Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6930,2,Mod(1,6930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6930, 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("6930.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6930 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6930.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: | \(55.3363286007\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2310) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6930.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.46410 | −0.960769 | −0.480384 | − | 0.877058i | \(-0.659503\pi\) | ||||
−0.480384 | + | 0.877058i | \(0.659503\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −5.46410 | −1.13934 | −0.569672 | − | 0.821872i | \(-0.692930\pi\) | ||||
−0.569672 | + | 0.821872i | \(0.692930\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.46410 | 0.679366 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.92820 | −1.24434 | −0.622171 | − | 0.782881i | \(-0.713749\pi\) | ||||
−0.622171 | + | 0.782881i | \(0.713749\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.46410 | 0.594089 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.535898 | 0.0881012 | 0.0440506 | − | 0.999029i | \(-0.485974\pi\) | ||||
0.0440506 | + | 0.999029i | \(0.485974\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −4.92820 | −0.769656 | −0.384828 | − | 0.922988i | \(-0.625739\pi\) | ||||
−0.384828 | + | 0.922988i | \(0.625739\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.9282 | 1.66654 | 0.833268 | − | 0.552870i | \(-0.186467\pi\) | ||||
0.833268 | + | 0.552870i | \(0.186467\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.46410 | 0.805638 | ||||||||
\(47\) | 6.92820 | 1.01058 | 0.505291 | − | 0.862949i | \(-0.331385\pi\) | ||||
0.505291 | + | 0.862949i | \(0.331385\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.46410 | −0.480384 | ||||||||
\(53\) | 0.928203 | 0.127499 | 0.0637493 | − | 0.997966i | \(-0.479694\pi\) | ||||
0.0637493 | + | 0.997966i | \(0.479694\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.00000 | 0.262613 | ||||||||
\(59\) | −10.9282 | −1.42273 | −0.711365 | − | 0.702822i | \(-0.751923\pi\) | ||||
−0.711365 | + | 0.702822i | \(0.751923\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.92820 | 1.14314 | 0.571570 | − | 0.820554i | \(-0.306335\pi\) | ||||
0.571570 | + | 0.820554i | \(0.306335\pi\) | |||||||
\(62\) | 6.92820 | 0.879883 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.46410 | −0.429669 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.53590 | 0.309809 | 0.154905 | − | 0.987929i | \(-0.450493\pi\) | ||||
0.154905 | + | 0.987929i | \(0.450493\pi\) | |||||||
\(68\) | −3.46410 | −0.420084 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | 4.00000 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.9282 | 1.51313 | 0.756566 | − | 0.653917i | \(-0.226876\pi\) | ||||
0.756566 | + | 0.653917i | \(0.226876\pi\) | |||||||
\(74\) | −0.535898 | −0.0622969 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.92820 | 0.544229 | ||||||||
\(83\) | 6.92820 | 0.760469 | 0.380235 | − | 0.924890i | \(-0.375843\pi\) | ||||
0.380235 | + | 0.924890i | \(0.375843\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.46410 | −0.375735 | ||||||||
\(86\) | −10.9282 | −1.17842 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 3.46410 | 0.367194 | 0.183597 | − | 0.983002i | \(-0.441226\pi\) | ||||
0.183597 | + | 0.983002i | \(0.441226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.46410 | −0.363137 | ||||||||
\(92\) | −5.46410 | −0.569672 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.92820 | −0.714590 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.8564 | 1.60997 | 0.804987 | − | 0.593292i | \(-0.202172\pi\) | ||||
0.804987 | + | 0.593292i | \(0.202172\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 15.8564 | 1.57777 | 0.788886 | − | 0.614540i | \(-0.210658\pi\) | ||||
0.788886 | + | 0.614540i | \(0.210658\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.0000 | 1.57653 | 0.788263 | − | 0.615338i | \(-0.210980\pi\) | ||||
0.788263 | + | 0.615338i | \(0.210980\pi\) | |||||||
\(104\) | 3.46410 | 0.339683 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.928203 | −0.0901551 | ||||||||
\(107\) | −6.92820 | −0.669775 | −0.334887 | − | 0.942258i | \(-0.608698\pi\) | ||||
−0.334887 | + | 0.942258i | \(0.608698\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.39230 | −0.612272 | −0.306136 | − | 0.951988i | \(-0.599036\pi\) | ||||
−0.306136 | + | 0.951988i | \(0.599036\pi\) | |||||||
\(110\) | 1.00000 | 0.0953463 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −4.53590 | −0.426701 | −0.213351 | − | 0.976976i | \(-0.568438\pi\) | ||||
−0.213351 | + | 0.976976i | \(0.568438\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.46410 | −0.509530 | ||||||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.9282 | 1.00602 | ||||||||
\(119\) | −3.46410 | −0.317554 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −8.92820 | −0.808322 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.92820 | −0.622171 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.92820 | −0.259836 | −0.129918 | − | 0.991525i | \(-0.541471\pi\) | ||||
−0.129918 | + | 0.991525i | \(0.541471\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.46410 | 0.303822 | ||||||||
\(131\) | 14.9282 | 1.30428 | 0.652142 | − | 0.758097i | \(-0.273871\pi\) | ||||
0.652142 | + | 0.758097i | \(0.273871\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.53590 | −0.219068 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.46410 | 0.297044 | ||||||||
\(137\) | 11.4641 | 0.979444 | 0.489722 | − | 0.871879i | \(-0.337098\pi\) | ||||
0.489722 | + | 0.871879i | \(0.337098\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.9282 | 0.926918 | 0.463459 | − | 0.886118i | \(-0.346608\pi\) | ||||
0.463459 | + | 0.886118i | \(0.346608\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.00000 | −0.335673 | ||||||||
\(143\) | 3.46410 | 0.289683 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | −12.9282 | −1.06995 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.535898 | 0.0440506 | ||||||||
\(149\) | 0.928203 | 0.0760414 | 0.0380207 | − | 0.999277i | \(-0.487895\pi\) | ||||
0.0380207 | + | 0.999277i | \(0.487895\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | −6.92820 | −0.556487 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.7846 | 1.81841 | 0.909205 | − | 0.416349i | \(-0.136691\pi\) | ||||
0.909205 | + | 0.416349i | \(0.136691\pi\) | |||||||
\(158\) | −8.00000 | −0.636446 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −5.46410 | −0.430632 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.53590 | 0.198627 | 0.0993134 | − | 0.995056i | \(-0.468335\pi\) | ||||
0.0993134 | + | 0.995056i | \(0.468335\pi\) | |||||||
\(164\) | −4.92820 | −0.384828 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.92820 | −0.537733 | ||||||||
\(167\) | 2.53590 | 0.196234 | 0.0981169 | − | 0.995175i | \(-0.468718\pi\) | ||||
0.0981169 | + | 0.995175i | \(0.468718\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 3.46410 | 0.265684 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.9282 | 0.833268 | ||||||||
\(173\) | −4.92820 | −0.374684 | −0.187342 | − | 0.982295i | \(-0.559987\pi\) | ||||
−0.187342 | + | 0.982295i | \(0.559987\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.46410 | −0.259645 | ||||||||
\(179\) | −20.7846 | −1.55351 | −0.776757 | − | 0.629800i | \(-0.783137\pi\) | ||||
−0.776757 | + | 0.629800i | \(0.783137\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.4641 | −1.74407 | −0.872036 | − | 0.489441i | \(-0.837201\pi\) | ||||
−0.872036 | + | 0.489441i | \(0.837201\pi\) | |||||||
\(182\) | 3.46410 | 0.256776 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.46410 | 0.402819 | ||||||||
\(185\) | 0.535898 | 0.0394000 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.46410 | 0.253320 | ||||||||
\(188\) | 6.92820 | 0.505291 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.07180 | −0.0775525 | −0.0387762 | − | 0.999248i | \(-0.512346\pi\) | ||||
−0.0387762 | + | 0.999248i | \(0.512346\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.9282 | 1.79437 | 0.897186 | − | 0.441654i | \(-0.145608\pi\) | ||||
0.897186 | + | 0.441654i | \(0.145608\pi\) | |||||||
\(194\) | −15.8564 | −1.13842 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.92820 | 0.491127 | 0.245564 | − | 0.969380i | \(-0.421027\pi\) | ||||
0.245564 | + | 0.969380i | \(0.421027\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.8564 | −1.11565 | ||||||||
\(203\) | −2.00000 | −0.140372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.92820 | −0.344201 | ||||||||
\(206\) | −16.0000 | −1.11477 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.46410 | −0.240192 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.3205 | 0.779336 | 0.389668 | − | 0.920955i | \(-0.372590\pi\) | ||||
0.389668 | + | 0.920955i | \(0.372590\pi\) | |||||||
\(212\) | 0.928203 | 0.0637493 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.92820 | 0.473602 | ||||||||
\(215\) | 10.9282 | 0.745297 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.92820 | −0.470317 | ||||||||
\(218\) | 6.39230 | 0.432942 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.7846 | −1.12398 | −0.561990 | − | 0.827144i | \(-0.689964\pi\) | ||||
−0.561990 | + | 0.827144i | \(0.689964\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.53590 | 0.301723 | ||||||||
\(227\) | 6.92820 | 0.459841 | 0.229920 | − | 0.973209i | \(-0.426153\pi\) | ||||
0.229920 | + | 0.973209i | \(0.426153\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.3923 | −1.21540 | −0.607699 | − | 0.794168i | \(-0.707907\pi\) | ||||
−0.607699 | + | 0.794168i | \(0.707907\pi\) | |||||||
\(230\) | 5.46410 | 0.360292 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.00000 | 0.131306 | ||||||||
\(233\) | −2.00000 | −0.131024 | −0.0655122 | − | 0.997852i | \(-0.520868\pi\) | ||||
−0.0655122 | + | 0.997852i | \(0.520868\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.92820 | 0.451946 | ||||||||
\(236\) | −10.9282 | −0.711365 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.46410 | 0.224544 | ||||||||
\(239\) | 16.3923 | 1.06033 | 0.530165 | − | 0.847894i | \(-0.322130\pi\) | ||||
0.530165 | + | 0.847894i | \(0.322130\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.9282 | −1.34810 | −0.674052 | − | 0.738684i | \(-0.735448\pi\) | ||||
−0.674052 | + | 0.738684i | \(0.735448\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.92820 | 0.571570 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.92820 | 0.439941 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 18.9282 | 1.19474 | 0.597369 | − | 0.801967i | \(-0.296213\pi\) | ||||
0.597369 | + | 0.801967i | \(0.296213\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.46410 | 0.343525 | ||||||||
\(254\) | 2.92820 | 0.183732 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.07180 | 0.191613 | 0.0958067 | − | 0.995400i | \(-0.469457\pi\) | ||||
0.0958067 | + | 0.995400i | \(0.469457\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.535898 | 0.0332991 | ||||||||
\(260\) | −3.46410 | −0.214834 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −14.9282 | −0.922267 | ||||||||
\(263\) | −24.7846 | −1.52828 | −0.764142 | − | 0.645048i | \(-0.776837\pi\) | ||||
−0.764142 | + | 0.645048i | \(0.776837\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.928203 | 0.0570191 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.53590 | 0.154905 | ||||||||
\(269\) | 3.07180 | 0.187291 | 0.0936454 | − | 0.995606i | \(-0.470148\pi\) | ||||
0.0936454 | + | 0.995606i | \(0.470148\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.8564 | 1.32768 | 0.663841 | − | 0.747874i | \(-0.268925\pi\) | ||||
0.663841 | + | 0.747874i | \(0.268925\pi\) | |||||||
\(272\) | −3.46410 | −0.210042 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.4641 | −0.692572 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.0000 | −0.600842 | −0.300421 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300421 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(278\) | −10.9282 | −0.655430 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −6.39230 | −0.381333 | −0.190666 | − | 0.981655i | \(-0.561065\pi\) | ||||
−0.190666 | + | 0.981655i | \(0.561065\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.46410 | −0.324807 | −0.162404 | − | 0.986724i | \(-0.551925\pi\) | ||||
−0.162404 | + | 0.986724i | \(0.551925\pi\) | |||||||
\(284\) | 4.00000 | 0.237356 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.46410 | −0.204837 | ||||||||
\(287\) | −4.92820 | −0.290903 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 2.00000 | 0.117444 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.9282 | 0.756566 | ||||||||
\(293\) | 14.0000 | 0.817889 | 0.408944 | − | 0.912559i | \(-0.365897\pi\) | ||||
0.408944 | + | 0.912559i | \(0.365897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.9282 | −0.636265 | ||||||||
\(296\) | −0.535898 | −0.0311485 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.928203 | −0.0537694 | ||||||||
\(299\) | 18.9282 | 1.09465 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.9282 | 0.629891 | ||||||||
\(302\) | −8.00000 | −0.460348 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.92820 | 0.511227 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.3205 | −1.55926 | −0.779632 | − | 0.626238i | \(-0.784594\pi\) | ||||
−0.779632 | + | 0.626238i | \(0.784594\pi\) | |||||||
\(308\) | −1.00000 | −0.0569803 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.92820 | 0.393496 | ||||||||
\(311\) | −13.4641 | −0.763479 | −0.381740 | − | 0.924270i | \(-0.624675\pi\) | ||||
−0.381740 | + | 0.924270i | \(0.624675\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −33.7128 | −1.90556 | −0.952780 | − | 0.303660i | \(-0.901791\pi\) | ||||
−0.952780 | + | 0.303660i | \(0.901791\pi\) | |||||||
\(314\) | −22.7846 | −1.28581 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.00000 | 0.450035 | ||||||||
\(317\) | 16.9282 | 0.950783 | 0.475391 | − | 0.879774i | \(-0.342306\pi\) | ||||
0.475391 | + | 0.879774i | \(0.342306\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.00000 | 0.111979 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.46410 | 0.304502 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.46410 | −0.192154 | ||||||||
\(326\) | −2.53590 | −0.140450 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.92820 | 0.272115 | ||||||||
\(329\) | 6.92820 | 0.381964 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(332\) | 6.92820 | 0.380235 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.53590 | −0.138758 | ||||||||
\(335\) | 2.53590 | 0.138551 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.7846 | −1.02326 | −0.511631 | − | 0.859205i | \(-0.670959\pi\) | ||||
−0.511631 | + | 0.859205i | \(0.670959\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.46410 | −0.187867 | ||||||||
\(341\) | 6.92820 | 0.375183 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −10.9282 | −0.589209 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.92820 | 0.264942 | ||||||||
\(347\) | 14.9282 | 0.801388 | 0.400694 | − | 0.916212i | \(-0.368769\pi\) | ||||
0.400694 | + | 0.916212i | \(0.368769\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.0718 | −0.806775 | −0.403387 | − | 0.915029i | \(-0.632167\pi\) | ||||
−0.403387 | + | 0.915029i | \(0.632167\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −7.07180 | −0.376394 | −0.188197 | − | 0.982131i | \(-0.560264\pi\) | ||||
−0.188197 | + | 0.982131i | \(0.560264\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.00000 | 0.212298 | ||||||||
\(356\) | 3.46410 | 0.183597 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.7846 | 1.09850 | ||||||||
\(359\) | −2.53590 | −0.133840 | −0.0669198 | − | 0.997758i | \(-0.521317\pi\) | ||||
−0.0669198 | + | 0.997758i | \(0.521317\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 23.4641 | 1.23325 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.46410 | −0.181568 | ||||||||
\(365\) | 12.9282 | 0.676693 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.0000 | 0.835193 | 0.417597 | − | 0.908633i | \(-0.362873\pi\) | ||||
0.417597 | + | 0.908633i | \(0.362873\pi\) | |||||||
\(368\) | −5.46410 | −0.284836 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.535898 | −0.0278600 | ||||||||
\(371\) | 0.928203 | 0.0481899 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.92820 | 0.462285 | 0.231142 | − | 0.972920i | \(-0.425754\pi\) | ||||
0.231142 | + | 0.972920i | \(0.425754\pi\) | |||||||
\(374\) | −3.46410 | −0.179124 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.92820 | −0.357295 | ||||||||
\(377\) | 6.92820 | 0.356821 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.0000 | −1.43826 | −0.719132 | − | 0.694874i | \(-0.755460\pi\) | ||||
−0.719132 | + | 0.694874i | \(0.755460\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.07180 | 0.0548379 | ||||||||
\(383\) | −28.7846 | −1.47082 | −0.735412 | − | 0.677620i | \(-0.763012\pi\) | ||||
−0.735412 | + | 0.677620i | \(0.763012\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.00000 | −0.0509647 | ||||||||
\(386\) | −24.9282 | −1.26881 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 15.8564 | 0.804987 | ||||||||
\(389\) | 33.7128 | 1.70931 | 0.854654 | − | 0.519198i | \(-0.173769\pi\) | ||||
0.854654 | + | 0.519198i | \(0.173769\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.9282 | 0.957240 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.0000 | −0.906827 | ||||||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.0000 | −0.501886 | −0.250943 | − | 0.968002i | \(-0.580741\pi\) | ||||
−0.250943 | + | 0.968002i | \(0.580741\pi\) | |||||||
\(398\) | −6.92820 | −0.347279 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −29.7128 | −1.48379 | −0.741894 | − | 0.670518i | \(-0.766072\pi\) | ||||
−0.741894 | + | 0.670518i | \(0.766072\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.0000 | 1.19553 | ||||||||
\(404\) | 15.8564 | 0.788886 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.00000 | 0.0992583 | ||||||||
\(407\) | −0.535898 | −0.0265635 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.928203 | 0.0458967 | 0.0229483 | − | 0.999737i | \(-0.492695\pi\) | ||||
0.0229483 | + | 0.999737i | \(0.492695\pi\) | |||||||
\(410\) | 4.92820 | 0.243387 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 16.0000 | 0.788263 | ||||||||
\(413\) | −10.9282 | −0.537742 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.92820 | 0.340092 | ||||||||
\(416\) | 3.46410 | 0.169842 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.8564 | 0.676930 | 0.338465 | − | 0.940979i | \(-0.390092\pi\) | ||||
0.338465 | + | 0.940979i | \(0.390092\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.0000 | −1.26716 | −0.633581 | − | 0.773676i | \(-0.718416\pi\) | ||||
−0.633581 | + | 0.773676i | \(0.718416\pi\) | |||||||
\(422\) | −11.3205 | −0.551074 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.928203 | −0.0450775 | ||||||||
\(425\) | −3.46410 | −0.168034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.92820 | 0.432066 | ||||||||
\(428\) | −6.92820 | −0.334887 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10.9282 | −0.527005 | ||||||||
\(431\) | −11.3205 | −0.545290 | −0.272645 | − | 0.962115i | \(-0.587898\pi\) | ||||
−0.272645 | + | 0.962115i | \(0.587898\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.7128 | 1.81236 | 0.906181 | − | 0.422890i | \(-0.138984\pi\) | ||||
0.906181 | + | 0.422890i | \(0.138984\pi\) | |||||||
\(434\) | 6.92820 | 0.332564 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.39230 | −0.306136 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.7846 | 1.18290 | 0.591452 | − | 0.806340i | \(-0.298555\pi\) | ||||
0.591452 | + | 0.806340i | \(0.298555\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.0000 | −0.570782 | ||||||||
\(443\) | −13.0718 | −0.621060 | −0.310530 | − | 0.950564i | \(-0.600506\pi\) | ||||
−0.310530 | + | 0.950564i | \(0.600506\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.46410 | 0.164214 | ||||||||
\(446\) | 16.7846 | 0.794774 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 22.0000 | 1.03824 | 0.519122 | − | 0.854700i | \(-0.326259\pi\) | ||||
0.519122 | + | 0.854700i | \(0.326259\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.92820 | 0.232060 | ||||||||
\(452\) | −4.53590 | −0.213351 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.92820 | −0.325157 | ||||||||
\(455\) | −3.46410 | −0.162400 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.9282 | 1.54032 | 0.770158 | − | 0.637853i | \(-0.220177\pi\) | ||||
0.770158 | + | 0.637853i | \(0.220177\pi\) | |||||||
\(458\) | 18.3923 | 0.859416 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.46410 | −0.254765 | ||||||||
\(461\) | 18.0000 | 0.838344 | 0.419172 | − | 0.907907i | \(-0.362320\pi\) | ||||
0.419172 | + | 0.907907i | \(0.362320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.7846 | −0.965943 | −0.482971 | − | 0.875636i | \(-0.660442\pi\) | ||||
−0.482971 | + | 0.875636i | \(0.660442\pi\) | |||||||
\(464\) | −2.00000 | −0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.00000 | 0.0926482 | ||||||||
\(467\) | 17.0718 | 0.789989 | 0.394994 | − | 0.918684i | \(-0.370747\pi\) | ||||
0.394994 | + | 0.918684i | \(0.370747\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.53590 | 0.117097 | ||||||||
\(470\) | −6.92820 | −0.319574 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.9282 | 0.503011 | ||||||||
\(473\) | −10.9282 | −0.502479 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.46410 | −0.158777 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −16.3923 | −0.749767 | ||||||||
\(479\) | 13.8564 | 0.633115 | 0.316558 | − | 0.948573i | \(-0.397473\pi\) | ||||
0.316558 | + | 0.948573i | \(0.397473\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.85641 | −0.0846448 | ||||||||
\(482\) | 20.9282 | 0.953254 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 15.8564 | 0.720002 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.9282 | 0.676461 | 0.338231 | − | 0.941063i | \(-0.390172\pi\) | ||||
0.338231 | + | 0.941063i | \(0.390172\pi\) | |||||||
\(488\) | −8.92820 | −0.404161 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 25.8564 | 1.16688 | 0.583442 | − | 0.812155i | \(-0.301706\pi\) | ||||
0.583442 | + | 0.812155i | \(0.301706\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.92820 | 0.312031 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.92820 | −0.311086 | ||||||||
\(497\) | 4.00000 | 0.179425 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.9282 | 1.38454 | 0.692268 | − | 0.721640i | \(-0.256611\pi\) | ||||
0.692268 | + | 0.721640i | \(0.256611\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.9282 | −0.844807 | ||||||||
\(503\) | 8.39230 | 0.374194 | 0.187097 | − | 0.982341i | \(-0.440092\pi\) | ||||
0.187097 | + | 0.982341i | \(0.440092\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.8564 | 0.705601 | ||||||||
\(506\) | −5.46410 | −0.242909 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.92820 | −0.129918 | ||||||||
\(509\) | 19.0718 | 0.845343 | 0.422671 | − | 0.906283i | \(-0.361092\pi\) | ||||
0.422671 | + | 0.906283i | \(0.361092\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.9282 | 0.571910 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.07180 | −0.135491 | ||||||||
\(515\) | 16.0000 | 0.705044 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.92820 | −0.304702 | ||||||||
\(518\) | −0.535898 | −0.0235460 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.46410 | 0.151911 | ||||||||
\(521\) | −20.5359 | −0.899694 | −0.449847 | − | 0.893106i | \(-0.648521\pi\) | ||||
−0.449847 | + | 0.893106i | \(0.648521\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.6077 | 1.03229 | 0.516146 | − | 0.856500i | \(-0.327366\pi\) | ||||
0.516146 | + | 0.856500i | \(0.327366\pi\) | |||||||
\(524\) | 14.9282 | 0.652142 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.7846 | 1.08066 | ||||||||
\(527\) | 24.0000 | 1.04546 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.85641 | 0.298105 | ||||||||
\(530\) | −0.928203 | −0.0403186 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.0718 | 0.739462 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.92820 | −0.299532 | ||||||||
\(536\) | −2.53590 | −0.109534 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.07180 | −0.132435 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.3205 | −1.08861 | −0.544307 | − | 0.838886i | \(-0.683207\pi\) | ||||
−0.544307 | + | 0.838886i | \(0.683207\pi\) | |||||||
\(542\) | −21.8564 | −0.938813 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.46410 | 0.148522 | ||||||||
\(545\) | −6.39230 | −0.273816 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.00000 | −0.342055 | −0.171028 | − | 0.985266i | \(-0.554709\pi\) | ||||
−0.171028 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(548\) | 11.4641 | 0.489722 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00000 | 0.340195 | ||||||||
\(554\) | 10.0000 | 0.424859 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.9282 | 0.463459 | ||||||||
\(557\) | 4.14359 | 0.175570 | 0.0877848 | − | 0.996139i | \(-0.472021\pi\) | ||||
0.0877848 | + | 0.996139i | \(0.472021\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −37.8564 | −1.60116 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.39230 | 0.269643 | ||||||||
\(563\) | −23.7128 | −0.999376 | −0.499688 | − | 0.866205i | \(-0.666552\pi\) | ||||
−0.499688 | + | 0.866205i | \(0.666552\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.53590 | −0.190827 | ||||||||
\(566\) | 5.46410 | 0.229673 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.00000 | −0.167836 | ||||||||
\(569\) | −23.1769 | −0.971627 | −0.485813 | − | 0.874063i | \(-0.661477\pi\) | ||||
−0.485813 | + | 0.874063i | \(0.661477\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.3205 | −0.473749 | −0.236874 | − | 0.971540i | \(-0.576123\pi\) | ||||
−0.236874 | + | 0.971540i | \(0.576123\pi\) | |||||||
\(572\) | 3.46410 | 0.144841 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.92820 | 0.205699 | ||||||||
\(575\) | −5.46410 | −0.227869 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.71281 | −0.404350 | −0.202175 | − | 0.979349i | \(-0.564801\pi\) | ||||
−0.202175 | + | 0.979349i | \(0.564801\pi\) | |||||||
\(578\) | 5.00000 | 0.207973 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.00000 | −0.0830455 | ||||||||
\(581\) | 6.92820 | 0.287430 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.928203 | −0.0384422 | ||||||||
\(584\) | −12.9282 | −0.534973 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.0000 | −0.578335 | ||||||||
\(587\) | −20.7846 | −0.857873 | −0.428936 | − | 0.903335i | \(-0.641112\pi\) | ||||
−0.428936 | + | 0.903335i | \(0.641112\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 10.9282 | 0.449907 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.535898 | 0.0220253 | ||||||||
\(593\) | 35.1769 | 1.44454 | 0.722271 | − | 0.691610i | \(-0.243098\pi\) | ||||
0.722271 | + | 0.691610i | \(0.243098\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.46410 | −0.142014 | ||||||||
\(596\) | 0.928203 | 0.0380207 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −18.9282 | −0.774032 | ||||||||
\(599\) | 44.7846 | 1.82985 | 0.914925 | − | 0.403624i | \(-0.132250\pi\) | ||||
0.914925 | + | 0.403624i | \(0.132250\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.9282 | −1.50633 | −0.753166 | − | 0.657830i | \(-0.771475\pi\) | ||||
−0.753166 | + | 0.657830i | \(0.771475\pi\) | |||||||
\(602\) | −10.9282 | −0.445400 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.0000 | 0.649420 | 0.324710 | − | 0.945814i | \(-0.394733\pi\) | ||||
0.324710 | + | 0.945814i | \(0.394733\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.92820 | −0.361492 | ||||||||
\(611\) | −24.0000 | −0.970936 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.00000 | −0.0807792 | −0.0403896 | − | 0.999184i | \(-0.512860\pi\) | ||||
−0.0403896 | + | 0.999184i | \(0.512860\pi\) | |||||||
\(614\) | 27.3205 | 1.10257 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | −18.3923 | −0.740446 | −0.370223 | − | 0.928943i | \(-0.620719\pi\) | ||||
−0.370223 | + | 0.928943i | \(0.620719\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.3205 | −0.776557 | −0.388278 | − | 0.921542i | \(-0.626930\pi\) | ||||
−0.388278 | + | 0.921542i | \(0.626930\pi\) | |||||||
\(620\) | −6.92820 | −0.278243 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13.4641 | 0.539861 | ||||||||
\(623\) | 3.46410 | 0.138786 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 33.7128 | 1.34743 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.7846 | 0.909205 | ||||||||
\(629\) | −1.85641 | −0.0740198 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.7846 | −0.986660 | −0.493330 | − | 0.869842i | \(-0.664220\pi\) | ||||
−0.493330 | + | 0.869842i | \(0.664220\pi\) | |||||||
\(632\) | −8.00000 | −0.318223 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16.9282 | −0.672305 | ||||||||
\(635\) | −2.92820 | −0.116202 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.46410 | −0.137253 | ||||||||
\(638\) | −2.00000 | −0.0791808 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 6.00000 | 0.236986 | 0.118493 | − | 0.992955i | \(-0.462194\pi\) | ||||
0.118493 | + | 0.992955i | \(0.462194\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.7128 | 1.25063 | 0.625316 | − | 0.780372i | \(-0.284970\pi\) | ||||
0.625316 | + | 0.780372i | \(0.284970\pi\) | |||||||
\(644\) | −5.46410 | −0.215316 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.07180 | 0.356649 | 0.178325 | − | 0.983972i | \(-0.442932\pi\) | ||||
0.178325 | + | 0.983972i | \(0.442932\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.9282 | 0.428969 | ||||||||
\(650\) | 3.46410 | 0.135873 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.53590 | 0.0993134 | ||||||||
\(653\) | −4.14359 | −0.162151 | −0.0810757 | − | 0.996708i | \(-0.525836\pi\) | ||||
−0.0810757 | + | 0.996708i | \(0.525836\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.9282 | 0.583293 | ||||||||
\(656\) | −4.92820 | −0.192414 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.92820 | −0.270089 | ||||||||
\(659\) | −15.7128 | −0.612084 | −0.306042 | − | 0.952018i | \(-0.599005\pi\) | ||||
−0.306042 | + | 0.952018i | \(0.599005\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.3923 | 0.870960 | 0.435480 | − | 0.900198i | \(-0.356579\pi\) | ||||
0.435480 | + | 0.900198i | \(0.356579\pi\) | |||||||
\(662\) | 4.00000 | 0.155464 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.92820 | −0.268866 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.9282 | 0.423142 | ||||||||
\(668\) | 2.53590 | 0.0981169 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.53590 | −0.0979703 | ||||||||
\(671\) | −8.92820 | −0.344669 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.9282 | −1.11510 | −0.557550 | − | 0.830143i | \(-0.688259\pi\) | ||||
−0.557550 | + | 0.830143i | \(0.688259\pi\) | |||||||
\(674\) | 18.7846 | 0.723556 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.00000 | −0.0384615 | ||||||||
\(677\) | 27.0718 | 1.04045 | 0.520227 | − | 0.854028i | \(-0.325847\pi\) | ||||
0.520227 | + | 0.854028i | \(0.325847\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.8564 | 0.608513 | ||||||||
\(680\) | 3.46410 | 0.132842 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.92820 | −0.265295 | ||||||||
\(683\) | −13.0718 | −0.500178 | −0.250089 | − | 0.968223i | \(-0.580460\pi\) | ||||
−0.250089 | + | 0.968223i | \(0.580460\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.4641 | 0.438021 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.9282 | 0.416634 | ||||||||
\(689\) | −3.21539 | −0.122497 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.3923 | 0.927927 | 0.463964 | − | 0.885854i | \(-0.346427\pi\) | ||||
0.463964 | + | 0.885854i | \(0.346427\pi\) | |||||||
\(692\) | −4.92820 | −0.187342 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.9282 | −0.566667 | ||||||||
\(695\) | 10.9282 | 0.414530 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.0718 | 0.646640 | ||||||||
\(698\) | 15.0718 | 0.570476 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −2.00000 | −0.0755390 | −0.0377695 | − | 0.999286i | \(-0.512025\pi\) | ||||
−0.0377695 | + | 0.999286i | \(0.512025\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.07180 | 0.266151 | ||||||||
\(707\) | 15.8564 | 0.596342 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.8564 | 0.745723 | 0.372861 | − | 0.927887i | \(-0.378377\pi\) | ||||
0.372861 | + | 0.927887i | \(0.378377\pi\) | |||||||
\(710\) | −4.00000 | −0.150117 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.46410 | −0.129823 | ||||||||
\(713\) | 37.8564 | 1.41773 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.46410 | 0.129550 | ||||||||
\(716\) | −20.7846 | −0.776757 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.53590 | 0.0946389 | ||||||||
\(719\) | −16.3923 | −0.611330 | −0.305665 | − | 0.952139i | \(-0.598879\pi\) | ||||
−0.305665 | + | 0.952139i | \(0.598879\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | 0.595871 | ||||||||
\(722\) | 19.0000 | 0.707107 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −23.4641 | −0.872036 | ||||||||
\(725\) | −2.00000 | −0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.9282 | 0.998712 | 0.499356 | − | 0.866397i | \(-0.333570\pi\) | ||||
0.499356 | + | 0.866397i | \(0.333570\pi\) | |||||||
\(728\) | 3.46410 | 0.128388 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12.9282 | −0.478494 | ||||||||
\(731\) | −37.8564 | −1.40017 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.2487 | 0.895647 | 0.447823 | − | 0.894122i | \(-0.352199\pi\) | ||||
0.447823 | + | 0.894122i | \(0.352199\pi\) | |||||||
\(734\) | −16.0000 | −0.590571 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.46410 | 0.201409 | ||||||||
\(737\) | −2.53590 | −0.0934110 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.3205 | −0.710716 | −0.355358 | − | 0.934730i | \(-0.615641\pi\) | ||||
−0.355358 | + | 0.934730i | \(0.615641\pi\) | |||||||
\(740\) | 0.535898 | 0.0197000 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.928203 | −0.0340754 | ||||||||
\(743\) | 13.8564 | 0.508342 | 0.254171 | − | 0.967159i | \(-0.418197\pi\) | ||||
0.254171 | + | 0.967159i | \(0.418197\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.928203 | 0.0340067 | ||||||||
\(746\) | −8.92820 | −0.326885 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.46410 | 0.126660 | ||||||||
\(749\) | −6.92820 | −0.253151 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.7846 | 1.48825 | 0.744126 | − | 0.668040i | \(-0.232866\pi\) | ||||
0.744126 | + | 0.668040i | \(0.232866\pi\) | |||||||
\(752\) | 6.92820 | 0.252646 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.92820 | −0.252310 | ||||||||
\(755\) | 8.00000 | 0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.1051 | 0.948807 | 0.474403 | − | 0.880308i | \(-0.342664\pi\) | ||||
0.474403 | + | 0.880308i | \(0.342664\pi\) | |||||||
\(758\) | 28.0000 | 1.01701 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.78461 | −0.100942 | −0.0504710 | − | 0.998726i | \(-0.516072\pi\) | ||||
−0.0504710 | + | 0.998726i | \(0.516072\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.39230 | −0.231417 | ||||||||
\(764\) | −1.07180 | −0.0387762 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28.7846 | 1.04003 | ||||||||
\(767\) | 37.8564 | 1.36692 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.78461 | −0.100416 | −0.0502078 | − | 0.998739i | \(-0.515988\pi\) | ||||
−0.0502078 | + | 0.998739i | \(0.515988\pi\) | |||||||
\(770\) | 1.00000 | 0.0360375 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 24.9282 | 0.897186 | ||||||||
\(773\) | −26.0000 | −0.935155 | −0.467578 | − | 0.883952i | \(-0.654873\pi\) | ||||
−0.467578 | + | 0.883952i | \(0.654873\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.92820 | −0.248868 | ||||||||
\(776\) | −15.8564 | −0.569212 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −33.7128 | −1.20866 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00000 | −0.143131 | ||||||||
\(782\) | −18.9282 | −0.676871 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 22.7846 | 0.813218 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.5359 | 1.23107 | 0.615536 | − | 0.788109i | \(-0.288940\pi\) | ||||
0.615536 | + | 0.788109i | \(0.288940\pi\) | |||||||
\(788\) | 18.0000 | 0.641223 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.00000 | −0.284627 | ||||||||
\(791\) | −4.53590 | −0.161278 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.9282 | −1.09829 | ||||||||
\(794\) | 10.0000 | 0.354887 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.92820 | 0.245564 | ||||||||
\(797\) | −4.14359 | −0.146774 | −0.0733868 | − | 0.997304i | \(-0.523381\pi\) | ||||
−0.0733868 | + | 0.997304i | \(0.523381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 29.7128 | 1.04920 | ||||||||
\(803\) | −12.9282 | −0.456226 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.46410 | −0.192584 | ||||||||
\(806\) | −24.0000 | −0.845364 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.8564 | −0.557826 | ||||||||
\(809\) | 4.53590 | 0.159474 | 0.0797368 | − | 0.996816i | \(-0.474592\pi\) | ||||
0.0797368 | + | 0.996816i | \(0.474592\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.8564 | −0.486564 | −0.243282 | − | 0.969956i | \(-0.578224\pi\) | ||||
−0.243282 | + | 0.969956i | \(0.578224\pi\) | |||||||
\(812\) | −2.00000 | −0.0701862 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.535898 | 0.0187832 | ||||||||
\(815\) | 2.53590 | 0.0888286 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −0.928203 | −0.0324539 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.92820 | −0.172100 | ||||||||
\(821\) | −39.8564 | −1.39100 | −0.695499 | − | 0.718527i | \(-0.744817\pi\) | ||||
−0.695499 | + | 0.718527i | \(0.744817\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.1436 | 0.771877 | 0.385939 | − | 0.922524i | \(-0.373878\pi\) | ||||
0.385939 | + | 0.922524i | \(0.373878\pi\) | |||||||
\(824\) | −16.0000 | −0.557386 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.9282 | 0.380241 | ||||||||
\(827\) | 20.7846 | 0.722752 | 0.361376 | − | 0.932420i | \(-0.382307\pi\) | ||||
0.361376 | + | 0.932420i | \(0.382307\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.1769 | −0.388190 | −0.194095 | − | 0.980983i | \(-0.562177\pi\) | ||||
−0.194095 | + | 0.980983i | \(0.562177\pi\) | |||||||
\(830\) | −6.92820 | −0.240481 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.46410 | −0.120096 | ||||||||
\(833\) | −3.46410 | −0.120024 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.53590 | 0.0877584 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.8564 | −0.478662 | ||||||||
\(839\) | −37.4641 | −1.29340 | −0.646702 | − | 0.762743i | \(-0.723852\pi\) | ||||
−0.646702 | + | 0.762743i | \(0.723852\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 26.0000 | 0.896019 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.3205 | 0.389668 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0.928203 | 0.0318746 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.46410 | 0.118818 | ||||||||
\(851\) | −2.92820 | −0.100378 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.1769 | −1.61531 | −0.807653 | − | 0.589658i | \(-0.799263\pi\) | ||||
−0.807653 | + | 0.589658i | \(0.799263\pi\) | |||||||
\(854\) | −8.92820 | −0.305517 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.92820 | 0.236801 | ||||||||
\(857\) | 7.46410 | 0.254969 | 0.127484 | − | 0.991841i | \(-0.459310\pi\) | ||||
0.127484 | + | 0.991841i | \(0.459310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.392305 | −0.0133853 | −0.00669263 | − | 0.999978i | \(-0.502130\pi\) | ||||
−0.00669263 | + | 0.999978i | \(0.502130\pi\) | |||||||
\(860\) | 10.9282 | 0.372649 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11.3205 | 0.385578 | ||||||||
\(863\) | 6.24871 | 0.212709 | 0.106354 | − | 0.994328i | \(-0.466082\pi\) | ||||
0.106354 | + | 0.994328i | \(0.466082\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.92820 | −0.167564 | ||||||||
\(866\) | −37.7128 | −1.28153 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.92820 | −0.235159 | ||||||||
\(869\) | −8.00000 | −0.271381 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.78461 | −0.297655 | ||||||||
\(872\) | 6.39230 | 0.216471 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.8564 | 0.670503 | 0.335252 | − | 0.942129i | \(-0.391179\pi\) | ||||
0.335252 | + | 0.942129i | \(0.391179\pi\) | |||||||
\(878\) | −24.7846 | −0.836440 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | 17.3205 | 0.583543 | 0.291771 | − | 0.956488i | \(-0.405755\pi\) | ||||
0.291771 | + | 0.956488i | \(0.405755\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.1051 | 0.945813 | 0.472906 | − | 0.881113i | \(-0.343205\pi\) | ||||
0.472906 | + | 0.881113i | \(0.343205\pi\) | |||||||
\(884\) | 12.0000 | 0.403604 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.0718 | 0.439156 | ||||||||
\(887\) | 51.3205 | 1.72317 | 0.861587 | − | 0.507610i | \(-0.169471\pi\) | ||||
0.861587 | + | 0.507610i | \(0.169471\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.92820 | −0.0982088 | ||||||||
\(890\) | −3.46410 | −0.116117 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16.7846 | −0.561990 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.7846 | −0.694753 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.0000 | −0.734150 | ||||||||
\(899\) | 13.8564 | 0.462137 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.21539 | −0.107120 | ||||||||
\(902\) | −4.92820 | −0.164091 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.53590 | 0.150862 | ||||||||
\(905\) | −23.4641 | −0.779973 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.1769 | 1.36726 | 0.683629 | − | 0.729830i | \(-0.260401\pi\) | ||||
0.683629 | + | 0.729830i | \(0.260401\pi\) | |||||||
\(908\) | 6.92820 | 0.229920 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.46410 | 0.114834 | ||||||||
\(911\) | 4.00000 | 0.132526 | 0.0662630 | − | 0.997802i | \(-0.478892\pi\) | ||||
0.0662630 | + | 0.997802i | \(0.478892\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.92820 | −0.229290 | ||||||||
\(914\) | −32.9282 | −1.08917 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18.3923 | −0.607699 | ||||||||
\(917\) | 14.9282 | 0.492973 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 58.9282 | 1.94386 | 0.971931 | − | 0.235266i | \(-0.0755961\pi\) | ||||
0.971931 | + | 0.235266i | \(0.0755961\pi\) | |||||||
\(920\) | 5.46410 | 0.180146 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18.0000 | −0.592798 | ||||||||
\(923\) | −13.8564 | −0.456089 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.535898 | 0.0176202 | ||||||||
\(926\) | 20.7846 | 0.683025 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.00000 | 0.0656532 | ||||||||
\(929\) | 46.3923 | 1.52208 | 0.761041 | − | 0.648704i | \(-0.224689\pi\) | ||||
0.761041 | + | 0.648704i | \(0.224689\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.00000 | −0.0655122 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17.0718 | −0.558606 | ||||||||
\(935\) | 3.46410 | 0.113288 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.8564 | 0.779355 | 0.389677 | − | 0.920951i | \(-0.372587\pi\) | ||||
0.389677 | + | 0.920951i | \(0.372587\pi\) | |||||||
\(938\) | −2.53590 | −0.0828000 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.92820 | 0.225973 | ||||||||
\(941\) | −22.0000 | −0.717180 | −0.358590 | − | 0.933495i | \(-0.616742\pi\) | ||||
−0.358590 | + | 0.933495i | \(0.616742\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.9282 | 0.876903 | ||||||||
\(944\) | −10.9282 | −0.355683 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.9282 | 0.355307 | ||||||||
\(947\) | 37.8564 | 1.23017 | 0.615084 | − | 0.788462i | \(-0.289122\pi\) | ||||
0.615084 | + | 0.788462i | \(0.289122\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −44.7846 | −1.45377 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.46410 | 0.112272 | ||||||||
\(953\) | −40.6410 | −1.31649 | −0.658246 | − | 0.752803i | \(-0.728701\pi\) | ||||
−0.658246 | + | 0.752803i | \(0.728701\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.07180 | −0.0346825 | ||||||||
\(956\) | 16.3923 | 0.530165 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13.8564 | −0.447680 | ||||||||
\(959\) | 11.4641 | 0.370195 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.0000 | 0.548387 | ||||||||
\(962\) | 1.85641 | 0.0598529 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −20.9282 | −0.674052 | ||||||||
\(965\) | 24.9282 | 0.802467 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.0718 | −0.420361 | −0.210180 | − | 0.977663i | \(-0.567405\pi\) | ||||
−0.210180 | + | 0.977663i | \(0.567405\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −15.8564 | −0.509119 | ||||||||
\(971\) | 19.7128 | 0.632614 | 0.316307 | − | 0.948657i | \(-0.397557\pi\) | ||||
0.316307 | + | 0.948657i | \(0.397557\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.9282 | 0.350342 | ||||||||
\(974\) | −14.9282 | −0.478330 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.92820 | 0.285785 | ||||||||
\(977\) | 2.67949 | 0.0857245 | 0.0428623 | − | 0.999081i | \(-0.486352\pi\) | ||||
0.0428623 | + | 0.999081i | \(0.486352\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.46410 | −0.110713 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −25.8564 | −0.825111 | ||||||||
\(983\) | −44.7846 | −1.42841 | −0.714204 | − | 0.699938i | \(-0.753211\pi\) | ||||
−0.714204 | + | 0.699938i | \(0.753211\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.0000 | 0.573528 | ||||||||
\(986\) | −6.92820 | −0.220639 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −59.7128 | −1.89876 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.784610 | 0.0249239 | 0.0124620 | − | 0.999922i | \(-0.496033\pi\) | ||||
0.0124620 | + | 0.999922i | \(0.496033\pi\) | |||||||
\(992\) | 6.92820 | 0.219971 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.00000 | −0.126872 | ||||||||
\(995\) | 6.92820 | 0.219639 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 53.3205 | 1.68868 | 0.844339 | − | 0.535810i | \(-0.179994\pi\) | ||||
0.844339 | + | 0.535810i | \(0.179994\pi\) | |||||||
\(998\) | −30.9282 | −0.979015 | ||||||||
\(999\) | 0 | 0 |
(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 | 6930.2.a.bt.1.1 | 2 | ||
3.2 | odd | 2 | 2310.2.a.bb.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2310.2.a.bb.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
6930.2.a.bt.1.1 | 2 | 1.1 | even | 1 | trivial |