Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9025,2,Mod(1,9025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9025 = 5^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9025.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: | \(72.0649878242\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.4227136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 6x^{4} + 7x^{2} - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.15904\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.862781 | −0.610078 | −0.305039 | − | 0.952340i | \(-0.598670\pi\) | ||||
−0.305039 | + | 0.952340i | \(0.598670\pi\) | |||||||
\(3\) | −3.07914 | −1.77774 | −0.888870 | − | 0.458159i | \(-0.848509\pi\) | ||||
−0.888870 | + | 0.458159i | \(0.848509\pi\) | |||||||
\(4\) | −1.25561 | −0.627804 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.65662 | 1.08456 | ||||||||
\(7\) | 0.566520 | 0.214124 | 0.107062 | − | 0.994252i | \(-0.465856\pi\) | ||||
0.107062 | + | 0.994252i | \(0.465856\pi\) | |||||||
\(8\) | 2.80888 | 0.993088 | ||||||||
\(9\) | 6.48108 | 2.16036 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.91223 | −0.576559 | −0.288279 | − | 0.957546i | \(-0.593083\pi\) | ||||
−0.288279 | + | 0.957546i | \(0.593083\pi\) | |||||||
\(12\) | 3.86619 | 1.11607 | ||||||||
\(13\) | −0.194531 | −0.0539533 | −0.0269766 | − | 0.999636i | \(-0.508588\pi\) | ||||
−0.0269766 | + | 0.999636i | \(0.508588\pi\) | |||||||
\(14\) | −0.488783 | −0.130633 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.0877708 | 0.0219427 | ||||||||
\(17\) | 5.29549 | 1.28435 | 0.642173 | − | 0.766560i | \(-0.278033\pi\) | ||||
0.642173 | + | 0.766560i | \(0.278033\pi\) | |||||||
\(18\) | −5.59175 | −1.31799 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.74439 | −0.380657 | ||||||||
\(22\) | 1.64984 | 0.351746 | ||||||||
\(23\) | 3.37540 | 0.703819 | 0.351910 | − | 0.936034i | \(-0.385532\pi\) | ||||
0.351910 | + | 0.936034i | \(0.385532\pi\) | |||||||
\(24\) | −8.64892 | −1.76545 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.167838 | 0.0329157 | ||||||||
\(27\) | −10.7187 | −2.06282 | ||||||||
\(28\) | −0.711327 | −0.134428 | ||||||||
\(29\) | 8.73669 | 1.62236 | 0.811181 | − | 0.584795i | \(-0.198825\pi\) | ||||
0.811181 | + | 0.584795i | \(0.198825\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.65662 | −1.01596 | −0.507980 | − | 0.861369i | \(-0.669607\pi\) | ||||
−0.507980 | + | 0.861369i | \(0.669607\pi\) | |||||||
\(32\) | −5.69348 | −1.00648 | ||||||||
\(33\) | 5.88801 | 1.02497 | ||||||||
\(34\) | −4.56885 | −0.783551 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −8.13770 | −1.35628 | ||||||||
\(37\) | −0.955582 | −0.157097 | −0.0785484 | − | 0.996910i | \(-0.525029\pi\) | ||||
−0.0785484 | + | 0.996910i | \(0.525029\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.598988 | 0.0959149 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.0499 | −1.56954 | −0.784768 | − | 0.619790i | \(-0.787218\pi\) | ||||
−0.784768 | + | 0.619790i | \(0.787218\pi\) | |||||||
\(42\) | 1.50503 | 0.232231 | ||||||||
\(43\) | −4.93243 | −0.752189 | −0.376094 | − | 0.926581i | \(-0.622733\pi\) | ||||
−0.376094 | + | 0.926581i | \(0.622733\pi\) | |||||||
\(44\) | 2.40101 | 0.361966 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.91223 | −0.429385 | ||||||||
\(47\) | 8.83942 | 1.28936 | 0.644681 | − | 0.764452i | \(-0.276990\pi\) | ||||
0.644681 | + | 0.764452i | \(0.276990\pi\) | |||||||
\(48\) | −0.270258 | −0.0390084 | ||||||||
\(49\) | −6.67906 | −0.954151 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.3055 | −2.28323 | ||||||||
\(52\) | 0.244255 | 0.0338721 | ||||||||
\(53\) | 8.20610 | 1.12719 | 0.563597 | − | 0.826050i | \(-0.309417\pi\) | ||||
0.563597 | + | 0.826050i | \(0.309417\pi\) | |||||||
\(54\) | 9.24791 | 1.25848 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.59128 | 0.212644 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.53785 | −0.989768 | ||||||||
\(59\) | −3.71425 | −0.483554 | −0.241777 | − | 0.970332i | \(-0.577730\pi\) | ||||
−0.241777 | + | 0.970332i | \(0.577730\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.51122 | −0.449565 | −0.224783 | − | 0.974409i | \(-0.572167\pi\) | ||||
−0.224783 | + | 0.974409i | \(0.572167\pi\) | |||||||
\(62\) | 4.88043 | 0.619815 | ||||||||
\(63\) | 3.67166 | 0.462586 | ||||||||
\(64\) | 4.73669 | 0.592086 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.08007 | −0.625313 | ||||||||
\(67\) | −4.04365 | −0.494010 | −0.247005 | − | 0.969014i | \(-0.579446\pi\) | ||||
−0.247005 | + | 0.969014i | \(0.579446\pi\) | |||||||
\(68\) | −6.64906 | −0.806318 | ||||||||
\(69\) | −10.3933 | −1.25121 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.19533 | −0.616572 | −0.308286 | − | 0.951294i | \(-0.599755\pi\) | ||||
−0.308286 | + | 0.951294i | \(0.599755\pi\) | |||||||
\(72\) | 18.2046 | 2.14543 | ||||||||
\(73\) | 8.60409 | 1.00703 | 0.503516 | − | 0.863986i | \(-0.332039\pi\) | ||||
0.503516 | + | 0.863986i | \(0.332039\pi\) | |||||||
\(74\) | 0.824458 | 0.0958413 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.08332 | −0.123455 | ||||||||
\(78\) | −0.516796 | −0.0585156 | ||||||||
\(79\) | −6.62648 | −0.745537 | −0.372769 | − | 0.927924i | \(-0.621592\pi\) | ||||
−0.372769 | + | 0.927924i | \(0.621592\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 13.5611 | 1.50679 | ||||||||
\(82\) | 8.67089 | 0.957539 | ||||||||
\(83\) | −4.51737 | −0.495845 | −0.247923 | − | 0.968780i | \(-0.579748\pi\) | ||||
−0.247923 | + | 0.968780i | \(0.579748\pi\) | |||||||
\(84\) | 2.19027 | 0.238978 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.25561 | 0.458894 | ||||||||
\(87\) | −26.9014 | −2.88414 | ||||||||
\(88\) | −5.37122 | −0.572574 | ||||||||
\(89\) | −3.37352 | −0.357592 | −0.178796 | − | 0.983886i | \(-0.557220\pi\) | ||||
−0.178796 | + | 0.983886i | \(0.557220\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.110206 | −0.0115527 | ||||||||
\(92\) | −4.23818 | −0.441861 | ||||||||
\(93\) | 17.4175 | 1.80611 | ||||||||
\(94\) | −7.62648 | −0.786612 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 17.5310 | 1.78925 | ||||||||
\(97\) | −15.1922 | −1.54254 | −0.771268 | − | 0.636510i | \(-0.780377\pi\) | ||||
−0.771268 | + | 0.636510i | \(0.780377\pi\) | |||||||
\(98\) | 5.76256 | 0.582107 | ||||||||
\(99\) | −12.3933 | −1.24557 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.54136 | 0.352378 | 0.176189 | − | 0.984356i | \(-0.443623\pi\) | ||||
0.176189 | + | 0.984356i | \(0.443623\pi\) | |||||||
\(102\) | 14.0681 | 1.39295 | ||||||||
\(103\) | −15.6919 | −1.54617 | −0.773086 | − | 0.634301i | \(-0.781288\pi\) | ||||
−0.773086 | + | 0.634301i | \(0.781288\pi\) | |||||||
\(104\) | −0.546415 | −0.0535804 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.08007 | −0.687677 | ||||||||
\(107\) | −1.05731 | −0.102214 | −0.0511071 | − | 0.998693i | \(-0.516275\pi\) | ||||
−0.0511071 | + | 0.998693i | \(0.516275\pi\) | |||||||
\(108\) | 13.4585 | 1.29505 | ||||||||
\(109\) | 6.74439 | 0.645996 | 0.322998 | − | 0.946400i | \(-0.395309\pi\) | ||||
0.322998 | + | 0.946400i | \(0.395309\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.94237 | 0.279277 | ||||||||
\(112\) | 0.0497239 | 0.00469847 | ||||||||
\(113\) | 7.90091 | 0.743255 | 0.371627 | − | 0.928382i | \(-0.378800\pi\) | ||||
0.371627 | + | 0.928382i | \(0.378800\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −10.9699 | −1.01853 | ||||||||
\(117\) | −1.26077 | −0.116558 | ||||||||
\(118\) | 3.20459 | 0.295006 | ||||||||
\(119\) | 3.00000 | 0.275010 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.34338 | −0.667580 | ||||||||
\(122\) | 3.02941 | 0.274270 | ||||||||
\(123\) | 30.9451 | 2.79023 | ||||||||
\(124\) | 7.10250 | 0.637824 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.16784 | −0.282213 | ||||||||
\(127\) | 8.47636 | 0.752155 | 0.376078 | − | 0.926588i | \(-0.377273\pi\) | ||||
0.376078 | + | 0.926588i | \(0.377273\pi\) | |||||||
\(128\) | 7.30024 | 0.645256 | ||||||||
\(129\) | 15.1876 | 1.33720 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.87439 | 0.163766 | 0.0818830 | − | 0.996642i | \(-0.473907\pi\) | ||||
0.0818830 | + | 0.996642i | \(0.473907\pi\) | |||||||
\(132\) | −7.39304 | −0.643482 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.48878 | 0.301385 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14.8744 | 1.27547 | ||||||||
\(137\) | 12.4614 | 1.06465 | 0.532323 | − | 0.846542i | \(-0.321319\pi\) | ||||
0.532323 | + | 0.846542i | \(0.321319\pi\) | |||||||
\(138\) | 8.96715 | 0.763334 | ||||||||
\(139\) | −0.313241 | −0.0265687 | −0.0132844 | − | 0.999912i | \(-0.504229\pi\) | ||||
−0.0132844 | + | 0.999912i | \(0.504229\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −27.2178 | −2.29215 | ||||||||
\(142\) | 4.48243 | 0.376157 | ||||||||
\(143\) | 0.371988 | 0.0311072 | ||||||||
\(144\) | 0.568850 | 0.0474041 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.42345 | −0.614369 | ||||||||
\(147\) | 20.5657 | 1.69623 | ||||||||
\(148\) | 1.19984 | 0.0986260 | ||||||||
\(149\) | 4.36581 | 0.357661 | 0.178831 | − | 0.983880i | \(-0.442769\pi\) | ||||
0.178831 | + | 0.983880i | \(0.442769\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.197977 | −0.0161111 | −0.00805555 | − | 0.999968i | \(-0.502564\pi\) | ||||
−0.00805555 | + | 0.999968i | \(0.502564\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 34.3205 | 2.77465 | ||||||||
\(154\) | 0.934664 | 0.0753174 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.752095 | −0.0602158 | ||||||||
\(157\) | 15.7700 | 1.25858 | 0.629290 | − | 0.777171i | \(-0.283346\pi\) | ||||
0.629290 | + | 0.777171i | \(0.283346\pi\) | |||||||
\(158\) | 5.71720 | 0.454836 | ||||||||
\(159\) | −25.2677 | −2.00386 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.91223 | 0.150705 | ||||||||
\(162\) | −11.7003 | −0.919262 | ||||||||
\(163\) | 9.18768 | 0.719635 | 0.359817 | − | 0.933023i | \(-0.382839\pi\) | ||||
0.359817 | + | 0.933023i | \(0.382839\pi\) | |||||||
\(164\) | 12.6188 | 0.985361 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.89750 | 0.302505 | ||||||||
\(167\) | 3.07021 | 0.237580 | 0.118790 | − | 0.992919i | \(-0.462099\pi\) | ||||
0.118790 | + | 0.992919i | \(0.462099\pi\) | |||||||
\(168\) | −4.89978 | −0.378026 | ||||||||
\(169\) | −12.9622 | −0.997089 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.19320 | 0.472227 | ||||||||
\(173\) | −10.4135 | −0.791726 | −0.395863 | − | 0.918310i | \(-0.629554\pi\) | ||||
−0.395863 | + | 0.918310i | \(0.629554\pi\) | |||||||
\(174\) | 23.2101 | 1.75955 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.167838 | −0.0126513 | ||||||||
\(177\) | 11.4367 | 0.859634 | ||||||||
\(178\) | 2.91061 | 0.218159 | ||||||||
\(179\) | 13.4432 | 1.00479 | 0.502397 | − | 0.864637i | \(-0.332451\pi\) | ||||
0.502397 | + | 0.864637i | \(0.332451\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.96216 | −0.591823 | −0.295911 | − | 0.955215i | \(-0.595623\pi\) | ||||
−0.295911 | + | 0.955215i | \(0.595623\pi\) | |||||||
\(182\) | 0.0950835 | 0.00704806 | ||||||||
\(183\) | 10.8115 | 0.799210 | ||||||||
\(184\) | 9.48108 | 0.698954 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −15.0275 | −1.10187 | ||||||||
\(187\) | −10.1262 | −0.740501 | ||||||||
\(188\) | −11.0988 | −0.809467 | ||||||||
\(189\) | −6.07236 | −0.441699 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.0999 | −1.02023 | −0.510115 | − | 0.860106i | \(-0.670397\pi\) | ||||
−0.510115 | + | 0.860106i | \(0.670397\pi\) | |||||||
\(192\) | −14.5849 | −1.05257 | ||||||||
\(193\) | −3.97685 | −0.286260 | −0.143130 | − | 0.989704i | \(-0.545717\pi\) | ||||
−0.143130 | + | 0.989704i | \(0.545717\pi\) | |||||||
\(194\) | 13.1076 | 0.941068 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.38628 | 0.599020 | ||||||||
\(197\) | 18.3494 | 1.30734 | 0.653669 | − | 0.756781i | \(-0.273229\pi\) | ||||
0.653669 | + | 0.756781i | \(0.273229\pi\) | |||||||
\(198\) | 10.6927 | 0.759898 | ||||||||
\(199\) | −1.60669 | −0.113895 | −0.0569477 | − | 0.998377i | \(-0.518137\pi\) | ||||
−0.0569477 | + | 0.998377i | \(0.518137\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.4509 | 0.878222 | ||||||||
\(202\) | −3.05542 | −0.214978 | ||||||||
\(203\) | 4.94951 | 0.347387 | ||||||||
\(204\) | 20.4734 | 1.43342 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 13.5387 | 0.943287 | ||||||||
\(207\) | 21.8762 | 1.52050 | ||||||||
\(208\) | −0.0170742 | −0.00118388 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.09986 | 0.419931 | 0.209966 | − | 0.977709i | \(-0.432665\pi\) | ||||
0.209966 | + | 0.977709i | \(0.432665\pi\) | |||||||
\(212\) | −10.3036 | −0.707658 | ||||||||
\(213\) | 15.9971 | 1.09611 | ||||||||
\(214\) | 0.912229 | 0.0623587 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −30.1076 | −2.04856 | ||||||||
\(217\) | −3.20459 | −0.217542 | ||||||||
\(218\) | −5.81893 | −0.394108 | ||||||||
\(219\) | −26.4932 | −1.79024 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.03014 | −0.0692946 | ||||||||
\(222\) | −2.53862 | −0.170381 | ||||||||
\(223\) | −17.2253 | −1.15349 | −0.576744 | − | 0.816925i | \(-0.695677\pi\) | ||||
−0.576744 | + | 0.816925i | \(0.695677\pi\) | |||||||
\(224\) | −3.22547 | −0.215511 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.81675 | −0.453444 | ||||||||
\(227\) | −1.18505 | −0.0786542 | −0.0393271 | − | 0.999226i | \(-0.512521\pi\) | ||||
−0.0393271 | + | 0.999226i | \(0.512521\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.24791 | 0.412873 | 0.206437 | − | 0.978460i | \(-0.433813\pi\) | ||||
0.206437 | + | 0.978460i | \(0.433813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.33568 | 0.219471 | ||||||||
\(232\) | 24.5403 | 1.61115 | ||||||||
\(233\) | −2.75687 | −0.180609 | −0.0903043 | − | 0.995914i | \(-0.528784\pi\) | ||||
−0.0903043 | + | 0.995914i | \(0.528784\pi\) | |||||||
\(234\) | 1.08777 | 0.0711098 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.66365 | 0.303578 | ||||||||
\(237\) | 20.4038 | 1.32537 | ||||||||
\(238\) | −2.58834 | −0.167777 | ||||||||
\(239\) | 17.3055 | 1.11940 | 0.559701 | − | 0.828695i | \(-0.310916\pi\) | ||||
0.559701 | + | 0.828695i | \(0.310916\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.78662 | 0.308333 | 0.154167 | − | 0.988045i | \(-0.450731\pi\) | ||||
0.154167 | + | 0.988045i | \(0.450731\pi\) | |||||||
\(242\) | 6.33573 | 0.407276 | ||||||||
\(243\) | −9.60047 | −0.615870 | ||||||||
\(244\) | 4.40872 | 0.282239 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −26.6988 | −1.70226 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −15.8888 | −1.00894 | ||||||||
\(249\) | 13.9096 | 0.881484 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.2479 | −1.65675 | −0.828377 | − | 0.560172i | \(-0.810735\pi\) | ||||
−0.828377 | + | 0.560172i | \(0.810735\pi\) | |||||||
\(252\) | −4.61017 | −0.290413 | ||||||||
\(253\) | −6.45453 | −0.405793 | ||||||||
\(254\) | −7.31324 | −0.458874 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.7719 | −0.985743 | ||||||||
\(257\) | 22.2505 | 1.38795 | 0.693974 | − | 0.720000i | \(-0.255858\pi\) | ||||
0.693974 | + | 0.720000i | \(0.255858\pi\) | |||||||
\(258\) | −13.1036 | −0.815794 | ||||||||
\(259\) | −0.541356 | −0.0336382 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 56.6232 | 3.50489 | ||||||||
\(262\) | −1.61719 | −0.0999101 | ||||||||
\(263\) | 8.81341 | 0.543458 | 0.271729 | − | 0.962374i | \(-0.412405\pi\) | ||||
0.271729 | + | 0.962374i | \(0.412405\pi\) | |||||||
\(264\) | 16.5387 | 1.01789 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.3875 | 0.635706 | ||||||||
\(268\) | 5.07724 | 0.310142 | ||||||||
\(269\) | 4.76418 | 0.290477 | 0.145239 | − | 0.989397i | \(-0.453605\pi\) | ||||
0.145239 | + | 0.989397i | \(0.453605\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.51892 | 0.213759 | 0.106880 | − | 0.994272i | \(-0.465914\pi\) | ||||
0.106880 | + | 0.994272i | \(0.465914\pi\) | |||||||
\(272\) | 0.464790 | 0.0281820 | ||||||||
\(273\) | 0.339339 | 0.0205377 | ||||||||
\(274\) | −10.7514 | −0.649517 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 13.0499 | 0.785513 | ||||||||
\(277\) | 32.7724 | 1.96910 | 0.984551 | − | 0.175098i | \(-0.0560242\pi\) | ||||
0.984551 | + | 0.175098i | \(0.0560242\pi\) | |||||||
\(278\) | 0.270258 | 0.0162090 | ||||||||
\(279\) | −36.6610 | −2.19484 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.91993 | −0.591774 | −0.295887 | − | 0.955223i | \(-0.595615\pi\) | ||||
−0.295887 | + | 0.955223i | \(0.595615\pi\) | |||||||
\(282\) | 23.4830 | 1.39839 | ||||||||
\(283\) | −2.47182 | −0.146935 | −0.0734673 | − | 0.997298i | \(-0.523406\pi\) | ||||
−0.0734673 | + | 0.997298i | \(0.523406\pi\) | |||||||
\(284\) | 6.52330 | 0.387087 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.320945 | −0.0189779 | ||||||||
\(287\) | −5.69348 | −0.336076 | ||||||||
\(288\) | −36.8999 | −2.17435 | ||||||||
\(289\) | 11.0422 | 0.649543 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 46.7789 | 2.74223 | ||||||||
\(292\) | −10.8034 | −0.632219 | ||||||||
\(293\) | −17.0284 | −0.994812 | −0.497406 | − | 0.867518i | \(-0.665714\pi\) | ||||
−0.497406 | + | 0.867518i | \(0.665714\pi\) | |||||||
\(294\) | −17.7437 | −1.03483 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.68411 | −0.156011 | ||||||||
\(297\) | 20.4966 | 1.18934 | ||||||||
\(298\) | −3.76674 | −0.218202 | ||||||||
\(299\) | −0.656620 | −0.0379733 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.79432 | −0.161062 | ||||||||
\(302\) | 0.170810 | 0.00982904 | ||||||||
\(303\) | −10.9043 | −0.626437 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −29.6111 | −1.69275 | ||||||||
\(307\) | 20.9793 | 1.19735 | 0.598676 | − | 0.800992i | \(-0.295694\pi\) | ||||
0.598676 | + | 0.800992i | \(0.295694\pi\) | |||||||
\(308\) | 1.36022 | 0.0775058 | ||||||||
\(309\) | 48.3176 | 2.74869 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.14805 | −0.178509 | −0.0892547 | − | 0.996009i | \(-0.528449\pi\) | ||||
−0.0892547 | + | 0.996009i | \(0.528449\pi\) | |||||||
\(312\) | 1.68248 | 0.0952520 | ||||||||
\(313\) | −12.2928 | −0.694831 | −0.347416 | − | 0.937711i | \(-0.612941\pi\) | ||||
−0.347416 | + | 0.937711i | \(0.612941\pi\) | |||||||
\(314\) | −13.6060 | −0.767832 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.32027 | 0.468052 | ||||||||
\(317\) | −11.4619 | −0.643765 | −0.321882 | − | 0.946780i | \(-0.604316\pi\) | ||||
−0.321882 | + | 0.946780i | \(0.604316\pi\) | |||||||
\(318\) | 21.8005 | 1.22251 | ||||||||
\(319\) | −16.7065 | −0.935387 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.25561 | 0.181710 | ||||||||
\(322\) | −1.64984 | −0.0919417 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −17.0275 | −0.945972 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7.92696 | −0.439034 | ||||||||
\(327\) | −20.7669 | −1.14841 | ||||||||
\(328\) | −28.2290 | −1.55869 | ||||||||
\(329\) | 5.00770 | 0.276084 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.85724 | −0.321943 | −0.160972 | − | 0.986959i | \(-0.551463\pi\) | ||||
−0.160972 | + | 0.986959i | \(0.551463\pi\) | |||||||
\(332\) | 5.67204 | 0.311294 | ||||||||
\(333\) | −6.19320 | −0.339385 | ||||||||
\(334\) | −2.64892 | −0.144942 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.153107 | −0.00835265 | ||||||||
\(337\) | −8.60995 | −0.469014 | −0.234507 | − | 0.972114i | \(-0.575348\pi\) | ||||
−0.234507 | + | 0.972114i | \(0.575348\pi\) | |||||||
\(338\) | 11.1835 | 0.608302 | ||||||||
\(339\) | −24.3280 | −1.32131 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.8168 | 0.585760 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.74945 | −0.418431 | ||||||||
\(344\) | −13.8546 | −0.746990 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.98459 | 0.483015 | ||||||||
\(347\) | −12.0901 | −0.649033 | −0.324517 | − | 0.945880i | \(-0.605202\pi\) | ||||
−0.324517 | + | 0.945880i | \(0.605202\pi\) | |||||||
\(348\) | 33.7777 | 1.81067 | ||||||||
\(349\) | 18.9819 | 1.01608 | 0.508040 | − | 0.861333i | \(-0.330370\pi\) | ||||
0.508040 | + | 0.861333i | \(0.330370\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.08513 | 0.111296 | ||||||||
\(352\) | 10.8872 | 0.580292 | ||||||||
\(353\) | −7.71759 | −0.410766 | −0.205383 | − | 0.978682i | \(-0.565844\pi\) | ||||
−0.205383 | + | 0.978682i | \(0.565844\pi\) | |||||||
\(354\) | −9.86736 | −0.524444 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.23582 | 0.224498 | ||||||||
\(357\) | −9.23741 | −0.488895 | ||||||||
\(358\) | −11.5986 | −0.613003 | ||||||||
\(359\) | −7.03014 | −0.371037 | −0.185518 | − | 0.982641i | \(-0.559396\pi\) | ||||
−0.185518 | + | 0.982641i | \(0.559396\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 6.86960 | 0.361058 | ||||||||
\(363\) | 22.6113 | 1.18678 | ||||||||
\(364\) | 0.138375 | 0.00725284 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.32797 | −0.487581 | ||||||||
\(367\) | −33.7109 | −1.75969 | −0.879847 | − | 0.475257i | \(-0.842355\pi\) | ||||
−0.879847 | + | 0.475257i | \(0.842355\pi\) | |||||||
\(368\) | 0.296261 | 0.0154437 | ||||||||
\(369\) | −65.1344 | −3.39076 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.64892 | 0.241360 | ||||||||
\(372\) | −21.8696 | −1.13388 | ||||||||
\(373\) | −10.0097 | −0.518281 | −0.259141 | − | 0.965840i | \(-0.583439\pi\) | ||||
−0.259141 | + | 0.965840i | \(0.583439\pi\) | |||||||
\(374\) | 8.73669 | 0.451763 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 24.8288 | 1.28045 | ||||||||
\(377\) | −1.69956 | −0.0875317 | ||||||||
\(378\) | 5.23912 | 0.269471 | ||||||||
\(379\) | 35.8064 | 1.83925 | 0.919626 | − | 0.392796i | \(-0.128492\pi\) | ||||
0.919626 | + | 0.392796i | \(0.128492\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.0999 | −1.33714 | ||||||||
\(382\) | 12.1651 | 0.622420 | ||||||||
\(383\) | 16.2495 | 0.830312 | 0.415156 | − | 0.909750i | \(-0.363727\pi\) | ||||
0.415156 | + | 0.909750i | \(0.363727\pi\) | |||||||
\(384\) | −22.4784 | −1.14710 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.43115 | 0.174641 | ||||||||
\(387\) | −31.9675 | −1.62500 | ||||||||
\(388\) | 19.0755 | 0.968411 | ||||||||
\(389\) | −19.3856 | −0.982889 | −0.491445 | − | 0.870909i | \(-0.663531\pi\) | ||||
−0.491445 | + | 0.870909i | \(0.663531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.8744 | 0.903947 | ||||||||
\(392\) | −18.7607 | −0.947556 | ||||||||
\(393\) | −5.77149 | −0.291133 | ||||||||
\(394\) | −15.8315 | −0.797579 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 15.5611 | 0.781977 | ||||||||
\(397\) | 5.35414 | 0.268717 | 0.134358 | − | 0.990933i | \(-0.457103\pi\) | ||||
0.134358 | + | 0.990933i | \(0.457103\pi\) | |||||||
\(398\) | 1.38622 | 0.0694851 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.33832 | −0.416396 | −0.208198 | − | 0.978087i | \(-0.566760\pi\) | ||||
−0.208198 | + | 0.978087i | \(0.566760\pi\) | |||||||
\(402\) | −10.7424 | −0.535784 | ||||||||
\(403\) | 1.10039 | 0.0548143 | ||||||||
\(404\) | −4.44656 | −0.221225 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.27034 | −0.211933 | ||||||||
\(407\) | 1.82729 | 0.0905755 | ||||||||
\(408\) | −45.8003 | −2.26745 | ||||||||
\(409\) | 35.3227 | 1.74659 | 0.873297 | − | 0.487188i | \(-0.161977\pi\) | ||||
0.873297 | + | 0.487188i | \(0.161977\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −38.3702 | −1.89266 | ||||||||
\(412\) | 19.7029 | 0.970694 | ||||||||
\(413\) | −2.10420 | −0.103541 | ||||||||
\(414\) | −18.8744 | −0.927626 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.10756 | 0.0543026 | ||||||||
\(417\) | 0.964511 | 0.0472323 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.2453 | 1.03790 | 0.518949 | − | 0.854805i | \(-0.326323\pi\) | ||||
0.518949 | + | 0.854805i | \(0.326323\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.8744 | 0.724933 | 0.362467 | − | 0.931997i | \(-0.381935\pi\) | ||||
0.362467 | + | 0.931997i | \(0.381935\pi\) | |||||||
\(422\) | −5.26284 | −0.256191 | ||||||||
\(423\) | 57.2890 | 2.78548 | ||||||||
\(424\) | 23.0499 | 1.11940 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −13.8020 | −0.668710 | ||||||||
\(427\) | −1.98917 | −0.0962629 | ||||||||
\(428\) | 1.32757 | 0.0641706 | ||||||||
\(429\) | −1.14540 | −0.0553006 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.9518 | 0.816540 | 0.408270 | − | 0.912861i | \(-0.366132\pi\) | ||||
0.408270 | + | 0.912861i | \(0.366132\pi\) | |||||||
\(432\) | −0.940790 | −0.0452638 | ||||||||
\(433\) | −23.1459 | −1.11232 | −0.556161 | − | 0.831075i | \(-0.687726\pi\) | ||||
−0.556161 | + | 0.831075i | \(0.687726\pi\) | |||||||
\(434\) | 2.76486 | 0.132717 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.46832 | −0.405559 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 22.8578 | 1.09219 | ||||||||
\(439\) | −33.5457 | −1.60105 | −0.800525 | − | 0.599299i | \(-0.795446\pi\) | ||||
−0.800525 | + | 0.599299i | \(0.795446\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −43.2875 | −2.06131 | ||||||||
\(442\) | 0.888784 | 0.0422752 | ||||||||
\(443\) | −31.3579 | −1.48986 | −0.744929 | − | 0.667144i | \(-0.767517\pi\) | ||||
−0.744929 | + | 0.667144i | \(0.767517\pi\) | |||||||
\(444\) | −3.69446 | −0.175331 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14.8616 | 0.703718 | ||||||||
\(447\) | −13.4429 | −0.635829 | ||||||||
\(448\) | 2.68343 | 0.126780 | ||||||||
\(449\) | 16.0301 | 0.756509 | 0.378255 | − | 0.925702i | \(-0.376524\pi\) | ||||
0.378255 | + | 0.925702i | \(0.376524\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.2178 | 0.904929 | ||||||||
\(452\) | −9.92045 | −0.466619 | ||||||||
\(453\) | 0.609597 | 0.0286414 | ||||||||
\(454\) | 1.02243 | 0.0479853 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.3980 | −0.720286 | −0.360143 | − | 0.932897i | \(-0.617272\pi\) | ||||
−0.360143 | + | 0.932897i | \(0.617272\pi\) | |||||||
\(458\) | −5.39057 | −0.251885 | ||||||||
\(459\) | −56.7609 | −2.64937 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.81411 | −0.270790 | −0.135395 | − | 0.990792i | \(-0.543230\pi\) | ||||
−0.135395 | + | 0.990792i | \(0.543230\pi\) | |||||||
\(462\) | −2.87796 | −0.133895 | ||||||||
\(463\) | −32.6788 | −1.51871 | −0.759356 | − | 0.650675i | \(-0.774486\pi\) | ||||
−0.759356 | + | 0.650675i | \(0.774486\pi\) | |||||||
\(464\) | 0.766826 | 0.0355990 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.37858 | 0.110185 | ||||||||
\(467\) | 6.59041 | 0.304968 | 0.152484 | − | 0.988306i | \(-0.451273\pi\) | ||||
0.152484 | + | 0.988306i | \(0.451273\pi\) | |||||||
\(468\) | 1.58304 | 0.0731759 | ||||||||
\(469\) | −2.29081 | −0.105780 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −48.5578 | −2.23743 | ||||||||
\(472\) | −10.4329 | −0.480212 | ||||||||
\(473\) | 9.43194 | 0.433681 | ||||||||
\(474\) | −17.6040 | −0.808581 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.76683 | −0.172652 | ||||||||
\(477\) | 53.1844 | 2.43515 | ||||||||
\(478\) | −14.9309 | −0.682923 | ||||||||
\(479\) | −36.8064 | −1.68173 | −0.840864 | − | 0.541247i | \(-0.817952\pi\) | ||||
−0.840864 | + | 0.541247i | \(0.817952\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.185891 | 0.00847588 | ||||||||
\(482\) | −4.12980 | −0.188107 | ||||||||
\(483\) | −5.88801 | −0.267914 | ||||||||
\(484\) | 9.22041 | 0.419110 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.28310 | 0.375729 | ||||||||
\(487\) | 2.45475 | 0.111235 | 0.0556176 | − | 0.998452i | \(-0.482287\pi\) | ||||
0.0556176 | + | 0.998452i | \(0.482287\pi\) | |||||||
\(488\) | −9.86258 | −0.446458 | ||||||||
\(489\) | −28.2901 | −1.27932 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.7943 | 0.803046 | 0.401523 | − | 0.915849i | \(-0.368481\pi\) | ||||
0.401523 | + | 0.915849i | \(0.368481\pi\) | |||||||
\(492\) | −38.8549 | −1.75172 | ||||||||
\(493\) | 46.2651 | 2.08367 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.496486 | −0.0222929 | ||||||||
\(497\) | −2.94326 | −0.132023 | ||||||||
\(498\) | −12.0009 | −0.537774 | ||||||||
\(499\) | −29.2798 | −1.31074 | −0.655371 | − | 0.755307i | \(-0.727488\pi\) | ||||
−0.655371 | + | 0.755307i | \(0.727488\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.45359 | −0.422355 | ||||||||
\(502\) | 22.6462 | 1.01075 | ||||||||
\(503\) | 29.4378 | 1.31257 | 0.656283 | − | 0.754515i | \(-0.272128\pi\) | ||||
0.656283 | + | 0.754515i | \(0.272128\pi\) | |||||||
\(504\) | 10.3132 | 0.459388 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.56885 | 0.247566 | ||||||||
\(507\) | 39.9122 | 1.77257 | ||||||||
\(508\) | −10.6430 | −0.472206 | ||||||||
\(509\) | −6.69446 | −0.296727 | −0.148363 | − | 0.988933i | \(-0.547401\pi\) | ||||
−0.148363 | + | 0.988933i | \(0.547401\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.87439 | 0.215630 | ||||||||
\(512\) | −0.992797 | −0.0438758 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.1973 | −0.846757 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −19.0697 | −0.839498 | ||||||||
\(517\) | −16.9030 | −0.743393 | ||||||||
\(518\) | 0.467072 | 0.0205220 | ||||||||
\(519\) | 32.0647 | 1.40748 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.0801 | −0.879724 | −0.439862 | − | 0.898065i | \(-0.644973\pi\) | ||||
−0.439862 | + | 0.898065i | \(0.644973\pi\) | |||||||
\(522\) | −48.8534 | −2.13825 | ||||||||
\(523\) | 36.4440 | 1.59359 | 0.796793 | − | 0.604252i | \(-0.206528\pi\) | ||||
0.796793 | + | 0.604252i | \(0.206528\pi\) | |||||||
\(524\) | −2.35350 | −0.102813 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.60405 | −0.331552 | ||||||||
\(527\) | −29.9546 | −1.30484 | ||||||||
\(528\) | 0.516796 | 0.0224907 | ||||||||
\(529\) | −11.6067 | −0.504639 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −24.0724 | −1.04465 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.95503 | 0.0846816 | ||||||||
\(534\) | −8.96216 | −0.387830 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −11.3581 | −0.490596 | ||||||||
\(537\) | −41.3936 | −1.78626 | ||||||||
\(538\) | −4.11045 | −0.177214 | ||||||||
\(539\) | 12.7719 | 0.550124 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.6291 | −0.628955 | −0.314478 | − | 0.949265i | \(-0.601829\pi\) | ||||
−0.314478 | + | 0.949265i | \(0.601829\pi\) | |||||||
\(542\) | −3.03606 | −0.130410 | ||||||||
\(543\) | 24.5166 | 1.05211 | ||||||||
\(544\) | −30.1498 | −1.29266 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.292775 | −0.0125296 | ||||||||
\(547\) | −20.4186 | −0.873038 | −0.436519 | − | 0.899695i | \(-0.643789\pi\) | ||||
−0.436519 | + | 0.899695i | \(0.643789\pi\) | |||||||
\(548\) | −15.6466 | −0.668389 | ||||||||
\(549\) | −22.7565 | −0.971223 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −29.1935 | −1.24256 | ||||||||
\(553\) | −3.75403 | −0.159638 | ||||||||
\(554\) | −28.2754 | −1.20131 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.393308 | 0.0166800 | ||||||||
\(557\) | 35.8798 | 1.52028 | 0.760138 | − | 0.649761i | \(-0.225131\pi\) | ||||
0.760138 | + | 0.649761i | \(0.225131\pi\) | |||||||
\(558\) | 31.6304 | 1.33902 | ||||||||
\(559\) | 0.959512 | 0.0405830 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 31.1799 | 1.31642 | ||||||||
\(562\) | 8.55873 | 0.361028 | ||||||||
\(563\) | −37.7708 | −1.59185 | −0.795925 | − | 0.605395i | \(-0.793015\pi\) | ||||
−0.795925 | + | 0.605395i | \(0.793015\pi\) | |||||||
\(564\) | 34.1749 | 1.43902 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.13264 | 0.0896416 | ||||||||
\(567\) | 7.68266 | 0.322641 | ||||||||
\(568\) | −14.5931 | −0.612311 | ||||||||
\(569\) | −28.0844 | −1.17736 | −0.588681 | − | 0.808366i | \(-0.700352\pi\) | ||||
−0.588681 | + | 0.808366i | \(0.700352\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.6040 | 0.862253 | 0.431126 | − | 0.902292i | \(-0.358116\pi\) | ||||
0.431126 | + | 0.902292i | \(0.358116\pi\) | |||||||
\(572\) | −0.467072 | −0.0195293 | ||||||||
\(573\) | 43.4154 | 1.81370 | ||||||||
\(574\) | 4.91223 | 0.205032 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 30.6988 | 1.27912 | ||||||||
\(577\) | −43.8371 | −1.82496 | −0.912481 | − | 0.409119i | \(-0.865836\pi\) | ||||
−0.912481 | + | 0.409119i | \(0.865836\pi\) | |||||||
\(578\) | −9.52702 | −0.396272 | ||||||||
\(579\) | 12.2453 | 0.508896 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.55918 | −0.106173 | ||||||||
\(582\) | −40.3600 | −1.67297 | ||||||||
\(583\) | −15.6919 | −0.649894 | ||||||||
\(584\) | 24.1678 | 1.00007 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.6918 | 0.606913 | ||||||||
\(587\) | −37.9809 | −1.56764 | −0.783821 | − | 0.620987i | \(-0.786732\pi\) | ||||
−0.783821 | + | 0.620987i | \(0.786732\pi\) | |||||||
\(588\) | −25.8225 | −1.06490 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −56.5002 | −2.32411 | ||||||||
\(592\) | −0.0838722 | −0.00344713 | ||||||||
\(593\) | 5.38015 | 0.220936 | 0.110468 | − | 0.993880i | \(-0.464765\pi\) | ||||
0.110468 | + | 0.993880i | \(0.464765\pi\) | |||||||
\(594\) | −17.6841 | −0.725588 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.48175 | −0.224541 | ||||||||
\(597\) | 4.94722 | 0.202476 | ||||||||
\(598\) | 0.566520 | 0.0231667 | ||||||||
\(599\) | −22.4285 | −0.916404 | −0.458202 | − | 0.888848i | \(-0.651506\pi\) | ||||
−0.458202 | + | 0.888848i | \(0.651506\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.5732 | 1.20632 | 0.603159 | − | 0.797621i | \(-0.293909\pi\) | ||||
0.603159 | + | 0.797621i | \(0.293909\pi\) | |||||||
\(602\) | 2.41089 | 0.0982604 | ||||||||
\(603\) | −26.2072 | −1.06724 | ||||||||
\(604\) | 0.248581 | 0.0101146 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.40804 | 0.382175 | ||||||||
\(607\) | 24.5915 | 0.998139 | 0.499069 | − | 0.866562i | \(-0.333675\pi\) | ||||
0.499069 | + | 0.866562i | \(0.333675\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.2402 | −0.617564 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.71954 | −0.0695653 | ||||||||
\(612\) | −43.0931 | −1.74194 | ||||||||
\(613\) | −29.8901 | −1.20725 | −0.603624 | − | 0.797269i | \(-0.706277\pi\) | ||||
−0.603624 | + | 0.797269i | \(0.706277\pi\) | |||||||
\(614\) | −18.1005 | −0.730478 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.04290 | −0.122602 | ||||||||
\(617\) | −40.7141 | −1.63909 | −0.819544 | − | 0.573017i | \(-0.805773\pi\) | ||||
−0.819544 | + | 0.573017i | \(0.805773\pi\) | |||||||
\(618\) | −41.6875 | −1.67692 | ||||||||
\(619\) | −28.4784 | −1.14464 | −0.572322 | − | 0.820029i | \(-0.693957\pi\) | ||||
−0.572322 | + | 0.820029i | \(0.693957\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −36.1799 | −1.45185 | ||||||||
\(622\) | 2.71608 | 0.108905 | ||||||||
\(623\) | −1.91116 | −0.0765692 | ||||||||
\(624\) | 0.0525737 | 0.00210463 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.6060 | 0.423902 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −19.8009 | −0.790141 | ||||||||
\(629\) | −5.06028 | −0.201766 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.4201 | 1.68872 | 0.844359 | − | 0.535777i | \(-0.179981\pi\) | ||||
0.844359 | + | 0.535777i | \(0.179981\pi\) | |||||||
\(632\) | −18.6130 | −0.740384 | ||||||||
\(633\) | −18.7823 | −0.746529 | ||||||||
\(634\) | 9.88912 | 0.392747 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 31.7263 | 1.25803 | ||||||||
\(637\) | 1.29929 | 0.0514796 | ||||||||
\(638\) | 14.4141 | 0.570659 | ||||||||
\(639\) | −33.6714 | −1.33202 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.5259 | 1.16620 | 0.583102 | − | 0.812399i | \(-0.301839\pi\) | ||||
0.583102 | + | 0.812399i | \(0.301839\pi\) | |||||||
\(642\) | −2.80888 | −0.110858 | ||||||||
\(643\) | 21.5970 | 0.851704 | 0.425852 | − | 0.904793i | \(-0.359974\pi\) | ||||
0.425852 | + | 0.904793i | \(0.359974\pi\) | |||||||
\(644\) | −2.40101 | −0.0946131 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.6128 | −0.495861 | −0.247930 | − | 0.968778i | \(-0.579750\pi\) | ||||
−0.247930 | + | 0.968778i | \(0.579750\pi\) | |||||||
\(648\) | 38.0916 | 1.49638 | ||||||||
\(649\) | 7.10250 | 0.278798 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.86736 | 0.386732 | ||||||||
\(652\) | −11.5361 | −0.451790 | ||||||||
\(653\) | −26.6312 | −1.04216 | −0.521080 | − | 0.853508i | \(-0.674471\pi\) | ||||
−0.521080 | + | 0.853508i | \(0.674471\pi\) | |||||||
\(654\) | 17.9173 | 0.700621 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.882090 | −0.0344398 | ||||||||
\(657\) | 55.7638 | 2.17555 | ||||||||
\(658\) | −4.32055 | −0.168433 | ||||||||
\(659\) | −39.9545 | −1.55640 | −0.778202 | − | 0.628014i | \(-0.783868\pi\) | ||||
−0.778202 | + | 0.628014i | \(0.783868\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.5233 | 0.525996 | 0.262998 | − | 0.964796i | \(-0.415289\pi\) | ||||
0.262998 | + | 0.964796i | \(0.415289\pi\) | |||||||
\(662\) | 5.05352 | 0.196411 | ||||||||
\(663\) | 3.17194 | 0.123188 | ||||||||
\(664\) | −12.6887 | −0.492418 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.34338 | 0.207052 | ||||||||
\(667\) | 29.4898 | 1.14185 | ||||||||
\(668\) | −3.85498 | −0.149154 | ||||||||
\(669\) | 53.0389 | 2.05060 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.71425 | 0.259201 | ||||||||
\(672\) | 9.93166 | 0.383122 | ||||||||
\(673\) | −34.4110 | −1.32645 | −0.663224 | − | 0.748421i | \(-0.730812\pi\) | ||||
−0.663224 | + | 0.748421i | \(0.730812\pi\) | |||||||
\(674\) | 7.42851 | 0.286135 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.2754 | 0.625977 | ||||||||
\(677\) | 29.6650 | 1.14012 | 0.570059 | − | 0.821604i | \(-0.306920\pi\) | ||||
0.570059 | + | 0.821604i | \(0.306920\pi\) | |||||||
\(678\) | 20.9897 | 0.806105 | ||||||||
\(679\) | −8.60669 | −0.330295 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.64892 | 0.139827 | ||||||||
\(682\) | −9.33249 | −0.357360 | ||||||||
\(683\) | 27.8978 | 1.06748 | 0.533740 | − | 0.845648i | \(-0.320786\pi\) | ||||
0.533740 | + | 0.845648i | \(0.320786\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.68608 | 0.255276 | ||||||||
\(687\) | −19.2381 | −0.733981 | ||||||||
\(688\) | −0.432924 | −0.0165051 | ||||||||
\(689\) | −1.59634 | −0.0608158 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −49.6386 | −1.88834 | −0.944170 | − | 0.329459i | \(-0.893134\pi\) | ||||
−0.944170 | + | 0.329459i | \(0.893134\pi\) | |||||||
\(692\) | 13.0753 | 0.497049 | ||||||||
\(693\) | −7.02105 | −0.266708 | ||||||||
\(694\) | 10.4312 | 0.395961 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −75.5629 | −2.86420 | ||||||||
\(697\) | −53.2193 | −2.01582 | ||||||||
\(698\) | −16.3773 | −0.619889 | ||||||||
\(699\) | 8.48878 | 0.321075 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −49.9813 | −1.88777 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(702\) | −1.79901 | −0.0678991 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −9.05763 | −0.341372 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.65859 | 0.250599 | ||||||||
\(707\) | 2.00625 | 0.0754527 | ||||||||
\(708\) | −14.3600 | −0.539682 | ||||||||
\(709\) | 25.1876 | 0.945941 | 0.472971 | − | 0.881078i | \(-0.343182\pi\) | ||||
0.472971 | + | 0.881078i | \(0.343182\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −42.9468 | −1.61063 | ||||||||
\(712\) | −9.47580 | −0.355121 | ||||||||
\(713\) | −19.0933 | −0.715051 | ||||||||
\(714\) | 7.96986 | 0.298265 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16.8794 | −0.630814 | ||||||||
\(717\) | −53.2861 | −1.99001 | ||||||||
\(718\) | 6.06547 | 0.226361 | ||||||||
\(719\) | 17.1755 | 0.640540 | 0.320270 | − | 0.947326i | \(-0.396226\pi\) | ||||
0.320270 | + | 0.947326i | \(0.396226\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.88979 | −0.331073 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.7386 | −0.548136 | ||||||||
\(724\) | 9.99735 | 0.371549 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −19.5086 | −0.724031 | ||||||||
\(727\) | −1.05653 | −0.0391845 | −0.0195922 | − | 0.999808i | \(-0.506237\pi\) | ||||
−0.0195922 | + | 0.999808i | \(0.506237\pi\) | |||||||
\(728\) | −0.309555 | −0.0114729 | ||||||||
\(729\) | −11.1223 | −0.411937 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.1196 | −0.966070 | ||||||||
\(732\) | −13.5750 | −0.501748 | ||||||||
\(733\) | 20.5025 | 0.757277 | 0.378639 | − | 0.925545i | \(-0.376392\pi\) | ||||
0.378639 | + | 0.925545i | \(0.376392\pi\) | |||||||
\(734\) | 29.0851 | 1.07355 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.2178 | −0.708376 | ||||||||
\(737\) | 7.73238 | 0.284826 | ||||||||
\(738\) | 56.1967 | 2.06863 | ||||||||
\(739\) | 24.9096 | 0.916314 | 0.458157 | − | 0.888871i | \(-0.348510\pi\) | ||||
0.458157 | + | 0.888871i | \(0.348510\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.01100 | −0.147248 | ||||||||
\(743\) | −13.2573 | −0.486364 | −0.243182 | − | 0.969981i | \(-0.578191\pi\) | ||||
−0.243182 | + | 0.969981i | \(0.578191\pi\) | |||||||
\(744\) | 48.9236 | 1.79363 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8.63615 | 0.316192 | ||||||||
\(747\) | −29.2774 | −1.07120 | ||||||||
\(748\) | 12.7145 | 0.464889 | ||||||||
\(749\) | −0.598988 | −0.0218866 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.8365 | −0.906298 | −0.453149 | − | 0.891435i | \(-0.649700\pi\) | ||||
−0.453149 | + | 0.891435i | \(0.649700\pi\) | |||||||
\(752\) | 0.775843 | 0.0282921 | ||||||||
\(753\) | 80.8209 | 2.94528 | ||||||||
\(754\) | 1.46635 | 0.0534012 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 7.62451 | 0.277301 | ||||||||
\(757\) | 48.4658 | 1.76152 | 0.880760 | − | 0.473562i | \(-0.157032\pi\) | ||||
0.880760 | + | 0.473562i | \(0.157032\pi\) | |||||||
\(758\) | −30.8931 | −1.12209 | ||||||||
\(759\) | 19.8744 | 0.721395 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.3726 | 1.46351 | 0.731753 | − | 0.681570i | \(-0.238702\pi\) | ||||
0.731753 | + | 0.681570i | \(0.238702\pi\) | |||||||
\(762\) | 22.5185 | 0.815758 | ||||||||
\(763\) | 3.82083 | 0.138323 | ||||||||
\(764\) | 17.7039 | 0.640505 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.0198 | −0.506556 | ||||||||
\(767\) | 0.722538 | 0.0260893 | ||||||||
\(768\) | 48.5638 | 1.75239 | ||||||||
\(769\) | −44.9545 | −1.62110 | −0.810550 | − | 0.585670i | \(-0.800831\pi\) | ||||
−0.810550 | + | 0.585670i | \(0.800831\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −68.5123 | −2.46741 | ||||||||
\(772\) | 4.99337 | 0.179715 | ||||||||
\(773\) | −3.68645 | −0.132592 | −0.0662962 | − | 0.997800i | \(-0.521118\pi\) | ||||
−0.0662962 | + | 0.997800i | \(0.521118\pi\) | |||||||
\(774\) | 27.5809 | 0.991376 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −42.6731 | −1.53187 | ||||||||
\(777\) | 1.66691 | 0.0598000 | ||||||||
\(778\) | 16.7255 | 0.599639 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.93466 | 0.355490 | ||||||||
\(782\) | −15.4217 | −0.551478 | ||||||||
\(783\) | −93.6461 | −3.34664 | ||||||||
\(784\) | −0.586226 | −0.0209366 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.97953 | 0.177614 | ||||||||
\(787\) | −45.7141 | −1.62953 | −0.814766 | − | 0.579790i | \(-0.803135\pi\) | ||||
−0.814766 | + | 0.579790i | \(0.803135\pi\) | |||||||
\(788\) | −23.0396 | −0.820753 | ||||||||
\(789\) | −27.1377 | −0.966128 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.47602 | 0.159149 | ||||||||
\(792\) | −34.8113 | −1.23697 | ||||||||
\(793\) | 0.683042 | 0.0242555 | ||||||||
\(794\) | −4.61945 | −0.163938 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.01738 | 0.0715040 | ||||||||
\(797\) | 30.3378 | 1.07462 | 0.537310 | − | 0.843385i | \(-0.319441\pi\) | ||||
0.537310 | + | 0.843385i | \(0.319441\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 46.8091 | 1.65599 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −21.8640 | −0.772528 | ||||||||
\(802\) | 7.19415 | 0.254034 | ||||||||
\(803\) | −16.4530 | −0.580614 | ||||||||
\(804\) | −15.6335 | −0.551351 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.949395 | −0.0334410 | ||||||||
\(807\) | −14.6696 | −0.516393 | ||||||||
\(808\) | 9.94724 | 0.349943 | ||||||||
\(809\) | 34.5585 | 1.21501 | 0.607506 | − | 0.794315i | \(-0.292170\pi\) | ||||
0.607506 | + | 0.794315i | \(0.292170\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.2754 | −1.16846 | −0.584229 | − | 0.811589i | \(-0.698603\pi\) | ||||
−0.584229 | + | 0.811589i | \(0.698603\pi\) | |||||||
\(812\) | −6.21464 | −0.218091 | ||||||||
\(813\) | −10.8352 | −0.380008 | ||||||||
\(814\) | −1.57655 | −0.0552582 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.43115 | −0.0501003 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −30.4757 | −1.06556 | ||||||||
\(819\) | −0.714253 | −0.0249580 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.7013 | 0.443277 | 0.221638 | − | 0.975129i | \(-0.428860\pi\) | ||||
0.221638 | + | 0.975129i | \(0.428860\pi\) | |||||||
\(822\) | 33.1051 | 1.15467 | ||||||||
\(823\) | −12.0091 | −0.418610 | −0.209305 | − | 0.977850i | \(-0.567120\pi\) | ||||
−0.209305 | + | 0.977850i | \(0.567120\pi\) | |||||||
\(824\) | −44.0767 | −1.53549 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.81546 | 0.0631680 | ||||||||
\(827\) | −8.54544 | −0.297154 | −0.148577 | − | 0.988901i | \(-0.547469\pi\) | ||||
−0.148577 | + | 0.988901i | \(0.547469\pi\) | |||||||
\(828\) | −27.4680 | −0.954578 | ||||||||
\(829\) | 27.1042 | 0.941369 | 0.470685 | − | 0.882302i | \(-0.344007\pi\) | ||||
0.470685 | + | 0.882302i | \(0.344007\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −100.911 | −3.50055 | ||||||||
\(832\) | −0.921434 | −0.0319450 | ||||||||
\(833\) | −35.3689 | −1.22546 | ||||||||
\(834\) | −0.832162 | −0.0288154 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 60.6317 | 2.09574 | ||||||||
\(838\) | −18.3300 | −0.633200 | ||||||||
\(839\) | 36.4379 | 1.25798 | 0.628989 | − | 0.777414i | \(-0.283469\pi\) | ||||
0.628989 | + | 0.777414i | \(0.283469\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.3297 | 1.63206 | ||||||||
\(842\) | −12.8333 | −0.442266 | ||||||||
\(843\) | 30.5448 | 1.05202 | ||||||||
\(844\) | −7.65903 | −0.263635 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −49.4278 | −1.69936 | ||||||||
\(847\) | −4.16017 | −0.142945 | ||||||||
\(848\) | 0.720256 | 0.0247337 | ||||||||
\(849\) | 7.61107 | 0.261211 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.22547 | −0.110568 | ||||||||
\(852\) | −20.0861 | −0.688140 | ||||||||
\(853\) | −18.3471 | −0.628192 | −0.314096 | − | 0.949391i | \(-0.601701\pi\) | ||||
−0.314096 | + | 0.949391i | \(0.601701\pi\) | |||||||
\(854\) | 1.71622 | 0.0587279 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.96986 | −0.101508 | ||||||||
\(857\) | 7.85783 | 0.268418 | 0.134209 | − | 0.990953i | \(-0.457151\pi\) | ||||
0.134209 | + | 0.990953i | \(0.457151\pi\) | |||||||
\(858\) | 0.988232 | 0.0337377 | ||||||||
\(859\) | −34.3022 | −1.17038 | −0.585188 | − | 0.810897i | \(-0.698979\pi\) | ||||
−0.585188 | + | 0.810897i | \(0.698979\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.5310 | 0.597455 | ||||||||
\(862\) | −14.6257 | −0.498153 | ||||||||
\(863\) | 35.9451 | 1.22359 | 0.611793 | − | 0.791018i | \(-0.290449\pi\) | ||||
0.611793 | + | 0.791018i | \(0.290449\pi\) | |||||||
\(864\) | 61.0268 | 2.07617 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 19.9699 | 0.678604 | ||||||||
\(867\) | −34.0005 | −1.15472 | ||||||||
\(868\) | 4.02371 | 0.136574 | ||||||||
\(869\) | 12.6714 | 0.429846 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.786616 | 0.0266535 | ||||||||
\(872\) | 18.9442 | 0.641531 | ||||||||
\(873\) | −98.4620 | −3.33243 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 33.2650 | 1.12392 | ||||||||
\(877\) | 25.2516 | 0.852686 | 0.426343 | − | 0.904561i | \(-0.359802\pi\) | ||||
0.426343 | + | 0.904561i | \(0.359802\pi\) | |||||||
\(878\) | 28.9426 | 0.976766 | ||||||||
\(879\) | 52.4329 | 1.76852 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.7796 | 0.599010 | 0.299505 | − | 0.954095i | \(-0.403179\pi\) | ||||
0.299505 | + | 0.954095i | \(0.403179\pi\) | |||||||
\(882\) | 37.3476 | 1.25756 | ||||||||
\(883\) | 7.55342 | 0.254193 | 0.127096 | − | 0.991890i | \(-0.459434\pi\) | ||||
0.127096 | + | 0.991890i | \(0.459434\pi\) | |||||||
\(884\) | 1.29345 | 0.0435035 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27.0550 | 0.908930 | ||||||||
\(887\) | 16.2406 | 0.545306 | 0.272653 | − | 0.962112i | \(-0.412099\pi\) | ||||
0.272653 | + | 0.962112i | \(0.412099\pi\) | |||||||
\(888\) | 8.26475 | 0.277347 | ||||||||
\(889\) | 4.80202 | 0.161055 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −25.9320 | −0.868755 | ||||||||
\(892\) | 21.6282 | 0.724165 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 11.5983 | 0.387906 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.13573 | 0.138165 | ||||||||
\(897\) | 2.02182 | 0.0675067 | ||||||||
\(898\) | −13.8305 | −0.461530 | ||||||||
\(899\) | −49.4201 | −1.64825 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.4553 | 1.44771 | ||||||||
\(902\) | −16.5807 | −0.552078 | ||||||||
\(903\) | 8.60409 | 0.286326 | ||||||||
\(904\) | 22.1927 | 0.738118 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.525949 | −0.0174735 | ||||||||
\(907\) | 18.2535 | 0.606097 | 0.303049 | − | 0.952975i | \(-0.401996\pi\) | ||||
0.303049 | + | 0.952975i | \(0.401996\pi\) | |||||||
\(908\) | 1.48795 | 0.0493795 | ||||||||
\(909\) | 22.9518 | 0.761263 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.9019 | −0.526853 | −0.263426 | − | 0.964679i | \(-0.584853\pi\) | ||||
−0.263426 | + | 0.964679i | \(0.584853\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.63824 | 0.285884 | ||||||||
\(914\) | 13.2851 | 0.439431 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.84492 | −0.259204 | ||||||||
\(917\) | 1.06188 | 0.0350663 | ||||||||
\(918\) | 48.9722 | 1.61632 | ||||||||
\(919\) | −30.0748 | −0.992075 | −0.496038 | − | 0.868301i | \(-0.665212\pi\) | ||||
−0.496038 | + | 0.868301i | \(0.665212\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −64.5981 | −2.12858 | ||||||||
\(922\) | 5.01630 | 0.165203 | ||||||||
\(923\) | 1.01065 | 0.0332661 | ||||||||
\(924\) | −4.18830 | −0.137785 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 28.1947 | 0.926534 | ||||||||
\(927\) | −101.701 | −3.34029 | ||||||||
\(928\) | −49.7422 | −1.63287 | ||||||||
\(929\) | −36.8442 | −1.20882 | −0.604410 | − | 0.796673i | \(-0.706591\pi\) | ||||
−0.604410 | + | 0.796673i | \(0.706591\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.46155 | 0.113387 | ||||||||
\(933\) | 9.69327 | 0.317343 | ||||||||
\(934\) | −5.68608 | −0.186054 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.54136 | −0.115753 | ||||||||
\(937\) | −43.2321 | −1.41233 | −0.706165 | − | 0.708047i | \(-0.749576\pi\) | ||||
−0.706165 | + | 0.708047i | \(0.749576\pi\) | |||||||
\(938\) | 1.97646 | 0.0645338 | ||||||||
\(939\) | 37.8513 | 1.23523 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.3203 | 0.662422 | 0.331211 | − | 0.943557i | \(-0.392543\pi\) | ||||
0.331211 | + | 0.943557i | \(0.392543\pi\) | |||||||
\(942\) | 41.8948 | 1.36501 | ||||||||
\(943\) | −33.9225 | −1.10467 | ||||||||
\(944\) | −0.326003 | −0.0106105 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.13770 | −0.264579 | ||||||||
\(947\) | −21.5050 | −0.698819 | −0.349409 | − | 0.936970i | \(-0.613618\pi\) | ||||
−0.349409 | + | 0.936970i | \(0.613618\pi\) | |||||||
\(948\) | −25.6192 | −0.832074 | ||||||||
\(949\) | −1.67376 | −0.0543327 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 35.2928 | 1.14445 | ||||||||
\(952\) | 8.42663 | 0.273109 | ||||||||
\(953\) | −17.7301 | −0.574333 | −0.287166 | − | 0.957881i | \(-0.592713\pi\) | ||||
−0.287166 | + | 0.957881i | \(0.592713\pi\) | |||||||
\(954\) | −45.8865 | −1.48563 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −21.7290 | −0.702766 | ||||||||
\(957\) | 51.4417 | 1.66288 | ||||||||
\(958\) | 31.7559 | 1.02599 | ||||||||
\(959\) | 7.05960 | 0.227966 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.997355 | 0.0321727 | ||||||||
\(962\) | −0.160383 | −0.00517095 | ||||||||
\(963\) | −6.85253 | −0.220820 | ||||||||
\(964\) | −6.01012 | −0.193573 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5.08007 | 0.163448 | ||||||||
\(967\) | −13.6530 | −0.439052 | −0.219526 | − | 0.975607i | \(-0.570451\pi\) | ||||
−0.219526 | + | 0.975607i | \(0.570451\pi\) | |||||||
\(968\) | −20.6267 | −0.662966 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.9595 | −0.897263 | −0.448632 | − | 0.893717i | \(-0.648089\pi\) | ||||
−0.448632 | + | 0.893717i | \(0.648089\pi\) | |||||||
\(972\) | 12.0544 | 0.386646 | ||||||||
\(973\) | −0.177457 | −0.00568901 | ||||||||
\(974\) | −2.11791 | −0.0678622 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.308182 | −0.00986468 | ||||||||
\(977\) | −17.8540 | −0.571200 | −0.285600 | − | 0.958349i | \(-0.592193\pi\) | ||||
−0.285600 | + | 0.958349i | \(0.592193\pi\) | |||||||
\(978\) | 24.4082 | 0.780488 | ||||||||
\(979\) | 6.45094 | 0.206173 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 43.7109 | 1.39558 | ||||||||
\(982\) | −15.3526 | −0.489921 | ||||||||
\(983\) | 49.0443 | 1.56427 | 0.782136 | − | 0.623108i | \(-0.214130\pi\) | ||||
0.782136 | + | 0.623108i | \(0.214130\pi\) | |||||||
\(984\) | 86.9210 | 2.77094 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −39.9166 | −1.27120 | ||||||||
\(987\) | −15.4194 | −0.490805 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.6489 | −0.529405 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.0673 | 0.796289 | 0.398145 | − | 0.917323i | \(-0.369654\pi\) | ||||
0.398145 | + | 0.917323i | \(0.369654\pi\) | |||||||
\(992\) | 32.2059 | 1.02254 | ||||||||
\(993\) | 18.0352 | 0.572331 | ||||||||
\(994\) | 2.53939 | 0.0805445 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −17.4650 | −0.553400 | ||||||||
\(997\) | 30.0222 | 0.950811 | 0.475406 | − | 0.879767i | \(-0.342301\pi\) | ||||
0.475406 | + | 0.879767i | \(0.342301\pi\) | |||||||
\(998\) | 25.2620 | 0.799656 | ||||||||
\(999\) | 10.2426 | 0.324062 |
(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 | 9025.2.a.bt.1.2 | 6 | ||
5.2 | odd | 4 | 1805.2.b.g.1084.2 | 6 | |||
5.3 | odd | 4 | 1805.2.b.g.1084.5 | 6 | |||
5.4 | even | 2 | inner | 9025.2.a.bt.1.5 | 6 | ||
19.8 | odd | 6 | 475.2.e.g.26.2 | 12 | |||
19.12 | odd | 6 | 475.2.e.g.201.2 | 12 | |||
19.18 | odd | 2 | 9025.2.a.bu.1.5 | 6 | |||
95.8 | even | 12 | 95.2.i.b.64.2 | yes | 12 | ||
95.12 | even | 12 | 95.2.i.b.49.2 | ✓ | 12 | ||
95.18 | even | 4 | 1805.2.b.f.1084.2 | 6 | |||
95.27 | even | 12 | 95.2.i.b.64.5 | yes | 12 | ||
95.37 | even | 4 | 1805.2.b.f.1084.5 | 6 | |||
95.69 | odd | 6 | 475.2.e.g.201.5 | 12 | |||
95.84 | odd | 6 | 475.2.e.g.26.5 | 12 | |||
95.88 | even | 12 | 95.2.i.b.49.5 | yes | 12 | ||
95.94 | odd | 2 | 9025.2.a.bu.1.2 | 6 | |||
285.8 | odd | 12 | 855.2.be.d.64.5 | 12 | |||
285.107 | odd | 12 | 855.2.be.d.334.5 | 12 | |||
285.122 | odd | 12 | 855.2.be.d.64.2 | 12 | |||
285.278 | odd | 12 | 855.2.be.d.334.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.i.b.49.2 | ✓ | 12 | 95.12 | even | 12 | ||
95.2.i.b.49.5 | yes | 12 | 95.88 | even | 12 | ||
95.2.i.b.64.2 | yes | 12 | 95.8 | even | 12 | ||
95.2.i.b.64.5 | yes | 12 | 95.27 | even | 12 | ||
475.2.e.g.26.2 | 12 | 19.8 | odd | 6 | |||
475.2.e.g.26.5 | 12 | 95.84 | odd | 6 | |||
475.2.e.g.201.2 | 12 | 19.12 | odd | 6 | |||
475.2.e.g.201.5 | 12 | 95.69 | odd | 6 | |||
855.2.be.d.64.2 | 12 | 285.122 | odd | 12 | |||
855.2.be.d.64.5 | 12 | 285.8 | odd | 12 | |||
855.2.be.d.334.2 | 12 | 285.278 | odd | 12 | |||
855.2.be.d.334.5 | 12 | 285.107 | odd | 12 | |||
1805.2.b.f.1084.2 | 6 | 95.18 | even | 4 | |||
1805.2.b.f.1084.5 | 6 | 95.37 | even | 4 | |||
1805.2.b.g.1084.2 | 6 | 5.2 | odd | 4 | |||
1805.2.b.g.1084.5 | 6 | 5.3 | odd | 4 | |||
9025.2.a.bt.1.2 | 6 | 1.1 | even | 1 | trivial | ||
9025.2.a.bt.1.5 | 6 | 5.4 | even | 2 | inner | ||
9025.2.a.bu.1.2 | 6 | 95.94 | odd | 2 | |||
9025.2.a.bu.1.5 | 6 | 19.18 | odd | 2 |