Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2366,2,Mod(1,2366)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2366, 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("2366.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2366 = 2 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2366.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: | \(18.8926051182\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.285686784.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 10x^{4} + 12x^{3} + 21x^{2} + 2x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 182) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.865515\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2366.1 |
$q$-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 | ||||||||
\(3\) | −0.865515 | −0.499705 | −0.249853 | − | 0.968284i | \(-0.580382\pi\) | ||||
−0.249853 | + | 0.968284i | \(0.580382\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.71131 | 1.65975 | 0.829875 | − | 0.557950i | \(-0.188412\pi\) | ||||
0.829875 | + | 0.557950i | \(0.188412\pi\) | |||||||
\(6\) | 0.865515 | 0.353345 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.25088 | −0.750295 | ||||||||
\(10\) | −3.71131 | −1.17362 | ||||||||
\(11\) | 5.77486 | 1.74119 | 0.870594 | − | 0.492003i | \(-0.163735\pi\) | ||||
0.870594 | + | 0.492003i | \(0.163735\pi\) | |||||||
\(12\) | −0.865515 | −0.249853 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −3.21220 | −0.829386 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.212197 | −0.0514653 | −0.0257327 | − | 0.999669i | \(-0.508192\pi\) | ||||
−0.0257327 | + | 0.999669i | \(0.508192\pi\) | |||||||
\(18\) | 2.25088 | 0.530538 | ||||||||
\(19\) | −2.13714 | −0.490293 | −0.245146 | − | 0.969486i | \(-0.578836\pi\) | ||||
−0.245146 | + | 0.969486i | \(0.578836\pi\) | |||||||
\(20\) | 3.71131 | 0.829875 | ||||||||
\(21\) | 0.865515 | 0.188871 | ||||||||
\(22\) | −5.77486 | −1.23121 | ||||||||
\(23\) | 2.47940 | 0.516990 | 0.258495 | − | 0.966013i | \(-0.416773\pi\) | ||||
0.258495 | + | 0.966013i | \(0.416773\pi\) | |||||||
\(24\) | 0.865515 | 0.176673 | ||||||||
\(25\) | 8.77384 | 1.75477 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.54472 | 0.874632 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −0.0985660 | −0.0183032 | −0.00915162 | − | 0.999958i | \(-0.502913\pi\) | ||||
−0.00915162 | + | 0.999958i | \(0.502913\pi\) | |||||||
\(30\) | 3.21220 | 0.586464 | ||||||||
\(31\) | −2.31076 | −0.415025 | −0.207513 | − | 0.978232i | \(-0.566537\pi\) | ||||
−0.207513 | + | 0.978232i | \(0.566537\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.99823 | −0.870080 | ||||||||
\(34\) | 0.212197 | 0.0363915 | ||||||||
\(35\) | −3.71131 | −0.627326 | ||||||||
\(36\) | −2.25088 | −0.375147 | ||||||||
\(37\) | −7.87343 | −1.29438 | −0.647192 | − | 0.762327i | \(-0.724057\pi\) | ||||
−0.647192 | + | 0.762327i | \(0.724057\pi\) | |||||||
\(38\) | 2.13714 | 0.346689 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.71131 | −0.586810 | ||||||||
\(41\) | 7.52119 | 1.17461 | 0.587306 | − | 0.809365i | \(-0.300188\pi\) | ||||
0.587306 | + | 0.809365i | \(0.300188\pi\) | |||||||
\(42\) | −0.865515 | −0.133552 | ||||||||
\(43\) | 4.57973 | 0.698403 | 0.349201 | − | 0.937048i | \(-0.386453\pi\) | ||||
0.349201 | + | 0.937048i | \(0.386453\pi\) | |||||||
\(44\) | 5.77486 | 0.870594 | ||||||||
\(45\) | −8.35373 | −1.24530 | ||||||||
\(46\) | −2.47940 | −0.365567 | ||||||||
\(47\) | 9.15570 | 1.33550 | 0.667748 | − | 0.744388i | \(-0.267258\pi\) | ||||
0.667748 | + | 0.744388i | \(0.267258\pi\) | |||||||
\(48\) | −0.865515 | −0.124926 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −8.77384 | −1.24081 | ||||||||
\(51\) | 0.183660 | 0.0257175 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.0948 | 1.66135 | 0.830674 | − | 0.556759i | \(-0.187955\pi\) | ||||
0.830674 | + | 0.556759i | \(0.187955\pi\) | |||||||
\(54\) | −4.54472 | −0.618458 | ||||||||
\(55\) | 21.4323 | 2.88993 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 1.84972 | 0.245002 | ||||||||
\(58\) | 0.0985660 | 0.0129423 | ||||||||
\(59\) | −0.231914 | −0.0301926 | −0.0150963 | − | 0.999886i | \(-0.504805\pi\) | ||||
−0.0150963 | + | 0.999886i | \(0.504805\pi\) | |||||||
\(60\) | −3.21220 | −0.414693 | ||||||||
\(61\) | 8.03211 | 1.02841 | 0.514203 | − | 0.857668i | \(-0.328088\pi\) | ||||
0.514203 | + | 0.857668i | \(0.328088\pi\) | |||||||
\(62\) | 2.31076 | 0.293467 | ||||||||
\(63\) | 2.25088 | 0.283585 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.99823 | 0.615240 | ||||||||
\(67\) | −12.9700 | −1.58454 | −0.792269 | − | 0.610172i | \(-0.791100\pi\) | ||||
−0.792269 | + | 0.610172i | \(0.791100\pi\) | |||||||
\(68\) | −0.212197 | −0.0257327 | ||||||||
\(69\) | −2.14596 | −0.258343 | ||||||||
\(70\) | 3.71131 | 0.443587 | ||||||||
\(71\) | −7.36377 | −0.873918 | −0.436959 | − | 0.899481i | \(-0.643945\pi\) | ||||
−0.436959 | + | 0.899481i | \(0.643945\pi\) | |||||||
\(72\) | 2.25088 | 0.265269 | ||||||||
\(73\) | 5.60414 | 0.655915 | 0.327958 | − | 0.944692i | \(-0.393640\pi\) | ||||
0.327958 | + | 0.944692i | \(0.393640\pi\) | |||||||
\(74\) | 7.87343 | 0.915268 | ||||||||
\(75\) | −7.59389 | −0.876867 | ||||||||
\(76\) | −2.13714 | −0.245146 | ||||||||
\(77\) | −5.77486 | −0.658107 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.19749 | −1.03480 | −0.517399 | − | 0.855744i | \(-0.673100\pi\) | ||||
−0.517399 | + | 0.855744i | \(0.673100\pi\) | |||||||
\(80\) | 3.71131 | 0.414937 | ||||||||
\(81\) | 2.81913 | 0.313237 | ||||||||
\(82\) | −7.52119 | −0.830577 | ||||||||
\(83\) | −3.17186 | −0.348157 | −0.174078 | − | 0.984732i | \(-0.555695\pi\) | ||||
−0.174078 | + | 0.984732i | \(0.555695\pi\) | |||||||
\(84\) | 0.865515 | 0.0944354 | ||||||||
\(85\) | −0.787529 | −0.0854196 | ||||||||
\(86\) | −4.57973 | −0.493845 | ||||||||
\(87\) | 0.0853103 | 0.00914623 | ||||||||
\(88\) | −5.77486 | −0.615603 | ||||||||
\(89\) | 11.8167 | 1.25256 | 0.626282 | − | 0.779597i | \(-0.284576\pi\) | ||||
0.626282 | + | 0.779597i | \(0.284576\pi\) | |||||||
\(90\) | 8.35373 | 0.880561 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.47940 | 0.258495 | ||||||||
\(93\) | 2.00000 | 0.207390 | ||||||||
\(94\) | −9.15570 | −0.944338 | ||||||||
\(95\) | −7.93158 | −0.813763 | ||||||||
\(96\) | 0.865515 | 0.0883363 | ||||||||
\(97\) | −14.0819 | −1.42980 | −0.714898 | − | 0.699229i | \(-0.753527\pi\) | ||||
−0.714898 | + | 0.699229i | \(0.753527\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −12.9985 | −1.30640 | ||||||||
\(100\) | 8.77384 | 0.877384 | ||||||||
\(101\) | −6.15243 | −0.612190 | −0.306095 | − | 0.952001i | \(-0.599023\pi\) | ||||
−0.306095 | + | 0.952001i | \(0.599023\pi\) | |||||||
\(102\) | −0.183660 | −0.0181850 | ||||||||
\(103\) | −19.3491 | −1.90652 | −0.953260 | − | 0.302152i | \(-0.902295\pi\) | ||||
−0.953260 | + | 0.302152i | \(0.902295\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.21220 | 0.313478 | ||||||||
\(106\) | −12.0948 | −1.17475 | ||||||||
\(107\) | 11.6501 | 1.12626 | 0.563130 | − | 0.826368i | \(-0.309597\pi\) | ||||
0.563130 | + | 0.826368i | \(0.309597\pi\) | |||||||
\(108\) | 4.54472 | 0.437316 | ||||||||
\(109\) | 5.73307 | 0.549129 | 0.274564 | − | 0.961569i | \(-0.411466\pi\) | ||||
0.274564 | + | 0.961569i | \(0.411466\pi\) | |||||||
\(110\) | −21.4323 | −2.04349 | ||||||||
\(111\) | 6.81457 | 0.646811 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 16.5194 | 1.55402 | 0.777008 | − | 0.629490i | \(-0.216736\pi\) | ||||
0.777008 | + | 0.629490i | \(0.216736\pi\) | |||||||
\(114\) | −1.84972 | −0.173243 | ||||||||
\(115\) | 9.20183 | 0.858075 | ||||||||
\(116\) | −0.0985660 | −0.00915162 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.231914 | 0.0213494 | ||||||||
\(119\) | 0.212197 | 0.0194521 | ||||||||
\(120\) | 3.21220 | 0.293232 | ||||||||
\(121\) | 22.3491 | 2.03173 | ||||||||
\(122\) | −8.03211 | −0.727193 | ||||||||
\(123\) | −6.50970 | −0.586960 | ||||||||
\(124\) | −2.31076 | −0.207513 | ||||||||
\(125\) | 14.0059 | 1.25273 | ||||||||
\(126\) | −2.25088 | −0.200525 | ||||||||
\(127\) | −11.7884 | −1.04605 | −0.523025 | − | 0.852317i | \(-0.675197\pi\) | ||||
−0.523025 | + | 0.852317i | \(0.675197\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.96383 | −0.348996 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.12859 | −0.448087 | −0.224043 | − | 0.974579i | \(-0.571926\pi\) | ||||
−0.224043 | + | 0.974579i | \(0.571926\pi\) | |||||||
\(132\) | −4.99823 | −0.435040 | ||||||||
\(133\) | 2.13714 | 0.185313 | ||||||||
\(134\) | 12.9700 | 1.12044 | ||||||||
\(135\) | 16.8669 | 1.45167 | ||||||||
\(136\) | 0.212197 | 0.0181957 | ||||||||
\(137\) | −9.39328 | −0.802522 | −0.401261 | − | 0.915964i | \(-0.631428\pi\) | ||||
−0.401261 | + | 0.915964i | \(0.631428\pi\) | |||||||
\(138\) | 2.14596 | 0.182676 | ||||||||
\(139\) | 15.1413 | 1.28427 | 0.642133 | − | 0.766594i | \(-0.278050\pi\) | ||||
0.642133 | + | 0.766594i | \(0.278050\pi\) | |||||||
\(140\) | −3.71131 | −0.313663 | ||||||||
\(141\) | −7.92439 | −0.667354 | ||||||||
\(142\) | 7.36377 | 0.617954 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.25088 | −0.187574 | ||||||||
\(145\) | −0.365809 | −0.0303788 | ||||||||
\(146\) | −5.60414 | −0.463802 | ||||||||
\(147\) | −0.865515 | −0.0713865 | ||||||||
\(148\) | −7.87343 | −0.647192 | ||||||||
\(149\) | 20.6027 | 1.68784 | 0.843919 | − | 0.536470i | \(-0.180243\pi\) | ||||
0.843919 | + | 0.536470i | \(0.180243\pi\) | |||||||
\(150\) | 7.59389 | 0.620039 | ||||||||
\(151\) | 11.9407 | 0.971721 | 0.485861 | − | 0.874036i | \(-0.338506\pi\) | ||||
0.485861 | + | 0.874036i | \(0.338506\pi\) | |||||||
\(152\) | 2.13714 | 0.173345 | ||||||||
\(153\) | 0.477631 | 0.0386142 | ||||||||
\(154\) | 5.77486 | 0.465352 | ||||||||
\(155\) | −8.57596 | −0.688838 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.34022 | 0.745431 | 0.372715 | − | 0.927946i | \(-0.378427\pi\) | ||||
0.372715 | + | 0.927946i | \(0.378427\pi\) | |||||||
\(158\) | 9.19749 | 0.731713 | ||||||||
\(159\) | −10.4682 | −0.830185 | ||||||||
\(160\) | −3.71131 | −0.293405 | ||||||||
\(161\) | −2.47940 | −0.195404 | ||||||||
\(162\) | −2.81913 | −0.221492 | ||||||||
\(163\) | 4.47730 | 0.350689 | 0.175345 | − | 0.984507i | \(-0.443896\pi\) | ||||
0.175345 | + | 0.984507i | \(0.443896\pi\) | |||||||
\(164\) | 7.52119 | 0.587306 | ||||||||
\(165\) | −18.5500 | −1.44412 | ||||||||
\(166\) | 3.17186 | 0.246184 | ||||||||
\(167\) | −14.7068 | −1.13805 | −0.569025 | − | 0.822321i | \(-0.692679\pi\) | ||||
−0.569025 | + | 0.822321i | \(0.692679\pi\) | |||||||
\(168\) | −0.865515 | −0.0667759 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.787529 | 0.0604008 | ||||||||
\(171\) | 4.81045 | 0.367864 | ||||||||
\(172\) | 4.57973 | 0.349201 | ||||||||
\(173\) | 13.7657 | 1.04659 | 0.523294 | − | 0.852152i | \(-0.324703\pi\) | ||||
0.523294 | + | 0.852152i | \(0.324703\pi\) | |||||||
\(174\) | −0.0853103 | −0.00646736 | ||||||||
\(175\) | −8.77384 | −0.663240 | ||||||||
\(176\) | 5.77486 | 0.435297 | ||||||||
\(177\) | 0.200725 | 0.0150874 | ||||||||
\(178\) | −11.8167 | −0.885696 | ||||||||
\(179\) | 15.2787 | 1.14198 | 0.570992 | − | 0.820955i | \(-0.306559\pi\) | ||||
0.570992 | + | 0.820955i | \(0.306559\pi\) | |||||||
\(180\) | −8.35373 | −0.622651 | ||||||||
\(181\) | 1.66748 | 0.123943 | 0.0619713 | − | 0.998078i | \(-0.480261\pi\) | ||||
0.0619713 | + | 0.998078i | \(0.480261\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.95191 | −0.513900 | ||||||||
\(184\) | −2.47940 | −0.182784 | ||||||||
\(185\) | −29.2208 | −2.14835 | ||||||||
\(186\) | −2.00000 | −0.146647 | ||||||||
\(187\) | −1.22541 | −0.0896108 | ||||||||
\(188\) | 9.15570 | 0.667748 | ||||||||
\(189\) | −4.54472 | −0.330580 | ||||||||
\(190\) | 7.93158 | 0.575418 | ||||||||
\(191\) | 0.120976 | 0.00875351 | 0.00437676 | − | 0.999990i | \(-0.498607\pi\) | ||||
0.00437676 | + | 0.999990i | \(0.498607\pi\) | |||||||
\(192\) | −0.865515 | −0.0624632 | ||||||||
\(193\) | 2.75550 | 0.198345 | 0.0991725 | − | 0.995070i | \(-0.468380\pi\) | ||||
0.0991725 | + | 0.995070i | \(0.468380\pi\) | |||||||
\(194\) | 14.0819 | 1.01102 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −15.1253 | −1.07764 | −0.538818 | − | 0.842422i | \(-0.681129\pi\) | ||||
−0.538818 | + | 0.842422i | \(0.681129\pi\) | |||||||
\(198\) | 12.9985 | 0.923767 | ||||||||
\(199\) | 5.30640 | 0.376161 | 0.188080 | − | 0.982154i | \(-0.439773\pi\) | ||||
0.188080 | + | 0.982154i | \(0.439773\pi\) | |||||||
\(200\) | −8.77384 | −0.620404 | ||||||||
\(201\) | 11.2257 | 0.791802 | ||||||||
\(202\) | 6.15243 | 0.432884 | ||||||||
\(203\) | 0.0985660 | 0.00691798 | ||||||||
\(204\) | 0.183660 | 0.0128587 | ||||||||
\(205\) | 27.9135 | 1.94956 | ||||||||
\(206\) | 19.3491 | 1.34811 | ||||||||
\(207\) | −5.58084 | −0.387895 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.3417 | −0.853691 | ||||||||
\(210\) | −3.21220 | −0.221663 | ||||||||
\(211\) | 17.8982 | 1.23216 | 0.616081 | − | 0.787682i | \(-0.288719\pi\) | ||||
0.616081 | + | 0.787682i | \(0.288719\pi\) | |||||||
\(212\) | 12.0948 | 0.830674 | ||||||||
\(213\) | 6.37345 | 0.436702 | ||||||||
\(214\) | −11.6501 | −0.796386 | ||||||||
\(215\) | 16.9968 | 1.15917 | ||||||||
\(216\) | −4.54472 | −0.309229 | ||||||||
\(217\) | 2.31076 | 0.156865 | ||||||||
\(218\) | −5.73307 | −0.388293 | ||||||||
\(219\) | −4.85047 | −0.327764 | ||||||||
\(220\) | 21.4323 | 1.44497 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.81457 | −0.457364 | ||||||||
\(223\) | −16.4385 | −1.10080 | −0.550402 | − | 0.834900i | \(-0.685525\pi\) | ||||
−0.550402 | + | 0.834900i | \(0.685525\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −19.7489 | −1.31659 | ||||||||
\(226\) | −16.5194 | −1.09886 | ||||||||
\(227\) | 5.63095 | 0.373739 | 0.186870 | − | 0.982385i | \(-0.440166\pi\) | ||||
0.186870 | + | 0.982385i | \(0.440166\pi\) | |||||||
\(228\) | 1.84972 | 0.122501 | ||||||||
\(229\) | 27.7225 | 1.83196 | 0.915978 | − | 0.401228i | \(-0.131416\pi\) | ||||
0.915978 | + | 0.401228i | \(0.131416\pi\) | |||||||
\(230\) | −9.20183 | −0.606750 | ||||||||
\(231\) | 4.99823 | 0.328860 | ||||||||
\(232\) | 0.0985660 | 0.00647117 | ||||||||
\(233\) | 20.1104 | 1.31747 | 0.658737 | − | 0.752374i | \(-0.271091\pi\) | ||||
0.658737 | + | 0.752374i | \(0.271091\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 33.9797 | 2.21659 | ||||||||
\(236\) | −0.231914 | −0.0150963 | ||||||||
\(237\) | 7.96057 | 0.517094 | ||||||||
\(238\) | −0.212197 | −0.0137547 | ||||||||
\(239\) | −6.62968 | −0.428838 | −0.214419 | − | 0.976742i | \(-0.568786\pi\) | ||||
−0.214419 | + | 0.976742i | \(0.568786\pi\) | |||||||
\(240\) | −3.21220 | −0.207346 | ||||||||
\(241\) | 1.61687 | 0.104151 | 0.0520757 | − | 0.998643i | \(-0.483416\pi\) | ||||
0.0520757 | + | 0.998643i | \(0.483416\pi\) | |||||||
\(242\) | −22.3491 | −1.43665 | ||||||||
\(243\) | −16.0742 | −1.03116 | ||||||||
\(244\) | 8.03211 | 0.514203 | ||||||||
\(245\) | 3.71131 | 0.237107 | ||||||||
\(246\) | 6.50970 | 0.415044 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.31076 | 0.146734 | ||||||||
\(249\) | 2.74529 | 0.173976 | ||||||||
\(250\) | −14.0059 | −0.885812 | ||||||||
\(251\) | 0.507011 | 0.0320023 | 0.0160011 | − | 0.999872i | \(-0.494906\pi\) | ||||
0.0160011 | + | 0.999872i | \(0.494906\pi\) | |||||||
\(252\) | 2.25088 | 0.141792 | ||||||||
\(253\) | 14.3182 | 0.900177 | ||||||||
\(254\) | 11.7884 | 0.739670 | ||||||||
\(255\) | 0.681619 | 0.0426846 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.64063 | −0.601366 | −0.300683 | − | 0.953724i | \(-0.597215\pi\) | ||||
−0.300683 | + | 0.953724i | \(0.597215\pi\) | |||||||
\(258\) | 3.96383 | 0.246777 | ||||||||
\(259\) | 7.87343 | 0.489231 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.221861 | 0.0137328 | ||||||||
\(262\) | 5.12859 | 0.316845 | ||||||||
\(263\) | −7.34617 | −0.452985 | −0.226492 | − | 0.974013i | \(-0.572726\pi\) | ||||
−0.226492 | + | 0.974013i | \(0.572726\pi\) | |||||||
\(264\) | 4.99823 | 0.307620 | ||||||||
\(265\) | 44.8876 | 2.75742 | ||||||||
\(266\) | −2.13714 | −0.131036 | ||||||||
\(267\) | −10.2275 | −0.625912 | ||||||||
\(268\) | −12.9700 | −0.792269 | ||||||||
\(269\) | 22.3541 | 1.36295 | 0.681476 | − | 0.731841i | \(-0.261338\pi\) | ||||
0.681476 | + | 0.731841i | \(0.261338\pi\) | |||||||
\(270\) | −16.8669 | −1.02649 | ||||||||
\(271\) | 9.61740 | 0.584215 | 0.292108 | − | 0.956385i | \(-0.405643\pi\) | ||||
0.292108 | + | 0.956385i | \(0.405643\pi\) | |||||||
\(272\) | −0.212197 | −0.0128663 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.39328 | 0.567469 | ||||||||
\(275\) | 50.6678 | 3.05538 | ||||||||
\(276\) | −2.14596 | −0.129171 | ||||||||
\(277\) | 10.1789 | 0.611590 | 0.305795 | − | 0.952097i | \(-0.401078\pi\) | ||||
0.305795 | + | 0.952097i | \(0.401078\pi\) | |||||||
\(278\) | −15.1413 | −0.908113 | ||||||||
\(279\) | 5.20126 | 0.311391 | ||||||||
\(280\) | 3.71131 | 0.221793 | ||||||||
\(281\) | 14.1692 | 0.845265 | 0.422633 | − | 0.906301i | \(-0.361106\pi\) | ||||
0.422633 | + | 0.906301i | \(0.361106\pi\) | |||||||
\(282\) | 7.92439 | 0.471891 | ||||||||
\(283\) | 18.9326 | 1.12543 | 0.562714 | − | 0.826652i | \(-0.309757\pi\) | ||||
0.562714 | + | 0.826652i | \(0.309757\pi\) | |||||||
\(284\) | −7.36377 | −0.436959 | ||||||||
\(285\) | 6.86490 | 0.406642 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.52119 | −0.443962 | ||||||||
\(288\) | 2.25088 | 0.132635 | ||||||||
\(289\) | −16.9550 | −0.997351 | ||||||||
\(290\) | 0.365809 | 0.0214811 | ||||||||
\(291\) | 12.1881 | 0.714477 | ||||||||
\(292\) | 5.60414 | 0.327958 | ||||||||
\(293\) | 3.65982 | 0.213809 | 0.106905 | − | 0.994269i | \(-0.465906\pi\) | ||||
0.106905 | + | 0.994269i | \(0.465906\pi\) | |||||||
\(294\) | 0.865515 | 0.0504779 | ||||||||
\(295\) | −0.860706 | −0.0501122 | ||||||||
\(296\) | 7.87343 | 0.457634 | ||||||||
\(297\) | 26.2451 | 1.52290 | ||||||||
\(298\) | −20.6027 | −1.19348 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −7.59389 | −0.438434 | ||||||||
\(301\) | −4.57973 | −0.263971 | ||||||||
\(302\) | −11.9407 | −0.687111 | ||||||||
\(303\) | 5.32502 | 0.305915 | ||||||||
\(304\) | −2.13714 | −0.122573 | ||||||||
\(305\) | 29.8097 | 1.70690 | ||||||||
\(306\) | −0.477631 | −0.0273043 | ||||||||
\(307\) | −19.6987 | −1.12426 | −0.562132 | − | 0.827048i | \(-0.690019\pi\) | ||||
−0.562132 | + | 0.827048i | \(0.690019\pi\) | |||||||
\(308\) | −5.77486 | −0.329053 | ||||||||
\(309\) | 16.7469 | 0.952698 | ||||||||
\(310\) | 8.57596 | 0.487082 | ||||||||
\(311\) | −16.9685 | −0.962195 | −0.481098 | − | 0.876667i | \(-0.659762\pi\) | ||||
−0.481098 | + | 0.876667i | \(0.659762\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.53794 | −0.256500 | −0.128250 | − | 0.991742i | \(-0.540936\pi\) | ||||
−0.128250 | + | 0.991742i | \(0.540936\pi\) | |||||||
\(314\) | −9.34022 | −0.527099 | ||||||||
\(315\) | 8.35373 | 0.470680 | ||||||||
\(316\) | −9.19749 | −0.517399 | ||||||||
\(317\) | −29.1866 | −1.63928 | −0.819641 | − | 0.572877i | \(-0.805827\pi\) | ||||
−0.819641 | + | 0.572877i | \(0.805827\pi\) | |||||||
\(318\) | 10.4682 | 0.587029 | ||||||||
\(319\) | −0.569205 | −0.0318694 | ||||||||
\(320\) | 3.71131 | 0.207469 | ||||||||
\(321\) | −10.0834 | −0.562798 | ||||||||
\(322\) | 2.47940 | 0.138171 | ||||||||
\(323\) | 0.453494 | 0.0252331 | ||||||||
\(324\) | 2.81913 | 0.156618 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.47730 | −0.247975 | ||||||||
\(327\) | −4.96206 | −0.274403 | ||||||||
\(328\) | −7.52119 | −0.415288 | ||||||||
\(329\) | −9.15570 | −0.504770 | ||||||||
\(330\) | 18.5500 | 1.02114 | ||||||||
\(331\) | −4.80542 | −0.264130 | −0.132065 | − | 0.991241i | \(-0.542161\pi\) | ||||
−0.132065 | + | 0.991241i | \(0.542161\pi\) | |||||||
\(332\) | −3.17186 | −0.174078 | ||||||||
\(333\) | 17.7222 | 0.971169 | ||||||||
\(334\) | 14.7068 | 0.804722 | ||||||||
\(335\) | −48.1357 | −2.62994 | ||||||||
\(336\) | 0.865515 | 0.0472177 | ||||||||
\(337\) | −17.7312 | −0.965883 | −0.482941 | − | 0.875653i | \(-0.660432\pi\) | ||||
−0.482941 | + | 0.875653i | \(0.660432\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.2978 | −0.776550 | ||||||||
\(340\) | −0.787529 | −0.0427098 | ||||||||
\(341\) | −13.3443 | −0.722637 | ||||||||
\(342\) | −4.81045 | −0.260119 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −4.57973 | −0.246923 | ||||||||
\(345\) | −7.96432 | −0.428784 | ||||||||
\(346\) | −13.7657 | −0.740049 | ||||||||
\(347\) | −16.7048 | −0.896760 | −0.448380 | − | 0.893843i | \(-0.647999\pi\) | ||||
−0.448380 | + | 0.893843i | \(0.647999\pi\) | |||||||
\(348\) | 0.0853103 | 0.00457311 | ||||||||
\(349\) | −0.0200475 | −0.00107312 | −0.000536559 | − | 1.00000i | \(-0.500171\pi\) | ||||
−0.000536559 | 1.00000i | \(0.500171\pi\) | ||||||||
\(350\) | 8.77384 | 0.468982 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.77486 | −0.307801 | ||||||||
\(353\) | 29.8258 | 1.58747 | 0.793734 | − | 0.608265i | \(-0.208134\pi\) | ||||
0.793734 | + | 0.608265i | \(0.208134\pi\) | |||||||
\(354\) | −0.200725 | −0.0106684 | ||||||||
\(355\) | −27.3292 | −1.45049 | ||||||||
\(356\) | 11.8167 | 0.626282 | ||||||||
\(357\) | −0.183660 | −0.00972030 | ||||||||
\(358\) | −15.2787 | −0.807505 | ||||||||
\(359\) | −18.3351 | −0.967687 | −0.483844 | − | 0.875154i | \(-0.660760\pi\) | ||||
−0.483844 | + | 0.875154i | \(0.660760\pi\) | |||||||
\(360\) | 8.35373 | 0.440280 | ||||||||
\(361\) | −14.4326 | −0.759613 | ||||||||
\(362\) | −1.66748 | −0.0876407 | ||||||||
\(363\) | −19.3434 | −1.01527 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.7987 | 1.08866 | ||||||||
\(366\) | 6.95191 | 0.363382 | ||||||||
\(367\) | 1.34485 | 0.0702007 | 0.0351004 | − | 0.999384i | \(-0.488825\pi\) | ||||
0.0351004 | + | 0.999384i | \(0.488825\pi\) | |||||||
\(368\) | 2.47940 | 0.129248 | ||||||||
\(369\) | −16.9293 | −0.881306 | ||||||||
\(370\) | 29.2208 | 1.51912 | ||||||||
\(371\) | −12.0948 | −0.627931 | ||||||||
\(372\) | 2.00000 | 0.103695 | ||||||||
\(373\) | −11.0715 | −0.573261 | −0.286630 | − | 0.958041i | \(-0.592535\pi\) | ||||
−0.286630 | + | 0.958041i | \(0.592535\pi\) | |||||||
\(374\) | 1.22541 | 0.0633644 | ||||||||
\(375\) | −12.1223 | −0.625994 | ||||||||
\(376\) | −9.15570 | −0.472169 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 4.54472 | 0.233755 | ||||||||
\(379\) | 16.8105 | 0.863495 | 0.431747 | − | 0.901995i | \(-0.357897\pi\) | ||||
0.431747 | + | 0.901995i | \(0.357897\pi\) | |||||||
\(380\) | −7.93158 | −0.406882 | ||||||||
\(381\) | 10.2030 | 0.522717 | ||||||||
\(382\) | −0.120976 | −0.00618967 | ||||||||
\(383\) | −16.5771 | −0.847051 | −0.423525 | − | 0.905884i | \(-0.639208\pi\) | ||||
−0.423525 | + | 0.905884i | \(0.639208\pi\) | |||||||
\(384\) | 0.865515 | 0.0441681 | ||||||||
\(385\) | −21.4323 | −1.09229 | ||||||||
\(386\) | −2.75550 | −0.140251 | ||||||||
\(387\) | −10.3084 | −0.524008 | ||||||||
\(388\) | −14.0819 | −0.714898 | ||||||||
\(389\) | 1.17013 | 0.0593280 | 0.0296640 | − | 0.999560i | \(-0.490556\pi\) | ||||
0.0296640 | + | 0.999560i | \(0.490556\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.526121 | −0.0266071 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 4.43887 | 0.223911 | ||||||||
\(394\) | 15.1253 | 0.762003 | ||||||||
\(395\) | −34.1348 | −1.71751 | ||||||||
\(396\) | −12.9985 | −0.653202 | ||||||||
\(397\) | 26.1975 | 1.31481 | 0.657406 | − | 0.753536i | \(-0.271654\pi\) | ||||
0.657406 | + | 0.753536i | \(0.271654\pi\) | |||||||
\(398\) | −5.30640 | −0.265986 | ||||||||
\(399\) | −1.84972 | −0.0926020 | ||||||||
\(400\) | 8.77384 | 0.438692 | ||||||||
\(401\) | 11.3687 | 0.567726 | 0.283863 | − | 0.958865i | \(-0.408384\pi\) | ||||
0.283863 | + | 0.958865i | \(0.408384\pi\) | |||||||
\(402\) | −11.2257 | −0.559888 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.15243 | −0.306095 | ||||||||
\(405\) | 10.4627 | 0.519894 | ||||||||
\(406\) | −0.0985660 | −0.00489175 | ||||||||
\(407\) | −45.4680 | −2.25376 | ||||||||
\(408\) | −0.183660 | −0.00909251 | ||||||||
\(409\) | 23.3314 | 1.15366 | 0.576832 | − | 0.816863i | \(-0.304289\pi\) | ||||
0.576832 | + | 0.816863i | \(0.304289\pi\) | |||||||
\(410\) | −27.9135 | −1.37855 | ||||||||
\(411\) | 8.13003 | 0.401025 | ||||||||
\(412\) | −19.3491 | −0.953260 | ||||||||
\(413\) | 0.231914 | 0.0114117 | ||||||||
\(414\) | 5.58084 | 0.274283 | ||||||||
\(415\) | −11.7718 | −0.577853 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.1050 | −0.641754 | ||||||||
\(418\) | 12.3417 | 0.603651 | ||||||||
\(419\) | −12.6680 | −0.618875 | −0.309437 | − | 0.950920i | \(-0.600141\pi\) | ||||
−0.309437 | + | 0.950920i | \(0.600141\pi\) | |||||||
\(420\) | 3.21220 | 0.156739 | ||||||||
\(421\) | −27.6625 | −1.34819 | −0.674094 | − | 0.738646i | \(-0.735466\pi\) | ||||
−0.674094 | + | 0.738646i | \(0.735466\pi\) | |||||||
\(422\) | −17.8982 | −0.871271 | ||||||||
\(423\) | −20.6084 | −1.00202 | ||||||||
\(424\) | −12.0948 | −0.587375 | ||||||||
\(425\) | −1.86178 | −0.0903098 | ||||||||
\(426\) | −6.37345 | −0.308795 | ||||||||
\(427\) | −8.03211 | −0.388701 | ||||||||
\(428\) | 11.6501 | 0.563130 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −16.9968 | −0.819660 | ||||||||
\(431\) | 6.41393 | 0.308948 | 0.154474 | − | 0.987997i | \(-0.450632\pi\) | ||||
0.154474 | + | 0.987997i | \(0.450632\pi\) | |||||||
\(432\) | 4.54472 | 0.218658 | ||||||||
\(433\) | −0.0650270 | −0.00312500 | −0.00156250 | − | 0.999999i | \(-0.500497\pi\) | ||||
−0.00156250 | + | 0.999999i | \(0.500497\pi\) | |||||||
\(434\) | −2.31076 | −0.110920 | ||||||||
\(435\) | 0.316613 | 0.0151804 | ||||||||
\(436\) | 5.73307 | 0.274564 | ||||||||
\(437\) | −5.29881 | −0.253477 | ||||||||
\(438\) | 4.85047 | 0.231764 | ||||||||
\(439\) | 36.7778 | 1.75531 | 0.877655 | − | 0.479294i | \(-0.159107\pi\) | ||||
0.877655 | + | 0.479294i | \(0.159107\pi\) | |||||||
\(440\) | −21.4323 | −1.02175 | ||||||||
\(441\) | −2.25088 | −0.107185 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.46383 | −0.402129 | −0.201064 | − | 0.979578i | \(-0.564440\pi\) | ||||
−0.201064 | + | 0.979578i | \(0.564440\pi\) | |||||||
\(444\) | 6.81457 | 0.323405 | ||||||||
\(445\) | 43.8553 | 2.07894 | ||||||||
\(446\) | 16.4385 | 0.778385 | ||||||||
\(447\) | −17.8319 | −0.843422 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −22.6303 | −1.06799 | −0.533995 | − | 0.845488i | \(-0.679310\pi\) | ||||
−0.533995 | + | 0.845488i | \(0.679310\pi\) | |||||||
\(450\) | 19.7489 | 0.930972 | ||||||||
\(451\) | 43.4339 | 2.04522 | ||||||||
\(452\) | 16.5194 | 0.777008 | ||||||||
\(453\) | −10.3349 | −0.485574 | ||||||||
\(454\) | −5.63095 | −0.264274 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.84972 | −0.0866213 | ||||||||
\(457\) | −16.3170 | −0.763278 | −0.381639 | − | 0.924311i | \(-0.624640\pi\) | ||||
−0.381639 | + | 0.924311i | \(0.624640\pi\) | |||||||
\(458\) | −27.7225 | −1.29539 | ||||||||
\(459\) | −0.964376 | −0.0450132 | ||||||||
\(460\) | 9.20183 | 0.429037 | ||||||||
\(461\) | −19.2778 | −0.897858 | −0.448929 | − | 0.893567i | \(-0.648194\pi\) | ||||
−0.448929 | + | 0.893567i | \(0.648194\pi\) | |||||||
\(462\) | −4.99823 | −0.232539 | ||||||||
\(463\) | −2.70218 | −0.125581 | −0.0627904 | − | 0.998027i | \(-0.520000\pi\) | ||||
−0.0627904 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(464\) | −0.0985660 | −0.00457581 | ||||||||
\(465\) | 7.42263 | 0.344216 | ||||||||
\(466\) | −20.1104 | −0.931594 | ||||||||
\(467\) | 18.3906 | 0.851014 | 0.425507 | − | 0.904955i | \(-0.360096\pi\) | ||||
0.425507 | + | 0.904955i | \(0.360096\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.9700 | 0.598899 | ||||||||
\(470\) | −33.9797 | −1.56736 | ||||||||
\(471\) | −8.08410 | −0.372496 | ||||||||
\(472\) | 0.231914 | 0.0106747 | ||||||||
\(473\) | 26.4473 | 1.21605 | ||||||||
\(474\) | −7.96057 | −0.365641 | ||||||||
\(475\) | −18.7509 | −0.860350 | ||||||||
\(476\) | 0.212197 | 0.00972603 | ||||||||
\(477\) | −27.2240 | −1.24650 | ||||||||
\(478\) | 6.62968 | 0.303234 | ||||||||
\(479\) | −40.8708 | −1.86743 | −0.933717 | − | 0.358012i | \(-0.883455\pi\) | ||||
−0.933717 | + | 0.358012i | \(0.883455\pi\) | |||||||
\(480\) | 3.21220 | 0.146616 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1.61687 | −0.0736462 | ||||||||
\(483\) | 2.14596 | 0.0976444 | ||||||||
\(484\) | 22.3491 | 1.01587 | ||||||||
\(485\) | −52.2622 | −2.37310 | ||||||||
\(486\) | 16.0742 | 0.729138 | ||||||||
\(487\) | −17.6293 | −0.798861 | −0.399430 | − | 0.916764i | \(-0.630792\pi\) | ||||
−0.399430 | + | 0.916764i | \(0.630792\pi\) | |||||||
\(488\) | −8.03211 | −0.363597 | ||||||||
\(489\) | −3.87517 | −0.175241 | ||||||||
\(490\) | −3.71131 | −0.167660 | ||||||||
\(491\) | −18.8599 | −0.851137 | −0.425569 | − | 0.904926i | \(-0.639926\pi\) | ||||
−0.425569 | + | 0.904926i | \(0.639926\pi\) | |||||||
\(492\) | −6.50970 | −0.293480 | ||||||||
\(493\) | 0.0209154 | 0.000941982 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −48.2417 | −2.16830 | ||||||||
\(496\) | −2.31076 | −0.103756 | ||||||||
\(497\) | 7.36377 | 0.330310 | ||||||||
\(498\) | −2.74529 | −0.123019 | ||||||||
\(499\) | −2.10742 | −0.0943410 | −0.0471705 | − | 0.998887i | \(-0.515020\pi\) | ||||
−0.0471705 | + | 0.998887i | \(0.515020\pi\) | |||||||
\(500\) | 14.0059 | 0.626364 | ||||||||
\(501\) | 12.7290 | 0.568689 | ||||||||
\(502\) | −0.507011 | −0.0226290 | ||||||||
\(503\) | 21.7884 | 0.971498 | 0.485749 | − | 0.874098i | \(-0.338547\pi\) | ||||
0.485749 | + | 0.874098i | \(0.338547\pi\) | |||||||
\(504\) | −2.25088 | −0.100262 | ||||||||
\(505\) | −22.8336 | −1.01608 | ||||||||
\(506\) | −14.3182 | −0.636521 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.7884 | −0.523025 | ||||||||
\(509\) | −12.1977 | −0.540655 | −0.270328 | − | 0.962768i | \(-0.587132\pi\) | ||||
−0.270328 | + | 0.962768i | \(0.587132\pi\) | |||||||
\(510\) | −0.681619 | −0.0301826 | ||||||||
\(511\) | −5.60414 | −0.247913 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −9.71268 | −0.428826 | ||||||||
\(514\) | 9.64063 | 0.425230 | ||||||||
\(515\) | −71.8104 | −3.16435 | ||||||||
\(516\) | −3.96383 | −0.174498 | ||||||||
\(517\) | 52.8729 | 2.32535 | ||||||||
\(518\) | −7.87343 | −0.345939 | ||||||||
\(519\) | −11.9144 | −0.522986 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.9765 | −1.18186 | −0.590932 | − | 0.806722i | \(-0.701240\pi\) | ||||
−0.590932 | + | 0.806722i | \(0.701240\pi\) | |||||||
\(522\) | −0.221861 | −0.00971057 | ||||||||
\(523\) | −3.75365 | −0.164136 | −0.0820679 | − | 0.996627i | \(-0.526152\pi\) | ||||
−0.0820679 | + | 0.996627i | \(0.526152\pi\) | |||||||
\(524\) | −5.12859 | −0.224043 | ||||||||
\(525\) | 7.59389 | 0.331425 | ||||||||
\(526\) | 7.34617 | 0.320308 | ||||||||
\(527\) | 0.490337 | 0.0213594 | ||||||||
\(528\) | −4.99823 | −0.217520 | ||||||||
\(529\) | −16.8526 | −0.732721 | ||||||||
\(530\) | −44.8876 | −1.94979 | ||||||||
\(531\) | 0.522012 | 0.0226534 | ||||||||
\(532\) | 2.13714 | 0.0926566 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 10.2275 | 0.442587 | ||||||||
\(535\) | 43.2372 | 1.86931 | ||||||||
\(536\) | 12.9700 | 0.560219 | ||||||||
\(537\) | −13.2240 | −0.570656 | ||||||||
\(538\) | −22.3541 | −0.963752 | ||||||||
\(539\) | 5.77486 | 0.248741 | ||||||||
\(540\) | 16.8669 | 0.725835 | ||||||||
\(541\) | −0.0135705 | −0.000583440 0 | −0.000291720 | − | 1.00000i | \(-0.500093\pi\) | ||||
−0.000291720 | 1.00000i | \(0.500093\pi\) | ||||||||
\(542\) | −9.61740 | −0.413103 | ||||||||
\(543\) | −1.44323 | −0.0619348 | ||||||||
\(544\) | 0.212197 | 0.00909787 | ||||||||
\(545\) | 21.2772 | 0.911416 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.66115 | −0.413081 | −0.206540 | − | 0.978438i | \(-0.566220\pi\) | ||||
−0.206540 | + | 0.978438i | \(0.566220\pi\) | |||||||
\(548\) | −9.39328 | −0.401261 | ||||||||
\(549\) | −18.0793 | −0.771608 | ||||||||
\(550\) | −50.6678 | −2.16048 | ||||||||
\(551\) | 0.210649 | 0.00897395 | ||||||||
\(552\) | 2.14596 | 0.0913380 | ||||||||
\(553\) | 9.19749 | 0.391117 | ||||||||
\(554\) | −10.1789 | −0.432460 | ||||||||
\(555\) | 25.2910 | 1.07354 | ||||||||
\(556\) | 15.1413 | 0.642133 | ||||||||
\(557\) | 24.9582 | 1.05751 | 0.528757 | − | 0.848773i | \(-0.322658\pi\) | ||||
0.528757 | + | 0.848773i | \(0.322658\pi\) | |||||||
\(558\) | −5.20126 | −0.220187 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3.71131 | −0.156832 | ||||||||
\(561\) | 1.06061 | 0.0447790 | ||||||||
\(562\) | −14.1692 | −0.597693 | ||||||||
\(563\) | 15.8994 | 0.670080 | 0.335040 | − | 0.942204i | \(-0.391250\pi\) | ||||
0.335040 | + | 0.942204i | \(0.391250\pi\) | |||||||
\(564\) | −7.92439 | −0.333677 | ||||||||
\(565\) | 61.3088 | 2.57928 | ||||||||
\(566\) | −18.9326 | −0.795798 | ||||||||
\(567\) | −2.81913 | −0.118392 | ||||||||
\(568\) | 7.36377 | 0.308977 | ||||||||
\(569\) | −17.9093 | −0.750797 | −0.375398 | − | 0.926864i | \(-0.622494\pi\) | ||||
−0.375398 | + | 0.926864i | \(0.622494\pi\) | |||||||
\(570\) | −6.86490 | −0.287539 | ||||||||
\(571\) | 12.5123 | 0.523623 | 0.261812 | − | 0.965119i | \(-0.415680\pi\) | ||||
0.261812 | + | 0.965119i | \(0.415680\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.104707 | −0.00437418 | ||||||||
\(574\) | 7.52119 | 0.313928 | ||||||||
\(575\) | 21.7539 | 0.907199 | ||||||||
\(576\) | −2.25088 | −0.0937868 | ||||||||
\(577\) | −22.0910 | −0.919662 | −0.459831 | − | 0.888007i | \(-0.652090\pi\) | ||||
−0.459831 | + | 0.888007i | \(0.652090\pi\) | |||||||
\(578\) | 16.9550 | 0.705234 | ||||||||
\(579\) | −2.38492 | −0.0991141 | ||||||||
\(580\) | −0.365809 | −0.0151894 | ||||||||
\(581\) | 3.17186 | 0.131591 | ||||||||
\(582\) | −12.1881 | −0.505211 | ||||||||
\(583\) | 69.8458 | 2.89272 | ||||||||
\(584\) | −5.60414 | −0.231901 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.65982 | −0.151186 | ||||||||
\(587\) | −21.1319 | −0.872205 | −0.436102 | − | 0.899897i | \(-0.643641\pi\) | ||||
−0.436102 | + | 0.899897i | \(0.643641\pi\) | |||||||
\(588\) | −0.865515 | −0.0356932 | ||||||||
\(589\) | 4.93842 | 0.203484 | ||||||||
\(590\) | 0.860706 | 0.0354347 | ||||||||
\(591\) | 13.0912 | 0.538500 | ||||||||
\(592\) | −7.87343 | −0.323596 | ||||||||
\(593\) | −8.95493 | −0.367735 | −0.183867 | − | 0.982951i | \(-0.558862\pi\) | ||||
−0.183867 | + | 0.982951i | \(0.558862\pi\) | |||||||
\(594\) | −26.2451 | −1.07685 | ||||||||
\(595\) | 0.787529 | 0.0322856 | ||||||||
\(596\) | 20.6027 | 0.843919 | ||||||||
\(597\) | −4.59277 | −0.187970 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.7996 | 1.70788 | 0.853942 | − | 0.520368i | \(-0.174205\pi\) | ||||
0.853942 | + | 0.520368i | \(0.174205\pi\) | |||||||
\(600\) | 7.59389 | 0.310019 | ||||||||
\(601\) | 15.2896 | 0.623676 | 0.311838 | − | 0.950135i | \(-0.399055\pi\) | ||||
0.311838 | + | 0.950135i | \(0.399055\pi\) | |||||||
\(602\) | 4.57973 | 0.186656 | ||||||||
\(603\) | 29.1940 | 1.18887 | ||||||||
\(604\) | 11.9407 | 0.485861 | ||||||||
\(605\) | 82.9444 | 3.37217 | ||||||||
\(606\) | −5.32502 | −0.216314 | ||||||||
\(607\) | 14.6087 | 0.592948 | 0.296474 | − | 0.955041i | \(-0.404189\pi\) | ||||
0.296474 | + | 0.955041i | \(0.404189\pi\) | |||||||
\(608\) | 2.13714 | 0.0866723 | ||||||||
\(609\) | −0.0853103 | −0.00345695 | ||||||||
\(610\) | −29.8097 | −1.20696 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.477631 | 0.0193071 | ||||||||
\(613\) | −39.2163 | −1.58393 | −0.791965 | − | 0.610566i | \(-0.790942\pi\) | ||||
−0.791965 | + | 0.610566i | \(0.790942\pi\) | |||||||
\(614\) | 19.6987 | 0.794975 | ||||||||
\(615\) | −24.1595 | −0.974207 | ||||||||
\(616\) | 5.77486 | 0.232676 | ||||||||
\(617\) | −9.35868 | −0.376766 | −0.188383 | − | 0.982096i | \(-0.560325\pi\) | ||||
−0.188383 | + | 0.982096i | \(0.560325\pi\) | |||||||
\(618\) | −16.7469 | −0.673659 | ||||||||
\(619\) | 43.7075 | 1.75675 | 0.878376 | − | 0.477970i | \(-0.158627\pi\) | ||||
0.878376 | + | 0.477970i | \(0.158627\pi\) | |||||||
\(620\) | −8.57596 | −0.344419 | ||||||||
\(621\) | 11.2682 | 0.452176 | ||||||||
\(622\) | 16.9685 | 0.680375 | ||||||||
\(623\) | −11.8167 | −0.473424 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.11112 | 0.324445 | ||||||||
\(626\) | 4.53794 | 0.181373 | ||||||||
\(627\) | 10.6819 | 0.426594 | ||||||||
\(628\) | 9.34022 | 0.372715 | ||||||||
\(629\) | 1.67072 | 0.0666159 | ||||||||
\(630\) | −8.35373 | −0.332821 | ||||||||
\(631\) | −20.7957 | −0.827864 | −0.413932 | − | 0.910308i | \(-0.635845\pi\) | ||||
−0.413932 | + | 0.910308i | \(0.635845\pi\) | |||||||
\(632\) | 9.19749 | 0.365857 | ||||||||
\(633\) | −15.4912 | −0.615718 | ||||||||
\(634\) | 29.1866 | 1.15915 | ||||||||
\(635\) | −43.7504 | −1.73618 | ||||||||
\(636\) | −10.4682 | −0.415092 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.569205 | 0.0225350 | ||||||||
\(639\) | 16.5750 | 0.655696 | ||||||||
\(640\) | −3.71131 | −0.146703 | ||||||||
\(641\) | −7.23795 | −0.285882 | −0.142941 | − | 0.989731i | \(-0.545656\pi\) | ||||
−0.142941 | + | 0.989731i | \(0.545656\pi\) | |||||||
\(642\) | 10.0834 | 0.397958 | ||||||||
\(643\) | −40.1718 | −1.58422 | −0.792111 | − | 0.610377i | \(-0.791018\pi\) | ||||
−0.792111 | + | 0.610377i | \(0.791018\pi\) | |||||||
\(644\) | −2.47940 | −0.0977020 | ||||||||
\(645\) | −14.7110 | −0.579245 | ||||||||
\(646\) | −0.453494 | −0.0178425 | ||||||||
\(647\) | 14.5512 | 0.572068 | 0.286034 | − | 0.958220i | \(-0.407663\pi\) | ||||
0.286034 | + | 0.958220i | \(0.407663\pi\) | |||||||
\(648\) | −2.81913 | −0.110746 | ||||||||
\(649\) | −1.33927 | −0.0525710 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.00000 | −0.0783862 | ||||||||
\(652\) | 4.47730 | 0.175345 | ||||||||
\(653\) | −49.7267 | −1.94596 | −0.972978 | − | 0.230896i | \(-0.925834\pi\) | ||||
−0.972978 | + | 0.230896i | \(0.925834\pi\) | |||||||
\(654\) | 4.96206 | 0.194032 | ||||||||
\(655\) | −19.0338 | −0.743712 | ||||||||
\(656\) | 7.52119 | 0.293653 | ||||||||
\(657\) | −12.6143 | −0.492130 | ||||||||
\(658\) | 9.15570 | 0.356926 | ||||||||
\(659\) | −31.5977 | −1.23087 | −0.615436 | − | 0.788187i | \(-0.711020\pi\) | ||||
−0.615436 | + | 0.788187i | \(0.711020\pi\) | |||||||
\(660\) | −18.5500 | −0.722058 | ||||||||
\(661\) | 24.8712 | 0.967379 | 0.483689 | − | 0.875240i | \(-0.339296\pi\) | ||||
0.483689 | + | 0.875240i | \(0.339296\pi\) | |||||||
\(662\) | 4.80542 | 0.186768 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.17186 | 0.123092 | ||||||||
\(665\) | 7.93158 | 0.307574 | ||||||||
\(666\) | −17.7222 | −0.686720 | ||||||||
\(667\) | −0.244384 | −0.00946260 | ||||||||
\(668\) | −14.7068 | −0.569025 | ||||||||
\(669\) | 14.2278 | 0.550077 | ||||||||
\(670\) | 48.1357 | 1.85964 | ||||||||
\(671\) | 46.3843 | 1.79065 | ||||||||
\(672\) | −0.865515 | −0.0333880 | ||||||||
\(673\) | −21.6490 | −0.834508 | −0.417254 | − | 0.908790i | \(-0.637007\pi\) | ||||
−0.417254 | + | 0.908790i | \(0.637007\pi\) | |||||||
\(674\) | 17.7312 | 0.682982 | ||||||||
\(675\) | 39.8747 | 1.53478 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.3935 | 0.553187 | 0.276594 | − | 0.960987i | \(-0.410794\pi\) | ||||
0.276594 | + | 0.960987i | \(0.410794\pi\) | |||||||
\(678\) | 14.2978 | 0.549104 | ||||||||
\(679\) | 14.0819 | 0.540412 | ||||||||
\(680\) | 0.787529 | 0.0302004 | ||||||||
\(681\) | −4.87367 | −0.186759 | ||||||||
\(682\) | 13.3443 | 0.510981 | ||||||||
\(683\) | −42.3738 | −1.62139 | −0.810694 | − | 0.585471i | \(-0.800910\pi\) | ||||
−0.810694 | + | 0.585471i | \(0.800910\pi\) | |||||||
\(684\) | 4.81045 | 0.183932 | ||||||||
\(685\) | −34.8614 | −1.33199 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −23.9943 | −0.915438 | ||||||||
\(688\) | 4.57973 | 0.174601 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 7.96432 | 0.303196 | ||||||||
\(691\) | −22.9382 | −0.872610 | −0.436305 | − | 0.899799i | \(-0.643713\pi\) | ||||
−0.436305 | + | 0.899799i | \(0.643713\pi\) | |||||||
\(692\) | 13.7657 | 0.523294 | ||||||||
\(693\) | 12.9985 | 0.493774 | ||||||||
\(694\) | 16.7048 | 0.634105 | ||||||||
\(695\) | 56.1940 | 2.13156 | ||||||||
\(696\) | −0.0853103 | −0.00323368 | ||||||||
\(697\) | −1.59597 | −0.0604518 | ||||||||
\(698\) | 0.0200475 | 0.000758808 0 | ||||||||
\(699\) | −17.4058 | −0.658348 | ||||||||
\(700\) | −8.77384 | −0.331620 | ||||||||
\(701\) | −1.70699 | −0.0644723 | −0.0322361 | − | 0.999480i | \(-0.510263\pi\) | ||||
−0.0322361 | + | 0.999480i | \(0.510263\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.8266 | 0.634627 | ||||||||
\(704\) | 5.77486 | 0.217648 | ||||||||
\(705\) | −29.4099 | −1.10764 | ||||||||
\(706\) | −29.8258 | −1.12251 | ||||||||
\(707\) | 6.15243 | 0.231386 | ||||||||
\(708\) | 0.200725 | 0.00754371 | ||||||||
\(709\) | −18.2131 | −0.684009 | −0.342005 | − | 0.939698i | \(-0.611106\pi\) | ||||
−0.342005 | + | 0.939698i | \(0.611106\pi\) | |||||||
\(710\) | 27.3292 | 1.02565 | ||||||||
\(711\) | 20.7025 | 0.776404 | ||||||||
\(712\) | −11.8167 | −0.442848 | ||||||||
\(713\) | −5.72930 | −0.214564 | ||||||||
\(714\) | 0.183660 | 0.00687329 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.2787 | 0.570992 | ||||||||
\(717\) | 5.73808 | 0.214293 | ||||||||
\(718\) | 18.3351 | 0.684258 | ||||||||
\(719\) | 3.58214 | 0.133591 | 0.0667956 | − | 0.997767i | \(-0.478722\pi\) | ||||
0.0667956 | + | 0.997767i | \(0.478722\pi\) | |||||||
\(720\) | −8.35373 | −0.311325 | ||||||||
\(721\) | 19.3491 | 0.720597 | ||||||||
\(722\) | 14.4326 | 0.537128 | ||||||||
\(723\) | −1.39942 | −0.0520450 | ||||||||
\(724\) | 1.66748 | 0.0619713 | ||||||||
\(725\) | −0.864802 | −0.0321180 | ||||||||
\(726\) | 19.3434 | 0.717903 | ||||||||
\(727\) | −3.21747 | −0.119329 | −0.0596647 | − | 0.998218i | \(-0.519003\pi\) | ||||
−0.0596647 | + | 0.998218i | \(0.519003\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.45503 | 0.202038 | ||||||||
\(730\) | −20.7987 | −0.769796 | ||||||||
\(731\) | −0.971806 | −0.0359435 | ||||||||
\(732\) | −6.95191 | −0.256950 | ||||||||
\(733\) | 4.79233 | 0.177009 | 0.0885043 | − | 0.996076i | \(-0.471791\pi\) | ||||
0.0885043 | + | 0.996076i | \(0.471791\pi\) | |||||||
\(734\) | −1.34485 | −0.0496394 | ||||||||
\(735\) | −3.21220 | −0.118484 | ||||||||
\(736\) | −2.47940 | −0.0913919 | ||||||||
\(737\) | −74.9000 | −2.75898 | ||||||||
\(738\) | 16.9293 | 0.623177 | ||||||||
\(739\) | −11.1989 | −0.411958 | −0.205979 | − | 0.978556i | \(-0.566038\pi\) | ||||
−0.205979 | + | 0.978556i | \(0.566038\pi\) | |||||||
\(740\) | −29.2208 | −1.07418 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.0948 | 0.444014 | ||||||||
\(743\) | −38.2570 | −1.40351 | −0.701757 | − | 0.712417i | \(-0.747601\pi\) | ||||
−0.701757 | + | 0.712417i | \(0.747601\pi\) | |||||||
\(744\) | −2.00000 | −0.0733236 | ||||||||
\(745\) | 76.4630 | 2.80139 | ||||||||
\(746\) | 11.0715 | 0.405357 | ||||||||
\(747\) | 7.13948 | 0.261220 | ||||||||
\(748\) | −1.22541 | −0.0448054 | ||||||||
\(749\) | −11.6501 | −0.425686 | ||||||||
\(750\) | 12.1223 | 0.442645 | ||||||||
\(751\) | −1.84025 | −0.0671517 | −0.0335758 | − | 0.999436i | \(-0.510690\pi\) | ||||
−0.0335758 | + | 0.999436i | \(0.510690\pi\) | |||||||
\(752\) | 9.15570 | 0.333874 | ||||||||
\(753\) | −0.438826 | −0.0159917 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 44.3157 | 1.61281 | ||||||||
\(756\) | −4.54472 | −0.165290 | ||||||||
\(757\) | −21.1921 | −0.770241 | −0.385120 | − | 0.922866i | \(-0.625840\pi\) | ||||
−0.385120 | + | 0.922866i | \(0.625840\pi\) | |||||||
\(758\) | −16.8105 | −0.610583 | ||||||||
\(759\) | −12.3926 | −0.449823 | ||||||||
\(760\) | 7.93158 | 0.287709 | ||||||||
\(761\) | −14.1313 | −0.512260 | −0.256130 | − | 0.966642i | \(-0.582447\pi\) | ||||
−0.256130 | + | 0.966642i | \(0.582447\pi\) | |||||||
\(762\) | −10.2030 | −0.369617 | ||||||||
\(763\) | −5.73307 | −0.207551 | ||||||||
\(764\) | 0.120976 | 0.00437676 | ||||||||
\(765\) | 1.77264 | 0.0640898 | ||||||||
\(766\) | 16.5771 | 0.598955 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.865515 | −0.0312316 | ||||||||
\(769\) | −30.6249 | −1.10436 | −0.552181 | − | 0.833725i | \(-0.686204\pi\) | ||||
−0.552181 | + | 0.833725i | \(0.686204\pi\) | |||||||
\(770\) | 21.4323 | 0.772368 | ||||||||
\(771\) | 8.34411 | 0.300506 | ||||||||
\(772\) | 2.75550 | 0.0991725 | ||||||||
\(773\) | 9.79479 | 0.352294 | 0.176147 | − | 0.984364i | \(-0.443637\pi\) | ||||
0.176147 | + | 0.984364i | \(0.443637\pi\) | |||||||
\(774\) | 10.3084 | 0.370529 | ||||||||
\(775\) | −20.2743 | −0.728273 | ||||||||
\(776\) | 14.0819 | 0.505509 | ||||||||
\(777\) | −6.81457 | −0.244471 | ||||||||
\(778\) | −1.17013 | −0.0419512 | ||||||||
\(779\) | −16.0738 | −0.575904 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42.5248 | −1.52166 | ||||||||
\(782\) | 0.526121 | 0.0188140 | ||||||||
\(783\) | −0.447955 | −0.0160086 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 34.6645 | 1.23723 | ||||||||
\(786\) | −4.43887 | −0.158329 | ||||||||
\(787\) | 20.6305 | 0.735397 | 0.367699 | − | 0.929945i | \(-0.380146\pi\) | ||||
0.367699 | + | 0.929945i | \(0.380146\pi\) | |||||||
\(788\) | −15.1253 | −0.538818 | ||||||||
\(789\) | 6.35822 | 0.226359 | ||||||||
\(790\) | 34.1348 | 1.21446 | ||||||||
\(791\) | −16.5194 | −0.587363 | ||||||||
\(792\) | 12.9985 | 0.461883 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −26.1975 | −0.929713 | ||||||||
\(795\) | −38.8509 | −1.37790 | ||||||||
\(796\) | 5.30640 | 0.188080 | ||||||||
\(797\) | 7.77168 | 0.275287 | 0.137643 | − | 0.990482i | \(-0.456047\pi\) | ||||
0.137643 | + | 0.990482i | \(0.456047\pi\) | |||||||
\(798\) | 1.84972 | 0.0654795 | ||||||||
\(799\) | −1.94281 | −0.0687317 | ||||||||
\(800\) | −8.77384 | −0.310202 | ||||||||
\(801\) | −26.5979 | −0.939791 | ||||||||
\(802\) | −11.3687 | −0.401443 | ||||||||
\(803\) | 32.3632 | 1.14207 | ||||||||
\(804\) | 11.2257 | 0.395901 | ||||||||
\(805\) | −9.20183 | −0.324322 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.3478 | −0.681074 | ||||||||
\(808\) | 6.15243 | 0.216442 | ||||||||
\(809\) | 42.5430 | 1.49573 | 0.747866 | − | 0.663850i | \(-0.231078\pi\) | ||||
0.747866 | + | 0.663850i | \(0.231078\pi\) | |||||||
\(810\) | −10.4627 | −0.367621 | ||||||||
\(811\) | −22.1131 | −0.776494 | −0.388247 | − | 0.921555i | \(-0.626919\pi\) | ||||
−0.388247 | + | 0.921555i | \(0.626919\pi\) | |||||||
\(812\) | 0.0985660 | 0.00345899 | ||||||||
\(813\) | −8.32400 | −0.291936 | ||||||||
\(814\) | 45.4680 | 1.59365 | ||||||||
\(815\) | 16.6167 | 0.582056 | ||||||||
\(816\) | 0.183660 | 0.00642937 | ||||||||
\(817\) | −9.78752 | −0.342422 | ||||||||
\(818\) | −23.3314 | −0.815763 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 27.9135 | 0.974782 | ||||||||
\(821\) | 24.3549 | 0.849992 | 0.424996 | − | 0.905195i | \(-0.360275\pi\) | ||||
0.424996 | + | 0.905195i | \(0.360275\pi\) | |||||||
\(822\) | −8.13003 | −0.283567 | ||||||||
\(823\) | −4.75914 | −0.165893 | −0.0829465 | − | 0.996554i | \(-0.526433\pi\) | ||||
−0.0829465 | + | 0.996554i | \(0.526433\pi\) | |||||||
\(824\) | 19.3491 | 0.674056 | ||||||||
\(825\) | −43.8537 | −1.52679 | ||||||||
\(826\) | −0.231914 | −0.00806932 | ||||||||
\(827\) | −7.00333 | −0.243530 | −0.121765 | − | 0.992559i | \(-0.538855\pi\) | ||||
−0.121765 | + | 0.992559i | \(0.538855\pi\) | |||||||
\(828\) | −5.58084 | −0.193948 | ||||||||
\(829\) | −5.75238 | −0.199788 | −0.0998941 | − | 0.994998i | \(-0.531850\pi\) | ||||
−0.0998941 | + | 0.994998i | \(0.531850\pi\) | |||||||
\(830\) | 11.7718 | 0.408604 | ||||||||
\(831\) | −8.80998 | −0.305615 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.212197 | −0.00735219 | ||||||||
\(834\) | 13.1050 | 0.453789 | ||||||||
\(835\) | −54.5817 | −1.88888 | ||||||||
\(836\) | −12.3417 | −0.426846 | ||||||||
\(837\) | −10.5018 | −0.362994 | ||||||||
\(838\) | 12.6680 | 0.437610 | ||||||||
\(839\) | −41.2070 | −1.42262 | −0.711311 | − | 0.702877i | \(-0.751898\pi\) | ||||
−0.711311 | + | 0.702877i | \(0.751898\pi\) | |||||||
\(840\) | −3.21220 | −0.110831 | ||||||||
\(841\) | −28.9903 | −0.999665 | ||||||||
\(842\) | 27.6625 | 0.953312 | ||||||||
\(843\) | −12.2637 | −0.422384 | ||||||||
\(844\) | 17.8982 | 0.616081 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 20.6084 | 0.708532 | ||||||||
\(847\) | −22.3491 | −0.767923 | ||||||||
\(848\) | 12.0948 | 0.415337 | ||||||||
\(849\) | −16.3865 | −0.562382 | ||||||||
\(850\) | 1.86178 | 0.0638586 | ||||||||
\(851\) | −19.5214 | −0.669184 | ||||||||
\(852\) | 6.37345 | 0.218351 | ||||||||
\(853\) | 2.38939 | 0.0818113 | 0.0409056 | − | 0.999163i | \(-0.486976\pi\) | ||||
0.0409056 | + | 0.999163i | \(0.486976\pi\) | |||||||
\(854\) | 8.03211 | 0.274853 | ||||||||
\(855\) | 17.8531 | 0.610562 | ||||||||
\(856\) | −11.6501 | −0.398193 | ||||||||
\(857\) | 13.8037 | 0.471526 | 0.235763 | − | 0.971811i | \(-0.424241\pi\) | ||||
0.235763 | + | 0.971811i | \(0.424241\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.7276 | −1.28725 | −0.643624 | − | 0.765342i | \(-0.722570\pi\) | ||||
−0.643624 | + | 0.765342i | \(0.722570\pi\) | |||||||
\(860\) | 16.9968 | 0.579587 | ||||||||
\(861\) | 6.50970 | 0.221850 | ||||||||
\(862\) | −6.41393 | −0.218459 | ||||||||
\(863\) | 25.5180 | 0.868643 | 0.434322 | − | 0.900758i | \(-0.356988\pi\) | ||||
0.434322 | + | 0.900758i | \(0.356988\pi\) | |||||||
\(864\) | −4.54472 | −0.154614 | ||||||||
\(865\) | 51.0889 | 1.73707 | ||||||||
\(866\) | 0.0650270 | 0.00220971 | ||||||||
\(867\) | 14.6748 | 0.498382 | ||||||||
\(868\) | 2.31076 | 0.0784324 | ||||||||
\(869\) | −53.1143 | −1.80178 | ||||||||
\(870\) | −0.316613 | −0.0107342 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −5.73307 | −0.194146 | ||||||||
\(873\) | 31.6966 | 1.07277 | ||||||||
\(874\) | 5.29881 | 0.179235 | ||||||||
\(875\) | −14.0059 | −0.473486 | ||||||||
\(876\) | −4.85047 | −0.163882 | ||||||||
\(877\) | −12.4391 | −0.420039 | −0.210019 | − | 0.977697i | \(-0.567353\pi\) | ||||
−0.210019 | + | 0.977697i | \(0.567353\pi\) | |||||||
\(878\) | −36.7778 | −1.24119 | ||||||||
\(879\) | −3.16763 | −0.106842 | ||||||||
\(880\) | 21.4323 | 0.722484 | ||||||||
\(881\) | −22.5419 | −0.759457 | −0.379728 | − | 0.925098i | \(-0.623983\pi\) | ||||
−0.379728 | + | 0.925098i | \(0.623983\pi\) | |||||||
\(882\) | 2.25088 | 0.0757912 | ||||||||
\(883\) | 15.1548 | 0.509998 | 0.254999 | − | 0.966941i | \(-0.417925\pi\) | ||||
0.254999 | + | 0.966941i | \(0.417925\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.744954 | 0.0250413 | ||||||||
\(886\) | 8.46383 | 0.284348 | ||||||||
\(887\) | 41.7749 | 1.40266 | 0.701332 | − | 0.712835i | \(-0.252589\pi\) | ||||
0.701332 | + | 0.712835i | \(0.252589\pi\) | |||||||
\(888\) | −6.81457 | −0.228682 | ||||||||
\(889\) | 11.7884 | 0.395370 | ||||||||
\(890\) | −43.8553 | −1.47003 | ||||||||
\(891\) | 16.2801 | 0.545404 | ||||||||
\(892\) | −16.4385 | −0.550402 | ||||||||
\(893\) | −19.5670 | −0.654784 | ||||||||
\(894\) | 17.8319 | 0.596389 | ||||||||
\(895\) | 56.7041 | 1.89541 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.6303 | 0.755183 | ||||||||
\(899\) | 0.227763 | 0.00759631 | ||||||||
\(900\) | −19.7489 | −0.658297 | ||||||||
\(901\) | −2.56648 | −0.0855018 | ||||||||
\(902\) | −43.4339 | −1.44619 | ||||||||
\(903\) | 3.96383 | 0.131908 | ||||||||
\(904\) | −16.5194 | −0.549428 | ||||||||
\(905\) | 6.18853 | 0.205714 | ||||||||
\(906\) | 10.3349 | 0.343353 | ||||||||
\(907\) | 4.28751 | 0.142365 | 0.0711823 | − | 0.997463i | \(-0.477323\pi\) | ||||
0.0711823 | + | 0.997463i | \(0.477323\pi\) | |||||||
\(908\) | 5.63095 | 0.186870 | ||||||||
\(909\) | 13.8484 | 0.459323 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.87618 | −0.128423 | −0.0642117 | − | 0.997936i | \(-0.520453\pi\) | ||||
−0.0642117 | + | 0.997936i | \(0.520453\pi\) | |||||||
\(912\) | 1.84972 | 0.0612505 | ||||||||
\(913\) | −18.3171 | −0.606206 | ||||||||
\(914\) | 16.3170 | 0.539719 | ||||||||
\(915\) | −25.8007 | −0.852945 | ||||||||
\(916\) | 27.7225 | 0.915978 | ||||||||
\(917\) | 5.12859 | 0.169361 | ||||||||
\(918\) | 0.964376 | 0.0318291 | ||||||||
\(919\) | 45.9047 | 1.51426 | 0.757129 | − | 0.653266i | \(-0.226601\pi\) | ||||
0.757129 | + | 0.653266i | \(0.226601\pi\) | |||||||
\(920\) | −9.20183 | −0.303375 | ||||||||
\(921\) | 17.0495 | 0.561801 | ||||||||
\(922\) | 19.2778 | 0.634882 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 4.99823 | 0.164430 | ||||||||
\(925\) | −69.0802 | −2.27134 | ||||||||
\(926\) | 2.70218 | 0.0887990 | ||||||||
\(927\) | 43.5525 | 1.43045 | ||||||||
\(928\) | 0.0985660 | 0.00323559 | ||||||||
\(929\) | −9.83612 | −0.322713 | −0.161356 | − | 0.986896i | \(-0.551587\pi\) | ||||
−0.161356 | + | 0.986896i | \(0.551587\pi\) | |||||||
\(930\) | −7.42263 | −0.243397 | ||||||||
\(931\) | −2.13714 | −0.0700418 | ||||||||
\(932\) | 20.1104 | 0.658737 | ||||||||
\(933\) | 14.6865 | 0.480814 | ||||||||
\(934\) | −18.3906 | −0.601758 | ||||||||
\(935\) | −4.54788 | −0.148731 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.5135 | 0.702815 | 0.351407 | − | 0.936223i | \(-0.385703\pi\) | ||||
0.351407 | + | 0.936223i | \(0.385703\pi\) | |||||||
\(938\) | −12.9700 | −0.423485 | ||||||||
\(939\) | 3.92766 | 0.128174 | ||||||||
\(940\) | 33.9797 | 1.10829 | ||||||||
\(941\) | 6.41845 | 0.209236 | 0.104618 | − | 0.994513i | \(-0.466638\pi\) | ||||
0.104618 | + | 0.994513i | \(0.466638\pi\) | |||||||
\(942\) | 8.08410 | 0.263394 | ||||||||
\(943\) | 18.6480 | 0.607264 | ||||||||
\(944\) | −0.231914 | −0.00754816 | ||||||||
\(945\) | −16.8669 | −0.548679 | ||||||||
\(946\) | −26.4473 | −0.859877 | ||||||||
\(947\) | −7.57266 | −0.246078 | −0.123039 | − | 0.992402i | \(-0.539264\pi\) | ||||
−0.123039 | + | 0.992402i | \(0.539264\pi\) | |||||||
\(948\) | 7.96057 | 0.258547 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 18.7509 | 0.608360 | ||||||||
\(951\) | 25.2614 | 0.819158 | ||||||||
\(952\) | −0.212197 | −0.00687734 | ||||||||
\(953\) | −35.8044 | −1.15982 | −0.579909 | − | 0.814681i | \(-0.696912\pi\) | ||||
−0.579909 | + | 0.814681i | \(0.696912\pi\) | |||||||
\(954\) | 27.2240 | 0.881409 | ||||||||
\(955\) | 0.448980 | 0.0145286 | ||||||||
\(956\) | −6.62968 | −0.214419 | ||||||||
\(957\) | 0.492656 | 0.0159253 | ||||||||
\(958\) | 40.8708 | 1.32048 | ||||||||
\(959\) | 9.39328 | 0.303325 | ||||||||
\(960\) | −3.21220 | −0.103673 | ||||||||
\(961\) | −25.6604 | −0.827754 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −26.2231 | −0.845027 | ||||||||
\(964\) | 1.61687 | 0.0520757 | ||||||||
\(965\) | 10.2265 | 0.329203 | ||||||||
\(966\) | −2.14596 | −0.0690450 | ||||||||
\(967\) | −32.3876 | −1.04152 | −0.520758 | − | 0.853704i | \(-0.674351\pi\) | ||||
−0.520758 | + | 0.853704i | \(0.674351\pi\) | |||||||
\(968\) | −22.3491 | −0.718326 | ||||||||
\(969\) | −0.392506 | −0.0126091 | ||||||||
\(970\) | 52.2622 | 1.67804 | ||||||||
\(971\) | 34.4065 | 1.10416 | 0.552079 | − | 0.833792i | \(-0.313835\pi\) | ||||
0.552079 | + | 0.833792i | \(0.313835\pi\) | |||||||
\(972\) | −16.0742 | −0.515579 | ||||||||
\(973\) | −15.1413 | −0.485407 | ||||||||
\(974\) | 17.6293 | 0.564880 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.03211 | 0.257102 | ||||||||
\(977\) | 23.1484 | 0.740583 | 0.370291 | − | 0.928916i | \(-0.379258\pi\) | ||||
0.370291 | + | 0.928916i | \(0.379258\pi\) | |||||||
\(978\) | 3.87517 | 0.123914 | ||||||||
\(979\) | 68.2396 | 2.18095 | ||||||||
\(980\) | 3.71131 | 0.118554 | ||||||||
\(981\) | −12.9045 | −0.412008 | ||||||||
\(982\) | 18.8599 | 0.601845 | ||||||||
\(983\) | −47.0579 | −1.50092 | −0.750458 | − | 0.660919i | \(-0.770167\pi\) | ||||
−0.750458 | + | 0.660919i | \(0.770167\pi\) | |||||||
\(984\) | 6.50970 | 0.207522 | ||||||||
\(985\) | −56.1349 | −1.78861 | ||||||||
\(986\) | −0.0209154 | −0.000666082 0 | ||||||||
\(987\) | 7.92439 | 0.252236 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.3550 | 0.361068 | ||||||||
\(990\) | 48.2417 | 1.53322 | ||||||||
\(991\) | −11.9010 | −0.378049 | −0.189025 | − | 0.981972i | \(-0.560533\pi\) | ||||
−0.189025 | + | 0.981972i | \(0.560533\pi\) | |||||||
\(992\) | 2.31076 | 0.0733668 | ||||||||
\(993\) | 4.15916 | 0.131987 | ||||||||
\(994\) | −7.36377 | −0.233565 | ||||||||
\(995\) | 19.6937 | 0.624333 | ||||||||
\(996\) | 2.74529 | 0.0869879 | ||||||||
\(997\) | 13.0143 | 0.412166 | 0.206083 | − | 0.978534i | \(-0.433928\pi\) | ||||
0.206083 | + | 0.978534i | \(0.433928\pi\) | |||||||
\(998\) | 2.10742 | 0.0667092 | ||||||||
\(999\) | −35.7825 | −1.13211 |
(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 | 2366.2.a.bf.1.2 | 6 | ||
13.2 | odd | 12 | 182.2.m.b.43.3 | ✓ | 12 | ||
13.5 | odd | 4 | 2366.2.d.r.337.8 | 12 | |||
13.7 | odd | 12 | 182.2.m.b.127.3 | yes | 12 | ||
13.8 | odd | 4 | 2366.2.d.r.337.2 | 12 | |||
13.12 | even | 2 | 2366.2.a.bh.1.2 | 6 | |||
39.2 | even | 12 | 1638.2.bj.g.1135.6 | 12 | |||
39.20 | even | 12 | 1638.2.bj.g.127.4 | 12 | |||
52.7 | even | 12 | 1456.2.cc.d.673.2 | 12 | |||
52.15 | even | 12 | 1456.2.cc.d.225.2 | 12 | |||
91.2 | odd | 12 | 1274.2.o.d.459.6 | 12 | |||
91.20 | even | 12 | 1274.2.m.c.491.1 | 12 | |||
91.33 | even | 12 | 1274.2.v.d.361.6 | 12 | |||
91.41 | even | 12 | 1274.2.m.c.589.1 | 12 | |||
91.46 | odd | 12 | 1274.2.o.d.569.3 | 12 | |||
91.54 | even | 12 | 1274.2.o.e.459.4 | 12 | |||
91.59 | even | 12 | 1274.2.o.e.569.1 | 12 | |||
91.67 | odd | 12 | 1274.2.v.e.667.4 | 12 | |||
91.72 | odd | 12 | 1274.2.v.e.361.4 | 12 | |||
91.80 | even | 12 | 1274.2.v.d.667.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
182.2.m.b.43.3 | ✓ | 12 | 13.2 | odd | 12 | ||
182.2.m.b.127.3 | yes | 12 | 13.7 | odd | 12 | ||
1274.2.m.c.491.1 | 12 | 91.20 | even | 12 | |||
1274.2.m.c.589.1 | 12 | 91.41 | even | 12 | |||
1274.2.o.d.459.6 | 12 | 91.2 | odd | 12 | |||
1274.2.o.d.569.3 | 12 | 91.46 | odd | 12 | |||
1274.2.o.e.459.4 | 12 | 91.54 | even | 12 | |||
1274.2.o.e.569.1 | 12 | 91.59 | even | 12 | |||
1274.2.v.d.361.6 | 12 | 91.33 | even | 12 | |||
1274.2.v.d.667.6 | 12 | 91.80 | even | 12 | |||
1274.2.v.e.361.4 | 12 | 91.72 | odd | 12 | |||
1274.2.v.e.667.4 | 12 | 91.67 | odd | 12 | |||
1456.2.cc.d.225.2 | 12 | 52.15 | even | 12 | |||
1456.2.cc.d.673.2 | 12 | 52.7 | even | 12 | |||
1638.2.bj.g.127.4 | 12 | 39.20 | even | 12 | |||
1638.2.bj.g.1135.6 | 12 | 39.2 | even | 12 | |||
2366.2.a.bf.1.2 | 6 | 1.1 | even | 1 | trivial | ||
2366.2.a.bh.1.2 | 6 | 13.12 | even | 2 | |||
2366.2.d.r.337.2 | 12 | 13.8 | odd | 4 | |||
2366.2.d.r.337.8 | 12 | 13.5 | odd | 4 |