Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [418,2,Mod(115,418)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(418, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("418.115");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 418 = 2 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 418.f (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.33774680449\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + 7 x^{14} - 13 x^{13} + 51 x^{12} - 74 x^{11} + 332 x^{10} - 614 x^{9} + 1832 x^{8} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 267.1 | ||
Root | \(-0.744204 - 2.29042i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.267 |
Dual form | 418.2.f.g.191.1 |
$q$-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 \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(343\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | − | 0.587785i | 0.572061 | − | 0.415627i | ||||
\(3\) | −0.744204 | − | 2.29042i | −0.429666 | − | 1.32238i | −0.898455 | − | 0.439066i | \(-0.855309\pi\) |
0.468789 | − | 0.883310i | \(-0.344691\pi\) | |||||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | 2.77774 | + | 2.01814i | 1.24224 | + | 0.902541i | 0.997746 | − | 0.0671088i | \(-0.0213775\pi\) |
0.244496 | + | 0.969650i | \(0.421377\pi\) | |||||||
\(6\) | −1.94835 | − | 1.41556i | −0.795411 | − | 0.577900i | ||||
\(7\) | 0.326530 | − | 1.00496i | 0.123417 | − | 0.379838i | −0.870192 | − | 0.492712i | \(-0.836006\pi\) |
0.993609 | + | 0.112874i | \(0.0360056\pi\) | |||||||
\(8\) | −0.309017 | − | 0.951057i | −0.109254 | − | 0.336249i | ||||
\(9\) | −2.26515 | + | 1.64573i | −0.755049 | + | 0.548575i | ||||
\(10\) | 3.43347 | 1.08576 | ||||||||
\(11\) | 0.637485 | − | 3.25478i | 0.192209 | − | 0.981354i | ||||
\(12\) | −2.40829 | −0.695214 | ||||||||
\(13\) | 0.266156 | − | 0.193374i | 0.0738185 | − | 0.0536323i | −0.550264 | − | 0.834991i | \(-0.685473\pi\) |
0.624082 | + | 0.781358i | \(0.285473\pi\) | |||||||
\(14\) | −0.326530 | − | 1.00496i | −0.0872689 | − | 0.268586i | ||||
\(15\) | 2.55520 | − | 7.86410i | 0.659750 | − | 2.03050i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | 2.82037 | + | 2.04912i | 0.684041 | + | 0.496985i | 0.874696 | − | 0.484672i | \(-0.161061\pi\) |
−0.190655 | + | 0.981657i | \(0.561061\pi\) | |||||||
\(18\) | −0.865209 | + | 2.66284i | −0.203932 | + | 0.627638i | ||||
\(19\) | 0.309017 | + | 0.951057i | 0.0708934 | + | 0.218187i | ||||
\(20\) | 2.77774 | − | 2.01814i | 0.621121 | − | 0.451271i | ||||
\(21\) | −2.54478 | −0.555317 | ||||||||
\(22\) | −1.39738 | − | 3.00788i | −0.297922 | − | 0.641282i | ||||
\(23\) | −7.90827 | −1.64899 | −0.824495 | − | 0.565870i | \(-0.808540\pi\) | ||||
−0.824495 | + | 0.565870i | \(0.808540\pi\) | |||||||
\(24\) | −1.94835 | + | 1.41556i | −0.397705 | + | 0.288950i | ||||
\(25\) | 2.09783 | + | 6.45646i | 0.419566 | + | 1.29129i | ||||
\(26\) | 0.101663 | − | 0.312886i | 0.0199377 | − | 0.0613619i | ||||
\(27\) | −0.389910 | − | 0.283287i | −0.0750383 | − | 0.0545185i | ||||
\(28\) | −0.854868 | − | 0.621098i | −0.161555 | − | 0.117376i | ||||
\(29\) | −1.91607 | + | 5.89707i | −0.355806 | + | 1.09506i | 0.599735 | + | 0.800199i | \(0.295273\pi\) |
−0.955541 | + | 0.294859i | \(0.904727\pi\) | |||||||
\(30\) | −2.55520 | − | 7.86410i | −0.466514 | − | 1.43578i | ||||
\(31\) | −1.78552 | + | 1.29725i | −0.320688 | + | 0.232994i | −0.736469 | − | 0.676471i | \(-0.763508\pi\) |
0.415781 | + | 0.909465i | \(0.363508\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −7.92925 | + | 0.962110i | −1.38031 | + | 0.167482i | ||||
\(34\) | 3.48617 | 0.597874 | ||||||||
\(35\) | 2.93516 | − | 2.13252i | 0.496133 | − | 0.360462i | ||||
\(36\) | 0.865209 | + | 2.66284i | 0.144202 | + | 0.443807i | ||||
\(37\) | 1.98483 | − | 6.10867i | 0.326303 | − | 1.00426i | −0.644545 | − | 0.764566i | \(-0.722953\pi\) |
0.970849 | − | 0.239693i | \(-0.0770467\pi\) | |||||||
\(38\) | 0.809017 | + | 0.587785i | 0.131240 | + | 0.0953514i | ||||
\(39\) | −0.640983 | − | 0.465701i | −0.102639 | − | 0.0745719i | ||||
\(40\) | 1.06100 | − | 3.26543i | 0.167759 | − | 0.516309i | ||||
\(41\) | −1.26074 | − | 3.88017i | −0.196895 | − | 0.605980i | −0.999949 | − | 0.0100745i | \(-0.996793\pi\) |
0.803054 | − | 0.595906i | \(-0.203207\pi\) | |||||||
\(42\) | −2.05877 | + | 1.49579i | −0.317675 | + | 0.230805i | ||||
\(43\) | 4.47258 | 0.682062 | 0.341031 | − | 0.940052i | \(-0.389224\pi\) | ||||
0.341031 | + | 0.940052i | \(0.389224\pi\) | |||||||
\(44\) | −2.89849 | − | 1.61207i | −0.436964 | − | 0.243028i | ||||
\(45\) | −9.61330 | −1.43307 | ||||||||
\(46\) | −6.39793 | + | 4.64837i | −0.943323 | + | 0.685364i | ||||
\(47\) | 3.18543 | + | 9.80375i | 0.464643 | + | 1.43002i | 0.859431 | + | 0.511251i | \(0.170818\pi\) |
−0.394789 | + | 0.918772i | \(0.629182\pi\) | |||||||
\(48\) | −0.744204 | + | 2.29042i | −0.107417 | + | 0.330594i | ||||
\(49\) | 4.75980 | + | 3.45820i | 0.679972 | + | 0.494028i | ||||
\(50\) | 5.49220 | + | 3.99031i | 0.776714 | + | 0.564316i | ||||
\(51\) | 2.59442 | − | 7.98481i | 0.363292 | − | 1.11810i | ||||
\(52\) | −0.101663 | − | 0.312886i | −0.0140981 | − | 0.0433894i | ||||
\(53\) | −0.313656 | + | 0.227885i | −0.0430840 | + | 0.0313024i | −0.609119 | − | 0.793079i | \(-0.708477\pi\) |
0.566035 | + | 0.824381i | \(0.308477\pi\) | |||||||
\(54\) | −0.481956 | −0.0655859 | ||||||||
\(55\) | 8.33939 | − | 7.75439i | 1.12448 | − | 1.04560i | ||||
\(56\) | −1.05667 | −0.141204 | ||||||||
\(57\) | 1.94835 | − | 1.41556i | 0.258065 | − | 0.187495i | ||||
\(58\) | 1.91607 | + | 5.89707i | 0.251593 | + | 0.774323i | ||||
\(59\) | −0.235855 | + | 0.725888i | −0.0307057 | + | 0.0945025i | −0.965235 | − | 0.261384i | \(-0.915821\pi\) |
0.934529 | + | 0.355887i | \(0.115821\pi\) | |||||||
\(60\) | −6.68961 | − | 4.86028i | −0.863624 | − | 0.627460i | ||||
\(61\) | 2.77448 | + | 2.01578i | 0.355236 | + | 0.258094i | 0.751062 | − | 0.660231i | \(-0.229542\pi\) |
−0.395826 | + | 0.918325i | \(0.629542\pi\) | |||||||
\(62\) | −0.682007 | + | 2.09900i | −0.0866150 | + | 0.266573i | ||||
\(63\) | 0.914245 | + | 2.81376i | 0.115184 | + | 0.354500i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 1.12957 | 0.140106 | ||||||||
\(66\) | −5.84938 | + | 5.43906i | −0.720009 | + | 0.669502i | ||||
\(67\) | −11.9017 | −1.45402 | −0.727012 | − | 0.686625i | \(-0.759091\pi\) | ||||
−0.727012 | + | 0.686625i | \(0.759091\pi\) | |||||||
\(68\) | 2.82037 | − | 2.04912i | 0.342020 | − | 0.248492i | ||||
\(69\) | 5.88537 | + | 18.1133i | 0.708515 | + | 2.18058i | ||||
\(70\) | 1.12113 | − | 3.45049i | 0.134001 | − | 0.412413i | ||||
\(71\) | 10.1982 | + | 7.40946i | 1.21031 | + | 0.879341i | 0.995259 | − | 0.0972622i | \(-0.0310085\pi\) |
0.215050 | + | 0.976603i | \(0.431009\pi\) | |||||||
\(72\) | 2.26515 | + | 1.64573i | 0.266950 | + | 0.193951i | ||||
\(73\) | −1.34810 | + | 4.14903i | −0.157783 | + | 0.485607i | −0.998432 | − | 0.0559731i | \(-0.982174\pi\) |
0.840649 | + | 0.541581i | \(0.182174\pi\) | |||||||
\(74\) | −1.98483 | − | 6.10867i | −0.230731 | − | 0.710118i | ||||
\(75\) | 13.2268 | − | 9.60985i | 1.52730 | − | 1.10965i | ||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −3.06276 | − | 1.70343i | −0.349034 | − | 0.194124i | ||||
\(78\) | −0.792298 | −0.0897101 | ||||||||
\(79\) | 12.2517 | − | 8.90136i | 1.37842 | − | 1.00148i | 0.381395 | − | 0.924412i | \(-0.375444\pi\) |
0.997026 | − | 0.0770688i | \(-0.0245561\pi\) | |||||||
\(80\) | −1.06100 | − | 3.26543i | −0.118624 | − | 0.365086i | ||||
\(81\) | −2.95430 | + | 9.09241i | −0.328256 | + | 1.01027i | ||||
\(82\) | −3.30067 | − | 2.39808i | −0.364498 | − | 0.264823i | ||||
\(83\) | 7.76891 | + | 5.64444i | 0.852748 | + | 0.619558i | 0.925902 | − | 0.377763i | \(-0.123307\pi\) |
−0.0731543 | + | 0.997321i | \(0.523307\pi\) | |||||||
\(84\) | −0.786381 | + | 2.42023i | −0.0858012 | + | 0.264069i | ||||
\(85\) | 3.69883 | + | 11.3838i | 0.401195 | + | 1.23475i | ||||
\(86\) | 3.61839 | − | 2.62892i | 0.390181 | − | 0.283483i | ||||
\(87\) | 14.9327 | 1.60096 | ||||||||
\(88\) | −3.29248 | + | 0.399499i | −0.350979 | + | 0.0425867i | ||||
\(89\) | −6.50467 | −0.689493 | −0.344747 | − | 0.938696i | \(-0.612035\pi\) | ||||
−0.344747 | + | 0.938696i | \(0.612035\pi\) | |||||||
\(90\) | −7.77732 | + | 5.65055i | −0.819802 | + | 0.595621i | ||||
\(91\) | −0.107424 | − | 0.330618i | −0.0112611 | − | 0.0346582i | ||||
\(92\) | −2.44379 | + | 7.52122i | −0.254783 | + | 0.784141i | ||||
\(93\) | 4.30005 | + | 3.12417i | 0.445894 | + | 0.323961i | ||||
\(94\) | 8.33956 | + | 6.05905i | 0.860160 | + | 0.624943i | ||||
\(95\) | −1.06100 | + | 3.26543i | −0.108856 | + | 0.335026i | ||||
\(96\) | 0.744204 | + | 2.29042i | 0.0759550 | + | 0.233765i | ||||
\(97\) | 3.88851 | − | 2.82517i | 0.394818 | − | 0.286852i | −0.372609 | − | 0.927988i | \(-0.621537\pi\) |
0.767427 | + | 0.641136i | \(0.221537\pi\) | |||||||
\(98\) | 5.88344 | 0.594317 | ||||||||
\(99\) | 3.91248 | + | 8.42169i | 0.393219 | + | 0.846412i | ||||
\(100\) | 6.78873 | 0.678873 | ||||||||
\(101\) | 4.36800 | − | 3.17354i | 0.434632 | − | 0.315779i | −0.348866 | − | 0.937173i | \(-0.613433\pi\) |
0.783499 | + | 0.621394i | \(0.213433\pi\) | |||||||
\(102\) | −2.59442 | − | 7.98481i | −0.256886 | − | 0.790614i | ||||
\(103\) | −3.36832 | + | 10.3666i | −0.331891 | + | 1.02145i | 0.636343 | + | 0.771406i | \(0.280446\pi\) |
−0.968233 | + | 0.250048i | \(0.919554\pi\) | |||||||
\(104\) | −0.266156 | − | 0.193374i | −0.0260988 | − | 0.0189619i | ||||
\(105\) | −7.06873 | − | 5.13574i | −0.689838 | − | 0.501197i | ||||
\(106\) | −0.119806 | + | 0.368725i | −0.0116366 | + | 0.0358137i | ||||
\(107\) | 1.65702 | + | 5.09978i | 0.160190 | + | 0.493014i | 0.998650 | − | 0.0519495i | \(-0.0165435\pi\) |
−0.838460 | + | 0.544964i | \(0.816543\pi\) | |||||||
\(108\) | −0.389910 | + | 0.283287i | −0.0375191 | + | 0.0272593i | ||||
\(109\) | −2.66422 | −0.255186 | −0.127593 | − | 0.991827i | \(-0.540725\pi\) | ||||
−0.127593 | + | 0.991827i | \(0.540725\pi\) | |||||||
\(110\) | 2.18879 | − | 11.1752i | 0.208693 | − | 1.06551i | ||||
\(111\) | −15.4685 | −1.46821 | ||||||||
\(112\) | −0.854868 | + | 0.621098i | −0.0807774 | + | 0.0586882i | ||||
\(113\) | −4.96552 | − | 15.2823i | −0.467117 | − | 1.43764i | −0.856300 | − | 0.516479i | \(-0.827243\pi\) |
0.389183 | − | 0.921161i | \(-0.372757\pi\) | |||||||
\(114\) | 0.744204 | − | 2.29042i | 0.0697010 | − | 0.214518i | ||||
\(115\) | −21.9671 | − | 15.9600i | −2.04844 | − | 1.48828i | ||||
\(116\) | 5.01635 | + | 3.64459i | 0.465756 | + | 0.338392i | ||||
\(117\) | −0.284643 | + | 0.876041i | −0.0263152 | + | 0.0809900i | ||||
\(118\) | 0.235855 | + | 0.725888i | 0.0217122 | + | 0.0668234i | ||||
\(119\) | 2.98022 | − | 2.16525i | 0.273196 | − | 0.198488i | ||||
\(120\) | −8.26881 | −0.754835 | ||||||||
\(121\) | −10.1872 | − | 4.14975i | −0.926111 | − | 0.377250i | ||||
\(122\) | 3.42944 | 0.310487 | ||||||||
\(123\) | −7.94898 | + | 5.77527i | −0.716735 | + | 0.520739i | ||||
\(124\) | 0.682007 | + | 2.09900i | 0.0612460 | + | 0.188496i | ||||
\(125\) | −1.89784 | + | 5.84096i | −0.169748 | + | 0.522431i | ||||
\(126\) | 2.39352 | + | 1.73900i | 0.213232 | + | 0.154922i | ||||
\(127\) | −14.4279 | − | 10.4825i | −1.28027 | − | 0.930170i | −0.280708 | − | 0.959793i | \(-0.590569\pi\) |
−0.999561 | + | 0.0296235i | \(0.990569\pi\) | |||||||
\(128\) | −0.309017 | + | 0.951057i | −0.0273135 | + | 0.0840623i | ||||
\(129\) | −3.32851 | − | 10.2441i | −0.293059 | − | 0.901943i | ||||
\(130\) | 0.913840 | − | 0.663944i | 0.0801491 | − | 0.0582317i | ||||
\(131\) | −1.04772 | −0.0915400 | −0.0457700 | − | 0.998952i | \(-0.514574\pi\) | ||||
−0.0457700 | + | 0.998952i | \(0.514574\pi\) | |||||||
\(132\) | −1.53525 | + | 7.83847i | −0.133627 | + | 0.682251i | ||||
\(133\) | 1.05667 | 0.0916253 | ||||||||
\(134\) | −9.62867 | + | 6.99564i | −0.831791 | + | 0.604331i | ||||
\(135\) | −0.511356 | − | 1.57379i | −0.0440105 | − | 0.135450i | ||||
\(136\) | 1.07729 | − | 3.31555i | 0.0923766 | − | 0.284306i | ||||
\(137\) | −7.79713 | − | 5.66494i | −0.666153 | − | 0.483989i | 0.202582 | − | 0.979265i | \(-0.435067\pi\) |
−0.868735 | + | 0.495277i | \(0.835067\pi\) | |||||||
\(138\) | 15.4081 | + | 11.1946i | 1.31162 | + | 0.952950i | ||||
\(139\) | −1.19610 | + | 3.68121i | −0.101452 | + | 0.312236i | −0.988881 | − | 0.148707i | \(-0.952489\pi\) |
0.887430 | + | 0.460943i | \(0.152489\pi\) | |||||||
\(140\) | −1.12113 | − | 3.45049i | −0.0947530 | − | 0.291620i | ||||
\(141\) | 20.0841 | − | 14.5920i | 1.69139 | − | 1.22887i | ||||
\(142\) | 12.6057 | 1.05785 | ||||||||
\(143\) | −0.459719 | − | 0.989554i | −0.0384437 | − | 0.0827507i | ||||
\(144\) | 2.79988 | 0.233323 | ||||||||
\(145\) | −17.2235 | + | 12.5136i | −1.43033 | + | 1.03920i | ||||
\(146\) | 1.34810 | + | 4.14903i | 0.111570 | + | 0.343376i | ||||
\(147\) | 4.37848 | − | 13.4756i | 0.361131 | − | 1.11145i | ||||
\(148\) | −5.19634 | − | 3.77536i | −0.427137 | − | 0.310333i | ||||
\(149\) | 11.1463 | + | 8.09826i | 0.913140 | + | 0.663435i | 0.941807 | − | 0.336154i | \(-0.109126\pi\) |
−0.0286669 | + | 0.999589i | \(0.509126\pi\) | |||||||
\(150\) | 5.05220 | − | 15.5491i | 0.412510 | − | 1.26958i | ||||
\(151\) | 5.60789 | + | 17.2593i | 0.456363 | + | 1.40454i | 0.869527 | + | 0.493885i | \(0.164424\pi\) |
−0.413164 | + | 0.910657i | \(0.635576\pi\) | |||||||
\(152\) | 0.809017 | − | 0.587785i | 0.0656199 | − | 0.0476757i | ||||
\(153\) | −9.76085 | −0.789118 | ||||||||
\(154\) | −3.47908 | + | 0.422140i | −0.280352 | + | 0.0340170i | ||||
\(155\) | −7.57774 | −0.608659 | ||||||||
\(156\) | −0.640983 | + | 0.465701i | −0.0513197 | + | 0.0372859i | ||||
\(157\) | −5.77683 | − | 17.7793i | −0.461041 | − | 1.41894i | −0.863894 | − | 0.503674i | \(-0.831981\pi\) |
0.402852 | − | 0.915265i | \(-0.368019\pi\) | |||||||
\(158\) | 4.67972 | − | 14.4027i | 0.372299 | − | 1.14582i | ||||
\(159\) | 0.755376 | + | 0.548813i | 0.0599052 | + | 0.0435237i | ||||
\(160\) | −2.77774 | − | 2.01814i | −0.219599 | − | 0.159548i | ||||
\(161\) | −2.58229 | + | 7.94748i | −0.203513 | + | 0.626349i | ||||
\(162\) | 2.95430 | + | 9.09241i | 0.232112 | + | 0.714367i | ||||
\(163\) | −18.2254 | + | 13.2415i | −1.42752 | + | 1.03716i | −0.437050 | + | 0.899437i | \(0.643977\pi\) |
−0.990471 | + | 0.137718i | \(0.956023\pi\) | |||||||
\(164\) | −4.07985 | −0.318583 | ||||||||
\(165\) | −23.9670 | − | 13.3299i | −1.86583 | − | 1.03773i | ||||
\(166\) | 9.60289 | 0.745329 | ||||||||
\(167\) | 10.2303 | − | 7.43277i | 0.791647 | − | 0.575165i | −0.116805 | − | 0.993155i | \(-0.537265\pi\) |
0.908452 | + | 0.417990i | \(0.137265\pi\) | |||||||
\(168\) | 0.786381 | + | 2.42023i | 0.0606706 | + | 0.186725i | ||||
\(169\) | −3.98378 | + | 12.2608i | −0.306444 | + | 0.943138i | ||||
\(170\) | 9.68367 | + | 7.03560i | 0.742704 | + | 0.539606i | ||||
\(171\) | −2.26515 | − | 1.64573i | −0.173220 | − | 0.125852i | ||||
\(172\) | 1.38210 | − | 4.25368i | 0.105384 | − | 0.324340i | ||||
\(173\) | 4.50828 | + | 13.8751i | 0.342758 | + | 1.05490i | 0.962773 | + | 0.270311i | \(0.0871265\pi\) |
−0.620015 | + | 0.784590i | \(0.712874\pi\) | |||||||
\(174\) | 12.0808 | − | 8.77724i | 0.915846 | − | 0.665401i | ||||
\(175\) | 7.17348 | 0.542264 | ||||||||
\(176\) | −2.42885 | + | 2.25847i | −0.183081 | + | 0.170239i | ||||
\(177\) | 1.83811 | 0.138161 | ||||||||
\(178\) | −5.26239 | + | 3.82335i | −0.394433 | + | 0.286572i | ||||
\(179\) | 1.74130 | + | 5.35917i | 0.130151 | + | 0.400563i | 0.994804 | − | 0.101806i | \(-0.0324620\pi\) |
−0.864653 | + | 0.502369i | \(0.832462\pi\) | |||||||
\(180\) | −2.97067 | + | 9.14279i | −0.221421 | + | 0.681463i | ||||
\(181\) | 0.324711 | + | 0.235917i | 0.0241356 | + | 0.0175355i | 0.599788 | − | 0.800159i | \(-0.295252\pi\) |
−0.575652 | + | 0.817695i | \(0.695252\pi\) | |||||||
\(182\) | −0.281241 | − | 0.204333i | −0.0208469 | − | 0.0151462i | ||||
\(183\) | 2.55221 | − | 7.85488i | 0.188664 | − | 0.580649i | ||||
\(184\) | 2.44379 | + | 7.52122i | 0.180159 | + | 0.554471i | ||||
\(185\) | 17.8415 | − | 12.9626i | 1.31173 | − | 0.953030i | ||||
\(186\) | 5.31515 | 0.389726 | ||||||||
\(187\) | 8.46739 | − | 7.87342i | 0.619197 | − | 0.575761i | ||||
\(188\) | 10.3083 | 0.751808 | ||||||||
\(189\) | −0.412008 | + | 0.299342i | −0.0299692 | + | 0.0217739i | ||||
\(190\) | 1.06100 | + | 3.26543i | 0.0769731 | + | 0.236899i | ||||
\(191\) | −3.45316 | + | 10.6277i | −0.249862 | + | 0.768995i | 0.744937 | + | 0.667135i | \(0.232479\pi\) |
−0.994799 | + | 0.101860i | \(0.967521\pi\) | |||||||
\(192\) | 1.94835 | + | 1.41556i | 0.140610 | + | 0.102159i | ||||
\(193\) | −19.3491 | − | 14.0579i | −1.39278 | − | 1.01191i | −0.995554 | − | 0.0941884i | \(-0.969974\pi\) |
−0.397222 | − | 0.917723i | \(-0.630026\pi\) | |||||||
\(194\) | 1.48528 | − | 4.57122i | 0.106637 | − | 0.328194i | ||||
\(195\) | −0.840629 | − | 2.58719i | −0.0601987 | − | 0.185273i | ||||
\(196\) | 4.75980 | − | 3.45820i | 0.339986 | − | 0.247014i | ||||
\(197\) | 24.8502 | 1.77050 | 0.885251 | − | 0.465114i | \(-0.153987\pi\) | ||||
0.885251 | + | 0.465114i | \(0.153987\pi\) | |||||||
\(198\) | 8.11541 | + | 4.51359i | 0.576737 | + | 0.320767i | ||||
\(199\) | −24.4565 | −1.73368 | −0.866838 | − | 0.498589i | \(-0.833852\pi\) | ||||
−0.866838 | + | 0.498589i | \(0.833852\pi\) | |||||||
\(200\) | 5.49220 | − | 3.99031i | 0.388357 | − | 0.282158i | ||||
\(201\) | 8.85728 | + | 27.2599i | 0.624745 | + | 1.92277i | ||||
\(202\) | 1.66843 | − | 5.13489i | 0.117390 | − | 0.361290i | ||||
\(203\) | 5.30064 | + | 3.85114i | 0.372032 | + | 0.270297i | ||||
\(204\) | −6.79228 | − | 4.93488i | −0.475555 | − | 0.345511i | ||||
\(205\) | 4.32873 | − | 13.3224i | 0.302331 | − | 0.930480i | ||||
\(206\) | 3.36832 | + | 10.3666i | 0.234682 | + | 0.722277i | ||||
\(207\) | 17.9134 | − | 13.0149i | 1.24507 | − | 0.904595i | ||||
\(208\) | −0.328987 | −0.0228112 | ||||||||
\(209\) | 3.29248 | − | 0.399499i | 0.227745 | − | 0.0276339i | ||||
\(210\) | −8.73744 | −0.602940 | ||||||||
\(211\) | −2.82564 | + | 2.05295i | −0.194525 | + | 0.141331i | −0.680785 | − | 0.732484i | \(-0.738361\pi\) |
0.486259 | + | 0.873814i | \(0.338361\pi\) | |||||||
\(212\) | 0.119806 | + | 0.368725i | 0.00822831 | + | 0.0253241i | ||||
\(213\) | 9.38122 | − | 28.8724i | 0.642791 | − | 1.97831i | ||||
\(214\) | 4.33813 | + | 3.15184i | 0.296548 | + | 0.215455i | ||||
\(215\) | 12.4236 | + | 9.02631i | 0.847286 | + | 0.615589i | ||||
\(216\) | −0.148933 | + | 0.458367i | −0.0101336 | + | 0.0311879i | ||||
\(217\) | 0.720659 | + | 2.21796i | 0.0489215 | + | 0.150565i | ||||
\(218\) | −2.15540 | + | 1.56599i | −0.145982 | + | 0.106062i | ||||
\(219\) | 10.5063 | 0.709950 | ||||||||
\(220\) | −4.79785 | − | 10.3275i | −0.323471 | − | 0.696278i | ||||
\(221\) | 1.14691 | 0.0771493 | ||||||||
\(222\) | −12.5143 | + | 9.09218i | −0.839906 | + | 0.610227i | ||||
\(223\) | −5.48537 | − | 16.8822i | −0.367328 | − | 1.13052i | −0.948511 | − | 0.316745i | \(-0.897410\pi\) |
0.581183 | − | 0.813773i | \(-0.302590\pi\) | |||||||
\(224\) | −0.326530 | + | 1.00496i | −0.0218172 | + | 0.0671465i | ||||
\(225\) | −15.3775 | − | 11.1724i | −1.02516 | − | 0.744826i | ||||
\(226\) | −12.9999 | − | 9.44499i | −0.864741 | − | 0.628271i | ||||
\(227\) | 5.85007 | − | 18.0047i | 0.388283 | − | 1.19501i | −0.545788 | − | 0.837924i | \(-0.683769\pi\) |
0.934071 | − | 0.357088i | \(-0.116231\pi\) | |||||||
\(228\) | −0.744204 | − | 2.29042i | −0.0492861 | − | 0.151687i | ||||
\(229\) | −2.44841 | + | 1.77888i | −0.161796 | + | 0.117552i | −0.665737 | − | 0.746186i | \(-0.731883\pi\) |
0.503941 | + | 0.863738i | \(0.331883\pi\) | |||||||
\(230\) | −27.1528 | −1.79041 | ||||||||
\(231\) | −1.62226 | + | 8.28271i | −0.106737 | + | 0.544962i | ||||
\(232\) | 6.20055 | 0.407086 | ||||||||
\(233\) | −13.4216 | + | 9.75133i | −0.879276 | + | 0.638831i | −0.933060 | − | 0.359721i | \(-0.882872\pi\) |
0.0537841 | + | 0.998553i | \(0.482872\pi\) | |||||||
\(234\) | 0.284643 | + | 0.876041i | 0.0186077 | + | 0.0572686i | ||||
\(235\) | −10.9371 | + | 33.6609i | −0.713457 | + | 2.19579i | ||||
\(236\) | 0.617477 | + | 0.448623i | 0.0401943 | + | 0.0292029i | ||||
\(237\) | −29.5056 | − | 21.4371i | −1.91660 | − | 1.39249i | ||||
\(238\) | 1.13834 | − | 3.50345i | 0.0737877 | − | 0.227095i | ||||
\(239\) | 4.94944 | + | 15.2328i | 0.320153 | + | 0.985329i | 0.973581 | + | 0.228341i | \(0.0733300\pi\) |
−0.653429 | + | 0.756988i | \(0.726670\pi\) | |||||||
\(240\) | −6.68961 | + | 4.86028i | −0.431812 | + | 0.313730i | ||||
\(241\) | −22.3425 | −1.43921 | −0.719604 | − | 0.694384i | \(-0.755677\pi\) | ||||
−0.719604 | + | 0.694384i | \(0.755677\pi\) | |||||||
\(242\) | −10.6808 | + | 2.63068i | −0.686588 | + | 0.169107i | ||||
\(243\) | 21.5782 | 1.38424 | ||||||||
\(244\) | 2.77448 | − | 2.01578i | 0.177618 | − | 0.129047i | ||||
\(245\) | 6.24234 | + | 19.2119i | 0.398808 | + | 1.22741i | ||||
\(246\) | −3.03624 | + | 9.34458i | −0.193584 | + | 0.595789i | ||||
\(247\) | 0.266156 | + | 0.193374i | 0.0169351 | + | 0.0123041i | ||||
\(248\) | 1.78552 | + | 1.29725i | 0.113380 | + | 0.0823757i | ||||
\(249\) | 7.14651 | − | 21.9947i | 0.452892 | − | 1.39386i | ||||
\(250\) | 1.89784 | + | 5.84096i | 0.120030 | + | 0.369415i | ||||
\(251\) | −3.19923 | + | 2.32438i | −0.201934 | + | 0.146713i | −0.684157 | − | 0.729335i | \(-0.739830\pi\) |
0.482223 | + | 0.876049i | \(0.339830\pi\) | |||||||
\(252\) | 2.95856 | 0.186372 | ||||||||
\(253\) | −5.04141 | + | 25.7397i | −0.316951 | + | 1.61824i | ||||
\(254\) | −17.8339 | −1.11900 | ||||||||
\(255\) | 23.3211 | − | 16.9438i | 1.46042 | − | 1.06106i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | 7.81691 | − | 24.0580i | 0.487605 | − | 1.50069i | −0.340567 | − | 0.940220i | \(-0.610619\pi\) |
0.828172 | − | 0.560474i | \(-0.189381\pi\) | |||||||
\(258\) | −8.71415 | − | 6.33120i | −0.542519 | − | 0.394163i | ||||
\(259\) | −5.49084 | − | 3.98933i | −0.341184 | − | 0.247885i | ||||
\(260\) | 0.349056 | − | 1.07428i | 0.0216475 | − | 0.0666242i | ||||
\(261\) | −5.36477 | − | 16.5111i | −0.332071 | − | 1.02201i | ||||
\(262\) | −0.847626 | + | 0.615836i | −0.0523665 | + | 0.0380465i | ||||
\(263\) | −14.7586 | −0.910056 | −0.455028 | − | 0.890477i | \(-0.650371\pi\) | ||||
−0.455028 | + | 0.890477i | \(0.650371\pi\) | |||||||
\(264\) | 3.36529 | + | 7.24386i | 0.207120 | + | 0.445828i | ||||
\(265\) | −1.33116 | −0.0817724 | ||||||||
\(266\) | 0.854868 | − | 0.621098i | 0.0524153 | − | 0.0380819i | ||||
\(267\) | 4.84080 | + | 14.8984i | 0.296252 | + | 0.911770i | ||||
\(268\) | −3.67783 | + | 11.3192i | −0.224659 | + | 0.691429i | ||||
\(269\) | −16.1888 | − | 11.7619i | −0.987049 | − | 0.717133i | −0.0277761 | − | 0.999614i | \(-0.508843\pi\) |
−0.959273 | + | 0.282481i | \(0.908843\pi\) | |||||||
\(270\) | −1.33875 | − | 0.972656i | −0.0814735 | − | 0.0591940i | ||||
\(271\) | 7.25670 | − | 22.3338i | 0.440813 | − | 1.35668i | −0.446197 | − | 0.894935i | \(-0.647222\pi\) |
0.887010 | − | 0.461749i | \(-0.152778\pi\) | |||||||
\(272\) | −1.07729 | − | 3.31555i | −0.0653201 | − | 0.201035i | ||||
\(273\) | −0.677310 | + | 0.492094i | −0.0409927 | + | 0.0297829i | ||||
\(274\) | −9.63778 | −0.582239 | ||||||||
\(275\) | 22.3517 | − | 2.71209i | 1.34786 | − | 0.163545i | ||||
\(276\) | 19.0454 | 1.14640 | ||||||||
\(277\) | 14.6899 | − | 10.6729i | 0.882632 | − | 0.641270i | −0.0513142 | − | 0.998683i | \(-0.516341\pi\) |
0.933947 | + | 0.357413i | \(0.116341\pi\) | |||||||
\(278\) | 1.19610 | + | 3.68121i | 0.0717371 | + | 0.220784i | ||||
\(279\) | 1.90954 | − | 5.87695i | 0.114321 | − | 0.351844i | ||||
\(280\) | −2.93516 | − | 2.13252i | −0.175410 | − | 0.127443i | ||||
\(281\) | −2.22572 | − | 1.61708i | −0.132775 | − | 0.0964668i | 0.519415 | − | 0.854522i | \(-0.326150\pi\) |
−0.652191 | + | 0.758055i | \(0.726150\pi\) | |||||||
\(282\) | 7.67145 | − | 23.6103i | 0.456828 | − | 1.40597i | ||||
\(283\) | −7.83172 | − | 24.1036i | −0.465548 | − | 1.43281i | −0.858292 | − | 0.513161i | \(-0.828474\pi\) |
0.392745 | − | 0.919648i | \(-0.371526\pi\) | |||||||
\(284\) | 10.1982 | − | 7.40946i | 0.605154 | − | 0.439670i | ||||
\(285\) | 8.26881 | 0.489802 | ||||||||
\(286\) | −0.953566 | − | 0.530350i | −0.0563855 | − | 0.0313602i | ||||
\(287\) | −4.31107 | −0.254475 | ||||||||
\(288\) | 2.26515 | − | 1.64573i | 0.133475 | − | 0.0969753i | ||||
\(289\) | −1.49768 | − | 4.60939i | −0.0880990 | − | 0.271141i | ||||
\(290\) | −6.57879 | + | 20.2474i | −0.386320 | + | 1.18897i | ||||
\(291\) | −9.36467 | − | 6.80383i | −0.548967 | − | 0.398848i | ||||
\(292\) | 3.52938 | + | 2.56424i | 0.206541 | + | 0.150061i | ||||
\(293\) | 0.154794 | − | 0.476408i | 0.00904319 | − | 0.0278321i | −0.946433 | − | 0.322900i | \(-0.895342\pi\) |
0.955476 | + | 0.295068i | \(0.0953423\pi\) | |||||||
\(294\) | −4.37848 | − | 13.4756i | −0.255358 | − | 0.785911i | ||||
\(295\) | −2.12009 | + | 1.54034i | −0.123436 | + | 0.0896818i | ||||
\(296\) | −6.42303 | −0.373331 | ||||||||
\(297\) | −1.17060 | + | 1.08848i | −0.0679250 | + | 0.0631602i | ||||
\(298\) | 13.7776 | 0.798114 | ||||||||
\(299\) | −2.10484 | + | 1.52925i | −0.121726 | + | 0.0884390i | ||||
\(300\) | −5.05220 | − | 15.5491i | −0.291689 | − | 0.897725i | ||||
\(301\) | 1.46043 | − | 4.49475i | 0.0841779 | − | 0.259073i | ||||
\(302\) | 14.6816 | + | 10.6668i | 0.844833 | + | 0.613807i | ||||
\(303\) | −10.5194 | − | 7.64281i | −0.604325 | − | 0.439068i | ||||
\(304\) | 0.309017 | − | 0.951057i | 0.0177233 | − | 0.0545468i | ||||
\(305\) | 3.63864 | + | 11.1986i | 0.208348 | + | 0.641230i | ||||
\(306\) | −7.89670 | + | 5.73729i | −0.451424 | + | 0.327979i | ||||
\(307\) | 10.6138 | 0.605762 | 0.302881 | − | 0.953028i | \(-0.402052\pi\) | ||||
0.302881 | + | 0.953028i | \(0.402052\pi\) | |||||||
\(308\) | −2.56650 | + | 2.38647i | −0.146240 | + | 0.135982i | ||||
\(309\) | 26.2507 | 1.49335 | ||||||||
\(310\) | −6.13052 | + | 4.45409i | −0.348190 | + | 0.252975i | ||||
\(311\) | −3.12776 | − | 9.62626i | −0.177359 | − | 0.545855i | 0.822374 | − | 0.568947i | \(-0.192649\pi\) |
−0.999733 | + | 0.0230917i | \(0.992649\pi\) | |||||||
\(312\) | −0.244834 | + | 0.753520i | −0.0138610 | + | 0.0426597i | ||||
\(313\) | 7.80229 | + | 5.66869i | 0.441011 | + | 0.320414i | 0.786037 | − | 0.618180i | \(-0.212130\pi\) |
−0.345025 | + | 0.938593i | \(0.612130\pi\) | |||||||
\(314\) | −15.1239 | − | 10.9882i | −0.853493 | − | 0.620099i | ||||
\(315\) | −3.13903 | + | 9.66095i | −0.176864 | + | 0.544333i | ||||
\(316\) | −4.67972 | − | 14.4027i | −0.263255 | − | 0.810215i | ||||
\(317\) | −22.5821 | + | 16.4069i | −1.26834 | + | 0.921502i | −0.999135 | − | 0.0415818i | \(-0.986760\pi\) |
−0.269203 | + | 0.963083i | \(0.586760\pi\) | |||||||
\(318\) | 0.933696 | 0.0523591 | ||||||||
\(319\) | 17.9722 | + | 9.99570i | 1.00625 | + | 0.559652i | ||||
\(320\) | −3.43347 | −0.191937 | ||||||||
\(321\) | 10.4475 | − | 7.59054i | 0.583122 | − | 0.423663i | ||||
\(322\) | 2.58229 | + | 7.94748i | 0.143905 | + | 0.442896i | ||||
\(323\) | −1.07729 | + | 3.31555i | −0.0599418 | + | 0.184482i | ||||
\(324\) | 7.73446 | + | 5.61942i | 0.429692 | + | 0.312190i | ||||
\(325\) | 1.80686 | + | 1.31276i | 0.100227 | + | 0.0728190i | ||||
\(326\) | −6.96147 | + | 21.4252i | −0.385560 | + | 1.18663i | ||||
\(327\) | 1.98272 | + | 6.10219i | 0.109645 | + | 0.337452i | ||||
\(328\) | −3.30067 | + | 2.39808i | −0.182249 | + | 0.132412i | ||||
\(329\) | 10.8925 | 0.600522 | ||||||||
\(330\) | −27.2249 | + | 3.30338i | −1.49868 | + | 0.181845i | ||||
\(331\) | 1.00668 | 0.0553319 | 0.0276659 | − | 0.999617i | \(-0.491193\pi\) | ||||
0.0276659 | + | 0.999617i | \(0.491193\pi\) | |||||||
\(332\) | 7.76891 | − | 5.64444i | 0.426374 | − | 0.309779i | ||||
\(333\) | 5.55727 | + | 17.1035i | 0.304536 | + | 0.937267i | ||||
\(334\) | 3.90764 | − | 12.0265i | 0.213816 | − | 0.658059i | ||||
\(335\) | −33.0598 | − | 24.0193i | −1.80625 | − | 1.31232i | ||||
\(336\) | 2.05877 | + | 1.49579i | 0.112315 | + | 0.0816018i | ||||
\(337\) | 2.79242 | − | 8.59418i | 0.152113 | − | 0.468155i | −0.845744 | − | 0.533589i | \(-0.820843\pi\) |
0.997857 | + | 0.0654337i | \(0.0208431\pi\) | |||||||
\(338\) | 3.98378 | + | 12.2608i | 0.216689 | + | 0.666900i | ||||
\(339\) | −31.3076 | + | 22.7463i | −1.70040 | + | 1.23541i | ||||
\(340\) | 11.9697 | 0.649147 | ||||||||
\(341\) | 3.08404 | + | 6.63845i | 0.167010 | + | 0.359492i | ||||
\(342\) | −2.79988 | −0.151400 | ||||||||
\(343\) | 11.0136 | − | 8.00187i | 0.594680 | − | 0.432061i | ||||
\(344\) | −1.38210 | − | 4.25368i | −0.0745180 | − | 0.229343i | ||||
\(345\) | −20.2072 | + | 62.1915i | −1.08792 | + | 3.34828i | ||||
\(346\) | 11.8028 | + | 8.57525i | 0.634524 | + | 0.461009i | ||||
\(347\) | 23.1396 | + | 16.8119i | 1.24220 | + | 0.902511i | 0.997743 | − | 0.0671488i | \(-0.0213902\pi\) |
0.244457 | + | 0.969660i | \(0.421390\pi\) | |||||||
\(348\) | 4.61447 | − | 14.2019i | 0.247361 | − | 0.761300i | ||||
\(349\) | 2.03829 | + | 6.27322i | 0.109107 | + | 0.335798i | 0.990672 | − | 0.136265i | \(-0.0435097\pi\) |
−0.881565 | + | 0.472062i | \(0.843510\pi\) | |||||||
\(350\) | 5.80346 | − | 4.21646i | 0.310208 | − | 0.225379i | ||||
\(351\) | −0.158557 | −0.00846317 | ||||||||
\(352\) | −0.637485 | + | 3.25478i | −0.0339781 | + | 0.173481i | ||||
\(353\) | −10.2956 | −0.547980 | −0.273990 | − | 0.961732i | \(-0.588344\pi\) | ||||
−0.273990 | + | 0.961732i | \(0.588344\pi\) | |||||||
\(354\) | 1.48707 | − | 1.08042i | 0.0790366 | − | 0.0574235i | ||||
\(355\) | 13.3747 | + | 41.1630i | 0.709855 | + | 2.18471i | ||||
\(356\) | −2.01005 | + | 6.18631i | −0.106533 | + | 0.327874i | ||||
\(357\) | −7.17723 | − | 5.21457i | −0.379859 | − | 0.275984i | ||||
\(358\) | 4.55878 | + | 3.31215i | 0.240939 | + | 0.175053i | ||||
\(359\) | 6.23315 | − | 19.1837i | 0.328973 | − | 1.01248i | −0.640642 | − | 0.767840i | \(-0.721332\pi\) |
0.969615 | − | 0.244636i | \(-0.0786684\pi\) | |||||||
\(360\) | 2.97067 | + | 9.14279i | 0.156568 | + | 0.481867i | ||||
\(361\) | −0.809017 | + | 0.587785i | −0.0425798 | + | 0.0309361i | ||||
\(362\) | 0.401365 | 0.0210953 | ||||||||
\(363\) | −1.92332 | + | 26.4213i | −0.100948 | + | 1.38676i | ||||
\(364\) | −0.347632 | −0.0182209 | ||||||||
\(365\) | −12.1180 | + | 8.80425i | −0.634286 | + | 0.460836i | ||||
\(366\) | −2.55221 | − | 7.85488i | −0.133406 | − | 0.410581i | ||||
\(367\) | 9.84135 | − | 30.2886i | 0.513714 | − | 1.58105i | −0.271895 | − | 0.962327i | \(-0.587650\pi\) |
0.785609 | − | 0.618723i | \(-0.212350\pi\) | |||||||
\(368\) | 6.39793 | + | 4.64837i | 0.333515 | + | 0.242313i | ||||
\(369\) | 9.24146 | + | 6.71432i | 0.481091 | + | 0.349533i | ||||
\(370\) | 6.81485 | − | 20.9739i | 0.354287 | − | 1.09038i | ||||
\(371\) | 0.126596 | + | 0.389622i | 0.00657253 | + | 0.0202282i | ||||
\(372\) | 4.30005 | − | 3.12417i | 0.222947 | − | 0.161981i | ||||
\(373\) | 24.0754 | 1.24658 | 0.623290 | − | 0.781991i | \(-0.285796\pi\) | ||||
0.623290 | + | 0.781991i | \(0.285796\pi\) | |||||||
\(374\) | 2.22238 | − | 11.3467i | 0.114917 | − | 0.586726i | ||||
\(375\) | 14.7906 | 0.763786 | ||||||||
\(376\) | 8.33956 | − | 6.05905i | 0.430080 | − | 0.312472i | ||||
\(377\) | 0.630364 | + | 1.94006i | 0.0324654 | + | 0.0999182i | ||||
\(378\) | −0.157373 | + | 0.484345i | −0.00809440 | + | 0.0249120i | ||||
\(379\) | 3.49284 | + | 2.53770i | 0.179415 | + | 0.130353i | 0.673868 | − | 0.738852i | \(-0.264632\pi\) |
−0.494453 | + | 0.869204i | \(0.664632\pi\) | |||||||
\(380\) | 2.77774 | + | 2.01814i | 0.142495 | + | 0.103529i | ||||
\(381\) | −13.2720 | + | 40.8471i | −0.679946 | + | 2.09266i | ||||
\(382\) | 3.45316 | + | 10.6277i | 0.176679 | + | 0.543761i | ||||
\(383\) | 6.92535 | − | 5.03156i | 0.353869 | − | 0.257101i | −0.396621 | − | 0.917982i | \(-0.629817\pi\) |
0.750490 | + | 0.660882i | \(0.229817\pi\) | |||||||
\(384\) | 2.40829 | 0.122898 | ||||||||
\(385\) | −5.06977 | − | 10.9128i | −0.258379 | − | 0.556166i | ||||
\(386\) | −23.9168 | −1.21733 | ||||||||
\(387\) | −10.1311 | + | 7.36064i | −0.514990 | + | 0.374162i | ||||
\(388\) | −1.48528 | − | 4.57122i | −0.0754036 | − | 0.232068i | ||||
\(389\) | 3.28968 | − | 10.1246i | 0.166793 | − | 0.513337i | −0.832371 | − | 0.554219i | \(-0.813017\pi\) |
0.999164 | + | 0.0408822i | \(0.0130168\pi\) | |||||||
\(390\) | −2.20080 | − | 1.59897i | −0.111442 | − | 0.0809671i | ||||
\(391\) | −22.3043 | − | 16.2050i | −1.12798 | − | 0.819523i | ||||
\(392\) | 1.81808 | − | 5.59548i | 0.0918270 | − | 0.282615i | ||||
\(393\) | 0.779719 | + | 2.39973i | 0.0393316 | + | 0.121050i | ||||
\(394\) | 20.1042 | − | 14.6066i | 1.01284 | − | 0.735868i | ||||
\(395\) | 51.9961 | 2.61621 | ||||||||
\(396\) | 9.21853 | − | 1.11855i | 0.463248 | − | 0.0562091i | ||||
\(397\) | −19.1392 | −0.960569 | −0.480285 | − | 0.877113i | \(-0.659467\pi\) | ||||
−0.480285 | + | 0.877113i | \(0.659467\pi\) | |||||||
\(398\) | −19.7857 | + | 14.3752i | −0.991769 | + | 0.720563i | ||||
\(399\) | −0.786381 | − | 2.42023i | −0.0393683 | − | 0.121163i | ||||
\(400\) | 2.09783 | − | 6.45646i | 0.104892 | − | 0.322823i | ||||
\(401\) | 4.13138 | + | 3.00163i | 0.206311 | + | 0.149894i | 0.686143 | − | 0.727466i | \(-0.259302\pi\) |
−0.479832 | + | 0.877360i | \(0.659302\pi\) | |||||||
\(402\) | 23.1887 | + | 16.8476i | 1.15655 | + | 0.840280i | ||||
\(403\) | −0.224372 | + | 0.690545i | −0.0111767 | + | 0.0343985i | ||||
\(404\) | −1.66843 | − | 5.13489i | −0.0830074 | − | 0.255471i | ||||
\(405\) | −26.5561 | + | 19.2941i | −1.31958 | + | 0.958732i | ||||
\(406\) | 6.55196 | 0.325168 | ||||||||
\(407\) | −18.6171 | − | 10.3544i | −0.922815 | − | 0.513247i | ||||
\(408\) | −8.39573 | −0.415650 | ||||||||
\(409\) | 15.6587 | − | 11.3767i | 0.774271 | − | 0.562541i | −0.128983 | − | 0.991647i | \(-0.541171\pi\) |
0.903254 | + | 0.429106i | \(0.141171\pi\) | |||||||
\(410\) | −4.32873 | − | 13.3224i | −0.213781 | − | 0.657949i | ||||
\(411\) | −7.17247 | + | 22.0746i | −0.353792 | + | 1.08886i | ||||
\(412\) | 8.81838 | + | 6.40693i | 0.434450 | + | 0.315647i | ||||
\(413\) | 0.652472 | + | 0.474049i | 0.0321061 | + | 0.0233264i | ||||
\(414\) | 6.84231 | − | 21.0585i | 0.336281 | − | 1.03497i | ||||
\(415\) | 10.1887 | + | 31.3575i | 0.500143 | + | 1.53928i | ||||
\(416\) | −0.266156 | + | 0.193374i | −0.0130494 | + | 0.00948094i | ||||
\(417\) | 9.32166 | 0.456483 | ||||||||
\(418\) | 2.42885 | − | 2.25847i | 0.118799 | − | 0.110465i | ||||
\(419\) | −9.86427 | −0.481901 | −0.240951 | − | 0.970537i | \(-0.577459\pi\) | ||||
−0.240951 | + | 0.970537i | \(0.577459\pi\) | |||||||
\(420\) | −7.06873 | + | 5.13574i | −0.344919 | + | 0.250598i | ||||
\(421\) | 7.53847 | + | 23.2010i | 0.367403 | + | 1.13075i | 0.948463 | + | 0.316888i | \(0.102638\pi\) |
−0.581060 | + | 0.813860i | \(0.697362\pi\) | |||||||
\(422\) | −1.07930 | + | 3.32174i | −0.0525394 | + | 0.161700i | ||||
\(423\) | −23.3497 | − | 16.9646i | −1.13530 | − | 0.824846i | ||||
\(424\) | 0.313656 | + | 0.227885i | 0.0152325 | + | 0.0110671i | ||||
\(425\) | −7.31341 | + | 22.5083i | −0.354752 | + | 1.09182i | ||||
\(426\) | −9.38122 | − | 28.8724i | −0.454522 | − | 1.39887i | ||||
\(427\) | 2.93172 | − | 2.13002i | 0.141876 | − | 0.103079i | ||||
\(428\) | 5.36222 | 0.259193 | ||||||||
\(429\) | −1.92437 | + | 1.78938i | −0.0929096 | + | 0.0863921i | ||||
\(430\) | 15.3565 | 0.740555 | ||||||||
\(431\) | −12.8013 | + | 9.30069i | −0.616617 | + | 0.447998i | −0.851738 | − | 0.523968i | \(-0.824451\pi\) |
0.235121 | + | 0.971966i | \(0.424451\pi\) | |||||||
\(432\) | 0.148933 | + | 0.458367i | 0.00716552 | + | 0.0220532i | ||||
\(433\) | 3.08362 | − | 9.49041i | 0.148189 | − | 0.456080i | −0.849218 | − | 0.528043i | \(-0.822926\pi\) |
0.997407 | + | 0.0719624i | \(0.0229261\pi\) | |||||||
\(434\) | 1.88671 | + | 1.37078i | 0.0905650 | + | 0.0657993i | ||||
\(435\) | 41.4792 | + | 30.1364i | 1.98878 | + | 1.44493i | ||||
\(436\) | −0.823290 | + | 2.53383i | −0.0394284 | + | 0.121348i | ||||
\(437\) | −2.44379 | − | 7.52122i | −0.116902 | − | 0.359789i | ||||
\(438\) | 8.49978 | − | 6.17545i | 0.406135 | − | 0.295074i | ||||
\(439\) | −26.9775 | −1.28757 | −0.643783 | − | 0.765208i | \(-0.722636\pi\) | ||||
−0.643783 | + | 0.765208i | \(0.722636\pi\) | |||||||
\(440\) | −9.95188 | − | 5.53499i | −0.474437 | − | 0.263870i | ||||
\(441\) | −16.4729 | −0.784424 | ||||||||
\(442\) | 0.927867 | − | 0.674135i | 0.0441341 | − | 0.0320653i | ||||
\(443\) | −6.29218 | − | 19.3653i | −0.298951 | − | 0.920075i | −0.981866 | − | 0.189578i | \(-0.939288\pi\) |
0.682915 | − | 0.730498i | \(-0.260712\pi\) | |||||||
\(444\) | −4.78004 | + | 14.7115i | −0.226851 | + | 0.698175i | ||||
\(445\) | −18.0683 | − | 13.1274i | −0.856518 | − | 0.622296i | ||||
\(446\) | −14.3609 | − | 10.4338i | −0.680008 | − | 0.494055i | ||||
\(447\) | 10.2533 | − | 31.5565i | 0.484966 | − | 1.49257i | ||||
\(448\) | 0.326530 | + | 1.00496i | 0.0154271 | + | 0.0474798i | ||||
\(449\) | −7.46859 | + | 5.42625i | −0.352465 | + | 0.256081i | −0.749902 | − | 0.661549i | \(-0.769900\pi\) |
0.397438 | + | 0.917629i | \(0.369900\pi\) | |||||||
\(450\) | −19.0076 | −0.896027 | ||||||||
\(451\) | −13.4328 | + | 1.62989i | −0.632526 | + | 0.0767487i | ||||
\(452\) | −16.0688 | −0.755812 | ||||||||
\(453\) | 35.3577 | − | 25.6889i | 1.66125 | − | 1.20697i | ||||
\(454\) | −5.85007 | − | 18.0047i | −0.274557 | − | 0.845001i | ||||
\(455\) | 0.368838 | − | 1.13517i | 0.0172914 | − | 0.0532175i | ||||
\(456\) | −1.94835 | − | 1.41556i | −0.0912399 | − | 0.0662896i | ||||
\(457\) | −15.5083 | − | 11.2675i | −0.725450 | − | 0.527070i | 0.162671 | − | 0.986680i | \(-0.447989\pi\) |
−0.888121 | + | 0.459610i | \(0.847989\pi\) | |||||||
\(458\) | −0.935211 | + | 2.87828i | −0.0436995 | + | 0.134493i | ||||
\(459\) | −0.519204 | − | 1.59795i | −0.0242344 | − | 0.0745858i | ||||
\(460\) | −21.9671 | + | 15.9600i | −1.02422 | + | 0.744141i | ||||
\(461\) | 34.2672 | 1.59598 | 0.797991 | − | 0.602669i | \(-0.205896\pi\) | ||||
0.797991 | + | 0.602669i | \(0.205896\pi\) | |||||||
\(462\) | 3.55602 | + | 7.65440i | 0.165441 | + | 0.356115i | ||||
\(463\) | −1.71478 | −0.0796927 | −0.0398463 | − | 0.999206i | \(-0.512687\pi\) | ||||
−0.0398463 | + | 0.999206i | \(0.512687\pi\) | |||||||
\(464\) | 5.01635 | − | 3.64459i | 0.232878 | − | 0.169196i | ||||
\(465\) | 5.63938 | + | 17.3562i | 0.261520 | + | 0.804876i | ||||
\(466\) | −5.12658 | + | 15.7780i | −0.237484 | + | 0.730901i | ||||
\(467\) | 25.2744 | + | 18.3630i | 1.16956 | + | 0.849736i | 0.990956 | − | 0.134185i | \(-0.0428415\pi\) |
0.178605 | + | 0.983921i | \(0.442842\pi\) | |||||||
\(468\) | 0.745205 | + | 0.541423i | 0.0344471 | + | 0.0250273i | ||||
\(469\) | −3.88626 | + | 11.9607i | −0.179451 | + | 0.552293i | ||||
\(470\) | 10.9371 | + | 33.6609i | 0.504490 | + | 1.55266i | ||||
\(471\) | −36.4229 | + | 26.4628i | −1.67828 | + | 1.21934i | ||||
\(472\) | 0.763244 | 0.0351311 | ||||||||
\(473\) | 2.85120 | − | 14.5573i | 0.131098 | − | 0.669344i | ||||
\(474\) | −36.4709 | −1.67517 | ||||||||
\(475\) | −5.49220 | + | 3.99031i | −0.251999 | + | 0.183088i | ||||
\(476\) | −1.13834 | − | 3.50345i | −0.0521758 | − | 0.160581i | ||||
\(477\) | 0.335442 | − | 1.03238i | 0.0153588 | − | 0.0472696i | ||||
\(478\) | 12.9578 | + | 9.41440i | 0.592676 | + | 0.430605i | ||||
\(479\) | 33.8867 | + | 24.6201i | 1.54832 | + | 1.12492i | 0.944835 | + | 0.327548i | \(0.106222\pi\) |
0.603486 | + | 0.797373i | \(0.293778\pi\) | |||||||
\(480\) | −2.55520 | + | 7.86410i | −0.116628 | + | 0.358946i | ||||
\(481\) | −0.652983 | − | 2.00967i | −0.0297735 | − | 0.0916333i | ||||
\(482\) | −18.0755 | + | 13.1326i | −0.823316 | + | 0.598174i | ||||
\(483\) | 20.1248 | 0.915712 | ||||||||
\(484\) | −7.09468 | + | 8.40628i | −0.322485 | + | 0.382104i | ||||
\(485\) | 16.5028 | 0.749356 | ||||||||
\(486\) | 17.4571 | − | 12.6833i | 0.791871 | − | 0.575328i | ||||
\(487\) | −5.75022 | − | 17.6973i | −0.260567 | − | 0.801943i | −0.992682 | − | 0.120762i | \(-0.961466\pi\) |
0.732114 | − | 0.681182i | \(-0.238534\pi\) | |||||||
\(488\) | 1.05976 | − | 3.26160i | 0.0479729 | − | 0.147646i | ||||
\(489\) | 43.8921 | + | 31.8894i | 1.98487 | + | 1.44209i | ||||
\(490\) | 16.3426 | + | 11.8736i | 0.738286 | + | 0.536396i | ||||
\(491\) | −1.42767 | + | 4.39391i | −0.0644298 | + | 0.198294i | −0.978089 | − | 0.208186i | \(-0.933244\pi\) |
0.913659 | + | 0.406480i | \(0.133244\pi\) | |||||||
\(492\) | 3.03624 | + | 9.34458i | 0.136884 | + | 0.421286i | ||||
\(493\) | −17.4878 | + | 12.7057i | −0.787613 | + | 0.572234i | ||||
\(494\) | 0.328987 | 0.0148018 | ||||||||
\(495\) | −6.12834 | + | 31.2892i | −0.275448 | + | 1.40634i | ||||
\(496\) | 2.20702 | 0.0990982 | ||||||||
\(497\) | 10.7762 | − | 7.82938i | 0.483380 | − | 0.351196i | ||||
\(498\) | −7.14651 | − | 21.9947i | −0.320243 | − | 0.985606i | ||||
\(499\) | 3.30931 | − | 10.1850i | 0.148145 | − | 0.455943i | −0.849257 | − | 0.527979i | \(-0.822950\pi\) |
0.997402 | + | 0.0720364i | \(0.0229498\pi\) | |||||||
\(500\) | 4.96862 | + | 3.60991i | 0.222203 | + | 0.161440i | ||||
\(501\) | −24.6376 | − | 17.9003i | −1.10073 | − | 0.799726i | ||||
\(502\) | −1.22200 | + | 3.76092i | −0.0545404 | + | 0.167858i | ||||
\(503\) | −6.74982 | − | 20.7738i | −0.300959 | − | 0.926258i | −0.981154 | − | 0.193227i | \(-0.938105\pi\) |
0.680195 | − | 0.733031i | \(-0.261895\pi\) | |||||||
\(504\) | 2.39352 | − | 1.73900i | 0.106616 | − | 0.0774611i | ||||
\(505\) | 18.5378 | 0.824922 | ||||||||
\(506\) | 11.0508 | + | 23.7871i | 0.491270 | + | 1.05747i | ||||
\(507\) | 31.0472 | 1.37885 | ||||||||
\(508\) | −14.4279 | + | 10.4825i | −0.640134 | + | 0.465085i | ||||
\(509\) | 11.6423 | + | 35.8314i | 0.516037 | + | 1.58820i | 0.781388 | + | 0.624045i | \(0.214512\pi\) |
−0.265352 | + | 0.964152i | \(0.585488\pi\) | |||||||
\(510\) | 8.90787 | − | 27.4156i | 0.394447 | − | 1.21398i | ||||
\(511\) | 3.72940 | + | 2.70957i | 0.164979 | + | 0.119864i | ||||
\(512\) | 0.809017 | + | 0.587785i | 0.0357538 | + | 0.0259767i | ||||
\(513\) | 0.148933 | − | 0.458367i | 0.00657553 | − | 0.0202374i | ||||
\(514\) | −7.81691 | − | 24.0580i | −0.344789 | − | 1.06115i | ||||
\(515\) | −30.2777 | + | 21.9980i | −1.33419 | + | 0.969348i | ||||
\(516\) | −10.7713 | −0.474179 | ||||||||
\(517\) | 33.9397 | − | 4.11814i | 1.49267 | − | 0.181116i | ||||
\(518\) | −6.78705 | −0.298206 | ||||||||
\(519\) | 28.4247 | − | 20.6517i | 1.24770 | − | 0.906510i | ||||
\(520\) | −0.349056 | − | 1.07428i | −0.0153071 | − | 0.0471105i | ||||
\(521\) | 1.18872 | − | 3.65850i | 0.0520786 | − | 0.160282i | −0.921635 | − | 0.388059i | \(-0.873146\pi\) |
0.973713 | + | 0.227777i | \(0.0731458\pi\) | |||||||
\(522\) | −14.0452 | − | 10.2044i | −0.614740 | − | 0.446634i | ||||
\(523\) | −26.4220 | − | 19.1967i | −1.15535 | − | 0.839414i | −0.166171 | − | 0.986097i | \(-0.553140\pi\) |
−0.989184 | + | 0.146682i | \(0.953140\pi\) | |||||||
\(524\) | −0.323764 | + | 0.996444i | −0.0141437 | + | 0.0435299i | ||||
\(525\) | −5.33853 | − | 16.4303i | −0.232992 | − | 0.717077i | ||||
\(526\) | −11.9400 | + | 8.67490i | −0.520608 | + | 0.378244i | ||||
\(527\) | −7.69406 | −0.335158 | ||||||||
\(528\) | 6.98041 | + | 3.88233i | 0.303783 | + | 0.168957i | ||||
\(529\) | 39.5408 | 1.71917 | ||||||||
\(530\) | −1.07693 | + | 0.782435i | −0.0467788 | + | 0.0339868i | ||||
\(531\) | −0.660365 | − | 2.03240i | −0.0286574 | − | 0.0881985i | ||||
\(532\) | 0.326530 | − | 1.00496i | 0.0141569 | − | 0.0435704i | ||||
\(533\) | −1.08588 | − | 0.788937i | −0.0470346 | − | 0.0341726i | ||||
\(534\) | 12.6734 | + | 9.20774i | 0.548430 | + | 0.398458i | ||||
\(535\) | −5.68932 | + | 17.5099i | −0.245971 | + | 0.757021i | ||||
\(536\) | 3.67783 | + | 11.3192i | 0.158858 | + | 0.488914i | ||||
\(537\) | 10.9789 | − | 7.97663i | 0.473774 | − | 0.344217i | ||||
\(538\) | −20.0105 | −0.862712 | ||||||||
\(539\) | 14.2900 | − | 13.2876i | 0.615513 | − | 0.572336i | ||||
\(540\) | −1.65478 | −0.0712105 | ||||||||
\(541\) | −26.8602 | + | 19.5151i | −1.15481 | + | 0.839020i | −0.989113 | − | 0.147156i | \(-0.952988\pi\) |
−0.165699 | + | 0.986176i | \(0.552988\pi\) | |||||||
\(542\) | −7.25670 | − | 22.3338i | −0.311702 | − | 0.959321i | ||||
\(543\) | 0.298698 | − | 0.919297i | 0.0128183 | − | 0.0394508i | ||||
\(544\) | −2.82037 | − | 2.04912i | −0.120922 | − | 0.0878553i | ||||
\(545\) | −7.40051 | − | 5.37678i | −0.317003 | − | 0.230316i | ||||
\(546\) | −0.258709 | + | 0.796225i | −0.0110717 | + | 0.0340753i | ||||
\(547\) | 11.5142 | + | 35.4372i | 0.492313 | + | 1.51518i | 0.821103 | + | 0.570781i | \(0.193359\pi\) |
−0.328790 | + | 0.944403i | \(0.606641\pi\) | |||||||
\(548\) | −7.79713 | + | 5.66494i | −0.333077 | + | 0.241994i | ||||
\(549\) | −9.60202 | −0.409804 | ||||||||
\(550\) | 16.4888 | − | 15.3321i | 0.703085 | − | 0.653765i | ||||
\(551\) | −6.20055 | −0.264152 | ||||||||
\(552\) | 15.4081 | − | 11.1946i | 0.655812 | − | 0.476475i | ||||
\(553\) | −4.94494 | − | 15.2190i | −0.210280 | − | 0.647176i | ||||
\(554\) | 5.61105 | − | 17.2690i | 0.238391 | − | 0.733692i | ||||
\(555\) | −42.9676 | − | 31.2178i | −1.82387 | − | 1.32512i | ||||
\(556\) | 3.13142 | + | 2.27511i | 0.132802 | + | 0.0964862i | ||||
\(557\) | 1.69335 | − | 5.21159i | 0.0717495 | − | 0.220822i | −0.908751 | − | 0.417339i | \(-0.862963\pi\) |
0.980501 | + | 0.196516i | \(0.0629629\pi\) | |||||||
\(558\) | −1.90954 | − | 5.87695i | −0.0808371 | − | 0.248791i | ||||
\(559\) | 1.19041 | − | 0.864880i | 0.0503488 | − | 0.0365805i | ||||
\(560\) | −3.62806 | −0.153314 | ||||||||
\(561\) | −24.3349 | − | 13.5345i | −1.02742 | − | 0.571426i | ||||
\(562\) | −2.75114 | −0.116050 | ||||||||
\(563\) | −32.5043 | + | 23.6158i | −1.36989 | + | 0.995287i | −0.372150 | + | 0.928173i | \(0.621379\pi\) |
−0.997745 | + | 0.0671142i | \(0.978621\pi\) | |||||||
\(564\) | −7.67145 | − | 23.6103i | −0.323026 | − | 0.994173i | ||||
\(565\) | 17.0490 | − | 52.4714i | 0.717256 | − | 2.20749i | ||||
\(566\) | −20.5037 | − | 14.8968i | −0.861836 | − | 0.626160i | ||||
\(567\) | 8.17281 | + | 5.93789i | 0.343226 | + | 0.249368i | ||||
\(568\) | 3.89538 | − | 11.9888i | 0.163447 | − | 0.503037i | ||||
\(569\) | −10.3170 | − | 31.7524i | −0.432511 | − | 1.33113i | −0.895616 | − | 0.444828i | \(-0.853265\pi\) |
0.463106 | − | 0.886303i | \(-0.346735\pi\) | |||||||
\(570\) | 6.68961 | − | 4.86028i | 0.280197 | − | 0.203575i | ||||
\(571\) | −30.1103 | −1.26008 | −0.630038 | − | 0.776564i | \(-0.716961\pi\) | ||||
−0.630038 | + | 0.776564i | \(0.716961\pi\) | |||||||
\(572\) | −1.08318 | + | 0.131430i | −0.0452902 | + | 0.00549536i | ||||
\(573\) | 26.9118 | 1.12426 | ||||||||
\(574\) | −3.48773 | + | 2.53399i | −0.145575 | + | 0.105767i | ||||
\(575\) | −16.5902 | − | 51.0595i | −0.691861 | − | 2.12933i | ||||
\(576\) | 0.865209 | − | 2.66284i | 0.0360504 | − | 0.110952i | ||||
\(577\) | 9.24959 | + | 6.72022i | 0.385066 | + | 0.279767i | 0.763430 | − | 0.645890i | \(-0.223514\pi\) |
−0.378365 | + | 0.925657i | \(0.623514\pi\) | |||||||
\(578\) | −3.92098 | − | 2.84876i | −0.163091 | − | 0.118493i | ||||
\(579\) | −17.7989 | + | 54.7795i | −0.739699 | + | 2.27656i | ||||
\(580\) | 6.57879 | + | 20.2474i | 0.273169 | + | 0.840728i | ||||
\(581\) | 8.20920 | − | 5.96434i | 0.340575 | − | 0.247442i | ||||
\(582\) | −11.5754 | −0.479814 | ||||||||
\(583\) | 0.541764 | + | 1.16616i | 0.0224376 | + | 0.0482972i | ||||
\(584\) | 4.36255 | 0.180524 | ||||||||
\(585\) | −2.55864 | + | 1.85896i | −0.105787 | + | 0.0768586i | ||||
\(586\) | −0.154794 | − | 0.476408i | −0.00639450 | − | 0.0196802i | ||||
\(587\) | −1.13763 | + | 3.50125i | −0.0469548 | + | 0.144512i | −0.971785 | − | 0.235868i | \(-0.924207\pi\) |
0.924830 | + | 0.380380i | \(0.124207\pi\) | |||||||
\(588\) | −11.4630 | − | 8.32836i | −0.472726 | − | 0.343456i | ||||
\(589\) | −1.78552 | − | 1.29725i | −0.0735710 | − | 0.0534524i | ||||
\(590\) | −0.809802 | + | 2.49231i | −0.0333390 | + | 0.102607i | ||||
\(591\) | −18.4936 | − | 56.9174i | −0.760725 | − | 2.34127i | ||||
\(592\) | −5.19634 | + | 3.77536i | −0.213568 | + | 0.155167i | ||||
\(593\) | −9.81520 | −0.403062 | −0.201531 | − | 0.979482i | \(-0.564592\pi\) | ||||
−0.201531 | + | 0.979482i | \(0.564592\pi\) | |||||||
\(594\) | −0.307240 | + | 1.56866i | −0.0126062 | + | 0.0643630i | ||||
\(595\) | 12.6480 | 0.518519 | ||||||||
\(596\) | 11.1463 | − | 8.09826i | 0.456570 | − | 0.331718i | ||||
\(597\) | 18.2006 | + | 56.0158i | 0.744902 | + | 2.29257i | ||||
\(598\) | −0.803976 | + | 2.47438i | −0.0328770 | + | 0.101185i | ||||
\(599\) | 3.11410 | + | 2.26252i | 0.127239 | + | 0.0924443i | 0.649584 | − | 0.760290i | \(-0.274943\pi\) |
−0.522346 | + | 0.852734i | \(0.674943\pi\) | |||||||
\(600\) | −13.2268 | − | 9.60985i | −0.539983 | − | 0.392320i | ||||
\(601\) | 6.14577 | − | 18.9148i | 0.250691 | − | 0.771549i | −0.743957 | − | 0.668228i | \(-0.767053\pi\) |
0.994648 | − | 0.103321i | \(-0.0329469\pi\) | |||||||
\(602\) | −1.46043 | − | 4.49475i | −0.0595228 | − | 0.183192i | ||||
\(603\) | 26.9591 | − | 19.5869i | 1.09786 | − | 0.797641i | ||||
\(604\) | 18.1475 | 0.738411 | ||||||||
\(605\) | −19.9226 | − | 32.0862i | −0.809970 | − | 1.30449i | ||||
\(606\) | −13.0027 | −0.528200 | ||||||||
\(607\) | −6.07452 | + | 4.41340i | −0.246557 | + | 0.179134i | −0.704200 | − | 0.710002i | \(-0.748694\pi\) |
0.457642 | + | 0.889136i | \(0.348694\pi\) | |||||||
\(608\) | −0.309017 | − | 0.951057i | −0.0125323 | − | 0.0385704i | ||||
\(609\) | 4.87599 | − | 15.0068i | 0.197585 | − | 0.608104i | ||||
\(610\) | 9.52610 | + | 6.92111i | 0.385700 | + | 0.280228i | ||||
\(611\) | 2.74361 | + | 1.99335i | 0.110995 | + | 0.0806423i | ||||
\(612\) | −3.01627 | + | 9.28312i | −0.121925 | + | 0.375248i | ||||
\(613\) | 0.214923 | + | 0.661466i | 0.00868067 | + | 0.0267164i | 0.955303 | − | 0.295628i | \(-0.0955290\pi\) |
−0.946622 | + | 0.322345i | \(0.895529\pi\) | |||||||
\(614\) | 8.58675 | − | 6.23864i | 0.346533 | − | 0.251771i | ||||
\(615\) | −33.7355 | −1.36035 | ||||||||
\(616\) | −0.673614 | + | 3.43925i | −0.0271407 | + | 0.138571i | ||||
\(617\) | −0.548806 | −0.0220941 | −0.0110471 | − | 0.999939i | \(-0.503516\pi\) | ||||
−0.0110471 | + | 0.999939i | \(0.503516\pi\) | |||||||
\(618\) | 21.2372 | − | 15.4298i | 0.854287 | − | 0.620676i | ||||
\(619\) | −12.7916 | − | 39.3685i | −0.514138 | − | 1.58236i | −0.784844 | − | 0.619693i | \(-0.787257\pi\) |
0.270706 | − | 0.962662i | \(-0.412743\pi\) | |||||||
\(620\) | −2.34165 | + | 7.20686i | −0.0940430 | + | 0.289435i | ||||
\(621\) | 3.08352 | + | 2.24031i | 0.123737 | + | 0.0899004i | ||||
\(622\) | −8.18859 | − | 5.94936i | −0.328332 | − | 0.238547i | ||||
\(623\) | −2.12397 | + | 6.53691i | −0.0850951 | + | 0.261896i | ||||
\(624\) | 0.244834 | + | 0.753520i | 0.00980119 | + | 0.0301649i | ||||
\(625\) | 10.4014 | − | 7.55704i | 0.416055 | − | 0.302282i | ||||
\(626\) | 9.64416 | 0.385458 | ||||||||
\(627\) | −3.36529 | − | 7.24386i | −0.134397 | − | 0.289292i | ||||
\(628\) | −18.6942 | −0.745980 | ||||||||
\(629\) | 18.1153 | − | 13.1616i | 0.722306 | − | 0.524786i | ||||
\(630\) | 3.13903 | + | 9.66095i | 0.125062 | + | 0.384902i | ||||
\(631\) | −2.19126 | + | 6.74401i | −0.0872328 | + | 0.268475i | −0.985152 | − | 0.171686i | \(-0.945079\pi\) |
0.897919 | + | 0.440161i | \(0.145079\pi\) | |||||||
\(632\) | −12.2517 | − | 8.90136i | −0.487345 | − | 0.354077i | ||||
\(633\) | 6.80497 | + | 4.94410i | 0.270473 | + | 0.196510i | ||||
\(634\) | −8.62560 | + | 26.5469i | −0.342566 | + | 1.05431i | ||||
\(635\) | −18.9217 | − | 58.2352i | −0.750887 | − | 2.31099i | ||||
\(636\) | 0.755376 | − | 0.548813i | 0.0299526 | − | 0.0217618i | ||||
\(637\) | 1.93558 | 0.0766903 | ||||||||
\(638\) | 20.4151 | − | 2.47711i | 0.808243 | − | 0.0980697i | ||||
\(639\) | −35.2945 | −1.39623 | ||||||||
\(640\) | −2.77774 | + | 2.01814i | −0.109800 | + | 0.0797741i | ||||
\(641\) | 6.94537 | + | 21.3756i | 0.274326 | + | 0.844287i | 0.989397 | + | 0.145236i | \(0.0463941\pi\) |
−0.715071 | + | 0.699051i | \(0.753606\pi\) | |||||||
\(642\) | 3.99058 | − | 12.2818i | 0.157496 | − | 0.484722i | ||||
\(643\) | −3.13820 | − | 2.28004i | −0.123759 | − | 0.0899158i | 0.524184 | − | 0.851605i | \(-0.324370\pi\) |
−0.647943 | + | 0.761689i | \(0.724370\pi\) | |||||||
\(644\) | 6.76053 | + | 4.91181i | 0.266402 | + | 0.193552i | ||||
\(645\) | 11.4283 | − | 35.1728i | 0.449991 | − | 1.38493i | ||||
\(646\) | 1.07729 | + | 3.31555i | 0.0423853 | + | 0.130448i | ||||
\(647\) | −8.28292 | + | 6.01790i | −0.325635 | + | 0.236588i | −0.738576 | − | 0.674170i | \(-0.764502\pi\) |
0.412941 | + | 0.910758i | \(0.364502\pi\) | |||||||
\(648\) | 9.56032 | 0.375565 | ||||||||
\(649\) | 2.21225 | + | 1.23040i | 0.0868385 | + | 0.0482974i | ||||
\(650\) | 2.23341 | 0.0876014 | ||||||||
\(651\) | 4.54375 | − | 3.30123i | 0.178084 | − | 0.129385i | ||||
\(652\) | 6.96147 | + | 21.4252i | 0.272632 | + | 0.839076i | ||||
\(653\) | −4.52089 | + | 13.9139i | −0.176916 | + | 0.544491i | −0.999716 | − | 0.0238399i | \(-0.992411\pi\) |
0.822800 | + | 0.568331i | \(0.192411\pi\) | |||||||
\(654\) | 5.19084 | + | 3.77136i | 0.202978 | + | 0.147472i | ||||
\(655\) | −2.91030 | − | 2.11446i | −0.113715 | − | 0.0826187i | ||||
\(656\) | −1.26074 | + | 3.88017i | −0.0492237 | + | 0.151495i | ||||
\(657\) | −3.77452 | − | 11.6168i | −0.147258 | − | 0.453214i | ||||
\(658\) | 8.81220 | − | 6.40244i | 0.343535 | − | 0.249593i | ||||
\(659\) | 23.4146 | 0.912102 | 0.456051 | − | 0.889954i | \(-0.349263\pi\) | ||||
0.456051 | + | 0.889954i | \(0.349263\pi\) | |||||||
\(660\) | −20.0837 | + | 18.6749i | −0.781757 | + | 0.726918i | ||||
\(661\) | 5.06352 | 0.196948 | 0.0984740 | − | 0.995140i | \(-0.468604\pi\) | ||||
0.0984740 | + | 0.995140i | \(0.468604\pi\) | |||||||
\(662\) | 0.814417 | − | 0.591709i | 0.0316532 | − | 0.0229974i | ||||
\(663\) | −0.853532 | − | 2.62690i | −0.0331484 | − | 0.102020i | ||||
\(664\) | 2.96746 | − | 9.13290i | 0.115160 | − | 0.354425i | ||||
\(665\) | 2.93516 | + | 2.13252i | 0.113821 | + | 0.0826956i | ||||
\(666\) | 14.5491 | + | 10.5706i | 0.563767 | + | 0.409601i | ||||
\(667\) | 15.1528 | − | 46.6356i | 0.586720 | − | 1.80574i | ||||
\(668\) | −3.90764 | − | 12.0265i | −0.151191 | − | 0.465318i | ||||
\(669\) | −34.5852 | + | 25.1276i | −1.33714 | + | 0.971491i | ||||
\(670\) | −40.8641 | −1.57872 | ||||||||
\(671\) | 8.32961 | − | 7.74530i | 0.321561 | − | 0.299004i | ||||
\(672\) | 2.54478 | 0.0981671 | ||||||||
\(673\) | −10.9078 | + | 7.92501i | −0.420466 | + | 0.305486i | −0.777825 | − | 0.628481i | \(-0.783677\pi\) |
0.357359 | + | 0.933967i | \(0.383677\pi\) | |||||||
\(674\) | −2.79242 | − | 8.59418i | −0.107560 | − | 0.331035i | ||||
\(675\) | 1.01106 | − | 3.11173i | 0.0389158 | − | 0.119771i | ||||
\(676\) | 10.4297 | + | 7.57759i | 0.401141 | + | 0.291446i | ||||
\(677\) | 21.2023 | + | 15.4044i | 0.814871 | + | 0.592039i | 0.915239 | − | 0.402912i | \(-0.132002\pi\) |
−0.100368 | + | 0.994950i | \(0.532002\pi\) | |||||||
\(678\) | −11.9584 | + | 36.8043i | −0.459261 | + | 1.41346i | ||||
\(679\) | −1.56946 | − | 4.83029i | −0.0602302 | − | 0.185369i | ||||
\(680\) | 9.68367 | − | 7.03560i | 0.371352 | − | 0.269803i | ||||
\(681\) | −45.5920 | −1.74709 | ||||||||
\(682\) | 6.39703 | + | 3.55787i | 0.244955 | + | 0.136238i | ||||
\(683\) | −24.1621 | −0.924536 | −0.462268 | − | 0.886740i | \(-0.652964\pi\) | ||||
−0.462268 | + | 0.886740i | \(0.652964\pi\) | |||||||
\(684\) | −2.26515 | + | 1.64573i | −0.0866101 | + | 0.0629259i | ||||
\(685\) | −10.2257 | − | 31.4714i | −0.390704 | − | 1.20246i | ||||
\(686\) | 4.20683 | − | 12.9473i | 0.160618 | − | 0.494330i | ||||
\(687\) | 5.89650 | + | 4.28406i | 0.224966 | + | 0.163447i | ||||
\(688\) | −3.61839 | − | 2.62892i | −0.137950 | − | 0.100226i | ||||
\(689\) | −0.0394147 | + | 0.121306i | −0.00150158 | + | 0.00462138i | ||||
\(690\) | 20.2072 | + | 62.1915i | 0.769276 | + | 2.36759i | ||||
\(691\) | 27.5510 | − | 20.0169i | 1.04809 | − | 0.761480i | 0.0762400 | − | 0.997089i | \(-0.475708\pi\) |
0.971848 | + | 0.235609i | \(0.0757085\pi\) | |||||||
\(692\) | 14.5891 | 0.554594 | ||||||||
\(693\) | 9.74098 | − | 1.18194i | 0.370029 | − | 0.0448982i | ||||
\(694\) | 28.6021 | 1.08572 | ||||||||
\(695\) | −10.7516 | + | 7.81153i | −0.407833 | + | 0.296308i | ||||
\(696\) | −4.61447 | − | 14.2019i | −0.174911 | − | 0.538321i | ||||
\(697\) | 4.39517 | − | 13.5269i | 0.166479 | − | 0.512369i | ||||
\(698\) | 5.33632 | + | 3.87706i | 0.201983 | + | 0.146749i | ||||
\(699\) | 32.3231 | + | 23.4841i | 1.22257 | + | 0.888249i | ||||
\(700\) | 2.21673 | − | 6.82238i | 0.0837844 | − | 0.257862i | ||||
\(701\) | −6.51256 | − | 20.0436i | −0.245976 | − | 0.757036i | −0.995474 | − | 0.0950300i | \(-0.969705\pi\) |
0.749499 | − | 0.662006i | \(-0.230295\pi\) | |||||||
\(702\) | −0.128276 | + | 0.0931977i | −0.00484145 | + | 0.00351752i | ||||
\(703\) | 6.42303 | 0.242249 | ||||||||
\(704\) | 1.39738 | + | 3.00788i | 0.0526656 | + | 0.113364i | ||||
\(705\) | 85.2371 | 3.21021 | ||||||||
\(706\) | −8.32933 | + | 6.05161i | −0.313478 | + | 0.227755i | ||||
\(707\) | −1.76299 | − | 5.42591i | −0.0663039 | − | 0.204062i | ||||
\(708\) | 0.568009 | − | 1.74815i | 0.0213471 | − | 0.0656995i | ||||
\(709\) | 8.50727 | + | 6.18089i | 0.319497 | + | 0.232128i | 0.735961 | − | 0.677024i | \(-0.236731\pi\) |
−0.416464 | + | 0.909152i | \(0.636731\pi\) | |||||||
\(710\) | 35.0154 | + | 25.4402i | 1.31410 | + | 0.954752i | ||||
\(711\) | −13.1026 | + | 40.3258i | −0.491387 | + | 1.51234i | ||||
\(712\) | 2.01005 | + | 6.18631i | 0.0753299 | + | 0.231842i | ||||
\(713\) | 14.1204 | − | 10.2590i | 0.528812 | − | 0.384204i | ||||
\(714\) | −8.87155 | −0.332009 | ||||||||
\(715\) | 0.720083 | − | 3.67650i | 0.0269296 | − | 0.137493i | ||||
\(716\) | 5.63497 | 0.210589 | ||||||||
\(717\) | 31.2062 | − | 22.6726i | 1.16542 | − | 0.846725i | ||||
\(718\) | −6.23315 | − | 19.1837i | −0.232619 | − | 0.715928i | ||||
\(719\) | 13.2455 | − | 40.7654i | 0.493973 | − | 1.52029i | −0.324579 | − | 0.945859i | \(-0.605223\pi\) |
0.818552 | − | 0.574433i | \(-0.194777\pi\) | |||||||
\(720\) | 7.77732 | + | 5.65055i | 0.289844 | + | 0.210584i | ||||
\(721\) | 9.31816 | + | 6.77004i | 0.347026 | + | 0.252129i | ||||
\(722\) | −0.309017 | + | 0.951057i | −0.0115004 | + | 0.0353947i | ||||
\(723\) | 16.6274 | + | 51.1738i | 0.618379 | + | 1.90318i | ||||
\(724\) | 0.324711 | − | 0.235917i | 0.0120678 | − | 0.00876777i | ||||
\(725\) | −42.0938 | −1.56333 | ||||||||
\(726\) | 13.9741 | + | 22.5058i | 0.518626 | + | 0.835268i | ||||
\(727\) | −17.8183 | −0.660843 | −0.330422 | − | 0.943833i | \(-0.607191\pi\) | ||||
−0.330422 | + | 0.943833i | \(0.607191\pi\) | |||||||
\(728\) | −0.281241 | + | 0.204333i | −0.0104235 | + | 0.00757309i | ||||
\(729\) | −7.19566 | − | 22.1460i | −0.266506 | − | 0.820221i | ||||
\(730\) | −4.62867 | + | 14.2456i | −0.171315 | + | 0.527253i | ||||
\(731\) | 12.6143 | + | 9.16485i | 0.466558 | + | 0.338974i | ||||
\(732\) | −6.68176 | − | 4.85458i | −0.246965 | − | 0.179431i | ||||
\(733\) | 14.3337 | − | 44.1145i | 0.529426 | − | 1.62941i | −0.225967 | − | 0.974135i | \(-0.572554\pi\) |
0.755393 | − | 0.655272i | \(-0.227446\pi\) | |||||||
\(734\) | −9.84135 | − | 30.2886i | −0.363251 | − | 1.11797i | ||||
\(735\) | 39.3579 | − | 28.5952i | 1.45174 | − | 1.05475i | ||||
\(736\) | 7.90827 | 0.291503 | ||||||||
\(737\) | −7.58716 | + | 38.7374i | −0.279476 | + | 1.42691i | ||||
\(738\) | 11.4231 | 0.420489 | ||||||||
\(739\) | −36.3539 | + | 26.4127i | −1.33730 | + | 0.971605i | −0.337761 | + | 0.941232i | \(0.609670\pi\) |
−0.999539 | + | 0.0303734i | \(0.990330\pi\) | |||||||
\(740\) | −6.81485 | − | 20.9739i | −0.250519 | − | 0.771017i | ||||
\(741\) | 0.244834 | − | 0.753520i | 0.00899418 | − | 0.0276813i | ||||
\(742\) | 0.331432 | + | 0.240800i | 0.0121673 | + | 0.00884004i | ||||
\(743\) | −38.8009 | − | 28.1905i | −1.42347 | − | 1.03421i | −0.991187 | − | 0.132472i | \(-0.957709\pi\) |
−0.432281 | − | 0.901739i | \(-0.642291\pi\) | |||||||
\(744\) | 1.64247 | − | 5.05501i | 0.0602160 | − | 0.185326i | ||||
\(745\) | 14.6180 | + | 44.9897i | 0.535563 | + | 1.64829i | ||||
\(746\) | 19.4774 | − | 14.1512i | 0.713120 | − | 0.518112i | ||||
\(747\) | −26.8869 | −0.983741 | ||||||||
\(748\) | −4.87150 | − | 10.4860i | −0.178120 | − | 0.383406i | ||||
\(749\) | 5.66612 | 0.207036 | ||||||||
\(750\) | 11.9659 | − | 8.69372i | 0.436932 | − | 0.317450i | ||||
\(751\) | 14.2888 | + | 43.9765i | 0.521407 | + | 1.60473i | 0.771313 | + | 0.636456i | \(0.219600\pi\) |
−0.249906 | + | 0.968270i | \(0.580400\pi\) | |||||||
\(752\) | 3.18543 | − | 9.80375i | 0.116161 | − | 0.357506i | ||||
\(753\) | 7.70468 | + | 5.59778i | 0.280774 | + | 0.203994i | ||||
\(754\) | 1.65031 | + | 1.19902i | 0.0601009 | + | 0.0436659i | ||||
\(755\) | −19.2545 | + | 59.2593i | −0.700744 | + | 2.15667i | ||||
\(756\) | 0.157373 | + | 0.484345i | 0.00572361 | + | 0.0176155i | ||||
\(757\) | −11.6191 | + | 8.44181i | −0.422305 | + | 0.306823i | −0.778565 | − | 0.627564i | \(-0.784052\pi\) |
0.356259 | + | 0.934387i | \(0.384052\pi\) | |||||||
\(758\) | 4.31739 | 0.156815 | ||||||||
\(759\) | 62.7067 | − | 7.60863i | 2.27611 | − | 0.276176i | ||||
\(760\) | 3.43347 | 0.124545 | ||||||||
\(761\) | −3.14574 | + | 2.28551i | −0.114033 | + | 0.0828497i | −0.643340 | − | 0.765580i | \(-0.722452\pi\) |
0.529307 | + | 0.848430i | \(0.322452\pi\) | |||||||
\(762\) | 13.2720 | + | 40.8471i | 0.480795 | + | 1.47973i | ||||
\(763\) | −0.869949 | + | 2.67743i | −0.0314943 | + | 0.0969294i | ||||
\(764\) | 9.04048 | + | 6.56829i | 0.327073 | + | 0.237632i | ||||
\(765\) | −27.1131 | − | 19.6988i | −0.980275 | − | 0.712212i | ||||
\(766\) | 2.64525 | − | 8.14124i | 0.0955767 | − | 0.294155i | ||||
\(767\) | 0.0775934 | + | 0.238808i | 0.00280173 | + | 0.00862285i | ||||
\(768\) | 1.94835 | − | 1.41556i | 0.0703050 | − | 0.0510796i | ||||
\(769\) | −38.5275 | −1.38934 | −0.694669 | − | 0.719329i | \(-0.744449\pi\) | ||||
−0.694669 | + | 0.719329i | \(0.744449\pi\) | |||||||
\(770\) | −10.5159 | − | 5.84868i | −0.378967 | − | 0.210772i | ||||
\(771\) | −60.9203 | −2.19399 | ||||||||
\(772\) | −19.3491 | + | 14.0579i | −0.696388 | + | 0.505956i | ||||
\(773\) | 11.7057 | + | 36.0264i | 0.421024 | + | 1.29578i | 0.906750 | + | 0.421668i | \(0.138555\pi\) |
−0.485726 | + | 0.874111i | \(0.661445\pi\) | |||||||
\(774\) | −3.86972 | + | 11.9098i | −0.139094 | + | 0.428088i | ||||
\(775\) | −12.1214 | − | 8.80671i | −0.435413 | − | 0.316346i | ||||
\(776\) | −3.88851 | − | 2.82517i | −0.139589 | − | 0.101418i | ||||
\(777\) | −5.05095 | + | 15.5452i | −0.181202 | + | 0.557682i | ||||
\(778\) | −3.28968 | − | 10.1246i | −0.117941 | − | 0.362984i | ||||
\(779\) | 3.30067 | − | 2.39808i | 0.118259 | − | 0.0859200i | ||||
\(780\) | −2.72033 | −0.0974035 | ||||||||
\(781\) | 30.6174 | − | 28.4696i | 1.09558 | − | 1.01872i | ||||
\(782\) | −27.5696 | −0.985887 | ||||||||
\(783\) | 2.41766 | − | 1.75653i | 0.0864000 | − | 0.0627733i | ||||
\(784\) | −1.81808 | − | 5.59548i | −0.0649315 | − | 0.199839i | ||||
\(785\) | 19.8346 | − | 61.0446i | 0.707927 | − | 2.17877i | ||||
\(786\) | 2.04133 | + | 1.48311i | 0.0728119 | + | 0.0529009i | ||||
\(787\) | 38.1058 | + | 27.6854i | 1.35832 | + | 0.986880i | 0.998550 | + | 0.0538401i | \(0.0171461\pi\) |
0.359774 | + | 0.933040i | \(0.382854\pi\) | |||||||
\(788\) | 7.67913 | − | 23.6339i | 0.273558 | − | 0.841924i | ||||
\(789\) | 10.9834 | + | 33.8035i | 0.391020 | + | 1.20344i | ||||
\(790\) | 42.0658 | − | 30.5626i | 1.49663 | − | 1.08737i | ||||
\(791\) | −16.9795 | −0.603720 | ||||||||
\(792\) | 6.80048 | − | 6.32344i | 0.241645 | − | 0.224694i | ||||
\(793\) | 1.12824 | 0.0400651 | ||||||||
\(794\) | −15.4839 | + | 11.2497i | −0.549504 | + | 0.399238i | ||||
\(795\) | 0.990653 | + | 3.04892i | 0.0351348 | + | 0.108134i | ||||
\(796\) | −7.55748 | + | 23.2595i | −0.267868 | + | 0.824412i | ||||
\(797\) | 1.92672 | + | 1.39984i | 0.0682479 | + | 0.0495850i | 0.621386 | − | 0.783505i | \(-0.286570\pi\) |
−0.553138 | + | 0.833090i | \(0.686570\pi\) | |||||||
\(798\) | −2.05877 | − | 1.49579i | −0.0728797 | − | 0.0529502i | ||||
\(799\) | −11.1050 | + | 34.1775i | −0.392865 | + | 1.20911i | ||||
\(800\) | −2.09783 | − | 6.45646i | −0.0741696 | − | 0.228270i | ||||
\(801\) | 14.7340 | − | 10.7049i | 0.520602 | − | 0.378239i | ||||
\(802\) | 5.10667 | 0.180323 | ||||||||
\(803\) | 12.6448 | + | 7.03273i | 0.446225 | + | 0.248180i | ||||
\(804\) | 28.6628 | 1.01086 | ||||||||
\(805\) | −23.2121 | + | 16.8646i | −0.818118 | + | 0.594398i | ||||
\(806\) | 0.224372 | + | 0.690545i | 0.00790315 | + | 0.0243234i | ||||
\(807\) | −14.8919 | + | 45.8324i | −0.524218 | + | 1.61338i | ||||
\(808\) | −4.36800 | − | 3.17354i | −0.153666 | − | 0.111645i | ||||
\(809\) | 2.99939 | + | 2.17918i | 0.105453 | + | 0.0766159i | 0.639262 | − | 0.768989i | \(-0.279240\pi\) |
−0.533809 | + | 0.845605i | \(0.679240\pi\) | |||||||
\(810\) | −10.1435 | + | 31.2185i | −0.356407 | + | 1.09691i | ||||
\(811\) | 11.6487 | + | 35.8511i | 0.409042 | + | 1.25890i | 0.917472 | + | 0.397800i | \(0.130226\pi\) |
−0.508430 | + | 0.861103i | \(0.669774\pi\) | |||||||
\(812\) | 5.30064 | − | 3.85114i | 0.186016 | − | 0.135149i | ||||
\(813\) | −56.5544 | −1.98345 | ||||||||
\(814\) | −21.1477 | + | 2.56599i | −0.741226 | + | 0.0899380i | ||||
\(815\) | −77.3486 | −2.70940 | ||||||||
\(816\) | −6.79228 | + | 4.93488i | −0.237778 | + | 0.172755i | ||||
\(817\) | 1.38210 | + | 4.25368i | 0.0483537 | + | 0.148817i | ||||
\(818\) | 5.98107 | − | 18.4079i | 0.209123 | − | 0.643616i | ||||
\(819\) | 0.787439 | + | 0.572108i | 0.0275153 | + | 0.0199911i | ||||
\(820\) | −11.3328 | − | 8.23373i | −0.395757 | − | 0.287534i | ||||
\(821\) | 7.82745 | − | 24.0904i | 0.273180 | − | 0.840761i | −0.716515 | − | 0.697571i | \(-0.754264\pi\) |
0.989695 | − | 0.143190i | \(-0.0457359\pi\) | |||||||
\(822\) | 7.17247 | + | 22.0746i | 0.250169 | + | 0.769940i | ||||
\(823\) | −4.54680 | + | 3.30344i | −0.158491 | + | 0.115151i | −0.664204 | − | 0.747551i | \(-0.731229\pi\) |
0.505713 | + | 0.862702i | \(0.331229\pi\) | |||||||
\(824\) | 10.9001 | 0.379724 | ||||||||
\(825\) | −22.8461 | − | 49.1766i | −0.795398 | − | 1.71211i | ||||
\(826\) | 0.806500 | 0.0280617 | ||||||||
\(827\) | −3.03197 | + | 2.20285i | −0.105432 | + | 0.0766008i | −0.639252 | − | 0.768997i | \(-0.720756\pi\) |
0.533820 | + | 0.845598i | \(0.320756\pi\) | |||||||
\(828\) | −6.84231 | − | 21.0585i | −0.237787 | − | 0.731833i | ||||
\(829\) | 9.83014 | − | 30.2541i | 0.341415 | − | 1.05077i | −0.622060 | − | 0.782969i | \(-0.713704\pi\) |
0.963475 | − | 0.267798i | \(-0.0862959\pi\) | |||||||
\(830\) | 26.6743 | + | 19.3800i | 0.925879 | + | 0.672690i | ||||
\(831\) | −35.3777 | − | 25.7034i | −1.22724 | − | 0.891640i | ||||
\(832\) | −0.101663 | + | 0.312886i | −0.00352452 | + | 0.0108474i | ||||
\(833\) | 6.33815 | + | 19.5068i | 0.219604 | + | 0.675871i | ||||
\(834\) | 7.54138 | − | 5.47913i | 0.261137 | − | 0.189727i | ||||
\(835\) | 43.4176 | 1.50253 | ||||||||
\(836\) | 0.637485 | − | 3.25478i | 0.0220479 | − | 0.112569i | ||||
\(837\) | 1.06369 | 0.0367664 | ||||||||
\(838\) | −7.98036 | + | 5.79807i | −0.275677 | + | 0.200291i | ||||
\(839\) | −14.6207 | − | 44.9978i | −0.504761 | − | 1.55350i | −0.801171 | − | 0.598435i | \(-0.795789\pi\) |
0.296410 | − | 0.955061i | \(-0.404211\pi\) | |||||||
\(840\) | −2.70002 | + | 8.30980i | −0.0931594 | + | 0.286715i | ||||
\(841\) | −7.64259 | − | 5.55267i | −0.263538 | − | 0.191471i | ||||
\(842\) | 19.7360 | + | 14.3390i | 0.680146 | + | 0.494155i | ||||
\(843\) | −2.04741 | + | 6.30127i | −0.0705165 | + | 0.217027i | ||||
\(844\) | 1.07930 | + | 3.32174i | 0.0371510 | + | 0.114339i | ||||
\(845\) | −35.8099 | + | 26.0174i | −1.23190 | + | 0.895027i | ||||
\(846\) | −28.8619 | −0.992292 | ||||||||
\(847\) | −7.49676 | + | 8.88270i | −0.257592 | + | 0.305213i | ||||
\(848\) | 0.387700 | 0.0133137 | ||||||||
\(849\) | −49.3790 | + | 35.8759i | −1.69468 | + | 1.23126i | ||||
\(850\) | 7.31341 | + | 22.5083i | 0.250848 | + | 0.772030i | ||||
\(851\) | −15.6966 | + | 48.3090i | −0.538071 | + | 1.65601i | ||||
\(852\) | −24.5604 | − | 17.8441i | −0.841424 | − | 0.611330i | ||||
\(853\) | 10.5580 | + | 7.67083i | 0.361499 | + | 0.262644i | 0.753677 | − | 0.657245i | \(-0.228278\pi\) |
−0.392178 | + | 0.919889i | \(0.628278\pi\) | |||||||
\(854\) | 1.11982 | − | 3.44645i | 0.0383194 | − | 0.117935i | ||||
\(855\) | −2.97067 | − | 9.14279i | −0.101595 | − | 0.312677i | ||||
\(856\) | 4.33813 | − | 3.15184i | 0.148274 | − | 0.107728i | ||||
\(857\) | 11.1935 | 0.382363 | 0.191181 | − | 0.981555i | \(-0.438768\pi\) | ||||
0.191181 | + | 0.981555i | \(0.438768\pi\) | |||||||
\(858\) | −0.505078 | + | 2.57876i | −0.0172431 | + | 0.0880373i | ||||
\(859\) | −17.1818 | −0.586237 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(860\) | 12.4236 | − | 9.02631i | 0.423643 | − | 0.307795i | ||||
\(861\) | 3.20832 | + | 9.87418i | 0.109339 | + | 0.336511i | ||||
\(862\) | −4.88966 | + | 15.0488i | −0.166542 | + | 0.512565i | ||||
\(863\) | 1.83060 | + | 1.33001i | 0.0623143 | + | 0.0452740i | 0.618506 | − | 0.785780i | \(-0.287738\pi\) |
−0.556192 | + | 0.831054i | \(0.687738\pi\) | |||||||
\(864\) | 0.389910 | + | 0.283287i | 0.0132650 | + | 0.00963760i | ||||
\(865\) | −15.4790 | + | 47.6396i | −0.526303 | + | 1.61980i | ||||
\(866\) | −3.08362 | − | 9.49041i | −0.104786 | − | 0.322497i | ||||
\(867\) | −9.44288 | + | 6.86065i | −0.320697 | + | 0.233000i | ||||
\(868\) | 2.33210 | 0.0791567 | ||||||||
\(869\) | −21.1617 | − | 45.5510i | −0.717863 | − | 1.54521i | ||||
\(870\) | 51.2711 | 1.73825 | ||||||||
\(871\) | −3.16771 | + | 2.30148i | −0.107334 | + | 0.0779826i | ||||
\(872\) | 0.823290 | + | 2.53383i | 0.0278801 | + | 0.0858061i | ||||
\(873\) | −4.15859 | + | 12.7988i | −0.140747 | + | 0.433175i | ||||
\(874\) | −6.39793 | − | 4.64837i | −0.216413 | − | 0.157233i | ||||
\(875\) | 5.25021 | + | 3.81450i | 0.177489 | + | 0.128954i | ||||
\(876\) | 3.24663 | − | 9.99209i | 0.109693 | − | 0.337601i | ||||
\(877\) | −2.21835 | − | 6.82736i | −0.0749082 | − | 0.230544i | 0.906591 | − | 0.422011i | \(-0.138676\pi\) |
−0.981499 | + | 0.191467i | \(0.938676\pi\) | |||||||
\(878\) | −21.8253 | + | 15.8570i | −0.736567 | + | 0.535147i | ||||
\(879\) | −1.20638 | −0.0406900 | ||||||||
\(880\) | −11.3046 | + | 1.37167i | −0.381079 | + | 0.0462389i | ||||
\(881\) | 35.0751 | 1.18171 | 0.590854 | − | 0.806778i | \(-0.298791\pi\) | ||||
0.590854 | + | 0.806778i | \(0.298791\pi\) | |||||||
\(882\) | −13.3269 | + | 9.68253i | −0.448739 | + | 0.326028i | ||||
\(883\) | −9.02356 | − | 27.7717i | −0.303667 | − | 0.934591i | −0.980171 | − | 0.198152i | \(-0.936506\pi\) |
0.676504 | − | 0.736439i | \(-0.263494\pi\) | |||||||
\(884\) | 0.354414 | − | 1.09077i | 0.0119202 | − | 0.0366867i | ||||
\(885\) | 5.10580 | + | 3.70958i | 0.171630 | + | 0.124696i | ||||
\(886\) | −16.4731 | − | 11.9684i | −0.553426 | − | 0.402088i | ||||
\(887\) | 11.8163 | − | 36.3668i | 0.396752 | − | 1.22108i | −0.530836 | − | 0.847474i | \(-0.678122\pi\) |
0.927588 | − | 0.373604i | \(-0.121878\pi\) | |||||||
\(888\) | 4.78004 | + | 14.7115i | 0.160408 | + | 0.493684i | ||||
\(889\) | −15.2456 | + | 11.0766i | −0.511321 | + | 0.371496i | ||||
\(890\) | −22.3336 | −0.748624 | ||||||||
\(891\) | 27.7105 | + | 15.4119i | 0.928336 | + | 0.516318i | ||||
\(892\) | −17.7510 | −0.594349 | ||||||||
\(893\) | −8.33956 | + | 6.05905i | −0.279073 | + | 0.202758i | ||||
\(894\) | −10.2533 | − | 31.5565i | −0.342922 | − | 1.05541i | ||||
\(895\) | −5.97871 | + | 18.4006i | −0.199846 | + | 0.615063i | ||||
\(896\) | 0.854868 | + | 0.621098i | 0.0285591 | + | 0.0207494i | ||||
\(897\) | 5.06907 | + | 3.68289i | 0.169251 | + | 0.122968i | ||||
\(898\) | −2.85275 | + | 8.77986i | −0.0951974 | + | 0.292988i | ||||
\(899\) | −4.22882 | − | 13.0150i | −0.141039 | − | 0.434073i | ||||
\(900\) | −15.3775 | + | 11.1724i | −0.512582 | + | 0.372413i | ||||
\(901\) | −1.35159 | −0.0450280 | ||||||||
\(902\) | −9.90934 | + | 9.21422i | −0.329945 | + | 0.306800i | ||||
\(903\) | −11.3817 | −0.378761 | ||||||||
\(904\) | −12.9999 | + | 9.44499i | −0.432371 | + | 0.314136i | ||||
\(905\) | 0.425849 | + | 1.31063i | 0.0141557 | + | 0.0435668i | ||||
\(906\) | 13.5054 | − | 41.5654i | 0.448688 | − | 1.38092i | ||||
\(907\) | 18.4491 | + | 13.4041i | 0.612592 | + | 0.445074i | 0.850326 | − | 0.526256i | \(-0.176405\pi\) |
−0.237734 | + | 0.971330i | \(0.576405\pi\) | |||||||
\(908\) | −15.3157 | − | 11.1275i | −0.508269 | − | 0.369279i | ||||
\(909\) | −4.67139 | + | 14.3771i | −0.154940 | + | 0.476857i | ||||
\(910\) | −0.368838 | − | 1.13517i | −0.0122269 | − | 0.0376305i | ||||
\(911\) | 11.4175 | − | 8.29528i | 0.378278 | − | 0.274835i | −0.382357 | − | 0.924015i | \(-0.624888\pi\) |
0.760635 | + | 0.649180i | \(0.224888\pi\) | |||||||
\(912\) | −2.40829 | −0.0797466 | ||||||||
\(913\) | 23.3240 | − | 21.6879i | 0.771911 | − | 0.717763i | ||||
\(914\) | −19.1694 | −0.634066 | ||||||||
\(915\) | 22.9416 | − | 16.6681i | 0.758427 | − | 0.551029i | ||||
\(916\) | 0.935211 | + | 2.87828i | 0.0309002 | + | 0.0951012i | ||||
\(917\) | −0.342113 | + | 1.05292i | −0.0112976 | + | 0.0347704i | ||||
\(918\) | −1.35929 | − | 0.987586i | −0.0448634 | − | 0.0325952i | ||||
\(919\) | −23.2763 | − | 16.9112i | −0.767813 | − | 0.557849i | 0.133484 | − | 0.991051i | \(-0.457384\pi\) |
−0.901297 | + | 0.433202i | \(0.857384\pi\) | |||||||
\(920\) | −8.39069 | + | 25.8239i | −0.276633 | + | 0.851388i | ||||
\(921\) | −7.89883 | − | 24.3101i | −0.260275 | − | 0.801045i | ||||
\(922\) | 27.7227 | − | 20.1417i | 0.913000 | − | 0.663333i | ||||
\(923\) | 4.14712 | 0.136504 | ||||||||
\(924\) | 7.37602 | + | 4.10236i | 0.242653 | + | 0.134958i | ||||
\(925\) | 43.6042 | 1.43370 | ||||||||
\(926\) | −1.38729 | + | 1.00792i | −0.0455891 | + | 0.0331224i | ||||
\(927\) | −9.43089 | − | 29.0253i | −0.309751 | − | 0.953315i | ||||
\(928\) | 1.91607 | − | 5.89707i | 0.0628982 | − | 0.193581i | ||||
\(929\) | −20.8634 | − | 15.1581i | −0.684506 | − | 0.497323i | 0.190344 | − | 0.981718i | \(-0.439040\pi\) |
−0.874849 | + | 0.484395i | \(0.839040\pi\) | |||||||
\(930\) | 14.7641 | + | 10.7267i | 0.484134 | + | 0.351744i | ||||
\(931\) | −1.81808 | + | 5.59548i | −0.0595853 | + | 0.183385i | ||||
\(932\) | 5.12658 | + | 15.7780i | 0.167927 | + | 0.516825i | ||||
\(933\) | −19.7205 | + | 14.3278i | −0.645621 | + | 0.469071i | ||||
\(934\) | 31.2409 | 1.02223 | ||||||||
\(935\) | 39.4099 | − | 4.78187i | 1.28884 | − | 0.156384i | ||||
\(936\) | 0.921124 | 0.0301079 | ||||||||
\(937\) | −40.3494 | + | 29.3156i | −1.31816 | + | 0.957698i | −0.318204 | + | 0.948022i | \(0.603080\pi\) |
−0.999953 | + | 0.00967549i | \(0.996920\pi\) | |||||||
\(938\) | 3.88626 | + | 11.9607i | 0.126891 | + | 0.390530i | ||||
\(939\) | 7.17722 | − | 22.0892i | 0.234220 | − | 0.720854i | ||||
\(940\) | 28.6337 | + | 20.8036i | 0.933927 | + | 0.678538i | ||||
\(941\) | 11.1746 | + | 8.11881i | 0.364281 | + | 0.264665i | 0.754835 | − | 0.655914i | \(-0.227717\pi\) |
−0.390555 | + | 0.920580i | \(0.627717\pi\) | |||||||
\(942\) | −13.9123 | + | 42.8177i | −0.453287 | + | 1.39507i | ||||
\(943\) | 9.97030 | + | 30.6854i | 0.324678 | + | 0.999255i | ||||
\(944\) | 0.617477 | − | 0.448623i | 0.0200972 | − | 0.0146014i | ||||
\(945\) | −1.74857 | −0.0568808 | ||||||||
\(946\) | −6.24988 | − | 13.4530i | −0.203201 | − | 0.437394i | ||||
\(947\) | 40.7217 | 1.32328 | 0.661638 | − | 0.749823i | \(-0.269862\pi\) | ||||
0.661638 | + | 0.749823i | \(0.269862\pi\) | |||||||
\(948\) | −29.5056 | + | 21.4371i | −0.958298 | + | 0.696244i | ||||
\(949\) | 0.443509 | + | 1.36498i | 0.0143969 | + | 0.0443091i | ||||
\(950\) | −2.09783 | + | 6.45646i | −0.0680627 | + | 0.209475i | ||||
\(951\) | 54.3844 | + | 39.5126i | 1.76353 | + | 1.28128i | ||||
\(952\) | −2.98022 | − | 2.16525i | −0.0965893 | − | 0.0701763i | ||||
\(953\) | −4.12190 | + | 12.6859i | −0.133522 | + | 0.410937i | −0.995357 | − | 0.0962508i | \(-0.969315\pi\) |
0.861836 | + | 0.507188i | \(0.169315\pi\) | |||||||
\(954\) | −0.335442 | − | 1.03238i | −0.0108603 | − | 0.0334247i | ||||
\(955\) | −31.0402 | + | 22.5520i | −1.00444 | + | 0.729767i | ||||
\(956\) | 16.0167 | 0.518018 | ||||||||
\(957\) | 9.51940 | − | 48.6028i | 0.307718 | − | 1.57111i | ||||
\(958\) | 41.8862 | 1.35328 | ||||||||
\(959\) | −8.23902 | + | 5.98600i | −0.266052 | + | 0.193298i | ||||
\(960\) | 2.55520 | + | 7.86410i | 0.0824688 | + | 0.253813i | ||||
\(961\) | −8.07432 | + | 24.8502i | −0.260462 | + | 0.801620i | ||||
\(962\) | −1.70953 | − | 1.24205i | −0.0551175 | − | 0.0400452i | ||||
\(963\) | −12.1462 | − | 8.82475i | −0.391407 | − | 0.284374i | ||||
\(964\) | −6.90422 | + | 21.2490i | −0.222370 | + | 0.684384i | ||||
\(965\) | −25.3757 | − | 78.0984i | −0.816873 | − | 2.51408i | ||||
\(966\) | 16.2813 | − | 11.8291i | 0.523843 | − | 0.380594i | ||||
\(967\) | 20.4739 | 0.658395 | 0.329197 | − | 0.944261i | \(-0.393222\pi\) | ||||
0.329197 | + | 0.944261i | \(0.393222\pi\) | |||||||
\(968\) | −0.798624 | + | 10.9710i | −0.0256687 | + | 0.352620i | ||||
\(969\) | 8.39573 | 0.269710 | ||||||||
\(970\) | 13.3511 | − | 9.70013i | 0.428677 | − | 0.311452i | ||||
\(971\) | 10.0151 | + | 30.8233i | 0.321399 | + | 0.989166i | 0.973040 | + | 0.230638i | \(0.0740812\pi\) |
−0.651640 | + | 0.758528i | \(0.725919\pi\) | |||||||
\(972\) | 6.66803 | − | 20.5221i | 0.213877 | − | 0.658246i | ||||
\(973\) | 3.30889 | + | 2.40405i | 0.106078 | + | 0.0770703i | ||||
\(974\) | −15.0543 | − | 10.9376i | −0.482370 | − | 0.350462i | ||||
\(975\) | 1.66211 | − | 5.11544i | 0.0532301 | − | 0.163825i | ||||
\(976\) | −1.05976 | − | 3.26160i | −0.0339220 | − | 0.104401i | ||||
\(977\) | −25.1349 | + | 18.2616i | −0.804136 | + | 0.584239i | −0.912125 | − | 0.409913i | \(-0.865559\pi\) |
0.107989 | + | 0.994152i | \(0.465559\pi\) | |||||||
\(978\) | 54.2536 | 1.73484 | ||||||||
\(979\) | −4.14663 | + | 21.1713i | −0.132527 | + | 0.676637i | ||||
\(980\) | 20.2006 | 0.645285 | ||||||||
\(981\) | 6.03486 | − | 4.38458i | 0.192678 | − | 0.139989i | ||||
\(982\) | 1.42767 | + | 4.39391i | 0.0455587 | + | 0.140215i | ||||
\(983\) | −5.88037 | + | 18.0979i | −0.187555 | + | 0.577234i | −0.999983 | − | 0.00582712i | \(-0.998145\pi\) |
0.812428 | + | 0.583061i | \(0.198145\pi\) | |||||||
\(984\) | 7.94898 | + | 5.77527i | 0.253404 | + | 0.184109i | ||||
\(985\) | 69.0272 | + | 50.1512i | 2.19939 | + | 1.59795i | ||||
\(986\) | −6.67976 | + | 20.5582i | −0.212727 | + | 0.654706i | ||||
\(987\) | −8.10622 | − | 24.9484i | −0.258024 | − | 0.794116i | ||||
\(988\) | 0.266156 | − | 0.193374i | 0.00846756 | − | 0.00615204i | ||||
\(989\) | −35.3704 | −1.12471 | ||||||||
\(990\) | 13.4334 | + | 28.9156i | 0.426941 | + | 0.918999i | ||||
\(991\) | 20.3068 | 0.645065 | 0.322533 | − | 0.946558i | \(-0.395466\pi\) | ||||
0.322533 | + | 0.946558i | \(0.395466\pi\) | |||||||
\(992\) | 1.78552 | − | 1.29725i | 0.0566902 | − | 0.0411879i | ||||
\(993\) | −0.749171 | − | 2.30571i | −0.0237742 | − | 0.0731696i | ||||
\(994\) | 4.11615 | − | 12.6682i | 0.130556 | − | 0.401811i | ||||
\(995\) | −67.9338 | − | 49.3568i | −2.15365 | − | 1.56472i | ||||
\(996\) | −18.7098 | − | 13.5935i | −0.592843 | − | 0.430725i | ||||
\(997\) | −5.16849 | + | 15.9070i | −0.163688 | + | 0.503779i | −0.998937 | − | 0.0460924i | \(-0.985323\pi\) |
0.835250 | + | 0.549871i | \(0.185323\pi\) | |||||||
\(998\) | −3.30931 | − | 10.1850i | −0.104754 | − | 0.322400i | ||||
\(999\) | −2.50441 | + | 1.81956i | −0.0792360 | + | 0.0575683i |
(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 | 418.2.f.g.267.1 | yes | 16 | |
11.2 | odd | 10 | 4598.2.a.bz.1.1 | 8 | |||
11.4 | even | 5 | inner | 418.2.f.g.191.1 | ✓ | 16 | |
11.9 | even | 5 | 4598.2.a.bw.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.f.g.191.1 | ✓ | 16 | 11.4 | even | 5 | inner | |
418.2.f.g.267.1 | yes | 16 | 1.1 | even | 1 | trivial | |
4598.2.a.bw.1.1 | 8 | 11.9 | even | 5 | |||
4598.2.a.bz.1.1 | 8 | 11.2 | odd | 10 |