Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [342,2,Mod(65,342)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(342, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("342.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 342 = 2 \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 342.j (of order \(6\), 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: | \(2.73088374913\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 5 x^{17} + 13 x^{16} - 30 x^{15} + 54 x^{14} - 69 x^{13} + 66 x^{12} + 36 x^{11} - 243 x^{10} + 432 x^{9} - 729 x^{8} + 324 x^{7} + 1782 x^{6} - 5589 x^{5} + 13122 x^{4} + \cdots + 19683 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.3 | ||
Root | \(0.565455 + 1.63715i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 342.65 |
Dual form | 342.2.j.f.221.3 |
$q$-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 \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −1.13509 | − | 1.30827i | −0.655342 | − | 0.755332i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 2.55258i | 1.14155i | 0.821107 | + | 0.570775i | \(0.193357\pi\) | ||||
−0.821107 | + | 0.570775i | \(0.806643\pi\) | |||||||
\(6\) | −0.565455 | + | 1.63715i | −0.230846 | + | 0.668364i | ||||
\(7\) | 0.762878 | − | 1.32134i | 0.288341 | − | 0.499421i | −0.685073 | − | 0.728474i | \(-0.740230\pi\) |
0.973414 | + | 0.229053i | \(0.0735631\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.423160 | + | 2.97001i | −0.141053 | + | 0.990002i | ||||
\(10\) | 2.21060 | − | 1.27629i | 0.699053 | − | 0.403599i | ||||
\(11\) | 1.01188 | + | 0.584208i | 0.305093 | + | 0.176145i | 0.644729 | − | 0.764412i | \(-0.276970\pi\) |
−0.339636 | + | 0.940557i | \(0.610304\pi\) | |||||||
\(12\) | 1.70054 | − | 0.328876i | 0.490904 | − | 0.0949384i | ||||
\(13\) | 1.91472 | + | 1.10547i | 0.531048 | + | 0.306601i | 0.741443 | − | 0.671016i | \(-0.234142\pi\) |
−0.210395 | + | 0.977616i | \(0.567475\pi\) | |||||||
\(14\) | −1.52576 | −0.407776 | ||||||||
\(15\) | 3.33948 | − | 2.89740i | 0.862249 | − | 0.748105i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 6.71222 | + | 3.87530i | 1.62795 | + | 0.939899i | 0.984703 | + | 0.174244i | \(0.0557481\pi\) |
0.643251 | + | 0.765655i | \(0.277585\pi\) | |||||||
\(18\) | 2.78368 | − | 1.11854i | 0.656120 | − | 0.263641i | ||||
\(19\) | −1.14556 | − | 4.20567i | −0.262810 | − | 0.964848i | ||||
\(20\) | −2.21060 | − | 1.27629i | −0.494305 | − | 0.285387i | ||||
\(21\) | −2.59461 | + | 0.501785i | −0.566191 | + | 0.109498i | ||||
\(22\) | − | 1.16842i | − | 0.249107i | ||||||
\(23\) | −0.116908 | − | 0.0674966i | −0.0243769 | − | 0.0140740i | 0.487762 | − | 0.872977i | \(-0.337813\pi\) |
−0.512139 | + | 0.858903i | \(0.671147\pi\) | |||||||
\(24\) | −1.13509 | − | 1.30827i | −0.231698 | − | 0.267050i | ||||
\(25\) | −1.51567 | −0.303134 | ||||||||
\(26\) | − | 2.21093i | − | 0.433599i | ||||||
\(27\) | 4.36590 | − | 2.81760i | 0.840219 | − | 0.542248i | ||||
\(28\) | 0.762878 | + | 1.32134i | 0.144170 | + | 0.249710i | ||||
\(29\) | 4.13926 | 0.768641 | 0.384321 | − | 0.923200i | \(-0.374436\pi\) | ||||
0.384321 | + | 0.923200i | \(0.374436\pi\) | |||||||
\(30\) | −4.17896 | − | 1.44337i | −0.762970 | − | 0.263522i | ||||
\(31\) | 0.334751 | − | 0.193269i | 0.0601231 | − | 0.0347121i | −0.469637 | − | 0.882860i | \(-0.655615\pi\) |
0.529760 | + | 0.848147i | \(0.322282\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −0.384265 | − | 1.98694i | −0.0668919 | − | 0.345882i | ||||
\(34\) | − | 7.75061i | − | 1.32922i | ||||||
\(35\) | 3.37284 | + | 1.94731i | 0.570114 | + | 0.329155i | ||||
\(36\) | −2.36052 | − | 1.85147i | −0.393420 | − | 0.308578i | ||||
\(37\) | − | 8.30368i | − | 1.36512i | −0.730832 | − | 0.682558i | \(-0.760867\pi\) | ||
0.730832 | − | 0.682558i | \(-0.239133\pi\) | |||||||
\(38\) | −3.06944 | + | 3.09492i | −0.497929 | + | 0.502063i | ||||
\(39\) | −0.727123 | − | 3.75978i | −0.116433 | − | 0.602047i | ||||
\(40\) | 2.55258i | 0.403599i | ||||||||
\(41\) | −6.75990 | −1.05572 | −0.527859 | − | 0.849332i | \(-0.677005\pi\) | ||||
−0.527859 | + | 0.849332i | \(0.677005\pi\) | |||||||
\(42\) | 1.73186 | + | 1.99611i | 0.267232 | + | 0.308006i | ||||
\(43\) | 0.944197 | + | 1.63540i | 0.143989 | + | 0.249396i | 0.928995 | − | 0.370092i | \(-0.120674\pi\) |
−0.785006 | + | 0.619488i | \(0.787340\pi\) | |||||||
\(44\) | −1.01188 | + | 0.584208i | −0.152546 | + | 0.0880727i | ||||
\(45\) | −7.58118 | − | 1.08015i | −1.13014 | − | 0.161019i | ||||
\(46\) | 0.134993i | 0.0199037i | ||||||||
\(47\) | 9.81867i | 1.43220i | 0.697998 | + | 0.716100i | \(0.254074\pi\) | ||||
−0.697998 | + | 0.716100i | \(0.745926\pi\) | |||||||
\(48\) | −0.565455 | + | 1.63715i | −0.0816164 | + | 0.236302i | ||||
\(49\) | 2.33603 | + | 4.04613i | 0.333719 | + | 0.578018i | ||||
\(50\) | 0.757836 | + | 1.31261i | 0.107174 | + | 0.185631i | ||||
\(51\) | −2.54899 | − | 13.1802i | −0.356930 | − | 1.84560i | ||||
\(52\) | −1.91472 | + | 1.10547i | −0.265524 | + | 0.153300i | ||||
\(53\) | 4.43603 | + | 7.68344i | 0.609336 | + | 1.05540i | 0.991350 | + | 0.131245i | \(0.0418973\pi\) |
−0.382014 | + | 0.924157i | \(0.624769\pi\) | |||||||
\(54\) | −4.62307 | − | 2.37218i | −0.629120 | − | 0.322813i | ||||
\(55\) | −1.49124 | + | 2.58290i | −0.201079 | + | 0.348279i | ||||
\(56\) | 0.762878 | − | 1.32134i | 0.101944 | − | 0.176572i | ||||
\(57\) | −4.20186 | + | 6.27251i | −0.556550 | + | 0.830814i | ||||
\(58\) | −2.06963 | − | 3.58471i | −0.271756 | − | 0.470695i | ||||
\(59\) | 7.77614 | 1.01237 | 0.506183 | − | 0.862426i | \(-0.331056\pi\) | ||||
0.506183 | + | 0.862426i | \(0.331056\pi\) | |||||||
\(60\) | 0.839484 | + | 4.34077i | 0.108377 | + | 0.560391i | ||||
\(61\) | 0.918405 | 0.117590 | 0.0587949 | − | 0.998270i | \(-0.481274\pi\) | ||||
0.0587949 | + | 0.998270i | \(0.481274\pi\) | |||||||
\(62\) | −0.334751 | − | 0.193269i | −0.0425135 | − | 0.0245452i | ||||
\(63\) | 3.60158 | + | 2.82489i | 0.453756 | + | 0.355903i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.82179 | + | 4.88749i | −0.350000 | + | 0.606218i | ||||
\(66\) | −1.52861 | + | 1.32625i | −0.188159 | + | 0.163251i | ||||
\(67\) | 6.16782 | + | 3.56099i | 0.753519 | + | 0.435044i | 0.826964 | − | 0.562255i | \(-0.190066\pi\) |
−0.0734452 | + | 0.997299i | \(0.523399\pi\) | |||||||
\(68\) | −6.71222 | + | 3.87530i | −0.813977 | + | 0.469950i | ||||
\(69\) | 0.0443961 | + | 0.229562i | 0.00534466 | + | 0.0276360i | ||||
\(70\) | − | 3.89462i | − | 0.465496i | ||||||
\(71\) | −4.47829 | + | 7.75662i | −0.531475 | + | 0.920541i | 0.467850 | + | 0.883808i | \(0.345029\pi\) |
−0.999325 | + | 0.0367336i | \(0.988305\pi\) | |||||||
\(72\) | −0.423160 | + | 2.97001i | −0.0498699 | + | 0.350019i | ||||
\(73\) | −5.36599 | + | 9.29417i | −0.628042 | + | 1.08780i | 0.359902 | + | 0.932990i | \(0.382810\pi\) |
−0.987944 | + | 0.154810i | \(0.950523\pi\) | |||||||
\(74\) | −7.19119 | + | 4.15184i | −0.835959 | + | 0.482641i | ||||
\(75\) | 1.72042 | + | 1.98291i | 0.198657 | + | 0.228967i | ||||
\(76\) | 4.21500 | + | 1.11075i | 0.483494 | + | 0.127412i | ||||
\(77\) | 1.54388 | − | 0.891360i | 0.175941 | − | 0.101580i | ||||
\(78\) | −2.89250 | + | 2.50960i | −0.327511 | + | 0.284156i | ||||
\(79\) | 8.72967 | − | 5.04008i | 0.982165 | − | 0.567053i | 0.0792420 | − | 0.996855i | \(-0.474750\pi\) |
0.902923 | + | 0.429802i | \(0.141417\pi\) | |||||||
\(80\) | 2.21060 | − | 1.27629i | 0.247153 | − | 0.142694i | ||||
\(81\) | −8.64187 | − | 2.51358i | −0.960208 | − | 0.279286i | ||||
\(82\) | 3.37995 | + | 5.85424i | 0.373253 | + | 0.646493i | ||||
\(83\) | −13.4929 | − | 7.79012i | −1.48104 | − | 0.855076i | −0.481267 | − | 0.876574i | \(-0.659823\pi\) |
−0.999769 | + | 0.0214976i | \(0.993157\pi\) | |||||||
\(84\) | 0.862747 | − | 2.49789i | 0.0941334 | − | 0.272542i | ||||
\(85\) | −9.89203 | + | 17.1335i | −1.07294 | + | 1.85839i | ||||
\(86\) | 0.944197 | − | 1.63540i | 0.101815 | − | 0.176349i | ||||
\(87\) | −4.69842 | − | 5.41529i | −0.503723 | − | 0.580580i | ||||
\(88\) | 1.01188 | + | 0.584208i | 0.107867 | + | 0.0622768i | ||||
\(89\) | −3.33058 | − | 5.76874i | −0.353041 | − | 0.611485i | 0.633739 | − | 0.773547i | \(-0.281519\pi\) |
−0.986781 | + | 0.162061i | \(0.948186\pi\) | |||||||
\(90\) | 2.85515 | + | 7.10557i | 0.300960 | + | 0.748993i | ||||
\(91\) | 2.92140 | − | 1.68667i | 0.306246 | − | 0.176811i | ||||
\(92\) | 0.116908 | − | 0.0674966i | 0.0121885 | − | 0.00703701i | ||||
\(93\) | −0.632820 | − | 0.218570i | −0.0656204 | − | 0.0226646i | ||||
\(94\) | 8.50321 | − | 4.90933i | 0.877040 | − | 0.506359i | ||||
\(95\) | 10.7353 | − | 2.92414i | 1.10142 | − | 0.300011i | ||||
\(96\) | 1.70054 | − | 0.328876i | 0.173561 | − | 0.0335658i | ||||
\(97\) | −0.462464 | + | 0.267004i | −0.0469561 | + | 0.0271101i | −0.523294 | − | 0.852152i | \(-0.675297\pi\) |
0.476338 | + | 0.879262i | \(0.341964\pi\) | |||||||
\(98\) | 2.33603 | − | 4.04613i | 0.235975 | − | 0.408721i | ||||
\(99\) | −2.16329 | + | 2.75807i | −0.217419 | + | 0.277197i | ||||
\(100\) | 0.757836 | − | 1.31261i | 0.0757836 | − | 0.131261i | ||||
\(101\) | − | 18.6864i | − | 1.85937i | −0.368360 | − | 0.929683i | \(-0.620080\pi\) | ||
0.368360 | − | 0.929683i | \(-0.379920\pi\) | |||||||
\(102\) | −10.1399 | + | 8.79761i | −1.00400 | + | 0.871093i | ||||
\(103\) | 5.51194 | − | 3.18232i | 0.543108 | − | 0.313563i | −0.203230 | − | 0.979131i | \(-0.565144\pi\) |
0.746337 | + | 0.665568i | \(0.231811\pi\) | |||||||
\(104\) | 1.91472 | + | 1.10547i | 0.187754 | + | 0.108400i | ||||
\(105\) | −1.28085 | − | 6.62296i | −0.124998 | − | 0.646334i | ||||
\(106\) | 4.43603 | − | 7.68344i | 0.430866 | − | 0.746281i | ||||
\(107\) | −9.68605 | −0.936386 | −0.468193 | − | 0.883626i | \(-0.655095\pi\) | ||||
−0.468193 | + | 0.883626i | \(0.655095\pi\) | |||||||
\(108\) | 0.257164 | + | 5.18978i | 0.0247456 | + | 0.499387i | ||||
\(109\) | −11.7103 | − | 6.76093i | −1.12164 | − | 0.647580i | −0.179822 | − | 0.983699i | \(-0.557552\pi\) |
−0.941819 | + | 0.336120i | \(0.890885\pi\) | |||||||
\(110\) | 2.98248 | 0.284368 | ||||||||
\(111\) | −10.8635 | + | 9.42538i | −1.03112 | + | 0.894618i | ||||
\(112\) | −1.52576 | −0.144170 | ||||||||
\(113\) | −2.63721 | − | 4.56778i | −0.248088 | − | 0.429701i | 0.714907 | − | 0.699219i | \(-0.246469\pi\) |
−0.962995 | + | 0.269518i | \(0.913136\pi\) | |||||||
\(114\) | 7.53308 | + | 0.502660i | 0.705538 | + | 0.0470785i | ||||
\(115\) | 0.172291 | − | 0.298416i | 0.0160662 | − | 0.0278274i | ||||
\(116\) | −2.06963 | + | 3.58471i | −0.192160 | + | 0.332832i | ||||
\(117\) | −4.09347 | + | 5.21895i | −0.378442 | + | 0.482492i | ||||
\(118\) | −3.88807 | − | 6.73433i | −0.357926 | − | 0.619946i | ||||
\(119\) | 10.2412 | − | 5.91277i | 0.938811 | − | 0.542023i | ||||
\(120\) | 3.33948 | − | 2.89740i | 0.304851 | − | 0.264495i | ||||
\(121\) | −4.81740 | − | 8.34398i | −0.437946 | − | 0.758544i | ||||
\(122\) | −0.459203 | − | 0.795362i | −0.0415743 | − | 0.0720087i | ||||
\(123\) | 7.67307 | + | 8.84380i | 0.691857 | + | 0.797418i | ||||
\(124\) | 0.386537i | 0.0347121i | ||||||||
\(125\) | 8.89403i | 0.795506i | ||||||||
\(126\) | 0.645639 | − | 4.53151i | 0.0575181 | − | 0.403699i | ||||
\(127\) | −5.70970 | + | 3.29650i | −0.506654 | + | 0.292517i | −0.731457 | − | 0.681887i | \(-0.761159\pi\) |
0.224803 | + | 0.974404i | \(0.427826\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 1.06780 | − | 3.09158i | 0.0940148 | − | 0.272199i | ||||
\(130\) | 5.64358 | 0.494975 | ||||||||
\(131\) | − | 0.750276i | − | 0.0655519i | −0.999463 | − | 0.0327760i | \(-0.989565\pi\) | ||
0.999463 | − | 0.0327760i | \(-0.0104348\pi\) | |||||||
\(132\) | 1.91287 | + | 0.660688i | 0.166494 | + | 0.0575055i | ||||
\(133\) | −6.43106 | − | 1.69473i | −0.557644 | − | 0.146952i | ||||
\(134\) | − | 7.12198i | − | 0.615245i | ||||||
\(135\) | 7.19216 | + | 11.1443i | 0.619003 | + | 0.959151i | ||||
\(136\) | 6.71222 | + | 3.87530i | 0.575568 | + | 0.332305i | ||||
\(137\) | 2.01675i | 0.172303i | 0.996282 | + | 0.0861513i | \(0.0274568\pi\) | ||||
−0.996282 | + | 0.0861513i | \(0.972543\pi\) | |||||||
\(138\) | 0.176608 | − | 0.153229i | 0.0150339 | − | 0.0130437i | ||||
\(139\) | −0.470675 | + | 0.815232i | −0.0399221 | + | 0.0691471i | −0.885296 | − | 0.465028i | \(-0.846044\pi\) |
0.845374 | + | 0.534175i | \(0.179378\pi\) | |||||||
\(140\) | −3.37284 | + | 1.94731i | −0.285057 | + | 0.164578i | ||||
\(141\) | 12.8455 | − | 11.1450i | 1.08179 | − | 0.938581i | ||||
\(142\) | 8.95657 | 0.751619 | ||||||||
\(143\) | 1.29164 | + | 2.23719i | 0.108013 | + | 0.187084i | ||||
\(144\) | 2.78368 | − | 1.11854i | 0.231973 | − | 0.0932113i | ||||
\(145\) | 10.5658i | 0.877442i | ||||||||
\(146\) | 10.7320 | 0.888185 | ||||||||
\(147\) | 2.64185 | − | 7.64888i | 0.217896 | − | 0.630869i | ||||
\(148\) | 7.19119 | + | 4.15184i | 0.591112 | + | 0.341279i | ||||
\(149\) | − | 14.2026i | − | 1.16352i | −0.813361 | − | 0.581760i | \(-0.802364\pi\) | ||
0.813361 | − | 0.581760i | \(-0.197636\pi\) | |||||||
\(150\) | 0.857045 | − | 2.48138i | 0.0699774 | − | 0.202604i | ||||
\(151\) | −1.58378 | − | 0.914396i | −0.128886 | − | 0.0744125i | 0.434171 | − | 0.900831i | \(-0.357041\pi\) |
−0.563057 | + | 0.826418i | \(0.690375\pi\) | |||||||
\(152\) | −1.14556 | − | 4.20567i | −0.0929175 | − | 0.341125i | ||||
\(153\) | −14.3500 | + | 18.2955i | −1.16013 | + | 1.47910i | ||||
\(154\) | −1.54388 | − | 0.891360i | −0.124409 | − | 0.0718278i | ||||
\(155\) | 0.493334 | + | 0.854480i | 0.0396256 | + | 0.0686335i | ||||
\(156\) | 3.61963 | + | 1.25018i | 0.289802 | + | 0.100095i | ||||
\(157\) | 20.9348 | 1.67078 | 0.835390 | − | 0.549658i | \(-0.185242\pi\) | ||||
0.835390 | + | 0.549658i | \(0.185242\pi\) | |||||||
\(158\) | −8.72967 | − | 5.04008i | −0.694496 | − | 0.400967i | ||||
\(159\) | 5.01676 | − | 14.5249i | 0.397855 | − | 1.15190i | ||||
\(160\) | −2.21060 | − | 1.27629i | −0.174763 | − | 0.100900i | ||||
\(161\) | −0.178372 | + | 0.102983i | −0.0140577 | + | 0.00811623i | ||||
\(162\) | 2.14411 | + | 8.74087i | 0.168458 | + | 0.686747i | ||||
\(163\) | −17.9035 | −1.40231 | −0.701156 | − | 0.713008i | \(-0.747333\pi\) | ||||
−0.701156 | + | 0.713008i | \(0.747333\pi\) | |||||||
\(164\) | 3.37995 | − | 5.85424i | 0.263930 | − | 0.457140i | ||||
\(165\) | 5.07183 | − | 0.980867i | 0.394841 | − | 0.0763604i | ||||
\(166\) | 15.5802i | 1.20926i | ||||||||
\(167\) | 0.368544 | − | 0.638336i | 0.0285188 | − | 0.0493959i | −0.851414 | − | 0.524495i | \(-0.824254\pi\) |
0.879933 | + | 0.475099i | \(0.157588\pi\) | |||||||
\(168\) | −2.59461 | + | 0.501785i | −0.200179 | + | 0.0387136i | ||||
\(169\) | −4.05589 | − | 7.02501i | −0.311992 | − | 0.540385i | ||||
\(170\) | 19.7841 | 1.51737 | ||||||||
\(171\) | 12.9756 | − | 1.62266i | 0.992271 | − | 0.124088i | ||||
\(172\) | −1.88839 | −0.143989 | ||||||||
\(173\) | 5.01877 | + | 8.69276i | 0.381570 | + | 0.660898i | 0.991287 | − | 0.131721i | \(-0.0420502\pi\) |
−0.609717 | + | 0.792619i | \(0.708717\pi\) | |||||||
\(174\) | −2.34057 | + | 6.77659i | −0.177438 | + | 0.513732i | ||||
\(175\) | −1.15627 | + | 2.00272i | −0.0874060 | + | 0.151392i | ||||
\(176\) | − | 1.16842i | − | 0.0880727i | ||||||
\(177\) | −8.82658 | − | 10.1733i | −0.663447 | − | 0.764673i | ||||
\(178\) | −3.33058 | + | 5.76874i | −0.249638 | + | 0.432386i | ||||
\(179\) | −9.74221 | −0.728167 | −0.364083 | − | 0.931366i | \(-0.618618\pi\) | ||||
−0.364083 | + | 0.931366i | \(0.618618\pi\) | |||||||
\(180\) | 4.72603 | − | 6.02542i | 0.352257 | − | 0.449108i | ||||
\(181\) | −11.9960 | + | 6.92591i | −0.891658 | + | 0.514799i | −0.874484 | − | 0.485054i | \(-0.838800\pi\) |
−0.0171734 | + | 0.999853i | \(0.505467\pi\) | |||||||
\(182\) | −2.92140 | − | 1.68667i | −0.216549 | − | 0.125024i | ||||
\(183\) | −1.04247 | − | 1.20153i | −0.0770615 | − | 0.0888193i | ||||
\(184\) | −0.116908 | − | 0.0674966i | −0.00861854 | − | 0.00497592i | ||||
\(185\) | 21.1958 | 1.55835 | ||||||||
\(186\) | 0.127123 | + | 0.657323i | 0.00932111 | + | 0.0481973i | ||||
\(187\) | 4.52797 | + | 7.84268i | 0.331118 | + | 0.573513i | ||||
\(188\) | −8.50321 | − | 4.90933i | −0.620161 | − | 0.358050i | ||||
\(189\) | −0.392369 | − | 7.91835i | −0.0285406 | − | 0.575975i | ||||
\(190\) | −7.90004 | − | 7.83499i | −0.573129 | − | 0.568410i | ||||
\(191\) | 0.945198 | + | 0.545710i | 0.0683921 | + | 0.0394862i | 0.533806 | − | 0.845607i | \(-0.320761\pi\) |
−0.465414 | + | 0.885093i | \(0.654095\pi\) | |||||||
\(192\) | −1.13509 | − | 1.30827i | −0.0819178 | − | 0.0944165i | ||||
\(193\) | − | 1.82307i | − | 0.131227i | −0.997845 | − | 0.0656136i | \(-0.979100\pi\) | ||
0.997845 | − | 0.0656136i | \(-0.0209005\pi\) | |||||||
\(194\) | 0.462464 | + | 0.267004i | 0.0332030 | + | 0.0191697i | ||||
\(195\) | 9.59714 | − | 1.85604i | 0.687266 | − | 0.132914i | ||||
\(196\) | −4.67207 | −0.333719 | ||||||||
\(197\) | − | 19.6968i | − | 1.40334i | −0.712504 | − | 0.701668i | \(-0.752439\pi\) | ||
0.712504 | − | 0.701668i | \(-0.247561\pi\) | |||||||
\(198\) | 3.47021 | + | 0.494427i | 0.246617 | + | 0.0351374i | ||||
\(199\) | 4.29440 | + | 7.43811i | 0.304422 | + | 0.527274i | 0.977132 | − | 0.212632i | \(-0.0682035\pi\) |
−0.672711 | + | 0.739906i | \(0.734870\pi\) | |||||||
\(200\) | −1.51567 | −0.107174 | ||||||||
\(201\) | −2.34225 | − | 12.1112i | −0.165210 | − | 0.854260i | ||||
\(202\) | −16.1829 | + | 9.34320i | −1.13862 | + | 0.657385i | ||||
\(203\) | 3.15775 | − | 5.46939i | 0.221631 | − | 0.383876i | ||||
\(204\) | 12.6889 | + | 4.38262i | 0.888401 | + | 0.306845i | ||||
\(205\) | − | 17.2552i | − | 1.20515i | ||||||
\(206\) | −5.51194 | − | 3.18232i | −0.384035 | − | 0.221723i | ||||
\(207\) | 0.249936 | − | 0.318654i | 0.0173717 | − | 0.0221480i | ||||
\(208\) | − | 2.21093i | − | 0.153300i | ||||||
\(209\) | 1.29782 | − | 4.92488i | 0.0897720 | − | 0.340661i | ||||
\(210\) | −5.09523 | + | 4.42072i | −0.351604 | + | 0.305059i | ||||
\(211\) | − | 23.4844i | − | 1.61673i | −0.588681 | − | 0.808366i | \(-0.700352\pi\) | ||
0.588681 | − | 0.808366i | \(-0.299648\pi\) | |||||||
\(212\) | −8.87207 | −0.609336 | ||||||||
\(213\) | 15.2310 | − | 2.94561i | 1.04361 | − | 0.201830i | ||||
\(214\) | 4.84302 | + | 8.38837i | 0.331062 | + | 0.573417i | ||||
\(215\) | −4.17448 | + | 2.41014i | −0.284697 | + | 0.164370i | ||||
\(216\) | 4.36590 | − | 2.81760i | 0.297062 | − | 0.191714i | ||||
\(217\) | − | 0.589762i | − | 0.0400357i | ||||||
\(218\) | 13.5219i | 0.915816i | ||||||||
\(219\) | 18.2502 | − | 3.52950i | 1.23323 | − | 0.238501i | ||||
\(220\) | −1.49124 | − | 2.58290i | −0.100539 | − | 0.174139i | ||||
\(221\) | 8.56803 | + | 14.8403i | 0.576348 | + | 0.998264i | ||||
\(222\) | 13.5944 | + | 4.69536i | 0.912394 | + | 0.315132i | ||||
\(223\) | 4.53089 | − | 2.61591i | 0.303411 | − | 0.175174i | −0.340563 | − | 0.940222i | \(-0.610618\pi\) |
0.643974 | + | 0.765047i | \(0.277284\pi\) | |||||||
\(224\) | 0.762878 | + | 1.32134i | 0.0509719 | + | 0.0882860i | ||||
\(225\) | 0.641372 | − | 4.50155i | 0.0427581 | − | 0.300104i | ||||
\(226\) | −2.63721 | + | 4.56778i | −0.175425 | + | 0.303844i | ||||
\(227\) | 4.12452 | − | 7.14387i | 0.273754 | − | 0.474156i | −0.696066 | − | 0.717978i | \(-0.745068\pi\) |
0.969820 | + | 0.243822i | \(0.0784013\pi\) | |||||||
\(228\) | −3.33122 | − | 6.77517i | −0.220616 | − | 0.448697i | ||||
\(229\) | 9.53515 | + | 16.5154i | 0.630101 | + | 1.09137i | 0.987531 | + | 0.157427i | \(0.0503197\pi\) |
−0.357430 | + | 0.933940i | \(0.616347\pi\) | |||||||
\(230\) | −0.344581 | −0.0227210 | ||||||||
\(231\) | −2.91858 | − | 1.00805i | −0.192028 | − | 0.0663247i | ||||
\(232\) | 4.13926 | 0.271756 | ||||||||
\(233\) | 7.66969 | + | 4.42810i | 0.502458 | + | 0.290094i | 0.729728 | − | 0.683738i | \(-0.239647\pi\) |
−0.227270 | + | 0.973832i | \(0.572980\pi\) | |||||||
\(234\) | 6.56648 | + | 0.935578i | 0.429264 | + | 0.0611606i | ||||
\(235\) | −25.0629 | −1.63493 | ||||||||
\(236\) | −3.88807 | + | 6.73433i | −0.253092 | + | 0.438368i | ||||
\(237\) | −16.5027 | − | 5.69988i | −1.07197 | − | 0.370247i | ||||
\(238\) | −10.2412 | − | 5.91277i | −0.663840 | − | 0.383268i | ||||
\(239\) | 4.98254 | − | 2.87667i | 0.322293 | − | 0.186076i | −0.330121 | − | 0.943939i | \(-0.607090\pi\) |
0.652414 | + | 0.757862i | \(0.273756\pi\) | |||||||
\(240\) | −4.17896 | − | 1.44337i | −0.269751 | − | 0.0931692i | ||||
\(241\) | 27.1682i | 1.75006i | 0.484071 | + | 0.875029i | \(0.339158\pi\) | ||||
−0.484071 | + | 0.875029i | \(0.660842\pi\) | |||||||
\(242\) | −4.81740 | + | 8.34398i | −0.309674 | + | 0.536372i | ||||
\(243\) | 6.52082 | + | 14.1591i | 0.418311 | + | 0.908304i | ||||
\(244\) | −0.459203 | + | 0.795362i | −0.0293974 | + | 0.0509179i | ||||
\(245\) | −10.3281 | + | 5.96292i | −0.659836 | + | 0.380957i | ||||
\(246\) | 3.82242 | − | 11.0670i | 0.243709 | − | 0.705604i | ||||
\(247\) | 2.45579 | − | 9.31908i | 0.156258 | − | 0.592959i | ||||
\(248\) | 0.334751 | − | 0.193269i | 0.0212567 | − | 0.0122726i | ||||
\(249\) | 5.12397 | + | 26.4948i | 0.324718 | + | 1.67904i | ||||
\(250\) | 7.70246 | − | 4.44702i | 0.487146 | − | 0.281254i | ||||
\(251\) | −24.1315 | + | 13.9323i | −1.52316 | + | 0.879399i | −0.523539 | + | 0.852002i | \(0.675389\pi\) |
−0.999625 | + | 0.0273973i | \(0.991278\pi\) | |||||||
\(252\) | −4.24722 | + | 1.70661i | −0.267550 | + | 0.107506i | ||||
\(253\) | −0.0788642 | − | 0.136597i | −0.00495815 | − | 0.00858776i | ||||
\(254\) | 5.70970 | + | 3.29650i | 0.358258 | + | 0.206841i | ||||
\(255\) | 33.6436 | − | 6.50651i | 2.10684 | − | 0.407453i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 2.30383 | − | 3.99035i | 0.143709 | − | 0.248911i | −0.785182 | − | 0.619266i | \(-0.787430\pi\) |
0.928891 | + | 0.370354i | \(0.120764\pi\) | |||||||
\(258\) | −3.21129 | + | 0.621048i | −0.199926 | + | 0.0386648i | ||||
\(259\) | −10.9720 | − | 6.33469i | −0.681767 | − | 0.393619i | ||||
\(260\) | −2.82179 | − | 4.88749i | −0.175000 | − | 0.303109i | ||||
\(261\) | −1.75157 | + | 12.2936i | −0.108419 | + | 0.760957i | ||||
\(262\) | −0.649758 | + | 0.375138i | −0.0401422 | + | 0.0231761i | ||||
\(263\) | 8.47535 | − | 4.89325i | 0.522612 | − | 0.301730i | −0.215390 | − | 0.976528i | \(-0.569102\pi\) |
0.738003 | + | 0.674798i | \(0.235769\pi\) | |||||||
\(264\) | −0.384265 | − | 1.98694i | −0.0236499 | − | 0.122288i | ||||
\(265\) | −19.6126 | + | 11.3233i | −1.20479 | + | 0.695587i | ||||
\(266\) | 1.74785 | + | 6.41683i | 0.107168 | + | 0.393441i | ||||
\(267\) | −3.76659 | + | 10.9053i | −0.230512 | + | 0.667396i | ||||
\(268\) | −6.16782 | + | 3.56099i | −0.376759 | + | 0.217522i | ||||
\(269\) | 10.4195 | − | 18.0472i | 0.635290 | − | 1.10035i | −0.351164 | − | 0.936314i | \(-0.614214\pi\) |
0.986454 | − | 0.164040i | \(-0.0524527\pi\) | |||||||
\(270\) | 6.05519 | − | 11.8008i | 0.368507 | − | 0.718171i | ||||
\(271\) | 10.4430 | − | 18.0878i | 0.634366 | − | 1.09875i | −0.352283 | − | 0.935893i | \(-0.614595\pi\) |
0.986649 | − | 0.162861i | \(-0.0520721\pi\) | |||||||
\(272\) | − | 7.75061i | − | 0.469950i | ||||||
\(273\) | −5.52267 | − | 1.90747i | −0.334247 | − | 0.115446i | ||||
\(274\) | 1.74656 | − | 1.00838i | 0.105513 | − | 0.0609182i | ||||
\(275\) | −1.53368 | − | 0.885468i | −0.0924842 | − | 0.0533957i | ||||
\(276\) | −0.221004 | − | 0.0763326i | −0.0133029 | − | 0.00459468i | ||||
\(277\) | 10.1903 | − | 17.6502i | 0.612279 | − | 1.06050i | −0.378577 | − | 0.925570i | \(-0.623586\pi\) |
0.990855 | − | 0.134928i | \(-0.0430802\pi\) | |||||||
\(278\) | 0.941349 | 0.0564584 | ||||||||
\(279\) | 0.432356 | + | 1.07600i | 0.0258845 | + | 0.0644183i | ||||
\(280\) | 3.37284 | + | 1.94731i | 0.201566 | + | 0.116374i | ||||
\(281\) | −32.0813 | −1.91381 | −0.956904 | − | 0.290405i | \(-0.906210\pi\) | ||||
−0.956904 | + | 0.290405i | \(0.906210\pi\) | |||||||
\(282\) | −16.0746 | − | 5.55202i | −0.957230 | − | 0.330618i | ||||
\(283\) | −19.1782 | −1.14003 | −0.570013 | − | 0.821636i | \(-0.693062\pi\) | ||||
−0.570013 | + | 0.821636i | \(0.693062\pi\) | |||||||
\(284\) | −4.47829 | − | 7.75662i | −0.265737 | − | 0.460271i | ||||
\(285\) | −16.0111 | − | 10.7256i | −0.948415 | − | 0.635329i | ||||
\(286\) | 1.29164 | − | 2.23719i | 0.0763766 | − | 0.132288i | ||||
\(287\) | −5.15698 | + | 8.93215i | −0.304407 | + | 0.527248i | ||||
\(288\) | −2.36052 | − | 1.85147i | −0.139095 | − | 0.109099i | ||||
\(289\) | 21.5360 | + | 37.3014i | 1.26682 | + | 2.19420i | ||||
\(290\) | 9.15025 | − | 5.28290i | 0.537321 | − | 0.310223i | ||||
\(291\) | 0.874250 | + | 0.301957i | 0.0512494 | + | 0.0177010i | ||||
\(292\) | −5.36599 | − | 9.29417i | −0.314021 | − | 0.543900i | ||||
\(293\) | −3.09233 | − | 5.35608i | −0.180656 | − | 0.312905i | 0.761448 | − | 0.648226i | \(-0.224489\pi\) |
−0.942104 | + | 0.335320i | \(0.891155\pi\) | |||||||
\(294\) | −7.94504 | + | 1.53653i | −0.463364 | + | 0.0896124i | ||||
\(295\) | 19.8492i | 1.15567i | ||||||||
\(296\) | − | 8.30368i | − | 0.482641i | ||||||
\(297\) | 6.06383 | − | 0.300474i | 0.351859 | − | 0.0174353i | ||||
\(298\) | −12.2998 | + | 7.10128i | −0.712507 | + | 0.411366i | ||||
\(299\) | −0.149230 | − | 0.258475i | −0.00863021 | − | 0.0149480i | ||||
\(300\) | −2.57746 | + | 0.498469i | −0.148810 | + | 0.0287791i | ||||
\(301\) | 2.88123 | 0.166071 | ||||||||
\(302\) | 1.82879i | 0.105235i | ||||||||
\(303\) | −24.4469 | + | 21.2107i | −1.40444 | + | 1.21852i | ||||
\(304\) | −3.06944 | + | 3.09492i | −0.176044 | + | 0.177506i | ||||
\(305\) | 2.34430i | 0.134234i | ||||||||
\(306\) | 23.0194 | + | 3.27975i | 1.31593 | + | 0.187491i | ||||
\(307\) | 14.0179 | + | 8.09326i | 0.800046 | + | 0.461907i | 0.843487 | − | 0.537149i | \(-0.180499\pi\) |
−0.0434413 | + | 0.999056i | \(0.513832\pi\) | |||||||
\(308\) | 1.78272i | 0.101580i | ||||||||
\(309\) | −10.4199 | − | 3.59892i | −0.592766 | − | 0.204735i | ||||
\(310\) | 0.493334 | − | 0.854480i | 0.0280195 | − | 0.0485312i | ||||
\(311\) | −24.8337 | + | 14.3377i | −1.40819 | + | 0.813017i | −0.995213 | − | 0.0977254i | \(-0.968843\pi\) |
−0.412974 | + | 0.910743i | \(0.635510\pi\) | |||||||
\(312\) | −0.727123 | − | 3.75978i | −0.0411652 | − | 0.212856i | ||||
\(313\) | −7.21649 | −0.407900 | −0.203950 | − | 0.978981i | \(-0.565378\pi\) | ||||
−0.203950 | + | 0.978981i | \(0.565378\pi\) | |||||||
\(314\) | −10.4674 | − | 18.1301i | −0.590710 | − | 1.02314i | ||||
\(315\) | −7.21077 | + | 9.19332i | −0.406281 | + | 0.517985i | ||||
\(316\) | 10.0802i | 0.567053i | ||||||||
\(317\) | −5.39047 | −0.302759 | −0.151379 | − | 0.988476i | \(-0.548372\pi\) | ||||
−0.151379 | + | 0.988476i | \(0.548372\pi\) | |||||||
\(318\) | −15.0873 | + | 2.91781i | −0.846055 | + | 0.163623i | ||||
\(319\) | 4.18843 | + | 2.41819i | 0.234507 | + | 0.135393i | ||||
\(320\) | 2.55258i | 0.142694i | ||||||||
\(321\) | 10.9945 | + | 12.6720i | 0.613653 | + | 0.707282i | ||||
\(322\) | 0.178372 | + | 0.102983i | 0.00994031 | + | 0.00573904i | ||||
\(323\) | 8.60898 | − | 32.6688i | 0.479017 | − | 1.81774i | ||||
\(324\) | 6.49776 | − | 6.22729i | 0.360986 | − | 0.345961i | ||||
\(325\) | −2.90209 | − | 1.67552i | −0.160979 | − | 0.0929413i | ||||
\(326\) | 8.95176 | + | 15.5049i | 0.495792 | + | 0.858738i | ||||
\(327\) | 4.44702 | + | 22.9945i | 0.245921 | + | 1.27160i | ||||
\(328\) | −6.75990 | −0.373253 | ||||||||
\(329\) | 12.9738 | + | 7.49045i | 0.715271 | + | 0.412962i | ||||
\(330\) | −3.38537 | − | 3.90190i | −0.186358 | − | 0.214792i | ||||
\(331\) | −20.6131 | − | 11.9010i | −1.13300 | − | 0.654138i | −0.188313 | − | 0.982109i | \(-0.560302\pi\) |
−0.944688 | + | 0.327971i | \(0.893635\pi\) | |||||||
\(332\) | 13.4929 | − | 7.79012i | 0.740518 | − | 0.427538i | ||||
\(333\) | 24.6620 | + | 3.51378i | 1.35147 | + | 0.192554i | ||||
\(334\) | −0.737087 | −0.0403316 | ||||||||
\(335\) | −9.08972 | + | 15.7439i | −0.496624 | + | 0.860179i | ||||
\(336\) | 1.73186 | + | 1.99611i | 0.0944809 | + | 0.108897i | ||||
\(337\) | 6.06350i | 0.330300i | 0.986268 | + | 0.165150i | \(0.0528109\pi\) | ||||
−0.986268 | + | 0.165150i | \(0.947189\pi\) | |||||||
\(338\) | −4.05589 | + | 7.02501i | −0.220611 | + | 0.382110i | ||||
\(339\) | −2.98245 | + | 8.63502i | −0.161984 | + | 0.468990i | ||||
\(340\) | −9.89203 | − | 17.1335i | −0.536471 | − | 0.929194i | ||||
\(341\) | 0.451637 | 0.0244575 | ||||||||
\(342\) | −7.89308 | − | 10.4259i | −0.426809 | − | 0.563768i | ||||
\(343\) | 17.8087 | 0.961581 | ||||||||
\(344\) | 0.944197 | + | 1.63540i | 0.0509077 | + | 0.0881747i | ||||
\(345\) | −0.585974 | + | 0.113325i | −0.0315478 | + | 0.00610119i | ||||
\(346\) | 5.01877 | − | 8.69276i | 0.269811 | − | 0.467326i | ||||
\(347\) | 19.5061i | 1.04714i | 0.851982 | + | 0.523572i | \(0.175401\pi\) | ||||
−0.851982 | + | 0.523572i | \(0.824599\pi\) | |||||||
\(348\) | 7.03898 | − | 1.36131i | 0.377329 | − | 0.0729736i | ||||
\(349\) | 12.3916 | − | 21.4628i | 0.663306 | − | 1.14888i | −0.316436 | − | 0.948614i | \(-0.602486\pi\) |
0.979742 | − | 0.200266i | \(-0.0641805\pi\) | |||||||
\(350\) | 2.31255 | 0.123611 | ||||||||
\(351\) | 11.4743 | − | 0.568571i | 0.612451 | − | 0.0303481i | ||||
\(352\) | −1.01188 | + | 0.584208i | −0.0539333 | + | 0.0311384i | ||||
\(353\) | 10.2539 | + | 5.92008i | 0.545759 | + | 0.315094i | 0.747410 | − | 0.664364i | \(-0.231297\pi\) |
−0.201651 | + | 0.979457i | \(0.564631\pi\) | |||||||
\(354\) | −4.39706 | + | 12.7307i | −0.233701 | + | 0.676629i | ||||
\(355\) | −19.7994 | − | 11.4312i | −1.05084 | − | 0.606705i | ||||
\(356\) | 6.66117 | 0.353041 | ||||||||
\(357\) | −19.3602 | − | 6.68681i | −1.02465 | − | 0.353904i | ||||
\(358\) | 4.87110 | + | 8.43700i | 0.257446 | + | 0.445909i | ||||
\(359\) | −13.8289 | − | 7.98410i | −0.729859 | − | 0.421384i | 0.0885114 | − | 0.996075i | \(-0.471789\pi\) |
−0.818371 | + | 0.574691i | \(0.805122\pi\) | |||||||
\(360\) | −7.58118 | − | 1.08015i | −0.399563 | − | 0.0569289i | ||||
\(361\) | −16.3754 | + | 9.63573i | −0.861861 | + | 0.507144i | ||||
\(362\) | 11.9960 | + | 6.92591i | 0.630497 | + | 0.364018i | ||||
\(363\) | −5.44805 | + | 15.7736i | −0.285948 | + | 0.827900i | ||||
\(364\) | 3.37334i | 0.176811i | ||||||||
\(365\) | −23.7241 | − | 13.6971i | −1.24178 | − | 0.716941i | ||||
\(366\) | −0.519317 | + | 1.50357i | −0.0271451 | + | 0.0785927i | ||||
\(367\) | 22.6343 | 1.18150 | 0.590750 | − | 0.806854i | \(-0.298832\pi\) | ||||
0.590750 | + | 0.806854i | \(0.298832\pi\) | |||||||
\(368\) | 0.134993i | 0.00703701i | ||||||||
\(369\) | 2.86052 | − | 20.0769i | 0.148913 | − | 1.04516i | ||||
\(370\) | −10.5979 | − | 18.3561i | −0.550959 | − | 0.954289i | ||||
\(371\) | 13.5366 | 0.702786 | ||||||||
\(372\) | 0.505697 | − | 0.438753i | 0.0262192 | − | 0.0227483i | ||||
\(373\) | −7.71350 | + | 4.45339i | −0.399390 | + | 0.230588i | −0.686221 | − | 0.727393i | \(-0.740732\pi\) |
0.286831 | + | 0.957981i | \(0.407398\pi\) | |||||||
\(374\) | 4.52797 | − | 7.84268i | 0.234136 | − | 0.405535i | ||||
\(375\) | 11.6358 | − | 10.0955i | 0.600872 | − | 0.521329i | ||||
\(376\) | 9.81867i | 0.506359i | ||||||||
\(377\) | 7.92554 | + | 4.57581i | 0.408186 | + | 0.235666i | ||||
\(378\) | −6.66130 | + | 4.29897i | −0.342621 | + | 0.221115i | ||||
\(379\) | − | 34.4271i | − | 1.76840i | −0.467109 | − | 0.884200i | \(-0.654704\pi\) | ||
0.467109 | − | 0.884200i | \(-0.345296\pi\) | |||||||
\(380\) | −2.83528 | + | 10.7591i | −0.145447 | + | 0.551932i | ||||
\(381\) | 10.7937 | + | 3.72804i | 0.552979 | + | 0.190993i | ||||
\(382\) | − | 1.09142i | − | 0.0558419i | ||||||
\(383\) | −35.4244 | −1.81010 | −0.905052 | − | 0.425301i | \(-0.860168\pi\) | ||||
−0.905052 | + | 0.425301i | \(0.860168\pi\) | |||||||
\(384\) | −0.565455 | + | 1.63715i | −0.0288558 | + | 0.0835455i | ||||
\(385\) | 2.27527 | + | 3.94088i | 0.115958 | + | 0.200846i | ||||
\(386\) | −1.57882 | + | 0.911533i | −0.0803599 | + | 0.0463958i | ||||
\(387\) | −5.25669 | + | 2.11224i | −0.267212 | + | 0.107371i | ||||
\(388\) | − | 0.534007i | − | 0.0271101i | ||||||
\(389\) | − | 12.3362i | − | 0.625471i | −0.949840 | − | 0.312735i | \(-0.898755\pi\) | ||
0.949840 | − | 0.312735i | \(-0.101245\pi\) | |||||||
\(390\) | −6.40595 | − | 7.38335i | −0.324378 | − | 0.373870i | ||||
\(391\) | −0.523140 | − | 0.906105i | −0.0264563 | − | 0.0458237i | ||||
\(392\) | 2.33603 | + | 4.04613i | 0.117988 | + | 0.204360i | ||||
\(393\) | −0.981567 | + | 0.851628i | −0.0495135 | + | 0.0429589i | ||||
\(394\) | −17.0579 | + | 9.84838i | −0.859364 | + | 0.496154i | ||||
\(395\) | 12.8652 | + | 22.2832i | 0.647319 | + | 1.12119i | ||||
\(396\) | −1.30692 | − | 3.25250i | −0.0656750 | − | 0.163444i | ||||
\(397\) | −10.2049 | + | 17.6754i | −0.512168 | + | 0.887101i | 0.487733 | + | 0.872993i | \(0.337824\pi\) |
−0.999900 | + | 0.0141076i | \(0.995509\pi\) | |||||||
\(398\) | 4.29440 | − | 7.43811i | 0.215259 | − | 0.372839i | ||||
\(399\) | 5.08264 | + | 10.3373i | 0.254450 | + | 0.517510i | ||||
\(400\) | 0.757836 | + | 1.31261i | 0.0378918 | + | 0.0656305i | ||||
\(401\) | 0.691367 | 0.0345252 | 0.0172626 | − | 0.999851i | \(-0.494505\pi\) | ||||
0.0172626 | + | 0.999851i | \(0.494505\pi\) | |||||||
\(402\) | −9.31750 | + | 8.08406i | −0.464715 | + | 0.403196i | ||||
\(403\) | 0.854608 | 0.0425710 | ||||||||
\(404\) | 16.1829 | + | 9.34320i | 0.805129 | + | 0.464842i | ||||
\(405\) | 6.41611 | − | 22.0591i | 0.318819 | − | 1.09612i | ||||
\(406\) | −6.31550 | −0.313433 | ||||||||
\(407\) | 4.85108 | − | 8.40231i | 0.240459 | − | 0.416487i | ||||
\(408\) | −2.54899 | − | 13.1802i | −0.126194 | − | 0.652519i | ||||
\(409\) | 28.3434 | + | 16.3641i | 1.40149 | + | 0.809151i | 0.994546 | − | 0.104301i | \(-0.0332606\pi\) |
0.406945 | + | 0.913452i | \(0.366594\pi\) | |||||||
\(410\) | −14.9434 | + | 8.62760i | −0.738004 | + | 0.426087i | ||||
\(411\) | 2.63846 | − | 2.28918i | 0.130146 | − | 0.112917i | ||||
\(412\) | 6.36464i | 0.313563i | ||||||||
\(413\) | 5.93225 | − | 10.2750i | 0.291907 | − | 0.505597i | ||||
\(414\) | −0.400931 | − | 0.0571237i | −0.0197047 | − | 0.00280748i | ||||
\(415\) | 19.8849 | − | 34.4417i | 0.976112 | − | 1.69068i | ||||
\(416\) | −1.91472 | + | 1.10547i | −0.0938770 | + | 0.0541999i | ||||
\(417\) | 1.60080 | − | 0.309587i | 0.0783917 | − | 0.0151606i | ||||
\(418\) | −4.91398 | + | 1.33850i | −0.240351 | + | 0.0654680i | ||||
\(419\) | 31.5759 | − | 18.2304i | 1.54258 | − | 0.890611i | 0.543909 | − | 0.839144i | \(-0.316944\pi\) |
0.998675 | − | 0.0514673i | \(-0.0163898\pi\) | |||||||
\(420\) | 6.37607 | + | 2.20223i | 0.311120 | + | 0.107458i | ||||
\(421\) | −11.3869 | + | 6.57421i | −0.554962 | + | 0.320408i | −0.751121 | − | 0.660165i | \(-0.770487\pi\) |
0.196159 | + | 0.980572i | \(0.437153\pi\) | |||||||
\(422\) | −20.3381 | + | 11.7422i | −0.990042 | + | 0.571601i | ||||
\(423\) | −29.1615 | − | 4.15487i | −1.41788 | − | 0.202017i | ||||
\(424\) | 4.43603 | + | 7.68344i | 0.215433 | + | 0.373141i | ||||
\(425\) | −10.1735 | − | 5.87369i | −0.493489 | − | 0.284916i | ||||
\(426\) | −10.1665 | − | 11.7176i | −0.492568 | − | 0.567722i | ||||
\(427\) | 0.700631 | − | 1.21353i | 0.0339059 | − | 0.0587268i | ||||
\(428\) | 4.84302 | − | 8.38837i | 0.234096 | − | 0.405467i | ||||
\(429\) | 1.46073 | − | 4.22923i | 0.0705249 | − | 0.204189i | ||||
\(430\) | 4.17448 | + | 2.41014i | 0.201312 | + | 0.116227i | ||||
\(431\) | 0.191860 | + | 0.332312i | 0.00924158 | + | 0.0160069i | 0.870609 | − | 0.491975i | \(-0.163725\pi\) |
−0.861368 | + | 0.507982i | \(0.830392\pi\) | |||||||
\(432\) | −4.62307 | − | 2.37218i | −0.222427 | − | 0.114132i | ||||
\(433\) | 15.6280 | − | 9.02281i | 0.751032 | − | 0.433609i | −0.0750344 | − | 0.997181i | \(-0.523907\pi\) |
0.826067 | + | 0.563572i | \(0.190573\pi\) | |||||||
\(434\) | −0.510749 | + | 0.294881i | −0.0245167 | + | 0.0141547i | ||||
\(435\) | 13.8230 | − | 11.9931i | 0.662760 | − | 0.575025i | ||||
\(436\) | 11.7103 | − | 6.76093i | 0.560820 | − | 0.323790i | ||||
\(437\) | −0.149944 | + | 0.568997i | −0.00717277 | + | 0.0272188i | ||||
\(438\) | −12.1817 | − | 14.0404i | −0.582065 | − | 0.670875i | ||||
\(439\) | −9.32231 | + | 5.38224i | −0.444930 | + | 0.256880i | −0.705686 | − | 0.708524i | \(-0.749361\pi\) |
0.260757 | + | 0.965405i | \(0.416028\pi\) | |||||||
\(440\) | −1.49124 | + | 2.58290i | −0.0710921 | + | 0.123135i | ||||
\(441\) | −13.0055 | + | 5.22587i | −0.619312 | + | 0.248851i | ||||
\(442\) | 8.56803 | − | 14.8403i | 0.407540 | − | 0.705879i | ||||
\(443\) | − | 6.32546i | − | 0.300532i | −0.988646 | − | 0.150266i | \(-0.951987\pi\) | ||
0.988646 | − | 0.150266i | \(-0.0480129\pi\) | |||||||
\(444\) | −2.73088 | − | 14.1207i | −0.129602 | − | 0.670141i | ||||
\(445\) | 14.7252 | − | 8.50159i | 0.698041 | − | 0.403014i | ||||
\(446\) | −4.53089 | − | 2.61591i | −0.214544 | − | 0.123867i | ||||
\(447\) | −18.5808 | + | 16.1211i | −0.878844 | + | 0.762503i | ||||
\(448\) | 0.762878 | − | 1.32134i | 0.0360426 | − | 0.0624276i | ||||
\(449\) | 14.5374 | 0.686063 | 0.343032 | − | 0.939324i | \(-0.388546\pi\) | ||||
0.343032 | + | 0.939324i | \(0.388546\pi\) | |||||||
\(450\) | −4.21915 | + | 1.69533i | −0.198892 | + | 0.0799188i | ||||
\(451\) | −6.84020 | − | 3.94919i | −0.322092 | − | 0.185960i | ||||
\(452\) | 5.27442 | 0.248088 | ||||||||
\(453\) | 0.601446 | + | 3.10994i | 0.0282584 | + | 0.146118i | ||||
\(454\) | −8.24904 | −0.387146 | ||||||||
\(455\) | 4.30537 | + | 7.45711i | 0.201839 | + | 0.349595i | ||||
\(456\) | −4.20186 | + | 6.27251i | −0.196770 | + | 0.293737i | ||||
\(457\) | −6.55232 | + | 11.3489i | −0.306505 | + | 0.530881i | −0.977595 | − | 0.210494i | \(-0.932493\pi\) |
0.671091 | + | 0.741375i | \(0.265826\pi\) | |||||||
\(458\) | 9.53515 | − | 16.5154i | 0.445548 | − | 0.771713i | ||||
\(459\) | 40.2240 | − | 1.99317i | 1.87750 | − | 0.0930334i | ||||
\(460\) | 0.172291 | + | 0.298416i | 0.00803309 | + | 0.0139137i | ||||
\(461\) | 12.1860 | − | 7.03557i | 0.567557 | − | 0.327679i | −0.188616 | − | 0.982051i | \(-0.560400\pi\) |
0.756173 | + | 0.654372i | \(0.227067\pi\) | |||||||
\(462\) | 0.586294 | + | 3.03159i | 0.0272769 | + | 0.141042i | ||||
\(463\) | 13.6189 | + | 23.5886i | 0.632925 | + | 1.09626i | 0.986951 | + | 0.161022i | \(0.0514790\pi\) |
−0.354026 | + | 0.935235i | \(0.615188\pi\) | |||||||
\(464\) | −2.06963 | − | 3.58471i | −0.0960802 | − | 0.166416i | ||||
\(465\) | 0.557917 | − | 1.61532i | 0.0258728 | − | 0.0749089i | ||||
\(466\) | − | 8.85619i | − | 0.410255i | ||||||
\(467\) | 16.8983i | 0.781961i | 0.920399 | + | 0.390981i | \(0.127864\pi\) | ||||
−0.920399 | + | 0.390981i | \(0.872136\pi\) | |||||||
\(468\) | −2.47301 | − | 6.15453i | −0.114315 | − | 0.284493i | ||||
\(469\) | 9.41058 | − | 5.43320i | 0.434540 | − | 0.250882i | ||||
\(470\) | 12.5315 | + | 21.7051i | 0.578034 | + | 1.00118i | ||||
\(471\) | −23.7628 | − | 27.3885i | −1.09493 | − | 1.26199i | ||||
\(472\) | 7.77614 | 0.357926 | ||||||||
\(473\) | 2.20643i | 0.101452i | ||||||||
\(474\) | 3.31513 | + | 17.1417i | 0.152269 | + | 0.787346i | ||||
\(475\) | 1.73630 | + | 6.37442i | 0.0796668 | + | 0.292478i | ||||
\(476\) | 11.8255i | 0.542023i | ||||||||
\(477\) | −24.6970 | + | 9.92372i | −1.13080 | + | 0.454376i | ||||
\(478\) | −4.98254 | − | 2.87667i | −0.227896 | − | 0.131576i | ||||
\(479\) | − | 40.7634i | − | 1.86253i | −0.364349 | − | 0.931263i | \(-0.618708\pi\) | ||
0.364349 | − | 0.931263i | \(-0.381292\pi\) | |||||||
\(480\) | 0.839484 | + | 4.34077i | 0.0383170 | + | 0.198128i | ||||
\(481\) | 9.17943 | − | 15.8992i | 0.418546 | − | 0.724943i | ||||
\(482\) | 23.5284 | − | 13.5841i | 1.07169 | − | 0.618739i | ||||
\(483\) | 0.337198 | + | 0.116465i | 0.0153431 | + | 0.00529934i | ||||
\(484\) | 9.63480 | 0.437946 | ||||||||
\(485\) | −0.681548 | − | 1.18048i | −0.0309475 | − | 0.0536027i | ||||
\(486\) | 9.00169 | − | 12.7267i | 0.408325 | − | 0.577296i | ||||
\(487\) | − | 23.9395i | − | 1.08480i | −0.840120 | − | 0.542401i | \(-0.817515\pi\) | ||
0.840120 | − | 0.542401i | \(-0.182485\pi\) | |||||||
\(488\) | 0.918405 | 0.0415743 | ||||||||
\(489\) | 20.3220 | + | 23.4227i | 0.918995 | + | 1.05921i | ||||
\(490\) | 10.3281 | + | 5.96292i | 0.466575 | + | 0.269377i | ||||
\(491\) | 29.0305i | 1.31013i | 0.755573 | + | 0.655064i | \(0.227359\pi\) | ||||
−0.755573 | + | 0.655064i | \(0.772641\pi\) | |||||||
\(492\) | −11.4955 | + | 2.22317i | −0.518257 | + | 0.100228i | ||||
\(493\) | 27.7836 | + | 16.0409i | 1.25131 | + | 0.722446i | ||||
\(494\) | −9.29845 | + | 2.53276i | −0.418357 | + | 0.113954i | ||||
\(495\) | −7.04020 | − | 5.52197i | −0.316434 | − | 0.248194i | ||||
\(496\) | −0.334751 | − | 0.193269i | −0.0150308 | − | 0.00867802i | ||||
\(497\) | 6.83277 | + | 11.8347i | 0.306492 | + | 0.530859i | ||||
\(498\) | 20.3832 | − | 17.6849i | 0.913394 | − | 0.792480i | ||||
\(499\) | 2.96806 | 0.132868 | 0.0664342 | − | 0.997791i | \(-0.478838\pi\) | ||||
0.0664342 | + | 0.997791i | \(0.478838\pi\) | |||||||
\(500\) | −7.70246 | − | 4.44702i | −0.344464 | − | 0.198877i | ||||
\(501\) | −1.25345 | + | 0.242411i | −0.0559999 | + | 0.0108301i | ||||
\(502\) | 24.1315 | + | 13.9323i | 1.07704 | + | 0.621829i | ||||
\(503\) | −33.9493 | + | 19.6006i | −1.51372 | + | 0.873949i | −0.513853 | + | 0.857878i | \(0.671782\pi\) |
−0.999871 | + | 0.0160702i | \(0.994884\pi\) | |||||||
\(504\) | 3.60158 | + | 2.82489i | 0.160427 | + | 0.125831i | ||||
\(505\) | 47.6986 | 2.12256 | ||||||||
\(506\) | −0.0788642 | + | 0.136597i | −0.00350594 | + | 0.00607247i | ||||
\(507\) | −4.58685 | + | 13.2802i | −0.203709 | + | 0.589795i | ||||
\(508\) | − | 6.59299i | − | 0.292517i | ||||||
\(509\) | −15.0166 | + | 26.0096i | −0.665600 | + | 1.15285i | 0.313522 | + | 0.949581i | \(0.398491\pi\) |
−0.979122 | + | 0.203272i | \(0.934842\pi\) | |||||||
\(510\) | −22.4566 | − | 25.8830i | −0.994395 | − | 1.14612i | ||||
\(511\) | 8.18720 | + | 14.1806i | 0.362180 | + | 0.627315i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −16.8513 | − | 15.1338i | −0.744005 | − | 0.668174i | ||||
\(514\) | −4.60766 | −0.203235 | ||||||||
\(515\) | 8.12313 | + | 14.0697i | 0.357948 | + | 0.619984i | ||||
\(516\) | 2.14349 | + | 2.47054i | 0.0943619 | + | 0.108759i | ||||
\(517\) | −5.73615 | + | 9.93530i | −0.252275 | + | 0.436954i | ||||
\(518\) | 12.6694i | 0.556661i | ||||||||
\(519\) | 5.67578 | − | 16.4330i | 0.249139 | − | 0.721327i | ||||
\(520\) | −2.82179 | + | 4.88749i | −0.123744 | + | 0.214330i | ||||
\(521\) | 20.7192 | 0.907724 | 0.453862 | − | 0.891072i | \(-0.350046\pi\) | ||||
0.453862 | + | 0.891072i | \(0.350046\pi\) | |||||||
\(522\) | 11.5224 | − | 4.62991i | 0.504321 | − | 0.202646i | ||||
\(523\) | −1.90320 | + | 1.09881i | −0.0832212 | + | 0.0480478i | −0.541033 | − | 0.841001i | \(-0.681967\pi\) |
0.457812 | + | 0.889049i | \(0.348633\pi\) | |||||||
\(524\) | 0.649758 | + | 0.375138i | 0.0283848 | + | 0.0163880i | ||||
\(525\) | 3.93258 | − | 0.760542i | 0.171632 | − | 0.0331928i | ||||
\(526\) | −8.47535 | − | 4.89325i | −0.369543 | − | 0.213356i | ||||
\(527\) | 2.99590 | 0.130503 | ||||||||
\(528\) | −1.52861 | + | 1.32625i | −0.0665242 | + | 0.0577178i | ||||
\(529\) | −11.4909 | − | 19.9028i | −0.499604 | − | 0.865339i | ||||
\(530\) | 19.6126 | + | 11.3233i | 0.851917 | + | 0.491854i | ||||
\(531\) | −3.29055 | + | 23.0952i | −0.142798 | + | 1.00225i | ||||
\(532\) | 4.68321 | − | 4.72210i | 0.203043 | − | 0.204729i | ||||
\(533\) | −12.9433 | − | 7.47284i | −0.560638 | − | 0.323684i | ||||
\(534\) | 11.3276 | − | 2.19070i | 0.490193 | − | 0.0948009i | ||||
\(535\) | − | 24.7244i | − | 1.06893i | ||||||
\(536\) | 6.16782 | + | 3.56099i | 0.266409 | + | 0.153811i | ||||
\(537\) | 11.0582 | + | 12.7455i | 0.477198 | + | 0.550008i | ||||
\(538\) | −20.8391 | −0.898436 | ||||||||
\(539\) | 5.45892i | 0.235132i | ||||||||
\(540\) | −13.2473 | + | 0.656431i | −0.570075 | + | 0.0282483i | ||||
\(541\) | −1.95051 | − | 3.37838i | −0.0838589 | − | 0.145248i | 0.821045 | − | 0.570863i | \(-0.193391\pi\) |
−0.904904 | + | 0.425615i | \(0.860058\pi\) | |||||||
\(542\) | −20.8860 | −0.897129 | ||||||||
\(543\) | 22.6775 | + | 7.83259i | 0.973185 | + | 0.336128i | ||||
\(544\) | −6.71222 | + | 3.87530i | −0.287784 | + | 0.166152i | ||||
\(545\) | 17.2578 | − | 29.8914i | 0.739244 | − | 1.28041i | ||||
\(546\) | 1.10941 | + | 5.73651i | 0.0474785 | + | 0.245500i | ||||
\(547\) | − | 45.5556i | − | 1.94782i | −0.226944 | − | 0.973908i | \(-0.572874\pi\) | ||
0.226944 | − | 0.973908i | \(-0.427126\pi\) | |||||||
\(548\) | −1.74656 | − | 1.00838i | −0.0746092 | − | 0.0430757i | ||||
\(549\) | −0.388633 | + | 2.72767i | −0.0165864 | + | 0.116414i | ||||
\(550\) | 1.77094i | 0.0755130i | ||||||||
\(551\) | −4.74179 | − | 17.4084i | −0.202007 | − | 0.741622i | ||||
\(552\) | 0.0443961 | + | 0.229562i | 0.00188962 | + | 0.00977079i | ||||
\(553\) | − | 15.3799i | − | 0.654018i | ||||||
\(554\) | −20.3807 | −0.865893 | ||||||||
\(555\) | −24.0591 | − | 27.7299i | −1.02125 | − | 1.17707i | ||||
\(556\) | −0.470675 | − | 0.815232i | −0.0199610 | − | 0.0345735i | ||||
\(557\) | −34.7750 | + | 20.0774i | −1.47346 | + | 0.850705i | −0.999554 | − | 0.0298686i | \(-0.990491\pi\) |
−0.473910 | + | 0.880573i | \(0.657158\pi\) | |||||||
\(558\) | 0.715663 | − | 0.912430i | 0.0302964 | − | 0.0386262i | ||||
\(559\) | 4.17511i | 0.176588i | ||||||||
\(560\) | − | 3.89462i | − | 0.164578i | ||||||
\(561\) | 5.12073 | − | 14.8259i | 0.216197 | − | 0.625952i | ||||
\(562\) | 16.0406 | + | 27.7832i | 0.676633 | + | 1.17196i | ||||
\(563\) | 16.8303 | + | 29.1508i | 0.709311 | + | 1.22856i | 0.965113 | + | 0.261833i | \(0.0843269\pi\) |
−0.255803 | + | 0.966729i | \(0.582340\pi\) | |||||||
\(564\) | 3.22913 | + | 16.6970i | 0.135971 | + | 0.703072i | ||||
\(565\) | 11.6596 | − | 6.73169i | 0.490525 | − | 0.283204i | ||||
\(566\) | 9.58910 | + | 16.6088i | 0.403060 | + | 0.698120i | ||||
\(567\) | −9.91399 | + | 9.50133i | −0.416349 | + | 0.399018i | ||||
\(568\) | −4.47829 | + | 7.75662i | −0.187905 | + | 0.325461i | ||||
\(569\) | −13.9198 | + | 24.1099i | −0.583550 | + | 1.01074i | 0.411505 | + | 0.911408i | \(0.365003\pi\) |
−0.995055 | + | 0.0993302i | \(0.968330\pi\) | |||||||
\(570\) | −1.28308 | + | 19.2288i | −0.0537424 | + | 0.805406i | ||||
\(571\) | −6.57983 | − | 11.3966i | −0.275357 | − | 0.476933i | 0.694868 | − | 0.719137i | \(-0.255463\pi\) |
−0.970225 | + | 0.242205i | \(0.922129\pi\) | |||||||
\(572\) | −2.58329 | −0.108013 | ||||||||
\(573\) | −0.358942 | − | 1.85601i | −0.0149950 | − | 0.0775357i | ||||
\(574\) | 10.3140 | 0.430496 | ||||||||
\(575\) | 0.177193 | + | 0.102303i | 0.00738948 | + | 0.00426632i | ||||
\(576\) | −0.423160 | + | 2.97001i | −0.0176317 | + | 0.123750i | ||||
\(577\) | 39.9592 | 1.66352 | 0.831761 | − | 0.555134i | \(-0.187333\pi\) | ||||
0.831761 | + | 0.555134i | \(0.187333\pi\) | |||||||
\(578\) | 21.5360 | − | 37.3014i | 0.895778 | − | 1.55153i | ||||
\(579\) | −2.38507 | + | 2.06934i | −0.0991201 | + | 0.0859987i | ||||
\(580\) | −9.15025 | − | 5.28290i | −0.379944 | − | 0.219361i | ||||
\(581\) | −20.5868 | + | 11.8858i | −0.854086 | + | 0.493107i | ||||
\(582\) | −0.175622 | − | 0.908101i | −0.00727978 | − | 0.0376420i | ||||
\(583\) | 10.3663i | 0.429327i | ||||||||
\(584\) | −5.36599 | + | 9.29417i | −0.222046 | + | 0.384596i | ||||
\(585\) | −13.3218 | − | 10.4489i | −0.550788 | − | 0.432010i | ||||
\(586\) | −3.09233 | + | 5.35608i | −0.127743 | + | 0.221258i | ||||
\(587\) | −7.15130 | + | 4.12880i | −0.295166 | + | 0.170414i | −0.640269 | − | 0.768151i | \(-0.721177\pi\) |
0.345104 | + | 0.938565i | \(0.387844\pi\) | |||||||
\(588\) | 5.30320 | + | 6.11234i | 0.218700 | + | 0.252069i | ||||
\(589\) | −1.19630 | − | 1.18645i | −0.0492928 | − | 0.0488869i | ||||
\(590\) | 17.1899 | − | 9.92461i | 0.707698 | − | 0.408590i | ||||
\(591\) | −25.7688 | + | 22.3575i | −1.05999 | + | 0.919665i | ||||
\(592\) | −7.19119 | + | 4.15184i | −0.295556 | + | 0.170639i | ||||
\(593\) | −3.01185 | + | 1.73889i | −0.123682 | + | 0.0714078i | −0.560565 | − | 0.828111i | \(-0.689416\pi\) |
0.436883 | + | 0.899519i | \(0.356083\pi\) | |||||||
\(594\) | −3.29213 | − | 5.10120i | −0.135078 | − | 0.209305i | ||||
\(595\) | 15.0928 | + | 26.1415i | 0.618746 | + | 1.07170i | ||||
\(596\) | 12.2998 | + | 7.10128i | 0.503819 | + | 0.290880i | ||||
\(597\) | 4.85658 | − | 14.0611i | 0.198767 | − | 0.575484i | ||||
\(598\) | −0.149230 | + | 0.258475i | −0.00610248 | + | 0.0105698i | ||||
\(599\) | 2.87651 | − | 4.98225i | 0.117531 | − | 0.203569i | −0.801258 | − | 0.598319i | \(-0.795835\pi\) |
0.918789 | + | 0.394750i | \(0.129169\pi\) | |||||||
\(600\) | 1.72042 | + | 1.98291i | 0.0702358 | + | 0.0809521i | ||||
\(601\) | 3.74377 | + | 2.16147i | 0.152712 | + | 0.0881681i | 0.574409 | − | 0.818569i | \(-0.305232\pi\) |
−0.421697 | + | 0.906737i | \(0.638565\pi\) | |||||||
\(602\) | −1.44061 | − | 2.49522i | −0.0587151 | − | 0.101697i | ||||
\(603\) | −13.1861 | + | 16.8116i | −0.536981 | + | 0.684620i | ||||
\(604\) | 1.58378 | − | 0.914396i | 0.0644431 | − | 0.0372062i | ||||
\(605\) | 21.2987 | − | 12.2968i | 0.865915 | − | 0.499936i | ||||
\(606\) | 30.5924 | + | 10.5663i | 1.24273 | + | 0.429228i | ||||
\(607\) | 24.0328 | − | 13.8753i | 0.975461 | − | 0.563183i | 0.0745645 | − | 0.997216i | \(-0.476243\pi\) |
0.900897 | + | 0.434033i | \(0.142910\pi\) | |||||||
\(608\) | 4.21500 | + | 1.11075i | 0.170941 | + | 0.0450468i | ||||
\(609\) | −10.7398 | + | 2.07702i | −0.435198 | + | 0.0841651i | ||||
\(610\) | 2.03023 | − | 1.17215i | 0.0822015 | − | 0.0474591i | ||||
\(611\) | −10.8542 | + | 18.8000i | −0.439114 | + | 0.760567i | ||||
\(612\) | −8.66933 | − | 21.5752i | −0.350437 | − | 0.872127i | ||||
\(613\) | 23.6861 | − | 41.0255i | 0.956672 | − | 1.65700i | 0.226176 | − | 0.974086i | \(-0.427378\pi\) |
0.730496 | − | 0.682917i | \(-0.239289\pi\) | |||||||
\(614\) | − | 16.1865i | − | 0.653235i | ||||||
\(615\) | −22.5745 | + | 19.5861i | −0.910292 | + | 0.789789i | ||||
\(616\) | 1.54388 | − | 0.891360i | 0.0622047 | − | 0.0359139i | ||||
\(617\) | 2.44932 | + | 1.41412i | 0.0986061 | + | 0.0569302i | 0.548492 | − | 0.836156i | \(-0.315202\pi\) |
−0.449886 | + | 0.893086i | \(0.648535\pi\) | |||||||
\(618\) | 2.09318 | + | 10.8233i | 0.0842000 | + | 0.435378i | ||||
\(619\) | −7.27971 | + | 12.6088i | −0.292596 | + | 0.506792i | −0.974423 | − | 0.224722i | \(-0.927853\pi\) |
0.681827 | + | 0.731514i | \(0.261186\pi\) | |||||||
\(620\) | −0.986668 | −0.0396256 | ||||||||
\(621\) | −0.700586 | + | 0.0347153i | −0.0281135 | + | 0.00139308i | ||||
\(622\) | 24.8337 | + | 14.3377i | 0.995739 | + | 0.574890i | ||||
\(623\) | −10.1633 | −0.407185 | ||||||||
\(624\) | −2.89250 | + | 2.50960i | −0.115793 | + | 0.100464i | ||||
\(625\) | −30.2811 | −1.21124 | ||||||||
\(626\) | 3.60825 | + | 6.24967i | 0.144215 | + | 0.249787i | ||||
\(627\) | −7.91622 | + | 3.89226i | −0.316144 | + | 0.155442i | ||||
\(628\) | −10.4674 | + | 18.1301i | −0.417695 | + | 0.723469i | ||||
\(629\) | 32.1793 | − | 55.7361i | 1.28307 | − | 2.22235i | ||||
\(630\) | 11.5670 | + | 1.64805i | 0.460842 | + | 0.0656597i | ||||
\(631\) | 6.40998 | + | 11.1024i | 0.255177 | + | 0.441980i | 0.964944 | − | 0.262457i | \(-0.0845328\pi\) |
−0.709766 | + | 0.704437i | \(0.751199\pi\) | |||||||
\(632\) | 8.72967 | − | 5.04008i | 0.347248 | − | 0.200484i | ||||
\(633\) | −30.7240 | + | 26.6568i | −1.22117 | + | 1.05951i | ||||
\(634\) | 2.69523 | + | 4.66828i | 0.107041 | + | 0.185401i | ||||
\(635\) | −8.41458 | − | 14.5745i | −0.333922 | − | 0.578370i | ||||
\(636\) | 10.0706 | + | 11.6071i | 0.399324 | + | 0.460251i | ||||
\(637\) | 10.3296i | 0.409274i | ||||||||
\(638\) | − | 4.83638i | − | 0.191474i | ||||||
\(639\) | −21.1422 | − | 16.5828i | −0.836371 | − | 0.656007i | ||||
\(640\) | 2.21060 | − | 1.27629i | 0.0873817 | − | 0.0504498i | ||||
\(641\) | −14.2475 | − | 24.6774i | −0.562742 | − | 0.974698i | −0.997256 | − | 0.0740328i | \(-0.976413\pi\) |
0.434514 | − | 0.900665i | \(-0.356920\pi\) | |||||||
\(642\) | 5.47703 | − | 15.8575i | 0.216161 | − | 0.625846i | ||||
\(643\) | 4.59459 | 0.181193 | 0.0905964 | − | 0.995888i | \(-0.471123\pi\) | ||||
0.0905964 | + | 0.995888i | \(0.471123\pi\) | |||||||
\(644\) | − | 0.205967i | − | 0.00811623i | ||||||
\(645\) | 7.89152 | + | 2.72565i | 0.310728 | + | 0.107322i | ||||
\(646\) | −32.5965 | + | 8.87882i | −1.28249 | + | 0.349332i | ||||
\(647\) | 9.46727i | 0.372197i | 0.982531 | + | 0.186098i | \(0.0595843\pi\) | ||||
−0.982531 | + | 0.186098i | \(0.940416\pi\) | |||||||
\(648\) | −8.64187 | − | 2.51358i | −0.339485 | − | 0.0987426i | ||||
\(649\) | 7.86851 | + | 4.54289i | 0.308866 | + | 0.178324i | ||||
\(650\) | 3.35105i | 0.131439i | ||||||||
\(651\) | −0.771570 | + | 0.669430i | −0.0302402 | + | 0.0262370i | ||||
\(652\) | 8.95176 | − | 15.5049i | 0.350578 | − | 0.607219i | ||||
\(653\) | 34.4306 | − | 19.8785i | 1.34737 | − | 0.777905i | 0.359495 | − | 0.933147i | \(-0.382949\pi\) |
0.987877 | + | 0.155242i | \(0.0496156\pi\) | |||||||
\(654\) | 17.6903 | − | 15.3485i | 0.691745 | − | 0.600173i | ||||
\(655\) | 1.91514 | 0.0748308 | ||||||||
\(656\) | 3.37995 | + | 5.85424i | 0.131965 | + | 0.228570i | ||||
\(657\) | −25.3331 | − | 19.8700i | −0.988337 | − | 0.775201i | ||||
\(658\) | − | 14.9809i | − | 0.584016i | ||||||
\(659\) | −48.5702 | −1.89203 | −0.946014 | − | 0.324125i | \(-0.894930\pi\) | ||||
−0.946014 | + | 0.324125i | \(0.894930\pi\) | |||||||
\(660\) | −1.68646 | + | 4.88277i | −0.0656453 | + | 0.190061i | ||||
\(661\) | −20.9317 | − | 12.0849i | −0.814151 | − | 0.470050i | 0.0342446 | − | 0.999413i | \(-0.489097\pi\) |
−0.848395 | + | 0.529363i | \(0.822431\pi\) | |||||||
\(662\) | 23.8020i | 0.925091i | ||||||||
\(663\) | 9.68968 | − | 28.0543i | 0.376316 | − | 1.08954i | ||||
\(664\) | −13.4929 | − | 7.79012i | −0.523625 | − | 0.302315i | ||||
\(665\) | 4.32594 | − | 16.4158i | 0.167753 | − | 0.636578i | ||||
\(666\) | −9.28796 | − | 23.1148i | −0.359901 | − | 0.895680i | ||||
\(667\) | −0.483911 | − | 0.279386i | −0.0187371 | − | 0.0108179i | ||||
\(668\) | 0.368544 | + | 0.638336i | 0.0142594 | + | 0.0246980i | ||||
\(669\) | −8.56528 | − | 2.95836i | −0.331153 | − | 0.114377i | ||||
\(670\) | 18.1794 | 0.702333 | ||||||||
\(671\) | 0.929315 | + | 0.536540i | 0.0358758 | + | 0.0207129i | ||||
\(672\) | 0.862747 | − | 2.49789i | 0.0332812 | − | 0.0963583i | ||||
\(673\) | −0.599468 | − | 0.346103i | −0.0231078 | − | 0.0133413i | 0.488402 | − | 0.872619i | \(-0.337580\pi\) |
−0.511509 | + | 0.859278i | \(0.670913\pi\) | |||||||
\(674\) | 5.25115 | − | 3.03175i | 0.202267 | − | 0.116779i | ||||
\(675\) | −6.61728 | + | 4.27056i | −0.254699 | + | 0.164374i | ||||
\(676\) | 8.11178 | 0.311992 | ||||||||
\(677\) | −12.3134 | + | 21.3274i | −0.473242 | + | 0.819680i | −0.999531 | − | 0.0306263i | \(-0.990250\pi\) |
0.526289 | + | 0.850306i | \(0.323583\pi\) | |||||||
\(678\) | 8.96937 | − | 1.73463i | 0.344467 | − | 0.0666181i | ||||
\(679\) | 0.814765i | 0.0312678i | ||||||||
\(680\) | −9.89203 | + | 17.1335i | −0.379342 | + | 0.657040i | ||||
\(681\) | −14.0278 | + | 2.71291i | −0.537547 | + | 0.103959i | ||||
\(682\) | −0.225818 | − | 0.391129i | −0.00864704 | − | 0.0149771i | ||||
\(683\) | 8.41338 | 0.321929 | 0.160965 | − | 0.986960i | \(-0.448540\pi\) | ||||
0.160965 | + | 0.986960i | \(0.448540\pi\) | |||||||
\(684\) | −5.08255 | + | 12.0486i | −0.194336 | + | 0.460688i | ||||
\(685\) | −5.14792 | −0.196692 | ||||||||
\(686\) | −8.90437 | − | 15.4228i | −0.339970 | − | 0.588846i | ||||
\(687\) | 10.7834 | − | 31.2210i | 0.411413 | − | 1.19115i | ||||
\(688\) | 0.944197 | − | 1.63540i | 0.0359972 | − | 0.0623489i | ||||
\(689\) | 19.6155i | 0.747292i | ||||||||
\(690\) | 0.391129 | + | 0.450806i | 0.0148900 | + | 0.0171619i | ||||
\(691\) | −5.59480 | + | 9.69047i | −0.212836 | + | 0.368643i | −0.952601 | − | 0.304223i | \(-0.901603\pi\) |
0.739765 | + | 0.672865i | \(0.234937\pi\) | |||||||
\(692\) | −10.0375 | −0.381570 | ||||||||
\(693\) | 1.99404 | + | 4.96252i | 0.0757471 | + | 0.188511i | ||||
\(694\) | 16.8928 | − | 9.75306i | 0.641242 | − | 0.370221i | ||||
\(695\) | −2.08095 | − | 1.20144i | −0.0789348 | − | 0.0455730i | ||||
\(696\) | −4.69842 | − | 5.41529i | −0.178093 | − | 0.205266i | ||||
\(697\) | −45.3740 | − | 26.1967i | −1.71866 | − | 0.992270i | ||||
\(698\) | −24.7832 | −0.938056 | ||||||||
\(699\) | −2.91259 | − | 15.0603i | −0.110164 | − | 0.569634i | ||||
\(700\) | −1.15627 | − | 2.00272i | −0.0437030 | − | 0.0756958i | ||||
\(701\) | 31.3712 | + | 18.1121i | 1.18487 | + | 0.684086i | 0.957137 | − | 0.289637i | \(-0.0935345\pi\) |
0.227736 | + | 0.973723i | \(0.426868\pi\) | |||||||
\(702\) | −6.22953 | − | 9.65271i | −0.235118 | − | 0.364318i | ||||
\(703\) | −34.9225 | + | 9.51239i | −1.31713 | + | 0.358767i | ||||
\(704\) | 1.01188 | + | 0.584208i | 0.0381366 | + | 0.0220182i | ||||
\(705\) | 28.4486 | + | 32.7892i | 1.07144 | + | 1.23491i | ||||
\(706\) | − | 11.8402i | − | 0.445610i | ||||||
\(707\) | −24.6912 | − | 14.2554i | −0.928607 | − | 0.536131i | ||||
\(708\) | 13.2236 | − | 2.55739i | 0.496975 | − | 0.0961125i | ||||
\(709\) | −33.3507 | −1.25251 | −0.626255 | − | 0.779618i | \(-0.715413\pi\) | ||||
−0.626255 | + | 0.779618i | \(0.715413\pi\) | |||||||
\(710\) | 22.8624i | 0.858010i | ||||||||
\(711\) | 11.2750 | + | 28.0599i | 0.422846 | + | 1.05233i | ||||
\(712\) | −3.33058 | − | 5.76874i | −0.124819 | − | 0.216193i | ||||
\(713\) | −0.0521799 | −0.00195415 | ||||||||
\(714\) | 3.88914 | + | 20.1098i | 0.145547 | + | 0.752591i | ||||
\(715\) | −5.71062 | + | 3.29703i | −0.213565 | + | 0.123302i | ||||
\(716\) | 4.87110 | − | 8.43700i | 0.182042 | − | 0.315305i | ||||
\(717\) | −9.41908 | − | 3.25325i | −0.351762 | − | 0.121495i | ||||
\(718\) | 15.9682i | 0.595928i | ||||||||
\(719\) | −24.1012 | − | 13.9149i | −0.898825 | − | 0.518937i | −0.0220061 | − | 0.999758i | \(-0.507005\pi\) |
−0.876819 | + | 0.480821i | \(0.840339\pi\) | |||||||
\(720\) | 2.85515 | + | 7.10557i | 0.106405 | + | 0.264809i | ||||
\(721\) | − | 9.71089i | − | 0.361652i | ||||||
\(722\) | 16.5325 | + | 9.36362i | 0.615275 | + | 0.348478i | ||||
\(723\) | 35.5434 | − | 30.8382i | 1.32187 | − | 1.14689i | ||||
\(724\) | − | 13.8518i | − | 0.514799i | ||||||
\(725\) | −6.27376 | −0.233002 | ||||||||
\(726\) | 16.3844 | − | 3.16866i | 0.608081 | − | 0.117600i | ||||
\(727\) | −20.3335 | − | 35.2187i | −0.754128 | − | 1.30619i | −0.945807 | − | 0.324731i | \(-0.894726\pi\) |
0.191678 | − | 0.981458i | \(-0.438607\pi\) | |||||||
\(728\) | 2.92140 | − | 1.68667i | 0.108274 | − | 0.0625122i | ||||
\(729\) | 11.1222 | − | 24.6028i | 0.411934 | − | 0.911213i | ||||
\(730\) | 27.3943i | 1.01391i | ||||||||
\(731\) | 14.6362i | 0.541340i | ||||||||
\(732\) | 1.56179 | − | 0.302042i | 0.0577253 | − | 0.0111638i | ||||
\(733\) | −4.36371 | − | 7.55816i | −0.161177 | − | 0.279167i | 0.774114 | − | 0.633046i | \(-0.218196\pi\) |
−0.935291 | + | 0.353879i | \(0.884862\pi\) | |||||||
\(734\) | −11.3171 | − | 19.6019i | −0.417724 | − | 0.723518i | ||||
\(735\) | 19.5244 | + | 6.74353i | 0.720168 | + | 0.248739i | ||||
\(736\) | 0.116908 | − | 0.0674966i | 0.00430927 | − | 0.00248796i | ||||
\(737\) | 4.16072 | + | 7.20658i | 0.153262 | + | 0.265458i | ||||
\(738\) | −18.8174 | + | 7.56119i | −0.692678 | + | 0.278331i | ||||
\(739\) | −1.87473 | + | 3.24713i | −0.0689630 | + | 0.119447i | −0.898445 | − | 0.439086i | \(-0.855302\pi\) |
0.829482 | + | 0.558533i | \(0.188636\pi\) | |||||||
\(740\) | −10.5979 | + | 18.3561i | −0.389587 | + | 0.674784i | ||||
\(741\) | −14.9794 | + | 7.36511i | −0.550283 | + | 0.270564i | ||||
\(742\) | −6.76831 | − | 11.7231i | −0.248472 | − | 0.430367i | ||||
\(743\) | −8.47663 | −0.310977 | −0.155489 | − | 0.987838i | \(-0.549695\pi\) | ||||
−0.155489 | + | 0.987838i | \(0.549695\pi\) | |||||||
\(744\) | −0.632820 | − | 0.218570i | −0.0232003 | − | 0.00801315i | ||||
\(745\) | 36.2532 | 1.32821 | ||||||||
\(746\) | 7.71350 | + | 4.45339i | 0.282411 | + | 0.163050i | ||||
\(747\) | 28.8463 | − | 36.7775i | 1.05543 | − | 1.34562i | ||||
\(748\) | −9.05594 | −0.331118 | ||||||||
\(749\) | −7.38928 | + | 12.7986i | −0.269998 | + | 0.467651i | ||||
\(750\) | −14.5609 | − | 5.02918i | −0.531688 | − | 0.183640i | ||||
\(751\) | 4.53004 | + | 2.61542i | 0.165303 | + | 0.0954380i | 0.580369 | − | 0.814353i | \(-0.302908\pi\) |
−0.415066 | + | 0.909791i | \(0.636242\pi\) | |||||||
\(752\) | 8.50321 | − | 4.90933i | 0.310080 | − | 0.179025i | ||||
\(753\) | 45.6185 | + | 15.7562i | 1.66243 | + | 0.574187i | ||||
\(754\) | − | 9.15162i | − | 0.333282i | ||||||
\(755\) | 2.33407 | − | 4.04273i | 0.0849455 | − | 0.147130i | ||||
\(756\) | 7.05367 | + | 3.61937i | 0.256540 | + | 0.131635i | ||||
\(757\) | 6.65825 | − | 11.5324i | 0.241998 | − | 0.419153i | −0.719285 | − | 0.694715i | \(-0.755531\pi\) |
0.961283 | + | 0.275562i | \(0.0888639\pi\) | |||||||
\(758\) | −29.8147 | + | 17.2135i | −1.08292 | + | 0.625224i | ||||
\(759\) | −0.0891883 | + | 0.258225i | −0.00323733 | + | 0.00937297i | ||||
\(760\) | 10.7353 | − | 2.92414i | 0.389411 | − | 0.106070i | ||||
\(761\) | 15.2464 | − | 8.80251i | 0.552681 | − | 0.319091i | −0.197521 | − | 0.980299i | \(-0.563289\pi\) |
0.750203 | + | 0.661208i | \(0.229956\pi\) | |||||||
\(762\) | −2.16828 | − | 11.2117i | −0.0785485 | − | 0.406156i | ||||
\(763\) | −17.8670 | + | 10.3155i | −0.646830 | + | 0.373447i | ||||
\(764\) | −0.945198 | + | 0.545710i | −0.0341961 | + | 0.0197431i | ||||
\(765\) | −46.7007 | − | 36.6296i | −1.68847 | − | 1.32435i | ||||
\(766\) | 17.7122 | + | 30.6785i | 0.639968 | + | 1.10846i | ||||
\(767\) | 14.8891 | + | 8.59625i | 0.537616 | + | 0.310393i | ||||
\(768\) | 1.70054 | − | 0.328876i | 0.0613630 | − | 0.0118673i | ||||
\(769\) | −14.0382 | + | 24.3149i | −0.506231 | + | 0.876817i | 0.493743 | + | 0.869608i | \(0.335628\pi\) |
−0.999974 | + | 0.00720967i | \(0.997705\pi\) | |||||||
\(770\) | 2.27527 | − | 3.94088i | 0.0819950 | − | 0.142019i | ||||
\(771\) | −7.83551 | + | 1.51535i | −0.282189 | + | 0.0545740i | ||||
\(772\) | 1.57882 | + | 0.911533i | 0.0568230 | + | 0.0328068i | ||||
\(773\) | −1.52748 | − | 2.64567i | −0.0549395 | − | 0.0951580i | 0.837248 | − | 0.546824i | \(-0.184163\pi\) |
−0.892187 | + | 0.451666i | \(0.850830\pi\) | |||||||
\(774\) | 4.45759 | + | 3.49631i | 0.160225 | + | 0.125672i | ||||
\(775\) | −0.507373 | + | 0.292932i | −0.0182254 | + | 0.0105224i | ||||
\(776\) | −0.462464 | + | 0.267004i | −0.0166015 | + | 0.00958487i | ||||
\(777\) | 4.16666 | + | 21.5448i | 0.149478 | + | 0.772916i | ||||
\(778\) | −10.6835 | + | 6.16811i | −0.383021 | + | 0.221137i | ||||
\(779\) | 7.74390 | + | 28.4299i | 0.277454 | + | 1.01861i | ||||
\(780\) | −3.19119 | + | 9.23939i | −0.114263 | + | 0.330823i | ||||
\(781\) | −9.06297 | + | 5.23251i | −0.324298 | + | 0.187234i | ||||
\(782\) | −0.523140 | + | 0.906105i | −0.0187074 | + | 0.0324022i | ||||
\(783\) | 18.0716 | − | 11.6628i | 0.645827 | − | 0.416794i | ||||
\(784\) | 2.33603 | − | 4.04613i | 0.0834298 | − | 0.144505i | ||||
\(785\) | 53.4378i | 1.90728i | ||||||||
\(786\) | 1.22831 | + | 0.424248i | 0.0438125 | + | 0.0151324i | ||||
\(787\) | −39.5679 | + | 22.8445i | −1.41044 | + | 0.814320i | −0.995430 | − | 0.0954955i | \(-0.969556\pi\) |
−0.415013 | + | 0.909815i | \(0.636223\pi\) | |||||||
\(788\) | 17.0579 | + | 9.84838i | 0.607662 | + | 0.350834i | ||||
\(789\) | −16.0220 | − | 5.53382i | −0.570397 | − | 0.197009i | ||||
\(790\) | 12.8652 | − | 22.2832i | 0.457724 | − | 0.792801i | ||||
\(791\) | −8.04748 | −0.286135 | ||||||||
\(792\) | −2.16329 | + | 2.75807i | −0.0768691 | + | 0.0980038i | ||||
\(793\) | 1.75849 | + | 1.01527i | 0.0624459 | + | 0.0360531i | ||||
\(794\) | 20.4097 | 0.724315 | ||||||||
\(795\) | 37.0760 | + | 12.8057i | 1.31495 | + | 0.454171i | ||||
\(796\) | −8.58879 | −0.304422 | ||||||||
\(797\) | −3.74913 | − | 6.49368i | −0.132801 | − | 0.230018i | 0.791954 | − | 0.610580i | \(-0.209064\pi\) |
−0.924755 | + | 0.380562i | \(0.875730\pi\) | |||||||
\(798\) | 6.41101 | − | 9.57032i | 0.226947 | − | 0.338786i | ||||
\(799\) | −38.0503 | + | 65.9051i | −1.34612 | + | 2.33155i | ||||
\(800\) | 0.757836 | − | 1.31261i | 0.0267935 | − | 0.0464078i | ||||
\(801\) | 18.5426 | − | 7.45076i | 0.655169 | − | 0.263259i | ||||
\(802\) | −0.345683 | − | 0.598741i | −0.0122065 | − | 0.0211423i | ||||
\(803\) | −10.8595 | + | 6.26972i | −0.383222 | + | 0.221253i | ||||
\(804\) | 11.6598 | + | 4.02716i | 0.411208 | + | 0.142027i | ||||
\(805\) | −0.262873 | − | 0.455310i | −0.00926507 | − | 0.0160476i | ||||
\(806\) | −0.427304 | − | 0.740112i | −0.0150511 | − | 0.0260693i | ||||
\(807\) | −35.4377 | + | 6.85347i | −1.24747 | + | 0.241254i | ||||
\(808\) | − | 18.6864i | − | 0.657385i | ||||||
\(809\) | 9.70609i | 0.341248i | 0.985336 | + | 0.170624i | \(0.0545784\pi\) | ||||
−0.985336 | + | 0.170624i | \(0.945422\pi\) | |||||||
\(810\) | −22.3118 | + | 5.47303i | −0.783956 | + | 0.192303i | ||||
\(811\) | −26.3705 | + | 15.2250i | −0.925995 | + | 0.534623i | −0.885543 | − | 0.464558i | \(-0.846213\pi\) |
−0.0404523 | + | 0.999181i | \(0.512880\pi\) | |||||||
\(812\) | 3.15775 | + | 5.46939i | 0.110815 | + | 0.191938i | ||||
\(813\) | −35.5174 | + | 6.86890i | −1.24565 | + | 0.240903i | ||||
\(814\) | −9.70215 | −0.340060 | ||||||||
\(815\) | − | 45.7002i | − | 1.60081i | ||||||
\(816\) | −10.1399 | + | 8.79761i | −0.354968 | + | 0.307978i | ||||
\(817\) | 5.79631 | − | 5.84444i | 0.202787 | − | 0.204471i | ||||
\(818\) | − | 32.7281i | − | 1.14431i | ||||||
\(819\) | 3.77320 | + | 9.39031i | 0.131846 | + | 0.328124i | ||||
\(820\) | 14.9434 | + | 8.62760i | 0.521847 | + | 0.301289i | ||||
\(821\) | − | 17.7758i | − | 0.620378i | −0.950675 | − | 0.310189i | \(-0.899608\pi\) | ||
0.950675 | − | 0.310189i | \(-0.100392\pi\) | |||||||
\(822\) | −3.30172 | − | 1.14038i | −0.115161 | − | 0.0397754i | ||||
\(823\) | −2.81911 | + | 4.88284i | −0.0982679 | + | 0.170205i | −0.910968 | − | 0.412478i | \(-0.864664\pi\) |
0.812700 | + | 0.582682i | \(0.197997\pi\) | |||||||
\(824\) | 5.51194 | − | 3.18232i | 0.192018 | − | 0.110861i | ||||
\(825\) | 0.582419 | + | 3.01155i | 0.0202772 | + | 0.104849i | ||||
\(826\) | −11.8645 | −0.412818 | ||||||||
\(827\) | 14.2242 | + | 24.6371i | 0.494625 | + | 0.856716i | 0.999981 | − | 0.00619548i | \(-0.00197210\pi\) |
−0.505356 | + | 0.862911i | \(0.668639\pi\) | |||||||
\(828\) | 0.150995 | + | 0.375778i | 0.00524743 | + | 0.0130592i | ||||
\(829\) | − | 35.2950i | − | 1.22584i | −0.790143 | − | 0.612922i | \(-0.789994\pi\) | ||
0.790143 | − | 0.612922i | \(-0.210006\pi\) | |||||||
\(830\) | −39.7698 | −1.38043 | ||||||||
\(831\) | −34.6582 | + | 6.70273i | −1.20228 | + | 0.232515i | ||||
\(832\) | 1.91472 | + | 1.10547i | 0.0663811 | + | 0.0383251i | ||||
\(833\) | 36.2114i | 1.25465i | ||||||||
\(834\) | −1.06851 | − | 1.23154i | −0.0369995 | − | 0.0426448i | ||||
\(835\) | 1.62941 | + | 0.940738i | 0.0563879 | + | 0.0325556i | ||||
\(836\) | 3.61616 | + | 3.58638i | 0.125068 | + | 0.124038i | ||||
\(837\) | 0.916937 | − | 1.78699i | 0.0316940 | − | 0.0617674i | ||||
\(838\) | −31.5759 | − | 18.2304i | −1.09077 | − | 0.629757i | ||||
\(839\) | 12.2589 | + | 21.2330i | 0.423224 | + | 0.733046i | 0.996253 | − | 0.0864896i | \(-0.0275649\pi\) |
−0.573029 | + | 0.819535i | \(0.694232\pi\) | |||||||
\(840\) | −1.28085 | − | 6.62296i | −0.0441934 | − | 0.228514i | ||||
\(841\) | −11.8665 | −0.409190 | ||||||||
\(842\) | 11.3869 | + | 6.57421i | 0.392418 | + | 0.226562i | ||||
\(843\) | 36.4150 | + | 41.9711i | 1.25420 | + | 1.44556i | ||||
\(844\) | 20.3381 | + | 11.7422i | 0.700065 | + | 0.404183i | ||||
\(845\) | 17.9319 | − | 10.3530i | 0.616876 | − | 0.356154i | ||||
\(846\) | 10.9825 | + | 27.3320i | 0.377587 | + | 0.939695i | ||||
\(847\) | −14.7004 | −0.505110 | ||||||||
\(848\) | 4.43603 | − | 7.68344i | 0.152334 | − | 0.263850i | ||||
\(849\) | 21.7689 | + | 25.0903i | 0.747107 | + | 0.861098i | ||||
\(850\) | 11.7474i | 0.402932i | ||||||||
\(851\) | −0.560470 | + | 0.970762i | −0.0192127 | + | 0.0332773i | ||||
\(852\) | −5.06454 | + | 14.6633i | −0.173508 | + | 0.502355i | ||||
\(853\) | 3.17813 | + | 5.50468i | 0.108817 | + | 0.188477i | 0.915291 | − | 0.402793i | \(-0.131960\pi\) |
−0.806474 | + | 0.591269i | \(0.798627\pi\) | |||||||
\(854\) | −1.40126 | −0.0479502 | ||||||||
\(855\) | 4.14197 | + | 33.1214i | 0.141652 | + | 1.13273i | ||||
\(856\) | −9.68605 | −0.331062 | ||||||||
\(857\) | 0.502103 | + | 0.869669i | 0.0171515 | + | 0.0297073i | 0.874474 | − | 0.485073i | \(-0.161207\pi\) |
−0.857322 | + | 0.514780i | \(0.827874\pi\) | |||||||
\(858\) | −4.39299 | + | 0.849583i | −0.149974 | + | 0.0290043i | ||||
\(859\) | −10.5678 | + | 18.3040i | −0.360570 | + | 0.624525i | −0.988055 | − | 0.154104i | \(-0.950751\pi\) |
0.627485 | + | 0.778629i | \(0.284084\pi\) | |||||||
\(860\) | − | 4.82028i | − | 0.164370i | ||||||
\(861\) | 17.5393 | − | 3.39202i | 0.597738 | − | 0.115600i | ||||
\(862\) | 0.191860 | − | 0.332312i | 0.00653479 | − | 0.0113186i | ||||
\(863\) | −19.7281 | −0.671551 | −0.335776 | − | 0.941942i | \(-0.608998\pi\) | ||||
−0.335776 | + | 0.941942i | \(0.608998\pi\) | |||||||
\(864\) | 0.257164 | + | 5.18978i | 0.00874888 | + | 0.176560i | ||||
\(865\) | −22.1890 | + | 12.8108i | −0.754448 | + | 0.435581i | ||||
\(866\) | −15.6280 | − | 9.02281i | −0.531060 | − | 0.306608i | ||||
\(867\) | 24.3553 | − | 70.5152i | 0.827148 | − | 2.39482i | ||||
\(868\) | 0.510749 | + | 0.294881i | 0.0173359 | + | 0.0100089i | ||||
\(869\) | 11.7778 | 0.399535 | ||||||||
\(870\) | −17.2978 | − | 5.97449i | −0.586450 | − | 0.202554i | ||||
\(871\) | 7.87310 | + | 13.6366i | 0.266770 | + | 0.462059i | ||||
\(872\) | −11.7103 | − | 6.76093i | −0.396560 | − | 0.228954i | ||||
\(873\) | −0.597306 | − | 1.48651i | −0.0202157 | − | 0.0503106i | ||||
\(874\) | 0.567737 | − | 0.154643i | 0.0192040 | − | 0.00523089i | ||||
\(875\) | 11.7521 | + | 6.78506i | 0.397293 | + | 0.229377i | ||||
\(876\) | −6.06846 | + | 17.5699i | −0.205034 | + | 0.593631i | ||||
\(877\) | 8.07401i | 0.272640i | 0.990665 | + | 0.136320i | \(0.0435275\pi\) | ||||
−0.990665 | + | 0.136320i | \(0.956472\pi\) | |||||||
\(878\) | 9.32231 | + | 5.38224i | 0.314613 | + | 0.181642i | ||||
\(879\) | −3.49715 | + | 10.1252i | −0.117956 | + | 0.341515i | ||||
\(880\) | 2.98248 | 0.100539 | ||||||||
\(881\) | − | 3.75576i | − | 0.126535i | −0.997997 | − | 0.0632674i | \(-0.979848\pi\) | ||
0.997997 | − | 0.0632674i | \(-0.0201521\pi\) | |||||||
\(882\) | 11.0285 | + | 8.65020i | 0.371349 | + | 0.291267i | ||||
\(883\) | 10.2193 | + | 17.7004i | 0.343907 | + | 0.595664i | 0.985155 | − | 0.171670i | \(-0.0549162\pi\) |
−0.641248 | + | 0.767334i | \(0.721583\pi\) | |||||||
\(884\) | −17.1361 | −0.576348 | ||||||||
\(885\) | 25.9682 | − | 22.5306i | 0.872912 | − | 0.757357i | ||||
\(886\) | −5.47801 | + | 3.16273i | −0.184037 | + | 0.106254i | ||||
\(887\) | 21.7923 | − | 37.7453i | 0.731713 | − | 1.26736i | −0.224438 | − | 0.974488i | \(-0.572054\pi\) |
0.956151 | − | 0.292876i | \(-0.0946122\pi\) | |||||||
\(888\) | −10.8635 | + | 9.42538i | −0.364555 | + | 0.316295i | ||||
\(889\) | 10.0593i | 0.337378i | ||||||||
\(890\) | −14.7252 | − | 8.50159i | −0.493589 | − | 0.284974i | ||||
\(891\) | −7.27607 | − | 7.59209i | −0.243758 | − | 0.254345i | ||||
\(892\) | 5.23183i | 0.175174i | ||||||||
\(893\) | 41.2941 | − | 11.2479i | 1.38185 | − | 0.376397i | ||||
\(894\) | 23.2517 | + | 8.03092i | 0.777654 | + | 0.268594i | ||||
\(895\) | − | 24.8678i | − | 0.831238i | ||||||
\(896\) | −1.52576 | −0.0509719 | ||||||||
\(897\) | −0.168766 | + | 0.488625i | −0.00563494 | + | 0.0163147i | ||||
\(898\) | −7.26871 | − | 12.5898i | −0.242560 | − | 0.420126i | ||||
\(899\) | 1.38562 | − | 0.799990i | 0.0462131 | − | 0.0266812i | ||||
\(900\) | 3.57777 | + | 2.80622i | 0.119259 | + | 0.0935407i | ||||
\(901\) | 68.7639i | 2.29086i | ||||||||
\(902\) | 7.89838i | 0.262987i | ||||||||
\(903\) | −3.27044 | − | 3.76944i | −0.108834 | − | 0.125439i | ||||
\(904\) | −2.63721 | − | 4.56778i | −0.0877123 | − | 0.151922i | ||||
\(905\) | −17.6790 | − | 30.6208i | −0.587668 | − | 1.01787i | ||||
\(906\) | 2.39256 | − | 2.07584i | 0.0794875 | − | 0.0689650i | ||||
\(907\) | 41.0312 | − | 23.6894i | 1.36242 | − | 0.786593i | 0.372473 | − | 0.928043i | \(-0.378510\pi\) |
0.989945 | + | 0.141450i | \(0.0451766\pi\) | |||||||
\(908\) | 4.12452 | + | 7.14387i | 0.136877 | + | 0.237078i | ||||
\(909\) | 55.4987 | + | 7.90734i | 1.84078 | + | 0.262270i | ||||
\(910\) | 4.30537 | − | 7.45711i | 0.142721 | − | 0.247201i | ||||
\(911\) | 14.3777 | − | 24.9029i | 0.476354 | − | 0.825070i | −0.523279 | − | 0.852162i | \(-0.675291\pi\) |
0.999633 | + | 0.0270919i | \(0.00862468\pi\) | |||||||
\(912\) | 7.53308 | + | 0.502660i | 0.249445 | + | 0.0166447i | ||||
\(913\) | −9.10210 | − | 15.7653i | −0.301236 | − | 0.521756i | ||||
\(914\) | 13.1046 | 0.433463 | ||||||||
\(915\) | 3.06699 | − | 2.66099i | 0.101392 | − | 0.0879695i | ||||
\(916\) | −19.0703 | −0.630101 | ||||||||
\(917\) | −0.991373 | − | 0.572369i | −0.0327380 | − | 0.0189013i | ||||
\(918\) | −21.8381 | − | 33.8384i | −0.720766 | − | 1.11683i | ||||
\(919\) | −35.0205 | −1.15522 | −0.577610 | − | 0.816313i | \(-0.696015\pi\) | ||||
−0.577610 | + | 0.816313i | \(0.696015\pi\) | |||||||
\(920\) | 0.172291 | − | 0.298416i | 0.00568025 | − | 0.00983849i | ||||
\(921\) | −5.32336 | − | 27.5258i | −0.175411 | − | 0.907007i | ||||
\(922\) | −12.1860 | − | 7.03557i | −0.401323 | − | 0.231704i | ||||
\(923\) | −17.1494 | + | 9.90118i | −0.564478 | + | 0.325901i | ||||
\(924\) | 2.33228 | − | 2.02354i | 0.0767265 | − | 0.0665696i | ||||
\(925\) | 12.5856i | 0.413814i | ||||||||
\(926\) | 13.6189 | − | 23.5886i | 0.447545 | − | 0.775171i | ||||
\(927\) | 7.11908 | + | 17.7171i | 0.233821 | + | 0.581907i | ||||
\(928\) | −2.06963 | + | 3.58471i | −0.0679390 | + | 0.117674i | ||||
\(929\) | 12.9759 | − | 7.49164i | 0.425725 | − | 0.245793i | −0.271798 | − | 0.962354i | \(-0.587618\pi\) |
0.697524 | + | 0.716561i | \(0.254285\pi\) | |||||||
\(930\) | −1.67787 | + | 0.324492i | −0.0550195 | + | 0.0106405i | ||||
\(931\) | 14.3406 | − | 14.4597i | 0.469995 | − | 0.473897i | ||||
\(932\) | −7.66969 | + | 4.42810i | −0.251229 | + | 0.145047i | ||||
\(933\) | 46.9460 | + | 16.2147i | 1.53694 | + | 0.530845i | ||||
\(934\) | 14.6344 | − | 8.44916i | 0.478852 | − | 0.276465i | ||||
\(935\) | −20.0191 | + | 11.5580i | −0.654694 | + | 0.377988i | ||||
\(936\) | −4.09347 | + | 5.21895i | −0.133799 | + | 0.170587i | ||||
\(937\) | 3.76912 | + | 6.52830i | 0.123132 | + | 0.213270i | 0.921001 | − | 0.389560i | \(-0.127373\pi\) |
−0.797869 | + | 0.602830i | \(0.794040\pi\) | |||||||
\(938\) | −9.41058 | − | 5.43320i | −0.307266 | − | 0.177400i | ||||
\(939\) | 8.19134 | + | 9.44115i | 0.267314 | + | 0.308100i | ||||
\(940\) | 12.5315 | − | 21.7051i | 0.408732 | − | 0.707944i | ||||
\(941\) | 23.0496 | − | 39.9231i | 0.751397 | − | 1.30146i | −0.195749 | − | 0.980654i | \(-0.562714\pi\) |
0.947146 | − | 0.320803i | \(-0.103953\pi\) | |||||||
\(942\) | −11.8377 | + | 34.2734i | −0.385693 | + | 1.11669i | ||||
\(943\) | 0.790283 | + | 0.456270i | 0.0257352 | + | 0.0148582i | ||||
\(944\) | −3.88807 | − | 6.73433i | −0.126546 | − | 0.219184i | ||||
\(945\) | 20.2122 | − | 1.00155i | 0.657504 | − | 0.0325805i | ||||
\(946\) | 1.91083 | − | 1.10322i | 0.0621263 | − | 0.0358686i | ||||
\(947\) | −22.0863 | + | 12.7515i | −0.717707 | + | 0.414368i | −0.813908 | − | 0.580993i | \(-0.802664\pi\) |
0.0962010 | + | 0.995362i | \(0.469331\pi\) | |||||||
\(948\) | 13.1876 | − | 11.4418i | 0.428314 | − | 0.371614i | ||||
\(949\) | −20.5488 | + | 11.8638i | −0.667041 | + | 0.385117i | ||||
\(950\) | 4.65226 | − | 4.69089i | 0.150939 | − | 0.152193i | ||||
\(951\) | 6.11865 | + | 7.05221i | 0.198411 | + | 0.228684i | ||||
\(952\) | 10.2412 | − | 5.91277i | 0.331920 | − | 0.191634i | ||||
\(953\) | 0.323565 | − | 0.560431i | 0.0104813 | − | 0.0181542i | −0.860737 | − | 0.509050i | \(-0.829997\pi\) |
0.871218 | + | 0.490895i | \(0.163330\pi\) | |||||||
\(954\) | 20.9427 | + | 16.4264i | 0.678045 | + | 0.531823i | ||||
\(955\) | −1.39297 | + | 2.41269i | −0.0450754 | + | 0.0780730i | ||||
\(956\) | 5.75334i | 0.186076i | ||||||||
\(957\) | −1.59057 | − | 8.22447i | −0.0514159 | − | 0.265859i | ||||
\(958\) | −35.3021 | + | 20.3817i | −1.14056 | + | 0.658502i | ||||
\(959\) | 2.66482 | + | 1.53853i | 0.0860515 | + | 0.0496819i | ||||
\(960\) | 3.33948 | − | 2.89740i | 0.107781 | − | 0.0935132i | ||||
\(961\) | −15.4253 | + | 26.7174i | −0.497590 | + | 0.861851i | ||||
\(962\) | −18.3589 | −0.591913 | ||||||||
\(963\) | 4.09875 | − | 28.7676i | 0.132080 | − | 0.927024i | ||||
\(964\) | −23.5284 | − | 13.5841i | −0.757797 | − | 0.437514i | ||||
\(965\) | 4.65352 | 0.149802 | ||||||||
\(966\) | −0.0677376 | − | 0.350255i | −0.00217942 | − | 0.0112693i | ||||
\(967\) | 42.2076 | 1.35730 | 0.678652 | − | 0.734460i | \(-0.262564\pi\) | ||||
0.678652 | + | 0.734460i | \(0.262564\pi\) | |||||||
\(968\) | −4.81740 | − | 8.34398i | −0.154837 | − | 0.268186i | ||||
\(969\) | −52.5117 | + | 25.8190i | −1.68692 | + | 0.829426i | ||||
\(970\) | −0.681548 | + | 1.18048i | −0.0218832 | + | 0.0379028i | ||||
\(971\) | 16.2173 | − | 28.0891i | 0.520437 | − | 0.901423i | −0.479281 | − | 0.877662i | \(-0.659102\pi\) |
0.999718 | − | 0.0237614i | \(-0.00756421\pi\) | |||||||
\(972\) | −15.5225 | − | 1.43233i | −0.497885 | − | 0.0459421i | ||||
\(973\) | 0.718135 | + | 1.24385i | 0.0230223 | + | 0.0398759i | ||||
\(974\) | −20.7322 | + | 11.9697i | −0.664303 | + | 0.383535i | ||||
\(975\) | 1.10208 | + | 5.69859i | 0.0352948 | + | 0.182501i | ||||
\(976\) | −0.459203 | − | 0.795362i | −0.0146987 | − | 0.0254589i | ||||
\(977\) | −11.1431 | − | 19.3004i | −0.356500 | − | 0.617475i | 0.630874 | − | 0.775885i | \(-0.282697\pi\) |
−0.987373 | + | 0.158410i | \(0.949363\pi\) | |||||||
\(978\) | 10.1236 | − | 29.3108i | 0.323719 | − | 0.937255i | ||||
\(979\) | − | 7.78302i | − | 0.248747i | ||||||
\(980\) | − | 11.9258i | − | 0.380957i | ||||||
\(981\) | 25.0353 | − | 31.9186i | 0.799316 | − | 1.01908i | ||||
\(982\) | 25.1412 | − | 14.5153i | 0.802287 | − | 0.463200i | ||||
\(983\) | −2.39962 | − | 4.15627i | −0.0765361 | − | 0.132564i | 0.825217 | − | 0.564816i | \(-0.191053\pi\) |
−0.901753 | + | 0.432251i | \(0.857719\pi\) | |||||||
\(984\) | 7.67307 | + | 8.84380i | 0.244608 | + | 0.281930i | ||||
\(985\) | 50.2776 | 1.60198 | ||||||||
\(986\) | − | 32.0818i | − | 1.02169i | ||||||
\(987\) | −4.92686 | − | 25.4756i | −0.156824 | − | 0.810898i | ||||
\(988\) | 6.84266 | + | 6.78632i | 0.217694 | + | 0.215901i | ||||
\(989\) | − | 0.254920i | − | 0.00810600i | ||||||
\(990\) | −1.26207 | + | 8.85798i | −0.0401111 | + | 0.281525i | ||||
\(991\) | −11.2116 | − | 6.47302i | −0.356148 | − | 0.205622i | 0.311242 | − | 0.950331i | \(-0.399255\pi\) |
−0.667390 | + | 0.744709i | \(0.732588\pi\) | |||||||
\(992\) | 0.386537i | 0.0122726i | ||||||||
\(993\) | 7.82792 | + | 40.4763i | 0.248411 | + | 1.28448i | ||||
\(994\) | 6.83277 | − | 11.8347i | 0.216722 | − | 0.375374i | ||||
\(995\) | −18.9864 | + | 10.9618i | −0.601909 | + | 0.347512i | ||||
\(996\) | −25.5072 | − | 8.80993i | −0.808226 | − | 0.279153i | ||||
\(997\) | −9.60690 | −0.304254 | −0.152127 | − | 0.988361i | \(-0.548612\pi\) | ||||
−0.152127 | + | 0.988361i | \(0.548612\pi\) | |||||||
\(998\) | −1.48403 | − | 2.57041i | −0.0469761 | − | 0.0813650i | ||||
\(999\) | −23.3965 | − | 36.2530i | −0.740231 | − | 1.14700i |
(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 | 342.2.j.f.65.3 | ✓ | 18 | |
3.2 | odd | 2 | 1026.2.j.f.521.3 | 18 | |||
9.4 | even | 3 | 1026.2.n.f.179.7 | 18 | |||
9.5 | odd | 6 | 342.2.n.f.293.1 | yes | 18 | ||
19.12 | odd | 6 | 342.2.n.f.335.1 | yes | 18 | ||
57.50 | even | 6 | 1026.2.n.f.791.7 | 18 | |||
171.31 | odd | 6 | 1026.2.j.f.449.7 | 18 | |||
171.50 | even | 6 | inner | 342.2.j.f.221.3 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
342.2.j.f.65.3 | ✓ | 18 | 1.1 | even | 1 | trivial | |
342.2.j.f.221.3 | yes | 18 | 171.50 | even | 6 | inner | |
342.2.n.f.293.1 | yes | 18 | 9.5 | odd | 6 | ||
342.2.n.f.335.1 | yes | 18 | 19.12 | odd | 6 | ||
1026.2.j.f.449.7 | 18 | 171.31 | odd | 6 | |||
1026.2.j.f.521.3 | 18 | 3.2 | odd | 2 | |||
1026.2.n.f.179.7 | 18 | 9.4 | even | 3 | |||
1026.2.n.f.791.7 | 18 | 57.50 | even | 6 |