Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [420,2,Mod(239,420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(420, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("420.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 420.l (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.35371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 9 x^{14} - 16 x^{13} + 18 x^{12} - 4 x^{11} - 36 x^{10} + 102 x^{9} - 170 x^{8} + 204 x^{7} - 144 x^{6} - 32 x^{5} + 288 x^{4} - 512 x^{3} + 576 x^{2} - 512 x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 239.13 | ||
Root | \(-0.167106 + 1.40431i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 420.239 |
Dual form | 420.2.l.h.239.14 |
$q$-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 \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(241\) | \(281\) | \(337\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.25945 | − | 0.643263i | 0.890565 | − | 0.454856i | ||||
\(3\) | 1.48716 | − | 0.887900i | 0.858610 | − | 0.512629i | ||||
\(4\) | 1.17242 | − | 1.62032i | 0.586212 | − | 0.810158i | ||||
\(5\) | −2.05223 | + | 0.887900i | −0.917784 | + | 0.397081i | ||||
\(6\) | 1.30184 | − | 2.07490i | 0.531476 | − | 0.847074i | ||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0.434319 | − | 2.79488i | 0.153555 | − | 0.988140i | ||||
\(9\) | 1.42327 | − | 2.64089i | 0.474422 | − | 0.880297i | ||||
\(10\) | −2.01352 | + | 2.43839i | −0.636731 | + | 0.771086i | ||||
\(11\) | 2.75993 | 0.832151 | 0.416076 | − | 0.909330i | \(-0.363405\pi\) | ||||
0.416076 | + | 0.909330i | \(0.363405\pi\) | |||||||
\(12\) | 0.304900 | − | 3.45066i | 0.0880170 | − | 0.996119i | ||||
\(13\) | 1.90761i | 0.529076i | 0.964375 | + | 0.264538i | \(0.0852195\pi\) | ||||
−0.964375 | + | 0.264538i | \(0.914781\pi\) | |||||||
\(14\) | 1.25945 | − | 0.643263i | 0.336602 | − | 0.171919i | ||||
\(15\) | −2.26361 | + | 3.14262i | −0.584463 | + | 0.811421i | ||||
\(16\) | −1.25084 | − | 3.79939i | −0.312711 | − | 0.949848i | ||||
\(17\) | −5.03780 | −1.22185 | −0.610923 | − | 0.791690i | \(-0.709201\pi\) | ||||
−0.610923 | + | 0.791690i | \(0.709201\pi\) | |||||||
\(18\) | 0.0937425 | − | 4.24160i | 0.0220953 | − | 0.999756i | ||||
\(19\) | − | 1.90761i | − | 0.437636i | −0.975766 | − | 0.218818i | \(-0.929780\pi\) | ||
0.975766 | − | 0.218818i | \(-0.0702201\pi\) | |||||||
\(20\) | −0.967402 | + | 4.36625i | −0.216318 | + | 0.976323i | ||||
\(21\) | 1.48716 | − | 0.887900i | 0.324524 | − | 0.193756i | ||||
\(22\) | 3.47600 | − | 1.77536i | 0.741085 | − | 0.378509i | ||||
\(23\) | 2.05073i | 0.427607i | 0.976877 | + | 0.213804i | \(0.0685853\pi\) | ||||
−0.976877 | + | 0.213804i | \(0.931415\pi\) | |||||||
\(24\) | −1.83568 | − | 4.54206i | −0.374706 | − | 0.927144i | ||||
\(25\) | 3.42327 | − | 3.64434i | 0.684653 | − | 0.728869i | ||||
\(26\) | 1.22710 | + | 2.40254i | 0.240653 | + | 0.471177i | ||||
\(27\) | −0.228229 | − | 5.19114i | −0.0439227 | − | 0.999035i | ||||
\(28\) | 1.17242 | − | 1.62032i | 0.221567 | − | 0.306211i | ||||
\(29\) | 4.94433i | 0.918140i | 0.888400 | + | 0.459070i | \(0.151817\pi\) | ||||
−0.888400 | + | 0.459070i | \(0.848183\pi\) | |||||||
\(30\) | −0.829376 | + | 5.41407i | −0.151423 | + | 0.988469i | ||||
\(31\) | 6.92361i | 1.24352i | 0.783209 | + | 0.621758i | \(0.213581\pi\) | ||||
−0.783209 | + | 0.621758i | \(0.786419\pi\) | |||||||
\(32\) | −4.01938 | − | 3.98052i | −0.710533 | − | 0.703664i | ||||
\(33\) | 4.10445 | − | 2.45055i | 0.714494 | − | 0.426585i | ||||
\(34\) | −6.34485 | + | 3.24063i | −1.08813 | + | 0.555764i | ||||
\(35\) | −2.05223 | + | 0.887900i | −0.346890 | + | 0.150083i | ||||
\(36\) | −2.61041 | − | 5.40239i | −0.435068 | − | 0.900398i | ||||
\(37\) | 6.48126i | 1.06551i | 0.846269 | + | 0.532756i | \(0.178844\pi\) | ||||
−0.846269 | + | 0.532756i | \(0.821156\pi\) | |||||||
\(38\) | −1.22710 | − | 2.40254i | −0.199061 | − | 0.389743i | ||||
\(39\) | 1.69377 | + | 2.83692i | 0.271220 | + | 0.454270i | ||||
\(40\) | 1.59025 | + | 6.12136i | 0.251441 | + | 0.967873i | ||||
\(41\) | 11.1795i | 1.74595i | 0.487766 | + | 0.872975i | \(0.337812\pi\) | ||||
−0.487766 | + | 0.872975i | \(0.662188\pi\) | |||||||
\(42\) | 1.30184 | − | 2.07490i | 0.200879 | − | 0.320164i | ||||
\(43\) | −9.36439 | −1.42806 | −0.714028 | − | 0.700117i | \(-0.753131\pi\) | ||||
−0.714028 | + | 0.700117i | \(0.753131\pi\) | |||||||
\(44\) | 3.23581 | − | 4.47196i | 0.487817 | − | 0.674174i | ||||
\(45\) | −0.576017 | + | 6.68343i | −0.0858675 | + | 0.996307i | ||||
\(46\) | 1.31916 | + | 2.58279i | 0.194500 | + | 0.380812i | ||||
\(47\) | − | 7.51739i | − | 1.09652i | −0.836307 | − | 0.548262i | \(-0.815290\pi\) | ||
0.836307 | − | 0.548262i | \(-0.184710\pi\) | |||||||
\(48\) | −5.23368 | − | 4.53967i | −0.755417 | − | 0.655245i | ||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.96716 | − | 6.79193i | 0.278198 | − | 0.960524i | ||||
\(51\) | −7.49199 | + | 4.47306i | −1.04909 | + | 0.626354i | ||||
\(52\) | 3.09093 | + | 2.23653i | 0.428635 | + | 0.310151i | ||||
\(53\) | 6.14747 | 0.844420 | 0.422210 | − | 0.906498i | \(-0.361254\pi\) | ||||
0.422210 | + | 0.906498i | \(0.361254\pi\) | |||||||
\(54\) | −3.62671 | − | 6.39116i | −0.493533 | − | 0.869727i | ||||
\(55\) | −5.66401 | + | 2.45055i | −0.763735 | + | 0.330432i | ||||
\(56\) | 0.434319 | − | 2.79488i | 0.0580384 | − | 0.373482i | ||||
\(57\) | −1.69377 | − | 2.83692i | −0.224345 | − | 0.375759i | ||||
\(58\) | 3.18051 | + | 6.22714i | 0.417621 | + | 0.817663i | ||||
\(59\) | 0.716916 | 0.0933345 | 0.0466672 | − | 0.998910i | \(-0.485140\pi\) | ||||
0.0466672 | + | 0.998910i | \(0.485140\pi\) | |||||||
\(60\) | 2.43812 | + | 7.35225i | 0.314759 | + | 0.949172i | ||||
\(61\) | 5.13115 | 0.656976 | 0.328488 | − | 0.944508i | \(-0.393461\pi\) | ||||
0.328488 | + | 0.944508i | \(0.393461\pi\) | |||||||
\(62\) | 4.45370 | + | 8.71993i | 0.565621 | + | 1.10743i | ||||
\(63\) | 1.42327 | − | 2.64089i | 0.179315 | − | 0.332721i | ||||
\(64\) | −7.62273 | − | 2.42774i | −0.952842 | − | 0.303468i | ||||
\(65\) | −1.69377 | − | 3.91485i | −0.210086 | − | 0.485577i | ||||
\(66\) | 3.59300 | − | 5.72658i | 0.442268 | − | 0.704894i | ||||
\(67\) | 3.58761 | 0.438296 | 0.219148 | − | 0.975692i | \(-0.429672\pi\) | ||||
0.219148 | + | 0.975692i | \(0.429672\pi\) | |||||||
\(68\) | −5.90644 | + | 8.16282i | −0.716261 | + | 0.989887i | ||||
\(69\) | 1.82085 | + | 3.04976i | 0.219204 | + | 0.367148i | ||||
\(70\) | −2.01352 | + | 2.43839i | −0.240662 | + | 0.291443i | ||||
\(71\) | 4.49721 | 0.533721 | 0.266860 | − | 0.963735i | \(-0.414014\pi\) | ||||
0.266860 | + | 0.963735i | \(0.414014\pi\) | |||||||
\(72\) | −6.76283 | − | 5.12485i | −0.797007 | − | 0.603970i | ||||
\(73\) | 6.11618i | 0.715845i | 0.933751 | + | 0.357922i | \(0.116515\pi\) | ||||
−0.933751 | + | 0.357922i | \(0.883485\pi\) | |||||||
\(74\) | 4.16916 | + | 8.16282i | 0.484655 | + | 0.948908i | ||||
\(75\) | 1.85512 | − | 8.45923i | 0.214211 | − | 0.976788i | ||||
\(76\) | −3.09093 | − | 2.23653i | −0.354554 | − | 0.256548i | ||||
\(77\) | 2.75993 | 0.314524 | ||||||||
\(78\) | 3.95810 | + | 2.48341i | 0.448167 | + | 0.281191i | ||||
\(79\) | − | 14.6546i | − | 1.64878i | −0.566025 | − | 0.824388i | \(-0.691520\pi\) | ||
0.566025 | − | 0.824388i | \(-0.308480\pi\) | |||||||
\(80\) | 5.94049 | + | 6.68659i | 0.664167 | + | 0.747584i | ||||
\(81\) | −4.94862 | − | 7.51739i | −0.549847 | − | 0.835265i | ||||
\(82\) | 7.19138 | + | 14.0800i | 0.794155 | + | 1.55488i | ||||
\(83\) | 7.71558i | 0.846895i | 0.905921 | + | 0.423448i | \(0.139180\pi\) | ||||
−0.905921 | + | 0.423448i | \(0.860820\pi\) | |||||||
\(84\) | 0.304900 | − | 3.45066i | 0.0332673 | − | 0.376498i | ||||
\(85\) | 10.3387 | − | 4.47306i | 1.12139 | − | 0.485172i | ||||
\(86\) | −11.7940 | + | 6.02377i | −1.27178 | + | 0.649560i | ||||
\(87\) | 4.39007 | + | 7.35300i | 0.470665 | + | 0.788324i | ||||
\(88\) | 1.19869 | − | 7.71369i | 0.127781 | − | 0.822282i | ||||
\(89\) | − | 13.5677i | − | 1.43817i | −0.694920 | − | 0.719087i | \(-0.744560\pi\) | ||
0.694920 | − | 0.719087i | \(-0.255440\pi\) | |||||||
\(90\) | 3.57374 | + | 8.78797i | 0.376705 | + | 0.926333i | ||||
\(91\) | 1.90761i | 0.199972i | ||||||||
\(92\) | 3.32283 | + | 2.40433i | 0.346429 | + | 0.250669i | ||||
\(93\) | 6.14747 | + | 10.2965i | 0.637463 | + | 1.06770i | ||||
\(94\) | −4.83566 | − | 9.46777i | −0.498760 | − | 0.976526i | ||||
\(95\) | 1.69377 | + | 3.91485i | 0.173777 | + | 0.401655i | ||||
\(96\) | −9.51176 | − | 2.35085i | −0.970790 | − | 0.239932i | ||||
\(97\) | − | 16.6772i | − | 1.69331i | −0.532143 | − | 0.846654i | \(-0.678613\pi\) | ||
0.532143 | − | 0.846654i | \(-0.321387\pi\) | |||||||
\(98\) | 1.25945 | − | 0.643263i | 0.127224 | − | 0.0649794i | ||||
\(99\) | 3.92812 | − | 7.28869i | 0.394791 | − | 0.732541i | ||||
\(100\) | −1.89147 | − | 9.81949i | −0.189147 | − | 0.981949i | ||||
\(101\) | 7.71558i | 0.767729i | 0.923389 | + | 0.383865i | \(0.125407\pi\) | ||||
−0.923389 | + | 0.383865i | \(0.874593\pi\) | |||||||
\(102\) | −6.55842 | + | 10.4529i | −0.649381 | + | 1.03499i | ||||
\(103\) | −20.2109 | −1.99144 | −0.995721 | − | 0.0924150i | \(-0.970541\pi\) | ||||
−0.995721 | + | 0.0924150i | \(0.970541\pi\) | |||||||
\(104\) | 5.33155 | + | 0.828513i | 0.522801 | + | 0.0812424i | ||||
\(105\) | −2.26361 | + | 3.14262i | −0.220906 | + | 0.306688i | ||||
\(106\) | 7.74243 | − | 3.95444i | 0.752011 | − | 0.384089i | ||||
\(107\) | 1.27396i | 0.123158i | 0.998102 | + | 0.0615791i | \(0.0196136\pi\) | ||||
−0.998102 | + | 0.0615791i | \(0.980386\pi\) | |||||||
\(108\) | −8.67886 | − | 5.71641i | −0.835124 | − | 0.550062i | ||||
\(109\) | −14.6383 | −1.40210 | −0.701048 | − | 0.713114i | \(-0.747284\pi\) | ||||
−0.701048 | + | 0.713114i | \(0.747284\pi\) | |||||||
\(110\) | −5.55719 | + | 6.72979i | −0.529857 | + | 0.641660i | ||||
\(111\) | 5.75471 | + | 9.63865i | 0.546213 | + | 0.914860i | ||||
\(112\) | −1.25084 | − | 3.79939i | −0.118193 | − | 0.359009i | ||||
\(113\) | 8.83651 | 0.831269 | 0.415634 | − | 0.909532i | \(-0.363560\pi\) | ||||
0.415634 | + | 0.909532i | \(0.363560\pi\) | |||||||
\(114\) | −3.95810 | − | 2.48341i | −0.370710 | − | 0.232593i | ||||
\(115\) | −1.82085 | − | 4.20857i | −0.169795 | − | 0.392451i | ||||
\(116\) | 8.01138 | + | 5.79686i | 0.743838 | + | 0.538225i | ||||
\(117\) | 5.03780 | + | 2.71504i | 0.465744 | + | 0.251006i | ||||
\(118\) | 0.902919 | − | 0.461166i | 0.0831204 | − | 0.0424537i | ||||
\(119\) | −5.03780 | −0.461814 | ||||||||
\(120\) | 7.80012 | + | 7.69144i | 0.712050 | + | 0.702129i | ||||
\(121\) | −3.38276 | −0.307524 | ||||||||
\(122\) | 6.46242 | − | 3.30068i | 0.585080 | − | 0.298830i | ||||
\(123\) | 9.92631 | + | 16.6257i | 0.895025 | + | 1.49909i | ||||
\(124\) | 11.2184 | + | 8.11740i | 1.00744 | + | 0.728964i | ||||
\(125\) | −3.78950 | + | 10.5185i | −0.338944 | + | 0.940807i | ||||
\(126\) | 0.0937425 | − | 4.24160i | 0.00835125 | − | 0.377872i | ||||
\(127\) | −2.15684 | −0.191388 | −0.0956941 | − | 0.995411i | \(-0.530507\pi\) | ||||
−0.0956941 | + | 0.995411i | \(0.530507\pi\) | |||||||
\(128\) | −11.1621 | + | 1.84581i | −0.986602 | + | 0.163148i | ||||
\(129\) | −13.9263 | + | 8.31464i | −1.22614 | + | 0.732063i | ||||
\(130\) | −4.65150 | − | 3.84102i | −0.407963 | − | 0.336879i | ||||
\(131\) | −2.93626 | −0.256543 | −0.128271 | − | 0.991739i | \(-0.540943\pi\) | ||||
−0.128271 | + | 0.991739i | \(0.540943\pi\) | |||||||
\(132\) | 0.841504 | − | 9.52359i | 0.0732435 | − | 0.828922i | ||||
\(133\) | − | 1.90761i | − | 0.165411i | ||||||
\(134\) | 4.51841 | − | 2.30778i | 0.390331 | − | 0.199361i | ||||
\(135\) | 5.07759 | + | 10.4507i | 0.437009 | + | 0.899457i | ||||
\(136\) | −2.18801 | + | 14.0800i | −0.187621 | + | 1.20735i | ||||
\(137\) | −16.4887 | −1.40873 | −0.704363 | − | 0.709840i | \(-0.748767\pi\) | ||||
−0.704363 | + | 0.709840i | \(0.748767\pi\) | |||||||
\(138\) | 4.25506 | + | 2.66973i | 0.362215 | + | 0.227263i | ||||
\(139\) | − | 10.8537i | − | 0.920602i | −0.887763 | − | 0.460301i | \(-0.847742\pi\) | ||
0.887763 | − | 0.460301i | \(-0.152258\pi\) | |||||||
\(140\) | −0.967402 | + | 4.36625i | −0.0817604 | + | 0.369015i | ||||
\(141\) | −6.67469 | − | 11.1795i | −0.562110 | − | 0.941486i | ||||
\(142\) | 5.66401 | − | 2.89289i | 0.475313 | − | 0.242766i | ||||
\(143\) | 5.26488i | 0.440272i | ||||||||
\(144\) | −11.8141 | − | 2.10421i | −0.984506 | − | 0.175351i | ||||
\(145\) | −4.39007 | − | 10.1469i | −0.364576 | − | 0.842654i | ||||
\(146\) | 3.93431 | + | 7.70302i | 0.325606 | + | 0.637506i | ||||
\(147\) | 1.48716 | − | 0.887900i | 0.122659 | − | 0.0732328i | ||||
\(148\) | 10.5017 | + | 7.59879i | 0.863233 | + | 0.624617i | ||||
\(149\) | − | 13.6420i | − | 1.11760i | −0.829303 | − | 0.558800i | \(-0.811262\pi\) | ||
0.829303 | − | 0.558800i | \(-0.188738\pi\) | |||||||
\(150\) | −3.10509 | − | 11.8473i | −0.253529 | − | 0.967328i | ||||
\(151\) | 1.35036i | 0.109891i | 0.998489 | + | 0.0549455i | \(0.0174985\pi\) | ||||
−0.998489 | + | 0.0549455i | \(0.982501\pi\) | |||||||
\(152\) | −5.33155 | − | 0.828513i | −0.432446 | − | 0.0672013i | ||||
\(153\) | −7.17013 | + | 13.3043i | −0.579670 | + | 1.07559i | ||||
\(154\) | 3.47600 | − | 1.77536i | 0.280104 | − | 0.143063i | ||||
\(155\) | −6.14747 | − | 14.2088i | −0.493777 | − | 1.14128i | ||||
\(156\) | 6.58251 | + | 0.581631i | 0.527023 | + | 0.0465677i | ||||
\(157\) | − | 1.90761i | − | 0.152244i | −0.997099 | − | 0.0761220i | \(-0.975746\pi\) | ||
0.997099 | − | 0.0761220i | \(-0.0242538\pi\) | |||||||
\(158\) | −9.42679 | − | 18.4568i | −0.749955 | − | 1.46834i | ||||
\(159\) | 9.14225 | − | 5.45834i | 0.725028 | − | 0.432875i | ||||
\(160\) | 11.7830 | + | 4.60012i | 0.931527 | + | 0.363672i | ||||
\(161\) | 2.05073i | 0.161620i | ||||||||
\(162\) | −11.0682 | − | 6.28450i | −0.869600 | − | 0.493757i | ||||
\(163\) | 24.4368 | 1.91404 | 0.957021 | − | 0.290019i | \(-0.0936617\pi\) | ||||
0.957021 | + | 0.290019i | \(0.0936617\pi\) | |||||||
\(164\) | 18.1144 | + | 13.1072i | 1.41449 | + | 1.02350i | ||||
\(165\) | −6.24743 | + | 8.67342i | −0.486361 | + | 0.675225i | ||||
\(166\) | 4.96315 | + | 9.71739i | 0.385215 | + | 0.754215i | ||||
\(167\) | 3.53470i | 0.273523i | 0.990604 | + | 0.136762i | \(0.0436694\pi\) | ||||
−0.990604 | + | 0.136762i | \(0.956331\pi\) | |||||||
\(168\) | −1.83568 | − | 4.54206i | −0.141625 | − | 0.350427i | ||||
\(169\) | 9.36102 | 0.720078 | ||||||||
\(170\) | 10.1437 | − | 12.2841i | 0.777987 | − | 0.942147i | ||||
\(171\) | −5.03780 | − | 2.71504i | −0.385250 | − | 0.207624i | ||||
\(172\) | −10.9790 | + | 15.1733i | −0.837144 | + | 1.15695i | ||||
\(173\) | 16.8691 | 1.28253 | 0.641266 | − | 0.767318i | \(-0.278409\pi\) | ||||
0.641266 | + | 0.767318i | \(0.278409\pi\) | |||||||
\(174\) | 10.2590 | + | 6.43675i | 0.777732 | + | 0.487969i | ||||
\(175\) | 3.42327 | − | 3.64434i | 0.258775 | − | 0.275487i | ||||
\(176\) | −3.45224 | − | 10.4861i | −0.260223 | − | 0.790418i | ||||
\(177\) | 1.06617 | − | 0.636550i | 0.0801379 | − | 0.0478460i | ||||
\(178\) | −8.72761 | − | 17.0878i | −0.654162 | − | 1.28079i | ||||
\(179\) | 4.19377 | 0.313457 | 0.156728 | − | 0.987642i | \(-0.449905\pi\) | ||||
0.156728 | + | 0.987642i | \(0.449905\pi\) | |||||||
\(180\) | 10.1539 | + | 8.76914i | 0.756829 | + | 0.653613i | ||||
\(181\) | −9.70038 | −0.721023 | −0.360512 | − | 0.932755i | \(-0.617398\pi\) | ||||
−0.360512 | + | 0.932755i | \(0.617398\pi\) | |||||||
\(182\) | 1.22710 | + | 2.40254i | 0.0909585 | + | 0.178088i | ||||
\(183\) | 7.63082 | − | 4.55595i | 0.564086 | − | 0.336785i | ||||
\(184\) | 5.73155 | + | 0.890673i | 0.422536 | + | 0.0656613i | ||||
\(185\) | −5.75471 | − | 13.3010i | −0.423095 | − | 0.977910i | ||||
\(186\) | 14.3658 | + | 9.01345i | 1.05335 | + | 0.660899i | ||||
\(187\) | −13.9040 | −1.01676 | ||||||||
\(188\) | −12.1805 | − | 8.81357i | −0.888357 | − | 0.642796i | ||||
\(189\) | −0.228229 | − | 5.19114i | −0.0166012 | − | 0.377600i | ||||
\(190\) | 4.65150 | + | 3.84102i | 0.337455 | + | 0.278657i | ||||
\(191\) | −7.79773 | −0.564224 | −0.282112 | − | 0.959381i | \(-0.591035\pi\) | ||||
−0.282112 | + | 0.959381i | \(0.591035\pi\) | |||||||
\(192\) | −13.4918 | + | 3.15779i | −0.973686 | + | 0.227894i | ||||
\(193\) | − | 2.15779i | − | 0.155321i | −0.996980 | − | 0.0776606i | \(-0.975255\pi\) | ||
0.996980 | − | 0.0776606i | \(-0.0247451\pi\) | |||||||
\(194\) | −10.7278 | − | 21.0040i | −0.770211 | − | 1.50800i | ||||
\(195\) | −5.99489 | − | 4.31810i | −0.429303 | − | 0.309225i | ||||
\(196\) | 1.17242 | − | 1.62032i | 0.0837446 | − | 0.115737i | ||||
\(197\) | 14.9679 | 1.06642 | 0.533208 | − | 0.845984i | \(-0.320986\pi\) | ||||
0.533208 | + | 0.845984i | \(0.320986\pi\) | |||||||
\(198\) | 0.258723 | − | 11.7066i | 0.0183867 | − | 0.831948i | ||||
\(199\) | 10.7388i | 0.761255i | 0.924728 | + | 0.380628i | \(0.124292\pi\) | ||||
−0.924728 | + | 0.380628i | \(0.875708\pi\) | |||||||
\(200\) | −8.69872 | − | 11.1504i | −0.615093 | − | 0.788455i | ||||
\(201\) | 5.33533 | − | 3.18544i | 0.376325 | − | 0.224683i | ||||
\(202\) | 4.96315 | + | 9.71739i | 0.349206 | + | 0.683713i | ||||
\(203\) | 4.94433i | 0.347024i | ||||||||
\(204\) | −1.53602 | + | 17.3837i | −0.107543 | + | 1.21710i | ||||
\(205\) | −9.92631 | − | 22.9429i | −0.693283 | − | 1.60240i | ||||
\(206\) | −25.4546 | + | 13.0009i | −1.77351 | + | 0.905819i | ||||
\(207\) | 5.41576 | + | 2.91874i | 0.376422 | + | 0.202866i | ||||
\(208\) | 7.24777 | − | 2.38612i | 0.502542 | − | 0.165448i | ||||
\(209\) | − | 5.26488i | − | 0.364180i | ||||||
\(210\) | −0.829376 | + | 5.41407i | −0.0572324 | + | 0.373606i | ||||
\(211\) | − | 13.5827i | − | 0.935073i | −0.883974 | − | 0.467536i | \(-0.845142\pi\) | ||
0.883974 | − | 0.467536i | \(-0.154858\pi\) | |||||||
\(212\) | 7.20745 | − | 9.96084i | 0.495009 | − | 0.684113i | ||||
\(213\) | 6.68806 | − | 3.99308i | 0.458258 | − | 0.273601i | ||||
\(214\) | 0.819491 | + | 1.60449i | 0.0560192 | + | 0.109680i | ||||
\(215\) | 19.2178 | − | 8.31464i | 1.31065 | − | 0.567054i | ||||
\(216\) | −14.6077 | − | 1.61674i | −0.993931 | − | 0.110005i | ||||
\(217\) | 6.92361i | 0.470005i | ||||||||
\(218\) | −18.4362 | + | 9.41630i | −1.24866 | + | 0.637752i | ||||
\(219\) | 5.43056 | + | 9.09571i | 0.366963 | + | 0.614631i | ||||
\(220\) | −2.66997 | + | 12.0506i | −0.180009 | + | 0.812449i | ||||
\(221\) | − | 9.61016i | − | 0.646449i | ||||||
\(222\) | 13.4480 | + | 8.43759i | 0.902568 | + | 0.566294i | ||||
\(223\) | −11.6417 | −0.779585 | −0.389793 | − | 0.920903i | \(-0.627453\pi\) | ||||
−0.389793 | + | 0.920903i | \(0.627453\pi\) | |||||||
\(224\) | −4.01938 | − | 3.98052i | −0.268556 | − | 0.265960i | ||||
\(225\) | −4.75210 | − | 14.2274i | −0.316807 | − | 0.948490i | ||||
\(226\) | 11.1291 | − | 5.68420i | 0.740299 | − | 0.378108i | ||||
\(227\) | − | 3.16030i | − | 0.209756i | −0.994485 | − | 0.104878i | \(-0.966555\pi\) | ||
0.994485 | − | 0.104878i | \(-0.0334453\pi\) | |||||||
\(228\) | −6.58251 | − | 0.581631i | −0.435938 | − | 0.0385194i | ||||
\(229\) | −3.43808 | −0.227195 | −0.113597 | − | 0.993527i | \(-0.536237\pi\) | ||||
−0.113597 | + | 0.993527i | \(0.536237\pi\) | |||||||
\(230\) | −5.00048 | − | 4.12919i | −0.329722 | − | 0.272271i | ||||
\(231\) | 4.10445 | − | 2.45055i | 0.270053 | − | 0.161234i | ||||
\(232\) | 13.8188 | + | 2.14742i | 0.907251 | + | 0.140985i | ||||
\(233\) | −17.5699 | −1.15104 | −0.575520 | − | 0.817787i | \(-0.695200\pi\) | ||||
−0.575520 | + | 0.817787i | \(0.695200\pi\) | |||||||
\(234\) | 8.09133 | + | 0.178824i | 0.528947 | + | 0.0116901i | ||||
\(235\) | 6.67469 | + | 15.4274i | 0.435409 | + | 1.00637i | ||||
\(236\) | 0.840529 | − | 1.16163i | 0.0547138 | − | 0.0756156i | ||||
\(237\) | −13.0119 | − | 21.7937i | −0.845211 | − | 1.41566i | ||||
\(238\) | −6.34485 | + | 3.24063i | −0.411275 | + | 0.210059i | ||||
\(239\) | −17.5275 | −1.13376 | −0.566879 | − | 0.823801i | \(-0.691849\pi\) | ||||
−0.566879 | + | 0.823801i | \(0.691849\pi\) | |||||||
\(240\) | 14.7715 | + | 4.66944i | 0.953494 | + | 0.301411i | ||||
\(241\) | 6.21092 | 0.400081 | 0.200040 | − | 0.979788i | \(-0.435893\pi\) | ||||
0.200040 | + | 0.979788i | \(0.435893\pi\) | |||||||
\(242\) | −4.26042 | + | 2.17601i | −0.273870 | + | 0.139879i | ||||
\(243\) | −14.0341 | − | 6.78564i | −0.900286 | − | 0.435299i | ||||
\(244\) | 6.01588 | − | 8.31408i | 0.385127 | − | 0.532254i | ||||
\(245\) | −2.05223 | + | 0.887900i | −0.131112 | + | 0.0567259i | ||||
\(246\) | 23.1964 | + | 14.5540i | 1.47895 | + | 0.927929i | ||||
\(247\) | 3.63898 | 0.231543 | ||||||||
\(248\) | 19.3507 | + | 3.00706i | 1.22877 | + | 0.190948i | ||||
\(249\) | 6.85067 | + | 11.4743i | 0.434143 | + | 0.727153i | ||||
\(250\) | 1.99350 | + | 15.6852i | 0.126080 | + | 0.992020i | ||||
\(251\) | 22.4760 | 1.41867 | 0.709335 | − | 0.704871i | \(-0.248995\pi\) | ||||
0.709335 | + | 0.704871i | \(0.248995\pi\) | |||||||
\(252\) | −2.61041 | − | 5.40239i | −0.164440 | − | 0.340318i | ||||
\(253\) | 5.65989i | 0.355834i | ||||||||
\(254\) | −2.71642 | + | 1.38741i | −0.170444 | + | 0.0870541i | ||||
\(255\) | 11.4036 | − | 15.8319i | 0.714123 | − | 0.991430i | ||||
\(256\) | −12.8708 | + | 9.50488i | −0.804424 | + | 0.594055i | ||||
\(257\) | −7.25715 | −0.452688 | −0.226344 | − | 0.974047i | \(-0.572677\pi\) | ||||
−0.226344 | + | 0.974047i | \(0.572677\pi\) | |||||||
\(258\) | −12.1910 | + | 19.4302i | −0.758977 | + | 1.20967i | ||||
\(259\) | 6.48126i | 0.402726i | ||||||||
\(260\) | −8.32911 | − | 1.84543i | −0.516549 | − | 0.114449i | ||||
\(261\) | 13.0575 | + | 7.03711i | 0.808236 | + | 0.435586i | ||||
\(262\) | −3.69808 | + | 1.88879i | −0.228468 | + | 0.116690i | ||||
\(263\) | − | 16.3928i | − | 1.01082i | −0.862878 | − | 0.505412i | \(-0.831341\pi\) | ||
0.862878 | − | 0.505412i | \(-0.168659\pi\) | |||||||
\(264\) | −5.06634 | − | 12.5358i | −0.311812 | − | 0.771524i | ||||
\(265\) | −12.6160 | + | 5.45834i | −0.774995 | + | 0.335303i | ||||
\(266\) | −1.22710 | − | 2.40254i | −0.0752381 | − | 0.147309i | ||||
\(267\) | −12.0468 | − | 20.1773i | −0.737251 | − | 1.23483i | ||||
\(268\) | 4.20620 | − | 5.81305i | 0.256934 | − | 0.355089i | ||||
\(269\) | − | 4.53372i | − | 0.276426i | −0.990403 | − | 0.138213i | \(-0.955864\pi\) | ||
0.990403 | − | 0.138213i | \(-0.0441359\pi\) | |||||||
\(270\) | 13.1175 | + | 9.89595i | 0.798309 | + | 0.602249i | ||||
\(271\) | − | 27.5166i | − | 1.67151i | −0.549100 | − | 0.835756i | \(-0.685030\pi\) | ||
0.549100 | − | 0.835756i | \(-0.314970\pi\) | |||||||
\(272\) | 6.30149 | + | 19.1406i | 0.382084 | + | 1.16057i | ||||
\(273\) | 1.69377 | + | 2.83692i | 0.102512 | + | 0.171698i | ||||
\(274\) | −20.7667 | + | 10.6066i | −1.25456 | + | 0.640767i | ||||
\(275\) | 9.44799 | − | 10.0582i | 0.569735 | − | 0.606529i | ||||
\(276\) | 7.07637 | + | 0.625268i | 0.425948 | + | 0.0376367i | ||||
\(277\) | 24.3449i | 1.46274i | 0.681980 | + | 0.731371i | \(0.261119\pi\) | ||||
−0.681980 | + | 0.731371i | \(0.738881\pi\) | |||||||
\(278\) | −6.98181 | − | 13.6697i | −0.418741 | − | 0.819856i | ||||
\(279\) | 18.2845 | + | 9.85414i | 1.09466 | + | 0.589952i | ||||
\(280\) | 1.59025 | + | 6.12136i | 0.0950359 | + | 0.365821i | ||||
\(281\) | − | 10.5636i | − | 0.630170i | −0.949064 | − | 0.315085i | \(-0.897967\pi\) | ||
0.949064 | − | 0.315085i | \(-0.102033\pi\) | |||||||
\(282\) | −15.5978 | − | 9.78646i | −0.928836 | − | 0.582775i | ||||
\(283\) | −5.53680 | −0.329129 | −0.164564 | − | 0.986366i | \(-0.552622\pi\) | ||||
−0.164564 | + | 0.986366i | \(0.552622\pi\) | |||||||
\(284\) | 5.27264 | − | 7.28690i | 0.312874 | − | 0.432398i | ||||
\(285\) | 5.99489 | + | 4.31810i | 0.355107 | + | 0.255782i | ||||
\(286\) | 3.38671 | + | 6.63085i | 0.200260 | + | 0.392090i | ||||
\(287\) | 11.1795i | 0.659907i | ||||||||
\(288\) | −16.2328 | + | 4.94941i | −0.956526 | + | 0.291647i | ||||
\(289\) | 8.37939 | 0.492906 | ||||||||
\(290\) | −12.0562 | − | 9.95552i | −0.707965 | − | 0.584608i | ||||
\(291\) | −14.8076 | − | 24.8015i | −0.868040 | − | 1.45389i | ||||
\(292\) | 9.91014 | + | 7.17076i | 0.579947 | + | 0.419637i | ||||
\(293\) | 25.2198 | 1.47336 | 0.736678 | − | 0.676244i | \(-0.236393\pi\) | ||||
0.736678 | + | 0.676244i | \(0.236393\pi\) | |||||||
\(294\) | 1.30184 | − | 2.07490i | 0.0759251 | − | 0.121011i | ||||
\(295\) | −1.47127 | + | 0.636550i | −0.0856608 | + | 0.0370613i | ||||
\(296\) | 18.1144 | + | 2.81494i | 1.05288 | + | 0.163615i | ||||
\(297\) | −0.629897 | − | 14.3272i | −0.0365504 | − | 0.831348i | ||||
\(298\) | −8.77543 | − | 17.1815i | −0.508347 | − | 0.995295i | ||||
\(299\) | −3.91200 | −0.226237 | ||||||||
\(300\) | −11.5316 | − | 12.9237i | −0.665779 | − | 0.746149i | ||||
\(301\) | −9.36439 | −0.539754 | ||||||||
\(302\) | 0.868639 | + | 1.70071i | 0.0499846 | + | 0.0978650i | ||||
\(303\) | 6.85067 | + | 11.4743i | 0.393561 | + | 0.659180i | ||||
\(304\) | −7.24777 | + | 2.38612i | −0.415688 | + | 0.136853i | ||||
\(305\) | −10.5303 | + | 4.55595i | −0.602962 | + | 0.260873i | ||||
\(306\) | −0.472256 | + | 21.3683i | −0.0269971 | + | 1.22155i | ||||
\(307\) | 19.0825 | 1.08909 | 0.544547 | − | 0.838730i | \(-0.316701\pi\) | ||||
0.544547 | + | 0.838730i | \(0.316701\pi\) | |||||||
\(308\) | 3.23581 | − | 4.47196i | 0.184378 | − | 0.254814i | ||||
\(309\) | −30.0568 | + | 17.9453i | −1.70987 | + | 1.02087i | ||||
\(310\) | −16.8824 | − | 13.9408i | −0.958858 | − | 0.791786i | ||||
\(311\) | −6.95370 | −0.394308 | −0.197154 | − | 0.980373i | \(-0.563170\pi\) | ||||
−0.197154 | + | 0.980373i | \(0.563170\pi\) | |||||||
\(312\) | 8.66448 | − | 3.50176i | 0.490530 | − | 0.198248i | ||||
\(313\) | − | 34.5408i | − | 1.95236i | −0.216963 | − | 0.976180i | \(-0.569615\pi\) | ||
0.216963 | − | 0.976180i | \(-0.430385\pi\) | |||||||
\(314\) | −1.22710 | − | 2.40254i | −0.0692491 | − | 0.135583i | ||||
\(315\) | −0.576017 | + | 6.68343i | −0.0324549 | + | 0.376568i | ||||
\(316\) | −23.7451 | − | 17.1815i | −1.33577 | − | 0.966533i | ||||
\(317\) | 8.19278 | 0.460153 | 0.230076 | − | 0.973173i | \(-0.426102\pi\) | ||||
0.230076 | + | 0.973173i | \(0.426102\pi\) | |||||||
\(318\) | 8.00305 | − | 12.7554i | 0.448789 | − | 0.715286i | ||||
\(319\) | 13.6460i | 0.764031i | ||||||||
\(320\) | 17.7992 | − | 1.78595i | 0.995004 | − | 0.0998375i | ||||
\(321\) | 1.13115 | + | 1.89458i | 0.0631345 | + | 0.105745i | ||||
\(322\) | 1.31916 | + | 2.58279i | 0.0735140 | + | 0.143933i | ||||
\(323\) | 9.61016i | 0.534724i | ||||||||
\(324\) | −17.9824 | − | 0.795237i | −0.999024 | − | 0.0441799i | ||||
\(325\) | 6.95199 | + | 6.53026i | 0.385627 | + | 0.362234i | ||||
\(326\) | 30.7770 | − | 15.7193i | 1.70458 | − | 0.870613i | ||||
\(327\) | −21.7695 | + | 12.9974i | −1.20385 | + | 0.718756i | ||||
\(328\) | 31.2455 | + | 4.85549i | 1.72524 | + | 0.268099i | ||||
\(329\) | − | 7.51739i | − | 0.414447i | ||||||
\(330\) | −2.28902 | + | 14.9425i | −0.126007 | + | 0.822556i | ||||
\(331\) | 4.63660i | 0.254850i | 0.991848 | + | 0.127425i | \(0.0406713\pi\) | ||||
−0.991848 | + | 0.127425i | \(0.959329\pi\) | |||||||
\(332\) | 12.5017 | + | 9.04594i | 0.686119 | + | 0.496460i | ||||
\(333\) | 17.1163 | + | 9.22456i | 0.937968 | + | 0.505503i | ||||
\(334\) | 2.27374 | + | 4.45177i | 0.124414 | + | 0.243590i | ||||
\(335\) | −7.36258 | + | 3.18544i | −0.402261 | + | 0.174039i | ||||
\(336\) | −5.23368 | − | 4.53967i | −0.285521 | − | 0.247659i | ||||
\(337\) | 18.4352i | 1.00423i | 0.864801 | + | 0.502114i | \(0.167444\pi\) | ||||
−0.864801 | + | 0.502114i | \(0.832556\pi\) | |||||||
\(338\) | 11.7897 | − | 6.02160i | 0.641277 | − | 0.327532i | ||||
\(339\) | 13.1413 | − | 7.84594i | 0.713736 | − | 0.426133i | ||||
\(340\) | 4.87358 | − | 21.9963i | 0.264307 | − | 1.19292i | ||||
\(341\) | 19.1087i | 1.03479i | ||||||||
\(342\) | −8.09133 | − | 0.178824i | −0.437529 | − | 0.00966971i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −4.06714 | + | 26.1724i | −0.219285 | + | 1.41112i | ||||
\(345\) | −6.44467 | − | 4.64207i | −0.346969 | − | 0.249920i | ||||
\(346\) | 21.2458 | − | 10.8513i | 1.14218 | − | 0.583368i | ||||
\(347\) | 2.86847i | 0.153987i | 0.997032 | + | 0.0769936i | \(0.0245321\pi\) | ||||
−0.997032 | + | 0.0769936i | \(0.975468\pi\) | |||||||
\(348\) | 17.0612 | + | 1.50753i | 0.914576 | + | 0.0808119i | ||||
\(349\) | −2.76610 | −0.148066 | −0.0740330 | − | 0.997256i | \(-0.523587\pi\) | ||||
−0.0740330 | + | 0.997256i | \(0.523587\pi\) | |||||||
\(350\) | 1.96716 | − | 6.79193i | 0.105149 | − | 0.363044i | ||||
\(351\) | 9.90267 | − | 0.435373i | 0.528566 | − | 0.0232385i | ||||
\(352\) | −11.0932 | − | 10.9860i | −0.591271 | − | 0.585555i | ||||
\(353\) | 23.6750 | 1.26009 | 0.630045 | − | 0.776558i | \(-0.283036\pi\) | ||||
0.630045 | + | 0.776558i | \(0.283036\pi\) | |||||||
\(354\) | 0.933312 | − | 1.48753i | 0.0496050 | − | 0.0790612i | ||||
\(355\) | −9.22930 | + | 3.99308i | −0.489840 | + | 0.211930i | ||||
\(356\) | −21.9840 | − | 15.9071i | −1.16515 | − | 0.843075i | ||||
\(357\) | −7.49199 | + | 4.47306i | −0.396518 | + | 0.236739i | ||||
\(358\) | 5.28183 | − | 2.69770i | 0.279154 | − | 0.142578i | ||||
\(359\) | −15.7410 | −0.830778 | −0.415389 | − | 0.909644i | \(-0.636355\pi\) | ||||
−0.415389 | + | 0.909644i | \(0.636355\pi\) | |||||||
\(360\) | 18.4292 | + | 4.51264i | 0.971305 | + | 0.237837i | ||||
\(361\) | 15.3610 | 0.808475 | ||||||||
\(362\) | −12.2171 | + | 6.23990i | −0.642118 | + | 0.327962i | ||||
\(363\) | −5.03070 | + | 3.00356i | −0.264043 | + | 0.157646i | ||||
\(364\) | 3.09093 | + | 2.23653i | 0.162009 | + | 0.117226i | ||||
\(365\) | −5.43056 | − | 12.5518i | −0.284248 | − | 0.656990i | ||||
\(366\) | 6.67995 | − | 10.6466i | 0.349167 | − | 0.556507i | ||||
\(367\) | 19.3280 | 1.00891 | 0.504457 | − | 0.863437i | \(-0.331693\pi\) | ||||
0.504457 | + | 0.863437i | \(0.331693\pi\) | |||||||
\(368\) | 7.79154 | − | 2.56514i | 0.406162 | − | 0.133717i | ||||
\(369\) | 29.5239 | + | 15.9114i | 1.53695 | + | 0.828317i | ||||
\(370\) | −15.8038 | − | 13.0502i | −0.821602 | − | 0.678445i | ||||
\(371\) | 6.14747 | 0.319161 | ||||||||
\(372\) | 23.8910 | + | 2.11101i | 1.23869 | + | 0.109451i | ||||
\(373\) | 34.4749i | 1.78504i | 0.451007 | + | 0.892520i | \(0.351065\pi\) | ||||
−0.451007 | + | 0.892520i | \(0.648935\pi\) | |||||||
\(374\) | −17.5114 | + | 8.94393i | −0.905491 | + | 0.462479i | ||||
\(375\) | 3.70383 | + | 19.0074i | 0.191265 | + | 0.981538i | ||||
\(376\) | −21.0102 | − | 3.26495i | −1.08352 | − | 0.168377i | ||||
\(377\) | −9.43187 | −0.485766 | ||||||||
\(378\) | −3.62671 | − | 6.39116i | −0.186538 | − | 0.328726i | ||||
\(379\) | 16.3121i | 0.837895i | 0.908010 | + | 0.418947i | \(0.137601\pi\) | ||||
−0.908010 | + | 0.418947i | \(0.862399\pi\) | |||||||
\(380\) | 8.32911 | + | 1.84543i | 0.427274 | + | 0.0946684i | ||||
\(381\) | −3.20755 | + | 1.91505i | −0.164328 | + | 0.0981112i | ||||
\(382\) | −9.82085 | + | 5.01599i | −0.502478 | + | 0.256641i | ||||
\(383\) | − | 20.4691i | − | 1.04592i | −0.852356 | − | 0.522962i | \(-0.824827\pi\) | ||
0.852356 | − | 0.522962i | \(-0.175173\pi\) | |||||||
\(384\) | −14.9609 | + | 12.6559i | −0.763472 | + | 0.645841i | ||||
\(385\) | −5.66401 | + | 2.45055i | −0.288665 | + | 0.124891i | ||||
\(386\) | −1.38803 | − | 2.71763i | −0.0706488 | − | 0.138324i | ||||
\(387\) | −13.3280 | + | 24.7303i | −0.677501 | + | 1.25711i | ||||
\(388\) | −27.0222 | − | 19.5527i | −1.37185 | − | 0.992638i | ||||
\(389\) | 12.5062i | 0.634088i | 0.948411 | + | 0.317044i | \(0.102690\pi\) | ||||
−0.948411 | + | 0.317044i | \(0.897310\pi\) | |||||||
\(390\) | −10.3279 | − | 1.58213i | −0.522976 | − | 0.0801141i | ||||
\(391\) | − | 10.3312i | − | 0.522470i | ||||||
\(392\) | 0.434319 | − | 2.79488i | 0.0219364 | − | 0.141163i | ||||
\(393\) | −4.36668 | + | 2.60711i | −0.220270 | + | 0.131511i | ||||
\(394\) | 18.8513 | − | 9.62828i | 0.949713 | − | 0.485066i | ||||
\(395\) | 13.0119 | + | 30.0746i | 0.654698 | + | 1.51322i | ||||
\(396\) | −7.20455 | − | 14.9102i | −0.362042 | − | 0.749267i | ||||
\(397\) | 7.33769i | 0.368268i | 0.982901 | + | 0.184134i | \(0.0589481\pi\) | ||||
−0.982901 | + | 0.184134i | \(0.941052\pi\) | |||||||
\(398\) | 6.90790 | + | 13.5250i | 0.346262 | + | 0.677947i | ||||
\(399\) | −1.69377 | − | 2.83692i | −0.0847945 | − | 0.142023i | ||||
\(400\) | −18.1283 | − | 8.44784i | −0.906413 | − | 0.422392i | ||||
\(401\) | − | 11.3403i | − | 0.566310i | −0.959074 | − | 0.283155i | \(-0.908619\pi\) | ||
0.959074 | − | 0.283155i | \(-0.0913810\pi\) | |||||||
\(402\) | 4.67050 | − | 7.44392i | 0.232944 | − | 0.371269i | ||||
\(403\) | −13.2076 | −0.657915 | ||||||||
\(404\) | 12.5017 | + | 9.04594i | 0.621982 | + | 0.450052i | ||||
\(405\) | 16.8304 | + | 11.0335i | 0.836309 | + | 0.548259i | ||||
\(406\) | 3.18051 | + | 6.22714i | 0.157846 | + | 0.309048i | ||||
\(407\) | 17.8879i | 0.886668i | ||||||||
\(408\) | 9.24776 | + | 22.8820i | 0.457832 | + | 1.13283i | ||||
\(409\) | 10.5692 | 0.522615 | 0.261307 | − | 0.965256i | \(-0.415846\pi\) | ||||
0.261307 | + | 0.965256i | \(0.415846\pi\) | |||||||
\(410\) | −27.2600 | − | 22.5102i | −1.34628 | − | 1.11170i | ||||
\(411\) | −24.5213 | + | 14.6403i | −1.20955 | + | 0.722154i | ||||
\(412\) | −23.6958 | + | 32.7481i | −1.16741 | + | 1.61338i | ||||
\(413\) | 0.716916 | 0.0352771 | ||||||||
\(414\) | 8.69840 | + | 0.192241i | 0.427503 | + | 0.00944812i | ||||
\(415\) | −6.85067 | − | 15.8341i | −0.336286 | − | 0.777267i | ||||
\(416\) | 7.59329 | − | 7.66742i | 0.372292 | − | 0.375926i | ||||
\(417\) | −9.63703 | − | 16.1412i | −0.471927 | − | 0.790438i | ||||
\(418\) | −3.38671 | − | 6.63085i | −0.165649 | − | 0.324326i | ||||
\(419\) | −39.1526 | −1.91273 | −0.956365 | − | 0.292175i | \(-0.905621\pi\) | ||||
−0.956365 | + | 0.292175i | \(0.905621\pi\) | |||||||
\(420\) | 2.43812 | + | 7.35225i | 0.118968 | + | 0.358753i | ||||
\(421\) | 28.0122 | 1.36523 | 0.682614 | − | 0.730779i | \(-0.260843\pi\) | ||||
0.682614 | + | 0.730779i | \(0.260843\pi\) | |||||||
\(422\) | −8.73727 | − | 17.1067i | −0.425323 | − | 0.832743i | ||||
\(423\) | −19.8526 | − | 10.6992i | −0.965267 | − | 0.520215i | ||||
\(424\) | 2.66997 | − | 17.1815i | 0.129665 | − | 0.834405i | ||||
\(425\) | −17.2457 | + | 18.3595i | −0.836540 | + | 0.890565i | ||||
\(426\) | 5.85467 | − | 9.33126i | 0.283660 | − | 0.452101i | ||||
\(427\) | 5.13115 | 0.248314 | ||||||||
\(428\) | 2.06421 | + | 1.49362i | 0.0997776 | + | 0.0721968i | ||||
\(429\) | 4.67469 | + | 7.82970i | 0.225696 | + | 0.378022i | ||||
\(430\) | 18.8554 | − | 22.8340i | 0.909288 | − | 1.10115i | ||||
\(431\) | −37.8527 | −1.82330 | −0.911650 | − | 0.410967i | \(-0.865191\pi\) | ||||
−0.911650 | + | 0.410967i | \(0.865191\pi\) | |||||||
\(432\) | −19.4377 | + | 7.36043i | −0.935197 | + | 0.354129i | ||||
\(433\) | 18.2920i | 0.879058i | 0.898228 | + | 0.439529i | \(0.144855\pi\) | ||||
−0.898228 | + | 0.439529i | \(0.855145\pi\) | |||||||
\(434\) | 4.45370 | + | 8.71993i | 0.213785 | + | 0.418570i | ||||
\(435\) | −15.5382 | − | 11.1921i | −0.744997 | − | 0.536618i | ||||
\(436\) | −17.1623 | + | 23.7187i | −0.821926 | + | 1.13592i | ||||
\(437\) | 3.91200 | 0.187136 | ||||||||
\(438\) | 12.6904 | + | 7.96231i | 0.606373 | + | 0.380454i | ||||
\(439\) | 12.5549i | 0.599211i | 0.954063 | + | 0.299605i | \(0.0968550\pi\) | ||||
−0.954063 | + | 0.299605i | \(0.903145\pi\) | |||||||
\(440\) | 4.38900 | + | 16.8946i | 0.209237 | + | 0.805417i | ||||
\(441\) | 1.42327 | − | 2.64089i | 0.0677746 | − | 0.125757i | ||||
\(442\) | −6.18186 | − | 12.1035i | −0.294041 | − | 0.575705i | ||||
\(443\) | 29.7757i | 1.41468i | 0.706872 | + | 0.707342i | \(0.250106\pi\) | ||||
−0.706872 | + | 0.707342i | \(0.749894\pi\) | |||||||
\(444\) | 22.3646 | + | 1.97614i | 1.06138 | + | 0.0937833i | ||||
\(445\) | 12.0468 | + | 27.8440i | 0.571072 | + | 1.31993i | ||||
\(446\) | −14.6621 | + | 7.48867i | −0.694271 | + | 0.354599i | ||||
\(447\) | −12.1128 | − | 20.2878i | −0.572914 | − | 0.959582i | ||||
\(448\) | −7.62273 | − | 2.42774i | −0.360140 | − | 0.114700i | ||||
\(449\) | 23.7253i | 1.11967i | 0.828605 | + | 0.559834i | \(0.189135\pi\) | ||||
−0.828605 | + | 0.559834i | \(0.810865\pi\) | |||||||
\(450\) | −15.1370 | − | 14.8618i | −0.713563 | − | 0.700591i | ||||
\(451\) | 30.8548i | 1.45289i | ||||||||
\(452\) | 10.3601 | − | 14.3179i | 0.487300 | − | 0.673459i | ||||
\(453\) | 1.19899 | + | 2.00820i | 0.0563333 | + | 0.0943535i | ||||
\(454\) | −2.03290 | − | 3.98024i | −0.0954090 | − | 0.186802i | ||||
\(455\) | −1.69377 | − | 3.91485i | −0.0794051 | − | 0.183531i | ||||
\(456\) | −8.66448 | + | 3.50176i | −0.405752 | + | 0.163985i | ||||
\(457\) | 5.67383i | 0.265411i | 0.991156 | + | 0.132705i | \(0.0423664\pi\) | ||||
−0.991156 | + | 0.132705i | \(0.957634\pi\) | |||||||
\(458\) | −4.33009 | + | 2.21159i | −0.202332 | + | 0.103341i | ||||
\(459\) | 1.14977 | + | 26.1519i | 0.0536668 | + | 1.22067i | ||||
\(460\) | −8.95401 | − | 1.98388i | −0.417483 | − | 0.0924990i | ||||
\(461\) | − | 12.2891i | − | 0.572360i | −0.958176 | − | 0.286180i | \(-0.907614\pi\) | ||
0.958176 | − | 0.286180i | \(-0.0923856\pi\) | |||||||
\(462\) | 3.59300 | − | 5.72658i | 0.167162 | − | 0.266425i | ||||
\(463\) | 0.893880 | 0.0415421 | 0.0207711 | − | 0.999784i | \(-0.493388\pi\) | ||||
0.0207711 | + | 0.999784i | \(0.493388\pi\) | |||||||
\(464\) | 18.7855 | − | 6.18458i | 0.872094 | − | 0.287112i | ||||
\(465\) | −21.7583 | − | 15.6724i | −1.00901 | − | 0.726789i | ||||
\(466\) | −22.1284 | + | 11.3021i | −1.02508 | + | 0.523558i | ||||
\(467\) | − | 29.0874i | − | 1.34601i | −0.739640 | − | 0.673003i | \(-0.765004\pi\) | ||
0.739640 | − | 0.673003i | \(-0.234996\pi\) | |||||||
\(468\) | 10.3057 | − | 4.97964i | 0.476379 | − | 0.230184i | ||||
\(469\) | 3.58761 | 0.165660 | ||||||||
\(470\) | 18.3303 | + | 15.1364i | 0.845514 | + | 0.698191i | ||||
\(471\) | −1.69377 | − | 2.83692i | −0.0780447 | − | 0.130718i | ||||
\(472\) | 0.311370 | − | 2.00369i | 0.0143320 | − | 0.0922275i | ||||
\(473\) | −25.8451 | −1.18836 | ||||||||
\(474\) | −30.4069 | − | 19.0781i | −1.39663 | − | 0.876284i | ||||
\(475\) | −6.95199 | − | 6.53026i | −0.318979 | − | 0.299629i | ||||
\(476\) | −5.90644 | + | 8.16282i | −0.270721 | + | 0.374142i | ||||
\(477\) | 8.74949 | − | 16.2348i | 0.400612 | − | 0.743341i | ||||
\(478\) | −22.0750 | + | 11.2748i | −1.00969 | + | 0.515697i | ||||
\(479\) | −24.2741 | −1.10911 | −0.554555 | − | 0.832147i | \(-0.687111\pi\) | ||||
−0.554555 | + | 0.832147i | \(0.687111\pi\) | |||||||
\(480\) | 21.6076 | − | 3.62102i | 0.986247 | − | 0.165276i | ||||
\(481\) | −12.3637 | −0.563737 | ||||||||
\(482\) | 7.82234 | − | 3.99526i | 0.356298 | − | 0.181979i | ||||
\(483\) | 1.82085 | + | 3.04976i | 0.0828513 | + | 0.138769i | ||||
\(484\) | −3.96603 | + | 5.48114i | −0.180274 | + | 0.249143i | ||||
\(485\) | 14.8076 | + | 34.2253i | 0.672381 | + | 1.55409i | ||||
\(486\) | −22.0402 | + | 0.481428i | −0.999762 | + | 0.0218380i | ||||
\(487\) | 38.1623 | 1.72930 | 0.864648 | − | 0.502378i | \(-0.167541\pi\) | ||||
0.864648 | + | 0.502378i | \(0.167541\pi\) | |||||||
\(488\) | 2.22856 | − | 14.3410i | 0.100882 | − | 0.649184i | ||||
\(489\) | 36.3414 | − | 21.6975i | 1.64342 | − | 0.981194i | ||||
\(490\) | −2.01352 | + | 2.43839i | −0.0909616 | + | 0.110155i | ||||
\(491\) | 26.4225 | 1.19243 | 0.596216 | − | 0.802824i | \(-0.296670\pi\) | ||||
0.596216 | + | 0.802824i | \(0.296670\pi\) | |||||||
\(492\) | 38.5767 | + | 3.40864i | 1.73917 | + | 0.153673i | ||||
\(493\) | − | 24.9085i | − | 1.12182i | ||||||
\(494\) | 4.58311 | − | 2.34082i | 0.206204 | − | 0.105319i | ||||
\(495\) | −1.58977 | + | 18.4458i | −0.0714547 | + | 0.829078i | ||||
\(496\) | 26.3055 | − | 8.66034i | 1.18115 | − | 0.388861i | ||||
\(497\) | 4.49721 | 0.201728 | ||||||||
\(498\) | 16.0091 | + | 10.0445i | 0.717383 | + | 0.450104i | ||||
\(499\) | 34.9059i | 1.56260i | 0.624155 | + | 0.781300i | \(0.285443\pi\) | ||||
−0.624155 | + | 0.781300i | \(0.714557\pi\) | |||||||
\(500\) | 12.6004 | + | 18.4724i | 0.563509 | + | 0.826110i | ||||
\(501\) | 3.13846 | + | 5.25665i | 0.140216 | + | 0.234850i | ||||
\(502\) | 28.3073 | − | 14.4580i | 1.26342 | − | 0.645291i | ||||
\(503\) | − | 8.03971i | − | 0.358473i | −0.983806 | − | 0.179236i | \(-0.942637\pi\) | ||
0.983806 | − | 0.179236i | \(-0.0573627\pi\) | |||||||
\(504\) | −6.76283 | − | 5.12485i | −0.301240 | − | 0.228279i | ||||
\(505\) | −6.85067 | − | 15.8341i | −0.304851 | − | 0.704609i | ||||
\(506\) | 3.64080 | + | 7.12834i | 0.161853 | + | 0.316893i | ||||
\(507\) | 13.9213 | − | 8.31165i | 0.618266 | − | 0.369133i | ||||
\(508\) | −2.52873 | + | 3.49475i | −0.112194 | + | 0.155055i | ||||
\(509\) | − | 5.53741i | − | 0.245441i | −0.992441 | − | 0.122721i | \(-0.960838\pi\) | ||
0.992441 | − | 0.122721i | \(-0.0391619\pi\) | |||||||
\(510\) | 4.17823 | − | 27.2750i | 0.185015 | − | 1.20776i | ||||
\(511\) | 6.11618i | 0.270564i | ||||||||
\(512\) | −10.0960 | + | 20.2502i | −0.446183 | + | 0.894942i | ||||
\(513\) | −9.90267 | + | 0.435373i | −0.437214 | + | 0.0192222i | ||||
\(514\) | −9.14001 | + | 4.66826i | −0.403148 | + | 0.205908i | ||||
\(515\) | 41.4774 | − | 17.9453i | 1.82771 | − | 0.790763i | ||||
\(516\) | −2.85520 | + | 32.3133i | −0.125693 | + | 1.42251i | ||||
\(517\) | − | 20.7475i | − | 0.912474i | ||||||
\(518\) | 4.16916 | + | 8.16282i | 0.183182 | + | 0.358654i | ||||
\(519\) | 25.0870 | − | 14.9781i | 1.10120 | − | 0.657464i | ||||
\(520\) | −11.6772 | + | 3.03359i | −0.512078 | + | 0.133032i | ||||
\(521\) | 12.7331i | 0.557846i | 0.960313 | + | 0.278923i | \(0.0899775\pi\) | ||||
−0.960313 | + | 0.278923i | \(0.910023\pi\) | |||||||
\(522\) | 20.9719 | + | 0.463494i | 0.917916 | + | 0.0202866i | ||||
\(523\) | 22.8415 | 0.998791 | 0.499396 | − | 0.866374i | \(-0.333555\pi\) | ||||
0.499396 | + | 0.866374i | \(0.333555\pi\) | |||||||
\(524\) | −3.44255 | + | 4.75767i | −0.150388 | + | 0.207840i | ||||
\(525\) | 1.85512 | − | 8.45923i | 0.0809640 | − | 0.369191i | ||||
\(526\) | −10.5449 | − | 20.6459i | −0.459779 | − | 0.900205i | ||||
\(527\) | − | 34.8797i | − | 1.51938i | ||||||
\(528\) | −14.4446 | − | 12.5292i | −0.628621 | − | 0.545263i | ||||
\(529\) | 18.7945 | 0.817152 | ||||||||
\(530\) | −12.3781 | + | 14.9899i | −0.537669 | + | 0.651120i | ||||
\(531\) | 1.02036 | − | 1.89330i | 0.0442799 | − | 0.0821621i | ||||
\(532\) | −3.09093 | − | 2.23653i | −0.134009 | − | 0.0969659i | ||||
\(533\) | −21.3262 | −0.923740 | ||||||||
\(534\) | −28.1516 | − | 17.6630i | −1.21824 | − | 0.764355i | ||||
\(535\) | −1.13115 | − | 2.61445i | −0.0489038 | − | 0.113033i | ||||
\(536\) | 1.55817 | − | 10.0269i | 0.0673026 | − | 0.433098i | ||||
\(537\) | 6.23678 | − | 3.72364i | 0.269137 | − | 0.160687i | ||||
\(538\) | −2.91638 | − | 5.71000i | −0.125734 | − | 0.246175i | ||||
\(539\) | 2.75993 | 0.118879 | ||||||||
\(540\) | 22.8866 | + | 4.02541i | 0.984882 | + | 0.173226i | ||||
\(541\) | −16.5179 | −0.710158 | −0.355079 | − | 0.934836i | \(-0.615546\pi\) | ||||
−0.355079 | + | 0.934836i | \(0.615546\pi\) | |||||||
\(542\) | −17.7004 | − | 34.6557i | −0.760297 | − | 1.48859i | ||||
\(543\) | −14.4260 | + | 8.61297i | −0.619078 | + | 0.369618i | ||||
\(544\) | 20.2488 | + | 20.0531i | 0.868162 | + | 0.859768i | ||||
\(545\) | 30.0412 | − | 12.9974i | 1.28682 | − | 0.556746i | ||||
\(546\) | 3.95810 | + | 2.48341i | 0.169391 | + | 0.106280i | ||||
\(547\) | −22.5719 | −0.965106 | −0.482553 | − | 0.875867i | \(-0.660290\pi\) | ||||
−0.482553 | + | 0.875867i | \(0.660290\pi\) | |||||||
\(548\) | −19.3318 | + | 26.7169i | −0.825812 | + | 1.14129i | ||||
\(549\) | 7.30299 | − | 13.5508i | 0.311684 | − | 0.578334i | ||||
\(550\) | 5.42922 | − | 18.7453i | 0.231503 | − | 0.799301i | ||||
\(551\) | 9.43187 | 0.401811 | ||||||||
\(552\) | 9.31455 | − | 3.76448i | 0.396453 | − | 0.160227i | ||||
\(553\) | − | 14.6546i | − | 0.623179i | ||||||
\(554\) | 15.6602 | + | 30.6611i | 0.665337 | + | 1.30267i | ||||
\(555\) | −20.3681 | − | 14.6711i | −0.864579 | − | 0.622752i | ||||
\(556\) | −17.5865 | − | 12.7252i | −0.745832 | − | 0.539668i | ||||
\(557\) | −9.27395 | −0.392950 | −0.196475 | − | 0.980509i | \(-0.562949\pi\) | ||||
−0.196475 | + | 0.980509i | \(0.562949\pi\) | |||||||
\(558\) | 29.3672 | + | 0.649036i | 1.24321 | + | 0.0274759i | ||||
\(559\) | − | 17.8636i | − | 0.755550i | ||||||
\(560\) | 5.94049 | + | 6.68659i | 0.251032 | + | 0.282560i | ||||
\(561\) | −20.6774 | + | 12.3454i | −0.873000 | + | 0.521221i | ||||
\(562\) | −6.79516 | − | 13.3043i | −0.286636 | − | 0.561207i | ||||
\(563\) | 13.5713i | 0.571962i | 0.958235 | + | 0.285981i | \(0.0923194\pi\) | ||||
−0.958235 | + | 0.285981i | \(0.907681\pi\) | |||||||
\(564\) | −25.9399 | − | 2.29205i | −1.09227 | − | 0.0965128i | ||||
\(565\) | −18.1345 | + | 7.84594i | −0.762925 | + | 0.330081i | ||||
\(566\) | −6.97332 | + | 3.56162i | −0.293111 | + | 0.149706i | ||||
\(567\) | −4.94862 | − | 7.51739i | −0.207823 | − | 0.315701i | ||||
\(568\) | 1.95323 | − | 12.5692i | 0.0819556 | − | 0.527391i | ||||
\(569\) | 16.4865i | 0.691148i | 0.938392 | + | 0.345574i | \(0.112316\pi\) | ||||
−0.938392 | + | 0.345574i | \(0.887684\pi\) | |||||||
\(570\) | 10.3279 | + | 1.58213i | 0.432590 | + | 0.0662680i | ||||
\(571\) | 7.86631i | 0.329195i | 0.986361 | + | 0.164597i | \(0.0526325\pi\) | ||||
−0.986361 | + | 0.164597i | \(0.947368\pi\) | |||||||
\(572\) | 8.53077 | + | 6.17268i | 0.356689 | + | 0.258093i | ||||
\(573\) | −11.5964 | + | 6.92361i | −0.484448 | + | 0.289238i | ||||
\(574\) | 7.19138 | + | 14.0800i | 0.300162 | + | 0.587690i | ||||
\(575\) | 7.47357 | + | 7.02020i | 0.311670 | + | 0.292763i | ||||
\(576\) | −17.2606 | + | 16.6755i | −0.719191 | + | 0.694812i | ||||
\(577\) | 31.2545i | 1.30114i | 0.759445 | + | 0.650572i | \(0.225471\pi\) | ||||
−0.759445 | + | 0.650572i | \(0.774529\pi\) | |||||||
\(578\) | 10.5534 | − | 5.39016i | 0.438964 | − | 0.224201i | ||||
\(579\) | −1.91590 | − | 3.20897i | −0.0796222 | − | 0.133360i | ||||
\(580\) | −21.5882 | − | 4.78316i | −0.896401 | − | 0.198610i | ||||
\(581\) | 7.71558i | 0.320096i | ||||||||
\(582\) | −34.6034 | − | 21.7111i | −1.43436 | − | 0.899952i | ||||
\(583\) | 16.9666 | 0.702685 | ||||||||
\(584\) | 17.0940 | + | 2.65638i | 0.707355 | + | 0.109922i | ||||
\(585\) | −12.7494 | − | 1.09882i | −0.527122 | − | 0.0454304i | ||||
\(586\) | 31.7630 | − | 16.2230i | 1.31212 | − | 0.670164i | ||||
\(587\) | 2.10458i | 0.0868654i | 0.999056 | + | 0.0434327i | \(0.0138294\pi\) | ||||
−0.999056 | + | 0.0434327i | \(0.986171\pi\) | |||||||
\(588\) | 0.304900 | − | 3.45066i | 0.0125739 | − | 0.142303i | ||||
\(589\) | 13.2076 | 0.544208 | ||||||||
\(590\) | −1.44352 | + | 1.74812i | −0.0594290 | + | 0.0719689i | ||||
\(591\) | 22.2595 | − | 13.2900i | 0.915635 | − | 0.546676i | ||||
\(592\) | 24.6249 | − | 8.10703i | 1.01208 | − | 0.333197i | ||||
\(593\) | −3.52377 | −0.144704 | −0.0723520 | − | 0.997379i | \(-0.523050\pi\) | ||||
−0.0723520 | + | 0.997379i | \(0.523050\pi\) | |||||||
\(594\) | −10.0095 | − | 17.6392i | −0.410694 | − | 0.723745i | ||||
\(595\) | 10.3387 | − | 4.47306i | 0.423845 | − | 0.183378i | ||||
\(596\) | −22.1044 | − | 15.9943i | −0.905432 | − | 0.655151i | ||||
\(597\) | 9.53501 | + | 15.9703i | 0.390242 | + | 0.653622i | ||||
\(598\) | −4.92697 | + | 2.51645i | −0.201479 | + | 0.102905i | ||||
\(599\) | −13.1436 | −0.537031 | −0.268516 | − | 0.963275i | \(-0.586533\pi\) | ||||
−0.268516 | + | 0.963275i | \(0.586533\pi\) | |||||||
\(600\) | −22.8368 | − | 8.85884i | −0.932310 | − | 0.361661i | ||||
\(601\) | −15.5022 | −0.632347 | −0.316174 | − | 0.948701i | \(-0.602398\pi\) | ||||
−0.316174 | + | 0.948701i | \(0.602398\pi\) | |||||||
\(602\) | −11.7940 | + | 6.02377i | −0.480686 | + | 0.245510i | ||||
\(603\) | 5.10612 | − | 9.47448i | 0.207937 | − | 0.385831i | ||||
\(604\) | 2.18801 | + | 1.58320i | 0.0890290 | + | 0.0644194i | ||||
\(605\) | 6.94220 | − | 3.00356i | 0.282240 | − | 0.122112i | ||||
\(606\) | 16.0091 | + | 10.0445i | 0.650323 | + | 0.408029i | ||||
\(607\) | 8.78015 | 0.356375 | 0.178188 | − | 0.983997i | \(-0.442977\pi\) | ||||
0.178188 | + | 0.983997i | \(0.442977\pi\) | |||||||
\(608\) | −7.59329 | + | 7.66742i | −0.307949 | + | 0.310955i | ||||
\(609\) | 4.39007 | + | 7.35300i | 0.177895 | + | 0.297958i | ||||
\(610\) | −10.3317 | + | 12.5117i | −0.418317 | + | 0.506585i | ||||
\(611\) | 14.3403 | 0.580145 | ||||||||
\(612\) | 13.1507 | + | 27.2161i | 0.531585 | + | 1.10015i | ||||
\(613\) | 7.21143i | 0.291267i | 0.989339 | + | 0.145633i | \(0.0465220\pi\) | ||||
−0.989339 | + | 0.145633i | \(0.953478\pi\) | |||||||
\(614\) | 24.0334 | − | 12.2751i | 0.969910 | − | 0.495381i | ||||
\(615\) | −35.1330 | − | 25.3061i | −1.41670 | − | 1.02044i | ||||
\(616\) | 1.19869 | − | 7.71369i | 0.0482967 | − | 0.310793i | ||||
\(617\) | −4.53960 | −0.182758 | −0.0913788 | − | 0.995816i | \(-0.529127\pi\) | ||||
−0.0913788 | + | 0.995816i | \(0.529127\pi\) | |||||||
\(618\) | −26.3115 | + | 41.9356i | −1.05840 | + | 1.68690i | ||||
\(619\) | − | 18.1564i | − | 0.729766i | −0.931053 | − | 0.364883i | \(-0.881109\pi\) | ||
0.931053 | − | 0.364883i | \(-0.118891\pi\) | |||||||
\(620\) | −30.2302 | − | 6.69791i | −1.21407 | − | 0.268995i | ||||
\(621\) | 10.6456 | − | 0.468037i | 0.427195 | − | 0.0187817i | ||||
\(622\) | −8.75783 | + | 4.47306i | −0.351157 | + | 0.179353i | ||||
\(623\) | − | 13.5677i | − | 0.543579i | ||||||
\(624\) | 8.65992 | − | 9.98383i | 0.346674 | − | 0.399673i | ||||
\(625\) | −1.56249 | − | 24.9511i | −0.0624997 | − | 0.998045i | ||||
\(626\) | −22.2188 | − | 43.5023i | −0.888042 | − | 1.73870i | ||||
\(627\) | −4.67469 | − | 7.82970i | −0.186689 | − | 0.312688i | ||||
\(628\) | −3.09093 | − | 2.23653i | −0.123342 | − | 0.0892473i | ||||
\(629\) | − | 32.6513i | − | 1.30189i | ||||||
\(630\) | 3.57374 | + | 8.78797i | 0.142381 | + | 0.350121i | ||||
\(631\) | 46.0384i | 1.83276i | 0.400310 | + | 0.916380i | \(0.368902\pi\) | ||||
−0.400310 | + | 0.916380i | \(0.631098\pi\) | |||||||
\(632\) | −40.9580 | − | 6.36480i | −1.62922 | − | 0.253178i | ||||
\(633\) | −12.0601 | − | 20.1996i | −0.479346 | − | 0.802863i | ||||
\(634\) | 10.3184 | − | 5.27012i | 0.409796 | − | 0.209303i | ||||
\(635\) | 4.42632 | − | 1.91505i | 0.175653 | − | 0.0759966i | ||||
\(636\) | 1.87436 | − | 21.2128i | 0.0743234 | − | 0.841143i | ||||
\(637\) | 1.90761i | 0.0755823i | ||||||||
\(638\) | 8.77800 | + | 17.1865i | 0.347524 | + | 0.680420i | ||||
\(639\) | 6.40073 | − | 11.8767i | 0.253209 | − | 0.469833i | ||||
\(640\) | 21.2683 | − | 13.6989i | 0.840704 | − | 0.541495i | ||||
\(641\) | − | 28.5533i | − | 1.12779i | −0.825847 | − | 0.563894i | \(-0.809303\pi\) | ||
0.825847 | − | 0.563894i | \(-0.190697\pi\) | |||||||
\(642\) | 2.64333 | + | 1.65849i | 0.104324 | + | 0.0654556i | ||||
\(643\) | 28.9229 | 1.14061 | 0.570305 | − | 0.821433i | \(-0.306825\pi\) | ||||
0.570305 | + | 0.821433i | \(0.306825\pi\) | |||||||
\(644\) | 3.32283 | + | 2.40433i | 0.130938 | + | 0.0947438i | ||||
\(645\) | 21.1974 | − | 29.4287i | 0.834645 | − | 1.15875i | ||||
\(646\) | 6.18186 | + | 12.1035i | 0.243222 | + | 0.476206i | ||||
\(647\) | − | 5.44152i | − | 0.213928i | −0.994263 | − | 0.106964i | \(-0.965887\pi\) | ||
0.994263 | − | 0.106964i | \(-0.0341130\pi\) | |||||||
\(648\) | −23.1595 | + | 10.5659i | −0.909791 | + | 0.415067i | ||||
\(649\) | 1.97864 | 0.0776684 | ||||||||
\(650\) | 12.9564 | + | 3.75257i | 0.508190 | + | 0.147188i | ||||
\(651\) | 6.14747 | + | 10.2965i | 0.240938 | + | 0.403551i | ||||
\(652\) | 28.6504 | − | 39.5954i | 1.12203 | − | 1.55068i | ||||
\(653\) | −36.5529 | −1.43042 | −0.715212 | − | 0.698907i | \(-0.753670\pi\) | ||||
−0.715212 | + | 0.698907i | \(0.753670\pi\) | |||||||
\(654\) | −19.0568 | + | 30.3730i | −0.745180 | + | 1.18768i | ||||
\(655\) | 6.02588 | − | 2.60711i | 0.235451 | − | 0.101868i | ||||
\(656\) | 42.4754 | − | 13.9838i | 1.65839 | − | 0.545977i | ||||
\(657\) | 16.1522 | + | 8.70495i | 0.630156 | + | 0.339613i | ||||
\(658\) | −4.83566 | − | 9.46777i | −0.188514 | − | 0.369092i | ||||
\(659\) | 9.10215 | 0.354570 | 0.177285 | − | 0.984160i | \(-0.443269\pi\) | ||||
0.177285 | + | 0.984160i | \(0.443269\pi\) | |||||||
\(660\) | 6.72904 | + | 20.2917i | 0.261927 | + | 0.789854i | ||||
\(661\) | −1.54757 | −0.0601935 | −0.0300968 | − | 0.999547i | \(-0.509582\pi\) | ||||
−0.0300968 | + | 0.999547i | \(0.509582\pi\) | |||||||
\(662\) | 2.98255 | + | 5.83956i | 0.115920 | + | 0.226961i | ||||
\(663\) | −8.53286 | − | 14.2918i | −0.331389 | − | 0.555048i | ||||
\(664\) | 21.5641 | + | 3.35103i | 0.836851 | + | 0.130045i | ||||
\(665\) | 1.69377 | + | 3.91485i | 0.0656815 | + | 0.151811i | ||||
\(666\) | 27.4909 | + | 0.607570i | 1.06525 | + | 0.0235428i | ||||
\(667\) | −10.1395 | −0.392603 | ||||||||
\(668\) | 5.72732 | + | 4.14417i | 0.221597 | + | 0.160343i | ||||
\(669\) | −17.3130 | + | 10.3367i | −0.669360 | + | 0.399638i | ||||
\(670\) | −7.22372 | + | 8.74797i | −0.279077 | + | 0.337964i | ||||
\(671\) | 14.1616 | 0.546704 | ||||||||
\(672\) | −9.51176 | − | 2.35085i | −0.366924 | − | 0.0906859i | ||||
\(673\) | − | 3.16034i | − | 0.121822i | −0.998143 | − | 0.0609110i | \(-0.980599\pi\) | ||
0.998143 | − | 0.0609110i | \(-0.0194006\pi\) | |||||||
\(674\) | 11.8587 | + | 23.2182i | 0.456779 | + | 0.894330i | ||||
\(675\) | −19.6996 | − | 16.9389i | −0.758237 | − | 0.651979i | ||||
\(676\) | 10.9751 | − | 15.1678i | 0.422119 | − | 0.583377i | ||||
\(677\) | 11.8437 | 0.455189 | 0.227595 | − | 0.973756i | \(-0.426914\pi\) | ||||
0.227595 | + | 0.973756i | \(0.426914\pi\) | |||||||
\(678\) | 11.5038 | − | 18.3349i | 0.441799 | − | 0.704146i | ||||
\(679\) | − | 16.6772i | − | 0.640010i | ||||||
\(680\) | −8.01138 | − | 30.8382i | −0.307222 | − | 1.18259i | ||||
\(681\) | −2.80603 | − | 4.69986i | −0.107527 | − | 0.180099i | ||||
\(682\) | 12.2919 | + | 24.0664i | 0.470682 | + | 0.921551i | ||||
\(683\) | − | 4.05943i | − | 0.155330i | −0.996980 | − | 0.0776648i | \(-0.975254\pi\) | ||
0.996980 | − | 0.0776648i | \(-0.0247464\pi\) | |||||||
\(684\) | −10.3057 | + | 4.97964i | −0.394047 | + | 0.190401i | ||||
\(685\) | 33.8386 | − | 14.6403i | 1.29291 | − | 0.559378i | ||||
\(686\) | 1.25945 | − | 0.643263i | 0.0480860 | − | 0.0245599i | ||||
\(687\) | −5.11296 | + | 3.05267i | −0.195072 | + | 0.116467i | ||||
\(688\) | 11.7134 | + | 35.5790i | 0.446568 | + | 1.35644i | ||||
\(689\) | 11.7270i | 0.446763i | ||||||||
\(690\) | −11.1028 | − | 1.70083i | −0.422677 | − | 0.0647494i | ||||
\(691\) | − | 40.8932i | − | 1.55565i | −0.628481 | − | 0.777825i | \(-0.716323\pi\) | ||
0.628481 | − | 0.777825i | \(-0.283677\pi\) | |||||||
\(692\) | 19.7777 | − | 27.3332i | 0.751836 | − | 1.03905i | ||||
\(693\) | 3.92812 | − | 7.28869i | 0.149217 | − | 0.276874i | ||||
\(694\) | 1.84518 | + | 3.61269i | 0.0700420 | + | 0.137136i | ||||
\(695\) | 9.63703 | + | 22.2743i | 0.365553 | + | 0.844913i | ||||
\(696\) | 22.4575 | − | 9.07619i | 0.851248 | − | 0.344032i | ||||
\(697\) | − | 56.3202i | − | 2.13328i | ||||||
\(698\) | −3.48376 | + | 1.77933i | −0.131862 | + | 0.0673487i | ||||
\(699\) | −26.1292 | + | 15.6003i | −0.988295 | + | 0.590057i | ||||
\(700\) | −1.89147 | − | 9.81949i | −0.0714907 | − | 0.371142i | ||||
\(701\) | 34.0369i | 1.28555i | 0.766053 | + | 0.642777i | \(0.222218\pi\) | ||||
−0.766053 | + | 0.642777i | \(0.777782\pi\) | |||||||
\(702\) | 12.1919 | − | 6.91836i | 0.460152 | − | 0.261117i | ||||
\(703\) | 12.3637 | 0.466307 | ||||||||
\(704\) | −21.0382 | − | 6.70041i | −0.792909 | − | 0.252531i | ||||
\(705\) | 23.6243 | + | 17.0165i | 0.889742 | + | 0.640877i | ||||
\(706\) | 29.8174 | − | 15.2292i | 1.12219 | − | 0.573160i | ||||
\(707\) | 7.71558i | 0.290174i | ||||||||
\(708\) | 0.218588 | − | 2.47383i | 0.00821502 | − | 0.0929722i | ||||
\(709\) | −38.5746 | −1.44870 | −0.724351 | − | 0.689432i | \(-0.757860\pi\) | ||||
−0.724351 | + | 0.689432i | \(0.757860\pi\) | |||||||
\(710\) | −9.05523 | + | 10.9659i | −0.339837 | + | 0.411545i | ||||
\(711\) | −38.7013 | − | 20.8575i | −1.45141 | − | 0.782216i | ||||
\(712\) | −37.9202 | − | 5.89272i | −1.42112 | − | 0.220839i | ||||
\(713\) | −14.1985 | −0.531737 | ||||||||
\(714\) | −6.55842 | + | 10.4529i | −0.245443 | + | 0.391191i | ||||
\(715\) | −4.67469 | − | 10.8047i | −0.174823 | − | 0.404074i | ||||
\(716\) | 4.91687 | − | 6.79522i | 0.183752 | − | 0.253949i | ||||
\(717\) | −26.0661 | + | 15.5627i | −0.973457 | + | 0.581198i | ||||
\(718\) | −19.8250 | + | 10.1256i | −0.739862 | + | 0.377884i | ||||
\(719\) | 10.8657 | 0.405222 | 0.202611 | − | 0.979259i | \(-0.435057\pi\) | ||||
0.202611 | + | 0.979259i | \(0.435057\pi\) | |||||||
\(720\) | 26.1135 | − | 6.17140i | 0.973192 | − | 0.229994i | ||||
\(721\) | −20.2109 | −0.752694 | ||||||||
\(722\) | 19.3464 | − | 9.88118i | 0.719999 | − | 0.367739i | ||||
\(723\) | 9.23661 | − | 5.51468i | 0.343513 | − | 0.205093i | ||||
\(724\) | −11.3730 | + | 15.7177i | −0.422673 | + | 0.584143i | ||||
\(725\) | 18.0189 | + | 16.9258i | 0.669203 | + | 0.628607i | ||||
\(726\) | −4.40383 | + | 7.01889i | −0.163441 | + | 0.260495i | ||||
\(727\) | 4.65736 | 0.172732 | 0.0863659 | − | 0.996263i | \(-0.472475\pi\) | ||||
0.0863659 | + | 0.996263i | \(0.472475\pi\) | |||||||
\(728\) | 5.33155 | + | 0.828513i | 0.197600 | + | 0.0307067i | ||||
\(729\) | −26.8958 | + | 2.36954i | −0.996142 | + | 0.0877607i | ||||
\(730\) | −14.9136 | − | 12.3151i | −0.551978 | − | 0.455801i | ||||
\(731\) | 47.1759 | 1.74486 | ||||||||
\(732\) | 1.56449 | − | 17.7058i | 0.0578251 | − | 0.654426i | ||||
\(733\) | − | 7.36632i | − | 0.272081i | −0.990703 | − | 0.136041i | \(-0.956562\pi\) | ||
0.990703 | − | 0.136041i | \(-0.0434378\pi\) | |||||||
\(734\) | 24.3427 | − | 12.4330i | 0.898504 | − | 0.458911i | ||||
\(735\) | −2.26361 | + | 3.14262i | −0.0834947 | + | 0.115917i | ||||
\(736\) | 8.16299 | − | 8.24268i | 0.300892 | − | 0.303829i | ||||
\(737\) | 9.90156 | 0.364729 | ||||||||
\(738\) | 47.4191 | + | 1.04800i | 1.74552 | + | 0.0385773i | ||||
\(739\) | − | 33.9459i | − | 1.24872i | −0.781137 | − | 0.624360i | \(-0.785360\pi\) | ||
0.781137 | − | 0.624360i | \(-0.214640\pi\) | |||||||
\(740\) | −28.2988 | − | 6.26999i | −1.04028 | − | 0.230489i | ||||
\(741\) | 5.41173 | − | 3.23105i | 0.198805 | − | 0.118696i | ||||
\(742\) | 7.74243 | − | 3.95444i | 0.284233 | − | 0.145172i | ||||
\(743\) | − | 5.51110i | − | 0.202183i | −0.994877 | − | 0.101091i | \(-0.967767\pi\) | ||
0.994877 | − | 0.101091i | \(-0.0322334\pi\) | |||||||
\(744\) | 31.4474 | − | 12.7095i | 1.15292 | − | 0.465953i | ||||
\(745\) | 12.1128 | + | 27.9966i | 0.443778 | + | 1.02571i | ||||
\(746\) | 22.1764 | + | 43.4193i | 0.811936 | + | 1.58970i | ||||
\(747\) | 20.3760 | + | 10.9813i | 0.745520 | + | 0.401786i | ||||
\(748\) | −16.3014 | + | 22.5288i | −0.596037 | + | 0.823736i | ||||
\(749\) | 1.27396i | 0.0465494i | ||||||||
\(750\) | 16.8916 | + | 21.5563i | 0.616792 | + | 0.787126i | ||||
\(751\) | − | 19.4438i | − | 0.709514i | −0.934959 | − | 0.354757i | \(-0.884564\pi\) | ||
0.934959 | − | 0.354757i | \(-0.115436\pi\) | |||||||
\(752\) | −28.5615 | + | 9.40307i | −1.04153 | + | 0.342895i | ||||
\(753\) | 33.4253 | − | 19.9564i | 1.21808 | − | 0.727252i | ||||
\(754\) | −11.8790 | + | 6.06718i | −0.432606 | + | 0.220954i | ||||
\(755\) | −1.19899 | − | 2.77125i | −0.0436356 | − | 0.100856i | ||||
\(756\) | −8.67886 | − | 5.71641i | −0.315647 | − | 0.207904i | ||||
\(757\) | 26.8731i | 0.976718i | 0.872643 | + | 0.488359i | \(0.162404\pi\) | ||||
−0.872643 | + | 0.488359i | \(0.837596\pi\) | |||||||
\(758\) | 10.4930 | + | 20.5442i | 0.381121 | + | 0.746200i | ||||
\(759\) | 5.02541 | + | 8.41713i | 0.182411 | + | 0.305523i | ||||
\(760\) | 11.6772 | − | 3.03359i | 0.423576 | − | 0.110040i | ||||
\(761\) | − | 43.9086i | − | 1.59169i | −0.605503 | − | 0.795843i | \(-0.707028\pi\) | ||
0.605503 | − | 0.795843i | \(-0.292972\pi\) | |||||||
\(762\) | −2.80786 | + | 4.47521i | −0.101718 | + | 0.162120i | ||||
\(763\) | −14.6383 | −0.529943 | ||||||||
\(764\) | −9.14225 | + | 12.6348i | −0.330755 | + | 0.457110i | ||||
\(765\) | 2.90185 | − | 33.6697i | 0.104917 | − | 1.21733i | ||||
\(766\) | −13.1670 | − | 25.7798i | −0.475745 | − | 0.931464i | ||||
\(767\) | 1.36760i | 0.0493811i | ||||||||
\(768\) | −10.7015 | + | 25.5632i | −0.386156 | + | 0.922433i | ||||
\(769\) | −24.2477 | −0.874393 | −0.437197 | − | 0.899366i | \(-0.644029\pi\) | ||||
−0.437197 | + | 0.899366i | \(0.644029\pi\) | |||||||
\(770\) | −5.55719 | + | 6.72979i | −0.200267 | + | 0.242525i | ||||
\(771\) | −10.7925 | + | 6.44362i | −0.388683 | + | 0.232061i | ||||
\(772\) | −3.49630 | − | 2.52985i | −0.125835 | − | 0.0910512i | ||||
\(773\) | −17.0431 | −0.612998 | −0.306499 | − | 0.951871i | \(-0.599158\pi\) | ||||
−0.306499 | + | 0.951871i | \(0.599158\pi\) | |||||||
\(774\) | −0.877841 | + | 39.7200i | −0.0315533 | + | 1.42771i | ||||
\(775\) | 25.2320 | + | 23.7014i | 0.906360 | + | 0.851378i | ||||
\(776\) | −46.6107 | − | 7.24321i | −1.67323 | − | 0.260016i | ||||
\(777\) | 5.75471 | + | 9.63865i | 0.206449 | + | 0.345785i | ||||
\(778\) | 8.04476 | + | 15.7509i | 0.288419 | + | 0.564696i | ||||
\(779\) | 21.3262 | 0.764090 | ||||||||
\(780\) | −14.0252 | + | 4.65098i | −0.502184 | + | 0.166532i | ||||
\(781\) | 12.4120 | 0.444137 | ||||||||
\(782\) | −6.64566 | − | 13.0116i | −0.237648 | − | 0.465293i | ||||
\(783\) | 25.6667 | − | 1.12844i | 0.917254 | − | 0.0403272i | ||||
\(784\) | −1.25084 | − | 3.79939i | −0.0446729 | − | 0.135693i | ||||
\(785\) | 1.69377 | + | 3.91485i | 0.0604532 | + | 0.139727i | ||||
\(786\) | −3.82256 | + | 6.09245i | −0.136346 | + | 0.217311i | ||||
\(787\) | −11.5435 | −0.411483 | −0.205741 | − | 0.978606i | \(-0.565961\pi\) | ||||
−0.205741 | + | 0.978606i | \(0.565961\pi\) | |||||||
\(788\) | 17.5487 | − | 24.2526i | 0.625146 | − | 0.863965i | ||||
\(789\) | −14.5552 | − | 24.3787i | −0.518178 | − | 0.867904i | ||||
\(790\) | 35.7337 | + | 29.5074i | 1.27135 | + | 1.04983i | ||||
\(791\) | 8.83651 | 0.314190 | ||||||||
\(792\) | −18.6650 | − | 14.1443i | −0.663231 | − | 0.502594i | ||||
\(793\) | 9.78824i | 0.347590i | ||||||||
\(794\) | 4.72007 | + | 9.24145i | 0.167509 | + | 0.327967i | ||||
\(795\) | −13.9155 | + | 19.3192i | −0.493532 | + | 0.685180i | ||||
\(796\) | 17.4003 | + | 12.5905i | 0.616737 | + | 0.446257i | ||||
\(797\) | 8.66018 | 0.306759 | 0.153380 | − | 0.988167i | \(-0.450984\pi\) | ||||
0.153380 | + | 0.988167i | \(0.450984\pi\) | |||||||
\(798\) | −3.95810 | − | 2.48341i | −0.140115 | − | 0.0879118i | ||||
\(799\) | 37.8711i | 1.33978i | ||||||||
\(800\) | −28.2658 | + | 1.02163i | −0.999347 | + | 0.0361200i | ||||
\(801\) | −35.8309 | − | 19.3105i | −1.26602 | − | 0.682302i | ||||
\(802\) | −7.29483 | − | 14.2826i | −0.257589 | − | 0.504336i | ||||
\(803\) | 16.8802i | 0.595691i | ||||||||
\(804\) | 1.09386 | − | 12.3796i | 0.0385775 | − | 0.436595i | ||||
\(805\) | −1.82085 | − | 4.20857i | −0.0641764 | − | 0.148332i | ||||
\(806\) | −16.6342 | + | 8.49593i | −0.585916 | + | 0.299257i | ||||
\(807\) | −4.02550 | − | 6.74236i | −0.141704 | − | 0.237342i | ||||
\(808\) | 21.5641 | + | 3.35103i | 0.758624 | + | 0.117889i | ||||
\(809\) | − | 29.1441i | − | 1.02465i | −0.858791 | − | 0.512326i | \(-0.828784\pi\) | ||
0.858791 | − | 0.512326i | \(-0.171216\pi\) | |||||||
\(810\) | 28.2945 | + | 3.06976i | 0.994166 | + | 0.107860i | ||||
\(811\) | 37.4623i | 1.31548i | 0.753246 | + | 0.657739i | \(0.228487\pi\) | ||||
−0.753246 | + | 0.657739i | \(0.771513\pi\) | |||||||
\(812\) | 8.01138 | + | 5.79686i | 0.281144 | + | 0.203430i | ||||
\(813\) | −24.4320 | − | 40.9214i | −0.856867 | − | 1.43518i | ||||
\(814\) | 11.5066 | + | 22.5288i | 0.403306 | + | 0.789635i | ||||
\(815\) | −50.1499 | + | 21.6975i | −1.75668 | + | 0.760030i | ||||
\(816\) | 26.3662 | + | 22.8699i | 0.923002 | + | 0.800608i | ||||
\(817\) | 17.8636i | 0.624969i | ||||||||
\(818\) | 13.3114 | − | 6.79880i | 0.465422 | − | 0.237714i | ||||
\(819\) | 5.03780 | + | 2.71504i | 0.176035 | + | 0.0948712i | ||||
\(820\) | −48.8126 | − | 10.8151i | −1.70461 | − | 0.377680i | ||||
\(821\) | 22.2823i | 0.777658i | 0.921310 | + | 0.388829i | \(0.127120\pi\) | ||||
−0.921310 | + | 0.388829i | \(0.872880\pi\) | |||||||
\(822\) | −21.4657 | + | 34.2124i | −0.748703 | + | 1.19329i | ||||
\(823\) | −12.5937 | −0.438988 | −0.219494 | − | 0.975614i | \(-0.570441\pi\) | ||||
−0.219494 | + | 0.975614i | \(0.570441\pi\) | |||||||
\(824\) | −8.77800 | + | 56.4871i | −0.305796 | + | 1.96782i | ||||
\(825\) | 5.12000 | − | 23.3469i | 0.178256 | − | 0.812835i | ||||
\(826\) | 0.902919 | − | 0.461166i | 0.0314166 | − | 0.0160460i | ||||
\(827\) | 32.6595i | 1.13568i | 0.823138 | + | 0.567841i | \(0.192221\pi\) | ||||
−0.823138 | + | 0.567841i | \(0.807779\pi\) | |||||||
\(828\) | 11.0788 | − | 5.35324i | 0.385017 | − | 0.186038i | ||||
\(829\) | −19.9927 | −0.694375 | −0.347187 | − | 0.937796i | \(-0.612863\pi\) | ||||
−0.347187 | + | 0.937796i | \(0.612863\pi\) | |||||||
\(830\) | −18.8136 | − | 15.5355i | −0.653029 | − | 0.539245i | ||||
\(831\) | 21.6158 | + | 36.2046i | 0.749844 | + | 1.25592i | ||||
\(832\) | 4.63119 | − | 14.5412i | 0.160558 | − | 0.504126i | ||||
\(833\) | −5.03780 | −0.174549 | ||||||||
\(834\) | −22.5204 | − | 14.1299i | −0.779817 | − | 0.489277i | ||||
\(835\) | −3.13846 | − | 7.25400i | −0.108611 | − | 0.251035i | ||||
\(836\) | −8.53077 | − | 6.17268i | −0.295043 | − | 0.213486i | ||||
\(837\) | 35.9414 | − | 1.58017i | 1.24232 | − | 0.0546186i | ||||
\(838\) | −49.3107 | + | 25.1854i | −1.70341 | + | 0.870016i | ||||
\(839\) | −7.38656 | −0.255012 | −0.127506 | − | 0.991838i | \(-0.540697\pi\) | ||||
−0.127506 | + | 0.991838i | \(0.540697\pi\) | |||||||
\(840\) | 7.80012 | + | 7.69144i | 0.269130 | + | 0.265380i | ||||
\(841\) | 4.55356 | 0.157019 | ||||||||
\(842\) | 35.2799 | − | 18.0192i | 1.21583 | − | 0.620982i | ||||
\(843\) | −9.37939 | − | 15.7097i | −0.323044 | − | 0.541070i | ||||
\(844\) | −22.0083 | − | 15.9247i | −0.757556 | − | 0.548151i | ||||
\(845\) | −19.2109 | + | 8.31165i | −0.660876 | + | 0.285929i | ||||
\(846\) | −31.8858 | − | 0.704699i | −1.09626 | − | 0.0242280i | ||||
\(847\) | −3.38276 | −0.116233 | ||||||||
\(848\) | −7.68952 | − | 23.3567i | −0.264059 | − | 0.802071i | ||||
\(849\) | −8.23409 | + | 4.91613i | −0.282593 | + | 0.168721i | ||||
\(850\) | −9.91014 | + | 34.2164i | −0.339915 | + | 1.17361i | ||||
\(851\) | −13.2913 | −0.455621 | ||||||||
\(852\) | 1.37120 | − | 15.5183i | 0.0469765 | − | 0.531649i | ||||
\(853\) | 0.362131i | 0.0123991i | 0.999981 | + | 0.00619956i | \(0.00197339\pi\) | ||||
−0.999981 | + | 0.00619956i | \(0.998027\pi\) | |||||||
\(854\) | 6.46242 | − | 3.30068i | 0.221139 | − | 0.112947i | ||||
\(855\) | 12.7494 | + | 1.09882i | 0.436020 | + | 0.0375787i | ||||
\(856\) | 3.56056 | + | 0.553305i | 0.121698 | + | 0.0189116i | ||||
\(857\) | −4.56811 | −0.156044 | −0.0780218 | − | 0.996952i | \(-0.524860\pi\) | ||||
−0.0780218 | + | 0.996952i | \(0.524860\pi\) | |||||||
\(858\) | 10.9241 | + | 6.85405i | 0.372942 | + | 0.233994i | ||||
\(859\) | − | 16.7842i | − | 0.572669i | −0.958130 | − | 0.286334i | \(-0.907563\pi\) | ||
0.958130 | − | 0.286334i | \(-0.0924368\pi\) | |||||||
\(860\) | 9.05913 | − | 40.8872i | 0.308914 | − | 1.39424i | ||||
\(861\) | 9.92631 | + | 16.6257i | 0.338288 | + | 0.566602i | ||||
\(862\) | −47.6736 | + | 24.3493i | −1.62377 | + | 0.829339i | ||||
\(863\) | − | 26.2477i | − | 0.893481i | −0.894664 | − | 0.446741i | \(-0.852585\pi\) | ||
0.894664 | − | 0.446741i | \(-0.147415\pi\) | |||||||
\(864\) | −19.7461 | + | 21.7736i | −0.671776 | + | 0.740754i | ||||
\(865\) | −34.6192 | + | 14.9781i | −1.17709 | + | 0.509269i | ||||
\(866\) | 11.7666 | + | 23.0379i | 0.399845 | + | 0.782858i | ||||
\(867\) | 12.4615 | − | 7.44007i | 0.423214 | − | 0.252678i | ||||
\(868\) | 11.2184 | + | 8.11740i | 0.380778 | + | 0.275523i | ||||
\(869\) | − | 40.4458i | − | 1.37203i | ||||||
\(870\) | −26.7690 | − | 4.10071i | −0.907553 | − | 0.139027i | ||||
\(871\) | 6.84376i | 0.231892i | ||||||||
\(872\) | −6.35771 | + | 40.9124i | −0.215299 | + | 1.38547i | ||||
\(873\) | −44.0426 | − | 23.7360i | −1.49062 | − | 0.803343i | ||||
\(874\) | 4.92697 | − | 2.51645i | 0.166657 | − | 0.0851201i | ||||
\(875\) | −3.78950 | + | 10.5185i | −0.128109 | + | 0.355592i | ||||
\(876\) | 21.1048 | + | 1.86482i | 0.713066 | + | 0.0630065i | ||||
\(877\) | − | 30.5051i | − | 1.03008i | −0.857165 | − | 0.515042i | \(-0.827776\pi\) | ||
0.857165 | − | 0.515042i | \(-0.172224\pi\) | |||||||
\(878\) | 8.07608 | + | 15.8122i | 0.272555 | + | 0.533636i | ||||
\(879\) | 37.5058 | − | 22.3926i | 1.26504 | − | 0.755285i | ||||
\(880\) | 16.3954 | + | 18.4546i | 0.552688 | + | 0.622103i | ||||
\(881\) | 21.4921i | 0.724088i | 0.932161 | + | 0.362044i | \(0.117921\pi\) | ||||
−0.932161 | + | 0.362044i | \(0.882079\pi\) | |||||||
\(882\) | 0.0937425 | − | 4.24160i | 0.00315647 | − | 0.142822i | ||||
\(883\) | 26.3164 | 0.885617 | 0.442808 | − | 0.896616i | \(-0.353982\pi\) | ||||
0.442808 | + | 0.896616i | \(0.353982\pi\) | |||||||
\(884\) | −15.5715 | − | 11.2672i | −0.523726 | − | 0.378956i | ||||
\(885\) | −1.62282 | + | 2.25299i | −0.0545505 | + | 0.0757335i | ||||
\(886\) | 19.1536 | + | 37.5009i | 0.643477 | + | 1.25987i | ||||
\(887\) | 58.2531i | 1.95595i | 0.208727 | + | 0.977974i | \(0.433068\pi\) | ||||
−0.208727 | + | 0.977974i | \(0.566932\pi\) | |||||||
\(888\) | 29.4383 | − | 11.8975i | 0.987883 | − | 0.399254i | ||||
\(889\) | −2.15684 | −0.0723379 | ||||||||
\(890\) | 33.0833 | + | 27.3189i | 1.10896 | + | 0.915731i | ||||
\(891\) | −13.6579 | − | 20.7475i | −0.457556 | − | 0.695067i | ||||
\(892\) | −13.6490 | + | 18.8632i | −0.457002 | + | 0.631587i | ||||
\(893\) | −14.3403 | −0.479878 | ||||||||
\(894\) | −28.3058 | − | 17.7598i | −0.946689 | − | 0.593977i | ||||
\(895\) | −8.60656 | + | 3.72364i | −0.287685 | + | 0.124468i | ||||
\(896\) | −11.1621 | + | 1.84581i | −0.372900 | + | 0.0616641i | ||||
\(897\) | −5.81776 | + | 3.47347i | −0.194249 | + | 0.115976i | ||||
\(898\) | 15.2616 | + | 29.8808i | 0.509287 | + | 0.997137i | ||||
\(899\) | −34.2326 | −1.14172 | ||||||||
\(900\) | −28.6243 | − | 8.98059i | −0.954142 | − | 0.299353i | ||||
\(901\) | −30.9697 | −1.03175 | ||||||||
\(902\) | 19.8477 | + | 38.8600i | 0.660857 | + | 1.29390i | ||||
\(903\) | −13.9263 | + | 8.31464i | −0.463438 | + | 0.276694i | ||||
\(904\) | 3.83787 | − | 24.6970i | 0.127646 | − | 0.821410i | ||||
\(905\) | 19.9074 | − | 8.61297i | 0.661743 | − | 0.286305i | ||||
\(906\) | 2.80187 | + | 1.75796i | 0.0930857 | + | 0.0584044i | ||||
\(907\) | −28.7261 | −0.953833 | −0.476917 | − | 0.878949i | \(-0.658246\pi\) | ||||
−0.476917 | + | 0.878949i | \(0.658246\pi\) | |||||||
\(908\) | −5.12068 | − | 3.70521i | −0.169936 | − | 0.122962i | ||||
\(909\) | 20.3760 | + | 10.9813i | 0.675830 | + | 0.364228i | ||||
\(910\) | −4.65150 | − | 3.84102i | −0.154196 | − | 0.127328i | ||||
\(911\) | −1.93202 | −0.0640108 | −0.0320054 | − | 0.999488i | \(-0.510189\pi\) | ||||
−0.0320054 | + | 0.999488i | \(0.510189\pi\) | |||||||
\(912\) | −8.65992 | + | 9.98383i | −0.286759 | + | 0.330598i | ||||
\(913\) | 21.2945i | 0.704745i | ||||||||
\(914\) | 3.64977 | + | 7.14590i | 0.120724 | + | 0.236365i | ||||
\(915\) | −11.6149 | + | 16.1252i | −0.383978 | + | 0.533084i | ||||
\(916\) | −4.03089 | + | 5.57078i | −0.133184 | + | 0.184064i | ||||
\(917\) | −2.93626 | −0.0969640 | ||||||||
\(918\) | 18.2706 | + | 32.1974i | 0.603021 | + | 1.06267i | ||||
\(919\) | 39.8495i | 1.31451i | 0.753666 | + | 0.657257i | \(0.228283\pi\) | ||||
−0.753666 | + | 0.657257i | \(0.771717\pi\) | |||||||
\(920\) | −12.5533 | + | 3.26119i | −0.413869 | + | 0.107518i | ||||
\(921\) | 28.3786 | − | 16.9433i | 0.935108 | − | 0.558302i | ||||
\(922\) | −7.90513 | − | 15.4775i | −0.260341 | − | 0.509724i | ||||
\(923\) | 8.57893i | 0.282379i | ||||||||
\(924\) | 0.841504 | − | 9.52359i | 0.0276834 | − | 0.313303i | ||||
\(925\) | 23.6199 | + | 22.1871i | 0.776619 | + | 0.729507i | ||||
\(926\) | 1.12580 | − | 0.575000i | 0.0369960 | − | 0.0188957i | ||||
\(927\) | −28.7655 | + | 53.3749i | −0.944784 | + | 1.75306i | ||||
\(928\) | 19.6810 | − | 19.8732i | 0.646062 | − | 0.652369i | ||||
\(929\) | 33.7414i | 1.10702i | 0.832842 | + | 0.553510i | \(0.186712\pi\) | ||||
−0.832842 | + | 0.553510i | \(0.813288\pi\) | |||||||
\(930\) | −37.4849 | − | 5.74227i | −1.22918 | − | 0.188297i | ||||
\(931\) | − | 1.90761i | − | 0.0625194i | ||||||
\(932\) | −20.5994 | + | 28.4687i | −0.674754 | + | 0.932525i | ||||
\(933\) | −10.3412 | + | 6.17419i | −0.338557 | + | 0.202134i | ||||
\(934\) | −18.7109 | − | 36.6341i | −0.612239 | − | 1.19871i | ||||
\(935\) | 28.5341 | − | 12.3454i | 0.933166 | − | 0.403736i | ||||
\(936\) | 9.77623 | − | 12.9009i | 0.319546 | − | 0.421678i | ||||
\(937\) | 2.95584i | 0.0965631i | 0.998834 | + | 0.0482816i | \(0.0153745\pi\) | ||||
−0.998834 | + | 0.0482816i | \(0.984626\pi\) | |||||||
\(938\) | 4.51841 | − | 2.30778i | 0.147531 | − | 0.0753516i | ||||
\(939\) | −30.6688 | − | 51.3675i | −1.00084 | − | 1.67632i | ||||
\(940\) | 32.8228 | + | 7.27234i | 1.07056 | + | 0.237197i | ||||
\(941\) | − | 10.7787i | − | 0.351375i | −0.984446 | − | 0.175687i | \(-0.943785\pi\) | ||
0.984446 | − | 0.175687i | \(-0.0562148\pi\) | |||||||
\(942\) | −3.95810 | − | 2.48341i | −0.128962 | − | 0.0809139i | ||||
\(943\) | −22.9262 | −0.746580 | ||||||||
\(944\) | −0.896748 | − | 2.72384i | −0.0291867 | − | 0.0886536i | ||||
\(945\) | 5.07759 | + | 10.4507i | 0.165174 | + | 0.339963i | ||||
\(946\) | −32.5506 | + | 16.6252i | −1.05831 | + | 0.540532i | ||||
\(947\) | 34.5592i | 1.12302i | 0.827469 | + | 0.561511i | \(0.189780\pi\) | ||||
−0.827469 | + | 0.561511i | \(0.810220\pi\) | |||||||
\(948\) | −50.5681 | − | 4.46820i | −1.64238 | − | 0.145120i | ||||
\(949\) | −11.6673 | −0.378736 | ||||||||
\(950\) | −12.9564 | − | 3.75257i | −0.420360 | − | 0.121749i | ||||
\(951\) | 12.1839 | − | 7.27437i | 0.395092 | − | 0.235888i | ||||
\(952\) | −2.18801 | + | 14.0800i | −0.0709139 | + | 0.456337i | ||||
\(953\) | 32.9065 | 1.06595 | 0.532973 | − | 0.846132i | \(-0.321075\pi\) | ||||
0.532973 | + | 0.846132i | \(0.321075\pi\) | |||||||
\(954\) | 0.576279 | − | 26.0751i | 0.0186577 | − | 0.844214i | ||||
\(955\) | 16.0027 | − | 6.92361i | 0.517836 | − | 0.224043i | ||||
\(956\) | −20.5497 | + | 28.4001i | −0.664623 | + | 0.918523i | ||||
\(957\) | 12.1163 | + | 20.2938i | 0.391665 | + | 0.656005i | ||||
\(958\) | −30.5719 | + | 15.6146i | −0.987735 | + | 0.504485i | ||||
\(959\) | −16.4887 | −0.532448 | ||||||||
\(960\) | 24.8844 | − | 18.4599i | 0.803141 | − | 0.595790i | ||||
\(961\) | −16.9363 | −0.546333 | ||||||||
\(962\) | −15.5715 | + | 7.95313i | −0.502045 | + | 0.256419i | ||||
\(963\) | 3.36439 | + | 1.81318i | 0.108416 | + | 0.0584290i | ||||
\(964\) | 7.28183 | − | 10.0636i | 0.234532 | − | 0.324128i | ||||
\(965\) | 1.91590 | + | 4.42828i | 0.0616751 | + | 0.142551i | ||||
\(966\) | 4.25506 | + | 2.66973i | 0.136904 | + | 0.0858972i | ||||
\(967\) | 0.335417 | 0.0107863 | 0.00539314 | − | 0.999985i | \(-0.498283\pi\) | ||||
0.00539314 | + | 0.999985i | \(0.498283\pi\) | |||||||
\(968\) | −1.46920 | + | 9.45443i | −0.0472219 | + | 0.303877i | ||||
\(969\) | 8.53286 | + | 14.2918i | 0.274115 | + | 0.459119i | ||||
\(970\) | 40.6654 | + | 33.5798i | 1.30569 | + | 1.07818i | ||||
\(971\) | −56.6148 | −1.81685 | −0.908427 | − | 0.418044i | \(-0.862716\pi\) | ||||
−0.908427 | + | 0.418044i | \(0.862716\pi\) | |||||||
\(972\) | −27.4488 | + | 14.7840i | −0.880420 | + | 0.474196i | ||||
\(973\) | − | 10.8537i | − | 0.347955i | ||||||
\(974\) | 48.0634 | − | 24.5484i | 1.54005 | − | 0.786581i | ||||
\(975\) | 16.1369 | + | 3.53884i | 0.516795 | + | 0.113334i | ||||
\(976\) | −6.41826 | − | 19.4953i | −0.205443 | − | 0.624028i | ||||
\(977\) | 59.0104 | 1.88791 | 0.943955 | − | 0.330073i | \(-0.107073\pi\) | ||||
0.943955 | + | 0.330073i | \(0.107073\pi\) | |||||||
\(978\) | 31.8130 | − | 50.7040i | 1.01727 | − | 1.62133i | ||||
\(979\) | − | 37.4460i | − | 1.19678i | ||||||
\(980\) | −0.967402 | + | 4.36625i | −0.0309025 | + | 0.139475i | ||||
\(981\) | −20.8342 | + | 38.6582i | −0.665186 | + | 1.23426i | ||||
\(982\) | 33.2778 | − | 16.9966i | 1.06194 | − | 0.542384i | ||||
\(983\) | − | 37.6136i | − | 1.19969i | −0.800117 | − | 0.599844i | \(-0.795229\pi\) | ||
0.800117 | − | 0.599844i | \(-0.204771\pi\) | |||||||
\(984\) | 50.7781 | − | 20.5220i | 1.61875 | − | 0.654217i | ||||
\(985\) | −30.7174 | + | 13.2900i | −0.978739 | + | 0.423453i | ||||
\(986\) | −16.0228 | − | 31.3711i | −0.510269 | − | 0.999058i | ||||
\(987\) | −6.67469 | − | 11.1795i | −0.212458 | − | 0.355848i | ||||
\(988\) | 4.26643 | − | 5.89630i | 0.135733 | − | 0.187586i | ||||
\(989\) | − | 19.2038i | − | 0.610647i | ||||||
\(990\) | 9.86329 | + | 24.2542i | 0.313476 | + | 0.770849i | ||||
\(991\) | − | 45.8372i | − | 1.45607i | −0.685541 | − | 0.728034i | \(-0.740434\pi\) | ||
0.685541 | − | 0.728034i | \(-0.259566\pi\) | |||||||
\(992\) | 27.5596 | − | 27.8286i | 0.875017 | − | 0.883560i | ||||
\(993\) | 4.11684 | + | 6.89535i | 0.130644 | + | 0.218817i | ||||
\(994\) | 5.66401 | − | 2.89289i | 0.179651 | − | 0.0917570i | ||||
\(995\) | −9.53501 | − | 22.0385i | −0.302280 | − | 0.698668i | ||||
\(996\) | 26.6238 | + | 2.35248i | 0.843609 | + | 0.0745412i | ||||
\(997\) | − | 13.7556i | − | 0.435645i | −0.975988 | − | 0.217823i | \(-0.930105\pi\) | ||
0.975988 | − | 0.217823i | \(-0.0698954\pi\) | |||||||
\(998\) | 22.4537 | + | 43.9621i | 0.710758 | + | 1.39160i | ||||
\(999\) | 33.6451 | − | 1.47921i | 1.06448 | − | 0.0468002i |
(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 | 420.2.l.h.239.13 | yes | 16 | |
3.2 | odd | 2 | inner | 420.2.l.h.239.4 | yes | 16 | |
4.3 | odd | 2 | 420.2.l.g.239.14 | yes | 16 | ||
5.4 | even | 2 | 420.2.l.g.239.4 | yes | 16 | ||
12.11 | even | 2 | 420.2.l.g.239.3 | ✓ | 16 | ||
15.14 | odd | 2 | 420.2.l.g.239.13 | yes | 16 | ||
20.19 | odd | 2 | inner | 420.2.l.h.239.3 | yes | 16 | |
60.59 | even | 2 | inner | 420.2.l.h.239.14 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.l.g.239.3 | ✓ | 16 | 12.11 | even | 2 | ||
420.2.l.g.239.4 | yes | 16 | 5.4 | even | 2 | ||
420.2.l.g.239.13 | yes | 16 | 15.14 | odd | 2 | ||
420.2.l.g.239.14 | yes | 16 | 4.3 | odd | 2 | ||
420.2.l.h.239.3 | yes | 16 | 20.19 | odd | 2 | inner | |
420.2.l.h.239.4 | yes | 16 | 3.2 | odd | 2 | inner | |
420.2.l.h.239.13 | yes | 16 | 1.1 | even | 1 | trivial | |
420.2.l.h.239.14 | yes | 16 | 60.59 | even | 2 | inner |