Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [115,2,Mod(22,115)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(115, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("115.22");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 115 = 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 115.e (of order \(4\), degree \(2\), 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: | \(0.918279623245\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 6 x^{18} + 3 x^{16} + 80 x^{14} - 600 x^{12} + 3500 x^{10} - 15000 x^{8} + 50000 x^{6} + \cdots + 9765625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 68.9 | ||
Root | \(1.20735 + 1.88210i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 115.68 |
Dual form | 115.2.e.a.22.9 |
$q$-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 \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.40095 | − | 1.40095i | 0.990623 | − | 0.990623i | −0.00933298 | − | 0.999956i | \(-0.502971\pi\) |
0.999956 | + | 0.00933298i | \(0.00297082\pi\) | |||||||
\(3\) | −1.47890 | − | 1.47890i | −0.853845 | − | 0.853845i | 0.136759 | − | 0.990604i | \(-0.456331\pi\) |
−0.990604 | + | 0.136759i | \(0.956331\pi\) | |||||||
\(4\) | − | 1.92534i | − | 0.962670i | ||||||
\(5\) | −1.88210 | − | 1.20735i | −0.841703 | − | 0.539941i | ||||
\(6\) | −4.14375 | −1.69168 | ||||||||
\(7\) | 2.58659 | + | 2.58659i | 0.977639 | + | 0.977639i | 0.999755 | − | 0.0221167i | \(-0.00704053\pi\) |
−0.0221167 | + | 0.999755i | \(0.507041\pi\) | |||||||
\(8\) | 0.104596 | + | 0.104596i | 0.0369803 | + | 0.0369803i | ||||
\(9\) | 1.37431i | 0.458102i | ||||||||
\(10\) | −4.32817 | + | 0.945306i | −1.36869 | + | 0.298932i | ||||
\(11\) | − | 4.24585i | − | 1.28017i | −0.768303 | − | 0.640086i | \(-0.778899\pi\) | ||
0.768303 | − | 0.640086i | \(-0.221101\pi\) | |||||||
\(12\) | −2.84739 | + | 2.84739i | −0.821971 | + | 0.821971i | ||||
\(13\) | 1.82074 | + | 1.82074i | 0.504983 | + | 0.504983i | 0.912982 | − | 0.407999i | \(-0.133773\pi\) |
−0.407999 | + | 0.912982i | \(0.633773\pi\) | |||||||
\(14\) | 7.24738 | 1.93694 | ||||||||
\(15\) | 0.997903 | + | 4.56900i | 0.257657 | + | 1.17971i | ||||
\(16\) | 4.14375 | 1.03594 | ||||||||
\(17\) | 0.884201 | + | 0.884201i | 0.214450 | + | 0.214450i | 0.806155 | − | 0.591705i | \(-0.201545\pi\) |
−0.591705 | + | 0.806155i | \(0.701545\pi\) | |||||||
\(18\) | 1.92534 | + | 1.92534i | 0.453807 | + | 0.453807i | ||||
\(19\) | −0.524079 | −0.120232 | −0.0601160 | − | 0.998191i | \(-0.519147\pi\) | ||||
−0.0601160 | + | 0.998191i | \(0.519147\pi\) | |||||||
\(20\) | −2.32455 | + | 3.62369i | −0.519785 | + | 0.810282i | ||||
\(21\) | − | 7.65063i | − | 1.66950i | ||||||
\(22\) | −5.94824 | − | 5.94824i | −1.26817 | − | 1.26817i | ||||
\(23\) | −3.80809 | + | 2.91521i | −0.794041 | + | 0.607864i | ||||
\(24\) | − | 0.309375i | − | 0.0631508i | ||||||
\(25\) | 2.08463 | + | 4.54470i | 0.416927 | + | 0.908940i | ||||
\(26\) | 5.10155 | 1.00050 | ||||||||
\(27\) | −2.40424 | + | 2.40424i | −0.462697 | + | 0.462697i | ||||
\(28\) | 4.98006 | − | 4.98006i | 0.941143 | − | 0.941143i | ||||
\(29\) | 4.01110i | 0.744842i | 0.928064 | + | 0.372421i | \(0.121472\pi\) | ||||
−0.928064 | + | 0.372421i | \(0.878528\pi\) | |||||||
\(30\) | 7.79896 | + | 5.00293i | 1.42389 | + | 0.913407i | ||||
\(31\) | −7.49669 | −1.34644 | −0.673222 | − | 0.739440i | \(-0.735090\pi\) | ||||
−0.673222 | + | 0.739440i | \(0.735090\pi\) | |||||||
\(32\) | 5.59600 | − | 5.59600i | 0.989243 | − | 0.989243i | ||||
\(33\) | −6.27920 | + | 6.27920i | −1.09307 | + | 1.09307i | ||||
\(34\) | 2.47745 | 0.424879 | ||||||||
\(35\) | −1.74532 | − | 7.99114i | −0.295014 | − | 1.35075i | ||||
\(36\) | 2.64601 | 0.441001 | ||||||||
\(37\) | 5.58812 | + | 5.58812i | 0.918681 | + | 0.918681i | 0.996934 | − | 0.0782528i | \(-0.0249341\pi\) |
−0.0782528 | + | 0.996934i | \(0.524934\pi\) | |||||||
\(38\) | −0.734210 | + | 0.734210i | −0.119105 | + | 0.119105i | ||||
\(39\) | − | 5.38541i | − | 0.862355i | ||||||
\(40\) | −0.0705771 | − | 0.323144i | −0.0111592 | − | 0.0510936i | ||||
\(41\) | −4.85068 | −0.757549 | −0.378774 | − | 0.925489i | \(-0.623654\pi\) | ||||
−0.378774 | + | 0.925489i | \(0.623654\pi\) | |||||||
\(42\) | −10.7182 | − | 10.7182i | −1.65385 | − | 1.65385i | ||||
\(43\) | 6.47232 | − | 6.47232i | 0.987019 | − | 0.987019i | −0.0128975 | − | 0.999917i | \(-0.504106\pi\) |
0.999917 | + | 0.0128975i | \(0.00410553\pi\) | |||||||
\(44\) | −8.17471 | −1.23238 | ||||||||
\(45\) | 1.65926 | − | 2.58659i | 0.247348 | − | 0.385586i | ||||
\(46\) | −1.25087 | + | 9.41903i | −0.184431 | + | 1.38876i | ||||
\(47\) | −2.08135 | + | 2.08135i | −0.303595 | + | 0.303595i | −0.842419 | − | 0.538823i | \(-0.818869\pi\) |
0.538823 | + | 0.842419i | \(0.318869\pi\) | |||||||
\(48\) | −6.12820 | − | 6.12820i | −0.884529 | − | 0.884529i | ||||
\(49\) | 6.38088i | 0.911555i | ||||||||
\(50\) | 9.28739 | + | 3.44644i | 1.31343 | + | 0.487400i | ||||
\(51\) | − | 2.61530i | − | 0.366215i | ||||||
\(52\) | 3.50555 | − | 3.50555i | 0.486132 | − | 0.486132i | ||||
\(53\) | −0.553239 | + | 0.553239i | −0.0759932 | + | 0.0759932i | −0.744082 | − | 0.668089i | \(-0.767113\pi\) |
0.668089 | + | 0.744082i | \(0.267113\pi\) | |||||||
\(54\) | 6.73646i | 0.916716i | ||||||||
\(55\) | −5.12621 | + | 7.99114i | −0.691218 | + | 1.07752i | ||||
\(56\) | 0.541094i | 0.0723067i | ||||||||
\(57\) | 0.775062 | + | 0.775062i | 0.102659 | + | 0.102659i | ||||
\(58\) | 5.61936 | + | 5.61936i | 0.737858 | + | 0.737858i | ||||
\(59\) | − | 13.5774i | − | 1.76763i | −0.467838 | − | 0.883814i | \(-0.654967\pi\) | ||
0.467838 | − | 0.883814i | \(-0.345033\pi\) | |||||||
\(60\) | 8.79687 | − | 1.92130i | 1.13567 | − | 0.248039i | ||||
\(61\) | 3.54262i | 0.453586i | 0.973943 | + | 0.226793i | \(0.0728241\pi\) | ||||
−0.973943 | + | 0.226793i | \(0.927176\pi\) | |||||||
\(62\) | −10.5025 | + | 10.5025i | −1.33382 | + | 1.33382i | ||||
\(63\) | −3.55477 | + | 3.55477i | −0.447859 | + | 0.447859i | ||||
\(64\) | − | 7.39198i | − | 0.923998i | ||||||
\(65\) | −1.22856 | − | 5.62510i | −0.152385 | − | 0.697707i | ||||
\(66\) | 17.5937i | 2.16564i | ||||||||
\(67\) | −9.83397 | − | 9.83397i | −1.20141 | − | 1.20141i | −0.973738 | − | 0.227673i | \(-0.926888\pi\) |
−0.227673 | − | 0.973738i | \(-0.573112\pi\) | |||||||
\(68\) | 1.70239 | − | 1.70239i | 0.206445 | − | 0.206445i | ||||
\(69\) | 9.94311 | + | 1.32047i | 1.19701 | + | 0.158966i | ||||
\(70\) | −13.6403 | − | 8.75009i | −1.63033 | − | 1.04584i | ||||
\(71\) | 6.28522 | 0.745919 | 0.372959 | − | 0.927848i | \(-0.378343\pi\) | ||||
0.372959 | + | 0.927848i | \(0.378343\pi\) | |||||||
\(72\) | −0.143747 | + | 0.143747i | −0.0169407 | + | 0.0169407i | ||||
\(73\) | −3.78828 | − | 3.78828i | −0.443384 | − | 0.443384i | 0.449763 | − | 0.893148i | \(-0.351508\pi\) |
−0.893148 | + | 0.449763i | \(0.851508\pi\) | |||||||
\(74\) | 15.6574 | 1.82013 | ||||||||
\(75\) | 3.63820 | − | 9.80414i | 0.420103 | − | 1.13208i | ||||
\(76\) | 1.00903i | 0.115744i | ||||||||
\(77\) | 10.9823 | − | 10.9823i | 1.25155 | − | 1.25155i | ||||
\(78\) | −7.54470 | − | 7.54470i | −0.854269 | − | 0.854269i | ||||
\(79\) | −10.4842 | −1.17956 | −0.589782 | − | 0.807562i | \(-0.700787\pi\) | ||||
−0.589782 | + | 0.807562i | \(0.700787\pi\) | |||||||
\(80\) | −7.79896 | − | 5.00293i | −0.871951 | − | 0.559345i | ||||
\(81\) | 11.2342 | 1.24824 | ||||||||
\(82\) | −6.79557 | + | 6.79557i | −0.750446 | + | 0.750446i | ||||
\(83\) | −8.53483 | + | 8.53483i | −0.936819 | + | 0.936819i | −0.998119 | − | 0.0613002i | \(-0.980475\pi\) |
0.0613002 | + | 0.998119i | \(0.480475\pi\) | |||||||
\(84\) | −14.7301 | −1.60718 | ||||||||
\(85\) | −0.596623 | − | 2.73170i | −0.0647128 | − | 0.296294i | ||||
\(86\) | − | 18.1348i | − | 1.95553i | ||||||
\(87\) | 5.93202 | − | 5.93202i | 0.635980 | − | 0.635980i | ||||
\(88\) | 0.444099 | − | 0.444099i | 0.0473411 | − | 0.0473411i | ||||
\(89\) | 10.8704 | 1.15226 | 0.576132 | − | 0.817357i | \(-0.304561\pi\) | ||||
0.576132 | + | 0.817357i | \(0.304561\pi\) | |||||||
\(90\) | −1.29914 | − | 5.94824i | −0.136941 | − | 0.626999i | ||||
\(91\) | 9.41903i | 0.987383i | ||||||||
\(92\) | 5.61278 | + | 7.33186i | 0.585172 | + | 0.764399i | ||||
\(93\) | 11.0869 | + | 11.0869i | 1.14965 | + | 1.14965i | ||||
\(94\) | 5.83173i | 0.601498i | ||||||||
\(95\) | 0.986371 | + | 0.632744i | 0.101200 | + | 0.0649182i | ||||
\(96\) | −16.5519 | −1.68932 | ||||||||
\(97\) | 2.73658 | + | 2.73658i | 0.277858 | + | 0.277858i | 0.832253 | − | 0.554396i | \(-0.187051\pi\) |
−0.554396 | + | 0.832253i | \(0.687051\pi\) | |||||||
\(98\) | 8.93932 | + | 8.93932i | 0.903008 | + | 0.903008i | ||||
\(99\) | 5.83510 | 0.586450 | ||||||||
\(100\) | 8.75009 | − | 4.01363i | 0.875009 | − | 0.401363i | ||||
\(101\) | 0.488012 | 0.0485590 | 0.0242795 | − | 0.999705i | \(-0.492271\pi\) | ||||
0.0242795 | + | 0.999705i | \(0.492271\pi\) | |||||||
\(102\) | −3.66391 | − | 3.66391i | −0.362781 | − | 0.362781i | ||||
\(103\) | 3.91489 | − | 3.91489i | 0.385746 | − | 0.385746i | −0.487421 | − | 0.873167i | \(-0.662062\pi\) |
0.873167 | + | 0.487421i | \(0.162062\pi\) | |||||||
\(104\) | 0.380885i | 0.0373488i | ||||||||
\(105\) | −9.23695 | + | 14.3993i | −0.901434 | + | 1.40523i | ||||
\(106\) | 1.55012i | 0.150561i | ||||||||
\(107\) | 4.87092 | + | 4.87092i | 0.470890 | + | 0.470890i | 0.902203 | − | 0.431313i | \(-0.141949\pi\) |
−0.431313 | + | 0.902203i | \(0.641949\pi\) | |||||||
\(108\) | 4.62898 | + | 4.62898i | 0.445424 | + | 0.445424i | ||||
\(109\) | −6.58545 | −0.630772 | −0.315386 | − | 0.948963i | \(-0.602134\pi\) | ||||
−0.315386 | + | 0.948963i | \(0.602134\pi\) | |||||||
\(110\) | 4.01363 | + | 18.3768i | 0.382685 | + | 1.75216i | ||||
\(111\) | − | 16.5286i | − | 1.56882i | ||||||
\(112\) | 10.7182 | + | 10.7182i | 1.01277 | + | 1.01277i | ||||
\(113\) | −3.11067 | + | 3.11067i | −0.292627 | + | 0.292627i | −0.838117 | − | 0.545490i | \(-0.816344\pi\) |
0.545490 | + | 0.838117i | \(0.316344\pi\) | |||||||
\(114\) | 2.17165 | 0.203394 | ||||||||
\(115\) | 10.6869 | − | 0.889061i | 0.996557 | − | 0.0829053i | ||||
\(116\) | 7.72273 | 0.717037 | ||||||||
\(117\) | −2.50226 | + | 2.50226i | −0.231334 | + | 0.231334i | ||||
\(118\) | −19.0213 | − | 19.0213i | −1.75105 | − | 1.75105i | ||||
\(119\) | 4.57413i | 0.419310i | ||||||||
\(120\) | −0.373522 | + | 0.582275i | −0.0340977 | + | 0.0531542i | ||||
\(121\) | −7.02726 | −0.638842 | ||||||||
\(122\) | 4.96305 | + | 4.96305i | 0.449333 | + | 0.449333i | ||||
\(123\) | 7.17368 | + | 7.17368i | 0.646829 | + | 0.646829i | ||||
\(124\) | 14.4337i | 1.29618i | ||||||||
\(125\) | 1.56352 | − | 11.0705i | 0.139846 | − | 0.990173i | ||||
\(126\) | 9.96012i | 0.887318i | ||||||||
\(127\) | −11.5902 | + | 11.5902i | −1.02846 | + | 1.02846i | −0.0288796 | + | 0.999583i | \(0.509194\pi\) |
−0.999583 | + | 0.0288796i | \(0.990806\pi\) | |||||||
\(128\) | 0.836185 | + | 0.836185i | 0.0739090 | + | 0.0739090i | ||||
\(129\) | −19.1439 | −1.68552 | ||||||||
\(130\) | −9.60165 | − | 6.15934i | −0.842121 | − | 0.540209i | ||||
\(131\) | 7.75071 | 0.677183 | 0.338591 | − | 0.940934i | \(-0.390050\pi\) | ||||
0.338591 | + | 0.940934i | \(0.390050\pi\) | |||||||
\(132\) | 12.0896 | + | 12.0896i | 1.05226 | + | 1.05226i | ||||
\(133\) | −1.35558 | − | 1.35558i | −0.117543 | − | 0.117543i | ||||
\(134\) | −27.5539 | −2.38029 | ||||||||
\(135\) | 7.42779 | − | 1.62228i | 0.639282 | − | 0.139624i | ||||
\(136\) | 0.184968i | 0.0158609i | ||||||||
\(137\) | 7.12655 | + | 7.12655i | 0.608862 | + | 0.608862i | 0.942649 | − | 0.333787i | \(-0.108326\pi\) |
−0.333787 | + | 0.942649i | \(0.608326\pi\) | |||||||
\(138\) | 15.7797 | − | 12.0799i | 1.34326 | − | 1.02831i | ||||
\(139\) | 9.78245i | 0.829737i | 0.909881 | + | 0.414868i | \(0.136172\pi\) | ||||
−0.909881 | + | 0.414868i | \(0.863828\pi\) | |||||||
\(140\) | −15.3857 | + | 3.36034i | −1.30032 | + | 0.284001i | ||||
\(141\) | 6.15622 | 0.518447 | ||||||||
\(142\) | 8.80530 | − | 8.80530i | 0.738925 | − | 0.738925i | ||||
\(143\) | 7.73061 | − | 7.73061i | 0.646466 | − | 0.646466i | ||||
\(144\) | 5.69478i | 0.474565i | ||||||||
\(145\) | 4.84278 | − | 7.54931i | 0.402171 | − | 0.626936i | ||||
\(146\) | −10.6144 | −0.878454 | ||||||||
\(147\) | 9.43671 | − | 9.43671i | 0.778327 | − | 0.778327i | ||||
\(148\) | 10.7590 | − | 10.7590i | 0.884386 | − | 0.884386i | ||||
\(149\) | −17.5133 | −1.43475 | −0.717373 | − | 0.696689i | \(-0.754656\pi\) | ||||
−0.717373 | + | 0.696689i | \(0.754656\pi\) | |||||||
\(150\) | −8.63820 | − | 18.8321i | −0.705306 | − | 1.53763i | ||||
\(151\) | 8.88661 | 0.723182 | 0.361591 | − | 0.932337i | \(-0.382234\pi\) | ||||
0.361591 | + | 0.932337i | \(0.382234\pi\) | |||||||
\(152\) | −0.0548165 | − | 0.0548165i | −0.00444621 | − | 0.00444621i | ||||
\(153\) | −1.21516 | + | 1.21516i | −0.0982402 | + | 0.0982402i | ||||
\(154\) | − | 30.7713i | − | 2.47962i | ||||||
\(155\) | 14.1095 | + | 9.05109i | 1.13331 | + | 0.727001i | ||||
\(156\) | −10.3687 | −0.830163 | ||||||||
\(157\) | 4.46767 | + | 4.46767i | 0.356559 | + | 0.356559i | 0.862543 | − | 0.505984i | \(-0.168870\pi\) |
−0.505984 | + | 0.862543i | \(0.668870\pi\) | |||||||
\(158\) | −14.6879 | + | 14.6879i | −1.16850 | + | 1.16850i | ||||
\(159\) | 1.63637 | 0.129773 | ||||||||
\(160\) | −17.2886 | + | 3.77595i | −1.36678 | + | 0.298515i | ||||
\(161\) | −17.3904 | − | 2.30950i | −1.37056 | − | 0.182014i | ||||
\(162\) | 15.7386 | − | 15.7386i | 1.23654 | − | 1.23654i | ||||
\(163\) | −16.1787 | − | 16.1787i | −1.26721 | − | 1.26721i | −0.947522 | − | 0.319691i | \(-0.896421\pi\) |
−0.319691 | − | 0.947522i | \(-0.603579\pi\) | |||||||
\(164\) | 9.33920i | 0.729269i | ||||||||
\(165\) | 19.3993 | − | 4.23695i | 1.51023 | − | 0.329846i | ||||
\(166\) | 23.9138i | 1.85607i | ||||||||
\(167\) | 4.56719 | − | 4.56719i | 0.353420 | − | 0.353420i | −0.507960 | − | 0.861380i | \(-0.669600\pi\) |
0.861380 | + | 0.507960i | \(0.169600\pi\) | |||||||
\(168\) | 0.800225 | − | 0.800225i | 0.0617387 | − | 0.0617387i | ||||
\(169\) | − | 6.36979i | − | 0.489984i | ||||||
\(170\) | −4.66282 | − | 2.99114i | −0.357622 | − | 0.229410i | ||||
\(171\) | − | 0.720245i | − | 0.0550785i | ||||||
\(172\) | −12.4614 | − | 12.4614i | −0.950174 | − | 0.950174i | ||||
\(173\) | −5.73382 | − | 5.73382i | −0.435935 | − | 0.435935i | 0.454707 | − | 0.890641i | \(-0.349744\pi\) |
−0.890641 | + | 0.454707i | \(0.849744\pi\) | |||||||
\(174\) | − | 16.6210i | − | 1.26003i | ||||||
\(175\) | −6.36318 | + | 17.1474i | −0.481011 | + | 1.29622i | ||||
\(176\) | − | 17.5937i | − | 1.32618i | ||||||
\(177\) | −20.0797 | + | 20.0797i | −1.50928 | + | 1.50928i | ||||
\(178\) | 15.2290 | − | 15.2290i | 1.14146 | − | 1.14146i | ||||
\(179\) | − | 3.90640i | − | 0.291978i | −0.989286 | − | 0.145989i | \(-0.953364\pi\) | ||
0.989286 | − | 0.145989i | \(-0.0466364\pi\) | |||||||
\(180\) | −4.98006 | − | 3.19464i | −0.371192 | − | 0.238115i | ||||
\(181\) | − | 21.2572i | − | 1.58003i | −0.613085 | − | 0.790017i | \(-0.710072\pi\) | ||
0.613085 | − | 0.790017i | \(-0.289928\pi\) | |||||||
\(182\) | 13.1956 | + | 13.1956i | 0.978124 | + | 0.978124i | ||||
\(183\) | 5.23919 | − | 5.23919i | 0.387292 | − | 0.387292i | ||||
\(184\) | −0.703230 | − | 0.0933910i | −0.0518428 | − | 0.00688487i | ||||
\(185\) | −3.77063 | − | 17.2642i | −0.277222 | − | 1.26929i | ||||
\(186\) | 31.0644 | 2.27775 | ||||||||
\(187\) | 3.75419 | − | 3.75419i | 0.274533 | − | 0.274533i | ||||
\(188\) | 4.00730 | + | 4.00730i | 0.292262 | + | 0.292262i | ||||
\(189\) | −12.4376 | −0.904700 | ||||||||
\(190\) | 2.26830 | − | 0.495415i | 0.164560 | − | 0.0359412i | ||||
\(191\) | − | 2.78325i | − | 0.201389i | −0.994917 | − | 0.100694i | \(-0.967894\pi\) | ||
0.994917 | − | 0.100694i | \(-0.0321064\pi\) | |||||||
\(192\) | −10.9320 | + | 10.9320i | −0.788951 | + | 0.788951i | ||||
\(193\) | 9.50337 | + | 9.50337i | 0.684068 | + | 0.684068i | 0.960914 | − | 0.276847i | \(-0.0892894\pi\) |
−0.276847 | + | 0.960914i | \(0.589289\pi\) | |||||||
\(194\) | 7.66764 | 0.550505 | ||||||||
\(195\) | −6.50204 | + | 10.1359i | −0.465621 | + | 0.725847i | ||||
\(196\) | 12.2854 | 0.877526 | ||||||||
\(197\) | −1.97143 | + | 1.97143i | −0.140459 | + | 0.140459i | −0.773840 | − | 0.633381i | \(-0.781667\pi\) |
0.633381 | + | 0.773840i | \(0.281667\pi\) | |||||||
\(198\) | 8.17471 | − | 8.17471i | 0.580951 | − | 0.580951i | ||||
\(199\) | 10.5829 | 0.750203 | 0.375102 | − | 0.926984i | \(-0.377608\pi\) | ||||
0.375102 | + | 0.926984i | \(0.377608\pi\) | |||||||
\(200\) | −0.257313 | + | 0.693402i | −0.0181948 | + | 0.0490309i | ||||
\(201\) | 29.0870i | 2.05164i | ||||||||
\(202\) | 0.683681 | − | 0.683681i | 0.0481037 | − | 0.0481037i | ||||
\(203\) | −10.3751 | + | 10.3751i | −0.728187 | + | 0.728187i | ||||
\(204\) | −5.03533 | −0.352544 | ||||||||
\(205\) | 9.12948 | + | 5.85644i | 0.637631 | + | 0.409032i | ||||
\(206\) | − | 10.9692i | − | 0.764257i | ||||||
\(207\) | −4.00640 | − | 5.23348i | −0.278464 | − | 0.363752i | ||||
\(208\) | 7.54470 | + | 7.54470i | 0.523131 | + | 0.523131i | ||||
\(209\) | 2.22516i | 0.153918i | ||||||||
\(210\) | 7.23218 | + | 33.1132i | 0.499068 | + | 2.28503i | ||||
\(211\) | −7.53925 | −0.519023 | −0.259512 | − | 0.965740i | \(-0.583562\pi\) | ||||
−0.259512 | + | 0.965740i | \(0.583562\pi\) | |||||||
\(212\) | 1.06517 | + | 1.06517i | 0.0731563 | + | 0.0731563i | ||||
\(213\) | −9.29523 | − | 9.29523i | −0.636899 | − | 0.636899i | ||||
\(214\) | 13.6479 | 0.932949 | ||||||||
\(215\) | −19.9959 | + | 4.36726i | −1.36371 | + | 0.297844i | ||||
\(216\) | −0.502948 | −0.0342213 | ||||||||
\(217\) | −19.3908 | − | 19.3908i | −1.31634 | − | 1.31634i | ||||
\(218\) | −9.22591 | + | 9.22591i | −0.624858 | + | 0.624858i | ||||
\(219\) | 11.2050i | 0.757163i | ||||||||
\(220\) | 15.3857 | + | 9.86969i | 1.03730 | + | 0.665415i | ||||
\(221\) | 3.21981i | 0.216588i | ||||||||
\(222\) | −23.1557 | − | 23.1557i | −1.55411 | − | 1.55411i | ||||
\(223\) | 10.7644 | + | 10.7644i | 0.720838 | + | 0.720838i | 0.968776 | − | 0.247938i | \(-0.0797529\pi\) |
−0.247938 | + | 0.968776i | \(0.579753\pi\) | |||||||
\(224\) | 28.9491 | 1.93424 | ||||||||
\(225\) | −6.24581 | + | 2.86493i | −0.416387 | + | 0.190995i | ||||
\(226\) | 8.71580i | 0.579766i | ||||||||
\(227\) | −15.6982 | − | 15.6982i | −1.04193 | − | 1.04193i | −0.999082 | − | 0.0428466i | \(-0.986357\pi\) |
−0.0428466 | − | 0.999082i | \(-0.513643\pi\) | |||||||
\(228\) | 1.49226 | − | 1.49226i | 0.0988271 | − | 0.0988271i | ||||
\(229\) | 0.305799 | 0.0202078 | 0.0101039 | − | 0.999949i | \(-0.496784\pi\) | ||||
0.0101039 | + | 0.999949i | \(0.496784\pi\) | |||||||
\(230\) | 13.7263 | − | 16.2174i | 0.905085 | − | 1.06934i | ||||
\(231\) | −32.4834 | −2.13725 | ||||||||
\(232\) | −0.419545 | + | 0.419545i | −0.0275445 | + | 0.0275445i | ||||
\(233\) | −12.4523 | − | 12.4523i | −0.815779 | − | 0.815779i | 0.169714 | − | 0.985493i | \(-0.445716\pi\) |
−0.985493 | + | 0.169714i | \(0.945716\pi\) | |||||||
\(234\) | 7.01110i | 0.458330i | ||||||||
\(235\) | 6.43021 | − | 1.40441i | 0.419461 | − | 0.0916134i | ||||
\(236\) | −26.1411 | −1.70164 | ||||||||
\(237\) | 15.5051 | + | 15.5051i | 1.00717 | + | 1.00717i | ||||
\(238\) | 6.40814 | + | 6.40814i | 0.415378 | + | 0.415378i | ||||
\(239\) | − | 9.23593i | − | 0.597423i | −0.954344 | − | 0.298711i | \(-0.903443\pi\) | ||
0.954344 | − | 0.298711i | \(-0.0965568\pi\) | |||||||
\(240\) | 4.13506 | + | 18.9328i | 0.266917 | + | 1.22210i | ||||
\(241\) | 2.91528i | 0.187790i | 0.995582 | + | 0.0938948i | \(0.0299317\pi\) | ||||
−0.995582 | + | 0.0938948i | \(0.970068\pi\) | |||||||
\(242\) | −9.84486 | + | 9.84486i | −0.632852 | + | 0.632852i | ||||
\(243\) | −9.40156 | − | 9.40156i | −0.603111 | − | 0.603111i | ||||
\(244\) | 6.82075 | 0.436654 | ||||||||
\(245\) | 7.70393 | − | 12.0095i | 0.492186 | − | 0.767258i | ||||
\(246\) | 20.1000 | 1.28153 | ||||||||
\(247\) | −0.954213 | − | 0.954213i | −0.0607151 | − | 0.0607151i | ||||
\(248\) | −0.784123 | − | 0.784123i | −0.0497919 | − | 0.0497919i | ||||
\(249\) | 25.2444 | 1.59980 | ||||||||
\(250\) | −13.3188 | − | 17.6996i | −0.842354 | − | 1.11942i | ||||
\(251\) | 19.1830i | 1.21082i | 0.795914 | + | 0.605410i | \(0.206991\pi\) | ||||
−0.795914 | + | 0.605410i | \(0.793009\pi\) | |||||||
\(252\) | 6.84413 | + | 6.84413i | 0.431140 | + | 0.431140i | ||||
\(253\) | 12.3776 | + | 16.1686i | 0.778171 | + | 1.01651i | ||||
\(254\) | 32.4746i | 2.03764i | ||||||||
\(255\) | −3.15756 | + | 4.92226i | −0.197734 | + | 0.308244i | ||||
\(256\) | 17.1269 | 1.07043 | ||||||||
\(257\) | −5.08878 | + | 5.08878i | −0.317429 | + | 0.317429i | −0.847779 | − | 0.530350i | \(-0.822061\pi\) |
0.530350 | + | 0.847779i | \(0.322061\pi\) | |||||||
\(258\) | −26.8196 | + | 26.8196i | −1.66972 | + | 1.66972i | ||||
\(259\) | 28.9083i | 1.79628i | ||||||||
\(260\) | −10.8302 | + | 2.36540i | −0.671662 | + | 0.146696i | ||||
\(261\) | −5.51248 | −0.341214 | ||||||||
\(262\) | 10.8584 | − | 10.8584i | 0.670833 | − | 0.670833i | ||||
\(263\) | 5.79825 | − | 5.79825i | 0.357535 | − | 0.357535i | −0.505368 | − | 0.862904i | \(-0.668643\pi\) |
0.862904 | + | 0.505368i | \(0.168643\pi\) | |||||||
\(264\) | −1.31356 | −0.0808439 | ||||||||
\(265\) | 1.70920 | − | 0.373303i | 0.104996 | − | 0.0229318i | ||||
\(266\) | −3.79820 | −0.232882 | ||||||||
\(267\) | −16.0763 | − | 16.0763i | −0.983855 | − | 0.983855i | ||||
\(268\) | −18.9337 | + | 18.9337i | −1.15656 | + | 1.15656i | ||||
\(269\) | − | 6.52449i | − | 0.397805i | −0.980019 | − | 0.198902i | \(-0.936262\pi\) | ||
0.980019 | − | 0.198902i | \(-0.0637377\pi\) | |||||||
\(270\) | 8.13324 | − | 12.6787i | 0.494973 | − | 0.771603i | ||||
\(271\) | 15.6908 | 0.953148 | 0.476574 | − | 0.879134i | \(-0.341879\pi\) | ||||
0.476574 | + | 0.879134i | \(0.341879\pi\) | |||||||
\(272\) | 3.66391 | + | 3.66391i | 0.222157 | + | 0.222157i | ||||
\(273\) | 13.9298 | − | 13.9298i | 0.843072 | − | 0.843072i | ||||
\(274\) | 19.9679 | 1.20631 | ||||||||
\(275\) | 19.2961 | − | 8.85105i | 1.16360 | − | 0.533738i | ||||
\(276\) | 2.54236 | − | 19.1439i | 0.153032 | − | 1.15232i | ||||
\(277\) | 12.5541 | − | 12.5541i | 0.754300 | − | 0.754300i | −0.220979 | − | 0.975279i | \(-0.570925\pi\) |
0.975279 | + | 0.220979i | \(0.0709251\pi\) | |||||||
\(278\) | 13.7048 | + | 13.7048i | 0.821956 | + | 0.821956i | ||||
\(279\) | − | 10.3027i | − | 0.616809i | ||||||
\(280\) | 0.653287 | − | 1.01839i | 0.0390414 | − | 0.0608607i | ||||
\(281\) | − | 5.68024i | − | 0.338855i | −0.985543 | − | 0.169427i | \(-0.945808\pi\) | ||
0.985543 | − | 0.169427i | \(-0.0541918\pi\) | |||||||
\(282\) | 8.62457 | − | 8.62457i | 0.513586 | − | 0.513586i | ||||
\(283\) | −4.72681 | + | 4.72681i | −0.280979 | + | 0.280979i | −0.833500 | − | 0.552520i | \(-0.813666\pi\) |
0.552520 | + | 0.833500i | \(0.313666\pi\) | |||||||
\(284\) | − | 12.1012i | − | 0.718073i | ||||||
\(285\) | −0.522980 | − | 2.39451i | −0.0309787 | − | 0.141839i | ||||
\(286\) | − | 21.6604i | − | 1.28081i | ||||||
\(287\) | −12.5467 | − | 12.5467i | −0.740609 | − | 0.740609i | ||||
\(288\) | 7.69063 | + | 7.69063i | 0.453174 | + | 0.453174i | ||||
\(289\) | − | 15.4364i | − | 0.908022i | ||||||
\(290\) | −3.79171 | − | 17.3607i | −0.222657 | − | 1.01946i | ||||
\(291\) | − | 8.09427i | − | 0.474495i | ||||||
\(292\) | −7.29372 | + | 7.29372i | −0.426833 | + | 0.426833i | ||||
\(293\) | −15.5891 | + | 15.5891i | −0.910724 | + | 0.910724i | −0.996329 | − | 0.0856047i | \(-0.972718\pi\) |
0.0856047 | + | 0.996329i | \(0.472718\pi\) | |||||||
\(294\) | − | 26.4408i | − | 1.54206i | ||||||
\(295\) | −16.3926 | + | 25.5541i | −0.954416 | + | 1.48782i | ||||
\(296\) | 1.16899i | 0.0679461i | ||||||||
\(297\) | 10.2081 | + | 10.2081i | 0.592331 | + | 0.592331i | ||||
\(298\) | −24.5353 | + | 24.5353i | −1.42129 | + | 1.42129i | ||||
\(299\) | −12.2414 | − | 1.62569i | −0.707939 | − | 0.0940163i | ||||
\(300\) | −18.8763 | − | 7.00477i | −1.08982 | − | 0.404420i | ||||
\(301\) | 33.4825 | 1.92990 | ||||||||
\(302\) | 12.4497 | − | 12.4497i | 0.716401 | − | 0.716401i | ||||
\(303\) | −0.721722 | − | 0.721722i | −0.0414618 | − | 0.0414618i | ||||
\(304\) | −2.17165 | −0.124553 | ||||||||
\(305\) | 4.27717 | − | 6.66758i | 0.244910 | − | 0.381785i | ||||
\(306\) | 3.40478i | 0.194638i | ||||||||
\(307\) | −0.539934 | + | 0.539934i | −0.0308157 | + | 0.0308157i | −0.722347 | − | 0.691531i | \(-0.756937\pi\) |
0.691531 | + | 0.722347i | \(0.256937\pi\) | |||||||
\(308\) | −21.1446 | − | 21.1446i | −1.20483 | − | 1.20483i | ||||
\(309\) | −11.5795 | −0.658734 | ||||||||
\(310\) | 32.4470 | − | 7.08666i | 1.84286 | − | 0.402495i | ||||
\(311\) | 13.9115 | 0.788846 | 0.394423 | − | 0.918929i | \(-0.370944\pi\) | ||||
0.394423 | + | 0.918929i | \(0.370944\pi\) | |||||||
\(312\) | 0.563292 | − | 0.563292i | 0.0318901 | − | 0.0318901i | ||||
\(313\) | 16.3093 | − | 16.3093i | 0.921858 | − | 0.921858i | −0.0753025 | − | 0.997161i | \(-0.523992\pi\) |
0.997161 | + | 0.0753025i | \(0.0239922\pi\) | |||||||
\(314\) | 12.5180 | 0.706432 | ||||||||
\(315\) | 10.9823 | − | 2.39861i | 0.618781 | − | 0.135146i | ||||
\(316\) | 20.1856i | 1.13553i | ||||||||
\(317\) | −10.0129 | + | 10.0129i | −0.562378 | + | 0.562378i | −0.929982 | − | 0.367604i | \(-0.880178\pi\) |
0.367604 | + | 0.929982i | \(0.380178\pi\) | |||||||
\(318\) | 2.29248 | − | 2.29248i | 0.128556 | − | 0.128556i | ||||
\(319\) | 17.0305 | 0.953527 | ||||||||
\(320\) | −8.92468 | + | 13.9125i | −0.498905 | + | 0.777732i | ||||
\(321\) | − | 14.4072i | − | 0.804134i | ||||||
\(322\) | −27.5987 | + | 21.1277i | −1.53801 | + | 1.17740i | ||||
\(323\) | −0.463391 | − | 0.463391i | −0.0257838 | − | 0.0257838i | ||||
\(324\) | − | 21.6297i | − | 1.20165i | ||||||
\(325\) | −4.47915 | + | 12.0703i | −0.248458 | + | 0.669541i | ||||
\(326\) | −45.3312 | −2.51066 | ||||||||
\(327\) | 9.73925 | + | 9.73925i | 0.538582 | + | 0.538582i | ||||
\(328\) | −0.507361 | − | 0.507361i | −0.0280144 | − | 0.0280144i | ||||
\(329\) | −10.7672 | −0.593613 | ||||||||
\(330\) | 21.2417 | − | 33.1132i | 1.16932 | − | 1.82282i | ||||
\(331\) | −14.0712 | −0.773422 | −0.386711 | − | 0.922201i | \(-0.626389\pi\) | ||||
−0.386711 | + | 0.922201i | \(0.626389\pi\) | |||||||
\(332\) | 16.4324 | + | 16.4324i | 0.901847 | + | 0.901847i | ||||
\(333\) | −7.67979 | + | 7.67979i | −0.420850 | + | 0.420850i | ||||
\(334\) | − | 12.7968i | − | 0.700212i | ||||||
\(335\) | 6.63556 | + | 30.3816i | 0.362539 | + | 1.65992i | ||||
\(336\) | − | 31.7023i | − | 1.72950i | ||||||
\(337\) | −2.71142 | − | 2.71142i | −0.147700 | − | 0.147700i | 0.629390 | − | 0.777090i | \(-0.283305\pi\) |
−0.777090 | + | 0.629390i | \(0.783305\pi\) | |||||||
\(338\) | −8.92377 | − | 8.92377i | −0.485389 | − | 0.485389i | ||||
\(339\) | 9.20075 | 0.499716 | ||||||||
\(340\) | −5.25944 | + | 1.14870i | −0.285233 | + | 0.0622971i | ||||
\(341\) | 31.8298i | 1.72368i | ||||||||
\(342\) | −1.00903 | − | 1.00903i | −0.0545621 | − | 0.0545621i | ||||
\(343\) | 1.60140 | − | 1.60140i | 0.0864673 | − | 0.0864673i | ||||
\(344\) | 1.35396 | 0.0730005 | ||||||||
\(345\) | −17.1197 | − | 14.4900i | −0.921694 | − | 0.780117i | ||||
\(346\) | −16.0656 | −0.863694 | ||||||||
\(347\) | −22.3073 | + | 22.3073i | −1.19752 | + | 1.19752i | −0.222609 | + | 0.974908i | \(0.571457\pi\) |
−0.974908 | + | 0.222609i | \(0.928543\pi\) | |||||||
\(348\) | −11.4212 | − | 11.4212i | −0.612238 | − | 0.612238i | ||||
\(349\) | − | 5.25900i | − | 0.281508i | −0.990045 | − | 0.140754i | \(-0.955047\pi\) | ||
0.990045 | − | 0.140754i | \(-0.0449526\pi\) | |||||||
\(350\) | 15.1081 | + | 32.9372i | 0.807564 | + | 1.76057i | ||||
\(351\) | −8.75502 | −0.467308 | ||||||||
\(352\) | −23.7598 | − | 23.7598i | −1.26640 | − | 1.26640i | ||||
\(353\) | 22.9940 | + | 22.9940i | 1.22385 | + | 1.22385i | 0.966253 | + | 0.257595i | \(0.0829301\pi\) |
0.257595 | + | 0.966253i | \(0.417070\pi\) | |||||||
\(354\) | 56.2614i | 2.99026i | ||||||||
\(355\) | −11.8294 | − | 7.58843i | −0.627842 | − | 0.402752i | ||||
\(356\) | − | 20.9293i | − | 1.10925i | ||||||
\(357\) | 6.76469 | − | 6.76469i | 0.358026 | − | 0.358026i | ||||
\(358\) | −5.47268 | − | 5.47268i | −0.289240 | − | 0.289240i | ||||
\(359\) | −6.80373 | −0.359087 | −0.179544 | − | 0.983750i | \(-0.557462\pi\) | ||||
−0.179544 | + | 0.983750i | \(0.557462\pi\) | |||||||
\(360\) | 0.444099 | − | 0.0969946i | 0.0234061 | − | 0.00511206i | ||||
\(361\) | −18.7253 | −0.985544 | ||||||||
\(362\) | −29.7803 | − | 29.7803i | −1.56522 | − | 1.56522i | ||||
\(363\) | 10.3926 | + | 10.3926i | 0.545472 | + | 0.545472i | ||||
\(364\) | 18.1348 | 0.950523 | ||||||||
\(365\) | 2.55617 | + | 11.7037i | 0.133796 | + | 0.612599i | ||||
\(366\) | − | 14.6797i | − | 0.767322i | ||||||
\(367\) | −3.54662 | − | 3.54662i | −0.185132 | − | 0.185132i | 0.608456 | − | 0.793588i | \(-0.291789\pi\) |
−0.793588 | + | 0.608456i | \(0.791789\pi\) | |||||||
\(368\) | −15.7797 | + | 12.0799i | −0.822576 | + | 0.629709i | ||||
\(369\) | − | 6.66632i | − | 0.347035i | ||||||
\(370\) | −29.4688 | − | 18.9039i | −1.53201 | − | 0.982765i | ||||
\(371\) | −2.86200 | −0.148588 | ||||||||
\(372\) | 21.3460 | − | 21.3460i | 1.10674 | − | 1.10674i | ||||
\(373\) | 4.61812 | − | 4.61812i | 0.239117 | − | 0.239117i | −0.577367 | − | 0.816485i | \(-0.695920\pi\) |
0.816485 | + | 0.577367i | \(0.195920\pi\) | |||||||
\(374\) | − | 10.5189i | − | 0.543918i | ||||||
\(375\) | −18.6845 | + | 14.0599i | −0.964861 | + | 0.726048i | ||||
\(376\) | −0.435401 | −0.0224541 | ||||||||
\(377\) | −7.30318 | + | 7.30318i | −0.376133 | + | 0.376133i | ||||
\(378\) | −17.4245 | + | 17.4245i | −0.896217 | + | 0.896217i | ||||
\(379\) | 28.0276 | 1.43968 | 0.719841 | − | 0.694139i | \(-0.244215\pi\) | ||||
0.719841 | + | 0.694139i | \(0.244215\pi\) | |||||||
\(380\) | 1.21825 | − | 1.89910i | 0.0624948 | − | 0.0974217i | ||||
\(381\) | 34.2815 | 1.75629 | ||||||||
\(382\) | −3.89920 | − | 3.89920i | −0.199500 | − | 0.199500i | ||||
\(383\) | 24.8950 | − | 24.8950i | 1.27207 | − | 1.27207i | 0.327076 | − | 0.944998i | \(-0.393937\pi\) |
0.944998 | − | 0.327076i | \(-0.106063\pi\) | |||||||
\(384\) | − | 2.47327i | − | 0.126214i | ||||||
\(385\) | −33.9292 | + | 7.41039i | −1.72919 | + | 0.377668i | ||||
\(386\) | 26.6276 | 1.35531 | ||||||||
\(387\) | 8.89495 | + | 8.89495i | 0.452156 | + | 0.452156i | ||||
\(388\) | 5.26885 | − | 5.26885i | 0.267485 | − | 0.267485i | ||||
\(389\) | −12.7847 | −0.648209 | −0.324104 | − | 0.946021i | \(-0.605063\pi\) | ||||
−0.324104 | + | 0.946021i | \(0.605063\pi\) | |||||||
\(390\) | 5.09086 | + | 23.3090i | 0.257785 | + | 1.18030i | ||||
\(391\) | −5.94475 | − | 0.789480i | −0.300639 | − | 0.0399257i | ||||
\(392\) | −0.667415 | + | 0.667415i | −0.0337095 | + | 0.0337095i | ||||
\(393\) | −11.4625 | − | 11.4625i | −0.578209 | − | 0.578209i | ||||
\(394\) | 5.52377i | 0.278284i | ||||||||
\(395\) | 19.7324 | + | 12.6581i | 0.992843 | + | 0.636896i | ||||
\(396\) | − | 11.2346i | − | 0.564558i | ||||||
\(397\) | 27.1558 | − | 27.1558i | 1.36291 | − | 1.36291i | 0.492727 | − | 0.870184i | \(-0.336000\pi\) |
0.870184 | − | 0.492727i | \(-0.164000\pi\) | |||||||
\(398\) | 14.8262 | − | 14.8262i | 0.743169 | − | 0.743169i | ||||
\(399\) | 4.00953i | 0.200728i | ||||||||
\(400\) | 8.63820 | + | 18.8321i | 0.431910 | + | 0.941604i | ||||
\(401\) | 10.6634i | 0.532502i | 0.963904 | + | 0.266251i | \(0.0857851\pi\) | ||||
−0.963904 | + | 0.266251i | \(0.914215\pi\) | |||||||
\(402\) | 40.7495 | + | 40.7495i | 2.03240 | + | 2.03240i | ||||
\(403\) | −13.6495 | − | 13.6495i | −0.679932 | − | 0.679932i | ||||
\(404\) | − | 0.939588i | − | 0.0467462i | ||||||
\(405\) | −21.1439 | − | 13.5636i | −1.05065 | − | 0.673979i | ||||
\(406\) | 29.0700i | 1.44272i | ||||||||
\(407\) | 23.7263 | − | 23.7263i | 1.17607 | − | 1.17607i | ||||
\(408\) | 0.273549 | − | 0.273549i | 0.0135427 | − | 0.0135427i | ||||
\(409\) | 23.2475i | 1.14951i | 0.818324 | + | 0.574757i | \(0.194904\pi\) | ||||
−0.818324 | + | 0.574757i | \(0.805096\pi\) | |||||||
\(410\) | 20.9946 | − | 4.58538i | 1.03685 | − | 0.226456i | ||||
\(411\) | − | 21.0789i | − | 1.03975i | ||||||
\(412\) | −7.53749 | − | 7.53749i | −0.371346 | − | 0.371346i | ||||
\(413\) | 35.1192 | − | 35.1192i | 1.72810 | − | 1.72810i | ||||
\(414\) | −12.9446 | − | 1.71908i | −0.636194 | − | 0.0844884i | ||||
\(415\) | 26.3679 | − | 5.75895i | 1.29435 | − | 0.282696i | ||||
\(416\) | 20.3778 | 0.999103 | ||||||||
\(417\) | 14.4673 | − | 14.4673i | 0.708466 | − | 0.708466i | ||||
\(418\) | 3.11735 | + | 3.11735i | 0.152474 | + | 0.152474i | ||||
\(419\) | 29.1857 | 1.42581 | 0.712907 | − | 0.701259i | \(-0.247378\pi\) | ||||
0.712907 | + | 0.701259i | \(0.247378\pi\) | |||||||
\(420\) | 27.7235 | + | 17.7843i | 1.35277 | + | 0.867783i | ||||
\(421\) | 1.45722i | 0.0710206i | 0.999369 | + | 0.0355103i | \(0.0113057\pi\) | ||||
−0.999369 | + | 0.0355103i | \(0.988694\pi\) | |||||||
\(422\) | −10.5621 | + | 10.5621i | −0.514156 | + | 0.514156i | ||||
\(423\) | −2.86041 | − | 2.86041i | −0.139078 | − | 0.139078i | ||||
\(424\) | −0.115733 | −0.00562050 | ||||||||
\(425\) | −2.17519 | + | 5.86167i | −0.105512 | + | 0.284333i | ||||
\(426\) | −26.0444 | −1.26185 | ||||||||
\(427\) | −9.16331 | + | 9.16331i | −0.443443 | + | 0.443443i | ||||
\(428\) | 9.37818 | − | 9.37818i | 0.453311 | − | 0.453311i | ||||
\(429\) | −22.8656 | −1.10396 | ||||||||
\(430\) | −21.8950 | + | 34.1316i | −1.05587 | + | 1.64597i | ||||
\(431\) | − | 0.582399i | − | 0.0280532i | −0.999902 | − | 0.0140266i | \(-0.995535\pi\) | ||
0.999902 | − | 0.0140266i | \(-0.00446495\pi\) | |||||||
\(432\) | −9.96257 | + | 9.96257i | −0.479324 | + | 0.479324i | ||||
\(433\) | 10.9710 | − | 10.9710i | 0.527231 | − | 0.527231i | −0.392515 | − | 0.919746i | \(-0.628395\pi\) |
0.919746 | + | 0.392515i | \(0.128395\pi\) | |||||||
\(434\) | −54.3313 | −2.60799 | ||||||||
\(435\) | −18.3267 | + | 4.00269i | −0.878698 | + | 0.191914i | ||||
\(436\) | 12.6792i | 0.607225i | ||||||||
\(437\) | 1.99574 | − | 1.52780i | 0.0954691 | − | 0.0730847i | ||||
\(438\) | 15.6977 | + | 15.6977i | 0.750063 | + | 0.750063i | ||||
\(439\) | − | 16.6345i | − | 0.793923i | −0.917835 | − | 0.396962i | \(-0.870065\pi\) | ||
0.917835 | − | 0.396962i | \(-0.129935\pi\) | |||||||
\(440\) | −1.37202 | + | 0.299660i | −0.0654086 | + | 0.0142857i | ||||
\(441\) | −8.76929 | −0.417585 | ||||||||
\(442\) | 4.51080 | + | 4.51080i | 0.214557 | + | 0.214557i | ||||
\(443\) | 10.7205 | + | 10.7205i | 0.509347 | + | 0.509347i | 0.914326 | − | 0.404979i | \(-0.132721\pi\) |
−0.404979 | + | 0.914326i | \(0.632721\pi\) | |||||||
\(444\) | −31.8231 | −1.51026 | ||||||||
\(445\) | −20.4593 | − | 13.1244i | −0.969864 | − | 0.622155i | ||||
\(446\) | 30.1609 | 1.42816 | ||||||||
\(447\) | 25.9005 | + | 25.9005i | 1.22505 | + | 1.22505i | ||||
\(448\) | 19.1200 | − | 19.1200i | 0.903336 | − | 0.903336i | ||||
\(449\) | 6.41439i | 0.302714i | 0.988479 | + | 0.151357i | \(0.0483643\pi\) | ||||
−0.988479 | + | 0.151357i | \(0.951636\pi\) | |||||||
\(450\) | −4.73646 | + | 12.7637i | −0.223279 | + | 0.601687i | ||||
\(451\) | 20.5953i | 0.969793i | ||||||||
\(452\) | 5.98909 | + | 5.98909i | 0.281703 | + | 0.281703i | ||||
\(453\) | −13.1424 | − | 13.1424i | −0.617485 | − | 0.617485i | ||||
\(454\) | −43.9850 | −2.06432 | ||||||||
\(455\) | 11.3720 | − | 17.7276i | 0.533129 | − | 0.831083i | ||||
\(456\) | 0.162137i | 0.00759274i | ||||||||
\(457\) | 10.2641 | + | 10.2641i | 0.480134 | + | 0.480134i | 0.905175 | − | 0.425040i | \(-0.139740\pi\) |
−0.425040 | + | 0.905175i | \(0.639740\pi\) | |||||||
\(458\) | 0.428411 | − | 0.428411i | 0.0200183 | − | 0.0200183i | ||||
\(459\) | −4.25167 | −0.198451 | ||||||||
\(460\) | −1.71174 | − | 20.5759i | −0.0798105 | − | 0.959356i | ||||
\(461\) | 15.0573 | 0.701286 | 0.350643 | − | 0.936509i | \(-0.385963\pi\) | ||||
0.350643 | + | 0.936509i | \(0.385963\pi\) | |||||||
\(462\) | −45.5078 | + | 45.5078i | −2.11721 | + | 2.11721i | ||||
\(463\) | 8.68190 | + | 8.68190i | 0.403482 | + | 0.403482i | 0.879458 | − | 0.475976i | \(-0.157905\pi\) |
−0.475976 | + | 0.879458i | \(0.657905\pi\) | |||||||
\(464\) | 16.6210i | 0.771609i | ||||||||
\(465\) | −7.48097 | − | 34.2523i | −0.346922 | − | 1.58841i | ||||
\(466\) | −34.8903 | −1.61626 | ||||||||
\(467\) | −20.4003 | − | 20.4003i | −0.944015 | − | 0.944015i | 0.0544992 | − | 0.998514i | \(-0.482644\pi\) |
−0.998514 | + | 0.0544992i | \(0.982644\pi\) | |||||||
\(468\) | 4.81770 | + | 4.81770i | 0.222698 | + | 0.222698i | ||||
\(469\) | − | 50.8729i | − | 2.34909i | ||||||
\(470\) | 7.04092 | − | 10.9759i | 0.324773 | − | 0.506282i | ||||
\(471\) | − | 13.2145i | − | 0.608893i | ||||||
\(472\) | 1.42014 | − | 1.42014i | 0.0653674 | − | 0.0653674i | ||||
\(473\) | −27.4805 | − | 27.4805i | −1.26355 | − | 1.26355i | ||||
\(474\) | 43.4439 | 1.99544 | ||||||||
\(475\) | −1.09251 | − | 2.38178i | −0.0501279 | − | 0.109284i | ||||
\(476\) | 8.80675 | 0.403657 | ||||||||
\(477\) | −0.760320 | − | 0.760320i | −0.0348127 | − | 0.0348127i | ||||
\(478\) | −12.9391 | − | 12.9391i | −0.591821 | − | 0.591821i | ||||
\(479\) | −22.4278 | −1.02475 | −0.512376 | − | 0.858761i | \(-0.671235\pi\) | ||||
−0.512376 | + | 0.858761i | \(0.671235\pi\) | |||||||
\(480\) | 31.1524 | + | 19.9838i | 1.42191 | + | 0.912134i | ||||
\(481\) | 20.3491i | 0.927837i | ||||||||
\(482\) | 4.08417 | + | 4.08417i | 0.186029 | + | 0.186029i | ||||
\(483\) | 22.3032 | + | 29.1343i | 1.01483 | + | 1.32565i | ||||
\(484\) | 13.5299i | 0.614993i | ||||||||
\(485\) | −1.84653 | − | 8.45453i | −0.0838467 | − | 0.383900i | ||||
\(486\) | −26.3423 | −1.19491 | ||||||||
\(487\) | −3.84312 | + | 3.84312i | −0.174148 | + | 0.174148i | −0.788799 | − | 0.614651i | \(-0.789297\pi\) |
0.614651 | + | 0.788799i | \(0.289297\pi\) | |||||||
\(488\) | −0.370544 | + | 0.370544i | −0.0167737 | + | 0.0167737i | ||||
\(489\) | 47.8534i | 2.16401i | ||||||||
\(490\) | −6.03189 | − | 27.6176i | −0.272493 | − | 1.24764i | ||||
\(491\) | 22.5199 | 1.01631 | 0.508155 | − | 0.861266i | \(-0.330328\pi\) | ||||
0.508155 | + | 0.861266i | \(0.330328\pi\) | |||||||
\(492\) | 13.8118 | − | 13.8118i | 0.622683 | − | 0.622683i | ||||
\(493\) | −3.54662 | + | 3.54662i | −0.159732 | + | 0.159732i | ||||
\(494\) | −2.67362 | −0.120292 | ||||||||
\(495\) | −10.9823 | − | 7.04498i | −0.493616 | − | 0.316649i | ||||
\(496\) | −31.0644 | −1.39483 | ||||||||
\(497\) | 16.2573 | + | 16.2573i | 0.729239 | + | 0.729239i | ||||
\(498\) | 35.3662 | − | 35.3662i | 1.58480 | − | 1.58480i | ||||
\(499\) | 8.97150i | 0.401620i | 0.979630 | + | 0.200810i | \(0.0643573\pi\) | ||||
−0.979630 | + | 0.200810i | \(0.935643\pi\) | |||||||
\(500\) | −21.3144 | − | 3.01031i | −0.953210 | − | 0.134625i | ||||
\(501\) | −13.5089 | −0.603532 | ||||||||
\(502\) | 26.8745 | + | 26.8745i | 1.19947 | + | 1.19947i | ||||
\(503\) | −19.4362 | + | 19.4362i | −0.866619 | + | 0.866619i | −0.992096 | − | 0.125477i | \(-0.959954\pi\) |
0.125477 | + | 0.992096i | \(0.459954\pi\) | |||||||
\(504\) | −0.743629 | −0.0331239 | ||||||||
\(505\) | −0.918489 | − | 0.589198i | −0.0408722 | − | 0.0262190i | ||||
\(506\) | 39.9918 | + | 5.31102i | 1.77785 | + | 0.236104i | ||||
\(507\) | −9.42030 | + | 9.42030i | −0.418370 | + | 0.418370i | ||||
\(508\) | 22.3150 | + | 22.3150i | 0.990070 | + | 0.990070i | ||||
\(509\) | 14.8111i | 0.656491i | 0.944592 | + | 0.328246i | \(0.106457\pi\) | ||||
−0.944592 | + | 0.328246i | \(0.893543\pi\) | |||||||
\(510\) | 2.47225 | + | 11.3195i | 0.109473 | + | 0.501234i | ||||
\(511\) | − | 19.5974i | − | 0.866939i | ||||||
\(512\) | 22.3216 | − | 22.3216i | 0.986484 | − | 0.986484i | ||||
\(513\) | 1.26001 | − | 1.26001i | 0.0556309 | − | 0.0556309i | ||||
\(514\) | 14.2583i | 0.628906i | ||||||||
\(515\) | −12.0949 | + | 2.64161i | −0.532963 | + | 0.116403i | ||||
\(516\) | 36.8584i | 1.62260i | ||||||||
\(517\) | 8.83708 | + | 8.83708i | 0.388655 | + | 0.388655i | ||||
\(518\) | 40.4992 | + | 40.4992i | 1.77943 | + | 1.77943i | ||||
\(519\) | 16.9595i | 0.744441i | ||||||||
\(520\) | 0.459860 | − | 0.716865i | 0.0201662 | − | 0.0314366i | ||||
\(521\) | 14.1668i | 0.620661i | 0.950629 | + | 0.310330i | \(0.100440\pi\) | ||||
−0.950629 | + | 0.310330i | \(0.899560\pi\) | |||||||
\(522\) | −7.72273 | + | 7.72273i | −0.338015 | + | 0.338015i | ||||
\(523\) | −12.7188 | + | 12.7188i | −0.556155 | + | 0.556155i | −0.928211 | − | 0.372055i | \(-0.878653\pi\) |
0.372055 | + | 0.928211i | \(0.378653\pi\) | |||||||
\(524\) | − | 14.9227i | − | 0.651903i | ||||||
\(525\) | 34.7698 | − | 15.9488i | 1.51748 | − | 0.696061i | ||||
\(526\) | − | 16.2461i | − | 0.708366i | ||||||
\(527\) | −6.62858 | − | 6.62858i | −0.288745 | − | 0.288745i | ||||
\(528\) | −26.0194 | + | 26.0194i | −1.13235 | + | 1.13235i | ||||
\(529\) | 6.00306 | − | 22.2028i | 0.261002 | − | 0.965338i | ||||
\(530\) | 1.87153 | − | 2.91749i | 0.0812942 | − | 0.126728i | ||||
\(531\) | 18.6595 | 0.809755 | ||||||||
\(532\) | −2.60994 | + | 2.60994i | −0.113155 | + | 0.113155i | ||||
\(533\) | −8.83184 | − | 8.83184i | −0.382550 | − | 0.382550i | ||||
\(534\) | −45.0443 | −1.94926 | ||||||||
\(535\) | −3.28670 | − | 15.0485i | −0.142096 | − | 0.650602i | ||||
\(536\) | − | 2.05719i | − | 0.0888570i | ||||||
\(537\) | −5.77718 | + | 5.77718i | −0.249304 | + | 0.249304i | ||||
\(538\) | −9.14050 | − | 9.14050i | −0.394075 | − | 0.394075i | ||||
\(539\) | 27.0923 | 1.16695 | ||||||||
\(540\) | −3.12345 | − | 14.3010i | −0.134412 | − | 0.615417i | ||||
\(541\) | 5.11180 | 0.219773 | 0.109887 | − | 0.993944i | \(-0.464951\pi\) | ||||
0.109887 | + | 0.993944i | \(0.464951\pi\) | |||||||
\(542\) | 21.9821 | − | 21.9821i | 0.944210 | − | 0.944210i | ||||
\(543\) | −31.4373 | + | 31.4373i | −1.34910 | + | 1.34910i | ||||
\(544\) | 9.89599 | 0.424287 | ||||||||
\(545\) | 12.3945 | + | 7.95092i | 0.530923 | + | 0.340580i | ||||
\(546\) | − | 39.0301i | − | 1.67033i | ||||||
\(547\) | −13.4172 | + | 13.4172i | −0.573680 | + | 0.573680i | −0.933155 | − | 0.359475i | \(-0.882956\pi\) |
0.359475 | + | 0.933155i | \(0.382956\pi\) | |||||||
\(548\) | 13.7210 | − | 13.7210i | 0.586133 | − | 0.586133i | ||||
\(549\) | −4.86865 | −0.207789 | ||||||||
\(550\) | 14.6331 | − | 39.4329i | 0.623956 | − | 1.68142i | ||||
\(551\) | − | 2.10213i | − | 0.0895538i | ||||||
\(552\) | 0.901893 | + | 1.17813i | 0.0383871 | + | 0.0501443i | ||||
\(553\) | −27.1183 | − | 27.1183i | −1.15319 | − | 1.15319i | ||||
\(554\) | − | 35.1753i | − | 1.49445i | ||||||
\(555\) | −19.9557 | + | 31.1085i | −0.847072 | + | 1.32048i | ||||
\(556\) | 18.8345 | 0.798762 | ||||||||
\(557\) | −14.6983 | − | 14.6983i | −0.622787 | − | 0.622787i | 0.323456 | − | 0.946243i | \(-0.395155\pi\) |
−0.946243 | + | 0.323456i | \(0.895155\pi\) | |||||||
\(558\) | −14.4337 | − | 14.4337i | −0.611026 | − | 0.611026i | ||||
\(559\) | 23.5689 | 0.996857 | ||||||||
\(560\) | −7.23218 | − | 33.1132i | −0.305616 | − | 1.39929i | ||||
\(561\) | −11.1042 | −0.468818 | ||||||||
\(562\) | −7.95775 | − | 7.95775i | −0.335678 | − | 0.335678i | ||||
\(563\) | −5.00617 | + | 5.00617i | −0.210985 | + | 0.210985i | −0.804686 | − | 0.593701i | \(-0.797666\pi\) |
0.593701 | + | 0.804686i | \(0.297666\pi\) | |||||||
\(564\) | − | 11.8528i | − | 0.499093i | ||||||
\(565\) | 9.61025 | − | 2.09895i | 0.404306 | − | 0.0883036i | ||||
\(566\) | 13.2441i | 0.556690i | ||||||||
\(567\) | 29.0583 | + | 29.0583i | 1.22033 | + | 1.22033i | ||||
\(568\) | 0.657409 | + | 0.657409i | 0.0275843 | + | 0.0275843i | ||||
\(569\) | −15.2554 | −0.639540 | −0.319770 | − | 0.947495i | \(-0.603606\pi\) | ||||
−0.319770 | + | 0.947495i | \(0.603606\pi\) | |||||||
\(570\) | −4.08727 | − | 2.62193i | −0.171197 | − | 0.109821i | ||||
\(571\) | − | 31.6677i | − | 1.32525i | −0.748951 | − | 0.662626i | \(-0.769442\pi\) | ||
0.748951 | − | 0.662626i | \(-0.230558\pi\) | |||||||
\(572\) | −14.8840 | − | 14.8840i | −0.622333 | − | 0.622333i | ||||
\(573\) | −4.11615 | + | 4.11615i | −0.171955 | + | 0.171955i | ||||
\(574\) | −35.1547 | −1.46733 | ||||||||
\(575\) | −21.1872 | − | 11.2295i | −0.883569 | − | 0.468301i | ||||
\(576\) | 10.1589 | 0.423286 | ||||||||
\(577\) | 2.19187 | − | 2.19187i | 0.0912488 | − | 0.0912488i | −0.660009 | − | 0.751258i | \(-0.729448\pi\) |
0.751258 | + | 0.660009i | \(0.229448\pi\) | |||||||
\(578\) | −21.6256 | − | 21.6256i | −0.899508 | − | 0.899508i | ||||
\(579\) | − | 28.1091i | − | 1.16818i | ||||||
\(580\) | −14.5350 | − | 9.32400i | −0.603532 | − | 0.387158i | ||||
\(581\) | −44.1522 | −1.83174 | ||||||||
\(582\) | −11.3397 | − | 11.3397i | −0.470046 | − | 0.470046i | ||||
\(583\) | 2.34897 | + | 2.34897i | 0.0972844 | + | 0.0972844i | ||||
\(584\) | − | 0.792477i | − | 0.0327929i | ||||||
\(585\) | 7.73061 | − | 1.68842i | 0.319621 | − | 0.0698077i | ||||
\(586\) | 43.6792i | 1.80437i | ||||||||
\(587\) | 0.610131 | − | 0.610131i | 0.0251828 | − | 0.0251828i | −0.694403 | − | 0.719586i | \(-0.744332\pi\) |
0.719586 | + | 0.694403i | \(0.244332\pi\) | |||||||
\(588\) | −18.1689 | − | 18.1689i | −0.749271 | − | 0.749271i | ||||
\(589\) | 3.92885 | 0.161886 | ||||||||
\(590\) | 12.8348 | + | 58.7654i | 0.528401 | + | 2.41933i | ||||
\(591\) | 5.83112 | 0.239860 | ||||||||
\(592\) | 23.1557 | + | 23.1557i | 0.951695 | + | 0.951695i | ||||
\(593\) | −20.2560 | − | 20.2560i | −0.831816 | − | 0.831816i | 0.155950 | − | 0.987765i | \(-0.450156\pi\) |
−0.987765 | + | 0.155950i | \(0.950156\pi\) | |||||||
\(594\) | 28.6020 | 1.17355 | ||||||||
\(595\) | 5.52256 | − | 8.60899i | 0.226403 | − | 0.352934i | ||||
\(596\) | 33.7191i | 1.38119i | ||||||||
\(597\) | −15.6511 | − | 15.6511i | −0.640557 | − | 0.640557i | ||||
\(598\) | −19.4272 | + | 14.8721i | −0.794436 | + | 0.608166i | ||||
\(599\) | − | 14.9856i | − | 0.612293i | −0.951984 | − | 0.306147i | \(-0.900960\pi\) | ||
0.951984 | − | 0.306147i | \(-0.0990398\pi\) | |||||||
\(600\) | 1.40601 | − | 0.644933i | 0.0574003 | − | 0.0263293i | ||||
\(601\) | −9.54167 | −0.389213 | −0.194606 | − | 0.980881i | \(-0.562343\pi\) | ||||
−0.194606 | + | 0.980881i | \(0.562343\pi\) | |||||||
\(602\) | 46.9073 | − | 46.9073i | 1.91180 | − | 1.91180i | ||||
\(603\) | 13.5149 | − | 13.5149i | 0.550369 | − | 0.550369i | ||||
\(604\) | − | 17.1097i | − | 0.696186i | ||||||
\(605\) | 13.2260 | + | 8.48433i | 0.537715 | + | 0.344937i | ||||
\(606\) | −2.02220 | −0.0821461 | ||||||||
\(607\) | −4.08607 | + | 4.08607i | −0.165849 | + | 0.165849i | −0.785152 | − | 0.619303i | \(-0.787415\pi\) |
0.619303 | + | 0.785152i | \(0.287415\pi\) | |||||||
\(608\) | −2.93275 | + | 2.93275i | −0.118939 | + | 0.118939i | ||||
\(609\) | 30.6874 | 1.24352 | ||||||||
\(610\) | −3.34886 | − | 15.3331i | −0.135591 | − | 0.620818i | ||||
\(611\) | −7.57919 | −0.306621 | ||||||||
\(612\) | 2.33960 | + | 2.33960i | 0.0945728 | + | 0.0945728i | ||||
\(613\) | −28.0640 | + | 28.0640i | −1.13349 | + | 1.13349i | −0.143901 | + | 0.989592i | \(0.545965\pi\) |
−0.989592 | + | 0.143901i | \(0.954035\pi\) | |||||||
\(614\) | 1.51285i | 0.0610535i | ||||||||
\(615\) | −4.84051 | − | 22.1627i | −0.195188 | − | 0.893688i | ||||
\(616\) | 2.29740 | 0.0925650 | ||||||||
\(617\) | −24.8729 | − | 24.8729i | −1.00134 | − | 1.00134i | −0.999999 | − | 0.00134503i | \(-0.999572\pi\) |
−0.00134503 | − | 0.999999i | \(-0.500428\pi\) | |||||||
\(618\) | −16.2223 | + | 16.2223i | −0.652557 | + | 0.652557i | ||||
\(619\) | 13.5552 | 0.544831 | 0.272416 | − | 0.962180i | \(-0.412177\pi\) | ||||
0.272416 | + | 0.962180i | \(0.412177\pi\) | |||||||
\(620\) | 17.4264 | − | 27.1657i | 0.699862 | − | 1.09100i | ||||
\(621\) | 2.14668 | − | 16.1644i | 0.0861434 | − | 0.648657i | ||||
\(622\) | 19.4893 | − | 19.4893i | 0.781450 | − | 0.781450i | ||||
\(623\) | 28.1173 | + | 28.1173i | 1.12650 | + | 1.12650i | ||||
\(624\) | − | 22.3158i | − | 0.893345i | ||||||
\(625\) | −16.3086 | + | 18.9481i | −0.652344 | + | 0.757923i | ||||
\(626\) | − | 45.6972i | − | 1.82643i | ||||||
\(627\) | 3.29080 | − | 3.29080i | 0.131422 | − | 0.131422i | ||||
\(628\) | 8.60179 | − | 8.60179i | 0.343249 | − | 0.343249i | ||||
\(629\) | 9.88204i | 0.394023i | ||||||||
\(630\) | 12.0253 | − | 18.7460i | 0.479100 | − | 0.746858i | ||||
\(631\) | − | 16.9812i | − | 0.676012i | −0.941144 | − | 0.338006i | \(-0.890248\pi\) | ||
0.941144 | − | 0.338006i | \(-0.109752\pi\) | |||||||
\(632\) | −1.09661 | − | 1.09661i | −0.0436206 | − | 0.0436206i | ||||
\(633\) | 11.1498 | + | 11.1498i | 0.443165 | + | 0.443165i | ||||
\(634\) | 28.0551i | 1.11421i | ||||||||
\(635\) | 35.8073 | − | 7.82058i | 1.42097 | − | 0.310350i | ||||
\(636\) | − | 3.15057i | − | 0.124928i | ||||||
\(637\) | −11.6180 | + | 11.6180i | −0.460320 | + | 0.460320i | ||||
\(638\) | 23.8590 | − | 23.8590i | 0.944586 | − | 0.944586i | ||||
\(639\) | 8.63782i | 0.341707i | ||||||||
\(640\) | −0.564223 | − | 2.58335i | −0.0223029 | − | 0.102116i | ||||
\(641\) | 48.2196i | 1.90456i | 0.305225 | + | 0.952280i | \(0.401268\pi\) | ||||
−0.305225 | + | 0.952280i | \(0.598732\pi\) | |||||||
\(642\) | −20.1839 | − | 20.1839i | −0.796594 | − | 0.796594i | ||||
\(643\) | −19.8040 | + | 19.8040i | −0.780992 | + | 0.780992i | −0.979998 | − | 0.199006i | \(-0.936229\pi\) |
0.199006 | + | 0.979998i | \(0.436229\pi\) | |||||||
\(644\) | −4.44656 | + | 33.4825i | −0.175219 | + | 1.31939i | ||||
\(645\) | 36.0307 | + | 23.1132i | 1.41871 | + | 0.910083i | ||||
\(646\) | −1.29838 | −0.0510840 | ||||||||
\(647\) | 7.63032 | − | 7.63032i | 0.299979 | − | 0.299979i | −0.541027 | − | 0.841005i | \(-0.681964\pi\) |
0.841005 | + | 0.541027i | \(0.181964\pi\) | |||||||
\(648\) | 1.17505 | + | 1.17505i | 0.0461604 | + | 0.0461604i | ||||
\(649\) | −57.6477 | −2.26287 | ||||||||
\(650\) | 10.6349 | + | 23.1850i | 0.417134 | + | 0.909392i | ||||
\(651\) | 57.3543i | 2.24789i | ||||||||
\(652\) | −31.1495 | + | 31.1495i | −1.21991 | + | 1.21991i | ||||
\(653\) | 28.6922 | + | 28.6922i | 1.12281 | + | 1.12281i | 0.991317 | + | 0.131497i | \(0.0419784\pi\) |
0.131497 | + | 0.991317i | \(0.458022\pi\) | |||||||
\(654\) | 27.2885 | 1.06706 | ||||||||
\(655\) | −14.5876 | − | 9.35778i | −0.569986 | − | 0.365639i | ||||
\(656\) | −20.1000 | −0.784773 | ||||||||
\(657\) | 5.20626 | − | 5.20626i | 0.203115 | − | 0.203115i | ||||
\(658\) | −15.0843 | + | 15.0843i | −0.588047 | + | 0.588047i | ||||
\(659\) | 42.3419 | 1.64941 | 0.824704 | − | 0.565564i | \(-0.191342\pi\) | ||||
0.824704 | + | 0.565564i | \(0.191342\pi\) | |||||||
\(660\) | −8.15756 | − | 37.3502i | −0.317533 | − | 1.45385i | ||||
\(661\) | − | 16.0529i | − | 0.624385i | −0.950019 | − | 0.312192i | \(-0.898937\pi\) | ||
0.950019 | − | 0.312192i | \(-0.101063\pi\) | |||||||
\(662\) | −19.7131 | + | 19.7131i | −0.766170 | + | 0.766170i | ||||
\(663\) | 4.76178 | − | 4.76178i | 0.184932 | − | 0.184932i | ||||
\(664\) | −1.78542 | −0.0692876 | ||||||||
\(665\) | 0.914688 | + | 4.18799i | 0.0354701 | + | 0.162403i | ||||
\(666\) | 21.5180i | 0.833807i | ||||||||
\(667\) | −11.6932 | − | 15.2746i | −0.452763 | − | 0.591435i | ||||
\(668\) | −8.79340 | − | 8.79340i | −0.340227 | − | 0.340227i | ||||
\(669\) | − | 31.8390i | − | 1.23097i | ||||||
\(670\) | 51.8592 | + | 33.2670i | 2.00350 | + | 1.28522i | ||||
\(671\) | 15.0414 | 0.580669 | ||||||||
\(672\) | −42.8129 | − | 42.8129i | −1.65154 | − | 1.65154i | ||||
\(673\) | 12.1544 | + | 12.1544i | 0.468518 | + | 0.468518i | 0.901434 | − | 0.432916i | \(-0.142515\pi\) |
−0.432916 | + | 0.901434i | \(0.642515\pi\) | |||||||
\(674\) | −7.59714 | −0.292631 | ||||||||
\(675\) | −15.9385 | − | 5.91459i | −0.613474 | − | 0.227653i | ||||
\(676\) | −12.2640 | −0.471692 | ||||||||
\(677\) | 9.71268 | + | 9.71268i | 0.373289 | + | 0.373289i | 0.868674 | − | 0.495385i | \(-0.164973\pi\) |
−0.495385 | + | 0.868674i | \(0.664973\pi\) | |||||||
\(678\) | 12.8898 | − | 12.8898i | 0.495031 | − | 0.495031i | ||||
\(679\) | 14.1568i | 0.543289i | ||||||||
\(680\) | 0.223320 | − | 0.348129i | 0.00856393 | − | 0.0133501i | ||||
\(681\) | 46.4323i | 1.77929i | ||||||||
\(682\) | 44.5921 | + | 44.5921i | 1.70752 | + | 1.70752i | ||||
\(683\) | −6.18689 | − | 6.18689i | −0.236735 | − | 0.236735i | 0.578762 | − | 0.815497i | \(-0.303536\pi\) |
−0.815497 | + | 0.578762i | \(0.803536\pi\) | |||||||
\(684\) | −1.38672 | −0.0530224 | ||||||||
\(685\) | −4.80870 | − | 22.0171i | −0.183731 | − | 0.841231i | ||||
\(686\) | − | 4.48696i | − | 0.171313i | ||||||
\(687\) | −0.452247 | − | 0.452247i | −0.0172543 | − | 0.0172543i | ||||
\(688\) | 26.8196 | − | 26.8196i | 1.02249 | − | 1.02249i | ||||
\(689\) | −2.01461 | −0.0767506 | ||||||||
\(690\) | −44.2838 | + | 3.68404i | −1.68585 | + | 0.140249i | ||||
\(691\) | −4.66320 | −0.177396 | −0.0886982 | − | 0.996059i | \(-0.528271\pi\) | ||||
−0.0886982 | + | 0.996059i | \(0.528271\pi\) | |||||||
\(692\) | −11.0396 | + | 11.0396i | −0.419661 | + | 0.419661i | ||||
\(693\) | 15.0930 | + | 15.0930i | 0.573336 | + | 0.573336i | ||||
\(694\) | 62.5029i | 2.37258i | ||||||||
\(695\) | 11.8108 | − | 18.4116i | 0.448009 | − | 0.698391i | ||||
\(696\) | 1.24093 | 0.0470374 | ||||||||
\(697\) | −4.28898 | − | 4.28898i | −0.162457 | − | 0.162457i | ||||
\(698\) | −7.36761 | − | 7.36761i | −0.278868 | − | 0.278868i | ||||
\(699\) | 36.8316i | 1.39310i | ||||||||
\(700\) | 33.0145 | + | 12.2513i | 1.24783 | + | 0.463055i | ||||
\(701\) | − | 13.2720i | − | 0.501276i | −0.968081 | − | 0.250638i | \(-0.919360\pi\) | ||
0.968081 | − | 0.250638i | \(-0.0806404\pi\) | |||||||
\(702\) | −12.2654 | + | 12.2654i | −0.462926 | + | 0.462926i | ||||
\(703\) | −2.92861 | − | 2.92861i | −0.110455 | − | 0.110455i | ||||
\(704\) | −31.3853 | −1.18288 | ||||||||
\(705\) | −11.5866 | − | 7.43268i | −0.436378 | − | 0.279931i | ||||
\(706\) | 64.4271 | 2.42475 | ||||||||
\(707\) | 1.26229 | + | 1.26229i | 0.0474731 | + | 0.0474731i | ||||
\(708\) | 38.6602 | + | 38.6602i | 1.45294 | + | 1.45294i | ||||
\(709\) | 29.4992 | 1.10787 | 0.553934 | − | 0.832561i | \(-0.313126\pi\) | ||||
0.553934 | + | 0.832561i | \(0.313126\pi\) | |||||||
\(710\) | −27.2035 | + | 5.94146i | −1.02093 | + | 0.222979i | ||||
\(711\) | − | 14.4085i | − | 0.540361i | ||||||
\(712\) | 1.13700 | + | 1.13700i | 0.0426110 | + | 0.0426110i | ||||
\(713\) | 28.5480 | − | 21.8544i | 1.06913 | − | 0.818455i | ||||
\(714\) | − | 18.9540i | − | 0.709337i | ||||||
\(715\) | −23.8833 | + | 5.21630i | −0.893186 | + | 0.195078i | ||||
\(716\) | −7.52114 | −0.281078 | ||||||||
\(717\) | −13.6590 | + | 13.6590i | −0.510106 | + | 0.510106i | ||||
\(718\) | −9.53171 | + | 9.53171i | −0.355720 | + | 0.355720i | ||||
\(719\) | 13.9897i | 0.521729i | 0.965375 | + | 0.260865i | \(0.0840076\pi\) | ||||
−0.965375 | + | 0.260865i | \(0.915992\pi\) | |||||||
\(720\) | 6.87557 | − | 10.7182i | 0.256237 | − | 0.399443i | ||||
\(721\) | 20.2524 | 0.754239 | ||||||||
\(722\) | −26.2333 | + | 26.2333i | −0.976303 | + | 0.976303i | ||||
\(723\) | 4.31141 | − | 4.31141i | 0.160343 | − | 0.160343i | ||||
\(724\) | −40.9273 | −1.52105 | ||||||||
\(725\) | −18.2292 | + | 8.36167i | −0.677017 | + | 0.310545i | ||||
\(726\) | 29.1192 | 1.08071 | ||||||||
\(727\) | 6.81675 | + | 6.81675i | 0.252819 | + | 0.252819i | 0.822126 | − | 0.569306i | \(-0.192788\pi\) |
−0.569306 | + | 0.822126i | \(0.692788\pi\) | |||||||
\(728\) | −0.985193 | + | 0.985193i | −0.0365137 | + | 0.0365137i | ||||
\(729\) | − | 5.89460i | − | 0.218319i | ||||||
\(730\) | 19.9774 | + | 12.8152i | 0.739397 | + | 0.474313i | ||||
\(731\) | 11.4457 | 0.423333 | ||||||||
\(732\) | −10.0872 | − | 10.0872i | −0.372835 | − | 0.372835i | ||||
\(733\) | 19.6235 | − | 19.6235i | 0.724812 | − | 0.724812i | −0.244769 | − | 0.969581i | \(-0.578712\pi\) |
0.969581 | + | 0.244769i | \(0.0787122\pi\) | |||||||
\(734\) | −9.93729 | −0.366792 | ||||||||
\(735\) | −29.1542 | + | 6.36751i | −1.07537 | + | 0.234869i | ||||
\(736\) | −4.99652 | + | 37.6236i | −0.184174 | + | 1.38682i | ||||
\(737\) | −41.7536 | + | 41.7536i | −1.53801 | + | 1.53801i | ||||
\(738\) | −9.33920 | − | 9.33920i | −0.343781 | − | 0.343781i | ||||
\(739\) | − | 20.0313i | − | 0.736864i | −0.929655 | − | 0.368432i | \(-0.879895\pi\) | ||
0.929655 | − | 0.368432i | \(-0.120105\pi\) | |||||||
\(740\) | −33.2395 | + | 7.25975i | −1.22191 | + | 0.266874i | ||||
\(741\) | 2.82238i | 0.103683i | ||||||||
\(742\) | −4.00953 | + | 4.00953i | −0.147195 | + | 0.147195i | ||||
\(743\) | −18.2305 | + | 18.2305i | −0.668812 | + | 0.668812i | −0.957441 | − | 0.288629i | \(-0.906801\pi\) |
0.288629 | + | 0.957441i | \(0.406801\pi\) | |||||||
\(744\) | 2.31928i | 0.0850291i | ||||||||
\(745\) | 32.9619 | + | 21.1446i | 1.20763 | + | 0.774678i | ||||
\(746\) | − | 12.9395i | − | 0.473750i | ||||||
\(747\) | −11.7295 | − | 11.7295i | −0.429159 | − | 0.429159i | ||||
\(748\) | −7.22809 | − | 7.22809i | −0.264285 | − | 0.264285i | ||||
\(749\) | 25.1981i | 0.920720i | ||||||||
\(750\) | −6.47884 | + | 45.8732i | −0.236574 | + | 1.67505i | ||||
\(751\) | 24.9495i | 0.910419i | 0.890384 | + | 0.455210i | \(0.150436\pi\) | ||||
−0.890384 | + | 0.455210i | \(0.849564\pi\) | |||||||
\(752\) | −8.62457 | + | 8.62457i | −0.314506 | + | 0.314506i | ||||
\(753\) | 28.3698 | − | 28.3698i | 1.03385 | − | 1.03385i | ||||
\(754\) | 20.4628i | 0.745212i | ||||||||
\(755\) | −16.7255 | − | 10.7292i | −0.608704 | − | 0.390476i | ||||
\(756\) | 23.9465i | 0.870928i | ||||||||
\(757\) | 14.3452 | + | 14.3452i | 0.521386 | + | 0.521386i | 0.917990 | − | 0.396604i | \(-0.129811\pi\) |
−0.396604 | + | 0.917990i | \(0.629811\pi\) | |||||||
\(758\) | 39.2654 | − | 39.2654i | 1.42618 | − | 1.42618i | ||||
\(759\) | 5.60653 | − | 42.2170i | 0.203504 | − | 1.53238i | ||||
\(760\) | 0.0369880 | + | 0.169353i | 0.00134169 | + | 0.00614308i | ||||
\(761\) | −17.8213 | −0.646023 | −0.323012 | − | 0.946395i | \(-0.604695\pi\) | ||||
−0.323012 | + | 0.946395i | \(0.604695\pi\) | |||||||
\(762\) | 48.0268 | − | 48.0268i | 1.73983 | − | 1.73983i | ||||
\(763\) | −17.0339 | − | 17.0339i | −0.616667 | − | 0.616667i | ||||
\(764\) | −5.35870 | −0.193871 | ||||||||
\(765\) | 3.75419 | − | 0.819943i | 0.135733 | − | 0.0296451i | ||||
\(766\) | − | 69.7534i | − | 2.52029i | ||||||
\(767\) | 24.7210 | − | 24.7210i | 0.892623 | − | 0.892623i | ||||
\(768\) | −25.3290 | − | 25.3290i | −0.913981 | − | 0.913981i | ||||
\(769\) | 10.1694 | 0.366717 | 0.183359 | − | 0.983046i | \(-0.441303\pi\) | ||||
0.183359 | + | 0.983046i | \(0.441303\pi\) | |||||||
\(770\) | −37.1516 | + | 57.9148i | −1.33885 | + | 2.08710i | ||||
\(771\) | 15.0516 | 0.542071 | ||||||||
\(772\) | 18.2972 | − | 18.2972i | 0.658531 | − | 0.658531i | ||||
\(773\) | 0.320217 | − | 0.320217i | 0.0115174 | − | 0.0115174i | −0.701325 | − | 0.712842i | \(-0.747408\pi\) |
0.712842 | + | 0.701325i | \(0.247408\pi\) | |||||||
\(774\) | 24.9228 | 0.895832 | ||||||||
\(775\) | −15.6278 | − | 34.0702i | −0.561369 | − | 1.22384i | ||||
\(776\) | 0.572471i | 0.0205505i | ||||||||
\(777\) | 42.7526 | − | 42.7526i | 1.53374 | − | 1.53374i | ||||
\(778\) | −17.9107 | + | 17.9107i | −0.642131 | + | 0.642131i | ||||
\(779\) | 2.54214 | 0.0910815 | ||||||||
\(780\) | 19.5150 | + | 12.5186i | 0.698750 | + | 0.448239i | ||||
\(781\) | − | 26.6861i | − | 0.954905i | ||||||
\(782\) | −9.43434 | + | 7.22229i | −0.337371 | + | 0.258269i | ||||
\(783\) | −9.64365 | − | 9.64365i | −0.344636 | − | 0.344636i | ||||
\(784\) | 26.4408i | 0.944313i | ||||||||
\(785\) | −3.01460 | − | 13.8027i | −0.107596 | − | 0.492638i | ||||
\(786\) | −32.1170 | −1.14557 | ||||||||
\(787\) | −14.4826 | − | 14.4826i | −0.516249 | − | 0.516249i | 0.400185 | − | 0.916434i | \(-0.368946\pi\) |
−0.916434 | + | 0.400185i | \(0.868946\pi\) | |||||||
\(788\) | 3.79568 | + | 3.79568i | 0.135216 | + | 0.135216i | ||||
\(789\) | −17.1501 | −0.610559 | ||||||||
\(790\) | 45.3775 | − | 9.91078i | 1.61446 | − | 0.352610i | ||||
\(791\) | −16.0920 | −0.572167 | ||||||||
\(792\) | 0.610328 | + | 0.610328i | 0.0216871 | + | 0.0216871i | ||||
\(793\) | −6.45021 | + | 6.45021i | −0.229053 | + | 0.229053i | ||||
\(794\) | − | 76.0880i | − | 2.70026i | ||||||
\(795\) | −3.07982 | − | 1.97567i | −0.109230 | − | 0.0700697i | ||||
\(796\) | − | 20.3757i | − | 0.722198i | ||||||
\(797\) | −14.6932 | − | 14.6932i | −0.520460 | − | 0.520460i | 0.397250 | − | 0.917710i | \(-0.369964\pi\) |
−0.917710 | + | 0.397250i | \(0.869964\pi\) | |||||||
\(798\) | 5.61717 | + | 5.61717i | 0.198846 | + | 0.198846i | ||||
\(799\) | −3.68066 | −0.130212 | ||||||||
\(800\) | 37.0978 | + | 13.7665i | 1.31160 | + | 0.486721i | ||||
\(801\) | 14.9393i | 0.527855i | ||||||||
\(802\) | 14.9389 | + | 14.9389i | 0.527509 | + | 0.527509i | ||||
\(803\) | −16.0845 | + | 16.0845i | −0.567608 | + | 0.567608i | ||||
\(804\) | 56.0023 | 1.97505 | ||||||||
\(805\) | 29.9422 | + | 25.3430i | 1.05532 | + | 0.893222i | ||||
\(806\) | −38.2447 | −1.34711 | ||||||||
\(807\) | −9.64908 | + | 9.64908i | −0.339664 | + | 0.339664i | ||||
\(808\) | 0.0510440 | + | 0.0510440i | 0.00179572 | + | 0.00179572i | ||||
\(809\) | − | 33.3168i | − | 1.17136i | −0.810544 | − | 0.585678i | \(-0.800828\pi\) | ||
0.810544 | − | 0.585678i | \(-0.199172\pi\) | |||||||
\(810\) | −48.6236 | + | 10.6198i | −1.70846 | + | 0.373140i | ||||
\(811\) | 24.0519 | 0.844575 | 0.422288 | − | 0.906462i | \(-0.361227\pi\) | ||||
0.422288 | + | 0.906462i | \(0.361227\pi\) | |||||||
\(812\) | 19.9755 | + | 19.9755i | 0.701003 | + | 0.701003i | ||||
\(813\) | −23.2052 | − | 23.2052i | −0.813840 | − | 0.813840i | ||||
\(814\) | − | 66.4789i | − | 2.33008i | ||||||
\(815\) | 10.9167 | + | 49.9833i | 0.382396 | + | 1.75084i | ||||
\(816\) | − | 10.8371i | − | 0.379375i | ||||||
\(817\) | −3.39200 | + | 3.39200i | −0.118671 | + | 0.118671i | ||||
\(818\) | 32.5687 | + | 32.5687i | 1.13874 | + | 1.13874i | ||||
\(819\) | −12.9446 | −0.452322 | ||||||||
\(820\) | 11.2756 | − | 17.5774i | 0.393763 | − | 0.613828i | ||||
\(821\) | −11.2195 | −0.391563 | −0.195781 | − | 0.980648i | \(-0.562724\pi\) | ||||
−0.195781 | + | 0.980648i | \(0.562724\pi\) | |||||||
\(822\) | −29.5306 | − | 29.5306i | −1.03000 | − | 1.03000i | ||||
\(823\) | −16.9341 | − | 16.9341i | −0.590286 | − | 0.590286i | 0.347423 | − | 0.937709i | \(-0.387057\pi\) |
−0.937709 | + | 0.347423i | \(0.887057\pi\) | |||||||
\(824\) | 0.818963 | 0.0285299 | ||||||||
\(825\) | −41.6269 | − | 15.4472i | −1.44926 | − | 0.537804i | ||||
\(826\) | − | 98.4007i | − | 3.42380i | ||||||
\(827\) | −2.86855 | − | 2.86855i | −0.0997493 | − | 0.0997493i | 0.655471 | − | 0.755220i | \(-0.272470\pi\) |
−0.755220 | + | 0.655471i | \(0.772470\pi\) | |||||||
\(828\) | −10.0762 | + | 7.71368i | −0.350173 | + | 0.268069i | ||||
\(829\) | 43.1039i | 1.49706i | 0.663100 | + | 0.748531i | \(0.269240\pi\) | ||||
−0.663100 | + | 0.748531i | \(0.730760\pi\) | |||||||
\(830\) | 28.8722 | − | 45.0083i | 1.00217 | − | 1.56226i | ||||
\(831\) | −37.1325 | −1.28811 | ||||||||
\(832\) | 13.4589 | − | 13.4589i | 0.466604 | − | 0.466604i | ||||
\(833\) | −5.64199 | + | 5.64199i | −0.195483 | + | 0.195483i | ||||
\(834\) | − | 40.5360i | − | 1.40365i | ||||||
\(835\) | −14.1101 | + | 3.08175i | −0.488301 | + | 0.106649i | ||||
\(836\) | 4.28419 | 0.148172 | ||||||||
\(837\) | 18.0238 | − | 18.0238i | 0.622995 | − | 0.622995i | ||||
\(838\) | 40.8878 | − | 40.8878i | 1.41244 | − | 1.41244i | ||||
\(839\) | 3.14028 | 0.108415 | 0.0542073 | − | 0.998530i | \(-0.482737\pi\) | ||||
0.0542073 | + | 0.998530i | \(0.482737\pi\) | |||||||
\(840\) | −2.47225 | + | 0.539959i | −0.0853009 | + | 0.0186304i | ||||
\(841\) | 12.9111 | 0.445210 | ||||||||
\(842\) | 2.04150 | + | 2.04150i | 0.0703547 | + | 0.0703547i | ||||
\(843\) | −8.40053 | + | 8.40053i | −0.289329 | + | 0.289329i | ||||
\(844\) | 14.5156i | 0.499648i | ||||||||
\(845\) | −7.69053 | + | 11.9886i | −0.264562 | + | 0.412421i | ||||
\(846\) | −8.01459 | −0.275547 | ||||||||
\(847\) | −18.1766 | − | 18.1766i | −0.624556 | − | 0.624556i | ||||
\(848\) | −2.29248 | + | 2.29248i | −0.0787241 | + | 0.0787241i | ||||
\(849\) | 13.9810 | 0.479826 | ||||||||
\(850\) | 5.16458 | + | 11.2593i | 0.177143 | + | 0.386190i | ||||
\(851\) | −37.5706 | − | 4.98948i | −1.28790 | − | 0.171037i | ||||
\(852\) | −17.8965 | + | 17.8965i | −0.613123 | + | 0.613123i | ||||
\(853\) | 25.8718 | + | 25.8718i | 0.885834 | + | 0.885834i | 0.994120 | − | 0.108286i | \(-0.0345361\pi\) |
−0.108286 | + | 0.994120i | \(0.534536\pi\) | |||||||
\(854\) | 25.6747i | 0.878571i | ||||||||
\(855\) | −0.869584 | + | 1.35558i | −0.0297392 | + | 0.0463597i | ||||
\(856\) | 1.01896i | 0.0348273i | ||||||||
\(857\) | −4.61744 | + | 4.61744i | −0.157729 | + | 0.157729i | −0.781560 | − | 0.623831i | \(-0.785575\pi\) |
0.623831 | + | 0.781560i | \(0.285575\pi\) | |||||||
\(858\) | −32.0337 | + | 32.0337i | −1.09361 | + | 1.09361i | ||||
\(859\) | − | 14.4628i | − | 0.493464i | −0.969084 | − | 0.246732i | \(-0.920643\pi\) | ||
0.969084 | − | 0.246732i | \(-0.0793568\pi\) | |||||||
\(860\) | 8.40845 | + | 38.4989i | 0.286726 | + | 1.31280i | ||||
\(861\) | 37.1107i | 1.26473i | ||||||||
\(862\) | −0.815913 | − | 0.815913i | −0.0277901 | − | 0.0277901i | ||||
\(863\) | 0.0304482 | + | 0.0304482i | 0.00103647 | + | 0.00103647i | 0.707625 | − | 0.706588i | \(-0.249767\pi\) |
−0.706588 | + | 0.707625i | \(0.749767\pi\) | |||||||
\(864\) | 26.9083i | 0.915439i | ||||||||
\(865\) | 3.86895 | + | 17.7144i | 0.131548 | + | 0.602306i | ||||
\(866\) | − | 30.7396i | − | 1.04458i | ||||||
\(867\) | −22.8289 | + | 22.8289i | −0.775310 | + | 0.775310i | ||||
\(868\) | −37.3340 | + | 37.3340i | −1.26720 | + | 1.26720i | ||||
\(869\) | 44.5144i | 1.51005i | ||||||||
\(870\) | −20.0673 | + | 31.2824i | −0.680344 | + | 1.06057i | ||||
\(871\) | − | 35.8103i | − | 1.21338i | ||||||
\(872\) | −0.688812 | − | 0.688812i | −0.0233261 | − | 0.0233261i | ||||
\(873\) | −3.76090 | + | 3.76090i | −0.127287 | + | 0.127287i | ||||
\(874\) | 0.655556 | − | 4.93631i | 0.0221745 | − | 0.166973i | ||||
\(875\) | 32.6790 | − | 24.5906i | 1.10475 | − | 0.831313i | ||||
\(876\) | 21.5734 | 0.728898 | ||||||||
\(877\) | 10.1873 | − | 10.1873i | 0.344000 | − | 0.344000i | −0.513869 | − | 0.857869i | \(-0.671788\pi\) |
0.857869 | + | 0.513869i | \(0.171788\pi\) | |||||||
\(878\) | −23.3042 | − | 23.3042i | −0.786479 | − | 0.786479i | ||||
\(879\) | 46.1095 | 1.55523 | ||||||||
\(880\) | −21.2417 | + | 33.1132i | −0.716058 | + | 1.11625i | ||||
\(881\) | − | 13.2383i | − | 0.446008i | −0.974818 | − | 0.223004i | \(-0.928414\pi\) | ||
0.974818 | − | 0.223004i | \(-0.0715863\pi\) | |||||||
\(882\) | −12.2854 | + | 12.2854i | −0.413670 | + | 0.413670i | ||||
\(883\) | 1.75780 | + | 1.75780i | 0.0591547 | + | 0.0591547i | 0.736065 | − | 0.676911i | \(-0.236682\pi\) |
−0.676911 | + | 0.736065i | \(0.736682\pi\) | |||||||
\(884\) | 6.19922 | 0.208502 | ||||||||
\(885\) | 62.0351 | − | 13.5489i | 2.08529 | − | 0.455443i | ||||
\(886\) | 30.0379 | 1.00914 | ||||||||
\(887\) | 7.26411 | − | 7.26411i | 0.243905 | − | 0.243905i | −0.574558 | − | 0.818464i | \(-0.694826\pi\) |
0.818464 | + | 0.574558i | \(0.194826\pi\) | |||||||
\(888\) | 1.72882 | − | 1.72882i | 0.0580154 | − | 0.0580154i | ||||
\(889\) | −59.9581 | −2.01093 | ||||||||
\(890\) | −47.0491 | + | 10.2759i | −1.57709 | + | 0.344448i | ||||
\(891\) | − | 47.6988i | − | 1.59797i | ||||||
\(892\) | 20.7251 | − | 20.7251i | 0.693929 | − | 0.693929i | ||||
\(893\) | 1.09079 | − | 1.09079i | 0.0365019 | − | 0.0365019i | ||||
\(894\) | 72.5707 | 2.42713 | ||||||||
\(895\) | −4.71637 | + | 7.35224i | −0.157651 | + | 0.245758i | ||||
\(896\) | 4.32573i | 0.144513i | ||||||||
\(897\) | 15.6996 | + | 20.5081i | 0.524195 | + | 0.684745i | ||||
\(898\) | 8.98626 | + | 8.98626i | 0.299876 | + | 0.299876i | ||||
\(899\) | − | 30.0699i | − | 1.00289i | ||||||
\(900\) | 5.51596 | + | 12.0253i | 0.183865 | + | 0.400844i | ||||
\(901\) | −0.978349 | −0.0325935 | ||||||||
\(902\) | 28.8530 | + | 28.8530i | 0.960700 | + | 0.960700i | ||||
\(903\) | −49.5173 | − | 49.5173i | −1.64783 | − | 1.64783i | ||||
\(904\) | −0.650727 | −0.0216428 | ||||||||
\(905\) | −25.6648 | + | 40.0083i | −0.853126 | + | 1.32992i | ||||
\(906\) | −36.8239 | −1.22339 | ||||||||
\(907\) | 33.1581 | + | 33.1581i | 1.10100 | + | 1.10100i | 0.994291 | + | 0.106707i | \(0.0340306\pi\) |
0.106707 | + | 0.994291i | \(0.465969\pi\) | |||||||
\(908\) | −30.2244 | + | 30.2244i | −1.00303 | + | 1.00303i | ||||
\(909\) | 0.670678i | 0.0222450i | ||||||||
\(910\) | −8.90386 | − | 40.7672i | −0.295160 | − | 1.35142i | ||||
\(911\) | − | 15.3817i | − | 0.509618i | −0.966991 | − | 0.254809i | \(-0.917987\pi\) | ||
0.966991 | − | 0.254809i | \(-0.0820126\pi\) | |||||||
\(912\) | 3.21166 | + | 3.21166i | 0.106349 | + | 0.106349i | ||||
\(913\) | 36.2376 | + | 36.2376i | 1.19929 | + | 1.19929i | ||||
\(914\) | 28.7591 | 0.951265 | ||||||||
\(915\) | −16.1862 | + | 3.53519i | −0.535100 | + | 0.116870i | ||||
\(916\) | − | 0.588767i | − | 0.0194534i | ||||||
\(917\) | 20.0479 | + | 20.0479i | 0.662040 | + | 0.662040i | ||||
\(918\) | −5.95639 | + | 5.95639i | −0.196590 | + | 0.196590i | ||||
\(919\) | 38.8730 | 1.28230 | 0.641152 | − | 0.767414i | \(-0.278457\pi\) | ||||
0.641152 | + | 0.767414i | \(0.278457\pi\) | |||||||
\(920\) | 1.21080 | + | 1.02481i | 0.0399188 | + | 0.0337871i | ||||
\(921\) | 1.59702 | 0.0526236 | ||||||||
\(922\) | 21.0945 | − | 21.0945i | 0.694711 | − | 0.694711i | ||||
\(923\) | 11.4438 | + | 11.4438i | 0.376677 | + | 0.376677i | ||||
\(924\) | 62.5416i | 2.05747i | ||||||||
\(925\) | −13.7471 | + | 37.0455i | −0.452003 | + | 1.21805i | ||||
\(926\) | 24.3259 | 0.799398 | ||||||||
\(927\) | 5.38026 | + | 5.38026i | 0.176711 | + | 0.176711i | ||||
\(928\) | 22.4461 | + | 22.4461i | 0.736830 | + | 0.736830i | ||||
\(929\) | − | 6.87353i | − | 0.225513i | −0.993623 | − | 0.112757i | \(-0.964032\pi\) | ||
0.993623 | − | 0.112757i | \(-0.0359680\pi\) | |||||||
\(930\) | −58.4664 | − | 37.5054i | −1.91719 | − | 1.22985i | ||||
\(931\) | − | 3.34409i | − | 0.109598i | ||||||
\(932\) | −23.9750 | + | 23.9750i | −0.785326 | + | 0.785326i | ||||
\(933\) | −20.5737 | − | 20.5737i | −0.673552 | − | 0.673552i | ||||
\(934\) | −57.1598 | −1.87033 | ||||||||
\(935\) | −11.5984 | + | 2.53317i | −0.379307 | + | 0.0828436i | ||||
\(936\) | −0.523453 | −0.0171096 | ||||||||
\(937\) | −8.27388 | − | 8.27388i | −0.270296 | − | 0.270296i | 0.558923 | − | 0.829219i | \(-0.311215\pi\) |
−0.829219 | + | 0.558923i | \(0.811215\pi\) | |||||||
\(938\) | −71.2705 | − | 71.2705i | −2.32706 | − | 2.32706i | ||||
\(939\) | −48.2398 | −1.57425 | ||||||||
\(940\) | −2.70396 | − | 12.3803i | −0.0881934 | − | 0.403802i | ||||
\(941\) | − | 54.9307i | − | 1.79069i | −0.445372 | − | 0.895346i | \(-0.646929\pi\) | ||
0.445372 | − | 0.895346i | \(-0.353071\pi\) | |||||||
\(942\) | −18.5129 | − | 18.5129i | −0.603183 | − | 0.603183i | ||||
\(943\) | 18.4718 | − | 14.1408i | 0.601525 | − | 0.460487i | ||||
\(944\) | − | 56.2614i | − | 1.83115i | ||||||
\(945\) | 23.4088 | + | 15.0164i | 0.761489 | + | 0.488485i | ||||
\(946\) | −76.9978 | −2.50341 | ||||||||
\(947\) | 29.9981 | − | 29.9981i | 0.974808 | − | 0.974808i | −0.0248820 | − | 0.999690i | \(-0.507921\pi\) |
0.999690 | + | 0.0248820i | \(0.00792099\pi\) | |||||||
\(948\) | 29.8526 | − | 29.8526i | 0.969568 | − | 0.969568i | ||||
\(949\) | − | 13.7950i | − | 0.447803i | ||||||
\(950\) | −4.86732 | − | 1.80620i | −0.157917 | − | 0.0586010i | ||||
\(951\) | 29.6161 | 0.960367 | ||||||||
\(952\) | −0.478436 | + | 0.478436i | −0.0155062 | + | 0.0155062i | ||||
\(953\) | 17.8604 | − | 17.8604i | 0.578555 | − | 0.578555i | −0.355950 | − | 0.934505i | \(-0.615843\pi\) |
0.934505 | + | 0.355950i | \(0.115843\pi\) | |||||||
\(954\) | −2.13034 | −0.0689725 | ||||||||
\(955\) | −3.36034 | + | 5.23836i | −0.108738 | + | 0.169509i | ||||
\(956\) | −17.7823 | −0.575121 | ||||||||
\(957\) | −25.1865 | − | 25.1865i | −0.814164 | − | 0.814164i | ||||
\(958\) | −31.4203 | + | 31.4203i | −1.01514 | + | 1.01514i | ||||
\(959\) | 36.8669i | 1.19049i | ||||||||
\(960\) | 33.7739 | − | 7.37648i | 1.09005 | − | 0.238075i | ||||
\(961\) | 25.2003 | 0.812913 | ||||||||
\(962\) | 28.5081 | + | 28.5081i | 0.919137 | + | 0.919137i | ||||
\(963\) | −6.69414 | + | 6.69414i | −0.215716 | + | 0.215716i | ||||
\(964\) | 5.61290 | 0.180779 | ||||||||
\(965\) | −6.41249 | − | 29.3602i | −0.206425 | − | 0.945138i | ||||
\(966\) | 72.0615 | + | 9.56997i | 2.31854 | + | 0.307909i | ||||
\(967\) | −41.0798 | + | 41.0798i | −1.32104 | + | 1.32104i | −0.408098 | + | 0.912938i | \(0.633808\pi\) |
−0.912938 | + | 0.408098i | \(0.866192\pi\) | |||||||
\(968\) | −0.735023 | − | 0.735023i | −0.0236245 | − | 0.0236245i | ||||
\(969\) | 1.37062i | 0.0440307i | ||||||||
\(970\) | −14.4313 | − | 9.25749i | −0.463361 | − | 0.297240i | ||||
\(971\) | 60.3006i | 1.93514i | 0.252604 | + | 0.967570i | \(0.418713\pi\) | ||||
−0.252604 | + | 0.967570i | \(0.581287\pi\) | |||||||
\(972\) | −18.1012 | + | 18.1012i | −0.580596 | + | 0.580596i | ||||
\(973\) | −25.3032 | + | 25.3032i | −0.811183 | + | 0.811183i | ||||
\(974\) | 10.7680i | 0.345031i | ||||||||
\(975\) | 24.4751 | − | 11.2266i | 0.783829 | − | 0.359539i | ||||
\(976\) | 14.6797i | 0.469887i | ||||||||
\(977\) | −9.21244 | − | 9.21244i | −0.294732 | − | 0.294732i | 0.544214 | − | 0.838946i | \(-0.316828\pi\) |
−0.838946 | + | 0.544214i | \(0.816828\pi\) | |||||||
\(978\) | 67.0404 | + | 67.0404i | 2.14372 | + | 2.14372i | ||||
\(979\) | − | 46.1543i | − | 1.47510i | ||||||
\(980\) | −23.1223 | − | 14.8327i | −0.738616 | − | 0.473813i | ||||
\(981\) | − | 9.05044i | − | 0.288958i | ||||||
\(982\) | 31.5493 | − | 31.5493i | 1.00678 | − | 1.00678i | ||||
\(983\) | 0.800718 | − | 0.800718i | 0.0255389 | − | 0.0255389i | −0.694222 | − | 0.719761i | \(-0.744251\pi\) |
0.719761 | + | 0.694222i | \(0.244251\pi\) | |||||||
\(984\) | 1.50068i | 0.0478398i | ||||||||
\(985\) | 6.09065 | − | 1.33024i | 0.194064 | − | 0.0423851i | ||||
\(986\) | 9.93729i | 0.316468i | ||||||||
\(987\) | 15.9236 | + | 15.9236i | 0.506854 | + | 0.506854i | ||||
\(988\) | −1.83718 | + | 1.83718i | −0.0584486 | + | 0.0584486i | ||||
\(989\) | −5.77896 | + | 43.5153i | −0.183760 | + | 1.38371i | ||||
\(990\) | −25.2553 | + | 5.51596i | −0.802668 | + | 0.175309i | ||||
\(991\) | −45.5190 | −1.44596 | −0.722979 | − | 0.690870i | \(-0.757228\pi\) | ||||
−0.722979 | + | 0.690870i | \(0.757228\pi\) | |||||||
\(992\) | −41.9515 | + | 41.9515i | −1.33196 | + | 1.33196i | ||||
\(993\) | 20.8099 | + | 20.8099i | 0.660383 | + | 0.660383i | ||||
\(994\) | 45.5514 | 1.44480 | ||||||||
\(995\) | −19.9182 | − | 12.7772i | −0.631448 | − | 0.405066i | ||||
\(996\) | − | 48.6040i | − | 1.54008i | ||||||
\(997\) | −16.3776 | + | 16.3776i | −0.518683 | + | 0.518683i | −0.917173 | − | 0.398490i | \(-0.869534\pi\) |
0.398490 | + | 0.917173i | \(0.369534\pi\) | |||||||
\(998\) | 12.5687 | + | 12.5687i | 0.397854 | + | 0.397854i | ||||
\(999\) | −26.8704 | −0.850141 |
(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 | 115.2.e.a.68.9 | yes | 20 | |
5.2 | odd | 4 | inner | 115.2.e.a.22.10 | yes | 20 | |
5.3 | odd | 4 | 575.2.e.d.482.2 | 20 | |||
5.4 | even | 2 | 575.2.e.d.68.1 | 20 | |||
23.22 | odd | 2 | inner | 115.2.e.a.68.10 | yes | 20 | |
115.22 | even | 4 | inner | 115.2.e.a.22.9 | ✓ | 20 | |
115.68 | even | 4 | 575.2.e.d.482.1 | 20 | |||
115.114 | odd | 2 | 575.2.e.d.68.2 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.2.e.a.22.9 | ✓ | 20 | 115.22 | even | 4 | inner | |
115.2.e.a.22.10 | yes | 20 | 5.2 | odd | 4 | inner | |
115.2.e.a.68.9 | yes | 20 | 1.1 | even | 1 | trivial | |
115.2.e.a.68.10 | yes | 20 | 23.22 | odd | 2 | inner | |
575.2.e.d.68.1 | 20 | 5.4 | even | 2 | |||
575.2.e.d.68.2 | 20 | 115.114 | odd | 2 | |||
575.2.e.d.482.1 | 20 | 115.68 | even | 4 | |||
575.2.e.d.482.2 | 20 | 5.3 | odd | 4 |