Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,2,Mod(32,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.32");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.p (of order \(12\), 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: | \(1.79663404548\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 32.2 | ||
Root | \(-0.186243 + 0.0499037i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.32 |
Dual form | 225.2.p.b.218.2 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.186243 | − | 0.0499037i | −0.131694 | − | 0.0352872i | 0.192370 | − | 0.981322i | \(-0.438383\pi\) |
−0.324064 | + | 0.946035i | \(0.605049\pi\) | |||||||
\(3\) | −1.53295 | − | 0.806271i | −0.885048 | − | 0.465501i | ||||
\(4\) | −1.69985 | − | 0.981412i | −0.849927 | − | 0.490706i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.245265 | + | 0.226662i | 0.100129 | + | 0.0925344i | ||||
\(7\) | −0.632007 | + | 2.35868i | −0.238876 | + | 0.891499i | 0.737487 | + | 0.675362i | \(0.236012\pi\) |
−0.976363 | + | 0.216137i | \(0.930654\pi\) | |||||||
\(8\) | 0.540289 | + | 0.540289i | 0.191021 | + | 0.191021i | ||||
\(9\) | 1.69985 | + | 2.47194i | 0.566618 | + | 0.823980i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.14390 | + | 1.23778i | −0.646409 | + | 0.373204i | −0.787079 | − | 0.616852i | \(-0.788408\pi\) |
0.140670 | + | 0.990057i | \(0.455074\pi\) | |||||||
\(12\) | 1.81450 | + | 2.87500i | 0.523802 | + | 0.829940i | ||||
\(13\) | 0.422032 | + | 1.57505i | 0.117051 | + | 0.436839i | 0.999432 | − | 0.0336956i | \(-0.0107277\pi\) |
−0.882381 | + | 0.470535i | \(0.844061\pi\) | |||||||
\(14\) | 0.235414 | − | 0.407749i | 0.0629170 | − | 0.108975i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.88916 | + | 3.27212i | 0.472290 | + | 0.818031i | ||||
\(17\) | −0.403949 | + | 0.403949i | −0.0979721 | + | 0.0979721i | −0.754394 | − | 0.656422i | \(-0.772069\pi\) |
0.656422 | + | 0.754394i | \(0.272069\pi\) | |||||||
\(18\) | −0.193227 | − | 0.545211i | −0.0455441 | − | 0.128507i | ||||
\(19\) | 4.28779i | 0.983687i | 0.870684 | + | 0.491843i | \(0.163677\pi\) | ||||
−0.870684 | + | 0.491843i | \(0.836323\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.87057 | − | 3.10617i | 0.626410 | − | 0.677822i | ||||
\(22\) | 0.461055 | − | 0.123539i | 0.0982973 | − | 0.0263387i | ||||
\(23\) | −6.82387 | + | 1.82845i | −1.42288 | + | 0.381258i | −0.886503 | − | 0.462723i | \(-0.846872\pi\) |
−0.536373 | + | 0.843981i | \(0.680206\pi\) | |||||||
\(24\) | −0.392615 | − | 1.26385i | −0.0801422 | − | 0.257983i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 0.314402i | − | 0.0616594i | ||||||
\(27\) | −0.612733 | − | 5.15990i | −0.117921 | − | 0.993023i | ||||
\(28\) | 3.38916 | − | 3.38916i | 0.640491 | − | 0.640491i | ||||
\(29\) | −3.20524 | − | 5.55164i | −0.595199 | − | 1.03091i | −0.993519 | − | 0.113668i | \(-0.963740\pi\) |
0.398320 | − | 0.917247i | \(-0.369593\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.97194 | + | 3.41550i | −0.354171 | + | 0.613442i | −0.986976 | − | 0.160869i | \(-0.948570\pi\) |
0.632805 | + | 0.774312i | \(0.281904\pi\) | |||||||
\(32\) | −0.584071 | − | 2.17978i | −0.103250 | − | 0.385335i | ||||
\(33\) | 4.28446 | − | 0.168889i | 0.745829 | − | 0.0293998i | ||||
\(34\) | 0.0953913 | − | 0.0550742i | 0.0163595 | − | 0.00944515i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.463514 | − | 5.87020i | −0.0772524 | − | 0.978366i | ||||
\(37\) | 0.171954 | + | 0.171954i | 0.0282691 | + | 0.0282691i | 0.721100 | − | 0.692831i | \(-0.243637\pi\) |
−0.692831 | + | 0.721100i | \(0.743637\pi\) | |||||||
\(38\) | 0.213977 | − | 0.798571i | 0.0347116 | − | 0.129545i | ||||
\(39\) | 0.622960 | − | 2.75474i | 0.0997535 | − | 0.441111i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.52359 | − | 3.76639i | −1.01881 | − | 0.588212i | −0.105053 | − | 0.994467i | \(-0.533501\pi\) |
−0.913760 | + | 0.406255i | \(0.866835\pi\) | |||||||
\(42\) | −0.689633 | + | 0.435250i | −0.106413 | + | 0.0671606i | ||||
\(43\) | 4.95226 | + | 1.32695i | 0.755213 | + | 0.202359i | 0.615829 | − | 0.787880i | \(-0.288821\pi\) |
0.139384 | + | 0.990238i | \(0.455488\pi\) | |||||||
\(44\) | 4.85908 | 0.732534 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.36214 | 0.200837 | ||||||||
\(47\) | −2.91430 | − | 0.780885i | −0.425095 | − | 0.113904i | 0.0399279 | − | 0.999203i | \(-0.487287\pi\) |
−0.465023 | + | 0.885299i | \(0.653954\pi\) | |||||||
\(48\) | −0.257767 | − | 6.53917i | −0.0372055 | − | 0.943847i | ||||
\(49\) | 0.898221 | + | 0.518588i | 0.128317 | + | 0.0740841i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.944926 | − | 0.293541i | 0.132316 | − | 0.0411039i | ||||
\(52\) | 0.828375 | − | 3.09154i | 0.114875 | − | 0.428719i | ||||
\(53\) | 6.12030 | + | 6.12030i | 0.840688 | + | 0.840688i | 0.988948 | − | 0.148260i | \(-0.0473672\pi\) |
−0.148260 | + | 0.988948i | \(0.547367\pi\) | |||||||
\(54\) | −0.143381 | + | 0.991573i | −0.0195116 | + | 0.134936i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.61584 | + | 0.932904i | −0.215925 | + | 0.124665i | ||||
\(57\) | 3.45712 | − | 6.57296i | 0.457907 | − | 0.870610i | ||||
\(58\) | 0.319907 | + | 1.19391i | 0.0420058 | + | 0.156768i | ||||
\(59\) | −2.27234 | + | 3.93581i | −0.295833 | + | 0.512399i | −0.975178 | − | 0.221421i | \(-0.928931\pi\) |
0.679345 | + | 0.733819i | \(0.262264\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.235795 | − | 0.408408i | −0.0301904 | − | 0.0522913i | 0.850535 | − | 0.525918i | \(-0.176278\pi\) |
−0.880726 | + | 0.473626i | \(0.842945\pi\) | |||||||
\(62\) | 0.537706 | − | 0.537706i | 0.0682888 | − | 0.0682888i | ||||
\(63\) | −6.90485 | + | 2.44713i | −0.869929 | + | 0.308310i | ||||
\(64\) | − | 7.12153i | − | 0.890191i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.806380 | − | 0.182356i | −0.0992585 | − | 0.0224465i | ||||
\(67\) | −1.65496 | + | 0.443446i | −0.202186 | + | 0.0541756i | −0.358491 | − | 0.933533i | \(-0.616709\pi\) |
0.156305 | + | 0.987709i | \(0.450042\pi\) | |||||||
\(68\) | 1.08310 | − | 0.290215i | 0.131345 | − | 0.0351937i | ||||
\(69\) | 11.9349 | + | 2.69897i | 1.43679 | + | 0.324918i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.50583i | 0.416065i | 0.978122 | + | 0.208032i | \(0.0667060\pi\) | ||||
−0.978122 | + | 0.208032i | \(0.933294\pi\) | |||||||
\(72\) | −0.417150 | + | 2.25397i | −0.0491616 | + | 0.265633i | ||||
\(73\) | −6.88847 | + | 6.88847i | −0.806234 | + | 0.806234i | −0.984062 | − | 0.177827i | \(-0.943093\pi\) |
0.177827 | + | 0.984062i | \(0.443093\pi\) | |||||||
\(74\) | −0.0234441 | − | 0.0406064i | −0.00272533 | − | 0.00472040i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.20809 | − | 7.28862i | 0.482701 | − | 0.836062i | ||||
\(77\) | −1.56457 | − | 5.83906i | −0.178299 | − | 0.665422i | ||||
\(78\) | −0.253493 | + | 0.481962i | −0.0287025 | + | 0.0545715i | ||||
\(79\) | −6.50159 | + | 3.75369i | −0.731485 | + | 0.422323i | −0.818965 | − | 0.573843i | \(-0.805452\pi\) |
0.0874799 | + | 0.996166i | \(0.472119\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.22099 | + | 8.40388i | −0.357888 | + | 0.933765i | ||||
\(82\) | 1.02702 | + | 1.02702i | 0.113415 | + | 0.113415i | ||||
\(83\) | 2.85794 | − | 10.6660i | 0.313700 | − | 1.17074i | −0.611493 | − | 0.791249i | \(-0.709431\pi\) |
0.925194 | − | 0.379495i | \(-0.123902\pi\) | |||||||
\(84\) | −7.92799 | + | 2.46282i | −0.865014 | + | 0.268716i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.856104 | − | 0.494272i | −0.0923161 | − | 0.0532987i | ||||
\(87\) | 0.437340 | + | 11.0947i | 0.0468878 | + | 1.18947i | ||||
\(88\) | −1.82708 | − | 0.489565i | −0.194767 | − | 0.0521878i | ||||
\(89\) | 2.90124 | 0.307531 | 0.153765 | − | 0.988107i | \(-0.450860\pi\) | ||||
0.153765 | + | 0.988107i | \(0.450860\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.98176 | −0.417402 | ||||||||
\(92\) | 13.3941 | + | 3.58893i | 1.39643 | + | 0.374171i | ||||
\(93\) | 5.77670 | − | 3.64587i | 0.599016 | − | 0.378059i | ||||
\(94\) | 0.503800 | + | 0.290869i | 0.0519630 | + | 0.0300008i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.862145 | + | 3.81241i | −0.0879923 | + | 0.389103i | ||||
\(97\) | 0.379633 | − | 1.41681i | 0.0385459 | − | 0.143855i | −0.943971 | − | 0.330028i | \(-0.892942\pi\) |
0.982517 | + | 0.186173i | \(0.0596084\pi\) | |||||||
\(98\) | −0.141408 | − | 0.141408i | −0.0142844 | − | 0.0142844i | ||||
\(99\) | −6.70403 | − | 3.19554i | −0.673780 | − | 0.321164i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.3563 | − | 8.86596i | 1.52801 | − | 0.882196i | 0.528563 | − | 0.848894i | \(-0.322731\pi\) |
0.999445 | − | 0.0333015i | \(-0.0106022\pi\) | |||||||
\(102\) | −0.190635 | + | 0.00751461i | −0.0188756 | + | 0.000744058i | ||||
\(103\) | −2.74330 | − | 10.2381i | −0.270305 | − | 1.00879i | −0.958922 | − | 0.283668i | \(-0.908449\pi\) |
0.688617 | − | 0.725125i | \(-0.258218\pi\) | |||||||
\(104\) | −0.622960 | + | 1.07900i | −0.0610863 | + | 0.105805i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.834438 | − | 1.44529i | −0.0810478 | − | 0.140379i | ||||
\(107\) | −10.4591 | + | 10.4591i | −1.01112 | + | 1.01112i | −0.0111806 | + | 0.999937i | \(0.503559\pi\) |
−0.999937 | + | 0.0111806i | \(0.996441\pi\) | |||||||
\(108\) | −4.02243 | + | 9.37242i | −0.387058 | + | 0.901862i | ||||
\(109\) | 0.343204i | 0.0328730i | 0.999865 | + | 0.0164365i | \(0.00523214\pi\) | ||||
−0.999865 | + | 0.0164365i | \(0.994768\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.124955 | − | 0.402239i | −0.0118602 | − | 0.0381788i | ||||
\(112\) | −8.91187 | + | 2.38793i | −0.842092 | + | 0.225638i | ||||
\(113\) | −5.19250 | + | 1.39133i | −0.488469 | + | 0.130885i | −0.494643 | − | 0.869096i | \(-0.664701\pi\) |
0.00617426 | + | 0.999981i | \(0.498035\pi\) | |||||||
\(114\) | −0.971879 | + | 1.05164i | −0.0910248 | + | 0.0984955i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 12.5827i | 1.16827i | ||||||||
\(117\) | −3.17603 | + | 3.72059i | −0.293624 | + | 0.343969i | ||||
\(118\) | 0.619619 | − | 0.619619i | 0.0570405 | − | 0.0570405i | ||||
\(119\) | −0.697490 | − | 1.20809i | −0.0639388 | − | 0.110745i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.43581 | + | 4.21894i | −0.221437 | + | 0.383540i | ||||
\(122\) | 0.0235340 | + | 0.0878302i | 0.00213067 | + | 0.00795177i | ||||
\(123\) | 6.96358 | + | 11.0335i | 0.627885 | + | 0.994854i | ||||
\(124\) | 6.70403 | − | 3.87057i | 0.602039 | − | 0.347588i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.40810 | − | 0.111184i | 0.125444 | − | 0.00990510i | ||||
\(127\) | 3.59190 | + | 3.59190i | 0.318729 | + | 0.318729i | 0.848279 | − | 0.529550i | \(-0.177639\pi\) |
−0.529550 | + | 0.848279i | \(0.677639\pi\) | |||||||
\(128\) | −1.52353 | + | 5.68590i | −0.134662 | + | 0.502567i | ||||
\(129\) | −6.52167 | − | 6.02702i | −0.574201 | − | 0.530649i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.5188 | + | 8.38241i | 1.26851 | + | 0.732375i | 0.974706 | − | 0.223491i | \(-0.0717453\pi\) |
0.293804 | + | 0.955866i | \(0.405079\pi\) | |||||||
\(132\) | −7.44872 | − | 3.91774i | −0.648327 | − | 0.340995i | ||||
\(133\) | −10.1135 | − | 2.70992i | −0.876956 | − | 0.234980i | ||||
\(134\) | 0.330355 | 0.0285383 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.436499 | −0.0374295 | ||||||||
\(137\) | 6.17718 | + | 1.65517i | 0.527752 | + | 0.141411i | 0.512850 | − | 0.858478i | \(-0.328590\pi\) |
0.0149021 | + | 0.999889i | \(0.495256\pi\) | |||||||
\(138\) | −2.08810 | − | 1.09826i | −0.177751 | − | 0.0934899i | ||||
\(139\) | 9.09433 | + | 5.25061i | 0.771371 | + | 0.445351i | 0.833364 | − | 0.552725i | \(-0.186412\pi\) |
−0.0619924 | + | 0.998077i | \(0.519745\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.83787 | + | 3.54677i | 0.323207 | + | 0.298692i | ||||
\(142\) | 0.174954 | − | 0.652936i | 0.0146818 | − | 0.0547931i | ||||
\(143\) | −2.85435 | − | 2.85435i | −0.238693 | − | 0.238693i | ||||
\(144\) | −4.87720 | + | 10.2320i | −0.406433 | + | 0.852669i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.62669 | − | 0.939170i | 0.134626 | − | 0.0777262i | ||||
\(147\) | −0.958803 | − | 1.51918i | −0.0790808 | − | 0.125300i | ||||
\(148\) | −0.123539 | − | 0.461055i | −0.0101549 | − | 0.0378985i | ||||
\(149\) | −4.96581 | + | 8.60103i | −0.406815 | + | 0.704624i | −0.994531 | − | 0.104443i | \(-0.966694\pi\) |
0.587716 | + | 0.809067i | \(0.300027\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.95939 | − | 12.0540i | −0.566347 | − | 0.980942i | −0.996923 | − | 0.0783879i | \(-0.975023\pi\) |
0.430576 | − | 0.902555i | \(-0.358311\pi\) | |||||||
\(152\) | −2.31665 | + | 2.31665i | −0.187905 | + | 0.187905i | ||||
\(153\) | −1.68519 | − | 0.311884i | −0.136240 | − | 0.0252143i | ||||
\(154\) | 1.16556i | 0.0939236i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.76247 | + | 4.07127i | −0.301239 | + | 0.325962i | ||||
\(157\) | 20.2365 | − | 5.42234i | 1.61505 | − | 0.432750i | 0.665504 | − | 0.746394i | \(-0.268216\pi\) |
0.949541 | + | 0.313644i | \(0.101550\pi\) | |||||||
\(158\) | 1.39820 | − | 0.374646i | 0.111235 | − | 0.0298052i | ||||
\(159\) | −4.44748 | − | 14.3167i | −0.352708 | − | 1.13539i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 17.2510i | − | 1.35957i | ||||||
\(162\) | 1.01927 | − | 1.40443i | 0.0800815 | − | 0.110342i | ||||
\(163\) | 2.42872 | − | 2.42872i | 0.190232 | − | 0.190232i | −0.605564 | − | 0.795796i | \(-0.707052\pi\) |
0.795796 | + | 0.605564i | \(0.207052\pi\) | |||||||
\(164\) | 7.39277 | + | 12.8046i | 0.577278 | + | 0.999875i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.06454 | + | 1.84385i | −0.0826247 | + | 0.143110i | ||||
\(167\) | 2.20590 | + | 8.23252i | 0.170697 | + | 0.637052i | 0.997245 | + | 0.0741841i | \(0.0236352\pi\) |
−0.826547 | + | 0.562868i | \(0.809698\pi\) | |||||||
\(168\) | 3.22917 | − | 0.127290i | 0.249136 | − | 0.00982066i | ||||
\(169\) | 8.95567 | − | 5.17056i | 0.688898 | − | 0.397735i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.5992 | + | 7.28862i | −0.810539 | + | 0.557375i | ||||
\(172\) | −7.11584 | − | 7.11584i | −0.542577 | − | 0.542577i | ||||
\(173\) | 4.57458 | − | 17.0726i | 0.347799 | − | 1.29800i | −0.541509 | − | 0.840695i | \(-0.682147\pi\) |
0.889308 | − | 0.457308i | \(-0.151186\pi\) | |||||||
\(174\) | 0.472213 | − | 2.08813i | 0.0357984 | − | 0.158301i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.10033 | − | 4.67673i | −0.610585 | − | 0.352521i | ||||
\(177\) | 6.65670 | − | 4.20126i | 0.500348 | − | 0.315786i | ||||
\(178\) | −0.540336 | − | 0.144783i | −0.0404999 | − | 0.0108519i | ||||
\(179\) | −8.30788 | −0.620960 | −0.310480 | − | 0.950580i | \(-0.600490\pi\) | ||||
−0.310480 | + | 0.950580i | \(0.600490\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.73429 | −0.351897 | −0.175948 | − | 0.984399i | \(-0.556299\pi\) | ||||
−0.175948 | + | 0.984399i | \(0.556299\pi\) | |||||||
\(182\) | 0.741576 | + | 0.198705i | 0.0549693 | + | 0.0147290i | ||||
\(183\) | 0.0321731 | + | 0.816183i | 0.00237830 | + | 0.0603340i | ||||
\(184\) | −4.67475 | − | 2.69897i | −0.344627 | − | 0.198971i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.25781 | + | 0.390739i | −0.0922273 | + | 0.0286503i | ||||
\(187\) | 0.366025 | − | 1.36603i | 0.0267664 | − | 0.0998937i | ||||
\(188\) | 4.18752 | + | 4.18752i | 0.305406 | + | 0.305406i | ||||
\(189\) | 12.5578 | + | 1.81585i | 0.913447 | + | 0.132084i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.34902 | + | 1.93356i | −0.242327 | + | 0.139907i | −0.616246 | − | 0.787554i | \(-0.711347\pi\) |
0.373919 | + | 0.927461i | \(0.378014\pi\) | |||||||
\(192\) | −5.74188 | + | 10.9169i | −0.414384 | + | 0.787861i | ||||
\(193\) | 4.44530 | + | 16.5901i | 0.319979 | + | 1.19418i | 0.919263 | + | 0.393643i | \(0.128785\pi\) |
−0.599284 | + | 0.800536i | \(0.704548\pi\) | |||||||
\(194\) | −0.141408 | + | 0.244926i | −0.0101525 | + | 0.0175847i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.01790 | − | 1.76305i | −0.0727070 | − | 0.125932i | ||||
\(197\) | 11.0386 | − | 11.0386i | 0.786469 | − | 0.786469i | −0.194445 | − | 0.980913i | \(-0.562291\pi\) |
0.980913 | + | 0.194445i | \(0.0622905\pi\) | |||||||
\(198\) | 1.08911 | + | 0.929703i | 0.0773996 | + | 0.0660711i | ||||
\(199\) | − | 3.60138i | − | 0.255295i | −0.991820 | − | 0.127648i | \(-0.959257\pi\) | ||
0.991820 | − | 0.127648i | \(-0.0407427\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.89451 | + | 0.654569i | 0.204163 | + | 0.0461698i | ||||
\(202\) | −3.30245 | + | 0.884888i | −0.232359 | + | 0.0622605i | ||||
\(203\) | 15.1203 | − | 4.05148i | 1.06124 | − | 0.284358i | ||||
\(204\) | −1.89432 | − | 0.428385i | −0.132629 | − | 0.0299929i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.04368i | 0.142390i | ||||||||
\(207\) | −16.1194 | − | 13.7601i | −1.12038 | − | 0.956394i | ||||
\(208\) | −4.35646 | + | 4.35646i | −0.302066 | + | 0.302066i | ||||
\(209\) | −5.30734 | − | 9.19258i | −0.367116 | − | 0.635864i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.56007 | − | 16.5585i | 0.658142 | − | 1.13994i | −0.322954 | − | 0.946415i | \(-0.604676\pi\) |
0.981096 | − | 0.193521i | \(-0.0619909\pi\) | |||||||
\(212\) | −4.39709 | − | 16.4102i | −0.301993 | − | 1.12705i | ||||
\(213\) | 2.82664 | − | 5.37425i | 0.193678 | − | 0.368237i | ||||
\(214\) | 2.46988 | − | 1.42599i | 0.168837 | − | 0.0974783i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.45678 | − | 3.11889i | 0.167163 | − | 0.212213i | ||||
\(217\) | −6.80981 | − | 6.80981i | −0.462280 | − | 0.462280i | ||||
\(218\) | 0.0171272 | − | 0.0639194i | 0.00116000 | − | 0.00432917i | ||||
\(219\) | 16.1136 | − | 5.00569i | 1.08886 | − | 0.338253i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.806719 | − | 0.465759i | −0.0542658 | − | 0.0313304i | ||||
\(222\) | 0.00319884 | + | 0.0811499i | 0.000214692 | + | 0.00544642i | ||||
\(223\) | −4.03530 | − | 1.08126i | −0.270224 | − | 0.0724062i | 0.121163 | − | 0.992633i | \(-0.461338\pi\) |
−0.391386 | + | 0.920226i | \(0.628004\pi\) | |||||||
\(224\) | 5.51055 | 0.368189 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.03650 | 0.0689469 | ||||||||
\(227\) | −13.2857 | − | 3.55990i | −0.881803 | − | 0.236279i | −0.210618 | − | 0.977568i | \(-0.567548\pi\) |
−0.671185 | + | 0.741290i | \(0.734214\pi\) | |||||||
\(228\) | −12.3274 | + | 7.78022i | −0.816401 | + | 0.515257i | ||||
\(229\) | −13.2694 | − | 7.66109i | −0.876866 | − | 0.506259i | −0.00724242 | − | 0.999974i | \(-0.502305\pi\) |
−0.869624 | + | 0.493715i | \(0.835639\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.30946 | + | 10.2124i | −0.151951 | + | 0.671929i | ||||
\(232\) | 1.26773 | − | 4.73125i | 0.0832308 | − | 0.310622i | ||||
\(233\) | 2.98562 | + | 2.98562i | 0.195595 | + | 0.195595i | 0.798108 | − | 0.602514i | \(-0.205834\pi\) |
−0.602514 | + | 0.798108i | \(0.705834\pi\) | |||||||
\(234\) | 0.777184 | − | 0.534438i | 0.0508061 | − | 0.0349373i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.72529 | − | 4.46020i | 0.502874 | − | 0.290334i | ||||
\(237\) | 12.9931 | − | 0.512173i | 0.843991 | − | 0.0332692i | ||||
\(238\) | 0.0696146 | + | 0.259805i | 0.00451245 | + | 0.0168407i | ||||
\(239\) | 2.59439 | − | 4.49362i | 0.167817 | − | 0.290668i | −0.769835 | − | 0.638243i | \(-0.779661\pi\) |
0.937652 | + | 0.347575i | \(0.112995\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.85872 | + | 3.21939i | 0.119730 | + | 0.207379i | 0.919661 | − | 0.392714i | \(-0.128464\pi\) |
−0.799930 | + | 0.600093i | \(0.795130\pi\) | |||||||
\(242\) | 0.664193 | − | 0.664193i | 0.0426959 | − | 0.0426959i | ||||
\(243\) | 11.7134 | − | 10.2857i | 0.751416 | − | 0.659829i | ||||
\(244\) | 0.925646i | 0.0592584i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.746308 | − | 2.40241i | −0.0475829 | − | 0.153172i | ||||
\(247\) | −6.75347 | + | 1.80959i | −0.429713 | + | 0.115141i | ||||
\(248\) | −2.91078 | + | 0.779940i | −0.184834 | + | 0.0495262i | ||||
\(249\) | −12.9808 | + | 14.0461i | −0.822622 | + | 0.890137i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.97271i | 0.250755i | 0.992109 | + | 0.125378i | \(0.0400142\pi\) | ||||
−0.992109 | + | 0.125378i | \(0.959986\pi\) | |||||||
\(252\) | 14.1389 | + | 2.61673i | 0.890666 | + | 0.164838i | ||||
\(253\) | 12.3665 | − | 12.3665i | 0.777472 | − | 0.777472i | ||||
\(254\) | −0.489717 | − | 0.848215i | −0.0307276 | − | 0.0532217i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.55403 | + | 11.3519i | −0.409627 | + | 0.709495i | ||||
\(257\) | 4.42437 | + | 16.5120i | 0.275985 | + | 1.02999i | 0.955179 | + | 0.296030i | \(0.0956628\pi\) |
−0.679194 | + | 0.733959i | \(0.737671\pi\) | |||||||
\(258\) | 0.913846 | + | 1.44794i | 0.0568935 | + | 0.0901451i | ||||
\(259\) | −0.514262 | + | 0.296909i | −0.0319547 | + | 0.0184491i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.27489 | − | 17.3602i | 0.512203 | − | 1.07457i | ||||
\(262\) | −2.28571 | − | 2.28571i | −0.141211 | − | 0.141211i | ||||
\(263\) | −2.77155 | + | 10.3436i | −0.170901 | + | 0.637812i | 0.826312 | + | 0.563212i | \(0.190435\pi\) |
−0.997214 | + | 0.0746001i | \(0.976232\pi\) | |||||||
\(264\) | 2.40610 | + | 2.22360i | 0.148085 | + | 0.136853i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.74834 | + | 1.00941i | 0.107198 | + | 0.0618907i | ||||
\(267\) | −4.44745 | − | 2.33919i | −0.272179 | − | 0.143156i | ||||
\(268\) | 3.24840 | + | 0.870407i | 0.198428 | + | 0.0531685i | ||||
\(269\) | 15.8925 | 0.968985 | 0.484492 | − | 0.874796i | \(-0.339004\pi\) | ||||
0.484492 | + | 0.874796i | \(0.339004\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.974200 | 0.0591785 | 0.0295892 | − | 0.999562i | \(-0.490580\pi\) | ||||
0.0295892 | + | 0.999562i | \(0.490580\pi\) | |||||||
\(272\) | −2.08490 | − | 0.558646i | −0.126415 | − | 0.0338729i | ||||
\(273\) | 6.10383 | + | 3.21038i | 0.369421 | + | 0.194301i | ||||
\(274\) | −1.06786 | − | 0.616528i | −0.0645117 | − | 0.0372458i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −17.6387 | − | 16.3009i | −1.06173 | − | 0.981197i | ||||
\(277\) | −6.18395 | + | 23.0788i | −0.371557 | + | 1.38667i | 0.486753 | + | 0.873540i | \(0.338181\pi\) |
−0.858310 | + | 0.513131i | \(0.828485\pi\) | |||||||
\(278\) | −1.43173 | − | 1.43173i | −0.0858695 | − | 0.0858695i | ||||
\(279\) | −11.7949 | + | 0.931335i | −0.706144 | + | 0.0557576i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.9241 | + | 13.8126i | −1.42720 | + | 0.823991i | −0.996899 | − | 0.0786961i | \(-0.974924\pi\) |
−0.430296 | + | 0.902688i | \(0.641591\pi\) | |||||||
\(282\) | −0.537779 | − | 0.852086i | −0.0320243 | − | 0.0507410i | ||||
\(283\) | −4.40870 | − | 16.4535i | −0.262070 | − | 0.978058i | −0.964020 | − | 0.265831i | \(-0.914354\pi\) |
0.701950 | − | 0.712227i | \(-0.252313\pi\) | |||||||
\(284\) | 3.44066 | − | 5.95939i | 0.204165 | − | 0.353625i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.389161 | + | 0.674046i | 0.0230115 | + | 0.0398572i | ||||
\(287\) | 13.0067 | − | 13.0067i | 0.767761 | − | 0.767761i | ||||
\(288\) | 4.39546 | − | 5.14910i | 0.259005 | − | 0.303414i | ||||
\(289\) | 16.6736i | 0.980803i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.72429 | + | 1.86581i | −0.101080 | + | 0.109376i | ||||
\(292\) | 18.4698 | − | 4.94897i | 1.08086 | − | 0.289617i | ||||
\(293\) | −25.7566 | + | 6.90146i | −1.50472 | + | 0.403188i | −0.914677 | − | 0.404186i | \(-0.867555\pi\) |
−0.590041 | + | 0.807374i | \(0.700888\pi\) | |||||||
\(294\) | 0.102758 | + | 0.330784i | 0.00599296 | + | 0.0192917i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.185810i | 0.0108000i | ||||||||
\(297\) | 7.70045 | + | 10.3039i | 0.446825 | + | 0.597890i | ||||
\(298\) | 1.35407 | − | 1.35407i | 0.0784392 | − | 0.0784392i | ||||
\(299\) | −5.75979 | − | 9.97625i | −0.333097 | − | 0.576941i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.25973 | + | 10.8422i | −0.360805 | + | 0.624933i | ||||
\(302\) | 0.694599 | + | 2.59228i | 0.0399697 | + | 0.149169i | ||||
\(303\) | −30.6887 | + | 1.20972i | −1.76302 | + | 0.0694965i | ||||
\(304\) | −14.0302 | + | 8.10033i | −0.804686 | + | 0.464586i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.298292 | + | 0.142184i | 0.0170522 | + | 0.00812810i | ||||
\(307\) | 12.3556 | + | 12.3556i | 0.705171 | + | 0.705171i | 0.965516 | − | 0.260345i | \(-0.0838363\pi\) |
−0.260345 | + | 0.965516i | \(0.583836\pi\) | |||||||
\(308\) | −3.07098 | + | 11.4610i | −0.174985 | + | 0.653053i | ||||
\(309\) | −4.04938 | + | 17.9064i | −0.230361 | + | 1.01866i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.49228 | + | 4.32567i | 0.424848 | + | 0.245286i | 0.697149 | − | 0.716926i | \(-0.254451\pi\) |
−0.272301 | + | 0.962212i | \(0.587785\pi\) | |||||||
\(312\) | 1.82493 | − | 1.15177i | 0.103316 | − | 0.0652064i | ||||
\(313\) | 18.1094 | + | 4.85240i | 1.02360 | + | 0.274274i | 0.731303 | − | 0.682052i | \(-0.238912\pi\) |
0.292301 | + | 0.956326i | \(0.405579\pi\) | |||||||
\(314\) | −4.03949 | −0.227962 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.7357 | 0.828946 | ||||||||
\(317\) | −18.7418 | − | 5.02186i | −1.05265 | − | 0.282056i | −0.309301 | − | 0.950964i | \(-0.600095\pi\) |
−0.743345 | + | 0.668908i | \(0.766762\pi\) | |||||||
\(318\) | 0.113855 | + | 2.88834i | 0.00638468 | + | 0.161970i | ||||
\(319\) | 13.7434 | + | 7.93476i | 0.769484 | + | 0.444262i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.4661 | − | 7.60037i | 1.36556 | − | 0.424211i | ||||
\(322\) | −0.860886 | + | 3.21287i | −0.0479753 | + | 0.179046i | ||||
\(323\) | −1.73205 | − | 1.73205i | −0.0963739 | − | 0.0963739i | ||||
\(324\) | 13.7229 | − | 11.1243i | 0.762382 | − | 0.618015i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.573535 | + | 0.331131i | −0.0317652 | + | 0.0183396i | ||||
\(327\) | 0.276716 | − | 0.526114i | 0.0153024 | − | 0.0290942i | ||||
\(328\) | −1.48968 | − | 5.55956i | −0.0822538 | − | 0.306975i | ||||
\(329\) | 3.68372 | − | 6.38039i | 0.203090 | − | 0.351763i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.1969 | + | 29.7859i | 0.945226 | + | 1.63718i | 0.755298 | + | 0.655382i | \(0.227492\pi\) |
0.189929 | + | 0.981798i | \(0.439174\pi\) | |||||||
\(332\) | −15.3258 | + | 15.3258i | −0.841114 | + | 0.841114i | ||||
\(333\) | −0.132764 | + | 0.717358i | −0.00727540 | + | 0.0393110i | ||||
\(334\) | − | 1.64333i | − | 0.0899191i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 15.5867 | + | 3.52481i | 0.850326 | + | 0.192294i | ||||
\(337\) | −30.9291 | + | 8.28744i | −1.68482 | + | 0.451445i | −0.969044 | − | 0.246888i | \(-0.920592\pi\) |
−0.715773 | + | 0.698333i | \(0.753925\pi\) | |||||||
\(338\) | −1.92596 | + | 0.516060i | −0.104758 | + | 0.0280700i | ||||
\(339\) | 9.08161 | + | 2.05373i | 0.493245 | + | 0.111543i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 9.76331i | − | 0.528713i | ||||||
\(342\) | 2.33775 | − | 0.828518i | 0.126411 | − | 0.0448011i | ||||
\(343\) | −13.8776 | + | 13.8776i | −0.749320 | + | 0.749320i | ||||
\(344\) | 1.95871 | + | 3.39259i | 0.105607 | + | 0.182916i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.70397 | + | 2.95136i | −0.0916059 | + | 0.158666i | ||||
\(347\) | 4.15647 | + | 15.5122i | 0.223131 | + | 0.832737i | 0.983145 | + | 0.182829i | \(0.0585256\pi\) |
−0.760014 | + | 0.649907i | \(0.774808\pi\) | |||||||
\(348\) | 10.1450 | − | 19.2885i | 0.543830 | − | 1.03397i | ||||
\(349\) | −15.1664 | + | 8.75630i | −0.811837 | + | 0.468714i | −0.847593 | − | 0.530646i | \(-0.821949\pi\) |
0.0357566 | + | 0.999361i | \(0.488616\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.86849 | − | 3.14273i | 0.419989 | − | 0.167746i | ||||
\(352\) | 3.95028 | + | 3.95028i | 0.210550 | + | 0.210550i | ||||
\(353\) | −4.95294 | + | 18.4846i | −0.263618 | + | 0.983837i | 0.699472 | + | 0.714660i | \(0.253418\pi\) |
−0.963091 | + | 0.269177i | \(0.913248\pi\) | |||||||
\(354\) | −1.44942 | + | 0.450262i | −0.0770360 | + | 0.0239312i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.93169 | − | 2.84731i | −0.261379 | − | 0.150907i | ||||
\(357\) | 0.0951692 | + | 2.41430i | 0.00503689 | + | 0.127778i | ||||
\(358\) | 1.54728 | + | 0.414594i | 0.0817766 | + | 0.0219120i | ||||
\(359\) | −23.0127 | −1.21457 | −0.607283 | − | 0.794486i | \(-0.707741\pi\) | ||||
−0.607283 | + | 0.794486i | \(0.707741\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.614846 | 0.0323603 | ||||||||
\(362\) | 0.881728 | + | 0.236258i | 0.0463426 | + | 0.0124175i | ||||
\(363\) | 7.13557 | − | 4.50350i | 0.374521 | − | 0.236372i | ||||
\(364\) | 6.76842 | + | 3.90775i | 0.354762 | + | 0.204822i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.0347385 | − | 0.153614i | 0.00181581 | − | 0.00802953i | ||||
\(367\) | 7.01692 | − | 26.1875i | 0.366280 | − | 1.36698i | −0.499397 | − | 0.866373i | \(-0.666445\pi\) |
0.865677 | − | 0.500603i | \(-0.166888\pi\) | |||||||
\(368\) | −18.8743 | − | 18.8743i | −0.983891 | − | 0.983891i | ||||
\(369\) | −1.77884 | − | 22.5282i | −0.0926029 | − | 1.17277i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.3039 | + | 10.5678i | −0.950293 | + | 0.548652i | ||||
\(372\) | −13.3977 | + | 0.528121i | −0.694636 | + | 0.0273818i | ||||
\(373\) | 7.76440 | + | 28.9771i | 0.402025 | + | 1.50038i | 0.809477 | + | 0.587152i | \(0.199751\pi\) |
−0.407451 | + | 0.913227i | \(0.633582\pi\) | |||||||
\(374\) | −0.136339 | + | 0.236147i | −0.00704994 | + | 0.0122109i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.15266 | − | 1.99647i | −0.0594440 | − | 0.102960i | ||||
\(377\) | 7.39138 | − | 7.39138i | 0.380675 | − | 0.380675i | ||||
\(378\) | −2.24819 | − | 0.964871i | −0.115634 | − | 0.0496276i | ||||
\(379\) | − | 20.0943i | − | 1.03218i | −0.856535 | − | 0.516089i | \(-0.827388\pi\) | ||
0.856535 | − | 0.516089i | \(-0.172612\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.61015 | − | 8.40224i | −0.133722 | − | 0.430460i | ||||
\(382\) | 0.720223 | − | 0.192983i | 0.0368498 | − | 0.00987388i | ||||
\(383\) | 26.6536 | − | 7.14181i | 1.36194 | − | 0.364929i | 0.497409 | − | 0.867516i | \(-0.334285\pi\) |
0.864527 | + | 0.502587i | \(0.167618\pi\) | |||||||
\(384\) | 6.91987 | − | 7.48780i | 0.353128 | − | 0.382110i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 3.31162i | − | 0.168557i | ||||||
\(387\) | 5.13797 | + | 14.4973i | 0.261178 | + | 0.736941i | ||||
\(388\) | −2.03579 | + | 2.03579i | −0.103352 | + | 0.103352i | ||||
\(389\) | 6.71184 | + | 11.6253i | 0.340304 | + | 0.589424i | 0.984489 | − | 0.175446i | \(-0.0561367\pi\) |
−0.644185 | + | 0.764870i | \(0.722803\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.01790 | − | 3.49510i | 0.102049 | − | 0.176755i | ||||
\(392\) | 0.205111 | + | 0.765487i | 0.0103597 | + | 0.0386629i | ||||
\(393\) | −15.4980 | − | 24.5558i | −0.781771 | − | 1.23868i | ||||
\(394\) | −2.60673 | + | 1.50500i | −0.131325 | + | 0.0758207i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.25973 | + | 12.0114i | 0.415067 | + | 0.603594i | ||||
\(397\) | 12.8716 | + | 12.8716i | 0.646008 | + | 0.646008i | 0.952026 | − | 0.306018i | \(-0.0989967\pi\) |
−0.306018 | + | 0.952026i | \(0.598997\pi\) | |||||||
\(398\) | −0.179722 | + | 0.670732i | −0.00900866 | + | 0.0336208i | ||||
\(399\) | 13.3186 | + | 12.3084i | 0.666764 | + | 0.616191i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.7606 | − | 12.5635i | −1.08667 | − | 0.627391i | −0.153985 | − | 0.988073i | \(-0.549211\pi\) |
−0.932689 | + | 0.360682i | \(0.882544\pi\) | |||||||
\(402\) | −0.506417 | − | 0.266356i | −0.0252578 | − | 0.0132846i | ||||
\(403\) | −6.21180 | − | 1.66445i | −0.309432 | − | 0.0829120i | ||||
\(404\) | −34.8046 | −1.73159 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.01824 | −0.149793 | ||||||||
\(407\) | −0.581494 | − | 0.155811i | −0.0288236 | − | 0.00772325i | ||||
\(408\) | 0.669129 | + | 0.351936i | 0.0331268 | + | 0.0174234i | ||||
\(409\) | −9.81878 | − | 5.66888i | −0.485508 | − | 0.280308i | 0.237201 | − | 0.971461i | \(-0.423770\pi\) |
−0.722709 | + | 0.691153i | \(0.757103\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.13478 | − | 7.51777i | −0.401259 | − | 0.370824i | ||||
\(412\) | −5.38461 | + | 20.0957i | −0.265281 | + | 0.990042i | ||||
\(413\) | −7.84719 | − | 7.84719i | −0.386135 | − | 0.386135i | ||||
\(414\) | 2.31545 | + | 3.36714i | 0.113798 | + | 0.165486i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.18676 | − | 1.83988i | 0.156244 | − | 0.0902074i | ||||
\(417\) | −9.70771 | − | 15.3814i | −0.475389 | − | 0.753231i | ||||
\(418\) | 0.529711 | + | 1.97691i | 0.0259090 | + | 0.0966938i | ||||
\(419\) | 4.26264 | − | 7.38311i | 0.208244 | − | 0.360688i | −0.742918 | − | 0.669383i | \(-0.766559\pi\) |
0.951161 | + | 0.308694i | \(0.0998920\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.10329 | + | 1.91095i | 0.0537710 | + | 0.0931341i | 0.891658 | − | 0.452710i | \(-0.149543\pi\) |
−0.837887 | + | 0.545844i | \(0.816209\pi\) | |||||||
\(422\) | −2.60683 | + | 2.60683i | −0.126898 | + | 0.126898i | ||||
\(423\) | −3.02359 | − | 8.53138i | −0.147012 | − | 0.414810i | ||||
\(424\) | 6.61346i | 0.321178i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.794637 | + | 0.859856i | −0.0385003 | + | 0.0416601i | ||||
\(427\) | 1.11233 | − | 0.298048i | 0.0538294 | − | 0.0144235i | ||||
\(428\) | 28.0436 | − | 7.51426i | 1.35554 | − | 0.363215i | ||||
\(429\) | 2.07419 | + | 6.67695i | 0.100143 | + | 0.322366i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 1.95738i | − | 0.0942838i | −0.998888 | − | 0.0471419i | \(-0.984989\pi\) | ||
0.998888 | − | 0.0471419i | \(-0.0150113\pi\) | |||||||
\(432\) | 15.7263 | − | 11.7528i | 0.756630 | − | 0.565458i | ||||
\(433\) | 9.71652 | − | 9.71652i | 0.466946 | − | 0.466946i | −0.433978 | − | 0.900924i | \(-0.642890\pi\) |
0.900924 | + | 0.433978i | \(0.142890\pi\) | |||||||
\(434\) | 0.928445 | + | 1.60811i | 0.0445668 | + | 0.0771919i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.336825 | − | 0.583398i | 0.0161310 | − | 0.0279397i | ||||
\(437\) | −7.84002 | − | 29.2593i | −0.375039 | − | 1.39966i | ||||
\(438\) | −3.25085 | + | 0.128145i | −0.155332 | + | 0.00612302i | ||||
\(439\) | −4.68008 | + | 2.70205i | −0.223368 | + | 0.128962i | −0.607509 | − | 0.794313i | \(-0.707831\pi\) |
0.384141 | + | 0.923275i | \(0.374498\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.244926 | + | 3.10188i | 0.0116631 | + | 0.147708i | ||||
\(442\) | 0.127003 | + | 0.127003i | 0.00604090 | + | 0.00604090i | ||||
\(443\) | −6.98940 | + | 26.0848i | −0.332077 | + | 1.23933i | 0.574927 | + | 0.818204i | \(0.305030\pi\) |
−0.907004 | + | 0.421122i | \(0.861636\pi\) | |||||||
\(444\) | −0.182356 | + | 0.806380i | −0.00865424 | + | 0.0382691i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.697588 | + | 0.402752i | 0.0330317 | + | 0.0190709i | ||||
\(447\) | 14.5471 | − | 9.18114i | 0.688053 | − | 0.434253i | ||||
\(448\) | 16.7974 | + | 4.50086i | 0.793604 | + | 0.212646i | ||||
\(449\) | 23.8541 | 1.12574 | 0.562872 | − | 0.826544i | \(-0.309696\pi\) | ||||
0.562872 | + | 0.826544i | \(0.309696\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.6479 | 0.878093 | ||||||||
\(452\) | 10.1920 | + | 2.73093i | 0.479389 | + | 0.128452i | ||||
\(453\) | 0.949576 | + | 24.0893i | 0.0446150 | + | 1.13182i | ||||
\(454\) | 2.29672 | + | 1.32601i | 0.107790 | + | 0.0622328i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.41914 | − | 1.68345i | 0.253774 | − | 0.0788349i | ||||
\(457\) | 5.13035 | − | 19.1467i | 0.239988 | − | 0.895647i | −0.735849 | − | 0.677146i | \(-0.763217\pi\) |
0.975837 | − | 0.218501i | \(-0.0701167\pi\) | |||||||
\(458\) | 2.08902 | + | 2.08902i | 0.0976133 | + | 0.0976133i | ||||
\(459\) | 2.33185 | + | 1.83682i | 0.108842 | + | 0.0857356i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.14371 | + | 0.660321i | −0.0532679 | + | 0.0307542i | −0.526397 | − | 0.850239i | \(-0.676458\pi\) |
0.473130 | + | 0.880993i | \(0.343124\pi\) | |||||||
\(462\) | 0.939758 | − | 1.78674i | 0.0437215 | − | 0.0831269i | ||||
\(463\) | −3.98780 | − | 14.8827i | −0.185329 | − | 0.691656i | −0.994560 | − | 0.104166i | \(-0.966783\pi\) |
0.809231 | − | 0.587490i | \(-0.199884\pi\) | |||||||
\(464\) | 12.1104 | − | 20.9759i | 0.562213 | − | 0.973782i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.407058 | − | 0.705045i | −0.0188566 | − | 0.0326606i | ||||
\(467\) | 1.77645 | − | 1.77645i | 0.0822044 | − | 0.0822044i | −0.664809 | − | 0.747013i | \(-0.731487\pi\) |
0.747013 | + | 0.664809i | \(0.231487\pi\) | |||||||
\(468\) | 9.05022 | − | 3.20747i | 0.418346 | − | 0.148265i | ||||
\(469\) | − | 4.18380i | − | 0.193190i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −35.3933 | − | 8.00390i | −1.63084 | − | 0.368800i | ||||
\(472\) | −3.35419 | + | 0.898753i | −0.154389 | + | 0.0413685i | ||||
\(473\) | −12.2596 | + | 3.28495i | −0.563697 | + | 0.151042i | ||||
\(474\) | −2.44543 | − | 0.553014i | −0.112322 | − | 0.0254008i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.73810i | 0.125501i | ||||||||
\(477\) | −4.72541 | + | 25.5327i | −0.216361 | + | 1.16906i | ||||
\(478\) | −0.707436 | + | 0.707436i | −0.0323574 | + | 0.0323574i | ||||
\(479\) | 18.9907 | + | 32.8928i | 0.867705 | + | 1.50291i | 0.864336 | + | 0.502915i | \(0.167739\pi\) |
0.00336919 | + | 0.999994i | \(0.498928\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.198266 | + | 0.343406i | −0.00904014 | + | 0.0156580i | ||||
\(482\) | −0.185513 | − | 0.692346i | −0.00844991 | − | 0.0315355i | ||||
\(483\) | −13.9089 | + | 26.4448i | −0.632879 | + | 1.20328i | ||||
\(484\) | 8.28104 | − | 4.78106i | 0.376411 | − | 0.217321i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.69484 | + | 1.33110i | −0.122240 | + | 0.0603800i | ||||
\(487\) | −23.6900 | − | 23.6900i | −1.07350 | − | 1.07350i | −0.997076 | − | 0.0764213i | \(-0.975651\pi\) |
−0.0764213 | − | 0.997076i | \(-0.524349\pi\) | |||||||
\(488\) | 0.0932612 | − | 0.348056i | 0.00422174 | − | 0.0157557i | ||||
\(489\) | −5.68131 | + | 1.76490i | −0.256918 | + | 0.0798114i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.9114 | + | 10.9185i | 0.853460 | + | 0.492746i | 0.861817 | − | 0.507220i | \(-0.169327\pi\) |
−0.00835660 | + | 0.999965i | \(0.502660\pi\) | |||||||
\(492\) | −1.00871 | − | 25.5894i | −0.0454761 | − | 1.15366i | ||||
\(493\) | 3.53734 | + | 0.947827i | 0.159314 | + | 0.0426880i | ||||
\(494\) | 1.34809 | 0.0606535 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.9013 | −0.669086 | ||||||||
\(497\) | −8.26913 | − | 2.21571i | −0.370921 | − | 0.0993881i | ||||
\(498\) | 3.11853 | − | 1.96821i | 0.139745 | − | 0.0881974i | ||||
\(499\) | −2.74862 | − | 1.58691i | −0.123045 | − | 0.0710401i | 0.437214 | − | 0.899357i | \(-0.355965\pi\) |
−0.560259 | + | 0.828317i | \(0.689298\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.25612 | − | 14.3986i | 0.145473 | − | 0.643281i | ||||
\(502\) | 0.198253 | − | 0.739889i | 0.00884845 | − | 0.0330229i | ||||
\(503\) | 7.00484 | + | 7.00484i | 0.312330 | + | 0.312330i | 0.845812 | − | 0.533481i | \(-0.179117\pi\) |
−0.533481 | + | 0.845812i | \(0.679117\pi\) | |||||||
\(504\) | −5.05277 | − | 2.40845i | −0.225068 | − | 0.107281i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.92030 | + | 1.68603i | −0.129823 | + | 0.0749534i | ||||
\(507\) | −17.8974 | + | 0.705498i | −0.794853 | + | 0.0313323i | ||||
\(508\) | −2.58058 | − | 9.63084i | −0.114495 | − | 0.427299i | ||||
\(509\) | 8.36206 | − | 14.4835i | 0.370642 | − | 0.641971i | −0.619023 | − | 0.785373i | \(-0.712471\pi\) |
0.989664 | + | 0.143403i | \(0.0458044\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.8942 | − | 20.6013i | −0.526167 | − | 0.911347i | ||||
\(512\) | 10.1119 | − | 10.1119i | 0.446886 | − | 0.446886i | ||||
\(513\) | 22.1246 | − | 2.62727i | 0.976824 | − | 0.115997i | ||||
\(514\) | − | 3.29603i | − | 0.145382i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.17091 | + | 16.6455i | 0.227637 | + | 0.732777i | ||||
\(517\) | 7.21452 | − | 1.93313i | 0.317294 | − | 0.0850188i | ||||
\(518\) | 0.110595 | − | 0.0296337i | 0.00485925 | − | 0.00130203i | ||||
\(519\) | −20.7777 | + | 22.4830i | −0.912040 | + | 0.986894i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.34092i | 0.0587466i | 0.999569 | + | 0.0293733i | \(0.00935116\pi\) | ||||
−0.999569 | + | 0.0293733i | \(0.990649\pi\) | |||||||
\(522\) | −2.40748 | + | 2.82026i | −0.105372 | + | 0.123440i | ||||
\(523\) | 9.19187 | − | 9.19187i | 0.401933 | − | 0.401933i | −0.476981 | − | 0.878914i | \(-0.658269\pi\) |
0.878914 | + | 0.476981i | \(0.158269\pi\) | |||||||
\(524\) | −16.4532 | − | 28.4978i | −0.718761 | − | 1.24493i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.03237 | − | 1.78811i | 0.0450133 | − | 0.0779653i | ||||
\(527\) | −0.583126 | − | 2.17625i | −0.0254014 | − | 0.0947991i | ||||
\(528\) | 8.64667 | + | 13.7002i | 0.376298 | + | 0.596226i | ||||
\(529\) | 23.3034 | − | 13.4542i | 1.01319 | − | 0.584967i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.5917 | + | 1.07321i | −0.589831 | + | 0.0465734i | ||||
\(532\) | 14.5320 | + | 14.5320i | 0.630043 | + | 0.630043i | ||||
\(533\) | 3.17908 | − | 11.8645i | 0.137701 | − | 0.513908i | ||||
\(534\) | 0.711572 | + | 0.657601i | 0.0307927 | + | 0.0284572i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.13375 | − | 0.654569i | −0.0489704 | − | 0.0282731i | ||||
\(537\) | 12.7355 | + | 6.69840i | 0.549579 | + | 0.289057i | ||||
\(538\) | −2.95987 | − | 0.793096i | −0.127609 | − | 0.0341928i | ||||
\(539\) | −2.56759 | −0.110594 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.0389 | −1.46345 | −0.731724 | − | 0.681601i | \(-0.761284\pi\) | ||||
−0.731724 | + | 0.681601i | \(0.761284\pi\) | |||||||
\(542\) | −0.181438 | − | 0.0486162i | −0.00779343 | − | 0.00208824i | ||||
\(543\) | 7.25741 | + | 3.81712i | 0.311445 | + | 0.163808i | ||||
\(544\) | 1.11646 | + | 0.644587i | 0.0478677 | + | 0.0276364i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.976587 | − | 0.902515i | −0.0417941 | − | 0.0386241i | ||||
\(547\) | −2.44487 | + | 9.12437i | −0.104535 | + | 0.390130i | −0.998292 | − | 0.0584215i | \(-0.981393\pi\) |
0.893757 | + | 0.448552i | \(0.148060\pi\) | |||||||
\(548\) | −8.87591 | − | 8.87591i | −0.379160 | − | 0.379160i | ||||
\(549\) | 0.608745 | − | 1.27711i | 0.0259806 | − | 0.0545055i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.8043 | − | 13.7434i | 1.01410 | − | 0.585489i | ||||
\(552\) | 4.99005 | + | 7.90650i | 0.212391 | + | 0.336523i | ||||
\(553\) | −4.74472 | − | 17.7075i | −0.201766 | − | 0.753001i | ||||
\(554\) | 2.30343 | − | 3.98967i | 0.0978636 | − | 0.169505i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.3060 | − | 17.8506i | −0.437073 | − | 0.757033i | ||||
\(557\) | −1.48579 | + | 1.48579i | −0.0629551 | + | 0.0629551i | −0.737883 | − | 0.674928i | \(-0.764175\pi\) |
0.674928 | + | 0.737883i | \(0.264175\pi\) | |||||||
\(558\) | 2.24320 | + | 0.415156i | 0.0949623 | + | 0.0175750i | ||||
\(559\) | 8.36006i | 0.353593i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.66248 | + | 1.79893i | −0.0701901 | + | 0.0759509i | ||||
\(562\) | 5.14501 | − | 1.37860i | 0.217029 | − | 0.0581527i | ||||
\(563\) | 20.6371 | − | 5.52969i | 0.869750 | − | 0.233049i | 0.203770 | − | 0.979019i | \(-0.434681\pi\) |
0.665979 | + | 0.745970i | \(0.268014\pi\) | |||||||
\(564\) | −3.04297 | − | 9.79553i | −0.128132 | − | 0.412466i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.28436i | 0.138052i | ||||||||
\(567\) | −17.7864 | − | 12.9086i | −0.746959 | − | 0.542111i | ||||
\(568\) | −1.89416 | + | 1.89416i | −0.0794771 | + | 0.0794771i | ||||
\(569\) | 5.82589 | + | 10.0907i | 0.244234 | + | 0.423026i | 0.961916 | − | 0.273345i | \(-0.0881301\pi\) |
−0.717682 | + | 0.696371i | \(0.754797\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.5623 | − | 18.2945i | 0.442020 | − | 0.765601i | −0.555819 | − | 0.831303i | \(-0.687595\pi\) |
0.997839 | + | 0.0657023i | \(0.0209288\pi\) | |||||||
\(572\) | 2.05069 | + | 7.65328i | 0.0857436 | + | 0.320000i | ||||
\(573\) | 6.69284 | − | 0.263825i | 0.279598 | − | 0.0110214i | ||||
\(574\) | −3.07149 | + | 1.77332i | −0.128201 | + | 0.0740171i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 17.6040 | − | 12.1056i | 0.733500 | − | 0.504398i | ||||
\(577\) | −30.1119 | − | 30.1119i | −1.25357 | − | 1.25357i | −0.954106 | − | 0.299469i | \(-0.903191\pi\) |
−0.299469 | − | 0.954106i | \(-0.596809\pi\) | |||||||
\(578\) | 0.832076 | − | 3.10535i | 0.0346098 | − | 0.129166i | ||||
\(579\) | 6.56168 | − | 29.0158i | 0.272694 | − | 1.20586i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23.3515 | + | 13.4820i | 0.968782 | + | 0.559327i | ||||
\(582\) | 0.414248 | − | 0.261445i | 0.0171711 | − | 0.0108373i | ||||
\(583\) | −20.6969 | − | 5.54571i | −0.857177 | − | 0.229680i | ||||
\(584\) | −7.44353 | −0.308015 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.14140 | 0.212389 | ||||||||
\(587\) | 8.53262 | + | 2.28631i | 0.352179 | + | 0.0943661i | 0.430571 | − | 0.902556i | \(-0.358312\pi\) |
−0.0783924 | + | 0.996923i | \(0.524979\pi\) | |||||||
\(588\) | 0.138887 | + | 3.52336i | 0.00572761 | + | 0.145301i | ||||
\(589\) | −14.6450 | − | 8.45527i | −0.603435 | − | 0.348393i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.8217 | + | 8.02150i | −1.06216 | + | 0.329960i | ||||
\(592\) | −0.237806 | + | 0.887505i | −0.00977377 | + | 0.0364762i | ||||
\(593\) | −24.5829 | − | 24.5829i | −1.00950 | − | 1.00950i | −0.999954 | − | 0.00954475i | \(-0.996962\pi\) |
−0.00954475 | − | 0.999954i | \(-0.503038\pi\) | |||||||
\(594\) | −0.919955 | − | 2.30330i | −0.0377462 | − | 0.0945056i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.8823 | − | 9.74700i | 0.691526 | − | 0.399253i | ||||
\(597\) | −2.90369 | + | 5.52073i | −0.118840 | + | 0.225948i | ||||
\(598\) | 0.574869 | + | 2.14544i | 0.0235082 | + | 0.0877336i | ||||
\(599\) | −18.8291 | + | 32.6129i | −0.769335 | + | 1.33253i | 0.168590 | + | 0.985686i | \(0.446079\pi\) |
−0.937924 | + | 0.346840i | \(0.887255\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.1158 | + | 19.2532i | 0.453424 | + | 0.785354i | 0.998596 | − | 0.0529703i | \(-0.0168689\pi\) |
−0.545172 | + | 0.838324i | \(0.683536\pi\) | |||||||
\(602\) | 1.70690 | − | 1.70690i | 0.0695679 | − | 0.0695679i | ||||
\(603\) | −3.90937 | − | 3.33718i | −0.159202 | − | 0.135900i | ||||
\(604\) | 27.3201i | 1.11164i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.77593 | + | 1.30618i | 0.234631 | + | 0.0530599i | ||||
\(607\) | 20.8988 | − | 5.59982i | 0.848257 | − | 0.227290i | 0.191594 | − | 0.981474i | \(-0.438634\pi\) |
0.656663 | + | 0.754184i | \(0.271968\pi\) | |||||||
\(608\) | 9.34645 | − | 2.50437i | 0.379049 | − | 0.101566i | ||||
\(609\) | −26.4452 | − | 5.98037i | −1.07161 | − | 0.242337i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 4.91972i | − | 0.199031i | ||||||
\(612\) | 2.55850 | + | 2.18403i | 0.103421 | + | 0.0882841i | ||||
\(613\) | −15.7726 | + | 15.7726i | −0.637051 | + | 0.637051i | −0.949827 | − | 0.312776i | \(-0.898741\pi\) |
0.312776 | + | 0.949827i | \(0.398741\pi\) | |||||||
\(614\) | −1.68455 | − | 2.91773i | −0.0679830 | − | 0.117750i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.30946 | − | 4.00010i | 0.0930507 | − | 0.161169i | ||||
\(617\) | 10.9568 | + | 40.8914i | 0.441104 | + | 1.64622i | 0.726021 | + | 0.687672i | \(0.241367\pi\) |
−0.284917 | + | 0.958552i | \(0.591966\pi\) | |||||||
\(618\) | 1.64776 | − | 3.13286i | 0.0662827 | − | 0.126022i | ||||
\(619\) | 27.5855 | − | 15.9265i | 1.10876 | − | 0.640141i | 0.170250 | − | 0.985401i | \(-0.445543\pi\) |
0.938507 | + | 0.345260i | \(0.112209\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.6158 | + | 34.0901i | 0.546385 | + | 1.36799i | ||||
\(622\) | −1.17952 | − | 1.17952i | −0.0472944 | − | 0.0472944i | ||||
\(623\) | −1.83361 | + | 6.84311i | −0.0734619 | + | 0.274163i | ||||
\(624\) | 10.1907 | − | 3.16573i | 0.407955 | − | 0.126731i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.13060 | − | 1.80745i | −0.125124 | − | 0.0722403i | ||||
\(627\) | 0.724161 | + | 18.3709i | 0.0289202 | + | 0.733663i | ||||
\(628\) | −39.7206 | − | 10.6431i | −1.58502 | − | 0.424706i | ||||
\(629\) | −0.138922 | −0.00553917 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.7931 | 0.628713 | 0.314356 | − | 0.949305i | \(-0.398211\pi\) | ||||
0.314356 | + | 0.949305i | \(0.398211\pi\) | |||||||
\(632\) | −5.54081 | − | 1.48466i | −0.220402 | − | 0.0590564i | ||||
\(633\) | −28.0057 | + | 17.6753i | −1.11313 | + | 0.702532i | ||||
\(634\) | 3.23993 | + | 1.87057i | 0.128674 | + | 0.0742899i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.49053 | + | 28.7012i | −0.257366 | + | 1.13808i | ||||
\(637\) | −0.437722 | + | 1.63360i | −0.0173432 | + | 0.0647256i | ||||
\(638\) | −2.16364 | − | 2.16364i | −0.0856594 | − | 0.0856594i | ||||
\(639\) | −8.66619 | + | 5.95939i | −0.342829 | + | 0.235750i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.57453 | + | 4.95051i | −0.338673 | + | 0.195533i | −0.659685 | − | 0.751542i | \(-0.729310\pi\) |
0.321012 | + | 0.947075i | \(0.395977\pi\) | |||||||
\(642\) | −4.93592 | + | 0.194569i | −0.194805 | + | 0.00767902i | ||||
\(643\) | 12.2247 | + | 45.6232i | 0.482095 | + | 1.79920i | 0.592801 | + | 0.805349i | \(0.298022\pi\) |
−0.110706 | + | 0.993853i | \(0.535311\pi\) | |||||||
\(644\) | −16.9303 | + | 29.3241i | −0.667147 | + | 1.15553i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.236147 | + | 0.409018i | 0.00929107 | + | 0.0160926i | ||||
\(647\) | 9.75824 | − | 9.75824i | 0.383636 | − | 0.383636i | −0.488774 | − | 0.872410i | \(-0.662556\pi\) |
0.872410 | + | 0.488774i | \(0.162556\pi\) | |||||||
\(648\) | −6.28079 | + | 2.80026i | −0.246733 | + | 0.110005i | ||||
\(649\) | − | 11.2506i | − | 0.441625i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.94853 | + | 15.9296i | 0.193948 | + | 0.624331i | ||||
\(652\) | −6.51206 | + | 1.74490i | −0.255032 | + | 0.0683356i | ||||
\(653\) | 2.99335 | − | 0.802065i | 0.117139 | − | 0.0313872i | −0.199773 | − | 0.979842i | \(-0.564021\pi\) |
0.316912 | + | 0.948455i | \(0.397354\pi\) | |||||||
\(654\) | −0.0777914 | + | 0.0841760i | −0.00304189 | + | 0.00329154i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 28.4613i | − | 1.11123i | ||||||
\(657\) | −28.7373 | − | 5.31850i | −1.12115 | − | 0.207494i | ||||
\(658\) | −1.00447 | + | 1.00447i | −0.0391584 | + | 0.0391584i | ||||
\(659\) | 13.5644 | + | 23.4942i | 0.528393 | + | 0.915204i | 0.999452 | + | 0.0331023i | \(0.0105387\pi\) |
−0.471059 | + | 0.882102i | \(0.656128\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.54526 | + | 16.5329i | −0.371268 | + | 0.643055i | −0.989761 | − | 0.142736i | \(-0.954410\pi\) |
0.618493 | + | 0.785790i | \(0.287743\pi\) | |||||||
\(662\) | −1.71638 | − | 6.40560i | −0.0667088 | − | 0.248961i | ||||
\(663\) | 0.861129 | + | 1.36442i | 0.0334435 | + | 0.0529896i | ||||
\(664\) | 7.30683 | − | 4.21860i | 0.283560 | − | 0.163713i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.0605251 | − | 0.126978i | 0.00234530 | − | 0.00492028i | ||||
\(667\) | 32.0231 | + | 32.0231i | 1.23994 | + | 1.23994i | ||||
\(668\) | 4.32979 | − | 16.1590i | 0.167524 | − | 0.625210i | ||||
\(669\) | 5.31412 | + | 4.91105i | 0.205456 | + | 0.189872i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.01104 | + | 0.583723i | 0.0390307 | + | 0.0225344i | ||||
\(672\) | −8.44739 | − | 4.44300i | −0.325865 | − | 0.171392i | ||||
\(673\) | 0.134287 | + | 0.0359820i | 0.00517638 | + | 0.00138701i | 0.261406 | − | 0.965229i | \(-0.415814\pi\) |
−0.256230 | + | 0.966616i | \(0.582480\pi\) | |||||||
\(674\) | 6.17391 | 0.237810 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.2978 | −0.780684 | ||||||||
\(677\) | 7.80401 | + | 2.09108i | 0.299933 | + | 0.0803667i | 0.405647 | − | 0.914030i | \(-0.367046\pi\) |
−0.105714 | + | 0.994397i | \(0.533713\pi\) | |||||||
\(678\) | −1.58890 | − | 0.835699i | −0.0610213 | − | 0.0320948i | ||||
\(679\) | 3.10188 | + | 1.79087i | 0.119039 | + | 0.0687272i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.4961 | + | 16.1690i | 0.670450 | + | 0.619598i | ||||
\(682\) | −0.487225 | + | 1.81835i | −0.0186568 | + | 0.0696281i | ||||
\(683\) | 35.0271 | + | 35.0271i | 1.34027 | + | 1.34027i | 0.895784 | + | 0.444490i | \(0.146615\pi\) |
0.444490 | + | 0.895784i | \(0.353385\pi\) | |||||||
\(684\) | 25.1702 | − | 1.98745i | 0.962406 | − | 0.0759921i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.27715 | − | 1.89206i | 0.125122 | − | 0.0722393i | ||||
\(687\) | 14.1644 | + | 22.4428i | 0.540404 | + | 0.856245i | ||||
\(688\) | 5.01366 | + | 18.7112i | 0.191144 | + | 0.713359i | ||||
\(689\) | −7.05680 | + | 12.2227i | −0.268843 | + | 0.465649i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.5195 | − | 35.5408i | −0.780597 | − | 1.35203i | −0.931594 | − | 0.363500i | \(-0.881582\pi\) |
0.150997 | − | 0.988534i | \(-0.451752\pi\) | |||||||
\(692\) | −24.5313 | + | 24.5313i | −0.932541 | + | 0.932541i | ||||
\(693\) | 11.7743 | − | 13.7931i | 0.447267 | − | 0.523956i | ||||
\(694\) | − | 3.09646i | − | 0.117540i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.75804 | + | 6.23062i | −0.218258 | + | 0.236171i | ||||
\(697\) | 4.15663 | − | 1.11377i | 0.157444 | − | 0.0421869i | ||||
\(698\) | 3.26160 | − | 0.873943i | 0.123453 | − | 0.0330792i | ||||
\(699\) | −2.16958 | − | 6.98402i | −0.0820611 | − | 0.264160i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.2173i | 1.40568i | 0.711348 | + | 0.702840i | \(0.248085\pi\) | ||||
−0.711348 | + | 0.702840i | \(0.751915\pi\) | |||||||
\(702\) | −1.62228 | + | 0.192645i | −0.0612292 | + | 0.00727091i | ||||
\(703\) | −0.737304 | + | 0.737304i | −0.0278080 | + | 0.0278080i | ||||
\(704\) | 8.81487 | + | 15.2678i | 0.332223 | + | 0.575427i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.84490 | − | 3.19546i | 0.0694337 | − | 0.120263i | ||||
\(707\) | 11.2067 | + | 41.8240i | 0.421471 | + | 1.57295i | ||||
\(708\) | −15.4386 | + | 0.608573i | −0.580218 | + | 0.0228716i | ||||
\(709\) | −13.3449 | + | 7.70466i | −0.501177 | + | 0.289355i | −0.729199 | − | 0.684301i | \(-0.760107\pi\) |
0.228023 | + | 0.973656i | \(0.426774\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.3307 | − | 9.69081i | −0.762459 | − | 0.363434i | ||||
\(712\) | 1.56751 | + | 1.56751i | 0.0587448 | + | 0.0587448i | ||||
\(713\) | 7.21120 | − | 26.9125i | 0.270061 | − | 1.00788i | ||||
\(714\) | 0.102758 | − | 0.454396i | 0.00384562 | − | 0.0170053i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.1222 | + | 8.15345i | 0.527771 | + | 0.304709i | ||||
\(717\) | −7.60014 | + | 4.79670i | −0.283833 | + | 0.179136i | ||||
\(718\) | 4.28596 | + | 1.14842i | 0.159951 | + | 0.0428587i | ||||
\(719\) | −11.9324 | −0.445002 | −0.222501 | − | 0.974932i | \(-0.571422\pi\) | ||||
−0.222501 | + | 0.974932i | \(0.571422\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.8823 | 0.963908 | ||||||||
\(722\) | −0.114511 | − | 0.0306831i | −0.00426165 | − | 0.00114191i | ||||
\(723\) | −0.253613 | − | 6.43378i | −0.00943196 | − | 0.239275i | ||||
\(724\) | 8.04760 | + | 4.64628i | 0.299087 | + | 0.172678i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.55369 | + | 0.482653i | −0.0576629 | + | 0.0179129i | ||||
\(727\) | −1.12575 | + | 4.20134i | −0.0417516 | + | 0.155819i | −0.983654 | − | 0.180066i | \(-0.942369\pi\) |
0.941903 | + | 0.335885i | \(0.109035\pi\) | |||||||
\(728\) | −2.15130 | − | 2.15130i | −0.0797326 | − | 0.0797326i | ||||
\(729\) | −26.2491 | + | 6.32329i | −0.972189 | + | 0.234196i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.53649 | + | 1.46444i | −0.0938153 | + | 0.0541643i | ||||
\(732\) | 0.746322 | − | 1.41897i | 0.0275848 | − | 0.0524465i | ||||
\(733\) | −12.7796 | − | 47.6943i | −0.472027 | − | 1.76163i | −0.632473 | − | 0.774583i | \(-0.717960\pi\) |
0.160446 | − | 0.987045i | \(-0.448707\pi\) | |||||||
\(734\) | −2.61370 | + | 4.52707i | −0.0964736 | + | 0.167097i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.97125 | + | 13.8066i | 0.293824 | + | 0.508918i | ||||
\(737\) | 2.99918 | − | 2.99918i | 0.110476 | − | 0.110476i | ||||
\(738\) | −0.792945 | + | 4.28450i | −0.0291887 | + | 0.157715i | ||||
\(739\) | − | 16.1890i | − | 0.595523i | −0.954640 | − | 0.297761i | \(-0.903760\pi\) | ||
0.954640 | − | 0.297761i | \(-0.0962400\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.8117 | + | 2.67112i | 0.433915 | + | 0.0981262i | ||||
\(742\) | 3.93635 | − | 1.05474i | 0.144508 | − | 0.0387208i | ||||
\(743\) | −19.2021 | + | 5.14520i | −0.704458 | + | 0.188759i | −0.593227 | − | 0.805035i | \(-0.702146\pi\) |
−0.111232 | + | 0.993795i | \(0.535480\pi\) | |||||||
\(744\) | 5.09091 | + | 1.15127i | 0.186642 | + | 0.0422075i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 5.78426i | − | 0.211777i | ||||||
\(747\) | 31.2238 | − | 11.0660i | 1.14242 | − | 0.404883i | ||||
\(748\) | −1.96282 | + | 1.96282i | −0.0717679 | + | 0.0717679i | ||||
\(749\) | −18.0595 | − | 31.2799i | −0.659878 | − | 1.14294i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.95061 | − | 13.7709i | 0.290122 | − | 0.502506i | −0.683716 | − | 0.729748i | \(-0.739637\pi\) |
0.973838 | + | 0.227242i | \(0.0729708\pi\) | |||||||
\(752\) | −2.95043 | − | 11.0112i | −0.107591 | − | 0.401536i | ||||
\(753\) | 3.20308 | − | 6.08995i | 0.116727 | − | 0.221930i | ||||
\(754\) | −1.74545 | + | 1.00774i | −0.0635655 | + | 0.0366996i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −19.5644 | − | 15.4111i | −0.711550 | − | 0.560495i | ||||
\(757\) | −21.3482 | − | 21.3482i | −0.775914 | − | 0.775914i | 0.203219 | − | 0.979133i | \(-0.434860\pi\) |
−0.979133 | + | 0.203219i | \(0.934860\pi\) | |||||||
\(758\) | −1.00278 | + | 3.74243i | −0.0364227 | + | 0.135931i | ||||
\(759\) | −28.9278 | + | 8.98641i | −1.05001 | + | 0.326186i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.74778 | + | 2.74113i | 0.172107 | + | 0.0993659i | 0.583579 | − | 0.812056i | \(-0.301652\pi\) |
−0.411472 | + | 0.911422i | \(0.634985\pi\) | |||||||
\(762\) | 0.0668196 | + | 1.69511i | 0.00242062 | + | 0.0614075i | ||||
\(763\) | −0.809511 | − | 0.216908i | −0.0293063 | − | 0.00785259i | ||||
\(764\) | 7.59046 | 0.274613 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.32045 | −0.192236 | ||||||||
\(767\) | −7.15808 | − | 1.91800i | −0.258463 | − | 0.0692550i | ||||
\(768\) | 19.1997 | − | 12.1176i | 0.692810 | − | 0.437255i | ||||
\(769\) | −7.13004 | − | 4.11653i | −0.257116 | − | 0.148446i | 0.365902 | − | 0.930653i | \(-0.380760\pi\) |
−0.623018 | + | 0.782207i | \(0.714094\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.53080 | − | 28.8792i | 0.235201 | − | 1.04006i | ||||
\(772\) | 8.72533 | − | 32.5634i | 0.314031 | − | 1.17198i | ||||
\(773\) | 14.0889 | + | 14.0889i | 0.506743 | + | 0.506743i | 0.913525 | − | 0.406782i | \(-0.133349\pi\) |
−0.406782 | + | 0.913525i | \(0.633349\pi\) | |||||||
\(774\) | −0.233441 | − | 2.95643i | −0.00839088 | − | 0.106267i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.970598 | − | 0.560375i | 0.0348424 | − | 0.0201163i | ||||
\(777\) | 1.02773 | − | 0.0405119i | 0.0368695 | − | 0.00145336i | ||||
\(778\) | −0.669891 | − | 2.50007i | −0.0240168 | − | 0.0896318i | ||||
\(779\) | 16.1495 | − | 27.9718i | 0.578616 | − | 1.00219i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.33944 | − | 7.51612i | −0.155277 | − | 0.268948i | ||||
\(782\) | −0.550238 | + | 0.550238i | −0.0196765 | + | 0.0196765i | ||||
\(783\) | −26.6820 | + | 19.9404i | −0.953536 | + | 0.712612i | ||||
\(784\) | 3.91879i | 0.139957i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.66097 | + | 5.34676i | 0.0592448 | + | 0.190713i | ||||
\(787\) | −19.4505 | + | 5.21175i | −0.693336 | + | 0.185779i | −0.588244 | − | 0.808684i | \(-0.700180\pi\) |
−0.105092 | + | 0.994462i | \(0.533514\pi\) | |||||||
\(788\) | −29.5975 | + | 7.93062i | −1.05437 | + | 0.282516i | ||||
\(789\) | 12.5884 | − | 13.6215i | 0.448158 | − | 0.484940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 13.1268i | − | 0.466735i | ||||||
\(792\) | −1.89560 | − | 5.34863i | −0.0673571 | − | 0.190055i | ||||
\(793\) | 0.543749 | − | 0.543749i | 0.0193091 | − | 0.0193091i | ||||
\(794\) | −1.75491 | − | 3.03959i | −0.0622793 | − | 0.107871i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.53444 | + | 6.12183i | −0.125275 | + | 0.216982i | ||||
\(797\) | −11.4576 | − | 42.7605i | −0.405850 | − | 1.51465i | −0.802483 | − | 0.596676i | \(-0.796488\pi\) |
0.396632 | − | 0.917978i | \(-0.370179\pi\) | |||||||
\(798\) | −1.86626 | − | 2.95700i | −0.0660650 | − | 0.104677i | ||||
\(799\) | 1.49267 | − | 0.861793i | 0.0528068 | − | 0.0304880i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.93169 | + | 7.17170i | 0.174253 | + | 0.253399i | ||||
\(802\) | 3.42580 | + | 3.42580i | 0.120969 | + | 0.120969i | ||||
\(803\) | 6.24176 | − | 23.2946i | 0.220267 | − | 0.822047i | ||||
\(804\) | −4.27784 | − | 3.95338i | −0.150868 | − | 0.139425i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.07384 | + | 0.619983i | 0.0378245 | + | 0.0218380i | ||||
\(807\) | −24.3624 | − | 12.8137i | −0.857597 | − | 0.451063i | ||||
\(808\) | 13.0870 | + | 3.50665i | 0.460399 | + | 0.123364i | ||||
\(809\) | 35.4591 | 1.24667 | 0.623337 | − | 0.781953i | \(-0.285777\pi\) | ||||
0.623337 | + | 0.781953i | \(0.285777\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.68119 | −0.339952 | −0.169976 | − | 0.985448i | \(-0.554369\pi\) | ||||
−0.169976 | + | 0.985448i | \(0.554369\pi\) | |||||||
\(812\) | −29.6785 | − | 7.95233i | −1.04151 | − | 0.279072i | ||||
\(813\) | −1.49340 | − | 0.785469i | −0.0523757 | − | 0.0275476i | ||||
\(814\) | 0.100524 | + | 0.0580373i | 0.00352335 | + | 0.00203421i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.74562 | + | 2.53737i | 0.0961158 | + | 0.0888256i | ||||
\(817\) | −5.68970 | + | 21.2343i | −0.199058 | + | 0.742893i | ||||
\(818\) | 1.54578 | + | 1.54578i | 0.0540470 | + | 0.0540470i | ||||
\(819\) | −6.76842 | − | 9.84269i | −0.236508 | − | 0.343931i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.6602 | − | 8.46408i | 0.511645 | − | 0.295398i | −0.221865 | − | 0.975077i | \(-0.571214\pi\) |
0.733510 | + | 0.679679i | \(0.237881\pi\) | |||||||
\(822\) | 1.13988 | + | 1.80609i | 0.0397579 | + | 0.0629945i | ||||
\(823\) | −9.19340 | − | 34.3102i | −0.320462 | − | 1.19598i | −0.918796 | − | 0.394733i | \(-0.870837\pi\) |
0.598334 | − | 0.801247i | \(-0.295830\pi\) | |||||||
\(824\) | 4.04938 | − | 7.01372i | 0.141067 | − | 0.244335i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.06988 | + | 1.85309i | 0.0372259 | + | 0.0644772i | ||||
\(827\) | 31.4545 | − | 31.4545i | 1.09378 | − | 1.09378i | 0.0986577 | − | 0.995121i | \(-0.468545\pi\) |
0.995121 | − | 0.0986577i | \(-0.0314549\pi\) | |||||||
\(828\) | 13.8963 | + | 39.2100i | 0.482931 | + | 1.36264i | ||||
\(829\) | − | 17.3376i | − | 0.602161i | −0.953599 | − | 0.301081i | \(-0.902653\pi\) | ||
0.953599 | − | 0.301081i | \(-0.0973474\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.0874 | − | 30.3927i | 0.974342 | − | 1.05431i | ||||
\(832\) | 11.2167 | − | 3.00551i | 0.388870 | − | 0.104197i | ||||
\(833\) | −0.572320 | + | 0.153353i | −0.0198297 | + | 0.00531335i | ||||
\(834\) | 1.04041 | + | 3.34913i | 0.0360263 | + | 0.115971i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 20.8347i | 0.720584i | ||||||||
\(837\) | 18.8319 | + | 8.08223i | 0.650926 | + | 0.279363i | ||||
\(838\) | −1.16233 | + | 1.16233i | −0.0401521 | + | 0.0401521i | ||||
\(839\) | −12.8988 | − | 22.3413i | −0.445315 | − | 0.771308i | 0.552759 | − | 0.833341i | \(-0.313575\pi\) |
−0.998074 | + | 0.0620331i | \(0.980242\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.04717 | + | 10.4740i | −0.208523 | + | 0.361173i | ||||
\(842\) | −0.110116 | − | 0.410960i | −0.00379486 | − | 0.0141626i | ||||
\(843\) | 47.8112 | − | 1.88467i | 1.64670 | − | 0.0649113i | ||||
\(844\) | −32.5015 | + | 18.7647i | −1.11875 | + | 0.645909i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.137375 | + | 1.73980i | 0.00472306 | + | 0.0598155i | ||||
\(847\) | −8.41170 | − | 8.41170i | −0.289030 | − | 0.289030i | ||||
\(848\) | −8.46415 | + | 31.5886i | −0.290660 | + | 1.08476i | ||||
\(849\) | −6.50766 | + | 28.7769i | −0.223342 | + | 0.987622i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.48780 | − | 0.858984i | −0.0510013 | − | 0.0294456i | ||||
\(852\) | −10.0792 | + | 6.36133i | −0.345309 | + | 0.217936i | ||||
\(853\) | 13.7160 | + | 3.67518i | 0.469626 | + | 0.125836i | 0.485868 | − | 0.874032i | \(-0.338504\pi\) |
−0.0162423 | + | 0.999868i | \(0.505170\pi\) | |||||||
\(854\) | −0.222037 | −0.00759796 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.3019 | −0.386289 | ||||||||
\(857\) | 48.2115 | + | 12.9182i | 1.64687 | + | 0.441278i | 0.958735 | − | 0.284303i | \(-0.0917620\pi\) |
0.688137 | + | 0.725581i | \(0.258429\pi\) | |||||||
\(858\) | −0.0530991 | − | 1.34705i | −0.00181277 | − | 0.0459874i | ||||
\(859\) | 35.6374 | + | 20.5752i | 1.21593 | + | 0.702018i | 0.964045 | − | 0.265739i | \(-0.0856158\pi\) |
0.251886 | + | 0.967757i | \(0.418949\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −30.4255 | + | 9.45165i | −1.03690 | + | 0.322112i | ||||
\(862\) | −0.0976806 | + | 0.364549i | −0.00332701 | + | 0.0124166i | ||||
\(863\) | −20.5637 | − | 20.5637i | −0.699996 | − | 0.699996i | 0.264413 | − | 0.964410i | \(-0.414822\pi\) |
−0.964410 | + | 0.264413i | \(0.914822\pi\) | |||||||
\(864\) | −10.8896 | + | 4.34937i | −0.370471 | + | 0.147969i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.29452 | + | 1.32474i | −0.0779711 | + | 0.0450166i | ||||
\(867\) | 13.4435 | − | 25.5598i | 0.456564 | − | 0.868057i | ||||
\(868\) | 4.89246 | + | 18.2589i | 0.166061 | + | 0.619748i | ||||
\(869\) | 9.29248 | − | 16.0950i | 0.315226 | − | 0.545987i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.39690 | − | 2.41950i | −0.0473320 | − | 0.0819815i | ||||
\(872\) | −0.185430 | + | 0.185430i | −0.00627944 | + | 0.00627944i | ||||
\(873\) | 4.14759 | − | 1.46994i | 0.140375 | − | 0.0497499i | ||||
\(874\) | 5.84059i | 0.197561i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −32.3035 | − | 7.30516i | −1.09143 | − | 0.246819i | ||||
\(877\) | −48.3556 | + | 12.9568i | −1.63285 | + | 0.437521i | −0.954741 | − | 0.297438i | \(-0.903868\pi\) |
−0.678111 | + | 0.734959i | \(0.737201\pi\) | |||||||
\(878\) | 1.00647 | − | 0.269684i | 0.0339669 | − | 0.00910140i | ||||
\(879\) | 45.0480 | + | 10.1872i | 1.51943 | + | 0.343607i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 25.4215i | − | 0.856471i | −0.903667 | − | 0.428235i | \(-0.859135\pi\) | ||
0.903667 | − | 0.428235i | \(-0.140865\pi\) | |||||||
\(882\) | 0.109179 | − | 0.589925i | 0.00367626 | − | 0.0198638i | ||||
\(883\) | 27.7207 | − | 27.7207i | 0.932874 | − | 0.932874i | −0.0650103 | − | 0.997885i | \(-0.520708\pi\) |
0.997885 | + | 0.0650103i | \(0.0207080\pi\) | |||||||
\(884\) | 0.914203 | + | 1.58345i | 0.0307480 | + | 0.0532571i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.60346 | − | 4.50932i | 0.0874648 | − | 0.151493i | ||||
\(887\) | −5.34114 | − | 19.9334i | −0.179338 | − | 0.669298i | −0.995772 | − | 0.0918595i | \(-0.970719\pi\) |
0.816434 | − | 0.577439i | \(-0.195948\pi\) | |||||||
\(888\) | 0.149813 | − | 0.284837i | 0.00502740 | − | 0.00955850i | ||||
\(889\) | −10.7423 | + | 6.20205i | −0.360284 | + | 0.208010i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.49668 | − | 22.0039i | −0.117143 | − | 0.737159i | ||||
\(892\) | 5.79827 | + | 5.79827i | 0.194140 | + | 0.194140i | ||||
\(893\) | 3.34827 | − | 12.4959i | 0.112046 | − | 0.418160i | ||||
\(894\) | −3.16746 | + | 0.983971i | −0.105936 | + | 0.0329089i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −12.4484 | − | 7.18706i | −0.415870 | − | 0.240103i | ||||
\(897\) | 0.785896 | + | 19.9370i | 0.0262403 | + | 0.665677i | ||||
\(898\) | −4.44266 | − | 1.19041i | −0.148253 | − | 0.0397244i | ||||
\(899\) | 25.2822 | 0.843209 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.94459 | −0.164728 | ||||||||
\(902\) | −3.47303 | − | 0.930596i | −0.115639 | − | 0.0309855i | ||||
\(903\) | 18.3376 | − | 11.5734i | 0.610236 | − | 0.385140i | ||||
\(904\) | −3.55717 | − | 2.05373i | −0.118310 | − | 0.0683061i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.02529 | − | 4.53386i | 0.0340631 | − | 0.150627i | ||||
\(907\) | 10.1886 | − | 38.0242i | 0.338305 | − | 1.26257i | −0.561935 | − | 0.827181i | \(-0.689943\pi\) |
0.900241 | − | 0.435392i | \(-0.143390\pi\) | |||||||
\(908\) | 19.0901 | + | 19.0901i | 0.633526 | + | 0.633526i | ||||
\(909\) | 48.0196 | + | 22.8890i | 1.59271 | + | 0.759180i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.5747 | + | 24.5805i | −1.41056 | + | 0.814389i | −0.995441 | − | 0.0953768i | \(-0.969594\pi\) |
−0.415122 | + | 0.909766i | \(0.636261\pi\) | |||||||
\(912\) | 28.0386 | − | 1.10525i | 0.928450 | − | 0.0365985i | ||||
\(913\) | 7.07501 | + | 26.4043i | 0.234149 | + | 0.873854i | ||||
\(914\) | −1.91099 | + | 3.30992i | −0.0632098 | + | 0.109483i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.0374 | + | 26.0455i | 0.496848 | + | 0.860567i | ||||
\(917\) | −28.9474 | + | 28.9474i | −0.955928 | + | 0.955928i | ||||
\(918\) | −0.342627 | − | 0.458464i | −0.0113084 | − | 0.0151316i | ||||
\(919\) | 7.00522i | 0.231081i | 0.993303 | + | 0.115540i | \(0.0368600\pi\) | ||||
−0.993303 | + | 0.115540i | \(0.963140\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.97851 | − | 28.9024i | −0.295852 | − | 0.952367i | ||||
\(922\) | 0.245960 | − | 0.0659049i | 0.00810028 | − | 0.00217046i | ||||
\(923\) | −5.52184 | + | 1.47957i | −0.181753 | + | 0.0487007i | ||||
\(924\) | 13.9483 | − | 15.0931i | 0.458867 | − | 0.496527i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.97080i | 0.0976265i | ||||||||
\(927\) | 20.6449 | − | 24.1846i | 0.678066 | − | 0.794327i | ||||
\(928\) | −10.2293 | + | 10.2293i | −0.335793 | + | 0.335793i | ||||
\(929\) | −1.96179 | − | 3.39791i | −0.0643641 | − | 0.111482i | 0.832048 | − | 0.554704i | \(-0.187169\pi\) |
−0.896412 | + | 0.443222i | \(0.853835\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.22360 | + | 3.85139i | −0.0728755 | + | 0.126224i | ||||
\(932\) | −2.14500 | − | 8.00525i | −0.0702618 | − | 0.262221i | ||||
\(933\) | −7.99761 | − | 12.6718i | −0.261830 | − | 0.414857i | ||||
\(934\) | −0.419503 | + | 0.242200i | −0.0137266 | + | 0.00792504i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.72616 | + | 0.294220i | −0.121794 | + | 0.00961688i | ||||
\(937\) | 28.6351 | + | 28.6351i | 0.935468 | + | 0.935468i | 0.998040 | − | 0.0625728i | \(-0.0199305\pi\) |
−0.0625728 | + | 0.998040i | \(0.519931\pi\) | |||||||
\(938\) | −0.208787 | + | 0.779203i | −0.00681713 | + | 0.0254419i | ||||
\(939\) | −23.8484 | − | 22.0396i | −0.778264 | − | 0.719234i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −50.0184 | − | 28.8781i | −1.63055 | − | 0.941400i | −0.983922 | − | 0.178596i | \(-0.942844\pi\) |
−0.646630 | − | 0.762804i | \(-0.723822\pi\) | |||||||
\(942\) | 6.19233 | + | 3.25693i | 0.201757 | + | 0.106116i | ||||
\(943\) | 51.4028 | + | 13.7733i | 1.67390 | + | 0.448521i | ||||
\(944\) | −17.1713 | −0.558877 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.44720 | 0.0795653 | ||||||||
\(947\) | −8.02351 | − | 2.14989i | −0.260729 | − | 0.0698622i | 0.126086 | − | 0.992019i | \(-0.459758\pi\) |
−0.386816 | + | 0.922157i | \(0.626425\pi\) | |||||||
\(948\) | −22.5890 | − | 11.8809i | −0.733657 | − | 0.385875i | ||||
\(949\) | −13.7568 | − | 7.94250i | −0.446565 | − | 0.257824i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.6813 | + | 22.8092i | 0.800345 | + | 0.739640i | ||||
\(952\) | 0.275870 | − | 1.02956i | 0.00894101 | − | 0.0333683i | ||||
\(953\) | 27.2237 | + | 27.2237i | 0.881861 | + | 0.881861i | 0.993724 | − | 0.111862i | \(-0.0356816\pi\) |
−0.111862 | + | 0.993724i | \(0.535682\pi\) | |||||||
\(954\) | 2.15425 | − | 4.51947i | 0.0697463 | − | 0.146323i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −8.82018 | + | 5.09233i | −0.285265 | + | 0.164698i | ||||
\(957\) | −14.6704 | − | 23.2445i | −0.474225 | − | 0.751388i | ||||
\(958\) | −1.89541 | − | 7.07375i | −0.0612378 | − | 0.228543i | ||||
\(959\) | −7.80805 | + | 13.5239i | −0.252135 | + | 0.436711i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.72289 | + | 13.3764i | 0.249126 | + | 0.431498i | ||||
\(962\) | 0.0540628 | − | 0.0540628i | 0.00174306 | − | 0.00174306i | ||||
\(963\) | −43.6332 | − | 8.07532i | −1.40606 | − | 0.260224i | ||||
\(964\) | − | 7.29666i | − | 0.235010i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.91014 | − | 4.23105i | 0.125807 | − | 0.136132i | ||||
\(967\) | 45.5627 | − | 12.2085i | 1.46520 | − | 0.392598i | 0.563916 | − | 0.825832i | \(-0.309294\pi\) |
0.901282 | + | 0.433234i | \(0.142628\pi\) | |||||||
\(968\) | −3.59549 | + | 0.963408i | −0.115563 | + | 0.0309651i | ||||
\(969\) | 1.25864 | + | 4.05164i | 0.0404334 | + | 0.130158i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.4752i | 0.657080i | 0.944490 | + | 0.328540i | \(0.106557\pi\) | ||||
−0.944490 | + | 0.328540i | \(0.893443\pi\) | |||||||
\(972\) | −30.0056 | + | 5.98855i | −0.962431 | + | 0.192083i | ||||
\(973\) | −18.1322 | + | 18.1322i | −0.581292 | + | 0.581292i | ||||
\(974\) | 3.22988 | + | 5.59432i | 0.103492 | + | 0.179254i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.890908 | − | 1.54310i | 0.0285173 | − | 0.0493934i | ||||
\(977\) | −9.36214 | − | 34.9400i | −0.299521 | − | 1.11783i | −0.937560 | − | 0.347824i | \(-0.886921\pi\) |
0.638038 | − | 0.770005i | \(-0.279746\pi\) | |||||||
\(978\) | 1.14618 | − | 0.0451812i | 0.0366508 | − | 0.00144474i | ||||
\(979\) | −6.21996 | + | 3.59109i | −0.198791 | + | 0.114772i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.848381 | + | 0.583398i | −0.0270867 | + | 0.0186265i | ||||
\(982\) | −2.97725 | − | 2.97725i | −0.0950077 | − | 0.0950077i | ||||
\(983\) | −5.10700 | + | 19.0596i | −0.162888 | + | 0.607906i | 0.835412 | + | 0.549624i | \(0.185229\pi\) |
−0.998300 | + | 0.0582820i | \(0.981438\pi\) | |||||||
\(984\) | −2.19891 | + | 9.72360i | −0.0700987 | + | 0.309977i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.611505 | − | 0.353052i | −0.0194743 | − | 0.0112435i | ||||
\(987\) | −10.7913 | + | 6.81073i | −0.343490 | + | 0.216788i | ||||
\(988\) | 13.2559 | + | 3.55190i | 0.421725 | + | 0.113001i | ||||
\(989\) | −36.2199 | −1.15172 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.0916 | 1.68651 | 0.843255 | − | 0.537513i | \(-0.180636\pi\) | ||||
0.843255 | + | 0.537513i | \(0.180636\pi\) | |||||||
\(992\) | 8.59681 | + | 2.30351i | 0.272949 | + | 0.0731364i | ||||
\(993\) | −2.34643 | − | 59.5255i | −0.0744618 | − | 1.88899i | ||||
\(994\) | 1.42950 | + | 0.825320i | 0.0453409 | + | 0.0261776i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 35.8504 | − | 11.1369i | 1.13596 | − | 0.352887i | ||||
\(997\) | −9.82689 | + | 36.6745i | −0.311221 | + | 1.16149i | 0.616236 | + | 0.787562i | \(0.288657\pi\) |
−0.927457 | + | 0.373930i | \(0.878010\pi\) | |||||||
\(998\) | 0.432718 | + | 0.432718i | 0.0136974 | + | 0.0136974i | ||||
\(999\) | 0.781905 | − | 0.992629i | 0.0247384 | − | 0.0314054i |
(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 | 225.2.p.b.32.2 | 16 | ||
3.2 | odd | 2 | 675.2.q.a.557.3 | 16 | |||
5.2 | odd | 4 | 45.2.l.a.23.3 | yes | 16 | ||
5.3 | odd | 4 | inner | 225.2.p.b.68.2 | 16 | ||
5.4 | even | 2 | 45.2.l.a.32.3 | yes | 16 | ||
9.2 | odd | 6 | inner | 225.2.p.b.182.2 | 16 | ||
9.7 | even | 3 | 675.2.q.a.332.3 | 16 | |||
15.2 | even | 4 | 135.2.m.a.98.2 | 16 | |||
15.8 | even | 4 | 675.2.q.a.368.3 | 16 | |||
15.14 | odd | 2 | 135.2.m.a.17.2 | 16 | |||
20.7 | even | 4 | 720.2.cu.c.113.2 | 16 | |||
20.19 | odd | 2 | 720.2.cu.c.257.1 | 16 | |||
45.2 | even | 12 | 45.2.l.a.38.3 | yes | 16 | ||
45.4 | even | 6 | 405.2.f.a.242.4 | 16 | |||
45.7 | odd | 12 | 135.2.m.a.8.2 | 16 | |||
45.14 | odd | 6 | 405.2.f.a.242.5 | 16 | |||
45.22 | odd | 12 | 405.2.f.a.323.5 | 16 | |||
45.29 | odd | 6 | 45.2.l.a.2.3 | ✓ | 16 | ||
45.32 | even | 12 | 405.2.f.a.323.4 | 16 | |||
45.34 | even | 6 | 135.2.m.a.62.2 | 16 | |||
45.38 | even | 12 | inner | 225.2.p.b.218.2 | 16 | ||
45.43 | odd | 12 | 675.2.q.a.143.3 | 16 | |||
180.47 | odd | 12 | 720.2.cu.c.353.1 | 16 | |||
180.119 | even | 6 | 720.2.cu.c.497.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.2.l.a.2.3 | ✓ | 16 | 45.29 | odd | 6 | ||
45.2.l.a.23.3 | yes | 16 | 5.2 | odd | 4 | ||
45.2.l.a.32.3 | yes | 16 | 5.4 | even | 2 | ||
45.2.l.a.38.3 | yes | 16 | 45.2 | even | 12 | ||
135.2.m.a.8.2 | 16 | 45.7 | odd | 12 | |||
135.2.m.a.17.2 | 16 | 15.14 | odd | 2 | |||
135.2.m.a.62.2 | 16 | 45.34 | even | 6 | |||
135.2.m.a.98.2 | 16 | 15.2 | even | 4 | |||
225.2.p.b.32.2 | 16 | 1.1 | even | 1 | trivial | ||
225.2.p.b.68.2 | 16 | 5.3 | odd | 4 | inner | ||
225.2.p.b.182.2 | 16 | 9.2 | odd | 6 | inner | ||
225.2.p.b.218.2 | 16 | 45.38 | even | 12 | inner | ||
405.2.f.a.242.4 | 16 | 45.4 | even | 6 | |||
405.2.f.a.242.5 | 16 | 45.14 | odd | 6 | |||
405.2.f.a.323.4 | 16 | 45.32 | even | 12 | |||
405.2.f.a.323.5 | 16 | 45.22 | odd | 12 | |||
675.2.q.a.143.3 | 16 | 45.43 | odd | 12 | |||
675.2.q.a.332.3 | 16 | 9.7 | even | 3 | |||
675.2.q.a.368.3 | 16 | 15.8 | even | 4 | |||
675.2.q.a.557.3 | 16 | 3.2 | odd | 2 | |||
720.2.cu.c.113.2 | 16 | 20.7 | even | 4 | |||
720.2.cu.c.257.1 | 16 | 20.19 | odd | 2 | |||
720.2.cu.c.353.1 | 16 | 180.47 | odd | 12 | |||
720.2.cu.c.497.2 | 16 | 180.119 | even | 6 |