Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1104,2,Mod(1,1104)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1104, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1104.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1104 = 2^{4} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1104.a (trivial) |
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: | yes |
Analytic conductor: | \(8.81548438315\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 69) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1104.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.23607 | 0.552786 | 0.276393 | − | 0.961045i | \(-0.410861\pi\) | ||||
0.276393 | + | 0.961045i | \(0.410861\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.23607 | −1.22312 | −0.611559 | − | 0.791199i | \(-0.709457\pi\) | ||||
−0.611559 | + | 0.791199i | \(0.709457\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.47214 | −1.24035 | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.23607 | 0.319151 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.76393 | −0.670352 | −0.335176 | − | 0.942156i | \(-0.608796\pi\) | ||||
−0.335176 | + | 0.942156i | \(0.608796\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.23607 | −1.66007 | −0.830034 | − | 0.557713i | \(-0.811679\pi\) | ||||
−0.830034 | + | 0.557713i | \(0.811679\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.23607 | −0.706168 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.47214 | −0.694427 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.47214 | 1.16243 | 0.581215 | − | 0.813750i | \(-0.302578\pi\) | ||||
0.581215 | + | 0.813750i | \(0.302578\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | −0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.00000 | −0.676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.47214 | 0.735215 | 0.367607 | − | 0.929981i | \(-0.380177\pi\) | ||||
0.367607 | + | 0.929981i | \(0.380177\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.47214 | −0.716115 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.9443 | −1.70921 | −0.854604 | − | 0.519280i | \(-0.826200\pi\) | ||||
−0.854604 | + | 0.519280i | \(0.826200\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.70820 | 0.870493 | 0.435246 | − | 0.900311i | \(-0.356661\pi\) | ||||
0.435246 | + | 0.900311i | \(0.356661\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.23607 | 0.184262 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.00000 | 0.583460 | 0.291730 | − | 0.956501i | \(-0.405769\pi\) | ||||
0.291730 | + | 0.956501i | \(0.405769\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.47214 | 0.496019 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.76393 | −0.387028 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.23607 | −0.719229 | −0.359615 | − | 0.933101i | \(-0.617092\pi\) | ||||
−0.359615 | + | 0.933101i | \(0.617092\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.94427 | −0.666685 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.23607 | −0.958441 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.94427 | 0.643689 | 0.321845 | − | 0.946792i | \(-0.395697\pi\) | ||||
0.321845 | + | 0.946792i | \(0.395697\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.47214 | 0.572598 | 0.286299 | − | 0.958140i | \(-0.407575\pi\) | ||||
0.286299 | + | 0.958140i | \(0.407575\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.23607 | −0.407706 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.52786 | −0.685647 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.763932 | −0.0933292 | −0.0466646 | − | 0.998911i | \(-0.514859\pi\) | ||||
−0.0466646 | + | 0.998911i | \(0.514859\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.94427 | 0.812766 | 0.406383 | − | 0.913703i | \(-0.366790\pi\) | ||||
0.406383 | + | 0.913703i | \(0.366790\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.47214 | −0.400928 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.9443 | 1.47514 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.70820 | −1.09226 | −0.546129 | − | 0.837701i | \(-0.683899\pi\) | ||||
−0.546129 | + | 0.837701i | \(0.683899\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.41641 | −0.370561 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.47214 | 0.479463 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.23607 | −0.131023 | −0.0655115 | − | 0.997852i | \(-0.520868\pi\) | ||||
−0.0655115 | + | 0.997852i | \(0.520868\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.4721 | 1.51709 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.47214 | 0.671129 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.94427 | −0.917663 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.47214 | 0.860215 | 0.430108 | − | 0.902778i | \(-0.358476\pi\) | ||||
0.430108 | + | 0.902778i | \(0.358476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.94427 | −0.690981 | −0.345490 | − | 0.938422i | \(-0.612287\pi\) | ||||
−0.345490 | + | 0.938422i | \(0.612287\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.2361 | 1.10712 | 0.553561 | − | 0.832808i | \(-0.313268\pi\) | ||||
0.553561 | + | 0.832808i | \(0.313268\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.00000 | −0.390360 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.9443 | −1.63806 | −0.819032 | − | 0.573747i | \(-0.805489\pi\) | ||||
−0.819032 | + | 0.573747i | \(0.805489\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.9443 | −1.43140 | −0.715701 | − | 0.698407i | \(-0.753893\pi\) | ||||
−0.715701 | + | 0.698407i | \(0.753893\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.47214 | 0.424476 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.18034 | −0.581397 | −0.290699 | − | 0.956815i | \(-0.593888\pi\) | ||||
−0.290699 | + | 0.956815i | \(0.593888\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.23607 | −0.115264 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.47214 | −0.413449 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.94427 | 0.819920 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.9443 | −0.986812 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.4721 | −0.936656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.52786 | −0.135576 | −0.0677880 | − | 0.997700i | \(-0.521594\pi\) | ||||
−0.0677880 | + | 0.997700i | \(0.521594\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.70820 | 0.502579 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.9443 | −1.48043 | −0.740214 | − | 0.672371i | \(-0.765276\pi\) | ||||
−0.740214 | + | 0.672371i | \(0.765276\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23.4164 | 2.03046 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.23607 | 0.106384 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.23607 | −0.105604 | −0.0528022 | − | 0.998605i | \(-0.516815\pi\) | ||||
−0.0528022 | + | 0.998605i | \(0.516815\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.94427 | 0.758643 | 0.379322 | − | 0.925265i | \(-0.376157\pi\) | ||||
0.379322 | + | 0.925265i | \(0.376157\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.00000 | 0.336861 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.8885 | 1.49592 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.52786 | 0.459064 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.47214 | 0.286377 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.7082 | −0.959173 | −0.479587 | − | 0.877494i | \(-0.659213\pi\) | ||||
−0.479587 | + | 0.877494i | \(0.659213\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0000 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.76393 | −0.223451 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000 | 0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.52786 | −0.281554 | −0.140777 | − | 0.990041i | \(-0.544960\pi\) | ||||
−0.140777 | + | 0.990041i | \(0.544960\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.23607 | −0.415247 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.23607 | 0.255038 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.41641 | −0.580898 | −0.290449 | − | 0.956890i | \(-0.593805\pi\) | ||||
−0.290449 | + | 0.956890i | \(0.593805\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.94427 | −0.384911 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.9443 | −1.00166 | −0.500829 | − | 0.865546i | \(-0.666971\pi\) | ||||
−0.500829 | + | 0.865546i | \(0.666971\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.23607 | −0.553356 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.47214 | 0.340010 | 0.170005 | − | 0.985443i | \(-0.445622\pi\) | ||||
0.170005 | + | 0.985443i | \(0.445622\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.2361 | 0.849367 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.94427 | 0.371634 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.9443 | −1.56545 | −0.782724 | − | 0.622369i | \(-0.786170\pi\) | ||||
−0.782724 | + | 0.622369i | \(0.786170\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.8885 | −0.883669 | −0.441834 | − | 0.897097i | \(-0.645672\pi\) | ||||
−0.441834 | + | 0.897097i | \(0.645672\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.47214 | 0.330590 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.52786 | 0.406417 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.0557 | 0.808475 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.23607 | −0.235389 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.52786 | −0.110552 | −0.0552762 | − | 0.998471i | \(-0.517604\pi\) | ||||
−0.0552762 | + | 0.998471i | \(0.517604\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.4164 | 1.25366 | 0.626830 | − | 0.779156i | \(-0.284352\pi\) | ||||
0.626830 | + | 0.779156i | \(0.284352\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.52786 | −0.395859 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.4164 | 1.24087 | 0.620434 | − | 0.784259i | \(-0.286957\pi\) | ||||
0.620434 | + | 0.784259i | \(0.286957\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.70820 | −0.688196 | −0.344098 | − | 0.938934i | \(-0.611815\pi\) | ||||
−0.344098 | + | 0.938934i | \(0.611815\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.763932 | −0.0538836 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.4721 | −1.01574 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.5279 | −0.944827 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 28.9443 | 2.00212 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.5279 | −0.931297 | −0.465648 | − | 0.884970i | \(-0.654179\pi\) | ||||
−0.465648 | + | 0.884970i | \(0.654179\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.00000 | 0.548151 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.05573 | 0.481197 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.9443 | −1.42179 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.94427 | 0.469250 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.3607 | 0.831469 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.8885 | 1.73363 | 0.866813 | − | 0.498634i | \(-0.166165\pi\) | ||||
0.866813 | + | 0.498634i | \(0.166165\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.47214 | −0.231476 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.5279 | 0.897876 | 0.448938 | − | 0.893563i | \(-0.351802\pi\) | ||||
0.448938 | + | 0.893563i | \(0.351802\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.94427 | 0.194563 | 0.0972815 | − | 0.995257i | \(-0.468985\pi\) | ||||
0.0972815 | + | 0.995257i | \(0.468985\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.9443 | 0.851671 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.0000 | −0.917170 | −0.458585 | − | 0.888650i | \(-0.651644\pi\) | ||||
−0.458585 | + | 0.888650i | \(0.651644\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.94427 | 0.322529 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.70820 | −0.630616 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.94427 | −0.319818 | −0.159909 | − | 0.987132i | \(-0.551120\pi\) | ||||
−0.159909 | + | 0.987132i | \(0.551120\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.5279 | 1.25790 | 0.628950 | − | 0.777446i | \(-0.283485\pi\) | ||||
0.628950 | + | 0.777446i | \(0.283485\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.29180 | 0.274193 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 32.3607 | 2.05906 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.00000 | −0.253490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.4721 | 0.660995 | 0.330498 | − | 0.943807i | \(-0.392783\pi\) | ||||
0.330498 | + | 0.943807i | \(0.392783\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.41641 | −0.213944 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.0000 | −1.37232 | −0.686161 | − | 0.727450i | \(-0.740706\pi\) | ||||
−0.686161 | + | 0.727450i | \(0.740706\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.4721 | −0.899255 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.47214 | 0.276818 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.47214 | −0.399089 | −0.199544 | − | 0.979889i | \(-0.563946\pi\) | ||||
−0.199544 | + | 0.979889i | \(0.563946\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.47214 | −0.397580 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.23607 | −0.0756461 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.472136 | −0.0287866 | −0.0143933 | − | 0.999896i | \(-0.504582\pi\) | ||||
−0.0143933 | + | 0.999896i | \(0.504582\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.5279 | 1.06474 | 0.532371 | − | 0.846511i | \(-0.321301\pi\) | ||||
0.532371 | + | 0.846511i | \(0.321301\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.4721 | 0.875894 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.8885 | 0.837511 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.8885 | 0.954650 | 0.477325 | − | 0.878727i | \(-0.341606\pi\) | ||||
0.477325 | + | 0.878727i | \(0.341606\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.47214 | 0.387477 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.6525 | 1.47064 | 0.735322 | − | 0.677718i | \(-0.237031\pi\) | ||||
0.735322 | + | 0.677718i | \(0.237031\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.70820 | −0.339318 | −0.169659 | − | 0.985503i | \(-0.554267\pi\) | ||||
−0.169659 | + | 0.985503i | \(0.554267\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.94427 | −0.529813 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 35.4164 | 2.09056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.36068 | −0.550628 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.47214 | 0.496645 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.70820 | 0.450318 | 0.225159 | − | 0.974322i | \(-0.427710\pi\) | ||||
0.225159 | + | 0.974322i | \(0.427710\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.11146 | 0.355823 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.00000 | −0.232104 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.47214 | 0.258630 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.4721 | −1.06472 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.94427 | −0.398938 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.52786 | 0.316525 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.47214 | −0.141092 | −0.0705461 | − | 0.997509i | \(-0.522474\pi\) | ||||
−0.0705461 | + | 0.997509i | \(0.522474\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.2361 | 0.639198 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.05573 | −0.400094 | −0.200047 | − | 0.979786i | \(-0.564109\pi\) | ||||
−0.200047 | + | 0.979786i | \(0.564109\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.05573 | 0.285767 | 0.142883 | − | 0.989740i | \(-0.454363\pi\) | ||||
0.142883 | + | 0.989740i | \(0.454363\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.00000 | −0.225374 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.58359 | 0.145109 | 0.0725545 | − | 0.997364i | \(-0.476885\pi\) | ||||
0.0725545 | + | 0.997364i | \(0.476885\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.8885 | −1.00157 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.9443 | −0.945737 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.0000 | 1.11283 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.5279 | 0.861331 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.9443 | −0.826420 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.9443 | −0.713641 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.4164 | −1.28708 | −0.643541 | − | 0.765412i | \(-0.722535\pi\) | ||||
−0.643541 | + | 0.765412i | \(0.722535\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.47214 | 0.245072 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.944272 | −0.0515911 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.3607 | −0.782276 | −0.391138 | − | 0.920332i | \(-0.627918\pi\) | ||||
−0.391138 | + | 0.920332i | \(0.627918\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.18034 | −0.335670 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25.8885 | −1.40194 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.4164 | 0.616428 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.23607 | −0.0665477 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.88854 | 0.530845 | 0.265422 | − | 0.964132i | \(-0.414489\pi\) | ||||
0.265422 | + | 0.964132i | \(0.414489\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.5279 | −1.25942 | −0.629709 | − | 0.776831i | \(-0.716826\pi\) | ||||
−0.629709 | + | 0.776831i | \(0.716826\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.47214 | −0.238705 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.4164 | −0.926982 | −0.463491 | − | 0.886102i | \(-0.653403\pi\) | ||||
−0.463491 | + | 0.886102i | \(0.653403\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.88854 | 0.524829 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.94427 | 0.473381 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.47214 | −0.341586 | −0.170793 | − | 0.985307i | \(-0.554633\pi\) | ||||
−0.170793 | + | 0.985307i | \(0.554633\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 33.3607 | 1.75583 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.00000 | 0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.58359 | 0.449286 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.7082 | −1.34196 | −0.670979 | − | 0.741477i | \(-0.734126\pi\) | ||||
−0.670979 | + | 0.741477i | \(0.734126\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.9443 | −0.569736 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.9443 | 0.879703 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.4721 | 1.06001 | 0.530004 | − | 0.847995i | \(-0.322191\pi\) | ||||
0.530004 | + | 0.847995i | \(0.322191\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.4721 | −0.540779 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −20.0000 | −1.03005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.0689 | −1.54453 | −0.772267 | − | 0.635298i | \(-0.780877\pi\) | ||||
−0.772267 | + | 0.635298i | \(0.780877\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.52786 | −0.0782748 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.5279 | −1.30441 | −0.652206 | − | 0.758041i | \(-0.726156\pi\) | ||||
−0.652206 | + | 0.758041i | \(0.726156\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.0000 | 0.815436 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.70820 | 0.290164 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.6525 | 1.04712 | 0.523561 | − | 0.851988i | \(-0.324603\pi\) | ||||
0.523561 | + | 0.851988i | \(0.324603\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.76393 | 0.139778 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.9443 | −0.854725 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.0000 | −0.603786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.00000 | −0.100377 | −0.0501886 | − | 0.998740i | \(-0.515982\pi\) | ||||
−0.0501886 | + | 0.998740i | \(0.515982\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 23.4164 | 1.17229 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.0689 | 1.00219 | 0.501096 | − | 0.865392i | \(-0.332930\pi\) | ||||
0.501096 | + | 0.865392i | \(0.332930\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.9443 | −1.44182 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.23607 | 0.0614207 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.8885 | −0.886702 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.4164 | 0.861186 | 0.430593 | − | 0.902546i | \(-0.358304\pi\) | ||||
0.430593 | + | 0.902546i | \(0.358304\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.23607 | −0.0609707 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.0000 | −0.787309 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.94427 | −0.242705 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.94427 | 0.438003 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.8885 | −0.678500 | −0.339250 | − | 0.940696i | \(-0.610173\pi\) | ||||
−0.339250 | + | 0.940696i | \(0.610173\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.9443 | −1.50813 | −0.754066 | − | 0.656799i | \(-0.771910\pi\) | ||||
−0.754066 | + | 0.656799i | \(0.771910\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.00000 | 0.194487 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.59675 | 0.465511 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.4721 | −0.700356 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17.8885 | 0.863667 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.00000 | −0.385346 | −0.192673 | − | 0.981263i | \(-0.561716\pi\) | ||||
−0.192673 | + | 0.981263i | \(0.561716\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.8885 | 1.34024 | 0.670119 | − | 0.742254i | \(-0.266243\pi\) | ||||
0.670119 | + | 0.742254i | \(0.266243\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.52786 | 0.265041 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.23607 | 0.346148 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.88854 | 0.471954 | 0.235977 | − | 0.971759i | \(-0.424171\pi\) | ||||
0.235977 | + | 0.971759i | \(0.424171\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.47214 | 0.165340 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.8328 | 1.65496 | 0.827479 | − | 0.561497i | \(-0.189775\pi\) | ||||
0.827479 | + | 0.561497i | \(0.189775\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.52786 | −0.0724277 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.7082 | −0.553779 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.9443 | 0.705264 | 0.352632 | − | 0.935762i | \(-0.385287\pi\) | ||||
0.352632 | + | 0.935762i | \(0.385287\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 43.7771 | 2.06138 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.0000 | 0.751746 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.8885 | 0.838628 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.47214 | 0.396310 | 0.198155 | − | 0.980171i | \(-0.436505\pi\) | ||||
0.198155 | + | 0.980171i | \(0.436505\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.76393 | −0.129009 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.41641 | −0.252267 | −0.126134 | − | 0.992013i | \(-0.540257\pi\) | ||||
−0.126134 | + | 0.992013i | \(0.540257\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.9443 | 0.601571 | 0.300786 | − | 0.953692i | \(-0.402751\pi\) | ||||
0.300786 | + | 0.953692i | \(0.402751\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.00000 | 0.370991 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.3607 | −0.942180 | −0.471090 | − | 0.882085i | \(-0.656139\pi\) | ||||
−0.471090 | + | 0.882085i | \(0.656139\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.47214 | 0.114153 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.52786 | −0.162555 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.8328 | −1.04985 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.1246 | 1.15280 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.23607 | −0.239743 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.8885 | 1.54841 | 0.774204 | − | 0.632937i | \(-0.218151\pi\) | ||||
0.774204 | + | 0.632937i | \(0.218151\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0000 | −0.911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.23607 | 0.147246 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.4721 | 0.475515 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.0000 | −1.08754 | −0.543772 | − | 0.839233i | \(-0.683004\pi\) | ||||
−0.543772 | + | 0.839233i | \(0.683004\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.41641 | −0.335382 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −40.0000 | −1.80517 | −0.902587 | − | 0.430507i | \(-0.858335\pi\) | ||||
−0.902587 | + | 0.430507i | \(0.858335\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.3607 | −0.556697 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.94427 | −0.222228 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.8885 | −1.16126 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.3607 | 0.553340 | 0.276670 | − | 0.960965i | \(-0.410769\pi\) | ||||
0.276670 | + | 0.960965i | \(0.410769\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.9443 | −0.578307 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.0557 | 0.849653 | 0.424826 | − | 0.905275i | \(-0.360335\pi\) | ||||
0.424826 | + | 0.905275i | \(0.360335\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.58359 | −0.381965 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.00000 | 0.310881 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.4721 | −0.730115 | −0.365057 | − | 0.930985i | \(-0.618951\pi\) | ||||
−0.365057 | + | 0.930985i | \(0.618951\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.4721 | −0.994109 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.23607 | −0.319480 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.8885 | 0.612002 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.0000 | −0.703679 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.47214 | 0.196305 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.2361 | −1.45610 | −0.728049 | − | 0.685525i | \(-0.759573\pi\) | ||||
−0.728049 | + | 0.685525i | \(0.759573\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.5967 | −0.681998 | −0.340999 | − | 0.940064i | \(-0.610765\pi\) | ||||
−0.340999 | + | 0.940064i | \(0.610765\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.2361 | 0.490382 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.8885 | −0.779237 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.94427 | 0.214563 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 48.9443 | 2.12001 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.9443 | −0.905500 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.9443 | −0.903812 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.8885 | −0.598222 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.5279 | −0.667595 | −0.333798 | − | 0.942645i | \(-0.608330\pi\) | ||||
−0.333798 | + | 0.942645i | \(0.608330\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.8885 | −0.510186 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.4721 | −0.791259 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.5279 | −0.578410 | −0.289205 | − | 0.957267i | \(-0.593391\pi\) | ||||
−0.289205 | + | 0.957267i | \(0.593391\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.47214 | 0.190866 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −32.3607 | −1.37861 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 31.4164 | 1.33596 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.52786 | 0.234645 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −42.1803 | −1.78724 | −0.893619 | − | 0.448826i | \(-0.851842\pi\) | ||||
−0.893619 | + | 0.448826i | \(0.851842\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.5279 | −1.07971 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.0557 | 0.466773 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.41641 | 0.312564 | 0.156282 | − | 0.987712i | \(-0.450049\pi\) | ||||
0.156282 | + | 0.987712i | \(0.450049\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.63932 | −0.321389 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.23607 | −0.135902 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.7639 | −0.451248 | −0.225624 | − | 0.974215i | \(-0.572442\pi\) | ||||
−0.225624 | + | 0.974215i | \(0.572442\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.7082 | −1.24325 | −0.621625 | − | 0.783315i | \(-0.713527\pi\) | ||||
−0.621625 | + | 0.783315i | \(0.713527\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.52786 | −0.0638274 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.47214 | 0.144798 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.52786 | 0.313389 | 0.156695 | − | 0.987647i | \(-0.449916\pi\) | ||||
0.156695 | + | 0.987647i | \(0.449916\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.4164 | 0.723801 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.9443 | 0.537019 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.9443 | 0.867423 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.52786 | −0.228549 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.944272 | 0.0389743 | 0.0194871 | − | 0.999810i | \(-0.493797\pi\) | ||||
0.0194871 | + | 0.999810i | \(0.493797\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −46.8328 | −1.92971 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.4164 | 0.716415 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.0000 | 1.39621 | 0.698106 | − | 0.715994i | \(-0.254026\pi\) | ||||
0.698106 | + | 0.715994i | \(0.254026\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.0557 | 0.453241 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.70820 | −0.397330 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.05573 | 0.124854 | 0.0624268 | − | 0.998050i | \(-0.480116\pi\) | ||||
0.0624268 | + | 0.998050i | \(0.480116\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −42.3607 | −1.72793 | −0.863964 | − | 0.503553i | \(-0.832026\pi\) | ||||
−0.863964 | + | 0.503553i | \(0.832026\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.763932 | −0.0311097 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.18034 | 0.251267 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.8328 | 0.602045 | 0.301023 | − | 0.953617i | \(-0.402672\pi\) | ||||
0.301023 | + | 0.953617i | \(0.402672\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.4721 | −0.586441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.8885 | −0.723693 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −40.4721 | −1.63465 | −0.817327 | − | 0.576174i | \(-0.804545\pi\) | ||||
−0.817327 | + | 0.576174i | \(0.804545\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13.5279 | −0.545496 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.2918 | −0.816917 | −0.408458 | − | 0.912777i | \(-0.633934\pi\) | ||||
−0.408458 | + | 0.912777i | \(0.633934\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.12461 | 0.366749 | 0.183375 | − | 0.983043i | \(-0.441298\pi\) | ||||
0.183375 | + | 0.983043i | \(0.441298\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.00000 | 0.160257 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 28.9443 | 1.15592 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.3607 | −0.492853 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.1803 | 0.644129 | 0.322065 | − | 0.946718i | \(-0.395623\pi\) | ||||
0.322065 | + | 0.946718i | \(0.395623\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.5279 | −0.537684 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.88854 | −0.0749446 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.5279 | −0.615236 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.00000 | 0.316475 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 49.0132 | 1.93590 | 0.967952 | − | 0.251137i | \(-0.0808044\pi\) | ||||
0.967952 | + | 0.251137i | \(0.0808044\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.0689 | −1.50129 | −0.750645 | − | 0.660706i | \(-0.770257\pi\) | ||||
−0.750645 | + | 0.660706i | \(0.770257\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.05573 | 0.277819 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.0000 | −0.471769 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.7771 | −0.776319 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.9443 | −0.820871 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.9443 | −0.897879 | −0.448939 | − | 0.893562i | \(-0.648198\pi\) | ||||
−0.448939 | + | 0.893562i | \(0.648198\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.9443 | −0.818360 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.94427 | 0.270922 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.3607 | −1.41641 | −0.708205 | − | 0.706006i | \(-0.750495\pi\) | ||||
−0.708205 | + | 0.706006i | \(0.750495\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.5279 | −0.448382 | −0.224191 | − | 0.974545i | \(-0.571974\pi\) | ||||
−0.224191 | + | 0.974545i | \(0.571974\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.3607 | 0.480049 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 28.9443 | 1.12241 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.47214 | −0.173162 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25.8885 | 1.00091 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.8885 | −0.690580 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.58359 | 0.0995902 | 0.0497951 | − | 0.998759i | \(-0.484143\pi\) | ||||
0.0497951 | + | 0.998759i | \(0.484143\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.47214 | −0.133643 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −47.4853 | −1.82501 | −0.912504 | − | 0.409068i | \(-0.865854\pi\) | ||||
−0.912504 | + | 0.409068i | \(0.865854\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.4164 | −1.05215 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.5279 | 0.518389 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.0000 | 0.765279 | 0.382639 | − | 0.923898i | \(-0.375015\pi\) | ||||
0.382639 | + | 0.923898i | \(0.375015\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.52786 | −0.0583767 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.94427 | 0.112331 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 23.4164 | 0.892094 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.36068 | −0.165888 | −0.0829440 | − | 0.996554i | \(-0.526432\pi\) | ||||
−0.0829440 | + | 0.996554i | \(0.526432\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.9443 | 0.491712 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.0557 | 0.419368 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.2492 | 1.14577 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.0000 | −0.529529 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.2361 | 0.953153 | 0.476577 | − | 0.879133i | \(-0.341878\pi\) | ||||
0.476577 | + | 0.879133i | \(0.341878\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.3607 | −1.22051 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.94427 | 0.186212 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.4721 | 0.845152 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.8328 | −1.23306 | −0.616531 | − | 0.787331i | \(-0.711463\pi\) | ||||
−0.616531 | + | 0.787331i | \(0.711463\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.70820 | −0.364086 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.47214 | −0.242383 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.1115 | 0.826922 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.94427 | −0.184647 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.00000 | −0.149175 | −0.0745874 | − | 0.997214i | \(-0.523764\pi\) | ||||
−0.0745874 | + | 0.997214i | \(0.523764\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −36.3607 | −1.35414 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.5279 | 0.726249 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.5279 | −0.576690 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.34752 | −0.0499769 | −0.0249885 | − | 0.999688i | \(-0.507955\pi\) | ||||
−0.0249885 | + | 0.999688i | \(0.507955\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.7771 | −0.583537 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.0000 | 0.812589 | 0.406294 | − | 0.913742i | \(-0.366821\pi\) | ||||
0.406294 | + | 0.913742i | \(0.366821\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.29180 | 0.158305 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.05573 | 0.112559 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.8328 | 0.987061 | 0.493531 | − | 0.869728i | \(-0.335706\pi\) | ||||
0.493531 | + | 0.869728i | \(0.335706\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 32.3607 | 1.18880 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.3607 | 0.893707 | 0.446853 | − | 0.894607i | \(-0.352545\pi\) | ||||
0.446853 | + | 0.894607i | \(0.352545\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.4721 | −0.530218 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.00000 | −0.146352 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 54.8328 | 2.00355 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −50.0689 | −1.82704 | −0.913520 | − | 0.406794i | \(-0.866647\pi\) | ||||
−0.913520 | + | 0.406794i | \(0.866647\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.4721 | 0.381626 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.7771 | 0.719762 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.8885 | 1.44977 | 0.724887 | − | 0.688868i | \(-0.241892\pi\) | ||||
0.724887 | + | 0.688868i | \(0.241892\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.00000 | 0.145191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.3607 | 1.53557 | 0.767787 | − | 0.640706i | \(-0.221358\pi\) | ||||
0.767787 | + | 0.640706i | \(0.221358\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 48.3607 | 1.75077 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.41641 | −0.123520 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22.1115 | −0.798398 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.8328 | 0.607007 | 0.303503 | − | 0.952830i | \(-0.401844\pi\) | ||||
0.303503 | + | 0.952830i | \(0.401844\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.0000 | −0.792311 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.2918 | 1.30533 | 0.652663 | − | 0.757649i | \(-0.273652\pi\) | ||||
0.652663 | + | 0.757649i | \(0.273652\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.4721 | −0.807223 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.4721 | −0.519185 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 79.1935 | 2.83740 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.0000 | −1.14505 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.47214 | 0.159821 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.36068 | −0.155639 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.7082 | 0.488645 | 0.244322 | − | 0.969694i | \(-0.421434\pi\) | ||||
0.244322 | + | 0.969694i | \(0.421434\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.47214 | −0.230414 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.0000 | 0.711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.0000 | −0.710221 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.47214 | −0.229543 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.6525 | 0.448174 | 0.224087 | − | 0.974569i | \(-0.428060\pi\) | ||||
0.224087 | + | 0.974569i | \(0.428060\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.0557 | −0.391124 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.23607 | −0.0436743 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −27.7771 | −0.980232 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.00000 | 0.140981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.472136 | −0.0166200 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.3050 | −1.52252 | −0.761261 | − | 0.648446i | \(-0.775419\pi\) | ||||
−0.761261 | + | 0.648446i | \(0.775419\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.4164 | 0.822261 | 0.411131 | − | 0.911576i | \(-0.365134\pi\) | ||||
0.411131 | + | 0.911576i | \(0.365134\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.5279 | 0.614729 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.16718 | −0.321112 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −41.3050 | −1.44508 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.4721 | 0.505697 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.1115 | 0.422693 | 0.211346 | − | 0.977411i | \(-0.432215\pi\) | ||||
0.211346 | + | 0.977411i | \(0.432215\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.5279 | 0.889845 | 0.444923 | − | 0.895569i | \(-0.353231\pi\) | ||||
0.444923 | + | 0.895569i | \(0.353231\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.8885 | 0.483537 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.58359 | −0.298481 | −0.149240 | − | 0.988801i | \(-0.547683\pi\) | ||||
−0.149240 | + | 0.988801i | \(0.547683\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.3607 | 0.359841 | 0.179921 | − | 0.983681i | \(-0.442416\pi\) | ||||
0.179921 | + | 0.983681i | \(0.442416\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.8885 | 0.551167 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.59675 | −0.332508 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.0000 | −0.553703 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.47214 | 0.223710 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.5836 | 0.434434 | 0.217217 | − | 0.976123i | \(-0.430302\pi\) | ||||
0.217217 | + | 0.976123i | \(0.430302\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.6525 | 0.849076 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.65248 | 0.297654 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.1803 | −0.555963 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.70820 | −0.195905 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.47214 | −0.153303 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.0000 | 0.753266 | 0.376633 | − | 0.926363i | \(-0.377082\pi\) | ||||
0.376633 | + | 0.926363i | \(0.377082\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.94427 | −0.305888 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −42.9443 | −1.46695 | −0.733474 | − | 0.679717i | \(-0.762102\pi\) | ||||
−0.733474 | + | 0.679717i | \(0.762102\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.05573 | 0.240738 | 0.120369 | − | 0.992729i | \(-0.461592\pi\) | ||||
0.120369 | + | 0.992729i | \(0.461592\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35.4164 | 1.20699 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.00000 | 0.136162 | 0.0680808 | − | 0.997680i | \(-0.478312\pi\) | ||||
0.0680808 | + | 0.997680i | \(0.478312\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.52786 | 0.187953 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.36068 | −0.317905 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 38.8328 | 1.31731 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.41641 | 0.115761 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.47214 | 0.286738 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 33.8885 | 1.14564 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.0557 | 1.11621 | 0.558106 | − | 0.829769i | \(-0.311528\pi\) | ||||
0.558106 | + | 0.829769i | \(0.311528\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.70820 | 0.259991 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.5410 | 0.894190 | 0.447095 | − | 0.894487i | \(-0.352459\pi\) | ||||
0.447095 | + | 0.894487i | \(0.352459\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.41641 | 0.249582 | 0.124791 | − | 0.992183i | \(-0.460174\pi\) | ||||
0.124791 | + | 0.992183i | \(0.460174\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.11146 | 0.205434 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31.0557 | −1.04275 | −0.521375 | − | 0.853328i | \(-0.674581\pi\) | ||||
−0.521375 | + | 0.853328i | \(0.674581\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.94427 | 0.165826 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.00000 | −0.134005 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.9443 | −0.968583 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.8885 | −0.865359 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.47214 | 0.149320 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 28.9443 | 0.965346 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.4721 | 0.482137 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.4721 | −0.614714 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.6950 | −0.488480 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.12461 | 0.0373421 | 0.0186711 | − | 0.999826i | \(-0.494056\pi\) | ||||
0.0186711 | + | 0.999826i | \(0.494056\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.94427 | −0.230327 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.7214 | 1.34916 | 0.674579 | − | 0.738202i | \(-0.264325\pi\) | ||||
0.674579 | + | 0.738202i | \(0.264325\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.0000 | 0.529523 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.52786 | 0.182746 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 54.8328 | 1.81074 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.0132 | 0.759134 | 0.379567 | − | 0.925164i | \(-0.376073\pi\) | ||||
0.379567 | + | 0.925164i | \(0.376073\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.47214 | −0.0814596 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −35.7771 | −1.17762 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.5279 | −0.510553 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.2361 | 0.369041 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.8328 | −0.945974 | −0.472987 | − | 0.881069i | \(-0.656824\pi\) | ||||
−0.472987 | + | 0.881069i | \(0.656824\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.1246 | −0.823426 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.05573 | −0.230994 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.6656 | 0.446914 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.8328 | −0.419230 | −0.209615 | − | 0.977784i | \(-0.567221\pi\) | ||||
−0.209615 | + | 0.977784i | \(0.567221\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.05573 | 0.164987 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.5410 | −1.38680 | −0.693399 | − | 0.720554i | \(-0.743888\pi\) | ||||
−0.693399 | + | 0.720554i | \(0.743888\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.9443 | 0.356395 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.00000 | −0.130120 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.16718 | 0.0379284 | 0.0189642 | − | 0.999820i | \(-0.493963\pi\) | ||||
0.0189642 | + | 0.999820i | \(0.493963\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31.0557 | −1.00811 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.58359 | 0.0837787 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.0689 | 0.390949 | 0.195475 | − | 0.980709i | \(-0.437375\pi\) | ||||
0.195475 | + | 0.980709i | \(0.437375\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.88854 | −0.0611118 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −17.8885 | −0.578254 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.00000 | 0.129167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.8885 | 0.351243 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.9443 | −0.546022 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.5279 | 0.693006 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.63932 | 0.245664 | 0.122832 | − | 0.992427i | \(-0.460802\pi\) | ||||
0.122832 | + | 0.992427i | \(0.460802\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 20.0000 | 0.642493 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.3050 | −0.555342 | −0.277671 | − | 0.960676i | \(-0.589563\pi\) | ||||
−0.277671 | + | 0.960676i | \(0.589563\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.9443 | −0.927911 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15.5279 | 0.497290 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32.0689 | −1.02597 | −0.512987 | − | 0.858396i | \(-0.671461\pi\) | ||||
−0.512987 | + | 0.858396i | \(0.671461\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.94427 | 0.158020 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.9443 | −0.477134 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.8328 | −0.728254 | −0.364127 | − | 0.931349i | \(-0.618633\pi\) | ||||
−0.364127 | + | 0.931349i | \(0.618633\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.5279 | 0.685935 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.9443 | −0.412021 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.70820 | −0.181510 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.52786 | 0.0485342 | 0.0242671 | − | 0.999706i | \(-0.492275\pi\) | ||||
0.0242671 | + | 0.999706i | \(0.492275\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23.4164 | −0.743097 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.0000 | −0.380426 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.3607 | 1.34158 | 0.670788 | − | 0.741649i | \(-0.265956\pi\) | ||||
0.670788 | + | 0.741649i | \(0.265956\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.47214 | 0.141492 |
(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 | 1104.2.a.m.1.2 | 2 | ||
3.2 | odd | 2 | 3312.2.a.bb.1.1 | 2 | |||
4.3 | odd | 2 | 69.2.a.b.1.1 | ✓ | 2 | ||
8.3 | odd | 2 | 4416.2.a.bm.1.1 | 2 | |||
8.5 | even | 2 | 4416.2.a.bg.1.1 | 2 | |||
12.11 | even | 2 | 207.2.a.c.1.2 | 2 | |||
20.3 | even | 4 | 1725.2.b.o.1174.3 | 4 | |||
20.7 | even | 4 | 1725.2.b.o.1174.2 | 4 | |||
20.19 | odd | 2 | 1725.2.a.ba.1.2 | 2 | |||
28.27 | even | 2 | 3381.2.a.t.1.1 | 2 | |||
44.43 | even | 2 | 8349.2.a.i.1.2 | 2 | |||
60.59 | even | 2 | 5175.2.a.bk.1.1 | 2 | |||
92.91 | even | 2 | 1587.2.a.i.1.1 | 2 | |||
276.275 | odd | 2 | 4761.2.a.v.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.2.a.b.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
207.2.a.c.1.2 | 2 | 12.11 | even | 2 | |||
1104.2.a.m.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1587.2.a.i.1.1 | 2 | 92.91 | even | 2 | |||
1725.2.a.ba.1.2 | 2 | 20.19 | odd | 2 | |||
1725.2.b.o.1174.2 | 4 | 20.7 | even | 4 | |||
1725.2.b.o.1174.3 | 4 | 20.3 | even | 4 | |||
3312.2.a.bb.1.1 | 2 | 3.2 | odd | 2 | |||
3381.2.a.t.1.1 | 2 | 28.27 | even | 2 | |||
4416.2.a.bg.1.1 | 2 | 8.5 | even | 2 | |||
4416.2.a.bm.1.1 | 2 | 8.3 | odd | 2 | |||
4761.2.a.v.1.2 | 2 | 276.275 | odd | 2 | |||
5175.2.a.bk.1.1 | 2 | 60.59 | even | 2 | |||
8349.2.a.i.1.2 | 2 | 44.43 | even | 2 |