Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1471,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("5520.1471");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.be (of order \(2\), degree \(1\), 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: | \(44.0774219157\) |
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: | \( x^{16} - 4 x^{15} + 8 x^{14} + 28 x^{13} + 373 x^{12} - 920 x^{11} + 1088 x^{10} - 168 x^{9} + 16460 x^{8} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.7 | ||
Root | \(0.476829 + 0.476829i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5520.1471 |
Dual form | 5520.2.be.b.1471.15 |
$q$-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 \(\left(\mathbb{Z}/5520\mathbb{Z}\right)^\times\).
\(n\) | \(1201\) | \(1381\) | \(1841\) | \(4417\) | \(4831\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.79952 | 1.43608 | 0.718042 | − | 0.696000i | \(-0.245039\pi\) | ||||
0.718042 | + | 0.696000i | \(0.245039\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.69013 | 1.11262 | 0.556308 | − | 0.830976i | \(-0.312217\pi\) | ||||
0.556308 | + | 0.830976i | \(0.312217\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.60963 | 0.723781 | 0.361891 | − | 0.932221i | \(-0.382131\pi\) | ||||
0.361891 | + | 0.932221i | \(0.382131\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.60151i | 0.388424i | 0.980960 | + | 0.194212i | \(0.0622150\pi\) | ||||
−0.980960 | + | 0.194212i | \(0.937785\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.20535 | −1.88244 | −0.941218 | − | 0.337801i | \(-0.890317\pi\) | ||||
−0.941218 | + | 0.337801i | \(0.890317\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 3.79952i | − | 0.829123i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.19801 | − | 4.64379i | 0.249802 | − | 0.968297i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.706420 | 0.131179 | 0.0655894 | − | 0.997847i | \(-0.479107\pi\) | ||||
0.0655894 | + | 0.997847i | \(0.479107\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.46598i | − | 1.16132i | −0.814145 | − | 0.580662i | \(-0.802794\pi\) | ||
0.814145 | − | 0.580662i | \(-0.197206\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 3.69013i | − | 0.642369i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 3.79952i | − | 0.642236i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.01787i | − | 0.824933i | −0.910973 | − | 0.412466i | \(-0.864667\pi\) | ||
0.910973 | − | 0.412466i | \(-0.135333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 2.60963i | − | 0.417875i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.6396 | −1.66162 | −0.830812 | − | 0.556553i | \(-0.812124\pi\) | ||||
−0.830812 | + | 0.556553i | \(0.812124\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.94134 | −0.906045 | −0.453023 | − | 0.891499i | \(-0.649654\pi\) | ||||
−0.453023 | + | 0.891499i | \(0.649654\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.46270i | − | 0.650952i | −0.945550 | − | 0.325476i | \(-0.894476\pi\) | ||
0.945550 | − | 0.325476i | \(-0.105524\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.43635 | 1.06234 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.60151 | 0.224257 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 7.25579i | − | 0.996660i | −0.866987 | − | 0.498330i | \(-0.833947\pi\) | ||
0.866987 | − | 0.498330i | \(-0.166053\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.69013i | − | 0.497577i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.20535i | 1.08682i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.04730i | 0.787291i | 0.919262 | + | 0.393646i | \(0.128786\pi\) | ||||
−0.919262 | + | 0.393646i | \(0.871214\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.36597i | 0.430968i | 0.976507 | + | 0.215484i | \(0.0691329\pi\) | ||||
−0.976507 | + | 0.215484i | \(0.930867\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.79952 | −0.478695 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.60963i | − | 0.323685i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.5383 | 1.65397 | 0.826984 | − | 0.562226i | \(-0.190055\pi\) | ||||
0.826984 | + | 0.562226i | \(0.190055\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.64379 | − | 1.19801i | −0.559047 | − | 0.144223i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.69292i | − | 1.03166i | −0.856691 | − | 0.515830i | \(-0.827484\pi\) | ||
0.856691 | − | 0.515830i | \(-0.172516\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.516947 | −0.0605040 | −0.0302520 | − | 0.999542i | \(-0.509631\pi\) | ||||
−0.0302520 | + | 0.999542i | \(0.509631\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000i | 0.115470i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.0207 | 1.59781 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.23175 | −0.363600 | −0.181800 | − | 0.983336i | \(-0.558192\pi\) | ||||
−0.181800 | + | 0.983336i | \(0.558192\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.10586 | 0.450677 | 0.225338 | − | 0.974281i | \(-0.427651\pi\) | ||||
0.225338 | + | 0.974281i | \(0.427651\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.60151 | 0.173709 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 0.706420i | − | 0.0757361i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5.11034i | − | 0.541695i | −0.962622 | − | 0.270848i | \(-0.912696\pi\) | ||
0.962622 | − | 0.270848i | \(-0.0873040\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.91534 | 1.03941 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.46598 | −0.670491 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.20535i | 0.841851i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 19.4018i | − | 1.96996i | −0.172675 | − | 0.984979i | \(-0.555241\pi\) | ||
0.172675 | − | 0.984979i | \(-0.444759\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.69013 | −0.370872 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.1514 | 1.30861 | 0.654305 | − | 0.756231i | \(-0.272961\pi\) | ||||
0.654305 | + | 0.756231i | \(0.272961\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.37041 | 0.529162 | 0.264581 | − | 0.964363i | \(-0.414766\pi\) | ||||
0.264581 | + | 0.964363i | \(0.414766\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.79952 | −0.370795 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.9219 | 1.73258 | 0.866290 | − | 0.499542i | \(-0.166498\pi\) | ||||
0.866290 | + | 0.499542i | \(0.166498\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.27328i | − | 0.121958i | −0.998139 | − | 0.0609792i | \(-0.980578\pi\) | ||
0.998139 | − | 0.0609792i | \(-0.0194223\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.01787 | −0.476275 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.32431i | − | 0.312725i | −0.987700 | − | 0.156362i | \(-0.950023\pi\) | ||
0.987700 | − | 0.156362i | \(-0.0499768\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.64379 | − | 1.19801i | −0.433036 | − | 0.111715i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.60963 | −0.241260 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.08498i | 0.557810i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.61707 | 0.237915 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.6396i | 0.959339i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.7160i | 1.39457i | 0.716793 | + | 0.697286i | \(0.245609\pi\) | ||||
−0.716793 | + | 0.697286i | \(0.754391\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.94134i | 0.523106i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 10.5445i | − | 0.921280i | −0.887587 | − | 0.460640i | \(-0.847620\pi\) | ||
0.887587 | − | 0.460640i | \(-0.152380\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −31.1764 | −2.70333 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.67864i | 0.143416i | 0.997426 | + | 0.0717081i | \(0.0228450\pi\) | ||||
−0.997426 | + | 0.0717081i | \(0.977155\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.7161i | 1.16338i | 0.813410 | + | 0.581691i | \(0.197609\pi\) | ||||
−0.813410 | + | 0.581691i | \(0.802391\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.46270 | −0.375827 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.62988 | 0.805291 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 0.706420i | − | 0.0586650i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 7.43635i | − | 0.613340i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 22.3923i | − | 1.83445i | −0.398368 | − | 0.917226i | \(-0.630423\pi\) | ||
0.398368 | − | 0.917226i | \(-0.369577\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.9206i | 1.86526i | 0.360840 | + | 0.932628i | \(0.382490\pi\) | ||||
−0.360840 | + | 0.932628i | \(0.617510\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.60151i | − | 0.129475i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.46598 | −0.519360 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 14.5054i | − | 1.15765i | −0.815450 | − | 0.578827i | \(-0.803511\pi\) | ||
0.815450 | − | 0.578827i | \(-0.196489\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.25579 | −0.575422 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.55185 | − | 17.6442i | 0.358736 | − | 1.39056i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.70939i | 0.525520i | 0.964861 | + | 0.262760i | \(0.0846327\pi\) | ||||
−0.964861 | + | 0.262760i | \(0.915367\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.69013 | −0.287276 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.17703i | 0.400611i | 0.979734 | + | 0.200305i | \(0.0641934\pi\) | ||||
−0.979734 | + | 0.200305i | \(0.935807\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.18983 | −0.476141 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.20535 | 0.627478 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.0638 | 1.06925 | 0.534624 | − | 0.845090i | \(-0.320453\pi\) | ||||
0.534624 | + | 0.845090i | \(0.320453\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.79952 | −0.287217 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.04730 | 0.454543 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.9606i | 0.893975i | 0.894540 | + | 0.446988i | \(0.147503\pi\) | ||||
−0.894540 | + | 0.446988i | \(0.852497\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.90385i | 0.141512i | 0.997494 | + | 0.0707561i | \(0.0225412\pi\) | ||||
−0.997494 | + | 0.0707561i | \(0.977459\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.36597 | 0.248819 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.01787 | −0.368921 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.90980i | 0.432167i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.79952i | 0.276374i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.6906 | 1.20769 | 0.603845 | − | 0.797102i | \(-0.293635\pi\) | ||||
0.603845 | + | 0.797102i | \(0.293635\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.9024 | −0.856751 | −0.428376 | − | 0.903601i | \(-0.640914\pi\) | ||||
−0.428376 | + | 0.903601i | \(0.640914\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.60963 | −0.186879 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.3515 | 1.09375 | 0.546876 | − | 0.837214i | \(-0.315817\pi\) | ||||
0.546876 | + | 0.837214i | \(0.315817\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.4361 | −1.23601 | −0.618006 | − | 0.786173i | \(-0.712059\pi\) | ||||
−0.618006 | + | 0.786173i | \(0.712059\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 13.5383i | − | 0.954919i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.68406 | 0.188384 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.6396i | 0.743101i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.19801 | + | 4.64379i | −0.0832672 | + | 0.322766i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −30.2788 | −2.09443 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 7.11509i | − | 0.489823i | −0.969545 | − | 0.244911i | \(-0.921241\pi\) | ||
0.969545 | − | 0.244911i | \(-0.0787589\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.69292 | −0.595629 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.94134i | 0.405196i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 24.5676i | − | 1.66776i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.516947i | 0.0349320i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.17936i | 0.281134i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.92403i | 0.195808i | 0.995196 | + | 0.0979038i | \(0.0312137\pi\) | ||||
−0.995196 | + | 0.0979038i | \(0.968786\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.86711 | 0.588531 | 0.294265 | − | 0.955724i | \(-0.404925\pi\) | ||||
0.294265 | + | 0.955724i | \(0.404925\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.81117i | 0.516177i | 0.966121 | + | 0.258088i | \(0.0830926\pi\) | ||||
−0.966121 | + | 0.258088i | \(0.916907\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 14.0207i | − | 0.922496i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.09372 | −0.333701 | −0.166850 | − | 0.985982i | \(-0.553360\pi\) | ||||
−0.166850 | + | 0.985982i | \(0.553360\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.46270 | −0.291114 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.23175i | 0.209925i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 19.5551i | − | 1.26491i | −0.774595 | − | 0.632457i | \(-0.782046\pi\) | ||
0.774595 | − | 0.632457i | \(-0.217954\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 8.39986i | − | 0.541083i | −0.962708 | − | 0.270541i | \(-0.912797\pi\) | ||
0.962708 | − | 0.270541i | \(-0.0872027\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 7.43635i | − | 0.475091i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.4129 | −1.36247 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 4.10586i | − | 0.260198i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.84091 | 0.494914 | 0.247457 | − | 0.968899i | \(-0.420405\pi\) | ||||
0.247457 | + | 0.968899i | \(0.420405\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.42080 | − | 17.1362i | 0.277933 | − | 1.07734i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 1.60151i | − | 0.100291i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.18308 | −0.323312 | −0.161656 | − | 0.986847i | \(-0.551683\pi\) | ||||
−0.161656 | + | 0.986847i | \(0.551683\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 19.0655i | − | 1.18467i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.706420 | −0.0437263 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.41083 | 0.395309 | 0.197654 | − | 0.980272i | \(-0.436668\pi\) | ||||
0.197654 | + | 0.980272i | \(0.436668\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.25579 | −0.445720 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.11034 | −0.312748 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.1418 | 1.71584 | 0.857919 | − | 0.513785i | \(-0.171757\pi\) | ||||
0.857919 | + | 0.513785i | \(0.171757\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 23.8196i | − | 1.44694i | −0.690356 | − | 0.723470i | \(-0.742546\pi\) | ||
0.690356 | − | 0.723470i | \(-0.257454\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 9.91534i | − | 0.600104i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.69013 | −0.222523 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.1168 | −1.32887 | −0.664436 | − | 0.747345i | \(-0.731328\pi\) | ||||
−0.664436 | + | 0.747345i | \(0.731328\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.46598i | 0.387108i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10.5452i | − | 0.629075i | −0.949245 | − | 0.314538i | \(-0.898151\pi\) | ||
0.949245 | − | 0.314538i | \(-0.101849\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.3512 | 0.793648 | 0.396824 | − | 0.917895i | \(-0.370112\pi\) | ||||
0.396824 | + | 0.917895i | \(0.370112\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.20535 | 0.486043 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −40.4253 | −2.38623 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.4352 | 0.849127 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.4018 | −1.13736 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.0456i | 0.762129i | 0.924548 | + | 0.381065i | \(0.124443\pi\) | ||||
−0.924548 | + | 0.381065i | \(0.875557\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.04730 | 0.352087 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.69013i | 0.214123i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.12635 | − | 12.1186i | 0.180802 | − | 0.700835i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.5742 | −1.30116 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 13.1514i | − | 0.755526i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.36597 | 0.192735 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 24.4269i | − | 1.39412i | −0.717015 | − | 0.697058i | \(-0.754492\pi\) | ||
0.717015 | − | 0.697058i | \(-0.245508\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 5.37041i | − | 0.305512i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 2.74305i | − | 0.155544i | −0.996971 | − | 0.0777721i | \(-0.975219\pi\) | ||
0.996971 | − | 0.0777721i | \(-0.0247807\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.88307i | 0.219484i | 0.993960 | + | 0.109742i | \(0.0350025\pi\) | ||||
−0.993960 | + | 0.109742i | \(0.964998\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.79952i | 0.214079i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.5346 | −1.49033 | −0.745166 | − | 0.666879i | \(-0.767630\pi\) | ||||
−0.745166 | + | 0.666879i | \(0.767630\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.60678 | 0.145952 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 17.9219i | − | 1.00031i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 13.1410i | − | 0.731183i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.60963 | −0.144756 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.27328 | −0.0704127 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 16.9561i | − | 0.934821i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.5918i | 1.57155i | 0.618515 | + | 0.785773i | \(0.287735\pi\) | ||||
−0.618515 | + | 0.785773i | \(0.712265\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.01787i | 0.274978i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 13.5383i | − | 0.739677i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.76479i | 0.368501i | 0.982879 | + | 0.184251i | \(0.0589858\pi\) | ||||
−0.982879 | + | 0.184251i | \(0.941014\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.32431 | −0.180552 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 23.8603i | − | 1.29211i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.65793 | 0.0895200 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.19801 | + | 4.64379i | −0.0644985 | + | 0.250013i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.0461i | 1.55927i | 0.626231 | + | 0.779637i | \(0.284597\pi\) | ||||
−0.626231 | + | 0.779637i | \(0.715403\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.4208 | −1.09310 | −0.546550 | − | 0.837427i | \(-0.684059\pi\) | ||||
−0.546550 | + | 0.837427i | \(0.684059\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.60963i | 0.139292i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.6709 | −0.993751 | −0.496876 | − | 0.867822i | \(-0.665519\pi\) | ||||
−0.496876 | + | 0.867822i | \(0.665519\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.69292 | −0.461372 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.08498 | 0.322052 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.96281 | 0.314705 | 0.157353 | − | 0.987542i | \(-0.449704\pi\) | ||||
0.157353 | + | 0.987542i | \(0.449704\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 48.3277 | 2.54356 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 2.61707i | − | 0.137360i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.516947i | 0.0270582i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.4914 | −1.22624 | −0.613121 | − | 0.789989i | \(-0.710086\pi\) | ||||
−0.613121 | + | 0.789989i | \(0.710086\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.6396 | 0.553875 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 27.5685i | − | 1.43129i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.8948i | 1.08189i | 0.841057 | + | 0.540946i | \(0.181934\pi\) | ||||
−0.841057 | + | 0.540946i | \(0.818066\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.84349 | 0.0949447 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.21337 | 0.421892 | 0.210946 | − | 0.977498i | \(-0.432346\pi\) | ||||
0.210946 | + | 0.977498i | \(0.432346\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.7160 | 0.805156 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.84776 | 0.401002 | 0.200501 | − | 0.979694i | \(-0.435743\pi\) | ||||
0.200501 | + | 0.979694i | \(0.435743\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 14.0207i | − | 0.714562i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.94134 | 0.302015 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 25.0255i | − | 1.26884i | −0.772988 | − | 0.634421i | \(-0.781239\pi\) | ||
0.772988 | − | 0.634421i | \(-0.218761\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.43709 | + | 1.91862i | 0.376110 | + | 0.0970290i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.5445 | −0.531901 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.23175i | 0.162607i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.5249 | 0.979928 | 0.489964 | − | 0.871743i | \(-0.337010\pi\) | ||||
0.489964 | + | 0.871743i | \(0.337010\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 31.1764i | 1.56077i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.8201i | 1.38927i | 0.719363 | + | 0.694634i | \(0.244434\pi\) | ||||
−0.719363 | + | 0.694634i | \(0.755566\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 16.8738i | − | 0.840545i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1.00000i | − | 0.0496904i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 18.5166i | − | 0.917834i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.0574 | −0.892882 | −0.446441 | − | 0.894813i | \(-0.647309\pi\) | ||||
−0.446441 | + | 0.894813i | \(0.647309\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.67864 | 0.0828014 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.9768i | 1.13062i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4.10586i | − | 0.201549i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.7161 | 0.671679 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.4005 | −0.556952 | −0.278476 | − | 0.960443i | \(-0.589829\pi\) | ||||
−0.278476 | + | 0.960443i | \(0.589829\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.5611i | 1.00209i | 0.865422 | + | 0.501044i | \(0.167051\pi\) | ||||
−0.865422 | + | 0.501044i | \(0.832949\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.46270i | 0.216984i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.60151i | − | 0.0776848i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.7891i | 0.618906i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 9.62988i | − | 0.464935i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.10368 | −0.149499 | −0.0747496 | − | 0.997202i | \(-0.523816\pi\) | ||||
−0.0747496 | + | 0.997202i | \(0.523816\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9.48758i | − | 0.455944i | −0.973668 | − | 0.227972i | \(-0.926791\pi\) | ||
0.973668 | − | 0.227972i | \(-0.0732095\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.706420 | −0.0338702 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.83005 | + | 38.1039i | −0.470235 | + | 1.82276i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.16012i | 0.198551i | 0.995060 | + | 0.0992757i | \(0.0316526\pi\) | ||||
−0.995060 | + | 0.0992757i | \(0.968347\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.43635 | −0.354112 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.5136i | 1.49726i | 0.662990 | + | 0.748629i | \(0.269287\pi\) | ||||
−0.662990 | + | 0.748629i | \(0.730713\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.11034 | −0.242254 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22.3923 | −1.05912 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.5729 | −0.734930 | −0.367465 | − | 0.930037i | \(-0.619774\pi\) | ||||
−0.367465 | + | 0.930037i | \(0.619774\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −39.2615 | −1.84875 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.9206 | 1.07691 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 9.91534i | − | 0.464838i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 30.9828i | − | 1.44931i | −0.689110 | − | 0.724657i | \(-0.741998\pi\) | ||
0.689110 | − | 0.724657i | \(-0.258002\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.60151 | −0.0747523 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.7446 | 0.733301 | 0.366651 | − | 0.930359i | \(-0.380504\pi\) | ||||
0.366651 | + | 0.930359i | \(0.380504\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.71750i | − | 0.0798191i | −0.999203 | − | 0.0399096i | \(-0.987293\pi\) | ||
0.999203 | − | 0.0399096i | \(-0.0127070\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.46598i | 0.299853i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.3495 | 1.63578 | 0.817891 | − | 0.575373i | \(-0.195143\pi\) | ||||
0.817891 | + | 0.575373i | \(0.195143\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 51.4391 | 2.37524 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.5054 | −0.668372 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.9243 | −1.00808 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.20535 | 0.376487 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.25579i | 0.332220i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.0253 | 1.23482 | 0.617408 | − | 0.786643i | \(-0.288183\pi\) | ||||
0.617408 | + | 0.786643i | \(0.288183\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 13.0948i | − | 0.597071i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −17.6442 | − | 4.55185i | −0.802838 | − | 0.207116i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.4018 | −0.880992 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 42.0999i | 1.90773i | 0.300237 | + | 0.953865i | \(0.402934\pi\) | ||||
−0.300237 | + | 0.953865i | \(0.597066\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.70939 | 0.303409 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.3694i | 0.648480i | 0.945975 | + | 0.324240i | \(0.105109\pi\) | ||||
−0.945975 | + | 0.324240i | \(0.894891\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.13134i | 0.0509530i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.69013i | 0.165859i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 33.0289i | − | 1.48155i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.1409i | 0.498734i | 0.968409 | + | 0.249367i | \(0.0802226\pi\) | ||||
−0.968409 | + | 0.249367i | \(0.919777\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.17703 | 0.231293 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.8161 | 0.705207 | 0.352603 | − | 0.935773i | \(-0.385297\pi\) | ||||
0.352603 | + | 0.935773i | \(0.385297\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 13.1514i | − | 0.585228i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.18983i | 0.274900i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.3061 | −1.38762 | −0.693809 | − | 0.720159i | \(-0.744069\pi\) | ||||
−0.693809 | + | 0.720159i | \(0.744069\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.96415 | −0.0868888 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 8.20535i | − | 0.362275i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 5.37041i | − | 0.236648i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 16.4679i | − | 0.724259i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 14.0638i | − | 0.617331i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 23.5026i | − | 1.02967i | −0.857290 | − | 0.514833i | \(-0.827854\pi\) | ||
0.857290 | − | 0.514833i | \(-0.172146\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.4909 | −1.55191 | −0.775954 | − | 0.630789i | \(-0.782731\pi\) | ||||
−0.775954 | + | 0.630789i | \(0.782731\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.79952i | 0.165825i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.3554 | 0.451087 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.1296 | − | 11.1266i | −0.875198 | − | 0.483764i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 6.04730i | − | 0.262430i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −27.7654 | −1.20265 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 17.9219i | − | 0.774833i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.9606 | 0.516137 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27.4411 | 1.18197 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.7968 | 1.36705 | 0.683525 | − | 0.729927i | \(-0.260446\pi\) | ||||
0.683525 | + | 0.729927i | \(0.260446\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.90385 | 0.0817022 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.27328 | −0.0545415 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 21.8699i | − | 0.935090i | −0.883969 | − | 0.467545i | \(-0.845139\pi\) | ||
0.883969 | − | 0.467545i | \(-0.154861\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 3.36597i | − | 0.143656i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.79642 | −0.246936 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.2791 | −0.522160 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.01787i | 0.212997i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 1.91446i | − | 0.0811182i | −0.999177 | − | 0.0405591i | \(-0.987086\pi\) | ||
0.999177 | − | 0.0405591i | \(-0.0129139\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.5047 | −0.655779 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.90980 | 0.249512 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.0420 | 1.39255 | 0.696277 | − | 0.717773i | \(-0.254838\pi\) | ||||
0.696277 | + | 0.717773i | \(0.254838\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.32431 | −0.139855 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.79952 | 0.159565 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 10.1677i | − | 0.426250i | −0.977025 | − | 0.213125i | \(-0.931636\pi\) | ||
0.977025 | − | 0.213125i | \(-0.0683642\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.6137 | −0.946355 | −0.473177 | − | 0.880967i | \(-0.656893\pi\) | ||||
−0.473177 | + | 0.880967i | \(0.656893\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 16.6906i | − | 0.697260i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.19801 | + | 4.64379i | −0.0499603 | + | 0.193659i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.0069 | −0.416591 | −0.208295 | − | 0.978066i | \(-0.566792\pi\) | ||||
−0.208295 | + | 0.978066i | \(0.566792\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.9024i | 0.494646i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.6003 | 0.647210 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 26.7748i | − | 1.10890i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.60963i | 0.107895i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 20.6747i | − | 0.853336i | −0.904408 | − | 0.426668i | \(-0.859687\pi\) | ||
0.904408 | − | 0.426668i | \(-0.140313\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 53.0556i | 2.18612i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 15.3515i | − | 0.631478i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.2092 | −1.40480 | −0.702402 | − | 0.711780i | \(-0.747889\pi\) | ||||
−0.702402 | + | 0.711780i | \(0.747889\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.08498 | 0.249460 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.4361i | 0.713612i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.2726i | 1.19605i | 0.801479 | + | 0.598023i | \(0.204047\pi\) | ||||
−0.801479 | + | 0.598023i | \(0.795953\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.7471 | 1.33578 | 0.667891 | − | 0.744259i | \(-0.267197\pi\) | ||||
0.667891 | + | 0.744259i | \(0.267197\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.5383 | −0.551323 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 2.61707i | − | 0.106399i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.9681i | 1.21637i | 0.793796 | + | 0.608185i | \(0.208102\pi\) | ||||
−0.793796 | + | 0.608185i | \(0.791898\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 2.68406i | − | 0.108763i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 11.6460i | − | 0.471146i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 12.6769i | − | 0.512014i | −0.966675 | − | 0.256007i | \(-0.917593\pi\) | ||
0.966675 | − | 0.256007i | \(-0.0824070\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.6396 | 0.429029 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.68220i | − | 0.269015i | −0.990913 | − | 0.134508i | \(-0.957055\pi\) | ||
0.990913 | − | 0.134508i | \(-0.0429453\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.1774 | −0.489451 | −0.244725 | − | 0.969592i | \(-0.578698\pi\) | ||||
−0.244725 | + | 0.969592i | \(0.578698\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.64379 | + | 1.19801i | 0.186349 | + | 0.0480743i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 19.4169i | − | 0.777920i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 30.2788i | 1.20922i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.03619 | 0.320424 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.6325 | −0.821365 | −0.410683 | − | 0.911778i | \(-0.634710\pi\) | ||||
−0.410683 | + | 0.911778i | \(0.634710\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.11509 | −0.282799 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.7160 | 0.623671 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.4061 | 0.768899 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.69292i | 0.343887i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.8025i | 0.742655i | 0.928502 | + | 0.371328i | \(0.121097\pi\) | ||||
−0.928502 | + | 0.371328i | \(0.878903\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.17101 | 0.243361 | 0.121680 | − | 0.992569i | \(-0.461172\pi\) | ||||
0.121680 | + | 0.992569i | \(0.461172\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.94134 | 0.233940 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.0800i | 0.435601i | 0.975993 | + | 0.217801i | \(0.0698882\pi\) | ||||
−0.975993 | + | 0.217801i | \(0.930112\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.3153i | 0.875953i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.5676 | −0.962881 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.6281 | −0.572441 | −0.286221 | − | 0.958164i | \(-0.592399\pi\) | ||||
−0.286221 | + | 0.958164i | \(0.592399\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.5445 | −0.412009 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.516947 | 0.0201680 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.1684 | −0.746694 | −0.373347 | − | 0.927692i | \(-0.621790\pi\) | ||||
−0.373347 | + | 0.927692i | \(0.621790\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 32.1112i | − | 1.24898i | −0.781033 | − | 0.624490i | \(-0.785307\pi\) | ||
0.781033 | − | 0.624490i | \(-0.214693\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.17936 | 0.162313 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 31.1764i | 1.20897i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.846295 | − | 3.28046i | 0.0327687 | − | 0.127020i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.92403 | 0.113050 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.4209i | 0.479502i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.150913 | 0.00581729 | 0.00290864 | − | 0.999996i | \(-0.499074\pi\) | ||||
0.00290864 | + | 0.999996i | \(0.499074\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 1.00000i | − | 0.0384900i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.2608i | 1.58578i | 0.609365 | + | 0.792890i | \(0.291425\pi\) | ||||
−0.609365 | + | 0.792890i | \(0.708575\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 73.7177i | − | 2.82902i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 8.86711i | − | 0.339788i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 20.7486i | − | 0.793925i | −0.917835 | − | 0.396963i | \(-0.870064\pi\) | ||
0.917835 | − | 0.396963i | \(-0.129936\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.67864 | 0.0641377 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.81117 | 0.298015 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 18.9349i | − | 0.721364i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 4.48560i | − | 0.170640i | −0.996354 | − | 0.0853202i | \(-0.972809\pi\) | ||
0.996354 | − | 0.0853202i | \(-0.0271913\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.0207 | −0.532603 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.7161 | 0.520280 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 17.0394i | − | 0.645415i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.09372i | 0.192662i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.49486i | 0.0564601i | 0.999601 | + | 0.0282301i | \(0.00898710\pi\) | ||||
−0.999601 | + | 0.0282301i | \(0.991013\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.1734i | 1.55288i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.46270i | 0.168075i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 49.9689 | 1.87927 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 48.1753i | 1.80926i | 0.426194 | + | 0.904632i | \(0.359854\pi\) | ||||
−0.426194 | + | 0.904632i | \(0.640146\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.23175 | 0.121200 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −30.0267 | − | 7.74629i | −1.12451 | − | 0.290101i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 9.62988i | − | 0.360137i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19.5551 | −0.730299 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.1017i | 0.488610i | 0.969698 | + | 0.244305i | \(0.0785599\pi\) | ||||
−0.969698 | + | 0.244305i | \(0.921440\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.4050 | 0.759921 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.39986 | −0.312394 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.706420 | −0.0262358 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.30395 | 0.270888 | 0.135444 | − | 0.990785i | \(-0.456754\pi\) | ||||
0.135444 | + | 0.990785i | \(0.456754\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 9.51513i | − | 0.351930i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.8028i | 0.657563i | 0.944406 | + | 0.328781i | \(0.106638\pi\) | ||||
−0.944406 | + | 0.328781i | \(0.893362\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.43635 | −0.274294 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 49.9581 | 1.84023 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.6415i | 1.12716i | 0.826060 | + | 0.563582i | \(0.190577\pi\) | ||||
−0.826060 | + | 0.563582i | \(0.809423\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.4129i | 0.786623i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.7573 | −0.871572 | −0.435786 | − | 0.900050i | \(-0.643530\pi\) | ||||
−0.435786 | + | 0.900050i | \(0.643530\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.3923 | −0.820392 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.10586 | −0.150226 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 68.0948 | 2.48813 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.6741 | 0.425996 | 0.212998 | − | 0.977053i | \(-0.431677\pi\) | ||||
0.212998 | + | 0.977053i | \(0.431677\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 7.84091i | − | 0.285739i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.9206 | 0.834167 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 16.7159i | − | 0.607551i | −0.952744 | − | 0.303776i | \(-0.901753\pi\) | ||
0.952744 | − | 0.303776i | \(-0.0982473\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17.1362 | − | 4.42080i | −0.622004 | − | 0.160465i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.0602 | 0.908430 | 0.454215 | − | 0.890892i | \(-0.349920\pi\) | ||||
0.454215 | + | 0.890892i | \(0.349920\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 4.83786i | − | 0.175142i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.60151 | −0.0579029 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.7812i | 0.569826i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 21.2483i | − | 0.766234i | −0.923700 | − | 0.383117i | \(-0.874851\pi\) | ||
0.923700 | − | 0.383117i | \(-0.125149\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.18308i | 0.186664i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 19.8965i | − | 0.715628i | −0.933793 | − | 0.357814i | \(-0.883522\pi\) | ||
0.933793 | − | 0.357814i | \(-0.116478\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.46598i | 0.232265i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −19.0655 | −0.683971 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 87.3015 | 3.12790 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 32.0780i | − | 1.14784i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.706420i | 0.0252454i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.5054 | −0.517719 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.36272 | −0.333745 | −0.166873 | − | 0.985978i | \(-0.553367\pi\) | ||||
−0.166873 | + | 0.985978i | \(0.553367\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 6.41083i | − | 0.228232i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 12.6308i | − | 0.449099i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.78393i | 0.311926i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.25579i | 0.257336i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43.4609i | 1.53946i | 0.638367 | + | 0.769732i | \(0.279610\pi\) | ||||
−0.638367 | + | 0.769732i | \(0.720390\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.14708 | 0.252845 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.11034i | 0.180565i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.90760 | −0.0673178 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.6442 | − | 4.55185i | −0.621875 | − | 0.160432i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 28.1418i | − | 0.990640i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.4500 | 1.49246 | 0.746232 | − | 0.665686i | \(-0.231861\pi\) | ||||
0.746232 | + | 0.665686i | \(0.231861\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 38.4953i | − | 1.35175i | −0.737015 | − | 0.675876i | \(-0.763765\pi\) | ||
0.737015 | − | 0.675876i | \(-0.236235\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.8196 | −0.835391 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.70939 | 0.235020 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 48.7507 | 1.70557 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.91534 | −0.346470 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.0615 | 1.15386 | 0.576928 | − | 0.816795i | \(-0.304251\pi\) | ||||
0.576928 | + | 0.816795i | \(0.304251\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.4029i | 1.75693i | 0.477802 | + | 0.878467i | \(0.341434\pi\) | ||||
−0.477802 | + | 0.878467i | \(0.658566\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.69013i | 0.128474i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.6674 | 0.927318 | 0.463659 | − | 0.886014i | \(-0.346536\pi\) | ||||
0.463659 | + | 0.886014i | \(0.346536\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.4837 | 1.54498 | 0.772492 | − | 0.635025i | \(-0.219010\pi\) | ||||
0.772492 | + | 0.635025i | \(0.219010\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.1168i | 0.767224i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.9094i | 0.412637i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.17703 | 0.179159 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.46598 | 0.223497 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.8945 | −0.790404 | −0.395202 | − | 0.918594i | \(-0.629325\pi\) | ||||
−0.395202 | + | 0.918594i | \(0.629325\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5010 | −0.982792 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.5452 | −0.363197 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.18983i | 0.212937i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.94360 | 0.341666 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 13.3512i | − | 0.458213i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.3019 | − | 6.01144i | −0.798780 | − | 0.206070i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.5273 | −0.942516 | −0.471258 | − | 0.881995i | \(-0.656200\pi\) | ||||
−0.471258 | + | 0.881995i | \(0.656200\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 8.20535i | − | 0.280617i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.4676 | 0.938276 | 0.469138 | − | 0.883125i | \(-0.344565\pi\) | ||||
0.469138 | + | 0.883125i | \(0.344565\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 26.7023i | − | 0.911071i | −0.890218 | − | 0.455536i | \(-0.849448\pi\) | ||
0.890218 | − | 0.455536i | \(-0.150552\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 40.4253i | 1.37769i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.7892i | 1.55868i | 0.626600 | + | 0.779341i | \(0.284446\pi\) | ||||
−0.626600 | + | 0.779341i | \(0.715554\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 14.0638i | − | 0.478182i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 14.4352i | − | 0.490243i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.9256 | −0.404547 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.3300 | 1.19711 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 19.4018i | 0.656653i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.79952i | 0.128447i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.1607 | −1.66004 | −0.830019 | − | 0.557735i | \(-0.811671\pi\) | ||||
−0.830019 | + | 0.557735i | \(0.811671\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.0456 | 0.440016 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.3938i | 0.687085i | 0.939137 | + | 0.343543i | \(0.111627\pi\) | ||||
−0.939137 | + | 0.343543i | \(0.888373\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.8470i | 1.67749i | 0.544527 | + | 0.838743i | \(0.316709\pi\) | ||||
−0.544527 | + | 0.838743i | \(0.683291\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 6.04730i | − | 0.203278i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 30.4376i | − | 1.02200i | −0.859582 | − | 0.510998i | \(-0.829276\pi\) | ||
0.859582 | − | 0.510998i | \(-0.170724\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 59.7133i | 2.00272i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.69013 | 0.123624 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36.6180i | 1.22537i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.9606 | 0.399798 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.1186 | − | 3.12635i | −0.404627 | − | 0.104386i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 4.56770i | − | 0.152341i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.6203 | 0.387127 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22.5742i | 0.751223i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.90385 | 0.0632862 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.3539 | 0.343795 | 0.171898 | − | 0.985115i | \(-0.445010\pi\) | ||||
0.171898 | + | 0.985115i | \(0.445010\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.1514 | −0.436203 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.1853 | 1.33140 | 0.665699 | − | 0.746220i | \(-0.268133\pi\) | ||||
0.665699 | + | 0.746220i | \(0.268133\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.1512 | 0.501430 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 3.36597i | − | 0.111275i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 40.0641i | − | 1.32303i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.2326 | 1.19520 | 0.597601 | − | 0.801793i | \(-0.296121\pi\) | ||||
0.597601 | + | 0.801793i | \(0.296121\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.4269 | −0.804893 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 22.6853i | − | 0.746696i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.01787i | 0.164987i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.37041 | −0.176387 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −58.9418 | −1.93382 | −0.966909 | − | 0.255121i | \(-0.917885\pi\) | ||||
−0.966909 | + | 0.255121i | \(0.917885\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −61.0179 | −1.99978 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.74305 | −0.0898035 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.90980 | 0.193271 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 60.0374i | 1.96134i | 0.195681 | + | 0.980668i | \(0.437308\pi\) | ||||
−0.195681 | + | 0.980668i | \(0.562692\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.88307 | 0.126719 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 54.3566i | 1.77198i | 0.463709 | + | 0.885988i | \(0.346518\pi\) | ||||
−0.463709 | + | 0.885988i | \(0.653482\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.7463 | + | 49.4080i | −0.415076 | + | 1.60895i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.79952 | 0.123598 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.9091i | 0.386995i | 0.981101 | + | 0.193498i | \(0.0619832\pi\) | ||||
−0.981101 | + | 0.193498i | \(0.938017\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.34904 | −0.0437917 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.5346i | 0.860444i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.43091i | 0.273104i | 0.990633 | + | 0.136552i | \(0.0436021\pi\) | ||||
−0.990633 | + | 0.136552i | \(0.956398\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 16.6906i | − | 0.540096i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 2.60678i | − | 0.0842653i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.37804i | 0.205958i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.8089 | −0.348675 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.9219 | −0.577526 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.9024i | 0.383151i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.93945i | 0.0623686i | 0.999514 | + | 0.0311843i | \(0.00992788\pi\) | ||||
−0.999514 | + | 0.0311843i | \(0.990072\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.1410 | −0.422149 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.00608 | −0.224836 | −0.112418 | − | 0.993661i | \(-0.535860\pi\) | ||||
−0.112418 | + | 0.993661i | \(0.535860\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 52.1145i | 1.67071i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.60963i | 0.0835750i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 18.8261i | − | 0.602302i | −0.953576 | − | 0.301151i | \(-0.902629\pi\) | ||
0.953576 | − | 0.301151i | \(-0.0973708\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 18.8578i | − | 0.602699i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.27328i | 0.0406528i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −46.2604 | −1.47548 | −0.737740 | − | 0.675085i | \(-0.764107\pi\) | ||||
−0.737740 | + | 0.675085i | \(0.764107\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 15.3515i | − | 0.489141i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.9561 | −0.539719 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.11776 | + | 27.5903i | −0.226332 | + | 0.877321i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.0493i | 0.319228i | 0.987180 | + | 0.159614i | \(0.0510249\pi\) | ||||
−0.987180 | + | 0.159614i | \(0.948975\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.5918 | 0.907333 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.4361i | 0.552761i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.7460 | −1.10042 | −0.550209 | − | 0.835027i | \(-0.685452\pi\) | ||||
−0.550209 | + | 0.835027i | \(0.685452\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.01787 | 0.158758 |
(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 | 5520.2.be.b.1471.7 | yes | 16 | |
4.3 | odd | 2 | 5520.2.be.a.1471.10 | yes | 16 | ||
23.22 | odd | 2 | 5520.2.be.a.1471.2 | ✓ | 16 | ||
92.91 | even | 2 | inner | 5520.2.be.b.1471.15 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5520.2.be.a.1471.2 | ✓ | 16 | 23.22 | odd | 2 | ||
5520.2.be.a.1471.10 | yes | 16 | 4.3 | odd | 2 | ||
5520.2.be.b.1471.7 | yes | 16 | 1.1 | even | 1 | trivial | |
5520.2.be.b.1471.15 | yes | 16 | 92.91 | even | 2 | inner |