Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,3,Mod(721,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.721");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.o (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(74.5506003290\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-7}, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 15x^{2} + 16x + 134 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 171) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 721.2 | ||
Root | \(3.66228 + 1.32288i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.721 |
Dual form | 2736.3.o.j.721.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.32456 | −1.26491 | −0.632456 | − | 0.774597i | \(-0.717953\pi\) | ||||
−0.632456 | + | 0.774597i | \(0.717953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | 0.285714 | 0.142857 | − | 0.989743i | \(-0.454371\pi\) | ||||
0.142857 | + | 0.989743i | \(0.454371\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.6491 | 1.14992 | 0.574960 | − | 0.818182i | \(-0.305018\pi\) | ||||
0.574960 | + | 0.818182i | \(0.305018\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 16.7332i | 1.28717i | 0.765375 | + | 0.643585i | \(0.222554\pi\) | ||||
−0.765375 | + | 0.643585i | \(0.777446\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.00000 | + | 16.7332i | 0.473684 | + | 0.880695i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.32456 | −0.274981 | −0.137490 | − | 0.990503i | \(-0.543904\pi\) | ||||
−0.137490 | + | 0.990503i | \(0.543904\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 15.0000 | 0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 21.1660i | − | 0.729862i | −0.931034 | − | 0.364931i | \(-0.881093\pi\) | ||
0.931034 | − | 0.364931i | \(-0.118907\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 16.7332i | 0.539781i | 0.962891 | + | 0.269890i | \(0.0869875\pi\) | ||||
−0.962891 | + | 0.269890i | \(0.913013\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −12.6491 | −0.361403 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 50.1996i | − | 1.35675i | −0.734718 | − | 0.678373i | \(-0.762685\pi\) | ||
0.734718 | − | 0.678373i | \(-0.237315\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 21.1660i | 0.516244i | 0.966112 | + | 0.258122i | \(0.0831037\pi\) | ||||
−0.966112 | + | 0.258122i | \(0.916896\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −34.0000 | −0.790698 | −0.395349 | − | 0.918531i | \(-0.629376\pi\) | ||||
−0.395349 | + | 0.918531i | \(0.629376\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 82.2192 | 1.74935 | 0.874673 | − | 0.484714i | \(-0.161076\pi\) | ||||
0.874673 | + | 0.484714i | \(0.161076\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −45.0000 | −0.918367 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 63.4980i | − | 1.19808i | −0.800721 | − | 0.599038i | \(-0.795550\pi\) | ||
0.800721 | − | 0.599038i | \(-0.204450\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −80.0000 | −1.45455 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 21.1660i | 0.358746i | 0.983781 | + | 0.179373i | \(0.0574069\pi\) | ||||
−0.983781 | + | 0.179373i | \(0.942593\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 86.0000 | 1.40984 | 0.704918 | − | 0.709289i | \(-0.250984\pi\) | ||||
0.704918 | + | 0.709289i | \(0.250984\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 105.830i | − | 1.62815i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 66.9328i | 0.998997i | 0.866315 | + | 0.499499i | \(0.166482\pi\) | ||||
−0.866315 | + | 0.499499i | \(0.833518\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 126.996i | − | 1.78868i | −0.447391 | − | 0.894338i | \(-0.647647\pi\) | ||
0.447391 | − | 0.894338i | \(-0.352353\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −102.000 | −1.39726 | −0.698630 | − | 0.715483i | \(-0.746207\pi\) | ||||
−0.698630 | + | 0.715483i | \(0.746207\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 25.2982 | 0.328548 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 117.132i | 1.48269i | 0.671125 | + | 0.741344i | \(0.265811\pi\) | ||||
−0.671125 | + | 0.741344i | \(0.734189\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −25.2982 | −0.304798 | −0.152399 | − | 0.988319i | \(-0.548700\pi\) | ||||
−0.152399 | + | 0.988319i | \(0.548700\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 126.996i | 1.42692i | 0.700695 | + | 0.713461i | \(0.252873\pi\) | ||||
−0.700695 | + | 0.713461i | \(0.747127\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 33.4664i | 0.367763i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −56.9210 | − | 105.830i | −0.599168 | − | 1.11400i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 33.4664i | − | 0.345014i | −0.985008 | − | 0.172507i | \(-0.944813\pi\) | ||
0.985008 | − | 0.172507i | \(-0.0551868\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 145.465 | 1.44025 | 0.720123 | − | 0.693847i | \(-0.244086\pi\) | ||||
0.720123 | + | 0.693847i | \(0.244086\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 117.132i | − | 1.13721i | −0.822611 | − | 0.568604i | \(-0.807484\pi\) | ||
0.822611 | − | 0.568604i | \(-0.192516\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 63.4980i | 0.593440i | 0.954965 | + | 0.296720i | \(0.0958927\pi\) | ||||
−0.954965 | + | 0.296720i | \(0.904107\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 184.065i | 1.68867i | 0.535814 | + | 0.844336i | \(0.320005\pi\) | ||||
−0.535814 | + | 0.844336i | \(0.679995\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 105.830i | 0.936549i | 0.883583 | + | 0.468275i | \(0.155124\pi\) | ||||
−0.883583 | + | 0.468275i | \(0.844876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 40.0000 | 0.347826 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 39.0000 | 0.322314 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 63.2456 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 50.1996i | 0.395272i | 0.980275 | + | 0.197636i | \(0.0633265\pi\) | ||||
−0.980275 | + | 0.197636i | \(0.936674\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −88.5438 | −0.675907 | −0.337953 | − | 0.941163i | \(-0.609735\pi\) | ||||
−0.337953 | + | 0.941163i | \(0.609735\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.0000 | + | 33.4664i | 0.135338 | + | 0.251627i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −164.438 | −1.20028 | −0.600140 | − | 0.799895i | \(-0.704889\pi\) | ||||
−0.600140 | + | 0.799895i | \(0.704889\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −134.000 | −0.964029 | −0.482014 | − | 0.876163i | \(-0.660095\pi\) | ||||
−0.482014 | + | 0.876163i | \(0.660095\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 211.660i | 1.48014i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 133.866i | 0.923211i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −82.2192 | −0.551807 | −0.275903 | − | 0.961185i | \(-0.588977\pi\) | ||||
−0.275903 | + | 0.961185i | \(0.588977\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 184.065i | 1.21897i | 0.792796 | + | 0.609487i | \(0.208625\pi\) | ||||
−0.792796 | + | 0.609487i | \(0.791375\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 105.830i | − | 0.682775i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −122.000 | −0.777070 | −0.388535 | − | 0.921434i | \(-0.627019\pi\) | ||||
−0.388535 | + | 0.921434i | \(0.627019\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.6491 | −0.0785659 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 138.000 | 0.846626 | 0.423313 | − | 0.905984i | \(-0.360867\pi\) | ||||
0.423313 | + | 0.905984i | \(0.360867\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 169.328i | 1.01394i | 0.861964 | + | 0.506970i | \(0.169235\pi\) | ||||
−0.861964 | + | 0.506970i | \(0.830765\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −111.000 | −0.656805 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 148.162i | − | 0.856428i | −0.903677 | − | 0.428214i | \(-0.859143\pi\) | ||
0.903677 | − | 0.428214i | \(-0.140857\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 30.0000 | 0.171429 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 296.324i | 1.65544i | 0.561140 | + | 0.827721i | \(0.310363\pi\) | ||||
−0.561140 | + | 0.827721i | \(0.689637\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 50.1996i | 0.277346i | 0.990338 | + | 0.138673i | \(0.0442837\pi\) | ||||
−0.990338 | + | 0.138673i | \(0.955716\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 317.490i | 1.71616i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −259.307 | −1.35763 | −0.678814 | − | 0.734311i | \(-0.737506\pi\) | ||||
−0.678814 | + | 0.734311i | \(0.737506\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 334.664i | 1.73401i | 0.498299 | + | 0.867005i | \(0.333958\pi\) | ||||
−0.498299 | + | 0.867005i | \(0.666042\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −246.658 | −1.25207 | −0.626035 | − | 0.779795i | \(-0.715323\pi\) | ||||
−0.626035 | + | 0.779795i | \(0.715323\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −66.0000 | −0.331658 | −0.165829 | − | 0.986154i | \(-0.553030\pi\) | ||||
−0.165829 | + | 0.986154i | \(0.553030\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 42.3320i | − | 0.208532i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 133.866i | − | 0.653003i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 113.842 | + | 211.660i | 0.544699 | + | 1.01273i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 66.9328i | − | 0.317217i | −0.987342 | − | 0.158609i | \(-0.949299\pi\) | ||
0.987342 | − | 0.158609i | \(-0.0507008\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 215.035 | 1.00016 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 33.4664i | 0.154223i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 284.464i | 1.27563i | 0.770192 | + | 0.637813i | \(0.220161\pi\) | ||||
−0.770192 | + | 0.637813i | \(0.779839\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 169.328i | − | 0.745939i | −0.927844 | − | 0.372969i | \(-0.878340\pi\) | ||
0.927844 | − | 0.372969i | \(-0.121660\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −298.000 | −1.30131 | −0.650655 | − | 0.759373i | \(-0.725506\pi\) | ||||
−0.650655 | + | 0.759373i | \(0.725506\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −265.631 | −1.14005 | −0.570024 | − | 0.821628i | \(-0.693066\pi\) | ||||
−0.570024 | + | 0.821628i | \(0.693066\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −520.000 | −2.21277 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −44.2719 | −0.185238 | −0.0926190 | − | 0.995702i | \(-0.529524\pi\) | ||||
−0.0926190 | + | 0.995702i | \(0.529524\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 334.664i | 1.38865i | 0.719663 | + | 0.694324i | \(0.244296\pi\) | ||||
−0.719663 | + | 0.694324i | \(0.755704\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 284.605 | 1.16165 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −280.000 | + | 150.599i | −1.13360 | + | 0.609712i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 151.789 | 0.604738 | 0.302369 | − | 0.953191i | \(-0.402222\pi\) | ||||
0.302369 | + | 0.953191i | \(0.402222\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −80.0000 | −0.316206 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 169.328i | − | 0.658864i | −0.944179 | − | 0.329432i | \(-0.893143\pi\) | ||
0.944179 | − | 0.329432i | \(-0.106857\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 100.399i | − | 0.387642i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 309.903 | 1.17834 | 0.589170 | − | 0.808009i | \(-0.299455\pi\) | ||||
0.589170 | + | 0.808009i | \(0.299455\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 401.597i | 1.51546i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 317.490i | − | 1.18026i | −0.807308 | − | 0.590130i | \(-0.799076\pi\) | ||
0.807308 | − | 0.590130i | \(-0.200924\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 366.000 | 1.35055 | 0.675277 | − | 0.737564i | \(-0.264024\pi\) | ||||
0.675277 | + | 0.737564i | \(0.264024\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 189.737 | 0.689951 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −122.000 | −0.440433 | −0.220217 | − | 0.975451i | \(-0.570676\pi\) | ||||
−0.220217 | + | 0.975451i | \(0.570676\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 105.830i | − | 0.376619i | −0.982110 | − | 0.188310i | \(-0.939699\pi\) | ||
0.982110 | − | 0.188310i | \(-0.0603009\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 326.000 | 1.15194 | 0.575972 | − | 0.817470i | \(-0.304624\pi\) | ||||
0.575972 | + | 0.817470i | \(0.304624\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 42.3320i | 0.147498i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −289.000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 105.830i | 0.361195i | 0.983557 | + | 0.180597i | \(0.0578031\pi\) | ||||
−0.983557 | + | 0.180597i | \(0.942197\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 133.866i | − | 0.453782i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 105.830i | − | 0.353947i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −68.0000 | −0.225914 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −543.912 | −1.78332 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 200.798i | 0.654066i | 0.945013 | + | 0.327033i | \(0.106049\pi\) | ||||
−0.945013 | + | 0.327033i | \(0.893951\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −309.903 | −0.996473 | −0.498237 | − | 0.867041i | \(-0.666019\pi\) | ||||
−0.498237 | + | 0.867041i | \(0.666019\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 86.0000 | 0.274760 | 0.137380 | − | 0.990518i | \(-0.456132\pi\) | ||||
0.137380 | + | 0.990518i | \(0.456132\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 486.818i | − | 1.53570i | −0.640627 | − | 0.767852i | \(-0.721326\pi\) | ||
0.640627 | − | 0.767852i | \(-0.278674\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 267.731i | − | 0.839283i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 250.998i | 0.772302i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 164.438 | 0.499813 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 267.731i | 0.808856i | 0.914570 | + | 0.404428i | \(0.132529\pi\) | ||||
−0.914570 | + | 0.404428i | \(0.867471\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 423.320i | − | 1.26364i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 167.332i | 0.496534i | 0.968692 | + | 0.248267i | \(0.0798611\pi\) | ||||
−0.968692 | + | 0.248267i | \(0.920139\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 211.660i | 0.620704i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −188.000 | −0.548105 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.6491 | 0.0364528 | 0.0182264 | − | 0.999834i | \(-0.494198\pi\) | ||||
0.0182264 | + | 0.999834i | \(0.494198\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 506.000 | 1.44986 | 0.724928 | − | 0.688824i | \(-0.241873\pi\) | ||||
0.724928 | + | 0.688824i | \(0.241873\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 619.806 | 1.75583 | 0.877913 | − | 0.478821i | \(-0.158936\pi\) | ||||
0.877913 | + | 0.478821i | \(0.158936\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 803.194i | 2.26252i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −94.8683 | −0.264257 | −0.132129 | − | 0.991233i | \(-0.542181\pi\) | ||||
−0.132129 | + | 0.991233i | \(0.542181\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −199.000 | + | 301.198i | −0.551247 | + | 0.834342i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 645.105 | 1.76741 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −386.000 | −1.05177 | −0.525886 | − | 0.850555i | \(-0.676266\pi\) | ||||
−0.525886 | + | 0.850555i | \(0.676266\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 126.996i | − | 0.342307i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 317.931i | − | 0.852361i | −0.904638 | − | 0.426181i | \(-0.859859\pi\) | ||
0.904638 | − | 0.426181i | \(-0.140141\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 354.175 | 0.939456 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 301.198i | − | 0.794717i | −0.917664 | − | 0.397358i | \(-0.869927\pi\) | ||
0.917664 | − | 0.397358i | \(-0.130073\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 592.648i | 1.54738i | 0.633562 | + | 0.773692i | \(0.281592\pi\) | ||||
−0.633562 | + | 0.773692i | \(0.718408\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −160.000 | −0.415584 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −221.359 | −0.569047 | −0.284524 | − | 0.958669i | \(-0.591835\pi\) | ||||
−0.284524 | + | 0.958669i | \(0.591835\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 740.810i | − | 1.87547i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 186.000 | 0.468514 | 0.234257 | − | 0.972175i | \(-0.424734\pi\) | ||||
0.234257 | + | 0.972175i | \(0.424734\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 105.830i | − | 0.263915i | −0.991255 | − | 0.131958i | \(-0.957874\pi\) | ||
0.991255 | − | 0.131958i | \(-0.0421263\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −280.000 | −0.694789 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 634.980i | − | 1.56015i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 167.332i | − | 0.409125i | −0.978854 | − | 0.204562i | \(-0.934423\pi\) | ||
0.978854 | − | 0.204562i | \(-0.0655771\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 42.3320i | 0.102499i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 160.000 | 0.385542 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −771.596 | −1.84152 | −0.920759 | − | 0.390133i | \(-0.872429\pi\) | ||||
−0.920759 | + | 0.390133i | \(0.872429\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 284.464i | − | 0.675687i | −0.941202 | − | 0.337844i | \(-0.890302\pi\) | ||
0.941202 | − | 0.337844i | \(-0.109698\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 172.000 | 0.402810 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 761.976i | 1.76793i | 0.467556 | + | 0.883963i | \(0.345135\pi\) | ||||
−0.467556 | + | 0.883963i | \(0.654865\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 100.399i | 0.231869i | 0.993257 | + | 0.115934i | \(0.0369862\pi\) | ||||
−0.993257 | + | 0.115934i | \(0.963014\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −56.9210 | − | 105.830i | −0.130254 | − | 0.242174i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 485.263i | 1.10538i | 0.833386 | + | 0.552691i | \(0.186399\pi\) | ||||
−0.833386 | + | 0.552691i | \(0.813601\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 442.719 | 0.999365 | 0.499683 | − | 0.866209i | \(-0.333450\pi\) | ||||
0.499683 | + | 0.866209i | \(0.333450\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 803.194i | − | 1.80493i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 296.324i | 0.659965i | 0.943987 | + | 0.329982i | \(0.107043\pi\) | ||||
−0.943987 | + | 0.329982i | \(0.892957\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 267.731i | 0.593639i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 211.660i | − | 0.465187i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 82.0000 | 0.179431 | 0.0897155 | − | 0.995967i | \(-0.471404\pi\) | ||||
0.0897155 | + | 0.995967i | \(0.471404\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −423.745 | −0.919187 | −0.459593 | − | 0.888129i | \(-0.652005\pi\) | ||||
−0.459593 | + | 0.888129i | \(0.652005\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.0000 | −0.0734341 | −0.0367171 | − | 0.999326i | \(-0.511690\pi\) | ||||
−0.0367171 | + | 0.999326i | \(0.511690\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 404.772 | 0.866748 | 0.433374 | − | 0.901214i | \(-0.357323\pi\) | ||||
0.433374 | + | 0.901214i | \(0.357323\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 133.866i | 0.285428i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −430.070 | −0.909238 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 135.000 | + | 250.998i | 0.284211 | + | 0.528417i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.6228 | 0.0660183 | 0.0330092 | − | 0.999455i | \(-0.489491\pi\) | ||||
0.0330092 | + | 0.999455i | \(0.489491\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 840.000 | 1.74636 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 211.660i | 0.436413i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 552.196i | 1.13387i | 0.823762 | + | 0.566936i | \(0.191871\pi\) | ||||
−0.823762 | + | 0.566936i | \(0.808129\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 290.930 | 0.592525 | 0.296262 | − | 0.955107i | \(-0.404260\pi\) | ||||
0.296262 | + | 0.955107i | \(0.404260\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 253.992i | − | 0.511051i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −254.000 | −0.509018 | −0.254509 | − | 0.967070i | \(-0.581914\pi\) | ||||
−0.254509 | + | 0.967070i | \(0.581914\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −284.605 | −0.565815 | −0.282908 | − | 0.959147i | \(-0.591299\pi\) | ||||
−0.282908 | + | 0.959147i | \(0.591299\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −920.000 | −1.82178 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 867.806i | 1.70492i | 0.522789 | + | 0.852462i | \(0.324892\pi\) | ||||
−0.522789 | + | 0.852462i | \(0.675108\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −204.000 | −0.399217 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 740.810i | 1.43847i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1040.00 | 2.01161 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 296.324i | 0.568760i | 0.958712 | + | 0.284380i | \(0.0917878\pi\) | ||||
−0.958712 | + | 0.284380i | \(0.908212\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 501.996i | − | 0.959839i | −0.877312 | − | 0.479920i | \(-0.840666\pi\) | ||
0.877312 | − | 0.479920i | \(-0.159334\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −489.000 | −0.924386 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −354.175 | −0.664494 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 401.597i | − | 0.750648i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −569.210 | −1.05605 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −198.000 | −0.365989 | −0.182994 | − | 0.983114i | \(-0.558579\pi\) | ||||
−0.182994 | + | 0.983114i | \(0.558579\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1164.13i | − | 2.13602i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 234.265i | − | 0.428272i | −0.976804 | − | 0.214136i | \(-0.931306\pi\) | ||
0.976804 | − | 0.214136i | \(-0.0686936\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 354.175 | − | 190.494i | 0.642786 | − | 0.345724i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 234.265i | 0.423625i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 917.061 | 1.64643 | 0.823214 | − | 0.567731i | \(-0.192179\pi\) | ||||
0.823214 | + | 0.567731i | \(0.192179\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 568.929i | − | 1.01776i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 275.158i | − | 0.488736i | −0.969683 | − | 0.244368i | \(-0.921420\pi\) | ||
0.969683 | − | 0.244368i | \(-0.0785804\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 669.328i | − | 1.18465i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 84.6640i | 0.148794i | 0.997229 | + | 0.0743972i | \(0.0237033\pi\) | ||||
−0.997229 | + | 0.0743972i | \(0.976297\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 46.0000 | 0.0805604 | 0.0402802 | − | 0.999188i | \(-0.487175\pi\) | ||||
0.0402802 | + | 0.999188i | \(0.487175\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −94.8683 | −0.164988 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −66.0000 | −0.114385 | −0.0571924 | − | 0.998363i | \(-0.518215\pi\) | ||||
−0.0571924 | + | 0.998363i | \(0.518215\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −50.5964 | −0.0870851 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 803.194i | − | 1.37769i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −177.088 | −0.301682 | −0.150841 | − | 0.988558i | \(-0.548198\pi\) | ||||
−0.150841 | + | 0.988558i | \(0.548198\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −280.000 | + | 150.599i | −0.475382 | + | 0.255686i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −493.315 | −0.831898 | −0.415949 | − | 0.909388i | \(-0.636550\pi\) | ||||
−0.415949 | + | 0.909388i | \(0.636550\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 423.320i | − | 0.706712i | −0.935489 | − | 0.353356i | \(-0.885041\pi\) | ||
0.935489 | − | 0.353356i | \(-0.114959\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 167.332i | − | 0.278423i | −0.990263 | − | 0.139211i | \(-0.955543\pi\) | ||
0.990263 | − | 0.139211i | \(-0.0444567\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −246.658 | −0.407699 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 719.528i | 1.18538i | 0.805429 | + | 0.592692i | \(0.201935\pi\) | ||||
−0.805429 | + | 0.592692i | \(0.798065\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1375.79i | 2.25170i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 342.000 | 0.557912 | 0.278956 | − | 0.960304i | \(-0.410012\pi\) | ||||
0.278956 | + | 0.960304i | \(0.410012\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 505.964 | 0.820040 | 0.410020 | − | 0.912077i | \(-0.365522\pi\) | ||||
0.410020 | + | 0.912077i | \(0.365522\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −494.000 | −0.798061 | −0.399031 | − | 0.916938i | \(-0.630653\pi\) | ||||
−0.399031 | + | 0.916938i | \(0.630653\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 253.992i | 0.407692i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −775.000 | −1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −78.0000 | −0.123613 | −0.0618067 | − | 0.998088i | \(-0.519686\pi\) | ||||
−0.0618067 | + | 0.998088i | \(0.519686\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 317.490i | − | 0.499984i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 752.994i | − | 1.18209i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 423.320i | − | 0.660406i | −0.943910 | − | 0.330203i | \(-0.892883\pi\) | ||
0.943910 | − | 0.330203i | \(-0.107117\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 502.000 | 0.780715 | 0.390358 | − | 0.920663i | \(-0.372351\pi\) | ||||
0.390358 | + | 0.920663i | \(0.372351\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −56.9210 | −0.0879768 | −0.0439884 | − | 0.999032i | \(-0.514006\pi\) | ||||
−0.0439884 | + | 0.999032i | \(0.514006\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 267.731i | 0.412529i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1283.88 | −1.96613 | −0.983066 | − | 0.183250i | \(-0.941338\pi\) | ||||
−0.983066 | + | 0.183250i | \(0.941338\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 560.000 | 0.854962 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1058.30i | 1.60592i | 0.596034 | + | 0.802959i | \(0.296742\pi\) | ||||
−0.596034 | + | 0.802959i | \(0.703258\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 384.864i | − | 0.582244i | −0.956686 | − | 0.291122i | \(-0.905971\pi\) | ||
0.956686 | − | 0.291122i | \(-0.0940286\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −113.842 | − | 211.660i | −0.171191 | − | 0.318286i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 133.866i | 0.200698i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1087.82 | 1.62120 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 769.727i | 1.14373i | 0.820349 | + | 0.571863i | \(0.193779\pi\) | ||||
−0.820349 | + | 0.571863i | \(0.806221\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 910.138i | 1.34437i | 0.740383 | + | 0.672185i | \(0.234644\pi\) | ||||
−0.740383 | + | 0.672185i | \(0.765356\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 66.9328i | − | 0.0985756i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 380.988i | − | 0.557816i | −0.960318 | − | 0.278908i | \(-0.910028\pi\) | ||
0.960318 | − | 0.278908i | \(-0.0899724\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1040.00 | 1.51825 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1062.53 | 1.54213 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −242.000 | −0.350217 | −0.175109 | − | 0.984549i | \(-0.556028\pi\) | ||||
−0.175109 | + | 0.984549i | \(0.556028\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 847.490 | 1.21941 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1081.50 | −1.54279 | −0.771397 | − | 0.636354i | \(-0.780442\pi\) | ||||
−0.771397 | + | 0.636354i | \(0.780442\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 840.000 | − | 451.796i | 1.19488 | − | 0.642669i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 290.930 | 0.411499 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 586.000 | 0.826516 | 0.413258 | − | 0.910614i | \(-0.364391\pi\) | ||||
0.413258 | + | 0.910614i | \(0.364391\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 105.830i | − | 0.148429i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1338.66i | − | 1.87225i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −929.710 | −1.29306 | −0.646530 | − | 0.762889i | \(-0.723780\pi\) | ||||
−0.646530 | + | 0.762889i | \(0.723780\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 234.265i | − | 0.324917i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 317.490i | − | 0.437917i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1198.00 | 1.64787 | 0.823934 | − | 0.566686i | \(-0.191775\pi\) | ||||
0.823934 | + | 0.566686i | \(0.191775\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 298.000 | 0.406548 | 0.203274 | − | 0.979122i | \(-0.434842\pi\) | ||||
0.203274 | + | 0.979122i | \(0.434842\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 846.640i | 1.14877i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 106.000 | 0.143437 | 0.0717185 | − | 0.997425i | \(-0.477152\pi\) | ||||
0.0717185 | + | 0.997425i | \(0.477152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 42.3320i | 0.0569745i | 0.999594 | + | 0.0284872i | \(0.00906899\pi\) | ||||
−0.999594 | + | 0.0284872i | \(0.990931\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 520.000 | 0.697987 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 126.996i | 0.169554i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 217.532i | − | 0.289656i | −0.989457 | − | 0.144828i | \(-0.953737\pi\) | ||
0.989457 | − | 0.144828i | \(-0.0462629\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1164.13i | − | 1.54189i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 918.000 | 1.21268 | 0.606341 | − | 0.795205i | \(-0.292637\pi\) | ||||
0.606341 | + | 0.795205i | \(0.292637\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −923.385 | −1.21338 | −0.606692 | − | 0.794937i | \(-0.707504\pi\) | ||||
−0.606692 | + | 0.794937i | \(0.707504\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 368.130i | 0.482478i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −354.175 | −0.461767 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −986.000 | −1.28218 | −0.641092 | − | 0.767464i | \(-0.721518\pi\) | ||||
−0.641092 | + | 0.767464i | \(0.721518\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 275.158i | 0.355961i | 0.984034 | + | 0.177981i | \(0.0569565\pi\) | ||||
−0.984034 | + | 0.177981i | \(0.943044\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 250.998i | 0.323868i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −354.175 | + | 190.494i | −0.454654 | + | 0.244537i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1606.39i | − | 2.05683i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 771.596 | 0.982925 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 568.929i | − | 0.722908i | −0.932390 | − | 0.361454i | \(-0.882280\pi\) | ||
0.932390 | − | 0.361454i | \(-0.117720\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 211.660i | 0.267585i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1439.06i | 1.81470i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 275.158i | 0.345242i | 0.984988 | + | 0.172621i | \(0.0552236\pi\) | ||||
−0.984988 | + | 0.172621i | \(0.944776\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1290.21 | −1.60674 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 80.0000 | 0.0993789 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 632.456 | 0.781774 | 0.390887 | − | 0.920439i | \(-0.372168\pi\) | ||||
0.390887 | + | 0.920439i | \(0.372168\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 301.198i | 0.371390i | 0.982607 | + | 0.185695i | \(0.0594537\pi\) | ||||
−0.982607 | + | 0.185695i | \(0.940546\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −872.789 | −1.07091 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −306.000 | − | 568.929i | −0.374541 | − | 0.696363i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 537.587 | 0.654796 | 0.327398 | − | 0.944887i | \(-0.393828\pi\) | ||||
0.327398 | + | 0.944887i | \(0.393828\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −382.000 | −0.464156 | −0.232078 | − | 0.972697i | \(-0.574552\pi\) | ||||
−0.232078 | + | 0.972697i | \(0.574552\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 634.980i | 0.767812i | 0.923372 | + | 0.383906i | \(0.125421\pi\) | ||||
−0.923372 | + | 0.383906i | \(0.874579\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 50.1996i | − | 0.0605544i | −0.999542 | − | 0.0302772i | \(-0.990361\pi\) | ||
0.999542 | − | 0.0302772i | \(-0.00963901\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1070.92i | − | 1.28254i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1354.62i | − | 1.61457i | −0.590161 | − | 0.807285i | \(-0.700936\pi\) | ||
0.590161 | − | 0.807285i | \(-0.299064\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 393.000 | 0.467301 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 702.026 | 0.830800 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 78.0000 | 0.0920897 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 317.490i | 0.373079i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1142.00 | −1.33880 | −0.669402 | − | 0.742900i | \(-0.733450\pi\) | ||||
−0.669402 | + | 0.742900i | \(0.733450\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1100.63i | − | 1.28429i | −0.766585 | − | 0.642143i | \(-0.778046\pi\) | ||
0.766585 | − | 0.642143i | \(-0.221954\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 866.000 | 1.00815 | 0.504075 | − | 0.863660i | \(-0.331834\pi\) | ||||
0.504075 | + | 0.863660i | \(0.331834\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1015.97i | 1.17725i | 0.808405 | + | 0.588626i | \(0.200331\pi\) | ||||
−0.808405 | + | 0.588626i | \(0.799669\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 937.059i | 1.08331i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1481.62i | 1.70497i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1120.00 | −1.28588 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 126.491 | 0.144561 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 786.460i | − | 0.896762i | −0.893842 | − | 0.448381i | \(-0.852001\pi\) | ||
0.893842 | − | 0.448381i | \(-0.147999\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 265.631 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1458.00 | 1.65119 | 0.825595 | − | 0.564264i | \(-0.190840\pi\) | ||||
0.825595 | + | 0.564264i | \(0.190840\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 423.320i | − | 0.477249i | −0.971112 | − | 0.238625i | \(-0.923303\pi\) | ||
0.971112 | − | 0.238625i | \(-0.0766966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 100.399i | 0.112935i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 739.973 | + | 1375.79i | 0.828637 | + | 1.54064i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1874.12i | − | 2.09399i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 354.175 | 0.393966 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 317.490i | − | 0.350818i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1773.72i | − | 1.95559i | −0.209566 | − | 0.977795i | \(-0.567205\pi\) | ||
0.209566 | − | 0.977795i | \(-0.432795\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 550.316i | − | 0.604079i | −0.953295 | − | 0.302040i | \(-0.902332\pi\) | ||
0.953295 | − | 0.302040i | \(-0.0976675\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −320.000 | −0.350493 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −177.088 | −0.193116 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1374.00 | −1.49510 | −0.747552 | − | 0.664204i | \(-0.768771\pi\) | ||||
−0.747552 | + | 0.664204i | \(0.768771\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2125.05 | 2.30233 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 752.994i | − | 0.814048i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −670.403 | −0.721639 | −0.360820 | − | 0.932636i | \(-0.617503\pi\) | ||||
−0.360820 | + | 0.932636i | \(0.617503\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −405.000 | − | 752.994i | −0.435016 | − | 0.808801i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −918.000 | −0.979723 | −0.489861 | − | 0.871800i | \(-0.662953\pi\) | ||||
−0.489861 | + | 0.871800i | \(0.662953\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1164.13i | − | 1.23712i | −0.785737 | − | 0.618560i | \(-0.787716\pi\) | ||
0.785737 | − | 0.618560i | \(-0.212284\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 133.866i | − | 0.141957i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1682.33 | −1.77649 | −0.888243 | − | 0.459374i | \(-0.848074\pi\) | ||||
−0.888243 | + | 0.459374i | \(0.848074\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1706.79i | − | 1.79851i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1206.46i | − | 1.26596i | −0.774167 | − | 0.632981i | \(-0.781831\pi\) | ||
0.774167 | − | 0.632981i | \(-0.218169\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1640.00 | 1.71728 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −328.877 | −0.342937 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 681.000 | 0.708637 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 2116.60i | − | 2.19337i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1682.00 | 1.73940 | 0.869700 | − | 0.493581i | \(-0.164312\pi\) | ||||
0.869700 | + | 0.493581i | \(0.164312\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1142.96i | − | 1.17710i | −0.808461 | − | 0.588550i | \(-0.799699\pi\) | ||
0.808461 | − | 0.588550i | \(-0.200301\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −268.000 | −0.275437 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 740.810i | − | 0.758250i | −0.925345 | − | 0.379125i | \(-0.876225\pi\) | ||
0.925345 | − | 0.379125i | \(-0.123775\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1606.39i | 1.64084i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 423.320i | 0.430641i | 0.976543 | + | 0.215321i | \(0.0690796\pi\) | ||||
−0.976543 | + | 0.215321i | \(0.930920\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1560.00 | 1.58376 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 215.035 | 0.217427 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 853.393i | − | 0.861144i | −0.902556 | − | 0.430572i | \(-0.858312\pi\) | ||
0.902556 | − | 0.430572i | \(-0.141688\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 417.421 | 0.419518 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 454.000 | 0.455366 | 0.227683 | − | 0.973735i | \(-0.426885\pi\) | ||||
0.227683 | + | 0.973735i | \(0.426885\pi\) | |||||||
\(998\) | 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 | 2736.3.o.j.721.2 | 4 | ||
3.2 | odd | 2 | inner | 2736.3.o.j.721.4 | 4 | ||
4.3 | odd | 2 | 171.3.c.e.37.1 | ✓ | 4 | ||
12.11 | even | 2 | 171.3.c.e.37.4 | yes | 4 | ||
19.18 | odd | 2 | inner | 2736.3.o.j.721.1 | 4 | ||
57.56 | even | 2 | inner | 2736.3.o.j.721.3 | 4 | ||
76.75 | even | 2 | 171.3.c.e.37.3 | yes | 4 | ||
228.227 | odd | 2 | 171.3.c.e.37.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
171.3.c.e.37.1 | ✓ | 4 | 4.3 | odd | 2 | ||
171.3.c.e.37.2 | yes | 4 | 228.227 | odd | 2 | ||
171.3.c.e.37.3 | yes | 4 | 76.75 | even | 2 | ||
171.3.c.e.37.4 | yes | 4 | 12.11 | even | 2 | ||
2736.3.o.j.721.1 | 4 | 19.18 | odd | 2 | inner | ||
2736.3.o.j.721.2 | 4 | 1.1 | even | 1 | trivial | ||
2736.3.o.j.721.3 | 4 | 57.56 | even | 2 | inner | ||
2736.3.o.j.721.4 | 4 | 3.2 | odd | 2 | inner |