Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6762,2,Mod(1,6762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6762, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6762.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: | \(53.9948418468\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.16448.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.18398\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6762.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.183979 | 0.0822781 | 0.0411390 | − | 0.999153i | \(-0.486901\pi\) | ||||
0.0411390 | + | 0.999153i | \(0.486901\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.183979 | 0.0581794 | ||||||||
\(11\) | 3.08861 | 0.931252 | 0.465626 | − | 0.884982i | \(-0.345829\pi\) | ||||
0.465626 | + | 0.884982i | \(0.345829\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −5.85838 | −1.62482 | −0.812411 | − | 0.583085i | \(-0.801845\pi\) | ||||
−0.812411 | + | 0.583085i | \(0.801845\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.183979 | 0.0475033 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.36796 | −1.54446 | −0.772228 | − | 0.635345i | \(-0.780858\pi\) | ||||
−0.772228 | + | 0.635345i | \(0.780858\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.41421 | −0.783274 | −0.391637 | − | 0.920120i | \(-0.628091\pi\) | ||||
−0.391637 | + | 0.920120i | \(0.628091\pi\) | |||||||
\(20\) | 0.183979 | 0.0411390 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.08861 | 0.658495 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.96615 | −0.993230 | ||||||||
\(26\) | −5.85838 | −1.14892 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.68681 | −0.870318 | −0.435159 | − | 0.900354i | \(-0.643308\pi\) | ||||
−0.435159 | + | 0.900354i | \(0.643308\pi\) | |||||||
\(30\) | 0.183979 | 0.0335899 | ||||||||
\(31\) | −3.41421 | −0.613211 | −0.306605 | − | 0.951837i | \(-0.599193\pi\) | ||||
−0.306605 | + | 0.951837i | \(0.599193\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.08861 | 0.537659 | ||||||||
\(34\) | −6.36796 | −1.09210 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.49042 | −0.245024 | −0.122512 | − | 0.992467i | \(-0.539095\pi\) | ||||
−0.122512 | + | 0.992467i | \(0.539095\pi\) | |||||||
\(38\) | −3.41421 | −0.553859 | ||||||||
\(39\) | −5.85838 | −0.938091 | ||||||||
\(40\) | 0.183979 | 0.0290897 | ||||||||
\(41\) | −2.07621 | −0.324249 | −0.162125 | − | 0.986770i | \(-0.551835\pi\) | ||||
−0.162125 | + | 0.986770i | \(0.551835\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.94699 | 0.754409 | 0.377205 | − | 0.926130i | \(-0.376885\pi\) | ||||
0.377205 | + | 0.926130i | \(0.376885\pi\) | |||||||
\(44\) | 3.08861 | 0.465626 | ||||||||
\(45\) | 0.183979 | 0.0274260 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −5.01241 | −0.731135 | −0.365567 | − | 0.930785i | \(-0.619125\pi\) | ||||
−0.365567 | + | 0.930785i | \(0.619125\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.96615 | −0.702320 | ||||||||
\(51\) | −6.36796 | −0.891693 | ||||||||
\(52\) | −5.85838 | −0.812411 | ||||||||
\(53\) | −1.79972 | −0.247210 | −0.123605 | − | 0.992331i | \(-0.539446\pi\) | ||||
−0.123605 | + | 0.992331i | \(0.539446\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.568241 | 0.0766216 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.41421 | −0.452224 | ||||||||
\(58\) | −4.68681 | −0.615408 | ||||||||
\(59\) | −7.91704 | −1.03071 | −0.515355 | − | 0.856977i | \(-0.672340\pi\) | ||||
−0.515355 | + | 0.856977i | \(0.672340\pi\) | |||||||
\(60\) | 0.183979 | 0.0237516 | ||||||||
\(61\) | 2.30254 | 0.294811 | 0.147405 | − | 0.989076i | \(-0.452908\pi\) | ||||
0.147405 | + | 0.989076i | \(0.452908\pi\) | |||||||
\(62\) | −3.41421 | −0.433606 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.07782 | −0.133687 | ||||||||
\(66\) | 3.08861 | 0.380182 | ||||||||
\(67\) | −1.53953 | −0.188084 | −0.0940419 | − | 0.995568i | \(-0.529979\pi\) | ||||
−0.0940419 | + | 0.995568i | \(0.529979\pi\) | |||||||
\(68\) | −6.36796 | −0.772228 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.08861 | −0.366551 | −0.183275 | − | 0.983062i | \(-0.558670\pi\) | ||||
−0.183275 | + | 0.983062i | \(0.558670\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 5.13097 | 0.600535 | 0.300267 | − | 0.953855i | \(-0.402924\pi\) | ||||
0.300267 | + | 0.953855i | \(0.402924\pi\) | |||||||
\(74\) | −1.49042 | −0.173258 | ||||||||
\(75\) | −4.96615 | −0.573442 | ||||||||
\(76\) | −3.41421 | −0.391637 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.85838 | −0.663331 | ||||||||
\(79\) | −9.08861 | −1.02255 | −0.511274 | − | 0.859418i | \(-0.670826\pi\) | ||||
−0.511274 | + | 0.859418i | \(0.670826\pi\) | |||||||
\(80\) | 0.183979 | 0.0205695 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.07621 | −0.229279 | ||||||||
\(83\) | −0.0175454 | −0.00192586 | −0.000962929 | − | 1.00000i | \(-0.500307\pi\) | ||||
−0.000962929 | 1.00000i | \(0.500307\pi\) | ||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.17157 | −0.127075 | ||||||||
\(86\) | 4.94699 | 0.533448 | ||||||||
\(87\) | −4.68681 | −0.502478 | ||||||||
\(88\) | 3.08861 | 0.329247 | ||||||||
\(89\) | 9.63380 | 1.02118 | 0.510590 | − | 0.859824i | \(-0.329427\pi\) | ||||
0.510590 | + | 0.859824i | \(0.329427\pi\) | |||||||
\(90\) | 0.183979 | 0.0193931 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −3.41421 | −0.354037 | ||||||||
\(94\) | −5.01241 | −0.516990 | ||||||||
\(95\) | −0.628145 | −0.0644463 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 4.60385 | 0.467450 | 0.233725 | − | 0.972303i | \(-0.424908\pi\) | ||||
0.233725 | + | 0.972303i | \(0.424908\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.08861 | 0.310417 | ||||||||
\(100\) | −4.96615 | −0.496615 | ||||||||
\(101\) | −5.39667 | −0.536989 | −0.268494 | − | 0.963281i | \(-0.586526\pi\) | ||||
−0.268494 | + | 0.963281i | \(0.586526\pi\) | |||||||
\(102\) | −6.36796 | −0.630522 | ||||||||
\(103\) | −0.141621 | −0.0139543 | −0.00697717 | − | 0.999976i | \(-0.502221\pi\) | ||||
−0.00697717 | + | 0.999976i | \(0.502221\pi\) | |||||||
\(104\) | −5.85838 | −0.574461 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.79972 | −0.174804 | ||||||||
\(107\) | −16.5452 | −1.59948 | −0.799742 | − | 0.600344i | \(-0.795030\pi\) | ||||
−0.799742 | + | 0.600344i | \(0.795030\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 15.9431 | 1.52707 | 0.763536 | − | 0.645765i | \(-0.223462\pi\) | ||||
0.763536 | + | 0.645765i | \(0.223462\pi\) | |||||||
\(110\) | 0.568241 | 0.0541797 | ||||||||
\(111\) | −1.49042 | −0.141464 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.42097 | 0.133673 | 0.0668366 | − | 0.997764i | \(-0.478709\pi\) | ||||
0.0668366 | + | 0.997764i | \(0.478709\pi\) | |||||||
\(114\) | −3.41421 | −0.319770 | ||||||||
\(115\) | −0.183979 | −0.0171562 | ||||||||
\(116\) | −4.68681 | −0.435159 | ||||||||
\(117\) | −5.85838 | −0.541607 | ||||||||
\(118\) | −7.91704 | −0.728823 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.183979 | 0.0167949 | ||||||||
\(121\) | −1.46047 | −0.132770 | ||||||||
\(122\) | 2.30254 | 0.208463 | ||||||||
\(123\) | −2.07621 | −0.187205 | ||||||||
\(124\) | −3.41421 | −0.306605 | ||||||||
\(125\) | −1.83357 | −0.163999 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0356 | −1.06799 | −0.533994 | − | 0.845488i | \(-0.679309\pi\) | ||||
−0.533994 | + | 0.845488i | \(0.679309\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 4.94699 | 0.435558 | ||||||||
\(130\) | −1.07782 | −0.0945311 | ||||||||
\(131\) | −2.47573 | −0.216306 | −0.108153 | − | 0.994134i | \(-0.534494\pi\) | ||||
−0.108153 | + | 0.994134i | \(0.534494\pi\) | |||||||
\(132\) | 3.08861 | 0.268829 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.53953 | −0.132995 | ||||||||
\(135\) | 0.183979 | 0.0158344 | ||||||||
\(136\) | −6.36796 | −0.546048 | ||||||||
\(137\) | 17.6230 | 1.50563 | 0.752817 | − | 0.658229i | \(-0.228694\pi\) | ||||
0.752817 | + | 0.658229i | \(0.228694\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | 17.9526 | 1.52272 | 0.761362 | − | 0.648327i | \(-0.224531\pi\) | ||||
0.761362 | + | 0.648327i | \(0.224531\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.01241 | −0.422121 | ||||||||
\(142\) | −3.08861 | −0.259191 | ||||||||
\(143\) | −18.0943 | −1.51312 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.862276 | −0.0716081 | ||||||||
\(146\) | 5.13097 | 0.424642 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.49042 | −0.122512 | ||||||||
\(149\) | 1.33925 | 0.109716 | 0.0548578 | − | 0.998494i | \(-0.482529\pi\) | ||||
0.0548578 | + | 0.998494i | \(0.482529\pi\) | |||||||
\(150\) | −4.96615 | −0.405485 | ||||||||
\(151\) | 9.05476 | 0.736866 | 0.368433 | − | 0.929654i | \(-0.379894\pi\) | ||||
0.368433 | + | 0.929654i | \(0.379894\pi\) | |||||||
\(152\) | −3.41421 | −0.276929 | ||||||||
\(153\) | −6.36796 | −0.514819 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.628145 | −0.0504538 | ||||||||
\(156\) | −5.85838 | −0.469046 | ||||||||
\(157\) | 9.98421 | 0.796827 | 0.398413 | − | 0.917206i | \(-0.369561\pi\) | ||||
0.398413 | + | 0.917206i | \(0.369561\pi\) | |||||||
\(158\) | −9.08861 | −0.723051 | ||||||||
\(159\) | −1.79972 | −0.142727 | ||||||||
\(160\) | 0.183979 | 0.0145448 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 8.48528 | 0.664619 | 0.332309 | − | 0.943170i | \(-0.392172\pi\) | ||||
0.332309 | + | 0.943170i | \(0.392172\pi\) | |||||||
\(164\) | −2.07621 | −0.162125 | ||||||||
\(165\) | 0.568241 | 0.0442375 | ||||||||
\(166\) | −0.0175454 | −0.00136179 | ||||||||
\(167\) | 12.1845 | 0.942864 | 0.471432 | − | 0.881902i | \(-0.343737\pi\) | ||||
0.471432 | + | 0.881902i | \(0.343737\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.3206 | 1.64005 | ||||||||
\(170\) | −1.17157 | −0.0898555 | ||||||||
\(171\) | −3.41421 | −0.261091 | ||||||||
\(172\) | 4.94699 | 0.377205 | ||||||||
\(173\) | 6.21555 | 0.472559 | 0.236280 | − | 0.971685i | \(-0.424072\pi\) | ||||
0.236280 | + | 0.971685i | \(0.424072\pi\) | |||||||
\(174\) | −4.68681 | −0.355306 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.08861 | 0.232813 | ||||||||
\(177\) | −7.91704 | −0.595081 | ||||||||
\(178\) | 9.63380 | 0.722084 | ||||||||
\(179\) | 12.6422 | 0.944920 | 0.472460 | − | 0.881352i | \(-0.343366\pi\) | ||||
0.472460 | + | 0.881352i | \(0.343366\pi\) | |||||||
\(180\) | 0.183979 | 0.0137130 | ||||||||
\(181\) | −18.4893 | −1.37430 | −0.687150 | − | 0.726515i | \(-0.741139\pi\) | ||||
−0.687150 | + | 0.726515i | \(0.741139\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.30254 | 0.170209 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −0.274207 | −0.0201601 | ||||||||
\(186\) | −3.41421 | −0.250342 | ||||||||
\(187\) | −19.6682 | −1.43828 | ||||||||
\(188\) | −5.01241 | −0.365567 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.628145 | −0.0455704 | ||||||||
\(191\) | −13.1230 | −0.949545 | −0.474773 | − | 0.880108i | \(-0.657470\pi\) | ||||
−0.474773 | + | 0.880108i | \(0.657470\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 14.6038 | 1.05121 | 0.525604 | − | 0.850729i | \(-0.323839\pi\) | ||||
0.525604 | + | 0.850729i | \(0.323839\pi\) | |||||||
\(194\) | 4.60385 | 0.330537 | ||||||||
\(195\) | −1.07782 | −0.0771843 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.5751 | 1.25218 | 0.626088 | − | 0.779752i | \(-0.284655\pi\) | ||||
0.626088 | + | 0.779752i | \(0.284655\pi\) | |||||||
\(198\) | 3.08861 | 0.219498 | ||||||||
\(199\) | 1.39791 | 0.0990953 | 0.0495476 | − | 0.998772i | \(-0.484222\pi\) | ||||
0.0495476 | + | 0.998772i | \(0.484222\pi\) | |||||||
\(200\) | −4.96615 | −0.351160 | ||||||||
\(201\) | −1.53953 | −0.108590 | ||||||||
\(202\) | −5.39667 | −0.379708 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.36796 | −0.445846 | ||||||||
\(205\) | −0.381979 | −0.0266786 | ||||||||
\(206\) | −0.141621 | −0.00986720 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −5.85838 | −0.406205 | ||||||||
\(209\) | −10.5452 | −0.729426 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.9419 | −1.23517 | −0.617584 | − | 0.786505i | \(-0.711888\pi\) | ||||
−0.617584 | + | 0.786505i | \(0.711888\pi\) | |||||||
\(212\) | −1.79972 | −0.123605 | ||||||||
\(213\) | −3.08861 | −0.211628 | ||||||||
\(214\) | −16.5452 | −1.13101 | ||||||||
\(215\) | 0.910144 | 0.0620713 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 15.9431 | 1.07980 | ||||||||
\(219\) | 5.13097 | 0.346719 | ||||||||
\(220\) | 0.568241 | 0.0383108 | ||||||||
\(221\) | 37.3059 | 2.50947 | ||||||||
\(222\) | −1.49042 | −0.100030 | ||||||||
\(223\) | −23.9013 | −1.60055 | −0.800273 | − | 0.599636i | \(-0.795312\pi\) | ||||
−0.800273 | + | 0.599636i | \(0.795312\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.96615 | −0.331077 | ||||||||
\(226\) | 1.42097 | 0.0945213 | ||||||||
\(227\) | 8.81212 | 0.584881 | 0.292441 | − | 0.956284i | \(-0.405533\pi\) | ||||
0.292441 | + | 0.956284i | \(0.405533\pi\) | |||||||
\(228\) | −3.41421 | −0.226112 | ||||||||
\(229\) | 0.194772 | 0.0128709 | 0.00643544 | − | 0.999979i | \(-0.497952\pi\) | ||||
0.00643544 | + | 0.999979i | \(0.497952\pi\) | |||||||
\(230\) | −0.183979 | −0.0121312 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.68681 | −0.307704 | ||||||||
\(233\) | 9.79972 | 0.642001 | 0.321000 | − | 0.947079i | \(-0.395981\pi\) | ||||
0.321000 | + | 0.947079i | \(0.395981\pi\) | |||||||
\(234\) | −5.85838 | −0.382974 | ||||||||
\(235\) | −0.922179 | −0.0601563 | ||||||||
\(236\) | −7.91704 | −0.515355 | ||||||||
\(237\) | −9.08861 | −0.590369 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.5835 | 0.684590 | 0.342295 | − | 0.939593i | \(-0.388796\pi\) | ||||
0.342295 | + | 0.939593i | \(0.388796\pi\) | |||||||
\(240\) | 0.183979 | 0.0118758 | ||||||||
\(241\) | −6.17847 | −0.397990 | −0.198995 | − | 0.980000i | \(-0.563768\pi\) | ||||
−0.198995 | + | 0.980000i | \(0.563768\pi\) | |||||||
\(242\) | −1.46047 | −0.0938825 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.30254 | 0.147405 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.07621 | −0.132374 | ||||||||
\(247\) | 20.0018 | 1.27268 | ||||||||
\(248\) | −3.41421 | −0.216803 | ||||||||
\(249\) | −0.0175454 | −0.00111189 | ||||||||
\(250\) | −1.83357 | −0.115965 | ||||||||
\(251\) | −18.6845 | −1.17936 | −0.589678 | − | 0.807638i | \(-0.700745\pi\) | ||||
−0.589678 | + | 0.807638i | \(0.700745\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.08861 | −0.194179 | ||||||||
\(254\) | −12.0356 | −0.755181 | ||||||||
\(255\) | −1.17157 | −0.0733667 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.76691 | 0.110217 | 0.0551084 | − | 0.998480i | \(-0.482450\pi\) | ||||
0.0551084 | + | 0.998480i | \(0.482450\pi\) | |||||||
\(258\) | 4.94699 | 0.307986 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.07782 | −0.0668436 | ||||||||
\(261\) | −4.68681 | −0.290106 | ||||||||
\(262\) | −2.47573 | −0.152951 | ||||||||
\(263\) | −7.58864 | −0.467936 | −0.233968 | − | 0.972244i | \(-0.575171\pi\) | ||||
−0.233968 | + | 0.972244i | \(0.575171\pi\) | |||||||
\(264\) | 3.08861 | 0.190091 | ||||||||
\(265\) | −0.331111 | −0.0203400 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.63380 | 0.589579 | ||||||||
\(268\) | −1.53953 | −0.0940419 | ||||||||
\(269\) | −24.6452 | −1.50264 | −0.751321 | − | 0.659937i | \(-0.770583\pi\) | ||||
−0.751321 | + | 0.659937i | \(0.770583\pi\) | |||||||
\(270\) | 0.183979 | 0.0111966 | ||||||||
\(271\) | 18.8261 | 1.14361 | 0.571803 | − | 0.820391i | \(-0.306244\pi\) | ||||
0.571803 | + | 0.820391i | \(0.306244\pi\) | |||||||
\(272\) | −6.36796 | −0.386114 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.6230 | 1.06464 | ||||||||
\(275\) | −15.3385 | −0.924948 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 11.8571 | 0.712426 | 0.356213 | − | 0.934405i | \(-0.384068\pi\) | ||||
0.356213 | + | 0.934405i | \(0.384068\pi\) | |||||||
\(278\) | 17.9526 | 1.07673 | ||||||||
\(279\) | −3.41421 | −0.204404 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.48652 | 0.506264 | 0.253132 | − | 0.967432i | \(-0.418539\pi\) | ||||
0.253132 | + | 0.967432i | \(0.418539\pi\) | |||||||
\(282\) | −5.01241 | −0.298484 | ||||||||
\(283\) | −5.34329 | −0.317626 | −0.158813 | − | 0.987309i | \(-0.550767\pi\) | ||||
−0.158813 | + | 0.987309i | \(0.550767\pi\) | |||||||
\(284\) | −3.08861 | −0.183275 | ||||||||
\(285\) | −0.628145 | −0.0372081 | ||||||||
\(286\) | −18.0943 | −1.06994 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 23.5509 | 1.38535 | ||||||||
\(290\) | −0.862276 | −0.0506346 | ||||||||
\(291\) | 4.60385 | 0.269882 | ||||||||
\(292\) | 5.13097 | 0.300267 | ||||||||
\(293\) | −17.9148 | −1.04659 | −0.523296 | − | 0.852151i | \(-0.675298\pi\) | ||||
−0.523296 | + | 0.852151i | \(0.675298\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.45657 | −0.0848049 | ||||||||
\(296\) | −1.49042 | −0.0866289 | ||||||||
\(297\) | 3.08861 | 0.179220 | ||||||||
\(298\) | 1.33925 | 0.0775806 | ||||||||
\(299\) | 5.85838 | 0.338799 | ||||||||
\(300\) | −4.96615 | −0.286721 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.05476 | 0.521043 | ||||||||
\(303\) | −5.39667 | −0.310030 | ||||||||
\(304\) | −3.41421 | −0.195819 | ||||||||
\(305\) | 0.423621 | 0.0242564 | ||||||||
\(306\) | −6.36796 | −0.364032 | ||||||||
\(307\) | 6.99339 | 0.399134 | 0.199567 | − | 0.979884i | \(-0.436046\pi\) | ||||
0.199567 | + | 0.979884i | \(0.436046\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.141621 | −0.00805654 | ||||||||
\(310\) | −0.628145 | −0.0356762 | ||||||||
\(311\) | −19.9013 | −1.12850 | −0.564248 | − | 0.825605i | \(-0.690834\pi\) | ||||
−0.564248 | + | 0.825605i | \(0.690834\pi\) | |||||||
\(312\) | −5.85838 | −0.331665 | ||||||||
\(313\) | −17.0440 | −0.963382 | −0.481691 | − | 0.876341i | \(-0.659977\pi\) | ||||
−0.481691 | + | 0.876341i | \(0.659977\pi\) | |||||||
\(314\) | 9.98421 | 0.563442 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.08861 | −0.511274 | ||||||||
\(317\) | −6.47449 | −0.363644 | −0.181822 | − | 0.983332i | \(-0.558199\pi\) | ||||
−0.181822 | + | 0.983332i | \(0.558199\pi\) | |||||||
\(318\) | −1.79972 | −0.100923 | ||||||||
\(319\) | −14.4757 | −0.810485 | ||||||||
\(320\) | 0.183979 | 0.0102848 | ||||||||
\(321\) | −16.5452 | −0.923462 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.7416 | 1.20973 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 29.0936 | 1.61382 | ||||||||
\(326\) | 8.48528 | 0.469956 | ||||||||
\(327\) | 15.9431 | 0.881655 | ||||||||
\(328\) | −2.07621 | −0.114639 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.568241 | 0.0312806 | ||||||||
\(331\) | −17.4909 | −0.961389 | −0.480694 | − | 0.876888i | \(-0.659615\pi\) | ||||
−0.480694 | + | 0.876888i | \(0.659615\pi\) | |||||||
\(332\) | −0.0175454 | −0.000962929 0 | ||||||||
\(333\) | −1.49042 | −0.0816745 | ||||||||
\(334\) | 12.1845 | 0.666706 | ||||||||
\(335\) | −0.283242 | −0.0154752 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.0999 | −1.14939 | −0.574693 | − | 0.818369i | \(-0.694879\pi\) | ||||
−0.574693 | + | 0.818369i | \(0.694879\pi\) | |||||||
\(338\) | 21.3206 | 1.15969 | ||||||||
\(339\) | 1.42097 | 0.0771763 | ||||||||
\(340\) | −1.17157 | −0.0635375 | ||||||||
\(341\) | −10.5452 | −0.571054 | ||||||||
\(342\) | −3.41421 | −0.184620 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.94699 | 0.266724 | ||||||||
\(345\) | −0.183979 | −0.00990512 | ||||||||
\(346\) | 6.21555 | 0.334150 | ||||||||
\(347\) | 12.1976 | 0.654800 | 0.327400 | − | 0.944886i | \(-0.393828\pi\) | ||||
0.327400 | + | 0.944886i | \(0.393828\pi\) | |||||||
\(348\) | −4.68681 | −0.251239 | ||||||||
\(349\) | −25.3353 | −1.35617 | −0.678084 | − | 0.734985i | \(-0.737189\pi\) | ||||
−0.678084 | + | 0.734985i | \(0.737189\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.85838 | −0.312697 | ||||||||
\(352\) | 3.08861 | 0.164624 | ||||||||
\(353\) | 26.9816 | 1.43608 | 0.718042 | − | 0.696000i | \(-0.245039\pi\) | ||||
0.718042 | + | 0.696000i | \(0.245039\pi\) | |||||||
\(354\) | −7.91704 | −0.420786 | ||||||||
\(355\) | −0.568241 | −0.0301591 | ||||||||
\(356\) | 9.63380 | 0.510590 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.6422 | 0.668159 | ||||||||
\(359\) | 3.43623 | 0.181357 | 0.0906786 | − | 0.995880i | \(-0.471096\pi\) | ||||
0.0906786 | + | 0.995880i | \(0.471096\pi\) | |||||||
\(360\) | 0.183979 | 0.00969656 | ||||||||
\(361\) | −7.34315 | −0.386481 | ||||||||
\(362\) | −18.4893 | −0.971777 | ||||||||
\(363\) | −1.46047 | −0.0766547 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.943993 | 0.0494108 | ||||||||
\(366\) | 2.30254 | 0.120356 | ||||||||
\(367\) | 21.8481 | 1.14046 | 0.570231 | − | 0.821485i | \(-0.306854\pi\) | ||||
0.570231 | + | 0.821485i | \(0.306854\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −2.07621 | −0.108083 | ||||||||
\(370\) | −0.274207 | −0.0142553 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.41421 | −0.177019 | ||||||||
\(373\) | −33.9436 | −1.75753 | −0.878767 | − | 0.477251i | \(-0.841633\pi\) | ||||
−0.878767 | + | 0.477251i | \(0.841633\pi\) | |||||||
\(374\) | −19.6682 | −1.01702 | ||||||||
\(375\) | −1.83357 | −0.0946849 | ||||||||
\(376\) | −5.01241 | −0.258495 | ||||||||
\(377\) | 27.4571 | 1.41411 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.7563 | −1.47711 | −0.738555 | − | 0.674193i | \(-0.764491\pi\) | ||||
−0.738555 | + | 0.674193i | \(0.764491\pi\) | |||||||
\(380\) | −0.628145 | −0.0322231 | ||||||||
\(381\) | −12.0356 | −0.616603 | ||||||||
\(382\) | −13.1230 | −0.671430 | ||||||||
\(383\) | −2.94648 | −0.150558 | −0.0752790 | − | 0.997163i | \(-0.523985\pi\) | ||||
−0.0752790 | + | 0.997163i | \(0.523985\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.6038 | 0.743316 | ||||||||
\(387\) | 4.94699 | 0.251470 | ||||||||
\(388\) | 4.60385 | 0.233725 | ||||||||
\(389\) | 17.7742 | 0.901187 | 0.450593 | − | 0.892729i | \(-0.351212\pi\) | ||||
0.450593 | + | 0.892729i | \(0.351212\pi\) | |||||||
\(390\) | −1.07782 | −0.0545776 | ||||||||
\(391\) | 6.36796 | 0.322042 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.47573 | −0.124884 | ||||||||
\(394\) | 17.5751 | 0.885423 | ||||||||
\(395\) | −1.67212 | −0.0841333 | ||||||||
\(396\) | 3.08861 | 0.155209 | ||||||||
\(397\) | −22.6026 | −1.13439 | −0.567196 | − | 0.823583i | \(-0.691972\pi\) | ||||
−0.567196 | + | 0.823583i | \(0.691972\pi\) | |||||||
\(398\) | 1.39791 | 0.0700709 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.96615 | −0.248308 | ||||||||
\(401\) | −31.8047 | −1.58825 | −0.794126 | − | 0.607754i | \(-0.792071\pi\) | ||||
−0.794126 | + | 0.607754i | \(0.792071\pi\) | |||||||
\(402\) | −1.53953 | −0.0767849 | ||||||||
\(403\) | 20.0018 | 0.996358 | ||||||||
\(404\) | −5.39667 | −0.268494 | ||||||||
\(405\) | 0.183979 | 0.00914201 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.60333 | −0.228179 | ||||||||
\(408\) | −6.36796 | −0.315261 | ||||||||
\(409\) | −11.3082 | −0.559154 | −0.279577 | − | 0.960123i | \(-0.590194\pi\) | ||||
−0.279577 | + | 0.960123i | \(0.590194\pi\) | |||||||
\(410\) | −0.381979 | −0.0188646 | ||||||||
\(411\) | 17.6230 | 0.869279 | ||||||||
\(412\) | −0.141621 | −0.00697717 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | −0.00322799 | −0.000158456 0 | ||||||||
\(416\) | −5.85838 | −0.287231 | ||||||||
\(417\) | 17.9526 | 0.879145 | ||||||||
\(418\) | −10.5452 | −0.515782 | ||||||||
\(419\) | 30.3833 | 1.48432 | 0.742161 | − | 0.670222i | \(-0.233801\pi\) | ||||
0.742161 | + | 0.670222i | \(0.233801\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.4149 | 0.897486 | 0.448743 | − | 0.893661i | \(-0.351872\pi\) | ||||
0.448743 | + | 0.893661i | \(0.351872\pi\) | |||||||
\(422\) | −17.9419 | −0.873396 | ||||||||
\(423\) | −5.01241 | −0.243712 | ||||||||
\(424\) | −1.79972 | −0.0874020 | ||||||||
\(425\) | 31.6242 | 1.53400 | ||||||||
\(426\) | −3.08861 | −0.149644 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −16.5452 | −0.799742 | ||||||||
\(429\) | −18.0943 | −0.873599 | ||||||||
\(430\) | 0.910144 | 0.0438911 | ||||||||
\(431\) | −0.811922 | −0.0391089 | −0.0195544 | − | 0.999809i | \(-0.506225\pi\) | ||||
−0.0195544 | + | 0.999809i | \(0.506225\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −35.7020 | −1.71573 | −0.857865 | − | 0.513876i | \(-0.828209\pi\) | ||||
−0.857865 | + | 0.513876i | \(0.828209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.862276 | −0.0413429 | ||||||||
\(436\) | 15.9431 | 0.763536 | ||||||||
\(437\) | 3.41421 | 0.163324 | ||||||||
\(438\) | 5.13097 | 0.245167 | ||||||||
\(439\) | −12.0193 | −0.573650 | −0.286825 | − | 0.957983i | \(-0.592600\pi\) | ||||
−0.286825 | + | 0.957983i | \(0.592600\pi\) | |||||||
\(440\) | 0.568241 | 0.0270898 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 37.3059 | 1.77446 | ||||||||
\(443\) | −36.0622 | −1.71337 | −0.856683 | − | 0.515844i | \(-0.827479\pi\) | ||||
−0.856683 | + | 0.515844i | \(0.827479\pi\) | |||||||
\(444\) | −1.49042 | −0.0707322 | ||||||||
\(445\) | 1.77242 | 0.0840208 | ||||||||
\(446\) | −23.9013 | −1.13176 | ||||||||
\(447\) | 1.33925 | 0.0633443 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.0867970 | 0.00409620 | 0.00204810 | − | 0.999998i | \(-0.499348\pi\) | ||||
0.00204810 | + | 0.999998i | \(0.499348\pi\) | |||||||
\(450\) | −4.96615 | −0.234107 | ||||||||
\(451\) | −6.41260 | −0.301958 | ||||||||
\(452\) | 1.42097 | 0.0668366 | ||||||||
\(453\) | 9.05476 | 0.425430 | ||||||||
\(454\) | 8.81212 | 0.413573 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.41421 | −0.159885 | ||||||||
\(457\) | −37.6005 | −1.75888 | −0.879438 | − | 0.476014i | \(-0.842081\pi\) | ||||
−0.879438 | + | 0.476014i | \(0.842081\pi\) | |||||||
\(458\) | 0.194772 | 0.00910109 | ||||||||
\(459\) | −6.36796 | −0.297231 | ||||||||
\(460\) | −0.183979 | −0.00857808 | ||||||||
\(461\) | 33.2804 | 1.55002 | 0.775011 | − | 0.631948i | \(-0.217744\pi\) | ||||
0.775011 | + | 0.631948i | \(0.217744\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.4036 | −0.855286 | −0.427643 | − | 0.903948i | \(-0.640656\pi\) | ||||
−0.427643 | + | 0.903948i | \(0.640656\pi\) | |||||||
\(464\) | −4.68681 | −0.217580 | ||||||||
\(465\) | −0.628145 | −0.0291295 | ||||||||
\(466\) | 9.79972 | 0.453963 | ||||||||
\(467\) | −32.6327 | −1.51006 | −0.755031 | − | 0.655690i | \(-0.772378\pi\) | ||||
−0.755031 | + | 0.655690i | \(0.772378\pi\) | |||||||
\(468\) | −5.85838 | −0.270804 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.922179 | −0.0425370 | ||||||||
\(471\) | 9.98421 | 0.460048 | ||||||||
\(472\) | −7.91704 | −0.364411 | ||||||||
\(473\) | 15.2793 | 0.702545 | ||||||||
\(474\) | −9.08861 | −0.417454 | ||||||||
\(475\) | 16.9555 | 0.777972 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.79972 | −0.0824034 | ||||||||
\(478\) | 10.5835 | 0.484078 | ||||||||
\(479\) | 33.0578 | 1.51045 | 0.755224 | − | 0.655467i | \(-0.227528\pi\) | ||||
0.755224 | + | 0.655467i | \(0.227528\pi\) | |||||||
\(480\) | 0.183979 | 0.00839747 | ||||||||
\(481\) | 8.73145 | 0.398120 | ||||||||
\(482\) | −6.17847 | −0.281422 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.46047 | −0.0663849 | ||||||||
\(485\) | 0.847013 | 0.0384609 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 24.1562 | 1.09462 | 0.547310 | − | 0.836930i | \(-0.315652\pi\) | ||||
0.547310 | + | 0.836930i | \(0.315652\pi\) | |||||||
\(488\) | 2.30254 | 0.104231 | ||||||||
\(489\) | 8.48528 | 0.383718 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.6320 | 1.24702 | 0.623508 | − | 0.781817i | \(-0.285707\pi\) | ||||
0.623508 | + | 0.781817i | \(0.285707\pi\) | |||||||
\(492\) | −2.07621 | −0.0936026 | ||||||||
\(493\) | 29.8454 | 1.34417 | ||||||||
\(494\) | 20.0018 | 0.899922 | ||||||||
\(495\) | 0.568241 | 0.0255405 | ||||||||
\(496\) | −3.41421 | −0.153303 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.0175454 | −0.000786228 0 | ||||||||
\(499\) | −33.9787 | −1.52110 | −0.760548 | − | 0.649282i | \(-0.775070\pi\) | ||||
−0.760548 | + | 0.649282i | \(0.775070\pi\) | |||||||
\(500\) | −1.83357 | −0.0819996 | ||||||||
\(501\) | 12.1845 | 0.544363 | ||||||||
\(502\) | −18.6845 | −0.833931 | ||||||||
\(503\) | −25.6451 | −1.14346 | −0.571729 | − | 0.820442i | \(-0.693727\pi\) | ||||
−0.571729 | + | 0.820442i | \(0.693727\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.992875 | −0.0441824 | ||||||||
\(506\) | −3.08861 | −0.137306 | ||||||||
\(507\) | 21.3206 | 0.946881 | ||||||||
\(508\) | −12.0356 | −0.533994 | ||||||||
\(509\) | −29.1631 | −1.29263 | −0.646315 | − | 0.763071i | \(-0.723691\pi\) | ||||
−0.646315 | + | 0.763071i | \(0.723691\pi\) | |||||||
\(510\) | −1.17157 | −0.0518781 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.41421 | −0.150741 | ||||||||
\(514\) | 1.76691 | 0.0779350 | ||||||||
\(515\) | −0.0260553 | −0.00114814 | ||||||||
\(516\) | 4.94699 | 0.217779 | ||||||||
\(517\) | −15.4814 | −0.680871 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.21555 | 0.272832 | ||||||||
\(520\) | −1.07782 | −0.0472656 | ||||||||
\(521\) | −43.0011 | −1.88391 | −0.941956 | − | 0.335736i | \(-0.891015\pi\) | ||||
−0.941956 | + | 0.335736i | \(0.891015\pi\) | |||||||
\(522\) | −4.68681 | −0.205136 | ||||||||
\(523\) | −19.3202 | −0.844815 | −0.422407 | − | 0.906406i | \(-0.638815\pi\) | ||||
−0.422407 | + | 0.906406i | \(0.638815\pi\) | |||||||
\(524\) | −2.47573 | −0.108153 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.58864 | −0.330881 | ||||||||
\(527\) | 21.7416 | 0.947078 | ||||||||
\(528\) | 3.08861 | 0.134415 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −0.331111 | −0.0143825 | ||||||||
\(531\) | −7.91704 | −0.343570 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.1632 | 0.526847 | ||||||||
\(534\) | 9.63380 | 0.416895 | ||||||||
\(535\) | −3.04397 | −0.131602 | ||||||||
\(536\) | −1.53953 | −0.0664976 | ||||||||
\(537\) | 12.6422 | 0.545550 | ||||||||
\(538\) | −24.6452 | −1.06253 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.183979 | 0.00791721 | ||||||||
\(541\) | −33.7203 | −1.44975 | −0.724874 | − | 0.688882i | \(-0.758102\pi\) | ||||
−0.724874 | + | 0.688882i | \(0.758102\pi\) | |||||||
\(542\) | 18.8261 | 0.808652 | ||||||||
\(543\) | −18.4893 | −0.793453 | ||||||||
\(544\) | −6.36796 | −0.273024 | ||||||||
\(545\) | 2.93320 | 0.125644 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.6275 | −1.18127 | −0.590633 | − | 0.806940i | \(-0.701122\pi\) | ||||
−0.590633 | + | 0.806940i | \(0.701122\pi\) | |||||||
\(548\) | 17.6230 | 0.752817 | ||||||||
\(549\) | 2.30254 | 0.0982702 | ||||||||
\(550\) | −15.3385 | −0.654037 | ||||||||
\(551\) | 16.0018 | 0.681698 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 11.8571 | 0.503761 | ||||||||
\(555\) | −0.274207 | −0.0116394 | ||||||||
\(556\) | 17.9526 | 0.761362 | ||||||||
\(557\) | −1.65685 | −0.0702032 | −0.0351016 | − | 0.999384i | \(-0.511175\pi\) | ||||
−0.0351016 | + | 0.999384i | \(0.511175\pi\) | |||||||
\(558\) | −3.41421 | −0.144535 | ||||||||
\(559\) | −28.9814 | −1.22578 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.6682 | −0.830390 | ||||||||
\(562\) | 8.48652 | 0.357982 | ||||||||
\(563\) | 38.9217 | 1.64035 | 0.820176 | − | 0.572111i | \(-0.193875\pi\) | ||||
0.820176 | + | 0.572111i | \(0.193875\pi\) | |||||||
\(564\) | −5.01241 | −0.211060 | ||||||||
\(565\) | 0.261428 | 0.0109984 | ||||||||
\(566\) | −5.34329 | −0.224595 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.08861 | −0.129595 | ||||||||
\(569\) | 10.3093 | 0.432188 | 0.216094 | − | 0.976373i | \(-0.430668\pi\) | ||||
0.216094 | + | 0.976373i | \(0.430668\pi\) | |||||||
\(570\) | −0.628145 | −0.0263101 | ||||||||
\(571\) | 23.3137 | 0.975648 | 0.487824 | − | 0.872942i | \(-0.337791\pi\) | ||||
0.487824 | + | 0.872942i | \(0.337791\pi\) | |||||||
\(572\) | −18.0943 | −0.756559 | ||||||||
\(573\) | −13.1230 | −0.548220 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.96615 | 0.207103 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 33.2716 | 1.38512 | 0.692558 | − | 0.721362i | \(-0.256484\pi\) | ||||
0.692558 | + | 0.721362i | \(0.256484\pi\) | |||||||
\(578\) | 23.5509 | 0.979588 | ||||||||
\(579\) | 14.6038 | 0.606915 | ||||||||
\(580\) | −0.862276 | −0.0358040 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4.60385 | 0.190836 | ||||||||
\(583\) | −5.55863 | −0.230215 | ||||||||
\(584\) | 5.13097 | 0.212321 | ||||||||
\(585\) | −1.07782 | −0.0445624 | ||||||||
\(586\) | −17.9148 | −0.740052 | ||||||||
\(587\) | 35.4328 | 1.46247 | 0.731234 | − | 0.682127i | \(-0.238945\pi\) | ||||
0.731234 | + | 0.682127i | \(0.238945\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.6569 | 0.480312 | ||||||||
\(590\) | −1.45657 | −0.0599661 | ||||||||
\(591\) | 17.5751 | 0.722945 | ||||||||
\(592\) | −1.49042 | −0.0612559 | ||||||||
\(593\) | 8.28604 | 0.340267 | 0.170133 | − | 0.985421i | \(-0.445580\pi\) | ||||
0.170133 | + | 0.985421i | \(0.445580\pi\) | |||||||
\(594\) | 3.08861 | 0.126727 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.33925 | 0.0548578 | ||||||||
\(597\) | 1.39791 | 0.0572127 | ||||||||
\(598\) | 5.85838 | 0.239567 | ||||||||
\(599\) | 17.3392 | 0.708463 | 0.354231 | − | 0.935158i | \(-0.384743\pi\) | ||||
0.354231 | + | 0.935158i | \(0.384743\pi\) | |||||||
\(600\) | −4.96615 | −0.202742 | ||||||||
\(601\) | 18.1214 | 0.739186 | 0.369593 | − | 0.929194i | \(-0.379497\pi\) | ||||
0.369593 | + | 0.929194i | \(0.379497\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.53953 | −0.0626946 | ||||||||
\(604\) | 9.05476 | 0.368433 | ||||||||
\(605\) | −0.268696 | −0.0109240 | ||||||||
\(606\) | −5.39667 | −0.219225 | ||||||||
\(607\) | 23.3663 | 0.948411 | 0.474205 | − | 0.880414i | \(-0.342735\pi\) | ||||
0.474205 | + | 0.880414i | \(0.342735\pi\) | |||||||
\(608\) | −3.41421 | −0.138465 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.423621 | 0.0171519 | ||||||||
\(611\) | 29.3646 | 1.18796 | ||||||||
\(612\) | −6.36796 | −0.257409 | ||||||||
\(613\) | −37.9353 | −1.53219 | −0.766096 | − | 0.642726i | \(-0.777803\pi\) | ||||
−0.766096 | + | 0.642726i | \(0.777803\pi\) | |||||||
\(614\) | 6.99339 | 0.282230 | ||||||||
\(615\) | −0.381979 | −0.0154029 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.6274 | 1.31353 | 0.656765 | − | 0.754095i | \(-0.271924\pi\) | ||||
0.656765 | + | 0.754095i | \(0.271924\pi\) | |||||||
\(618\) | −0.141621 | −0.00569683 | ||||||||
\(619\) | 31.1150 | 1.25062 | 0.625308 | − | 0.780378i | \(-0.284973\pi\) | ||||
0.625308 | + | 0.780378i | \(0.284973\pi\) | |||||||
\(620\) | −0.628145 | −0.0252269 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −19.9013 | −0.797968 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.85838 | −0.234523 | ||||||||
\(625\) | 24.4934 | 0.979737 | ||||||||
\(626\) | −17.0440 | −0.681214 | ||||||||
\(627\) | −10.5452 | −0.421134 | ||||||||
\(628\) | 9.98421 | 0.398413 | ||||||||
\(629\) | 9.49093 | 0.378428 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.9556 | 0.794422 | 0.397211 | − | 0.917727i | \(-0.369978\pi\) | ||||
0.397211 | + | 0.917727i | \(0.369978\pi\) | |||||||
\(632\) | −9.08861 | −0.361526 | ||||||||
\(633\) | −17.9419 | −0.713125 | ||||||||
\(634\) | −6.47449 | −0.257135 | ||||||||
\(635\) | −2.21430 | −0.0878719 | ||||||||
\(636\) | −1.79972 | −0.0713634 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.4757 | −0.573100 | ||||||||
\(639\) | −3.08861 | −0.122184 | ||||||||
\(640\) | 0.183979 | 0.00727242 | ||||||||
\(641\) | −1.72123 | −0.0679844 | −0.0339922 | − | 0.999422i | \(-0.510822\pi\) | ||||
−0.0339922 | + | 0.999422i | \(0.510822\pi\) | |||||||
\(642\) | −16.5452 | −0.652986 | ||||||||
\(643\) | −6.02885 | −0.237755 | −0.118877 | − | 0.992909i | \(-0.537930\pi\) | ||||
−0.118877 | + | 0.992909i | \(0.537930\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.910144 | 0.0358369 | ||||||||
\(646\) | 21.7416 | 0.855411 | ||||||||
\(647\) | −19.9498 | −0.784309 | −0.392155 | − | 0.919899i | \(-0.628270\pi\) | ||||
−0.392155 | + | 0.919899i | \(0.628270\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −24.4527 | −0.959851 | ||||||||
\(650\) | 29.0936 | 1.14114 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.48528 | 0.332309 | ||||||||
\(653\) | 41.8484 | 1.63765 | 0.818827 | − | 0.574040i | \(-0.194625\pi\) | ||||
0.818827 | + | 0.574040i | \(0.194625\pi\) | |||||||
\(654\) | 15.9431 | 0.623424 | ||||||||
\(655\) | −0.455483 | −0.0177972 | ||||||||
\(656\) | −2.07621 | −0.0810623 | ||||||||
\(657\) | 5.13097 | 0.200178 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.6721 | 0.688408 | 0.344204 | − | 0.938895i | \(-0.388149\pi\) | ||||
0.344204 | + | 0.938895i | \(0.388149\pi\) | |||||||
\(660\) | 0.568241 | 0.0221188 | ||||||||
\(661\) | 45.0019 | 1.75037 | 0.875186 | − | 0.483787i | \(-0.160739\pi\) | ||||
0.875186 | + | 0.483787i | \(0.160739\pi\) | |||||||
\(662\) | −17.4909 | −0.679804 | ||||||||
\(663\) | 37.3059 | 1.44884 | ||||||||
\(664\) | −0.0175454 | −0.000680894 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.49042 | −0.0577526 | ||||||||
\(667\) | 4.68681 | 0.181474 | ||||||||
\(668\) | 12.1845 | 0.471432 | ||||||||
\(669\) | −23.9013 | −0.924076 | ||||||||
\(670\) | −0.283242 | −0.0109426 | ||||||||
\(671\) | 7.11167 | 0.274543 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.0948 | 0.697503 | 0.348751 | − | 0.937215i | \(-0.386606\pi\) | ||||
0.348751 | + | 0.937215i | \(0.386606\pi\) | |||||||
\(674\) | −21.0999 | −0.812739 | ||||||||
\(675\) | −4.96615 | −0.191147 | ||||||||
\(676\) | 21.3206 | 0.820023 | ||||||||
\(677\) | −34.4000 | −1.32210 | −0.661050 | − | 0.750341i | \(-0.729889\pi\) | ||||
−0.661050 | + | 0.750341i | \(0.729889\pi\) | |||||||
\(678\) | 1.42097 | 0.0545719 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.17157 | −0.0449278 | ||||||||
\(681\) | 8.81212 | 0.337681 | ||||||||
\(682\) | −10.5452 | −0.403796 | ||||||||
\(683\) | −39.2300 | −1.50110 | −0.750548 | − | 0.660816i | \(-0.770210\pi\) | ||||
−0.750548 | + | 0.660816i | \(0.770210\pi\) | |||||||
\(684\) | −3.41421 | −0.130546 | ||||||||
\(685\) | 3.24227 | 0.123881 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.194772 | 0.00743101 | ||||||||
\(688\) | 4.94699 | 0.188602 | ||||||||
\(689\) | 10.5434 | 0.401673 | ||||||||
\(690\) | −0.183979 | −0.00700397 | ||||||||
\(691\) | 23.2054 | 0.882776 | 0.441388 | − | 0.897316i | \(-0.354486\pi\) | ||||
0.441388 | + | 0.897316i | \(0.354486\pi\) | |||||||
\(692\) | 6.21555 | 0.236280 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.1976 | 0.463013 | ||||||||
\(695\) | 3.30292 | 0.125287 | ||||||||
\(696\) | −4.68681 | −0.177653 | ||||||||
\(697\) | 13.2212 | 0.500789 | ||||||||
\(698\) | −25.3353 | −0.958955 | ||||||||
\(699\) | 9.79972 | 0.370659 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.82271 | −0.257690 | −0.128845 | − | 0.991665i | \(-0.541127\pi\) | ||||
−0.128845 | + | 0.991665i | \(0.541127\pi\) | |||||||
\(702\) | −5.85838 | −0.221110 | ||||||||
\(703\) | 5.08861 | 0.191921 | ||||||||
\(704\) | 3.08861 | 0.116406 | ||||||||
\(705\) | −0.922179 | −0.0347313 | ||||||||
\(706\) | 26.9816 | 1.01546 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.91704 | −0.297541 | ||||||||
\(709\) | −36.6309 | −1.37570 | −0.687852 | − | 0.725851i | \(-0.741446\pi\) | ||||
−0.687852 | + | 0.725851i | \(0.741446\pi\) | |||||||
\(710\) | −0.568241 | −0.0213257 | ||||||||
\(711\) | −9.08861 | −0.340850 | ||||||||
\(712\) | 9.63380 | 0.361042 | ||||||||
\(713\) | 3.41421 | 0.127863 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.32897 | −0.124496 | ||||||||
\(716\) | 12.6422 | 0.472460 | ||||||||
\(717\) | 10.5835 | 0.395248 | ||||||||
\(718\) | 3.43623 | 0.128239 | ||||||||
\(719\) | 43.5746 | 1.62506 | 0.812529 | − | 0.582920i | \(-0.198090\pi\) | ||||
0.812529 | + | 0.582920i | \(0.198090\pi\) | |||||||
\(720\) | 0.183979 | 0.00685651 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7.34315 | −0.273284 | ||||||||
\(723\) | −6.17847 | −0.229780 | ||||||||
\(724\) | −18.4893 | −0.687150 | ||||||||
\(725\) | 23.2754 | 0.864426 | ||||||||
\(726\) | −1.46047 | −0.0542031 | ||||||||
\(727\) | −15.5859 | −0.578050 | −0.289025 | − | 0.957322i | \(-0.593331\pi\) | ||||
−0.289025 | + | 0.957322i | \(0.593331\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.943993 | 0.0349387 | ||||||||
\(731\) | −31.5022 | −1.16515 | ||||||||
\(732\) | 2.30254 | 0.0851045 | ||||||||
\(733\) | −1.66485 | −0.0614926 | −0.0307463 | − | 0.999527i | \(-0.509788\pi\) | ||||
−0.0307463 | + | 0.999527i | \(0.509788\pi\) | |||||||
\(734\) | 21.8481 | 0.806428 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −4.75502 | −0.175153 | ||||||||
\(738\) | −2.07621 | −0.0764262 | ||||||||
\(739\) | 27.3856 | 1.00740 | 0.503699 | − | 0.863879i | \(-0.331972\pi\) | ||||
0.503699 | + | 0.863879i | \(0.331972\pi\) | |||||||
\(740\) | −0.274207 | −0.0100800 | ||||||||
\(741\) | 20.0018 | 0.734783 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.1775 | −1.03373 | −0.516866 | − | 0.856066i | \(-0.672902\pi\) | ||||
−0.516866 | + | 0.856066i | \(0.672902\pi\) | |||||||
\(744\) | −3.41421 | −0.125171 | ||||||||
\(745\) | 0.246394 | 0.00902718 | ||||||||
\(746\) | −33.9436 | −1.24276 | ||||||||
\(747\) | −0.0175454 | −0.000641953 0 | ||||||||
\(748\) | −19.6682 | −0.719139 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.83357 | −0.0669524 | ||||||||
\(751\) | 22.1439 | 0.808042 | 0.404021 | − | 0.914750i | \(-0.367612\pi\) | ||||
0.404021 | + | 0.914750i | \(0.367612\pi\) | |||||||
\(752\) | −5.01241 | −0.182784 | ||||||||
\(753\) | −18.6845 | −0.680902 | ||||||||
\(754\) | 27.4571 | 0.999928 | ||||||||
\(755\) | 1.66589 | 0.0606279 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.1748 | −0.406155 | −0.203078 | − | 0.979163i | \(-0.565094\pi\) | ||||
−0.203078 | + | 0.979163i | \(0.565094\pi\) | |||||||
\(758\) | −28.7563 | −1.04447 | ||||||||
\(759\) | −3.08861 | −0.112110 | ||||||||
\(760\) | −0.628145 | −0.0227852 | ||||||||
\(761\) | 8.27141 | 0.299838 | 0.149919 | − | 0.988698i | \(-0.452099\pi\) | ||||
0.149919 | + | 0.988698i | \(0.452099\pi\) | |||||||
\(762\) | −12.0356 | −0.436004 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −13.1230 | −0.474773 | ||||||||
\(765\) | −1.17157 | −0.0423583 | ||||||||
\(766\) | −2.94648 | −0.106461 | ||||||||
\(767\) | 46.3810 | 1.67472 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 5.44007 | 0.196174 | 0.0980869 | − | 0.995178i | \(-0.468728\pi\) | ||||
0.0980869 | + | 0.995178i | \(0.468728\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.76691 | 0.0636337 | ||||||||
\(772\) | 14.6038 | 0.525604 | ||||||||
\(773\) | −42.6671 | −1.53463 | −0.767314 | − | 0.641272i | \(-0.778407\pi\) | ||||
−0.767314 | + | 0.641272i | \(0.778407\pi\) | |||||||
\(774\) | 4.94699 | 0.177816 | ||||||||
\(775\) | 16.9555 | 0.609060 | ||||||||
\(776\) | 4.60385 | 0.165268 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.7742 | 0.637235 | ||||||||
\(779\) | 7.08861 | 0.253976 | ||||||||
\(780\) | −1.07782 | −0.0385922 | ||||||||
\(781\) | −9.53953 | −0.341351 | ||||||||
\(782\) | 6.36796 | 0.227718 | ||||||||
\(783\) | −4.68681 | −0.167493 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.83689 | 0.0655614 | ||||||||
\(786\) | −2.47573 | −0.0883064 | ||||||||
\(787\) | 7.86897 | 0.280498 | 0.140249 | − | 0.990116i | \(-0.455210\pi\) | ||||
0.140249 | + | 0.990116i | \(0.455210\pi\) | |||||||
\(788\) | 17.5751 | 0.626088 | ||||||||
\(789\) | −7.58864 | −0.270163 | ||||||||
\(790\) | −1.67212 | −0.0594913 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.08861 | 0.109749 | ||||||||
\(793\) | −13.4892 | −0.479015 | ||||||||
\(794\) | −22.6026 | −0.802136 | ||||||||
\(795\) | −0.331111 | −0.0117433 | ||||||||
\(796\) | 1.39791 | 0.0495476 | ||||||||
\(797\) | −13.0748 | −0.463133 | −0.231567 | − | 0.972819i | \(-0.574385\pi\) | ||||
−0.231567 | + | 0.972819i | \(0.574385\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.9188 | 1.12921 | ||||||||
\(800\) | −4.96615 | −0.175580 | ||||||||
\(801\) | 9.63380 | 0.340394 | ||||||||
\(802\) | −31.8047 | −1.12306 | ||||||||
\(803\) | 15.8476 | 0.559249 | ||||||||
\(804\) | −1.53953 | −0.0542951 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20.0018 | 0.704532 | ||||||||
\(807\) | −24.6452 | −0.867551 | ||||||||
\(808\) | −5.39667 | −0.189854 | ||||||||
\(809\) | −28.0188 | −0.985088 | −0.492544 | − | 0.870288i | \(-0.663933\pi\) | ||||
−0.492544 | + | 0.870288i | \(0.663933\pi\) | |||||||
\(810\) | 0.183979 | 0.00646438 | ||||||||
\(811\) | 17.1104 | 0.600828 | 0.300414 | − | 0.953809i | \(-0.402875\pi\) | ||||
0.300414 | + | 0.953809i | \(0.402875\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.8261 | 0.660262 | ||||||||
\(814\) | −4.60333 | −0.161347 | ||||||||
\(815\) | 1.56112 | 0.0546835 | ||||||||
\(816\) | −6.36796 | −0.222923 | ||||||||
\(817\) | −16.8901 | −0.590909 | ||||||||
\(818\) | −11.3082 | −0.395382 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.381979 | −0.0133393 | ||||||||
\(821\) | 18.0857 | 0.631197 | 0.315598 | − | 0.948893i | \(-0.397795\pi\) | ||||
0.315598 | + | 0.948893i | \(0.397795\pi\) | |||||||
\(822\) | 17.6230 | 0.614673 | ||||||||
\(823\) | −24.7219 | −0.861751 | −0.430876 | − | 0.902411i | \(-0.641795\pi\) | ||||
−0.430876 | + | 0.902411i | \(0.641795\pi\) | |||||||
\(824\) | −0.141621 | −0.00493360 | ||||||||
\(825\) | −15.3385 | −0.534019 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.39843 | 0.326815 | 0.163408 | − | 0.986559i | \(-0.447751\pi\) | ||||
0.163408 | + | 0.986559i | \(0.447751\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | 2.43566 | 0.0845938 | 0.0422969 | − | 0.999105i | \(-0.486532\pi\) | ||||
0.0422969 | + | 0.999105i | \(0.486532\pi\) | |||||||
\(830\) | −0.00322799 | −0.000112045 0 | ||||||||
\(831\) | 11.8571 | 0.411320 | ||||||||
\(832\) | −5.85838 | −0.203103 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 17.9526 | 0.621649 | ||||||||
\(835\) | 2.24170 | 0.0775771 | ||||||||
\(836\) | −10.5452 | −0.364713 | ||||||||
\(837\) | −3.41421 | −0.118012 | ||||||||
\(838\) | 30.3833 | 1.04957 | ||||||||
\(839\) | 6.62007 | 0.228550 | 0.114275 | − | 0.993449i | \(-0.463545\pi\) | ||||
0.114275 | + | 0.993449i | \(0.463545\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.03385 | −0.242546 | ||||||||
\(842\) | 18.4149 | 0.634618 | ||||||||
\(843\) | 8.48652 | 0.292291 | ||||||||
\(844\) | −17.9419 | −0.617584 | ||||||||
\(845\) | 3.92255 | 0.134940 | ||||||||
\(846\) | −5.01241 | −0.172330 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.79972 | −0.0618026 | ||||||||
\(849\) | −5.34329 | −0.183381 | ||||||||
\(850\) | 31.6242 | 1.08470 | ||||||||
\(851\) | 1.49042 | 0.0510909 | ||||||||
\(852\) | −3.08861 | −0.105814 | ||||||||
\(853\) | −7.63256 | −0.261334 | −0.130667 | − | 0.991426i | \(-0.541712\pi\) | ||||
−0.130667 | + | 0.991426i | \(0.541712\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.628145 | −0.0214821 | ||||||||
\(856\) | −16.5452 | −0.565503 | ||||||||
\(857\) | −14.0772 | −0.480869 | −0.240435 | − | 0.970665i | \(-0.577290\pi\) | ||||
−0.240435 | + | 0.970665i | \(0.577290\pi\) | |||||||
\(858\) | −18.0943 | −0.617728 | ||||||||
\(859\) | 2.16468 | 0.0738578 | 0.0369289 | − | 0.999318i | \(-0.488242\pi\) | ||||
0.0369289 | + | 0.999318i | \(0.488242\pi\) | |||||||
\(860\) | 0.910144 | 0.0310357 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.811922 | −0.0276542 | ||||||||
\(863\) | −4.31054 | −0.146732 | −0.0733662 | − | 0.997305i | \(-0.523374\pi\) | ||||
−0.0733662 | + | 0.997305i | \(0.523374\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 1.14353 | 0.0388813 | ||||||||
\(866\) | −35.7020 | −1.21320 | ||||||||
\(867\) | 23.5509 | 0.799830 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.0712 | −0.952251 | ||||||||
\(870\) | −0.862276 | −0.0292339 | ||||||||
\(871\) | 9.01916 | 0.305603 | ||||||||
\(872\) | 15.9431 | 0.539901 | ||||||||
\(873\) | 4.60385 | 0.155817 | ||||||||
\(874\) | 3.41421 | 0.115487 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.13097 | 0.173359 | ||||||||
\(877\) | −13.8015 | −0.466043 | −0.233021 | − | 0.972472i | \(-0.574861\pi\) | ||||
−0.233021 | + | 0.972472i | \(0.574861\pi\) | |||||||
\(878\) | −12.0193 | −0.405632 | ||||||||
\(879\) | −17.9148 | −0.604250 | ||||||||
\(880\) | 0.568241 | 0.0191554 | ||||||||
\(881\) | 23.6955 | 0.798320 | 0.399160 | − | 0.916881i | \(-0.369302\pi\) | ||||
0.399160 | + | 0.916881i | \(0.369302\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 54.3484 | 1.82897 | 0.914485 | − | 0.404620i | \(-0.132596\pi\) | ||||
0.914485 | + | 0.404620i | \(0.132596\pi\) | |||||||
\(884\) | 37.3059 | 1.25473 | ||||||||
\(885\) | −1.45657 | −0.0489621 | ||||||||
\(886\) | −36.0622 | −1.21153 | ||||||||
\(887\) | −14.5547 | −0.488697 | −0.244349 | − | 0.969687i | \(-0.578574\pi\) | ||||
−0.244349 | + | 0.969687i | \(0.578574\pi\) | |||||||
\(888\) | −1.49042 | −0.0500152 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.77242 | 0.0594117 | ||||||||
\(891\) | 3.08861 | 0.103472 | ||||||||
\(892\) | −23.9013 | −0.800273 | ||||||||
\(893\) | 17.1134 | 0.572679 | ||||||||
\(894\) | 1.33925 | 0.0447912 | ||||||||
\(895\) | 2.32590 | 0.0777462 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.85838 | 0.195606 | ||||||||
\(898\) | 0.0867970 | 0.00289645 | ||||||||
\(899\) | 16.0018 | 0.533688 | ||||||||
\(900\) | −4.96615 | −0.165538 | ||||||||
\(901\) | 11.4605 | 0.381806 | ||||||||
\(902\) | −6.41260 | −0.213516 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.42097 | 0.0472606 | ||||||||
\(905\) | −3.40165 | −0.113075 | ||||||||
\(906\) | 9.05476 | 0.300824 | ||||||||
\(907\) | −6.69884 | −0.222431 | −0.111216 | − | 0.993796i | \(-0.535474\pi\) | ||||
−0.111216 | + | 0.993796i | \(0.535474\pi\) | |||||||
\(908\) | 8.81212 | 0.292441 | ||||||||
\(909\) | −5.39667 | −0.178996 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.3660 | −0.475966 | −0.237983 | − | 0.971269i | \(-0.576486\pi\) | ||||
−0.237983 | + | 0.971269i | \(0.576486\pi\) | |||||||
\(912\) | −3.41421 | −0.113056 | ||||||||
\(913\) | −0.0541910 | −0.00179346 | ||||||||
\(914\) | −37.6005 | −1.24371 | ||||||||
\(915\) | 0.423621 | 0.0140045 | ||||||||
\(916\) | 0.194772 | 0.00643544 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6.36796 | −0.210174 | ||||||||
\(919\) | 26.4314 | 0.871891 | 0.435945 | − | 0.899973i | \(-0.356414\pi\) | ||||
0.435945 | + | 0.899973i | \(0.356414\pi\) | |||||||
\(920\) | −0.183979 | −0.00606562 | ||||||||
\(921\) | 6.99339 | 0.230440 | ||||||||
\(922\) | 33.2804 | 1.09603 | ||||||||
\(923\) | 18.0943 | 0.595580 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.40165 | 0.243365 | ||||||||
\(926\) | −18.4036 | −0.604779 | ||||||||
\(927\) | −0.141621 | −0.00465144 | ||||||||
\(928\) | −4.68681 | −0.153852 | ||||||||
\(929\) | 42.6352 | 1.39882 | 0.699408 | − | 0.714723i | \(-0.253447\pi\) | ||||
0.699408 | + | 0.714723i | \(0.253447\pi\) | |||||||
\(930\) | −0.628145 | −0.0205977 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9.79972 | 0.321000 | ||||||||
\(933\) | −19.9013 | −0.651538 | ||||||||
\(934\) | −32.6327 | −1.06777 | ||||||||
\(935\) | −3.61854 | −0.118339 | ||||||||
\(936\) | −5.85838 | −0.191487 | ||||||||
\(937\) | −15.7651 | −0.515025 | −0.257512 | − | 0.966275i | \(-0.582903\pi\) | ||||
−0.257512 | + | 0.966275i | \(0.582903\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.0440 | −0.556209 | ||||||||
\(940\) | −0.922179 | −0.0300782 | ||||||||
\(941\) | 24.8387 | 0.809718 | 0.404859 | − | 0.914379i | \(-0.367321\pi\) | ||||
0.404859 | + | 0.914379i | \(0.367321\pi\) | |||||||
\(942\) | 9.98421 | 0.325303 | ||||||||
\(943\) | 2.07621 | 0.0676106 | ||||||||
\(944\) | −7.91704 | −0.257678 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.2793 | 0.496774 | ||||||||
\(947\) | −27.4245 | −0.891176 | −0.445588 | − | 0.895238i | \(-0.647005\pi\) | ||||
−0.445588 | + | 0.895238i | \(0.647005\pi\) | |||||||
\(948\) | −9.08861 | −0.295184 | ||||||||
\(949\) | −30.0592 | −0.975762 | ||||||||
\(950\) | 16.9555 | 0.550109 | ||||||||
\(951\) | −6.47449 | −0.209950 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.2045 | −0.427735 | −0.213867 | − | 0.976863i | \(-0.568606\pi\) | ||||
−0.213867 | + | 0.976863i | \(0.568606\pi\) | |||||||
\(954\) | −1.79972 | −0.0582680 | ||||||||
\(955\) | −2.41436 | −0.0781267 | ||||||||
\(956\) | 10.5835 | 0.342295 | ||||||||
\(957\) | −14.4757 | −0.467934 | ||||||||
\(958\) | 33.0578 | 1.06805 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.183979 | 0.00593791 | ||||||||
\(961\) | −19.3431 | −0.623972 | ||||||||
\(962\) | 8.73145 | 0.281513 | ||||||||
\(963\) | −16.5452 | −0.533161 | ||||||||
\(964\) | −6.17847 | −0.198995 | ||||||||
\(965\) | 2.68681 | 0.0864913 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.8950 | −1.47588 | −0.737942 | − | 0.674864i | \(-0.764202\pi\) | ||||
−0.737942 | + | 0.674864i | \(0.764202\pi\) | |||||||
\(968\) | −1.46047 | −0.0469412 | ||||||||
\(969\) | 21.7416 | 0.698440 | ||||||||
\(970\) | 0.847013 | 0.0271959 | ||||||||
\(971\) | −22.5411 | −0.723380 | −0.361690 | − | 0.932298i | \(-0.617800\pi\) | ||||
−0.361690 | + | 0.932298i | \(0.617800\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 24.1562 | 0.774013 | ||||||||
\(975\) | 29.0936 | 0.931741 | ||||||||
\(976\) | 2.30254 | 0.0737027 | ||||||||
\(977\) | 25.9073 | 0.828847 | 0.414424 | − | 0.910084i | \(-0.363983\pi\) | ||||
0.414424 | + | 0.910084i | \(0.363983\pi\) | |||||||
\(978\) | 8.48528 | 0.271329 | ||||||||
\(979\) | 29.7551 | 0.950976 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.9431 | 0.509024 | ||||||||
\(982\) | 27.6320 | 0.881774 | ||||||||
\(983\) | −34.7320 | −1.10778 | −0.553889 | − | 0.832591i | \(-0.686857\pi\) | ||||
−0.553889 | + | 0.832591i | \(0.686857\pi\) | |||||||
\(984\) | −2.07621 | −0.0661871 | ||||||||
\(985\) | 3.23346 | 0.103027 | ||||||||
\(986\) | 29.8454 | 0.950471 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20.0018 | 0.636341 | ||||||||
\(989\) | −4.94699 | −0.157305 | ||||||||
\(990\) | 0.568241 | 0.0180599 | ||||||||
\(991\) | −32.9187 | −1.04570 | −0.522849 | − | 0.852425i | \(-0.675131\pi\) | ||||
−0.522849 | + | 0.852425i | \(0.675131\pi\) | |||||||
\(992\) | −3.41421 | −0.108401 | ||||||||
\(993\) | −17.4909 | −0.555058 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.257187 | 0.00815337 | ||||||||
\(996\) | −0.0175454 | −0.000555947 0 | ||||||||
\(997\) | 12.6320 | 0.400059 | 0.200029 | − | 0.979790i | \(-0.435896\pi\) | ||||
0.200029 | + | 0.979790i | \(0.435896\pi\) | |||||||
\(998\) | −33.9787 | −1.07558 | ||||||||
\(999\) | −1.49042 | −0.0471548 |
(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 | 6762.2.a.co.1.3 | yes | 4 | |
7.6 | odd | 2 | 6762.2.a.cn.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6762.2.a.cn.1.2 | ✓ | 4 | 7.6 | odd | 2 | ||
6762.2.a.co.1.3 | yes | 4 | 1.1 | even | 1 | trivial |