Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3120,2,Mod(1,3120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("3120.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3120.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: | \(24.9133254306\) |
Analytic rank: | \(1\) |
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 | \(\chi\) | \(=\) | 3120.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843 | 1.06904 | 0.534522 | − | 0.845154i | \(-0.320491\pi\) | ||||
0.534522 | + | 0.845154i | \(0.320491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.65685 | −1.70561 | −0.852803 | − | 0.522233i | \(-0.825099\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.828427 | 0.200923 | 0.100462 | − | 0.994941i | \(-0.467968\pi\) | ||||
0.100462 | + | 0.994941i | \(0.467968\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.82843 | −0.648886 | −0.324443 | − | 0.945905i | \(-0.605177\pi\) | ||||
−0.324443 | + | 0.945905i | \(0.605177\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.82843 | −0.617213 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.48528 | 1.76930 | 0.884652 | − | 0.466252i | \(-0.154396\pi\) | ||||
0.884652 | + | 0.466252i | \(0.154396\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.82843 | −1.63940 | −0.819699 | − | 0.572795i | \(-0.805859\pi\) | ||||
−0.819699 | + | 0.572795i | \(0.805859\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.65685 | 0.984732 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.82843 | 0.478091 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.6569 | −1.91638 | −0.958188 | − | 0.286141i | \(-0.907627\pi\) | ||||
−0.958188 | + | 0.286141i | \(0.907627\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.65685 | −1.19580 | −0.597900 | − | 0.801571i | \(-0.703998\pi\) | ||||
−0.597900 | + | 0.801571i | \(0.703998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.65685 | −1.47266 | −0.736328 | − | 0.676625i | \(-0.763442\pi\) | ||||
−0.736328 | + | 0.676625i | \(0.763442\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.828427 | −0.116003 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.3137 | 1.82878 | 0.914389 | − | 0.404836i | \(-0.132671\pi\) | ||||
0.914389 | + | 0.404836i | \(0.132671\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.65685 | −0.762770 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.82843 | 0.374634 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.34315 | 0.305052 | 0.152526 | − | 0.988299i | \(-0.451259\pi\) | ||||
0.152526 | + | 0.988299i | \(0.451259\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.82843 | 0.356348 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.65685 | −0.691095 | −0.345547 | − | 0.938401i | \(-0.612307\pi\) | ||||
−0.345547 | + | 0.938401i | \(0.612307\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.48528 | −1.02151 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.65685 | 0.671345 | 0.335673 | − | 0.941979i | \(-0.391036\pi\) | ||||
0.335673 | + | 0.941979i | \(0.391036\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.4853 | −1.69537 | −0.847687 | − | 0.530497i | \(-0.822005\pi\) | ||||
−0.847687 | + | 0.530497i | \(0.822005\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.0000 | −1.82337 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.34315 | −0.263624 | −0.131812 | − | 0.991275i | \(-0.542080\pi\) | ||||
−0.131812 | + | 0.991275i | \(0.542080\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.34315 | −0.696251 | −0.348125 | − | 0.937448i | \(-0.613182\pi\) | ||||
−0.348125 | + | 0.937448i | \(0.613182\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.828427 | 0.0898555 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.82843 | 0.946507 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.6569 | −1.65962 | −0.829812 | − | 0.558044i | \(-0.811552\pi\) | ||||
−0.829812 | + | 0.558044i | \(0.811552\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.82843 | −0.296500 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.00000 | 0.414781 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.82843 | −0.290191 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.17157 | −0.322024 | −0.161012 | − | 0.986952i | \(-0.551476\pi\) | ||||
−0.161012 | + | 0.986952i | \(0.551476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.65685 | −0.568535 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.1421 | 1.60620 | 0.803101 | − | 0.595843i | \(-0.203182\pi\) | ||||
0.803101 | + | 0.595843i | \(0.203182\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.65685 | 0.163255 | 0.0816274 | − | 0.996663i | \(-0.473988\pi\) | ||||
0.0816274 | + | 0.996663i | \(0.473988\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.82843 | −0.276026 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.82843 | 0.845610 | 0.422805 | − | 0.906221i | \(-0.361046\pi\) | ||||
0.422805 | + | 0.906221i | \(0.361046\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.6569 | 1.10642 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.48528 | 0.610084 | 0.305042 | − | 0.952339i | \(-0.401330\pi\) | ||||
0.305042 | + | 0.952339i | \(0.401330\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.48528 | 0.791257 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.34315 | 0.214796 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.0000 | 1.90909 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.65685 | 0.690395 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.65685 | −0.856907 | −0.428454 | − | 0.903564i | \(-0.640941\pi\) | ||||
−0.428454 | + | 0.903564i | \(0.640941\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.65685 | 0.850239 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.14214 | 0.536641 | 0.268320 | − | 0.963330i | \(-0.413531\pi\) | ||||
0.268320 | + | 0.963330i | \(0.413531\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | −0.693688 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.3137 | −1.47921 | −0.739605 | − | 0.673041i | \(-0.764988\pi\) | ||||
−0.739605 | + | 0.673041i | \(0.764988\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.34315 | −0.538019 | −0.269009 | − | 0.963138i | \(-0.586696\pi\) | ||||
−0.269009 | + | 0.963138i | \(0.586696\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.00000 | −0.673722 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.65685 | 0.473050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.82843 | −0.733161 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.65685 | 0.299581 | 0.149791 | − | 0.988718i | \(-0.452140\pi\) | ||||
0.149791 | + | 0.988718i | \(0.452140\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.828427 | 0.0669744 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.31371 | 0.424080 | 0.212040 | − | 0.977261i | \(-0.431989\pi\) | ||||
0.212040 | + | 0.977261i | \(0.431989\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.3137 | −1.05585 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.0000 | 1.89146 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.3137 | −0.886158 | −0.443079 | − | 0.896483i | \(-0.646114\pi\) | ||||
−0.443079 | + | 0.896483i | \(0.646114\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.65685 | 0.440386 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.97056 | −0.694163 | −0.347081 | − | 0.937835i | \(-0.612827\pi\) | ||||
−0.347081 | + | 0.937835i | \(0.612827\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.82843 | −0.216295 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.31371 | −0.708108 | −0.354054 | − | 0.935225i | \(-0.615197\pi\) | ||||
−0.354054 | + | 0.935225i | \(0.615197\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.82843 | 0.213809 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.34315 | −0.176122 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.51472 | −0.561676 | −0.280838 | − | 0.959755i | \(-0.590612\pi\) | ||||
−0.280838 | + | 0.959755i | \(0.590612\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −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 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.6569 | −0.857029 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.68629 | −0.342696 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.82843 | −0.205738 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.3137 | −0.818631 | −0.409316 | − | 0.912393i | \(-0.634232\pi\) | ||||
−0.409316 | + | 0.912393i | \(0.634232\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.48528 | 0.178894 | 0.0894472 | − | 0.995992i | \(-0.471490\pi\) | ||||
0.0894472 | + | 0.995992i | \(0.471490\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.00000 | 0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.3137 | −0.948562 | −0.474281 | − | 0.880373i | \(-0.657292\pi\) | ||||
−0.474281 | + | 0.880373i | \(0.657292\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.3431 | −0.733206 | −0.366603 | − | 0.930377i | \(-0.619479\pi\) | ||||
−0.366603 | + | 0.930377i | \(0.619479\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.65685 | 0.399004 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −24.9706 | −1.75259 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.65685 | −0.534778 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.48528 | 0.589768 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0000 | 1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.686292 | −0.0472463 | −0.0236231 | − | 0.999721i | \(-0.507520\pi\) | ||||
−0.0236231 | + | 0.999721i | \(0.507520\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.65685 | −0.387601 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.65685 | −0.658592 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.3137 | −0.768025 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.4853 | 0.978825 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.828427 | −0.0557260 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.8284 | −0.725125 | −0.362563 | − | 0.931959i | \(-0.618098\pi\) | ||||
−0.362563 | + | 0.931959i | \(0.618098\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.00000 | −0.265489 | −0.132745 | − | 0.991150i | \(-0.542379\pi\) | ||||
−0.132745 | + | 0.991150i | \(0.542379\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.14214 | 0.273720 | 0.136860 | − | 0.990590i | \(-0.456299\pi\) | ||||
0.136860 | + | 0.990590i | \(0.456299\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.0000 | 1.05272 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 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 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.34315 | 0.152204 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.31371 | 0.342286 | 0.171143 | − | 0.985246i | \(-0.445254\pi\) | ||||
0.171143 | + | 0.985246i | \(0.445254\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.82843 | 0.179969 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.34315 | 0.401981 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.8284 | −0.683484 | −0.341742 | − | 0.939794i | \(-0.611017\pi\) | ||||
−0.341742 | + | 0.939794i | \(0.611017\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −48.0000 | −3.01773 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.828427 | −0.0518781 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.82843 | −0.301189 | −0.150595 | − | 0.988596i | \(-0.548119\pi\) | ||||
−0.150595 | + | 0.988596i | \(0.548119\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −32.9706 | −2.04869 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.82843 | −0.546466 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.4853 | −1.01653 | −0.508263 | − | 0.861202i | \(-0.669712\pi\) | ||||
−0.508263 | + | 0.861202i | \(0.669712\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.3137 | 0.817855 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.6569 | 0.958184 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.4853 | −0.883183 | −0.441592 | − | 0.897216i | \(-0.645586\pi\) | ||||
−0.441592 | + | 0.897216i | \(0.645586\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.31371 | −0.444276 | −0.222138 | − | 0.975015i | \(-0.571304\pi\) | ||||
−0.222138 | + | 0.975015i | \(0.571304\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.82843 | 0.171184 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.65685 | −0.341121 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.0000 | 1.56219 | 0.781094 | − | 0.624413i | \(-0.214662\pi\) | ||||
0.781094 | + | 0.624413i | \(0.214662\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.34315 | 0.497710 | 0.248855 | − | 0.968541i | \(-0.419946\pi\) | ||||
0.248855 | + | 0.968541i | \(0.419946\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.6569 | 1.04959 | 0.524796 | − | 0.851228i | \(-0.324142\pi\) | ||||
0.524796 | + | 0.851228i | \(0.324142\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.82843 | 0.167542 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.6569 | −1.27836 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3137 | −0.959630 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.17157 | 0.185921 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.6274 | −0.971384 | −0.485692 | − | 0.874130i | \(-0.661432\pi\) | ||||
−0.485692 | + | 0.874130i | \(0.661432\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.34315 | 0.136423 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.65685 | 0.328244 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.48528 | −0.490716 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.3137 | −1.57434 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.1421 | −0.927341 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.00000 | 0.343559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.6569 | 1.23602 | 0.618011 | − | 0.786169i | \(-0.287939\pi\) | ||||
0.618011 | + | 0.786169i | \(0.287939\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.65685 | −0.0942551 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.0000 | 1.36092 | 0.680458 | − | 0.732787i | \(-0.261781\pi\) | ||||
0.680458 | + | 0.732787i | \(0.261781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.9706 | −1.75056 | −0.875280 | − | 0.483617i | \(-0.839323\pi\) | ||||
−0.875280 | + | 0.483617i | \(0.839323\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.82843 | 0.159364 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.3137 | 1.42176 | 0.710880 | − | 0.703314i | \(-0.248297\pi\) | ||||
0.710880 | + | 0.703314i | \(0.248297\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 49.9411 | 2.79617 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.34315 | −0.130376 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.82843 | −0.488213 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.6274 | 1.24749 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.48528 | 0.466393 | 0.233197 | − | 0.972430i | \(-0.425081\pi\) | ||||
0.233197 | + | 0.972430i | \(0.425081\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.6569 | −0.638792 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.65685 | −0.309067 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 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 | 0 | ||||||||
\(341\) | 22.6274 | 1.22534 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.48528 | −0.456832 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.65685 | 0.518407 | 0.259204 | − | 0.965823i | \(-0.416540\pi\) | ||||
0.259204 | + | 0.965823i | \(0.416540\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.1421 | 0.649954 | 0.324977 | − | 0.945722i | \(-0.394644\pi\) | ||||
0.324977 | + | 0.945722i | \(0.394644\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.31371 | 0.282820 | 0.141410 | − | 0.989951i | \(-0.454836\pi\) | ||||
0.141410 | + | 0.989951i | \(0.454836\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.65685 | 0.300235 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.34315 | −0.124012 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.2843 | 1.49279 | 0.746393 | − | 0.665505i | \(-0.231784\pi\) | ||||
0.746393 | + | 0.665505i | \(0.231784\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.0000 | −1.10221 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.4853 | −0.758194 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.6569 | −1.33928 | −0.669638 | − | 0.742687i | \(-0.733551\pi\) | ||||
−0.669638 | + | 0.742687i | \(0.733551\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.65685 | −0.398600 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 37.6569 | 1.95505 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.68629 | −0.139091 | −0.0695455 | − | 0.997579i | \(-0.522155\pi\) | ||||
−0.0695455 | + | 0.997579i | \(0.522155\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.82843 | 0.454687 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.51472 | 0.386005 | 0.193003 | − | 0.981198i | \(-0.438177\pi\) | ||||
0.193003 | + | 0.981198i | \(0.438177\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.65685 | 0.494736 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.6569 | 1.51539 | 0.757697 | − | 0.652606i | \(-0.226324\pi\) | ||||
0.757697 | + | 0.652606i | \(0.226324\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.0000 | −0.815436 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.65685 | −0.490885 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −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 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.14214 | −0.309830 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.34315 | −0.117896 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.2843 | 1.51992 | 0.759962 | − | 0.649968i | \(-0.225218\pi\) | ||||
0.759962 | + | 0.649968i | \(0.225218\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.00000 | 0.400501 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.9706 | −1.34685 | −0.673423 | − | 0.739258i | \(-0.735177\pi\) | ||||
−0.673423 | + | 0.739258i | \(0.735177\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000 | 0.199254 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 65.9411 | 3.26858 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.65685 | −0.180820 | −0.0904099 | − | 0.995905i | \(-0.528818\pi\) | ||||
−0.0904099 | + | 0.995905i | \(0.528818\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.3137 | 0.854022 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.62742 | 0.326114 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.34315 | −0.311373 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.34315 | 0.310625 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.8284 | 0.529003 | 0.264502 | − | 0.964385i | \(-0.414793\pi\) | ||||
0.264502 | + | 0.964385i | \(0.414793\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.1421 | −1.17662 | −0.588308 | − | 0.808637i | \(-0.700206\pi\) | ||||
−0.588308 | + | 0.808637i | \(0.700206\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.00000 | 0.388973 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.828427 | 0.0401846 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.9706 | 0.821263 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.65685 | −0.273115 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.9706 | −1.10389 | −0.551947 | − | 0.833879i | \(-0.686115\pi\) | ||||
−0.551947 | + | 0.833879i | \(0.686115\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.82843 | 0.423291 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −24.0000 | −1.14808 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.6274 | −1.07995 | −0.539974 | − | 0.841682i | \(-0.681566\pi\) | ||||
−0.539974 | + | 0.841682i | \(0.681566\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.3431 | −1.44165 | −0.720823 | − | 0.693119i | \(-0.756236\pi\) | ||||
−0.720823 | + | 0.693119i | \(0.756236\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.6569 | −0.742206 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.65685 | −0.172963 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.2843 | 1.24043 | 0.620216 | − | 0.784431i | \(-0.287045\pi\) | ||||
0.620216 | + | 0.784431i | \(0.287045\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 43.3137 | 2.03956 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.0000 | 0.563809 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.82843 | −0.132599 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.8284 | 0.974313 | 0.487156 | − | 0.873315i | \(-0.338034\pi\) | ||||
0.487156 | + | 0.873315i | \(0.338034\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.828427 | −0.0386677 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0000 | 0.652045 | 0.326023 | − | 0.945362i | \(-0.394291\pi\) | ||||
0.326023 | + | 0.945362i | \(0.394291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.79899 | 0.176554 | 0.0882770 | − | 0.996096i | \(-0.471864\pi\) | ||||
0.0882770 | + | 0.996096i | \(0.471864\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.00000 | 0.185496 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.31371 | −0.338438 | −0.169219 | − | 0.985578i | \(-0.554125\pi\) | ||||
−0.169219 | + | 0.985578i | \(0.554125\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.31371 | −0.244843 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 54.6274 | 2.51177 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.82843 | −0.129777 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.3137 | 0.609593 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.3137 | 0.516937 | 0.258468 | − | 0.966020i | \(-0.416782\pi\) | ||||
0.258468 | + | 0.966020i | \(0.416782\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.6569 | 0.531507 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −24.0000 | −1.09204 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.17157 | −0.144014 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.4853 | −0.747019 | −0.373510 | − | 0.927626i | \(-0.621846\pi\) | ||||
−0.373510 | + | 0.927626i | \(0.621846\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.3137 | 0.511624 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.1421 | 1.72133 | 0.860665 | − | 0.509171i | \(-0.170048\pi\) | ||||
0.860665 | + | 0.509171i | \(0.170048\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.31371 | −0.329393 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.65685 | −0.254257 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.0000 | 0.717698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.485281 | −0.0217242 | −0.0108621 | − | 0.999941i | \(-0.503458\pi\) | ||||
−0.0108621 | + | 0.999941i | \(0.503458\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.97056 | 0.400775 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.5147 | 1.04847 | 0.524235 | − | 0.851574i | \(-0.324351\pi\) | ||||
0.524235 | + | 0.851574i | \(0.324351\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.1421 | 0.718316 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −37.3137 | −1.65390 | −0.826951 | − | 0.562275i | \(-0.809926\pi\) | ||||
−0.826951 | + | 0.562275i | \(0.809926\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −40.9706 | −1.81243 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.82843 | 0.124878 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.65685 | 0.0730097 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −45.2548 | −1.99031 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.31371 | 0.408826 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.9706 | 1.18160 | 0.590801 | − | 0.806817i | \(-0.298812\pi\) | ||||
0.590801 | + | 0.806817i | \(0.298812\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.6274 | 0.464704 | 0.232352 | − | 0.972632i | \(-0.425358\pi\) | ||||
0.232352 | + | 0.972632i | \(0.425358\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.82843 | −0.123443 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.31371 | −0.144347 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 49.0000 | 2.13043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.34315 | 0.101684 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.65685 | 0.331655 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.00000 | 0.172935 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.51472 | 0.324284 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.65685 | −0.243658 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.4853 | 0.622771 | 0.311385 | − | 0.950284i | \(-0.399207\pi\) | ||||
0.311385 | + | 0.950284i | \(0.399207\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.65685 | 0.328587 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.82843 | 0.378168 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.686292 | −0.0293437 | −0.0146719 | − | 0.999892i | \(-0.504670\pi\) | ||||
−0.0146719 | + | 0.999892i | \(0.504670\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.9706 | 1.06378 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.62742 | −0.281826 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11.6569 | 0.494806 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.6863 | 0.452793 | 0.226396 | − | 0.974035i | \(-0.427306\pi\) | ||||
0.226396 | + | 0.974035i | \(0.427306\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.65685 | 0.408441 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.68629 | 0.197855 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.3431 | 1.27881 | 0.639406 | − | 0.768870i | \(-0.279181\pi\) | ||||
0.639406 | + | 0.768870i | \(0.279181\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.48528 | 0.272838 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.82843 | 0.118783 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.6569 | 1.32712 | 0.663562 | − | 0.748121i | \(-0.269044\pi\) | ||||
0.663562 | + | 0.748121i | \(0.269044\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.9706 | −0.877591 | −0.438795 | − | 0.898587i | \(-0.644595\pi\) | ||||
−0.438795 | + | 0.898587i | \(0.644595\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.3137 | 0.472637 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.48528 | 0.353861 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.4558 | −0.976480 | −0.488240 | − | 0.872710i | \(-0.662361\pi\) | ||||
−0.488240 | + | 0.872710i | \(0.662361\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.48528 | −0.103285 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.9411 | −0.744323 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −75.3137 | −3.11918 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.00000 | −0.0413449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.62742 | −0.108445 | −0.0542226 | − | 0.998529i | \(-0.517268\pi\) | ||||
−0.0542226 | + | 0.998529i | \(0.517268\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.3137 | 0.466173 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.3137 | 0.547653 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.343146 | −0.0140913 | −0.00704565 | − | 0.999975i | \(-0.502243\pi\) | ||||
−0.00704565 | + | 0.999975i | \(0.502243\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.34315 | 0.0960596 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.3431 | 0.423317 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −40.0000 | −1.63436 | −0.817178 | − | 0.576386i | \(-0.804463\pi\) | ||||
−0.817178 | + | 0.576386i | \(0.804463\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.3137 | 1.19573 | 0.597866 | − | 0.801596i | \(-0.296016\pi\) | ||||
0.597866 | + | 0.801596i | \(0.296016\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.65685 | −0.230365 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.0000 | 0.853771 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.9706 | −1.17588 | −0.587939 | − | 0.808905i | \(-0.700061\pi\) | ||||
−0.587939 | + | 0.808905i | \(0.700061\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 24.9706 | 1.01186 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.00000 | −0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.2843 | 0.900053 | 0.450027 | − | 0.893015i | \(-0.351414\pi\) | ||||
0.450027 | + | 0.893015i | \(0.351414\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.65685 | 0.308754 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.00000 | 0.0805170 | 0.0402585 | − | 0.999189i | \(-0.487182\pi\) | ||||
0.0402585 | + | 0.999189i | \(0.487182\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.8284 | 1.39987 | 0.699936 | − | 0.714205i | \(-0.253212\pi\) | ||||
0.699936 | + | 0.714205i | \(0.253212\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.48528 | −0.340503 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −44.2843 | −1.77421 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.0000 | −0.638978 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.65685 | −0.385044 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.6569 | 1.33986 | 0.669929 | − | 0.742425i | \(-0.266324\pi\) | ||||
0.669929 | + | 0.742425i | \(0.266324\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.686292 | 0.0272776 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.65685 | −0.383221 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.65685 | 0.223782 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.62742 | −0.182772 | −0.0913860 | − | 0.995816i | \(-0.529130\pi\) | ||||
−0.0913860 | + | 0.995816i | \(0.529130\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.5980 | −1.56159 | −0.780796 | − | 0.624786i | \(-0.785186\pi\) | ||||
−0.780796 | + | 0.624786i | \(0.785186\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.65685 | 0.380238 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.48528 | −0.333591 | −0.166795 | − | 0.985992i | \(-0.553342\pi\) | ||||
−0.166795 | + | 0.985992i | \(0.553342\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.2548 | −0.520298 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.3137 | 0.443419 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −42.2843 | −1.65471 | −0.827356 | − | 0.561678i | \(-0.810156\pi\) | ||||
−0.827356 | + | 0.561678i | \(0.810156\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.14214 | 0.239993 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.4853 | −0.565125 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.51472 | 0.292732 | 0.146366 | − | 0.989231i | \(-0.453242\pi\) | ||||
0.146366 | + | 0.989231i | \(0.453242\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.14214 | −0.316692 | −0.158346 | − | 0.987384i | \(-0.550616\pi\) | ||||
−0.158346 | + | 0.987384i | \(0.550616\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.828427 | 0.0321734 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.00000 | −0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −74.9117 | −2.90059 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.8284 | 0.418651 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.9411 | −1.31028 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.6274 | 1.25769 | 0.628847 | − | 0.777529i | \(-0.283527\pi\) | ||||
0.628847 | + | 0.777529i | \(0.283527\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.3431 | 0.474386 | 0.237193 | − | 0.971463i | \(-0.423773\pi\) | ||||
0.237193 | + | 0.971463i | \(0.423773\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.97056 | −0.344259 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.00000 | 0.153280 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.6569 | −1.28784 | −0.643922 | − | 0.765091i | \(-0.722694\pi\) | ||||
−0.643922 | + | 0.765091i | \(0.722694\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.3137 | −0.661523 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.14214 | −0.158032 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.3137 | −0.507212 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.7990 | 1.05752 | 0.528762 | − | 0.848770i | \(-0.322657\pi\) | ||||
0.528762 | + | 0.848770i | \(0.322657\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.0000 | −0.607790 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.34315 | −0.240609 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.34315 | −0.240264 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.51472 | −0.208586 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 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 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.00000 | −0.301297 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 45.6569 | 1.71710 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.17157 | −0.269334 | −0.134667 | − | 0.990891i | \(-0.542996\pi\) | ||||
−0.134667 | + | 0.990891i | \(0.542996\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.34315 | −0.0878748 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −33.9411 | −1.27111 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.65685 | 0.211554 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.0000 | 0.597531 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.6569 | 1.10601 | 0.553007 | − | 0.833177i | \(-0.313480\pi\) | ||||
0.553007 | + | 0.833177i | \(0.313480\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.68629 | 0.174527 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.31371 | −0.197619 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.82843 | −0.327880 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.9411 | 1.70386 | 0.851931 | − | 0.523654i | \(-0.175432\pi\) | ||||
0.851931 | + | 0.523654i | \(0.175432\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.00000 | −0.295891 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.343146 | −0.0126744 | −0.00633719 | − | 0.999980i | \(-0.502017\pi\) | ||||
−0.00633719 | + | 0.999980i | \(0.502017\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.0000 | 1.17874 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.1421 | 0.520227 | 0.260113 | − | 0.965578i | \(-0.416240\pi\) | ||||
0.260113 | + | 0.965578i | \(0.416240\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.82843 | −0.103905 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.2843 | 1.33114 | 0.665570 | − | 0.746335i | \(-0.268188\pi\) | ||||
0.665570 | + | 0.746335i | \(0.268188\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.65685 | 0.133977 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.34315 | −0.232084 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.3137 | 0.413394 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.3137 | −0.412843 | −0.206422 | − | 0.978463i | \(-0.566182\pi\) | ||||
−0.206422 | + | 0.978463i | \(0.566182\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.8284 | 0.394610 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.0000 | −0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.9411 | 0.724773 | 0.362386 | − | 0.932028i | \(-0.381962\pi\) | ||||
0.362386 | + | 0.932028i | \(0.381962\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 48.0000 | 1.74229 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.6569 | 1.00256 | 0.501280 | − | 0.865285i | \(-0.332863\pi\) | ||||
0.501280 | + | 0.865285i | \(0.332863\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.9706 | 0.903995 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.828427 | 0.0299518 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.34315 | −0.0846061 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.0000 | −0.504853 | −0.252426 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252426 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.82843 | 0.173892 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −53.3137 | −1.91756 | −0.958780 | − | 0.284148i | \(-0.908289\pi\) | ||||
−0.958780 | + | 0.284148i | \(0.908289\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 32.9706 | 1.18281 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21.6569 | 0.775937 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.0000 | −1.14505 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.82843 | 0.315502 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.31371 | 0.189654 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.0000 | 0.855508 | 0.427754 | − | 0.903895i | \(-0.359305\pi\) | ||||
0.427754 | + | 0.903895i | \(0.359305\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.4853 | 0.586892 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.3431 | 0.652207 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.00000 | −0.213066 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.3137 | −0.472189 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.6274 | 0.588973 | 0.294487 | − | 0.955656i | \(-0.404851\pi\) | ||||
0.294487 | + | 0.955656i | \(0.404851\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.62742 | 0.234461 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.6569 | −0.553208 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 81.9411 | 2.89164 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.0000 | 0.845889 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.4853 | 0.509906 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.3137 | 0.468085 | 0.234043 | − | 0.972226i | \(-0.424804\pi\) | ||||
0.234043 | + | 0.972226i | \(0.424804\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.85786 | 0.0652384 | 0.0326192 | − | 0.999468i | \(-0.489615\pi\) | ||||
0.0326192 | + | 0.999468i | \(0.489615\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.31371 | 0.256503 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.3137 | −0.396302 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.3137 | 0.955586 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.82843 | −0.0988332 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.2843 | 1.19653 | 0.598265 | − | 0.801299i | \(-0.295857\pi\) | ||||
0.598265 | + | 0.801299i | \(0.295857\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 52.9706 | 1.84644 | 0.923219 | − | 0.384275i | \(-0.125548\pi\) | ||||
0.923219 | + | 0.384275i | \(0.125548\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.65685 | 0.196946 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.65685 | −0.335802 | −0.167901 | − | 0.985804i | \(-0.553699\pi\) | ||||
−0.167901 | + | 0.985804i | \(0.553699\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −53.3137 | −1.85166 | −0.925831 | − | 0.377938i | \(-0.876633\pi\) | ||||
−0.925831 | + | 0.377938i | \(0.876633\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.0000 | −0.901930 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.828427 | 0.0287033 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.97056 | −0.310439 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.00000 | 0.138260 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 48.9411 | 1.68763 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.34315 | −0.287353 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 59.3970 | 2.04090 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.6569 | −0.605982 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −98.9117 | −3.39065 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.2843 | 1.31083 | 0.655414 | − | 0.755270i | \(-0.272494\pi\) | ||||
0.655414 | + | 0.755270i | \(0.272494\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.82843 | −0.0967302 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −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 | \(-0.724088\pi\) | ||||
−0.647267 | + | 0.762263i | \(0.724088\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.6569 | 0.738064 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.2843 | 0.962808 | 0.481404 | − | 0.876499i | \(-0.340127\pi\) | ||||
0.481404 | + | 0.876499i | \(0.340127\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.31371 | −0.316676 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.3137 | 0.554043 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.2548 | 0.449639 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.65685 | 0.191675 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.17157 | −0.107341 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.82843 | 0.0956183 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −51.2548 | −1.73075 | −0.865376 | − | 0.501122i | \(-0.832921\pi\) | ||||
−0.865376 | + | 0.501122i | \(0.832921\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.6274 | 0.560829 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.2843 | −0.346486 | −0.173243 | − | 0.984879i | \(-0.555425\pi\) | ||||
−0.173243 | + | 0.984879i | \(0.555425\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.3137 | −1.05379 | −0.526895 | − | 0.849930i | \(-0.676644\pi\) | ||||
−0.526895 | + | 0.849930i | \(0.676644\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.34315 | −0.0787640 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40.4853 | 1.35936 | 0.679681 | − | 0.733508i | \(-0.262118\pi\) | ||||
0.679681 | + | 0.733508i | \(0.262118\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.3137 | −0.916072 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.65685 | −0.189512 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.6274 | −0.757198 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.51472 | −0.251189 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.48528 | 0.283315 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.3137 | 1.17778 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.0294 | 0.367444 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27.3137 | 0.908943 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.65685 | −0.254522 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.28427 | −0.275075 | −0.137537 | − | 0.990497i | \(-0.543919\pi\) | ||||
−0.137537 | + | 0.990497i | \(0.543919\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.1421 | 0.535401 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.9706 | −0.827312 | −0.413656 | − | 0.910433i | \(-0.635748\pi\) | ||||
−0.413656 | + | 0.910433i | \(0.635748\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 35.8823 | 1.18753 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.00000 | −0.198354 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.3726 | 0.573693 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.9411 | −1.38351 | −0.691755 | − | 0.722132i | \(-0.743162\pi\) | ||||
−0.691755 | + | 0.722132i | \(0.743162\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.6569 | −0.713618 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.65685 | −0.186198 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.6569 | −0.383275 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.65685 | 0.0544182 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.5980 | −1.10231 | −0.551157 | − | 0.834402i | \(-0.685813\pi\) | ||||
−0.551157 | + | 0.834402i | \(0.685813\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.82843 | −0.0926980 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.0000 | −0.785725 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.68629 | −0.153258 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.6274 | 0.543194 | 0.271597 | − | 0.962411i | \(-0.412448\pi\) | ||||
0.271597 | + | 0.962411i | \(0.412448\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.9706 | 1.01069 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 54.9706 | 1.79199 | 0.895995 | − | 0.444065i | \(-0.146464\pi\) | ||||
0.895995 | + | 0.444065i | \(0.146464\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −64.9706 | −2.11573 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.82843 | −0.0920087 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.3431 | −0.986020 | −0.493010 | − | 0.870024i | \(-0.664103\pi\) | ||||
−0.493010 | + | 0.870024i | \(0.664103\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.4853 | 0.470212 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.3137 | −0.820853 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.8579 | −0.902405 | −0.451202 | − | 0.892422i | \(-0.649005\pi\) | ||||
−0.451202 | + | 0.892422i | \(0.649005\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.3137 | −0.366103 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −49.9411 | −1.61437 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −48.9706 | −1.58134 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.00000 | 0.128898 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.48528 | 0.0800040 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.51472 | 0.241657 | 0.120829 | − | 0.992673i | \(-0.461445\pi\) | ||||
0.120829 | + | 0.992673i | \(0.461445\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.34315 | 0.0752727 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.5147 | −0.497891 | −0.248946 | − | 0.968517i | \(-0.580084\pi\) | ||||
−0.248946 | + | 0.968517i | \(0.580084\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.9411 | −0.575166 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.00000 | 0.0320256 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.34315 | −0.266921 | −0.133460 | − | 0.991054i | \(-0.542609\pi\) | ||||
−0.133460 | + | 0.991054i | \(0.542609\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 88.5685 | 2.83066 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.82843 | 0.281870 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.34315 | 0.0747347 | 0.0373674 | − | 0.999302i | \(-0.488103\pi\) | ||||
0.0373674 | + | 0.999302i | \(0.488103\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.3137 | −0.424210 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.6274 | −0.720239 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −81.9411 | −2.60558 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.9117 | 1.36313 | 0.681567 | − | 0.731755i | \(-0.261299\pi\) | ||||
0.681567 | + | 0.731755i | \(0.261299\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.48528 | −0.269272 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.3431 | −0.327900 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 61.3137 | 1.94182 | 0.970912 | − | 0.239435i | \(-0.0769623\pi\) | ||||
0.970912 | + | 0.239435i | \(0.0769623\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 3120.2.a.bc.1.2 | 2 | ||
3.2 | odd | 2 | 9360.2.a.ch.1.2 | 2 | |||
4.3 | odd | 2 | 390.2.a.h.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 1170.2.a.o.1.1 | 2 | |||
20.3 | even | 4 | 1950.2.e.o.1249.2 | 4 | |||
20.7 | even | 4 | 1950.2.e.o.1249.3 | 4 | |||
20.19 | odd | 2 | 1950.2.a.bd.1.2 | 2 | |||
52.31 | even | 4 | 5070.2.b.q.1351.1 | 4 | |||
52.47 | even | 4 | 5070.2.b.q.1351.4 | 4 | |||
52.51 | odd | 2 | 5070.2.a.bc.1.2 | 2 | |||
60.23 | odd | 4 | 5850.2.e.bk.5149.4 | 4 | |||
60.47 | odd | 4 | 5850.2.e.bk.5149.1 | 4 | |||
60.59 | even | 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 | 4.3 | odd | 2 | ||
1170.2.a.o.1.1 | 2 | 12.11 | even | 2 | |||
1950.2.a.bd.1.2 | 2 | 20.19 | odd | 2 | |||
1950.2.e.o.1249.2 | 4 | 20.3 | even | 4 | |||
1950.2.e.o.1249.3 | 4 | 20.7 | even | 4 | |||
3120.2.a.bc.1.2 | 2 | 1.1 | even | 1 | trivial | ||
5070.2.a.bc.1.2 | 2 | 52.51 | odd | 2 | |||
5070.2.b.q.1351.1 | 4 | 52.31 | even | 4 | |||
5070.2.b.q.1351.4 | 4 | 52.47 | even | 4 | |||
5850.2.a.cl.1.2 | 2 | 60.59 | even | 2 | |||
5850.2.e.bk.5149.1 | 4 | 60.47 | odd | 4 | |||
5850.2.e.bk.5149.4 | 4 | 60.23 | odd | 4 | |||
9360.2.a.ch.1.2 | 2 | 3.2 | odd | 2 |