||||
\(891\) | −4.72001 | −0.158126 | ||||||||
\(892\) | −1.50399 | + | 2.60499i | −0.0503574 | + | 0.0872216i | ||||
\(893\) | −3.73242 | − | 6.46474i | −0.124901 | − | 0.216334i | ||||
\(894\) | −1.65032 | + | 2.85843i | −0.0551949 | + | 0.0956003i | ||||
\(895\) | 15.7905 | + | 27.3499i | 0.527818 | + | 0.914208i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.345925 | − | 13.4659i | −0.0115501 | − | 0.449613i | ||||
\(898\) | 8.37780 | + | 14.5108i | 0.279571 | + | 0.484231i | ||||
\(899\) | −16.7692 | −0.559283 | ||||||||
\(900\) | 22.3726 | 0.745755 | ||||||||
\(901\) | 18.1798 | 0.605658 | ||||||||
\(902\) | 4.07480 | 0.135676 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.1942 | + | 33.2453i | −0.638388 | + | 1.10572i | ||||
\(905\) | −10.3328 | − | 17.8970i | −0.343475 | − | 0.594917i | ||||
\(906\) | 4.74337 | + | 8.21575i | 0.157588 | + | 0.272950i | ||||
\(907\) | 9.73642 | 0.323292 | 0.161646 | − | 0.986849i | \(-0.448320\pi\) | ||||
0.161646 | + | 0.986849i | \(0.448320\pi\) | |||||||
\(908\) | −16.7692 | + | 29.0452i | −0.556507 | + | 0.963898i | ||||
\(909\) | −15.3422 | −0.508869 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.4372 | −1.27348 | −0.636740 | − | 0.771078i | \(-0.719718\pi\) | ||||
−0.636740 | + | 0.771078i | \(0.719718\pi\) | |||||||
\(912\) | −0.0611867 | + | 0.105979i | −0.00202609 | + | 0.00350930i | ||||
\(913\) | 1.36197 | 0.0450746 | ||||||||
\(914\) | −0.317871 | − | 0.550568i | −0.0105142 | − | 0.0182112i | ||||
\(915\) | 1.63409 | + | 2.83032i | 0.0540212 | + | 0.0935675i | ||||
\(916\) | −0.0437242 | + | 0.0757325i | −0.00144469 | + | 0.00250227i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.06346 | 0.200124 | ||||||||
\(919\) | 54.2804 | 1.79055 | 0.895273 | − | 0.445519i | \(-0.146981\pi\) | ||||
0.895273 | + | 0.445519i | \(0.146981\pi\) | |||||||
\(920\) | −54.2108 | −1.78728 | ||||||||
\(921\) | 14.6880 | 0.483985 | ||||||||
\(922\) | 14.1164 | + | 24.4502i | 0.464897 | + | 0.805226i | ||||
\(923\) | −0.319293 | − | 12.4292i | −0.0105097 | − | 0.409112i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.2721 | + | 62.8251i | 1.19262 | + | 2.06568i | ||||
\(926\) | −13.0869 | + | 22.6673i | −0.430064 | + | 0.744892i | ||||
\(927\) | 5.29602 | + | 9.17297i | 0.173944 | + | 0.301280i | ||||
\(928\) | −5.25777 | + | 9.10673i | −0.172595 | + | 0.298943i | ||||
\(929\) | 38.1920 | 1.25304 | 0.626519 | − | 0.779406i | \(-0.284479\pi\) | ||||
0.626519 | + | 0.779406i | \(0.284479\pi\) | |||||||
\(930\) | 8.84526 | − | 15.3204i | 0.290047 | − | 0.502377i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9.35660 | − | 16.2061i | 0.306486 | − | 0.530849i | ||||
\(933\) | −3.25408 | + | 5.63622i | −0.106534 | + | 0.184522i | ||||
\(934\) | −25.1988 | −0.824531 | ||||||||
\(935\) | 2.99276 | − | 5.18361i | 0.0978736 | − | 0.169522i | ||||
\(936\) | −21.9717 | + | 13.4493i | −0.718168 | + | 0.439604i | ||||
\(937\) | 19.0376 | 0.621931 | 0.310966 | − | 0.950421i | \(-0.399348\pi\) | ||||
0.310966 | + | 0.950421i | \(0.399348\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.91392 | + | 11.9753i | 0.225627 | + | 0.390798i | ||||
\(940\) | −31.5691 | −1.02967 | ||||||||
\(941\) | 23.0811 | − | 39.9776i | 0.752422 | − | 1.30323i | −0.194224 | − | 0.980957i | \(-0.562219\pi\) |
0.946646 | − | 0.322275i | \(-0.104448\pi\) | |||||||
\(942\) | −0.545619 | − | 0.945040i | −0.0177772 | − | 0.0307911i | ||||
\(943\) | 30.1232 | 0.980948 | ||||||||
\(944\) | 0.0910198 | 0.00296244 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.49598 | + | 2.59111i | 0.0486385 | + | 0.0842443i | ||||
\(947\) | 4.59687 | − | 7.96201i | 0.149378 | − | 0.258730i | −0.781620 | − | 0.623755i | \(-0.785606\pi\) |
0.930998 | + | 0.365025i | \(0.118940\pi\) | |||||||
\(948\) | 5.09938 | − | 8.83239i | 0.165620 | − | 0.286863i | ||||
\(949\) | −1.00930 | − | 39.2894i | −0.0327634 | − | 1.27539i | ||||
\(950\) | −3.02324 | − | 5.23641i | −0.0980869 | − | 0.169892i | ||||
\(951\) | −8.38440 | − | 14.5222i | −0.271883 | − | 0.470915i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.3232 | − | 38.6648i | 0.723118 | − | 1.25248i | −0.236626 | − | 0.971601i | \(-0.576042\pi\) |
0.959744 | − | 0.280876i | \(-0.0906250\pi\) | |||||||
\(954\) | 10.2371 | + | 17.7312i | 0.331440 | + | 0.574070i | ||||
\(955\) | 2.26470 | + | 3.92258i | 0.0732841 | + | 0.126932i | ||||
\(956\) | 2.13937 | + | 3.70550i | 0.0691923 | + | 0.119844i | ||||
\(957\) | 0.545062 | + | 0.944075i | 0.0176194 | + | 0.0305176i | ||||
\(958\) | −5.99641 | + | 10.3861i | −0.193735 | + | 0.335559i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −5.14093 | − | 8.90436i | −0.165923 | − | 0.287387i | ||||
\(961\) | −26.2136 | − | 45.4032i | −0.845599 | − | 1.46462i | ||||
\(962\) | −28.5794 | − | 15.5357i | −0.921437 | − | 0.500892i | ||||
\(963\) | −18.0976 | + | 31.3459i | −0.583186 | + | 1.01011i | ||||
\(964\) | 5.47212 | − | 9.47799i | 0.176245 | − | 0.305266i | ||||
\(965\) | −28.2638 | − | 48.9544i | −0.909845 | − | 1.57590i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.8268 | 0.444639 | 0.222320 | − | 0.974974i | \(-0.428637\pi\) | ||||
0.222320 | + | 0.974974i | \(0.428637\pi\) | |||||||
\(968\) | −28.4191 | −0.913426 | ||||||||
\(969\) | 0.664689 | + | 1.15128i | 0.0213529 | + | 0.0369843i | ||||
\(970\) | 0.741422 | − | 1.28418i | 0.0238056 | − | 0.0412326i | ||||
\(971\) | −7.26873 | −0.233265 | −0.116632 | − | 0.993175i | \(-0.537210\pi\) | ||||
−0.116632 | + | 0.993175i | \(0.537210\pi\) | |||||||
\(972\) | −9.25454 | − | 16.0293i | −0.296839 | − | 0.514141i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 14.2950 | 0.458043 | ||||||||
\(975\) | −0.419005 | − | 16.3107i | −0.0134189 | − | 0.522360i | ||||
\(976\) | 0.128029 | − | 0.221752i | 0.00409810 | − | 0.00709811i | ||||
\(977\) | 42.8101 | 1.36962 | 0.684808 | − | 0.728723i | \(-0.259886\pi\) | ||||
0.684808 | + | 0.728723i | \(0.259886\pi\) | |||||||
\(978\) | 3.34742 | − | 5.79790i | 0.107039 | − | 0.185397i | ||||
\(979\) | −6.10982 | + | 10.5825i | −0.195271 | + | 0.338219i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.38489 | + | 9.32690i | −0.171926 | + | 0.297785i | ||||
\(982\) | −18.4430 | −0.588541 | ||||||||
\(983\) | −23.1544 | + | 40.1046i | −0.738511 | + | 1.27914i | 0.214655 | + | 0.976690i | \(0.431137\pi\) |
−0.953166 | + | 0.302448i | \(0.902196\pi\) | |||||||
\(984\) | 4.91410 | + | 8.51147i | 0.156656 | + | 0.271336i | ||||
\(985\) | −44.0294 | + | 76.2612i | −1.40289 | + | 2.42988i | ||||
\(986\) | 1.51324 | + | 2.62101i | 0.0481914 | + | 0.0834700i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.19446 | − | 2.28010i | −0.133444 | − | 0.0725398i | ||||
\(989\) | 11.0591 | + | 19.1550i | 0.351660 | + | 0.609092i | ||||
\(990\) | 6.74094 | 0.214241 | ||||||||
\(991\) | −58.2324 | −1.84981 | −0.924907 | − | 0.380194i | \(-0.875857\pi\) | ||||
−0.924907 | + | 0.380194i | \(0.875857\pi\) | |||||||
\(992\) | −52.3151 | −1.66101 | ||||||||
\(993\) | −1.17885 | −0.0374097 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 43.6703 | − | 75.6392i | 1.38444 | − | 2.39792i | ||||
\(996\) | 0.639625 | + | 1.10786i | 0.0202673 | + | 0.0351040i | ||||
\(997\) | −2.24739 | − | 3.89260i | −0.0711757 | − | 0.123280i | 0.828241 | − | 0.560372i | \(-0.189342\pi\) |
−0.899417 | + | 0.437092i | \(0.856008\pi\) | |||||||
\(998\) | 19.8353 | 0.627875 | ||||||||
\(999\) | 19.4947 | − | 33.7658i | 0.616786 | − | 1.06830i |
(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 | 637.2.g.l.263.4 | 12 | ||
7.2 | even | 3 | 637.2.h.l.471.3 | 12 | |||
7.3 | odd | 6 | 637.2.f.k.393.4 | 12 | |||
7.4 | even | 3 | 637.2.f.j.393.4 | 12 | |||
7.5 | odd | 6 | 91.2.h.b.16.3 | yes | 12 | ||
7.6 | odd | 2 | 91.2.g.b.81.4 | yes | 12 | ||
13.9 | even | 3 | 637.2.h.l.165.3 | 12 | |||
21.5 | even | 6 | 819.2.s.d.289.4 | 12 | |||
21.20 | even | 2 | 819.2.n.d.172.3 | 12 | |||
91.3 | odd | 6 | 8281.2.a.bz.1.3 | 6 | |||
91.9 | even | 3 | inner | 637.2.g.l.373.4 | 12 | ||
91.10 | odd | 6 | 8281.2.a.ce.1.4 | 6 | |||
91.48 | odd | 6 | 91.2.h.b.74.3 | yes | 12 | ||
91.55 | odd | 6 | 1183.2.e.h.508.4 | 12 | |||
91.61 | odd | 6 | 91.2.g.b.9.4 | ✓ | 12 | ||
91.62 | odd | 6 | 1183.2.e.g.508.3 | 12 | |||
91.68 | odd | 6 | 1183.2.e.h.170.4 | 12 | |||
91.74 | even | 3 | 637.2.f.j.295.4 | 12 | |||
91.75 | odd | 6 | 1183.2.e.g.170.3 | 12 | |||
91.81 | even | 3 | 8281.2.a.ca.1.3 | 6 | |||
91.87 | odd | 6 | 637.2.f.k.295.4 | 12 | |||
91.88 | even | 6 | 8281.2.a.cf.1.4 | 6 | |||
273.152 | even | 6 | 819.2.n.d.100.3 | 12 | |||
273.230 | even | 6 | 819.2.s.d.802.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.g.b.9.4 | ✓ | 12 | 91.61 | odd | 6 | ||
91.2.g.b.81.4 | yes | 12 | 7.6 | odd | 2 | ||
91.2.h.b.16.3 | yes | 12 | 7.5 | odd | 6 | ||
91.2.h.b.74.3 | yes | 12 | 91.48 | odd | 6 | ||
637.2.f.j.295.4 | 12 | 91.74 | even | 3 | |||
637.2.f.j.393.4 | 12 | 7.4 | even | 3 | |||
637.2.f.k.295.4 | 12 | 91.87 | odd | 6 | |||
637.2.f.k.393.4 | 12 | 7.3 | odd | 6 | |||
637.2.g.l.263.4 | 12 | 1.1 | even | 1 | trivial | ||
637.2.g.l.373.4 | 12 | 91.9 | even | 3 | inner | ||
637.2.h.l.165.3 | 12 | 13.9 | even | 3 | |||
637.2.h.l.471.3 | 12 | 7.2 | even | 3 | |||
819.2.n.d.100.3 | 12 | 273.152 | even | 6 | |||
819.2.n.d.172.3 | 12 | 21.20 | even | 2 | |||
819.2.s.d.289.4 | 12 | 21.5 | even | 6 | |||
819.2.s.d.802.4 | 12 | 273.230 | even | 6 | |||
1183.2.e.g.170.3 | 12 | 91.75 | odd | 6 | |||
1183.2.e.g.508.3 | 12 | 91.62 | odd | 6 | |||
1183.2.e.h.170.4 | 12 | 91.68 | odd | 6 | |||
1183.2.e.h.508.4 | 12 | 91.55 | odd | 6 | |||
8281.2.a.bz.1.3 | 6 | 91.3 | odd | 6 | |||
8281.2.a.ca.1.3 | 6 | 91.81 | even | 3 | |||
8281.2.a.ce.1.4 | 6 | 91.10 | odd | 6 | |||
8281.2.a.cf.1.4 | 6 | 91.88 | even | 6 |