Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6013,2,Mod(1,6013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6013 = 7 \cdot 859 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6013.a (trivial) |
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: | yes |
Analytic conductor: | \(48.0140467354\) |
Analytic rank: | \(0\) |
Dimension: | \(110\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6013.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.23147 | −1.57789 | −0.788944 | − | 0.614465i | \(-0.789372\pi\) | ||||
−0.788944 | + | 0.614465i | \(0.789372\pi\) | |||||||
\(3\) | 2.27145 | 1.31142 | 0.655710 | − | 0.755013i | \(-0.272369\pi\) | ||||
0.655710 | + | 0.755013i | \(0.272369\pi\) | |||||||
\(4\) | 2.97947 | 1.48973 | ||||||||
\(5\) | −3.38307 | −1.51295 | −0.756477 | − | 0.654020i | \(-0.773081\pi\) | ||||
−0.756477 | + | 0.654020i | \(0.773081\pi\) | |||||||
\(6\) | −5.06867 | −2.06928 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.18565 | −0.772745 | ||||||||
\(9\) | 2.15947 | 0.719823 | ||||||||
\(10\) | 7.54923 | 2.38727 | ||||||||
\(11\) | −1.25111 | −0.377224 | −0.188612 | − | 0.982052i | \(-0.560399\pi\) | ||||
−0.188612 | + | 0.982052i | \(0.560399\pi\) | |||||||
\(12\) | 6.76770 | 1.95367 | ||||||||
\(13\) | −4.40536 | −1.22183 | −0.610913 | − | 0.791698i | \(-0.709197\pi\) | ||||
−0.610913 | + | 0.791698i | \(0.709197\pi\) | |||||||
\(14\) | 2.23147 | 0.596386 | ||||||||
\(15\) | −7.68446 | −1.98412 | ||||||||
\(16\) | −1.08171 | −0.270428 | ||||||||
\(17\) | −7.52986 | −1.82626 | −0.913130 | − | 0.407669i | \(-0.866342\pi\) | ||||
−0.913130 | + | 0.407669i | \(0.866342\pi\) | |||||||
\(18\) | −4.81880 | −1.13580 | ||||||||
\(19\) | −0.544700 | −0.124963 | −0.0624814 | − | 0.998046i | \(-0.519901\pi\) | ||||
−0.0624814 | + | 0.998046i | \(0.519901\pi\) | |||||||
\(20\) | −10.0797 | −2.25390 | ||||||||
\(21\) | −2.27145 | −0.495670 | ||||||||
\(22\) | 2.79182 | 0.595218 | ||||||||
\(23\) | 7.05915 | 1.47193 | 0.735967 | − | 0.677017i | \(-0.236728\pi\) | ||||
0.735967 | + | 0.677017i | \(0.236728\pi\) | |||||||
\(24\) | −4.96459 | −1.01339 | ||||||||
\(25\) | 6.44516 | 1.28903 | ||||||||
\(26\) | 9.83043 | 1.92791 | ||||||||
\(27\) | −1.90922 | −0.367429 | ||||||||
\(28\) | −2.97947 | −0.563066 | ||||||||
\(29\) | 4.54232 | 0.843487 | 0.421744 | − | 0.906715i | \(-0.361418\pi\) | ||||
0.421744 | + | 0.906715i | \(0.361418\pi\) | |||||||
\(30\) | 17.1477 | 3.13072 | ||||||||
\(31\) | −7.89947 | −1.41879 | −0.709394 | − | 0.704812i | \(-0.751031\pi\) | ||||
−0.709394 | + | 0.704812i | \(0.751031\pi\) | |||||||
\(32\) | 6.78511 | 1.19945 | ||||||||
\(33\) | −2.84183 | −0.494700 | ||||||||
\(34\) | 16.8027 | 2.88163 | ||||||||
\(35\) | 3.38307 | 0.571843 | ||||||||
\(36\) | 6.43407 | 1.07234 | ||||||||
\(37\) | −0.578275 | −0.0950678 | −0.0475339 | − | 0.998870i | \(-0.515136\pi\) | ||||
−0.0475339 | + | 0.998870i | \(0.515136\pi\) | |||||||
\(38\) | 1.21548 | 0.197177 | ||||||||
\(39\) | −10.0065 | −1.60233 | ||||||||
\(40\) | 7.39422 | 1.16913 | ||||||||
\(41\) | −0.546589 | −0.0853629 | −0.0426815 | − | 0.999089i | \(-0.513590\pi\) | ||||
−0.0426815 | + | 0.999089i | \(0.513590\pi\) | |||||||
\(42\) | 5.06867 | 0.782113 | ||||||||
\(43\) | −6.25284 | −0.953549 | −0.476774 | − | 0.879026i | \(-0.658194\pi\) | ||||
−0.476774 | + | 0.879026i | \(0.658194\pi\) | |||||||
\(44\) | −3.72765 | −0.561964 | ||||||||
\(45\) | −7.30564 | −1.08906 | ||||||||
\(46\) | −15.7523 | −2.32255 | ||||||||
\(47\) | 0.251029 | 0.0366163 | 0.0183082 | − | 0.999832i | \(-0.494172\pi\) | ||||
0.0183082 | + | 0.999832i | \(0.494172\pi\) | |||||||
\(48\) | −2.45705 | −0.354644 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −14.3822 | −2.03395 | ||||||||
\(51\) | −17.1037 | −2.39499 | ||||||||
\(52\) | −13.1256 | −1.82020 | ||||||||
\(53\) | −11.3467 | −1.55859 | −0.779294 | − | 0.626659i | \(-0.784422\pi\) | ||||
−0.779294 | + | 0.626659i | \(0.784422\pi\) | |||||||
\(54\) | 4.26037 | 0.579763 | ||||||||
\(55\) | 4.23260 | 0.570723 | ||||||||
\(56\) | 2.18565 | 0.292070 | ||||||||
\(57\) | −1.23726 | −0.163879 | ||||||||
\(58\) | −10.1361 | −1.33093 | ||||||||
\(59\) | −4.98797 | −0.649379 | −0.324689 | − | 0.945821i | \(-0.605260\pi\) | ||||
−0.324689 | + | 0.945821i | \(0.605260\pi\) | |||||||
\(60\) | −22.8956 | −2.95581 | ||||||||
\(61\) | −2.93734 | −0.376088 | −0.188044 | − | 0.982161i | \(-0.560215\pi\) | ||||
−0.188044 | + | 0.982161i | \(0.560215\pi\) | |||||||
\(62\) | 17.6275 | 2.23869 | ||||||||
\(63\) | −2.15947 | −0.272068 | ||||||||
\(64\) | −12.9774 | −1.62217 | ||||||||
\(65\) | 14.9036 | 1.84857 | ||||||||
\(66\) | 6.34147 | 0.780581 | ||||||||
\(67\) | 6.89699 | 0.842602 | 0.421301 | − | 0.906921i | \(-0.361574\pi\) | ||||
0.421301 | + | 0.906921i | \(0.361574\pi\) | |||||||
\(68\) | −22.4350 | −2.72064 | ||||||||
\(69\) | 16.0345 | 1.93032 | ||||||||
\(70\) | −7.54923 | −0.902305 | ||||||||
\(71\) | 6.94602 | 0.824341 | 0.412171 | − | 0.911107i | \(-0.364771\pi\) | ||||
0.412171 | + | 0.911107i | \(0.364771\pi\) | |||||||
\(72\) | −4.71985 | −0.556240 | ||||||||
\(73\) | −0.847622 | −0.0992066 | −0.0496033 | − | 0.998769i | \(-0.515796\pi\) | ||||
−0.0496033 | + | 0.998769i | \(0.515796\pi\) | |||||||
\(74\) | 1.29040 | 0.150006 | ||||||||
\(75\) | 14.6398 | 1.69046 | ||||||||
\(76\) | −1.62292 | −0.186161 | ||||||||
\(77\) | 1.25111 | 0.142577 | ||||||||
\(78\) | 22.3293 | 2.52829 | ||||||||
\(79\) | −15.2146 | −1.71177 | −0.855886 | − | 0.517165i | \(-0.826987\pi\) | ||||
−0.855886 | + | 0.517165i | \(0.826987\pi\) | |||||||
\(80\) | 3.65950 | 0.409145 | ||||||||
\(81\) | −10.8151 | −1.20168 | ||||||||
\(82\) | 1.21970 | 0.134693 | ||||||||
\(83\) | 8.11205 | 0.890414 | 0.445207 | − | 0.895428i | \(-0.353130\pi\) | ||||
0.445207 | + | 0.895428i | \(0.353130\pi\) | |||||||
\(84\) | −6.76770 | −0.738417 | ||||||||
\(85\) | 25.4740 | 2.76305 | ||||||||
\(86\) | 13.9530 | 1.50459 | ||||||||
\(87\) | 10.3176 | 1.10617 | ||||||||
\(88\) | 2.73450 | 0.291498 | ||||||||
\(89\) | 0.924246 | 0.0979699 | 0.0489849 | − | 0.998800i | \(-0.484401\pi\) | ||||
0.0489849 | + | 0.998800i | \(0.484401\pi\) | |||||||
\(90\) | 16.3023 | 1.71842 | ||||||||
\(91\) | 4.40536 | 0.461807 | ||||||||
\(92\) | 21.0325 | 2.19279 | ||||||||
\(93\) | −17.9432 | −1.86063 | ||||||||
\(94\) | −0.560164 | −0.0577765 | ||||||||
\(95\) | 1.84276 | 0.189063 | ||||||||
\(96\) | 15.4120 | 1.57298 | ||||||||
\(97\) | −2.56900 | −0.260843 | −0.130421 | − | 0.991459i | \(-0.541633\pi\) | ||||
−0.130421 | + | 0.991459i | \(0.541633\pi\) | |||||||
\(98\) | −2.23147 | −0.225413 | ||||||||
\(99\) | −2.70174 | −0.271535 | ||||||||
\(100\) | 19.2032 | 1.92032 | ||||||||
\(101\) | 1.13625 | 0.113061 | 0.0565307 | − | 0.998401i | \(-0.481996\pi\) | ||||
0.0565307 | + | 0.998401i | \(0.481996\pi\) | |||||||
\(102\) | 38.1664 | 3.77903 | ||||||||
\(103\) | 2.81818 | 0.277684 | 0.138842 | − | 0.990315i | \(-0.455662\pi\) | ||||
0.138842 | + | 0.990315i | \(0.455662\pi\) | |||||||
\(104\) | 9.62858 | 0.944160 | ||||||||
\(105\) | 7.68446 | 0.749927 | ||||||||
\(106\) | 25.3198 | 2.45928 | ||||||||
\(107\) | −5.60690 | −0.542040 | −0.271020 | − | 0.962574i | \(-0.587361\pi\) | ||||
−0.271020 | + | 0.962574i | \(0.587361\pi\) | |||||||
\(108\) | −5.68845 | −0.547372 | ||||||||
\(109\) | 3.16393 | 0.303049 | 0.151525 | − | 0.988453i | \(-0.451582\pi\) | ||||
0.151525 | + | 0.988453i | \(0.451582\pi\) | |||||||
\(110\) | −9.44492 | −0.900538 | ||||||||
\(111\) | −1.31352 | −0.124674 | ||||||||
\(112\) | 1.08171 | 0.102212 | ||||||||
\(113\) | −2.00506 | −0.188621 | −0.0943103 | − | 0.995543i | \(-0.530065\pi\) | ||||
−0.0943103 | + | 0.995543i | \(0.530065\pi\) | |||||||
\(114\) | 2.76091 | 0.258583 | ||||||||
\(115\) | −23.8816 | −2.22697 | ||||||||
\(116\) | 13.5337 | 1.25657 | ||||||||
\(117\) | −9.51324 | −0.879499 | ||||||||
\(118\) | 11.1305 | 1.02465 | ||||||||
\(119\) | 7.52986 | 0.690261 | ||||||||
\(120\) | 16.7956 | 1.53322 | ||||||||
\(121\) | −9.43472 | −0.857702 | ||||||||
\(122\) | 6.55460 | 0.593425 | ||||||||
\(123\) | −1.24155 | −0.111947 | ||||||||
\(124\) | −23.5362 | −2.11362 | ||||||||
\(125\) | −4.88909 | −0.437293 | ||||||||
\(126\) | 4.81880 | 0.429293 | ||||||||
\(127\) | 5.38996 | 0.478281 | 0.239141 | − | 0.970985i | \(-0.423134\pi\) | ||||
0.239141 | + | 0.970985i | \(0.423134\pi\) | |||||||
\(128\) | 15.3884 | 1.36016 | ||||||||
\(129\) | −14.2030 | −1.25050 | ||||||||
\(130\) | −33.2570 | −2.91683 | ||||||||
\(131\) | 20.2237 | 1.76695 | 0.883475 | − | 0.468478i | \(-0.155197\pi\) | ||||
0.883475 | + | 0.468478i | \(0.155197\pi\) | |||||||
\(132\) | −8.46715 | −0.736971 | ||||||||
\(133\) | 0.544700 | 0.0472315 | ||||||||
\(134\) | −15.3904 | −1.32953 | ||||||||
\(135\) | 6.45902 | 0.555904 | ||||||||
\(136\) | 16.4577 | 1.41123 | ||||||||
\(137\) | 6.14206 | 0.524752 | 0.262376 | − | 0.964966i | \(-0.415494\pi\) | ||||
0.262376 | + | 0.964966i | \(0.415494\pi\) | |||||||
\(138\) | −35.7805 | −3.04584 | ||||||||
\(139\) | 3.61692 | 0.306783 | 0.153392 | − | 0.988165i | \(-0.450980\pi\) | ||||
0.153392 | + | 0.988165i | \(0.450980\pi\) | |||||||
\(140\) | 10.0797 | 0.851894 | ||||||||
\(141\) | 0.570199 | 0.0480194 | ||||||||
\(142\) | −15.4999 | −1.30072 | ||||||||
\(143\) | 5.51159 | 0.460902 | ||||||||
\(144\) | −2.33592 | −0.194660 | ||||||||
\(145\) | −15.3670 | −1.27616 | ||||||||
\(146\) | 1.89144 | 0.156537 | ||||||||
\(147\) | 2.27145 | 0.187346 | ||||||||
\(148\) | −1.72295 | −0.141626 | ||||||||
\(149\) | −6.33298 | −0.518818 | −0.259409 | − | 0.965768i | \(-0.583528\pi\) | ||||
−0.259409 | + | 0.965768i | \(0.583528\pi\) | |||||||
\(150\) | −32.6684 | −2.66736 | ||||||||
\(151\) | 8.40014 | 0.683593 | 0.341797 | − | 0.939774i | \(-0.388965\pi\) | ||||
0.341797 | + | 0.939774i | \(0.388965\pi\) | |||||||
\(152\) | 1.19053 | 0.0965644 | ||||||||
\(153\) | −16.2605 | −1.31458 | ||||||||
\(154\) | −2.79182 | −0.224971 | ||||||||
\(155\) | 26.7245 | 2.14656 | ||||||||
\(156\) | −29.8141 | −2.38704 | ||||||||
\(157\) | −19.6202 | −1.56587 | −0.782933 | − | 0.622106i | \(-0.786277\pi\) | ||||
−0.782933 | + | 0.622106i | \(0.786277\pi\) | |||||||
\(158\) | 33.9509 | 2.70099 | ||||||||
\(159\) | −25.7734 | −2.04396 | ||||||||
\(160\) | −22.9545 | −1.81471 | ||||||||
\(161\) | −7.05915 | −0.556339 | ||||||||
\(162\) | 24.1336 | 1.89611 | ||||||||
\(163\) | 20.9355 | 1.63979 | 0.819896 | − | 0.572512i | \(-0.194031\pi\) | ||||
0.819896 | + | 0.572512i | \(0.194031\pi\) | |||||||
\(164\) | −1.62855 | −0.127168 | ||||||||
\(165\) | 9.61412 | 0.748458 | ||||||||
\(166\) | −18.1018 | −1.40497 | ||||||||
\(167\) | 10.7398 | 0.831072 | 0.415536 | − | 0.909577i | \(-0.363594\pi\) | ||||
0.415536 | + | 0.909577i | \(0.363594\pi\) | |||||||
\(168\) | 4.96459 | 0.383027 | ||||||||
\(169\) | 6.40717 | 0.492859 | ||||||||
\(170\) | −56.8446 | −4.35978 | ||||||||
\(171\) | −1.17626 | −0.0899512 | ||||||||
\(172\) | −18.6301 | −1.42053 | ||||||||
\(173\) | −22.4178 | −1.70439 | −0.852197 | − | 0.523221i | \(-0.824730\pi\) | ||||
−0.852197 | + | 0.523221i | \(0.824730\pi\) | |||||||
\(174\) | −23.0235 | −1.74541 | ||||||||
\(175\) | −6.44516 | −0.487209 | ||||||||
\(176\) | 1.35334 | 0.102012 | ||||||||
\(177\) | −11.3299 | −0.851609 | ||||||||
\(178\) | −2.06243 | −0.154586 | ||||||||
\(179\) | 11.4219 | 0.853709 | 0.426855 | − | 0.904320i | \(-0.359622\pi\) | ||||
0.426855 | + | 0.904320i | \(0.359622\pi\) | |||||||
\(180\) | −21.7669 | −1.62241 | ||||||||
\(181\) | 8.95619 | 0.665709 | 0.332854 | − | 0.942978i | \(-0.391988\pi\) | ||||
0.332854 | + | 0.942978i | \(0.391988\pi\) | |||||||
\(182\) | −9.83043 | −0.728680 | ||||||||
\(183\) | −6.67202 | −0.493210 | ||||||||
\(184\) | −15.4288 | −1.13743 | ||||||||
\(185\) | 1.95634 | 0.143833 | ||||||||
\(186\) | 40.0398 | 2.93586 | ||||||||
\(187\) | 9.42069 | 0.688909 | ||||||||
\(188\) | 0.747932 | 0.0545486 | ||||||||
\(189\) | 1.90922 | 0.138875 | ||||||||
\(190\) | −4.11207 | −0.298321 | ||||||||
\(191\) | 0.506428 | 0.0366438 | 0.0183219 | − | 0.999832i | \(-0.494168\pi\) | ||||
0.0183219 | + | 0.999832i | \(0.494168\pi\) | |||||||
\(192\) | −29.4774 | −2.12735 | ||||||||
\(193\) | 16.8603 | 1.21363 | 0.606814 | − | 0.794844i | \(-0.292447\pi\) | ||||
0.606814 | + | 0.794844i | \(0.292447\pi\) | |||||||
\(194\) | 5.73266 | 0.411581 | ||||||||
\(195\) | 33.8528 | 2.42425 | ||||||||
\(196\) | 2.97947 | 0.212819 | ||||||||
\(197\) | 23.7570 | 1.69262 | 0.846308 | − | 0.532694i | \(-0.178820\pi\) | ||||
0.846308 | + | 0.532694i | \(0.178820\pi\) | |||||||
\(198\) | 6.02885 | 0.428452 | ||||||||
\(199\) | −25.8468 | −1.83223 | −0.916116 | − | 0.400914i | \(-0.868693\pi\) | ||||
−0.916116 | + | 0.400914i | \(0.868693\pi\) | |||||||
\(200\) | −14.0869 | −0.996094 | ||||||||
\(201\) | 15.6662 | 1.10501 | ||||||||
\(202\) | −2.53552 | −0.178398 | ||||||||
\(203\) | −4.54232 | −0.318808 | ||||||||
\(204\) | −50.9598 | −3.56790 | ||||||||
\(205\) | 1.84915 | 0.129150 | ||||||||
\(206\) | −6.28869 | −0.438154 | ||||||||
\(207\) | 15.2440 | 1.05953 | ||||||||
\(208\) | 4.76532 | 0.330416 | ||||||||
\(209\) | 0.681481 | 0.0471390 | ||||||||
\(210\) | −17.1477 | −1.18330 | ||||||||
\(211\) | −22.9983 | −1.58327 | −0.791636 | − | 0.610993i | \(-0.790770\pi\) | ||||
−0.791636 | + | 0.610993i | \(0.790770\pi\) | |||||||
\(212\) | −33.8071 | −2.32188 | ||||||||
\(213\) | 15.7775 | 1.08106 | ||||||||
\(214\) | 12.5116 | 0.855279 | ||||||||
\(215\) | 21.1538 | 1.44268 | ||||||||
\(216\) | 4.17289 | 0.283929 | ||||||||
\(217\) | 7.89947 | 0.536251 | ||||||||
\(218\) | −7.06021 | −0.478178 | ||||||||
\(219\) | −1.92533 | −0.130102 | ||||||||
\(220\) | 12.6109 | 0.850226 | ||||||||
\(221\) | 33.1717 | 2.23137 | ||||||||
\(222\) | 2.93108 | 0.196721 | ||||||||
\(223\) | 18.7442 | 1.25520 | 0.627602 | − | 0.778534i | \(-0.284037\pi\) | ||||
0.627602 | + | 0.778534i | \(0.284037\pi\) | |||||||
\(224\) | −6.78511 | −0.453349 | ||||||||
\(225\) | 13.9181 | 0.927876 | ||||||||
\(226\) | 4.47424 | 0.297622 | ||||||||
\(227\) | 4.25365 | 0.282324 | 0.141162 | − | 0.989986i | \(-0.454916\pi\) | ||||
0.141162 | + | 0.989986i | \(0.454916\pi\) | |||||||
\(228\) | −3.68637 | −0.244136 | ||||||||
\(229\) | −3.77045 | −0.249159 | −0.124579 | − | 0.992210i | \(-0.539758\pi\) | ||||
−0.124579 | + | 0.992210i | \(0.539758\pi\) | |||||||
\(230\) | 53.2911 | 3.51391 | ||||||||
\(231\) | 2.84183 | 0.186979 | ||||||||
\(232\) | −9.92793 | −0.651801 | ||||||||
\(233\) | 4.52884 | 0.296694 | 0.148347 | − | 0.988935i | \(-0.452605\pi\) | ||||
0.148347 | + | 0.988935i | \(0.452605\pi\) | |||||||
\(234\) | 21.2285 | 1.38775 | ||||||||
\(235\) | −0.849248 | −0.0553989 | ||||||||
\(236\) | −14.8615 | −0.967402 | ||||||||
\(237\) | −34.5591 | −2.24485 | ||||||||
\(238\) | −16.8027 | −1.08916 | ||||||||
\(239\) | −3.40685 | −0.220371 | −0.110185 | − | 0.993911i | \(-0.535144\pi\) | ||||
−0.110185 | + | 0.993911i | \(0.535144\pi\) | |||||||
\(240\) | 8.31237 | 0.536561 | ||||||||
\(241\) | −0.898375 | −0.0578694 | −0.0289347 | − | 0.999581i | \(-0.509211\pi\) | ||||
−0.0289347 | + | 0.999581i | \(0.509211\pi\) | |||||||
\(242\) | 21.0533 | 1.35336 | ||||||||
\(243\) | −18.8383 | −1.20848 | ||||||||
\(244\) | −8.75172 | −0.560271 | ||||||||
\(245\) | −3.38307 | −0.216136 | ||||||||
\(246\) | 2.77048 | 0.176639 | ||||||||
\(247\) | 2.39960 | 0.152683 | ||||||||
\(248\) | 17.2655 | 1.09636 | ||||||||
\(249\) | 18.4261 | 1.16771 | ||||||||
\(250\) | 10.9099 | 0.690000 | ||||||||
\(251\) | 21.7755 | 1.37446 | 0.687228 | − | 0.726442i | \(-0.258827\pi\) | ||||
0.687228 | + | 0.726442i | \(0.258827\pi\) | |||||||
\(252\) | −6.43407 | −0.405308 | ||||||||
\(253\) | −8.83178 | −0.555249 | ||||||||
\(254\) | −12.0275 | −0.754675 | ||||||||
\(255\) | 57.8629 | 3.62352 | ||||||||
\(256\) | −8.38406 | −0.524004 | ||||||||
\(257\) | 10.5212 | 0.656292 | 0.328146 | − | 0.944627i | \(-0.393576\pi\) | ||||
0.328146 | + | 0.944627i | \(0.393576\pi\) | |||||||
\(258\) | 31.6936 | 1.97316 | ||||||||
\(259\) | 0.578275 | 0.0359322 | ||||||||
\(260\) | 44.4049 | 2.75387 | ||||||||
\(261\) | 9.80900 | 0.607162 | ||||||||
\(262\) | −45.1286 | −2.78805 | ||||||||
\(263\) | −11.4838 | −0.708124 | −0.354062 | − | 0.935222i | \(-0.615200\pi\) | ||||
−0.354062 | + | 0.935222i | \(0.615200\pi\) | |||||||
\(264\) | 6.21126 | 0.382277 | ||||||||
\(265\) | 38.3866 | 2.35807 | ||||||||
\(266\) | −1.21548 | −0.0745261 | ||||||||
\(267\) | 2.09938 | 0.128480 | ||||||||
\(268\) | 20.5494 | 1.25525 | ||||||||
\(269\) | 5.98881 | 0.365144 | 0.182572 | − | 0.983192i | \(-0.441558\pi\) | ||||
0.182572 | + | 0.983192i | \(0.441558\pi\) | |||||||
\(270\) | −14.4131 | −0.877155 | ||||||||
\(271\) | −7.82828 | −0.475534 | −0.237767 | − | 0.971322i | \(-0.576415\pi\) | ||||
−0.237767 | + | 0.971322i | \(0.576415\pi\) | |||||||
\(272\) | 8.14513 | 0.493871 | ||||||||
\(273\) | 10.0065 | 0.605623 | ||||||||
\(274\) | −13.7058 | −0.828000 | ||||||||
\(275\) | −8.06362 | −0.486254 | ||||||||
\(276\) | 47.7742 | 2.87567 | ||||||||
\(277\) | 31.3248 | 1.88212 | 0.941062 | − | 0.338233i | \(-0.109829\pi\) | ||||
0.941062 | + | 0.338233i | \(0.109829\pi\) | |||||||
\(278\) | −8.07106 | −0.484070 | ||||||||
\(279\) | −17.0587 | −1.02128 | ||||||||
\(280\) | −7.39422 | −0.441889 | ||||||||
\(281\) | 29.9083 | 1.78418 | 0.892089 | − | 0.451861i | \(-0.149240\pi\) | ||||
0.892089 | + | 0.451861i | \(0.149240\pi\) | |||||||
\(282\) | −1.27238 | −0.0757693 | ||||||||
\(283\) | −21.2362 | −1.26236 | −0.631181 | − | 0.775636i | \(-0.717430\pi\) | ||||
−0.631181 | + | 0.775636i | \(0.717430\pi\) | |||||||
\(284\) | 20.6954 | 1.22805 | ||||||||
\(285\) | 4.18573 | 0.247941 | ||||||||
\(286\) | −12.2990 | −0.727253 | ||||||||
\(287\) | 0.546589 | 0.0322642 | ||||||||
\(288\) | 14.6522 | 0.863392 | ||||||||
\(289\) | 39.6988 | 2.33522 | ||||||||
\(290\) | 34.2910 | 2.01364 | ||||||||
\(291\) | −5.83535 | −0.342074 | ||||||||
\(292\) | −2.52546 | −0.147791 | ||||||||
\(293\) | −14.8950 | −0.870173 | −0.435086 | − | 0.900389i | \(-0.643282\pi\) | ||||
−0.435086 | + | 0.900389i | \(0.643282\pi\) | |||||||
\(294\) | −5.06867 | −0.295611 | ||||||||
\(295\) | 16.8747 | 0.982481 | ||||||||
\(296\) | 1.26391 | 0.0734631 | ||||||||
\(297\) | 2.38865 | 0.138603 | ||||||||
\(298\) | 14.1319 | 0.818638 | ||||||||
\(299\) | −31.0981 | −1.79845 | ||||||||
\(300\) | 43.6189 | 2.51834 | ||||||||
\(301\) | 6.25284 | 0.360408 | ||||||||
\(302\) | −18.7447 | −1.07863 | ||||||||
\(303\) | 2.58094 | 0.148271 | ||||||||
\(304\) | 0.589208 | 0.0337934 | ||||||||
\(305\) | 9.93724 | 0.569004 | ||||||||
\(306\) | 36.2849 | 2.07427 | ||||||||
\(307\) | −1.43001 | −0.0816149 | −0.0408075 | − | 0.999167i | \(-0.512993\pi\) | ||||
−0.0408075 | + | 0.999167i | \(0.512993\pi\) | |||||||
\(308\) | 3.72765 | 0.212402 | ||||||||
\(309\) | 6.40135 | 0.364160 | ||||||||
\(310\) | −59.6349 | −3.38704 | ||||||||
\(311\) | 19.0043 | 1.07763 | 0.538817 | − | 0.842423i | \(-0.318871\pi\) | ||||
0.538817 | + | 0.842423i | \(0.318871\pi\) | |||||||
\(312\) | 21.8708 | 1.23819 | ||||||||
\(313\) | 15.9971 | 0.904211 | 0.452106 | − | 0.891964i | \(-0.350673\pi\) | ||||
0.452106 | + | 0.891964i | \(0.350673\pi\) | |||||||
\(314\) | 43.7820 | 2.47076 | ||||||||
\(315\) | 7.30564 | 0.411626 | ||||||||
\(316\) | −45.3313 | −2.55008 | ||||||||
\(317\) | 14.1550 | 0.795021 | 0.397511 | − | 0.917598i | \(-0.369874\pi\) | ||||
0.397511 | + | 0.917598i | \(0.369874\pi\) | |||||||
\(318\) | 57.5126 | 3.22515 | ||||||||
\(319\) | −5.68295 | −0.318184 | ||||||||
\(320\) | 43.9033 | 2.45427 | ||||||||
\(321\) | −12.7358 | −0.710842 | ||||||||
\(322\) | 15.7523 | 0.877841 | ||||||||
\(323\) | 4.10152 | 0.228215 | ||||||||
\(324\) | −32.2232 | −1.79018 | ||||||||
\(325\) | −28.3932 | −1.57497 | ||||||||
\(326\) | −46.7169 | −2.58741 | ||||||||
\(327\) | 7.18669 | 0.397425 | ||||||||
\(328\) | 1.19465 | 0.0659638 | ||||||||
\(329\) | −0.251029 | −0.0138397 | ||||||||
\(330\) | −21.4536 | −1.18098 | ||||||||
\(331\) | −15.7787 | −0.867278 | −0.433639 | − | 0.901087i | \(-0.642771\pi\) | ||||
−0.433639 | + | 0.901087i | \(0.642771\pi\) | |||||||
\(332\) | 24.1696 | 1.32648 | ||||||||
\(333\) | −1.24877 | −0.0684320 | ||||||||
\(334\) | −23.9656 | −1.31134 | ||||||||
\(335\) | −23.3330 | −1.27482 | ||||||||
\(336\) | 2.45705 | 0.134043 | ||||||||
\(337\) | −0.912483 | −0.0497061 | −0.0248530 | − | 0.999691i | \(-0.507912\pi\) | ||||
−0.0248530 | + | 0.999691i | \(0.507912\pi\) | |||||||
\(338\) | −14.2974 | −0.777677 | ||||||||
\(339\) | −4.55440 | −0.247361 | ||||||||
\(340\) | 75.8991 | 4.11621 | ||||||||
\(341\) | 9.88312 | 0.535201 | ||||||||
\(342\) | 2.62480 | 0.141933 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 13.6665 | 0.736850 | ||||||||
\(345\) | −54.2458 | −2.92049 | ||||||||
\(346\) | 50.0247 | 2.68934 | ||||||||
\(347\) | −4.87937 | −0.261938 | −0.130969 | − | 0.991386i | \(-0.541809\pi\) | ||||
−0.130969 | + | 0.991386i | \(0.541809\pi\) | |||||||
\(348\) | 30.7411 | 1.64789 | ||||||||
\(349\) | −29.6797 | −1.58872 | −0.794358 | − | 0.607450i | \(-0.792193\pi\) | ||||
−0.794358 | + | 0.607450i | \(0.792193\pi\) | |||||||
\(350\) | 14.3822 | 0.768761 | ||||||||
\(351\) | 8.41079 | 0.448935 | ||||||||
\(352\) | −8.48893 | −0.452462 | ||||||||
\(353\) | 5.94182 | 0.316251 | 0.158126 | − | 0.987419i | \(-0.449455\pi\) | ||||
0.158126 | + | 0.987419i | \(0.449455\pi\) | |||||||
\(354\) | 25.2824 | 1.34374 | ||||||||
\(355\) | −23.4989 | −1.24719 | ||||||||
\(356\) | 2.75376 | 0.145949 | ||||||||
\(357\) | 17.1037 | 0.905223 | ||||||||
\(358\) | −25.4875 | −1.34706 | ||||||||
\(359\) | −27.4000 | −1.44612 | −0.723059 | − | 0.690786i | \(-0.757264\pi\) | ||||
−0.723059 | + | 0.690786i | \(0.757264\pi\) | |||||||
\(360\) | 15.9676 | 0.841566 | ||||||||
\(361\) | −18.7033 | −0.984384 | ||||||||
\(362\) | −19.9855 | −1.05041 | ||||||||
\(363\) | −21.4305 | −1.12481 | ||||||||
\(364\) | 13.1256 | 0.687969 | ||||||||
\(365\) | 2.86756 | 0.150095 | ||||||||
\(366\) | 14.8884 | 0.778230 | ||||||||
\(367\) | 0.373548 | 0.0194990 | 0.00974952 | − | 0.999952i | \(-0.496897\pi\) | ||||
0.00974952 | + | 0.999952i | \(0.496897\pi\) | |||||||
\(368\) | −7.63596 | −0.398052 | ||||||||
\(369\) | −1.18034 | −0.0614462 | ||||||||
\(370\) | −4.36553 | −0.226953 | ||||||||
\(371\) | 11.3467 | 0.589091 | ||||||||
\(372\) | −53.4613 | −2.77184 | ||||||||
\(373\) | −25.9007 | −1.34109 | −0.670545 | − | 0.741869i | \(-0.733940\pi\) | ||||
−0.670545 | + | 0.741869i | \(0.733940\pi\) | |||||||
\(374\) | −21.0220 | −1.08702 | ||||||||
\(375\) | −11.1053 | −0.573476 | ||||||||
\(376\) | −0.548662 | −0.0282951 | ||||||||
\(377\) | −20.0105 | −1.03059 | ||||||||
\(378\) | −4.26037 | −0.219130 | ||||||||
\(379\) | −28.1494 | −1.44594 | −0.722970 | − | 0.690880i | \(-0.757223\pi\) | ||||
−0.722970 | + | 0.690880i | \(0.757223\pi\) | |||||||
\(380\) | 5.49044 | 0.281654 | ||||||||
\(381\) | 12.2430 | 0.627228 | ||||||||
\(382\) | −1.13008 | −0.0578199 | ||||||||
\(383\) | 8.49187 | 0.433914 | 0.216957 | − | 0.976181i | \(-0.430387\pi\) | ||||
0.216957 | + | 0.976181i | \(0.430387\pi\) | |||||||
\(384\) | 34.9539 | 1.78374 | ||||||||
\(385\) | −4.23260 | −0.215713 | ||||||||
\(386\) | −37.6232 | −1.91497 | ||||||||
\(387\) | −13.5028 | −0.686387 | ||||||||
\(388\) | −7.65426 | −0.388586 | ||||||||
\(389\) | 6.17570 | 0.313120 | 0.156560 | − | 0.987668i | \(-0.449959\pi\) | ||||
0.156560 | + | 0.987668i | \(0.449959\pi\) | |||||||
\(390\) | −75.5416 | −3.82520 | ||||||||
\(391\) | −53.1544 | −2.68813 | ||||||||
\(392\) | −2.18565 | −0.110392 | ||||||||
\(393\) | 45.9370 | 2.31721 | ||||||||
\(394\) | −53.0131 | −2.67076 | ||||||||
\(395\) | 51.4719 | 2.58983 | ||||||||
\(396\) | −8.04974 | −0.404515 | ||||||||
\(397\) | 29.2827 | 1.46966 | 0.734828 | − | 0.678253i | \(-0.237263\pi\) | ||||
0.734828 | + | 0.678253i | \(0.237263\pi\) | |||||||
\(398\) | 57.6764 | 2.89106 | ||||||||
\(399\) | 1.23726 | 0.0619404 | ||||||||
\(400\) | −6.97180 | −0.348590 | ||||||||
\(401\) | −29.9593 | −1.49610 | −0.748048 | − | 0.663645i | \(-0.769009\pi\) | ||||
−0.748048 | + | 0.663645i | \(0.769009\pi\) | |||||||
\(402\) | −34.9586 | −1.74358 | ||||||||
\(403\) | 34.8000 | 1.73351 | ||||||||
\(404\) | 3.38543 | 0.168431 | ||||||||
\(405\) | 36.5882 | 1.81808 | ||||||||
\(406\) | 10.1361 | 0.503044 | ||||||||
\(407\) | 0.723486 | 0.0358619 | ||||||||
\(408\) | 37.3827 | 1.85072 | ||||||||
\(409\) | −0.0225409 | −0.00111458 | −0.000557289 | − | 1.00000i | \(-0.500177\pi\) | ||||
−0.000557289 | 1.00000i | \(0.500177\pi\) | ||||||||
\(410\) | −4.12633 | −0.203785 | ||||||||
\(411\) | 13.9514 | 0.688170 | ||||||||
\(412\) | 8.39668 | 0.413675 | ||||||||
\(413\) | 4.98797 | 0.245442 | ||||||||
\(414\) | −34.0166 | −1.67183 | ||||||||
\(415\) | −27.4436 | −1.34716 | ||||||||
\(416\) | −29.8908 | −1.46552 | ||||||||
\(417\) | 8.21565 | 0.402322 | ||||||||
\(418\) | −1.52071 | −0.0743801 | ||||||||
\(419\) | 30.6438 | 1.49705 | 0.748523 | − | 0.663109i | \(-0.230764\pi\) | ||||
0.748523 | + | 0.663109i | \(0.230764\pi\) | |||||||
\(420\) | 22.8956 | 1.11719 | ||||||||
\(421\) | 20.7079 | 1.00924 | 0.504621 | − | 0.863341i | \(-0.331632\pi\) | ||||
0.504621 | + | 0.863341i | \(0.331632\pi\) | |||||||
\(422\) | 51.3202 | 2.49823 | ||||||||
\(423\) | 0.542089 | 0.0263573 | ||||||||
\(424\) | 24.7999 | 1.20439 | ||||||||
\(425\) | −48.5312 | −2.35411 | ||||||||
\(426\) | −35.2071 | −1.70579 | ||||||||
\(427\) | 2.93734 | 0.142148 | ||||||||
\(428\) | −16.7056 | −0.807495 | ||||||||
\(429\) | 12.5193 | 0.604437 | ||||||||
\(430\) | −47.2041 | −2.27638 | ||||||||
\(431\) | −2.86069 | −0.137795 | −0.0688973 | − | 0.997624i | \(-0.521948\pi\) | ||||
−0.0688973 | + | 0.997624i | \(0.521948\pi\) | |||||||
\(432\) | 2.06522 | 0.0993631 | ||||||||
\(433\) | −26.3432 | −1.26597 | −0.632987 | − | 0.774163i | \(-0.718171\pi\) | ||||
−0.632987 | + | 0.774163i | \(0.718171\pi\) | |||||||
\(434\) | −17.6275 | −0.846145 | ||||||||
\(435\) | −34.9053 | −1.67358 | ||||||||
\(436\) | 9.42682 | 0.451463 | ||||||||
\(437\) | −3.84512 | −0.183937 | ||||||||
\(438\) | 4.29631 | 0.205286 | ||||||||
\(439\) | −11.9257 | −0.569184 | −0.284592 | − | 0.958649i | \(-0.591858\pi\) | ||||
−0.284592 | + | 0.958649i | \(0.591858\pi\) | |||||||
\(440\) | −9.25099 | −0.441024 | ||||||||
\(441\) | 2.15947 | 0.102832 | ||||||||
\(442\) | −74.0218 | −3.52086 | ||||||||
\(443\) | 21.0508 | 1.00015 | 0.500076 | − | 0.865982i | \(-0.333305\pi\) | ||||
0.500076 | + | 0.865982i | \(0.333305\pi\) | |||||||
\(444\) | −3.91359 | −0.185731 | ||||||||
\(445\) | −3.12679 | −0.148224 | ||||||||
\(446\) | −41.8271 | −1.98057 | ||||||||
\(447\) | −14.3850 | −0.680389 | ||||||||
\(448\) | 12.9774 | 0.613123 | ||||||||
\(449\) | 27.8890 | 1.31616 | 0.658081 | − | 0.752947i | \(-0.271368\pi\) | ||||
0.658081 | + | 0.752947i | \(0.271368\pi\) | |||||||
\(450\) | −31.0579 | −1.46409 | ||||||||
\(451\) | 0.683844 | 0.0322010 | ||||||||
\(452\) | −5.97402 | −0.280994 | ||||||||
\(453\) | 19.0805 | 0.896478 | ||||||||
\(454\) | −9.49189 | −0.445477 | ||||||||
\(455\) | −14.9036 | −0.698693 | ||||||||
\(456\) | 2.70422 | 0.126637 | ||||||||
\(457\) | 32.0010 | 1.49694 | 0.748471 | − | 0.663167i | \(-0.230788\pi\) | ||||
0.748471 | + | 0.663167i | \(0.230788\pi\) | |||||||
\(458\) | 8.41366 | 0.393145 | ||||||||
\(459\) | 14.3762 | 0.671021 | ||||||||
\(460\) | −71.1544 | −3.31759 | ||||||||
\(461\) | 27.0463 | 1.25967 | 0.629837 | − | 0.776727i | \(-0.283122\pi\) | ||||
0.629837 | + | 0.776727i | \(0.283122\pi\) | |||||||
\(462\) | −6.34147 | −0.295032 | ||||||||
\(463\) | 22.7241 | 1.05608 | 0.528038 | − | 0.849220i | \(-0.322928\pi\) | ||||
0.528038 | + | 0.849220i | \(0.322928\pi\) | |||||||
\(464\) | −4.91348 | −0.228102 | ||||||||
\(465\) | 60.7032 | 2.81504 | ||||||||
\(466\) | −10.1060 | −0.468151 | ||||||||
\(467\) | 14.5631 | 0.673899 | 0.336950 | − | 0.941523i | \(-0.390605\pi\) | ||||
0.336950 | + | 0.941523i | \(0.390605\pi\) | |||||||
\(468\) | −28.3444 | −1.31022 | ||||||||
\(469\) | −6.89699 | −0.318474 | ||||||||
\(470\) | 1.89507 | 0.0874132 | ||||||||
\(471\) | −44.5663 | −2.05351 | ||||||||
\(472\) | 10.9020 | 0.501804 | ||||||||
\(473\) | 7.82300 | 0.359702 | ||||||||
\(474\) | 77.1176 | 3.54213 | ||||||||
\(475\) | −3.51068 | −0.161081 | ||||||||
\(476\) | 22.4350 | 1.02831 | ||||||||
\(477\) | −24.5028 | −1.12191 | ||||||||
\(478\) | 7.60229 | 0.347721 | ||||||||
\(479\) | −29.2601 | −1.33693 | −0.668465 | − | 0.743744i | \(-0.733048\pi\) | ||||
−0.668465 | + | 0.743744i | \(0.733048\pi\) | |||||||
\(480\) | −52.1400 | −2.37985 | ||||||||
\(481\) | 2.54751 | 0.116156 | ||||||||
\(482\) | 2.00470 | 0.0913115 | ||||||||
\(483\) | −16.0345 | −0.729594 | ||||||||
\(484\) | −28.1104 | −1.27775 | ||||||||
\(485\) | 8.69112 | 0.394643 | ||||||||
\(486\) | 42.0371 | 1.90684 | ||||||||
\(487\) | −22.6707 | −1.02731 | −0.513654 | − | 0.857997i | \(-0.671709\pi\) | ||||
−0.513654 | + | 0.857997i | \(0.671709\pi\) | |||||||
\(488\) | 6.42001 | 0.290620 | ||||||||
\(489\) | 47.5538 | 2.15046 | ||||||||
\(490\) | 7.54923 | 0.341039 | ||||||||
\(491\) | 27.1569 | 1.22557 | 0.612787 | − | 0.790248i | \(-0.290049\pi\) | ||||
0.612787 | + | 0.790248i | \(0.290049\pi\) | |||||||
\(492\) | −3.69915 | −0.166771 | ||||||||
\(493\) | −34.2030 | −1.54043 | ||||||||
\(494\) | −5.35464 | −0.240917 | ||||||||
\(495\) | 9.14017 | 0.410820 | ||||||||
\(496\) | 8.54495 | 0.383679 | ||||||||
\(497\) | −6.94602 | −0.311572 | ||||||||
\(498\) | −41.1173 | −1.84251 | ||||||||
\(499\) | 8.26118 | 0.369821 | 0.184911 | − | 0.982755i | \(-0.440800\pi\) | ||||
0.184911 | + | 0.982755i | \(0.440800\pi\) | |||||||
\(500\) | −14.5669 | −0.651451 | ||||||||
\(501\) | 24.3949 | 1.08988 | ||||||||
\(502\) | −48.5914 | −2.16874 | ||||||||
\(503\) | −32.7531 | −1.46039 | −0.730194 | − | 0.683240i | \(-0.760570\pi\) | ||||
−0.730194 | + | 0.683240i | \(0.760570\pi\) | |||||||
\(504\) | 4.71985 | 0.210239 | ||||||||
\(505\) | −3.84402 | −0.171057 | ||||||||
\(506\) | 19.7079 | 0.876122 | ||||||||
\(507\) | 14.5535 | 0.646345 | ||||||||
\(508\) | 16.0592 | 0.712512 | ||||||||
\(509\) | −2.18381 | −0.0967955 | −0.0483978 | − | 0.998828i | \(-0.515412\pi\) | ||||
−0.0483978 | + | 0.998828i | \(0.515412\pi\) | |||||||
\(510\) | −129.120 | −5.71751 | ||||||||
\(511\) | 0.847622 | 0.0374966 | ||||||||
\(512\) | −12.0680 | −0.533336 | ||||||||
\(513\) | 1.03995 | 0.0459150 | ||||||||
\(514\) | −23.4777 | −1.03556 | ||||||||
\(515\) | −9.53411 | −0.420123 | ||||||||
\(516\) | −42.3173 | −1.86292 | ||||||||
\(517\) | −0.314065 | −0.0138126 | ||||||||
\(518\) | −1.29040 | −0.0566971 | ||||||||
\(519\) | −50.9208 | −2.23518 | ||||||||
\(520\) | −32.5742 | −1.42847 | ||||||||
\(521\) | −20.9230 | −0.916654 | −0.458327 | − | 0.888784i | \(-0.651551\pi\) | ||||
−0.458327 | + | 0.888784i | \(0.651551\pi\) | |||||||
\(522\) | −21.8885 | −0.958034 | ||||||||
\(523\) | 23.2523 | 1.01675 | 0.508377 | − | 0.861135i | \(-0.330246\pi\) | ||||
0.508377 | + | 0.861135i | \(0.330246\pi\) | |||||||
\(524\) | 60.2558 | 2.63229 | ||||||||
\(525\) | −14.6398 | −0.638935 | ||||||||
\(526\) | 25.6259 | 1.11734 | ||||||||
\(527\) | 59.4819 | 2.59107 | ||||||||
\(528\) | 3.07404 | 0.133780 | ||||||||
\(529\) | 26.8316 | 1.16659 | ||||||||
\(530\) | −85.6587 | −3.72078 | ||||||||
\(531\) | −10.7714 | −0.467438 | ||||||||
\(532\) | 1.62292 | 0.0703624 | ||||||||
\(533\) | 2.40792 | 0.104299 | ||||||||
\(534\) | −4.68470 | −0.202727 | ||||||||
\(535\) | 18.9685 | 0.820082 | ||||||||
\(536\) | −15.0744 | −0.651116 | ||||||||
\(537\) | 25.9441 | 1.11957 | ||||||||
\(538\) | −13.3639 | −0.576157 | ||||||||
\(539\) | −1.25111 | −0.0538892 | ||||||||
\(540\) | 19.2444 | 0.828149 | ||||||||
\(541\) | −15.5941 | −0.670441 | −0.335221 | − | 0.942140i | \(-0.608811\pi\) | ||||
−0.335221 | + | 0.942140i | \(0.608811\pi\) | |||||||
\(542\) | 17.4686 | 0.750340 | ||||||||
\(543\) | 20.3435 | 0.873024 | ||||||||
\(544\) | −51.0910 | −2.19051 | ||||||||
\(545\) | −10.7038 | −0.458500 | ||||||||
\(546\) | −22.3293 | −0.955606 | ||||||||
\(547\) | 16.9059 | 0.722842 | 0.361421 | − | 0.932403i | \(-0.382292\pi\) | ||||
0.361421 | + | 0.932403i | \(0.382292\pi\) | |||||||
\(548\) | 18.3001 | 0.781740 | ||||||||
\(549\) | −6.34310 | −0.270717 | ||||||||
\(550\) | 17.9937 | 0.767255 | ||||||||
\(551\) | −2.47420 | −0.105405 | ||||||||
\(552\) | −35.0458 | −1.49165 | ||||||||
\(553\) | 15.2146 | 0.646989 | ||||||||
\(554\) | −69.9004 | −2.96978 | ||||||||
\(555\) | 4.44373 | 0.188626 | ||||||||
\(556\) | 10.7765 | 0.457026 | ||||||||
\(557\) | −31.5914 | −1.33857 | −0.669286 | − | 0.743005i | \(-0.733400\pi\) | ||||
−0.669286 | + | 0.743005i | \(0.733400\pi\) | |||||||
\(558\) | 38.0660 | 1.61146 | ||||||||
\(559\) | 27.5460 | 1.16507 | ||||||||
\(560\) | −3.65950 | −0.154642 | ||||||||
\(561\) | 21.3986 | 0.903450 | ||||||||
\(562\) | −66.7394 | −2.81523 | ||||||||
\(563\) | −18.2500 | −0.769147 | −0.384573 | − | 0.923094i | \(-0.625651\pi\) | ||||
−0.384573 | + | 0.923094i | \(0.625651\pi\) | |||||||
\(564\) | 1.69889 | 0.0715361 | ||||||||
\(565\) | 6.78327 | 0.285374 | ||||||||
\(566\) | 47.3880 | 1.99187 | ||||||||
\(567\) | 10.8151 | 0.454191 | ||||||||
\(568\) | −15.1816 | −0.637006 | ||||||||
\(569\) | −25.7110 | −1.07786 | −0.538930 | − | 0.842351i | \(-0.681171\pi\) | ||||
−0.538930 | + | 0.842351i | \(0.681171\pi\) | |||||||
\(570\) | −9.34034 | −0.391224 | ||||||||
\(571\) | 11.3801 | 0.476244 | 0.238122 | − | 0.971235i | \(-0.423468\pi\) | ||||
0.238122 | + | 0.971235i | \(0.423468\pi\) | |||||||
\(572\) | 16.4216 | 0.686622 | ||||||||
\(573\) | 1.15032 | 0.0480555 | ||||||||
\(574\) | −1.21970 | −0.0509092 | ||||||||
\(575\) | 45.4974 | 1.89737 | ||||||||
\(576\) | −28.0242 | −1.16768 | ||||||||
\(577\) | 23.8859 | 0.994384 | 0.497192 | − | 0.867641i | \(-0.334364\pi\) | ||||
0.497192 | + | 0.867641i | \(0.334364\pi\) | |||||||
\(578\) | −88.5868 | −3.68472 | ||||||||
\(579\) | 38.2972 | 1.59158 | ||||||||
\(580\) | −45.7854 | −1.90114 | ||||||||
\(581\) | −8.11205 | −0.336545 | ||||||||
\(582\) | 13.0214 | 0.539756 | ||||||||
\(583\) | 14.1960 | 0.587937 | ||||||||
\(584\) | 1.85261 | 0.0766614 | ||||||||
\(585\) | 32.1839 | 1.33064 | ||||||||
\(586\) | 33.2377 | 1.37304 | ||||||||
\(587\) | −12.7728 | −0.527192 | −0.263596 | − | 0.964633i | \(-0.584909\pi\) | ||||
−0.263596 | + | 0.964633i | \(0.584909\pi\) | |||||||
\(588\) | 6.76770 | 0.279095 | ||||||||
\(589\) | 4.30285 | 0.177296 | ||||||||
\(590\) | −37.6553 | −1.55025 | ||||||||
\(591\) | 53.9628 | 2.21973 | ||||||||
\(592\) | 0.625526 | 0.0257090 | ||||||||
\(593\) | −39.5261 | −1.62314 | −0.811571 | − | 0.584254i | \(-0.801387\pi\) | ||||
−0.811571 | + | 0.584254i | \(0.801387\pi\) | |||||||
\(594\) | −5.33020 | −0.218701 | ||||||||
\(595\) | −25.4740 | −1.04433 | ||||||||
\(596\) | −18.8689 | −0.772901 | ||||||||
\(597\) | −58.7096 | −2.40283 | ||||||||
\(598\) | 69.3945 | 2.83775 | ||||||||
\(599\) | 11.7371 | 0.479564 | 0.239782 | − | 0.970827i | \(-0.422924\pi\) | ||||
0.239782 | + | 0.970827i | \(0.422924\pi\) | |||||||
\(600\) | −31.9976 | −1.30630 | ||||||||
\(601\) | −23.6931 | −0.966460 | −0.483230 | − | 0.875493i | \(-0.660537\pi\) | ||||
−0.483230 | + | 0.875493i | \(0.660537\pi\) | |||||||
\(602\) | −13.9530 | −0.568683 | ||||||||
\(603\) | 14.8939 | 0.606525 | ||||||||
\(604\) | 25.0279 | 1.01837 | ||||||||
\(605\) | 31.9183 | 1.29766 | ||||||||
\(606\) | −5.75929 | −0.233955 | ||||||||
\(607\) | 42.0122 | 1.70522 | 0.852611 | − | 0.522546i | \(-0.175018\pi\) | ||||
0.852611 | + | 0.522546i | \(0.175018\pi\) | |||||||
\(608\) | −3.69585 | −0.149887 | ||||||||
\(609\) | −10.3176 | −0.418092 | ||||||||
\(610\) | −22.1747 | −0.897826 | ||||||||
\(611\) | −1.10587 | −0.0447388 | ||||||||
\(612\) | −48.4476 | −1.95838 | ||||||||
\(613\) | 13.2379 | 0.534674 | 0.267337 | − | 0.963603i | \(-0.413856\pi\) | ||||
0.267337 | + | 0.963603i | \(0.413856\pi\) | |||||||
\(614\) | 3.19103 | 0.128779 | ||||||||
\(615\) | 4.20025 | 0.169370 | ||||||||
\(616\) | −2.73450 | −0.110176 | ||||||||
\(617\) | 31.3521 | 1.26219 | 0.631095 | − | 0.775706i | \(-0.282606\pi\) | ||||
0.631095 | + | 0.775706i | \(0.282606\pi\) | |||||||
\(618\) | −14.2844 | −0.574604 | ||||||||
\(619\) | 4.83758 | 0.194439 | 0.0972194 | − | 0.995263i | \(-0.469005\pi\) | ||||
0.0972194 | + | 0.995263i | \(0.469005\pi\) | |||||||
\(620\) | 79.6247 | 3.19780 | ||||||||
\(621\) | −13.4775 | −0.540832 | ||||||||
\(622\) | −42.4076 | −1.70039 | ||||||||
\(623\) | −0.924246 | −0.0370291 | ||||||||
\(624\) | 10.8242 | 0.433314 | ||||||||
\(625\) | −15.6857 | −0.627427 | ||||||||
\(626\) | −35.6972 | −1.42675 | ||||||||
\(627\) | 1.54795 | 0.0618191 | ||||||||
\(628\) | −58.4578 | −2.33272 | ||||||||
\(629\) | 4.35433 | 0.173618 | ||||||||
\(630\) | −16.3023 | −0.649500 | ||||||||
\(631\) | 29.7327 | 1.18364 | 0.591820 | − | 0.806070i | \(-0.298410\pi\) | ||||
0.591820 | + | 0.806070i | \(0.298410\pi\) | |||||||
\(632\) | 33.2537 | 1.32276 | ||||||||
\(633\) | −52.2395 | −2.07633 | ||||||||
\(634\) | −31.5864 | −1.25446 | ||||||||
\(635\) | −18.2346 | −0.723618 | ||||||||
\(636\) | −76.7910 | −3.04496 | ||||||||
\(637\) | −4.40536 | −0.174547 | ||||||||
\(638\) | 12.6813 | 0.502059 | ||||||||
\(639\) | 14.9997 | 0.593380 | ||||||||
\(640\) | −52.0601 | −2.05785 | ||||||||
\(641\) | 6.19788 | 0.244802 | 0.122401 | − | 0.992481i | \(-0.460941\pi\) | ||||
0.122401 | + | 0.992481i | \(0.460941\pi\) | |||||||
\(642\) | 28.4195 | 1.12163 | ||||||||
\(643\) | 1.44309 | 0.0569098 | 0.0284549 | − | 0.999595i | \(-0.490941\pi\) | ||||
0.0284549 | + | 0.999595i | \(0.490941\pi\) | |||||||
\(644\) | −21.0325 | −0.828797 | ||||||||
\(645\) | 48.0497 | 1.89195 | ||||||||
\(646\) | −9.15242 | −0.360097 | ||||||||
\(647\) | −6.58237 | −0.258780 | −0.129390 | − | 0.991594i | \(-0.541302\pi\) | ||||
−0.129390 | + | 0.991594i | \(0.541302\pi\) | |||||||
\(648\) | 23.6381 | 0.928590 | ||||||||
\(649\) | 6.24051 | 0.244962 | ||||||||
\(650\) | 63.3587 | 2.48513 | ||||||||
\(651\) | 17.9432 | 0.703251 | ||||||||
\(652\) | 62.3765 | 2.44285 | ||||||||
\(653\) | −20.2903 | −0.794019 | −0.397010 | − | 0.917814i | \(-0.629952\pi\) | ||||
−0.397010 | + | 0.917814i | \(0.629952\pi\) | |||||||
\(654\) | −16.0369 | −0.627092 | ||||||||
\(655\) | −68.4181 | −2.67332 | ||||||||
\(656\) | 0.591252 | 0.0230845 | ||||||||
\(657\) | −1.83041 | −0.0714112 | ||||||||
\(658\) | 0.560164 | 0.0218375 | ||||||||
\(659\) | 23.8434 | 0.928805 | 0.464403 | − | 0.885624i | \(-0.346269\pi\) | ||||
0.464403 | + | 0.885624i | \(0.346269\pi\) | |||||||
\(660\) | 28.6450 | 1.11500 | ||||||||
\(661\) | 44.4651 | 1.72949 | 0.864745 | − | 0.502211i | \(-0.167480\pi\) | ||||
0.864745 | + | 0.502211i | \(0.167480\pi\) | |||||||
\(662\) | 35.2098 | 1.36847 | ||||||||
\(663\) | 75.3478 | 2.92627 | ||||||||
\(664\) | −17.7301 | −0.688063 | ||||||||
\(665\) | −1.84276 | −0.0714592 | ||||||||
\(666\) | 2.78659 | 0.107978 | ||||||||
\(667\) | 32.0649 | 1.24156 | ||||||||
\(668\) | 31.9989 | 1.23808 | ||||||||
\(669\) | 42.5764 | 1.64610 | ||||||||
\(670\) | 52.0670 | 2.01152 | ||||||||
\(671\) | 3.67494 | 0.141870 | ||||||||
\(672\) | −15.4120 | −0.594532 | ||||||||
\(673\) | 4.18712 | 0.161402 | 0.0807009 | − | 0.996738i | \(-0.474284\pi\) | ||||
0.0807009 | + | 0.996738i | \(0.474284\pi\) | |||||||
\(674\) | 2.03618 | 0.0784307 | ||||||||
\(675\) | −12.3052 | −0.473628 | ||||||||
\(676\) | 19.0899 | 0.734228 | ||||||||
\(677\) | −3.59693 | −0.138241 | −0.0691206 | − | 0.997608i | \(-0.522019\pi\) | ||||
−0.0691206 | + | 0.997608i | \(0.522019\pi\) | |||||||
\(678\) | 10.1630 | 0.390308 | ||||||||
\(679\) | 2.56900 | 0.0985893 | ||||||||
\(680\) | −55.6774 | −2.13513 | ||||||||
\(681\) | 9.66193 | 0.370246 | ||||||||
\(682\) | −22.0539 | −0.844488 | ||||||||
\(683\) | 27.5424 | 1.05388 | 0.526939 | − | 0.849903i | \(-0.323339\pi\) | ||||
0.526939 | + | 0.849903i | \(0.323339\pi\) | |||||||
\(684\) | −3.50464 | −0.134003 | ||||||||
\(685\) | −20.7790 | −0.793926 | ||||||||
\(686\) | 2.23147 | 0.0851980 | ||||||||
\(687\) | −8.56439 | −0.326752 | ||||||||
\(688\) | 6.76376 | 0.257866 | ||||||||
\(689\) | 49.9862 | 1.90432 | ||||||||
\(690\) | 121.048 | 4.60822 | ||||||||
\(691\) | −46.0906 | −1.75337 | −0.876685 | − | 0.481066i | \(-0.840250\pi\) | ||||
−0.876685 | + | 0.481066i | \(0.840250\pi\) | |||||||
\(692\) | −66.7931 | −2.53909 | ||||||||
\(693\) | 2.70174 | 0.102631 | ||||||||
\(694\) | 10.8882 | 0.413310 | ||||||||
\(695\) | −12.2363 | −0.464149 | ||||||||
\(696\) | −22.5508 | −0.854785 | ||||||||
\(697\) | 4.11574 | 0.155895 | ||||||||
\(698\) | 66.2293 | 2.50682 | ||||||||
\(699\) | 10.2870 | 0.389091 | ||||||||
\(700\) | −19.2032 | −0.725811 | ||||||||
\(701\) | −7.73041 | −0.291974 | −0.145987 | − | 0.989287i | \(-0.546636\pi\) | ||||
−0.145987 | + | 0.989287i | \(0.546636\pi\) | |||||||
\(702\) | −18.7684 | −0.708369 | ||||||||
\(703\) | 0.314986 | 0.0118799 | ||||||||
\(704\) | 16.2361 | 0.611922 | ||||||||
\(705\) | −1.92902 | −0.0726512 | ||||||||
\(706\) | −13.2590 | −0.499009 | ||||||||
\(707\) | −1.13625 | −0.0427332 | ||||||||
\(708\) | −33.7571 | −1.26867 | ||||||||
\(709\) | 19.0508 | 0.715469 | 0.357735 | − | 0.933823i | \(-0.383549\pi\) | ||||
0.357735 | + | 0.933823i | \(0.383549\pi\) | |||||||
\(710\) | 52.4371 | 1.96793 | ||||||||
\(711\) | −32.8554 | −1.23217 | ||||||||
\(712\) | −2.02008 | −0.0757057 | ||||||||
\(713\) | −55.7636 | −2.08836 | ||||||||
\(714\) | −38.1664 | −1.42834 | ||||||||
\(715\) | −18.6461 | −0.697325 | ||||||||
\(716\) | 34.0310 | 1.27180 | ||||||||
\(717\) | −7.73848 | −0.288999 | ||||||||
\(718\) | 61.1424 | 2.28181 | ||||||||
\(719\) | −45.7794 | −1.70728 | −0.853642 | − | 0.520860i | \(-0.825611\pi\) | ||||
−0.853642 | + | 0.520860i | \(0.825611\pi\) | |||||||
\(720\) | 7.90259 | 0.294512 | ||||||||
\(721\) | −2.81818 | −0.104955 | ||||||||
\(722\) | 41.7359 | 1.55325 | ||||||||
\(723\) | −2.04061 | −0.0758911 | ||||||||
\(724\) | 26.6847 | 0.991728 | ||||||||
\(725\) | 29.2760 | 1.08728 | ||||||||
\(726\) | 47.8215 | 1.77482 | ||||||||
\(727\) | −29.3335 | −1.08792 | −0.543960 | − | 0.839111i | \(-0.683076\pi\) | ||||
−0.543960 | + | 0.839111i | \(0.683076\pi\) | |||||||
\(728\) | −9.62858 | −0.356859 | ||||||||
\(729\) | −10.3448 | −0.383141 | ||||||||
\(730\) | −6.39889 | −0.236833 | ||||||||
\(731\) | 47.0830 | 1.74143 | ||||||||
\(732\) | −19.8791 | −0.734751 | ||||||||
\(733\) | −21.3349 | −0.788022 | −0.394011 | − | 0.919106i | \(-0.628913\pi\) | ||||
−0.394011 | + | 0.919106i | \(0.628913\pi\) | |||||||
\(734\) | −0.833562 | −0.0307673 | ||||||||
\(735\) | −7.68446 | −0.283446 | ||||||||
\(736\) | 47.8971 | 1.76551 | ||||||||
\(737\) | −8.62891 | −0.317850 | ||||||||
\(738\) | 2.63390 | 0.0969553 | ||||||||
\(739\) | −5.27844 | −0.194171 | −0.0970853 | − | 0.995276i | \(-0.530952\pi\) | ||||
−0.0970853 | + | 0.995276i | \(0.530952\pi\) | |||||||
\(740\) | 5.82886 | 0.214273 | ||||||||
\(741\) | 5.45056 | 0.200231 | ||||||||
\(742\) | −25.3198 | −0.929520 | ||||||||
\(743\) | −24.6117 | −0.902916 | −0.451458 | − | 0.892292i | \(-0.649096\pi\) | ||||
−0.451458 | + | 0.892292i | \(0.649096\pi\) | |||||||
\(744\) | 39.2177 | 1.43779 | ||||||||
\(745\) | 21.4249 | 0.784949 | ||||||||
\(746\) | 57.7968 | 2.11609 | ||||||||
\(747\) | 17.5177 | 0.640941 | ||||||||
\(748\) | 28.0686 | 1.02629 | ||||||||
\(749\) | 5.60690 | 0.204872 | ||||||||
\(750\) | 24.7812 | 0.904881 | ||||||||
\(751\) | 43.6644 | 1.59334 | 0.796668 | − | 0.604418i | \(-0.206594\pi\) | ||||
0.796668 | + | 0.604418i | \(0.206594\pi\) | |||||||
\(752\) | −0.271541 | −0.00990207 | ||||||||
\(753\) | 49.4619 | 1.80249 | ||||||||
\(754\) | 44.6529 | 1.62616 | ||||||||
\(755\) | −28.4182 | −1.03425 | ||||||||
\(756\) | 5.68845 | 0.206887 | ||||||||
\(757\) | 30.6179 | 1.11283 | 0.556413 | − | 0.830906i | \(-0.312177\pi\) | ||||
0.556413 | + | 0.830906i | \(0.312177\pi\) | |||||||
\(758\) | 62.8147 | 2.28153 | ||||||||
\(759\) | −20.0609 | −0.728165 | ||||||||
\(760\) | −4.02763 | −0.146098 | ||||||||
\(761\) | 25.4933 | 0.924131 | 0.462065 | − | 0.886846i | \(-0.347109\pi\) | ||||
0.462065 | + | 0.886846i | \(0.347109\pi\) | |||||||
\(762\) | −27.3199 | −0.989696 | ||||||||
\(763\) | −3.16393 | −0.114542 | ||||||||
\(764\) | 1.50888 | 0.0545895 | ||||||||
\(765\) | 55.0104 | 1.98891 | ||||||||
\(766\) | −18.9494 | −0.684669 | ||||||||
\(767\) | 21.9738 | 0.793428 | ||||||||
\(768\) | −19.0439 | −0.687189 | ||||||||
\(769\) | −28.6493 | −1.03312 | −0.516560 | − | 0.856251i | \(-0.672788\pi\) | ||||
−0.516560 | + | 0.856251i | \(0.672788\pi\) | |||||||
\(770\) | 9.44492 | 0.340371 | ||||||||
\(771\) | 23.8983 | 0.860675 | ||||||||
\(772\) | 50.2346 | 1.80798 | ||||||||
\(773\) | −48.0951 | −1.72986 | −0.864929 | − | 0.501894i | \(-0.832637\pi\) | ||||
−0.864929 | + | 0.501894i | \(0.832637\pi\) | |||||||
\(774\) | 30.1312 | 1.08304 | ||||||||
\(775\) | −50.9134 | −1.82886 | ||||||||
\(776\) | 5.61495 | 0.201565 | ||||||||
\(777\) | 1.31352 | 0.0471223 | ||||||||
\(778\) | −13.7809 | −0.494069 | ||||||||
\(779\) | 0.297727 | 0.0106672 | ||||||||
\(780\) | 100.863 | 3.61149 | ||||||||
\(781\) | −8.69025 | −0.310962 | ||||||||
\(782\) | 118.613 | 4.24158 | ||||||||
\(783\) | −8.67228 | −0.309922 | ||||||||
\(784\) | −1.08171 | −0.0386325 | ||||||||
\(785\) | 66.3766 | 2.36908 | ||||||||
\(786\) | −102.507 | −3.65631 | ||||||||
\(787\) | −18.0545 | −0.643575 | −0.321787 | − | 0.946812i | \(-0.604284\pi\) | ||||
−0.321787 | + | 0.946812i | \(0.604284\pi\) | |||||||
\(788\) | 70.7832 | 2.52155 | ||||||||
\(789\) | −26.0849 | −0.928648 | ||||||||
\(790\) | −114.858 | −4.08647 | ||||||||
\(791\) | 2.00506 | 0.0712919 | ||||||||
\(792\) | 5.90506 | 0.209827 | ||||||||
\(793\) | 12.9400 | 0.459514 | ||||||||
\(794\) | −65.3435 | −2.31896 | ||||||||
\(795\) | 87.1932 | 3.09242 | ||||||||
\(796\) | −77.0097 | −2.72954 | ||||||||
\(797\) | 20.3503 | 0.720846 | 0.360423 | − | 0.932789i | \(-0.382632\pi\) | ||||
0.360423 | + | 0.932789i | \(0.382632\pi\) | |||||||
\(798\) | −2.76091 | −0.0977350 | ||||||||
\(799\) | −1.89021 | −0.0668709 | ||||||||
\(800\) | 43.7312 | 1.54613 | ||||||||
\(801\) | 1.99588 | 0.0705210 | ||||||||
\(802\) | 66.8533 | 2.36067 | ||||||||
\(803\) | 1.06047 | 0.0374231 | ||||||||
\(804\) | 46.6768 | 1.64616 | ||||||||
\(805\) | 23.8816 | 0.841716 | ||||||||
\(806\) | −77.6552 | −2.73529 | ||||||||
\(807\) | 13.6033 | 0.478857 | ||||||||
\(808\) | −2.48345 | −0.0873676 | ||||||||
\(809\) | 51.2660 | 1.80242 | 0.901209 | − | 0.433385i | \(-0.142681\pi\) | ||||
0.901209 | + | 0.433385i | \(0.142681\pi\) | |||||||
\(810\) | −81.6456 | −2.86873 | ||||||||
\(811\) | −1.84372 | −0.0647418 | −0.0323709 | − | 0.999476i | \(-0.510306\pi\) | ||||
−0.0323709 | + | 0.999476i | \(0.510306\pi\) | |||||||
\(812\) | −13.5337 | −0.474939 | ||||||||
\(813\) | −17.7815 | −0.623625 | ||||||||
\(814\) | −1.61444 | −0.0565861 | ||||||||
\(815\) | −70.8261 | −2.48093 | ||||||||
\(816\) | 18.5012 | 0.647673 | ||||||||
\(817\) | 3.40592 | 0.119158 | ||||||||
\(818\) | 0.0502995 | 0.00175868 | ||||||||
\(819\) | 9.51324 | 0.332419 | ||||||||
\(820\) | 5.50948 | 0.192399 | ||||||||
\(821\) | 20.7700 | 0.724879 | 0.362439 | − | 0.932007i | \(-0.381944\pi\) | ||||
0.362439 | + | 0.932007i | \(0.381944\pi\) | |||||||
\(822\) | −31.1321 | −1.08586 | ||||||||
\(823\) | −20.7678 | −0.723921 | −0.361961 | − | 0.932193i | \(-0.617892\pi\) | ||||
−0.361961 | + | 0.932193i | \(0.617892\pi\) | |||||||
\(824\) | −6.15957 | −0.214579 | ||||||||
\(825\) | −18.3161 | −0.637684 | ||||||||
\(826\) | −11.1305 | −0.387281 | ||||||||
\(827\) | 29.0443 | 1.00997 | 0.504985 | − | 0.863128i | \(-0.331498\pi\) | ||||
0.504985 | + | 0.863128i | \(0.331498\pi\) | |||||||
\(828\) | 45.4191 | 1.57842 | ||||||||
\(829\) | 3.66633 | 0.127337 | 0.0636685 | − | 0.997971i | \(-0.479720\pi\) | ||||
0.0636685 | + | 0.997971i | \(0.479720\pi\) | |||||||
\(830\) | 61.2397 | 2.12566 | ||||||||
\(831\) | 71.1526 | 2.46826 | ||||||||
\(832\) | 57.1699 | 1.98201 | ||||||||
\(833\) | −7.52986 | −0.260894 | ||||||||
\(834\) | −18.3330 | −0.634819 | ||||||||
\(835\) | −36.3335 | −1.25737 | ||||||||
\(836\) | 2.03045 | 0.0702246 | ||||||||
\(837\) | 15.0818 | 0.521304 | ||||||||
\(838\) | −68.3807 | −2.36217 | ||||||||
\(839\) | −17.1701 | −0.592777 | −0.296389 | − | 0.955067i | \(-0.595782\pi\) | ||||
−0.296389 | + | 0.955067i | \(0.595782\pi\) | |||||||
\(840\) | −16.7956 | −0.579502 | ||||||||
\(841\) | −8.36734 | −0.288529 | ||||||||
\(842\) | −46.2091 | −1.59247 | ||||||||
\(843\) | 67.9350 | 2.33981 | ||||||||
\(844\) | −68.5228 | −2.35865 | ||||||||
\(845\) | −21.6759 | −0.745673 | ||||||||
\(846\) | −1.20966 | −0.0415889 | ||||||||
\(847\) | 9.43472 | 0.324181 | ||||||||
\(848\) | 12.2738 | 0.421485 | ||||||||
\(849\) | −48.2369 | −1.65549 | ||||||||
\(850\) | 108.296 | 3.71452 | ||||||||
\(851\) | −4.08213 | −0.139934 | ||||||||
\(852\) | 47.0086 | 1.61049 | ||||||||
\(853\) | 21.6515 | 0.741332 | 0.370666 | − | 0.928766i | \(-0.379129\pi\) | ||||
0.370666 | + | 0.928766i | \(0.379129\pi\) | |||||||
\(854\) | −6.55460 | −0.224294 | ||||||||
\(855\) | 3.97938 | 0.136092 | ||||||||
\(856\) | 12.2547 | 0.418859 | ||||||||
\(857\) | 32.5424 | 1.11163 | 0.555814 | − | 0.831307i | \(-0.312407\pi\) | ||||
0.555814 | + | 0.831307i | \(0.312407\pi\) | |||||||
\(858\) | −27.9364 | −0.953734 | ||||||||
\(859\) | 1.00000 | 0.0341196 | ||||||||
\(860\) | 63.0270 | 2.14920 | ||||||||
\(861\) | 1.24155 | 0.0423119 | ||||||||
\(862\) | 6.38355 | 0.217425 | ||||||||
\(863\) | 24.9076 | 0.847865 | 0.423933 | − | 0.905694i | \(-0.360649\pi\) | ||||
0.423933 | + | 0.905694i | \(0.360649\pi\) | |||||||
\(864\) | −12.9543 | −0.440713 | ||||||||
\(865\) | 75.8410 | 2.57867 | ||||||||
\(866\) | 58.7841 | 1.99756 | ||||||||
\(867\) | 90.1737 | 3.06246 | ||||||||
\(868\) | 23.5362 | 0.798871 | ||||||||
\(869\) | 19.0351 | 0.645722 | ||||||||
\(870\) | 77.8902 | 2.64072 | ||||||||
\(871\) | −30.3837 | −1.02951 | ||||||||
\(872\) | −6.91525 | −0.234180 | ||||||||
\(873\) | −5.54769 | −0.187761 | ||||||||
\(874\) | 8.58028 | 0.290232 | ||||||||
\(875\) | 4.88909 | 0.165281 | ||||||||
\(876\) | −5.73645 | −0.193817 | ||||||||
\(877\) | 28.2725 | 0.954693 | 0.477347 | − | 0.878715i | \(-0.341599\pi\) | ||||
0.477347 | + | 0.878715i | \(0.341599\pi\) | |||||||
\(878\) | 26.6119 | 0.898108 | ||||||||
\(879\) | −33.8331 | −1.14116 | ||||||||
\(880\) | −4.57845 | −0.154339 | ||||||||
\(881\) | 9.56875 | 0.322379 | 0.161190 | − | 0.986923i | \(-0.448467\pi\) | ||||
0.161190 | + | 0.986923i | \(0.448467\pi\) | |||||||
\(882\) | −4.81880 | −0.162257 | ||||||||
\(883\) | −15.1023 | −0.508234 | −0.254117 | − | 0.967174i | \(-0.581785\pi\) | ||||
−0.254117 | + | 0.967174i | \(0.581785\pi\) | |||||||
\(884\) | 98.8340 | 3.32415 | ||||||||
\(885\) | 38.3299 | 1.28845 | ||||||||
\(886\) | −46.9742 | −1.57813 | ||||||||
\(887\) | −12.6415 | −0.424461 | −0.212231 | − | 0.977220i | \(-0.568073\pi\) | ||||
−0.212231 | + | 0.977220i | \(0.568073\pi\) | |||||||
\(888\) | 2.87090 | 0.0963411 | ||||||||
\(889\) | −5.38996 | −0.180773 | ||||||||
\(890\) | 6.97734 | 0.233881 | ||||||||
\(891\) | 13.5309 | 0.453302 | ||||||||
\(892\) | 55.8477 | 1.86992 | ||||||||
\(893\) | −0.136736 | −0.00457568 | ||||||||
\(894\) | 32.0998 | 1.07358 | ||||||||
\(895\) | −38.6409 | −1.29162 | ||||||||
\(896\) | −15.3884 | −0.514091 | ||||||||
\(897\) | −70.6376 | −2.35852 | ||||||||
\(898\) | −62.2335 | −2.07676 | ||||||||
\(899\) | −35.8819 | −1.19673 | ||||||||
\(900\) | 41.4686 | 1.38229 | ||||||||
\(901\) | 85.4390 | 2.84639 | ||||||||
\(902\) | −1.52598 | −0.0508096 | ||||||||
\(903\) | 14.2030 | 0.472646 | ||||||||
\(904\) | 4.38237 | 0.145756 | ||||||||
\(905\) | −30.2994 | −1.00719 | ||||||||
\(906\) | −42.5775 | −1.41454 | ||||||||
\(907\) | −16.7565 | −0.556389 | −0.278194 | − | 0.960525i | \(-0.589736\pi\) | ||||
−0.278194 | + | 0.960525i | \(0.589736\pi\) | |||||||
\(908\) | 12.6736 | 0.420588 | ||||||||
\(909\) | 2.45370 | 0.0813842 | ||||||||
\(910\) | 33.2570 | 1.10246 | ||||||||
\(911\) | −6.86506 | −0.227450 | −0.113725 | − | 0.993512i | \(-0.536278\pi\) | ||||
−0.113725 | + | 0.993512i | \(0.536278\pi\) | |||||||
\(912\) | 1.33836 | 0.0443174 | ||||||||
\(913\) | −10.1491 | −0.335886 | ||||||||
\(914\) | −71.4093 | −2.36201 | ||||||||
\(915\) | 22.5719 | 0.746204 | ||||||||
\(916\) | −11.2339 | −0.371180 | ||||||||
\(917\) | −20.2237 | −0.667844 | ||||||||
\(918\) | −32.0800 | −1.05880 | ||||||||
\(919\) | −48.3632 | −1.59535 | −0.797677 | − | 0.603085i | \(-0.793938\pi\) | ||||
−0.797677 | + | 0.603085i | \(0.793938\pi\) | |||||||
\(920\) | 52.1969 | 1.72088 | ||||||||
\(921\) | −3.24819 | −0.107031 | ||||||||
\(922\) | −60.3532 | −1.98763 | ||||||||
\(923\) | −30.5997 | −1.00720 | ||||||||
\(924\) | 8.46715 | 0.278549 | ||||||||
\(925\) | −3.72707 | −0.122545 | ||||||||
\(926\) | −50.7081 | −1.66637 | ||||||||
\(927\) | 6.08578 | 0.199883 | ||||||||
\(928\) | 30.8201 | 1.01172 | ||||||||
\(929\) | 0.608949 | 0.0199790 | 0.00998949 | − | 0.999950i | \(-0.496820\pi\) | ||||
0.00998949 | + | 0.999950i | \(0.496820\pi\) | |||||||
\(930\) | −135.458 | −4.44183 | ||||||||
\(931\) | −0.544700 | −0.0178518 | ||||||||
\(932\) | 13.4935 | 0.441996 | ||||||||
\(933\) | 43.1672 | 1.41323 | ||||||||
\(934\) | −32.4971 | −1.06334 | ||||||||
\(935\) | −31.8709 | −1.04229 | ||||||||
\(936\) | 20.7926 | 0.679628 | ||||||||
\(937\) | 50.2766 | 1.64246 | 0.821232 | − | 0.570595i | \(-0.193287\pi\) | ||||
0.821232 | + | 0.570595i | \(0.193287\pi\) | |||||||
\(938\) | 15.3904 | 0.502516 | ||||||||
\(939\) | 36.3366 | 1.18580 | ||||||||
\(940\) | −2.53031 | −0.0825295 | ||||||||
\(941\) | 21.2326 | 0.692162 | 0.346081 | − | 0.938205i | \(-0.387512\pi\) | ||||
0.346081 | + | 0.938205i | \(0.387512\pi\) | |||||||
\(942\) | 99.4485 | 3.24021 | ||||||||
\(943\) | −3.85846 | −0.125649 | ||||||||
\(944\) | 5.39555 | 0.175610 | ||||||||
\(945\) | −6.45902 | −0.210112 | ||||||||
\(946\) | −17.4568 | −0.567569 | ||||||||
\(947\) | −52.8484 | −1.71734 | −0.858672 | − | 0.512526i | \(-0.828710\pi\) | ||||
−0.858672 | + | 0.512526i | \(0.828710\pi\) | |||||||
\(948\) | −102.968 | −3.34423 | ||||||||
\(949\) | 3.73407 | 0.121213 | ||||||||
\(950\) | 7.83399 | 0.254168 | ||||||||
\(951\) | 32.1522 | 1.04261 | ||||||||
\(952\) | −16.4577 | −0.533396 | ||||||||
\(953\) | −15.8047 | −0.511965 | −0.255983 | − | 0.966681i | \(-0.582399\pi\) | ||||
−0.255983 | + | 0.966681i | \(0.582399\pi\) | |||||||
\(954\) | 54.6774 | 1.77025 | ||||||||
\(955\) | −1.71328 | −0.0554404 | ||||||||
\(956\) | −10.1506 | −0.328294 | ||||||||
\(957\) | −12.9085 | −0.417273 | ||||||||
\(958\) | 65.2932 | 2.10953 | ||||||||
\(959\) | −6.14206 | −0.198338 | ||||||||
\(960\) | 99.7241 | 3.21858 | ||||||||
\(961\) | 31.4017 | 1.01296 | ||||||||
\(962\) | −5.68469 | −0.183282 | ||||||||
\(963\) | −12.1079 | −0.390173 | ||||||||
\(964\) | −2.67668 | −0.0862100 | ||||||||
\(965\) | −57.0395 | −1.83617 | ||||||||
\(966\) | 35.7805 | 1.15122 | ||||||||
\(967\) | −37.3530 | −1.20119 | −0.600596 | − | 0.799552i | \(-0.705070\pi\) | ||||
−0.600596 | + | 0.799552i | \(0.705070\pi\) | |||||||
\(968\) | 20.6210 | 0.662785 | ||||||||
\(969\) | 9.31638 | 0.299285 | ||||||||
\(970\) | −19.3940 | −0.622703 | ||||||||
\(971\) | −19.6029 | −0.629087 | −0.314543 | − | 0.949243i | \(-0.601851\pi\) | ||||
−0.314543 | + | 0.949243i | \(0.601851\pi\) | |||||||
\(972\) | −56.1280 | −1.80031 | ||||||||
\(973\) | −3.61692 | −0.115953 | ||||||||
\(974\) | 50.5891 | 1.62098 | ||||||||
\(975\) | −64.4937 | −2.06545 | ||||||||
\(976\) | 3.17736 | 0.101705 | ||||||||
\(977\) | 5.52603 | 0.176793 | 0.0883967 | − | 0.996085i | \(-0.471826\pi\) | ||||
0.0883967 | + | 0.996085i | \(0.471826\pi\) | |||||||
\(978\) | −106.115 | −3.39318 | ||||||||
\(979\) | −1.15633 | −0.0369566 | ||||||||
\(980\) | −10.0797 | −0.321986 | ||||||||
\(981\) | 6.83241 | 0.218142 | ||||||||
\(982\) | −60.5998 | −1.93382 | ||||||||
\(983\) | 23.9019 | 0.762351 | 0.381175 | − | 0.924503i | \(-0.375519\pi\) | ||||
0.381175 | + | 0.924503i | \(0.375519\pi\) | |||||||
\(984\) | 2.71359 | 0.0865062 | ||||||||
\(985\) | −80.3716 | −2.56085 | ||||||||
\(986\) | 76.3231 | 2.43062 | ||||||||
\(987\) | −0.570199 | −0.0181496 | ||||||||
\(988\) | 7.14953 | 0.227457 | ||||||||
\(989\) | −44.1397 | −1.40356 | ||||||||
\(990\) | −20.3960 | −0.648228 | ||||||||
\(991\) | −9.78457 | −0.310817 | −0.155409 | − | 0.987850i | \(-0.549669\pi\) | ||||
−0.155409 | + | 0.987850i | \(0.549669\pi\) | |||||||
\(992\) | −53.5988 | −1.70176 | ||||||||
\(993\) | −35.8406 | −1.13737 | ||||||||
\(994\) | 15.4999 | 0.491625 | ||||||||
\(995\) | 87.4415 | 2.77208 | ||||||||
\(996\) | 54.9000 | 1.73957 | ||||||||
\(997\) | −34.6072 | −1.09602 | −0.548011 | − | 0.836471i | \(-0.684615\pi\) | ||||
−0.548011 | + | 0.836471i | \(0.684615\pi\) | |||||||
\(998\) | −18.4346 | −0.583537 | ||||||||
\(999\) | 1.10405 | 0.0349307 |
(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 | 6013.2.a.f.1.13 | ✓ | 110 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6013.2.a.f.1.13 | ✓ | 110 | 1.1 | even | 1 | trivial |