Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [196,2,Mod(19,196)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(196, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("196.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 196 = 2^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 196.f (of order \(6\), 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: | \(1.56506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 4x^{14} + 6x^{12} + 8x^{10} + 20x^{8} + 32x^{6} + 96x^{4} + 256x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.2 | ||
Root | \(-0.264742 + 1.38921i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 196.19 |
Dual form | 196.2.f.d.31.2 |
$q$-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 \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).
\(n\) | \(99\) | \(101\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.31509 | − | 0.520123i | −0.929912 | − | 0.367783i | ||||
\(3\) | 1.07072 | + | 1.85455i | 0.618182 | + | 1.07072i | 0.989817 | + | 0.142344i | \(0.0454638\pi\) |
−0.371635 | + | 0.928379i | \(0.621203\pi\) | |||||||
\(4\) | 1.45894 | + | 1.36802i | 0.729472 | + | 0.684011i | ||||
\(5\) | 2.26303 | + | 1.30656i | 1.01206 | + | 0.584313i | 0.911794 | − | 0.410648i | \(-0.134697\pi\) |
0.100265 | + | 0.994961i | \(0.468031\pi\) | |||||||
\(6\) | −0.443508 | − | 2.99581i | −0.181061 | − | 1.22303i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.20711 | − | 2.55791i | −0.426777 | − | 0.904357i | ||||
\(9\) | −0.792893 | + | 1.37333i | −0.264298 | + | 0.457777i | ||||
\(10\) | −2.29653 | − | 2.89531i | −0.726226 | − | 0.915577i | ||||
\(11\) | −3.42675 | + | 1.97844i | −1.03321 | + | 0.596521i | −0.917901 | − | 0.396809i | \(-0.870118\pi\) |
−0.115304 | + | 0.993330i | \(0.536784\pi\) | |||||||
\(12\) | −0.974936 | + | 4.17045i | −0.281440 | + | 1.20390i | ||||
\(13\) | − | 1.08239i | − | 0.300202i | −0.988671 | − | 0.150101i | \(-0.952040\pi\) | ||
0.988671 | − | 0.150101i | \(-0.0479598\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.59587i | 1.44485i | ||||||||
\(16\) | 0.257031 | + | 3.99173i | 0.0642577 | + | 0.997933i | ||||
\(17\) | −0.274552 | + | 0.158513i | −0.0665886 | + | 0.0384450i | −0.532925 | − | 0.846163i | \(-0.678907\pi\) |
0.466336 | + | 0.884608i | \(0.345574\pi\) | |||||||
\(18\) | 1.75703 | − | 1.39366i | 0.414136 | − | 0.328488i | ||||
\(19\) | 2.58495 | − | 4.47727i | 0.593029 | − | 1.02716i | −0.400793 | − | 0.916169i | \(-0.631265\pi\) |
0.993822 | − | 0.110987i | \(-0.0354013\pi\) | |||||||
\(20\) | 1.51423 | + | 5.00208i | 0.338592 | + | 1.11850i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.53553 | − | 0.819496i | 1.18018 | − | 0.174717i | ||||
\(23\) | 2.00735 | + | 1.15894i | 0.418561 | + | 0.241656i | 0.694461 | − | 0.719530i | \(-0.255643\pi\) |
−0.275901 | + | 0.961186i | \(0.588976\pi\) | |||||||
\(24\) | 3.45128 | − | 4.97744i | 0.704490 | − | 1.01602i | ||||
\(25\) | 0.914214 | + | 1.58346i | 0.182843 | + | 0.316693i | ||||
\(26\) | −0.562978 | + | 1.42345i | −0.110409 | + | 0.279161i | ||||
\(27\) | 3.02846 | 0.582827 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.82843 | −1.26801 | −0.634004 | − | 0.773330i | \(-0.718590\pi\) | ||||
−0.634004 | + | 0.773330i | \(0.718590\pi\) | |||||||
\(30\) | 2.91054 | − | 7.35909i | 0.531390 | − | 1.34358i | ||||
\(31\) | 3.02846 | + | 5.24545i | 0.543928 | + | 0.942110i | 0.998674 | + | 0.0514890i | \(0.0163967\pi\) |
−0.454746 | + | 0.890621i | \(0.650270\pi\) | |||||||
\(32\) | 1.73817 | − | 5.38319i | 0.307269 | − | 0.951623i | ||||
\(33\) | −7.33820 | − | 4.23671i | −1.27742 | − | 0.737517i | ||||
\(34\) | 0.443508 | − | 0.0656581i | 0.0760610 | − | 0.0112603i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.03553 | + | 0.918917i | −0.505922 | + | 0.153153i | ||||
\(37\) | 2.00000 | − | 3.46410i | 0.328798 | − | 0.569495i | −0.653476 | − | 0.756948i | \(-0.726690\pi\) |
0.982274 | + | 0.187453i | \(0.0600231\pi\) | |||||||
\(38\) | −5.72819 | + | 4.54353i | −0.929235 | + | 0.737059i | ||||
\(39\) | 2.00735 | − | 1.15894i | 0.321433 | − | 0.185579i | ||||
\(40\) | 0.610345 | − | 7.36579i | 0.0965040 | − | 1.16463i | ||||
\(41\) | 2.29610i | 0.358591i | 0.983795 | + | 0.179295i | \(0.0573818\pi\) | ||||
−0.983795 | + | 0.179295i | \(0.942618\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.23486i | − | 1.10331i | −0.834074 | − | 0.551653i | \(-0.813997\pi\) | ||
0.834074 | − | 0.551653i | \(-0.186003\pi\) | |||||||
\(44\) | −7.70598 | − | 1.80145i | −1.16172 | − | 0.271578i | ||||
\(45\) | −3.58869 | + | 2.07193i | −0.534970 | + | 0.308865i | ||||
\(46\) | −2.03706 | − | 2.56818i | −0.300347 | − | 0.378658i | ||||
\(47\) | −2.14144 | + | 3.70909i | −0.312362 | + | 0.541027i | −0.978873 | − | 0.204468i | \(-0.934453\pi\) |
0.666511 | + | 0.745495i | \(0.267787\pi\) | |||||||
\(48\) | −7.12764 | + | 4.75071i | −1.02879 | + | 0.685706i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.378680 | − | 2.55791i | −0.0535534 | − | 0.361743i | ||||
\(51\) | −0.587938 | − | 0.339446i | −0.0823278 | − | 0.0475320i | ||||
\(52\) | 1.48074 | − | 1.57915i | 0.205341 | − | 0.218989i | ||||
\(53\) | −5.24264 | − | 9.08052i | −0.720132 | − | 1.24731i | −0.960947 | − | 0.276734i | \(-0.910748\pi\) |
0.240814 | − | 0.970571i | \(-0.422585\pi\) | |||||||
\(54\) | −3.98271 | − | 1.57517i | −0.541978 | − | 0.214354i | ||||
\(55\) | −10.3398 | −1.39422 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.0711 | 1.46640 | ||||||||
\(58\) | 8.98002 | + | 3.55162i | 1.17913 | + | 0.466351i | ||||
\(59\) | −5.61341 | − | 9.72272i | −0.730804 | − | 1.26579i | −0.956540 | − | 0.291601i | \(-0.905812\pi\) |
0.225736 | − | 0.974189i | \(-0.427521\pi\) | |||||||
\(60\) | −7.65527 | + | 8.16405i | −0.988291 | + | 1.05397i | ||||
\(61\) | 4.68690 | + | 2.70598i | 0.600096 | + | 0.346465i | 0.769079 | − | 0.639154i | \(-0.220715\pi\) |
−0.168984 | + | 0.985619i | \(0.554049\pi\) | |||||||
\(62\) | −1.25443 | − | 8.47343i | −0.159313 | − | 1.07613i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.08579 | + | 6.17534i | −0.635723 | + | 0.771917i | ||||
\(65\) | 1.41421 | − | 2.44949i | 0.175412 | − | 0.303822i | ||||
\(66\) | 7.44681 | + | 9.38845i | 0.916639 | + | 1.15564i | ||||
\(67\) | 2.83882 | − | 1.63899i | 0.346817 | − | 0.200235i | −0.316466 | − | 0.948604i | \(-0.602496\pi\) |
0.663282 | + | 0.748369i | \(0.269163\pi\) | |||||||
\(68\) | −0.617405 | − | 0.144332i | −0.0748713 | − | 0.0175029i | ||||
\(69\) | 4.96362i | 0.597550i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 4.46996 | + | 0.370390i | 0.526790 | + | 0.0436509i | ||||
\(73\) | 12.1388 | − | 7.00835i | 1.42074 | − | 0.820266i | 0.424380 | − | 0.905484i | \(-0.360492\pi\) |
0.996362 | + | 0.0852188i | \(0.0271589\pi\) | |||||||
\(74\) | −4.43195 | + | 3.51537i | −0.515203 | + | 0.408654i | ||||
\(75\) | −1.95774 | + | 3.39090i | −0.226060 | + | 0.391548i | ||||
\(76\) | 9.89630 | − | 2.99581i | 1.13518 | − | 0.343643i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.24264 | + | 0.480049i | −0.367157 | + | 0.0543549i | ||||
\(79\) | −6.85351 | − | 3.95687i | −0.771080 | − | 0.445183i | 0.0621799 | − | 0.998065i | \(-0.480195\pi\) |
−0.833260 | + | 0.552882i | \(0.813528\pi\) | |||||||
\(80\) | −4.63378 | + | 9.36925i | −0.518073 | + | 1.04751i | ||||
\(81\) | 5.62132 | + | 9.73641i | 0.624591 | + | 1.08182i | ||||
\(82\) | 1.19426 | − | 3.01959i | 0.131883 | − | 0.333458i | ||||
\(83\) | 9.45280 | 1.03758 | 0.518790 | − | 0.854902i | \(-0.326383\pi\) | ||||
0.518790 | + | 0.854902i | \(0.326383\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.828427 | −0.0898555 | ||||||||
\(86\) | −3.76302 | + | 9.51451i | −0.405777 | + | 1.02598i | ||||
\(87\) | −7.31135 | − | 12.6636i | −0.783859 | − | 1.35768i | ||||
\(88\) | 9.19712 | + | 6.37714i | 0.980416 | + | 0.679805i | ||||
\(89\) | 5.18889 | + | 2.99581i | 0.550022 | + | 0.317555i | 0.749131 | − | 0.662422i | \(-0.230471\pi\) |
−0.199109 | + | 0.979977i | \(0.563805\pi\) | |||||||
\(90\) | 5.79712 | − | 0.858221i | 0.611070 | − | 0.0904645i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.34315 | + | 4.43692i | 0.140033 | + | 0.462581i | ||||
\(93\) | −6.48528 | + | 11.2328i | −0.672492 | + | 1.16479i | ||||
\(94\) | 4.74539 | − | 3.76399i | 0.489449 | − | 0.388226i | ||||
\(95\) | 11.6997 | − | 6.75481i | 1.20036 | − | 0.693029i | ||||
\(96\) | 11.8445 | − | 2.54038i | 1.20887 | − | 0.259276i | ||||
\(97\) | − | 9.23880i | − | 0.938058i | −0.883183 | − | 0.469029i | \(-0.844604\pi\) | ||
0.883183 | − | 0.469029i | \(-0.155396\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 6.27476i | − | 0.630637i | ||||||
\(100\) | −0.832429 | + | 3.56085i | −0.0832429 | + | 0.356085i | ||||
\(101\) | −13.1899 | + | 7.61521i | −1.31245 | + | 0.757741i | −0.982501 | − | 0.186258i | \(-0.940364\pi\) |
−0.329946 | + | 0.944000i | \(0.607030\pi\) | |||||||
\(102\) | 0.596640 | + | 0.752204i | 0.0590761 | + | 0.0744793i | ||||
\(103\) | −6.05692 | + | 10.4909i | −0.596806 | + | 1.03370i | 0.396483 | + | 0.918042i | \(0.370231\pi\) |
−0.993289 | + | 0.115657i | \(0.963103\pi\) | |||||||
\(104\) | −2.76866 | + | 1.30656i | −0.271489 | + | 0.128119i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.17157 | + | 14.6686i | 0.210922 | + | 1.42474i | ||||
\(107\) | 2.00735 | + | 1.15894i | 0.194057 | + | 0.112039i | 0.593881 | − | 0.804553i | \(-0.297595\pi\) |
−0.399823 | + | 0.916592i | \(0.630928\pi\) | |||||||
\(108\) | 4.41835 | + | 4.14300i | 0.425156 | + | 0.398660i | ||||
\(109\) | 2.82843 | + | 4.89898i | 0.270914 | + | 0.469237i | 0.969096 | − | 0.246683i | \(-0.0793407\pi\) |
−0.698182 | + | 0.715920i | \(0.746007\pi\) | |||||||
\(110\) | 13.5978 | + | 5.37798i | 1.29650 | + | 0.512770i | ||||
\(111\) | 8.56578 | 0.813028 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.24264 | −0.399114 | −0.199557 | − | 0.979886i | \(-0.563950\pi\) | ||||
−0.199557 | + | 0.979886i | \(0.563950\pi\) | |||||||
\(114\) | −14.5595 | − | 5.75832i | −1.36362 | − | 0.539316i | ||||
\(115\) | 3.02846 | + | 5.24545i | 0.282405 | + | 0.489140i | ||||
\(116\) | −9.96229 | − | 9.34144i | −0.924975 | − | 0.867331i | ||||
\(117\) | 1.48648 | + | 0.858221i | 0.137425 | + | 0.0793426i | ||||
\(118\) | 2.32515 | + | 15.7060i | 0.214048 | + | 1.44585i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 14.3137 | − | 6.75481i | 1.30666 | − | 0.616627i | ||||
\(121\) | 2.32843 | − | 4.03295i | 0.211675 | − | 0.366632i | ||||
\(122\) | −4.75626 | − | 5.99638i | −0.430612 | − | 0.542887i | ||||
\(123\) | −4.25822 | + | 2.45849i | −0.383951 | + | 0.221674i | ||||
\(124\) | −2.75754 | + | 11.7958i | −0.247634 | + | 1.05930i | ||||
\(125\) | − | 8.28772i | − | 0.741276i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.2316i | − | 0.907911i | −0.891024 | − | 0.453955i | \(-0.850013\pi\) | ||
0.891024 | − | 0.453955i | \(-0.149987\pi\) | |||||||
\(128\) | 9.90022 | − | 5.47591i | 0.875064 | − | 0.484007i | ||||
\(129\) | 13.4174 | − | 7.74652i | 1.18133 | − | 0.682043i | ||||
\(130\) | −3.13386 | + | 2.48574i | −0.274858 | + | 0.218014i | ||||
\(131\) | −0.183707 | + | 0.318190i | −0.0160505 | + | 0.0278004i | −0.873939 | − | 0.486035i | \(-0.838443\pi\) |
0.857889 | + | 0.513836i | \(0.171776\pi\) | |||||||
\(132\) | −4.91010 | − | 16.2200i | −0.427370 | − | 1.41177i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.58579 | + | 0.678892i | −0.396152 | + | 0.0586474i | ||||
\(135\) | 6.85351 | + | 3.95687i | 0.589856 | + | 0.340554i | ||||
\(136\) | 0.736874 | + | 0.510937i | 0.0631865 | + | 0.0438125i | ||||
\(137\) | 4.12132 | + | 7.13834i | 0.352108 | + | 0.609869i | 0.986619 | − | 0.163045i | \(-0.0521316\pi\) |
−0.634510 | + | 0.772914i | \(0.718798\pi\) | |||||||
\(138\) | 2.58169 | − | 6.52763i | 0.219768 | − | 0.555668i | ||||
\(139\) | −22.8211 | −1.93566 | −0.967829 | − | 0.251610i | \(-0.919040\pi\) | ||||
−0.967829 | + | 0.251610i | \(0.919040\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.17157 | −0.772386 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.14144 | + | 3.70909i | 0.179077 | + | 0.310170i | ||||
\(144\) | −5.68577 | − | 2.81203i | −0.473814 | − | 0.234336i | ||||
\(145\) | −15.4530 | − | 8.92177i | −1.28330 | − | 0.740913i | ||||
\(146\) | −19.6089 | + | 2.90295i | −1.62284 | + | 0.240250i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.65685 | − | 2.31788i | 0.629390 | − | 0.190529i | ||||
\(149\) | −2.41421 | + | 4.18154i | −0.197780 | + | 0.342565i | −0.947808 | − | 0.318841i | \(-0.896707\pi\) |
0.750028 | + | 0.661406i | \(0.230040\pi\) | |||||||
\(150\) | 4.33830 | − | 3.44109i | 0.354220 | − | 0.280964i | ||||
\(151\) | −18.5532 | + | 10.7117i | −1.50984 | + | 0.871704i | −0.509902 | + | 0.860233i | \(0.670318\pi\) |
−0.999934 | + | 0.0114717i | \(0.996348\pi\) | |||||||
\(152\) | −14.5728 | − | 1.20753i | −1.18201 | − | 0.0979435i | ||||
\(153\) | − | 0.502734i | − | 0.0406437i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.8275i | 1.27130i | ||||||||
\(156\) | 4.51406 | + | 1.05526i | 0.361414 | + | 0.0844887i | ||||
\(157\) | −16.6178 | + | 9.59428i | −1.32624 | + | 0.765707i | −0.984717 | − | 0.174165i | \(-0.944277\pi\) |
−0.341527 | + | 0.939872i | \(0.610944\pi\) | |||||||
\(158\) | 6.95494 | + | 8.76833i | 0.553305 | + | 0.697571i | ||||
\(159\) | 11.2268 | − | 19.4454i | 0.890345 | − | 1.54212i | ||||
\(160\) | 10.9670 | − | 9.91131i | 0.867019 | − | 0.783558i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.32843 | − | 15.7281i | −0.182939 | − | 1.23571i | ||||
\(163\) | −13.1191 | − | 7.57430i | −1.02757 | − | 0.593265i | −0.111279 | − | 0.993789i | \(-0.535495\pi\) |
−0.916286 | + | 0.400524i | \(0.868828\pi\) | |||||||
\(164\) | −3.14112 | + | 3.34988i | −0.245280 | + | 0.261582i | ||||
\(165\) | −11.0711 | − | 19.1757i | −0.861881 | − | 1.49282i | ||||
\(166\) | −12.4313 | − | 4.91662i | −0.964857 | − | 0.381604i | ||||
\(167\) | 7.83095 | 0.605977 | 0.302989 | − | 0.952994i | \(-0.402016\pi\) | ||||
0.302989 | + | 0.952994i | \(0.402016\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8284 | 0.909879 | ||||||||
\(170\) | 1.08946 | + | 0.430884i | 0.0835577 | + | 0.0330473i | ||||
\(171\) | 4.09918 | + | 7.09999i | 0.313472 | + | 0.542950i | ||||
\(172\) | 9.89744 | − | 10.5552i | 0.754673 | − | 0.804830i | ||||
\(173\) | 5.69089 | + | 3.28564i | 0.432671 | + | 0.249802i | 0.700484 | − | 0.713668i | \(-0.252968\pi\) |
−0.267813 | + | 0.963471i | \(0.586301\pi\) | |||||||
\(174\) | 3.02846 | + | 20.4567i | 0.229587 | + | 1.55082i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.77817 | − | 13.1702i | −0.661680 | − | 0.992739i | ||||
\(177\) | 12.0208 | − | 20.8207i | 0.903540 | − | 1.56498i | ||||
\(178\) | −5.26569 | − | 6.63864i | −0.394680 | − | 0.497587i | ||||
\(179\) | 11.6997 | − | 6.75481i | 0.874474 | − | 0.504878i | 0.00564179 | − | 0.999984i | \(-0.498204\pi\) |
0.868833 | + | 0.495106i | \(0.164871\pi\) | |||||||
\(180\) | −8.07014 | − | 1.88658i | −0.601513 | − | 0.140617i | ||||
\(181\) | 21.9874i | 1.63431i | 0.576418 | + | 0.817155i | \(0.304450\pi\) | ||||
−0.576418 | + | 0.817155i | \(0.695550\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.5894i | 0.856714i | ||||||||
\(184\) | 0.541385 | − | 6.53357i | 0.0399115 | − | 0.481661i | ||||
\(185\) | 9.05213 | − | 5.22625i | 0.665526 | − | 0.384242i | ||||
\(186\) | 14.3712 | − | 11.3991i | 1.05375 | − | 0.835822i | ||||
\(187\) | 0.627215 | − | 1.08637i | 0.0458665 | − | 0.0794431i | ||||
\(188\) | −8.19837 | + | 2.48181i | −0.597927 | + | 0.181005i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.8995 | + | 2.79793i | −1.37111 | + | 0.202983i | ||||
\(191\) | 5.67763 | + | 3.27798i | 0.410819 | + | 0.237186i | 0.691142 | − | 0.722719i | \(-0.257108\pi\) |
−0.280323 | + | 0.959906i | \(0.590441\pi\) | |||||||
\(192\) | −16.8979 | − | 2.81975i | −1.21950 | − | 0.203498i | ||||
\(193\) | −7.29289 | − | 12.6317i | −0.524954 | − | 0.909247i | −0.999578 | − | 0.0290581i | \(-0.990749\pi\) |
0.474624 | − | 0.880189i | \(-0.342584\pi\) | |||||||
\(194\) | −4.80531 | + | 12.1499i | −0.345001 | + | 0.872311i | ||||
\(195\) | 6.05692 | 0.433745 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | −3.26365 | + | 8.25189i | −0.231937 | + | 0.586437i | ||||
\(199\) | 8.56578 | + | 14.8364i | 0.607212 | + | 1.05172i | 0.991698 | + | 0.128591i | \(0.0410455\pi\) |
−0.384486 | + | 0.923131i | \(0.625621\pi\) | |||||||
\(200\) | 2.94680 | − | 4.24988i | 0.208370 | − | 0.300512i | ||||
\(201\) | 6.07917 | + | 3.50981i | 0.428791 | + | 0.247563i | ||||
\(202\) | 21.3068 | − | 3.15432i | 1.49914 | − | 0.221937i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.393398 | − | 1.29954i | −0.0275434 | − | 0.0909863i | ||||
\(205\) | −3.00000 | + | 5.19615i | −0.209529 | + | 0.362915i | ||||
\(206\) | 13.4220 | − | 10.6462i | 0.935154 | − | 0.741753i | ||||
\(207\) | −3.18322 | + | 1.83783i | −0.221249 | + | 0.127738i | ||||
\(208\) | 4.32062 | − | 0.278208i | 0.299581 | − | 0.0192903i | ||||
\(209\) | 20.4567i | 1.41502i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.4697i | 0.996136i | 0.867138 | + | 0.498068i | \(0.165957\pi\) | ||||
−0.867138 | + | 0.498068i | \(0.834043\pi\) | |||||||
\(212\) | 4.77364 | − | 20.4200i | 0.327855 | − | 1.40245i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.03706 | − | 2.56818i | −0.139250 | − | 0.175557i | ||||
\(215\) | 9.45280 | − | 16.3727i | 0.644675 | − | 1.11661i | ||||
\(216\) | −3.65568 | − | 7.74652i | −0.248737 | − | 0.527084i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.17157 | − | 7.91375i | −0.0793489 | − | 0.535987i | ||||
\(219\) | 25.9946 | + | 15.0080i | 1.75655 | + | 1.01415i | ||||
\(220\) | −15.0852 | − | 14.1451i | −1.01704 | − | 0.953662i | ||||
\(221\) | 0.171573 | + | 0.297173i | 0.0115412 | + | 0.0199900i | ||||
\(222\) | −11.2648 | − | 4.45526i | −0.756044 | − | 0.299018i | ||||
\(223\) | 7.83095 | 0.524399 | 0.262200 | − | 0.965014i | \(-0.415552\pi\) | ||||
0.262200 | + | 0.965014i | \(0.415552\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.89949 | −0.193300 | ||||||||
\(226\) | 5.57947 | + | 2.20670i | 0.371141 | + | 0.146787i | ||||
\(227\) | 4.98620 | + | 8.63635i | 0.330946 | + | 0.573215i | 0.982698 | − | 0.185218i | \(-0.0592990\pi\) |
−0.651752 | + | 0.758432i | \(0.725966\pi\) | |||||||
\(228\) | 16.1521 | + | 15.1455i | 1.06970 | + | 1.00303i | ||||
\(229\) | −1.16483 | − | 0.672512i | −0.0769738 | − | 0.0444409i | 0.461019 | − | 0.887390i | \(-0.347484\pi\) |
−0.537993 | + | 0.842949i | \(0.680817\pi\) | |||||||
\(230\) | −1.25443 | − | 8.47343i | −0.0827146 | − | 0.558721i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.24264 | + | 17.4665i | 0.541156 | + | 1.14673i | ||||
\(233\) | −8.12132 | + | 14.0665i | −0.532045 | + | 0.921530i | 0.467255 | + | 0.884123i | \(0.345243\pi\) |
−0.999300 | + | 0.0374069i | \(0.988090\pi\) | |||||||
\(234\) | −1.50848 | − | 1.90180i | −0.0986127 | − | 0.124324i | ||||
\(235\) | −9.69232 | + | 5.59587i | −0.632257 | + | 0.365034i | ||||
\(236\) | 5.11124 | − | 21.8642i | 0.332713 | − | 1.42324i | ||||
\(237\) | − | 16.9469i | − | 1.10082i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.2316i | − | 0.661829i | −0.943661 | − | 0.330915i | \(-0.892643\pi\) | ||
0.943661 | − | 0.330915i | \(-0.107357\pi\) | |||||||
\(240\) | −22.3372 | + | 1.43831i | −1.44186 | + | 0.0928425i | ||||
\(241\) | −4.41234 | + | 2.54747i | −0.284224 | + | 0.164097i | −0.635334 | − | 0.772237i | \(-0.719138\pi\) |
0.351110 | + | 0.936334i | \(0.385804\pi\) | |||||||
\(242\) | −5.15973 | + | 4.09264i | −0.331680 | + | 0.263085i | ||||
\(243\) | −7.49506 | + | 12.9818i | −0.480808 | + | 0.832784i | ||||
\(244\) | 3.13607 | + | 10.3596i | 0.200767 | + | 0.663209i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.87868 | − | 1.01834i | 0.438569 | − | 0.0649269i | ||||
\(247\) | −4.84616 | − | 2.79793i | −0.308354 | − | 0.178028i | ||||
\(248\) | 9.76170 | − | 14.0783i | 0.619868 | − | 0.893975i | ||||
\(249\) | 10.1213 | + | 17.5306i | 0.641413 | + | 1.11096i | ||||
\(250\) | −4.31064 | + | 10.8991i | −0.272629 | + | 0.689321i | ||||
\(251\) | −3.91548 | −0.247143 | −0.123571 | − | 0.992336i | \(-0.539435\pi\) | ||||
−0.123571 | + | 0.992336i | \(0.539435\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.17157 | −0.576612 | ||||||||
\(254\) | −5.32171 | + | 13.4556i | −0.333914 | + | 0.844277i | ||||
\(255\) | −0.887016 | − | 1.53636i | −0.0555471 | − | 0.0962103i | ||||
\(256\) | −15.8679 | + | 2.05200i | −0.991742 | + | 0.128250i | ||||
\(257\) | −16.5041 | − | 9.52862i | −1.02950 | − | 0.594379i | −0.112655 | − | 0.993634i | \(-0.535936\pi\) |
−0.916840 | + | 0.399255i | \(0.869269\pi\) | |||||||
\(258\) | −21.6743 | + | 3.20871i | −1.34938 | + | 0.199766i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.41421 | − | 1.63899i | 0.335775 | − | 0.101646i | ||||
\(261\) | 5.41421 | − | 9.37769i | 0.335131 | − | 0.580465i | ||||
\(262\) | 0.407090 | − | 0.322899i | 0.0251501 | − | 0.0199488i | ||||
\(263\) | −22.2235 | + | 12.8307i | −1.37036 | + | 0.791176i | −0.990973 | − | 0.134063i | \(-0.957198\pi\) |
−0.379385 | + | 0.925239i | \(0.623864\pi\) | |||||||
\(264\) | −1.97913 | + | 23.8846i | −0.121807 | + | 1.47000i | ||||
\(265\) | − | 27.3994i | − | 1.68313i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.8307i | 0.785227i | ||||||||
\(268\) | 6.38385 | + | 1.49237i | 0.389956 | + | 0.0911609i | ||||
\(269\) | 4.36524 | − | 2.52027i | 0.266153 | − | 0.153664i | −0.360985 | − | 0.932572i | \(-0.617559\pi\) |
0.627138 | + | 0.778908i | \(0.284226\pi\) | |||||||
\(270\) | −6.95494 | − | 8.76833i | −0.423264 | − | 0.533624i | ||||
\(271\) | −2.14144 | + | 3.70909i | −0.130084 | + | 0.225311i | −0.923709 | − | 0.383096i | \(-0.874858\pi\) |
0.793625 | + | 0.608407i | \(0.208191\pi\) | |||||||
\(272\) | −0.703309 | − | 1.05520i | −0.0426443 | − | 0.0639806i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.70711 | − | 11.5312i | −0.103130 | − | 0.696624i | ||||
\(275\) | −6.26557 | − | 3.61743i | −0.377828 | − | 0.218139i | ||||
\(276\) | −6.79034 | + | 7.24164i | −0.408731 | + | 0.435895i | ||||
\(277\) | 2.07107 | + | 3.58719i | 0.124438 | + | 0.215534i | 0.921513 | − | 0.388347i | \(-0.126954\pi\) |
−0.797075 | + | 0.603880i | \(0.793620\pi\) | |||||||
\(278\) | 30.0118 | + | 11.8698i | 1.79999 | + | 0.711902i | ||||
\(279\) | −9.60498 | −0.575035 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3848 | 0.619504 | 0.309752 | − | 0.950817i | \(-0.399754\pi\) | ||||
0.309752 | + | 0.950817i | \(0.399754\pi\) | |||||||
\(282\) | 12.0615 | + | 4.77035i | 0.718251 | + | 0.284070i | ||||
\(283\) | −1.69794 | − | 2.94091i | −0.100932 | − | 0.174819i | 0.811137 | − | 0.584856i | \(-0.198849\pi\) |
−0.912069 | + | 0.410037i | \(0.865516\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 25.0542 | + | 14.4650i | 1.48408 | + | 0.856835i | ||||
\(286\) | −0.887016 | − | 5.99162i | −0.0524503 | − | 0.354292i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6.01472 | + | 6.65539i | 0.354421 | + | 0.392172i | ||||
\(289\) | −8.44975 | + | 14.6354i | −0.497044 | + | 0.860905i | ||||
\(290\) | 15.6817 | + | 19.7704i | 0.920859 | + | 1.16096i | ||||
\(291\) | 17.1338 | − | 9.89219i | 1.00440 | − | 0.579890i | ||||
\(292\) | 27.2974 | + | 6.38139i | 1.59746 | + | 0.373443i | ||||
\(293\) | − | 11.7975i | − | 0.689219i | −0.938746 | − | 0.344609i | \(-0.888011\pi\) | ||
0.938746 | − | 0.344609i | \(-0.111989\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 29.3371i | − | 1.70807i | ||||||
\(296\) | −11.2751 | − | 0.934275i | −0.655350 | − | 0.0543037i | ||||
\(297\) | −10.3778 | + | 5.99162i | −0.602180 | + | 0.347669i | ||||
\(298\) | 5.34983 | − | 4.24343i | 0.309908 | − | 0.245815i | ||||
\(299\) | 1.25443 | − | 2.17274i | 0.0725455 | − | 0.125653i | ||||
\(300\) | −7.49506 | + | 2.26890i | −0.432727 | + | 0.130995i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 29.9706 | − | 4.43692i | 1.72461 | − | 0.255316i | ||||
\(303\) | −28.2455 | − | 16.3075i | −1.62266 | − | 0.936844i | ||||
\(304\) | 18.5365 | + | 9.16765i | 1.06314 | + | 0.525801i | ||||
\(305\) | 7.07107 | + | 12.2474i | 0.404888 | + | 0.701287i | ||||
\(306\) | −0.261484 | + | 0.661143i | −0.0149480 | + | 0.0377950i | ||||
\(307\) | −3.91548 | −0.223468 | −0.111734 | − | 0.993738i | \(-0.535640\pi\) | ||||
−0.111734 | + | 0.993738i | \(0.535640\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.9411 | −1.47574 | ||||||||
\(310\) | 8.23225 | − | 20.8146i | 0.467561 | − | 1.18219i | ||||
\(311\) | −10.3398 | − | 17.9091i | −0.586317 | − | 1.01553i | −0.994710 | − | 0.102724i | \(-0.967244\pi\) |
0.408393 | − | 0.912806i | \(-0.366089\pi\) | |||||||
\(312\) | −5.38755 | − | 3.73564i | −0.305010 | − | 0.211489i | ||||
\(313\) | 11.0406 | + | 6.37430i | 0.624052 | + | 0.360297i | 0.778445 | − | 0.627713i | \(-0.216009\pi\) |
−0.154393 | + | 0.988010i | \(0.549342\pi\) | |||||||
\(314\) | 26.8442 | − | 3.97408i | 1.51490 | − | 0.224270i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.58579 | − | 15.1486i | −0.257971 | − | 0.852176i | ||||
\(317\) | 2.75736 | − | 4.77589i | 0.154869 | − | 0.268241i | −0.778142 | − | 0.628088i | \(-0.783838\pi\) |
0.933011 | + | 0.359847i | \(0.117171\pi\) | |||||||
\(318\) | −24.8784 | + | 19.7332i | −1.39511 | + | 1.10658i | ||||
\(319\) | 23.3993 | − | 13.5096i | 1.31011 | − | 0.756393i | ||||
\(320\) | −19.5778 | + | 7.33009i | −1.09443 | + | 0.409765i | ||||
\(321\) | 4.96362i | 0.277042i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.63899i | 0.0911959i | ||||||||
\(324\) | −5.11844 | + | 21.8950i | −0.284358 | + | 1.21639i | ||||
\(325\) | 1.71393 | − | 0.989538i | 0.0950717 | − | 0.0548897i | ||||
\(326\) | 13.3132 | + | 16.7845i | 0.737352 | + | 0.929605i | ||||
\(327\) | −6.05692 | + | 10.4909i | −0.334948 | + | 0.580148i | ||||
\(328\) | 5.87321 | − | 2.77164i | 0.324294 | − | 0.153038i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 4.58579 | + | 30.9761i | 0.252439 | + | 1.70518i | ||||
\(331\) | −13.1191 | − | 7.57430i | −0.721090 | − | 0.416321i | 0.0940639 | − | 0.995566i | \(-0.470014\pi\) |
−0.815154 | + | 0.579245i | \(0.803348\pi\) | |||||||
\(332\) | 13.7911 | + | 12.9316i | 0.756884 | + | 0.709716i | ||||
\(333\) | 3.17157 | + | 5.49333i | 0.173801 | + | 0.301032i | ||||
\(334\) | −10.2984 | − | 4.07306i | −0.563505 | − | 0.222868i | ||||
\(335\) | 8.56578 | 0.467999 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.8284 | 0.589862 | 0.294931 | − | 0.955519i | \(-0.404703\pi\) | ||||
0.294931 | + | 0.955519i | \(0.404703\pi\) | |||||||
\(338\) | −15.5555 | − | 6.15224i | −0.846107 | − | 0.334638i | ||||
\(339\) | −4.54269 | − | 7.86817i | −0.246725 | − | 0.427340i | ||||
\(340\) | −1.20863 | − | 1.13331i | −0.0655471 | − | 0.0614622i | ||||
\(341\) | −20.7556 | − | 11.9832i | −1.12398 | − | 0.648929i | ||||
\(342\) | −1.69794 | − | 11.4692i | −0.0918139 | − | 0.620185i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −18.5061 | + | 8.73324i | −0.997782 | + | 0.470865i | ||||
\(345\) | −6.48528 | + | 11.2328i | −0.349156 | + | 0.604756i | ||||
\(346\) | −5.77512 | − | 7.28089i | −0.310472 | − | 0.391423i | ||||
\(347\) | −3.42675 | + | 1.97844i | −0.183958 | + | 0.106208i | −0.589151 | − | 0.808023i | \(-0.700538\pi\) |
0.405193 | + | 0.914231i | \(0.367204\pi\) | |||||||
\(348\) | 6.65728 | − | 28.4776i | 0.356868 | − | 1.52656i | ||||
\(349\) | 8.47343i | 0.453572i | 0.973945 | + | 0.226786i | \(0.0728218\pi\) | ||||
−0.973945 | + | 0.226786i | \(0.927178\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 3.27798i | − | 0.174966i | ||||||
\(352\) | 4.69401 | + | 21.8857i | 0.250192 | + | 1.16651i | ||||
\(353\) | 8.71096 | − | 5.02928i | 0.463638 | − | 0.267681i | −0.249935 | − | 0.968263i | \(-0.580409\pi\) |
0.713573 | + | 0.700581i | \(0.247076\pi\) | |||||||
\(354\) | −26.6378 | + | 21.1288i | −1.41578 | + | 1.12298i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.47197 | + | 11.4692i | 0.184014 | + | 0.607868i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.8995 | + | 2.79793i | −0.998869 | + | 0.147875i | ||||
\(359\) | 27.0696 | + | 15.6287i | 1.42868 | + | 0.824849i | 0.997017 | − | 0.0771860i | \(-0.0245935\pi\) |
0.431663 | + | 0.902035i | \(0.357927\pi\) | |||||||
\(360\) | 9.63174 | + | 6.67849i | 0.507637 | + | 0.351987i | ||||
\(361\) | −3.86396 | − | 6.69258i | −0.203366 | − | 0.352241i | ||||
\(362\) | 11.4362 | − | 28.9155i | 0.601071 | − | 1.51976i | ||||
\(363\) | 9.97240 | 0.523415 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.6274 | 1.91717 | ||||||||
\(366\) | 6.02793 | − | 15.2412i | 0.315085 | − | 0.796669i | ||||
\(367\) | −6.42433 | − | 11.1273i | −0.335348 | − | 0.580839i | 0.648204 | − | 0.761467i | \(-0.275520\pi\) |
−0.983552 | + | 0.180628i | \(0.942187\pi\) | |||||||
\(368\) | −4.11024 | + | 8.31067i | −0.214261 | + | 0.433224i | ||||
\(369\) | −3.15331 | − | 1.82056i | −0.164155 | − | 0.0947747i | ||||
\(370\) | −14.6227 | + | 2.16478i | −0.760198 | + | 0.112542i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −24.8284 | + | 7.51606i | −1.28729 | + | 0.389690i | ||||
\(373\) | 10.0711 | − | 17.4436i | 0.521460 | − | 0.903195i | −0.478228 | − | 0.878236i | \(-0.658721\pi\) |
0.999688 | − | 0.0249599i | \(-0.00794580\pi\) | |||||||
\(374\) | −1.38989 | + | 1.10245i | −0.0718696 | + | 0.0570061i | ||||
\(375\) | 15.3700 | − | 8.87385i | 0.793701 | − | 0.458244i | ||||
\(376\) | 12.0725 | + | 1.00035i | 0.622590 | + | 0.0515891i | ||||
\(377\) | 7.39104i | 0.380658i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 21.7046i | − | 1.11489i | −0.830214 | − | 0.557444i | \(-0.811782\pi\) | ||
0.830214 | − | 0.557444i | \(-0.188218\pi\) | |||||||
\(380\) | 26.3099 | + | 6.15053i | 1.34967 | + | 0.315515i | ||||
\(381\) | 18.9750 | − | 10.9552i | 0.972120 | − | 0.561254i | ||||
\(382\) | −5.76166 | − | 7.26392i | −0.294792 | − | 0.371655i | ||||
\(383\) | −15.5097 | + | 26.8636i | −0.792509 | + | 1.37267i | 0.131899 | + | 0.991263i | \(0.457892\pi\) |
−0.924409 | + | 0.381404i | \(0.875441\pi\) | |||||||
\(384\) | 20.7557 | + | 12.4972i | 1.05919 | + | 0.637747i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.02082 | + | 20.4050i | 0.153755 | + | 1.03859i | ||||
\(387\) | 9.93585 | + | 5.73647i | 0.505068 | + | 0.291601i | ||||
\(388\) | 12.6389 | − | 13.4789i | 0.641642 | − | 0.684286i | ||||
\(389\) | −7.07107 | − | 12.2474i | −0.358517 | − | 0.620970i | 0.629196 | − | 0.777247i | \(-0.283384\pi\) |
−0.987713 | + | 0.156276i | \(0.950051\pi\) | |||||||
\(390\) | −7.96542 | − | 3.15035i | −0.403345 | − | 0.159524i | ||||
\(391\) | −0.734828 | −0.0371618 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.786797 | −0.0396886 | ||||||||
\(394\) | −2.63019 | − | 1.04025i | −0.132507 | − | 0.0524069i | ||||
\(395\) | −10.3398 | − | 17.9091i | −0.520252 | − | 0.901103i | ||||
\(396\) | 8.58401 | − | 9.15452i | 0.431363 | − | 0.460032i | ||||
\(397\) | 13.9665 | + | 8.06355i | 0.700957 | + | 0.404698i | 0.807704 | − | 0.589588i | \(-0.200710\pi\) |
−0.106747 | + | 0.994286i | \(0.534043\pi\) | |||||||
\(398\) | −3.54806 | − | 23.9665i | −0.177848 | − | 1.20133i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.08579 | + | 4.05630i | −0.304289 | + | 0.202815i | ||||
\(401\) | 6.41421 | − | 11.1097i | 0.320311 | − | 0.554794i | −0.660242 | − | 0.751053i | \(-0.729546\pi\) |
0.980552 | + | 0.196259i | \(0.0628794\pi\) | |||||||
\(402\) | −6.16914 | − | 7.77765i | −0.307689 | − | 0.387914i | ||||
\(403\) | 5.67763 | − | 3.27798i | 0.282823 | − | 0.163288i | ||||
\(404\) | −29.6611 | − | 6.93396i | −1.47570 | − | 0.344977i | ||||
\(405\) | 29.3784i | 1.45983i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.8275i | 0.784540i | ||||||||
\(408\) | −0.158568 | + | 1.91364i | −0.00785029 | + | 0.0947392i | ||||
\(409\) | −11.9780 | + | 6.91550i | −0.592274 | + | 0.341949i | −0.765996 | − | 0.642845i | \(-0.777754\pi\) |
0.173722 | + | 0.984795i | \(0.444420\pi\) | |||||||
\(410\) | 6.64792 | − | 5.27306i | 0.328317 | − | 0.260418i | ||||
\(411\) | −8.82558 | + | 15.2864i | −0.435334 | + | 0.754020i | ||||
\(412\) | −23.1885 | + | 7.01962i | −1.14241 | + | 0.345832i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.14214 | − | 0.761256i | 0.252722 | − | 0.0374137i | ||||
\(415\) | 21.3920 | + | 12.3507i | 1.05009 | + | 0.606271i | ||||
\(416\) | −5.82672 | − | 1.88139i | −0.285679 | − | 0.0922426i | ||||
\(417\) | −24.4350 | − | 42.3227i | −1.19659 | − | 2.07255i | ||||
\(418\) | 10.6400 | − | 26.9024i | 0.520419 | − | 1.31584i | ||||
\(419\) | −17.2837 | −0.844366 | −0.422183 | − | 0.906511i | \(-0.638736\pi\) | ||||
−0.422183 | + | 0.906511i | \(0.638736\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.4853 | −0.511021 | −0.255511 | − | 0.966806i | \(-0.582244\pi\) | ||||
−0.255511 | + | 0.966806i | \(0.582244\pi\) | |||||||
\(422\) | 7.52604 | − | 19.0290i | 0.366362 | − | 0.926319i | ||||
\(423\) | −3.39587 | − | 5.88183i | −0.165113 | − | 0.285984i | ||||
\(424\) | −16.8987 | + | 24.3713i | −0.820674 | + | 1.18358i | ||||
\(425\) | −0.501998 | − | 0.289829i | −0.0243505 | − | 0.0140588i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.34315 | + | 4.43692i | 0.0649234 | + | 0.214467i | ||||
\(429\) | −4.58579 | + | 7.94282i | −0.221404 | + | 0.383483i | ||||
\(430\) | −20.9471 | + | 16.6150i | −1.01016 | + | 0.801249i | ||||
\(431\) | −0.831470 | + | 0.480049i | −0.0400505 | + | 0.0231232i | −0.519892 | − | 0.854232i | \(-0.674028\pi\) |
0.479841 | + | 0.877355i | \(0.340694\pi\) | |||||||
\(432\) | 0.778407 | + | 12.0888i | 0.0374511 | + | 0.581623i | ||||
\(433\) | 26.1857i | 1.25840i | 0.777243 | + | 0.629201i | \(0.216618\pi\) | ||||
−0.777243 | + | 0.629201i | \(0.783382\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 38.2110i | − | 1.83208i | ||||||
\(436\) | −2.57540 | + | 11.0167i | −0.123339 | + | 0.527603i | ||||
\(437\) | 10.3778 | − | 5.99162i | 0.496437 | − | 0.286618i | ||||
\(438\) | −26.3794 | − | 33.2573i | −1.26045 | − | 1.58910i | ||||
\(439\) | 11.2268 | − | 19.4454i | 0.535827 | − | 0.928080i | −0.463296 | − | 0.886204i | \(-0.653333\pi\) |
0.999123 | − | 0.0418761i | \(-0.0133335\pi\) | |||||||
\(440\) | 12.4813 | + | 26.4483i | 0.595021 | + | 1.26087i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.0710678 | − | 0.480049i | −0.00338035 | − | 0.0228336i | ||||
\(443\) | −24.5752 | − | 14.1885i | −1.16760 | − | 0.674116i | −0.214489 | − | 0.976726i | \(-0.568809\pi\) |
−0.953114 | + | 0.302610i | \(0.902142\pi\) | |||||||
\(444\) | 12.4970 | + | 11.7182i | 0.593081 | + | 0.556120i | ||||
\(445\) | 7.82843 | + | 13.5592i | 0.371103 | + | 0.642769i | ||||
\(446\) | −10.2984 | − | 4.07306i | −0.487645 | − | 0.192865i | ||||
\(447\) | −10.3398 | −0.489056 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.2843 | −0.768502 | −0.384251 | − | 0.923229i | \(-0.625540\pi\) | ||||
−0.384251 | + | 0.923229i | \(0.625540\pi\) | |||||||
\(450\) | 3.81311 | + | 1.50810i | 0.179752 | + | 0.0710923i | ||||
\(451\) | −4.54269 | − | 7.86817i | −0.213907 | − | 0.370498i | ||||
\(452\) | −6.18977 | − | 5.80403i | −0.291142 | − | 0.272998i | ||||
\(453\) | −39.7306 | − | 22.9385i | −1.86671 | − | 1.07774i | ||||
\(454\) | −2.06535 | − | 13.9510i | −0.0969317 | − | 0.654755i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.3640 | − | 28.3188i | −0.625825 | − | 1.32615i | ||||
\(457\) | −0.363961 | + | 0.630399i | −0.0170254 | + | 0.0294888i | −0.874413 | − | 0.485183i | \(-0.838753\pi\) |
0.857387 | + | 0.514672i | \(0.172086\pi\) | |||||||
\(458\) | 1.18207 | + | 1.49027i | 0.0552343 | + | 0.0696357i | ||||
\(459\) | −0.831470 | + | 0.480049i | −0.0388097 | + | 0.0224068i | ||||
\(460\) | −2.75754 | + | 11.7958i | −0.128571 | + | 0.549983i | ||||
\(461\) | − | 29.7499i | − | 1.38559i | −0.721135 | − | 0.692794i | \(-0.756379\pi\) | ||
0.721135 | − | 0.692794i | \(-0.243621\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.9330i | 1.62347i | 0.584024 | + | 0.811737i | \(0.301477\pi\) | ||||
−0.584024 | + | 0.811737i | \(0.698523\pi\) | |||||||
\(464\) | −1.75512 | − | 27.2573i | −0.0814792 | − | 1.26539i | ||||
\(465\) | −29.3528 | + | 16.9469i | −1.36120 | + | 0.785892i | ||||
\(466\) | 17.9966 | − | 14.2747i | 0.833678 | − | 0.661264i | ||||
\(467\) | 12.0377 | − | 20.8500i | 0.557041 | − | 0.964823i | −0.440701 | − | 0.897654i | \(-0.645270\pi\) |
0.997742 | − | 0.0671686i | \(-0.0213965\pi\) | |||||||
\(468\) | 0.994629 | + | 3.28564i | 0.0459767 | + | 0.151879i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 15.6569 | − | 2.31788i | 0.722197 | − | 0.106916i | ||||
\(471\) | −35.5861 | − | 20.5456i | −1.63972 | − | 0.946693i | ||||
\(472\) | −18.0938 | + | 26.0950i | −0.832836 | + | 1.20112i | ||||
\(473\) | 14.3137 | + | 24.7921i | 0.658145 | + | 1.13994i | ||||
\(474\) | −8.81446 | + | 22.2867i | −0.404861 | + | 1.02366i | ||||
\(475\) | 9.45280 | 0.433724 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.6274 | 0.761317 | ||||||||
\(478\) | −5.32171 | + | 13.4556i | −0.243409 | + | 0.615443i | ||||
\(479\) | 16.3967 | + | 28.4000i | 0.749186 | + | 1.29763i | 0.948213 | + | 0.317634i | \(0.102888\pi\) |
−0.199028 | + | 0.979994i | \(0.563778\pi\) | |||||||
\(480\) | 30.1236 | + | 9.72659i | 1.37495 | + | 0.443956i | ||||
\(481\) | −3.74952 | − | 2.16478i | −0.170963 | − | 0.0987057i | ||||
\(482\) | 7.12764 | − | 1.05520i | 0.324655 | − | 0.0480628i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.91421 | − | 2.69851i | 0.405192 | − | 0.122660i | ||||
\(485\) | 12.0711 | − | 20.9077i | 0.548119 | − | 0.949370i | ||||
\(486\) | 16.6089 | − | 13.1740i | 0.753393 | − | 0.597583i | ||||
\(487\) | 16.8902 | − | 9.75158i | 0.765370 | − | 0.441886i | −0.0658507 | − | 0.997829i | \(-0.520976\pi\) |
0.831220 | + | 0.555943i | \(0.187643\pi\) | |||||||
\(488\) | 1.26407 | − | 15.2551i | 0.0572216 | − | 0.690564i | ||||
\(489\) | − | 32.4399i | − | 1.46698i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14.4697i | − | 0.653009i | −0.945196 | − | 0.326504i | \(-0.894129\pi\) | ||
0.945196 | − | 0.326504i | \(-0.105871\pi\) | |||||||
\(492\) | −9.57577 | − | 2.23855i | −0.431709 | − | 0.100922i | ||||
\(493\) | 1.87476 | − | 1.08239i | 0.0844349 | − | 0.0487485i | ||||
\(494\) | 4.91789 | + | 6.20015i | 0.221266 | + | 0.278958i | ||||
\(495\) | 8.19837 | − | 14.2000i | 0.368489 | − | 0.638242i | ||||
\(496\) | −20.1600 | + | 13.4370i | −0.905212 | + | 0.603341i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.19239 | − | 28.3188i | −0.187865 | − | 1.26899i | ||||
\(499\) | 10.8682 | + | 6.27476i | 0.486527 | + | 0.280897i | 0.723133 | − | 0.690709i | \(-0.242701\pi\) |
−0.236605 | + | 0.971606i | \(0.576035\pi\) | |||||||
\(500\) | 11.3378 | − | 12.0913i | 0.507041 | − | 0.540740i | ||||
\(501\) | 8.38478 | + | 14.5229i | 0.374604 | + | 0.648833i | ||||
\(502\) | 5.14922 | + | 2.03653i | 0.229821 | + | 0.0908948i | ||||
\(503\) | −7.83095 | −0.349165 | −0.174582 | − | 0.984643i | \(-0.555858\pi\) | ||||
−0.174582 | + | 0.984643i | \(0.555858\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39.7990 | −1.77103 | ||||||||
\(506\) | 12.0615 | + | 4.77035i | 0.536198 | + | 0.212068i | ||||
\(507\) | 12.6650 | + | 21.9364i | 0.562471 | + | 0.974228i | ||||
\(508\) | 13.9971 | − | 14.9274i | 0.621021 | − | 0.662295i | ||||
\(509\) | 5.69089 | + | 3.28564i | 0.252244 | + | 0.145633i | 0.620791 | − | 0.783976i | \(-0.286811\pi\) |
−0.368547 | + | 0.929609i | \(0.620145\pi\) | |||||||
\(510\) | 0.367414 | + | 2.48181i | 0.0162694 | + | 0.109896i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 21.9350 | + | 5.55468i | 0.969400 | + | 0.245485i | ||||
\(513\) | 7.82843 | − | 13.5592i | 0.345634 | − | 0.598655i | ||||
\(514\) | 16.7483 | + | 21.1152i | 0.738737 | + | 0.931351i | ||||
\(515\) | −27.4140 | + | 15.8275i | −1.20801 | + | 0.697443i | ||||
\(516\) | 30.1726 | + | 7.05352i | 1.32827 | + | 0.310514i | ||||
\(517\) | − | 16.9469i | − | 0.745322i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.0720i | 0.617693i | ||||||||
\(520\) | −7.97268 | − | 0.660632i | −0.349625 | − | 0.0289707i | ||||
\(521\) | 10.4249 | − | 6.01882i | 0.456723 | − | 0.263689i | −0.253942 | − | 0.967219i | \(-0.581727\pi\) |
0.710665 | + | 0.703530i | \(0.248394\pi\) | |||||||
\(522\) | −11.9978 | + | 9.51649i | −0.525128 | + | 0.416525i | ||||
\(523\) | 3.73177 | − | 6.46361i | 0.163179 | − | 0.282634i | −0.772828 | − | 0.634615i | \(-0.781159\pi\) |
0.936007 | + | 0.351981i | \(0.114492\pi\) | |||||||
\(524\) | −0.703309 | + | 0.212906i | −0.0307242 | + | 0.00930083i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 35.8995 | − | 5.31466i | 1.56529 | − | 0.231730i | ||||
\(527\) | −1.66294 | − | 0.960099i | −0.0724388 | − | 0.0418226i | ||||
\(528\) | 15.0257 | − | 30.3811i | 0.653909 | − | 1.32217i | ||||
\(529\) | −8.81371 | − | 15.2658i | −0.383205 | − | 0.663730i | ||||
\(530\) | −14.2510 | + | 36.0327i | −0.619026 | + | 1.56516i | ||||
\(531\) | 17.8033 | 0.772600 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.48528 | 0.107649 | ||||||||
\(534\) | 6.67356 | − | 16.8736i | 0.288793 | − | 0.730192i | ||||
\(535\) | 3.02846 | + | 5.24545i | 0.130932 | + | 0.226780i | ||||
\(536\) | −7.61914 | − | 5.28299i | −0.329097 | − | 0.228191i | ||||
\(537\) | 25.0542 | + | 14.4650i | 1.08117 | + | 0.624213i | ||||
\(538\) | −7.05155 | + | 1.04393i | −0.304014 | + | 0.0450070i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.58579 | + | 15.1486i | 0.197341 | + | 0.651892i | ||||
\(541\) | −22.6569 | + | 39.2428i | −0.974094 | + | 1.68718i | −0.291202 | + | 0.956662i | \(0.594055\pi\) |
−0.682892 | + | 0.730519i | \(0.739278\pi\) | |||||||
\(542\) | 4.74539 | − | 3.76399i | 0.203832 | − | 0.161677i | ||||
\(543\) | −40.7766 | + | 23.5424i | −1.74989 | + | 1.01030i | ||||
\(544\) | 0.376085 | + | 1.75349i | 0.0161245 | + | 0.0751802i | ||||
\(545\) | 14.7821i | 0.633194i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.6981i | 1.18429i | 0.805833 | + | 0.592143i | \(0.201718\pi\) | ||||
−0.805833 | + | 0.592143i | \(0.798282\pi\) | |||||||
\(548\) | −3.75263 | + | 16.0525i | −0.160304 | + | 0.685728i | ||||
\(549\) | −7.43242 | + | 4.29111i | −0.317208 | + | 0.183140i | ||||
\(550\) | 6.35830 | + | 8.01613i | 0.271119 | + | 0.341809i | ||||
\(551\) | −17.6512 | + | 30.5727i | −0.751965 | + | 1.30244i | ||||
\(552\) | 12.6965 | − | 5.99162i | 0.540398 | − | 0.255020i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.857864 | − | 5.79471i | −0.0364472 | − | 0.246194i | ||||
\(555\) | 19.3846 | + | 11.1917i | 0.822832 | + | 0.475063i | ||||
\(556\) | −33.2946 | − | 31.2197i | −1.41201 | − | 1.32401i | ||||
\(557\) | 9.82843 | + | 17.0233i | 0.416444 | + | 0.721302i | 0.995579 | − | 0.0939298i | \(-0.0299429\pi\) |
−0.579135 | + | 0.815232i | \(0.696610\pi\) | |||||||
\(558\) | 12.6315 | + | 4.99578i | 0.534732 | + | 0.211488i | ||||
\(559\) | −7.83095 | −0.331214 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.68629 | 0.113415 | ||||||||
\(562\) | −13.6570 | − | 5.40137i | −0.576084 | − | 0.227843i | ||||
\(563\) | 10.5235 | + | 18.2273i | 0.443513 | + | 0.768188i | 0.997947 | − | 0.0640400i | \(-0.0203985\pi\) |
−0.554434 | + | 0.832228i | \(0.687065\pi\) | |||||||
\(564\) | −13.3808 | − | 12.5469i | −0.563433 | − | 0.528320i | ||||
\(565\) | −9.60124 | − | 5.54328i | −0.403927 | − | 0.233207i | ||||
\(566\) | 0.703309 | + | 4.75071i | 0.0295623 | + | 0.199687i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.41421 | + | 16.3059i | −0.394664 | + | 0.683579i | −0.993058 | − | 0.117623i | \(-0.962472\pi\) |
0.598394 | + | 0.801202i | \(0.295806\pi\) | |||||||
\(570\) | −25.4250 | − | 32.0542i | −1.06494 | − | 1.34260i | ||||
\(571\) | −8.61732 | + | 4.97521i | −0.360624 | + | 0.208206i | −0.669354 | − | 0.742943i | \(-0.733429\pi\) |
0.308731 | + | 0.951150i | \(0.400096\pi\) | |||||||
\(572\) | −1.94987 | + | 8.34090i | −0.0815283 | + | 0.348750i | ||||
\(573\) | 14.0392i | 0.586497i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.23808i | 0.176740i | ||||||||
\(576\) | −4.44830 | − | 11.8809i | −0.185346 | − | 0.495036i | ||||
\(577\) | 0.729445 | − | 0.421145i | 0.0303672 | − | 0.0175325i | −0.484740 | − | 0.874659i | \(-0.661086\pi\) |
0.515107 | + | 0.857126i | \(0.327752\pi\) | |||||||
\(578\) | 18.7244 | − | 14.8520i | 0.778833 | − | 0.617762i | ||||
\(579\) | 15.6173 | − | 27.0500i | 0.649034 | − | 1.12416i | ||||
\(580\) | −10.3398 | − | 34.1563i | −0.429337 | − | 1.41827i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −27.6777 | + | 4.09748i | −1.14728 | + | 0.169846i | ||||
\(583\) | 35.9305 | + | 20.7445i | 1.48809 | + | 0.859148i | ||||
\(584\) | −32.5796 | − | 22.5902i | −1.34815 | − | 0.934788i | ||||
\(585\) | 2.24264 | + | 3.88437i | 0.0927218 | + | 0.160599i | ||||
\(586\) | −6.13617 | + | 15.5149i | −0.253483 | + | 0.640913i | ||||
\(587\) | 22.8211 | 0.941926 | 0.470963 | − | 0.882153i | \(-0.343906\pi\) | ||||
0.470963 | + | 0.882153i | \(0.343906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.3137 | 1.29026 | ||||||||
\(590\) | −15.2589 | + | 38.5811i | −0.628200 | + | 1.58836i | ||||
\(591\) | 2.14144 | + | 3.70909i | 0.0880873 | + | 0.152572i | ||||
\(592\) | 14.3418 | + | 7.09309i | 0.589446 | + | 0.291524i | ||||
\(593\) | 32.4395 | + | 18.7290i | 1.33213 | + | 0.769106i | 0.985626 | − | 0.168942i | \(-0.0540351\pi\) |
0.346505 | + | 0.938048i | \(0.387368\pi\) | |||||||
\(594\) | 16.7641 | − | 2.48181i | 0.687841 | − | 0.101830i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.24264 | + | 2.79793i | −0.378593 | + | 0.114608i | ||||
\(597\) | −18.3431 | + | 31.7713i | −0.750735 | + | 1.30031i | ||||
\(598\) | −2.77978 | + | 2.20489i | −0.113674 | + | 0.0901648i | ||||
\(599\) | 27.9011 | − | 16.1087i | 1.14001 | − | 0.658184i | 0.193575 | − | 0.981085i | \(-0.437992\pi\) |
0.946433 | + | 0.322902i | \(0.104658\pi\) | |||||||
\(600\) | 11.0368 | + | 0.914533i | 0.450576 | + | 0.0373357i | ||||
\(601\) | − | 25.5516i | − | 1.04227i | −0.853474 | − | 0.521136i | \(-0.825509\pi\) | ||
0.853474 | − | 0.521136i | \(-0.174491\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.19818i | 0.211686i | ||||||||
\(604\) | −41.7218 | − | 9.75342i | −1.69764 | − | 0.396861i | ||||
\(605\) | 10.5386 | − | 6.08447i | 0.428456 | − | 0.247369i | ||||
\(606\) | 28.6635 | + | 36.1371i | 1.16438 | + | 1.46797i | ||||
\(607\) | −6.05692 | + | 10.4909i | −0.245843 | + | 0.425812i | −0.962368 | − | 0.271749i | \(-0.912398\pi\) |
0.716525 | + | 0.697561i | \(0.245731\pi\) | |||||||
\(608\) | −19.6089 | − | 21.6976i | −0.795246 | − | 0.879953i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.92893 | − | 19.7844i | −0.118589 | − | 0.801046i | ||||
\(611\) | 4.01469 | + | 2.31788i | 0.162417 | + | 0.0937715i | ||||
\(612\) | 0.687752 | − | 0.733461i | 0.0278007 | − | 0.0296484i | ||||
\(613\) | 4.34315 | + | 7.52255i | 0.175418 | + | 0.303833i | 0.940306 | − | 0.340331i | \(-0.110539\pi\) |
−0.764888 | + | 0.644163i | \(0.777206\pi\) | |||||||
\(614\) | 5.14922 | + | 2.03653i | 0.207806 | + | 0.0821877i | ||||
\(615\) | −12.8487 | −0.518108 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.4558 | −1.42740 | −0.713699 | − | 0.700452i | \(-0.752982\pi\) | ||||
−0.713699 | + | 0.700452i | \(0.752982\pi\) | |||||||
\(618\) | 34.1150 | + | 13.4926i | 1.37231 | + | 0.542751i | ||||
\(619\) | −6.76023 | − | 11.7091i | −0.271717 | − | 0.470627i | 0.697585 | − | 0.716502i | \(-0.254258\pi\) |
−0.969301 | + | 0.245875i | \(0.920925\pi\) | |||||||
\(620\) | −21.6524 | + | 23.0914i | −0.869580 | + | 0.927374i | ||||
\(621\) | 6.07917 | + | 3.50981i | 0.243949 | + | 0.140844i | ||||
\(622\) | 4.28289 | + | 28.9301i | 0.171728 | + | 1.15999i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.14214 | + | 7.71491i | 0.205850 | + | 0.308843i | ||||
\(625\) | 15.3995 | − | 26.6727i | 0.615980 | − | 1.06691i | ||||
\(626\) | −11.2040 | − | 14.1253i | −0.447803 | − | 0.564560i | ||||
\(627\) | −37.9378 | + | 21.9034i | −1.51509 | + | 0.874738i | ||||
\(628\) | −37.3696 | − | 8.73598i | −1.49121 | − | 0.348604i | ||||
\(629\) | 1.26810i | 0.0505625i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.4633i | 0.814630i | 0.913288 | + | 0.407315i | \(0.133535\pi\) | ||||
−0.913288 | + | 0.407315i | \(0.866465\pi\) | |||||||
\(632\) | −1.84841 | + | 22.3070i | −0.0735256 | + | 0.887325i | ||||
\(633\) | −26.8347 | + | 15.4930i | −1.06659 | + | 0.615793i | ||||
\(634\) | −6.11024 | + | 4.84657i | −0.242668 | + | 0.192482i | ||||
\(635\) | 13.3683 | − | 23.1545i | 0.530504 | − | 0.918859i | ||||
\(636\) | 42.9811 | − | 13.0112i | 1.70431 | − | 0.515929i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −37.7990 | + | 5.59587i | −1.49648 | + | 0.221542i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 29.5592 | + | 0.543099i | 1.16843 | + | 0.0214679i | ||||
\(641\) | −24.7279 | − | 42.8300i | −0.976694 | − | 1.69168i | −0.674227 | − | 0.738524i | \(-0.735523\pi\) |
−0.302467 | − | 0.953160i | \(-0.597810\pi\) | |||||||
\(642\) | 2.58169 | − | 6.52763i | 0.101891 | − | 0.257625i | ||||
\(643\) | 41.7267 | 1.64554 | 0.822769 | − | 0.568375i | \(-0.192428\pi\) | ||||
0.822769 | + | 0.568375i | \(0.192428\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 40.4853 | 1.59411 | ||||||||
\(646\) | 0.852478 | − | 2.15543i | 0.0335403 | − | 0.0848041i | ||||
\(647\) | 21.9341 | + | 37.9909i | 0.862317 | + | 1.49358i | 0.869687 | + | 0.493603i | \(0.164320\pi\) |
−0.00737070 | + | 0.999973i | \(0.502346\pi\) | |||||||
\(648\) | 18.1193 | − | 26.1317i | 0.711794 | − | 1.02655i | ||||
\(649\) | 38.4716 | + | 22.2116i | 1.51014 | + | 0.871880i | ||||
\(650\) | −2.76866 | + | 0.409880i | −0.108596 | + | 0.0160768i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.77817 | − | 28.9977i | −0.343780 | − | 1.13564i | ||||
\(653\) | 11.8995 | − | 20.6105i | 0.465663 | − | 0.806552i | −0.533568 | − | 0.845757i | \(-0.679149\pi\) |
0.999231 | + | 0.0392048i | \(0.0124825\pi\) | |||||||
\(654\) | 13.4220 | − | 10.6462i | 0.524841 | − | 0.416298i | ||||
\(655\) | −0.831470 | + | 0.480049i | −0.0324882 | + | 0.0187571i | ||||
\(656\) | −9.16542 | + | 0.590168i | −0.357850 | + | 0.0230422i | ||||
\(657\) | 22.2275i | 0.867177i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.2284i | 0.515306i | 0.966238 | + | 0.257653i | \(0.0829491\pi\) | ||||
−0.966238 | + | 0.257653i | \(0.917051\pi\) | |||||||
\(660\) | 10.0807 | − | 43.1217i | 0.392389 | − | 1.67851i | ||||
\(661\) | 32.6198 | − | 18.8331i | 1.26877 | − | 0.732522i | 0.294011 | − | 0.955802i | \(-0.405010\pi\) |
0.974754 | + | 0.223280i | \(0.0716765\pi\) | |||||||
\(662\) | 13.3132 | + | 16.7845i | 0.517434 | + | 0.652346i | ||||
\(663\) | −0.367414 | + | 0.636379i | −0.0142692 | + | 0.0247149i | ||||
\(664\) | −11.4105 | − | 24.1794i | −0.442815 | − | 0.938342i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.31371 | − | 8.87385i | −0.0509052 | − | 0.343855i | ||||
\(667\) | −13.7070 | − | 7.91375i | −0.530738 | − | 0.306422i | ||||
\(668\) | 11.4249 | + | 10.7129i | 0.442043 | + | 0.414495i | ||||
\(669\) | 8.38478 | + | 14.5229i | 0.324174 | + | 0.561486i | ||||
\(670\) | −11.2648 | − | 4.45526i | −0.435197 | − | 0.172122i | ||||
\(671\) | −21.4144 | −0.826696 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.3848 | 0.400304 | 0.200152 | − | 0.979765i | \(-0.435856\pi\) | ||||
0.200152 | + | 0.979765i | \(0.435856\pi\) | |||||||
\(674\) | −14.2404 | − | 5.63212i | −0.548520 | − | 0.216941i | ||||
\(675\) | 2.76866 | + | 4.79546i | 0.106566 | + | 0.184577i | ||||
\(676\) | 17.2570 | + | 16.1816i | 0.663731 | + | 0.622367i | ||||
\(677\) | −24.9876 | − | 14.4266i | −0.960351 | − | 0.554459i | −0.0640697 | − | 0.997945i | \(-0.520408\pi\) |
−0.896281 | + | 0.443487i | \(0.853741\pi\) | |||||||
\(678\) | 1.88164 | + | 12.7101i | 0.0722641 | + | 0.488130i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.00000 | + | 2.11904i | 0.0383482 | + | 0.0812615i | ||||
\(681\) | −10.6777 | + | 18.4943i | −0.409169 | + | 0.708702i | ||||
\(682\) | 21.0628 | + | 26.5545i | 0.806535 | + | 1.01683i | ||||
\(683\) | 27.9011 | − | 16.1087i | 1.06761 | − | 0.616382i | 0.140079 | − | 0.990140i | \(-0.455264\pi\) |
0.927526 | + | 0.373758i | \(0.121931\pi\) | |||||||
\(684\) | −3.73247 | + | 15.9663i | −0.142715 | + | 0.610485i | ||||
\(685\) | 21.5391i | 0.822965i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 2.88030i | − | 0.109890i | ||||||
\(688\) | 28.8796 | − | 1.85958i | 1.10103 | − | 0.0708958i | ||||
\(689\) | −9.82868 | + | 5.67459i | −0.374443 | + | 0.216185i | ||||
\(690\) | 14.3712 | − | 11.3991i | 0.547103 | − | 0.433956i | ||||
\(691\) | −4.09918 | + | 7.09999i | −0.155940 | + | 0.270096i | −0.933401 | − | 0.358835i | \(-0.883174\pi\) |
0.777461 | + | 0.628931i | \(0.216507\pi\) | |||||||
\(692\) | 3.80786 | + | 12.5788i | 0.144753 | + | 0.478175i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.53553 | − | 0.819496i | 0.210126 | − | 0.0311076i | ||||
\(695\) | −51.6448 | − | 29.8172i | −1.95900 | − | 1.13103i | ||||
\(696\) | −23.5668 | + | 33.9881i | −0.893298 | + | 1.28832i | ||||
\(697\) | −0.363961 | − | 0.630399i | −0.0137860 | − | 0.0238781i | ||||
\(698\) | 4.40723 | − | 11.1434i | 0.166816 | − | 0.421782i | ||||
\(699\) | −34.7827 | −1.31560 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.0000 | 0.604312 | 0.302156 | − | 0.953259i | \(-0.402294\pi\) | ||||
0.302156 | + | 0.953259i | \(0.402294\pi\) | |||||||
\(702\) | −1.70496 | + | 4.31085i | −0.0643494 | + | 0.162703i | ||||
\(703\) | −10.3398 | − | 17.9091i | −0.389973 | − | 0.675454i | ||||
\(704\) | 5.21022 | − | 31.2233i | 0.196368 | − | 1.17677i | ||||
\(705\) | −20.7556 | − | 11.9832i | −0.781700 | − | 0.451315i | ||||
\(706\) | −14.0716 | + | 2.08319i | −0.529591 | + | 0.0784021i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 46.0208 | − | 13.9314i | 1.72957 | − | 0.523575i | ||||
\(709\) | 23.3137 | − | 40.3805i | 0.875565 | − | 1.51652i | 0.0194047 | − | 0.999812i | \(-0.493823\pi\) |
0.856160 | − | 0.516711i | \(-0.172844\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.8682 | − | 6.27476i | 0.407589 | − | 0.235322i | ||||
\(712\) | 1.39946 | − | 16.8890i | 0.0524468 | − | 0.632941i | ||||
\(713\) | 14.0392i | 0.525774i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.1917i | 0.418547i | ||||||||
\(716\) | 26.3099 | + | 6.15053i | 0.983246 | + | 0.229856i | ||||
\(717\) | 18.9750 | − | 10.9552i | 0.708635 | − | 0.409131i | ||||
\(718\) | −27.4703 | − | 34.6327i | −1.02518 | − | 1.29248i | ||||
\(719\) | 16.7641 | − | 29.0364i | 0.625197 | − | 1.08287i | −0.363306 | − | 0.931670i | \(-0.618352\pi\) |
0.988503 | − | 0.151203i | \(-0.0483148\pi\) | |||||||
\(720\) | −9.19299 | − | 13.7925i | −0.342603 | − | 0.514017i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.60051 | + | 10.8111i | 0.0595646 | + | 0.402348i | ||||
\(723\) | −9.44879 | − | 5.45526i | −0.351404 | − | 0.202883i | ||||
\(724\) | −30.0792 | + | 32.0784i | −1.11789 | + | 1.19218i | ||||
\(725\) | −6.24264 | − | 10.8126i | −0.231846 | − | 0.401569i | ||||
\(726\) | −13.1146 | − | 5.18688i | −0.486730 | − | 0.192503i | ||||
\(727\) | 29.9802 | 1.11191 | 0.555953 | − | 0.831214i | \(-0.312354\pi\) | ||||
0.555953 | + | 0.831214i | \(0.312354\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.62742 | 0.0602747 | ||||||||
\(730\) | −48.1685 | − | 19.0508i | −1.78280 | − | 0.705101i | ||||
\(731\) | 1.14682 | + | 1.98634i | 0.0424165 | + | 0.0734676i | ||||
\(732\) | −15.8546 | + | 16.9083i | −0.586002 | + | 0.624949i | ||||
\(733\) | −17.7160 | − | 10.2283i | −0.654355 | − | 0.377792i | 0.135768 | − | 0.990741i | \(-0.456650\pi\) |
−0.790123 | + | 0.612949i | \(0.789983\pi\) | |||||||
\(734\) | 2.66105 | + | 17.9749i | 0.0982210 | + | 0.663464i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.72792 | − | 8.79148i | 0.358576 | − | 0.324058i | ||||
\(737\) | −6.48528 | + | 11.2328i | −0.238888 | + | 0.413767i | ||||
\(738\) | 3.19998 | + | 4.03432i | 0.117793 | + | 0.148505i | ||||
\(739\) | −10.7673 | + | 6.21652i | −0.396082 | + | 0.228678i | −0.684792 | − | 0.728738i | \(-0.740107\pi\) |
0.288710 | + | 0.957417i | \(0.406774\pi\) | |||||||
\(740\) | 20.3562 | + | 4.75871i | 0.748308 | + | 0.174934i | ||||
\(741\) | − | 11.9832i | − | 0.440215i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 45.1646i | − | 1.65693i | −0.560042 | − | 0.828464i | \(-0.689215\pi\) | ||
0.560042 | − | 0.828464i | \(-0.310785\pi\) | |||||||
\(744\) | 36.5610 | + | 3.02952i | 1.34039 | + | 0.111068i | ||||
\(745\) | −10.9269 | + | 6.30864i | −0.400330 | + | 0.231131i | ||||
\(746\) | −22.3172 | + | 17.7018i | −0.817092 | + | 0.648108i | ||||
\(747\) | −7.49506 | + | 12.9818i | −0.274230 | + | 0.474980i | ||||
\(748\) | 2.40125 | − | 0.726905i | 0.0877982 | − | 0.0265783i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −24.8284 | + | 3.67567i | −0.906606 | + | 0.134216i | ||||
\(751\) | 32.2602 | + | 18.6254i | 1.17719 | + | 0.679652i | 0.955363 | − | 0.295434i | \(-0.0954643\pi\) |
0.221828 | + | 0.975086i | \(0.428798\pi\) | |||||||
\(752\) | −15.3561 | − | 7.59473i | −0.559980 | − | 0.276951i | ||||
\(753\) | −4.19239 | − | 7.26143i | −0.152779 | − | 0.264621i | ||||
\(754\) | 3.84425 | − | 9.71991i | 0.139999 | − | 0.353978i | ||||
\(755\) | −55.9819 | −2.03739 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.2843 | −1.60954 | −0.804770 | − | 0.593587i | \(-0.797711\pi\) | ||||
−0.804770 | + | 0.593587i | \(0.797711\pi\) | |||||||
\(758\) | −11.2891 | + | 28.5435i | −0.410037 | + | 1.03675i | ||||
\(759\) | −9.82021 | − | 17.0091i | −0.356451 | − | 0.617391i | ||||
\(760\) | −31.4009 | − | 21.7729i | −1.13903 | − | 0.789786i | ||||
\(761\) | 0.0471057 | + | 0.0271965i | 0.00170758 | + | 0.000985871i | 0.500854 | − | 0.865532i | \(-0.333020\pi\) |
−0.499146 | + | 0.866518i | \(0.666353\pi\) | |||||||
\(762\) | −30.6520 | + | 4.53781i | −1.11041 | + | 0.164387i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.79899 | + | 12.5495i | 0.137443 | + | 0.454026i | ||||
\(765\) | 0.656854 | − | 1.13770i | 0.0237486 | − | 0.0411338i | ||||
\(766\) | 34.3691 | − | 27.2612i | 1.24181 | − | 0.984987i | ||||
\(767\) | −10.5238 | + | 6.07591i | −0.379992 | + | 0.219389i | ||||
\(768\) | −20.7956 | − | 27.2306i | −0.750397 | − | 0.982599i | ||||
\(769\) | − | 19.1342i | − | 0.689996i | −0.938603 | − | 0.344998i | \(-0.887880\pi\) | ||
0.938603 | − | 0.344998i | \(-0.112120\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 40.8100i | − | 1.46974i | ||||||
\(772\) | 6.64048 | − | 28.4057i | 0.238996 | − | 1.02234i | ||||
\(773\) | −42.8644 | + | 24.7478i | −1.54173 | + | 0.890116i | −0.542995 | + | 0.839736i | \(0.682710\pi\) |
−0.998730 | + | 0.0503797i | \(0.983957\pi\) | |||||||
\(774\) | −10.0829 | − | 12.7119i | −0.362423 | − | 0.456919i | ||||
\(775\) | −5.53732 | + | 9.59092i | −0.198906 | + | 0.344516i | ||||
\(776\) | −23.6320 | + | 11.1522i | −0.848339 | + | 0.400341i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.92893 | + | 19.7844i | 0.105007 | + | 0.709304i | ||||
\(779\) | 10.2803 | + | 5.93531i | 0.368329 | + | 0.212655i | ||||
\(780\) | 8.83670 | + | 8.28600i | 0.316405 | + | 0.296686i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.966367 | + | 0.382201i | 0.0345572 | + | 0.0136675i | ||||
\(783\) | −20.6796 | −0.739029 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −50.1421 | −1.78965 | ||||||||
\(786\) | 1.03471 | + | 0.409231i | 0.0369069 | + | 0.0145968i | ||||
\(787\) | −20.6035 | − | 35.6864i | −0.734436 | − | 1.27208i | −0.954970 | − | 0.296702i | \(-0.904113\pi\) |
0.220534 | − | 0.975379i | \(-0.429220\pi\) | |||||||
\(788\) | 2.91789 | + | 2.73604i | 0.103945 | + | 0.0974675i | ||||
\(789\) | −47.5903 | − | 27.4763i | −1.69426 | − | 0.978182i | ||||
\(790\) | 4.28289 | + | 28.9301i | 0.152378 | + | 1.02929i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −16.0503 | + | 7.57430i | −0.570321 | + | 0.269141i | ||||
\(793\) | 2.92893 | − | 5.07306i | 0.104009 | − | 0.180150i | ||||
\(794\) | −14.1732 | − | 17.8686i | −0.502988 | − | 0.634133i | ||||
\(795\) | 50.8134 | − | 29.3371i | 1.80216 | − | 1.04048i | ||||
\(796\) | −7.79949 | + | 33.3636i | −0.276446 | + | 1.18254i | ||||
\(797\) | − | 20.1940i | − | 0.715309i | −0.933854 | − | 0.357655i | \(-0.883576\pi\) | ||
0.933854 | − | 0.357655i | \(-0.116424\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.35778i | − | 0.0480350i | ||||||
\(800\) | 10.1132 | − | 2.16905i | 0.357554 | − | 0.0766875i | ||||
\(801\) | −8.22848 | + | 4.75071i | −0.290739 | + | 0.167858i | ||||
\(802\) | −14.2137 | + | 11.2742i | −0.501904 | + | 0.398105i | ||||
\(803\) | −27.7312 | + | 48.0318i | −0.978612 | + | 1.69501i | ||||
\(804\) | 4.06766 | + | 13.4370i | 0.143455 | + | 0.473888i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.17157 | + | 1.35778i | −0.323055 | + | 0.0478259i | ||||
\(807\) | 9.34792 | + | 5.39702i | 0.329062 | + | 0.189984i | ||||
\(808\) | 35.4006 | + | 24.5462i | 1.24539 | + | 0.863534i | ||||
\(809\) | 0.0208153 | + | 0.0360531i | 0.000731826 | + | 0.00126756i | 0.866391 | − | 0.499366i | \(-0.166434\pi\) |
−0.865659 | + | 0.500634i | \(0.833100\pi\) | |||||||
\(810\) | 15.2804 | − | 38.6354i | 0.536899 | − | 1.35751i | ||||
\(811\) | 39.4330 | 1.38468 | 0.692340 | − | 0.721571i | \(-0.256580\pi\) | ||||
0.692340 | + | 0.721571i | \(0.256580\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.17157 | −0.321661 | ||||||||
\(814\) | 8.23225 | − | 20.8146i | 0.288540 | − | 0.729553i | ||||
\(815\) | −19.7926 | − | 34.2818i | −0.693305 | − | 1.20084i | ||||
\(816\) | 1.20386 | − | 2.43414i | 0.0421435 | − | 0.0852119i | ||||
\(817\) | −32.3924 | − | 18.7018i | −1.13327 | − | 0.654292i | ||||
\(818\) | 19.3491 | − | 2.86449i | 0.676525 | − | 0.100155i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.4853 | + | 3.47682i | −0.401083 | + | 0.121416i | ||||
\(821\) | 9.00000 | − | 15.5885i | 0.314102 | − | 0.544041i | −0.665144 | − | 0.746715i | \(-0.731630\pi\) |
0.979246 | + | 0.202674i | \(0.0649632\pi\) | |||||||
\(822\) | 19.5573 | − | 15.5126i | 0.682138 | − | 0.541064i | ||||
\(823\) | −14.8829 | + | 8.59264i | −0.518785 | + | 0.299521i | −0.736437 | − | 0.676506i | \(-0.763493\pi\) |
0.217652 | + | 0.976026i | \(0.430160\pi\) | |||||||
\(824\) | 34.1461 | + | 2.82942i | 1.18954 | + | 0.0985674i | ||||
\(825\) | − | 15.4930i | − | 0.539399i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 45.1646i | − | 1.57053i | −0.619162 | − | 0.785264i | \(-0.712527\pi\) | ||
0.619162 | − | 0.785264i | \(-0.287473\pi\) | |||||||
\(828\) | −7.15834 | − | 1.67342i | −0.248769 | − | 0.0581555i | ||||
\(829\) | 40.8954 | − | 23.6110i | 1.42036 | − | 0.820044i | 0.424028 | − | 0.905649i | \(-0.360616\pi\) |
0.996329 | + | 0.0856056i | \(0.0272825\pi\) | |||||||
\(830\) | −21.7086 | − | 27.3688i | −0.753517 | − | 0.949984i | ||||
\(831\) | −4.43508 | + | 7.68178i | −0.153851 | + | 0.266478i | ||||
\(832\) | 6.68414 | + | 5.50482i | 0.231731 | + | 0.190845i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.1213 | + | 68.3676i | 0.350473 | + | 2.36738i | ||||
\(835\) | 17.7217 | + | 10.2316i | 0.613285 | + | 0.354080i | ||||
\(836\) | −27.9852 | + | 29.8451i | −0.967887 | + | 1.03221i | ||||
\(837\) | 9.17157 | + | 15.8856i | 0.317016 | + | 0.549088i | ||||
\(838\) | 22.7297 | + | 8.98968i | 0.785186 | + | 0.310543i | ||||
\(839\) | 42.3984 | 1.46376 | 0.731878 | − | 0.681435i | \(-0.238644\pi\) | ||||
0.731878 | + | 0.681435i | \(0.238644\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.6274 | 0.607842 | ||||||||
\(842\) | 13.7891 | + | 5.45364i | 0.475205 | + | 0.187945i | ||||
\(843\) | 11.1192 | + | 19.2590i | 0.382966 | + | 0.663317i | ||||
\(844\) | −19.7949 | + | 21.1105i | −0.681368 | + | 0.726653i | ||||
\(845\) | 26.7681 | + | 15.4546i | 0.920852 | + | 0.531654i | ||||
\(846\) | 1.40662 | + | 9.50143i | 0.0483605 | + | 0.326666i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 34.8995 | − | 23.2612i | 1.19845 | − | 0.798793i | ||||
\(849\) | 3.63604 | − | 6.29780i | 0.124789 | − | 0.216140i | ||||
\(850\) | 0.509428 | + | 0.642253i | 0.0174732 | + | 0.0220291i | ||||
\(851\) | 8.02938 | − | 4.63577i | 0.275244 | − | 0.158912i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.3002i | 1.31137i | 0.755033 | + | 0.655687i | \(0.227621\pi\) | ||||
−0.755033 | + | 0.655687i | \(0.772379\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21.4234i | 0.732664i | ||||||||
\(856\) | 0.541385 | − | 6.53357i | 0.0185042 | − | 0.223313i | ||||
\(857\) | −2.99248 | + | 1.72771i | −0.102221 | + | 0.0590174i | −0.550239 | − | 0.835007i | \(-0.685463\pi\) |
0.448018 | + | 0.894025i | \(0.352130\pi\) | |||||||
\(858\) | 10.1620 | − | 8.06037i | 0.346924 | − | 0.275177i | ||||
\(859\) | −1.33052 | + | 2.30453i | −0.0453969 | + | 0.0786297i | −0.887831 | − | 0.460170i | \(-0.847789\pi\) |
0.842434 | + | 0.538799i | \(0.181122\pi\) | |||||||
\(860\) | 36.1893 | − | 10.9552i | 1.23405 | − | 0.373571i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.34315 | − | 0.198843i | 0.0457477 | − | 0.00677262i | ||||
\(863\) | 10.8682 | + | 6.27476i | 0.369958 | + | 0.213595i | 0.673440 | − | 0.739242i | \(-0.264816\pi\) |
−0.303482 | + | 0.952837i | \(0.598149\pi\) | |||||||
\(864\) | 5.26399 | − | 16.3028i | 0.179085 | − | 0.554632i | ||||
\(865\) | 8.58579 | + | 14.8710i | 0.291925 | + | 0.505630i | ||||
\(866\) | 13.6198 | − | 34.4366i | 0.462819 | − | 1.17020i | ||||
\(867\) | −36.1893 | −1.22905 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31.3137 | 1.06224 | ||||||||
\(870\) | −19.8744 | + | 50.2510i | −0.673806 | + | 1.70367i | ||||
\(871\) | −1.77403 | − | 3.07271i | −0.0601107 | − | 0.104115i | ||||
\(872\) | 9.11693 | − | 13.1484i | 0.308738 | − | 0.445263i | ||||
\(873\) | 12.6879 | + | 7.32538i | 0.429421 | + | 0.247926i | ||||
\(874\) | −16.7641 | + | 2.48181i | −0.567056 | + | 0.0839485i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 17.3934 | + | 57.4570i | 0.587668 | + | 1.94129i | ||||
\(877\) | −15.2132 | + | 26.3500i | −0.513713 | + | 0.889778i | 0.486160 | + | 0.873870i | \(0.338397\pi\) |
−0.999873 | + | 0.0159079i | \(0.994936\pi\) | |||||||
\(878\) | −24.8784 | + | 19.7332i | −0.839604 | + | 0.665964i | ||||
\(879\) | 21.8791 | − | 12.6319i | 0.737962 | − | 0.426063i | ||||
\(880\) | −2.65765 | − | 41.2738i | −0.0895893 | − | 1.39134i | ||||
\(881\) | 26.1857i | 0.882217i | 0.897454 | + | 0.441109i | \(0.145415\pi\) | ||||
−0.897454 | + | 0.441109i | \(0.854585\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.7013i | 0.831266i | 0.909532 | + | 0.415633i | \(0.136440\pi\) | ||||
−0.909532 | + | 0.415633i | \(0.863560\pi\) | |||||||
\(884\) | −0.156224 | + | 0.668274i | −0.00525438 | + | 0.0224765i | ||||
\(885\) | 54.4070 | − | 31.4119i | 1.82887 | − | 1.05590i | ||||
\(886\) | 24.9389 | + | 31.4414i | 0.837840 | + | 1.05629i | ||||
\(887\) | 11.2268 | − | 19.4454i | 0.376960 | − | 0.652914i | −0.613658 | − | 0.789572i | \(-0.710303\pi\) |
0.990618 | + | 0.136658i | \(0.0436361\pi\) | |||||||
\(888\) | −10.3398 | − | 21.9105i | −0.346981 | − | 0.735267i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −3.24264 | − | 21.9034i | −0.108694 | − | 0.734204i | ||||
\(891\) | −38.5258 | − | 22.2429i | −1.29066 | − | 0.745164i | ||||
\(892\) | 11.4249 | + | 10.7129i | 0.382534 | + | 0.358695i | ||||
\(893\) | 11.0711 | + | 19.1757i | 0.370479 | + | 0.641689i | ||||
\(894\) | 13.5978 | + | 5.37798i | 0.454779 | + | 0.179866i | ||||
\(895\) | 35.3023 | 1.18003 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.37258 | 0.179385 | ||||||||
\(898\) | 21.4153 | + | 8.46983i | 0.714639 | + | 0.282642i | ||||
\(899\) | −20.6796 | − | 35.8182i | −0.689704 | − | 1.19460i | ||||
\(900\) | −4.23020 | − | 3.96657i | −0.141007 | − | 0.132219i | ||||
\(901\) | 2.87875 | + | 1.66205i | 0.0959052 | + | 0.0553709i | ||||
\(902\) | 1.88164 | + | 12.7101i | 0.0626519 | + | 0.423201i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.12132 | + | 10.8523i | 0.170333 | + | 0.360942i | ||||
\(905\) | −28.7279 | + | 49.7582i | −0.954948 | + | 1.65402i | ||||
\(906\) | 40.3186 | + | 50.8311i | 1.33950 | + | 1.68875i | ||||
\(907\) | 29.4214 | − | 16.9864i | 0.976921 | − | 0.564025i | 0.0755817 | − | 0.997140i | \(-0.475919\pi\) |
0.901339 | + | 0.433114i | \(0.142585\pi\) | |||||||
\(908\) | −4.54014 | + | 19.4212i | −0.150670 | + | 0.644514i | ||||
\(909\) | − | 24.1522i | − | 0.801077i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 18.7078i | − | 0.619817i | −0.950766 | − | 0.309908i | \(-0.899702\pi\) | ||
0.950766 | − | 0.309908i | \(-0.100298\pi\) | |||||||
\(912\) | 2.84560 | + | 44.1928i | 0.0942274 | + | 1.46337i | ||||
\(913\) | −32.3924 | + | 18.7018i | −1.07203 | + | 0.618938i | ||||
\(914\) | 0.806528 | − | 0.639729i | 0.0266776 | − | 0.0211604i | ||||
\(915\) | −15.1423 | + | 26.2272i | −0.500589 | + | 0.867046i | ||||
\(916\) | −0.779403 | − | 2.57466i | −0.0257522 | − | 0.0850693i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.34315 | − | 0.198843i | 0.0443304 | − | 0.00656280i | ||||
\(919\) | −42.2969 | − | 24.4201i | −1.39525 | − | 0.805546i | −0.401357 | − | 0.915922i | \(-0.631461\pi\) |
−0.993890 | + | 0.110376i | \(0.964795\pi\) | |||||||
\(920\) | 9.76170 | − | 14.0783i | 0.321834 | − | 0.464149i | ||||
\(921\) | −4.19239 | − | 7.26143i | −0.138144 | − | 0.239272i | ||||
\(922\) | −15.4736 | + | 39.1238i | −0.509596 | + | 1.28848i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.31371 | 0.240473 | ||||||||
\(926\) | 18.1695 | − | 45.9401i | 0.597085 | − | 1.50969i | ||||
\(927\) | −9.60498 | − | 16.6363i | −0.315469 | − | 0.546408i | ||||
\(928\) | −11.8690 | + | 36.7587i | −0.389619 | + | 1.20666i | ||||
\(929\) | 25.8779 | + | 14.9406i | 0.849025 | + | 0.490185i | 0.860322 | − | 0.509751i | \(-0.170263\pi\) |
−0.0112969 | + | 0.999936i | \(0.503596\pi\) | |||||||
\(930\) | 47.4162 | − | 7.01962i | 1.55484 | − | 0.230182i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −31.0919 | + | 9.41214i | −1.01845 | + | 0.308305i | ||||
\(933\) | 22.1421 | − | 38.3513i | 0.724901 | − | 1.25557i | ||||
\(934\) | −26.6753 | + | 21.1586i | −0.872844 | + | 0.692330i | ||||
\(935\) | 2.83882 | − | 1.63899i | 0.0928392 | − | 0.0536007i | ||||
\(936\) | 0.400908 | − | 4.83825i | 0.0131041 | − | 0.158143i | ||||
\(937\) | 29.8042i | 0.973662i | 0.873496 | + | 0.486831i | \(0.161847\pi\) | ||||
−0.873496 | + | 0.486831i | \(0.838153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.3004i | 0.890916i | ||||||||
\(940\) | −21.7958 | − | 5.09526i | −0.710901 | − | 0.166189i | ||||
\(941\) | −21.4655 | + | 12.3931i | −0.699756 | + | 0.404004i | −0.807256 | − | 0.590201i | \(-0.799049\pi\) |
0.107501 | + | 0.994205i | \(0.465715\pi\) | |||||||
\(942\) | 36.1128 | + | 45.5286i | 1.17662 | + | 1.48340i | ||||
\(943\) | −2.66105 | + | 4.60907i | −0.0866556 | + | 0.150092i | ||||
\(944\) | 37.3677 | − | 24.9063i | 1.21621 | − | 0.810631i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.92893 | − | 40.0488i | −0.192766 | − | 1.30210i | ||||
\(947\) | −7.92851 | − | 4.57753i | −0.257642 | − | 0.148750i | 0.365616 | − | 0.930766i | \(-0.380858\pi\) |
−0.623258 | + | 0.782016i | \(0.714192\pi\) | |||||||
\(948\) | 23.1837 | − | 24.7245i | 0.752971 | − | 0.803015i | ||||
\(949\) | −7.58579 | − | 13.1390i | −0.246245 | − | 0.426509i | ||||
\(950\) | −12.4313 | − | 4.91662i | −0.403325 | − | 0.159516i | ||||
\(951\) | 11.8095 | 0.382948 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.3431 | 0.853338 | 0.426669 | − | 0.904408i | \(-0.359687\pi\) | ||||
0.426669 | + | 0.904408i | \(0.359687\pi\) | |||||||
\(954\) | −21.8666 | − | 8.64831i | −0.707958 | − | 0.279999i | ||||
\(955\) | 8.56578 | + | 14.8364i | 0.277182 | + | 0.480094i | ||||
\(956\) | 13.9971 | − | 14.9274i | 0.452699 | − | 0.482786i | ||||
\(957\) | 50.1084 | + | 28.9301i | 1.61977 | + | 0.935177i | ||||
\(958\) | −6.79175 | − | 45.8770i | −0.219431 | − | 1.48222i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −34.5563 | − | 28.4594i | −1.11530 | − | 0.918522i | ||||
\(961\) | −2.84315 | + | 4.92447i | −0.0917144 | + | 0.158854i | ||||
\(962\) | 3.80501 | + | 4.79711i | 0.122678 | + | 0.154665i | ||||
\(963\) | −3.18322 | + | 1.83783i | −0.102578 | + | 0.0592234i | ||||
\(964\) | −9.92235 | − | 2.31957i | −0.319577 | − | 0.0747084i | ||||
\(965\) | − | 38.1145i | − | 1.22695i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 45.1646i | − | 1.45240i | −0.687486 | − | 0.726198i | \(-0.741286\pi\) | ||
0.687486 | − | 0.726198i | \(-0.258714\pi\) | |||||||
\(968\) | −13.1266 | − | 1.08770i | −0.421904 | − | 0.0349599i | ||||
\(969\) | −3.03958 | + | 1.75490i | −0.0976455 | + | 0.0563757i | ||||
\(970\) | −26.7492 | + | 21.2171i | −0.858864 | + | 0.681241i | ||||
\(971\) | 6.50043 | − | 11.2591i | 0.208609 | − | 0.361321i | −0.742668 | − | 0.669660i | \(-0.766440\pi\) |
0.951276 | + | 0.308339i | \(0.0997732\pi\) | |||||||
\(972\) | −28.6943 | + | 8.68633i | −0.920369 | + | 0.278614i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −27.2843 | + | 4.03924i | −0.874244 | + | 0.129426i | ||||
\(975\) | 3.67029 | + | 2.11904i | 0.117543 | + | 0.0678636i | ||||
\(976\) | −9.59688 | + | 19.4044i | −0.307189 | + | 0.621118i | ||||
\(977\) | −8.80761 | − | 15.2552i | −0.281780 | − | 0.488058i | 0.690043 | − | 0.723768i | \(-0.257592\pi\) |
−0.971823 | + | 0.235710i | \(0.924258\pi\) | |||||||
\(978\) | −16.8728 | + | 42.6615i | −0.539531 | + | 1.36416i | ||||
\(979\) | −23.7081 | −0.757714 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.97056 | −0.286408 | ||||||||
\(982\) | −7.52604 | + | 19.0290i | −0.240165 | + | 0.607241i | ||||
\(983\) | −4.80249 | − | 8.31816i | −0.153176 | − | 0.265308i | 0.779218 | − | 0.626754i | \(-0.215617\pi\) |
−0.932393 | + | 0.361445i | \(0.882283\pi\) | |||||||
\(984\) | 11.4287 | + | 7.92449i | 0.364334 | + | 0.252623i | ||||
\(985\) | 4.52607 | + | 2.61313i | 0.144212 | + | 0.0832611i | ||||
\(986\) | −3.02846 | + | 0.448342i | −0.0964458 | + | 0.0142781i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.24264 | − | 10.7117i | −0.103162 | − | 0.340784i | ||||
\(989\) | 8.38478 | − | 14.5229i | 0.266620 | − | 0.461800i | ||||
\(990\) | −18.1674 | + | 14.4102i | −0.577397 | + | 0.457985i | ||||
\(991\) | −22.2235 | + | 12.8307i | −0.705952 | + | 0.407581i | −0.809560 | − | 0.587037i | \(-0.800294\pi\) |
0.103609 | + | 0.994618i | \(0.466961\pi\) | |||||||
\(992\) | 33.5012 | − | 7.18528i | 1.06367 | − | 0.228133i | ||||
\(993\) | − | 32.4399i | − | 1.02945i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 44.7669i | 1.41921i | ||||||||
\(996\) | −9.21587 | + | 39.4224i | −0.292016 | + | 1.24915i | ||||
\(997\) | 26.7681 | − | 15.4546i | 0.847755 | − | 0.489452i | −0.0121377 | − | 0.999926i | \(-0.503864\pi\) |
0.859893 | + | 0.510475i | \(0.170530\pi\) | |||||||
\(998\) | −11.0291 | − | 13.9047i | −0.349119 | − | 0.440146i | ||||
\(999\) | 6.05692 | − | 10.4909i | 0.191632 | − | 0.331917i |
(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 | 196.2.f.d.19.2 | 16 | ||
4.3 | odd | 2 | inner | 196.2.f.d.19.5 | 16 | ||
7.2 | even | 3 | 196.2.d.c.195.7 | yes | 8 | ||
7.3 | odd | 6 | inner | 196.2.f.d.31.5 | 16 | ||
7.4 | even | 3 | inner | 196.2.f.d.31.6 | 16 | ||
7.5 | odd | 6 | 196.2.d.c.195.8 | yes | 8 | ||
7.6 | odd | 2 | inner | 196.2.f.d.19.1 | 16 | ||
21.2 | odd | 6 | 1764.2.b.k.1567.2 | 8 | |||
21.5 | even | 6 | 1764.2.b.k.1567.1 | 8 | |||
28.3 | even | 6 | inner | 196.2.f.d.31.2 | 16 | ||
28.11 | odd | 6 | inner | 196.2.f.d.31.1 | 16 | ||
28.19 | even | 6 | 196.2.d.c.195.5 | ✓ | 8 | ||
28.23 | odd | 6 | 196.2.d.c.195.6 | yes | 8 | ||
28.27 | even | 2 | inner | 196.2.f.d.19.6 | 16 | ||
56.5 | odd | 6 | 3136.2.f.i.3135.3 | 8 | |||
56.19 | even | 6 | 3136.2.f.i.3135.5 | 8 | |||
56.37 | even | 6 | 3136.2.f.i.3135.6 | 8 | |||
56.51 | odd | 6 | 3136.2.f.i.3135.4 | 8 | |||
84.23 | even | 6 | 1764.2.b.k.1567.4 | 8 | |||
84.47 | odd | 6 | 1764.2.b.k.1567.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
196.2.d.c.195.5 | ✓ | 8 | 28.19 | even | 6 | ||
196.2.d.c.195.6 | yes | 8 | 28.23 | odd | 6 | ||
196.2.d.c.195.7 | yes | 8 | 7.2 | even | 3 | ||
196.2.d.c.195.8 | yes | 8 | 7.5 | odd | 6 | ||
196.2.f.d.19.1 | 16 | 7.6 | odd | 2 | inner | ||
196.2.f.d.19.2 | 16 | 1.1 | even | 1 | trivial | ||
196.2.f.d.19.5 | 16 | 4.3 | odd | 2 | inner | ||
196.2.f.d.19.6 | 16 | 28.27 | even | 2 | inner | ||
196.2.f.d.31.1 | 16 | 28.11 | odd | 6 | inner | ||
196.2.f.d.31.2 | 16 | 28.3 | even | 6 | inner | ||
196.2.f.d.31.5 | 16 | 7.3 | odd | 6 | inner | ||
196.2.f.d.31.6 | 16 | 7.4 | even | 3 | inner | ||
1764.2.b.k.1567.1 | 8 | 21.5 | even | 6 | |||
1764.2.b.k.1567.2 | 8 | 21.2 | odd | 6 | |||
1764.2.b.k.1567.3 | 8 | 84.47 | odd | 6 | |||
1764.2.b.k.1567.4 | 8 | 84.23 | even | 6 | |||
3136.2.f.i.3135.3 | 8 | 56.5 | odd | 6 | |||
3136.2.f.i.3135.4 | 8 | 56.51 | odd | 6 | |||
3136.2.f.i.3135.5 | 8 | 56.19 | even | 6 | |||
3136.2.f.i.3135.6 | 8 | 56.37 | even | 6 |