Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2960,2,Mod(1,2960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2960, 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("2960.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2960 = 2^{4} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2960.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: | \(23.6357189983\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1480) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.363328\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2960.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.363328 | 0.209768 | 0.104884 | − | 0.994484i | \(-0.466553\pi\) | ||||
0.104884 | + | 0.994484i | \(0.466553\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.363328 | −0.137325 | −0.0686626 | − | 0.997640i | \(-0.521873\pi\) | ||||
−0.0686626 | + | 0.997640i | \(0.521873\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.86799 | −0.955998 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.14134 | 0.344126 | 0.172063 | − | 0.985086i | \(-0.444957\pi\) | ||||
0.172063 | + | 0.985086i | \(0.444957\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.363328 | 0.0938109 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.77801 | −1.09615 | −0.548075 | − | 0.836429i | \(-0.684639\pi\) | ||||
−0.548075 | + | 0.836429i | \(0.684639\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.132007 | −0.0288064 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.13201 | −0.410305 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.28267 | 0.795272 | 0.397636 | − | 0.917543i | \(-0.369831\pi\) | ||||
0.397636 | + | 0.917543i | \(0.369831\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.50466 | −0.988667 | −0.494333 | − | 0.869272i | \(-0.664588\pi\) | ||||
−0.494333 | + | 0.869272i | \(0.664588\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.414680 | 0.0721865 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.363328 | −0.0614137 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.86799 | 0.604079 | 0.302039 | − | 0.953295i | \(-0.402333\pi\) | ||||
0.302039 | + | 0.953295i | \(0.402333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.28267 | 0.348104 | 0.174052 | − | 0.984736i | \(-0.444314\pi\) | ||||
0.174052 | + | 0.984736i | \(0.444314\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.86799 | −0.427535 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.9287 | −1.88584 | −0.942920 | − | 0.333018i | \(-0.891933\pi\) | ||||
−0.942920 | + | 0.333018i | \(0.891933\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.86799 | −0.981142 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.15066 | −0.844859 | −0.422429 | − | 0.906396i | \(-0.638823\pi\) | ||||
−0.422429 | + | 0.906396i | \(0.638823\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.14134 | 0.153898 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.73599 | −0.229937 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.78734 | −1.01382 | −0.506912 | − | 0.861998i | \(-0.669213\pi\) | ||||
−0.506912 | + | 0.861998i | \(0.669213\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.546687 | −0.0699961 | −0.0349981 | − | 0.999387i | \(-0.511143\pi\) | ||||
−0.0349981 | + | 0.999387i | \(0.511143\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.04202 | 0.131283 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.212663 | −0.0259810 | −0.0129905 | − | 0.999916i | \(-0.504135\pi\) | ||||
−0.0129905 | + | 0.999916i | \(0.504135\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.45331 | −0.174958 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.58532 | −0.425499 | −0.212750 | − | 0.977107i | \(-0.568242\pi\) | ||||
−0.212750 | + | 0.977107i | \(0.568242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.69735 | 1.01795 | 0.508974 | − | 0.860782i | \(-0.330025\pi\) | ||||
0.508974 | + | 0.860782i | \(0.330025\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.363328 | 0.0419535 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.414680 | −0.0472571 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.06068 | 0.794389 | 0.397194 | − | 0.917735i | \(-0.369984\pi\) | ||||
0.397194 | + | 0.917735i | \(0.369984\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.82936 | 0.869929 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.466031 | 0.0511536 | 0.0255768 | − | 0.999673i | \(-0.491858\pi\) | ||||
0.0255768 | + | 0.999673i | \(0.491858\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.55602 | 0.166822 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.0187 | −1.69797 | −0.848987 | − | 0.528414i | \(-0.822787\pi\) | ||||
−0.848987 | + | 0.528414i | \(0.822787\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | −0.207390 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.77801 | −0.490213 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000 | 0.609208 | 0.304604 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304604 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.27334 | −0.328983 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.6040 | 1.35365 | 0.676823 | − | 0.736146i | \(-0.263356\pi\) | ||||
0.676823 | + | 0.736146i | \(0.263356\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.17997 | −0.608930 | −0.304465 | − | 0.952523i | \(-0.598478\pi\) | ||||
−0.304465 | + | 0.952523i | \(0.598478\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.132007 | −0.0128826 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.7967 | −1.81714 | −0.908571 | − | 0.417730i | \(-0.862826\pi\) | ||||
−0.908571 | + | 0.417730i | \(0.862826\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.54669 | −0.435494 | −0.217747 | − | 0.976005i | \(-0.569871\pi\) | ||||
−0.217747 | + | 0.976005i | \(0.569871\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.363328 | 0.0344856 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.82936 | −0.830596 | −0.415298 | − | 0.909685i | \(-0.636323\pi\) | ||||
−0.415298 | + | 0.909685i | \(0.636323\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | −0.373002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.69735 | −0.881577 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.40535 | 0.126716 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.7487 | −0.953793 | −0.476897 | − | 0.878959i | \(-0.658238\pi\) | ||||
−0.476897 | + | 0.878959i | \(0.658238\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.829359 | 0.0730210 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.50466 | 0.480945 | 0.240472 | − | 0.970656i | \(-0.422698\pi\) | ||||
0.240472 | + | 0.970656i | \(0.422698\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.73599 | 0.150529 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.13201 | −0.183494 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.45331 | 0.295036 | 0.147518 | − | 0.989059i | \(-0.452871\pi\) | ||||
0.147518 | + | 0.989059i | \(0.452871\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.0187 | −0.849771 | −0.424886 | − | 0.905247i | \(-0.639686\pi\) | ||||
−0.424886 | + | 0.905247i | \(0.639686\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.69735 | −0.395588 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.28267 | 0.355657 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.49534 | −0.205812 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.86799 | −0.153032 | −0.0765160 | − | 0.997068i | \(-0.524380\pi\) | ||||
−0.0765160 | + | 0.997068i | \(0.524380\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.46264 | 0.363165 | 0.181582 | − | 0.983376i | \(-0.441878\pi\) | ||||
0.181582 | + | 0.983376i | \(0.441878\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.50466 | −0.442145 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.1693 | 1.60969 | 0.804844 | − | 0.593487i | \(-0.202249\pi\) | ||||
0.804844 | + | 0.593487i | \(0.202249\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.23471 | −0.177224 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.45331 | 0.114537 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.55602 | −0.748485 | −0.374242 | − | 0.927331i | \(-0.622097\pi\) | ||||
−0.374242 | + | 0.927331i | \(0.622097\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.414680 | 0.0322828 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.8387 | 1.22563 | 0.612817 | − | 0.790225i | \(-0.290036\pi\) | ||||
0.612817 | + | 0.790225i | \(0.290036\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.7033 | 1.04792 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.8680 | 1.20642 | 0.603211 | − | 0.797582i | \(-0.293888\pi\) | ||||
0.603211 | + | 0.797582i | \(0.293888\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.363328 | −0.0274650 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.82936 | −0.212668 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.34335 | 0.698355 | 0.349177 | − | 0.937057i | \(-0.386461\pi\) | ||||
0.349177 | + | 0.937057i | \(0.386461\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.2627 | −1.43178 | −0.715892 | − | 0.698211i | \(-0.753980\pi\) | ||||
−0.715892 | + | 0.698211i | \(0.753980\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.198627 | −0.0146829 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.00000 | 0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.774618 | 0.0563452 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.32469 | −0.240566 | −0.120283 | − | 0.992740i | \(-0.538380\pi\) | ||||
−0.120283 | + | 0.992740i | \(0.538380\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.73599 | −0.124959 | −0.0624795 | − | 0.998046i | \(-0.519901\pi\) | ||||
−0.0624795 | + | 0.998046i | \(0.519901\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.41468 | −0.172039 | −0.0860194 | − | 0.996293i | \(-0.527415\pi\) | ||||
−0.0860194 | + | 0.996293i | \(0.527415\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.05135 | −0.287193 | −0.143596 | − | 0.989636i | \(-0.545867\pi\) | ||||
−0.143596 | + | 0.989636i | \(0.545867\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.0772666 | −0.00544997 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.55602 | −0.109211 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.86799 | 0.270152 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.4720 | 0.797357 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.45331 | −0.377214 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.56666 | 0.107854 | 0.0539268 | − | 0.998545i | \(-0.482826\pi\) | ||||
0.0539268 | + | 0.998545i | \(0.482826\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.30265 | −0.0892560 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.28267 | 0.155677 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.15999 | 0.213533 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.0900 | 1.14443 | 0.572215 | − | 0.820104i | \(-0.306084\pi\) | ||||
0.572215 | + | 0.820104i | \(0.306084\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.86799 | −0.191200 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.99067 | −0.331242 | −0.165621 | − | 0.986189i | \(-0.552963\pi\) | ||||
−0.165621 | + | 0.986189i | \(0.552963\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.1693 | −1.86148 | −0.930741 | − | 0.365680i | \(-0.880836\pi\) | ||||
−0.930741 | + | 0.365680i | \(0.880836\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.150665 | −0.00991302 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.9287 | −0.843374 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.56534 | 0.166637 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.9766 | 1.35687 | 0.678433 | − | 0.734662i | \(-0.262659\pi\) | ||||
0.678433 | + | 0.734662i | \(0.262659\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.30133 | 0.148242 | 0.0741208 | − | 0.997249i | \(-0.476385\pi\) | ||||
0.0741208 | + | 0.997249i | \(0.476385\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.24065 | 0.592788 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.86799 | −0.438780 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.169322 | 0.0107304 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.7967 | −1.69139 | −0.845695 | − | 0.533666i | \(-0.820814\pi\) | ||||
−0.845695 | + | 0.533666i | \(0.820814\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.56534 | −0.287021 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.8294 | 1.04979 | 0.524893 | − | 0.851168i | \(-0.324105\pi\) | ||||
0.524893 | + | 0.851168i | \(0.324105\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.363328 | −0.0225761 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.2827 | −0.760278 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.91934 | −0.118352 | −0.0591759 | − | 0.998248i | \(-0.518847\pi\) | ||||
−0.0591759 | + | 0.998248i | \(0.518847\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.15066 | −0.377832 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.82003 | −0.356180 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.3013 | 0.750025 | 0.375013 | − | 0.927020i | \(-0.377638\pi\) | ||||
0.375013 | + | 0.927020i | \(0.377638\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.8867 | 1.69399 | 0.846997 | − | 0.531598i | \(-0.178408\pi\) | ||||
0.846997 | + | 0.531598i | \(0.178408\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.14134 | 0.0688252 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.3013 | −0.979452 | −0.489726 | − | 0.871876i | \(-0.662903\pi\) | ||||
−0.489726 | + | 0.871876i | \(0.662903\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 15.7873 | 0.945163 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.90663 | −0.531325 | −0.265662 | − | 0.964066i | \(-0.585591\pi\) | ||||
−0.265662 | + | 0.964066i | \(0.585591\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5747 | 0.925818 | 0.462909 | − | 0.886406i | \(-0.346806\pi\) | ||||
0.462909 | + | 0.886406i | \(0.346806\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.73599 | −0.102831 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.40535 | −0.0829552 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.17997 | 0.127792 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.0000 | −0.584206 | −0.292103 | − | 0.956387i | \(-0.594355\pi\) | ||||
−0.292103 | + | 0.956387i | \(0.594355\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.78734 | −0.453396 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.43334 | −0.141197 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.829359 | −0.0478035 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.94271 | 0.283951 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.546687 | −0.0313032 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.3727 | −0.649072 | −0.324536 | − | 0.945873i | \(-0.605208\pi\) | ||||
−0.324536 | + | 0.945873i | \(0.605208\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.24536 | −0.127734 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.24065 | −0.0703508 | −0.0351754 | − | 0.999381i | \(-0.511199\pi\) | ||||
−0.0351754 | + | 0.999381i | \(0.511199\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.9066 | −0.729526 | −0.364763 | − | 0.931100i | \(-0.618850\pi\) | ||||
−0.364763 | + | 0.931100i | \(0.618850\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.04202 | 0.0587113 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.0186574 | −0.00104790 | −0.000523952 | − | 1.00000i | \(-0.500167\pi\) | ||||
−0.000523952 | 1.00000i | \(0.500167\pi\) | ||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.88797 | 0.273674 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.82936 | −0.381178 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.65194 | −0.0913525 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.69735 | 0.258973 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.24065 | −0.507912 | −0.253956 | − | 0.967216i | \(-0.581732\pi\) | ||||
−0.253956 | + | 0.967216i | \(0.581732\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.86799 | −0.157165 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.212663 | −0.0116190 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.6226 | 1.39575 | 0.697877 | − | 0.716218i | \(-0.254128\pi\) | ||||
0.697877 | + | 0.716218i | \(0.254128\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.20796 | −0.174232 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.28267 | −0.340226 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.03863 | 0.272061 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.45331 | −0.0782437 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.45331 | −0.507480 | −0.253740 | − | 0.967272i | \(-0.581661\pi\) | ||||
−0.253740 | + | 0.967272i | \(0.581661\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.2640 | −0.870593 | −0.435296 | − | 0.900287i | \(-0.643356\pi\) | ||||
−0.435296 | + | 0.900287i | \(0.643356\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.43466 | 0.289258 | 0.144629 | − | 0.989486i | \(-0.453801\pi\) | ||||
0.144629 | + | 0.989486i | \(0.453801\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.58532 | −0.190289 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.85866 | 0.150875 | 0.0754373 | − | 0.997151i | \(-0.475965\pi\) | ||||
0.0754373 | + | 0.997151i | \(0.475965\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.82936 | 0.201545 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.52332 | −0.184926 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.69735 | 0.455240 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.77801 | 0.249410 | 0.124705 | − | 0.992194i | \(-0.460202\pi\) | ||||
0.124705 | + | 0.992194i | \(0.460202\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.0934 | −0.577498 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.23471 | 0.116020 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.433337 | 0.0224373 | 0.0112187 | − | 0.999937i | \(-0.496429\pi\) | ||||
0.0112187 | + | 0.999937i | \(0.496429\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.363328 | 0.0187622 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.8587 | −0.763238 | −0.381619 | − | 0.924320i | \(-0.624633\pi\) | ||||
−0.381619 | + | 0.924320i | \(0.624633\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.90531 | −0.200075 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.73599 | 0.395290 | 0.197645 | − | 0.980274i | \(-0.436671\pi\) | ||||
0.197645 | + | 0.980274i | \(0.436671\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.414680 | −0.0211340 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.54669 | −0.332787 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.7546 | −0.798792 | −0.399396 | − | 0.916778i | \(-0.630780\pi\) | ||||
−0.399396 | + | 0.916778i | \(0.630780\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.00000 | 0.100887 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.06068 | 0.355261 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.58532 | 0.280319 | 0.140160 | − | 0.990129i | \(-0.455238\pi\) | ||||
0.140160 | + | 0.990129i | \(0.455238\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.630732 | 0.0315761 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.11203 | −0.0555322 | −0.0277661 | − | 0.999614i | \(-0.508839\pi\) | ||||
−0.0277661 | + | 0.999614i | \(0.508839\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.82936 | 0.389044 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.14134 | 0.0565739 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.8480 | −0.833081 | −0.416540 | − | 0.909117i | \(-0.636758\pi\) | ||||
−0.416540 | + | 0.909117i | \(0.636758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.25469 | 0.0618891 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.82936 | 0.139224 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.466031 | 0.0228766 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.64006 | −0.178255 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.8960 | −1.31395 | −0.656977 | − | 0.753910i | \(-0.728165\pi\) | ||||
−0.656977 | + | 0.753910i | \(0.728165\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.8480 | 0.821122 | 0.410561 | − | 0.911833i | \(-0.365333\pi\) | ||||
0.410561 | + | 0.911833i | \(0.365333\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 37.0793 | 1.80286 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.198627 | 0.00961223 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.11929 | 0.150251 | 0.0751254 | − | 0.997174i | \(-0.476064\pi\) | ||||
0.0751254 | + | 0.997174i | \(0.476064\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.43334 | 0.405280 | 0.202640 | − | 0.979253i | \(-0.435048\pi\) | ||||
0.202640 | + | 0.979253i | \(0.435048\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.55602 | 0.0746052 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.1120 | 0.914252 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.3434 | 1.20957 | 0.604786 | − | 0.796388i | \(-0.293259\pi\) | ||||
0.604786 | + | 0.796388i | \(0.293259\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.6974 | 0.937969 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.8446 | 1.27543 | 0.637713 | − | 0.770274i | \(-0.279880\pi\) | ||||
0.637713 | + | 0.770274i | \(0.279880\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.0187 | −0.759357 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.678694 | −0.0321011 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.0000 | 0.660701 | 0.330350 | − | 0.943858i | \(-0.392833\pi\) | ||||
0.330350 | + | 0.943858i | \(0.392833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.41468 | 0.207879 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.62140 | 0.0761802 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.6587 | −0.919596 | −0.459798 | − | 0.888024i | \(-0.652078\pi\) | ||||
−0.459798 | + | 0.888024i | \(0.652078\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.6027 | 1.79791 | 0.898953 | − | 0.438046i | \(-0.144329\pi\) | ||||
0.898953 | + | 0.438046i | \(0.144329\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.7546 | 1.75461 | 0.877304 | − | 0.479936i | \(-0.159340\pi\) | ||||
0.877304 | + | 0.479936i | \(0.159340\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.00000 | −0.0927478 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.9507 | −0.691837 | −0.345918 | − | 0.938265i | \(-0.612433\pi\) | ||||
−0.345918 | + | 0.938265i | \(0.612433\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.0772666 | 0.00356784 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.32808 | 0.337660 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.60530 | 0.119792 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.77801 | −0.219230 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.6401 | 0.807683 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.21266 | −0.375246 | −0.187623 | − | 0.982241i | \(-0.560078\pi\) | ||||
−0.187623 | + | 0.982241i | \(0.560078\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.528030 | 0.0240262 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.00000 | 0.272446 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.5747 | 1.24953 | 0.624764 | − | 0.780814i | \(-0.285195\pi\) | ||||
0.624764 | + | 0.780814i | \(0.285195\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.47197 | −0.157008 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.4906 | 1.15038 | 0.575188 | − | 0.818021i | \(-0.304929\pi\) | ||||
0.575188 | + | 0.818021i | \(0.304929\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.27334 | −0.147126 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.30265 | 0.0584318 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.4020 | −0.958083 | −0.479042 | − | 0.877792i | \(-0.659016\pi\) | ||||
−0.479042 | + | 0.877792i | \(0.659016\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.75464 | 0.257098 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.45331 | 0.243151 | 0.121576 | − | 0.992582i | \(-0.461205\pi\) | ||||
0.121576 | + | 0.992582i | \(0.461205\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.6040 | 0.605369 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.72327 | −0.209768 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.4333 | −1.61488 | −0.807440 | − | 0.589950i | \(-0.799147\pi\) | ||||
−0.807440 | + | 0.589950i | \(0.799147\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.15999 | −0.139790 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.1867 | 0.449756 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.17997 | −0.272322 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.7560 | −0.648966 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.76529 | 0.253068 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.6040 | 0.771244 | 0.385622 | − | 0.922657i | \(-0.373987\pi\) | ||||
0.385622 | + | 0.922657i | \(0.373987\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.71733 | 0.250001 | 0.125001 | − | 0.992157i | \(-0.460107\pi\) | ||||
0.125001 | + | 0.992157i | \(0.460107\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.132007 | −0.00576128 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.3340 | 0.969214 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.7967 | −0.812651 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.39470 | 0.146492 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.83869 | −0.337636 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.90663 | −0.382926 | −0.191463 | − | 0.981500i | \(-0.561323\pi\) | ||||
−0.191463 | + | 0.981500i | \(0.561323\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.99868 | −0.300342 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.54669 | −0.194759 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.8133 | −0.932667 | −0.466334 | − | 0.884609i | \(-0.654425\pi\) | ||||
−0.466334 | + | 0.884609i | \(0.654425\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.56789 | 0.0669161 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.4626 | −0.871738 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.56534 | −0.109090 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.363328 | 0.0154224 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 41.1307 | 1.74276 | 0.871382 | − | 0.490606i | \(-0.163224\pi\) | ||||
0.871382 | + | 0.490606i | \(0.163224\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.5467 | −0.613070 | −0.306535 | − | 0.951859i | \(-0.599170\pi\) | ||||
−0.306535 | + | 0.951859i | \(0.599170\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.82936 | −0.371454 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.84463 | −0.119463 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.5467 | 1.02905 | 0.514525 | − | 0.857475i | \(-0.327968\pi\) | ||||
0.514525 | + | 0.857475i | \(0.327968\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.1693 | 0.760362 | 0.380181 | − | 0.924912i | \(-0.375862\pi\) | ||||
0.380181 | + | 0.924912i | \(0.375862\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.20796 | −0.0504631 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.65872 | 0.402098 | 0.201049 | − | 0.979581i | \(-0.435565\pi\) | ||||
0.201049 | + | 0.979581i | \(0.435565\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.630732 | −0.0262123 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.169322 | −0.00702467 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.01998 | −0.290738 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.3200 | 1.25144 | 0.625720 | − | 0.780048i | \(-0.284805\pi\) | ||||
0.625720 | + | 0.780048i | \(0.284805\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.3013 | 1.08373 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.877321 | −0.0360882 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.8280 | 1.22489 | 0.612445 | − | 0.790513i | \(-0.290186\pi\) | ||||
0.612445 | + | 0.790513i | \(0.290186\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.47197 | −0.0602437 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.95204 | 0.324911 | 0.162456 | − | 0.986716i | \(-0.448059\pi\) | ||||
0.162456 | + | 0.986716i | \(0.448059\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.3947 | −1.03587 | −0.517936 | − | 0.855420i | \(-0.673299\pi\) | ||||
−0.517936 | + | 0.855420i | \(0.673299\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.609917 | 0.0248377 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.69735 | −0.394253 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.4533 | 1.19547 | 0.597737 | − | 0.801693i | \(-0.296067\pi\) | ||||
0.597737 | + | 0.801693i | \(0.296067\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.565344 | −0.0229089 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.32131 | −0.0533670 | −0.0266835 | − | 0.999644i | \(-0.508495\pi\) | ||||
−0.0266835 | + | 0.999644i | \(0.508495\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.40535 | 0.0566692 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 43.6999 | 1.75929 | 0.879646 | − | 0.475629i | \(-0.157780\pi\) | ||||
0.879646 | + | 0.475629i | \(0.157780\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.209274 | −0.00841143 | −0.00420572 | − | 0.999991i | \(-0.501339\pi\) | ||||
−0.00420572 | + | 0.999991i | \(0.501339\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.52803 | 0.342218 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.82003 | 0.233175 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.98134 | −0.0791272 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.0700 | 1.03783 | 0.518915 | − | 0.854826i | \(-0.326336\pi\) | ||||
0.518915 | + | 0.854826i | \(0.326336\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.569213 | 0.0226242 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.7487 | −0.426549 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.2827 | 0.406776 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.0921 | −0.951579 | −0.475789 | − | 0.879559i | \(-0.657838\pi\) | ||||
−0.475789 | + | 0.879559i | \(0.657838\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.5933 | −1.16705 | −0.583524 | − | 0.812096i | \(-0.698326\pi\) | ||||
−0.583524 | + | 0.812096i | \(0.698326\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.829359 | 0.0326560 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.7733 | −1.40639 | −0.703197 | − | 0.710995i | \(-0.748245\pi\) | ||||
−0.703197 | + | 0.710995i | \(0.748245\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.88797 | −0.348883 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.726656 | 0.0284799 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.3786 | 0.954008 | 0.477004 | − | 0.878901i | \(-0.341723\pi\) | ||||
0.477004 | + | 0.878901i | \(0.341723\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.50466 | 0.215085 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −24.9439 | −0.973156 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.5454 | 0.683471 | 0.341735 | − | 0.939796i | \(-0.388985\pi\) | ||||
0.341735 | + | 0.939796i | \(0.388985\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.0560 | 1.24683 | 0.623416 | − | 0.781890i | \(-0.285744\pi\) | ||||
0.623416 | + | 0.781890i | \(0.285744\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.73599 | 0.0673186 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.1307 | −0.663303 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.20927 | 0.240064 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.623954 | −0.0240875 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.2440 | 0.895992 | 0.447996 | − | 0.894036i | \(-0.352138\pi\) | ||||
0.447996 | + | 0.894036i | \(0.352138\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.13201 | −0.0820610 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.0734 | 0.771483 | 0.385742 | − | 0.922607i | \(-0.373946\pi\) | ||||
0.385742 | + | 0.922607i | \(0.373946\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.17997 | −0.0836595 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.81325 | −0.0694840 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.4533 | 0.973944 | 0.486972 | − | 0.873418i | \(-0.338101\pi\) | ||||
0.486972 | + | 0.873418i | \(0.338101\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.45331 | 0.131944 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.2347 | −0.390479 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.19608 | −0.0455009 | −0.0227505 | − | 0.999741i | \(-0.507242\pi\) | ||||
−0.0227505 | + | 0.999741i | \(0.507242\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.18930 | 0.0451777 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.0187 | −0.380029 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.17997 | −0.0824540 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.9414 | 1.13087 | 0.565435 | − | 0.824793i | \(-0.308708\pi\) | ||||
0.565435 | + | 0.824793i | \(0.308708\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.77801 | −0.180206 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.69735 | −0.176913 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.94271 | −0.185890 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.0959 | −0.980053 | −0.490026 | − | 0.871708i | \(-0.663013\pi\) | ||||
−0.490026 | + | 0.871708i | \(0.663013\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.2500 | −0.759434 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.0187 | 0.824605 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.62140 | 0.284627 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.5360 | −0.691278 | −0.345639 | − | 0.938368i | \(-0.612338\pi\) | ||||
−0.345639 | + | 0.938368i | \(0.612338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.24536 | 0.0836215 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.836138 | 0.0310963 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.28267 | 0.159054 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.0959 | 1.33872 | 0.669362 | − | 0.742937i | \(-0.266568\pi\) | ||||
0.669362 | + | 0.742937i | \(0.266568\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.1307 | −0.745581 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.13201 | 0.300363 | 0.150181 | − | 0.988658i | \(-0.452014\pi\) | ||||
0.150181 | + | 0.988658i | \(0.452014\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.49534 | −0.0920418 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.242720 | −0.00894072 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.942709 | −0.0346781 | −0.0173391 | − | 0.999850i | \(-0.505519\pi\) | ||||
−0.0173391 | + | 0.999850i | \(0.505519\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.8446 | 1.27833 | 0.639163 | − | 0.769072i | \(-0.279281\pi\) | ||||
0.639163 | + | 0.769072i | \(0.279281\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.86799 | −0.0684380 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.33657 | −0.0489027 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.82936 | 0.249539 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.8587 | 0.396238 | 0.198119 | − | 0.980178i | \(-0.436517\pi\) | ||||
0.198119 | + | 0.980178i | \(0.436517\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.73599 | −0.354799 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.46264 | 0.162412 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.3386 | −1.39344 | −0.696721 | − | 0.717342i | \(-0.745358\pi\) | ||||
−0.696721 | + | 0.717342i | \(0.745358\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.65872 | −0.0602077 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.4333 | −0.885708 | −0.442854 | − | 0.896594i | \(-0.646034\pi\) | ||||
−0.442854 | + | 0.896594i | \(0.646034\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.65194 | 0.0598042 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.84802 | 0.319068 | 0.159534 | − | 0.987192i | \(-0.449001\pi\) | ||||
0.159534 | + | 0.987192i | \(0.449001\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.11458 | 0.220211 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.58532 | 0.200890 | 0.100445 | − | 0.994943i | \(-0.467973\pi\) | ||||
0.100445 | + | 0.994943i | \(0.467973\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.50466 | −0.197733 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.132007 | −0.00473574 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.4813 | −0.662161 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.09206 | −0.146425 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.13069 | −0.326304 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.1693 | 0.719874 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.4754 | −0.979391 | −0.489695 | − | 0.871894i | \(-0.662892\pi\) | ||||
−0.489695 | + | 0.871894i | \(0.662892\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.697352 | −0.0248264 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.20796 | 0.114062 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.23471 | −0.0792570 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.90663 | −0.102958 | −0.0514790 | − | 0.998674i | \(-0.516394\pi\) | ||||
−0.0514790 | + | 0.998674i | \(0.516394\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 45.9414 | 1.62326 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.92660 | 0.350302 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.45331 | 0.0512226 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.46942 | 0.157331 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.82936 | 0.0994750 | 0.0497375 | − | 0.998762i | \(-0.484162\pi\) | ||||
0.0497375 | + | 0.998762i | \(0.484162\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.9053 | −1.33104 | −0.665518 | − | 0.746382i | \(-0.731789\pi\) | ||||
−0.665518 | + | 0.746382i | \(0.731789\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.1320 | 0.355345 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.55602 | −0.334733 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.9066 | −0.381575 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.2093 | −0.495907 | −0.247954 | − | 0.968772i | \(-0.579758\pi\) | ||||
−0.247954 | + | 0.968772i | \(0.579758\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.3713 | −0.919247 | −0.459624 | − | 0.888114i | \(-0.652016\pi\) | ||||
−0.459624 | + | 0.888114i | \(0.652016\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.414680 | 0.0144373 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.10270 | −0.281759 | −0.140879 | − | 0.990027i | \(-0.544993\pi\) | ||||
−0.140879 | + | 0.990027i | \(0.544993\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.20796 | −0.180880 | −0.0904399 | − | 0.995902i | \(-0.528827\pi\) | ||||
−0.0904399 | + | 0.995902i | \(0.528827\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.92273 | −0.205457 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.8387 | 0.548120 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.7360 | 0.405655 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.98134 | −0.344594 | −0.172297 | − | 0.985045i | \(-0.555119\pi\) | ||||
−0.172297 | + | 0.985045i | \(0.555119\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.6587 | −0.367542 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.23603 | −0.111455 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.0000 | −0.447214 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.52332 | 0.121063 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.65872 | 0.194207 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.00000 | −0.137118 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.4320 | 0.665340 | 0.332670 | − | 0.943043i | \(-0.392051\pi\) | ||||
0.332670 | + | 0.943043i | \(0.392051\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.7033 | 0.468643 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.5653 | 0.634180 | 0.317090 | − | 0.948395i | \(-0.397294\pi\) | ||||
0.317090 | + | 0.948395i | \(0.397294\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.7687 | −0.606260 | −0.303130 | − | 0.952949i | \(-0.598032\pi\) | ||||
−0.303130 | + | 0.952949i | \(0.598032\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.510604 | −0.0174013 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.4647 | 1.34339 | 0.671697 | − | 0.740826i | \(-0.265566\pi\) | ||||
0.671697 | + | 0.740826i | \(0.265566\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.8680 | 0.539528 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.17658 | −0.209768 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.05861 | 0.273370 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −17.2080 | −0.582401 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.363328 | −0.0122827 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.0373 | 0.338936 | 0.169468 | − | 0.985536i | \(-0.445795\pi\) | ||||
0.169468 | + | 0.985536i | \(0.445795\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.63328 | −0.122548 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 52.8667 | 1.78112 | 0.890562 | − | 0.454862i | \(-0.150312\pi\) | ||||
0.890562 | + | 0.454862i | \(0.150312\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.5560 | −1.12925 | −0.564625 | − | 0.825348i | \(-0.690979\pi\) | ||||
−0.564625 | + | 0.825348i | \(0.690979\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.82936 | −0.0951079 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 53.3259 | 1.79051 | 0.895255 | − | 0.445555i | \(-0.146994\pi\) | ||||
0.895255 | + | 0.445555i | \(0.146994\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.90531 | 0.130980 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.93593 | 0.299365 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 61.7733 | 2.06716 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.34335 | 0.312314 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −23.5747 | −0.786259 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.301330 | −0.0100276 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.2627 | −0.640314 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.2173 | 0.472077 | 0.236039 | − | 0.971744i | \(-0.424151\pi\) | ||||
0.236039 | + | 0.971744i | \(0.424151\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −39.0161 | −1.29408 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.08867 | 0.267989 | 0.133995 | − | 0.990982i | \(-0.457219\pi\) | ||||
0.133995 | + | 0.990982i | \(0.457219\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.531898 | 0.0176033 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.198627 | −0.00656640 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.00000 | −0.0660458 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.3620 | −1.29843 | −0.649216 | − | 0.760604i | \(-0.724903\pi\) | ||||
−0.649216 | + | 0.760604i | \(0.724903\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.13201 | −0.136154 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00000 | 0.0328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.7241 | 0.582136 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.0000 | 0.984268 | 0.492134 | − | 0.870519i | \(-0.336217\pi\) | ||||
0.492134 | + | 0.870519i | \(0.336217\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.8153 | 1.07548 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.450763 | −0.0147573 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.0946926 | −0.00309347 | −0.00154674 | − | 0.999999i | \(-0.500492\pi\) | ||||
−0.00154674 | + | 0.999999i | \(0.500492\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.68934 | −0.153031 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.8667 | −0.680234 | −0.340117 | − | 0.940383i | \(-0.610467\pi\) | ||||
−0.340117 | + | 0.940383i | \(0.610467\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.4720 | −0.503837 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.774618 | 0.0251983 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.4813 | −0.600562 | −0.300281 | − | 0.953851i | \(-0.597080\pi\) | ||||
−0.300281 | + | 0.953851i | \(0.597080\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.00677877 | −0.000219817 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.660037 | −0.0213807 | −0.0106903 | − | 0.999943i | \(-0.503403\pi\) | ||||
−0.0106903 | + | 0.999943i | \(0.503403\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.32469 | −0.107585 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.77594 | 0.0574079 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.25469 | −0.0405159 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.698670 | −0.0225378 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 53.9087 | 1.73718 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.73599 | −0.0558833 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.4413 | −1.55777 | −0.778884 | − | 0.627168i | \(-0.784214\pi\) | ||||
−0.778884 | + | 0.627168i | \(0.784214\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.1120 | 0.484968 | 0.242484 | − | 0.970155i | \(-0.422038\pi\) | ||||
0.242484 | + | 0.970155i | \(0.422038\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.64006 | 0.116695 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.2640 | 0.328375 | 0.164187 | − | 0.986429i | \(-0.447500\pi\) | ||||
0.164187 | + | 0.986429i | \(0.447500\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.2827 | −0.584317 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.0399 | 0.416331 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.10864 | −0.226730 | −0.113365 | − | 0.993553i | \(-0.536163\pi\) | ||||
−0.113365 | + | 0.993553i | \(0.536163\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.41468 | −0.0769381 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.70668 | 0.0543242 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.13069 | −0.290339 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.94865 | −0.125433 | −0.0627165 | − | 0.998031i | \(-0.519976\pi\) | ||||
−0.0627165 | + | 0.998031i | \(0.519976\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.35739 | −0.106544 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.05135 | −0.128436 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −49.7733 | −1.57634 | −0.788168 | − | 0.615460i | \(-0.788970\pi\) | ||||
−0.788168 | + | 0.615460i | \(0.788970\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.13201 | −0.0674537 |
(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 | 2960.2.a.s.1.2 | 3 | ||
4.3 | odd | 2 | 1480.2.a.f.1.2 | ✓ | 3 | ||
20.19 | odd | 2 | 7400.2.a.m.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1480.2.a.f.1.2 | ✓ | 3 | 4.3 | odd | 2 | ||
2960.2.a.s.1.2 | 3 | 1.1 | even | 1 | trivial | ||
7400.2.a.m.1.2 | 3 | 20.19 | odd | 2 |