Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2535,2,Mod(1,2535)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2535, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2535.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2535 = 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2535.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: | \(20.2420769124\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.756.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 195) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.26180\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2535.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.26180 | 1.59934 | 0.799668 | − | 0.600443i | \(-0.205009\pi\) | ||||
0.799668 | + | 0.600443i | \(0.205009\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.11575 | 1.55787 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.26180 | −0.923377 | ||||||||
\(7\) | 1.26180 | 0.476916 | 0.238458 | − | 0.971153i | \(-0.423358\pi\) | ||||
0.238458 | + | 0.971153i | \(0.423358\pi\) | |||||||
\(8\) | 2.52360 | 0.892229 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.26180 | −0.715245 | ||||||||
\(11\) | −4.52360 | −1.36392 | −0.681959 | − | 0.731390i | \(-0.738872\pi\) | ||||
−0.681959 | + | 0.731390i | \(0.738872\pi\) | |||||||
\(12\) | −3.11575 | −0.899439 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.85395 | 0.762749 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −0.523604 | −0.130901 | ||||||||
\(17\) | −4.49330 | −1.08979 | −0.544893 | − | 0.838506i | \(-0.683430\pi\) | ||||
−0.544893 | + | 0.838506i | \(0.683430\pi\) | |||||||
\(18\) | 2.26180 | 0.533112 | ||||||||
\(19\) | −5.11575 | −1.17363 | −0.586817 | − | 0.809720i | \(-0.699619\pi\) | ||||
−0.586817 | + | 0.809720i | \(0.699619\pi\) | |||||||
\(20\) | −3.11575 | −0.696703 | ||||||||
\(21\) | −1.26180 | −0.275348 | ||||||||
\(22\) | −10.2315 | −2.18136 | ||||||||
\(23\) | 2.23150 | 0.465300 | 0.232650 | − | 0.972561i | \(-0.425260\pi\) | ||||
0.232650 | + | 0.972561i | \(0.425260\pi\) | |||||||
\(24\) | −2.52360 | −0.515129 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.93146 | 0.742976 | ||||||||
\(29\) | −1.37755 | −0.255805 | −0.127902 | − | 0.991787i | \(-0.540824\pi\) | ||||
−0.127902 | + | 0.991787i | \(0.540824\pi\) | |||||||
\(30\) | 2.26180 | 0.412947 | ||||||||
\(31\) | −8.87085 | −1.59325 | −0.796626 | − | 0.604472i | \(-0.793384\pi\) | ||||
−0.796626 | + | 0.604472i | \(0.793384\pi\) | |||||||
\(32\) | −6.23150 | −1.10158 | ||||||||
\(33\) | 4.52360 | 0.787458 | ||||||||
\(34\) | −10.1630 | −1.74293 | ||||||||
\(35\) | −1.26180 | −0.213284 | ||||||||
\(36\) | 3.11575 | 0.519292 | ||||||||
\(37\) | 0.231499 | 0.0380582 | 0.0190291 | − | 0.999819i | \(-0.493942\pi\) | ||||
0.0190291 | + | 0.999819i | \(0.493942\pi\) | |||||||
\(38\) | −11.5708 | −1.87703 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.52360 | −0.399017 | ||||||||
\(41\) | −1.14605 | −0.178983 | −0.0894917 | − | 0.995988i | \(-0.528524\pi\) | ||||
−0.0894917 | + | 0.995988i | \(0.528524\pi\) | |||||||
\(42\) | −2.85395 | −0.440374 | ||||||||
\(43\) | 6.37755 | 0.972568 | 0.486284 | − | 0.873801i | \(-0.338352\pi\) | ||||
0.486284 | + | 0.873801i | \(0.338352\pi\) | |||||||
\(44\) | −14.0944 | −2.12481 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 5.04721 | 0.744170 | ||||||||
\(47\) | 10.7854 | 1.57321 | 0.786607 | − | 0.617454i | \(-0.211836\pi\) | ||||
0.786607 | + | 0.617454i | \(0.211836\pi\) | |||||||
\(48\) | 0.523604 | 0.0755758 | ||||||||
\(49\) | −5.40786 | −0.772551 | ||||||||
\(50\) | 2.26180 | 0.319867 | ||||||||
\(51\) | 4.49330 | 0.629188 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.52360 | 0.621365 | 0.310682 | − | 0.950514i | \(-0.399442\pi\) | ||||
0.310682 | + | 0.950514i | \(0.399442\pi\) | |||||||
\(54\) | −2.26180 | −0.307792 | ||||||||
\(55\) | 4.52360 | 0.609963 | ||||||||
\(56\) | 3.18429 | 0.425519 | ||||||||
\(57\) | 5.11575 | 0.677598 | ||||||||
\(58\) | −3.11575 | −0.409118 | ||||||||
\(59\) | 0.853947 | 0.111174 | 0.0555872 | − | 0.998454i | \(-0.482297\pi\) | ||||
0.0555872 | + | 0.998454i | \(0.482297\pi\) | |||||||
\(60\) | 3.11575 | 0.402242 | ||||||||
\(61\) | 4.63935 | 0.594008 | 0.297004 | − | 0.954876i | \(-0.404012\pi\) | ||||
0.297004 | + | 0.954876i | \(0.404012\pi\) | |||||||
\(62\) | −20.0641 | −2.54815 | ||||||||
\(63\) | 1.26180 | 0.158972 | ||||||||
\(64\) | −13.0472 | −1.63090 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 10.2315 | 1.25941 | ||||||||
\(67\) | −13.1327 | −1.60441 | −0.802205 | − | 0.597049i | \(-0.796340\pi\) | ||||
−0.802205 | + | 0.597049i | \(0.796340\pi\) | |||||||
\(68\) | −14.0000 | −1.69775 | ||||||||
\(69\) | −2.23150 | −0.268641 | ||||||||
\(70\) | −2.85395 | −0.341112 | ||||||||
\(71\) | 9.60905 | 1.14038 | 0.570192 | − | 0.821511i | \(-0.306869\pi\) | ||||
0.570192 | + | 0.821511i | \(0.306869\pi\) | |||||||
\(72\) | 2.52360 | 0.297410 | ||||||||
\(73\) | −13.7854 | −1.61346 | −0.806730 | − | 0.590920i | \(-0.798765\pi\) | ||||
−0.806730 | + | 0.590920i | \(0.798765\pi\) | |||||||
\(74\) | 0.523604 | 0.0608678 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −15.9394 | −1.82837 | ||||||||
\(77\) | −5.70789 | −0.650475 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.87085 | −0.998049 | −0.499024 | − | 0.866588i | \(-0.666308\pi\) | ||||
−0.499024 | + | 0.866588i | \(0.666308\pi\) | |||||||
\(80\) | 0.523604 | 0.0585408 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.59214 | −0.286255 | ||||||||
\(83\) | 8.23150 | 0.903524 | 0.451762 | − | 0.892138i | \(-0.350796\pi\) | ||||
0.451762 | + | 0.892138i | \(0.350796\pi\) | |||||||
\(84\) | −3.93146 | −0.428957 | ||||||||
\(85\) | 4.49330 | 0.487367 | ||||||||
\(86\) | 14.4248 | 1.55546 | ||||||||
\(87\) | 1.37755 | 0.147689 | ||||||||
\(88\) | −11.4158 | −1.21693 | ||||||||
\(89\) | −6.62245 | −0.701978 | −0.350989 | − | 0.936380i | \(-0.614155\pi\) | ||||
−0.350989 | + | 0.936380i | \(0.614155\pi\) | |||||||
\(90\) | −2.26180 | −0.238415 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.95279 | 0.724879 | ||||||||
\(93\) | 8.87085 | 0.919865 | ||||||||
\(94\) | 24.3945 | 2.51610 | ||||||||
\(95\) | 5.11575 | 0.524865 | ||||||||
\(96\) | 6.23150 | 0.636000 | ||||||||
\(97\) | −10.6697 | −1.08334 | −0.541670 | − | 0.840591i | \(-0.682208\pi\) | ||||
−0.541670 | + | 0.840591i | \(0.682208\pi\) | |||||||
\(98\) | −12.2315 | −1.23557 | ||||||||
\(99\) | −4.52360 | −0.454639 | ||||||||
\(100\) | 3.11575 | 0.311575 | ||||||||
\(101\) | −17.0472 | −1.69626 | −0.848130 | − | 0.529788i | \(-0.822272\pi\) | ||||
−0.848130 | + | 0.529788i | \(0.822272\pi\) | |||||||
\(102\) | 10.1630 | 1.00628 | ||||||||
\(103\) | −13.9484 | −1.37437 | −0.687187 | − | 0.726481i | \(-0.741155\pi\) | ||||
−0.687187 | + | 0.726481i | \(0.741155\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.26180 | 0.123139 | ||||||||
\(106\) | 10.2315 | 0.993771 | ||||||||
\(107\) | 12.4933 | 1.20777 | 0.603886 | − | 0.797070i | \(-0.293618\pi\) | ||||
0.603886 | + | 0.797070i | \(0.293618\pi\) | |||||||
\(108\) | −3.11575 | −0.299813 | ||||||||
\(109\) | 2.27871 | 0.218261 | 0.109130 | − | 0.994027i | \(-0.465193\pi\) | ||||
0.109130 | + | 0.994027i | \(0.465193\pi\) | |||||||
\(110\) | 10.2315 | 0.975535 | ||||||||
\(111\) | −0.231499 | −0.0219729 | ||||||||
\(112\) | −0.660685 | −0.0624289 | ||||||||
\(113\) | −1.47640 | −0.138888 | −0.0694438 | − | 0.997586i | \(-0.522122\pi\) | ||||
−0.0694438 | + | 0.997586i | \(0.522122\pi\) | |||||||
\(114\) | 11.5708 | 1.08371 | ||||||||
\(115\) | −2.23150 | −0.208088 | ||||||||
\(116\) | −4.29211 | −0.398512 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.93146 | 0.177805 | ||||||||
\(119\) | −5.66966 | −0.519737 | ||||||||
\(120\) | 2.52360 | 0.230373 | ||||||||
\(121\) | 9.46300 | 0.860273 | ||||||||
\(122\) | 10.4933 | 0.950019 | ||||||||
\(123\) | 1.14605 | 0.103336 | ||||||||
\(124\) | −27.6394 | −2.48209 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.85395 | 0.254250 | ||||||||
\(127\) | −17.7854 | −1.57820 | −0.789100 | − | 0.614265i | \(-0.789453\pi\) | ||||
−0.789100 | + | 0.614265i | \(0.789453\pi\) | |||||||
\(128\) | −17.0472 | −1.50677 | ||||||||
\(129\) | −6.37755 | −0.561512 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.6697 | 1.01958 | 0.509791 | − | 0.860298i | \(-0.329723\pi\) | ||||
0.509791 | + | 0.860298i | \(0.329723\pi\) | |||||||
\(132\) | 14.0944 | 1.22676 | ||||||||
\(133\) | −6.45506 | −0.559725 | ||||||||
\(134\) | −29.7035 | −2.56599 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −11.3393 | −0.972338 | ||||||||
\(137\) | 20.0641 | 1.71419 | 0.857096 | − | 0.515156i | \(-0.172266\pi\) | ||||
0.857096 | + | 0.515156i | \(0.172266\pi\) | |||||||
\(138\) | −5.04721 | −0.429647 | ||||||||
\(139\) | 16.3393 | 1.38588 | 0.692941 | − | 0.720994i | \(-0.256314\pi\) | ||||
0.692941 | + | 0.720994i | \(0.256314\pi\) | |||||||
\(140\) | −3.93146 | −0.332269 | ||||||||
\(141\) | −10.7854 | −0.908295 | ||||||||
\(142\) | 21.7338 | 1.82386 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.523604 | −0.0436337 | ||||||||
\(145\) | 1.37755 | 0.114399 | ||||||||
\(146\) | −31.1799 | −2.58046 | ||||||||
\(147\) | 5.40786 | 0.446032 | ||||||||
\(148\) | 0.721292 | 0.0592899 | ||||||||
\(149\) | 3.24490 | 0.265832 | 0.132916 | − | 0.991127i | \(-0.457566\pi\) | ||||
0.132916 | + | 0.991127i | \(0.457566\pi\) | |||||||
\(150\) | −2.26180 | −0.184675 | ||||||||
\(151\) | −5.69996 | −0.463856 | −0.231928 | − | 0.972733i | \(-0.574503\pi\) | ||||
−0.231928 | + | 0.972733i | \(0.574503\pi\) | |||||||
\(152\) | −12.9101 | −1.04715 | ||||||||
\(153\) | −4.49330 | −0.363262 | ||||||||
\(154\) | −12.9101 | −1.04033 | ||||||||
\(155\) | 8.87085 | 0.712524 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.85395 | −0.307578 | −0.153789 | − | 0.988104i | \(-0.549148\pi\) | ||||
−0.153789 | + | 0.988104i | \(0.549148\pi\) | |||||||
\(158\) | −20.0641 | −1.59622 | ||||||||
\(159\) | −4.52360 | −0.358745 | ||||||||
\(160\) | 6.23150 | 0.492643 | ||||||||
\(161\) | 2.81571 | 0.221909 | ||||||||
\(162\) | 2.26180 | 0.177704 | ||||||||
\(163\) | 9.72480 | 0.761705 | 0.380853 | − | 0.924636i | \(-0.375631\pi\) | ||||
0.380853 | + | 0.924636i | \(0.375631\pi\) | |||||||
\(164\) | −3.57081 | −0.278834 | ||||||||
\(165\) | −4.52360 | −0.352162 | ||||||||
\(166\) | 18.6180 | 1.44504 | ||||||||
\(167\) | 19.2787 | 1.49183 | 0.745916 | − | 0.666040i | \(-0.232012\pi\) | ||||
0.745916 | + | 0.666040i | \(0.232012\pi\) | |||||||
\(168\) | −3.18429 | −0.245673 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 10.1630 | 0.779463 | ||||||||
\(171\) | −5.11575 | −0.391211 | ||||||||
\(172\) | 19.8709 | 1.51514 | ||||||||
\(173\) | −3.01691 | −0.229371 | −0.114686 | − | 0.993402i | \(-0.536586\pi\) | ||||
−0.114686 | + | 0.993402i | \(0.536586\pi\) | |||||||
\(174\) | 3.11575 | 0.236204 | ||||||||
\(175\) | 1.26180 | 0.0953833 | ||||||||
\(176\) | 2.36858 | 0.178538 | ||||||||
\(177\) | −0.853947 | −0.0641866 | ||||||||
\(178\) | −14.9787 | −1.12270 | ||||||||
\(179\) | −5.31694 | −0.397407 | −0.198704 | − | 0.980060i | \(-0.563673\pi\) | ||||
−0.198704 | + | 0.980060i | \(0.563673\pi\) | |||||||
\(180\) | −3.11575 | −0.232234 | ||||||||
\(181\) | 25.8709 | 1.92297 | 0.961483 | − | 0.274866i | \(-0.0886333\pi\) | ||||
0.961483 | + | 0.274866i | \(0.0886333\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.63935 | −0.342951 | ||||||||
\(184\) | 5.63142 | 0.415154 | ||||||||
\(185\) | −0.231499 | −0.0170201 | ||||||||
\(186\) | 20.0641 | 1.47117 | ||||||||
\(187\) | 20.3259 | 1.48638 | ||||||||
\(188\) | 33.6046 | 2.45087 | ||||||||
\(189\) | −1.26180 | −0.0917826 | ||||||||
\(190\) | 11.5708 | 0.839435 | ||||||||
\(191\) | 10.6563 | 0.771060 | 0.385530 | − | 0.922695i | \(-0.374019\pi\) | ||||
0.385530 | + | 0.922695i | \(0.374019\pi\) | |||||||
\(192\) | 13.0472 | 0.941601 | ||||||||
\(193\) | −7.98309 | −0.574636 | −0.287318 | − | 0.957835i | \(-0.592764\pi\) | ||||
−0.287318 | + | 0.957835i | \(0.592764\pi\) | |||||||
\(194\) | −24.1327 | −1.73262 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −16.8495 | −1.20354 | ||||||||
\(197\) | −17.3393 | −1.23538 | −0.617688 | − | 0.786424i | \(-0.711930\pi\) | ||||
−0.617688 | + | 0.786424i | \(0.711930\pi\) | |||||||
\(198\) | −10.2315 | −0.727121 | ||||||||
\(199\) | −1.23150 | −0.0872986 | −0.0436493 | − | 0.999047i | \(-0.513898\pi\) | ||||
−0.0436493 | + | 0.999047i | \(0.513898\pi\) | |||||||
\(200\) | 2.52360 | 0.178446 | ||||||||
\(201\) | 13.1327 | 0.926306 | ||||||||
\(202\) | −38.5574 | −2.71289 | ||||||||
\(203\) | −1.73820 | −0.121998 | ||||||||
\(204\) | 14.0000 | 0.980196 | ||||||||
\(205\) | 1.14605 | 0.0800438 | ||||||||
\(206\) | −31.5484 | −2.19808 | ||||||||
\(207\) | 2.23150 | 0.155100 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 23.1416 | 1.60074 | ||||||||
\(210\) | 2.85395 | 0.196941 | ||||||||
\(211\) | 10.3393 | 0.711788 | 0.355894 | − | 0.934526i | \(-0.384176\pi\) | ||||
0.355894 | + | 0.934526i | \(0.384176\pi\) | |||||||
\(212\) | 14.0944 | 0.968009 | ||||||||
\(213\) | −9.60905 | −0.658401 | ||||||||
\(214\) | 28.2574 | 1.93163 | ||||||||
\(215\) | −6.37755 | −0.434945 | ||||||||
\(216\) | −2.52360 | −0.171710 | ||||||||
\(217\) | −11.1933 | −0.759848 | ||||||||
\(218\) | 5.15399 | 0.349072 | ||||||||
\(219\) | 13.7854 | 0.931531 | ||||||||
\(220\) | 14.0944 | 0.950245 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.523604 | −0.0351420 | ||||||||
\(223\) | −21.5708 | −1.44449 | −0.722244 | − | 0.691638i | \(-0.756889\pi\) | ||||
−0.722244 | + | 0.691638i | \(0.756889\pi\) | |||||||
\(224\) | −7.86292 | −0.525363 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −3.33931 | −0.222128 | ||||||||
\(227\) | −5.44609 | −0.361470 | −0.180735 | − | 0.983532i | \(-0.557848\pi\) | ||||
−0.180735 | + | 0.983532i | \(0.557848\pi\) | |||||||
\(228\) | 15.9394 | 1.05561 | ||||||||
\(229\) | −21.9315 | −1.44927 | −0.724636 | − | 0.689132i | \(-0.757992\pi\) | ||||
−0.724636 | + | 0.689132i | \(0.757992\pi\) | |||||||
\(230\) | −5.04721 | −0.332803 | ||||||||
\(231\) | 5.70789 | 0.375552 | ||||||||
\(232\) | −3.47640 | −0.228237 | ||||||||
\(233\) | 25.3125 | 1.65828 | 0.829139 | − | 0.559042i | \(-0.188831\pi\) | ||||
0.829139 | + | 0.559042i | \(0.188831\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.7854 | −0.703562 | ||||||||
\(236\) | 2.66069 | 0.173196 | ||||||||
\(237\) | 8.87085 | 0.576224 | ||||||||
\(238\) | −12.8236 | −0.831233 | ||||||||
\(239\) | −22.5236 | −1.45693 | −0.728465 | − | 0.685083i | \(-0.759766\pi\) | ||||
−0.728465 | + | 0.685083i | \(0.759766\pi\) | |||||||
\(240\) | −0.523604 | −0.0337985 | ||||||||
\(241\) | −11.1157 | −0.716028 | −0.358014 | − | 0.933716i | \(-0.616546\pi\) | ||||
−0.358014 | + | 0.933716i | \(0.616546\pi\) | |||||||
\(242\) | 21.4034 | 1.37586 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 14.4551 | 0.925391 | ||||||||
\(245\) | 5.40786 | 0.345495 | ||||||||
\(246\) | 2.59214 | 0.165269 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −22.3865 | −1.42155 | ||||||||
\(249\) | −8.23150 | −0.521650 | ||||||||
\(250\) | −2.26180 | −0.143049 | ||||||||
\(251\) | 11.0472 | 0.697294 | 0.348647 | − | 0.937254i | \(-0.386641\pi\) | ||||
0.348647 | + | 0.937254i | \(0.386641\pi\) | |||||||
\(252\) | 3.93146 | 0.247659 | ||||||||
\(253\) | −10.0944 | −0.634631 | ||||||||
\(254\) | −40.2271 | −2.52407 | ||||||||
\(255\) | −4.49330 | −0.281381 | ||||||||
\(256\) | −12.4630 | −0.778937 | ||||||||
\(257\) | −2.03030 | −0.126647 | −0.0633234 | − | 0.997993i | \(-0.520170\pi\) | ||||
−0.0633234 | + | 0.997993i | \(0.520170\pi\) | |||||||
\(258\) | −14.4248 | −0.898046 | ||||||||
\(259\) | 0.292106 | 0.0181506 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.37755 | −0.0852683 | ||||||||
\(262\) | 26.3945 | 1.63066 | ||||||||
\(263\) | 3.24840 | 0.200305 | 0.100153 | − | 0.994972i | \(-0.468067\pi\) | ||||
0.100153 | + | 0.994972i | \(0.468067\pi\) | |||||||
\(264\) | 11.4158 | 0.702593 | ||||||||
\(265\) | −4.52360 | −0.277883 | ||||||||
\(266\) | −14.6001 | −0.895188 | ||||||||
\(267\) | 6.62245 | 0.405287 | ||||||||
\(268\) | −40.9181 | −2.49947 | ||||||||
\(269\) | 26.9484 | 1.64307 | 0.821535 | − | 0.570157i | \(-0.193118\pi\) | ||||
0.821535 | + | 0.570157i | \(0.193118\pi\) | |||||||
\(270\) | 2.26180 | 0.137649 | ||||||||
\(271\) | 19.8495 | 1.20577 | 0.602886 | − | 0.797827i | \(-0.294017\pi\) | ||||
0.602886 | + | 0.797827i | \(0.294017\pi\) | |||||||
\(272\) | 2.35271 | 0.142654 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 45.3811 | 2.74157 | ||||||||
\(275\) | −4.52360 | −0.272784 | ||||||||
\(276\) | −6.95279 | −0.418509 | ||||||||
\(277\) | 16.0944 | 0.967020 | 0.483510 | − | 0.875339i | \(-0.339362\pi\) | ||||
0.483510 | + | 0.875339i | \(0.339362\pi\) | |||||||
\(278\) | 36.9563 | 2.21649 | ||||||||
\(279\) | −8.87085 | −0.531084 | ||||||||
\(280\) | −3.18429 | −0.190298 | ||||||||
\(281\) | 5.37755 | 0.320798 | 0.160399 | − | 0.987052i | \(-0.448722\pi\) | ||||
0.160399 | + | 0.987052i | \(0.448722\pi\) | |||||||
\(282\) | −24.3945 | −1.45267 | ||||||||
\(283\) | 26.8664 | 1.59704 | 0.798522 | − | 0.601966i | \(-0.205616\pi\) | ||||
0.798522 | + | 0.601966i | \(0.205616\pi\) | |||||||
\(284\) | 29.9394 | 1.77658 | ||||||||
\(285\) | −5.11575 | −0.303031 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.44609 | −0.0853601 | ||||||||
\(288\) | −6.23150 | −0.367195 | ||||||||
\(289\) | 3.18975 | 0.187633 | ||||||||
\(290\) | 3.11575 | 0.182963 | ||||||||
\(291\) | 10.6697 | 0.625466 | ||||||||
\(292\) | −42.9519 | −2.51357 | ||||||||
\(293\) | −21.4193 | −1.25133 | −0.625664 | − | 0.780092i | \(-0.715172\pi\) | ||||
−0.625664 | + | 0.780092i | \(0.715172\pi\) | |||||||
\(294\) | 12.2315 | 0.713355 | ||||||||
\(295\) | −0.853947 | −0.0497187 | ||||||||
\(296\) | 0.584211 | 0.0339566 | ||||||||
\(297\) | 4.52360 | 0.262486 | ||||||||
\(298\) | 7.33931 | 0.425155 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.11575 | −0.179888 | ||||||||
\(301\) | 8.04721 | 0.463833 | ||||||||
\(302\) | −12.8922 | −0.741862 | ||||||||
\(303\) | 17.0472 | 0.979337 | ||||||||
\(304\) | 2.67863 | 0.153630 | ||||||||
\(305\) | −4.63935 | −0.265649 | ||||||||
\(306\) | −10.1630 | −0.580978 | ||||||||
\(307\) | 7.85395 | 0.448248 | 0.224124 | − | 0.974561i | \(-0.428048\pi\) | ||||
0.224124 | + | 0.974561i | \(0.428048\pi\) | |||||||
\(308\) | −17.7844 | −1.01336 | ||||||||
\(309\) | 13.9484 | 0.793495 | ||||||||
\(310\) | 20.0641 | 1.13957 | ||||||||
\(311\) | −27.8744 | −1.58061 | −0.790305 | − | 0.612714i | \(-0.790078\pi\) | ||||
−0.790305 | + | 0.612714i | \(0.790078\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.88776 | 0.445842 | 0.222921 | − | 0.974836i | \(-0.428441\pi\) | ||||
0.222921 | + | 0.974836i | \(0.428441\pi\) | |||||||
\(314\) | −8.71687 | −0.491921 | ||||||||
\(315\) | −1.26180 | −0.0710945 | ||||||||
\(316\) | −27.6394 | −1.55484 | ||||||||
\(317\) | −13.2181 | −0.742403 | −0.371201 | − | 0.928552i | \(-0.621054\pi\) | ||||
−0.371201 | + | 0.928552i | \(0.621054\pi\) | |||||||
\(318\) | −10.2315 | −0.573754 | ||||||||
\(319\) | 6.23150 | 0.348897 | ||||||||
\(320\) | 13.0472 | 0.729361 | ||||||||
\(321\) | −12.4933 | −0.697308 | ||||||||
\(322\) | 6.36858 | 0.354907 | ||||||||
\(323\) | 22.9866 | 1.27901 | ||||||||
\(324\) | 3.11575 | 0.173097 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 21.9956 | 1.21822 | ||||||||
\(327\) | −2.27871 | −0.126013 | ||||||||
\(328\) | −2.89218 | −0.159694 | ||||||||
\(329\) | 13.6091 | 0.750291 | ||||||||
\(330\) | −10.2315 | −0.563225 | ||||||||
\(331\) | 23.8495 | 1.31089 | 0.655444 | − | 0.755244i | \(-0.272481\pi\) | ||||
0.655444 | + | 0.755244i | \(0.272481\pi\) | |||||||
\(332\) | 25.6473 | 1.40758 | ||||||||
\(333\) | 0.231499 | 0.0126861 | ||||||||
\(334\) | 43.6046 | 2.38594 | ||||||||
\(335\) | 13.1327 | 0.717514 | ||||||||
\(336\) | 0.660685 | 0.0360433 | ||||||||
\(337\) | 5.68306 | 0.309576 | 0.154788 | − | 0.987948i | \(-0.450531\pi\) | ||||
0.154788 | + | 0.987948i | \(0.450531\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.47640 | 0.0801868 | ||||||||
\(340\) | 14.0000 | 0.759257 | ||||||||
\(341\) | 40.1282 | 2.17307 | ||||||||
\(342\) | −11.5708 | −0.625678 | ||||||||
\(343\) | −15.6563 | −0.845359 | ||||||||
\(344\) | 16.0944 | 0.867753 | ||||||||
\(345\) | 2.23150 | 0.120140 | ||||||||
\(346\) | −6.82364 | −0.366841 | ||||||||
\(347\) | −21.4496 | −1.15147 | −0.575737 | − | 0.817635i | \(-0.695285\pi\) | ||||
−0.575737 | + | 0.817635i | \(0.695285\pi\) | |||||||
\(348\) | 4.29211 | 0.230081 | ||||||||
\(349\) | −6.87085 | −0.367788 | −0.183894 | − | 0.982946i | \(-0.558870\pi\) | ||||
−0.183894 | + | 0.982946i | \(0.558870\pi\) | |||||||
\(350\) | 2.85395 | 0.152550 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 28.1888 | 1.50247 | ||||||||
\(353\) | −34.4968 | −1.83608 | −0.918040 | − | 0.396488i | \(-0.870229\pi\) | ||||
−0.918040 | + | 0.396488i | \(0.870229\pi\) | |||||||
\(354\) | −1.93146 | −0.102656 | ||||||||
\(355\) | −9.60905 | −0.509995 | ||||||||
\(356\) | −20.6339 | −1.09359 | ||||||||
\(357\) | 5.66966 | 0.300070 | ||||||||
\(358\) | −12.0259 | −0.635587 | ||||||||
\(359\) | 8.15945 | 0.430639 | 0.215320 | − | 0.976544i | \(-0.430921\pi\) | ||||
0.215320 | + | 0.976544i | \(0.430921\pi\) | |||||||
\(360\) | −2.52360 | −0.133006 | ||||||||
\(361\) | 7.17089 | 0.377415 | ||||||||
\(362\) | 58.5148 | 3.07547 | ||||||||
\(363\) | −9.46300 | −0.496679 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.7854 | 0.721561 | ||||||||
\(366\) | −10.4933 | −0.548494 | ||||||||
\(367\) | −6.84055 | −0.357074 | −0.178537 | − | 0.983933i | \(-0.557136\pi\) | ||||
−0.178537 | + | 0.983933i | \(0.557136\pi\) | |||||||
\(368\) | −1.16842 | −0.0609082 | ||||||||
\(369\) | −1.14605 | −0.0596611 | ||||||||
\(370\) | −0.523604 | −0.0272209 | ||||||||
\(371\) | 5.70789 | 0.296339 | ||||||||
\(372\) | 27.6394 | 1.43303 | ||||||||
\(373\) | 13.8192 | 0.715532 | 0.357766 | − | 0.933811i | \(-0.383539\pi\) | ||||
0.357766 | + | 0.933811i | \(0.383539\pi\) | |||||||
\(374\) | 45.9732 | 2.37722 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 27.2181 | 1.40367 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.85395 | −0.146791 | ||||||||
\(379\) | −11.5157 | −0.591520 | −0.295760 | − | 0.955262i | \(-0.595573\pi\) | ||||
−0.295760 | + | 0.955262i | \(0.595573\pi\) | |||||||
\(380\) | 15.9394 | 0.817674 | ||||||||
\(381\) | 17.7854 | 0.911174 | ||||||||
\(382\) | 24.1024 | 1.23318 | ||||||||
\(383\) | −22.8798 | −1.16910 | −0.584552 | − | 0.811356i | \(-0.698730\pi\) | ||||
−0.584552 | + | 0.811356i | \(0.698730\pi\) | |||||||
\(384\) | 17.0472 | 0.869937 | ||||||||
\(385\) | 5.70789 | 0.290901 | ||||||||
\(386\) | −18.0562 | −0.919035 | ||||||||
\(387\) | 6.37755 | 0.324189 | ||||||||
\(388\) | −33.2440 | −1.68771 | ||||||||
\(389\) | −4.35271 | −0.220691 | −0.110346 | − | 0.993893i | \(-0.535196\pi\) | ||||
−0.110346 | + | 0.993893i | \(0.535196\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.0268 | −0.507077 | ||||||||
\(392\) | −13.6473 | −0.689292 | ||||||||
\(393\) | −11.6697 | −0.588656 | ||||||||
\(394\) | −39.2181 | −1.97578 | ||||||||
\(395\) | 8.87085 | 0.446341 | ||||||||
\(396\) | −14.0944 | −0.708271 | ||||||||
\(397\) | −7.62245 | −0.382560 | −0.191280 | − | 0.981536i | \(-0.561264\pi\) | ||||
−0.191280 | + | 0.981536i | \(0.561264\pi\) | |||||||
\(398\) | −2.78541 | −0.139620 | ||||||||
\(399\) | 6.45506 | 0.323157 | ||||||||
\(400\) | −0.523604 | −0.0261802 | ||||||||
\(401\) | −20.8495 | −1.04118 | −0.520588 | − | 0.853808i | \(-0.674287\pi\) | ||||
−0.520588 | + | 0.853808i | \(0.674287\pi\) | |||||||
\(402\) | 29.7035 | 1.48147 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −53.1148 | −2.64256 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −3.93146 | −0.195115 | ||||||||
\(407\) | −1.04721 | −0.0519082 | ||||||||
\(408\) | 11.3393 | 0.561380 | ||||||||
\(409\) | 16.9653 | 0.838879 | 0.419439 | − | 0.907783i | \(-0.362227\pi\) | ||||
0.419439 | + | 0.907783i | \(0.362227\pi\) | |||||||
\(410\) | 2.59214 | 0.128017 | ||||||||
\(411\) | −20.0641 | −0.989690 | ||||||||
\(412\) | −43.4596 | −2.14110 | ||||||||
\(413\) | 1.07751 | 0.0530209 | ||||||||
\(414\) | 5.04721 | 0.248057 | ||||||||
\(415\) | −8.23150 | −0.404068 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.3393 | −0.800140 | ||||||||
\(418\) | 52.3418 | 2.56012 | ||||||||
\(419\) | 2.09884 | 0.102535 | 0.0512676 | − | 0.998685i | \(-0.483674\pi\) | ||||
0.0512676 | + | 0.998685i | \(0.483674\pi\) | |||||||
\(420\) | 3.93146 | 0.191836 | ||||||||
\(421\) | 39.6598 | 1.93290 | 0.966449 | − | 0.256857i | \(-0.0826870\pi\) | ||||
0.966449 | + | 0.256857i | \(0.0826870\pi\) | |||||||
\(422\) | 23.3855 | 1.13839 | ||||||||
\(423\) | 10.7854 | 0.524404 | ||||||||
\(424\) | 11.4158 | 0.554400 | ||||||||
\(425\) | −4.49330 | −0.217957 | ||||||||
\(426\) | −21.7338 | −1.05300 | ||||||||
\(427\) | 5.85395 | 0.283292 | ||||||||
\(428\) | 38.9260 | 1.88156 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14.4248 | −0.695624 | ||||||||
\(431\) | 22.1282 | 1.06588 | 0.532940 | − | 0.846153i | \(-0.321087\pi\) | ||||
0.532940 | + | 0.846153i | \(0.321087\pi\) | |||||||
\(432\) | 0.523604 | 0.0251919 | ||||||||
\(433\) | −31.3562 | −1.50688 | −0.753442 | − | 0.657515i | \(-0.771608\pi\) | ||||
−0.753442 | + | 0.657515i | \(0.771608\pi\) | |||||||
\(434\) | −25.3169 | −1.21525 | ||||||||
\(435\) | −1.37755 | −0.0660485 | ||||||||
\(436\) | 7.09988 | 0.340023 | ||||||||
\(437\) | −11.4158 | −0.546091 | ||||||||
\(438\) | 31.1799 | 1.48983 | ||||||||
\(439\) | 4.31344 | 0.205869 | 0.102935 | − | 0.994688i | \(-0.467177\pi\) | ||||
0.102935 | + | 0.994688i | \(0.467177\pi\) | |||||||
\(440\) | 11.4158 | 0.544226 | ||||||||
\(441\) | −5.40786 | −0.257517 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.493301 | 0.0234374 | 0.0117187 | − | 0.999931i | \(-0.496270\pi\) | ||||
0.0117187 | + | 0.999931i | \(0.496270\pi\) | |||||||
\(444\) | −0.721292 | −0.0342310 | ||||||||
\(445\) | 6.62245 | 0.313934 | ||||||||
\(446\) | −48.7889 | −2.31022 | ||||||||
\(447\) | −3.24490 | −0.153478 | ||||||||
\(448\) | −16.4630 | −0.777804 | ||||||||
\(449\) | 23.3125 | 1.10019 | 0.550093 | − | 0.835103i | \(-0.314592\pi\) | ||||
0.550093 | + | 0.835103i | \(0.314592\pi\) | |||||||
\(450\) | 2.26180 | 0.106622 | ||||||||
\(451\) | 5.18429 | 0.244119 | ||||||||
\(452\) | −4.60008 | −0.216369 | ||||||||
\(453\) | 5.69996 | 0.267808 | ||||||||
\(454\) | −12.3180 | −0.578112 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.9101 | 0.604572 | ||||||||
\(457\) | −6.66966 | −0.311993 | −0.155997 | − | 0.987758i | \(-0.549859\pi\) | ||||
−0.155997 | + | 0.987758i | \(0.549859\pi\) | |||||||
\(458\) | −49.6046 | −2.31787 | ||||||||
\(459\) | 4.49330 | 0.209729 | ||||||||
\(460\) | −6.95279 | −0.324176 | ||||||||
\(461\) | −29.1193 | −1.35622 | −0.678110 | − | 0.734961i | \(-0.737200\pi\) | ||||
−0.678110 | + | 0.734961i | \(0.737200\pi\) | |||||||
\(462\) | 12.9101 | 0.600634 | ||||||||
\(463\) | 1.79334 | 0.0833436 | 0.0416718 | − | 0.999131i | \(-0.486732\pi\) | ||||
0.0416718 | + | 0.999131i | \(0.486732\pi\) | |||||||
\(464\) | 0.721292 | 0.0334852 | ||||||||
\(465\) | −8.87085 | −0.411376 | ||||||||
\(466\) | 57.2519 | 2.65214 | ||||||||
\(467\) | 16.8192 | 0.778301 | 0.389150 | − | 0.921174i | \(-0.372769\pi\) | ||||
0.389150 | + | 0.921174i | \(0.372769\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.5708 | −0.765169 | ||||||||
\(470\) | −24.3945 | −1.12523 | ||||||||
\(471\) | 3.85395 | 0.177581 | ||||||||
\(472\) | 2.15502 | 0.0991931 | ||||||||
\(473\) | −28.8495 | −1.32650 | ||||||||
\(474\) | 20.0641 | 0.921575 | ||||||||
\(475\) | −5.11575 | −0.234727 | ||||||||
\(476\) | −17.6652 | −0.809685 | ||||||||
\(477\) | 4.52360 | 0.207122 | ||||||||
\(478\) | −50.9439 | −2.33012 | ||||||||
\(479\) | −35.1531 | −1.60618 | −0.803092 | − | 0.595855i | \(-0.796813\pi\) | ||||
−0.803092 | + | 0.595855i | \(0.796813\pi\) | |||||||
\(480\) | −6.23150 | −0.284428 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −25.1416 | −1.14517 | ||||||||
\(483\) | −2.81571 | −0.128119 | ||||||||
\(484\) | 29.4843 | 1.34020 | ||||||||
\(485\) | 10.6697 | 0.484484 | ||||||||
\(486\) | −2.26180 | −0.102597 | ||||||||
\(487\) | 8.62596 | 0.390879 | 0.195440 | − | 0.980716i | \(-0.437387\pi\) | ||||
0.195440 | + | 0.980716i | \(0.437387\pi\) | |||||||
\(488\) | 11.7079 | 0.529991 | ||||||||
\(489\) | −9.72480 | −0.439771 | ||||||||
\(490\) | 12.2315 | 0.552563 | ||||||||
\(491\) | −23.2137 | −1.04762 | −0.523809 | − | 0.851836i | \(-0.675490\pi\) | ||||
−0.523809 | + | 0.851836i | \(0.675490\pi\) | |||||||
\(492\) | 3.57081 | 0.160985 | ||||||||
\(493\) | 6.18975 | 0.278773 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.52360 | 0.203321 | ||||||||
\(496\) | 4.64482 | 0.208558 | ||||||||
\(497\) | 12.1247 | 0.543868 | ||||||||
\(498\) | −18.6180 | −0.834294 | ||||||||
\(499\) | −29.0393 | −1.29998 | −0.649988 | − | 0.759944i | \(-0.725226\pi\) | ||||
−0.649988 | + | 0.759944i | \(0.725226\pi\) | |||||||
\(500\) | −3.11575 | −0.139341 | ||||||||
\(501\) | −19.2787 | −0.861309 | ||||||||
\(502\) | 24.9866 | 1.11521 | ||||||||
\(503\) | −17.3999 | −0.775824 | −0.387912 | − | 0.921696i | \(-0.626804\pi\) | ||||
−0.387912 | + | 0.921696i | \(0.626804\pi\) | |||||||
\(504\) | 3.18429 | 0.141840 | ||||||||
\(505\) | 17.0472 | 0.758591 | ||||||||
\(506\) | −22.8316 | −1.01499 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −55.4149 | −2.45864 | ||||||||
\(509\) | 22.8763 | 1.01397 | 0.506987 | − | 0.861953i | \(-0.330759\pi\) | ||||
0.506987 | + | 0.861953i | \(0.330759\pi\) | |||||||
\(510\) | −10.1630 | −0.450023 | ||||||||
\(511\) | −17.3945 | −0.769485 | ||||||||
\(512\) | 5.90558 | 0.260992 | ||||||||
\(513\) | 5.11575 | 0.225866 | ||||||||
\(514\) | −4.59214 | −0.202551 | ||||||||
\(515\) | 13.9484 | 0.614638 | ||||||||
\(516\) | −19.8709 | −0.874766 | ||||||||
\(517\) | −48.7889 | −2.14573 | ||||||||
\(518\) | 0.660685 | 0.0290288 | ||||||||
\(519\) | 3.01691 | 0.132427 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.3642 | −1.15503 | −0.577517 | − | 0.816378i | \(-0.695978\pi\) | ||||
−0.577517 | + | 0.816378i | \(0.695978\pi\) | |||||||
\(522\) | −3.11575 | −0.136373 | ||||||||
\(523\) | −26.2921 | −1.14967 | −0.574837 | − | 0.818268i | \(-0.694934\pi\) | ||||
−0.574837 | + | 0.818268i | \(0.694934\pi\) | |||||||
\(524\) | 36.3597 | 1.58838 | ||||||||
\(525\) | −1.26180 | −0.0550696 | ||||||||
\(526\) | 7.34725 | 0.320355 | ||||||||
\(527\) | 39.8594 | 1.73630 | ||||||||
\(528\) | −2.36858 | −0.103079 | ||||||||
\(529\) | −18.0204 | −0.783496 | ||||||||
\(530\) | −10.2315 | −0.444428 | ||||||||
\(531\) | 0.853947 | 0.0370581 | ||||||||
\(532\) | −20.1124 | −0.871981 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 14.9787 | 0.648190 | ||||||||
\(535\) | −12.4933 | −0.540133 | ||||||||
\(536\) | −33.1416 | −1.43150 | ||||||||
\(537\) | 5.31694 | 0.229443 | ||||||||
\(538\) | 60.9519 | 2.62782 | ||||||||
\(539\) | 24.4630 | 1.05370 | ||||||||
\(540\) | 3.11575 | 0.134081 | ||||||||
\(541\) | 0.107816 | 0.00463537 | 0.00231768 | − | 0.999997i | \(-0.499262\pi\) | ||||
0.00231768 | + | 0.999997i | \(0.499262\pi\) | |||||||
\(542\) | 44.8957 | 1.92844 | ||||||||
\(543\) | −25.8709 | −1.11022 | ||||||||
\(544\) | 28.0000 | 1.20049 | ||||||||
\(545\) | −2.27871 | −0.0976091 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.1193 | 0.518182 | 0.259091 | − | 0.965853i | \(-0.416577\pi\) | ||||
0.259091 | + | 0.965853i | \(0.416577\pi\) | |||||||
\(548\) | 62.5148 | 2.67050 | ||||||||
\(549\) | 4.63935 | 0.198003 | ||||||||
\(550\) | −10.2315 | −0.436273 | ||||||||
\(551\) | 7.04721 | 0.300221 | ||||||||
\(552\) | −5.63142 | −0.239689 | ||||||||
\(553\) | −11.1933 | −0.475986 | ||||||||
\(554\) | 36.4024 | 1.54659 | ||||||||
\(555\) | 0.231499 | 0.00982658 | ||||||||
\(556\) | 50.9092 | 2.15903 | ||||||||
\(557\) | −38.0070 | −1.61041 | −0.805204 | − | 0.592997i | \(-0.797944\pi\) | ||||
−0.805204 | + | 0.592997i | \(0.797944\pi\) | |||||||
\(558\) | −20.0641 | −0.849382 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.660685 | 0.0279191 | ||||||||
\(561\) | −20.3259 | −0.858161 | ||||||||
\(562\) | 12.1630 | 0.513063 | ||||||||
\(563\) | 15.5102 | 0.653677 | 0.326839 | − | 0.945080i | \(-0.394017\pi\) | ||||
0.326839 | + | 0.945080i | \(0.394017\pi\) | |||||||
\(564\) | −33.6046 | −1.41501 | ||||||||
\(565\) | 1.47640 | 0.0621124 | ||||||||
\(566\) | 60.7665 | 2.55421 | ||||||||
\(567\) | 1.26180 | 0.0529907 | ||||||||
\(568\) | 24.2494 | 1.01748 | ||||||||
\(569\) | 19.2405 | 0.806602 | 0.403301 | − | 0.915067i | \(-0.367863\pi\) | ||||
0.403301 | + | 0.915067i | \(0.367863\pi\) | |||||||
\(570\) | −11.5708 | −0.484648 | ||||||||
\(571\) | 27.7338 | 1.16062 | 0.580311 | − | 0.814395i | \(-0.302931\pi\) | ||||
0.580311 | + | 0.814395i | \(0.302931\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.6563 | −0.445172 | ||||||||
\(574\) | −3.27077 | −0.136519 | ||||||||
\(575\) | 2.23150 | 0.0930599 | ||||||||
\(576\) | −13.0472 | −0.543634 | ||||||||
\(577\) | −26.9866 | −1.12347 | −0.561733 | − | 0.827318i | \(-0.689865\pi\) | ||||
−0.561733 | + | 0.827318i | \(0.689865\pi\) | |||||||
\(578\) | 7.21459 | 0.300088 | ||||||||
\(579\) | 7.98309 | 0.331766 | ||||||||
\(580\) | 4.29211 | 0.178220 | ||||||||
\(581\) | 10.3865 | 0.430906 | ||||||||
\(582\) | 24.1327 | 1.00033 | ||||||||
\(583\) | −20.4630 | −0.847491 | ||||||||
\(584\) | −34.7889 | −1.43958 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −48.4462 | −2.00129 | ||||||||
\(587\) | 30.8530 | 1.27344 | 0.636720 | − | 0.771095i | \(-0.280291\pi\) | ||||
0.636720 | + | 0.771095i | \(0.280291\pi\) | |||||||
\(588\) | 16.8495 | 0.694863 | ||||||||
\(589\) | 45.3811 | 1.86989 | ||||||||
\(590\) | −1.93146 | −0.0795169 | ||||||||
\(591\) | 17.3393 | 0.713244 | ||||||||
\(592\) | −0.121214 | −0.00498186 | ||||||||
\(593\) | −4.29211 | −0.176256 | −0.0881278 | − | 0.996109i | \(-0.528088\pi\) | ||||
−0.0881278 | + | 0.996109i | \(0.528088\pi\) | |||||||
\(594\) | 10.2315 | 0.419803 | ||||||||
\(595\) | 5.66966 | 0.232433 | ||||||||
\(596\) | 10.1103 | 0.414133 | ||||||||
\(597\) | 1.23150 | 0.0504019 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0224 | −0.981527 | −0.490764 | − | 0.871293i | \(-0.663282\pi\) | ||||
−0.490764 | + | 0.871293i | \(0.663282\pi\) | |||||||
\(600\) | −2.52360 | −0.103026 | ||||||||
\(601\) | 2.53154 | 0.103264 | 0.0516318 | − | 0.998666i | \(-0.483558\pi\) | ||||
0.0516318 | + | 0.998666i | \(0.483558\pi\) | |||||||
\(602\) | 18.2012 | 0.741825 | ||||||||
\(603\) | −13.1327 | −0.534803 | ||||||||
\(604\) | −17.7596 | −0.722630 | ||||||||
\(605\) | −9.46300 | −0.384726 | ||||||||
\(606\) | 38.5574 | 1.56629 | ||||||||
\(607\) | 11.4417 | 0.464403 | 0.232201 | − | 0.972668i | \(-0.425407\pi\) | ||||
0.232201 | + | 0.972668i | \(0.425407\pi\) | |||||||
\(608\) | 31.8788 | 1.29286 | ||||||||
\(609\) | 1.73820 | 0.0704353 | ||||||||
\(610\) | −10.4933 | −0.424861 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −14.0000 | −0.565916 | ||||||||
\(613\) | 7.19326 | 0.290533 | 0.145267 | − | 0.989393i | \(-0.453596\pi\) | ||||
0.145267 | + | 0.989393i | \(0.453596\pi\) | |||||||
\(614\) | 17.7641 | 0.716900 | ||||||||
\(615\) | −1.14605 | −0.0462133 | ||||||||
\(616\) | −14.4045 | −0.580373 | ||||||||
\(617\) | −25.5708 | −1.02944 | −0.514721 | − | 0.857358i | \(-0.672105\pi\) | ||||
−0.514721 | + | 0.857358i | \(0.672105\pi\) | |||||||
\(618\) | 31.5484 | 1.26906 | ||||||||
\(619\) | −5.98660 | −0.240622 | −0.120311 | − | 0.992736i | \(-0.538389\pi\) | ||||
−0.120311 | + | 0.992736i | \(0.538389\pi\) | |||||||
\(620\) | 27.6394 | 1.11002 | ||||||||
\(621\) | −2.23150 | −0.0895470 | ||||||||
\(622\) | −63.0463 | −2.52793 | ||||||||
\(623\) | −8.35622 | −0.334785 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 17.8405 | 0.713052 | ||||||||
\(627\) | −23.1416 | −0.924188 | ||||||||
\(628\) | −12.0079 | −0.479169 | ||||||||
\(629\) | −1.04019 | −0.0414752 | ||||||||
\(630\) | −2.85395 | −0.113704 | ||||||||
\(631\) | 43.0259 | 1.71283 | 0.856417 | − | 0.516285i | \(-0.172686\pi\) | ||||
0.856417 | + | 0.516285i | \(0.172686\pi\) | |||||||
\(632\) | −22.3865 | −0.890488 | ||||||||
\(633\) | −10.3393 | −0.410951 | ||||||||
\(634\) | −29.8967 | −1.18735 | ||||||||
\(635\) | 17.7854 | 0.705792 | ||||||||
\(636\) | −14.0944 | −0.558880 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 14.0944 | 0.558003 | ||||||||
\(639\) | 9.60905 | 0.380128 | ||||||||
\(640\) | 17.0472 | 0.673850 | ||||||||
\(641\) | −6.69450 | −0.264417 | −0.132208 | − | 0.991222i | \(-0.542207\pi\) | ||||
−0.132208 | + | 0.991222i | \(0.542207\pi\) | |||||||
\(642\) | −28.2574 | −1.11523 | ||||||||
\(643\) | −8.18078 | −0.322619 | −0.161309 | − | 0.986904i | \(-0.551572\pi\) | ||||
−0.161309 | + | 0.986904i | \(0.551572\pi\) | |||||||
\(644\) | 8.77305 | 0.345706 | ||||||||
\(645\) | 6.37755 | 0.251116 | ||||||||
\(646\) | 51.9911 | 2.04556 | ||||||||
\(647\) | −11.2787 | −0.443412 | −0.221706 | − | 0.975114i | \(-0.571162\pi\) | ||||
−0.221706 | + | 0.975114i | \(0.571162\pi\) | |||||||
\(648\) | 2.52360 | 0.0991365 | ||||||||
\(649\) | −3.86292 | −0.151633 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.1933 | 0.438699 | ||||||||
\(652\) | 30.3000 | 1.18664 | ||||||||
\(653\) | 27.2484 | 1.06631 | 0.533156 | − | 0.846017i | \(-0.321006\pi\) | ||||
0.533156 | + | 0.846017i | \(0.321006\pi\) | |||||||
\(654\) | −5.15399 | −0.201537 | ||||||||
\(655\) | −11.6697 | −0.455971 | ||||||||
\(656\) | 0.600078 | 0.0234291 | ||||||||
\(657\) | −13.7854 | −0.537820 | ||||||||
\(658\) | 30.7810 | 1.19997 | ||||||||
\(659\) | 6.75510 | 0.263141 | 0.131571 | − | 0.991307i | \(-0.457998\pi\) | ||||
0.131571 | + | 0.991307i | \(0.457998\pi\) | |||||||
\(660\) | −14.0944 | −0.548624 | ||||||||
\(661\) | 26.5102 | 1.03113 | 0.515564 | − | 0.856851i | \(-0.327583\pi\) | ||||
0.515564 | + | 0.856851i | \(0.327583\pi\) | |||||||
\(662\) | 53.9429 | 2.09655 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20.7730 | 0.806151 | ||||||||
\(665\) | 6.45506 | 0.250317 | ||||||||
\(666\) | 0.523604 | 0.0202893 | ||||||||
\(667\) | −3.07400 | −0.119026 | ||||||||
\(668\) | 60.0676 | 2.32409 | ||||||||
\(669\) | 21.5708 | 0.833976 | ||||||||
\(670\) | 29.7035 | 1.14755 | ||||||||
\(671\) | −20.9866 | −0.810179 | ||||||||
\(672\) | 7.86292 | 0.303319 | ||||||||
\(673\) | −0.677591 | −0.0261192 | −0.0130596 | − | 0.999915i | \(-0.504157\pi\) | ||||
−0.0130596 | + | 0.999915i | \(0.504157\pi\) | |||||||
\(674\) | 12.8539 | 0.495116 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.4630 | −0.402126 | −0.201063 | − | 0.979578i | \(-0.564440\pi\) | ||||
−0.201063 | + | 0.979578i | \(0.564440\pi\) | |||||||
\(678\) | 3.33931 | 0.128246 | ||||||||
\(679\) | −13.4630 | −0.516662 | ||||||||
\(680\) | 11.3393 | 0.434843 | ||||||||
\(681\) | 5.44609 | 0.208695 | ||||||||
\(682\) | 90.7621 | 3.47546 | ||||||||
\(683\) | 18.7516 | 0.717510 | 0.358755 | − | 0.933432i | \(-0.383201\pi\) | ||||
0.358755 | + | 0.933432i | \(0.383201\pi\) | |||||||
\(684\) | −15.9394 | −0.609458 | ||||||||
\(685\) | −20.0641 | −0.766610 | ||||||||
\(686\) | −35.4114 | −1.35201 | ||||||||
\(687\) | 21.9315 | 0.836737 | ||||||||
\(688\) | −3.33931 | −0.127310 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 5.04721 | 0.192144 | ||||||||
\(691\) | −43.5653 | −1.65730 | −0.828652 | − | 0.559764i | \(-0.810892\pi\) | ||||
−0.828652 | + | 0.559764i | \(0.810892\pi\) | |||||||
\(692\) | −9.39992 | −0.357331 | ||||||||
\(693\) | −5.70789 | −0.216825 | ||||||||
\(694\) | −48.5148 | −1.84159 | ||||||||
\(695\) | −16.3393 | −0.619786 | ||||||||
\(696\) | 3.47640 | 0.131772 | ||||||||
\(697\) | 5.14956 | 0.195054 | ||||||||
\(698\) | −15.5405 | −0.588217 | ||||||||
\(699\) | −25.3125 | −0.957407 | ||||||||
\(700\) | 3.93146 | 0.148595 | ||||||||
\(701\) | −19.0810 | −0.720680 | −0.360340 | − | 0.932821i | \(-0.617339\pi\) | ||||
−0.360340 | + | 0.932821i | \(0.617339\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.18429 | −0.0446663 | ||||||||
\(704\) | 59.0204 | 2.22442 | ||||||||
\(705\) | 10.7854 | 0.406202 | ||||||||
\(706\) | −78.0250 | −2.93651 | ||||||||
\(707\) | −21.5102 | −0.808975 | ||||||||
\(708\) | −2.66069 | −0.0999947 | ||||||||
\(709\) | −44.6046 | −1.67516 | −0.837581 | − | 0.546313i | \(-0.816031\pi\) | ||||
−0.837581 | + | 0.546313i | \(0.816031\pi\) | |||||||
\(710\) | −21.7338 | −0.815654 | ||||||||
\(711\) | −8.87085 | −0.332683 | ||||||||
\(712\) | −16.7124 | −0.626325 | ||||||||
\(713\) | −19.7953 | −0.741340 | ||||||||
\(714\) | 12.8236 | 0.479913 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16.5663 | −0.619110 | ||||||||
\(717\) | 22.5236 | 0.841159 | ||||||||
\(718\) | 18.4551 | 0.688737 | ||||||||
\(719\) | −12.9822 | −0.484153 | −0.242077 | − | 0.970257i | \(-0.577829\pi\) | ||||
−0.242077 | + | 0.970257i | \(0.577829\pi\) | |||||||
\(720\) | 0.523604 | 0.0195136 | ||||||||
\(721\) | −17.6001 | −0.655461 | ||||||||
\(722\) | 16.2191 | 0.603614 | ||||||||
\(723\) | 11.1157 | 0.413399 | ||||||||
\(724\) | 80.6071 | 2.99574 | ||||||||
\(725\) | −1.37755 | −0.0511610 | ||||||||
\(726\) | −21.4034 | −0.794356 | ||||||||
\(727\) | 17.3980 | 0.645255 | 0.322627 | − | 0.946526i | \(-0.395434\pi\) | ||||
0.322627 | + | 0.946526i | \(0.395434\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 31.1799 | 1.15402 | ||||||||
\(731\) | −28.6563 | −1.05989 | ||||||||
\(732\) | −14.4551 | −0.534275 | ||||||||
\(733\) | −45.8272 | −1.69266 | −0.846332 | − | 0.532655i | \(-0.821194\pi\) | ||||
−0.846332 | + | 0.532655i | \(0.821194\pi\) | |||||||
\(734\) | −15.4720 | −0.571081 | ||||||||
\(735\) | −5.40786 | −0.199472 | ||||||||
\(736\) | −13.9056 | −0.512567 | ||||||||
\(737\) | 59.4069 | 2.18828 | ||||||||
\(738\) | −2.59214 | −0.0954182 | ||||||||
\(739\) | −17.5708 | −0.646353 | −0.323176 | − | 0.946339i | \(-0.604751\pi\) | ||||
−0.323176 | + | 0.946339i | \(0.604751\pi\) | |||||||
\(740\) | −0.721292 | −0.0265152 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.9101 | 0.473946 | ||||||||
\(743\) | 30.3562 | 1.11366 | 0.556831 | − | 0.830626i | \(-0.312017\pi\) | ||||
0.556831 | + | 0.830626i | \(0.312017\pi\) | |||||||
\(744\) | 22.3865 | 0.820730 | ||||||||
\(745\) | −3.24490 | −0.118884 | ||||||||
\(746\) | 31.2563 | 1.14438 | ||||||||
\(747\) | 8.23150 | 0.301175 | ||||||||
\(748\) | 63.3305 | 2.31559 | ||||||||
\(749\) | 15.7641 | 0.576007 | ||||||||
\(750\) | 2.26180 | 0.0825893 | ||||||||
\(751\) | 3.80323 | 0.138782 | 0.0693909 | − | 0.997590i | \(-0.477894\pi\) | ||||
0.0693909 | + | 0.997590i | \(0.477894\pi\) | |||||||
\(752\) | −5.64729 | −0.205935 | ||||||||
\(753\) | −11.0472 | −0.402583 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.69996 | 0.207443 | ||||||||
\(756\) | −3.93146 | −0.142986 | ||||||||
\(757\) | −3.40786 | −0.123861 | −0.0619303 | − | 0.998080i | \(-0.519726\pi\) | ||||
−0.0619303 | + | 0.998080i | \(0.519726\pi\) | |||||||
\(758\) | −26.0462 | −0.946040 | ||||||||
\(759\) | 10.0944 | 0.366404 | ||||||||
\(760\) | 12.9101 | 0.468300 | ||||||||
\(761\) | −7.24490 | −0.262627 | −0.131314 | − | 0.991341i | \(-0.541919\pi\) | ||||
−0.131314 | + | 0.991341i | \(0.541919\pi\) | |||||||
\(762\) | 40.2271 | 1.45727 | ||||||||
\(763\) | 2.87528 | 0.104092 | ||||||||
\(764\) | 33.2022 | 1.20121 | ||||||||
\(765\) | 4.49330 | 0.162456 | ||||||||
\(766\) | −51.7496 | −1.86979 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 12.4630 | 0.449720 | ||||||||
\(769\) | −31.1764 | −1.12425 | −0.562124 | − | 0.827053i | \(-0.690016\pi\) | ||||
−0.562124 | + | 0.827053i | \(0.690016\pi\) | |||||||
\(770\) | 12.9101 | 0.465249 | ||||||||
\(771\) | 2.03030 | 0.0731196 | ||||||||
\(772\) | −24.8733 | −0.895210 | ||||||||
\(773\) | −19.4605 | −0.699947 | −0.349973 | − | 0.936760i | \(-0.613809\pi\) | ||||
−0.349973 | + | 0.936760i | \(0.613809\pi\) | |||||||
\(774\) | 14.4248 | 0.518487 | ||||||||
\(775\) | −8.87085 | −0.318650 | ||||||||
\(776\) | −26.9260 | −0.966587 | ||||||||
\(777\) | −0.292106 | −0.0104792 | ||||||||
\(778\) | −9.84498 | −0.352959 | ||||||||
\(779\) | 5.86292 | 0.210061 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43.4675 | −1.55539 | ||||||||
\(782\) | −22.6786 | −0.810986 | ||||||||
\(783\) | 1.37755 | 0.0492297 | ||||||||
\(784\) | 2.83158 | 0.101128 | ||||||||
\(785\) | 3.85395 | 0.137553 | ||||||||
\(786\) | −26.3945 | −0.941459 | ||||||||
\(787\) | −14.4034 | −0.513427 | −0.256713 | − | 0.966488i | \(-0.582640\pi\) | ||||
−0.256713 | + | 0.966488i | \(0.582640\pi\) | |||||||
\(788\) | −54.0250 | −1.92456 | ||||||||
\(789\) | −3.24840 | −0.115646 | ||||||||
\(790\) | 20.0641 | 0.713849 | ||||||||
\(791\) | −1.86292 | −0.0662378 | ||||||||
\(792\) | −11.4158 | −0.405642 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −17.2405 | −0.611841 | ||||||||
\(795\) | 4.52360 | 0.160436 | ||||||||
\(796\) | −3.83704 | −0.136000 | ||||||||
\(797\) | −23.6011 | −0.835994 | −0.417997 | − | 0.908448i | \(-0.637268\pi\) | ||||
−0.417997 | + | 0.908448i | \(0.637268\pi\) | |||||||
\(798\) | 14.6001 | 0.516837 | ||||||||
\(799\) | −48.4621 | −1.71447 | ||||||||
\(800\) | −6.23150 | −0.220317 | ||||||||
\(801\) | −6.62245 | −0.233993 | ||||||||
\(802\) | −47.1575 | −1.66519 | ||||||||
\(803\) | 62.3597 | 2.20063 | ||||||||
\(804\) | 40.9181 | 1.44307 | ||||||||
\(805\) | −2.81571 | −0.0992407 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.9484 | −0.948627 | ||||||||
\(808\) | −43.0204 | −1.51345 | ||||||||
\(809\) | 26.7551 | 0.940659 | 0.470330 | − | 0.882491i | \(-0.344135\pi\) | ||||
0.470330 | + | 0.882491i | \(0.344135\pi\) | |||||||
\(810\) | −2.26180 | −0.0794716 | ||||||||
\(811\) | 3.58421 | 0.125859 | 0.0629293 | − | 0.998018i | \(-0.479956\pi\) | ||||
0.0629293 | + | 0.998018i | \(0.479956\pi\) | |||||||
\(812\) | −5.41579 | −0.190057 | ||||||||
\(813\) | −19.8495 | −0.696153 | ||||||||
\(814\) | −2.36858 | −0.0830187 | ||||||||
\(815\) | −9.72480 | −0.340645 | ||||||||
\(816\) | −2.35271 | −0.0823614 | ||||||||
\(817\) | −32.6260 | −1.14144 | ||||||||
\(818\) | 38.3721 | 1.34165 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.57081 | 0.124698 | ||||||||
\(821\) | −15.8361 | −0.552685 | −0.276342 | − | 0.961059i | \(-0.589122\pi\) | ||||
−0.276342 | + | 0.961059i | \(0.589122\pi\) | |||||||
\(822\) | −45.3811 | −1.58285 | ||||||||
\(823\) | 7.41579 | 0.258498 | 0.129249 | − | 0.991612i | \(-0.458743\pi\) | ||||
0.129249 | + | 0.991612i | \(0.458743\pi\) | |||||||
\(824\) | −35.2002 | −1.22626 | ||||||||
\(825\) | 4.52360 | 0.157492 | ||||||||
\(826\) | 2.43712 | 0.0847983 | ||||||||
\(827\) | 16.6036 | 0.577363 | 0.288682 | − | 0.957425i | \(-0.406783\pi\) | ||||
0.288682 | + | 0.957425i | \(0.406783\pi\) | |||||||
\(828\) | 6.95279 | 0.241626 | ||||||||
\(829\) | −29.2842 | −1.01708 | −0.508541 | − | 0.861038i | \(-0.669815\pi\) | ||||
−0.508541 | + | 0.861038i | \(0.669815\pi\) | |||||||
\(830\) | −18.6180 | −0.646241 | ||||||||
\(831\) | −16.0944 | −0.558309 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.2991 | 0.841915 | ||||||||
\(834\) | −36.9563 | −1.27969 | ||||||||
\(835\) | −19.2787 | −0.667167 | ||||||||
\(836\) | 72.1035 | 2.49375 | ||||||||
\(837\) | 8.87085 | 0.306622 | ||||||||
\(838\) | 4.74717 | 0.163988 | ||||||||
\(839\) | 30.1620 | 1.04131 | 0.520655 | − | 0.853767i | \(-0.325688\pi\) | ||||
0.520655 | + | 0.853767i | \(0.325688\pi\) | |||||||
\(840\) | 3.18429 | 0.109868 | ||||||||
\(841\) | −27.1024 | −0.934564 | ||||||||
\(842\) | 89.7026 | 3.09135 | ||||||||
\(843\) | −5.37755 | −0.185213 | ||||||||
\(844\) | 32.2147 | 1.10888 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 24.3945 | 0.838699 | ||||||||
\(847\) | 11.9404 | 0.410278 | ||||||||
\(848\) | −2.36858 | −0.0813374 | ||||||||
\(849\) | −26.8664 | −0.922053 | ||||||||
\(850\) | −10.1630 | −0.348587 | ||||||||
\(851\) | 0.516589 | 0.0177085 | ||||||||
\(852\) | −29.9394 | −1.02571 | ||||||||
\(853\) | 2.50670 | 0.0858277 | 0.0429139 | − | 0.999079i | \(-0.486336\pi\) | ||||
0.0429139 | + | 0.999079i | \(0.486336\pi\) | |||||||
\(854\) | 13.2405 | 0.453080 | ||||||||
\(855\) | 5.11575 | 0.174955 | ||||||||
\(856\) | 31.5282 | 1.07761 | ||||||||
\(857\) | −24.4327 | −0.834605 | −0.417302 | − | 0.908768i | \(-0.637024\pi\) | ||||
−0.417302 | + | 0.908768i | \(0.637024\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.10235 | −0.242329 | −0.121165 | − | 0.992632i | \(-0.538663\pi\) | ||||
−0.121165 | + | 0.992632i | \(0.538663\pi\) | |||||||
\(860\) | −19.8709 | −0.677590 | ||||||||
\(861\) | 1.44609 | 0.0492827 | ||||||||
\(862\) | 50.0497 | 1.70470 | ||||||||
\(863\) | 3.24490 | 0.110458 | 0.0552288 | − | 0.998474i | \(-0.482411\pi\) | ||||
0.0552288 | + | 0.998474i | \(0.482411\pi\) | |||||||
\(864\) | 6.23150 | 0.212000 | ||||||||
\(865\) | 3.01691 | 0.102578 | ||||||||
\(866\) | −70.9216 | −2.41001 | ||||||||
\(867\) | −3.18975 | −0.108330 | ||||||||
\(868\) | −34.8754 | −1.18375 | ||||||||
\(869\) | 40.1282 | 1.36126 | ||||||||
\(870\) | −3.11575 | −0.105634 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 5.75056 | 0.194738 | ||||||||
\(873\) | −10.6697 | −0.361113 | ||||||||
\(874\) | −25.8203 | −0.873383 | ||||||||
\(875\) | −1.26180 | −0.0426567 | ||||||||
\(876\) | 42.9519 | 1.45121 | ||||||||
\(877\) | −18.9866 | −0.641132 | −0.320566 | − | 0.947226i | \(-0.603873\pi\) | ||||
−0.320566 | + | 0.947226i | \(0.603873\pi\) | |||||||
\(878\) | 9.75614 | 0.329254 | ||||||||
\(879\) | 21.4193 | 0.722455 | ||||||||
\(880\) | −2.36858 | −0.0798448 | ||||||||
\(881\) | −19.4764 | −0.656176 | −0.328088 | − | 0.944647i | \(-0.606404\pi\) | ||||
−0.328088 | + | 0.944647i | \(0.606404\pi\) | |||||||
\(882\) | −12.2315 | −0.411856 | ||||||||
\(883\) | −50.5664 | −1.70169 | −0.850847 | − | 0.525413i | \(-0.823911\pi\) | ||||
−0.850847 | + | 0.525413i | \(0.823911\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.853947 | 0.0287051 | ||||||||
\(886\) | 1.11575 | 0.0374843 | ||||||||
\(887\) | −12.5271 | −0.420619 | −0.210310 | − | 0.977635i | \(-0.567447\pi\) | ||||
−0.210310 | + | 0.977635i | \(0.567447\pi\) | |||||||
\(888\) | −0.584211 | −0.0196049 | ||||||||
\(889\) | −22.4417 | −0.752669 | ||||||||
\(890\) | 14.9787 | 0.502086 | ||||||||
\(891\) | −4.52360 | −0.151546 | ||||||||
\(892\) | −67.2092 | −2.25033 | ||||||||
\(893\) | −55.1754 | −1.84638 | ||||||||
\(894\) | −7.33931 | −0.245463 | ||||||||
\(895\) | 5.31694 | 0.177726 | ||||||||
\(896\) | −21.5102 | −0.718606 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 52.7283 | 1.75957 | ||||||||
\(899\) | 12.2201 | 0.407562 | ||||||||
\(900\) | 3.11575 | 0.103858 | ||||||||
\(901\) | −20.3259 | −0.677154 | ||||||||
\(902\) | 11.7258 | 0.390428 | ||||||||
\(903\) | −8.04721 | −0.267794 | ||||||||
\(904\) | −3.72584 | −0.123920 | ||||||||
\(905\) | −25.8709 | −0.859976 | ||||||||
\(906\) | 12.8922 | 0.428314 | ||||||||
\(907\) | 28.0417 | 0.931111 | 0.465555 | − | 0.885019i | \(-0.345855\pi\) | ||||
0.465555 | + | 0.885019i | \(0.345855\pi\) | |||||||
\(908\) | −16.9687 | −0.563125 | ||||||||
\(909\) | −17.0472 | −0.565420 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.1977 | 0.536653 | 0.268327 | − | 0.963328i | \(-0.413529\pi\) | ||||
0.268327 | + | 0.963328i | \(0.413529\pi\) | |||||||
\(912\) | −2.67863 | −0.0886983 | ||||||||
\(913\) | −37.2360 | −1.23233 | ||||||||
\(914\) | −15.0854 | −0.498982 | ||||||||
\(915\) | 4.63935 | 0.153372 | ||||||||
\(916\) | −68.3329 | −2.25778 | ||||||||
\(917\) | 14.7248 | 0.486256 | ||||||||
\(918\) | 10.1630 | 0.335428 | ||||||||
\(919\) | −43.2778 | −1.42760 | −0.713801 | − | 0.700348i | \(-0.753028\pi\) | ||||
−0.713801 | + | 0.700348i | \(0.753028\pi\) | |||||||
\(920\) | −5.63142 | −0.185662 | ||||||||
\(921\) | −7.85395 | −0.258796 | ||||||||
\(922\) | −65.8620 | −2.16905 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 17.7844 | 0.585063 | ||||||||
\(925\) | 0.231499 | 0.00761163 | ||||||||
\(926\) | 4.05618 | 0.133294 | ||||||||
\(927\) | −13.9484 | −0.458124 | ||||||||
\(928\) | 8.58421 | 0.281791 | ||||||||
\(929\) | −13.7685 | −0.451730 | −0.225865 | − | 0.974159i | \(-0.572521\pi\) | ||||
−0.225865 | + | 0.974159i | \(0.572521\pi\) | |||||||
\(930\) | −20.0641 | −0.657928 | ||||||||
\(931\) | 27.6652 | 0.906691 | ||||||||
\(932\) | 78.8675 | 2.58339 | ||||||||
\(933\) | 27.8744 | 0.912566 | ||||||||
\(934\) | 38.0417 | 1.24476 | ||||||||
\(935\) | −20.3259 | −0.664729 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.1888 | −1.24757 | −0.623787 | − | 0.781594i | \(-0.714407\pi\) | ||||
−0.623787 | + | 0.781594i | \(0.714407\pi\) | |||||||
\(938\) | −37.4799 | −1.22376 | ||||||||
\(939\) | −7.88776 | −0.257407 | ||||||||
\(940\) | −33.6046 | −1.09606 | ||||||||
\(941\) | 13.9618 | 0.455140 | 0.227570 | − | 0.973762i | \(-0.426922\pi\) | ||||
0.227570 | + | 0.973762i | \(0.426922\pi\) | |||||||
\(942\) | 8.71687 | 0.284011 | ||||||||
\(943\) | −2.55742 | −0.0832809 | ||||||||
\(944\) | −0.447131 | −0.0145529 | ||||||||
\(945\) | 1.26180 | 0.0410464 | ||||||||
\(946\) | −65.2519 | −2.12152 | ||||||||
\(947\) | −7.36962 | −0.239480 | −0.119740 | − | 0.992805i | \(-0.538206\pi\) | ||||
−0.119740 | + | 0.992805i | \(0.538206\pi\) | |||||||
\(948\) | 27.6394 | 0.897684 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −11.5708 | −0.375407 | ||||||||
\(951\) | 13.2181 | 0.428626 | ||||||||
\(952\) | −14.3080 | −0.463724 | ||||||||
\(953\) | 23.2181 | 0.752108 | 0.376054 | − | 0.926598i | \(-0.377281\pi\) | ||||
0.376054 | + | 0.926598i | \(0.377281\pi\) | |||||||
\(954\) | 10.2315 | 0.331257 | ||||||||
\(955\) | −10.6563 | −0.344828 | ||||||||
\(956\) | −70.1779 | −2.26972 | ||||||||
\(957\) | −6.23150 | −0.201436 | ||||||||
\(958\) | −79.5093 | −2.56883 | ||||||||
\(959\) | 25.3169 | 0.817527 | ||||||||
\(960\) | −13.0472 | −0.421097 | ||||||||
\(961\) | 47.6920 | 1.53845 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.4933 | 0.402591 | ||||||||
\(964\) | −34.6339 | −1.11548 | ||||||||
\(965\) | 7.98309 | 0.256985 | ||||||||
\(966\) | −6.36858 | −0.204906 | ||||||||
\(967\) | 7.54402 | 0.242599 | 0.121300 | − | 0.992616i | \(-0.461294\pi\) | ||||
0.121300 | + | 0.992616i | \(0.461294\pi\) | |||||||
\(968\) | 23.8809 | 0.767560 | ||||||||
\(969\) | −22.9866 | −0.738436 | ||||||||
\(970\) | 24.1327 | 0.774853 | ||||||||
\(971\) | −30.5842 | −0.981494 | −0.490747 | − | 0.871302i | \(-0.663276\pi\) | ||||
−0.490747 | + | 0.871302i | \(0.663276\pi\) | |||||||
\(972\) | −3.11575 | −0.0999377 | ||||||||
\(973\) | 20.6170 | 0.660950 | ||||||||
\(974\) | 19.5102 | 0.625147 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.42919 | −0.0777564 | ||||||||
\(977\) | 35.6811 | 1.14154 | 0.570770 | − | 0.821110i | \(-0.306645\pi\) | ||||
0.570770 | + | 0.821110i | \(0.306645\pi\) | |||||||
\(978\) | −21.9956 | −0.703341 | ||||||||
\(979\) | 29.9573 | 0.957441 | ||||||||
\(980\) | 16.8495 | 0.538238 | ||||||||
\(981\) | 2.27871 | 0.0727535 | ||||||||
\(982\) | −52.5047 | −1.67549 | ||||||||
\(983\) | −12.9866 | −0.414208 | −0.207104 | − | 0.978319i | \(-0.566404\pi\) | ||||
−0.207104 | + | 0.978319i | \(0.566404\pi\) | |||||||
\(984\) | 2.89218 | 0.0921995 | ||||||||
\(985\) | 17.3393 | 0.552477 | ||||||||
\(986\) | 14.0000 | 0.445851 | ||||||||
\(987\) | −13.6091 | −0.433181 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.2315 | 0.452535 | ||||||||
\(990\) | 10.2315 | 0.325178 | ||||||||
\(991\) | −22.7472 | −0.722588 | −0.361294 | − | 0.932452i | \(-0.617665\pi\) | ||||
−0.361294 | + | 0.932452i | \(0.617665\pi\) | |||||||
\(992\) | 55.2787 | 1.75510 | ||||||||
\(993\) | −23.8495 | −0.756842 | ||||||||
\(994\) | 27.4237 | 0.869828 | ||||||||
\(995\) | 1.23150 | 0.0390411 | ||||||||
\(996\) | −25.6473 | −0.812665 | ||||||||
\(997\) | −13.8460 | −0.438508 | −0.219254 | − | 0.975668i | \(-0.570362\pi\) | ||||
−0.219254 | + | 0.975668i | \(0.570362\pi\) | |||||||
\(998\) | −65.6811 | −2.07910 | ||||||||
\(999\) | −0.231499 | −0.00732430 |
(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 | 2535.2.a.ba.1.3 | 3 | ||
3.2 | odd | 2 | 7605.2.a.bw.1.1 | 3 | |||
13.4 | even | 6 | 195.2.i.d.16.3 | ✓ | 6 | ||
13.10 | even | 6 | 195.2.i.d.61.3 | yes | 6 | ||
13.12 | even | 2 | 2535.2.a.bb.1.1 | 3 | |||
39.17 | odd | 6 | 585.2.j.f.406.1 | 6 | |||
39.23 | odd | 6 | 585.2.j.f.451.1 | 6 | |||
39.38 | odd | 2 | 7605.2.a.bv.1.3 | 3 | |||
65.4 | even | 6 | 975.2.i.l.601.1 | 6 | |||
65.17 | odd | 12 | 975.2.bb.k.874.2 | 12 | |||
65.23 | odd | 12 | 975.2.bb.k.724.2 | 12 | |||
65.43 | odd | 12 | 975.2.bb.k.874.5 | 12 | |||
65.49 | even | 6 | 975.2.i.l.451.1 | 6 | |||
65.62 | odd | 12 | 975.2.bb.k.724.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.i.d.16.3 | ✓ | 6 | 13.4 | even | 6 | ||
195.2.i.d.61.3 | yes | 6 | 13.10 | even | 6 | ||
585.2.j.f.406.1 | 6 | 39.17 | odd | 6 | |||
585.2.j.f.451.1 | 6 | 39.23 | odd | 6 | |||
975.2.i.l.451.1 | 6 | 65.49 | even | 6 | |||
975.2.i.l.601.1 | 6 | 65.4 | even | 6 | |||
975.2.bb.k.724.2 | 12 | 65.23 | odd | 12 | |||
975.2.bb.k.724.5 | 12 | 65.62 | odd | 12 | |||
975.2.bb.k.874.2 | 12 | 65.17 | odd | 12 | |||
975.2.bb.k.874.5 | 12 | 65.43 | odd | 12 | |||
2535.2.a.ba.1.3 | 3 | 1.1 | even | 1 | trivial | ||
2535.2.a.bb.1.1 | 3 | 13.12 | even | 2 | |||
7605.2.a.bv.1.3 | 3 | 39.38 | odd | 2 | |||
7605.2.a.bw.1.1 | 3 | 3.2 | odd | 2 |