Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, 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("5070.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.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: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 390) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 2.82843 | 1.06904 | 0.534522 | − | 0.845154i | \(-0.320491\pi\) | ||||
0.534522 | + | 0.845154i | \(0.320491\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −5.65685 | −1.70561 | −0.852803 | − | 0.522233i | \(-0.825099\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.82843 | −0.755929 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.828427 | 0.200923 | 0.100462 | − | 0.994941i | \(-0.467968\pi\) | ||||
0.100462 | + | 0.994941i | \(0.467968\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.82843 | −0.648886 | −0.324443 | − | 0.945905i | \(-0.605177\pi\) | ||||
−0.324443 | + | 0.945905i | \(0.605177\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 2.82843 | 0.617213 | ||||||||
\(22\) | 5.65685 | 1.20605 | ||||||||
\(23\) | −8.48528 | −1.76930 | −0.884652 | − | 0.466252i | \(-0.845604\pi\) | ||||
−0.884652 | + | 0.466252i | \(0.845604\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.82843 | 0.534522 | ||||||||
\(29\) | −8.82843 | −1.63940 | −0.819699 | − | 0.572795i | \(-0.805859\pi\) | ||||
−0.819699 | + | 0.572795i | \(0.805859\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.65685 | −0.984732 | ||||||||
\(34\) | −0.828427 | −0.142074 | ||||||||
\(35\) | −2.82843 | −0.478091 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 11.6569 | 1.91638 | 0.958188 | − | 0.286141i | \(-0.0923726\pi\) | ||||
0.958188 | + | 0.286141i | \(0.0923726\pi\) | |||||||
\(38\) | 2.82843 | 0.458831 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 7.65685 | 1.19580 | 0.597900 | − | 0.801571i | \(-0.296002\pi\) | ||||
0.597900 | + | 0.801571i | \(0.296002\pi\) | |||||||
\(42\) | −2.82843 | −0.436436 | ||||||||
\(43\) | 9.65685 | 1.47266 | 0.736328 | − | 0.676625i | \(-0.236558\pi\) | ||||
0.736328 | + | 0.676625i | \(0.236558\pi\) | |||||||
\(44\) | −5.65685 | −0.852803 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 8.48528 | 1.25109 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0.828427 | 0.116003 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.3137 | 1.82878 | 0.914389 | − | 0.404836i | \(-0.132671\pi\) | ||||
0.914389 | + | 0.404836i | \(0.132671\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 5.65685 | 0.762770 | ||||||||
\(56\) | −2.82843 | −0.377964 | ||||||||
\(57\) | −2.82843 | −0.374634 | ||||||||
\(58\) | 8.82843 | 1.15923 | ||||||||
\(59\) | 2.34315 | 0.305052 | 0.152526 | − | 0.988299i | \(-0.451259\pi\) | ||||
0.152526 | + | 0.988299i | \(0.451259\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 4.00000 | 0.508001 | ||||||||
\(63\) | 2.82843 | 0.356348 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.65685 | 0.696311 | ||||||||
\(67\) | −5.65685 | −0.691095 | −0.345547 | − | 0.938401i | \(-0.612307\pi\) | ||||
−0.345547 | + | 0.938401i | \(0.612307\pi\) | |||||||
\(68\) | 0.828427 | 0.100462 | ||||||||
\(69\) | −8.48528 | −1.02151 | ||||||||
\(70\) | 2.82843 | 0.338062 | ||||||||
\(71\) | 5.65685 | 0.671345 | 0.335673 | − | 0.941979i | \(-0.391036\pi\) | ||||
0.335673 | + | 0.941979i | \(0.391036\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 14.4853 | 1.69537 | 0.847687 | − | 0.530497i | \(-0.177995\pi\) | ||||
0.847687 | + | 0.530497i | \(0.177995\pi\) | |||||||
\(74\) | −11.6569 | −1.35508 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −2.82843 | −0.324443 | ||||||||
\(77\) | −16.0000 | −1.82337 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.34315 | 0.263624 | 0.131812 | − | 0.991275i | \(-0.457920\pi\) | ||||
0.131812 | + | 0.991275i | \(0.457920\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.65685 | −0.845558 | ||||||||
\(83\) | −6.34315 | −0.696251 | −0.348125 | − | 0.937448i | \(-0.613182\pi\) | ||||
−0.348125 | + | 0.937448i | \(0.613182\pi\) | |||||||
\(84\) | 2.82843 | 0.308607 | ||||||||
\(85\) | −0.828427 | −0.0898555 | ||||||||
\(86\) | −9.65685 | −1.04133 | ||||||||
\(87\) | −8.82843 | −0.946507 | ||||||||
\(88\) | 5.65685 | 0.603023 | ||||||||
\(89\) | 15.6569 | 1.65962 | 0.829812 | − | 0.558044i | \(-0.188448\pi\) | ||||
0.829812 | + | 0.558044i | \(0.188448\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.48528 | −0.884652 | ||||||||
\(93\) | −4.00000 | −0.414781 | ||||||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | 2.82843 | 0.290191 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 3.17157 | 0.322024 | 0.161012 | − | 0.986952i | \(-0.448524\pi\) | ||||
0.161012 | + | 0.986952i | \(0.448524\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −5.65685 | −0.568535 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 16.1421 | 1.60620 | 0.803101 | − | 0.595843i | \(-0.203182\pi\) | ||||
0.803101 | + | 0.595843i | \(0.203182\pi\) | |||||||
\(102\) | −0.828427 | −0.0820265 | ||||||||
\(103\) | −1.65685 | −0.163255 | −0.0816274 | − | 0.996663i | \(-0.526012\pi\) | ||||
−0.0816274 | + | 0.996663i | \(0.526012\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.82843 | −0.276026 | ||||||||
\(106\) | −13.3137 | −1.29314 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −8.82843 | −0.845610 | −0.422805 | − | 0.906221i | \(-0.638954\pi\) | ||||
−0.422805 | + | 0.906221i | \(0.638954\pi\) | |||||||
\(110\) | −5.65685 | −0.539360 | ||||||||
\(111\) | 11.6569 | 1.10642 | ||||||||
\(112\) | 2.82843 | 0.267261 | ||||||||
\(113\) | 6.48528 | 0.610084 | 0.305042 | − | 0.952339i | \(-0.401330\pi\) | ||||
0.305042 | + | 0.952339i | \(0.401330\pi\) | |||||||
\(114\) | 2.82843 | 0.264906 | ||||||||
\(115\) | 8.48528 | 0.791257 | ||||||||
\(116\) | −8.82843 | −0.819699 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.34315 | −0.215704 | ||||||||
\(119\) | 2.34315 | 0.214796 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 21.0000 | 1.90909 | ||||||||
\(122\) | −6.00000 | −0.543214 | ||||||||
\(123\) | 7.65685 | 0.690395 | ||||||||
\(124\) | −4.00000 | −0.359211 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.82843 | −0.251976 | ||||||||
\(127\) | 9.65685 | 0.856907 | 0.428454 | − | 0.903564i | \(-0.359059\pi\) | ||||
0.428454 | + | 0.903564i | \(0.359059\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 9.65685 | 0.850239 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.14214 | −0.536641 | −0.268320 | − | 0.963330i | \(-0.586469\pi\) | ||||
−0.268320 | + | 0.963330i | \(0.586469\pi\) | |||||||
\(132\) | −5.65685 | −0.492366 | ||||||||
\(133\) | −8.00000 | −0.693688 | ||||||||
\(134\) | 5.65685 | 0.488678 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −0.828427 | −0.0710370 | ||||||||
\(137\) | 17.3137 | 1.47921 | 0.739605 | − | 0.673041i | \(-0.235012\pi\) | ||||
0.739605 | + | 0.673041i | \(0.235012\pi\) | |||||||
\(138\) | 8.48528 | 0.722315 | ||||||||
\(139\) | 6.34315 | 0.538019 | 0.269009 | − | 0.963138i | \(-0.413304\pi\) | ||||
0.269009 | + | 0.963138i | \(0.413304\pi\) | |||||||
\(140\) | −2.82843 | −0.239046 | ||||||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | −5.65685 | −0.474713 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 8.82843 | 0.733161 | ||||||||
\(146\) | −14.4853 | −1.19881 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 11.6569 | 0.958188 | ||||||||
\(149\) | −3.65685 | −0.299581 | −0.149791 | − | 0.988718i | \(-0.547860\pi\) | ||||
−0.149791 | + | 0.988718i | \(0.547860\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 2.82843 | 0.229416 | ||||||||
\(153\) | 0.828427 | 0.0669744 | ||||||||
\(154\) | 16.0000 | 1.28932 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.31371 | 0.424080 | 0.212040 | − | 0.977261i | \(-0.431989\pi\) | ||||
0.212040 | + | 0.977261i | \(0.431989\pi\) | |||||||
\(158\) | −2.34315 | −0.186411 | ||||||||
\(159\) | 13.3137 | 1.05585 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −24.0000 | −1.89146 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −11.3137 | −0.886158 | −0.443079 | − | 0.896483i | \(-0.646114\pi\) | ||||
−0.443079 | + | 0.896483i | \(0.646114\pi\) | |||||||
\(164\) | 7.65685 | 0.597900 | ||||||||
\(165\) | 5.65685 | 0.440386 | ||||||||
\(166\) | 6.34315 | 0.492324 | ||||||||
\(167\) | −8.97056 | −0.694163 | −0.347081 | − | 0.937835i | \(-0.612827\pi\) | ||||
−0.347081 | + | 0.937835i | \(0.612827\pi\) | |||||||
\(168\) | −2.82843 | −0.218218 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.828427 | 0.0635375 | ||||||||
\(171\) | −2.82843 | −0.216295 | ||||||||
\(172\) | 9.65685 | 0.736328 | ||||||||
\(173\) | −9.31371 | −0.708108 | −0.354054 | − | 0.935225i | \(-0.615197\pi\) | ||||
−0.354054 | + | 0.935225i | \(0.615197\pi\) | |||||||
\(174\) | 8.82843 | 0.669281 | ||||||||
\(175\) | 2.82843 | 0.213809 | ||||||||
\(176\) | −5.65685 | −0.426401 | ||||||||
\(177\) | 2.34315 | 0.176122 | ||||||||
\(178\) | −15.6569 | −1.17353 | ||||||||
\(179\) | 7.51472 | 0.561676 | 0.280838 | − | 0.959755i | \(-0.409388\pi\) | ||||
0.280838 | + | 0.959755i | \(0.409388\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | −7.65685 | −0.569129 | −0.284565 | − | 0.958657i | \(-0.591849\pi\) | ||||
−0.284565 | + | 0.958657i | \(0.591849\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.00000 | 0.443533 | ||||||||
\(184\) | 8.48528 | 0.625543 | ||||||||
\(185\) | −11.6569 | −0.857029 | ||||||||
\(186\) | 4.00000 | 0.293294 | ||||||||
\(187\) | −4.68629 | −0.342696 | ||||||||
\(188\) | 8.00000 | 0.583460 | ||||||||
\(189\) | 2.82843 | 0.205738 | ||||||||
\(190\) | −2.82843 | −0.205196 | ||||||||
\(191\) | 11.3137 | 0.818631 | 0.409316 | − | 0.912393i | \(-0.365768\pi\) | ||||
0.409316 | + | 0.912393i | \(0.365768\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −2.48528 | −0.178894 | −0.0894472 | − | 0.995992i | \(-0.528510\pi\) | ||||
−0.0894472 | + | 0.995992i | \(0.528510\pi\) | |||||||
\(194\) | −3.17157 | −0.227706 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 13.3137 | 0.948562 | 0.474281 | − | 0.880373i | \(-0.342708\pi\) | ||||
0.474281 | + | 0.880373i | \(0.342708\pi\) | |||||||
\(198\) | 5.65685 | 0.402015 | ||||||||
\(199\) | 10.3431 | 0.733206 | 0.366603 | − | 0.930377i | \(-0.380521\pi\) | ||||
0.366603 | + | 0.930377i | \(0.380521\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −5.65685 | −0.399004 | ||||||||
\(202\) | −16.1421 | −1.13576 | ||||||||
\(203\) | −24.9706 | −1.75259 | ||||||||
\(204\) | 0.828427 | 0.0580015 | ||||||||
\(205\) | −7.65685 | −0.534778 | ||||||||
\(206\) | 1.65685 | 0.115439 | ||||||||
\(207\) | −8.48528 | −0.589768 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0000 | 1.10674 | ||||||||
\(210\) | 2.82843 | 0.195180 | ||||||||
\(211\) | 0.686292 | 0.0472463 | 0.0236231 | − | 0.999721i | \(-0.492480\pi\) | ||||
0.0236231 | + | 0.999721i | \(0.492480\pi\) | |||||||
\(212\) | 13.3137 | 0.914389 | ||||||||
\(213\) | 5.65685 | 0.387601 | ||||||||
\(214\) | 4.00000 | 0.273434 | ||||||||
\(215\) | −9.65685 | −0.658592 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −11.3137 | −0.768025 | ||||||||
\(218\) | 8.82843 | 0.597937 | ||||||||
\(219\) | 14.4853 | 0.978825 | ||||||||
\(220\) | 5.65685 | 0.381385 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −11.6569 | −0.782357 | ||||||||
\(223\) | −10.8284 | −0.725125 | −0.362563 | − | 0.931959i | \(-0.618098\pi\) | ||||
−0.362563 | + | 0.931959i | \(0.618098\pi\) | |||||||
\(224\) | −2.82843 | −0.188982 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −6.48528 | −0.431394 | ||||||||
\(227\) | −4.00000 | −0.265489 | −0.132745 | − | 0.991150i | \(-0.542379\pi\) | ||||
−0.132745 | + | 0.991150i | \(0.542379\pi\) | |||||||
\(228\) | −2.82843 | −0.187317 | ||||||||
\(229\) | −4.14214 | −0.273720 | −0.136860 | − | 0.990590i | \(-0.543701\pi\) | ||||
−0.136860 | + | 0.990590i | \(0.543701\pi\) | |||||||
\(230\) | −8.48528 | −0.559503 | ||||||||
\(231\) | −16.0000 | −1.05272 | ||||||||
\(232\) | 8.82843 | 0.579615 | ||||||||
\(233\) | 5.51472 | 0.361281 | 0.180641 | − | 0.983549i | \(-0.442183\pi\) | ||||
0.180641 | + | 0.983549i | \(0.442183\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | −0.521862 | ||||||||
\(236\) | 2.34315 | 0.152526 | ||||||||
\(237\) | 2.34315 | 0.152204 | ||||||||
\(238\) | −2.34315 | −0.151884 | ||||||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −5.31371 | −0.342286 | −0.171143 | − | 0.985246i | \(-0.554746\pi\) | ||||
−0.171143 | + | 0.985246i | \(0.554746\pi\) | |||||||
\(242\) | −21.0000 | −1.34993 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −7.65685 | −0.488183 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | −6.34315 | −0.401981 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 10.8284 | 0.683484 | 0.341742 | − | 0.939794i | \(-0.388983\pi\) | ||||
0.341742 | + | 0.939794i | \(0.388983\pi\) | |||||||
\(252\) | 2.82843 | 0.178174 | ||||||||
\(253\) | 48.0000 | 3.01773 | ||||||||
\(254\) | −9.65685 | −0.605925 | ||||||||
\(255\) | −0.828427 | −0.0518781 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.82843 | −0.301189 | −0.150595 | − | 0.988596i | \(-0.548119\pi\) | ||||
−0.150595 | + | 0.988596i | \(0.548119\pi\) | |||||||
\(258\) | −9.65685 | −0.601209 | ||||||||
\(259\) | 32.9706 | 2.04869 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.82843 | −0.546466 | ||||||||
\(262\) | 6.14214 | 0.379462 | ||||||||
\(263\) | 16.4853 | 1.01653 | 0.508263 | − | 0.861202i | \(-0.330288\pi\) | ||||
0.508263 | + | 0.861202i | \(0.330288\pi\) | |||||||
\(264\) | 5.65685 | 0.348155 | ||||||||
\(265\) | −13.3137 | −0.817855 | ||||||||
\(266\) | 8.00000 | 0.490511 | ||||||||
\(267\) | 15.6569 | 0.958184 | ||||||||
\(268\) | −5.65685 | −0.345547 | ||||||||
\(269\) | −14.4853 | −0.883183 | −0.441592 | − | 0.897216i | \(-0.645586\pi\) | ||||
−0.441592 | + | 0.897216i | \(0.645586\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | −7.31371 | −0.444276 | −0.222138 | − | 0.975015i | \(-0.571304\pi\) | ||||
−0.222138 | + | 0.975015i | \(0.571304\pi\) | |||||||
\(272\) | 0.828427 | 0.0502308 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.3137 | −1.04596 | ||||||||
\(275\) | −5.65685 | −0.341121 | ||||||||
\(276\) | −8.48528 | −0.510754 | ||||||||
\(277\) | 26.0000 | 1.56219 | 0.781094 | − | 0.624413i | \(-0.214662\pi\) | ||||
0.781094 | + | 0.624413i | \(0.214662\pi\) | |||||||
\(278\) | −6.34315 | −0.380437 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 2.82843 | 0.169031 | ||||||||
\(281\) | −8.34315 | −0.497710 | −0.248855 | − | 0.968541i | \(-0.580054\pi\) | ||||
−0.248855 | + | 0.968541i | \(0.580054\pi\) | |||||||
\(282\) | −8.00000 | −0.476393 | ||||||||
\(283\) | −17.6569 | −1.04959 | −0.524796 | − | 0.851228i | \(-0.675858\pi\) | ||||
−0.524796 | + | 0.851228i | \(0.675858\pi\) | |||||||
\(284\) | 5.65685 | 0.335673 | ||||||||
\(285\) | 2.82843 | 0.167542 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.6569 | 1.27836 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.3137 | −0.959630 | ||||||||
\(290\) | −8.82843 | −0.518423 | ||||||||
\(291\) | 3.17157 | 0.185921 | ||||||||
\(292\) | 14.4853 | 0.847687 | ||||||||
\(293\) | 16.6274 | 0.971384 | 0.485692 | − | 0.874130i | \(-0.338568\pi\) | ||||
0.485692 | + | 0.874130i | \(0.338568\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −2.34315 | −0.136423 | ||||||||
\(296\) | −11.6569 | −0.677541 | ||||||||
\(297\) | −5.65685 | −0.328244 | ||||||||
\(298\) | 3.65685 | 0.211836 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 27.3137 | 1.57434 | ||||||||
\(302\) | 12.0000 | 0.690522 | ||||||||
\(303\) | 16.1421 | 0.927341 | ||||||||
\(304\) | −2.82843 | −0.162221 | ||||||||
\(305\) | −6.00000 | −0.343559 | ||||||||
\(306\) | −0.828427 | −0.0473580 | ||||||||
\(307\) | 21.6569 | 1.23602 | 0.618011 | − | 0.786169i | \(-0.287939\pi\) | ||||
0.618011 | + | 0.786169i | \(0.287939\pi\) | |||||||
\(308\) | −16.0000 | −0.911685 | ||||||||
\(309\) | −1.65685 | −0.0942551 | ||||||||
\(310\) | −4.00000 | −0.227185 | ||||||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.9706 | −1.75056 | −0.875280 | − | 0.483617i | \(-0.839323\pi\) | ||||
−0.875280 | + | 0.483617i | \(0.839323\pi\) | |||||||
\(314\) | −5.31371 | −0.299870 | ||||||||
\(315\) | −2.82843 | −0.159364 | ||||||||
\(316\) | 2.34315 | 0.131812 | ||||||||
\(317\) | −25.3137 | −1.42176 | −0.710880 | − | 0.703314i | \(-0.751703\pi\) | ||||
−0.710880 | + | 0.703314i | \(0.751703\pi\) | |||||||
\(318\) | −13.3137 | −0.746596 | ||||||||
\(319\) | 49.9411 | 2.79617 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 24.0000 | 1.33747 | ||||||||
\(323\) | −2.34315 | −0.130376 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.3137 | 0.626608 | ||||||||
\(327\) | −8.82843 | −0.488213 | ||||||||
\(328\) | −7.65685 | −0.422779 | ||||||||
\(329\) | 22.6274 | 1.24749 | ||||||||
\(330\) | −5.65685 | −0.311400 | ||||||||
\(331\) | 8.48528 | 0.466393 | 0.233197 | − | 0.972430i | \(-0.425081\pi\) | ||||
0.233197 | + | 0.972430i | \(0.425081\pi\) | |||||||
\(332\) | −6.34315 | −0.348125 | ||||||||
\(333\) | 11.6569 | 0.638792 | ||||||||
\(334\) | 8.97056 | 0.490847 | ||||||||
\(335\) | 5.65685 | 0.309067 | ||||||||
\(336\) | 2.82843 | 0.154303 | ||||||||
\(337\) | 10.9706 | 0.597605 | 0.298802 | − | 0.954315i | \(-0.403413\pi\) | ||||
0.298802 | + | 0.954315i | \(0.403413\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.48528 | 0.352232 | ||||||||
\(340\) | −0.828427 | −0.0449278 | ||||||||
\(341\) | 22.6274 | 1.22534 | ||||||||
\(342\) | 2.82843 | 0.152944 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | −9.65685 | −0.520663 | ||||||||
\(345\) | 8.48528 | 0.456832 | ||||||||
\(346\) | 9.31371 | 0.500708 | ||||||||
\(347\) | −9.65685 | −0.518407 | −0.259204 | − | 0.965823i | \(-0.583460\pi\) | ||||
−0.259204 | + | 0.965823i | \(0.583460\pi\) | |||||||
\(348\) | −8.82843 | −0.473253 | ||||||||
\(349\) | −12.1421 | −0.649954 | −0.324977 | − | 0.945722i | \(-0.605356\pi\) | ||||
−0.324977 | + | 0.945722i | \(0.605356\pi\) | |||||||
\(350\) | −2.82843 | −0.151186 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.65685 | 0.301511 | ||||||||
\(353\) | −5.31371 | −0.282820 | −0.141410 | − | 0.989951i | \(-0.545164\pi\) | ||||
−0.141410 | + | 0.989951i | \(0.545164\pi\) | |||||||
\(354\) | −2.34315 | −0.124537 | ||||||||
\(355\) | −5.65685 | −0.300235 | ||||||||
\(356\) | 15.6569 | 0.829812 | ||||||||
\(357\) | 2.34315 | 0.124012 | ||||||||
\(358\) | −7.51472 | −0.397165 | ||||||||
\(359\) | 28.2843 | 1.49279 | 0.746393 | − | 0.665505i | \(-0.231784\pi\) | ||||
0.746393 | + | 0.665505i | \(0.231784\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 7.65685 | 0.402435 | ||||||||
\(363\) | 21.0000 | 1.10221 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.4853 | −0.758194 | ||||||||
\(366\) | −6.00000 | −0.313625 | ||||||||
\(367\) | 25.6569 | 1.33928 | 0.669638 | − | 0.742687i | \(-0.266449\pi\) | ||||
0.669638 | + | 0.742687i | \(0.266449\pi\) | |||||||
\(368\) | −8.48528 | −0.442326 | ||||||||
\(369\) | 7.65685 | 0.398600 | ||||||||
\(370\) | 11.6569 | 0.606011 | ||||||||
\(371\) | 37.6569 | 1.95505 | ||||||||
\(372\) | −4.00000 | −0.207390 | ||||||||
\(373\) | −2.68629 | −0.139091 | −0.0695455 | − | 0.997579i | \(-0.522155\pi\) | ||||
−0.0695455 | + | 0.997579i | \(0.522155\pi\) | |||||||
\(374\) | 4.68629 | 0.242322 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −8.00000 | −0.412568 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.82843 | −0.145479 | ||||||||
\(379\) | 7.51472 | 0.386005 | 0.193003 | − | 0.981198i | \(-0.438177\pi\) | ||||
0.193003 | + | 0.981198i | \(0.438177\pi\) | |||||||
\(380\) | 2.82843 | 0.145095 | ||||||||
\(381\) | 9.65685 | 0.494736 | ||||||||
\(382\) | −11.3137 | −0.578860 | ||||||||
\(383\) | 29.6569 | 1.51539 | 0.757697 | − | 0.652606i | \(-0.226324\pi\) | ||||
0.757697 | + | 0.652606i | \(0.226324\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 16.0000 | 0.815436 | ||||||||
\(386\) | 2.48528 | 0.126497 | ||||||||
\(387\) | 9.65685 | 0.490885 | ||||||||
\(388\) | 3.17157 | 0.161012 | ||||||||
\(389\) | −6.48528 | −0.328817 | −0.164408 | − | 0.986392i | \(-0.552571\pi\) | ||||
−0.164408 | + | 0.986392i | \(0.552571\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.02944 | −0.355494 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −6.14214 | −0.309830 | ||||||||
\(394\) | −13.3137 | −0.670735 | ||||||||
\(395\) | −2.34315 | −0.117896 | ||||||||
\(396\) | −5.65685 | −0.284268 | ||||||||
\(397\) | −30.2843 | −1.51992 | −0.759962 | − | 0.649968i | \(-0.774782\pi\) | ||||
−0.759962 | + | 0.649968i | \(0.774782\pi\) | |||||||
\(398\) | −10.3431 | −0.518455 | ||||||||
\(399\) | −8.00000 | −0.400501 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 26.9706 | 1.34685 | 0.673423 | − | 0.739258i | \(-0.264823\pi\) | ||||
0.673423 | + | 0.739258i | \(0.264823\pi\) | |||||||
\(402\) | 5.65685 | 0.282138 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 16.1421 | 0.803101 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 24.9706 | 1.23927 | ||||||||
\(407\) | −65.9411 | −3.26858 | ||||||||
\(408\) | −0.828427 | −0.0410133 | ||||||||
\(409\) | 3.65685 | 0.180820 | 0.0904099 | − | 0.995905i | \(-0.471182\pi\) | ||||
0.0904099 | + | 0.995905i | \(0.471182\pi\) | |||||||
\(410\) | 7.65685 | 0.378145 | ||||||||
\(411\) | 17.3137 | 0.854022 | ||||||||
\(412\) | −1.65685 | −0.0816274 | ||||||||
\(413\) | 6.62742 | 0.326114 | ||||||||
\(414\) | 8.48528 | 0.417029 | ||||||||
\(415\) | 6.34315 | 0.311373 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.34315 | 0.310625 | ||||||||
\(418\) | −16.0000 | −0.782586 | ||||||||
\(419\) | −10.8284 | −0.529003 | −0.264502 | − | 0.964385i | \(-0.585207\pi\) | ||||
−0.264502 | + | 0.964385i | \(0.585207\pi\) | |||||||
\(420\) | −2.82843 | −0.138013 | ||||||||
\(421\) | 24.1421 | 1.17662 | 0.588308 | − | 0.808637i | \(-0.299794\pi\) | ||||
0.588308 | + | 0.808637i | \(0.299794\pi\) | |||||||
\(422\) | −0.686292 | −0.0334081 | ||||||||
\(423\) | 8.00000 | 0.388973 | ||||||||
\(424\) | −13.3137 | −0.646571 | ||||||||
\(425\) | 0.828427 | 0.0401846 | ||||||||
\(426\) | −5.65685 | −0.274075 | ||||||||
\(427\) | 16.9706 | 0.821263 | ||||||||
\(428\) | −4.00000 | −0.193347 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.65685 | 0.465695 | ||||||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −22.9706 | −1.10389 | −0.551947 | − | 0.833879i | \(-0.686115\pi\) | ||||
−0.551947 | + | 0.833879i | \(0.686115\pi\) | |||||||
\(434\) | 11.3137 | 0.543075 | ||||||||
\(435\) | 8.82843 | 0.423291 | ||||||||
\(436\) | −8.82843 | −0.422805 | ||||||||
\(437\) | 24.0000 | 1.14808 | ||||||||
\(438\) | −14.4853 | −0.692134 | ||||||||
\(439\) | 22.6274 | 1.07995 | 0.539974 | − | 0.841682i | \(-0.318434\pi\) | ||||
0.539974 | + | 0.841682i | \(0.318434\pi\) | |||||||
\(440\) | −5.65685 | −0.269680 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.3431 | 1.44165 | 0.720823 | − | 0.693119i | \(-0.243764\pi\) | ||||
0.720823 | + | 0.693119i | \(0.243764\pi\) | |||||||
\(444\) | 11.6569 | 0.553210 | ||||||||
\(445\) | −15.6569 | −0.742206 | ||||||||
\(446\) | 10.8284 | 0.512741 | ||||||||
\(447\) | −3.65685 | −0.172963 | ||||||||
\(448\) | 2.82843 | 0.133631 | ||||||||
\(449\) | −26.2843 | −1.24043 | −0.620216 | − | 0.784431i | \(-0.712955\pi\) | ||||
−0.620216 | + | 0.784431i | \(0.712955\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | −43.3137 | −2.03956 | ||||||||
\(452\) | 6.48528 | 0.305042 | ||||||||
\(453\) | −12.0000 | −0.563809 | ||||||||
\(454\) | 4.00000 | 0.187729 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.82843 | 0.132453 | ||||||||
\(457\) | −20.8284 | −0.974313 | −0.487156 | − | 0.873315i | \(-0.661966\pi\) | ||||
−0.487156 | + | 0.873315i | \(0.661966\pi\) | |||||||
\(458\) | 4.14214 | 0.193549 | ||||||||
\(459\) | 0.828427 | 0.0386677 | ||||||||
\(460\) | 8.48528 | 0.395628 | ||||||||
\(461\) | −14.0000 | −0.652045 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(462\) | 16.0000 | 0.744387 | ||||||||
\(463\) | 3.79899 | 0.176554 | 0.0882770 | − | 0.996096i | \(-0.471864\pi\) | ||||
0.0882770 | + | 0.996096i | \(0.471864\pi\) | |||||||
\(464\) | −8.82843 | −0.409849 | ||||||||
\(465\) | 4.00000 | 0.185496 | ||||||||
\(466\) | −5.51472 | −0.255464 | ||||||||
\(467\) | 7.31371 | 0.338438 | 0.169219 | − | 0.985578i | \(-0.445875\pi\) | ||||
0.169219 | + | 0.985578i | \(0.445875\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | 8.00000 | 0.369012 | ||||||||
\(471\) | 5.31371 | 0.244843 | ||||||||
\(472\) | −2.34315 | −0.107852 | ||||||||
\(473\) | −54.6274 | −2.51177 | ||||||||
\(474\) | −2.34315 | −0.107624 | ||||||||
\(475\) | −2.82843 | −0.129777 | ||||||||
\(476\) | 2.34315 | 0.107398 | ||||||||
\(477\) | 13.3137 | 0.609593 | ||||||||
\(478\) | 16.0000 | 0.731823 | ||||||||
\(479\) | 11.3137 | 0.516937 | 0.258468 | − | 0.966020i | \(-0.416782\pi\) | ||||
0.258468 | + | 0.966020i | \(0.416782\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 5.31371 | 0.242033 | ||||||||
\(483\) | −24.0000 | −1.09204 | ||||||||
\(484\) | 21.0000 | 0.954545 | ||||||||
\(485\) | −3.17157 | −0.144014 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −16.4853 | −0.747019 | −0.373510 | − | 0.927626i | \(-0.621846\pi\) | ||||
−0.373510 | + | 0.927626i | \(0.621846\pi\) | |||||||
\(488\) | −6.00000 | −0.271607 | ||||||||
\(489\) | −11.3137 | −0.511624 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | −38.1421 | −1.72133 | −0.860665 | − | 0.509171i | \(-0.829952\pi\) | ||||
−0.860665 | + | 0.509171i | \(0.829952\pi\) | |||||||
\(492\) | 7.65685 | 0.345198 | ||||||||
\(493\) | −7.31371 | −0.329393 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.65685 | 0.254257 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 16.0000 | 0.717698 | ||||||||
\(498\) | 6.34315 | 0.284243 | ||||||||
\(499\) | −0.485281 | −0.0217242 | −0.0108621 | − | 0.999941i | \(-0.503458\pi\) | ||||
−0.0108621 | + | 0.999941i | \(0.503458\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −8.97056 | −0.400775 | ||||||||
\(502\) | −10.8284 | −0.483296 | ||||||||
\(503\) | −23.5147 | −1.04847 | −0.524235 | − | 0.851574i | \(-0.675649\pi\) | ||||
−0.524235 | + | 0.851574i | \(0.675649\pi\) | |||||||
\(504\) | −2.82843 | −0.125988 | ||||||||
\(505\) | −16.1421 | −0.718316 | ||||||||
\(506\) | −48.0000 | −2.13386 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.65685 | 0.428454 | ||||||||
\(509\) | 37.3137 | 1.65390 | 0.826951 | − | 0.562275i | \(-0.190074\pi\) | ||||
0.826951 | + | 0.562275i | \(0.190074\pi\) | |||||||
\(510\) | 0.828427 | 0.0366834 | ||||||||
\(511\) | 40.9706 | 1.81243 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.82843 | −0.124878 | ||||||||
\(514\) | 4.82843 | 0.212973 | ||||||||
\(515\) | 1.65685 | 0.0730097 | ||||||||
\(516\) | 9.65685 | 0.425119 | ||||||||
\(517\) | −45.2548 | −1.99031 | ||||||||
\(518\) | −32.9706 | −1.44864 | ||||||||
\(519\) | −9.31371 | −0.408826 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.9706 | 1.18160 | 0.590801 | − | 0.806817i | \(-0.298812\pi\) | ||||
0.590801 | + | 0.806817i | \(0.298812\pi\) | |||||||
\(522\) | 8.82843 | 0.386410 | ||||||||
\(523\) | −10.6274 | −0.464704 | −0.232352 | − | 0.972632i | \(-0.574642\pi\) | ||||
−0.232352 | + | 0.972632i | \(0.574642\pi\) | |||||||
\(524\) | −6.14214 | −0.268320 | ||||||||
\(525\) | 2.82843 | 0.123443 | ||||||||
\(526\) | −16.4853 | −0.718792 | ||||||||
\(527\) | −3.31371 | −0.144347 | ||||||||
\(528\) | −5.65685 | −0.246183 | ||||||||
\(529\) | 49.0000 | 2.13043 | ||||||||
\(530\) | 13.3137 | 0.578311 | ||||||||
\(531\) | 2.34315 | 0.101684 | ||||||||
\(532\) | −8.00000 | −0.346844 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −15.6569 | −0.677538 | ||||||||
\(535\) | 4.00000 | 0.172935 | ||||||||
\(536\) | 5.65685 | 0.244339 | ||||||||
\(537\) | 7.51472 | 0.324284 | ||||||||
\(538\) | 14.4853 | 0.624505 | ||||||||
\(539\) | −5.65685 | −0.243658 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −14.4853 | −0.622771 | −0.311385 | − | 0.950284i | \(-0.600793\pi\) | ||||
−0.311385 | + | 0.950284i | \(0.600793\pi\) | |||||||
\(542\) | 7.31371 | 0.314151 | ||||||||
\(543\) | −7.65685 | −0.328587 | ||||||||
\(544\) | −0.828427 | −0.0355185 | ||||||||
\(545\) | 8.82843 | 0.378168 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.686292 | 0.0293437 | 0.0146719 | − | 0.999892i | \(-0.495330\pi\) | ||||
0.0146719 | + | 0.999892i | \(0.495330\pi\) | |||||||
\(548\) | 17.3137 | 0.739605 | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | 5.65685 | 0.241209 | ||||||||
\(551\) | 24.9706 | 1.06378 | ||||||||
\(552\) | 8.48528 | 0.361158 | ||||||||
\(553\) | 6.62742 | 0.281826 | ||||||||
\(554\) | −26.0000 | −1.10463 | ||||||||
\(555\) | −11.6569 | −0.494806 | ||||||||
\(556\) | 6.34315 | 0.269009 | ||||||||
\(557\) | −10.6863 | −0.452793 | −0.226396 | − | 0.974035i | \(-0.572694\pi\) | ||||
−0.226396 | + | 0.974035i | \(0.572694\pi\) | |||||||
\(558\) | 4.00000 | 0.169334 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.82843 | −0.119523 | ||||||||
\(561\) | −4.68629 | −0.197855 | ||||||||
\(562\) | 8.34315 | 0.351934 | ||||||||
\(563\) | −30.3431 | −1.27881 | −0.639406 | − | 0.768870i | \(-0.720819\pi\) | ||||
−0.639406 | + | 0.768870i | \(0.720819\pi\) | |||||||
\(564\) | 8.00000 | 0.336861 | ||||||||
\(565\) | −6.48528 | −0.272838 | ||||||||
\(566\) | 17.6569 | 0.742173 | ||||||||
\(567\) | 2.82843 | 0.118783 | ||||||||
\(568\) | −5.65685 | −0.237356 | ||||||||
\(569\) | 31.6569 | 1.32712 | 0.663562 | − | 0.748121i | \(-0.269044\pi\) | ||||
0.663562 | + | 0.748121i | \(0.269044\pi\) | |||||||
\(570\) | −2.82843 | −0.118470 | ||||||||
\(571\) | 20.9706 | 0.877591 | 0.438795 | − | 0.898587i | \(-0.355405\pi\) | ||||
0.438795 | + | 0.898587i | \(0.355405\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.3137 | 0.472637 | ||||||||
\(574\) | −21.6569 | −0.903940 | ||||||||
\(575\) | −8.48528 | −0.353861 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 23.4558 | 0.976480 | 0.488240 | − | 0.872710i | \(-0.337639\pi\) | ||||
0.488240 | + | 0.872710i | \(0.337639\pi\) | |||||||
\(578\) | 16.3137 | 0.678561 | ||||||||
\(579\) | −2.48528 | −0.103285 | ||||||||
\(580\) | 8.82843 | 0.366580 | ||||||||
\(581\) | −17.9411 | −0.744323 | ||||||||
\(582\) | −3.17157 | −0.131466 | ||||||||
\(583\) | −75.3137 | −3.11918 | ||||||||
\(584\) | −14.4853 | −0.599405 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.6274 | −0.686872 | ||||||||
\(587\) | −2.62742 | −0.108445 | −0.0542226 | − | 0.998529i | \(-0.517268\pi\) | ||||
−0.0542226 | + | 0.998529i | \(0.517268\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | 11.3137 | 0.466173 | ||||||||
\(590\) | 2.34315 | 0.0964658 | ||||||||
\(591\) | 13.3137 | 0.547653 | ||||||||
\(592\) | 11.6569 | 0.479094 | ||||||||
\(593\) | 0.343146 | 0.0140913 | 0.00704565 | − | 0.999975i | \(-0.497757\pi\) | ||||
0.00704565 | + | 0.999975i | \(0.497757\pi\) | |||||||
\(594\) | 5.65685 | 0.232104 | ||||||||
\(595\) | −2.34315 | −0.0960596 | ||||||||
\(596\) | −3.65685 | −0.149791 | ||||||||
\(597\) | 10.3431 | 0.423317 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.0000 | 1.63436 | 0.817178 | − | 0.576386i | \(-0.195537\pi\) | ||||
0.817178 | + | 0.576386i | \(0.195537\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | 29.3137 | 1.19573 | 0.597866 | − | 0.801596i | \(-0.296016\pi\) | ||||
0.597866 | + | 0.801596i | \(0.296016\pi\) | |||||||
\(602\) | −27.3137 | −1.11322 | ||||||||
\(603\) | −5.65685 | −0.230365 | ||||||||
\(604\) | −12.0000 | −0.488273 | ||||||||
\(605\) | −21.0000 | −0.853771 | ||||||||
\(606\) | −16.1421 | −0.655729 | ||||||||
\(607\) | 28.9706 | 1.17588 | 0.587939 | − | 0.808905i | \(-0.299939\pi\) | ||||
0.587939 | + | 0.808905i | \(0.299939\pi\) | |||||||
\(608\) | 2.82843 | 0.114708 | ||||||||
\(609\) | −24.9706 | −1.01186 | ||||||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.828427 | 0.0334872 | ||||||||
\(613\) | −22.2843 | −0.900053 | −0.450027 | − | 0.893015i | \(-0.648586\pi\) | ||||
−0.450027 | + | 0.893015i | \(0.648586\pi\) | |||||||
\(614\) | −21.6569 | −0.874000 | ||||||||
\(615\) | −7.65685 | −0.308754 | ||||||||
\(616\) | 16.0000 | 0.644658 | ||||||||
\(617\) | −2.00000 | −0.0805170 | −0.0402585 | − | 0.999189i | \(-0.512818\pi\) | ||||
−0.0402585 | + | 0.999189i | \(0.512818\pi\) | |||||||
\(618\) | 1.65685 | 0.0666485 | ||||||||
\(619\) | 34.8284 | 1.39987 | 0.699936 | − | 0.714205i | \(-0.253212\pi\) | ||||
0.699936 | + | 0.714205i | \(0.253212\pi\) | |||||||
\(620\) | 4.00000 | 0.160644 | ||||||||
\(621\) | −8.48528 | −0.340503 | ||||||||
\(622\) | 24.0000 | 0.962312 | ||||||||
\(623\) | 44.2843 | 1.77421 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 30.9706 | 1.23783 | ||||||||
\(627\) | 16.0000 | 0.638978 | ||||||||
\(628\) | 5.31371 | 0.212040 | ||||||||
\(629\) | 9.65685 | 0.385044 | ||||||||
\(630\) | 2.82843 | 0.112687 | ||||||||
\(631\) | 33.6569 | 1.33986 | 0.669929 | − | 0.742425i | \(-0.266324\pi\) | ||||
0.669929 | + | 0.742425i | \(0.266324\pi\) | |||||||
\(632\) | −2.34315 | −0.0932053 | ||||||||
\(633\) | 0.686292 | 0.0272776 | ||||||||
\(634\) | 25.3137 | 1.00534 | ||||||||
\(635\) | −9.65685 | −0.383221 | ||||||||
\(636\) | 13.3137 | 0.527923 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −49.9411 | −1.97719 | ||||||||
\(639\) | 5.65685 | 0.223782 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −4.62742 | −0.182772 | −0.0913860 | − | 0.995816i | \(-0.529130\pi\) | ||||
−0.0913860 | + | 0.995816i | \(0.529130\pi\) | |||||||
\(642\) | 4.00000 | 0.157867 | ||||||||
\(643\) | −39.5980 | −1.56159 | −0.780796 | − | 0.624786i | \(-0.785186\pi\) | ||||
−0.780796 | + | 0.624786i | \(0.785186\pi\) | |||||||
\(644\) | −24.0000 | −0.945732 | ||||||||
\(645\) | −9.65685 | −0.380238 | ||||||||
\(646\) | 2.34315 | 0.0921898 | ||||||||
\(647\) | 8.48528 | 0.333591 | 0.166795 | − | 0.985992i | \(-0.446658\pi\) | ||||
0.166795 | + | 0.985992i | \(0.446658\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −13.2548 | −0.520298 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.3137 | −0.443419 | ||||||||
\(652\) | −11.3137 | −0.443079 | ||||||||
\(653\) | −42.2843 | −1.65471 | −0.827356 | − | 0.561678i | \(-0.810156\pi\) | ||||
−0.827356 | + | 0.561678i | \(0.810156\pi\) | |||||||
\(654\) | 8.82843 | 0.345219 | ||||||||
\(655\) | 6.14214 | 0.239993 | ||||||||
\(656\) | 7.65685 | 0.298950 | ||||||||
\(657\) | 14.4853 | 0.565125 | ||||||||
\(658\) | −22.6274 | −0.882109 | ||||||||
\(659\) | −7.51472 | −0.292732 | −0.146366 | − | 0.989231i | \(-0.546758\pi\) | ||||
−0.146366 | + | 0.989231i | \(0.546758\pi\) | |||||||
\(660\) | 5.65685 | 0.220193 | ||||||||
\(661\) | 8.14214 | 0.316692 | 0.158346 | − | 0.987384i | \(-0.449384\pi\) | ||||
0.158346 | + | 0.987384i | \(0.449384\pi\) | |||||||
\(662\) | −8.48528 | −0.329790 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.34315 | 0.246162 | ||||||||
\(665\) | 8.00000 | 0.310227 | ||||||||
\(666\) | −11.6569 | −0.451694 | ||||||||
\(667\) | 74.9117 | 2.90059 | ||||||||
\(668\) | −8.97056 | −0.347081 | ||||||||
\(669\) | −10.8284 | −0.418651 | ||||||||
\(670\) | −5.65685 | −0.218543 | ||||||||
\(671\) | −33.9411 | −1.31028 | ||||||||
\(672\) | −2.82843 | −0.109109 | ||||||||
\(673\) | 32.6274 | 1.25769 | 0.628847 | − | 0.777529i | \(-0.283527\pi\) | ||||
0.628847 | + | 0.777529i | \(0.283527\pi\) | |||||||
\(674\) | −10.9706 | −0.422570 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.3431 | 0.474386 | 0.237193 | − | 0.971463i | \(-0.423773\pi\) | ||||
0.237193 | + | 0.971463i | \(0.423773\pi\) | |||||||
\(678\) | −6.48528 | −0.249066 | ||||||||
\(679\) | 8.97056 | 0.344259 | ||||||||
\(680\) | 0.828427 | 0.0317687 | ||||||||
\(681\) | −4.00000 | −0.153280 | ||||||||
\(682\) | −22.6274 | −0.866449 | ||||||||
\(683\) | −33.6569 | −1.28784 | −0.643922 | − | 0.765091i | \(-0.722694\pi\) | ||||
−0.643922 | + | 0.765091i | \(0.722694\pi\) | |||||||
\(684\) | −2.82843 | −0.108148 | ||||||||
\(685\) | −17.3137 | −0.661523 | ||||||||
\(686\) | 16.9706 | 0.647939 | ||||||||
\(687\) | −4.14214 | −0.158032 | ||||||||
\(688\) | 9.65685 | 0.368164 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −8.48528 | −0.323029 | ||||||||
\(691\) | 27.7990 | 1.05752 | 0.528762 | − | 0.848770i | \(-0.322657\pi\) | ||||
0.528762 | + | 0.848770i | \(0.322657\pi\) | |||||||
\(692\) | −9.31371 | −0.354054 | ||||||||
\(693\) | −16.0000 | −0.607790 | ||||||||
\(694\) | 9.65685 | 0.366569 | ||||||||
\(695\) | −6.34315 | −0.240609 | ||||||||
\(696\) | 8.82843 | 0.334641 | ||||||||
\(697\) | 6.34315 | 0.240264 | ||||||||
\(698\) | 12.1421 | 0.459587 | ||||||||
\(699\) | 5.51472 | 0.208586 | ||||||||
\(700\) | 2.82843 | 0.106904 | ||||||||
\(701\) | 0.142136 | 0.00536839 | 0.00268419 | − | 0.999996i | \(-0.499146\pi\) | ||||
0.00268419 | + | 0.999996i | \(0.499146\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.9706 | −1.24351 | ||||||||
\(704\) | −5.65685 | −0.213201 | ||||||||
\(705\) | −8.00000 | −0.301297 | ||||||||
\(706\) | 5.31371 | 0.199984 | ||||||||
\(707\) | 45.6569 | 1.71710 | ||||||||
\(708\) | 2.34315 | 0.0880608 | ||||||||
\(709\) | 7.17157 | 0.269334 | 0.134667 | − | 0.990891i | \(-0.457004\pi\) | ||||
0.134667 | + | 0.990891i | \(0.457004\pi\) | |||||||
\(710\) | 5.65685 | 0.212298 | ||||||||
\(711\) | 2.34315 | 0.0878748 | ||||||||
\(712\) | −15.6569 | −0.586765 | ||||||||
\(713\) | 33.9411 | 1.27111 | ||||||||
\(714\) | −2.34315 | −0.0876900 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.51472 | 0.280838 | ||||||||
\(717\) | −16.0000 | −0.597531 | ||||||||
\(718\) | −28.2843 | −1.05556 | ||||||||
\(719\) | −29.6569 | −1.10601 | −0.553007 | − | 0.833177i | \(-0.686520\pi\) | ||||
−0.553007 | + | 0.833177i | \(0.686520\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | −4.68629 | −0.174527 | ||||||||
\(722\) | 11.0000 | 0.409378 | ||||||||
\(723\) | −5.31371 | −0.197619 | ||||||||
\(724\) | −7.65685 | −0.284565 | ||||||||
\(725\) | −8.82843 | −0.327880 | ||||||||
\(726\) | −21.0000 | −0.779383 | ||||||||
\(727\) | −45.9411 | −1.70386 | −0.851931 | − | 0.523654i | \(-0.824568\pi\) | ||||
−0.851931 | + | 0.523654i | \(0.824568\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 14.4853 | 0.536124 | ||||||||
\(731\) | 8.00000 | 0.295891 | ||||||||
\(732\) | 6.00000 | 0.221766 | ||||||||
\(733\) | 0.343146 | 0.0126744 | 0.00633719 | − | 0.999980i | \(-0.497983\pi\) | ||||
0.00633719 | + | 0.999980i | \(0.497983\pi\) | |||||||
\(734\) | −25.6569 | −0.947012 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | 8.48528 | 0.312772 | ||||||||
\(737\) | 32.0000 | 1.17874 | ||||||||
\(738\) | −7.65685 | −0.281853 | ||||||||
\(739\) | 14.1421 | 0.520227 | 0.260113 | − | 0.965578i | \(-0.416240\pi\) | ||||
0.260113 | + | 0.965578i | \(0.416240\pi\) | |||||||
\(740\) | −11.6569 | −0.428514 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −37.6569 | −1.38243 | ||||||||
\(743\) | 36.2843 | 1.33114 | 0.665570 | − | 0.746335i | \(-0.268188\pi\) | ||||
0.665570 | + | 0.746335i | \(0.268188\pi\) | |||||||
\(744\) | 4.00000 | 0.146647 | ||||||||
\(745\) | 3.65685 | 0.133977 | ||||||||
\(746\) | 2.68629 | 0.0983521 | ||||||||
\(747\) | −6.34315 | −0.232084 | ||||||||
\(748\) | −4.68629 | −0.171348 | ||||||||
\(749\) | −11.3137 | −0.413394 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 11.3137 | 0.412843 | 0.206422 | − | 0.978463i | \(-0.433818\pi\) | ||||
0.206422 | + | 0.978463i | \(0.433818\pi\) | |||||||
\(752\) | 8.00000 | 0.291730 | ||||||||
\(753\) | 10.8284 | 0.394610 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0000 | 0.436725 | ||||||||
\(756\) | 2.82843 | 0.102869 | ||||||||
\(757\) | 19.9411 | 0.724773 | 0.362386 | − | 0.932028i | \(-0.381962\pi\) | ||||
0.362386 | + | 0.932028i | \(0.381962\pi\) | |||||||
\(758\) | −7.51472 | −0.272947 | ||||||||
\(759\) | 48.0000 | 1.74229 | ||||||||
\(760\) | −2.82843 | −0.102598 | ||||||||
\(761\) | −27.6569 | −1.00256 | −0.501280 | − | 0.865285i | \(-0.667137\pi\) | ||||
−0.501280 | + | 0.865285i | \(0.667137\pi\) | |||||||
\(762\) | −9.65685 | −0.349831 | ||||||||
\(763\) | −24.9706 | −0.903995 | ||||||||
\(764\) | 11.3137 | 0.409316 | ||||||||
\(765\) | −0.828427 | −0.0299518 | ||||||||
\(766\) | −29.6569 | −1.07155 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | −16.0000 | −0.576600 | ||||||||
\(771\) | −4.82843 | −0.173892 | ||||||||
\(772\) | −2.48528 | −0.0894472 | ||||||||
\(773\) | 53.3137 | 1.91756 | 0.958780 | − | 0.284148i | \(-0.0917107\pi\) | ||||
0.958780 | + | 0.284148i | \(0.0917107\pi\) | |||||||
\(774\) | −9.65685 | −0.347108 | ||||||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | −3.17157 | −0.113853 | ||||||||
\(777\) | 32.9706 | 1.18281 | ||||||||
\(778\) | 6.48528 | 0.232509 | ||||||||
\(779\) | −21.6569 | −0.775937 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.0000 | −1.14505 | ||||||||
\(782\) | 7.02944 | 0.251372 | ||||||||
\(783\) | −8.82843 | −0.315502 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −5.31371 | −0.189654 | ||||||||
\(786\) | 6.14214 | 0.219083 | ||||||||
\(787\) | 24.0000 | 0.855508 | 0.427754 | − | 0.903895i | \(-0.359305\pi\) | ||||
0.427754 | + | 0.903895i | \(0.359305\pi\) | |||||||
\(788\) | 13.3137 | 0.474281 | ||||||||
\(789\) | 16.4853 | 0.586892 | ||||||||
\(790\) | 2.34315 | 0.0833654 | ||||||||
\(791\) | 18.3431 | 0.652207 | ||||||||
\(792\) | 5.65685 | 0.201008 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 30.2843 | 1.07475 | ||||||||
\(795\) | −13.3137 | −0.472189 | ||||||||
\(796\) | 10.3431 | 0.366603 | ||||||||
\(797\) | 16.6274 | 0.588973 | 0.294487 | − | 0.955656i | \(-0.404851\pi\) | ||||
0.294487 | + | 0.955656i | \(0.404851\pi\) | |||||||
\(798\) | 8.00000 | 0.283197 | ||||||||
\(799\) | 6.62742 | 0.234461 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 15.6569 | 0.553208 | ||||||||
\(802\) | −26.9706 | −0.952364 | ||||||||
\(803\) | −81.9411 | −2.89164 | ||||||||
\(804\) | −5.65685 | −0.199502 | ||||||||
\(805\) | 24.0000 | 0.845889 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.4853 | −0.509906 | ||||||||
\(808\) | −16.1421 | −0.567878 | ||||||||
\(809\) | 13.3137 | 0.468085 | 0.234043 | − | 0.972226i | \(-0.424804\pi\) | ||||
0.234043 | + | 0.972226i | \(0.424804\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 1.85786 | 0.0652384 | 0.0326192 | − | 0.999468i | \(-0.489615\pi\) | ||||
0.0326192 | + | 0.999468i | \(0.489615\pi\) | |||||||
\(812\) | −24.9706 | −0.876295 | ||||||||
\(813\) | −7.31371 | −0.256503 | ||||||||
\(814\) | 65.9411 | 2.31124 | ||||||||
\(815\) | 11.3137 | 0.396302 | ||||||||
\(816\) | 0.828427 | 0.0290008 | ||||||||
\(817\) | −27.3137 | −0.955586 | ||||||||
\(818\) | −3.65685 | −0.127859 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.65685 | −0.267389 | ||||||||
\(821\) | −34.2843 | −1.19653 | −0.598265 | − | 0.801299i | \(-0.704143\pi\) | ||||
−0.598265 | + | 0.801299i | \(0.704143\pi\) | |||||||
\(822\) | −17.3137 | −0.603885 | ||||||||
\(823\) | −52.9706 | −1.84644 | −0.923219 | − | 0.384275i | \(-0.874452\pi\) | ||||
−0.923219 | + | 0.384275i | \(0.874452\pi\) | |||||||
\(824\) | 1.65685 | 0.0577193 | ||||||||
\(825\) | −5.65685 | −0.196946 | ||||||||
\(826\) | −6.62742 | −0.230597 | ||||||||
\(827\) | −9.65685 | −0.335802 | −0.167901 | − | 0.985804i | \(-0.553699\pi\) | ||||
−0.167901 | + | 0.985804i | \(0.553699\pi\) | |||||||
\(828\) | −8.48528 | −0.294884 | ||||||||
\(829\) | −53.3137 | −1.85166 | −0.925831 | − | 0.377938i | \(-0.876633\pi\) | ||||
−0.925831 | + | 0.377938i | \(0.876633\pi\) | |||||||
\(830\) | −6.34315 | −0.220174 | ||||||||
\(831\) | 26.0000 | 0.901930 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.828427 | 0.0287033 | ||||||||
\(834\) | −6.34315 | −0.219645 | ||||||||
\(835\) | 8.97056 | 0.310439 | ||||||||
\(836\) | 16.0000 | 0.553372 | ||||||||
\(837\) | −4.00000 | −0.138260 | ||||||||
\(838\) | 10.8284 | 0.374062 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 2.82843 | 0.0975900 | ||||||||
\(841\) | 48.9411 | 1.68763 | ||||||||
\(842\) | −24.1421 | −0.831993 | ||||||||
\(843\) | −8.34315 | −0.287353 | ||||||||
\(844\) | 0.686292 | 0.0236231 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.00000 | −0.275046 | ||||||||
\(847\) | 59.3970 | 2.04090 | ||||||||
\(848\) | 13.3137 | 0.457195 | ||||||||
\(849\) | −17.6569 | −0.605982 | ||||||||
\(850\) | −0.828427 | −0.0284148 | ||||||||
\(851\) | −98.9117 | −3.39065 | ||||||||
\(852\) | 5.65685 | 0.193801 | ||||||||
\(853\) | −38.2843 | −1.31083 | −0.655414 | − | 0.755270i | \(-0.727506\pi\) | ||||
−0.655414 | + | 0.755270i | \(0.727506\pi\) | |||||||
\(854\) | −16.9706 | −0.580721 | ||||||||
\(855\) | 2.82843 | 0.0967302 | ||||||||
\(856\) | 4.00000 | 0.136717 | ||||||||
\(857\) | −20.8284 | −0.711486 | −0.355743 | − | 0.934584i | \(-0.615772\pi\) | ||||
−0.355743 | + | 0.934584i | \(0.615772\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.9411 | 1.29453 | 0.647267 | − | 0.762263i | \(-0.275912\pi\) | ||||
0.647267 | + | 0.762263i | \(0.275912\pi\) | |||||||
\(860\) | −9.65685 | −0.329296 | ||||||||
\(861\) | 21.6569 | 0.738064 | ||||||||
\(862\) | −16.0000 | −0.544962 | ||||||||
\(863\) | 28.2843 | 0.962808 | 0.481404 | − | 0.876499i | \(-0.340127\pi\) | ||||
0.481404 | + | 0.876499i | \(0.340127\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 9.31371 | 0.316676 | ||||||||
\(866\) | 22.9706 | 0.780571 | ||||||||
\(867\) | −16.3137 | −0.554043 | ||||||||
\(868\) | −11.3137 | −0.384012 | ||||||||
\(869\) | −13.2548 | −0.449639 | ||||||||
\(870\) | −8.82843 | −0.299312 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.82843 | 0.298968 | ||||||||
\(873\) | 3.17157 | 0.107341 | ||||||||
\(874\) | −24.0000 | −0.811812 | ||||||||
\(875\) | −2.82843 | −0.0956183 | ||||||||
\(876\) | 14.4853 | 0.489412 | ||||||||
\(877\) | 51.2548 | 1.73075 | 0.865376 | − | 0.501122i | \(-0.167079\pi\) | ||||
0.865376 | + | 0.501122i | \(0.167079\pi\) | |||||||
\(878\) | −22.6274 | −0.763638 | ||||||||
\(879\) | 16.6274 | 0.560829 | ||||||||
\(880\) | 5.65685 | 0.190693 | ||||||||
\(881\) | −10.2843 | −0.346486 | −0.173243 | − | 0.984879i | \(-0.555425\pi\) | ||||
−0.173243 | + | 0.984879i | \(0.555425\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | 31.3137 | 1.05379 | 0.526895 | − | 0.849930i | \(-0.323356\pi\) | ||||
0.526895 | + | 0.849930i | \(0.323356\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.34315 | −0.0787640 | ||||||||
\(886\) | −30.3431 | −1.01940 | ||||||||
\(887\) | −40.4853 | −1.35936 | −0.679681 | − | 0.733508i | \(-0.737882\pi\) | ||||
−0.679681 | + | 0.733508i | \(0.737882\pi\) | |||||||
\(888\) | −11.6569 | −0.391178 | ||||||||
\(889\) | 27.3137 | 0.916072 | ||||||||
\(890\) | 15.6569 | 0.524819 | ||||||||
\(891\) | −5.65685 | −0.189512 | ||||||||
\(892\) | −10.8284 | −0.362563 | ||||||||
\(893\) | −22.6274 | −0.757198 | ||||||||
\(894\) | 3.65685 | 0.122304 | ||||||||
\(895\) | −7.51472 | −0.251189 | ||||||||
\(896\) | −2.82843 | −0.0944911 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 26.2843 | 0.877117 | ||||||||
\(899\) | 35.3137 | 1.17778 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 11.0294 | 0.367444 | ||||||||
\(902\) | 43.3137 | 1.44219 | ||||||||
\(903\) | 27.3137 | 0.908943 | ||||||||
\(904\) | −6.48528 | −0.215697 | ||||||||
\(905\) | 7.65685 | 0.254522 | ||||||||
\(906\) | 12.0000 | 0.398673 | ||||||||
\(907\) | 8.28427 | 0.275075 | 0.137537 | − | 0.990497i | \(-0.456081\pi\) | ||||
0.137537 | + | 0.990497i | \(0.456081\pi\) | |||||||
\(908\) | −4.00000 | −0.132745 | ||||||||
\(909\) | 16.1421 | 0.535401 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.9706 | 0.827312 | 0.413656 | − | 0.910433i | \(-0.364252\pi\) | ||||
0.413656 | + | 0.910433i | \(0.364252\pi\) | |||||||
\(912\) | −2.82843 | −0.0936586 | ||||||||
\(913\) | 35.8823 | 1.18753 | ||||||||
\(914\) | 20.8284 | 0.688943 | ||||||||
\(915\) | −6.00000 | −0.198354 | ||||||||
\(916\) | −4.14214 | −0.136860 | ||||||||
\(917\) | −17.3726 | −0.573693 | ||||||||
\(918\) | −0.828427 | −0.0273422 | ||||||||
\(919\) | 41.9411 | 1.38351 | 0.691755 | − | 0.722132i | \(-0.256838\pi\) | ||||
0.691755 | + | 0.722132i | \(0.256838\pi\) | |||||||
\(920\) | −8.48528 | −0.279751 | ||||||||
\(921\) | 21.6569 | 0.713618 | ||||||||
\(922\) | 14.0000 | 0.461065 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −16.0000 | −0.526361 | ||||||||
\(925\) | 11.6569 | 0.383275 | ||||||||
\(926\) | −3.79899 | −0.124843 | ||||||||
\(927\) | −1.65685 | −0.0544182 | ||||||||
\(928\) | 8.82843 | 0.289807 | ||||||||
\(929\) | 33.5980 | 1.10231 | 0.551157 | − | 0.834402i | \(-0.314187\pi\) | ||||
0.551157 | + | 0.834402i | \(0.314187\pi\) | |||||||
\(930\) | −4.00000 | −0.131165 | ||||||||
\(931\) | −2.82843 | −0.0926980 | ||||||||
\(932\) | 5.51472 | 0.180641 | ||||||||
\(933\) | −24.0000 | −0.785725 | ||||||||
\(934\) | −7.31371 | −0.239312 | ||||||||
\(935\) | 4.68629 | 0.153258 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.6274 | 0.543194 | 0.271597 | − | 0.962411i | \(-0.412448\pi\) | ||||
0.271597 | + | 0.962411i | \(0.412448\pi\) | |||||||
\(938\) | 16.0000 | 0.522419 | ||||||||
\(939\) | −30.9706 | −1.01069 | ||||||||
\(940\) | −8.00000 | −0.260931 | ||||||||
\(941\) | −54.9706 | −1.79199 | −0.895995 | − | 0.444065i | \(-0.853536\pi\) | ||||
−0.895995 | + | 0.444065i | \(0.853536\pi\) | |||||||
\(942\) | −5.31371 | −0.173130 | ||||||||
\(943\) | −64.9706 | −2.11573 | ||||||||
\(944\) | 2.34315 | 0.0762629 | ||||||||
\(945\) | −2.82843 | −0.0920087 | ||||||||
\(946\) | 54.6274 | 1.77609 | ||||||||
\(947\) | −30.3431 | −0.986020 | −0.493010 | − | 0.870024i | \(-0.664103\pi\) | ||||
−0.493010 | + | 0.870024i | \(0.664103\pi\) | |||||||
\(948\) | 2.34315 | 0.0761018 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.82843 | 0.0917663 | ||||||||
\(951\) | −25.3137 | −0.820853 | ||||||||
\(952\) | −2.34315 | −0.0759418 | ||||||||
\(953\) | −27.8579 | −0.902405 | −0.451202 | − | 0.892422i | \(-0.649005\pi\) | ||||
−0.451202 | + | 0.892422i | \(0.649005\pi\) | |||||||
\(954\) | −13.3137 | −0.431047 | ||||||||
\(955\) | −11.3137 | −0.366103 | ||||||||
\(956\) | −16.0000 | −0.517477 | ||||||||
\(957\) | 49.9411 | 1.61437 | ||||||||
\(958\) | −11.3137 | −0.365529 | ||||||||
\(959\) | 48.9706 | 1.58134 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.00000 | −0.128898 | ||||||||
\(964\) | −5.31371 | −0.171143 | ||||||||
\(965\) | 2.48528 | 0.0800040 | ||||||||
\(966\) | 24.0000 | 0.772187 | ||||||||
\(967\) | 7.51472 | 0.241657 | 0.120829 | − | 0.992673i | \(-0.461445\pi\) | ||||
0.120829 | + | 0.992673i | \(0.461445\pi\) | |||||||
\(968\) | −21.0000 | −0.674966 | ||||||||
\(969\) | −2.34315 | −0.0752727 | ||||||||
\(970\) | 3.17157 | 0.101833 | ||||||||
\(971\) | 15.5147 | 0.497891 | 0.248946 | − | 0.968517i | \(-0.419916\pi\) | ||||
0.248946 | + | 0.968517i | \(0.419916\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 17.9411 | 0.575166 | ||||||||
\(974\) | 16.4853 | 0.528222 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.00000 | 0.192055 | ||||||||
\(977\) | 8.34315 | 0.266921 | 0.133460 | − | 0.991054i | \(-0.457391\pi\) | ||||
0.133460 | + | 0.991054i | \(0.457391\pi\) | |||||||
\(978\) | 11.3137 | 0.361773 | ||||||||
\(979\) | −88.5685 | −2.83066 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −8.82843 | −0.281870 | ||||||||
\(982\) | 38.1421 | 1.21716 | ||||||||
\(983\) | 2.34315 | 0.0747347 | 0.0373674 | − | 0.999302i | \(-0.488103\pi\) | ||||
0.0373674 | + | 0.999302i | \(0.488103\pi\) | |||||||
\(984\) | −7.65685 | −0.244092 | ||||||||
\(985\) | −13.3137 | −0.424210 | ||||||||
\(986\) | 7.31371 | 0.232916 | ||||||||
\(987\) | 22.6274 | 0.720239 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −81.9411 | −2.60558 | ||||||||
\(990\) | −5.65685 | −0.179787 | ||||||||
\(991\) | −42.9117 | −1.36313 | −0.681567 | − | 0.731755i | \(-0.738701\pi\) | ||||
−0.681567 | + | 0.731755i | \(0.738701\pi\) | |||||||
\(992\) | 4.00000 | 0.127000 | ||||||||
\(993\) | 8.48528 | 0.269272 | ||||||||
\(994\) | −16.0000 | −0.507489 | ||||||||
\(995\) | −10.3431 | −0.327900 | ||||||||
\(996\) | −6.34315 | −0.200990 | ||||||||
\(997\) | 61.3137 | 1.94182 | 0.970912 | − | 0.239435i | \(-0.0769623\pi\) | ||||
0.970912 | + | 0.239435i | \(0.0769623\pi\) | |||||||
\(998\) | 0.485281 | 0.0153613 | ||||||||
\(999\) | 11.6569 | 0.368807 |
(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 | 5070.2.a.bc.1.2 | 2 | ||
13.5 | odd | 4 | 5070.2.b.q.1351.4 | 4 | |||
13.8 | odd | 4 | 5070.2.b.q.1351.1 | 4 | |||
13.12 | even | 2 | 390.2.a.h.1.1 | ✓ | 2 | ||
39.38 | odd | 2 | 1170.2.a.o.1.1 | 2 | |||
52.51 | odd | 2 | 3120.2.a.bc.1.2 | 2 | |||
65.12 | odd | 4 | 1950.2.e.o.1249.3 | 4 | |||
65.38 | odd | 4 | 1950.2.e.o.1249.2 | 4 | |||
65.64 | even | 2 | 1950.2.a.bd.1.2 | 2 | |||
156.155 | even | 2 | 9360.2.a.ch.1.2 | 2 | |||
195.38 | even | 4 | 5850.2.e.bk.5149.4 | 4 | |||
195.77 | even | 4 | 5850.2.e.bk.5149.1 | 4 | |||
195.194 | odd | 2 | 5850.2.a.cl.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.a.h.1.1 | ✓ | 2 | 13.12 | even | 2 | ||
1170.2.a.o.1.1 | 2 | 39.38 | odd | 2 | |||
1950.2.a.bd.1.2 | 2 | 65.64 | even | 2 | |||
1950.2.e.o.1249.2 | 4 | 65.38 | odd | 4 | |||
1950.2.e.o.1249.3 | 4 | 65.12 | odd | 4 | |||
3120.2.a.bc.1.2 | 2 | 52.51 | odd | 2 | |||
5070.2.a.bc.1.2 | 2 | 1.1 | even | 1 | trivial | ||
5070.2.b.q.1351.1 | 4 | 13.8 | odd | 4 | |||
5070.2.b.q.1351.4 | 4 | 13.5 | odd | 4 | |||
5850.2.a.cl.1.2 | 2 | 195.194 | odd | 2 | |||
5850.2.e.bk.5149.1 | 4 | 195.77 | even | 4 | |||
5850.2.e.bk.5149.4 | 4 | 195.38 | even | 4 | |||
9360.2.a.ch.1.2 | 2 | 156.155 | even | 2 |