Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7500,2,Mod(1249,7500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7500, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7500.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7500 = 2^{2} \cdot 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7500.d (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: | \(59.8878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.7 | ||
Character | \(\chi\) | \(=\) | 7500.1249 |
Dual form | 7500.2.d.g.1249.18 |
$q$-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 \(\left(\mathbb{Z}/7500\mathbb{Z}\right)^\times\).
\(n\) | \(2501\) | \(3751\) | \(6877\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.04684i | 0.395667i | 0.980236 | + | 0.197833i | \(0.0633905\pi\) | ||||
−0.980236 | + | 0.197833i | \(0.936610\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.28891 | 1.89618 | 0.948088 | − | 0.318008i | \(-0.103014\pi\) | ||||
0.948088 | + | 0.318008i | \(0.103014\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00629i | 0.279096i | 0.990215 | + | 0.139548i | \(0.0445649\pi\) | ||||
−0.990215 | + | 0.139548i | \(0.955435\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 4.69165i | − 1.13789i | −0.822375 | − | 0.568946i | \(-0.807351\pi\) | ||||
0.822375 | − | 0.568946i | \(-0.192649\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.97554 | 1.37088 | 0.685441 | − | 0.728128i | \(-0.259609\pi\) | ||||
0.685441 | + | 0.728128i | \(0.259609\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.04684 | 0.228438 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 8.05101i | − 1.67875i | −0.543551 | − | 0.839376i | \(-0.682920\pi\) | ||||
0.543551 | − | 0.839376i | \(-0.317080\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.91519 | −1.28412 | −0.642059 | − | 0.766655i | \(-0.721920\pi\) | ||||
−0.642059 | + | 0.766655i | \(0.721920\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.52414 | −1.71059 | −0.855293 | − | 0.518145i | \(-0.826623\pi\) | ||||
−0.855293 | + | 0.518145i | \(0.826623\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 6.28891i | − 1.09476i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.69791i | 1.26553i | 0.774344 | + | 0.632765i | \(0.218080\pi\) | ||||
−0.774344 | + | 0.632765i | \(0.781920\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00629 | 0.161136 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.56932 | 0.245086 | 0.122543 | − | 0.992463i | \(-0.460895\pi\) | ||||
0.122543 | + | 0.992463i | \(0.460895\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 9.94897i | − 1.51720i | −0.651555 | − | 0.758602i | \(-0.725883\pi\) | ||||
0.651555 | − | 0.758602i | \(-0.274117\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 4.84659i | − 0.706948i | −0.935444 | − | 0.353474i | \(-0.885000\pi\) | ||||
0.935444 | − | 0.353474i | \(-0.115000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.90413 | 0.843448 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.69165 | −0.656962 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 2.82635i | − 0.388229i | −0.980979 | − | 0.194114i | \(-0.937817\pi\) | ||||
0.980979 | − | 0.194114i | \(-0.0621833\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 5.97554i | − 0.791479i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.08209 | −0.531443 | −0.265721 | − | 0.964050i | \(-0.585610\pi\) | ||||
−0.265721 | + | 0.964050i | \(0.585610\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.16053 | 0.404665 | 0.202332 | − | 0.979317i | \(-0.435148\pi\) | ||||
0.202332 | + | 0.979317i | \(0.435148\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 1.04684i | − 0.131889i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.17036i | 0.387321i | 0.981069 | + | 0.193660i | \(0.0620360\pi\) | ||||
−0.981069 | + | 0.193660i | \(0.937964\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.05101 | −0.969228 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.50896 | 0.772472 | 0.386236 | − | 0.922400i | \(-0.373775\pi\) | ||||
0.386236 | + | 0.922400i | \(0.373775\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.367806i | 0.0430485i | 0.999768 | + | 0.0215242i | \(0.00685190\pi\) | ||||
−0.999768 | + | 0.0215242i | \(0.993148\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.58345i | 0.750254i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.32009 | 0.373539 | 0.186770 | − | 0.982404i | \(-0.440198\pi\) | ||||
0.186770 | + | 0.982404i | \(0.440198\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 13.8579i | − 1.52110i | −0.649281 | − | 0.760549i | \(-0.724930\pi\) | ||||
0.649281 | − | 0.760549i | \(-0.275070\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.91519i | 0.741386i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.50645 | 0.265683 | 0.132842 | − | 0.991137i | \(-0.457590\pi\) | ||||
0.132842 | + | 0.991137i | \(0.457590\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.05342 | −0.110429 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.52414i | 0.987607i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.182689i | 0.0185493i | 0.999957 | + | 0.00927465i | \(0.00295226\pi\) | ||||
−0.999957 | + | 0.00927465i | \(0.997048\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.28891 | −0.632059 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.96970 | −0.594008 | −0.297004 | − | 0.954876i | \(-0.595987\pi\) | ||||
−0.297004 | + | 0.954876i | \(0.595987\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.95864i | 0.882721i | 0.897330 | + | 0.441360i | \(0.145504\pi\) | ||||
−0.897330 | + | 0.441360i | \(0.854496\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 2.69495i | − 0.260530i | −0.991479 | − | 0.130265i | \(-0.958417\pi\) | ||||
0.991479 | − | 0.130265i | \(-0.0415829\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.2999 | −0.986549 | −0.493275 | − | 0.869874i | \(-0.664200\pi\) | ||||
−0.493275 | + | 0.869874i | \(0.664200\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.69791 | 0.730654 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.38070i | 0.318029i | 0.987276 | + | 0.159015i | \(0.0508317\pi\) | ||||
−0.987276 | + | 0.159015i | \(0.949168\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 1.00629i | − 0.0930319i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.91139 | 0.450226 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 28.5503 | 2.59548 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1.56932i | − 0.141501i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 5.97421i | − 0.530126i | −0.964231 | − | 0.265063i | \(-0.914607\pi\) | ||||
0.964231 | − | 0.265063i | \(-0.0853927\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.94897 | −0.875958 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.20733 | 0.542337 | 0.271168 | − | 0.962532i | \(-0.412590\pi\) | ||||
0.271168 | + | 0.962532i | \(0.412590\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.25541i | 0.542413i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.9777i | 1.10876i | 0.832263 | + | 0.554381i | \(0.187045\pi\) | ||||
−0.832263 | + | 0.554381i | \(0.812955\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.99948 | −0.339231 | −0.169616 | − | 0.985510i | \(-0.554253\pi\) | ||||
−0.169616 | + | 0.985510i | \(0.554253\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.84659 | −0.408156 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.32849i | 0.529215i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 5.90413i | − 0.486965i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.68762 | −0.465948 | −0.232974 | − | 0.972483i | \(-0.574846\pi\) | ||||
−0.232974 | + | 0.972483i | \(0.574846\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.51150 | −0.448519 | −0.224260 | − | 0.974529i | \(-0.571996\pi\) | ||||
−0.224260 | + | 0.974529i | \(0.571996\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.69165i | 0.379297i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.0217i | 1.35848i | 0.733915 | + | 0.679242i | \(0.237691\pi\) | ||||
−0.733915 | + | 0.679242i | \(0.762309\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.82635 | −0.224144 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.42809 | 0.664227 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 12.2958i | − 0.963078i | −0.876425 | − | 0.481539i | \(-0.840078\pi\) | ||||
0.876425 | − | 0.481539i | \(-0.159922\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 5.42858i | − 0.420076i | −0.977693 | − | 0.210038i | \(-0.932641\pi\) | ||||
0.977693 | − | 0.210038i | \(-0.0673589\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.9874 | 0.922106 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.97554 | −0.456961 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 10.7456i | − 0.816973i | −0.912764 | − | 0.408486i | \(-0.866057\pi\) | ||||
0.912764 | − | 0.408486i | \(-0.133943\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.08209i | 0.306829i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.3062 | 1.44302 | 0.721508 | − | 0.692406i | \(-0.243449\pi\) | ||||
0.721508 | + | 0.692406i | \(0.243449\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.7512 | 1.24511 | 0.622555 | − | 0.782576i | \(-0.286095\pi\) | ||||
0.622555 | + | 0.782576i | \(0.286095\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 3.16053i | − 0.233633i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 29.5053i | − 2.15764i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.04684 | −0.0761461 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.9454 | −0.864336 | −0.432168 | − | 0.901793i | \(-0.642251\pi\) | ||||
−0.432168 | + | 0.901793i | \(0.642251\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 26.4298i | − 1.90246i | −0.308485 | − | 0.951229i | \(-0.599822\pi\) | ||||
0.308485 | − | 0.951229i | \(-0.400178\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 11.0718i | − 0.788833i | −0.918932 | − | 0.394417i | \(-0.870947\pi\) | ||||
0.918932 | − | 0.394417i | \(-0.129053\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.5548 | 1.17354 | 0.586768 | − | 0.809755i | \(-0.300400\pi\) | ||||
0.586768 | + | 0.809755i | \(0.300400\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.17036 | 0.223620 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 7.23907i | − 0.508083i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.05101i | 0.559584i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 37.5796 | 2.59944 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.10714 | −0.282747 | −0.141373 | − | 0.989956i | \(-0.545152\pi\) | ||||
−0.141373 | + | 0.989956i | \(0.545152\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 6.50896i | − 0.445987i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 9.97021i | − 0.676822i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.367806 | 0.0248540 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.72118 | 0.317581 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.26147i | 0.419299i | 0.977777 | + | 0.209650i | \(0.0672323\pi\) | ||||
−0.977777 | + | 0.209650i | \(0.932768\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 10.4817i | − 0.695697i | −0.937551 | − | 0.347849i | \(-0.886912\pi\) | ||||
0.937551 | − | 0.347849i | \(-0.113088\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.56679 | −0.500028 | −0.250014 | − | 0.968242i | \(-0.580435\pi\) | ||||
−0.250014 | + | 0.968242i | \(0.580435\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.58345 | 0.433159 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.9832i | 1.04709i | 0.851997 | + | 0.523547i | \(0.175392\pi\) | ||||
−0.851997 | + | 0.523547i | \(0.824608\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 3.32009i | − 0.215663i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.91998 | 0.188877 | 0.0944387 | − | 0.995531i | \(-0.469894\pi\) | ||||
0.0944387 | + | 0.995531i | \(0.469894\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.0477 | −1.48463 | −0.742315 | − | 0.670051i | \(-0.766272\pi\) | ||||
−0.742315 | + | 0.670051i | \(0.766272\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.01315i | 0.382607i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.8579 | −0.878206 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.79130 | −0.618021 | −0.309011 | − | 0.951059i | \(-0.599998\pi\) | ||||
−0.309011 | + | 0.951059i | \(0.599998\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 50.6321i | − 3.18321i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 22.3147i | − 1.39195i | −0.718066 | − | 0.695975i | \(-0.754973\pi\) | ||||
0.718066 | − | 0.695975i | \(-0.245027\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.05845 | −0.500728 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.91519 | 0.428039 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 0.729154i | − 0.0449615i | −0.999747 | − | 0.0224808i | \(-0.992844\pi\) | ||||
0.999747 | − | 0.0224808i | \(-0.00715645\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 2.50645i | − 0.153392i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.85922 | 0.113359 | 0.0566794 | − | 0.998392i | \(-0.481949\pi\) | ||||
0.0566794 | + | 0.998392i | \(0.481949\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.5534 | 1.18778 | 0.593891 | − | 0.804545i | \(-0.297591\pi\) | ||||
0.593891 | + | 0.804545i | \(0.297591\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.05342i | 0.0637561i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 16.9612i | − 1.01910i | −0.860441 | − | 0.509551i | \(-0.829812\pi\) | ||||
0.860441 | − | 0.509551i | \(-0.170188\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.52414 | 0.570195 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.0879 | −1.55627 | −0.778135 | − | 0.628096i | \(-0.783834\pi\) | ||||
−0.778135 | + | 0.628096i | \(0.783834\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 25.6093i | − 1.52232i | −0.648565 | − | 0.761159i | \(-0.724631\pi\) | ||||
0.648565 | − | 0.761159i | \(-0.275369\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.64282i | 0.0969724i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.01158 | −0.294799 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.182689 | 0.0107094 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 27.7845i | − 1.62319i | −0.584220 | − | 0.811595i | \(-0.698600\pi\) | ||||
0.584220 | − | 0.811595i | \(-0.301400\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.28891i | 0.364919i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.10169 | 0.468533 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.4149 | 0.600307 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.96970i | 0.342951i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.1422i | 0.921283i | 0.887586 | + | 0.460642i | \(0.152381\pi\) | ||||
−0.887586 | + | 0.460642i | \(0.847619\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.95864 | 0.509639 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.7381 | 1.62959 | 0.814795 | − | 0.579749i | \(-0.196850\pi\) | ||||
0.814795 | + | 0.579749i | \(0.196850\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 26.4864i | − 1.49710i | −0.663079 | − | 0.748550i | \(-0.730751\pi\) | ||||
0.663079 | − | 0.748550i | \(-0.269249\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.2980i | 1.47705i | 0.674229 | + | 0.738523i | \(0.264476\pi\) | ||||
−0.674229 | + | 0.738523i | \(0.735524\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −43.4890 | −2.43491 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.69495 | −0.150417 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 28.0351i | − 1.55992i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.2999i | 0.569585i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.07358 | 0.279716 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.2634 | −1.71839 | −0.859195 | − | 0.511649i | \(-0.829035\pi\) | ||||
−0.859195 | + | 0.511649i | \(0.829035\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 7.69791i | − 0.421843i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.90526i | 0.485101i | 0.970139 | + | 0.242550i | \(0.0779839\pi\) | ||||
−0.970139 | + | 0.242550i | \(0.922016\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.38070 | 0.183614 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −59.8964 | −3.24357 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.5085i | 0.729391i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.5530i | 1.15702i | 0.815674 | + | 0.578512i | \(0.196366\pi\) | ||||
−0.815674 | + | 0.578512i | \(0.803634\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.3958 | −0.931178 | −0.465589 | − | 0.885001i | \(-0.654158\pi\) | ||||
−0.465589 | + | 0.885001i | \(0.654158\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00629 | −0.0537120 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 17.8613i | − 0.950661i | −0.879807 | − | 0.475331i | \(-0.842328\pi\) | ||||
0.879807 | − | 0.475331i | \(-0.157672\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 4.91139i | − 0.259938i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.65870 | −0.193099 | −0.0965493 | − | 0.995328i | \(-0.530781\pi\) | ||||
−0.0965493 | + | 0.995328i | \(0.530781\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.7071 | 0.879319 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 28.5503i | − 1.49850i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.0423i | 1.35940i | 0.733492 | + | 0.679698i | \(0.237889\pi\) | ||||
−0.733492 | + | 0.679698i | \(0.762111\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.56932 | −0.0816954 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.95872 | 0.153609 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.2609i | 1.51507i | 0.652792 | + | 0.757537i | \(0.273597\pi\) | ||||
−0.652792 | + | 0.757537i | \(0.726403\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 6.95871i | − 0.358392i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.2669 | 0.527374 | 0.263687 | − | 0.964608i | \(-0.415061\pi\) | ||||
0.263687 | + | 0.964608i | \(0.415061\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.97421 | −0.306068 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.6479i | 1.31055i | 0.755392 | + | 0.655273i | \(0.227446\pi\) | ||||
−0.755392 | + | 0.655273i | \(0.772554\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.94897i | 0.505735i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.58813 | 0.486137 | 0.243069 | − | 0.970009i | \(-0.421846\pi\) | ||||
0.243069 | + | 0.970009i | \(0.421846\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −37.7725 | −1.91024 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 6.20733i | − 0.313118i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 12.3309i | − 0.618869i | −0.950921 | − | 0.309435i | \(-0.899860\pi\) | ||||
0.950921 | − | 0.309435i | \(-0.100140\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.25541 | 0.313162 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.9779 | 0.947709 | 0.473855 | − | 0.880603i | \(-0.342862\pi\) | ||||
0.473855 | + | 0.880603i | \(0.342862\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 9.58408i | − 0.477417i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 48.4115i | 2.39967i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.5102 | −0.964719 | −0.482359 | − | 0.875973i | \(-0.660220\pi\) | ||||
−0.482359 | + | 0.875973i | \(0.660220\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.9777 | 0.640144 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 4.27328i | − 0.210274i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.99948i | 0.195855i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.84915 | −0.0903370 | −0.0451685 | − | 0.998979i | \(-0.514382\pi\) | ||||
−0.0451685 | + | 0.998979i | \(0.514382\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.67752 | −0.325443 | −0.162721 | − | 0.986672i | \(-0.552027\pi\) | ||||
−0.162721 | + | 0.986672i | \(0.552027\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.84659i | 0.235649i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.30856i | 0.160112i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.32849 | 0.305542 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.6459 | 1.42799 | 0.713996 | − | 0.700150i | \(-0.246884\pi\) | ||||
0.713996 | + | 0.700150i | \(0.246884\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 28.0178i | − 1.34645i | −0.739438 | − | 0.673225i | \(-0.764909\pi\) | ||||
0.739438 | − | 0.673225i | \(-0.235091\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 48.1091i | − 2.30137i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.2248 | −0.488004 | −0.244002 | − | 0.969775i | \(-0.578460\pi\) | ||||
−0.244002 | + | 0.969775i | \(0.578460\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.90413 | −0.281149 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 26.5115i | − 1.25960i | −0.776757 | − | 0.629800i | \(-0.783137\pi\) | ||||
0.776757 | − | 0.629800i | \(-0.216863\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.68762i | 0.269015i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.39692 | 0.301889 | 0.150945 | − | 0.988542i | \(-0.451768\pi\) | ||||
0.150945 | + | 0.988542i | \(0.451768\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.86929 | 0.464727 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.51150i | 0.258953i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 14.9784i | − 0.700661i | −0.936626 | − | 0.350330i | \(-0.886069\pi\) | ||||
0.936626 | − | 0.350330i | \(-0.113931\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.69165 | 0.218987 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.1832 | −0.567429 | −0.283715 | − | 0.958909i | \(-0.591567\pi\) | ||||
−0.283715 | + | 0.958909i | \(0.591567\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 8.31956i | − 0.386643i | −0.981135 | − | 0.193321i | \(-0.938074\pi\) | ||||
0.981135 | − | 0.193321i | \(-0.0619260\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 8.30463i | − 0.384293i | −0.981366 | − | 0.192146i | \(-0.938455\pi\) | ||||
0.981366 | − | 0.192146i | \(-0.0615448\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.31884 | −0.153250 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.0217 | 0.784321 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 62.5681i | − 2.87689i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.82635i | 0.129410i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.05639 | 0.139650 | 0.0698249 | − | 0.997559i | \(-0.477756\pi\) | ||||
0.0698249 | + | 0.997559i | \(0.477756\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.74636 | −0.353204 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 8.42809i | − 0.383491i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 11.7187i | − 0.531026i | −0.964107 | − | 0.265513i | \(-0.914459\pi\) | ||||
0.964107 | − | 0.265513i | \(-0.0855412\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.2958 | −0.556033 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.9523 | 0.765048 | 0.382524 | − | 0.923946i | \(-0.375055\pi\) | ||||
0.382524 | + | 0.923946i | \(0.375055\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.4436i | 1.46119i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.81381i | 0.305641i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0674 | −0.629742 | −0.314871 | − | 0.949135i | \(-0.601961\pi\) | ||||
−0.314871 | + | 0.949135i | \(0.601961\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.42858 | −0.242531 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 5.60755i | − 0.250028i | −0.992155 | − | 0.125014i | \(-0.960102\pi\) | ||||
0.992155 | − | 0.125014i | \(-0.0398976\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 11.9874i | − 0.532378i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.4650 | 0.508176 | 0.254088 | − | 0.967181i | \(-0.418225\pi\) | ||||
0.254088 | + | 0.967181i | \(0.418225\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.385033 | −0.0170328 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.97554i | 0.263826i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 30.4797i | − 1.34050i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.7456 | −0.471680 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.9012 | 0.784267 | 0.392133 | − | 0.919908i | \(-0.371737\pi\) | ||||
0.392133 | + | 0.919908i | \(0.371737\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.34677i | − 0.0588899i | −0.999566 | − | 0.0294450i | \(-0.990626\pi\) | ||||
0.999566 | − | 0.0294450i | \(-0.00937398\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 44.6839i | 1.94646i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −41.8188 | −1.81821 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.08209 | 0.177148 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.57919i | 0.0684025i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 19.3062i | − 0.833126i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 37.1305 | 1.59933 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.2977 | 0.485725 | 0.242862 | − | 0.970061i | \(-0.421914\pi\) | ||||
0.242862 | + | 0.970061i | \(0.421914\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 16.7512i | − 0.718864i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.8147i | 1.10376i | 0.833924 | + | 0.551879i | \(0.186089\pi\) | ||||
−0.833924 | + | 0.551879i | \(0.813911\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.16053 | −0.134888 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −41.3220 | −1.76037 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.47559i | 0.147797i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 35.3575i | − 1.49814i | −0.662489 | − | 0.749072i | \(-0.730500\pi\) | ||||
0.662489 | − | 0.749072i | \(-0.269500\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.0116 | 0.423445 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −29.5053 | −1.24572 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.55427i | 0.191940i | 0.995384 | + | 0.0959698i | \(0.0305952\pi\) | ||||
−0.995384 | + | 0.0959698i | \(0.969405\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.04684i | 0.0439630i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.1409 | 1.55703 | 0.778514 | − | 0.627627i | \(-0.215974\pi\) | ||||
0.778514 | + | 0.627627i | \(0.215974\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.30015 | −0.179956 | −0.0899778 | − | 0.995944i | \(-0.528680\pi\) | ||||
−0.0899778 | + | 0.995944i | \(0.528680\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.9454i | 0.499025i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.467179i | 0.0194489i | 0.999953 | + | 0.00972445i | \(0.00309544\pi\) | ||||
−0.999953 | + | 0.00972445i | \(0.996905\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −26.4298 | −1.09838 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.5069 | 0.601848 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 17.7746i | − 0.736150i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.9548i | 1.36019i | 0.733124 | + | 0.680095i | \(0.238062\pi\) | ||||
−0.733124 | + | 0.680095i | \(0.761938\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −56.9119 | −2.34501 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.0718 | −0.455433 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.5285i | 0.637680i | 0.947809 | + | 0.318840i | \(0.103293\pi\) | ||||
−0.947809 | + | 0.318840i | \(0.896707\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 16.5548i | − 0.677542i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.0116 | 1.47140 | 0.735698 | − | 0.677310i | \(-0.236854\pi\) | ||||
0.735698 | + | 0.677310i | \(0.236854\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.1503 | −0.985112 | −0.492556 | − | 0.870281i | \(-0.663937\pi\) | ||||
−0.492556 | + | 0.870281i | \(0.663937\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 3.17036i | − 0.129107i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 29.8098i | − 1.20994i | −0.796248 | − | 0.604970i | \(-0.793185\pi\) | ||||
0.796248 | − | 0.604970i | \(-0.206815\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.23907 | −0.293342 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.87709 | 0.197306 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.1330i | 1.29784i | 0.760857 | + | 0.648919i | \(0.224779\pi\) | ||||
−0.760857 | + | 0.648919i | \(0.775221\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 17.2509i | − 0.694493i | −0.937774 | − | 0.347247i | \(-0.887117\pi\) | ||||
0.937774 | − | 0.347247i | \(-0.112883\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.06017 | −0.283772 | −0.141886 | − | 0.989883i | \(-0.545317\pi\) | ||||
−0.141886 | + | 0.989883i | \(0.545317\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.05101 | 0.323076 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.62384i | 0.105122i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 37.5796i | − 1.50078i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 36.1159 | 1.44004 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.78513 | −0.389540 | −0.194770 | − | 0.980849i | \(-0.562396\pi\) | ||||
−0.194770 | + | 0.980849i | \(0.562396\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.10714i | 0.163244i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.94129i | 0.235403i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.50896 | −0.257491 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.6701 | 0.618930 | 0.309465 | − | 0.950911i | \(-0.399850\pi\) | ||||
0.309465 | + | 0.950911i | \(0.399850\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 0.766747i | − 0.0302375i | −0.999886 | − | 0.0151188i | \(-0.995187\pi\) | ||||
0.999886 | − | 0.0151188i | \(-0.00481264\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 13.1728i | − 0.517878i | −0.965894 | − | 0.258939i | \(-0.916627\pi\) | ||||
0.965894 | − | 0.258939i | \(-0.0833728\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.6719 | −1.00771 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.97021 | −0.390763 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 13.0921i | − 0.512335i | −0.966632 | − | 0.256167i | \(-0.917540\pi\) | ||||
0.966632 | − | 0.256167i | \(-0.0824598\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 0.367806i | − 0.0143495i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.46731 | 0.368794 | 0.184397 | − | 0.982852i | \(-0.440967\pi\) | ||||
0.184397 | + | 0.982852i | \(0.440967\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.55884 | 0.216214 | 0.108107 | − | 0.994139i | \(-0.465521\pi\) | ||||
0.108107 | + | 0.994139i | \(0.465521\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 4.72118i | − 0.183355i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 55.6743i | 2.15572i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.26147 | 0.242083 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.8763 | 0.767316 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.304023i | 0.0117192i | 0.999983 | + | 0.00585962i | \(0.00186519\pi\) | ||||
−0.999983 | + | 0.00585962i | \(0.998135\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 39.5278i | − 1.51918i | −0.650404 | − | 0.759589i | \(-0.725400\pi\) | ||||
0.650404 | − | 0.759589i | \(-0.274600\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.191246 | −0.00733934 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.4817 | −0.401661 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.5480i | 1.20715i | 0.797305 | + | 0.603576i | \(0.206258\pi\) | ||||
−0.797305 | + | 0.603576i | \(0.793742\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.56679i | 0.288691i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.84414 | 0.108353 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.38385 | 0.356978 | 0.178489 | − | 0.983942i | \(-0.442879\pi\) | ||||
0.178489 | + | 0.983942i | \(0.442879\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 6.58345i | − 0.250085i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 7.36269i | − 0.278882i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.9832 | 0.604540 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.4347 | −0.771809 | −0.385904 | − | 0.922539i | \(-0.626111\pi\) | ||||
−0.385904 | + | 0.922539i | \(0.626111\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 45.9992i | 1.73489i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 6.24930i | − 0.235029i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.91798 | 0.222254 | 0.111127 | − | 0.993806i | \(-0.464554\pi\) | ||||
0.111127 | + | 0.993806i | \(0.464554\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.32009 | −0.124513 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 76.6790i | 2.87165i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2.91998i | − 0.109048i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.00127 | 0.298397 | 0.149199 | − | 0.988807i | \(-0.452331\pi\) | ||||
0.149199 | + | 0.988807i | \(0.452331\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.37822 | −0.349263 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.0477i | 0.857152i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.2787i | 1.49385i | 0.664907 | + | 0.746926i | \(0.268471\pi\) | ||||
−0.664907 | + | 0.746926i | \(0.731529\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −46.6771 | −1.72641 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.5973i | 0.391420i | 0.980662 | + | 0.195710i | \(0.0627011\pi\) | ||||
−0.980662 | + | 0.195710i | \(0.937299\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.9381i | 0.734428i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 45.5094 | 1.67409 | 0.837044 | − | 0.547135i | \(-0.184282\pi\) | ||||
0.837044 | + | 0.547135i | \(0.184282\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.01315 | 0.220898 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 8.64344i | − 0.317097i | −0.987351 | − | 0.158549i | \(-0.949319\pi\) | ||||
0.987351 | − | 0.158549i | \(-0.0506814\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.8579i | 0.507032i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.82117 | 0.103083 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −54.4382 | −1.98648 | −0.993239 | − | 0.116086i | \(-0.962965\pi\) | ||||
−0.993239 | + | 0.116086i | \(0.962965\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.79130i | 0.356815i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 34.1378i | − 1.24076i | −0.784302 | − | 0.620380i | \(-0.786978\pi\) | ||||
0.784302 | − | 0.620380i | \(-0.213022\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −50.6321 | −1.83783 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.12475 | 0.113272 | 0.0566361 | − | 0.998395i | \(-0.481963\pi\) | ||||
0.0566361 | + | 0.998395i | \(0.481963\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 10.7823i | − 0.390345i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 4.10778i | − 0.148323i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 53.3949 | 1.92547 | 0.962735 | − | 0.270446i | \(-0.0871712\pi\) | ||||
0.962735 | + | 0.270446i | \(0.0871712\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.3147 | −0.803642 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.797218i | 0.0286739i | 0.999897 | + | 0.0143370i | \(0.00456375\pi\) | ||||
−0.999897 | + | 0.0143370i | \(0.995436\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.05845i | 0.289095i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.37751 | 0.335984 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.9342 | 1.46474 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 6.91519i | − 0.247129i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.7571i | 1.48848i | 0.667913 | + | 0.744239i | \(0.267188\pi\) | ||||
−0.667913 | + | 0.744239i | \(0.732812\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.729154 | −0.0259586 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.53904 | −0.125834 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.18042i | 0.112940i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27.6513i | 0.979458i | 0.871875 | + | 0.489729i | \(0.162904\pi\) | ||||
−0.871875 | + | 0.489729i | \(0.837096\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.7385 | −0.804430 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.50645 | −0.0885611 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.31310i | 0.0816275i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 1.85922i | − 0.0654477i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.9805 | −1.22985 | −0.614924 | − | 0.788586i | \(-0.710813\pi\) | ||||
−0.614924 | + | 0.788586i | \(0.710813\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.15152 | 0.321353 | 0.160677 | − | 0.987007i | \(-0.448632\pi\) | ||||
0.160677 | + | 0.987007i | \(0.448632\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 19.5534i | − 0.685767i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 59.4504i | − 2.07991i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.05342 | 0.0368096 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.23251 | −0.112815 | −0.0564077 | − | 0.998408i | \(-0.517965\pi\) | ||||
−0.0564077 | + | 0.998408i | \(0.517965\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 45.2046i | − 1.57573i | −0.615846 | − | 0.787867i | \(-0.711186\pi\) | ||||
0.615846 | − | 0.787867i | \(-0.288814\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.6568i | 0.822629i | 0.911493 | + | 0.411314i | \(0.134930\pi\) | ||||
−0.911493 | + | 0.411314i | \(0.865070\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.7644 | −0.443326 | −0.221663 | − | 0.975123i | \(-0.571148\pi\) | ||||
−0.221663 | + | 0.975123i | \(0.571148\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.9612 | −0.588379 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 27.7001i | − 0.959753i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 9.52414i | − 0.329202i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 52.0352 | 1.79646 | 0.898228 | − | 0.439530i | \(-0.144855\pi\) | ||||
0.898228 | + | 0.439530i | \(0.144855\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.8198 | 0.648959 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26.0879i | 0.898513i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.8875i | 1.02695i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.6093 | −0.878911 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 61.9760 | 2.12451 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.6260i | 1.21981i | 0.792474 | + | 0.609905i | \(0.208792\pi\) | ||||
−0.792474 | + | 0.609905i | \(0.791208\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.6745i | 0.842866i | 0.906860 | + | 0.421433i | \(0.138473\pi\) | ||||
−0.906860 | + | 0.421433i | \(0.861527\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.9223 | −0.747978 | −0.373989 | − | 0.927433i | \(-0.622010\pi\) | ||||
−0.373989 | + | 0.927433i | \(0.622010\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.64282 | 0.0559871 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.5761i | 0.938702i | 0.883012 | + | 0.469351i | \(0.155512\pi\) | ||||
−0.883012 | + | 0.469351i | \(0.844488\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.01158i | 0.170202i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.8797 | 0.708296 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.19031 | −0.108100 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 0.182689i | − 0.00618310i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.6879i | 0.698579i | 0.937015 | + | 0.349290i | \(0.113577\pi\) | ||||
−0.937015 | + | 0.349290i | \(0.886423\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.7845 | −0.937149 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.8861 | −1.27641 | −0.638207 | − | 0.769865i | \(-0.720324\pi\) | ||||
−0.638207 | + | 0.769865i | \(0.720324\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 39.3444i | − 1.32404i | −0.749484 | − | 0.662022i | \(-0.769698\pi\) | ||||
0.749484 | − | 0.662022i | \(-0.230302\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 24.2764i | − 0.815121i | −0.913178 | − | 0.407560i | \(-0.866380\pi\) | ||||
0.913178 | − | 0.407560i | \(-0.133620\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.25402 | 0.209753 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.28891 | 0.210686 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 28.9610i | − 0.969142i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 8.10169i | − 0.270507i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 65.8612 | 2.19659 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.2602 | −0.441762 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 10.4149i | − 0.346587i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.1961i | 0.438169i | 0.975706 | + | 0.219085i | \(0.0703071\pi\) | ||||
−0.975706 | + | 0.219085i | \(0.929693\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.96970 | 0.198003 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.6036 | −0.914547 | −0.457274 | − | 0.889326i | \(-0.651174\pi\) | ||||
−0.457274 | + | 0.889326i | \(0.651174\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 87.1508i | − 2.88427i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.49805i | 0.214585i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.1492 | −0.400764 | −0.200382 | − | 0.979718i | \(-0.564218\pi\) | ||||
−0.200382 | + | 0.979718i | \(0.564218\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.1422 | 0.531903 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.54993i | 0.215593i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 8.95864i | − 0.294240i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.2346 | −1.15601 | −0.578005 | − | 0.816033i | \(-0.696169\pi\) | ||||
−0.578005 | + | 0.816033i | \(0.696169\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35.2804 | 1.15627 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 28.7381i | − 0.940844i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 6.81965i | − 0.222788i | −0.993776 | − | 0.111394i | \(-0.964468\pi\) | ||||
0.993776 | − | 0.111394i | \(-0.0355316\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.4864 | −0.864351 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.2034 | 1.01720 | 0.508601 | − | 0.861002i | \(-0.330163\pi\) | ||||
0.508601 | + | 0.861002i | \(0.330163\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 12.6346i | − 0.411439i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 28.3989i | − 0.922842i | −0.887181 | − | 0.461421i | \(-0.847340\pi\) | ||||
0.887181 | − | 0.461421i | \(-0.152660\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.370121 | −0.0120146 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.2980 | 0.852772 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 11.7015i | − 0.379049i | −0.981876 | − | 0.189525i | \(-0.939305\pi\) | ||||
0.981876 | − | 0.189525i | \(-0.0606947\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 43.4890i | 1.40580i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.5855 | −0.438700 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 59.7092 | 1.92610 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.69495i | 0.0868435i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 16.9318i | − 0.544490i | −0.962228 | − | 0.272245i | \(-0.912234\pi\) | ||||
0.962228 | − | 0.272245i | \(-0.0877661\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −28.0351 | −0.900618 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.3229 | −0.395460 | −0.197730 | − | 0.980257i | \(-0.563357\pi\) | ||||
−0.197730 | + | 0.980257i | \(0.563357\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 4.18679i | − 0.134222i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.15644i | 0.132976i | 0.997787 | + | 0.0664882i | \(0.0211795\pi\) | ||||
−0.997787 | + | 0.0664882i | \(0.978821\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.7628 | 0.503782 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.2999 | 0.328850 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.6896i | 0.436632i | 0.975878 | + | 0.218316i | \(0.0700563\pi\) | ||||
−0.975878 | + | 0.218316i | \(0.929944\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 5.07358i | − 0.161494i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −80.0993 | −2.54701 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.65679 | −0.243226 | −0.121613 | − | 0.992578i | \(-0.538807\pi\) | ||||
−0.121613 | + | 0.992578i | \(0.538807\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 31.2634i | 0.992113i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 51.5223i | − 1.63173i | −0.578244 | − | 0.815864i | \(-0.696262\pi\) | ||||
0.578244 | − | 0.815864i | \(-0.303738\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.69791 | −0.243551 |
(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 | 7500.2.d.g.1249.7 | 24 | ||
5.2 | odd | 4 | 7500.2.a.m.1.6 | 12 | |||
5.3 | odd | 4 | 7500.2.a.n.1.7 | 12 | |||
5.4 | even | 2 | inner | 7500.2.d.g.1249.18 | 24 | ||
25.3 | odd | 20 | 1500.2.m.c.1201.4 | 24 | |||
25.4 | even | 10 | 300.2.o.a.109.3 | ✓ | 24 | ||
25.6 | even | 5 | 300.2.o.a.289.3 | yes | 24 | ||
25.8 | odd | 20 | 1500.2.m.c.301.4 | 24 | |||
25.17 | odd | 20 | 1500.2.m.d.301.3 | 24 | |||
25.19 | even | 10 | 1500.2.o.c.949.4 | 24 | |||
25.21 | even | 5 | 1500.2.o.c.49.4 | 24 | |||
25.22 | odd | 20 | 1500.2.m.d.1201.3 | 24 | |||
75.29 | odd | 10 | 900.2.w.c.109.2 | 24 | |||
75.56 | odd | 10 | 900.2.w.c.289.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.109.3 | ✓ | 24 | 25.4 | even | 10 | ||
300.2.o.a.289.3 | yes | 24 | 25.6 | even | 5 | ||
900.2.w.c.109.2 | 24 | 75.29 | odd | 10 | |||
900.2.w.c.289.2 | 24 | 75.56 | odd | 10 | |||
1500.2.m.c.301.4 | 24 | 25.8 | odd | 20 | |||
1500.2.m.c.1201.4 | 24 | 25.3 | odd | 20 | |||
1500.2.m.d.301.3 | 24 | 25.17 | odd | 20 | |||
1500.2.m.d.1201.3 | 24 | 25.22 | odd | 20 | |||
1500.2.o.c.49.4 | 24 | 25.21 | even | 5 | |||
1500.2.o.c.949.4 | 24 | 25.19 | even | 10 | |||
7500.2.a.m.1.6 | 12 | 5.2 | odd | 4 | |||
7500.2.a.n.1.7 | 12 | 5.3 | odd | 4 | |||
7500.2.d.g.1249.7 | 24 | 1.1 | even | 1 | trivial | ||
7500.2.d.g.1249.18 | 24 | 5.4 | even | 2 | inner |