Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(25,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.l (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Relative dimension: | \(34\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 25.20 | ||
Character | \(\chi\) | \(=\) | 403.25 |
Dual form | 403.2.l.c.129.15 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.216546i | 0.153121i | 0.997065 | + | 0.0765606i | \(0.0243939\pi\) | ||||
−0.997065 | + | 0.0765606i | \(0.975606\pi\) | |||||||
\(3\) | 1.35890 | + | 2.35368i | 0.784561 | + | 1.35890i | 0.929261 | + | 0.369424i | \(0.120445\pi\) |
−0.144700 | + | 0.989476i | \(0.546222\pi\) | |||||||
\(4\) | 1.95311 | 0.976554 | ||||||||
\(5\) | −0.933057 | − | 0.538701i | −0.417276 | − | 0.240914i | 0.276635 | − | 0.960975i | \(-0.410781\pi\) |
−0.693911 | + | 0.720061i | \(0.744114\pi\) | |||||||
\(6\) | −0.509681 | + | 0.294264i | −0.208076 | + | 0.120133i | ||||
\(7\) | 2.50436 | − | 1.44590i | 0.946560 | − | 0.546497i | 0.0545497 | − | 0.998511i | \(-0.482628\pi\) |
0.892011 | + | 0.452014i | \(0.149294\pi\) | |||||||
\(8\) | 0.856030i | 0.302652i | ||||||||
\(9\) | −2.19321 | + | 3.79876i | −0.731071 | + | 1.26625i | ||||
\(10\) | 0.116654 | − | 0.202050i | 0.0368891 | − | 0.0638938i | ||||
\(11\) | −1.69734 | − | 0.979961i | −0.511768 | − | 0.295469i | 0.221792 | − | 0.975094i | \(-0.428809\pi\) |
−0.733560 | + | 0.679625i | \(0.762143\pi\) | |||||||
\(12\) | 2.65408 | + | 4.59700i | 0.766166 | + | 1.32704i | ||||
\(13\) | 3.03278 | + | 1.94993i | 0.841143 | + | 0.540813i | ||||
\(14\) | 0.313103 | + | 0.542310i | 0.0836803 | + | 0.144938i | ||||
\(15\) | − | 2.92816i | − | 0.756048i | ||||||
\(16\) | 3.72085 | 0.930211 | ||||||||
\(17\) | −2.22424 | − | 3.85250i | −0.539457 | − | 0.934368i | −0.998933 | − | 0.0461774i | \(-0.985296\pi\) |
0.459476 | − | 0.888190i | \(-0.348037\pi\) | |||||||
\(18\) | −0.822606 | − | 0.474932i | −0.193890 | − | 0.111943i | ||||
\(19\) | −3.53832 | + | 2.04285i | −0.811746 | + | 0.468662i | −0.847562 | − | 0.530696i | \(-0.821930\pi\) |
0.0358156 | + | 0.999358i | \(0.488597\pi\) | |||||||
\(20\) | −1.82236 | − | 1.05214i | −0.407492 | − | 0.235266i | ||||
\(21\) | 6.80636 | + | 3.92965i | 1.48527 | + | 0.857520i | ||||
\(22\) | 0.212207 | − | 0.367553i | 0.0452426 | − | 0.0783625i | ||||
\(23\) | −0.663330 | −0.138314 | −0.0691570 | − | 0.997606i | \(-0.522031\pi\) | ||||
−0.0691570 | + | 0.997606i | \(0.522031\pi\) | |||||||
\(24\) | −2.01482 | + | 1.16326i | −0.411274 | + | 0.237449i | ||||
\(25\) | −1.91960 | − | 3.32485i | −0.383921 | − | 0.664970i | ||||
\(26\) | −0.422249 | + | 0.656737i | −0.0828099 | + | 0.128797i | ||||
\(27\) | −3.76803 | −0.725159 | ||||||||
\(28\) | 4.89129 | − | 2.82399i | 0.924367 | − | 0.533684i | ||||
\(29\) | −4.34035 | −0.805982 | −0.402991 | − | 0.915204i | \(-0.632029\pi\) | ||||
−0.402991 | + | 0.915204i | \(0.632029\pi\) | |||||||
\(30\) | 0.634082 | 0.115767 | ||||||||
\(31\) | −5.33130 | + | 1.60538i | −0.957529 | + | 0.288336i | ||||
\(32\) | 2.51779i | 0.445087i | ||||||||
\(33\) | − | 5.32668i | − | 0.927255i | ||||||
\(34\) | 0.834243 | − | 0.481650i | 0.143071 | − | 0.0826024i | ||||
\(35\) | −3.11562 | −0.526636 | ||||||||
\(36\) | −4.28358 | + | 7.41939i | −0.713931 | + | 1.23656i | ||||
\(37\) | −0.514023 | + | 0.296771i | −0.0845048 | + | 0.0487889i | −0.541657 | − | 0.840600i | \(-0.682203\pi\) |
0.457152 | + | 0.889389i | \(0.348869\pi\) | |||||||
\(38\) | −0.442371 | − | 0.766209i | −0.0717621 | − | 0.124296i | ||||
\(39\) | −0.468267 | + | 9.78797i | −0.0749828 | + | 1.56733i | ||||
\(40\) | 0.461144 | − | 0.798725i | 0.0729133 | − | 0.126289i | ||||
\(41\) | −6.64980 | − | 3.83926i | −1.03852 | − | 0.599592i | −0.119109 | − | 0.992881i | \(-0.538004\pi\) |
−0.919415 | + | 0.393289i | \(0.871337\pi\) | |||||||
\(42\) | −0.850950 | + | 1.47389i | −0.131305 | + | 0.227426i | ||||
\(43\) | 2.15673 | + | 3.73557i | 0.328899 | + | 0.569669i | 0.982294 | − | 0.187348i | \(-0.0599892\pi\) |
−0.653395 | + | 0.757017i | \(0.726656\pi\) | |||||||
\(44\) | −3.31509 | − | 1.91397i | −0.499769 | − | 0.288542i | ||||
\(45\) | 4.09279 | − | 2.36297i | 0.610117 | − | 0.352251i | ||||
\(46\) | − | 0.143642i | − | 0.0211788i | ||||||
\(47\) | − | 0.255427i | − | 0.0372579i | −0.999826 | − | 0.0186289i | \(-0.994070\pi\) | ||
0.999826 | − | 0.0186289i | \(-0.00593012\pi\) | |||||||
\(48\) | 5.05625 | + | 8.75769i | 0.729807 | + | 1.26406i | ||||
\(49\) | 0.681225 | − | 1.17992i | 0.0973178 | − | 0.168559i | ||||
\(50\) | 0.719983 | − | 0.415682i | 0.101821 | − | 0.0587864i | ||||
\(51\) | 6.04504 | − | 10.4703i | 0.846474 | − | 1.46614i | ||||
\(52\) | 5.92335 | + | 3.80842i | 0.821421 | + | 0.528133i | ||||
\(53\) | 1.64889 | − | 2.85596i | 0.226492 | − | 0.392296i | −0.730274 | − | 0.683155i | \(-0.760608\pi\) |
0.956766 | + | 0.290858i | \(0.0939409\pi\) | |||||||
\(54\) | − | 0.815953i | − | 0.111037i | ||||||
\(55\) | 1.05581 | + | 1.82872i | 0.142366 | + | 0.246585i | ||||
\(56\) | 1.23773 | + | 2.14381i | 0.165399 | + | 0.286479i | ||||
\(57\) | −9.61644 | − | 5.55206i | −1.27373 | − | 0.735388i | ||||
\(58\) | − | 0.939885i | − | 0.123413i | ||||||
\(59\) | 9.81008 | − | 5.66385i | 1.27716 | − | 0.737371i | 0.300838 | − | 0.953675i | \(-0.402734\pi\) |
0.976326 | + | 0.216304i | \(0.0694004\pi\) | |||||||
\(60\) | − | 5.71901i | − | 0.738321i | ||||||
\(61\) | 5.31550 | 0.680580 | 0.340290 | − | 0.940321i | \(-0.389475\pi\) | ||||
0.340290 | + | 0.940321i | \(0.389475\pi\) | |||||||
\(62\) | −0.347640 | − | 1.15447i | −0.0441503 | − | 0.146618i | ||||
\(63\) | 12.6846i | 1.59811i | ||||||||
\(64\) | 6.89647 | 0.862059 | ||||||||
\(65\) | −1.77933 | − | 3.45316i | −0.220699 | − | 0.428312i | ||||
\(66\) | 1.15347 | 0.141982 | ||||||||
\(67\) | −8.18899 | − | 4.72791i | −1.00044 | − | 0.577607i | −0.0920644 | − | 0.995753i | \(-0.529347\pi\) |
−0.908380 | + | 0.418146i | \(0.862680\pi\) | |||||||
\(68\) | −4.34418 | − | 7.52434i | −0.526809 | − | 0.912460i | ||||
\(69\) | −0.901399 | − | 1.56127i | −0.108516 | − | 0.187955i | ||||
\(70\) | − | 0.674675i | − | 0.0806391i | ||||||
\(71\) | 6.83812 | + | 3.94799i | 0.811535 | + | 0.468540i | 0.847489 | − | 0.530813i | \(-0.178113\pi\) |
−0.0359533 | + | 0.999353i | \(0.511447\pi\) | |||||||
\(72\) | −3.25185 | − | 1.87746i | −0.383234 | − | 0.221260i | ||||
\(73\) | 0.249101 | + | 0.143819i | 0.0291551 | + | 0.0168327i | 0.514507 | − | 0.857486i | \(-0.327975\pi\) |
−0.485352 | + | 0.874319i | \(0.661308\pi\) | |||||||
\(74\) | −0.0642646 | − | 0.111310i | −0.00747061 | − | 0.0129395i | ||||
\(75\) | 5.21709 | − | 9.03627i | 0.602418 | − | 1.04342i | ||||
\(76\) | −6.91072 | + | 3.98991i | −0.792714 | + | 0.457674i | ||||
\(77\) | −5.66768 | −0.645893 | ||||||||
\(78\) | −2.11955 | − | 0.101401i | −0.239991 | − | 0.0114815i | ||||
\(79\) | −2.03383 | − | 3.52270i | −0.228824 | − | 0.396334i | 0.728636 | − | 0.684901i | \(-0.240155\pi\) |
−0.957460 | + | 0.288567i | \(0.906821\pi\) | |||||||
\(80\) | −3.47176 | − | 2.00442i | −0.388155 | − | 0.224101i | ||||
\(81\) | 1.45926 | + | 2.52752i | 0.162140 | + | 0.280835i | ||||
\(82\) | 0.831377 | − | 1.43999i | 0.0918103 | − | 0.159020i | ||||
\(83\) | 12.3268 | + | 7.11691i | 1.35305 | + | 0.781182i | 0.988675 | − | 0.150071i | \(-0.0479503\pi\) |
0.364372 | + | 0.931253i | \(0.381284\pi\) | |||||||
\(84\) | 13.2935 | + | 7.67503i | 1.45044 | + | 0.837415i | ||||
\(85\) | 4.79280i | 0.519852i | ||||||||
\(86\) | −0.808923 | + | 0.467032i | −0.0872284 | + | 0.0503613i | ||||
\(87\) | −5.89810 | − | 10.2158i | −0.632342 | − | 1.09525i | ||||
\(88\) | 0.838876 | − | 1.45298i | 0.0894245 | − | 0.154888i | ||||
\(89\) | 5.37232i | 0.569464i | 0.958607 | + | 0.284732i | \(0.0919047\pi\) | ||||
−0.958607 | + | 0.284732i | \(0.908095\pi\) | |||||||
\(90\) | 0.511692 | + | 0.886277i | 0.0539371 | + | 0.0934218i | ||||
\(91\) | 10.4146 | + | 0.498246i | 1.09175 | + | 0.0522303i | ||||
\(92\) | −1.29556 | −0.135071 | ||||||||
\(93\) | −11.0233 | − | 10.3666i | −1.14306 | − | 1.07497i | ||||
\(94\) | 0.0553117 | 0.00570497 | ||||||||
\(95\) | 4.40194 | 0.451630 | ||||||||
\(96\) | −5.92609 | + | 3.42143i | −0.604829 | + | 0.349198i | ||||
\(97\) | − | 1.70597i | − | 0.173216i | −0.996242 | − | 0.0866078i | \(-0.972397\pi\) | ||
0.996242 | − | 0.0866078i | \(-0.0276027\pi\) | |||||||
\(98\) | 0.255506 | + | 0.147517i | 0.0258100 | + | 0.0149014i | ||||
\(99\) | 7.44527 | − | 4.29853i | 0.748278 | − | 0.432019i | ||||
\(100\) | −3.74919 | − | 6.49379i | −0.374919 | − | 0.649379i | ||||
\(101\) | −8.31840 | −0.827711 | −0.413856 | − | 0.910342i | \(-0.635818\pi\) | ||||
−0.413856 | + | 0.910342i | \(0.635818\pi\) | |||||||
\(102\) | 2.26730 | + | 1.30903i | 0.224497 | + | 0.129613i | ||||
\(103\) | −1.71285 | + | 2.96674i | −0.168772 | + | 0.292322i | −0.937988 | − | 0.346667i | \(-0.887314\pi\) |
0.769216 | + | 0.638989i | \(0.220647\pi\) | |||||||
\(104\) | −1.66920 | + | 2.59615i | −0.163678 | + | 0.254574i | ||||
\(105\) | −4.23381 | − | 7.33318i | −0.413178 | − | 0.715645i | ||||
\(106\) | 0.618447 | + | 0.357060i | 0.0600688 | + | 0.0346808i | ||||
\(107\) | −7.21523 | − | 12.4972i | −0.697523 | − | 1.20815i | −0.969323 | − | 0.245792i | \(-0.920952\pi\) |
0.271800 | − | 0.962354i | \(-0.412381\pi\) | |||||||
\(108\) | −7.35938 | −0.708156 | ||||||||
\(109\) | − | 14.1796i | − | 1.35816i | −0.734064 | − | 0.679080i | \(-0.762379\pi\) | ||
0.734064 | − | 0.679080i | \(-0.237621\pi\) | |||||||
\(110\) | −0.396002 | + | 0.228632i | −0.0377573 | + | 0.0217992i | ||||
\(111\) | −1.39701 | − | 0.806565i | −0.132598 | − | 0.0765557i | ||||
\(112\) | 9.31835 | − | 5.37995i | 0.880501 | − | 0.508358i | ||||
\(113\) | −2.72624 | + | 4.72198i | −0.256463 | + | 0.444207i | −0.965292 | − | 0.261174i | \(-0.915890\pi\) |
0.708829 | + | 0.705380i | \(0.249224\pi\) | |||||||
\(114\) | 1.20228 | − | 2.08240i | 0.112603 | − | 0.195035i | ||||
\(115\) | 0.618925 | + | 0.357337i | 0.0577151 | + | 0.0333218i | ||||
\(116\) | −8.47717 | −0.787085 | ||||||||
\(117\) | −14.0589 | + | 7.24420i | −1.29974 | + | 0.669727i | ||||
\(118\) | 1.22648 | + | 2.12433i | 0.112907 | + | 0.195561i | ||||
\(119\) | −11.1406 | − | 6.43204i | −1.02126 | − | 0.589624i | ||||
\(120\) | 2.50659 | 0.228820 | ||||||||
\(121\) | −3.57935 | − | 6.19962i | −0.325396 | − | 0.563602i | ||||
\(122\) | 1.15105i | 0.104211i | ||||||||
\(123\) | − | 20.8687i | − | 1.88167i | ||||||
\(124\) | −10.4126 | + | 3.13549i | −0.935079 | + | 0.281575i | ||||
\(125\) | 9.52337i | 0.851797i | ||||||||
\(126\) | −2.74681 | −0.244705 | ||||||||
\(127\) | −9.01988 | − | 15.6229i | −0.800385 | − | 1.38631i | −0.919363 | − | 0.393411i | \(-0.871295\pi\) |
0.118978 | − | 0.992897i | \(-0.462038\pi\) | |||||||
\(128\) | 6.52899i | 0.577087i | ||||||||
\(129\) | −5.86156 | + | 10.1525i | −0.516082 | + | 0.893880i | ||||
\(130\) | 0.747768 | − | 0.385307i | 0.0655836 | − | 0.0337937i | ||||
\(131\) | 2.44773 | + | 4.23960i | 0.213859 | + | 0.370415i | 0.952919 | − | 0.303225i | \(-0.0980632\pi\) |
−0.739060 | + | 0.673640i | \(0.764730\pi\) | |||||||
\(132\) | − | 10.4036i | − | 0.905515i | ||||||
\(133\) | −5.90749 | + | 10.2321i | −0.512245 | + | 0.887234i | ||||
\(134\) | 1.02381 | − | 1.77329i | 0.0884438 | − | 0.153189i | ||||
\(135\) | 3.51579 | + | 2.02984i | 0.302591 | + | 0.174701i | ||||
\(136\) | 3.29785 | − | 1.90402i | 0.282788 | − | 0.163268i | ||||
\(137\) | 12.5462 | + | 7.24358i | 1.07190 | + | 0.618860i | 0.928699 | − | 0.370834i | \(-0.120928\pi\) |
0.143198 | + | 0.989694i | \(0.454261\pi\) | |||||||
\(138\) | 0.338087 | − | 0.195194i | 0.0287798 | − | 0.0166160i | ||||
\(139\) | 21.1636 | 1.79508 | 0.897538 | − | 0.440936i | \(-0.145354\pi\) | ||||
0.897538 | + | 0.440936i | \(0.145354\pi\) | |||||||
\(140\) | −6.08514 | −0.514288 | ||||||||
\(141\) | 0.601194 | − | 0.347100i | 0.0506297 | − | 0.0292311i | ||||
\(142\) | −0.854922 | + | 1.48077i | −0.0717434 | + | 0.124263i | ||||
\(143\) | −3.23682 | − | 6.28171i | −0.270676 | − | 0.525303i | ||||
\(144\) | −8.16061 | + | 14.1346i | −0.680051 | + | 1.17788i | ||||
\(145\) | 4.04979 | + | 2.33815i | 0.336317 | + | 0.194173i | ||||
\(146\) | −0.0311434 | + | 0.0539419i | −0.00257745 | + | 0.00446427i | ||||
\(147\) | 3.70286 | 0.305407 | ||||||||
\(148\) | −1.00394 | + | 0.579626i | −0.0825235 | + | 0.0476450i | ||||
\(149\) | 11.3091 | − | 6.52932i | 0.926478 | − | 0.534902i | 0.0407821 | − | 0.999168i | \(-0.487015\pi\) |
0.885696 | + | 0.464266i | \(0.153682\pi\) | |||||||
\(150\) | 1.95677 | + | 1.12974i | 0.159770 | + | 0.0922430i | ||||
\(151\) | 21.4537i | 1.74587i | 0.487833 | + | 0.872937i | \(0.337788\pi\) | ||||
−0.487833 | + | 0.872937i | \(0.662212\pi\) | |||||||
\(152\) | −1.74874 | − | 3.02891i | −0.141842 | − | 0.245677i | ||||
\(153\) | 19.5129 | 1.57753 | ||||||||
\(154\) | − | 1.22731i | − | 0.0988998i | ||||||
\(155\) | 5.83923 | + | 1.37406i | 0.469018 | + | 0.110367i | ||||
\(156\) | −0.914577 | + | 19.1170i | −0.0732248 | + | 1.53058i | ||||
\(157\) | −0.204180 | −0.0162954 | −0.00814768 | − | 0.999967i | \(-0.502594\pi\) | ||||
−0.00814768 | + | 0.999967i | \(0.502594\pi\) | |||||||
\(158\) | 0.762826 | − | 0.440418i | 0.0606872 | − | 0.0350377i | ||||
\(159\) | 8.96269 | 0.710788 | ||||||||
\(160\) | 1.35634 | − | 2.34925i | 0.107228 | − | 0.185724i | ||||
\(161\) | −1.66122 | + | 0.959106i | −0.130922 | + | 0.0755881i | ||||
\(162\) | −0.547324 | + | 0.315998i | −0.0430019 | + | 0.0248271i | ||||
\(163\) | − | 8.34506i | − | 0.653636i | −0.945087 | − | 0.326818i | \(-0.894024\pi\) | ||
0.945087 | − | 0.326818i | \(-0.105976\pi\) | |||||||
\(164\) | −12.9878 | − | 7.49849i | −1.01417 | − | 0.585534i | ||||
\(165\) | −2.86948 | + | 4.97009i | −0.223389 | + | 0.386921i | ||||
\(166\) | −1.54114 | + | 2.66933i | −0.119616 | + | 0.207180i | ||||
\(167\) | −7.36470 | + | 4.25201i | −0.569898 | + | 0.329031i | −0.757108 | − | 0.653289i | \(-0.773389\pi\) |
0.187211 | + | 0.982320i | \(0.440055\pi\) | |||||||
\(168\) | −3.36390 | + | 5.82644i | −0.259530 | + | 0.449520i | ||||
\(169\) | 5.39555 | + | 11.8274i | 0.415042 | + | 0.909802i | ||||
\(170\) | −1.03786 | −0.0796004 | ||||||||
\(171\) | − | 17.9216i | − | 1.37050i | ||||||
\(172\) | 4.21233 | + | 7.29597i | 0.321187 | + | 0.556312i | ||||
\(173\) | −12.3780 | + | 21.4393i | −0.941079 | + | 1.63000i | −0.177661 | + | 0.984092i | \(0.556853\pi\) |
−0.763418 | + | 0.645905i | \(0.776480\pi\) | |||||||
\(174\) | 2.21219 | − | 1.27721i | 0.167706 | − | 0.0968250i | ||||
\(175\) | −9.61477 | − | 5.55109i | −0.726808 | − | 0.419623i | ||||
\(176\) | −6.31555 | − | 3.64629i | −0.476053 | − | 0.274849i | ||||
\(177\) | 26.6618 | + | 15.3932i | 2.00403 | + | 1.15702i | ||||
\(178\) | −1.16335 | −0.0871971 | ||||||||
\(179\) | 7.81732 | + | 13.5400i | 0.584294 | + | 1.01203i | 0.994963 | + | 0.100242i | \(0.0319618\pi\) |
−0.410669 | + | 0.911784i | \(0.634705\pi\) | |||||||
\(180\) | 7.99366 | − | 4.61514i | 0.595812 | − | 0.343992i | ||||
\(181\) | 0.0959588 | − | 0.166206i | 0.00713256 | − | 0.0123540i | −0.862437 | − | 0.506164i | \(-0.831063\pi\) |
0.869570 | + | 0.493810i | \(0.164396\pi\) | |||||||
\(182\) | −0.107893 | + | 2.25524i | −0.00799757 | + | 0.167169i | ||||
\(183\) | 7.22323 | + | 12.5110i | 0.533957 | + | 0.924840i | ||||
\(184\) | − | 0.567830i | − | 0.0418610i | ||||||
\(185\) | 0.639484 | 0.0470158 | ||||||||
\(186\) | 2.24485 | − | 2.38704i | 0.164601 | − | 0.175027i | ||||
\(187\) | 8.71868i | 0.637573i | ||||||||
\(188\) | − | 0.498876i | − | 0.0363843i | ||||||
\(189\) | −9.43653 | + | 5.44818i | −0.686406 | + | 0.396297i | ||||
\(190\) | 0.953223i | 0.0691540i | ||||||||
\(191\) | 10.8919 | − | 18.8654i | 0.788112 | − | 1.36505i | −0.139010 | − | 0.990291i | \(-0.544392\pi\) |
0.927122 | − | 0.374759i | \(-0.122275\pi\) | |||||||
\(192\) | 9.37161 | + | 16.2321i | 0.676338 | + | 1.17145i | ||||
\(193\) | −20.9910 | + | 12.1192i | −1.51097 | + | 0.872357i | −0.511048 | + | 0.859552i | \(0.670743\pi\) |
−0.999918 | + | 0.0128045i | \(0.995924\pi\) | |||||||
\(194\) | 0.369422 | 0.0265230 | ||||||||
\(195\) | 5.70971 | − | 8.88048i | 0.408881 | − | 0.635944i | ||||
\(196\) | 1.33051 | − | 2.30450i | 0.0950361 | − | 0.164607i | ||||
\(197\) | 4.91380 | + | 2.83698i | 0.350093 | + | 0.202127i | 0.664726 | − | 0.747087i | \(-0.268548\pi\) |
−0.314633 | + | 0.949213i | \(0.601881\pi\) | |||||||
\(198\) | 0.930830 | + | 1.61224i | 0.0661512 | + | 0.114577i | ||||
\(199\) | −8.04415 | + | 13.9329i | −0.570235 | + | 0.987676i | 0.426307 | + | 0.904579i | \(0.359814\pi\) |
−0.996541 | + | 0.0830970i | \(0.973519\pi\) | |||||||
\(200\) | 2.84617 | − | 1.64324i | 0.201255 | − | 0.116194i | ||||
\(201\) | − | 25.6990i | − | 1.81267i | ||||||
\(202\) | − | 1.80132i | − | 0.126740i | ||||||
\(203\) | −10.8698 | + | 6.27569i | −0.762911 | + | 0.440467i | ||||
\(204\) | 11.8066 | − | 20.4496i | 0.826628 | − | 1.43176i | ||||
\(205\) | 4.13643 | + | 7.16450i | 0.288901 | + | 0.500391i | ||||
\(206\) | −0.642437 | − | 0.370911i | −0.0447607 | − | 0.0258426i | ||||
\(207\) | 1.45483 | − | 2.51983i | 0.101117 | − | 0.175140i | ||||
\(208\) | 11.2845 | + | 7.25539i | 0.782441 | + | 0.503071i | ||||
\(209\) | 8.00766 | 0.553901 | ||||||||
\(210\) | 1.58797 | − | 0.916815i | 0.109580 | − | 0.0632663i | ||||
\(211\) | −3.65726 | − | 6.33456i | −0.251776 | − | 0.436089i | 0.712239 | − | 0.701937i | \(-0.247681\pi\) |
−0.964015 | + | 0.265848i | \(0.914348\pi\) | |||||||
\(212\) | 3.22046 | − | 5.57800i | 0.221182 | − | 0.383098i | ||||
\(213\) | 21.4597i | 1.47039i | ||||||||
\(214\) | 2.70621 | − | 1.56243i | 0.184993 | − | 0.106806i | ||||
\(215\) | − | 4.64733i | − | 0.316946i | ||||||
\(216\) | − | 3.22555i | − | 0.219471i | ||||||
\(217\) | −11.0303 | + | 11.7290i | −0.748785 | + | 0.796214i | ||||
\(218\) | 3.07054 | 0.207963 | ||||||||
\(219\) | 0.781741i | 0.0528252i | ||||||||
\(220\) | 2.06211 | + | 3.57169i | 0.139028 | + | 0.240803i | ||||
\(221\) | 0.766458 | − | 16.0209i | 0.0515575 | − | 1.07768i | ||||
\(222\) | 0.174658 | − | 0.302517i | 0.0117223 | − | 0.0203036i | ||||
\(223\) | 24.4234 | − | 14.1009i | 1.63551 | − | 0.944263i | 0.653159 | − | 0.757220i | \(-0.273443\pi\) |
0.982352 | − | 0.187042i | \(-0.0598902\pi\) | |||||||
\(224\) | 3.64047 | + | 6.30547i | 0.243239 | + | 0.421302i | ||||
\(225\) | 16.8404 | 1.12269 | ||||||||
\(226\) | −1.02253 | − | 0.590356i | −0.0680175 | − | 0.0392699i | ||||
\(227\) | −19.4653 | − | 11.2383i | −1.29196 | − | 0.745913i | −0.312957 | − | 0.949767i | \(-0.601320\pi\) |
−0.979001 | + | 0.203855i | \(0.934653\pi\) | |||||||
\(228\) | −18.7819 | − | 10.8438i | −1.24386 | − | 0.718146i | ||||
\(229\) | −7.09051 | + | 4.09371i | −0.468554 | + | 0.270520i | −0.715634 | − | 0.698475i | \(-0.753862\pi\) |
0.247080 | + | 0.968995i | \(0.420529\pi\) | |||||||
\(230\) | −0.0773798 | + | 0.134026i | −0.00510227 | + | 0.00883740i | ||||
\(231\) | −7.70181 | − | 13.3399i | −0.506742 | − | 0.877703i | ||||
\(232\) | − | 3.71547i | − | 0.243932i | ||||||
\(233\) | 2.12578 | 0.139265 | 0.0696323 | − | 0.997573i | \(-0.477817\pi\) | ||||
0.0696323 | + | 0.997573i | \(0.477817\pi\) | |||||||
\(234\) | −1.56870 | − | 3.04439i | −0.102549 | − | 0.199018i | ||||
\(235\) | −0.137599 | + | 0.238328i | −0.00897595 | + | 0.0155468i | ||||
\(236\) | 19.1601 | − | 11.0621i | 1.24722 | − | 0.720082i | ||||
\(237\) | 5.52754 | − | 9.57398i | 0.359052 | − | 0.621897i | ||||
\(238\) | 1.39283 | − | 2.41246i | 0.0902839 | − | 0.156376i | ||||
\(239\) | 7.07031 | + | 4.08204i | 0.457340 | + | 0.264045i | 0.710925 | − | 0.703268i | \(-0.248276\pi\) |
−0.253585 | + | 0.967313i | \(0.581610\pi\) | |||||||
\(240\) | − | 10.8952i | − | 0.703284i | ||||||
\(241\) | 19.6980 | − | 11.3727i | 1.26886 | − | 0.732577i | 0.294088 | − | 0.955778i | \(-0.404984\pi\) |
0.974772 | + | 0.223201i | \(0.0716506\pi\) | |||||||
\(242\) | 1.34250 | − | 0.775094i | 0.0862994 | − | 0.0498250i | ||||
\(243\) | −9.61804 | + | 16.6589i | −0.616997 | + | 1.06867i | ||||
\(244\) | 10.3817 | 0.664623 | ||||||||
\(245\) | −1.27124 | + | 0.733953i | −0.0812168 | + | 0.0468905i | ||||
\(246\) | 4.51903 | 0.288123 | ||||||||
\(247\) | −14.7144 | − | 0.703952i | −0.936253 | − | 0.0447914i | ||||
\(248\) | −1.37426 | − | 4.56375i | −0.0872654 | − | 0.289798i | ||||
\(249\) | 38.6846i | 2.45154i | ||||||||
\(250\) | −2.06225 | −0.130428 | ||||||||
\(251\) | 8.40806 | + | 14.5632i | 0.530712 | + | 0.919221i | 0.999358 | + | 0.0358343i | \(0.0114088\pi\) |
−0.468646 | + | 0.883386i | \(0.655258\pi\) | |||||||
\(252\) | 24.7745i | 1.56064i | ||||||||
\(253\) | 1.12590 | + | 0.650038i | 0.0707847 | + | 0.0408675i | ||||
\(254\) | 3.38308 | − | 1.95322i | 0.212273 | − | 0.122556i | ||||
\(255\) | −11.2807 | + | 6.51293i | −0.706427 | + | 0.407856i | ||||
\(256\) | 12.3791 | 0.773695 | ||||||||
\(257\) | −11.6255 | + | 20.1359i | −0.725177 | + | 1.25604i | 0.233725 | + | 0.972303i | \(0.424909\pi\) |
−0.958901 | + | 0.283740i | \(0.908425\pi\) | |||||||
\(258\) | −2.19849 | − | 1.26930i | −0.136872 | − | 0.0790231i | ||||
\(259\) | −0.858200 | + | 1.48645i | −0.0533260 | + | 0.0923633i | ||||
\(260\) | −3.47523 | − | 6.74439i | −0.215524 | − | 0.418269i | ||||
\(261\) | 9.51931 | − | 16.4879i | 0.589231 | − | 1.02058i | ||||
\(262\) | −0.918068 | + | 0.530047i | −0.0567184 | + | 0.0327464i | ||||
\(263\) | −21.7782 | −1.34290 | −0.671451 | − | 0.741049i | \(-0.734328\pi\) | ||||
−0.671451 | + | 0.741049i | \(0.734328\pi\) | |||||||
\(264\) | 4.55979 | 0.280636 | ||||||||
\(265\) | −3.07701 | + | 1.77652i | −0.189020 | + | 0.109130i | ||||
\(266\) | −2.21572 | − | 1.27924i | −0.135854 | − | 0.0784355i | ||||
\(267\) | −12.6447 | + | 7.30044i | −0.773845 | + | 0.446779i | ||||
\(268\) | −15.9940 | − | 9.23413i | −0.976988 | − | 0.564064i | ||||
\(269\) | −13.7118 | + | 23.7495i | −0.836020 | + | 1.44803i | 0.0571764 | + | 0.998364i | \(0.481790\pi\) |
−0.893197 | + | 0.449666i | \(0.851543\pi\) | |||||||
\(270\) | −0.439555 | + | 0.761331i | −0.0267504 | + | 0.0463331i | ||||
\(271\) | 10.2933i | 0.625271i | 0.949873 | + | 0.312635i | \(0.101212\pi\) | ||||
−0.949873 | + | 0.312635i | \(0.898788\pi\) | |||||||
\(272\) | −8.27605 | − | 14.3345i | −0.501810 | − | 0.869160i | ||||
\(273\) | 12.9797 | + | 25.1897i | 0.785565 | + | 1.52455i | ||||
\(274\) | −1.56857 | + | 2.71684i | −0.0947606 | + | 0.164130i | ||||
\(275\) | 7.52455i | 0.453747i | ||||||||
\(276\) | −1.76053 | − | 3.04933i | −0.105971 | − | 0.183548i | ||||
\(277\) | −25.6564 | −1.54154 | −0.770772 | − | 0.637111i | \(-0.780129\pi\) | ||||
−0.770772 | + | 0.637111i | \(0.780129\pi\) | |||||||
\(278\) | 4.58290i | 0.274864i | ||||||||
\(279\) | 5.59421 | − | 23.7733i | 0.334917 | − | 1.42327i | ||||
\(280\) | − | 2.66706i | − | 0.159388i | ||||||
\(281\) | − | 10.7924i | − | 0.643819i | −0.946771 | − | 0.321909i | \(-0.895675\pi\) | ||
0.946771 | − | 0.321909i | \(-0.104325\pi\) | |||||||
\(282\) | 0.0751630 | + | 0.130186i | 0.00447589 | + | 0.00775248i | ||||
\(283\) | −1.13064 | −0.0672096 | −0.0336048 | − | 0.999435i | \(-0.510699\pi\) | ||||
−0.0336048 | + | 0.999435i | \(0.510699\pi\) | |||||||
\(284\) | 13.3556 | + | 7.71085i | 0.792508 | + | 0.457555i | ||||
\(285\) | 5.98179 | + | 10.3608i | 0.354331 | + | 0.613719i | ||||
\(286\) | 1.36028 | − | 0.700920i | 0.0804350 | − | 0.0414463i | ||||
\(287\) | −22.2047 | −1.31070 | ||||||||
\(288\) | −9.56449 | − | 5.52206i | −0.563593 | − | 0.325391i | ||||
\(289\) | −1.39449 | + | 2.41532i | −0.0820287 | + | 0.142078i | ||||
\(290\) | −0.506317 | + | 0.876967i | −0.0297320 | + | 0.0514973i | ||||
\(291\) | 4.01532 | − | 2.31825i | 0.235382 | − | 0.135898i | ||||
\(292\) | 0.486522 | + | 0.280894i | 0.0284715 | + | 0.0164381i | ||||
\(293\) | 8.91703 | − | 5.14825i | 0.520938 | − | 0.300764i | −0.216380 | − | 0.976309i | \(-0.569425\pi\) |
0.737318 | + | 0.675545i | \(0.236092\pi\) | |||||||
\(294\) | 0.801840i | 0.0467643i | ||||||||
\(295\) | −12.2045 | −0.710573 | ||||||||
\(296\) | −0.254045 | − | 0.440019i | −0.0147661 | − | 0.0255756i | ||||
\(297\) | 6.39565 | + | 3.69253i | 0.371113 | + | 0.214262i | ||||
\(298\) | 1.41390 | + | 2.44894i | 0.0819049 | + | 0.141863i | ||||
\(299\) | −2.01174 | − | 1.29345i | −0.116342 | − | 0.0748020i | ||||
\(300\) | 10.1895 | − | 17.6488i | 0.588294 | − | 1.01895i | ||||
\(301\) | 10.8025 | + | 6.23682i | 0.622645 | + | 0.359484i | ||||
\(302\) | −4.64571 | −0.267330 | ||||||||
\(303\) | −11.3039 | − | 19.5789i | −0.649390 | − | 1.12478i | ||||
\(304\) | −13.1655 | + | 7.60113i | −0.755096 | + | 0.435955i | ||||
\(305\) | −4.95967 | − | 2.86346i | −0.283990 | − | 0.163962i | ||||
\(306\) | 4.22545i | 0.241553i | ||||||||
\(307\) | −2.74732 | + | 1.58616i | −0.156798 | + | 0.0905272i | −0.576346 | − | 0.817206i | \(-0.695522\pi\) |
0.419548 | + | 0.907733i | \(0.362189\pi\) | |||||||
\(308\) | −11.0696 | −0.630749 | ||||||||
\(309\) | −9.31036 | −0.529648 | ||||||||
\(310\) | −0.297547 | + | 1.26446i | −0.0168995 | + | 0.0718166i | ||||
\(311\) | −12.7270 | −0.721682 | −0.360841 | − | 0.932627i | \(-0.617510\pi\) | ||||
−0.360841 | + | 0.932627i | \(0.617510\pi\) | |||||||
\(312\) | −8.37879 | − | 0.400851i | −0.474356 | − | 0.0226937i | ||||
\(313\) | 5.03964 | + | 8.72891i | 0.284857 | + | 0.493387i | 0.972575 | − | 0.232592i | \(-0.0747205\pi\) |
−0.687717 | + | 0.725978i | \(0.741387\pi\) | |||||||
\(314\) | − | 0.0442144i | − | 0.00249517i | ||||||
\(315\) | 6.83322 | − | 11.8355i | 0.385008 | − | 0.666854i | ||||
\(316\) | −3.97229 | − | 6.88020i | −0.223459 | − | 0.387042i | ||||
\(317\) | −28.7576 | + | 16.6032i | −1.61519 | + | 0.932530i | −0.627049 | + | 0.778980i | \(0.715737\pi\) |
−0.988141 | + | 0.153550i | \(0.950929\pi\) | |||||||
\(318\) | 1.94084i | 0.108837i | ||||||||
\(319\) | 7.36706 | + | 4.25337i | 0.412476 | + | 0.238143i | ||||
\(320\) | −6.43480 | − | 3.71514i | −0.359716 | − | 0.207682i | ||||
\(321\) | 19.6096 | − | 33.9647i | 1.09450 | − | 1.89573i | ||||
\(322\) | −0.207691 | − | 0.359731i | −0.0115741 | − | 0.0200470i | ||||
\(323\) | 15.7401 | + | 9.08758i | 0.875805 | + | 0.505646i | ||||
\(324\) | 2.85010 | + | 4.93652i | 0.158339 | + | 0.274251i | ||||
\(325\) | 0.661482 | − | 13.8266i | 0.0366924 | − | 0.766964i | ||||
\(326\) | 1.80709 | 0.100085 | ||||||||
\(327\) | 33.3743 | − | 19.2687i | 1.84560 | − | 1.06556i | ||||
\(328\) | 3.28652 | − | 5.69243i | 0.181468 | − | 0.314312i | ||||
\(329\) | −0.369321 | − | 0.639682i | −0.0203613 | − | 0.0352668i | ||||
\(330\) | −1.07625 | − | 0.621375i | −0.0592458 | − | 0.0342056i | ||||
\(331\) | −4.91037 | − | 2.83500i | −0.269898 | − | 0.155826i | 0.358943 | − | 0.933359i | \(-0.383137\pi\) |
−0.628841 | + | 0.777534i | \(0.716471\pi\) | |||||||
\(332\) | 24.0757 | + | 13.9001i | 1.32132 | + | 0.762867i | ||||
\(333\) | − | 2.60353i | − | 0.142673i | ||||||
\(334\) | −0.920756 | − | 1.59480i | −0.0503815 | − | 0.0872634i | ||||
\(335\) | 5.09386 | + | 8.82283i | 0.278307 | + | 0.482043i | ||||
\(336\) | 25.3254 | + | 14.6216i | 1.38161 | + | 0.797675i | ||||
\(337\) | 21.0424 | 1.14625 | 0.573127 | − | 0.819467i | \(-0.305730\pi\) | ||||
0.573127 | + | 0.819467i | \(0.305730\pi\) | |||||||
\(338\) | −2.56118 | + | 1.16839i | −0.139310 | + | 0.0635518i | ||||
\(339\) | −14.8187 | −0.804843 | ||||||||
\(340\) | 9.36085i | 0.507664i | ||||||||
\(341\) | 10.6223 | + | 2.49958i | 0.575227 | + | 0.135360i | ||||
\(342\) | 3.88086 | 0.209853 | ||||||||
\(343\) | 16.3026i | 0.880258i | ||||||||
\(344\) | −3.19776 | + | 1.84623i | −0.172412 | + | 0.0995419i | ||||
\(345\) | 1.94234i | 0.104572i | ||||||||
\(346\) | −4.64259 | − | 2.68040i | −0.249587 | − | 0.144099i | ||||
\(347\) | −3.45932 | − | 5.99172i | −0.185706 | − | 0.321653i | 0.758108 | − | 0.652129i | \(-0.226124\pi\) |
−0.943814 | + | 0.330476i | \(0.892791\pi\) | |||||||
\(348\) | −11.5196 | − | 19.9526i | −0.617516 | − | 1.06957i | ||||
\(349\) | − | 20.4459i | − | 1.09444i | −0.836988 | − | 0.547221i | \(-0.815686\pi\) | ||
0.836988 | − | 0.547221i | \(-0.184314\pi\) | |||||||
\(350\) | 1.20207 | − | 2.08204i | 0.0642531 | − | 0.111290i | ||||
\(351\) | −11.4276 | − | 7.34740i | −0.609962 | − | 0.392175i | ||||
\(352\) | 2.46734 | − | 4.27356i | 0.131510 | − | 0.227782i | ||||
\(353\) | 10.3755 | − | 5.99032i | 0.552234 | − | 0.318832i | −0.197789 | − | 0.980245i | \(-0.563376\pi\) |
0.750022 | + | 0.661412i | \(0.230043\pi\) | |||||||
\(354\) | −3.33334 | + | 5.77351i | −0.177165 | + | 0.306859i | ||||
\(355\) | −4.25357 | − | 7.36740i | −0.225756 | − | 0.391021i | ||||
\(356\) | 10.4927i | 0.556113i | ||||||||
\(357\) | − | 34.9620i | − | 1.85038i | ||||||
\(358\) | −2.93203 | + | 1.69281i | −0.154963 | + | 0.0894678i | ||||
\(359\) | −26.0022 | − | 15.0124i | −1.37234 | − | 0.792322i | −0.381119 | − | 0.924526i | \(-0.624461\pi\) |
−0.991223 | + | 0.132204i | \(0.957795\pi\) | |||||||
\(360\) | 2.02278 | + | 3.50355i | 0.106610 | + | 0.184653i | ||||
\(361\) | −1.15353 | + | 1.99797i | −0.0607120 | + | 0.105156i | ||||
\(362\) | 0.0359912 | + | 0.0207795i | 0.00189165 | + | 0.00109215i | ||||
\(363\) | 9.72796 | − | 16.8493i | 0.510585 | − | 0.884360i | ||||
\(364\) | 20.3408 | + | 0.973127i | 1.06615 | + | 0.0510057i | ||||
\(365\) | −0.154951 | − | 0.268382i | −0.00811049 | − | 0.0140478i | ||||
\(366\) | −2.70921 | + | 1.56416i | −0.141613 | + | 0.0817601i | ||||
\(367\) | −4.65412 | + | 8.06117i | −0.242943 | + | 0.420790i | −0.961551 | − | 0.274626i | \(-0.911446\pi\) |
0.718608 | + | 0.695415i | \(0.244779\pi\) | |||||||
\(368\) | −2.46815 | −0.128661 | ||||||||
\(369\) | 29.1689 | − | 16.8407i | 1.51847 | − | 0.876689i | ||||
\(370\) | 0.138478i | 0.00719911i | ||||||||
\(371\) | − | 9.53648i | − | 0.495109i | ||||||
\(372\) | −21.5296 | − | 20.2471i | −1.11626 | − | 1.04977i | ||||
\(373\) | 22.1171 | 1.14518 | 0.572589 | − | 0.819843i | \(-0.305939\pi\) | ||||
0.572589 | + | 0.819843i | \(0.305939\pi\) | |||||||
\(374\) | −1.88800 | −0.0976259 | ||||||||
\(375\) | −22.4150 | + | 12.9413i | −1.15751 | + | 0.668286i | ||||
\(376\) | 0.218653 | 0.0112762 | ||||||||
\(377\) | −13.1633 | − | 8.46337i | −0.677946 | − | 0.435886i | ||||
\(378\) | −1.17978 | − | 2.04344i | −0.0606815 | − | 0.105103i | ||||
\(379\) | −3.68888 | + | 2.12978i | −0.189485 | + | 0.109399i | −0.591742 | − | 0.806128i | \(-0.701559\pi\) |
0.402256 | + | 0.915527i | \(0.368226\pi\) | |||||||
\(380\) | 8.59746 | 0.441041 | ||||||||
\(381\) | 24.5142 | − | 42.4599i | 1.25590 | − | 2.17529i | ||||
\(382\) | 4.08522 | + | 2.35860i | 0.209018 | + | 0.120677i | ||||
\(383\) | −19.5460 | − | 11.2849i | −0.998751 | − | 0.576629i | −0.0908728 | − | 0.995863i | \(-0.528966\pi\) |
−0.907879 | + | 0.419233i | \(0.862299\pi\) | |||||||
\(384\) | −15.3672 | + | 8.87224i | −0.784203 | + | 0.452760i | ||||
\(385\) | 5.28827 | + | 3.05319i | 0.269515 | + | 0.155605i | ||||
\(386\) | −2.62436 | − | 4.54552i | −0.133576 | − | 0.231361i | ||||
\(387\) | −18.9207 | −0.961793 | ||||||||
\(388\) | − | 3.33195i | − | 0.169154i | ||||||
\(389\) | −3.81794 | − | 6.61287i | −0.193577 | − | 0.335286i | 0.752856 | − | 0.658185i | \(-0.228676\pi\) |
−0.946433 | + | 0.322900i | \(0.895342\pi\) | |||||||
\(390\) | 1.92303 | + | 1.23641i | 0.0973765 | + | 0.0626083i | ||||
\(391\) | 1.47541 | + | 2.55548i | 0.0746145 | + | 0.129236i | ||||
\(392\) | 1.01004 | + | 0.583149i | 0.0510149 | + | 0.0294535i | ||||
\(393\) | −6.65244 | + | 11.5224i | −0.335571 | + | 0.581227i | ||||
\(394\) | −0.614337 | + | 1.06406i | −0.0309499 | + | 0.0536067i | ||||
\(395\) | 4.38250i | 0.220508i | ||||||||
\(396\) | 14.5414 | − | 8.39549i | 0.730734 | − | 0.421889i | ||||
\(397\) | 7.76424 | − | 4.48269i | 0.389676 | − | 0.224980i | −0.292344 | − | 0.956313i | \(-0.594435\pi\) |
0.682020 | + | 0.731334i | \(0.261102\pi\) | |||||||
\(398\) | −3.01711 | − | 1.74193i | −0.151234 | − | 0.0873150i | ||||
\(399\) | −32.1108 | −1.60755 | ||||||||
\(400\) | −7.14255 | − | 12.3713i | −0.357127 | − | 0.618563i | ||||
\(401\) | 35.4154i | 1.76856i | 0.466955 | + | 0.884281i | \(0.345351\pi\) | ||||
−0.466955 | + | 0.884281i | \(0.654649\pi\) | |||||||
\(402\) | 5.56502 | 0.277558 | ||||||||
\(403\) | −19.2991 | − | 5.52687i | −0.961355 | − | 0.275313i | ||||
\(404\) | −16.2467 | −0.808305 | ||||||||
\(405\) | − | 3.14443i | − | 0.156248i | ||||||
\(406\) | −1.35898 | − | 2.35381i | −0.0674448 | − | 0.116818i | ||||
\(407\) | 1.16330 | 0.0576625 | ||||||||
\(408\) | 8.96290 | + | 5.17473i | 0.443730 | + | 0.256187i | ||||
\(409\) | −14.9021 | + | 8.60372i | −0.736860 | + | 0.425426i | −0.820927 | − | 0.571034i | \(-0.806543\pi\) |
0.0840665 | + | 0.996460i | \(0.473209\pi\) | |||||||
\(410\) | −1.55145 | + | 0.895727i | −0.0766204 | + | 0.0442368i | ||||
\(411\) | 39.3732i | 1.94213i | ||||||||
\(412\) | −3.34538 | + | 5.79437i | −0.164815 | + | 0.285468i | ||||
\(413\) | 16.3787 | − | 28.3687i | 0.805942 | − | 1.39593i | ||||
\(414\) | 0.545660 | + | 0.315037i | 0.0268177 | + | 0.0154832i | ||||
\(415\) | −7.66777 | − | 13.2810i | −0.376396 | − | 0.651937i | ||||
\(416\) | −4.90952 | + | 7.63592i | −0.240709 | + | 0.374382i | ||||
\(417\) | 28.7593 | + | 49.8125i | 1.40835 | + | 2.43933i | ||||
\(418\) | 1.73403i | 0.0848140i | ||||||||
\(419\) | 26.3377 | 1.28668 | 0.643341 | − | 0.765580i | \(-0.277548\pi\) | ||||
0.643341 | + | 0.765580i | \(0.277548\pi\) | |||||||
\(420\) | −8.26909 | − | 14.3225i | −0.403490 | − | 0.698866i | ||||
\(421\) | 10.0044 | + | 5.77603i | 0.487583 | + | 0.281506i | 0.723571 | − | 0.690250i | \(-0.242499\pi\) |
−0.235988 | + | 0.971756i | \(0.575833\pi\) | |||||||
\(422\) | 1.37172 | − | 0.791965i | 0.0667744 | − | 0.0385522i | ||||
\(423\) | 0.970306 | + | 0.560206i | 0.0471779 | + | 0.0272382i | ||||
\(424\) | 2.44479 | + | 1.41150i | 0.118729 | + | 0.0685484i | ||||
\(425\) | −8.53932 | + | 14.7905i | −0.414218 | + | 0.717446i | ||||
\(426\) | −4.64701 | −0.225148 | ||||||||
\(427\) | 13.3119 | − | 7.68566i | 0.644210 | − | 0.371935i | ||||
\(428\) | −14.0921 | − | 24.4083i | −0.681169 | − | 1.17982i | ||||
\(429\) | 10.3866 | − | 16.1547i | 0.501472 | − | 0.779954i | ||||
\(430\) | 1.00636 | 0.0485311 | ||||||||
\(431\) | 0.0776939 | − | 0.0448566i | 0.00374239 | − | 0.00216067i | −0.498128 | − | 0.867104i | \(-0.665979\pi\) |
0.501870 | + | 0.864943i | \(0.332646\pi\) | |||||||
\(432\) | −14.0203 | −0.674551 | ||||||||
\(433\) | 26.7326 | 1.28469 | 0.642344 | − | 0.766416i | \(-0.277962\pi\) | ||||
0.642344 | + | 0.766416i | \(0.277962\pi\) | |||||||
\(434\) | −2.53986 | − | 2.38857i | −0.121917 | − | 0.114655i | ||||
\(435\) | 12.7092i | 0.609361i | ||||||||
\(436\) | − | 27.6943i | − | 1.32632i | ||||||
\(437\) | 2.34707 | − | 1.35508i | 0.112276 | − | 0.0648225i | ||||
\(438\) | −0.169283 | −0.00808865 | ||||||||
\(439\) | 0.475013 | − | 0.822747i | 0.0226711 | − | 0.0392676i | −0.854467 | − | 0.519505i | \(-0.826116\pi\) |
0.877138 | + | 0.480238i | \(0.159450\pi\) | |||||||
\(440\) | −1.56544 | + | 0.903807i | −0.0746294 | + | 0.0430873i | ||||
\(441\) | 2.98814 | + | 5.17562i | 0.142293 | + | 0.246458i | ||||
\(442\) | 3.46926 | + | 0.165973i | 0.165016 | + | 0.00789455i | ||||
\(443\) | 14.3958 | − | 24.9342i | 0.683964 | − | 1.18466i | −0.289797 | − | 0.957088i | \(-0.593588\pi\) |
0.973761 | − | 0.227573i | \(-0.0730790\pi\) | |||||||
\(444\) | −2.72851 | − | 1.57531i | −0.129489 | − | 0.0747608i | ||||
\(445\) | 2.89407 | − | 5.01268i | 0.137192 | − | 0.237624i | ||||
\(446\) | 3.05348 | + | 5.28879i | 0.144587 | + | 0.250431i | ||||
\(447\) | 30.7359 | + | 17.7454i | 1.45376 | + | 0.839327i | ||||
\(448\) | 17.2713 | − | 9.97158i | 0.815991 | − | 0.471113i | ||||
\(449\) | 27.7320i | 1.30875i | 0.756169 | + | 0.654377i | \(0.227069\pi\) | ||||
−0.756169 | + | 0.654377i | \(0.772931\pi\) | |||||||
\(450\) | 3.64672i | 0.171908i | ||||||||
\(451\) | 7.52466 | + | 13.0331i | 0.354322 | + | 0.613704i | ||||
\(452\) | −5.32464 | + | 9.22254i | −0.250450 | + | 0.433792i | ||||
\(453\) | −50.4951 | + | 29.1534i | −2.37247 | + | 1.36974i | ||||
\(454\) | 2.43361 | − | 4.21514i | 0.114215 | − | 0.197826i | ||||
\(455\) | −9.44900 | − | 6.07524i | −0.442976 | − | 0.284812i | ||||
\(456\) | 4.75272 | − | 8.23196i | 0.222567 | − | 0.385497i | ||||
\(457\) | − | 26.0706i | − | 1.21953i | −0.792582 | − | 0.609765i | \(-0.791264\pi\) | ||
0.792582 | − | 0.609765i | \(-0.208736\pi\) | |||||||
\(458\) | −0.886477 | − | 1.53542i | −0.0414223 | − | 0.0717456i | ||||
\(459\) | 8.38101 | + | 14.5163i | 0.391192 | + | 0.677565i | ||||
\(460\) | 1.20883 | + | 0.697917i | 0.0563619 | + | 0.0325405i | ||||
\(461\) | − | 1.87261i | − | 0.0872160i | −0.999049 | − | 0.0436080i | \(-0.986115\pi\) | ||
0.999049 | − | 0.0436080i | \(-0.0138853\pi\) | |||||||
\(462\) | 2.88871 | − | 1.66780i | 0.134395 | − | 0.0775929i | ||||
\(463\) | 2.06017i | 0.0957441i | 0.998853 | + | 0.0478720i | \(0.0152440\pi\) | ||||
−0.998853 | + | 0.0478720i | \(0.984756\pi\) | |||||||
\(464\) | −16.1498 | −0.749734 | ||||||||
\(465\) | 4.70082 | + | 15.6109i | 0.217995 | + | 0.723938i | ||||
\(466\) | 0.460330i | 0.0213244i | ||||||||
\(467\) | 25.5423 | 1.18196 | 0.590979 | − | 0.806687i | \(-0.298741\pi\) | ||||
0.590979 | + | 0.806687i | \(0.298741\pi\) | |||||||
\(468\) | −27.4585 | + | 14.1487i | −1.26927 | + | 0.654024i | ||||
\(469\) | −27.3443 | −1.26264 | ||||||||
\(470\) | −0.0516090 | − | 0.0297965i | −0.00238054 | − | 0.00137441i | ||||
\(471\) | −0.277461 | − | 0.480576i | −0.0127847 | − | 0.0221438i | ||||
\(472\) | 4.84843 | + | 8.39772i | 0.223167 | + | 0.386536i | ||||
\(473\) | − | 8.45406i | − | 0.388718i | ||||||
\(474\) | 2.07321 | + | 1.19697i | 0.0952255 | + | 0.0549785i | ||||
\(475\) | 13.5843 | + | 7.84292i | 0.623292 | + | 0.359858i | ||||
\(476\) | −21.7588 | − | 12.5625i | −0.997314 | − | 0.575799i | ||||
\(477\) | 7.23273 | + | 12.5275i | 0.331164 | + | 0.573593i | ||||
\(478\) | −0.883950 | + | 1.53105i | −0.0404309 | + | 0.0700284i | ||||
\(479\) | 35.3344 | − | 20.4004i | 1.61447 | − | 0.932116i | 0.626156 | − | 0.779698i | \(-0.284627\pi\) |
0.988316 | − | 0.152418i | \(-0.0487060\pi\) | |||||||
\(480\) | 7.37251 | 0.336507 | ||||||||
\(481\) | −2.13760 | − | 0.102265i | −0.0974663 | − | 0.00466290i | ||||
\(482\) | 2.46270 | + | 4.26553i | 0.112173 | + | 0.194289i | ||||
\(483\) | −4.51486 | − | 2.60666i | −0.205433 | − | 0.118607i | ||||
\(484\) | −6.99086 | − | 12.1085i | −0.317766 | − | 0.550387i | ||||
\(485\) | −0.919010 | + | 1.59177i | −0.0417301 | + | 0.0722786i | ||||
\(486\) | −3.60743 | − | 2.08275i | −0.163636 | − | 0.0944754i | ||||
\(487\) | −25.0470 | − | 14.4609i | −1.13499 | − | 0.655287i | −0.189805 | − | 0.981822i | \(-0.560785\pi\) |
−0.945185 | + | 0.326535i | \(0.894119\pi\) | |||||||
\(488\) | 4.55023i | 0.205979i | ||||||||
\(489\) | 19.6416 | − | 11.3401i | 0.888225 | − | 0.512817i | ||||
\(490\) | −0.158935 | − | 0.275283i | −0.00717993 | − | 0.0124360i | ||||
\(491\) | 14.1441 | − | 24.4983i | 0.638313 | − | 1.10559i | −0.347489 | − | 0.937684i | \(-0.612966\pi\) |
0.985803 | − | 0.167907i | \(-0.0537010\pi\) | |||||||
\(492\) | − | 40.7588i | − | 1.83755i | ||||||
\(493\) | 9.65398 | + | 16.7212i | 0.434793 | + | 0.753084i | ||||
\(494\) | 0.152438 | − | 3.18634i | 0.00685851 | − | 0.143360i | ||||
\(495\) | −9.26249 | −0.416318 | ||||||||
\(496\) | −19.8369 | + | 5.97339i | −0.890705 | + | 0.268213i | ||||
\(497\) | 22.8335 | 1.02422 | ||||||||
\(498\) | −8.37701 | −0.375383 | ||||||||
\(499\) | 14.5917 | − | 8.42449i | 0.653212 | − | 0.377132i | −0.136474 | − | 0.990644i | \(-0.543577\pi\) |
0.789686 | + | 0.613512i | \(0.210244\pi\) | |||||||
\(500\) | 18.6002i | 0.831825i | ||||||||
\(501\) | −20.0158 | − | 11.5561i | −0.894239 | − | 0.516289i | ||||
\(502\) | −3.15360 | + | 1.82073i | −0.140752 | + | 0.0812633i | ||||
\(503\) | 6.38581 | + | 11.0605i | 0.284729 | + | 0.493165i | 0.972543 | − | 0.232721i | \(-0.0747630\pi\) |
−0.687814 | + | 0.725887i | \(0.741430\pi\) | |||||||
\(504\) | −10.8584 | −0.483673 | ||||||||
\(505\) | 7.76154 | + | 4.48113i | 0.345384 | + | 0.199408i | ||||
\(506\) | −0.140763 | + | 0.243809i | −0.00625769 | + | 0.0108386i | ||||
\(507\) | −20.5060 | + | 28.7717i | −0.910703 | + | 1.27780i | ||||
\(508\) | −17.6168 | − | 30.5132i | −0.781619 | − | 1.35380i | ||||
\(509\) | 20.0967 | + | 11.6028i | 0.890770 | + | 0.514286i | 0.874194 | − | 0.485577i | \(-0.161390\pi\) |
0.0165755 | + | 0.999863i | \(0.494724\pi\) | |||||||
\(510\) | −1.41035 | − | 2.44280i | −0.0624513 | − | 0.108169i | ||||
\(511\) | 0.831787 | 0.0367961 | ||||||||
\(512\) | 15.7386i | 0.695556i | ||||||||
\(513\) | 13.3325 | − | 7.69753i | 0.588645 | − | 0.339854i | ||||
\(514\) | −4.36035 | − | 2.51745i | −0.192327 | − | 0.111040i | ||||
\(515\) | 3.19637 | − | 1.84543i | 0.140849 | − | 0.0813193i | ||||
\(516\) | −11.4483 | + | 19.8290i | −0.503982 | + | 0.872922i | ||||
\(517\) | −0.250309 | + | 0.433547i | −0.0110086 | + | 0.0190674i | ||||
\(518\) | −0.321884 | − | 0.185840i | −0.0141428 | − | 0.00816533i | ||||
\(519\) | −67.2816 | −2.95333 | ||||||||
\(520\) | 2.95601 | − | 1.52316i | 0.129629 | − | 0.0667950i | ||||
\(521\) | 8.40806 | + | 14.5632i | 0.368364 | + | 0.638025i | 0.989310 | − | 0.145828i | \(-0.0465847\pi\) |
−0.620946 | + | 0.783853i | \(0.713251\pi\) | |||||||
\(522\) | 3.57040 | + | 2.06137i | 0.156272 | + | 0.0902237i | ||||
\(523\) | −9.01605 | −0.394244 | −0.197122 | − | 0.980379i | \(-0.563160\pi\) | ||||
−0.197122 | + | 0.980379i | \(0.563160\pi\) | |||||||
\(524\) | 4.78069 | + | 8.28039i | 0.208845 | + | 0.361731i | ||||
\(525\) | − | 30.1735i | − | 1.31688i | ||||||
\(526\) | − | 4.71598i | − | 0.205627i | ||||||
\(527\) | 18.0428 | + | 16.9680i | 0.785958 | + | 0.739140i | ||||
\(528\) | − | 19.8197i | − | 0.862543i | ||||||
\(529\) | −22.5600 | −0.980869 | ||||||||
\(530\) | −0.384697 | − | 0.666315i | −0.0167102 | − | 0.0289429i | ||||
\(531\) | 49.6882i | 2.15628i | ||||||||
\(532\) | −11.5380 | + | 19.9844i | −0.500235 | + | 0.866432i | ||||
\(533\) | −12.6811 | − | 24.6103i | −0.549280 | − | 1.06599i | ||||
\(534\) | −1.58088 | − | 2.73817i | −0.0684114 | − | 0.118492i | ||||
\(535\) | 15.5474i | 0.672173i | ||||||||
\(536\) | 4.04724 | − | 7.01002i | 0.174814 | − | 0.302787i | ||||
\(537\) | −21.2459 | + | 36.7990i | −0.916828 | + | 1.58799i | ||||
\(538\) | −5.14285 | − | 2.96923i | −0.221724 | − | 0.128012i | ||||
\(539\) | −2.31254 | + | 1.33515i | −0.0996083 | + | 0.0575089i | ||||
\(540\) | 6.86672 | + | 3.96450i | 0.295497 | + | 0.170605i | ||||
\(541\) | 12.7800 | − | 7.37852i | 0.549454 | − | 0.317227i | −0.199448 | − | 0.979908i | \(-0.563915\pi\) |
0.748902 | + | 0.662681i | \(0.230582\pi\) | |||||||
\(542\) | −2.22896 | −0.0957422 | ||||||||
\(543\) | 0.521593 | 0.0223837 | ||||||||
\(544\) | 9.69979 | − | 5.60018i | 0.415875 | − | 0.240106i | ||||
\(545\) | −7.63857 | + | 13.2304i | −0.327200 | + | 0.566728i | ||||
\(546\) | −5.45473 | + | 2.81069i | −0.233441 | + | 0.120287i | ||||
\(547\) | −7.94526 | + | 13.7616i | −0.339715 | + | 0.588403i | −0.984379 | − | 0.176063i | \(-0.943664\pi\) |
0.644664 | + | 0.764466i | \(0.276997\pi\) | |||||||
\(548\) | 24.5042 | + | 14.1475i | 1.04677 | + | 0.604351i | ||||
\(549\) | −11.6580 | + | 20.1923i | −0.497553 | + | 0.861787i | ||||
\(550\) | −1.62941 | −0.0694783 | ||||||||
\(551\) | 15.3575 | − | 8.86668i | 0.654253 | − | 0.377733i | ||||
\(552\) | 1.33649 | − | 0.771624i | 0.0568849 | − | 0.0328425i | ||||
\(553\) | −10.1869 | − | 5.88141i | −0.433191 | − | 0.250103i | ||||
\(554\) | − | 5.55579i | − | 0.236043i | ||||||
\(555\) | 0.868994 | + | 1.50514i | 0.0368867 | + | 0.0638897i | ||||
\(556\) | 41.3349 | 1.75299 | ||||||||
\(557\) | − | 11.7837i | − | 0.499291i | −0.968337 | − | 0.249645i | \(-0.919686\pi\) | ||
0.968337 | − | 0.249645i | \(-0.0803140\pi\) | |||||||
\(558\) | 5.14801 | + | 1.21140i | 0.217933 | + | 0.0512828i | ||||
\(559\) | −0.743195 | + | 15.5346i | −0.0314338 | + | 0.657046i | ||||
\(560\) | −11.5927 | −0.489883 | ||||||||
\(561\) | −20.5210 | + | 11.8478i | −0.866397 | + | 0.500215i | ||||
\(562\) | 2.33704 | 0.0985823 | ||||||||
\(563\) | −4.86382 | + | 8.42438i | −0.204985 | + | 0.355045i | −0.950128 | − | 0.311860i | \(-0.899048\pi\) |
0.745143 | + | 0.666905i | \(0.232381\pi\) | |||||||
\(564\) | 1.17420 | − | 0.677923i | 0.0494426 | − | 0.0285457i | ||||
\(565\) | 5.08747 | − | 2.93725i | 0.214032 | − | 0.123571i | ||||
\(566\) | − | 0.244836i | − | 0.0102912i | ||||||
\(567\) | 7.30905 | + | 4.21988i | 0.306951 | + | 0.177219i | ||||
\(568\) | −3.37960 | + | 5.85363i | −0.141805 | + | 0.245613i | ||||
\(569\) | −18.4922 | + | 32.0295i | −0.775234 | + | 1.34275i | 0.159429 | + | 0.987209i | \(0.449035\pi\) |
−0.934663 | + | 0.355536i | \(0.884298\pi\) | |||||||
\(570\) | −2.24358 | + | 1.29533i | −0.0939734 | + | 0.0542556i | ||||
\(571\) | 23.0626 | − | 39.9456i | 0.965141 | − | 1.67167i | 0.255905 | − | 0.966702i | \(-0.417627\pi\) |
0.709236 | − | 0.704971i | \(-0.249040\pi\) | |||||||
\(572\) | −6.32185 | − | 12.2689i | −0.264330 | − | 0.512987i | ||||
\(573\) | 59.2041 | 2.47329 | ||||||||
\(574\) | − | 4.80834i | − | 0.200696i | ||||||
\(575\) | 1.27333 | + | 2.20547i | 0.0531016 | + | 0.0919746i | ||||
\(576\) | −15.1254 | + | 26.1980i | −0.630227 | + | 1.09158i | ||||
\(577\) | −28.8138 | + | 16.6356i | −1.19953 | + | 0.692550i | −0.960451 | − | 0.278449i | \(-0.910180\pi\) |
−0.239081 | + | 0.971000i | \(0.576846\pi\) | |||||||
\(578\) | −0.523029 | − | 0.301971i | −0.0217551 | − | 0.0125603i | ||||
\(579\) | −57.0493 | − | 32.9375i | −2.37089 | − | 1.36883i | ||||
\(580\) | 7.90968 | + | 4.56666i | 0.328432 | + | 0.189620i | ||||
\(581\) | 41.1612 | 1.70765 | ||||||||
\(582\) | 0.502007 | + | 0.869502i | 0.0208089 | + | 0.0360420i | ||||
\(583\) | −5.59746 | + | 3.23169i | −0.231823 | + | 0.133843i | ||||
\(584\) | −0.123113 | + | 0.213238i | −0.00509446 | + | 0.00882386i | ||||
\(585\) | 17.0202 | + | 0.814264i | 0.703698 | + | 0.0336657i | ||||
\(586\) | 1.11483 | + | 1.93095i | 0.0460533 | + | 0.0797667i | ||||
\(587\) | 6.92154i | 0.285683i | 0.989746 | + | 0.142841i | \(0.0456238\pi\) | ||||
−0.989746 | + | 0.142841i | \(0.954376\pi\) | |||||||
\(588\) | 7.23209 | 0.298246 | ||||||||
\(589\) | 15.5843 | − | 16.5714i | 0.642139 | − | 0.682813i | ||||
\(590\) | − | 2.64283i | − | 0.108804i | ||||||
\(591\) | 15.4207i | 0.634322i | ||||||||
\(592\) | −1.91260 | + | 1.10424i | −0.0786074 | + | 0.0453840i | ||||
\(593\) | − | 14.0226i | − | 0.575839i | −0.957655 | − | 0.287919i | \(-0.907036\pi\) | ||
0.957655 | − | 0.287919i | \(-0.0929635\pi\) | |||||||
\(594\) | −0.799602 | + | 1.38495i | −0.0328081 | + | 0.0568253i | ||||
\(595\) | 6.92989 | + | 12.0029i | 0.284098 | + | 0.492071i | ||||
\(596\) | 22.0879 | − | 12.7525i | 0.904756 | − | 0.522361i | ||||
\(597\) | −43.7248 | −1.78954 | ||||||||
\(598\) | 0.280091 | − | 0.435634i | 0.0114538 | − | 0.0178144i | ||||
\(599\) | 5.52124 | − | 9.56307i | 0.225592 | − | 0.390736i | −0.730905 | − | 0.682479i | \(-0.760902\pi\) |
0.956497 | + | 0.291743i | \(0.0942351\pi\) | |||||||
\(600\) | 7.73532 | + | 4.46599i | 0.315793 | + | 0.182323i | ||||
\(601\) | 2.59974 | + | 4.50288i | 0.106046 | + | 0.183676i | 0.914165 | − | 0.405343i | \(-0.132848\pi\) |
−0.808119 | + | 0.589019i | \(0.799514\pi\) | |||||||
\(602\) | −1.35056 | + | 2.33923i | −0.0550446 | + | 0.0953401i | ||||
\(603\) | 35.9204 | − | 20.7387i | 1.46279 | − | 0.844544i | ||||
\(604\) | 41.9013i | 1.70494i | ||||||||
\(605\) | 7.71280i | 0.313570i | ||||||||
\(606\) | 4.23973 | − | 2.44781i | 0.172227 | − | 0.0994354i | ||||
\(607\) | 19.7074 | − | 34.1341i | 0.799897 | − | 1.38546i | −0.119786 | − | 0.992800i | \(-0.538221\pi\) |
0.919683 | − | 0.392662i | \(-0.128446\pi\) | |||||||
\(608\) | −5.14348 | − | 8.90876i | −0.208595 | − | 0.361298i | ||||
\(609\) | −29.5420 | − | 17.0561i | −1.19710 | − | 0.691146i | ||||
\(610\) | 0.620072 | − | 1.07400i | 0.0251060 | − | 0.0434848i | ||||
\(611\) | 0.498065 | − | 0.774655i | 0.0201495 | − | 0.0313392i | ||||
\(612\) | 38.1109 | 1.54054 | ||||||||
\(613\) | −11.5373 | + | 6.66106i | −0.465987 | + | 0.269038i | −0.714558 | − | 0.699576i | \(-0.753372\pi\) |
0.248571 | + | 0.968614i | \(0.420039\pi\) | |||||||
\(614\) | −0.343478 | − | 0.594921i | −0.0138616 | − | 0.0240091i | ||||
\(615\) | −11.2420 | + | 19.4717i | −0.453320 | + | 0.785174i | ||||
\(616\) | − | 4.85171i | − | 0.195481i | ||||||
\(617\) | −2.04390 | + | 1.18005i | −0.0822843 | + | 0.0475069i | −0.540578 | − | 0.841294i | \(-0.681794\pi\) |
0.458293 | + | 0.888801i | \(0.348461\pi\) | |||||||
\(618\) | − | 2.01612i | − | 0.0811003i | ||||||
\(619\) | − | 9.60526i | − | 0.386068i | −0.981192 | − | 0.193034i | \(-0.938167\pi\) | ||
0.981192 | − | 0.193034i | \(-0.0618328\pi\) | |||||||
\(620\) | 11.4046 | + | 2.68369i | 0.458021 | + | 0.107779i | ||||
\(621\) | 2.49945 | 0.100300 | ||||||||
\(622\) | − | 2.75598i | − | 0.110505i | ||||||
\(623\) | 7.76780 | + | 13.4542i | 0.311211 | + | 0.539032i | ||||
\(624\) | −1.74235 | + | 36.4195i | −0.0697499 | + | 1.45795i | ||||
\(625\) | −4.46776 | + | 7.73839i | −0.178711 | + | 0.309536i | ||||
\(626\) | −1.89021 | + | 1.09131i | −0.0755480 | + | 0.0436177i | ||||
\(627\) | 10.8816 | + | 18.8475i | 0.434569 | + | 0.752696i | ||||
\(628\) | −0.398786 | −0.0159133 | ||||||||
\(629\) | 2.28662 | + | 1.32018i | 0.0911735 | + | 0.0526391i | ||||
\(630\) | 2.56293 | + | 1.47971i | 0.102109 | + | 0.0589529i | ||||
\(631\) | −17.6572 | − | 10.1944i | −0.702922 | − | 0.405832i | 0.105513 | − | 0.994418i | \(-0.466352\pi\) |
−0.808435 | + | 0.588586i | \(0.799685\pi\) | |||||||
\(632\) | 3.01553 | − | 1.74102i | 0.119951 | − | 0.0692540i | ||||
\(633\) | 9.93969 | − | 17.2160i | 0.395067 | − | 0.684277i | ||||
\(634\) | −3.59536 | − | 6.22735i | −0.142790 | − | 0.247320i | ||||
\(635\) | 19.4361i | 0.771297i | ||||||||
\(636\) | 17.5051 | 0.694123 | ||||||||
\(637\) | 4.36676 | − | 2.25009i | 0.173017 | − | 0.0891518i | ||||
\(638\) | −0.921051 | + | 1.59531i | −0.0364648 | + | 0.0631588i | ||||
\(639\) | −29.9949 | + | 17.3176i | −1.18658 | + | 0.685073i | ||||
\(640\) | 3.51717 | − | 6.09192i | 0.139028 | − | 0.240804i | ||||
\(641\) | 16.7963 | − | 29.0920i | 0.663413 | − | 1.14907i | −0.316300 | − | 0.948659i | \(-0.602441\pi\) |
0.979713 | − | 0.200406i | \(-0.0642261\pi\) | |||||||
\(642\) | 7.35493 | + | 4.24637i | 0.290276 | + | 0.167591i | ||||
\(643\) | 0.727035i | 0.0286714i | 0.999897 | + | 0.0143357i | \(0.00456336\pi\) | ||||
−0.999897 | + | 0.0143357i | \(0.995437\pi\) | |||||||
\(644\) | −3.24454 | + | 1.87324i | −0.127853 | + | 0.0738159i | ||||
\(645\) | 10.9383 | − | 6.31526i | 0.430697 | − | 0.248663i | ||||
\(646\) | −1.96788 | + | 3.40847i | −0.0774252 | + | 0.134104i | ||||
\(647\) | 32.8776 | 1.29255 | 0.646276 | − | 0.763104i | \(-0.276325\pi\) | ||||
0.646276 | + | 0.763104i | \(0.276325\pi\) | |||||||
\(648\) | −2.16363 | + | 1.24917i | −0.0849955 | + | 0.0490722i | ||||
\(649\) | −22.2014 | −0.871482 | ||||||||
\(650\) | 2.99410 | + | 0.143241i | 0.117438 | + | 0.00561839i | ||||
\(651\) | −42.5953 | − | 10.0233i | −1.66944 | − | 0.392845i | ||||
\(652\) | − | 16.2988i | − | 0.638311i | ||||||
\(653\) | 8.29740 | 0.324702 | 0.162351 | − | 0.986733i | \(-0.448092\pi\) | ||||
0.162351 | + | 0.986733i | \(0.448092\pi\) | |||||||
\(654\) | 4.17255 | + | 7.22708i | 0.163160 | + | 0.282601i | ||||
\(655\) | − | 5.27438i | − | 0.206087i | ||||||
\(656\) | −24.7429 | − | 14.2853i | −0.966047 | − | 0.557747i | ||||
\(657\) | −1.09267 | + | 0.630851i | −0.0426290 | + | 0.0246118i | ||||
\(658\) | 0.138521 | − | 0.0799749i | 0.00540010 | − | 0.00311775i | ||||
\(659\) | 27.7760 | 1.08200 | 0.541000 | − | 0.841023i | \(-0.318046\pi\) | ||||
0.541000 | + | 0.841023i | \(0.318046\pi\) | |||||||
\(660\) | −5.60441 | + | 9.70713i | −0.218151 | + | 0.377849i | ||||
\(661\) | −5.17216 | − | 2.98615i | −0.201174 | − | 0.116148i | 0.396029 | − | 0.918238i | \(-0.370388\pi\) |
−0.597203 | + | 0.802090i | \(0.703721\pi\) | |||||||
\(662\) | 0.613908 | − | 1.06332i | 0.0238602 | − | 0.0413271i | ||||
\(663\) | 38.7497 | − | 19.9668i | 1.50491 | − | 0.775446i | ||||
\(664\) | −6.09229 | + | 10.5521i | −0.236427 | + | 0.409503i | ||||
\(665\) | 11.0241 | − | 6.36474i | 0.427495 | − | 0.246814i | ||||
\(666\) | 0.563785 | 0.0218462 | ||||||||
\(667\) | 2.87908 | 0.111479 | ||||||||
\(668\) | −14.3841 | + | 8.30464i | −0.556536 | + | 0.321316i | ||||
\(669\) | 66.3779 | + | 38.3233i | 2.56632 | + | 1.48166i | ||||
\(670\) | −1.91055 | + | 1.10306i | −0.0738109 | + | 0.0426148i | ||||
\(671\) | −9.02223 | − | 5.20899i | −0.348299 | − | 0.201091i | ||||
\(672\) | −9.89405 | + | 17.1370i | −0.381671 | + | 0.661074i | ||||
\(673\) | −7.18552 | + | 12.4457i | −0.276982 | + | 0.479746i | −0.970633 | − | 0.240565i | \(-0.922667\pi\) |
0.693652 | + | 0.720311i | \(0.256001\pi\) | |||||||
\(674\) | 4.55665i | 0.175516i | ||||||||
\(675\) | 7.23313 | + | 12.5281i | 0.278403 | + | 0.482209i | ||||
\(676\) | 10.5381 | + | 23.1002i | 0.405311 | + | 0.888471i | ||||
\(677\) | 6.22535 | − | 10.7826i | 0.239260 | − | 0.414410i | −0.721242 | − | 0.692683i | \(-0.756429\pi\) |
0.960502 | + | 0.278273i | \(0.0897619\pi\) | |||||||
\(678\) | − | 3.20894i | − | 0.123238i | ||||||
\(679\) | −2.46666 | − | 4.27238i | −0.0946617 | − | 0.163959i | ||||
\(680\) | −4.10278 | −0.157334 | ||||||||
\(681\) | − | 61.0869i | − | 2.34086i | ||||||
\(682\) | −0.541274 | + | 2.30021i | −0.0207264 | + | 0.0880795i | ||||
\(683\) | − | 38.4734i | − | 1.47214i | −0.676903 | − | 0.736072i | \(-0.736678\pi\) | ||
0.676903 | − | 0.736072i | \(-0.263322\pi\) | |||||||
\(684\) | − | 35.0029i | − | 1.33837i | ||||||
\(685\) | −7.80424 | − | 13.5173i | −0.298185 | − | 0.516471i | ||||
\(686\) | −3.53027 | −0.134786 | ||||||||
\(687\) | −19.2706 | − | 11.1259i | −0.735219 | − | 0.424479i | ||||
\(688\) | 8.02487 | + | 13.8995i | 0.305945 | + | 0.529913i | ||||
\(689\) | 10.5696 | − | 5.44629i | 0.402671 | − | 0.207487i | ||||
\(690\) | −0.420605 | −0.0160122 | ||||||||
\(691\) | 17.3900 | + | 10.0401i | 0.661548 | + | 0.381945i | 0.792867 | − | 0.609395i | \(-0.208588\pi\) |
−0.131318 | + | 0.991340i | \(0.541921\pi\) | |||||||
\(692\) | −24.1755 | + | 41.8732i | −0.919014 | + | 1.59178i | ||||
\(693\) | 12.4304 | − | 21.5302i | 0.472194 | − | 0.817863i | ||||
\(694\) | 1.29748 | − | 0.749103i | 0.0492518 | − | 0.0284355i | ||||
\(695\) | −19.7469 | − | 11.4009i | −0.749042 | − | 0.432460i | ||||
\(696\) | 8.74503 | − | 5.04895i | 0.331480 | − | 0.191380i | ||||
\(697\) | 34.1578i | 1.29382i | ||||||||
\(698\) | 4.42747 | 0.167582 | ||||||||
\(699\) | 2.88872 | + | 5.00342i | 0.109262 | + | 0.189247i | ||||
\(700\) | −18.7787 | − | 10.8419i | −0.709767 | − | 0.409784i | ||||
\(701\) | 11.6336 | + | 20.1499i | 0.439394 | + | 0.761053i | 0.997643 | − | 0.0686208i | \(-0.0218599\pi\) |
−0.558249 | + | 0.829674i | \(0.688527\pi\) | |||||||
\(702\) | 1.59105 | − | 2.47461i | 0.0600503 | − | 0.0933981i | ||||
\(703\) | 1.21252 | − | 2.10014i | 0.0457310 | − | 0.0792084i | ||||
\(704\) | −11.7057 | − | 6.75828i | −0.441174 | − | 0.254712i | ||||
\(705\) | −0.747931 | −0.0281687 | ||||||||
\(706\) | 1.29718 | + | 2.24678i | 0.0488200 | + | 0.0845587i | ||||
\(707\) | −20.8323 | + | 12.0275i | −0.783479 | + | 0.452342i | ||||
\(708\) | 52.0734 | + | 30.0646i | 1.95704 | + | 1.12990i | ||||
\(709\) | 3.26759i | 0.122717i | 0.998116 | + | 0.0613584i | \(0.0195433\pi\) | ||||
−0.998116 | + | 0.0613584i | \(0.980457\pi\) | |||||||
\(710\) | 1.59538 | − | 0.921094i | 0.0598736 | − | 0.0345680i | ||||
\(711\) | 17.8425 | 0.669146 | ||||||||
\(712\) | −4.59886 | −0.172350 | ||||||||
\(713\) | 3.53641 | − | 1.06490i | 0.132440 | − | 0.0398808i | ||||
\(714\) | 7.57087 | 0.283333 | ||||||||
\(715\) | −0.363826 | + | 7.60487i | −0.0136063 | + | 0.284406i | ||||
\(716\) | 15.2681 | + | 26.4451i | 0.570595 | + | 0.988299i | ||||
\(717\) | 22.1883i | 0.828639i | ||||||||
\(718\) | 3.25087 | − | 5.63067i | 0.121321 | − | 0.210135i | ||||
\(719\) | −6.07474 | − | 10.5218i | −0.226549 | − | 0.392395i | 0.730234 | − | 0.683197i | \(-0.239411\pi\) |
−0.956783 | + | 0.290802i | \(0.906078\pi\) | |||||||
\(720\) | 15.2286 | − | 8.79226i | 0.567538 | − | 0.327668i | ||||
\(721\) | 9.90641i | 0.368934i | ||||||||
\(722\) | −0.432652 | − | 0.249792i | −0.0161016 | − | 0.00929629i | ||||
\(723\) | 53.5352 | + | 30.9086i | 1.99100 | + | 1.14950i | ||||
\(724\) | 0.187418 | − | 0.324617i | 0.00696533 | − | 0.0120643i | ||||
\(725\) | 8.33174 | + | 14.4310i | 0.309433 | + | 0.535954i | ||||
\(726\) | 3.64865 | + | 2.10655i | 0.135414 | + | 0.0781814i | ||||
\(727\) | 15.3228 | + | 26.5399i | 0.568293 | + | 0.984312i | 0.996735 | + | 0.0807426i | \(0.0257292\pi\) |
−0.428442 | + | 0.903569i | \(0.640937\pi\) | |||||||
\(728\) | −0.426513 | + | 8.91520i | −0.0158076 | + | 0.330419i | ||||
\(729\) | −43.5242 | −1.61201 | ||||||||
\(730\) | 0.0581171 | − | 0.0335539i | 0.00215101 | − | 0.00124189i | ||||
\(731\) | 9.59418 | − | 16.6176i | 0.354854 | − | 0.614624i | ||||
\(732\) | 14.1077 | + | 24.4353i | 0.521437 | + | 0.903156i | ||||
\(733\) | −18.8745 | − | 10.8972i | −0.697146 | − | 0.402498i | 0.109137 | − | 0.994027i | \(-0.465191\pi\) |
−0.806284 | + | 0.591529i | \(0.798525\pi\) | |||||||
\(734\) | −1.74561 | − | 1.00783i | −0.0644318 | − | 0.0371997i | ||||
\(735\) | −3.45498 | − | 1.99474i | −0.127439 | − | 0.0735769i | ||||
\(736\) | − | 1.67013i | − | 0.0615618i | ||||||
\(737\) | 9.26635 | + | 16.0498i | 0.341330 | + | 0.591201i | ||||
\(738\) | 3.64678 | + | 6.31640i | 0.134240 | + | 0.232510i | ||||
\(739\) | 17.6198 | + | 10.1728i | 0.648156 | + | 0.374213i | 0.787750 | − | 0.615996i | \(-0.211246\pi\) |
−0.139593 | + | 0.990209i | \(0.544579\pi\) | |||||||
\(740\) | 1.24898 | 0.0459134 | ||||||||
\(741\) | −18.3385 | − | 35.5896i | −0.673681 | − | 1.30742i | ||||
\(742\) | 2.06509 | 0.0758117 | ||||||||
\(743\) | − | 41.2679i | − | 1.51397i | −0.653431 | − | 0.756986i | \(-0.726671\pi\) | ||
0.653431 | − | 0.756986i | \(-0.273329\pi\) | |||||||
\(744\) | 8.87414 | − | 9.43624i | 0.325342 | − | 0.345949i | ||||
\(745\) | −14.0694 | −0.515463 | ||||||||
\(746\) | 4.78936i | 0.175351i | ||||||||
\(747\) | −54.0708 | + | 31.2178i | −1.97835 | + | 1.14220i | ||||
\(748\) | 17.0285i | 0.622624i | ||||||||
\(749\) | −36.1391 | − | 20.8649i | −1.32050 | − | 0.762388i | ||||
\(750\) | −2.80239 | − | 4.85388i | −0.102329 | − | 0.177239i | ||||
\(751\) | −25.0093 | − | 43.3173i | −0.912602 | − | 1.58067i | −0.810375 | − | 0.585911i | \(-0.800737\pi\) |
−0.102226 | − | 0.994761i | \(-0.532597\pi\) | |||||||
\(752\) | − | 0.950404i | − | 0.0346577i | ||||||
\(753\) | −22.8514 | + | 39.5798i | −0.832752 | + | 1.44237i | ||||
\(754\) | 1.83271 | − | 2.85047i | 0.0667434 | − | 0.103808i | ||||
\(755\) | 11.5571 | − | 20.0175i | 0.420606 | − | 0.728511i | ||||
\(756\) | −18.4306 | + | 10.6409i | −0.670313 | + | 0.387005i | ||||
\(757\) | −15.6416 | + | 27.0921i | −0.568505 | + | 0.984680i | 0.428209 | + | 0.903680i | \(0.359145\pi\) |
−0.996714 | + | 0.0810000i | \(0.974189\pi\) | |||||||
\(758\) | −0.461195 | − | 0.798813i | −0.0167514 | − | 0.0290142i | ||||
\(759\) | 3.53334i | 0.128252i | ||||||||
\(760\) | 3.76819i | 0.136687i | ||||||||
\(761\) | 34.9676 | − | 20.1885i | 1.26757 | − | 0.731834i | 0.293045 | − | 0.956099i | \(-0.405331\pi\) |
0.974528 | + | 0.224265i | \(0.0719981\pi\) | |||||||
\(762\) | 9.19452 | + | 5.30846i | 0.333082 | + | 0.192305i | ||||
\(763\) | −20.5022 | − | 35.5109i | −0.742231 | − | 1.28558i | ||||
\(764\) | 21.2731 | − | 36.8461i | 0.769634 | − | 1.33305i | ||||
\(765\) | −18.2067 | − | 10.5116i | −0.658264 | − | 0.380049i | ||||
\(766\) | 2.44369 | − | 4.23260i | 0.0882942 | − | 0.152930i | ||||
\(767\) | 40.7960 | + | 1.95173i | 1.47306 | + | 0.0704727i | ||||
\(768\) | 16.8220 | + | 29.1365i | 0.607011 | + | 1.05137i | ||||
\(769\) | −9.31755 | + | 5.37949i | −0.336000 | + | 0.193989i | −0.658502 | − | 0.752579i | \(-0.728809\pi\) |
0.322502 | + | 0.946569i | \(0.395476\pi\) | |||||||
\(770\) | −0.661155 | + | 1.14515i | −0.0238264 | + | 0.0412685i | ||||
\(771\) | −63.1913 | −2.27578 | ||||||||
\(772\) | −40.9977 | + | 23.6700i | −1.47554 | + | 0.851903i | ||||
\(773\) | 15.4275i | 0.554889i | 0.960742 | + | 0.277445i | \(0.0894875\pi\) | ||||
−0.960742 | + | 0.277445i | \(0.910513\pi\) | |||||||
\(774\) | − | 4.09720i | − | 0.147271i | ||||||
\(775\) | 15.5716 | + | 14.6441i | 0.559350 | + | 0.526030i | ||||
\(776\) | 1.46037 | 0.0524241 | ||||||||
\(777\) | −4.66483 | −0.167350 | ||||||||
\(778\) | 1.43199 | − | 0.826761i | 0.0513394 | − | 0.0296408i | ||||
\(779\) | 31.3722 | 1.12402 | ||||||||
\(780\) | 11.1517 | − | 17.3445i | 0.399294 | − | 0.621034i | ||||
\(781\) | −7.73776 | − | 13.4022i | −0.276879 | − | 0.479568i | ||||
\(782\) | −0.553379 | + | 0.319493i | −0.0197888 | + | 0.0114251i | ||||
\(783\) | 16.3546 | 0.584465 | ||||||||
\(784\) | 2.53473 | − | 4.39029i | 0.0905262 | − | 0.156796i | ||||
\(785\) | 0.190512 | + | 0.109992i | 0.00679966 | + | 0.00392579i | ||||
\(786\) | −2.49512 | − | 1.44056i | −0.0889981 | − | 0.0513831i | ||||
\(787\) | 39.8468 | − | 23.0055i | 1.42038 | − | 0.820059i | 0.424053 | − | 0.905637i | \(-0.360607\pi\) |
0.996331 | + | 0.0855783i | \(0.0272738\pi\) | |||||||
\(788\) | 9.59717 | + | 5.54093i | 0.341885 | + | 0.197387i | ||||
\(789\) | −29.5944 | − | 51.2590i | −1.05359 | − | 1.82487i | ||||
\(790\) | −0.949013 | −0.0337644 | ||||||||
\(791\) | 15.7674i | 0.560625i | ||||||||
\(792\) | 3.67967 | + | 6.37338i | 0.130751 | + | 0.226468i | ||||
\(793\) | 16.1208 | + | 10.3649i | 0.572465 | + | 0.368067i | ||||
\(794\) | 0.970708 | + | 1.68132i | 0.0344491 | + | 0.0596677i | ||||
\(795\) | −8.36271 | − | 4.82821i | −0.296595 | − | 0.171239i | ||||
\(796\) | −15.7111 | + | 27.2124i | −0.556865 | + | 0.964519i | ||||
\(797\) | 10.7954 | − | 18.6982i | 0.382392 | − | 0.662323i | −0.609011 | − | 0.793162i | \(-0.708434\pi\) |
0.991404 | + | 0.130839i | \(0.0417669\pi\) | |||||||
\(798\) | − | 6.95346i | − | 0.246150i | ||||||
\(799\) | −0.984032 | + | 0.568131i | −0.0348125 | + | 0.0200990i | ||||
\(800\) | 8.37129 | − | 4.83316i | 0.295970 | − | 0.170878i | ||||
\(801\) | −20.4081 | − | 11.7826i | −0.721086 | − | 0.416319i | ||||
\(802\) | −7.66907 | −0.270804 | ||||||||
\(803\) | −0.281874 | − | 0.488220i | −0.00994711 | − | 0.0172289i | ||||
\(804\) | − | 50.1930i | − | 1.77017i | ||||||
\(805\) | 2.06668 | 0.0728411 | ||||||||
\(806\) | 1.19682 | − | 4.17913i | 0.0421563 | − | 0.147204i | ||||
\(807\) | −74.5316 | −2.62364 | ||||||||
\(808\) | − | 7.12080i | − | 0.250509i | ||||||
\(809\) | −17.4746 | − | 30.2669i | −0.614374 | − | 1.06413i | −0.990494 | − | 0.137557i | \(-0.956075\pi\) |
0.376119 | − | 0.926571i | \(-0.377258\pi\) | |||||||
\(810\) | 0.680913 | 0.0239248 | ||||||||
\(811\) | −34.6528 | − | 20.0068i | −1.21682 | − | 0.702533i | −0.252586 | − | 0.967574i | \(-0.581281\pi\) |
−0.964237 | + | 0.265041i | \(0.914615\pi\) | |||||||
\(812\) | −21.2299 | + | 12.2571i | −0.745024 | + | 0.430140i | ||||
\(813\) | −24.2271 | + | 13.9875i | −0.849680 | + | 0.490563i | ||||
\(814\) | 0.251907i | 0.00882935i | ||||||||
\(815\) | −4.49549 | + | 7.78642i | −0.157470 | + | 0.272746i | ||||
\(816\) | 22.4926 | − | 38.9584i | 0.787400 | − | 1.36382i | ||||
\(817\) | −15.2624 | − | 8.81176i | −0.533964 | − | 0.308284i | ||||
\(818\) | −1.86310 | − | 3.22698i | −0.0651418 | − | 0.112829i | ||||
\(819\) | −24.7341 | + | 38.4697i | −0.864281 | + | 1.34424i | ||||
\(820\) | 8.07889 | + | 13.9930i | 0.282127 | + | 0.488658i | ||||
\(821\) | 42.5223i | 1.48404i | 0.670379 | + | 0.742019i | \(0.266132\pi\) | ||||
−0.670379 | + | 0.742019i | \(0.733868\pi\) | |||||||
\(822\) | −8.52610 | −0.297382 | ||||||||
\(823\) | −7.30664 | − | 12.6555i | −0.254693 | − | 0.441142i | 0.710119 | − | 0.704082i | \(-0.248641\pi\) |
−0.964812 | + | 0.262940i | \(0.915308\pi\) | |||||||
\(824\) | −2.53962 | − | 1.46625i | −0.0884719 | − | 0.0510793i | ||||
\(825\) | −17.7104 | + | 10.2251i | −0.616597 | + | 0.355992i | ||||
\(826\) | 6.14313 | + | 3.54674i | 0.213747 | + | 0.123407i | ||||
\(827\) | −8.28137 | − | 4.78125i | −0.287971 | − | 0.166260i | 0.349055 | − | 0.937102i | \(-0.386503\pi\) |
−0.637027 | + | 0.770842i | \(0.719836\pi\) | |||||||
\(828\) | 2.84143 | − | 4.92150i | 0.0987466 | − | 0.171034i | ||||
\(829\) | −38.5950 | −1.34046 | −0.670230 | − | 0.742153i | \(-0.733805\pi\) | ||||
−0.670230 | + | 0.742153i | \(0.733805\pi\) | |||||||
\(830\) | 2.87594 | − | 1.66043i | 0.0998254 | − | 0.0576342i | ||||
\(831\) | −34.8645 | − | 60.3870i | −1.20944 | − | 2.09480i | ||||
\(832\) | 20.9155 | + | 13.4476i | 0.725115 | + | 0.466213i | ||||
\(833\) | −6.06083 | −0.209995 | ||||||||
\(834\) | −10.7867 | + | 6.22770i | −0.373513 | + | 0.215648i | ||||
\(835\) | 9.16225 | 0.317073 | ||||||||
\(836\) | 15.6398 | 0.540914 | ||||||||
\(837\) | 20.0885 | − | 6.04914i | 0.694361 | − | 0.209089i | ||||
\(838\) | 5.70333i | 0.197018i | ||||||||
\(839\) | 32.8723i | 1.13488i | 0.823416 | + | 0.567439i | \(0.192066\pi\) | ||||
−0.823416 | + | 0.567439i | \(0.807934\pi\) | |||||||
\(840\) | 6.27742 | − | 3.62427i | 0.216592 | − | 0.125049i | ||||
\(841\) | −10.1614 | −0.350392 | ||||||||
\(842\) | −1.25078 | + | 2.16641i | −0.0431046 | + | 0.0746594i | ||||
\(843\) | 25.4018 | − | 14.6657i | 0.874885 | − | 0.505115i | ||||
\(844\) | −7.14302 | − | 12.3721i | −0.245873 | − | 0.425864i | ||||
\(845\) | 1.33709 | − | 13.9423i | 0.0459972 | − | 0.479628i | ||||
\(846\) | −0.121310 | + | 0.210116i | −0.00417074 | + | 0.00722393i | ||||
\(847\) | −17.9280 | − | 10.3507i | −0.616013 | − | 0.355655i | ||||
\(848\) | 6.13526 | − | 10.6266i | 0.210686 | − | 0.364918i | ||||
\(849\) | −1.53643 | − | 2.66117i | −0.0527300 | − | 0.0913311i | ||||
\(850\) | −3.20283 | − | 1.84915i | −0.109856 | − | 0.0634255i | ||||
\(851\) | 0.340967 | − | 0.196857i | 0.0116882 | − | 0.00674818i | ||||
\(852\) | 41.9131i | 1.43592i | ||||||||
\(853\) | 35.8035i | 1.22589i | 0.790126 | + | 0.612945i | \(0.210015\pi\) | ||||
−0.790126 | + | 0.612945i | \(0.789985\pi\) | |||||||
\(854\) | 1.66430 | + | 2.88265i | 0.0569511 | + | 0.0986422i | ||||
\(855\) | −9.65440 | + | 16.7219i | −0.330173 | + | 0.571877i | ||||
\(856\) | 10.6979 | − | 6.17646i | 0.365648 | − | 0.211107i | ||||
\(857\) | −4.43656 | + | 7.68434i | −0.151550 | + | 0.262492i | −0.931797 | − | 0.362979i | \(-0.881760\pi\) |
0.780248 | + | 0.625471i | \(0.215093\pi\) | |||||||
\(858\) | 3.49823 | + | 2.24919i | 0.119427 | + | 0.0767859i | ||||
\(859\) | 25.0291 | − | 43.3516i | 0.853981 | − | 1.47914i | −0.0236058 | − | 0.999721i | \(-0.507515\pi\) |
0.877587 | − | 0.479417i | \(-0.159152\pi\) | |||||||
\(860\) | − | 9.07674i | − | 0.309514i | ||||||
\(861\) | −30.1739 | − | 52.2628i | −1.02832 | − | 1.78111i | ||||
\(862\) | 0.00971352 | + | 0.0168243i | 0.000330844 | + | 0.000573039i | ||||
\(863\) | −28.9654 | − | 16.7232i | −0.985994 | − | 0.569264i | −0.0819193 | − | 0.996639i | \(-0.526105\pi\) |
−0.904074 | + | 0.427375i | \(0.859438\pi\) | |||||||
\(864\) | − | 9.48714i | − | 0.322759i | ||||||
\(865\) | 23.0987 | − | 13.3360i | 0.785379 | − | 0.453439i | ||||
\(866\) | 5.78885i | 0.196713i | ||||||||
\(867\) | −7.57988 | −0.257426 | ||||||||
\(868\) | −21.5434 | + | 22.9079i | −0.731229 | + | 0.777546i | ||||
\(869\) | 7.97230i | 0.270442i | ||||||||
\(870\) | −2.75213 | −0.0933061 | ||||||||
\(871\) | −15.6163 | − | 30.3067i | −0.529139 | − | 1.02690i | ||||
\(872\) | 12.1382 | 0.411050 | ||||||||
\(873\) | 6.48059 | + | 3.74157i | 0.219335 | + | 0.126633i | ||||
\(874\) | 0.293438 | + | 0.508250i | 0.00992569 | + | 0.0171918i | ||||
\(875\) | 13.7698 | + | 23.8500i | 0.465504 | + | 0.806277i | ||||
\(876\) | 1.52682i | 0.0515866i | ||||||||
\(877\) | 28.2565 | + | 16.3139i | 0.954154 | + | 0.550881i | 0.894369 | − | 0.447330i | \(-0.147625\pi\) |
0.0597853 | + | 0.998211i | \(0.480958\pi\) | |||||||
\(878\) | 0.178163 | + | 0.102862i | 0.00601270 | + | 0.00347143i | ||||
\(879\) | 24.2347 | + | 13.9919i | 0.817415 | + | 0.471935i | ||||
\(880\) | 3.92851 | + | 6.80439i | 0.132430 | + | 0.229376i | ||||
\(881\) | 9.23635 | − | 15.9978i | 0.311180 | − | 0.538980i | −0.667438 | − | 0.744666i | \(-0.732609\pi\) |
0.978618 | + | 0.205685i | \(0.0659423\pi\) | |||||||
\(882\) | −1.12076 | + | 0.647071i | −0.0377379 | + | 0.0217880i | ||||
\(883\) | −53.6613 | −1.80584 | −0.902922 | − | 0.429803i | \(-0.858583\pi\) | ||||
−0.902922 | + | 0.429803i | \(0.858583\pi\) | |||||||
\(884\) | 1.49698 | − | 31.2905i | 0.0503487 | − | 1.05241i | ||||
\(885\) | −16.5847 | − | 28.7255i | −0.557488 | − | 0.965597i | ||||
\(886\) | 5.39941 | + | 3.11735i | 0.181397 | + | 0.104729i | ||||
\(887\) | −9.86117 | − | 17.0800i | −0.331106 | − | 0.573492i | 0.651623 | − | 0.758543i | \(-0.274088\pi\) |
−0.982729 | + | 0.185051i | \(0.940755\pi\) | |||||||
\(888\) | 0.690443 | − | 1.19588i | 0.0231698 | − | 0.0401312i | ||||
\(889\) | −45.1781 | − | 26.0836i | −1.51523 | − | 0.874816i | ||||
\(890\) | 1.08548 | + | 0.626700i | 0.0363852 | + | 0.0210070i | ||||
\(891\) | − | 5.72009i | − | 0.191630i | ||||||
\(892\) | 47.7015 | − | 27.5405i | 1.59716 | − | 0.922124i | ||||
\(893\) | 0.521799 | + | 0.903783i | 0.0174613 | + | 0.0302439i | ||||
\(894\) | −3.84269 | + | 6.65573i | −0.128519 | + | 0.222601i | ||||
\(895\) | − | 16.8448i | − | 0.563059i | ||||||
\(896\) | 9.44024 | + | 16.3510i | 0.315376 | + | 0.546248i | ||||
\(897\) | 0.310616 | − | 6.49265i | 0.0103712 | − | 0.216783i | ||||
\(898\) | −6.00525 | −0.200398 | ||||||||
\(899\) | 23.1397 | − | 6.96793i | 0.771752 | − | 0.232393i | ||||
\(900\) | 32.8911 | 1.09637 | ||||||||
\(901\) | −14.6701 | −0.488732 | ||||||||
\(902\) | −2.82226 | + | 1.62944i | −0.0939711 | + | 0.0542543i | ||||
\(903\) | 33.9008i | 1.12815i | ||||||||
\(904\) | −4.04216 | − | 2.33374i | −0.134440 | − | 0.0776191i | ||||
\(905\) | −0.179070 | + | 0.103386i | −0.00595249 | + | 0.00343667i | ||||
\(906\) | −6.31305 | − | 10.9345i | −0.209737 | − | 0.363275i | ||||
\(907\) | 23.2079 | 0.770607 | 0.385303 | − | 0.922790i | \(-0.374097\pi\) | ||||
0.385303 | + | 0.922790i | \(0.374097\pi\) | |||||||
\(908\) | −38.0179 | − | 21.9496i | −1.26167 | − | 0.728424i | ||||
\(909\) | 18.2440 | − | 31.5996i | 0.605116 | − | 1.04809i | ||||
\(910\) | 1.31557 | − | 2.04614i | 0.0436107 | − | 0.0678290i | ||||
\(911\) | 13.1869 | + | 22.8405i | 0.436903 | + | 0.756738i | 0.997449 | − | 0.0713851i | \(-0.0227419\pi\) |
−0.560546 | + | 0.828123i | \(0.689409\pi\) | |||||||
\(912\) | −35.7813 | − | 20.6583i | −1.18484 | − | 0.684066i | ||||
\(913\) | −13.9486 | − | 24.1597i | −0.461631 | − | 0.799568i | ||||
\(914\) | 5.64548 | 0.186736 | ||||||||
\(915\) | − | 15.5646i | − | 0.514551i | ||||||
\(916\) | −13.8485 | + | 7.99546i | −0.457569 | + | 0.264177i | ||||
\(917\) | 12.2600 | + | 7.07833i | 0.404862 | + | 0.233747i | ||||
\(918\) | −3.14346 | + | 1.81488i | −0.103750 | + | 0.0598998i | ||||
\(919\) | −16.7700 | + | 29.0465i | −0.553191 | + | 0.958155i | 0.444851 | + | 0.895605i | \(0.353257\pi\) |
−0.998042 | + | 0.0625502i | \(0.980077\pi\) | |||||||
\(920\) | −0.305891 | + | 0.529818i | −0.0100849 | + | 0.0174676i | ||||
\(921\) | −7.46666 | − | 4.31088i | −0.246035 | − | 0.142048i | ||||
\(922\) | 0.405506 | 0.0133546 | ||||||||
\(923\) | 13.0402 | + | 25.3072i | 0.429225 | + | 0.832998i | ||||
\(924\) | −15.0425 | − | 26.0543i | −0.494861 | − | 0.857124i | ||||
\(925\) | 1.97344 | + | 1.13937i | 0.0648863 | + | 0.0374621i | ||||
\(926\) | −0.446121 | −0.0146604 | ||||||||
\(927\) | −7.51330 | − | 13.0134i | −0.246769 | − | 0.427416i | ||||
\(928\) | − | 10.9281i | − | 0.358733i | ||||||
\(929\) | 42.4547i | 1.39289i | 0.717609 | + | 0.696446i | \(0.245237\pi\) | ||||
−0.717609 | + | 0.696446i | \(0.754763\pi\) | |||||||
\(930\) | −3.38048 | + | 1.01794i | −0.110850 | + | 0.0333797i | ||||
\(931\) | 5.56656i | 0.182437i | ||||||||
\(932\) | 4.15188 | 0.135999 | ||||||||
\(933\) | −17.2947 | − | 29.9553i | −0.566204 | − | 0.980693i | ||||
\(934\) | 5.53109i | 0.180983i | ||||||||
\(935\) | 4.69676 | − | 8.13502i | 0.153600 | − | 0.266044i | ||||
\(936\) | −6.20125 | − | 12.0348i | −0.202694 | − | 0.393370i | ||||
\(937\) | 9.98063 | + | 17.2870i | 0.326053 | + | 0.564740i | 0.981725 | − | 0.190306i | \(-0.0609479\pi\) |
−0.655672 | + | 0.755046i | \(0.727615\pi\) | |||||||
\(938\) | − | 5.92129i | − | 0.193337i | ||||||
\(939\) | −13.6967 | + | 23.7234i | −0.446975 | + | 0.774184i | ||||
\(940\) | −0.268745 | + | 0.465480i | −0.00876550 | + | 0.0151823i | ||||
\(941\) | −20.5620 | − | 11.8715i | −0.670302 | − | 0.386999i | 0.125889 | − | 0.992044i | \(-0.459822\pi\) |
−0.796191 | + | 0.605045i | \(0.793155\pi\) | |||||||
\(942\) | 0.104067 | − | 0.0600830i | 0.00339068 | − | 0.00195761i | ||||
\(943\) | 4.41101 | + | 2.54670i | 0.143642 | + | 0.0829319i | ||||
\(944\) | 36.5018 | − | 21.0743i | 1.18803 | − | 0.685911i | ||||
\(945\) | 11.7398 | 0.381894 | ||||||||
\(946\) | 1.83069 | 0.0595209 | ||||||||
\(947\) | 27.9672 | − | 16.1469i | 0.908811 | − | 0.524702i | 0.0287625 | − | 0.999586i | \(-0.490843\pi\) |
0.880048 | + | 0.474884i | \(0.157510\pi\) | |||||||
\(948\) | 10.7959 | − | 18.6990i | 0.350634 | − | 0.607316i | ||||
\(949\) | 0.475034 | + | 0.921901i | 0.0154203 | + | 0.0299262i | ||||
\(950\) | −1.69835 | + | 2.94163i | −0.0551019 | + | 0.0954392i | ||||
\(951\) | −78.1575 | − | 45.1242i | −2.53443 | − | 1.46325i | ||||
\(952\) | 5.50601 | − | 9.53670i | 0.178451 | − | 0.309086i | ||||
\(953\) | −13.0405 | −0.422423 | −0.211211 | − | 0.977440i | \(-0.567741\pi\) | ||||
−0.211211 | + | 0.977440i | \(0.567741\pi\) | |||||||
\(954\) | −2.71277 | + | 1.56622i | −0.0878292 | + | 0.0507082i | ||||
\(955\) | −20.3256 | + | 11.7350i | −0.657720 | + | 0.379735i | ||||
\(956\) | 13.8091 | + | 7.97267i | 0.446617 | + | 0.257855i | ||||
\(957\) | 23.1196i | 0.747351i | ||||||||
\(958\) | 4.41762 | + | 7.65153i | 0.142727 | + | 0.247210i | ||||
\(959\) | 41.8938 | 1.35282 | ||||||||
\(960\) | − | 20.1940i | − | 0.651758i | ||||||
\(961\) | 25.8455 | − | 17.1176i | 0.833725 | − | 0.552180i | ||||
\(962\) | 0.0221452 | − | 0.462889i | 0.000713989 | − | 0.0149242i | ||||
\(963\) | 63.2982 | 2.03976 | ||||||||
\(964\) | 38.4724 | − | 22.2120i | 1.23911 | − | 0.715401i | ||||
\(965\) | 26.1144 | 0.840653 | ||||||||
\(966\) | 0.564461 | − | 0.977675i | 0.0181612 | − | 0.0314562i | ||||
\(967\) | 18.0955 | − | 10.4474i | 0.581911 | − | 0.335966i | −0.179982 | − | 0.983670i | \(-0.557604\pi\) |
0.761892 | + | 0.647704i | \(0.224270\pi\) | |||||||
\(968\) | 5.30706 | − | 3.06403i | 0.170575 | − | 0.0984817i | ||||
\(969\) | 49.3964i | 1.58684i | ||||||||
\(970\) | −0.344692 | − | 0.199008i | −0.0110674 | − | 0.00638976i | ||||
\(971\) | −5.61491 | + | 9.72530i | −0.180191 | + | 0.312100i | −0.941945 | − | 0.335766i | \(-0.891005\pi\) |
0.761755 | + | 0.647866i | \(0.224338\pi\) | |||||||
\(972\) | −18.7851 | + | 32.5367i | −0.602531 | + | 1.04361i | ||||
\(973\) | 53.0015 | − | 30.6004i | 1.69915 | − | 0.981004i | ||||
\(974\) | 3.13145 | − | 5.42384i | 0.100338 | − | 0.173791i | ||||
\(975\) | 33.4424 | − | 17.2321i | 1.07101 | − | 0.551869i | ||||
\(976\) | 19.7782 | 0.633083 | ||||||||
\(977\) | 26.4825i | 0.847250i | 0.905838 | + | 0.423625i | \(0.139243\pi\) | ||||
−0.905838 | + | 0.423625i | \(0.860757\pi\) | |||||||
\(978\) | 2.45565 | + | 4.25332i | 0.0785231 | + | 0.136006i | ||||
\(979\) | 5.26466 | − | 9.11866i | 0.168259 | − | 0.291434i | ||||
\(980\) | −2.48288 | + | 1.43349i | −0.0793125 | + | 0.0457911i | ||||
\(981\) | 53.8649 | + | 31.0989i | 1.71978 | + | 0.992913i | ||||
\(982\) | 5.30500 | + | 3.06284i | 0.169289 | + | 0.0977393i | ||||
\(983\) | −25.3799 | − | 14.6531i | −0.809493 | − | 0.467361i | 0.0372866 | − | 0.999305i | \(-0.488129\pi\) |
−0.846780 | + | 0.531943i | \(0.821462\pi\) | |||||||
\(984\) | 17.8642 | 0.569491 | ||||||||
\(985\) | −3.05657 | − | 5.29413i | −0.0973904 | − | 0.168685i | ||||
\(986\) | −3.62090 | + | 2.09053i | −0.115313 | + | 0.0665761i | ||||
\(987\) | 1.00374 | − | 1.73853i | 0.0319494 | − | 0.0553379i | ||||
\(988\) | −28.7388 | − | 1.37489i | −0.914302 | − | 0.0437412i | ||||
\(989\) | −1.43063 | − | 2.47792i | −0.0454912 | − | 0.0787932i | ||||
\(990\) | − | 2.00576i | − | 0.0637471i | ||||||
\(991\) | 14.7838 | 0.469622 | 0.234811 | − | 0.972041i | \(-0.424553\pi\) | ||||
0.234811 | + | 0.972041i | \(0.424553\pi\) | |||||||
\(992\) | −4.04203 | − | 13.4231i | −0.128334 | − | 0.426184i | ||||
\(993\) | − | 15.4099i | − | 0.489019i | ||||||
\(994\) | 4.94451i | 0.156830i | ||||||||
\(995\) | 15.0113 | − | 8.66678i | 0.475890 | − | 0.274755i | ||||
\(996\) | 75.5553i | 2.39406i | ||||||||
\(997\) | 11.1436 | − | 19.3013i | 0.352921 | − | 0.611277i | −0.633839 | − | 0.773465i | \(-0.718522\pi\) |
0.986760 | + | 0.162188i | \(0.0518551\pi\) | |||||||
\(998\) | 1.82429 | + | 3.15976i | 0.0577469 | + | 0.100021i | ||||
\(999\) | 1.93686 | − | 1.11824i | 0.0612794 | − | 0.0353797i |
(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 | 403.2.l.c.25.20 | yes | 68 | |
13.12 | even | 2 | inner | 403.2.l.c.25.15 | ✓ | 68 | |
31.5 | even | 3 | inner | 403.2.l.c.129.20 | yes | 68 | |
403.129 | even | 6 | inner | 403.2.l.c.129.15 | yes | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.l.c.25.15 | ✓ | 68 | 13.12 | even | 2 | inner | |
403.2.l.c.25.20 | yes | 68 | 1.1 | even | 1 | trivial | |
403.2.l.c.129.15 | yes | 68 | 403.129 | even | 6 | inner | |
403.2.l.c.129.20 | yes | 68 | 31.5 | even | 3 | inner |