Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [308,2,Mod(1,308)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(308, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("308.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 308 = 2^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 308.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: | \(2.45939238226\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 308.1 |
$q$-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 | ||||||||
\(3\) | 2.44949 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.449490 | −0.124666 | −0.0623330 | − | 0.998055i | \(-0.519854\pi\) | ||||
−0.0623330 | + | 0.998055i | \(0.519854\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.89898 | 1.26491 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.449490 | −0.109017 | −0.0545086 | − | 0.998513i | \(-0.517359\pi\) | ||||
−0.0545086 | + | 0.998513i | \(0.517359\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.89898 | −1.12390 | −0.561951 | − | 0.827170i | \(-0.689949\pi\) | ||||
−0.561951 | + | 0.827170i | \(0.689949\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.44949 | −0.534522 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.898979 | −0.187450 | −0.0937251 | − | 0.995598i | \(-0.529877\pi\) | ||||
−0.0937251 | + | 0.995598i | \(0.529877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.89898 | 0.538327 | 0.269163 | − | 0.963095i | \(-0.413253\pi\) | ||||
0.269163 | + | 0.963095i | \(0.413253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.44949 | 1.15836 | 0.579181 | − | 0.815199i | \(-0.303372\pi\) | ||||
0.579181 | + | 0.815199i | \(0.303372\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.44949 | −0.426401 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.10102 | −0.176304 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.34847 | −1.45999 | −0.729993 | − | 0.683455i | \(-0.760477\pi\) | ||||
−0.729993 | + | 0.683455i | \(0.760477\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.89898 | 0.442090 | 0.221045 | − | 0.975264i | \(-0.429053\pi\) | ||||
0.221045 | + | 0.975264i | \(0.429053\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.00000 | 0.894427 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.44949 | −0.940755 | −0.470377 | − | 0.882465i | \(-0.655882\pi\) | ||||
−0.470377 | + | 0.882465i | \(0.655882\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.10102 | −0.154174 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.79796 | 1.34585 | 0.672927 | − | 0.739709i | \(-0.265037\pi\) | ||||
0.672927 | + | 0.739709i | \(0.265037\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.0000 | −1.58944 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.34847 | 0.956689 | 0.478345 | − | 0.878172i | \(-0.341237\pi\) | ||||
0.478345 | + | 0.878172i | \(0.341237\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.34847 | 0.684801 | 0.342401 | − | 0.939554i | \(-0.388760\pi\) | ||||
0.342401 | + | 0.939554i | \(0.388760\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.00000 | −0.377964 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.898979 | −0.111505 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.6969 | −1.79552 | −0.897758 | − | 0.440488i | \(-0.854805\pi\) | ||||
−0.897758 | + | 0.440488i | \(0.854805\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.20204 | −0.265095 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.8990 | −1.53083 | −0.765414 | − | 0.643539i | \(-0.777466\pi\) | ||||
−0.765414 | + | 0.643539i | \(0.777466\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.4495 | 1.45710 | 0.728551 | − | 0.684991i | \(-0.240194\pi\) | ||||
0.728551 | + | 0.684991i | \(0.240194\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.44949 | −0.282843 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.8990 | −1.22623 | −0.613115 | − | 0.789993i | \(-0.710084\pi\) | ||||
−0.613115 | + | 0.789993i | \(0.710084\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.8990 | −1.85490 | −0.927452 | − | 0.373942i | \(-0.878006\pi\) | ||||
−0.927452 | + | 0.373942i | \(0.878006\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.898979 | −0.0975080 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.10102 | 0.761309 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.449490 | 0.0471193 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.7980 | 1.63817 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.79796 | −1.00525 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.10102 | 0.517930 | 0.258965 | − | 0.965887i | \(-0.416619\pi\) | ||||
0.258965 | + | 0.965887i | \(0.416619\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.44949 | −0.840756 | −0.420378 | − | 0.907349i | \(-0.638102\pi\) | ||||
−0.420378 | + | 0.907349i | \(0.638102\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.4495 | 1.42375 | 0.711875 | − | 0.702306i | \(-0.247846\pi\) | ||||
0.711875 | + | 0.702306i | \(0.247846\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.89898 | −0.478091 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.8990 | 1.42706 | 0.713532 | − | 0.700623i | \(-0.247094\pi\) | ||||
0.713532 | + | 0.700623i | \(0.247094\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.79796 | 0.929981 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0000 | −0.940721 | −0.470360 | − | 0.882474i | \(-0.655876\pi\) | ||||
−0.470360 | + | 0.882474i | \(0.655876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.79796 | −0.167661 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.34847 | −0.124666 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.449490 | 0.0412047 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −22.8990 | −2.06473 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.79796 | −0.159543 | −0.0797715 | − | 0.996813i | \(-0.525419\pi\) | ||||
−0.0797715 | + | 0.996813i | \(0.525419\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.10102 | 0.625210 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.79796 | 0.856052 | 0.428026 | − | 0.903767i | \(-0.359209\pi\) | ||||
0.428026 | + | 0.903767i | \(0.359209\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.89898 | 0.424795 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.79796 | 0.837096 | 0.418548 | − | 0.908195i | \(-0.362539\pi\) | ||||
0.418548 | + | 0.908195i | \(0.362539\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.6969 | 1.92513 | 0.962565 | − | 0.271052i | \(-0.0873717\pi\) | ||||
0.962565 | + | 0.271052i | \(0.0873717\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.7980 | −1.33043 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.449490 | 0.0375882 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.79796 | 0.481494 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.44949 | 0.202031 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.7980 | 0.966526 | 0.483263 | − | 0.875475i | \(-0.339451\pi\) | ||||
0.483263 | + | 0.875475i | \(0.339451\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.69694 | 0.707747 | 0.353873 | − | 0.935293i | \(-0.384864\pi\) | ||||
0.353873 | + | 0.935293i | \(0.384864\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.34847 | −0.109017 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.8990 | 1.03607 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 24.0000 | 1.90332 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.898979 | 0.0708495 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.89898 | 0.697022 | 0.348511 | − | 0.937305i | \(-0.386687\pi\) | ||||
0.348511 | + | 0.937305i | \(0.386687\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.89898 | −0.381385 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.7980 | 1.06772 | 0.533859 | − | 0.845573i | \(-0.320741\pi\) | ||||
0.533859 | + | 0.845573i | \(0.320741\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7980 | −0.984458 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.6969 | −1.12390 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.2474 | 0.779099 | 0.389550 | − | 0.921006i | \(-0.372631\pi\) | ||||
0.389550 | + | 0.921006i | \(0.372631\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 18.0000 | 1.35296 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.5959 | −1.16569 | −0.582847 | − | 0.812582i | \(-0.698061\pi\) | ||||
−0.582847 | + | 0.812582i | \(0.698061\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.10102 | 0.676474 | 0.338237 | − | 0.941061i | \(-0.390170\pi\) | ||||
0.338237 | + | 0.941061i | \(0.390170\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.1010 | 0.968455 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.00000 | 0.588172 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.449490 | 0.0328699 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.79796 | −0.130096 | −0.0650479 | − | 0.997882i | \(-0.520720\pi\) | ||||
−0.0650479 | + | 0.997882i | \(0.520720\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.5959 | 1.55451 | 0.777254 | − | 0.629187i | \(-0.216612\pi\) | ||||
0.777254 | + | 0.629187i | \(0.216612\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.20204 | −0.157691 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.5959 | −1.82363 | −0.911817 | − | 0.410597i | \(-0.865320\pi\) | ||||
−0.911817 | + | 0.410597i | \(0.865320\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.0454 | 1.84631 | 0.923155 | − | 0.384428i | \(-0.125601\pi\) | ||||
0.923155 | + | 0.384428i | \(0.125601\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −36.0000 | −2.53924 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.89898 | −0.203468 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.6969 | −1.30585 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.69694 | −0.187450 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.89898 | 0.338869 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.0000 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −31.5959 | −2.16492 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.79796 | 0.395418 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.44949 | −0.437820 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 30.4949 | 2.06065 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.202041 | 0.0135908 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.1464 | −0.880350 | −0.440175 | − | 0.897912i | \(-0.645084\pi\) | ||||
−0.440175 | + | 0.897912i | \(0.645084\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.79796 | 0.119335 | 0.0596674 | − | 0.998218i | \(-0.480996\pi\) | ||||
0.0596674 | + | 0.998218i | \(0.480996\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.10102 | −0.337085 | −0.168542 | − | 0.985694i | \(-0.553906\pi\) | ||||
−0.168542 | + | 0.985694i | \(0.553906\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.44949 | 0.161165 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.10102 | −0.0721303 | −0.0360651 | − | 0.999349i | \(-0.511482\pi\) | ||||
−0.0360651 | + | 0.999349i | \(0.511482\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.8990 | −0.841437 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −26.6969 | −1.73415 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.0000 | 1.03495 | 0.517477 | − | 0.855697i | \(-0.326871\pi\) | ||||
0.517477 | + | 0.855697i | \(0.326871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.34847 | −0.0868625 | −0.0434313 | − | 0.999056i | \(-0.513829\pi\) | ||||
−0.0434313 | + | 0.999056i | \(0.513829\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.0454 | −1.41421 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.00000 | 0.127775 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.20204 | 0.140113 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −41.3939 | −2.62323 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.44949 | 0.154610 | 0.0773052 | − | 0.997007i | \(-0.475368\pi\) | ||||
0.0773052 | + | 0.997007i | \(0.475368\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.898979 | 0.0565184 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.20204 | −0.137897 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.79796 | −0.236910 | −0.118455 | − | 0.992959i | \(-0.537794\pi\) | ||||
−0.118455 | + | 0.992959i | \(0.537794\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00000 | −0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.69694 | 0.538327 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.5959 | 1.20834 | 0.604168 | − | 0.796857i | \(-0.293506\pi\) | ||||
0.604168 | + | 0.796857i | \(0.293506\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.5959 | 1.20377 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.6969 | 0.899438 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.1010 | −0.798783 | −0.399392 | − | 0.916780i | \(-0.630779\pi\) | ||||
−0.399392 | + | 0.916780i | \(0.630779\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.30306 | 0.0791554 | 0.0395777 | − | 0.999216i | \(-0.487399\pi\) | ||||
0.0395777 | + | 0.999216i | \(0.487399\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.10102 | 0.0666368 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.7980 | 0.949207 | 0.474604 | − | 0.880200i | \(-0.342591\pi\) | ||||
0.474604 | + | 0.880200i | \(0.342591\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 19.3485 | 1.15836 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.10102 | −0.304301 | −0.152151 | − | 0.988357i | \(-0.548620\pi\) | ||||
−0.152151 | + | 0.988357i | \(0.548620\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.0000 | −1.42665 | −0.713326 | − | 0.700832i | \(-0.752812\pi\) | ||||
−0.713326 | + | 0.700832i | \(0.752812\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −24.0000 | −1.42164 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.34847 | 0.551823 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7980 | −0.988115 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.4949 | 0.732464 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.6515 | −0.622269 | −0.311135 | − | 0.950366i | \(-0.600709\pi\) | ||||
−0.311135 | + | 0.950366i | \(0.600709\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.6969 | 0.855689 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.404082 | 0.0233687 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.89898 | −0.167094 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −20.6969 | −1.18901 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.6969 | 0.612505 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.79796 | −0.102615 | −0.0513075 | − | 0.998683i | \(-0.516339\pi\) | ||||
−0.0513075 | + | 0.998683i | \(0.516339\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 35.3939 | 2.01349 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.55051 | −0.0879214 | −0.0439607 | − | 0.999033i | \(-0.513998\pi\) | ||||
−0.0439607 | + | 0.999033i | \(0.513998\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.59592 | 0.316300 | 0.158150 | − | 0.987415i | \(-0.449447\pi\) | ||||
0.158150 | + | 0.987415i | \(0.449447\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.00000 | −0.338062 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.5959 | −0.763623 | −0.381811 | − | 0.924240i | \(-0.624700\pi\) | ||||
−0.381811 | + | 0.924240i | \(0.624700\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.89898 | −0.162312 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.79796 | −0.546869 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.20204 | 0.122525 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.449490 | 0.0249332 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 36.4949 | 2.01817 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.44949 | 0.355572 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.0000 | −1.75888 | −0.879440 | − | 0.476011i | \(-0.842082\pi\) | ||||
−0.879440 | + | 0.476011i | \(0.842082\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.0000 | 0.657596 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −29.3939 | −1.60596 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.6969 | 1.12743 | 0.563717 | − | 0.825968i | \(-0.309371\pi\) | ||||
0.563717 | + | 0.825968i | \(0.309371\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −24.4949 | −1.33038 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.44949 | −0.349259 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.40408 | −0.237108 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.4949 | 1.42232 | 0.711160 | − | 0.703030i | \(-0.248170\pi\) | ||||
0.711160 | + | 0.703030i | \(0.248170\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.75255 | 0.0938119 | 0.0469060 | − | 0.998899i | \(-0.485064\pi\) | ||||
0.0469060 | + | 0.998899i | \(0.485064\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.5959 | 1.36233 | 0.681167 | − | 0.732128i | \(-0.261473\pi\) | ||||
0.681167 | + | 0.732128i | \(0.261473\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.7980 | −1.36921 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.10102 | 0.0582722 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.6969 | −1.30345 | −0.651727 | − | 0.758453i | \(-0.725955\pi\) | ||||
−0.651727 | + | 0.758453i | \(0.725955\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.00000 | 0.263158 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.44949 | 0.128565 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.8990 | 1.30327 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.1464 | 1.10383 | 0.551917 | − | 0.833899i | \(-0.313896\pi\) | ||||
0.551917 | + | 0.833899i | \(0.313896\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −28.0454 | −1.45999 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.79796 | −0.508685 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.20204 | 0.217573 | 0.108787 | − | 0.994065i | \(-0.465303\pi\) | ||||
0.108787 | + | 0.994065i | \(0.465303\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −29.3939 | −1.51789 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.30306 | −0.0671111 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.10102 | −0.159289 | −0.0796444 | − | 0.996823i | \(-0.525378\pi\) | ||||
−0.0796444 | + | 0.996823i | \(0.525378\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.40408 | −0.225628 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.3485 | 1.39744 | 0.698721 | − | 0.715395i | \(-0.253753\pi\) | ||||
0.698721 | + | 0.715395i | \(0.253753\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.00000 | 0.101929 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.69694 | 0.442090 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.5959 | −0.689340 | −0.344670 | − | 0.938724i | \(-0.612009\pi\) | ||||
−0.344670 | + | 0.938724i | \(0.612009\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.404082 | 0.0204353 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.0000 | 1.21064 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.7980 | −1.09677 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.5959 | −1.28462 | −0.642311 | − | 0.766444i | \(-0.722024\pi\) | ||||
−0.642311 | + | 0.766444i | \(0.722024\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.0000 | 0.600751 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.7980 | −1.38816 | −0.694082 | − | 0.719896i | \(-0.744189\pi\) | ||||
−0.694082 | + | 0.719896i | \(0.744189\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.89898 | −0.144408 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.0000 | −0.894427 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.00000 | −0.198273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.5505 | −0.571136 | −0.285568 | − | 0.958358i | \(-0.592182\pi\) | ||||
−0.285568 | + | 0.958358i | \(0.592182\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.0000 | 1.18383 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.34847 | −0.361595 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −33.7980 | −1.65908 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 55.5959 | 2.72254 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.4495 | 0.901317 | 0.450658 | − | 0.892697i | \(-0.351189\pi\) | ||||
0.450658 | + | 0.892697i | \(0.351189\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.79796 | −0.282575 | −0.141288 | − | 0.989969i | \(-0.545124\pi\) | ||||
−0.141288 | + | 0.989969i | \(0.545124\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −19.3485 | −0.940755 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.449490 | 0.0218035 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.34847 | −0.258831 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.10102 | 0.0531578 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.10102 | −0.438381 | −0.219190 | − | 0.975682i | \(-0.570342\pi\) | ||||
−0.219190 | + | 0.975682i | \(0.570342\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.1010 | 1.01405 | 0.507025 | − | 0.861931i | \(-0.330745\pi\) | ||||
0.507025 | + | 0.861931i | \(0.330745\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.2020 | 0.680936 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.40408 | 0.210676 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.8990 | −1.18836 | −0.594182 | − | 0.804331i | \(-0.702524\pi\) | ||||
−0.594182 | + | 0.804331i | \(0.702524\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.0000 | 1.14027 | 0.570137 | − | 0.821549i | \(-0.306890\pi\) | ||||
0.570137 | + | 0.821549i | \(0.306890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.0000 | 0.568855 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 28.8990 | 1.36687 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.5959 | 0.924789 | 0.462394 | − | 0.886674i | \(-0.346990\pi\) | ||||
0.462394 | + | 0.886674i | \(0.346990\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.34847 | 0.440202 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.3031 | 1.00091 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.898979 | 0.0421448 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.3939 | 0.907207 | 0.453604 | − | 0.891204i | \(-0.350138\pi\) | ||||
0.453604 | + | 0.891204i | \(0.350138\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.3485 | −1.73949 | −0.869746 | − | 0.493500i | \(-0.835717\pi\) | ||||
−0.869746 | + | 0.493500i | \(0.835717\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.8990 | −1.15715 | −0.578577 | − | 0.815628i | \(-0.696392\pi\) | ||||
−0.578577 | + | 0.815628i | \(0.696392\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 31.5959 | 1.46523 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.34847 | 0.340047 | 0.170023 | − | 0.985440i | \(-0.445616\pi\) | ||||
0.170023 | + | 0.985440i | \(0.445616\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.6969 | 0.678642 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 24.4949 | 1.12867 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.89898 | −0.133295 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.89898 | 0.224781 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29.3939 | 1.34585 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.898979 | 0.0410754 | 0.0205377 | − | 0.999789i | \(-0.493462\pi\) | ||||
0.0205377 | + | 0.999789i | \(0.493462\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.79796 | −0.0819799 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.20204 | 0.100196 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.2020 | 0.463251 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.8990 | 1.67205 | 0.836026 | − | 0.548690i | \(-0.184873\pi\) | ||||
0.836026 | + | 0.548690i | \(0.184873\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.7980 | 0.985738 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.6969 | 1.47559 | 0.737796 | − | 0.675024i | \(-0.235867\pi\) | ||||
0.737796 | + | 0.675024i | \(0.235867\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.30306 | −0.0586869 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.00000 | −0.269680 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.8990 | 0.578598 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −42.6969 | −1.91138 | −0.955689 | − | 0.294379i | \(-0.904887\pi\) | ||||
−0.955689 | + | 0.294379i | \(0.904887\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 33.7980 | 1.50998 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.4949 | −1.09217 | −0.546087 | − | 0.837729i | \(-0.683883\pi\) | ||||
−0.546087 | + | 0.837729i | \(0.683883\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.8990 | −0.751995 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −31.3485 | −1.39223 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.6969 | −1.09467 | −0.547336 | − | 0.836913i | \(-0.684358\pi\) | ||||
−0.547336 | + | 0.836913i | \(0.684358\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.4495 | −0.550733 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.8990 | 1.27344 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.44949 | 0.283648 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25.1010 | 1.10181 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.10102 | −0.398723 | −0.199361 | − | 0.979926i | \(-0.563887\pi\) | ||||
−0.199361 | + | 0.979926i | \(0.563887\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.3939 | 1.11040 | 0.555198 | − | 0.831718i | \(-0.312642\pi\) | ||||
0.555198 | + | 0.831718i | \(0.312642\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.44949 | 0.106904 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.89898 | −0.126282 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.1918 | −0.964862 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.0454 | 0.956689 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.20204 | 0.182011 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.00000 | −0.345870 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −38.2020 | −1.64854 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.5959 | −0.756508 | −0.378254 | − | 0.925702i | \(-0.623475\pi\) | ||||
−0.378254 | + | 0.925702i | \(0.623475\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22.2929 | 0.956678 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 29.7980 | 1.27640 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0000 | −0.513083 | −0.256541 | − | 0.966533i | \(-0.582583\pi\) | ||||
−0.256541 | + | 0.966533i | \(0.582583\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.0454 | 0.684801 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.2020 | −0.605027 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.8990 | 0.463472 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19.5959 | 0.831800 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −43.7980 | −1.85578 | −0.927890 | − | 0.372855i | \(-0.878379\pi\) | ||||
−0.927890 | + | 0.372855i | \(0.878379\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.30306 | −0.0551136 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.10102 | 0.0464851 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26.2929 | −1.10811 | −0.554056 | − | 0.832479i | \(-0.686921\pi\) | ||||
−0.554056 | + | 0.832479i | \(0.686921\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.0000 | −0.841406 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.00000 | 0.377964 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.69694 | −0.364595 | −0.182297 | − | 0.983243i | \(-0.558353\pi\) | ||||
−0.182297 | + | 0.983243i | \(0.558353\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.2020 | −0.426942 | −0.213471 | − | 0.976949i | \(-0.568477\pi\) | ||||
−0.213471 | + | 0.976949i | \(0.568477\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.40408 | −0.183983 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.898979 | 0.0374900 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.4949 | −0.936475 | −0.468237 | − | 0.883603i | \(-0.655111\pi\) | ||||
−0.468237 | + | 0.883603i | \(0.655111\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 52.8990 | 2.19841 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.8990 | 0.701088 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.79796 | −0.405790 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.69694 | −0.111505 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.5505 | 0.889485 | 0.444742 | − | 0.895659i | \(-0.353295\pi\) | ||||
0.444742 | + | 0.895659i | \(0.353295\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.5959 | −1.30189 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −62.6969 | −2.57901 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.853572 | −0.0350520 | −0.0175260 | − | 0.999846i | \(-0.505579\pi\) | ||||
−0.0175260 | + | 0.999846i | \(0.505579\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.898979 | 0.0368546 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 63.7980 | 2.61108 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.10102 | −0.290140 | −0.145070 | − | 0.989421i | \(-0.546341\pi\) | ||||
−0.145070 | + | 0.989421i | \(0.546341\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.65153 | 0.271322 | 0.135661 | − | 0.990755i | \(-0.456684\pi\) | ||||
0.135661 | + | 0.990755i | \(0.456684\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −44.0908 | −1.79552 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.00000 | 0.0813116 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.5959 | 0.633019 | 0.316509 | − | 0.948589i | \(-0.397489\pi\) | ||||
0.316509 | + | 0.948589i | \(0.397489\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.10102 | −0.287748 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.89898 | 0.117280 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.6969 | −0.674383 | −0.337191 | − | 0.941436i | \(-0.609477\pi\) | ||||
−0.337191 | + | 0.941436i | \(0.609477\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −45.7980 | −1.84675 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.3939 | −1.18335 | −0.591676 | − | 0.806176i | \(-0.701534\pi\) | ||||
−0.591676 | + | 0.806176i | \(0.701534\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.55051 | 0.223094 | 0.111547 | − | 0.993759i | \(-0.464419\pi\) | ||||
0.111547 | + | 0.993759i | \(0.464419\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.00000 | −0.240385 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.0000 | 0.479234 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.79796 | −0.0716893 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.20204 | −0.0876619 | −0.0438309 | − | 0.999039i | \(-0.513956\pi\) | ||||
−0.0438309 | + | 0.999039i | \(0.513956\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −48.9898 | −1.94717 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.59592 | −0.142700 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.449490 | −0.0178094 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −38.6969 | −1.53083 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.59592 | −0.300021 | −0.150010 | − | 0.988684i | \(-0.547931\pi\) | ||||
−0.150010 | + | 0.988684i | \(0.547931\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.24745 | 0.167503 | 0.0837515 | − | 0.996487i | \(-0.473310\pi\) | ||||
0.0837515 | + | 0.996487i | \(0.473310\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.2020 | 0.559205 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.247449 | 0.00972821 | 0.00486411 | − | 0.999988i | \(-0.498452\pi\) | ||||
0.00486411 | + | 0.999988i | \(0.498452\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.34847 | −0.288453 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.7980 | −0.619171 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.3939 | 0.602409 | 0.301204 | − | 0.953560i | \(-0.402611\pi\) | ||||
0.301204 | + | 0.953560i | \(0.402611\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.5959 | 0.765676 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 37.3485 | 1.45710 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.10102 | 0.198708 | 0.0993538 | − | 0.995052i | \(-0.468322\pi\) | ||||
0.0993538 | + | 0.995052i | \(0.468322\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.5959 | −1.15115 | −0.575574 | − | 0.817750i | \(-0.695221\pi\) | ||||
−0.575574 | + | 0.817750i | \(0.695221\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.494897 | 0.0192202 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.79796 | 0.379949 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.60612 | −0.100909 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −32.2020 | −1.24500 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.34847 | −0.206475 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.30306 | 0.281512 | 0.140756 | − | 0.990044i | \(-0.455047\pi\) | ||||
0.140756 | + | 0.990044i | \(0.455047\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.9444 | 1.11242 | 0.556212 | − | 0.831041i | \(-0.312254\pi\) | ||||
0.556212 | + | 0.831041i | \(0.312254\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.10102 | −0.195759 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.40408 | 0.168765 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.2020 | −1.00259 | −0.501297 | − | 0.865276i | \(-0.667143\pi\) | ||||
−0.501297 | + | 0.865276i | \(0.667143\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.5959 | 0.748722 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.4949 | −0.476710 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.40408 | −0.167782 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.1464 | −1.56528 | −0.782642 | − | 0.622472i | \(-0.786128\pi\) | ||||
−0.782642 | + | 0.622472i | \(0.786128\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.00000 | 0.113961 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 45.3939 | 1.72189 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.20204 | 0.159164 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.69694 | −0.102008 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.6969 | −0.781713 | −0.390856 | − | 0.920452i | \(-0.627821\pi\) | ||||
−0.390856 | + | 0.920452i | \(0.627821\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.5959 | −0.739074 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −31.5959 | −1.18997 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.44949 | 0.317776 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.79796 | 0.142635 | 0.0713177 | − | 0.997454i | \(-0.477280\pi\) | ||||
0.0713177 | + | 0.997454i | \(0.477280\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −32.6969 | −1.22623 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.79796 | −0.217135 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.898979 | 0.0336199 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 39.1918 | 1.46365 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.1464 | 1.68368 | 0.841839 | − | 0.539729i | \(-0.181473\pi\) | ||||
0.841839 | + | 0.539729i | \(0.181473\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.4495 | −0.538127 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.30306 | −0.122842 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.89898 | −0.107665 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.55051 | −0.0575052 | −0.0287526 | − | 0.999587i | \(-0.509154\pi\) | ||||
−0.0287526 | + | 0.999587i | \(0.509154\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.30306 | −0.0481955 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.3485 | 1.67498 | 0.837492 | − | 0.546450i | \(-0.184021\pi\) | ||||
0.837492 | + | 0.546450i | \(0.184021\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.89898 | 0.180702 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.6969 | 0.541369 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.3939 | −1.52270 | −0.761349 | − | 0.648342i | \(-0.775463\pi\) | ||||
−0.761349 | + | 0.648342i | \(0.775463\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.39388 | 0.198149 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.5959 | −0.718905 | −0.359452 | − | 0.933163i | \(-0.617036\pi\) | ||||
−0.359452 | + | 0.933163i | \(0.617036\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.5959 | 0.864488 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −50.6969 | −1.85490 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.00000 | 0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.8990 | −0.470690 | −0.235345 | − | 0.971912i | \(-0.575622\pi\) | ||||
−0.235345 | + | 0.971912i | \(0.575622\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.00000 | 0.218652 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.3939 | 0.633028 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.20204 | 0.0799290 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 49.8434 | 1.80682 | 0.903410 | − | 0.428777i | \(-0.141055\pi\) | ||||
0.903410 | + | 0.428777i | \(0.141055\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.8990 | −0.539379 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.69694 | −0.0975080 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.30306 | −0.119267 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.1464 | 1.41166 | 0.705828 | − | 0.708383i | \(-0.250575\pi\) | ||||
0.705828 | + | 0.708383i | \(0.250575\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.30306 | −0.335042 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.30306 | 0.118803 | 0.0594014 | − | 0.998234i | \(-0.481081\pi\) | ||||
0.0594014 | + | 0.998234i | \(0.481081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.44949 | −0.231673 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.79796 | −0.351500 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 45.7980 | 1.64088 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.8990 | 0.461562 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.0000 | 0.713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.6969 | 0.381305 | 0.190652 | − | 0.981658i | \(-0.438940\pi\) | ||||
0.190652 | + | 0.981658i | \(0.438940\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 48.0000 | 1.70885 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.0000 | 0.355559 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.40408 | −0.0853715 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 48.0000 | 1.70238 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.7980 | −1.12634 | −0.563171 | − | 0.826341i | \(-0.690419\pi\) | ||||
−0.563171 | + | 0.826341i | \(0.690419\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.89898 | 0.102559 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.0000 | 0.635999 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.4495 | −0.439333 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.79796 | 0.0633697 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −32.0908 | −1.12965 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.5959 | −0.899905 | −0.449952 | − | 0.893053i | \(-0.648559\pi\) | ||||
−0.449952 | + | 0.893053i | \(0.648559\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.5959 | −0.828565 | −0.414282 | − | 0.910148i | \(-0.635967\pi\) | ||||
−0.414282 | + | 0.910148i | \(0.635967\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.19184 | 0.111943 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.7980 | 0.623435 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.2020 | −0.496867 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.34847 | 0.0471193 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.7980 | −0.551353 | −0.275676 | − | 0.961251i | \(-0.588902\pi\) | ||||
−0.275676 | + | 0.961251i | \(0.588902\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.1918 | 1.22671 | 0.613355 | − | 0.789807i | \(-0.289819\pi\) | ||||
0.613355 | + | 0.789807i | \(0.289819\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.44949 | 0.0852803 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.6969 | 1.83245 | 0.916226 | − | 0.400662i | \(-0.131220\pi\) | ||||
0.916226 | + | 0.400662i | \(0.131220\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.0000 | −0.486240 | −0.243120 | − | 0.969996i | \(-0.578171\pi\) | ||||
−0.243120 | + | 0.969996i | \(0.578171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 38.6969 | 1.34238 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.449490 | −0.0155739 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.5959 | 0.954996 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.55051 | 0.329720 | 0.164860 | − | 0.986317i | \(-0.447283\pi\) | ||||
0.164860 | + | 0.986317i | \(0.447283\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.5959 | −0.710204 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.4949 | −0.430347 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.5959 | −0.880526 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −58.7878 | −2.01759 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.59592 | −0.123266 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.1464 | 1.47731 | 0.738653 | − | 0.674086i | \(-0.235462\pi\) | ||||
0.738653 | + | 0.674086i | \(0.235462\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −29.3939 | −1.00525 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.85357 | 0.302432 | 0.151216 | − | 0.988501i | \(-0.451681\pi\) | ||||
0.151216 | + | 0.988501i | \(0.451681\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.8434 | 0.813525 | 0.406763 | − | 0.913534i | \(-0.366658\pi\) | ||||
0.406763 | + | 0.913534i | \(0.366658\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 22.8990 | 0.780395 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.0000 | −1.08929 | −0.544646 | − | 0.838666i | \(-0.683336\pi\) | ||||
−0.544646 | + | 0.838666i | \(0.683336\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.4949 | 0.696847 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −41.1464 | −1.39741 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.8990 | 0.369723 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.60612 | 0.223840 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.3031 | 0.517930 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.0000 | 0.405674 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.6969 | 1.23917 | 0.619584 | − | 0.784931i | \(-0.287301\pi\) | ||||
0.619584 | + | 0.784931i | \(0.287301\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.0908 | −0.880021 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.6969 | −0.697298 | −0.348649 | − | 0.937253i | \(-0.613359\pi\) | ||||
−0.348649 | + | 0.937253i | \(0.613359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.7980 | −1.00278 | −0.501391 | − | 0.865221i | \(-0.667178\pi\) | ||||
−0.501391 | + | 0.865221i | \(0.667178\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 36.0000 | 1.21013 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30.2929 | −1.01713 | −0.508567 | − | 0.861022i | \(-0.669825\pi\) | ||||
−0.508567 | + | 0.861022i | \(0.669825\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.79796 | 0.0603016 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.00000 | 0.301511 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 31.5959 | 1.05732 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.1918 | −1.04263 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.989795 | 0.0330483 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.6969 | 0.623578 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.40408 | −0.146721 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.10102 | −0.236307 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.2020 | 0.605056 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.10102 | 0.102968 | 0.0514838 | − | 0.998674i | \(-0.483605\pi\) | ||||
0.0514838 | + | 0.998674i | \(0.483605\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −25.3485 | −0.840756 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.4949 | 1.20913 | 0.604565 | − | 0.796556i | \(-0.293347\pi\) | ||||
0.604565 | + | 0.796556i | \(0.293347\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.8990 | 0.559275 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 26.2020 | 0.866213 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.79796 | −0.323557 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.40408 | 0.145277 | 0.0726386 | − | 0.997358i | \(-0.476858\pi\) | ||||
0.0726386 | + | 0.997358i | \(0.476858\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.40408 | −0.145119 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.79796 | 0.190842 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 43.3485 | 1.42375 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −52.2929 | −1.71567 | −0.857836 | − | 0.513923i | \(-0.828192\pi\) | ||||
−0.857836 | + | 0.513923i | \(0.828192\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.89898 | −0.160558 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.79796 | −0.124340 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.898979 | 0.0293998 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.9444 | 1.07625 | 0.538123 | − | 0.842866i | \(-0.319134\pi\) | ||||
0.538123 | + | 0.842866i | \(0.319134\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.7071 | 0.447316 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.5505 | 1.41971 | 0.709853 | − | 0.704350i | \(-0.248761\pi\) | ||||
0.709853 | + | 0.704350i | \(0.248761\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.40408 | 0.273675 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.404082 | 0.0131309 | 0.00656545 | − | 0.999978i | \(-0.497910\pi\) | ||||
0.00656545 | + | 0.999978i | \(0.497910\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.59592 | −0.181651 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −33.3031 | −1.07993 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43.7980 | −1.41876 | −0.709378 | − | 0.704829i | \(-0.751024\pi\) | ||||
−0.709378 | + | 0.704829i | \(0.751024\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.59592 | −0.116361 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.10102 | −0.229543 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.79796 | −0.316393 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.5959 | 0.341804 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.0000 | −0.386695 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 43.1918 | 1.39039 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.8990 | −1.25091 | −0.625453 | − | 0.780262i | \(-0.715086\pi\) | ||||
−0.625453 | + | 0.780262i | \(0.715086\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.39388 | 0.173276 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.0454 | −1.22094 | −0.610468 | − | 0.792041i | \(-0.709018\pi\) | ||||
−0.610468 | + | 0.792041i | \(0.709018\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.6969 | −0.727630 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.10102 | 0.0352609 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.20204 | 0.134435 | 0.0672176 | − | 0.997738i | \(-0.478588\pi\) | ||||
0.0672176 | + | 0.997738i | \(0.478588\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 44.6969 | 1.42706 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.3485 | 0.617120 | 0.308560 | − | 0.951205i | \(-0.400153\pi\) | ||||
0.308560 | + | 0.951205i | \(0.400153\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −51.1918 | −1.63111 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.7980 | 0.502855 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.60612 | −0.0828699 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 60.0908 | 1.90885 | 0.954424 | − | 0.298455i | \(-0.0964711\pi\) | ||||
0.954424 | + | 0.298455i | \(0.0964711\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −78.3837 | −2.48743 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 52.0908 | 1.65139 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.9444 | −0.663315 | −0.331658 | − | 0.943400i | \(-0.607608\pi\) | ||||
−0.331658 | + | 0.943400i | \(0.607608\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 308.2.a.b.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 2772.2.a.n.1.1 | 2 | |||
4.3 | odd | 2 | 1232.2.a.n.1.1 | 2 | |||
5.2 | odd | 4 | 7700.2.e.j.1849.1 | 4 | |||
5.3 | odd | 4 | 7700.2.e.j.1849.4 | 4 | |||
5.4 | even | 2 | 7700.2.a.s.1.1 | 2 | |||
7.2 | even | 3 | 2156.2.i.e.1145.1 | 4 | |||
7.3 | odd | 6 | 2156.2.i.i.177.2 | 4 | |||
7.4 | even | 3 | 2156.2.i.e.177.1 | 4 | |||
7.5 | odd | 6 | 2156.2.i.i.1145.2 | 4 | |||
7.6 | odd | 2 | 2156.2.a.c.1.1 | 2 | |||
8.3 | odd | 2 | 4928.2.a.bq.1.2 | 2 | |||
8.5 | even | 2 | 4928.2.a.bp.1.1 | 2 | |||
11.10 | odd | 2 | 3388.2.a.h.1.2 | 2 | |||
28.27 | even | 2 | 8624.2.a.bj.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
308.2.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1232.2.a.n.1.1 | 2 | 4.3 | odd | 2 | |||
2156.2.a.c.1.1 | 2 | 7.6 | odd | 2 | |||
2156.2.i.e.177.1 | 4 | 7.4 | even | 3 | |||
2156.2.i.e.1145.1 | 4 | 7.2 | even | 3 | |||
2156.2.i.i.177.2 | 4 | 7.3 | odd | 6 | |||
2156.2.i.i.1145.2 | 4 | 7.5 | odd | 6 | |||
2772.2.a.n.1.1 | 2 | 3.2 | odd | 2 | |||
3388.2.a.h.1.2 | 2 | 11.10 | odd | 2 | |||
4928.2.a.bp.1.1 | 2 | 8.5 | even | 2 | |||
4928.2.a.bq.1.2 | 2 | 8.3 | odd | 2 | |||
7700.2.a.s.1.1 | 2 | 5.4 | even | 2 | |||
7700.2.e.j.1849.1 | 4 | 5.2 | odd | 4 | |||
7700.2.e.j.1849.4 | 4 | 5.3 | odd | 4 | |||
8624.2.a.bj.1.2 | 2 | 28.27 | even | 2 |