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 | 729.1 | ||
Root | \(0.544351 - 1.67534i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.729 |
Dual form | 847.2.f.t.323.1 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 | −0.662834 | + | 0.748766i | \(0.730647\pi\) |
−0.916946 | + | 0.399011i | \(0.869353\pi\) | |||||||
\(3\) | 0.544351 | + | 1.67534i | 0.314281 | + | 0.967258i | 0.976049 | + | 0.217550i | \(0.0698064\pi\) |
−0.661768 | + | 0.749709i | \(0.730194\pi\) | |||||||
\(4\) | 1.73859 | − | 5.35083i | 0.869295 | − | 2.67542i | ||||
\(5\) | 2.12464 | + | 1.54364i | 0.950167 | + | 0.690337i | 0.950846 | − | 0.309663i | \(-0.100216\pi\) |
−0.000679067 | 1.00000i | \(0.500216\pi\) | ||||||||
\(6\) | −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 | \(-0.592573\pi\) |
0.822510 | + | 0.568750i | \(0.192573\pi\) | |||||||
\(14\) | 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 | \(-0.206492\pi\) |
−0.328348 | + | 0.944557i | \(0.606492\pi\) | |||||||
\(18\) | 0.0879683 | − | 0.270739i | 0.0207343 | − | 0.0638137i | ||||
\(19\) | −0.534377 | − | 1.64464i | −0.122595 | − | 0.377307i | 0.870861 | − | 0.491530i | \(-0.163562\pi\) |
−0.993455 | + | 0.114223i | \(0.963562\pi\) | |||||||
\(20\) | 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 | \(-0.848670\pi\) |
0.988333 | + | 0.152306i | \(0.0486701\pi\) | |||||||
\(30\) | −3.94785 | − | 12.1502i | −0.720775 | − | 2.21832i | ||||
\(31\) | 1.81094 | − | 1.31572i | 0.325254 | − | 0.236311i | −0.413160 | − | 0.910658i | \(-0.635575\pi\) |
0.738414 | + | 0.674347i | \(0.235575\pi\) | |||||||
\(32\) | 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 | 0.608264 | + | 0.793735i | \(0.291866\pi\) |
−0.958641 | + | 0.284617i | \(0.908134\pi\) | |||||||
\(38\) | 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 | 0.806876 | + | 0.590721i | \(0.201157\pi\) |
−0.305559 | + | 0.952173i | \(0.598843\pi\) | |||||||
\(42\) | −3.93558 | + | 2.85936i | −0.607273 | + | 0.441209i | ||||
\(43\) | 7.25240 | 1.10598 | 0.552990 | − | 0.833188i | \(-0.313487\pi\) | ||||
0.552990 | + | 0.833188i | \(0.313487\pi\) | |||||||
\(44\) | 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 | 0.985506 | + | 0.169640i | \(0.0542603\pi\) |
−0.697580 | + | 0.716507i | \(0.745740\pi\) | |||||||
\(48\) | 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 | 0.0602454 | − | 0.998184i | \(-0.480812\pi\) |
0.967946 | + | 0.251159i | \(0.0808117\pi\) | |||||||
\(54\) | −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 | −0.980218 | − | 0.197923i | \(-0.936580\pi\) |
0.909349 | + | 0.416034i | \(0.136580\pi\) | |||||||
\(60\) | 21.0570 | + | 15.2988i | 2.71845 | + | 1.97507i | ||||
\(61\) | 8.40387 | + | 6.10577i | 1.07601 | + | 0.781764i | 0.976982 | − | 0.213321i | \(-0.0684282\pi\) |
0.0990233 | + | 0.995085i | \(0.468428\pi\) | |||||||
\(62\) | −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 | 0.127609 | − | 0.991825i | \(-0.459270\pi\) |
−0.903848 | + | 0.427854i | \(0.859270\pi\) | |||||||
\(72\) | −0.835128 | − | 0.606756i | −0.0984208 | − | 0.0715069i | ||||
\(73\) | 3.20999 | − | 9.87934i | 0.375701 | − | 1.15629i | −0.567303 | − | 0.823509i | \(-0.692013\pi\) |
0.943004 | − | 0.332780i | \(-0.107987\pi\) | |||||||
\(74\) | −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 | −0.392247 | + | 0.919860i | \(0.628302\pi\) |
−0.996050 | + | 0.0887962i | \(0.971698\pi\) | |||||||
\(80\) | −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 | \(-0.547328\pi\) |
−0.986341 | + | 0.164718i | \(0.947328\pi\) | |||||||
\(84\) | 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 | −0.189111 | − | 0.981956i | \(-0.560561\pi\) |
0.875457 | + | 0.483296i | \(0.160561\pi\) | |||||||
\(98\) | 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 | \(-0.458103\pi\) |
0.983387 | + | 0.181523i | \(0.0581026\pi\) | |||||||
\(102\) | −3.58941 | − | 11.0471i | −0.355404 | − | 1.09382i | ||||
\(103\) | −0.905170 | + | 2.78583i | −0.0891891 | + | 0.274496i | −0.985696 | − | 0.168534i | \(-0.946097\pi\) |
0.896507 | + | 0.443030i | \(0.146097\pi\) | |||||||
\(104\) | 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 | \(-0.0465352\pi\) |
−0.886012 | + | 0.463662i | \(0.846535\pi\) | |||||||
\(108\) | 23.2277 | − | 16.8759i | 2.23508 | − | 1.62388i | ||||
\(109\) | −16.2341 | −1.55494 | −0.777471 | − | 0.628919i | \(-0.783498\pi\) | ||||
−0.777471 | + | 0.628919i | \(0.783498\pi\) | |||||||
\(110\) | 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 | 0.999649 | + | 0.0264888i | \(0.00843265\pi\) |
−0.793163 | + | 0.609009i | \(0.791567\pi\) | |||||||
\(114\) | −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 | \(-0.235420\pi\) |
−0.412718 | + | 0.910859i | \(0.635420\pi\) | |||||||
\(128\) | 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 | \(-0.588326\pi\) | ||||
−0.273938 | + | 0.961747i | \(0.588326\pi\) | |||||||
\(132\) | 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 | 0.213379 | − | 0.976970i | \(-0.431553\pi\) |
−0.863216 | + | 0.504836i | \(0.831553\pi\) | |||||||
\(138\) | 2.46445 | + | 1.79053i | 0.209788 | + | 0.152420i | ||||
\(139\) | 4.88919 | − | 15.0474i | 0.414695 | − | 1.27630i | −0.497828 | − | 0.867276i | \(-0.665869\pi\) |
0.912523 | − | 0.409025i | \(-0.134131\pi\) | |||||||
\(140\) | −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 | \(-0.345247\pi\) |
−0.696469 | + | 0.717587i | \(0.745247\pi\) | |||||||
\(150\) | 2.85155 | − | 8.77618i | 0.232828 | − | 0.716572i | ||||
\(151\) | −3.18245 | − | 9.79457i | −0.258984 | − | 0.797071i | −0.993018 | − | 0.117959i | \(-0.962365\pi\) |
0.734034 | − | 0.679112i | \(-0.237635\pi\) | |||||||
\(152\) | 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 | 0.987966 | + | 0.154674i | \(0.0494327\pi\) |
−0.708366 | + | 0.705845i | \(0.750567\pi\) | |||||||
\(158\) | 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 | −0.235187 | − | 0.971950i | \(-0.575570\pi\) |
0.851703 | + | 0.524025i | \(0.175570\pi\) | |||||||
\(164\) | 58.4436 | 4.56368 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 35.2803 | 2.73828 | ||||||||
\(167\) | −18.2068 | + | 13.2280i | −1.40888 | + | 1.02361i | −0.415397 | + | 0.909640i | \(0.636357\pi\) |
−0.993484 | + | 0.113972i | \(0.963643\pi\) | |||||||
\(168\) | 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 | \(-0.0151533\pi\) |
−0.836072 | + | 0.548620i | \(0.815153\pi\) | |||||||
\(174\) | −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 | 0.972757 | + | 0.231828i | \(0.0744706\pi\) |
−0.650712 | + | 0.759325i | \(0.725529\pi\) | |||||||
\(180\) | −0.470668 | + | 1.44857i | −0.0350815 | + | 0.107970i | ||||
\(181\) | −2.56267 | − | 1.86189i | −0.190482 | − | 0.138393i | 0.488457 | − | 0.872588i | \(-0.337560\pi\) |
−0.678939 | + | 0.734195i | \(0.737560\pi\) | |||||||
\(182\) | 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 | −0.505859 | − | 0.862616i | \(-0.668824\pi\) |
0.916281 | − | 0.400535i | \(-0.131176\pi\) | |||||||
\(192\) | −52.6885 | − | 38.2805i | −3.80247 | − | 2.76265i | ||||
\(193\) | 2.46445 | + | 1.79053i | 0.177395 | + | 0.128885i | 0.672939 | − | 0.739698i | \(-0.265031\pi\) |
−0.495544 | + | 0.868583i | \(0.665031\pi\) | |||||||
\(194\) | −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 | \(-0.443532\pi\) | ||||
0.176471 | + | 0.984306i | \(0.443532\pi\) | |||||||
\(198\) | 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 | \(-0.906480\pi\) |
−0.0203551 | + | 0.999793i | \(0.506480\pi\) | |||||||
\(212\) | −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 | −0.863525 | − | 0.504305i | \(-0.831749\pi\) |
0.402183 | − | 0.915559i | \(-0.368251\pi\) | |||||||
\(224\) | 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 | −0.691291 | − | 0.722576i | \(-0.742958\pi\) |
0.983986 | − | 0.178246i | \(-0.0570423\pi\) | |||||||
\(228\) | −5.29615 | − | 16.2999i | −0.350746 | − | 1.07948i | ||||
\(229\) | 3.13785 | − | 2.27978i | 0.207355 | − | 0.150652i | −0.479261 | − | 0.877672i | \(-0.659095\pi\) |
0.686616 | + | 0.727020i | \(0.259095\pi\) | |||||||
\(230\) | 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 | \(-0.770250\pi\) |
0.396426 | + | 0.918067i | \(0.370250\pi\) | |||||||
\(234\) | −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 | \(-0.146923\pi\) |
−0.986130 | + | 0.165974i | \(0.946923\pi\) | |||||||
\(240\) | 61.3862 | − | 44.5997i | 3.96246 | − | 2.87890i | ||||
\(241\) | −3.70470 | −0.238641 | −0.119320 | − | 0.992856i | \(-0.538072\pi\) | ||||
−0.119320 | + | 0.992856i | \(0.538072\pi\) | |||||||
\(242\) | 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 | −0.783453 | − | 0.621451i | \(-0.786543\pi\) |
0.348935 | + | 0.937147i | \(0.386543\pi\) | |||||||
\(252\) | 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 | −0.975480 | − | 0.220086i | \(-0.929366\pi\) |
0.918544 | + | 0.395320i | \(0.129366\pi\) | |||||||
\(258\) | −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 | \(-0.664210\pi\) | ||||
−0.493301 | + | 0.869859i | \(0.664210\pi\) | |||||||
\(264\) | 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 | 0.742216 | − | 0.670160i | \(-0.233775\pi\) |
−0.408003 | + | 0.912981i | \(0.633775\pi\) | |||||||
\(270\) | −29.9414 | − | 21.7537i | −1.82217 | − | 1.32389i | ||||
\(271\) | 1.06875 | − | 3.28929i | 0.0649222 | − | 0.199810i | −0.913334 | − | 0.407212i | \(-0.866501\pi\) |
0.978256 | + | 0.207402i | \(0.0665009\pi\) | |||||||
\(272\) | −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 | \(-0.588137\pi\) |
0.830356 | + | 0.557233i | \(0.188137\pi\) | |||||||
\(278\) | 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 | \(-0.0680287\pi\) |
0.100272 | + | 0.994960i | \(0.468029\pi\) | |||||||
\(282\) | 9.60244 | − | 29.5533i | 0.571817 | − | 1.75987i | ||||
\(283\) | −3.82043 | − | 11.7581i | −0.227101 | − | 0.698945i | −0.998072 | − | 0.0620743i | \(-0.980228\pi\) |
0.770970 | − | 0.636871i | \(-0.219772\pi\) | |||||||
\(284\) | −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 | \(-0.879962\pi\) |
0.968613 | + | 0.248574i | \(0.0799620\pi\) | |||||||
\(294\) | 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 | \(-0.862453\pi\) | ||||
−0.908081 | + | 0.418794i | \(0.862453\pi\) | |||||||
\(308\) | 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 | −1.00000 | 0.000895774i | \(-0.999715\pi\) | |
0.808490 | − | 0.588510i | \(-0.200285\pi\) | |||||||
\(312\) | −13.0159 | + | 40.0588i | −0.736881 | + | 2.26789i | ||||
\(313\) | −5.98811 | − | 4.35062i | −0.338468 | − | 0.245911i | 0.405547 | − | 0.914074i | \(-0.367081\pi\) |
−0.744015 | + | 0.668163i | \(0.767081\pi\) | |||||||
\(314\) | −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 | −0.367010 | − | 0.930217i | \(-0.619619\pi\) |
0.771276 | + | 0.636500i | \(0.219619\pi\) | |||||||
\(318\) | −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 | \(-0.985370\pi\) |
0.835169 | + | 0.549994i | \(0.185370\pi\) | |||||||
\(338\) | −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 | \(-0.430409\pi\) |
−0.861396 | + | 0.507934i | \(0.830409\pi\) | |||||||
\(348\) | 5.29615 | − | 16.2999i | 0.283903 | − | 0.873764i | ||||
\(349\) | 5.02033 | + | 15.4510i | 0.268732 | + | 0.827073i | 0.990810 | + | 0.135261i | \(0.0431873\pi\) |
−0.722078 | + | 0.691812i | \(0.756813\pi\) | |||||||
\(350\) | −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 | 0.807648 | + | 0.589665i | \(0.200740\pi\) |
−0.999997 | + | 0.00232497i | \(0.999260\pi\) | |||||||
\(360\) | −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 | −0.975628 | − | 0.219430i | \(-0.929580\pi\) |
0.918278 | + | 0.395937i | \(0.129580\pi\) | |||||||
\(368\) | 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 | \(-0.302025\pi\) | ||||
0.582627 | + | 0.812740i | \(0.302025\pi\) | |||||||
\(374\) | 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 | −0.0173701 | − | 0.999849i | \(-0.505529\pi\) |
−0.956281 | + | 0.292450i | \(0.905529\pi\) | |||||||
\(380\) | −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 | −0.514709 | − | 0.857365i | \(-0.672100\pi\) |
0.656348 | + | 0.754458i | \(0.272100\pi\) | |||||||
\(384\) | 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 | −0.867891 | − | 0.496755i | \(-0.834525\pi\) |
0.994124 | + | 0.108250i | \(0.0345247\pi\) | |||||||
\(390\) | −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 | 0.941756 | − | 0.336297i | \(-0.109175\pi\) |
−0.0288186 | + | 0.999585i | \(0.509175\pi\) | |||||||
\(402\) | 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 | \(-0.773888\pi\) |
0.385907 | + | 0.922538i | \(0.373888\pi\) | |||||||
\(410\) | −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 | −0.735910 | − | 0.677079i | \(-0.763245\pi\) |
0.197387 | − | 0.980326i | \(-0.436755\pi\) | |||||||
\(422\) | 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 | \(-0.428106\pi\) |
0.996104 | + | 0.0881844i | \(0.0281065\pi\) | |||||||
\(432\) | −25.8645 | − | 79.6028i | −1.24441 | − | 3.82989i | ||||
\(433\) | 6.67720 | − | 20.5503i | 0.320886 | − | 0.987585i | −0.652378 | − | 0.757894i | \(-0.726228\pi\) |
0.973264 | − | 0.229691i | \(-0.0737716\pi\) | |||||||
\(434\) | 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 | \(-0.378679\pi\) | ||||
0.371979 | + | 0.928241i | \(0.378679\pi\) | |||||||
\(440\) | 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 | 0.961617 | + | 0.274395i | \(0.0884774\pi\) |
−0.616680 | + | 0.787214i | \(0.711523\pi\) | |||||||
\(444\) | −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 | −0.930549 | − | 0.366166i | \(-0.880670\pi\) |
0.0606894 | + | 0.998157i | \(0.480670\pi\) | |||||||
\(450\) | 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 | \(-0.189826\pi\) |
−0.278466 | + | 0.960446i | \(0.589826\pi\) | |||||||
\(458\) | −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 | \(-0.758488\pi\) | ||||
−0.725709 | + | 0.688002i | \(0.758488\pi\) | |||||||
\(462\) | 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 | 0.935404 | − | 0.353580i | \(-0.115036\pi\) |
−0.0472185 | + | 0.998885i | \(0.515036\pi\) | |||||||
\(468\) | 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 | \(-0.361557\pi\) |
−0.732309 | + | 0.680973i | \(0.761557\pi\) | |||||||
\(480\) | −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 | 0.960389 | + | 0.278663i | \(0.0898912\pi\) |
−0.613177 | + | 0.789946i | \(0.710109\pi\) | |||||||
\(488\) | −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 | \(-0.811180\pi\) |
0.999383 | + | 0.0351168i | \(0.0111803\pi\) | |||||||
\(492\) | 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 | −0.669357 | − | 0.742941i | \(-0.733430\pi\) |
0.978211 | − | 0.207614i | \(-0.0665698\pi\) | |||||||
\(500\) | −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 | \(-0.132283\pi\) |
−0.977456 | + | 0.211138i | \(0.932283\pi\) | |||||||
\(504\) | −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 | 0.975306 | − | 0.220857i | \(-0.0708853\pi\) |
−0.918856 | + | 0.394594i | \(0.870885\pi\) | |||||||
\(510\) | 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 | −0.218379 | − | 0.975864i | \(-0.570077\pi\) |
0.750271 | − | 0.661131i | \(-0.229923\pi\) | |||||||
\(522\) | −0.398261 | − | 0.289353i | −0.0174314 | − | 0.0126647i | ||||
\(523\) | 1.73260 | + | 1.25881i | 0.0757615 | + | 0.0550439i | 0.625021 | − | 0.780608i | \(-0.285090\pi\) |
−0.549260 | + | 0.835652i | \(0.685090\pi\) | |||||||
\(524\) | −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 | 0.525788 | − | 0.850615i | \(-0.323770\pi\) |
0.971461 | − | 0.237200i | \(-0.0762296\pi\) | |||||||
\(542\) | 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 | −0.937711 | − | 0.347415i | \(-0.887060\pi\) |
0.554419 | − | 0.832238i | \(-0.312940\pi\) | |||||||
\(548\) | −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 | \(-0.910085\pi\) |
0.940791 | + | 0.338989i | \(0.110085\pi\) | |||||||
\(558\) | −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 | \(-0.742185\pi\) |
0.475728 | + | 0.879593i | \(0.342185\pi\) | |||||||
\(564\) | 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 | \(-0.0475757\pi\) |
−0.887523 | + | 0.460763i | \(0.847576\pi\) | |||||||
\(570\) | −17.8732 | + | 12.9856i | −0.748625 | + | 0.543908i | ||||
\(571\) | −15.1753 | −0.635068 | −0.317534 | − | 0.948247i | \(-0.602855\pi\) | ||||
−0.317534 | + | 0.948247i | \(0.602855\pi\) | |||||||
\(572\) | 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 | 0.113496 | − | 0.993538i | \(-0.463795\pi\) |
−0.909839 | + | 0.414961i | \(0.863795\pi\) | |||||||
\(578\) | 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 | −0.994695 | − | 0.102869i | \(-0.967198\pi\) |
0.865190 | + | 0.501444i | \(0.167198\pi\) | |||||||
\(588\) | −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 | \(-0.255873\pi\) | ||||
0.693942 | + | 0.720031i | \(0.255873\pi\) | |||||||
\(594\) | 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 | 0.847931 | − | 0.530107i | \(-0.177848\pi\) |
−0.242137 | + | 0.970242i | \(0.577848\pi\) | |||||||
\(600\) | −27.0712 | − | 19.6684i | −1.10518 | − | 0.802959i | ||||
\(601\) | 14.9812 | − | 46.1074i | 0.611096 | − | 1.88076i | 0.163446 | − | 0.986552i | \(-0.447739\pi\) |
0.447650 | − | 0.894209i | \(-0.352261\pi\) | |||||||
\(602\) | 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 | \(-0.562728\pi\) |
0.872145 | + | 0.489247i | \(0.162728\pi\) | |||||||
\(608\) | −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 | 0.997148 | + | 0.0754656i | \(0.0240443\pi\) |
−0.762352 | + | 0.647162i | \(0.775956\pi\) | |||||||
\(614\) | 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 | −0.999906 | − | 0.0137029i | \(-0.995638\pi\) |
0.800887 | − | 0.598816i | \(-0.204362\pi\) | |||||||
\(620\) | 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 | −0.813044 | − | 0.582202i | \(-0.802191\pi\) |
0.999976 | + | 0.00688413i | \(0.00219131\pi\) | |||||||
\(632\) | −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 | 0.869050 | − | 0.494724i | \(-0.164731\pi\) |
−0.993868 | + | 0.110575i | \(0.964731\pi\) | |||||||
\(642\) | 5.19911 | − | 16.0012i | 0.205192 | − | 0.631517i | ||||
\(643\) | −16.6374 | − | 12.0878i | −0.656116 | − | 0.476696i | 0.209233 | − | 0.977866i | \(-0.432903\pi\) |
−0.865349 | + | 0.501170i | \(0.832903\pi\) | |||||||
\(644\) | 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 | −0.104122 | − | 0.994565i | \(-0.533203\pi\) |
0.913712 | + | 0.406363i | \(0.133203\pi\) | |||||||
\(648\) | −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 | 0.168452 | + | 0.985710i | \(0.446123\pi\) |
−0.715666 | + | 0.698442i | \(0.753877\pi\) | |||||||
\(654\) | 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 | \(-0.937467\pi\) | ||||
−0.980765 | + | 0.195191i | \(0.937467\pi\) | |||||||
\(660\) | 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 | \(-0.680205\pi\) |
0.636927 | + | 0.770924i | \(0.280205\pi\) | |||||||
\(674\) | −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 | −0.999851 | − | 0.0172658i | \(-0.994504\pi\) |
−0.325392 | − | 0.945579i | \(-0.605496\pi\) | |||||||
\(678\) | 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 | −0.999815 | − | 0.0192259i | \(-0.993880\pi\) |
−0.290675 | + | 0.956822i | \(0.593880\pi\) | |||||||
\(692\) | 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 | \(-0.193989\pi\) |
−0.999822 | + | 0.0188835i | \(0.993989\pi\) | |||||||
\(702\) | −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 | 0.543485 | − | 0.839419i | \(-0.317105\pi\) |
−0.630389 | + | 0.776279i | \(0.717105\pi\) | |||||||
\(710\) | 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 | 0.529901 | + | 0.848059i | \(0.322229\pi\) |
−0.927176 | + | 0.374626i | \(0.877771\pi\) | |||||||
\(720\) | 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 | 0.641628 | + | 0.767016i | \(0.278259\pi\) |
−0.969929 | + | 0.243389i | \(0.921741\pi\) | |||||||
\(734\) | −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 | \(-0.923403\pi\) |
−0.0734563 | + | 0.997298i | \(0.523403\pi\) | |||||||
\(740\) | 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 | \(-0.0969261\pi\) |
0.00965687 | + | 0.999953i | \(0.496926\pi\) | |||||||
\(744\) | −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 | −0.973623 | − | 0.228163i | \(-0.926728\pi\) |
0.653566 | − | 0.756869i | \(-0.273272\pi\) | |||||||
\(752\) | 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 | −0.308256 | − | 0.951303i | \(-0.599745\pi\) |
0.809487 | + | 0.587138i | \(0.199745\pi\) | |||||||
\(758\) | 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 | \(-0.869020\pi\) |
0.0971719 | + | 0.995268i | \(0.469020\pi\) | |||||||
\(762\) | −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 | \(-0.461481\pi\) | ||||
0.120716 | + | 0.992687i | \(0.461481\pi\) | |||||||
\(770\) | 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 | 0.977664 | + | 0.210174i | \(0.0674030\pi\) |
−0.667410 | + | 0.744691i | \(0.732597\pi\) | |||||||
\(774\) | 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 | \(-0.427381\pi\) |
−0.856525 | + | 0.516106i | \(0.827381\pi\) | |||||||
\(788\) | 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 | 0.960419 | − | 0.278560i | \(-0.0898572\pi\) |
0.0318591 | + | 0.999492i | \(0.489857\pi\) | |||||||
\(798\) | 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 | \(-0.511280\pi\) |
−0.961408 | + | 0.275127i | \(0.911280\pi\) | |||||||
\(810\) | 20.8393 | − | 64.1367i | 0.732217 | − | 2.25353i | ||||
\(811\) | −5.60607 | − | 17.2537i | −0.196856 | − | 0.605859i | −0.999950 | − | 0.0100074i | \(-0.996814\pi\) |
0.803094 | − | 0.595852i | \(-0.203186\pi\) | |||||||
\(812\) | −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 | \(-0.919222\pi\) |
0.930673 | + | 0.365852i | \(0.119222\pi\) | |||||||
\(822\) | 14.1332 | + | 43.4975i | 0.492951 | + | 1.51715i | ||||
\(823\) | 27.1270 | − | 19.7089i | 0.945588 | − | 0.687010i | −0.00417155 | − | 0.999991i | \(-0.501328\pi\) |
0.949759 | + | 0.312982i | \(0.101328\pi\) | |||||||
\(824\) | −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 | \(-0.548836\pi\) |
0.892661 | + | 0.450729i | \(0.148836\pi\) | |||||||
\(828\) | −0.112227 | − | 0.345401i | −0.00390017 | − | 0.0120035i | ||||
\(829\) | −8.96208 | + | 27.5824i | −0.311266 | + | 0.957978i | 0.665999 | + | 0.745953i | \(0.268006\pi\) |
−0.977264 | + | 0.212025i | \(0.931994\pi\) | |||||||
\(830\) | 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 | 0.977287 | + | 0.211921i | \(0.0679718\pi\) |
−0.666078 | + | 0.745882i | \(0.732028\pi\) | |||||||
\(840\) | −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 | \(-0.358206\pi\) |
−0.725099 | + | 0.688645i | \(0.758206\pi\) | |||||||
\(854\) | −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 | \(-0.276273\pi\) | ||||
0.646403 | + | 0.762996i | \(0.276273\pi\) | |||||||
\(858\) | 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 | 0.423175 | − | 0.906048i | \(-0.360916\pi\) |
−0.730935 | + | 0.682447i | \(0.760916\pi\) | |||||||
\(864\) | 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 | \(-0.131536\pi\) |
−0.976958 | + | 0.213431i | \(0.931536\pi\) | |||||||
\(878\) | −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 | 0.996274 | − | 0.0862449i | \(-0.0274868\pi\) |
−0.856696 | + | 0.515822i | \(0.827487\pi\) | |||||||
\(884\) | 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 | 0.269101 | + | 0.963112i | \(0.413274\pi\) |
−0.783810 | + | 0.621001i | \(0.786726\pi\) | |||||||
\(888\) | −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 | 0.999720 | − | 0.0236757i | \(-0.00753690\pi\) |
0.286413 | + | 0.958106i | \(0.407537\pi\) | |||||||
\(908\) | −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 | −0.849927 | − | 0.526901i | \(-0.823354\pi\) |
0.238471 | + | 0.971150i | \(0.423354\pi\) | |||||||
\(912\) | −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 | \(-0.0706668\pi\) |
0.0920227 | + | 0.995757i | \(0.470667\pi\) | |||||||
\(920\) | 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 | 0.779911 | − | 0.625890i | \(-0.215264\pi\) |
−0.354251 | + | 0.935150i | \(0.615264\pi\) | |||||||
\(930\) | −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 | \(-0.564363\pi\) |
0.869621 | + | 0.493720i | \(0.164363\pi\) | |||||||
\(938\) | −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 | \(-0.408608\pi\) |
−0.824614 | + | 0.565696i | \(0.808608\pi\) | |||||||
\(942\) | 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 | −0.101963 | − | 0.994788i | \(-0.532512\pi\) |
0.667212 | − | 0.744868i | \(-0.267488\pi\) | |||||||
\(954\) | −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 | \(-0.224873\pi\) | ||||
0.760665 | + | 0.649145i | \(0.224873\pi\) | |||||||
\(968\) | 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 | −0.994727 | − | 0.102555i | \(-0.967298\pi\) |
0.744471 | − | 0.667655i | \(-0.232702\pi\) | |||||||
\(972\) | −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 | −0.675902 | − | 0.736991i | \(-0.736246\pi\) |
0.492055 | + | 0.870564i | \(0.336246\pi\) | |||||||
\(978\) | −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 | −0.996313 | − | 0.0857927i | \(-0.972658\pi\) |
0.856462 | + | 0.516210i | \(0.172658\pi\) | |||||||
\(984\) | −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 | 0.719079 | + | 0.694928i | \(0.244564\pi\) |
−0.990216 | + | 0.139545i | \(0.955436\pi\) | |||||||
\(998\) | 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.t.729.1 | 12 | ||
11.2 | odd | 10 | 847.2.a.i.1.1 | ✓ | 3 | ||
11.3 | even | 5 | inner | 847.2.f.t.148.3 | 12 | ||
11.4 | even | 5 | inner | 847.2.f.t.323.1 | 12 | ||
11.5 | even | 5 | inner | 847.2.f.t.372.3 | 12 | ||
11.6 | odd | 10 | 847.2.f.u.372.1 | 12 | |||
11.7 | odd | 10 | 847.2.f.u.323.3 | 12 | |||
11.8 | odd | 10 | 847.2.f.u.148.1 | 12 | |||
11.9 | even | 5 | 847.2.a.j.1.3 | yes | 3 | ||
11.10 | odd | 2 | 847.2.f.u.729.3 | 12 | |||
33.2 | even | 10 | 7623.2.a.ce.1.3 | 3 | |||
33.20 | odd | 10 | 7623.2.a.bz.1.1 | 3 | |||
77.13 | even | 10 | 5929.2.a.t.1.1 | 3 | |||
77.20 | odd | 10 | 5929.2.a.y.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.i.1.1 | ✓ | 3 | 11.2 | odd | 10 | ||
847.2.a.j.1.3 | yes | 3 | 11.9 | even | 5 | ||
847.2.f.t.148.3 | 12 | 11.3 | even | 5 | inner | ||
847.2.f.t.323.1 | 12 | 11.4 | even | 5 | inner | ||
847.2.f.t.372.3 | 12 | 11.5 | even | 5 | inner | ||
847.2.f.t.729.1 | 12 | 1.1 | even | 1 | trivial | ||
847.2.f.u.148.1 | 12 | 11.8 | odd | 10 | |||
847.2.f.u.323.3 | 12 | 11.7 | odd | 10 | |||
847.2.f.u.372.1 | 12 | 11.6 | odd | 10 | |||
847.2.f.u.729.3 | 12 | 11.10 | odd | 2 | |||
5929.2.a.t.1.1 | 3 | 77.13 | even | 10 | |||
5929.2.a.y.1.3 | 3 | 77.20 | odd | 10 | |||
7623.2.a.bz.1.1 | 3 | 33.20 | odd | 10 | |||
7623.2.a.ce.1.3 | 3 | 33.2 | even | 10 |