Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(163,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.163");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.w (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 5x^{12} + 28x^{8} + 80x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 307.8 | ||
Root | \(0.512386 + 1.31813i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 360.307 |
Dual form | 360.2.w.d.163.8 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.31813 | − | 0.512386i | 0.932057 | − | 0.362312i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.47492 | − | 1.35078i | 0.737460 | − | 0.675391i | ||||
\(5\) | −1.83051 | + | 1.28422i | −0.818631 | + | 0.574320i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.94984 | − | 2.94984i | 1.11494 | − | 1.11494i | 0.122462 | − | 0.992473i | \(-0.460921\pi\) |
0.992473 | − | 0.122462i | \(-0.0390789\pi\) | |||||||
\(8\) | 1.25201 | − | 2.53623i | 0.442653 | − | 0.896693i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.75483 | + | 2.63069i | −0.554927 | + | 0.831899i | ||||
\(11\) | 1.61148 | 0.485880 | 0.242940 | − | 0.970041i | \(-0.421888\pi\) | ||||
0.242940 | + | 0.970041i | \(0.421888\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.50967 | − | 2.50967i | −0.696057 | − | 0.696057i | 0.267501 | − | 0.963558i | \(-0.413802\pi\) |
−0.963558 | + | 0.267501i | \(0.913802\pi\) | |||||||
\(14\) | 2.37681 | − | 5.39972i | 0.635229 | − | 1.44314i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.350781 | − | 3.98459i | 0.0876953 | − | 0.996147i | ||||
\(17\) | 4.59398 | + | 4.59398i | 1.11420 | + | 1.11420i | 0.992576 | + | 0.121629i | \(0.0388118\pi\) |
0.121629 | + | 0.992576i | \(0.461188\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | −0.965164 | + | 4.36674i | −0.215817 | + | 0.976434i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.12414 | − | 0.825702i | 0.452868 | − | 0.176040i | ||||
\(23\) | −1.09259 | − | 1.09259i | −0.227821 | − | 0.227821i | 0.583961 | − | 0.811782i | \(-0.301502\pi\) |
−0.811782 | + | 0.583961i | \(0.801502\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.70156 | − | 4.70156i | 0.340312 | − | 0.940312i | ||||
\(26\) | −4.59398 | − | 2.02214i | −0.900954 | − | 0.396575i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.366192 | − | 8.33537i | 0.0692037 | − | 1.57524i | ||||
\(29\) | −4.75362 | −0.882725 | −0.441362 | − | 0.897329i | \(-0.645505\pi\) | ||||
−0.441362 | + | 0.897329i | \(0.645505\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.01934i | 0.901500i | 0.892650 | + | 0.450750i | \(0.148843\pi\) | ||||
−0.892650 | + | 0.450750i | \(0.851157\pi\) | |||||||
\(32\) | −1.57927 | − | 5.43193i | −0.279179 | − | 0.960239i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.40935 | + | 3.70156i | 1.44219 | + | 0.634813i | ||||
\(35\) | −1.61148 | + | 9.18797i | −0.272390 | + | 1.55305i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.50967 | − | 2.50967i | 0.412587 | − | 0.412587i | −0.470052 | − | 0.882639i | \(-0.655765\pi\) |
0.882639 | + | 0.470052i | \(0.155765\pi\) | |||||||
\(38\) | 2.04955 | + | 5.27251i | 0.332480 | + | 0.855314i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.965252 | + | 6.25046i | 0.152620 | + | 0.988285i | ||||
\(41\) | −9.18797 | −1.43492 | −0.717460 | − | 0.696600i | \(-0.754695\pi\) | ||||
−0.717460 | + | 0.696600i | \(0.754695\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.40312 | + | 7.40312i | −1.12897 | + | 1.12897i | −0.138620 | + | 0.990346i | \(0.544267\pi\) |
−0.990346 | + | 0.138620i | \(0.955733\pi\) | |||||||
\(44\) | 2.37681 | − | 2.17676i | 0.358317 | − | 0.328159i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.00000 | − | 0.880344i | −0.294884 | − | 0.129800i | ||||
\(47\) | −7.32206 | + | 7.32206i | −1.06803 | + | 1.06803i | −0.0705213 | + | 0.997510i | \(0.522466\pi\) |
−0.997510 | + | 0.0705213i | \(0.977534\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 10.4031i | − | 1.48616i | ||||||
\(50\) | −0.166140 | − | 7.06912i | −0.0234958 | − | 0.999724i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.09158 | − | 0.311549i | −0.983425 | − | 0.0432041i | ||||
\(53\) | 3.11473 | + | 3.11473i | 0.427841 | + | 0.427841i | 0.887892 | − | 0.460051i | \(-0.152169\pi\) |
−0.460051 | + | 0.887892i | \(0.652169\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.94984 | + | 2.06950i | −0.397756 | + | 0.279051i | ||||
\(56\) | −3.78824 | − | 11.1747i | −0.506225 | − | 1.49328i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.26587 | + | 2.43569i | −0.822750 | + | 0.319822i | ||||
\(59\) | − | 1.61148i | − | 0.209797i | −0.994483 | − | 0.104899i | \(-0.966548\pi\) | ||
0.994483 | − | 0.104899i | \(-0.0334518\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.78003i | 0.868093i | 0.900890 | + | 0.434047i | \(0.142915\pi\) | ||||
−0.900890 | + | 0.434047i | \(0.857085\pi\) | |||||||
\(62\) | 2.57184 | + | 6.61613i | 0.326624 | + | 0.840249i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.86493 | − | 6.35078i | −0.608117 | − | 0.793848i | ||||
\(65\) | 7.81695 | + | 1.37102i | 0.969573 | + | 0.170054i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.40312 | + | 7.40312i | 0.904436 | + | 0.904436i | 0.995816 | − | 0.0913805i | \(-0.0291279\pi\) |
−0.0913805 | + | 0.995816i | \(0.529128\pi\) | |||||||
\(68\) | 12.9812 | + | 0.570295i | 1.57421 | + | 0.0691584i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.58365 | + | 12.9366i | 0.308805 | + | 1.54622i | ||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.00000 | − | 5.00000i | 0.585206 | − | 0.585206i | −0.351123 | − | 0.936329i | \(-0.614200\pi\) |
0.936329 | + | 0.351123i | \(0.114200\pi\) | |||||||
\(74\) | 2.02214 | − | 4.59398i | 0.235069 | − | 0.534040i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.40312 | + | 5.89968i | 0.619781 | + | 0.676740i | ||||
\(77\) | 4.75362 | − | 4.75362i | 0.541725 | − | 0.541725i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.01934 | 0.564720 | 0.282360 | − | 0.959309i | \(-0.408883\pi\) | ||||
0.282360 | + | 0.959309i | \(0.408883\pi\) | |||||||
\(80\) | 4.47498 | + | 7.74433i | 0.500318 | + | 0.865842i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −12.1109 | + | 4.70779i | −1.33743 | + | 0.519888i | ||||
\(83\) | 7.57648 | − | 7.57648i | 0.831627 | − | 0.831627i | −0.156112 | − | 0.987739i | \(-0.549896\pi\) |
0.987739 | + | 0.156112i | \(0.0498961\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.3090 | − | 2.50967i | −1.55203 | − | 0.272212i | ||||
\(86\) | −5.96500 | + | 13.5515i | −0.643223 | + | 1.46130i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.01759 | − | 4.08709i | 0.215076 | − | 0.435685i | ||||
\(89\) | − | 2.74204i | − | 0.290655i | −0.989384 | − | 0.145328i | \(-0.953576\pi\) | ||
0.989384 | − | 0.145328i | \(-0.0464236\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.8062 | −1.55212 | ||||||||
\(92\) | −3.08733 | − | 0.135633i | −0.321877 | − | 0.0141408i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.89968 | + | 13.4031i | −0.608506 | + | 1.38243i | ||||
\(95\) | −5.13688 | − | 7.32206i | −0.527032 | − | 0.751227i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.40312 | + | 2.40312i | 0.244000 | + | 0.244000i | 0.818503 | − | 0.574503i | \(-0.194804\pi\) |
−0.574503 | + | 0.818503i | \(0.694804\pi\) | |||||||
\(98\) | −5.33042 | − | 13.7126i | −0.538454 | − | 1.38519i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.84111 | − | 9.23287i | −0.384111 | − | 0.923287i | ||||
\(101\) | − | 8.79790i | − | 0.875424i | −0.899115 | − | 0.437712i | \(-0.855789\pi\) | ||
0.899115 | − | 0.437712i | \(-0.144211\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.96918 | + | 7.96918i | 0.785227 | + | 0.785227i | 0.980707 | − | 0.195481i | \(-0.0626268\pi\) |
−0.195481 | + | 0.980707i | \(0.562627\pi\) | |||||||
\(104\) | −9.50723 | + | 3.22296i | −0.932261 | + | 0.316038i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.70156 | + | 2.50967i | 0.553785 | + | 0.243761i | ||||
\(107\) | 1.61148 | + | 1.61148i | 0.155788 | + | 0.155788i | 0.780697 | − | 0.624909i | \(-0.214864\pi\) |
−0.624909 | + | 0.780697i | \(0.714864\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.7994 | −1.13017 | −0.565087 | − | 0.825031i | \(-0.691157\pi\) | ||||
−0.565087 | + | 0.825031i | \(0.691157\pi\) | |||||||
\(110\) | −2.82788 | + | 4.23932i | −0.269628 | + | 0.404203i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.7192 | − | 12.7887i | −1.01287 | − | 1.20841i | ||||
\(113\) | 4.59398 | − | 4.59398i | 0.432166 | − | 0.432166i | −0.457199 | − | 0.889364i | \(-0.651147\pi\) |
0.889364 | + | 0.457199i | \(0.151147\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.40312 | + | 0.596876i | 0.317343 | + | 0.0556590i | ||||
\(116\) | −7.01121 | + | 6.42110i | −0.650974 | + | 0.596184i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.825702 | − | 2.12414i | −0.0760120 | − | 0.195543i | ||||
\(119\) | 27.1030 | 2.48453 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.40312 | −0.763920 | ||||||||
\(122\) | 3.47399 | + | 8.93694i | 0.314521 | + | 0.809112i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.78003 | + | 7.40312i | 0.608864 | + | 0.664820i | ||||
\(125\) | 2.92310 | + | 10.7915i | 0.261450 | + | 0.965217i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.83019 | − | 3.83019i | 0.339874 | − | 0.339874i | −0.516446 | − | 0.856320i | \(-0.672745\pi\) |
0.856320 | + | 0.516446i | \(0.172745\pi\) | |||||||
\(128\) | −9.66666 | − | 5.87841i | −0.854420 | − | 0.519583i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 11.0062 | − | 2.19812i | 0.965310 | − | 0.192788i | ||||
\(131\) | −13.5415 | −1.18313 | −0.591563 | − | 0.806259i | \(-0.701489\pi\) | ||||
−0.591563 | + | 0.806259i | \(0.701489\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.7994 | + | 11.7994i | 1.02313 | + | 1.02313i | ||||
\(134\) | 13.5515 | + | 5.96500i | 1.17067 | + | 0.515298i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 17.4031 | − | 5.89968i | 1.49231 | − | 0.505894i | ||||
\(137\) | −11.0399 | − | 11.0399i | −0.943203 | − | 0.943203i | 0.0552681 | − | 0.998472i | \(-0.482399\pi\) |
−0.998472 | + | 0.0552681i | \(0.982399\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.00000i | − | 0.339276i | −0.985506 | − | 0.169638i | \(-0.945740\pi\) | ||
0.985506 | − | 0.169638i | \(-0.0542598\pi\) | |||||||
\(140\) | 10.0341 | + | 15.7283i | 0.848038 | + | 1.32928i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.04429 | − | 4.04429i | −0.338200 | − | 0.338200i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.70156 | − | 6.10469i | 0.722625 | − | 0.506967i | ||||
\(146\) | 4.02871 | − | 9.15257i | 0.333418 | − | 0.757472i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.311549 | − | 7.09158i | 0.0256092 | − | 0.582924i | ||||
\(149\) | −8.79790 | −0.720752 | −0.360376 | − | 0.932807i | \(-0.617352\pi\) | ||||
−0.360376 | + | 0.932807i | \(0.617352\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.880344i | 0.0716414i | 0.999358 | + | 0.0358207i | \(0.0114045\pi\) | ||||
−0.999358 | + | 0.0358207i | \(0.988595\pi\) | |||||||
\(152\) | 10.1449 | + | 5.00805i | 0.822862 | + | 0.406206i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.83019 | − | 8.70156i | 0.308645 | − | 0.701192i | ||||
\(155\) | −6.44593 | − | 9.18797i | −0.517750 | − | 0.737995i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.28970 | − | 9.28970i | 0.741398 | − | 0.741398i | −0.231449 | − | 0.972847i | \(-0.574347\pi\) |
0.972847 | + | 0.231449i | \(0.0743465\pi\) | |||||||
\(158\) | 6.61613 | − | 2.57184i | 0.526351 | − | 0.204605i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.86668 | + | 7.91509i | 0.780029 | + | 0.625743i | ||||
\(161\) | −6.44593 | −0.508010 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(164\) | −13.5515 | + | 12.4109i | −1.05820 | + | 0.969131i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.10469 | − | 13.8689i | 0.473816 | − | 1.07643i | ||||
\(167\) | 7.32206 | − | 7.32206i | 0.566598 | − | 0.566598i | −0.364576 | − | 0.931174i | \(-0.618786\pi\) |
0.931174 | + | 0.364576i | \(0.118786\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 0.403124i | − | 0.0310096i | ||||||
\(170\) | −20.1471 | + | 4.02369i | −1.54521 | + | 0.308603i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.919020 | + | 20.9190i | −0.0700746 | + | 1.59506i | ||||
\(173\) | 7.86835 | + | 7.86835i | 0.598220 | + | 0.598220i | 0.939839 | − | 0.341619i | \(-0.110975\pi\) |
−0.341619 | + | 0.939839i | \(0.610975\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.84952 | − | 18.8882i | −0.668961 | − | 1.42781i | ||||
\(176\) | 0.565278 | − | 6.42110i | 0.0426094 | − | 0.484008i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.40498 | − | 3.61436i | −0.105308 | − | 0.270907i | ||||
\(179\) | − | 26.4333i | − | 1.97572i | −0.155343 | − | 0.987861i | \(-0.549648\pi\) | ||
0.155343 | − | 0.987861i | \(-0.450352\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.7994i | − | 0.877040i | −0.898721 | − | 0.438520i | \(-0.855503\pi\) | ||
0.898721 | − | 0.438520i | \(-0.144497\pi\) | |||||||
\(182\) | −19.5165 | + | 7.58652i | −1.44666 | + | 0.562350i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.13899 | + | 1.40312i | −0.305131 | + | 0.103440i | ||||
\(185\) | −1.37102 | + | 7.81695i | −0.100799 | + | 0.574713i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.40312 | + | 7.40312i | 0.541370 | + | 0.541370i | ||||
\(188\) | −0.908956 | + | 20.6899i | −0.0662924 | + | 1.50897i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.5228 | − | 7.01934i | −0.763403 | − | 0.509236i | ||||
\(191\) | 19.0145i | 1.37584i | 0.725787 | + | 0.687919i | \(0.241476\pi\) | ||||
−0.725787 | + | 0.687919i | \(0.758524\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.4031 | + | 12.4031i | −0.892796 | + | 0.892796i | −0.994786 | − | 0.101989i | \(-0.967479\pi\) |
0.101989 | + | 0.994786i | \(0.467479\pi\) | |||||||
\(194\) | 4.39895 | + | 1.93630i | 0.315826 | + | 0.139018i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0523 | − | 15.3438i | −1.00374 | − | 1.09598i | ||||
\(197\) | 9.34420 | − | 9.34420i | 0.665747 | − | 0.665747i | −0.290982 | − | 0.956729i | \(-0.593982\pi\) |
0.956729 | + | 0.290982i | \(0.0939820\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.9577 | −1.48565 | −0.742826 | − | 0.669485i | \(-0.766515\pi\) | ||||
−0.742826 | + | 0.669485i | \(0.766515\pi\) | |||||||
\(200\) | −9.79387 | − | 10.2020i | −0.692531 | − | 0.721388i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.50793 | − | 11.5968i | −0.317177 | − | 0.815945i | ||||
\(203\) | −14.0224 | + | 14.0224i | −0.984181 | + | 0.984181i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.8187 | − | 11.7994i | 1.17467 | − | 0.824103i | ||||
\(206\) | 14.5877 | + | 6.42110i | 1.01637 | + | 0.447379i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −10.8803 | + | 9.11966i | −0.754416 | + | 0.632334i | ||||
\(209\) | 6.44593i | 0.445874i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 8.80131 | + | 0.386661i | 0.604476 | + | 0.0265560i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.94984 | + | 1.29844i | 0.201647 | + | 0.0887594i | ||||
\(215\) | 4.04429 | − | 23.0588i | 0.275818 | − | 1.57259i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.8062 | + | 14.8062i | 1.00511 | + | 1.00511i | ||||
\(218\) | −15.5531 | + | 6.04583i | −1.05339 | + | 0.409475i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.55534 | + | 7.03693i | −0.104861 | + | 0.474430i | ||||
\(221\) | − | 23.0588i | − | 1.55110i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.83019 | + | 3.83019i | 0.256488 | + | 0.256488i | 0.823624 | − | 0.567136i | \(-0.191949\pi\) |
−0.567136 | + | 0.823624i | \(0.691949\pi\) | |||||||
\(224\) | −20.6819 | − | 11.3647i | −1.38187 | − | 0.759338i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.70156 | − | 8.40935i | 0.246224 | − | 0.559382i | ||||
\(227\) | 15.6339 | + | 15.6339i | 1.03766 | + | 1.03766i | 0.999263 | + | 0.0383956i | \(0.0122247\pi\) |
0.0383956 | + | 0.999263i | \(0.487775\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.78003 | 0.448037 | 0.224018 | − | 0.974585i | \(-0.428082\pi\) | ||||
0.224018 | + | 0.974585i | \(0.428082\pi\) | |||||||
\(230\) | 4.79158 | − | 0.956956i | 0.315948 | − | 0.0630998i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.95158 | + | 12.0563i | −0.390741 | + | 0.791533i | ||||
\(233\) | 11.0399 | − | 11.0399i | 0.723249 | − | 0.723249i | −0.246017 | − | 0.969266i | \(-0.579122\pi\) |
0.969266 | + | 0.246017i | \(0.0791218\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | − | 22.8062i | 0.260931 | − | 1.48772i | ||||
\(236\) | −2.17676 | − | 2.37681i | −0.141695 | − | 0.154717i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 35.7253 | − | 13.8872i | 2.31573 | − | 0.900175i | ||||
\(239\) | −8.08857 | −0.523206 | −0.261603 | − | 0.965176i | \(-0.584251\pi\) | ||||
−0.261603 | + | 0.965176i | \(0.584251\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.80625 | −0.438429 | −0.219215 | − | 0.975677i | \(-0.570349\pi\) | ||||
−0.219215 | + | 0.975677i | \(0.570349\pi\) | |||||||
\(242\) | −11.0764 | + | 4.30565i | −0.712017 | + | 0.276777i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.15833 | + | 10.0000i | 0.586302 | + | 0.640184i | ||||
\(245\) | 13.3599 | + | 19.0431i | 0.853532 | + | 1.21662i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.0387 | − | 10.0387i | 0.638746 | − | 0.638746i | ||||
\(248\) | 12.7302 | + | 6.28427i | 0.808368 | + | 0.399051i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.38242 | + | 12.7268i | 0.593396 | + | 0.804911i | ||||
\(251\) | 19.9874 | 1.26159 | 0.630797 | − | 0.775948i | \(-0.282728\pi\) | ||||
0.630797 | + | 0.775948i | \(0.282728\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.76069 | − | 1.76069i | −0.110694 | − | 0.110694i | ||||
\(254\) | 3.08614 | − | 7.01121i | 0.193642 | − | 0.439922i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.7539 | − | 2.79544i | −0.984619 | − | 0.174715i | ||||
\(257\) | −13.7820 | − | 13.7820i | −0.859694 | − | 0.859694i | 0.131607 | − | 0.991302i | \(-0.457986\pi\) |
−0.991302 | + | 0.131607i | \(0.957986\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 14.8062i | − | 0.920016i | ||||||
\(260\) | 13.3813 | − | 8.53684i | 0.829874 | − | 0.529432i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −17.8494 | + | 6.93847i | −1.10274 | + | 0.428660i | ||||
\(263\) | 2.95170 | + | 2.95170i | 0.182009 | + | 0.182009i | 0.792231 | − | 0.610221i | \(-0.208920\pi\) |
−0.610221 | + | 0.792231i | \(0.708920\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.70156 | − | 1.70156i | −0.595962 | − | 0.104526i | ||||
\(266\) | 21.5989 | + | 9.50723i | 1.32431 | + | 0.582926i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 20.9190 | + | 0.919020i | 1.27783 | + | 0.0561381i | ||||
\(269\) | −18.3051 | −1.11608 | −0.558042 | − | 0.829813i | \(-0.688447\pi\) | ||||
−0.558042 | + | 0.829813i | \(0.688447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.6797i | 0.770237i | 0.922867 | + | 0.385119i | \(0.125840\pi\) | ||||
−0.922867 | + | 0.385119i | \(0.874160\pi\) | |||||||
\(272\) | 19.9166 | − | 16.6937i | 1.20762 | − | 1.01220i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.2087 | − | 8.89531i | −1.22085 | − | 0.537386i | ||||
\(275\) | 2.74204 | − | 7.57648i | 0.165351 | − | 0.456879i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.52901 | + | 7.52901i | −0.452374 | + | 0.452374i | −0.896142 | − | 0.443768i | \(-0.853642\pi\) |
0.443768 | + | 0.896142i | \(0.353642\pi\) | |||||||
\(278\) | −2.04955 | − | 5.27251i | −0.122924 | − | 0.316224i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 21.2852 | + | 15.5905i | 1.27203 | + | 0.931713i | ||||
\(281\) | 27.5639 | 1.64432 | 0.822162 | − | 0.569253i | \(-0.192768\pi\) | ||||
0.822162 | + | 0.569253i | \(0.192768\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.40312 | − | 7.40312i | 0.440070 | − | 0.440070i | −0.451965 | − | 0.892035i | \(-0.649277\pi\) |
0.892035 | + | 0.451965i | \(0.149277\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.40312 | − | 3.25865i | −0.437756 | − | 0.192688i | ||||
\(287\) | −27.1030 | + | 27.1030i | −1.59984 | + | 1.59984i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.2094i | 1.48290i | ||||||||
\(290\) | 8.34181 | − | 12.5053i | 0.489848 | − | 0.734337i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.620697 | − | 14.1285i | 0.0363236 | − | 0.826808i | ||||
\(293\) | −3.11473 | − | 3.11473i | −0.181965 | − | 0.181965i | 0.610247 | − | 0.792211i | \(-0.291070\pi\) |
−0.792211 | + | 0.610247i | \(0.791070\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.06950 | + | 2.94984i | 0.120491 | + | 0.171746i | ||||
\(296\) | −3.22296 | − | 9.50723i | −0.187331 | − | 0.552597i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.5968 | + | 4.50793i | −0.671782 | + | 0.261137i | ||||
\(299\) | 5.48408i | 0.317152i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 43.6761i | 2.51745i | ||||||||
\(302\) | 0.451076 | + | 1.16041i | 0.0259565 | + | 0.0667739i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 15.9384 | + | 1.40312i | 0.914128 | + | 0.0804747i | ||||
\(305\) | −8.70704 | − | 12.4109i | −0.498564 | − | 0.710648i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.0000 | − | 20.0000i | −1.14146 | − | 1.14146i | −0.988183 | − | 0.153277i | \(-0.951017\pi\) |
−0.153277 | − | 0.988183i | \(-0.548983\pi\) | |||||||
\(308\) | 0.590111 | − | 13.4323i | 0.0336247 | − | 0.765377i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −13.2043 | − | 8.80811i | −0.749956 | − | 0.500267i | ||||
\(311\) | 8.08857i | 0.458661i | 0.973349 | + | 0.229330i | \(0.0736537\pi\) | ||||
−0.973349 | + | 0.229330i | \(0.926346\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.8062 | + | 19.8062i | −1.11952 | + | 1.11952i | −0.127703 | + | 0.991812i | \(0.540760\pi\) |
−0.991812 | + | 0.127703i | \(0.959240\pi\) | |||||||
\(314\) | 7.48509 | − | 17.0049i | 0.422408 | − | 0.959643i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.40312 | − | 6.78003i | 0.416458 | − | 0.381406i | ||||
\(317\) | 4.59058 | − | 4.59058i | 0.257833 | − | 0.257833i | −0.566339 | − | 0.824172i | \(-0.691641\pi\) |
0.824172 | + | 0.566339i | \(0.191641\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.66037 | −0.428898 | ||||||||
\(320\) | 17.0611 | + | 5.37755i | 0.953746 | + | 0.300614i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.49656 | + | 3.30281i | −0.473495 | + | 0.184058i | ||||
\(323\) | −18.3759 | + | 18.3759i | −1.02246 | + | 1.02246i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.0697 | + | 7.52901i | −0.891388 | + | 0.417634i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −11.5034 | + | 23.3028i | −0.635171 | + | 1.28668i | ||||
\(329\) | 43.1978i | 2.38157i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.80625 | 0.154245 | 0.0771227 | − | 0.997022i | \(-0.475427\pi\) | ||||
0.0771227 | + | 0.997022i | \(0.475427\pi\) | |||||||
\(332\) | 0.940541 | − | 21.4089i | 0.0516189 | − | 1.17497i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.89968 | − | 13.4031i | 0.322816 | − | 0.733386i | ||||
\(335\) | −23.0588 | − | 4.04429i | −1.25983 | − | 0.220963i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.40312 | − | 2.40312i | −0.130907 | − | 0.130907i | 0.638618 | − | 0.769524i | \(-0.279507\pi\) |
−0.769524 | + | 0.638618i | \(0.779507\pi\) | |||||||
\(338\) | −0.206555 | − | 0.531369i | −0.0112351 | − | 0.0289027i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −24.4947 | + | 15.6268i | −1.32841 | + | 0.847483i | ||||
\(341\) | 8.08857i | 0.438021i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0387 | − | 10.0387i | −0.542038 | − | 0.542038i | ||||
\(344\) | 9.50723 | + | 28.0448i | 0.512596 | + | 1.51208i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.4031 | + | 6.33985i | 0.774317 | + | 0.340833i | ||||
\(347\) | −2.74204 | − | 2.74204i | −0.147200 | − | 0.147200i | 0.629666 | − | 0.776866i | \(-0.283192\pi\) |
−0.776866 | + | 0.629666i | \(0.783192\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.78003 | −0.362926 | −0.181463 | − | 0.983398i | \(-0.558083\pi\) | ||||
−0.181463 | + | 0.983398i | \(0.558083\pi\) | |||||||
\(350\) | −21.3429 | − | 20.3627i | −1.14082 | − | 1.08843i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.54497 | − | 8.75346i | −0.135648 | − | 0.466561i | ||||
\(353\) | −13.7820 | + | 13.7820i | −0.733539 | + | 0.733539i | −0.971319 | − | 0.237780i | \(-0.923580\pi\) |
0.237780 | + | 0.971319i | \(0.423580\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.70389 | − | 4.04429i | −0.196306 | − | 0.214347i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.5441 | − | 34.8425i | −0.715827 | − | 1.84148i | ||||
\(359\) | 35.1916 | 1.85734 | 0.928671 | − | 0.370904i | \(-0.120952\pi\) | ||||
0.928671 | + | 0.370904i | \(0.120952\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | −6.04583 | − | 15.5531i | −0.317762 | − | 0.817451i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −21.8380 | + | 20.0000i | −1.14462 | + | 1.04828i | ||||
\(365\) | −2.73147 | + | 15.5737i | −0.142972 | + | 0.815163i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.7492 | + | 14.7492i | −0.769902 | + | 0.769902i | −0.978089 | − | 0.208187i | \(-0.933244\pi\) |
0.208187 | + | 0.978089i | \(0.433244\pi\) | |||||||
\(368\) | −4.73678 | + | 3.97026i | −0.246922 | + | 0.206964i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.19812 | + | 11.0062i | 0.114275 | + | 0.572186i | ||||
\(371\) | 18.3759 | 0.954031 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.3090 | + | 14.3090i | 0.740894 | + | 0.740894i | 0.972750 | − | 0.231856i | \(-0.0744799\pi\) |
−0.231856 | + | 0.972750i | \(0.574480\pi\) | |||||||
\(374\) | 13.5515 | + | 5.96500i | 0.700733 | + | 0.308443i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.40312 | + | 27.7377i | 0.484929 | + | 1.43046i | ||||
\(377\) | 11.9300 | + | 11.9300i | 0.614427 | + | 0.614427i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 18.8062i | − | 0.966012i | −0.875617 | − | 0.483006i | \(-0.839545\pi\) | ||
0.875617 | − | 0.483006i | \(-0.160455\pi\) | |||||||
\(380\) | −17.4670 | − | 3.86065i | −0.896037 | − | 0.198047i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.74275 | + | 25.0635i | 0.498483 | + | 1.28236i | ||||
\(383\) | −26.0105 | − | 26.0105i | −1.32907 | − | 1.32907i | −0.906180 | − | 0.422892i | \(-0.861015\pi\) |
−0.422892 | − | 0.906180i | \(-0.638985\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.59688 | + | 14.8062i | −0.132349 | + | 0.754596i | ||||
\(386\) | −9.99371 | + | 22.7041i | −0.508666 | + | 1.15561i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.79051 | + | 0.298323i | 0.344736 | + | 0.0151450i | ||||
\(389\) | −37.3196 | −1.89218 | −0.946090 | − | 0.323905i | \(-0.895004\pi\) | ||||
−0.946090 | + | 0.323905i | \(0.895004\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10.0387i | − | 0.507678i | ||||||
\(392\) | −26.3847 | − | 13.0248i | −1.33263 | − | 0.657853i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.52901 | − | 17.1047i | 0.379306 | − | 0.861722i | ||||
\(395\) | −9.18797 | + | 6.44593i | −0.462297 | + | 0.324330i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.3284 | − | 19.3284i | 0.970063 | − | 0.970063i | −0.0295016 | − | 0.999565i | \(-0.509392\pi\) |
0.999565 | + | 0.0295016i | \(0.00939202\pi\) | |||||||
\(398\) | −27.6249 | + | 10.7384i | −1.38471 | + | 0.538269i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18.1369 | − | 8.42925i | −0.906846 | − | 0.421462i | ||||
\(401\) | −12.8919 | −0.643789 | −0.321894 | − | 0.946776i | \(-0.604320\pi\) | ||||
−0.321894 | + | 0.946776i | \(0.604320\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.5969 | − | 12.5969i | 0.627495 | − | 0.627495i | ||||
\(404\) | −11.8840 | − | 12.9762i | −0.591253 | − | 0.645591i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.2984 | + | 25.6682i | −0.560732 | + | 1.27389i | ||||
\(407\) | 4.04429 | − | 4.04429i | 0.200468 | − | 0.200468i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.40312i | 0.168274i | 0.996454 | + | 0.0841368i | \(0.0268133\pi\) | ||||
−0.996454 | + | 0.0841368i | \(0.973187\pi\) | |||||||
\(410\) | 16.1234 | − | 24.1707i | 0.796276 | − | 1.19371i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 22.5185 | + | 0.989290i | 1.10941 | + | 0.0487388i | ||||
\(413\) | −4.75362 | − | 4.75362i | −0.233910 | − | 0.233910i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.13899 | + | 23.5987i | −0.203175 | + | 1.15842i | ||||
\(416\) | −9.66889 | + | 17.5958i | −0.474057 | + | 0.862706i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.30281 | + | 8.49656i | 0.161546 | + | 0.415580i | ||||
\(419\) | 31.9174i | 1.55927i | 0.626235 | + | 0.779634i | \(0.284595\pi\) | ||||
−0.626235 | + | 0.779634i | \(0.715405\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 30.3788i | − | 1.48057i | −0.672293 | − | 0.740285i | \(-0.734691\pi\) | ||
0.672293 | − | 0.740285i | \(-0.265309\pi\) | |||||||
\(422\) | 15.8175 | − | 6.14864i | 0.769985 | − | 0.299311i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.7994 | − | 4.00000i | 0.573028 | − | 0.194257i | ||||
\(425\) | 29.4158 | − | 13.7820i | 1.42688 | − | 0.668523i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.0000 | + | 20.0000i | 0.967868 | + | 0.967868i | ||||
\(428\) | 4.55357 | + | 0.200049i | 0.220105 | + | 0.00966971i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.48410 | − | 32.4666i | −0.312691 | − | 1.56568i | ||||
\(431\) | 27.1030i | 1.30551i | 0.757570 | + | 0.652754i | \(0.226386\pi\) | ||||
−0.757570 | + | 0.652754i | \(0.773614\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.4031 | − | 12.4031i | 0.596056 | − | 0.596056i | −0.343205 | − | 0.939261i | \(-0.611512\pi\) |
0.939261 | + | 0.343205i | \(0.111512\pi\) | |||||||
\(434\) | 27.1030 | + | 11.9300i | 1.30099 | + | 0.572659i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.4031 | + | 15.9384i | −0.833458 | + | 0.763309i | ||||
\(437\) | 4.37036 | − | 4.37036i | 0.209063 | − | 0.209063i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.9190 | 0.521136 | 0.260568 | − | 0.965455i | \(-0.416090\pi\) | ||||
0.260568 | + | 0.965455i | \(0.416090\pi\) | |||||||
\(440\) | 1.55549 | + | 10.0725i | 0.0741549 | + | 0.480188i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.8150 | − | 30.3944i | −0.561982 | − | 1.44571i | ||||
\(443\) | 15.6339 | − | 15.6339i | 0.742789 | − | 0.742789i | −0.230325 | − | 0.973114i | \(-0.573979\pi\) |
0.973114 | + | 0.230325i | \(0.0739789\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.52138 | + | 5.01934i | 0.166929 | + | 0.237939i | ||||
\(446\) | 7.01121 | + | 3.08614i | 0.331990 | + | 0.146133i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −33.0846 | − | 4.38301i | −1.56310 | − | 0.207078i | ||||
\(449\) | 6.44593i | 0.304202i | 0.988365 | + | 0.152101i | \(0.0486039\pi\) | ||||
−0.988365 | + | 0.152101i | \(0.951396\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.8062 | −0.697199 | ||||||||
\(452\) | 0.570295 | − | 12.9812i | 0.0268244 | − | 0.610586i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 28.6181 | + | 12.5969i | 1.34311 | + | 0.591201i | ||||
\(455\) | 27.1030 | − | 19.0145i | 1.27061 | − | 0.891412i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.80625 | − | 9.80625i | −0.458717 | − | 0.458717i | 0.439517 | − | 0.898234i | \(-0.355150\pi\) |
−0.898234 | + | 0.439517i | \(0.855150\pi\) | |||||||
\(458\) | 8.93694 | − | 3.47399i | 0.417596 | − | 0.162329i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.82559 | − | 3.71653i | 0.271619 | − | 0.173284i | ||||
\(461\) | 18.3051i | 0.852555i | 0.904592 | + | 0.426278i | \(0.140175\pi\) | ||||
−0.904592 | + | 0.426278i | \(0.859825\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.7492 | − | 14.7492i | −0.685454 | − | 0.685454i | 0.275770 | − | 0.961224i | \(-0.411067\pi\) |
−0.961224 | + | 0.275770i | \(0.911067\pi\) | |||||||
\(464\) | −1.66748 | + | 18.9412i | −0.0774108 | + | 0.879324i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.89531 | − | 20.2087i | 0.412067 | − | 0.936151i | ||||
\(467\) | −10.7994 | − | 10.7994i | −0.499739 | − | 0.499739i | 0.411618 | − | 0.911357i | \(-0.364964\pi\) |
−0.911357 | + | 0.411618i | \(0.864964\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 43.6761 | 2.01677 | ||||||||
\(470\) | −6.41310 | − | 32.1111i | −0.295814 | − | 1.48117i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.08709 | − | 2.01759i | −0.188124 | − | 0.0928673i | ||||
\(473\) | −11.9300 | + | 11.9300i | −0.548542 | + | 0.548542i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.8062 | + | 6.80625i | 0.862890 | + | 0.312292i | ||||
\(476\) | 39.9748 | − | 36.6103i | 1.83224 | − | 1.67803i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.6618 | + | 4.14448i | −0.487658 | + | 0.189564i | ||||
\(479\) | −8.08857 | −0.369576 | −0.184788 | − | 0.982778i | \(-0.559160\pi\) | ||||
−0.184788 | + | 0.982778i | \(0.559160\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.5969 | −0.574368 | ||||||||
\(482\) | −8.97150 | + | 3.48743i | −0.408641 | + | 0.158848i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.3939 | + | 11.3508i | −0.563361 | + | 0.515945i | ||||
\(485\) | −7.48509 | − | 1.31281i | −0.339880 | − | 0.0596118i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.06950 | + | 2.06950i | −0.0937778 | + | 0.0937778i | −0.752439 | − | 0.658662i | \(-0.771123\pi\) |
0.658662 | + | 0.752439i | \(0.271123\pi\) | |||||||
\(488\) | 17.1957 | + | 8.48867i | 0.778413 | + | 0.384264i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 27.3674 | + | 18.2558i | 1.23634 | + | 0.824711i | ||||
\(491\) | 11.2804 | 0.509076 | 0.254538 | − | 0.967063i | \(-0.418077\pi\) | ||||
0.254538 | + | 0.967063i | \(0.418077\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.8380 | − | 21.8380i | −0.983536 | − | 0.983536i | ||||
\(494\) | 8.08857 | − | 18.3759i | 0.363922 | − | 0.826772i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.0000 | + | 1.76069i | 0.898027 | + | 0.0790573i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.8062i | 0.841883i | 0.907088 | + | 0.420942i | \(0.138300\pi\) | ||||
−0.907088 | + | 0.420942i | \(0.861700\pi\) | |||||||
\(500\) | 18.8882 | + | 11.9681i | 0.844708 | + | 0.535228i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 26.3460 | − | 10.2413i | 1.17588 | − | 0.457091i | ||||
\(503\) | 5.13688 | + | 5.13688i | 0.229042 | + | 0.229042i | 0.812292 | − | 0.583250i | \(-0.198219\pi\) |
−0.583250 | + | 0.812292i | \(0.698219\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.2984 | + | 16.1047i | 0.502774 | + | 0.716649i | ||||
\(506\) | −3.22296 | − | 1.41866i | −0.143278 | − | 0.0630671i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.475477 | − | 10.8230i | 0.0210959 | − | 0.480191i | ||||
\(509\) | −12.8422 | −0.569220 | −0.284610 | − | 0.958643i | \(-0.591864\pi\) | ||||
−0.284610 | + | 0.958643i | \(0.591864\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 29.4984i | − | 1.30493i | ||||||
\(512\) | −22.1980 | + | 4.38734i | −0.981022 | + | 0.193895i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −25.2281 | − | 11.1047i | −1.11276 | − | 0.489807i | ||||
\(515\) | −24.8219 | − | 4.35352i | −1.09378 | − | 0.191839i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.7994 | + | 11.7994i | −0.518935 | + | 0.518935i | ||||
\(518\) | −7.58652 | − | 19.5165i | −0.333333 | − | 0.857507i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 13.2641 | − | 18.1091i | 0.581671 | − | 0.794135i | ||||
\(521\) | −6.44593 | −0.282401 | −0.141201 | − | 0.989981i | \(-0.545096\pi\) | ||||
−0.141201 | + | 0.989981i | \(0.545096\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.19375 | + | 5.19375i | −0.227107 | + | 0.227107i | −0.811483 | − | 0.584376i | \(-0.801339\pi\) |
0.584376 | + | 0.811483i | \(0.301339\pi\) | |||||||
\(524\) | −19.9726 | + | 18.2916i | −0.872508 | + | 0.799072i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.40312 | + | 2.37830i | 0.235587 | + | 0.103699i | ||||
\(527\) | −23.0588 | + | 23.0588i | −1.00446 | + | 1.00446i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 20.6125i | − | 0.896196i | ||||||
\(530\) | −13.6598 | + | 2.72807i | −0.593342 | + | 0.118500i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 33.3415 | + | 1.46477i | 1.44554 | + | 0.0635057i | ||||
\(533\) | 23.0588 | + | 23.0588i | 0.998786 | + | 0.998786i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.01934 | − | 0.880344i | −0.217005 | − | 0.0380606i | ||||
\(536\) | 28.0448 | − | 9.50723i | 1.21135 | − | 0.410650i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −24.1285 | + | 9.37930i | −1.04025 | + | 0.404370i | ||||
\(539\) | − | 16.7645i | − | 0.722096i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 8.27799i | − | 0.355898i | −0.984040 | − | 0.177949i | \(-0.943054\pi\) | ||
0.984040 | − | 0.177949i | \(-0.0569463\pi\) | |||||||
\(542\) | 6.49691 | + | 16.7135i | 0.279066 | + | 0.717905i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 17.6990 | − | 32.2094i | 0.758840 | − | 1.38097i | ||||
\(545\) | 21.5989 | − | 15.1530i | 0.925195 | − | 0.649082i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.2094 | − | 22.2094i | −0.949604 | − | 0.949604i | 0.0491855 | − | 0.998790i | \(-0.484337\pi\) |
−0.998790 | + | 0.0491855i | \(0.984337\pi\) | |||||||
\(548\) | −31.1955 | − | 1.37049i | −1.33261 | − | 0.0585444i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.267732 | − | 11.3918i | −0.0114161 | − | 0.485746i | ||||
\(551\) | − | 19.0145i | − | 0.810044i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.8062 | − | 14.8062i | 0.629626 | − | 0.629626i | ||||
\(554\) | −6.06643 | + | 13.7820i | −0.257738 | + | 0.585539i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.40312 | − | 5.89968i | −0.229144 | − | 0.250202i | ||||
\(557\) | 13.7146 | − | 13.7146i | 0.581104 | − | 0.581104i | −0.354102 | − | 0.935207i | \(-0.615214\pi\) |
0.935207 | + | 0.354102i | \(0.115214\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 37.1588 | 1.57165 | ||||||||
\(560\) | 36.0450 | + | 9.64406i | 1.52318 | + | 0.407536i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 36.3327 | − | 14.1234i | 1.53260 | − | 0.595758i | ||||
\(563\) | 2.74204 | − | 2.74204i | 0.115563 | − | 0.115563i | −0.646960 | − | 0.762524i | \(-0.723960\pi\) |
0.762524 | + | 0.646960i | \(0.223960\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.50967 | + | 14.3090i | −0.105583 | + | 0.601986i | ||||
\(566\) | 5.96500 | − | 13.5515i | 0.250728 | − | 0.569613i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 36.7519i | − | 1.54072i | −0.637610 | − | 0.770359i | \(-0.720077\pi\) | ||
0.637610 | − | 0.770359i | \(-0.279923\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.6125 | 0.737060 | 0.368530 | − | 0.929616i | \(-0.379861\pi\) | ||||
0.368530 | + | 0.929616i | \(0.379861\pi\) | |||||||
\(572\) | −11.4279 | − | 0.502056i | −0.477827 | − | 0.0209920i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −21.8380 | + | 49.6125i | −0.911502 | + | 2.07079i | ||||
\(575\) | −6.99599 | + | 3.27777i | −0.291753 | + | 0.136692i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.4031 | + | 12.4031i | 0.516349 | + | 0.516349i | 0.916465 | − | 0.400116i | \(-0.131030\pi\) |
−0.400116 | + | 0.916465i | \(0.631030\pi\) | |||||||
\(578\) | 12.9169 | + | 33.2292i | 0.537274 | + | 1.38215i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.58802 | − | 20.7578i | 0.190507 | − | 0.861922i | ||||
\(581\) | − | 44.6989i | − | 1.85442i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.01934 | + | 5.01934i | 0.207880 | + | 0.207880i | ||||
\(584\) | −6.42110 | − | 18.9412i | −0.265707 | − | 0.783793i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.70156 | − | 2.50967i | −0.235529 | − | 0.103673i | ||||
\(587\) | −1.61148 | − | 1.61148i | −0.0665130 | − | 0.0665130i | 0.673068 | − | 0.739581i | \(-0.264976\pi\) |
−0.739581 | + | 0.673068i | \(0.764976\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.0774 | −0.827273 | ||||||||
\(590\) | 4.23932 | + | 2.82788i | 0.174530 | + | 0.116422i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.11966 | − | 10.8803i | −0.374816 | − | 0.447179i | ||||
\(593\) | −4.59398 | + | 4.59398i | −0.188652 | + | 0.188652i | −0.795113 | − | 0.606461i | \(-0.792589\pi\) |
0.606461 | + | 0.795113i | \(0.292589\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −49.6125 | + | 34.8062i | −2.03391 | + | 1.42692i | ||||
\(596\) | −12.9762 | + | 11.8840i | −0.531526 | + | 0.486789i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.80997 | + | 7.22871i | 0.114908 | + | 0.295604i | ||||
\(599\) | 27.1030 | 1.10740 | 0.553700 | − | 0.832716i | \(-0.313215\pi\) | ||||
0.553700 | + | 0.832716i | \(0.313215\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.2094 | 0.824358 | 0.412179 | − | 0.911103i | \(-0.364768\pi\) | ||||
0.412179 | + | 0.911103i | \(0.364768\pi\) | |||||||
\(602\) | 22.3790 | + | 57.5706i | 0.912101 | + | 2.34640i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.18915 | + | 1.29844i | 0.0483859 | + | 0.0528327i | ||||
\(605\) | 15.3820 | − | 10.7915i | 0.625369 | − | 0.438735i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.8882 | − | 18.8882i | 0.766648 | − | 0.766648i | −0.210867 | − | 0.977515i | \(-0.567629\pi\) |
0.977515 | + | 0.210867i | \(0.0676285\pi\) | |||||||
\(608\) | 21.7277 | − | 6.31710i | 0.881176 | − | 0.256192i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −17.8362 | − | 11.8978i | −0.722166 | − | 0.481729i | ||||
\(611\) | 36.7519 | 1.48682 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.3284 | − | 19.3284i | −0.780666 | − | 0.780666i | 0.199278 | − | 0.979943i | \(-0.436140\pi\) |
−0.979943 | + | 0.199278i | \(0.936140\pi\) | |||||||
\(614\) | −36.6103 | − | 16.1148i | −1.47747 | − | 0.650341i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.10469 | − | 18.0079i | −0.245965 | − | 0.725557i | ||||
\(617\) | −7.33602 | − | 7.33602i | −0.295337 | − | 0.295337i | 0.543847 | − | 0.839184i | \(-0.316967\pi\) |
−0.839184 | + | 0.543847i | \(0.816967\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.8062i | 0.434340i | 0.976134 | + | 0.217170i | \(0.0696826\pi\) | ||||
−0.976134 | + | 0.217170i | \(0.930317\pi\) | |||||||
\(620\) | −21.9182 | − | 4.84448i | −0.880255 | − | 0.194559i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.14448 | + | 10.6618i | 0.166178 | + | 0.427498i | ||||
\(623\) | −8.08857 | − | 8.08857i | −0.324062 | − | 0.324062i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.2094 | − | 16.0000i | −0.768375 | − | 0.640000i | ||||
\(626\) | −15.9587 | + | 36.2556i | −0.637838 | + | 1.44907i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.15322 | − | 26.2499i | 0.0460184 | − | 1.04749i | ||||
\(629\) | 23.0588 | 0.919413 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.0967i | 0.999083i | 0.866290 | + | 0.499542i | \(0.166498\pi\) | ||||
−0.866290 | + | 0.499542i | \(0.833502\pi\) | |||||||
\(632\) | 6.28427 | − | 12.7302i | 0.249975 | − | 0.506380i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.69882 | − | 8.40312i | 0.146899 | − | 0.333731i | ||||
\(635\) | −2.09241 | + | 11.9300i | −0.0830348 | + | 0.473428i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.1084 | + | 26.1084i | −1.03445 | + | 1.03445i | ||||
\(638\) | −10.0973 | + | 3.92507i | −0.399758 | + | 0.155395i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 25.2441 | − | 1.65359i | 0.997862 | − | 0.0653638i | ||||
\(641\) | −2.74204 | −0.108304 | −0.0541520 | − | 0.998533i | \(-0.517246\pi\) | ||||
−0.0541520 | + | 0.998533i | \(0.517246\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(644\) | −9.50723 | + | 8.70704i | −0.374638 | + | 0.343105i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.8062 | + | 33.6374i | −0.582544 | + | 1.32345i | ||||
\(647\) | 19.7810 | − | 19.7810i | 0.777671 | − | 0.777671i | −0.201763 | − | 0.979434i | \(-0.564667\pi\) |
0.979434 | + | 0.201763i | \(0.0646672\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 2.59688i | − | 0.101936i | ||||||
\(650\) | −17.3242 | + | 18.1581i | −0.679510 | + | 0.712219i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.1904 | + | 15.1904i | 0.594447 | + | 0.594447i | 0.938829 | − | 0.344383i | \(-0.111912\pi\) |
−0.344383 | + | 0.938829i | \(0.611912\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.7879 | − | 17.3902i | 0.968543 | − | 0.679493i | ||||
\(656\) | −3.22296 | + | 36.6103i | −0.125836 | + | 1.42939i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 22.1340 | + | 56.9402i | 0.862872 | + | 2.21976i | ||||
\(659\) | − | 4.83445i | − | 0.188323i | −0.995557 | − | 0.0941617i | \(-0.969983\pi\) | ||
0.995557 | − | 0.0941617i | \(-0.0300171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 26.8574i | − | 1.04463i | −0.852752 | − | 0.522315i | \(-0.825068\pi\) | ||
0.852752 | − | 0.522315i | \(-0.174932\pi\) | |||||||
\(662\) | 3.69899 | − | 1.43788i | 0.143765 | − | 0.0558849i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.72987 | − | 28.7016i | −0.377592 | − | 1.11384i | ||||
\(665\) | −36.7519 | − | 6.44593i | −1.42518 | − | 0.249962i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.19375 | + | 5.19375i | 0.201103 | + | 0.201103i | ||||
\(668\) | 0.908956 | − | 20.6899i | 0.0351686 | − | 0.800518i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −32.4666 | + | 6.48410i | −1.25429 | + | 0.250503i | ||||
\(671\) | 10.9259i | 0.421789i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.0000 | − | 15.0000i | 0.578208 | − | 0.578208i | −0.356202 | − | 0.934409i | \(-0.615928\pi\) |
0.934409 | + | 0.356202i | \(0.115928\pi\) | |||||||
\(674\) | −4.39895 | − | 1.93630i | −0.169441 | − | 0.0745833i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.544533 | − | 0.594576i | −0.0209436 | − | 0.0228683i | ||||
\(677\) | 18.1421 | − | 18.1421i | 0.697258 | − | 0.697258i | −0.266560 | − | 0.963818i | \(-0.585887\pi\) |
0.963818 | + | 0.266560i | \(0.0858872\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.1777 | 0.544089 | ||||||||
\(680\) | −24.2802 | + | 33.1489i | −0.931102 | + | 1.27120i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.14448 | + | 10.6618i | 0.158700 | + | 0.408260i | ||||
\(683\) | 1.13056 | − | 1.13056i | 0.0432595 | − | 0.0432595i | −0.685146 | − | 0.728406i | \(-0.740262\pi\) |
0.728406 | + | 0.685146i | \(0.240262\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34.3864 | + | 6.03105i | 1.31384 | + | 0.230434i | ||||
\(686\) | −18.3759 | − | 8.08857i | −0.701596 | − | 0.308823i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 26.9015 | + | 32.0953i | 1.02561 | + | 1.22362i | ||||
\(689\) | − | 15.6339i | − | 0.595604i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.0000 | 1.06517 | 0.532585 | − | 0.846376i | \(-0.321221\pi\) | ||||
0.532585 | + | 0.846376i | \(0.321221\pi\) | |||||||
\(692\) | 22.2336 | + | 0.976773i | 0.845195 | + | 0.0371313i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.01934 | − | 2.20937i | −0.190531 | − | 0.0838666i | ||||
\(695\) | 5.13688 | + | 7.32206i | 0.194853 | + | 0.277741i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −42.2094 | − | 42.2094i | −1.59879 | − | 1.59879i | ||||
\(698\) | −8.93694 | + | 3.47399i | −0.338268 | + | 0.131493i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −38.5662 | − | 15.9048i | −1.45766 | − | 0.601146i | ||||
\(701\) | − | 3.33496i | − | 0.125960i | −0.998015 | − | 0.0629798i | \(-0.979940\pi\) | ||
0.998015 | − | 0.0629798i | \(-0.0200604\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.0387 | + | 10.0387i | 0.378616 | + | 0.378616i | ||||
\(704\) | −7.83976 | − | 10.2342i | −0.295472 | − | 0.385715i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.1047 | + | 25.2281i | −0.417930 | + | 0.949470i | ||||
\(707\) | −25.9524 | − | 25.9524i | −0.976041 | − | 0.976041i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.8574 | −1.00865 | −0.504325 | − | 0.863514i | \(-0.668259\pi\) | ||||
−0.504325 | + | 0.863514i | \(0.668259\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.95444 | − | 3.43306i | −0.260629 | − | 0.128659i | ||||
\(713\) | 5.48408 | − | 5.48408i | 0.205380 | − | 0.205380i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.5969 | + | 2.20937i | 0.471096 | + | 0.0826259i | ||||
\(716\) | −35.7057 | − | 38.9871i | −1.33438 | − | 1.45702i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 46.3870 | − | 18.0317i | 1.73115 | − | 0.672937i | ||||
\(719\) | −8.08857 | −0.301653 | −0.150826 | − | 0.988560i | \(-0.548193\pi\) | ||||
−0.150826 | + | 0.988560i | \(0.548193\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 47.0156 | 1.75095 | ||||||||
\(722\) | 3.95438 | − | 1.53716i | 0.147167 | − | 0.0572071i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −15.9384 | − | 17.4031i | −0.592344 | − | 0.646782i | ||||
\(725\) | −8.08857 | + | 22.3494i | −0.300402 | + | 0.830037i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.7069 | + | 35.7069i | −1.32430 | + | 1.32430i | −0.414034 | + | 0.910261i | \(0.635881\pi\) |
−0.910261 | + | 0.414034i | \(0.864119\pi\) | |||||||
\(728\) | −18.5376 | + | 37.5521i | −0.687049 | + | 1.39177i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.37930 | + | 21.9276i | 0.162085 | + | 0.811579i | ||||
\(731\) | −68.0197 | −2.51580 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.50967 | − | 2.50967i | −0.0926967 | − | 0.0926967i | 0.659238 | − | 0.751935i | \(-0.270879\pi\) |
−0.751935 | + | 0.659238i | \(0.770879\pi\) | |||||||
\(734\) | −11.8840 | + | 26.9986i | −0.438648 | + | 0.996537i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.20937 | + | 7.66037i | −0.155160 | + | 0.282365i | ||||
\(737\) | 11.9300 | + | 11.9300i | 0.439447 | + | 0.439447i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.4187i | 1.78111i | 0.454873 | + | 0.890556i | \(0.349685\pi\) | ||||
−0.454873 | + | 0.890556i | \(0.650315\pi\) | |||||||
\(740\) | 8.53684 | + | 13.3813i | 0.313821 | + | 0.491907i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 24.2218 | − | 9.41558i | 0.889211 | − | 0.345657i | ||||
\(743\) | 9.18116 | + | 9.18116i | 0.336824 | + | 0.336824i | 0.855171 | − | 0.518346i | \(-0.173452\pi\) |
−0.518346 | + | 0.855171i | \(0.673452\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.1047 | − | 11.2984i | 0.590030 | − | 0.413943i | ||||
\(746\) | 26.1929 | + | 11.5294i | 0.958990 | + | 0.422121i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 20.9190 | + | 0.919020i | 0.764875 | + | 0.0336027i | ||||
\(749\) | 9.50723 | 0.347387 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.0580i | 0.549475i | 0.961519 | + | 0.274737i | \(0.0885909\pi\) | ||||
−0.961519 | + | 0.274737i | \(0.911409\pi\) | |||||||
\(752\) | 26.6069 | + | 31.7438i | 0.970256 | + | 1.15758i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 21.8380 | + | 9.61250i | 0.795294 | + | 0.350066i | ||||
\(755\) | −1.13056 | − | 1.61148i | −0.0411451 | − | 0.0586479i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.0504 | + | 11.0504i | −0.401633 | + | 0.401633i | −0.878808 | − | 0.477175i | \(-0.841661\pi\) |
0.477175 | + | 0.878808i | \(0.341661\pi\) | |||||||
\(758\) | −9.63606 | − | 24.7890i | −0.349998 | − | 0.900378i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −25.0019 | + | 3.86101i | −0.906913 | + | 0.140053i | ||||
\(761\) | −43.1978 | −1.56592 | −0.782960 | − | 0.622073i | \(-0.786291\pi\) | ||||
−0.782960 | + | 0.622073i | \(0.786291\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.8062 | + | 34.8062i | −1.26007 | + | 1.26007i | ||||
\(764\) | 25.6844 | + | 28.0448i | 0.929228 | + | 1.01463i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −47.6125 | − | 20.9577i | −1.72031 | − | 0.757232i | ||||
\(767\) | −4.04429 | + | 4.04429i | −0.146031 | + | 0.146031i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.40312i | 0.0505980i | 0.999680 | + | 0.0252990i | \(0.00805377\pi\) | ||||
−0.999680 | + | 0.0252990i | \(0.991946\pi\) | |||||||
\(770\) | 4.16351 | + | 20.8471i | 0.150042 | + | 0.751278i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.53972 | + | 35.0475i | −0.0554156 | + | 1.26139i | ||||
\(773\) | −25.4642 | − | 25.4642i | −0.915882 | − | 0.915882i | 0.0808446 | − | 0.996727i | \(-0.474238\pi\) |
−0.996727 | + | 0.0808446i | \(0.974238\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.5987 | + | 8.54071i | 0.847691 | + | 0.306792i | ||||
\(776\) | 9.10362 | − | 3.08614i | 0.326801 | − | 0.110786i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −49.1920 | + | 19.1221i | −1.76362 | + | 0.685559i | ||||
\(779\) | − | 36.7519i | − | 1.31677i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −5.14368 | − | 13.2323i | −0.183938 | − | 0.473184i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −41.4522 | − | 3.64922i | −1.48043 | − | 0.130329i | ||||
\(785\) | −5.07491 | + | 28.9349i | −0.181131 | + | 1.03273i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.0000 | − | 20.0000i | −0.712923 | − | 0.712923i | 0.254223 | − | 0.967146i | \(-0.418180\pi\) |
−0.967146 | + | 0.254223i | \(0.918180\pi\) | |||||||
\(788\) | 1.15998 | − | 26.4039i | 0.0413227 | − | 0.940601i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.80811 | + | 13.2043i | −0.313378 | + | 0.469790i | ||||
\(791\) | − | 27.1030i | − | 0.963673i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.0156 | − | 17.0156i | 0.604242 | − | 0.604242i | ||||
\(794\) | 15.5737 | − | 35.3809i | 0.552689 | − | 1.25562i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −30.9109 | + | 28.3093i | −1.09561 | + | 1.00340i | ||||
\(797\) | −6.00924 | + | 6.00924i | −0.212858 | + | 0.212858i | −0.805481 | − | 0.592622i | \(-0.798093\pi\) |
0.592622 | + | 0.805481i | \(0.298093\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −67.2748 | −2.38001 | ||||||||
\(800\) | −28.2258 | − | 1.81771i | −0.997933 | − | 0.0642658i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −16.9931 | + | 6.60561i | −0.600048 | + | 0.233252i | ||||
\(803\) | 8.05741 | − | 8.05741i | 0.284340 | − | 0.284340i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.7994 | − | 8.27799i | 0.415873 | − | 0.291761i | ||||
\(806\) | 10.1498 | − | 23.0588i | 0.357512 | − | 0.812210i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −22.3135 | − | 11.0151i | −0.784987 | − | 0.387509i | ||||
\(809\) | − | 2.74204i | − | 0.0964049i | −0.998838 | − | 0.0482025i | \(-0.984651\pi\) | ||
0.998838 | − | 0.0482025i | \(-0.0153493\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.8062 | −1.50313 | −0.751565 | − | 0.659659i | \(-0.770701\pi\) | ||||
−0.751565 | + | 0.659659i | \(0.770701\pi\) | |||||||
\(812\) | −1.74073 | + | 39.6232i | −0.0610878 | + | 1.39050i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.25865 | − | 7.40312i | 0.114216 | − | 0.259479i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29.6125 | − | 29.6125i | −1.03601 | − | 1.03601i | ||||
\(818\) | 1.74371 | + | 4.48575i | 0.0609675 | + | 0.156841i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.86789 | − | 40.1215i | 0.309680 | − | 1.40110i | ||||
\(821\) | 39.9452i | 1.39410i | 0.717023 | + | 0.697049i | \(0.245504\pi\) | ||||
−0.717023 | + | 0.697049i | \(0.754496\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.59087 | − | 5.59087i | −0.194886 | − | 0.194886i | 0.602918 | − | 0.797803i | \(-0.294005\pi\) |
−0.797803 | + | 0.602918i | \(0.794005\pi\) | |||||||
\(824\) | 30.1892 | − | 10.2342i | 1.05169 | − | 0.356524i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.70156 | − | 3.83019i | −0.302766 | − | 0.133269i | ||||
\(827\) | 36.7519 | + | 36.7519i | 1.27799 | + | 1.27799i | 0.941792 | + | 0.336196i | \(0.109140\pi\) |
0.336196 | + | 0.941792i | \(0.390860\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.27799 | 0.287506 | 0.143753 | − | 0.989614i | \(-0.454083\pi\) | ||||
0.143753 | + | 0.989614i | \(0.454083\pi\) | |||||||
\(830\) | 6.63594 | + | 33.2269i | 0.230337 | + | 1.15332i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.72898 | + | 28.1477i | −0.129279 | + | 0.975847i | ||||
\(833\) | 47.7918 | − | 47.7918i | 1.65589 | − | 1.65589i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.00000 | + | 22.8062i | −0.138426 | + | 0.789243i | ||||
\(836\) | 8.70704 | + | 9.50723i | 0.301139 | + | 0.328815i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.3541 | + | 42.0712i | 0.564941 | + | 1.45333i | ||||
\(839\) | 27.1030 | 0.935701 | 0.467850 | − | 0.883808i | \(-0.345029\pi\) | ||||
0.467850 | + | 0.883808i | \(0.345029\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.40312 | −0.220797 | ||||||||
\(842\) | −15.5657 | − | 40.0431i | −0.536428 | − | 1.37998i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 17.6990 | − | 16.2094i | 0.609226 | − | 0.557950i | ||||
\(845\) | 0.517700 | + | 0.737925i | 0.0178094 | + | 0.0253854i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.7879 | + | 24.7879i | −0.851722 | + | 0.851722i | ||||
\(848\) | 13.5035 | − | 11.3183i | 0.463713 | − | 0.388673i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 31.7122 | − | 33.2386i | 1.08772 | − | 1.14008i | ||||
\(851\) | −5.48408 | −0.187992 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.3090 | + | 14.3090i | 0.489932 | + | 0.489932i | 0.908285 | − | 0.418353i | \(-0.137392\pi\) |
−0.418353 | + | 0.908285i | \(0.637392\pi\) | |||||||
\(854\) | 36.6103 | + | 16.1148i | 1.25278 | + | 0.551438i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.10469 | − | 2.06950i | 0.208654 | − | 0.0707339i | ||||
\(857\) | −13.7820 | − | 13.7820i | −0.470782 | − | 0.470782i | 0.431385 | − | 0.902168i | \(-0.358025\pi\) |
−0.902168 | + | 0.431385i | \(0.858025\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.6125i | 0.873887i | 0.899489 | + | 0.436944i | \(0.143939\pi\) | ||||
−0.899489 | + | 0.436944i | \(0.856061\pi\) | |||||||
\(860\) | −25.1823 | − | 39.4728i | −0.858710 | − | 1.34601i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.8872 | + | 35.7253i | 0.473001 | + | 1.21681i | ||||
\(863\) | 21.9662 | + | 21.9662i | 0.747737 | + | 0.747737i | 0.974054 | − | 0.226317i | \(-0.0726684\pi\) |
−0.226317 | + | 0.974054i | \(0.572668\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.5078 | − | 4.29844i | −0.833291 | − | 0.146151i | ||||
\(866\) | 9.99371 | − | 22.7041i | 0.339600 | − | 0.771516i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 41.8380 | + | 1.83804i | 1.42008 | + | 0.0623871i | ||||
\(869\) | 8.08857 | 0.274386 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 37.1588i | − | 1.25908i | ||||||
\(872\) | −14.7729 | + | 29.9259i | −0.500275 | + | 1.01342i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.52138 | − | 8.00000i | 0.119112 | − | 0.270604i | ||||
\(875\) | 40.4558 | + | 23.2104i | 1.36765 | + | 0.784654i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.3090 | + | 14.3090i | −0.483182 | + | 0.483182i | −0.906146 | − | 0.422965i | \(-0.860989\pi\) |
0.422965 | + | 0.906146i | \(0.360989\pi\) | |||||||
\(878\) | 14.3927 | − | 5.59476i | 0.485729 | − | 0.188814i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.21135 | + | 12.4798i | 0.243094 | + | 0.420696i | ||||
\(881\) | 46.9017 | 1.58016 | 0.790079 | − | 0.613005i | \(-0.210039\pi\) | ||||
0.790079 | + | 0.613005i | \(0.210039\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.8062 | − | 14.8062i | 0.498270 | − | 0.498270i | −0.412629 | − | 0.910899i | \(-0.635389\pi\) |
0.910899 | + | 0.412629i | \(0.135389\pi\) | |||||||
\(884\) | −31.1473 | − | 34.0098i | −1.04760 | − | 1.14387i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.5969 | − | 28.6181i | 0.423200 | − | 0.961443i | ||||
\(887\) | 26.3365 | − | 26.3365i | 0.884294 | − | 0.884294i | −0.109674 | − | 0.993968i | \(-0.534981\pi\) |
0.993968 | + | 0.109674i | \(0.0349806\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 22.5969i | − | 0.757875i | ||||||
\(890\) | 7.21346 | + | 4.81182i | 0.241796 | + | 0.161293i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.8230 | + | 0.475477i | 0.362380 | + | 0.0159202i | ||||
\(893\) | −29.2882 | − | 29.2882i | −0.980093 | − | 0.980093i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 33.9462 | + | 48.3866i | 1.13470 | + | 1.61739i | ||||
\(896\) | −45.8555 | + | 11.1747i | −1.53192 | + | 0.373321i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.30281 | + | 8.49656i | 0.110216 | + | 0.283534i | ||||
\(899\) | − | 23.8600i | − | 0.795776i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.6181i | 0.953406i | ||||||||
\(902\) | −19.5165 | + | 7.58652i | −0.649829 | + | 0.252603i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.89968 | − | 17.4031i | −0.196221 | − | 0.578819i | ||||
\(905\) | 15.1530 | + | 21.5989i | 0.503702 | + | 0.717972i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.5969 | + | 12.5969i | 0.418272 | + | 0.418272i | 0.884608 | − | 0.466336i | \(-0.154426\pi\) |
−0.466336 | + | 0.884608i | \(0.654426\pi\) | |||||||
\(908\) | 44.1767 | + | 1.94078i | 1.46606 | + | 0.0644072i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 25.9825 | − | 38.9507i | 0.861312 | − | 1.29120i | ||||
\(911\) | − | 27.1030i | − | 0.897964i | −0.893541 | − | 0.448982i | \(-0.851787\pi\) | ||
0.893541 | − | 0.448982i | \(-0.148213\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.2094 | − | 12.2094i | 0.404071 | − | 0.404071i | ||||
\(914\) | −17.9505 | − | 7.90130i | −0.593749 | − | 0.261352i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.0000 | − | 9.15833i | 0.330409 | − | 0.302600i | ||||
\(917\) | −39.9452 | + | 39.9452i | −1.31911 | + | 1.31911i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.2168 | 1.72247 | 0.861237 | − | 0.508204i | \(-0.169691\pi\) | ||||
0.861237 | + | 0.508204i | \(0.169691\pi\) | |||||||
\(920\) | 5.77457 | − | 7.88381i | 0.190382 | − | 0.259922i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.37930 | + | 24.1285i | 0.308891 | + | 0.794630i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.52901 | − | 16.0697i | −0.247552 | − | 0.528369i | ||||
\(926\) | −26.9986 | − | 11.8840i | −0.887230 | − | 0.390534i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.50727 | + | 25.8213i | 0.246438 | + | 0.847627i | ||||
\(929\) | 43.1978i | 1.41727i | 0.705573 | + | 0.708637i | \(0.250690\pi\) | ||||
−0.705573 | + | 0.708637i | \(0.749310\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 41.6125 | 1.36379 | ||||||||
\(932\) | 1.37049 | − | 31.1955i | 0.0448919 | − | 1.02184i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −19.7685 | − | 8.70156i | −0.646846 | − | 0.284724i | ||||
\(935\) | −23.0588 | − | 4.04429i | −0.754102 | − | 0.132262i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.4031 | + | 22.4031i | 0.731878 | + | 0.731878i | 0.970992 | − | 0.239113i | \(-0.0768568\pi\) |
−0.239113 | + | 0.970992i | \(0.576857\pi\) | |||||||
\(938\) | 57.5706 | − | 22.3790i | 1.87975 | − | 0.730701i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −24.9066 | − | 39.0405i | −0.812363 | − | 1.27336i | ||||
\(941\) | − | 10.2166i | − | 0.333050i | −0.986037 | − | 0.166525i | \(-0.946745\pi\) | ||
0.986037 | − | 0.166525i | \(-0.0532547\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.0387 | + | 10.0387i | 0.326904 | + | 0.326904i | ||||
\(944\) | −6.42110 | − | 0.565278i | −0.208989 | − | 0.0183982i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.61250 | + | 21.8380i | −0.312529 | + | 0.710016i | ||||
\(947\) | 18.3759 | + | 18.3759i | 0.597138 | + | 0.597138i | 0.939550 | − | 0.342412i | \(-0.111244\pi\) |
−0.342412 | + | 0.939550i | \(0.611244\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.0967 | −0.814673 | ||||||||
\(950\) | 28.2765 | − | 0.664561i | 0.917410 | − | 0.0215612i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 33.9333 | − | 68.7396i | 1.09979 | − | 2.22786i | ||||
\(953\) | −1.85195 | + | 1.85195i | −0.0599904 | + | 0.0599904i | −0.736466 | − | 0.676475i | \(-0.763507\pi\) |
0.676475 | + | 0.736466i | \(0.263507\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.4187 | − | 34.8062i | −0.790172 | − | 1.12630i | ||||
\(956\) | −11.9300 | + | 10.9259i | −0.385844 | + | 0.353369i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10.6618 | + | 4.14448i | −0.344466 | + | 0.133902i | ||||
\(959\) | −65.1320 | −2.10322 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.80625 | 0.187298 | ||||||||
\(962\) | −16.6043 | + | 6.45447i | −0.535344 | + | 0.208100i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.0387 | + | 9.19375i | −0.323324 | + | 0.296111i | ||||
\(965\) | 6.77576 | − | 38.6324i | 0.218119 | − | 1.24362i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.06950 | + | 2.06950i | −0.0665505 | + | 0.0665505i | −0.739599 | − | 0.673048i | \(-0.764985\pi\) |
0.673048 | + | 0.739599i | \(0.264985\pi\) | |||||||
\(968\) | −10.5208 | + | 21.3123i | −0.338152 | + | 0.685002i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10.5390 | + | 2.10480i | −0.338386 | + | 0.0675811i | ||||
\(971\) | −38.3634 | −1.23114 | −0.615569 | − | 0.788083i | \(-0.711074\pi\) | ||||
−0.615569 | + | 0.788083i | \(0.711074\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.7994 | − | 11.7994i | −0.378270 | − | 0.378270i | ||||
\(974\) | −1.66748 | + | 3.78824i | −0.0534295 | + | 0.121383i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 27.0156 | + | 2.37830i | 0.864749 | + | 0.0761277i | ||||
\(977\) | 7.33602 | + | 7.33602i | 0.234700 | + | 0.234700i | 0.814651 | − | 0.579951i | \(-0.196928\pi\) |
−0.579951 | + | 0.814651i | \(0.696928\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 4.41875i | − | 0.141224i | ||||||
\(980\) | 45.4278 | + | 10.0407i | 1.45114 | + | 0.320739i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 14.8690 | − | 5.77991i | 0.474488 | − | 0.184444i | ||||
\(983\) | 9.18116 | + | 9.18116i | 0.292834 | + | 0.292834i | 0.838199 | − | 0.545365i | \(-0.183609\pi\) |
−0.545365 | + | 0.838199i | \(0.683609\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.10469 | + | 29.1047i | −0.162649 | + | 0.927352i | ||||
\(986\) | −39.9748 | − | 17.5958i | −1.27306 | − | 0.560365i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.24620 | − | 28.3663i | 0.0396468 | − | 0.902452i | ||||
\(989\) | 16.1771 | 0.514403 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 42.7957i | − | 1.35945i | −0.733466 | − | 0.679726i | \(-0.762099\pi\) | ||
0.733466 | − | 0.679726i | \(-0.237901\pi\) | |||||||
\(992\) | 27.2647 | − | 7.92691i | 0.865655 | − | 0.251680i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 38.3634 | − | 26.9143i | 1.21620 | − | 0.853240i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.50967 | − | 2.50967i | 0.0794820 | − | 0.0794820i | −0.666248 | − | 0.745730i | \(-0.732101\pi\) |
0.745730 | + | 0.666248i | \(0.232101\pi\) | |||||||
\(998\) | 9.63606 | + | 24.7890i | 0.305024 | + | 0.784683i | ||||
\(999\) | 0 | 0 |
(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 | 360.2.w.d.307.8 | yes | 16 | |
3.2 | odd | 2 | inner | 360.2.w.d.307.1 | yes | 16 | |
4.3 | odd | 2 | 1440.2.bi.d.847.1 | 16 | |||
5.3 | odd | 4 | inner | 360.2.w.d.163.4 | yes | 16 | |
8.3 | odd | 2 | inner | 360.2.w.d.307.4 | yes | 16 | |
8.5 | even | 2 | 1440.2.bi.d.847.8 | 16 | |||
12.11 | even | 2 | 1440.2.bi.d.847.7 | 16 | |||
15.8 | even | 4 | inner | 360.2.w.d.163.5 | yes | 16 | |
20.3 | even | 4 | 1440.2.bi.d.1423.8 | 16 | |||
24.5 | odd | 2 | 1440.2.bi.d.847.2 | 16 | |||
24.11 | even | 2 | inner | 360.2.w.d.307.5 | yes | 16 | |
40.3 | even | 4 | inner | 360.2.w.d.163.8 | yes | 16 | |
40.13 | odd | 4 | 1440.2.bi.d.1423.1 | 16 | |||
60.23 | odd | 4 | 1440.2.bi.d.1423.2 | 16 | |||
120.53 | even | 4 | 1440.2.bi.d.1423.7 | 16 | |||
120.83 | odd | 4 | inner | 360.2.w.d.163.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.w.d.163.1 | ✓ | 16 | 120.83 | odd | 4 | inner | |
360.2.w.d.163.4 | yes | 16 | 5.3 | odd | 4 | inner | |
360.2.w.d.163.5 | yes | 16 | 15.8 | even | 4 | inner | |
360.2.w.d.163.8 | yes | 16 | 40.3 | even | 4 | inner | |
360.2.w.d.307.1 | yes | 16 | 3.2 | odd | 2 | inner | |
360.2.w.d.307.4 | yes | 16 | 8.3 | odd | 2 | inner | |
360.2.w.d.307.5 | yes | 16 | 24.11 | even | 2 | inner | |
360.2.w.d.307.8 | yes | 16 | 1.1 | even | 1 | trivial | |
1440.2.bi.d.847.1 | 16 | 4.3 | odd | 2 | |||
1440.2.bi.d.847.2 | 16 | 24.5 | odd | 2 | |||
1440.2.bi.d.847.7 | 16 | 12.11 | even | 2 | |||
1440.2.bi.d.847.8 | 16 | 8.5 | even | 2 | |||
1440.2.bi.d.1423.1 | 16 | 40.13 | odd | 4 | |||
1440.2.bi.d.1423.2 | 16 | 60.23 | odd | 4 | |||
1440.2.bi.d.1423.7 | 16 | 120.53 | even | 4 | |||
1440.2.bi.d.1423.8 | 16 | 20.3 | even | 4 |