Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(459,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.459");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.k (of order \(6\), degree \(2\), not 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.2346760387617129.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 459.4 | ||
Root | \(-1.18541 + 0.771231i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.459 |
Dual form | 637.2.k.i.569.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.499987i | 0.353544i | 0.984252 | + | 0.176772i | \(0.0565655\pi\) | ||||
−0.984252 | + | 0.176772i | \(0.943434\pi\) | |||||||
\(3\) | 0.424801 | + | 0.735776i | 0.245259 | + | 0.424801i | 0.962204 | − | 0.272328i | \(-0.0877937\pi\) |
−0.716946 | + | 0.697129i | \(0.754460\pi\) | |||||||
\(4\) | 1.75001 | 0.875007 | ||||||||
\(5\) | 0.902810 | − | 0.521238i | 0.403749 | − | 0.233105i | −0.284351 | − | 0.958720i | \(-0.591778\pi\) |
0.688100 | + | 0.725616i | \(0.258445\pi\) | |||||||
\(6\) | −0.367878 | + | 0.212395i | −0.150186 | + | 0.0867098i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.87496i | 0.662897i | ||||||||
\(9\) | 1.13909 | − | 1.97296i | 0.379696 | − | 0.657653i | ||||
\(10\) | 0.260612 | + | 0.451393i | 0.0824127 | + | 0.142743i | ||||
\(11\) | −3.43579 | + | 1.98365i | −1.03593 | + | 0.598094i | −0.918677 | − | 0.395009i | \(-0.870742\pi\) |
−0.117251 | + | 0.993102i | \(0.537408\pi\) | |||||||
\(12\) | 0.743407 | + | 1.28762i | 0.214603 | + | 0.371703i | ||||
\(13\) | 3.57504 | − | 0.468096i | 0.991537 | − | 0.129827i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.767029 | + | 0.442844i | 0.198046 | + | 0.114342i | ||||
\(16\) | 2.56257 | 0.640643 | ||||||||
\(17\) | −0.142035 | −0.0344486 | −0.0172243 | − | 0.999852i | \(-0.505483\pi\) | ||||
−0.0172243 | + | 0.999852i | \(0.505483\pi\) | |||||||
\(18\) | 0.986453 | + | 0.569529i | 0.232509 | + | 0.134239i | ||||
\(19\) | 4.77160 | + | 2.75488i | 1.09468 | + | 0.632014i | 0.934818 | − | 0.355126i | \(-0.115562\pi\) |
0.159861 | + | 0.987140i | \(0.448895\pi\) | |||||||
\(20\) | 1.57993 | − | 0.912173i | 0.353283 | − | 0.203968i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.991800 | − | 1.71785i | −0.211452 | − | 0.366246i | ||||
\(23\) | −4.39098 | −0.915582 | −0.457791 | − | 0.889060i | \(-0.651359\pi\) | ||||
−0.457791 | + | 0.889060i | \(0.651359\pi\) | |||||||
\(24\) | −1.37955 | + | 0.796483i | −0.281599 | + | 0.162581i | ||||
\(25\) | −1.95662 | + | 3.38897i | −0.391325 | + | 0.677794i | ||||
\(26\) | 0.234042 | + | 1.78747i | 0.0458994 | + | 0.350552i | ||||
\(27\) | 4.48435 | 0.863013 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.19880 | − | 7.27253i | 0.779697 | − | 1.35047i | −0.152419 | − | 0.988316i | \(-0.548706\pi\) |
0.932116 | − | 0.362159i | \(-0.117960\pi\) | |||||||
\(30\) | −0.221416 | + | 0.383504i | −0.0404249 | + | 0.0700179i | ||||
\(31\) | −2.46516 | − | 1.42326i | −0.442756 | − | 0.255625i | 0.262010 | − | 0.965065i | \(-0.415615\pi\) |
−0.704766 | + | 0.709440i | \(0.748948\pi\) | |||||||
\(32\) | 5.03117i | 0.889393i | ||||||||
\(33\) | −2.91905 | − | 1.68531i | −0.508141 | − | 0.293376i | ||||
\(34\) | − | 0.0710158i | − | 0.0121791i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.99342 | − | 3.45271i | 0.332237 | − | 0.575451i | ||||
\(37\) | − | 0.843187i | − | 0.138619i | −0.997595 | − | 0.0693095i | \(-0.977920\pi\) | ||
0.997595 | − | 0.0693095i | \(-0.0220796\pi\) | |||||||
\(38\) | −1.37740 | + | 2.38574i | −0.223445 | + | 0.387017i | ||||
\(39\) | 1.86309 | + | 2.43158i | 0.298334 | + | 0.389364i | ||||
\(40\) | 0.977298 | + | 1.69273i | 0.154524 | + | 0.267644i | ||||
\(41\) | −10.4766 | − | 6.04869i | −1.63618 | − | 0.944647i | −0.982133 | − | 0.188190i | \(-0.939738\pi\) |
−0.654044 | − | 0.756457i | \(-0.726929\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.41161 | + | 4.17704i | 0.367768 | + | 0.636993i | 0.989216 | − | 0.146463i | \(-0.0467888\pi\) |
−0.621448 | + | 0.783455i | \(0.713455\pi\) | |||||||
\(44\) | −6.01267 | + | 3.47142i | −0.906444 | + | 0.523336i | ||||
\(45\) | − | 2.37494i | − | 0.354036i | ||||||
\(46\) | − | 2.19543i | − | 0.323699i | ||||||
\(47\) | 3.94602 | − | 2.27824i | 0.575587 | − | 0.332315i | −0.183791 | − | 0.982965i | \(-0.558837\pi\) |
0.759378 | + | 0.650650i | \(0.225504\pi\) | |||||||
\(48\) | 1.08858 | + | 1.88548i | 0.157123 | + | 0.272146i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.69444 | − | 0.978285i | −0.239630 | − | 0.138350i | ||||
\(51\) | −0.0603367 | − | 0.104506i | −0.00844883 | − | 0.0146338i | ||||
\(52\) | 6.25636 | − | 0.819175i | 0.867601 | − | 0.113599i | ||||
\(53\) | 0.139800 | − | 0.242141i | 0.0192030 | − | 0.0332606i | −0.856264 | − | 0.516538i | \(-0.827220\pi\) |
0.875467 | + | 0.483278i | \(0.160554\pi\) | |||||||
\(54\) | 2.24211i | 0.305113i | ||||||||
\(55\) | −2.06791 | + | 3.58172i | −0.278837 | + | 0.482959i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.68111i | 0.620028i | ||||||||
\(58\) | 3.63617 | + | 2.09934i | 0.477452 | + | 0.275657i | ||||
\(59\) | 10.7815i | 1.40363i | 0.712359 | + | 0.701815i | \(0.247627\pi\) | ||||
−0.712359 | + | 0.701815i | \(0.752373\pi\) | |||||||
\(60\) | 1.34231 | + | 0.774983i | 0.173292 | + | 0.100050i | ||||
\(61\) | −2.93177 | + | 5.07797i | −0.375374 | + | 0.650168i | −0.990383 | − | 0.138353i | \(-0.955819\pi\) |
0.615009 | + | 0.788520i | \(0.289153\pi\) | |||||||
\(62\) | 0.711612 | − | 1.23255i | 0.0903748 | − | 0.156534i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.60963 | 0.326204 | ||||||||
\(65\) | 2.98359 | − | 2.28605i | 0.370069 | − | 0.283549i | ||||
\(66\) | 0.842634 | − | 1.45949i | 0.103721 | − | 0.179650i | ||||
\(67\) | −4.45524 | + | 2.57223i | −0.544294 | + | 0.314248i | −0.746818 | − | 0.665029i | \(-0.768419\pi\) |
0.202523 | + | 0.979277i | \(0.435086\pi\) | |||||||
\(68\) | −0.248564 | −0.0301428 | ||||||||
\(69\) | −1.86529 | − | 3.23078i | −0.224555 | − | 0.388940i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.20326 | + | 1.84940i | −0.380157 | + | 0.219484i | −0.677887 | − | 0.735167i | \(-0.737104\pi\) |
0.297730 | + | 0.954650i | \(0.403771\pi\) | |||||||
\(72\) | 3.69921 | + | 2.13574i | 0.435956 | + | 0.251700i | ||||
\(73\) | −5.72686 | − | 3.30640i | −0.670278 | − | 0.386985i | 0.125904 | − | 0.992042i | \(-0.459817\pi\) |
−0.796182 | + | 0.605057i | \(0.793150\pi\) | |||||||
\(74\) | 0.421582 | 0.0490079 | ||||||||
\(75\) | −3.32470 | −0.383903 | ||||||||
\(76\) | 8.35036 | + | 4.82108i | 0.957852 | + | 0.553016i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.21576 | + | 0.931521i | −0.137657 | + | 0.105474i | ||||
\(79\) | −5.96135 | − | 10.3254i | −0.670705 | − | 1.16169i | −0.977705 | − | 0.209985i | \(-0.932658\pi\) |
0.307000 | − | 0.951710i | \(-0.400675\pi\) | |||||||
\(80\) | 2.31352 | − | 1.33571i | 0.258659 | − | 0.149337i | ||||
\(81\) | −1.51231 | − | 2.61940i | −0.168035 | − | 0.291045i | ||||
\(82\) | 3.02426 | − | 5.23818i | 0.333974 | − | 0.578460i | ||||
\(83\) | 2.87321i | 0.315376i | 0.987489 | + | 0.157688i | \(0.0504040\pi\) | ||||
−0.987489 | + | 0.157688i | \(0.949596\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.128231 | + | 0.0740342i | −0.0139086 | + | 0.00803013i | ||||
\(86\) | −2.08846 | + | 1.20578i | −0.225205 | + | 0.130022i | ||||
\(87\) | 7.13461 | 0.764910 | ||||||||
\(88\) | −3.71926 | − | 6.44195i | −0.396475 | − | 0.686714i | ||||
\(89\) | − | 1.74765i | − | 0.185250i | −0.995701 | − | 0.0926252i | \(-0.970474\pi\) | ||
0.995701 | − | 0.0926252i | \(-0.0295258\pi\) | |||||||
\(90\) | 1.18744 | 0.125167 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.68427 | −0.801141 | ||||||||
\(93\) | − | 2.41841i | − | 0.250777i | ||||||
\(94\) | 1.13909 | + | 1.97296i | 0.117488 | + | 0.203495i | ||||
\(95\) | 5.74379 | 0.589301 | ||||||||
\(96\) | −3.70181 | + | 2.13724i | −0.377815 | + | 0.218131i | ||||
\(97\) | −2.34079 | + | 1.35145i | −0.237671 | + | 0.137219i | −0.614106 | − | 0.789224i | \(-0.710483\pi\) |
0.376435 | + | 0.926443i | \(0.377150\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.03822i | 0.908376i | ||||||||
\(100\) | −3.42412 | + | 5.93074i | −0.342412 | + | 0.593074i | ||||
\(101\) | −5.73612 | − | 9.93524i | −0.570765 | − | 0.988594i | −0.996488 | − | 0.0837401i | \(-0.973313\pi\) |
0.425723 | − | 0.904854i | \(-0.360020\pi\) | |||||||
\(102\) | 0.0522517 | − | 0.0301676i | 0.00517369 | − | 0.00298703i | ||||
\(103\) | −2.08475 | − | 3.61090i | −0.205417 | − | 0.355792i | 0.744849 | − | 0.667233i | \(-0.232522\pi\) |
−0.950265 | + | 0.311441i | \(0.899188\pi\) | |||||||
\(104\) | 0.877660 | + | 6.70304i | 0.0860617 | + | 0.657287i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.121067 | + | 0.0698982i | 0.0117591 | + | 0.00678911i | ||||
\(107\) | 8.48742 | 0.820510 | 0.410255 | − | 0.911971i | \(-0.365440\pi\) | ||||
0.410255 | + | 0.911971i | \(0.365440\pi\) | |||||||
\(108\) | 7.84767 | 0.755142 | ||||||||
\(109\) | 5.56886 | + | 3.21518i | 0.533400 | + | 0.307958i | 0.742400 | − | 0.669957i | \(-0.233688\pi\) |
−0.209000 | + | 0.977916i | \(0.567021\pi\) | |||||||
\(110\) | −1.79081 | − | 1.03393i | −0.170747 | − | 0.0985810i | ||||
\(111\) | 0.620397 | − | 0.358186i | 0.0588855 | − | 0.0339975i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.48164 | − | 9.49448i | −0.515670 | − | 0.893166i | −0.999835 | − | 0.0181892i | \(-0.994210\pi\) |
0.484165 | − | 0.874977i | \(-0.339123\pi\) | |||||||
\(114\) | −2.34049 | −0.219207 | ||||||||
\(115\) | −3.96422 | + | 2.28874i | −0.369665 | + | 0.213426i | ||||
\(116\) | 7.34795 | − | 12.7270i | 0.682240 | − | 1.18167i | ||||
\(117\) | 3.14875 | − | 7.58661i | 0.291102 | − | 0.701382i | ||||
\(118\) | −5.39060 | −0.496245 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.830314 | + | 1.43815i | −0.0757969 | + | 0.131284i | ||||
\(121\) | 2.36975 | − | 4.10453i | 0.215432 | − | 0.373139i | ||||
\(122\) | −2.53892 | − | 1.46584i | −0.229863 | − | 0.132711i | ||||
\(123\) | − | 10.2780i | − | 0.926732i | ||||||
\(124\) | −4.31406 | − | 2.49073i | −0.387414 | − | 0.223674i | ||||
\(125\) | 9.29184i | 0.831087i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00394 | + | 1.73887i | −0.0890849 | + | 0.154300i | −0.907125 | − | 0.420862i | \(-0.861728\pi\) |
0.818040 | + | 0.575162i | \(0.195061\pi\) | |||||||
\(128\) | 11.3671i | 1.00472i | ||||||||
\(129\) | −2.04891 | + | 3.54882i | −0.180397 | + | 0.312456i | ||||
\(130\) | 1.14299 | + | 1.49175i | 0.100247 | + | 0.130836i | ||||
\(131\) | −6.22511 | − | 10.7822i | −0.543890 | − | 0.942046i | −0.998676 | − | 0.0514449i | \(-0.983617\pi\) |
0.454785 | − | 0.890601i | \(-0.349716\pi\) | |||||||
\(132\) | −5.10838 | − | 2.94932i | −0.444627 | − | 0.256706i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.28608 | − | 2.22756i | −0.111101 | − | 0.192432i | ||||
\(135\) | 4.04851 | − | 2.33741i | 0.348441 | − | 0.201172i | ||||
\(136\) | − | 0.266310i | − | 0.0228359i | ||||||
\(137\) | − | 5.24518i | − | 0.448126i | −0.974575 | − | 0.224063i | \(-0.928068\pi\) | ||
0.974575 | − | 0.224063i | \(-0.0719321\pi\) | |||||||
\(138\) | 1.61535 | − | 0.932620i | 0.137507 | − | 0.0793899i | ||||
\(139\) | −10.3693 | − | 17.9601i | −0.879510 | − | 1.52336i | −0.851880 | − | 0.523737i | \(-0.824537\pi\) |
−0.0276301 | − | 0.999618i | \(-0.508796\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.35255 | + | 1.93559i | 0.282335 | + | 0.163006i | ||||
\(142\) | −0.924676 | − | 1.60159i | −0.0775971 | − | 0.134402i | ||||
\(143\) | −11.3545 | + | 8.69991i | −0.949513 | + | 0.727523i | ||||
\(144\) | 2.91900 | − | 5.05585i | 0.243250 | − | 0.421321i | ||||
\(145\) | − | 8.75428i | − | 0.727004i | ||||||
\(146\) | 1.65316 | − | 2.86335i | 0.136816 | − | 0.236973i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.47559i | − | 0.121293i | ||||||
\(149\) | 0.00985188 | + | 0.00568799i | 0.000807098 | + | 0.000465978i | 0.500403 | − | 0.865792i | \(-0.333185\pi\) |
−0.499596 | + | 0.866258i | \(0.666518\pi\) | |||||||
\(150\) | − | 1.66231i | − | 0.135727i | ||||||
\(151\) | −16.3726 | − | 9.45271i | −1.33238 | − | 0.769251i | −0.346717 | − | 0.937970i | \(-0.612704\pi\) |
−0.985664 | + | 0.168719i | \(0.946037\pi\) | |||||||
\(152\) | −5.16529 | + | 8.94654i | −0.418960 | + | 0.725660i | ||||
\(153\) | −0.161791 | + | 0.280230i | −0.0130800 | + | 0.0226553i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.96743 | −0.238350 | ||||||||
\(156\) | 3.26044 | + | 4.25530i | 0.261044 | + | 0.340696i | ||||
\(157\) | 9.89687 | − | 17.1419i | 0.789856 | − | 1.36807i | −0.136198 | − | 0.990682i | \(-0.543488\pi\) |
0.926054 | − | 0.377390i | \(-0.123178\pi\) | |||||||
\(158\) | 5.16255 | − | 2.98060i | 0.410710 | − | 0.237124i | ||||
\(159\) | 0.237549 | 0.0188388 | ||||||||
\(160\) | 2.62243 | + | 4.54219i | 0.207321 | + | 0.359091i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.30967 | − | 0.756136i | 0.102897 | − | 0.0594076i | ||||
\(163\) | 7.73581 | + | 4.46627i | 0.605915 | + | 0.349825i | 0.771365 | − | 0.636393i | \(-0.219574\pi\) |
−0.165450 | + | 0.986218i | \(0.552908\pi\) | |||||||
\(164\) | −18.3343 | − | 10.5853i | −1.43167 | − | 0.826572i | ||||
\(165\) | −3.51380 | −0.273549 | ||||||||
\(166\) | −1.43657 | −0.111499 | ||||||||
\(167\) | −5.31279 | − | 3.06734i | −0.411116 | − | 0.237358i | 0.280153 | − | 0.959955i | \(-0.409615\pi\) |
−0.691269 | + | 0.722597i | \(0.742948\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5618 | − | 3.34692i | 0.966290 | − | 0.257456i | ||||
\(170\) | −0.0370161 | − | 0.0641138i | −0.00283900 | − | 0.00491730i | ||||
\(171\) | 10.8705 | − | 6.27611i | 0.831291 | − | 0.479946i | ||||
\(172\) | 4.22036 | + | 7.30987i | 0.321799 | + | 0.557373i | ||||
\(173\) | −12.1314 | + | 21.0122i | −0.922332 | + | 1.59753i | −0.126535 | + | 0.991962i | \(0.540386\pi\) |
−0.795797 | + | 0.605563i | \(0.792948\pi\) | |||||||
\(174\) | 3.56721i | 0.270429i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.80446 | + | 5.08325i | −0.663661 | + | 0.383165i | ||||
\(177\) | −7.93277 | + | 4.57999i | −0.596263 | + | 0.344253i | ||||
\(178\) | 0.873801 | 0.0654942 | ||||||||
\(179\) | −2.06838 | − | 3.58253i | −0.154598 | − | 0.267771i | 0.778315 | − | 0.627874i | \(-0.216075\pi\) |
−0.932912 | + | 0.360103i | \(0.882741\pi\) | |||||||
\(180\) | − | 4.15618i | − | 0.309784i | ||||||
\(181\) | 7.86568 | 0.584651 | 0.292326 | − | 0.956319i | \(-0.405571\pi\) | ||||
0.292326 | + | 0.956319i | \(0.405571\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.98167 | −0.368256 | ||||||||
\(184\) | − | 8.23289i | − | 0.606937i | ||||||
\(185\) | −0.439501 | − | 0.761237i | −0.0323127 | − | 0.0559673i | ||||
\(186\) | 1.20917 | 0.0886608 | ||||||||
\(187\) | 0.488003 | − | 0.281749i | 0.0356863 | − | 0.0206035i | ||||
\(188\) | 6.90560 | − | 3.98695i | 0.503642 | − | 0.290778i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.87182i | 0.208344i | ||||||||
\(191\) | 3.23933 | − | 5.61069i | 0.234390 | − | 0.405975i | −0.724705 | − | 0.689059i | \(-0.758024\pi\) |
0.959095 | + | 0.283084i | \(0.0913574\pi\) | |||||||
\(192\) | 1.10857 | + | 1.92011i | 0.0800044 | + | 0.138572i | ||||
\(193\) | 4.18228 | − | 2.41464i | 0.301047 | − | 0.173810i | −0.341866 | − | 0.939749i | \(-0.611059\pi\) |
0.642913 | + | 0.765939i | \(0.277726\pi\) | |||||||
\(194\) | −0.675708 | − | 1.17036i | −0.0485130 | − | 0.0840270i | ||||
\(195\) | 2.94945 | + | 1.22414i | 0.211214 | + | 0.0876626i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.3748 | − | 12.9181i | −1.59414 | − | 0.920377i | −0.992586 | − | 0.121545i | \(-0.961215\pi\) |
−0.601554 | − | 0.798832i | \(-0.705452\pi\) | |||||||
\(198\) | −4.51899 | −0.321151 | ||||||||
\(199\) | 17.1146 | 1.21322 | 0.606612 | − | 0.794998i | \(-0.292528\pi\) | ||||
0.606612 | + | 0.794998i | \(0.292528\pi\) | |||||||
\(200\) | −6.35417 | − | 3.66858i | −0.449308 | − | 0.259408i | ||||
\(201\) | −3.78518 | − | 2.18537i | −0.266986 | − | 0.154144i | ||||
\(202\) | 4.96749 | − | 2.86798i | 0.349511 | − | 0.201790i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.105590 | − | 0.182887i | −0.00739278 | − | 0.0128047i | ||||
\(205\) | −12.6112 | −0.880806 | ||||||||
\(206\) | 1.80540 | − | 1.04235i | 0.125788 | − | 0.0726238i | ||||
\(207\) | −5.00171 | + | 8.66322i | −0.347643 | + | 0.602136i | ||||
\(208\) | 9.16129 | − | 1.19953i | 0.635221 | − | 0.0831725i | ||||
\(209\) | −21.8589 | −1.51201 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.14557 | + | 15.8406i | −0.629607 | + | 1.09051i | 0.358024 | + | 0.933713i | \(0.383451\pi\) |
−0.987631 | + | 0.156799i | \(0.949883\pi\) | |||||||
\(212\) | 0.244652 | − | 0.423750i | 0.0168028 | − | 0.0291032i | ||||
\(213\) | −2.72149 | − | 1.57125i | −0.186474 | − | 0.107661i | ||||
\(214\) | 4.24360i | 0.290086i | ||||||||
\(215\) | 4.35446 | + | 2.51405i | 0.296972 | + | 0.171457i | ||||
\(216\) | 8.40796i | 0.572089i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.60755 | + | 2.78435i | −0.108877 | + | 0.188580i | ||||
\(219\) | − | 5.61825i | − | 0.379646i | ||||||
\(220\) | −3.61887 | + | 6.26806i | −0.243984 | + | 0.422593i | ||||
\(221\) | −0.507782 | + | 0.0664862i | −0.0341571 | + | 0.00447235i | ||||
\(222\) | 0.179088 | + | 0.310190i | 0.0120196 | + | 0.0208186i | ||||
\(223\) | 9.96682 | + | 5.75435i | 0.667428 | + | 0.385340i | 0.795101 | − | 0.606477i | \(-0.207418\pi\) |
−0.127674 | + | 0.991816i | \(0.540751\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.45753 | + | 7.72067i | 0.297169 | + | 0.514712i | ||||
\(226\) | 4.74711 | − | 2.74075i | 0.315773 | − | 0.182312i | ||||
\(227\) | 17.9045i | 1.18836i | 0.804332 | + | 0.594181i | \(0.202524\pi\) | ||||
−0.804332 | + | 0.594181i | \(0.797476\pi\) | |||||||
\(228\) | 8.19200i | 0.542528i | ||||||||
\(229\) | 3.34589 | − | 1.93175i | 0.221103 | − | 0.127654i | −0.385358 | − | 0.922767i | \(-0.625922\pi\) |
0.606461 | + | 0.795113i | \(0.292589\pi\) | |||||||
\(230\) | −1.14434 | − | 1.98206i | −0.0754556 | − | 0.130693i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13.6357 | + | 7.87256i | 0.895226 | + | 0.516859i | ||||
\(233\) | 12.5321 | + | 21.7062i | 0.821004 | + | 1.42202i | 0.904935 | + | 0.425549i | \(0.139919\pi\) |
−0.0839312 | + | 0.996472i | \(0.526748\pi\) | |||||||
\(234\) | 3.79320 | + | 1.57433i | 0.247969 | + | 0.102917i | ||||
\(235\) | 2.37501 | − | 4.11363i | 0.154928 | − | 0.268344i | ||||
\(236\) | 18.8678i | 1.22819i | ||||||||
\(237\) | 5.06477 | − | 8.77245i | 0.328992 | − | 0.569832i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 7.80462i | − | 0.504839i | −0.967618 | − | 0.252419i | \(-0.918774\pi\) | ||
0.967618 | − | 0.252419i | \(-0.0812263\pi\) | |||||||
\(240\) | 1.96557 | + | 1.13482i | 0.126877 | + | 0.0732524i | ||||
\(241\) | 21.7653i | 1.40202i | 0.713150 | + | 0.701012i | \(0.247268\pi\) | ||||
−0.713150 | + | 0.701012i | \(0.752732\pi\) | |||||||
\(242\) | 2.05221 | + | 1.18484i | 0.131921 | + | 0.0761647i | ||||
\(243\) | 8.01138 | − | 13.8761i | 0.513930 | − | 0.890154i | ||||
\(244\) | −5.13063 | + | 8.88652i | −0.328455 | + | 0.568901i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.13884 | 0.327640 | ||||||||
\(247\) | 18.3482 | + | 7.61524i | 1.16747 | + | 0.484546i | ||||
\(248\) | 2.66855 | − | 4.62207i | 0.169453 | − | 0.293502i | ||||
\(249\) | −2.11404 | + | 1.22054i | −0.133972 | + | 0.0773488i | ||||
\(250\) | −4.64579 | −0.293826 | ||||||||
\(251\) | −3.83990 | − | 6.65090i | −0.242372 | − | 0.419801i | 0.719017 | − | 0.694992i | \(-0.244592\pi\) |
−0.961390 | + | 0.275191i | \(0.911259\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.0865 | − | 8.71017i | 0.948478 | − | 0.547604i | ||||
\(254\) | −0.869411 | − | 0.501955i | −0.0545517 | − | 0.0314954i | ||||
\(255\) | −0.108945 | − | 0.0628995i | −0.00682241 | − | 0.00393892i | ||||
\(256\) | −0.464141 | −0.0290088 | ||||||||
\(257\) | 13.6237 | 0.849826 | 0.424913 | − | 0.905234i | \(-0.360305\pi\) | ||||
0.424913 | + | 0.905234i | \(0.360305\pi\) | |||||||
\(258\) | −1.77436 | − | 1.02443i | −0.110467 | − | 0.0637781i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.22132 | − | 4.00061i | 0.323813 | − | 0.248107i | ||||
\(261\) | −9.56560 | − | 16.5681i | −0.592096 | − | 1.02554i | ||||
\(262\) | 5.39096 | − | 3.11247i | 0.333055 | − | 0.192289i | ||||
\(263\) | 5.86158 | + | 10.1525i | 0.361440 | + | 0.626033i | 0.988198 | − | 0.153181i | \(-0.0489518\pi\) |
−0.626758 | + | 0.779214i | \(0.715618\pi\) | |||||||
\(264\) | 3.15989 | − | 5.47309i | 0.194478 | − | 0.336845i | ||||
\(265\) | − | 0.291476i | − | 0.0179052i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.28588 | − | 0.742403i | 0.0786945 | − | 0.0454343i | ||||
\(268\) | −7.79673 | + | 4.50144i | −0.476261 | + | 0.274970i | ||||
\(269\) | −9.19876 | −0.560858 | −0.280429 | − | 0.959875i | \(-0.590477\pi\) | ||||
−0.280429 | + | 0.959875i | \(0.590477\pi\) | |||||||
\(270\) | 1.16867 | + | 2.02420i | 0.0711232 | + | 0.123189i | ||||
\(271\) | − | 2.56369i | − | 0.155733i | −0.996964 | − | 0.0778665i | \(-0.975189\pi\) | ||
0.996964 | − | 0.0778665i | \(-0.0248108\pi\) | |||||||
\(272\) | −0.363976 | −0.0220693 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.62252 | 0.158432 | ||||||||
\(275\) | − | 15.5250i | − | 0.936195i | ||||||
\(276\) | −3.26428 | − | 5.65391i | −0.196487 | − | 0.340325i | ||||
\(277\) | 0.933882 | 0.0561115 | 0.0280558 | − | 0.999606i | \(-0.491068\pi\) | ||||
0.0280558 | + | 0.999606i | \(0.491068\pi\) | |||||||
\(278\) | 8.97981 | − | 5.18450i | 0.538573 | − | 0.310945i | ||||
\(279\) | −5.61607 | + | 3.24244i | −0.336226 | + | 0.194120i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.45288i | − | 0.384947i | −0.981302 | − | 0.192473i | \(-0.938349\pi\) | ||
0.981302 | − | 0.192473i | \(-0.0616509\pi\) | |||||||
\(282\) | −0.967771 | + | 1.67623i | −0.0576299 | + | 0.0998180i | ||||
\(283\) | −11.0873 | − | 19.2037i | −0.659071 | − | 1.14154i | −0.980857 | − | 0.194731i | \(-0.937616\pi\) |
0.321786 | − | 0.946812i | \(-0.395717\pi\) | |||||||
\(284\) | −5.60575 | + | 3.23648i | −0.332640 | + | 0.192050i | ||||
\(285\) | 2.43997 | + | 4.22615i | 0.144531 | + | 0.250335i | ||||
\(286\) | −4.34984 | − | 5.67711i | −0.257211 | − | 0.335695i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 9.92629 | + | 5.73094i | 0.584912 | + | 0.337699i | ||||
\(289\) | −16.9798 | −0.998813 | ||||||||
\(290\) | 4.37702 | 0.257028 | ||||||||
\(291\) | −1.98873 | − | 1.14820i | −0.116582 | − | 0.0673085i | ||||
\(292\) | −10.0221 | − | 5.78625i | −0.586498 | − | 0.338615i | ||||
\(293\) | 20.9600 | − | 12.1013i | 1.22450 | − | 0.706964i | 0.258624 | − | 0.965978i | \(-0.416731\pi\) |
0.965874 | + | 0.259014i | \(0.0833976\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.61972 | + | 9.73364i | 0.327193 | + | 0.566714i | ||||
\(296\) | 1.58094 | 0.0918902 | ||||||||
\(297\) | −15.4073 | + | 8.89539i | −0.894020 | + | 0.516163i | ||||
\(298\) | −0.00284392 | + | 0.00492581i | −0.000164744 | + | 0.000285345i | ||||
\(299\) | −15.6979 | + | 2.05540i | −0.907833 | + | 0.118867i | ||||
\(300\) | −5.81827 | −0.335918 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.72623 | − | 8.18607i | 0.271964 | − | 0.471055i | ||||
\(303\) | 4.87341 | − | 8.44100i | 0.279970 | − | 0.484923i | ||||
\(304\) | 12.2276 | + | 7.05959i | 0.701299 | + | 0.404895i | ||||
\(305\) | 6.11259i | 0.350006i | ||||||||
\(306\) | −0.140111 | − | 0.0808933i | −0.00800963 | − | 0.00462436i | ||||
\(307\) | 24.2924i | 1.38644i | 0.720726 | + | 0.693220i | \(0.243809\pi\) | ||||
−0.720726 | + | 0.693220i | \(0.756191\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.77121 | − | 3.06782i | 0.100761 | − | 0.174522i | ||||
\(310\) | − | 1.48367i | − | 0.0842671i | ||||||
\(311\) | −1.99355 | + | 3.45294i | −0.113044 | + | 0.195798i | −0.916996 | − | 0.398896i | \(-0.869393\pi\) |
0.803952 | + | 0.594694i | \(0.202727\pi\) | |||||||
\(312\) | −4.55911 | + | 3.49322i | −0.258109 | + | 0.197764i | ||||
\(313\) | 14.2377 | + | 24.6604i | 0.804763 | + | 1.39389i | 0.916451 | + | 0.400147i | \(0.131041\pi\) |
−0.111688 | + | 0.993743i | \(0.535626\pi\) | |||||||
\(314\) | 8.57071 | + | 4.94830i | 0.483673 | + | 0.279249i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.4324 | − | 18.0695i | −0.586871 | − | 1.01649i | ||||
\(317\) | −14.5632 | + | 8.40806i | −0.817950 | + | 0.472244i | −0.849709 | − | 0.527252i | \(-0.823222\pi\) |
0.0317591 | + | 0.999496i | \(0.489889\pi\) | |||||||
\(318\) | 0.118771i | 0.00666036i | ||||||||
\(319\) | 33.3158i | 1.86533i | ||||||||
\(320\) | 2.35600 | − | 1.36024i | 0.131704 | − | 0.0760396i | ||||
\(321\) | 3.60546 | + | 6.24485i | 0.201237 | + | 0.348553i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.677736 | − | 0.391291i | −0.0377102 | − | 0.0217720i | ||||
\(324\) | −2.64657 | − | 4.58399i | −0.147031 | − | 0.254666i | ||||
\(325\) | −5.40863 | + | 13.0316i | −0.300017 | + | 0.722862i | ||||
\(326\) | −2.23308 | + | 3.86780i | −0.123679 | + | 0.214218i | ||||
\(327\) | 5.46324i | 0.302118i | ||||||||
\(328\) | 11.3410 | − | 19.6432i | 0.626204 | − | 1.08462i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 1.75685i | − | 0.0967115i | ||||||
\(331\) | 5.37730 | + | 3.10459i | 0.295563 | + | 0.170644i | 0.640448 | − | 0.768002i | \(-0.278749\pi\) |
−0.344885 | + | 0.938645i | \(0.612082\pi\) | |||||||
\(332\) | 5.02816i | 0.275956i | ||||||||
\(333\) | −1.66357 | − | 0.960464i | −0.0911632 | − | 0.0526331i | ||||
\(334\) | 1.53363 | − | 2.65633i | 0.0839165 | − | 0.145348i | ||||
\(335\) | −2.68149 | + | 4.64448i | −0.146505 | + | 0.253755i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.69650 | 0.419255 | 0.209628 | − | 0.977781i | \(-0.432775\pi\) | ||||
0.209628 | + | 0.977781i | \(0.432775\pi\) | |||||||
\(338\) | 1.67342 | + | 6.28072i | 0.0910219 | + | 0.341626i | ||||
\(339\) | 4.65721 | − | 8.06653i | 0.252945 | − | 0.438114i | ||||
\(340\) | −0.224406 | + | 0.129561i | −0.0121701 | + | 0.00702642i | ||||
\(341\) | 11.2930 | 0.611552 | ||||||||
\(342\) | 3.13797 | + | 5.43513i | 0.169682 | + | 0.293898i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.83177 | + | 4.52167i | −0.422261 | + | 0.243792i | ||||
\(345\) | −3.36801 | − | 1.94452i | −0.181327 | − | 0.104689i | ||||
\(346\) | −10.5058 | − | 6.06553i | −0.564795 | − | 0.326085i | ||||
\(347\) | 30.4094 | 1.63246 | 0.816231 | − | 0.577725i | \(-0.196059\pi\) | ||||
0.816231 | + | 0.577725i | \(0.196059\pi\) | |||||||
\(348\) | 12.4857 | 0.669302 | ||||||||
\(349\) | 13.9933 | + | 8.07906i | 0.749046 | + | 0.432462i | 0.825349 | − | 0.564623i | \(-0.190978\pi\) |
−0.0763028 | + | 0.997085i | \(0.524312\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.0317 | − | 2.09911i | 0.855709 | − | 0.112042i | ||||
\(352\) | −9.98008 | − | 17.2860i | −0.531940 | − | 0.921347i | ||||
\(353\) | 10.2558 | − | 5.92119i | 0.545861 | − | 0.315153i | −0.201590 | − | 0.979470i | \(-0.564611\pi\) |
0.747451 | + | 0.664317i | \(0.231277\pi\) | |||||||
\(354\) | −2.28993 | − | 3.96628i | −0.121709 | − | 0.210805i | ||||
\(355\) | −1.92796 | + | 3.33932i | −0.102325 | + | 0.177233i | ||||
\(356\) | − | 3.05841i | − | 0.162095i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.79122 | − | 1.03416i | 0.0946688 | − | 0.0546571i | ||||
\(359\) | −27.1631 | + | 15.6826i | −1.43362 | + | 0.827698i | −0.997394 | − | 0.0721417i | \(-0.977017\pi\) |
−0.436221 | + | 0.899840i | \(0.643683\pi\) | |||||||
\(360\) | 4.45292 | 0.234689 | ||||||||
\(361\) | 5.67876 | + | 9.83591i | 0.298882 | + | 0.517679i | ||||
\(362\) | 3.93273i | 0.206700i | ||||||||
\(363\) | 4.02669 | 0.211346 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.89369 | −0.360832 | ||||||||
\(366\) | − | 2.49077i | − | 0.130195i | ||||||
\(367\) | 12.0387 | + | 20.8517i | 0.628415 | + | 1.08845i | 0.987870 | + | 0.155285i | \(0.0496295\pi\) |
−0.359454 | + | 0.933163i | \(0.617037\pi\) | |||||||
\(368\) | −11.2522 | −0.586562 | ||||||||
\(369\) | −23.8676 | + | 13.7800i | −1.24250 | + | 0.717358i | ||||
\(370\) | 0.380608 | − | 0.219744i | 0.0197869 | − | 0.0114240i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 4.23225i | − | 0.219432i | ||||||
\(373\) | 9.19612 | − | 15.9281i | 0.476157 | − | 0.824728i | −0.523470 | − | 0.852044i | \(-0.675363\pi\) |
0.999627 | + | 0.0273160i | \(0.00869604\pi\) | |||||||
\(374\) | 0.140871 | + | 0.243995i | 0.00728425 | + | 0.0126167i | ||||
\(375\) | −6.83672 | + | 3.94718i | −0.353046 | + | 0.203831i | ||||
\(376\) | 4.27160 | + | 7.39862i | 0.220291 | + | 0.381555i | ||||
\(377\) | 11.6066 | − | 27.9650i | 0.597771 | − | 1.44027i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.04719 | − | 4.06870i | −0.361990 | − | 0.208995i | 0.307963 | − | 0.951398i | \(-0.400353\pi\) |
−0.669953 | + | 0.742403i | \(0.733686\pi\) | |||||||
\(380\) | 10.0517 | 0.515642 | ||||||||
\(381\) | −1.70589 | −0.0873955 | ||||||||
\(382\) | 2.80527 | + | 1.61962i | 0.143530 | + | 0.0828671i | ||||
\(383\) | 19.3739 | + | 11.1856i | 0.989962 | + | 0.571555i | 0.905263 | − | 0.424852i | \(-0.139674\pi\) |
0.0846992 | + | 0.996407i | \(0.473007\pi\) | |||||||
\(384\) | −8.36365 | + | 4.82876i | −0.426806 | + | 0.246417i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.20729 | + | 2.09108i | 0.0614493 | + | 0.106433i | ||||
\(387\) | 10.9882 | 0.558560 | ||||||||
\(388\) | −4.09641 | + | 2.36506i | −0.207963 | + | 0.120068i | ||||
\(389\) | −10.6973 | + | 18.5283i | −0.542374 | + | 0.939420i | 0.456393 | + | 0.889778i | \(0.349141\pi\) |
−0.998767 | + | 0.0496415i | \(0.984192\pi\) | |||||||
\(390\) | −0.612054 | + | 1.47469i | −0.0309926 | + | 0.0746736i | ||||
\(391\) | 0.623674 | 0.0315406 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.28886 | − | 9.16058i | 0.266788 | − | 0.462090i | ||||
\(394\) | 6.45888 | − | 11.1871i | 0.325394 | − | 0.563599i | ||||
\(395\) | −10.7639 | − | 6.21456i | −0.541592 | − | 0.312689i | ||||
\(396\) | 15.8170i | 0.794835i | ||||||||
\(397\) | −1.03640 | − | 0.598365i | −0.0520154 | − | 0.0300311i | 0.473767 | − | 0.880650i | \(-0.342894\pi\) |
−0.525782 | + | 0.850619i | \(0.676227\pi\) | |||||||
\(398\) | 8.55708i | 0.428928i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.01399 | + | 8.68449i | −0.250699 | + | 0.434224i | ||||
\(401\) | 36.2749i | 1.81148i | 0.423831 | + | 0.905741i | \(0.360685\pi\) | ||||
−0.423831 | + | 0.905741i | \(0.639315\pi\) | |||||||
\(402\) | 1.09266 | − | 1.89254i | 0.0544968 | − | 0.0943913i | ||||
\(403\) | −9.47926 | − | 3.93428i | −0.472196 | − | 0.195980i | ||||
\(404\) | −10.0383 | − | 17.3868i | −0.499423 | − | 0.865026i | ||||
\(405\) | −2.73066 | − | 1.57655i | −0.135688 | − | 0.0783393i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.67259 | + | 2.89701i | 0.0829072 | + | 0.143599i | ||||
\(408\) | 0.195945 | − | 0.113129i | 0.00970071 | − | 0.00560071i | ||||
\(409\) | − | 14.6723i | − | 0.725500i | −0.931887 | − | 0.362750i | \(-0.881838\pi\) | ||
0.931887 | − | 0.362750i | \(-0.118162\pi\) | |||||||
\(410\) | − | 6.30544i | − | 0.311404i | ||||||
\(411\) | 3.85928 | − | 2.22816i | 0.190364 | − | 0.109907i | ||||
\(412\) | −3.64834 | − | 6.31912i | −0.179741 | − | 0.311321i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.33150 | − | 2.50079i | −0.212881 | − | 0.122907i | ||||
\(415\) | 1.49763 | + | 2.59397i | 0.0735156 | + | 0.127333i | ||||
\(416\) | 2.35507 | + | 17.9866i | 0.115467 | + | 0.881866i | ||||
\(417\) | 8.80975 | − | 15.2589i | 0.431415 | − | 0.747233i | ||||
\(418\) | − | 10.9292i | − | 0.534563i | ||||||
\(419\) | −2.96674 | + | 5.13855i | −0.144935 | + | 0.251034i | −0.929349 | − | 0.369203i | \(-0.879631\pi\) |
0.784414 | + | 0.620238i | \(0.212964\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.63174i | 0.128263i | 0.997941 | + | 0.0641317i | \(0.0204278\pi\) | ||||
−0.997941 | + | 0.0641317i | \(0.979572\pi\) | |||||||
\(422\) | −7.92008 | − | 4.57266i | −0.385544 | − | 0.222594i | ||||
\(423\) | − | 10.3805i | − | 0.504715i | ||||||
\(424\) | 0.454004 | + | 0.262119i | 0.0220484 | + | 0.0127296i | ||||
\(425\) | 0.277910 | − | 0.481354i | 0.0134806 | − | 0.0233491i | ||||
\(426\) | 0.785606 | − | 1.36071i | 0.0380628 | − | 0.0659266i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 14.8531 | 0.717952 | ||||||||
\(429\) | −11.2246 | − | 4.65866i | −0.541929 | − | 0.224922i | ||||
\(430\) | −1.25699 | + | 2.17717i | −0.0606175 | + | 0.104993i | ||||
\(431\) | 16.3139 | − | 9.41883i | 0.785812 | − | 0.453689i | −0.0526738 | − | 0.998612i | \(-0.516774\pi\) |
0.838486 | + | 0.544923i | \(0.183441\pi\) | |||||||
\(432\) | 11.4915 | 0.552884 | ||||||||
\(433\) | −9.56773 | − | 16.5718i | −0.459796 | − | 0.796389i | 0.539154 | − | 0.842207i | \(-0.318744\pi\) |
−0.998950 | + | 0.0458176i | \(0.985411\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.44119 | − | 3.71883i | 0.308832 | − | 0.178304i | ||||
\(436\) | 9.74557 | + | 5.62661i | 0.466728 | + | 0.269466i | ||||
\(437\) | −20.9520 | − | 12.0966i | −1.00227 | − | 0.578660i | ||||
\(438\) | 2.80905 | 0.134222 | ||||||||
\(439\) | −1.26511 | −0.0603803 | −0.0301901 | − | 0.999544i | \(-0.509611\pi\) | ||||
−0.0301901 | + | 0.999544i | \(0.509611\pi\) | |||||||
\(440\) | −6.71557 | − | 3.87724i | −0.320152 | − | 0.184840i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.0332422 | − | 0.253884i | −0.00158117 | − | 0.0120760i | ||||
\(443\) | 10.4696 | + | 18.1339i | 0.497426 | + | 0.861568i | 0.999996 | − | 0.00296930i | \(-0.000945159\pi\) |
−0.502569 | + | 0.864537i | \(0.667612\pi\) | |||||||
\(444\) | 1.08570 | − | 0.626831i | 0.0515252 | − | 0.0297481i | ||||
\(445\) | −0.910940 | − | 1.57779i | −0.0431827 | − | 0.0747946i | ||||
\(446\) | −2.87710 | + | 4.98328i | −0.136234 | + | 0.235965i | ||||
\(447\) | 0.00966505i | 0.000457141i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.4700 | − | 8.93162i | 0.730075 | − | 0.421509i | −0.0883746 | − | 0.996087i | \(-0.528167\pi\) |
0.818450 | + | 0.574578i | \(0.194834\pi\) | |||||||
\(450\) | −3.86023 | + | 2.22871i | −0.181973 | + | 0.105062i | ||||
\(451\) | 47.9940 | 2.25995 | ||||||||
\(452\) | −9.59295 | − | 16.6155i | −0.451214 | − | 0.781526i | ||||
\(453\) | − | 16.0621i | − | 0.754662i | ||||||
\(454\) | −8.95199 | −0.420138 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.77687 | −0.411015 | ||||||||
\(457\) | − | 6.56597i | − | 0.307143i | −0.988138 | − | 0.153571i | \(-0.950922\pi\) | ||
0.988138 | − | 0.153571i | \(-0.0490775\pi\) | |||||||
\(458\) | 0.965850 | + | 1.67290i | 0.0451312 | + | 0.0781695i | ||||
\(459\) | −0.636936 | −0.0297296 | ||||||||
\(460\) | −6.93744 | + | 4.00533i | −0.323460 | + | 0.186749i | ||||
\(461\) | 4.42854 | − | 2.55682i | 0.206258 | − | 0.119083i | −0.393313 | − | 0.919404i | \(-0.628671\pi\) |
0.599571 | + | 0.800322i | \(0.295338\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.3239i | 1.54869i | 0.632761 | + | 0.774347i | \(0.281921\pi\) | ||||
−0.632761 | + | 0.774347i | \(0.718079\pi\) | |||||||
\(464\) | 10.7597 | − | 18.6364i | 0.499508 | − | 0.865173i | ||||
\(465\) | −1.26057 | − | 2.18336i | −0.0584574 | − | 0.101251i | ||||
\(466\) | −10.8528 | + | 6.26587i | −0.502747 | + | 0.290261i | ||||
\(467\) | 6.47472 | + | 11.2145i | 0.299614 | + | 0.518947i | 0.976048 | − | 0.217557i | \(-0.0698087\pi\) |
−0.676433 | + | 0.736504i | \(0.736475\pi\) | |||||||
\(468\) | 5.51035 | − | 13.2767i | 0.254716 | − | 0.613714i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.05676 | + | 1.18747i | 0.0948713 | + | 0.0547740i | ||||
\(471\) | 16.8168 | 0.774877 | ||||||||
\(472\) | −20.2148 | −0.930463 | ||||||||
\(473\) | −16.5716 | − | 9.56761i | −0.761962 | − | 0.439919i | ||||
\(474\) | 4.38611 | + | 2.53232i | 0.201461 | + | 0.116313i | ||||
\(475\) | −18.6724 | + | 10.7805i | −0.856750 | + | 0.494645i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.318489 | − | 0.551640i | −0.0145826 | − | 0.0252578i | ||||
\(478\) | 3.90221 | 0.178483 | ||||||||
\(479\) | −23.3930 | + | 13.5060i | −1.06885 | + | 0.617104i | −0.927868 | − | 0.372908i | \(-0.878361\pi\) |
−0.140987 | + | 0.990012i | \(0.545027\pi\) | |||||||
\(480\) | −2.22802 | + | 3.85905i | −0.101695 | + | 0.176141i | ||||
\(481\) | −0.394692 | − | 3.01442i | −0.0179964 | − | 0.137446i | ||||
\(482\) | −10.8823 | −0.495677 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.14710 | − | 7.18299i | 0.188505 | − | 0.326499i | ||||
\(485\) | −1.40886 | + | 2.44021i | −0.0639729 | + | 0.110804i | ||||
\(486\) | 6.93788 | + | 4.00558i | 0.314708 | + | 0.181697i | ||||
\(487\) | − | 32.0838i | − | 1.45386i | −0.686713 | − | 0.726928i | \(-0.740947\pi\) | ||
0.686713 | − | 0.726928i | \(-0.259053\pi\) | |||||||
\(488\) | −9.52097 | − | 5.49694i | −0.430994 | − | 0.248835i | ||||
\(489\) | 7.58910i | 0.343191i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.3020 | + | 24.7718i | −0.645440 | + | 1.11793i | 0.338760 | + | 0.940873i | \(0.389992\pi\) |
−0.984200 | + | 0.177061i | \(0.943341\pi\) | |||||||
\(492\) | − | 17.9866i | − | 0.810897i | ||||||
\(493\) | −0.596378 | + | 1.03296i | −0.0268595 | + | 0.0465220i | ||||
\(494\) | −3.80752 | + | 9.17385i | −0.171308 | + | 0.412751i | ||||
\(495\) | 4.71106 | + | 8.15980i | 0.211746 | + | 0.366756i | ||||
\(496\) | −6.31716 | − | 3.64721i | −0.283649 | − | 0.163765i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.610255 | − | 1.05699i | −0.0273462 | − | 0.0473650i | ||||
\(499\) | 1.55726 | − | 0.899082i | 0.0697123 | − | 0.0402484i | −0.464739 | − | 0.885448i | \(-0.653852\pi\) |
0.534451 | + | 0.845199i | \(0.320518\pi\) | |||||||
\(500\) | 16.2608i | 0.727207i | ||||||||
\(501\) | − | 5.21204i | − | 0.232857i | ||||||
\(502\) | 3.32536 | − | 1.91990i | 0.148418 | − | 0.0856893i | ||||
\(503\) | 14.5386 | + | 25.1816i | 0.648245 | + | 1.12279i | 0.983542 | + | 0.180681i | \(0.0578300\pi\) |
−0.335297 | + | 0.942112i | \(0.608837\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.3572 | − | 5.97976i | −0.460891 | − | 0.266096i | ||||
\(506\) | 4.35497 | + | 7.54303i | 0.193602 | + | 0.335329i | ||||
\(507\) | 7.79884 | + | 7.82088i | 0.346359 | + | 0.347338i | ||||
\(508\) | −1.75690 | + | 3.04304i | −0.0779499 | + | 0.135013i | ||||
\(509\) | − | 23.1913i | − | 1.02794i | −0.857809 | − | 0.513969i | \(-0.828175\pi\) | ||
0.857809 | − | 0.513969i | \(-0.171825\pi\) | |||||||
\(510\) | 0.0314489 | − | 0.0544711i | 0.00139258 | − | 0.00241202i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.5022i | 0.994464i | ||||||||
\(513\) | 21.3975 | + | 12.3539i | 0.944723 | + | 0.545436i | ||||
\(514\) | 6.81169i | 0.300451i | ||||||||
\(515\) | −3.76427 | − | 2.17330i | −0.165874 | − | 0.0957671i | ||||
\(516\) | −3.58562 | + | 6.21048i | −0.157848 | + | 0.273401i | ||||
\(517\) | −9.03847 | + | 15.6551i | −0.397511 | + | 0.688510i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.6137 | −0.904840 | ||||||||
\(520\) | 4.28624 | + | 5.59410i | 0.187964 | + | 0.245318i | ||||
\(521\) | 16.6255 | − | 28.7962i | 0.728376 | − | 1.26158i | −0.229193 | − | 0.973381i | \(-0.573609\pi\) |
0.957569 | − | 0.288203i | \(-0.0930579\pi\) | |||||||
\(522\) | 8.28383 | − | 4.78267i | 0.362574 | − | 0.209332i | ||||
\(523\) | −38.7121 | −1.69276 | −0.846380 | − | 0.532579i | \(-0.821223\pi\) | ||||
−0.846380 | + | 0.532579i | \(0.821223\pi\) | |||||||
\(524\) | −10.8940 | − | 18.8690i | −0.475908 | − | 0.824296i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.07614 | + | 2.93071i | −0.221330 | + | 0.127785i | ||||
\(527\) | 0.350140 | + | 0.202153i | 0.0152523 | + | 0.00880594i | ||||
\(528\) | −7.48028 | − | 4.31874i | −0.325537 | − | 0.187949i | ||||
\(529\) | −3.71931 | −0.161709 | ||||||||
\(530\) | 0.145734 | 0.00633029 | ||||||||
\(531\) | 21.2714 | + | 12.2811i | 0.923102 | + | 0.532953i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −40.2857 | − | 16.7202i | −1.74497 | − | 0.724233i | ||||
\(534\) | 0.371191 | + | 0.642922i | 0.0160630 | + | 0.0278220i | ||||
\(535\) | 7.66253 | − | 4.42396i | 0.331280 | − | 0.191265i | ||||
\(536\) | −4.82283 | − | 8.35338i | −0.208314 | − | 0.360811i | ||||
\(537\) | 1.75730 | − | 3.04372i | 0.0758329 | − | 0.131346i | ||||
\(538\) | − | 4.59926i | − | 0.198288i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.08495 | − | 4.09050i | 0.304888 | − | 0.176027i | ||||
\(541\) | −19.6306 | + | 11.3337i | −0.843986 | + | 0.487275i | −0.858617 | − | 0.512618i | \(-0.828676\pi\) |
0.0146313 | + | 0.999893i | \(0.495343\pi\) | |||||||
\(542\) | 1.28181 | 0.0550585 | ||||||||
\(543\) | 3.34135 | + | 5.78738i | 0.143391 | + | 0.248360i | ||||
\(544\) | − | 0.714603i | − | 0.0306384i | ||||||
\(545\) | 6.70349 | 0.287146 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.21134 | −0.393848 | −0.196924 | − | 0.980419i | \(-0.563095\pi\) | ||||
−0.196924 | + | 0.980419i | \(0.563095\pi\) | |||||||
\(548\) | − | 9.17913i | − | 0.392113i | ||||||
\(549\) | 6.67909 | + | 11.5685i | 0.285056 | + | 0.493732i | ||||
\(550\) | 7.76231 | 0.330986 | ||||||||
\(551\) | 40.0699 | − | 23.1344i | 1.70704 | − | 0.985558i | ||||
\(552\) | 6.05757 | − | 3.49734i | 0.257827 | − | 0.148857i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.466928i | 0.0198379i | ||||||||
\(555\) | 0.373400 | − | 0.646748i | 0.0158500 | − | 0.0274529i | ||||
\(556\) | −18.1464 | − | 31.4304i | −0.769577 | − | 1.33295i | ||||
\(557\) | 9.81039 | − | 5.66403i | 0.415680 | − | 0.239993i | −0.277547 | − | 0.960712i | \(-0.589522\pi\) |
0.693227 | + | 0.720719i | \(0.256188\pi\) | |||||||
\(558\) | −1.62118 | − | 2.80796i | −0.0686299 | − | 0.118871i | ||||
\(559\) | 10.5769 | + | 13.8042i | 0.447354 | + | 0.583855i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.414608 | + | 0.239374i | 0.0175048 | + | 0.0101064i | ||||
\(562\) | 3.22636 | 0.136096 | ||||||||
\(563\) | 32.6386 | 1.37555 | 0.687777 | − | 0.725922i | \(-0.258586\pi\) | ||||
0.687777 | + | 0.725922i | \(0.258586\pi\) | |||||||
\(564\) | 5.86700 | + | 3.38732i | 0.247045 | + | 0.142632i | ||||
\(565\) | −9.89776 | − | 5.71448i | −0.416402 | − | 0.240410i | ||||
\(566\) | 9.60161 | − | 5.54349i | 0.403586 | − | 0.233010i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.46755 | − | 6.00597i | −0.145495 | − | 0.252005i | ||||
\(569\) | −35.0091 | −1.46766 | −0.733829 | − | 0.679335i | \(-0.762269\pi\) | ||||
−0.733829 | + | 0.679335i | \(0.762269\pi\) | |||||||
\(570\) | −2.11302 | + | 1.21995i | −0.0885046 | + | 0.0510981i | ||||
\(571\) | 13.1273 | − | 22.7371i | 0.549360 | − | 0.951519i | −0.448959 | − | 0.893552i | \(-0.648205\pi\) |
0.998319 | − | 0.0579663i | \(-0.0184616\pi\) | |||||||
\(572\) | −19.8706 | + | 15.2250i | −0.830830 | + | 0.636587i | ||||
\(573\) | 5.50428 | 0.229945 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.59149 | − | 14.8809i | 0.358290 | − | 0.620576i | ||||
\(576\) | 2.97260 | − | 5.14870i | 0.123858 | − | 0.214529i | ||||
\(577\) | −21.2806 | − | 12.2863i | −0.885922 | − | 0.511487i | −0.0133154 | − | 0.999911i | \(-0.504239\pi\) |
−0.872606 | + | 0.488424i | \(0.837572\pi\) | |||||||
\(578\) | − | 8.48969i | − | 0.353124i | ||||||
\(579\) | 3.55327 | + | 2.05148i | 0.147669 | + | 0.0852567i | ||||
\(580\) | − | 15.3201i | − | 0.636133i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.574083 | − | 0.994341i | 0.0237965 | − | 0.0412167i | ||||
\(583\) | 1.10926i | 0.0459408i | ||||||||
\(584\) | 6.19936 | − | 10.7376i | 0.256531 | − | 0.444325i | ||||
\(585\) | −1.11170 | − | 8.49051i | −0.0459632 | − | 0.351039i | ||||
\(586\) | 6.05048 | + | 10.4797i | 0.249943 | + | 0.432914i | ||||
\(587\) | −17.7777 | − | 10.2640i | −0.733765 | − | 0.423639i | 0.0860331 | − | 0.996292i | \(-0.472581\pi\) |
−0.819798 | + | 0.572653i | \(0.805914\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.84184 | − | 13.5825i | −0.323117 | − | 0.559656i | ||||
\(590\) | −4.86669 | + | 2.80978i | −0.200358 | + | 0.115677i | ||||
\(591\) | − | 21.9505i | − | 0.902923i | ||||||
\(592\) | − | 2.16073i | − | 0.0888054i | ||||||
\(593\) | −33.1545 | + | 19.1417i | −1.36149 | + | 0.786057i | −0.989822 | − | 0.142308i | \(-0.954548\pi\) |
−0.371669 | + | 0.928365i | \(0.621214\pi\) | |||||||
\(594\) | −4.44757 | − | 7.70342i | −0.182486 | − | 0.316075i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.0172409 | + | 0.00995405i | 0.000706216 | + | 0.000407734i | ||||
\(597\) | 7.27030 | + | 12.5925i | 0.297554 | + | 0.515378i | ||||
\(598\) | −1.02767 | − | 7.84874i | −0.0420247 | − | 0.320959i | ||||
\(599\) | −7.03567 | + | 12.1861i | −0.287470 | + | 0.497912i | −0.973205 | − | 0.229939i | \(-0.926147\pi\) |
0.685735 | + | 0.727851i | \(0.259481\pi\) | |||||||
\(600\) | − | 6.23367i | − | 0.254488i | ||||||
\(601\) | −10.1171 | + | 17.5233i | −0.412685 | + | 0.714791i | −0.995182 | − | 0.0980417i | \(-0.968742\pi\) |
0.582498 | + | 0.812832i | \(0.302075\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.7200i | 0.477276i | ||||||||
\(604\) | −28.6522 | − | 16.5424i | −1.16584 | − | 0.673099i | ||||
\(605\) | − | 4.94082i | − | 0.200873i | ||||||
\(606\) | 4.22039 | + | 2.43664i | 0.171441 | + | 0.0989818i | ||||
\(607\) | 3.27563 | − | 5.67356i | 0.132954 | − | 0.230283i | −0.791860 | − | 0.610703i | \(-0.790887\pi\) |
0.924814 | + | 0.380420i | \(0.124220\pi\) | |||||||
\(608\) | −13.8603 | + | 24.0067i | −0.562108 | + | 0.973600i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.05621 | −0.123742 | ||||||||
\(611\) | 13.0407 | − | 9.99190i | 0.527572 | − | 0.404229i | ||||
\(612\) | −0.283136 | + | 0.490406i | −0.0114451 | + | 0.0198235i | ||||
\(613\) | 28.8598 | − | 16.6622i | 1.16564 | − | 0.672980i | 0.212988 | − | 0.977055i | \(-0.431681\pi\) |
0.952648 | + | 0.304075i | \(0.0983472\pi\) | |||||||
\(614\) | −12.1459 | −0.490168 | ||||||||
\(615\) | −5.35726 | − | 9.27904i | −0.216025 | − | 0.374167i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.85466 | − | 3.38019i | 0.235700 | − | 0.136081i | −0.377499 | − | 0.926010i | \(-0.623216\pi\) |
0.613199 | + | 0.789929i | \(0.289883\pi\) | |||||||
\(618\) | 1.53387 | + | 0.885581i | 0.0617013 | + | 0.0356233i | ||||
\(619\) | −15.2582 | − | 8.80931i | −0.613278 | − | 0.354076i | 0.160970 | − | 0.986959i | \(-0.448538\pi\) |
−0.774247 | + | 0.632883i | \(0.781871\pi\) | |||||||
\(620\) | −5.19304 | −0.208558 | ||||||||
\(621\) | −19.6907 | −0.790159 | ||||||||
\(622\) | −1.72642 | − | 0.996751i | −0.0692233 | − | 0.0399661i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.77431 | + | 6.23110i | 0.191125 | + | 0.249444i | ||||
\(625\) | −4.93986 | − | 8.55609i | −0.197594 | − | 0.342244i | ||||
\(626\) | −12.3299 | + | 7.11866i | −0.492801 | + | 0.284519i | ||||
\(627\) | −9.28569 | − | 16.0833i | −0.370835 | − | 0.642304i | ||||
\(628\) | 17.3197 | − | 29.9985i | 0.691130 | − | 1.19707i | ||||
\(629\) | 0.119762i | 0.00477524i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.6416 | − | 7.87596i | 0.543062 | − | 0.313537i | −0.203257 | − | 0.979125i | \(-0.565153\pi\) |
0.746319 | + | 0.665588i | \(0.231819\pi\) | |||||||
\(632\) | 19.3596 | − | 11.1773i | 0.770084 | − | 0.444608i | ||||
\(633\) | −15.5402 | −0.617667 | ||||||||
\(634\) | −4.20392 | − | 7.28140i | −0.166959 | − | 0.289181i | ||||
\(635\) | 2.09316i | 0.0830644i | ||||||||
\(636\) | 0.415713 | 0.0164841 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −16.6575 | −0.659475 | ||||||||
\(639\) | 8.42653i | 0.333348i | ||||||||
\(640\) | 5.92497 | + | 10.2623i | 0.234205 | + | 0.405655i | ||||
\(641\) | 20.9405 | 0.827099 | 0.413550 | − | 0.910482i | \(-0.364289\pi\) | ||||
0.413550 | + | 0.910482i | \(0.364289\pi\) | |||||||
\(642\) | −3.12234 | + | 1.80268i | −0.123229 | + | 0.0711463i | ||||
\(643\) | 16.3952 | − | 9.46576i | 0.646563 | − | 0.373293i | −0.140575 | − | 0.990070i | \(-0.544895\pi\) |
0.787138 | + | 0.616777i | \(0.211562\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.27188i | 0.168205i | ||||||||
\(646\) | 0.195640 | − | 0.338859i | 0.00769736 | − | 0.0133322i | ||||
\(647\) | 18.8384 | + | 32.6291i | 0.740614 | + | 1.28278i | 0.952216 | + | 0.305426i | \(0.0987988\pi\) |
−0.211601 | + | 0.977356i | \(0.567868\pi\) | |||||||
\(648\) | 4.91126 | − | 2.83552i | 0.192933 | − | 0.111390i | ||||
\(649\) | −21.3867 | − | 37.0429i | −0.839503 | − | 1.45406i | ||||
\(650\) | −6.51562 | − | 2.70424i | −0.255563 | − | 0.106069i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.5378 | + | 7.81604i | 0.530180 | + | 0.306100i | ||||
\(653\) | 29.0326 | 1.13613 | 0.568066 | − | 0.822983i | \(-0.307692\pi\) | ||||
0.568066 | + | 0.822983i | \(0.307692\pi\) | |||||||
\(654\) | −2.73155 | −0.106812 | ||||||||
\(655\) | −11.2402 | − | 6.48952i | −0.439190 | − | 0.253567i | ||||
\(656\) | −26.8472 | − | 15.5002i | −1.04821 | − | 0.605182i | ||||
\(657\) | −13.0468 | + | 7.53257i | −0.509004 | + | 0.293874i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.709152 | + | 1.22829i | 0.0276247 | + | 0.0478473i | 0.879507 | − | 0.475886i | \(-0.157872\pi\) |
−0.851883 | + | 0.523733i | \(0.824539\pi\) | |||||||
\(660\) | −6.14919 | −0.239357 | ||||||||
\(661\) | 3.97764 | − | 2.29649i | 0.154712 | − | 0.0893231i | −0.420645 | − | 0.907225i | \(-0.638196\pi\) |
0.575357 | + | 0.817902i | \(0.304863\pi\) | |||||||
\(662\) | −1.55225 | + | 2.68858i | −0.0603300 | + | 0.104495i | ||||
\(663\) | −0.264625 | − | 0.345370i | −0.0102772 | − | 0.0134131i | ||||
\(664\) | −5.38715 | −0.209062 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.480219 | − | 0.831764i | 0.0186081 | − | 0.0322302i | ||||
\(667\) | −18.4368 | + | 31.9335i | −0.713877 | + | 1.23647i | ||||
\(668\) | −9.29746 | − | 5.36789i | −0.359730 | − | 0.207690i | ||||
\(669\) | 9.77780i | 0.378032i | ||||||||
\(670\) | −2.32218 | − | 1.34071i | −0.0897135 | − | 0.0517961i | ||||
\(671\) | − | 23.2624i | − | 0.898036i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.10111 | + | 3.63924i | −0.0809920 | + | 0.140282i | −0.903676 | − | 0.428216i | \(-0.859142\pi\) |
0.822684 | + | 0.568499i | \(0.192475\pi\) | |||||||
\(674\) | 3.84815i | 0.148225i | ||||||||
\(675\) | −8.77418 | + | 15.1973i | −0.337718 | + | 0.584945i | ||||
\(676\) | 21.9833 | − | 5.85716i | 0.845510 | − | 0.225275i | ||||
\(677\) | 4.04354 | + | 7.00361i | 0.155406 | + | 0.269171i | 0.933207 | − | 0.359340i | \(-0.116998\pi\) |
−0.777801 | + | 0.628511i | \(0.783665\pi\) | |||||||
\(678\) | 4.03316 | + | 2.32854i | 0.154892 | + | 0.0894272i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.138811 | − | 0.240427i | −0.00532315 | − | 0.00921997i | ||||
\(681\) | −13.1737 | + | 7.60583i | −0.504817 | + | 0.291456i | ||||
\(682\) | 5.64636i | 0.216210i | ||||||||
\(683\) | − | 24.6865i | − | 0.944604i | −0.881437 | − | 0.472302i | \(-0.843423\pi\) | ||
0.881437 | − | 0.472302i | \(-0.156577\pi\) | |||||||
\(684\) | 19.0236 | − | 10.9833i | 0.727386 | − | 0.419956i | ||||
\(685\) | −2.73398 | − | 4.73540i | −0.104460 | − | 0.180930i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.84267 | + | 1.64122i | 0.108455 | + | 0.0626164i | ||||
\(688\) | 6.17994 | + | 10.7040i | 0.235608 | + | 0.408085i | ||||
\(689\) | 0.386445 | − | 0.931102i | 0.0147224 | − | 0.0354722i | ||||
\(690\) | 0.972234 | − | 1.68396i | 0.0370123 | − | 0.0641072i | ||||
\(691\) | 11.2567i | 0.428225i | 0.976809 | + | 0.214113i | \(0.0686859\pi\) | ||||
−0.976809 | + | 0.214113i | \(0.931314\pi\) | |||||||
\(692\) | −21.2301 | + | 36.7716i | −0.807047 | + | 1.39785i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.2043i | 0.577147i | ||||||||
\(695\) | −18.7230 | − | 10.8097i | −0.710202 | − | 0.410035i | ||||
\(696\) | 13.3771i | 0.507057i | ||||||||
\(697\) | 1.48805 | + | 0.859128i | 0.0563640 | + | 0.0325418i | ||||
\(698\) | −4.03942 | + | 6.99648i | −0.152894 | + | 0.264821i | ||||
\(699\) | −10.6473 | + | 18.4416i | −0.402717 | + | 0.697526i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.2305 | 0.839635 | 0.419818 | − | 0.907608i | \(-0.362094\pi\) | ||||
0.419818 | + | 0.907608i | \(0.362094\pi\) | |||||||
\(702\) | 1.04953 | + | 8.01564i | 0.0396118 | + | 0.302531i | ||||
\(703\) | 2.32288 | − | 4.02335i | 0.0876091 | − | 0.151743i | ||||
\(704\) | −8.96614 | + | 5.17660i | −0.337924 | + | 0.195101i | ||||
\(705\) | 4.03562 | 0.151990 | ||||||||
\(706\) | 2.96052 | + | 5.12776i | 0.111420 | + | 0.192986i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −13.8825 | + | 8.01504i | −0.521734 | + | 0.301224i | ||||
\(709\) | 20.5889 | + | 11.8870i | 0.773234 | + | 0.446427i | 0.834027 | − | 0.551723i | \(-0.186030\pi\) |
−0.0607929 | + | 0.998150i | \(0.519363\pi\) | |||||||
\(710\) | −1.66961 | − | 0.963952i | −0.0626595 | − | 0.0361765i | ||||
\(711\) | −27.1620 | −1.01866 | ||||||||
\(712\) | 3.27677 | 0.122802 | ||||||||
\(713\) | 10.8245 | + | 6.24951i | 0.405380 | + | 0.234046i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.71626 | + | 13.7728i | −0.213776 | + | 0.515072i | ||||
\(716\) | −3.61969 | − | 6.26948i | −0.135274 | − | 0.234301i | ||||
\(717\) | 5.74246 | − | 3.31541i | 0.214456 | − | 0.123816i | ||||
\(718\) | −7.84111 | − | 13.5812i | −0.292628 | − | 0.506846i | ||||
\(719\) | −10.3904 | + | 17.9967i | −0.387496 | + | 0.671163i | −0.992112 | − | 0.125354i | \(-0.959993\pi\) |
0.604616 | + | 0.796517i | \(0.293327\pi\) | |||||||
\(720\) | − | 6.08597i | − | 0.226811i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −4.91782 | + | 2.83931i | −0.183022 | + | 0.105668i | ||||
\(723\) | −16.0144 | + | 9.24589i | −0.595580 | + | 0.343859i | ||||
\(724\) | 13.7650 | 0.511574 | ||||||||
\(725\) | 16.4309 | + | 28.4592i | 0.610229 | + | 1.05695i | ||||
\(726\) | 2.01329i | 0.0747203i | ||||||||
\(727\) | 26.7719 | 0.992915 | 0.496457 | − | 0.868061i | \(-0.334634\pi\) | ||||
0.496457 | + | 0.868061i | \(0.334634\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.53910 | 0.168115 | ||||||||
\(730\) | − | 3.44675i | − | 0.127570i | ||||||
\(731\) | −0.342535 | − | 0.593287i | −0.0126691 | − | 0.0219435i | ||||
\(732\) | −8.71799 | −0.322226 | ||||||||
\(733\) | −4.55224 | + | 2.62824i | −0.168141 | + | 0.0970761i | −0.581709 | − | 0.813397i | \(-0.697616\pi\) |
0.413568 | + | 0.910473i | \(0.364282\pi\) | |||||||
\(734\) | −10.4255 | + | 6.01919i | −0.384814 | + | 0.222172i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 22.0917i | − | 0.814312i | ||||||
\(737\) | 10.2048 | − | 17.6753i | 0.375900 | − | 0.651078i | ||||
\(738\) | −6.88981 | − | 11.9335i | −0.253617 | − | 0.439278i | ||||
\(739\) | 6.19209 | − | 3.57501i | 0.227780 | − | 0.131509i | −0.381768 | − | 0.924258i | \(-0.624685\pi\) |
0.609547 | + | 0.792750i | \(0.291351\pi\) | |||||||
\(740\) | −0.769132 | − | 1.33218i | −0.0282738 | − | 0.0489717i | ||||
\(741\) | 2.19121 | + | 16.7351i | 0.0804960 | + | 0.614780i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.618032 | − | 0.356821i | −0.0226734 | − | 0.0130905i | 0.488620 | − | 0.872496i | \(-0.337500\pi\) |
−0.511294 | + | 0.859406i | \(0.670834\pi\) | |||||||
\(744\) | 4.53441 | 0.166240 | ||||||||
\(745\) | 0.0118592 | 0.000434486 | ||||||||
\(746\) | 7.96386 | + | 4.59794i | 0.291578 | + | 0.168342i | ||||
\(747\) | 5.66873 | + | 3.27284i | 0.207408 | + | 0.119747i | ||||
\(748\) | 0.854012 | − | 0.493064i | 0.0312258 | − | 0.0180282i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.97354 | − | 3.41827i | −0.0720634 | − | 0.124817i | ||||
\(751\) | 25.7013 | 0.937854 | 0.468927 | − | 0.883237i | \(-0.344641\pi\) | ||||
0.468927 | + | 0.883237i | \(0.344641\pi\) | |||||||
\(752\) | 10.1120 | − | 5.83815i | 0.368746 | − | 0.212896i | ||||
\(753\) | 3.26238 | − | 5.65062i | 0.118888 | − | 0.205920i | ||||
\(754\) | 13.9821 | + | 5.80315i | 0.509199 | + | 0.211338i | ||||
\(755\) | −19.7084 | −0.717263 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.19425 | + | 14.1928i | −0.297825 | + | 0.515848i | −0.975638 | − | 0.219386i | \(-0.929594\pi\) |
0.677813 | + | 0.735234i | \(0.262928\pi\) | |||||||
\(758\) | 2.03430 | − | 3.52350i | 0.0738889 | − | 0.127979i | ||||
\(759\) | 12.8175 | + | 7.40018i | 0.465245 | + | 0.268609i | ||||
\(760\) | 10.7694i | 0.390646i | ||||||||
\(761\) | −7.20531 | − | 4.15999i | −0.261192 | − | 0.150800i | 0.363686 | − | 0.931522i | \(-0.381518\pi\) |
−0.624878 | + | 0.780722i | \(0.714851\pi\) | |||||||
\(762\) | − | 0.852923i | − | 0.0308981i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5.66888 | − | 9.81878i | 0.205093 | − | 0.355231i | ||||
\(765\) | 0.337326i | 0.0121960i | ||||||||
\(766\) | −5.59263 | + | 9.68671i | −0.202070 | + | 0.349995i | ||||
\(767\) | 5.04678 | + | 38.5442i | 0.182229 | + | 1.39175i | ||||
\(768\) | −0.197167 | − | 0.341504i | −0.00711466 | − | 0.0123230i | ||||
\(769\) | −22.1346 | − | 12.7794i | −0.798194 | − | 0.460838i | 0.0446452 | − | 0.999003i | \(-0.485784\pi\) |
−0.842839 | + | 0.538165i | \(0.819118\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.78738 | + | 10.0240i | 0.208427 | + | 0.361007i | ||||
\(772\) | 7.31905 | − | 4.22565i | 0.263418 | − | 0.152085i | ||||
\(773\) | 8.40077i | 0.302155i | 0.988522 | + | 0.151077i | \(0.0482742\pi\) | ||||
−0.988522 | + | 0.151077i | \(0.951726\pi\) | |||||||
\(774\) | 5.49394i | 0.197476i | ||||||||
\(775\) | 9.64678 | − | 5.56957i | 0.346523 | − | 0.200065i | ||||
\(776\) | −2.53392 | − | 4.38887i | −0.0909623 | − | 0.157551i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.26388 | − | 5.34850i | −0.332126 | − | 0.191753i | ||||
\(779\) | −33.3269 | − | 57.7238i | −1.19406 | − | 2.06817i | ||||
\(780\) | 5.16158 | + | 2.14226i | 0.184814 | + | 0.0767053i | ||||
\(781\) | 7.33714 | − | 12.7083i | 0.262544 | − | 0.454739i | ||||
\(782\) | 0.311829i | 0.0111510i | ||||||||
\(783\) | 18.8289 | − | 32.6125i | 0.672889 | − | 1.16548i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 20.6345i | − | 0.736476i | ||||||
\(786\) | 4.58017 | + | 2.64436i | 0.163369 | + | 0.0943212i | ||||
\(787\) | − | 35.0644i | − | 1.24991i | −0.780660 | − | 0.624956i | \(-0.785117\pi\) | ||
0.780660 | − | 0.624956i | \(-0.214883\pi\) | |||||||
\(788\) | −39.1562 | − | 22.6069i | −1.39488 | − | 0.805336i | ||||
\(789\) | −4.98000 | + | 8.62562i | −0.177293 | + | 0.307080i | ||||
\(790\) | 3.10720 | − | 5.38182i | 0.110549 | − | 0.191477i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −16.9463 | −0.602160 | ||||||||
\(793\) | −8.10420 | + | 19.5263i | −0.287788 | + | 0.693399i | ||||
\(794\) | 0.299175 | − | 0.518186i | 0.0106173 | − | 0.0183897i | ||||
\(795\) | 0.214461 | − | 0.123819i | 0.00760616 | − | 0.00439142i | ||||
\(796\) | 29.9508 | 1.06158 | ||||||||
\(797\) | 12.2876 | + | 21.2828i | 0.435250 | + | 0.753875i | 0.997316 | − | 0.0732173i | \(-0.0233267\pi\) |
−0.562066 | + | 0.827092i | \(0.689993\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.560475 | + | 0.323590i | −0.0198282 | + | 0.0114478i | ||||
\(800\) | −17.0505 | − | 9.84409i | −0.602825 | − | 0.348041i | ||||
\(801\) | −3.44804 | − | 1.99073i | −0.121831 | − | 0.0703389i | ||||
\(802\) | −18.1370 | −0.640439 | ||||||||
\(803\) | 26.2350 | 0.925814 | ||||||||
\(804\) | −6.62411 | − | 3.82443i | −0.233615 | − | 0.134877i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.96709 | − | 4.73951i | 0.0692877 | − | 0.166942i | ||||
\(807\) | −3.90764 | − | 6.76823i | −0.137555 | − | 0.238253i | ||||
\(808\) | 18.6282 | − | 10.7550i | 0.655336 | − | 0.378358i | ||||
\(809\) | 15.9006 | + | 27.5406i | 0.559035 | + | 0.968277i | 0.997577 | + | 0.0695667i | \(0.0221617\pi\) |
−0.438542 | + | 0.898711i | \(0.644505\pi\) | |||||||
\(810\) | 0.788253 | − | 1.36529i | 0.0276964 | − | 0.0479715i | ||||
\(811\) | 10.3633i | 0.363905i | 0.983307 | + | 0.181953i | \(0.0582418\pi\) | ||||
−0.983307 | + | 0.181953i | \(0.941758\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.88630 | − | 1.08906i | 0.0661555 | − | 0.0381949i | ||||
\(814\) | −1.44847 | + | 0.836272i | −0.0507687 | + | 0.0293113i | ||||
\(815\) | 9.31196 | 0.326184 | ||||||||
\(816\) | −0.154617 | − | 0.267805i | −0.00541269 | − | 0.00937505i | ||||
\(817\) | 26.5749i | 0.929737i | ||||||||
\(818\) | 7.33597 | 0.256496 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22.0698 | −0.770711 | ||||||||
\(821\) | 4.05592i | 0.141552i | 0.997492 | + | 0.0707762i | \(0.0225476\pi\) | ||||
−0.997492 | + | 0.0707762i | \(0.977452\pi\) | |||||||
\(822\) | 1.11405 | + | 1.92959i | 0.0388569 | + | 0.0673021i | ||||
\(823\) | −8.71697 | −0.303854 | −0.151927 | − | 0.988392i | \(-0.548548\pi\) | ||||
−0.151927 | + | 0.988392i | \(0.548548\pi\) | |||||||
\(824\) | 6.77027 | − | 3.90882i | 0.235854 | − | 0.136170i | ||||
\(825\) | 11.4230 | − | 6.59505i | 0.397696 | − | 0.229610i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.5788i | 0.819915i | 0.912105 | + | 0.409957i | \(0.134456\pi\) | ||||
−0.912105 | + | 0.409957i | \(0.865544\pi\) | |||||||
\(828\) | −8.75307 | + | 15.1608i | −0.304190 | + | 0.526873i | ||||
\(829\) | 14.5203 | + | 25.1499i | 0.504311 | + | 0.873492i | 0.999988 | + | 0.00498467i | \(0.00158668\pi\) |
−0.495677 | + | 0.868507i | \(0.665080\pi\) | |||||||
\(830\) | −1.29695 | + | 0.748793i | −0.0450177 | + | 0.0259910i | ||||
\(831\) | 0.396714 | + | 0.687128i | 0.0137618 | + | 0.0238362i | ||||
\(832\) | 9.32953 | − | 1.22156i | 0.323443 | − | 0.0423499i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 7.62926 | + | 4.40475i | 0.264180 | + | 0.152524i | ||||
\(835\) | −6.39526 | −0.221317 | ||||||||
\(836\) | −38.2534 | −1.32302 | ||||||||
\(837\) | −11.0546 | − | 6.38240i | −0.382104 | − | 0.220608i | ||||
\(838\) | −2.56921 | − | 1.48333i | −0.0887517 | − | 0.0512408i | ||||
\(839\) | 10.0090 | − | 5.77871i | 0.345550 | − | 0.199503i | −0.317174 | − | 0.948367i | \(-0.602734\pi\) |
0.662723 | + | 0.748864i | \(0.269400\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.7598 | − | 35.9570i | −0.715855 | − | 1.23990i | ||||
\(842\) | −1.31584 | −0.0453467 | ||||||||
\(843\) | 4.74788 | − | 2.74119i | 0.163526 | − | 0.0944116i | ||||
\(844\) | −16.0049 | + | 27.7212i | −0.550910 | + | 0.954205i | ||||
\(845\) | 9.59635 | − | 9.56930i | 0.330124 | − | 0.329194i | ||||
\(846\) | 5.19009 | 0.178439 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.358248 | − | 0.620504i | 0.0123023 | − | 0.0213082i | ||||
\(849\) | 9.41977 | − | 16.3155i | 0.323286 | − | 0.559947i | ||||
\(850\) | 0.240670 | + | 0.138951i | 0.00825493 | + | 0.00476598i | ||||
\(851\) | 3.70241i | 0.126917i | ||||||||
\(852\) | −4.76265 | − | 2.74972i | −0.163166 | − | 0.0942038i | ||||
\(853\) | − | 1.51845i | − | 0.0519906i | −0.999662 | − | 0.0259953i | \(-0.991725\pi\) | ||
0.999662 | − | 0.0259953i | \(-0.00827550\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.54269 | − | 11.3323i | 0.223755 | − | 0.387556i | ||||
\(856\) | 15.9136i | 0.543914i | ||||||||
\(857\) | 3.00060 | − | 5.19718i | 0.102498 | − | 0.177532i | −0.810215 | − | 0.586133i | \(-0.800650\pi\) |
0.912713 | + | 0.408600i | \(0.133983\pi\) | |||||||
\(858\) | 2.32927 | − | 5.61215i | 0.0795199 | − | 0.191596i | ||||
\(859\) | 0.838021 | + | 1.45150i | 0.0285929 | + | 0.0495244i | 0.879968 | − | 0.475033i | \(-0.157564\pi\) |
−0.851375 | + | 0.524558i | \(0.824231\pi\) | |||||||
\(860\) | 7.62036 | + | 4.39962i | 0.259852 | + | 0.150026i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.70929 | + | 8.15673i | 0.160399 | + | 0.277819i | ||||
\(863\) | 36.4167 | − | 21.0252i | 1.23964 | − | 0.715706i | 0.270619 | − | 0.962687i | \(-0.412772\pi\) |
0.969021 | + | 0.246980i | \(0.0794383\pi\) | |||||||
\(864\) | 22.5615i | 0.767558i | ||||||||
\(865\) | 25.2933i | 0.859999i | ||||||||
\(866\) | 8.28567 | − | 4.78374i | 0.281559 | − | 0.162558i | ||||
\(867\) | −7.21304 | − | 12.4934i | −0.244968 | − | 0.424297i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 40.9639 | + | 23.6505i | 1.38960 | + | 0.802288i | ||||
\(870\) | 1.85936 | + | 3.22051i | 0.0630383 | + | 0.109186i | ||||
\(871\) | −14.7236 | + | 11.2813i | −0.498890 | + | 0.382253i | ||||
\(872\) | −6.02832 | + | 10.4414i | −0.204145 | + | 0.353589i | ||||
\(873\) | 6.15770i | 0.208407i | ||||||||
\(874\) | 6.04815 | − | 10.4757i | 0.204582 | − | 0.354346i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 9.83201i | − | 0.332193i | ||||||
\(877\) | 26.7281 | + | 15.4315i | 0.902545 | + | 0.521084i | 0.878025 | − | 0.478615i | \(-0.158861\pi\) |
0.0245198 | + | 0.999699i | \(0.492194\pi\) | |||||||
\(878\) | − | 0.632537i | − | 0.0213471i | ||||||
\(879\) | 17.8077 | + | 10.2813i | 0.600638 | + | 0.346778i | ||||
\(880\) | −5.29917 | + | 9.17843i | −0.178635 | + | 0.309405i | ||||
\(881\) | 27.8669 | − | 48.2669i | 0.938860 | − | 1.62615i | 0.171260 | − | 0.985226i | \(-0.445216\pi\) |
0.767601 | − | 0.640928i | \(-0.221450\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.92007 | −0.0982681 | −0.0491341 | − | 0.998792i | \(-0.515646\pi\) | ||||
−0.0491341 | + | 0.998792i | \(0.515646\pi\) | |||||||
\(884\) | −0.888625 | + | 0.116352i | −0.0298877 | + | 0.00391333i | ||||
\(885\) | −4.77452 | + | 8.26971i | −0.160494 | + | 0.277983i | ||||
\(886\) | −9.06671 | + | 5.23467i | −0.304602 | + | 0.175862i | ||||
\(887\) | −1.87909 | −0.0630937 | −0.0315468 | − | 0.999502i | \(-0.510043\pi\) | ||||
−0.0315468 | + | 0.999502i | \(0.510043\pi\) | |||||||
\(888\) | 0.671584 | + | 1.16322i | 0.0225369 | + | 0.0390350i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.788876 | − | 0.455458i | 0.0264432 | − | 0.0152670i | ||||
\(891\) | 10.3920 | + | 5.99980i | 0.348144 | + | 0.201001i | ||||
\(892\) | 17.4421 | + | 10.0702i | 0.584004 | + | 0.337175i | ||||
\(893\) | 25.1051 | 0.840111 | ||||||||
\(894\) | −0.00483239 | −0.000161619 | ||||||||
\(895\) | −3.73470 | − | 2.15623i | −0.124837 | − | 0.0720748i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.18080 | − | 10.6770i | −0.273149 | − | 0.356495i | ||||
\(898\) | 4.46569 | + | 7.73480i | 0.149022 | + | 0.258114i | ||||
\(899\) | −20.7014 | + | 11.9520i | −0.690431 | + | 0.398621i | ||||
\(900\) | 7.80074 | + | 13.5113i | 0.260025 | + | 0.450376i | ||||
\(901\) | −0.0198566 | + | 0.0343926i | −0.000661518 | + | 0.00114578i | ||||
\(902\) | 23.9964i | 0.798991i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.8017 | − | 10.2778i | 0.592077 | − | 0.341836i | ||||
\(905\) | 7.10121 | − | 4.09989i | 0.236052 | − | 0.136285i | ||||
\(906\) | 8.03082 | 0.266806 | ||||||||
\(907\) | −17.8082 | − | 30.8447i | −0.591311 | − | 1.02418i | −0.994056 | − | 0.108868i | \(-0.965277\pi\) |
0.402745 | − | 0.915312i | \(-0.368056\pi\) | |||||||
\(908\) | 31.3331i | 1.03982i | ||||||||
\(909\) | −26.1358 | −0.866869 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.2844 | 1.46721 | 0.733604 | − | 0.679577i | \(-0.237837\pi\) | ||||
0.733604 | + | 0.679577i | \(0.237837\pi\) | |||||||
\(912\) | 11.9957i | 0.397217i | ||||||||
\(913\) | −5.69946 | − | 9.87175i | −0.188624 | − | 0.326707i | ||||
\(914\) | 3.28290 | 0.108589 | ||||||||
\(915\) | −4.49750 | + | 2.59663i | −0.148683 | + | 0.0858420i | ||||
\(916\) | 5.85535 | − | 3.38059i | 0.193466 | − | 0.111698i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 0.318459i | − | 0.0105107i | ||||||
\(919\) | −13.0564 | + | 22.6144i | −0.430691 | + | 0.745979i | −0.996933 | − | 0.0782603i | \(-0.975063\pi\) |
0.566242 | + | 0.824239i | \(0.308397\pi\) | |||||||
\(920\) | −4.29129 | − | 7.43274i | −0.141480 | − | 0.245050i | ||||
\(921\) | −17.8738 | + | 10.3194i | −0.588961 | + | 0.340037i | ||||
\(922\) | 1.27838 | + | 2.21421i | 0.0421010 | + | 0.0729211i | ||||
\(923\) | −10.5861 | + | 8.11111i | −0.348445 | + | 0.266981i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.85753 | + | 1.64980i | 0.0939551 | + | 0.0542450i | ||||
\(926\) | −16.6615 | −0.547531 | ||||||||
\(927\) | −9.49887 | −0.311984 | ||||||||
\(928\) | 36.5893 | + | 21.1248i | 1.20110 | + | 0.693457i | ||||
\(929\) | 8.68030 | + | 5.01157i | 0.284791 | + | 0.164424i | 0.635591 | − | 0.772026i | \(-0.280757\pi\) |
−0.350799 | + | 0.936451i | \(0.614090\pi\) | |||||||
\(930\) | 1.09165 | − | 0.630266i | 0.0357967 | − | 0.0206672i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 21.9313 | + | 37.9861i | 0.718384 | + | 1.24428i | ||||
\(933\) | −3.38745 | −0.110900 | ||||||||
\(934\) | −5.60712 | + | 3.23727i | −0.183471 | + | 0.105927i | ||||
\(935\) | 0.293716 | − | 0.508731i | 0.00960554 | − | 0.0166373i | ||||
\(936\) | 14.2246 | + | 5.90377i | 0.464944 | + | 0.192971i | ||||
\(937\) | 0.916838 | 0.0299518 | 0.0149759 | − | 0.999888i | \(-0.495233\pi\) | ||||
0.0149759 | + | 0.999888i | \(0.495233\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.0964 | + | 20.9515i | −0.394750 | + | 0.683728i | ||||
\(940\) | 4.15629 | − | 7.19891i | 0.135563 | − | 0.234803i | ||||
\(941\) | 14.8001 | + | 8.54482i | 0.482468 | + | 0.278553i | 0.721445 | − | 0.692472i | \(-0.243478\pi\) |
−0.238976 | + | 0.971025i | \(0.576812\pi\) | |||||||
\(942\) | 8.40817i | 0.273953i | ||||||||
\(943\) | 46.0027 | + | 26.5597i | 1.49805 | + | 0.864902i | ||||
\(944\) | 27.6284i | 0.899227i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.78368 | − | 8.28557i | 0.155531 | − | 0.269387i | ||||
\(947\) | 21.7555i | 0.706957i | 0.935443 | + | 0.353479i | \(0.115001\pi\) | ||||
−0.935443 | + | 0.353479i | \(0.884999\pi\) | |||||||
\(948\) | 8.86342 | − | 15.3519i | 0.287871 | − | 0.498607i | ||||
\(949\) | −22.0214 | − | 9.13979i | −0.714846 | − | 0.296690i | ||||
\(950\) | −5.39012 | − | 9.33597i | −0.174879 | − | 0.302899i | ||||
\(951\) | −12.3729 | − | 7.14350i | −0.401219 | − | 0.231644i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.90406 | − | 15.4223i | −0.288431 | − | 0.499577i | 0.685005 | − | 0.728539i | \(-0.259800\pi\) |
−0.973435 | + | 0.228962i | \(0.926467\pi\) | |||||||
\(954\) | 0.275812 | − | 0.159240i | 0.00892976 | − | 0.00515560i | ||||
\(955\) | − | 6.75385i | − | 0.218549i | ||||||
\(956\) | − | 13.6582i | − | 0.441737i | ||||||
\(957\) | −24.5130 | + | 14.1526i | −0.792392 | + | 0.457488i | ||||
\(958\) | −6.75281 | − | 11.6962i | −0.218173 | − | 0.377887i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.00166 | + | 1.15566i | 0.0646034 | + | 0.0372988i | ||||
\(961\) | −11.4487 | − | 19.8297i | −0.369311 | − | 0.639666i | ||||
\(962\) | 1.50717 | − | 0.197341i | 0.0485931 | − | 0.00636253i | ||||
\(963\) | 9.66793 | − | 16.7453i | 0.311545 | − | 0.539611i | ||||
\(964\) | 38.0895i | 1.22678i | ||||||||
\(965\) | 2.51720 | − | 4.35992i | 0.0810316 | − | 0.140351i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 35.3813i | − | 1.13779i | −0.822412 | − | 0.568893i | \(-0.807372\pi\) | ||
0.822412 | − | 0.568893i | \(-0.192628\pi\) | |||||||
\(968\) | 7.69582 | + | 4.44318i | 0.247353 | + | 0.142809i | ||||
\(969\) | − | 0.664883i | − | 0.0213591i | ||||||
\(970\) | −1.22007 | − | 0.704409i | −0.0391742 | − | 0.0226172i | ||||
\(971\) | 24.8533 | − | 43.0472i | 0.797582 | − | 1.38145i | −0.123605 | − | 0.992331i | \(-0.539446\pi\) |
0.921187 | − | 0.389120i | \(-0.127221\pi\) | |||||||
\(972\) | 14.0200 | − | 24.2834i | 0.449693 | − | 0.778890i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 16.0415 | 0.514002 | ||||||||
\(975\) | −11.8859 | + | 1.55628i | −0.380654 | + | 0.0498408i | ||||
\(976\) | −7.51287 | + | 13.0127i | −0.240481 | + | 0.416526i | ||||
\(977\) | −53.0701 | + | 30.6401i | −1.69786 | + | 0.980262i | −0.750081 | + | 0.661346i | \(0.769986\pi\) |
−0.947783 | + | 0.318917i | \(0.896681\pi\) | |||||||
\(978\) | −3.79445 | −0.121333 | ||||||||
\(979\) | 3.46673 | + | 6.00455i | 0.110797 | + | 0.191906i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.6868 | − | 7.32475i | 0.405060 | − | 0.233861i | ||||
\(982\) | −12.3856 | − | 7.15080i | −0.395239 | − | 0.228191i | ||||
\(983\) | 6.05318 | + | 3.49481i | 0.193067 | + | 0.111467i | 0.593417 | − | 0.804895i | \(-0.297778\pi\) |
−0.400351 | + | 0.916362i | \(0.631112\pi\) | |||||||
\(984\) | 19.2707 | 0.614328 | ||||||||
\(985\) | −26.9336 | −0.858176 | ||||||||
\(986\) | −0.516464 | − | 0.298181i | −0.0164476 | − | 0.00949601i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 32.1096 | + | 13.3268i | 1.02154 | + | 0.423981i | ||||
\(989\) | −10.5893 | − | 18.3413i | −0.336722 | − | 0.583219i | ||||
\(990\) | −4.07979 | + | 2.35547i | −0.129664 | + | 0.0748617i | ||||
\(991\) | 16.3671 | + | 28.3486i | 0.519917 | + | 0.900522i | 0.999732 | + | 0.0231525i | \(0.00737033\pi\) |
−0.479815 | + | 0.877370i | \(0.659296\pi\) | |||||||
\(992\) | 7.16066 | − | 12.4026i | 0.227351 | − | 0.393784i | ||||
\(993\) | 5.27532i | 0.167407i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.4512 | − | 8.92078i | 0.489838 | − | 0.282808i | ||||
\(996\) | −3.69960 | + | 2.13597i | −0.117226 | + | 0.0676807i | ||||
\(997\) | −57.7897 | −1.83022 | −0.915109 | − | 0.403207i | \(-0.867896\pi\) | ||||
−0.915109 | + | 0.403207i | \(0.867896\pi\) | |||||||
\(998\) | 0.449529 | + | 0.778607i | 0.0142296 | + | 0.0246464i | ||||
\(999\) | − | 3.78114i | − | 0.119630i |
(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 | 637.2.k.i.459.4 | 12 | ||
7.2 | even | 3 | 637.2.u.g.30.4 | 12 | |||
7.3 | odd | 6 | 637.2.q.g.589.3 | 12 | |||
7.4 | even | 3 | 637.2.q.i.589.3 | 12 | |||
7.5 | odd | 6 | 91.2.u.b.30.4 | yes | 12 | ||
7.6 | odd | 2 | 91.2.k.b.4.4 | ✓ | 12 | ||
13.10 | even | 6 | 637.2.u.g.361.4 | 12 | |||
21.5 | even | 6 | 819.2.do.e.667.3 | 12 | |||
21.20 | even | 2 | 819.2.bm.f.550.3 | 12 | |||
91.6 | even | 12 | 1183.2.e.j.508.5 | 24 | |||
91.10 | odd | 6 | 637.2.q.g.491.3 | 12 | |||
91.19 | even | 12 | 1183.2.e.j.170.5 | 24 | |||
91.20 | even | 12 | 1183.2.e.j.508.8 | 24 | |||
91.23 | even | 6 | inner | 637.2.k.i.569.3 | 12 | ||
91.32 | odd | 12 | 8281.2.a.co.1.8 | 12 | |||
91.33 | even | 12 | 1183.2.e.j.170.8 | 24 | |||
91.45 | even | 12 | 8281.2.a.cp.1.8 | 12 | |||
91.46 | odd | 12 | 8281.2.a.co.1.5 | 12 | |||
91.59 | even | 12 | 8281.2.a.cp.1.5 | 12 | |||
91.62 | odd | 6 | 91.2.u.b.88.4 | yes | 12 | ||
91.75 | odd | 6 | 91.2.k.b.23.3 | yes | 12 | ||
91.88 | even | 6 | 637.2.q.i.491.3 | 12 | |||
273.62 | even | 6 | 819.2.do.e.361.3 | 12 | |||
273.257 | even | 6 | 819.2.bm.f.478.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.4 | ✓ | 12 | 7.6 | odd | 2 | ||
91.2.k.b.23.3 | yes | 12 | 91.75 | odd | 6 | ||
91.2.u.b.30.4 | yes | 12 | 7.5 | odd | 6 | ||
91.2.u.b.88.4 | yes | 12 | 91.62 | odd | 6 | ||
637.2.k.i.459.4 | 12 | 1.1 | even | 1 | trivial | ||
637.2.k.i.569.3 | 12 | 91.23 | even | 6 | inner | ||
637.2.q.g.491.3 | 12 | 91.10 | odd | 6 | |||
637.2.q.g.589.3 | 12 | 7.3 | odd | 6 | |||
637.2.q.i.491.3 | 12 | 91.88 | even | 6 | |||
637.2.q.i.589.3 | 12 | 7.4 | even | 3 | |||
637.2.u.g.30.4 | 12 | 7.2 | even | 3 | |||
637.2.u.g.361.4 | 12 | 13.10 | even | 6 | |||
819.2.bm.f.478.4 | 12 | 273.257 | even | 6 | |||
819.2.bm.f.550.3 | 12 | 21.20 | even | 2 | |||
819.2.do.e.361.3 | 12 | 273.62 | even | 6 | |||
819.2.do.e.667.3 | 12 | 21.5 | even | 6 | |||
1183.2.e.j.170.5 | 24 | 91.19 | even | 12 | |||
1183.2.e.j.170.8 | 24 | 91.33 | even | 12 | |||
1183.2.e.j.508.5 | 24 | 91.6 | even | 12 | |||
1183.2.e.j.508.8 | 24 | 91.20 | even | 12 | |||
8281.2.a.co.1.5 | 12 | 91.46 | odd | 12 | |||
8281.2.a.co.1.8 | 12 | 91.32 | odd | 12 | |||
8281.2.a.cp.1.5 | 12 | 91.59 | even | 12 | |||
8281.2.a.cp.1.8 | 12 | 91.45 | even | 12 |