Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(136,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 2, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.136");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.et (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 273) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 136.3 | ||
Character | \(\chi\) | \(=\) | 819.136 |
Dual form | 819.2.et.c.271.3 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.09987 | + | 1.09987i | −0.777729 | + | 0.777729i | −0.979444 | − | 0.201716i | \(-0.935348\pi\) |
0.201716 | + | 0.979444i | \(0.435348\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 0.419447i | − | 0.209723i | ||||||
\(5\) | −0.745735 | + | 2.78312i | −0.333503 | + | 1.24465i | 0.571981 | + | 0.820267i | \(0.306175\pi\) |
−0.905483 | + | 0.424382i | \(0.860491\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.80794 | + | 1.93167i | −0.683336 | + | 0.730104i | ||||
\(8\) | −1.73841 | − | 1.73841i | −0.614621 | − | 0.614621i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.24087 | − | 3.88130i | −0.708624 | − | 1.22737i | ||||
\(11\) | −1.41711 | + | 5.28871i | −0.427273 | + | 1.59461i | 0.331635 | + | 0.943408i | \(0.392400\pi\) |
−0.758908 | + | 0.651198i | \(0.774267\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.662549 | + | 3.54415i | −0.183758 | + | 0.982972i | ||||
\(14\) | −0.136094 | − | 4.11310i | −0.0363725 | − | 1.09927i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.66296 | 1.16574 | ||||||||
\(17\) | 4.36465 | 1.05858 | 0.529292 | − | 0.848440i | \(-0.322458\pi\) | ||||
0.529292 | + | 0.848440i | \(0.322458\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.39486 | + | 0.373751i | −0.320003 | + | 0.0857444i | −0.415245 | − | 0.909710i | \(-0.636304\pi\) |
0.0952423 | + | 0.995454i | \(0.469637\pi\) | |||||||
\(20\) | 1.16737 | + | 0.312796i | 0.261032 | + | 0.0699433i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.25828 | − | 7.37555i | −0.907868 | − | 1.57247i | ||||
\(23\) | − | 8.37225i | − | 1.74573i | −0.487958 | − | 0.872867i | \(-0.662258\pi\) | ||
0.487958 | − | 0.872867i | \(-0.337742\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.85951 | − | 1.65094i | −0.571901 | − | 0.330187i | ||||
\(26\) | −3.16940 | − | 4.62684i | −0.621571 | − | 0.907399i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.810234 | + | 0.758334i | 0.153120 | + | 0.143312i | ||||
\(29\) | −0.882488 | + | 1.52851i | −0.163874 | + | 0.283838i | −0.936255 | − | 0.351322i | \(-0.885732\pi\) |
0.772381 | + | 0.635160i | \(0.219066\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.770818 | − | 0.206540i | 0.138443 | − | 0.0370957i | −0.188932 | − | 0.981990i | \(-0.560503\pi\) |
0.327375 | + | 0.944894i | \(0.393836\pi\) | |||||||
\(32\) | −1.65185 | + | 1.65185i | −0.292008 | + | 0.292008i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.80057 | + | 4.80057i | −0.823290 | + | 0.823290i | ||||
\(35\) | −4.02784 | − | 6.47222i | −0.680829 | − | 1.09401i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.86358 | + | 3.86358i | 0.635169 | + | 0.635169i | 0.949360 | − | 0.314191i | \(-0.101733\pi\) |
−0.314191 | + | 0.949360i | \(0.601733\pi\) | |||||||
\(38\) | 1.12309 | − | 1.94525i | 0.182189 | − | 0.315561i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.13459 | − | 3.54181i | 0.969965 | − | 0.560009i | ||||
\(41\) | −3.88124 | + | 1.03997i | −0.606147 | + | 0.162417i | −0.548823 | − | 0.835939i | \(-0.684924\pi\) |
−0.0573248 | + | 0.998356i | \(0.518257\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.58033 | + | 3.22180i | −0.850992 | + | 0.491320i | −0.860985 | − | 0.508630i | \(-0.830152\pi\) |
0.00999354 | + | 0.999950i | \(0.496819\pi\) | |||||||
\(44\) | 2.21833 | + | 0.594400i | 0.334426 | + | 0.0896092i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.20842 | + | 9.20842i | 1.35771 | + | 1.35771i | ||||
\(47\) | 8.52304 | + | 2.28374i | 1.24321 | + | 0.333118i | 0.819711 | − | 0.572777i | \(-0.194134\pi\) |
0.423502 | + | 0.905895i | \(0.360800\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.462723 | − | 6.98469i | −0.0661033 | − | 0.997813i | ||||
\(50\) | 4.96092 | − | 1.32927i | 0.701580 | − | 0.187988i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.48658 | + | 0.277904i | 0.206152 | + | 0.0385384i | ||||
\(53\) | −0.139208 | + | 0.241116i | −0.0191217 | + | 0.0331198i | −0.875428 | − | 0.483349i | \(-0.839420\pi\) |
0.856306 | + | 0.516468i | \(0.172754\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.6623 | − | 7.88795i | −1.84223 | − | 1.06361i | ||||
\(56\) | 6.50098 | − | 0.215103i | 0.868729 | − | 0.0287444i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.710548 | − | 2.65180i | −0.0932995 | − | 0.348198i | ||||
\(59\) | 5.16369 | − | 5.16369i | 0.672255 | − | 0.672255i | −0.285980 | − | 0.958235i | \(-0.592319\pi\) |
0.958235 | + | 0.285980i | \(0.0923192\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.10703 | + | 2.37119i | 0.525851 | + | 0.303600i | 0.739325 | − | 0.673348i | \(-0.235145\pi\) |
−0.213474 | + | 0.976949i | \(0.568478\pi\) | |||||||
\(62\) | −0.620634 | + | 1.07497i | −0.0788207 | + | 0.136521i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.69226i | 0.711533i | ||||||||
\(65\) | −9.36972 | − | 4.48695i | −1.16217 | − | 0.556538i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.87565 | + | 0.502580i | 0.229148 | + | 0.0613999i | 0.371566 | − | 0.928407i | \(-0.378821\pi\) |
−0.142418 | + | 0.989807i | \(0.545488\pi\) | |||||||
\(68\) | − | 1.83074i | − | 0.222010i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 11.5487 | + | 2.68852i | 1.38034 | + | 0.321339i | ||||
\(71\) | −11.3490 | − | 3.04095i | −1.34688 | − | 0.360894i | −0.487895 | − | 0.872902i | \(-0.662235\pi\) |
−0.858981 | + | 0.512008i | \(0.828902\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.72736 | − | 13.9107i | −0.436254 | − | 1.62812i | −0.738047 | − | 0.674749i | \(-0.764252\pi\) |
0.301793 | − | 0.953373i | \(-0.402415\pi\) | |||||||
\(74\) | −8.49891 | −0.987978 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.156769 | + | 0.585069i | 0.0179826 | + | 0.0671121i | ||||
\(77\) | −7.65402 | − | 12.2990i | −0.872256 | − | 1.40161i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.431242 | − | 0.746933i | −0.0485185 | − | 0.0840365i | 0.840746 | − | 0.541429i | \(-0.182117\pi\) |
−0.889265 | + | 0.457393i | \(0.848783\pi\) | |||||||
\(80\) | −3.47733 | + | 12.9776i | −0.388777 | + | 1.45094i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.12503 | − | 5.41271i | 0.345102 | − | 0.597734i | ||||
\(83\) | −4.29551 | − | 4.29551i | −0.471494 | − | 0.471494i | 0.430904 | − | 0.902398i | \(-0.358195\pi\) |
−0.902398 | + | 0.430904i | \(0.858195\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.25487 | + | 12.1473i | −0.353040 | + | 1.31756i | ||||
\(86\) | 2.59408 | − | 9.68124i | 0.279727 | − | 1.04395i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 11.6575 | − | 6.73043i | 1.24269 | − | 0.717467i | ||||
\(89\) | −4.21484 | + | 4.21484i | −0.446772 | + | 0.446772i | −0.894280 | − | 0.447508i | \(-0.852312\pi\) |
0.447508 | + | 0.894280i | \(0.352312\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.64830 | − | 7.68744i | −0.592103 | − | 0.805862i | ||||
\(92\) | −3.51171 | −0.366121 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −11.8861 | + | 6.86245i | −1.22596 | + | 0.707807i | ||||
\(95\) | − | 4.16078i | − | 0.426887i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.575652 | + | 2.14836i | −0.0584486 | + | 0.218133i | −0.988973 | − | 0.148097i | \(-0.952685\pi\) |
0.930524 | + | 0.366230i | \(0.119352\pi\) | |||||||
\(98\) | 8.19122 | + | 7.17334i | 0.827438 | + | 0.724617i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.692481 | + | 1.19941i | −0.0692481 | + | 0.119941i | ||||
\(101\) | 7.92218 | + | 13.7216i | 0.788287 | + | 1.36535i | 0.927016 | + | 0.375023i | \(0.122365\pi\) |
−0.138729 | + | 0.990330i | \(0.544302\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.32654 | − | 9.22583i | −0.524839 | − | 0.909048i | −0.999582 | − | 0.0289234i | \(-0.990792\pi\) |
0.474742 | − | 0.880125i | \(-0.342541\pi\) | |||||||
\(104\) | 7.31297 | − | 5.00941i | 0.717096 | − | 0.491213i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.112085 | − | 0.418309i | −0.0108867 | − | 0.0406297i | ||||
\(107\) | 14.5513 | 1.40672 | 0.703361 | − | 0.710833i | \(-0.251682\pi\) | ||||
0.703361 | + | 0.710833i | \(0.251682\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.22729 | − | 8.31237i | −0.213336 | − | 0.796181i | −0.986746 | − | 0.162274i | \(-0.948117\pi\) |
0.773410 | − | 0.633906i | \(-0.218550\pi\) | |||||||
\(110\) | 23.7026 | − | 6.35109i | 2.25995 | − | 0.605553i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.43034 | + | 9.00731i | −0.796592 | + | 0.851111i | ||||
\(113\) | 6.81406 | + | 11.8023i | 0.641013 | + | 1.11027i | 0.985207 | + | 0.171368i | \(0.0548187\pi\) |
−0.344195 | + | 0.938898i | \(0.611848\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 23.3010 | + | 6.24347i | 2.17283 | + | 0.582207i | ||||
\(116\) | 0.641131 | + | 0.370157i | 0.0595275 | + | 0.0343682i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.3588i | 1.04566i | ||||||||
\(119\) | −7.89102 | + | 8.43108i | −0.723368 | + | 0.772876i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.4360 | − | 9.48931i | −1.49418 | − | 0.862665i | ||||
\(122\) | −7.12523 | + | 1.90920i | −0.645088 | + | 0.172851i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.0866325 | − | 0.323317i | −0.00777983 | − | 0.0290347i | ||||
\(125\) | −3.45974 | + | 3.45974i | −0.309448 | + | 0.309448i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.01715 | + | 1.74195i | 0.267728 | + | 0.154573i | 0.627855 | − | 0.778330i | \(-0.283933\pi\) |
−0.360126 | + | 0.932904i | \(0.617266\pi\) | |||||||
\(128\) | −9.56447 | − | 9.56447i | −0.845388 | − | 0.845388i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 15.2406 | − | 5.37043i | 1.33669 | − | 0.471018i | ||||
\(131\) | 5.01539 | − | 2.89564i | 0.438197 | − | 0.252993i | −0.264636 | − | 0.964348i | \(-0.585252\pi\) |
0.702832 | + | 0.711356i | \(0.251918\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.79985 | − | 3.37013i | 0.156067 | − | 0.292227i | ||||
\(134\) | −2.61576 | + | 1.51021i | −0.225967 | + | 0.130462i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.58755 | − | 7.58755i | −0.650627 | − | 0.650627i | ||||
\(137\) | 2.42365 | + | 2.42365i | 0.207067 | + | 0.207067i | 0.803019 | − | 0.595953i | \(-0.203226\pi\) |
−0.595953 | + | 0.803019i | \(0.703226\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.1580 | + | 9.32882i | −1.37050 | + | 0.791260i | −0.990991 | − | 0.133927i | \(-0.957241\pi\) |
−0.379512 | + | 0.925187i | \(0.623908\pi\) | |||||||
\(140\) | −2.71475 | + | 1.68946i | −0.229439 | + | 0.142786i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15.8271 | − | 9.13779i | 1.32818 | − | 0.766826i | ||||
\(143\) | −17.8051 | − | 8.52647i | −1.48894 | − | 0.713019i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.59594 | − | 3.59594i | −0.298626 | − | 0.298626i | ||||
\(146\) | 19.3996 | + | 11.2004i | 1.60552 | + | 0.926950i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.62057 | − | 1.62057i | 0.133210 | − | 0.133210i | ||||
\(149\) | 3.69990 | + | 13.8082i | 0.303108 | + | 1.13121i | 0.934562 | + | 0.355801i | \(0.115792\pi\) |
−0.631454 | + | 0.775413i | \(0.717542\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.0198676 | + | 0.00532352i | −0.00161681 | + | 0.000433222i | −0.259627 | − | 0.965709i | \(-0.583600\pi\) |
0.258011 | + | 0.966142i | \(0.416933\pi\) | |||||||
\(152\) | 3.07457 | + | 1.77510i | 0.249381 | + | 0.143980i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 21.9459 | + | 5.10894i | 1.76845 | + | 0.411690i | ||||
\(155\) | 2.29930i | 0.184684i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.26575 | + | 3.04018i | 0.420253 | + | 0.242633i | 0.695185 | − | 0.718830i | \(-0.255322\pi\) |
−0.274933 | + | 0.961463i | \(0.588656\pi\) | |||||||
\(158\) | 1.29584 | + | 0.347220i | 0.103092 | + | 0.0276234i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.36545 | − | 5.82913i | −0.266062 | − | 0.460833i | ||||
\(161\) | 16.1724 | + | 15.1365i | 1.27457 | + | 1.19292i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.7573 | − | 3.68627i | 1.07756 | − | 0.288731i | 0.323963 | − | 0.946070i | \(-0.394985\pi\) |
0.753595 | + | 0.657339i | \(0.228318\pi\) | |||||||
\(164\) | 0.436214 | + | 1.62797i | 0.0340626 | + | 0.127123i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.44905 | 0.733388 | ||||||||
\(167\) | 0.579671 | + | 2.16336i | 0.0448563 | + | 0.167406i | 0.984720 | − | 0.174142i | \(-0.0557153\pi\) |
−0.939864 | + | 0.341548i | \(0.889049\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.1221 | − | 4.69635i | −0.932466 | − | 0.361258i | ||||
\(170\) | −9.78060 | − | 16.9405i | −0.750138 | − | 1.29928i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.35138 | + | 2.34065i | 0.103041 | + | 0.178473i | ||||
\(173\) | 1.62494 | − | 2.81448i | 0.123542 | − | 0.213981i | −0.797620 | − | 0.603160i | \(-0.793908\pi\) |
0.921162 | + | 0.389179i | \(0.127241\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.35888 | − | 2.53884i | 0.631872 | − | 0.191918i | ||||
\(176\) | −6.60790 | + | 24.6610i | −0.498089 | + | 1.85889i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 9.27158i | − | 0.694934i | ||||||
\(179\) | −18.3339 | + | 10.5851i | −1.37034 | + | 0.791165i | −0.990970 | − | 0.134081i | \(-0.957192\pi\) |
−0.379367 | + | 0.925246i | \(0.623858\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.5217 | 1.37671 | 0.688353 | − | 0.725376i | \(-0.258334\pi\) | ||||
0.688353 | + | 0.725376i | \(0.258334\pi\) | |||||||
\(182\) | 14.6676 | + | 2.24279i | 1.08724 | + | 0.166247i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −14.5544 | + | 14.5544i | −1.07296 | + | 1.07296i | ||||
\(185\) | −13.6340 | + | 7.87160i | −1.00239 | + | 0.578732i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.18517 | + | 23.0834i | −0.452304 | + | 1.68802i | ||||
\(188\) | 0.957909 | − | 3.57496i | 0.0698627 | − | 0.260731i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.57633 | + | 4.57633i | 0.332002 | + | 0.332002i | ||||
\(191\) | −13.7090 | + | 23.7447i | −0.991948 | + | 1.71810i | −0.386292 | + | 0.922376i | \(0.626244\pi\) |
−0.605655 | + | 0.795727i | \(0.707089\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.93597 | + | 18.4213i | −0.355299 | + | 1.32599i | 0.524809 | + | 0.851220i | \(0.324137\pi\) |
−0.880108 | + | 0.474774i | \(0.842530\pi\) | |||||||
\(194\) | −1.72978 | − | 2.99607i | −0.124191 | − | 0.215105i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.92971 | + | 0.194088i | −0.209265 | + | 0.0138634i | ||||
\(197\) | −1.20155 | − | 4.48424i | −0.0856068 | − | 0.319489i | 0.909822 | − | 0.415000i | \(-0.136218\pi\) |
−0.995428 | + | 0.0955106i | \(0.969552\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.447121 | −0.0316956 | −0.0158478 | − | 0.999874i | \(-0.505045\pi\) | ||||
−0.0158478 | + | 0.999874i | \(0.505045\pi\) | |||||||
\(200\) | 2.10099 | + | 7.84100i | 0.148562 | + | 0.554442i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −23.8055 | − | 6.37866i | −1.67495 | − | 0.448801i | ||||
\(203\) | −1.35711 | − | 4.46814i | −0.0952502 | − | 0.313602i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 11.5775i | − | 0.808607i | ||||||
\(206\) | 16.0058 | + | 4.28873i | 1.11518 | + | 0.298810i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.08944 | + | 16.5262i | −0.214214 | + | 1.14589i | ||||
\(209\) | − | 7.90665i | − | 0.546914i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.3795 | + | 24.9060i | −0.989924 | + | 1.71460i | −0.372331 | + | 0.928100i | \(0.621442\pi\) |
−0.617592 | + | 0.786498i | \(0.711892\pi\) | |||||||
\(212\) | 0.101135 | + | 0.0583905i | 0.00694600 | + | 0.00401028i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −16.0045 | + | 16.0045i | −1.09405 | + | 1.09405i | ||||
\(215\) | −4.80522 | − | 17.9333i | −0.327713 | − | 1.22304i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.994622 | + | 1.86238i | −0.0675194 | + | 0.126427i | ||||
\(218\) | 11.5923 | + | 6.69282i | 0.785130 | + | 0.453295i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.30857 | + | 5.73062i | −0.223064 | + | 0.386358i | ||||
\(221\) | −2.89179 | + | 15.4690i | −0.194523 | + | 1.04056i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.0758 | − | 3.77160i | 0.942586 | − | 0.252565i | 0.245372 | − | 0.969429i | \(-0.421090\pi\) |
0.697213 | + | 0.716864i | \(0.254423\pi\) | |||||||
\(224\) | −0.204392 | − | 6.17727i | −0.0136565 | − | 0.412736i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −20.4756 | − | 5.48643i | −1.36202 | − | 0.364952i | ||||
\(227\) | −12.6759 | − | 12.6759i | −0.841326 | − | 0.841326i | 0.147705 | − | 0.989031i | \(-0.452811\pi\) |
−0.989031 | + | 0.147705i | \(0.952811\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.61427 | − | 1.77229i | −0.437083 | − | 0.117116i | 0.0335661 | − | 0.999437i | \(-0.489314\pi\) |
−0.470649 | + | 0.882320i | \(0.655980\pi\) | |||||||
\(230\) | −32.4952 | + | 18.7611i | −2.14267 | + | 1.23707i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.19131 | − | 1.12306i | 0.275173 | − | 0.0737324i | ||||
\(233\) | −6.74247 | + | 3.89276i | −0.441714 | + | 0.255023i | −0.704324 | − | 0.709878i | \(-0.748750\pi\) |
0.262611 | + | 0.964902i | \(0.415417\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.7119 | + | 22.0176i | −0.829230 | + | 1.43627i | ||||
\(236\) | −2.16589 | − | 2.16589i | −0.140988 | − | 0.140988i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.594001 | − | 17.9523i | −0.0385034 | − | 1.16367i | ||||
\(239\) | 2.22428 | − | 2.22428i | 0.143877 | − | 0.143877i | −0.631499 | − | 0.775376i | \(-0.717560\pi\) |
0.775376 | + | 0.631499i | \(0.217560\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.34946 | − | 6.34946i | 0.409005 | − | 0.409005i | −0.472387 | − | 0.881391i | \(-0.656607\pi\) |
0.881391 | + | 0.472387i | \(0.156607\pi\) | |||||||
\(242\) | 28.5146 | − | 7.64045i | 1.83298 | − | 0.491147i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.994590 | − | 1.72268i | 0.0636721 | − | 0.110283i | ||||
\(245\) | 19.7843 | + | 3.92091i | 1.26397 | + | 0.250498i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.400470 | − | 5.19122i | −0.0254813 | − | 0.330310i | ||||
\(248\) | −1.69905 | − | 0.980946i | −0.107890 | − | 0.0622901i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 7.61055i | − | 0.481333i | ||||||
\(251\) | −12.3486 | − | 21.3883i | −0.779434 | − | 1.35002i | −0.932269 | − | 0.361767i | \(-0.882174\pi\) |
0.152835 | − | 0.988252i | \(-0.451160\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 44.2784 | + | 11.8644i | 2.78376 | + | 0.745905i | ||||
\(254\) | −5.23441 | + | 1.40256i | −0.328436 | + | 0.0880042i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.65491 | 0.603432 | ||||||||
\(257\) | 6.15108 | 0.383694 | 0.191847 | − | 0.981425i | \(-0.438552\pi\) | ||||
0.191847 | + | 0.981425i | \(0.438552\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.4483 | + | 0.478063i | −0.897773 | + | 0.0297054i | ||||
\(260\) | −1.88204 | + | 3.93010i | −0.116719 | + | 0.243734i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.33146 | + | 8.70113i | −0.144038 | + | 0.537558i | ||||
\(263\) | 8.57461 | + | 14.8517i | 0.528733 | + | 0.915792i | 0.999439 | + | 0.0335020i | \(0.0106660\pi\) |
−0.470706 | + | 0.882290i | \(0.656001\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.567242 | − | 0.567242i | −0.0348454 | − | 0.0348454i | ||||
\(266\) | 1.72711 | + | 5.68633i | 0.105896 | + | 0.348651i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.210806 | − | 0.786737i | 0.0128770 | − | 0.0480576i | ||||
\(269\) | − | 2.31154i | − | 0.140937i | −0.997514 | − | 0.0704685i | \(-0.977551\pi\) | ||
0.997514 | − | 0.0704685i | \(-0.0224494\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.58217 | + | 4.58217i | −0.278347 | + | 0.278347i | −0.832449 | − | 0.554102i | \(-0.813062\pi\) |
0.554102 | + | 0.832449i | \(0.313062\pi\) | |||||||
\(272\) | 20.3522 | 1.23403 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.33142 | −0.322083 | ||||||||
\(275\) | 12.7835 | − | 12.7835i | 0.770877 | − | 0.770877i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.1768i | 1.45265i | 0.687354 | + | 0.726323i | \(0.258772\pi\) | ||||
−0.687354 | + | 0.726323i | \(0.741228\pi\) | |||||||
\(278\) | 7.51123 | − | 28.0323i | 0.450494 | − | 1.68127i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.24934 | + | 18.2534i | −0.253947 | + | 1.09085i | ||||
\(281\) | −18.6196 | − | 18.6196i | −1.11075 | − | 1.11075i | −0.993049 | − | 0.117703i | \(-0.962447\pi\) |
−0.117703 | − | 0.993049i | \(-0.537553\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.25230 | − | 10.8293i | −0.371661 | − | 0.643736i | 0.618160 | − | 0.786052i | \(-0.287878\pi\) |
−0.989821 | + | 0.142317i | \(0.954545\pi\) | |||||||
\(284\) | −1.27552 | + | 4.76029i | −0.0756880 | + | 0.282472i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 28.9614 | − | 10.2053i | 1.71252 | − | 0.603454i | ||||
\(287\) | 5.00814 | − | 9.37749i | 0.295621 | − | 0.553536i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.05017 | 0.120598 | ||||||||
\(290\) | 7.91016 | 0.464500 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.83479 | + | 1.56343i | −0.341455 | + | 0.0914927i | ||||
\(293\) | 0.0851383 | + | 0.0228127i | 0.00497383 | + | 0.00133274i | 0.261305 | − | 0.965256i | \(-0.415847\pi\) |
−0.256331 | + | 0.966589i | \(0.582514\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.5204 | + | 18.2219i | 0.612523 | + | 1.06092i | ||||
\(296\) | − | 13.4330i | − | 0.780776i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.2567 | − | 11.1179i | −1.11551 | − | 0.644042i | ||||
\(299\) | 29.6725 | + | 5.54702i | 1.71601 | + | 0.320793i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.86541 | − | 16.6042i | 0.222799 | − | 0.957049i | ||||
\(302\) | 0.0159967 | − | 0.0277071i | 0.000920507 | − | 0.00159436i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.50417 | + | 1.74279i | −0.373040 | + | 0.0999557i | ||||
\(305\) | −9.66207 | + | 9.66207i | −0.553248 | + | 0.553248i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.58728 | + | 7.58728i | −0.433029 | + | 0.433029i | −0.889658 | − | 0.456628i | \(-0.849057\pi\) |
0.456628 | + | 0.889658i | \(0.349057\pi\) | |||||||
\(308\) | −5.15879 | + | 3.21045i | −0.293950 | + | 0.182933i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.52894 | − | 2.52894i | −0.143634 | − | 0.143634i | ||||
\(311\) | 15.1148 | − | 26.1796i | 0.857082 | − | 1.48451i | −0.0176172 | − | 0.999845i | \(-0.505608\pi\) |
0.874700 | − | 0.484665i | \(-0.161059\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.9891 | − | 14.4275i | 1.41247 | − | 0.815489i | 0.416849 | − | 0.908976i | \(-0.363135\pi\) |
0.995621 | + | 0.0934866i | \(0.0298012\pi\) | |||||||
\(314\) | −9.13548 | + | 2.44784i | −0.515545 | + | 0.138140i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.313299 | + | 0.180883i | −0.0176244 | + | 0.0101755i | ||||
\(317\) | −16.2082 | − | 4.34297i | −0.910343 | − | 0.243926i | −0.226890 | − | 0.973920i | \(-0.572856\pi\) |
−0.683453 | + | 0.729995i | \(0.739523\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.83329 | − | 6.83329i | −0.382591 | − | 0.382591i | ||||
\(320\) | −15.8423 | − | 4.24492i | −0.885609 | − | 0.237298i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −34.4359 | + | 1.13941i | −1.91904 | + | 0.0634968i | ||||
\(323\) | −6.08807 | + | 1.63129i | −0.338749 | + | 0.0907676i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.74574 | − | 9.04071i | 0.429656 | − | 0.501488i | ||||
\(326\) | −11.0769 | + | 19.1858i | −0.613493 | + | 1.06260i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.55508 | + | 4.93928i | 0.472375 | + | 0.272726i | ||||
\(329\) | −19.8206 | + | 12.3349i | −1.09274 | + | 0.680044i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.62870 | + | 6.07840i | 0.0895215 | + | 0.334099i | 0.996132 | − | 0.0878697i | \(-0.0280059\pi\) |
−0.906610 | + | 0.421969i | \(0.861339\pi\) | |||||||
\(332\) | −1.80174 | + | 1.80174i | −0.0988833 | + | 0.0988833i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.01699 | − | 1.74186i | −0.165083 | − | 0.0953104i | ||||
\(335\) | −2.79748 | + | 4.84538i | −0.152843 | + | 0.264731i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 17.1415i | − | 0.933758i | −0.884321 | − | 0.466879i | \(-0.845378\pi\) | ||
0.884321 | − | 0.466879i | \(-0.154622\pi\) | |||||||
\(338\) | 18.4981 | − | 8.16734i | 1.00617 | − | 0.444245i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.09517 | + | 1.36525i | 0.276324 | + | 0.0740408i | ||||
\(341\) | 4.36932i | 0.236612i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.3287 | + | 11.7341i | 0.773678 | + | 0.633579i | ||||
\(344\) | 15.3017 | + | 4.10008i | 0.825013 | + | 0.221062i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.30834 | + | 4.88281i | 0.0703370 | + | 0.262501i | ||||
\(347\) | −4.22975 | −0.227065 | −0.113532 | − | 0.993534i | \(-0.536217\pi\) | ||||
−0.113532 | + | 0.993534i | \(0.536217\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.82352 | + | 18.0016i | 0.258197 | + | 0.963605i | 0.966284 | + | 0.257479i | \(0.0828919\pi\) |
−0.708087 | + | 0.706125i | \(0.750441\pi\) | |||||||
\(350\) | −6.40131 | + | 11.9861i | −0.342165 | + | 0.640685i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.39530 | − | 11.0770i | −0.340871 | − | 0.590405i | ||||
\(353\) | 1.15293 | − | 4.30278i | 0.0613641 | − | 0.229014i | −0.928433 | − | 0.371501i | \(-0.878843\pi\) |
0.989797 | + | 0.142487i | \(0.0455099\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.9267 | − | 29.3178i | 0.898373 | − | 1.55603i | ||||
\(356\) | 1.76790 | + | 1.76790i | 0.0936985 | + | 0.0936985i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.52271 | − | 31.8072i | 0.450439 | − | 1.68106i | ||||
\(359\) | 4.24764 | − | 15.8524i | 0.224182 | − | 0.836657i | −0.758549 | − | 0.651616i | \(-0.774091\pi\) |
0.982731 | − | 0.185041i | \(-0.0592420\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.6485 | + | 8.45734i | −0.770976 | + | 0.445123i | ||||
\(362\) | −20.3715 | + | 20.3715i | −1.07070 | + | 1.07070i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.22447 | + | 2.36916i | −0.169008 | + | 0.124178i | ||||
\(365\) | 41.4947 | 2.17193 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.1880 | + | 13.9650i | −1.26260 | + | 0.728964i | −0.973578 | − | 0.228357i | \(-0.926665\pi\) |
−0.289026 | + | 0.957321i | \(0.593331\pi\) | |||||||
\(368\) | − | 39.0394i | − | 2.03507i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.33793 | − | 23.6535i | 0.329493 | − | 1.22969i | ||||
\(371\) | −0.214077 | − | 0.704827i | −0.0111143 | − | 0.0365928i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.92406 | − | 5.06463i | 0.151402 | − | 0.262237i | −0.780341 | − | 0.625354i | \(-0.784954\pi\) |
0.931743 | + | 0.363118i | \(0.118288\pi\) | |||||||
\(374\) | −18.5859 | − | 32.1917i | −0.961054 | − | 1.66459i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.8465 | − | 18.7866i | −0.559364 | − | 0.968846i | ||||
\(377\) | −4.83260 | − | 4.14039i | −0.248892 | − | 0.213241i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.411597 | − | 1.53610i | −0.0211423 | − | 0.0789043i | 0.954549 | − | 0.298055i | \(-0.0963380\pi\) |
−0.975691 | + | 0.219151i | \(0.929671\pi\) | |||||||
\(380\) | −1.74523 | −0.0895282 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.0380 | − | 41.1943i | −0.564752 | − | 2.10768i | ||||
\(383\) | 13.6049 | − | 3.64543i | 0.695179 | − | 0.186273i | 0.106109 | − | 0.994355i | \(-0.466161\pi\) |
0.589070 | + | 0.808082i | \(0.299494\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 39.9376 | − | 12.1302i | 2.03541 | − | 0.618214i | ||||
\(386\) | −14.8322 | − | 25.6901i | −0.754937 | − | 1.30759i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.901124 | + | 0.241455i | 0.0457476 | + | 0.0122580i | ||||
\(389\) | −0.216783 | − | 0.125160i | −0.0109913 | − | 0.00634584i | 0.494494 | − | 0.869181i | \(-0.335353\pi\) |
−0.505486 | + | 0.862835i | \(0.668687\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 36.5419i | − | 1.84800i | ||||||
\(392\) | −11.3378 | + | 12.9467i | −0.572648 | + | 0.653905i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.25365 | + | 3.61055i | 0.315055 | + | 0.181897i | ||||
\(395\) | 2.40040 | − | 0.643184i | 0.120777 | − | 0.0323621i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.74276 | + | 6.50408i | 0.0874668 | + | 0.326430i | 0.995770 | − | 0.0918822i | \(-0.0292883\pi\) |
−0.908303 | + | 0.418313i | \(0.862622\pi\) | |||||||
\(398\) | 0.491777 | − | 0.491777i | 0.0246505 | − | 0.0246505i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.3338 | − | 7.69825i | −0.666688 | − | 0.384913i | ||||
\(401\) | 20.3892 | + | 20.3892i | 1.01819 | + | 1.01819i | 0.999831 | + | 0.0183568i | \(0.00584349\pi\) |
0.0183568 | + | 0.999831i | \(0.494157\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.221305 | + | 2.86874i | 0.0110240 | + | 0.142902i | ||||
\(404\) | 5.75549 | − | 3.32294i | 0.286347 | − | 0.165322i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.40704 | + | 3.42174i | 0.317976 | + | 0.169818i | ||||
\(407\) | −25.9085 | + | 14.9583i | −1.28423 | + | 0.741453i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.0625 | + | 19.0625i | 0.942582 | + | 0.942582i | 0.998439 | − | 0.0558573i | \(-0.0177892\pi\) |
−0.0558573 | + | 0.998439i | \(0.517789\pi\) | |||||||
\(410\) | 12.7338 | + | 12.7338i | 0.628877 | + | 0.628877i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.86975 | + | 2.23420i | −0.190649 | + | 0.110071i | ||||
\(413\) | 0.638932 | + | 19.3102i | 0.0314398 | + | 0.950192i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.1582 | − | 8.75161i | 0.744089 | − | 0.429600i | ||||
\(416\) | −4.75998 | − | 6.94884i | −0.233377 | − | 0.340695i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.69632 | + | 8.69632i | 0.425351 | + | 0.425351i | ||||
\(419\) | −12.0707 | − | 6.96900i | −0.589691 | − | 0.340458i | 0.175284 | − | 0.984518i | \(-0.443916\pi\) |
−0.764975 | + | 0.644060i | \(0.777249\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.9864 | − | 15.9864i | 0.779131 | − | 0.779131i | −0.200552 | − | 0.979683i | \(-0.564274\pi\) |
0.979683 | + | 0.200552i | \(0.0642735\pi\) | |||||||
\(422\) | −11.5778 | − | 43.2091i | −0.563600 | − | 2.10338i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.661159 | − | 0.177157i | 0.0321087 | − | 0.00860351i | ||||
\(425\) | −12.4807 | − | 7.20576i | −0.605405 | − | 0.349531i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.0056 | + | 3.64647i | −0.580993 | + | 0.176465i | ||||
\(428\) | − | 6.10348i | − | 0.295023i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 25.0095 | + | 14.4393i | 1.20607 | + | 0.696323i | ||||
\(431\) | −3.10956 | − | 0.833204i | −0.149782 | − | 0.0401340i | 0.183149 | − | 0.983085i | \(-0.441371\pi\) |
−0.332931 | + | 0.942951i | \(0.608038\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.34137 | − | 9.25152i | −0.256690 | − | 0.444600i | 0.708663 | − | 0.705547i | \(-0.249299\pi\) |
−0.965353 | + | 0.260947i | \(0.915965\pi\) | |||||||
\(434\) | −0.954423 | − | 3.14234i | −0.0458138 | − | 0.150837i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.48660 | + | 0.934231i | −0.166978 | + | 0.0447416i | ||||
\(437\) | 3.12914 | + | 11.6781i | 0.149687 | + | 0.558639i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.5610 | 0.694961 | 0.347480 | − | 0.937687i | \(-0.387037\pi\) | ||||
0.347480 | + | 0.937687i | \(0.387037\pi\) | |||||||
\(440\) | 10.0382 | + | 37.4632i | 0.478554 | + | 1.78599i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.8333 | − | 20.1946i | −0.657985 | − | 0.960557i | ||||
\(443\) | 2.49941 | + | 4.32911i | 0.118751 | + | 0.205682i | 0.919273 | − | 0.393621i | \(-0.128778\pi\) |
−0.800522 | + | 0.599303i | \(0.795444\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.58724 | − | 14.8735i | −0.407074 | − | 0.705073i | ||||
\(446\) | −11.3333 | + | 19.6299i | −0.536649 | + | 0.929503i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10.9956 | − | 10.2913i | −0.519493 | − | 0.486216i | ||||
\(449\) | −6.89362 | + | 25.7273i | −0.325330 | + | 1.21415i | 0.588650 | + | 0.808388i | \(0.299660\pi\) |
−0.913980 | + | 0.405760i | \(0.867007\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 22.0005i | − | 1.03596i | ||||||
\(452\) | 4.95044 | − | 2.85814i | 0.232849 | − | 0.134435i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 27.8837 | 1.30865 | ||||||||
\(455\) | 25.6072 | − | 9.98711i | 1.20048 | − | 0.468203i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.85252 | + | 8.85252i | −0.414103 | + | 0.414103i | −0.883165 | − | 0.469062i | \(-0.844592\pi\) |
0.469062 | + | 0.883165i | \(0.344592\pi\) | |||||||
\(458\) | 9.22416 | − | 5.32557i | 0.431017 | − | 0.248848i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.61881 | − | 9.77352i | 0.122102 | − | 0.455693i | ||||
\(461\) | −2.58295 | + | 9.63971i | −0.120300 | + | 0.448966i | −0.999629 | − | 0.0272495i | \(-0.991325\pi\) |
0.879329 | + | 0.476216i | \(0.157992\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.87215 | − | 8.87215i | −0.412324 | − | 0.412324i | 0.470224 | − | 0.882547i | \(-0.344173\pi\) |
−0.882547 | + | 0.470224i | \(0.844173\pi\) | |||||||
\(464\) | −4.11501 | + | 7.12740i | −0.191034 | + | 0.330881i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.13431 | − | 11.6974i | 0.145194 | − | 0.541872i | ||||
\(467\) | −7.33629 | − | 12.7068i | −0.339483 | − | 0.588002i | 0.644853 | − | 0.764307i | \(-0.276919\pi\) |
−0.984336 | + | 0.176305i | \(0.943585\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.36188 | + | 2.71452i | −0.201413 | + | 0.125345i | ||||
\(470\) | −10.2351 | − | 38.1980i | −0.472111 | − | 1.76194i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −17.9532 | −0.826364 | ||||||||
\(473\) | −9.13127 | − | 34.0784i | −0.419856 | − | 1.56692i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.60565 | + | 1.23408i | 0.211322 | + | 0.0566235i | ||||
\(476\) | 3.53639 | + | 3.30986i | 0.162090 | + | 0.151707i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.89286i | 0.223794i | ||||||||
\(479\) | −13.3439 | − | 3.57549i | −0.609699 | − | 0.163368i | −0.0592583 | − | 0.998243i | \(-0.518874\pi\) |
−0.550441 | + | 0.834874i | \(0.685540\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.2529 | + | 11.1333i | −0.741070 | + | 0.507636i | ||||
\(482\) | 13.9672i | 0.636189i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.98026 | + | 6.89402i | −0.180921 | + | 0.313364i | ||||
\(485\) | −5.54986 | − | 3.20421i | −0.252006 | − | 0.145496i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.2572 | − | 21.2572i | 0.963257 | − | 0.963257i | −0.0360915 | − | 0.999348i | \(-0.511491\pi\) |
0.999348 | + | 0.0360915i | \(0.0114908\pi\) | |||||||
\(488\) | −3.01759 | − | 11.2618i | −0.136600 | − | 0.509798i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −26.0727 | + | 17.4477i | −1.17785 | + | 0.788208i | ||||
\(491\) | −27.2827 | − | 15.7517i | −1.23125 | − | 0.710863i | −0.263961 | − | 0.964533i | \(-0.585029\pi\) |
−0.967291 | + | 0.253670i | \(0.918362\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.85175 | + | 6.67143i | −0.173474 | + | 0.300466i | ||||
\(494\) | 6.15016 | + | 5.26923i | 0.276709 | + | 0.237074i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.59429 | − | 0.963087i | 0.161388 | − | 0.0432439i | ||||
\(497\) | 26.3924 | − | 16.4247i | 1.18386 | − | 0.736747i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.5875 | − | 6.05231i | −1.01116 | − | 0.270938i | −0.285044 | − | 0.958515i | \(-0.592008\pi\) |
−0.726112 | + | 0.687576i | \(0.758675\pi\) | |||||||
\(500\) | 1.45118 | + | 1.45118i | 0.0648985 | + | 0.0648985i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 37.1063 | + | 9.94261i | 1.65614 | + | 0.443760i | ||||
\(503\) | 7.16456 | − | 4.13646i | 0.319452 | − | 0.184436i | −0.331696 | − | 0.943386i | \(-0.607621\pi\) |
0.651148 | + | 0.758951i | \(0.274288\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −44.0968 | + | 11.8157i | −1.96228 | + | 0.525792i | ||||
\(506\) | −61.7499 | + | 35.6513i | −2.74512 | + | 1.58490i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.730656 | − | 1.26553i | 0.0324176 | − | 0.0561489i | ||||
\(509\) | 6.51433 | + | 6.51433i | 0.288742 | + | 0.288742i | 0.836583 | − | 0.547840i | \(-0.184550\pi\) |
−0.547840 | + | 0.836583i | \(0.684550\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 33.6097 | + | 17.9496i | 1.48681 | + | 0.794044i | ||||
\(512\) | 8.50976 | − | 8.50976i | 0.376082 | − | 0.376082i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.76541 | + | 6.76541i | −0.298409 | + | 0.298409i | ||||
\(515\) | 29.6488 | − | 7.94436i | 1.30648 | − | 0.350071i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.1561 | + | 41.8396i | −1.06238 | + | 1.84010i | ||||
\(518\) | 15.3655 | − | 16.4171i | 0.675121 | − | 0.721326i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.48825 | + | 24.0886i | 0.372234 | + | 1.05635i | ||||
\(521\) | −5.78613 | − | 3.34062i | −0.253495 | − | 0.146355i | 0.367869 | − | 0.929878i | \(-0.380088\pi\) |
−0.621364 | + | 0.783522i | \(0.713421\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 32.1180i | − | 1.40442i | −0.711969 | − | 0.702211i | \(-0.752196\pi\) | ||
0.711969 | − | 0.702211i | \(-0.247804\pi\) | |||||||
\(524\) | −1.21457 | − | 2.10369i | −0.0530586 | − | 0.0919001i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −25.7659 | − | 6.90396i | −1.12345 | − | 0.301027i | ||||
\(527\) | 3.36435 | − | 0.901475i | 0.146553 | − | 0.0392689i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −47.0945 | −2.04759 | ||||||||
\(530\) | 1.24779 | 0.0542005 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.41359 | − | 0.754943i | −0.0612869 | − | 0.0327309i | ||||
\(533\) | −1.11432 | − | 14.4447i | −0.0482665 | − | 0.625671i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.8514 | + | 40.4979i | −0.469146 | + | 1.75088i | ||||
\(536\) | −2.38696 | − | 4.13434i | −0.103101 | − | 0.178576i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.54240 | + | 2.54240i | 0.109611 | + | 0.109611i | ||||
\(539\) | 37.5957 | + | 7.45083i | 1.61936 | + | 0.320930i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.62221 | + | 6.05418i | −0.0697443 | + | 0.260289i | −0.991990 | − | 0.126314i | \(-0.959685\pi\) |
0.922246 | + | 0.386604i | \(0.126352\pi\) | |||||||
\(542\) | − | 10.0796i | − | 0.432957i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.20974 | + | 7.20974i | −0.309115 | + | 0.309115i | ||||
\(545\) | 24.7953 | 1.06211 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.9848 | −0.768973 | −0.384487 | − | 0.923131i | \(-0.625622\pi\) | ||||
−0.384487 | + | 0.923131i | \(0.625622\pi\) | |||||||
\(548\) | 1.01659 | − | 1.01659i | 0.0434267 | − | 0.0434267i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 28.1206i | 1.19907i | ||||||||
\(551\) | 0.659662 | − | 2.46189i | 0.0281026 | − | 0.104880i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.22249 | + | 0.517390i | 0.0945099 | + | 0.0220017i | ||||
\(554\) | −26.5915 | − | 26.5915i | −1.12976 | − | 1.12976i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.91295 | + | 6.77742i | 0.165946 | + | 0.287427i | ||||
\(557\) | −9.77773 | + | 36.4910i | −0.414296 | + | 1.54617i | 0.371946 | + | 0.928254i | \(0.378691\pi\) |
−0.786242 | + | 0.617919i | \(0.787976\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.72133 | − | 21.9121i | −0.326577 | − | 0.926785i | ||||
\(560\) | −18.7816 | − | 30.1797i | −0.793669 | − | 1.27533i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 40.9584 | 1.72773 | ||||||||
\(563\) | 6.37316 | 0.268596 | 0.134298 | − | 0.990941i | \(-0.457122\pi\) | ||||
0.134298 | + | 0.990941i | \(0.457122\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −37.9287 | + | 10.1630i | −1.59567 | + | 0.427559i | ||||
\(566\) | 18.7876 | + | 5.03413i | 0.789703 | + | 0.211600i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.4428 | + | 25.0156i | 0.606005 | + | 1.04963i | ||||
\(569\) | 4.40653i | 0.184731i | 0.995725 | + | 0.0923657i | \(0.0294429\pi\) | ||||
−0.995725 | + | 0.0923657i | \(0.970557\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.2682 | + | 7.08302i | 0.513406 | + | 0.296415i | 0.734233 | − | 0.678898i | \(-0.237542\pi\) |
−0.220826 | + | 0.975313i | \(0.570875\pi\) | |||||||
\(572\) | −3.57640 | + | 7.46829i | −0.149537 | + | 0.312265i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.80573 | + | 15.8224i | 0.200587 | + | 0.660414i | ||||
\(575\) | −13.8221 | + | 23.9405i | −0.576419 | + | 0.998388i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.98371 | − | 2.40718i | 0.373997 | − | 0.100212i | −0.0669241 | − | 0.997758i | \(-0.521319\pi\) |
0.440921 | + | 0.897546i | \(0.354652\pi\) | |||||||
\(578\) | −2.25493 | + | 2.25493i | −0.0937929 | + | 0.0937929i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.50830 | + | 1.50830i | −0.0626289 | + | 0.0626289i | ||||
\(581\) | 16.0635 | − | 0.531508i | 0.666428 | − | 0.0220507i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.07792 | − | 1.07792i | −0.0446428 | − | 0.0446428i | ||||
\(584\) | −17.7028 | + | 30.6621i | −0.732547 | + | 1.26881i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.118733 | + | 0.0685503i | −0.00490480 | + | 0.00283179i | ||||
\(587\) | 10.0172 | − | 2.68411i | 0.413455 | − | 0.110785i | −0.0460944 | − | 0.998937i | \(-0.514678\pi\) |
0.459550 | + | 0.888152i | \(0.348011\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.997987 | + | 0.576188i | −0.0411213 | + | 0.0237414i | ||||
\(590\) | −31.6130 | − | 8.47066i | −1.30148 | − | 0.348732i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 18.0157 | + | 18.0157i | 0.740441 | + | 0.740441i | ||||
\(593\) | −11.6126 | − | 3.11158i | −0.476871 | − | 0.127777i | 0.0123741 | − | 0.999923i | \(-0.496061\pi\) |
−0.489245 | + | 0.872146i | \(0.662728\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.5801 | − | 28.2490i | −0.720714 | − | 1.15810i | ||||
\(596\) | 5.79182 | − | 1.55191i | 0.237242 | − | 0.0635688i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −38.7371 | + | 26.5350i | −1.58408 | + | 1.08510i | ||||
\(599\) | 9.16962 | − | 15.8822i | 0.374660 | − | 0.648931i | −0.615616 | − | 0.788046i | \(-0.711093\pi\) |
0.990276 | + | 0.139116i | \(0.0444260\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.4396 | + | 16.9969i | 1.20086 | + | 0.693319i | 0.960747 | − | 0.277424i | \(-0.0894808\pi\) |
0.240117 | + | 0.970744i | \(0.422814\pi\) | |||||||
\(602\) | 14.0111 | + | 22.5140i | 0.571048 | + | 0.917602i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.00223293 | + | 0.00833342i | 9.08568e−5 | + | 0.000339082i | ||||
\(605\) | 38.6668 | − | 38.6668i | 1.57203 | − | 1.57203i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.5453 | + | 20.5221i | 1.44274 | + | 0.832965i | 0.998032 | − | 0.0627107i | \(-0.0199745\pi\) |
0.444707 | + | 0.895676i | \(0.353308\pi\) | |||||||
\(608\) | 1.68672 | − | 2.92148i | 0.0684053 | − | 0.118482i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 21.2541i | − | 0.860554i | ||||||
\(611\) | −13.7409 | + | 28.6939i | −0.555896 | + | 1.16083i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.8999 | − | 6.93987i | −1.04609 | − | 0.280299i | −0.305454 | − | 0.952207i | \(-0.598808\pi\) |
−0.740635 | + | 0.671908i | \(0.765475\pi\) | |||||||
\(614\) | − | 16.6901i | − | 0.673558i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.07495 | + | 34.6866i | −0.325349 | + | 1.39756i | ||||
\(617\) | 10.2681 | + | 2.75133i | 0.413378 | + | 0.110764i | 0.459513 | − | 0.888171i | \(-0.348024\pi\) |
−0.0461351 | + | 0.998935i | \(0.514690\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.23874 | − | 27.0153i | −0.290949 | − | 1.08584i | −0.944381 | − | 0.328853i | \(-0.893338\pi\) |
0.653432 | − | 0.756985i | \(-0.273329\pi\) | |||||||
\(620\) | 0.964435 | 0.0387326 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.1699 | + | 45.4187i | 0.487969 | + | 1.82112i | ||||
\(623\) | −0.521525 | − | 15.7618i | −0.0208945 | − | 0.631485i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.3035 | − | 26.5064i | −0.612140 | − | 1.06026i | ||||
\(626\) | −11.6165 | + | 43.3533i | −0.464288 | + | 1.73275i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.27520 | − | 2.20870i | 0.0508858 | − | 0.0881368i | ||||
\(629\) | 16.8632 | + | 16.8632i | 0.672379 | + | 0.672379i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.748324 | + | 2.79278i | −0.0297903 | + | 0.111179i | −0.979220 | − | 0.202801i | \(-0.934996\pi\) |
0.949430 | + | 0.313980i | \(0.101662\pi\) | |||||||
\(632\) | −0.548800 | + | 2.04815i | −0.0218301 | + | 0.0814711i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 22.6037 | − | 13.0503i | 0.897708 | − | 0.518292i | ||||
\(635\) | −7.09805 | + | 7.09805i | −0.281677 | + | 0.281677i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.0614 | + | 2.98774i | 0.992969 | + | 0.118378i | ||||
\(638\) | 15.0315 | 0.595103 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 33.7516 | − | 19.4865i | 1.33415 | − | 0.770272i | ||||
\(641\) | − | 15.0751i | − | 0.595431i | −0.954655 | − | 0.297715i | \(-0.903775\pi\) | ||
0.954655 | − | 0.297715i | \(-0.0962246\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.7996 | − | 40.3048i | 0.425896 | − | 1.58946i | −0.336063 | − | 0.941839i | \(-0.609096\pi\) |
0.761959 | − | 0.647625i | \(-0.224238\pi\) | |||||||
\(644\) | 6.34896 | − | 6.78348i | 0.250184 | − | 0.267307i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.90190 | − | 8.49033i | 0.192863 | − | 0.334048i | ||||
\(647\) | 0.214109 | + | 0.370847i | 0.00841747 | + | 0.0145795i | 0.870203 | − | 0.492693i | \(-0.163987\pi\) |
−0.861786 | + | 0.507272i | \(0.830654\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.9918 | + | 34.6267i | 0.784745 | + | 1.35922i | ||||
\(650\) | 1.42430 | + | 18.4630i | 0.0558657 | + | 0.724178i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.54619 | − | 5.77047i | −0.0605536 | − | 0.225989i | ||||
\(653\) | 16.3850 | 0.641195 | 0.320597 | − | 0.947216i | \(-0.396116\pi\) | ||||
0.320597 | + | 0.947216i | \(0.396116\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.31875 | + | 16.1178i | 0.168748 | + | 0.629775i | ||||
\(656\) | −18.0980 | + | 4.84936i | −0.706610 | + | 0.189336i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.23334 | − | 35.3670i | 0.320969 | − | 1.37875i | ||||
\(659\) | 13.2020 | + | 22.8666i | 0.514278 | + | 0.890755i | 0.999863 | + | 0.0165659i | \(0.00527333\pi\) |
−0.485585 | + | 0.874190i | \(0.661393\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.7452 | + | 7.16635i | 1.04027 | + | 0.278739i | 0.738224 | − | 0.674555i | \(-0.235665\pi\) |
0.302043 | + | 0.953294i | \(0.402331\pi\) | |||||||
\(662\) | −8.47684 | − | 4.89411i | −0.329462 | − | 0.190215i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.9347i | 0.579580i | ||||||||
\(665\) | 8.03726 | + | 7.52243i | 0.311672 | + | 0.291707i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.7971 | + | 7.38841i | 0.495506 | + | 0.286080i | ||||
\(668\) | 0.907416 | − | 0.243141i | 0.0351090 | − | 0.00940742i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.25243 | − | 8.40618i | −0.0870189 | − | 0.324759i | ||||
\(671\) | −18.3606 | + | 18.3606i | −0.708805 | + | 0.708805i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.8918 | − | 9.75249i | −0.651131 | − | 0.375931i | 0.137758 | − | 0.990466i | \(-0.456010\pi\) |
−0.788889 | + | 0.614535i | \(0.789344\pi\) | |||||||
\(674\) | 18.8535 | + | 18.8535i | 0.726210 | + | 0.726210i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.96987 | + | 5.08456i | −0.0757642 | + | 0.195560i | ||||
\(677\) | 1.91182 | − | 1.10379i | 0.0734772 | − | 0.0424221i | −0.462811 | − | 0.886457i | \(-0.653159\pi\) |
0.536288 | + | 0.844035i | \(0.319826\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.10919 | − | 4.99607i | −0.119320 | − | 0.191732i | ||||
\(680\) | 26.7754 | − | 15.4588i | 1.02679 | − | 0.592816i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.80570 | − | 4.80570i | −0.184020 | − | 0.184020i | ||||
\(683\) | 9.24232 | + | 9.24232i | 0.353647 | + | 0.353647i | 0.861465 | − | 0.507817i | \(-0.169548\pi\) |
−0.507817 | + | 0.861465i | \(0.669548\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.55271 | + | 4.93791i | −0.326782 | + | 0.188668i | ||||
\(686\) | −28.6658 | + | 2.85380i | −1.09446 | + | 0.108959i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −26.0208 | + | 15.0231i | −0.992035 | + | 0.572752i | ||||
\(689\) | −0.762319 | − | 0.653127i | −0.0290421 | − | 0.0248821i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.9312 | − | 35.9312i | −1.36689 | − | 1.36689i | −0.864842 | − | 0.502045i | \(-0.832581\pi\) |
−0.502045 | − | 0.864842i | \(-0.667419\pi\) | |||||||
\(692\) | −1.18053 | − | 0.681577i | −0.0448768 | − | 0.0259097i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.65219 | − | 4.65219i | 0.176595 | − | 0.176595i | ||||
\(695\) | −13.9137 | − | 51.9265i | −0.527775 | − | 1.96968i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.9402 | + | 4.53912i | −0.641657 | + | 0.171932i | ||||
\(698\) | −25.1048 | − | 14.4943i | −0.950230 | − | 0.548616i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.06491 | − | 3.50611i | −0.0402498 | − | 0.132518i | ||||
\(701\) | 12.9407i | 0.488765i | 0.969679 | + | 0.244383i | \(0.0785853\pi\) | ||||
−0.969679 | + | 0.244383i | \(0.921415\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.83317 | − | 3.94513i | −0.257718 | − | 0.148793i | ||||
\(704\) | −30.1047 | − | 8.06654i | −1.13461 | − | 0.304019i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.46444 | + | 6.00059i | 0.130386 | + | 0.225835i | ||||
\(707\) | −40.8285 | − | 9.50477i | −1.53551 | − | 0.357464i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.8425 | + | 6.38859i | −0.895426 | + | 0.239929i | −0.677051 | − | 0.735936i | \(-0.736742\pi\) |
−0.218375 | + | 0.975865i | \(0.570076\pi\) | |||||||
\(710\) | 13.6287 | + | 50.8631i | 0.511477 | + | 1.90886i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.6542 | 0.549190 | ||||||||
\(713\) | −1.72920 | − | 6.45347i | −0.0647592 | − | 0.241684i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37.0081 | − | 43.1952i | 1.38402 | − | 1.61541i | ||||
\(716\) | 4.43987 | + | 7.69008i | 0.165926 | + | 0.287392i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12.7638 | + | 22.1075i | 0.476340 | + | 0.825045i | ||||
\(719\) | 7.46614 | − | 12.9317i | 0.278440 | − | 0.482273i | −0.692557 | − | 0.721363i | \(-0.743516\pi\) |
0.970997 | + | 0.239091i | \(0.0768493\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.4513 | + | 6.39060i | 1.02234 | + | 0.237998i | ||||
\(722\) | 6.80954 | − | 25.4136i | 0.253425 | − | 0.945795i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 7.76886i | − | 0.288727i | ||||||
\(725\) | 5.04696 | − | 2.91387i | 0.187439 | − | 0.108218i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.06701 | 0.299189 | 0.149595 | − | 0.988747i | \(-0.452203\pi\) | ||||
0.149595 | + | 0.988747i | \(0.452203\pi\) | |||||||
\(728\) | −3.54486 | + | 23.1830i | −0.131381 | + | 0.859218i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −45.6390 | + | 45.6390i | −1.68917 | + | 1.68917i | ||||
\(731\) | −24.3562 | + | 14.0620i | −0.900846 | + | 0.520104i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.991378 | − | 3.69987i | 0.0366174 | − | 0.136658i | −0.945197 | − | 0.326500i | \(-0.894131\pi\) |
0.981815 | + | 0.189842i | \(0.0607975\pi\) | |||||||
\(734\) | 11.2441 | − | 41.9635i | 0.415026 | − | 1.54890i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.8297 | + | 13.8297i | 0.509769 | + | 0.509769i | ||||
\(737\) | −5.31600 | + | 9.20757i | −0.195817 | + | 0.339165i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.96535 | − | 18.5309i | 0.182653 | − | 0.681671i | −0.812467 | − | 0.583007i | \(-0.801876\pi\) |
0.995121 | − | 0.0986647i | \(-0.0314571\pi\) | |||||||
\(740\) | 3.30172 | + | 5.71875i | 0.121374 | + | 0.210225i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.01068 | + | 0.539764i | 0.0371032 | + | 0.0198153i | ||||
\(743\) | −2.24541 | − | 8.37997i | −0.0823759 | − | 0.307431i | 0.912428 | − | 0.409236i | \(-0.134205\pi\) |
−0.994804 | + | 0.101805i | \(0.967538\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −41.1891 | −1.50905 | ||||||||
\(746\) | 2.35435 | + | 8.78656i | 0.0861989 | + | 0.321699i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.68225 | + | 2.59435i | 0.354018 | + | 0.0948588i | ||||
\(749\) | −26.3078 | + | 28.1083i | −0.961264 | + | 1.02705i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.1279i | 1.09938i | 0.835367 | + | 0.549692i | \(0.185255\pi\) | ||||
−0.835367 | + | 0.549692i | \(0.814745\pi\) | |||||||
\(752\) | 39.7426 | + | 10.6490i | 1.44926 | + | 0.388329i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.86916 | − | 0.761343i | 0.359414 | − | 0.0277265i | ||||
\(755\) | − | 0.0592640i | − | 0.00215684i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.444897 | + | 0.770584i | −0.0161700 | + | 0.0280073i | −0.873997 | − | 0.485931i | \(-0.838481\pi\) |
0.857827 | + | 0.513938i | \(0.171814\pi\) | |||||||
\(758\) | 2.14223 | + | 1.23681i | 0.0778091 | + | 0.0449231i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.23314 | + | 7.23314i | −0.262373 | + | 0.262373i | ||||
\(761\) | 12.4145 | + | 46.3316i | 0.450026 | + | 1.67952i | 0.702314 | + | 0.711867i | \(0.252150\pi\) |
−0.252288 | + | 0.967652i | \(0.581183\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.0836 | + | 10.7258i | 0.727075 | + | 0.388302i | ||||
\(764\) | 9.95963 | + | 5.75019i | 0.360327 | + | 0.208035i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.9542 | + | 18.9732i | −0.395791 | + | 0.685530i | ||||
\(767\) | 14.8797 | + | 21.7221i | 0.537275 | + | 0.784340i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.85396 | − | 1.30061i | 0.175038 | − | 0.0469013i | −0.170235 | − | 0.985403i | \(-0.554453\pi\) |
0.345274 | + | 0.938502i | \(0.387786\pi\) | |||||||
\(770\) | −30.5846 | + | 57.2680i | −1.10219 | + | 2.06380i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.72676 | + | 2.07038i | 0.278092 | + | 0.0745146i | ||||
\(773\) | −9.15642 | − | 9.15642i | −0.329333 | − | 0.329333i | 0.523000 | − | 0.852333i | \(-0.324813\pi\) |
−0.852333 | + | 0.523000i | \(0.824813\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.54514 | − | 0.681969i | −0.0914242 | − | 0.0244970i | ||||
\(776\) | 4.73545 | − | 2.73401i | 0.169993 | − | 0.0981454i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.376093 | − | 0.100774i | 0.0134836 | − | 0.00361292i | ||||
\(779\) | 5.02509 | − | 2.90123i | 0.180042 | − | 0.103948i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.1654 | − | 55.7121i | 1.15097 | − | 1.99354i | ||||
\(782\) | 40.1915 | + | 40.1915i | 1.43725 | + | 1.43725i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.15766 | − | 32.5693i | −0.0770592 | − | 1.16319i | ||||
\(785\) | −12.3880 | + | 12.3880i | −0.442148 | + | 0.442148i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.63546 | − | 1.63546i | 0.0582978 | − | 0.0582978i | −0.677357 | − | 0.735655i | \(-0.736875\pi\) |
0.735655 | + | 0.677357i | \(0.236875\pi\) | |||||||
\(788\) | −1.88090 | + | 0.503986i | −0.0670043 | + | 0.0179538i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.93271 | + | 3.34756i | −0.0687628 | + | 0.119101i | ||||
\(791\) | −35.1176 | − | 8.17528i | −1.24864 | − | 0.290679i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.1250 | + | 12.9849i | −0.395060 | + | 0.461108i | ||||
\(794\) | −9.07049 | − | 5.23685i | −0.321900 | − | 0.185849i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.187543i | 0.00664730i | ||||||||
\(797\) | −22.4781 | − | 38.9332i | −0.796216 | − | 1.37909i | −0.922064 | − | 0.387037i | \(-0.873499\pi\) |
0.125848 | − | 0.992049i | \(-0.459835\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.2001 | + | 9.96774i | 1.31605 | + | 0.352633i | ||||
\(800\) | 7.45057 | − | 1.99637i | 0.263417 | − | 0.0705825i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −44.8511 | −1.58375 | ||||||||
\(803\) | 78.8516 | 2.78261 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −54.1870 | + | 33.7220i | −1.90984 | + | 1.18855i | ||||
\(806\) | −3.39866 | − | 2.91184i | −0.119713 | − | 0.102565i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.0818 | − | 37.6258i | 0.354677 | − | 1.32367i | ||||
\(809\) | −7.19827 | − | 12.4678i | −0.253078 | − | 0.438343i | 0.711294 | − | 0.702895i | \(-0.248109\pi\) |
−0.964372 | + | 0.264551i | \(0.914776\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.3043 | + | 15.3043i | 0.537406 | + | 0.537406i | 0.922766 | − | 0.385360i | \(-0.125923\pi\) |
−0.385360 | + | 0.922766i | \(0.625923\pi\) | |||||||
\(812\) | −1.87415 | + | 0.569234i | −0.0657697 | + | 0.0199762i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.0438 | − | 44.9482i | 0.422137 | − | 1.57544i | ||||
\(815\) | 41.0373i | 1.43747i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.57962 | − | 6.57962i | 0.230192 | − | 0.230192i | ||||
\(818\) | −41.9328 | −1.46615 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.85614 | −0.169584 | ||||||||
\(821\) | 25.9843 | − | 25.9843i | 0.906858 | − | 0.906858i | −0.0891592 | − | 0.996017i | \(-0.528418\pi\) |
0.996017 | + | 0.0891592i | \(0.0284180\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.4449i | 1.13096i | 0.824762 | + | 0.565480i | \(0.191309\pi\) | ||||
−0.824762 | + | 0.565480i | \(0.808691\pi\) | |||||||
\(824\) | −6.77857 | + | 25.2980i | −0.236143 | + | 0.881297i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −21.9415 | − | 20.5360i | −0.763443 | − | 0.714540i | ||||
\(827\) | 32.5966 | + | 32.5966i | 1.13349 | + | 1.13349i | 0.989592 | + | 0.143901i | \(0.0459647\pi\) |
0.143901 | + | 0.989592i | \(0.454035\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.7107 | + | 41.0681i | 0.823507 | + | 1.42636i | 0.903055 | + | 0.429524i | \(0.141319\pi\) |
−0.0795487 | + | 0.996831i | \(0.525348\pi\) | |||||||
\(830\) | −7.04648 | + | 26.2978i | −0.244587 | + | 0.912811i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20.1743 | − | 3.77140i | −0.699417 | − | 0.130750i | ||||
\(833\) | −2.01962 | − | 30.4857i | −0.0699758 | − | 1.05627i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.45318 | −0.223321 | ||||||||
\(836\) | −3.31642 | −0.114701 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 20.9412 | − | 5.61119i | 0.723403 | − | 0.193835i | ||||
\(839\) | 3.74709 | + | 1.00403i | 0.129364 | + | 0.0346629i | 0.322920 | − | 0.946426i | \(-0.395336\pi\) |
−0.193556 | + | 0.981089i | \(0.562002\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.9424 | + | 22.4169i | 0.446291 | + | 0.772998i | ||||
\(842\) | 35.1661i | 1.21191i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.4467 | + | 6.03143i | 0.359591 | + | 0.207610i | ||||
\(845\) | 22.1103 | − | 30.2349i | 0.760619 | − | 1.04011i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48.0455 | − | 14.5928i | 1.65086 | − | 0.501416i | ||||
\(848\) | −0.649122 | + | 1.12431i | −0.0222910 | + | 0.0386091i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 21.6527 | − | 5.80182i | 0.742681 | − | 0.199001i | ||||
\(851\) | 32.3469 | − | 32.3469i | 1.10884 | − | 1.10884i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.3977 | + | 23.3977i | −0.801122 | + | 0.801122i | −0.983271 | − | 0.182149i | \(-0.941695\pi\) |
0.182149 | + | 0.983271i | \(0.441695\pi\) | |||||||
\(854\) | 9.19402 | − | 17.2153i | 0.314613 | − | 0.589096i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25.2960 | − | 25.2960i | −0.864601 | − | 0.864601i | ||||
\(857\) | 7.09899 | − | 12.2958i | 0.242497 | − | 0.420017i | −0.718928 | − | 0.695084i | \(-0.755367\pi\) |
0.961425 | + | 0.275068i | \(0.0887003\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.7926 | + | 24.1290i | −1.42595 | + | 0.823270i | −0.996798 | − | 0.0799637i | \(-0.974520\pi\) |
−0.429148 | + | 0.903234i | \(0.641186\pi\) | |||||||
\(860\) | −7.52208 | + | 2.01553i | −0.256501 | + | 0.0687292i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.33655 | − | 2.50371i | 0.147703 | − | 0.0852766i | ||||
\(863\) | 39.8830 | + | 10.6866i | 1.35763 | + | 0.363776i | 0.862946 | − | 0.505296i | \(-0.168617\pi\) |
0.494686 | + | 0.869072i | \(0.335283\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.62126 | + | 6.62126i | 0.225130 | + | 0.225130i | ||||
\(866\) | 16.0503 | + | 4.30068i | 0.545413 | + | 0.146143i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.781169 | + | 0.417191i | 0.0265146 | + | 0.0141604i | ||||
\(869\) | 4.56143 | − | 1.22223i | 0.154736 | − | 0.0414613i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.02393 | + | 6.31462i | −0.102462 | + | 0.213963i | ||||
\(872\) | −10.5784 | + | 18.3223i | −0.358228 | + | 0.620470i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −16.2861 | − | 9.40279i | −0.550886 | − | 0.318054i | ||||
\(875\) | −0.428092 | − | 12.9381i | −0.0144722 | − | 0.437386i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.12324 | + | 19.1202i | 0.173000 | + | 0.645643i | 0.996884 | + | 0.0788850i | \(0.0251360\pi\) |
−0.823884 | + | 0.566758i | \(0.808197\pi\) | |||||||
\(878\) | −16.0153 | + | 16.0153i | −0.540491 | + | 0.540491i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −63.7068 | − | 36.7812i | −2.14756 | − | 1.23989i | ||||
\(881\) | −4.58892 | + | 7.94824i | −0.154605 | + | 0.267783i | −0.932915 | − | 0.360097i | \(-0.882744\pi\) |
0.778310 | + | 0.627880i | \(0.216077\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.23790i | 0.0753113i | 0.999291 | + | 0.0376556i | \(0.0119890\pi\) | ||||
−0.999291 | + | 0.0376556i | \(0.988011\pi\) | |||||||
\(884\) | 6.48842 | + | 1.21295i | 0.218229 | + | 0.0407961i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.51051 | − | 2.01244i | −0.252321 | − | 0.0676091i | ||||
\(887\) | − | 10.1980i | − | 0.342415i | −0.985235 | − | 0.171207i | \(-0.945233\pi\) | ||
0.985235 | − | 0.171207i | \(-0.0547668\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.81969 | + | 2.67880i | −0.295803 | + | 0.0898442i | ||||
\(890\) | 25.8039 | + | 6.91414i | 0.864949 | + | 0.231762i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.58199 | − | 5.90405i | −0.0529688 | − | 0.197682i | ||||
\(893\) | −12.7420 | −0.426395 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.7873 | − | 58.9190i | −0.527711 | − | 1.96944i | ||||
\(896\) | 35.7674 | − | 1.18347i | 1.19491 | − | 0.0395368i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20.7147 | − | 35.8790i | −0.691259 | − | 1.19730i | ||||
\(899\) | −0.364538 | + | 1.36047i | −0.0121580 | + | 0.0453744i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.607596 | + | 1.05239i | −0.0202419 | + | 0.0350601i | ||||
\(902\) | 24.1978 | + | 24.1978i | 0.805697 | + | 0.805697i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.67160 | − | 32.3628i | 0.288413 | − | 1.07637i | ||||
\(905\) | −13.8123 | + | 51.5480i | −0.459135 | + | 1.71351i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.4824 | − | 20.4858i | 1.17817 | − | 0.680219i | 0.222582 | − | 0.974914i | \(-0.428551\pi\) |
0.955591 | + | 0.294695i | \(0.0952181\pi\) | |||||||
\(908\) | −5.31685 | + | 5.31685i | −0.176446 | + | 0.176446i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −17.1801 | + | 39.1493i | −0.569516 | + | 1.29779i | ||||
\(911\) | −45.1869 | −1.49711 | −0.748554 | − | 0.663074i | \(-0.769252\pi\) | ||||
−0.748554 | + | 0.663074i | \(0.769252\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.8049 | − | 16.6305i | 0.953303 | − | 0.550390i | ||||
\(914\) | − | 19.4733i | − | 0.644120i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.743381 | + | 2.77433i | −0.0245620 | + | 0.0916666i | ||||
\(917\) | −3.47409 | + | 14.9232i | −0.114724 | + | 0.492808i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.4121 | + | 18.0342i | −0.343463 | + | 0.594895i | −0.985073 | − | 0.172136i | \(-0.944933\pi\) |
0.641611 | + | 0.767030i | \(0.278267\pi\) | |||||||
\(920\) | −29.6529 | − | 51.3603i | −0.977627 | − | 1.69330i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7.76155 | − | 13.4434i | −0.255613 | − | 0.442735i | ||||
\(923\) | 18.2968 | − | 38.2078i | 0.602248 | − | 1.25762i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.66941 | − | 17.4265i | −0.153529 | − | 0.572979i | ||||
\(926\) | 19.5165 | 0.641352 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.06714 | − | 3.98261i | −0.0350305 | − | 0.130736i | ||||
\(929\) | −54.2535 | + | 14.5372i | −1.78000 | + | 0.476949i | −0.990584 | − | 0.136910i | \(-0.956283\pi\) |
−0.789416 | + | 0.613859i | \(0.789616\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.25597 | + | 9.56971i | 0.106710 | + | 0.313635i | ||||
\(932\) | 1.63281 | + | 2.82811i | 0.0534844 | + | 0.0926377i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 22.0449 | + | 5.90691i | 0.721331 | + | 0.193280i | ||||
\(935\) | −59.6313 | − | 34.4281i | −1.95015 | − | 1.12592i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.6449i | 0.413092i | 0.978437 | + | 0.206546i | \(0.0662223\pi\) | ||||
−0.978437 | + | 0.206546i | \(0.933778\pi\) | |||||||
\(938\) | 1.81190 | − | 7.78315i | 0.0591605 | − | 0.254129i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.23521 | + | 5.33195i | 0.301219 | + | 0.173909i | ||||
\(941\) | 1.15761 | − | 0.310180i | 0.0377369 | − | 0.0101116i | −0.239901 | − | 0.970797i | \(-0.577115\pi\) |
0.277638 | + | 0.960686i | \(0.410448\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.70692 | + | 32.4947i | 0.283536 | + | 1.05817i | ||||
\(944\) | 24.0781 | − | 24.0781i | 0.783674 | − | 0.783674i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 47.5252 | + | 27.4387i | 1.54518 | + | 0.892108i | ||||
\(947\) | −22.5630 | − | 22.5630i | −0.733199 | − | 0.733199i | 0.238053 | − | 0.971252i | \(-0.423491\pi\) |
−0.971252 | + | 0.238053i | \(0.923491\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 51.7712 | − | 3.99382i | 1.68056 | − | 0.129645i | ||||
\(950\) | −6.42297 | + | 3.70830i | −0.208389 | + | 0.120313i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 28.3745 | − | 0.938850i | 0.919622 | − | 0.0304283i | ||||
\(953\) | −9.16224 | + | 5.28982i | −0.296794 | + | 0.171354i | −0.641002 | − | 0.767539i | \(-0.721481\pi\) |
0.344208 | + | 0.938894i | \(0.388148\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −55.8610 | − | 55.8610i | −1.80762 | − | 1.80762i | ||||
\(956\) | −0.932968 | − | 0.932968i | −0.0301743 | − | 0.0301743i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 18.6092 | − | 10.7440i | 0.601236 | − | 0.347124i | ||||
\(959\) | −9.06351 | + | 0.299892i | −0.292676 | + | 0.00968402i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.2953 | + | 15.1816i | −0.848235 | + | 0.489729i | ||||
\(962\) | 5.63094 | − | 30.1214i | 0.181549 | − | 0.971154i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.66326 | − | 2.66326i | −0.0857779 | − | 0.0857779i | ||||
\(965\) | −47.5878 | − | 27.4748i | −1.53190 | − | 0.884445i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.9761 | − | 23.9761i | 0.771021 | − | 0.771021i | −0.207264 | − | 0.978285i | \(-0.566456\pi\) |
0.978285 | + | 0.207264i | \(0.0664560\pi\) | |||||||
\(968\) | 12.0761 | + | 45.0688i | 0.388142 | + | 1.44856i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.62838 | − | 2.57992i | 0.309149 | − | 0.0828362i | ||||
\(971\) | −21.6257 | − | 12.4856i | −0.694002 | − | 0.400682i | 0.111108 | − | 0.993808i | \(-0.464560\pi\) |
−0.805109 | + | 0.593126i | \(0.797893\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.1924 | − | 48.0779i | 0.358812 | − | 1.54131i | ||||
\(974\) | 46.7606i | 1.49831i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 19.1509 | + | 11.0568i | 0.613005 | + | 0.353919i | ||||
\(977\) | −16.3501 | − | 4.38099i | −0.523085 | − | 0.140160i | −0.0123917 | − | 0.999923i | \(-0.503945\pi\) |
−0.510693 | + | 0.859763i | \(0.670611\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.3182 | − | 28.2639i | −0.521531 | − | 0.903318i | ||||
\(980\) | 1.64461 | − | 8.29846i | 0.0525353 | − | 0.265085i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 47.3324 | − | 12.6827i | 1.51044 | − | 0.404721i | ||||
\(983\) | 7.16888 | + | 26.7546i | 0.228652 | + | 0.853340i | 0.980908 | + | 0.194470i | \(0.0622987\pi\) |
−0.752257 | + | 0.658870i | \(0.771035\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.3762 | 0.426202 | ||||||||
\(986\) | −3.10129 | − | 11.5742i | −0.0987653 | − | 0.368597i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.17744 | + | 0.167976i | −0.0692737 | + | 0.00534403i | ||||
\(989\) | 26.9737 | + | 46.7199i | 0.857715 | + | 1.48561i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.15625 | − | 10.6629i | −0.195560 | − | 0.338720i | 0.751524 | − | 0.659706i | \(-0.229319\pi\) |
−0.947084 | + | 0.320986i | \(0.895986\pi\) | |||||||
\(992\) | −0.932101 | + | 1.61445i | −0.0295942 | + | 0.0512587i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10.9632 | + | 47.0934i | −0.347732 | + | 1.49371i | ||||
\(995\) | 0.333433 | − | 1.24439i | 0.0105706 | − | 0.0394498i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.5696i | 0.398082i | 0.979991 | + | 0.199041i | \(0.0637827\pi\) | ||||
−0.979991 | + | 0.199041i | \(0.936217\pi\) | |||||||
\(998\) | 31.5002 | − | 18.1866i | 0.997121 | − | 0.575688i | ||||
\(999\) | 0 | 0 |
(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 | 819.2.et.c.136.3 | 36 | ||
3.2 | odd | 2 | 273.2.bt.a.136.7 | ✓ | 36 | ||
7.5 | odd | 6 | 819.2.gh.c.19.7 | 36 | |||
13.11 | odd | 12 | 819.2.gh.c.388.7 | 36 | |||
21.5 | even | 6 | 273.2.cg.a.19.3 | yes | 36 | ||
39.11 | even | 12 | 273.2.cg.a.115.3 | yes | 36 | ||
91.89 | even | 12 | inner | 819.2.et.c.271.3 | 36 | ||
273.89 | odd | 12 | 273.2.bt.a.271.7 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.bt.a.136.7 | ✓ | 36 | 3.2 | odd | 2 | ||
273.2.bt.a.271.7 | yes | 36 | 273.89 | odd | 12 | ||
273.2.cg.a.19.3 | yes | 36 | 21.5 | even | 6 | ||
273.2.cg.a.115.3 | yes | 36 | 39.11 | even | 12 | ||
819.2.et.c.136.3 | 36 | 1.1 | even | 1 | trivial | ||
819.2.et.c.271.3 | 36 | 91.89 | even | 12 | inner | ||
819.2.gh.c.19.7 | 36 | 7.5 | odd | 6 | |||
819.2.gh.c.388.7 | 36 | 13.11 | odd | 12 |