Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9680,2,Mod(1,9680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9680.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9680 = 2^{4} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9680.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: | \(77.2951891566\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 4840) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9680.1 |
$q$-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 | ||||||||
\(3\) | −2.41421 | −1.39385 | −0.696923 | − | 0.717146i | \(-0.745448\pi\) | ||||
−0.696923 | + | 0.717146i | \(0.745448\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.41421 | 0.912487 | 0.456243 | − | 0.889855i | \(-0.349195\pi\) | ||||
0.456243 | + | 0.889855i | \(0.349195\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.41421 | −0.623347 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.65685 | −1.37199 | −0.685994 | − | 0.727607i | \(-0.740633\pi\) | ||||
−0.685994 | + | 0.727607i | \(0.740633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.82843 | 1.10772 | 0.553859 | − | 0.832611i | \(-0.313155\pi\) | ||||
0.553859 | + | 0.832611i | \(0.313155\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.82843 | −1.27187 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.65685 | −0.762507 | −0.381253 | − | 0.924471i | \(-0.624507\pi\) | ||||
−0.381253 | + | 0.924471i | \(0.624507\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.414214 | 0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.65685 | 1.01600 | 0.508001 | − | 0.861357i | \(-0.330385\pi\) | ||||
0.508001 | + | 0.861357i | \(0.330385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.41421 | 0.408077 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.82843 | 0.773167 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.48528 | 1.48135 | 0.740676 | − | 0.671862i | \(-0.234505\pi\) | ||||
0.740676 | + | 0.671862i | \(0.234505\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.58579 | 0.546827 | 0.273414 | − | 0.961897i | \(-0.411847\pi\) | ||||
0.273414 | + | 0.961897i | \(0.411847\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.82843 | 0.421637 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.58579 | −1.10650 | −0.553250 | − | 0.833015i | \(-0.686613\pi\) | ||||
−0.553250 | + | 0.833015i | \(0.686613\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.17157 | −0.167368 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.6569 | 1.91234 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.65685 | −1.05175 | −0.525875 | − | 0.850562i | \(-0.676262\pi\) | ||||
−0.525875 | + | 0.850562i | \(0.676262\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.6569 | −1.54399 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.3137 | 1.47292 | 0.736460 | − | 0.676481i | \(-0.236496\pi\) | ||||
0.736460 | + | 0.676481i | \(0.236496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) | ||||
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.82843 | 0.860301 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.00000 | −0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.41421 | 0.783621 | 0.391810 | − | 0.920046i | \(-0.371849\pi\) | ||||
0.391810 | + | 0.920046i | \(0.371849\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.82843 | 1.06282 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.00000 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.41421 | −0.278769 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.4853 | −1.62972 | −0.814861 | − | 0.579657i | \(-0.803187\pi\) | ||||
−0.814861 | + | 0.579657i | \(0.803187\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.3137 | −1.46137 | −0.730685 | − | 0.682715i | \(-0.760799\pi\) | ||||
−0.730685 | + | 0.682715i | \(0.760799\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.65685 | −0.613572 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.82843 | 0.517662 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.65685 | 0.281626 | 0.140813 | − | 0.990036i | \(-0.455028\pi\) | ||||
0.140813 | + | 0.990036i | \(0.455028\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.82843 | −0.506157 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.6569 | −1.41615 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.82843 | 0.495386 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.3137 | −1.75794 | −0.878970 | − | 0.476876i | \(-0.841769\pi\) | ||||
−0.878970 | + | 0.476876i | \(0.841769\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.1716 | −1.01211 | −0.506055 | − | 0.862501i | \(-0.668897\pi\) | ||||
−0.506055 | + | 0.862501i | \(0.668897\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.3137 | −1.31184 | −0.655919 | − | 0.754831i | \(-0.727719\pi\) | ||||
−0.655919 | + | 0.754831i | \(0.727719\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.82843 | −0.568796 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.2426 | 1.47356 | 0.736781 | − | 0.676132i | \(-0.236345\pi\) | ||||
0.736781 | + | 0.676132i | \(0.236345\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.6569 | −1.59544 | −0.797719 | − | 0.603030i | \(-0.793960\pi\) | ||||
−0.797719 | + | 0.603030i | \(0.793960\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.65685 | 0.916588 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3137 | 1.62874 | 0.814368 | − | 0.580348i | \(-0.197084\pi\) | ||||
0.814368 | + | 0.580348i | \(0.197084\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.65685 | −0.341003 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.65685 | −0.522976 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.6569 | −1.25192 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −22.8995 | −2.06478 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.41421 | −0.391698 | −0.195849 | − | 0.980634i | \(-0.562746\pi\) | ||||
−0.195849 | + | 0.980634i | \(0.562746\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.65685 | −0.762194 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.48528 | −0.217140 | −0.108570 | − | 0.994089i | \(-0.534627\pi\) | ||||
−0.108570 | + | 0.994089i | \(0.534627\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.6569 | 1.01078 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.414214 | 0.0356498 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.3137 | 1.13747 | 0.568733 | − | 0.822522i | \(-0.307434\pi\) | ||||
0.568733 | + | 0.822522i | \(0.307434\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000 | 1.01783 | 0.508913 | − | 0.860818i | \(-0.330047\pi\) | ||||
0.508913 | + | 0.860818i | \(0.330047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.3137 | 1.54229 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.82843 | 0.233285 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.0000 | 1.39269 | 0.696347 | − | 0.717705i | \(-0.254807\pi\) | ||||
0.696347 | + | 0.717705i | \(0.254807\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.65685 | 0.460348 | 0.230174 | − | 0.973149i | \(-0.426070\pi\) | ||||
0.230174 | + | 0.973149i | \(0.426070\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.0000 | −1.29352 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.65685 | 0.454369 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.6569 | 1.40917 | 0.704585 | − | 0.709619i | \(-0.251133\pi\) | ||||
0.704585 | + | 0.709619i | \(0.251133\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 18.4853 | 1.46598 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.82843 | −0.695778 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.58579 | −0.594165 | −0.297082 | − | 0.954852i | \(-0.596014\pi\) | ||||
−0.297082 | + | 0.954852i | \(0.596014\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.41421 | 0.496347 | 0.248173 | − | 0.968716i | \(-0.420170\pi\) | ||||
0.248173 | + | 0.968716i | \(0.420170\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.6569 | 1.04437 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.65685 | 0.278025 | 0.139013 | − | 0.990291i | \(-0.455607\pi\) | ||||
0.139013 | + | 0.990291i | \(0.455607\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.41421 | 0.182497 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −27.3137 | −2.05302 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.7990 | 1.33036 | 0.665179 | − | 0.746684i | \(-0.268355\pi\) | ||||
0.665179 | + | 0.746684i | \(0.268355\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.8284 | −1.91981 | −0.959906 | − | 0.280322i | \(-0.909559\pi\) | ||||
−0.959906 | + | 0.280322i | \(0.909559\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.41421 | 0.178464 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00000 | −0.294086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.8284 | −1.21766 | −0.608831 | − | 0.793300i | \(-0.708361\pi\) | ||||
−0.608831 | + | 0.793300i | \(0.708361\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.31371 | −0.0945628 | −0.0472814 | − | 0.998882i | \(-0.515056\pi\) | ||||
−0.0472814 | + | 0.998882i | \(0.515056\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.82843 | 0.345771 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.97056 | 0.496632 | 0.248316 | − | 0.968679i | \(-0.420123\pi\) | ||||
0.248316 | + | 0.968679i | \(0.420123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.17157 | 0.508379 | 0.254190 | − | 0.967154i | \(-0.418191\pi\) | ||||
0.254190 | + | 0.967154i | \(0.418191\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.4853 | −1.09225 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.82843 | −0.338889 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.48528 | 0.662481 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.3431 | −0.718898 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.65685 | −0.661677 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.58579 | 0.244549 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.6569 | 0.927088 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.65685 | 0.652550 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.3137 | 0.761042 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.92893 | −0.530961 | −0.265480 | − | 0.964116i | \(-0.585531\pi\) | ||||
−0.265480 | + | 0.964116i | \(0.585531\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.82843 | 0.188562 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 26.0711 | 1.73040 | 0.865199 | − | 0.501429i | \(-0.167192\pi\) | ||||
0.865199 | + | 0.501429i | \(0.167192\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.4853 | 0.758969 | 0.379484 | − | 0.925198i | \(-0.376101\pi\) | ||||
0.379484 | + | 0.925198i | \(0.376101\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.34315 | −0.284529 | −0.142264 | − | 0.989829i | \(-0.545438\pi\) | ||||
−0.142264 | + | 0.989829i | \(0.545438\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.58579 | −0.494842 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 34.9706 | 2.27158 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.1421 | −1.56162 | −0.780812 | − | 0.624765i | \(-0.785195\pi\) | ||||
−0.780812 | + | 0.624765i | \(0.785195\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.1716 | −1.04170 | −0.520851 | − | 0.853647i | \(-0.674385\pi\) | ||||
−0.520851 | + | 0.853647i | \(0.674385\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.6569 | 1.38929 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.17157 | −0.0748490 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.65685 | −0.614451 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 32.1421 | 2.03693 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.686292 | −0.0433183 | −0.0216592 | − | 0.999765i | \(-0.506895\pi\) | ||||
−0.0216592 | + | 0.999765i | \(0.506895\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.6569 | 0.855225 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.9706 | 0.809081 | 0.404541 | − | 0.914520i | \(-0.367431\pi\) | ||||
0.404541 | + | 0.914520i | \(0.367431\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.65685 | −0.600048 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.65685 | −0.350150 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.6274 | 1.51859 | 0.759296 | − | 0.650746i | \(-0.225544\pi\) | ||||
0.759296 | + | 0.650746i | \(0.225544\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.65685 | −0.470357 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.41421 | −0.392543 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.3137 | −0.994664 | −0.497332 | − | 0.867560i | \(-0.665687\pi\) | ||||
−0.497332 | + | 0.867560i | \(0.665687\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.3137 | −0.687259 | −0.343629 | − | 0.939105i | \(-0.611656\pi\) | ||||
−0.343629 | + | 0.939105i | \(0.611656\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.6569 | 0.705505 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.6274 | −1.72005 | −0.860027 | − | 0.510248i | \(-0.829554\pi\) | ||||
−0.860027 | + | 0.510248i | \(0.829554\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16.0000 | 0.957895 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.31371 | 0.316989 | 0.158495 | − | 0.987360i | \(-0.449336\pi\) | ||||
0.158495 | + | 0.987360i | \(0.449336\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.2132 | −1.20155 | −0.600775 | − | 0.799418i | \(-0.705141\pi\) | ||||
−0.600775 | + | 0.799418i | \(0.705141\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −11.6569 | −0.690492 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.8995 | 1.35171 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.0000 | 0.882353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 41.7990 | 2.45030 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.3137 | 1.12832 | 0.564159 | − | 0.825666i | \(-0.309200\pi\) | ||||
0.564159 | + | 0.825666i | \(0.309200\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.3137 | 0.658710 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.31371 | 0.422963 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.65685 | 0.498973 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24.5563 | 1.41073 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.00000 | −0.0572598 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.3137 | −1.44473 | −0.722365 | − | 0.691512i | \(-0.756945\pi\) | ||||
−0.722365 | + | 0.691512i | \(0.756945\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 32.1421 | 1.82850 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.8284 | −0.727433 | −0.363717 | − | 0.931510i | \(-0.618492\pi\) | ||||
−0.363717 | + | 0.931510i | \(0.618492\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.3137 | −1.20472 | −0.602361 | − | 0.798224i | \(-0.705773\pi\) | ||||
−0.602361 | + | 0.798224i | \(0.705773\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.82843 | 0.384738 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.68629 | −0.150877 | −0.0754386 | − | 0.997150i | \(-0.524036\pi\) | ||||
−0.0754386 | + | 0.997150i | \(0.524036\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −36.7990 | −2.05392 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −27.3137 | −1.51978 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.00000 | −0.110940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 40.2132 | 2.22380 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18.3137 | −1.00967 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.82843 | −0.265394 | −0.132697 | − | 0.991157i | \(-0.542364\pi\) | ||||
−0.132697 | + | 0.991157i | \(0.542364\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.3137 | −0.619987 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.41421 | 0.350446 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000 | 0.108947 | 0.0544735 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544735 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −41.7990 | −2.27021 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.7279 | −1.06521 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.82843 | 0.475307 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.38478 | 0.0743387 | 0.0371693 | − | 0.999309i | \(-0.488166\pi\) | ||||
0.0371693 | + | 0.999309i | \(0.488166\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.31371 | 0.284436 | 0.142218 | − | 0.989835i | \(-0.454577\pi\) | ||||
0.142218 | + | 0.989835i | \(0.454577\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.828427 | −0.0442182 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −34.6274 | −1.84303 | −0.921516 | − | 0.388341i | \(-0.873048\pi\) | ||||
−0.921516 | + | 0.388341i | \(0.873048\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.00000 | 0.212298 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 32.9706 | 1.74499 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.17157 | −0.167389 | −0.0836946 | − | 0.996491i | \(-0.526672\pi\) | ||||
−0.0836946 | + | 0.996491i | \(0.526672\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.31371 | 0.227037 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.00000 | −0.209370 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.24264 | −0.273664 | −0.136832 | − | 0.990594i | \(-0.543692\pi\) | ||||
−0.136832 | + | 0.990594i | \(0.543692\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 26.8284 | 1.39663 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.4853 | −0.959708 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.9706 | 1.08581 | 0.542907 | − | 0.839793i | \(-0.317323\pi\) | ||||
0.542907 | + | 0.839793i | \(0.317323\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.41421 | −0.124669 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.00000 | 0.206010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.1421 | 1.03463 | 0.517316 | − | 0.855794i | \(-0.326931\pi\) | ||||
0.517316 | + | 0.855794i | \(0.326931\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.6569 | 0.545967 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.9706 | −1.58252 | −0.791261 | − | 0.611479i | \(-0.790575\pi\) | ||||
−0.791261 | + | 0.611479i | \(0.790575\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.1421 | 0.515554 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.3137 | 1.33416 | 0.667079 | − | 0.744987i | \(-0.267544\pi\) | ||||
0.667079 | + | 0.744987i | \(0.267544\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.6863 | 1.04615 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.00000 | 0.302660 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.4853 | −0.728834 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.0000 | −1.20453 | −0.602263 | − | 0.798298i | \(-0.705734\pi\) | ||||
−0.602263 | + | 0.798298i | \(0.705734\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −28.1421 | −1.40887 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.31371 | 0.315292 | 0.157646 | − | 0.987496i | \(-0.449610\pi\) | ||||
0.157646 | + | 0.987496i | \(0.449610\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.3137 | −0.563576 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.48528 | −0.471327 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 39.7696 | 1.96648 | 0.983239 | − | 0.182322i | \(-0.0583613\pi\) | ||||
0.983239 | + | 0.182322i | \(0.0583613\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −32.1421 | −1.58545 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 27.3137 | 1.34402 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.3137 | −0.653544 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −28.9706 | −1.41869 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.5147 | 0.855650 | 0.427825 | − | 0.903862i | \(-0.359280\pi\) | ||||
0.427825 | + | 0.903862i | \(0.359280\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.68629 | −0.374607 | −0.187303 | − | 0.982302i | \(-0.559975\pi\) | ||||
−0.187303 | + | 0.982302i | \(0.559975\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21.4558 | −1.04322 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.65685 | −0.274398 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.41421 | −0.116832 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.5147 | 0.843654 | 0.421827 | − | 0.906676i | \(-0.361389\pi\) | ||||
0.421827 | + | 0.906676i | \(0.361389\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.9706 | −1.39224 | −0.696118 | − | 0.717927i | \(-0.745091\pi\) | ||||
−0.696118 | + | 0.717927i | \(0.745091\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.82843 | 0.231505 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −17.6569 | −0.844642 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.2843 | −1.15903 | −0.579513 | − | 0.814963i | \(-0.696757\pi\) | ||||
−0.579513 | + | 0.814963i | \(0.696757\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.31371 | −0.157796 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.24264 | −0.439131 | −0.219566 | − | 0.975598i | \(-0.570464\pi\) | ||||
−0.219566 | + | 0.975598i | \(0.570464\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.65685 | 0.125947 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −41.0416 | −1.94120 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −40.4558 | −1.90923 | −0.954615 | − | 0.297844i | \(-0.903733\pi\) | ||||
−0.954615 | + | 0.297844i | \(0.903733\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.6569 | −0.641655 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.82843 | −0.226360 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.31371 | −0.155009 | −0.0775044 | − | 0.996992i | \(-0.524695\pi\) | ||||
−0.0775044 | + | 0.996992i | \(0.524695\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.34315 | −0.109369 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.14214 | 0.425792 | 0.212896 | − | 0.977075i | \(-0.431710\pi\) | ||||
0.212896 | + | 0.977075i | \(0.431710\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.2426 | −0.708386 | −0.354193 | − | 0.935172i | \(-0.615244\pi\) | ||||
−0.354193 | + | 0.935172i | \(0.615244\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.6569 | −0.633321 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −42.5563 | −1.96927 | −0.984636 | − | 0.174617i | \(-0.944131\pi\) | ||||
−0.984636 | + | 0.174617i | \(0.944131\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.4853 | 0.715044 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −42.6274 | −1.96417 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.82843 | 0.221543 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.6569 | −0.991599 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.79899 | −0.0821979 | −0.0410990 | − | 0.999155i | \(-0.513086\pi\) | ||||
−0.0410990 | + | 0.999155i | \(0.513086\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.00000 | 0.364769 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 21.3137 | 0.969807 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.3137 | −0.786175 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.6863 | −0.846757 | −0.423378 | − | 0.905953i | \(-0.639156\pi\) | ||||
−0.423378 | + | 0.905953i | \(0.639156\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.3137 | 0.828175 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.5147 | 0.790428 | 0.395214 | − | 0.918589i | \(-0.370670\pi\) | ||||
0.395214 | + | 0.918589i | \(0.370670\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.3137 | 0.509544 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.65685 | 0.433169 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.7990 | 1.69212 | 0.846058 | − | 0.533092i | \(-0.178970\pi\) | ||||
0.846058 | + | 0.533092i | \(0.178970\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.4853 | −0.691831 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.38478 | 0.418446 | 0.209223 | − | 0.977868i | \(-0.432906\pi\) | ||||
0.209223 | + | 0.977868i | \(0.432906\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.1716 | −0.452629 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.7279 | 0.964971 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.4853 | 0.509076 | 0.254538 | − | 0.967063i | \(-0.418077\pi\) | ||||
0.254538 | + | 0.967063i | \(0.418077\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.65685 | −0.427194 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.00000 | 0.0883022 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.3137 | −0.586672 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.82843 | −0.387525 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.02944 | 0.264154 | 0.132077 | − | 0.991239i | \(-0.457835\pi\) | ||||
0.132077 | + | 0.991239i | \(0.457835\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.3137 | −0.582168 | −0.291084 | − | 0.956698i | \(-0.594016\pi\) | ||||
−0.291084 | + | 0.956698i | \(0.594016\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.82843 | −0.254373 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −32.0000 | −1.39394 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.62742 | −0.418583 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 32.0000 | 1.38868 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.9706 | −0.821706 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.2426 | 0.658997 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −42.9706 | −1.85432 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.14214 | 0.221078 | 0.110539 | − | 0.993872i | \(-0.464742\pi\) | ||||
0.110539 | + | 0.993872i | \(0.464742\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 62.3553 | 2.67592 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.6569 | −0.713501 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.0000 | 1.11168 | 0.555840 | − | 0.831289i | \(-0.312397\pi\) | ||||
0.555840 | + | 0.831289i | \(0.312397\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.82843 | −0.120714 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.65685 | −0.411396 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −34.9706 | −1.48710 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.65685 | 0.409911 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.6274 | −0.958754 | −0.479377 | − | 0.877609i | \(-0.659137\pi\) | ||||
−0.479377 | + | 0.877609i | \(0.659137\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.17157 | −0.303325 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.89949 | 0.122199 | 0.0610996 | − | 0.998132i | \(-0.480539\pi\) | ||||
0.0610996 | + | 0.998132i | \(0.480539\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.3137 | 0.728393 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.8995 | −0.961688 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.4558 | 0.689865 | 0.344932 | − | 0.938628i | \(-0.387902\pi\) | ||||
0.344932 | + | 0.938628i | \(0.387902\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.4558 | 0.981597 | 0.490798 | − | 0.871273i | \(-0.336705\pi\) | ||||
0.490798 | + | 0.871273i | \(0.336705\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 40.6274 | 1.69723 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.65685 | −0.152501 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.9411 | −1.41299 | −0.706494 | − | 0.707719i | \(-0.749724\pi\) | ||||
−0.706494 | + | 0.707719i | \(0.749724\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.17157 | 0.131806 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.1421 | −1.33348 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.65685 | −0.233882 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.6985 | −1.51471 | −0.757354 | − | 0.653004i | \(-0.773508\pi\) | ||||
−0.757354 | + | 0.653004i | \(0.773508\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.3137 | 1.12544 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.8284 | −0.692229 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.6569 | 0.971471 | 0.485735 | − | 0.874106i | \(-0.338552\pi\) | ||||
0.485735 | + | 0.874106i | \(0.338552\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.6569 | −0.559876 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.3137 | −0.708603 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.8579 | −0.647935 | −0.323967 | − | 0.946068i | \(-0.605017\pi\) | ||||
−0.323967 | + | 0.946068i | \(0.605017\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.9411 | −1.62923 | −0.814616 | − | 0.580000i | \(-0.803052\pi\) | ||||
−0.814616 | + | 0.580000i | \(0.803052\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.1421 | 0.738805 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.5980 | 1.36370 | 0.681850 | − | 0.731492i | \(-0.261176\pi\) | ||||
0.681850 | + | 0.731492i | \(0.261176\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.6569 | 0.472360 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.1716 | 0.613776 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.9706 | −0.604655 | −0.302328 | − | 0.953204i | \(-0.597764\pi\) | ||||
−0.302328 | + | 0.953204i | \(0.597764\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −22.8995 | −0.923397 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.0000 | −1.61034 | −0.805170 | − | 0.593045i | \(-0.797926\pi\) | ||||
−0.805170 | + | 0.593045i | \(0.797926\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.31371 | −0.293963 | −0.146981 | − | 0.989139i | \(-0.546956\pi\) | ||||
−0.146981 | + | 0.989139i | \(0.546956\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.51472 | −0.0607836 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.41421 | 0.256980 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.6274 | 0.902214 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.3431 | −1.36718 | −0.683590 | − | 0.729867i | \(-0.739582\pi\) | ||||
−0.683590 | + | 0.729867i | \(0.739582\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.3137 | 0.767651 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.41421 | −0.175173 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.34315 | 0.0928388 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.3137 | 0.447563 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −48.6274 | −1.92067 | −0.960334 | − | 0.278853i | \(-0.910046\pi\) | ||||
−0.960334 | + | 0.278853i | \(0.910046\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.272078 | −0.0107297 | −0.00536485 | − | 0.999986i | \(-0.501708\pi\) | ||||
−0.00536485 | + | 0.999986i | \(0.501708\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.65685 | −0.340863 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.8701 | 1.17431 | 0.587157 | − | 0.809473i | \(-0.300247\pi\) | ||||
0.587157 | + | 0.809473i | \(0.300247\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −32.9706 | −1.29222 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.65685 | −0.299636 | −0.149818 | − | 0.988714i | \(-0.547869\pi\) | ||||
−0.149818 | + | 0.988714i | \(0.547869\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.48528 | −0.0971080 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.3137 | −0.441390 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.1716 | −0.902636 | −0.451318 | − | 0.892363i | \(-0.649046\pi\) | ||||
−0.451318 | + | 0.892363i | \(0.649046\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.3431 | 1.37469 | 0.687345 | − | 0.726332i | \(-0.258776\pi\) | ||||
0.687345 | + | 0.726332i | \(0.258776\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −27.3137 | −1.06078 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.6569 | 0.452033 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.31371 | 0.283188 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.1421 | 0.740078 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.9706 | −0.654167 | −0.327084 | − | 0.944995i | \(-0.606066\pi\) | ||||
−0.327084 | + | 0.944995i | \(0.606066\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.414214 | 0.0159431 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.68629 | 0.333841 | 0.166921 | − | 0.985970i | \(-0.446618\pi\) | ||||
0.166921 | + | 0.985970i | \(0.446618\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −41.7990 | −1.60410 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −62.9411 | −2.41191 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.8701 | −0.760307 | −0.380153 | − | 0.924923i | \(-0.624129\pi\) | ||||
−0.380153 | + | 0.924923i | \(0.624129\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.3137 | 0.508691 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27.7279 | −1.05789 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.3137 | 0.583406 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.4853 | 0.551046 | 0.275523 | − | 0.961294i | \(-0.411149\pi\) | ||||
0.275523 | + | 0.961294i | \(0.411149\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.0000 | 0.455186 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −53.6569 | −2.03240 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.4853 | 0.396590 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.9411 | −1.50856 | −0.754278 | − | 0.656555i | \(-0.772013\pi\) | ||||
−0.754278 | + | 0.656555i | \(0.772013\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.3137 | −0.728430 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.3137 | 0.689734 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.5563 | −0.923537 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.1421 | −1.31979 | −0.659895 | − | 0.751358i | \(-0.729399\pi\) | ||||
−0.659895 | + | 0.751358i | \(0.729399\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −40.9706 | −1.53652 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.6863 | −0.774708 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 58.2843 | 2.17667 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.1716 | 1.16250 | 0.581252 | − | 0.813724i | \(-0.302563\pi\) | ||||
0.581252 | + | 0.813724i | \(0.302563\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.1421 | −1.19704 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 39.0416 | 1.45197 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.00000 | −0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −52.0711 | −1.93121 | −0.965605 | − | 0.260015i | \(-0.916272\pi\) | ||||
−0.965605 | + | 0.260015i | \(0.916272\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.2843 | −0.750241 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.2843 | −1.48793 | −0.743967 | − | 0.668217i | \(-0.767058\pi\) | ||||
−0.743967 | + | 0.668217i | \(0.767058\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.82843 | 0.104328 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.5147 | −1.23286 | −0.616429 | − | 0.787410i | \(-0.711421\pi\) | ||||
−0.616429 | + | 0.787410i | \(0.711421\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 23.3137 | 0.856450 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.4142 | 1.18916 | 0.594581 | − | 0.804036i | \(-0.297318\pi\) | ||||
0.594581 | + | 0.804036i | \(0.297318\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.0000 | 0.622832 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −37.6569 | −1.37779 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 36.7990 | 1.34461 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.82843 | −0.176192 | −0.0880959 | − | 0.996112i | \(-0.528078\pi\) | ||||
−0.0880959 | + | 0.996112i | \(0.528078\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.65685 | 0.0603791 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.65685 | 0.205874 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.9706 | −1.12564 | −0.562822 | − | 0.826578i | \(-0.690284\pi\) | ||||
−0.562822 | + | 0.826578i | \(0.690284\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.00000 | −0.217500 | −0.108750 | − | 0.994069i | \(-0.534685\pi\) | ||||
−0.108750 | + | 0.994069i | \(0.534685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −40.2132 | −1.45582 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.0000 | −0.578481 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22.6274 | −0.817029 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.0000 | 0.649097 | 0.324548 | − | 0.945869i | \(-0.394788\pi\) | ||||
0.324548 | + | 0.945869i | \(0.394788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.3137 | −1.12774 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.9706 | −1.04200 | −0.520999 | − | 0.853557i | \(-0.674441\pi\) | ||||
−0.520999 | + | 0.853557i | \(0.674441\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.65685 | 0.203200 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 23.3137 | 0.836375 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 45.7990 | 1.64092 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.828427 | −0.0296056 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.6569 | 0.630200 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.213203 | 0.00759988 | 0.00379994 | − | 0.999993i | \(-0.498790\pi\) | ||||
0.00379994 | + | 0.999993i | \(0.498790\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −59.4558 | −2.11668 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 41.7990 | 1.48620 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.00000 | 0.0710221 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.4853 | 0.655605 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.3431 | 1.21650 | 0.608248 | − | 0.793747i | \(-0.291872\pi\) | ||||
0.608248 | + | 0.793747i | \(0.291872\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.9117 | 1.51811 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.51472 | 0.265520 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.82843 | −0.311161 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 39.3848 | 1.38641 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.6274 | −0.865854 | −0.432927 | − | 0.901429i | \(-0.642519\pi\) | ||||
−0.432927 | + | 0.901429i | \(0.642519\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.65685 | −0.198639 | −0.0993195 | − | 0.995056i | \(-0.531667\pi\) | ||||
−0.0993195 | + | 0.995056i | \(0.531667\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.3137 | 0.957934 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.58579 | −0.265719 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.3137 | 0.605730 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.6569 | −0.477209 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.97056 | 0.138574 | 0.0692868 | − | 0.997597i | \(-0.477928\pi\) | ||||
0.0692868 | + | 0.997597i | \(0.477928\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.92893 | 0.0672383 | 0.0336192 | − | 0.999435i | \(-0.489297\pi\) | ||||
0.0336192 | + | 0.999435i | \(0.489297\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.3553 | −1.12511 | −0.562553 | − | 0.826761i | \(-0.690181\pi\) | ||||
−0.562553 | + | 0.826761i | \(0.690181\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.9411 | 1.14409 | 0.572046 | − | 0.820221i | \(-0.306150\pi\) | ||||
0.572046 | + | 0.820221i | \(0.306150\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 69.1127 | 2.39749 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.62742 | 0.229626 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.41421 | 0.221973 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.34315 | 0.0809910 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41.7990 | −1.44306 | −0.721531 | − | 0.692382i | \(-0.756561\pi\) | ||||
−0.721531 | + | 0.692382i | \(0.756561\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.8284 | −0.441834 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.00000 | −0.309609 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 48.7990 | 1.67478 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.6274 | 0.501421 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.6569 | 1.01543 | 0.507716 | − | 0.861525i | \(-0.330490\pi\) | ||||
0.507716 | + | 0.861525i | \(0.330490\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.6569 | 0.467055 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.9706 | 0.374747 | 0.187374 | − | 0.982289i | \(-0.440002\pi\) | ||||
0.187374 | + | 0.982289i | \(0.440002\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.85786 | 0.268107 | 0.134053 | − | 0.990974i | \(-0.457201\pi\) | ||||
0.134053 | + | 0.990974i | \(0.457201\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −55.2843 | −1.88408 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.87006 | 0.267900 | 0.133950 | − | 0.990988i | \(-0.457234\pi\) | ||||
0.133950 | + | 0.990988i | \(0.457234\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.65685 | 0.124337 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −36.2132 | −1.22986 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.8284 | −0.434675 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −48.9706 | −1.65740 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.41421 | 0.0816153 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.3137 | 1.59767 | 0.798835 | − | 0.601550i | \(-0.205450\pi\) | ||||
0.798835 | + | 0.601550i | \(0.205450\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −46.6274 | −1.57270 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.51472 | 0.0847230 | 0.0423615 | − | 0.999102i | \(-0.486512\pi\) | ||||
0.0423615 | + | 0.999102i | \(0.486512\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.3431 | 1.08843 | 0.544217 | − | 0.838945i | \(-0.316827\pi\) | ||||
0.544217 | + | 0.838945i | \(0.316827\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −27.3137 | −0.918140 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.615224 | −0.0206572 | −0.0103286 | − | 0.999947i | \(-0.503288\pi\) | ||||
−0.0103286 | + | 0.999947i | \(0.503288\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.6569 | −0.357419 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −36.6274 | −1.22569 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.7990 | 0.594955 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.6569 | −0.589545 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.3137 | −0.377333 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.3137 | 1.44299 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.8995 | −0.695492 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.8284 | −0.858566 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.6985 | −1.35137 | −0.675686 | − | 0.737190i | \(-0.736152\pi\) | ||||
−0.675686 | + | 0.737190i | \(0.736152\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28.7696 | −0.954226 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.1716 | 0.900234 | 0.450117 | − | 0.892969i | \(-0.351382\pi\) | ||||
0.450117 | + | 0.892969i | \(0.351382\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.41421 | 0.0798114 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.00000 | −0.198137 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.4264 | 1.06965 | 0.534824 | − | 0.844963i | \(-0.320378\pi\) | ||||
0.534824 | + | 0.844963i | \(0.320378\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 61.1127 | 2.01373 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.00000 | −0.263323 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −37.6569 | −1.23681 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.0000 | 1.11550 | 0.557752 | − | 0.830008i | \(-0.311664\pi\) | ||||
0.557752 | + | 0.830008i | \(0.311664\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.65685 | −0.185396 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 30.9706 | 1.01393 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.0000 | 0.980057 | 0.490029 | − | 0.871706i | \(-0.336986\pi\) | ||||
0.490029 | + | 0.871706i | \(0.336986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 51.4558 | 1.67920 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −51.8284 | −1.68956 | −0.844779 | − | 0.535115i | \(-0.820268\pi\) | ||||
−0.844779 | + | 0.535115i | \(0.820268\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34.6863 | −1.12954 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.0000 | −0.324956 | −0.162478 | − | 0.986712i | \(-0.551949\pi\) | ||||
−0.162478 | + | 0.986712i | \(0.551949\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.00000 | 0.259691 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.48528 | 0.210300 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.2843 | −0.786645 | −0.393322 | − | 0.919401i | \(-0.628674\pi\) | ||||
−0.393322 | + | 0.919401i | \(0.628674\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.8284 | −0.544555 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 32.1421 | 1.03792 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 43.1127 | 1.38929 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.31371 | −0.0422898 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.5980 | 1.33770 | 0.668850 | − | 0.743397i | \(-0.266787\pi\) | ||||
0.668850 | + | 0.743397i | \(0.266787\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 65.9411 | 2.11833 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.71573 | 0.119243 | 0.0596217 | − | 0.998221i | \(-0.481011\pi\) | ||||
0.0596217 | + | 0.998221i | \(0.481011\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.9706 | 0.928754 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.82843 | 0.154633 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.62742 | 0.0840585 | 0.0420293 | − | 0.999116i | \(-0.486618\pi\) | ||||
0.0420293 | + | 0.999116i | \(0.486618\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −47.1127 | −1.50419 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.92893 | 0.189104 | 0.0945518 | − | 0.995520i | \(-0.469858\pi\) | ||||
0.0945518 | + | 0.995520i | \(0.469858\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.97056 | 0.222101 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 44.2132 | 1.40732 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.1127 | −0.416960 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −58.4853 | −1.85785 | −0.928923 | − | 0.370273i | \(-0.879264\pi\) | ||||
−0.928923 | + | 0.370273i | \(0.879264\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.6569 | 0.369919 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.17157 | 0.227354 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.3137 | 0.928374 | 0.464187 | − | 0.885737i | \(-0.346346\pi\) | ||||
0.464187 | + | 0.885737i | \(0.346346\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.65685 | −0.0524205 |
(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 | 9680.2.a.bk.1.1 | 2 | ||
4.3 | odd | 2 | 4840.2.a.o.1.2 | ✓ | 2 | ||
11.10 | odd | 2 | 9680.2.a.bj.1.1 | 2 | |||
44.43 | even | 2 | 4840.2.a.p.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4840.2.a.o.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
4840.2.a.p.1.2 | yes | 2 | 44.43 | even | 2 | ||
9680.2.a.bj.1.1 | 2 | 11.10 | odd | 2 | |||
9680.2.a.bk.1.1 | 2 | 1.1 | even | 1 | trivial |