Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [156,2,Mod(155,156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(156, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("156.155");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 156 = 2^{2} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 156.h (of order \(2\), degree \(1\), 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: | \(1.24566627153\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 43x^{12} + 517x^{8} + 1804x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 155.7 | ||
Root | \(1.58894 + 1.58894i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 156.155 |
Dual form | 156.2.h.b.155.5 |
$q$-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 \(\left(\mathbb{Z}/156\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(79\) | \(145\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.599676 | + | 1.28078i | −0.424035 | + | 0.905646i | ||||
\(3\) | −1.62493 | − | 0.599676i | −0.938152 | − | 0.346223i | ||||
\(4\) | −1.28078 | − | 1.53610i | −0.640388 | − | 0.768051i | ||||
\(5\) | 2.13578 | 0.955149 | 0.477575 | − | 0.878591i | \(-0.341516\pi\) | ||||
0.477575 | + | 0.878591i | \(0.341516\pi\) | |||||||
\(6\) | 1.74248 | − | 1.72156i | 0.711365 | − | 0.702823i | ||||
\(7\) | 1.52162 | 0.575120 | 0.287560 | − | 0.957763i | \(-0.407156\pi\) | ||||
0.287560 | + | 0.957763i | \(0.407156\pi\) | |||||||
\(8\) | 2.73546 | − | 0.719224i | 0.967130 | − | 0.254284i | ||||
\(9\) | 2.28078 | + | 1.94886i | 0.760259 | + | 0.649620i | ||||
\(10\) | −1.28078 | + | 2.73546i | −0.405017 | + | 0.865027i | ||||
\(11\) | 2.00000i | 0.603023i | 0.953463 | + | 0.301511i | \(0.0974911\pi\) | ||||
−0.953463 | + | 0.301511i | \(0.902509\pi\) | |||||||
\(12\) | 1.16000 | + | 3.26411i | 0.334864 | + | 0.942266i | ||||
\(13\) | 1.56155 | + | 3.24985i | 0.433097 | + | 0.901347i | ||||
\(14\) | −0.912482 | + | 1.94886i | −0.243871 | + | 0.520855i | ||||
\(15\) | −3.47049 | − | 1.28078i | −0.896076 | − | 0.330695i | ||||
\(16\) | −0.719224 | + | 3.93481i | −0.179806 | + | 0.983702i | ||||
\(17\) | − | 6.94097i | − | 1.68343i | −0.539920 | − | 0.841716i | \(-0.681545\pi\) | ||
0.539920 | − | 0.841716i | \(-0.318455\pi\) | |||||||
\(18\) | −3.86378 | + | 1.75248i | −0.910702 | + | 0.413063i | ||||
\(19\) | 5.41935 | 1.24328 | 0.621642 | − | 0.783302i | \(-0.286466\pi\) | ||||
0.621642 | + | 0.783302i | \(0.286466\pi\) | |||||||
\(20\) | −2.73546 | − | 3.28078i | −0.611666 | − | 0.733604i | ||||
\(21\) | −2.47253 | − | 0.912482i | −0.539550 | − | 0.199120i | ||||
\(22\) | −2.56155 | − | 1.19935i | −0.546125 | − | 0.255703i | ||||
\(23\) | 5.07482 | 1.05817 | 0.529086 | − | 0.848568i | \(-0.322535\pi\) | ||||
0.529086 | + | 0.848568i | \(0.322535\pi\) | |||||||
\(24\) | −4.87622 | − | 0.471702i | −0.995354 | − | 0.0962858i | ||||
\(25\) | −0.438447 | −0.0876894 | ||||||||
\(26\) | −5.09876 | + | 0.0511391i | −0.999950 | + | 0.0100292i | ||||
\(27\) | −2.53741 | − | 4.53448i | −0.488325 | − | 0.872662i | ||||
\(28\) | −1.94886 | − | 2.33737i | −0.368300 | − | 0.441722i | ||||
\(29\) | 3.04325i | 0.565117i | 0.959250 | + | 0.282559i | \(0.0911832\pi\) | ||||
−0.959250 | + | 0.282559i | \(0.908817\pi\) | |||||||
\(30\) | 3.72156 | − | 3.67686i | 0.679460 | − | 0.671301i | ||||
\(31\) | −5.41935 | −0.973343 | −0.486672 | − | 0.873585i | \(-0.661789\pi\) | ||||
−0.486672 | + | 0.873585i | \(0.661789\pi\) | |||||||
\(32\) | −4.60831 | − | 3.28078i | −0.814642 | − | 0.579965i | ||||
\(33\) | 1.19935 | − | 3.24985i | 0.208781 | − | 0.565727i | ||||
\(34\) | 8.88983 | + | 4.16234i | 1.52459 | + | 0.713835i | ||||
\(35\) | 3.24985 | 0.549326 | ||||||||
\(36\) | 0.0724861 | − | 5.99956i | 0.0120810 | − | 0.999927i | ||||
\(37\) | 1.82496i | 0.300022i | 0.988684 | + | 0.150011i | \(0.0479310\pi\) | ||||
−0.988684 | + | 0.150011i | \(0.952069\pi\) | |||||||
\(38\) | −3.24985 | + | 6.94097i | −0.527196 | + | 1.12597i | ||||
\(39\) | −0.588549 | − | 6.21720i | −0.0942432 | − | 0.995549i | ||||
\(40\) | 5.84233 | − | 1.53610i | 0.923753 | − | 0.242879i | ||||
\(41\) | −5.73384 | −0.895475 | −0.447737 | − | 0.894165i | \(-0.647770\pi\) | ||||
−0.447737 | + | 0.894165i | \(0.647770\pi\) | |||||||
\(42\) | 2.65140 | − | 2.61956i | 0.409120 | − | 0.404207i | ||||
\(43\) | − | 3.07221i | − | 0.468507i | −0.972176 | − | 0.234253i | \(-0.924735\pi\) | ||
0.972176 | − | 0.234253i | \(-0.0752646\pi\) | |||||||
\(44\) | 3.07221 | − | 2.56155i | 0.463152 | − | 0.386169i | ||||
\(45\) | 4.87123 | + | 4.16234i | 0.726161 | + | 0.620485i | ||||
\(46\) | −3.04325 | + | 6.49971i | −0.448703 | + | 0.958330i | ||||
\(47\) | − | 5.68466i | − | 0.829193i | −0.910005 | − | 0.414596i | \(-0.863923\pi\) | ||
0.910005 | − | 0.414596i | \(-0.136077\pi\) | |||||||
\(48\) | 3.52830 | − | 5.96248i | 0.509266 | − | 0.860609i | ||||
\(49\) | −4.68466 | −0.669237 | ||||||||
\(50\) | 0.262926 | − | 0.561553i | 0.0371834 | − | 0.0794156i | ||||
\(51\) | −4.16234 | + | 11.2786i | −0.582844 | + | 1.57932i | ||||
\(52\) | 2.99211 | − | 6.56104i | 0.414931 | − | 0.909853i | ||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 7.32929 | − | 0.530631i | 0.997389 | − | 0.0722097i | ||||
\(55\) | 4.27156i | 0.575977i | ||||||||
\(56\) | 4.16234 | − | 1.09439i | 0.556216 | − | 0.146244i | ||||
\(57\) | −8.80604 | − | 3.24985i | −1.16639 | − | 0.430454i | ||||
\(58\) | −3.89772 | − | 1.82496i | −0.511796 | − | 0.239630i | ||||
\(59\) | 11.1231i | 1.44811i | 0.689745 | + | 0.724053i | \(0.257723\pi\) | ||||
−0.689745 | + | 0.724053i | \(0.742277\pi\) | |||||||
\(60\) | 2.47751 | + | 6.97141i | 0.319845 | + | 0.900005i | ||||
\(61\) | −5.12311 | −0.655946 | −0.327973 | − | 0.944687i | \(-0.606366\pi\) | ||||
−0.327973 | + | 0.944687i | \(0.606366\pi\) | |||||||
\(62\) | 3.24985 | − | 6.94097i | 0.412732 | − | 0.881504i | ||||
\(63\) | 3.47049 | + | 2.96543i | 0.437240 | + | 0.373610i | ||||
\(64\) | 6.96543 | − | 3.93481i | 0.870679 | − | 0.491851i | ||||
\(65\) | 3.33513 | + | 6.94097i | 0.413672 | + | 0.860922i | ||||
\(66\) | 3.44311 | + | 3.48496i | 0.423818 | + | 0.428969i | ||||
\(67\) | −8.46260 | −1.03387 | −0.516935 | − | 0.856024i | \(-0.672927\pi\) | ||||
−0.516935 | + | 0.856024i | \(0.672927\pi\) | |||||||
\(68\) | −10.6620 | + | 8.88983i | −1.29296 | + | 1.07805i | ||||
\(69\) | −8.24621 | − | 3.04325i | −0.992727 | − | 0.366364i | ||||
\(70\) | −1.94886 | + | 4.16234i | −0.232933 | + | 0.497494i | ||||
\(71\) | − | 2.31534i | − | 0.274780i | −0.990517 | − | 0.137390i | \(-0.956129\pi\) | ||
0.990517 | − | 0.137390i | \(-0.0438714\pi\) | |||||||
\(72\) | 7.64063 | + | 3.69063i | 0.900457 | + | 0.434945i | ||||
\(73\) | − | 10.1496i | − | 1.18793i | −0.804493 | − | 0.593963i | \(-0.797563\pi\) | ||
0.804493 | − | 0.593963i | \(-0.202437\pi\) | |||||||
\(74\) | −2.33737 | − | 1.09439i | −0.271714 | − | 0.127220i | ||||
\(75\) | 0.712445 | + | 0.262926i | 0.0822660 | + | 0.0303601i | ||||
\(76\) | −6.94097 | − | 8.32467i | −0.796184 | − | 0.954906i | ||||
\(77\) | 3.04325i | 0.346810i | ||||||||
\(78\) | 8.31579 | + | 2.97451i | 0.941577 | + | 0.336797i | ||||
\(79\) | 9.06897i | 1.02034i | 0.860074 | + | 0.510169i | \(0.170417\pi\) | ||||
−0.860074 | + | 0.510169i | \(0.829583\pi\) | |||||||
\(80\) | −1.53610 | + | 8.40388i | −0.171742 | + | 0.939583i | ||||
\(81\) | 1.40388 | + | 8.88983i | 0.155987 | + | 0.987759i | ||||
\(82\) | 3.43845 | − | 7.34376i | 0.379713 | − | 0.810983i | ||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | 1.76509 | + | 4.96674i | 0.192587 | + | 0.541916i | ||||
\(85\) | − | 14.8244i | − | 1.60793i | ||||||
\(86\) | 3.93481 | + | 1.84233i | 0.424301 | + | 0.198663i | ||||
\(87\) | 1.82496 | − | 4.94506i | 0.195657 | − | 0.530166i | ||||
\(88\) | 1.43845 | + | 5.47091i | 0.153339 | + | 0.583201i | ||||
\(89\) | 11.3524 | 1.20335 | 0.601676 | − | 0.798740i | \(-0.294500\pi\) | ||||
0.601676 | + | 0.798740i | \(0.294500\pi\) | |||||||
\(90\) | −8.25219 | + | 3.74291i | −0.869857 | + | 0.394537i | ||||
\(91\) | 2.37610 | + | 4.94506i | 0.249083 | + | 0.518383i | ||||
\(92\) | −6.49971 | − | 7.79544i | −0.677641 | − | 0.812731i | ||||
\(93\) | 8.80604 | + | 3.24985i | 0.913144 | + | 0.336994i | ||||
\(94\) | 7.28078 | + | 3.40896i | 0.750955 | + | 0.351607i | ||||
\(95\) | 11.5745 | 1.18752 | ||||||||
\(96\) | 5.52076 | + | 8.09452i | 0.563460 | + | 0.826143i | ||||
\(97\) | 16.6493i | 1.69049i | 0.534383 | + | 0.845243i | \(0.320544\pi\) | ||||
−0.534383 | + | 0.845243i | \(0.679456\pi\) | |||||||
\(98\) | 2.80928 | − | 6.00000i | 0.283780 | − | 0.606092i | ||||
\(99\) | −3.89772 | + | 4.56155i | −0.391736 | + | 0.458453i | ||||
\(100\) | 0.561553 | + | 0.673500i | 0.0561553 | + | 0.0673500i | ||||
\(101\) | − | 6.08650i | − | 0.605629i | −0.953049 | − | 0.302815i | \(-0.902074\pi\) | ||
0.953049 | − | 0.302815i | \(-0.0979263\pi\) | |||||||
\(102\) | −11.9493 | − | 12.0945i | −1.18315 | − | 1.19754i | ||||
\(103\) | − | 19.4849i | − | 1.91991i | −0.280157 | − | 0.959954i | \(-0.590387\pi\) | ||
0.280157 | − | 0.959954i | \(-0.409613\pi\) | |||||||
\(104\) | 6.60893 | + | 7.76673i | 0.648059 | + | 0.761590i | ||||
\(105\) | −5.28078 | − | 1.94886i | −0.515351 | − | 0.190189i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.1496 | −0.981203 | −0.490601 | − | 0.871384i | \(-0.663223\pi\) | ||||
−0.490601 | + | 0.871384i | \(0.663223\pi\) | |||||||
\(108\) | −3.71558 | + | 9.70538i | −0.357532 | + | 0.933901i | ||||
\(109\) | − | 8.32467i | − | 0.797359i | −0.917090 | − | 0.398680i | \(-0.869469\pi\) | ||
0.917090 | − | 0.398680i | \(-0.130531\pi\) | |||||||
\(110\) | −5.47091 | − | 2.56155i | −0.521631 | − | 0.244234i | ||||
\(111\) | 1.09439 | − | 2.96543i | 0.103875 | − | 0.281467i | ||||
\(112\) | −1.09439 | + | 5.98730i | −0.103410 | + | 0.565747i | ||||
\(113\) | − | 10.8387i | − | 1.01962i | −0.860287 | − | 0.509809i | \(-0.829716\pi\) | ||
0.860287 | − | 0.509809i | \(-0.170284\pi\) | |||||||
\(114\) | 9.44311 | − | 9.32971i | 0.884429 | − | 0.873808i | ||||
\(115\) | 10.8387 | 1.01071 | ||||||||
\(116\) | 4.67474 | − | 3.89772i | 0.434039 | − | 0.361894i | ||||
\(117\) | −2.77196 | + | 10.4554i | −0.256268 | + | 0.966606i | ||||
\(118\) | −14.2462 | − | 6.67026i | −1.31147 | − | 0.614048i | ||||
\(119\) | − | 10.5616i | − | 0.968176i | ||||||
\(120\) | −10.4145 | − | 1.00745i | −0.950712 | − | 0.0919674i | ||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 3.07221 | − | 6.56155i | 0.278144 | − | 0.594055i | ||||
\(123\) | 9.31707 | + | 3.43845i | 0.840092 | + | 0.310034i | ||||
\(124\) | 6.94097 | + | 8.32467i | 0.623318 | + | 0.747578i | ||||
\(125\) | −11.6153 | −1.03891 | ||||||||
\(126\) | −5.87923 | + | 2.66661i | −0.523763 | + | 0.237561i | ||||
\(127\) | − | 6.67026i | − | 0.591890i | −0.955205 | − | 0.295945i | \(-0.904365\pi\) | ||
0.955205 | − | 0.295945i | \(-0.0956346\pi\) | |||||||
\(128\) | 0.862603 | + | 11.2808i | 0.0762440 | + | 0.997089i | ||||
\(129\) | −1.84233 | + | 4.99211i | −0.162208 | + | 0.439531i | ||||
\(130\) | −10.8898 | + | 0.109222i | −0.955101 | + | 0.00957938i | ||||
\(131\) | 1.82496 | 0.159448 | 0.0797240 | − | 0.996817i | \(-0.474596\pi\) | ||||
0.0797240 | + | 0.996817i | \(0.474596\pi\) | |||||||
\(132\) | −6.52821 | + | 2.32001i | −0.568208 | + | 0.201931i | ||||
\(133\) | 8.24621 | 0.715037 | ||||||||
\(134\) | 5.07482 | − | 10.8387i | 0.438398 | − | 0.936320i | ||||
\(135\) | −5.41935 | − | 9.68466i | −0.466423 | − | 0.833523i | ||||
\(136\) | −4.99211 | − | 18.9867i | −0.428070 | − | 1.62810i | ||||
\(137\) | −8.95369 | −0.764965 | −0.382483 | − | 0.923963i | \(-0.624931\pi\) | ||||
−0.382483 | + | 0.923963i | \(0.624931\pi\) | |||||||
\(138\) | 8.84278 | − | 8.73659i | 0.752747 | − | 0.743708i | ||||
\(139\) | 6.81791i | 0.578288i | 0.957286 | + | 0.289144i | \(0.0933706\pi\) | ||||
−0.957286 | + | 0.289144i | \(0.906629\pi\) | |||||||
\(140\) | −4.16234 | − | 4.99211i | −0.351782 | − | 0.421910i | ||||
\(141\) | −3.40896 | + | 9.23716i | −0.287086 | + | 0.777909i | ||||
\(142\) | 2.96543 | + | 1.38846i | 0.248854 | + | 0.116517i | ||||
\(143\) | −6.49971 | + | 3.12311i | −0.543533 | + | 0.261167i | ||||
\(144\) | −9.30878 | + | 7.57275i | −0.775732 | + | 0.631063i | ||||
\(145\) | 6.49971i | 0.539771i | ||||||||
\(146\) | 12.9994 | + | 6.08650i | 1.07584 | + | 0.503722i | ||||
\(147\) | 7.61223 | + | 2.80928i | 0.627846 | + | 0.231705i | ||||
\(148\) | 2.80333 | − | 2.33737i | 0.230433 | − | 0.192131i | ||||
\(149\) | 0.410574 | 0.0336355 | 0.0168177 | − | 0.999859i | \(-0.494646\pi\) | ||||
0.0168177 | + | 0.999859i | \(0.494646\pi\) | |||||||
\(150\) | −0.763986 | + | 0.754812i | −0.0623792 | + | 0.0616301i | ||||
\(151\) | −17.1125 | −1.39260 | −0.696298 | − | 0.717753i | \(-0.745171\pi\) | ||||
−0.696298 | + | 0.717753i | \(0.745171\pi\) | |||||||
\(152\) | 14.8244 | − | 3.89772i | 1.20242 | − | 0.316147i | ||||
\(153\) | 13.5270 | − | 15.8308i | 1.09359 | − | 1.27984i | ||||
\(154\) | −3.89772 | − | 1.82496i | −0.314087 | − | 0.147060i | ||||
\(155\) | −11.5745 | −0.929688 | ||||||||
\(156\) | −8.79646 | + | 8.86692i | −0.704281 | + | 0.709922i | ||||
\(157\) | 6.24621 | 0.498502 | 0.249251 | − | 0.968439i | \(-0.419816\pi\) | ||||
0.249251 | + | 0.968439i | \(0.419816\pi\) | |||||||
\(158\) | −11.6153 | − | 5.43845i | −0.924065 | − | 0.432660i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.84233 | − | 7.00701i | −0.778104 | − | 0.553953i | ||||
\(161\) | 7.72197 | 0.608576 | ||||||||
\(162\) | −12.2278 | − | 3.53296i | −0.960704 | − | 0.277576i | ||||
\(163\) | −13.2148 | −1.03506 | −0.517531 | − | 0.855664i | \(-0.673149\pi\) | ||||
−0.517531 | + | 0.855664i | \(0.673149\pi\) | |||||||
\(164\) | 7.34376 | + | 8.80776i | 0.573452 | + | 0.687771i | ||||
\(165\) | 2.56155 | − | 6.94097i | 0.199417 | − | 0.540354i | ||||
\(166\) | −7.68466 | − | 3.59806i | −0.596445 | − | 0.279263i | ||||
\(167\) | − | 17.3693i | − | 1.34408i | −0.740516 | − | 0.672039i | \(-0.765419\pi\) | ||
0.740516 | − | 0.672039i | \(-0.234581\pi\) | |||||||
\(168\) | −7.41977 | − | 0.717754i | −0.572448 | − | 0.0553759i | ||||
\(169\) | −8.12311 | + | 10.1496i | −0.624854 | + | 0.780741i | ||||
\(170\) | 18.9867 | + | 8.88983i | 1.45621 | + | 0.681819i | ||||
\(171\) | 12.3603 | + | 10.5616i | 0.945217 | + | 0.807662i | ||||
\(172\) | −4.71922 | + | 3.93481i | −0.359837 | + | 0.300026i | ||||
\(173\) | 7.79544i | 0.592677i | 0.955083 | + | 0.296338i | \(0.0957656\pi\) | ||||
−0.955083 | + | 0.296338i | \(0.904234\pi\) | |||||||
\(174\) | 5.23913 | + | 5.30281i | 0.397177 | + | 0.402005i | ||||
\(175\) | −0.667152 | −0.0504320 | ||||||||
\(176\) | −7.86962 | − | 1.43845i | −0.593195 | − | 0.108427i | ||||
\(177\) | 6.67026 | − | 18.0742i | 0.501368 | − | 1.35854i | ||||
\(178\) | −6.80776 | + | 14.5399i | −0.510263 | + | 1.08981i | ||||
\(179\) | −1.82496 | −0.136404 | −0.0682021 | − | 0.997672i | \(-0.521726\pi\) | ||||
−0.0682021 | + | 0.997672i | \(0.521726\pi\) | |||||||
\(180\) | 0.154814 | − | 12.8137i | 0.0115392 | − | 0.955080i | ||||
\(181\) | 19.3693 | 1.43971 | 0.719855 | − | 0.694124i | \(-0.244208\pi\) | ||||
0.719855 | + | 0.694124i | \(0.244208\pi\) | |||||||
\(182\) | −7.75840 | + | 0.0778144i | −0.575091 | + | 0.00576799i | ||||
\(183\) | 8.32467 | + | 3.07221i | 0.615378 | + | 0.227104i | ||||
\(184\) | 13.8819 | − | 3.64993i | 1.02339 | − | 0.269076i | ||||
\(185\) | 3.89772i | 0.286566i | ||||||||
\(186\) | −9.44311 | + | 9.32971i | −0.692403 | + | 0.684088i | ||||
\(187\) | 13.8819 | 1.01515 | ||||||||
\(188\) | −8.73222 | + | 7.28078i | −0.636863 | + | 0.531005i | ||||
\(189\) | −3.86098 | − | 6.89978i | −0.280845 | − | 0.501885i | ||||
\(190\) | −6.94097 | + | 14.8244i | −0.503551 | + | 1.07547i | ||||
\(191\) | −11.5745 | −0.837503 | −0.418752 | − | 0.908101i | \(-0.637532\pi\) | ||||
−0.418752 | + | 0.908101i | \(0.637532\pi\) | |||||||
\(192\) | −13.6779 | + | 2.21677i | −0.987120 | + | 0.159982i | ||||
\(193\) | 19.4991i | 1.40358i | 0.712385 | + | 0.701789i | \(0.247615\pi\) | ||||
−0.712385 | + | 0.701789i | \(0.752385\pi\) | |||||||
\(194\) | −21.3241 | − | 9.98422i | −1.53098 | − | 0.716825i | ||||
\(195\) | −1.25701 | − | 13.2786i | −0.0900163 | − | 0.950898i | ||||
\(196\) | 6.00000 | + | 7.19612i | 0.428571 | + | 0.514008i | ||||
\(197\) | −8.28019 | −0.589939 | −0.294970 | − | 0.955507i | \(-0.595310\pi\) | ||||
−0.294970 | + | 0.955507i | \(0.595310\pi\) | |||||||
\(198\) | −3.50496 | − | 7.72757i | −0.249086 | − | 0.549174i | ||||
\(199\) | − | 5.61856i | − | 0.398289i | −0.979970 | − | 0.199145i | \(-0.936184\pi\) | ||
0.979970 | − | 0.199145i | \(-0.0638163\pi\) | |||||||
\(200\) | −1.19935 | + | 0.315342i | −0.0848071 | + | 0.0222980i | ||||
\(201\) | 13.7511 | + | 5.07482i | 0.969928 | + | 0.357950i | ||||
\(202\) | 7.79544 | + | 3.64993i | 0.548486 | + | 0.256808i | ||||
\(203\) | 4.63068i | 0.325010i | ||||||||
\(204\) | 22.6561 | − | 8.05155i | 1.58624 | − | 0.563721i | ||||
\(205\) | −12.2462 | −0.855312 | ||||||||
\(206\) | 24.9559 | + | 11.6847i | 1.73876 | + | 0.814109i | ||||
\(207\) | 11.5745 | + | 9.89012i | 0.804485 | + | 0.687411i | ||||
\(208\) | −13.9107 | + | 3.80704i | −0.964531 | + | 0.263971i | ||||
\(209\) | 10.8387i | 0.749728i | ||||||||
\(210\) | 5.66281 | − | 5.59481i | 0.390771 | − | 0.386078i | ||||
\(211\) | − | 1.19935i | − | 0.0825669i | −0.999147 | − | 0.0412834i | \(-0.986855\pi\) | ||
0.999147 | − | 0.0412834i | \(-0.0131447\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.38846 | + | 3.76226i | −0.0951354 | + | 0.257786i | ||||
\(214\) | 6.08650 | − | 12.9994i | 0.416064 | − | 0.888622i | ||||
\(215\) | − | 6.56155i | − | 0.447494i | ||||||
\(216\) | −10.2023 | − | 10.5789i | −0.694177 | − | 0.719804i | ||||
\(217\) | −8.24621 | −0.559789 | ||||||||
\(218\) | 10.6620 | + | 4.99211i | 0.722125 | + | 0.338108i | ||||
\(219\) | −6.08650 | + | 16.4924i | −0.411287 | + | 1.11445i | ||||
\(220\) | 6.56155 | − | 5.47091i | 0.442380 | − | 0.368849i | ||||
\(221\) | 22.5571 | − | 10.8387i | 1.51736 | − | 0.729089i | ||||
\(222\) | 3.14178 | + | 3.17997i | 0.210862 | + | 0.213425i | ||||
\(223\) | 29.2855 | 1.96110 | 0.980551 | − | 0.196263i | \(-0.0628805\pi\) | ||||
0.980551 | + | 0.196263i | \(0.0628805\pi\) | |||||||
\(224\) | −7.01212 | − | 4.99211i | −0.468517 | − | 0.333549i | ||||
\(225\) | −1.00000 | − | 0.854473i | −0.0666667 | − | 0.0569648i | ||||
\(226\) | 13.8819 | + | 6.49971i | 0.923413 | + | 0.432354i | ||||
\(227\) | − | 7.75379i | − | 0.514637i | −0.966327 | − | 0.257319i | \(-0.917161\pi\) | ||
0.966327 | − | 0.257319i | \(-0.0828390\pi\) | |||||||
\(228\) | 6.28646 | + | 17.6893i | 0.416331 | + | 1.17150i | ||||
\(229\) | − | 27.8238i | − | 1.83865i | −0.393501 | − | 0.919324i | \(-0.628736\pi\) | ||
0.393501 | − | 0.919324i | \(-0.371264\pi\) | |||||||
\(230\) | −6.49971 | + | 13.8819i | −0.428578 | + | 0.915348i | ||||
\(231\) | 1.82496 | − | 4.94506i | 0.120074 | − | 0.325361i | ||||
\(232\) | 2.18878 | + | 8.32467i | 0.143700 | + | 0.546542i | ||||
\(233\) | 11.6932i | 0.766045i | 0.923739 | + | 0.383022i | \(0.125117\pi\) | ||||
−0.923739 | + | 0.383022i | \(0.874883\pi\) | |||||||
\(234\) | −11.7288 | − | 9.82014i | −0.766736 | − | 0.641963i | ||||
\(235\) | − | 12.1412i | − | 0.792003i | ||||||
\(236\) | 17.0862 | − | 14.2462i | 1.11222 | − | 0.927349i | ||||
\(237\) | 5.43845 | − | 14.7364i | 0.353265 | − | 0.957233i | ||||
\(238\) | 13.5270 | + | 6.33351i | 0.876824 | + | 0.410541i | ||||
\(239\) | 19.9309i | 1.28922i | 0.764511 | + | 0.644610i | \(0.222980\pi\) | ||||
−0.764511 | + | 0.644610i | \(0.777020\pi\) | |||||||
\(240\) | 7.53566 | − | 12.7345i | 0.486425 | − | 0.822010i | ||||
\(241\) | − | 3.64993i | − | 0.235113i | −0.993066 | − | 0.117556i | \(-0.962494\pi\) | ||
0.993066 | − | 0.117556i | \(-0.0375061\pi\) | |||||||
\(242\) | −4.19773 | + | 8.96543i | −0.269841 | + | 0.576320i | ||||
\(243\) | 3.04982 | − | 15.2872i | 0.195646 | − | 0.980675i | ||||
\(244\) | 6.56155 | + | 7.86962i | 0.420060 | + | 0.503801i | ||||
\(245\) | −10.0054 | −0.639221 | ||||||||
\(246\) | −9.99111 | + | 9.87113i | −0.637010 | + | 0.629360i | ||||
\(247\) | 8.46260 | + | 17.6121i | 0.538462 | + | 1.12063i | ||||
\(248\) | −14.8244 | + | 3.89772i | −0.941349 | + | 0.247506i | ||||
\(249\) | 3.59806 | − | 9.74956i | 0.228018 | − | 0.617853i | ||||
\(250\) | 6.96543 | − | 14.8766i | 0.440533 | − | 0.940881i | ||||
\(251\) | −18.0742 | −1.14084 | −0.570418 | − | 0.821355i | \(-0.693219\pi\) | ||||
−0.570418 | + | 0.821355i | \(0.693219\pi\) | |||||||
\(252\) | 0.110297 | − | 9.12908i | 0.00694804 | − | 0.575078i | ||||
\(253\) | 10.1496i | 0.638102i | ||||||||
\(254\) | 8.54312 | + | 4.00000i | 0.536043 | + | 0.250982i | ||||
\(255\) | −8.88983 | + | 24.0885i | −0.556703 | + | 1.50848i | ||||
\(256\) | −14.9654 | − | 5.66001i | −0.935340 | − | 0.353751i | ||||
\(257\) | 2.18878i | 0.136532i | 0.997667 | + | 0.0682661i | \(0.0217467\pi\) | ||||
−0.997667 | + | 0.0682661i | \(0.978253\pi\) | |||||||
\(258\) | −5.28898 | − | 5.35326i | −0.329277 | − | 0.333280i | ||||
\(259\) | 2.77691i | 0.172549i | ||||||||
\(260\) | 6.39049 | − | 14.0129i | 0.396321 | − | 0.869046i | ||||
\(261\) | −5.93087 | + | 6.94097i | −0.367112 | + | 0.429635i | ||||
\(262\) | −1.09439 | + | 2.33737i | −0.0676115 | + | 0.144403i | ||||
\(263\) | 3.64993 | 0.225064 | 0.112532 | − | 0.993648i | \(-0.464104\pi\) | ||||
0.112532 | + | 0.993648i | \(0.464104\pi\) | |||||||
\(264\) | 0.943405 | − | 9.75243i | 0.0580625 | − | 0.600221i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.94506 | + | 10.5616i | −0.303201 | + | 0.647570i | ||||
\(267\) | −18.4468 | − | 6.80776i | −1.12893 | − | 0.416628i | ||||
\(268\) | 10.8387 | + | 12.9994i | 0.662079 | + | 0.794066i | ||||
\(269\) | 18.6341i | 1.13614i | 0.822979 | + | 0.568072i | \(0.192310\pi\) | ||||
−0.822979 | + | 0.568072i | \(0.807690\pi\) | |||||||
\(270\) | 15.6537 | − | 1.13331i | 0.952656 | − | 0.0689710i | ||||
\(271\) | −7.60812 | −0.462161 | −0.231080 | − | 0.972935i | \(-0.574226\pi\) | ||||
−0.231080 | + | 0.972935i | \(0.574226\pi\) | |||||||
\(272\) | 27.3114 | + | 4.99211i | 1.65600 | + | 0.302691i | ||||
\(273\) | −0.895550 | − | 9.46025i | −0.0542012 | − | 0.572560i | ||||
\(274\) | 5.36932 | − | 11.4677i | 0.324372 | − | 0.692788i | ||||
\(275\) | − | 0.876894i | − | 0.0528787i | ||||||
\(276\) | 5.88681 | + | 16.5648i | 0.354344 | + | 0.997081i | ||||
\(277\) | −3.75379 | −0.225543 | −0.112772 | − | 0.993621i | \(-0.535973\pi\) | ||||
−0.112772 | + | 0.993621i | \(0.535973\pi\) | |||||||
\(278\) | −8.73222 | − | 4.08854i | −0.523724 | − | 0.245214i | ||||
\(279\) | −12.3603 | − | 10.5616i | −0.739993 | − | 0.632304i | ||||
\(280\) | 8.88983 | − | 2.33737i | 0.531269 | − | 0.139685i | ||||
\(281\) | −17.2015 | −1.02616 | −0.513078 | − | 0.858342i | \(-0.671495\pi\) | ||||
−0.513078 | + | 0.858342i | \(0.671495\pi\) | |||||||
\(282\) | −9.78646 | − | 9.90541i | −0.582775 | − | 0.589859i | ||||
\(283\) | 16.5604i | 0.984412i | 0.870479 | + | 0.492206i | \(0.163809\pi\) | ||||
−0.870479 | + | 0.492206i | \(0.836191\pi\) | |||||||
\(284\) | −3.55660 | + | 2.96543i | −0.211046 | + | 0.175966i | ||||
\(285\) | −18.8078 | − | 6.94097i | −1.11408 | − | 0.411148i | ||||
\(286\) | −0.102278 | − | 10.1975i | −0.00604783 | − | 0.602992i | ||||
\(287\) | −8.72475 | −0.515006 | ||||||||
\(288\) | −4.11674 | − | 16.4637i | −0.242581 | − | 0.970131i | ||||
\(289\) | −31.1771 | −1.83395 | ||||||||
\(290\) | −8.32467 | − | 3.89772i | −0.488842 | − | 0.228882i | ||||
\(291\) | 9.98422 | − | 27.0540i | 0.585285 | − | 1.58593i | ||||
\(292\) | −15.5909 | + | 12.9994i | −0.912388 | + | 0.760733i | ||||
\(293\) | 2.66163 | 0.155494 | 0.0777471 | − | 0.996973i | \(-0.475227\pi\) | ||||
0.0777471 | + | 0.996973i | \(0.475227\pi\) | |||||||
\(294\) | −8.16293 | + | 8.06490i | −0.476072 | + | 0.470355i | ||||
\(295\) | 23.7565i | 1.38316i | ||||||||
\(296\) | 1.31256 | + | 4.99211i | 0.0762909 | + | 0.290161i | ||||
\(297\) | 9.06897 | − | 5.07482i | 0.526235 | − | 0.294471i | ||||
\(298\) | −0.246211 | + | 0.525853i | −0.0142626 | + | 0.0304618i | ||||
\(299\) | 7.92460 | + | 16.4924i | 0.458291 | + | 0.953781i | ||||
\(300\) | −0.508600 | − | 1.43114i | −0.0293641 | − | 0.0826268i | ||||
\(301\) | − | 4.67474i | − | 0.269448i | ||||||
\(302\) | 10.2620 | − | 21.9173i | 0.590510 | − | 1.26120i | ||||
\(303\) | −3.64993 | + | 9.89012i | −0.209683 | + | 0.568172i | ||||
\(304\) | −3.89772 | + | 21.3241i | −0.223550 | + | 1.22302i | ||||
\(305\) | −10.9418 | −0.626527 | ||||||||
\(306\) | 12.1639 | + | 26.8184i | 0.695364 | + | 1.53311i | ||||
\(307\) | −2.37610 | −0.135611 | −0.0678055 | − | 0.997699i | \(-0.521600\pi\) | ||||
−0.0678055 | + | 0.997699i | \(0.521600\pi\) | |||||||
\(308\) | 4.67474 | − | 3.89772i | 0.266368 | − | 0.222093i | ||||
\(309\) | −11.6847 | + | 31.6616i | −0.664717 | + | 1.80117i | ||||
\(310\) | 6.94097 | − | 14.8244i | 0.394221 | − | 0.841968i | ||||
\(311\) | 24.5739 | 1.39346 | 0.696730 | − | 0.717333i | \(-0.254637\pi\) | ||||
0.696730 | + | 0.717333i | \(0.254637\pi\) | |||||||
\(312\) | −6.08151 | − | 16.5836i | −0.344298 | − | 0.938861i | ||||
\(313\) | 7.43845 | 0.420446 | 0.210223 | − | 0.977653i | \(-0.432581\pi\) | ||||
0.210223 | + | 0.977653i | \(0.432581\pi\) | |||||||
\(314\) | −3.74571 | + | 8.00000i | −0.211382 | + | 0.451466i | ||||
\(315\) | 7.41219 | + | 6.33351i | 0.417630 | + | 0.356853i | ||||
\(316\) | 13.9309 | − | 11.6153i | 0.783673 | − | 0.653413i | ||||
\(317\) | −0.410574 | −0.0230601 | −0.0115301 | − | 0.999934i | \(-0.503670\pi\) | ||||
−0.0115301 | + | 0.999934i | \(0.503670\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.08650 | −0.340778 | ||||||||
\(320\) | 14.8766 | − | 8.40388i | 0.831629 | − | 0.469791i | ||||
\(321\) | 16.4924 | + | 6.08650i | 0.920517 | + | 0.339715i | ||||
\(322\) | −4.63068 | + | 9.89012i | −0.258058 | + | 0.551155i | ||||
\(323\) | − | 37.6155i | − | 2.09298i | ||||||
\(324\) | 11.8576 | − | 13.5424i | 0.658758 | − | 0.752355i | ||||
\(325\) | −0.684658 | − | 1.42489i | −0.0379780 | − | 0.0790386i | ||||
\(326\) | 7.92460 | − | 16.9252i | 0.438903 | − | 0.937400i | ||||
\(327\) | −4.99211 | + | 13.5270i | −0.276064 | + | 0.748044i | ||||
\(328\) | −15.6847 | + | 4.12391i | −0.866040 | + | 0.227705i | ||||
\(329\) | − | 8.64992i | − | 0.476885i | ||||||
\(330\) | 7.35373 | + | 7.44311i | 0.404809 | + | 0.409730i | ||||
\(331\) | 5.41935 | 0.297874 | 0.148937 | − | 0.988847i | \(-0.452415\pi\) | ||||
0.148937 | + | 0.988847i | \(0.452415\pi\) | |||||||
\(332\) | 9.21662 | − | 7.68466i | 0.505828 | − | 0.421750i | ||||
\(333\) | −3.55660 | + | 4.16234i | −0.194901 | + | 0.228095i | ||||
\(334\) | 22.2462 | + | 10.4160i | 1.21726 | + | 0.569936i | ||||
\(335\) | −18.0742 | −0.987501 | ||||||||
\(336\) | 5.36874 | − | 9.07265i | 0.292889 | − | 0.494954i | ||||
\(337\) | −9.68466 | −0.527557 | −0.263778 | − | 0.964583i | \(-0.584969\pi\) | ||||
−0.263778 | + | 0.964583i | \(0.584969\pi\) | |||||||
\(338\) | −8.12818 | − | 16.4904i | −0.442115 | − | 0.896958i | ||||
\(339\) | −6.49971 | + | 17.6121i | −0.353016 | + | 0.956557i | ||||
\(340\) | −22.7718 | + | 18.9867i | −1.23497 | + | 1.02970i | ||||
\(341\) | − | 10.8387i | − | 0.586948i | ||||||
\(342\) | −20.9392 | + | 9.49729i | −1.13226 | + | 0.513555i | ||||
\(343\) | −17.7797 | −0.960012 | ||||||||
\(344\) | −2.20960 | − | 8.40388i | −0.119134 | − | 0.453107i | ||||
\(345\) | −17.6121 | − | 6.49971i | −0.948203 | − | 0.349933i | ||||
\(346\) | −9.98422 | − | 4.67474i | −0.536755 | − | 0.251316i | ||||
\(347\) | 19.8992 | 1.06825 | 0.534123 | − | 0.845407i | \(-0.320642\pi\) | ||||
0.534123 | + | 0.845407i | \(0.320642\pi\) | |||||||
\(348\) | −9.93349 | + | 3.53018i | −0.532491 | + | 0.189238i | ||||
\(349\) | 1.82496i | 0.0976881i | 0.998806 | + | 0.0488441i | \(0.0155537\pi\) | ||||
−0.998806 | + | 0.0488441i | \(0.984446\pi\) | |||||||
\(350\) | 0.400075 | − | 0.854473i | 0.0213849 | − | 0.0456735i | ||||
\(351\) | 10.7741 | − | 15.3270i | 0.575080 | − | 0.818097i | ||||
\(352\) | 6.56155 | − | 9.21662i | 0.349732 | − | 0.491247i | ||||
\(353\) | 26.5658 | 1.41395 | 0.706977 | − | 0.707237i | \(-0.250058\pi\) | ||||
0.706977 | + | 0.707237i | \(0.250058\pi\) | |||||||
\(354\) | 19.1491 | + | 19.3818i | 1.01776 | + | 1.03013i | ||||
\(355\) | − | 4.94506i | − | 0.262456i | ||||||
\(356\) | −14.5399 | − | 17.4384i | −0.770612 | − | 0.924236i | ||||
\(357\) | −6.33351 | + | 17.1618i | −0.335205 | + | 0.908296i | ||||
\(358\) | 1.09439 | − | 2.33737i | 0.0578402 | − | 0.123534i | ||||
\(359\) | − | 11.1231i | − | 0.587055i | −0.955951 | − | 0.293528i | \(-0.905171\pi\) | ||
0.955951 | − | 0.293528i | \(-0.0948292\pi\) | |||||||
\(360\) | 16.3187 | + | 7.88238i | 0.860071 | + | 0.415438i | ||||
\(361\) | 10.3693 | 0.545754 | ||||||||
\(362\) | −11.6153 | + | 24.8078i | −0.610488 | + | 1.30387i | ||||
\(363\) | −11.3745 | − | 4.19773i | −0.597006 | − | 0.220324i | ||||
\(364\) | 4.55287 | − | 9.98344i | 0.238635 | − | 0.523275i | ||||
\(365\) | − | 21.6774i | − | 1.13465i | ||||||
\(366\) | −8.92692 | + | 8.81972i | −0.466618 | + | 0.461014i | ||||
\(367\) | − | 21.8836i | − | 1.14232i | −0.820840 | − | 0.571158i | \(-0.806494\pi\) | ||
0.820840 | − | 0.571158i | \(-0.193506\pi\) | |||||||
\(368\) | −3.64993 | + | 19.9684i | −0.190266 | + | 1.04093i | ||||
\(369\) | −13.0776 | − | 11.1745i | −0.680793 | − | 0.581719i | ||||
\(370\) | −4.99211 | − | 2.33737i | −0.259527 | − | 0.121514i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.28646 | − | 17.6893i | −0.325938 | − | 0.917149i | ||||
\(373\) | −0.876894 | −0.0454039 | −0.0227019 | − | 0.999742i | \(-0.507227\pi\) | ||||
−0.0227019 | + | 0.999742i | \(0.507227\pi\) | |||||||
\(374\) | −8.32467 | + | 17.7797i | −0.430459 | + | 0.919365i | ||||
\(375\) | 18.8741 | + | 6.96543i | 0.974652 | + | 0.359694i | ||||
\(376\) | −4.08854 | − | 15.5501i | −0.210850 | − | 0.801937i | ||||
\(377\) | −9.89012 | + | 4.75219i | −0.509367 | + | 0.244750i | ||||
\(378\) | 11.1524 | − | 0.807421i | 0.573619 | − | 0.0415292i | ||||
\(379\) | −8.46260 | −0.434694 | −0.217347 | − | 0.976094i | \(-0.569740\pi\) | ||||
−0.217347 | + | 0.976094i | \(0.569740\pi\) | |||||||
\(380\) | −14.8244 | − | 17.7797i | −0.760475 | − | 0.912078i | ||||
\(381\) | −4.00000 | + | 10.8387i | −0.204926 | + | 0.555283i | ||||
\(382\) | 6.94097 | − | 14.8244i | 0.355131 | − | 0.758481i | ||||
\(383\) | 19.4384i | 0.993258i | 0.867963 | + | 0.496629i | \(0.165429\pi\) | ||||
−0.867963 | + | 0.496629i | \(0.834571\pi\) | |||||||
\(384\) | 5.36315 | − | 18.8477i | 0.273687 | − | 0.961819i | ||||
\(385\) | 6.49971i | 0.331256i | ||||||||
\(386\) | −24.9740 | − | 11.6932i | −1.27114 | − | 0.595166i | ||||
\(387\) | 5.98730 | − | 7.00701i | 0.304352 | − | 0.356187i | ||||
\(388\) | 25.5751 | − | 21.3241i | 1.29838 | − | 1.08257i | ||||
\(389\) | − | 32.5161i | − | 1.64863i | −0.566131 | − | 0.824315i | \(-0.691560\pi\) | ||
0.566131 | − | 0.824315i | \(-0.308440\pi\) | |||||||
\(390\) | 17.7607 | + | 6.35290i | 0.899347 | + | 0.321691i | ||||
\(391\) | − | 35.2242i | − | 1.78136i | ||||||
\(392\) | −12.8147 | + | 3.36932i | −0.647239 | + | 0.170176i | ||||
\(393\) | −2.96543 | − | 1.09439i | −0.149586 | − | 0.0552046i | ||||
\(394\) | 4.96543 | − | 10.6051i | 0.250155 | − | 0.534276i | ||||
\(395\) | 19.3693i | 0.974576i | ||||||||
\(396\) | 11.9991 | + | 0.144972i | 0.602979 | + | 0.00728513i | ||||
\(397\) | − | 3.64993i | − | 0.183185i | −0.995797 | − | 0.0915924i | \(-0.970804\pi\) | ||
0.995797 | − | 0.0915924i | \(-0.0291957\pi\) | |||||||
\(398\) | 7.19612 | + | 3.36932i | 0.360709 | + | 0.168889i | ||||
\(399\) | −13.3995 | − | 4.94506i | −0.670814 | − | 0.247563i | ||||
\(400\) | 0.315342 | − | 1.72521i | 0.0157671 | − | 0.0862603i | ||||
\(401\) | −15.8545 | −0.791737 | −0.395868 | − | 0.918307i | \(-0.629556\pi\) | ||||
−0.395868 | + | 0.918307i | \(0.629556\pi\) | |||||||
\(402\) | −14.7459 | + | 14.5688i | −0.735460 | + | 0.726628i | ||||
\(403\) | −8.46260 | − | 17.6121i | −0.421552 | − | 0.877321i | ||||
\(404\) | −9.34949 | + | 7.79544i | −0.465154 | + | 0.387838i | ||||
\(405\) | 2.99838 | + | 18.9867i | 0.148991 | + | 0.943458i | ||||
\(406\) | −5.93087 | − | 2.77691i | −0.294344 | − | 0.137816i | ||||
\(407\) | −3.64993 | −0.180920 | ||||||||
\(408\) | −3.27407 | + | 33.8457i | −0.162091 | + | 1.67561i | ||||
\(409\) | 2.84978i | 0.140912i | 0.997515 | + | 0.0704562i | \(0.0224455\pi\) | ||||
−0.997515 | + | 0.0704562i | \(0.977554\pi\) | |||||||
\(410\) | 7.34376 | − | 15.6847i | 0.362683 | − | 0.774610i | ||||
\(411\) | 14.5491 | + | 5.36932i | 0.717654 | + | 0.264849i | ||||
\(412\) | −29.9309 | + | 24.9559i | −1.47459 | + | 1.22949i | ||||
\(413\) | 16.9252i | 0.832834i | ||||||||
\(414\) | −19.6080 | + | 8.89351i | −0.963681 | + | 0.437092i | ||||
\(415\) | 12.8147i | 0.629048i | ||||||||
\(416\) | 3.46593 | − | 20.0994i | 0.169931 | − | 0.985456i | ||||
\(417\) | 4.08854 | − | 11.0786i | 0.200217 | − | 0.542522i | ||||
\(418\) | −13.8819 | − | 6.49971i | −0.678988 | − | 0.317911i | ||||
\(419\) | 35.1237 | 1.71590 | 0.857951 | − | 0.513731i | \(-0.171737\pi\) | ||||
0.857951 | + | 0.513731i | \(0.171737\pi\) | |||||||
\(420\) | 3.76984 | + | 10.6079i | 0.183950 | + | 0.517611i | ||||
\(421\) | − | 8.32467i | − | 0.405720i | −0.979208 | − | 0.202860i | \(-0.934976\pi\) | ||
0.979208 | − | 0.202860i | \(-0.0650236\pi\) | |||||||
\(422\) | 1.53610 | + | 0.719224i | 0.0747763 | + | 0.0350113i | ||||
\(423\) | 11.0786 | − | 12.9654i | 0.538660 | − | 0.630401i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.04325i | 0.147619i | ||||||||
\(426\) | −3.98599 | − | 4.03444i | −0.193122 | − | 0.195469i | ||||
\(427\) | −7.79544 | −0.377248 | ||||||||
\(428\) | 12.9994 | + | 15.5909i | 0.628351 | + | 0.753614i | ||||
\(429\) | 12.4344 | − | 1.17710i | 0.600339 | − | 0.0568308i | ||||
\(430\) | 8.40388 | + | 3.93481i | 0.405271 | + | 0.189753i | ||||
\(431\) | 9.19224i | 0.442774i | 0.975186 | + | 0.221387i | \(0.0710585\pi\) | ||||
−0.975186 | + | 0.221387i | \(0.928942\pi\) | |||||||
\(432\) | 19.6673 | − | 6.72291i | 0.946243 | − | 0.323456i | ||||
\(433\) | 36.1771 | 1.73856 | 0.869280 | − | 0.494320i | \(-0.164583\pi\) | ||||
0.869280 | + | 0.494320i | \(0.164583\pi\) | |||||||
\(434\) | 4.94506 | − | 10.5616i | 0.237370 | − | 0.506971i | ||||
\(435\) | 3.89772 | − | 10.5616i | 0.186881 | − | 0.506388i | ||||
\(436\) | −12.7876 | + | 10.6620i | −0.612413 | + | 0.510619i | ||||
\(437\) | 27.5022 | 1.31561 | ||||||||
\(438\) | −17.4732 | − | 17.6856i | −0.834901 | − | 0.845049i | ||||
\(439\) | 25.6294i | 1.22322i | 0.791159 | + | 0.611611i | \(0.209478\pi\) | ||||
−0.791159 | + | 0.611611i | \(0.790522\pi\) | |||||||
\(440\) | 3.07221 | + | 11.6847i | 0.146462 | + | 0.557044i | ||||
\(441\) | −10.6847 | − | 9.12975i | −0.508793 | − | 0.434750i | ||||
\(442\) | 0.354955 | + | 35.3904i | 0.0168835 | + | 1.68335i | ||||
\(443\) | 1.82496 | 0.0867067 | 0.0433533 | − | 0.999060i | \(-0.486196\pi\) | ||||
0.0433533 | + | 0.999060i | \(0.486196\pi\) | |||||||
\(444\) | −5.95688 | + | 2.11697i | −0.282701 | + | 0.100467i | ||||
\(445\) | 24.2462 | 1.14938 | ||||||||
\(446\) | −17.5618 | + | 37.5082i | −0.831577 | + | 1.77606i | ||||
\(447\) | −0.667152 | − | 0.246211i | −0.0315552 | − | 0.0116454i | ||||
\(448\) | 10.5988 | − | 5.98730i | 0.500745 | − | 0.282873i | ||||
\(449\) | 14.2770 | 0.673771 | 0.336886 | − | 0.941546i | \(-0.390626\pi\) | ||||
0.336886 | + | 0.941546i | \(0.390626\pi\) | |||||||
\(450\) | 1.69406 | − | 0.768369i | 0.0798590 | − | 0.0362213i | ||||
\(451\) | − | 11.4677i | − | 0.539992i | ||||||
\(452\) | −16.6493 | + | 13.8819i | −0.783119 | + | 0.652952i | ||||
\(453\) | 27.8066 | + | 10.2620i | 1.30647 | + | 0.482149i | ||||
\(454\) | 9.93087 | + | 4.64976i | 0.466079 | + | 0.218224i | ||||
\(455\) | 5.07482 | + | 10.5616i | 0.237911 | + | 0.495133i | ||||
\(456\) | −26.4259 | − | 2.55632i | −1.23751 | − | 0.119711i | ||||
\(457\) | − | 6.49971i | − | 0.304044i | −0.988377 | − | 0.152022i | \(-0.951422\pi\) | ||
0.988377 | − | 0.152022i | \(-0.0485784\pi\) | |||||||
\(458\) | 35.6361 | + | 16.6853i | 1.66516 | + | 0.779652i | ||||
\(459\) | −31.4737 | + | 17.6121i | −1.46907 | + | 0.822062i | ||||
\(460\) | −13.8819 | − | 16.6493i | −0.647249 | − | 0.776280i | ||||
\(461\) | 25.0711 | 1.16768 | 0.583839 | − | 0.811869i | \(-0.301550\pi\) | ||||
0.583839 | + | 0.811869i | \(0.301550\pi\) | |||||||
\(462\) | 5.23913 | + | 5.30281i | 0.243746 | + | 0.246709i | ||||
\(463\) | 27.0967 | 1.25929 | 0.629646 | − | 0.776882i | \(-0.283200\pi\) | ||||
0.629646 | + | 0.776882i | \(0.283200\pi\) | |||||||
\(464\) | −11.9746 | − | 2.18878i | −0.555907 | − | 0.101611i | ||||
\(465\) | 18.8078 | + | 6.94097i | 0.872189 | + | 0.321880i | ||||
\(466\) | −14.9763 | − | 7.01212i | −0.693765 | − | 0.324830i | ||||
\(467\) | −10.7744 | −0.498579 | −0.249289 | − | 0.968429i | \(-0.580197\pi\) | ||||
−0.249289 | + | 0.968429i | \(0.580197\pi\) | |||||||
\(468\) | 19.6109 | − | 9.13306i | 0.906514 | − | 0.422176i | ||||
\(469\) | −12.8769 | −0.594600 | ||||||||
\(470\) | 15.5501 | + | 7.28078i | 0.717274 | + | 0.335837i | ||||
\(471\) | −10.1496 | − | 3.74571i | −0.467671 | − | 0.172593i | ||||
\(472\) | 8.00000 | + | 30.4268i | 0.368230 | + | 1.40051i | ||||
\(473\) | 6.14441 | 0.282520 | ||||||||
\(474\) | 15.6127 | + | 15.8025i | 0.717117 | + | 0.725834i | ||||
\(475\) | −2.37610 | −0.109023 | ||||||||
\(476\) | −16.2236 | + | 13.5270i | −0.743609 | + | 0.620008i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −25.5270 | − | 11.9521i | −1.16758 | − | 0.546675i | ||||
\(479\) | 7.43845i | 0.339871i | 0.985455 | + | 0.169936i | \(0.0543560\pi\) | ||||
−0.985455 | + | 0.169936i | \(0.945644\pi\) | |||||||
\(480\) | 11.7911 | + | 17.2881i | 0.538189 | + | 0.789090i | ||||
\(481\) | −5.93087 | + | 2.84978i | −0.270424 | + | 0.129939i | ||||
\(482\) | 4.67474 | + | 2.18878i | 0.212929 | + | 0.0996960i | ||||
\(483\) | −12.5476 | − | 4.63068i | −0.570937 | − | 0.210703i | ||||
\(484\) | −8.96543 | − | 10.7527i | −0.407520 | − | 0.488760i | ||||
\(485\) | 35.5593i | 1.61467i | ||||||||
\(486\) | 17.7506 | + | 13.0735i | 0.805183 | + | 0.593026i | ||||
\(487\) | 5.41935 | 0.245574 | 0.122787 | − | 0.992433i | \(-0.460817\pi\) | ||||
0.122787 | + | 0.992433i | \(0.460817\pi\) | |||||||
\(488\) | −14.0140 | + | 3.68466i | −0.634385 | + | 0.166797i | ||||
\(489\) | 21.4731 | + | 7.92460i | 0.971046 | + | 0.358363i | ||||
\(490\) | 6.00000 | − | 12.8147i | 0.271052 | − | 0.578908i | ||||
\(491\) | 22.7490 | 1.02665 | 0.513324 | − | 0.858195i | \(-0.328414\pi\) | ||||
0.513324 | + | 0.858195i | \(0.328414\pi\) | |||||||
\(492\) | −6.65127 | − | 18.7159i | −0.299863 | − | 0.843776i | ||||
\(493\) | 21.1231 | 0.951337 | ||||||||
\(494\) | −27.6320 | + | 0.277140i | −1.24322 | + | 0.0124691i | ||||
\(495\) | −8.32467 | + | 9.74247i | −0.374166 | + | 0.437891i | ||||
\(496\) | 3.89772 | − | 21.3241i | 0.175013 | − | 0.957480i | ||||
\(497\) | − | 3.52308i | − | 0.158032i | ||||||
\(498\) | 10.3293 | + | 10.4549i | 0.462869 | + | 0.468495i | ||||
\(499\) | −5.41935 | −0.242603 | −0.121302 | − | 0.992616i | \(-0.538707\pi\) | ||||
−0.121302 | + | 0.992616i | \(0.538707\pi\) | |||||||
\(500\) | 14.8766 | + | 17.8423i | 0.665303 | + | 0.797933i | ||||
\(501\) | −10.4160 | + | 28.2239i | −0.465351 | + | 1.26095i | ||||
\(502\) | 10.8387 | − | 23.1491i | 0.483755 | − | 1.03319i | ||||
\(503\) | −22.3489 | −0.996488 | −0.498244 | − | 0.867037i | \(-0.666022\pi\) | ||||
−0.498244 | + | 0.867037i | \(0.666022\pi\) | |||||||
\(504\) | 11.6262 | + | 5.61576i | 0.517871 | + | 0.250146i | ||||
\(505\) | − | 12.9994i | − | 0.578466i | ||||||
\(506\) | −12.9994 | − | 6.08650i | −0.577895 | − | 0.270578i | ||||
\(507\) | 19.2860 | − | 11.6212i | 0.856519 | − | 0.516115i | ||||
\(508\) | −10.2462 | + | 8.54312i | −0.454602 | + | 0.379040i | ||||
\(509\) | −32.9407 | −1.46007 | −0.730036 | − | 0.683408i | \(-0.760497\pi\) | ||||
−0.730036 | + | 0.683408i | \(0.760497\pi\) | |||||||
\(510\) | −25.5210 | − | 25.8312i | −1.13009 | − | 1.14383i | ||||
\(511\) | − | 15.4439i | − | 0.683200i | ||||||
\(512\) | 16.2236 | − | 15.7732i | 0.716990 | − | 0.697083i | ||||
\(513\) | −13.7511 | − | 24.5739i | −0.607126 | − | 1.08497i | ||||
\(514\) | −2.80333 | − | 1.31256i | −0.123650 | − | 0.0578944i | ||||
\(515\) | − | 41.6155i | − | 1.83380i | ||||||
\(516\) | 10.0280 | − | 3.56377i | 0.441458 | − | 0.156886i | ||||
\(517\) | 11.3693 | 0.500022 | ||||||||
\(518\) | −3.55660 | − | 1.66525i | −0.156268 | − | 0.0731668i | ||||
\(519\) | 4.67474 | − | 12.6670i | 0.205198 | − | 0.556021i | ||||
\(520\) | 14.1152 | + | 16.5880i | 0.618993 | + | 0.727432i | ||||
\(521\) | − | 14.7364i | − | 0.645614i | −0.946465 | − | 0.322807i | \(-0.895374\pi\) | ||
0.946465 | − | 0.322807i | \(-0.104626\pi\) | |||||||
\(522\) | −5.33323 | − | 11.7585i | −0.233429 | − | 0.514654i | ||||
\(523\) | 19.4849i | 0.852017i | 0.904719 | + | 0.426008i | \(0.140081\pi\) | ||||
−0.904719 | + | 0.426008i | \(0.859919\pi\) | |||||||
\(524\) | −2.33737 | − | 2.80333i | −0.102109 | − | 0.122464i | ||||
\(525\) | 1.08407 | + | 0.400075i | 0.0473128 | + | 0.0174607i | ||||
\(526\) | −2.18878 | + | 4.67474i | −0.0954352 | + | 0.203829i | ||||
\(527\) | 37.6155i | 1.63856i | ||||||||
\(528\) | 11.9250 | + | 7.05660i | 0.518967 | + | 0.307099i | ||||
\(529\) | 2.75379 | 0.119730 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21.6774 | + | 25.3693i | −0.940718 | + | 1.10093i | ||||
\(532\) | −10.5616 | − | 12.6670i | −0.457901 | − | 0.549185i | ||||
\(533\) | −8.95369 | − | 18.6341i | −0.387827 | − | 0.807134i | ||||
\(534\) | 19.7813 | − | 19.5438i | 0.856022 | − | 0.845743i | ||||
\(535\) | −21.6774 | −0.937195 | ||||||||
\(536\) | −23.1491 | + | 6.08650i | −0.999887 | + | 0.262897i | ||||
\(537\) | 2.96543 | + | 1.09439i | 0.127968 | + | 0.0472263i | ||||
\(538\) | −23.8662 | − | 11.1745i | −1.02894 | − | 0.481765i | ||||
\(539\) | − | 9.36932i | − | 0.403565i | ||||||
\(540\) | −7.93566 | + | 20.7286i | −0.341496 | + | 0.892015i | ||||
\(541\) | 21.3241i | 0.916794i | 0.888747 | + | 0.458397i | \(0.151576\pi\) | ||||
−0.888747 | + | 0.458397i | \(0.848424\pi\) | |||||||
\(542\) | 4.56241 | − | 9.74430i | 0.195972 | − | 0.418554i | ||||
\(543\) | −31.4737 | − | 11.6153i | −1.35067 | − | 0.498461i | ||||
\(544\) | −22.7718 | + | 31.9861i | −0.976332 | + | 1.37139i | ||||
\(545\) | − | 17.7797i | − | 0.761597i | ||||||
\(546\) | 12.6535 | + | 4.52609i | 0.541520 | + | 0.193699i | ||||
\(547\) | 24.6606i | 1.05441i | 0.849738 | + | 0.527205i | \(0.176760\pi\) | ||||
−0.849738 | + | 0.527205i | \(0.823240\pi\) | |||||||
\(548\) | 11.4677 | + | 13.7538i | 0.489875 | + | 0.587533i | ||||
\(549\) | −11.6847 | − | 9.98422i | −0.498689 | − | 0.426116i | ||||
\(550\) | 1.12311 | + | 0.525853i | 0.0478894 | + | 0.0224224i | ||||
\(551\) | 16.4924i | 0.702601i | ||||||||
\(552\) | −24.7459 | − | 2.39380i | −1.05326 | − | 0.101887i | ||||
\(553\) | 13.7996i | 0.586817i | ||||||||
\(554\) | 2.25106 | − | 4.80776i | 0.0956383 | − | 0.204262i | ||||
\(555\) | 2.33737 | − | 6.33351i | 0.0992159 | − | 0.268843i | ||||
\(556\) | 10.4730 | − | 8.73222i | 0.444155 | − | 0.370329i | ||||
\(557\) | −18.4009 | −0.779670 | −0.389835 | − | 0.920885i | \(-0.627468\pi\) | ||||
−0.389835 | + | 0.920885i | \(0.627468\pi\) | |||||||
\(558\) | 20.9392 | − | 9.49729i | 0.886426 | − | 0.402052i | ||||
\(559\) | 9.98422 | − | 4.79741i | 0.422288 | − | 0.202909i | ||||
\(560\) | −2.33737 | + | 12.7876i | −0.0987720 | + | 0.540373i | ||||
\(561\) | −22.5571 | − | 8.32467i | −0.952363 | − | 0.351468i | ||||
\(562\) | 10.3153 | − | 22.0313i | 0.435126 | − | 0.929334i | ||||
\(563\) | −11.1745 | −0.470947 | −0.235474 | − | 0.971881i | \(-0.575664\pi\) | ||||
−0.235474 | + | 0.971881i | \(0.575664\pi\) | |||||||
\(564\) | 18.5553 | − | 6.59422i | 0.781320 | − | 0.277667i | ||||
\(565\) | − | 23.1491i | − | 0.973888i | ||||||
\(566\) | −21.2101 | − | 9.93087i | −0.891529 | − | 0.417426i | ||||
\(567\) | 2.13618 | + | 13.5270i | 0.0897112 | + | 0.568080i | ||||
\(568\) | −1.66525 | − | 6.33351i | −0.0698723 | − | 0.265748i | ||||
\(569\) | 2.18878i | 0.0917583i | 0.998947 | + | 0.0458791i | \(0.0146089\pi\) | ||||
−0.998947 | + | 0.0458791i | \(0.985391\pi\) | |||||||
\(570\) | 20.1684 | − | 19.9262i | 0.844762 | − | 0.834617i | ||||
\(571\) | − | 22.0313i | − | 0.921981i | −0.887405 | − | 0.460990i | \(-0.847494\pi\) | ||
0.887405 | − | 0.460990i | \(-0.152506\pi\) | |||||||
\(572\) | 13.1221 | + | 5.98422i | 0.548662 | + | 0.250213i | ||||
\(573\) | 18.8078 | + | 6.94097i | 0.785706 | + | 0.289963i | ||||
\(574\) | 5.23203 | − | 11.1745i | 0.218381 | − | 0.466413i | ||||
\(575\) | −2.22504 | −0.0927906 | ||||||||
\(576\) | 23.5550 | + | 4.60025i | 0.981458 | + | 0.191677i | ||||
\(577\) | 23.1491i | 0.963708i | 0.876252 | + | 0.481854i | \(0.160036\pi\) | ||||
−0.876252 | + | 0.481854i | \(0.839964\pi\) | |||||||
\(578\) | 18.6962 | − | 39.9309i | 0.777658 | − | 1.66091i | ||||
\(579\) | 11.6932 | − | 31.6847i | 0.485951 | − | 1.31677i | ||||
\(580\) | 9.98422 | − | 8.32467i | 0.414572 | − | 0.345663i | ||||
\(581\) | 9.12975i | 0.378766i | ||||||||
\(582\) | 28.6628 | + | 29.0112i | 1.18811 | + | 1.20255i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −7.29986 | − | 27.7639i | −0.302070 | − | 1.14888i | ||||
\(585\) | −5.92030 | + | 22.3305i | −0.244774 | + | 0.923253i | ||||
\(586\) | −1.59612 | + | 3.40896i | −0.0659350 | + | 0.140823i | ||||
\(587\) | − | 15.6155i | − | 0.644522i | −0.946651 | − | 0.322261i | \(-0.895557\pi\) | ||
0.946651 | − | 0.322261i | \(-0.104443\pi\) | |||||||
\(588\) | −5.43422 | − | 15.2912i | −0.224104 | − | 0.630599i | ||||
\(589\) | −29.3693 | −1.21014 | ||||||||
\(590\) | −30.4268 | − | 14.2462i | −1.25265 | − | 0.586507i | ||||
\(591\) | 13.4547 | + | 4.96543i | 0.553453 | + | 0.204251i | ||||
\(592\) | −7.18089 | − | 1.31256i | −0.295133 | − | 0.0539458i | ||||
\(593\) | −31.3632 | −1.28793 | −0.643966 | − | 0.765054i | \(-0.722712\pi\) | ||||
−0.643966 | + | 0.765054i | \(0.722712\pi\) | |||||||
\(594\) | 1.06126 | + | 14.6586i | 0.0435441 | + | 0.601448i | ||||
\(595\) | − | 22.5571i | − | 0.924753i | ||||||
\(596\) | −0.525853 | − | 0.630683i | −0.0215398 | − | 0.0258338i | ||||
\(597\) | −3.36932 | + | 9.12975i | −0.137897 | + | 0.373656i | ||||
\(598\) | −25.8753 | + | 0.259521i | −1.05812 | + | 0.0106126i | ||||
\(599\) | 33.2987 | 1.36055 | 0.680274 | − | 0.732958i | \(-0.261861\pi\) | ||||
0.680274 | + | 0.732958i | \(0.261861\pi\) | |||||||
\(600\) | 2.13796 | + | 0.206817i | 0.0872820 | + | 0.00844325i | ||||
\(601\) | 2.80776 | 0.114531 | 0.0572655 | − | 0.998359i | \(-0.481762\pi\) | ||||
0.0572655 | + | 0.998359i | \(0.481762\pi\) | |||||||
\(602\) | 5.98730 | + | 2.80333i | 0.244024 | + | 0.114255i | ||||
\(603\) | −19.3013 | − | 16.4924i | −0.786009 | − | 0.671623i | ||||
\(604\) | 21.9173 | + | 26.2866i | 0.891802 | + | 1.06959i | ||||
\(605\) | 14.9505 | 0.607822 | ||||||||
\(606\) | −10.4783 | − | 10.6056i | −0.425650 | − | 0.430824i | ||||
\(607\) | 13.3405i | 0.541475i | 0.962653 | + | 0.270738i | \(0.0872676\pi\) | ||||
−0.962653 | + | 0.270738i | \(0.912732\pi\) | |||||||
\(608\) | −24.9740 | − | 17.7797i | −1.01283 | − | 0.721061i | ||||
\(609\) | 2.77691 | − | 7.52452i | 0.112526 | − | 0.304909i | ||||
\(610\) | 6.56155 | − | 14.0140i | 0.265670 | − | 0.567411i | ||||
\(611\) | 18.4743 | − | 8.87689i | 0.747391 | − | 0.359121i | ||||
\(612\) | −41.6428 | − | 0.503124i | −1.68331 | − | 0.0203376i | ||||
\(613\) | − | 6.49971i | − | 0.262521i | −0.991348 | − | 0.131260i | \(-0.958098\pi\) | ||
0.991348 | − | 0.131260i | \(-0.0419024\pi\) | |||||||
\(614\) | 1.42489 | − | 3.04325i | 0.0575039 | − | 0.122816i | ||||
\(615\) | 19.8992 | + | 7.34376i | 0.802413 | + | 0.296129i | ||||
\(616\) | 2.18878 | + | 8.32467i | 0.0881883 | + | 0.335411i | ||||
\(617\) | 18.5485 | 0.746735 | 0.373368 | − | 0.927684i | \(-0.378203\pi\) | ||||
0.373368 | + | 0.927684i | \(0.378203\pi\) | |||||||
\(618\) | −33.5444 | − | 33.9522i | −1.34935 | − | 1.36576i | ||||
\(619\) | 4.08504 | 0.164192 | 0.0820959 | − | 0.996624i | \(-0.473839\pi\) | ||||
0.0820959 | + | 0.996624i | \(0.473839\pi\) | |||||||
\(620\) | 14.8244 | + | 17.7797i | 0.595362 | + | 0.714048i | ||||
\(621\) | −12.8769 | − | 23.0117i | −0.516732 | − | 0.923427i | ||||
\(622\) | −14.7364 | + | 31.4737i | −0.590876 | + | 1.26198i | ||||
\(623\) | 17.2741 | 0.692072 | ||||||||
\(624\) | 24.8868 | + | 2.15573i | 0.996269 | + | 0.0862984i | ||||
\(625\) | −22.6155 | −0.904621 | ||||||||
\(626\) | −4.46066 | + | 9.52699i | −0.178284 | + | 0.380775i | ||||
\(627\) | 6.49971 | − | 17.6121i | 0.259573 | − | 0.703359i | ||||
\(628\) | −8.00000 | − | 9.59482i | −0.319235 | − | 0.382875i | ||||
\(629\) | 12.6670 | 0.505067 | ||||||||
\(630\) | −12.5567 | + | 5.69530i | −0.500272 | + | 0.226906i | ||||
\(631\) | 30.9945 | 1.23387 | 0.616935 | − | 0.787014i | \(-0.288374\pi\) | ||||
0.616935 | + | 0.787014i | \(0.288374\pi\) | |||||||
\(632\) | 6.52262 | + | 24.8078i | 0.259456 | + | 0.986800i | ||||
\(633\) | −0.719224 | + | 1.94886i | −0.0285866 | + | 0.0774603i | ||||
\(634\) | 0.246211 | − | 0.525853i | 0.00977830 | − | 0.0208843i | ||||
\(635\) | − | 14.2462i | − | 0.565344i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.31534 | − | 15.2245i | −0.289844 | − | 0.603215i | ||||
\(638\) | 3.64993 | − | 7.79544i | 0.144502 | − | 0.308625i | ||||
\(639\) | 4.51228 | − | 5.28078i | 0.178503 | − | 0.208904i | ||||
\(640\) | 1.84233 | + | 24.0932i | 0.0728245 | + | 0.952369i | ||||
\(641\) | 1.33430i | 0.0527018i | 0.999653 | + | 0.0263509i | \(0.00838873\pi\) | ||||
−0.999653 | + | 0.0263509i | \(0.991611\pi\) | |||||||
\(642\) | −17.6856 | + | 17.4732i | −0.697993 | + | 0.689611i | ||||
\(643\) | −1.04179 | −0.0410843 | −0.0205422 | − | 0.999789i | \(-0.506539\pi\) | ||||
−0.0205422 | + | 0.999789i | \(0.506539\pi\) | |||||||
\(644\) | −9.89012 | − | 11.8617i | −0.389725 | − | 0.467418i | ||||
\(645\) | −3.93481 | + | 10.6620i | −0.154933 | + | 0.419818i | ||||
\(646\) | 48.1771 | + | 22.5571i | 1.89550 | + | 0.887499i | ||||
\(647\) | −33.2987 | −1.30911 | −0.654553 | − | 0.756016i | \(-0.727143\pi\) | ||||
−0.654553 | + | 0.756016i | \(0.727143\pi\) | |||||||
\(648\) | 10.2340 | + | 23.3080i | 0.402031 | + | 0.915626i | ||||
\(649\) | −22.2462 | −0.873240 | ||||||||
\(650\) | 2.23554 | − | 0.0224218i | 0.0876850 | − | 0.000879454i | ||||
\(651\) | 13.3995 | + | 4.94506i | 0.525168 | + | 0.193812i | ||||
\(652\) | 16.9252 | + | 20.2993i | 0.662842 | + | 0.794981i | ||||
\(653\) | − | 26.4296i | − | 1.03427i | −0.855904 | − | 0.517135i | \(-0.826999\pi\) | ||
0.855904 | − | 0.517135i | \(-0.173001\pi\) | |||||||
\(654\) | −14.3314 | − | 14.5056i | −0.560402 | − | 0.567214i | ||||
\(655\) | 3.89772 | 0.152297 | ||||||||
\(656\) | 4.12391 | − | 22.5616i | 0.161012 | − | 0.880881i | ||||
\(657\) | 19.7802 | − | 23.1491i | 0.771700 | − | 0.903131i | ||||
\(658\) | 11.0786 | + | 5.18715i | 0.431889 | + | 0.202216i | ||||
\(659\) | 23.7738 | 0.926096 | 0.463048 | − | 0.886333i | \(-0.346756\pi\) | ||||
0.463048 | + | 0.886333i | \(0.346756\pi\) | |||||||
\(660\) | −13.9428 | + | 4.95502i | −0.542724 | + | 0.192874i | ||||
\(661\) | − | 29.6488i | − | 1.15320i | −0.817025 | − | 0.576602i | \(-0.804378\pi\) | ||
0.817025 | − | 0.576602i | \(-0.195622\pi\) | |||||||
\(662\) | −3.24985 | + | 6.94097i | −0.126309 | + | 0.269769i | ||||
\(663\) | −43.1534 | + | 4.08510i | −1.67594 | + | 0.158652i | ||||
\(664\) | 4.31534 | + | 16.4127i | 0.167468 | + | 0.636938i | ||||
\(665\) | 17.6121 | 0.682967 | ||||||||
\(666\) | −3.19821 | − | 7.05127i | −0.123928 | − | 0.273231i | ||||
\(667\) | 15.4439i | 0.597992i | ||||||||
\(668\) | −26.6811 | + | 22.2462i | −1.03232 | + | 0.860732i | ||||
\(669\) | −47.5868 | − | 17.5618i | −1.83981 | − | 0.678980i | ||||
\(670\) | 10.8387 | − | 23.1491i | 0.418735 | − | 0.894326i | ||||
\(671\) | − | 10.2462i | − | 0.395551i | ||||||
\(672\) | 8.40053 | + | 12.3168i | 0.324057 | + | 0.475131i | ||||
\(673\) | −11.6847 | −0.450410 | −0.225205 | − | 0.974311i | \(-0.572305\pi\) | ||||
−0.225205 | + | 0.974311i | \(0.572305\pi\) | |||||||
\(674\) | 5.80766 | − | 12.4039i | 0.223703 | − | 0.477780i | ||||
\(675\) | 1.11252 | + | 1.98813i | 0.0428209 | + | 0.0765232i | ||||
\(676\) | 25.9948 | − | 0.521492i | 0.999799 | − | 0.0200574i | ||||
\(677\) | 29.4728i | 1.13273i | 0.824154 | + | 0.566366i | \(0.191651\pi\) | ||||
−0.824154 | + | 0.566366i | \(0.808349\pi\) | |||||||
\(678\) | −18.6594 | − | 18.8862i | −0.716611 | − | 0.725321i | ||||
\(679\) | 25.3341i | 0.972232i | ||||||||
\(680\) | −10.6620 | − | 40.5514i | −0.408871 | − | 1.55508i | ||||
\(681\) | −4.64976 | + | 12.5993i | −0.178179 | + | 0.482808i | ||||
\(682\) | 13.8819 | + | 6.49971i | 0.531567 | + | 0.248887i | ||||
\(683\) | 38.9848i | 1.49171i | 0.666106 | + | 0.745857i | \(0.267960\pi\) | ||||
−0.666106 | + | 0.745857i | \(0.732040\pi\) | |||||||
\(684\) | 0.392827 | − | 32.5137i | 0.0150201 | − | 1.24319i | ||||
\(685\) | −19.1231 | −0.730656 | ||||||||
\(686\) | 10.6620 | − | 22.7718i | 0.407079 | − | 0.869430i | ||||
\(687\) | −16.6853 | + | 45.2116i | −0.636583 | + | 1.72493i | ||||
\(688\) | 12.0885 | + | 2.20960i | 0.460871 | + | 0.0842403i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 18.8862 | − | 18.6594i | 0.718986 | − | 0.710352i | ||||
\(691\) | −31.4743 | −1.19734 | −0.598669 | − | 0.800996i | \(-0.704304\pi\) | ||||
−0.598669 | + | 0.800996i | \(0.704304\pi\) | |||||||
\(692\) | 11.9746 | − | 9.98422i | 0.455206 | − | 0.379543i | ||||
\(693\) | −5.93087 | + | 6.94097i | −0.225295 | + | 0.263666i | ||||
\(694\) | −11.9331 | + | 25.4864i | −0.452974 | + | 0.967452i | ||||
\(695\) | 14.5616i | 0.552351i | ||||||||
\(696\) | 1.43551 | − | 14.8395i | 0.0544128 | − | 0.562492i | ||||
\(697\) | 39.7984i | 1.50747i | ||||||||
\(698\) | −2.33737 | − | 1.09439i | −0.0884708 | − | 0.0414232i | ||||
\(699\) | 7.01212 | − | 19.0005i | 0.265223 | − | 0.718667i | ||||
\(700\) | 0.854473 | + | 1.02481i | 0.0322960 | + | 0.0387343i | ||||
\(701\) | 26.4296i | 0.998231i | 0.866535 | + | 0.499116i | \(0.166342\pi\) | ||||
−0.866535 | + | 0.499116i | \(0.833658\pi\) | |||||||
\(702\) | 13.1695 | + | 22.9905i | 0.497052 | + | 0.867721i | ||||
\(703\) | 9.89012i | 0.373013i | ||||||||
\(704\) | 7.86962 | + | 13.9309i | 0.296597 | + | 0.525039i | ||||
\(705\) | −7.28078 | + | 19.7285i | −0.274210 | + | 0.743019i | ||||
\(706\) | −15.9309 | + | 34.0248i | −0.599566 | + | 1.28054i | ||||
\(707\) | − | 9.26137i | − | 0.348310i | ||||||
\(708\) | −36.3070 | + | 12.9028i | −1.36450 | + | 0.484919i | ||||
\(709\) | 23.9492i | 0.899431i | 0.893172 | + | 0.449716i | \(0.148475\pi\) | ||||
−0.893172 | + | 0.449716i | \(0.851525\pi\) | |||||||
\(710\) | 6.33351 | + | 2.96543i | 0.237693 | + | 0.111291i | ||||
\(711\) | −17.6742 | + | 20.6843i | −0.662833 | + | 0.775722i | ||||
\(712\) | 31.0540 | − | 8.16491i | 1.16380 | − | 0.305993i | ||||
\(713\) | −27.5022 | −1.02997 | ||||||||
\(714\) | −18.1823 | − | 18.4033i | −0.680456 | − | 0.688727i | ||||
\(715\) | −13.8819 | + | 6.67026i | −0.519155 | + | 0.249454i | ||||
\(716\) | 2.33737 | + | 2.80333i | 0.0873517 | + | 0.104765i | ||||
\(717\) | 11.9521 | − | 32.3862i | 0.446358 | − | 1.20949i | ||||
\(718\) | 14.2462 | + | 6.67026i | 0.531664 | + | 0.248932i | ||||
\(719\) | 31.0737 | 1.15885 | 0.579426 | − | 0.815025i | \(-0.303277\pi\) | ||||
0.579426 | + | 0.815025i | \(0.303277\pi\) | |||||||
\(720\) | −19.8815 | + | 16.1737i | −0.740940 | + | 0.602759i | ||||
\(721\) | − | 29.6488i | − | 1.10418i | ||||||
\(722\) | −6.21823 | + | 13.2808i | −0.231419 | + | 0.494259i | ||||
\(723\) | −2.18878 | + | 5.93087i | −0.0814015 | + | 0.220571i | ||||
\(724\) | −24.8078 | − | 29.7533i | −0.921973 | − | 1.10577i | ||||
\(725\) | − | 1.33430i | − | 0.0495548i | ||||||
\(726\) | 12.1974 | − | 12.0509i | 0.452687 | − | 0.447251i | ||||
\(727\) | − | 5.32326i | − | 0.197429i | −0.995116 | − | 0.0987145i | \(-0.968527\pi\) | ||
0.995116 | − | 0.0987145i | \(-0.0314730\pi\) | |||||||
\(728\) | 10.0563 | + | 11.8180i | 0.372712 | + | 0.438006i | ||||
\(729\) | −14.1231 | + | 23.0117i | −0.523078 | + | 0.852285i | ||||
\(730\) | 27.7639 | + | 12.9994i | 1.02759 | + | 0.481130i | ||||
\(731\) | −21.3241 | −0.788700 | ||||||||
\(732\) | −5.94282 | − | 16.7224i | −0.219653 | − | 0.618076i | ||||
\(733\) | 5.47489i | 0.202220i | 0.994875 | + | 0.101110i | \(0.0322394\pi\) | ||||
−0.994875 | + | 0.101110i | \(0.967761\pi\) | |||||||
\(734\) | 28.0281 | + | 13.1231i | 1.03453 | + | 0.484383i | ||||
\(735\) | 16.2580 | + | 6.00000i | 0.599687 | + | 0.221313i | ||||
\(736\) | −23.3863 | − | 16.6493i | −0.862032 | − | 0.613703i | ||||
\(737\) | − | 16.9252i | − | 0.623447i | ||||||
\(738\) | 22.1543 | − | 10.0484i | 0.815511 | − | 0.369888i | ||||
\(739\) | 23.6788 | 0.871040 | 0.435520 | − | 0.900179i | \(-0.356564\pi\) | ||||
0.435520 | + | 0.900179i | \(0.356564\pi\) | |||||||
\(740\) | 5.98730 | − | 4.99211i | 0.220098 | − | 0.183514i | ||||
\(741\) | −3.18955 | − | 33.6932i | −0.117171 | − | 1.23775i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 12.5616i | − | 0.460839i | −0.973091 | − | 0.230419i | \(-0.925990\pi\) | ||
0.973091 | − | 0.230419i | \(-0.0740098\pi\) | |||||||
\(744\) | 26.4259 | + | 2.55632i | 0.968821 | + | 0.0937192i | ||||
\(745\) | 0.876894 | 0.0321269 | ||||||||
\(746\) | 0.525853 | − | 1.12311i | 0.0192528 | − | 0.0411198i | ||||
\(747\) | −11.6932 | + | 13.6847i | −0.427831 | + | 0.500695i | ||||
\(748\) | −17.7797 | − | 21.3241i | −0.650089 | − | 0.779686i | ||||
\(749\) | −15.4439 | −0.564309 | ||||||||
\(750\) | −20.2395 | + | 19.9964i | −0.739042 | + | 0.730167i | ||||
\(751\) | 38.6746i | 1.41126i | 0.708583 | + | 0.705628i | \(0.249335\pi\) | ||||
−0.708583 | + | 0.705628i | \(0.750665\pi\) | |||||||
\(752\) | 22.3680 | + | 4.08854i | 0.815679 | + | 0.149094i | ||||
\(753\) | 29.3693 | + | 10.8387i | 1.07028 | + | 0.394984i | ||||
\(754\) | −0.155629 | − | 15.5168i | −0.00566767 | − | 0.565089i | ||||
\(755\) | −36.5485 | −1.33014 | ||||||||
\(756\) | −5.65372 | + | 14.7680i | −0.205624 | + | 0.537105i | ||||
\(757\) | −4.49242 | −0.163280 | −0.0816399 | − | 0.996662i | \(-0.526016\pi\) | ||||
−0.0816399 | + | 0.996662i | \(0.526016\pi\) | |||||||
\(758\) | 5.07482 | − | 10.8387i | 0.184326 | − | 0.393679i | ||||
\(759\) | 6.08650 | − | 16.4924i | 0.220926 | − | 0.598637i | ||||
\(760\) | 31.6616 | − | 8.32467i | 1.14849 | − | 0.301968i | ||||
\(761\) | 23.3459 | 0.846289 | 0.423145 | − | 0.906062i | \(-0.360926\pi\) | ||||
0.423145 | + | 0.906062i | \(0.360926\pi\) | |||||||
\(762\) | −11.4832 | − | 11.6228i | −0.415994 | − | 0.421050i | ||||
\(763\) | − | 12.6670i | − | 0.458577i | ||||||
\(764\) | 14.8244 | + | 17.7797i | 0.536327 | + | 0.643246i | ||||
\(765\) | 28.8907 | − | 33.8111i | 1.04454 | − | 1.22244i | ||||
\(766\) | −24.8963 | − | 11.6568i | −0.899540 | − | 0.421177i | ||||
\(767\) | −36.1485 | + | 17.3693i | −1.30525 | + | 0.627170i | ||||
\(768\) | 20.9236 | + | 18.1715i | 0.755014 | + | 0.655709i | ||||
\(769\) | 28.8486i | 1.04031i | 0.854073 | + | 0.520154i | \(0.174125\pi\) | ||||
−0.854073 | + | 0.520154i | \(0.825875\pi\) | |||||||
\(770\) | −8.32467 | − | 3.89772i | −0.300000 | − | 0.140464i | ||||
\(771\) | 1.31256 | − | 3.55660i | 0.0472706 | − | 0.128088i | ||||
\(772\) | 29.9527 | − | 24.9740i | 1.07802 | − | 0.898835i | ||||
\(773\) | −2.13578 | −0.0768186 | −0.0384093 | − | 0.999262i | \(-0.512229\pi\) | ||||
−0.0384093 | + | 0.999262i | \(0.512229\pi\) | |||||||
\(774\) | 5.38397 | + | 11.8703i | 0.193523 | + | 0.426670i | ||||
\(775\) | 2.37610 | 0.0853519 | ||||||||
\(776\) | 11.9746 | + | 45.5435i | 0.429863 | + | 1.63492i | ||||
\(777\) | 1.66525 | − | 4.51228i | 0.0597404 | − | 0.161877i | ||||
\(778\) | 41.6458 | + | 19.4991i | 1.49308 | + | 0.699078i | ||||
\(779\) | −31.0737 | −1.11333 | ||||||||
\(780\) | −18.7873 | + | 18.9378i | −0.672693 | + | 0.678081i | ||||
\(781\) | 4.63068 | 0.165699 | ||||||||
\(782\) | 45.1143 | + | 21.1231i | 1.61328 | + | 0.755361i | ||||
\(783\) | 13.7996 | − | 7.72197i | 0.493156 | − | 0.275961i | ||||
\(784\) | 3.36932 | − | 18.4332i | 0.120333 | − | 0.658330i | ||||
\(785\) | 13.3405 | 0.476144 | ||||||||
\(786\) | 3.17997 | − | 3.14178i | 0.113426 | − | 0.112064i | ||||
\(787\) | 39.2697 | 1.39981 | 0.699907 | − | 0.714234i | \(-0.253225\pi\) | ||||
0.699907 | + | 0.714234i | \(0.253225\pi\) | |||||||
\(788\) | 10.6051 | + | 12.7192i | 0.377790 | + | 0.453104i | ||||
\(789\) | −5.93087 | − | 2.18878i | −0.211145 | − | 0.0779225i | ||||
\(790\) | −24.8078 | − | 11.6153i | −0.882621 | − | 0.413255i | ||||
\(791\) | − | 16.4924i | − | 0.586403i | ||||||
\(792\) | −7.38127 | + | 15.2813i | −0.262282 | + | 0.542996i | ||||
\(793\) | −8.00000 | − | 16.6493i | −0.284088 | − | 0.591236i | ||||
\(794\) | 4.67474 | + | 2.18878i | 0.165900 | + | 0.0776768i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.63068 | + | 7.19612i | −0.305906 | + | 0.255060i | ||||
\(797\) | − | 15.2162i | − | 0.538987i | −0.963002 | − | 0.269494i | \(-0.913144\pi\) | ||
0.963002 | − | 0.269494i | \(-0.0868563\pi\) | |||||||
\(798\) | 14.3689 | − | 14.1963i | 0.508653 | − | 0.502544i | ||||
\(799\) | −39.4571 | −1.39589 | ||||||||
\(800\) | 2.02050 | + | 1.43845i | 0.0714355 | + | 0.0508568i | ||||
\(801\) | 25.8923 | + | 22.1242i | 0.914859 | + | 0.781722i | ||||
\(802\) | 9.50758 | − | 20.3061i | 0.335724 | − | 0.717033i | ||||
\(803\) | 20.2993 | 0.716346 | ||||||||
\(804\) | −9.81664 | − | 27.6228i | −0.346206 | − | 0.974182i | ||||
\(805\) | 16.4924 | 0.581282 | ||||||||
\(806\) | 27.6320 | − | 0.277140i | 0.973294 | − | 0.00976185i | ||||
\(807\) | 11.1745 | − | 30.2791i | 0.393359 | − | 1.06588i | ||||
\(808\) | −4.37755 | − | 16.6493i | −0.154002 | − | 0.585722i | ||||
\(809\) | 11.3185i | 0.397938i | 0.980006 | + | 0.198969i | \(0.0637593\pi\) | ||||
−0.980006 | + | 0.198969i | \(0.936241\pi\) | |||||||
\(810\) | −26.1158 | − | 7.54563i | −0.917616 | − | 0.265126i | ||||
\(811\) | 24.0535 | 0.844632 | 0.422316 | − | 0.906449i | \(-0.361217\pi\) | ||||
0.422316 | + | 0.906449i | \(0.361217\pi\) | |||||||
\(812\) | 7.11321 | − | 5.93087i | 0.249625 | − | 0.208133i | ||||
\(813\) | 12.3626 | + | 4.56241i | 0.433577 | + | 0.160011i | ||||
\(814\) | 2.18878 | − | 4.67474i | 0.0767166 | − | 0.163850i | ||||
\(815\) | −28.2239 | −0.988639 | ||||||||
\(816\) | −41.3854 | − | 24.4898i | −1.44878 | − | 0.857315i | ||||
\(817\) | − | 16.6493i | − | 0.582487i | ||||||
\(818\) | −3.64993 | − | 1.70895i | −0.127617 | − | 0.0597519i | ||||
\(819\) | −4.21788 | + | 15.9093i | −0.147385 | + | 0.555914i | ||||
\(820\) | 15.6847 | + | 18.8114i | 0.547732 | + | 0.656924i | ||||
\(821\) | 9.85775 | 0.344038 | 0.172019 | − | 0.985094i | \(-0.444971\pi\) | ||||
0.172019 | + | 0.985094i | \(0.444971\pi\) | |||||||
\(822\) | −15.6016 | + | 15.4143i | −0.544170 | + | 0.537635i | ||||
\(823\) | − | 9.59482i | − | 0.334454i | −0.985918 | − | 0.167227i | \(-0.946519\pi\) | ||
0.985918 | − | 0.167227i | \(-0.0534814\pi\) | |||||||
\(824\) | −14.0140 | − | 53.3002i | −0.488202 | − | 1.85680i | ||||
\(825\) | −0.525853 | + | 1.42489i | −0.0183078 | + | 0.0496083i | ||||
\(826\) | −21.6774 | − | 10.1496i | −0.754253 | − | 0.353151i | ||||
\(827\) | − | 13.5076i | − | 0.469704i | −0.972031 | − | 0.234852i | \(-0.924539\pi\) | ||
0.972031 | − | 0.234852i | \(-0.0754606\pi\) | |||||||
\(828\) | 0.367854 | − | 30.4467i | 0.0127838 | − | 1.05810i | ||||
\(829\) | 24.0000 | 0.833554 | 0.416777 | − | 0.909009i | \(-0.363160\pi\) | ||||
0.416777 | + | 0.909009i | \(0.363160\pi\) | |||||||
\(830\) | −16.4127 | − | 7.68466i | −0.569694 | − | 0.266738i | ||||
\(831\) | 6.09963 | + | 2.25106i | 0.211594 | + | 0.0780884i | ||||
\(832\) | 23.6644 | + | 16.4922i | 0.820417 | + | 0.571765i | ||||
\(833\) | 32.5161i | 1.12662i | ||||||||
\(834\) | 11.7374 | + | 11.8801i | 0.406434 | + | 0.411374i | ||||
\(835\) | − | 37.0970i | − | 1.28380i | ||||||
\(836\) | 16.6493 | − | 13.8819i | 0.575830 | − | 0.480117i | ||||
\(837\) | 13.7511 | + | 24.5739i | 0.475308 | + | 0.849400i | ||||
\(838\) | −21.0628 | + | 44.9856i | −0.727603 | + | 1.55400i | ||||
\(839\) | − | 19.1231i | − | 0.660203i | −0.943945 | − | 0.330101i | \(-0.892917\pi\) | ||
0.943945 | − | 0.330101i | \(-0.107083\pi\) | |||||||
\(840\) | −15.8470 | − | 1.53296i | −0.546773 | − | 0.0528923i | ||||
\(841\) | 19.7386 | 0.680643 | ||||||||
\(842\) | 10.6620 | + | 4.99211i | 0.367438 | + | 0.172039i | ||||
\(843\) | 27.9512 | + | 10.3153i | 0.962691 | + | 0.355279i | ||||
\(844\) | −1.84233 | + | 1.53610i | −0.0634156 | + | 0.0528748i | ||||
\(845\) | −17.3492 | + | 21.6774i | −0.596829 | + | 0.745725i | ||||
\(846\) | 9.96224 | + | 21.9643i | 0.342509 | + | 0.755148i | ||||
\(847\) | 10.6514 | 0.365985 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.93087 | − | 26.9094i | 0.340827 | − | 0.923529i | ||||
\(850\) | −3.89772 | − | 1.82496i | −0.133691 | − | 0.0625958i | ||||
\(851\) | 9.26137i | 0.317476i | ||||||||
\(852\) | 7.55752 | − | 2.68580i | 0.258916 | − | 0.0920142i | ||||
\(853\) | 21.3241i | 0.730123i | 0.930983 | + | 0.365061i | \(0.118952\pi\) | ||||
−0.930983 | + | 0.365061i | \(0.881048\pi\) | |||||||
\(854\) | 4.67474 | − | 9.98422i | 0.159966 | − | 0.341653i | ||||
\(855\) | 26.3989 | + | 22.5571i | 0.902824 | + | 0.771438i | ||||
\(856\) | −27.7639 | + | 7.29986i | −0.948950 | + | 0.249504i | ||||
\(857\) | 49.4413i | 1.68888i | 0.535649 | + | 0.844441i | \(0.320067\pi\) | ||||
−0.535649 | + | 0.844441i | \(0.679933\pi\) | |||||||
\(858\) | −5.94902 | + | 16.6316i | −0.203096 | + | 0.567792i | ||||
\(859\) | − | 9.06897i | − | 0.309429i | −0.987959 | − | 0.154715i | \(-0.950554\pi\) | ||
0.987959 | − | 0.154715i | \(-0.0494458\pi\) | |||||||
\(860\) | −10.0792 | + | 8.40388i | −0.343699 | + | 0.286570i | ||||
\(861\) | 14.1771 | + | 5.23203i | 0.483154 | + | 0.178307i | ||||
\(862\) | −11.7732 | − | 5.51237i | −0.400997 | − | 0.187752i | ||||
\(863\) | 0.561553i | 0.0191155i | 0.999954 | + | 0.00955774i | \(0.00304237\pi\) | ||||
−0.999954 | + | 0.00955774i | \(0.996958\pi\) | |||||||
\(864\) | −3.18347 | + | 29.2210i | −0.108304 | + | 0.994118i | ||||
\(865\) | 16.6493i | 0.566095i | ||||||||
\(866\) | −21.6945 | + | 46.3348i | −0.737211 | + | 1.57452i | ||||
\(867\) | 50.6605 | + | 18.6962i | 1.72052 | + | 0.634955i | ||||
\(868\) | 10.5616 | + | 12.6670i | 0.358482 | + | 0.429947i | ||||
\(869\) | −18.1379 | −0.615287 | ||||||||
\(870\) | 11.1896 | + | 11.3256i | 0.379364 | + | 0.383975i | ||||
\(871\) | −13.2148 | − | 27.5022i | −0.447766 | − | 0.931877i | ||||
\(872\) | −5.98730 | − | 22.7718i | −0.202756 | − | 0.771150i | ||||
\(873\) | −32.4473 | + | 37.9734i | −1.09817 | + | 1.28521i | ||||
\(874\) | −16.4924 | + | 35.2242i | −0.557865 | + | 1.19148i | ||||
\(875\) | −17.6742 | −0.597496 | ||||||||
\(876\) | 33.1295 | − | 11.7736i | 1.11934 | − | 0.397794i | ||||
\(877\) | − | 14.8244i | − | 0.500584i | −0.968170 | − | 0.250292i | \(-0.919473\pi\) | ||
0.968170 | − | 0.250292i | \(-0.0805266\pi\) | |||||||
\(878\) | −32.8255 | − | 15.3693i | −1.10781 | − | 0.518689i | ||||
\(879\) | −4.32496 | − | 1.59612i | −0.145877 | − | 0.0538357i | ||||
\(880\) | −16.8078 | − | 3.07221i | −0.566590 | − | 0.103564i | ||||
\(881\) | − | 43.8346i | − | 1.47683i | −0.674349 | − | 0.738413i | \(-0.735576\pi\) | ||
0.674349 | − | 0.738413i | \(-0.264424\pi\) | |||||||
\(882\) | 18.1005 | − | 8.20976i | 0.609476 | − | 0.276437i | ||||
\(883\) | 47.6606i | 1.60391i | 0.597386 | + | 0.801954i | \(0.296206\pi\) | ||||
−0.597386 | + | 0.801954i | \(0.703794\pi\) | |||||||
\(884\) | −45.5400 | − | 20.7682i | −1.53168 | − | 0.698509i | ||||
\(885\) | 14.2462 | − | 38.6026i | 0.478881 | − | 1.29761i | ||||
\(886\) | −1.09439 | + | 2.33737i | −0.0367667 | + | 0.0785255i | ||||
\(887\) | −34.7236 | −1.16590 | −0.582952 | − | 0.812507i | \(-0.698102\pi\) | ||||
−0.582952 | + | 0.812507i | \(0.698102\pi\) | |||||||
\(888\) | 0.860840 | − | 8.89893i | 0.0288879 | − | 0.298628i | ||||
\(889\) | − | 10.1496i | − | 0.340408i | ||||||
\(890\) | −14.5399 | + | 31.0540i | −0.487378 | + | 1.04093i | ||||
\(891\) | −17.7797 | + | 2.80776i | −0.595641 | + | 0.0940636i | ||||
\(892\) | −37.5082 | − | 44.9856i | −1.25587 | − | 1.50623i | ||||
\(893\) | − | 30.8071i | − | 1.03092i | ||||||
\(894\) | 0.715417 | − | 0.706826i | 0.0239271 | − | 0.0236398i | ||||
\(895\) | −3.89772 | −0.130286 | ||||||||
\(896\) | 1.31256 | + | 17.1651i | 0.0438495 | + | 0.573446i | ||||
\(897\) | −2.98678 | − | 31.5512i | −0.0997256 | − | 1.05346i | ||||
\(898\) | −8.56155 | + | 18.2856i | −0.285703 | + | 0.610198i | ||||
\(899\) | − | 16.4924i | − | 0.550053i | ||||||
\(900\) | −0.0317813 | + | 2.63049i | −0.00105938 | + | 0.0876830i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 14.6875 | + | 6.87689i | 0.489041 | + | 0.228976i | ||||
\(903\) | −2.80333 | + | 7.59612i | −0.0932891 | + | 0.252783i | ||||
\(904\) | −7.79544 | − | 29.6488i | −0.259273 | − | 0.986103i | ||||
\(905\) | 41.3686 | 1.37514 | ||||||||
\(906\) | −29.8182 | + | 29.4602i | −0.990645 | + | 0.978748i | ||||
\(907\) | − | 31.3308i | − | 1.04032i | −0.854068 | − | 0.520161i | \(-0.825872\pi\) | ||
0.854068 | − | 0.520161i | \(-0.174128\pi\) | |||||||
\(908\) | −11.9106 | + | 9.93087i | −0.395268 | + | 0.329567i | ||||
\(909\) | 11.8617 | − | 13.8819i | 0.393429 | − | 0.460435i | ||||
\(910\) | −16.5702 | + | 0.166194i | −0.549298 | + | 0.00550929i | ||||
\(911\) | 8.72475 | 0.289064 | 0.144532 | − | 0.989500i | \(-0.453832\pi\) | ||||
0.144532 | + | 0.989500i | \(0.453832\pi\) | |||||||
\(912\) | 19.1211 | − | 32.3127i | 0.633162 | − | 1.06998i | ||||
\(913\) | −12.0000 | −0.397142 | ||||||||
\(914\) | 8.32467 | + | 3.89772i | 0.275356 | + | 0.128925i | ||||
\(915\) | 17.7797 | + | 6.56155i | 0.587778 | + | 0.216918i | ||||
\(916\) | −42.7402 | + | 35.6361i | −1.41218 | + | 1.17745i | ||||
\(917\) | 2.77691 | 0.0917017 | ||||||||
\(918\) | −3.68309 | − | 50.8724i | −0.121560 | − | 1.67904i | ||||
\(919\) | − | 47.2824i | − | 1.55970i | −0.625964 | − | 0.779852i | \(-0.715294\pi\) | ||
0.625964 | − | 0.779852i | \(-0.284706\pi\) | |||||||
\(920\) | 29.6488 | − | 7.79544i | 0.977491 | − | 0.257008i | ||||
\(921\) | 3.86098 | + | 1.42489i | 0.127224 | + | 0.0469517i | ||||
\(922\) | −15.0346 | + | 32.1105i | −0.495137 | + | 1.05750i | ||||
\(923\) | 7.52452 | − | 3.61553i | 0.247673 | − | 0.119007i | ||||
\(924\) | −9.93349 | + | 3.53018i | −0.326788 | + | 0.116134i | ||||
\(925\) | − | 0.800151i | − | 0.0263088i | ||||||
\(926\) | −16.2493 | + | 34.7049i | −0.533984 | + | 1.14047i | ||||
\(927\) | 37.9734 | − | 44.4408i | 1.24721 | − | 1.45963i | ||||
\(928\) | 9.98422 | − | 14.0242i | 0.327748 | − | 0.460368i | ||||
\(929\) | −9.77484 | −0.320702 | −0.160351 | − | 0.987060i | \(-0.551263\pi\) | ||||
−0.160351 | + | 0.987060i | \(0.551263\pi\) | |||||||
\(930\) | −20.1684 | + | 19.9262i | −0.661348 | + | 0.653406i | ||||
\(931\) | −25.3878 | −0.832051 | ||||||||
\(932\) | 17.9619 | − | 14.9763i | 0.588362 | − | 0.490566i | ||||
\(933\) | −39.9309 | − | 14.7364i | −1.30728 | − | 0.482449i | ||||
\(934\) | 6.46114 | − | 13.7996i | 0.211415 | − | 0.451536i | ||||
\(935\) | 29.6488 | 0.969618 | ||||||||
\(936\) | −0.0627777 | + | 30.5941i | −0.00205195 | + | 0.999998i | ||||
\(937\) | 55.8617 | 1.82492 | 0.912462 | − | 0.409162i | \(-0.134179\pi\) | ||||
0.912462 | + | 0.409162i | \(0.134179\pi\) | |||||||
\(938\) | 7.72197 | − | 16.4924i | 0.252131 | − | 0.538497i | ||||
\(939\) | −12.0869 | − | 4.46066i | −0.394442 | − | 0.145568i | ||||
\(940\) | −18.6501 | + | 15.5501i | −0.608299 | + | 0.507189i | ||||
\(941\) | −49.4182 | −1.61099 | −0.805494 | − | 0.592604i | \(-0.798100\pi\) | ||||
−0.805494 | + | 0.592604i | \(0.798100\pi\) | |||||||
\(942\) | 10.8839 | − | 10.7532i | 0.354617 | − | 0.350358i | ||||
\(943\) | −29.0982 | −0.947567 | ||||||||
\(944\) | −43.7673 | − | 8.00000i | −1.42450 | − | 0.260378i | ||||
\(945\) | −8.24621 | − | 14.7364i | −0.268249 | − | 0.479376i | ||||
\(946\) | −3.68466 | + | 7.86962i | −0.119799 | + | 0.255863i | ||||
\(947\) | 2.00000i | 0.0649913i | 0.999472 | + | 0.0324956i | \(0.0103455\pi\) | ||||
−0.999472 | + | 0.0324956i | \(0.989654\pi\) | |||||||
\(948\) | −29.6021 | + | 10.5200i | −0.961431 | + | 0.341675i | ||||
\(949\) | 32.9848 | − | 15.8492i | 1.07073 | − | 0.514487i | ||||
\(950\) | 1.42489 | − | 3.04325i | 0.0462295 | − | 0.0987360i | ||||
\(951\) | 0.667152 | + | 0.246211i | 0.0216339 | + | 0.00798395i | ||||
\(952\) | −7.59612 | − | 28.8907i | −0.246192 | − | 0.936352i | ||||
\(953\) | − | 29.9527i | − | 0.970262i | −0.874442 | − | 0.485131i | \(-0.838772\pi\) | ||
0.874442 | − | 0.485131i | \(-0.161228\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.7206 | −0.799941 | ||||||||
\(956\) | 30.6159 | − | 25.5270i | 0.990188 | − | 0.825602i | ||||
\(957\) | 9.89012 | + | 3.64993i | 0.319702 | + | 0.117985i | ||||
\(958\) | −9.52699 | − | 4.46066i | −0.307803 | − | 0.144117i | ||||
\(959\) | −13.6242 | −0.439947 | ||||||||
\(960\) | −29.2131 | + | 4.73453i | −0.942847 | + | 0.152806i | ||||
\(961\) | −1.63068 | −0.0526027 | ||||||||
\(962\) | −0.0933270 | − | 9.30506i | −0.00300898 | − | 0.300007i | ||||
\(963\) | −23.1491 | − | 19.7802i | −0.745968 | − | 0.637409i | ||||
\(964\) | −5.60667 | + | 4.67474i | −0.180579 | + | 0.150563i | ||||
\(965\) | 41.6458i | 1.34063i | ||||||||
\(966\) | 13.4554 | − | 13.2938i | 0.432920 | − | 0.427721i | ||||
\(967\) | 38.7899 | 1.24740 | 0.623700 | − | 0.781664i | \(-0.285629\pi\) | ||||
0.623700 | + | 0.781664i | \(0.285629\pi\) | |||||||
\(968\) | 19.1482 | − | 5.03457i | 0.615446 | − | 0.161817i | ||||
\(969\) | −22.5571 | + | 61.1225i | −0.724640 | + | 1.96354i | ||||
\(970\) | −45.5435 | − | 21.3241i | −1.46232 | − | 0.684675i | ||||
\(971\) | 6.09963 | 0.195747 | 0.0978733 | − | 0.995199i | \(-0.468796\pi\) | ||||
0.0978733 | + | 0.995199i | \(0.468796\pi\) | |||||||
\(972\) | −27.3889 | + | 14.8947i | −0.878498 | + | 0.477746i | ||||
\(973\) | 10.3743i | 0.332585i | ||||||||
\(974\) | −3.24985 | + | 6.94097i | −0.104132 | + | 0.222403i | ||||
\(975\) | 0.258047 | + | 2.72592i | 0.00826413 | + | 0.0872991i | ||||
\(976\) | 3.68466 | − | 20.1584i | 0.117943 | − | 0.645256i | ||||
\(977\) | −28.9645 | −0.926656 | −0.463328 | − | 0.886187i | \(-0.653345\pi\) | ||||
−0.463328 | + | 0.886187i | \(0.653345\pi\) | |||||||
\(978\) | −23.0265 | + | 22.7500i | −0.736307 | + | 0.727465i | ||||
\(979\) | 22.7048i | 0.725648i | ||||||||
\(980\) | 12.8147 | + | 15.3693i | 0.409350 | + | 0.490955i | ||||
\(981\) | 16.2236 | − | 18.9867i | 0.517981 | − | 0.606199i | ||||
\(982\) | −13.6420 | + | 29.1364i | −0.435335 | + | 0.929779i | ||||
\(983\) | − | 35.9309i | − | 1.14602i | −0.819550 | − | 0.573008i | \(-0.805776\pi\) | ||
0.819550 | − | 0.573008i | \(-0.194224\pi\) | |||||||
\(984\) | 27.9594 | + | 2.70466i | 0.891314 | + | 0.0862215i | ||||
\(985\) | −17.6847 | −0.563480 | ||||||||
\(986\) | −12.6670 | + | 27.0540i | −0.403400 | + | 0.861574i | ||||
\(987\) | −5.18715 | + | 14.0555i | −0.165109 | + | 0.447391i | ||||
\(988\) | 16.2153 | − | 35.5566i | 0.515877 | − | 1.13120i | ||||
\(989\) | − | 15.5909i | − | 0.495761i | ||||||
\(990\) | −7.48582 | − | 16.5044i | −0.237915 | − | 0.524543i | ||||
\(991\) | 47.8083i | 1.51868i | 0.650694 | + | 0.759340i | \(0.274478\pi\) | ||||
−0.650694 | + | 0.759340i | \(0.725522\pi\) | |||||||
\(992\) | 24.9740 | + | 17.7797i | 0.792926 | + | 0.564505i | ||||
\(993\) | −8.80604 | − | 3.24985i | −0.279451 | − | 0.103131i | ||||
\(994\) | 4.51228 | + | 2.11271i | 0.143121 | + | 0.0670110i | ||||
\(995\) | − | 12.0000i | − | 0.380426i | ||||||
\(996\) | −19.5846 | + | 6.96002i | −0.620563 | + | 0.220537i | ||||
\(997\) | 10.0000 | 0.316703 | 0.158352 | − | 0.987383i | \(-0.449382\pi\) | ||||
0.158352 | + | 0.987383i | \(0.449382\pi\) | |||||||
\(998\) | 3.24985 | − | 6.94097i | 0.102872 | − | 0.219713i | ||||
\(999\) | 8.27528 | − | 4.63068i | 0.261818 | − | 0.146508i |
(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 | 156.2.h.b.155.7 | yes | 16 | |
3.2 | odd | 2 | inner | 156.2.h.b.155.10 | yes | 16 | |
4.3 | odd | 2 | inner | 156.2.h.b.155.6 | yes | 16 | |
12.11 | even | 2 | inner | 156.2.h.b.155.11 | yes | 16 | |
13.12 | even | 2 | inner | 156.2.h.b.155.9 | yes | 16 | |
39.38 | odd | 2 | inner | 156.2.h.b.155.8 | yes | 16 | |
52.51 | odd | 2 | inner | 156.2.h.b.155.12 | yes | 16 | |
156.155 | even | 2 | inner | 156.2.h.b.155.5 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
156.2.h.b.155.5 | ✓ | 16 | 156.155 | even | 2 | inner | |
156.2.h.b.155.6 | yes | 16 | 4.3 | odd | 2 | inner | |
156.2.h.b.155.7 | yes | 16 | 1.1 | even | 1 | trivial | |
156.2.h.b.155.8 | yes | 16 | 39.38 | odd | 2 | inner | |
156.2.h.b.155.9 | yes | 16 | 13.12 | even | 2 | inner | |
156.2.h.b.155.10 | yes | 16 | 3.2 | odd | 2 | inner | |
156.2.h.b.155.11 | yes | 16 | 12.11 | even | 2 | inner | |
156.2.h.b.155.12 | yes | 16 | 52.51 | odd | 2 | inner |