Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(71,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.n (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.682515625.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 421.2 | ||
Root | \(0.581882 + 1.79085i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.421 |
Dual form | 770.2.n.e.631.2 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | − | 0.587785i | 0.572061 | − | 0.415627i | ||||
\(3\) | 0.941506 | + | 2.89766i | 0.543578 | + | 1.67296i | 0.724346 | + | 0.689437i | \(0.242142\pi\) |
−0.180767 | + | 0.983526i | \(0.557858\pi\) | |||||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | 0.809017 | + | 0.587785i | 0.361803 | + | 0.262866i | ||||
\(6\) | 2.46489 | + | 1.79085i | 1.00629 | + | 0.731111i | ||||
\(7\) | −0.309017 | + | 0.951057i | −0.116797 | + | 0.359466i | ||||
\(8\) | −0.309017 | − | 0.951057i | −0.109254 | − | 0.336249i | ||||
\(9\) | −5.08293 | + | 3.69296i | −1.69431 | + | 1.23099i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 3.28837 | − | 0.432036i | 0.991479 | − | 0.130264i | ||||
\(12\) | 3.04678 | 0.879528 | ||||||||
\(13\) | 0.285629 | − | 0.207522i | 0.0792192 | − | 0.0575561i | −0.547471 | − | 0.836825i | \(-0.684409\pi\) |
0.626690 | + | 0.779269i | \(0.284409\pi\) | |||||||
\(14\) | 0.309017 | + | 0.951057i | 0.0825883 | + | 0.254181i | ||||
\(15\) | −0.941506 | + | 2.89766i | −0.243096 | + | 0.748172i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | 0.655877 | + | 0.476522i | 0.159073 | + | 0.115574i | 0.664474 | − | 0.747311i | \(-0.268655\pi\) |
−0.505401 | + | 0.862885i | \(0.668655\pi\) | |||||||
\(18\) | −1.94151 | + | 5.97534i | −0.457617 | + | 1.40840i | ||||
\(19\) | 0.801129 | + | 2.46562i | 0.183792 | + | 0.565652i | 0.999925 | − | 0.0122107i | \(-0.00388687\pi\) |
−0.816134 | + | 0.577863i | \(0.803887\pi\) | |||||||
\(20\) | 0.809017 | − | 0.587785i | 0.180902 | − | 0.131433i | ||||
\(21\) | −3.04678 | −0.664861 | ||||||||
\(22\) | 2.40640 | − | 2.28238i | 0.513046 | − | 0.486604i | ||||
\(23\) | −2.00000 | −0.417029 | −0.208514 | − | 0.978019i | \(-0.566863\pi\) | ||||
−0.208514 | + | 0.978019i | \(0.566863\pi\) | |||||||
\(24\) | 2.46489 | − | 1.79085i | 0.503144 | − | 0.365556i | ||||
\(25\) | 0.309017 | + | 0.951057i | 0.0618034 | + | 0.190211i | ||||
\(26\) | 0.109101 | − | 0.335777i | 0.0213964 | − | 0.0658513i | ||||
\(27\) | −8.09186 | − | 5.87908i | −1.55728 | − | 1.13143i | ||||
\(28\) | 0.809017 | + | 0.587785i | 0.152890 | + | 0.111081i | ||||
\(29\) | −2.95044 | + | 9.08052i | −0.547883 | + | 1.68621i | 0.166153 | + | 0.986100i | \(0.446866\pi\) |
−0.714035 | + | 0.700110i | \(0.753134\pi\) | |||||||
\(30\) | 0.941506 | + | 2.89766i | 0.171895 | + | 0.529037i | ||||
\(31\) | 4.61803 | − | 3.35520i | 0.829423 | − | 0.602611i | −0.0899727 | − | 0.995944i | \(-0.528678\pi\) |
0.919396 | + | 0.393333i | \(0.128678\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.34790 | + | 9.12179i | 0.756873 | + | 1.58790i | ||||
\(34\) | 0.810708 | 0.139035 | ||||||||
\(35\) | −0.809017 | + | 0.587785i | −0.136749 | + | 0.0993538i | ||||
\(36\) | 1.94151 | + | 5.97534i | 0.323584 | + | 0.995890i | ||||
\(37\) | 1.10121 | − | 3.38918i | 0.181038 | − | 0.557178i | −0.818819 | − | 0.574051i | \(-0.805371\pi\) |
0.999858 | + | 0.0168729i | \(0.00537106\pi\) | |||||||
\(38\) | 2.09738 | + | 1.52384i | 0.340240 | + | 0.247199i | ||||
\(39\) | 0.870248 | + | 0.632272i | 0.139351 | + | 0.101245i | ||||
\(40\) | 0.309017 | − | 0.951057i | 0.0488599 | − | 0.150375i | ||||
\(41\) | −2.55165 | − | 7.85318i | −0.398501 | − | 1.22646i | −0.926201 | − | 0.377029i | \(-0.876946\pi\) |
0.527700 | − | 0.849431i | \(-0.323054\pi\) | |||||||
\(42\) | −2.46489 | + | 1.79085i | −0.380341 | + | 0.276334i | ||||
\(43\) | −9.49338 | −1.44773 | −0.723864 | − | 0.689943i | \(-0.757636\pi\) | ||||
−0.723864 | + | 0.689943i | \(0.757636\pi\) | |||||||
\(44\) | 0.605270 | − | 3.26093i | 0.0912480 | − | 0.491603i | ||||
\(45\) | −6.28284 | −0.936591 | ||||||||
\(46\) | −1.61803 | + | 1.17557i | −0.238566 | + | 0.173328i | ||||
\(47\) | −2.65993 | − | 8.18644i | −0.387991 | − | 1.19411i | −0.934287 | − | 0.356522i | \(-0.883962\pi\) |
0.546296 | − | 0.837593i | \(-0.316038\pi\) | |||||||
\(48\) | 0.941506 | − | 2.89766i | 0.135895 | − | 0.418241i | ||||
\(49\) | −0.809017 | − | 0.587785i | −0.115574 | − | 0.0839693i | ||||
\(50\) | 0.809017 | + | 0.587785i | 0.114412 | + | 0.0831254i | ||||
\(51\) | −0.763286 | + | 2.34915i | −0.106881 | + | 0.328947i | ||||
\(52\) | −0.109101 | − | 0.335777i | −0.0151295 | − | 0.0465639i | ||||
\(53\) | 2.26498 | − | 1.64560i | 0.311119 | − | 0.226041i | −0.421258 | − | 0.906941i | \(-0.638411\pi\) |
0.732376 | + | 0.680900i | \(0.238411\pi\) | |||||||
\(54\) | −10.0021 | −1.36111 | ||||||||
\(55\) | 2.91429 | + | 1.58333i | 0.392962 | + | 0.213496i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −6.39025 | + | 4.64279i | −0.846410 | + | 0.614953i | ||||
\(58\) | 2.95044 | + | 9.08052i | 0.387412 | + | 1.19233i | ||||
\(59\) | 4.08188 | − | 12.5627i | 0.531416 | − | 1.63553i | −0.219853 | − | 0.975533i | \(-0.570558\pi\) |
0.751269 | − | 0.659997i | \(-0.229442\pi\) | |||||||
\(60\) | 2.46489 | + | 1.79085i | 0.318216 | + | 0.231198i | ||||
\(61\) | 5.42536 | + | 3.94175i | 0.694646 | + | 0.504690i | 0.878184 | − | 0.478323i | \(-0.158755\pi\) |
−0.183538 | + | 0.983013i | \(0.558755\pi\) | |||||||
\(62\) | 1.76393 | − | 5.42882i | 0.224020 | − | 0.689461i | ||||
\(63\) | −1.94151 | − | 5.97534i | −0.244607 | − | 0.752822i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 0.353057 | 0.0437913 | ||||||||
\(66\) | 8.87918 | + | 4.82405i | 1.09295 | + | 0.593799i | ||||
\(67\) | −1.40749 | −0.171953 | −0.0859763 | − | 0.996297i | \(-0.527401\pi\) | ||||
−0.0859763 | + | 0.996297i | \(0.527401\pi\) | |||||||
\(68\) | 0.655877 | − | 0.476522i | 0.0795367 | − | 0.0577868i | ||||
\(69\) | −1.88301 | − | 5.79531i | −0.226688 | − | 0.697674i | ||||
\(70\) | −0.309017 | + | 0.951057i | −0.0369346 | + | 0.113673i | ||||
\(71\) | 10.4515 | + | 7.59345i | 1.24036 | + | 0.901176i | 0.997623 | − | 0.0689148i | \(-0.0219537\pi\) |
0.242740 | + | 0.970091i | \(0.421954\pi\) | |||||||
\(72\) | 5.08293 | + | 3.69296i | 0.599029 | + | 0.435220i | ||||
\(73\) | −1.59146 | + | 4.89802i | −0.186267 | + | 0.573269i | −0.999968 | − | 0.00801375i | \(-0.997449\pi\) |
0.813701 | + | 0.581283i | \(0.197449\pi\) | |||||||
\(74\) | −1.10121 | − | 3.38918i | −0.128013 | − | 0.393985i | ||||
\(75\) | −2.46489 | + | 1.79085i | −0.284621 | + | 0.206790i | ||||
\(76\) | 2.59251 | 0.297381 | ||||||||
\(77\) | −0.605270 | + | 3.26093i | −0.0689770 | + | 0.371617i | ||||
\(78\) | 1.07569 | 0.121797 | ||||||||
\(79\) | 2.95044 | − | 2.14362i | 0.331950 | − | 0.241176i | −0.409307 | − | 0.912397i | \(-0.634230\pi\) |
0.741258 | + | 0.671221i | \(0.234230\pi\) | |||||||
\(80\) | −0.309017 | − | 0.951057i | −0.0345492 | − | 0.106331i | ||||
\(81\) | 3.59251 | − | 11.0566i | 0.399167 | − | 1.22851i | ||||
\(82\) | −6.68031 | − | 4.85353i | −0.737717 | − | 0.535983i | ||||
\(83\) | 2.15861 | + | 1.56832i | 0.236939 | + | 0.172146i | 0.699918 | − | 0.714223i | \(-0.253220\pi\) |
−0.462980 | + | 0.886369i | \(0.653220\pi\) | |||||||
\(84\) | −0.941506 | + | 2.89766i | −0.102727 | + | 0.316160i | ||||
\(85\) | 0.250523 | + | 0.771029i | 0.0271730 | + | 0.0836299i | ||||
\(86\) | −7.68031 | + | 5.58007i | −0.828189 | + | 0.601715i | ||||
\(87\) | −29.0901 | −3.11878 | ||||||||
\(88\) | −1.42705 | − | 2.99391i | −0.152124 | − | 0.319152i | ||||
\(89\) | 9.63799 | 1.02163 | 0.510813 | − | 0.859692i | \(-0.329345\pi\) | ||||
0.510813 | + | 0.859692i | \(0.329345\pi\) | |||||||
\(90\) | −5.08293 | + | 3.69296i | −0.535788 | + | 0.389272i | ||||
\(91\) | 0.109101 | + | 0.335777i | 0.0114368 | + | 0.0351990i | ||||
\(92\) | −0.618034 | + | 1.90211i | −0.0644345 | + | 0.198309i | ||||
\(93\) | 14.0701 | + | 10.2225i | 1.45900 | + | 1.06003i | ||||
\(94\) | −6.96380 | − | 5.05950i | −0.718261 | − | 0.521847i | ||||
\(95\) | −0.801129 | + | 2.46562i | −0.0821941 | + | 0.252967i | ||||
\(96\) | −0.941506 | − | 2.89766i | −0.0960920 | − | 0.295741i | ||||
\(97\) | 7.92705 | − | 5.75934i | 0.804870 | − | 0.584772i | −0.107469 | − | 0.994208i | \(-0.534275\pi\) |
0.912339 | + | 0.409436i | \(0.134275\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −15.1190 | + | 14.3398i | −1.51952 | + | 1.44121i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 0.731641 | − | 0.531568i | 0.0728010 | − | 0.0528930i | −0.550789 | − | 0.834644i | \(-0.685673\pi\) |
0.623590 | + | 0.781751i | \(0.285673\pi\) | |||||||
\(102\) | 0.763286 | + | 2.34915i | 0.0755766 | + | 0.232601i | ||||
\(103\) | 3.46726 | − | 10.6711i | 0.341639 | − | 1.05146i | −0.621719 | − | 0.783240i | \(-0.713565\pi\) |
0.963358 | − | 0.268217i | \(-0.0864346\pi\) | |||||||
\(104\) | −0.285629 | − | 0.207522i | −0.0280082 | − | 0.0203492i | ||||
\(105\) | −2.46489 | − | 1.79085i | −0.240549 | − | 0.174769i | ||||
\(106\) | 0.865144 | − | 2.66264i | 0.0840302 | − | 0.258618i | ||||
\(107\) | 2.74906 | + | 8.46074i | 0.265762 | + | 0.817930i | 0.991517 | + | 0.129977i | \(0.0414904\pi\) |
−0.725755 | + | 0.687953i | \(0.758510\pi\) | |||||||
\(108\) | −8.09186 | + | 5.87908i | −0.778640 | + | 0.565715i | ||||
\(109\) | 18.4763 | 1.76971 | 0.884855 | − | 0.465866i | \(-0.154257\pi\) | ||||
0.884855 | + | 0.465866i | \(0.154257\pi\) | |||||||
\(110\) | 3.28837 | − | 0.432036i | 0.313533 | − | 0.0411930i | ||||
\(111\) | 10.8575 | 1.03055 | ||||||||
\(112\) | 0.809017 | − | 0.587785i | 0.0764449 | − | 0.0555405i | ||||
\(113\) | −3.92150 | − | 12.0691i | −0.368904 | − | 1.13537i | −0.947500 | − | 0.319755i | \(-0.896399\pi\) |
0.578597 | − | 0.815614i | \(-0.303601\pi\) | |||||||
\(114\) | −2.44086 | + | 7.51219i | −0.228607 | + | 0.703581i | ||||
\(115\) | −1.61803 | − | 1.17557i | −0.150882 | − | 0.109623i | ||||
\(116\) | 7.72435 | + | 5.61207i | 0.717188 | + | 0.521067i | ||||
\(117\) | −0.685462 | + | 2.10963i | −0.0633710 | + | 0.195036i | ||||
\(118\) | −4.08188 | − | 12.5627i | −0.375768 | − | 1.15649i | ||||
\(119\) | −0.655877 | + | 0.476522i | −0.0601241 | + | 0.0436827i | ||||
\(120\) | 3.04678 | 0.278131 | ||||||||
\(121\) | 10.6267 | − | 2.84138i | 0.966063 | − | 0.258307i | ||||
\(122\) | 6.70611 | 0.607143 | ||||||||
\(123\) | 20.3534 | − | 14.7876i | 1.83520 | − | 1.33335i | ||||
\(124\) | −1.76393 | − | 5.42882i | −0.158406 | − | 0.487523i | ||||
\(125\) | −0.309017 | + | 0.951057i | −0.0276393 | + | 0.0850651i | ||||
\(126\) | −5.08293 | − | 3.69296i | −0.452823 | − | 0.328995i | ||||
\(127\) | −13.1369 | − | 9.54455i | −1.16572 | − | 0.846942i | −0.175226 | − | 0.984528i | \(-0.556066\pi\) |
−0.990490 | + | 0.137586i | \(0.956066\pi\) | |||||||
\(128\) | −0.309017 | + | 0.951057i | −0.0273135 | + | 0.0840623i | ||||
\(129\) | −8.93807 | − | 27.5086i | −0.786954 | − | 2.42199i | ||||
\(130\) | 0.285629 | − | 0.207522i | 0.0250513 | − | 0.0182008i | ||||
\(131\) | −8.08882 | −0.706723 | −0.353362 | − | 0.935487i | \(-0.614961\pi\) | ||||
−0.353362 | + | 0.935487i | \(0.614961\pi\) | |||||||
\(132\) | 10.0189 | − | 1.31632i | 0.872034 | − | 0.114571i | ||||
\(133\) | −2.59251 | −0.224799 | ||||||||
\(134\) | −1.13869 | + | 0.827304i | −0.0983675 | + | 0.0714682i | ||||
\(135\) | −3.09082 | − | 9.51255i | −0.266015 | − | 0.818710i | ||||
\(136\) | 0.250523 | − | 0.771029i | 0.0214821 | − | 0.0661152i | ||||
\(137\) | −8.41533 | − | 6.11410i | −0.718970 | − | 0.522363i | 0.167085 | − | 0.985943i | \(-0.446565\pi\) |
−0.886055 | + | 0.463580i | \(0.846565\pi\) | |||||||
\(138\) | −4.92979 | − | 3.58170i | −0.419651 | − | 0.304895i | ||||
\(139\) | 0.233978 | − | 0.720109i | 0.0198457 | − | 0.0610789i | −0.940643 | − | 0.339397i | \(-0.889777\pi\) |
0.960489 | + | 0.278318i | \(0.0897770\pi\) | |||||||
\(140\) | 0.309017 | + | 0.951057i | 0.0261167 | + | 0.0803789i | ||||
\(141\) | 21.2171 | − | 15.4152i | 1.78681 | − | 1.29819i | ||||
\(142\) | 12.9187 | 1.08412 | ||||||||
\(143\) | 0.849596 | − | 0.805809i | 0.0710468 | − | 0.0673851i | ||||
\(144\) | 6.28284 | 0.523570 | ||||||||
\(145\) | −7.72435 | + | 5.61207i | −0.641472 | + | 0.466057i | ||||
\(146\) | 1.59146 | + | 4.89802i | 0.131710 | + | 0.405363i | ||||
\(147\) | 0.941506 | − | 2.89766i | 0.0776541 | − | 0.238995i | ||||
\(148\) | −2.88301 | − | 2.09463i | −0.236982 | − | 0.172178i | ||||
\(149\) | 7.25672 | + | 5.27232i | 0.594494 | + | 0.431925i | 0.843920 | − | 0.536469i | \(-0.180242\pi\) |
−0.249426 | + | 0.968394i | \(0.580242\pi\) | |||||||
\(150\) | −0.941506 | + | 2.89766i | −0.0768736 | + | 0.236593i | ||||
\(151\) | −6.79006 | − | 20.8976i | −0.552567 | − | 1.70063i | −0.702284 | − | 0.711897i | \(-0.747836\pi\) |
0.149717 | − | 0.988729i | \(-0.452164\pi\) | |||||||
\(152\) | 2.09738 | − | 1.52384i | 0.170120 | − | 0.123600i | ||||
\(153\) | −5.09355 | −0.411789 | ||||||||
\(154\) | 1.42705 | + | 2.99391i | 0.114995 | + | 0.241257i | ||||
\(155\) | 5.70820 | 0.458494 | ||||||||
\(156\) | 0.870248 | − | 0.632272i | 0.0696756 | − | 0.0506223i | ||||
\(157\) | 0.0206519 | + | 0.0635599i | 0.00164820 | + | 0.00507263i | 0.951877 | − | 0.306480i | \(-0.0991511\pi\) |
−0.950229 | + | 0.311552i | \(0.899151\pi\) | |||||||
\(158\) | 1.12697 | − | 3.46845i | 0.0896567 | − | 0.275935i | ||||
\(159\) | 6.90088 | + | 5.01378i | 0.547275 | + | 0.397619i | ||||
\(160\) | −0.809017 | − | 0.587785i | −0.0639584 | − | 0.0464685i | ||||
\(161\) | 0.618034 | − | 1.90211i | 0.0487079 | − | 0.149908i | ||||
\(162\) | −3.59251 | − | 11.0566i | −0.282254 | − | 0.868688i | ||||
\(163\) | −18.0161 | + | 13.0895i | −1.41113 | + | 1.02525i | −0.417975 | + | 0.908458i | \(0.637260\pi\) |
−0.993157 | + | 0.116789i | \(0.962740\pi\) | |||||||
\(164\) | −8.25732 | −0.644788 | ||||||||
\(165\) | −1.84412 | + | 9.93532i | −0.143565 | + | 0.773463i | ||||
\(166\) | 2.66819 | 0.207092 | ||||||||
\(167\) | 9.70820 | − | 7.05342i | 0.751243 | − | 0.545810i | −0.144969 | − | 0.989436i | \(-0.546308\pi\) |
0.896212 | + | 0.443626i | \(0.146308\pi\) | |||||||
\(168\) | 0.941506 | + | 2.89766i | 0.0726387 | + | 0.223559i | ||||
\(169\) | −3.97870 | + | 12.2452i | −0.306054 | + | 0.941937i | ||||
\(170\) | 0.655877 | + | 0.476522i | 0.0503034 | + | 0.0365476i | ||||
\(171\) | −13.1775 | − | 9.57403i | −1.00771 | − | 0.732145i | ||||
\(172\) | −2.93362 | + | 9.02875i | −0.223686 | + | 0.688435i | ||||
\(173\) | 6.14010 | + | 18.8973i | 0.466823 | + | 1.43673i | 0.856675 | + | 0.515856i | \(0.172526\pi\) |
−0.389852 | + | 0.920878i | \(0.627474\pi\) | |||||||
\(174\) | −23.5344 | + | 17.0987i | −1.78414 | + | 1.29625i | ||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −2.91429 | − | 1.58333i | −0.219673 | − | 0.119348i | ||||
\(177\) | 40.2456 | 3.02505 | ||||||||
\(178\) | 7.79730 | − | 5.66507i | 0.584432 | − | 0.424615i | ||||
\(179\) | −2.66140 | − | 8.19094i | −0.198922 | − | 0.612220i | −0.999908 | − | 0.0135367i | \(-0.995691\pi\) |
0.800986 | − | 0.598683i | \(-0.204309\pi\) | |||||||
\(180\) | −1.94151 | + | 5.97534i | −0.144711 | + | 0.445376i | ||||
\(181\) | −9.49338 | − | 6.89735i | −0.705638 | − | 0.512676i | 0.176126 | − | 0.984368i | \(-0.443643\pi\) |
−0.881763 | + | 0.471692i | \(0.843643\pi\) | |||||||
\(182\) | 0.285629 | + | 0.207522i | 0.0211722 | + | 0.0153825i | ||||
\(183\) | −6.31384 | + | 19.4320i | −0.466733 | + | 1.43646i | ||||
\(184\) | 0.618034 | + | 1.90211i | 0.0455621 | + | 0.140226i | ||||
\(185\) | 2.88301 | − | 2.09463i | 0.211963 | − | 0.154000i | ||||
\(186\) | 17.3916 | 1.27522 | ||||||||
\(187\) | 2.36264 | + | 1.28362i | 0.172773 | + | 0.0938674i | ||||
\(188\) | −8.60773 | −0.627783 | ||||||||
\(189\) | 8.09186 | − | 5.87908i | 0.588596 | − | 0.427640i | ||||
\(190\) | 0.801129 | + | 2.46562i | 0.0581200 | + | 0.178875i | ||||
\(191\) | −2.51868 | + | 7.75171i | −0.182246 | + | 0.560894i | −0.999890 | − | 0.0148293i | \(-0.995280\pi\) |
0.817644 | + | 0.575723i | \(0.195280\pi\) | |||||||
\(192\) | −2.46489 | − | 1.79085i | −0.177888 | − | 0.129243i | ||||
\(193\) | −7.07230 | − | 5.13833i | −0.509076 | − | 0.369865i | 0.303397 | − | 0.952864i | \(-0.401879\pi\) |
−0.812473 | + | 0.582999i | \(0.801879\pi\) | |||||||
\(194\) | 3.02786 | − | 9.31881i | 0.217388 | − | 0.669051i | ||||
\(195\) | 0.332405 | + | 1.02304i | 0.0238040 | + | 0.0732612i | ||||
\(196\) | −0.809017 | + | 0.587785i | −0.0577869 | + | 0.0419847i | ||||
\(197\) | 14.4568 | 1.03001 | 0.515003 | − | 0.857189i | \(-0.327791\pi\) | ||||
0.515003 | + | 0.857189i | \(0.327791\pi\) | |||||||
\(198\) | −3.80282 | + | 20.4879i | −0.270255 | + | 1.45601i | ||||
\(199\) | −11.0446 | −0.782930 | −0.391465 | − | 0.920193i | \(-0.628032\pi\) | ||||
−0.391465 | + | 0.920193i | \(0.628032\pi\) | |||||||
\(200\) | 0.809017 | − | 0.587785i | 0.0572061 | − | 0.0415627i | ||||
\(201\) | −1.32516 | − | 4.07843i | −0.0934698 | − | 0.287670i | ||||
\(202\) | 0.279462 | − | 0.860095i | 0.0196629 | − | 0.0605161i | ||||
\(203\) | −7.72435 | − | 5.61207i | −0.542143 | − | 0.393890i | ||||
\(204\) | 1.99831 | + | 1.45186i | 0.139910 | + | 0.101650i | ||||
\(205\) | 2.55165 | − | 7.85318i | 0.178215 | − | 0.548490i | ||||
\(206\) | −3.46726 | − | 10.6711i | −0.241576 | − | 0.743493i | ||||
\(207\) | 10.1659 | − | 7.38593i | 0.706576 | − | 0.513357i | ||||
\(208\) | −0.353057 | −0.0244801 | ||||||||
\(209\) | 3.69964 | + | 7.76174i | 0.255909 | + | 0.536891i | ||||
\(210\) | −3.04678 | −0.210248 | ||||||||
\(211\) | −19.1820 | + | 13.9365i | −1.32054 | + | 0.959428i | −0.320615 | + | 0.947210i | \(0.603889\pi\) |
−0.999925 | + | 0.0122188i | \(0.996111\pi\) | |||||||
\(212\) | −0.865144 | − | 2.66264i | −0.0594184 | − | 0.182871i | ||||
\(213\) | −12.1631 | + | 37.4341i | −0.833400 | + | 2.56494i | ||||
\(214\) | 7.19713 | + | 5.22902i | 0.491986 | + | 0.357449i | ||||
\(215\) | −7.68031 | − | 5.58007i | −0.523793 | − | 0.380558i | ||||
\(216\) | −3.09082 | + | 9.51255i | −0.210303 | + | 0.647247i | ||||
\(217\) | 1.76393 | + | 5.42882i | 0.119744 | + | 0.368533i | ||||
\(218\) | 14.9477 | − | 10.8601i | 1.01238 | − | 0.735539i | ||||
\(219\) | −15.6911 | −1.06031 | ||||||||
\(220\) | 2.40640 | − | 2.28238i | 0.162239 | − | 0.153878i | ||||
\(221\) | 0.286226 | 0.0192536 | ||||||||
\(222\) | 8.78389 | − | 6.38187i | 0.589536 | − | 0.428323i | ||||
\(223\) | −1.72736 | − | 5.31628i | −0.115673 | − | 0.356004i | 0.876414 | − | 0.481558i | \(-0.159929\pi\) |
−0.992087 | + | 0.125554i | \(0.959929\pi\) | |||||||
\(224\) | 0.309017 | − | 0.951057i | 0.0206471 | − | 0.0635451i | ||||
\(225\) | −5.08293 | − | 3.69296i | −0.338862 | − | 0.246198i | ||||
\(226\) | −10.2666 | − | 7.45914i | −0.682925 | − | 0.496174i | ||||
\(227\) | −1.95362 | + | 6.01263i | −0.129667 | + | 0.399073i | −0.994722 | − | 0.102603i | \(-0.967283\pi\) |
0.865056 | + | 0.501676i | \(0.167283\pi\) | |||||||
\(228\) | 2.44086 | + | 7.51219i | 0.161650 | + | 0.497507i | ||||
\(229\) | 3.14799 | − | 2.28715i | 0.208025 | − | 0.151139i | −0.478895 | − | 0.877872i | \(-0.658962\pi\) |
0.686920 | + | 0.726733i | \(0.258962\pi\) | |||||||
\(230\) | −2.00000 | −0.131876 | ||||||||
\(231\) | −10.0189 | + | 1.31632i | −0.659196 | + | 0.0866072i | ||||
\(232\) | 9.54782 | 0.626845 | ||||||||
\(233\) | −12.2694 | + | 8.91427i | −0.803797 | + | 0.583993i | −0.912026 | − | 0.410133i | \(-0.865482\pi\) |
0.108228 | + | 0.994126i | \(0.465482\pi\) | |||||||
\(234\) | 0.685462 | + | 2.10963i | 0.0448100 | + | 0.137911i | ||||
\(235\) | 2.65993 | − | 8.18644i | 0.173515 | − | 0.534024i | ||||
\(236\) | −10.6865 | − | 7.76420i | −0.695632 | − | 0.505406i | ||||
\(237\) | 8.98933 | + | 6.53113i | 0.583920 | + | 0.424242i | ||||
\(238\) | −0.250523 | + | 0.771029i | −0.0162390 | + | 0.0499784i | ||||
\(239\) | −6.51868 | − | 20.0624i | −0.421659 | − | 1.29773i | −0.906158 | − | 0.422940i | \(-0.860998\pi\) |
0.484499 | − | 0.874792i | \(-0.339002\pi\) | |||||||
\(240\) | 2.46489 | − | 1.79085i | 0.159108 | − | 0.115599i | ||||
\(241\) | −11.9416 | −0.769228 | −0.384614 | − | 0.923078i | \(-0.625665\pi\) | ||||
−0.384614 | + | 0.923078i | \(0.625665\pi\) | |||||||
\(242\) | 6.92705 | − | 8.54494i | 0.445288 | − | 0.549289i | ||||
\(243\) | 5.41432 | 0.347329 | ||||||||
\(244\) | 5.42536 | − | 3.94175i | 0.347323 | − | 0.252345i | ||||
\(245\) | −0.309017 | − | 0.951057i | −0.0197424 | − | 0.0607608i | ||||
\(246\) | 7.77431 | − | 23.9269i | 0.495672 | − | 1.52552i | ||||
\(247\) | 0.740495 | + | 0.538001i | 0.0471166 | + | 0.0342322i | ||||
\(248\) | −4.61803 | − | 3.35520i | −0.293245 | − | 0.213055i | ||||
\(249\) | −2.51212 | + | 7.73150i | −0.159199 | + | 0.489964i | ||||
\(250\) | 0.309017 | + | 0.951057i | 0.0195440 | + | 0.0601501i | ||||
\(251\) | −1.71377 | + | 1.24513i | −0.108172 | + | 0.0785919i | −0.640556 | − | 0.767911i | \(-0.721296\pi\) |
0.532384 | + | 0.846503i | \(0.321296\pi\) | |||||||
\(252\) | −6.28284 | −0.395782 | ||||||||
\(253\) | −6.57673 | + | 0.864071i | −0.413475 | + | 0.0543237i | ||||
\(254\) | −16.2382 | −1.01887 | ||||||||
\(255\) | −1.99831 | + | 1.45186i | −0.125139 | + | 0.0909188i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | −6.40088 | + | 19.6999i | −0.399276 | + | 1.22884i | 0.526305 | + | 0.850296i | \(0.323577\pi\) |
−0.925581 | + | 0.378549i | \(0.876423\pi\) | |||||||
\(258\) | −23.4002 | − | 17.0012i | −1.45683 | − | 1.05845i | ||||
\(259\) | 2.88301 | + | 2.09463i | 0.179142 | + | 0.130154i | ||||
\(260\) | 0.109101 | − | 0.335777i | 0.00676613 | − | 0.0208240i | ||||
\(261\) | −18.5371 | − | 57.0515i | −1.14742 | − | 3.53140i | ||||
\(262\) | −6.54399 | + | 4.75449i | −0.404289 | + | 0.293733i | ||||
\(263\) | 3.89531 | 0.240195 | 0.120097 | − | 0.992762i | \(-0.461679\pi\) | ||||
0.120097 | + | 0.992762i | \(0.461679\pi\) | |||||||
\(264\) | 7.33176 | − | 6.95389i | 0.451239 | − | 0.427982i | ||||
\(265\) | 2.79967 | 0.171982 | ||||||||
\(266\) | −2.09738 | + | 1.52384i | −0.128599 | + | 0.0934325i | ||||
\(267\) | 9.07422 | + | 27.9276i | 0.555333 | + | 1.70914i | ||||
\(268\) | −0.434939 | + | 1.33861i | −0.0265681 | + | 0.0817683i | ||||
\(269\) | 18.5009 | + | 13.4417i | 1.12802 | + | 0.819556i | 0.985406 | − | 0.170222i | \(-0.0544483\pi\) |
0.142617 | + | 0.989778i | \(0.454448\pi\) | |||||||
\(270\) | −8.09186 | − | 5.87908i | −0.492455 | − | 0.357789i | ||||
\(271\) | 6.36828 | − | 19.5995i | 0.386845 | − | 1.19059i | −0.548287 | − | 0.836290i | \(-0.684720\pi\) |
0.935133 | − | 0.354298i | \(-0.115280\pi\) | |||||||
\(272\) | −0.250523 | − | 0.771029i | −0.0151902 | − | 0.0467505i | ||||
\(273\) | −0.870248 | + | 0.632272i | −0.0526698 | + | 0.0382668i | ||||
\(274\) | −10.4019 | −0.628403 | ||||||||
\(275\) | 1.42705 | + | 2.99391i | 0.0860544 | + | 0.180540i | ||||
\(276\) | −6.09355 | −0.366789 | ||||||||
\(277\) | −13.9187 | + | 10.1126i | −0.836296 | + | 0.607605i | −0.921334 | − | 0.388773i | \(-0.872899\pi\) |
0.0850373 | + | 0.996378i | \(0.472899\pi\) | |||||||
\(278\) | −0.233978 | − | 0.720109i | −0.0140331 | − | 0.0431893i | ||||
\(279\) | −11.0825 | + | 34.1085i | −0.663492 | + | 2.04202i | ||||
\(280\) | 0.809017 | + | 0.587785i | 0.0483480 | + | 0.0351269i | ||||
\(281\) | −24.6301 | − | 17.8948i | −1.46931 | − | 1.06751i | −0.980814 | − | 0.194945i | \(-0.937547\pi\) |
−0.488492 | − | 0.872569i | \(-0.662453\pi\) | |||||||
\(282\) | 8.10423 | − | 24.9422i | 0.482600 | − | 1.48529i | ||||
\(283\) | 3.08868 | + | 9.50597i | 0.183603 | + | 0.565071i | 0.999921 | − | 0.0125305i | \(-0.00398868\pi\) |
−0.816319 | + | 0.577602i | \(0.803989\pi\) | |||||||
\(284\) | 10.4515 | − | 7.59345i | 0.620181 | − | 0.450588i | ||||
\(285\) | −7.89879 | −0.467884 | ||||||||
\(286\) | 0.213695 | − | 1.15129i | 0.0126360 | − | 0.0680774i | ||||
\(287\) | 8.25732 | 0.487414 | ||||||||
\(288\) | 5.08293 | − | 3.69296i | 0.299514 | − | 0.217610i | ||||
\(289\) | −5.05019 | − | 15.5429i | −0.297070 | − | 0.914287i | ||||
\(290\) | −2.95044 | + | 9.08052i | −0.173256 | + | 0.533226i | ||||
\(291\) | 24.1519 | + | 17.5474i | 1.41581 | + | 1.02865i | ||||
\(292\) | 4.16650 | + | 3.02714i | 0.243826 | + | 0.177150i | ||||
\(293\) | −1.99871 | + | 6.15139i | −0.116766 | + | 0.359368i | −0.992311 | − | 0.123768i | \(-0.960502\pi\) |
0.875545 | + | 0.483136i | \(0.160502\pi\) | |||||||
\(294\) | −0.941506 | − | 2.89766i | −0.0549097 | − | 0.168995i | ||||
\(295\) | 10.6865 | − | 7.76420i | 0.622192 | − | 0.452049i | ||||
\(296\) | −3.56360 | −0.207130 | ||||||||
\(297\) | −29.1490 | − | 15.8366i | −1.69139 | − | 0.918932i | ||||
\(298\) | 8.96980 | 0.519607 | ||||||||
\(299\) | −0.571258 | + | 0.415043i | −0.0330367 | + | 0.0240026i | ||||
\(300\) | 0.941506 | + | 2.89766i | 0.0543578 | + | 0.167296i | ||||
\(301\) | 2.93362 | − | 9.02875i | 0.169091 | − | 0.520408i | ||||
\(302\) | −17.7766 | − | 12.9155i | −1.02293 | − | 0.743201i | ||||
\(303\) | 2.22915 | + | 1.61957i | 0.128061 | + | 0.0930418i | ||||
\(304\) | 0.801129 | − | 2.46562i | 0.0459479 | − | 0.141413i | ||||
\(305\) | 2.07230 | + | 6.37789i | 0.118660 | + | 0.365197i | ||||
\(306\) | −4.12077 | + | 2.99391i | −0.235569 | + | 0.171151i | ||||
\(307\) | −20.6473 | −1.17840 | −0.589202 | − | 0.807986i | \(-0.700558\pi\) | ||||
−0.589202 | + | 0.807986i | \(0.700558\pi\) | |||||||
\(308\) | 2.91429 | + | 1.58333i | 0.166057 | + | 0.0902185i | ||||
\(309\) | 34.1857 | 1.94476 | ||||||||
\(310\) | 4.61803 | − | 3.35520i | 0.262287 | − | 0.190562i | ||||
\(311\) | 7.24289 | + | 22.2913i | 0.410707 | + | 1.26403i | 0.916035 | + | 0.401098i | \(0.131371\pi\) |
−0.505328 | + | 0.862927i | \(0.668629\pi\) | |||||||
\(312\) | 0.332405 | − | 1.02304i | 0.0188187 | − | 0.0579181i | ||||
\(313\) | −9.63207 | − | 6.99811i | −0.544437 | − | 0.395557i | 0.281293 | − | 0.959622i | \(-0.409237\pi\) |
−0.825730 | + | 0.564065i | \(0.809237\pi\) | |||||||
\(314\) | 0.0540673 | + | 0.0392822i | 0.00305119 | + | 0.00221682i | ||||
\(315\) | 1.94151 | − | 5.97534i | 0.109391 | − | 0.336672i | ||||
\(316\) | −1.12697 | − | 3.46845i | −0.0633969 | − | 0.195116i | ||||
\(317\) | 27.8451 | − | 20.2307i | 1.56394 | − | 1.13627i | 0.631255 | − | 0.775575i | \(-0.282540\pi\) |
0.932685 | − | 0.360693i | \(-0.117460\pi\) | |||||||
\(318\) | 8.52995 | 0.478336 | ||||||||
\(319\) | −5.77901 | + | 31.1348i | −0.323563 | + | 1.74321i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −21.9280 | + | 15.9317i | −1.22390 | + | 0.889218i | ||||
\(322\) | −0.618034 | − | 1.90211i | −0.0344417 | − | 0.106001i | ||||
\(323\) | −0.649481 | + | 1.99890i | −0.0361381 | + | 0.111222i | ||||
\(324\) | −9.40531 | − | 6.83335i | −0.522517 | − | 0.379631i | ||||
\(325\) | 0.285629 | + | 0.207522i | 0.0158438 | + | 0.0115112i | ||||
\(326\) | −6.88155 | + | 21.1792i | −0.381134 | + | 1.17301i | ||||
\(327\) | 17.3956 | + | 53.5380i | 0.961976 | + | 2.96066i | ||||
\(328\) | −6.68031 | + | 4.85353i | −0.368858 | + | 0.267991i | ||||
\(329\) | 8.60773 | 0.474559 | ||||||||
\(330\) | 4.34790 | + | 9.12179i | 0.239344 | + | 0.502138i | ||||
\(331\) | −11.6770 | −0.641829 | −0.320914 | − | 0.947108i | \(-0.603990\pi\) | ||||
−0.320914 | + | 0.947108i | \(0.603990\pi\) | |||||||
\(332\) | 2.15861 | − | 1.56832i | 0.118469 | − | 0.0860730i | ||||
\(333\) | 6.91874 | + | 21.2937i | 0.379145 | + | 1.16689i | ||||
\(334\) | 3.70820 | − | 11.4127i | 0.202904 | − | 0.624474i | ||||
\(335\) | −1.13869 | − | 0.827304i | −0.0622131 | − | 0.0452004i | ||||
\(336\) | 2.46489 | + | 1.79085i | 0.134471 | + | 0.0976989i | ||||
\(337\) | −3.19330 | + | 9.82797i | −0.173950 | + | 0.535364i | −0.999584 | − | 0.0288428i | \(-0.990818\pi\) |
0.825634 | + | 0.564206i | \(0.190818\pi\) | |||||||
\(338\) | 3.97870 | + | 12.2452i | 0.216413 | + | 0.666050i | ||||
\(339\) | 31.2801 | − | 22.7263i | 1.69890 | − | 1.23432i | ||||
\(340\) | 0.810708 | 0.0439668 | ||||||||
\(341\) | 13.7362 | − | 13.0283i | 0.743858 | − | 0.705520i | ||||
\(342\) | −16.2883 | −0.880771 | ||||||||
\(343\) | 0.809017 | − | 0.587785i | 0.0436828 | − | 0.0317374i | ||||
\(344\) | 2.93362 | + | 9.02875i | 0.158170 | + | 0.486797i | ||||
\(345\) | 1.88301 | − | 5.79531i | 0.101378 | − | 0.312009i | ||||
\(346\) | 16.0750 | + | 11.6792i | 0.864197 | + | 0.627876i | ||||
\(347\) | 14.8214 | + | 10.7684i | 0.795652 | + | 0.578075i | 0.909635 | − | 0.415407i | \(-0.136361\pi\) |
−0.113983 | + | 0.993483i | \(0.536361\pi\) | |||||||
\(348\) | −8.98933 | + | 27.6663i | −0.481878 | + | 1.48307i | ||||
\(349\) | −9.24627 | − | 28.4571i | −0.494942 | − | 1.52327i | −0.817048 | − | 0.576570i | \(-0.804391\pi\) |
0.322106 | − | 0.946704i | \(-0.395609\pi\) | |||||||
\(350\) | −0.809017 | + | 0.587785i | −0.0432438 | + | 0.0314184i | ||||
\(351\) | −3.53131 | −0.188487 | ||||||||
\(352\) | −3.28837 | + | 0.432036i | −0.175270 | + | 0.0230276i | ||||
\(353\) | −8.93024 | −0.475309 | −0.237654 | − | 0.971350i | \(-0.576379\pi\) | ||||
−0.237654 | + | 0.971350i | \(0.576379\pi\) | |||||||
\(354\) | 32.5594 | − | 23.6558i | 1.73051 | − | 1.25729i | ||||
\(355\) | 3.99211 | + | 12.2865i | 0.211879 | + | 0.652097i | ||||
\(356\) | 2.97830 | − | 9.16627i | 0.157850 | − | 0.485812i | ||||
\(357\) | −1.99831 | − | 1.45186i | −0.105762 | − | 0.0768404i | ||||
\(358\) | −6.96763 | − | 5.06228i | −0.368251 | − | 0.267550i | ||||
\(359\) | −9.20610 | + | 28.3334i | −0.485879 | + | 1.49538i | 0.344824 | + | 0.938667i | \(0.387938\pi\) |
−0.830704 | + | 0.556715i | \(0.812062\pi\) | |||||||
\(360\) | 1.94151 | + | 5.97534i | 0.102326 | + | 0.314928i | ||||
\(361\) | 9.93385 | − | 7.21736i | 0.522834 | − | 0.379861i | ||||
\(362\) | −11.7345 | −0.616750 | ||||||||
\(363\) | 18.2384 | + | 28.1173i | 0.957270 | + | 1.47578i | ||||
\(364\) | 0.353057 | 0.0185052 | ||||||||
\(365\) | −4.16650 | + | 3.02714i | −0.218085 | + | 0.158448i | ||||
\(366\) | 6.31384 | + | 19.4320i | 0.330030 | + | 1.01573i | ||||
\(367\) | −7.64926 | + | 23.5420i | −0.399288 | + | 1.22888i | 0.526283 | + | 0.850309i | \(0.323585\pi\) |
−0.925571 | + | 0.378573i | \(0.876415\pi\) | |||||||
\(368\) | 1.61803 | + | 1.17557i | 0.0843459 | + | 0.0612808i | ||||
\(369\) | 41.9713 | + | 30.4940i | 2.18494 | + | 1.58745i | ||||
\(370\) | 1.10121 | − | 3.38918i | 0.0572493 | − | 0.176195i | ||||
\(371\) | 0.865144 | + | 2.66264i | 0.0449161 | + | 0.138237i | ||||
\(372\) | 14.0701 | − | 10.2225i | 0.729501 | − | 0.530014i | ||||
\(373\) | −9.75070 | −0.504872 | −0.252436 | − | 0.967614i | \(-0.581232\pi\) | ||||
−0.252436 | + | 0.967614i | \(0.581232\pi\) | |||||||
\(374\) | 2.66590 | − | 0.350255i | 0.137851 | − | 0.0181112i | ||||
\(375\) | −3.04678 | −0.157335 | ||||||||
\(376\) | −6.96380 | + | 5.05950i | −0.359131 | + | 0.260924i | ||||
\(377\) | 1.04167 | + | 3.20594i | 0.0536489 | + | 0.165114i | ||||
\(378\) | 3.09082 | − | 9.51255i | 0.158974 | − | 0.489273i | ||||
\(379\) | −17.0261 | − | 12.3702i | −0.874571 | − | 0.635413i | 0.0572388 | − | 0.998361i | \(-0.481770\pi\) |
−0.931810 | + | 0.362948i | \(0.881770\pi\) | |||||||
\(380\) | 2.09738 | + | 1.52384i | 0.107593 | + | 0.0781712i | ||||
\(381\) | 15.2883 | − | 47.0526i | 0.783244 | − | 2.41058i | ||||
\(382\) | 2.51868 | + | 7.75171i | 0.128867 | + | 0.396612i | ||||
\(383\) | 28.2208 | − | 20.5036i | 1.44202 | − | 1.04769i | 0.454398 | − | 0.890799i | \(-0.349854\pi\) |
0.987617 | − | 0.156887i | \(-0.0501457\pi\) | |||||||
\(384\) | −3.04678 | −0.155480 | ||||||||
\(385\) | −2.40640 | + | 2.28238i | −0.122641 | + | 0.116321i | ||||
\(386\) | −8.74185 | −0.444948 | ||||||||
\(387\) | 48.2542 | − | 35.0587i | 2.45290 | − | 1.78213i | ||||
\(388\) | −3.02786 | − | 9.31881i | −0.153717 | − | 0.473091i | ||||
\(389\) | −3.92663 | + | 12.0849i | −0.199088 | + | 0.612730i | 0.800816 | + | 0.598910i | \(0.204399\pi\) |
−0.999904 | + | 0.0138204i | \(0.995601\pi\) | |||||||
\(390\) | 0.870248 | + | 0.632272i | 0.0440667 | + | 0.0320163i | ||||
\(391\) | −1.31175 | − | 0.953044i | −0.0663382 | − | 0.0481975i | ||||
\(392\) | −0.309017 | + | 0.951057i | −0.0156077 | + | 0.0480356i | ||||
\(393\) | −7.61567 | − | 23.4386i | −0.384160 | − | 1.18232i | ||||
\(394\) | 11.6958 | − | 8.49750i | 0.589226 | − | 0.428098i | ||||
\(395\) | 3.64694 | 0.183498 | ||||||||
\(396\) | 8.96594 | + | 18.8103i | 0.450555 | + | 0.945253i | ||||
\(397\) | 3.33036 | 0.167146 | 0.0835729 | − | 0.996502i | \(-0.473367\pi\) | ||||
0.0835729 | + | 0.996502i | \(0.473367\pi\) | |||||||
\(398\) | −8.93526 | + | 6.49185i | −0.447884 | + | 0.325407i | ||||
\(399\) | −2.44086 | − | 7.51219i | −0.122196 | − | 0.376080i | ||||
\(400\) | 0.309017 | − | 0.951057i | 0.0154508 | − | 0.0475528i | ||||
\(401\) | 7.50159 | + | 5.45023i | 0.374612 | + | 0.272171i | 0.759121 | − | 0.650950i | \(-0.225629\pi\) |
−0.384509 | + | 0.923121i | \(0.625629\pi\) | |||||||
\(402\) | −3.46932 | − | 2.52061i | −0.173034 | − | 0.125717i | ||||
\(403\) | 0.622768 | − | 1.91668i | 0.0310223 | − | 0.0954768i | ||||
\(404\) | −0.279462 | − | 0.860095i | −0.0139038 | − | 0.0427913i | ||||
\(405\) | 9.40531 | − | 6.83335i | 0.467353 | − | 0.339552i | ||||
\(406\) | −9.54782 | −0.473850 | ||||||||
\(407\) | 2.15694 | − | 11.6206i | 0.106916 | − | 0.576013i | ||||
\(408\) | 2.47005 | 0.122285 | ||||||||
\(409\) | 0.282844 | − | 0.205498i | 0.0139857 | − | 0.0101612i | −0.580770 | − | 0.814067i | \(-0.697249\pi\) |
0.594756 | + | 0.803906i | \(0.297249\pi\) | |||||||
\(410\) | −2.55165 | − | 7.85318i | −0.126017 | − | 0.387841i | ||||
\(411\) | 9.79347 | − | 30.1412i | 0.483076 | − | 1.48676i | ||||
\(412\) | −9.07741 | − | 6.59512i | −0.447212 | − | 0.324918i | ||||
\(413\) | 10.6865 | + | 7.76420i | 0.525849 | + | 0.382051i | ||||
\(414\) | 3.88301 | − | 11.9507i | 0.190840 | − | 0.587344i | ||||
\(415\) | 0.824517 | + | 2.53760i | 0.0404739 | + | 0.124566i | ||||
\(416\) | −0.285629 | + | 0.207522i | −0.0140041 | + | 0.0101746i | ||||
\(417\) | 2.30692 | 0.112970 | ||||||||
\(418\) | 7.55531 | + | 4.10479i | 0.369542 | + | 0.200772i | ||||
\(419\) | 27.9340 | 1.36466 | 0.682332 | − | 0.731043i | \(-0.260966\pi\) | ||||
0.682332 | + | 0.731043i | \(0.260966\pi\) | |||||||
\(420\) | −2.46489 | + | 1.79085i | −0.120274 | + | 0.0873845i | ||||
\(421\) | 2.49445 | + | 7.67712i | 0.121572 | + | 0.374160i | 0.993261 | − | 0.115899i | \(-0.0369750\pi\) |
−0.871689 | + | 0.490060i | \(0.836975\pi\) | |||||||
\(422\) | −7.32685 | + | 22.5497i | −0.356666 | + | 1.09770i | ||||
\(423\) | 43.7525 | + | 31.7880i | 2.12732 | + | 1.54559i | ||||
\(424\) | −2.26498 | − | 1.64560i | −0.109997 | − | 0.0799175i | ||||
\(425\) | −0.250523 | + | 0.771029i | −0.0121521 | + | 0.0374004i | ||||
\(426\) | 12.1631 | + | 37.4341i | 0.589303 | + | 1.81369i | ||||
\(427\) | −5.42536 | + | 3.94175i | −0.262552 | + | 0.190755i | ||||
\(428\) | 8.89614 | 0.430011 | ||||||||
\(429\) | 3.13486 | + | 1.70316i | 0.151352 | + | 0.0822295i | ||||
\(430\) | −9.49338 | −0.457812 | ||||||||
\(431\) | −16.1875 | + | 11.7609i | −0.779723 | + | 0.566502i | −0.904896 | − | 0.425633i | \(-0.860051\pi\) |
0.125173 | + | 0.992135i | \(0.460051\pi\) | |||||||
\(432\) | 3.09082 | + | 9.51255i | 0.148707 | + | 0.457673i | ||||
\(433\) | −11.9728 | + | 36.8484i | −0.575375 | + | 1.77082i | 0.0595231 | + | 0.998227i | \(0.481042\pi\) |
−0.634898 | + | 0.772596i | \(0.718958\pi\) | |||||||
\(434\) | 4.61803 | + | 3.35520i | 0.221673 | + | 0.161055i | ||||
\(435\) | −23.5344 | − | 17.0987i | −1.12839 | − | 0.819821i | ||||
\(436\) | 5.70950 | − | 17.5720i | 0.273435 | − | 0.841547i | ||||
\(437\) | −1.60226 | − | 4.93124i | −0.0766464 | − | 0.235893i | ||||
\(438\) | −12.6944 | + | 9.22302i | −0.606562 | + | 0.440693i | ||||
\(439\) | 5.62560 | 0.268495 | 0.134248 | − | 0.990948i | \(-0.457138\pi\) | ||||
0.134248 | + | 0.990948i | \(0.457138\pi\) | |||||||
\(440\) | 0.605270 | − | 3.26093i | 0.0288551 | − | 0.155459i | ||||
\(441\) | 6.28284 | 0.299183 | ||||||||
\(442\) | 0.231562 | − | 0.168239i | 0.0110143 | − | 0.00800233i | ||||
\(443\) | −4.84425 | − | 14.9091i | −0.230157 | − | 0.708351i | −0.997727 | − | 0.0673854i | \(-0.978534\pi\) |
0.767570 | − | 0.640965i | \(-0.221466\pi\) | |||||||
\(444\) | 3.35515 | − | 10.3261i | 0.159228 | − | 0.490054i | ||||
\(445\) | 7.79730 | + | 5.66507i | 0.369627 | + | 0.268550i | ||||
\(446\) | −4.52229 | − | 3.28564i | −0.214137 | − | 0.155580i | ||||
\(447\) | −8.44512 | + | 25.9914i | −0.399440 | + | 1.22935i | ||||
\(448\) | −0.309017 | − | 0.951057i | −0.0145997 | − | 0.0449332i | ||||
\(449\) | 21.1179 | − | 15.3431i | 0.996617 | − | 0.724085i | 0.0352568 | − | 0.999378i | \(-0.488775\pi\) |
0.961360 | + | 0.275294i | \(0.0887751\pi\) | |||||||
\(450\) | −6.28284 | −0.296176 | ||||||||
\(451\) | −11.7836 | − | 24.7217i | −0.554869 | − | 1.16410i | ||||
\(452\) | −12.6902 | −0.596899 | ||||||||
\(453\) | 54.1613 | − | 39.3505i | 2.54472 | − | 1.84885i | ||||
\(454\) | 1.95362 | + | 6.01263i | 0.0916881 | + | 0.282187i | ||||
\(455\) | −0.109101 | + | 0.335777i | −0.00511471 | + | 0.0157415i | ||||
\(456\) | 6.39025 | + | 4.64279i | 0.299251 | + | 0.217419i | ||||
\(457\) | 28.7938 | + | 20.9199i | 1.34692 | + | 0.978593i | 0.999159 | + | 0.0410094i | \(0.0130573\pi\) |
0.347759 | + | 0.937584i | \(0.386943\pi\) | |||||||
\(458\) | 1.20242 | − | 3.70068i | 0.0561856 | − | 0.172922i | ||||
\(459\) | −2.50575 | − | 7.71190i | −0.116958 | − | 0.359961i | ||||
\(460\) | −1.61803 | + | 1.17557i | −0.0754412 | + | 0.0548113i | ||||
\(461\) | −9.66571 | −0.450177 | −0.225088 | − | 0.974338i | \(-0.572267\pi\) | ||||
−0.225088 | + | 0.974338i | \(0.572267\pi\) | |||||||
\(462\) | −7.33176 | + | 6.95389i | −0.341104 | + | 0.323524i | ||||
\(463\) | −29.9726 | −1.39295 | −0.696473 | − | 0.717583i | \(-0.745248\pi\) | ||||
−0.696473 | + | 0.717583i | \(0.745248\pi\) | |||||||
\(464\) | 7.72435 | − | 5.61207i | 0.358594 | − | 0.260534i | ||||
\(465\) | 5.37431 | + | 16.5404i | 0.249227 | + | 0.767043i | ||||
\(466\) | −4.68651 | + | 14.4236i | −0.217098 | + | 0.668160i | ||||
\(467\) | −24.6820 | − | 17.9325i | −1.14215 | − | 0.829818i | −0.154729 | − | 0.987957i | \(-0.549450\pi\) |
−0.987417 | + | 0.158139i | \(0.949450\pi\) | |||||||
\(468\) | 1.79456 | + | 1.30383i | 0.0829537 | + | 0.0602694i | ||||
\(469\) | 0.434939 | − | 1.33861i | 0.0200836 | − | 0.0618111i | ||||
\(470\) | −2.65993 | − | 8.18644i | −0.122694 | − | 0.377612i | ||||
\(471\) | −0.164731 | + | 0.119684i | −0.00759040 | + | 0.00551475i | ||||
\(472\) | −13.2092 | −0.608005 | ||||||||
\(473\) | −31.2177 | + | 4.10148i | −1.43539 | + | 0.188586i | ||||
\(474\) | 11.1114 | 0.510364 | ||||||||
\(475\) | −2.09738 | + | 1.52384i | −0.0962345 | + | 0.0699185i | ||||
\(476\) | 0.250523 | + | 0.771029i | 0.0114827 | + | 0.0353401i | ||||
\(477\) | −5.43557 | + | 16.7290i | −0.248877 | + | 0.765966i | ||||
\(478\) | −17.0661 | − | 12.3993i | −0.780587 | − | 0.567130i | ||||
\(479\) | 31.3192 | + | 22.7547i | 1.43101 | + | 1.03969i | 0.989827 | + | 0.142274i | \(0.0454415\pi\) |
0.441184 | + | 0.897417i | \(0.354559\pi\) | |||||||
\(480\) | 0.941506 | − | 2.89766i | 0.0429737 | − | 0.132259i | ||||
\(481\) | −0.388791 | − | 1.19657i | −0.0177273 | − | 0.0545591i | ||||
\(482\) | −9.66098 | + | 7.01911i | −0.440046 | + | 0.319712i | ||||
\(483\) | 6.09355 | 0.277266 | ||||||||
\(484\) | 0.581513 | − | 10.9846i | 0.0264324 | − | 0.499301i | ||||
\(485\) | 9.79837 | 0.444921 | ||||||||
\(486\) | 4.38027 | − | 3.18246i | 0.198693 | − | 0.144359i | ||||
\(487\) | 10.4564 | + | 32.1814i | 0.473823 | + | 1.45828i | 0.847539 | + | 0.530734i | \(0.178084\pi\) |
−0.373716 | + | 0.927543i | \(0.621916\pi\) | |||||||
\(488\) | 2.07230 | − | 6.37789i | 0.0938088 | − | 0.288714i | ||||
\(489\) | −54.8911 | − | 39.8807i | −2.48226 | − | 1.80347i | ||||
\(490\) | −0.809017 | − | 0.587785i | −0.0365477 | − | 0.0265534i | ||||
\(491\) | −5.74014 | + | 17.6663i | −0.259049 | + | 0.797271i | 0.733956 | + | 0.679197i | \(0.237672\pi\) |
−0.993005 | + | 0.118074i | \(0.962328\pi\) | |||||||
\(492\) | −7.77431 | − | 23.9269i | −0.350493 | − | 1.07871i | ||||
\(493\) | −6.26219 | + | 4.54975i | −0.282035 | + | 0.204910i | ||||
\(494\) | 0.915302 | 0.0411814 | ||||||||
\(495\) | −20.6603 | + | 2.71441i | −0.928611 | + | 0.122004i | ||||
\(496\) | −5.70820 | −0.256306 | ||||||||
\(497\) | −10.4515 | + | 7.59345i | −0.468813 | + | 0.340613i | ||||
\(498\) | 2.51212 | + | 7.73150i | 0.112571 | + | 0.346457i | ||||
\(499\) | −4.54469 | + | 13.9871i | −0.203448 | + | 0.626149i | 0.796325 | + | 0.604868i | \(0.206774\pi\) |
−0.999774 | + | 0.0212804i | \(0.993226\pi\) | |||||||
\(500\) | 0.809017 | + | 0.587785i | 0.0361803 | + | 0.0262866i | ||||
\(501\) | 29.5787 | + | 21.4902i | 1.32148 | + | 0.960111i | ||||
\(502\) | −0.654603 | + | 2.01466i | −0.0292164 | + | 0.0899188i | ||||
\(503\) | 1.70032 | + | 5.23303i | 0.0758133 | + | 0.233329i | 0.981781 | − | 0.190018i | \(-0.0608548\pi\) |
−0.905967 | + | 0.423348i | \(0.860855\pi\) | |||||||
\(504\) | −5.08293 | + | 3.69296i | −0.226412 | + | 0.164498i | ||||
\(505\) | 0.904358 | 0.0402434 | ||||||||
\(506\) | −4.81280 | + | 4.56475i | −0.213955 | + | 0.202928i | ||||
\(507\) | −39.2283 | −1.74219 | ||||||||
\(508\) | −13.1369 | + | 9.54455i | −0.582858 | + | 0.423471i | ||||
\(509\) | 7.44870 | + | 22.9247i | 0.330158 | + | 1.01612i | 0.969058 | + | 0.246832i | \(0.0793895\pi\) |
−0.638901 | + | 0.769289i | \(0.720610\pi\) | |||||||
\(510\) | −0.763286 | + | 2.34915i | −0.0337989 | + | 0.104022i | ||||
\(511\) | −4.16650 | − | 3.02714i | −0.184315 | − | 0.133913i | ||||
\(512\) | 0.809017 | + | 0.587785i | 0.0357538 | + | 0.0259767i | ||||
\(513\) | 8.01296 | − | 24.6614i | 0.353781 | − | 1.08883i | ||||
\(514\) | 6.40088 | + | 19.6999i | 0.282331 | + | 0.868924i | ||||
\(515\) | 9.07741 | − | 6.59512i | 0.399998 | − | 0.290616i | ||||
\(516\) | −28.9242 | −1.27332 | ||||||||
\(517\) | −12.2837 | − | 25.7708i | −0.540235 | − | 1.13340i | ||||
\(518\) | 3.56360 | 0.156575 | ||||||||
\(519\) | −48.9769 | + | 35.5838i | −2.14985 | + | 1.56196i | ||||
\(520\) | −0.109101 | − | 0.335777i | −0.00478438 | − | 0.0147248i | ||||
\(521\) | 2.69862 | − | 8.30551i | 0.118229 | − | 0.363871i | −0.874378 | − | 0.485246i | \(-0.838730\pi\) |
0.992607 | + | 0.121374i | \(0.0387302\pi\) | |||||||
\(522\) | −48.5309 | − | 35.2598i | −2.12414 | − | 1.54328i | ||||
\(523\) | −35.7970 | − | 26.0080i | −1.56529 | − | 1.13725i | −0.931495 | − | 0.363754i | \(-0.881495\pi\) |
−0.633799 | − | 0.773498i | \(-0.718505\pi\) | |||||||
\(524\) | −2.49958 | + | 7.69292i | −0.109195 | + | 0.336067i | ||||
\(525\) | −0.941506 | − | 2.89766i | −0.0410907 | − | 0.126464i | ||||
\(526\) | 3.15137 | − | 2.28960i | 0.137406 | − | 0.0998315i | ||||
\(527\) | 4.62769 | 0.201585 | ||||||||
\(528\) | 1.84412 | − | 9.93532i | 0.0802552 | − | 0.432379i | ||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | 2.26498 | − | 1.64560i | 0.0983843 | − | 0.0714804i | ||||
\(531\) | 25.6458 | + | 78.9298i | 1.11293 | + | 3.42526i | ||||
\(532\) | −0.801129 | + | 2.46562i | −0.0347333 | + | 0.106898i | ||||
\(533\) | −2.35853 | − | 1.71357i | −0.102159 | − | 0.0742230i | ||||
\(534\) | 23.7566 | + | 17.2602i | 1.02805 | + | 0.746922i | ||||
\(535\) | −2.74906 | + | 8.46074i | −0.118852 | + | 0.365789i | ||||
\(536\) | 0.434939 | + | 1.33861i | 0.0187865 | + | 0.0578190i | ||||
\(537\) | 21.2288 | − | 15.4236i | 0.916091 | − | 0.665579i | ||||
\(538\) | 22.8684 | 0.985928 | ||||||||
\(539\) | −2.91429 | − | 1.58333i | −0.125527 | − | 0.0681988i | ||||
\(540\) | −10.0021 | −0.430421 | ||||||||
\(541\) | −11.3591 | + | 8.25289i | −0.488367 | + | 0.354819i | −0.804556 | − | 0.593877i | \(-0.797597\pi\) |
0.316189 | + | 0.948696i | \(0.397597\pi\) | |||||||
\(542\) | −6.36828 | − | 19.5995i | −0.273541 | − | 0.841873i | ||||
\(543\) | 11.0481 | − | 34.0025i | 0.474118 | − | 1.45919i | ||||
\(544\) | −0.655877 | − | 0.476522i | −0.0281205 | − | 0.0204307i | ||||
\(545\) | 14.9477 | + | 10.8601i | 0.640287 | + | 0.465196i | ||||
\(546\) | −0.332405 | + | 1.02304i | −0.0142256 | + | 0.0437820i | ||||
\(547\) | 2.00272 | + | 6.16373i | 0.0856300 | + | 0.263542i | 0.984699 | − | 0.174266i | \(-0.0557551\pi\) |
−0.899069 | + | 0.437808i | \(0.855755\pi\) | |||||||
\(548\) | −8.41533 | + | 6.11410i | −0.359485 | + | 0.261181i | ||||
\(549\) | −42.1335 | −1.79821 | ||||||||
\(550\) | 2.91429 | + | 1.58333i | 0.124266 | + | 0.0675133i | ||||
\(551\) | −24.7528 | −1.05450 | ||||||||
\(552\) | −4.92979 | + | 3.58170i | −0.209826 | + | 0.152447i | ||||
\(553\) | 1.12697 | + | 3.46845i | 0.0479235 | + | 0.147493i | ||||
\(554\) | −5.31649 | + | 16.3625i | −0.225876 | + | 0.695175i | ||||
\(555\) | 8.78389 | + | 6.38187i | 0.372855 | + | 0.270895i | ||||
\(556\) | −0.612562 | − | 0.445052i | −0.0259784 | − | 0.0188744i | ||||
\(557\) | 3.09355 | − | 9.52097i | 0.131078 | − | 0.403417i | −0.863881 | − | 0.503695i | \(-0.831973\pi\) |
0.994959 | + | 0.100279i | \(0.0319734\pi\) | |||||||
\(558\) | 11.0825 | + | 34.1085i | 0.469160 | + | 1.44393i | ||||
\(559\) | −2.71159 | + | 1.97008i | −0.114688 | + | 0.0833256i | ||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | −1.49505 | + | 8.05464i | −0.0631209 | + | 0.340067i | ||||
\(562\) | −30.4444 | −1.28422 | ||||||||
\(563\) | −2.68760 | + | 1.95266i | −0.113269 | + | 0.0822947i | −0.642978 | − | 0.765885i | \(-0.722301\pi\) |
0.529709 | + | 0.848180i | \(0.322301\pi\) | |||||||
\(564\) | −8.10423 | − | 24.9422i | −0.341249 | − | 1.05026i | ||||
\(565\) | 3.92150 | − | 12.0691i | 0.164979 | − | 0.507752i | ||||
\(566\) | 8.08626 | + | 5.87501i | 0.339891 | + | 0.246945i | ||||
\(567\) | 9.40531 | + | 6.83335i | 0.394986 | + | 0.286974i | ||||
\(568\) | 3.99211 | − | 12.2865i | 0.167505 | − | 0.515528i | ||||
\(569\) | 9.42871 | + | 29.0186i | 0.395272 | + | 1.21652i | 0.928749 | + | 0.370708i | \(0.120885\pi\) |
−0.533477 | + | 0.845814i | \(0.679115\pi\) | |||||||
\(570\) | −6.39025 | + | 4.64279i | −0.267658 | + | 0.194465i | ||||
\(571\) | 2.37904 | 0.0995597 | 0.0497799 | − | 0.998760i | \(-0.484148\pi\) | ||||
0.0497799 | + | 0.998760i | \(0.484148\pi\) | |||||||
\(572\) | −0.503830 | − | 1.05702i | −0.0210662 | − | 0.0441963i | ||||
\(573\) | −24.8332 | −1.03742 | ||||||||
\(574\) | 6.68031 | − | 4.85353i | 0.278831 | − | 0.202582i | ||||
\(575\) | −0.618034 | − | 1.90211i | −0.0257738 | − | 0.0793236i | ||||
\(576\) | 1.94151 | − | 5.97534i | 0.0808961 | − | 0.248972i | ||||
\(577\) | 10.1438 | + | 7.36989i | 0.422291 | + | 0.306813i | 0.778559 | − | 0.627571i | \(-0.215951\pi\) |
−0.356268 | + | 0.934384i | \(0.615951\pi\) | |||||||
\(578\) | −13.2216 | − | 9.60603i | −0.549945 | − | 0.399558i | ||||
\(579\) | 8.23050 | − | 25.3309i | 0.342048 | − | 1.05271i | ||||
\(580\) | 2.95044 | + | 9.08052i | 0.122510 | + | 0.377048i | ||||
\(581\) | −2.15861 | + | 1.56832i | −0.0895543 | + | 0.0650650i | ||||
\(582\) | 29.8535 | 1.23747 | ||||||||
\(583\) | 6.73711 | − | 6.38989i | 0.279023 | − | 0.264642i | ||||
\(584\) | 5.15008 | 0.213112 | ||||||||
\(585\) | −1.79456 | + | 1.30383i | −0.0741960 | + | 0.0539066i | ||||
\(586\) | 1.99871 | + | 6.15139i | 0.0825659 | + | 0.254112i | ||||
\(587\) | 13.4670 | − | 41.4471i | 0.555841 | − | 1.71070i | −0.137870 | − | 0.990450i | \(-0.544026\pi\) |
0.693712 | − | 0.720253i | \(-0.255974\pi\) | |||||||
\(588\) | −2.46489 | − | 1.79085i | −0.101650 | − | 0.0738534i | ||||
\(589\) | 11.9723 | + | 8.69837i | 0.493309 | + | 0.358410i | ||||
\(590\) | 4.08188 | − | 12.5627i | 0.168048 | − | 0.517200i | ||||
\(591\) | 13.6112 | + | 41.8909i | 0.559889 | + | 1.72316i | ||||
\(592\) | −2.88301 | + | 2.09463i | −0.118491 | + | 0.0860888i | ||||
\(593\) | 0.0535401 | 0.00219863 | 0.00109931 | − | 0.999999i | \(-0.499650\pi\) | ||||
0.00109931 | + | 0.999999i | \(0.499650\pi\) | |||||||
\(594\) | −32.8905 | + | 4.32126i | −1.34951 | + | 0.177303i | ||||
\(595\) | −0.810708 | −0.0332358 | ||||||||
\(596\) | 7.25672 | − | 5.27232i | 0.297247 | − | 0.215962i | ||||
\(597\) | −10.3985 | − | 32.0034i | −0.425584 | − | 1.30981i | ||||
\(598\) | −0.218201 | + | 0.671554i | −0.00892291 | + | 0.0274619i | ||||
\(599\) | −23.4214 | − | 17.0166i | −0.956971 | − | 0.695280i | −0.00452535 | − | 0.999990i | \(-0.501440\pi\) |
−0.952445 | + | 0.304710i | \(0.901440\pi\) | |||||||
\(600\) | 2.46489 | + | 1.79085i | 0.100629 | + | 0.0731111i | ||||
\(601\) | 9.59206 | − | 29.5213i | 0.391268 | − | 1.20420i | −0.540562 | − | 0.841304i | \(-0.681788\pi\) |
0.931830 | − | 0.362895i | \(-0.118212\pi\) | |||||||
\(602\) | −2.93362 | − | 9.02875i | −0.119565 | − | 0.367984i | ||||
\(603\) | 7.15419 | − | 5.19782i | 0.291341 | − | 0.211672i | ||||
\(604\) | −21.9731 | −0.894072 | ||||||||
\(605\) | 10.2673 | + | 3.94749i | 0.417425 | + | 0.160488i | ||||
\(606\) | 2.75538 | 0.111929 | ||||||||
\(607\) | −6.63627 | + | 4.82153i | −0.269358 | + | 0.195700i | −0.714262 | − | 0.699878i | \(-0.753238\pi\) |
0.444904 | + | 0.895578i | \(0.353238\pi\) | |||||||
\(608\) | −0.801129 | − | 2.46562i | −0.0324901 | − | 0.0999941i | ||||
\(609\) | 8.98933 | − | 27.6663i | 0.364266 | − | 1.12110i | ||||
\(610\) | 5.42536 | + | 3.94175i | 0.219666 | + | 0.159597i | ||||
\(611\) | −2.45862 | − | 1.78629i | −0.0994650 | − | 0.0722656i | ||||
\(612\) | −1.57399 | + | 4.84426i | −0.0636249 | + | 0.195817i | ||||
\(613\) | −6.67585 | − | 20.5462i | −0.269635 | − | 0.829852i | −0.990589 | − | 0.136869i | \(-0.956296\pi\) |
0.720954 | − | 0.692983i | \(-0.243704\pi\) | |||||||
\(614\) | −16.7040 | + | 12.1362i | −0.674119 | + | 0.489776i | ||||
\(615\) | 25.1582 | 1.01448 | ||||||||
\(616\) | 3.28837 | − | 0.432036i | 0.132492 | − | 0.0174072i | ||||
\(617\) | 16.5772 | 0.667372 | 0.333686 | − | 0.942684i | \(-0.391707\pi\) | ||||
0.333686 | + | 0.942684i | \(0.391707\pi\) | |||||||
\(618\) | 27.6568 | − | 20.0939i | 1.11252 | − | 0.808294i | ||||
\(619\) | −5.50460 | − | 16.9414i | −0.221248 | − | 0.680933i | −0.998651 | − | 0.0519291i | \(-0.983463\pi\) |
0.777402 | − | 0.629004i | \(-0.216537\pi\) | |||||||
\(620\) | 1.76393 | − | 5.42882i | 0.0708412 | − | 0.218027i | ||||
\(621\) | 16.1837 | + | 11.7582i | 0.649430 | + | 0.471839i | ||||
\(622\) | 18.9621 | + | 13.7768i | 0.760312 | + | 0.552399i | ||||
\(623\) | −2.97830 | + | 9.16627i | −0.119323 | + | 0.367239i | ||||
\(624\) | −0.332405 | − | 1.02304i | −0.0133068 | − | 0.0409543i | ||||
\(625\) | −0.809017 | + | 0.587785i | −0.0323607 | + | 0.0235114i | ||||
\(626\) | −11.9059 | −0.475855 | ||||||||
\(627\) | −19.0076 | + | 18.0280i | −0.759092 | + | 0.719969i | ||||
\(628\) | 0.0668308 | 0.00266684 | ||||||||
\(629\) | 2.33728 | − | 1.69813i | 0.0931935 | − | 0.0677090i | ||||
\(630\) | −1.94151 | − | 5.97534i | −0.0773514 | − | 0.238063i | ||||
\(631\) | 4.17546 | − | 12.8508i | 0.166223 | − | 0.511581i | −0.832902 | − | 0.553421i | \(-0.813322\pi\) |
0.999124 | + | 0.0418403i | \(0.0133221\pi\) | |||||||
\(632\) | −2.95044 | − | 2.14362i | −0.117362 | − | 0.0852686i | ||||
\(633\) | −58.4431 | − | 42.4614i | −2.32291 | − | 1.68769i | ||||
\(634\) | 10.6359 | − | 32.7339i | 0.422406 | − | 1.30003i | ||||
\(635\) | −5.01787 | − | 15.4434i | −0.199128 | − | 0.612853i | ||||
\(636\) | 6.90088 | − | 5.01378i | 0.273638 | − | 0.198809i | ||||
\(637\) | −0.353057 | −0.0139886 | ||||||||
\(638\) | 13.6252 | + | 28.5854i | 0.539428 | + | 1.13171i | ||||
\(639\) | −81.1665 | −3.21090 | ||||||||
\(640\) | −0.809017 | + | 0.587785i | −0.0319792 | + | 0.0232343i | ||||
\(641\) | 13.6930 | + | 42.1429i | 0.540843 | + | 1.66454i | 0.730674 | + | 0.682726i | \(0.239206\pi\) |
−0.189832 | + | 0.981817i | \(0.560794\pi\) | |||||||
\(642\) | −8.37577 | + | 25.7780i | −0.330565 | + | 1.01738i | ||||
\(643\) | −27.7373 | − | 20.1524i | −1.09385 | − | 0.794731i | −0.113808 | − | 0.993503i | \(-0.536305\pi\) |
−0.980046 | + | 0.198772i | \(0.936305\pi\) | |||||||
\(644\) | −1.61803 | − | 1.17557i | −0.0637595 | − | 0.0463240i | ||||
\(645\) | 8.93807 | − | 27.5086i | 0.351936 | − | 1.08315i | ||||
\(646\) | 0.649481 | + | 1.99890i | 0.0255535 | + | 0.0786456i | ||||
\(647\) | −22.5507 | + | 16.3841i | −0.886561 | + | 0.644124i | −0.934979 | − | 0.354703i | \(-0.884582\pi\) |
0.0484181 | + | 0.998827i | \(0.484582\pi\) | |||||||
\(648\) | −11.6256 | −0.456697 | ||||||||
\(649\) | 7.99517 | − | 43.0744i | 0.313838 | − | 1.69082i | ||||
\(650\) | 0.353057 | 0.0138480 | ||||||||
\(651\) | −14.0701 | + | 10.2225i | −0.551451 | + | 0.400653i | ||||
\(652\) | 6.88155 | + | 21.1792i | 0.269502 | + | 0.829443i | ||||
\(653\) | −8.52365 | + | 26.2331i | −0.333556 | + | 1.02658i | 0.633873 | + | 0.773437i | \(0.281464\pi\) |
−0.967429 | + | 0.253143i | \(0.918536\pi\) | |||||||
\(654\) | 45.5422 | + | 33.0883i | 1.78084 | + | 1.29386i | ||||
\(655\) | −6.54399 | − | 4.75449i | −0.255695 | − | 0.185773i | ||||
\(656\) | −2.55165 | + | 7.85318i | −0.0996252 | + | 0.306615i | ||||
\(657\) | −9.99891 | − | 30.7735i | −0.390094 | − | 1.20059i | ||||
\(658\) | 6.96380 | − | 5.05950i | 0.271477 | − | 0.197240i | ||||
\(659\) | 2.49969 | 0.0973742 | 0.0486871 | − | 0.998814i | \(-0.484496\pi\) | ||||
0.0486871 | + | 0.998814i | \(0.484496\pi\) | |||||||
\(660\) | 8.87918 | + | 4.82405i | 0.345622 | + | 0.187776i | ||||
\(661\) | 10.1499 | 0.394785 | 0.197393 | − | 0.980325i | \(-0.436753\pi\) | ||||
0.197393 | + | 0.980325i | \(0.436753\pi\) | |||||||
\(662\) | −9.44693 | + | 6.86360i | −0.367165 | + | 0.266761i | ||||
\(663\) | 0.269483 | + | 0.829385i | 0.0104659 | + | 0.0322106i | ||||
\(664\) | 0.824517 | − | 2.53760i | 0.0319975 | − | 0.0984780i | ||||
\(665\) | −2.09738 | − | 1.52384i | −0.0813330 | − | 0.0590919i | ||||
\(666\) | 18.1135 | + | 13.1602i | 0.701884 | + | 0.509949i | ||||
\(667\) | 5.90088 | − | 18.1610i | 0.228483 | − | 0.703198i | ||||
\(668\) | −3.70820 | − | 11.4127i | −0.143475 | − | 0.441570i | ||||
\(669\) | 13.7784 | − | 10.0106i | 0.532704 | − | 0.387032i | ||||
\(670\) | −1.40749 | −0.0543762 | ||||||||
\(671\) | 19.5435 | + | 10.6180i | 0.754470 | + | 0.409903i | ||||
\(672\) | 3.04678 | 0.117532 | ||||||||
\(673\) | −29.8922 | + | 21.7180i | −1.15226 | + | 0.837166i | −0.988780 | − | 0.149381i | \(-0.952272\pi\) |
−0.163480 | + | 0.986547i | \(0.552272\pi\) | |||||||
\(674\) | 3.19330 | + | 9.82797i | 0.123001 | + | 0.378559i | ||||
\(675\) | 3.09082 | − | 9.51255i | 0.118966 | − | 0.366138i | ||||
\(676\) | 10.4164 | + | 7.56794i | 0.400630 | + | 0.291075i | ||||
\(677\) | −7.14971 | − | 5.19457i | −0.274786 | − | 0.199643i | 0.441854 | − | 0.897087i | \(-0.354321\pi\) |
−0.716640 | + | 0.697443i | \(0.754321\pi\) | |||||||
\(678\) | 11.9479 | − | 36.7720i | 0.458858 | − | 1.41222i | ||||
\(679\) | 3.02786 | + | 9.31881i | 0.116199 | + | 0.357623i | ||||
\(680\) | 0.655877 | − | 0.476522i | 0.0251517 | − | 0.0182738i | ||||
\(681\) | −19.2619 | −0.738117 | ||||||||
\(682\) | 3.45501 | − | 18.6140i | 0.132299 | − | 0.712768i | ||||
\(683\) | 33.0803 | 1.26578 | 0.632892 | − | 0.774240i | \(-0.281868\pi\) | ||||
0.632892 | + | 0.774240i | \(0.281868\pi\) | |||||||
\(684\) | −13.1775 | + | 9.57403i | −0.503855 | + | 0.366072i | ||||
\(685\) | −3.21437 | − | 9.89282i | −0.122815 | − | 0.377985i | ||||
\(686\) | 0.309017 | − | 0.951057i | 0.0117983 | − | 0.0363115i | ||||
\(687\) | 9.59122 | + | 6.96843i | 0.365928 | + | 0.265862i | ||||
\(688\) | 7.68031 | + | 5.58007i | 0.292809 | + | 0.212738i | ||||
\(689\) | 0.305445 | − | 0.940063i | 0.0116365 | − | 0.0358136i | ||||
\(690\) | −1.88301 | − | 5.79531i | −0.0716850 | − | 0.220624i | ||||
\(691\) | 7.46019 | − | 5.42014i | 0.283799 | − | 0.206192i | −0.436774 | − | 0.899571i | \(-0.643879\pi\) |
0.720573 | + | 0.693379i | \(0.243879\pi\) | |||||||
\(692\) | 19.8698 | 0.755336 | ||||||||
\(693\) | −8.96594 | − | 18.8103i | −0.340588 | − | 0.714544i | ||||
\(694\) | 18.3202 | 0.695426 | ||||||||
\(695\) | 0.612562 | − | 0.445052i | 0.0232358 | − | 0.0168818i | ||||
\(696\) | 8.98933 | + | 27.6663i | 0.340740 | + | 1.04869i | ||||
\(697\) | 2.06864 | − | 6.36663i | 0.0783555 | − | 0.241153i | ||||
\(698\) | −24.2071 | − | 17.5875i | −0.916251 | − | 0.665695i | ||||
\(699\) | −37.3822 | − | 27.1598i | −1.41393 | − | 1.02728i | ||||
\(700\) | −0.309017 | + | 0.951057i | −0.0116797 | + | 0.0359466i | ||||
\(701\) | 8.12619 | + | 25.0098i | 0.306922 | + | 0.944608i | 0.978953 | + | 0.204085i | \(0.0654220\pi\) |
−0.672031 | + | 0.740523i | \(0.734578\pi\) | |||||||
\(702\) | −2.85689 | + | 2.07565i | −0.107826 | + | 0.0783404i | ||||
\(703\) | 9.23865 | 0.348442 | ||||||||
\(704\) | −2.40640 | + | 2.28238i | −0.0906946 | + | 0.0860203i | ||||
\(705\) | 26.2258 | 0.987722 | ||||||||
\(706\) | −7.22472 | + | 5.24907i | −0.271906 | + | 0.197551i | ||||
\(707\) | 0.279462 | + | 0.860095i | 0.0105102 | + | 0.0323472i | ||||
\(708\) | 12.4366 | − | 38.2759i | 0.467395 | − | 1.43849i | ||||
\(709\) | 28.0104 | + | 20.3508i | 1.05195 | + | 0.764289i | 0.972583 | − | 0.232557i | \(-0.0747091\pi\) |
0.0793701 | + | 0.996845i | \(0.474709\pi\) | |||||||
\(710\) | 10.4515 | + | 7.59345i | 0.392237 | + | 0.284977i | ||||
\(711\) | −7.08056 | + | 21.7917i | −0.265542 | + | 0.817254i | ||||
\(712\) | −2.97830 | − | 9.16627i | −0.111617 | − | 0.343521i | ||||
\(713\) | −9.23607 | + | 6.71040i | −0.345893 | + | 0.251306i | ||||
\(714\) | −2.47005 | −0.0924391 | ||||||||
\(715\) | 1.16098 | − | 0.152533i | 0.0434182 | − | 0.00570442i | ||||
\(716\) | −8.61246 | −0.321863 | ||||||||
\(717\) | 51.9967 | − | 37.7778i | 1.94185 | − | 1.41084i | ||||
\(718\) | 9.20610 | + | 28.3334i | 0.343568 | + | 1.05739i | ||||
\(719\) | −11.4905 | + | 35.3640i | −0.428522 | + | 1.31885i | 0.471060 | + | 0.882101i | \(0.343872\pi\) |
−0.899581 | + | 0.436753i | \(0.856128\pi\) | |||||||
\(720\) | 5.08293 | + | 3.69296i | 0.189430 | + | 0.137629i | ||||
\(721\) | 9.07741 | + | 6.59512i | 0.338060 | + | 0.245615i | ||||
\(722\) | 3.79439 | − | 11.6779i | 0.141213 | − | 0.434608i | ||||
\(723\) | −11.2431 | − | 34.6027i | −0.418136 | − | 1.28689i | ||||
\(724\) | −9.49338 | + | 6.89735i | −0.352819 | + | 0.256338i | ||||
\(725\) | −9.54782 | −0.354597 | ||||||||
\(726\) | 31.2821 | + | 12.0271i | 1.16099 | + | 0.446368i | ||||
\(727\) | 16.8666 | 0.625547 | 0.312773 | − | 0.949828i | \(-0.398742\pi\) | ||||
0.312773 | + | 0.949828i | \(0.398742\pi\) | |||||||
\(728\) | 0.285629 | − | 0.207522i | 0.0105861 | − | 0.00769126i | ||||
\(729\) | −5.67991 | − | 17.4810i | −0.210367 | − | 0.647443i | ||||
\(730\) | −1.59146 | + | 4.89802i | −0.0589026 | + | 0.181284i | ||||
\(731\) | −6.22649 | − | 4.52381i | −0.230295 | − | 0.167319i | ||||
\(732\) | 16.5299 | + | 12.0096i | 0.610961 | + | 0.443889i | ||||
\(733\) | 10.8449 | − | 33.3771i | 0.400564 | − | 1.23281i | −0.523979 | − | 0.851731i | \(-0.675553\pi\) |
0.924543 | − | 0.381078i | \(-0.124447\pi\) | |||||||
\(734\) | 7.64926 | + | 23.5420i | 0.282339 | + | 0.868951i | ||||
\(735\) | 2.46489 | − | 1.79085i | 0.0909190 | − | 0.0660565i | ||||
\(736\) | 2.00000 | 0.0737210 | ||||||||
\(737\) | −4.62835 | + | 0.608087i | −0.170488 | + | 0.0223992i | ||||
\(738\) | 51.8794 | 1.90971 | ||||||||
\(739\) | 7.27016 | − | 5.28208i | 0.267437 | − | 0.194304i | −0.445982 | − | 0.895042i | \(-0.647146\pi\) |
0.713419 | + | 0.700737i | \(0.247146\pi\) | |||||||
\(740\) | −1.10121 | − | 3.38918i | −0.0404814 | − | 0.124589i | ||||
\(741\) | −0.861762 | + | 2.65223i | −0.0316576 | + | 0.0974322i | ||||
\(742\) | 2.26498 | + | 1.64560i | 0.0831499 | + | 0.0604120i | ||||
\(743\) | 7.76383 | + | 5.64076i | 0.284827 | + | 0.206939i | 0.721020 | − | 0.692914i | \(-0.243673\pi\) |
−0.436193 | + | 0.899853i | \(0.643673\pi\) | |||||||
\(744\) | 5.37431 | − | 16.5404i | 0.197032 | − | 0.606401i | ||||
\(745\) | 2.77182 | + | 8.53079i | 0.101552 | + | 0.312544i | ||||
\(746\) | −7.88848 | + | 5.73132i | −0.288818 | + | 0.209838i | ||||
\(747\) | −16.7638 | −0.613357 | ||||||||
\(748\) | 1.95089 | − | 1.85034i | 0.0713315 | − | 0.0676552i | ||||
\(749\) | −8.89614 | −0.325058 | ||||||||
\(750\) | −2.46489 | + | 1.79085i | −0.0900052 | + | 0.0653926i | ||||
\(751\) | −4.37232 | − | 13.4566i | −0.159548 | − | 0.491039i | 0.839045 | − | 0.544062i | \(-0.183114\pi\) |
−0.998593 | + | 0.0530230i | \(0.983114\pi\) | |||||||
\(752\) | −2.65993 | + | 8.18644i | −0.0969978 | + | 0.298529i | ||||
\(753\) | −5.22149 | − | 3.79363i | −0.190282 | − | 0.138248i | ||||
\(754\) | 2.72713 | + | 1.98138i | 0.0993164 | + | 0.0721576i | ||||
\(755\) | 6.79006 | − | 20.8976i | 0.247115 | − | 0.760543i | ||||
\(756\) | −3.09082 | − | 9.51255i | −0.112412 | − | 0.345968i | ||||
\(757\) | −36.9530 | + | 26.8479i | −1.34308 | + | 0.975805i | −0.343756 | + | 0.939059i | \(0.611699\pi\) |
−0.999325 | + | 0.0367462i | \(0.988301\pi\) | |||||||
\(758\) | −21.0454 | −0.764403 | ||||||||
\(759\) | −8.69581 | − | 18.2436i | −0.315638 | − | 0.662200i | ||||
\(760\) | 2.59251 | 0.0940401 | ||||||||
\(761\) | 13.3680 | − | 9.71241i | 0.484589 | − | 0.352075i | −0.318510 | − | 0.947919i | \(-0.603183\pi\) |
0.803100 | + | 0.595845i | \(0.203183\pi\) | |||||||
\(762\) | −15.2883 | − | 47.0526i | −0.553837 | − | 1.70454i | ||||
\(763\) | −5.70950 | + | 17.5720i | −0.206698 | + | 0.636150i | ||||
\(764\) | 6.59400 | + | 4.79082i | 0.238563 | + | 0.173326i | ||||
\(765\) | −4.12077 | − | 2.99391i | −0.148987 | − | 0.108245i | ||||
\(766\) | 10.7794 | − | 33.1755i | 0.389475 | − | 1.19868i | ||||
\(767\) | −1.44114 | − | 4.43536i | −0.0520364 | − | 0.160152i | ||||
\(768\) | −2.46489 | + | 1.79085i | −0.0889442 | + | 0.0646217i | ||||
\(769\) | 26.5929 | 0.958963 | 0.479482 | − | 0.877552i | \(-0.340825\pi\) | ||||
0.479482 | + | 0.877552i | \(0.340825\pi\) | |||||||
\(770\) | −0.605270 | + | 3.26093i | −0.0218124 | + | 0.117516i | ||||
\(771\) | −63.1099 | −2.27285 | ||||||||
\(772\) | −7.07230 | + | 5.13833i | −0.254538 | + | 0.184933i | ||||
\(773\) | 10.9632 | + | 33.7413i | 0.394319 | + | 1.21359i | 0.929491 | + | 0.368846i | \(0.120247\pi\) |
−0.535172 | + | 0.844743i | \(0.679753\pi\) | |||||||
\(774\) | 18.4315 | − | 56.7262i | 0.662505 | − | 2.03898i | ||||
\(775\) | 4.61803 | + | 3.35520i | 0.165885 | + | 0.120522i | ||||
\(776\) | −7.92705 | − | 5.75934i | −0.284565 | − | 0.206748i | ||||
\(777\) | −3.35515 | + | 10.3261i | −0.120365 | + | 0.370446i | ||||
\(778\) | 3.92663 | + | 12.0849i | 0.140777 | + | 0.433266i | ||||
\(779\) | 17.3187 | − | 12.5828i | 0.620509 | − | 0.450826i | ||||
\(780\) | 1.07569 | 0.0385157 | ||||||||
\(781\) | 37.6489 | + | 20.4546i | 1.34718 | + | 0.731924i | ||||
\(782\) | −1.62142 | −0.0579817 | ||||||||
\(783\) | 77.2596 | − | 56.1324i | 2.76103 | − | 2.00601i | ||||
\(784\) | 0.309017 | + | 0.951057i | 0.0110363 | + | 0.0339663i | ||||
\(785\) | −0.0206519 | + | 0.0635599i | −0.000737097 | + | 0.00226855i | ||||
\(786\) | −19.9381 | − | 14.4859i | −0.711168 | − | 0.516693i | ||||
\(787\) | 13.0244 | + | 9.46277i | 0.464269 | + | 0.337311i | 0.795204 | − | 0.606342i | \(-0.207364\pi\) |
−0.330934 | + | 0.943654i | \(0.607364\pi\) | |||||||
\(788\) | 4.46740 | − | 13.7492i | 0.159145 | − | 0.489797i | ||||
\(789\) | 3.66745 | + | 11.2873i | 0.130565 | + | 0.401837i | ||||
\(790\) | 2.95044 | − | 2.14362i | 0.104972 | − | 0.0762666i | ||||
\(791\) | 12.6902 | 0.451213 | ||||||||
\(792\) | 18.3100 | + | 9.94781i | 0.650618 | + | 0.353480i | ||||
\(793\) | 2.36764 | 0.0840773 | ||||||||
\(794\) | 2.69432 | − | 1.95754i | 0.0956177 | − | 0.0694703i | ||||
\(795\) | 2.63590 | + | 8.11247i | 0.0934858 | + | 0.287720i | ||||
\(796\) | −3.41297 | + | 10.5040i | −0.120969 | + | 0.372305i | ||||
\(797\) | −30.7797 | − | 22.3627i | −1.09027 | − | 0.792128i | −0.110826 | − | 0.993840i | \(-0.535350\pi\) |
−0.979445 | + | 0.201711i | \(0.935350\pi\) | |||||||
\(798\) | −6.39025 | − | 4.64279i | −0.226213 | − | 0.164353i | ||||
\(799\) | 2.15643 | − | 6.63681i | 0.0762890 | − | 0.234793i | ||||
\(800\) | −0.309017 | − | 0.951057i | −0.0109254 | − | 0.0336249i | ||||
\(801\) | −48.9892 | + | 35.5927i | −1.73095 | + | 1.25761i | ||||
\(802\) | 9.27248 | 0.327423 | ||||||||
\(803\) | −3.11719 | + | 16.7940i | −0.110003 | + | 0.592649i | ||||
\(804\) | −4.28832 | −0.151237 | ||||||||
\(805\) | 1.61803 | − | 1.17557i | 0.0570282 | − | 0.0414334i | ||||
\(806\) | −0.622768 | − | 1.91668i | −0.0219361 | − | 0.0675123i | ||||
\(807\) | −21.5308 | + | 66.2648i | −0.757918 | + | 2.33263i | ||||
\(808\) | −0.731641 | − | 0.531568i | −0.0257390 | − | 0.0187005i | ||||
\(809\) | −11.9721 | − | 8.69827i | −0.420918 | − | 0.305815i | 0.357089 | − | 0.934070i | \(-0.383769\pi\) |
−0.778007 | + | 0.628256i | \(0.783769\pi\) | |||||||
\(810\) | 3.59251 | − | 11.0566i | 0.126228 | − | 0.388489i | ||||
\(811\) | −0.217015 | − | 0.667904i | −0.00762043 | − | 0.0234533i | 0.947174 | − | 0.320720i | \(-0.103925\pi\) |
−0.954794 | + | 0.297267i | \(0.903925\pi\) | |||||||
\(812\) | −7.72435 | + | 5.61207i | −0.271072 | + | 0.196945i | ||||
\(813\) | 62.7885 | 2.20209 | ||||||||
\(814\) | −5.08544 | − | 10.6691i | −0.178244 | − | 0.373952i | ||||
\(815\) | −22.2692 | −0.780055 | ||||||||
\(816\) | 1.99831 | − | 1.45186i | 0.0699548 | − | 0.0508251i | ||||
\(817\) | −7.60542 | − | 23.4071i | −0.266080 | − | 0.818910i | ||||
\(818\) | 0.108037 | − | 0.332503i | 0.00377742 | − | 0.0116257i | ||||
\(819\) | −1.79456 | − | 1.30383i | −0.0627071 | − | 0.0455594i | ||||
\(820\) | −6.68031 | − | 4.85353i | −0.233287 | − | 0.169493i | ||||
\(821\) | −0.465627 | + | 1.43305i | −0.0162505 | + | 0.0500138i | −0.958853 | − | 0.283903i | \(-0.908371\pi\) |
0.942602 | + | 0.333917i | \(0.108371\pi\) | |||||||
\(822\) | −9.79347 | − | 30.1412i | −0.341586 | − | 1.05129i | ||||
\(823\) | 24.9977 | − | 18.1619i | 0.871366 | − | 0.633084i | −0.0595875 | − | 0.998223i | \(-0.518979\pi\) |
0.930953 | + | 0.365139i | \(0.118979\pi\) | |||||||
\(824\) | −11.2203 | −0.390877 | ||||||||
\(825\) | −7.33176 | + | 6.95389i | −0.255259 | + | 0.242103i | ||||
\(826\) | 13.2092 | 0.459609 | ||||||||
\(827\) | 42.6884 | − | 31.0149i | 1.48442 | − | 1.07850i | 0.508323 | − | 0.861167i | \(-0.330266\pi\) |
0.976099 | − | 0.217328i | \(-0.0697343\pi\) | |||||||
\(828\) | −3.88301 | − | 11.9507i | −0.134944 | − | 0.415315i | ||||
\(829\) | −8.57753 | + | 26.3989i | −0.297910 | + | 0.916872i | 0.684319 | + | 0.729183i | \(0.260100\pi\) |
−0.982228 | + | 0.187689i | \(0.939900\pi\) | |||||||
\(830\) | 2.15861 | + | 1.56832i | 0.0749265 | + | 0.0544373i | ||||
\(831\) | −42.4073 | − | 30.8107i | −1.47109 | − | 1.06881i | ||||
\(832\) | −0.109101 | + | 0.335777i | −0.00378238 | + | 0.0116410i | ||||
\(833\) | −0.250523 | − | 0.771029i | −0.00868009 | − | 0.0267146i | ||||
\(834\) | 1.86634 | − | 1.35597i | 0.0646260 | − | 0.0469535i | ||||
\(835\) | 12.0000 | 0.415277 | ||||||||
\(836\) | 8.52511 | − | 1.12006i | 0.294847 | − | 0.0387379i | ||||
\(837\) | −57.0940 | −1.97346 | ||||||||
\(838\) | 22.5991 | − | 16.4192i | 0.780671 | − | 0.567191i | ||||
\(839\) | −14.8401 | − | 45.6732i | −0.512338 | − | 1.57682i | −0.788073 | − | 0.615581i | \(-0.788921\pi\) |
0.275735 | − | 0.961234i | \(-0.411079\pi\) | |||||||
\(840\) | −0.941506 | + | 2.89766i | −0.0324850 | + | 0.0999786i | ||||
\(841\) | −50.2892 | − | 36.5373i | −1.73411 | − | 1.25991i | ||||
\(842\) | 6.53055 | + | 4.74472i | 0.225058 | + | 0.163514i | ||||
\(843\) | 28.6636 | − | 88.2175i | 0.987227 | − | 3.03837i | ||||
\(844\) | 7.32685 | + | 22.5497i | 0.252201 | + | 0.776194i | ||||
\(845\) | −10.4164 | + | 7.56794i | −0.358334 | + | 0.260345i | ||||
\(846\) | 54.0810 | 1.85934 | ||||||||
\(847\) | −0.581513 | + | 10.9846i | −0.0199810 | + | 0.377436i | ||||
\(848\) | −2.79967 | −0.0961409 | ||||||||
\(849\) | −24.6370 | + | 17.8998i | −0.845541 | + | 0.614321i | ||||
\(850\) | 0.250523 | + | 0.771029i | 0.00859285 | + | 0.0264461i | ||||
\(851\) | −2.20242 | + | 6.77837i | −0.0754981 | + | 0.232359i | ||||
\(852\) | 31.8433 | + | 23.1355i | 1.09093 | + | 0.792610i | ||||
\(853\) | −29.1396 | − | 21.1712i | −0.997722 | − | 0.724887i | −0.0361235 | − | 0.999347i | \(-0.511501\pi\) |
−0.961599 | + | 0.274460i | \(0.911501\pi\) | |||||||
\(854\) | −2.07230 | + | 6.37789i | −0.0709128 | + | 0.218247i | ||||
\(855\) | −5.03337 | − | 15.4911i | −0.172138 | − | 0.529785i | ||||
\(856\) | 7.19713 | − | 5.22902i | 0.245993 | − | 0.178724i | ||||
\(857\) | −5.73142 | −0.195782 | −0.0978908 | − | 0.995197i | \(-0.531210\pi\) | ||||
−0.0978908 | + | 0.995197i | \(0.531210\pi\) | |||||||
\(858\) | 3.53725 | − | 0.464734i | 0.120760 | − | 0.0158658i | ||||
\(859\) | 33.4569 | 1.14153 | 0.570767 | − | 0.821112i | \(-0.306646\pi\) | ||||
0.570767 | + | 0.821112i | \(0.306646\pi\) | |||||||
\(860\) | −7.68031 | + | 5.58007i | −0.261896 | + | 0.190279i | ||||
\(861\) | 7.77431 | + | 23.9269i | 0.264948 | + | 0.815425i | ||||
\(862\) | −6.18306 | + | 19.0295i | −0.210596 | + | 0.648148i | ||||
\(863\) | −8.77961 | − | 6.37876i | −0.298861 | − | 0.217136i | 0.428241 | − | 0.903665i | \(-0.359133\pi\) |
−0.727102 | + | 0.686529i | \(0.759133\pi\) | |||||||
\(864\) | 8.09186 | + | 5.87908i | 0.275291 | + | 0.200010i | ||||
\(865\) | −6.14010 | + | 18.8973i | −0.208770 | + | 0.642527i | ||||
\(866\) | 11.9728 | + | 36.8484i | 0.406852 | + | 1.25216i | ||||
\(867\) | 40.2831 | − | 29.2674i | 1.36809 | − | 0.993974i | ||||
\(868\) | 5.70820 | 0.193749 | ||||||||
\(869\) | 8.77600 | − | 8.32370i | 0.297705 | − | 0.282362i | ||||
\(870\) | −29.0901 | −0.986246 | ||||||||
\(871\) | −0.402021 | + | 0.292085i | −0.0136220 | + | 0.00989693i | ||||
\(872\) | −5.70950 | − | 17.5720i | −0.193348 | − | 0.595064i | ||||
\(873\) | −19.0236 | + | 58.5486i | −0.643851 | + | 1.98157i | ||||
\(874\) | −4.19476 | − | 3.04767i | −0.141890 | − | 0.103089i | ||||
\(875\) | −0.809017 | − | 0.587785i | −0.0273498 | − | 0.0198708i | ||||
\(876\) | −4.84883 | + | 14.9232i | −0.163827 | + | 0.504207i | ||||
\(877\) | 6.52912 | + | 20.0946i | 0.220473 | + | 0.678545i | 0.998720 | + | 0.0505868i | \(0.0161092\pi\) |
−0.778247 | + | 0.627958i | \(0.783891\pi\) | |||||||
\(878\) | 4.55120 | − | 3.30664i | 0.153596 | − | 0.111594i | ||||
\(879\) | −19.7064 | −0.664681 | ||||||||
\(880\) | −1.42705 | − | 2.99391i | −0.0481059 | − | 0.100925i | ||||
\(881\) | 24.5805 | 0.828137 | 0.414069 | − | 0.910246i | \(-0.364107\pi\) | ||||
0.414069 | + | 0.910246i | \(0.364107\pi\) | |||||||
\(882\) | 5.08293 | − | 3.69296i | 0.171151 | − | 0.124349i | ||||
\(883\) | −4.78135 | − | 14.7155i | −0.160905 | − | 0.495215i | 0.837806 | − | 0.545968i | \(-0.183838\pi\) |
−0.998711 | + | 0.0507526i | \(0.983838\pi\) | |||||||
\(884\) | 0.0884487 | − | 0.272217i | 0.00297485 | − | 0.00915565i | ||||
\(885\) | 32.5594 | + | 23.6558i | 1.09447 | + | 0.795180i | ||||
\(886\) | −12.6824 | − | 9.21430i | −0.426074 | − | 0.309561i | ||||
\(887\) | 6.31499 | − | 19.4356i | 0.212037 | − | 0.652582i | −0.787314 | − | 0.616552i | \(-0.788529\pi\) |
0.999351 | − | 0.0360297i | \(-0.0114711\pi\) | |||||||
\(888\) | −3.35515 | − | 10.3261i | −0.112591 | − | 0.346521i | ||||
\(889\) | 13.1369 | − | 9.54455i | 0.440599 | − | 0.320114i | ||||
\(890\) | 9.63799 | 0.323066 | ||||||||
\(891\) | 7.03663 | − | 37.9102i | 0.235736 | − | 1.27004i | ||||
\(892\) | −5.58986 | −0.187162 | ||||||||
\(893\) | 18.0537 | − | 13.1168i | 0.604144 | − | 0.438936i | ||||
\(894\) | 8.44512 | + | 25.9914i | 0.282447 | + | 0.869282i | ||||
\(895\) | 2.66140 | − | 8.19094i | 0.0889607 | − | 0.273793i | ||||
\(896\) | −0.809017 | − | 0.587785i | −0.0270274 | − | 0.0196365i | ||||
\(897\) | −1.74050 | − | 1.26454i | −0.0581134 | − | 0.0422219i | ||||
\(898\) | 8.06633 | − | 24.8256i | 0.269177 | − | 0.828442i | ||||
\(899\) | 16.8417 | + | 51.8334i | 0.561702 | + | 1.72874i | ||||
\(900\) | −5.08293 | + | 3.69296i | −0.169431 | + | 0.123099i | ||||
\(901\) | 2.26971 | 0.0756151 | ||||||||
\(902\) | −24.0642 | − | 13.0740i | −0.801250 | − | 0.435318i | ||||
\(903\) | 28.9242 | 0.962538 | ||||||||
\(904\) | −10.2666 | + | 7.45914i | −0.341463 | + | 0.248087i | ||||
\(905\) | −3.62615 | − | 11.1601i | −0.120537 | − | 0.370976i | ||||
\(906\) | 20.6878 | − | 63.6704i | 0.687305 | − | 2.11531i | ||||
\(907\) | −25.0615 | − | 18.2082i | −0.832152 | − | 0.604594i | 0.0880154 | − | 0.996119i | \(-0.471948\pi\) |
−0.920167 | + | 0.391525i | \(0.871948\pi\) | |||||||
\(908\) | 5.11465 | + | 3.71601i | 0.169736 | + | 0.123320i | ||||
\(909\) | −1.75582 | + | 5.40384i | −0.0582367 | + | 0.179234i | ||||
\(910\) | 0.109101 | + | 0.335777i | 0.00361665 | + | 0.0111309i | ||||
\(911\) | 23.5171 | − | 17.0862i | 0.779156 | − | 0.566090i | −0.125570 | − | 0.992085i | \(-0.540076\pi\) |
0.904726 | + | 0.425995i | \(0.140076\pi\) | |||||||
\(912\) | 7.89879 | 0.261555 | ||||||||
\(913\) | 7.77588 | + | 4.22462i | 0.257344 | + | 0.139815i | ||||
\(914\) | 35.5911 | 1.17725 | ||||||||
\(915\) | −16.5299 | + | 12.0096i | −0.546460 | + | 0.397027i | ||||
\(916\) | −1.20242 | − | 3.70068i | −0.0397292 | − | 0.122274i | ||||
\(917\) | 2.49958 | − | 7.69292i | 0.0825435 | − | 0.254043i | ||||
\(918\) | −6.56014 | − | 4.76622i | −0.216517 | − | 0.157309i | ||||
\(919\) | −30.9348 | − | 22.4754i | −1.02044 | − | 0.741396i | −0.0540707 | − | 0.998537i | \(-0.517220\pi\) |
−0.966374 | + | 0.257141i | \(0.917220\pi\) | |||||||
\(920\) | −0.618034 | + | 1.90211i | −0.0203760 | + | 0.0627108i | ||||
\(921\) | −19.4395 | − | 59.8288i | −0.640555 | − | 1.97143i | ||||
\(922\) | −7.81972 | + | 5.68136i | −0.257529 | + | 0.187106i | ||||
\(923\) | 4.56105 | 0.150129 | ||||||||
\(924\) | −1.84412 | + | 9.93532i | −0.0606672 | + | 0.326848i | ||||
\(925\) | 3.56360 | 0.117170 | ||||||||
\(926\) | −24.2484 | + | 17.6175i | −0.796851 | + | 0.578946i | ||||
\(927\) | 21.7843 | + | 67.0451i | 0.715489 | + | 2.20205i | ||||
\(928\) | 2.95044 | − | 9.08052i | 0.0968529 | − | 0.298083i | ||||
\(929\) | −31.3555 | − | 22.7811i | −1.02874 | − | 0.747424i | −0.0606843 | − | 0.998157i | \(-0.519328\pi\) |
−0.968056 | + | 0.250733i | \(0.919328\pi\) | |||||||
\(930\) | 14.0701 | + | 10.2225i | 0.461377 | + | 0.335210i | ||||
\(931\) | 0.801129 | − | 2.46562i | 0.0262559 | − | 0.0808075i | ||||
\(932\) | 4.68651 | + | 14.4236i | 0.153512 | + | 0.472460i | ||||
\(933\) | −57.7734 | + | 41.9748i | −1.89142 | + | 1.37419i | ||||
\(934\) | −30.5086 | −0.998272 | ||||||||
\(935\) | 1.15692 | + | 2.42719i | 0.0378354 | + | 0.0793776i | ||||
\(936\) | 2.21820 | 0.0725042 | ||||||||
\(937\) | −8.49443 | + | 6.17156i | −0.277501 | + | 0.201616i | −0.717827 | − | 0.696222i | \(-0.754863\pi\) |
0.440326 | + | 0.897838i | \(0.354863\pi\) | |||||||
\(938\) | −0.434939 | − | 1.33861i | −0.0142013 | − | 0.0437070i | ||||
\(939\) | 11.2095 | − | 34.4992i | 0.365807 | − | 1.12584i | ||||
\(940\) | −6.96380 | − | 5.05950i | −0.227134 | − | 0.165023i | ||||
\(941\) | 8.24846 | + | 5.99286i | 0.268892 | + | 0.195362i | 0.714058 | − | 0.700087i | \(-0.246855\pi\) |
−0.445166 | + | 0.895448i | \(0.646855\pi\) | |||||||
\(942\) | −0.0629216 | + | 0.193653i | −0.00205010 | + | 0.00630955i | ||||
\(943\) | 5.10330 | + | 15.7064i | 0.166186 | + | 0.511469i | ||||
\(944\) | −10.6865 | + | 7.76420i | −0.347816 | + | 0.252703i | ||||
\(945\) | 10.0021 | 0.325368 | ||||||||
\(946\) | −22.8449 | + | 21.6675i | −0.742751 | + | 0.704471i | ||||
\(947\) | −47.2023 | −1.53387 | −0.766934 | − | 0.641726i | \(-0.778219\pi\) | ||||
−0.766934 | + | 0.641726i | \(0.778219\pi\) | |||||||
\(948\) | 8.98933 | − | 6.53113i | 0.291960 | − | 0.212121i | ||||
\(949\) | 0.561876 | + | 1.72928i | 0.0182393 | + | 0.0561347i | ||||
\(950\) | −0.801129 | + | 2.46562i | −0.0259920 | + | 0.0799953i | ||||
\(951\) | 84.8379 | + | 61.6384i | 2.75106 | + | 1.99876i | ||||
\(952\) | 0.655877 | + | 0.476522i | 0.0212571 | + | 0.0154442i | ||||
\(953\) | 1.60316 | − | 4.93402i | 0.0519315 | − | 0.159829i | −0.921727 | − | 0.387839i | \(-0.873222\pi\) |
0.973659 | + | 0.228010i | \(0.0732218\pi\) | |||||||
\(954\) | 5.43557 | + | 16.7290i | 0.175983 | + | 0.541620i | ||||
\(955\) | −6.59400 | + | 4.79082i | −0.213377 | + | 0.155027i | ||||
\(956\) | −21.0949 | −0.682258 | ||||||||
\(957\) | −95.6588 | + | 12.5679i | −3.09221 | + | 0.406264i | ||||
\(958\) | 38.7127 | 1.25075 | ||||||||
\(959\) | 8.41533 | − | 6.11410i | 0.271745 | − | 0.197434i | ||||
\(960\) | −0.941506 | − | 2.89766i | −0.0303870 | − | 0.0935215i | ||||
\(961\) | 0.489357 | − | 1.50609i | 0.0157857 | − | 0.0485834i | ||||
\(962\) | −1.01787 | − | 0.739524i | −0.0328173 | − | 0.0238432i | ||||
\(963\) | −45.2185 | − | 32.8531i | −1.45714 | − | 1.05868i | ||||
\(964\) | −3.69017 | + | 11.3572i | −0.118852 | + | 0.365790i | ||||
\(965\) | −2.70138 | − | 8.31399i | −0.0869605 | − | 0.267637i | ||||
\(966\) | 4.92979 | − | 3.58170i | 0.158613 | − | 0.115239i | ||||
\(967\) | 18.9841 | 0.610486 | 0.305243 | − | 0.952274i | \(-0.401262\pi\) | ||||
0.305243 | + | 0.952274i | \(0.401262\pi\) | |||||||
\(968\) | −5.98614 | − | 9.22855i | −0.192402 | − | 0.296617i | ||||
\(969\) | −6.40361 | −0.205714 | ||||||||
\(970\) | 7.92705 | − | 5.75934i | 0.254522 | − | 0.184921i | ||||
\(971\) | −12.9503 | − | 39.8569i | −0.415595 | − | 1.27907i | −0.911718 | − | 0.410817i | \(-0.865243\pi\) |
0.496123 | − | 0.868252i | \(-0.334757\pi\) | |||||||
\(972\) | 1.67312 | − | 5.14932i | 0.0536652 | − | 0.165165i | ||||
\(973\) | 0.612562 | + | 0.445052i | 0.0196378 | + | 0.0142677i | ||||
\(974\) | 27.3751 | + | 19.8892i | 0.877155 | + | 0.637290i | ||||
\(975\) | −0.332405 | + | 1.02304i | −0.0106455 | + | 0.0327634i | ||||
\(976\) | −2.07230 | − | 6.37789i | −0.0663328 | − | 0.204151i | ||||
\(977\) | −6.56981 | + | 4.77324i | −0.210187 | + | 0.152710i | −0.687898 | − | 0.725807i | \(-0.741466\pi\) |
0.477711 | + | 0.878517i | \(0.341466\pi\) | |||||||
\(978\) | −67.8491 | −2.16958 | ||||||||
\(979\) | 31.6932 | − | 4.16396i | 1.01292 | − | 0.133081i | ||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −93.9138 | + | 68.2324i | −2.99844 | + | 2.17849i | ||||
\(982\) | 5.74014 | + | 17.6663i | 0.183175 | + | 0.563756i | ||||
\(983\) | −11.9943 | + | 36.9146i | −0.382558 | + | 1.17739i | 0.555678 | + | 0.831398i | \(0.312459\pi\) |
−0.938236 | + | 0.345996i | \(0.887541\pi\) | |||||||
\(984\) | −20.3534 | − | 14.7876i | −0.648843 | − | 0.471412i | ||||
\(985\) | 11.6958 | + | 8.49750i | 0.372659 | + | 0.270753i | ||||
\(986\) | −2.39194 | + | 7.36165i | −0.0761750 | + | 0.234443i | ||||
\(987\) | 8.10423 | + | 24.9422i | 0.257960 | + | 0.793920i | ||||
\(988\) | 0.740495 | − | 0.538001i | 0.0235583 | − | 0.0171161i | ||||
\(989\) | 18.9868 | 0.603744 | ||||||||
\(990\) | −15.1190 | + | 14.3398i | −0.480514 | + | 0.455749i | ||||
\(991\) | 1.30139 | 0.0413400 | 0.0206700 | − | 0.999786i | \(-0.493420\pi\) | ||||
0.0206700 | + | 0.999786i | \(0.493420\pi\) | |||||||
\(992\) | −4.61803 | + | 3.35520i | −0.146623 | + | 0.106528i | ||||
\(993\) | −10.9940 | − | 33.8361i | −0.348884 | − | 1.07376i | ||||
\(994\) | −3.99211 | + | 12.2865i | −0.126622 | + | 0.389703i | ||||
\(995\) | −8.93526 | − | 6.49185i | −0.283267 | − | 0.205805i | ||||
\(996\) | 6.57681 | + | 4.77833i | 0.208394 | + | 0.151407i | ||||
\(997\) | 4.57401 | − | 14.0773i | 0.144860 | − | 0.445834i | −0.852133 | − | 0.523326i | \(-0.824691\pi\) |
0.996993 | + | 0.0774917i | \(0.0246911\pi\) | |||||||
\(998\) | 4.54469 | + | 13.9871i | 0.143860 | + | 0.442754i | ||||
\(999\) | −28.8361 | + | 20.9507i | −0.912335 | + | 0.662850i |
(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 | 770.2.n.e.421.2 | ✓ | 8 | |
11.2 | odd | 10 | 8470.2.a.ct.1.4 | 4 | |||
11.4 | even | 5 | inner | 770.2.n.e.631.2 | yes | 8 | |
11.9 | even | 5 | 8470.2.a.cq.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.e.421.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
770.2.n.e.631.2 | yes | 8 | 11.4 | even | 5 | inner | |
8470.2.a.cq.1.4 | 4 | 11.9 | even | 5 | |||
8470.2.a.ct.1.4 | 4 | 11.2 | odd | 10 |