Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,2,Mod(1241,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("4140.1241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.i (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: | \(33.0580664368\) |
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: | \( x^{16} + 62x^{14} + 1303x^{12} + 12842x^{10} + 65359x^{8} + 170834x^{6} + 207293x^{4} + 91366x^{2} + 9604 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1241.5 | ||
Root | \(-2.31631i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4140.1241 |
Dual form | 4140.2.i.a.1241.12 |
$q$-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 \(\left(\mathbb{Z}/4140\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(2071\) | \(3961\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.73994i | − | 0.657637i | −0.944393 | − | 0.328818i | \(-0.893350\pi\) | ||
0.944393 | − | 0.328818i | \(-0.106650\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.48546 | −0.447884 | −0.223942 | − | 0.974603i | \(-0.571893\pi\) | ||||
−0.223942 | + | 0.974603i | \(0.571893\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.14610 | −0.595222 | −0.297611 | − | 0.954687i | \(-0.596190\pi\) | ||||
−0.297611 | + | 0.954687i | \(0.596190\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.22657 | 0.782558 | 0.391279 | − | 0.920272i | \(-0.372033\pi\) | ||||
0.391279 | + | 0.920272i | \(0.372033\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.06099i | 1.16107i | 0.814235 | + | 0.580535i | \(0.197157\pi\) | ||||
−0.814235 | + | 0.580535i | \(0.802843\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.42186 | + | 1.85665i | 0.922022 | + | 0.387137i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.21742i | − | 0.968851i | −0.874832 | − | 0.484426i | \(-0.839029\pi\) | ||
0.874832 | − | 0.484426i | \(-0.160971\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.45116 | −0.979057 | −0.489528 | − | 0.871987i | \(-0.662831\pi\) | ||||
−0.489528 | + | 0.871987i | \(0.662831\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.73994i | 0.294104i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.87861i | − | 0.473241i | −0.971602 | − | 0.236620i | \(-0.923960\pi\) | ||
0.971602 | − | 0.236620i | \(-0.0760398\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.9887i | − | 1.71615i | −0.513525 | − | 0.858074i | \(-0.671661\pi\) | ||
0.513525 | − | 0.858074i | \(-0.328339\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.50476i | 0.686969i | 0.939158 | + | 0.343485i | \(0.111607\pi\) | ||||
−0.939158 | + | 0.343485i | \(0.888393\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.76294i | − | 0.694746i | −0.937727 | − | 0.347373i | \(-0.887074\pi\) | ||
0.937727 | − | 0.347373i | \(-0.112926\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.97260 | 0.567514 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.239954 | 0.0329601 | 0.0164801 | − | 0.999864i | \(-0.494754\pi\) | ||||
0.0164801 | + | 0.999864i | \(0.494754\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.48546 | 0.200300 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 5.20247i | − | 0.677304i | −0.940912 | − | 0.338652i | \(-0.890029\pi\) | ||
0.940912 | − | 0.338652i | \(-0.109971\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.30502i | 0.807275i | 0.914919 | + | 0.403638i | \(0.132254\pi\) | ||||
−0.914919 | + | 0.403638i | \(0.867746\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.14610 | 0.266191 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.61074i | 0.318952i | 0.987202 | + | 0.159476i | \(0.0509805\pi\) | ||||
−0.987202 | + | 0.159476i | \(0.949019\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.17216i | − | 0.376466i | −0.982124 | − | 0.188233i | \(-0.939724\pi\) | ||
0.982124 | − | 0.188233i | \(-0.0602760\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.7765 | −1.84649 | −0.923247 | − | 0.384207i | \(-0.874475\pi\) | ||||
−0.923247 | + | 0.384207i | \(0.874475\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.58462i | 0.294545i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 16.1921i | − | 1.82175i | −0.412682 | − | 0.910875i | \(-0.635408\pi\) | ||
0.412682 | − | 0.910875i | \(-0.364592\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.583836 | 0.0640843 | 0.0320421 | − | 0.999487i | \(-0.489799\pi\) | ||||
0.0320421 | + | 0.999487i | \(0.489799\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.22657 | −0.349971 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.7009 | −1.55829 | −0.779147 | − | 0.626842i | \(-0.784347\pi\) | ||||
−0.779147 | + | 0.626842i | \(0.784347\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.73410i | 0.391440i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 5.06099i | − | 0.519246i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.66138i | − | 0.168687i | −0.996437 | − | 0.0843436i | \(-0.973121\pi\) | ||
0.996437 | − | 0.0843436i | \(-0.0268793\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.21263i | 0.618180i | 0.951033 | + | 0.309090i | \(0.100024\pi\) | ||||
−0.951033 | + | 0.309090i | \(0.899976\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.57047i | 0.351809i | 0.984407 | + | 0.175904i | \(0.0562850\pi\) | ||||
−0.984407 | + | 0.175904i | \(0.943715\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.4060 | −1.77938 | −0.889689 | − | 0.456566i | \(-0.849079\pi\) | ||||
−0.889689 | + | 0.456566i | \(0.849079\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.6728i | 1.69275i | 0.532590 | + | 0.846374i | \(0.321219\pi\) | ||||
−0.532590 | + | 0.846374i | \(0.678781\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.9644 | −1.12551 | −0.562757 | − | 0.826622i | \(-0.690259\pi\) | ||||
−0.562757 | + | 0.826622i | \(0.690259\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.42186 | − | 1.85665i | −0.412341 | − | 0.173133i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 5.61405i | − | 0.514639i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.79340 | −0.799400 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.2155 | −1.35016 | −0.675081 | − | 0.737744i | \(-0.735891\pi\) | ||||
−0.675081 | + | 0.737744i | \(0.735891\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 21.1936i | − | 1.85170i | −0.377897 | − | 0.925848i | \(-0.623353\pi\) | ||
0.377897 | − | 0.925848i | \(-0.376647\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.80583 | 0.763562 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.3615 | −1.65417 | −0.827084 | − | 0.562078i | \(-0.810002\pi\) | ||||
−0.827084 | + | 0.562078i | \(0.810002\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.3341 | −1.04617 | −0.523083 | − | 0.852282i | \(-0.675218\pi\) | ||||
−0.523083 | + | 0.852282i | \(0.675218\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.18795 | 0.266590 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.21742i | 0.433283i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.5487 | 1.02803 | 0.514015 | − | 0.857781i | \(-0.328158\pi\) | ||||
0.514015 | + | 0.857781i | \(0.328158\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.3650 | 1.41314 | 0.706570 | − | 0.707643i | \(-0.250242\pi\) | ||||
0.706570 | + | 0.707643i | \(0.250242\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.45116 | 0.437847 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 17.5785i | − | 1.40291i | −0.712711 | − | 0.701457i | \(-0.752533\pi\) | ||
0.712711 | − | 0.701457i | \(-0.247467\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.23046 | − | 7.69379i | 0.254596 | − | 0.606356i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.0296 | 1.17721 | 0.588606 | − | 0.808420i | \(-0.299677\pi\) | ||||
0.588606 | + | 0.808420i | \(0.299677\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.4559i | 0.886485i | 0.896402 | + | 0.443242i | \(0.146172\pi\) | ||||
−0.896402 | + | 0.443242i | \(0.853828\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.39424 | −0.645711 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 7.36507i | − | 0.559956i | −0.960006 | − | 0.279978i | \(-0.909673\pi\) | ||
0.960006 | − | 0.279978i | \(-0.0903272\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.73994i | − | 0.131527i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.0710i | 0.976975i | 0.872571 | + | 0.488487i | \(0.162451\pi\) | ||||
−0.872571 | + | 0.488487i | \(0.837549\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.0486i | 1.41587i | 0.706276 | + | 0.707937i | \(0.250374\pi\) | ||||
−0.706276 | + | 0.707937i | \(0.749626\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.87861i | 0.211640i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.79295 | −0.350495 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.27526 | 0.309347 | 0.154673 | − | 0.987966i | \(-0.450567\pi\) | ||||
0.154673 | + | 0.987966i | \(0.450567\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.8399 | −1.35613 | −0.678063 | − | 0.735004i | \(-0.737180\pi\) | ||||
−0.678063 | + | 0.735004i | \(0.737180\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 26.8545i | − | 1.91330i | −0.291233 | − | 0.956652i | \(-0.594065\pi\) | ||
0.291233 | − | 0.956652i | \(-0.405935\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 10.8944i | − | 0.772282i | −0.922440 | − | 0.386141i | \(-0.873808\pi\) | ||
0.922440 | − | 0.386141i | \(-0.126192\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.07802 | −0.637152 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.9887i | 0.767485i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 7.51790i | − | 0.520024i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.8858 | 0.955941 | 0.477970 | − | 0.878376i | \(-0.341373\pi\) | ||||
0.477970 | + | 0.878376i | \(0.341373\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 4.50476i | − | 0.307222i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.48470i | 0.643864i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.92455 | −0.465796 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.1599 | −1.35001 | −0.675003 | − | 0.737815i | \(-0.735858\pi\) | ||||
−0.675003 | + | 0.737815i | \(0.735858\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.4260 | 1.35572 | 0.677861 | − | 0.735190i | \(-0.262907\pi\) | ||||
0.677861 | + | 0.735190i | \(0.262907\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 12.6822i | − | 0.838064i | −0.907971 | − | 0.419032i | \(-0.862369\pi\) | ||
0.907971 | − | 0.419032i | \(-0.137631\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 18.4814i | − | 1.21076i | −0.795938 | − | 0.605378i | \(-0.793022\pi\) | ||
0.795938 | − | 0.605378i | \(-0.206978\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.76294i | 0.310700i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.96320i | 0.644466i | 0.946660 | + | 0.322233i | \(0.104433\pi\) | ||||
−0.946660 | + | 0.322233i | \(0.895567\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.57276i | 0.294557i | 0.989095 | + | 0.147279i | \(0.0470514\pi\) | ||||
−0.989095 | + | 0.147279i | \(0.952949\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.97260 | −0.253800 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 10.8614i | − | 0.691094i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.15628 | 0.136103 | 0.0680515 | − | 0.997682i | \(-0.478322\pi\) | ||||
0.0680515 | + | 0.997682i | \(0.478322\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.56851 | − | 2.75798i | −0.412959 | − | 0.173392i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 18.9962i | − | 1.18495i | −0.805589 | − | 0.592474i | \(-0.798151\pi\) | ||
0.805589 | − | 0.592474i | \(-0.201849\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.00862 | −0.311221 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.44986 | 0.0894022 | 0.0447011 | − | 0.999000i | \(-0.485766\pi\) | ||||
0.0447011 | + | 0.999000i | \(0.485766\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.239954 | −0.0147402 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 10.9723i | − | 0.668992i | −0.942397 | − | 0.334496i | \(-0.891434\pi\) | ||
0.942397 | − | 0.334496i | \(-0.108566\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.9514 | −1.15122 | −0.575608 | − | 0.817726i | \(-0.695235\pi\) | ||||
−0.575608 | + | 0.817726i | \(0.695235\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.48546 | −0.0895767 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.76990 | 0.286595 | 0.143298 | − | 0.989680i | \(-0.454229\pi\) | ||||
0.143298 | + | 0.989680i | \(0.454229\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.47200 | 0.505397 | 0.252699 | − | 0.967545i | \(-0.418682\pi\) | ||||
0.252699 | + | 0.967545i | \(0.418682\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 3.48520i | − | 0.207174i | −0.994620 | − | 0.103587i | \(-0.966968\pi\) | ||
0.994620 | − | 0.103587i | \(-0.0330320\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −19.1197 | −1.12860 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.58925 | −0.387603 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.5320 | −0.965811 | −0.482905 | − | 0.875672i | \(-0.660419\pi\) | ||||
−0.482905 | + | 0.875672i | \(0.660419\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.20247i | 0.302899i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.48977 | − | 3.98455i | −0.548808 | − | 0.230433i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.83802 | 0.451776 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 6.30502i | − | 0.361024i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.9569 | −0.739491 | −0.369746 | − | 0.929133i | \(-0.620555\pi\) | ||||
−0.369746 | + | 0.929133i | \(0.620555\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.07291i | 0.117544i | 0.998271 | + | 0.0587720i | \(0.0187185\pi\) | ||||
−0.998271 | + | 0.0587720i | \(0.981282\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.21330i | 0.520767i | 0.965505 | + | 0.260383i | \(0.0838489\pi\) | ||||
−0.965505 | + | 0.260383i | \(0.916151\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.62477i | − | 0.0912560i | −0.998958 | − | 0.0456280i | \(-0.985471\pi\) | ||
0.998958 | − | 0.0456280i | \(-0.0145289\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.75028i | 0.433933i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.3296i | 0.908605i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.14610 | −0.119044 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.28725 | −0.456891 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.7992 | 0.868402 | 0.434201 | − | 0.900816i | \(-0.357031\pi\) | ||||
0.434201 | + | 0.900816i | \(0.357031\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 2.61074i | − | 0.142640i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.58536i | 0.140834i | 0.997518 | + | 0.0704169i | \(0.0224330\pi\) | ||||
−0.997518 | + | 0.0704169i | \(0.977567\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.09748 | 0.438503 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.0917i | − | 1.03085i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.459390i | 0.0246614i | 0.999924 | + | 0.0123307i | \(0.00392508\pi\) | ||||
−0.999924 | + | 0.0123307i | \(0.996075\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.8616 | −1.11670 | −0.558348 | − | 0.829607i | \(-0.688565\pi\) | ||||
−0.558348 | + | 0.829607i | \(0.688565\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 27.4459i | − | 1.46080i | −0.683020 | − | 0.730400i | \(-0.739334\pi\) | ||
0.683020 | − | 0.730400i | \(-0.260666\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.17216i | 0.168361i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.9440 | −0.788716 | −0.394358 | − | 0.918957i | \(-0.629033\pi\) | ||||
−0.394358 | + | 0.918957i | \(0.629033\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.61358 | −0.348083 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.7765 | 0.825777 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 10.6253i | − | 0.554636i | −0.960778 | − | 0.277318i | \(-0.910554\pi\) | ||
0.960778 | − | 0.277318i | \(-0.0894456\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 0.417505i | − | 0.0216758i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.2372i | 0.737173i | 0.929593 | + | 0.368587i | \(0.120158\pi\) | ||||
−0.929593 | + | 0.368587i | \(0.879842\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.1971i | 0.576681i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7.81778i | − | 0.401572i | −0.979635 | − | 0.200786i | \(-0.935650\pi\) | ||
0.979635 | − | 0.200786i | \(-0.0643496\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.0636 | 1.68947 | 0.844737 | − | 0.535182i | \(-0.179757\pi\) | ||||
0.844737 | + | 0.535182i | \(0.179757\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 2.58462i | − | 0.131724i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.1348 | 0.615259 | 0.307630 | − | 0.951506i | \(-0.400464\pi\) | ||||
0.307630 | + | 0.951506i | \(0.400464\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.2674 | + | 5.99060i | 0.721536 | + | 0.302957i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.1921i | 0.814711i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.46588 | −0.0735704 | −0.0367852 | − | 0.999323i | \(-0.511712\pi\) | ||||
−0.0367852 | + | 0.999323i | \(0.511712\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.10416 | −0.155014 | −0.0775071 | − | 0.996992i | \(-0.524696\pi\) | ||||
−0.0775071 | + | 0.996992i | \(0.524696\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.6987 | 0.582756 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.27607i | 0.211957i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.1259 | −1.19295 | −0.596475 | − | 0.802632i | \(-0.703432\pi\) | ||||
−0.596475 | + | 0.802632i | \(0.703432\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.05200 | −0.445420 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.583836 | −0.0286594 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.4432 | −0.852158 | −0.426079 | − | 0.904686i | \(-0.640105\pi\) | ||||
−0.426079 | + | 0.904686i | \(0.640105\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.3486i | 0.991729i | 0.868400 | + | 0.495864i | \(0.165149\pi\) | ||||
−0.868400 | + | 0.495864i | \(0.834851\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.22657 | 0.156512 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.9704 | 0.530894 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.4974 | 1.46901 | 0.734505 | − | 0.678603i | \(-0.237414\pi\) | ||||
0.734505 | + | 0.678603i | \(0.237414\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 19.0844i | − | 0.917137i | −0.888659 | − | 0.458568i | \(-0.848362\pi\) | ||
0.888659 | − | 0.458568i | \(-0.151638\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.39646 | + | 22.3790i | −0.449494 | + | 1.07053i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.7420 | 1.41951 | 0.709753 | − | 0.704451i | \(-0.248807\pi\) | ||||
0.709753 | + | 0.704451i | \(0.248807\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 11.9964i | − | 0.569965i | −0.958533 | − | 0.284983i | \(-0.908012\pi\) | ||
0.958533 | − | 0.284983i | \(-0.0919878\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.7009 | 0.696890 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.01821i | 0.0480525i | 0.999711 | + | 0.0240263i | \(0.00764853\pi\) | ||||
−0.999711 | + | 0.0240263i | \(0.992351\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.3233i | 0.768635i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 3.73410i | − | 0.175057i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 26.4418i | − | 1.23689i | −0.785826 | − | 0.618447i | \(-0.787762\pi\) | ||
0.785826 | − | 0.618447i | \(-0.212238\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 35.5680i | − | 1.65657i | −0.560309 | − | 0.828284i | \(-0.689317\pi\) | ||
0.560309 | − | 0.828284i | \(-0.310683\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.1095 | 1.07399 | 0.536995 | − | 0.843586i | \(-0.319560\pi\) | ||||
0.536995 | + | 0.843586i | \(0.319560\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.60164 | 0.259213 | 0.129607 | − | 0.991566i | \(-0.458629\pi\) | ||||
0.129607 | + | 0.991566i | \(0.458629\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.54254 | 0.209755 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 6.69165i | − | 0.307682i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.06099i | 0.232214i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.0470 | −0.641825 | −0.320912 | − | 0.947109i | \(-0.603990\pi\) | ||||
−0.320912 | + | 0.947109i | \(0.603990\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.17780i | 0.281683i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.66138i | 0.0754392i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.3972 | −1.55868 | −0.779342 | − | 0.626598i | \(-0.784447\pi\) | ||||
−0.779342 | + | 0.626598i | \(0.784447\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.4728i | 1.78138i | 0.454610 | + | 0.890691i | \(0.349779\pi\) | ||||
−0.454610 | + | 0.890691i | \(0.650221\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 16.8344i | − | 0.758182i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.51938 | −0.247578 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.1017 | 0.855108 | 0.427554 | − | 0.903990i | \(-0.359375\pi\) | ||||
0.427554 | + | 0.903990i | \(0.359375\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.1989 | −0.454749 | −0.227374 | − | 0.973807i | \(-0.573014\pi\) | ||||
−0.227374 | + | 0.973807i | \(0.573014\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 6.21263i | − | 0.276458i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 0.706053i | − | 0.0312953i | −0.999878 | − | 0.0156476i | \(-0.995019\pi\) | ||
0.999878 | − | 0.0156476i | \(-0.00498100\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.4501i | 1.21432i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 3.57047i | − | 0.157334i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.07517i | 0.311166i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.3159 | 1.67865 | 0.839325 | − | 0.543630i | \(-0.182951\pi\) | ||||
0.839325 | + | 0.543630i | \(0.182951\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.1352i | 1.23027i | 0.788423 | + | 0.615133i | \(0.210898\pi\) | ||||
−0.788423 | + | 0.615133i | \(0.789102\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.5885 | −0.766169 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.1057 | + | 16.4197i | 0.700249 | + | 0.713898i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.5829i | 1.02149i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.4060 | 0.795762 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.90114 | −0.254180 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.9400 | −0.943272 | −0.471636 | − | 0.881793i | \(-0.656336\pi\) | ||||
−0.471636 | + | 0.881793i | \(0.656336\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 17.6728i | − | 0.757020i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.611160 | −0.0261313 | −0.0130657 | − | 0.999915i | \(-0.504159\pi\) | ||||
−0.0130657 | + | 0.999915i | \(0.504159\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26.4053 | 1.12490 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.1733 | −1.19805 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.5939 | 1.04208 | 0.521039 | − | 0.853533i | \(-0.325545\pi\) | ||||
0.521039 | + | 0.853533i | \(0.325545\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.66767i | − | 0.408899i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.35384 | −0.225637 | −0.112819 | − | 0.993616i | \(-0.535988\pi\) | ||||
−0.112819 | + | 0.993616i | \(0.535988\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.9644 | 0.503345 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.18277 | −0.133429 | −0.0667144 | − | 0.997772i | \(-0.521252\pi\) | ||||
−0.0667144 | + | 0.997772i | \(0.521252\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 20.9849i | − | 0.878191i | −0.898440 | − | 0.439096i | \(-0.855299\pi\) | ||
0.898440 | − | 0.439096i | \(-0.144701\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.42186 | + | 1.85665i | 0.184404 | + | 0.0774275i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.1387 | −0.838384 | −0.419192 | − | 0.907897i | \(-0.637687\pi\) | ||||
−0.419192 | + | 0.907897i | \(0.637687\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1.01584i | − | 0.0421442i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.356442 | −0.0147623 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 45.4769i | 1.87703i | 0.345237 | + | 0.938516i | \(0.387799\pi\) | ||||
−0.345237 | + | 0.938516i | \(0.612201\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 27.5882i | − | 1.13675i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.0282i | 0.986722i | 0.869825 | + | 0.493361i | \(0.164232\pi\) | ||||
−0.869825 | + | 0.493361i | \(0.835768\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.61405i | 0.230154i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.54733i | 0.104081i | 0.998645 | + | 0.0520406i | \(0.0165725\pi\) | ||||
−0.998645 | + | 0.0520406i | \(0.983427\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.7927 | 0.521825 | 0.260913 | − | 0.965362i | \(-0.415977\pi\) | ||||
0.260913 | + | 0.965362i | \(0.415977\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.79340 | 0.357503 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.4815 | 0.912497 | 0.456248 | − | 0.889852i | \(-0.349193\pi\) | ||||
0.456248 | + | 0.889852i | \(0.349193\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.2218i | 0.413528i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1.99075i | − | 0.0804055i | −0.999192 | − | 0.0402027i | \(-0.987200\pi\) | ||
0.999192 | − | 0.0402027i | \(-0.0128004\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −46.5579 | −1.87435 | −0.937175 | − | 0.348860i | \(-0.886569\pi\) | ||||
−0.937175 | + | 0.348860i | \(0.886569\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 25.2164i | − | 1.01353i | −0.862084 | − | 0.506766i | \(-0.830841\pi\) | ||
0.862084 | − | 0.506766i | \(-0.169159\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 25.5787i | 1.02479i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 9.28804i | − | 0.370338i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 49.3547i | 1.96478i | 0.186840 | + | 0.982390i | \(0.440175\pi\) | ||||
−0.186840 | + | 0.982390i | \(0.559825\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.2155 | 0.603810 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.52560 | −0.337797 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.85956 | −0.310434 | −0.155217 | − | 0.987880i | \(-0.549608\pi\) | ||||
−0.155217 | + | 0.987880i | \(0.549608\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.93166i | 0.352230i | 0.984370 | + | 0.176115i | \(0.0563531\pi\) | ||||
−0.984370 | + | 0.176115i | \(0.943647\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 3.29757i | − | 0.129641i | −0.997897 | − | 0.0648204i | \(-0.979353\pi\) | ||
0.997897 | − | 0.0648204i | \(-0.0206474\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.72807i | 0.303353i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.1565i | 1.29752i | 0.760995 | + | 0.648758i | \(0.224711\pi\) | ||||
−0.760995 | + | 0.648758i | \(0.775289\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.1936i | 0.828103i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.27163 | −0.127444 | −0.0637222 | − | 0.997968i | \(-0.520297\pi\) | ||||
−0.0637222 | + | 0.997968i | \(0.520297\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.2040i | 1.79713i | 0.438844 | + | 0.898563i | \(0.355388\pi\) | ||||
−0.438844 | + | 0.898563i | \(0.644612\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.80583 | −0.341475 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.68690 | − | 23.0707i | 0.375078 | − | 0.893302i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 9.36587i | − | 0.361565i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.4260 | 1.63540 | 0.817701 | − | 0.575643i | \(-0.195248\pi\) | ||||
0.817701 | + | 0.575643i | \(0.195248\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.8444 | −1.18545 | −0.592723 | − | 0.805407i | \(-0.701947\pi\) | ||||
−0.592723 | + | 0.805407i | \(0.701947\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.89070 | −0.110935 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 12.4892i | − | 0.477887i | −0.971033 | − | 0.238944i | \(-0.923199\pi\) | ||
0.971033 | − | 0.238944i | \(-0.0768011\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.3615 | 0.739767 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.514965 | −0.0196186 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.2420 | 1.07438 | 0.537189 | − | 0.843462i | \(-0.319486\pi\) | ||||
0.537189 | + | 0.843462i | \(0.319486\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.3341 | 0.467859 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 35.4558i | − | 1.34299i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.8720 | 0.561708 | 0.280854 | − | 0.959751i | \(-0.409382\pi\) | ||||
0.280854 | + | 0.959751i | \(0.409382\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.5686 | 0.549466 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.8096 | 0.406538 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 24.4780i | − | 0.919290i | −0.888103 | − | 0.459645i | \(-0.847977\pi\) | ||
0.888103 | − | 0.459645i | \(-0.152023\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.1043 | − | 10.1209i | −0.902712 | − | 0.379029i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.18795 | −0.119223 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.4680i | 0.539566i | 0.962921 | + | 0.269783i | \(0.0869520\pi\) | ||||
−0.962921 | + | 0.269783i | \(0.913048\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.21242 | 0.231362 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 5.21742i | − | 0.193770i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 36.4058i | − | 1.35022i | −0.737718 | − | 0.675109i | \(-0.764097\pi\) | ||
0.737718 | − | 0.675109i | \(-0.235903\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.5349i | 0.537593i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 39.6907i | − | 1.46601i | −0.680223 | − | 0.733005i | \(-0.738117\pi\) | ||
0.680223 | − | 0.733005i | \(-0.261883\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 3.87815i | − | 0.142854i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.6534 | −0.980462 | −0.490231 | − | 0.871592i | \(-0.663088\pi\) | ||||
−0.490231 | + | 0.871592i | \(0.663088\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.33994 | −0.159217 | −0.0796085 | − | 0.996826i | \(-0.525367\pi\) | ||||
−0.0796085 | + | 0.996826i | \(0.525367\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.5487 | −0.459749 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 32.0255i | 1.17018i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.0717i | 0.805408i | 0.915330 | + | 0.402704i | \(0.131930\pi\) | ||||
−0.915330 | + | 0.402704i | \(0.868070\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.3650 | −0.631975 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 28.4839i | − | 1.03527i | −0.855603 | − | 0.517633i | \(-0.826813\pi\) | ||
0.855603 | − | 0.517633i | \(-0.173187\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 29.8896i | − | 1.08350i | −0.840540 | − | 0.541749i | \(-0.817762\pi\) | ||
0.840540 | − | 0.541749i | \(-0.182238\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.7497 | 1.11321 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.1650i | 0.403146i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.87428i | − | 0.0675881i | −0.999429 | − | 0.0337941i | \(-0.989241\pi\) | ||
0.999429 | − | 0.0337941i | \(-0.0107590\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.80634 | −0.244807 | −0.122404 | − | 0.992480i | \(-0.539060\pi\) | ||||
−0.122404 | + | 0.992480i | \(0.539060\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.45116 | −0.195811 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 55.6137 | 1.99257 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.71212i | 0.168613i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.5785i | 0.627403i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 33.9079i | − | 1.20869i | −0.796724 | − | 0.604344i | \(-0.793435\pi\) | ||
0.796724 | − | 0.604344i | \(-0.206565\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.8173i | 0.740179i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 13.5312i | − | 0.480508i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.345368 | 0.0122336 | 0.00611678 | − | 0.999981i | \(-0.498053\pi\) | ||||
0.00611678 | + | 0.999981i | \(0.498053\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 15.3680i | − | 0.543679i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.4353 | 0.827014 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.23046 | + | 7.69379i | −0.113859 | + | 0.271170i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 8.81115i | − | 0.309784i | −0.987931 | − | 0.154892i | \(-0.950497\pi\) | ||
0.987931 | − | 0.154892i | \(-0.0495029\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.96662 | 0.349975 | 0.174988 | − | 0.984571i | \(-0.444011\pi\) | ||||
0.174988 | + | 0.984571i | \(0.444011\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.0296 | −0.526466 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.7985 | −0.797619 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.9308i | 1.00969i | 0.863210 | + | 0.504845i | \(0.168450\pi\) | ||||
−0.863210 | + | 0.504845i | \(0.831550\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.4278 | 1.16522 | 0.582610 | − | 0.812752i | \(-0.302032\pi\) | ||||
0.582610 | + | 0.812752i | \(0.302032\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.3409 | 0.394363 | 0.197182 | − | 0.980367i | \(-0.436821\pi\) | ||||
0.197182 | + | 0.980367i | \(0.436821\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.900479 | 0.0312749 | 0.0156375 | − | 0.999878i | \(-0.495022\pi\) | ||||
0.0156375 | + | 0.999878i | \(0.495022\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.8179 | 0.444113 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 11.4559i | − | 0.396448i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.8397 | 1.27185 | 0.635924 | − | 0.771751i | \(-0.280619\pi\) | ||||
0.635924 | + | 0.771751i | \(0.280619\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.77850 | 0.0613275 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.39424 | 0.288771 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.3000i | 0.525715i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.34456 | − | 12.7288i | 0.183209 | − | 0.436338i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.7815 | −0.574588 | −0.287294 | − | 0.957843i | \(-0.592756\pi\) | ||||
−0.287294 | + | 0.957843i | \(0.592756\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 22.6280i | − | 0.772957i | −0.922298 | − | 0.386479i | \(-0.873691\pi\) | ||
0.922298 | − | 0.386479i | \(-0.126309\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.122682 | −0.00418587 | −0.00209293 | − | 0.999998i | \(-0.500666\pi\) | ||||
−0.00209293 | + | 0.999998i | \(0.500666\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.3766i | 0.421306i | 0.977561 | + | 0.210653i | \(0.0675590\pi\) | ||||
−0.977561 | + | 0.210653i | \(0.932441\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.36507i | 0.250420i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.0527i | 0.815932i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 5.60291i | − | 0.189847i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.73994i | 0.0588208i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.1426 | −1.65943 | −0.829714 | − | 0.558188i | \(-0.811497\pi\) | ||||
−0.829714 | + | 0.558188i | \(0.811497\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.8206 | −0.364554 | −0.182277 | − | 0.983247i | \(-0.558347\pi\) | ||||
−0.182277 | + | 0.983247i | \(0.558347\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.8514 | −1.37476 | −0.687380 | − | 0.726298i | \(-0.741239\pi\) | ||||
−0.687380 | + | 0.726298i | \(0.741239\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45.5013i | 1.52779i | 0.645343 | + | 0.763893i | \(0.276714\pi\) | ||||
−0.645343 | + | 0.763893i | \(0.723286\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.4742i | 0.887916i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.1052 | 0.806649 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 13.0710i | − | 0.436916i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 28.4410i | 0.948560i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.774227 | 0.0257932 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 19.0486i | − | 0.633198i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 40.4240i | − | 1.34226i | −0.741341 | − | 0.671129i | \(-0.765810\pi\) | ||
0.741341 | − | 0.671129i | \(-0.234190\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.5112 | 0.480776 | 0.240388 | − | 0.970677i | \(-0.422725\pi\) | ||||
0.240388 | + | 0.970677i | \(0.422725\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.867265 | −0.0287023 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36.8757 | −1.21774 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 57.0808i | − | 1.88292i | −0.337124 | − | 0.941460i | \(-0.609454\pi\) | ||
0.337124 | − | 0.941460i | \(-0.390546\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.80778i | 0.224081i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.87861i | − | 0.0946482i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.48787i | 0.245669i | 0.992427 | + | 0.122835i | \(0.0391984\pi\) | ||||
−0.992427 | + | 0.122835i | \(0.960802\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.1053i | 0.658923i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.79295 | 0.156746 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.76692i | 0.188397i | 0.995553 | + | 0.0941986i | \(0.0300289\pi\) | ||||
−0.995553 | + | 0.0941986i | \(0.969971\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.0222 | 0.717902 | 0.358951 | − | 0.933356i | \(-0.383134\pi\) | ||||
0.358951 | + | 0.933356i | \(0.383134\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.4021 | − | 48.5906i | 0.664385 | − | 1.58233i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.0318i | 1.30086i | 0.759567 | + | 0.650429i | \(0.225411\pi\) | ||||
−0.759567 | + | 0.650429i | \(0.774589\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.8579 | 1.09907 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.9291 | 0.937105 | 0.468553 | − | 0.883436i | \(-0.344776\pi\) | ||||
0.468553 | + | 0.883436i | \(0.344776\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.27526 | −0.138344 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 33.6880i | 1.08784i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.28490 | −0.0414484 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.8399 | 0.606478 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.3299 | 1.52203 | 0.761014 | − | 0.648736i | \(-0.224702\pi\) | ||||
0.761014 | + | 0.648736i | \(0.224702\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.0244 | 1.22026 | 0.610131 | − | 0.792301i | \(-0.291117\pi\) | ||||
0.610131 | + | 0.792301i | \(0.291117\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.4606i | 0.687997i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.4601 | −0.654575 | −0.327288 | − | 0.944925i | \(-0.606135\pi\) | ||||
−0.327288 | + | 0.944925i | \(0.606135\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.8376 | 0.697934 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.7804 | 0.662792 | 0.331396 | − | 0.943492i | \(-0.392480\pi\) | ||||
0.331396 | + | 0.943492i | \(0.392480\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.8545i | 0.855656i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.36374 | + | 19.9194i | −0.265951 | + | 0.633401i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.91895 | 0.315086 | 0.157543 | − | 0.987512i | \(-0.449643\pi\) | ||||
0.157543 | + | 0.987512i | \(0.449643\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.8944i | 0.345375i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.8855 | 1.10484 | 0.552418 | − | 0.833568i | \(-0.313705\pi\) | ||||
0.552418 | + | 0.833568i | \(0.313705\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4140.2.i.a.1241.5 | ✓ | 16 | |
3.2 | odd | 2 | 4140.2.i.b.1241.5 | yes | 16 | ||
23.22 | odd | 2 | 4140.2.i.b.1241.12 | yes | 16 | ||
69.68 | even | 2 | inner | 4140.2.i.a.1241.12 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.2.i.a.1241.5 | ✓ | 16 | 1.1 | even | 1 | trivial | |
4140.2.i.a.1241.12 | yes | 16 | 69.68 | even | 2 | inner | |
4140.2.i.b.1241.5 | yes | 16 | 3.2 | odd | 2 | ||
4140.2.i.b.1241.12 | yes | 16 | 23.22 | odd | 2 |