Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.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: | \(38.8392355432\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2432) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-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 | 0.288675 | − | 0.957427i | \(-0.406785\pi\) | ||||
0.288675 | + | 0.957427i | \(0.406785\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.46410 | −0.931343 | −0.465671 | − | 0.884958i | \(-0.654187\pi\) | ||||
−0.465671 | + | 0.884958i | \(0.654187\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.46410 | 0.683419 | 0.341709 | − | 0.939806i | \(-0.388994\pi\) | ||||
0.341709 | + | 0.939806i | \(0.388994\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00000 | 0.516398 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.92820 | 1.43780 | 0.718900 | − | 0.695113i | \(-0.244646\pi\) | ||||
0.718900 | + | 0.695113i | \(0.244646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.46410 | −0.537711 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.464102 | 0.0967719 | 0.0483859 | − | 0.998829i | \(-0.484592\pi\) | ||||
0.0483859 | + | 0.998829i | \(0.484592\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.46410 | −0.828963 | −0.414481 | − | 0.910058i | \(-0.636037\pi\) | ||||
−0.414481 | + | 0.910058i | \(0.636037\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.92820 | −1.60355 | −0.801776 | − | 0.597624i | \(-0.796111\pi\) | ||||
−0.801776 | + | 0.597624i | \(0.796111\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | −0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.92820 | −0.833018 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.46410 | 0.394572 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.92820 | 1.08200 | 0.541002 | − | 0.841021i | \(-0.318045\pi\) | ||||
0.541002 | + | 0.841021i | \(0.318045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.92820 | −1.36154 | −0.680769 | − | 0.732498i | \(-0.738354\pi\) | ||||
−0.680769 | + | 0.732498i | \(0.738354\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.00000 | −0.596285 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.92820 | 1.01058 | 0.505291 | − | 0.862949i | \(-0.331385\pi\) | ||||
0.505291 | + | 0.862949i | \(0.331385\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.928203 | −0.132600 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.92820 | 0.830114 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.53590 | −0.760414 | −0.380207 | − | 0.924901i | \(-0.624147\pi\) | ||||
−0.380207 | + | 0.924901i | \(0.624147\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.00000 | −1.07872 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.92820 | 0.511409 | 0.255704 | − | 0.966755i | \(-0.417693\pi\) | ||||
0.255704 | + | 0.966755i | \(0.417693\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.92820 | −0.630992 | −0.315496 | − | 0.948927i | \(-0.602171\pi\) | ||||
−0.315496 | + | 0.948927i | \(0.602171\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.92820 | 0.620895 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.92820 | 0.611268 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.92820 | 0.968584 | 0.484292 | − | 0.874906i | \(-0.339077\pi\) | ||||
0.484292 | + | 0.874906i | \(0.339077\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.464102 | 0.0558713 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.0000 | −1.66149 | −0.830747 | − | 0.556650i | \(-0.812086\pi\) | ||||
−0.830747 | + | 0.556650i | \(0.812086\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.00000 | −0.819288 | −0.409644 | − | 0.912245i | \(-0.634347\pi\) | ||||
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.85641 | 1.12324 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | 0.225018 | 0.112509 | − | 0.993651i | \(-0.464111\pi\) | ||||
0.112509 | + | 0.993651i | \(0.464111\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.9282 | −1.19953 | −0.599763 | − | 0.800178i | \(-0.704739\pi\) | ||||
−0.599763 | + | 0.800178i | \(0.704739\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.8564 | 1.28601 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.46410 | −0.478602 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.9282 | 1.37039 | 0.685193 | − | 0.728361i | \(-0.259718\pi\) | ||||
0.685193 | + | 0.728361i | \(0.259718\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.07180 | −0.636497 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.92820 | −0.925812 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | 0.205196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.928203 | −0.0942448 | −0.0471224 | − | 0.998889i | \(-0.515005\pi\) | ||||
−0.0471224 | + | 0.998889i | \(0.515005\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.00000 | 0.804030 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.8564 | −1.77678 | −0.888389 | − | 0.459091i | \(-0.848175\pi\) | ||||
−0.888389 | + | 0.459091i | \(0.848175\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.9282 | −1.07679 | −0.538394 | − | 0.842693i | \(-0.680969\pi\) | ||||
−0.538394 | + | 0.842693i | \(0.680969\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.92820 | −0.480943 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.0717968 | 0.00694086 | 0.00347043 | − | 0.999994i | \(-0.498895\pi\) | ||||
0.00347043 | + | 0.999994i | \(0.498895\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.3923 | −1.28275 | −0.641375 | − | 0.767227i | \(-0.721636\pi\) | ||||
−0.641375 | + | 0.767227i | \(0.721636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.928203 | −0.0873180 | −0.0436590 | − | 0.999046i | \(-0.513902\pi\) | ||||
−0.0436590 | + | 0.999046i | \(0.513902\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.928203 | 0.0865554 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.92820 | −0.455613 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.6077 | −1.33909 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.92820 | 0.624695 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.9282 | −1.14719 | −0.573596 | − | 0.819138i | \(-0.694452\pi\) | ||||
−0.573596 | + | 0.819138i | \(0.694452\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.92820 | −0.786084 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.9282 | 1.82851 | 0.914253 | − | 0.405144i | \(-0.132779\pi\) | ||||
0.914253 | + | 0.405144i | \(0.132779\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.46410 | −0.213665 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.0000 | −0.860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.8564 | −1.61101 | −0.805506 | − | 0.592588i | \(-0.798106\pi\) | ||||
−0.805506 | + | 0.592588i | \(0.798106\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.8564 | 1.00565 | 0.502824 | − | 0.864389i | \(-0.332295\pi\) | ||||
0.502824 | + | 0.864389i | \(0.332295\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.92820 | 0.583460 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.85641 | −0.824234 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.92820 | −0.741447 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.928203 | −0.0765569 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.92820 | 0.239888 | 0.119944 | − | 0.992781i | \(-0.461729\pi\) | ||||
0.119944 | + | 0.992781i | \(0.461729\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0000 | −1.30206 | −0.651031 | − | 0.759051i | \(-0.725663\pi\) | ||||
−0.651031 | + | 0.759051i | \(0.725663\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.8564 | −0.958534 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.8564 | −1.43426 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.53590 | −0.439025 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.14359 | −0.0901278 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.85641 | −0.302057 | −0.151029 | − | 0.988529i | \(-0.548259\pi\) | ||||
−0.151029 | + | 0.988529i | \(0.548259\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.00000 | −0.622799 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.9282 | −1.46471 | −0.732354 | − | 0.680924i | \(-0.761578\pi\) | ||||
−0.732354 | + | 0.680924i | \(0.761578\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.92820 | −0.532939 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | −0.152944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.0000 | 0.760286 | 0.380143 | − | 0.924928i | \(-0.375875\pi\) | ||||
0.380143 | + | 0.924928i | \(0.375875\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.46410 | 0.186269 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.92820 | 0.295262 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.85641 | −0.138754 | −0.0693772 | − | 0.997591i | \(-0.522101\pi\) | ||||
−0.0693772 | + | 0.997591i | \(0.522101\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.92820 | −0.364303 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.00000 | 0.294086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −23.7128 | −1.73405 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.3205 | 0.896185 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.4641 | −0.757156 | −0.378578 | − | 0.925569i | \(-0.623587\pi\) | ||||
−0.378578 | + | 0.925569i | \(0.623587\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.8564 | −1.28533 | −0.642666 | − | 0.766146i | \(-0.722172\pi\) | ||||
−0.642666 | + | 0.766146i | \(0.722172\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.92820 | 0.352916 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.92820 | −0.493614 | −0.246807 | − | 0.969065i | \(-0.579381\pi\) | ||||
−0.246807 | + | 0.969065i | \(0.579381\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.4641 | 1.45066 | 0.725331 | − | 0.688400i | \(-0.241687\pi\) | ||||
0.725331 | + | 0.688400i | \(0.241687\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.92820 | 0.559212 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.0000 | 0.772049 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.8564 | 0.967773 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.928203 | −0.0645146 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.85641 | 0.196643 | 0.0983216 | − | 0.995155i | \(-0.468653\pi\) | ||||
0.0983216 | + | 0.995155i | \(0.468653\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.0000 | −0.959264 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.8564 | −1.21780 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.0000 | 1.49346 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.00000 | −0.473016 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.6077 | 0.982620 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.0718 | −0.875352 | −0.437676 | − | 0.899133i | \(-0.644198\pi\) | ||||
−0.437676 | + | 0.899133i | \(0.644198\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.00000 | 0.133333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.9282 | 0.791703 | 0.395851 | − | 0.918315i | \(-0.370450\pi\) | ||||
0.395851 | + | 0.918315i | \(0.370450\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.9282 | 1.11865 | 0.559324 | − | 0.828949i | \(-0.311061\pi\) | ||||
0.559324 | + | 0.828949i | \(0.311061\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.85641 | 0.648504 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.8564 | 0.776739 | 0.388370 | − | 0.921504i | \(-0.373038\pi\) | ||||
0.388370 | + | 0.921504i | \(0.373038\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.8564 | 0.903892 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.00000 | 0.129914 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.3205 | 1.18506 | 0.592528 | − | 0.805550i | \(-0.298130\pi\) | ||||
0.592528 | + | 0.805550i | \(0.298130\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.7846 | 1.08119 | 0.540596 | − | 0.841282i | \(-0.318199\pi\) | ||||
0.540596 | + | 0.841282i | \(0.318199\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0000 | 1.02640 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.85641 | −0.118601 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.46410 | 0.156787 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.9282 | −0.692547 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.928203 | −0.0585877 | −0.0292938 | − | 0.999571i | \(-0.509326\pi\) | ||||
−0.0292938 | + | 0.999571i | \(0.509326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.85641 | −0.116711 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.8564 | 0.742477 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.9282 | 0.806439 | 0.403220 | − | 0.915103i | \(-0.367891\pi\) | ||||
0.403220 | + | 0.915103i | \(0.367891\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.92820 | −0.306224 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.92820 | 0.552642 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.9282 | 0.673862 | 0.336931 | − | 0.941529i | \(-0.390611\pi\) | ||||
0.336931 | + | 0.941529i | \(0.390611\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.0718 | −0.680135 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.9282 | 0.791193 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.8564 | −1.21067 | −0.605333 | − | 0.795972i | \(-0.706960\pi\) | ||||
−0.605333 | + | 0.795972i | \(0.706960\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.3923 | −1.54247 | −0.771236 | − | 0.636549i | \(-0.780361\pi\) | ||||
−0.771236 | + | 0.636549i | \(0.780361\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.07180 | −0.367482 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.00000 | 0.241209 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0718 | 0.665240 | 0.332620 | − | 0.943061i | \(-0.392067\pi\) | ||||
0.332620 | + | 0.943061i | \(0.392067\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.8564 | 1.06904 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.00000 | −0.238620 | −0.119310 | − | 0.992857i | \(-0.538068\pi\) | ||||
−0.119310 | + | 0.992857i | \(0.538068\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.07180 | −0.301487 | −0.150744 | − | 0.988573i | \(-0.548167\pi\) | ||||
−0.150744 | + | 0.988573i | \(0.548167\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.00000 | 0.118470 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.0718 | −1.00772 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.1436 | 1.06727 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.928203 | −0.0544122 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.3205 | 1.53766 | 0.768830 | − | 0.639453i | \(-0.220839\pi\) | ||||
0.768830 | + | 0.639453i | \(0.220839\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.85641 | 0.457418 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 20.0000 | 1.16052 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.14359 | 0.0661357 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.0000 | 1.26806 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.8564 | −1.02582 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.85641 | −0.564376 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.8564 | −1.47570 | −0.737852 | − | 0.674963i | \(-0.764160\pi\) | ||||
−0.737852 | + | 0.674963i | \(0.764160\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.9282 | −0.621684 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.3923 | −0.759408 | −0.379704 | − | 0.925108i | \(-0.623974\pi\) | ||||
−0.379704 | + | 0.925108i | \(0.623974\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.8564 | 0.613640 | 0.306820 | − | 0.951767i | \(-0.400735\pi\) | ||||
0.306820 | + | 0.951767i | \(0.400735\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.85641 | 0.555346 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.53590 | −0.423258 | −0.211629 | − | 0.977350i | \(-0.567877\pi\) | ||||
−0.211629 | + | 0.977350i | \(0.567877\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.8564 | 0.999767 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.0717968 | 0.00400730 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.92820 | 0.329854 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.46410 | −0.136684 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.3923 | −0.740596 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.0718 | −0.941199 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.7846 | 1.74704 | 0.873520 | − | 0.486788i | \(-0.161832\pi\) | ||||
0.873520 | + | 0.486788i | \(0.161832\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.00000 | −0.219199 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.8564 | 0.866328 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.9282 | −1.14003 | −0.570016 | − | 0.821634i | \(-0.693063\pi\) | ||||
−0.570016 | + | 0.821634i | \(0.693063\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.928203 | −0.0504131 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 35.7128 | 1.93396 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5359 | 1.05484 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.928203 | 0.0499728 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.143594 | −0.00770851 | −0.00385425 | − | 0.999993i | \(-0.501227\pi\) | ||||
−0.00385425 | + | 0.999993i | \(0.501227\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0000 | −0.749403 | −0.374701 | − | 0.927146i | \(-0.622255\pi\) | ||||
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.3205 | −0.657620 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.9282 | 1.27357 | 0.636785 | − | 0.771042i | \(-0.280264\pi\) | ||||
0.636785 | + | 0.771042i | \(0.280264\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −28.0000 | −1.48609 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.6077 | −0.773121 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.5359 | −0.925509 | −0.462755 | − | 0.886486i | \(-0.653139\pi\) | ||||
−0.462755 | + | 0.886486i | \(0.653139\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.00000 | 0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.0000 | −0.732793 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.9282 | −1.40564 | −0.702820 | − | 0.711367i | \(-0.748076\pi\) | ||||
−0.702820 | + | 0.711367i | \(0.748076\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.8564 | −0.721336 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.6410 | 0.708206 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.39230 | −0.486315 | −0.243158 | − | 0.969987i | \(-0.578183\pi\) | ||||
−0.243158 | + | 0.969987i | \(0.578183\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.0000 | −0.619677 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.0000 | −0.566529 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.8564 | −1.07132 | −0.535661 | − | 0.844433i | \(-0.679937\pi\) | ||||
−0.535661 | + | 0.844433i | \(0.679937\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.9282 | −0.662332 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.7846 | −0.857653 | −0.428827 | − | 0.903387i | \(-0.641073\pi\) | ||||
−0.428827 | + | 0.903387i | \(0.641073\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.7128 | 1.00466 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.8564 | 0.907692 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.85641 | −0.0941235 | −0.0470618 | − | 0.998892i | \(-0.514986\pi\) | ||||
−0.0470618 | + | 0.998892i | \(0.514986\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.75129 | 0.139139 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.9282 | 1.05569 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.00000 | 0.201262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.92820 | −0.247339 | −0.123670 | − | 0.992323i | \(-0.539466\pi\) | ||||
−0.123670 | + | 0.992323i | \(0.539466\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.46410 | −0.123359 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.0000 | −0.599251 | −0.299626 | − | 0.954057i | \(-0.596862\pi\) | ||||
−0.299626 | + | 0.954057i | \(0.596862\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.0000 | −1.09590 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.00000 | 0.0993808 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.00000 | 0.296681 | 0.148340 | − | 0.988936i | \(-0.452607\pi\) | ||||
0.148340 | + | 0.988936i | \(0.452607\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.8564 | −0.930118 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.67949 | −0.476297 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.8564 | −1.07289 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.8564 | 0.580611 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.7846 | 0.526863 | 0.263431 | − | 0.964678i | \(-0.415146\pi\) | ||||
0.263431 | + | 0.964678i | \(0.415146\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.4641 | 0.899885 | 0.449943 | − | 0.893057i | \(-0.351444\pi\) | ||||
0.449943 | + | 0.893057i | \(0.351444\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.8564 | −0.673722 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.92820 | −0.287560 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.1436 | 0.587670 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.85641 | −0.475872 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.928203 | 0.0447100 | 0.0223550 | − | 0.999750i | \(-0.492884\pi\) | ||||
0.0223550 | + | 0.999750i | \(0.492884\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.7846 | 0.806617 | 0.403308 | − | 0.915064i | \(-0.367860\pi\) | ||||
0.403308 | + | 0.915064i | \(0.367860\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.92820 | −0.428075 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.464102 | 0.0222010 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.00000 | 0.190910 | 0.0954548 | − | 0.995434i | \(-0.469569\pi\) | ||||
0.0954548 | + | 0.995434i | \(0.469569\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.85641 | 0.0884003 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.85641 | 0.468292 | 0.234146 | − | 0.972201i | \(-0.424771\pi\) | ||||
0.234146 | + | 0.972201i | \(0.424771\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.8564 | 1.22571 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.92820 | 0.138499 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.0000 | 0.943858 | 0.471929 | − | 0.881636i | \(-0.343558\pi\) | ||||
0.471929 | + | 0.881636i | \(0.343558\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.7128 | −1.30495 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.0000 | −0.751746 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.1436 | −0.569300 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.0000 | −1.45012 | −0.725059 | − | 0.688686i | \(-0.758188\pi\) | ||||
−0.725059 | + | 0.688686i | \(0.758188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −29.6410 | −1.38352 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.8564 | 0.645357 | 0.322679 | − | 0.946509i | \(-0.395417\pi\) | ||||
0.322679 | + | 0.946509i | \(0.395417\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.7846 | 1.15184 | 0.575919 | − | 0.817507i | \(-0.304644\pi\) | ||||
0.575919 | + | 0.817507i | \(0.304644\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17.8564 | −0.828071 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −38.7846 | −1.79474 | −0.897369 | − | 0.441281i | \(-0.854524\pi\) | ||||
−0.897369 | + | 0.441281i | \(0.854524\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.5359 | −0.902084 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.0000 | 0.460776 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 35.7128 | 1.64208 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.0718 | 0.506943 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.7846 | −1.13244 | −0.566219 | − | 0.824255i | \(-0.691594\pi\) | ||||
−0.566219 | + | 0.824255i | \(0.691594\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.92820 | 0.224707 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.14359 | −0.0520353 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.85641 | −0.0842951 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.6410 | 1.56973 | 0.784867 | − | 0.619664i | \(-0.212731\pi\) | ||||
0.784867 | + | 0.619664i | \(0.212731\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.85641 | −0.174393 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 41.8564 | 1.88895 | 0.944477 | − | 0.328579i | \(-0.106570\pi\) | ||||
0.944477 | + | 0.328579i | \(0.106570\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.4641 | −1.19188 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.0000 | 0.719147 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 34.4974 | 1.54742 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.7846 | 0.840915 | 0.420457 | − | 0.907312i | \(-0.361870\pi\) | ||||
0.420457 | + | 0.907312i | \(0.361870\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.9282 | −0.845650 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.3205 | −0.549344 | −0.274672 | − | 0.961538i | \(-0.588569\pi\) | ||||
−0.274672 | + | 0.961538i | \(0.588569\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −35.7128 | −1.58920 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.92820 | −0.307692 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.0000 | 0.797836 | 0.398918 | − | 0.916987i | \(-0.369386\pi\) | ||||
0.398918 | + | 0.916987i | \(0.369386\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.2487 | 0.763038 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.00000 | −0.220755 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −21.8564 | −0.963108 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.7128 | −1.21881 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.0000 | 0.438951 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.9282 | 1.17975 | 0.589873 | − | 0.807496i | \(-0.299178\pi\) | ||||
0.589873 | + | 0.807496i | \(0.299178\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.0000 | 1.35554 | 0.677768 | − | 0.735276i | \(-0.262948\pi\) | ||||
0.677768 | + | 0.735276i | \(0.262948\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.46410 | 0.107542 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −52.9282 | −2.30559 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7846 | −0.990635 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.85641 | −0.340939 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.0718 | 0.739462 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.143594 | 0.00620809 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.85641 | −0.0801099 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.71281 | 0.159922 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.7846 | 1.23755 | 0.618774 | − | 0.785569i | \(-0.287630\pi\) | ||||
0.618774 | + | 0.785569i | \(0.287630\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.0000 | 0.429141 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.7846 | −1.14733 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.8564 | −1.44760 | −0.723798 | − | 0.690012i | \(-0.757605\pi\) | ||||
−0.723798 | + | 0.690012i | \(0.757605\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.85641 | 0.420661 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.46410 | −0.190177 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.92820 | −0.209569 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.00000 | 0.169791 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.0000 | 0.932170 | 0.466085 | − | 0.884740i | \(-0.345664\pi\) | ||||
0.466085 | + | 0.884740i | \(0.345664\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.0000 | −0.930501 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23.7128 | −1.00116 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.7128 | −0.999376 | −0.499688 | − | 0.866205i | \(-0.666552\pi\) | ||||
−0.499688 | + | 0.866205i | \(0.666552\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.85641 | −0.0780996 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.46410 | −0.103483 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.7846 | −1.37440 | −0.687201 | − | 0.726467i | \(-0.741161\pi\) | ||||
−0.687201 | + | 0.726467i | \(0.741161\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.7846 | 0.535019 | 0.267510 | − | 0.963555i | \(-0.413799\pi\) | ||||
0.267510 | + | 0.963555i | \(0.413799\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.4641 | −0.437144 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.464102 | −0.0193544 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.7846 | −1.23995 | −0.619975 | − | 0.784622i | \(-0.712857\pi\) | ||||
−0.619975 | + | 0.784622i | \(0.712857\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.8564 | −0.742087 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.9282 | 1.11717 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.1436 | 0.917094 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.85641 | −0.407512 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.92820 | −0.367880 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.92820 | −0.284988 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 43.8564 | 1.80097 | 0.900483 | − | 0.434890i | \(-0.143213\pi\) | ||||
0.900483 | + | 0.434890i | \(0.143213\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −29.2154 | −1.19771 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.4641 | 0.837540 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.8564 | 0.729593 | 0.364796 | − | 0.931087i | \(-0.381139\pi\) | ||||
0.364796 | + | 0.931087i | \(0.381139\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.143594 | 0.00585730 | 0.00292865 | − | 0.999996i | \(-0.499068\pi\) | ||||
0.00292865 | + | 0.999996i | \(0.499068\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.8564 | −0.645723 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.0000 | 0.406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.1436 | −0.492893 | −0.246447 | − | 0.969156i | \(-0.579263\pi\) | ||||
−0.246447 | + | 0.969156i | \(0.579263\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.0000 | 0.445742 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.0718 | 0.690651 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.6410 | 1.39914 | 0.699569 | − | 0.714565i | \(-0.253375\pi\) | ||||
0.699569 | + | 0.714565i | \(0.253375\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.8564 | 0.558744 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.0000 | −0.563619 | −0.281809 | − | 0.959470i | \(-0.590935\pi\) | ||||
−0.281809 | + | 0.959470i | \(0.590935\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.143594 | 0.00577151 | 0.00288576 | − | 0.999996i | \(-0.499081\pi\) | ||||
0.00288576 | + | 0.999996i | \(0.499081\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.32051 | −0.0931188 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −31.8564 | −1.27630 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.00000 | −0.159745 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.8564 | 0.472746 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.6410 | 1.21980 | 0.609900 | − | 0.792479i | \(-0.291210\pi\) | ||||
0.609900 | + | 0.792479i | \(0.291210\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.85641 | 0.113532 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −25.8564 | −1.02608 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.28719 | −0.0906217 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.0000 | 1.10766 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.7846 | −1.29491 | −0.647457 | − | 0.762102i | \(-0.724168\pi\) | ||||
−0.647457 | + | 0.762102i | \(0.724168\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.0718 | −0.752118 | −0.376059 | − | 0.926596i | \(-0.622721\pi\) | ||||
−0.376059 | + | 0.926596i | \(0.622721\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.8564 | −0.703095 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.4641 | 0.804527 | 0.402263 | − | 0.915524i | \(-0.368224\pi\) | ||||
0.402263 | + | 0.915524i | \(0.368224\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.7128 | −0.616782 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.0000 | 0.862248 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −34.7846 | −1.36123 | −0.680613 | − | 0.732643i | \(-0.738287\pi\) | ||||
−0.680613 | + | 0.732643i | \(0.738287\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 41.8564 | 1.63547 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.0000 | 0.546192 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.8564 | 0.968268 | 0.484134 | − | 0.874994i | \(-0.339135\pi\) | ||||
0.484134 | + | 0.874994i | \(0.339135\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.5359 | −0.915440 | −0.457720 | − | 0.889096i | \(-0.651334\pi\) | ||||
−0.457720 | + | 0.889096i | \(0.651334\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 14.6077 | 0.567316 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.92820 | −0.191108 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.07180 | −0.0802203 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.0718 | −0.505385 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.7128 | 0.761005 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.9282 | 0.883817 | 0.441909 | − | 0.897060i | \(-0.354302\pi\) | ||||
0.441909 | + | 0.897060i | \(0.354302\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.00000 | 0.192450 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.3923 | −0.514708 | −0.257354 | − | 0.966317i | \(-0.582851\pi\) | ||||
−0.257354 | + | 0.966317i | \(0.582851\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.28719 | 0.0877742 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.9282 | 0.457090 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.85641 | −0.377145 | −0.188572 | − | 0.982059i | \(-0.560386\pi\) | ||||
−0.188572 | + | 0.982059i | \(0.560386\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.7128 | −1.44093 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.9282 | 0.645851 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.6410 | −0.519681 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.8564 | 0.755373 | 0.377687 | − | 0.925933i | \(-0.376720\pi\) | ||||
0.377687 | + | 0.925933i | \(0.376720\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −19.7128 | −0.748828 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.7128 | 0.899478 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 41.0718 | 1.55571 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.8564 | 0.448450 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 47.7128 | 1.80209 | 0.901044 | − | 0.433728i | \(-0.142802\pi\) | ||||
0.901044 | + | 0.433728i | \(0.142802\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.00000 | 0.0754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.8564 | 0.521862 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 44.0000 | 1.65479 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.7846 | 1.15614 | 0.578070 | − | 0.815987i | \(-0.303806\pi\) | ||||
0.578070 | + | 0.815987i | \(0.303806\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.00000 | −0.150012 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.14359 | −0.155179 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.7128 | −0.737217 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.3205 | 0.684192 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.39230 | 0.275686 | 0.137843 | − | 0.990454i | \(-0.455983\pi\) | ||||
0.137843 | + | 0.990454i | \(0.455983\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.9282 | 1.00286 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.7846 | 0.624226 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.46410 | 0.165793 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.3205 | 1.27288 | 0.636439 | − | 0.771327i | \(-0.280407\pi\) | ||||
0.636439 | + | 0.771327i | \(0.280407\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −52.9282 | −1.95762 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.1436 | −0.596277 | −0.298139 | − | 0.954523i | \(-0.596366\pi\) | ||||
−0.298139 | + | 0.954523i | \(0.596366\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.85641 | −0.0684746 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −31.7128 | −1.16816 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.8564 | 0.656859 | 0.328429 | − | 0.944529i | \(-0.393481\pi\) | ||||
0.328429 | + | 0.944529i | \(0.393481\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.46410 | 0.0905210 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.07180 | 0.112693 | 0.0563466 | − | 0.998411i | \(-0.482055\pi\) | ||||
0.0563466 | + | 0.998411i | \(0.482055\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.85641 | 0.214562 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.8564 | 0.799684 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.176915 | −0.00646432 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.9282 | −1.71243 | −0.856217 | − | 0.516616i | \(-0.827192\pi\) | ||||
−0.856217 | + | 0.516616i | \(0.827192\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.928203 | −0.0338256 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −32.0000 | −1.16460 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.7846 | −1.55503 | −0.777517 | − | 0.628862i | \(-0.783521\pi\) | ||||
−0.777517 | + | 0.628862i | \(0.783521\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.85641 | −0.0673833 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.71281 | 0.243339 | 0.121670 | − | 0.992571i | \(-0.461175\pi\) | ||||
0.121670 | + | 0.992571i | \(0.461175\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33.0000 | 1.19468 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −23.7128 | −0.857339 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.67949 | 0.349506 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.0000 | −1.69486 | −0.847432 | − | 0.530904i | \(-0.821852\pi\) | ||||
−0.847432 | + | 0.530904i | \(0.821852\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.9282 | 0.465598 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −47.5359 | −1.70975 | −0.854874 | − | 0.518836i | \(-0.826365\pi\) | ||||
−0.854874 | + | 0.518836i | \(0.826365\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.92820 | 0.320711 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.92820 | −0.176798 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.92820 | 0.248229 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 56.0000 | 2.00384 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22.3205 | 0.797670 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.0000 | 0.713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.7846 | 0.776537 | 0.388269 | − | 0.921546i | \(-0.373073\pi\) | ||||
0.388269 | + | 0.921546i | \(0.373073\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.9282 | 0.389054 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.28719 | 0.0813230 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.1436 | −0.431232 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.0718 | −0.392676 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.1769 | −1.13976 | −0.569882 | − | 0.821726i | \(-0.693011\pi\) | ||||
−0.569882 | + | 0.821726i | \(0.693011\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 41.0718 | 1.45302 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −25.8564 | −0.913591 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.0000 | 0.988099 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.28719 | −0.0806128 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.8564 | −0.698979 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.9282 | 1.12254 | 0.561268 | − | 0.827634i | \(-0.310314\pi\) | ||||
0.561268 | + | 0.827634i | \(0.310314\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.8564 | 1.01329 | 0.506643 | − | 0.862156i | \(-0.330886\pi\) | ||||
0.506643 | + | 0.862156i | \(0.330886\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.3923 | −0.890547 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.71281 | −0.270168 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.92820 | −0.312358 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.1436 | 0.424331 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.6410 | 0.859977 | 0.429989 | − | 0.902834i | \(-0.358518\pi\) | ||||
0.429989 | + | 0.902834i | \(0.358518\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.4641 | 1.06191 | 0.530956 | − | 0.847399i | \(-0.321833\pi\) | ||||
0.530956 | + | 0.847399i | \(0.321833\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.00000 | 0.139262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.7128 | 1.41572 | 0.707862 | − | 0.706351i | \(-0.249660\pi\) | ||||
0.707862 | + | 0.706351i | \(0.249660\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.3205 | 0.775223 | 0.387612 | − | 0.921823i | \(-0.373300\pi\) | ||||
0.387612 | + | 0.921823i | \(0.373300\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.0718 | 0.384076 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.50258 | −0.190653 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −37.8564 | −1.31007 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 44.6410 | 1.54302 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.0000 | −0.759524 | −0.379762 | − | 0.925084i | \(-0.623994\pi\) | ||||
−0.379762 | + | 0.925084i | \(0.623994\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.07180 | −0.312821 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.00000 | −0.137767 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.8564 | −0.476675 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.3205 | −0.423338 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.07180 | −0.174064 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.928203 | 0.0318184 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.9282 | −0.922004 | −0.461002 | − | 0.887399i | \(-0.652510\pi\) | ||||
−0.461002 | + | 0.887399i | \(0.652510\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.00000 | −0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.1436 | 0.756411 | 0.378205 | − | 0.925722i | \(-0.376541\pi\) | ||||
0.378205 | + | 0.925722i | \(0.376541\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.9282 | −1.19173 | −0.595867 | − | 0.803083i | \(-0.703192\pi\) | ||||
−0.595867 | + | 0.803083i | \(0.703192\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.0718 | −0.581805 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.7846 | −0.911759 | −0.455879 | − | 0.890042i | \(-0.650675\pi\) | ||||
−0.455879 | + | 0.890042i | \(0.650675\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.0000 | 0.680020 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.1436 | 0.616189 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.00000 | −0.271381 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.5359 | 0.661949 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.85641 | 0.0628298 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 29.5692 | 0.999622 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.2487 | 0.582448 | 0.291224 | − | 0.956655i | \(-0.405938\pi\) | ||||
0.291224 | + | 0.956655i | \(0.405938\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.3205 | 0.887769 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.0000 | −0.741199 | −0.370599 | − | 0.928793i | \(-0.620848\pi\) | ||||
−0.370599 | + | 0.928793i | \(0.620848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.71281 | −0.192251 | −0.0961257 | − | 0.995369i | \(-0.530645\pi\) | ||||
−0.0961257 | + | 0.995369i | \(0.530645\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.85641 | 0.264090 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.928203 | 0.0311660 | 0.0155830 | − | 0.999879i | \(-0.495040\pi\) | ||||
0.0155830 | + | 0.999879i | \(0.495040\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.8564 | 1.06843 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.00000 | −0.134005 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.92820 | 0.231843 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.71281 | −0.124106 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.14359 | 0.0381835 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 39.8564 | 1.32929 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.8179 | −1.09332 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22.0000 | 0.732114 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.0000 | 0.664822 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.8564 | 1.35661 | 0.678307 | − | 0.734778i | \(-0.262714\pi\) | ||||
0.678307 | + | 0.734778i | \(0.262714\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 35.7128 | 1.18452 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.8564 | 0.657872 | 0.328936 | − | 0.944352i | \(-0.393310\pi\) | ||||
0.328936 | + | 0.944352i | \(0.393310\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43.7128 | 1.44668 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.85641 | −0.325843 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −51.5692 | −1.70297 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.3923 | −0.507745 | −0.253873 | − | 0.967238i | \(-0.581704\pi\) | ||||
−0.253873 | + | 0.967238i | \(0.581704\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.8564 | −0.851998 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −34.4974 | −1.13550 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.00000 | −0.0657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 21.8564 | 0.717859 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.7128 | −1.53260 | −0.766299 | − | 0.642484i | \(-0.777904\pi\) | ||||
−0.766299 | + | 0.642484i | \(0.777904\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.928203 | −0.0304206 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.3923 | −0.438444 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −47.4256 | −1.55098 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.0718 | −0.525043 | −0.262521 | − | 0.964926i | \(-0.584554\pi\) | ||||
−0.262521 | + | 0.964926i | \(0.584554\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.8564 | 0.354285 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.1051 | −1.14439 | −0.572197 | − | 0.820116i | \(-0.693909\pi\) | ||||
−0.572197 | + | 0.820116i | \(0.693909\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.21539 | 0.104708 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 24.6410 | 0.801572 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.07180 | 0.0998200 | 0.0499100 | − | 0.998754i | \(-0.484107\pi\) | ||||
0.0499100 | + | 0.998754i | \(0.484107\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.2487 | −0.559917 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.53590 | −0.244368 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.7846 | −1.58029 | −0.790144 | − | 0.612921i | \(-0.789994\pi\) | ||||
−0.790144 | + | 0.612921i | \(0.789994\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.9282 | −0.677221 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.8564 | 0.577216 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 46.4641 | 1.50040 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 48.7128 | 1.57138 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.143594 | −0.00462724 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −35.7128 | −1.14964 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.7846 | 0.539757 | 0.269878 | − | 0.962894i | \(-0.413017\pi\) | ||||
0.269878 | + | 0.962894i | \(0.413017\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.92820 | 0.190441 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.85641 | −0.0595749 | −0.0297875 | − | 0.999556i | \(-0.509483\pi\) | ||||
−0.0297875 | + | 0.999556i | \(0.509483\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29.2154 | −0.936602 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.46410 | −0.0789144 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.00000 | 0.191957 | 0.0959785 | − | 0.995383i | \(-0.469402\pi\) | ||||
0.0959785 | + | 0.995383i | \(0.469402\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −51.7128 | −1.65275 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26.7846 | 0.855167 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48.6410 | 1.55141 | 0.775704 | − | 0.631097i | \(-0.217395\pi\) | ||||
0.775704 | + | 0.631097i | \(0.217395\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.8564 | −0.441502 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −17.0718 | −0.543401 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.14359 | −0.131759 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.5692 | 1.25696 | 0.628479 | − | 0.777827i | \(-0.283678\pi\) | ||||
0.628479 | + | 0.777827i | \(0.283678\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 31.7846 | 1.00865 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 40.9282 | 1.29751 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.21539 | −0.0384918 | −0.0192459 | − | 0.999815i | \(-0.506127\pi\) | ||||
−0.0192459 | + | 0.999815i | \(0.506127\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.0000 | −0.316386 |
(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 | 4864.2.a.x.1.1 | 2 | ||
4.3 | odd | 2 | 4864.2.a.u.1.2 | 2 | |||
8.3 | odd | 2 | 4864.2.a.v.1.2 | 2 | |||
8.5 | even | 2 | 4864.2.a.s.1.1 | 2 | |||
16.3 | odd | 4 | 2432.2.c.d.1217.1 | yes | 4 | ||
16.5 | even | 4 | 2432.2.c.c.1217.2 | ✓ | 4 | ||
16.11 | odd | 4 | 2432.2.c.d.1217.3 | yes | 4 | ||
16.13 | even | 4 | 2432.2.c.c.1217.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.c.1217.2 | ✓ | 4 | 16.5 | even | 4 | ||
2432.2.c.c.1217.4 | yes | 4 | 16.13 | even | 4 | ||
2432.2.c.d.1217.1 | yes | 4 | 16.3 | odd | 4 | ||
2432.2.c.d.1217.3 | yes | 4 | 16.11 | odd | 4 | ||
4864.2.a.s.1.1 | 2 | 8.5 | even | 2 | |||
4864.2.a.u.1.2 | 2 | 4.3 | odd | 2 | |||
4864.2.a.v.1.2 | 2 | 8.3 | odd | 2 | |||
4864.2.a.x.1.1 | 2 | 1.1 | even | 1 | trivial |