Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 13x^{7} + 32x^{6} + 40x^{5} - 79x^{4} - 39x^{3} + 58x^{2} + 9x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.511914\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.34732 | 0.602539 | 0.301270 | − | 0.953539i | \(-0.402590\pi\) | ||||
0.301270 | + | 0.953539i | \(0.402590\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.91839 | 1.10305 | 0.551523 | − | 0.834160i | \(-0.314047\pi\) | ||||
0.551523 | + | 0.834160i | \(0.314047\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.69746 | 1.11483 | 0.557413 | − | 0.830235i | \(-0.311794\pi\) | ||||
0.557413 | + | 0.830235i | \(0.311794\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.03680 | −1.67431 | −0.837153 | − | 0.546969i | \(-0.815782\pi\) | ||||
−0.837153 | + | 0.546969i | \(0.815782\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.34732 | −0.347876 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.75034 | 1.39466 | 0.697331 | − | 0.716750i | \(-0.254371\pi\) | ||||
0.697331 | + | 0.716750i | \(0.254371\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.30556 | −1.44659 | −0.723297 | − | 0.690537i | \(-0.757374\pi\) | ||||
−0.723297 | + | 0.690537i | \(0.757374\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.91839 | −0.636844 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.18473 | −0.636946 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.671792 | −0.120657 | −0.0603287 | − | 0.998179i | \(-0.519215\pi\) | ||||
−0.0603287 | + | 0.998179i | \(0.519215\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.69746 | −0.643645 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.93200 | 0.664629 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.42860 | −0.728058 | −0.364029 | − | 0.931388i | \(-0.618599\pi\) | ||||
−0.364029 | + | 0.931388i | \(0.618599\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.03680 | 0.966661 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.20091 | −0.343725 | −0.171862 | − | 0.985121i | \(-0.554978\pi\) | ||||
−0.171862 | + | 0.985121i | \(0.554978\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.58949 | −1.30988 | −0.654942 | − | 0.755679i | \(-0.727307\pi\) | ||||
−0.654942 | + | 0.755679i | \(0.727307\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.34732 | 0.200846 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.549485 | 0.0801506 | 0.0400753 | − | 0.999197i | \(-0.487240\pi\) | ||||
0.0400753 | + | 0.999197i | \(0.487240\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.51697 | 0.216711 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.75034 | −0.805208 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.93706 | −0.403436 | −0.201718 | − | 0.979444i | \(-0.564652\pi\) | ||||
−0.201718 | + | 0.979444i | \(0.564652\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.98166 | 0.671726 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.30556 | 0.835191 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.20516 | −0.547465 | −0.273733 | − | 0.961806i | \(-0.588258\pi\) | ||||
−0.273733 | + | 0.961806i | \(0.588258\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.6176 | −1.35945 | −0.679724 | − | 0.733468i | \(-0.737900\pi\) | ||||
−0.679724 | + | 0.733468i | \(0.737900\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.91839 | 0.367682 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.13349 | −1.00884 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.98884 | −0.487314 | −0.243657 | − | 0.969861i | \(-0.578347\pi\) | ||||
−0.243657 | + | 0.969861i | \(0.578347\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.08197 | −1.07783 | −0.538916 | − | 0.842359i | \(-0.681166\pi\) | ||||
−0.538916 | + | 0.842359i | \(0.681166\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.11062 | −0.247029 | −0.123515 | − | 0.992343i | \(-0.539417\pi\) | ||||
−0.123515 | + | 0.992343i | \(0.539417\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.18473 | 0.367741 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.7906 | 1.22970 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.8630 | −1.44720 | −0.723598 | − | 0.690222i | \(-0.757513\pi\) | ||||
−0.723598 | + | 0.690222i | \(0.757513\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.50563 | −0.714085 | −0.357043 | − | 0.934088i | \(-0.616215\pi\) | ||||
−0.357043 | + | 0.934088i | \(0.616215\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.74754 | 0.840338 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.64297 | 0.492154 | 0.246077 | − | 0.969250i | \(-0.420858\pi\) | ||||
0.246077 | + | 0.969250i | \(0.420858\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.6177 | −1.84684 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.671792 | 0.0696616 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.49560 | −0.871630 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.50834 | −0.153148 | −0.0765742 | − | 0.997064i | \(-0.524398\pi\) | ||||
−0.0765742 | + | 0.997064i | \(0.524398\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.69746 | 0.371609 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.26567 | 0.324946 | 0.162473 | − | 0.986713i | \(-0.448053\pi\) | ||||
0.162473 | + | 0.986713i | \(0.448053\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.93651 | −0.584942 | −0.292471 | − | 0.956274i | \(-0.594478\pi\) | ||||
−0.292471 | + | 0.956274i | \(0.594478\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.93200 | −0.383724 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.1575 | 1.07863 | 0.539317 | − | 0.842103i | \(-0.318682\pi\) | ||||
0.539317 | + | 0.842103i | \(0.318682\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.50930 | −0.144564 | −0.0722822 | − | 0.997384i | \(-0.523028\pi\) | ||||
−0.0722822 | + | 0.997384i | \(0.523028\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.42860 | 0.420345 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.54937 | −0.427968 | −0.213984 | − | 0.976837i | \(-0.568644\pi\) | ||||
−0.213984 | + | 0.976837i | \(0.568644\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.34732 | −0.125638 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.03680 | −0.558102 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.7817 | 1.53838 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.67121 | 0.242837 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.20091 | 0.198450 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.0274 | −0.986325 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.98492 | −0.353605 | −0.176802 | − | 0.984246i | \(-0.556575\pi\) | ||||
−0.176802 | + | 0.984246i | \(0.556575\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.58949 | 0.756262 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.73658 | 0.151726 | 0.0758628 | − | 0.997118i | \(-0.475829\pi\) | ||||
0.0758628 | + | 0.997118i | \(0.475829\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.4020 | −1.59566 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.34732 | −0.115959 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.15181 | −0.696456 | −0.348228 | − | 0.937410i | \(-0.613217\pi\) | ||||
−0.348228 | + | 0.937410i | \(0.613217\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.954858 | −0.0809900 | −0.0404950 | − | 0.999180i | \(-0.512893\pi\) | ||||
−0.0404950 | + | 0.999180i | \(0.512893\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.549485 | −0.0462750 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −22.3208 | −1.86656 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.34732 | 0.111889 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.51697 | −0.125118 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.579094 | −0.0474412 | −0.0237206 | − | 0.999719i | \(-0.507551\pi\) | ||||
−0.0237206 | + | 0.999719i | \(0.507551\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.8135 | 1.36827 | 0.684134 | − | 0.729357i | \(-0.260181\pi\) | ||||
0.684134 | + | 0.729357i | \(0.260181\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.75034 | 0.464887 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.905118 | −0.0727008 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.7695 | 0.939307 | 0.469654 | − | 0.882851i | \(-0.344379\pi\) | ||||
0.469654 | + | 0.882851i | \(0.344379\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.93706 | 0.232924 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.91839 | −0.230001 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.97311 | −0.154546 | −0.0772729 | − | 0.997010i | \(-0.524621\pi\) | ||||
−0.0772729 | + | 0.997010i | \(0.524621\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.98166 | −0.387821 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.3458 | 1.18750 | 0.593748 | − | 0.804651i | \(-0.297648\pi\) | ||||
0.593748 | + | 0.804651i | \(0.297648\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.4429 | 1.80330 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.30556 | −0.482198 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.507138 | 0.0385570 | 0.0192785 | − | 0.999814i | \(-0.493863\pi\) | ||||
0.0192785 | + | 0.999814i | \(0.493863\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.29428 | −0.702581 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.20516 | 0.316079 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.0584 | 1.27501 | 0.637503 | − | 0.770448i | \(-0.279967\pi\) | ||||
0.637503 | + | 0.770448i | \(0.279967\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.69457 | −0.646262 | −0.323131 | − | 0.946354i | \(-0.604735\pi\) | ||||
−0.323131 | + | 0.946354i | \(0.604735\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.6176 | 0.784877 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.96674 | −0.438684 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.2616 | 1.55480 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.91839 | −0.212281 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.97988 | 0.577404 | 0.288702 | − | 0.957419i | \(-0.406776\pi\) | ||||
0.288702 | + | 0.957419i | \(0.406776\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.3801 | 1.17906 | 0.589531 | − | 0.807746i | \(-0.299312\pi\) | ||||
0.589531 | + | 0.807746i | \(0.299312\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.13349 | 0.582451 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.4305 | −0.743140 | −0.371570 | − | 0.928405i | \(-0.621180\pi\) | ||||
−0.371570 | + | 0.928405i | \(0.621180\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.3102 | 1.51064 | 0.755321 | − | 0.655355i | \(-0.227481\pi\) | ||||
0.755321 | + | 0.655355i | \(0.227481\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.98884 | 0.281351 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.91839 | 0.204831 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.96533 | −0.207108 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.3145 | −1.61270 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.2304 | −1.53040 | −0.765201 | − | 0.643791i | \(-0.777360\pi\) | ||||
−0.765201 | + | 0.643791i | \(0.777360\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.08197 | 0.622287 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.5728 | −0.789257 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.96055 | −0.133091 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.11062 | 0.142622 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −34.7136 | −2.33509 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.34435 | 0.223955 | 0.111977 | − | 0.993711i | \(-0.464282\pi\) | ||||
0.111977 | + | 0.993711i | \(0.464282\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.18473 | −0.212315 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.7776 | −1.04720 | −0.523598 | − | 0.851965i | \(-0.675411\pi\) | ||||
−0.523598 | + | 0.851965i | \(0.675411\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.93012 | 0.325791 | 0.162896 | − | 0.986643i | \(-0.447917\pi\) | ||||
0.162896 | + | 0.986643i | \(0.447917\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.7906 | −0.709970 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.88297 | −0.188869 | −0.0944347 | − | 0.995531i | \(-0.530104\pi\) | ||||
−0.0944347 | + | 0.995531i | \(0.530104\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.740332 | 0.0482939 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.8630 | 0.835539 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.1677 | −0.851749 | −0.425874 | − | 0.904782i | \(-0.640033\pi\) | ||||
−0.425874 | + | 0.904782i | \(0.640033\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.71060 | −0.110189 | −0.0550947 | − | 0.998481i | \(-0.517546\pi\) | ||||
−0.0550947 | + | 0.998481i | \(0.517546\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.04385 | 0.130577 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 38.0654 | 2.42204 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.50563 | 0.412277 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.52631 | 0.538176 | 0.269088 | − | 0.963116i | \(-0.413278\pi\) | ||||
0.269088 | + | 0.963116i | \(0.413278\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.69746 | −0.232457 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.74754 | −0.485170 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.31579 | 0.581103 | 0.290551 | − | 0.956859i | \(-0.406161\pi\) | ||||
0.290551 | + | 0.956859i | \(0.406161\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.9244 | −0.803082 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 31.3704 | 1.93438 | 0.967190 | − | 0.254054i | \(-0.0817642\pi\) | ||||
0.967190 | + | 0.254054i | \(0.0817642\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.95715 | −0.243086 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.64297 | −0.284145 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.98936 | −0.304206 | −0.152103 | − | 0.988365i | \(-0.548605\pi\) | ||||
−0.152103 | + | 0.988365i | \(0.548605\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.3242 | 1.72057 | 0.860285 | − | 0.509813i | \(-0.170286\pi\) | ||||
0.860285 | + | 0.509813i | \(0.170286\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 17.6177 | 1.06627 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.7754 | −0.710084 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.33021 | −0.260177 | −0.130088 | − | 0.991502i | \(-0.541526\pi\) | ||||
−0.130088 | + | 0.991502i | \(0.541526\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.671792 | −0.0402191 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.22411 | −0.550264 | −0.275132 | − | 0.961406i | \(-0.588722\pi\) | ||||
−0.275132 | + | 0.961406i | \(0.588722\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.4601 | 1.21623 | 0.608114 | − | 0.793850i | \(-0.291927\pi\) | ||||
0.608114 | + | 0.793850i | \(0.291927\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.49560 | 0.503236 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.42311 | −0.379144 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.0664 | 0.945080 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.50834 | 0.0884203 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.53864 | 0.265150 | 0.132575 | − | 0.991173i | \(-0.457675\pi\) | ||||
0.132575 | + | 0.991173i | \(0.457675\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.66569 | −0.329869 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.69746 | −0.214548 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.03680 | 0.349117 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.0674 | −1.44486 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.26567 | −0.187608 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.3053 | −0.819120 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.5891 | −1.00387 | −0.501933 | − | 0.864907i | \(-0.667378\pi\) | ||||
−0.501933 | + | 0.864907i | \(0.667378\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.93651 | 0.337717 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.8397 | −1.46524 | −0.732618 | − | 0.680640i | \(-0.761702\pi\) | ||||
−0.732618 | + | 0.680640i | \(0.761702\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.28452 | −0.411745 | −0.205873 | − | 0.978579i | \(-0.566003\pi\) | ||||
−0.205873 | + | 0.978579i | \(0.566003\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.93200 | 0.221543 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.21892 | −0.461620 | −0.230810 | − | 0.972999i | \(-0.574138\pi\) | ||||
−0.230810 | + | 0.972999i | \(0.574138\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.69746 | 0.207018 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.1575 | −0.622750 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −36.2591 | −2.01751 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.2256 | 1.06644 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.50930 | 0.0834643 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.60361 | 0.0884098 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.55431 | 0.195363 | 0.0976813 | − | 0.995218i | \(-0.468857\pi\) | ||||
0.0976813 | + | 0.995218i | \(0.468857\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.42860 | −0.242686 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.37424 | −0.293626 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.7733 | −1.13160 | −0.565798 | − | 0.824544i | \(-0.691432\pi\) | ||||
−0.565798 | + | 0.824544i | \(0.691432\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.54937 | 0.247088 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.48392 | −0.134512 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.0016 | −0.864004 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.34732 | 0.0725372 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.56583 | −0.406155 | −0.203078 | − | 0.979163i | \(-0.565094\pi\) | ||||
−0.203078 | + | 0.979163i | \(0.565094\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.14262 | 0.489393 | 0.244697 | − | 0.969600i | \(-0.421312\pi\) | ||||
0.244697 | + | 0.969600i | \(0.421312\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.03680 | 0.322220 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.0243 | 1.11901 | 0.559506 | − | 0.828826i | \(-0.310991\pi\) | ||||
0.559506 | + | 0.828826i | \(0.310991\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.2363 | −0.649436 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −16.7817 | −0.888182 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.8797 | 0.996433 | 0.498216 | − | 0.867053i | \(-0.333989\pi\) | ||||
0.498216 | + | 0.867053i | \(0.333989\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.7600 | 1.09263 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.67121 | −0.140202 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.84368 | −0.148845 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.2455 | 1.05681 | 0.528404 | − | 0.848993i | \(-0.322791\pi\) | ||||
0.528404 | + | 0.848993i | \(0.322791\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.20091 | −0.114575 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.57147 | −0.445008 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.30473 | −0.430003 | −0.215001 | − | 0.976614i | \(-0.568976\pi\) | ||||
−0.215001 | + | 0.976614i | \(0.568976\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.0274 | 0.569455 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.03680 | −0.310911 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.1184 | −1.18751 | −0.593756 | − | 0.804645i | \(-0.702356\pi\) | ||||
−0.593756 | + | 0.804645i | \(0.702356\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.98492 | 0.204154 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.7677 | −0.907889 | −0.453945 | − | 0.891030i | \(-0.649984\pi\) | ||||
−0.453945 | + | 0.891030i | \(0.649984\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.5384 | 0.740945 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.58949 | −0.436628 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.16020 | −0.210930 | −0.105465 | − | 0.994423i | \(-0.533633\pi\) | ||||
−0.105465 | + | 0.994423i | \(0.533633\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.75034 | −0.290807 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.73658 | −0.0875988 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.3305 | −0.871992 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.81500 | −0.0910922 | −0.0455461 | − | 0.998962i | \(-0.514503\pi\) | ||||
−0.0455461 | + | 0.998962i | \(0.514503\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18.4020 | 0.921255 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.76103 | −0.237754 | −0.118877 | − | 0.992909i | \(-0.537929\pi\) | ||||
−0.118877 | + | 0.992909i | \(0.537929\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.05547 | 0.202017 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.34732 | 0.0669488 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.3746 | −0.811658 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.00888 | 0.148780 | 0.0743898 | − | 0.997229i | \(-0.476299\pi\) | ||||
0.0743898 | + | 0.997229i | \(0.476299\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.15181 | 0.402099 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.2723 | −0.603879 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.76515 | −0.430265 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.954858 | 0.0467596 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.26848 | 0.306236 | 0.153118 | − | 0.988208i | \(-0.451069\pi\) | ||||
0.153118 | + | 0.988208i | \(0.451069\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.78433 | 0.184437 | 0.0922184 | − | 0.995739i | \(-0.470604\pi\) | ||||
0.0922184 | + | 0.995739i | \(0.470604\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.549485 | 0.0267169 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.3133 | −0.888324 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.9863 | −1.49953 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 22.3208 | 1.07766 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.6641 | 1.42887 | 0.714435 | − | 0.699702i | \(-0.246684\pi\) | ||||
0.714435 | + | 0.699702i | \(0.246684\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.8508 | −1.33843 | −0.669213 | − | 0.743071i | \(-0.733369\pi\) | ||||
−0.669213 | + | 0.743071i | \(0.733369\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.34732 | −0.0645990 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.30556 | 0.301636 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.0457 | −0.574910 | −0.287455 | − | 0.957794i | \(-0.592809\pi\) | ||||
−0.287455 | + | 0.957794i | \(0.592809\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.51697 | 0.0722369 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.13889 | 0.0541102 | 0.0270551 | − | 0.999634i | \(-0.491387\pi\) | ||||
0.0270551 | + | 0.999634i | \(0.491387\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.25556 | 0.296542 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.579094 | 0.0273902 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.5017 | −0.778764 | −0.389382 | − | 0.921076i | \(-0.627311\pi\) | ||||
−0.389382 | + | 0.921076i | \(0.627311\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.13778 | −0.383193 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.8135 | −0.789969 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −23.7367 | −1.11279 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.941855 | 0.0440581 | 0.0220291 | − | 0.999757i | \(-0.492987\pi\) | ||||
0.0220291 | + | 0.999757i | \(0.492987\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.75034 | −0.268403 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.61417 | −0.354627 | −0.177314 | − | 0.984154i | \(-0.556741\pi\) | ||||
−0.177314 | + | 0.984154i | \(0.556741\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.38347 | 0.157243 | 0.0786217 | − | 0.996905i | \(-0.474948\pi\) | ||||
0.0786217 | + | 0.996905i | \(0.474948\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.905118 | 0.0419739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.0548 | 1.02057 | 0.510286 | − | 0.860005i | \(-0.329540\pi\) | ||||
0.510286 | + | 0.860005i | \(0.329540\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.6410 | −0.537530 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.7695 | −0.542309 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −31.7593 | −1.46029 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 20.0815 | 0.921403 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.93706 | −0.134479 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.8852 | 1.04565 | 0.522825 | − | 0.852440i | \(-0.324878\pi\) | ||||
0.522825 | + | 0.852440i | \(0.324878\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.7346 | 1.21899 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.91839 | 0.132791 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.03221 | −0.0922780 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.7383 | 1.48351 | 0.741756 | − | 0.670670i | \(-0.233993\pi\) | ||||
0.741756 | + | 0.670670i | \(0.233993\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.97311 | 0.0892271 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.7397 | −0.529805 | −0.264902 | − | 0.964275i | \(-0.585340\pi\) | ||||
−0.264902 | + | 0.964275i | \(0.585340\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.75034 | 0.258982 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.98166 | 0.223909 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −26.5047 | −1.18890 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.6706 | −1.50730 | −0.753651 | − | 0.657275i | \(-0.771709\pi\) | ||||
−0.753651 | + | 0.657275i | \(0.771709\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.3458 | −0.685601 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.0415 | −1.29490 | −0.647448 | − | 0.762110i | \(-0.724164\pi\) | ||||
−0.647448 | + | 0.762110i | \(0.724164\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.39990 | 0.195793 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.4429 | −1.04114 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.1695 | −1.51454 | −0.757269 | − | 0.653103i | \(-0.773467\pi\) | ||||
−0.757269 | + | 0.653103i | \(0.773467\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.15960 | −0.272485 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.30556 | 0.278397 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.99838 | −0.352451 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.03170 | 0.0893540 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.507138 | −0.0222609 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.6254 | −0.772185 | −0.386092 | − | 0.922460i | \(-0.626175\pi\) | ||||
−0.386092 | + | 0.922460i | \(0.626175\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.67968 | 0.117174 | 0.0585870 | − | 0.998282i | \(-0.481340\pi\) | ||||
0.0585870 | + | 0.998282i | \(0.481340\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.29428 | 0.405635 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.86303 | −0.168276 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.20516 | −0.182488 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.2865 | 0.575500 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.0327 | 0.649920 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17.0584 | −0.736125 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.60895 | 0.241595 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.691956 | −0.0297495 | −0.0148748 | − | 0.999889i | \(-0.504735\pi\) | ||||
−0.0148748 | + | 0.999889i | \(0.504735\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.69457 | 0.373120 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.03350 | −0.0871058 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.2353 | 0.608659 | 0.304330 | − | 0.952567i | \(-0.401568\pi\) | ||||
0.304330 | + | 0.952567i | \(0.401568\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.6176 | −0.453149 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.30556 | −0.268626 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −37.5391 | −1.59632 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.96674 | 0.253274 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.54928 | −0.235130 | −0.117565 | − | 0.993065i | \(-0.537509\pi\) | ||||
−0.117565 | + | 0.993065i | \(0.537509\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 51.8530 | 2.19315 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.2616 | −0.897667 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.6802 | 1.12444 | 0.562219 | − | 0.826989i | \(-0.309948\pi\) | ||||
0.562219 | + | 0.826989i | \(0.309948\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.12945 | −0.257868 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.91839 | 0.122561 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.81271 | −0.369448 | −0.184724 | − | 0.982790i | \(-0.559139\pi\) | ||||
−0.184724 | + | 0.982790i | \(0.559139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.6835 | −1.74440 | −0.872200 | − | 0.489150i | \(-0.837307\pi\) | ||||
−0.872200 | + | 0.489150i | \(0.837307\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.97988 | −0.333364 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.18473 | 0.132812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.8443 | −0.451452 | −0.225726 | − | 0.974191i | \(-0.572475\pi\) | ||||
−0.225726 | + | 0.974191i | \(0.572475\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.3801 | −0.680732 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.9859 | −0.787669 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.8597 | −0.449761 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.13349 | −0.336278 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.0198519 | 0.000819377 0 | 0.000409689 | − | 1.00000i | \(-0.499870\pi\) | ||||
0.000409689 | 1.00000i | \(0.499870\pi\) | ||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.23602 | 0.174542 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.4305 | 0.429052 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.59076 | 0.270650 | 0.135325 | − | 0.990801i | \(-0.456792\pi\) | ||||
0.135325 | + | 0.990801i | \(0.456792\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.6103 | 0.926932 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.3102 | −0.872169 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.4616 | 1.28549 | 0.642743 | − | 0.766082i | \(-0.277796\pi\) | ||||
0.642743 | + | 0.766082i | \(0.277796\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.9067 | −1.21992 | −0.609961 | − | 0.792432i | \(-0.708815\pi\) | ||||
−0.609961 | + | 0.792432i | \(0.708815\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.98884 | −0.162438 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.59897 | 0.146319 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.08762 | −0.206500 | −0.103250 | − | 0.994655i | \(-0.532924\pi\) | ||||
−0.103250 | + | 0.994655i | \(0.532924\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.91839 | −0.118259 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.31713 | −0.134197 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.8235 | 1.44690 | 0.723449 | − | 0.690378i | \(-0.242556\pi\) | ||||
0.723449 | + | 0.690378i | \(0.242556\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.96533 | 0.119574 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.2128 | 0.612442 | 0.306221 | − | 0.951960i | \(-0.400935\pi\) | ||||
0.306221 | + | 0.951960i | \(0.400935\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.5644 | 1.22849 | 0.614244 | − | 0.789116i | \(-0.289461\pi\) | ||||
0.614244 | + | 0.789116i | \(0.289461\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.5500 | 0.542869 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.06617 | 0.0426470 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 23.3145 | 0.931093 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −25.4660 | −1.01539 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.73458 | −0.387527 | −0.193764 | − | 0.981048i | \(-0.562070\pi\) | ||||
−0.193764 | + | 0.981048i | \(0.562070\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.2304 | 0.883578 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.36896 | −0.213061 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.15767 | −0.362840 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.08197 | −0.359277 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.9947 | −1.54020 | −0.770099 | − | 0.637924i | \(-0.779793\pi\) | ||||
−0.770099 | + | 0.637924i | \(0.779793\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.49902 | 0.177424 | 0.0887120 | − | 0.996057i | \(-0.471725\pi\) | ||||
0.0887120 | + | 0.996057i | \(0.471725\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.5728 | 0.455678 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.20597 | −0.204668 | −0.102334 | − | 0.994750i | \(-0.532631\pi\) | ||||
−0.102334 | + | 0.994750i | \(0.532631\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.5484 | −0.610328 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.96055 | 0.0768400 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.19073 | −0.0465968 | −0.0232984 | − | 0.999729i | \(-0.507417\pi\) | ||||
−0.0232984 | + | 0.999729i | \(0.507417\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.33972 | 0.0914206 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.11062 | −0.0823431 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.9964 | 1.67490 | 0.837450 | − | 0.546514i | \(-0.184045\pi\) | ||||
0.837450 | + | 0.546514i | \(0.184045\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.7967 | −1.66460 | −0.832300 | − | 0.554325i | \(-0.812976\pi\) | ||||
−0.832300 | + | 0.554325i | \(0.812976\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 34.7136 | 1.34816 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −24.7934 | −0.961448 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.34435 | −0.129300 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −39.2582 | −1.51555 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.7493 | −0.954015 | −0.477007 | − | 0.878899i | \(-0.658279\pi\) | ||||
−0.477007 | + | 0.878899i | \(0.658279\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.18473 | 0.122580 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.9081 | −0.957296 | −0.478648 | − | 0.878007i | \(-0.658873\pi\) | ||||
−0.478648 | + | 0.878007i | \(0.658873\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.40191 | −0.168930 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.7776 | 0.604599 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.7745 | 0.641860 | 0.320930 | − | 0.947103i | \(-0.396005\pi\) | ||||
0.320930 | + | 0.947103i | \(0.396005\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.9831 | −0.419642 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.93012 | −0.188096 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17.7304 | 0.675475 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.32052 | −0.0882768 | −0.0441384 | − | 0.999025i | \(-0.514054\pi\) | ||||
−0.0441384 | + | 0.999025i | \(0.514054\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.7906 | 0.409901 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.28650 | −0.0487997 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.6560 | −0.479380 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.88297 | 0.109044 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.11535 | 0.193204 | 0.0966020 | − | 0.995323i | \(-0.469203\pi\) | ||||
0.0966020 | + | 0.995323i | \(0.469203\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.9248 | 1.05320 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.740332 | −0.0278825 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.53049 | 0.358431 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.4887 | −1.14503 | −0.572514 | − | 0.819895i | \(-0.694032\pi\) | ||||
−0.572514 | + | 0.819895i | \(0.694032\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.8630 | −0.482399 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.671792 | 0.0251588 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −30.0733 | −1.12468 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.1677 | 0.491757 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.50338 | −0.279829 | −0.139914 | − | 0.990164i | \(-0.544683\pi\) | ||||
−0.139914 | + | 0.990164i | \(0.544683\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.3250 | −0.645218 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.71060 | 0.0636179 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.18473 | −0.118278 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.1529 | −0.932870 | −0.466435 | − | 0.884555i | \(-0.654462\pi\) | ||||
−0.466435 | + | 0.884555i | \(0.654462\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −49.3925 | −1.82685 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.5387 | −0.684742 | −0.342371 | − | 0.939565i | \(-0.611230\pi\) | ||||
−0.342371 | + | 0.939565i | \(0.611230\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.04385 | −0.0753885 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.7486 | −0.543271 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.1856 | 0.632184 | 0.316092 | − | 0.948729i | \(-0.397629\pi\) | ||||
0.316092 | + | 0.948729i | \(0.397629\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −38.0654 | −1.39837 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.9275 | −1.02456 | −0.512280 | − | 0.858818i | \(-0.671199\pi\) | ||||
−0.512280 | + | 0.858818i | \(0.671199\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.780224 | −0.0285852 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.50563 | −0.238028 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 32.5618 | 1.18978 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.7691 | −1.63365 | −0.816824 | − | 0.576888i | \(-0.804267\pi\) | ||||
−0.816824 | + | 0.576888i | \(0.804267\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.52631 | −0.310716 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.6532 | 0.824435 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.2317 | 1.38955 | 0.694777 | − | 0.719225i | \(-0.255503\pi\) | ||||
0.694777 | + | 0.719225i | \(0.255503\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.69746 | 0.134209 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.0194 | −1.45070 | −0.725350 | − | 0.688380i | \(-0.758322\pi\) | ||||
−0.725350 | + | 0.688380i | \(0.758322\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.40471 | −0.159461 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.74754 | 0.280113 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.3857 | 0.916624 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.6601 | −1.21381 | −0.606906 | − | 0.794773i | \(-0.707590\pi\) | ||||
−0.606906 | + | 0.794773i | \(0.707590\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.31579 | −0.335500 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.00330 | 0.0720536 | 0.0360268 | − | 0.999351i | \(-0.488530\pi\) | ||||
0.0360268 | + | 0.999351i | \(0.488530\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.13948 | 0.0768523 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.9244 | 0.463659 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.8780 | 0.497230 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.5802 | −1.20160 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.8572 | 0.565969 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.0531304 | −0.00189389 | −0.000946946 | − | 1.00000i | \(-0.500301\pi\) | ||||
−0.000946946 | 1.00000i | \(0.500301\pi\) | ||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −31.3704 | −1.11681 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.2768 | −0.472069 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 64.0964 | 2.27613 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.95715 | 0.140346 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.2146 | 1.10568 | 0.552839 | − | 0.833288i | \(-0.313545\pi\) | ||||
0.552839 | + | 0.833288i | \(0.313545\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.15972 | 0.111783 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.64297 | 0.164051 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.80393 | −0.275395 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.93200 | −0.138585 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.98936 | 0.175634 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.153360 | −0.00539185 | −0.00269592 | − | 0.999996i | \(-0.500858\pi\) | ||||
−0.00269592 | + | 0.999996i | \(0.500858\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.3984 | 0.400253 | 0.200126 | − | 0.979770i | \(-0.435865\pi\) | ||||
0.200126 | + | 0.979770i | \(0.435865\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.3242 | −0.993371 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.65841 | −0.0931199 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 54.1615 | 1.89487 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17.6177 | −0.615612 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.9338 | −0.660795 | −0.330397 | − | 0.943842i | \(-0.607183\pi\) | ||||
−0.330397 | + | 0.943842i | \(0.607183\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.4815 | 1.48081 | 0.740405 | − | 0.672161i | \(-0.234634\pi\) | ||||
0.740405 | + | 0.672161i | \(0.234634\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.7754 | 0.409967 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.4445 | 1.58026 | 0.790129 | − | 0.612940i | \(-0.210013\pi\) | ||||
0.790129 | + | 0.612940i | \(0.210013\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 49.6222 | 1.72345 | 0.861725 | − | 0.507375i | \(-0.169384\pi\) | ||||
0.861725 | + | 0.507375i | \(0.169384\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.33021 | 0.150213 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.72311 | 0.302238 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.6757 | 0.715513 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.671792 | 0.0232205 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 53.2719 | 1.83915 | 0.919576 | − | 0.392913i | \(-0.128533\pi\) | ||||
0.919576 | + | 0.392913i | \(0.128533\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.22411 | 0.317695 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 31.5851 | 1.08656 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.79561 | 0.267860 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.4601 | −0.702189 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.42860 | 0.151811 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.3344 | 0.833194 | 0.416597 | − | 0.909091i | \(-0.363223\pi\) | ||||
0.416597 | + | 0.909091i | \(0.363223\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.49560 | −0.290543 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.88014 | 0.166702 | 0.0833512 | − | 0.996520i | \(-0.473438\pi\) | ||||
0.0833512 | + | 0.996520i | \(0.473438\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.3449 | −1.44479 | −0.722394 | − | 0.691481i | \(-0.756958\pi\) | ||||
−0.722394 | + | 0.691481i | \(0.756958\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.42311 | 0.218899 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −55.7214 | −1.89678 | −0.948389 | − | 0.317110i | \(-0.897287\pi\) | ||||
−0.948389 | + | 0.317110i | \(0.897287\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.683277 | 0.0232321 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.0664 | −0.545642 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −47.5603 | −1.61337 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.0798 | 0.815913 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.50834 | −0.0510495 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −32.1823 | −1.08796 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.5958 | −1.40459 | −0.702295 | − | 0.711886i | \(-0.747841\pi\) | ||||
−0.702295 | + | 0.711886i | \(0.747841\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.53864 | −0.153084 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.9100 | 1.74889 | 0.874446 | − | 0.485122i | \(-0.161225\pi\) | ||||
0.874446 | + | 0.485122i | \(0.161225\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.84338 | −0.297604 | −0.148802 | − | 0.988867i | \(-0.547542\pi\) | ||||
−0.148802 | + | 0.988867i | \(0.547542\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.66569 | 0.190450 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.7401 | 0.494925 | 0.247462 | − | 0.968897i | \(-0.420403\pi\) | ||||
0.247462 | + | 0.968897i | \(0.420403\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.6295 | −0.390042 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.69746 | 0.123870 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.46481 | −0.115945 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.9831 | 0.768241 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.03680 | −0.201563 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.671792 | −0.0224055 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.8891 | −0.562657 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.0674 | 0.834192 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.7144 | −0.389398 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.0429 | −0.665515 | −0.332757 | − | 0.943012i | \(-0.607979\pi\) | ||||
−0.332757 | + | 0.943012i | \(0.607979\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.26567 | 0.108315 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.47857 | 0.148382 | 0.0741908 | − | 0.997244i | \(-0.476363\pi\) | ||||
0.0741908 | + | 0.997244i | \(0.476363\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.0543 | −0.796081 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.3053 | 0.472919 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.06800 | 0.167360 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.4388 | 0.674214 | 0.337107 | − | 0.941466i | \(-0.390552\pi\) | ||||
0.337107 | + | 0.941466i | \(0.390552\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.5891 | 0.579582 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 54.8260 | 1.80462 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.1039 | 0.463734 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.93651 | −0.194981 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.2202 | −1.02430 | −0.512151 | − | 0.858895i | \(-0.671151\pi\) | ||||
−0.512151 | + | 0.858895i | \(0.671151\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.56537 | −0.313492 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25.8397 | 0.845955 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 28.6462 | 0.936831 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.5696 | −1.16201 | −0.581005 | − | 0.813900i | \(-0.697340\pi\) | ||||
−0.581005 | + | 0.813900i | \(0.697340\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.28452 | 0.237721 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.409490 | 0.0133490 | 0.00667449 | − | 0.999978i | \(-0.497875\pi\) | ||||
0.00667449 | + | 0.999978i | \(0.497875\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.20091 | 0.0716716 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.93200 | −0.127908 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.0270 | 1.39819 | 0.699095 | − | 0.715029i | \(-0.253586\pi\) | ||||
0.699095 | + | 0.715029i | \(0.253586\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.7414 | 0.413603 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.21892 | 0.266517 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.1891 | 0.556808 | 0.278404 | − | 0.960464i | \(-0.410195\pi\) | ||||
0.278404 | + | 0.960464i | \(0.410195\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.7514 | 0.347908 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.69746 | −0.119522 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23.7901 | −0.768223 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5487 | −0.985442 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.1575 | 0.359545 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.0692 | 0.710432 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.03839 | 0.258497 | 0.129249 | − | 0.991612i | \(-0.458743\pi\) | ||||
0.129249 | + | 0.991612i | \(0.458743\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36.2591 | 1.16481 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.4945 | 1.45999 | 0.729995 | − | 0.683453i | \(-0.239522\pi\) | ||||
0.729995 | + | 0.683453i | \(0.239522\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.78664 | −0.0893357 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −19.2256 | −0.615711 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.6237 | −0.499846 | −0.249923 | − | 0.968266i | \(-0.580405\pi\) | ||||
−0.249923 | + | 0.968266i | \(0.580405\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.1672 | 0.548666 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.50930 | −0.0481882 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.8606 | 0.442084 | 0.221042 | − | 0.975264i | \(-0.429054\pi\) | ||||
0.221042 | + | 0.975264i | \(0.429054\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.0532 | −0.447771 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.60361 | −0.0510434 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.58949 | 0.273130 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.4027 | −1.02930 | −0.514652 | − | 0.857399i | \(-0.672079\pi\) | ||||
−0.514652 | + | 0.857399i | \(0.672079\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.55431 | −0.112793 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.7117 | 0.910221 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.7250 | −1.03641 | −0.518206 | − | 0.855256i | \(-0.673400\pi\) | ||||
−0.518206 | + | 0.855256i | \(0.673400\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.42860 | 0.140115 |
(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 | 8004.2.a.e.1.8 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.e.1.8 | ✓ | 9 | 1.1 | even | 1 | trivial |