Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(1,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, 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("4600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.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: | \(36.7311849298\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.1 |
$q$-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 | ||||||||
\(3\) | −3.23607 | −1.86834 | −0.934172 | − | 0.356822i | \(-0.883860\pi\) | ||||
−0.934172 | + | 0.356822i | \(0.883860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.23607 | 1.60108 | 0.800542 | − | 0.599277i | \(-0.204545\pi\) | ||||
0.800542 | + | 0.599277i | \(0.204545\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.47214 | 2.49071 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.23607 | 0.620174 | 0.310087 | − | 0.950708i | \(-0.399642\pi\) | ||||
0.310087 | + | 0.950708i | \(0.399642\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.47214 | −1.56972 | −0.784862 | − | 0.619671i | \(-0.787266\pi\) | ||||
−0.784862 | + | 0.619671i | \(0.787266\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | 0.114708 | − | 0.993399i | \(-0.463407\pi\) | ||||
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −13.7082 | −2.99138 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −14.4721 | −2.78516 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.76393 | −0.327554 | −0.163777 | − | 0.986497i | \(-0.552368\pi\) | ||||
−0.163777 | + | 0.986497i | \(0.552368\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.472136 | 0.0847981 | 0.0423991 | − | 0.999101i | \(-0.486500\pi\) | ||||
0.0423991 | + | 0.999101i | \(0.486500\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.23607 | −0.563327 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.2361 | −1.84720 | −0.923599 | − | 0.383360i | \(-0.874767\pi\) | ||||
−0.923599 | + | 0.383360i | \(0.874767\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.23607 | −1.15870 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.94427 | −0.928339 | −0.464170 | − | 0.885746i | \(-0.653647\pi\) | ||||
−0.464170 | + | 0.885746i | \(0.653647\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.52786 | −0.385496 | −0.192748 | − | 0.981248i | \(-0.561740\pi\) | ||||
−0.192748 | + | 0.981248i | \(0.561740\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.7082 | −1.70782 | −0.853909 | − | 0.520423i | \(-0.825774\pi\) | ||||
−0.853909 | + | 0.520423i | \(0.825774\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.9443 | 1.56347 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 20.9443 | 2.93278 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.23607 | −0.169787 | −0.0848935 | − | 0.996390i | \(-0.527055\pi\) | ||||
−0.0848935 | + | 0.996390i | \(0.527055\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.23607 | −0.428628 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.23607 | 0.421300 | 0.210650 | − | 0.977562i | \(-0.432442\pi\) | ||||
0.210650 | + | 0.977562i | \(0.432442\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.23607 | −0.926484 | −0.463242 | − | 0.886232i | \(-0.653314\pi\) | ||||
−0.463242 | + | 0.886232i | \(0.653314\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 31.6525 | 3.98784 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.9443 | −1.58139 | −0.790697 | − | 0.612207i | \(-0.790282\pi\) | ||||
−0.790697 | + | 0.612207i | \(0.790282\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.23607 | −0.389577 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0000 | 1.18678 | 0.593391 | − | 0.804914i | \(-0.297789\pi\) | ||||
0.593391 | + | 0.804914i | \(0.297789\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.47214 | 1.10863 | 0.554315 | − | 0.832307i | \(-0.312980\pi\) | ||||
0.554315 | + | 0.832307i | \(0.312980\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.23607 | 0.482745 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.1803 | 1.70792 | 0.853961 | − | 0.520337i | \(-0.174194\pi\) | ||||
0.853961 | + | 0.520337i | \(0.174194\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 24.4164 | 2.71293 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.00000 | −0.987878 | −0.493939 | − | 0.869496i | \(-0.664443\pi\) | ||||
−0.493939 | + | 0.869496i | \(0.664443\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.70820 | 0.611984 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.47214 | 0.992950 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.52786 | −0.158432 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.18034 | −0.627518 | −0.313759 | − | 0.949503i | \(-0.601588\pi\) | ||||
−0.313759 | + | 0.949503i | \(0.601588\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.47214 | 0.750978 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.9443 | −1.88503 | −0.942513 | − | 0.334170i | \(-0.891544\pi\) | ||||
−0.942513 | + | 0.334170i | \(0.891544\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.23607 | 0.220326 | 0.110163 | − | 0.993914i | \(-0.464863\pi\) | ||||
0.110163 | + | 0.993914i | \(0.464863\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.4164 | 1.87705 | 0.938527 | − | 0.345204i | \(-0.112190\pi\) | ||||
0.938527 | + | 0.345204i | \(0.112190\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.7639 | −1.22256 | −0.611281 | − | 0.791413i | \(-0.709346\pi\) | ||||
−0.611281 | + | 0.791413i | \(0.709346\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 36.3607 | 3.45120 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.76393 | −0.636297 | −0.318149 | − | 0.948041i | \(-0.603061\pi\) | ||||
−0.318149 | + | 0.948041i | \(0.603061\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.7082 | 1.54467 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −27.4164 | −2.51326 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 19.2361 | 1.73446 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.18034 | 0.370945 | 0.185473 | − | 0.982649i | \(-0.440618\pi\) | ||||
0.185473 | + | 0.982649i | \(0.440618\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.18034 | 0.720239 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.9443 | −1.30569 | −0.652844 | − | 0.757493i | \(-0.726424\pi\) | ||||
−0.652844 | + | 0.757493i | \(0.726424\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.23607 | 0.367314 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.5279 | −0.984892 | −0.492446 | − | 0.870343i | \(-0.663897\pi\) | ||||
−0.492446 | + | 0.870343i | \(0.663897\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.0000 | 1.69638 | 0.848189 | − | 0.529694i | \(-0.177693\pi\) | ||||
0.848189 | + | 0.529694i | \(0.177693\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 37.8885 | 3.19079 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.23607 | 0.186989 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −35.4164 | −2.92110 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.9443 | 0.896590 | 0.448295 | − | 0.893886i | \(-0.352031\pi\) | ||||
0.448295 | + | 0.893886i | \(0.352031\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5279 | 0.938124 | 0.469062 | − | 0.883165i | \(-0.344592\pi\) | ||||
0.469062 | + | 0.883165i | \(0.344592\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −48.3607 | −3.90973 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.291796 | −0.0232879 | −0.0116439 | − | 0.999932i | \(-0.503706\pi\) | ||||
−0.0116439 | + | 0.999932i | \(0.503706\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.00000 | 0.317221 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.23607 | 0.333849 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.7082 | 0.917057 | 0.458529 | − | 0.888680i | \(-0.348377\pi\) | ||||
0.458529 | + | 0.888680i | \(0.348377\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.41641 | 0.419134 | 0.209567 | − | 0.977794i | \(-0.432795\pi\) | ||||
0.209567 | + | 0.977794i | \(0.432795\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.00000 | −0.615385 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.47214 | 0.571409 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.2361 | −1.08235 | −0.541174 | − | 0.840911i | \(-0.682020\pi\) | ||||
−0.541174 | + | 0.840911i | \(0.682020\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.4721 | −0.787134 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.7082 | −1.17409 | −0.587043 | − | 0.809556i | \(-0.699708\pi\) | ||||
−0.587043 | + | 0.809556i | \(0.699708\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.944272 | −0.0701872 | −0.0350936 | − | 0.999384i | \(-0.511173\pi\) | ||||
−0.0350936 | + | 0.999384i | \(0.511173\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.4164 | 1.73099 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.47214 | −0.473289 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −61.3050 | −4.45928 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.1803 | −1.38784 | −0.693920 | − | 0.720052i | \(-0.744118\pi\) | ||||
−0.693920 | + | 0.720052i | \(0.744118\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.94427 | −0.211933 | −0.105967 | − | 0.994370i | \(-0.533794\pi\) | ||||
−0.105967 | + | 0.994370i | \(0.533794\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.23607 | 0.586796 | 0.293398 | − | 0.955990i | \(-0.405214\pi\) | ||||
0.293398 | + | 0.955990i | \(0.405214\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.7082 | 0.900861 | 0.450430 | − | 0.892812i | \(-0.351271\pi\) | ||||
0.450430 | + | 0.892812i | \(0.351271\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 41.8885 | 2.95459 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.47214 | −0.524441 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.47214 | 0.519349 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.9443 | −1.02881 | −0.514403 | − | 0.857549i | \(-0.671986\pi\) | ||||
−0.514403 | + | 0.857549i | \(0.671986\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −32.3607 | −2.21732 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −30.6525 | −2.07130 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.4721 | −0.973501 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.2361 | −0.886353 | −0.443176 | − | 0.896434i | \(-0.646148\pi\) | ||||
−0.443176 | + | 0.896434i | \(0.646148\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.9443 | −0.859142 | −0.429571 | − | 0.903033i | \(-0.641335\pi\) | ||||
−0.429571 | + | 0.903033i | \(0.641335\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.94427 | 0.458890 | 0.229445 | − | 0.973322i | \(-0.426309\pi\) | ||||
0.229445 | + | 0.973322i | \(0.426309\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.7082 | −0.901934 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.52786 | −0.296630 | −0.148315 | − | 0.988940i | \(-0.547385\pi\) | ||||
−0.148315 | + | 0.988940i | \(0.547385\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −49.1246 | −3.19099 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.76393 | 0.437522 | 0.218761 | − | 0.975778i | \(-0.429798\pi\) | ||||
0.218761 | + | 0.975778i | \(0.429798\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.2361 | 1.36794 | 0.683968 | − | 0.729512i | \(-0.260253\pi\) | ||||
0.683968 | + | 0.729512i | \(0.260253\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −35.5967 | −2.28353 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.23607 | 0.142278 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 29.1246 | 1.84570 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.52786 | −0.348916 | −0.174458 | − | 0.984665i | \(-0.555817\pi\) | ||||
−0.174458 | + | 0.984665i | \(0.555817\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.00000 | 0.0628695 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.0000 | 0.873296 | 0.436648 | − | 0.899632i | \(-0.356166\pi\) | ||||
0.436648 | + | 0.899632i | \(0.356166\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −47.5967 | −2.95752 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.1803 | −0.815843 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.00000 | −0.493301 | −0.246651 | − | 0.969104i | \(-0.579330\pi\) | ||||
−0.246651 | + | 0.969104i | \(0.579330\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.47214 | −0.396088 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.1803 | −1.53527 | −0.767636 | − | 0.640886i | \(-0.778567\pi\) | ||||
−0.767636 | + | 0.640886i | \(0.778567\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −32.0689 | −1.94805 | −0.974023 | − | 0.226449i | \(-0.927288\pi\) | ||||
−0.974023 | + | 0.226449i | \(0.927288\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −30.6525 | −1.85517 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.2361 | −0.855362 | −0.427681 | − | 0.903930i | \(-0.640669\pi\) | ||||
−0.427681 | + | 0.903930i | \(0.640669\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.52786 | 0.211208 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.1803 | −1.32317 | −0.661584 | − | 0.749871i | \(-0.730116\pi\) | ||||
−0.661584 | + | 0.749871i | \(0.730116\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.3607 | −1.68587 | −0.842934 | − | 0.538017i | \(-0.819173\pi\) | ||||
−0.842934 | + | 0.538017i | \(0.819173\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.1803 | −1.48635 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.8885 | 1.46403 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20.0000 | 1.17242 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.4721 | 0.845471 | 0.422736 | − | 0.906253i | \(-0.361070\pi\) | ||||
0.422736 | + | 0.906253i | \(0.361070\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −14.4721 | −0.839759 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.23607 | 0.129315 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.7082 | −0.617211 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 61.3050 | 3.52188 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.0000 | −1.36975 | −0.684876 | − | 0.728659i | \(-0.740144\pi\) | ||||
−0.684876 | + | 0.728659i | \(0.740144\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.23607 | −0.411646 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.23607 | −0.183501 | −0.0917503 | − | 0.995782i | \(-0.529246\pi\) | ||||
−0.0917503 | + | 0.995782i | \(0.529246\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.6525 | 0.602114 | 0.301057 | − | 0.953606i | \(-0.402661\pi\) | ||||
0.301057 | + | 0.953606i | \(0.402661\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.1246 | 1.24264 | 0.621321 | − | 0.783556i | \(-0.286596\pi\) | ||||
0.621321 | + | 0.783556i | \(0.286596\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.76393 | −0.0987612 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −62.8328 | −3.50699 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.47214 | −0.360119 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 41.3050 | 2.28417 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −49.5967 | −2.73436 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.9443 | 1.70085 | 0.850426 | − | 0.526095i | \(-0.176345\pi\) | ||||
0.850426 | + | 0.526095i | \(0.176345\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −83.9574 | −4.60084 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.6525 | 1.34291 | 0.671453 | − | 0.741047i | \(-0.265671\pi\) | ||||
0.671453 | + | 0.741047i | \(0.265671\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.8885 | 1.18882 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.472136 | 0.0255676 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.7082 | 0.902158 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.05573 | −0.164040 | −0.0820200 | − | 0.996631i | \(-0.526137\pi\) | ||||
−0.0820200 | + | 0.996631i | \(0.526137\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.18034 | −0.277297 | −0.138649 | − | 0.990342i | \(-0.544276\pi\) | ||||
−0.138649 | + | 0.990342i | \(0.544276\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −32.3607 | −1.72729 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.88854 | 0.260191 | 0.130095 | − | 0.991501i | \(-0.458472\pi\) | ||||
0.130095 | + | 0.991501i | \(0.458472\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 88.7214 | 4.69563 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.7639 | 1.04310 | 0.521550 | − | 0.853221i | \(-0.325354\pi\) | ||||
0.521550 | + | 0.853221i | \(0.325354\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 32.3607 | 1.69850 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.6525 | 1.23465 | 0.617325 | − | 0.786709i | \(-0.288217\pi\) | ||||
0.617325 | + | 0.786709i | \(0.288217\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −44.4164 | −2.31223 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.23607 | −0.271843 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.0000 | 0.621336 | 0.310668 | − | 0.950518i | \(-0.399447\pi\) | ||||
0.310668 | + | 0.950518i | \(0.399447\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.94427 | −0.203140 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.05573 | 0.156962 | 0.0784811 | − | 0.996916i | \(-0.474993\pi\) | ||||
0.0784811 | + | 0.996916i | \(0.474993\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.5279 | −0.693053 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.236068 | 0.0120625 | 0.00603126 | − | 0.999982i | \(-0.498080\pi\) | ||||
0.00603126 | + | 0.999982i | \(0.498080\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.8885 | −0.960159 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.18034 | 0.313356 | 0.156678 | − | 0.987650i | \(-0.449922\pi\) | ||||
0.156678 | + | 0.987650i | \(0.449922\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.47214 | −0.327310 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 48.3607 | 2.43947 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.3607 | −1.12225 | −0.561125 | − | 0.827731i | \(-0.689631\pi\) | ||||
−0.561125 | + | 0.827731i | \(0.689631\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.7082 | −0.686269 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.1246 | −0.655412 | −0.327706 | − | 0.944780i | \(-0.606276\pi\) | ||||
−0.327706 | + | 0.944780i | \(0.606276\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.05573 | 0.0525896 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.2361 | −0.556951 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.4164 | −1.30621 | −0.653104 | − | 0.757269i | \(-0.726533\pi\) | ||||
−0.653104 | + | 0.757269i | \(0.726533\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 37.3050 | 1.84012 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.7082 | 0.674537 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −64.7214 | −3.16942 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −36.7771 | −1.79668 | −0.898339 | − | 0.439303i | \(-0.855226\pi\) | ||||
−0.898339 | + | 0.439303i | \(0.855226\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.8885 | 0.774360 | 0.387180 | − | 0.922004i | \(-0.373449\pi\) | ||||
0.387180 | + | 0.922004i | \(0.373449\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −87.4853 | −4.25368 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.6525 | −1.48338 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.23607 | −0.349361 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.9443 | 0.623504 | 0.311752 | − | 0.950164i | \(-0.399084\pi\) | ||||
0.311752 | + | 0.950164i | \(0.399084\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.1246 | 1.39964 | 0.699820 | − | 0.714319i | \(-0.253264\pi\) | ||||
0.699820 | + | 0.714319i | \(0.253264\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.00000 | 0.0478365 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.3607 | 0.589943 | 0.294972 | − | 0.955506i | \(-0.404690\pi\) | ||||
0.294972 | + | 0.955506i | \(0.404690\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 81.7771 | 3.89415 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.0000 | 0.475114 | 0.237557 | − | 0.971374i | \(-0.423653\pi\) | ||||
0.237557 | + | 0.971374i | \(0.423653\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −35.4164 | −1.67514 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.8328 | −1.73825 | −0.869124 | − | 0.494594i | \(-0.835317\pi\) | ||||
−0.869124 | + | 0.494594i | \(0.835317\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.94427 | −0.279905 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −37.3050 | −1.75274 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.6525 | 0.966082 | 0.483041 | − | 0.875598i | \(-0.339532\pi\) | ||||
0.483041 | + | 0.875598i | \(0.339532\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 93.6656 | 4.37194 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.6525 | 1.56735 | 0.783676 | − | 0.621170i | \(-0.213342\pi\) | ||||
0.783676 | + | 0.621170i | \(0.213342\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.4721 | 1.23026 | 0.615132 | − | 0.788424i | \(-0.289103\pi\) | ||||
0.615132 | + | 0.788424i | \(0.289103\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.0000 | 0.786666 | 0.393333 | − | 0.919396i | \(-0.371322\pi\) | ||||
0.393333 | + | 0.919396i | \(0.371322\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −54.8328 | −2.53194 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.944272 | 0.0435098 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.52786 | −0.116231 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.23607 | −0.422891 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.1246 | −0.553988 | −0.276994 | − | 0.960872i | \(-0.589338\pi\) | ||||
−0.276994 | + | 0.960872i | \(0.589338\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.1246 | −1.14558 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.7082 | −0.623745 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.1246 | 1.77291 | 0.886453 | − | 0.462819i | \(-0.153162\pi\) | ||||
0.886453 | + | 0.462819i | \(0.153162\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −37.8885 | −1.71338 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.23607 | −0.146042 | −0.0730209 | − | 0.997330i | \(-0.523264\pi\) | ||||
−0.0730209 | + | 0.997330i | \(0.523264\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.4164 | 0.514169 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 42.3607 | 1.90014 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −42.5410 | −1.90440 | −0.952199 | − | 0.305479i | \(-0.901183\pi\) | ||||
−0.952199 | + | 0.305479i | \(0.901183\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.5279 | −0.783087 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.5967 | −0.740012 | −0.370006 | − | 0.929029i | \(-0.620644\pi\) | ||||
−0.370006 | + | 0.929029i | \(0.620644\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.8885 | 1.14975 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.3607 | 1.34571 | 0.672857 | − | 0.739773i | \(-0.265067\pi\) | ||||
0.672857 | + | 0.739773i | \(0.265067\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 40.1246 | 1.77501 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.4721 | −0.638960 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.7082 | −0.514926 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 46.0689 | 2.02220 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.34752 | 0.409522 | 0.204761 | − | 0.978812i | \(-0.434358\pi\) | ||||
0.204761 | + | 0.978812i | \(0.434358\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.8885 | 0.825938 | 0.412969 | − | 0.910745i | \(-0.364492\pi\) | ||||
0.412969 | + | 0.910745i | \(0.364492\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.05573 | −0.133110 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.1803 | 1.04934 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.2918 | −0.575732 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 50.8328 | 2.19360 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.9443 | 0.471403 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.70820 | 0.374395 | 0.187197 | − | 0.982322i | \(-0.440060\pi\) | ||||
0.187197 | + | 0.982322i | \(0.440060\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.05573 | 0.131134 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.7082 | 0.671634 | 0.335817 | − | 0.941927i | \(-0.390988\pi\) | ||||
0.335817 | + | 0.941927i | \(0.390988\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −54.0689 | −2.30760 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.76393 | −0.0751460 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 64.3050 | 2.73452 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.1803 | −1.53301 | −0.766505 | − | 0.642238i | \(-0.778006\pi\) | ||||
−0.766505 | + | 0.642238i | \(0.778006\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.65248 | −0.239074 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.9443 | 0.884268 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 39.3607 | 1.65885 | 0.829427 | − | 0.558614i | \(-0.188667\pi\) | ||||
0.829427 | + | 0.558614i | \(0.188667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 103.430 | 4.34363 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.5836 | 0.527532 | 0.263766 | − | 0.964587i | \(-0.415035\pi\) | ||||
0.263766 | + | 0.964587i | \(0.415035\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.0000 | 1.00437 | 0.502184 | − | 0.864761i | \(-0.332530\pi\) | ||||
0.502184 | + | 0.864761i | \(0.332530\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 62.0689 | 2.59296 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.00000 | −0.374675 | −0.187337 | − | 0.982296i | \(-0.559986\pi\) | ||||
−0.187337 | + | 0.982296i | \(0.559986\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.52786 | 0.395965 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −38.1246 | −1.58168 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.23607 | −0.0511927 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.5967 | −1.13904 | −0.569520 | − | 0.821978i | \(-0.692871\pi\) | ||||
−0.569520 | + | 0.821978i | \(0.692871\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.472136 | 0.0194540 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.6525 | −1.09634 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −44.8885 | −1.84335 | −0.921676 | − | 0.387961i | \(-0.873180\pi\) | ||||
−0.921676 | + | 0.387961i | \(0.873180\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −41.1246 | −1.68312 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.8328 | 0.687770 | 0.343885 | − | 0.939012i | \(-0.388257\pi\) | ||||
0.343885 | + | 0.939012i | \(0.388257\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.9443 | −0.609590 | −0.304795 | − | 0.952418i | \(-0.598588\pi\) | ||||
−0.304795 | + | 0.952418i | \(0.598588\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −96.7214 | −3.93880 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.1246 | −0.938599 | −0.469300 | − | 0.883039i | \(-0.655494\pi\) | ||||
−0.469300 | + | 0.883039i | \(0.655494\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 24.1803 | 0.979837 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.1803 | −1.05914 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.0689 | 0.729795 | 0.364898 | − | 0.931048i | \(-0.381104\pi\) | ||||
0.364898 | + | 0.931048i | \(0.381104\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.3050 | −1.01874 | −0.509369 | − | 0.860548i | \(-0.670121\pi\) | ||||
−0.509369 | + | 0.860548i | \(0.670121\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.52786 | −0.382957 | −0.191479 | − | 0.981497i | \(-0.561328\pi\) | ||||
−0.191479 | + | 0.981497i | \(0.561328\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.4721 | −0.580747 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.47214 | 0.339429 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.23607 | −0.129236 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 72.7214 | 2.89959 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.1246 | −0.960386 | −0.480193 | − | 0.877163i | \(-0.659433\pi\) | ||||
−0.480193 | + | 0.877163i | \(0.659433\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 48.3607 | 1.92216 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.4721 | 0.969621 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 74.7214 | 2.95593 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.7771 | 1.09713 | 0.548564 | − | 0.836108i | \(-0.315175\pi\) | ||||
0.548564 | + | 0.836108i | \(0.315175\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.94427 | −0.0766746 | −0.0383373 | − | 0.999265i | \(-0.512206\pi\) | ||||
−0.0383373 | + | 0.999265i | \(0.512206\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.1803 | −0.400230 | −0.200115 | − | 0.979772i | \(-0.564132\pi\) | ||||
−0.200115 | + | 0.979772i | \(0.564132\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.23607 | 0.127027 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.47214 | −0.253663 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.5410 | 1.54736 | 0.773680 | − | 0.633577i | \(-0.218414\pi\) | ||||
0.773680 | + | 0.633577i | \(0.218414\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 70.7771 | 2.76128 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.4721 | 0.524800 | 0.262400 | − | 0.964959i | \(-0.415486\pi\) | ||||
0.262400 | + | 0.964959i | \(0.415486\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.8197 | −0.848686 | −0.424343 | − | 0.905501i | \(-0.639495\pi\) | ||||
−0.424343 | + | 0.905501i | \(0.639495\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 46.8328 | 1.81884 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.76393 | −0.0682997 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 42.8328 | 1.65601 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.23607 | −0.279345 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.3050 | −1.86202 | −0.931010 | − | 0.364995i | \(-0.881071\pi\) | ||||
−0.931010 | + | 0.364995i | \(0.881071\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.7082 | 0.680582 | 0.340291 | − | 0.940320i | \(-0.389474\pi\) | ||||
0.340291 | + | 0.940320i | \(0.389474\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.1803 | −1.00471 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 41.8885 | 1.60517 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.7771 | −1.59856 | −0.799278 | − | 0.600962i | \(-0.794784\pi\) | ||||
−0.799278 | + | 0.600962i | \(0.794784\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22.4721 | −0.857365 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.76393 | −0.105297 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −42.4721 | −1.61572 | −0.807858 | − | 0.589377i | \(-0.799373\pi\) | ||||
−0.807858 | + | 0.589377i | \(0.799373\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 31.6525 | 1.20238 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.4721 | 1.45724 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.6525 | 0.554208 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.5279 | −1.41741 | −0.708704 | − | 0.705506i | \(-0.750720\pi\) | ||||
−0.708704 | + | 0.705506i | \(0.750720\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.2361 | −0.423776 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −80.2492 | −3.01808 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.41641 | 0.353641 | 0.176820 | − | 0.984243i | \(-0.443419\pi\) | ||||
0.176820 | + | 0.984243i | \(0.443419\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 113.430 | 4.25394 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.472136 | 0.0176816 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.8885 | −0.817443 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 37.7082 | 1.40628 | 0.703139 | − | 0.711052i | \(-0.251781\pi\) | ||||
0.703139 | + | 0.711052i | \(0.251781\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.47214 | 0.352761 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −68.7214 | −2.55577 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.7214 | −1.65862 | −0.829312 | − | 0.558786i | \(-0.811267\pi\) | ||||
−0.829312 | + | 0.558786i | \(0.811267\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 41.9443 | 1.55349 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.3607 | 0.605122 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.5279 | 1.45999 | 0.729997 | − | 0.683450i | \(-0.239521\pi\) | ||||
0.729997 | + | 0.683450i | \(0.239521\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.9443 | −0.476808 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.05573 | 0.333120 | 0.166560 | − | 0.986031i | \(-0.446734\pi\) | ||||
0.166560 | + | 0.986031i | \(0.446734\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.23607 | −0.265824 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −39.1803 | −1.43739 | −0.718694 | − | 0.695327i | \(-0.755260\pi\) | ||||
−0.718694 | + | 0.695327i | \(0.755260\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −67.2492 | −2.46052 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 82.2492 | 3.00532 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.5967 | −0.824567 | −0.412284 | − | 0.911056i | \(-0.635269\pi\) | ||||
−0.412284 | + | 0.911056i | \(0.635269\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.8885 | 0.651895 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.7639 | 0.609295 | 0.304648 | − | 0.952465i | \(-0.401461\pi\) | ||||
0.304648 | + | 0.952465i | \(0.401461\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.23607 | −0.117462 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −52.8885 | −1.91721 | −0.958604 | − | 0.284742i | \(-0.908092\pi\) | ||||
−0.958604 | + | 0.284742i | \(0.908092\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −54.0689 | −1.95743 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.23607 | 0.261279 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −46.0689 | −1.66129 | −0.830643 | − | 0.556805i | \(-0.812027\pi\) | ||||
−0.830643 | + | 0.556805i | \(0.812027\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −45.3050 | −1.63162 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.76393 | 0.171347 | 0.0856734 | − | 0.996323i | \(-0.472696\pi\) | ||||
0.0856734 | + | 0.996323i | \(0.472696\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 154.026 | 5.52566 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.94427 | −0.212976 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0000 | 0.357828 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 25.5279 | 0.912291 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.7214 | −1.41591 | −0.707957 | − | 0.706256i | \(-0.750383\pi\) | ||||
−0.707957 | + | 0.706256i | \(0.750383\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 25.8885 | 0.921657 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −28.6525 | −1.01876 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.1803 | −0.574581 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.2361 | −0.539689 | −0.269845 | − | 0.962904i | \(-0.586972\pi\) | ||||
−0.269845 | + | 0.962904i | \(0.586972\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 75.7771 | 2.68080 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.9443 | 0.528030 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.47214 | 0.334264 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 81.4853 | 2.86842 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.11146 | −0.320342 | −0.160171 | − | 0.987089i | \(-0.551205\pi\) | ||||
−0.160171 | + | 0.987089i | \(0.551205\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.4164 | 0.541343 | 0.270672 | − | 0.962672i | \(-0.412754\pi\) | ||||
0.270672 | + | 0.962672i | \(0.412754\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 103.777 | 3.63962 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.52786 | −0.0884388 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 70.7771 | 2.47315 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.2361 | −0.776044 | −0.388022 | − | 0.921650i | \(-0.626842\pi\) | ||||
−0.388022 | + | 0.921650i | \(0.626842\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.94427 | −0.311778 | −0.155889 | − | 0.987775i | \(-0.549824\pi\) | ||||
−0.155889 | + | 0.987775i | \(0.549824\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.00000 | −0.104320 | −0.0521601 | − | 0.998639i | \(-0.516611\pi\) | ||||
−0.0521601 | + | 0.998639i | \(0.516611\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.23607 | −0.147125 | −0.0735624 | − | 0.997291i | \(-0.523437\pi\) | ||||
−0.0735624 | + | 0.997291i | \(0.523437\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 46.0689 | 1.59811 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −70.8328 | −2.45421 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.83282 | −0.236177 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.59675 | 0.296793 | 0.148396 | − | 0.988928i | \(-0.452589\pi\) | ||||
0.148396 | + | 0.988928i | \(0.452589\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.8885 | −0.892708 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 71.7771 | 2.47213 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −42.3607 | −1.45553 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 91.7771 | 3.14978 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.2361 | −0.385167 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.2361 | −0.966785 | −0.483392 | − | 0.875404i | \(-0.660596\pi\) | ||||
−0.483392 | + | 0.875404i | \(0.660596\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.3050 | 1.20599 | 0.602997 | − | 0.797743i | \(-0.293973\pi\) | ||||
0.602997 | + | 0.797743i | \(0.293973\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.7082 | −0.740674 | −0.370337 | − | 0.928897i | \(-0.620758\pi\) | ||||
−0.370337 | + | 0.928897i | \(0.620758\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 81.4853 | 2.77701 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.5410 | 1.17579 | 0.587895 | − | 0.808937i | \(-0.299957\pi\) | ||||
0.587895 | + | 0.808937i | \(0.299957\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −80.5410 | −2.73532 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.1803 | 0.514958 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.9443 | −0.980739 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −46.1803 | −1.56297 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.58359 | 0.0872417 | 0.0436209 | − | 0.999048i | \(-0.486111\pi\) | ||||
0.0436209 | + | 0.999048i | \(0.486111\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −46.8328 | −1.57963 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.7082 | 1.27042 | 0.635211 | − | 0.772339i | \(-0.280913\pi\) | ||||
0.635211 | + | 0.772339i | \(0.280913\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.05573 | 0.102833 | 0.0514167 | − | 0.998677i | \(-0.483626\pi\) | ||||
0.0514167 | + | 0.998677i | \(0.483626\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.3607 | 0.415031 | 0.207516 | − | 0.978232i | \(-0.433462\pi\) | ||||
0.207516 | + | 0.978232i | \(0.433462\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.7082 | 0.593914 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.4164 | 0.817980 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.7082 | −0.391800 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.23607 | −0.241605 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.832816 | −0.0277760 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.00000 | 0.266519 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 34.6525 | 1.15316 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.58359 | 0.185400 | 0.0927001 | − | 0.995694i | \(-0.470450\pi\) | ||||
0.0927001 | + | 0.995694i | \(0.470450\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −141.554 | −4.69506 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.0689 | −1.02936 | −0.514679 | − | 0.857383i | \(-0.672089\pi\) | ||||
−0.514679 | + | 0.857383i | \(0.672089\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.00000 | −0.297857 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −63.3050 | −2.09051 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.7771 | 1.44407 | 0.722036 | − | 0.691855i | \(-0.243206\pi\) | ||||
0.722036 | + | 0.691855i | \(0.243206\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 77.6656 | 2.55917 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.3607 | 0.736011 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.7082 | 0.548769 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.0000 | 1.01708 | 0.508539 | − | 0.861039i | \(-0.330186\pi\) | ||||
0.508539 | + | 0.861039i | \(0.330186\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.9443 | 0.358684 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.4721 | 0.342842 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.12461 | −0.232751 | −0.116375 | − | 0.993205i | \(-0.537128\pi\) | ||||
−0.116375 | + | 0.993205i | \(0.537128\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −34.4721 | −1.12496 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.2361 | −0.431483 | −0.215742 | − | 0.976450i | \(-0.569217\pi\) | ||||
−0.215742 | + | 0.976450i | \(0.569217\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.94427 | −0.193572 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.1935 | −1.46859 | −0.734296 | − | 0.678830i | \(-0.762487\pi\) | ||||
−0.734296 | + | 0.678830i | \(0.762487\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.1803 | 0.687543 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −71.5967 | −2.32168 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.34752 | −0.173223 | −0.0866116 | − | 0.996242i | \(-0.527604\pi\) | ||||
−0.0866116 | + | 0.996242i | \(0.527604\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.70820 | 0.184520 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −48.8328 | −1.57689 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7771 | −0.992809 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 145.082 | 4.67520 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.88854 | −0.189363 | −0.0946814 | − | 0.995508i | \(-0.530183\pi\) | ||||
−0.0946814 | + | 0.995508i | \(0.530183\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 20.9443 | 0.672827 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.2492 | 1.19538 | 0.597692 | − | 0.801726i | \(-0.296084\pi\) | ||||
0.597692 | + | 0.801726i | \(0.296084\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 84.7214 | 2.71604 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.5410 | −0.721151 | −0.360576 | − | 0.932730i | \(-0.617420\pi\) | ||||
−0.360576 | + | 0.932730i | \(0.617420\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.00000 | 0.0639203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −95.3738 | −3.04505 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.6525 | −0.881977 | −0.440989 | − | 0.897513i | \(-0.645372\pi\) | ||||
−0.440989 | + | 0.897513i | \(0.645372\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 160.498 | 5.10872 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.52786 | −0.0803814 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.5967 | −1.32136 | −0.660682 | − | 0.750666i | \(-0.729733\pi\) | ||||
−0.660682 | + | 0.750666i | \(0.729733\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −100.138 | −3.17778 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.12461 | 0.0672871 | 0.0336436 | − | 0.999434i | \(-0.489289\pi\) | ||||
0.0336436 | + | 0.999434i | \(0.489289\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 162.610 | 5.14475 |
(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 | 4600.2.a.q.1.1 | ✓ | 2 | |
4.3 | odd | 2 | 9200.2.a.bz.1.2 | 2 | |||
5.2 | odd | 4 | 4600.2.e.l.4049.4 | 4 | |||
5.3 | odd | 4 | 4600.2.e.l.4049.1 | 4 | |||
5.4 | even | 2 | 4600.2.a.u.1.2 | yes | 2 | ||
20.19 | odd | 2 | 9200.2.a.bn.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.q.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
4600.2.a.u.1.2 | yes | 2 | 5.4 | even | 2 | ||
4600.2.e.l.4049.1 | 4 | 5.3 | odd | 4 | |||
4600.2.e.l.4049.4 | 4 | 5.2 | odd | 4 | |||
9200.2.a.bn.1.1 | 2 | 20.19 | odd | 2 | |||
9200.2.a.bz.1.2 | 2 | 4.3 | odd | 2 |