Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), 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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 7 x^{10} - 15 x^{9} + 59 x^{8} + 118 x^{7} + 266 x^{6} + 324 x^{5} + 1036 x^{4} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 323.3 | ||
Root | \(0.544351 + 1.67534i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.323 |
Dual form | 847.2.f.u.729.3 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.23415 | + | 1.62320i | 1.57978 | + | 1.14778i | 0.916946 | + | 0.399011i | \(0.130647\pi\) |
0.662834 | + | 0.748766i | \(0.269353\pi\) | |||||||
\(3\) | 0.544351 | − | 1.67534i | 0.314281 | − | 0.967258i | −0.661768 | − | 0.749709i | \(-0.730194\pi\) |
0.976049 | − | 0.217550i | \(-0.0698064\pi\) | |||||||
\(4\) | 1.73859 | + | 5.35083i | 0.869295 | + | 2.67542i | ||||
\(5\) | 2.12464 | − | 1.54364i | 0.950167 | − | 0.690337i | −0.000679067 | − | 1.00000i | \(-0.500216\pi\) |
0.950846 | + | 0.309663i | \(0.100216\pi\) | |||||||
\(6\) | 3.93558 | − | 2.85936i | 1.60669 | − | 1.16733i | ||||
\(7\) | −0.309017 | − | 0.951057i | −0.116797 | − | 0.359466i | ||||
\(8\) | −3.09448 | + | 9.52384i | −1.09406 | + | 3.36718i | ||||
\(9\) | −0.0833965 | − | 0.0605911i | −0.0277988 | − | 0.0201970i | ||||
\(10\) | 7.25240 | 2.29341 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 9.91087 | 2.86102 | ||||||||
\(13\) | −1.93173 | − | 1.40349i | −0.535767 | − | 0.389257i | 0.286744 | − | 0.958007i | \(-0.407427\pi\) |
−0.822510 | + | 0.568750i | \(0.807427\pi\) | |||||||
\(14\) | 0.853368 | − | 2.62640i | 0.228072 | − | 0.701934i | ||||
\(15\) | −1.42957 | − | 4.39978i | −0.369114 | − | 1.13602i | ||||
\(16\) | −13.2693 | + | 9.64068i | −3.31732 | + | 2.41017i | ||||
\(17\) | −1.93173 | + | 1.40349i | −0.468514 | + | 0.340396i | −0.796862 | − | 0.604161i | \(-0.793508\pi\) |
0.328348 | + | 0.944557i | \(0.393508\pi\) | |||||||
\(18\) | −0.0879683 | − | 0.270739i | −0.0207343 | − | 0.0638137i | ||||
\(19\) | 0.534377 | − | 1.64464i | 0.122595 | − | 0.377307i | −0.870861 | − | 0.491530i | \(-0.836438\pi\) |
0.993455 | + | 0.114223i | \(0.0364378\pi\) | |||||||
\(20\) | 11.9536 | + | 8.68483i | 2.67291 | + | 1.94199i | ||||
\(21\) | −1.76156 | −0.384403 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.626198 | −0.130571 | −0.0652857 | − | 0.997867i | \(-0.520796\pi\) | ||||
−0.0652857 | + | 0.997867i | \(0.520796\pi\) | |||||||
\(24\) | 14.2712 | + | 10.3686i | 2.91309 | + | 2.11649i | ||||
\(25\) | 0.586179 | − | 1.80407i | 0.117236 | − | 0.360815i | ||||
\(26\) | −2.03763 | − | 6.27119i | −0.399613 | − | 1.22988i | ||||
\(27\) | 4.12848 | − | 2.99952i | 0.794527 | − | 0.577257i | ||||
\(28\) | 4.55169 | − | 3.30700i | 0.860189 | − | 0.624964i | ||||
\(29\) | −0.534377 | − | 1.64464i | −0.0992314 | − | 0.305403i | 0.889102 | − | 0.457709i | \(-0.151330\pi\) |
−0.988333 | + | 0.152306i | \(0.951330\pi\) | |||||||
\(30\) | 3.94785 | − | 12.1502i | 0.720775 | − | 2.21832i | ||||
\(31\) | 1.81094 | + | 1.31572i | 0.325254 | + | 0.236311i | 0.738414 | − | 0.674347i | \(-0.235575\pi\) |
−0.413160 | + | 0.910658i | \(0.635575\pi\) | |||||||
\(32\) | −25.2663 | −4.46650 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.59392 | −1.13085 | ||||||||
\(35\) | −2.12464 | − | 1.54364i | −0.359130 | − | 0.260923i | ||||
\(36\) | 0.179220 | − | 0.551584i | 0.0298701 | − | 0.0919306i | ||||
\(37\) | −2.13126 | − | 6.55936i | −0.350378 | − | 1.07835i | −0.958641 | − | 0.284617i | \(-0.908134\pi\) |
0.608264 | − | 0.793735i | \(-0.291866\pi\) | |||||||
\(38\) | 3.86347 | − | 2.80697i | 0.626737 | − | 0.455351i | ||||
\(39\) | −3.40286 | + | 2.47232i | −0.544894 | + | 0.395889i | ||||
\(40\) | 8.12672 | + | 25.0115i | 1.28495 | + | 3.95466i | ||||
\(41\) | −3.20999 | + | 9.87934i | −0.501317 | + | 1.54289i | 0.305559 | + | 0.952173i | \(0.401157\pi\) |
−0.806876 | + | 0.590721i | \(0.798843\pi\) | |||||||
\(42\) | −3.93558 | − | 2.85936i | −0.607273 | − | 0.441209i | ||||
\(43\) | −7.25240 | −1.10598 | −0.552990 | − | 0.833188i | \(-0.686513\pi\) | ||||
−0.552990 | + | 0.833188i | \(0.686513\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.270718 | −0.0403563 | ||||||||
\(46\) | −1.39902 | − | 1.01645i | −0.206274 | − | 0.149867i | ||||
\(47\) | 1.97392 | − | 6.07512i | 0.287927 | − | 0.886147i | −0.697580 | − | 0.716507i | \(-0.745740\pi\) |
0.985506 | − | 0.169640i | \(-0.0542603\pi\) | |||||||
\(48\) | 8.92829 | + | 27.4784i | 1.28869 | + | 3.96617i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 4.23799 | − | 3.07908i | 0.599342 | − | 0.435448i | ||||
\(51\) | 1.29978 | + | 4.00030i | 0.182005 | + | 0.560154i | ||||
\(52\) | 4.15133 | − | 12.7765i | 0.575686 | − | 1.77178i | ||||
\(53\) | 7.48535 | + | 5.43842i | 1.02819 | + | 0.747025i | 0.967946 | − | 0.251159i | \(-0.0808117\pi\) |
0.0602454 | + | 0.998184i | \(0.480812\pi\) | |||||||
\(54\) | 14.0925 | 1.91774 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.0140 | 1.33817 | ||||||||
\(57\) | −2.46445 | − | 1.79053i | −0.326424 | − | 0.237161i | ||||
\(58\) | 1.47571 | − | 4.54178i | 0.193771 | − | 0.596365i | ||||
\(59\) | −0.544351 | − | 1.67534i | −0.0708685 | − | 0.218111i | 0.909349 | − | 0.416034i | \(-0.136580\pi\) |
−0.980218 | + | 0.197923i | \(0.936580\pi\) | |||||||
\(60\) | 21.0570 | − | 15.2988i | 2.71845 | − | 1.97507i | ||||
\(61\) | −8.40387 | + | 6.10577i | −1.07601 | + | 0.781764i | −0.976982 | − | 0.213321i | \(-0.931572\pi\) |
−0.0990233 | + | 0.995085i | \(0.531572\pi\) | |||||||
\(62\) | 1.91022 | + | 5.87904i | 0.242598 | + | 0.746639i | ||||
\(63\) | −0.0318546 | + | 0.0980384i | −0.00401330 | + | 0.0123517i | ||||
\(64\) | −29.9102 | − | 21.7310i | −3.73878 | − | 2.71638i | ||||
\(65\) | −6.27072 | −0.777787 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.42003 | −0.784332 | −0.392166 | − | 0.919895i | \(-0.628274\pi\) | ||||
−0.392166 | + | 0.919895i | \(0.628274\pi\) | |||||||
\(68\) | −10.8683 | − | 7.89630i | −1.31798 | − | 0.957567i | ||||
\(69\) | −0.340872 | + | 1.04909i | −0.0410361 | + | 0.126296i | ||||
\(70\) | −2.24111 | − | 6.89744i | −0.267864 | − | 0.824402i | ||||
\(71\) | −6.54071 | + | 4.75210i | −0.776239 | + | 0.563971i | −0.903848 | − | 0.427854i | \(-0.859270\pi\) |
0.127609 | + | 0.991825i | \(0.459270\pi\) | |||||||
\(72\) | 0.835128 | − | 0.606756i | 0.0984208 | − | 0.0715069i | ||||
\(73\) | −3.20999 | − | 9.87934i | −0.375701 | − | 1.15629i | −0.943004 | − | 0.332780i | \(-0.892013\pi\) |
0.567303 | − | 0.823509i | \(-0.307987\pi\) | |||||||
\(74\) | 5.88561 | − | 18.1140i | 0.684188 | − | 2.10571i | ||||
\(75\) | −2.70335 | − | 1.96410i | −0.312156 | − | 0.226795i | ||||
\(76\) | 9.72928 | 1.11603 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −11.6156 | −1.31520 | ||||||||
\(79\) | 12.3394 | + | 8.96513i | 1.38830 | + | 1.00866i | 0.996050 | + | 0.0887962i | \(0.0283020\pi\) |
0.392247 | + | 0.919860i | \(0.371698\pi\) | |||||||
\(80\) | −13.3106 | + | 40.9659i | −1.48817 | + | 4.58013i | ||||
\(81\) | −2.87343 | − | 8.84352i | −0.319270 | − | 0.982613i | ||||
\(82\) | −23.2078 | + | 16.8614i | −2.56287 | + | 1.86203i | ||||
\(83\) | 10.3356 | − | 7.50926i | 1.13448 | − | 0.824248i | 0.148139 | − | 0.988966i | \(-0.452672\pi\) |
0.986341 | + | 0.164718i | \(0.0526716\pi\) | |||||||
\(84\) | −3.06263 | − | 9.42580i | −0.334160 | − | 1.02844i | ||||
\(85\) | −1.93776 | + | 5.96381i | −0.210179 | + | 0.646866i | ||||
\(86\) | −16.2029 | − | 11.7721i | −1.74721 | − | 1.26942i | ||||
\(87\) | −3.04623 | −0.326590 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.1493 | −1.49982 | −0.749912 | − | 0.661538i | \(-0.769904\pi\) | ||||
−0.749912 | + | 0.661538i | \(0.769904\pi\) | |||||||
\(90\) | −0.604824 | − | 0.439431i | −0.0637541 | − | 0.0463200i | ||||
\(91\) | −0.737857 | + | 2.27089i | −0.0773484 | + | 0.238054i | ||||
\(92\) | −1.08870 | − | 3.35068i | −0.113505 | − | 0.349333i | ||||
\(93\) | 3.19007 | − | 2.31772i | 0.330795 | − | 0.240337i | ||||
\(94\) | 14.2712 | − | 10.3686i | 1.47196 | − | 1.06944i | ||||
\(95\) | −1.40338 | − | 4.31916i | −0.143984 | − | 0.443137i | ||||
\(96\) | −13.7538 | + | 42.3297i | −1.40374 | + | 4.32026i | ||||
\(97\) | 6.75973 | + | 4.91123i | 0.686346 | + | 0.498660i | 0.875457 | − | 0.483296i | \(-0.160561\pi\) |
−0.189111 | + | 0.981956i | \(0.560561\pi\) | |||||||
\(98\) | −2.76156 | −0.278959 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 10.6724 | 1.06724 | ||||||||
\(101\) | −11.2019 | − | 8.13866i | −1.11463 | − | 0.809827i | −0.131245 | − | 0.991350i | \(-0.541897\pi\) |
−0.983387 | + | 0.181523i | \(0.941897\pi\) | |||||||
\(102\) | −3.58941 | + | 11.0471i | −0.355404 | + | 1.09382i | ||||
\(103\) | −0.905170 | − | 2.78583i | −0.0891891 | − | 0.274496i | 0.896507 | − | 0.443030i | \(-0.146097\pi\) |
−0.985696 | + | 0.168534i | \(0.946097\pi\) | |||||||
\(104\) | 19.3443 | − | 14.0545i | 1.89686 | − | 1.37815i | ||||
\(105\) | −3.74267 | + | 2.71921i | −0.365247 | + | 0.265368i | ||||
\(106\) | 7.89570 | + | 24.3005i | 0.766898 | + | 2.36027i | ||||
\(107\) | −1.06875 | + | 3.28929i | −0.103320 | + | 0.317988i | −0.989333 | − | 0.145674i | \(-0.953465\pi\) |
0.886012 | + | 0.463662i | \(0.153465\pi\) | |||||||
\(108\) | 23.2277 | + | 16.8759i | 2.23508 | + | 1.62388i | ||||
\(109\) | 16.2341 | 1.55494 | 0.777471 | − | 0.628919i | \(-0.216502\pi\) | ||||
0.777471 | + | 0.628919i | \(0.216502\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.1493 | −1.15316 | ||||||||
\(112\) | 13.2693 | + | 9.64068i | 1.25383 | + | 0.910959i | ||||
\(113\) | 2.19497 | − | 6.75543i | 0.206486 | − | 0.635498i | −0.793163 | − | 0.609009i | \(-0.791567\pi\) |
0.999649 | − | 0.0264888i | \(-0.00843265\pi\) | |||||||
\(114\) | −2.59955 | − | 8.00061i | −0.243471 | − | 0.749325i | ||||
\(115\) | −1.33044 | + | 0.966625i | −0.124065 | + | 0.0901382i | ||||
\(116\) | 7.87115 | − | 5.71873i | 0.730818 | − | 0.530971i | ||||
\(117\) | 0.0760610 | + | 0.234092i | 0.00703184 | + | 0.0216418i | ||||
\(118\) | 1.50326 | − | 4.62655i | 0.138386 | − | 0.425908i | ||||
\(119\) | 1.93173 | + | 1.40349i | 0.177082 | + | 0.128657i | ||||
\(120\) | 46.3265 | 4.22901 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −28.6864 | −2.59714 | ||||||||
\(123\) | 14.8039 | + | 10.7557i | 1.33482 | + | 0.969805i | ||||
\(124\) | −3.89174 | + | 11.9775i | −0.349488 | + | 1.07561i | ||||
\(125\) | 2.51828 | + | 7.75046i | 0.225241 | + | 0.693222i | ||||
\(126\) | −0.230304 | + | 0.167326i | −0.0205171 | + | 0.0149066i | ||||
\(127\) | −3.67410 | + | 2.66939i | −0.326024 | + | 0.236870i | −0.738741 | − | 0.673989i | \(-0.764580\pi\) |
0.412718 | + | 0.910859i | \(0.364580\pi\) | |||||||
\(128\) | −15.9345 | − | 49.0412i | −1.40842 | − | 4.33467i | ||||
\(129\) | −3.94785 | + | 12.1502i | −0.347589 | + | 1.06977i | ||||
\(130\) | −14.0097 | − | 10.1786i | −1.22873 | − | 0.892726i | ||||
\(131\) | 6.27072 | 0.547875 | 0.273938 | − | 0.961747i | \(-0.411674\pi\) | ||||
0.273938 | + | 0.961747i | \(0.411674\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.72928 | −0.149948 | ||||||||
\(134\) | −14.3433 | − | 10.4210i | −1.23907 | − | 0.900238i | ||||
\(135\) | 4.14136 | − | 12.7458i | 0.356431 | − | 1.09698i | ||||
\(136\) | −7.38887 | − | 22.7406i | −0.633590 | − | 1.94999i | ||||
\(137\) | −7.60614 | + | 5.52619i | −0.649837 | + | 0.472134i | −0.863216 | − | 0.504836i | \(-0.831553\pi\) |
0.213379 | + | 0.976970i | \(0.431553\pi\) | |||||||
\(138\) | −2.46445 | + | 1.79053i | −0.209788 | + | 0.152420i | ||||
\(139\) | −4.88919 | − | 15.0474i | −0.414695 | − | 1.27630i | −0.912523 | − | 0.409025i | \(-0.865869\pi\) |
0.497828 | − | 0.867276i | \(-0.334131\pi\) | |||||||
\(140\) | 4.56588 | − | 14.0523i | 0.385888 | − | 1.18764i | ||||
\(141\) | −9.10338 | − | 6.61399i | −0.766643 | − | 0.556999i | ||||
\(142\) | −22.3265 | −1.87360 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.69075 | 0.140896 | ||||||||
\(145\) | −3.67410 | − | 2.66939i | −0.305117 | − | 0.221681i | ||||
\(146\) | 8.86458 | − | 27.2824i | 0.733638 | − | 2.25790i | ||||
\(147\) | 0.544351 | + | 1.67534i | 0.0448973 | + | 0.138180i | ||||
\(148\) | 31.3926 | − | 22.8081i | 2.58046 | − | 1.87481i | ||||
\(149\) | 2.79804 | − | 2.03289i | 0.229224 | − | 0.166541i | −0.467245 | − | 0.884128i | \(-0.654753\pi\) |
0.696469 | + | 0.717587i | \(0.254753\pi\) | |||||||
\(150\) | −2.85155 | − | 8.77618i | −0.232828 | − | 0.716572i | ||||
\(151\) | 3.18245 | − | 9.79457i | 0.258984 | − | 0.797071i | −0.734034 | − | 0.679112i | \(-0.762365\pi\) |
0.993018 | − | 0.117959i | \(-0.0376351\pi\) | |||||||
\(152\) | 14.0097 | + | 10.1786i | 1.13634 | + | 0.825597i | ||||
\(153\) | 0.246139 | 0.0198991 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.87859 | 0.472180 | ||||||||
\(156\) | −19.1452 | − | 13.9098i | −1.53284 | − | 1.11367i | ||||
\(157\) | 3.50337 | − | 10.7823i | 0.279600 | − | 0.860519i | −0.708366 | − | 0.705845i | \(-0.750567\pi\) |
0.987966 | − | 0.154674i | \(-0.0494327\pi\) | |||||||
\(158\) | 13.0159 | + | 40.0588i | 1.03549 | + | 3.18691i | ||||
\(159\) | 13.1859 | − | 9.58009i | 1.04571 | − | 0.759751i | ||||
\(160\) | −53.6819 | + | 39.0022i | −4.24392 | + | 3.08339i | ||||
\(161\) | 0.193506 | + | 0.595550i | 0.0152504 | + | 0.0469359i | ||||
\(162\) | 7.93515 | − | 24.4219i | 0.623444 | − | 1.91876i | ||||
\(163\) | 7.87115 | + | 5.71873i | 0.616516 | + | 0.447925i | 0.851703 | − | 0.524025i | \(-0.175570\pi\) |
−0.235187 | + | 0.971950i | \(0.575570\pi\) | |||||||
\(164\) | −58.4436 | −4.56368 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 35.2803 | 2.73828 | ||||||||
\(167\) | 18.2068 | + | 13.2280i | 1.40888 | + | 1.02361i | 0.993484 | + | 0.113972i | \(0.0363575\pi\) |
0.415397 | + | 0.909640i | \(0.363643\pi\) | |||||||
\(168\) | 5.45111 | − | 16.7768i | 0.420562 | − | 1.29436i | ||||
\(169\) | −2.25540 | − | 6.94140i | −0.173492 | − | 0.533954i | ||||
\(170\) | −14.0097 | + | 10.1786i | −1.07450 | + | 0.780667i | ||||
\(171\) | −0.144216 | + | 0.104779i | −0.0110285 | + | 0.00801265i | ||||
\(172\) | −12.6089 | − | 38.8064i | −0.961423 | − | 2.95896i | ||||
\(173\) | −2.14124 | + | 6.59005i | −0.162795 | + | 0.501032i | −0.998867 | − | 0.0475877i | \(-0.984847\pi\) |
0.836072 | + | 0.548620i | \(0.184847\pi\) | |||||||
\(174\) | −6.80572 | − | 4.94465i | −0.515940 | − | 0.374853i | ||||
\(175\) | −1.89692 | −0.143393 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.10308 | −0.233242 | ||||||||
\(178\) | −31.6116 | − | 22.9672i | −2.36939 | − | 1.72146i | ||||
\(179\) | 4.30867 | − | 13.2607i | 0.322045 | − | 0.991153i | −0.650712 | − | 0.759325i | \(-0.725529\pi\) |
0.972757 | − | 0.231828i | \(-0.0744706\pi\) | |||||||
\(180\) | −0.470668 | − | 1.44857i | −0.0350815 | − | 0.107970i | ||||
\(181\) | −2.56267 | + | 1.86189i | −0.190482 | + | 0.138393i | −0.678939 | − | 0.734195i | \(-0.737560\pi\) |
0.488457 | + | 0.872588i | \(0.337560\pi\) | |||||||
\(182\) | −5.33460 | + | 3.87581i | −0.395427 | + | 0.287294i | ||||
\(183\) | 5.65459 | + | 17.4030i | 0.417999 | + | 1.28647i | ||||
\(184\) | 1.93776 | − | 5.96381i | 0.142853 | − | 0.439658i | ||||
\(185\) | −14.6535 | − | 10.6464i | −1.07734 | − | 0.782736i | ||||
\(186\) | 10.8892 | 0.798436 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 35.9388 | 2.62110 | ||||||||
\(189\) | −4.12848 | − | 2.99952i | −0.300303 | − | 0.218183i | ||||
\(190\) | 3.87552 | − | 11.9276i | 0.281160 | − | 0.865320i | ||||
\(191\) | 5.67216 | + | 17.4571i | 0.410423 | + | 1.26315i | 0.916281 | + | 0.400535i | \(0.131176\pi\) |
−0.505859 | + | 0.862616i | \(0.668824\pi\) | |||||||
\(192\) | −52.6885 | + | 38.2805i | −3.80247 | + | 2.76265i | ||||
\(193\) | −2.46445 | + | 1.79053i | −0.177395 | + | 0.128885i | −0.672939 | − | 0.739698i | \(-0.734969\pi\) |
0.495544 | + | 0.868583i | \(0.334969\pi\) | |||||||
\(194\) | 7.13030 | + | 21.9448i | 0.511926 | + | 1.57555i | ||||
\(195\) | −3.41347 | + | 10.5056i | −0.244444 | + | 0.752321i | ||||
\(196\) | −4.55169 | − | 3.30700i | −0.325121 | − | 0.236214i | ||||
\(197\) | −4.95377 | −0.352942 | −0.176471 | − | 0.984306i | \(-0.556468\pi\) | ||||
−0.176471 | + | 0.984306i | \(0.556468\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.7047 | 1.11328 | 0.556638 | − | 0.830755i | \(-0.312091\pi\) | ||||
0.556638 | + | 0.830755i | \(0.312091\pi\) | |||||||
\(200\) | 15.3678 | + | 11.1654i | 1.08667 | + | 0.789510i | ||||
\(201\) | −3.49475 | + | 10.7557i | −0.246501 | + | 0.758651i | ||||
\(202\) | −11.8160 | − | 36.3659i | −0.831371 | − | 2.55870i | ||||
\(203\) | −1.39902 | + | 1.01645i | −0.0981918 | + | 0.0713405i | ||||
\(204\) | −19.1452 | + | 13.9098i | −1.34043 | + | 0.973879i | ||||
\(205\) | 8.43008 | + | 25.9451i | 0.588782 | + | 1.81209i | ||||
\(206\) | 2.49968 | − | 7.69322i | 0.174161 | − | 0.536012i | ||||
\(207\) | 0.0522227 | + | 0.0379420i | 0.00362973 | + | 0.00263715i | ||||
\(208\) | 39.1633 | 2.71548 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −12.7755 | −0.881594 | ||||||||
\(211\) | 14.1991 | + | 10.3162i | 0.977505 | + | 0.710199i | 0.957150 | − | 0.289594i | \(-0.0935203\pi\) |
0.0203551 | + | 0.999793i | \(0.493520\pi\) | |||||||
\(212\) | −16.0861 | + | 49.5080i | −1.10480 | + | 3.40022i | ||||
\(213\) | 4.40095 | + | 13.5447i | 0.301548 | + | 0.928069i | ||||
\(214\) | −7.72694 | + | 5.61395i | −0.528203 | + | 0.383762i | ||||
\(215\) | −15.4087 | + | 11.1951i | −1.05087 | + | 0.763499i | ||||
\(216\) | 15.7914 | + | 48.6009i | 1.07447 | + | 3.30687i | ||||
\(217\) | 0.691717 | − | 2.12889i | 0.0469568 | − | 0.144518i | ||||
\(218\) | 36.2693 | + | 26.3512i | 2.45647 | + | 1.78473i | ||||
\(219\) | −18.2986 | −1.23651 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.70138 | 0.383516 | ||||||||
\(222\) | −27.1433 | − | 19.7208i | −1.82174 | − | 1.32357i | ||||
\(223\) | −6.88930 | + | 21.2031i | −0.461342 | + | 1.41986i | 0.402183 | + | 0.915559i | \(0.368251\pi\) |
−0.863525 | + | 0.504305i | \(0.831749\pi\) | |||||||
\(224\) | 7.80773 | + | 24.0297i | 0.521676 | + | 1.60555i | ||||
\(225\) | −0.158196 | + | 0.114936i | −0.0105464 | + | 0.00766241i | ||||
\(226\) | 15.8693 | − | 11.5297i | 1.05561 | − | 0.766947i | ||||
\(227\) | −4.40989 | − | 13.5723i | −0.292695 | − | 0.900823i | −0.983986 | − | 0.178246i | \(-0.942958\pi\) |
0.691291 | − | 0.722576i | \(-0.257042\pi\) | |||||||
\(228\) | 5.29615 | − | 16.2999i | 0.350746 | − | 1.07948i | ||||
\(229\) | 3.13785 | + | 2.27978i | 0.207355 | + | 0.150652i | 0.686616 | − | 0.727020i | \(-0.259095\pi\) |
−0.479261 | + | 0.877672i | \(0.659095\pi\) | |||||||
\(230\) | −4.54144 | −0.299453 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 17.3169 | 1.13691 | ||||||||
\(233\) | 5.40670 | + | 3.92820i | 0.354205 | + | 0.257345i | 0.750631 | − | 0.660722i | \(-0.229750\pi\) |
−0.396426 | + | 0.918067i | \(0.629750\pi\) | |||||||
\(234\) | −0.210047 | + | 0.646458i | −0.0137312 | + | 0.0422603i | ||||
\(235\) | −5.18392 | − | 15.9545i | −0.338162 | − | 1.04075i | ||||
\(236\) | 8.01806 | − | 5.82546i | 0.521931 | − | 0.379205i | ||||
\(237\) | 21.7366 | − | 15.7926i | 1.41195 | − | 1.02584i | ||||
\(238\) | 2.03763 | + | 6.27119i | 0.132080 | + | 0.406501i | ||||
\(239\) | 1.40338 | − | 4.31916i | 0.0907772 | − | 0.279383i | −0.895353 | − | 0.445357i | \(-0.853077\pi\) |
0.986130 | + | 0.165974i | \(0.0530767\pi\) | |||||||
\(240\) | 61.3862 | + | 44.5997i | 3.96246 | + | 2.87890i | ||||
\(241\) | 3.70470 | 0.238641 | 0.119320 | − | 0.992856i | \(-0.461928\pi\) | ||||
0.119320 | + | 0.992856i | \(0.461928\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.07081 | −0.0686924 | ||||||||
\(244\) | −47.2818 | − | 34.3523i | −3.02691 | − | 2.19918i | ||||
\(245\) | −0.811540 | + | 2.49766i | −0.0518474 | + | 0.159570i | ||||
\(246\) | 15.6155 | + | 48.0595i | 0.995606 | + | 3.06416i | ||||
\(247\) | −3.34051 | + | 2.42703i | −0.212552 | + | 0.154428i | ||||
\(248\) | −18.1347 | + | 13.1756i | −1.15155 | + | 0.836651i | ||||
\(249\) | −6.95436 | − | 21.4033i | −0.440715 | − | 1.35638i | ||||
\(250\) | −6.95436 | + | 21.4033i | −0.439833 | + | 1.35367i | ||||
\(251\) | −6.88406 | − | 5.00156i | −0.434518 | − | 0.315696i | 0.348935 | − | 0.937147i | \(-0.386543\pi\) |
−0.783453 | + | 0.621451i | \(0.786543\pi\) | |||||||
\(252\) | −0.579969 | −0.0365346 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −12.5414 | −0.786920 | ||||||||
\(255\) | 8.93659 | + | 6.49281i | 0.559631 | + | 0.406596i | ||||
\(256\) | 21.1545 | − | 65.1070i | 1.32216 | − | 4.06919i | ||||
\(257\) | −0.912766 | − | 2.80920i | −0.0569367 | − | 0.175233i | 0.918544 | − | 0.395320i | \(-0.129366\pi\) |
−0.975480 | + | 0.220086i | \(0.929366\pi\) | |||||||
\(258\) | −28.5424 | + | 20.7372i | −1.77697 | + | 1.29104i | ||||
\(259\) | −5.57972 | + | 4.05391i | −0.346707 | + | 0.251897i | ||||
\(260\) | −10.9022 | − | 33.5536i | −0.676127 | − | 2.08090i | ||||
\(261\) | −0.0550856 | + | 0.169536i | −0.00340971 | + | 0.0104940i | ||||
\(262\) | 14.0097 | + | 10.1786i | 0.865522 | + | 0.628839i | ||||
\(263\) | 16.0000 | 0.986602 | 0.493301 | − | 0.869859i | \(-0.335790\pi\) | ||||
0.493301 | + | 0.869859i | \(0.335790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.2986 | 1.49265 | ||||||||
\(266\) | −3.86347 | − | 2.80697i | −0.236884 | − | 0.172107i | ||||
\(267\) | −7.70219 | + | 23.7049i | −0.471367 | + | 1.45072i | ||||
\(268\) | −11.1618 | − | 34.3525i | −0.681816 | − | 2.09841i | ||||
\(269\) | 5.48150 | − | 3.98255i | 0.334213 | − | 0.242820i | −0.408003 | − | 0.912981i | \(-0.633775\pi\) |
0.742216 | + | 0.670160i | \(0.233775\pi\) | |||||||
\(270\) | 29.9414 | − | 21.7537i | 1.82217 | − | 1.32389i | ||||
\(271\) | −1.06875 | − | 3.28929i | −0.0649222 | − | 0.199810i | 0.913334 | − | 0.407212i | \(-0.133499\pi\) |
−0.978256 | + | 0.207402i | \(0.933499\pi\) | |||||||
\(272\) | 12.1021 | − | 37.2465i | 0.733798 | − | 2.25840i | ||||
\(273\) | 3.40286 | + | 2.47232i | 0.205951 | + | 0.149632i | ||||
\(274\) | −25.9634 | −1.56850 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.20617 | −0.373567 | ||||||||
\(277\) | −9.27017 | − | 6.73517i | −0.556991 | − | 0.404677i | 0.273366 | − | 0.961910i | \(-0.411863\pi\) |
−0.830356 | + | 0.557233i | \(0.811863\pi\) | |||||||
\(278\) | 13.5018 | − | 41.5542i | 0.809782 | − | 2.49225i | ||||
\(279\) | −0.0713047 | − | 0.219453i | −0.00426890 | − | 0.0131383i | ||||
\(280\) | 21.2760 | − | 15.4579i | 1.27149 | − | 0.923789i | ||||
\(281\) | −18.0625 | + | 13.1232i | −1.07752 | + | 0.782865i | −0.977249 | − | 0.212095i | \(-0.931971\pi\) |
−0.100272 | + | 0.994960i | \(0.531971\pi\) | |||||||
\(282\) | −9.60244 | − | 29.5533i | −0.571817 | − | 1.75987i | ||||
\(283\) | 3.82043 | − | 11.7581i | 0.227101 | − | 0.698945i | −0.770970 | − | 0.636871i | \(-0.780228\pi\) |
0.998072 | − | 0.0620743i | \(-0.0197716\pi\) | |||||||
\(284\) | −36.7993 | − | 26.7363i | −2.18364 | − | 1.58651i | ||||
\(285\) | −8.00000 | −0.473879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.3878 | 0.613170 | ||||||||
\(288\) | 2.10712 | + | 1.53092i | 0.124163 | + | 0.0902101i | ||||
\(289\) | −3.49147 | + | 10.7456i | −0.205380 | + | 0.632096i | ||||
\(290\) | −3.87552 | − | 11.9276i | −0.227578 | − | 0.700414i | ||||
\(291\) | 11.9076 | − | 8.65141i | 0.698038 | − | 0.507155i | ||||
\(292\) | 47.2818 | − | 34.3523i | 2.76696 | − | 2.01031i | ||||
\(293\) | −0.665524 | − | 2.04827i | −0.0388803 | − | 0.119661i | 0.929733 | − | 0.368236i | \(-0.120038\pi\) |
−0.968613 | + | 0.248574i | \(0.920038\pi\) | |||||||
\(294\) | −1.50326 | + | 4.62655i | −0.0876717 | + | 0.269826i | ||||
\(295\) | −3.74267 | − | 2.71921i | −0.217907 | − | 0.158319i | ||||
\(296\) | 69.0654 | 4.01434 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.55102 | 0.553276 | ||||||||
\(299\) | 1.20965 | + | 0.878861i | 0.0699558 | + | 0.0508258i | ||||
\(300\) | 5.80955 | − | 17.8799i | 0.335414 | − | 1.03230i | ||||
\(301\) | 2.24111 | + | 6.89744i | 0.129176 | + | 0.397562i | ||||
\(302\) | 23.0086 | − | 16.7168i | 1.32400 | − | 0.961941i | ||||
\(303\) | −19.7328 | + | 14.3367i | −1.13362 | + | 0.823623i | ||||
\(304\) | 8.76470 | + | 26.9750i | 0.502690 | + | 1.54712i | ||||
\(305\) | −8.43008 | + | 25.9451i | −0.482705 | + | 1.48561i | ||||
\(306\) | 0.549910 | + | 0.399533i | 0.0314363 | + | 0.0228398i | ||||
\(307\) | 31.8217 | 1.81616 | 0.908081 | − | 0.418794i | \(-0.137547\pi\) | ||||
0.908081 | + | 0.418794i | \(0.137547\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.15994 | −0.293539 | ||||||||
\(310\) | 13.1336 | + | 9.54215i | 0.745941 | + | 0.541958i | ||||
\(311\) | −3.37731 | + | 10.3943i | −0.191509 | + | 0.589405i | 0.808490 | + | 0.588510i | \(0.200285\pi\) |
−1.00000 | 0.000895774i | \(0.999715\pi\) | ||||||||
\(312\) | −13.0159 | − | 40.0588i | −0.736881 | − | 2.26789i | ||||
\(313\) | −5.98811 | + | 4.35062i | −0.338468 | + | 0.245911i | −0.744015 | − | 0.668163i | \(-0.767081\pi\) |
0.405547 | + | 0.914074i | \(0.367081\pi\) | |||||||
\(314\) | 25.3289 | − | 18.4025i | 1.42939 | − | 1.03851i | ||||
\(315\) | 0.0836565 | + | 0.257468i | 0.00471351 | + | 0.0145067i | ||||
\(316\) | −26.5177 | + | 81.6130i | −1.49174 | + | 4.59109i | ||||
\(317\) | 7.19776 | + | 5.22948i | 0.404266 | + | 0.293717i | 0.771276 | − | 0.636500i | \(-0.219619\pi\) |
−0.367010 | + | 0.930217i | \(0.619619\pi\) | |||||||
\(318\) | 45.0096 | 2.52401 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −97.0933 | −5.42768 | ||||||||
\(321\) | 4.92890 | + | 3.58106i | 0.275104 | + | 0.199875i | ||||
\(322\) | −0.534377 | + | 1.64464i | −0.0297797 | + | 0.0916525i | ||||
\(323\) | 1.27596 | + | 3.92701i | 0.0709965 | + | 0.218505i | ||||
\(324\) | 42.3245 | − | 30.7505i | 2.35136 | − | 1.70836i | ||||
\(325\) | −3.66434 | + | 2.66230i | −0.203261 | + | 0.147678i | ||||
\(326\) | 8.30266 | + | 25.5530i | 0.459842 | + | 1.41525i | ||||
\(327\) | 8.83704 | − | 27.1976i | 0.488689 | − | 1.50403i | ||||
\(328\) | −84.1560 | − | 61.1429i | −4.64674 | − | 3.37605i | ||||
\(329\) | −6.38776 | −0.352168 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.56165 | 0.470591 | 0.235295 | − | 0.971924i | \(-0.424394\pi\) | ||||
0.235295 | + | 0.971924i | \(0.424394\pi\) | |||||||
\(332\) | 58.1502 | + | 42.2486i | 3.19140 | + | 2.31869i | ||||
\(333\) | −0.219699 | + | 0.676163i | −0.0120394 | + | 0.0370535i | ||||
\(334\) | 19.2049 | + | 59.1065i | 1.05084 | + | 3.23416i | ||||
\(335\) | −13.6402 | + | 9.91022i | −0.745246 | + | 0.541453i | ||||
\(336\) | 23.3746 | − | 16.9826i | 1.27519 | − | 0.926478i | ||||
\(337\) | 3.00651 | + | 9.25310i | 0.163775 | + | 0.504048i | 0.998944 | − | 0.0459455i | \(-0.0146301\pi\) |
−0.835169 | + | 0.549994i | \(0.814630\pi\) | |||||||
\(338\) | 6.22841 | − | 19.1691i | 0.338781 | − | 1.04266i | ||||
\(339\) | −10.1228 | − | 7.35466i | −0.549796 | − | 0.399450i | ||||
\(340\) | −35.2803 | −1.91334 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.492277 | −0.0266193 | ||||||||
\(343\) | 0.809017 | + | 0.587785i | 0.0436828 | + | 0.0317374i | ||||
\(344\) | 22.4424 | − | 69.0706i | 1.21001 | − | 3.72404i | ||||
\(345\) | 0.895196 | + | 2.75513i | 0.0481958 | + | 0.148331i | ||||
\(346\) | −15.4808 | + | 11.2475i | −0.832255 | + | 0.604668i | ||||
\(347\) | 12.0059 | − | 8.72277i | 0.644508 | − | 0.468263i | −0.216888 | − | 0.976197i | \(-0.569591\pi\) |
0.861396 | + | 0.507934i | \(0.169591\pi\) | |||||||
\(348\) | −5.29615 | − | 16.2999i | −0.283903 | − | 0.873764i | ||||
\(349\) | −5.02033 | + | 15.4510i | −0.268732 | + | 0.827073i | 0.722078 | + | 0.691812i | \(0.243187\pi\) |
−0.990810 | + | 0.135261i | \(0.956813\pi\) | |||||||
\(350\) | −4.23799 | − | 3.07908i | −0.226530 | − | 0.164584i | ||||
\(351\) | −12.1849 | −0.650383 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.8603 | 1.64253 | 0.821263 | − | 0.570549i | \(-0.193270\pi\) | ||||
0.821263 | + | 0.570549i | \(0.193270\pi\) | |||||||
\(354\) | −6.93274 | − | 5.03693i | −0.368471 | − | 0.267710i | ||||
\(355\) | −6.56111 | + | 20.1930i | −0.348227 | + | 1.07173i | ||||
\(356\) | −24.5999 | − | 75.7106i | −1.30379 | − | 4.01265i | ||||
\(357\) | 3.40286 | − | 2.47232i | 0.180098 | − | 0.130849i | ||||
\(358\) | 31.1510 | − | 22.6325i | 1.64638 | − | 1.19617i | ||||
\(359\) | 3.64449 | + | 11.2166i | 0.192349 | + | 0.591990i | 0.999997 | + | 0.00232497i | \(0.000740062\pi\) |
−0.807648 | + | 0.589665i | \(0.799260\pi\) | |||||||
\(360\) | 0.837733 | − | 2.57828i | 0.0441524 | − | 0.135887i | ||||
\(361\) | 12.9520 | + | 9.41020i | 0.681686 | + | 0.495274i | ||||
\(362\) | −8.74760 | −0.459764 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.4340 | −0.704132 | ||||||||
\(365\) | −22.0702 | − | 16.0350i | −1.15521 | − | 0.839308i | ||||
\(366\) | −15.6155 | + | 48.0595i | −0.816233 | + | 2.51211i | ||||
\(367\) | −1.09868 | − | 3.38138i | −0.0573504 | − | 0.176506i | 0.918278 | − | 0.395937i | \(-0.129580\pi\) |
−0.975628 | + | 0.219430i | \(0.929580\pi\) | |||||||
\(368\) | 8.30919 | − | 6.03698i | 0.433146 | − | 0.314699i | ||||
\(369\) | 0.866302 | − | 0.629405i | 0.0450979 | − | 0.0327655i | ||||
\(370\) | −15.4568 | − | 47.5711i | −0.803559 | − | 2.47310i | ||||
\(371\) | 2.85915 | − | 8.79955i | 0.148440 | − | 0.456850i | ||||
\(372\) | 17.9480 | + | 13.0400i | 0.930559 | + | 0.676091i | ||||
\(373\) | −22.5048 | −1.16525 | −0.582627 | − | 0.812740i | \(-0.697975\pi\) | ||||
−0.582627 | + | 0.812740i | \(0.697975\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.3555 | 0.741314 | ||||||||
\(376\) | 51.7501 | + | 37.5987i | 2.66881 | + | 1.93900i | ||||
\(377\) | −1.27596 | + | 3.92701i | −0.0657154 | + | 0.202251i | ||||
\(378\) | −4.35481 | − | 13.4027i | −0.223987 | − | 0.689362i | ||||
\(379\) | −18.9550 | + | 13.7716i | −0.973651 | + | 0.707399i | −0.956281 | − | 0.292450i | \(-0.905529\pi\) |
−0.0173701 | + | 0.999849i | \(0.505529\pi\) | |||||||
\(380\) | 20.6712 | − | 15.0185i | 1.06041 | − | 0.770433i | ||||
\(381\) | 2.47214 | + | 7.60845i | 0.126651 | + | 0.389793i | ||||
\(382\) | −15.6640 | + | 48.2088i | −0.801439 | + | 2.46658i | ||||
\(383\) | 2.77193 | + | 2.01392i | 0.141639 | + | 0.102907i | 0.656348 | − | 0.754458i | \(-0.272100\pi\) |
−0.514709 | + | 0.857365i | \(0.672100\pi\) | |||||||
\(384\) | −90.8347 | −4.63539 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.41233 | −0.428177 | ||||||||
\(387\) | 0.604824 | + | 0.439431i | 0.0307449 | + | 0.0223375i | ||||
\(388\) | −14.5268 | + | 44.7088i | −0.737485 | + | 2.26974i | ||||
\(389\) | 2.48971 | + | 7.66252i | 0.126233 | + | 0.388505i | 0.994124 | − | 0.108250i | \(-0.0345247\pi\) |
−0.867891 | + | 0.496755i | \(0.834525\pi\) | |||||||
\(390\) | −24.6789 | + | 17.9303i | −1.24966 | + | 0.907934i | ||||
\(391\) | 1.20965 | − | 0.878861i | 0.0611746 | − | 0.0444459i | ||||
\(392\) | −3.09448 | − | 9.52384i | −0.156295 | − | 0.481026i | ||||
\(393\) | 3.41347 | − | 10.5056i | 0.172187 | − | 0.529937i | ||||
\(394\) | −11.0675 | − | 8.04097i | −0.557570 | − | 0.405098i | ||||
\(395\) | 40.0558 | 2.01543 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.3632 | −1.32313 | −0.661565 | − | 0.749888i | \(-0.730107\pi\) | ||||
−0.661565 | + | 0.749888i | \(0.730107\pi\) | |||||||
\(398\) | 35.0866 | + | 25.4919i | 1.75873 | + | 1.27779i | ||||
\(399\) | −0.941336 | + | 2.89714i | −0.0471258 | + | 0.145038i | ||||
\(400\) | 9.61434 | + | 29.5899i | 0.480717 | + | 1.47950i | ||||
\(401\) | 18.2816 | − | 13.2823i | 0.912937 | − | 0.663288i | −0.0288186 | − | 0.999585i | \(-0.509175\pi\) |
0.941756 | + | 0.336297i | \(0.109175\pi\) | |||||||
\(402\) | −25.2665 | + | 18.3572i | −1.26018 | + | 0.915574i | ||||
\(403\) | −1.65165 | − | 5.08326i | −0.0822746 | − | 0.253215i | ||||
\(404\) | 24.0731 | − | 74.0893i | 1.19768 | − | 3.68608i | ||||
\(405\) | −19.7562 | − | 14.3537i | −0.981694 | − | 0.713243i | ||||
\(406\) | −4.77551 | −0.237005 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −42.1204 | −2.08527 | ||||||||
\(409\) | 7.52781 | + | 5.46927i | 0.372226 | + | 0.270438i | 0.758133 | − | 0.652099i | \(-0.226112\pi\) |
−0.385907 | + | 0.922538i | \(0.626112\pi\) | |||||||
\(410\) | −23.2801 | + | 71.6489i | −1.14972 | + | 3.53849i | ||||
\(411\) | 5.11783 | + | 15.7511i | 0.252444 | + | 0.776943i | ||||
\(412\) | 13.3328 | − | 9.68683i | 0.656859 | − | 0.477236i | ||||
\(413\) | −1.42513 | + | 1.03542i | −0.0701260 | + | 0.0509496i | ||||
\(414\) | 0.0550856 | + | 0.169536i | 0.00270731 | + | 0.00833224i | ||||
\(415\) | 10.3678 | − | 31.9089i | 0.508937 | − | 1.56635i | ||||
\(416\) | 48.8079 | + | 35.4610i | 2.39300 | + | 1.73862i | ||||
\(417\) | −27.8709 | −1.36484 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.8463 | −0.676437 | −0.338218 | − | 0.941068i | \(-0.609824\pi\) | ||||
−0.338218 | + | 0.941068i | \(0.609824\pi\) | |||||||
\(420\) | −21.0570 | − | 15.2988i | −1.02748 | − | 0.746506i | ||||
\(421\) | −11.0496 | + | 34.0071i | −0.538524 | + | 1.65740i | 0.197387 | + | 0.980326i | \(0.436755\pi\) |
−0.735910 | + | 0.677079i | \(0.763245\pi\) | |||||||
\(422\) | 14.9775 | + | 46.0959i | 0.729092 | + | 2.24392i | ||||
\(423\) | −0.532716 | + | 0.387041i | −0.0259015 | + | 0.0188186i | ||||
\(424\) | −74.9579 | + | 54.4601i | −3.64028 | + | 2.64482i | ||||
\(425\) | 1.39965 | + | 4.30769i | 0.0678931 | + | 0.208954i | ||||
\(426\) | −12.1535 | + | 37.4045i | −0.588838 | + | 1.81226i | ||||
\(427\) | 8.40387 | + | 6.10577i | 0.406692 | + | 0.295479i | ||||
\(428\) | −19.4586 | −0.940565 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −52.5972 | −2.53646 | ||||||||
\(431\) | −25.3289 | − | 18.4025i | −1.22005 | − | 0.886417i | −0.223945 | − | 0.974602i | \(-0.571894\pi\) |
−0.996104 | + | 0.0881844i | \(0.971894\pi\) | |||||||
\(432\) | −25.8645 | + | 79.6028i | −1.24441 | + | 3.82989i | ||||
\(433\) | 6.67720 | + | 20.5503i | 0.320886 | + | 0.987585i | 0.973264 | + | 0.229691i | \(0.0737716\pi\) |
−0.652378 | + | 0.757894i | \(0.726228\pi\) | |||||||
\(434\) | 5.00101 | − | 3.63345i | 0.240056 | − | 0.174411i | ||||
\(435\) | −6.47214 | + | 4.70228i | −0.310315 | + | 0.225457i | ||||
\(436\) | 28.2244 | + | 86.8658i | 1.35170 | + | 4.16012i | ||||
\(437\) | −0.334626 | + | 1.02987i | −0.0160073 | + | 0.0492655i | ||||
\(438\) | −40.8818 | − | 29.7024i | −1.95341 | − | 1.41923i | ||||
\(439\) | −15.5877 | −0.743959 | −0.371979 | − | 0.928241i | \(-0.621321\pi\) | ||||
−0.371979 | + | 0.928241i | \(0.621321\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.103084 | 0.00490875 | ||||||||
\(442\) | 12.7377 | + | 9.25449i | 0.605871 | + | 0.440191i | ||||
\(443\) | 7.26010 | − | 22.3443i | 0.344938 | − | 1.06161i | −0.616680 | − | 0.787214i | \(-0.711523\pi\) |
0.961617 | − | 0.274395i | \(-0.0884774\pi\) | |||||||
\(444\) | −21.1227 | − | 65.0089i | −1.00244 | − | 3.08519i | ||||
\(445\) | −30.0622 | + | 21.8415i | −1.42508 | + | 1.03538i | ||||
\(446\) | −49.8086 | + | 36.1881i | −2.35851 | + | 1.71356i | ||||
\(447\) | −1.88267 | − | 5.79427i | −0.0890474 | − | 0.274060i | ||||
\(448\) | −11.4247 | + | 35.1616i | −0.539766 | + | 1.66123i | ||||
\(449\) | −18.4320 | − | 13.3916i | −0.869860 | − | 0.631990i | 0.0606894 | − | 0.998157i | \(-0.480670\pi\) |
−0.930549 | + | 0.366166i | \(0.880670\pi\) | |||||||
\(450\) | −0.539998 | −0.0254558 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 39.9634 | 1.87972 | ||||||||
\(453\) | −14.6769 | − | 10.6634i | −0.689580 | − | 0.501009i | ||||
\(454\) | 12.1782 | − | 37.4806i | 0.571550 | − | 1.75905i | ||||
\(455\) | 1.93776 | + | 5.96381i | 0.0908435 | + | 0.279588i | ||||
\(456\) | 24.6789 | − | 17.9303i | 1.15570 | − | 0.839662i | ||||
\(457\) | −11.7346 | + | 8.52570i | −0.548923 | + | 0.398816i | −0.827388 | − | 0.561631i | \(-0.810174\pi\) |
0.278466 | + | 0.960446i | \(0.410174\pi\) | |||||||
\(458\) | 3.30987 | + | 10.1867i | 0.154660 | + | 0.475995i | ||||
\(459\) | −3.76535 | + | 11.5885i | −0.175751 | + | 0.540907i | ||||
\(460\) | −7.48535 | − | 5.43842i | −0.349006 | − | 0.253568i | ||||
\(461\) | 31.1633 | 1.45142 | 0.725709 | − | 0.688002i | \(-0.241512\pi\) | ||||
0.725709 | + | 0.688002i | \(0.241512\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.87859 | −0.273201 | −0.136601 | − | 0.990626i | \(-0.543618\pi\) | ||||
−0.136601 | + | 0.990626i | \(0.543618\pi\) | |||||||
\(464\) | 22.9463 | + | 16.6715i | 1.06525 | + | 0.773953i | ||||
\(465\) | 3.20002 | − | 9.84865i | 0.148397 | − | 0.456720i | ||||
\(466\) | 5.70310 | + | 17.5524i | 0.264191 | + | 0.813097i | ||||
\(467\) | 19.1939 | − | 13.9452i | 0.888186 | − | 0.645305i | −0.0472185 | − | 0.998885i | \(-0.515036\pi\) |
0.935404 | + | 0.353580i | \(0.115036\pi\) | |||||||
\(468\) | −1.12035 | + | 0.813980i | −0.0517881 | + | 0.0376262i | ||||
\(469\) | 1.98390 | + | 6.10581i | 0.0916079 | + | 0.281940i | ||||
\(470\) | 14.3157 | − | 44.0591i | 0.660333 | − | 2.03230i | ||||
\(471\) | −16.1569 | − | 11.7387i | −0.744472 | − | 0.540890i | ||||
\(472\) | 17.6402 | 0.811954 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 74.1974 | 3.40800 | ||||||||
\(475\) | −2.65382 | − | 1.92811i | −0.121766 | − | 0.0884679i | ||||
\(476\) | −4.15133 | + | 12.7765i | −0.190276 | + | 0.585609i | ||||
\(477\) | −0.294732 | − | 0.907090i | −0.0134948 | − | 0.0415328i | ||||
\(478\) | 10.1462 | − | 7.37167i | 0.464078 | − | 0.337172i | ||||
\(479\) | 6.80572 | − | 4.94465i | 0.310961 | − | 0.225927i | −0.421348 | − | 0.906899i | \(-0.638443\pi\) |
0.732309 | + | 0.680973i | \(0.238443\pi\) | |||||||
\(480\) | 36.1201 | + | 111.166i | 1.64865 | + | 5.07402i | ||||
\(481\) | −5.08894 | + | 15.6621i | −0.232036 | + | 0.714132i | ||||
\(482\) | 8.27685 | + | 6.01348i | 0.377000 | + | 0.273907i | ||||
\(483\) | 1.10308 | 0.0501920 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.9431 | 0.996387 | ||||||||
\(486\) | −2.39234 | − | 1.73814i | −0.108519 | − | 0.0788436i | ||||
\(487\) | 7.66230 | − | 23.5821i | 0.347212 | − | 1.06861i | −0.613177 | − | 0.789946i | \(-0.710109\pi\) |
0.960389 | − | 0.278663i | \(-0.0898912\pi\) | |||||||
\(488\) | −32.1447 | − | 98.9313i | −1.45512 | − | 4.47841i | ||||
\(489\) | 13.8655 | − | 10.0739i | 0.627019 | − | 0.455556i | ||||
\(490\) | −5.86731 | + | 4.26285i | −0.265058 | + | 0.192576i | ||||
\(491\) | −3.77191 | − | 11.6088i | −0.170224 | − | 0.523896i | 0.829159 | − | 0.559013i | \(-0.188820\pi\) |
−0.999383 | + | 0.0351168i | \(0.988820\pi\) | |||||||
\(492\) | −31.8138 | + | 97.9129i | −1.43428 | + | 4.41425i | ||||
\(493\) | 3.34051 | + | 2.42703i | 0.150449 | + | 0.109308i | ||||
\(494\) | −11.4028 | −0.513034 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −36.7143 | −1.64852 | ||||||||
\(497\) | 6.54071 | + | 4.75210i | 0.293391 | + | 0.213161i | ||||
\(498\) | 19.2049 | − | 59.1065i | 0.860591 | − | 2.64863i | ||||
\(499\) | 6.89928 | + | 21.2338i | 0.308854 | + | 0.950555i | 0.978211 | + | 0.207614i | \(0.0665698\pi\) |
−0.669357 | + | 0.742941i | \(0.733430\pi\) | |||||||
\(500\) | −37.0931 | + | 26.9497i | −1.65886 | + | 1.20523i | ||||
\(501\) | 32.0722 | − | 23.3019i | 1.43288 | − | 1.04105i | ||||
\(502\) | −7.26145 | − | 22.3484i | −0.324094 | − | 0.997459i | ||||
\(503\) | 1.40338 | − | 4.31916i | 0.0625737 | − | 0.192582i | −0.914883 | − | 0.403720i | \(-0.867717\pi\) |
0.977456 | + | 0.211138i | \(0.0677170\pi\) | |||||||
\(504\) | −0.835128 | − | 0.606756i | −0.0371996 | − | 0.0270271i | ||||
\(505\) | −36.3632 | −1.61814 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.8569 | −0.570997 | ||||||||
\(508\) | −20.6712 | − | 15.0185i | −0.917137 | − | 0.666339i | ||||
\(509\) | 1.27358 | − | 3.91969i | 0.0564506 | − | 0.173737i | −0.918856 | − | 0.394594i | \(-0.870885\pi\) |
0.975306 | + | 0.220857i | \(0.0708853\pi\) | |||||||
\(510\) | 9.42650 | + | 29.0118i | 0.417412 | + | 1.28466i | ||||
\(511\) | −8.40387 | + | 6.10577i | −0.371765 | + | 0.270103i | ||||
\(512\) | 69.5103 | − | 50.5022i | 3.07195 | − | 2.23190i | ||||
\(513\) | −2.72697 | − | 8.39276i | −0.120399 | − | 0.370549i | ||||
\(514\) | 2.52065 | − | 7.75778i | 0.111181 | − | 0.342181i | ||||
\(515\) | −6.22347 | − | 4.52162i | −0.274239 | − | 0.199246i | ||||
\(516\) | −71.8776 | −3.16423 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −19.0462 | −0.836843 | ||||||||
\(519\) | 9.87500 | + | 7.17461i | 0.433464 | + | 0.314930i | ||||
\(520\) | 19.4046 | − | 59.7213i | 0.850949 | − | 2.61895i | ||||
\(521\) | 12.1407 | + | 37.3651i | 0.531892 | + | 1.63700i | 0.750271 | + | 0.661131i | \(0.229923\pi\) |
−0.218379 | + | 0.975864i | \(0.570077\pi\) | |||||||
\(522\) | −0.398261 | + | 0.289353i | −0.0174314 | + | 0.0126647i | ||||
\(523\) | −1.73260 | + | 1.25881i | −0.0757615 | + | 0.0550439i | −0.625021 | − | 0.780608i | \(-0.714910\pi\) |
0.549260 | + | 0.835652i | \(0.314910\pi\) | |||||||
\(524\) | 10.9022 | + | 33.5536i | 0.476265 | + | 1.46579i | ||||
\(525\) | −1.03259 | + | 3.17798i | −0.0450659 | + | 0.138698i | ||||
\(526\) | 35.7463 | + | 25.9712i | 1.55861 | + | 1.13240i | ||||
\(527\) | −5.34485 | −0.232825 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6079 | −0.982951 | ||||||||
\(530\) | 54.2867 | + | 39.4416i | 2.35806 | + | 1.71323i | ||||
\(531\) | −0.0561137 | + | 0.172700i | −0.00243513 | + | 0.00749455i | ||||
\(532\) | −3.00651 | − | 9.25310i | −0.130349 | − | 0.401173i | ||||
\(533\) | 20.0664 | − | 14.5791i | 0.869172 | − | 0.631490i | ||||
\(534\) | −55.6857 | + | 40.4580i | −2.40976 | + | 1.75079i | ||||
\(535\) | 2.80676 | + | 8.63833i | 0.121347 | + | 0.373467i | ||||
\(536\) | 19.8667 | − | 61.1433i | 0.858109 | − | 2.64099i | ||||
\(537\) | −19.8708 | − | 14.4370i | −0.857488 | − | 0.623001i | ||||
\(538\) | 18.7110 | 0.806687 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 75.4007 | 3.24473 | ||||||||
\(541\) | −34.8251 | − | 25.3019i | −1.49725 | − | 1.08782i | −0.971461 | − | 0.237200i | \(-0.923770\pi\) |
−0.525788 | − | 0.850615i | \(-0.676230\pi\) | |||||||
\(542\) | 2.95143 | − | 9.08356i | 0.126775 | − | 0.390172i | ||||
\(543\) | 1.72431 | + | 5.30687i | 0.0739970 | + | 0.227739i | ||||
\(544\) | 48.8079 | − | 35.4610i | 2.09262 | − | 1.52038i | ||||
\(545\) | 34.4915 | − | 25.0596i | 1.47746 | − | 1.07343i | ||||
\(546\) | 3.58941 | + | 11.0471i | 0.153613 | + | 0.472771i | ||||
\(547\) | 8.96445 | − | 27.5898i | 0.383292 | − | 1.17965i | −0.554419 | − | 0.832238i | \(-0.687060\pi\) |
0.937711 | − | 0.347415i | \(-0.112940\pi\) | |||||||
\(548\) | −42.7937 | − | 31.0914i | −1.82805 | − | 1.32816i | ||||
\(549\) | 1.07081 | 0.0457010 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.99042 | −0.127396 | ||||||||
\(552\) | −8.93659 | − | 6.49281i | −0.380366 | − | 0.276352i | ||||
\(553\) | 4.71325 | − | 14.5059i | 0.200428 | − | 0.616853i | ||||
\(554\) | −9.77837 | − | 30.0947i | −0.415443 | − | 1.27860i | ||||
\(555\) | −25.8129 | + | 18.7542i | −1.09570 | + | 0.796070i | ||||
\(556\) | 72.0156 | − | 52.3224i | 3.05414 | − | 2.21897i | ||||
\(557\) | 0.462045 | + | 1.42203i | 0.0195775 | + | 0.0602532i | 0.960368 | − | 0.278735i | \(-0.0899152\pi\) |
−0.940791 | + | 0.338989i | \(0.889915\pi\) | |||||||
\(558\) | 0.196912 | − | 0.606033i | 0.00833595 | − | 0.0256554i | ||||
\(559\) | 14.0097 | + | 10.1786i | 0.592547 | + | 0.430511i | ||||
\(560\) | 43.0741 | 1.82021 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −61.6560 | −2.60080 | ||||||||
\(563\) | 5.07312 | + | 3.68584i | 0.213806 | + | 0.155339i | 0.689534 | − | 0.724253i | \(-0.257815\pi\) |
−0.475728 | + | 0.879593i | \(0.657815\pi\) | |||||||
\(564\) | 19.5633 | − | 60.2097i | 0.823764 | − | 2.53529i | ||||
\(565\) | −5.76444 | − | 17.7411i | −0.242512 | − | 0.746374i | ||||
\(566\) | 27.6211 | − | 20.0679i | 1.16100 | − | 0.843518i | ||||
\(567\) | −7.52275 | + | 5.46559i | −0.315926 | + | 0.229533i | ||||
\(568\) | −25.0181 | − | 76.9979i | −1.04974 | − | 3.23076i | ||||
\(569\) | −2.41705 | + | 7.43892i | −0.101328 | + | 0.311856i | −0.988851 | − | 0.148908i | \(-0.952424\pi\) |
0.887523 | + | 0.460763i | \(0.152424\pi\) | |||||||
\(570\) | −17.8732 | − | 12.9856i | −0.748625 | − | 0.543908i | ||||
\(571\) | 15.1753 | 0.635068 | 0.317534 | − | 0.948247i | \(-0.397145\pi\) | ||||
0.317534 | + | 0.948247i | \(0.397145\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 32.3342 | 1.35078 | ||||||||
\(574\) | 23.2078 | + | 16.8614i | 0.968674 | + | 0.703783i | ||||
\(575\) | −0.367064 | + | 1.12971i | −0.0153076 | + | 0.0471121i | ||||
\(576\) | 1.17770 | + | 3.62458i | 0.0490708 | + | 0.151024i | ||||
\(577\) | −19.1288 | + | 13.8979i | −0.796343 | + | 0.578577i | −0.909839 | − | 0.414961i | \(-0.863795\pi\) |
0.113496 | + | 0.993538i | \(0.463795\pi\) | |||||||
\(578\) | −25.2428 | + | 18.3400i | −1.04996 | + | 0.762842i | ||||
\(579\) | 1.65822 | + | 5.10347i | 0.0689132 | + | 0.212093i | ||||
\(580\) | 7.89570 | − | 24.3005i | 0.327851 | − | 1.00902i | ||||
\(581\) | −10.3356 | − | 7.50926i | −0.428793 | − | 0.311536i | ||||
\(582\) | 40.6464 | 1.68485 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 104.022 | 4.30448 | ||||||||
\(585\) | 0.522956 | + | 0.379950i | 0.0216216 | + | 0.0157090i | ||||
\(586\) | 1.83788 | − | 5.65642i | 0.0759222 | − | 0.233665i | ||||
\(587\) | −3.13766 | − | 9.65672i | −0.129505 | − | 0.398576i | 0.865190 | − | 0.501444i | \(-0.167198\pi\) |
−0.994695 | + | 0.102869i | \(0.967198\pi\) | |||||||
\(588\) | −8.01806 | + | 5.82546i | −0.330659 | + | 0.240238i | ||||
\(589\) | 3.13162 | − | 2.27526i | 0.129036 | − | 0.0937503i | ||||
\(590\) | −3.94785 | − | 12.1502i | −0.162530 | − | 0.500217i | ||||
\(591\) | −2.69659 | + | 8.29925i | −0.110923 | + | 0.341386i | ||||
\(592\) | 91.5170 | + | 66.4910i | 3.76132 | + | 2.73276i | ||||
\(593\) | −33.7972 | −1.38788 | −0.693942 | − | 0.720031i | \(-0.744127\pi\) | ||||
−0.693942 | + | 0.720031i | \(0.744127\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.27072 | 0.257074 | ||||||||
\(596\) | 15.7423 | + | 11.4375i | 0.644830 | + | 0.468496i | ||||
\(597\) | 8.54887 | − | 26.3107i | 0.349882 | − | 1.07683i | ||||
\(598\) | 1.27596 | + | 3.92701i | 0.0521780 | + | 0.160587i | ||||
\(599\) | 14.8265 | − | 10.7721i | 0.605793 | − | 0.440135i | −0.242137 | − | 0.970242i | \(-0.577848\pi\) |
0.847931 | + | 0.530107i | \(0.177848\pi\) | |||||||
\(600\) | 27.0712 | − | 19.6684i | 1.10518 | − | 0.802959i | ||||
\(601\) | −14.9812 | − | 46.1074i | −0.611096 | − | 1.88076i | −0.447650 | − | 0.894209i | \(-0.647739\pi\) |
−0.163446 | − | 0.986552i | \(-0.552261\pi\) | |||||||
\(602\) | −6.18896 | + | 19.0477i | −0.252243 | + | 0.776325i | ||||
\(603\) | 0.535408 | + | 0.388997i | 0.0218035 | + | 0.0158412i | ||||
\(604\) | 57.9421 | 2.35763 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −67.3574 | −2.73621 | ||||||||
\(607\) | −16.6635 | − | 12.1068i | −0.676352 | − | 0.491398i | 0.195794 | − | 0.980645i | \(-0.437272\pi\) |
−0.872145 | + | 0.489247i | \(0.837272\pi\) | |||||||
\(608\) | −13.5018 | + | 41.5542i | −0.547569 | + | 1.68524i | ||||
\(609\) | 0.941336 | + | 2.89714i | 0.0381449 | + | 0.117398i | ||||
\(610\) | −60.9482 | + | 44.2815i | −2.46772 | + | 1.79290i | ||||
\(611\) | −12.3394 | + | 8.96513i | −0.499201 | + | 0.362690i | ||||
\(612\) | 0.427934 | + | 1.31705i | 0.0172982 | + | 0.0532385i | ||||
\(613\) | −5.81328 | + | 17.8914i | −0.234796 | + | 0.722628i | 0.762352 | + | 0.647162i | \(0.224044\pi\) |
−0.997148 | + | 0.0754656i | \(0.975956\pi\) | |||||||
\(614\) | 71.0944 | + | 51.6531i | 2.86914 | + | 2.08455i | ||||
\(615\) | 48.0558 | 1.93780 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.2062 | −0.571919 | −0.285959 | − | 0.958242i | \(-0.592312\pi\) | ||||
−0.285959 | + | 0.958242i | \(0.592312\pi\) | |||||||
\(618\) | −11.5281 | − | 8.37563i | −0.463727 | − | 0.336917i | ||||
\(619\) | −4.95155 | + | 15.2393i | −0.199019 | + | 0.612519i | 0.800887 | + | 0.598816i | \(0.204362\pi\) |
−0.999906 | + | 0.0137029i | \(0.995638\pi\) | |||||||
\(620\) | 10.2205 | + | 31.4554i | 0.410464 | + | 1.26328i | ||||
\(621\) | −2.58525 | + | 1.87829i | −0.103742 | + | 0.0753733i | ||||
\(622\) | −24.4174 | + | 17.7403i | −0.979049 | + | 0.711321i | ||||
\(623\) | 4.37238 | + | 13.4568i | 0.175176 | + | 0.539135i | ||||
\(624\) | 21.3186 | − | 65.6118i | 0.853426 | − | 2.62657i | ||||
\(625\) | 24.9875 | + | 18.1545i | 0.999501 | + | 0.726180i | ||||
\(626\) | −20.4402 | −0.816956 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 63.7851 | 2.54530 | ||||||||
\(629\) | 13.3230 | + | 9.67973i | 0.531223 | + | 0.385956i | ||||
\(630\) | −0.231022 | + | 0.711014i | −0.00920415 | + | 0.0283275i | ||||
\(631\) | 4.69568 | + | 14.4518i | 0.186932 | + | 0.575318i | 0.999976 | − | 0.00688413i | \(-0.00219131\pi\) |
−0.813044 | + | 0.582202i | \(0.802191\pi\) | |||||||
\(632\) | −123.567 | + | 89.7764i | −4.91522 | + | 3.57111i | ||||
\(633\) | 25.0125 | − | 18.1726i | 0.994157 | − | 0.722297i | ||||
\(634\) | 7.59234 | + | 23.3668i | 0.301531 | + | 0.928016i | ||||
\(635\) | −3.68556 | + | 11.3430i | −0.146257 | + | 0.450132i | ||||
\(636\) | 74.1863 | + | 53.8995i | 2.94168 | + | 2.13725i | ||||
\(637\) | 2.38776 | 0.0946063 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.833407 | 0.0329691 | ||||||||
\(640\) | −109.557 | − | 79.5978i | −4.33062 | − | 3.14638i | ||||
\(641\) | −3.16012 | + | 9.72586i | −0.124817 | + | 0.384149i | −0.993868 | − | 0.110575i | \(-0.964731\pi\) |
0.869050 | + | 0.494724i | \(0.164731\pi\) | |||||||
\(642\) | 5.19911 | + | 16.0012i | 0.205192 | + | 0.631517i | ||||
\(643\) | −16.6374 | + | 12.0878i | −0.656116 | + | 0.476696i | −0.865349 | − | 0.501170i | \(-0.832903\pi\) |
0.209233 | + | 0.977866i | \(0.432903\pi\) | |||||||
\(644\) | −2.85026 | + | 2.07083i | −0.112316 | + | 0.0816023i | ||||
\(645\) | 10.3678 | + | 31.9089i | 0.408233 | + | 1.25641i | ||||
\(646\) | −3.52364 | + | 10.8447i | −0.138636 | + | 0.426677i | ||||
\(647\) | 20.5929 | + | 14.9616i | 0.809590 | + | 0.588201i | 0.913712 | − | 0.406363i | \(-0.133203\pi\) |
−0.104122 | + | 0.994565i | \(0.533203\pi\) | |||||||
\(648\) | 93.1160 | 3.65794 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −12.5081 | −0.490609 | ||||||||
\(651\) | −3.19007 | − | 2.31772i | −0.125029 | − | 0.0908387i | ||||
\(652\) | −16.9152 | + | 52.0598i | −0.662452 | + | 2.03882i | ||||
\(653\) | −13.9834 | − | 43.0366i | −0.547214 | − | 1.68415i | −0.715666 | − | 0.698442i | \(-0.753877\pi\) |
0.168452 | − | 0.985710i | \(-0.446123\pi\) | |||||||
\(654\) | 63.8905 | − | 46.4191i | 2.49831 | − | 1.81513i | ||||
\(655\) | 13.3230 | − | 9.67973i | 0.520573 | − | 0.378219i | ||||
\(656\) | −52.6494 | − | 162.038i | −2.05561 | − | 6.32652i | ||||
\(657\) | −0.330898 | + | 1.01840i | −0.0129096 | + | 0.0397315i | ||||
\(658\) | −14.2712 | − | 10.3686i | −0.556349 | − | 0.404211i | ||||
\(659\) | 50.3544 | 1.96153 | 0.980765 | − | 0.195191i | \(-0.0625327\pi\) | ||||
0.980765 | + | 0.195191i | \(0.0625327\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.2234 | −0.903287 | −0.451644 | − | 0.892198i | \(-0.649162\pi\) | ||||
−0.451644 | + | 0.892198i | \(0.649162\pi\) | |||||||
\(662\) | 19.1280 | + | 13.8973i | 0.743430 | + | 0.540133i | ||||
\(663\) | 3.10355 | − | 9.55174i | 0.120532 | − | 0.370959i | ||||
\(664\) | 39.5336 | + | 121.672i | 1.53420 | + | 4.72178i | ||||
\(665\) | −3.67410 | + | 2.66939i | −0.142475 | + | 0.103514i | ||||
\(666\) | −1.58839 | + | 1.15403i | −0.0615488 | + | 0.0447178i | ||||
\(667\) | 0.334626 | + | 1.02987i | 0.0129568 | + | 0.0398769i | ||||
\(668\) | −39.1266 | + | 120.419i | −1.51385 | + | 4.65917i | ||||
\(669\) | 31.7722 | + | 23.0839i | 1.22838 | + | 0.892474i | ||||
\(670\) | −46.5606 | −1.79879 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 44.5081 | 1.71694 | ||||||||
\(673\) | −2.60867 | − | 1.89531i | −0.100557 | − | 0.0730587i | 0.536371 | − | 0.843983i | \(-0.319795\pi\) |
−0.636927 | + | 0.770924i | \(0.719795\pi\) | |||||||
\(674\) | −8.30266 | + | 25.5530i | −0.319806 | + | 0.984263i | ||||
\(675\) | −2.99132 | − | 9.20634i | −0.115136 | − | 0.354352i | ||||
\(676\) | 33.2211 | − | 24.1365i | 1.27773 | − | 0.928328i | ||||
\(677\) | 34.4818 | − | 25.0525i | 1.32524 | − | 0.962845i | 0.325392 | − | 0.945579i | \(-0.394504\pi\) |
0.999851 | − | 0.0172658i | \(-0.00549615\pi\) | |||||||
\(678\) | −10.6778 | − | 32.8628i | −0.410077 | − | 1.26209i | ||||
\(679\) | 2.58199 | − | 7.94653i | 0.0990875 | − | 0.304960i | ||||
\(680\) | −50.8020 | − | 36.9098i | −1.94817 | − | 1.41543i | ||||
\(681\) | −25.1387 | −0.963317 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.5877 | 0.596445 | 0.298223 | − | 0.954496i | \(-0.403606\pi\) | ||||
0.298223 | + | 0.954496i | \(0.403606\pi\) | |||||||
\(684\) | −0.811388 | − | 0.589508i | −0.0310242 | − | 0.0225404i | ||||
\(685\) | −7.62986 | + | 23.4823i | −0.291522 | + | 0.897212i | ||||
\(686\) | 0.853368 | + | 2.62640i | 0.0325817 | + | 0.100276i | ||||
\(687\) | 5.52750 | − | 4.01596i | 0.210887 | − | 0.153219i | ||||
\(688\) | 96.2339 | − | 69.9180i | 3.66888 | − | 2.66560i | ||||
\(689\) | −6.82694 | − | 21.0112i | −0.260086 | − | 0.800462i | ||||
\(690\) | −2.47214 | + | 7.60845i | −0.0941126 | + | 0.289649i | ||||
\(691\) | −33.9230 | − | 24.6465i | −1.29049 | − | 0.937596i | −0.290675 | − | 0.956822i | \(-0.593880\pi\) |
−0.999815 | + | 0.0192259i | \(0.993880\pi\) | |||||||
\(692\) | −38.9850 | −1.48199 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 40.9817 | 1.55564 | ||||||||
\(695\) | −33.6155 | − | 24.4231i | −1.27511 | − | 0.926420i | ||||
\(696\) | 9.42650 | − | 29.0118i | 0.357311 | − | 1.09969i | ||||
\(697\) | −7.66468 | − | 23.5895i | −0.290320 | − | 0.893514i | ||||
\(698\) | −36.2963 | + | 26.3708i | −1.37383 | + | 0.998149i | ||||
\(699\) | 9.52422 | − | 6.91975i | 0.360239 | − | 0.261729i | ||||
\(700\) | −3.29796 | − | 10.1501i | −0.124651 | − | 0.383637i | ||||
\(701\) | 4.76177 | − | 14.6552i | 0.179849 | − | 0.553520i | −0.819972 | − | 0.572403i | \(-0.806011\pi\) |
0.999822 | + | 0.0188835i | \(0.00601117\pi\) | |||||||
\(702\) | −27.2229 | − | 19.7786i | −1.02746 | − | 0.746495i | ||||
\(703\) | −11.9267 | −0.449824 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −29.5510 | −1.11296 | ||||||||
\(706\) | 68.9464 | + | 50.0925i | 2.59483 | + | 1.88526i | ||||
\(707\) | −4.27875 | + | 13.1686i | −0.160919 | + | 0.495257i | ||||
\(708\) | −5.39499 | − | 16.6041i | −0.202756 | − | 0.624020i | ||||
\(709\) | −2.31401 | + | 1.68123i | −0.0869044 | + | 0.0631398i | −0.630389 | − | 0.776279i | \(-0.717105\pi\) |
0.543485 | + | 0.839419i | \(0.317105\pi\) | |||||||
\(710\) | −47.4358 | + | 34.4641i | −1.78023 | + | 1.29342i | ||||
\(711\) | −0.485859 | − | 1.49532i | −0.0182211 | − | 0.0560789i | ||||
\(712\) | 43.7848 | − | 134.756i | 1.64090 | − | 5.05018i | ||||
\(713\) | −1.13401 | − | 0.823904i | −0.0424689 | − | 0.0308554i | ||||
\(714\) | 11.6156 | 0.434702 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 78.4469 | 2.93170 | ||||||||
\(717\) | −6.47214 | − | 4.70228i | −0.241706 | − | 0.175610i | ||||
\(718\) | −10.0645 | + | 30.9753i | −0.375603 | + | 1.15599i | ||||
\(719\) | −10.6526 | − | 32.7853i | −0.397275 | − | 1.22269i | −0.927176 | − | 0.374626i | \(-0.877771\pi\) |
0.529901 | − | 0.848059i | \(-0.322229\pi\) | |||||||
\(720\) | 3.59223 | − | 2.60991i | 0.133875 | − | 0.0972655i | ||||
\(721\) | −2.36977 | + | 1.72174i | −0.0882547 | + | 0.0641208i | ||||
\(722\) | 13.6621 | + | 42.0475i | 0.508450 | + | 1.56485i | ||||
\(723\) | 2.01666 | − | 6.20664i | 0.0750003 | − | 0.230827i | ||||
\(724\) | −14.4181 | − | 10.4754i | −0.535844 | − | 0.389314i | ||||
\(725\) | −3.28030 | −0.121827 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.3309 | −1.49579 | −0.747895 | − | 0.663817i | \(-0.768935\pi\) | ||||
−0.747895 | + | 0.663817i | \(0.768935\pi\) | |||||||
\(728\) | −19.3443 | − | 14.0545i | −0.716947 | − | 0.520893i | ||||
\(729\) | 8.03740 | − | 24.7366i | 0.297682 | − | 0.916170i | ||||
\(730\) | −23.2801 | − | 71.6489i | −0.861637 | − | 2.65184i | ||||
\(731\) | 14.0097 | − | 10.1786i | 0.518168 | − | 0.376471i | ||||
\(732\) | −83.2897 | + | 60.5135i | −3.07847 | + | 2.23664i | ||||
\(733\) | 8.88839 | + | 27.3557i | 0.328300 | + | 1.01040i | 0.969929 | + | 0.243389i | \(0.0782591\pi\) |
−0.641628 | + | 0.767016i | \(0.721741\pi\) | |||||||
\(734\) | 3.03406 | − | 9.33786i | 0.111989 | − | 0.344667i | ||||
\(735\) | 3.74267 | + | 2.71921i | 0.138051 | + | 0.100300i | ||||
\(736\) | 15.8217 | 0.583197 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 2.95710 | 0.108852 | ||||||||
\(739\) | 28.3981 | + | 20.6325i | 1.04464 | + | 0.758977i | 0.971186 | − | 0.238321i | \(-0.0765970\pi\) |
0.0734563 | + | 0.997298i | \(0.476597\pi\) | |||||||
\(740\) | 31.4905 | − | 96.9179i | 1.15761 | − | 3.56277i | ||||
\(741\) | 2.24768 | + | 6.91765i | 0.0825706 | + | 0.254126i | ||||
\(742\) | 20.6712 | − | 15.0185i | 0.758864 | − | 0.551347i | ||||
\(743\) | −26.2673 | + | 19.0843i | −0.963653 | + | 0.700135i | −0.953996 | − | 0.299818i | \(-0.903074\pi\) |
−0.00965687 | + | 0.999953i | \(0.503074\pi\) | |||||||
\(744\) | 12.2020 | + | 37.5539i | 0.447347 | + | 1.37679i | ||||
\(745\) | 2.80676 | − | 8.63833i | 0.102832 | − | 0.316484i | ||||
\(746\) | −50.2790 | − | 36.5298i | −1.84085 | − | 1.33745i | ||||
\(747\) | −1.31695 | −0.0481846 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.45856 | 0.126373 | ||||||||
\(750\) | 32.0722 | + | 23.3019i | 1.17111 | + | 0.850863i | ||||
\(751\) | −8.77095 | + | 26.9942i | −0.320056 | + | 0.985033i | 0.653566 | + | 0.756869i | \(0.273272\pi\) |
−0.973623 | + | 0.228163i | \(0.926728\pi\) | |||||||
\(752\) | 32.3757 | + | 99.6423i | 1.18062 | + | 3.63358i | ||||
\(753\) | −12.1267 | + | 8.81053i | −0.441920 | + | 0.321074i | ||||
\(754\) | −9.22502 | + | 6.70237i | −0.335955 | + | 0.244086i | ||||
\(755\) | −8.35774 | − | 25.7225i | −0.304169 | − | 0.936137i | ||||
\(756\) | 8.87217 | − | 27.3057i | 0.322678 | − | 0.993100i | ||||
\(757\) | 13.7907 | + | 10.0195i | 0.501231 | + | 0.364166i | 0.809487 | − | 0.587138i | \(-0.199745\pi\) |
−0.308256 | + | 0.951303i | \(0.599745\pi\) | |||||||
\(758\) | −64.7022 | −2.35009 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 45.4777 | 1.64965 | ||||||||
\(761\) | 22.6029 | + | 16.4220i | 0.819356 | + | 0.595297i | 0.916528 | − | 0.399971i | \(-0.130980\pi\) |
−0.0971719 | + | 0.995268i | \(0.530980\pi\) | |||||||
\(762\) | −6.82694 | + | 21.0112i | −0.247314 | + | 0.761155i | ||||
\(763\) | −5.01660 | − | 15.4395i | −0.181613 | − | 0.558948i | ||||
\(764\) | −83.5485 | + | 60.7015i | −3.02268 | + | 2.19610i | ||||
\(765\) | 0.522956 | − | 0.379950i | 0.0189075 | − | 0.0137371i | ||||
\(766\) | 2.92388 | + | 8.99879i | 0.105644 | + | 0.325140i | ||||
\(767\) | −1.29978 | + | 4.00030i | −0.0469322 | + | 0.144443i | ||||
\(768\) | −97.5608 | − | 70.8821i | −3.52042 | − | 2.55774i | ||||
\(769\) | −6.69512 | −0.241432 | −0.120716 | − | 0.992687i | \(-0.538519\pi\) | ||||
−0.120716 | + | 0.992687i | \(0.538519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.20324 | −0.187390 | ||||||||
\(772\) | −13.8655 | − | 10.0739i | −0.499030 | − | 0.362566i | ||||
\(773\) | 8.62596 | − | 26.5480i | 0.310254 | − | 0.954864i | −0.667410 | − | 0.744691i | \(-0.732597\pi\) |
0.977664 | − | 0.210174i | \(-0.0674030\pi\) | |||||||
\(774\) | 0.637981 | + | 1.96350i | 0.0229318 | + | 0.0705767i | ||||
\(775\) | 3.43520 | − | 2.49582i | 0.123396 | − | 0.0896524i | ||||
\(776\) | −67.6916 | + | 49.1808i | −2.42999 | + | 1.76549i | ||||
\(777\) | 3.75434 | + | 11.5547i | 0.134686 | + | 0.414522i | ||||
\(778\) | −6.87546 | + | 21.1605i | −0.246497 | + | 0.758641i | ||||
\(779\) | 14.5327 | + | 10.5586i | 0.520687 | + | 0.378301i | ||||
\(780\) | −62.1483 | −2.22527 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 4.12910 | 0.147656 | ||||||||
\(783\) | −7.13931 | − | 5.18701i | −0.255138 | − | 0.185369i | ||||
\(784\) | 5.06841 | − | 15.5990i | 0.181015 | − | 0.557105i | ||||
\(785\) | −9.20056 | − | 28.3164i | −0.328382 | − | 1.01066i | ||||
\(786\) | 24.6789 | − | 17.9303i | 0.880267 | − | 0.639551i | ||||
\(787\) | 17.6838 | − | 12.8480i | 0.630360 | − | 0.457983i | −0.226165 | − | 0.974089i | \(-0.572619\pi\) |
0.856525 | + | 0.516106i | \(0.172619\pi\) | |||||||
\(788\) | −8.61258 | − | 26.5068i | −0.306811 | − | 0.944266i | ||||
\(789\) | 8.70962 | − | 26.8054i | 0.310071 | − | 0.954299i | ||||
\(790\) | 89.4906 | + | 65.0187i | 3.18393 | + | 2.31326i | ||||
\(791\) | −7.10308 | −0.252557 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.8034 | 0.880795 | ||||||||
\(794\) | −58.8992 | − | 42.7928i | −2.09025 | − | 1.51866i | ||||
\(795\) | 13.2270 | − | 40.7085i | 0.469113 | − | 1.44378i | ||||
\(796\) | 27.3041 | + | 84.0332i | 0.967766 | + | 2.97848i | ||||
\(797\) | 28.0132 | − | 20.3528i | 0.992278 | − | 0.720932i | 0.0318591 | − | 0.999492i | \(-0.489857\pi\) |
0.960419 | + | 0.278560i | \(0.0898572\pi\) | |||||||
\(798\) | −6.80572 | + | 4.94465i | −0.240920 | + | 0.175039i | ||||
\(799\) | 4.71325 | + | 14.5059i | 0.166743 | + | 0.513182i | ||||
\(800\) | −14.8106 | + | 45.5824i | −0.523634 | + | 1.61158i | ||||
\(801\) | 1.18000 | + | 0.857322i | 0.0416933 | + | 0.0302920i | ||||
\(802\) | 62.4036 | 2.20355 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −63.6281 | −2.24399 | ||||||||
\(805\) | 1.33044 | + | 0.966625i | 0.0468920 | + | 0.0340690i | ||||
\(806\) | 4.56113 | − | 14.0377i | 0.160659 | − | 0.494457i | ||||
\(807\) | −3.68826 | − | 11.3513i | −0.129833 | − | 0.399584i | ||||
\(808\) | 112.175 | − | 81.5002i | 3.94632 | − | 2.86717i | ||||
\(809\) | 28.3530 | − | 20.5997i | 0.996838 | − | 0.724245i | 0.0354303 | − | 0.999372i | \(-0.488720\pi\) |
0.961408 | + | 0.275127i | \(0.0887198\pi\) | |||||||
\(810\) | −20.8393 | − | 64.1367i | −0.732217 | − | 2.25353i | ||||
\(811\) | 5.60607 | − | 17.2537i | 0.196856 | − | 0.605859i | −0.803094 | − | 0.595852i | \(-0.796814\pi\) |
0.999950 | − | 0.0100074i | \(-0.00318552\pi\) | |||||||
\(812\) | −7.87115 | − | 5.71873i | −0.276223 | − | 0.200688i | ||||
\(813\) | −6.09246 | −0.213672 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 25.5510 | 0.895013 | ||||||||
\(816\) | −55.8127 | − | 40.5503i | −1.95384 | − | 1.41955i | ||||
\(817\) | −3.87552 | + | 11.9276i | −0.135587 | + | 0.417294i | ||||
\(818\) | 7.94049 | + | 24.4383i | 0.277633 | + | 0.854466i | ||||
\(819\) | 0.199130 | − | 0.144677i | 0.00695818 | − | 0.00505541i | ||||
\(820\) | −124.171 | + | 90.2159i | −4.33626 | + | 3.15047i | ||||
\(821\) | 1.06875 | + | 3.28929i | 0.0372998 | + | 0.114797i | 0.967973 | − | 0.251055i | \(-0.0807776\pi\) |
−0.930673 | + | 0.365852i | \(0.880778\pi\) | |||||||
\(822\) | −14.1332 | + | 43.4975i | −0.492951 | + | 1.51715i | ||||
\(823\) | 27.1270 | + | 19.7089i | 0.945588 | + | 0.687010i | 0.949759 | − | 0.312982i | \(-0.101328\pi\) |
−0.00417155 | + | 0.999991i | \(0.501328\pi\) | |||||||
\(824\) | 29.3328 | 1.02186 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.86464 | −0.169263 | ||||||||
\(827\) | −21.2760 | − | 15.4579i | −0.739840 | − | 0.537525i | 0.152821 | − | 0.988254i | \(-0.451164\pi\) |
−0.892661 | + | 0.450729i | \(0.851164\pi\) | |||||||
\(828\) | −0.112227 | + | 0.345401i | −0.00390017 | + | 0.0120035i | ||||
\(829\) | −8.96208 | − | 27.5824i | −0.311266 | − | 0.957978i | −0.977264 | − | 0.212025i | \(-0.931994\pi\) |
0.665999 | − | 0.745953i | \(-0.268006\pi\) | |||||||
\(830\) | 74.9579 | − | 54.4601i | 2.60183 | − | 1.89034i | ||||
\(831\) | −16.3299 | + | 11.8644i | −0.566479 | + | 0.411571i | ||||
\(832\) | 27.2793 | + | 83.9572i | 0.945741 | + | 2.91069i | ||||
\(833\) | 0.737857 | − | 2.27089i | 0.0255652 | − | 0.0786817i | ||||
\(834\) | −62.2677 | − | 45.2401i | −2.15615 | − | 1.56654i | ||||
\(835\) | 59.1020 | 2.04531 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.4230 | 0.394835 | ||||||||
\(838\) | −30.9347 | − | 22.4754i | −1.06862 | − | 0.776399i | ||||
\(839\) | 9.01432 | − | 27.7432i | 0.311209 | − | 0.957803i | −0.666078 | − | 0.745882i | \(-0.732028\pi\) |
0.977287 | − | 0.211921i | \(-0.0679718\pi\) | |||||||
\(840\) | −14.3157 | − | 44.0591i | −0.493938 | − | 1.52019i | ||||
\(841\) | 21.0422 | − | 15.2881i | 0.725593 | − | 0.527174i | ||||
\(842\) | −79.8868 | + | 58.0412i | −2.75308 | + | 2.00023i | ||||
\(843\) | 12.1535 | + | 37.4045i | 0.418588 | + | 1.28828i | ||||
\(844\) | −30.5140 | + | 93.9126i | −1.05034 | + | 3.23260i | ||||
\(845\) | −15.5069 | − | 11.2665i | −0.533455 | − | 0.387578i | ||||
\(846\) | −1.81841 | −0.0625183 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −151.755 | −5.21129 | ||||||||
\(849\) | −17.6191 | − | 12.8010i | −0.604687 | − | 0.439331i | ||||
\(850\) | −3.86522 | + | 11.8959i | −0.132576 | + | 0.408027i | ||||
\(851\) | 1.33459 | + | 4.10746i | 0.0457493 | + | 0.140802i | ||||
\(852\) | −64.8241 | + | 47.0975i | −2.22084 | + | 1.61353i | ||||
\(853\) | 8.59324 | − | 6.24335i | 0.294227 | − | 0.213768i | −0.430872 | − | 0.902413i | \(-0.641794\pi\) |
0.725099 | + | 0.688645i | \(0.241794\pi\) | |||||||
\(854\) | 8.86458 | + | 27.2824i | 0.303340 | + | 0.933583i | ||||
\(855\) | −0.144666 | + | 0.445235i | −0.00494746 | + | 0.0152267i | ||||
\(856\) | −28.0194 | − | 20.3573i | −0.957684 | − | 0.695798i | ||||
\(857\) | −37.8463 | −1.29281 | −0.646403 | − | 0.762996i | \(-0.723727\pi\) | ||||
−0.646403 | + | 0.762996i | \(0.723727\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.0785 | −0.650950 | −0.325475 | − | 0.945551i | \(-0.605524\pi\) | ||||
−0.325475 | + | 0.945551i | \(0.605524\pi\) | |||||||
\(860\) | −86.6925 | − | 62.9858i | −2.95619 | − | 2.14780i | ||||
\(861\) | 5.65459 | − | 17.4030i | 0.192708 | − | 0.593094i | ||||
\(862\) | −26.7174 | − | 82.2278i | −0.909999 | − | 2.80069i | ||||
\(863\) | −9.04103 | + | 6.56869i | −0.307760 | + | 0.223601i | −0.730935 | − | 0.682447i | \(-0.760916\pi\) |
0.423175 | + | 0.906048i | \(0.360916\pi\) | |||||||
\(864\) | −104.312 | + | 75.7869i | −3.54875 | + | 2.57832i | ||||
\(865\) | 5.62332 | + | 17.3068i | 0.191198 | + | 0.588448i | ||||
\(866\) | −18.4395 | + | 56.7509i | −0.626599 | + | 1.92847i | ||||
\(867\) | 16.1020 | + | 11.6988i | 0.546853 | + | 0.397312i | ||||
\(868\) | 12.5939 | 0.427466 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −22.0925 | −0.749004 | ||||||||
\(871\) | 12.4018 | + | 9.01043i | 0.420219 | + | 0.305307i | ||||
\(872\) | −50.2360 | + | 154.611i | −1.70121 | + | 5.23578i | ||||
\(873\) | −0.266161 | − | 0.819158i | −0.00900817 | − | 0.0277243i | ||||
\(874\) | −2.41930 | + | 1.75772i | −0.0818339 | + | 0.0594558i | ||||
\(875\) | 6.59293 | − | 4.79005i | 0.222882 | − | 0.161933i | ||||
\(876\) | −31.8138 | − | 97.9129i | −1.07489 | − | 3.30817i | ||||
\(877\) | 1.81034 | − | 5.57165i | 0.0611308 | − | 0.188141i | −0.915827 | − | 0.401572i | \(-0.868464\pi\) |
0.976958 | + | 0.213431i | \(0.0684638\pi\) | |||||||
\(878\) | −34.8251 | − | 25.3019i | −1.17529 | − | 0.853899i | ||||
\(879\) | −3.79383 | −0.127963 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.9065 | −0.872812 | −0.436406 | − | 0.899750i | \(-0.643749\pi\) | ||||
−0.436406 | + | 0.899750i | \(0.643749\pi\) | |||||||
\(882\) | 0.230304 | + | 0.167326i | 0.00775474 | + | 0.00563415i | ||||
\(883\) | 4.14760 | − | 12.7650i | 0.139578 | − | 0.429577i | −0.856696 | − | 0.515822i | \(-0.827487\pi\) |
0.996274 | + | 0.0862449i | \(0.0274868\pi\) | |||||||
\(884\) | 9.91236 | + | 30.5071i | 0.333389 | + | 1.02606i | ||||
\(885\) | −6.59293 | + | 4.79005i | −0.221619 | + | 0.161016i | ||||
\(886\) | 52.4894 | − | 38.1358i | 1.76342 | − | 1.28120i | ||||
\(887\) | 15.3294 | + | 47.1789i | 0.514709 | + | 1.58411i | 0.783810 | + | 0.621001i | \(0.213274\pi\) |
−0.269101 | + | 0.963112i | \(0.586726\pi\) | |||||||
\(888\) | 37.5958 | − | 115.708i | 1.26163 | − | 3.88291i | ||||
\(889\) | 3.67410 | + | 2.66939i | 0.123225 | + | 0.0895284i | ||||
\(890\) | −102.616 | −3.43971 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −125.432 | −4.19977 | ||||||||
\(893\) | −8.93659 | − | 6.49281i | −0.299051 | − | 0.217274i | ||||
\(894\) | 5.19911 | − | 16.0012i | 0.173884 | − | 0.535161i | ||||
\(895\) | −11.3154 | − | 34.8253i | −0.378233 | − | 1.16408i | ||||
\(896\) | −41.7169 | + | 30.3091i | −1.39367 | + | 1.01256i | ||||
\(897\) | 2.13086 | − | 1.54816i | 0.0711475 | − | 0.0516917i | ||||
\(898\) | −19.4425 | − | 59.8377i | −0.648803 | − | 1.99681i | ||||
\(899\) | 1.19617 | − | 3.68144i | 0.0398946 | − | 0.122783i | ||||
\(900\) | −0.890043 | − | 0.646654i | −0.0296681 | − | 0.0215551i | ||||
\(901\) | −22.0925 | −0.736006 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.7755 | 0.425142 | ||||||||
\(904\) | 57.5453 | + | 41.8091i | 1.91393 | + | 1.39055i | ||||
\(905\) | −2.57066 | + | 7.91168i | −0.0854517 | + | 0.262993i | ||||
\(906\) | −15.4815 | − | 47.6471i | −0.514338 | − | 1.58297i | ||||
\(907\) | 38.7338 | − | 28.1417i | 1.28613 | − | 0.934430i | 0.286413 | − | 0.958106i | \(-0.407537\pi\) |
0.999720 | + | 0.0236757i | \(0.00753690\pi\) | |||||||
\(908\) | 64.9559 | − | 47.1932i | 2.15564 | − | 1.56616i | ||||
\(909\) | 0.441069 | + | 1.35747i | 0.0146293 | + | 0.0450245i | ||||
\(910\) | −5.35123 | + | 16.4694i | −0.177392 | + | 0.545955i | ||||
\(911\) | −18.4554 | − | 13.4086i | −0.611455 | − | 0.444248i | 0.238471 | − | 0.971150i | \(-0.423354\pi\) |
−0.849927 | + | 0.526901i | \(0.823354\pi\) | |||||||
\(912\) | 49.9634 | 1.65445 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −40.0558 | −1.32493 | ||||||||
\(915\) | 38.8780 | + | 28.2465i | 1.28527 | + | 0.933800i | ||||
\(916\) | −6.74329 | + | 20.7537i | −0.222805 | + | 0.685722i | ||||
\(917\) | −1.93776 | − | 5.96381i | −0.0639904 | − | 0.196942i | ||||
\(918\) | −27.2229 | + | 19.7786i | −0.898489 | + | 0.652791i | ||||
\(919\) | −32.3607 | + | 23.5114i | −1.06748 | + | 0.775570i | −0.975458 | − | 0.220187i | \(-0.929333\pi\) |
−0.0920227 | + | 0.995757i | \(0.529333\pi\) | |||||||
\(920\) | −5.08894 | − | 15.6621i | −0.167777 | − | 0.516365i | ||||
\(921\) | 17.3222 | − | 53.3122i | 0.570786 | − | 1.75670i | ||||
\(922\) | 69.6233 | + | 50.5843i | 2.29292 | + | 1.66590i | ||||
\(923\) | 19.3044 | 0.635413 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.0829 | −0.430162 | ||||||||
\(926\) | −13.1336 | − | 9.54215i | −0.431598 | − | 0.313574i | ||||
\(927\) | −0.0933083 | + | 0.287173i | −0.00306465 | + | 0.00943201i | ||||
\(928\) | 13.5018 | + | 41.5542i | 0.443217 | + | 1.36408i | ||||
\(929\) | 12.9739 | − | 9.42610i | 0.425660 | − | 0.309260i | −0.354251 | − | 0.935150i | \(-0.615264\pi\) |
0.779911 | + | 0.625890i | \(0.215264\pi\) | |||||||
\(930\) | 23.1357 | − | 16.8090i | 0.758648 | − | 0.551190i | ||||
\(931\) | 0.534377 | + | 1.64464i | 0.0175135 | + | 0.0539011i | ||||
\(932\) | −11.6191 | + | 35.7599i | −0.380596 | + | 1.17135i | ||||
\(933\) | 15.5755 | + | 11.3163i | 0.509919 | + | 0.370478i | ||||
\(934\) | 65.5177 | 2.14380 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.46482 | −0.0805652 | ||||||||
\(937\) | −20.4721 | − | 14.8738i | −0.668794 | − | 0.485907i | 0.200827 | − | 0.979627i | \(-0.435637\pi\) |
−0.869621 | + | 0.493720i | \(0.835637\pi\) | |||||||
\(938\) | −5.47865 | + | 16.8615i | −0.178884 | + | 0.550549i | ||||
\(939\) | 4.02913 | + | 12.4004i | 0.131486 | + | 0.404671i | ||||
\(940\) | 76.3569 | − | 55.4766i | 2.49049 | − | 1.80945i | ||||
\(941\) | 16.6086 | − | 12.0669i | 0.541425 | − | 0.393368i | −0.283189 | − | 0.959064i | \(-0.591392\pi\) |
0.824614 | + | 0.565696i | \(0.191392\pi\) | |||||||
\(942\) | −17.0427 | − | 52.4519i | −0.555280 | − | 1.70898i | ||||
\(943\) | 2.01009 | − | 6.18643i | 0.0654576 | − | 0.201458i | ||||
\(944\) | 23.3746 | + | 16.9826i | 0.760777 | + | 0.552737i | ||||
\(945\) | −13.4017 | −0.435958 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.6907 | −0.542376 | −0.271188 | − | 0.962526i | \(-0.587417\pi\) | ||||
−0.271188 | + | 0.962526i | \(0.587417\pi\) | |||||||
\(948\) | 122.295 | + | 88.8523i | 3.97195 | + | 2.88579i | ||||
\(949\) | −7.66468 | + | 23.5895i | −0.248806 | + | 0.765746i | ||||
\(950\) | −2.79931 | − | 8.61538i | −0.0908215 | − | 0.279520i | ||||
\(951\) | 12.6793 | − | 9.21202i | 0.411153 | − | 0.298720i | ||||
\(952\) | −19.3443 | + | 14.0545i | −0.626952 | + | 0.455508i | ||||
\(953\) | −17.4496 | − | 53.7044i | −0.565249 | − | 1.73966i | −0.667212 | − | 0.744868i | \(-0.732512\pi\) |
0.101963 | − | 0.994788i | \(-0.467488\pi\) | |||||||
\(954\) | 0.813918 | − | 2.50498i | 0.0263516 | − | 0.0811018i | ||||
\(955\) | 38.9988 | + | 28.3343i | 1.26197 | + | 0.916875i | ||||
\(956\) | 25.5510 | 0.826379 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23.2311 | 0.750564 | ||||||||
\(959\) | 7.60614 | + | 5.52619i | 0.245615 | + | 0.178450i | ||||
\(960\) | −52.8528 | + | 162.664i | −1.70582 | + | 5.24997i | ||||
\(961\) | −8.03116 | − | 24.7174i | −0.259070 | − | 0.797334i | ||||
\(962\) | −36.7923 | + | 26.7311i | −1.18623 | + | 0.861847i | ||||
\(963\) | 0.288432 | − | 0.209558i | 0.00929459 | − | 0.00675292i | ||||
\(964\) | 6.44096 | + | 19.8232i | 0.207449 | + | 0.638464i | ||||
\(965\) | −2.47214 | + | 7.60845i | −0.0795809 | + | 0.244925i | ||||
\(966\) | 2.46445 | + | 1.79053i | 0.0792924 | + | 0.0576093i | ||||
\(967\) | −47.3082 | −1.52133 | −0.760665 | − | 0.649145i | \(-0.775127\pi\) | ||||
−0.760665 | + | 0.649145i | \(0.775127\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.27365 | 0.233663 | ||||||||
\(970\) | 49.0242 | + | 35.6182i | 1.57407 | + | 1.14363i | ||||
\(971\) | −7.79820 | + | 24.0004i | −0.250256 | + | 0.770209i | 0.744471 | + | 0.667655i | \(0.232702\pi\) |
−0.994727 | + | 0.102555i | \(0.967298\pi\) | |||||||
\(972\) | −1.86170 | − | 5.72972i | −0.0597140 | − | 0.183781i | ||||
\(973\) | −12.8001 | + | 9.29978i | −0.410351 | + | 0.298137i | ||||
\(974\) | 55.3973 | − | 40.2485i | 1.77504 | − | 1.28964i | ||||
\(975\) | 2.46557 | + | 7.58824i | 0.0789614 | + | 0.243018i | ||||
\(976\) | 52.6494 | − | 162.038i | 1.68527 | − | 5.18671i | ||||
\(977\) | −5.74652 | − | 4.17509i | −0.183847 | − | 0.133573i | 0.492055 | − | 0.870564i | \(-0.336246\pi\) |
−0.675902 | + | 0.736991i | \(0.736246\pi\) | |||||||
\(978\) | 47.3295 | 1.51343 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −14.7755 | −0.471986 | ||||||||
\(981\) | −1.35386 | − | 0.983640i | −0.0432256 | − | 0.0314052i | ||||
\(982\) | 10.4164 | − | 32.0582i | 0.332399 | − | 1.02302i | ||||
\(983\) | −4.38473 | − | 13.4948i | −0.139851 | − | 0.430418i | 0.856462 | − | 0.516210i | \(-0.172658\pi\) |
−0.996313 | + | 0.0857927i | \(0.972658\pi\) | |||||||
\(984\) | −148.246 | + | 107.707i | −4.72590 | + | 3.43356i | ||||
\(985\) | −10.5250 | + | 7.64684i | −0.335354 | + | 0.243649i | ||||
\(986\) | 3.52364 | + | 10.8447i | 0.112216 | + | 0.345364i | ||||
\(987\) | −3.47718 | + | 10.7017i | −0.110680 | + | 0.340638i | ||||
\(988\) | −18.7944 | − | 13.6549i | −0.597929 | − | 0.434421i | ||||
\(989\) | 4.54144 | 0.144409 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.23407 | 0.134500 | 0.0672499 | − | 0.997736i | \(-0.478578\pi\) | ||||
0.0672499 | + | 0.997736i | \(0.478578\pi\) | |||||||
\(992\) | −45.7558 | − | 33.2435i | −1.45275 | − | 1.05548i | ||||
\(993\) | 4.66054 | − | 14.3437i | 0.147898 | − | 0.455183i | ||||
\(994\) | 6.89928 | + | 21.2338i | 0.218832 | + | 0.673495i | ||||
\(995\) | 33.3668 | − | 24.2424i | 1.05780 | − | 0.768536i | ||||
\(996\) | 102.435 | − | 74.4233i | 3.24577 | − | 2.35819i | ||||
\(997\) | 8.56122 | + | 26.3487i | 0.271137 | + | 0.834473i | 0.990216 | + | 0.139545i | \(0.0445639\pi\) |
−0.719079 | + | 0.694928i | \(0.755436\pi\) | |||||||
\(998\) | −19.0527 | + | 58.6383i | −0.603104 | + | 1.85616i | ||||
\(999\) | −28.4738 | − | 20.6874i | −0.900871 | − | 0.654521i |
(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 | 847.2.f.u.323.3 | 12 | ||
11.2 | odd | 10 | 847.2.f.t.148.3 | 12 | |||
11.3 | even | 5 | inner | 847.2.f.u.729.3 | 12 | ||
11.4 | even | 5 | inner | 847.2.f.u.372.1 | 12 | ||
11.5 | even | 5 | 847.2.a.i.1.1 | ✓ | 3 | ||
11.6 | odd | 10 | 847.2.a.j.1.3 | yes | 3 | ||
11.7 | odd | 10 | 847.2.f.t.372.3 | 12 | |||
11.8 | odd | 10 | 847.2.f.t.729.1 | 12 | |||
11.9 | even | 5 | inner | 847.2.f.u.148.1 | 12 | ||
11.10 | odd | 2 | 847.2.f.t.323.1 | 12 | |||
33.5 | odd | 10 | 7623.2.a.ce.1.3 | 3 | |||
33.17 | even | 10 | 7623.2.a.bz.1.1 | 3 | |||
77.6 | even | 10 | 5929.2.a.y.1.3 | 3 | |||
77.27 | odd | 10 | 5929.2.a.t.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.i.1.1 | ✓ | 3 | 11.5 | even | 5 | ||
847.2.a.j.1.3 | yes | 3 | 11.6 | odd | 10 | ||
847.2.f.t.148.3 | 12 | 11.2 | odd | 10 | |||
847.2.f.t.323.1 | 12 | 11.10 | odd | 2 | |||
847.2.f.t.372.3 | 12 | 11.7 | odd | 10 | |||
847.2.f.t.729.1 | 12 | 11.8 | odd | 10 | |||
847.2.f.u.148.1 | 12 | 11.9 | even | 5 | inner | ||
847.2.f.u.323.3 | 12 | 1.1 | even | 1 | trivial | ||
847.2.f.u.372.1 | 12 | 11.4 | even | 5 | inner | ||
847.2.f.u.729.3 | 12 | 11.3 | even | 5 | inner | ||
5929.2.a.t.1.1 | 3 | 77.27 | odd | 10 | |||
5929.2.a.y.1.3 | 3 | 77.6 | even | 10 | |||
7623.2.a.bz.1.1 | 3 | 33.17 | even | 10 | |||
7623.2.a.ce.1.3 | 3 | 33.5 | odd | 10 |