Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(529,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.ba (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 529.5 | ||
Character | \(\chi\) | \(=\) | 1110.529 |
Dual form | 1110.2.ba.a.619.5 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.51023 | − | 1.64901i | 0.675393 | − | 0.737458i | ||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 0.0701099 | + | 0.0404780i | 0.0264990 | + | 0.0152992i | 0.513191 | − | 0.858274i | \(-0.328463\pi\) |
−0.486692 | + | 0.873574i | \(0.661797\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | −2.18319 | − | 0.483391i | −0.690386 | − | 0.152862i | ||||
\(11\) | −3.93468 | −1.18635 | −0.593176 | − | 0.805073i | \(-0.702126\pi\) | ||||
−0.593176 | + | 0.805073i | \(0.702126\pi\) | |||||||
\(12\) | 0.866025 | − | 0.500000i | 0.250000 | − | 0.144338i | ||||
\(13\) | 1.78579 | − | 3.09309i | 0.495290 | − | 0.857868i | −0.504695 | − | 0.863298i | \(-0.668395\pi\) |
0.999985 | + | 0.00542977i | \(0.00172836\pi\) | |||||||
\(14\) | − | 0.0809559i | − | 0.0216364i | ||||||
\(15\) | −2.13240 | + | 0.672968i | −0.550582 | + | 0.173760i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.563300 | + | 0.975664i | 0.136620 | + | 0.236633i | 0.926215 | − | 0.376995i | \(-0.123043\pi\) |
−0.789595 | + | 0.613628i | \(0.789709\pi\) | |||||||
\(18\) | 0.500000 | − | 0.866025i | 0.117851 | − | 0.204124i | ||||
\(19\) | −1.70412 | − | 0.983874i | −0.390952 | − | 0.225716i | 0.291621 | − | 0.956534i | \(-0.405805\pi\) |
−0.682572 | + | 0.730818i | \(0.739139\pi\) | |||||||
\(20\) | 0.672968 | + | 2.13240i | 0.150480 | + | 0.476818i | ||||
\(21\) | −0.0404780 | − | 0.0701099i | −0.00883302 | − | 0.0152992i | ||||
\(22\) | 1.96734 | + | 3.40754i | 0.419439 | + | 0.726489i | ||||
\(23\) | −2.93551 | −0.612096 | −0.306048 | − | 0.952016i | \(-0.599007\pi\) | ||||
−0.306048 | + | 0.952016i | \(0.599007\pi\) | |||||||
\(24\) | −0.866025 | − | 0.500000i | −0.176777 | − | 0.102062i | ||||
\(25\) | −0.438440 | − | 4.98074i | −0.0876879 | − | 0.996148i | ||||
\(26\) | −3.57159 | −0.700446 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −0.0701099 | + | 0.0404780i | −0.0132495 | + | 0.00764962i | ||||
\(29\) | 2.65993i | 0.493937i | 0.969023 | + | 0.246969i | \(0.0794345\pi\) | ||||
−0.969023 | + | 0.246969i | \(0.920566\pi\) | |||||||
\(30\) | 1.64901 | + | 1.51023i | 0.301066 | + | 0.275728i | ||||
\(31\) | − | 6.08031i | − | 1.09206i | −0.837767 | − | 0.546028i | \(-0.816139\pi\) | ||
0.837767 | − | 0.546028i | \(-0.183861\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 3.40754 | + | 1.96734i | 0.593176 | + | 0.342470i | ||||
\(34\) | 0.563300 | − | 0.975664i | 0.0966051 | − | 0.167325i | ||||
\(35\) | 0.172630 | − | 0.0544808i | 0.0291798 | − | 0.00920893i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 1.49939 | − | 5.89507i | 0.246498 | − | 0.969143i | ||||
\(38\) | 1.96775i | 0.319211i | ||||||||
\(39\) | −3.09309 | + | 1.78579i | −0.495290 | + | 0.285956i | ||||
\(40\) | 1.51023 | − | 1.64901i | 0.238788 | − | 0.260731i | ||||
\(41\) | −3.72081 | + | 6.44463i | −0.581093 | + | 1.00648i | 0.414257 | + | 0.910160i | \(0.364041\pi\) |
−0.995350 | + | 0.0963225i | \(0.969292\pi\) | |||||||
\(42\) | −0.0404780 | + | 0.0701099i | −0.00624589 | + | 0.0108182i | ||||
\(43\) | −5.69104 | −0.867876 | −0.433938 | − | 0.900943i | \(-0.642876\pi\) | ||||
−0.433938 | + | 0.900943i | \(0.642876\pi\) | |||||||
\(44\) | 1.96734 | − | 3.40754i | 0.296588 | − | 0.513705i | ||||
\(45\) | 2.18319 | + | 0.483391i | 0.325451 | + | 0.0720596i | ||||
\(46\) | 1.46775 | + | 2.54222i | 0.216409 | + | 0.374831i | ||||
\(47\) | − | 10.7878i | − | 1.57356i | −0.617235 | − | 0.786779i | \(-0.711747\pi\) | ||
0.617235 | − | 0.786779i | \(-0.288253\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −3.49672 | − | 6.05650i | −0.499532 | − | 0.865215i | ||||
\(50\) | −4.09423 | + | 2.87007i | −0.579011 | + | 0.405889i | ||||
\(51\) | − | 1.12660i | − | 0.157756i | ||||||
\(52\) | 1.78579 | + | 3.09309i | 0.247645 | + | 0.428934i | ||||
\(53\) | −0.118647 | + | 0.0685008i | −0.0162974 | + | 0.00940931i | −0.508127 | − | 0.861282i | \(-0.669662\pi\) |
0.491829 | + | 0.870692i | \(0.336328\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | −5.94226 | + | 6.48832i | −0.801254 | + | 0.874885i | ||||
\(56\) | 0.0701099 | + | 0.0404780i | 0.00936883 | + | 0.00540910i | ||||
\(57\) | 0.983874 | + | 1.70412i | 0.130317 | + | 0.225716i | ||||
\(58\) | 2.30357 | − | 1.32997i | 0.302474 | − | 0.174633i | ||||
\(59\) | −2.46559 | + | 1.42351i | −0.320992 | + | 0.185325i | −0.651835 | − | 0.758361i | \(-0.726000\pi\) |
0.330842 | + | 0.943686i | \(0.392667\pi\) | |||||||
\(60\) | 0.483391 | − | 2.18319i | 0.0624054 | − | 0.281849i | ||||
\(61\) | 8.34607 | + | 4.81861i | 1.06861 | + | 0.616960i | 0.927800 | − | 0.373078i | \(-0.121698\pi\) |
0.140805 | + | 0.990037i | \(0.455031\pi\) | |||||||
\(62\) | −5.26570 | + | 3.04016i | −0.668745 | + | 0.386100i | ||||
\(63\) | 0.0809559i | 0.0101995i | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.40357 | − | 7.61604i | −0.298126 | − | 0.944654i | ||||
\(66\) | − | 3.93468i | − | 0.484326i | ||||||
\(67\) | −3.06184 | − | 1.76776i | −0.374064 | − | 0.215966i | 0.301169 | − | 0.953571i | \(-0.402623\pi\) |
−0.675232 | + | 0.737605i | \(0.735957\pi\) | |||||||
\(68\) | −1.12660 | −0.136620 | ||||||||
\(69\) | 2.54222 | + | 1.46775i | 0.306048 | + | 0.176697i | ||||
\(70\) | −0.133497 | − | 0.122262i | −0.0159559 | − | 0.0146131i | ||||
\(71\) | −3.49001 | + | 6.04487i | −0.414188 | + | 0.717394i | −0.995343 | − | 0.0963986i | \(-0.969268\pi\) |
0.581155 | + | 0.813793i | \(0.302601\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | 5.98563i | 0.700565i | 0.936644 | + | 0.350282i | \(0.113914\pi\) | ||||
−0.936644 | + | 0.350282i | \(0.886086\pi\) | |||||||
\(74\) | −5.85497 | + | 1.64903i | −0.680627 | + | 0.191696i | ||||
\(75\) | −2.11067 | + | 4.53267i | −0.243719 | + | 0.523387i | ||||
\(76\) | 1.70412 | − | 0.983874i | 0.195476 | − | 0.112858i | ||||
\(77\) | −0.275860 | − | 0.159268i | −0.0314372 | − | 0.0181503i | ||||
\(78\) | 3.09309 | + | 1.78579i | 0.350223 | + | 0.202201i | ||||
\(79\) | −3.95064 | − | 2.28090i | −0.444481 | − | 0.256621i | 0.261015 | − | 0.965335i | \(-0.415943\pi\) |
−0.705497 | + | 0.708713i | \(0.749276\pi\) | |||||||
\(80\) | −2.18319 | − | 0.483391i | −0.244088 | − | 0.0540447i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 7.44162 | 0.821789 | ||||||||
\(83\) | −10.6365 | + | 6.14100i | −1.16751 | + | 0.674062i | −0.953092 | − | 0.302680i | \(-0.902119\pi\) |
−0.214418 | + | 0.976742i | \(0.568785\pi\) | |||||||
\(84\) | 0.0809559 | 0.00883302 | ||||||||
\(85\) | 2.45959 | + | 0.544588i | 0.266779 | + | 0.0590688i | ||||
\(86\) | 2.84552 | + | 4.92859i | 0.306840 | + | 0.531463i | ||||
\(87\) | 1.32997 | − | 2.30357i | 0.142587 | − | 0.246969i | ||||
\(88\) | −3.93468 | −0.419439 | ||||||||
\(89\) | −11.3025 | + | 6.52551i | −1.19806 | + | 0.691703i | −0.960123 | − | 0.279577i | \(-0.909806\pi\) |
−0.237941 | + | 0.971280i | \(0.576473\pi\) | |||||||
\(90\) | −0.672968 | − | 2.13240i | −0.0709371 | − | 0.224774i | ||||
\(91\) | 0.250404 | − | 0.144571i | 0.0262494 | − | 0.0151551i | ||||
\(92\) | 1.46775 | − | 2.54222i | 0.153024 | − | 0.265045i | ||||
\(93\) | −3.04016 | + | 5.26570i | −0.315249 | + | 0.546028i | ||||
\(94\) | −9.34248 | + | 5.39388i | −0.963603 | + | 0.556337i | ||||
\(95\) | −4.19602 | + | 1.32423i | −0.430502 | + | 0.135863i | ||||
\(96\) | 0.866025 | − | 0.500000i | 0.0883883 | − | 0.0510310i | ||||
\(97\) | 0.882847 | 0.0896396 | 0.0448198 | − | 0.998995i | \(-0.485729\pi\) | ||||
0.0448198 | + | 0.998995i | \(0.485729\pi\) | |||||||
\(98\) | −3.49672 | + | 6.05650i | −0.353222 | + | 0.611799i | ||||
\(99\) | −1.96734 | − | 3.40754i | −0.197725 | − | 0.342470i | ||||
\(100\) | 4.53267 | + | 2.11067i | 0.453267 | + | 0.211067i | ||||
\(101\) | −5.69660 | −0.566833 | −0.283417 | − | 0.958997i | \(-0.591468\pi\) | ||||
−0.283417 | + | 0.958997i | \(0.591468\pi\) | |||||||
\(102\) | −0.975664 | + | 0.563300i | −0.0966051 | + | 0.0557750i | ||||
\(103\) | −6.74171 | −0.664280 | −0.332140 | − | 0.943230i | \(-0.607771\pi\) | ||||
−0.332140 | + | 0.943230i | \(0.607771\pi\) | |||||||
\(104\) | 1.78579 | − | 3.09309i | 0.175112 | − | 0.303302i | ||||
\(105\) | −0.176742 | − | 0.0391333i | −0.0172483 | − | 0.00381902i | ||||
\(106\) | 0.118647 | + | 0.0685008i | 0.0115240 | + | 0.00665339i | ||||
\(107\) | −0.309869 | − | 0.178903i | −0.0299562 | − | 0.0172952i | 0.484947 | − | 0.874543i | \(-0.338839\pi\) |
−0.514903 | + | 0.857248i | \(0.672172\pi\) | |||||||
\(108\) | 0.866025 | + | 0.500000i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | −1.10002 | + | 0.635097i | −0.105363 | + | 0.0608312i | −0.551755 | − | 0.834006i | \(-0.686042\pi\) |
0.446393 | + | 0.894837i | \(0.352708\pi\) | |||||||
\(110\) | 8.59018 | + | 1.90199i | 0.819041 | + | 0.181348i | ||||
\(111\) | −4.24604 | + | 4.35559i | −0.403016 | + | 0.413414i | ||||
\(112\) | − | 0.0809559i | − | 0.00764962i | ||||||
\(113\) | −7.99299 | − | 13.8443i | −0.751917 | − | 1.30236i | −0.946892 | − | 0.321551i | \(-0.895796\pi\) |
0.194975 | − | 0.980808i | \(-0.437537\pi\) | |||||||
\(114\) | 0.983874 | − | 1.70412i | 0.0921482 | − | 0.159605i | ||||
\(115\) | −4.43328 | + | 4.84067i | −0.413405 | + | 0.451395i | ||||
\(116\) | −2.30357 | − | 1.32997i | −0.213881 | − | 0.123484i | ||||
\(117\) | 3.57159 | 0.330194 | ||||||||
\(118\) | 2.46559 | + | 1.42351i | 0.226976 | + | 0.131045i | ||||
\(119\) | 0.0912049i | 0.00836074i | ||||||||
\(120\) | −2.13240 | + | 0.672968i | −0.194660 | + | 0.0614333i | ||||
\(121\) | 4.48174 | 0.407431 | ||||||||
\(122\) | − | 9.63722i | − | 0.872513i | ||||||
\(123\) | 6.44463 | − | 3.72081i | 0.581093 | − | 0.335494i | ||||
\(124\) | 5.26570 | + | 3.04016i | 0.472874 | + | 0.273014i | ||||
\(125\) | −8.87541 | − | 6.79905i | −0.793841 | − | 0.608125i | ||||
\(126\) | 0.0701099 | − | 0.0404780i | 0.00624589 | − | 0.00360606i | ||||
\(127\) | 14.2361 | − | 8.21923i | 1.26325 | − | 0.729339i | 0.289550 | − | 0.957163i | \(-0.406494\pi\) |
0.973702 | + | 0.227824i | \(0.0731611\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 4.92859 | + | 2.84552i | 0.433938 | + | 0.250534i | ||||
\(130\) | −5.39390 | + | 5.88957i | −0.473077 | + | 0.516550i | ||||
\(131\) | 1.69785 | − | 0.980254i | 0.148342 | − | 0.0856452i | −0.423992 | − | 0.905666i | \(-0.639372\pi\) |
0.572334 | + | 0.820021i | \(0.306038\pi\) | |||||||
\(132\) | −3.40754 | + | 1.96734i | −0.296588 | + | 0.171235i | ||||
\(133\) | −0.0796504 | − | 0.137959i | −0.00690657 | − | 0.0119625i | ||||
\(134\) | 3.53551i | 0.305422i | ||||||||
\(135\) | −1.64901 | − | 1.51023i | −0.141924 | − | 0.129979i | ||||
\(136\) | 0.563300 | + | 0.975664i | 0.0483026 | + | 0.0836625i | ||||
\(137\) | − | 20.5579i | − | 1.75638i | −0.478314 | − | 0.878189i | \(-0.658752\pi\) | ||
0.478314 | − | 0.878189i | \(-0.341248\pi\) | |||||||
\(138\) | − | 2.93551i | − | 0.249887i | ||||||
\(139\) | 6.49951 | + | 11.2575i | 0.551281 | + | 0.954848i | 0.998182 | + | 0.0602641i | \(0.0191943\pi\) |
−0.446901 | + | 0.894583i | \(0.647472\pi\) | |||||||
\(140\) | −0.0391333 | + | 0.176742i | −0.00330737 | + | 0.0149375i | ||||
\(141\) | −5.39388 | + | 9.34248i | −0.454247 | + | 0.786779i | ||||
\(142\) | 6.98002 | 0.585750 | ||||||||
\(143\) | −7.02654 | + | 12.1703i | −0.587589 | + | 1.01773i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 4.38625 | + | 4.01710i | 0.364258 | + | 0.333602i | ||||
\(146\) | 5.18371 | − | 2.99281i | 0.429007 | − | 0.247687i | ||||
\(147\) | 6.99345i | 0.576810i | ||||||||
\(148\) | 4.35559 | + | 4.24604i | 0.358027 | + | 0.349022i | ||||
\(149\) | 22.5829 | 1.85006 | 0.925031 | − | 0.379891i | \(-0.124039\pi\) | ||||
0.925031 | + | 0.379891i | \(0.124039\pi\) | |||||||
\(150\) | 4.98074 | − | 0.438440i | 0.406676 | − | 0.0357985i | ||||
\(151\) | 3.99191 | − | 6.91418i | 0.324857 | − | 0.562668i | −0.656627 | − | 0.754216i | \(-0.728017\pi\) |
0.981483 | + | 0.191547i | \(0.0613506\pi\) | |||||||
\(152\) | −1.70412 | − | 0.983874i | −0.138222 | − | 0.0798027i | ||||
\(153\) | −0.563300 | + | 0.975664i | −0.0455401 | + | 0.0788778i | ||||
\(154\) | 0.318536i | 0.0256684i | ||||||||
\(155\) | −10.0265 | − | 9.18264i | −0.805345 | − | 0.737567i | ||||
\(156\) | − | 3.57159i | − | 0.285956i | ||||||
\(157\) | −4.93908 | + | 2.85158i | −0.394182 | + | 0.227581i | −0.683970 | − | 0.729510i | \(-0.739748\pi\) |
0.289789 | + | 0.957091i | \(0.406415\pi\) | |||||||
\(158\) | 4.56180i | 0.362917i | ||||||||
\(159\) | 0.137002 | 0.0108649 | ||||||||
\(160\) | 0.672968 | + | 2.13240i | 0.0532028 | + | 0.168581i | ||||
\(161\) | −0.205808 | − | 0.118823i | −0.0162200 | − | 0.00936460i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 5.46907 | + | 9.47271i | 0.428371 | + | 0.741960i | 0.996729 | − | 0.0808216i | \(-0.0257544\pi\) |
−0.568358 | + | 0.822781i | \(0.692421\pi\) | |||||||
\(164\) | −3.72081 | − | 6.44463i | −0.290546 | − | 0.503241i | ||||
\(165\) | 8.39031 | − | 2.64792i | 0.653184 | − | 0.206140i | ||||
\(166\) | 10.6365 | + | 6.14100i | 0.825554 | + | 0.476634i | ||||
\(167\) | 4.59649 | − | 7.96135i | 0.355687 | − | 0.616068i | −0.631548 | − | 0.775337i | \(-0.717580\pi\) |
0.987235 | + | 0.159268i | \(0.0509135\pi\) | |||||||
\(168\) | −0.0404780 | − | 0.0701099i | −0.00312294 | − | 0.00540910i | ||||
\(169\) | 0.121875 | + | 0.211094i | 0.00937502 | + | 0.0162380i | ||||
\(170\) | −0.758166 | − | 2.40236i | −0.0581487 | − | 0.184252i | ||||
\(171\) | − | 1.96775i | − | 0.150477i | ||||||
\(172\) | 2.84552 | − | 4.92859i | 0.216969 | − | 0.375801i | ||||
\(173\) | −4.32016 | + | 2.49425i | −0.328456 | + | 0.189634i | −0.655155 | − | 0.755494i | \(-0.727397\pi\) |
0.326700 | + | 0.945128i | \(0.394063\pi\) | |||||||
\(174\) | −2.65993 | −0.201649 | ||||||||
\(175\) | 0.170871 | − | 0.366946i | 0.0129167 | − | 0.0277385i | ||||
\(176\) | 1.96734 | + | 3.40754i | 0.148294 | + | 0.256853i | ||||
\(177\) | 2.84702 | 0.213995 | ||||||||
\(178\) | 11.3025 | + | 6.52551i | 0.847160 | + | 0.489108i | ||||
\(179\) | 9.29758i | 0.694934i | 0.937692 | + | 0.347467i | \(0.112958\pi\) | ||||
−0.937692 | + | 0.347467i | \(0.887042\pi\) | |||||||
\(180\) | −1.51023 | + | 1.64901i | −0.112566 | + | 0.122910i | ||||
\(181\) | 3.79019 | − | 6.56480i | 0.281722 | − | 0.487958i | −0.690087 | − | 0.723727i | \(-0.742428\pi\) |
0.971809 | + | 0.235769i | \(0.0757609\pi\) | |||||||
\(182\) | −0.250404 | − | 0.144571i | −0.0185612 | − | 0.0107163i | ||||
\(183\) | −4.81861 | − | 8.34607i | −0.356202 | − | 0.616960i | ||||
\(184\) | −2.93551 | −0.216409 | ||||||||
\(185\) | −7.45659 | − | 11.3754i | −0.548219 | − | 0.836335i | ||||
\(186\) | 6.08031 | 0.445830 | ||||||||
\(187\) | −2.21641 | − | 3.83893i | −0.162080 | − | 0.280730i | ||||
\(188\) | 9.34248 | + | 5.39388i | 0.681370 | + | 0.393389i | ||||
\(189\) | 0.0404780 | − | 0.0701099i | 0.00294434 | − | 0.00509974i | ||||
\(190\) | 3.24483 | + | 2.97174i | 0.235404 | + | 0.215593i | ||||
\(191\) | 0.0853502i | 0.00617573i | 0.999995 | + | 0.00308786i | \(0.000982899\pi\) | ||||
−0.999995 | + | 0.00308786i | \(0.999017\pi\) | |||||||
\(192\) | −0.866025 | − | 0.500000i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | 5.16516 | 0.371796 | 0.185898 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185898 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(194\) | −0.441424 | − | 0.764568i | −0.0316924 | − | 0.0548928i | ||||
\(195\) | −1.72647 | + | 7.79747i | −0.123635 | + | 0.558388i | ||||
\(196\) | 6.99345 | 0.499532 | ||||||||
\(197\) | 9.34387 | − | 5.39468i | 0.665723 | − | 0.384355i | −0.128731 | − | 0.991680i | \(-0.541090\pi\) |
0.794454 | + | 0.607324i | \(0.207757\pi\) | |||||||
\(198\) | −1.96734 | + | 3.40754i | −0.139813 | + | 0.242163i | ||||
\(199\) | − | 7.93361i | − | 0.562399i | −0.959649 | − | 0.281200i | \(-0.909268\pi\) | ||
0.959649 | − | 0.281200i | \(-0.0907323\pi\) | |||||||
\(200\) | −0.438440 | − | 4.98074i | −0.0310024 | − | 0.352192i | ||||
\(201\) | 1.76776 | + | 3.06184i | 0.124688 | + | 0.215966i | ||||
\(202\) | 2.84830 | + | 4.93340i | 0.200406 | + | 0.347113i | ||||
\(203\) | −0.107669 | + | 0.186488i | −0.00755686 | + | 0.0130889i | ||||
\(204\) | 0.975664 | + | 0.563300i | 0.0683101 | + | 0.0394389i | ||||
\(205\) | 5.00797 | + | 15.8685i | 0.349772 | + | 1.10830i | ||||
\(206\) | 3.37085 | + | 5.83849i | 0.234858 | + | 0.406787i | ||||
\(207\) | −1.46775 | − | 2.54222i | −0.102016 | − | 0.176697i | ||||
\(208\) | −3.57159 | −0.247645 | ||||||||
\(209\) | 6.70517 | + | 3.87123i | 0.463806 | + | 0.267779i | ||||
\(210\) | 0.0544808 | + | 0.172630i | 0.00375953 | + | 0.0119126i | ||||
\(211\) | 24.3190 | 1.67419 | 0.837093 | − | 0.547060i | \(-0.184253\pi\) | ||||
0.837093 | + | 0.547060i | \(0.184253\pi\) | |||||||
\(212\) | − | 0.137002i | − | 0.00940931i | ||||||
\(213\) | 6.04487 | − | 3.49001i | 0.414188 | − | 0.239131i | ||||
\(214\) | 0.357806i | 0.0244591i | ||||||||
\(215\) | −8.59476 | + | 9.38456i | −0.586158 | + | 0.640022i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 0.246119 | − | 0.426290i | 0.0167076 | − | 0.0289384i | ||||
\(218\) | 1.10002 | + | 0.635097i | 0.0745027 | + | 0.0430142i | ||||
\(219\) | 2.99281 | − | 5.18371i | 0.202236 | − | 0.350282i | ||||
\(220\) | −2.64792 | − | 8.39031i | −0.178523 | − | 0.565674i | ||||
\(221\) | 4.02375 | 0.270667 | ||||||||
\(222\) | 5.89507 | + | 1.49939i | 0.395651 | + | 0.100632i | ||||
\(223\) | − | 18.2474i | − | 1.22193i | −0.791656 | − | 0.610967i | \(-0.790781\pi\) | ||
0.791656 | − | 0.610967i | \(-0.209219\pi\) | |||||||
\(224\) | −0.0701099 | + | 0.0404780i | −0.00468441 | + | 0.00270455i | ||||
\(225\) | 4.09423 | − | 2.87007i | 0.272948 | − | 0.191338i | ||||
\(226\) | −7.99299 | + | 13.8443i | −0.531686 | + | 0.920907i | ||||
\(227\) | 4.95426 | − | 8.58102i | 0.328826 | − | 0.569543i | −0.653454 | − | 0.756967i | \(-0.726681\pi\) |
0.982279 | + | 0.187424i | \(0.0600138\pi\) | |||||||
\(228\) | −1.96775 | −0.130317 | ||||||||
\(229\) | 12.8080 | − | 22.1841i | 0.846376 | − | 1.46597i | −0.0380447 | − | 0.999276i | \(-0.512113\pi\) |
0.884421 | − | 0.466690i | \(-0.154554\pi\) | |||||||
\(230\) | 6.40878 | + | 1.41900i | 0.422583 | + | 0.0935659i | ||||
\(231\) | 0.159268 | + | 0.275860i | 0.0104791 | + | 0.0181503i | ||||
\(232\) | 2.65993i | 0.174633i | ||||||||
\(233\) | 3.44779i | 0.225872i | 0.993602 | + | 0.112936i | \(0.0360256\pi\) | ||||
−0.993602 | + | 0.112936i | \(0.963974\pi\) | |||||||
\(234\) | −1.78579 | − | 3.09309i | −0.116741 | − | 0.202201i | ||||
\(235\) | −17.7891 | − | 16.2920i | −1.16043 | − | 1.06277i | ||||
\(236\) | − | 2.84702i | − | 0.185325i | ||||||
\(237\) | 2.28090 | + | 3.95064i | 0.148160 | + | 0.256621i | ||||
\(238\) | 0.0789858 | − | 0.0456025i | 0.00511989 | − | 0.00295597i | ||||
\(239\) | 12.3341 | − | 7.12108i | 0.797824 | − | 0.460624i | −0.0448854 | − | 0.998992i | \(-0.514292\pi\) |
0.842710 | + | 0.538368i | \(0.180959\pi\) | |||||||
\(240\) | 1.64901 | + | 1.51023i | 0.106443 | + | 0.0974846i | ||||
\(241\) | −17.9025 | − | 10.3360i | −1.15320 | − | 0.665801i | −0.203536 | − | 0.979067i | \(-0.565244\pi\) |
−0.949665 | + | 0.313266i | \(0.898577\pi\) | |||||||
\(242\) | −2.24087 | − | 3.88130i | −0.144049 | − | 0.249500i | ||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | −8.34607 | + | 4.81861i | −0.534303 | + | 0.308480i | ||||
\(245\) | −15.2680 | − | 3.38057i | −0.975440 | − | 0.215976i | ||||
\(246\) | −6.44463 | − | 3.72081i | −0.410895 | − | 0.237230i | ||||
\(247\) | −6.08641 | + | 3.51399i | −0.387269 | + | 0.223590i | ||||
\(248\) | − | 6.08031i | − | 0.386100i | ||||||
\(249\) | 12.2820 | 0.778340 | ||||||||
\(250\) | −1.45044 | + | 11.0859i | −0.0917341 | + | 0.701131i | ||||
\(251\) | 8.24545i | 0.520448i | 0.965548 | + | 0.260224i | \(0.0837965\pi\) | ||||
−0.965548 | + | 0.260224i | \(0.916204\pi\) | |||||||
\(252\) | −0.0701099 | − | 0.0404780i | −0.00441651 | − | 0.00254987i | ||||
\(253\) | 11.5503 | 0.726161 | ||||||||
\(254\) | −14.2361 | − | 8.21923i | −0.893254 | − | 0.515721i | ||||
\(255\) | −1.85777 | − | 1.70142i | −0.116338 | − | 0.106547i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 3.41974 | + | 5.92316i | 0.213317 | + | 0.369476i | 0.952751 | − | 0.303753i | \(-0.0982399\pi\) |
−0.739433 | + | 0.673230i | \(0.764907\pi\) | |||||||
\(258\) | − | 5.69104i | − | 0.354309i | ||||||
\(259\) | 0.343742 | − | 0.352611i | 0.0213591 | − | 0.0219102i | ||||
\(260\) | 7.79747 | + | 1.72647i | 0.483579 | + | 0.107071i | ||||
\(261\) | −2.30357 | + | 1.32997i | −0.142587 | + | 0.0823229i | ||||
\(262\) | −1.69785 | − | 0.980254i | −0.104894 | − | 0.0605603i | ||||
\(263\) | −12.7454 | − | 7.35858i | −0.785917 | − | 0.453750i | 0.0526059 | − | 0.998615i | \(-0.483247\pi\) |
−0.838523 | + | 0.544866i | \(0.816581\pi\) | |||||||
\(264\) | 3.40754 | + | 1.96734i | 0.209719 | + | 0.121082i | ||||
\(265\) | −0.0662253 | + | 0.299101i | −0.00406819 | + | 0.0183736i | ||||
\(266\) | −0.0796504 | + | 0.137959i | −0.00488368 | + | 0.00845878i | ||||
\(267\) | 13.0510 | 0.798710 | ||||||||
\(268\) | 3.06184 | − | 1.76776i | 0.187032 | − | 0.107983i | ||||
\(269\) | 26.5270 | 1.61738 | 0.808691 | − | 0.588234i | \(-0.200177\pi\) | ||||
0.808691 | + | 0.588234i | \(0.200177\pi\) | |||||||
\(270\) | −0.483391 | + | 2.18319i | −0.0294182 | + | 0.132865i | ||||
\(271\) | 6.61234 | + | 11.4529i | 0.401671 | + | 0.695715i | 0.993928 | − | 0.110035i | \(-0.0350962\pi\) |
−0.592257 | + | 0.805749i | \(0.701763\pi\) | |||||||
\(272\) | 0.563300 | − | 0.975664i | 0.0341551 | − | 0.0591583i | ||||
\(273\) | −0.289141 | −0.0174996 | ||||||||
\(274\) | −17.8036 | + | 10.2789i | −1.07556 | + | 0.620973i | ||||
\(275\) | 1.72512 | + | 19.5976i | 0.104029 | + | 1.18178i | ||||
\(276\) | −2.54222 | + | 1.46775i | −0.153024 | + | 0.0883484i | ||||
\(277\) | 6.30776 | − | 10.9254i | 0.378997 | − | 0.656442i | −0.611920 | − | 0.790920i | \(-0.709602\pi\) |
0.990917 | + | 0.134478i | \(0.0429358\pi\) | |||||||
\(278\) | 6.49951 | − | 11.2575i | 0.389815 | − | 0.675179i | ||||
\(279\) | 5.26570 | − | 3.04016i | 0.315249 | − | 0.182009i | ||||
\(280\) | 0.172630 | − | 0.0544808i | 0.0103166 | − | 0.00325585i | ||||
\(281\) | −10.1405 | + | 5.85462i | −0.604931 | + | 0.349257i | −0.770979 | − | 0.636860i | \(-0.780233\pi\) |
0.166048 | + | 0.986118i | \(0.446899\pi\) | |||||||
\(282\) | 10.7878 | 0.642402 | ||||||||
\(283\) | −8.13334 | + | 14.0874i | −0.483477 | + | 0.837406i | −0.999820 | − | 0.0189756i | \(-0.993960\pi\) |
0.516343 | + | 0.856382i | \(0.327293\pi\) | |||||||
\(284\) | −3.49001 | − | 6.04487i | −0.207094 | − | 0.358697i | ||||
\(285\) | 4.29597 | + | 0.951190i | 0.254471 | + | 0.0563437i | ||||
\(286\) | 14.0531 | 0.830976 | ||||||||
\(287\) | −0.521731 | + | 0.301222i | −0.0307968 | + | 0.0177805i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 7.86539 | − | 13.6232i | 0.462670 | − | 0.801368i | ||||
\(290\) | 1.28579 | − | 5.80715i | 0.0755040 | − | 0.341008i | ||||
\(291\) | −0.764568 | − | 0.441424i | −0.0448198 | − | 0.0258767i | ||||
\(292\) | −5.18371 | − | 2.99281i | −0.303354 | − | 0.175141i | ||||
\(293\) | −4.62415 | − | 2.66975i | −0.270146 | − | 0.155969i | 0.358808 | − | 0.933411i | \(-0.383183\pi\) |
−0.628954 | + | 0.777443i | \(0.716517\pi\) | |||||||
\(294\) | 6.05650 | − | 3.49672i | 0.353222 | − | 0.203933i | ||||
\(295\) | −1.37622 | + | 6.21559i | −0.0801267 | + | 0.361886i | ||||
\(296\) | 1.49939 | − | 5.89507i | 0.0871501 | − | 0.342644i | ||||
\(297\) | 3.93468i | 0.228314i | ||||||||
\(298\) | −11.2914 | − | 19.5574i | −0.654096 | − | 1.13293i | ||||
\(299\) | −5.24221 | + | 9.07978i | −0.303165 | + | 0.525097i | ||||
\(300\) | −2.87007 | − | 4.09423i | −0.165704 | − | 0.236380i | ||||
\(301\) | −0.398998 | − | 0.230362i | −0.0229979 | − | 0.0132778i | ||||
\(302\) | −7.98381 | −0.459417 | ||||||||
\(303\) | 4.93340 | + | 2.84830i | 0.283417 | + | 0.163631i | ||||
\(304\) | 1.96775i | 0.112858i | ||||||||
\(305\) | 20.5504 | − | 6.48554i | 1.17671 | − | 0.371361i | ||||
\(306\) | 1.12660 | 0.0644034 | ||||||||
\(307\) | − | 23.4241i | − | 1.33689i | −0.743763 | − | 0.668443i | \(-0.766961\pi\) | ||
0.743763 | − | 0.668443i | \(-0.233039\pi\) | |||||||
\(308\) | 0.275860 | − | 0.159268i | 0.0157186 | − | 0.00907514i | ||||
\(309\) | 5.83849 | + | 3.37085i | 0.332140 | + | 0.191761i | ||||
\(310\) | −2.93916 | + | 13.2745i | −0.166933 | + | 0.753941i | ||||
\(311\) | 19.5018 | − | 11.2594i | 1.10584 | − | 0.638460i | 0.168095 | − | 0.985771i | \(-0.446239\pi\) |
0.937750 | + | 0.347311i | \(0.112905\pi\) | |||||||
\(312\) | −3.09309 | + | 1.78579i | −0.175112 | + | 0.101101i | ||||
\(313\) | −4.65775 | − | 8.06746i | −0.263272 | − | 0.456000i | 0.703838 | − | 0.710361i | \(-0.251468\pi\) |
−0.967109 | + | 0.254361i | \(0.918135\pi\) | |||||||
\(314\) | 4.93908 | + | 2.85158i | 0.278729 | + | 0.160924i | ||||
\(315\) | 0.133497 | + | 0.122262i | 0.00752169 | + | 0.00688867i | ||||
\(316\) | 3.95064 | − | 2.28090i | 0.222241 | − | 0.128311i | ||||
\(317\) | 18.6912 | − | 10.7914i | 1.04980 | − | 0.606104i | 0.127209 | − | 0.991876i | \(-0.459398\pi\) |
0.922594 | + | 0.385772i | \(0.126065\pi\) | |||||||
\(318\) | −0.0685008 | − | 0.118647i | −0.00384133 | − | 0.00665339i | ||||
\(319\) | − | 10.4660i | − | 0.585984i | ||||||
\(320\) | 1.51023 | − | 1.64901i | 0.0844242 | − | 0.0921822i | ||||
\(321\) | 0.178903 | + | 0.309869i | 0.00998540 | + | 0.0172952i | ||||
\(322\) | 0.237647i | 0.0132435i | ||||||||
\(323\) | − | 2.21686i | − | 0.123350i | ||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −16.1888 | − | 7.53845i | −0.897994 | − | 0.418158i | ||||
\(326\) | 5.46907 | − | 9.47271i | 0.302904 | − | 0.524645i | ||||
\(327\) | 1.27019 | 0.0702419 | ||||||||
\(328\) | −3.72081 | + | 6.44463i | −0.205447 | + | 0.355845i | ||||
\(329\) | 0.436667 | − | 0.756329i | 0.0240742 | − | 0.0416978i | ||||
\(330\) | −6.48832 | − | 5.94226i | −0.357170 | − | 0.327111i | ||||
\(331\) | 3.45970 | − | 1.99746i | 0.190162 | − | 0.109790i | −0.401896 | − | 0.915685i | \(-0.631649\pi\) |
0.592059 | + | 0.805895i | \(0.298315\pi\) | |||||||
\(332\) | − | 12.2820i | − | 0.674062i | ||||||
\(333\) | 5.85497 | − | 1.64903i | 0.320851 | − | 0.0903661i | ||||
\(334\) | −9.19298 | −0.503018 | ||||||||
\(335\) | −7.53911 | + | 2.37929i | −0.411906 | + | 0.129994i | ||||
\(336\) | −0.0404780 | + | 0.0701099i | −0.00220825 | + | 0.00382481i | ||||
\(337\) | 4.81065 | + | 2.77743i | 0.262053 | + | 0.151296i | 0.625271 | − | 0.780408i | \(-0.284989\pi\) |
−0.363218 | + | 0.931704i | \(0.618322\pi\) | |||||||
\(338\) | 0.121875 | − | 0.211094i | 0.00662914 | − | 0.0114820i | ||||
\(339\) | 15.9860i | 0.868239i | ||||||||
\(340\) | −1.70142 | + | 1.85777i | −0.0922724 | + | 0.100752i | ||||
\(341\) | 23.9241i | 1.29556i | ||||||||
\(342\) | −1.70412 | + | 0.983874i | −0.0921482 | + | 0.0532018i | ||||
\(343\) | − | 1.13285i | − | 0.0611683i | ||||||
\(344\) | −5.69104 | −0.306840 | ||||||||
\(345\) | 6.25967 | − | 1.97550i | 0.337009 | − | 0.106358i | ||||
\(346\) | 4.32016 | + | 2.49425i | 0.232253 | + | 0.134092i | ||||
\(347\) | −25.2200 | −1.35388 | −0.676940 | − | 0.736038i | \(-0.736694\pi\) | ||||
−0.676940 | + | 0.736038i | \(0.736694\pi\) | |||||||
\(348\) | 1.32997 | + | 2.30357i | 0.0712937 | + | 0.123484i | ||||
\(349\) | −4.14403 | − | 7.17766i | −0.221825 | − | 0.384211i | 0.733537 | − | 0.679649i | \(-0.237868\pi\) |
−0.955362 | + | 0.295438i | \(0.904535\pi\) | |||||||
\(350\) | −0.403220 | + | 0.0354943i | −0.0215530 | + | 0.00189725i | ||||
\(351\) | −3.09309 | − | 1.78579i | −0.165097 | − | 0.0953187i | ||||
\(352\) | 1.96734 | − | 3.40754i | 0.104860 | − | 0.181622i | ||||
\(353\) | 14.1316 | + | 24.4767i | 0.752150 | + | 1.30276i | 0.946779 | + | 0.321886i | \(0.104317\pi\) |
−0.194628 | + | 0.980877i | \(0.562350\pi\) | |||||||
\(354\) | −1.42351 | − | 2.46559i | −0.0756586 | − | 0.131045i | ||||
\(355\) | 4.69733 | + | 14.8842i | 0.249308 | + | 0.789969i | ||||
\(356\) | − | 13.0510i | − | 0.691703i | ||||||
\(357\) | 0.0456025 | − | 0.0789858i | 0.00241354 | − | 0.00418037i | ||||
\(358\) | 8.05194 | − | 4.64879i | 0.425558 | − | 0.245696i | ||||
\(359\) | 4.51937 | 0.238523 | 0.119262 | − | 0.992863i | \(-0.461947\pi\) | ||||
0.119262 | + | 0.992863i | \(0.461947\pi\) | |||||||
\(360\) | 2.18319 | + | 0.483391i | 0.115064 | + | 0.0254769i | ||||
\(361\) | −7.56399 | − | 13.1012i | −0.398105 | − | 0.689537i | ||||
\(362\) | −7.58038 | −0.398416 | ||||||||
\(363\) | −3.88130 | − | 2.24087i | −0.203716 | − | 0.117615i | ||||
\(364\) | 0.289141i | 0.0151551i | ||||||||
\(365\) | 9.87034 | + | 9.03965i | 0.516637 | + | 0.473157i | ||||
\(366\) | −4.81861 | + | 8.34607i | −0.251873 | + | 0.436256i | ||||
\(367\) | −13.0478 | − | 7.53314i | −0.681089 | − | 0.393227i | 0.119176 | − | 0.992873i | \(-0.461975\pi\) |
−0.800265 | + | 0.599646i | \(0.795308\pi\) | |||||||
\(368\) | 1.46775 | + | 2.54222i | 0.0765120 | + | 0.132523i | ||||
\(369\) | −7.44162 | −0.387395 | ||||||||
\(370\) | −6.12307 | + | 12.1453i | −0.318323 | + | 0.631403i | ||||
\(371\) | −0.0110911 | −0.000575821 | ||||||||
\(372\) | −3.04016 | − | 5.26570i | −0.157625 | − | 0.273014i | ||||
\(373\) | 25.0921 | + | 14.4869i | 1.29922 | + | 0.750105i | 0.980269 | − | 0.197667i | \(-0.0633364\pi\) |
0.318950 | + | 0.947772i | \(0.396670\pi\) | |||||||
\(374\) | −2.21641 | + | 3.83893i | −0.114608 | + | 0.198506i | ||||
\(375\) | 4.28681 | + | 10.3259i | 0.221370 | + | 0.533225i | ||||
\(376\) | − | 10.7878i | − | 0.556337i | ||||||
\(377\) | 8.22741 | + | 4.75010i | 0.423733 | + | 0.244642i | ||||
\(378\) | −0.0809559 | −0.00416392 | ||||||||
\(379\) | 13.4494 | + | 23.2950i | 0.690848 | + | 1.19658i | 0.971560 | + | 0.236792i | \(0.0760959\pi\) |
−0.280713 | + | 0.959792i | \(0.590571\pi\) | |||||||
\(380\) | 0.951190 | − | 4.29597i | 0.0487950 | − | 0.220379i | ||||
\(381\) | −16.4385 | −0.842168 | ||||||||
\(382\) | 0.0739155 | − | 0.0426751i | 0.00378184 | − | 0.00218345i | ||||
\(383\) | −4.83015 | + | 8.36606i | −0.246809 | + | 0.427486i | −0.962639 | − | 0.270789i | \(-0.912715\pi\) |
0.715830 | + | 0.698275i | \(0.246049\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | −0.679245 | + | 0.214365i | −0.0346175 | + | 0.0109250i | ||||
\(386\) | −2.58258 | − | 4.47316i | −0.131450 | − | 0.227678i | ||||
\(387\) | −2.84552 | − | 4.92859i | −0.144646 | − | 0.250534i | ||||
\(388\) | −0.441424 | + | 0.764568i | −0.0224099 | + | 0.0388151i | ||||
\(389\) | −21.6494 | − | 12.4993i | −1.09767 | − | 0.633739i | −0.162060 | − | 0.986781i | \(-0.551814\pi\) |
−0.935607 | + | 0.353042i | \(0.885147\pi\) | |||||||
\(390\) | 7.61604 | − | 2.40357i | 0.385653 | − | 0.121709i | ||||
\(391\) | −1.65357 | − | 2.86407i | −0.0836247 | − | 0.144842i | ||||
\(392\) | −3.49672 | − | 6.05650i | −0.176611 | − | 0.305900i | ||||
\(393\) | −1.96051 | −0.0988945 | ||||||||
\(394\) | −9.34387 | − | 5.39468i | −0.470737 | − | 0.271780i | ||||
\(395\) | −9.72757 | + | 3.06995i | −0.489447 | + | 0.154466i | ||||
\(396\) | 3.93468 | 0.197725 | ||||||||
\(397\) | 8.82419i | 0.442873i | 0.975175 | + | 0.221437i | \(0.0710746\pi\) | ||||
−0.975175 | + | 0.221437i | \(0.928925\pi\) | |||||||
\(398\) | −6.87071 | + | 3.96681i | −0.344398 | + | 0.198838i | ||||
\(399\) | 0.159301i | 0.00797501i | ||||||||
\(400\) | −4.09423 | + | 2.87007i | −0.204711 | + | 0.143503i | ||||
\(401\) | 21.1757i | 1.05746i | 0.848789 | + | 0.528732i | \(0.177332\pi\) | ||||
−0.848789 | + | 0.528732i | \(0.822668\pi\) | |||||||
\(402\) | 1.76776 | − | 3.06184i | 0.0881676 | − | 0.152711i | ||||
\(403\) | −18.8069 | − | 10.8582i | −0.936840 | − | 0.540885i | ||||
\(404\) | 2.84830 | − | 4.93340i | 0.141708 | − | 0.245446i | ||||
\(405\) | 0.672968 | + | 2.13240i | 0.0334401 | + | 0.105960i | ||||
\(406\) | 0.215337 | 0.0106870 | ||||||||
\(407\) | −5.89961 | + | 23.1952i | −0.292433 | + | 1.14975i | ||||
\(408\) | − | 1.12660i | − | 0.0557750i | ||||||
\(409\) | −19.6743 | + | 11.3590i | −0.972831 | + | 0.561664i | −0.900098 | − | 0.435687i | \(-0.856505\pi\) |
−0.0727331 | + | 0.997351i | \(0.523172\pi\) | |||||||
\(410\) | 11.2385 | − | 12.2713i | 0.555031 | − | 0.606035i | ||||
\(411\) | −10.2789 | + | 17.8036i | −0.507023 | + | 0.878189i | ||||
\(412\) | 3.37085 | − | 5.83849i | 0.166070 | − | 0.287642i | ||||
\(413\) | −0.230483 | −0.0113413 | ||||||||
\(414\) | −1.46775 | + | 2.54222i | −0.0721362 | + | 0.124944i | ||||
\(415\) | −5.93700 | + | 26.8140i | −0.291436 | + | 1.31625i | ||||
\(416\) | 1.78579 | + | 3.09309i | 0.0875558 | + | 0.151651i | ||||
\(417\) | − | 12.9990i | − | 0.636565i | ||||||
\(418\) | − | 7.74246i | − | 0.378696i | ||||||
\(419\) | −3.92133 | − | 6.79195i | −0.191570 | − | 0.331808i | 0.754201 | − | 0.656644i | \(-0.228024\pi\) |
−0.945771 | + | 0.324835i | \(0.894691\pi\) | |||||||
\(420\) | 0.122262 | − | 0.133497i | 0.00596576 | − | 0.00651398i | ||||
\(421\) | 10.2402i | 0.499077i | 0.968365 | + | 0.249539i | \(0.0802789\pi\) | ||||
−0.968365 | + | 0.249539i | \(0.919721\pi\) | |||||||
\(422\) | −12.1595 | − | 21.0608i | −0.591914 | − | 1.02523i | ||||
\(423\) | 9.34248 | − | 5.39388i | 0.454247 | − | 0.262260i | ||||
\(424\) | −0.118647 | + | 0.0685008i | −0.00576200 | + | 0.00332669i | ||||
\(425\) | 4.61256 | − | 3.23342i | 0.223742 | − | 0.156844i | ||||
\(426\) | −6.04487 | − | 3.49001i | −0.292875 | − | 0.169091i | ||||
\(427\) | 0.390095 | + | 0.675664i | 0.0188780 | + | 0.0326977i | ||||
\(428\) | 0.309869 | − | 0.178903i | 0.0149781 | − | 0.00864761i | ||||
\(429\) | 12.1703 | − | 7.02654i | 0.587589 | − | 0.339244i | ||||
\(430\) | 12.4246 | + | 2.75100i | 0.599170 | + | 0.132665i | ||||
\(431\) | −25.4351 | − | 14.6850i | −1.22517 | − | 0.707349i | −0.259150 | − | 0.965837i | \(-0.583443\pi\) |
−0.966015 | + | 0.258488i | \(0.916776\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 0.284291i | − | 0.0136621i | −0.999977 | − | 0.00683107i | \(-0.997826\pi\) | ||
0.999977 | − | 0.00683107i | \(-0.00217441\pi\) | |||||||
\(434\) | −0.492237 | −0.0236281 | ||||||||
\(435\) | −1.79005 | − | 5.67203i | −0.0858264 | − | 0.271953i | ||||
\(436\) | − | 1.27019i | − | 0.0608312i | ||||||
\(437\) | 5.00246 | + | 2.88817i | 0.239300 | + | 0.138160i | ||||
\(438\) | −5.98563 | −0.286004 | ||||||||
\(439\) | −0.313552 | − | 0.181029i | −0.0149650 | − | 0.00864004i | 0.492499 | − | 0.870313i | \(-0.336084\pi\) |
−0.507464 | + | 0.861673i | \(0.669417\pi\) | |||||||
\(440\) | −5.94226 | + | 6.48832i | −0.283286 | + | 0.309318i | ||||
\(441\) | 3.49672 | − | 6.05650i | 0.166511 | − | 0.288405i | ||||
\(442\) | −2.01188 | − | 3.48467i | −0.0956952 | − | 0.165749i | ||||
\(443\) | 31.7244i | 1.50727i | 0.657292 | + | 0.753636i | \(0.271702\pi\) | ||||
−0.657292 | + | 0.753636i | \(0.728298\pi\) | |||||||
\(444\) | −1.64903 | − | 5.85497i | −0.0782594 | − | 0.277865i | ||||
\(445\) | −6.30874 | + | 28.4929i | −0.299063 | + | 1.35069i | ||||
\(446\) | −15.8027 | + | 9.12368i | −0.748279 | + | 0.432019i | ||||
\(447\) | −19.5574 | − | 11.2914i | −0.925031 | − | 0.534067i | ||||
\(448\) | 0.0701099 | + | 0.0404780i | 0.00331238 | + | 0.00191240i | ||||
\(449\) | −4.41326 | − | 2.54800i | −0.208275 | − | 0.120248i | 0.392235 | − | 0.919865i | \(-0.371702\pi\) |
−0.600509 | + | 0.799618i | \(0.705035\pi\) | |||||||
\(450\) | −4.53267 | − | 2.11067i | −0.213672 | − | 0.0994979i | ||||
\(451\) | 14.6402 | − | 25.3576i | 0.689381 | − | 1.19404i | ||||
\(452\) | 15.9860 | 0.751917 | ||||||||
\(453\) | −6.91418 | + | 3.99191i | −0.324857 | + | 0.187556i | ||||
\(454\) | −9.90851 | −0.465030 | ||||||||
\(455\) | 0.139768 | − | 0.631251i | 0.00655243 | − | 0.0295935i | ||||
\(456\) | 0.983874 | + | 1.70412i | 0.0460741 | + | 0.0798027i | ||||
\(457\) | 15.4321 | − | 26.7292i | 0.721885 | − | 1.25034i | −0.238359 | − | 0.971177i | \(-0.576610\pi\) |
0.960244 | − | 0.279164i | \(-0.0900572\pi\) | |||||||
\(458\) | −25.6160 | −1.19696 | ||||||||
\(459\) | 0.975664 | − | 0.563300i | 0.0455401 | − | 0.0262926i | ||||
\(460\) | −1.97550 | − | 6.25967i | −0.0921083 | − | 0.291858i | ||||
\(461\) | 19.0806 | − | 11.0162i | 0.888670 | − | 0.513074i | 0.0151628 | − | 0.999885i | \(-0.495173\pi\) |
0.873507 | + | 0.486811i | \(0.161840\pi\) | |||||||
\(462\) | 0.159268 | − | 0.275860i | 0.00740982 | − | 0.0128342i | ||||
\(463\) | −17.1390 | + | 29.6855i | −0.796515 | + | 1.37960i | 0.125358 | + | 0.992112i | \(0.459992\pi\) |
−0.921873 | + | 0.387492i | \(0.873341\pi\) | |||||||
\(464\) | 2.30357 | − | 1.32997i | 0.106941 | − | 0.0617422i | ||||
\(465\) | 4.09186 | + | 12.9656i | 0.189755 | + | 0.601267i | ||||
\(466\) | 2.98587 | − | 1.72390i | 0.138318 | − | 0.0798579i | ||||
\(467\) | 25.6755 | 1.18812 | 0.594060 | − | 0.804421i | \(-0.297524\pi\) | ||||
0.594060 | + | 0.804421i | \(0.297524\pi\) | |||||||
\(468\) | −1.78579 | + | 3.09309i | −0.0825484 | + | 0.142978i | ||||
\(469\) | −0.143110 | − | 0.247874i | −0.00660822 | − | 0.0114458i | ||||
\(470\) | −5.21470 | + | 23.5518i | −0.240536 | + | 1.08636i | ||||
\(471\) | 5.70316 | 0.262788 | ||||||||
\(472\) | −2.46559 | + | 1.42351i | −0.113488 | + | 0.0655223i | ||||
\(473\) | 22.3925 | 1.02961 | ||||||||
\(474\) | 2.28090 | − | 3.95064i | 0.104765 | − | 0.181459i | ||||
\(475\) | −4.15326 | + | 8.91914i | −0.190565 | + | 0.409238i | ||||
\(476\) | −0.0789858 | − | 0.0456025i | −0.00362031 | − | 0.00209019i | ||||
\(477\) | −0.118647 | − | 0.0685008i | −0.00543247 | − | 0.00313644i | ||||
\(478\) | −12.3341 | − | 7.12108i | −0.564147 | − | 0.325710i | ||||
\(479\) | 30.5619 | − | 17.6449i | 1.39641 | − | 0.806217i | 0.402395 | − | 0.915466i | \(-0.368178\pi\) |
0.994014 | + | 0.109249i | \(0.0348446\pi\) | |||||||
\(480\) | 0.483391 | − | 2.18319i | 0.0220637 | − | 0.0996487i | ||||
\(481\) | −15.5564 | − | 15.1651i | −0.709309 | − | 0.691470i | ||||
\(482\) | 20.6720i | 0.941585i | ||||||||
\(483\) | 0.118823 | + | 0.205808i | 0.00540665 | + | 0.00936460i | ||||
\(484\) | −2.24087 | + | 3.88130i | −0.101858 | + | 0.176423i | ||||
\(485\) | 1.33330 | − | 1.45582i | 0.0605420 | − | 0.0661054i | ||||
\(486\) | −0.866025 | − | 0.500000i | −0.0392837 | − | 0.0226805i | ||||
\(487\) | 24.8974 | 1.12821 | 0.564105 | − | 0.825703i | \(-0.309221\pi\) | ||||
0.564105 | + | 0.825703i | \(0.309221\pi\) | |||||||
\(488\) | 8.34607 | + | 4.81861i | 0.377809 | + | 0.218128i | ||||
\(489\) | − | 10.9381i | − | 0.494640i | ||||||
\(490\) | 4.70637 | + | 14.9128i | 0.212612 | + | 0.673692i | ||||
\(491\) | −11.8114 | −0.533040 | −0.266520 | − | 0.963829i | \(-0.585874\pi\) | ||||
−0.266520 | + | 0.963829i | \(0.585874\pi\) | |||||||
\(492\) | 7.44162i | 0.335494i | ||||||||
\(493\) | −2.59520 | + | 1.49834i | −0.116882 | + | 0.0674819i | ||||
\(494\) | 6.08641 | + | 3.51399i | 0.273841 | + | 0.158102i | ||||
\(495\) | −8.59018 | − | 1.90199i | −0.386100 | − | 0.0854881i | ||||
\(496\) | −5.26570 | + | 3.04016i | −0.236437 | + | 0.136507i | ||||
\(497\) | −0.489368 | + | 0.282537i | −0.0219512 | + | 0.0126735i | ||||
\(498\) | −6.14100 | − | 10.6365i | −0.275185 | − | 0.476634i | ||||
\(499\) | 3.41972 | + | 1.97438i | 0.153088 | + | 0.0883852i | 0.574587 | − | 0.818444i | \(-0.305163\pi\) |
−0.421499 | + | 0.906829i | \(0.638496\pi\) | |||||||
\(500\) | 10.3259 | − | 4.28681i | 0.461786 | − | 0.191712i | ||||
\(501\) | −7.96135 | + | 4.59649i | −0.355687 | + | 0.205356i | ||||
\(502\) | 7.14077 | − | 4.12273i | 0.318708 | − | 0.184006i | ||||
\(503\) | 18.5458 | + | 32.1223i | 0.826916 | + | 1.43226i | 0.900446 | + | 0.434968i | \(0.143240\pi\) |
−0.0735293 | + | 0.997293i | \(0.523426\pi\) | |||||||
\(504\) | 0.0809559i | 0.00360606i | ||||||||
\(505\) | −8.60315 | + | 9.39373i | −0.382835 | + | 0.418016i | ||||
\(506\) | −5.77515 | − | 10.0029i | −0.256737 | − | 0.444681i | ||||
\(507\) | − | 0.243751i | − | 0.0108253i | ||||||
\(508\) | 16.4385i | 0.729339i | ||||||||
\(509\) | −0.0856429 | − | 0.148338i | −0.00379605 | − | 0.00657496i | 0.864121 | − | 0.503284i | \(-0.167875\pi\) |
−0.867917 | + | 0.496709i | \(0.834542\pi\) | |||||||
\(510\) | −0.544588 | + | 2.45959i | −0.0241147 | + | 0.108912i | ||||
\(511\) | −0.242286 | + | 0.419652i | −0.0107181 | + | 0.0185643i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.983874 | + | 1.70412i | −0.0434391 | + | 0.0752387i | ||||
\(514\) | 3.41974 | − | 5.92316i | 0.150838 | − | 0.261259i | ||||
\(515\) | −10.1815 | + | 11.1171i | −0.448650 | + | 0.489878i | ||||
\(516\) | −4.92859 | + | 2.84552i | −0.216969 | + | 0.125267i | ||||
\(517\) | 42.4465i | 1.86679i | ||||||||
\(518\) | −0.477241 | − | 0.121384i | −0.0209688 | − | 0.00533332i | ||||
\(519\) | 4.98849 | 0.218971 | ||||||||
\(520\) | −2.40357 | − | 7.61604i | −0.105403 | − | 0.333986i | ||||
\(521\) | −6.76509 | + | 11.7175i | −0.296384 | + | 0.513352i | −0.975306 | − | 0.220859i | \(-0.929114\pi\) |
0.678922 | + | 0.734210i | \(0.262447\pi\) | |||||||
\(522\) | 2.30357 | + | 1.32997i | 0.100825 | + | 0.0582111i | ||||
\(523\) | 16.3542 | − | 28.3263i | 0.715118 | − | 1.23862i | −0.247796 | − | 0.968812i | \(-0.579706\pi\) |
0.962914 | − | 0.269809i | \(-0.0869605\pi\) | |||||||
\(524\) | 1.96051i | 0.0856452i | ||||||||
\(525\) | −0.331452 | + | 0.232349i | −0.0144658 | + | 0.0101405i | ||||
\(526\) | 14.7172i | 0.641699i | ||||||||
\(527\) | 5.93234 | − | 3.42504i | 0.258417 | − | 0.149197i | ||||
\(528\) | − | 3.93468i | − | 0.171235i | ||||||
\(529\) | −14.3828 | −0.625339 | ||||||||
\(530\) | 0.292142 | − | 0.0921977i | 0.0126898 | − | 0.00400481i | ||||
\(531\) | −2.46559 | − | 1.42351i | −0.106997 | − | 0.0617750i | ||||
\(532\) | 0.159301 | 0.00690657 | ||||||||
\(533\) | 13.2892 | + | 23.0176i | 0.575619 | + | 0.997002i | ||||
\(534\) | −6.52551 | − | 11.3025i | −0.282387 | − | 0.489108i | ||||
\(535\) | −0.762985 | + | 0.240792i | −0.0329867 | + | 0.0104104i | ||||
\(536\) | −3.06184 | − | 1.76776i | −0.132251 | − | 0.0763554i | ||||
\(537\) | 4.64879 | − | 8.05194i | 0.200610 | − | 0.347467i | ||||
\(538\) | −13.2635 | − | 22.9731i | −0.571831 | − | 0.990440i | ||||
\(539\) | 13.7585 | + | 23.8304i | 0.592621 | + | 1.02645i | ||||
\(540\) | 2.13240 | − | 0.672968i | 0.0917637 | − | 0.0289599i | ||||
\(541\) | − | 29.1310i | − | 1.25244i | −0.779647 | − | 0.626220i | \(-0.784601\pi\) | ||
0.779647 | − | 0.626220i | \(-0.215399\pi\) | |||||||
\(542\) | 6.61234 | − | 11.4529i | 0.284024 | − | 0.491945i | ||||
\(543\) | −6.56480 | + | 3.79019i | −0.281722 | + | 0.162653i | ||||
\(544\) | −1.12660 | −0.0483026 | ||||||||
\(545\) | −0.613999 | + | 2.77308i | −0.0263008 | + | 0.118786i | ||||
\(546\) | 0.144571 | + | 0.250404i | 0.00618705 | + | 0.0107163i | ||||
\(547\) | −25.3366 | −1.08332 | −0.541658 | − | 0.840599i | \(-0.682203\pi\) | ||||
−0.541658 | + | 0.840599i | \(0.682203\pi\) | |||||||
\(548\) | 17.8036 | + | 10.2789i | 0.760534 | + | 0.439094i | ||||
\(549\) | 9.63722i | 0.411306i | ||||||||
\(550\) | 16.1095 | − | 11.2928i | 0.686911 | − | 0.481527i | ||||
\(551\) | 2.61704 | − | 4.53284i | 0.111490 | − | 0.193106i | ||||
\(552\) | 2.54222 | + | 1.46775i | 0.108204 | + | 0.0624718i | ||||
\(553\) | −0.184652 | − | 0.319827i | −0.00785222 | − | 0.0136004i | ||||
\(554\) | −12.6155 | −0.535982 | ||||||||
\(555\) | 0.769907 | + | 13.5797i | 0.0326807 | + | 0.576425i | ||||
\(556\) | −12.9990 | −0.551281 | ||||||||
\(557\) | 2.18960 | + | 3.79250i | 0.0927765 | + | 0.160694i | 0.908678 | − | 0.417497i | \(-0.137092\pi\) |
−0.815902 | + | 0.578190i | \(0.803759\pi\) | |||||||
\(558\) | −5.26570 | − | 3.04016i | −0.222915 | − | 0.128700i | ||||
\(559\) | −10.1630 | + | 17.6029i | −0.429851 | + | 0.744523i | ||||
\(560\) | −0.133497 | − | 0.122262i | −0.00564127 | − | 0.00516650i | ||||
\(561\) | 4.43281i | 0.187154i | ||||||||
\(562\) | 10.1405 | + | 5.85462i | 0.427751 | + | 0.246962i | ||||
\(563\) | 12.3285 | 0.519586 | 0.259793 | − | 0.965664i | \(-0.416346\pi\) | ||||
0.259793 | + | 0.965664i | \(0.416346\pi\) | |||||||
\(564\) | −5.39388 | − | 9.34248i | −0.227123 | − | 0.393389i | ||||
\(565\) | −34.9005 | − | 7.72747i | −1.46827 | − | 0.325097i | ||||
\(566\) | 16.2667 | 0.683739 | ||||||||
\(567\) | −0.0701099 | + | 0.0404780i | −0.00294434 | + | 0.00169991i | ||||
\(568\) | −3.49001 | + | 6.04487i | −0.146437 | + | 0.253637i | ||||
\(569\) | − | 33.7423i | − | 1.41455i | −0.706939 | − | 0.707274i | \(-0.749925\pi\) | ||
0.706939 | − | 0.707274i | \(-0.250075\pi\) | |||||||
\(570\) | −1.32423 | − | 4.19602i | −0.0554659 | − | 0.175752i | ||||
\(571\) | 1.27841 | + | 2.21428i | 0.0535000 | + | 0.0926647i | 0.891535 | − | 0.452952i | \(-0.149629\pi\) |
−0.838035 | + | 0.545616i | \(0.816296\pi\) | |||||||
\(572\) | −7.02654 | − | 12.1703i | −0.293794 | − | 0.508867i | ||||
\(573\) | 0.0426751 | − | 0.0739155i | 0.00178278 | − | 0.00308786i | ||||
\(574\) | 0.521731 | + | 0.301222i | 0.0217766 | + | 0.0125727i | ||||
\(575\) | 1.28704 | + | 14.6210i | 0.0536734 | + | 0.609738i | ||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 20.7924 | + | 36.0134i | 0.865598 | + | 1.49926i | 0.866453 | + | 0.499259i | \(0.166395\pi\) |
−0.000854926 | 1.00000i | \(0.500272\pi\) | ||||||||
\(578\) | −15.7308 | −0.654314 | ||||||||
\(579\) | −4.47316 | − | 2.58258i | −0.185898 | − | 0.107328i | ||||
\(580\) | −5.67203 | + | 1.79005i | −0.235518 | + | 0.0743278i | ||||
\(581\) | −0.994300 | −0.0412505 | ||||||||
\(582\) | 0.882847i | 0.0365952i | ||||||||
\(583\) | 0.466838 | − | 0.269529i | 0.0193345 | − | 0.0111628i | ||||
\(584\) | 5.98563i | 0.247687i | ||||||||
\(585\) | 5.39390 | − | 5.88957i | 0.223010 | − | 0.243504i | ||||
\(586\) | 5.33950i | 0.220573i | ||||||||
\(587\) | −5.77378 | + | 10.0005i | −0.238310 | + | 0.412764i | −0.960229 | − | 0.279213i | \(-0.909927\pi\) |
0.721920 | + | 0.691977i | \(0.243260\pi\) | |||||||
\(588\) | −6.05650 | − | 3.49672i | −0.249766 | − | 0.144202i | ||||
\(589\) | −5.98226 | + | 10.3616i | −0.246495 | + | 0.426941i | ||||
\(590\) | 6.07097 | − | 1.91595i | 0.249938 | − | 0.0788785i | ||||
\(591\) | −10.7894 | −0.443815 | ||||||||
\(592\) | −5.85497 | + | 1.64903i | −0.240638 | + | 0.0677746i | ||||
\(593\) | − | 2.72675i | − | 0.111974i | −0.998431 | − | 0.0559872i | \(-0.982169\pi\) | ||
0.998431 | − | 0.0559872i | \(-0.0178306\pi\) | |||||||
\(594\) | 3.40754 | − | 1.96734i | 0.139813 | − | 0.0807210i | ||||
\(595\) | 0.150397 | + | 0.137740i | 0.00616569 | + | 0.00564679i | ||||
\(596\) | −11.2914 | + | 19.5574i | −0.462516 | + | 0.801101i | ||||
\(597\) | −3.96681 | + | 6.87071i | −0.162351 | + | 0.281200i | ||||
\(598\) | 10.4844 | 0.428740 | ||||||||
\(599\) | 2.29323 | − | 3.97199i | 0.0936988 | − | 0.162291i | −0.815366 | − | 0.578946i | \(-0.803464\pi\) |
0.909065 | + | 0.416655i | \(0.136798\pi\) | |||||||
\(600\) | −2.11067 | + | 4.53267i | −0.0861677 | + | 0.185045i | ||||
\(601\) | 4.07826 | + | 7.06376i | 0.166356 | + | 0.288137i | 0.937136 | − | 0.348965i | \(-0.113467\pi\) |
−0.770780 | + | 0.637101i | \(0.780133\pi\) | |||||||
\(602\) | 0.460724i | 0.0187777i | ||||||||
\(603\) | − | 3.53551i | − | 0.143977i | ||||||
\(604\) | 3.99191 | + | 6.91418i | 0.162428 | + | 0.281334i | ||||
\(605\) | 6.76844 | − | 7.39042i | 0.275176 | − | 0.300463i | ||||
\(606\) | − | 5.69660i | − | 0.231409i | ||||||
\(607\) | −10.9036 | − | 18.8855i | −0.442562 | − | 0.766540i | 0.555317 | − | 0.831639i | \(-0.312597\pi\) |
−0.997879 | + | 0.0650990i | \(0.979264\pi\) | |||||||
\(608\) | 1.70412 | − | 0.983874i | 0.0691112 | − | 0.0399013i | ||||
\(609\) | 0.186488 | − | 0.107669i | 0.00755686 | − | 0.00436296i | ||||
\(610\) | −15.8918 | − | 14.5544i | −0.643441 | − | 0.589289i | ||||
\(611\) | −33.3675 | − | 19.2647i | −1.34990 | − | 0.779368i | ||||
\(612\) | −0.563300 | − | 0.975664i | −0.0227700 | − | 0.0394389i | ||||
\(613\) | −11.2580 | + | 6.49980i | −0.454706 | + | 0.262525i | −0.709816 | − | 0.704387i | \(-0.751222\pi\) |
0.255110 | + | 0.966912i | \(0.417888\pi\) | |||||||
\(614\) | −20.2859 | + | 11.7121i | −0.818672 | + | 0.472661i | ||||
\(615\) | 3.59721 | − | 16.2465i | 0.145053 | − | 0.655122i | ||||
\(616\) | −0.275860 | − | 0.159268i | −0.0111147 | − | 0.00641709i | ||||
\(617\) | 18.7829 | − | 10.8443i | 0.756170 | − | 0.436575i | −0.0717491 | − | 0.997423i | \(-0.522858\pi\) |
0.827919 | + | 0.560848i | \(0.189525\pi\) | |||||||
\(618\) | − | 6.74171i | − | 0.271191i | ||||||
\(619\) | −16.7055 | −0.671450 | −0.335725 | − | 0.941960i | \(-0.608981\pi\) | ||||
−0.335725 | + | 0.941960i | \(0.608981\pi\) | |||||||
\(620\) | 12.9656 | − | 4.09186i | 0.520712 | − | 0.164333i | ||||
\(621\) | 2.93551i | 0.117798i | ||||||||
\(622\) | −19.5018 | − | 11.2594i | −0.781950 | − | 0.451459i | ||||
\(623\) | −1.05656 | −0.0423301 | ||||||||
\(624\) | 3.09309 | + | 1.78579i | 0.123823 | + | 0.0714890i | ||||
\(625\) | −24.6155 | + | 4.36751i | −0.984622 | + | 0.174700i | ||||
\(626\) | −4.65775 | + | 8.06746i | −0.186161 | + | 0.322441i | ||||
\(627\) | −3.87123 | − | 6.70517i | −0.154602 | − | 0.267779i | ||||
\(628\) | − | 5.70316i | − | 0.227581i | ||||||
\(629\) | 6.59621 | − | 1.85779i | 0.263008 | − | 0.0740751i | ||||
\(630\) | 0.0391333 | − | 0.176742i | 0.00155911 | − | 0.00704159i | ||||
\(631\) | 12.8764 | − | 7.43418i | 0.512600 | − | 0.295950i | −0.221301 | − | 0.975205i | \(-0.571030\pi\) |
0.733902 | + | 0.679255i | \(0.237697\pi\) | |||||||
\(632\) | −3.95064 | − | 2.28090i | −0.157148 | − | 0.0907294i | ||||
\(633\) | −21.0608 | − | 12.1595i | −0.837093 | − | 0.483296i | ||||
\(634\) | −18.6912 | − | 10.7914i | −0.742323 | − | 0.428580i | ||||
\(635\) | 7.94620 | − | 35.8884i | 0.315335 | − | 1.42419i | ||||
\(636\) | −0.0685008 | + | 0.118647i | −0.00271623 | + | 0.00470465i | ||||
\(637\) | −24.9777 | −0.989653 | ||||||||
\(638\) | −9.06382 | + | 5.23300i | −0.358840 | + | 0.207176i | ||||
\(639\) | −6.98002 | −0.276125 | ||||||||
\(640\) | −2.18319 | − | 0.483391i | −0.0862983 | − | 0.0191077i | ||||
\(641\) | −22.7322 | − | 39.3734i | −0.897869 | − | 1.55516i | −0.830213 | − | 0.557447i | \(-0.811781\pi\) |
−0.0676565 | − | 0.997709i | \(-0.521552\pi\) | |||||||
\(642\) | 0.178903 | − | 0.309869i | 0.00706075 | − | 0.0122296i | ||||
\(643\) | −1.49694 | −0.0590335 | −0.0295167 | − | 0.999564i | \(-0.509397\pi\) | ||||
−0.0295167 | + | 0.999564i | \(0.509397\pi\) | |||||||
\(644\) | 0.205808 | − | 0.118823i | 0.00810998 | − | 0.00468230i | ||||
\(645\) | 12.1356 | − | 3.82989i | 0.477837 | − | 0.150802i | ||||
\(646\) | −1.91986 | + | 1.10843i | −0.0755359 | + | 0.0436107i | ||||
\(647\) | −8.29567 | + | 14.3685i | −0.326136 | + | 0.564885i | −0.981742 | − | 0.190219i | \(-0.939080\pi\) |
0.655605 | + | 0.755104i | \(0.272413\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | 9.70131 | − | 5.60106i | 0.380810 | − | 0.219861i | ||||
\(650\) | 1.56593 | + | 17.7892i | 0.0614207 | + | 0.697748i | ||||
\(651\) | −0.426290 | + | 0.246119i | −0.0167076 | + | 0.00964615i | ||||
\(652\) | −10.9381 | −0.428371 | ||||||||
\(653\) | 15.6069 | − | 27.0320i | 0.610747 | − | 1.05784i | −0.380368 | − | 0.924835i | \(-0.624203\pi\) |
0.991115 | − | 0.133009i | \(-0.0424640\pi\) | |||||||
\(654\) | −0.635097 | − | 1.10002i | −0.0248342 | − | 0.0430142i | ||||
\(655\) | 0.947691 | − | 4.28017i | 0.0370294 | − | 0.167240i | ||||
\(656\) | 7.44162 | 0.290546 | ||||||||
\(657\) | −5.18371 | + | 2.99281i | −0.202236 | + | 0.116761i | ||||
\(658\) | −0.873334 | −0.0340461 | ||||||||
\(659\) | −17.9421 | + | 31.0766i | −0.698925 | + | 1.21057i | 0.269914 | + | 0.962884i | \(0.413005\pi\) |
−0.968840 | + | 0.247689i | \(0.920329\pi\) | |||||||
\(660\) | −1.90199 | + | 8.59018i | −0.0740348 | + | 0.334372i | ||||
\(661\) | −10.6343 | − | 6.13969i | −0.413624 | − | 0.238806i | 0.278721 | − | 0.960372i | \(-0.410089\pi\) |
−0.692346 | + | 0.721566i | \(0.743423\pi\) | |||||||
\(662\) | −3.45970 | − | 1.99746i | −0.134465 | − | 0.0776334i | ||||
\(663\) | −3.48467 | − | 2.01188i | −0.135333 | − | 0.0781348i | ||||
\(664\) | −10.6365 | + | 6.14100i | −0.412777 | + | 0.238317i | ||||
\(665\) | −0.347784 | − | 0.0770045i | −0.0134865 | − | 0.00298611i | ||||
\(666\) | −4.35559 | − | 4.24604i | −0.168776 | − | 0.164531i | ||||
\(667\) | − | 7.80826i | − | 0.302337i | ||||||
\(668\) | 4.59649 | + | 7.96135i | 0.177844 | + | 0.308034i | ||||
\(669\) | −9.12368 | + | 15.8027i | −0.352742 | + | 0.610967i | ||||
\(670\) | 5.83008 | + | 5.33942i | 0.225236 | + | 0.206280i | ||||
\(671\) | −32.8392 | − | 18.9597i | −1.26774 | − | 0.731931i | ||||
\(672\) | 0.0809559 | 0.00312294 | ||||||||
\(673\) | 1.05405 | + | 0.608554i | 0.0406305 | + | 0.0234580i | 0.520178 | − | 0.854058i | \(-0.325866\pi\) |
−0.479547 | + | 0.877516i | \(0.659199\pi\) | |||||||
\(674\) | − | 5.55486i | − | 0.213965i | ||||||
\(675\) | −4.98074 | + | 0.438440i | −0.191709 | + | 0.0168756i | ||||
\(676\) | −0.243751 | −0.00937502 | ||||||||
\(677\) | 28.6640i | 1.10165i | 0.834622 | + | 0.550823i | \(0.185686\pi\) | ||||
−0.834622 | + | 0.550823i | \(0.814314\pi\) | |||||||
\(678\) | 13.8443 | − | 7.99299i | 0.531686 | − | 0.306969i | ||||
\(679\) | 0.0618963 | + | 0.0357359i | 0.00237536 | + | 0.00137142i | ||||
\(680\) | 2.45959 | + | 0.544588i | 0.0943208 | + | 0.0208840i | ||||
\(681\) | −8.58102 | + | 4.95426i | −0.328826 | + | 0.189848i | ||||
\(682\) | 20.7189 | − | 11.9621i | 0.793367 | − | 0.458051i | ||||
\(683\) | −18.2271 | − | 31.5702i | −0.697439 | − | 1.20800i | −0.969352 | − | 0.245677i | \(-0.920990\pi\) |
0.271913 | − | 0.962322i | \(-0.412344\pi\) | |||||||
\(684\) | 1.70412 | + | 0.983874i | 0.0651586 | + | 0.0376193i | ||||
\(685\) | −33.9001 | − | 31.0470i | −1.29525 | − | 1.18625i | ||||
\(686\) | −0.981079 | + | 0.566426i | −0.0374578 | + | 0.0216263i | ||||
\(687\) | −22.1841 | + | 12.8080i | −0.846376 | + | 0.488655i | ||||
\(688\) | 2.84552 | + | 4.92859i | 0.108484 | + | 0.187901i | ||||
\(689\) | 0.489313i | 0.0186414i | ||||||||
\(690\) | −4.84067 | − | 4.43328i | −0.184281 | − | 0.168772i | ||||
\(691\) | 4.52772 | + | 7.84224i | 0.172243 | + | 0.298333i | 0.939204 | − | 0.343361i | \(-0.111565\pi\) |
−0.766961 | + | 0.641694i | \(0.778232\pi\) | |||||||
\(692\) | − | 4.98849i | − | 0.189634i | ||||||
\(693\) | − | 0.318536i | − | 0.0121002i | ||||||
\(694\) | 12.6100 | + | 21.8412i | 0.478669 | + | 0.829079i | ||||
\(695\) | 28.3794 | + | 6.28361i | 1.07649 | + | 0.238351i | ||||
\(696\) | 1.32997 | − | 2.30357i | 0.0504123 | − | 0.0873166i | ||||
\(697\) | −8.38373 | −0.317556 | ||||||||
\(698\) | −4.14403 | + | 7.17766i | −0.156854 | + | 0.271679i | ||||
\(699\) | 1.72390 | − | 2.98587i | 0.0652037 | − | 0.112936i | ||||
\(700\) | 0.232349 | + | 0.331452i | 0.00878197 | + | 0.0125277i | ||||
\(701\) | −16.7531 | + | 9.67242i | −0.632757 | + | 0.365322i | −0.781819 | − | 0.623505i | \(-0.785708\pi\) |
0.149062 | + | 0.988828i | \(0.452375\pi\) | |||||||
\(702\) | 3.57159i | 0.134801i | ||||||||
\(703\) | −8.35514 | + | 8.57069i | −0.315120 | + | 0.323250i | ||||
\(704\) | −3.93468 | −0.148294 | ||||||||
\(705\) | 7.25983 | + | 23.0038i | 0.273421 | + | 0.866373i | ||||
\(706\) | 14.1316 | − | 24.4767i | 0.531851 | − | 0.921192i | ||||
\(707\) | −0.399388 | − | 0.230587i | −0.0150205 | − | 0.00867211i | ||||
\(708\) | −1.42351 | + | 2.46559i | −0.0534987 | + | 0.0926625i | ||||
\(709\) | 46.2387i | 1.73653i | 0.496100 | + | 0.868265i | \(0.334765\pi\) | ||||
−0.496100 | + | 0.868265i | \(0.665235\pi\) | |||||||
\(710\) | 10.5414 | − | 11.5101i | 0.395612 | − | 0.431966i | ||||
\(711\) | − | 4.56180i | − | 0.171081i | ||||||
\(712\) | −11.3025 | + | 6.52551i | −0.423580 | + | 0.244554i | ||||
\(713\) | 17.8488i | 0.668443i | ||||||||
\(714\) | −0.0912049 | −0.00341326 | ||||||||
\(715\) | 9.45727 | + | 29.9667i | 0.353682 | + | 1.12069i | ||||
\(716\) | −8.05194 | − | 4.64879i | −0.300915 | − | 0.173734i | ||||
\(717\) | −14.2422 | −0.531883 | ||||||||
\(718\) | −2.25969 | − | 3.91389i | −0.0843307 | − | 0.146065i | ||||
\(719\) | −12.4040 | − | 21.4844i | −0.462592 | − | 0.801233i | 0.536497 | − | 0.843902i | \(-0.319747\pi\) |
−0.999089 | + | 0.0426691i | \(0.986414\pi\) | |||||||
\(720\) | −0.672968 | − | 2.13240i | −0.0250800 | − | 0.0794697i | ||||
\(721\) | −0.472660 | − | 0.272891i | −0.0176028 | − | 0.0101630i | ||||
\(722\) | −7.56399 | + | 13.1012i | −0.281502 | + | 0.487576i | ||||
\(723\) | 10.3360 | + | 17.9025i | 0.384401 | + | 0.665801i | ||||
\(724\) | 3.79019 | + | 6.56480i | 0.140861 | + | 0.243979i | ||||
\(725\) | 13.2484 | − | 1.16622i | 0.492035 | − | 0.0433123i | ||||
\(726\) | 4.48174i | 0.166333i | ||||||||
\(727\) | 3.14633 | − | 5.44961i | 0.116691 | − | 0.202115i | −0.801763 | − | 0.597641i | \(-0.796105\pi\) |
0.918454 | + | 0.395527i | \(0.129438\pi\) | |||||||
\(728\) | 0.250404 | − | 0.144571i | 0.00928058 | − | 0.00535815i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 2.89340 | − | 13.0678i | 0.107089 | − | 0.483661i | ||||
\(731\) | −3.20576 | − | 5.55255i | −0.118569 | − | 0.205368i | ||||
\(732\) | 9.63722 | 0.356202 | ||||||||
\(733\) | −19.0928 | − | 11.0232i | −0.705210 | − | 0.407153i | 0.104075 | − | 0.994569i | \(-0.466812\pi\) |
−0.809285 | + | 0.587416i | \(0.800145\pi\) | |||||||
\(734\) | 15.0663i | 0.556107i | ||||||||
\(735\) | 11.5322 | + | 10.5617i | 0.425373 | + | 0.389573i | ||||
\(736\) | 1.46775 | − | 2.54222i | 0.0541021 | − | 0.0937077i | ||||
\(737\) | 12.0474 | + | 6.95556i | 0.443771 | + | 0.256211i | ||||
\(738\) | 3.72081 | + | 6.44463i | 0.136965 | + | 0.237230i | ||||
\(739\) | 43.2559 | 1.59120 | 0.795598 | − | 0.605825i | \(-0.207157\pi\) | ||||
0.795598 | + | 0.605825i | \(0.207157\pi\) | |||||||
\(740\) | 13.5797 | − | 0.769907i | 0.499198 | − | 0.0283024i | ||||
\(741\) | 7.02798 | 0.258179 | ||||||||
\(742\) | 0.00554555 | + | 0.00960517i | 0.000203583 | + | 0.000352617i | ||||
\(743\) | 0.357720 | + | 0.206529i | 0.0131235 | + | 0.00757683i | 0.506547 | − | 0.862212i | \(-0.330922\pi\) |
−0.493424 | + | 0.869789i | \(0.664255\pi\) | |||||||
\(744\) | −3.04016 | + | 5.26570i | −0.111458 | + | 0.193050i | ||||
\(745\) | 34.1053 | − | 37.2393i | 1.24952 | − | 1.36434i | ||||
\(746\) | − | 28.9739i | − | 1.06081i | ||||||
\(747\) | −10.6365 | − | 6.14100i | −0.389170 | − | 0.224687i | ||||
\(748\) | 4.43281 | 0.162080 | ||||||||
\(749\) | −0.0144833 | − | 0.0250858i | −0.000529207 | − | 0.000916614i | ||||
\(750\) | 6.79905 | − | 8.87541i | 0.248266 | − | 0.324084i | ||||
\(751\) | 43.8781 | 1.60114 | 0.800568 | − | 0.599243i | \(-0.204531\pi\) | ||||
0.800568 | + | 0.599243i | \(0.204531\pi\) | |||||||
\(752\) | −9.34248 | + | 5.39388i | −0.340685 | + | 0.196695i | ||||
\(753\) | 4.12273 | − | 7.14077i | 0.150241 | − | 0.260224i | ||||
\(754\) | − | 9.50019i | − | 0.345977i | ||||||
\(755\) | −5.37285 | − | 17.0247i | −0.195538 | − | 0.619591i | ||||
\(756\) | 0.0404780 | + | 0.0701099i | 0.00147217 | + | 0.00254987i | ||||
\(757\) | −12.6101 | − | 21.8413i | −0.458321 | − | 0.793835i | 0.540551 | − | 0.841311i | \(-0.318216\pi\) |
−0.998872 | + | 0.0474758i | \(0.984882\pi\) | |||||||
\(758\) | 13.4494 | − | 23.2950i | 0.488503 | − | 0.846112i | ||||
\(759\) | −10.0029 | − | 5.77515i | −0.363081 | − | 0.209625i | ||||
\(760\) | −4.19602 | + | 1.32423i | −0.152206 | + | 0.0480349i | ||||
\(761\) | 13.9826 | + | 24.2185i | 0.506868 | + | 0.877921i | 0.999968 | + | 0.00794833i | \(0.00253006\pi\) |
−0.493101 | + | 0.869972i | \(0.664137\pi\) | |||||||
\(762\) | 8.21923 | + | 14.2361i | 0.297751 | + | 0.515721i | ||||
\(763\) | −0.102830 | −0.00372268 | ||||||||
\(764\) | −0.0739155 | − | 0.0426751i | −0.00267417 | − | 0.00154393i | ||||
\(765\) | 0.758166 | + | 2.40236i | 0.0274115 | + | 0.0868574i | ||||
\(766\) | 9.66029 | 0.349041 | ||||||||
\(767\) | 10.1684i | 0.367159i | ||||||||
\(768\) | 0.866025 | − | 0.500000i | 0.0312500 | − | 0.0180422i | ||||
\(769\) | − | 51.0104i | − | 1.83948i | −0.392527 | − | 0.919740i | \(-0.628399\pi\) | ||
0.392527 | − | 0.919740i | \(-0.371601\pi\) | |||||||
\(770\) | 0.525268 | + | 0.481061i | 0.0189293 | + | 0.0173362i | ||||
\(771\) | − | 6.83947i | − | 0.246318i | ||||||
\(772\) | −2.58258 | + | 4.47316i | −0.0929490 | + | 0.160992i | ||||
\(773\) | −31.2064 | − | 18.0170i | −1.12242 | − | 0.648028i | −0.180400 | − | 0.983593i | \(-0.557739\pi\) |
−0.942017 | + | 0.335565i | \(0.891073\pi\) | |||||||
\(774\) | −2.84552 | + | 4.92859i | −0.102280 | + | 0.177154i | ||||
\(775\) | −30.2845 | + | 2.66585i | −1.08785 | + | 0.0957602i | ||||
\(776\) | 0.882847 | 0.0316924 | ||||||||
\(777\) | −0.473995 | + | 0.133499i | −0.0170045 | + | 0.00478923i | ||||
\(778\) | 24.9986i | 0.896242i | ||||||||
\(779\) | 12.6814 | − | 7.32161i | 0.454358 | − | 0.262324i | ||||
\(780\) | −5.88957 | − | 5.39390i | −0.210880 | − | 0.193133i | ||||
\(781\) | 13.7321 | − | 23.7847i | 0.491373 | − | 0.851082i | ||||
\(782\) | −1.65357 | + | 2.86407i | −0.0591316 | + | 0.102419i | ||||
\(783\) | 2.65993 | 0.0950583 | ||||||||
\(784\) | −3.49672 | + | 6.05650i | −0.124883 | + | 0.216304i | ||||
\(785\) | −2.75685 | + | 12.4511i | −0.0983964 | + | 0.444399i | ||||
\(786\) | 0.980254 | + | 1.69785i | 0.0349645 | + | 0.0605603i | ||||
\(787\) | 49.6923i | 1.77134i | 0.464317 | + | 0.885669i | \(0.346300\pi\) | ||||
−0.464317 | + | 0.885669i | \(0.653700\pi\) | |||||||
\(788\) | 10.7894i | 0.384355i | ||||||||
\(789\) | 7.35858 | + | 12.7454i | 0.261972 | + | 0.453750i | ||||
\(790\) | 7.52244 | + | 6.88935i | 0.267636 | + | 0.245112i | ||||
\(791\) | − | 1.29416i | − | 0.0460150i | ||||||
\(792\) | −1.96734 | − | 3.40754i | −0.0699065 | − | 0.121082i | ||||
\(793\) | 29.8087 | − | 17.2101i | 1.05854 | − | 0.611148i | ||||
\(794\) | 7.64197 | − | 4.41209i | 0.271203 | − | 0.156579i | ||||
\(795\) | 0.206903 | − | 0.225916i | 0.00733810 | − | 0.00801243i | ||||
\(796\) | 6.87071 | + | 3.96681i | 0.243526 | + | 0.140600i | ||||
\(797\) | 22.4128 | + | 38.8201i | 0.793902 | + | 1.37508i | 0.923534 | + | 0.383516i | \(0.125287\pi\) |
−0.129632 | + | 0.991562i | \(0.541380\pi\) | |||||||
\(798\) | 0.137959 | − | 0.0796504i | 0.00488368 | − | 0.00281959i | ||||
\(799\) | 10.5252 | − | 6.07675i | 0.372356 | − | 0.214980i | ||||
\(800\) | 4.53267 | + | 2.11067i | 0.160254 | + | 0.0746235i | ||||
\(801\) | −11.3025 | − | 6.52551i | −0.399355 | − | 0.230568i | ||||
\(802\) | 18.3387 | − | 10.5878i | 0.647561 | − | 0.373870i | ||||
\(803\) | − | 23.5516i | − | 0.831117i | ||||||
\(804\) | −3.53551 | −0.124688 | ||||||||
\(805\) | −0.506757 | + | 0.159929i | −0.0178608 | + | 0.00563675i | ||||
\(806\) | 21.7164i | 0.764927i | ||||||||
\(807\) | −22.9731 | − | 13.2635i | −0.808691 | − | 0.466898i | ||||
\(808\) | −5.69660 | −0.200406 | ||||||||
\(809\) | 36.6153 | + | 21.1399i | 1.28733 | + | 0.743238i | 0.978176 | − | 0.207776i | \(-0.0666225\pi\) |
0.309149 | + | 0.951014i | \(0.399956\pi\) | |||||||
\(810\) | 1.51023 | − | 1.64901i | 0.0530639 | − | 0.0579402i | ||||
\(811\) | 20.1394 | − | 34.8824i | 0.707189 | − | 1.22489i | −0.258707 | − | 0.965956i | \(-0.583296\pi\) |
0.965896 | − | 0.258931i | \(-0.0833702\pi\) | |||||||
\(812\) | −0.107669 | − | 0.186488i | −0.00377843 | − | 0.00654443i | ||||
\(813\) | − | 13.2247i | − | 0.463810i | ||||||
\(814\) | 23.0375 | − | 6.48840i | 0.807463 | − | 0.227418i | ||||
\(815\) | 23.8801 | + | 5.28739i | 0.836483 | + | 0.185209i | ||||
\(816\) | −0.975664 | + | 0.563300i | −0.0341551 | + | 0.0197194i | ||||
\(817\) | 9.69821 | + | 5.59927i | 0.339298 | + | 0.195894i | ||||
\(818\) | 19.6743 | + | 11.3590i | 0.687896 | + | 0.397157i | ||||
\(819\) | 0.250404 | + | 0.144571i | 0.00874981 | + | 0.00505171i | ||||
\(820\) | −16.2465 | − | 3.59721i | −0.567352 | − | 0.125620i | ||||
\(821\) | −13.3498 | + | 23.1225i | −0.465910 | + | 0.806980i | −0.999242 | − | 0.0389258i | \(-0.987606\pi\) |
0.533332 | + | 0.845906i | \(0.320940\pi\) | |||||||
\(822\) | 20.5579 | 0.717038 | ||||||||
\(823\) | −29.7911 | + | 17.1999i | −1.03845 | + | 0.599551i | −0.919395 | − | 0.393336i | \(-0.871321\pi\) |
−0.119058 | + | 0.992887i | \(0.537988\pi\) | |||||||
\(824\) | −6.74171 | −0.234858 | ||||||||
\(825\) | 8.30482 | − | 17.8346i | 0.289137 | − | 0.620922i | ||||
\(826\) | 0.115241 | + | 0.199604i | 0.00400976 | + | 0.00694511i | ||||
\(827\) | 20.7432 | − | 35.9282i | 0.721310 | − | 1.24935i | −0.239165 | − | 0.970979i | \(-0.576874\pi\) |
0.960475 | − | 0.278367i | \(-0.0897931\pi\) | |||||||
\(828\) | 2.93551 | 0.102016 | ||||||||
\(829\) | −22.2080 | + | 12.8218i | −0.771316 | + | 0.445319i | −0.833344 | − | 0.552755i | \(-0.813576\pi\) |
0.0620281 | + | 0.998074i | \(0.480243\pi\) | |||||||
\(830\) | 26.1901 | − | 8.26539i | 0.909071 | − | 0.286896i | ||||
\(831\) | −10.9254 | + | 6.30776i | −0.378997 | + | 0.218814i | ||||
\(832\) | 1.78579 | − | 3.09309i | 0.0619113 | − | 0.107233i | ||||
\(833\) | 3.93941 | − | 6.82325i | 0.136492 | − | 0.236412i | ||||
\(834\) | −11.2575 | + | 6.49951i | −0.389815 | + | 0.225060i | ||||
\(835\) | −6.18658 | − | 19.6031i | −0.214096 | − | 0.678392i | ||||
\(836\) | −6.70517 | + | 3.87123i | −0.231903 | + | 0.133889i | ||||
\(837\) | −6.08031 | −0.210166 | ||||||||
\(838\) | −3.92133 | + | 6.79195i | −0.135460 | + | 0.234624i | ||||
\(839\) | −21.5082 | − | 37.2532i | −0.742544 | − | 1.28612i | −0.951333 | − | 0.308163i | \(-0.900286\pi\) |
0.208789 | − | 0.977961i | \(-0.433048\pi\) | |||||||
\(840\) | −0.176742 | − | 0.0391333i | −0.00609819 | − | 0.00135023i | ||||
\(841\) | 21.9248 | 0.756026 | ||||||||
\(842\) | 8.86828 | − | 5.12010i | 0.305621 | − | 0.176450i | ||||
\(843\) | 11.7092 | 0.403287 | ||||||||
\(844\) | −12.1595 | + | 21.0608i | −0.418547 | + | 0.724944i | ||||
\(845\) | 0.532155 | + | 0.117827i | 0.0183067 | + | 0.00405336i | ||||
\(846\) | −9.34248 | − | 5.39388i | −0.321201 | − | 0.185446i | ||||
\(847\) | 0.314214 | + | 0.181412i | 0.0107965 | + | 0.00623338i | ||||
\(848\) | 0.118647 | + | 0.0685008i | 0.00407435 | + | 0.00235233i | ||||
\(849\) | 14.0874 | − | 8.13334i | 0.483477 | − | 0.279135i | ||||
\(850\) | −5.10650 | − | 2.37788i | −0.175152 | − | 0.0815606i | ||||
\(851\) | −4.40146 | + | 17.3050i | −0.150880 | + | 0.593209i | ||||
\(852\) | 6.98002i | 0.239131i | ||||||||
\(853\) | −16.9920 | − | 29.4310i | −0.581794 | − | 1.00770i | −0.995267 | − | 0.0971804i | \(-0.969018\pi\) |
0.413473 | − | 0.910517i | \(-0.364316\pi\) | |||||||
\(854\) | 0.390095 | − | 0.675664i | 0.0133488 | − | 0.0231208i | ||||
\(855\) | −3.24483 | − | 2.97174i | −0.110971 | − | 0.101631i | ||||
\(856\) | −0.309869 | − | 0.178903i | −0.0105911 | − | 0.00611479i | ||||
\(857\) | 21.8401 | 0.746044 | 0.373022 | − | 0.927822i | \(-0.378322\pi\) | ||||
0.373022 | + | 0.927822i | \(0.378322\pi\) | |||||||
\(858\) | −12.1703 | − | 7.02654i | −0.415488 | − | 0.239882i | ||||
\(859\) | 17.1572i | 0.585398i | 0.956205 | + | 0.292699i | \(0.0945534\pi\) | ||||
−0.956205 | + | 0.292699i | \(0.905447\pi\) | |||||||
\(860\) | −3.82989 | − | 12.1356i | −0.130598 | − | 0.413819i | ||||
\(861\) | 0.602443 | 0.0205312 | ||||||||
\(862\) | 29.3699i | 1.00034i | ||||||||
\(863\) | 22.0352 | − | 12.7221i | 0.750089 | − | 0.433064i | −0.0756373 | − | 0.997135i | \(-0.524099\pi\) |
0.825726 | + | 0.564072i | \(0.190766\pi\) | |||||||
\(864\) | 0.866025 | + | 0.500000i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | −2.41139 | + | 10.8908i | −0.0819897 | + | 0.370300i | ||||
\(866\) | −0.246203 | + | 0.142145i | −0.00836632 | + | 0.00483030i | ||||
\(867\) | −13.6232 | + | 7.86539i | −0.462670 | + | 0.267123i | ||||
\(868\) | 0.246119 | + | 0.426290i | 0.00835381 | + | 0.0144692i | ||||
\(869\) | 15.5445 | + | 8.97462i | 0.527311 | + | 0.304443i | ||||
\(870\) | −4.01710 | + | 4.38625i | −0.136192 | + | 0.148708i | ||||
\(871\) | −10.9356 | + | 6.31370i | −0.370540 | + | 0.213931i | ||||
\(872\) | −1.10002 | + | 0.635097i | −0.0372514 | + | 0.0215071i | ||||
\(873\) | 0.441424 | + | 0.764568i | 0.0149399 | + | 0.0258767i | ||||
\(874\) | − | 5.77634i | − | 0.195388i | ||||||
\(875\) | −0.347042 | − | 0.835939i | −0.0117322 | − | 0.0282599i | ||||
\(876\) | 2.99281 | + | 5.18371i | 0.101118 | + | 0.175141i | ||||
\(877\) | 47.4680i | 1.60288i | 0.598074 | + | 0.801441i | \(0.295933\pi\) | ||||
−0.598074 | + | 0.801441i | \(0.704067\pi\) | |||||||
\(878\) | 0.362058i | 0.0122189i | ||||||||
\(879\) | 2.66975 | + | 4.62415i | 0.0900485 | + | 0.155969i | ||||
\(880\) | 8.59018 | + | 1.90199i | 0.289575 | + | 0.0641160i | ||||
\(881\) | −8.58706 | + | 14.8732i | −0.289305 | + | 0.501091i | −0.973644 | − | 0.228073i | \(-0.926758\pi\) |
0.684339 | + | 0.729164i | \(0.260091\pi\) | |||||||
\(882\) | −6.99345 | −0.235482 | ||||||||
\(883\) | 6.83447 | − | 11.8376i | 0.229998 | − | 0.398369i | −0.727809 | − | 0.685780i | \(-0.759461\pi\) |
0.957807 | + | 0.287411i | \(0.0927946\pi\) | |||||||
\(884\) | −2.01188 | + | 3.48467i | −0.0676667 | + | 0.117202i | ||||
\(885\) | 4.29964 | − | 4.69475i | 0.144531 | − | 0.157812i | ||||
\(886\) | 27.4741 | − | 15.8622i | 0.923011 | − | 0.532901i | ||||
\(887\) | 2.71620i | 0.0912011i | 0.998960 | + | 0.0456006i | \(0.0145201\pi\) | ||||
−0.998960 | + | 0.0456006i | \(0.985480\pi\) | |||||||
\(888\) | −4.24604 | + | 4.35559i | −0.142488 | + | 0.146164i | ||||
\(889\) | 1.33079 | 0.0446333 | ||||||||
\(890\) | 27.8300 | − | 8.78292i | 0.932862 | − | 0.294404i | ||||
\(891\) | 1.96734 | − | 3.40754i | 0.0659084 | − | 0.114157i | ||||
\(892\) | 15.8027 | + | 9.12368i | 0.529113 | + | 0.305484i | ||||
\(893\) | −10.6138 | + | 18.3836i | −0.355177 | + | 0.615185i | ||||
\(894\) | 22.5829i | 0.755285i | ||||||||
\(895\) | 15.3318 | + | 14.0414i | 0.512485 | + | 0.469354i | ||||
\(896\) | − | 0.0809559i | − | 0.00270455i | ||||||
\(897\) | 9.07978 | − | 5.24221i | 0.303165 | − | 0.175032i | ||||
\(898\) | 5.09600i | 0.170056i | ||||||||
\(899\) | 16.1732 | 0.539407 | ||||||||
\(900\) | 0.438440 | + | 4.98074i | 0.0146147 | + | 0.166025i | ||||
\(901\) | −0.133668 | − | 0.0771730i | −0.00445311 | − | 0.00257100i | ||||
\(902\) | −29.2804 | −0.974931 | ||||||||
\(903\) | 0.230362 | + | 0.398998i | 0.00766596 | + | 0.0132778i | ||||
\(904\) | −7.99299 | − | 13.8443i | −0.265843 | − | 0.460453i | ||||
\(905\) | −5.10135 | − | 16.1644i | −0.169575 | − | 0.537322i | ||||
\(906\) | 6.91418 | + | 3.99191i | 0.229708 | + | 0.132622i | ||||
\(907\) | 20.3707 | − | 35.2832i | 0.676399 | − | 1.17156i | −0.299658 | − | 0.954047i | \(-0.596873\pi\) |
0.976058 | − | 0.217512i | \(-0.0697940\pi\) | |||||||
\(908\) | 4.95426 | + | 8.58102i | 0.164413 | + | 0.284771i | ||||
\(909\) | −2.84830 | − | 4.93340i | −0.0944722 | − | 0.163631i | ||||
\(910\) | −0.616564 | + | 0.194583i | −0.0204389 | + | 0.00645036i | ||||
\(911\) | − | 8.06856i | − | 0.267323i | −0.991027 | − | 0.133662i | \(-0.957326\pi\) | ||
0.991027 | − | 0.133662i | \(-0.0426736\pi\) | |||||||
\(912\) | 0.983874 | − | 1.70412i | 0.0325793 | − | 0.0564290i | ||||
\(913\) | 41.8514 | − | 24.1629i | 1.38508 | − | 0.799675i | ||||
\(914\) | −30.8643 | −1.02090 | ||||||||
\(915\) | −21.0399 | − | 4.65854i | −0.695558 | − | 0.154007i | ||||
\(916\) | 12.8080 | + | 22.1841i | 0.423188 | + | 0.732983i | ||||
\(917\) | 0.158715 | 0.00524122 | ||||||||
\(918\) | −0.975664 | − | 0.563300i | −0.0322017 | − | 0.0185917i | ||||
\(919\) | 43.7448i | 1.44301i | 0.692411 | + | 0.721504i | \(0.256549\pi\) | ||||
−0.692411 | + | 0.721504i | \(0.743451\pi\) | |||||||
\(920\) | −4.43328 | + | 4.84067i | −0.146161 | + | 0.159592i | ||||
\(921\) | −11.7121 | + | 20.2859i | −0.385926 | + | 0.668443i | ||||
\(922\) | −19.0806 | − | 11.0162i | −0.628385 | − | 0.362798i | ||||
\(923\) | 12.4649 | + | 21.5898i | 0.410286 | + | 0.710637i | ||||
\(924\) | −0.318536 | −0.0104791 | ||||||||
\(925\) | −30.0192 | − | 4.88342i | −0.987025 | − | 0.160566i | ||||
\(926\) | 34.2779 | 1.12644 | ||||||||
\(927\) | −3.37085 | − | 5.83849i | −0.110713 | − | 0.191761i | ||||
\(928\) | −2.30357 | − | 1.32997i | −0.0756184 | − | 0.0436583i | ||||
\(929\) | −12.0745 | + | 20.9137i | −0.396152 | + | 0.686155i | −0.993247 | − | 0.116015i | \(-0.962988\pi\) |
0.597095 | + | 0.802170i | \(0.296321\pi\) | |||||||
\(930\) | 9.18264 | − | 10.0265i | 0.301111 | − | 0.328781i | ||||
\(931\) | 13.7613i | 0.451009i | ||||||||
\(932\) | −2.98587 | − | 1.72390i | −0.0978056 | − | 0.0564681i | ||||
\(933\) | −22.5187 | −0.737230 | ||||||||
\(934\) | −12.8377 | − | 22.2356i | −0.420064 | − | 0.727572i | ||||
\(935\) | −9.67769 | − | 2.14278i | −0.316494 | − | 0.0700764i | ||||
\(936\) | 3.57159 | 0.116741 | ||||||||
\(937\) | −18.5144 | + | 10.6893i | −0.604840 | + | 0.349204i | −0.770943 | − | 0.636904i | \(-0.780215\pi\) |
0.166103 | + | 0.986108i | \(0.446881\pi\) | |||||||
\(938\) | −0.143110 | + | 0.247874i | −0.00467272 | + | 0.00809338i | ||||
\(939\) | 9.31550i | 0.304000i | ||||||||
\(940\) | 23.0038 | − | 7.25983i | 0.750301 | − | 0.236789i | ||||
\(941\) | −10.2496 | − | 17.7528i | −0.334127 | − | 0.578725i | 0.649190 | − | 0.760627i | \(-0.275108\pi\) |
−0.983317 | + | 0.181902i | \(0.941775\pi\) | |||||||
\(942\) | −2.85158 | − | 4.93908i | −0.0929095 | − | 0.160924i | ||||
\(943\) | 10.9225 | − | 18.9183i | 0.355684 | − | 0.616064i | ||||
\(944\) | 2.46559 | + | 1.42351i | 0.0802481 | + | 0.0463312i | ||||
\(945\) | −0.0544808 | − | 0.172630i | −0.00177226 | − | 0.00561566i | ||||
\(946\) | −11.1962 | − | 19.3924i | −0.364021 | − | 0.630503i | ||||
\(947\) | 8.96917 | + | 15.5351i | 0.291459 | + | 0.504822i | 0.974155 | − | 0.225881i | \(-0.0725260\pi\) |
−0.682696 | + | 0.730703i | \(0.739193\pi\) | |||||||
\(948\) | −4.56180 | −0.148160 | ||||||||
\(949\) | 18.5141 | + | 10.6891i | 0.600992 | + | 0.346983i | ||||
\(950\) | 9.80084 | − | 0.862739i | 0.317981 | − | 0.0279909i | ||||
\(951\) | −21.5828 | −0.699869 | ||||||||
\(952\) | 0.0912049i | 0.00295597i | ||||||||
\(953\) | 7.64774 | − | 4.41542i | 0.247734 | − | 0.143030i | −0.370992 | − | 0.928636i | \(-0.620982\pi\) |
0.618726 | + | 0.785607i | \(0.287649\pi\) | |||||||
\(954\) | 0.137002i | 0.00443559i | ||||||||
\(955\) | 0.140743 | + | 0.128898i | 0.00455434 | + | 0.00417104i | ||||
\(956\) | 14.2422i | 0.460624i | ||||||||
\(957\) | −5.23300 | + | 9.06382i | −0.169159 | + | 0.292992i | ||||
\(958\) | −30.5619 | − | 17.6449i | −0.987410 | − | 0.570082i | ||||
\(959\) | 0.832141 | − | 1.44131i | 0.0268712 | − | 0.0465423i | ||||
\(960\) | −2.13240 | + | 0.672968i | −0.0688228 | + | 0.0217200i | ||||
\(961\) | −5.97019 | −0.192587 | ||||||||
\(962\) | −5.35519 | + | 21.0548i | −0.172658 | + | 0.678833i | ||||
\(963\) | − | 0.357806i | − | 0.0115302i | ||||||
\(964\) | 17.9025 | − | 10.3360i | 0.576601 | − | 0.332901i | ||||
\(965\) | 7.80055 | − | 8.51737i | 0.251109 | − | 0.274184i | ||||
\(966\) | 0.118823 | − | 0.205808i | 0.00382308 | − | 0.00662177i | ||||
\(967\) | −2.30225 | + | 3.98762i | −0.0740354 | + | 0.128233i | −0.900666 | − | 0.434511i | \(-0.856921\pi\) |
0.826631 | + | 0.562744i | \(0.190254\pi\) | |||||||
\(968\) | 4.48174 | 0.144049 | ||||||||
\(969\) | −1.10843 | + | 1.91986i | −0.0356080 | + | 0.0616748i | ||||
\(970\) | −1.92743 | − | 0.426760i | −0.0618859 | − | 0.0137024i | ||||
\(971\) | 9.30668 | + | 16.1197i | 0.298666 | + | 0.517304i | 0.975831 | − | 0.218527i | \(-0.0701251\pi\) |
−0.677165 | + | 0.735831i | \(0.736792\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 1.05235i | 0.0337367i | ||||||||
\(974\) | −12.4487 | − | 21.5618i | −0.398882 | − | 0.690884i | ||||
\(975\) | 10.2507 | + | 14.6229i | 0.328285 | + | 0.468308i | ||||
\(976\) | − | 9.63722i | − | 0.308480i | ||||||
\(977\) | −0.151620 | − | 0.262614i | −0.00485076 | − | 0.00840176i | 0.863590 | − | 0.504195i | \(-0.168211\pi\) |
−0.868441 | + | 0.495793i | \(0.834877\pi\) | |||||||
\(978\) | −9.47271 | + | 5.46907i | −0.302904 | + | 0.174882i | ||||
\(979\) | 44.4718 | − | 25.6758i | 1.42133 | − | 0.820603i | ||||
\(980\) | 10.5617 | − | 11.5322i | 0.337380 | − | 0.368384i | ||||
\(981\) | −1.10002 | − | 0.635097i | −0.0351209 | − | 0.0202771i | ||||
\(982\) | 5.90569 | + | 10.2290i | 0.188458 | + | 0.326419i | ||||
\(983\) | 13.3666 | − | 7.71719i | 0.426327 | − | 0.246140i | −0.271454 | − | 0.962452i | \(-0.587504\pi\) |
0.697781 | + | 0.716311i | \(0.254171\pi\) | |||||||
\(984\) | 6.44463 | − | 3.72081i | 0.205447 | − | 0.118615i | ||||
\(985\) | 5.21548 | − | 23.5553i | 0.166179 | − | 0.750534i | ||||
\(986\) | 2.59520 | + | 1.49834i | 0.0826481 | + | 0.0477169i | ||||
\(987\) | −0.756329 | + | 0.436667i | −0.0240742 | + | 0.0138993i | ||||
\(988\) | − | 7.02798i | − | 0.223590i | ||||||
\(989\) | 16.7061 | 0.531223 | ||||||||
\(990\) | 2.64792 | + | 8.39031i | 0.0841563 | + | 0.266661i | ||||
\(991\) | − | 14.1840i | − | 0.450569i | −0.974293 | − | 0.225284i | \(-0.927669\pi\) | ||
0.974293 | − | 0.225284i | \(-0.0723311\pi\) | |||||||
\(992\) | 5.26570 | + | 3.04016i | 0.167186 | + | 0.0965250i | ||||
\(993\) | −3.99492 | −0.126775 | ||||||||
\(994\) | 0.489368 | + | 0.282537i | 0.0155218 | + | 0.00896153i | ||||
\(995\) | −13.0826 | − | 11.9815i | −0.414746 | − | 0.379841i | ||||
\(996\) | −6.14100 | + | 10.6365i | −0.194585 | + | 0.337031i | ||||
\(997\) | −19.4261 | − | 33.6469i | −0.615230 | − | 1.06561i | −0.990344 | − | 0.138631i | \(-0.955730\pi\) |
0.375114 | − | 0.926979i | \(-0.377603\pi\) | |||||||
\(998\) | − | 3.94875i | − | 0.124995i | ||||||
\(999\) | −5.89507 | − | 1.49939i | −0.186512 | − | 0.0474385i |
(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 | 1110.2.ba.a.529.5 | ✓ | 36 | |
5.4 | even | 2 | 1110.2.ba.b.529.14 | yes | 36 | ||
37.27 | even | 6 | 1110.2.ba.b.619.14 | yes | 36 | ||
185.64 | even | 6 | inner | 1110.2.ba.a.619.5 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.ba.a.529.5 | ✓ | 36 | 1.1 | even | 1 | trivial | |
1110.2.ba.a.619.5 | yes | 36 | 185.64 | even | 6 | inner | |
1110.2.ba.b.529.14 | yes | 36 | 5.4 | even | 2 | ||
1110.2.ba.b.619.14 | yes | 36 | 37.27 | even | 6 |