Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4002,2,Mod(1,4002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4002.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: | \(31.9561308889\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.16448.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.18398\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4002.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.59819 | 1.60916 | 0.804580 | − | 0.593844i | \(-0.202390\pi\) | ||||
0.804580 | + | 0.593844i | \(0.202390\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.23023 | 0.464985 | 0.232492 | − | 0.972598i | \(-0.425312\pi\) | ||||
0.232492 | + | 0.972598i | \(0.425312\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.59819 | −1.13785 | ||||||||
\(11\) | 0.260186 | 0.0784491 | 0.0392245 | − | 0.999230i | \(-0.487511\pi\) | ||||
0.0392245 | + | 0.999230i | \(0.487511\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 5.91704 | 1.64109 | 0.820546 | − | 0.571581i | \(-0.193670\pi\) | ||||
0.820546 | + | 0.571581i | \(0.193670\pi\) | |||||||
\(14\) | −1.23023 | −0.328794 | ||||||||
\(15\) | −3.59819 | −0.929049 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.05866 | −0.984370 | −0.492185 | − | 0.870491i | \(-0.663802\pi\) | ||||
−0.492185 | + | 0.870491i | \(0.663802\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 6.94699 | 1.59375 | 0.796875 | − | 0.604145i | \(-0.206485\pi\) | ||||
0.796875 | + | 0.604145i | \(0.206485\pi\) | |||||||
\(20\) | 3.59819 | 0.804580 | ||||||||
\(21\) | −1.23023 | −0.268459 | ||||||||
\(22\) | −0.260186 | −0.0554719 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 7.94699 | 1.58940 | ||||||||
\(26\) | −5.91704 | −1.16043 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.23023 | 0.232492 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 3.59819 | 0.656937 | ||||||||
\(31\) | 1.73981 | 0.312480 | 0.156240 | − | 0.987719i | \(-0.450063\pi\) | ||||
0.156240 | + | 0.987719i | \(0.450063\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.260186 | −0.0452926 | ||||||||
\(34\) | 4.05866 | 0.696055 | ||||||||
\(35\) | 4.42662 | 0.748235 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.95089 | 0.320724 | 0.160362 | − | 0.987058i | \(-0.448734\pi\) | ||||
0.160362 | + | 0.987058i | \(0.448734\pi\) | |||||||
\(38\) | −6.94699 | −1.12695 | ||||||||
\(39\) | −5.91704 | −0.947485 | ||||||||
\(40\) | −3.59819 | −0.568924 | ||||||||
\(41\) | 1.49042 | 0.232765 | 0.116382 | − | 0.993204i | \(-0.462870\pi\) | ||||
0.116382 | + | 0.993204i | \(0.462870\pi\) | |||||||
\(42\) | 1.23023 | 0.189829 | ||||||||
\(43\) | −2.42662 | −0.370056 | −0.185028 | − | 0.982733i | \(-0.559238\pi\) | ||||
−0.185028 | + | 0.982733i | \(0.559238\pi\) | |||||||
\(44\) | 0.260186 | 0.0392245 | ||||||||
\(45\) | 3.59819 | 0.536387 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 2.76977 | 0.404012 | 0.202006 | − | 0.979384i | \(-0.435254\pi\) | ||||
0.202006 | + | 0.979384i | \(0.435254\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −5.48652 | −0.783789 | ||||||||
\(50\) | −7.94699 | −1.12387 | ||||||||
\(51\) | 4.05866 | 0.568326 | ||||||||
\(52\) | 5.91704 | 0.820546 | ||||||||
\(53\) | −2.88833 | −0.396743 | −0.198371 | − | 0.980127i | \(-0.563565\pi\) | ||||
−0.198371 | + | 0.980127i | \(0.563565\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.936200 | 0.126237 | ||||||||
\(56\) | −1.23023 | −0.164397 | ||||||||
\(57\) | −6.94699 | −0.920152 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | 0.426620 | 0.0555412 | 0.0277706 | − | 0.999614i | \(-0.491159\pi\) | ||||
0.0277706 | + | 0.999614i | \(0.491159\pi\) | |||||||
\(60\) | −3.59819 | −0.464525 | ||||||||
\(61\) | −5.37361 | −0.688021 | −0.344010 | − | 0.938966i | \(-0.611786\pi\) | ||||
−0.344010 | + | 0.938966i | \(0.611786\pi\) | |||||||
\(62\) | −1.73981 | −0.220957 | ||||||||
\(63\) | 1.23023 | 0.154995 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 21.2907 | 2.64078 | ||||||||
\(66\) | 0.260186 | 0.0320267 | ||||||||
\(67\) | 15.5643 | 1.90149 | 0.950744 | − | 0.309978i | \(-0.100322\pi\) | ||||
0.950744 | + | 0.309978i | \(0.100322\pi\) | |||||||
\(68\) | −4.05866 | −0.492185 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | −4.42662 | −0.529082 | ||||||||
\(71\) | 12.9362 | 1.53524 | 0.767622 | − | 0.640903i | \(-0.221440\pi\) | ||||
0.767622 | + | 0.640903i | \(0.221440\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 1.07906 | 0.126295 | 0.0631474 | − | 0.998004i | \(-0.479886\pi\) | ||||
0.0631474 | + | 0.998004i | \(0.479886\pi\) | |||||||
\(74\) | −1.95089 | −0.226786 | ||||||||
\(75\) | −7.94699 | −0.917640 | ||||||||
\(76\) | 6.94699 | 0.796875 | ||||||||
\(77\) | 0.320090 | 0.0364776 | ||||||||
\(78\) | 5.91704 | 0.669973 | ||||||||
\(79\) | 5.02871 | 0.565774 | 0.282887 | − | 0.959153i | \(-0.408708\pi\) | ||||
0.282887 | + | 0.959153i | \(0.408708\pi\) | |||||||
\(80\) | 3.59819 | 0.402290 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.49042 | −0.164589 | ||||||||
\(83\) | 14.5452 | 1.59654 | 0.798271 | − | 0.602299i | \(-0.205748\pi\) | ||||
0.798271 | + | 0.602299i | \(0.205748\pi\) | |||||||
\(84\) | −1.23023 | −0.134230 | ||||||||
\(85\) | −14.6038 | −1.58401 | ||||||||
\(86\) | 2.42662 | 0.261669 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | −0.260186 | −0.0277359 | ||||||||
\(89\) | −10.4279 | −1.10535 | −0.552676 | − | 0.833396i | \(-0.686393\pi\) | ||||
−0.552676 | + | 0.833396i | \(0.686393\pi\) | |||||||
\(90\) | −3.59819 | −0.379283 | ||||||||
\(91\) | 7.27935 | 0.763083 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −1.73981 | −0.180410 | ||||||||
\(94\) | −2.76977 | −0.285680 | ||||||||
\(95\) | 24.9966 | 2.56460 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −11.3488 | −1.15230 | −0.576148 | − | 0.817345i | \(-0.695445\pi\) | ||||
−0.576148 | + | 0.817345i | \(0.695445\pi\) | |||||||
\(98\) | 5.48652 | 0.554223 | ||||||||
\(99\) | 0.260186 | 0.0261497 | ||||||||
\(100\) | 7.94699 | 0.794699 | ||||||||
\(101\) | −10.0000 | −0.995037 | −0.497519 | − | 0.867453i | \(-0.665755\pi\) | ||||
−0.497519 | + | 0.867453i | \(0.665755\pi\) | |||||||
\(102\) | −4.05866 | −0.401867 | ||||||||
\(103\) | −8.54394 | −0.841860 | −0.420930 | − | 0.907093i | \(-0.638296\pi\) | ||||
−0.420930 | + | 0.907093i | \(0.638296\pi\) | |||||||
\(104\) | −5.91704 | −0.580214 | ||||||||
\(105\) | −4.42662 | −0.431994 | ||||||||
\(106\) | 2.88833 | 0.280539 | ||||||||
\(107\) | 1.16078 | 0.112217 | 0.0561084 | − | 0.998425i | \(-0.482131\pi\) | ||||
0.0561084 | + | 0.998425i | \(0.482131\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −8.54519 | −0.818480 | −0.409240 | − | 0.912427i | \(-0.634206\pi\) | ||||
−0.409240 | + | 0.912427i | \(0.634206\pi\) | |||||||
\(110\) | −0.936200 | −0.0892631 | ||||||||
\(111\) | −1.95089 | −0.185170 | ||||||||
\(112\) | 1.23023 | 0.116246 | ||||||||
\(113\) | −10.9718 | −1.03214 | −0.516070 | − | 0.856546i | \(-0.672606\pi\) | ||||
−0.516070 | + | 0.856546i | \(0.672606\pi\) | |||||||
\(114\) | 6.94699 | 0.650645 | ||||||||
\(115\) | 3.59819 | 0.335533 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | 5.91704 | 0.547031 | ||||||||
\(118\) | −0.426620 | −0.0392736 | ||||||||
\(119\) | −4.99310 | −0.457717 | ||||||||
\(120\) | 3.59819 | 0.328469 | ||||||||
\(121\) | −10.9323 | −0.993846 | ||||||||
\(122\) | 5.37361 | 0.486504 | ||||||||
\(123\) | −1.49042 | −0.134387 | ||||||||
\(124\) | 1.73981 | 0.156240 | ||||||||
\(125\) | 10.6038 | 0.948437 | ||||||||
\(126\) | −1.23023 | −0.109598 | ||||||||
\(127\) | 21.3736 | 1.89660 | 0.948301 | − | 0.317373i | \(-0.102801\pi\) | ||||
0.948301 | + | 0.317373i | \(0.102801\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.42662 | 0.213652 | ||||||||
\(130\) | −21.2907 | −1.86731 | ||||||||
\(131\) | −20.1542 | −1.76088 | −0.880439 | − | 0.474159i | \(-0.842752\pi\) | ||||
−0.880439 | + | 0.474159i | \(0.842752\pi\) | |||||||
\(132\) | −0.260186 | −0.0226463 | ||||||||
\(133\) | 8.54643 | 0.741069 | ||||||||
\(134\) | −15.5643 | −1.34455 | ||||||||
\(135\) | −3.59819 | −0.309683 | ||||||||
\(136\) | 4.05866 | 0.348027 | ||||||||
\(137\) | −16.9380 | −1.44711 | −0.723554 | − | 0.690268i | \(-0.757493\pi\) | ||||
−0.723554 | + | 0.690268i | \(0.757493\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | −9.53953 | −0.809133 | −0.404566 | − | 0.914509i | \(-0.632577\pi\) | ||||
−0.404566 | + | 0.914509i | \(0.632577\pi\) | |||||||
\(140\) | 4.42662 | 0.374118 | ||||||||
\(141\) | −2.76977 | −0.233256 | ||||||||
\(142\) | −12.9362 | −1.08558 | ||||||||
\(143\) | 1.53953 | 0.128742 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −3.59819 | −0.298814 | ||||||||
\(146\) | −1.07906 | −0.0893039 | ||||||||
\(147\) | 5.48652 | 0.452521 | ||||||||
\(148\) | 1.95089 | 0.160362 | ||||||||
\(149\) | 8.75626 | 0.717341 | 0.358670 | − | 0.933464i | \(-0.383230\pi\) | ||||
0.358670 | + | 0.933464i | \(0.383230\pi\) | |||||||
\(150\) | 7.94699 | 0.648869 | ||||||||
\(151\) | −13.5999 | −1.10675 | −0.553374 | − | 0.832933i | \(-0.686660\pi\) | ||||
−0.553374 | + | 0.832933i | \(0.686660\pi\) | |||||||
\(152\) | −6.94699 | −0.563475 | ||||||||
\(153\) | −4.05866 | −0.328123 | ||||||||
\(154\) | −0.320090 | −0.0257936 | ||||||||
\(155\) | 6.26019 | 0.502830 | ||||||||
\(156\) | −5.91704 | −0.473742 | ||||||||
\(157\) | 7.49042 | 0.597801 | 0.298900 | − | 0.954284i | \(-0.403380\pi\) | ||||
0.298900 | + | 0.954284i | \(0.403380\pi\) | |||||||
\(158\) | −5.02871 | −0.400063 | ||||||||
\(159\) | 2.88833 | 0.229060 | ||||||||
\(160\) | −3.59819 | −0.284462 | ||||||||
\(161\) | 1.23023 | 0.0969560 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 9.66765 | 0.757229 | 0.378614 | − | 0.925555i | \(-0.376401\pi\) | ||||
0.378614 | + | 0.925555i | \(0.376401\pi\) | |||||||
\(164\) | 1.49042 | 0.116382 | ||||||||
\(165\) | −0.936200 | −0.0728831 | ||||||||
\(166\) | −14.5452 | −1.12893 | ||||||||
\(167\) | −14.8149 | −1.14641 | −0.573207 | − | 0.819411i | \(-0.694301\pi\) | ||||
−0.573207 | + | 0.819411i | \(0.694301\pi\) | |||||||
\(168\) | 1.23023 | 0.0949146 | ||||||||
\(169\) | 22.0114 | 1.69318 | ||||||||
\(170\) | 14.6038 | 1.12006 | ||||||||
\(171\) | 6.94699 | 0.531250 | ||||||||
\(172\) | −2.42662 | −0.185028 | ||||||||
\(173\) | 14.3437 | 1.09053 | 0.545264 | − | 0.838264i | \(-0.316429\pi\) | ||||
0.545264 | + | 0.838264i | \(0.316429\pi\) | |||||||
\(174\) | −1.00000 | −0.0758098 | ||||||||
\(175\) | 9.77666 | 0.739046 | ||||||||
\(176\) | 0.260186 | 0.0196123 | ||||||||
\(177\) | −0.426620 | −0.0320667 | ||||||||
\(178\) | 10.4279 | 0.781601 | ||||||||
\(179\) | −16.2371 | −1.21362 | −0.606810 | − | 0.794847i | \(-0.707551\pi\) | ||||
−0.606810 | + | 0.794847i | \(0.707551\pi\) | |||||||
\(180\) | 3.59819 | 0.268193 | ||||||||
\(181\) | 6.80537 | 0.505839 | 0.252920 | − | 0.967487i | \(-0.418609\pi\) | ||||
0.252920 | + | 0.967487i | \(0.418609\pi\) | |||||||
\(182\) | −7.27935 | −0.539581 | ||||||||
\(183\) | 5.37361 | 0.397229 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 7.01967 | 0.516097 | ||||||||
\(186\) | 1.73981 | 0.127569 | ||||||||
\(187\) | −1.05601 | −0.0772229 | ||||||||
\(188\) | 2.76977 | 0.202006 | ||||||||
\(189\) | −1.23023 | −0.0894864 | ||||||||
\(190\) | −24.9966 | −1.81345 | ||||||||
\(191\) | −10.0739 | −0.728924 | −0.364462 | − | 0.931218i | \(-0.618747\pi\) | ||||
−0.364462 | + | 0.931218i | \(0.618747\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −8.10953 | −0.583737 | −0.291868 | − | 0.956458i | \(-0.594277\pi\) | ||||
−0.291868 | + | 0.956458i | \(0.594277\pi\) | |||||||
\(194\) | 11.3488 | 0.814796 | ||||||||
\(195\) | −21.2907 | −1.52466 | ||||||||
\(196\) | −5.48652 | −0.391895 | ||||||||
\(197\) | 11.0300 | 0.785852 | 0.392926 | − | 0.919570i | \(-0.371463\pi\) | ||||
0.392926 | + | 0.919570i | \(0.371463\pi\) | |||||||
\(198\) | −0.260186 | −0.0184906 | ||||||||
\(199\) | −7.93230 | −0.562306 | −0.281153 | − | 0.959663i | \(-0.590717\pi\) | ||||
−0.281153 | + | 0.959663i | \(0.590717\pi\) | |||||||
\(200\) | −7.94699 | −0.561937 | ||||||||
\(201\) | −15.5643 | −1.09782 | ||||||||
\(202\) | 10.0000 | 0.703598 | ||||||||
\(203\) | −1.23023 | −0.0863455 | ||||||||
\(204\) | 4.05866 | 0.284163 | ||||||||
\(205\) | 5.36282 | 0.374556 | ||||||||
\(206\) | 8.54394 | 0.595285 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 5.91704 | 0.410273 | ||||||||
\(209\) | 1.80751 | 0.125028 | ||||||||
\(210\) | 4.42662 | 0.305466 | ||||||||
\(211\) | 5.76587 | 0.396939 | 0.198469 | − | 0.980107i | \(-0.436403\pi\) | ||||
0.198469 | + | 0.980107i | \(0.436403\pi\) | |||||||
\(212\) | −2.88833 | −0.198371 | ||||||||
\(213\) | −12.9362 | −0.886374 | ||||||||
\(214\) | −1.16078 | −0.0793493 | ||||||||
\(215\) | −8.73145 | −0.595480 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 2.14038 | 0.145298 | ||||||||
\(218\) | 8.54519 | 0.578753 | ||||||||
\(219\) | −1.07906 | −0.0729163 | ||||||||
\(220\) | 0.936200 | 0.0631186 | ||||||||
\(221\) | −24.0153 | −1.61544 | ||||||||
\(222\) | 1.95089 | 0.130935 | ||||||||
\(223\) | −13.6569 | −0.914531 | −0.457265 | − | 0.889330i | \(-0.651171\pi\) | ||||
−0.457265 | + | 0.889330i | \(0.651171\pi\) | |||||||
\(224\) | −1.23023 | −0.0821985 | ||||||||
\(225\) | 7.94699 | 0.529799 | ||||||||
\(226\) | 10.9718 | 0.729834 | ||||||||
\(227\) | 4.14162 | 0.274889 | 0.137445 | − | 0.990509i | \(-0.456111\pi\) | ||||
0.137445 | + | 0.990509i | \(0.456111\pi\) | |||||||
\(228\) | −6.94699 | −0.460076 | ||||||||
\(229\) | 20.9623 | 1.38522 | 0.692612 | − | 0.721310i | \(-0.256460\pi\) | ||||
0.692612 | + | 0.721310i | \(0.256460\pi\) | |||||||
\(230\) | −3.59819 | −0.237258 | ||||||||
\(231\) | −0.320090 | −0.0210604 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | 11.9401 | 0.782222 | 0.391111 | − | 0.920344i | \(-0.372091\pi\) | ||||
0.391111 | + | 0.920344i | \(0.372091\pi\) | |||||||
\(234\) | −5.91704 | −0.386809 | ||||||||
\(235\) | 9.96615 | 0.650120 | ||||||||
\(236\) | 0.426620 | 0.0277706 | ||||||||
\(237\) | −5.02871 | −0.326650 | ||||||||
\(238\) | 4.99310 | 0.323655 | ||||||||
\(239\) | 7.88268 | 0.509888 | 0.254944 | − | 0.966956i | \(-0.417943\pi\) | ||||
0.254944 | + | 0.966956i | \(0.417943\pi\) | |||||||
\(240\) | −3.59819 | −0.232262 | ||||||||
\(241\) | −2.22634 | −0.143411 | −0.0717055 | − | 0.997426i | \(-0.522844\pi\) | ||||
−0.0717055 | + | 0.997426i | \(0.522844\pi\) | |||||||
\(242\) | 10.9323 | 0.702755 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −5.37361 | −0.344010 | ||||||||
\(245\) | −19.7416 | −1.26124 | ||||||||
\(246\) | 1.49042 | 0.0950257 | ||||||||
\(247\) | 41.1056 | 2.61549 | ||||||||
\(248\) | −1.73981 | −0.110478 | ||||||||
\(249\) | −14.5452 | −0.921764 | ||||||||
\(250\) | −10.6038 | −0.670646 | ||||||||
\(251\) | 24.1095 | 1.52178 | 0.760890 | − | 0.648881i | \(-0.224763\pi\) | ||||
0.760890 | + | 0.648881i | \(0.224763\pi\) | |||||||
\(252\) | 1.23023 | 0.0774975 | ||||||||
\(253\) | 0.260186 | 0.0163578 | ||||||||
\(254\) | −21.3736 | −1.34110 | ||||||||
\(255\) | 14.6038 | 0.914528 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.23860 | −0.264397 | −0.132198 | − | 0.991223i | \(-0.542204\pi\) | ||||
−0.132198 | + | 0.991223i | \(0.542204\pi\) | |||||||
\(258\) | −2.42662 | −0.151075 | ||||||||
\(259\) | 2.40005 | 0.149132 | ||||||||
\(260\) | 21.2907 | 1.32039 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 20.1542 | 1.24513 | ||||||||
\(263\) | −23.5649 | −1.45307 | −0.726536 | − | 0.687129i | \(-0.758871\pi\) | ||||
−0.726536 | + | 0.687129i | \(0.758871\pi\) | |||||||
\(264\) | 0.260186 | 0.0160133 | ||||||||
\(265\) | −10.3928 | −0.638423 | ||||||||
\(266\) | −8.54643 | −0.524015 | ||||||||
\(267\) | 10.4279 | 0.638175 | ||||||||
\(268\) | 15.5643 | 0.950744 | ||||||||
\(269\) | 10.4374 | 0.636380 | 0.318190 | − | 0.948027i | \(-0.396925\pi\) | ||||
0.318190 | + | 0.948027i | \(0.396925\pi\) | |||||||
\(270\) | 3.59819 | 0.218979 | ||||||||
\(271\) | 25.4718 | 1.54730 | 0.773652 | − | 0.633611i | \(-0.218428\pi\) | ||||
0.773652 | + | 0.633611i | \(0.218428\pi\) | |||||||
\(272\) | −4.05866 | −0.246092 | ||||||||
\(273\) | −7.27935 | −0.440566 | ||||||||
\(274\) | 16.9380 | 1.02326 | ||||||||
\(275\) | 2.06770 | 0.124687 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 1.93863 | 0.116481 | 0.0582404 | − | 0.998303i | \(-0.481451\pi\) | ||||
0.0582404 | + | 0.998303i | \(0.481451\pi\) | |||||||
\(278\) | 9.53953 | 0.572143 | ||||||||
\(279\) | 1.73981 | 0.104160 | ||||||||
\(280\) | −4.42662 | −0.264541 | ||||||||
\(281\) | −21.8341 | −1.30251 | −0.651256 | − | 0.758858i | \(-0.725758\pi\) | ||||
−0.651256 | + | 0.758858i | \(0.725758\pi\) | |||||||
\(282\) | 2.76977 | 0.164937 | ||||||||
\(283\) | 17.4240 | 1.03575 | 0.517874 | − | 0.855457i | \(-0.326724\pi\) | ||||
0.517874 | + | 0.855457i | \(0.326724\pi\) | |||||||
\(284\) | 12.9362 | 0.767622 | ||||||||
\(285\) | −24.9966 | −1.48067 | ||||||||
\(286\) | −1.53953 | −0.0910344 | ||||||||
\(287\) | 1.83357 | 0.108232 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −0.527268 | −0.0310158 | ||||||||
\(290\) | 3.59819 | 0.211293 | ||||||||
\(291\) | 11.3488 | 0.665278 | ||||||||
\(292\) | 1.07906 | 0.0631474 | ||||||||
\(293\) | −21.9436 | −1.28196 | −0.640980 | − | 0.767558i | \(-0.721472\pi\) | ||||
−0.640980 | + | 0.767558i | \(0.721472\pi\) | |||||||
\(294\) | −5.48652 | −0.319981 | ||||||||
\(295\) | 1.53506 | 0.0893747 | ||||||||
\(296\) | −1.95089 | −0.113393 | ||||||||
\(297\) | −0.260186 | −0.0150975 | ||||||||
\(298\) | −8.75626 | −0.507237 | ||||||||
\(299\) | 5.91704 | 0.342191 | ||||||||
\(300\) | −7.94699 | −0.458820 | ||||||||
\(301\) | −2.98531 | −0.172070 | ||||||||
\(302\) | 13.5999 | 0.782589 | ||||||||
\(303\) | 10.0000 | 0.574485 | ||||||||
\(304\) | 6.94699 | 0.398437 | ||||||||
\(305\) | −19.3353 | −1.10714 | ||||||||
\(306\) | 4.05866 | 0.232018 | ||||||||
\(307\) | 14.3928 | 0.821439 | 0.410719 | − | 0.911762i | \(-0.365278\pi\) | ||||
0.410719 | + | 0.911762i | \(0.365278\pi\) | |||||||
\(308\) | 0.320090 | 0.0182388 | ||||||||
\(309\) | 8.54394 | 0.486048 | ||||||||
\(310\) | −6.26019 | −0.355555 | ||||||||
\(311\) | 2.31709 | 0.131390 | 0.0656951 | − | 0.997840i | \(-0.479074\pi\) | ||||
0.0656951 | + | 0.997840i | \(0.479074\pi\) | |||||||
\(312\) | 5.91704 | 0.334986 | ||||||||
\(313\) | 0.452161 | 0.0255576 | 0.0127788 | − | 0.999918i | \(-0.495932\pi\) | ||||
0.0127788 | + | 0.999918i | \(0.495932\pi\) | |||||||
\(314\) | −7.49042 | −0.422709 | ||||||||
\(315\) | 4.42662 | 0.249412 | ||||||||
\(316\) | 5.02871 | 0.282887 | ||||||||
\(317\) | 20.7625 | 1.16614 | 0.583069 | − | 0.812423i | \(-0.301852\pi\) | ||||
0.583069 | + | 0.812423i | \(0.301852\pi\) | |||||||
\(318\) | −2.88833 | −0.161970 | ||||||||
\(319\) | −0.260186 | −0.0145676 | ||||||||
\(320\) | 3.59819 | 0.201145 | ||||||||
\(321\) | −1.16078 | −0.0647884 | ||||||||
\(322\) | −1.23023 | −0.0685583 | ||||||||
\(323\) | −28.1955 | −1.56884 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 47.0227 | 2.60835 | ||||||||
\(326\) | −9.66765 | −0.535441 | ||||||||
\(327\) | 8.54519 | 0.472550 | ||||||||
\(328\) | −1.49042 | −0.0822947 | ||||||||
\(329\) | 3.40746 | 0.187859 | ||||||||
\(330\) | 0.936200 | 0.0515361 | ||||||||
\(331\) | 29.3142 | 1.61126 | 0.805628 | − | 0.592422i | \(-0.201828\pi\) | ||||
0.805628 | + | 0.592422i | \(0.201828\pi\) | |||||||
\(332\) | 14.5452 | 0.798271 | ||||||||
\(333\) | 1.95089 | 0.106908 | ||||||||
\(334\) | 14.8149 | 0.810636 | ||||||||
\(335\) | 56.0035 | 3.05980 | ||||||||
\(336\) | −1.23023 | −0.0671148 | ||||||||
\(337\) | 21.6739 | 1.18065 | 0.590326 | − | 0.807165i | \(-0.298999\pi\) | ||||
0.590326 | + | 0.807165i | \(0.298999\pi\) | |||||||
\(338\) | −22.0114 | −1.19726 | ||||||||
\(339\) | 10.9718 | 0.595907 | ||||||||
\(340\) | −14.6038 | −0.792005 | ||||||||
\(341\) | 0.452675 | 0.0245137 | ||||||||
\(342\) | −6.94699 | −0.375650 | ||||||||
\(343\) | −15.3613 | −0.829435 | ||||||||
\(344\) | 2.42662 | 0.130835 | ||||||||
\(345\) | −3.59819 | −0.193720 | ||||||||
\(346\) | −14.3437 | −0.771120 | ||||||||
\(347\) | −9.91653 | −0.532347 | −0.266173 | − | 0.963925i | \(-0.585759\pi\) | ||||
−0.266173 | + | 0.963925i | \(0.585759\pi\) | |||||||
\(348\) | 1.00000 | 0.0536056 | ||||||||
\(349\) | −11.6107 | −0.621509 | −0.310754 | − | 0.950490i | \(-0.600582\pi\) | ||||
−0.310754 | + | 0.950490i | \(0.600582\pi\) | |||||||
\(350\) | −9.77666 | −0.522585 | ||||||||
\(351\) | −5.91704 | −0.315828 | ||||||||
\(352\) | −0.260186 | −0.0138680 | ||||||||
\(353\) | 3.08686 | 0.164297 | 0.0821484 | − | 0.996620i | \(-0.473822\pi\) | ||||
0.0821484 | + | 0.996620i | \(0.473822\pi\) | |||||||
\(354\) | 0.426620 | 0.0226746 | ||||||||
\(355\) | 46.5469 | 2.47046 | ||||||||
\(356\) | −10.4279 | −0.552676 | ||||||||
\(357\) | 4.99310 | 0.264263 | ||||||||
\(358\) | 16.2371 | 0.858159 | ||||||||
\(359\) | −18.1451 | −0.957664 | −0.478832 | − | 0.877907i | \(-0.658940\pi\) | ||||
−0.478832 | + | 0.877907i | \(0.658940\pi\) | |||||||
\(360\) | −3.59819 | −0.189641 | ||||||||
\(361\) | 29.2607 | 1.54004 | ||||||||
\(362\) | −6.80537 | −0.357682 | ||||||||
\(363\) | 10.9323 | 0.573797 | ||||||||
\(364\) | 7.27935 | 0.381541 | ||||||||
\(365\) | 3.88268 | 0.203229 | ||||||||
\(366\) | −5.37361 | −0.280883 | ||||||||
\(367\) | −26.8359 | −1.40082 | −0.700411 | − | 0.713740i | \(-0.747000\pi\) | ||||
−0.700411 | + | 0.713740i | \(0.747000\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 1.49042 | 0.0775882 | ||||||||
\(370\) | −7.01967 | −0.364935 | ||||||||
\(371\) | −3.55332 | −0.184479 | ||||||||
\(372\) | −1.73981 | −0.0902051 | ||||||||
\(373\) | −17.9404 | −0.928918 | −0.464459 | − | 0.885595i | \(-0.653751\pi\) | ||||
−0.464459 | + | 0.885595i | \(0.653751\pi\) | |||||||
\(374\) | 1.05601 | 0.0546048 | ||||||||
\(375\) | −10.6038 | −0.547580 | ||||||||
\(376\) | −2.76977 | −0.142840 | ||||||||
\(377\) | −5.91704 | −0.304743 | ||||||||
\(378\) | 1.23023 | 0.0632764 | ||||||||
\(379\) | 0.913144 | 0.0469050 | 0.0234525 | − | 0.999725i | \(-0.492534\pi\) | ||||
0.0234525 | + | 0.999725i | \(0.492534\pi\) | |||||||
\(380\) | 24.9966 | 1.28230 | ||||||||
\(381\) | −21.3736 | −1.09500 | ||||||||
\(382\) | 10.0739 | 0.515427 | ||||||||
\(383\) | −27.2829 | −1.39409 | −0.697044 | − | 0.717028i | \(-0.745502\pi\) | ||||
−0.697044 | + | 0.717028i | \(0.745502\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 1.15174 | 0.0586984 | ||||||||
\(386\) | 8.10953 | 0.412764 | ||||||||
\(387\) | −2.42662 | −0.123352 | ||||||||
\(388\) | −11.3488 | −0.576148 | ||||||||
\(389\) | 24.9054 | 1.26275 | 0.631376 | − | 0.775477i | \(-0.282491\pi\) | ||||
0.631376 | + | 0.775477i | \(0.282491\pi\) | |||||||
\(390\) | 21.2907 | 1.07809 | ||||||||
\(391\) | −4.05866 | −0.205255 | ||||||||
\(392\) | 5.48652 | 0.277111 | ||||||||
\(393\) | 20.1542 | 1.01664 | ||||||||
\(394\) | −11.0300 | −0.555681 | ||||||||
\(395\) | 18.0943 | 0.910421 | ||||||||
\(396\) | 0.260186 | 0.0130748 | ||||||||
\(397\) | 36.5966 | 1.83673 | 0.918365 | − | 0.395735i | \(-0.129510\pi\) | ||||
0.918365 | + | 0.395735i | \(0.129510\pi\) | |||||||
\(398\) | 7.93230 | 0.397610 | ||||||||
\(399\) | −8.54643 | −0.427857 | ||||||||
\(400\) | 7.94699 | 0.397350 | ||||||||
\(401\) | −6.97056 | −0.348093 | −0.174047 | − | 0.984737i | \(-0.555684\pi\) | ||||
−0.174047 | + | 0.984737i | \(0.555684\pi\) | |||||||
\(402\) | 15.5643 | 0.776279 | ||||||||
\(403\) | 10.2945 | 0.512808 | ||||||||
\(404\) | −10.0000 | −0.497519 | ||||||||
\(405\) | 3.59819 | 0.178796 | ||||||||
\(406\) | 1.23023 | 0.0610555 | ||||||||
\(407\) | 0.507594 | 0.0251605 | ||||||||
\(408\) | −4.05866 | −0.200934 | ||||||||
\(409\) | −22.9578 | −1.13519 | −0.567595 | − | 0.823308i | \(-0.692126\pi\) | ||||
−0.567595 | + | 0.823308i | \(0.692126\pi\) | |||||||
\(410\) | −5.36282 | −0.264851 | ||||||||
\(411\) | 16.9380 | 0.835488 | ||||||||
\(412\) | −8.54394 | −0.420930 | ||||||||
\(413\) | 0.524843 | 0.0258258 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 52.3364 | 2.56909 | ||||||||
\(416\) | −5.91704 | −0.290107 | ||||||||
\(417\) | 9.53953 | 0.467153 | ||||||||
\(418\) | −1.80751 | −0.0884082 | ||||||||
\(419\) | 18.2512 | 0.891627 | 0.445814 | − | 0.895126i | \(-0.352914\pi\) | ||||
0.445814 | + | 0.895126i | \(0.352914\pi\) | |||||||
\(420\) | −4.42662 | −0.215997 | ||||||||
\(421\) | −25.9897 | −1.26666 | −0.633331 | − | 0.773881i | \(-0.718313\pi\) | ||||
−0.633331 | + | 0.773881i | \(0.718313\pi\) | |||||||
\(422\) | −5.76587 | −0.280678 | ||||||||
\(423\) | 2.76977 | 0.134671 | ||||||||
\(424\) | 2.88833 | 0.140270 | ||||||||
\(425\) | −32.2542 | −1.56456 | ||||||||
\(426\) | 12.9362 | 0.626761 | ||||||||
\(427\) | −6.61080 | −0.319919 | ||||||||
\(428\) | 1.16078 | 0.0561084 | ||||||||
\(429\) | −1.53953 | −0.0743293 | ||||||||
\(430\) | 8.73145 | 0.421068 | ||||||||
\(431\) | 4.08296 | 0.196669 | 0.0983346 | − | 0.995153i | \(-0.468648\pi\) | ||||
0.0983346 | + | 0.995153i | \(0.468648\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 8.66646 | 0.416484 | 0.208242 | − | 0.978077i | \(-0.433226\pi\) | ||||
0.208242 | + | 0.978077i | \(0.433226\pi\) | |||||||
\(434\) | −2.14038 | −0.102741 | ||||||||
\(435\) | 3.59819 | 0.172520 | ||||||||
\(436\) | −8.54519 | −0.409240 | ||||||||
\(437\) | 6.94699 | 0.332320 | ||||||||
\(438\) | 1.07906 | 0.0515596 | ||||||||
\(439\) | 17.8336 | 0.851150 | 0.425575 | − | 0.904923i | \(-0.360072\pi\) | ||||
0.425575 | + | 0.904923i | \(0.360072\pi\) | |||||||
\(440\) | −0.936200 | −0.0446316 | ||||||||
\(441\) | −5.48652 | −0.261263 | ||||||||
\(442\) | 24.0153 | 1.14229 | ||||||||
\(443\) | 26.3467 | 1.25177 | 0.625884 | − | 0.779916i | \(-0.284738\pi\) | ||||
0.625884 | + | 0.779916i | \(0.284738\pi\) | |||||||
\(444\) | −1.95089 | −0.0925851 | ||||||||
\(445\) | −37.5215 | −1.77869 | ||||||||
\(446\) | 13.6569 | 0.646671 | ||||||||
\(447\) | −8.75626 | −0.414157 | ||||||||
\(448\) | 1.23023 | 0.0581231 | ||||||||
\(449\) | 9.77718 | 0.461413 | 0.230707 | − | 0.973023i | \(-0.425896\pi\) | ||||
0.230707 | + | 0.973023i | \(0.425896\pi\) | |||||||
\(450\) | −7.94699 | −0.374625 | ||||||||
\(451\) | 0.387787 | 0.0182602 | ||||||||
\(452\) | −10.9718 | −0.516070 | ||||||||
\(453\) | 13.5999 | 0.638981 | ||||||||
\(454\) | −4.14162 | −0.194376 | ||||||||
\(455\) | 26.1925 | 1.22792 | ||||||||
\(456\) | 6.94699 | 0.325323 | ||||||||
\(457\) | 35.8371 | 1.67639 | 0.838194 | − | 0.545372i | \(-0.183612\pi\) | ||||
0.838194 | + | 0.545372i | \(0.183612\pi\) | |||||||
\(458\) | −20.9623 | −0.979502 | ||||||||
\(459\) | 4.05866 | 0.189442 | ||||||||
\(460\) | 3.59819 | 0.167767 | ||||||||
\(461\) | −12.3775 | −0.576478 | −0.288239 | − | 0.957558i | \(-0.593070\pi\) | ||||
−0.288239 | + | 0.957558i | \(0.593070\pi\) | |||||||
\(462\) | 0.320090 | 0.0148919 | ||||||||
\(463\) | −7.31619 | −0.340012 | −0.170006 | − | 0.985443i | \(-0.554379\pi\) | ||||
−0.170006 | + | 0.985443i | \(0.554379\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | −6.26019 | −0.290309 | ||||||||
\(466\) | −11.9401 | −0.553114 | ||||||||
\(467\) | 8.42713 | 0.389961 | 0.194981 | − | 0.980807i | \(-0.437536\pi\) | ||||
0.194981 | + | 0.980807i | \(0.437536\pi\) | |||||||
\(468\) | 5.91704 | 0.273515 | ||||||||
\(469\) | 19.1478 | 0.884163 | ||||||||
\(470\) | −9.96615 | −0.459704 | ||||||||
\(471\) | −7.49042 | −0.345140 | ||||||||
\(472\) | −0.426620 | −0.0196368 | ||||||||
\(473\) | −0.631373 | −0.0290306 | ||||||||
\(474\) | 5.02871 | 0.230976 | ||||||||
\(475\) | 55.2077 | 2.53310 | ||||||||
\(476\) | −4.99310 | −0.228859 | ||||||||
\(477\) | −2.88833 | −0.132248 | ||||||||
\(478\) | −7.88268 | −0.360545 | ||||||||
\(479\) | 2.15241 | 0.0983463 | 0.0491731 | − | 0.998790i | \(-0.484341\pi\) | ||||
0.0491731 | + | 0.998790i | \(0.484341\pi\) | |||||||
\(480\) | 3.59819 | 0.164234 | ||||||||
\(481\) | 11.5435 | 0.526338 | ||||||||
\(482\) | 2.22634 | 0.101407 | ||||||||
\(483\) | −1.23023 | −0.0559776 | ||||||||
\(484\) | −10.9323 | −0.496923 | ||||||||
\(485\) | −40.8352 | −1.85423 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −33.4837 | −1.51729 | −0.758645 | − | 0.651505i | \(-0.774138\pi\) | ||||
−0.758645 | + | 0.651505i | \(0.774138\pi\) | |||||||
\(488\) | 5.37361 | 0.243252 | ||||||||
\(489\) | −9.66765 | −0.437186 | ||||||||
\(490\) | 19.7416 | 0.891833 | ||||||||
\(491\) | −0.652958 | −0.0294676 | −0.0147338 | − | 0.999891i | \(-0.504690\pi\) | ||||
−0.0147338 | + | 0.999891i | \(0.504690\pi\) | |||||||
\(492\) | −1.49042 | −0.0671933 | ||||||||
\(493\) | 4.05866 | 0.182793 | ||||||||
\(494\) | −41.1056 | −1.84943 | ||||||||
\(495\) | 0.936200 | 0.0420790 | ||||||||
\(496\) | 1.73981 | 0.0781200 | ||||||||
\(497\) | 15.9146 | 0.713865 | ||||||||
\(498\) | 14.5452 | 0.651785 | ||||||||
\(499\) | 2.14286 | 0.0959277 | 0.0479639 | − | 0.998849i | \(-0.484727\pi\) | ||||
0.0479639 | + | 0.998849i | \(0.484727\pi\) | |||||||
\(500\) | 10.6038 | 0.474218 | ||||||||
\(501\) | 14.8149 | 0.661882 | ||||||||
\(502\) | −24.1095 | −1.07606 | ||||||||
\(503\) | 0.272736 | 0.0121607 | 0.00608034 | − | 0.999982i | \(-0.498065\pi\) | ||||
0.00608034 | + | 0.999982i | \(0.498065\pi\) | |||||||
\(504\) | −1.23023 | −0.0547990 | ||||||||
\(505\) | −35.9819 | −1.60117 | ||||||||
\(506\) | −0.260186 | −0.0115667 | ||||||||
\(507\) | −22.0114 | −0.977559 | ||||||||
\(508\) | 21.3736 | 0.948301 | ||||||||
\(509\) | 10.0413 | 0.445074 | 0.222537 | − | 0.974924i | \(-0.428566\pi\) | ||||
0.222537 | + | 0.974924i | \(0.428566\pi\) | |||||||
\(510\) | −14.6038 | −0.646669 | ||||||||
\(511\) | 1.32750 | 0.0587252 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.94699 | −0.306717 | ||||||||
\(514\) | 4.23860 | 0.186957 | ||||||||
\(515\) | −30.7428 | −1.35469 | ||||||||
\(516\) | 2.42662 | 0.106826 | ||||||||
\(517\) | 0.720655 | 0.0316943 | ||||||||
\(518\) | −2.40005 | −0.105452 | ||||||||
\(519\) | −14.3437 | −0.629617 | ||||||||
\(520\) | −21.2907 | −0.933657 | ||||||||
\(521\) | 27.9308 | 1.22367 | 0.611836 | − | 0.790985i | \(-0.290431\pi\) | ||||
0.611836 | + | 0.790985i | \(0.290431\pi\) | |||||||
\(522\) | 1.00000 | 0.0437688 | ||||||||
\(523\) | 37.3385 | 1.63270 | 0.816350 | − | 0.577558i | \(-0.195994\pi\) | ||||
0.816350 | + | 0.577558i | \(0.195994\pi\) | |||||||
\(524\) | −20.1542 | −0.880439 | ||||||||
\(525\) | −9.77666 | −0.426688 | ||||||||
\(526\) | 23.5649 | 1.02748 | ||||||||
\(527\) | −7.06132 | −0.307596 | ||||||||
\(528\) | −0.260186 | −0.0113231 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 10.3928 | 0.451433 | ||||||||
\(531\) | 0.426620 | 0.0185137 | ||||||||
\(532\) | 8.54643 | 0.370535 | ||||||||
\(533\) | 8.81888 | 0.381988 | ||||||||
\(534\) | −10.4279 | −0.451258 | ||||||||
\(535\) | 4.17671 | 0.180575 | ||||||||
\(536\) | −15.5643 | −0.672277 | ||||||||
\(537\) | 16.2371 | 0.700684 | ||||||||
\(538\) | −10.4374 | −0.449989 | ||||||||
\(539\) | −1.42752 | −0.0614875 | ||||||||
\(540\) | −3.59819 | −0.154842 | ||||||||
\(541\) | 34.0757 | 1.46503 | 0.732514 | − | 0.680752i | \(-0.238347\pi\) | ||||
0.732514 | + | 0.680752i | \(0.238347\pi\) | |||||||
\(542\) | −25.4718 | −1.09411 | ||||||||
\(543\) | −6.80537 | −0.292046 | ||||||||
\(544\) | 4.05866 | 0.174014 | ||||||||
\(545\) | −30.7472 | −1.31707 | ||||||||
\(546\) | 7.27935 | 0.311527 | ||||||||
\(547\) | −22.2945 | −0.953246 | −0.476623 | − | 0.879108i | \(-0.658139\pi\) | ||||
−0.476623 | + | 0.879108i | \(0.658139\pi\) | |||||||
\(548\) | −16.9380 | −0.723554 | ||||||||
\(549\) | −5.37361 | −0.229340 | ||||||||
\(550\) | −2.06770 | −0.0881669 | ||||||||
\(551\) | −6.94699 | −0.295952 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 6.18649 | 0.263076 | ||||||||
\(554\) | −1.93863 | −0.0823643 | ||||||||
\(555\) | −7.01967 | −0.297969 | ||||||||
\(556\) | −9.53953 | −0.404566 | ||||||||
\(557\) | 30.6071 | 1.29686 | 0.648432 | − | 0.761273i | \(-0.275425\pi\) | ||||
0.648432 | + | 0.761273i | \(0.275425\pi\) | |||||||
\(558\) | −1.73981 | −0.0736522 | ||||||||
\(559\) | −14.3584 | −0.607296 | ||||||||
\(560\) | 4.42662 | 0.187059 | ||||||||
\(561\) | 1.05601 | 0.0445847 | ||||||||
\(562\) | 21.8341 | 0.921015 | ||||||||
\(563\) | 21.0982 | 0.889182 | 0.444591 | − | 0.895734i | \(-0.353349\pi\) | ||||
0.444591 | + | 0.895734i | \(0.353349\pi\) | |||||||
\(564\) | −2.76977 | −0.116628 | ||||||||
\(565\) | −39.4787 | −1.66088 | ||||||||
\(566\) | −17.4240 | −0.732384 | ||||||||
\(567\) | 1.23023 | 0.0516650 | ||||||||
\(568\) | −12.9362 | −0.542791 | ||||||||
\(569\) | 6.02034 | 0.252386 | 0.126193 | − | 0.992006i | \(-0.459724\pi\) | ||||
0.126193 | + | 0.992006i | \(0.459724\pi\) | |||||||
\(570\) | 24.9966 | 1.04699 | ||||||||
\(571\) | −12.7071 | −0.531778 | −0.265889 | − | 0.964004i | \(-0.585665\pi\) | ||||
−0.265889 | + | 0.964004i | \(0.585665\pi\) | |||||||
\(572\) | 1.53953 | 0.0643710 | ||||||||
\(573\) | 10.0739 | 0.420844 | ||||||||
\(574\) | −1.83357 | −0.0765316 | ||||||||
\(575\) | 7.94699 | 0.331412 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 4.66075 | 0.194030 | 0.0970148 | − | 0.995283i | \(-0.469071\pi\) | ||||
0.0970148 | + | 0.995283i | \(0.469071\pi\) | |||||||
\(578\) | 0.527268 | 0.0219315 | ||||||||
\(579\) | 8.10953 | 0.337021 | ||||||||
\(580\) | −3.59819 | −0.149407 | ||||||||
\(581\) | 17.8940 | 0.742368 | ||||||||
\(582\) | −11.3488 | −0.470423 | ||||||||
\(583\) | −0.751504 | −0.0311241 | ||||||||
\(584\) | −1.07906 | −0.0446520 | ||||||||
\(585\) | 21.2907 | 0.880260 | ||||||||
\(586\) | 21.9436 | 0.906482 | ||||||||
\(587\) | 10.8871 | 0.449358 | 0.224679 | − | 0.974433i | \(-0.427867\pi\) | ||||
0.224679 | + | 0.974433i | \(0.427867\pi\) | |||||||
\(588\) | 5.48652 | 0.226260 | ||||||||
\(589\) | 12.0865 | 0.498014 | ||||||||
\(590\) | −1.53506 | −0.0631975 | ||||||||
\(591\) | −11.0300 | −0.453712 | ||||||||
\(592\) | 1.95089 | 0.0801810 | ||||||||
\(593\) | 16.2945 | 0.669137 | 0.334568 | − | 0.942371i | \(-0.391409\pi\) | ||||
0.334568 | + | 0.942371i | \(0.391409\pi\) | |||||||
\(594\) | 0.260186 | 0.0106756 | ||||||||
\(595\) | −17.9662 | −0.736540 | ||||||||
\(596\) | 8.75626 | 0.358670 | ||||||||
\(597\) | 7.93230 | 0.324648 | ||||||||
\(598\) | −5.91704 | −0.241966 | ||||||||
\(599\) | −17.4693 | −0.713778 | −0.356889 | − | 0.934147i | \(-0.616163\pi\) | ||||
−0.356889 | + | 0.934147i | \(0.616163\pi\) | |||||||
\(600\) | 7.94699 | 0.324435 | ||||||||
\(601\) | 2.30234 | 0.0939145 | 0.0469572 | − | 0.998897i | \(-0.485048\pi\) | ||||
0.0469572 | + | 0.998897i | \(0.485048\pi\) | |||||||
\(602\) | 2.98531 | 0.121672 | ||||||||
\(603\) | 15.5643 | 0.633829 | ||||||||
\(604\) | −13.5999 | −0.553374 | ||||||||
\(605\) | −39.3365 | −1.59926 | ||||||||
\(606\) | −10.0000 | −0.406222 | ||||||||
\(607\) | 26.0241 | 1.05629 | 0.528143 | − | 0.849156i | \(-0.322889\pi\) | ||||
0.528143 | + | 0.849156i | \(0.322889\pi\) | |||||||
\(608\) | −6.94699 | −0.281738 | ||||||||
\(609\) | 1.23023 | 0.0498516 | ||||||||
\(610\) | 19.3353 | 0.782863 | ||||||||
\(611\) | 16.3888 | 0.663021 | ||||||||
\(612\) | −4.05866 | −0.164062 | ||||||||
\(613\) | 14.2697 | 0.576349 | 0.288175 | − | 0.957578i | \(-0.406952\pi\) | ||||
0.288175 | + | 0.957578i | \(0.406952\pi\) | |||||||
\(614\) | −14.3928 | −0.580845 | ||||||||
\(615\) | −5.36282 | −0.216250 | ||||||||
\(616\) | −0.320090 | −0.0128968 | ||||||||
\(617\) | −43.8250 | −1.76433 | −0.882165 | − | 0.470941i | \(-0.843915\pi\) | ||||
−0.882165 | + | 0.470941i | \(0.843915\pi\) | |||||||
\(618\) | −8.54394 | −0.343688 | ||||||||
\(619\) | 6.40752 | 0.257540 | 0.128770 | − | 0.991674i | \(-0.458897\pi\) | ||||
0.128770 | + | 0.991674i | \(0.458897\pi\) | |||||||
\(620\) | 6.26019 | 0.251415 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −2.31709 | −0.0929069 | ||||||||
\(623\) | −12.8287 | −0.513972 | ||||||||
\(624\) | −5.91704 | −0.236871 | ||||||||
\(625\) | −1.58028 | −0.0632110 | ||||||||
\(626\) | −0.452161 | −0.0180720 | ||||||||
\(627\) | −1.80751 | −0.0721850 | ||||||||
\(628\) | 7.49042 | 0.298900 | ||||||||
\(629\) | −7.91800 | −0.315711 | ||||||||
\(630\) | −4.42662 | −0.176361 | ||||||||
\(631\) | −21.9176 | −0.872524 | −0.436262 | − | 0.899820i | \(-0.643698\pi\) | ||||
−0.436262 | + | 0.899820i | \(0.643698\pi\) | |||||||
\(632\) | −5.02871 | −0.200031 | ||||||||
\(633\) | −5.76587 | −0.229173 | ||||||||
\(634\) | −20.7625 | −0.824584 | ||||||||
\(635\) | 76.9064 | 3.05194 | ||||||||
\(636\) | 2.88833 | 0.114530 | ||||||||
\(637\) | −32.4640 | −1.28627 | ||||||||
\(638\) | 0.260186 | 0.0103009 | ||||||||
\(639\) | 12.9362 | 0.511748 | ||||||||
\(640\) | −3.59819 | −0.142231 | ||||||||
\(641\) | −16.9605 | −0.669899 | −0.334950 | − | 0.942236i | \(-0.608719\pi\) | ||||
−0.334950 | + | 0.942236i | \(0.608719\pi\) | |||||||
\(642\) | 1.16078 | 0.0458123 | ||||||||
\(643\) | 30.3474 | 1.19678 | 0.598392 | − | 0.801203i | \(-0.295807\pi\) | ||||
0.598392 | + | 0.801203i | \(0.295807\pi\) | |||||||
\(644\) | 1.23023 | 0.0484780 | ||||||||
\(645\) | 8.73145 | 0.343800 | ||||||||
\(646\) | 28.1955 | 1.10934 | ||||||||
\(647\) | 25.7398 | 1.01194 | 0.505968 | − | 0.862552i | \(-0.331135\pi\) | ||||
0.505968 | + | 0.862552i | \(0.331135\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0.111001 | 0.00435715 | ||||||||
\(650\) | −47.0227 | −1.84438 | ||||||||
\(651\) | −2.14038 | −0.0838881 | ||||||||
\(652\) | 9.66765 | 0.378614 | ||||||||
\(653\) | −32.7663 | −1.28225 | −0.641123 | − | 0.767438i | \(-0.721531\pi\) | ||||
−0.641123 | + | 0.767438i | \(0.721531\pi\) | |||||||
\(654\) | −8.54519 | −0.334143 | ||||||||
\(655\) | −72.5186 | −2.83354 | ||||||||
\(656\) | 1.49042 | 0.0581911 | ||||||||
\(657\) | 1.07906 | 0.0420983 | ||||||||
\(658\) | −3.40746 | −0.132837 | ||||||||
\(659\) | −31.4041 | −1.22333 | −0.611666 | − | 0.791116i | \(-0.709500\pi\) | ||||
−0.611666 | + | 0.791116i | \(0.709500\pi\) | |||||||
\(660\) | −0.936200 | −0.0364415 | ||||||||
\(661\) | 14.3218 | 0.557055 | 0.278528 | − | 0.960428i | \(-0.410154\pi\) | ||||
0.278528 | + | 0.960428i | \(0.410154\pi\) | |||||||
\(662\) | −29.3142 | −1.13933 | ||||||||
\(663\) | 24.0153 | 0.932676 | ||||||||
\(664\) | −14.5452 | −0.564463 | ||||||||
\(665\) | 30.7517 | 1.19250 | ||||||||
\(666\) | −1.95089 | −0.0755954 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −14.8149 | −0.573207 | ||||||||
\(669\) | 13.6569 | 0.528004 | ||||||||
\(670\) | −56.0035 | −2.16360 | ||||||||
\(671\) | −1.39814 | −0.0539746 | ||||||||
\(672\) | 1.23023 | 0.0474573 | ||||||||
\(673\) | 0.669058 | 0.0257903 | 0.0128952 | − | 0.999917i | \(-0.495895\pi\) | ||||
0.0128952 | + | 0.999917i | \(0.495895\pi\) | |||||||
\(674\) | −21.6739 | −0.834846 | ||||||||
\(675\) | −7.94699 | −0.305880 | ||||||||
\(676\) | 22.0114 | 0.846591 | ||||||||
\(677\) | −25.5892 | −0.983471 | −0.491736 | − | 0.870745i | \(-0.663637\pi\) | ||||
−0.491736 | + | 0.870745i | \(0.663637\pi\) | |||||||
\(678\) | −10.9718 | −0.421370 | ||||||||
\(679\) | −13.9617 | −0.535800 | ||||||||
\(680\) | 14.6038 | 0.560032 | ||||||||
\(681\) | −4.14162 | −0.158707 | ||||||||
\(682\) | −0.452675 | −0.0173338 | ||||||||
\(683\) | −19.3182 | −0.739190 | −0.369595 | − | 0.929193i | \(-0.620503\pi\) | ||||
−0.369595 | + | 0.929193i | \(0.620503\pi\) | |||||||
\(684\) | 6.94699 | 0.265625 | ||||||||
\(685\) | −60.9460 | −2.32863 | ||||||||
\(686\) | 15.3613 | 0.586499 | ||||||||
\(687\) | −20.9623 | −0.799760 | ||||||||
\(688\) | −2.42662 | −0.0925140 | ||||||||
\(689\) | −17.0904 | −0.651091 | ||||||||
\(690\) | 3.59819 | 0.136981 | ||||||||
\(691\) | −39.2116 | −1.49168 | −0.745841 | − | 0.666124i | \(-0.767952\pi\) | ||||
−0.745841 | + | 0.666124i | \(0.767952\pi\) | |||||||
\(692\) | 14.3437 | 0.545264 | ||||||||
\(693\) | 0.320090 | 0.0121592 | ||||||||
\(694\) | 9.91653 | 0.376426 | ||||||||
\(695\) | −34.3251 | −1.30202 | ||||||||
\(696\) | −1.00000 | −0.0379049 | ||||||||
\(697\) | −6.04911 | −0.229126 | ||||||||
\(698\) | 11.6107 | 0.439473 | ||||||||
\(699\) | −11.9401 | −0.451616 | ||||||||
\(700\) | 9.77666 | 0.369523 | ||||||||
\(701\) | −25.5634 | −0.965516 | −0.482758 | − | 0.875754i | \(-0.660365\pi\) | ||||
−0.482758 | + | 0.875754i | \(0.660365\pi\) | |||||||
\(702\) | 5.91704 | 0.223324 | ||||||||
\(703\) | 13.5528 | 0.511154 | ||||||||
\(704\) | 0.260186 | 0.00980613 | ||||||||
\(705\) | −9.96615 | −0.375347 | ||||||||
\(706\) | −3.08686 | −0.116175 | ||||||||
\(707\) | −12.3023 | −0.462677 | ||||||||
\(708\) | −0.426620 | −0.0160334 | ||||||||
\(709\) | −37.0999 | −1.39332 | −0.696658 | − | 0.717403i | \(-0.745331\pi\) | ||||
−0.696658 | + | 0.717403i | \(0.745331\pi\) | |||||||
\(710\) | −46.5469 | −1.74688 | ||||||||
\(711\) | 5.02871 | 0.188591 | ||||||||
\(712\) | 10.4279 | 0.390801 | ||||||||
\(713\) | 1.73981 | 0.0651565 | ||||||||
\(714\) | −4.99310 | −0.186862 | ||||||||
\(715\) | 5.53953 | 0.207167 | ||||||||
\(716\) | −16.2371 | −0.606810 | ||||||||
\(717\) | −7.88268 | −0.294384 | ||||||||
\(718\) | 18.1451 | 0.677170 | ||||||||
\(719\) | 17.2907 | 0.644833 | 0.322416 | − | 0.946598i | \(-0.395505\pi\) | ||||
0.322416 | + | 0.946598i | \(0.395505\pi\) | |||||||
\(720\) | 3.59819 | 0.134097 | ||||||||
\(721\) | −10.5111 | −0.391452 | ||||||||
\(722\) | −29.2607 | −1.08897 | ||||||||
\(723\) | 2.22634 | 0.0827984 | ||||||||
\(724\) | 6.80537 | 0.252920 | ||||||||
\(725\) | −7.94699 | −0.295144 | ||||||||
\(726\) | −10.9323 | −0.405736 | ||||||||
\(727\) | −19.3410 | −0.717318 | −0.358659 | − | 0.933469i | \(-0.616766\pi\) | ||||
−0.358659 | + | 0.933469i | \(0.616766\pi\) | |||||||
\(728\) | −7.27935 | −0.269790 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −3.88268 | −0.143704 | ||||||||
\(731\) | 9.84883 | 0.364272 | ||||||||
\(732\) | 5.37361 | 0.198614 | ||||||||
\(733\) | 1.32150 | 0.0488108 | 0.0244054 | − | 0.999702i | \(-0.492231\pi\) | ||||
0.0244054 | + | 0.999702i | \(0.492231\pi\) | |||||||
\(734\) | 26.8359 | 0.990531 | ||||||||
\(735\) | 19.7416 | 0.728179 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 4.04963 | 0.149170 | ||||||||
\(738\) | −1.49042 | −0.0548631 | ||||||||
\(739\) | −40.9741 | −1.50726 | −0.753628 | − | 0.657301i | \(-0.771698\pi\) | ||||
−0.753628 | + | 0.657301i | \(0.771698\pi\) | |||||||
\(740\) | 7.01967 | 0.258048 | ||||||||
\(741\) | −41.1056 | −1.51005 | ||||||||
\(742\) | 3.55332 | 0.130447 | ||||||||
\(743\) | −33.7691 | −1.23887 | −0.619434 | − | 0.785049i | \(-0.712638\pi\) | ||||
−0.619434 | + | 0.785049i | \(0.712638\pi\) | |||||||
\(744\) | 1.73981 | 0.0637847 | ||||||||
\(745\) | 31.5067 | 1.15432 | ||||||||
\(746\) | 17.9404 | 0.656844 | ||||||||
\(747\) | 14.5452 | 0.532180 | ||||||||
\(748\) | −1.05601 | −0.0386114 | ||||||||
\(749\) | 1.42803 | 0.0521791 | ||||||||
\(750\) | 10.6038 | 0.387198 | ||||||||
\(751\) | 0.658994 | 0.0240470 | 0.0120235 | − | 0.999928i | \(-0.496173\pi\) | ||||
0.0120235 | + | 0.999928i | \(0.496173\pi\) | |||||||
\(752\) | 2.76977 | 0.101003 | ||||||||
\(753\) | −24.1095 | −0.878600 | ||||||||
\(754\) | 5.91704 | 0.215486 | ||||||||
\(755\) | −48.9352 | −1.78094 | ||||||||
\(756\) | −1.23023 | −0.0447432 | ||||||||
\(757\) | 28.5833 | 1.03888 | 0.519438 | − | 0.854508i | \(-0.326141\pi\) | ||||
0.519438 | + | 0.854508i | \(0.326141\pi\) | |||||||
\(758\) | −0.913144 | −0.0331669 | ||||||||
\(759\) | −0.260186 | −0.00944416 | ||||||||
\(760\) | −24.9966 | −0.906723 | ||||||||
\(761\) | −24.1159 | −0.874199 | −0.437099 | − | 0.899413i | \(-0.643994\pi\) | ||||
−0.437099 | + | 0.899413i | \(0.643994\pi\) | |||||||
\(762\) | 21.3736 | 0.774284 | ||||||||
\(763\) | −10.5126 | −0.380581 | ||||||||
\(764\) | −10.0739 | −0.364462 | ||||||||
\(765\) | −14.6038 | −0.528003 | ||||||||
\(766\) | 27.2829 | 0.985770 | ||||||||
\(767\) | 2.52433 | 0.0911482 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −23.1676 | −0.835446 | −0.417723 | − | 0.908575i | \(-0.637172\pi\) | ||||
−0.417723 | + | 0.908575i | \(0.637172\pi\) | |||||||
\(770\) | −1.15174 | −0.0415060 | ||||||||
\(771\) | 4.23860 | 0.152649 | ||||||||
\(772\) | −8.10953 | −0.291868 | ||||||||
\(773\) | −10.0241 | −0.360541 | −0.180271 | − | 0.983617i | \(-0.557697\pi\) | ||||
−0.180271 | + | 0.983617i | \(0.557697\pi\) | |||||||
\(774\) | 2.42662 | 0.0872231 | ||||||||
\(775\) | 13.8263 | 0.496655 | ||||||||
\(776\) | 11.3488 | 0.407398 | ||||||||
\(777\) | −2.40005 | −0.0861013 | ||||||||
\(778\) | −24.9054 | −0.892900 | ||||||||
\(779\) | 10.3539 | 0.370968 | ||||||||
\(780\) | −21.2907 | −0.762328 | ||||||||
\(781\) | 3.36582 | 0.120438 | ||||||||
\(782\) | 4.05866 | 0.145137 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | −5.48652 | −0.195947 | ||||||||
\(785\) | 26.9520 | 0.961957 | ||||||||
\(786\) | −20.1542 | −0.718875 | ||||||||
\(787\) | 2.86279 | 0.102047 | 0.0510237 | − | 0.998697i | \(-0.483752\pi\) | ||||
0.0510237 | + | 0.998697i | \(0.483752\pi\) | |||||||
\(788\) | 11.0300 | 0.392926 | ||||||||
\(789\) | 23.5649 | 0.838931 | ||||||||
\(790\) | −18.0943 | −0.643765 | ||||||||
\(791\) | −13.4979 | −0.479930 | ||||||||
\(792\) | −0.260186 | −0.00924531 | ||||||||
\(793\) | −31.7959 | −1.12910 | ||||||||
\(794\) | −36.5966 | −1.29876 | ||||||||
\(795\) | 10.3928 | 0.368594 | ||||||||
\(796\) | −7.93230 | −0.281153 | ||||||||
\(797\) | −53.3899 | −1.89117 | −0.945584 | − | 0.325379i | \(-0.894508\pi\) | ||||
−0.945584 | + | 0.325379i | \(0.894508\pi\) | |||||||
\(798\) | 8.54643 | 0.302540 | ||||||||
\(799\) | −11.2415 | −0.397697 | ||||||||
\(800\) | −7.94699 | −0.280969 | ||||||||
\(801\) | −10.4279 | −0.368450 | ||||||||
\(802\) | 6.97056 | 0.246139 | ||||||||
\(803\) | 0.280757 | 0.00990771 | ||||||||
\(804\) | −15.5643 | −0.548912 | ||||||||
\(805\) | 4.42662 | 0.156018 | ||||||||
\(806\) | −10.2945 | −0.362610 | ||||||||
\(807\) | −10.4374 | −0.367414 | ||||||||
\(808\) | 10.0000 | 0.351799 | ||||||||
\(809\) | −8.89404 | −0.312698 | −0.156349 | − | 0.987702i | \(-0.549972\pi\) | ||||
−0.156349 | + | 0.987702i | \(0.549972\pi\) | |||||||
\(810\) | −3.59819 | −0.126428 | ||||||||
\(811\) | −36.1424 | −1.26913 | −0.634566 | − | 0.772869i | \(-0.718821\pi\) | ||||
−0.634566 | + | 0.772869i | \(0.718821\pi\) | |||||||
\(812\) | −1.23023 | −0.0431728 | ||||||||
\(813\) | −25.4718 | −0.893336 | ||||||||
\(814\) | −0.507594 | −0.0177912 | ||||||||
\(815\) | 34.7861 | 1.21850 | ||||||||
\(816\) | 4.05866 | 0.142082 | ||||||||
\(817\) | −16.8577 | −0.589777 | ||||||||
\(818\) | 22.9578 | 0.802700 | ||||||||
\(819\) | 7.27935 | 0.254361 | ||||||||
\(820\) | 5.36282 | 0.187278 | ||||||||
\(821\) | −17.6491 | −0.615956 | −0.307978 | − | 0.951393i | \(-0.599652\pi\) | ||||
−0.307978 | + | 0.951393i | \(0.599652\pi\) | |||||||
\(822\) | −16.9380 | −0.590779 | ||||||||
\(823\) | −11.0177 | −0.384052 | −0.192026 | − | 0.981390i | \(-0.561506\pi\) | ||||
−0.192026 | + | 0.981390i | \(0.561506\pi\) | |||||||
\(824\) | 8.54394 | 0.297642 | ||||||||
\(825\) | −2.06770 | −0.0719880 | ||||||||
\(826\) | −0.524843 | −0.0182616 | ||||||||
\(827\) | 21.4807 | 0.746956 | 0.373478 | − | 0.927639i | \(-0.378165\pi\) | ||||
0.373478 | + | 0.927639i | \(0.378165\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −38.3284 | −1.33120 | −0.665600 | − | 0.746309i | \(-0.731824\pi\) | ||||
−0.665600 | + | 0.746309i | \(0.731824\pi\) | |||||||
\(830\) | −52.3364 | −1.81662 | ||||||||
\(831\) | −1.93863 | −0.0672502 | ||||||||
\(832\) | 5.91704 | 0.205136 | ||||||||
\(833\) | 22.2679 | 0.771538 | ||||||||
\(834\) | −9.53953 | −0.330327 | ||||||||
\(835\) | −53.3069 | −1.84476 | ||||||||
\(836\) | 1.80751 | 0.0625141 | ||||||||
\(837\) | −1.73981 | −0.0601368 | ||||||||
\(838\) | −18.2512 | −0.630476 | ||||||||
\(839\) | −32.5560 | −1.12396 | −0.561979 | − | 0.827152i | \(-0.689960\pi\) | ||||
−0.561979 | + | 0.827152i | \(0.689960\pi\) | |||||||
\(840\) | 4.42662 | 0.152733 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 25.9897 | 0.895665 | ||||||||
\(843\) | 21.8341 | 0.752006 | ||||||||
\(844\) | 5.76587 | 0.198469 | ||||||||
\(845\) | 79.2011 | 2.72460 | ||||||||
\(846\) | −2.76977 | −0.0952265 | ||||||||
\(847\) | −13.4493 | −0.462123 | ||||||||
\(848\) | −2.88833 | −0.0991857 | ||||||||
\(849\) | −17.4240 | −0.597989 | ||||||||
\(850\) | 32.2542 | 1.10631 | ||||||||
\(851\) | 1.95089 | 0.0668756 | ||||||||
\(852\) | −12.9362 | −0.443187 | ||||||||
\(853\) | 12.3858 | 0.424082 | 0.212041 | − | 0.977261i | \(-0.431989\pi\) | ||||
0.212041 | + | 0.977261i | \(0.431989\pi\) | |||||||
\(854\) | 6.61080 | 0.226217 | ||||||||
\(855\) | 24.9966 | 0.854866 | ||||||||
\(856\) | −1.16078 | −0.0396747 | ||||||||
\(857\) | 5.65833 | 0.193285 | 0.0966424 | − | 0.995319i | \(-0.469190\pi\) | ||||
0.0966424 | + | 0.995319i | \(0.469190\pi\) | |||||||
\(858\) | 1.53953 | 0.0525587 | ||||||||
\(859\) | −48.8675 | −1.66734 | −0.833670 | − | 0.552264i | \(-0.813764\pi\) | ||||
−0.833670 | + | 0.552264i | \(0.813764\pi\) | |||||||
\(860\) | −8.73145 | −0.297740 | ||||||||
\(861\) | −1.83357 | −0.0624878 | ||||||||
\(862\) | −4.08296 | −0.139066 | ||||||||
\(863\) | 37.6019 | 1.27998 | 0.639992 | − | 0.768381i | \(-0.278937\pi\) | ||||
0.639992 | + | 0.768381i | \(0.278937\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 51.6113 | 1.75484 | ||||||||
\(866\) | −8.66646 | −0.294498 | ||||||||
\(867\) | 0.527268 | 0.0179070 | ||||||||
\(868\) | 2.14038 | 0.0726492 | ||||||||
\(869\) | 1.30840 | 0.0443844 | ||||||||
\(870\) | −3.59819 | −0.121990 | ||||||||
\(871\) | 92.0949 | 3.12052 | ||||||||
\(872\) | 8.54519 | 0.289376 | ||||||||
\(873\) | −11.3488 | −0.384099 | ||||||||
\(874\) | −6.94699 | −0.234986 | ||||||||
\(875\) | 13.0452 | 0.441009 | ||||||||
\(876\) | −1.07906 | −0.0364582 | ||||||||
\(877\) | 20.8111 | 0.702740 | 0.351370 | − | 0.936237i | \(-0.385716\pi\) | ||||
0.351370 | + | 0.936237i | \(0.385716\pi\) | |||||||
\(878\) | −17.8336 | −0.601854 | ||||||||
\(879\) | 21.9436 | 0.740140 | ||||||||
\(880\) | 0.936200 | 0.0315593 | ||||||||
\(881\) | 39.5870 | 1.33372 | 0.666859 | − | 0.745184i | \(-0.267638\pi\) | ||||
0.666859 | + | 0.745184i | \(0.267638\pi\) | |||||||
\(882\) | 5.48652 | 0.184741 | ||||||||
\(883\) | 15.8518 | 0.533456 | 0.266728 | − | 0.963772i | \(-0.414057\pi\) | ||||
0.266728 | + | 0.963772i | \(0.414057\pi\) | |||||||
\(884\) | −24.0153 | −0.807721 | ||||||||
\(885\) | −1.53506 | −0.0516005 | ||||||||
\(886\) | −26.3467 | −0.885133 | ||||||||
\(887\) | 16.0471 | 0.538810 | 0.269405 | − | 0.963027i | \(-0.413173\pi\) | ||||
0.269405 | + | 0.963027i | \(0.413173\pi\) | |||||||
\(888\) | 1.95089 | 0.0654675 | ||||||||
\(889\) | 26.2945 | 0.881891 | ||||||||
\(890\) | 37.5215 | 1.25772 | ||||||||
\(891\) | 0.260186 | 0.00871656 | ||||||||
\(892\) | −13.6569 | −0.457265 | ||||||||
\(893\) | 19.2415 | 0.643894 | ||||||||
\(894\) | 8.75626 | 0.292853 | ||||||||
\(895\) | −58.4243 | −1.95291 | ||||||||
\(896\) | −1.23023 | −0.0410992 | ||||||||
\(897\) | −5.91704 | −0.197564 | ||||||||
\(898\) | −9.77718 | −0.326269 | ||||||||
\(899\) | −1.73981 | −0.0580260 | ||||||||
\(900\) | 7.94699 | 0.264900 | ||||||||
\(901\) | 11.7228 | 0.390542 | ||||||||
\(902\) | −0.387787 | −0.0129119 | ||||||||
\(903\) | 2.98531 | 0.0993449 | ||||||||
\(904\) | 10.9718 | 0.364917 | ||||||||
\(905\) | 24.4870 | 0.813977 | ||||||||
\(906\) | −13.5999 | −0.451828 | ||||||||
\(907\) | −50.3850 | −1.67301 | −0.836503 | − | 0.547963i | \(-0.815404\pi\) | ||||
−0.836503 | + | 0.547963i | \(0.815404\pi\) | |||||||
\(908\) | 4.14162 | 0.137445 | ||||||||
\(909\) | −10.0000 | −0.331679 | ||||||||
\(910\) | −26.1925 | −0.868273 | ||||||||
\(911\) | 27.7391 | 0.919037 | 0.459518 | − | 0.888168i | \(-0.348022\pi\) | ||||
0.459518 | + | 0.888168i | \(0.348022\pi\) | |||||||
\(912\) | −6.94699 | −0.230038 | ||||||||
\(913\) | 3.78445 | 0.125247 | ||||||||
\(914\) | −35.8371 | −1.18539 | ||||||||
\(915\) | 19.3353 | 0.639205 | ||||||||
\(916\) | 20.9623 | 0.692612 | ||||||||
\(917\) | −24.7944 | −0.818782 | ||||||||
\(918\) | −4.05866 | −0.133956 | ||||||||
\(919\) | 48.3840 | 1.59604 | 0.798021 | − | 0.602630i | \(-0.205880\pi\) | ||||
0.798021 | + | 0.602630i | \(0.205880\pi\) | |||||||
\(920\) | −3.59819 | −0.118629 | ||||||||
\(921\) | −14.3928 | −0.474258 | ||||||||
\(922\) | 12.3775 | 0.407632 | ||||||||
\(923\) | 76.5440 | 2.51948 | ||||||||
\(924\) | −0.320090 | −0.0105302 | ||||||||
\(925\) | 15.5037 | 0.509758 | ||||||||
\(926\) | 7.31619 | 0.240425 | ||||||||
\(927\) | −8.54394 | −0.280620 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | −26.9976 | −0.885762 | −0.442881 | − | 0.896580i | \(-0.646044\pi\) | ||||
−0.442881 | + | 0.896580i | \(0.646044\pi\) | |||||||
\(930\) | 6.26019 | 0.205280 | ||||||||
\(931\) | −38.1148 | −1.24916 | ||||||||
\(932\) | 11.9401 | 0.391111 | ||||||||
\(933\) | −2.31709 | −0.0758581 | ||||||||
\(934\) | −8.42713 | −0.275744 | ||||||||
\(935\) | −3.79972 | −0.124264 | ||||||||
\(936\) | −5.91704 | −0.193405 | ||||||||
\(937\) | 40.6191 | 1.32697 | 0.663484 | − | 0.748190i | \(-0.269077\pi\) | ||||
0.663484 | + | 0.748190i | \(0.269077\pi\) | |||||||
\(938\) | −19.1478 | −0.625197 | ||||||||
\(939\) | −0.452161 | −0.0147557 | ||||||||
\(940\) | 9.96615 | 0.325060 | ||||||||
\(941\) | 17.9404 | 0.584840 | 0.292420 | − | 0.956290i | \(-0.405540\pi\) | ||||
0.292420 | + | 0.956290i | \(0.405540\pi\) | |||||||
\(942\) | 7.49042 | 0.244051 | ||||||||
\(943\) | 1.49042 | 0.0485348 | ||||||||
\(944\) | 0.426620 | 0.0138853 | ||||||||
\(945\) | −4.42662 | −0.143998 | ||||||||
\(946\) | 0.631373 | 0.0205277 | ||||||||
\(947\) | 17.6721 | 0.574267 | 0.287133 | − | 0.957891i | \(-0.407298\pi\) | ||||
0.287133 | + | 0.957891i | \(0.407298\pi\) | |||||||
\(948\) | −5.02871 | −0.163325 | ||||||||
\(949\) | 6.38486 | 0.207261 | ||||||||
\(950\) | −55.2077 | −1.79117 | ||||||||
\(951\) | −20.7625 | −0.673270 | ||||||||
\(952\) | 4.99310 | 0.161827 | ||||||||
\(953\) | 13.3623 | 0.432848 | 0.216424 | − | 0.976300i | \(-0.430561\pi\) | ||||
0.216424 | + | 0.976300i | \(0.430561\pi\) | |||||||
\(954\) | 2.88833 | 0.0935132 | ||||||||
\(955\) | −36.2479 | −1.17296 | ||||||||
\(956\) | 7.88268 | 0.254944 | ||||||||
\(957\) | 0.260186 | 0.00841062 | ||||||||
\(958\) | −2.15241 | −0.0695413 | ||||||||
\(959\) | −20.8377 | −0.672883 | ||||||||
\(960\) | −3.59819 | −0.116131 | ||||||||
\(961\) | −27.9730 | −0.902356 | ||||||||
\(962\) | −11.5435 | −0.372177 | ||||||||
\(963\) | 1.16078 | 0.0374056 | ||||||||
\(964\) | −2.22634 | −0.0717055 | ||||||||
\(965\) | −29.1797 | −0.939326 | ||||||||
\(966\) | 1.23023 | 0.0395821 | ||||||||
\(967\) | −15.7511 | −0.506522 | −0.253261 | − | 0.967398i | \(-0.581503\pi\) | ||||
−0.253261 | + | 0.967398i | \(0.581503\pi\) | |||||||
\(968\) | 10.9323 | 0.351378 | ||||||||
\(969\) | 28.1955 | 0.905770 | ||||||||
\(970\) | 40.8352 | 1.31114 | ||||||||
\(971\) | −21.5165 | −0.690497 | −0.345248 | − | 0.938511i | \(-0.612205\pi\) | ||||
−0.345248 | + | 0.938511i | \(0.612205\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −11.7359 | −0.376234 | ||||||||
\(974\) | 33.4837 | 1.07289 | ||||||||
\(975\) | −47.0227 | −1.50593 | ||||||||
\(976\) | −5.37361 | −0.172005 | ||||||||
\(977\) | −5.18112 | −0.165759 | −0.0828794 | − | 0.996560i | \(-0.526412\pi\) | ||||
−0.0828794 | + | 0.996560i | \(0.526412\pi\) | |||||||
\(978\) | 9.66765 | 0.309137 | ||||||||
\(979\) | −2.71318 | −0.0867138 | ||||||||
\(980\) | −19.7416 | −0.630621 | ||||||||
\(981\) | −8.54519 | −0.272827 | ||||||||
\(982\) | 0.652958 | 0.0208367 | ||||||||
\(983\) | 4.54270 | 0.144890 | 0.0724448 | − | 0.997372i | \(-0.476920\pi\) | ||||
0.0724448 | + | 0.997372i | \(0.476920\pi\) | |||||||
\(984\) | 1.49042 | 0.0475129 | ||||||||
\(985\) | 39.6879 | 1.26456 | ||||||||
\(986\) | −4.05866 | −0.129254 | ||||||||
\(987\) | −3.40746 | −0.108461 | ||||||||
\(988\) | 41.1056 | 1.30774 | ||||||||
\(989\) | −2.42662 | −0.0771620 | ||||||||
\(990\) | −0.936200 | −0.0297544 | ||||||||
\(991\) | −23.7556 | −0.754621 | −0.377311 | − | 0.926087i | \(-0.623151\pi\) | ||||
−0.377311 | + | 0.926087i | \(0.623151\pi\) | |||||||
\(992\) | −1.73981 | −0.0552391 | ||||||||
\(993\) | −29.3142 | −0.930259 | ||||||||
\(994\) | −15.9146 | −0.504779 | ||||||||
\(995\) | −28.5420 | −0.904841 | ||||||||
\(996\) | −14.5452 | −0.460882 | ||||||||
\(997\) | 25.9278 | 0.821143 | 0.410571 | − | 0.911828i | \(-0.365329\pi\) | ||||
0.410571 | + | 0.911828i | \(0.365329\pi\) | |||||||
\(998\) | −2.14286 | −0.0678312 | ||||||||
\(999\) | −1.95089 | −0.0617234 |
(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 | 4002.2.a.ba.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4002.2.a.ba.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial |