Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(49,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.bx (of order \(10\), degree \(4\), 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 499.1 | ||
Root | \(1.28932 + 0.418926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.499 |
Dual form | 825.2.bx.f.124.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.38463 | + | 1.90578i | −0.979082 | + | 1.34759i | −0.0417590 | + | 0.999128i | \(0.513296\pi\) |
−0.937323 | + | 0.348463i | \(0.886704\pi\) | |||||||
\(3\) | −0.951057 | − | 0.309017i | −0.549093 | − | 0.178411i | ||||
\(4\) | −1.09676 | − | 3.37549i | −0.548382 | − | 1.68775i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.90578 | − | 1.38463i | 0.778032 | − | 0.565273i | ||||
\(7\) | −0.184055 | + | 0.0598032i | −0.0695663 | + | 0.0226035i | −0.343593 | − | 0.939119i | \(-0.611644\pi\) |
0.274027 | + | 0.961722i | \(0.411644\pi\) | |||||||
\(8\) | 3.47080 | + | 1.12773i | 1.22711 | + | 0.398713i | ||||
\(9\) | 0.809017 | + | 0.587785i | 0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.96213 | − | 2.67395i | −0.591606 | − | 0.806227i | ||||
\(12\) | 3.54920i | 1.02457i | ||||||||
\(13\) | −0.572331 | + | 0.787747i | −0.158736 | + | 0.218482i | −0.880976 | − | 0.473161i | \(-0.843113\pi\) |
0.722240 | + | 0.691643i | \(0.243113\pi\) | |||||||
\(14\) | 0.140877 | − | 0.433574i | 0.0376509 | − | 0.115878i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.21225 | + | 0.880754i | −0.303063 | + | 0.220188i | ||||
\(17\) | 1.57274 | + | 2.16469i | 0.381446 | + | 0.525015i | 0.955967 | − | 0.293475i | \(-0.0948117\pi\) |
−0.574521 | + | 0.818490i | \(0.694812\pi\) | |||||||
\(18\) | −2.24038 | + | 0.727943i | −0.528062 | + | 0.171578i | ||||
\(19\) | 1.71480 | − | 5.27760i | 0.393402 | − | 1.21077i | −0.536798 | − | 0.843711i | \(-0.680366\pi\) |
0.930199 | − | 0.367055i | \(-0.119634\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.193527 | 0.0422311 | ||||||||
\(22\) | 7.81280 | − | 0.0369604i | 1.66569 | − | 0.00787998i | ||||
\(23\) | 4.80040i | 1.00095i | 0.865750 | + | 0.500476i | \(0.166842\pi\) | ||||
−0.865750 | + | 0.500476i | \(0.833158\pi\) | |||||||
\(24\) | −2.95244 | − | 2.14507i | −0.602664 | − | 0.437861i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.708805 | − | 2.18148i | −0.139008 | − | 0.427823i | ||||
\(27\) | −0.587785 | − | 0.809017i | −0.113119 | − | 0.155695i | ||||
\(28\) | 0.403730 | + | 0.555687i | 0.0762978 | + | 0.105015i | ||||
\(29\) | 3.12657 | + | 9.62260i | 0.580590 | + | 1.78687i | 0.616303 | + | 0.787509i | \(0.288630\pi\) |
−0.0357132 | + | 0.999362i | \(0.511370\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.02685 | + | 1.47259i | 0.364033 | + | 0.264486i | 0.754732 | − | 0.656033i | \(-0.227767\pi\) |
−0.390699 | + | 0.920518i | \(0.627767\pi\) | |||||||
\(32\) | 3.76902i | 0.666275i | ||||||||
\(33\) | 1.03980 | + | 3.14941i | 0.181007 | + | 0.548243i | ||||
\(34\) | −6.30309 | −1.08097 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.09676 | − | 3.37549i | 0.182794 | − | 0.562582i | ||||
\(37\) | −5.43260 | + | 1.76516i | −0.893114 | + | 0.290190i | −0.719392 | − | 0.694604i | \(-0.755579\pi\) |
−0.173722 | + | 0.984795i | \(0.555579\pi\) | |||||||
\(38\) | 7.68359 | + | 10.5756i | 1.24644 | + | 1.71558i | ||||
\(39\) | 0.787747 | − | 0.572331i | 0.126140 | − | 0.0916464i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.55823 | + | 7.87342i | −0.399529 | + | 1.22962i | 0.525850 | + | 0.850577i | \(0.323747\pi\) |
−0.925378 | + | 0.379045i | \(0.876253\pi\) | |||||||
\(42\) | −0.267964 | + | 0.368820i | −0.0413477 | + | 0.0569102i | ||||
\(43\) | − | 5.11353i | − | 0.779807i | −0.920856 | − | 0.389903i | \(-0.872508\pi\) | ||
0.920856 | − | 0.389903i | \(-0.127492\pi\) | |||||||
\(44\) | −6.87391 | + | 9.55586i | −1.03628 | + | 1.44060i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.14851 | − | 6.64678i | −1.34887 | − | 0.980014i | ||||
\(47\) | −10.3211 | − | 3.35354i | −1.50549 | − | 0.489164i | −0.563879 | − | 0.825857i | \(-0.690692\pi\) |
−0.941614 | + | 0.336693i | \(0.890692\pi\) | |||||||
\(48\) | 1.42509 | − | 0.463040i | 0.205694 | − | 0.0668340i | ||||
\(49\) | −5.63282 | + | 4.09248i | −0.804688 | + | 0.584640i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.826838 | − | 2.54475i | −0.115781 | − | 0.356336i | ||||
\(52\) | 3.28674 | + | 1.06793i | 0.455789 | + | 0.148095i | ||||
\(53\) | 5.45981 | − | 7.51479i | 0.749963 | − | 1.03224i | −0.248020 | − | 0.968755i | \(-0.579780\pi\) |
0.997983 | − | 0.0634803i | \(-0.0202200\pi\) | |||||||
\(54\) | 2.35567 | 0.320567 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.706260 | −0.0943780 | ||||||||
\(57\) | −3.26174 | + | 4.48940i | −0.432028 | + | 0.594635i | ||||
\(58\) | −22.6677 | − | 7.36518i | −2.97642 | − | 0.967096i | ||||
\(59\) | 3.46656 | + | 10.6690i | 0.451307 | + | 1.38898i | 0.875416 | + | 0.483369i | \(0.160587\pi\) |
−0.424109 | + | 0.905611i | \(0.639413\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.975693 | + | 0.708883i | −0.124925 | + | 0.0907631i | −0.648493 | − | 0.761221i | \(-0.724600\pi\) |
0.523568 | + | 0.851984i | \(0.324600\pi\) | |||||||
\(62\) | −5.61288 | + | 1.82374i | −0.712836 | + | 0.231615i | ||||
\(63\) | −0.184055 | − | 0.0598032i | −0.0231888 | − | 0.00753449i | ||||
\(64\) | −9.60743 | − | 6.98021i | −1.20093 | − | 0.872526i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.44184 | − | 2.37914i | −0.916027 | − | 0.292851i | ||||
\(67\) | 3.25922i | 0.398176i | 0.979982 | + | 0.199088i | \(0.0637980\pi\) | ||||
−0.979982 | + | 0.199088i | \(0.936202\pi\) | |||||||
\(68\) | 5.58197 | − | 7.68293i | 0.676914 | − | 0.931692i | ||||
\(69\) | 1.48341 | − | 4.56545i | 0.178581 | − | 0.549616i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.84664 | + | 3.52129i | −0.575191 | + | 0.417901i | −0.836987 | − | 0.547222i | \(-0.815685\pi\) |
0.261796 | + | 0.965123i | \(0.415685\pi\) | |||||||
\(72\) | 2.14507 | + | 2.95244i | 0.252799 | + | 0.347948i | ||||
\(73\) | 3.14442 | − | 1.02168i | 0.368026 | − | 0.119579i | −0.119165 | − | 0.992875i | \(-0.538022\pi\) |
0.487191 | + | 0.873296i | \(0.338022\pi\) | |||||||
\(74\) | 4.15814 | − | 12.7974i | 0.483374 | − | 1.48767i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −19.6952 | −2.25920 | ||||||||
\(77\) | 0.521052 | + | 0.374813i | 0.0593794 | + | 0.0427139i | ||||
\(78\) | 2.29374i | 0.259715i | ||||||||
\(79\) | 8.21389 | + | 5.96774i | 0.924135 | + | 0.671423i | 0.944550 | − | 0.328368i | \(-0.106499\pi\) |
−0.0204147 | + | 0.999792i | \(0.506499\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | −11.4628 | − | 15.7772i | −1.26586 | − | 1.74230i | ||||
\(83\) | 4.88748 | + | 6.72704i | 0.536471 | + | 0.738388i | 0.988099 | − | 0.153818i | \(-0.0491568\pi\) |
−0.451629 | + | 0.892206i | \(0.649157\pi\) | |||||||
\(84\) | −0.212253 | − | 0.653249i | −0.0231588 | − | 0.0712753i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.74527 | + | 7.08035i | 1.05086 | + | 0.763494i | ||||
\(87\) | − | 10.1178i | − | 1.08474i | ||||||
\(88\) | −3.79468 | − | 11.4935i | −0.404514 | − | 1.22521i | ||||
\(89\) | −7.34270 | −0.778325 | −0.389163 | − | 0.921169i | \(-0.627236\pi\) | ||||
−0.389163 | + | 0.921169i | \(0.627236\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0582308 | − | 0.179216i | 0.00610425 | − | 0.0187869i | ||||
\(92\) | 16.2037 | − | 5.26490i | 1.68935 | − | 0.548904i | ||||
\(93\) | −1.47259 | − | 2.02685i | −0.152701 | − | 0.210175i | ||||
\(94\) | 20.6821 | − | 15.0264i | 2.13319 | − | 1.54986i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.16469 | − | 3.58455i | 0.118871 | − | 0.365847i | ||||
\(97\) | −9.31774 | + | 12.8248i | −0.946074 | + | 1.30216i | 0.00717602 | + | 0.999974i | \(0.497716\pi\) |
−0.953250 | + | 0.302184i | \(0.902284\pi\) | |||||||
\(98\) | − | 16.4015i | − | 1.65680i | ||||||
\(99\) | −0.0156899 | − | 3.31659i | −0.00157690 | − | 0.333330i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.6460 | − | 7.73475i | −1.05931 | − | 0.769636i | −0.0853519 | − | 0.996351i | \(-0.527201\pi\) |
−0.973961 | + | 0.226715i | \(0.927201\pi\) | |||||||
\(102\) | 5.99460 | + | 1.94776i | 0.593553 | + | 0.192857i | ||||
\(103\) | 3.80172 | − | 1.23525i | 0.374595 | − | 0.121713i | −0.115668 | − | 0.993288i | \(-0.536901\pi\) |
0.490263 | + | 0.871575i | \(0.336901\pi\) | |||||||
\(104\) | −2.87481 | + | 2.08867i | −0.281899 | + | 0.204811i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.76171 | + | 20.8104i | 0.656755 | + | 2.02129i | ||||
\(107\) | 4.64764 | + | 1.51011i | 0.449304 | + | 0.145988i | 0.524924 | − | 0.851149i | \(-0.324094\pi\) |
−0.0756201 | + | 0.997137i | \(0.524094\pi\) | |||||||
\(108\) | −2.08617 | + | 2.87136i | −0.200742 | + | 0.276297i | ||||
\(109\) | 7.51977 | 0.720263 | 0.360131 | − | 0.932902i | \(-0.382732\pi\) | ||||
0.360131 | + | 0.932902i | \(0.382732\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.71217 | 0.542176 | ||||||||
\(112\) | 0.170450 | − | 0.234604i | 0.0161060 | − | 0.0221680i | ||||
\(113\) | −19.2339 | − | 6.24947i | −1.80937 | − | 0.587901i | −1.00000 | 0.000604375i | \(-0.999808\pi\) | |
−0.809372 | − | 0.587296i | \(-0.800192\pi\) | |||||||
\(114\) | −4.03950 | − | 12.4323i | −0.378334 | − | 1.16439i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 29.0519 | − | 21.1074i | 2.69740 | − | 1.95978i | ||||
\(117\) | −0.926052 | + | 0.300892i | −0.0856135 | + | 0.0278175i | ||||
\(118\) | −25.1326 | − | 8.16608i | −2.31364 | − | 0.751748i | ||||
\(119\) | −0.418926 | − | 0.304368i | −0.0384029 | − | 0.0279014i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.30005 | + | 10.4933i | −0.300005 | + | 0.953938i | ||||
\(122\) | − | 2.84100i | − | 0.257212i | ||||||
\(123\) | 4.86604 | − | 6.69754i | 0.438756 | − | 0.603896i | ||||
\(124\) | 2.74775 | − | 8.45670i | 0.246755 | − | 0.759434i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.368820 | − | 0.267964i | 0.0328571 | − | 0.0238721i | ||||
\(127\) | −4.17340 | − | 5.74419i | −0.370329 | − | 0.509715i | 0.582661 | − | 0.812715i | \(-0.302012\pi\) |
−0.952990 | + | 0.303001i | \(0.902012\pi\) | |||||||
\(128\) | 19.4364 | − | 6.31526i | 1.71795 | − | 0.558196i | ||||
\(129\) | −1.58017 | + | 4.86326i | −0.139126 | + | 0.428186i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.50024 | −0.218447 | −0.109223 | − | 0.994017i | \(-0.534836\pi\) | ||||
−0.109223 | + | 0.994017i | \(0.534836\pi\) | |||||||
\(132\) | 9.49040 | − | 6.96401i | 0.826033 | − | 0.606139i | ||||
\(133\) | 1.07392i | 0.0931207i | ||||||||
\(134\) | −6.21135 | − | 4.51281i | −0.536579 | − | 0.389847i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.01748 | + | 9.28684i | 0.258746 | + | 0.796340i | ||||
\(137\) | 8.98981 | + | 12.3734i | 0.768052 | + | 1.05713i | 0.996501 | + | 0.0835766i | \(0.0266343\pi\) |
−0.228450 | + | 0.973556i | \(0.573366\pi\) | |||||||
\(138\) | 6.64678 | + | 9.14851i | 0.565812 | + | 0.778773i | ||||
\(139\) | 6.07484 | + | 18.6964i | 0.515261 | + | 1.58581i | 0.782806 | + | 0.622266i | \(0.213788\pi\) |
−0.267544 | + | 0.963546i | \(0.586212\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.77969 | + | 6.37882i | 0.739383 | + | 0.537193i | ||||
\(142\) | − | 14.1123i | − | 1.18428i | ||||||
\(143\) | 3.22939 | − | 0.0152774i | 0.270055 | − | 0.00127756i | ||||
\(144\) | −1.49843 | −0.124869 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.40675 | + | 7.40722i | −0.199184 | + | 0.613026i | ||||
\(147\) | 6.62178 | − | 2.15155i | 0.546155 | − | 0.177456i | ||||
\(148\) | 11.9166 | + | 16.4017i | 0.979535 | + | 1.34821i | ||||
\(149\) | −8.19771 | + | 5.95599i | −0.671583 | + | 0.487933i | −0.870555 | − | 0.492072i | \(-0.836240\pi\) |
0.198972 | + | 0.980005i | \(0.436240\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.69682 | − | 11.3776i | 0.300843 | − | 0.925899i | −0.680353 | − | 0.732884i | \(-0.738174\pi\) |
0.981196 | − | 0.193015i | \(-0.0618264\pi\) | |||||||
\(152\) | 11.9034 | − | 16.3837i | 0.965496 | − | 1.32889i | ||||
\(153\) | 2.67571i | 0.216318i | ||||||||
\(154\) | −1.43578 | + | 0.474033i | −0.115698 | + | 0.0381987i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.79587 | − | 2.03132i | −0.223849 | − | 0.162636i | ||||
\(157\) | −2.49752 | − | 0.811494i | −0.199324 | − | 0.0647643i | 0.207654 | − | 0.978202i | \(-0.433417\pi\) |
−0.406978 | + | 0.913438i | \(0.633417\pi\) | |||||||
\(158\) | −22.7464 | + | 7.39076i | −1.80961 | + | 0.587977i | ||||
\(159\) | −7.51479 | + | 5.45981i | −0.595961 | + | 0.432991i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.287079 | − | 0.883539i | −0.0226250 | − | 0.0696326i | ||||
\(162\) | −2.24038 | − | 0.727943i | −0.176021 | − | 0.0571926i | ||||
\(163\) | −13.9443 | + | 19.1927i | −1.09220 | + | 1.50329i | −0.246868 | + | 0.969049i | \(0.579402\pi\) |
−0.845334 | + | 0.534238i | \(0.820598\pi\) | |||||||
\(164\) | 29.3825 | 2.29438 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −19.5876 | −1.52029 | ||||||||
\(167\) | 2.05240 | − | 2.82488i | 0.158819 | − | 0.218596i | −0.722190 | − | 0.691694i | \(-0.756865\pi\) |
0.881010 | + | 0.473098i | \(0.156865\pi\) | |||||||
\(168\) | 0.671694 | + | 0.218246i | 0.0518223 | + | 0.0168381i | ||||
\(169\) | 3.72424 | + | 11.4620i | 0.286480 | + | 0.881695i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.48940 | − | 3.26174i | 0.343313 | − | 0.249431i | ||||
\(172\) | −17.2607 | + | 5.60834i | −1.31612 | + | 0.427632i | ||||
\(173\) | 19.3631 | + | 6.29145i | 1.47215 | + | 0.478330i | 0.931757 | − | 0.363083i | \(-0.118276\pi\) |
0.540392 | + | 0.841413i | \(0.318276\pi\) | |||||||
\(174\) | 19.2823 | + | 14.0094i | 1.46179 | + | 1.06205i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.73370 | + | 1.51335i | 0.356816 | + | 0.114073i | ||||
\(177\) | − | 11.2180i | − | 0.843197i | ||||||
\(178\) | 10.1669 | − | 13.9936i | 0.762044 | − | 1.04886i | ||||
\(179\) | −1.19008 | + | 3.66268i | −0.0889506 | + | 0.273762i | −0.985630 | − | 0.168919i | \(-0.945972\pi\) |
0.896679 | + | 0.442681i | \(0.145972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.2509 | − | 10.3539i | 1.05926 | − | 0.769599i | 0.0853107 | − | 0.996354i | \(-0.472812\pi\) |
0.973952 | + | 0.226755i | \(0.0728117\pi\) | |||||||
\(182\) | 0.260918 | + | 0.359123i | 0.0193406 | + | 0.0266200i | ||||
\(183\) | 1.14700 | − | 0.372682i | 0.0847884 | − | 0.0275494i | ||||
\(184\) | −5.41356 | + | 16.6612i | −0.399093 | + | 1.22828i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.90173 | 0.432736 | ||||||||
\(187\) | 2.70236 | − | 8.45285i | 0.197616 | − | 0.618134i | ||||
\(188\) | 38.5170i | 2.80914i | ||||||||
\(189\) | 0.156567 | + | 0.113752i | 0.0113886 | + | 0.00827427i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.128891 | + | 0.396685i | 0.00932620 | + | 0.0287031i | 0.955611 | − | 0.294630i | \(-0.0951965\pi\) |
−0.946285 | + | 0.323333i | \(0.895196\pi\) | |||||||
\(192\) | 6.98021 | + | 9.60743i | 0.503753 | + | 0.693357i | ||||
\(193\) | 6.87505 | + | 9.46269i | 0.494877 | + | 0.681140i | 0.981278 | − | 0.192596i | \(-0.0616907\pi\) |
−0.486401 | + | 0.873736i | \(0.661691\pi\) | |||||||
\(194\) | −11.5396 | − | 35.5151i | −0.828493 | − | 2.54984i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 19.9920 | + | 14.5250i | 1.42800 | + | 1.03750i | ||||
\(197\) | 21.5958i | 1.53864i | 0.638863 | + | 0.769320i | \(0.279405\pi\) | ||||
−0.638863 | + | 0.769320i | \(0.720595\pi\) | |||||||
\(198\) | 6.34241 | + | 4.56235i | 0.450736 | + | 0.324232i | ||||
\(199\) | −7.76028 | −0.550111 | −0.275056 | − | 0.961428i | \(-0.588696\pi\) | ||||
−0.275056 | + | 0.961428i | \(0.588696\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00715 | − | 3.09970i | 0.0710391 | − | 0.218636i | ||||
\(202\) | 29.4815 | − | 9.57911i | 2.07431 | − | 0.673984i | ||||
\(203\) | −1.15092 | − | 1.58411i | −0.0807790 | − | 0.111183i | ||||
\(204\) | −7.68293 | + | 5.58197i | −0.537912 | + | 0.390816i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.90986 | + | 8.95561i | −0.202739 | + | 0.623967i | ||||
\(207\) | −2.82160 | + | 3.88361i | −0.196115 | + | 0.269929i | ||||
\(208\) | − | 1.45903i | − | 0.101166i | ||||||
\(209\) | −17.4767 | + | 5.77008i | −1.20889 | + | 0.399125i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1173 | + | 7.35065i | 0.696504 | + | 0.506040i | 0.878792 | − | 0.477205i | \(-0.158350\pi\) |
−0.182288 | + | 0.983245i | \(0.558350\pi\) | |||||||
\(212\) | −31.3542 | − | 10.1876i | −2.15342 | − | 0.699687i | ||||
\(213\) | 5.69757 | − | 1.85125i | 0.390391 | − | 0.126846i | ||||
\(214\) | −9.31320 | + | 6.76644i | −0.636637 | + | 0.462544i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.12773 | − | 3.47080i | −0.0767324 | − | 0.236158i | ||||
\(217\) | −0.461118 | − | 0.149826i | −0.0313027 | − | 0.0101709i | ||||
\(218\) | −10.4121 | + | 14.3310i | −0.705196 | + | 0.970619i | ||||
\(219\) | −3.30624 | −0.223415 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.60536 | −0.175255 | ||||||||
\(222\) | −7.90925 | + | 10.8861i | −0.530834 | + | 0.730631i | ||||
\(223\) | 5.11257 | + | 1.66118i | 0.342363 | + | 0.111241i | 0.475152 | − | 0.879904i | \(-0.342393\pi\) |
−0.132789 | + | 0.991144i | \(0.542393\pi\) | |||||||
\(224\) | −0.225399 | − | 0.693708i | −0.0150601 | − | 0.0463503i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 38.5419 | − | 28.0024i | 2.56377 | − | 1.86269i | ||||
\(227\) | 20.6882 | − | 6.72202i | 1.37313 | − | 0.446156i | 0.472723 | − | 0.881211i | \(-0.343271\pi\) |
0.900404 | + | 0.435055i | \(0.143271\pi\) | |||||||
\(228\) | 18.7313 | + | 6.08616i | 1.24051 | + | 0.403066i | ||||
\(229\) | 2.16068 | + | 1.56983i | 0.142782 | + | 0.103737i | 0.656883 | − | 0.753992i | \(-0.271874\pi\) |
−0.514101 | + | 0.857730i | \(0.671874\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.379726 | − | 0.517482i | −0.0249842 | − | 0.0340478i | ||||
\(232\) | 36.9240i | 2.42418i | ||||||||
\(233\) | 3.36624 | − | 4.63323i | 0.220530 | − | 0.303533i | −0.684389 | − | 0.729117i | \(-0.739931\pi\) |
0.904919 | + | 0.425584i | \(0.139931\pi\) | |||||||
\(234\) | 0.708805 | − | 2.18148i | 0.0463360 | − | 0.142608i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 32.2110 | − | 23.4027i | 2.09676 | − | 1.52338i | ||||
\(237\) | −5.96774 | − | 8.21389i | −0.387647 | − | 0.533550i | ||||
\(238\) | 1.16012 | − | 0.376945i | 0.0751992 | − | 0.0244337i | ||||
\(239\) | 7.53013 | − | 23.1754i | 0.487084 | − | 1.49909i | −0.341857 | − | 0.939752i | \(-0.611056\pi\) |
0.828940 | − | 0.559337i | \(-0.188944\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.7082 | −1.07627 | −0.538135 | − | 0.842859i | \(-0.680871\pi\) | ||||
−0.538135 | + | 0.842859i | \(0.680871\pi\) | |||||||
\(242\) | −15.4286 | − | 20.8185i | −0.991788 | − | 1.33827i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 3.46293 | + | 2.51597i | 0.221691 | + | 0.161068i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.02636 | + | 18.5472i | 0.384227 | + | 1.18253i | ||||
\(247\) | 3.17598 | + | 4.37136i | 0.202083 | + | 0.278143i | ||||
\(248\) | 5.37410 | + | 7.39682i | 0.341256 | + | 0.469698i | ||||
\(249\) | −2.56950 | − | 7.90811i | −0.162835 | − | 0.501156i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.0239 | + | 9.46240i | 0.822060 | + | 0.597262i | 0.917302 | − | 0.398193i | \(-0.130362\pi\) |
−0.0952418 | + | 0.995454i | \(0.530362\pi\) | |||||||
\(252\) | 0.686867i | 0.0432685i | ||||||||
\(253\) | 12.8360 | − | 9.41903i | 0.806995 | − | 0.592169i | ||||
\(254\) | 16.7258 | 1.04947 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.53728 | + | 23.1974i | −0.471080 | + | 1.44984i | ||||
\(257\) | −5.67662 | + | 1.84445i | −0.354098 | + | 0.115053i | −0.480664 | − | 0.876905i | \(-0.659604\pi\) |
0.126566 | + | 0.991958i | \(0.459604\pi\) | |||||||
\(258\) | −7.08035 | − | 9.74527i | −0.440804 | − | 0.606714i | ||||
\(259\) | 0.894336 | − | 0.649773i | 0.0555713 | − | 0.0403749i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.12657 | + | 9.62260i | −0.193530 | + | 0.595624i | ||||
\(262\) | 3.46191 | − | 4.76490i | 0.213877 | − | 0.294377i | ||||
\(263\) | 0.451149i | 0.0278190i | 0.999903 | + | 0.0139095i | \(0.00442768\pi\) | ||||
−0.999903 | + | 0.0139095i | \(0.995572\pi\) | |||||||
\(264\) | 0.0572591 | + | 12.1036i | 0.00352405 | + | 0.744925i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.04666 | − | 1.48698i | −0.125489 | − | 0.0911728i | ||||
\(267\) | 6.98333 | + | 2.26902i | 0.427373 | + | 0.138862i | ||||
\(268\) | 11.0015 | − | 3.57459i | 0.672021 | − | 0.218353i | ||||
\(269\) | 11.9085 | − | 8.65203i | 0.726074 | − | 0.527524i | −0.162245 | − | 0.986751i | \(-0.551873\pi\) |
0.888319 | + | 0.459227i | \(0.151873\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.36829 | + | 4.21115i | 0.0831175 | + | 0.255809i | 0.983975 | − | 0.178305i | \(-0.0570614\pi\) |
−0.900858 | + | 0.434114i | \(0.857061\pi\) | |||||||
\(272\) | −3.81312 | − | 1.23896i | −0.231204 | − | 0.0751228i | ||||
\(273\) | −0.110762 | + | 0.152450i | −0.00670360 | + | 0.00922671i | ||||
\(274\) | −36.0286 | −2.17657 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −17.0376 | −1.02554 | ||||||||
\(277\) | −0.0542702 | + | 0.0746965i | −0.00326078 | + | 0.00448808i | −0.810644 | − | 0.585539i | \(-0.800883\pi\) |
0.807383 | + | 0.590027i | \(0.200883\pi\) | |||||||
\(278\) | −44.0427 | − | 14.3104i | −2.64151 | − | 0.858278i | ||||
\(279\) | 0.774188 | + | 2.38271i | 0.0463494 | + | 0.142649i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.19314 | + | 3.04650i | −0.250142 | + | 0.181739i | −0.705790 | − | 0.708421i | \(-0.749408\pi\) |
0.455648 | + | 0.890160i | \(0.349408\pi\) | |||||||
\(282\) | −24.3133 | + | 7.89985i | −1.44783 | + | 0.470429i | ||||
\(283\) | −1.48805 | − | 0.483496i | −0.0884552 | − | 0.0287408i | 0.264455 | − | 0.964398i | \(-0.414808\pi\) |
−0.352910 | + | 0.935657i | \(0.614808\pi\) | |||||||
\(284\) | 17.2017 | + | 12.4978i | 1.02073 | + | 0.741607i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.44240 | + | 6.17566i | −0.262684 | + | 0.365174i | ||||
\(287\) | − | 1.60214i | − | 0.0945710i | ||||||
\(288\) | −2.21537 | + | 3.04920i | −0.130542 | + | 0.179676i | ||||
\(289\) | 3.04091 | − | 9.35897i | 0.178877 | − | 0.550527i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.8248 | − | 9.31774i | 0.751802 | − | 0.546216i | ||||
\(292\) | −6.89736 | − | 9.49341i | −0.403638 | − | 0.555560i | ||||
\(293\) | −22.0236 | + | 7.15592i | −1.28664 | + | 0.418053i | −0.870912 | − | 0.491438i | \(-0.836471\pi\) |
−0.415723 | + | 0.909491i | \(0.636471\pi\) | |||||||
\(294\) | −5.06834 | + | 15.5987i | −0.295592 | + | 0.909737i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −20.8461 | −1.21165 | ||||||||
\(297\) | −1.00996 | + | 3.15911i | −0.0586038 | + | 0.183310i | ||||
\(298\) | − | 23.8699i | − | 1.38274i | ||||||
\(299\) | −3.78150 | − | 2.74742i | −0.218690 | − | 0.158887i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.305805 | + | 0.941172i | 0.0176263 | + | 0.0542483i | ||||
\(302\) | 16.5646 | + | 22.7991i | 0.953183 | + | 1.31194i | ||||
\(303\) | 7.73475 | + | 10.6460i | 0.444350 | + | 0.611595i | ||||
\(304\) | 2.56950 | + | 7.90811i | 0.147371 | + | 0.453561i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.09931 | − | 3.70486i | −0.291508 | − | 0.211793i | ||||
\(307\) | − | 7.72480i | − | 0.440878i | −0.975401 | − | 0.220439i | \(-0.929251\pi\) | ||
0.975401 | − | 0.220439i | \(-0.0707490\pi\) | |||||||
\(308\) | 0.693708 | − | 2.16989i | 0.0395277 | − | 0.123641i | ||||
\(309\) | −3.99737 | −0.227402 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.90867 | + | 18.1850i | −0.335050 | + | 1.03118i | 0.631647 | + | 0.775256i | \(0.282379\pi\) |
−0.966697 | + | 0.255922i | \(0.917621\pi\) | |||||||
\(312\) | 3.37955 | − | 1.09808i | 0.191329 | − | 0.0621666i | ||||
\(313\) | 1.70638 | + | 2.34863i | 0.0964503 | + | 0.132752i | 0.854515 | − | 0.519427i | \(-0.173855\pi\) |
−0.758064 | + | 0.652180i | \(0.773855\pi\) | |||||||
\(314\) | 5.00468 | − | 3.63611i | 0.282430 | − | 0.205198i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.1354 | − | 34.2711i | 0.626413 | − | 1.92790i | ||||
\(317\) | 1.32930 | − | 1.82962i | 0.0746607 | − | 0.102762i | −0.770053 | − | 0.637979i | \(-0.779770\pi\) |
0.844714 | + | 0.535218i | \(0.179770\pi\) | |||||||
\(318\) | − | 21.8814i | − | 1.22705i | ||||||
\(319\) | 19.5956 | − | 27.2411i | 1.09714 | − | 1.52521i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.95352 | − | 2.87240i | −0.220664 | − | 0.160322i | ||||
\(322\) | 2.08133 | + | 0.676265i | 0.115988 | + | 0.0376868i | ||||
\(323\) | 14.1213 | − | 4.58829i | 0.785731 | − | 0.255299i | ||||
\(324\) | 2.87136 | − | 2.08617i | 0.159520 | − | 0.115898i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −17.2693 | − | 53.1496i | −0.956460 | − | 2.94368i | ||||
\(327\) | −7.15172 | − | 2.32374i | −0.395491 | − | 0.128503i | ||||
\(328\) | −17.7582 | + | 24.4421i | −0.980533 | + | 1.34959i | ||||
\(329\) | 2.10021 | 0.115788 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.02336 | 0.331074 | 0.165537 | − | 0.986204i | \(-0.447064\pi\) | ||||
0.165537 | + | 0.986204i | \(0.447064\pi\) | |||||||
\(332\) | 17.3466 | − | 23.8756i | 0.952021 | − | 1.31034i | ||||
\(333\) | −5.43260 | − | 1.76516i | −0.297705 | − | 0.0967301i | ||||
\(334\) | 2.54179 | + | 7.82284i | 0.139081 | + | 0.428047i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.234604 | + | 0.170450i | −0.0127987 | + | 0.00929879i | ||||
\(337\) | 13.8519 | − | 4.50076i | 0.754562 | − | 0.245172i | 0.0936187 | − | 0.995608i | \(-0.470157\pi\) |
0.660943 | + | 0.750436i | \(0.270157\pi\) | |||||||
\(338\) | −27.0008 | − | 8.77310i | −1.46865 | − | 0.477193i | ||||
\(339\) | 16.3613 | + | 11.8872i | 0.888625 | + | 0.645624i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.0393084 | − | 8.30913i | −0.00212867 | − | 0.449965i | ||||
\(342\) | 13.0721i | 0.706859i | ||||||||
\(343\) | 1.58827 | − | 2.18607i | 0.0857587 | − | 0.118037i | ||||
\(344\) | 5.76669 | − | 17.7480i | 0.310919 | − | 0.956911i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −38.8009 | + | 28.1905i | −2.08595 | + | 1.51553i | ||||
\(347\) | −16.9489 | − | 23.3281i | −0.909863 | − | 1.25232i | −0.967213 | − | 0.253965i | \(-0.918265\pi\) |
0.0573506 | − | 0.998354i | \(-0.481735\pi\) | |||||||
\(348\) | −34.1525 | + | 11.0968i | −1.83077 | + | 0.594853i | ||||
\(349\) | 0.504421 | − | 1.55245i | 0.0270010 | − | 0.0831006i | −0.936648 | − | 0.350272i | \(-0.886089\pi\) |
0.963649 | + | 0.267172i | \(0.0860891\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.973708 | 0.0519727 | ||||||||
\(352\) | 10.0782 | − | 7.39533i | 0.537169 | − | 0.394172i | ||||
\(353\) | − | 24.9297i | − | 1.32687i | −0.748232 | − | 0.663437i | \(-0.769097\pi\) | ||
0.748232 | − | 0.663437i | \(-0.230903\pi\) | |||||||
\(354\) | 21.3791 | + | 15.5328i | 1.13628 | + | 0.825559i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.05321 | + | 24.7852i | 0.426819 | + | 1.31361i | ||||
\(357\) | 0.304368 | + | 0.418926i | 0.0161089 | + | 0.0221719i | ||||
\(358\) | −5.33245 | − | 7.33949i | −0.281829 | − | 0.387904i | ||||
\(359\) | −8.78874 | − | 27.0489i | −0.463852 | − | 1.42759i | −0.860421 | − | 0.509584i | \(-0.829799\pi\) |
0.396569 | − | 0.918005i | \(-0.370201\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.54125 | − | 6.93213i | −0.502171 | − | 0.364849i | ||||
\(362\) | 41.4955i | 2.18095i | ||||||||
\(363\) | 6.38115 | − | 8.95996i | 0.334924 | − | 0.470276i | ||||
\(364\) | −0.668808 | −0.0350550 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.877916 | + | 2.70195i | −0.0458894 | + | 0.141233i | ||||
\(367\) | 9.93023 | − | 3.22653i | 0.518354 | − | 0.168423i | −0.0381442 | − | 0.999272i | \(-0.512145\pi\) |
0.556498 | + | 0.830849i | \(0.312145\pi\) | |||||||
\(368\) | −4.22797 | − | 5.81930i | −0.220398 | − | 0.303352i | ||||
\(369\) | −6.69754 | + | 4.86604i | −0.348660 | + | 0.253316i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.555499 | + | 1.70965i | −0.0288401 | + | 0.0887606i | ||||
\(372\) | −5.22653 | + | 7.19370i | −0.270983 | + | 0.372976i | ||||
\(373\) | 2.81747i | 0.145883i | 0.997336 | + | 0.0729416i | \(0.0232387\pi\) | ||||
−0.997336 | + | 0.0729416i | \(0.976761\pi\) | |||||||
\(374\) | 12.3675 | + | 16.8542i | 0.639509 | + | 0.871508i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −32.0407 | − | 23.2789i | −1.65237 | − | 1.20052i | ||||
\(377\) | −9.36960 | − | 3.04437i | −0.482559 | − | 0.156793i | ||||
\(378\) | −0.433574 | + | 0.140877i | −0.0223006 | + | 0.00724592i | ||||
\(379\) | 7.22711 | − | 5.25080i | 0.371231 | − | 0.269715i | −0.386490 | − | 0.922294i | \(-0.626313\pi\) |
0.757721 | + | 0.652578i | \(0.226313\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.19409 | + | 6.75270i | 0.112406 | + | 0.345951i | ||||
\(382\) | −0.934460 | − | 0.303625i | −0.0478111 | − | 0.0155348i | ||||
\(383\) | 5.01545 | − | 6.90317i | 0.256278 | − | 0.352736i | −0.661420 | − | 0.750016i | \(-0.730046\pi\) |
0.917697 | + | 0.397280i | \(0.130046\pi\) | |||||||
\(384\) | −20.4366 | −1.04290 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −27.5532 | −1.40242 | ||||||||
\(387\) | 3.00566 | − | 4.13694i | 0.152786 | − | 0.210292i | ||||
\(388\) | 53.5093 | + | 17.3862i | 2.71652 | + | 0.882651i | ||||
\(389\) | −3.63890 | − | 11.1994i | −0.184500 | − | 0.567832i | 0.815440 | − | 0.578842i | \(-0.196495\pi\) |
−0.999939 | + | 0.0110104i | \(0.996495\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.3914 | + | 7.54978i | −0.525515 | + | 0.381809i | ||||
\(392\) | −24.1656 | + | 7.85188i | −1.22055 | + | 0.396580i | ||||
\(393\) | 2.37787 | + | 0.772616i | 0.119948 | + | 0.0389733i | ||||
\(394\) | −41.1569 | − | 29.9023i | −2.07346 | − | 1.50645i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −11.1779 | + | 3.69047i | −0.561711 | + | 0.185453i | ||||
\(397\) | − | 1.41214i | − | 0.0708735i | −0.999372 | − | 0.0354368i | \(-0.988718\pi\) | ||
0.999372 | − | 0.0354368i | \(-0.0112822\pi\) | |||||||
\(398\) | 10.7451 | − | 14.7894i | 0.538604 | − | 0.741325i | ||||
\(399\) | 0.331860 | − | 1.02136i | 0.0166138 | − | 0.0511319i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.84361 | + | 4.97217i | −0.341753 | + | 0.248298i | −0.745401 | − | 0.666616i | \(-0.767742\pi\) |
0.403648 | + | 0.914914i | \(0.367742\pi\) | |||||||
\(402\) | 4.51281 | + | 6.21135i | 0.225078 | + | 0.309794i | ||||
\(403\) | −2.32006 | + | 0.753833i | −0.115570 | + | 0.0375511i | ||||
\(404\) | −14.4325 | + | 44.4185i | −0.718042 | + | 2.20991i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.61257 | 0.228918 | ||||||||
\(407\) | 15.3794 | + | 11.0630i | 0.762331 | + | 0.548375i | ||||
\(408\) | − | 9.76476i | − | 0.483428i | ||||||
\(409\) | 8.19172 | + | 5.95163i | 0.405054 | + | 0.294289i | 0.771597 | − | 0.636112i | \(-0.219458\pi\) |
−0.366542 | + | 0.930401i | \(0.619458\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.72622 | − | 14.5458i | −0.233127 | − | 0.717493i | ||||
\(412\) | −8.33918 | − | 11.4779i | −0.410842 | − | 0.565475i | ||||
\(413\) | −1.27608 | − | 1.75637i | −0.0627915 | − | 0.0864252i | ||||
\(414\) | −3.49442 | − | 10.7547i | −0.171741 | − | 0.528566i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.96903 | − | 2.15713i | −0.145569 | − | 0.105762i | ||||
\(417\) | − | 19.6586i | − | 0.962686i | ||||||
\(418\) | 13.2023 | − | 41.2962i | 0.645746 | − | 2.01987i | ||||
\(419\) | −32.8019 | −1.60248 | −0.801240 | − | 0.598343i | \(-0.795826\pi\) | ||||
−0.801240 | + | 0.598343i | \(0.795826\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.36619 | + | 13.4377i | −0.212795 | + | 0.654915i | 0.786508 | + | 0.617580i | \(0.211887\pi\) |
−0.999303 | + | 0.0373351i | \(0.988113\pi\) | |||||||
\(422\) | −28.0175 | + | 9.10342i | −1.36387 | + | 0.443148i | ||||
\(423\) | −6.37882 | − | 8.77969i | −0.310149 | − | 0.426883i | ||||
\(424\) | 27.4246 | − | 19.9251i | 1.33185 | − | 0.967649i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.36095 | + | 13.4216i | −0.211289 | + | 0.650280i | ||||
\(427\) | 0.137188 | − | 0.188823i | 0.00663899 | − | 0.00913779i | ||||
\(428\) | − | 17.3443i | − | 0.838368i | ||||||
\(429\) | −3.07605 | − | 0.983406i | −0.148513 | − | 0.0474793i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.4569 | − | 11.2301i | −0.744531 | − | 0.540933i | 0.149596 | − | 0.988747i | \(-0.452203\pi\) |
−0.894127 | + | 0.447814i | \(0.852203\pi\) | |||||||
\(432\) | 1.42509 | + | 0.463040i | 0.0685646 | + | 0.0222780i | ||||
\(433\) | 14.3800 | − | 4.67235i | 0.691059 | − | 0.224539i | 0.0576283 | − | 0.998338i | \(-0.481646\pi\) |
0.633431 | + | 0.773799i | \(0.281646\pi\) | |||||||
\(434\) | 0.924015 | − | 0.671336i | 0.0443541 | − | 0.0322252i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.24740 | − | 25.3829i | −0.394979 | − | 1.21562i | ||||
\(437\) | 25.3346 | + | 8.23171i | 1.21192 | + | 0.393776i | ||||
\(438\) | 4.57791 | − | 6.30096i | 0.218741 | − | 0.301071i | ||||
\(439\) | −37.1642 | −1.77375 | −0.886876 | − | 0.462008i | \(-0.847129\pi\) | ||||
−0.886876 | + | 0.462008i | \(0.847129\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.96255 | −0.331550 | ||||||||
\(442\) | 3.60746 | − | 4.96524i | 0.171589 | − | 0.236172i | ||||
\(443\) | 2.62539 | + | 0.853040i | 0.124736 | + | 0.0405291i | 0.370720 | − | 0.928745i | \(-0.379111\pi\) |
−0.245984 | + | 0.969274i | \(0.579111\pi\) | |||||||
\(444\) | −6.26490 | − | 19.2814i | −0.297319 | − | 0.915054i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.2449 | + | 7.44333i | −0.485108 | + | 0.352452i | ||||
\(447\) | 9.63699 | − | 3.13125i | 0.455814 | − | 0.148103i | ||||
\(448\) | 2.18574 | + | 0.710189i | 0.103266 | + | 0.0335533i | ||||
\(449\) | −14.4540 | − | 10.5015i | −0.682127 | − | 0.495594i | 0.191936 | − | 0.981408i | \(-0.438524\pi\) |
−0.874063 | + | 0.485813i | \(0.838524\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.0728 | − | 8.60813i | 1.22772 | − | 0.405341i | ||||
\(452\) | 71.7780i | 3.37615i | ||||||||
\(453\) | −7.03177 | + | 9.67840i | −0.330381 | + | 0.454731i | ||||
\(454\) | −15.8349 | + | 48.7348i | −0.743168 | + | 2.28724i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −16.3837 | + | 11.9034i | −0.767236 | + | 0.557429i | ||||
\(457\) | 12.4388 | + | 17.1205i | 0.581862 | + | 0.800864i | 0.993898 | − | 0.110304i | \(-0.0351823\pi\) |
−0.412036 | + | 0.911167i | \(0.635182\pi\) | |||||||
\(458\) | −5.98350 | + | 1.94416i | −0.279590 | + | 0.0908444i | ||||
\(459\) | 0.826838 | − | 2.54475i | 0.0385935 | − | 0.118779i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.3476 | −1.59973 | −0.799864 | − | 0.600181i | \(-0.795095\pi\) | ||||
−0.799864 | + | 0.600181i | \(0.795095\pi\) | |||||||
\(462\) | 1.51199 | − | 0.00715284i | 0.0703441 | − | 0.000332780i | ||||
\(463\) | − | 10.4516i | − | 0.485727i | −0.970060 | − | 0.242864i | \(-0.921913\pi\) | ||
0.970060 | − | 0.242864i | \(-0.0780867\pi\) | |||||||
\(464\) | −12.2653 | − | 8.91129i | −0.569404 | − | 0.413696i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.16892 | + | 12.8306i | 0.193122 | + | 0.594367i | ||||
\(467\) | −17.4239 | − | 23.9820i | −0.806284 | − | 1.10975i | −0.991886 | − | 0.127129i | \(-0.959424\pi\) |
0.185602 | − | 0.982625i | \(-0.440576\pi\) | |||||||
\(468\) | 2.03132 | + | 2.79587i | 0.0938978 | + | 0.129239i | ||||
\(469\) | −0.194911 | − | 0.599875i | −0.00900017 | − | 0.0276997i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.12452 | + | 1.54355i | 0.0978927 | + | 0.0711232i | ||||
\(472\) | 40.9392i | 1.88438i | ||||||||
\(473\) | −13.6734 | + | 10.0334i | −0.628701 | + | 0.461338i | ||||
\(474\) | 23.9170 | 1.09854 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.567928 | + | 1.74790i | −0.0260309 | + | 0.0801150i | ||||
\(477\) | 8.83416 | − | 2.87039i | 0.404488 | − | 0.131426i | ||||
\(478\) | 33.7407 | + | 46.4401i | 1.54326 | + | 2.12412i | ||||
\(479\) | −10.6941 | + | 7.76971i | −0.488625 | + | 0.355007i | −0.804655 | − | 0.593742i | \(-0.797650\pi\) |
0.316030 | + | 0.948749i | \(0.397650\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.71875 | − | 5.28977i | 0.0783682 | − | 0.241193i | ||||
\(482\) | 23.1347 | − | 31.8422i | 1.05376 | − | 1.45037i | ||||
\(483\) | 0.929007i | 0.0422713i | ||||||||
\(484\) | 39.0395 | − | 0.369380i | 1.77452 | − | 0.0167900i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.90578 | + | 1.38463i | 0.0864480 | + | 0.0628081i | ||||
\(487\) | −40.4176 | − | 13.1325i | −1.83150 | − | 0.595089i | −0.999167 | − | 0.0408075i | \(-0.987007\pi\) |
−0.832329 | − | 0.554282i | \(-0.812993\pi\) | |||||||
\(488\) | −4.18586 | + | 1.36007i | −0.189485 | + | 0.0615675i | ||||
\(489\) | 19.1927 | − | 13.9443i | 0.867923 | − | 0.630583i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.86568 | − | 14.9750i | −0.219585 | − | 0.675813i | −0.998796 | − | 0.0490515i | \(-0.984380\pi\) |
0.779211 | − | 0.626761i | \(-0.215620\pi\) | |||||||
\(492\) | −27.9444 | − | 9.07968i | −1.25983 | − | 0.409343i | ||||
\(493\) | −15.9127 | + | 21.9019i | −0.716670 | + | 0.986412i | ||||
\(494\) | −12.7284 | −0.572679 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.75405 | −0.168562 | ||||||||
\(497\) | 0.681466 | − | 0.937957i | 0.0305679 | − | 0.0420731i | ||||
\(498\) | 18.6289 | + | 6.05291i | 0.834782 | + | 0.271237i | ||||
\(499\) | 10.3607 | + | 31.8869i | 0.463808 | + | 1.42746i | 0.860475 | + | 0.509493i | \(0.170167\pi\) |
−0.396666 | + | 0.917963i | \(0.629833\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.82488 | + | 2.05240i | −0.126206 | + | 0.0916943i | ||||
\(502\) | −36.0665 | + | 11.7187i | −1.60973 | + | 0.523032i | ||||
\(503\) | 21.6996 | + | 7.05063i | 0.967537 | + | 0.314372i | 0.749821 | − | 0.661640i | \(-0.230139\pi\) |
0.217716 | + | 0.976012i | \(0.430139\pi\) | |||||||
\(504\) | −0.571377 | − | 0.415129i | −0.0254511 | − | 0.0184913i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.177425 | + | 37.5046i | 0.00788749 | + | 1.66728i | ||||
\(507\) | − | 12.0519i | − | 0.535243i | ||||||
\(508\) | −14.8122 | + | 20.3873i | −0.657187 | + | 0.904540i | ||||
\(509\) | −12.2731 | + | 37.7727i | −0.543996 | + | 1.67425i | 0.179370 | + | 0.983782i | \(0.442594\pi\) |
−0.723365 | + | 0.690465i | \(0.757406\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.517646 | + | 0.376092i | −0.0228993 | + | 0.0166373i | ||||
\(512\) | −9.74805 | − | 13.4170i | −0.430807 | − | 0.592955i | ||||
\(513\) | −5.27760 | + | 1.71480i | −0.233012 | + | 0.0757102i | ||||
\(514\) | 4.34491 | − | 13.3723i | 0.191646 | − | 0.589826i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 18.1490 | 0.798963 | ||||||||
\(517\) | 11.2843 | + | 34.1784i | 0.496281 | + | 1.50316i | ||||
\(518\) | 2.60410i | 0.114418i | ||||||||
\(519\) | −16.4712 | − | 11.9670i | −0.723007 | − | 0.525295i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.88005 | + | 24.2523i | 0.345231 | + | 1.06251i | 0.961460 | + | 0.274945i | \(0.0886597\pi\) |
−0.616229 | + | 0.787567i | \(0.711340\pi\) | |||||||
\(522\) | −14.0094 | − | 19.2823i | −0.613175 | − | 0.843963i | ||||
\(523\) | −9.06977 | − | 12.4835i | −0.396593 | − | 0.545864i | 0.563291 | − | 0.826258i | \(-0.309535\pi\) |
−0.959885 | + | 0.280394i | \(0.909535\pi\) | |||||||
\(524\) | 2.74217 | + | 8.43953i | 0.119792 | + | 0.368683i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.859791 | − | 0.624675i | −0.0374887 | − | 0.0272371i | ||||
\(527\) | 6.70351i | 0.292010i | ||||||||
\(528\) | −4.03436 | − | 2.90208i | −0.175573 | − | 0.126297i | ||||
\(529\) | −0.0438407 | −0.00190612 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.46656 | + | 10.6690i | −0.150436 | + | 0.462993i | ||||
\(532\) | 3.62501 | − | 1.17784i | 0.157164 | − | 0.0510657i | ||||
\(533\) | −4.73811 | − | 6.52145i | −0.205230 | − | 0.282475i | ||||
\(534\) | −13.9936 | + | 10.1669i | −0.605561 | + | 0.439966i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.67552 | + | 11.3121i | −0.158758 | + | 0.488607i | ||||
\(537\) | 2.26366 | − | 3.11567i | 0.0976843 | − | 0.134451i | ||||
\(538\) | 34.6749i | 1.49494i | ||||||||
\(539\) | 21.9955 | + | 7.03189i | 0.947411 | + | 0.302885i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.3294 | − | 16.2233i | −0.960018 | − | 0.697494i | −0.00686309 | − | 0.999976i | \(-0.502185\pi\) |
−0.953155 | + | 0.302483i | \(0.902185\pi\) | |||||||
\(542\) | −9.92010 | − | 3.22324i | −0.426105 | − | 0.138450i | ||||
\(543\) | −16.7530 | + | 5.44337i | −0.718938 | + | 0.233597i | ||||
\(544\) | −8.15877 | + | 5.92769i | −0.349804 | + | 0.254148i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.137173 | − | 0.422175i | −0.00587046 | − | 0.0180674i | ||||
\(547\) | 29.2626 | + | 9.50800i | 1.25118 | + | 0.406533i | 0.858343 | − | 0.513076i | \(-0.171494\pi\) |
0.392836 | + | 0.919608i | \(0.371494\pi\) | |||||||
\(548\) | 31.9067 | − | 43.9157i | 1.36298 | − | 1.87599i | ||||
\(549\) | −1.20602 | −0.0514718 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 56.1457 | 2.39189 | ||||||||
\(552\) | 10.2972 | − | 14.1729i | 0.438278 | − | 0.603238i | ||||
\(553\) | −1.86870 | − | 0.607177i | −0.0794652 | − | 0.0258198i | ||||
\(554\) | −0.0672109 | − | 0.206854i | −0.00285552 | − | 0.00878838i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 56.4470 | − | 41.0112i | 2.39389 | − | 1.73926i | ||||
\(557\) | 13.2538 | − | 4.30642i | 0.561582 | − | 0.182469i | −0.0144509 | − | 0.999896i | \(-0.504600\pi\) |
0.576033 | + | 0.817427i | \(0.304600\pi\) | |||||||
\(558\) | −5.61288 | − | 1.82374i | −0.237612 | − | 0.0772049i | ||||
\(559\) | 4.02817 | + | 2.92664i | 0.170373 | + | 0.123783i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.18217 | + | 7.20406i | −0.218791 | + | 0.304156i | ||||
\(562\) | − | 12.2095i | − | 0.515026i | ||||||
\(563\) | −3.43259 | + | 4.72456i | −0.144667 | + | 0.199117i | −0.875201 | − | 0.483759i | \(-0.839271\pi\) |
0.730534 | + | 0.682876i | \(0.239271\pi\) | |||||||
\(564\) | 11.9024 | − | 36.6318i | 0.501181 | − | 1.54248i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.98183 | − | 2.16643i | 0.125336 | − | 0.0910618i | ||||
\(567\) | −0.113752 | − | 0.156567i | −0.00477715 | − | 0.00657518i | ||||
\(568\) | −20.7928 | + | 6.75599i | −0.872447 | + | 0.283475i | ||||
\(569\) | 1.68536 | − | 5.18701i | 0.0706540 | − | 0.217451i | −0.909494 | − | 0.415716i | \(-0.863531\pi\) |
0.980148 | + | 0.198266i | \(0.0635309\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.2894 | 1.68606 | 0.843030 | − | 0.537866i | \(-0.180770\pi\) | ||||
0.843030 | + | 0.537866i | \(0.180770\pi\) | |||||||
\(572\) | −3.59344 | − | 10.8840i | −0.150249 | − | 0.455084i | ||||
\(573\) | − | 0.417099i | − | 0.0174246i | ||||||
\(574\) | 3.05332 | + | 2.21837i | 0.127443 | + | 0.0925928i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.66971 | − | 11.2942i | −0.152905 | − | 0.470592i | ||||
\(577\) | 14.0032 | + | 19.2737i | 0.582959 | + | 0.802374i | 0.994016 | − | 0.109236i | \(-0.0348403\pi\) |
−0.411057 | + | 0.911610i | \(0.634840\pi\) | |||||||
\(578\) | 13.6256 | + | 18.7540i | 0.566750 | + | 0.780065i | ||||
\(579\) | −3.61443 | − | 11.1241i | −0.150210 | − | 0.462300i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.30186 | − | 0.945860i | −0.0540104 | − | 0.0392409i | ||||
\(582\) | 37.3428i | 1.54791i | ||||||||
\(583\) | −30.8071 | + | 0.145740i | −1.27590 | + | 0.00603595i | ||||
\(584\) | 12.0658 | 0.499287 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.8570 | − | 51.8805i | 0.696357 | − | 2.14317i | ||||
\(587\) | −18.6483 | + | 6.05919i | −0.769697 | + | 0.250090i | −0.667435 | − | 0.744668i | \(-0.732608\pi\) |
−0.102262 | + | 0.994758i | \(0.532608\pi\) | |||||||
\(588\) | −14.5250 | − | 19.9920i | −0.599003 | − | 0.824457i | ||||
\(589\) | 11.2474 | − | 8.17172i | 0.463441 | − | 0.336710i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.67348 | − | 20.5389i | 0.274510 | − | 0.844856i | ||||
\(592\) | 5.03102 | − | 6.92460i | 0.206774 | − | 0.284599i | ||||
\(593\) | − | 3.31095i | − | 0.135964i | −0.997687 | − | 0.0679822i | \(-0.978344\pi\) | ||
0.997687 | − | 0.0679822i | \(-0.0216561\pi\) | |||||||
\(594\) | −4.62215 | − | 6.29896i | −0.189649 | − | 0.258450i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 29.0953 | + | 21.1390i | 1.19179 | + | 0.865887i | ||||
\(597\) | 7.38046 | + | 2.39806i | 0.302062 | + | 0.0981460i | ||||
\(598\) | 10.4720 | − | 3.40255i | 0.428230 | − | 0.139140i | ||||
\(599\) | 25.9460 | − | 18.8509i | 1.06012 | − | 0.770225i | 0.0860126 | − | 0.996294i | \(-0.472587\pi\) |
0.974111 | + | 0.226069i | \(0.0725875\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.05125 | − | 27.8569i | −0.369208 | − | 1.13631i | −0.947304 | − | 0.320337i | \(-0.896204\pi\) |
0.578095 | − | 0.815969i | \(-0.303796\pi\) | |||||||
\(602\) | −2.21710 | − | 0.720378i | −0.0903621 | − | 0.0293604i | ||||
\(603\) | −1.91572 | + | 2.63676i | −0.0780141 | + | 0.107377i | ||||
\(604\) | −42.4596 | −1.72766 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −30.9986 | −1.25923 | ||||||||
\(607\) | −22.9710 | + | 31.6169i | −0.932364 | + | 1.28329i | 0.0265657 | + | 0.999647i | \(0.491543\pi\) |
−0.958930 | + | 0.283642i | \(0.908457\pi\) | |||||||
\(608\) | 19.8914 | + | 6.46311i | 0.806703 | + | 0.262114i | ||||
\(609\) | 0.605076 | + | 1.86223i | 0.0245189 | + | 0.0754615i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.54886 | − | 6.21111i | 0.345850 | − | 0.251275i | ||||
\(612\) | 9.03182 | − | 2.93462i | 0.365090 | − | 0.118625i | ||||
\(613\) | 12.1092 | + | 3.93452i | 0.489086 | + | 0.158914i | 0.543170 | − | 0.839623i | \(-0.317224\pi\) |
−0.0540840 | + | 0.998536i | \(0.517224\pi\) | |||||||
\(614\) | 14.7218 | + | 10.6960i | 0.594123 | + | 0.431655i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.38578 | + | 1.88851i | 0.0558346 | + | 0.0760901i | ||||
\(617\) | − | 8.97789i | − | 0.361436i | −0.983535 | − | 0.180718i | \(-0.942158\pi\) | ||
0.983535 | − | 0.180718i | \(-0.0578422\pi\) | |||||||
\(618\) | 5.53487 | − | 7.61810i | 0.222645 | − | 0.306445i | ||||
\(619\) | 6.86392 | − | 21.1250i | 0.275884 | − | 0.849084i | −0.713100 | − | 0.701062i | \(-0.752710\pi\) |
0.988984 | − | 0.148022i | \(-0.0472905\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.88361 | − | 2.82160i | 0.155844 | − | 0.113227i | ||||
\(622\) | −26.4753 | − | 36.4402i | −1.06156 | − | 1.46112i | ||||
\(623\) | 1.35146 | − | 0.439117i | 0.0541452 | − | 0.0175928i | ||||
\(624\) | −0.450866 | + | 1.38762i | −0.0180491 | + | 0.0555493i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.83868 | −0.273329 | ||||||||
\(627\) | 18.4044 | − | 0.0870666i | 0.735001 | − | 0.00347711i | ||||
\(628\) | 9.32038i | 0.371924i | ||||||||
\(629\) | −12.3651 | − | 8.98377i | −0.493029 | − | 0.358206i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.27153 | + | 25.4572i | 0.329285 | + | 1.01343i | 0.969469 | + | 0.245213i | \(0.0788578\pi\) |
−0.640185 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(632\) | 21.7788 | + | 29.9759i | 0.866313 | + | 1.19238i | ||||
\(633\) | −7.35065 | − | 10.1173i | −0.292162 | − | 0.402127i | ||||
\(634\) | 1.64627 | + | 5.06670i | 0.0653817 | + | 0.201224i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 26.6715 | + | 19.3780i | 1.05759 | + | 0.768386i | ||||
\(637\) | − | 6.77949i | − | 0.268613i | ||||||
\(638\) | 24.7829 | + | 75.0639i | 0.981166 | + | 2.97181i | ||||
\(639\) | −5.99078 | −0.236992 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.65770 | − | 14.3349i | 0.183968 | − | 0.566195i | −0.815961 | − | 0.578107i | \(-0.803792\pi\) |
0.999929 | + | 0.0119117i | \(0.00379170\pi\) | |||||||
\(642\) | 10.9483 | − | 3.55733i | 0.432096 | − | 0.140396i | ||||
\(643\) | −23.0925 | − | 31.7840i | −0.910678 | − | 1.25344i | −0.966935 | − | 0.255024i | \(-0.917917\pi\) |
0.0562569 | − | 0.998416i | \(-0.482083\pi\) | |||||||
\(644\) | −2.66752 | + | 1.93807i | −0.105115 | + | 0.0763705i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.8085 | + | 33.2652i | −0.425256 | + | 1.30880i | ||||
\(647\) | 13.9973 | − | 19.2656i | 0.550289 | − | 0.757408i | −0.439762 | − | 0.898114i | \(-0.644937\pi\) |
0.990051 | + | 0.140706i | \(0.0449373\pi\) | |||||||
\(648\) | 3.64941i | 0.143363i | ||||||||
\(649\) | 21.7265 | − | 30.2033i | 0.852838 | − | 1.18559i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.392251 | + | 0.284987i | 0.0153735 | + | 0.0111695i | ||||
\(652\) | 80.0784 | + | 26.0190i | 3.13611 | + | 1.01898i | ||||
\(653\) | 6.56566 | − | 2.13331i | 0.256934 | − | 0.0834829i | −0.177718 | − | 0.984081i | \(-0.556871\pi\) |
0.434652 | + | 0.900599i | \(0.356871\pi\) | |||||||
\(654\) | 14.3310 | − | 10.4121i | 0.560387 | − | 0.407145i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.83332 | − | 11.7978i | −0.149666 | − | 0.460625i | ||||
\(657\) | 3.14442 | + | 1.02168i | 0.122675 | + | 0.0398596i | ||||
\(658\) | −2.90802 | + | 4.00254i | −0.113366 | + | 0.156035i | ||||
\(659\) | 20.3718 | 0.793571 | 0.396786 | − | 0.917911i | \(-0.370126\pi\) | ||||
0.396786 | + | 0.917911i | \(0.370126\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.7451 | −0.767994 | −0.383997 | − | 0.923334i | \(-0.625453\pi\) | ||||
−0.383997 | + | 0.923334i | \(0.625453\pi\) | |||||||
\(662\) | −8.34013 | + | 11.4792i | −0.324148 | + | 0.446152i | ||||
\(663\) | 2.47784 | + | 0.805099i | 0.0962314 | + | 0.0312675i | ||||
\(664\) | 9.37717 | + | 28.8600i | 0.363905 | + | 1.11998i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.8861 | − | 7.90925i | 0.421830 | − | 0.306477i | ||||
\(667\) | −46.1923 | + | 15.0088i | −1.78857 | + | 0.581143i | ||||
\(668\) | −11.7864 | − | 3.82962i | −0.456028 | − | 0.148172i | ||||
\(669\) | −4.34901 | − | 3.15974i | −0.168143 | − | 0.122163i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.80996 | + | 1.21803i | 0.147082 | + | 0.0470217i | ||||
\(672\) | 0.729407i | 0.0281375i | ||||||||
\(673\) | −21.5207 | + | 29.6207i | −0.829563 | + | 1.14180i | 0.158441 | + | 0.987368i | \(0.449353\pi\) |
−0.988004 | + | 0.154427i | \(0.950647\pi\) | |||||||
\(674\) | −10.6023 | + | 32.6306i | −0.408386 | + | 1.25688i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 34.6054 | − | 25.1423i | 1.33098 | − | 0.967011i | ||||
\(677\) | −4.33279 | − | 5.96357i | −0.166523 | − | 0.229199i | 0.717598 | − | 0.696458i | \(-0.245242\pi\) |
−0.884120 | + | 0.467259i | \(0.845242\pi\) | |||||||
\(678\) | −45.3088 | + | 14.7217i | −1.74007 | + | 0.565384i | ||||
\(679\) | 0.948017 | − | 2.91770i | 0.0363816 | − | 0.111971i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.7529 | −0.833573 | ||||||||
\(682\) | 15.8898 | + | 11.4302i | 0.608452 | + | 0.437684i | ||||
\(683\) | − | 24.5651i | − | 0.939959i | −0.882677 | − | 0.469979i | \(-0.844261\pi\) | ||
0.882677 | − | 0.469979i | \(-0.155739\pi\) | |||||||
\(684\) | −15.9338 | − | 11.5766i | −0.609243 | − | 0.442641i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.96700 | + | 6.05380i | 0.0751004 | + | 0.231135i | ||||
\(687\) | −1.56983 | − | 2.16068i | −0.0598927 | − | 0.0824352i | ||||
\(688\) | 4.50376 | + | 6.19890i | 0.171704 | + | 0.236331i | ||||
\(689\) | 2.79492 | + | 8.60189i | 0.106478 | + | 0.327706i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.1439 | − | 17.5416i | −0.918479 | − | 0.667314i | 0.0246662 | − | 0.999696i | \(-0.492148\pi\) |
−0.943145 | + | 0.332382i | \(0.892148\pi\) | |||||||
\(692\) | − | 72.2602i | − | 2.74692i | ||||||
\(693\) | 0.201230 | + | 0.609497i | 0.00764410 | + | 0.0231529i | ||||
\(694\) | 67.9262 | 2.57844 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 11.4102 | − | 35.1168i | 0.432501 | − | 1.33110i | ||||
\(697\) | −21.0670 | + | 6.84507i | −0.797968 | + | 0.259276i | ||||
\(698\) | 2.26019 | + | 3.11088i | 0.0855494 | + | 0.117749i | ||||
\(699\) | −4.63323 | + | 3.36624i | −0.175245 | + | 0.127323i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.45569 | + | 13.7132i | −0.168289 | + | 0.517940i | −0.999264 | − | 0.0383701i | \(-0.987783\pi\) |
0.830975 | + | 0.556310i | \(0.187783\pi\) | |||||||
\(702\) | −1.34823 | + | 1.85567i | −0.0508855 | + | 0.0700379i | ||||
\(703\) | 31.6980i | 1.19551i | ||||||||
\(704\) | 0.186325 | + | 39.3859i | 0.00702238 | + | 1.48441i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 47.5106 | + | 34.5184i | 1.78808 | + | 1.29912i | ||||
\(707\) | 2.42201 | + | 0.786958i | 0.0910890 | + | 0.0295966i | ||||
\(708\) | −37.8663 | + | 12.3035i | −1.42310 | + | 0.462394i | ||||
\(709\) | −36.0084 | + | 26.1616i | −1.35232 | + | 0.982520i | −0.353430 | + | 0.935461i | \(0.614985\pi\) |
−0.998892 | + | 0.0470585i | \(0.985015\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.13743 | + | 9.65601i | 0.117663 | + | 0.362129i | ||||
\(712\) | −25.4850 | − | 8.28059i | −0.955093 | − | 0.310328i | ||||
\(713\) | −7.06904 | + | 9.72970i | −0.264738 | + | 0.364380i | ||||
\(714\) | −1.21982 | −0.0456506 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13.6686 | 0.510819 | ||||||||
\(717\) | −14.3232 | + | 19.7141i | −0.534908 | + | 0.736238i | ||||
\(718\) | 63.7185 | + | 20.7034i | 2.37795 | + | 0.772644i | ||||
\(719\) | −1.11044 | − | 3.41758i | −0.0414124 | − | 0.127454i | 0.928213 | − | 0.372050i | \(-0.121345\pi\) |
−0.969625 | + | 0.244595i | \(0.921345\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.625854 | + | 0.454710i | −0.0233080 | + | 0.0169343i | ||||
\(722\) | 26.4222 | − | 8.58510i | 0.983333 | − | 0.319504i | ||||
\(723\) | 15.8904 | + | 5.16312i | 0.590972 | + | 0.192018i | ||||
\(724\) | −50.5794 | − | 36.7481i | −1.87977 | − | 1.36573i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.24018 | + | 24.5673i | 0.305822 | + | 0.911778i | ||||
\(727\) | − | 39.0846i | − | 1.44957i | −0.688976 | − | 0.724784i | \(-0.741940\pi\) | ||
0.688976 | − | 0.724784i | \(-0.258060\pi\) | |||||||
\(728\) | 0.404215 | − | 0.556354i | 0.0149812 | − | 0.0206199i | ||||
\(729\) | −0.309017 | + | 0.951057i | −0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.0692 | − | 8.04226i | 0.409410 | − | 0.297454i | ||||
\(732\) | −2.51597 | − | 3.46293i | −0.0929928 | − | 0.127994i | ||||
\(733\) | 35.8610 | − | 11.6519i | 1.32455 | − | 0.430374i | 0.440498 | − | 0.897753i | \(-0.354802\pi\) |
0.884057 | + | 0.467379i | \(0.154802\pi\) | |||||||
\(734\) | −7.60065 | + | 23.3924i | −0.280545 | + | 0.863429i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.0928 | −0.666910 | ||||||||
\(737\) | 8.71499 | − | 6.39502i | 0.321021 | − | 0.235564i | ||||
\(738\) | − | 19.5017i | − | 0.717868i | ||||||
\(739\) | 12.0806 | + | 8.77706i | 0.444392 | + | 0.322869i | 0.787377 | − | 0.616471i | \(-0.211438\pi\) |
−0.342986 | + | 0.939341i | \(0.611438\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.66971 | − | 5.13885i | −0.0613384 | − | 0.188780i | ||||
\(742\) | −2.48906 | − | 3.42589i | −0.0913761 | − | 0.125768i | ||||
\(743\) | 7.85749 | + | 10.8149i | 0.288263 | + | 0.396760i | 0.928449 | − | 0.371460i | \(-0.121143\pi\) |
−0.640186 | + | 0.768220i | \(0.721143\pi\) | |||||||
\(744\) | −2.82533 | − | 8.69548i | −0.103582 | − | 0.318792i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.36949 | − | 3.90116i | −0.196591 | − | 0.142832i | ||||
\(747\) | 8.31508i | 0.304233i | ||||||||
\(748\) | −31.4964 | + | 0.149001i | −1.15162 | + | 0.00544803i | ||||
\(749\) | −0.945731 | −0.0345563 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5045 | − | 38.4849i | 0.456296 | − | 1.40434i | −0.413310 | − | 0.910590i | \(-0.635627\pi\) |
0.869606 | − | 0.493745i | \(-0.164373\pi\) | |||||||
\(752\) | 15.4655 | − | 5.02504i | 0.563968 | − | 0.183244i | ||||
\(753\) | −9.46240 | − | 13.0239i | −0.344829 | − | 0.474617i | ||||
\(754\) | 18.7753 | − | 13.6411i | 0.683757 | − | 0.496779i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.212253 | − | 0.653249i | 0.00771958 | − | 0.0237584i | ||||
\(757\) | −5.01826 | + | 6.90704i | −0.182392 | + | 0.251040i | −0.890416 | − | 0.455147i | \(-0.849587\pi\) |
0.708025 | + | 0.706188i | \(0.249587\pi\) | |||||||
\(758\) | 21.0437i | 0.764341i | ||||||||
\(759\) | −15.1184 | + | 4.99148i | −0.548765 | + | 0.181179i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.2162 | + | 12.5083i | 0.624089 | + | 0.453427i | 0.854347 | − | 0.519703i | \(-0.173957\pi\) |
−0.230259 | + | 0.973129i | \(0.573957\pi\) | |||||||
\(762\) | −15.9072 | − | 5.16855i | −0.576256 | − | 0.187237i | ||||
\(763\) | −1.38405 | + | 0.449706i | −0.0501060 | + | 0.0162804i | ||||
\(764\) | 1.19764 | − | 0.870139i | 0.0433292 | − | 0.0314805i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.21139 | + | 19.1167i | 0.224427 | + | 0.690714i | ||||
\(767\) | −10.3885 | − | 3.37541i | −0.375105 | − | 0.121879i | ||||
\(768\) | 14.3368 | − | 19.7329i | 0.517333 | − | 0.712048i | ||||
\(769\) | 24.4717 | 0.882471 | 0.441235 | − | 0.897391i | \(-0.354540\pi\) | ||||
0.441235 | + | 0.897391i | \(0.354540\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.96875 | 0.214959 | ||||||||
\(772\) | 24.4009 | − | 33.5850i | 0.878209 | − | 1.20875i | ||||
\(773\) | −12.9792 | − | 4.21721i | −0.466830 | − | 0.151682i | 0.0661505 | − | 0.997810i | \(-0.478928\pi\) |
−0.532981 | + | 0.846127i | \(0.678928\pi\) | |||||||
\(774\) | 3.72236 | + | 11.4563i | 0.133798 | + | 0.411787i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −46.8029 | + | 34.0043i | −1.68013 | + | 1.22068i | ||||
\(777\) | −1.05136 | + | 0.341606i | −0.0377172 | + | 0.0122550i | ||||
\(778\) | 26.3821 | + | 8.57207i | 0.945845 | + | 0.307324i | ||||
\(779\) | 37.1660 | + | 27.0027i | 1.33161 | + | 0.967471i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.9255 | + | 6.05045i | 0.677209 | + | 0.216502i | ||||
\(782\) | − | 30.2574i | − | 1.08200i | ||||||
\(783\) | 5.94709 | − | 8.18547i | 0.212532 | − | 0.292525i | ||||
\(784\) | 3.22394 | − | 9.92225i | 0.115141 | − | 0.354366i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.76490 | + | 3.46191i | −0.169958 | + | 0.123482i | ||||
\(787\) | 4.38317 | + | 6.03291i | 0.156243 | + | 0.215050i | 0.879961 | − | 0.475046i | \(-0.157568\pi\) |
−0.723718 | + | 0.690096i | \(0.757568\pi\) | |||||||
\(788\) | 72.8966 | − | 23.6855i | 2.59683 | − | 0.843762i | ||||
\(789\) | 0.139413 | − | 0.429068i | 0.00496322 | − | 0.0152752i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.91383 | 0.139160 | ||||||||
\(792\) | 3.68576 | − | 11.5289i | 0.130968 | − | 0.409662i | ||||
\(793\) | − | 1.17431i | − | 0.0417011i | ||||||
\(794\) | 2.69124 | + | 1.95530i | 0.0955085 | + | 0.0693910i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.51119 | + | 26.1947i | 0.301671 | + | 0.928448i | ||||
\(797\) | −7.07379 | − | 9.73624i | −0.250567 | − | 0.344875i | 0.665143 | − | 0.746716i | \(-0.268371\pi\) |
−0.915710 | + | 0.401841i | \(0.868371\pi\) | |||||||
\(798\) | 1.48698 | + | 2.04666i | 0.0526386 | + | 0.0724509i | ||||
\(799\) | −8.97309 | − | 27.6163i | −0.317445 | − | 0.976996i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.94037 | − | 4.31593i | −0.209893 | − | 0.152496i | ||||
\(802\) | − | 19.9270i | − | 0.703648i | ||||||
\(803\) | −8.90170 | − | 6.40334i | −0.314134 | − | 0.225969i | ||||
\(804\) | −11.5676 | −0.407958 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.77579 | − | 5.46531i | 0.0625494 | − | 0.192507i | ||||
\(807\) | −13.9993 | + | 4.54864i | −0.492798 | + | 0.160120i | ||||
\(808\) | −28.2273 | − | 38.8515i | −0.993033 | − | 1.36679i | ||||
\(809\) | −40.4782 | + | 29.4091i | −1.42314 | + | 1.03397i | −0.431892 | + | 0.901925i | \(0.642154\pi\) |
−0.991244 | + | 0.132044i | \(0.957846\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.46678 | + | 10.6697i | −0.121735 | + | 0.374663i | −0.993292 | − | 0.115632i | \(-0.963111\pi\) |
0.871557 | + | 0.490294i | \(0.163111\pi\) | |||||||
\(812\) | −4.08486 | + | 5.62233i | −0.143350 | + | 0.197305i | ||||
\(813\) | − | 4.42787i | − | 0.155292i | ||||||
\(814\) | −42.3786 | + | 13.9916i | −1.48537 | + | 0.490406i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.24363 | + | 2.35664i | 0.113550 | + | 0.0824988i | ||||
\(817\) | −26.9872 | − | 8.76867i | −0.944163 | − | 0.306777i | ||||
\(818\) | −22.6850 | + | 7.37080i | −0.793163 | + | 0.257714i | ||||
\(819\) | 0.152450 | − | 0.110762i | 0.00532704 | − | 0.00387032i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.27969 | + | 7.01616i | 0.0795617 | + | 0.244866i | 0.982924 | − | 0.184013i | \(-0.0589088\pi\) |
−0.903362 | + | 0.428879i | \(0.858909\pi\) | |||||||
\(822\) | 34.2652 | + | 11.1334i | 1.19514 | + | 0.388323i | ||||
\(823\) | −20.9475 | + | 28.8318i | −0.730184 | + | 1.00501i | 0.268939 | + | 0.963157i | \(0.413327\pi\) |
−0.999124 | + | 0.0418554i | \(0.986673\pi\) | |||||||
\(824\) | 14.5880 | 0.508198 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.11414 | 0.177944 | ||||||||
\(827\) | −29.7003 | + | 40.8789i | −1.03278 | + | 1.42150i | −0.129940 | + | 0.991522i | \(0.541478\pi\) |
−0.902840 | + | 0.429977i | \(0.858522\pi\) | |||||||
\(828\) | 16.2037 | + | 5.26490i | 0.563118 | + | 0.182968i | ||||
\(829\) | 1.89888 | + | 5.84416i | 0.0659509 | + | 0.202976i | 0.978602 | − | 0.205765i | \(-0.0659681\pi\) |
−0.912651 | + | 0.408741i | \(0.865968\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.0746965 | − | 0.0542702i | 0.00259119 | − | 0.00188261i | ||||
\(832\) | 10.9973 | − | 3.57323i | 0.381262 | − | 0.123879i | ||||
\(833\) | −17.7179 | − | 5.75690i | −0.613890 | − | 0.199465i | ||||
\(834\) | 37.4650 | + | 27.2199i | 1.29731 | + | 0.942548i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 38.6447 | + | 52.6641i | 1.33655 | + | 1.82143i | ||||
\(837\) | − | 2.50533i | − | 0.0865967i | ||||||
\(838\) | 45.4186 | − | 62.5133i | 1.56896 | − | 2.15949i | ||||
\(839\) | 11.5953 | − | 35.6865i | 0.400312 | − | 1.23204i | −0.524434 | − | 0.851451i | \(-0.675723\pi\) |
0.924746 | − | 0.380584i | \(-0.124277\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −59.3574 | + | 43.1257i | −2.04681 | + | 1.48709i | ||||
\(842\) | −19.5638 | − | 26.9273i | −0.674214 | − | 0.927976i | ||||
\(843\) | 4.92934 | − | 1.60164i | 0.169775 | − | 0.0551633i | ||||
\(844\) | 13.7158 | − | 42.2128i | 0.472116 | − | 1.45302i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 25.5645 | 0.878924 | ||||||||
\(847\) | −0.0201412 | − | 2.12870i | −0.000692058 | − | 0.0731431i | ||||
\(848\) | 13.9186i | 0.477966i | ||||||||
\(849\) | 1.26581 | + | 0.919664i | 0.0434424 | + | 0.0315628i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.47347 | − | 26.0787i | −0.290467 | − | 0.893965i | ||||
\(852\) | −12.4978 | − | 17.2017i | −0.428167 | − | 0.589321i | ||||
\(853\) | −15.8774 | − | 21.8533i | −0.543631 | − | 0.748244i | 0.445500 | − | 0.895282i | \(-0.353026\pi\) |
−0.989131 | + | 0.147038i | \(0.953026\pi\) | |||||||
\(854\) | 0.169901 | + | 0.522900i | 0.00581388 | + | 0.0178933i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.4280 | + | 10.4826i | 0.493140 | + | 0.358287i | ||||
\(857\) | − | 2.51515i | − | 0.0859159i | −0.999077 | − | 0.0429580i | \(-0.986322\pi\) | ||
0.999077 | − | 0.0429580i | \(-0.0136782\pi\) | |||||||
\(858\) | 6.13335 | − | 4.50063i | 0.209389 | − | 0.153649i | ||||
\(859\) | −6.70885 | −0.228903 | −0.114451 | − | 0.993429i | \(-0.536511\pi\) | ||||
−0.114451 | + | 0.993429i | \(0.536511\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.495087 | + | 1.52372i | −0.0168725 | + | 0.0519283i | ||||
\(862\) | 42.8041 | − | 13.9079i | 1.45791 | − | 0.473705i | ||||
\(863\) | −1.94406 | − | 2.67577i | −0.0661767 | − | 0.0910844i | 0.774646 | − | 0.632395i | \(-0.217928\pi\) |
−0.840822 | + | 0.541311i | \(0.817928\pi\) | |||||||
\(864\) | 3.04920 | − | 2.21537i | 0.103736 | − | 0.0753686i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11.0065 | + | 33.8746i | −0.374017 | + | 1.15111i | ||||
\(867\) | −5.78416 | + | 7.96121i | −0.196440 | + | 0.270377i | ||||
\(868\) | 1.72082i | 0.0584086i | ||||||||
\(869\) | −0.159299 | − | 33.6731i | −0.00540384 | − | 1.14228i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.56744 | − | 1.86535i | −0.0869942 | − | 0.0632050i | ||||
\(872\) | 26.0996 | + | 8.48027i | 0.883844 | + | 0.287178i | ||||
\(873\) | −15.0764 | + | 4.89863i | −0.510260 | + | 0.165793i | ||||
\(874\) | −50.7669 | + | 36.8843i | −1.71722 | + | 1.24763i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.62616 | + | 11.1602i | 0.122517 | + | 0.377067i | ||||
\(877\) | 30.5293 | + | 9.91956i | 1.03090 | + | 0.334960i | 0.775146 | − | 0.631782i | \(-0.217676\pi\) |
0.255754 | + | 0.966742i | \(0.417676\pi\) | |||||||
\(878\) | 51.4587 | − | 70.8269i | 1.73665 | − | 2.39029i | ||||
\(879\) | 23.1570 | 0.781067 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.2547 | −1.18776 | −0.593881 | − | 0.804553i | \(-0.702405\pi\) | ||||
−0.593881 | + | 0.804553i | \(0.702405\pi\) | |||||||
\(882\) | 9.64056 | − | 13.2691i | 0.324614 | − | 0.446793i | ||||
\(883\) | 0.433541 | + | 0.140866i | 0.0145898 | + | 0.00474052i | 0.316303 | − | 0.948658i | \(-0.397558\pi\) |
−0.301713 | + | 0.953399i | \(0.597558\pi\) | |||||||
\(884\) | 2.85746 | + | 8.79436i | 0.0961068 | + | 0.295786i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.26090 | + | 3.82226i | −0.176743 | + | 0.128411i | ||||
\(887\) | 1.71342 | − | 0.556725i | 0.0575312 | − | 0.0186930i | −0.280110 | − | 0.959968i | \(-0.590371\pi\) |
0.337641 | + | 0.941275i | \(0.390371\pi\) | |||||||
\(888\) | 19.8258 | + | 6.44179i | 0.665310 | + | 0.216172i | ||||
\(889\) | 1.11166 | + | 0.807666i | 0.0372838 | + | 0.0270882i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.93675 | − | 2.69240i | 0.0648835 | − | 0.0901987i | ||||
\(892\) | − | 19.0794i | − | 0.638824i | ||||||
\(893\) | −35.3973 | + | 48.7203i | −1.18453 | + | 1.63036i | ||||
\(894\) | −7.37620 | + | 22.7016i | −0.246697 | + | 0.759255i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.19970 | + | 2.32471i | −0.106894 | + | 0.0776633i | ||||
\(897\) | 2.74742 | + | 3.78150i | 0.0917337 | + | 0.126261i | ||||
\(898\) | 40.0269 | − | 13.0055i | 1.33572 | − | 0.434001i | ||||
\(899\) | −7.83308 | + | 24.1077i | −0.261248 | + | 0.804038i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.8541 | 0.828009 | ||||||||
\(902\) | −19.6959 | + | 61.6080i | −0.655803 | + | 2.05132i | ||||
\(903\) | − | 0.989607i | − | 0.0329321i | ||||||
\(904\) | −59.7092 | − | 43.3813i | −1.98590 | − | 1.44284i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −8.70850 | − | 26.8020i | −0.289321 | − | 0.890437i | ||||
\(907\) | 20.7764 | + | 28.5962i | 0.689868 | + | 0.949522i | 0.999999 | − | 0.00117159i | \(-0.000372930\pi\) |
−0.310131 | + | 0.950694i | \(0.600373\pi\) | |||||||
\(908\) | −45.3802 | − | 62.4605i | −1.50600 | − | 2.07282i | ||||
\(909\) | −4.06640 | − | 12.5151i | −0.134874 | − | 0.415099i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.33388 | + | 0.969123i | 0.0441935 | + | 0.0321085i | 0.609663 | − | 0.792661i | \(-0.291305\pi\) |
−0.565469 | + | 0.824769i | \(0.691305\pi\) | |||||||
\(912\) | − | 8.31508i | − | 0.275340i | ||||||
\(913\) | 8.39789 | − | 26.2682i | 0.277930 | − | 0.869352i | ||||
\(914\) | −49.8511 | −1.64893 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.92918 | − | 9.01510i | 0.0967829 | − | 0.297867i | ||||
\(917\) | 0.460182 | − | 0.149522i | 0.0151965 | − | 0.00493765i | ||||
\(918\) | 3.70486 | + | 5.09931i | 0.122279 | + | 0.168302i | ||||
\(919\) | −0.258068 | + | 0.187498i | −0.00851288 | + | 0.00618497i | −0.592034 | − | 0.805913i | \(-0.701675\pi\) |
0.583521 | + | 0.812098i | \(0.301675\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.38710 | + | 7.34672i | −0.0786575 | + | 0.242083i | ||||
\(922\) | 47.5588 | − | 65.4590i | 1.56626 | − | 2.15578i | ||||
\(923\) | − | 5.83327i | − | 0.192005i | ||||||
\(924\) | −1.33029 | + | 1.84932i | −0.0437632 | + | 0.0608381i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 19.9185 | + | 14.4716i | 0.654561 | + | 0.475567i | ||||
\(927\) | 3.80172 | + | 1.23525i | 0.124865 | + | 0.0405711i | ||||
\(928\) | −36.2678 | + | 11.7841i | −1.19055 | + | 0.386832i | ||||
\(929\) | 45.4270 | − | 33.0046i | 1.49041 | − | 1.08285i | 0.516400 | − | 0.856347i | \(-0.327272\pi\) |
0.974011 | − | 0.226500i | \(-0.0727283\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.9394 | + | 36.7456i | 0.391297 | + | 1.20429i | ||||
\(932\) | −19.3314 | − | 6.28115i | −0.633221 | − | 0.205746i | ||||
\(933\) | 11.2390 | − | 15.4691i | 0.367947 | − | 0.506436i | ||||
\(934\) | 69.8301 | 2.28491 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.55346 | −0.116149 | ||||||||
\(937\) | 21.6554 | − | 29.8061i | 0.707452 | − | 0.973724i | −0.292396 | − | 0.956297i | \(-0.594453\pi\) |
0.999848 | − | 0.0174269i | \(-0.00554745\pi\) | |||||||
\(938\) | 1.41311 | + | 0.459148i | 0.0461397 | + | 0.0149917i | ||||
\(939\) | −0.897097 | − | 2.76098i | −0.0292756 | − | 0.0901012i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.3865 | − | 8.99929i | 0.403787 | − | 0.293368i | −0.367295 | − | 0.930105i | \(-0.619716\pi\) |
0.771082 | + | 0.636736i | \(0.219716\pi\) | |||||||
\(942\) | −5.88335 | + | 1.91162i | −0.191690 | + | 0.0622838i | ||||
\(943\) | −37.7956 | − | 12.2805i | −1.23079 | − | 0.399909i | ||||
\(944\) | −13.5991 | − | 9.88030i | −0.442612 | − | 0.321576i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.188998 | − | 39.9510i | −0.00614486 | − | 1.29892i | ||||
\(947\) | − | 22.6654i | − | 0.736526i | −0.929722 | − | 0.368263i | \(-0.879953\pi\) | ||
0.929722 | − | 0.368263i | \(-0.120047\pi\) | |||||||
\(948\) | −21.1807 | + | 29.1528i | −0.687918 | + | 0.946838i | ||||
\(949\) | −0.994821 | + | 3.06174i | −0.0322933 | + | 0.0993884i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.82962 | + | 1.32930i | −0.0593295 | + | 0.0431054i | ||||
\(952\) | −1.11076 | − | 1.52884i | −0.0360001 | − | 0.0495499i | ||||
\(953\) | 37.4074 | − | 12.1544i | 1.21174 | − | 0.393719i | 0.367675 | − | 0.929955i | \(-0.380154\pi\) |
0.844069 | + | 0.536235i | \(0.180154\pi\) | |||||||
\(954\) | −6.76171 | + | 20.8104i | −0.218918 | + | 0.673762i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −86.4870 | −2.79719 | ||||||||
\(957\) | −27.0545 | + | 19.8525i | −0.874548 | + | 0.641740i | ||||
\(958\) | − | 31.1388i | − | 1.00605i | ||||||
\(959\) | −2.39459 | − | 1.73977i | −0.0773254 | − | 0.0561802i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.63993 | − | 23.5133i | −0.246449 | − | 0.758493i | ||||
\(962\) | 7.70130 | + | 10.5999i | 0.248300 | + | 0.341756i | ||||
\(963\) | 2.87240 | + | 3.95352i | 0.0925618 | + | 0.127400i | ||||
\(964\) | 18.3249 | + | 56.3984i | 0.590207 | + | 1.81647i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.77048 | − | 1.28633i | −0.0569644 | − | 0.0413871i | ||||
\(967\) | 3.06103i | 0.0984360i | 0.998788 | + | 0.0492180i | \(0.0156729\pi\) | ||||
−0.998788 | + | 0.0492180i | \(0.984327\pi\) | |||||||
\(968\) | −23.2875 | + | 32.6986i | −0.748487 | + | 1.05097i | ||||
\(969\) | −14.8480 | −0.476987 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.90043 | − | 30.4704i | 0.317720 | − | 0.977841i | −0.656900 | − | 0.753977i | \(-0.728133\pi\) |
0.974620 | − | 0.223864i | \(-0.0718672\pi\) | |||||||
\(972\) | −3.37549 | + | 1.09676i | −0.108269 | + | 0.0351787i | ||||
\(973\) | −2.23621 | − | 3.07788i | −0.0716897 | − | 0.0986724i | ||||
\(974\) | 80.9911 | − | 58.8434i | 2.59512 | − | 1.88547i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.558436 | − | 1.71869i | 0.0178751 | − | 0.0550139i | ||||
\(977\) | −31.2679 | + | 43.0366i | −1.00035 | + | 1.37686i | −0.0752388 | + | 0.997166i | \(0.523972\pi\) |
−0.925111 | + | 0.379697i | \(0.876028\pi\) | |||||||
\(978\) | 55.8848i | 1.78700i | ||||||||
\(979\) | 14.4074 | + | 19.6340i | 0.460462 | + | 0.627507i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.08362 | + | 4.42001i | 0.194235 | + | 0.141120i | ||||
\(982\) | 35.2762 | + | 11.4619i | 1.12571 | + | 0.365765i | ||||
\(983\) | −23.3013 | + | 7.57104i | −0.743195 | + | 0.241479i | −0.656051 | − | 0.754717i | \(-0.727774\pi\) |
−0.0871446 | + | 0.996196i | \(0.527774\pi\) | |||||||
\(984\) | 24.4421 | − | 17.7582i | 0.779185 | − | 0.566111i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −19.7071 | − | 60.6521i | −0.627601 | − | 1.93156i | ||||
\(987\) | −1.99742 | − | 0.649001i | −0.0635786 | − | 0.0206579i | ||||
\(988\) | 11.2722 | − | 15.5149i | 0.358616 | − | 0.493593i | ||||
\(989\) | 24.5470 | 0.780549 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.34819 | −0.201657 | −0.100828 | − | 0.994904i | \(-0.532149\pi\) | ||||
−0.100828 | + | 0.994904i | \(0.532149\pi\) | |||||||
\(992\) | −5.55023 | + | 7.63924i | −0.176220 | + | 0.242546i | ||||
\(993\) | −5.72856 | − | 1.86132i | −0.181790 | − | 0.0590673i | ||||
\(994\) | 0.843962 | + | 2.59745i | 0.0267689 | + | 0.0823861i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −23.8756 | + | 17.3466i | −0.756528 | + | 0.549650i | ||||
\(997\) | 24.6761 | − | 8.01777i | 0.781501 | − | 0.253925i | 0.109020 | − | 0.994040i | \(-0.465229\pi\) |
0.672481 | + | 0.740114i | \(0.265229\pi\) | |||||||
\(998\) | −75.1152 | − | 24.4064i | −2.37773 | − | 0.772572i | ||||
\(999\) | 4.62125 | + | 3.35753i | 0.146210 | + | 0.106228i |
(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 | 825.2.bx.f.499.1 | 16 | ||
5.2 | odd | 4 | 825.2.n.g.301.1 | 8 | |||
5.3 | odd | 4 | 165.2.m.d.136.2 | yes | 8 | ||
5.4 | even | 2 | inner | 825.2.bx.f.499.4 | 16 | ||
11.3 | even | 5 | inner | 825.2.bx.f.124.4 | 16 | ||
15.8 | even | 4 | 495.2.n.a.136.1 | 8 | |||
55.3 | odd | 20 | 165.2.m.d.91.2 | ✓ | 8 | ||
55.14 | even | 10 | inner | 825.2.bx.f.124.1 | 16 | ||
55.17 | even | 20 | 9075.2.a.cm.1.1 | 4 | |||
55.27 | odd | 20 | 9075.2.a.di.1.4 | 4 | |||
55.28 | even | 20 | 1815.2.a.w.1.4 | 4 | |||
55.38 | odd | 20 | 1815.2.a.p.1.1 | 4 | |||
55.47 | odd | 20 | 825.2.n.g.751.1 | 8 | |||
165.38 | even | 20 | 5445.2.a.bt.1.4 | 4 | |||
165.83 | odd | 20 | 5445.2.a.bf.1.1 | 4 | |||
165.113 | even | 20 | 495.2.n.a.91.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.d.91.2 | ✓ | 8 | 55.3 | odd | 20 | ||
165.2.m.d.136.2 | yes | 8 | 5.3 | odd | 4 | ||
495.2.n.a.91.1 | 8 | 165.113 | even | 20 | |||
495.2.n.a.136.1 | 8 | 15.8 | even | 4 | |||
825.2.n.g.301.1 | 8 | 5.2 | odd | 4 | |||
825.2.n.g.751.1 | 8 | 55.47 | odd | 20 | |||
825.2.bx.f.124.1 | 16 | 55.14 | even | 10 | inner | ||
825.2.bx.f.124.4 | 16 | 11.3 | even | 5 | inner | ||
825.2.bx.f.499.1 | 16 | 1.1 | even | 1 | trivial | ||
825.2.bx.f.499.4 | 16 | 5.4 | even | 2 | inner | ||
1815.2.a.p.1.1 | 4 | 55.38 | odd | 20 | |||
1815.2.a.w.1.4 | 4 | 55.28 | even | 20 | |||
5445.2.a.bf.1.1 | 4 | 165.83 | odd | 20 | |||
5445.2.a.bt.1.4 | 4 | 165.38 | even | 20 | |||
9075.2.a.cm.1.1 | 4 | 55.17 | even | 20 | |||
9075.2.a.di.1.4 | 4 | 55.27 | odd | 20 |