Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2800,2,Mod(1,2800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2800, 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("2800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2800.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: | \(22.3581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1400) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2800.1 |
$q$-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 | ||||||||
\(3\) | −2.56155 | −1.47891 | −0.739457 | − | 0.673204i | \(-0.764917\pi\) | ||||
−0.739457 | + | 0.673204i | \(0.764917\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.56155 | 1.18718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.12311 | −0.640140 | −0.320070 | − | 0.947394i | \(-0.603707\pi\) | ||||
−0.320070 | + | 0.947394i | \(0.603707\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.56155 | −0.621268 | −0.310634 | − | 0.950530i | \(-0.600541\pi\) | ||||
−0.310634 | + | 0.950530i | \(0.600541\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.561553 | 0.128829 | 0.0644145 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644145 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.56155 | 0.558977 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.56155 | −1.15966 | −0.579832 | − | 0.814736i | \(-0.696882\pi\) | ||||
−0.579832 | + | 0.814736i | \(0.696882\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.43845 | −0.276829 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.56155 | 1.40415 | 0.702073 | − | 0.712105i | \(-0.252258\pi\) | ||||
0.702073 | + | 0.712105i | \(0.252258\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.876894 | 0.157495 | 0.0787474 | − | 0.996895i | \(-0.474908\pi\) | ||||
0.0787474 | + | 0.996895i | \(0.474908\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.43845 | 0.946712 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.8078 | −1.94118 | −0.970592 | − | 0.240730i | \(-0.922613\pi\) | ||||
−0.970592 | + | 0.240730i | \(0.922613\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.12311 | −0.820353 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.56155 | −1.02474 | −0.512371 | − | 0.858764i | \(-0.671233\pi\) | ||||
−0.512371 | + | 0.858764i | \(0.671233\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.43845 | −0.371860 | −0.185930 | − | 0.982563i | \(-0.559530\pi\) | ||||
−0.185930 | + | 0.982563i | \(0.559530\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.24621 | −1.20283 | −0.601417 | − | 0.798935i | \(-0.705397\pi\) | ||||
−0.601417 | + | 0.798935i | \(0.705397\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.56155 | 0.918801 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.12311 | 0.978434 | 0.489217 | − | 0.872162i | \(-0.337283\pi\) | ||||
0.489217 | + | 0.872162i | \(0.337283\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.43845 | −0.190527 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.3693 | 1.74054 | 0.870268 | − | 0.492578i | \(-0.163945\pi\) | ||||
0.870268 | + | 0.492578i | \(0.163945\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.87689 | 0.368349 | 0.184174 | − | 0.982894i | \(-0.441039\pi\) | ||||
0.184174 | + | 0.982894i | \(0.441039\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.56155 | −0.448713 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −16.1231 | −1.96975 | −0.984875 | − | 0.173264i | \(-0.944569\pi\) | ||||
−0.984875 | + | 0.173264i | \(0.944569\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.2462 | 1.71504 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.6847 | 1.26804 | 0.634018 | − | 0.773318i | \(-0.281405\pi\) | ||||
0.634018 | + | 0.773318i | \(0.281405\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.5616 | 1.23614 | 0.618068 | − | 0.786125i | \(-0.287916\pi\) | ||||
0.618068 | + | 0.786125i | \(0.287916\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.12311 | 0.241950 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.68466 | −0.752083 | −0.376041 | − | 0.926603i | \(-0.622715\pi\) | ||||
−0.376041 | + | 0.926603i | \(0.622715\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.6847 | 1.50209 | 0.751043 | − | 0.660253i | \(-0.229551\pi\) | ||||
0.751043 | + | 0.660253i | \(0.229551\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −19.3693 | −2.07661 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.8078 | −1.14562 | −0.572810 | − | 0.819688i | \(-0.694147\pi\) | ||||
−0.572810 | + | 0.819688i | \(0.694147\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.24621 | −0.232921 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000 | 0.609208 | 0.304604 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304604 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.56155 | −0.759965 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.12311 | −0.701860 | −0.350930 | − | 0.936402i | \(-0.614135\pi\) | ||||
−0.350930 | + | 0.936402i | \(0.614135\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.8078 | 1.23817 | 0.619087 | − | 0.785323i | \(-0.287503\pi\) | ||||
0.619087 | + | 0.785323i | \(0.287503\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.93087 | −0.855422 | −0.427711 | − | 0.903915i | \(-0.640680\pi\) | ||||
−0.427711 | + | 0.903915i | \(0.640680\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 30.2462 | 2.87084 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.753789 | 0.0709105 | 0.0354552 | − | 0.999371i | \(-0.488712\pi\) | ||||
0.0354552 | + | 0.999371i | \(0.488712\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.12311 | 0.658531 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.56155 | 0.234817 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.49242 | −0.590220 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.8078 | 1.51551 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.80776 | 0.870298 | 0.435149 | − | 0.900358i | \(-0.356696\pi\) | ||||
0.435149 | + | 0.900358i | \(0.356696\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.24621 | 0.549948 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.75379 | 0.153229 | 0.0766146 | − | 0.997061i | \(-0.475589\pi\) | ||||
0.0766146 | + | 0.997061i | \(0.475589\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.561553 | −0.0486928 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.31534 | −0.197813 | −0.0989065 | − | 0.995097i | \(-0.531534\pi\) | ||||
−0.0989065 | + | 0.995097i | \(0.531534\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.6847 | 1.66963 | 0.834815 | − | 0.550530i | \(-0.185574\pi\) | ||||
0.834815 | + | 0.550530i | \(0.185574\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.1231 | 1.77889 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.24621 | −0.355086 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.56155 | −0.211273 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.5616 | 1.43870 | 0.719349 | − | 0.694649i | \(-0.244440\pi\) | ||||
0.719349 | + | 0.694649i | \(0.244440\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.56155 | 0.452593 | 0.226296 | − | 0.974058i | \(-0.427338\pi\) | ||||
0.226296 | + | 0.974058i | \(0.427338\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.12311 | −0.737559 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.4924 | 1.95471 | 0.977354 | − | 0.211611i | \(-0.0678709\pi\) | ||||
0.977354 | + | 0.211611i | \(0.0678709\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.2462 | −1.44702 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.56155 | 0.438312 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.9309 | 1.09115 | 0.545575 | − | 0.838062i | \(-0.316311\pi\) | ||||
0.545575 | + | 0.838062i | \(0.316311\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.6155 | 1.51790 | 0.758948 | − | 0.651152i | \(-0.225714\pi\) | ||||
0.758948 | + | 0.651152i | \(0.225714\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00000 | 0.152944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.4924 | 1.10184 | 0.550919 | − | 0.834559i | \(-0.314277\pi\) | ||||
0.550919 | + | 0.834559i | \(0.314277\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −34.2462 | −2.57410 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.31534 | 0.621518 | 0.310759 | − | 0.950489i | \(-0.399417\pi\) | ||||
0.310759 | + | 0.950489i | \(0.399417\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.87689 | −0.213838 | −0.106919 | − | 0.994268i | \(-0.534099\pi\) | ||||
−0.106919 | + | 0.994268i | \(0.534099\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.36932 | −0.544756 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.43845 | 0.397699 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.43845 | 0.104632 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.630683 | −0.0456346 | −0.0228173 | − | 0.999740i | \(-0.507264\pi\) | ||||
−0.0228173 | + | 0.999740i | \(0.507264\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.6155 | 1.48394 | 0.741969 | − | 0.670434i | \(-0.233892\pi\) | ||||
0.741969 | + | 0.670434i | \(0.233892\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.56155 | −0.253750 | −0.126875 | − | 0.991919i | \(-0.540495\pi\) | ||||
−0.126875 | + | 0.991919i | \(0.540495\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.1231 | 0.930272 | 0.465136 | − | 0.885239i | \(-0.346005\pi\) | ||||
0.465136 | + | 0.885239i | \(0.346005\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 41.3002 | 2.91309 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.56155 | −0.530717 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −19.8078 | −1.37673 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.19224 | −0.0824687 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.5616 | −0.727087 | −0.363544 | − | 0.931577i | \(-0.618433\pi\) | ||||
−0.363544 | + | 0.931577i | \(0.618433\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −27.3693 | −1.87531 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.876894 | −0.0595275 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −27.0540 | −1.82814 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.12311 | −0.344617 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.630683 | 0.0422337 | 0.0211168 | − | 0.999777i | \(-0.493278\pi\) | ||||
0.0211168 | + | 0.999777i | \(0.493278\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.3693 | 0.887353 | 0.443676 | − | 0.896187i | \(-0.353674\pi\) | ||||
0.443676 | + | 0.896187i | \(0.353674\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0000 | −0.925146 | −0.462573 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462573 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.43845 | −0.357824 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.56155 | 0.233325 | 0.116663 | − | 0.993172i | \(-0.462780\pi\) | ||||
0.116663 | + | 0.993172i | \(0.462780\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 17.1231 | 1.11227 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.00000 | 0.258738 | 0.129369 | − | 0.991596i | \(-0.458705\pi\) | ||||
0.129369 | + | 0.991596i | \(0.458705\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.0540 | 1.61387 | 0.806934 | − | 0.590641i | \(-0.201125\pi\) | ||||
0.806934 | + | 0.590641i | \(0.201125\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.2462 | 1.42710 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.12311 | 0.0714615 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −35.0540 | −2.22146 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.3153 | 0.777337 | 0.388669 | − | 0.921378i | \(-0.372935\pi\) | ||||
0.388669 | + | 0.921378i | \(0.372935\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.8078 | 0.742348 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.24621 | −0.264871 | −0.132436 | − | 0.991192i | \(-0.542280\pi\) | ||||
−0.132436 | + | 0.991192i | \(0.542280\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.8078 | 0.733699 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 26.9309 | 1.66698 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.6847 | 0.658844 | 0.329422 | − | 0.944183i | \(-0.393146\pi\) | ||||
0.329422 | + | 0.944183i | \(0.393146\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27.6847 | 1.69427 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.7538 | 0.716641 | 0.358321 | − | 0.933599i | \(-0.383349\pi\) | ||||
0.358321 | + | 0.933599i | \(0.383349\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.2462 | −0.986887 | −0.493444 | − | 0.869778i | \(-0.664262\pi\) | ||||
−0.493444 | + | 0.869778i | \(0.664262\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.12311 | 0.310064 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.4924 | −0.630429 | −0.315214 | − | 0.949021i | \(-0.602076\pi\) | ||||
−0.315214 | + | 0.949021i | \(0.602076\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.12311 | 0.186975 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.5616 | 0.689704 | 0.344852 | − | 0.938657i | \(-0.387929\pi\) | ||||
0.344852 | + | 0.938657i | \(0.387929\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.6847 | 0.813469 | 0.406734 | − | 0.913547i | \(-0.366667\pi\) | ||||
0.406734 | + | 0.913547i | \(0.366667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.56155 | 0.387316 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.4384 | −0.614026 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.3693 | −0.900965 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −30.0000 | −1.75262 | −0.876309 | − | 0.481749i | \(-0.840002\pi\) | ||||
−0.876309 | + | 0.481749i | \(0.840002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.05398 | 0.177210 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.1231 | −0.643266 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.43845 | 0.140550 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.31534 | −0.246290 | −0.123145 | − | 0.992389i | \(-0.539298\pi\) | ||||
−0.123145 | + | 0.992389i | \(0.539298\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.2462 | 1.03799 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.87689 | −0.163134 | −0.0815669 | − | 0.996668i | \(-0.525992\pi\) | ||||
−0.0815669 | + | 0.996668i | \(0.525992\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.0000 | 1.24351 | 0.621757 | − | 0.783210i | \(-0.286419\pi\) | ||||
0.621757 | + | 0.783210i | \(0.286419\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.6847 | −1.16177 | −0.580883 | − | 0.813987i | \(-0.697293\pi\) | ||||
−0.580883 | + | 0.813987i | \(0.697293\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.0540 | −0.898850 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −32.8078 | −1.83115 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.43845 | −0.0800373 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 22.8769 | 1.26510 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.24621 | 0.454628 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.0000 | −1.48405 | −0.742027 | − | 0.670370i | \(-0.766135\pi\) | ||||
−0.742027 | + | 0.670370i | \(0.766135\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −42.0540 | −2.30454 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.68466 | −0.309663 | −0.154832 | − | 0.987941i | \(-0.549483\pi\) | ||||
−0.154832 | + | 0.987941i | \(0.549483\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.93087 | −0.104870 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.86174 | −0.100819 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.6155 | −1.21407 | −0.607033 | − | 0.794677i | \(-0.707640\pi\) | ||||
−0.607033 | + | 0.794677i | \(0.707640\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.8769 | −0.689284 | −0.344642 | − | 0.938734i | \(-0.612000\pi\) | ||||
−0.344642 | + | 0.938734i | \(0.612000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.87689 | −0.153557 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.7538 | −0.625591 | −0.312796 | − | 0.949820i | \(-0.601265\pi\) | ||||
−0.312796 | + | 0.949820i | \(0.601265\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.56155 | −0.347274 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.6847 | 0.775027 | 0.387513 | − | 0.921864i | \(-0.373334\pi\) | ||||
0.387513 | + | 0.921864i | \(0.373334\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6847 | −0.983403 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.6307 | 0.872884 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.7538 | −0.926740 | −0.463370 | − | 0.886165i | \(-0.653360\pi\) | ||||
−0.463370 | + | 0.886165i | \(0.653360\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −23.3693 | −1.21656 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.12311 | −0.369813 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.0540 | 0.727687 | 0.363844 | − | 0.931460i | \(-0.381464\pi\) | ||||
0.363844 | + | 0.931460i | \(0.381464\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.1231 | 0.778880 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.8617 | 1.27706 | 0.638531 | − | 0.769596i | \(-0.279542\pi\) | ||||
0.638531 | + | 0.769596i | \(0.279542\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −25.1231 | −1.28710 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.2462 | 1.03453 | 0.517267 | − | 0.855824i | \(-0.326950\pi\) | ||||
0.517267 | + | 0.855824i | \(0.326950\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.68466 | −0.441466 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.43845 | 0.123634 | 0.0618171 | − | 0.998087i | \(-0.480310\pi\) | ||||
0.0618171 | + | 0.998087i | \(0.480310\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.2462 | 0.720462 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.49242 | −0.226613 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 38.4924 | 1.93188 | 0.965940 | − | 0.258767i | \(-0.0833163\pi\) | ||||
0.965940 | + | 0.258767i | \(0.0833163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.43845 | 0.0720124 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.4924 | −1.57266 | −0.786328 | − | 0.617809i | \(-0.788021\pi\) | ||||
−0.786328 | + | 0.617809i | \(0.788021\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.75379 | 0.0873624 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.0691 | 1.24263 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.19224 | −0.256740 | −0.128370 | − | 0.991726i | \(-0.540974\pi\) | ||||
−0.128370 | + | 0.991726i | \(0.540974\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.93087 | 0.292548 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.3693 | −0.657861 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −50.4233 | −2.46924 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.8078 | 0.918819 | 0.459410 | − | 0.888224i | \(-0.348061\pi\) | ||||
0.459410 | + | 0.888224i | \(0.348061\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.06913 | 0.247054 | 0.123527 | − | 0.992341i | \(-0.460579\pi\) | ||||
0.123527 | + | 0.992341i | \(0.460579\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −29.3693 | −1.42799 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.87689 | −0.139223 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.8769 | 0.525141 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.7538 | 0.662497 | 0.331248 | − | 0.943544i | \(-0.392530\pi\) | ||||
0.331248 | + | 0.943544i | \(0.392530\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −35.5464 | −1.70825 | −0.854125 | − | 0.520067i | \(-0.825907\pi\) | ||||
−0.854125 | + | 0.520067i | \(0.825907\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.12311 | −0.149398 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.12311 | 0.339967 | 0.169984 | − | 0.985447i | \(-0.445629\pi\) | ||||
0.169984 | + | 0.985447i | \(0.445629\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.56155 | 0.169598 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.5616 | −1.07193 | −0.535966 | − | 0.844240i | \(-0.680052\pi\) | ||||
−0.535966 | + | 0.844240i | \(0.680052\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −44.9848 | −2.12771 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.3693 | 0.489358 | 0.244679 | − | 0.969604i | \(-0.421317\pi\) | ||||
0.244679 | + | 0.969604i | \(0.421317\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.9309 | 0.655979 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.2462 | −0.669345 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.1080 | 1.73584 | 0.867918 | − | 0.496707i | \(-0.165458\pi\) | ||||
0.867918 | + | 0.496707i | \(0.165458\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.68466 | 0.171985 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.49242 | 0.302382 | 0.151191 | − | 0.988505i | \(-0.451689\pi\) | ||||
0.151191 | + | 0.988505i | \(0.451689\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.4924 | 0.952364 | 0.476182 | − | 0.879347i | \(-0.342020\pi\) | ||||
0.476182 | + | 0.879347i | \(0.342020\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.8769 | 1.15117 | 0.575583 | − | 0.817744i | \(-0.304775\pi\) | ||||
0.575583 | + | 0.817744i | \(0.304775\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.1231 | 0.744496 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −62.7386 | −2.89084 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.17708 | 0.238042 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 25.3693 | 1.16158 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 40.7386 | 1.86140 | 0.930698 | − | 0.365789i | \(-0.119201\pi\) | ||||
0.930698 | + | 0.365789i | \(0.119201\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.6155 | −1.07678 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.2462 | −0.648225 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.5616 | −1.61145 | −0.805724 | − | 0.592291i | \(-0.798223\pi\) | ||||
−0.805724 | + | 0.592291i | \(0.798223\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −35.6847 | −1.61372 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.6847 | −0.933486 | −0.466743 | − | 0.884393i | \(-0.654573\pi\) | ||||
−0.466743 | + | 0.884393i | \(0.654573\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.3693 | −0.872350 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.6847 | −0.479272 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.4924 | 0.738302 | 0.369151 | − | 0.929369i | \(-0.379648\pi\) | ||||
0.369151 | + | 0.929369i | \(0.379648\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −50.2462 | −2.24484 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.7538 | −0.880778 | −0.440389 | − | 0.897807i | \(-0.645159\pi\) | ||||
−0.440389 | + | 0.897807i | \(0.645159\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.0540 | 1.02386 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.0000 | 1.15243 | 0.576215 | − | 0.817298i | \(-0.304529\pi\) | ||||
0.576215 | + | 0.817298i | \(0.304529\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.5616 | −0.467216 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.807764 | −0.0356637 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.5076 | 0.769982 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −37.1231 | −1.62952 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.4384 | −1.20210 | −0.601050 | − | 0.799211i | \(-0.705251\pi\) | ||||
−0.601050 | + | 0.799211i | \(0.705251\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.3153 | −1.23814 | −0.619072 | − | 0.785334i | \(-0.712491\pi\) | ||||
−0.619072 | + | 0.785334i | \(0.712491\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.24621 | −0.0978465 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.93087 | 0.344820 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 47.6155 | 2.06634 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.1231 | −0.568425 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.3002 | −0.919171 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.12311 | −0.0914486 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.4233 | 1.78093 | 0.890463 | − | 0.455055i | \(-0.150380\pi\) | ||||
0.890463 | + | 0.455055i | \(0.150380\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.36932 | 0.316248 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.7386 | −1.44256 | −0.721280 | − | 0.692644i | \(-0.756446\pi\) | ||||
−0.721280 | + | 0.692644i | \(0.756446\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.2462 | 0.437298 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.24621 | 0.180895 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.68466 | 0.284261 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.56155 | 0.405136 | 0.202568 | − | 0.979268i | \(-0.435071\pi\) | ||||
0.202568 | + | 0.979268i | \(0.435071\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.87689 | −0.206271 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.9309 | −0.588162 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.12311 | 0.300203 | 0.150102 | − | 0.988671i | \(-0.452040\pi\) | ||||
0.150102 | + | 0.988671i | \(0.452040\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.00000 | 0.293972 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.9848 | −0.837808 | −0.418904 | − | 0.908030i | \(-0.637586\pi\) | ||||
−0.418904 | + | 0.908030i | \(0.637586\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.3153 | −1.14311 | −0.571556 | − | 0.820563i | \(-0.693660\pi\) | ||||
−0.571556 | + | 0.820563i | \(0.693660\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.61553 | 0.0674897 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.5464 | −1.89612 | −0.948061 | − | 0.318090i | \(-0.896959\pi\) | ||||
−0.948061 | + | 0.318090i | \(0.896959\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −52.8078 | −2.19462 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.6847 | −0.567735 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.1231 | −0.626335 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.17708 | −0.337504 | −0.168752 | − | 0.985659i | \(-0.553974\pi\) | ||||
−0.168752 | + | 0.985659i | \(0.553974\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.492423 | 0.0202899 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.12311 | 0.375274 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.3153 | 0.505730 | 0.252865 | − | 0.967502i | \(-0.418627\pi\) | ||||
0.252865 | + | 0.967502i | \(0.418627\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −33.6155 | −1.37579 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.3002 | −0.992879 | −0.496439 | − | 0.868071i | \(-0.665359\pi\) | ||||
−0.496439 | + | 0.868071i | \(0.665359\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.94602 | −0.201753 | −0.100876 | − | 0.994899i | \(-0.532165\pi\) | ||||
−0.100876 | + | 0.994899i | \(0.532165\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −57.4233 | −2.33846 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.3693 | 1.51677 | 0.758387 | − | 0.651805i | \(-0.225988\pi\) | ||||
0.758387 | + | 0.651805i | \(0.225988\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.3693 | 0.784884 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.4924 | −0.667212 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.68466 | −0.269991 | −0.134995 | − | 0.990846i | \(-0.543102\pi\) | ||||
−0.134995 | + | 0.990846i | \(0.543102\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.8078 | 0.716914 | 0.358457 | − | 0.933546i | \(-0.383303\pi\) | ||||
0.358457 | + | 0.933546i | \(0.383303\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.3693 | −1.18045 | −0.590226 | − | 0.807238i | \(-0.700961\pi\) | ||||
−0.590226 | + | 0.807238i | \(0.700961\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.00000 | 0.321029 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.8078 | 0.433004 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.05398 | 0.121964 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 30.2462 | 1.20600 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.0540 | −1.35567 | −0.677834 | − | 0.735215i | \(-0.737081\pi\) | ||||
−0.677834 | + | 0.735215i | \(0.737081\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 27.0540 | 1.07530 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | 0.0792429 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 38.0540 | 1.50539 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.4384 | −0.649280 | −0.324640 | − | 0.945838i | \(-0.605243\pi\) | ||||
−0.324640 | + | 0.945838i | \(0.605243\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.73863 | −0.108001 | −0.0540006 | − | 0.998541i | \(-0.517197\pi\) | ||||
−0.0540006 | + | 0.998541i | \(0.517197\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.3693 | 0.997371 | 0.498685 | − | 0.866783i | \(-0.333816\pi\) | ||||
0.498685 | + | 0.866783i | \(0.333816\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.3845 | −1.11419 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.24621 | 0.0880360 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.8617 | 1.32511 | 0.662556 | − | 0.749012i | \(-0.269472\pi\) | ||||
0.662556 | + | 0.749012i | \(0.269472\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 37.6155 | 1.46752 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.5616 | −0.723055 | −0.361528 | − | 0.932361i | \(-0.617745\pi\) | ||||
−0.361528 | + | 0.932361i | \(0.617745\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.4924 | −0.874854 | −0.437427 | − | 0.899254i | \(-0.644110\pi\) | ||||
−0.437427 | + | 0.899254i | \(0.644110\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.1231 | 0.509659 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −42.0540 | −1.62834 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.61553 | −0.0624599 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.10795 | −0.235795 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 46.4924 | 1.79215 | 0.896076 | − | 0.443901i | \(-0.146406\pi\) | ||||
0.896076 | + | 0.443901i | \(0.146406\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.6307 | 0.562303 | 0.281151 | − | 0.959663i | \(-0.409284\pi\) | ||||
0.281151 | + | 0.959663i | \(0.409284\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.00000 | −0.230259 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −34.2462 | −1.31232 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −34.1231 | −1.30568 | −0.652842 | − | 0.757494i | \(-0.726424\pi\) | ||||
−0.652842 | + | 0.757494i | \(0.726424\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 35.8617 | 1.36821 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.2462 | 0.542737 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.4384 | 0.663390 | 0.331695 | − | 0.943387i | \(-0.392380\pi\) | ||||
0.331695 | + | 0.943387i | \(0.392380\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.56155 | 0.287240 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.8078 | 0.636639 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.12311 | −0.345068 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.1080 | 1.66593 | 0.832967 | − | 0.553322i | \(-0.186640\pi\) | ||||
0.832967 | + | 0.553322i | \(0.186640\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.63068 | −0.250081 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.3693 | 1.40343 | 0.701717 | − | 0.712456i | \(-0.252417\pi\) | ||||
0.701717 | + | 0.712456i | \(0.252417\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.8078 | −0.892861 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.87689 | −0.182641 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.2462 | −0.382652 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.2462 | −1.42634 | −0.713171 | − | 0.700990i | \(-0.752742\pi\) | ||||
−0.713171 | + | 0.700990i | \(0.752742\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.12311 | 0.265278 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −64.1771 | −2.38677 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.61553 | 0.0599166 | 0.0299583 | − | 0.999551i | \(-0.490463\pi\) | ||||
0.0299583 | + | 0.999551i | \(0.490463\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −35.9848 | −1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.24621 | 0.231024 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.2462 | 0.821683 | 0.410841 | − | 0.911707i | \(-0.365235\pi\) | ||||
0.410841 | + | 0.911707i | \(0.365235\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 34.2311 | 1.26092 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.1771 | −0.631869 | −0.315935 | − | 0.948781i | \(-0.602318\pi\) | ||||
−0.315935 | + | 0.948781i | \(0.602318\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.87689 | −0.105685 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.7386 | 0.687454 | 0.343727 | − | 0.939070i | \(-0.388311\pi\) | ||||
0.343727 | + | 0.939070i | \(0.388311\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 48.7386 | 1.78325 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.8078 | −0.467986 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.3693 | −0.998721 | −0.499360 | − | 0.866394i | \(-0.666432\pi\) | ||||
−0.499360 | + | 0.866394i | \(0.666432\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31.5464 | −1.14961 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.3153 | 0.483954 | 0.241977 | − | 0.970282i | \(-0.422204\pi\) | ||||
0.241977 | + | 0.970282i | \(0.422204\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −30.2462 | −1.09787 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.4233 | 1.24784 | 0.623922 | − | 0.781487i | \(-0.285538\pi\) | ||||
0.623922 | + | 0.781487i | \(0.285538\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.93087 | 0.323319 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 26.7386 | 0.965476 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.3002 | −1.20084 | −0.600418 | − | 0.799687i | \(-0.704999\pi\) | ||||
−0.600418 | + | 0.799687i | \(0.704999\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.8769 | 0.391722 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.6155 | −0.417782 | −0.208891 | − | 0.977939i | \(-0.566985\pi\) | ||||
−0.208891 | + | 0.977939i | \(0.566985\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −30.2462 | −1.08508 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.68466 | −0.132017 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.6847 | −0.811721 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.8769 | −0.388708 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.2462 | −0.935576 | −0.467788 | − | 0.883841i | \(-0.654949\pi\) | ||||
−0.467788 | + | 0.883841i | \(0.654949\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.3693 | −0.974373 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.753789 | −0.0268016 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.75379 | 0.204323 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.6155 | 1.47410 | 0.737049 | − | 0.675840i | \(-0.236219\pi\) | ||||
0.737049 | + | 0.675840i | \(0.236219\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.1231 | 0.747282 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −38.4924 | −1.36006 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.4233 | −0.791301 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.1080 | −1.05985 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.4233 | 1.73763 | 0.868815 | − | 0.495136i | \(-0.164882\pi\) | ||||
0.868815 | + | 0.495136i | \(0.164882\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.6155 | −1.53155 | −0.765774 | − | 0.643110i | \(-0.777644\pi\) | ||||
−0.765774 | + | 0.643110i | \(0.777644\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 41.6155 | 1.45952 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.36932 | −0.0479063 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.12311 | −0.248901 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45.8617 | 1.60059 | 0.800293 | − | 0.599609i | \(-0.204677\pi\) | ||||
0.800293 | + | 0.599609i | \(0.204677\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.4384 | −0.433577 | −0.216789 | − | 0.976219i | \(-0.569558\pi\) | ||||
−0.216789 | + | 0.976219i | \(0.569558\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.24621 | 0.321522 | 0.160761 | − | 0.986993i | \(-0.448605\pi\) | ||||
0.160761 | + | 0.986993i | \(0.448605\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.24621 | −0.0780141 | −0.0390071 | − | 0.999239i | \(-0.512419\pi\) | ||||
−0.0390071 | + | 0.999239i | \(0.512419\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.8769 | 0.932349 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.56155 | −0.0887525 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.26137 | −0.0435992 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.12311 | 0.0387739 | 0.0193870 | − | 0.999812i | \(-0.493829\pi\) | ||||
0.0193870 | + | 0.999812i | \(0.493829\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.1771 | 0.971623 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −29.6155 | −1.02001 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.49242 | 0.223082 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −35.0540 | −1.20305 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 65.6695 | 2.25112 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.8769 | 0.372418 | 0.186209 | − | 0.982510i | \(-0.440380\pi\) | ||||
0.186209 | + | 0.982510i | \(0.440380\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.94602 | 0.168953 | 0.0844765 | − | 0.996425i | \(-0.473078\pi\) | ||||
0.0844765 | + | 0.996425i | \(0.473078\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.1771 | −1.16611 | −0.583053 | − | 0.812434i | \(-0.698142\pi\) | ||||
−0.583053 | + | 0.812434i | \(0.698142\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.8078 | −0.572807 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.8078 | 0.810426 | 0.405213 | − | 0.914222i | \(-0.367197\pi\) | ||||
0.405213 | + | 0.914222i | \(0.367197\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.7386 | 0.908092 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.1922 | 0.481439 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.2462 | −1.09262 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.3693 | 0.723242 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.6155 | 0.797440 | 0.398720 | − | 0.917073i | \(-0.369455\pi\) | ||||
0.398720 | + | 0.917073i | \(0.369455\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 76.8466 | 2.59197 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.7386 | −1.37252 | −0.686260 | − | 0.727357i | \(-0.740749\pi\) | ||||
−0.686260 | + | 0.727357i | \(0.740749\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.49242 | 0.0502240 | 0.0251120 | − | 0.999685i | \(-0.492006\pi\) | ||||
0.0251120 | + | 0.999685i | \(0.492006\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 49.6155 | 1.66593 | 0.832963 | − | 0.553328i | \(-0.186643\pi\) | ||||
0.832963 | + | 0.553328i | \(0.186643\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.80776 | −0.328942 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.8617 | 0.497887 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.63068 | −0.154960 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28.4924 | 0.951334 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.63068 | 0.221146 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.2462 | −0.607869 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.24621 | −0.207861 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.00000 | −0.132818 | −0.0664089 | − | 0.997792i | \(-0.521154\pi\) | ||||
−0.0664089 | + | 0.997792i | \(0.521154\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.4233 | 1.30615 | 0.653076 | − | 0.757292i | \(-0.273478\pi\) | ||||
0.653076 | + | 0.757292i | \(0.273478\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29.0540 | −0.961546 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.75379 | −0.0579152 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.1922 | −0.600106 | −0.300053 | − | 0.953922i | \(-0.597004\pi\) | ||||
−0.300053 | + | 0.953922i | \(0.597004\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.0540 | 0.364241 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.3693 | 0.703380 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −25.3693 | −0.833238 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 56.3542 | 1.84892 | 0.924460 | − | 0.381279i | \(-0.124516\pi\) | ||||
0.924460 | + | 0.381279i | \(0.124516\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.561553 | 0.0184042 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.36932 | 0.241261 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.3002 | 0.695847 | 0.347923 | − | 0.937523i | \(-0.386887\pi\) | ||||
0.347923 | + | 0.937523i | \(0.386887\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −56.3542 | −1.83905 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.36932 | −0.0446385 | −0.0223192 | − | 0.999751i | \(-0.507105\pi\) | ||||
−0.0223192 | + | 0.999751i | \(0.507105\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.4924 | 1.18836 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.4924 | −0.535932 | −0.267966 | − | 0.963428i | \(-0.586351\pi\) | ||||
−0.267966 | + | 0.963428i | \(0.586351\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.1231 | 0.685685 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 52.9848 | 1.71815 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.8769 | −0.903021 | −0.451511 | − | 0.892266i | \(-0.649115\pi\) | ||||
−0.451511 | + | 0.892266i | \(0.649115\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 41.1231 | 1.32932 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.31534 | 0.0747663 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.2311 | −0.975195 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 45.6155 | 1.46994 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.6307 | 0.534807 | 0.267403 | − | 0.963585i | \(-0.413834\pi\) | ||||
0.267403 | + | 0.963585i | \(0.413834\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.68466 | 0.118368 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.31534 | 0.0743028 | 0.0371514 | − | 0.999310i | \(-0.488172\pi\) | ||||
0.0371514 | + | 0.999310i | \(0.488172\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.6847 | −0.631061 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.2462 | −1.06364 | −0.531820 | − | 0.846857i | \(-0.678492\pi\) | ||||
−0.531820 | + | 0.846857i | \(0.678492\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.9460 | 0.733358 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −31.8078 | −1.01554 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 62.3542 | 1.98879 | 0.994394 | − | 0.105734i | \(-0.0337192\pi\) | ||||
0.994394 | + | 0.105734i | \(0.0337192\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21.1231 | −0.672356 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.5616 | 0.431232 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.6695 | 0.942483 | 0.471241 | − | 0.882004i | \(-0.343806\pi\) | ||||
0.471241 | + | 0.882004i | \(0.343806\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 69.1619 | 2.19479 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.2462 | 0.387841 | 0.193921 | − | 0.981017i | \(-0.437880\pi\) | ||||
0.193921 | + | 0.981017i | \(0.437880\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.9848 | 0.537377 |
(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 | 2800.2.a.bj.1.1 | 2 | ||
4.3 | odd | 2 | 1400.2.a.q.1.2 | yes | 2 | ||
5.2 | odd | 4 | 2800.2.g.v.449.4 | 4 | |||
5.3 | odd | 4 | 2800.2.g.v.449.1 | 4 | |||
5.4 | even | 2 | 2800.2.a.bo.1.2 | 2 | |||
20.3 | even | 4 | 1400.2.g.j.449.4 | 4 | |||
20.7 | even | 4 | 1400.2.g.j.449.1 | 4 | |||
20.19 | odd | 2 | 1400.2.a.o.1.1 | ✓ | 2 | ||
28.27 | even | 2 | 9800.2.a.bt.1.1 | 2 | |||
140.139 | even | 2 | 9800.2.a.bx.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1400.2.a.o.1.1 | ✓ | 2 | 20.19 | odd | 2 | ||
1400.2.a.q.1.2 | yes | 2 | 4.3 | odd | 2 | ||
1400.2.g.j.449.1 | 4 | 20.7 | even | 4 | |||
1400.2.g.j.449.4 | 4 | 20.3 | even | 4 | |||
2800.2.a.bj.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2800.2.a.bo.1.2 | 2 | 5.4 | even | 2 | |||
2800.2.g.v.449.1 | 4 | 5.3 | odd | 4 | |||
2800.2.g.v.449.4 | 4 | 5.2 | odd | 4 | |||
9800.2.a.bt.1.1 | 2 | 28.27 | even | 2 | |||
9800.2.a.bx.1.2 | 2 | 140.139 | even | 2 |