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: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.47917 | −1.04593 | −0.522965 | − | 0.852354i | \(-0.675174\pi\) | ||||
−0.522965 | + | 0.852354i | \(0.675174\pi\) | |||||||
\(3\) | 2.48321 | 1.43368 | 0.716840 | − | 0.697238i | \(-0.245588\pi\) | ||||
0.716840 | + | 0.697238i | \(0.245588\pi\) | |||||||
\(4\) | 0.187941 | 0.0939705 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.67308 | −1.49953 | ||||||||
\(7\) | −3.24988 | −1.22834 | −0.614169 | − | 0.789175i | \(-0.710509\pi\) | ||||
−0.614169 | + | 0.789175i | \(0.710509\pi\) | |||||||
\(8\) | 2.68034 | 0.947644 | ||||||||
\(9\) | 3.16631 | 1.05544 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.18399 | −1.26152 | −0.630760 | − | 0.775978i | \(-0.717257\pi\) | ||||
−0.630760 | + | 0.775978i | \(0.717257\pi\) | |||||||
\(12\) | 0.466696 | 0.134724 | ||||||||
\(13\) | 1.78413 | 0.494830 | 0.247415 | − | 0.968910i | \(-0.420419\pi\) | ||||
0.247415 | + | 0.968910i | \(0.420419\pi\) | |||||||
\(14\) | 4.80712 | 1.28476 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.34056 | −1.08514 | ||||||||
\(17\) | 6.33226 | 1.53580 | 0.767899 | − | 0.640571i | \(-0.221302\pi\) | ||||
0.767899 | + | 0.640571i | \(0.221302\pi\) | |||||||
\(18\) | −4.68351 | −1.10391 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.07011 | −1.76104 | ||||||||
\(22\) | 6.18883 | 1.31946 | ||||||||
\(23\) | 1.43368 | 0.298942 | 0.149471 | − | 0.988766i | \(-0.452243\pi\) | ||||
0.149471 | + | 0.988766i | \(0.452243\pi\) | |||||||
\(24\) | 6.65584 | 1.35862 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.63904 | −0.517558 | ||||||||
\(27\) | 0.412988 | 0.0794796 | ||||||||
\(28\) | −0.610785 | −0.115428 | ||||||||
\(29\) | −0.339390 | −0.0630231 | −0.0315116 | − | 0.999503i | \(-0.510032\pi\) | ||||
−0.0315116 | + | 0.999503i | \(0.510032\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.77865 | −0.499060 | −0.249530 | − | 0.968367i | \(-0.580276\pi\) | ||||
−0.249530 | + | 0.968367i | \(0.580276\pi\) | |||||||
\(32\) | 1.05974 | 0.187337 | ||||||||
\(33\) | −10.3897 | −1.80862 | ||||||||
\(34\) | −9.36648 | −1.60634 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.595080 | 0.0991800 | ||||||||
\(37\) | −2.70482 | −0.444670 | −0.222335 | − | 0.974970i | \(-0.571368\pi\) | ||||
−0.222335 | + | 0.974970i | \(0.571368\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.43037 | 0.709427 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.13821 | −1.11480 | −0.557401 | − | 0.830244i | \(-0.688201\pi\) | ||||
−0.557401 | + | 0.830244i | \(0.688201\pi\) | |||||||
\(42\) | 11.9371 | 1.84193 | ||||||||
\(43\) | 9.89425 | 1.50886 | 0.754429 | − | 0.656381i | \(-0.227914\pi\) | ||||
0.754429 | + | 0.656381i | \(0.227914\pi\) | |||||||
\(44\) | −0.786344 | −0.118546 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.12065 | −0.312673 | ||||||||
\(47\) | −0.445441 | −0.0649743 | −0.0324871 | − | 0.999472i | \(-0.510343\pi\) | ||||
−0.0324871 | + | 0.999472i | \(0.510343\pi\) | |||||||
\(48\) | −10.7785 | −1.55574 | ||||||||
\(49\) | 3.56169 | 0.508813 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 15.7243 | 2.20184 | ||||||||
\(52\) | 0.335312 | 0.0464994 | ||||||||
\(53\) | −7.23734 | −0.994125 | −0.497062 | − | 0.867715i | \(-0.665588\pi\) | ||||
−0.497062 | + | 0.867715i | \(0.665588\pi\) | |||||||
\(54\) | −0.610879 | −0.0831301 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −8.71078 | −1.16403 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.502015 | 0.0659178 | ||||||||
\(59\) | 3.14263 | 0.409136 | 0.204568 | − | 0.978852i | \(-0.434421\pi\) | ||||
0.204568 | + | 0.978852i | \(0.434421\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.06562 | −0.392512 | −0.196256 | − | 0.980553i | \(-0.562878\pi\) | ||||
−0.196256 | + | 0.980553i | \(0.562878\pi\) | |||||||
\(62\) | 4.11009 | 0.521982 | ||||||||
\(63\) | −10.2901 | −1.29643 | ||||||||
\(64\) | 7.11359 | 0.889198 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 15.3681 | 1.89169 | ||||||||
\(67\) | 8.55254 | 1.04486 | 0.522430 | − | 0.852682i | \(-0.325026\pi\) | ||||
0.522430 | + | 0.852682i | \(0.325026\pi\) | |||||||
\(68\) | 1.19009 | 0.144320 | ||||||||
\(69\) | 3.56011 | 0.428587 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.8928 | 1.53009 | 0.765046 | − | 0.643975i | \(-0.222716\pi\) | ||||
0.765046 | + | 0.643975i | \(0.222716\pi\) | |||||||
\(72\) | 8.48680 | 1.00018 | ||||||||
\(73\) | −1.82227 | −0.213281 | −0.106640 | − | 0.994298i | \(-0.534009\pi\) | ||||
−0.106640 | + | 0.994298i | \(0.534009\pi\) | |||||||
\(74\) | 4.00089 | 0.465094 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.5974 | 1.54957 | ||||||||
\(78\) | −6.55327 | −0.742012 | ||||||||
\(79\) | 0.698700 | 0.0786099 | 0.0393050 | − | 0.999227i | \(-0.487486\pi\) | ||||
0.0393050 | + | 0.999227i | \(0.487486\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.47340 | −0.941489 | ||||||||
\(82\) | 10.5586 | 1.16600 | ||||||||
\(83\) | −0.552985 | −0.0606980 | −0.0303490 | − | 0.999539i | \(-0.509662\pi\) | ||||
−0.0303490 | + | 0.999539i | \(0.509662\pi\) | |||||||
\(84\) | −1.51671 | −0.165486 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −14.6353 | −1.57816 | ||||||||
\(87\) | −0.842775 | −0.0903550 | ||||||||
\(88\) | −11.2145 | −1.19547 | ||||||||
\(89\) | 6.82870 | 0.723841 | 0.361920 | − | 0.932209i | \(-0.382121\pi\) | ||||
0.361920 | + | 0.932209i | \(0.382121\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.79822 | −0.607818 | ||||||||
\(92\) | 0.269446 | 0.0280917 | ||||||||
\(93\) | −6.89995 | −0.715492 | ||||||||
\(94\) | 0.658883 | 0.0679586 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.63155 | 0.268582 | ||||||||
\(97\) | −13.2006 | −1.34032 | −0.670160 | − | 0.742217i | \(-0.733774\pi\) | ||||
−0.670160 | + | 0.742217i | \(0.733774\pi\) | |||||||
\(98\) | −5.26835 | −0.532183 | ||||||||
\(99\) | −13.2478 | −1.33146 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.2757 | 1.71899 | 0.859496 | − | 0.511142i | \(-0.170777\pi\) | ||||
0.859496 | + | 0.511142i | \(0.170777\pi\) | |||||||
\(102\) | −23.2589 | −2.30297 | ||||||||
\(103\) | 13.8286 | 1.36257 | 0.681286 | − | 0.732017i | \(-0.261421\pi\) | ||||
0.681286 | + | 0.732017i | \(0.261421\pi\) | |||||||
\(104\) | 4.78209 | 0.468922 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.7052 | 1.03979 | ||||||||
\(107\) | −3.26460 | −0.315600 | −0.157800 | − | 0.987471i | \(-0.550440\pi\) | ||||
−0.157800 | + | 0.987471i | \(0.550440\pi\) | |||||||
\(108\) | 0.0776174 | 0.00746874 | ||||||||
\(109\) | −3.22094 | −0.308510 | −0.154255 | − | 0.988031i | \(-0.549298\pi\) | ||||
−0.154255 | + | 0.988031i | \(0.549298\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.71663 | −0.637514 | ||||||||
\(112\) | 14.1063 | 1.33292 | ||||||||
\(113\) | 4.71007 | 0.443086 | 0.221543 | − | 0.975151i | \(-0.428891\pi\) | ||||
0.221543 | + | 0.975151i | \(0.428891\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.0637853 | −0.00592232 | ||||||||
\(117\) | 5.64913 | 0.522262 | ||||||||
\(118\) | −4.64849 | −0.427928 | ||||||||
\(119\) | −20.5791 | −1.88648 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.50577 | 0.591434 | ||||||||
\(122\) | 4.53457 | 0.410541 | ||||||||
\(123\) | −17.7257 | −1.59827 | ||||||||
\(124\) | −0.522222 | −0.0468969 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 15.2208 | 1.35598 | ||||||||
\(127\) | 0.592012 | 0.0525325 | 0.0262663 | − | 0.999655i | \(-0.491638\pi\) | ||||
0.0262663 | + | 0.999655i | \(0.491638\pi\) | |||||||
\(128\) | −12.6417 | −1.11738 | ||||||||
\(129\) | 24.5695 | 2.16322 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.5490 | −1.79538 | −0.897689 | − | 0.440629i | \(-0.854755\pi\) | ||||
−0.897689 | + | 0.440629i | \(0.854755\pi\) | |||||||
\(132\) | −1.95265 | −0.169957 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.6507 | −1.09285 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16.9726 | 1.45539 | ||||||||
\(137\) | 8.75406 | 0.747910 | 0.373955 | − | 0.927447i | \(-0.378001\pi\) | ||||
0.373955 | + | 0.927447i | \(0.378001\pi\) | |||||||
\(138\) | −5.26601 | −0.448272 | ||||||||
\(139\) | 7.68939 | 0.652205 | 0.326103 | − | 0.945334i | \(-0.394264\pi\) | ||||
0.326103 | + | 0.945334i | \(0.394264\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.10612 | −0.0931523 | ||||||||
\(142\) | −19.0706 | −1.60037 | ||||||||
\(143\) | −7.46480 | −0.624238 | ||||||||
\(144\) | −13.7436 | −1.14530 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.69545 | 0.223077 | ||||||||
\(147\) | 8.84442 | 0.729475 | ||||||||
\(148\) | −0.508347 | −0.0417859 | ||||||||
\(149\) | −14.9414 | −1.22404 | −0.612022 | − | 0.790841i | \(-0.709644\pi\) | ||||
−0.612022 | + | 0.790841i | \(0.709644\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.1424 | 1.06951 | 0.534757 | − | 0.845006i | \(-0.320403\pi\) | ||||
0.534757 | + | 0.845006i | \(0.320403\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.0499 | 1.62094 | ||||||||
\(154\) | −20.1129 | −1.62075 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.832649 | 0.0666653 | ||||||||
\(157\) | 10.8372 | 0.864902 | 0.432451 | − | 0.901657i | \(-0.357649\pi\) | ||||
0.432451 | + | 0.901657i | \(0.357649\pi\) | |||||||
\(158\) | −1.03350 | −0.0822205 | ||||||||
\(159\) | −17.9718 | −1.42526 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.65927 | −0.367202 | ||||||||
\(162\) | 12.5336 | 0.984732 | ||||||||
\(163\) | 8.44554 | 0.661506 | 0.330753 | − | 0.943717i | \(-0.392697\pi\) | ||||
0.330753 | + | 0.943717i | \(0.392697\pi\) | |||||||
\(164\) | −1.34156 | −0.104758 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.817959 | 0.0634859 | ||||||||
\(167\) | −19.9012 | −1.54000 | −0.770002 | − | 0.638041i | \(-0.779745\pi\) | ||||
−0.770002 | + | 0.638041i | \(0.779745\pi\) | |||||||
\(168\) | −21.6307 | −1.66884 | ||||||||
\(169\) | −9.81686 | −0.755143 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.85954 | 0.141788 | ||||||||
\(173\) | 11.7211 | 0.891135 | 0.445568 | − | 0.895248i | \(-0.353002\pi\) | ||||
0.445568 | + | 0.895248i | \(0.353002\pi\) | |||||||
\(174\) | 1.24661 | 0.0945050 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 18.1609 | 1.36893 | ||||||||
\(177\) | 7.80380 | 0.586570 | ||||||||
\(178\) | −10.1008 | −0.757087 | ||||||||
\(179\) | 7.08378 | 0.529467 | 0.264733 | − | 0.964322i | \(-0.414716\pi\) | ||||
0.264733 | + | 0.964322i | \(0.414716\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.28177 | 0.689908 | 0.344954 | − | 0.938620i | \(-0.387894\pi\) | ||||
0.344954 | + | 0.938620i | \(0.387894\pi\) | |||||||
\(182\) | 8.57654 | 0.635735 | ||||||||
\(183\) | −7.61257 | −0.562737 | ||||||||
\(184\) | 3.84274 | 0.283291 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 10.2062 | 0.748355 | ||||||||
\(187\) | −26.4941 | −1.93744 | ||||||||
\(188\) | −0.0837167 | −0.00610567 | ||||||||
\(189\) | −1.34216 | −0.0976277 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.12426 | 0.587850 | 0.293925 | − | 0.955828i | \(-0.405038\pi\) | ||||
0.293925 | + | 0.955828i | \(0.405038\pi\) | |||||||
\(192\) | 17.6645 | 1.27483 | ||||||||
\(193\) | 7.72342 | 0.555944 | 0.277972 | − | 0.960589i | \(-0.410338\pi\) | ||||
0.277972 | + | 0.960589i | \(0.410338\pi\) | |||||||
\(194\) | 19.5259 | 1.40188 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.669388 | 0.0478135 | ||||||||
\(197\) | 3.56762 | 0.254183 | 0.127091 | − | 0.991891i | \(-0.459436\pi\) | ||||
0.127091 | + | 0.991891i | \(0.459436\pi\) | |||||||
\(198\) | 19.5958 | 1.39261 | ||||||||
\(199\) | −8.76938 | −0.621645 | −0.310822 | − | 0.950468i | \(-0.600604\pi\) | ||||
−0.310822 | + | 0.950468i | \(0.600604\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.2377 | 1.49799 | ||||||||
\(202\) | −25.5536 | −1.79795 | ||||||||
\(203\) | 1.10298 | 0.0774137 | ||||||||
\(204\) | 2.95524 | 0.206908 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −20.4548 | −1.42516 | ||||||||
\(207\) | 4.53946 | 0.315515 | ||||||||
\(208\) | −7.74414 | −0.536960 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.8171 | 0.813526 | 0.406763 | − | 0.913534i | \(-0.366657\pi\) | ||||
0.406763 | + | 0.913534i | \(0.366657\pi\) | |||||||
\(212\) | −1.36019 | −0.0934184 | ||||||||
\(213\) | 32.0155 | 2.19366 | ||||||||
\(214\) | 4.82889 | 0.330096 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.10695 | 0.0753183 | ||||||||
\(217\) | 9.03026 | 0.613014 | ||||||||
\(218\) | 4.76431 | 0.322680 | ||||||||
\(219\) | −4.52507 | −0.305776 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.2976 | 0.759959 | ||||||||
\(222\) | 9.93503 | 0.666796 | ||||||||
\(223\) | 8.89760 | 0.595827 | 0.297914 | − | 0.954593i | \(-0.403709\pi\) | ||||
0.297914 | + | 0.954593i | \(0.403709\pi\) | |||||||
\(224\) | −3.44402 | −0.230113 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.96698 | −0.463437 | ||||||||
\(227\) | −26.4080 | −1.75276 | −0.876380 | − | 0.481620i | \(-0.840049\pi\) | ||||
−0.876380 | + | 0.481620i | \(0.840049\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.7852 | 1.43961 | 0.719804 | − | 0.694177i | \(-0.244232\pi\) | ||||
0.719804 | + | 0.694177i | \(0.244232\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 33.7653 | 2.22159 | ||||||||
\(232\) | −0.909681 | −0.0597235 | ||||||||
\(233\) | 10.0009 | 0.655183 | 0.327591 | − | 0.944820i | \(-0.393763\pi\) | ||||
0.327591 | + | 0.944820i | \(0.393763\pi\) | |||||||
\(234\) | −8.35601 | −0.546250 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.590630 | 0.0384467 | ||||||||
\(237\) | 1.73502 | 0.112701 | ||||||||
\(238\) | 30.4399 | 1.97313 | ||||||||
\(239\) | 17.8365 | 1.15374 | 0.576872 | − | 0.816834i | \(-0.304273\pi\) | ||||
0.576872 | + | 0.816834i | \(0.304273\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.1442 | −1.10435 | −0.552177 | − | 0.833727i | \(-0.686203\pi\) | ||||
−0.552177 | + | 0.833727i | \(0.686203\pi\) | |||||||
\(242\) | −9.62314 | −0.618599 | ||||||||
\(243\) | −22.2802 | −1.42927 | ||||||||
\(244\) | −0.576156 | −0.0368846 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 26.2192 | 1.67168 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −7.44772 | −0.472931 | ||||||||
\(249\) | −1.37318 | −0.0870215 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.69585 | 0.611997 | 0.305998 | − | 0.952032i | \(-0.401010\pi\) | ||||
0.305998 | + | 0.952032i | \(0.401010\pi\) | |||||||
\(252\) | −1.93394 | −0.121827 | ||||||||
\(253\) | −5.99848 | −0.377121 | ||||||||
\(254\) | −0.875685 | −0.0549454 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.47200 | 0.279500 | ||||||||
\(257\) | −10.0506 | −0.626942 | −0.313471 | − | 0.949598i | \(-0.601492\pi\) | ||||
−0.313471 | + | 0.949598i | \(0.601492\pi\) | |||||||
\(258\) | −36.3424 | −2.26258 | ||||||||
\(259\) | 8.79033 | 0.546205 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.07461 | −0.0665170 | ||||||||
\(262\) | 30.3955 | 1.87784 | ||||||||
\(263\) | −21.8306 | −1.34613 | −0.673065 | − | 0.739583i | \(-0.735023\pi\) | ||||
−0.673065 | + | 0.739583i | \(0.735023\pi\) | |||||||
\(264\) | −27.8480 | −1.71392 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.9571 | 1.03776 | ||||||||
\(268\) | 1.60737 | 0.0981860 | ||||||||
\(269\) | 15.4551 | 0.942312 | 0.471156 | − | 0.882050i | \(-0.343837\pi\) | ||||
0.471156 | + | 0.882050i | \(0.343837\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.16319 | 0.313642 | 0.156821 | − | 0.987627i | \(-0.449875\pi\) | ||||
0.156821 | + | 0.987627i | \(0.449875\pi\) | |||||||
\(272\) | −27.4855 | −1.66656 | ||||||||
\(273\) | −14.3982 | −0.871416 | ||||||||
\(274\) | −12.9487 | −0.782262 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.669091 | 0.0402746 | ||||||||
\(277\) | −5.57030 | −0.334687 | −0.167343 | − | 0.985899i | \(-0.553519\pi\) | ||||
−0.167343 | + | 0.985899i | \(0.553519\pi\) | |||||||
\(278\) | −11.3739 | −0.682161 | ||||||||
\(279\) | −8.79807 | −0.526726 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.2729 | 1.62697 | 0.813483 | − | 0.581589i | \(-0.197569\pi\) | ||||
0.813483 | + | 0.581589i | \(0.197569\pi\) | |||||||
\(282\) | 1.63614 | 0.0974308 | ||||||||
\(283\) | 15.0458 | 0.894379 | 0.447190 | − | 0.894439i | \(-0.352425\pi\) | ||||
0.447190 | + | 0.894439i | \(0.352425\pi\) | |||||||
\(284\) | 2.42308 | 0.143784 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.0417 | 0.652910 | ||||||||
\(287\) | 23.1983 | 1.36935 | ||||||||
\(288\) | 3.35547 | 0.197723 | ||||||||
\(289\) | 23.0975 | 1.35868 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −32.7799 | −1.92159 | ||||||||
\(292\) | −0.342479 | −0.0200421 | ||||||||
\(293\) | 7.82882 | 0.457364 | 0.228682 | − | 0.973501i | \(-0.426558\pi\) | ||||
0.228682 | + | 0.973501i | \(0.426558\pi\) | |||||||
\(294\) | −13.0824 | −0.762981 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.24985 | −0.421389 | ||||||||
\(297\) | −1.72794 | −0.100265 | ||||||||
\(298\) | 22.1008 | 1.28026 | ||||||||
\(299\) | 2.55787 | 0.147925 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −32.1551 | −1.85339 | ||||||||
\(302\) | −19.4398 | −1.11864 | ||||||||
\(303\) | 42.8990 | 2.46449 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −29.6572 | −1.69539 | ||||||||
\(307\) | 15.7146 | 0.896879 | 0.448439 | − | 0.893813i | \(-0.351980\pi\) | ||||
0.448439 | + | 0.893813i | \(0.351980\pi\) | |||||||
\(308\) | 2.55552 | 0.145614 | ||||||||
\(309\) | 34.3393 | 1.95349 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.9812 | 1.01962 | 0.509810 | − | 0.860287i | \(-0.329716\pi\) | ||||
0.509810 | + | 0.860287i | \(0.329716\pi\) | |||||||
\(312\) | 11.8749 | 0.672285 | ||||||||
\(313\) | −21.2005 | −1.19832 | −0.599161 | − | 0.800628i | \(-0.704499\pi\) | ||||
−0.599161 | + | 0.800628i | \(0.704499\pi\) | |||||||
\(314\) | −16.0300 | −0.904627 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.131314 | 0.00738702 | ||||||||
\(317\) | −3.06442 | −0.172115 | −0.0860575 | − | 0.996290i | \(-0.527427\pi\) | ||||
−0.0860575 | + | 0.996290i | \(0.527427\pi\) | |||||||
\(318\) | 26.5833 | 1.49072 | ||||||||
\(319\) | 1.42000 | 0.0795050 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.10666 | −0.452470 | ||||||||
\(322\) | 6.89184 | 0.384067 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.59250 | −0.0884722 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.4924 | −0.691889 | ||||||||
\(327\) | −7.99825 | −0.442304 | ||||||||
\(328\) | −19.1328 | −1.05643 | ||||||||
\(329\) | 1.44763 | 0.0798103 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.9509 | −1.42639 | −0.713195 | − | 0.700966i | \(-0.752753\pi\) | ||||
−0.713195 | + | 0.700966i | \(0.752753\pi\) | |||||||
\(332\) | −0.103929 | −0.00570383 | ||||||||
\(333\) | −8.56431 | −0.469321 | ||||||||
\(334\) | 29.4373 | 1.61074 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 35.0288 | 1.91098 | ||||||||
\(337\) | −10.0575 | −0.547865 | −0.273933 | − | 0.961749i | \(-0.588324\pi\) | ||||
−0.273933 | + | 0.961749i | \(0.588324\pi\) | |||||||
\(338\) | 14.5208 | 0.789828 | ||||||||
\(339\) | 11.6961 | 0.635243 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.6258 | 0.629574 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.1741 | 0.603343 | ||||||||
\(344\) | 26.5200 | 1.42986 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.3374 | −0.932065 | ||||||||
\(347\) | −6.81801 | −0.366010 | −0.183005 | − | 0.983112i | \(-0.558582\pi\) | ||||
−0.183005 | + | 0.983112i | \(0.558582\pi\) | |||||||
\(348\) | −0.158392 | −0.00849071 | ||||||||
\(349\) | 31.5966 | 1.69133 | 0.845663 | − | 0.533718i | \(-0.179205\pi\) | ||||
0.845663 | + | 0.533718i | \(0.179205\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.736826 | 0.0393289 | ||||||||
\(352\) | −4.43394 | −0.236330 | ||||||||
\(353\) | 6.30657 | 0.335665 | 0.167832 | − | 0.985816i | \(-0.446323\pi\) | ||||
0.167832 | + | 0.985816i | \(0.446323\pi\) | |||||||
\(354\) | −11.5431 | −0.613511 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.28339 | 0.0680197 | ||||||||
\(357\) | −51.1020 | −2.70461 | ||||||||
\(358\) | −10.4781 | −0.553785 | ||||||||
\(359\) | 4.17666 | 0.220436 | 0.110218 | − | 0.993907i | \(-0.464845\pi\) | ||||
0.110218 | + | 0.993907i | \(0.464845\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −13.7293 | −0.721596 | ||||||||
\(363\) | 16.1552 | 0.847927 | ||||||||
\(364\) | −1.08972 | −0.0571170 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.2603 | 0.588584 | ||||||||
\(367\) | 16.5710 | 0.864998 | 0.432499 | − | 0.901634i | \(-0.357632\pi\) | ||||
0.432499 | + | 0.901634i | \(0.357632\pi\) | |||||||
\(368\) | −6.22295 | −0.324394 | ||||||||
\(369\) | −22.6018 | −1.17660 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.5204 | 1.22112 | ||||||||
\(372\) | −1.29678 | −0.0672352 | ||||||||
\(373\) | 37.0004 | 1.91581 | 0.957905 | − | 0.287085i | \(-0.0926863\pi\) | ||||
0.957905 | + | 0.287085i | \(0.0926863\pi\) | |||||||
\(374\) | 39.1893 | 2.02643 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.19393 | −0.0615725 | ||||||||
\(377\) | −0.605517 | −0.0311857 | ||||||||
\(378\) | 1.98528 | 0.102112 | ||||||||
\(379\) | 31.5147 | 1.61880 | 0.809400 | − | 0.587257i | \(-0.199792\pi\) | ||||
0.809400 | + | 0.587257i | \(0.199792\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.47009 | 0.0753148 | ||||||||
\(382\) | −12.0171 | −0.614851 | ||||||||
\(383\) | 3.09813 | 0.158307 | 0.0791536 | − | 0.996862i | \(-0.474778\pi\) | ||||
0.0791536 | + | 0.996862i | \(0.474778\pi\) | |||||||
\(384\) | −31.3919 | −1.60196 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.4243 | −0.581479 | ||||||||
\(387\) | 31.3283 | 1.59251 | ||||||||
\(388\) | −2.48094 | −0.125951 | ||||||||
\(389\) | 26.0318 | 1.31986 | 0.659931 | − | 0.751326i | \(-0.270585\pi\) | ||||
0.659931 | + | 0.751326i | \(0.270585\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.07840 | 0.459115 | ||||||||
\(392\) | 9.54655 | 0.482174 | ||||||||
\(393\) | −51.0275 | −2.57400 | ||||||||
\(394\) | −5.27712 | −0.265857 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.48981 | −0.125118 | ||||||||
\(397\) | −12.6607 | −0.635423 | −0.317712 | − | 0.948187i | \(-0.602914\pi\) | ||||
−0.317712 | + | 0.948187i | \(0.602914\pi\) | |||||||
\(398\) | 12.9714 | 0.650197 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.22180 | −0.460515 | −0.230257 | − | 0.973130i | \(-0.573957\pi\) | ||||
−0.230257 | + | 0.973130i | \(0.573957\pi\) | |||||||
\(402\) | −31.4142 | −1.56680 | ||||||||
\(403\) | −4.95748 | −0.246950 | ||||||||
\(404\) | 3.24681 | 0.161535 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.63149 | −0.0809693 | ||||||||
\(407\) | 11.3169 | 0.560960 | ||||||||
\(408\) | 42.1465 | 2.08656 | ||||||||
\(409\) | 34.4572 | 1.70380 | 0.851899 | − | 0.523706i | \(-0.175451\pi\) | ||||
0.851899 | + | 0.523706i | \(0.175451\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.7381 | 1.07226 | ||||||||
\(412\) | 2.59896 | 0.128042 | ||||||||
\(413\) | −10.2132 | −0.502557 | ||||||||
\(414\) | −6.71464 | −0.330006 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.89072 | 0.0927001 | ||||||||
\(417\) | 19.0943 | 0.935053 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.86047 | −0.384009 | −0.192005 | − | 0.981394i | \(-0.561499\pi\) | ||||
−0.192005 | + | 0.981394i | \(0.561499\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.4922 | 0.511360 | 0.255680 | − | 0.966761i | \(-0.417701\pi\) | ||||
0.255680 | + | 0.966761i | \(0.417701\pi\) | |||||||
\(422\) | −17.4796 | −0.850892 | ||||||||
\(423\) | −1.41041 | −0.0685763 | ||||||||
\(424\) | −19.3985 | −0.942076 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −47.3563 | −2.29442 | ||||||||
\(427\) | 9.96288 | 0.482138 | ||||||||
\(428\) | −0.613552 | −0.0296571 | ||||||||
\(429\) | −18.5366 | −0.894957 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.8923 | 1.43986 | 0.719931 | − | 0.694046i | \(-0.244173\pi\) | ||||
0.719931 | + | 0.694046i | \(0.244173\pi\) | |||||||
\(432\) | −1.79260 | −0.0862465 | ||||||||
\(433\) | −6.79977 | −0.326776 | −0.163388 | − | 0.986562i | \(-0.552242\pi\) | ||||
−0.163388 | + | 0.986562i | \(0.552242\pi\) | |||||||
\(434\) | −13.3573 | −0.641170 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.605347 | −0.0289908 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 6.69335 | 0.319820 | ||||||||
\(439\) | 7.96606 | 0.380199 | 0.190100 | − | 0.981765i | \(-0.439119\pi\) | ||||
0.190100 | + | 0.981765i | \(0.439119\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.2774 | 0.537021 | ||||||||
\(442\) | −16.7111 | −0.794864 | ||||||||
\(443\) | 21.7893 | 1.03524 | 0.517621 | − | 0.855610i | \(-0.326818\pi\) | ||||
0.517621 | + | 0.855610i | \(0.326818\pi\) | |||||||
\(444\) | −1.26233 | −0.0599076 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −13.1611 | −0.623194 | ||||||||
\(447\) | −37.1025 | −1.75489 | ||||||||
\(448\) | −23.1183 | −1.09224 | ||||||||
\(449\) | 18.7837 | 0.886458 | 0.443229 | − | 0.896409i | \(-0.353833\pi\) | ||||
0.443229 | + | 0.896409i | \(0.353833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.8662 | 1.40634 | ||||||||
\(452\) | 0.885215 | 0.0416370 | ||||||||
\(453\) | 32.6353 | 1.53334 | ||||||||
\(454\) | 39.0619 | 1.83327 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.2368 | −1.32086 | −0.660431 | − | 0.750887i | \(-0.729627\pi\) | ||||
−0.660431 | + | 0.750887i | \(0.729627\pi\) | |||||||
\(458\) | −32.2240 | −1.50573 | ||||||||
\(459\) | 2.61515 | 0.122065 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.196008 | −0.00912900 | −0.00456450 | − | 0.999990i | \(-0.501453\pi\) | ||||
−0.00456450 | + | 0.999990i | \(0.501453\pi\) | |||||||
\(462\) | −49.9445 | −2.32363 | ||||||||
\(463\) | −13.9641 | −0.648967 | −0.324484 | − | 0.945891i | \(-0.605191\pi\) | ||||
−0.324484 | + | 0.945891i | \(0.605191\pi\) | |||||||
\(464\) | 1.47314 | 0.0683889 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.7931 | −0.685275 | ||||||||
\(467\) | 32.1025 | 1.48553 | 0.742763 | − | 0.669555i | \(-0.233515\pi\) | ||||
0.742763 | + | 0.669555i | \(0.233515\pi\) | |||||||
\(468\) | 1.06170 | 0.0490772 | ||||||||
\(469\) | −27.7947 | −1.28344 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 26.9110 | 1.23999 | ||||||||
\(472\) | 8.42333 | 0.387715 | ||||||||
\(473\) | −41.3974 | −1.90346 | ||||||||
\(474\) | −2.56638 | −0.117878 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.86765 | −0.177273 | ||||||||
\(477\) | −22.9157 | −1.04924 | ||||||||
\(478\) | −26.3831 | −1.20674 | ||||||||
\(479\) | −1.98226 | −0.0905717 | −0.0452858 | − | 0.998974i | \(-0.514420\pi\) | ||||
−0.0452858 | + | 0.998974i | \(0.514420\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.82576 | −0.220036 | ||||||||
\(482\) | 25.3591 | 1.15508 | ||||||||
\(483\) | −11.5699 | −0.526450 | ||||||||
\(484\) | 1.22270 | 0.0555774 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 32.9561 | 1.49492 | ||||||||
\(487\) | −8.58916 | −0.389212 | −0.194606 | − | 0.980881i | \(-0.562343\pi\) | ||||
−0.194606 | + | 0.980881i | \(0.562343\pi\) | |||||||
\(488\) | −8.21691 | −0.371962 | ||||||||
\(489\) | 20.9720 | 0.948387 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.9002 | 1.16886 | 0.584430 | − | 0.811444i | \(-0.301318\pi\) | ||||
0.584430 | + | 0.811444i | \(0.301318\pi\) | |||||||
\(492\) | −3.33138 | −0.150190 | ||||||||
\(493\) | −2.14910 | −0.0967908 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.0609 | 0.541550 | ||||||||
\(497\) | −41.9000 | −1.87947 | ||||||||
\(498\) | 2.03116 | 0.0910185 | ||||||||
\(499\) | −21.2038 | −0.949214 | −0.474607 | − | 0.880198i | \(-0.657410\pi\) | ||||
−0.474607 | + | 0.880198i | \(0.657410\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −49.4189 | −2.20787 | ||||||||
\(502\) | −14.3418 | −0.640106 | ||||||||
\(503\) | −25.5162 | −1.13771 | −0.568855 | − | 0.822438i | \(-0.692614\pi\) | ||||
−0.568855 | + | 0.822438i | \(0.692614\pi\) | |||||||
\(504\) | −27.5810 | −1.22856 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8.87277 | 0.394443 | ||||||||
\(507\) | −24.3773 | −1.08263 | ||||||||
\(508\) | 0.111263 | 0.00493651 | ||||||||
\(509\) | −17.0407 | −0.755314 | −0.377657 | − | 0.925946i | \(-0.623270\pi\) | ||||
−0.377657 | + | 0.925946i | \(0.623270\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.92215 | 0.261981 | ||||||||
\(512\) | 18.6685 | 0.825039 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.8666 | 0.655738 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.61761 | 0.203279 | ||||||||
\(517\) | 1.86372 | 0.0819664 | ||||||||
\(518\) | −13.0024 | −0.571292 | ||||||||
\(519\) | 29.1058 | 1.27760 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.7817 | 0.954274 | 0.477137 | − | 0.878829i | \(-0.341675\pi\) | ||||
0.477137 | + | 0.878829i | \(0.341675\pi\) | |||||||
\(522\) | 1.58954 | 0.0695721 | ||||||||
\(523\) | 17.4855 | 0.764589 | 0.382294 | − | 0.924041i | \(-0.375134\pi\) | ||||
0.382294 | + | 0.924041i | \(0.375134\pi\) | |||||||
\(524\) | −3.86201 | −0.168713 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 32.2911 | 1.40796 | ||||||||
\(527\) | −17.5951 | −0.766455 | ||||||||
\(528\) | 45.0972 | 1.96260 | ||||||||
\(529\) | −20.9446 | −0.910634 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.95056 | 0.431817 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.7355 | −0.551637 | ||||||||
\(534\) | −25.0824 | −1.08542 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 22.9237 | 0.990154 | ||||||||
\(537\) | 17.5905 | 0.759086 | ||||||||
\(538\) | −22.8607 | −0.985593 | ||||||||
\(539\) | −14.9021 | −0.641878 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.8091 | 0.636691 | 0.318346 | − | 0.947975i | \(-0.396873\pi\) | ||||
0.318346 | + | 0.947975i | \(0.396873\pi\) | |||||||
\(542\) | −7.63724 | −0.328047 | ||||||||
\(543\) | 23.0485 | 0.989108 | ||||||||
\(544\) | 6.71054 | 0.287712 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 21.2973 | 0.911441 | ||||||||
\(547\) | 26.5735 | 1.13620 | 0.568100 | − | 0.822959i | \(-0.307679\pi\) | ||||
0.568100 | + | 0.822959i | \(0.307679\pi\) | |||||||
\(548\) | 1.64525 | 0.0702815 | ||||||||
\(549\) | −9.70671 | −0.414272 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 9.54231 | 0.406148 | ||||||||
\(553\) | −2.27069 | −0.0965595 | ||||||||
\(554\) | 8.23942 | 0.350059 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.44515 | 0.0612881 | ||||||||
\(557\) | 16.0752 | 0.681129 | 0.340565 | − | 0.940221i | \(-0.389382\pi\) | ||||
0.340565 | + | 0.940221i | \(0.389382\pi\) | |||||||
\(558\) | 13.0138 | 0.550919 | ||||||||
\(559\) | 17.6527 | 0.746628 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −65.7903 | −2.77767 | ||||||||
\(562\) | −40.3413 | −1.70169 | ||||||||
\(563\) | 2.03145 | 0.0856155 | 0.0428078 | − | 0.999083i | \(-0.486370\pi\) | ||||
0.0428078 | + | 0.999083i | \(0.486370\pi\) | |||||||
\(564\) | −0.207886 | −0.00875357 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −22.2553 | −0.935459 | ||||||||
\(567\) | 27.5375 | 1.15647 | ||||||||
\(568\) | 34.5571 | 1.44998 | ||||||||
\(569\) | −12.8224 | −0.537543 | −0.268772 | − | 0.963204i | \(-0.586618\pi\) | ||||
−0.268772 | + | 0.963204i | \(0.586618\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.9168 | 0.540551 | 0.270276 | − | 0.962783i | \(-0.412885\pi\) | ||||
0.270276 | + | 0.962783i | \(0.412885\pi\) | |||||||
\(572\) | −1.40294 | −0.0586600 | ||||||||
\(573\) | 20.1742 | 0.842789 | ||||||||
\(574\) | −34.3142 | −1.43225 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 22.5238 | 0.938493 | ||||||||
\(577\) | 8.11359 | 0.337773 | 0.168887 | − | 0.985635i | \(-0.445983\pi\) | ||||
0.168887 | + | 0.985635i | \(0.445983\pi\) | |||||||
\(578\) | −34.1651 | −1.42108 | ||||||||
\(579\) | 19.1789 | 0.797046 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.79713 | 0.0745577 | ||||||||
\(582\) | 48.4869 | 2.00985 | ||||||||
\(583\) | 30.2809 | 1.25411 | ||||||||
\(584\) | −4.88431 | −0.202114 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.5801 | −0.478371 | ||||||||
\(587\) | −32.5617 | −1.34396 | −0.671982 | − | 0.740568i | \(-0.734557\pi\) | ||||
−0.671982 | + | 0.740568i | \(0.734557\pi\) | |||||||
\(588\) | 1.66223 | 0.0685492 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.85914 | 0.364416 | ||||||||
\(592\) | 11.7404 | 0.482529 | ||||||||
\(593\) | −11.4752 | −0.471231 | −0.235616 | − | 0.971846i | \(-0.575711\pi\) | ||||
−0.235616 | + | 0.971846i | \(0.575711\pi\) | |||||||
\(594\) | 2.55591 | 0.104870 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.80809 | −0.115024 | ||||||||
\(597\) | −21.7762 | −0.891239 | ||||||||
\(598\) | −3.78352 | −0.154720 | ||||||||
\(599\) | 33.2099 | 1.35692 | 0.678460 | − | 0.734637i | \(-0.262648\pi\) | ||||
0.678460 | + | 0.734637i | \(0.262648\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.3180 | 1.11433 | 0.557163 | − | 0.830403i | \(-0.311890\pi\) | ||||
0.557163 | + | 0.830403i | \(0.311890\pi\) | |||||||
\(602\) | 47.5628 | 1.93851 | ||||||||
\(603\) | 27.0800 | 1.10278 | ||||||||
\(604\) | 2.47000 | 0.100503 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −63.4549 | −2.57768 | ||||||||
\(607\) | 25.7405 | 1.04478 | 0.522388 | − | 0.852708i | \(-0.325041\pi\) | ||||
0.522388 | + | 0.852708i | \(0.325041\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.73892 | 0.110986 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.794727 | −0.0321512 | ||||||||
\(612\) | 3.76820 | 0.152320 | ||||||||
\(613\) | 40.6039 | 1.63997 | 0.819987 | − | 0.572382i | \(-0.193980\pi\) | ||||
0.819987 | + | 0.572382i | \(0.193980\pi\) | |||||||
\(614\) | −23.2445 | −0.938073 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 36.4458 | 1.46844 | ||||||||
\(617\) | 14.2113 | 0.572125 | 0.286063 | − | 0.958211i | \(-0.407653\pi\) | ||||
0.286063 | + | 0.958211i | \(0.407653\pi\) | |||||||
\(618\) | −50.7936 | −2.04322 | ||||||||
\(619\) | −29.5635 | −1.18826 | −0.594129 | − | 0.804370i | \(-0.702503\pi\) | ||||
−0.594129 | + | 0.804370i | \(0.702503\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.592091 | 0.0237598 | ||||||||
\(622\) | −26.5973 | −1.06645 | ||||||||
\(623\) | −22.1924 | −0.889121 | ||||||||
\(624\) | −19.2303 | −0.769828 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 31.3591 | 1.25336 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.03675 | 0.0812753 | ||||||||
\(629\) | −17.1276 | −0.682923 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.70763 | −0.0679798 | −0.0339899 | − | 0.999422i | \(-0.510821\pi\) | ||||
−0.0339899 | + | 0.999422i | \(0.510821\pi\) | |||||||
\(632\) | 1.87276 | 0.0744942 | ||||||||
\(633\) | 29.3444 | 1.16634 | ||||||||
\(634\) | 4.53280 | 0.180020 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.37764 | −0.133932 | ||||||||
\(637\) | 6.35454 | 0.251776 | ||||||||
\(638\) | −2.10043 | −0.0831567 | ||||||||
\(639\) | 40.8226 | 1.61492 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.76200 | 0.109092 | 0.0545462 | − | 0.998511i | \(-0.482629\pi\) | ||||
0.0545462 | + | 0.998511i | \(0.482629\pi\) | |||||||
\(642\) | 11.9911 | 0.473252 | ||||||||
\(643\) | 21.6971 | 0.855648 | 0.427824 | − | 0.903862i | \(-0.359280\pi\) | ||||
0.427824 | + | 0.903862i | \(0.359280\pi\) | |||||||
\(644\) | −0.875668 | −0.0345061 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.0268 | −1.10185 | −0.550923 | − | 0.834556i | \(-0.685724\pi\) | ||||
−0.550923 | + | 0.834556i | \(0.685724\pi\) | |||||||
\(648\) | −22.7116 | −0.892196 | ||||||||
\(649\) | −13.1487 | −0.516133 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.4240 | 0.878866 | ||||||||
\(652\) | 1.58726 | 0.0621620 | ||||||||
\(653\) | 7.59308 | 0.297140 | 0.148570 | − | 0.988902i | \(-0.452533\pi\) | ||||
0.148570 | + | 0.988902i | \(0.452533\pi\) | |||||||
\(654\) | 11.8308 | 0.462620 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 30.9838 | 1.20972 | ||||||||
\(657\) | −5.76988 | −0.225104 | ||||||||
\(658\) | −2.14129 | −0.0834761 | ||||||||
\(659\) | 7.18394 | 0.279847 | 0.139923 | − | 0.990162i | \(-0.455314\pi\) | ||||
0.139923 | + | 0.990162i | \(0.455314\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.8678 | −1.12283 | −0.561413 | − | 0.827536i | \(-0.689742\pi\) | ||||
−0.561413 | + | 0.827536i | \(0.689742\pi\) | |||||||
\(662\) | 38.3857 | 1.49190 | ||||||||
\(663\) | 28.0543 | 1.08954 | ||||||||
\(664\) | −1.48219 | −0.0575201 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.6681 | 0.490877 | ||||||||
\(667\) | −0.486575 | −0.0188403 | ||||||||
\(668\) | −3.74026 | −0.144715 | ||||||||
\(669\) | 22.0946 | 0.854226 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.8265 | 0.495162 | ||||||||
\(672\) | −8.55222 | −0.329909 | ||||||||
\(673\) | −23.3191 | −0.898885 | −0.449442 | − | 0.893309i | \(-0.648377\pi\) | ||||
−0.449442 | + | 0.893309i | \(0.648377\pi\) | |||||||
\(674\) | 14.8767 | 0.573029 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.84499 | −0.0709612 | ||||||||
\(677\) | 17.5099 | 0.672958 | 0.336479 | − | 0.941691i | \(-0.390764\pi\) | ||||
0.336479 | + | 0.941691i | \(0.390764\pi\) | |||||||
\(678\) | −17.3005 | −0.664420 | ||||||||
\(679\) | 42.9004 | 1.64636 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −65.5765 | −2.51290 | ||||||||
\(682\) | −17.1966 | −0.658491 | ||||||||
\(683\) | −22.0114 | −0.842243 | −0.421122 | − | 0.907004i | \(-0.638363\pi\) | ||||
−0.421122 | + | 0.907004i | \(0.638363\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −16.5283 | −0.631055 | ||||||||
\(687\) | 54.0972 | 2.06394 | ||||||||
\(688\) | −42.9466 | −1.63732 | ||||||||
\(689\) | −12.9124 | −0.491923 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.65623 | −0.101048 | −0.0505238 | − | 0.998723i | \(-0.516089\pi\) | ||||
−0.0505238 | + | 0.998723i | \(0.516089\pi\) | |||||||
\(692\) | 2.20287 | 0.0837404 | ||||||||
\(693\) | 43.0538 | 1.63548 | ||||||||
\(694\) | 10.0850 | 0.382821 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.25893 | −0.0856244 | ||||||||
\(697\) | −45.2010 | −1.71211 | ||||||||
\(698\) | −46.7367 | −1.76901 | ||||||||
\(699\) | 24.8344 | 0.939322 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.36728 | −0.278258 | −0.139129 | − | 0.990274i | \(-0.544430\pi\) | ||||
−0.139129 | + | 0.990274i | \(0.544430\pi\) | |||||||
\(702\) | −1.08989 | −0.0411352 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −29.7632 | −1.12174 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.32848 | −0.351082 | ||||||||
\(707\) | −56.1438 | −2.11150 | ||||||||
\(708\) | 1.46666 | 0.0551203 | ||||||||
\(709\) | −5.99178 | −0.225026 | −0.112513 | − | 0.993650i | \(-0.535890\pi\) | ||||
−0.112513 | + | 0.993650i | \(0.535890\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.21230 | 0.0829679 | ||||||||
\(712\) | 18.3032 | 0.685943 | ||||||||
\(713\) | −3.98368 | −0.149190 | ||||||||
\(714\) | 75.5885 | 2.82883 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.33133 | 0.0497543 | ||||||||
\(717\) | 44.2916 | 1.65410 | ||||||||
\(718\) | −6.17798 | −0.230560 | ||||||||
\(719\) | 13.5815 | 0.506504 | 0.253252 | − | 0.967400i | \(-0.418500\pi\) | ||||
0.253252 | + | 0.967400i | \(0.418500\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −44.9412 | −1.67370 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −42.5725 | −1.58329 | ||||||||
\(724\) | 1.74443 | 0.0648311 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −23.8962 | −0.886872 | ||||||||
\(727\) | −41.2448 | −1.52968 | −0.764842 | − | 0.644218i | \(-0.777183\pi\) | ||||
−0.764842 | + | 0.644218i | \(0.777183\pi\) | |||||||
\(728\) | −15.5412 | −0.575995 | ||||||||
\(729\) | −29.9060 | −1.10763 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 62.6529 | 2.31730 | ||||||||
\(732\) | −1.43071 | −0.0528807 | ||||||||
\(733\) | −0.123848 | −0.00457443 | −0.00228722 | − | 0.999997i | \(-0.500728\pi\) | ||||
−0.00228722 | + | 0.999997i | \(0.500728\pi\) | |||||||
\(734\) | −24.5113 | −0.904728 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.51932 | 0.0560030 | ||||||||
\(737\) | −35.7837 | −1.31811 | ||||||||
\(738\) | 33.4319 | 1.23065 | ||||||||
\(739\) | −36.5134 | −1.34317 | −0.671584 | − | 0.740928i | \(-0.734386\pi\) | ||||
−0.671584 | + | 0.740928i | \(0.734386\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −34.7907 | −1.27721 | ||||||||
\(743\) | 9.06197 | 0.332451 | 0.166226 | − | 0.986088i | \(-0.446842\pi\) | ||||
0.166226 | + | 0.986088i | \(0.446842\pi\) | |||||||
\(744\) | −18.4942 | −0.678032 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −54.7299 | −2.00380 | ||||||||
\(747\) | −1.75092 | −0.0640630 | ||||||||
\(748\) | −4.97933 | −0.182062 | ||||||||
\(749\) | 10.6095 | 0.387664 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.08610 | −0.149104 | −0.0745519 | − | 0.997217i | \(-0.523753\pi\) | ||||
−0.0745519 | + | 0.997217i | \(0.523753\pi\) | |||||||
\(752\) | 1.93346 | 0.0705062 | ||||||||
\(753\) | 24.0768 | 0.877407 | ||||||||
\(754\) | 0.895663 | 0.0326181 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.252247 | −0.00917413 | ||||||||
\(757\) | −34.4597 | −1.25246 | −0.626230 | − | 0.779638i | \(-0.715403\pi\) | ||||
−0.626230 | + | 0.779638i | \(0.715403\pi\) | |||||||
\(758\) | −46.6155 | −1.69315 | ||||||||
\(759\) | −14.8955 | −0.540671 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.5813 | 0.746072 | 0.373036 | − | 0.927817i | \(-0.378317\pi\) | ||||
0.373036 | + | 0.927817i | \(0.378317\pi\) | |||||||
\(762\) | −2.17451 | −0.0787741 | ||||||||
\(763\) | 10.4676 | 0.378954 | ||||||||
\(764\) | 1.52688 | 0.0552406 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.58266 | −0.165578 | ||||||||
\(767\) | 5.60688 | 0.202453 | ||||||||
\(768\) | 11.1049 | 0.400714 | ||||||||
\(769\) | −30.3550 | −1.09463 | −0.547315 | − | 0.836927i | \(-0.684350\pi\) | ||||
−0.547315 | + | 0.836927i | \(0.684350\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.9578 | −0.898834 | ||||||||
\(772\) | 1.45155 | 0.0522424 | ||||||||
\(773\) | 19.5225 | 0.702176 | 0.351088 | − | 0.936343i | \(-0.385812\pi\) | ||||
0.351088 | + | 0.936343i | \(0.385812\pi\) | |||||||
\(774\) | −46.3398 | −1.66565 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −35.3822 | −1.27015 | ||||||||
\(777\) | 21.8282 | 0.783083 | ||||||||
\(778\) | −38.5054 | −1.38048 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −53.9433 | −1.93024 | ||||||||
\(782\) | −13.4285 | −0.480202 | ||||||||
\(783\) | −0.140164 | −0.00500905 | ||||||||
\(784\) | −15.4597 | −0.552134 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 75.4783 | 2.69222 | ||||||||
\(787\) | −35.2236 | −1.25559 | −0.627793 | − | 0.778380i | \(-0.716042\pi\) | ||||
−0.627793 | + | 0.778380i | \(0.716042\pi\) | |||||||
\(788\) | 0.670503 | 0.0238857 | ||||||||
\(789\) | −54.2098 | −1.92992 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.3071 | −0.544259 | ||||||||
\(792\) | −35.5087 | −1.26175 | ||||||||
\(793\) | −5.46948 | −0.194227 | ||||||||
\(794\) | 18.7273 | 0.664608 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.64813 | −0.0584163 | ||||||||
\(797\) | 28.7940 | 1.01994 | 0.509969 | − | 0.860193i | \(-0.329657\pi\) | ||||
0.509969 | + | 0.860193i | \(0.329657\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.82065 | −0.0997874 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.6218 | 0.763969 | ||||||||
\(802\) | 13.6406 | 0.481666 | ||||||||
\(803\) | 7.62436 | 0.269058 | ||||||||
\(804\) | 3.99144 | 0.140767 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.33295 | 0.258292 | ||||||||
\(807\) | 38.3781 | 1.35097 | ||||||||
\(808\) | 46.3047 | 1.62899 | ||||||||
\(809\) | −48.0068 | −1.68783 | −0.843915 | − | 0.536478i | \(-0.819755\pi\) | ||||
−0.843915 | + | 0.536478i | \(0.819755\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.62886 | −0.338115 | −0.169057 | − | 0.985606i | \(-0.554072\pi\) | ||||
−0.169057 | + | 0.985606i | \(0.554072\pi\) | |||||||
\(812\) | 0.207294 | 0.00727461 | ||||||||
\(813\) | 12.8213 | 0.449662 | ||||||||
\(814\) | −16.7397 | −0.586725 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −68.2523 | −2.38931 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −50.9680 | −1.78205 | ||||||||
\(819\) | −18.3590 | −0.641514 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.7257 | −0.897834 | −0.448917 | − | 0.893573i | \(-0.648190\pi\) | ||||
−0.448917 | + | 0.893573i | \(0.648190\pi\) | |||||||
\(822\) | −32.1544 | −1.12151 | ||||||||
\(823\) | −13.4584 | −0.469132 | −0.234566 | − | 0.972100i | \(-0.575367\pi\) | ||||
−0.234566 | + | 0.972100i | \(0.575367\pi\) | |||||||
\(824\) | 37.0654 | 1.29123 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.1070 | 0.525640 | ||||||||
\(827\) | 0.172408 | 0.00599520 | 0.00299760 | − | 0.999996i | \(-0.499046\pi\) | ||||
0.00299760 | + | 0.999996i | \(0.499046\pi\) | |||||||
\(828\) | 0.853152 | 0.0296491 | ||||||||
\(829\) | −42.3791 | −1.47189 | −0.735943 | − | 0.677044i | \(-0.763261\pi\) | ||||
−0.735943 | + | 0.677044i | \(0.763261\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.8322 | −0.479834 | ||||||||
\(832\) | 12.6916 | 0.440002 | ||||||||
\(833\) | 22.5536 | 0.781435 | ||||||||
\(834\) | −28.2437 | −0.978001 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.14755 | −0.0396651 | ||||||||
\(838\) | 11.6270 | 0.401647 | ||||||||
\(839\) | 45.1399 | 1.55840 | 0.779200 | − | 0.626775i | \(-0.215625\pi\) | ||||
0.779200 | + | 0.626775i | \(0.215625\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8848 | −0.996028 | ||||||||
\(842\) | −15.5198 | −0.534847 | ||||||||
\(843\) | 67.7243 | 2.33255 | ||||||||
\(844\) | 2.22093 | 0.0764475 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.08623 | 0.0717260 | ||||||||
\(847\) | −21.1430 | −0.726481 | ||||||||
\(848\) | 31.4141 | 1.07876 | ||||||||
\(849\) | 37.3618 | 1.28225 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.87784 | −0.132931 | ||||||||
\(852\) | 6.01702 | 0.206140 | ||||||||
\(853\) | −46.3405 | −1.58667 | −0.793333 | − | 0.608787i | \(-0.791656\pi\) | ||||
−0.793333 | + | 0.608787i | \(0.791656\pi\) | |||||||
\(854\) | −14.7368 | −0.504283 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.75023 | −0.299077 | ||||||||
\(857\) | 21.8934 | 0.747863 | 0.373931 | − | 0.927456i | \(-0.378010\pi\) | ||||
0.373931 | + | 0.927456i | \(0.378010\pi\) | |||||||
\(858\) | 27.4188 | 0.936063 | ||||||||
\(859\) | 33.4020 | 1.13966 | 0.569830 | − | 0.821762i | \(-0.307009\pi\) | ||||
0.569830 | + | 0.821762i | \(0.307009\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 57.6062 | 1.96321 | ||||||||
\(862\) | −44.2158 | −1.50600 | ||||||||
\(863\) | −27.1254 | −0.923359 | −0.461680 | − | 0.887047i | \(-0.652753\pi\) | ||||
−0.461680 | + | 0.887047i | \(0.652753\pi\) | |||||||
\(864\) | 0.437660 | 0.0148895 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.0580 | 0.341785 | ||||||||
\(867\) | 57.3558 | 1.94791 | ||||||||
\(868\) | 1.69716 | 0.0576052 | ||||||||
\(869\) | −2.92335 | −0.0991680 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.2589 | 0.517027 | ||||||||
\(872\) | −8.63321 | −0.292358 | ||||||||
\(873\) | −41.7973 | −1.41462 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.850447 | −0.0287339 | ||||||||
\(877\) | −49.0823 | −1.65739 | −0.828695 | − | 0.559700i | \(-0.810916\pi\) | ||||
−0.828695 | + | 0.559700i | \(0.810916\pi\) | |||||||
\(878\) | −11.7832 | −0.397662 | ||||||||
\(879\) | 19.4406 | 0.655714 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.9778 | 1.27951 | 0.639753 | − | 0.768581i | \(-0.279037\pi\) | ||||
0.639753 | + | 0.768581i | \(0.279037\pi\) | |||||||
\(882\) | −16.6812 | −0.561686 | ||||||||
\(883\) | 33.2100 | 1.11761 | 0.558803 | − | 0.829300i | \(-0.311261\pi\) | ||||
0.558803 | + | 0.829300i | \(0.311261\pi\) | |||||||
\(884\) | 2.12328 | 0.0714137 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32.2301 | −1.08279 | ||||||||
\(887\) | 26.2525 | 0.881474 | 0.440737 | − | 0.897636i | \(-0.354717\pi\) | ||||
0.440737 | + | 0.897636i | \(0.354717\pi\) | |||||||
\(888\) | −18.0029 | −0.604136 | ||||||||
\(889\) | −1.92396 | −0.0645277 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 35.4526 | 1.18771 | ||||||||
\(892\) | 1.67222 | 0.0559902 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 54.8808 | 1.83549 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 41.0839 | 1.37252 | ||||||||
\(897\) | 6.35172 | 0.212078 | ||||||||
\(898\) | −27.7843 | −0.927173 | ||||||||
\(899\) | 0.943045 | 0.0314523 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −45.8287 | −1.52677 | ||||||||
\(902\) | −44.1772 | −1.47094 | ||||||||
\(903\) | −79.8477 | −2.65716 | ||||||||
\(904\) | 12.6246 | 0.419888 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −48.2731 | −1.60377 | ||||||||
\(907\) | 7.92760 | 0.263231 | 0.131616 | − | 0.991301i | \(-0.457983\pi\) | ||||
0.131616 | + | 0.991301i | \(0.457983\pi\) | |||||||
\(908\) | −4.96315 | −0.164708 | ||||||||
\(909\) | 54.7002 | 1.81429 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.619746 | −0.0205331 | −0.0102665 | − | 0.999947i | \(-0.503268\pi\) | ||||
−0.0102665 | + | 0.999947i | \(0.503268\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.31369 | 0.0765718 | ||||||||
\(914\) | 41.7670 | 1.38153 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.09434 | 0.135281 | ||||||||
\(917\) | 66.7818 | 2.20533 | ||||||||
\(918\) | −3.86824 | −0.127671 | ||||||||
\(919\) | −35.0574 | −1.15644 | −0.578219 | − | 0.815882i | \(-0.696252\pi\) | ||||
−0.578219 | + | 0.815882i | \(0.696252\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39.0226 | 1.28584 | ||||||||
\(922\) | 0.289929 | 0.00954830 | ||||||||
\(923\) | 23.0025 | 0.757135 | ||||||||
\(924\) | 6.34588 | 0.208764 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 20.6553 | 0.678775 | ||||||||
\(927\) | 43.7857 | 1.43811 | ||||||||
\(928\) | −0.359665 | −0.0118066 | ||||||||
\(929\) | 12.0434 | 0.395132 | 0.197566 | − | 0.980290i | \(-0.436696\pi\) | ||||
0.197566 | + | 0.980290i | \(0.436696\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.87959 | 0.0615679 | ||||||||
\(933\) | 44.6511 | 1.46181 | ||||||||
\(934\) | −47.4850 | −1.55376 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 15.1416 | 0.494918 | ||||||||
\(937\) | 14.9304 | 0.487757 | 0.243878 | − | 0.969806i | \(-0.421580\pi\) | ||||
0.243878 | + | 0.969806i | \(0.421580\pi\) | |||||||
\(938\) | 41.1131 | 1.34239 | ||||||||
\(939\) | −52.6452 | −1.71801 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.4198 | 0.633068 | 0.316534 | − | 0.948581i | \(-0.397481\pi\) | ||||
0.316534 | + | 0.948581i | \(0.397481\pi\) | |||||||
\(942\) | −39.8059 | −1.29695 | ||||||||
\(943\) | −10.2339 | −0.333261 | ||||||||
\(944\) | −13.6408 | −0.443970 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 61.2338 | 1.99088 | ||||||||
\(947\) | 16.7369 | 0.543878 | 0.271939 | − | 0.962315i | \(-0.412335\pi\) | ||||
0.271939 | + | 0.962315i | \(0.412335\pi\) | |||||||
\(948\) | 0.326081 | 0.0105906 | ||||||||
\(949\) | −3.25117 | −0.105538 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.60959 | −0.246758 | ||||||||
\(952\) | −55.1589 | −1.78771 | ||||||||
\(953\) | −53.1772 | −1.72258 | −0.861290 | − | 0.508114i | \(-0.830343\pi\) | ||||
−0.861290 | + | 0.508114i | \(0.830343\pi\) | |||||||
\(954\) | 33.8962 | 1.09743 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.35220 | 0.108418 | ||||||||
\(957\) | 3.52616 | 0.113985 | ||||||||
\(958\) | 2.93209 | 0.0947317 | ||||||||
\(959\) | −28.4496 | −0.918686 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.2791 | −0.750939 | ||||||||
\(962\) | 7.13812 | 0.230142 | ||||||||
\(963\) | −10.3367 | −0.333096 | ||||||||
\(964\) | −3.22209 | −0.103777 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 17.1139 | 0.550630 | ||||||||
\(967\) | 30.0281 | 0.965637 | 0.482819 | − | 0.875720i | \(-0.339613\pi\) | ||||
0.482819 | + | 0.875720i | \(0.339613\pi\) | |||||||
\(968\) | 17.4377 | 0.560469 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.1413 | 0.774732 | 0.387366 | − | 0.921926i | \(-0.373385\pi\) | ||||
0.387366 | + | 0.921926i | \(0.373385\pi\) | |||||||
\(972\) | −4.18736 | −0.134310 | ||||||||
\(973\) | −24.9896 | −0.801128 | ||||||||
\(974\) | 12.7048 | 0.407089 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.3065 | 0.425931 | ||||||||
\(977\) | −9.57680 | −0.306389 | −0.153195 | − | 0.988196i | \(-0.548956\pi\) | ||||
−0.153195 | + | 0.988196i | \(0.548956\pi\) | |||||||
\(978\) | −31.0211 | −0.991947 | ||||||||
\(979\) | −28.5712 | −0.913140 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.1985 | −0.325613 | ||||||||
\(982\) | −38.3108 | −1.22255 | ||||||||
\(983\) | 31.1715 | 0.994216 | 0.497108 | − | 0.867689i | \(-0.334395\pi\) | ||||
0.497108 | + | 0.867689i | \(0.334395\pi\) | |||||||
\(984\) | −47.5108 | −1.51459 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.17889 | 0.101236 | ||||||||
\(987\) | 3.59476 | 0.114422 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.1851 | 0.451061 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.6643 | −1.54587 | −0.772937 | − | 0.634483i | \(-0.781213\pi\) | ||||
−0.772937 | + | 0.634483i | \(0.781213\pi\) | |||||||
\(992\) | −2.94464 | −0.0934925 | ||||||||
\(993\) | −64.4414 | −2.04499 | ||||||||
\(994\) | 61.9771 | 1.96580 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.258076 | −0.00817746 | ||||||||
\(997\) | 31.8954 | 1.01014 | 0.505068 | − | 0.863080i | \(-0.331467\pi\) | ||||
0.505068 | + | 0.863080i | \(0.331467\pi\) | |||||||
\(998\) | 31.3641 | 0.992812 | ||||||||
\(999\) | −1.11706 | −0.0353422 |
(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.cu.1.7 | 24 | ||
5.2 | odd | 4 | 1805.2.b.k.1084.7 | 24 | |||
5.3 | odd | 4 | 1805.2.b.k.1084.18 | 24 | |||
5.4 | even | 2 | inner | 9025.2.a.cu.1.18 | 24 | ||
19.6 | even | 9 | 475.2.l.f.226.2 | 48 | |||
19.16 | even | 9 | 475.2.l.f.351.2 | 48 | |||
19.18 | odd | 2 | 9025.2.a.ct.1.18 | 24 | |||
95.18 | even | 4 | 1805.2.b.l.1084.7 | 24 | |||
95.37 | even | 4 | 1805.2.b.l.1084.18 | 24 | |||
95.44 | even | 18 | 475.2.l.f.226.7 | 48 | |||
95.54 | even | 18 | 475.2.l.f.351.7 | 48 | |||
95.63 | odd | 36 | 95.2.p.a.74.7 | yes | 48 | ||
95.73 | odd | 36 | 95.2.p.a.9.2 | ✓ | 48 | ||
95.82 | odd | 36 | 95.2.p.a.74.2 | yes | 48 | ||
95.92 | odd | 36 | 95.2.p.a.9.7 | yes | 48 | ||
95.94 | odd | 2 | 9025.2.a.ct.1.7 | 24 | |||
285.92 | even | 36 | 855.2.da.b.199.2 | 48 | |||
285.158 | even | 36 | 855.2.da.b.739.2 | 48 | |||
285.263 | even | 36 | 855.2.da.b.199.7 | 48 | |||
285.272 | even | 36 | 855.2.da.b.739.7 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.p.a.9.2 | ✓ | 48 | 95.73 | odd | 36 | ||
95.2.p.a.9.7 | yes | 48 | 95.92 | odd | 36 | ||
95.2.p.a.74.2 | yes | 48 | 95.82 | odd | 36 | ||
95.2.p.a.74.7 | yes | 48 | 95.63 | odd | 36 | ||
475.2.l.f.226.2 | 48 | 19.6 | even | 9 | |||
475.2.l.f.226.7 | 48 | 95.44 | even | 18 | |||
475.2.l.f.351.2 | 48 | 19.16 | even | 9 | |||
475.2.l.f.351.7 | 48 | 95.54 | even | 18 | |||
855.2.da.b.199.2 | 48 | 285.92 | even | 36 | |||
855.2.da.b.199.7 | 48 | 285.263 | even | 36 | |||
855.2.da.b.739.2 | 48 | 285.158 | even | 36 | |||
855.2.da.b.739.7 | 48 | 285.272 | even | 36 | |||
1805.2.b.k.1084.7 | 24 | 5.2 | odd | 4 | |||
1805.2.b.k.1084.18 | 24 | 5.3 | odd | 4 | |||
1805.2.b.l.1084.7 | 24 | 95.18 | even | 4 | |||
1805.2.b.l.1084.18 | 24 | 95.37 | even | 4 | |||
9025.2.a.ct.1.7 | 24 | 95.94 | odd | 2 | |||
9025.2.a.ct.1.18 | 24 | 19.18 | odd | 2 | |||
9025.2.a.cu.1.7 | 24 | 1.1 | even | 1 | trivial | ||
9025.2.a.cu.1.18 | 24 | 5.4 | even | 2 | inner |