Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,2,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, 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("1859.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(14.8441897358\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.756.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 143) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.60168\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-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 | 0.353553 | − | 0.935414i | \(-0.384973\pi\) | ||||
0.353553 | + | 0.935414i | \(0.384973\pi\) | |||||||
\(3\) | 2.60168 | 1.50208 | 0.751040 | − | 0.660257i | \(-0.229552\pi\) | ||||
0.751040 | + | 0.660257i | \(0.229552\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 3.76873 | 1.68543 | 0.842715 | − | 0.538361i | \(-0.180956\pi\) | ||||
0.842715 | + | 0.538361i | \(0.180956\pi\) | |||||||
\(6\) | 2.60168 | 1.06213 | ||||||||
\(7\) | 0.167055 | 0.0631409 | 0.0315705 | − | 0.999502i | \(-0.489949\pi\) | ||||
0.0315705 | + | 0.999502i | \(0.489949\pi\) | |||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 3.76873 | 1.25624 | ||||||||
\(10\) | 3.76873 | 1.19178 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −2.60168 | −0.751040 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.167055 | 0.0446474 | ||||||||
\(15\) | 9.80504 | 2.53165 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.37041 | 1.05998 | 0.529990 | − | 0.848004i | \(-0.322195\pi\) | ||||
0.529990 | + | 0.848004i | \(0.322195\pi\) | |||||||
\(18\) | 3.76873 | 0.888299 | ||||||||
\(19\) | −3.37041 | −0.773226 | −0.386613 | − | 0.922242i | \(-0.626355\pi\) | ||||
−0.386613 | + | 0.922242i | \(0.626355\pi\) | |||||||
\(20\) | −3.76873 | −0.842715 | ||||||||
\(21\) | 0.434624 | 0.0948427 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −5.20336 | −1.08498 | −0.542488 | − | 0.840064i | \(-0.682517\pi\) | ||||
−0.542488 | + | 0.840064i | \(0.682517\pi\) | |||||||
\(24\) | −7.80504 | −1.59320 | ||||||||
\(25\) | 9.20336 | 1.84067 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.00000 | 0.384900 | ||||||||
\(28\) | −0.167055 | −0.0315705 | ||||||||
\(29\) | 1.93579 | 0.359467 | 0.179734 | − | 0.983715i | \(-0.442476\pi\) | ||||
0.179734 | + | 0.983715i | \(0.442476\pi\) | |||||||
\(30\) | 9.80504 | 1.79015 | ||||||||
\(31\) | 6.86925 | 1.23375 | 0.616877 | − | 0.787060i | \(-0.288398\pi\) | ||||
0.616877 | + | 0.787060i | \(0.288398\pi\) | |||||||
\(32\) | 5.00000 | 0.883883 | ||||||||
\(33\) | 2.60168 | 0.452894 | ||||||||
\(34\) | 4.37041 | 0.749520 | ||||||||
\(35\) | 0.629587 | 0.106420 | ||||||||
\(36\) | −3.76873 | −0.628122 | ||||||||
\(37\) | 8.63798 | 1.42008 | 0.710038 | − | 0.704164i | \(-0.248678\pi\) | ||||
0.710038 | + | 0.704164i | \(0.248678\pi\) | |||||||
\(38\) | −3.37041 | −0.546753 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −11.3062 | −1.78767 | ||||||||
\(41\) | −1.26757 | −0.197961 | −0.0989805 | − | 0.995089i | \(-0.531558\pi\) | ||||
−0.0989805 | + | 0.995089i | \(0.531558\pi\) | |||||||
\(42\) | 0.434624 | 0.0670639 | ||||||||
\(43\) | −7.20336 | −1.09850 | −0.549251 | − | 0.835657i | \(-0.685087\pi\) | ||||
−0.549251 | + | 0.835657i | \(0.685087\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 14.2034 | 2.11731 | ||||||||
\(46\) | −5.20336 | −0.767193 | ||||||||
\(47\) | −10.1391 | −1.47895 | −0.739473 | − | 0.673186i | \(-0.764925\pi\) | ||||
−0.739473 | + | 0.673186i | \(0.764925\pi\) | |||||||
\(48\) | −2.60168 | −0.375520 | ||||||||
\(49\) | −6.97209 | −0.996013 | ||||||||
\(50\) | 9.20336 | 1.30155 | ||||||||
\(51\) | 11.3704 | 1.59218 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.33411 | 0.183254 | 0.0916271 | − | 0.995793i | \(-0.470793\pi\) | ||||
0.0916271 | + | 0.995793i | \(0.470793\pi\) | |||||||
\(54\) | 2.00000 | 0.272166 | ||||||||
\(55\) | 3.76873 | 0.508176 | ||||||||
\(56\) | −0.501166 | −0.0669711 | ||||||||
\(57\) | −8.76873 | −1.16145 | ||||||||
\(58\) | 1.93579 | 0.254182 | ||||||||
\(59\) | 2.13915 | 0.278493 | 0.139247 | − | 0.990258i | \(-0.455532\pi\) | ||||
0.139247 | + | 0.990258i | \(0.455532\pi\) | |||||||
\(60\) | −9.80504 | −1.26582 | ||||||||
\(61\) | −4.80504 | −0.615222 | −0.307611 | − | 0.951512i | \(-0.599530\pi\) | ||||
−0.307611 | + | 0.951512i | \(0.599530\pi\) | |||||||
\(62\) | 6.86925 | 0.872395 | ||||||||
\(63\) | 0.629587 | 0.0793205 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.60168 | 0.320245 | ||||||||
\(67\) | −4.13915 | −0.505677 | −0.252839 | − | 0.967508i | \(-0.581364\pi\) | ||||
−0.252839 | + | 0.967508i | \(0.581364\pi\) | |||||||
\(68\) | −4.37041 | −0.529990 | ||||||||
\(69\) | −13.5375 | −1.62972 | ||||||||
\(70\) | 0.629587 | 0.0752500 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | −11.3062 | −1.33245 | ||||||||
\(73\) | 14.2420 | 1.66690 | 0.833450 | − | 0.552596i | \(-0.186363\pi\) | ||||
0.833450 | + | 0.552596i | \(0.186363\pi\) | |||||||
\(74\) | 8.63798 | 1.00415 | ||||||||
\(75\) | 23.9442 | 2.76484 | ||||||||
\(76\) | 3.37041 | 0.386613 | ||||||||
\(77\) | 0.167055 | 0.0190377 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.5738 | −1.63968 | −0.819839 | − | 0.572595i | \(-0.805937\pi\) | ||||
−0.819839 | + | 0.572595i | \(0.805937\pi\) | |||||||
\(80\) | −3.76873 | −0.421357 | ||||||||
\(81\) | −6.10284 | −0.678094 | ||||||||
\(82\) | −1.26757 | −0.139980 | ||||||||
\(83\) | −10.5738 | −1.16062 | −0.580311 | − | 0.814395i | \(-0.697069\pi\) | ||||
−0.580311 | + | 0.814395i | \(0.697069\pi\) | |||||||
\(84\) | −0.434624 | −0.0474214 | ||||||||
\(85\) | 16.4709 | 1.78652 | ||||||||
\(86\) | −7.20336 | −0.776758 | ||||||||
\(87\) | 5.03630 | 0.539948 | ||||||||
\(88\) | −3.00000 | −0.319801 | ||||||||
\(89\) | 14.3062 | 1.51645 | 0.758227 | − | 0.651990i | \(-0.226066\pi\) | ||||
0.758227 | + | 0.651990i | \(0.226066\pi\) | |||||||
\(90\) | 14.2034 | 1.49717 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.20336 | 0.542488 | ||||||||
\(93\) | 17.8716 | 1.85320 | ||||||||
\(94\) | −10.1391 | −1.04577 | ||||||||
\(95\) | −12.7022 | −1.30322 | ||||||||
\(96\) | 13.0084 | 1.32766 | ||||||||
\(97\) | 3.56538 | 0.362009 | 0.181005 | − | 0.983482i | \(-0.442065\pi\) | ||||
0.181005 | + | 0.983482i | \(0.442065\pi\) | |||||||
\(98\) | −6.97209 | −0.704288 | ||||||||
\(99\) | 3.76873 | 0.378772 | ||||||||
\(100\) | −9.20336 | −0.920336 | ||||||||
\(101\) | −12.0363 | −1.19766 | −0.598828 | − | 0.800877i | \(-0.704367\pi\) | ||||
−0.598828 | + | 0.800877i | \(0.704367\pi\) | |||||||
\(102\) | 11.3704 | 1.12584 | ||||||||
\(103\) | −6.40672 | −0.631273 | −0.315636 | − | 0.948880i | \(-0.602218\pi\) | ||||
−0.315636 | + | 0.948880i | \(0.602218\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.63798 | 0.159851 | ||||||||
\(106\) | 1.33411 | 0.129580 | ||||||||
\(107\) | −13.7045 | −1.32487 | −0.662433 | − | 0.749121i | \(-0.730476\pi\) | ||||
−0.662433 | + | 0.749121i | \(0.730476\pi\) | |||||||
\(108\) | −2.00000 | −0.192450 | ||||||||
\(109\) | −8.84134 | −0.846847 | −0.423423 | − | 0.905932i | \(-0.639172\pi\) | ||||
−0.423423 | + | 0.905932i | \(0.639172\pi\) | |||||||
\(110\) | 3.76873 | 0.359335 | ||||||||
\(111\) | 22.4733 | 2.13307 | ||||||||
\(112\) | −0.167055 | −0.0157852 | ||||||||
\(113\) | 4.56538 | 0.429474 | 0.214737 | − | 0.976672i | \(-0.431110\pi\) | ||||
0.214737 | + | 0.976672i | \(0.431110\pi\) | |||||||
\(114\) | −8.76873 | −0.821267 | ||||||||
\(115\) | −19.6101 | −1.82865 | ||||||||
\(116\) | −1.93579 | −0.179734 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.13915 | 0.196925 | ||||||||
\(119\) | 0.730100 | 0.0669282 | ||||||||
\(120\) | −29.4151 | −2.68522 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −4.80504 | −0.435028 | ||||||||
\(123\) | −3.29781 | −0.297353 | ||||||||
\(124\) | −6.86925 | −0.616877 | ||||||||
\(125\) | 15.8413 | 1.41689 | ||||||||
\(126\) | 0.629587 | 0.0560880 | ||||||||
\(127\) | −1.33178 | −0.118176 | −0.0590882 | − | 0.998253i | \(-0.518819\pi\) | ||||
−0.0590882 | + | 0.998253i | \(0.518819\pi\) | |||||||
\(128\) | −3.00000 | −0.265165 | ||||||||
\(129\) | −18.7408 | −1.65004 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.7045 | 1.19737 | 0.598685 | − | 0.800985i | \(-0.295690\pi\) | ||||
0.598685 | + | 0.800985i | \(0.295690\pi\) | |||||||
\(132\) | −2.60168 | −0.226447 | ||||||||
\(133\) | −0.563045 | −0.0488222 | ||||||||
\(134\) | −4.13915 | −0.357568 | ||||||||
\(135\) | 7.53747 | 0.648722 | ||||||||
\(136\) | −13.1112 | −1.12428 | ||||||||
\(137\) | −13.6403 | −1.16537 | −0.582685 | − | 0.812698i | \(-0.697998\pi\) | ||||
−0.582685 | + | 0.812698i | \(0.697998\pi\) | |||||||
\(138\) | −13.5375 | −1.15239 | ||||||||
\(139\) | 0.869248 | 0.0737286 | 0.0368643 | − | 0.999320i | \(-0.488263\pi\) | ||||
0.0368643 | + | 0.999320i | \(0.488263\pi\) | |||||||
\(140\) | −0.629587 | −0.0532098 | ||||||||
\(141\) | −26.3788 | −2.22150 | ||||||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.76873 | −0.314061 | ||||||||
\(145\) | 7.29548 | 0.605856 | ||||||||
\(146\) | 14.2420 | 1.17868 | ||||||||
\(147\) | −18.1391 | −1.49609 | ||||||||
\(148\) | −8.63798 | −0.710038 | ||||||||
\(149\) | 1.16706 | 0.0956089 | 0.0478044 | − | 0.998857i | \(-0.484778\pi\) | ||||
0.0478044 | + | 0.998857i | \(0.484778\pi\) | |||||||
\(150\) | 23.9442 | 1.95503 | ||||||||
\(151\) | −10.7408 | −0.874076 | −0.437038 | − | 0.899443i | \(-0.643972\pi\) | ||||
−0.437038 | + | 0.899443i | \(0.643972\pi\) | |||||||
\(152\) | 10.1112 | 0.820130 | ||||||||
\(153\) | 16.4709 | 1.33160 | ||||||||
\(154\) | 0.167055 | 0.0134617 | ||||||||
\(155\) | 25.8884 | 2.07940 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.59328 | −0.366584 | −0.183292 | − | 0.983059i | \(-0.558675\pi\) | ||||
−0.183292 | + | 0.983059i | \(0.558675\pi\) | |||||||
\(158\) | −14.5738 | −1.15943 | ||||||||
\(159\) | 3.47093 | 0.275262 | ||||||||
\(160\) | 18.8437 | 1.48972 | ||||||||
\(161\) | −0.869248 | −0.0685063 | ||||||||
\(162\) | −6.10284 | −0.479485 | ||||||||
\(163\) | 11.3425 | 0.888414 | 0.444207 | − | 0.895924i | \(-0.353486\pi\) | ||||
0.444207 | + | 0.895924i | \(0.353486\pi\) | |||||||
\(164\) | 1.26757 | 0.0989805 | ||||||||
\(165\) | 9.80504 | 0.763321 | ||||||||
\(166\) | −10.5738 | −0.820684 | ||||||||
\(167\) | 17.2760 | 1.33685 | 0.668427 | − | 0.743778i | \(-0.266968\pi\) | ||||
0.668427 | + | 0.743778i | \(0.266968\pi\) | |||||||
\(168\) | −1.30387 | −0.100596 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 16.4709 | 1.26326 | ||||||||
\(171\) | −12.7022 | −0.971361 | ||||||||
\(172\) | 7.20336 | 0.549251 | ||||||||
\(173\) | −12.8413 | −0.976309 | −0.488155 | − | 0.872757i | \(-0.662330\pi\) | ||||
−0.488155 | + | 0.872757i | \(0.662330\pi\) | |||||||
\(174\) | 5.03630 | 0.381801 | ||||||||
\(175\) | 1.53747 | 0.116222 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 5.56538 | 0.418319 | ||||||||
\(178\) | 14.3062 | 1.07230 | ||||||||
\(179\) | −4.93579 | −0.368918 | −0.184459 | − | 0.982840i | \(-0.559053\pi\) | ||||
−0.184459 | + | 0.982840i | \(0.559053\pi\) | |||||||
\(180\) | −14.2034 | −1.05866 | ||||||||
\(181\) | 0.637982 | 0.0474208 | 0.0237104 | − | 0.999719i | \(-0.492452\pi\) | ||||
0.0237104 | + | 0.999719i | \(0.492452\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.5012 | −0.924113 | ||||||||
\(184\) | 15.6101 | 1.15079 | ||||||||
\(185\) | 32.5543 | 2.39344 | ||||||||
\(186\) | 17.8716 | 1.31041 | ||||||||
\(187\) | 4.37041 | 0.319596 | ||||||||
\(188\) | 10.1391 | 0.739473 | ||||||||
\(189\) | 0.334110 | 0.0243030 | ||||||||
\(190\) | −12.7022 | −0.921514 | ||||||||
\(191\) | 26.1391 | 1.89136 | 0.945681 | − | 0.325096i | \(-0.105396\pi\) | ||||
0.945681 | + | 0.325096i | \(0.105396\pi\) | |||||||
\(192\) | 18.2118 | 1.31432 | ||||||||
\(193\) | −11.1391 | −0.801813 | −0.400907 | − | 0.916119i | \(-0.631305\pi\) | ||||
−0.400907 | + | 0.916119i | \(0.631305\pi\) | |||||||
\(194\) | 3.56538 | 0.255979 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.97209 | 0.498007 | ||||||||
\(197\) | 15.5375 | 1.10700 | 0.553499 | − | 0.832850i | \(-0.313292\pi\) | ||||
0.553499 | + | 0.832850i | \(0.313292\pi\) | |||||||
\(198\) | 3.76873 | 0.267832 | ||||||||
\(199\) | −11.6766 | −0.827733 | −0.413867 | − | 0.910337i | \(-0.635822\pi\) | ||||
−0.413867 | + | 0.910337i | \(0.635822\pi\) | |||||||
\(200\) | −27.6101 | −1.95233 | ||||||||
\(201\) | −10.7687 | −0.759568 | ||||||||
\(202\) | −12.0363 | −0.846871 | ||||||||
\(203\) | 0.323384 | 0.0226971 | ||||||||
\(204\) | −11.3704 | −0.796088 | ||||||||
\(205\) | −4.77713 | −0.333649 | ||||||||
\(206\) | −6.40672 | −0.446377 | ||||||||
\(207\) | −19.6101 | −1.36299 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.37041 | −0.233136 | ||||||||
\(210\) | 1.63798 | 0.113032 | ||||||||
\(211\) | −4.57377 | −0.314871 | −0.157436 | − | 0.987529i | \(-0.550323\pi\) | ||||
−0.157436 | + | 0.987529i | \(0.550323\pi\) | |||||||
\(212\) | −1.33411 | −0.0916271 | ||||||||
\(213\) | 15.6101 | 1.06958 | ||||||||
\(214\) | −13.7045 | −0.936822 | ||||||||
\(215\) | −27.1475 | −1.85145 | ||||||||
\(216\) | −6.00000 | −0.408248 | ||||||||
\(217\) | 1.14754 | 0.0779003 | ||||||||
\(218\) | −8.84134 | −0.598811 | ||||||||
\(219\) | 37.0531 | 2.50382 | ||||||||
\(220\) | −3.76873 | −0.254088 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 22.4733 | 1.50831 | ||||||||
\(223\) | −9.06421 | −0.606984 | −0.303492 | − | 0.952834i | \(-0.598153\pi\) | ||||
−0.303492 | + | 0.952834i | \(0.598153\pi\) | |||||||
\(224\) | 0.835276 | 0.0558092 | ||||||||
\(225\) | 34.6850 | 2.31233 | ||||||||
\(226\) | 4.56538 | 0.303684 | ||||||||
\(227\) | −13.2034 | −0.876338 | −0.438169 | − | 0.898893i | \(-0.644373\pi\) | ||||
−0.438169 | + | 0.898893i | \(0.644373\pi\) | |||||||
\(228\) | 8.76873 | 0.580724 | ||||||||
\(229\) | 2.02791 | 0.134008 | 0.0670039 | − | 0.997753i | \(-0.478656\pi\) | ||||
0.0670039 | + | 0.997753i | \(0.478656\pi\) | |||||||
\(230\) | −19.6101 | −1.29305 | ||||||||
\(231\) | 0.434624 | 0.0285962 | ||||||||
\(232\) | −5.80737 | −0.381272 | ||||||||
\(233\) | −12.7408 | −0.834679 | −0.417340 | − | 0.908751i | \(-0.637037\pi\) | ||||
−0.417340 | + | 0.908751i | \(0.637037\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −38.2118 | −2.49266 | ||||||||
\(236\) | −2.13915 | −0.139247 | ||||||||
\(237\) | −37.9163 | −2.46293 | ||||||||
\(238\) | 0.730100 | 0.0473254 | ||||||||
\(239\) | 4.07261 | 0.263435 | 0.131717 | − | 0.991287i | \(-0.457951\pi\) | ||||
0.131717 | + | 0.991287i | \(0.457951\pi\) | |||||||
\(240\) | −9.80504 | −0.632912 | ||||||||
\(241\) | −18.9828 | −1.22279 | −0.611395 | − | 0.791325i | \(-0.709392\pi\) | ||||
−0.611395 | + | 0.791325i | \(0.709392\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −21.8776 | −1.40345 | ||||||||
\(244\) | 4.80504 | 0.307611 | ||||||||
\(245\) | −26.2760 | −1.67871 | ||||||||
\(246\) | −3.29781 | −0.210261 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −20.6077 | −1.30859 | ||||||||
\(249\) | −27.5096 | −1.74335 | ||||||||
\(250\) | 15.8413 | 1.00189 | ||||||||
\(251\) | 10.3402 | 0.652666 | 0.326333 | − | 0.945255i | \(-0.394187\pi\) | ||||
0.326333 | + | 0.945255i | \(0.394187\pi\) | |||||||
\(252\) | −0.629587 | −0.0396602 | ||||||||
\(253\) | −5.20336 | −0.327132 | ||||||||
\(254\) | −1.33178 | −0.0835633 | ||||||||
\(255\) | 42.8521 | 2.68350 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | 24.1755 | 1.50802 | 0.754012 | − | 0.656861i | \(-0.228116\pi\) | ||||
0.754012 | + | 0.656861i | \(0.228116\pi\) | |||||||
\(258\) | −18.7408 | −1.16675 | ||||||||
\(259\) | 1.44302 | 0.0896649 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.29548 | 0.451579 | ||||||||
\(262\) | 13.7045 | 0.846668 | ||||||||
\(263\) | −10.7408 | −0.662308 | −0.331154 | − | 0.943577i | \(-0.607438\pi\) | ||||
−0.331154 | + | 0.943577i | \(0.607438\pi\) | |||||||
\(264\) | −7.80504 | −0.480367 | ||||||||
\(265\) | 5.02791 | 0.308862 | ||||||||
\(266\) | −0.563045 | −0.0345225 | ||||||||
\(267\) | 37.2201 | 2.27784 | ||||||||
\(268\) | 4.13915 | 0.252839 | ||||||||
\(269\) | 17.6659 | 1.07711 | 0.538554 | − | 0.842591i | \(-0.318971\pi\) | ||||
0.538554 | + | 0.842591i | \(0.318971\pi\) | |||||||
\(270\) | 7.53747 | 0.458716 | ||||||||
\(271\) | 8.74083 | 0.530967 | 0.265484 | − | 0.964115i | \(-0.414468\pi\) | ||||
0.265484 | + | 0.964115i | \(0.414468\pi\) | |||||||
\(272\) | −4.37041 | −0.264995 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.6403 | −0.824041 | ||||||||
\(275\) | 9.20336 | 0.554983 | ||||||||
\(276\) | 13.5375 | 0.814860 | ||||||||
\(277\) | 29.2118 | 1.75516 | 0.877582 | − | 0.479426i | \(-0.159155\pi\) | ||||
0.877582 | + | 0.479426i | \(0.159155\pi\) | |||||||
\(278\) | 0.869248 | 0.0521340 | ||||||||
\(279\) | 25.8884 | 1.54990 | ||||||||
\(280\) | −1.88876 | −0.112875 | ||||||||
\(281\) | −10.8050 | −0.644574 | −0.322287 | − | 0.946642i | \(-0.604452\pi\) | ||||
−0.322287 | + | 0.946642i | \(0.604452\pi\) | |||||||
\(282\) | −26.3788 | −1.57084 | ||||||||
\(283\) | 10.2397 | 0.608685 | 0.304342 | − | 0.952563i | \(-0.401563\pi\) | ||||
0.304342 | + | 0.952563i | \(0.401563\pi\) | |||||||
\(284\) | −6.00000 | −0.356034 | ||||||||
\(285\) | −33.0470 | −1.95754 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.211754 | −0.0124994 | ||||||||
\(288\) | 18.8437 | 1.11037 | ||||||||
\(289\) | 2.10051 | 0.123560 | ||||||||
\(290\) | 7.29548 | 0.428405 | ||||||||
\(291\) | 9.27596 | 0.543767 | ||||||||
\(292\) | −14.2420 | −0.833450 | ||||||||
\(293\) | 3.96370 | 0.231562 | 0.115781 | − | 0.993275i | \(-0.463063\pi\) | ||||
0.115781 | + | 0.993275i | \(0.463063\pi\) | |||||||
\(294\) | −18.1391 | −1.05790 | ||||||||
\(295\) | 8.06188 | 0.469381 | ||||||||
\(296\) | −25.9139 | −1.50622 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | 1.16706 | 0.0676057 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −23.9442 | −1.38242 | ||||||||
\(301\) | −1.20336 | −0.0693604 | ||||||||
\(302\) | −10.7408 | −0.618065 | ||||||||
\(303\) | −31.3146 | −1.79898 | ||||||||
\(304\) | 3.37041 | 0.193306 | ||||||||
\(305\) | −18.1089 | −1.03691 | ||||||||
\(306\) | 16.4709 | 0.941580 | ||||||||
\(307\) | 14.2397 | 0.812700 | 0.406350 | − | 0.913717i | \(-0.366801\pi\) | ||||
0.406350 | + | 0.913717i | \(0.366801\pi\) | |||||||
\(308\) | −0.167055 | −0.00951885 | ||||||||
\(309\) | −16.6682 | −0.948222 | ||||||||
\(310\) | 25.8884 | 1.47036 | ||||||||
\(311\) | 11.8776 | 0.673519 | 0.336760 | − | 0.941591i | \(-0.390669\pi\) | ||||
0.336760 | + | 0.941591i | \(0.390669\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.89949 | 0.446505 | 0.223253 | − | 0.974761i | \(-0.428332\pi\) | ||||
0.223253 | + | 0.974761i | \(0.428332\pi\) | |||||||
\(314\) | −4.59328 | −0.259214 | ||||||||
\(315\) | 2.37274 | 0.133689 | ||||||||
\(316\) | 14.5738 | 0.819839 | ||||||||
\(317\) | 27.3230 | 1.53461 | 0.767306 | − | 0.641281i | \(-0.221597\pi\) | ||||
0.767306 | + | 0.641281i | \(0.221597\pi\) | |||||||
\(318\) | 3.47093 | 0.194640 | ||||||||
\(319\) | 1.93579 | 0.108383 | ||||||||
\(320\) | 26.3811 | 1.47475 | ||||||||
\(321\) | −35.6548 | −1.99006 | ||||||||
\(322\) | −0.869248 | −0.0484413 | ||||||||
\(323\) | −14.7301 | −0.819605 | ||||||||
\(324\) | 6.10284 | 0.339047 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.3425 | 0.628203 | ||||||||
\(327\) | −23.0023 | −1.27203 | ||||||||
\(328\) | 3.80271 | 0.209969 | ||||||||
\(329\) | −1.69380 | −0.0933821 | ||||||||
\(330\) | 9.80504 | 0.539750 | ||||||||
\(331\) | 4.74083 | 0.260579 | 0.130290 | − | 0.991476i | \(-0.458409\pi\) | ||||
0.130290 | + | 0.991476i | \(0.458409\pi\) | |||||||
\(332\) | 10.5738 | 0.580311 | ||||||||
\(333\) | 32.5543 | 1.78396 | ||||||||
\(334\) | 17.2760 | 0.945299 | ||||||||
\(335\) | −15.5993 | −0.852283 | ||||||||
\(336\) | −0.434624 | −0.0237107 | ||||||||
\(337\) | −32.4430 | −1.76728 | −0.883642 | − | 0.468163i | \(-0.844916\pi\) | ||||
−0.883642 | + | 0.468163i | \(0.844916\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.8776 | 0.645105 | ||||||||
\(340\) | −16.4709 | −0.893261 | ||||||||
\(341\) | 6.86925 | 0.371991 | ||||||||
\(342\) | −12.7022 | −0.686856 | ||||||||
\(343\) | −2.33411 | −0.126030 | ||||||||
\(344\) | 21.6101 | 1.16514 | ||||||||
\(345\) | −51.0191 | −2.74678 | ||||||||
\(346\) | −12.8413 | −0.690355 | ||||||||
\(347\) | −11.8329 | −0.635226 | −0.317613 | − | 0.948220i | \(-0.602881\pi\) | ||||
−0.317613 | + | 0.948220i | \(0.602881\pi\) | |||||||
\(348\) | −5.03630 | −0.269974 | ||||||||
\(349\) | 30.0000 | 1.60586 | 0.802932 | − | 0.596071i | \(-0.203272\pi\) | ||||
0.802932 | + | 0.596071i | \(0.203272\pi\) | |||||||
\(350\) | 1.53747 | 0.0821812 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.00000 | 0.266501 | ||||||||
\(353\) | −10.2034 | −0.543070 | −0.271535 | − | 0.962429i | \(-0.587531\pi\) | ||||
−0.271535 | + | 0.962429i | \(0.587531\pi\) | |||||||
\(354\) | 5.56538 | 0.295796 | ||||||||
\(355\) | 22.6124 | 1.20014 | ||||||||
\(356\) | −14.3062 | −0.758227 | ||||||||
\(357\) | 1.89949 | 0.100531 | ||||||||
\(358\) | −4.93579 | −0.260865 | ||||||||
\(359\) | −13.5375 | −0.714480 | −0.357240 | − | 0.934013i | \(-0.616282\pi\) | ||||
−0.357240 | + | 0.934013i | \(0.616282\pi\) | |||||||
\(360\) | −42.6101 | −2.24575 | ||||||||
\(361\) | −7.64031 | −0.402122 | ||||||||
\(362\) | 0.637982 | 0.0335316 | ||||||||
\(363\) | 2.60168 | 0.136553 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 53.6743 | 2.80944 | ||||||||
\(366\) | −12.5012 | −0.653446 | ||||||||
\(367\) | −11.1475 | −0.581897 | −0.290949 | − | 0.956739i | \(-0.593971\pi\) | ||||
−0.290949 | + | 0.956739i | \(0.593971\pi\) | |||||||
\(368\) | 5.20336 | 0.271244 | ||||||||
\(369\) | −4.77713 | −0.248687 | ||||||||
\(370\) | 32.5543 | 1.69242 | ||||||||
\(371\) | 0.222870 | 0.0115708 | ||||||||
\(372\) | −17.8716 | −0.926598 | ||||||||
\(373\) | −27.3123 | −1.41418 | −0.707088 | − | 0.707126i | \(-0.749991\pi\) | ||||
−0.707088 | + | 0.707126i | \(0.749991\pi\) | |||||||
\(374\) | 4.37041 | 0.225989 | ||||||||
\(375\) | 41.2141 | 2.12829 | ||||||||
\(376\) | 30.4174 | 1.56866 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.334110 | 0.0171848 | ||||||||
\(379\) | 18.4067 | 0.945490 | 0.472745 | − | 0.881199i | \(-0.343263\pi\) | ||||
0.472745 | + | 0.881199i | \(0.343263\pi\) | |||||||
\(380\) | 12.7022 | 0.651609 | ||||||||
\(381\) | −3.46486 | −0.177510 | ||||||||
\(382\) | 26.1391 | 1.33740 | ||||||||
\(383\) | −25.8716 | −1.32198 | −0.660988 | − | 0.750397i | \(-0.729863\pi\) | ||||
−0.660988 | + | 0.750397i | \(0.729863\pi\) | |||||||
\(384\) | −7.80504 | −0.398299 | ||||||||
\(385\) | 0.629587 | 0.0320867 | ||||||||
\(386\) | −11.1391 | −0.566968 | ||||||||
\(387\) | −27.1475 | −1.37999 | ||||||||
\(388\) | −3.56538 | −0.181005 | ||||||||
\(389\) | 20.7153 | 1.05030 | 0.525152 | − | 0.851008i | \(-0.324008\pi\) | ||||
0.525152 | + | 0.851008i | \(0.324008\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.7408 | −1.15005 | ||||||||
\(392\) | 20.9163 | 1.05643 | ||||||||
\(393\) | 35.6548 | 1.79855 | ||||||||
\(394\) | 15.5375 | 0.782766 | ||||||||
\(395\) | −54.9247 | −2.76356 | ||||||||
\(396\) | −3.76873 | −0.189386 | ||||||||
\(397\) | −21.5822 | −1.08318 | −0.541589 | − | 0.840643i | \(-0.682177\pi\) | ||||
−0.541589 | + | 0.840643i | \(0.682177\pi\) | |||||||
\(398\) | −11.6766 | −0.585296 | ||||||||
\(399\) | −1.46486 | −0.0733348 | ||||||||
\(400\) | −9.20336 | −0.460168 | ||||||||
\(401\) | 0.203358 | 0.0101552 | 0.00507761 | − | 0.999987i | \(-0.498384\pi\) | ||||
0.00507761 | + | 0.999987i | \(0.498384\pi\) | |||||||
\(402\) | −10.7687 | −0.537096 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 12.0363 | 0.598828 | ||||||||
\(405\) | −23.0000 | −1.14288 | ||||||||
\(406\) | 0.323384 | 0.0160493 | ||||||||
\(407\) | 8.63798 | 0.428169 | ||||||||
\(408\) | −34.1112 | −1.68876 | ||||||||
\(409\) | 0.0921180 | 0.00455494 | 0.00227747 | − | 0.999997i | \(-0.499275\pi\) | ||||
0.00227747 | + | 0.999997i | \(0.499275\pi\) | |||||||
\(410\) | −4.77713 | −0.235926 | ||||||||
\(411\) | −35.4877 | −1.75048 | ||||||||
\(412\) | 6.40672 | 0.315636 | ||||||||
\(413\) | 0.357356 | 0.0175843 | ||||||||
\(414\) | −19.6101 | −0.963783 | ||||||||
\(415\) | −39.8497 | −1.95615 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.26150 | 0.110746 | ||||||||
\(418\) | −3.37041 | −0.164852 | ||||||||
\(419\) | 10.1284 | 0.494806 | 0.247403 | − | 0.968913i | \(-0.420423\pi\) | ||||
0.247403 | + | 0.968913i | \(0.420423\pi\) | |||||||
\(420\) | −1.63798 | −0.0799253 | ||||||||
\(421\) | −6.58217 | −0.320795 | −0.160398 | − | 0.987052i | \(-0.551278\pi\) | ||||
−0.160398 | + | 0.987052i | \(0.551278\pi\) | |||||||
\(422\) | −4.57377 | −0.222648 | ||||||||
\(423\) | −38.2118 | −1.85792 | ||||||||
\(424\) | −4.00233 | −0.194370 | ||||||||
\(425\) | 40.2225 | 1.95108 | ||||||||
\(426\) | 15.6101 | 0.756311 | ||||||||
\(427\) | −0.802706 | −0.0388457 | ||||||||
\(428\) | 13.7045 | 0.662433 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −27.1475 | −1.30917 | ||||||||
\(431\) | 17.4988 | 0.842889 | 0.421445 | − | 0.906854i | \(-0.361523\pi\) | ||||
0.421445 | + | 0.906854i | \(0.361523\pi\) | |||||||
\(432\) | −2.00000 | −0.0962250 | ||||||||
\(433\) | −8.69380 | −0.417797 | −0.208899 | − | 0.977937i | \(-0.566988\pi\) | ||||
−0.208899 | + | 0.977937i | \(0.566988\pi\) | |||||||
\(434\) | 1.14754 | 0.0550838 | ||||||||
\(435\) | 18.9805 | 0.910045 | ||||||||
\(436\) | 8.84134 | 0.423423 | ||||||||
\(437\) | 17.5375 | 0.838931 | ||||||||
\(438\) | 37.0531 | 1.77047 | ||||||||
\(439\) | −24.5738 | −1.17284 | −0.586421 | − | 0.810006i | \(-0.699464\pi\) | ||||
−0.586421 | + | 0.810006i | \(0.699464\pi\) | |||||||
\(440\) | −11.3062 | −0.539002 | ||||||||
\(441\) | −26.2760 | −1.25124 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.2699 | −0.820518 | −0.410259 | − | 0.911969i | \(-0.634562\pi\) | ||||
−0.410259 | + | 0.911969i | \(0.634562\pi\) | |||||||
\(444\) | −22.4733 | −1.06653 | ||||||||
\(445\) | 53.9163 | 2.55588 | ||||||||
\(446\) | −9.06421 | −0.429203 | ||||||||
\(447\) | 3.03630 | 0.143612 | ||||||||
\(448\) | 1.16939 | 0.0552483 | ||||||||
\(449\) | 16.3230 | 0.770330 | 0.385165 | − | 0.922848i | \(-0.374145\pi\) | ||||
0.385165 | + | 0.922848i | \(0.374145\pi\) | |||||||
\(450\) | 34.6850 | 1.63507 | ||||||||
\(451\) | −1.26757 | −0.0596875 | ||||||||
\(452\) | −4.56538 | −0.214737 | ||||||||
\(453\) | −27.9442 | −1.31293 | ||||||||
\(454\) | −13.2034 | −0.619664 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 26.3062 | 1.23190 | ||||||||
\(457\) | 21.4174 | 1.00187 | 0.500933 | − | 0.865486i | \(-0.332990\pi\) | ||||
0.500933 | + | 0.865486i | \(0.332990\pi\) | |||||||
\(458\) | 2.02791 | 0.0947579 | ||||||||
\(459\) | 8.74083 | 0.407987 | ||||||||
\(460\) | 19.6101 | 0.914324 | ||||||||
\(461\) | −17.8074 | −0.829372 | −0.414686 | − | 0.909965i | \(-0.636109\pi\) | ||||
−0.414686 | + | 0.909965i | \(0.636109\pi\) | |||||||
\(462\) | 0.434624 | 0.0202205 | ||||||||
\(463\) | 4.80271 | 0.223201 | 0.111600 | − | 0.993753i | \(-0.464402\pi\) | ||||
0.111600 | + | 0.993753i | \(0.464402\pi\) | |||||||
\(464\) | −1.93579 | −0.0898668 | ||||||||
\(465\) | 67.3532 | 3.12343 | ||||||||
\(466\) | −12.7408 | −0.590207 | ||||||||
\(467\) | −2.80737 | −0.129910 | −0.0649548 | − | 0.997888i | \(-0.520690\pi\) | ||||
−0.0649548 | + | 0.997888i | \(0.520690\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.691466 | −0.0319289 | ||||||||
\(470\) | −38.2118 | −1.76258 | ||||||||
\(471\) | −11.9502 | −0.550638 | ||||||||
\(472\) | −6.41744 | −0.295387 | ||||||||
\(473\) | −7.20336 | −0.331211 | ||||||||
\(474\) | −37.9163 | −1.74155 | ||||||||
\(475\) | −31.0191 | −1.42325 | ||||||||
\(476\) | −0.730100 | −0.0334641 | ||||||||
\(477\) | 5.02791 | 0.230212 | ||||||||
\(478\) | 4.07261 | 0.186277 | ||||||||
\(479\) | 11.8329 | 0.540661 | 0.270331 | − | 0.962768i | \(-0.412867\pi\) | ||||
0.270331 | + | 0.962768i | \(0.412867\pi\) | |||||||
\(480\) | 49.0252 | 2.23768 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −18.9828 | −0.864644 | ||||||||
\(483\) | −2.26150 | −0.102902 | ||||||||
\(484\) | −1.00000 | −0.0454545 | ||||||||
\(485\) | 13.4370 | 0.610141 | ||||||||
\(486\) | −21.8776 | −0.992390 | ||||||||
\(487\) | −16.4174 | −0.743945 | −0.371973 | − | 0.928244i | \(-0.621318\pi\) | ||||
−0.371973 | + | 0.928244i | \(0.621318\pi\) | |||||||
\(488\) | 14.4151 | 0.652541 | ||||||||
\(489\) | 29.5096 | 1.33447 | ||||||||
\(490\) | −26.2760 | −1.18703 | ||||||||
\(491\) | 7.83294 | 0.353496 | 0.176748 | − | 0.984256i | \(-0.443442\pi\) | ||||
0.176748 | + | 0.984256i | \(0.443442\pi\) | |||||||
\(492\) | 3.29781 | 0.148677 | ||||||||
\(493\) | 8.46020 | 0.381028 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.2034 | 0.638393 | ||||||||
\(496\) | −6.86925 | −0.308438 | ||||||||
\(497\) | 1.00233 | 0.0449607 | ||||||||
\(498\) | −27.5096 | −1.23273 | ||||||||
\(499\) | 12.2722 | 0.549381 | 0.274690 | − | 0.961533i | \(-0.411425\pi\) | ||||
0.274690 | + | 0.961533i | \(0.411425\pi\) | |||||||
\(500\) | −15.8413 | −0.708446 | ||||||||
\(501\) | 44.9465 | 2.00806 | ||||||||
\(502\) | 10.3402 | 0.461505 | ||||||||
\(503\) | 1.10891 | 0.0494438 | 0.0247219 | − | 0.999694i | \(-0.492130\pi\) | ||||
0.0247219 | + | 0.999694i | \(0.492130\pi\) | |||||||
\(504\) | −1.88876 | −0.0841320 | ||||||||
\(505\) | −45.3616 | −2.01857 | ||||||||
\(506\) | −5.20336 | −0.231317 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.33178 | 0.0590882 | ||||||||
\(509\) | −23.8692 | −1.05799 | −0.528993 | − | 0.848626i | \(-0.677430\pi\) | ||||
−0.528993 | + | 0.848626i | \(0.677430\pi\) | |||||||
\(510\) | 42.8521 | 1.89752 | ||||||||
\(511\) | 2.37920 | 0.105250 | ||||||||
\(512\) | −11.0000 | −0.486136 | ||||||||
\(513\) | −6.74083 | −0.297615 | ||||||||
\(514\) | 24.1755 | 1.06633 | ||||||||
\(515\) | −24.1452 | −1.06397 | ||||||||
\(516\) | 18.7408 | 0.825019 | ||||||||
\(517\) | −10.1391 | −0.445919 | ||||||||
\(518\) | 1.44302 | 0.0634026 | ||||||||
\(519\) | −33.4090 | −1.46649 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.3318 | 0.803130 | 0.401565 | − | 0.915831i | \(-0.368466\pi\) | ||||
0.401565 | + | 0.915831i | \(0.368466\pi\) | |||||||
\(522\) | 7.29548 | 0.319314 | ||||||||
\(523\) | −10.4407 | −0.456539 | −0.228270 | − | 0.973598i | \(-0.573307\pi\) | ||||
−0.228270 | + | 0.973598i | \(0.573307\pi\) | |||||||
\(524\) | −13.7045 | −0.598685 | ||||||||
\(525\) | 4.00000 | 0.174574 | ||||||||
\(526\) | −10.7408 | −0.468322 | ||||||||
\(527\) | 30.0215 | 1.30776 | ||||||||
\(528\) | −2.60168 | −0.113224 | ||||||||
\(529\) | 4.07494 | 0.177171 | ||||||||
\(530\) | 5.02791 | 0.218398 | ||||||||
\(531\) | 8.06188 | 0.349856 | ||||||||
\(532\) | 0.563045 | 0.0244111 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 37.2201 | 1.61067 | ||||||||
\(535\) | −51.6487 | −2.23297 | ||||||||
\(536\) | 12.4174 | 0.536352 | ||||||||
\(537\) | −12.8413 | −0.554145 | ||||||||
\(538\) | 17.6659 | 0.761631 | ||||||||
\(539\) | −6.97209 | −0.300309 | ||||||||
\(540\) | −7.53747 | −0.324361 | ||||||||
\(541\) | −11.0554 | −0.475310 | −0.237655 | − | 0.971350i | \(-0.576379\pi\) | ||||
−0.237655 | + | 0.971350i | \(0.576379\pi\) | |||||||
\(542\) | 8.74083 | 0.375451 | ||||||||
\(543\) | 1.65983 | 0.0712299 | ||||||||
\(544\) | 21.8521 | 0.936900 | ||||||||
\(545\) | −33.3207 | −1.42730 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.3532 | 1.08403 | 0.542013 | − | 0.840370i | \(-0.317662\pi\) | ||||
0.542013 | + | 0.840370i | \(0.317662\pi\) | |||||||
\(548\) | 13.6403 | 0.582685 | ||||||||
\(549\) | −18.1089 | −0.772869 | ||||||||
\(550\) | 9.20336 | 0.392433 | ||||||||
\(551\) | −6.52441 | −0.277949 | ||||||||
\(552\) | 40.6124 | 1.72858 | ||||||||
\(553\) | −2.43462 | −0.103531 | ||||||||
\(554\) | 29.2118 | 1.24109 | ||||||||
\(555\) | 84.6957 | 3.59513 | ||||||||
\(556\) | −0.869248 | −0.0368643 | ||||||||
\(557\) | 20.3425 | 0.861940 | 0.430970 | − | 0.902366i | \(-0.358172\pi\) | ||||
0.430970 | + | 0.902366i | \(0.358172\pi\) | |||||||
\(558\) | 25.8884 | 1.09594 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.629587 | −0.0266049 | ||||||||
\(561\) | 11.3704 | 0.480059 | ||||||||
\(562\) | −10.8050 | −0.455783 | ||||||||
\(563\) | −6.77480 | −0.285524 | −0.142762 | − | 0.989757i | \(-0.545598\pi\) | ||||
−0.142762 | + | 0.989757i | \(0.545598\pi\) | |||||||
\(564\) | 26.3788 | 1.11075 | ||||||||
\(565\) | 17.2057 | 0.723849 | ||||||||
\(566\) | 10.2397 | 0.430405 | ||||||||
\(567\) | −1.01951 | −0.0428155 | ||||||||
\(568\) | −18.0000 | −0.755263 | ||||||||
\(569\) | 16.8739 | 0.707391 | 0.353696 | − | 0.935361i | \(-0.384925\pi\) | ||||
0.353696 | + | 0.935361i | \(0.384925\pi\) | |||||||
\(570\) | −33.0470 | −1.38419 | ||||||||
\(571\) | 44.9973 | 1.88308 | 0.941539 | − | 0.336905i | \(-0.109380\pi\) | ||||
0.941539 | + | 0.336905i | \(0.109380\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 68.0057 | 2.84098 | ||||||||
\(574\) | −0.211754 | −0.00883844 | ||||||||
\(575\) | −47.8884 | −1.99708 | ||||||||
\(576\) | 26.3811 | 1.09921 | ||||||||
\(577\) | −19.5119 | −0.812291 | −0.406145 | − | 0.913808i | \(-0.633127\pi\) | ||||
−0.406145 | + | 0.913808i | \(0.633127\pi\) | |||||||
\(578\) | 2.10051 | 0.0873698 | ||||||||
\(579\) | −28.9805 | −1.20439 | ||||||||
\(580\) | −7.29548 | −0.302928 | ||||||||
\(581\) | −1.76640 | −0.0732828 | ||||||||
\(582\) | 9.27596 | 0.384501 | ||||||||
\(583\) | 1.33411 | 0.0552532 | ||||||||
\(584\) | −42.7260 | −1.76801 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.96370 | 0.163739 | ||||||||
\(587\) | 16.6789 | 0.688414 | 0.344207 | − | 0.938894i | \(-0.388148\pi\) | ||||
0.344207 | + | 0.938894i | \(0.388148\pi\) | |||||||
\(588\) | 18.1391 | 0.748046 | ||||||||
\(589\) | −23.1522 | −0.953970 | ||||||||
\(590\) | 8.06188 | 0.331902 | ||||||||
\(591\) | 40.4235 | 1.66280 | ||||||||
\(592\) | −8.63798 | −0.355019 | ||||||||
\(593\) | −29.4128 | −1.20784 | −0.603919 | − | 0.797046i | \(-0.706395\pi\) | ||||
−0.603919 | + | 0.797046i | \(0.706395\pi\) | |||||||
\(594\) | 2.00000 | 0.0820610 | ||||||||
\(595\) | 2.75155 | 0.112803 | ||||||||
\(596\) | −1.16706 | −0.0478044 | ||||||||
\(597\) | −30.3788 | −1.24332 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.12842 | 0.250400 | 0.125200 | − | 0.992131i | \(-0.460043\pi\) | ||||
0.125200 | + | 0.992131i | \(0.460043\pi\) | |||||||
\(600\) | −71.8326 | −2.93255 | ||||||||
\(601\) | 25.0061 | 1.02002 | 0.510009 | − | 0.860169i | \(-0.329642\pi\) | ||||
0.510009 | + | 0.860169i | \(0.329642\pi\) | |||||||
\(602\) | −1.20336 | −0.0490452 | ||||||||
\(603\) | −15.5993 | −0.635255 | ||||||||
\(604\) | 10.7408 | 0.437038 | ||||||||
\(605\) | 3.76873 | 0.153221 | ||||||||
\(606\) | −31.3146 | −1.27207 | ||||||||
\(607\) | 32.4407 | 1.31673 | 0.658363 | − | 0.752700i | \(-0.271249\pi\) | ||||
0.658363 | + | 0.752700i | \(0.271249\pi\) | |||||||
\(608\) | −16.8521 | −0.683442 | ||||||||
\(609\) | 0.841340 | 0.0340928 | ||||||||
\(610\) | −18.1089 | −0.733208 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −16.4709 | −0.665798 | ||||||||
\(613\) | −16.5714 | −0.669314 | −0.334657 | − | 0.942340i | \(-0.608620\pi\) | ||||
−0.334657 | + | 0.942340i | \(0.608620\pi\) | |||||||
\(614\) | 14.2397 | 0.574666 | ||||||||
\(615\) | −12.4286 | −0.501168 | ||||||||
\(616\) | −0.501166 | −0.0201925 | ||||||||
\(617\) | −17.8692 | −0.719389 | −0.359694 | − | 0.933070i | \(-0.617119\pi\) | ||||
−0.359694 | + | 0.933070i | \(0.617119\pi\) | |||||||
\(618\) | −16.6682 | −0.670494 | ||||||||
\(619\) | −27.4151 | −1.10191 | −0.550953 | − | 0.834536i | \(-0.685736\pi\) | ||||
−0.550953 | + | 0.834536i | \(0.685736\pi\) | |||||||
\(620\) | −25.8884 | −1.03970 | ||||||||
\(621\) | −10.4067 | −0.417607 | ||||||||
\(622\) | 11.8776 | 0.476250 | ||||||||
\(623\) | 2.38993 | 0.0957503 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.6850 | 0.547400 | ||||||||
\(626\) | 7.89949 | 0.315727 | ||||||||
\(627\) | −8.76873 | −0.350190 | ||||||||
\(628\) | 4.59328 | 0.183292 | ||||||||
\(629\) | 37.7516 | 1.50525 | ||||||||
\(630\) | 2.37274 | 0.0945324 | ||||||||
\(631\) | 6.54586 | 0.260587 | 0.130293 | − | 0.991475i | \(-0.458408\pi\) | ||||
0.130293 | + | 0.991475i | \(0.458408\pi\) | |||||||
\(632\) | 43.7213 | 1.73914 | ||||||||
\(633\) | −11.8995 | −0.472962 | ||||||||
\(634\) | 27.3230 | 1.08513 | ||||||||
\(635\) | −5.01912 | −0.199178 | ||||||||
\(636\) | −3.47093 | −0.137631 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.93579 | 0.0766386 | ||||||||
\(639\) | 22.6124 | 0.894533 | ||||||||
\(640\) | −11.3062 | −0.446917 | ||||||||
\(641\) | 2.07494 | 0.0819551 | 0.0409775 | − | 0.999160i | \(-0.486953\pi\) | ||||
0.0409775 | + | 0.999160i | \(0.486953\pi\) | |||||||
\(642\) | −35.6548 | −1.40718 | ||||||||
\(643\) | −12.2676 | −0.483786 | −0.241893 | − | 0.970303i | \(-0.577768\pi\) | ||||
−0.241893 | + | 0.970303i | \(0.577768\pi\) | |||||||
\(644\) | 0.869248 | 0.0342532 | ||||||||
\(645\) | −70.6292 | −2.78102 | ||||||||
\(646\) | −14.7301 | −0.579548 | ||||||||
\(647\) | 47.0871 | 1.85118 | 0.925592 | − | 0.378523i | \(-0.123568\pi\) | ||||
0.925592 | + | 0.378523i | \(0.123568\pi\) | |||||||
\(648\) | 18.3085 | 0.719227 | ||||||||
\(649\) | 2.13915 | 0.0839689 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.98554 | 0.117013 | ||||||||
\(652\) | −11.3425 | −0.444207 | ||||||||
\(653\) | −21.1028 | −0.825818 | −0.412909 | − | 0.910772i | \(-0.635487\pi\) | ||||
−0.412909 | + | 0.910772i | \(0.635487\pi\) | |||||||
\(654\) | −23.0023 | −0.899462 | ||||||||
\(655\) | 51.6487 | 2.01808 | ||||||||
\(656\) | 1.26757 | 0.0494902 | ||||||||
\(657\) | 53.6743 | 2.09403 | ||||||||
\(658\) | −1.69380 | −0.0660311 | ||||||||
\(659\) | −18.3895 | −0.716355 | −0.358177 | − | 0.933654i | \(-0.616602\pi\) | ||||
−0.358177 | + | 0.933654i | \(0.616602\pi\) | |||||||
\(660\) | −9.80504 | −0.381661 | ||||||||
\(661\) | 16.6938 | 0.649313 | 0.324657 | − | 0.945832i | \(-0.394751\pi\) | ||||
0.324657 | + | 0.945832i | \(0.394751\pi\) | |||||||
\(662\) | 4.74083 | 0.184257 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 31.7213 | 1.23103 | ||||||||
\(665\) | −2.12197 | −0.0822864 | ||||||||
\(666\) | 32.5543 | 1.26145 | ||||||||
\(667\) | −10.0726 | −0.390013 | ||||||||
\(668\) | −17.2760 | −0.668427 | ||||||||
\(669\) | −23.5822 | −0.911739 | ||||||||
\(670\) | −15.5993 | −0.602655 | ||||||||
\(671\) | −4.80504 | −0.185496 | ||||||||
\(672\) | 2.17312 | 0.0838299 | ||||||||
\(673\) | 29.6185 | 1.14171 | 0.570854 | − | 0.821052i | \(-0.306612\pi\) | ||||
0.570854 | + | 0.821052i | \(0.306612\pi\) | |||||||
\(674\) | −32.4430 | −1.24966 | ||||||||
\(675\) | 18.4067 | 0.708475 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.6124 | −0.869065 | −0.434533 | − | 0.900656i | \(-0.643086\pi\) | ||||
−0.434533 | + | 0.900656i | \(0.643086\pi\) | |||||||
\(678\) | 11.8776 | 0.456158 | ||||||||
\(679\) | 0.595615 | 0.0228576 | ||||||||
\(680\) | −49.4128 | −1.89489 | ||||||||
\(681\) | −34.3509 | −1.31633 | ||||||||
\(682\) | 6.86925 | 0.263037 | ||||||||
\(683\) | 33.1429 | 1.26818 | 0.634089 | − | 0.773260i | \(-0.281375\pi\) | ||||
0.634089 | + | 0.773260i | \(0.281375\pi\) | |||||||
\(684\) | 12.7022 | 0.485680 | ||||||||
\(685\) | −51.4067 | −1.96415 | ||||||||
\(686\) | −2.33411 | −0.0891167 | ||||||||
\(687\) | 5.27596 | 0.201291 | ||||||||
\(688\) | 7.20336 | 0.274625 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −51.0191 | −1.94226 | ||||||||
\(691\) | 16.2057 | 0.616493 | 0.308247 | − | 0.951306i | \(-0.400258\pi\) | ||||
0.308247 | + | 0.951306i | \(0.400258\pi\) | |||||||
\(692\) | 12.8413 | 0.488155 | ||||||||
\(693\) | 0.629587 | 0.0239160 | ||||||||
\(694\) | −11.8329 | −0.449172 | ||||||||
\(695\) | 3.27596 | 0.124264 | ||||||||
\(696\) | −15.1089 | −0.572702 | ||||||||
\(697\) | −5.53980 | −0.209835 | ||||||||
\(698\) | 30.0000 | 1.13552 | ||||||||
\(699\) | −33.1475 | −1.25376 | ||||||||
\(700\) | −1.53747 | −0.0581109 | ||||||||
\(701\) | 16.7855 | 0.633981 | 0.316990 | − | 0.948429i | \(-0.397328\pi\) | ||||
0.316990 | + | 0.948429i | \(0.397328\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.1136 | −1.09804 | ||||||||
\(704\) | 7.00000 | 0.263822 | ||||||||
\(705\) | −99.4147 | −3.74418 | ||||||||
\(706\) | −10.2034 | −0.384008 | ||||||||
\(707\) | −2.01073 | −0.0756212 | ||||||||
\(708\) | −5.56538 | −0.209160 | ||||||||
\(709\) | 27.6292 | 1.03764 | 0.518818 | − | 0.854885i | \(-0.326372\pi\) | ||||
0.518818 | + | 0.854885i | \(0.326372\pi\) | |||||||
\(710\) | 22.6124 | 0.848628 | ||||||||
\(711\) | −54.9247 | −2.05984 | ||||||||
\(712\) | −42.9186 | −1.60844 | ||||||||
\(713\) | −35.7432 | −1.33859 | ||||||||
\(714\) | 1.89949 | 0.0710865 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.93579 | 0.184459 | ||||||||
\(717\) | 10.5956 | 0.395700 | ||||||||
\(718\) | −13.5375 | −0.505214 | ||||||||
\(719\) | 9.40905 | 0.350898 | 0.175449 | − | 0.984488i | \(-0.443862\pi\) | ||||
0.175449 | + | 0.984488i | \(0.443862\pi\) | |||||||
\(720\) | −14.2034 | −0.529328 | ||||||||
\(721\) | −1.07028 | −0.0398591 | ||||||||
\(722\) | −7.64031 | −0.284343 | ||||||||
\(723\) | −49.3872 | −1.83673 | ||||||||
\(724\) | −0.637982 | −0.0237104 | ||||||||
\(725\) | 17.8158 | 0.661661 | ||||||||
\(726\) | 2.60168 | 0.0965574 | ||||||||
\(727\) | 20.6682 | 0.766542 | 0.383271 | − | 0.923636i | \(-0.374798\pi\) | ||||
0.383271 | + | 0.923636i | \(0.374798\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −38.6101 | −1.43000 | ||||||||
\(730\) | 53.6743 | 1.98657 | ||||||||
\(731\) | −31.4817 | −1.16439 | ||||||||
\(732\) | 12.5012 | 0.462056 | ||||||||
\(733\) | 26.1368 | 0.965385 | 0.482693 | − | 0.875790i | \(-0.339659\pi\) | ||||
0.482693 | + | 0.875790i | \(0.339659\pi\) | |||||||
\(734\) | −11.1475 | −0.411463 | ||||||||
\(735\) | −68.3616 | −2.52156 | ||||||||
\(736\) | −26.0168 | −0.958992 | ||||||||
\(737\) | −4.13915 | −0.152467 | ||||||||
\(738\) | −4.77713 | −0.175849 | ||||||||
\(739\) | −16.4793 | −0.606202 | −0.303101 | − | 0.952958i | \(-0.598022\pi\) | ||||
−0.303101 | + | 0.952958i | \(0.598022\pi\) | |||||||
\(740\) | −32.5543 | −1.19672 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.222870 | 0.00818182 | ||||||||
\(743\) | 29.6440 | 1.08753 | 0.543767 | − | 0.839236i | \(-0.316997\pi\) | ||||
0.543767 | + | 0.839236i | \(0.316997\pi\) | |||||||
\(744\) | −53.6147 | −1.96561 | ||||||||
\(745\) | 4.39832 | 0.161142 | ||||||||
\(746\) | −27.3123 | −0.999973 | ||||||||
\(747\) | −39.8497 | −1.45803 | ||||||||
\(748\) | −4.37041 | −0.159798 | ||||||||
\(749\) | −2.28941 | −0.0836533 | ||||||||
\(750\) | 41.2141 | 1.50493 | ||||||||
\(751\) | 25.3486 | 0.924982 | 0.462491 | − | 0.886624i | \(-0.346956\pi\) | ||||
0.462491 | + | 0.886624i | \(0.346956\pi\) | |||||||
\(752\) | 10.1391 | 0.369737 | ||||||||
\(753\) | 26.9018 | 0.980357 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −40.4793 | −1.47319 | ||||||||
\(756\) | −0.334110 | −0.0121515 | ||||||||
\(757\) | 31.7320 | 1.15332 | 0.576660 | − | 0.816984i | \(-0.304356\pi\) | ||||
0.576660 | + | 0.816984i | \(0.304356\pi\) | |||||||
\(758\) | 18.4067 | 0.668562 | ||||||||
\(759\) | −13.5375 | −0.491379 | ||||||||
\(760\) | 38.1066 | 1.38227 | ||||||||
\(761\) | −43.8837 | −1.59078 | −0.795392 | − | 0.606096i | \(-0.792735\pi\) | ||||
−0.795392 | + | 0.606096i | \(0.792735\pi\) | |||||||
\(762\) | −3.46486 | −0.125519 | ||||||||
\(763\) | −1.47699 | −0.0534707 | ||||||||
\(764\) | −26.1391 | −0.945681 | ||||||||
\(765\) | 62.0745 | 2.24431 | ||||||||
\(766\) | −25.8716 | −0.934778 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −44.2285 | −1.59596 | ||||||||
\(769\) | −15.6147 | −0.563082 | −0.281541 | − | 0.959549i | \(-0.590846\pi\) | ||||
−0.281541 | + | 0.959549i | \(0.590846\pi\) | |||||||
\(770\) | 0.629587 | 0.0226887 | ||||||||
\(771\) | 62.8968 | 2.26517 | ||||||||
\(772\) | 11.1391 | 0.400907 | ||||||||
\(773\) | −22.2504 | −0.800291 | −0.400145 | − | 0.916452i | \(-0.631040\pi\) | ||||
−0.400145 | + | 0.916452i | \(0.631040\pi\) | |||||||
\(774\) | −27.1475 | −0.975798 | ||||||||
\(775\) | 63.2201 | 2.27093 | ||||||||
\(776\) | −10.6961 | −0.383969 | ||||||||
\(777\) | 3.75427 | 0.134684 | ||||||||
\(778\) | 20.7153 | 0.742678 | ||||||||
\(779\) | 4.27223 | 0.153069 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | 0.214697 | ||||||||
\(782\) | −22.7408 | −0.813210 | ||||||||
\(783\) | 3.87158 | 0.138359 | ||||||||
\(784\) | 6.97209 | 0.249003 | ||||||||
\(785\) | −17.3109 | −0.617851 | ||||||||
\(786\) | 35.6548 | 1.27176 | ||||||||
\(787\) | 53.9828 | 1.92428 | 0.962140 | − | 0.272556i | \(-0.0878691\pi\) | ||||
0.962140 | + | 0.272556i | \(0.0878691\pi\) | |||||||
\(788\) | −15.5375 | −0.553499 | ||||||||
\(789\) | −27.9442 | −0.994839 | ||||||||
\(790\) | −54.9247 | −1.95413 | ||||||||
\(791\) | 0.762670 | 0.0271174 | ||||||||
\(792\) | −11.3062 | −0.401748 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −21.5822 | −0.765922 | ||||||||
\(795\) | 13.0810 | 0.463935 | ||||||||
\(796\) | 11.6766 | 0.413867 | ||||||||
\(797\) | −32.9912 | −1.16861 | −0.584304 | − | 0.811535i | \(-0.698633\pi\) | ||||
−0.584304 | + | 0.811535i | \(0.698633\pi\) | |||||||
\(798\) | −1.46486 | −0.0518556 | ||||||||
\(799\) | −44.3123 | −1.56766 | ||||||||
\(800\) | 46.0168 | 1.62694 | ||||||||
\(801\) | 53.9163 | 1.90504 | ||||||||
\(802\) | 0.203358 | 0.00718083 | ||||||||
\(803\) | 14.2420 | 0.502589 | ||||||||
\(804\) | 10.7687 | 0.379784 | ||||||||
\(805\) | −3.27596 | −0.115463 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 45.9610 | 1.61790 | ||||||||
\(808\) | 36.1089 | 1.27031 | ||||||||
\(809\) | −32.7771 | −1.15238 | −0.576191 | − | 0.817315i | \(-0.695462\pi\) | ||||
−0.576191 | + | 0.817315i | \(0.695462\pi\) | |||||||
\(810\) | −23.0000 | −0.808138 | ||||||||
\(811\) | 4.94185 | 0.173532 | 0.0867660 | − | 0.996229i | \(-0.472347\pi\) | ||||
0.0867660 | + | 0.996229i | \(0.472347\pi\) | |||||||
\(812\) | −0.323384 | −0.0113485 | ||||||||
\(813\) | 22.7408 | 0.797556 | ||||||||
\(814\) | 8.63798 | 0.302761 | ||||||||
\(815\) | 42.7469 | 1.49736 | ||||||||
\(816\) | −11.3704 | −0.398044 | ||||||||
\(817\) | 24.2783 | 0.849390 | ||||||||
\(818\) | 0.0921180 | 0.00322083 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.77713 | 0.166825 | ||||||||
\(821\) | −19.8158 | −0.691575 | −0.345787 | − | 0.938313i | \(-0.612388\pi\) | ||||
−0.345787 | + | 0.938313i | \(0.612388\pi\) | |||||||
\(822\) | −35.4877 | −1.23778 | ||||||||
\(823\) | 28.1499 | 0.981243 | 0.490621 | − | 0.871373i | \(-0.336770\pi\) | ||||
0.490621 | + | 0.871373i | \(0.336770\pi\) | |||||||
\(824\) | 19.2201 | 0.669566 | ||||||||
\(825\) | 23.9442 | 0.833630 | ||||||||
\(826\) | 0.357356 | 0.0124340 | ||||||||
\(827\) | 33.0578 | 1.14953 | 0.574765 | − | 0.818318i | \(-0.305093\pi\) | ||||
0.574765 | + | 0.818318i | \(0.305093\pi\) | |||||||
\(828\) | 19.6101 | 0.681497 | ||||||||
\(829\) | −14.9721 | −0.520002 | −0.260001 | − | 0.965608i | \(-0.583723\pi\) | ||||
−0.260001 | + | 0.965608i | \(0.583723\pi\) | |||||||
\(830\) | −39.8497 | −1.38320 | ||||||||
\(831\) | 75.9996 | 2.63640 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −30.4709 | −1.05576 | ||||||||
\(834\) | 2.26150 | 0.0783095 | ||||||||
\(835\) | 65.1085 | 2.25317 | ||||||||
\(836\) | 3.37041 | 0.116568 | ||||||||
\(837\) | 13.7385 | 0.474872 | ||||||||
\(838\) | 10.1284 | 0.349880 | ||||||||
\(839\) | −13.0131 | −0.449261 | −0.224630 | − | 0.974444i | \(-0.572117\pi\) | ||||
−0.224630 | + | 0.974444i | \(0.572117\pi\) | |||||||
\(840\) | −4.91395 | −0.169547 | ||||||||
\(841\) | −25.2527 | −0.870783 | ||||||||
\(842\) | −6.58217 | −0.226836 | ||||||||
\(843\) | −28.1112 | −0.968203 | ||||||||
\(844\) | 4.57377 | 0.157436 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −38.2118 | −1.31375 | ||||||||
\(847\) | 0.167055 | 0.00574008 | ||||||||
\(848\) | −1.33411 | −0.0458135 | ||||||||
\(849\) | 26.6403 | 0.914293 | ||||||||
\(850\) | 40.2225 | 1.37962 | ||||||||
\(851\) | −44.9465 | −1.54075 | ||||||||
\(852\) | −15.6101 | −0.534792 | ||||||||
\(853\) | 25.3448 | 0.867791 | 0.433895 | − | 0.900963i | \(-0.357139\pi\) | ||||
0.433895 | + | 0.900963i | \(0.357139\pi\) | |||||||
\(854\) | −0.802706 | −0.0274680 | ||||||||
\(855\) | −47.8712 | −1.63716 | ||||||||
\(856\) | 41.1136 | 1.40523 | ||||||||
\(857\) | 49.5627 | 1.69303 | 0.846514 | − | 0.532366i | \(-0.178697\pi\) | ||||
0.846514 | + | 0.532366i | \(0.178697\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −55.6208 | −1.89776 | −0.948879 | − | 0.315641i | \(-0.897780\pi\) | ||||
−0.948879 | + | 0.315641i | \(0.897780\pi\) | |||||||
\(860\) | 27.1475 | 0.925724 | ||||||||
\(861\) | −0.550916 | −0.0187752 | ||||||||
\(862\) | 17.4988 | 0.596013 | ||||||||
\(863\) | 10.6124 | 0.361250 | 0.180625 | − | 0.983552i | \(-0.442188\pi\) | ||||
0.180625 | + | 0.983552i | \(0.442188\pi\) | |||||||
\(864\) | 10.0000 | 0.340207 | ||||||||
\(865\) | −48.3956 | −1.64550 | ||||||||
\(866\) | −8.69380 | −0.295427 | ||||||||
\(867\) | 5.46486 | 0.185596 | ||||||||
\(868\) | −1.14754 | −0.0389502 | ||||||||
\(869\) | −14.5738 | −0.494381 | ||||||||
\(870\) | 18.9805 | 0.643499 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 26.5240 | 0.898217 | ||||||||
\(873\) | 13.4370 | 0.454772 | ||||||||
\(874\) | 17.5375 | 0.593214 | ||||||||
\(875\) | 2.64638 | 0.0894639 | ||||||||
\(876\) | −37.0531 | −1.25191 | ||||||||
\(877\) | 53.8474 | 1.81830 | 0.909149 | − | 0.416471i | \(-0.136733\pi\) | ||||
0.909149 | + | 0.416471i | \(0.136733\pi\) | |||||||
\(878\) | −24.5738 | −0.829325 | ||||||||
\(879\) | 10.3123 | 0.347824 | ||||||||
\(880\) | −3.76873 | −0.127044 | ||||||||
\(881\) | −1.20103 | −0.0404636 | −0.0202318 | − | 0.999795i | \(-0.506440\pi\) | ||||
−0.0202318 | + | 0.999795i | \(0.506440\pi\) | |||||||
\(882\) | −26.2760 | −0.884758 | ||||||||
\(883\) | 58.4793 | 1.96799 | 0.983993 | − | 0.178207i | \(-0.0570298\pi\) | ||||
0.983993 | + | 0.178207i | \(0.0570298\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 20.9744 | 0.705048 | ||||||||
\(886\) | −17.2699 | −0.580194 | ||||||||
\(887\) | −27.3364 | −0.917868 | −0.458934 | − | 0.888470i | \(-0.651769\pi\) | ||||
−0.458934 | + | 0.888470i | \(0.651769\pi\) | |||||||
\(888\) | −67.4198 | −2.26246 | ||||||||
\(889\) | −0.222481 | −0.00746176 | ||||||||
\(890\) | 53.9163 | 1.80728 | ||||||||
\(891\) | −6.10284 | −0.204453 | ||||||||
\(892\) | 9.06421 | 0.303492 | ||||||||
\(893\) | 34.1731 | 1.14356 | ||||||||
\(894\) | 3.03630 | 0.101549 | ||||||||
\(895\) | −18.6017 | −0.621786 | ||||||||
\(896\) | −0.501166 | −0.0167428 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.3230 | 0.544705 | ||||||||
\(899\) | 13.2974 | 0.443494 | ||||||||
\(900\) | −34.6850 | −1.15617 | ||||||||
\(901\) | 5.83061 | 0.194246 | ||||||||
\(902\) | −1.26757 | −0.0422054 | ||||||||
\(903\) | −3.13075 | −0.104185 | ||||||||
\(904\) | −13.6961 | −0.455526 | ||||||||
\(905\) | 2.40439 | 0.0799245 | ||||||||
\(906\) | −27.9442 | −0.928383 | ||||||||
\(907\) | −17.6598 | −0.586385 | −0.293192 | − | 0.956053i | \(-0.594718\pi\) | ||||
−0.293192 | + | 0.956053i | \(0.594718\pi\) | |||||||
\(908\) | 13.2034 | 0.438169 | ||||||||
\(909\) | −45.3616 | −1.50455 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.8074 | −0.689379 | −0.344689 | − | 0.938717i | \(-0.612016\pi\) | ||||
−0.344689 | + | 0.938717i | \(0.612016\pi\) | |||||||
\(912\) | 8.76873 | 0.290362 | ||||||||
\(913\) | −10.5738 | −0.349941 | ||||||||
\(914\) | 21.4174 | 0.708426 | ||||||||
\(915\) | −47.1136 | −1.55753 | ||||||||
\(916\) | −2.02791 | −0.0670039 | ||||||||
\(917\) | 2.28941 | 0.0756030 | ||||||||
\(918\) | 8.74083 | 0.288490 | ||||||||
\(919\) | 57.3700 | 1.89246 | 0.946231 | − | 0.323491i | \(-0.104857\pi\) | ||||
0.946231 | + | 0.323491i | \(0.104857\pi\) | |||||||
\(920\) | 58.8302 | 1.93958 | ||||||||
\(921\) | 37.0470 | 1.22074 | ||||||||
\(922\) | −17.8074 | −0.586454 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.434624 | −0.0142981 | ||||||||
\(925\) | 79.4984 | 2.61389 | ||||||||
\(926\) | 4.80271 | 0.157827 | ||||||||
\(927\) | −24.1452 | −0.793033 | ||||||||
\(928\) | 9.67895 | 0.317727 | ||||||||
\(929\) | 47.1452 | 1.54678 | 0.773392 | − | 0.633928i | \(-0.218558\pi\) | ||||
0.773392 | + | 0.633928i | \(0.218558\pi\) | |||||||
\(930\) | 67.3532 | 2.20860 | ||||||||
\(931\) | 23.4988 | 0.770143 | ||||||||
\(932\) | 12.7408 | 0.417340 | ||||||||
\(933\) | 30.9018 | 1.01168 | ||||||||
\(934\) | −2.80737 | −0.0918599 | ||||||||
\(935\) | 16.4709 | 0.538657 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.2820 | 0.793259 | 0.396630 | − | 0.917979i | \(-0.370180\pi\) | ||||
0.396630 | + | 0.917979i | \(0.370180\pi\) | |||||||
\(938\) | −0.691466 | −0.0225772 | ||||||||
\(939\) | 20.5519 | 0.670687 | ||||||||
\(940\) | 38.2118 | 1.24633 | ||||||||
\(941\) | 12.7408 | 0.415339 | 0.207670 | − | 0.978199i | \(-0.433412\pi\) | ||||
0.207670 | + | 0.978199i | \(0.433412\pi\) | |||||||
\(942\) | −11.9502 | −0.389360 | ||||||||
\(943\) | 6.59561 | 0.214783 | ||||||||
\(944\) | −2.13915 | −0.0696233 | ||||||||
\(945\) | 1.25917 | 0.0409609 | ||||||||
\(946\) | −7.20336 | −0.234201 | ||||||||
\(947\) | −11.0749 | −0.359887 | −0.179944 | − | 0.983677i | \(-0.557592\pi\) | ||||
−0.179944 | + | 0.983677i | \(0.557592\pi\) | |||||||
\(948\) | 37.9163 | 1.23146 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −31.0191 | −1.00639 | ||||||||
\(951\) | 71.0857 | 2.30511 | ||||||||
\(952\) | −2.19030 | −0.0709880 | ||||||||
\(953\) | 50.3677 | 1.63157 | 0.815785 | − | 0.578356i | \(-0.196305\pi\) | ||||
0.815785 | + | 0.578356i | \(0.196305\pi\) | |||||||
\(954\) | 5.02791 | 0.162785 | ||||||||
\(955\) | 98.5115 | 3.18776 | ||||||||
\(956\) | −4.07261 | −0.131717 | ||||||||
\(957\) | 5.03630 | 0.162801 | ||||||||
\(958\) | 11.8329 | 0.382305 | ||||||||
\(959\) | −2.27868 | −0.0735826 | ||||||||
\(960\) | 68.6353 | 2.21519 | ||||||||
\(961\) | 16.1866 | 0.522147 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −51.6487 | −1.66436 | ||||||||
\(964\) | 18.9828 | 0.611395 | ||||||||
\(965\) | −41.9805 | −1.35140 | ||||||||
\(966\) | −2.26150 | −0.0727627 | ||||||||
\(967\) | 47.7213 | 1.53461 | 0.767307 | − | 0.641280i | \(-0.221596\pi\) | ||||
0.767307 | + | 0.641280i | \(0.221596\pi\) | |||||||
\(968\) | −3.00000 | −0.0964237 | ||||||||
\(969\) | −38.3230 | −1.23111 | ||||||||
\(970\) | 13.4370 | 0.431435 | ||||||||
\(971\) | −30.7469 | −0.986715 | −0.493357 | − | 0.869827i | \(-0.664231\pi\) | ||||
−0.493357 | + | 0.869827i | \(0.664231\pi\) | |||||||
\(972\) | 21.8776 | 0.701726 | ||||||||
\(973\) | 0.145212 | 0.00465529 | ||||||||
\(974\) | −16.4174 | −0.526049 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.80504 | 0.153805 | ||||||||
\(977\) | −22.6426 | −0.724402 | −0.362201 | − | 0.932100i | \(-0.617975\pi\) | ||||
−0.362201 | + | 0.932100i | \(0.617975\pi\) | |||||||
\(978\) | 29.5096 | 0.943612 | ||||||||
\(979\) | 14.3062 | 0.457228 | ||||||||
\(980\) | 26.2760 | 0.839355 | ||||||||
\(981\) | −33.3207 | −1.06385 | ||||||||
\(982\) | 7.83294 | 0.249959 | ||||||||
\(983\) | 2.40672 | 0.0767623 | 0.0383812 | − | 0.999263i | \(-0.487780\pi\) | ||||
0.0383812 | + | 0.999263i | \(0.487780\pi\) | |||||||
\(984\) | 9.89342 | 0.315391 | ||||||||
\(985\) | 58.5566 | 1.86577 | ||||||||
\(986\) | 8.46020 | 0.269428 | ||||||||
\(987\) | −4.40672 | −0.140267 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37.4817 | 1.19185 | ||||||||
\(990\) | 14.2034 | 0.451412 | ||||||||
\(991\) | 13.2094 | 0.419611 | 0.209806 | − | 0.977743i | \(-0.432717\pi\) | ||||
0.209806 | + | 0.977743i | \(0.432717\pi\) | |||||||
\(992\) | 34.3462 | 1.09049 | ||||||||
\(993\) | 12.3341 | 0.391411 | ||||||||
\(994\) | 1.00233 | 0.0317920 | ||||||||
\(995\) | −44.0061 | −1.39509 | ||||||||
\(996\) | 27.5096 | 0.871674 | ||||||||
\(997\) | 17.2565 | 0.546517 | 0.273259 | − | 0.961941i | \(-0.411899\pi\) | ||||
0.273259 | + | 0.961941i | \(0.411899\pi\) | |||||||
\(998\) | 12.2722 | 0.388471 | ||||||||
\(999\) | 17.2760 | 0.546587 |
(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 | 1859.2.a.h.1.3 | 3 | ||
13.3 | even | 3 | 143.2.e.a.100.1 | ✓ | 6 | ||
13.9 | even | 3 | 143.2.e.a.133.1 | yes | 6 | ||
13.12 | even | 2 | 1859.2.a.e.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.2.e.a.100.1 | ✓ | 6 | 13.3 | even | 3 | ||
143.2.e.a.133.1 | yes | 6 | 13.9 | even | 3 | ||
1859.2.a.e.1.3 | 3 | 13.12 | even | 2 | |||
1859.2.a.h.1.3 | 3 | 1.1 | even | 1 | trivial |