Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1791,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("2240.1791");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.k (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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 6 x^{14} + 68 x^{13} - 126 x^{12} - 148 x^{11} + 1006 x^{10} - 1516 x^{9} + \cdots + 5956 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | no (minimal twist has level 1120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1791.11 | ||
Root | \(0.715495 - 0.510550i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1791 |
Dual form | 2240.2.k.f.1791.12 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.02110 | 0.589533 | 0.294766 | − | 0.955569i | \(-0.404758\pi\) | ||||
0.294766 | + | 0.955569i | \(0.404758\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.49445 | + | 2.18326i | 0.564848 | + | 0.825195i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.95735 | −0.652451 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.58102i | 0.778206i | 0.921194 | + | 0.389103i | \(0.127215\pi\) | ||||
−0.921194 | + | 0.389103i | \(0.872785\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.79751i | 1.60794i | 0.594670 | + | 0.803970i | \(0.297283\pi\) | ||||
−0.594670 | + | 0.803970i | \(0.702717\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.02110i | − | 0.263647i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.41988i | − | 1.07198i | −0.844225 | − | 0.535990i | \(-0.819939\pi\) | ||
0.844225 | − | 0.535990i | \(-0.180061\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.62638 | −0.831949 | −0.415975 | − | 0.909376i | \(-0.636560\pi\) | ||||
−0.415975 | + | 0.909376i | \(0.636560\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.52598 | + | 2.22933i | 0.332996 | + | 0.486479i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.61528i | 1.37938i | 0.724104 | + | 0.689690i | \(0.242253\pi\) | ||||
−0.724104 | + | 0.689690i | \(0.757747\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.06196 | −0.974174 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.1146 | −1.87823 | −0.939117 | − | 0.343598i | \(-0.888354\pi\) | ||||
−0.939117 | + | 0.343598i | \(0.888354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.36590 | −0.245322 | −0.122661 | − | 0.992449i | \(-0.539143\pi\) | ||||
−0.122661 | + | 0.992449i | \(0.539143\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.63548i | 0.458778i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.18326 | − | 1.49445i | 0.369038 | − | 0.252608i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.44165 | 0.237006 | 0.118503 | − | 0.992954i | \(-0.462191\pi\) | ||||
0.118503 | + | 0.992954i | \(0.462191\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.91984i | 0.947933i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.41261i | − | 0.376786i | −0.982094 | − | 0.188393i | \(-0.939672\pi\) | ||
0.982094 | − | 0.188393i | \(-0.0603279\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.71716i | − | 1.32935i | −0.747131 | − | 0.664677i | \(-0.768569\pi\) | ||
0.747131 | − | 0.664677i | \(-0.231431\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.95735i | 0.291785i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.09441 | 1.03483 | 0.517413 | − | 0.855736i | \(-0.326895\pi\) | ||||
0.517413 | + | 0.855736i | \(0.326895\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.53326 | + | 6.52554i | −0.361894 | + | 0.932219i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 4.51315i | − | 0.631967i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.51402 | −1.30685 | −0.653426 | − | 0.756991i | \(-0.726669\pi\) | ||||
−0.653426 | + | 0.756991i | \(0.726669\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.58102 | 0.348024 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.70290 | −0.490461 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.4752 | −1.36376 | −0.681881 | − | 0.731464i | \(-0.738838\pi\) | ||||
−0.681881 | + | 0.731464i | \(0.738838\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.00793i | 1.15335i | 0.816975 | + | 0.576674i | \(0.195650\pi\) | ||||
−0.816975 | + | 0.576674i | \(0.804350\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.92516 | − | 4.27341i | −0.368536 | − | 0.538399i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.79751 | 0.719093 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.04086i | 0.982347i | 0.871062 | + | 0.491173i | \(0.163432\pi\) | ||||
−0.871062 | + | 0.491173i | \(0.836568\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.75486i | 0.813190i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.09463i | − | 0.723300i | −0.932314 | − | 0.361650i | \(-0.882214\pi\) | ||
0.932314 | − | 0.361650i | \(-0.117786\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.74076i | 0.671905i | 0.941879 | + | 0.335953i | \(0.109058\pi\) | ||||
−0.941879 | + | 0.335953i | \(0.890942\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.02110 | −0.117907 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.63503 | + | 3.85719i | −0.642172 | + | 0.439568i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.97180i | − | 0.784389i | −0.919882 | − | 0.392195i | \(-0.871716\pi\) | ||
0.919882 | − | 0.392195i | \(-0.128284\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.703293 | 0.0781436 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.92102 | 0.979210 | 0.489605 | − | 0.871944i | \(-0.337141\pi\) | ||||
0.489605 | + | 0.871944i | \(0.337141\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.41988 | −0.479404 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.3280 | −1.10728 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.519989i | 0.0551187i | 0.999620 | + | 0.0275594i | \(0.00877353\pi\) | ||||
−0.999620 | + | 0.0275594i | \(0.991226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.6575 | + | 8.66407i | −1.32686 | + | 0.908242i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.39472 | −0.144626 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.62638i | 0.372059i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.08985i | 0.922934i | 0.887157 | + | 0.461467i | \(0.152677\pi\) | ||||
−0.887157 | + | 0.461467i | \(0.847323\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 5.05196i | − | 0.507741i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.8656i | 1.87720i | 0.345012 | + | 0.938598i | \(0.387875\pi\) | ||||
−0.345012 | + | 0.938598i | \(0.612125\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.0722 | 1.58364 | 0.791819 | − | 0.610756i | \(-0.209134\pi\) | ||||
0.791819 | + | 0.610756i | \(0.209134\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.22933 | − | 1.52598i | 0.217560 | − | 0.148920i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 5.93693i | − | 0.573945i | −0.957939 | − | 0.286972i | \(-0.907351\pi\) | ||
0.957939 | − | 0.286972i | \(-0.0926488\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.4574 | 1.09742 | 0.548712 | − | 0.836011i | \(-0.315118\pi\) | ||||
0.548712 | + | 0.836011i | \(0.315118\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.47207 | 0.139723 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.6475 | 1.00163 | 0.500816 | − | 0.865554i | \(-0.333033\pi\) | ||||
0.500816 | + | 0.865554i | \(0.333033\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.61528 | 0.616878 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 11.3478i | − | 1.04910i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.64976 | − | 6.60528i | 0.884592 | − | 0.605505i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.33835 | 0.394396 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 2.46352i | − | 0.222128i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.8640i | 1.05276i | 0.850249 | + | 0.526380i | \(0.176451\pi\) | ||||
−0.850249 | + | 0.526380i | \(0.823549\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 8.90110i | − | 0.783698i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.91333 | −0.254539 | −0.127269 | − | 0.991868i | \(-0.540621\pi\) | ||||
−0.127269 | + | 0.991868i | \(0.540621\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.41944 | − | 7.91734i | −0.469925 | − | 0.686521i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.06196i | 0.435664i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.3320 | −1.65164 | −0.825822 | − | 0.563931i | \(-0.809288\pi\) | ||||
−0.825822 | + | 0.563931i | \(0.809288\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.9727 | 1.52443 | 0.762214 | − | 0.647326i | \(-0.224113\pi\) | ||||
0.762214 | + | 0.647326i | \(0.224113\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.24411 | 0.610064 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.9635 | −1.25131 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.1146i | 0.839972i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.58671 | + | 6.66323i | −0.213348 | + | 0.549574i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.37426 | −0.194507 | −0.0972533 | − | 0.995260i | \(-0.531006\pi\) | ||||
−0.0972533 | + | 0.995260i | \(0.531006\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.19781i | − | 0.178855i | −0.995993 | − | 0.0894276i | \(-0.971496\pi\) | ||
0.995993 | − | 0.0894276i | \(-0.0285038\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.65128i | 0.699414i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.36590i | 0.109711i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.0690i | 1.28244i | 0.767356 | + | 0.641221i | \(0.221572\pi\) | ||||
−0.767356 | + | 0.641221i | \(0.778428\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.71477 | −0.770432 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.4429 | + | 9.88618i | −1.13826 | + | 0.779140i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 0.289542i | − | 0.0226787i | −0.999936 | − | 0.0113393i | \(-0.996390\pi\) | ||
0.999936 | − | 0.0113393i | \(-0.00360950\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.63548 | 0.205172 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.9468 | 1.85306 | 0.926530 | − | 0.376220i | \(-0.122776\pi\) | ||||
0.926530 | + | 0.376220i | \(0.122776\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −20.6111 | −1.58547 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.09811 | 0.542806 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 12.3976i | − | 0.942573i | −0.881980 | − | 0.471287i | \(-0.843790\pi\) | ||
0.881980 | − | 0.471287i | \(-0.156210\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.49445 | − | 2.18326i | −0.112970 | − | 0.165039i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.6963 | −0.803982 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 2.91386i | − | 0.217792i | −0.994053 | − | 0.108896i | \(-0.965268\pi\) | ||
0.994053 | − | 0.108896i | \(-0.0347316\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.06385i | 0.153405i | 0.997054 | + | 0.0767023i | \(0.0244391\pi\) | ||||
−0.997054 | + | 0.0767023i | \(0.975561\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.19800i | 0.679936i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1.44165i | − | 0.105992i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.4078 | 0.834221 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.56483 | − | 11.0516i | −0.550260 | − | 0.803884i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 15.3564i | − | 1.11115i | −0.831467 | − | 0.555574i | \(-0.812499\pi\) | ||
0.831467 | − | 0.555574i | \(-0.187501\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.09771 | 0.438923 | 0.219462 | − | 0.975621i | \(-0.429570\pi\) | ||||
0.219462 | + | 0.975621i | \(0.429570\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.91984 | 0.423929 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.5165 | −0.820515 | −0.410258 | − | 0.911970i | \(-0.634561\pi\) | ||||
−0.410258 | + | 0.911970i | \(0.634561\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.5402 | −1.24339 | −0.621695 | − | 0.783259i | \(-0.713556\pi\) | ||||
−0.621695 | + | 0.783259i | \(0.713556\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.21052i | 0.579126i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.1157 | − | 22.0828i | −1.06092 | − | 1.54991i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.41261 | −0.168504 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 12.9484i | − | 0.899979i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 9.35976i | − | 0.647428i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.0289i | 1.65422i | 0.562041 | + | 0.827109i | \(0.310016\pi\) | ||||
−0.562041 | + | 0.827109i | \(0.689984\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 6.22323i | − | 0.426409i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.71716 | −0.594505 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.04126 | − | 2.98211i | −0.138570 | − | 0.202439i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.86190i | 0.396110i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.6243 | 1.72368 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.2618 | −1.69165 | −0.845827 | − | 0.533458i | \(-0.820892\pi\) | ||||
−0.845827 | + | 0.533458i | \(0.820892\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.95735 | 0.130490 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.16769 | 0.542109 | 0.271054 | − | 0.962564i | \(-0.412628\pi\) | ||||
0.271054 | + | 0.962564i | \(0.412628\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.20416i | 0.145655i | 0.997345 | + | 0.0728274i | \(0.0232022\pi\) | ||||
−0.997345 | + | 0.0728274i | \(0.976798\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.75394 | + | 3.93858i | −0.378581 | + | 0.259140i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.92417 | 0.453618 | 0.226809 | − | 0.973939i | \(-0.427171\pi\) | ||||
0.226809 | + | 0.973939i | \(0.427171\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 7.09441i | − | 0.462788i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 7.11891i | − | 0.462423i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.36537i | 0.282372i | 0.989983 | + | 0.141186i | \(0.0450916\pi\) | ||||
−0.989983 | + | 0.141186i | \(0.954908\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.62318i | 0.297805i | 0.988852 | + | 0.148903i | \(0.0475741\pi\) | ||||
−0.988852 | + | 0.148903i | \(0.952426\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.9040 | 1.02024 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.52554 | + | 2.53326i | 0.416901 | + | 0.161844i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 21.0240i | − | 1.33773i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.10926 | 0.577276 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.78316 | 0.365030 | 0.182515 | − | 0.983203i | \(-0.441576\pi\) | ||||
0.182515 | + | 0.983203i | \(0.441576\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.0741 | −1.07344 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.51315 | −0.282624 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.26190i | 0.328228i | 0.986441 | + | 0.164114i | \(0.0524766\pi\) | ||||
−0.986441 | + | 0.164114i | \(0.947523\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.15447 | + | 3.14750i | 0.133872 | + | 0.195576i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.7978 | 1.22546 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.921675i | 0.0568329i | 0.999596 | + | 0.0284165i | \(0.00904646\pi\) | ||||
−0.999596 | + | 0.0284165i | \(0.990954\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.51402i | 0.584442i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.530961i | 0.0324943i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.23020i | 0.196949i | 0.995140 | + | 0.0984743i | \(0.0313962\pi\) | ||||
−0.995140 | + | 0.0984743i | \(0.968604\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.5410 | 0.944051 | 0.472025 | − | 0.881585i | \(-0.343523\pi\) | ||||
0.472025 | + | 0.881585i | \(0.343523\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.9246 | + | 8.84689i | −0.782230 | + | 0.535438i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 2.58102i | − | 0.155641i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.9121 | −1.61699 | −0.808497 | − | 0.588501i | \(-0.799718\pi\) | ||||
−0.808497 | + | 0.588501i | \(0.799718\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.67354 | 0.160061 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.1430 | 0.963012 | 0.481506 | − | 0.876443i | \(-0.340090\pi\) | ||||
0.481506 | + | 0.876443i | \(0.340090\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.3611 | 0.615905 | 0.307953 | − | 0.951402i | \(-0.400356\pi\) | ||||
0.307953 | + | 0.951402i | \(0.400356\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.70290i | 0.219341i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.26736 | − | 3.60552i | 0.310922 | − | 0.212827i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.53537 | −0.149140 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.28165i | 0.544100i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8.52467i | − | 0.498017i | −0.968501 | − | 0.249008i | \(-0.919895\pi\) | ||
0.968501 | − | 0.249008i | \(-0.0801047\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.4752i | 0.609893i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 13.0650i | − | 0.758108i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −38.3521 | −2.21796 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.0318 | − | 13.0273i | 1.09698 | − | 0.750883i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.2637i | 1.10667i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.00793 | 0.515793 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.5082 | 0.656806 | 0.328403 | − | 0.944538i | \(-0.393490\pi\) | ||||
0.328403 | + | 0.944538i | \(0.393490\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.4113 | 0.933607 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.26053 | 0.0714782 | 0.0357391 | − | 0.999361i | \(-0.488621\pi\) | ||||
0.0357391 | + | 0.999361i | \(0.488621\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.5665i | 0.936394i | 0.883624 | + | 0.468197i | \(0.155096\pi\) | ||||
−0.883624 | + | 0.468197i | \(0.844904\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.27341 | + | 2.92516i | −0.240780 | + | 0.164814i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.8458 | 1.00232 | 0.501161 | − | 0.865354i | \(-0.332906\pi\) | ||||
0.501161 | + | 0.865354i | \(0.332906\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 26.1059i | − | 1.46165i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 6.06221i | − | 0.338359i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.0282i | 0.891833i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 5.79751i | − | 0.321588i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.6992 | 0.646968 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.6022 | + | 15.4890i | 0.584519 | + | 0.853934i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.38744i | 0.241156i | 0.992704 | + | 0.120578i | \(0.0384747\pi\) | ||||
−0.992704 | + | 0.120578i | \(0.961525\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.82182 | −0.154635 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.04086 | 0.439319 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −36.2982 | −1.97729 | −0.988643 | − | 0.150281i | \(-0.951982\pi\) | ||||
−0.988643 | + | 0.150281i | \(0.951982\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.8722 | 0.590494 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 3.52540i | − | 0.190911i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0328 | + | 4.22131i | −0.973678 | + | 0.227929i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.75486 | 0.363670 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.01135i | 0.376389i | 0.982132 | + | 0.188194i | \(0.0602635\pi\) | ||||
−0.982132 | + | 0.188194i | \(0.939736\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 23.7131i | − | 1.26933i | −0.772786 | − | 0.634667i | \(-0.781137\pi\) | ||
0.772786 | − | 0.634667i | \(-0.218863\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 29.3468i | − | 1.56641i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 27.7599i | − | 1.47751i | −0.673973 | − | 0.738756i | \(-0.735414\pi\) | ||
0.673973 | − | 0.738756i | \(-0.264586\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.09463 | −0.323469 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.85338 | − | 6.74466i | 0.521496 | − | 0.356965i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.6167i | 1.03533i | 0.855584 | + | 0.517664i | \(0.173198\pi\) | ||||
−0.855584 | + | 0.517664i | \(0.826802\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.84934 | −0.307860 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.42989 | 0.232509 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.74076 | 0.300485 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.7026 | −1.70706 | −0.853531 | − | 0.521041i | \(-0.825544\pi\) | ||||
−0.853531 | + | 0.521041i | \(0.825544\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.72233i | 0.245835i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.2182 | − | 20.7716i | −0.738172 | − | 1.07841i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.67865 | −0.242251 | −0.121126 | − | 0.992637i | \(-0.538650\pi\) | ||||
−0.121126 | + | 0.992637i | \(0.538650\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.02110i | 0.0527294i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 58.6395i | − | 3.02009i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 16.3039i | − | 0.837478i | −0.908107 | − | 0.418739i | \(-0.862472\pi\) | ||
0.908107 | − | 0.418739i | \(-0.137528\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.1143i | 0.620637i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.99798 | −0.306482 | −0.153241 | − | 0.988189i | \(-0.548971\pi\) | ||||
−0.153241 | + | 0.988189i | \(0.548971\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.85719 | + | 5.63503i | 0.196581 | + | 0.287188i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.0626i | 0.867339i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.81109 | −0.193230 | −0.0966149 | − | 0.995322i | \(-0.530802\pi\) | ||||
−0.0966149 | + | 0.995322i | \(0.530802\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 29.2388 | 1.47867 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.97480 | −0.150059 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.97180 | −0.350790 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 29.3567i | − | 1.47337i | −0.676234 | − | 0.736686i | \(-0.736389\pi\) | ||
0.676234 | − | 0.736686i | \(-0.263611\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.53379 | − | 8.08440i | −0.277036 | − | 0.404726i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.9716 | 1.29696 | 0.648479 | − | 0.761232i | \(-0.275405\pi\) | ||||
0.648479 | + | 0.761232i | \(0.275405\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 7.91880i | − | 0.394464i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 0.703293i | − | 0.0349469i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.72092i | 0.184439i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 18.6606i | − | 0.922709i | −0.887216 | − | 0.461355i | \(-0.847364\pi\) | ||
0.887216 | − | 0.461355i | \(-0.152636\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.7399 | −0.973698 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.6547 | − | 22.8702i | −0.770318 | − | 1.12537i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 8.92102i | − | 0.437916i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.3520 | 0.898700 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.2356 | 1.37940 | 0.689699 | − | 0.724096i | \(-0.257743\pi\) | ||||
0.689699 | + | 0.724096i | \(0.257743\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.85966 | 0.383056 | 0.191528 | − | 0.981487i | \(-0.438656\pi\) | ||||
0.191528 | + | 0.981487i | \(0.438656\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.8863 | −0.675174 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.41988i | 0.214396i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.6667 | + | 13.4619i | −0.951736 | + | 0.651466i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.2792 | −0.737687 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.1789i | 0.971983i | 0.873963 | + | 0.485992i | \(0.161541\pi\) | ||||
−0.873963 | + | 0.485992i | \(0.838459\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.74851i | 0.180142i | 0.995935 | + | 0.0900709i | \(0.0287094\pi\) | ||||
−0.995935 | + | 0.0900709i | \(0.971291\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.3280i | 0.495191i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 23.9895i | − | 1.14758i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.6858 | 1.27365 | 0.636823 | − | 0.771010i | \(-0.280248\pi\) | ||||
0.636823 | + | 0.771010i | \(0.280248\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.95848 | − | 12.7728i | 0.236118 | − | 0.608228i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 12.3567i | − | 0.587084i | −0.955946 | − | 0.293542i | \(-0.905166\pi\) | ||
0.955946 | − | 0.293542i | \(-0.0948341\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.519989 | 0.0246498 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.42435 | −0.114668 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.59414 | 0.405582 | 0.202791 | − | 0.979222i | \(-0.434999\pi\) | ||||
0.202791 | + | 0.979222i | \(0.434999\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.22699 | 0.293217 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 2.24419i | − | 0.105441i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.66407 | + | 12.6575i | 0.406178 | + | 0.593392i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.34157 | 0.436980 | 0.218490 | − | 0.975839i | \(-0.429887\pi\) | ||||
0.218490 | + | 0.975839i | \(0.429887\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 22.3733i | 1.04429i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.9266i | 1.71984i | 0.510425 | + | 0.859922i | \(0.329488\pi\) | ||||
−0.510425 | + | 0.859922i | \(0.670512\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.1423i | 0.936092i | 0.883704 | + | 0.468046i | \(0.155042\pi\) | ||||
−0.883704 | + | 0.468046i | \(0.844958\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.39472i | 0.0646785i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.86546 | 0.132598 | 0.0662988 | − | 0.997800i | \(-0.478881\pi\) | ||||
0.0662988 | + | 0.997800i | \(0.478881\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.5553 | + | 12.0166i | −0.810628 | + | 0.554877i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.4080i | 0.756042i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.4991 | 1.03451 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.62638 | 0.166390 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.6223 | 0.852657 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −23.9569 | −1.09462 | −0.547309 | − | 0.836931i | \(-0.684348\pi\) | ||||
−0.547309 | + | 0.836931i | \(0.684348\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.35798i | 0.381091i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.7476 | + | 10.0948i | −0.671040 | + | 0.459329i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.08985 | 0.412749 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.7786i | 0.896255i | 0.893970 | + | 0.448128i | \(0.147909\pi\) | ||||
−0.893970 | + | 0.448128i | \(0.852091\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 0.295652i | − | 0.0133698i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19.6113i | − | 0.885047i | −0.896757 | − | 0.442524i | \(-0.854083\pi\) | ||
0.896757 | − | 0.442524i | \(-0.145917\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 44.7054i | 2.01343i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.05196 | −0.227069 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.3062 | − | 9.10811i | 0.596863 | − | 0.408554i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.2166i | 0.770722i | 0.922766 | + | 0.385361i | \(0.125923\pi\) | ||||
−0.922766 | + | 0.385361i | \(0.874077\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.4521 | 1.09244 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.8339 | 1.24105 | 0.620526 | − | 0.784186i | \(-0.286919\pi\) | ||||
0.620526 | + | 0.784186i | \(0.286919\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.8656 | 0.839508 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.0460 | −0.934688 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.15369i | 0.272757i | 0.990657 | + | 0.136379i | \(0.0435464\pi\) | ||||
−0.990657 | + | 0.136379i | \(0.956454\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.5336 | + | 8.57927i | −0.554453 | + | 0.379524i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.3566 | 0.810464 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 16.0722i | − | 0.708225i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.3108i | 0.805308i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 12.6592i | − | 0.555678i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 11.9506i | − | 0.523565i | −0.965127 | − | 0.261782i | \(-0.915690\pi\) | ||
0.965127 | − | 0.261782i | \(-0.0843103\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.76482 | −0.0771700 | −0.0385850 | − | 0.999255i | \(-0.512285\pi\) | ||||
−0.0385850 | + | 0.999255i | \(0.512285\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.52598 | − | 2.22933i | −0.0665993 | − | 0.0972959i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.03710i | 0.262980i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.7619 | −0.902691 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.5038 | 0.889788 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.9871 | 0.605850 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.93693 | −0.256676 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 2.97534i | − | 0.128396i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.8425 | − | 6.53837i | −0.725459 | − | 0.281628i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.6583 | 1.18912 | 0.594561 | − | 0.804050i | \(-0.297326\pi\) | ||||
0.594561 | + | 0.804050i | \(0.297326\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.10740i | 0.0904370i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 11.4574i | − | 0.490783i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 16.1575i | − | 0.690845i | −0.938447 | − | 0.345422i | \(-0.887736\pi\) | ||
0.938447 | − | 0.345422i | \(-0.112264\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 17.6317i | − | 0.752503i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 36.6794 | 1.56260 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.2213 | − | 10.4190i | 0.647274 | − | 0.443061i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 1.47207i | − | 0.0624859i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.9564 | −1.26930 | −0.634648 | − | 0.772802i | \(-0.718855\pi\) | ||||
−0.634648 | + | 0.772802i | \(0.718855\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 50.5378 | 2.13752 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.6485 | 0.491800 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.4054 | −0.522827 | −0.261413 | − | 0.965227i | \(-0.584189\pi\) | ||||
−0.261413 | + | 0.965227i | \(0.584189\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 10.6475i | − | 0.447943i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.05103 | + | 1.53547i | 0.0441393 | + | 0.0644837i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.8500 | −0.748310 | −0.374155 | − | 0.927366i | \(-0.622067\pi\) | ||||
−0.374155 | + | 0.927366i | \(0.622067\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 32.7029i | − | 1.36857i | −0.729214 | − | 0.684286i | \(-0.760114\pi\) | ||
0.729214 | − | 0.684286i | \(-0.239886\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 15.6804i | − | 0.655058i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6.61528i | − | 0.275876i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 24.1299i | − | 1.00454i | −0.864710 | − | 0.502271i | \(-0.832498\pi\) | ||
0.864710 | − | 0.502271i | \(-0.167502\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.22638 | 0.258760 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.3320 | + | 19.4769i | 0.553105 | + | 0.808039i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 24.5558i | − | 1.01700i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11.3478 | −0.469173 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.2089 | 1.04048 | 0.520241 | − | 0.854020i | \(-0.325842\pi\) | ||||
0.520241 | + | 0.854020i | \(0.325842\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.95326 | 0.204096 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.7595 | −0.483721 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 47.1605i | − | 1.93665i | −0.249692 | − | 0.968325i | \(-0.580329\pi\) | ||
0.249692 | − | 0.968325i | \(-0.419671\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.60528 | − | 9.64976i | −0.270790 | − | 0.395602i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.9103 | −0.733019 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.0947i | 1.63823i | 0.573632 | + | 0.819113i | \(0.305534\pi\) | ||||
−0.573632 | + | 0.819113i | \(0.694466\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.9606i | 1.42607i | 0.701127 | + | 0.713036i | \(0.252680\pi\) | ||||
−0.701127 | + | 0.713036i | \(0.747320\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 15.7388i | − | 0.640933i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 4.33835i | − | 0.176379i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.1706 | −0.818698 | −0.409349 | − | 0.912378i | \(-0.634244\pi\) | ||||
−0.409349 | + | 0.912378i | \(0.634244\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.4347 | − | 22.5488i | −0.625445 | − | 0.913722i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 41.1299i | 1.66394i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.7382 | 1.03956 | 0.519779 | − | 0.854301i | \(-0.326014\pi\) | ||||
0.519779 | + | 0.854301i | \(0.326014\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.46352 | −0.0993386 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.7826 | −0.514607 | −0.257303 | − | 0.966331i | \(-0.582834\pi\) | ||||
−0.257303 | + | 0.966331i | \(0.582834\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.8997 | −0.679258 | −0.339629 | − | 0.940560i | \(-0.610301\pi\) | ||||
−0.339629 | + | 0.940560i | \(0.610301\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 33.4863i | − | 1.34376i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.13527 | + | 0.777096i | −0.0454837 | + | 0.0311337i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 9.55725i | − | 0.381680i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 6.37193i | − | 0.254065i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 45.5707i | − | 1.81414i | −0.420980 | − | 0.907070i | \(-0.638314\pi\) | ||
0.420980 | − | 0.907070i | \(-0.361686\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.5359i | 0.975216i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.8640 | 0.470809 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −37.8319 | − | 14.6866i | −1.49895 | − | 0.581903i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.9293i | 0.471918i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.3043 | 0.446493 | 0.223246 | − | 0.974762i | \(-0.428335\pi\) | ||||
0.223246 | + | 0.974762i | \(0.428335\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.74609 | 0.147732 | 0.0738658 | − | 0.997268i | \(-0.476466\pi\) | ||||
0.0738658 | + | 0.997268i | \(0.476466\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.90110 | −0.350480 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 34.4780 | 1.35547 | 0.677735 | − | 0.735306i | \(-0.262962\pi\) | ||||
0.677735 | + | 0.735306i | \(0.262962\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 27.0368i | − | 1.06129i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.08433 | − | 3.04503i | −0.0816914 | − | 0.119344i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.06377 | −0.276427 | −0.138213 | − | 0.990402i | \(-0.544136\pi\) | ||||
−0.138213 | + | 0.990402i | \(0.544136\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.91333i | 0.113833i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 11.2367i | − | 0.438386i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 11.0259i | − | 0.429508i | −0.976668 | − | 0.214754i | \(-0.931105\pi\) | ||
0.976668 | − | 0.214754i | \(-0.0688949\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.1116i | 0.898935i | 0.893297 | + | 0.449468i | \(0.148386\pi\) | ||||
−0.893297 | + | 0.449468i | \(0.851614\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 26.1650 | 1.01617 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.91734 | + | 5.41944i | −0.307021 | + | 0.210157i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 66.9109i | − | 2.59080i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.7948 | −0.997285 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23.2496 | −0.897541 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.8939 | −0.651214 | −0.325607 | − | 0.945505i | \(-0.605569\pi\) | ||||
−0.325607 | + | 0.945505i | \(0.605569\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.06196 | 0.194835 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.2595i | 0.432738i | 0.976312 | + | 0.216369i | \(0.0694215\pi\) | ||||
−0.976312 | + | 0.216369i | \(0.930579\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.8455 | + | 13.5843i | −0.761601 | + | 0.521317i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.34004 | 0.319591 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 14.6641i | − | 0.561106i | −0.959839 | − | 0.280553i | \(-0.909482\pi\) | ||
0.959839 | − | 0.280553i | \(-0.0905178\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.3320i | 0.738638i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.25067i | 0.0858682i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 55.1576i | − | 2.10134i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.3976 | 0.585754 | 0.292877 | − | 0.956150i | \(-0.405387\pi\) | ||||
0.292877 | + | 0.956150i | \(0.405387\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.0298 | − | 7.54989i | 0.418986 | − | 0.286797i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 17.9727i | − | 0.681745i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.6635 | −0.403907 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.07028 | 0.267422 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.8811 | −1.27967 | −0.639836 | − | 0.768512i | \(-0.720998\pi\) | ||||
−0.639836 | + | 0.768512i | \(0.720998\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.22798 | −0.197177 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 7.24411i | − | 0.272829i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −41.1885 | + | 28.1936i | −1.54905 | + | 1.06033i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.75297 | −0.103390 | −0.0516949 | − | 0.998663i | \(-0.516462\pi\) | ||||
−0.0516949 | + | 0.998663i | \(0.516462\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.6463i | 0.511776i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 9.03579i | − | 0.338393i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.9635i | 0.559602i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.45748i | 0.166468i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.2515 | 0.867135 | 0.433568 | − | 0.901121i | \(-0.357255\pi\) | ||||
0.433568 | + | 0.901121i | \(0.357255\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.0190 | + | 35.0897i | 0.894515 | + | 1.30681i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.72073i | 0.175566i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.1146 | 0.375647 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.7237 | −0.471894 | −0.235947 | − | 0.971766i | \(-0.575819\pi\) | ||||
−0.235947 | + | 0.971766i | \(0.575819\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.1297 | 0.523323 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −38.5288 | −1.42504 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 21.3314i | − | 0.787894i | −0.919133 | − | 0.393947i | \(-0.871109\pi\) | ||
0.919133 | − | 0.393947i | \(-0.128891\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.66323 | + | 2.58671i | 0.245777 | + | 0.0954122i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.7536 | −0.764468 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 12.0391i | − | 0.442864i | −0.975176 | − | 0.221432i | \(-0.928927\pi\) | ||
0.975176 | − | 0.221432i | \(-0.0710730\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 21.4676i | − | 0.788633i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 13.2484i | − | 0.486036i | −0.970022 | − | 0.243018i | \(-0.921863\pi\) | ||
0.970022 | − | 0.243018i | \(-0.0781374\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.37426i | 0.0869860i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17.4616 | −0.638886 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.9619 | − | 8.87243i | 0.473616 | − | 0.324192i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 6.61180i | − | 0.241268i | −0.992697 | − | 0.120634i | \(-0.961507\pi\) | ||
0.992697 | − | 0.120634i | \(-0.0384928\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.90518 | 0.215197 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.19781 | −0.0799865 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.89444 | 0.141546 | 0.0707730 | − | 0.997492i | \(-0.477453\pi\) | ||||
0.0707730 | + | 0.997492i | \(0.477453\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17.4344 | −0.632829 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 6.62391i | − | 0.240117i | −0.992767 | − | 0.120058i | \(-0.961692\pi\) | ||
0.992767 | − | 0.120058i | \(-0.0383082\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.1225 | + | 25.0146i | 0.619878 | + | 0.905589i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.65128 | 0.312788 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 60.7304i | − | 2.19285i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.8942i | 0.609220i | 0.952477 | + | 0.304610i | \(0.0985261\pi\) | ||||
−0.952477 | + | 0.304610i | \(0.901474\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.37293i | 0.193501i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.87500i | 0.175342i | 0.996150 | + | 0.0876708i | \(0.0279424\pi\) | ||||
−0.996150 | + | 0.0876708i | \(0.972058\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.36590 | 0.0490645 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.19993 | + | 3.21391i | 0.0789221 | + | 0.115298i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.74905i | 0.313467i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.7303 | 0.562876 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 51.1997 | 1.82973 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.0690 | 0.573526 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.84166 | 0.101294 | 0.0506471 | − | 0.998717i | \(-0.483872\pi\) | ||||
0.0506471 | + | 0.998717i | \(0.483872\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.941123i | 0.0335049i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.9121 | + | 23.2462i | 0.565769 | + | 0.826541i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −52.2236 | −1.85451 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.71477i | 0.344547i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.67920i | 0.201168i | 0.994929 | + | 0.100584i | \(0.0320711\pi\) | ||||
−0.994929 | + | 0.100584i | \(0.967929\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 31.3565i | − | 1.10931i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 1.01780i | − | 0.0359623i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.8170 | −0.522881 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.88618 | + | 14.4429i | 0.348442 | + | 0.509045i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.29836i | 0.116108i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 40.2852 | 1.41635 | 0.708176 | − | 0.706036i | \(-0.249518\pi\) | ||||
0.708176 | + | 0.706036i | \(0.249518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.14029 | −0.145385 | −0.0726926 | − | 0.997354i | \(-0.523159\pi\) | ||||
−0.0726926 | + | 0.997354i | \(0.523159\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.8690 | 0.556549 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.289542 | −0.0101422 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.6118i | 1.10596i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 24.7752 | − | 16.9587i | 0.865714 | − | 0.592583i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.7883 | −0.900018 | −0.450009 | − | 0.893024i | \(-0.648579\pi\) | ||||
−0.450009 | + | 0.893024i | \(0.648579\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 27.7051i | − | 0.965740i | −0.875692 | − | 0.482870i | \(-0.839594\pi\) | ||
0.875692 | − | 0.482870i | \(-0.160406\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 2.63548i | − | 0.0917556i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 6.36134i | − | 0.221205i | −0.993865 | − | 0.110603i | \(-0.964722\pi\) | ||
0.993865 | − | 0.110603i | \(-0.0352781\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.3234i | 0.636399i | 0.948024 | + | 0.318199i | \(0.103078\pi\) | ||||
−0.948024 | + | 0.318199i | \(0.896922\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.4800 | −0.953271 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.8421 | + | 11.1967i | 0.999320 | + | 0.387943i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 23.9468i | − | 0.828714i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.91411 | 0.238987 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.4848 | −0.500071 | −0.250036 | − | 0.968237i | \(-0.580442\pi\) | ||||
−0.250036 | + | 0.968237i | \(0.580442\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 73.3051 | 2.52776 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.4836 | 0.567727 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.6111i | 0.709045i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.48344 | + | 9.47176i | 0.222774 | + | 0.325453i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.5798 | 0.363096 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.53692i | 0.326921i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.520567i | 0.0178239i | 0.999960 | + | 0.00891193i | \(0.00283679\pi\) | ||||
−0.999960 | + | 0.00891193i | \(0.997163\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 7.09811i | − | 0.242750i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47.8352i | 1.63402i | 0.576624 | + | 0.817010i | \(0.304370\pi\) | ||||
−0.576624 | + | 0.817010i | \(0.695630\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.1624 | 0.551456 | 0.275728 | − | 0.961236i | \(-0.411081\pi\) | ||||
0.275728 | + | 0.961236i | \(0.411081\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.37850 | − | 3.68160i | 0.183299 | − | 0.125468i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.3447i | 0.590419i | 0.955433 | + | 0.295209i | \(0.0953894\pi\) | ||||
−0.955433 | + | 0.295209i | \(0.904611\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.3976 | −0.421532 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.58887 | −0.0879227 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.9943 | 0.610416 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −46.6170 | −1.57956 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 17.7920i | − | 0.602169i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.18326 | + | 1.49445i | −0.0738077 | + | 0.0505215i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.1021 | −1.18531 | −0.592657 | − | 0.805455i | \(-0.701921\pi\) | ||||
−0.592657 | + | 0.805455i | \(0.701921\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 8.70455i | − | 0.293597i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.12523i | − | 0.105292i | −0.998613 | − | 0.0526458i | \(-0.983235\pi\) | ||
0.998613 | − | 0.0526458i | \(-0.0167654\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.1541i | 0.947461i | 0.880670 | + | 0.473731i | \(0.157093\pi\) | ||||
−0.880670 | + | 0.473731i | \(0.842907\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.6963i | 0.359552i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30.7626 | −1.03291 | −0.516454 | − | 0.856315i | \(-0.672748\pi\) | ||||
−0.516454 | + | 0.856315i | \(0.672748\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.9022 | + | 17.7301i | −0.868733 | + | 0.594649i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.81521i | 0.0608118i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25.7271 | −0.860923 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.91386 | −0.0973996 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −39.1614 | −1.30756 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.8155 | 0.460773 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.0509i | 1.40092i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19.4334 | − | 13.3022i | 0.646704 | − | 0.442670i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.06385 | 0.0686046 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.4398i | 0.844716i | 0.906429 | + | 0.422358i | \(0.138798\pi\) | ||||
−0.906429 | + | 0.422358i | \(0.861202\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 36.9266i | − | 1.22478i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.6451i | 0.949054i | 0.880241 | + | 0.474527i | \(0.157381\pi\) | ||||
−0.880241 | + | 0.474527i | \(0.842619\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.0253i | 0.762027i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.19800 | 0.304077 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.35382 | − | 6.36056i | −0.143776 | − | 0.210044i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.3761i | 1.19994i | 0.800023 | + | 0.599969i | \(0.204820\pi\) | ||||
−0.800023 | + | 0.599969i | \(0.795180\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.7510 | 0.387209 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 35.3337 | 1.16302 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.44165 | −0.0474012 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −31.4589 | −1.03325 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 53.2086i | 1.74572i | 0.487974 | + | 0.872858i | \(0.337736\pi\) | ||||
−0.487974 | + | 0.872858i | \(0.662264\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.18656 | − | 23.6641i | 0.301077 | − | 0.775559i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.28713 | 0.0421388 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 11.4078i | − | 0.373075i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.6232i | 1.22910i | 0.788879 | + | 0.614549i | \(0.210662\pi\) | ||||
−0.788879 | + | 0.614549i | \(0.789338\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.9161i | 0.552035i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 31.0252i | − | 1.01139i | −0.862711 | − | 0.505697i | \(-0.831235\pi\) | ||
0.862711 | − | 0.505697i | \(-0.168765\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.9601 | 0.519732 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11.0516 | + | 7.56483i | −0.359508 | + | 0.246084i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 34.2651i | − | 1.11347i | −0.830691 | − | 0.556734i | \(-0.812054\pi\) | ||
0.830691 | − | 0.556734i | \(-0.187946\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33.2821 | −1.08038 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.2224 | 0.590902 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −49.5311 | −1.60447 | −0.802236 | − | 0.597007i | \(-0.796356\pi\) | ||||
−0.802236 | + | 0.597007i | \(0.796356\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.3564 | −0.496921 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 26.6568i | − | 0.861692i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.8906 | − | 42.2068i | −0.932928 | − | 1.36293i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1343 | −0.939817 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.6207i | 0.374471i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 6.09771i | − | 0.196292i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 59.9908i | 1.92917i | 0.263767 | + | 0.964587i | \(0.415035\pi\) | ||||
−0.263767 | + | 0.964587i | \(0.584965\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.3664i | 0.525765i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.5169 | 1.49280 | 0.746400 | − | 0.665498i | \(-0.231781\pi\) | ||||
0.746400 | + | 0.665498i | \(0.231781\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.8593 | + | 39.2392i | 0.861070 | + | 1.25795i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 5.91984i | − | 0.189587i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.576069 | 0.0184301 | 0.00921504 | − | 0.999958i | \(-0.497067\pi\) | ||||
0.00921504 | + | 0.999958i | \(0.497067\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.34210 | −0.0428937 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −22.4263 | −0.716016 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.50742 | −0.239449 | −0.119725 | − | 0.992807i | \(-0.538201\pi\) | ||||
−0.119725 | + | 0.992807i | \(0.538201\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.5165i | 0.366946i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.8259 | + | 15.8158i | 0.344593 | + | 0.503422i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 57.6664 | 1.83369 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.7914i | 1.29578i | 0.761734 | + | 0.647890i | \(0.224348\pi\) | ||||
−0.761734 | + | 0.647890i | \(0.775652\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.48002i | 0.142169i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.5402i | 0.556061i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 38.4148i | − | 1.21661i | −0.793704 | − | 0.608304i | \(-0.791850\pi\) | ||
0.793704 | − | 0.608304i | \(-0.208150\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.29757 | −0.230885 |
(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 | 2240.2.k.f.1791.11 | 16 | ||
4.3 | odd | 2 | 2240.2.k.g.1791.5 | 16 | |||
7.6 | odd | 2 | 2240.2.k.g.1791.6 | 16 | |||
8.3 | odd | 2 | 1120.2.k.b.671.12 | yes | 16 | ||
8.5 | even | 2 | 1120.2.k.a.671.6 | yes | 16 | ||
28.27 | even | 2 | inner | 2240.2.k.f.1791.12 | 16 | ||
56.13 | odd | 2 | 1120.2.k.b.671.11 | yes | 16 | ||
56.27 | even | 2 | 1120.2.k.a.671.5 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1120.2.k.a.671.5 | ✓ | 16 | 56.27 | even | 2 | ||
1120.2.k.a.671.6 | yes | 16 | 8.5 | even | 2 | ||
1120.2.k.b.671.11 | yes | 16 | 56.13 | odd | 2 | ||
1120.2.k.b.671.12 | yes | 16 | 8.3 | odd | 2 | ||
2240.2.k.f.1791.11 | 16 | 1.1 | even | 1 | trivial | ||
2240.2.k.f.1791.12 | 16 | 28.27 | even | 2 | inner | ||
2240.2.k.g.1791.5 | 16 | 4.3 | odd | 2 | |||
2240.2.k.g.1791.6 | 16 | 7.6 | odd | 2 |