Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2368,2,Mod(1,2368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2368, 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("2368.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2368 = 2^{6} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2368.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: | \(18.9085751986\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 74) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2368.1 |
$q$-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 | ||||||||
\(3\) | −0.302776 | −0.174808 | −0.0874038 | − | 0.996173i | \(-0.527857\pi\) | ||||
−0.0874038 | + | 0.996173i | \(0.527857\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.30278 | −0.582619 | −0.291309 | − | 0.956629i | \(-0.594091\pi\) | ||||
−0.291309 | + | 0.956629i | \(0.594091\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.60555 | −1.74073 | −0.870367 | − | 0.492403i | \(-0.836119\pi\) | ||||
−0.870367 | + | 0.492403i | \(0.836119\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.90833 | −0.969442 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.30278 | 0.392802 | 0.196401 | − | 0.980524i | \(-0.437075\pi\) | ||||
0.196401 | + | 0.980524i | \(0.437075\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.30278 | 0.638675 | 0.319338 | − | 0.947641i | \(-0.396540\pi\) | ||||
0.319338 | + | 0.947641i | \(0.396540\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.394449 | 0.101846 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.00000 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.39445 | 0.304294 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.90833 | 1.44049 | 0.720243 | − | 0.693722i | \(-0.244030\pi\) | ||||
0.720243 | + | 0.693722i | \(0.244030\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.30278 | −0.660555 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.78890 | 0.344273 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.90833 | −1.28284 | −0.641422 | − | 0.767188i | \(-0.721655\pi\) | ||||
−0.641422 | + | 0.767188i | \(0.721655\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.30278 | −0.593196 | −0.296598 | − | 0.955002i | \(-0.595852\pi\) | ||||
−0.296598 | + | 0.955002i | \(0.595852\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.394449 | −0.0686647 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.00000 | 1.01419 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.697224 | −0.111645 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.908327 | −0.141857 | −0.0709284 | − | 0.997481i | \(-0.522596\pi\) | ||||
−0.0709284 | + | 0.997481i | \(0.522596\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.60555 | −1.00734 | −0.503669 | − | 0.863897i | \(-0.668017\pi\) | ||||
−0.503669 | + | 0.863897i | \(0.668017\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.78890 | 0.564815 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.60555 | 0.380059 | 0.190029 | − | 0.981778i | \(-0.439142\pi\) | ||||
0.190029 | + | 0.981778i | \(0.439142\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.2111 | 2.03016 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.81665 | 0.254382 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.69722 | −0.228854 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.605551 | −0.0802072 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.39445 | 0.441920 | 0.220960 | − | 0.975283i | \(-0.429081\pi\) | ||||
0.220960 | + | 0.975283i | \(0.429081\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.5139 | 1.34616 | 0.673082 | − | 0.739568i | \(-0.264970\pi\) | ||||
0.673082 | + | 0.739568i | \(0.264970\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13.3944 | 1.68754 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.00000 | −0.372104 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.5139 | 1.77315 | 0.886576 | − | 0.462583i | \(-0.153077\pi\) | ||||
0.886576 | + | 0.462583i | \(0.153077\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.09167 | −0.251808 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.69722 | −1.01793 | −0.508967 | − | 0.860786i | \(-0.669972\pi\) | ||||
−0.508967 | + | 0.860786i | \(0.669972\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.00000 | −0.683763 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.1194 | 1.81358 | 0.906789 | − | 0.421585i | \(-0.138526\pi\) | ||||
0.906789 | + | 0.421585i | \(0.138526\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.18335 | 0.909261 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.2111 | 1.88916 | 0.944582 | − | 0.328276i | \(-0.106467\pi\) | ||||
0.944582 | + | 0.328276i | \(0.106467\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.81665 | 0.847835 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.09167 | 0.224251 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.21110 | 0.552376 | 0.276188 | − | 0.961104i | \(-0.410929\pi\) | ||||
0.276188 | + | 0.961104i | \(0.410929\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.6056 | −1.11176 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.00000 | 0.103695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.60555 | −0.267324 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.4222 | 1.26128 | 0.630642 | − | 0.776074i | \(-0.282792\pi\) | ||||
0.630642 | + | 0.776074i | \(0.282792\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.78890 | −0.380799 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.4222 | −1.63407 | −0.817035 | − | 0.576588i | \(-0.804384\pi\) | ||||
−0.817035 | + | 0.576588i | \(0.804384\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.30278 | −0.325432 | −0.162716 | − | 0.986673i | \(-0.552025\pi\) | ||||
−0.162716 | + | 0.986673i | \(0.552025\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.81665 | −0.177287 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.30278 | 0.415965 | 0.207983 | − | 0.978133i | \(-0.433310\pi\) | ||||
0.207983 | + | 0.978133i | \(0.433310\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.302776 | 0.0287382 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.2111 | 1.05465 | 0.527326 | − | 0.849663i | \(-0.323195\pi\) | ||||
0.527326 | + | 0.849663i | \(0.323195\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.00000 | −0.839254 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.69722 | −0.619159 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 27.6333 | 2.53314 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.30278 | −0.845707 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.275019 | 0.0247977 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.8167 | 0.967471 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.78890 | 0.424946 | 0.212473 | − | 0.977167i | \(-0.431848\pi\) | ||||
0.212473 | + | 0.977167i | \(0.431848\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.00000 | 0.176090 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.39445 | 0.296574 | 0.148287 | − | 0.988944i | \(-0.452624\pi\) | ||||
0.148287 | + | 0.988944i | \(0.452624\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.21110 | −0.798704 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.33053 | −0.200580 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.90833 | −0.846525 | −0.423263 | − | 0.906007i | \(-0.639115\pi\) | ||||
−0.423263 | + | 0.906007i | \(0.639115\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.90833 | 0.755594 | 0.377797 | − | 0.925888i | \(-0.376682\pi\) | ||||
0.377797 | + | 0.925888i | \(0.376682\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.788897 | −0.0664372 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.00000 | 0.250873 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.00000 | 0.747409 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.30278 | −0.354887 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.81665 | 0.148826 | 0.0744130 | − | 0.997228i | \(-0.476292\pi\) | ||||
0.0744130 | + | 0.997228i | \(0.476292\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.3944 | 1.09002 | 0.545012 | − | 0.838428i | \(-0.316525\pi\) | ||||
0.545012 | + | 0.838428i | \(0.316525\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 17.4500 | 1.41075 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.30278 | 0.345607 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.21110 | −0.575509 | −0.287754 | − | 0.957704i | \(-0.592909\pi\) | ||||
−0.287754 | + | 0.957704i | \(0.592909\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.81665 | −0.144070 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −31.8167 | −2.50750 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.4222 | −1.59959 | −0.799795 | − | 0.600273i | \(-0.795059\pi\) | ||||
−0.799795 | + | 0.600273i | \(0.795059\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.513878 | 0.0400054 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.5139 | −0.968353 | −0.484176 | − | 0.874970i | \(-0.660881\pi\) | ||||
−0.484176 | + | 0.874970i | \(0.660881\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.69722 | −0.592094 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.81665 | −0.444811 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.2111 | 1.76471 | 0.882354 | − | 0.470587i | \(-0.155958\pi\) | ||||
0.882354 | + | 0.470587i | \(0.155958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.2111 | 1.14985 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.02776 | −0.0772509 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.81665 | 0.584244 | 0.292122 | − | 0.956381i | \(-0.405639\pi\) | ||||
0.292122 | + | 0.956381i | \(0.405639\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.0000 | −1.48659 | −0.743294 | − | 0.668965i | \(-0.766738\pi\) | ||||
−0.743294 | + | 0.668965i | \(0.766738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.18335 | −0.235320 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.30278 | 0.0957820 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.81665 | −0.571610 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.23886 | −0.599289 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.5139 | −0.905472 | −0.452736 | − | 0.891644i | \(-0.649552\pi\) | ||||
−0.452736 | + | 0.891644i | \(0.649552\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.00000 | −0.287926 | −0.143963 | − | 0.989583i | \(-0.545985\pi\) | ||||
−0.143963 | + | 0.989583i | \(0.545985\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.908327 | 0.0650466 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.42221 | 0.171706 | 0.0858528 | − | 0.996308i | \(-0.472639\pi\) | ||||
0.0858528 | + | 0.996308i | \(0.472639\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.39445 | −0.309961 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 31.8167 | 2.23309 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.18335 | 0.0826485 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −20.0917 | −1.39647 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.60555 | 0.180230 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.69722 | 0.461056 | 0.230528 | − | 0.973066i | \(-0.425955\pi\) | ||||
0.230528 | + | 0.973066i | \(0.425955\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.81665 | 0.124475 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.60555 | 0.586894 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.2111 | 1.03260 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.63331 | 0.177942 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.8167 | −0.929409 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.8167 | −1.05916 | −0.529581 | − | 0.848260i | \(-0.677651\pi\) | ||||
−0.529581 | + | 0.848260i | \(0.677651\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.60555 | 0.640370 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.81665 | −0.518810 | −0.259405 | − | 0.965769i | \(-0.583526\pi\) | ||||
−0.259405 | + | 0.965769i | \(0.583526\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.3944 | −1.14946 | −0.574729 | − | 0.818344i | \(-0.694892\pi\) | ||||
−0.574729 | + | 0.818344i | \(0.694892\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.81665 | 0.119527 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.51388 | −0.623275 | −0.311637 | − | 0.950201i | \(-0.600877\pi\) | ||||
−0.311637 | + | 0.950201i | \(0.600877\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.39445 | −0.221429 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.88057 | −0.317027 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.513878 | −0.0332400 | −0.0166200 | − | 0.999862i | \(-0.505291\pi\) | ||||
−0.0166200 | + | 0.999862i | \(0.505291\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.00000 | 0.515325 | 0.257663 | − | 0.966235i | \(-0.417048\pi\) | ||||
0.257663 | + | 0.966235i | \(0.417048\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.84441 | −0.503219 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.5139 | −1.18281 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.60555 | 0.293044 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.21110 | −0.330240 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.78890 | −0.428511 | −0.214256 | − | 0.976778i | \(-0.568733\pi\) | ||||
−0.214256 | + | 0.976778i | \(0.568733\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.00000 | 0.565825 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.36669 | −0.148208 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.2111 | −0.699329 | −0.349665 | − | 0.936875i | \(-0.613704\pi\) | ||||
−0.349665 | + | 0.936875i | \(0.613704\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.60555 | 0.286175 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.0917 | 1.24364 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.81665 | 0.481996 | 0.240998 | − | 0.970526i | \(-0.422525\pi\) | ||||
0.240998 | + | 0.970526i | \(0.422525\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.81665 | −0.480173 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.57779 | −0.0965595 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.78890 | 0.413926 | 0.206963 | − | 0.978349i | \(-0.433642\pi\) | ||||
0.206963 | + | 0.978349i | \(0.433642\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.42221 | −0.390121 | −0.195061 | − | 0.980791i | \(-0.562490\pi\) | ||||
−0.195061 | + | 0.980791i | \(0.562490\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.21110 | 0.194345 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.30278 | −0.259467 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.1194 | 1.50928 | 0.754640 | − | 0.656139i | \(-0.227811\pi\) | ||||
0.754640 | + | 0.656139i | \(0.227811\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.60555 | 0.575069 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0000 | −0.715860 | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||||
−0.357930 | + | 0.933748i | \(0.616517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.3944 | 1.03399 | 0.516996 | − | 0.855988i | \(-0.327050\pi\) | ||||
0.516996 | + | 0.855988i | \(0.327050\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.788897 | 0.0467303 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.18335 | 0.246935 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.76114 | −0.220482 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.0278 | 1.46214 | 0.731069 | − | 0.682304i | \(-0.239022\pi\) | ||||
0.731069 | + | 0.682304i | \(0.239022\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.42221 | −0.257471 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.33053 | 0.135231 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.9083 | 0.920002 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 30.4222 | 1.75351 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.97224 | 0.285648 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.6972 | −0.784301 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.09167 | 0.404743 | 0.202372 | − | 0.979309i | \(-0.435135\pi\) | ||||
0.202372 | + | 0.979309i | \(0.435135\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.09167 | −0.288722 | −0.144361 | − | 0.989525i | \(-0.546113\pi\) | ||||
−0.144361 | + | 0.989525i | \(0.546113\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.0278 | 1.52770 | 0.763850 | − | 0.645394i | \(-0.223307\pi\) | ||||
0.763850 | + | 0.645394i | \(0.223307\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −17.4500 | −0.983194 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.21110 | 0.292685 | 0.146342 | − | 0.989234i | \(-0.453250\pi\) | ||||
0.146342 | + | 0.989234i | \(0.453250\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.00000 | −0.503903 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.30278 | −0.0727138 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.0000 | −0.667698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.60555 | −0.421880 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.605551 | 0.0334871 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.0000 | −0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.21110 | 0.0665682 | 0.0332841 | − | 0.999446i | \(-0.489403\pi\) | ||||
0.0332841 | + | 0.999446i | \(0.489403\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.90833 | 0.159375 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.9083 | −1.03307 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.1194 | −1.04150 | −0.520751 | − | 0.853709i | \(-0.674348\pi\) | ||||
−0.520751 | + | 0.853709i | \(0.674348\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.39445 | −0.184361 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.30278 | −0.233008 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −33.2111 | −1.79323 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.72498 | 0.146708 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.8167 | 1.70801 | 0.854004 | − | 0.520267i | \(-0.174168\pi\) | ||||
0.854004 | + | 0.520267i | \(0.174168\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.2389 | 1.19042 | 0.595209 | − | 0.803571i | \(-0.297069\pi\) | ||||
0.595209 | + | 0.803571i | \(0.297069\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.11943 | 0.219879 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.8167 | 1.69343 | 0.846715 | − | 0.532047i | \(-0.178577\pi\) | ||||
0.846715 | + | 0.532047i | \(0.178577\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.81665 | 0.414865 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.36669 | −0.442812 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.2111 | 0.591699 | 0.295850 | − | 0.955235i | \(-0.404397\pi\) | ||||
0.295850 | + | 0.955235i | \(0.404397\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.81665 | 0.147836 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.3305 | 0.593067 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.8167 | 0.930022 | 0.465011 | − | 0.885305i | \(-0.346050\pi\) | ||||
0.465011 | + | 0.885305i | \(0.346050\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.64171 | 0.137522 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −27.6333 | −1.43465 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.81665 | −0.197619 | −0.0988094 | − | 0.995106i | \(-0.531503\pi\) | ||||
−0.0988094 | + | 0.995106i | \(0.531503\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.27502 | −0.169121 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.9083 | −0.819321 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.3305 | −0.787477 | −0.393738 | − | 0.919223i | \(-0.628818\pi\) | ||||
−0.393738 | + | 0.919223i | \(0.628818\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.44996 | −0.0742838 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.8444 | −1.06510 | −0.532550 | − | 0.846399i | \(-0.678766\pi\) | ||||
−0.532550 | + | 0.846399i | \(0.678766\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.81665 | 0.398374 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 19.2111 | 0.976555 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.8806 | 0.602369 | 0.301184 | − | 0.953566i | \(-0.402618\pi\) | ||||
0.301184 | + | 0.953566i | \(0.402618\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −41.4500 | −2.09621 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.02776 | −0.0518435 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.0000 | −1.05662 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.8167 | −1.39608 | −0.698039 | − | 0.716060i | \(-0.745944\pi\) | ||||
−0.698039 | + | 0.716060i | \(0.745944\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.78890 | 0.139620 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.8167 | 0.689971 | 0.344985 | − | 0.938608i | \(-0.387884\pi\) | ||||
0.344985 | + | 0.938608i | \(0.387884\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.60555 | −0.378859 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.6611 | −0.529753 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.30278 | −0.0645762 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.02776 | −0.248607 | −0.124303 | − | 0.992244i | \(-0.539670\pi\) | ||||
−0.124303 | + | 0.992244i | \(0.539670\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.00000 | 0.147979 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.6333 | −0.769265 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.4222 | −1.10066 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.69722 | −0.132084 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.1472 | −1.22852 | −0.614260 | − | 0.789104i | \(-0.710545\pi\) | ||||
−0.614260 | + | 0.789104i | \(0.710545\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.7250 | −1.39997 | −0.699985 | − | 0.714158i | \(-0.746810\pi\) | ||||
−0.699985 | + | 0.714158i | \(0.746810\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.57779 | −0.368445 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 19.8167 | 0.961249 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −48.4222 | −2.34331 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.908327 | −0.0438544 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.21110 | 0.251010 | 0.125505 | − | 0.992093i | \(-0.459945\pi\) | ||||
0.125505 | + | 0.992093i | \(0.459945\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.9361 | −0.573612 | −0.286806 | − | 0.957989i | \(-0.592593\pi\) | ||||
−0.286806 | + | 0.957989i | \(0.592593\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.72498 | −0.130653 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.8167 | 0.660940 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.33053 | 0.445322 | 0.222661 | − | 0.974896i | \(-0.428526\pi\) | ||||
0.222661 | + | 0.974896i | \(0.428526\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −41.3305 | −1.96812 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.275019 | 0.0130666 | 0.00653328 | − | 0.999979i | \(-0.497920\pi\) | ||||
0.00653328 | + | 0.999979i | \(0.497920\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.78890 | −0.321825 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.550039 | −0.0260159 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.788897 | −0.0372304 | −0.0186152 | − | 0.999827i | \(-0.505926\pi\) | ||||
−0.0186152 | + | 0.999827i | \(0.505926\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.18335 | −0.0557216 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.05551 | −0.190545 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.8167 | 0.647735 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.60555 | 0.215439 | 0.107719 | − | 0.994181i | \(-0.465645\pi\) | ||||
0.107719 | + | 0.994181i | \(0.465645\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.7334 | −0.500991 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.4222 | 0.764858 | 0.382429 | − | 0.923985i | \(-0.375088\pi\) | ||||
0.382429 | + | 0.923985i | \(0.375088\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.3028 | −1.40829 | −0.704145 | − | 0.710056i | \(-0.748669\pi\) | ||||
−0.704145 | + | 0.710056i | \(0.748669\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.30278 | −0.0604148 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −66.8444 | −3.08659 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.18335 | 0.100603 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.60555 | −0.395684 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.60555 | −0.303083 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17.4500 | −0.798979 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.1194 | −0.553751 | −0.276875 | − | 0.960906i | \(-0.589299\pi\) | ||||
−0.276875 | + | 0.960906i | \(0.589299\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.30278 | −0.104998 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.63331 | 0.438331 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.1833 | −0.734848 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.7889 | 1.03266 | 0.516332 | − | 0.856389i | \(-0.327297\pi\) | ||||
0.516332 | + | 0.856389i | \(0.327297\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.18335 | 0.279621 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.7250 | −0.664529 | −0.332265 | − | 0.943186i | \(-0.607813\pi\) | ||||
−0.332265 | + | 0.943186i | \(0.607813\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 41.4500 | 1.86681 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.93608 | 0.221860 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.6333 | 1.23952 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.23886 | 0.368822 | 0.184411 | − | 0.982849i | \(-0.440962\pi\) | ||||
0.184411 | + | 0.982849i | \(0.440962\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.78890 | 0.169275 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.5139 | 1.09302 | 0.546510 | − | 0.837453i | \(-0.315956\pi\) | ||||
0.546510 | + | 0.837453i | \(0.315956\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.3944 | 0.952040 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.33053 | 0.103503 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.8167 | 1.14430 | 0.572152 | − | 0.820148i | \(-0.306109\pi\) | ||||
0.572152 | + | 0.820148i | \(0.306109\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 40.0555 | 1.77195 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.57779 | 0.157964 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.30278 | 0.189603 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.39445 | 0.149288 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.02776 | −0.308484 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.63331 | −0.422043 | −0.211021 | − | 0.977481i | \(-0.567679\pi\) | ||||
−0.211021 | + | 0.977481i | \(0.567679\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.2389 | 1.40971 | 0.704853 | − | 0.709353i | \(-0.251013\pi\) | ||||
0.704853 | + | 0.709353i | \(0.251013\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.60555 | −0.201003 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.8167 | 0.863227 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.7250 | 1.07500 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.87217 | −0.428416 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.09167 | −0.0906004 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.60555 | −0.242349 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.36669 | −0.102130 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.5139 | 0.797449 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.9361 | 0.900113 | 0.450056 | − | 0.893000i | \(-0.351404\pi\) | ||||
0.450056 | + | 0.893000i | \(0.351404\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.05551 | 0.259867 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.60555 | 0.111610 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.3944 | −0.572705 | −0.286353 | − | 0.958124i | \(-0.592443\pi\) | ||||
−0.286353 | + | 0.958124i | \(0.592443\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −30.5778 | −1.30503 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.8167 | −0.588609 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −74.2389 | −3.15696 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.394449 | −0.0167434 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.51388 | 0.276002 | 0.138001 | − | 0.990432i | \(-0.455932\pi\) | ||||
0.138001 | + | 0.990432i | \(0.455932\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.2111 | −0.643361 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.36669 | 0.0999218 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 44.0555 | 1.85672 | 0.928359 | − | 0.371684i | \(-0.121220\pi\) | ||||
0.928359 | + | 0.371684i | \(0.121220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.6056 | −0.614460 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −37.6888 | −1.58278 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.4222 | −0.436922 | −0.218461 | − | 0.975846i | \(-0.570104\pi\) | ||||
−0.218461 | + | 0.975846i | \(0.570104\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.3028 | −0.849645 | −0.424822 | − | 0.905277i | \(-0.639663\pi\) | ||||
−0.424822 | + | 0.905277i | \(0.639663\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.78890 | 0.158283 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.8167 | −0.951520 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.2389 | −1.17560 | −0.587800 | − | 0.809007i | \(-0.700006\pi\) | ||||
−0.587800 | + | 0.809007i | \(0.700006\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.21110 | 0.0503317 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −79.2666 | −3.28853 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.81665 | 0.323733 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.72498 | 0.360734 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.36669 | −0.0976838 | −0.0488419 | − | 0.998807i | \(-0.515553\pi\) | ||||
−0.0488419 | + | 0.998807i | \(0.515553\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.60555 | −0.272177 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.81665 | −0.0747272 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 36.5139 | 1.49945 | 0.749723 | − | 0.661752i | \(-0.230187\pi\) | ||||
0.749723 | + | 0.661752i | \(0.230187\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.0000 | −1.47586 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.733385 | −0.0300154 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.2111 | 1.43869 | 0.719343 | − | 0.694655i | \(-0.244443\pi\) | ||||
0.719343 | + | 0.694655i | \(0.244443\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.6972 | −0.844257 | −0.422129 | − | 0.906536i | \(-0.638717\pi\) | ||||
−0.422129 | + | 0.906536i | \(0.638717\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −42.2111 | −1.71897 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.1194 | 0.492725 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.5139 | 1.27911 | 0.639554 | − | 0.768746i | \(-0.279119\pi\) | ||||
0.639554 | + | 0.768746i | \(0.279119\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.63331 | −0.390361 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.00000 | 0.242734 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.18335 | 0.330522 | 0.165261 | − | 0.986250i | \(-0.447153\pi\) | ||||
0.165261 | + | 0.986250i | \(0.447153\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.358288 | −0.0144476 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 47.5694 | 1.91507 | 0.957536 | − | 0.288314i | \(-0.0930948\pi\) | ||||
0.957536 | + | 0.288314i | \(0.0930948\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.69722 | −0.108411 | −0.0542053 | − | 0.998530i | \(-0.517263\pi\) | ||||
−0.0542053 | + | 0.998530i | \(0.517263\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.3583 | 0.495921 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.0000 | −0.961540 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.42221 | 0.0968882 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.788897 | −0.0315055 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.00000 | 0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.3028 | −0.728622 | −0.364311 | − | 0.931277i | \(-0.618695\pi\) | ||||
−0.364311 | + | 0.931277i | \(0.618695\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.02776 | −0.0805961 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.23886 | −0.247582 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.7250 | 1.29661 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.4500 | 0.690310 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.48612 | −0.0981959 | −0.0490980 | − | 0.998794i | \(-0.515635\pi\) | ||||
−0.0490980 | + | 0.998794i | \(0.515635\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.8167 | −1.17585 | −0.587927 | − | 0.808914i | \(-0.700056\pi\) | ||||
−0.587927 | + | 0.808914i | \(0.700056\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.60555 | −0.102593 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.9361 | 1.01965 | 0.509826 | − | 0.860277i | \(-0.329710\pi\) | ||||
0.509826 | + | 0.860277i | \(0.329710\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.42221 | 0.173587 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.60555 | −0.180506 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.90833 | −0.270344 | −0.135172 | − | 0.990822i | \(-0.543159\pi\) | ||||
−0.135172 | + | 0.990822i | \(0.543159\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.42221 | −0.172790 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 25.2944 | 0.986827 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.1194 | −1.64074 | −0.820370 | − | 0.571833i | \(-0.806233\pi\) | ||||
−0.820370 | + | 0.571833i | \(0.806233\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.4861 | 0.485654 | 0.242827 | − | 0.970070i | \(-0.421925\pi\) | ||||
0.242827 | + | 0.970070i | \(0.421925\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.18335 | 0.162468 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.0000 | 0.465340 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −47.7250 | −1.84792 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.78890 | 0.185149 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.6972 | 0.528775 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.3028 | 0.936803 | 0.468402 | − | 0.883516i | \(-0.344830\pi\) | ||||
0.468402 | + | 0.883516i | \(0.344830\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.90833 | −0.227412 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.2389 | 1.39277 | 0.696386 | − | 0.717667i | \(-0.254790\pi\) | ||||
0.696386 | + | 0.717667i | \(0.254790\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −57.2111 | −2.19556 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.36669 | 0.0906918 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0000 | 0.459167 | 0.229584 | − | 0.973289i | \(-0.426264\pi\) | ||||
0.229584 | + | 0.973289i | \(0.426264\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.9083 | 0.493202 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.26662 | 0.200934 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.8167 | 0.526373 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.00000 | 0.304334 | 0.152167 | − | 0.988355i | \(-0.451375\pi\) | ||||
0.152167 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.4500 | 0.662869 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.6056 | −0.440224 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.44996 | 0.206432 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.88057 | 0.108953 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.8806 | −0.562031 | −0.281016 | − | 0.959703i | \(-0.590671\pi\) | ||||
−0.281016 | + | 0.959703i | \(0.590671\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.00000 | −0.0754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.02776 | 0.0387075 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 75.6333 | 2.84448 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.66947 | 0.0626982 | 0.0313491 | − | 0.999508i | \(-0.490020\pi\) | ||||
0.0313491 | + | 0.999508i | \(0.490020\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −46.8806 | −1.75816 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.8167 | −0.854490 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.90833 | −0.146163 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.155590 | 0.00581061 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.36669 | 0.312025 | 0.156012 | − | 0.987755i | \(-0.450136\pi\) | ||||
0.156012 | + | 0.987755i | \(0.450136\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.2111 | 0.566491 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.42221 | −0.0900828 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.8167 | 0.847389 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.9083 | −1.10924 | −0.554619 | − | 0.832104i | \(-0.687136\pi\) | ||||
−0.554619 | + | 0.832104i | \(0.687136\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.1749 | −0.821294 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.6333 | 1.46589 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.6333 | −1.09453 | −0.547266 | − | 0.836959i | \(-0.684331\pi\) | ||||
−0.547266 | + | 0.836959i | \(0.684331\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.60555 | 0.206764 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.9083 | 0.696497 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.3305 | −1.55715 | −0.778577 | − | 0.627549i | \(-0.784058\pi\) | ||||
−0.778577 | + | 0.627549i | \(0.784058\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.39445 | −0.0512264 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.4500 | −1.30053 | −0.650266 | − | 0.759706i | \(-0.725343\pi\) | ||||
−0.650266 | + | 0.759706i | \(0.725343\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.36669 | −0.0867089 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −50.0555 | −1.83144 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.8167 | −0.724085 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.0000 | −0.510867 | −0.255434 | − | 0.966827i | \(-0.582218\pi\) | ||||
−0.255434 | + | 0.966827i | \(0.582218\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.05551 | 0.0749070 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.4500 | −0.635069 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.30278 | −0.338115 | −0.169058 | − | 0.985606i | \(-0.554072\pi\) | ||||
−0.169058 | + | 0.985606i | \(0.554072\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.72498 | −0.0989105 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.1194 | 1.52683 | 0.763414 | − | 0.645909i | \(-0.223522\pi\) | ||||
0.763414 | + | 0.645909i | \(0.223522\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.21110 | 0.333464 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −22.7334 | −0.821927 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.81665 | 0.282243 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.39445 | 0.122248 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 50.0555 | 1.80037 | 0.900186 | − | 0.435506i | \(-0.143431\pi\) | ||||
0.900186 | + | 0.435506i | \(0.143431\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.9083 | 0.391839 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.39445 | −0.0500256 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.81665 | −0.0650884 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.81665 | −0.279702 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.3583 | −0.441649 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.39445 | 0.335302 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.2111 | 0.898679 | 0.449339 | − | 0.893361i | \(-0.351659\pi\) | ||||
0.449339 | + | 0.893361i | \(0.351659\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.36669 | −0.0842565 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −51.6333 | −1.83587 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.2111 | 0.859761 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.36669 | 0.0839379 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.3305 | 0.613879 | 0.306939 | − | 0.951729i | \(-0.400695\pi\) | ||||
0.306939 | + | 0.951729i | \(0.400695\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.6333 | −0.553067 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.1556 | −0.535496 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.3305 | −0.399846 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 41.4500 | 1.46092 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.05551 | −0.0723575 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.4500 | 1.03541 | 0.517703 | − | 0.855561i | \(-0.326787\pi\) | ||||
0.517703 | + | 0.855561i | \(0.326787\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.1472 | 1.90136 | 0.950682 | − | 0.310166i | \(-0.100385\pi\) | ||||
0.950682 | + | 0.310166i | \(0.100385\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.94449 | 0.0681961 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 26.6056 | 0.931952 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.2111 | −0.462198 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 30.8444 | 1.07779 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.2111 | −0.391270 | −0.195635 | − | 0.980677i | \(-0.562677\pi\) | ||||
−0.195635 | + | 0.980677i | \(0.562677\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.8444 | 0.447728 | 0.223864 | − | 0.974620i | \(-0.428133\pi\) | ||||
0.223864 | + | 0.974620i | \(0.428133\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.30278 | 0.0453568 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.3944 | 0.952598 | 0.476299 | − | 0.879283i | \(-0.341978\pi\) | ||||
0.476299 | + | 0.879283i | \(0.341978\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.72498 | −0.164105 | −0.0820527 | − | 0.996628i | \(-0.526148\pi\) | ||||
−0.0820527 | + | 0.996628i | \(0.526148\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.60555 | −0.263834 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −85.2666 | −2.95431 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.3028 | 0.564181 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.90833 | −0.204222 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 49.0278 | 1.69263 | 0.846313 | − | 0.532686i | \(-0.178817\pi\) | ||||
0.846313 | + | 0.532686i | \(0.178817\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.7250 | 0.645689 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.63331 | 0.125138 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.0278 | 0.344965 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 42.8444 | 1.47215 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.26662 | −0.180750 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.90833 | −0.236814 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.5416 | 0.395178 | 0.197589 | − | 0.980285i | \(-0.436689\pi\) | ||||
0.197589 | + | 0.980285i | \(0.436689\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.57779 | 0.259155 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.8444 | −0.507075 | −0.253538 | − | 0.967326i | \(-0.581594\pi\) | ||||
−0.253538 | + | 0.967326i | \(0.581594\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.0555 | −0.820764 | −0.410382 | − | 0.911914i | \(-0.634605\pi\) | ||||
−0.410382 | + | 0.911914i | \(0.634605\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.26662 | −0.0431661 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.0000 | −0.408485 | −0.204242 | − | 0.978920i | \(-0.565473\pi\) | ||||
−0.204242 | + | 0.978920i | \(0.565473\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.2389 | −1.02815 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.75274 | −0.195373 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.0000 | 0.712376 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.4222 | 1.13247 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −36.1278 | −1.22274 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −49.8167 | −1.68411 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.21110 | −0.243502 | −0.121751 | − | 0.992561i | \(-0.538851\pi\) | ||||
−0.121751 | + | 0.992561i | \(0.538851\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.57779 | −0.255593 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.5416 | 0.860520 | 0.430260 | − | 0.902705i | \(-0.358422\pi\) | ||||
0.430260 | + | 0.902705i | \(0.358422\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.42221 | −0.0815137 | −0.0407568 | − | 0.999169i | \(-0.512977\pi\) | ||||
−0.0407568 | + | 0.999169i | \(0.512977\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.33894 | 0.0450078 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.4222 | −0.954324 | −0.477162 | − | 0.878815i | \(-0.658335\pi\) | ||||
−0.477162 | + | 0.878815i | \(0.658335\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.0555 | −0.739718 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.6611 | 0.357159 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.21110 | 0.174383 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.1833 | −0.340392 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.81665 | −0.160823 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.8167 | 0.760978 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.21110 | −0.306526 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26.0555 | 0.866115 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.0000 | 0.863316 | 0.431658 | − | 0.902037i | \(-0.357929\pi\) | ||||
0.431658 | + | 0.902037i | \(0.357929\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 47.7611 | 1.58414 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.4222 | 1.53804 | 0.769018 | − | 0.639227i | \(-0.220746\pi\) | ||||
0.769018 | + | 0.639227i | \(0.220746\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.4222 | 0.742067 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.14719 | 0.137102 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.6333 | −0.516257 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.4222 | 1.26743 | 0.633716 | − | 0.773566i | \(-0.281529\pi\) | ||||
0.633716 | + | 0.773566i | \(0.281529\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.14719 | −0.0707522 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.8167 | −0.454781 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.30278 | 0.108595 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.60555 | 0.315488 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.5139 | −1.19798 | −0.598991 | − | 0.800756i | \(-0.704431\pi\) | ||||
−0.598991 | + | 0.800756i | \(0.704431\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.4222 | 0.931500 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.54163 | 0.0504708 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.1833 | 0.333031 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.9083 | −0.944394 | −0.472197 | − | 0.881493i | \(-0.656539\pi\) | ||||
−0.472197 | + | 0.881493i | \(0.656539\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.18335 | −0.267053 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.81665 | 0.254816 | 0.127408 | − | 0.991850i | \(-0.459334\pi\) | ||||
0.127408 | + | 0.991850i | \(0.459334\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.27502 | −0.204343 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.7334 | 0.349157 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.6333 | 1.28791 | 0.643955 | − | 0.765064i | \(-0.277293\pi\) | ||||
0.643955 | + | 0.765064i | \(0.277293\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.0278 | −0.650128 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.57779 | −0.0511635 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.7527 | −0.607461 | −0.303730 | − | 0.952758i | \(-0.598232\pi\) | ||||
−0.303730 | + | 0.952758i | \(0.598232\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.3028 | 0.527545 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.72498 | 0.0880861 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.6333 | 1.47358 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.0917 | −0.648118 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.5139 | −0.403254 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.21110 | 0.167751 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.7250 | −0.827260 | −0.413630 | − | 0.910445i | \(-0.635739\pi\) | ||||
−0.413630 | + | 0.910445i | \(0.635739\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.63331 | 0.116719 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.5416 | 1.01222 | 0.506110 | − | 0.862469i | \(-0.331083\pi\) | ||||
0.506110 | + | 0.862469i | \(0.331083\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −41.0278 | −1.31529 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.30278 | 0.0737478 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.0000 | 0.575871 | 0.287936 | − | 0.957650i | \(-0.407031\pi\) | ||||
0.287936 | + | 0.957650i | \(0.407031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.78890 | 0.216974 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.81665 | 0.185711 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.0000 | 0.382741 | 0.191370 | − | 0.981518i | \(-0.438707\pi\) | ||||
0.191370 | + | 0.981518i | \(0.438707\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.81665 | −0.249059 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.63331 | 0.115649 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −45.6333 | −1.45105 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.3028 | −1.72498 | −0.862492 | − | 0.506070i | \(-0.831098\pi\) | ||||
−0.862492 | + | 0.506070i | \(0.831098\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.366692 | −0.0116366 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.15559 | −0.100039 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.5778 | 0.746716 | 0.373358 | − | 0.927687i | \(-0.378206\pi\) | ||||
0.373358 | + | 0.927687i | \(0.378206\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.78890 | −0.0565982 |
(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 | 2368.2.a.ba.1.1 | 2 | ||
4.3 | odd | 2 | 2368.2.a.s.1.2 | 2 | |||
8.3 | odd | 2 | 74.2.a.a.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 592.2.a.f.1.2 | 2 | |||
24.5 | odd | 2 | 5328.2.a.bf.1.1 | 2 | |||
24.11 | even | 2 | 666.2.a.j.1.1 | 2 | |||
40.3 | even | 4 | 1850.2.b.i.149.3 | 4 | |||
40.19 | odd | 2 | 1850.2.a.u.1.2 | 2 | |||
40.27 | even | 4 | 1850.2.b.i.149.2 | 4 | |||
56.27 | even | 2 | 3626.2.a.a.1.2 | 2 | |||
88.43 | even | 2 | 8954.2.a.p.1.1 | 2 | |||
296.147 | odd | 2 | 2738.2.a.l.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.a.a.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
592.2.a.f.1.2 | 2 | 8.5 | even | 2 | |||
666.2.a.j.1.1 | 2 | 24.11 | even | 2 | |||
1850.2.a.u.1.2 | 2 | 40.19 | odd | 2 | |||
1850.2.b.i.149.2 | 4 | 40.27 | even | 4 | |||
1850.2.b.i.149.3 | 4 | 40.3 | even | 4 | |||
2368.2.a.s.1.2 | 2 | 4.3 | odd | 2 | |||
2368.2.a.ba.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2738.2.a.l.1.1 | 2 | 296.147 | odd | 2 | |||
3626.2.a.a.1.2 | 2 | 56.27 | even | 2 | |||
5328.2.a.bf.1.1 | 2 | 24.5 | odd | 2 | |||
8954.2.a.p.1.1 | 2 | 88.43 | even | 2 |