Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [619,2,Mod(1,619)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(619, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("619.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 619.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: | \(4.94273988512\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.27 | ||
Character | \(\chi\) | \(=\) | 619.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.46595 | 1.74369 | 0.871844 | − | 0.489784i | \(-0.162924\pi\) | ||||
0.871844 | + | 0.489784i | \(0.162924\pi\) | |||||||
\(3\) | −0.157868 | −0.0911449 | −0.0455725 | − | 0.998961i | \(-0.514511\pi\) | ||||
−0.0455725 | + | 0.998961i | \(0.514511\pi\) | |||||||
\(4\) | 4.08090 | 2.04045 | ||||||||
\(5\) | 2.37765 | 1.06332 | 0.531659 | − | 0.846959i | \(-0.321569\pi\) | ||||
0.531659 | + | 0.846959i | \(0.321569\pi\) | |||||||
\(6\) | −0.389293 | −0.158928 | ||||||||
\(7\) | 4.70879 | 1.77975 | 0.889877 | − | 0.456200i | \(-0.150790\pi\) | ||||
0.889877 | + | 0.456200i | \(0.150790\pi\) | |||||||
\(8\) | 5.13138 | 1.81422 | ||||||||
\(9\) | −2.97508 | −0.991693 | ||||||||
\(10\) | 5.86316 | 1.85409 | ||||||||
\(11\) | −3.89648 | −1.17483 | −0.587416 | − | 0.809285i | \(-0.699855\pi\) | ||||
−0.587416 | + | 0.809285i | \(0.699855\pi\) | |||||||
\(12\) | −0.644241 | −0.185976 | ||||||||
\(13\) | −6.62279 | −1.83683 | −0.918416 | − | 0.395617i | \(-0.870531\pi\) | ||||
−0.918416 | + | 0.395617i | \(0.870531\pi\) | |||||||
\(14\) | 11.6116 | 3.10334 | ||||||||
\(15\) | −0.375354 | −0.0969160 | ||||||||
\(16\) | 4.49192 | 1.12298 | ||||||||
\(17\) | −5.95137 | −1.44342 | −0.721710 | − | 0.692195i | \(-0.756644\pi\) | ||||
−0.721710 | + | 0.692195i | \(0.756644\pi\) | |||||||
\(18\) | −7.33638 | −1.72920 | ||||||||
\(19\) | −0.395246 | −0.0906757 | −0.0453378 | − | 0.998972i | \(-0.514436\pi\) | ||||
−0.0453378 | + | 0.998972i | \(0.514436\pi\) | |||||||
\(20\) | 9.70294 | 2.16964 | ||||||||
\(21\) | −0.743365 | −0.162216 | ||||||||
\(22\) | −9.60851 | −2.04854 | ||||||||
\(23\) | −1.84938 | −0.385623 | −0.192812 | − | 0.981236i | \(-0.561761\pi\) | ||||
−0.192812 | + | 0.981236i | \(0.561761\pi\) | |||||||
\(24\) | −0.810079 | −0.165357 | ||||||||
\(25\) | 0.653219 | 0.130644 | ||||||||
\(26\) | −16.3315 | −3.20286 | ||||||||
\(27\) | 0.943271 | 0.181533 | ||||||||
\(28\) | 19.2161 | 3.63150 | ||||||||
\(29\) | 10.6320 | 1.97432 | 0.987159 | − | 0.159743i | \(-0.0510667\pi\) | ||||
0.987159 | + | 0.159743i | \(0.0510667\pi\) | |||||||
\(30\) | −0.925603 | −0.168991 | ||||||||
\(31\) | 7.56721 | 1.35911 | 0.679556 | − | 0.733624i | \(-0.262173\pi\) | ||||
0.679556 | + | 0.733624i | \(0.262173\pi\) | |||||||
\(32\) | 0.814076 | 0.143910 | ||||||||
\(33\) | 0.615128 | 0.107080 | ||||||||
\(34\) | −14.6758 | −2.51687 | ||||||||
\(35\) | 11.1958 | 1.89244 | ||||||||
\(36\) | −12.1410 | −2.02350 | ||||||||
\(37\) | −5.85939 | −0.963278 | −0.481639 | − | 0.876370i | \(-0.659958\pi\) | ||||
−0.481639 | + | 0.876370i | \(0.659958\pi\) | |||||||
\(38\) | −0.974656 | −0.158110 | ||||||||
\(39\) | 1.04552 | 0.167418 | ||||||||
\(40\) | 12.2006 | 1.92909 | ||||||||
\(41\) | 1.13182 | 0.176760 | 0.0883801 | − | 0.996087i | \(-0.471831\pi\) | ||||
0.0883801 | + | 0.996087i | \(0.471831\pi\) | |||||||
\(42\) | −1.83310 | −0.282853 | ||||||||
\(43\) | 3.18315 | 0.485425 | 0.242713 | − | 0.970098i | \(-0.421963\pi\) | ||||
0.242713 | + | 0.970098i | \(0.421963\pi\) | |||||||
\(44\) | −15.9011 | −2.39719 | ||||||||
\(45\) | −7.07369 | −1.05448 | ||||||||
\(46\) | −4.56048 | −0.672406 | ||||||||
\(47\) | 0.625030 | 0.0911700 | 0.0455850 | − | 0.998960i | \(-0.485485\pi\) | ||||
0.0455850 | + | 0.998960i | \(0.485485\pi\) | |||||||
\(48\) | −0.709129 | −0.102354 | ||||||||
\(49\) | 15.1727 | 2.16753 | ||||||||
\(50\) | 1.61080 | 0.227802 | ||||||||
\(51\) | 0.939529 | 0.131560 | ||||||||
\(52\) | −27.0269 | −3.74796 | ||||||||
\(53\) | 12.8766 | 1.76874 | 0.884368 | − | 0.466790i | \(-0.154589\pi\) | ||||
0.884368 | + | 0.466790i | \(0.154589\pi\) | |||||||
\(54\) | 2.32606 | 0.316536 | ||||||||
\(55\) | −9.26447 | −1.24922 | ||||||||
\(56\) | 24.1626 | 3.22886 | ||||||||
\(57\) | 0.0623966 | 0.00826463 | ||||||||
\(58\) | 26.2180 | 3.44259 | ||||||||
\(59\) | −0.141655 | −0.0184419 | −0.00922096 | − | 0.999957i | \(-0.502935\pi\) | ||||
−0.00922096 | + | 0.999957i | \(0.502935\pi\) | |||||||
\(60\) | −1.53178 | −0.197752 | ||||||||
\(61\) | −3.91754 | −0.501589 | −0.250795 | − | 0.968040i | \(-0.580692\pi\) | ||||
−0.250795 | + | 0.968040i | \(0.580692\pi\) | |||||||
\(62\) | 18.6603 | 2.36987 | ||||||||
\(63\) | −14.0090 | −1.76497 | ||||||||
\(64\) | −6.97637 | −0.872046 | ||||||||
\(65\) | −15.7467 | −1.95313 | ||||||||
\(66\) | 1.51687 | 0.186714 | ||||||||
\(67\) | 0.202947 | 0.0247939 | 0.0123970 | − | 0.999923i | \(-0.496054\pi\) | ||||
0.0123970 | + | 0.999923i | \(0.496054\pi\) | |||||||
\(68\) | −24.2869 | −2.94522 | ||||||||
\(69\) | 0.291958 | 0.0351476 | ||||||||
\(70\) | 27.6084 | 3.29983 | ||||||||
\(71\) | 6.99318 | 0.829938 | 0.414969 | − | 0.909836i | \(-0.363792\pi\) | ||||
0.414969 | + | 0.909836i | \(0.363792\pi\) | |||||||
\(72\) | −15.2663 | −1.79915 | ||||||||
\(73\) | 0.952512 | 0.111483 | 0.0557415 | − | 0.998445i | \(-0.482248\pi\) | ||||
0.0557415 | + | 0.998445i | \(0.482248\pi\) | |||||||
\(74\) | −14.4490 | −1.67966 | ||||||||
\(75\) | −0.103122 | −0.0119075 | ||||||||
\(76\) | −1.61296 | −0.185019 | ||||||||
\(77\) | −18.3477 | −2.09091 | ||||||||
\(78\) | 2.57821 | 0.291924 | ||||||||
\(79\) | −8.10807 | −0.912229 | −0.456114 | − | 0.889921i | \(-0.650759\pi\) | ||||
−0.456114 | + | 0.889921i | \(0.650759\pi\) | |||||||
\(80\) | 10.6802 | 1.19408 | ||||||||
\(81\) | 8.77632 | 0.975147 | ||||||||
\(82\) | 2.79100 | 0.308215 | ||||||||
\(83\) | 9.46455 | 1.03887 | 0.519435 | − | 0.854510i | \(-0.326142\pi\) | ||||
0.519435 | + | 0.854510i | \(0.326142\pi\) | |||||||
\(84\) | −3.03360 | −0.330992 | ||||||||
\(85\) | −14.1503 | −1.53481 | ||||||||
\(86\) | 7.84947 | 0.846430 | ||||||||
\(87\) | −1.67845 | −0.179949 | ||||||||
\(88\) | −19.9943 | −2.13140 | ||||||||
\(89\) | 10.3042 | 1.09224 | 0.546121 | − | 0.837706i | \(-0.316104\pi\) | ||||
0.546121 | + | 0.837706i | \(0.316104\pi\) | |||||||
\(90\) | −17.4434 | −1.83869 | ||||||||
\(91\) | −31.1853 | −3.26911 | ||||||||
\(92\) | −7.54714 | −0.786844 | ||||||||
\(93\) | −1.19462 | −0.123876 | ||||||||
\(94\) | 1.54129 | 0.158972 | ||||||||
\(95\) | −0.939757 | −0.0964170 | ||||||||
\(96\) | −0.128516 | −0.0131166 | ||||||||
\(97\) | −12.2470 | −1.24350 | −0.621749 | − | 0.783216i | \(-0.713578\pi\) | ||||
−0.621749 | + | 0.783216i | \(0.713578\pi\) | |||||||
\(98\) | 37.4150 | 3.77949 | ||||||||
\(99\) | 11.5923 | 1.16507 | ||||||||
\(100\) | 2.66572 | 0.266572 | ||||||||
\(101\) | 14.8308 | 1.47572 | 0.737858 | − | 0.674956i | \(-0.235838\pi\) | ||||
0.737858 | + | 0.674956i | \(0.235838\pi\) | |||||||
\(102\) | 2.31683 | 0.229400 | ||||||||
\(103\) | −3.30296 | −0.325451 | −0.162725 | − | 0.986671i | \(-0.552028\pi\) | ||||
−0.162725 | + | 0.986671i | \(0.552028\pi\) | |||||||
\(104\) | −33.9840 | −3.33241 | ||||||||
\(105\) | −1.76746 | −0.172487 | ||||||||
\(106\) | 31.7530 | 3.08413 | ||||||||
\(107\) | −2.29757 | −0.222115 | −0.111057 | − | 0.993814i | \(-0.535424\pi\) | ||||
−0.111057 | + | 0.993814i | \(0.535424\pi\) | |||||||
\(108\) | 3.84939 | 0.370408 | ||||||||
\(109\) | 9.44203 | 0.904383 | 0.452191 | − | 0.891921i | \(-0.350642\pi\) | ||||
0.452191 | + | 0.891921i | \(0.350642\pi\) | |||||||
\(110\) | −22.8457 | −2.17825 | ||||||||
\(111\) | 0.925009 | 0.0877979 | ||||||||
\(112\) | 21.1515 | 1.99863 | ||||||||
\(113\) | −10.3934 | −0.977725 | −0.488862 | − | 0.872361i | \(-0.662588\pi\) | ||||
−0.488862 | + | 0.872361i | \(0.662588\pi\) | |||||||
\(114\) | 0.153867 | 0.0144109 | ||||||||
\(115\) | −4.39719 | −0.410040 | ||||||||
\(116\) | 43.3882 | 4.02849 | ||||||||
\(117\) | 19.7033 | 1.82157 | ||||||||
\(118\) | −0.349314 | −0.0321570 | ||||||||
\(119\) | −28.0238 | −2.56893 | ||||||||
\(120\) | −1.92608 | −0.175827 | ||||||||
\(121\) | 4.18256 | 0.380232 | ||||||||
\(122\) | −9.66044 | −0.874615 | ||||||||
\(123\) | −0.178677 | −0.0161108 | ||||||||
\(124\) | 30.8810 | 2.77320 | ||||||||
\(125\) | −10.3351 | −0.924402 | ||||||||
\(126\) | −34.5455 | −3.07756 | ||||||||
\(127\) | −3.47652 | −0.308491 | −0.154246 | − | 0.988033i | \(-0.549295\pi\) | ||||
−0.154246 | + | 0.988033i | \(0.549295\pi\) | |||||||
\(128\) | −18.8315 | −1.66449 | ||||||||
\(129\) | −0.502516 | −0.0442440 | ||||||||
\(130\) | −38.8305 | −3.40566 | ||||||||
\(131\) | −0.615745 | −0.0537979 | −0.0268989 | − | 0.999638i | \(-0.508563\pi\) | ||||
−0.0268989 | + | 0.999638i | \(0.508563\pi\) | |||||||
\(132\) | 2.51027 | 0.218491 | ||||||||
\(133\) | −1.86113 | −0.161380 | ||||||||
\(134\) | 0.500457 | 0.0432329 | ||||||||
\(135\) | 2.24277 | 0.193027 | ||||||||
\(136\) | −30.5388 | −2.61868 | ||||||||
\(137\) | 3.33652 | 0.285058 | 0.142529 | − | 0.989791i | \(-0.454477\pi\) | ||||
0.142529 | + | 0.989791i | \(0.454477\pi\) | |||||||
\(138\) | 0.719952 | 0.0612864 | ||||||||
\(139\) | −2.51131 | −0.213007 | −0.106503 | − | 0.994312i | \(-0.533965\pi\) | ||||
−0.106503 | + | 0.994312i | \(0.533965\pi\) | |||||||
\(140\) | 45.6891 | 3.86143 | ||||||||
\(141\) | −0.0986720 | −0.00830968 | ||||||||
\(142\) | 17.2448 | 1.44715 | ||||||||
\(143\) | 25.8056 | 2.15797 | ||||||||
\(144\) | −13.3638 | −1.11365 | ||||||||
\(145\) | 25.2792 | 2.09933 | ||||||||
\(146\) | 2.34884 | 0.194392 | ||||||||
\(147\) | −2.39528 | −0.197559 | ||||||||
\(148\) | −23.9116 | −1.96552 | ||||||||
\(149\) | 2.65229 | 0.217284 | 0.108642 | − | 0.994081i | \(-0.465350\pi\) | ||||
0.108642 | + | 0.994081i | \(0.465350\pi\) | |||||||
\(150\) | −0.254294 | −0.0207630 | ||||||||
\(151\) | −7.64268 | −0.621953 | −0.310976 | − | 0.950418i | \(-0.600656\pi\) | ||||
−0.310976 | + | 0.950418i | \(0.600656\pi\) | |||||||
\(152\) | −2.02816 | −0.164505 | ||||||||
\(153\) | 17.7058 | 1.43143 | ||||||||
\(154\) | −45.2445 | −3.64590 | ||||||||
\(155\) | 17.9922 | 1.44517 | ||||||||
\(156\) | 4.26667 | 0.341607 | ||||||||
\(157\) | −4.49351 | −0.358621 | −0.179311 | − | 0.983793i | \(-0.557387\pi\) | ||||
−0.179311 | + | 0.983793i | \(0.557387\pi\) | |||||||
\(158\) | −19.9941 | −1.59064 | ||||||||
\(159\) | −2.03280 | −0.161211 | ||||||||
\(160\) | 1.93559 | 0.153022 | ||||||||
\(161\) | −8.70835 | −0.686314 | ||||||||
\(162\) | 21.6419 | 1.70035 | ||||||||
\(163\) | 16.3285 | 1.27894 | 0.639472 | − | 0.768815i | \(-0.279153\pi\) | ||||
0.639472 | + | 0.768815i | \(0.279153\pi\) | |||||||
\(164\) | 4.61883 | 0.360670 | ||||||||
\(165\) | 1.46256 | 0.113860 | ||||||||
\(166\) | 23.3391 | 1.81146 | ||||||||
\(167\) | −21.8457 | −1.69047 | −0.845234 | − | 0.534396i | \(-0.820539\pi\) | ||||
−0.845234 | + | 0.534396i | \(0.820539\pi\) | |||||||
\(168\) | −3.81449 | −0.294294 | ||||||||
\(169\) | 30.8613 | 2.37395 | ||||||||
\(170\) | −34.8939 | −2.67624 | ||||||||
\(171\) | 1.17589 | 0.0899224 | ||||||||
\(172\) | 12.9901 | 0.990485 | ||||||||
\(173\) | −2.93795 | −0.223368 | −0.111684 | − | 0.993744i | \(-0.535625\pi\) | ||||
−0.111684 | + | 0.993744i | \(0.535625\pi\) | |||||||
\(174\) | −4.13897 | −0.313775 | ||||||||
\(175\) | 3.07587 | 0.232514 | ||||||||
\(176\) | −17.5027 | −1.31931 | ||||||||
\(177\) | 0.0223628 | 0.00168089 | ||||||||
\(178\) | 25.4096 | 1.90453 | ||||||||
\(179\) | 1.37373 | 0.102677 | 0.0513387 | − | 0.998681i | \(-0.483651\pi\) | ||||
0.0513387 | + | 0.998681i | \(0.483651\pi\) | |||||||
\(180\) | −28.8670 | −2.15162 | ||||||||
\(181\) | −12.3352 | −0.916865 | −0.458433 | − | 0.888729i | \(-0.651589\pi\) | ||||
−0.458433 | + | 0.888729i | \(0.651589\pi\) | |||||||
\(182\) | −76.9013 | −5.70031 | ||||||||
\(183\) | 0.618452 | 0.0457173 | ||||||||
\(184\) | −9.48989 | −0.699604 | ||||||||
\(185\) | −13.9316 | −1.02427 | ||||||||
\(186\) | −2.94587 | −0.216001 | ||||||||
\(187\) | 23.1894 | 1.69578 | ||||||||
\(188\) | 2.55068 | 0.186028 | ||||||||
\(189\) | 4.44166 | 0.323084 | ||||||||
\(190\) | −2.31739 | −0.168121 | ||||||||
\(191\) | −13.4793 | −0.975329 | −0.487665 | − | 0.873031i | \(-0.662151\pi\) | ||||
−0.487665 | + | 0.873031i | \(0.662151\pi\) | |||||||
\(192\) | 1.10134 | 0.0794826 | ||||||||
\(193\) | 12.6210 | 0.908483 | 0.454241 | − | 0.890879i | \(-0.349910\pi\) | ||||
0.454241 | + | 0.890879i | \(0.349910\pi\) | |||||||
\(194\) | −30.2006 | −2.16827 | ||||||||
\(195\) | 2.48589 | 0.178018 | ||||||||
\(196\) | 61.9181 | 4.42272 | ||||||||
\(197\) | 5.34673 | 0.380938 | 0.190469 | − | 0.981693i | \(-0.438999\pi\) | ||||
0.190469 | + | 0.981693i | \(0.438999\pi\) | |||||||
\(198\) | 28.5861 | 2.03152 | ||||||||
\(199\) | −27.4088 | −1.94296 | −0.971478 | − | 0.237129i | \(-0.923794\pi\) | ||||
−0.971478 | + | 0.237129i | \(0.923794\pi\) | |||||||
\(200\) | 3.35191 | 0.237016 | ||||||||
\(201\) | −0.0320388 | −0.00225984 | ||||||||
\(202\) | 36.5719 | 2.57319 | ||||||||
\(203\) | 50.0639 | 3.51380 | ||||||||
\(204\) | 3.83412 | 0.268442 | ||||||||
\(205\) | 2.69107 | 0.187952 | ||||||||
\(206\) | −8.14493 | −0.567484 | ||||||||
\(207\) | 5.50206 | 0.382420 | ||||||||
\(208\) | −29.7490 | −2.06272 | ||||||||
\(209\) | 1.54007 | 0.106529 | ||||||||
\(210\) | −4.35847 | −0.300763 | ||||||||
\(211\) | −0.948427 | −0.0652924 | −0.0326462 | − | 0.999467i | \(-0.510393\pi\) | ||||
−0.0326462 | + | 0.999467i | \(0.510393\pi\) | |||||||
\(212\) | 52.5481 | 3.60902 | ||||||||
\(213\) | −1.10400 | −0.0756446 | ||||||||
\(214\) | −5.66569 | −0.387299 | ||||||||
\(215\) | 7.56841 | 0.516161 | ||||||||
\(216\) | 4.84028 | 0.329340 | ||||||||
\(217\) | 35.6324 | 2.41888 | ||||||||
\(218\) | 23.2836 | 1.57696 | ||||||||
\(219\) | −0.150371 | −0.0101611 | ||||||||
\(220\) | −37.8073 | −2.54897 | ||||||||
\(221\) | 39.4147 | 2.65132 | ||||||||
\(222\) | 2.28102 | 0.153092 | ||||||||
\(223\) | −23.6431 | −1.58326 | −0.791631 | − | 0.611000i | \(-0.790768\pi\) | ||||
−0.791631 | + | 0.611000i | \(0.790768\pi\) | |||||||
\(224\) | 3.83331 | 0.256124 | ||||||||
\(225\) | −1.94338 | −0.129558 | ||||||||
\(226\) | −25.6295 | −1.70485 | ||||||||
\(227\) | 0.104193 | 0.00691552 | 0.00345776 | − | 0.999994i | \(-0.498899\pi\) | ||||
0.00345776 | + | 0.999994i | \(0.498899\pi\) | |||||||
\(228\) | 0.254634 | 0.0168635 | ||||||||
\(229\) | 15.8886 | 1.04995 | 0.524973 | − | 0.851119i | \(-0.324076\pi\) | ||||
0.524973 | + | 0.851119i | \(0.324076\pi\) | |||||||
\(230\) | −10.8432 | −0.714981 | ||||||||
\(231\) | 2.89651 | 0.190576 | ||||||||
\(232\) | 54.5569 | 3.58184 | ||||||||
\(233\) | 27.7194 | 1.81596 | 0.907978 | − | 0.419018i | \(-0.137626\pi\) | ||||
0.907978 | + | 0.419018i | \(0.137626\pi\) | |||||||
\(234\) | 48.5873 | 3.17625 | ||||||||
\(235\) | 1.48610 | 0.0969426 | ||||||||
\(236\) | −0.578080 | −0.0376298 | ||||||||
\(237\) | 1.28000 | 0.0831450 | ||||||||
\(238\) | −69.1051 | −4.47942 | ||||||||
\(239\) | 2.94936 | 0.190778 | 0.0953892 | − | 0.995440i | \(-0.469590\pi\) | ||||
0.0953892 | + | 0.995440i | \(0.469590\pi\) | |||||||
\(240\) | −1.68606 | −0.108835 | ||||||||
\(241\) | −11.3904 | −0.733722 | −0.366861 | − | 0.930276i | \(-0.619568\pi\) | ||||
−0.366861 | + | 0.930276i | \(0.619568\pi\) | |||||||
\(242\) | 10.3140 | 0.663007 | ||||||||
\(243\) | −4.21531 | −0.270412 | ||||||||
\(244\) | −15.9871 | −1.02347 | ||||||||
\(245\) | 36.0753 | 2.30477 | ||||||||
\(246\) | −0.440609 | −0.0280922 | ||||||||
\(247\) | 2.61763 | 0.166556 | ||||||||
\(248\) | 38.8302 | 2.46572 | ||||||||
\(249\) | −1.49415 | −0.0946877 | ||||||||
\(250\) | −25.4859 | −1.61187 | ||||||||
\(251\) | −16.0716 | −1.01443 | −0.507214 | − | 0.861820i | \(-0.669325\pi\) | ||||
−0.507214 | + | 0.861820i | \(0.669325\pi\) | |||||||
\(252\) | −57.1693 | −3.60133 | ||||||||
\(253\) | 7.20608 | 0.453043 | ||||||||
\(254\) | −8.57292 | −0.537913 | ||||||||
\(255\) | 2.23387 | 0.139890 | ||||||||
\(256\) | −32.4848 | −2.03030 | ||||||||
\(257\) | −18.2023 | −1.13543 | −0.567714 | − | 0.823226i | \(-0.692172\pi\) | ||||
−0.567714 | + | 0.823226i | \(0.692172\pi\) | |||||||
\(258\) | −1.23918 | −0.0771478 | ||||||||
\(259\) | −27.5906 | −1.71440 | ||||||||
\(260\) | −64.2605 | −3.98527 | ||||||||
\(261\) | −31.6311 | −1.95792 | ||||||||
\(262\) | −1.51839 | −0.0938067 | ||||||||
\(263\) | 9.11949 | 0.562332 | 0.281166 | − | 0.959659i | \(-0.409279\pi\) | ||||
0.281166 | + | 0.959659i | \(0.409279\pi\) | |||||||
\(264\) | 3.15646 | 0.194266 | ||||||||
\(265\) | 30.6160 | 1.88073 | ||||||||
\(266\) | −4.58945 | −0.281397 | ||||||||
\(267\) | −1.62670 | −0.0995524 | ||||||||
\(268\) | 0.828206 | 0.0505907 | ||||||||
\(269\) | −14.0578 | −0.857119 | −0.428559 | − | 0.903514i | \(-0.640979\pi\) | ||||
−0.428559 | + | 0.903514i | \(0.640979\pi\) | |||||||
\(270\) | 5.53055 | 0.336579 | ||||||||
\(271\) | −7.13801 | −0.433603 | −0.216801 | − | 0.976216i | \(-0.569562\pi\) | ||||
−0.216801 | + | 0.976216i | \(0.569562\pi\) | |||||||
\(272\) | −26.7331 | −1.62093 | ||||||||
\(273\) | 4.92315 | 0.297963 | ||||||||
\(274\) | 8.22767 | 0.497052 | ||||||||
\(275\) | −2.54525 | −0.153485 | ||||||||
\(276\) | 1.19145 | 0.0717168 | ||||||||
\(277\) | −4.64697 | −0.279210 | −0.139605 | − | 0.990207i | \(-0.544583\pi\) | ||||
−0.139605 | + | 0.990207i | \(0.544583\pi\) | |||||||
\(278\) | −6.19276 | −0.371417 | ||||||||
\(279\) | −22.5130 | −1.34782 | ||||||||
\(280\) | 57.4501 | 3.43330 | ||||||||
\(281\) | −24.4344 | −1.45763 | −0.728817 | − | 0.684708i | \(-0.759930\pi\) | ||||
−0.728817 | + | 0.684708i | \(0.759930\pi\) | |||||||
\(282\) | −0.243320 | −0.0144895 | ||||||||
\(283\) | −5.51364 | −0.327752 | −0.163876 | − | 0.986481i | \(-0.552400\pi\) | ||||
−0.163876 | + | 0.986481i | \(0.552400\pi\) | |||||||
\(284\) | 28.5384 | 1.69344 | ||||||||
\(285\) | 0.148357 | 0.00878792 | ||||||||
\(286\) | 63.6352 | 3.76283 | ||||||||
\(287\) | 5.32949 | 0.314590 | ||||||||
\(288\) | −2.42194 | −0.142714 | ||||||||
\(289\) | 18.4189 | 1.08346 | ||||||||
\(290\) | 62.3372 | 3.66057 | ||||||||
\(291\) | 1.93341 | 0.113339 | ||||||||
\(292\) | 3.88710 | 0.227475 | ||||||||
\(293\) | −0.925316 | −0.0540576 | −0.0270288 | − | 0.999635i | \(-0.508605\pi\) | ||||
−0.0270288 | + | 0.999635i | \(0.508605\pi\) | |||||||
\(294\) | −5.90662 | −0.344481 | ||||||||
\(295\) | −0.336806 | −0.0196096 | ||||||||
\(296\) | −30.0668 | −1.74760 | ||||||||
\(297\) | −3.67544 | −0.213271 | ||||||||
\(298\) | 6.54041 | 0.378876 | ||||||||
\(299\) | 12.2481 | 0.708324 | ||||||||
\(300\) | −0.420831 | −0.0242967 | ||||||||
\(301\) | 14.9888 | 0.863938 | ||||||||
\(302\) | −18.8465 | −1.08449 | ||||||||
\(303\) | −2.34130 | −0.134504 | ||||||||
\(304\) | −1.77541 | −0.101827 | ||||||||
\(305\) | −9.31453 | −0.533349 | ||||||||
\(306\) | 43.6616 | 2.49597 | ||||||||
\(307\) | −27.4310 | −1.56557 | −0.782785 | − | 0.622292i | \(-0.786202\pi\) | ||||
−0.782785 | + | 0.622292i | \(0.786202\pi\) | |||||||
\(308\) | −74.8750 | −4.26640 | ||||||||
\(309\) | 0.521431 | 0.0296632 | ||||||||
\(310\) | 44.3678 | 2.51992 | ||||||||
\(311\) | −22.0958 | −1.25294 | −0.626468 | − | 0.779447i | \(-0.715500\pi\) | ||||
−0.626468 | + | 0.779447i | \(0.715500\pi\) | |||||||
\(312\) | 5.36498 | 0.303732 | ||||||||
\(313\) | −12.0460 | −0.680881 | −0.340440 | − | 0.940266i | \(-0.610576\pi\) | ||||
−0.340440 | + | 0.940266i | \(0.610576\pi\) | |||||||
\(314\) | −11.0808 | −0.625323 | ||||||||
\(315\) | −33.3085 | −1.87672 | ||||||||
\(316\) | −33.0882 | −1.86136 | ||||||||
\(317\) | 7.65816 | 0.430125 | 0.215063 | − | 0.976600i | \(-0.431004\pi\) | ||||
0.215063 | + | 0.976600i | \(0.431004\pi\) | |||||||
\(318\) | −5.01277 | −0.281102 | ||||||||
\(319\) | −41.4275 | −2.31949 | ||||||||
\(320\) | −16.5874 | −0.927262 | ||||||||
\(321\) | 0.362712 | 0.0202446 | ||||||||
\(322\) | −21.4743 | −1.19672 | ||||||||
\(323\) | 2.35226 | 0.130883 | ||||||||
\(324\) | 35.8153 | 1.98974 | ||||||||
\(325\) | −4.32613 | −0.239971 | ||||||||
\(326\) | 40.2651 | 2.23008 | ||||||||
\(327\) | −1.49059 | −0.0824299 | ||||||||
\(328\) | 5.80779 | 0.320681 | ||||||||
\(329\) | 2.94313 | 0.162260 | ||||||||
\(330\) | 3.60659 | 0.198536 | ||||||||
\(331\) | 16.9303 | 0.930575 | 0.465287 | − | 0.885160i | \(-0.345951\pi\) | ||||
0.465287 | + | 0.885160i | \(0.345951\pi\) | |||||||
\(332\) | 38.6239 | 2.11976 | ||||||||
\(333\) | 17.4322 | 0.955276 | ||||||||
\(334\) | −53.8703 | −2.94765 | ||||||||
\(335\) | 0.482537 | 0.0263638 | ||||||||
\(336\) | −3.33914 | −0.182165 | ||||||||
\(337\) | 9.35829 | 0.509779 | 0.254889 | − | 0.966970i | \(-0.417961\pi\) | ||||
0.254889 | + | 0.966970i | \(0.417961\pi\) | |||||||
\(338\) | 76.1024 | 4.13943 | ||||||||
\(339\) | 1.64077 | 0.0891147 | ||||||||
\(340\) | −57.7458 | −3.13171 | ||||||||
\(341\) | −29.4855 | −1.59673 | ||||||||
\(342\) | 2.89968 | 0.156797 | ||||||||
\(343\) | 38.4834 | 2.07791 | ||||||||
\(344\) | 16.3339 | 0.880666 | ||||||||
\(345\) | 0.694173 | 0.0373730 | ||||||||
\(346\) | −7.24484 | −0.389485 | ||||||||
\(347\) | −35.5930 | −1.91073 | −0.955367 | − | 0.295421i | \(-0.904540\pi\) | ||||
−0.955367 | + | 0.295421i | \(0.904540\pi\) | |||||||
\(348\) | −6.84959 | −0.367176 | ||||||||
\(349\) | −11.8428 | −0.633930 | −0.316965 | − | 0.948437i | \(-0.602664\pi\) | ||||
−0.316965 | + | 0.948437i | \(0.602664\pi\) | |||||||
\(350\) | 7.58493 | 0.405432 | ||||||||
\(351\) | −6.24709 | −0.333445 | ||||||||
\(352\) | −3.17203 | −0.169070 | ||||||||
\(353\) | −3.61444 | −0.192377 | −0.0961886 | − | 0.995363i | \(-0.530665\pi\) | ||||
−0.0961886 | + | 0.995363i | \(0.530665\pi\) | |||||||
\(354\) | 0.0551454 | 0.00293094 | ||||||||
\(355\) | 16.6273 | 0.882487 | ||||||||
\(356\) | 42.0504 | 2.22866 | ||||||||
\(357\) | 4.42404 | 0.234145 | ||||||||
\(358\) | 3.38755 | 0.179037 | ||||||||
\(359\) | 19.2576 | 1.01638 | 0.508188 | − | 0.861246i | \(-0.330316\pi\) | ||||
0.508188 | + | 0.861246i | \(0.330316\pi\) | |||||||
\(360\) | −36.2978 | −1.91306 | ||||||||
\(361\) | −18.8438 | −0.991778 | ||||||||
\(362\) | −30.4179 | −1.59873 | ||||||||
\(363\) | −0.660290 | −0.0346562 | ||||||||
\(364\) | −127.264 | −6.67045 | ||||||||
\(365\) | 2.26474 | 0.118542 | ||||||||
\(366\) | 1.52507 | 0.0797167 | ||||||||
\(367\) | 29.0707 | 1.51748 | 0.758740 | − | 0.651393i | \(-0.225815\pi\) | ||||
0.758740 | + | 0.651393i | \(0.225815\pi\) | |||||||
\(368\) | −8.30728 | −0.433047 | ||||||||
\(369\) | −3.36725 | −0.175292 | ||||||||
\(370\) | −34.3546 | −1.78601 | ||||||||
\(371\) | 60.6332 | 3.14792 | ||||||||
\(372\) | −4.87511 | −0.252763 | ||||||||
\(373\) | 11.0922 | 0.574334 | 0.287167 | − | 0.957881i | \(-0.407287\pi\) | ||||
0.287167 | + | 0.957881i | \(0.407287\pi\) | |||||||
\(374\) | 57.1839 | 2.95691 | ||||||||
\(375\) | 1.63158 | 0.0842545 | ||||||||
\(376\) | 3.20727 | 0.165402 | ||||||||
\(377\) | −70.4137 | −3.62649 | ||||||||
\(378\) | 10.9529 | 0.563357 | ||||||||
\(379\) | 28.5334 | 1.46566 | 0.732830 | − | 0.680412i | \(-0.238199\pi\) | ||||
0.732830 | + | 0.680412i | \(0.238199\pi\) | |||||||
\(380\) | −3.83505 | −0.196734 | ||||||||
\(381\) | 0.548830 | 0.0281174 | ||||||||
\(382\) | −33.2393 | −1.70067 | ||||||||
\(383\) | −22.5616 | −1.15284 | −0.576422 | − | 0.817152i | \(-0.695552\pi\) | ||||
−0.576422 | + | 0.817152i | \(0.695552\pi\) | |||||||
\(384\) | 2.97289 | 0.151709 | ||||||||
\(385\) | −43.6244 | −2.22331 | ||||||||
\(386\) | 31.1228 | 1.58411 | ||||||||
\(387\) | −9.47011 | −0.481393 | ||||||||
\(388\) | −49.9789 | −2.53729 | ||||||||
\(389\) | −7.21475 | −0.365802 | −0.182901 | − | 0.983131i | \(-0.558549\pi\) | ||||
−0.182901 | + | 0.983131i | \(0.558549\pi\) | |||||||
\(390\) | 6.13007 | 0.310408 | ||||||||
\(391\) | 11.0064 | 0.556616 | ||||||||
\(392\) | 77.8568 | 3.93236 | ||||||||
\(393\) | 0.0972061 | 0.00490340 | ||||||||
\(394\) | 13.1847 | 0.664238 | ||||||||
\(395\) | −19.2781 | −0.969989 | ||||||||
\(396\) | 47.3071 | 2.37727 | ||||||||
\(397\) | 27.6931 | 1.38988 | 0.694939 | − | 0.719069i | \(-0.255431\pi\) | ||||
0.694939 | + | 0.719069i | \(0.255431\pi\) | |||||||
\(398\) | −67.5886 | −3.38791 | ||||||||
\(399\) | 0.293812 | 0.0147090 | ||||||||
\(400\) | 2.93421 | 0.146710 | ||||||||
\(401\) | 19.7647 | 0.987002 | 0.493501 | − | 0.869745i | \(-0.335717\pi\) | ||||
0.493501 | + | 0.869745i | \(0.335717\pi\) | |||||||
\(402\) | −0.0790059 | −0.00394046 | ||||||||
\(403\) | −50.1161 | −2.49646 | ||||||||
\(404\) | 60.5228 | 3.01112 | ||||||||
\(405\) | 20.8670 | 1.03689 | ||||||||
\(406\) | 123.455 | 6.12697 | ||||||||
\(407\) | 22.8310 | 1.13169 | ||||||||
\(408\) | 4.82108 | 0.238679 | ||||||||
\(409\) | −3.39180 | −0.167714 | −0.0838569 | − | 0.996478i | \(-0.526724\pi\) | ||||
−0.0838569 | + | 0.996478i | \(0.526724\pi\) | |||||||
\(410\) | 6.63603 | 0.327730 | ||||||||
\(411\) | −0.526728 | −0.0259816 | ||||||||
\(412\) | −13.4790 | −0.664065 | ||||||||
\(413\) | −0.667024 | −0.0328221 | ||||||||
\(414\) | 13.5678 | 0.666820 | ||||||||
\(415\) | 22.5034 | 1.10465 | ||||||||
\(416\) | −5.39146 | −0.264338 | ||||||||
\(417\) | 0.396455 | 0.0194145 | ||||||||
\(418\) | 3.79773 | 0.185753 | ||||||||
\(419\) | 34.8756 | 1.70379 | 0.851893 | − | 0.523716i | \(-0.175455\pi\) | ||||
0.851893 | + | 0.523716i | \(0.175455\pi\) | |||||||
\(420\) | −7.21283 | −0.351950 | ||||||||
\(421\) | −19.5846 | −0.954494 | −0.477247 | − | 0.878769i | \(-0.658365\pi\) | ||||
−0.477247 | + | 0.878769i | \(0.658365\pi\) | |||||||
\(422\) | −2.33877 | −0.113850 | ||||||||
\(423\) | −1.85951 | −0.0904126 | ||||||||
\(424\) | 66.0747 | 3.20887 | ||||||||
\(425\) | −3.88755 | −0.188574 | ||||||||
\(426\) | −2.72240 | −0.131901 | ||||||||
\(427\) | −18.4469 | −0.892706 | ||||||||
\(428\) | −9.37615 | −0.453214 | ||||||||
\(429\) | −4.07386 | −0.196688 | ||||||||
\(430\) | 18.6633 | 0.900024 | ||||||||
\(431\) | 38.4490 | 1.85202 | 0.926012 | − | 0.377493i | \(-0.123214\pi\) | ||||
0.926012 | + | 0.377493i | \(0.123214\pi\) | |||||||
\(432\) | 4.23710 | 0.203857 | ||||||||
\(433\) | 12.4697 | 0.599253 | 0.299627 | − | 0.954057i | \(-0.403138\pi\) | ||||
0.299627 | + | 0.954057i | \(0.403138\pi\) | |||||||
\(434\) | 87.8676 | 4.21778 | ||||||||
\(435\) | −3.99077 | −0.191343 | ||||||||
\(436\) | 38.5319 | 1.84535 | ||||||||
\(437\) | 0.730962 | 0.0349666 | ||||||||
\(438\) | −0.370806 | −0.0177178 | ||||||||
\(439\) | −20.4231 | −0.974741 | −0.487371 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487371 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(440\) | −47.5395 | −2.26636 | ||||||||
\(441\) | −45.1399 | −2.14952 | ||||||||
\(442\) | 97.1946 | 4.62307 | ||||||||
\(443\) | 32.8537 | 1.56093 | 0.780463 | − | 0.625202i | \(-0.214984\pi\) | ||||
0.780463 | + | 0.625202i | \(0.214984\pi\) | |||||||
\(444\) | 3.77486 | 0.179147 | ||||||||
\(445\) | 24.4998 | 1.16140 | ||||||||
\(446\) | −58.3027 | −2.76071 | ||||||||
\(447\) | −0.418711 | −0.0198043 | ||||||||
\(448\) | −32.8502 | −1.55203 | ||||||||
\(449\) | 17.9950 | 0.849238 | 0.424619 | − | 0.905372i | \(-0.360408\pi\) | ||||
0.424619 | + | 0.905372i | \(0.360408\pi\) | |||||||
\(450\) | −4.79227 | −0.225910 | ||||||||
\(451\) | −4.41011 | −0.207664 | ||||||||
\(452\) | −42.4142 | −1.99500 | ||||||||
\(453\) | 1.20653 | 0.0566878 | ||||||||
\(454\) | 0.256934 | 0.0120585 | ||||||||
\(455\) | −74.1477 | −3.47610 | ||||||||
\(456\) | 0.320180 | 0.0149938 | ||||||||
\(457\) | 37.3590 | 1.74758 | 0.873791 | − | 0.486302i | \(-0.161655\pi\) | ||||
0.873791 | + | 0.486302i | \(0.161655\pi\) | |||||||
\(458\) | 39.1803 | 1.83078 | ||||||||
\(459\) | −5.61376 | −0.262028 | ||||||||
\(460\) | −17.9445 | −0.836665 | ||||||||
\(461\) | 9.41308 | 0.438411 | 0.219205 | − | 0.975679i | \(-0.429654\pi\) | ||||
0.219205 | + | 0.975679i | \(0.429654\pi\) | |||||||
\(462\) | 7.14263 | 0.332305 | ||||||||
\(463\) | −29.5125 | −1.37156 | −0.685781 | − | 0.727808i | \(-0.740539\pi\) | ||||
−0.685781 | + | 0.727808i | \(0.740539\pi\) | |||||||
\(464\) | 47.7582 | 2.21712 | ||||||||
\(465\) | −2.84038 | −0.131720 | ||||||||
\(466\) | 68.3545 | 3.16646 | ||||||||
\(467\) | 15.7255 | 0.727690 | 0.363845 | − | 0.931460i | \(-0.381464\pi\) | ||||
0.363845 | + | 0.931460i | \(0.381464\pi\) | |||||||
\(468\) | 80.4072 | 3.71682 | ||||||||
\(469\) | 0.955634 | 0.0441271 | ||||||||
\(470\) | 3.66465 | 0.169038 | ||||||||
\(471\) | 0.709380 | 0.0326865 | ||||||||
\(472\) | −0.726886 | −0.0334576 | ||||||||
\(473\) | −12.4031 | −0.570294 | ||||||||
\(474\) | 3.15642 | 0.144979 | ||||||||
\(475\) | −0.258182 | −0.0118462 | ||||||||
\(476\) | −114.362 | −5.24178 | ||||||||
\(477\) | −38.3089 | −1.75404 | ||||||||
\(478\) | 7.27297 | 0.332658 | ||||||||
\(479\) | −19.5493 | −0.893232 | −0.446616 | − | 0.894726i | \(-0.647371\pi\) | ||||
−0.446616 | + | 0.894726i | \(0.647371\pi\) | |||||||
\(480\) | −0.305567 | −0.0139472 | ||||||||
\(481\) | 38.8055 | 1.76938 | ||||||||
\(482\) | −28.0882 | −1.27938 | ||||||||
\(483\) | 1.37477 | 0.0625541 | ||||||||
\(484\) | 17.0686 | 0.775844 | ||||||||
\(485\) | −29.1192 | −1.32223 | ||||||||
\(486\) | −10.3947 | −0.471515 | ||||||||
\(487\) | −16.1545 | −0.732030 | −0.366015 | − | 0.930609i | \(-0.619278\pi\) | ||||
−0.366015 | + | 0.930609i | \(0.619278\pi\) | |||||||
\(488\) | −20.1024 | −0.909992 | ||||||||
\(489\) | −2.57773 | −0.116569 | ||||||||
\(490\) | 88.9598 | 4.01880 | ||||||||
\(491\) | 28.8831 | 1.30348 | 0.651738 | − | 0.758444i | \(-0.274040\pi\) | ||||
0.651738 | + | 0.758444i | \(0.274040\pi\) | |||||||
\(492\) | −0.729164 | −0.0328733 | ||||||||
\(493\) | −63.2752 | −2.84977 | ||||||||
\(494\) | 6.45494 | 0.290422 | ||||||||
\(495\) | 27.5625 | 1.23884 | ||||||||
\(496\) | 33.9913 | 1.52625 | ||||||||
\(497\) | 32.9294 | 1.47709 | ||||||||
\(498\) | −3.68449 | −0.165106 | ||||||||
\(499\) | −1.88279 | −0.0842854 | −0.0421427 | − | 0.999112i | \(-0.513418\pi\) | ||||
−0.0421427 | + | 0.999112i | \(0.513418\pi\) | |||||||
\(500\) | −42.1766 | −1.88619 | ||||||||
\(501\) | 3.44872 | 0.154078 | ||||||||
\(502\) | −39.6316 | −1.76884 | ||||||||
\(503\) | 19.1927 | 0.855760 | 0.427880 | − | 0.903836i | \(-0.359261\pi\) | ||||
0.427880 | + | 0.903836i | \(0.359261\pi\) | |||||||
\(504\) | −71.8855 | −3.20204 | ||||||||
\(505\) | 35.2623 | 1.56915 | ||||||||
\(506\) | 17.7698 | 0.789965 | ||||||||
\(507\) | −4.87201 | −0.216373 | ||||||||
\(508\) | −14.1873 | −0.629461 | ||||||||
\(509\) | 25.9305 | 1.14935 | 0.574674 | − | 0.818383i | \(-0.305129\pi\) | ||||
0.574674 | + | 0.818383i | \(0.305129\pi\) | |||||||
\(510\) | 5.50861 | 0.243925 | ||||||||
\(511\) | 4.48517 | 0.198412 | ||||||||
\(512\) | −42.4427 | −1.87572 | ||||||||
\(513\) | −0.372824 | −0.0164606 | ||||||||
\(514\) | −44.8859 | −1.97983 | ||||||||
\(515\) | −7.85329 | −0.346057 | ||||||||
\(516\) | −2.05071 | −0.0902777 | ||||||||
\(517\) | −2.43542 | −0.107110 | ||||||||
\(518\) | −68.0371 | −2.98938 | ||||||||
\(519\) | 0.463808 | 0.0203589 | ||||||||
\(520\) | −80.8022 | −3.54341 | ||||||||
\(521\) | 21.8092 | 0.955478 | 0.477739 | − | 0.878502i | \(-0.341456\pi\) | ||||
0.477739 | + | 0.878502i | \(0.341456\pi\) | |||||||
\(522\) | −78.0006 | −3.41399 | ||||||||
\(523\) | 27.0965 | 1.18485 | 0.592423 | − | 0.805627i | \(-0.298172\pi\) | ||||
0.592423 | + | 0.805627i | \(0.298172\pi\) | |||||||
\(524\) | −2.51279 | −0.109772 | ||||||||
\(525\) | −0.485580 | −0.0211925 | ||||||||
\(526\) | 22.4882 | 0.980531 | ||||||||
\(527\) | −45.0353 | −1.96177 | ||||||||
\(528\) | 2.76311 | 0.120249 | ||||||||
\(529\) | −19.5798 | −0.851295 | ||||||||
\(530\) | 75.4975 | 3.27940 | ||||||||
\(531\) | 0.421435 | 0.0182887 | ||||||||
\(532\) | −7.59508 | −0.329288 | ||||||||
\(533\) | −7.49579 | −0.324679 | ||||||||
\(534\) | −4.01135 | −0.173588 | ||||||||
\(535\) | −5.46282 | −0.236178 | ||||||||
\(536\) | 1.04140 | 0.0449816 | ||||||||
\(537\) | −0.216868 | −0.00935852 | ||||||||
\(538\) | −34.6658 | −1.49455 | ||||||||
\(539\) | −59.1200 | −2.54648 | ||||||||
\(540\) | 9.15251 | 0.393861 | ||||||||
\(541\) | 17.7634 | 0.763707 | 0.381854 | − | 0.924223i | \(-0.375286\pi\) | ||||
0.381854 | + | 0.924223i | \(0.375286\pi\) | |||||||
\(542\) | −17.6019 | −0.756068 | ||||||||
\(543\) | 1.94732 | 0.0835676 | ||||||||
\(544\) | −4.84487 | −0.207722 | ||||||||
\(545\) | 22.4498 | 0.961646 | ||||||||
\(546\) | 12.1402 | 0.519554 | ||||||||
\(547\) | −30.2921 | −1.29520 | −0.647599 | − | 0.761982i | \(-0.724227\pi\) | ||||
−0.647599 | + | 0.761982i | \(0.724227\pi\) | |||||||
\(548\) | 13.6160 | 0.581646 | ||||||||
\(549\) | 11.6550 | 0.497422 | ||||||||
\(550\) | −6.27646 | −0.267629 | ||||||||
\(551\) | −4.20227 | −0.179023 | ||||||||
\(552\) | 1.49815 | 0.0637653 | ||||||||
\(553\) | −38.1792 | −1.62354 | ||||||||
\(554\) | −11.4592 | −0.486854 | ||||||||
\(555\) | 2.19935 | 0.0933571 | ||||||||
\(556\) | −10.2484 | −0.434629 | ||||||||
\(557\) | 5.30744 | 0.224883 | 0.112442 | − | 0.993658i | \(-0.464133\pi\) | ||||
0.112442 | + | 0.993658i | \(0.464133\pi\) | |||||||
\(558\) | −55.5160 | −2.35018 | ||||||||
\(559\) | −21.0813 | −0.891644 | ||||||||
\(560\) | 50.2908 | 2.12518 | ||||||||
\(561\) | −3.66086 | −0.154562 | ||||||||
\(562\) | −60.2540 | −2.54166 | ||||||||
\(563\) | 0.877218 | 0.0369703 | 0.0184852 | − | 0.999829i | \(-0.494116\pi\) | ||||
0.0184852 | + | 0.999829i | \(0.494116\pi\) | |||||||
\(564\) | −0.402670 | −0.0169555 | ||||||||
\(565\) | −24.7118 | −1.03963 | ||||||||
\(566\) | −13.5964 | −0.571498 | ||||||||
\(567\) | 41.3258 | 1.73552 | ||||||||
\(568\) | 35.8847 | 1.50569 | ||||||||
\(569\) | 5.25733 | 0.220399 | 0.110199 | − | 0.993910i | \(-0.464851\pi\) | ||||
0.110199 | + | 0.993910i | \(0.464851\pi\) | |||||||
\(570\) | 0.365841 | 0.0153234 | ||||||||
\(571\) | −35.4142 | −1.48204 | −0.741018 | − | 0.671485i | \(-0.765657\pi\) | ||||
−0.741018 | + | 0.671485i | \(0.765657\pi\) | |||||||
\(572\) | 105.310 | 4.40323 | ||||||||
\(573\) | 2.12795 | 0.0888963 | ||||||||
\(574\) | 13.1422 | 0.548547 | ||||||||
\(575\) | −1.20805 | −0.0503793 | ||||||||
\(576\) | 20.7552 | 0.864802 | ||||||||
\(577\) | −7.68971 | −0.320127 | −0.160063 | − | 0.987107i | \(-0.551170\pi\) | ||||
−0.160063 | + | 0.987107i | \(0.551170\pi\) | |||||||
\(578\) | 45.4199 | 1.88922 | ||||||||
\(579\) | −1.99245 | −0.0828036 | ||||||||
\(580\) | 103.162 | 4.28356 | ||||||||
\(581\) | 44.5666 | 1.84893 | ||||||||
\(582\) | 4.76769 | 0.197627 | ||||||||
\(583\) | −50.1734 | −2.07797 | ||||||||
\(584\) | 4.88770 | 0.202254 | ||||||||
\(585\) | 46.8476 | 1.93691 | ||||||||
\(586\) | −2.28178 | −0.0942595 | ||||||||
\(587\) | −15.4388 | −0.637226 | −0.318613 | − | 0.947885i | \(-0.603217\pi\) | ||||
−0.318613 | + | 0.947885i | \(0.603217\pi\) | |||||||
\(588\) | −9.77487 | −0.403109 | ||||||||
\(589\) | −2.99091 | −0.123238 | ||||||||
\(590\) | −0.830546 | −0.0341930 | ||||||||
\(591\) | −0.844075 | −0.0347206 | ||||||||
\(592\) | −26.3199 | −1.08174 | ||||||||
\(593\) | −23.4716 | −0.963865 | −0.481932 | − | 0.876208i | \(-0.660065\pi\) | ||||
−0.481932 | + | 0.876208i | \(0.660065\pi\) | |||||||
\(594\) | −9.06344 | −0.371877 | ||||||||
\(595\) | −66.6307 | −2.73159 | ||||||||
\(596\) | 10.8237 | 0.443357 | ||||||||
\(597\) | 4.32696 | 0.177091 | ||||||||
\(598\) | 30.2031 | 1.23510 | ||||||||
\(599\) | −4.63449 | −0.189360 | −0.0946801 | − | 0.995508i | \(-0.530183\pi\) | ||||
−0.0946801 | + | 0.995508i | \(0.530183\pi\) | |||||||
\(600\) | −0.529159 | −0.0216028 | ||||||||
\(601\) | 17.8220 | 0.726973 | 0.363486 | − | 0.931600i | \(-0.381586\pi\) | ||||
0.363486 | + | 0.931600i | \(0.381586\pi\) | |||||||
\(602\) | 36.9615 | 1.50644 | ||||||||
\(603\) | −0.603783 | −0.0245880 | ||||||||
\(604\) | −31.1890 | −1.26906 | ||||||||
\(605\) | 9.94465 | 0.404308 | ||||||||
\(606\) | −5.77351 | −0.234533 | ||||||||
\(607\) | 46.4186 | 1.88407 | 0.942036 | − | 0.335511i | \(-0.108909\pi\) | ||||
0.942036 | + | 0.335511i | \(0.108909\pi\) | |||||||
\(608\) | −0.321761 | −0.0130491 | ||||||||
\(609\) | −7.90348 | −0.320265 | ||||||||
\(610\) | −22.9691 | −0.929993 | ||||||||
\(611\) | −4.13944 | −0.167464 | ||||||||
\(612\) | 72.2555 | 2.92076 | ||||||||
\(613\) | 7.84940 | 0.317034 | 0.158517 | − | 0.987356i | \(-0.449329\pi\) | ||||
0.158517 | + | 0.987356i | \(0.449329\pi\) | |||||||
\(614\) | −67.6434 | −2.72987 | ||||||||
\(615\) | −0.424832 | −0.0171309 | ||||||||
\(616\) | −94.1490 | −3.79337 | ||||||||
\(617\) | −26.4714 | −1.06570 | −0.532849 | − | 0.846211i | \(-0.678879\pi\) | ||||
−0.532849 | + | 0.846211i | \(0.678879\pi\) | |||||||
\(618\) | 1.28582 | 0.0517233 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | 73.4242 | 2.94879 | ||||||||
\(621\) | −1.74447 | −0.0700032 | ||||||||
\(622\) | −54.4870 | −2.18473 | ||||||||
\(623\) | 48.5203 | 1.94392 | ||||||||
\(624\) | 4.69641 | 0.188007 | ||||||||
\(625\) | −27.8394 | −1.11358 | ||||||||
\(626\) | −29.7048 | −1.18724 | ||||||||
\(627\) | −0.243127 | −0.00970956 | ||||||||
\(628\) | −18.3375 | −0.731748 | ||||||||
\(629\) | 34.8714 | 1.39042 | ||||||||
\(630\) | −82.1371 | −3.27242 | ||||||||
\(631\) | −25.2324 | −1.00448 | −0.502242 | − | 0.864727i | \(-0.667491\pi\) | ||||
−0.502242 | + | 0.864727i | \(0.667491\pi\) | |||||||
\(632\) | −41.6056 | −1.65498 | ||||||||
\(633\) | 0.149726 | 0.00595107 | ||||||||
\(634\) | 18.8846 | 0.750004 | ||||||||
\(635\) | −8.26595 | −0.328024 | ||||||||
\(636\) | −8.29564 | −0.328943 | ||||||||
\(637\) | −100.485 | −3.98138 | ||||||||
\(638\) | −102.158 | −4.04447 | ||||||||
\(639\) | −20.8053 | −0.823043 | ||||||||
\(640\) | −44.7747 | −1.76988 | ||||||||
\(641\) | 24.4105 | 0.964159 | 0.482079 | − | 0.876128i | \(-0.339882\pi\) | ||||
0.482079 | + | 0.876128i | \(0.339882\pi\) | |||||||
\(642\) | 0.894430 | 0.0353003 | ||||||||
\(643\) | −5.52050 | −0.217707 | −0.108854 | − | 0.994058i | \(-0.534718\pi\) | ||||
−0.108854 | + | 0.994058i | \(0.534718\pi\) | |||||||
\(644\) | −35.5379 | −1.40039 | ||||||||
\(645\) | −1.19481 | −0.0470455 | ||||||||
\(646\) | 5.80054 | 0.228219 | ||||||||
\(647\) | 39.5404 | 1.55449 | 0.777247 | − | 0.629195i | \(-0.216615\pi\) | ||||
0.777247 | + | 0.629195i | \(0.216615\pi\) | |||||||
\(648\) | 45.0346 | 1.76913 | ||||||||
\(649\) | 0.551956 | 0.0216662 | ||||||||
\(650\) | −10.6680 | −0.418434 | ||||||||
\(651\) | −5.62520 | −0.220469 | ||||||||
\(652\) | 66.6347 | 2.60962 | ||||||||
\(653\) | 26.1438 | 1.02308 | 0.511542 | − | 0.859258i | \(-0.329074\pi\) | ||||
0.511542 | + | 0.859258i | \(0.329074\pi\) | |||||||
\(654\) | −3.67572 | −0.143732 | ||||||||
\(655\) | −1.46402 | −0.0572042 | ||||||||
\(656\) | 5.08403 | 0.198498 | ||||||||
\(657\) | −2.83380 | −0.110557 | ||||||||
\(658\) | 7.25761 | 0.282931 | ||||||||
\(659\) | 9.69906 | 0.377822 | 0.188911 | − | 0.981994i | \(-0.439504\pi\) | ||||
0.188911 | + | 0.981994i | \(0.439504\pi\) | |||||||
\(660\) | 5.96855 | 0.232326 | ||||||||
\(661\) | −3.26550 | −0.127013 | −0.0635067 | − | 0.997981i | \(-0.520228\pi\) | ||||
−0.0635067 | + | 0.997981i | \(0.520228\pi\) | |||||||
\(662\) | 41.7493 | 1.62263 | ||||||||
\(663\) | −6.22231 | −0.241654 | ||||||||
\(664\) | 48.5662 | 1.88473 | ||||||||
\(665\) | −4.42512 | −0.171599 | ||||||||
\(666\) | 42.9868 | 1.66570 | ||||||||
\(667\) | −19.6627 | −0.761342 | ||||||||
\(668\) | −89.1499 | −3.44931 | ||||||||
\(669\) | 3.73249 | 0.144306 | ||||||||
\(670\) | 1.18991 | 0.0459703 | ||||||||
\(671\) | 15.2646 | 0.589284 | ||||||||
\(672\) | −0.605156 | −0.0233444 | ||||||||
\(673\) | −22.2964 | −0.859462 | −0.429731 | − | 0.902957i | \(-0.641392\pi\) | ||||
−0.429731 | + | 0.902957i | \(0.641392\pi\) | |||||||
\(674\) | 23.0771 | 0.888895 | ||||||||
\(675\) | 0.616163 | 0.0237161 | ||||||||
\(676\) | 125.942 | 4.84392 | ||||||||
\(677\) | 5.74561 | 0.220822 | 0.110411 | − | 0.993886i | \(-0.464783\pi\) | ||||
0.110411 | + | 0.993886i | \(0.464783\pi\) | |||||||
\(678\) | 4.04606 | 0.155388 | ||||||||
\(679\) | −57.6687 | −2.21312 | ||||||||
\(680\) | −72.6105 | −2.78448 | ||||||||
\(681\) | −0.0164487 | −0.000630315 0 | ||||||||
\(682\) | −72.7097 | −2.78420 | ||||||||
\(683\) | 3.03267 | 0.116042 | 0.0580210 | − | 0.998315i | \(-0.481521\pi\) | ||||
0.0580210 | + | 0.998315i | \(0.481521\pi\) | |||||||
\(684\) | 4.79868 | 0.183482 | ||||||||
\(685\) | 7.93307 | 0.303107 | ||||||||
\(686\) | 94.8981 | 3.62323 | ||||||||
\(687\) | −2.50829 | −0.0956972 | ||||||||
\(688\) | 14.2984 | 0.545123 | ||||||||
\(689\) | −85.2790 | −3.24887 | ||||||||
\(690\) | 1.71179 | 0.0651669 | ||||||||
\(691\) | −12.7010 | −0.483168 | −0.241584 | − | 0.970380i | \(-0.577667\pi\) | ||||
−0.241584 | + | 0.970380i | \(0.577667\pi\) | |||||||
\(692\) | −11.9895 | −0.455772 | ||||||||
\(693\) | 54.5858 | 2.07354 | ||||||||
\(694\) | −87.7705 | −3.33172 | ||||||||
\(695\) | −5.97102 | −0.226494 | ||||||||
\(696\) | −8.61277 | −0.326466 | ||||||||
\(697\) | −6.73587 | −0.255139 | ||||||||
\(698\) | −29.2037 | −1.10538 | ||||||||
\(699\) | −4.37599 | −0.165515 | ||||||||
\(700\) | 12.5523 | 0.474432 | ||||||||
\(701\) | 9.73745 | 0.367778 | 0.183889 | − | 0.982947i | \(-0.441131\pi\) | ||||
0.183889 | + | 0.982947i | \(0.441131\pi\) | |||||||
\(702\) | −15.4050 | −0.581424 | ||||||||
\(703\) | 2.31590 | 0.0873459 | ||||||||
\(704\) | 27.1833 | 1.02451 | ||||||||
\(705\) | −0.234608 | −0.00883583 | ||||||||
\(706\) | −8.91302 | −0.335446 | ||||||||
\(707\) | 69.8349 | 2.62641 | ||||||||
\(708\) | 0.0912601 | 0.00342976 | ||||||||
\(709\) | −36.5973 | −1.37444 | −0.687220 | − | 0.726449i | \(-0.741169\pi\) | ||||
−0.687220 | + | 0.726449i | \(0.741169\pi\) | |||||||
\(710\) | 41.0021 | 1.53878 | ||||||||
\(711\) | 24.1221 | 0.904650 | ||||||||
\(712\) | 52.8747 | 1.98156 | ||||||||
\(713\) | −13.9947 | −0.524105 | ||||||||
\(714\) | 10.9095 | 0.408276 | ||||||||
\(715\) | 61.3566 | 2.29461 | ||||||||
\(716\) | 5.60605 | 0.209508 | ||||||||
\(717\) | −0.465609 | −0.0173885 | ||||||||
\(718\) | 47.4881 | 1.77224 | ||||||||
\(719\) | 8.17131 | 0.304739 | 0.152369 | − | 0.988324i | \(-0.451310\pi\) | ||||
0.152369 | + | 0.988324i | \(0.451310\pi\) | |||||||
\(720\) | −31.7745 | −1.18416 | ||||||||
\(721\) | −15.5530 | −0.579222 | ||||||||
\(722\) | −46.4678 | −1.72935 | ||||||||
\(723\) | 1.79818 | 0.0668750 | ||||||||
\(724\) | −50.3385 | −1.87082 | ||||||||
\(725\) | 6.94504 | 0.257932 | ||||||||
\(726\) | −1.62824 | −0.0604297 | ||||||||
\(727\) | 1.52574 | 0.0565864 | 0.0282932 | − | 0.999600i | \(-0.490993\pi\) | ||||
0.0282932 | + | 0.999600i | \(0.490993\pi\) | |||||||
\(728\) | −160.024 | −5.93087 | ||||||||
\(729\) | −25.6635 | −0.950500 | ||||||||
\(730\) | 5.58473 | 0.206700 | ||||||||
\(731\) | −18.9441 | −0.700673 | ||||||||
\(732\) | 2.52384 | 0.0932838 | ||||||||
\(733\) | −38.8518 | −1.43503 | −0.717513 | − | 0.696545i | \(-0.754719\pi\) | ||||
−0.717513 | + | 0.696545i | \(0.754719\pi\) | |||||||
\(734\) | 71.6869 | 2.64601 | ||||||||
\(735\) | −5.69513 | −0.210068 | ||||||||
\(736\) | −1.50554 | −0.0554949 | ||||||||
\(737\) | −0.790779 | −0.0291287 | ||||||||
\(738\) | −8.30345 | −0.305654 | ||||||||
\(739\) | 44.8177 | 1.64865 | 0.824323 | − | 0.566120i | \(-0.191556\pi\) | ||||
0.824323 | + | 0.566120i | \(0.191556\pi\) | |||||||
\(740\) | −56.8534 | −2.08997 | ||||||||
\(741\) | −0.413239 | −0.0151807 | ||||||||
\(742\) | 149.518 | 5.48899 | ||||||||
\(743\) | −0.348330 | −0.0127790 | −0.00638950 | − | 0.999980i | \(-0.502034\pi\) | ||||
−0.00638950 | + | 0.999980i | \(0.502034\pi\) | |||||||
\(744\) | −6.13004 | −0.224738 | ||||||||
\(745\) | 6.30622 | 0.231042 | ||||||||
\(746\) | 27.3528 | 1.00146 | ||||||||
\(747\) | −28.1578 | −1.03024 | ||||||||
\(748\) | 94.6336 | 3.46015 | ||||||||
\(749\) | −10.8188 | −0.395310 | ||||||||
\(750\) | 4.02339 | 0.146914 | ||||||||
\(751\) | 6.42985 | 0.234628 | 0.117314 | − | 0.993095i | \(-0.462572\pi\) | ||||
0.117314 | + | 0.993095i | \(0.462572\pi\) | |||||||
\(752\) | 2.80758 | 0.102382 | ||||||||
\(753\) | 2.53718 | 0.0924599 | ||||||||
\(754\) | −173.636 | −6.32346 | ||||||||
\(755\) | −18.1716 | −0.661333 | ||||||||
\(756\) | 18.1260 | 0.659235 | ||||||||
\(757\) | −33.2343 | −1.20792 | −0.603960 | − | 0.797014i | \(-0.706411\pi\) | ||||
−0.603960 | + | 0.797014i | \(0.706411\pi\) | |||||||
\(758\) | 70.3617 | 2.55565 | ||||||||
\(759\) | −1.13761 | −0.0412925 | ||||||||
\(760\) | −4.82225 | −0.174921 | ||||||||
\(761\) | −1.37647 | −0.0498969 | −0.0249484 | − | 0.999689i | \(-0.507942\pi\) | ||||
−0.0249484 | + | 0.999689i | \(0.507942\pi\) | |||||||
\(762\) | 1.35339 | 0.0490280 | ||||||||
\(763\) | 44.4605 | 1.60958 | ||||||||
\(764\) | −55.0077 | −1.99011 | ||||||||
\(765\) | 42.0982 | 1.52206 | ||||||||
\(766\) | −55.6357 | −2.01020 | ||||||||
\(767\) | 0.938152 | 0.0338747 | ||||||||
\(768\) | 5.12829 | 0.185051 | ||||||||
\(769\) | −4.55292 | −0.164183 | −0.0820913 | − | 0.996625i | \(-0.526160\pi\) | ||||
−0.0820913 | + | 0.996625i | \(0.526160\pi\) | |||||||
\(770\) | −107.575 | −3.87675 | ||||||||
\(771\) | 2.87355 | 0.103488 | ||||||||
\(772\) | 51.5052 | 1.85371 | ||||||||
\(773\) | −24.0249 | −0.864116 | −0.432058 | − | 0.901846i | \(-0.642212\pi\) | ||||
−0.432058 | + | 0.901846i | \(0.642212\pi\) | |||||||
\(774\) | −23.3528 | −0.839399 | ||||||||
\(775\) | 4.94305 | 0.177559 | ||||||||
\(776\) | −62.8442 | −2.25598 | ||||||||
\(777\) | 4.35567 | 0.156259 | ||||||||
\(778\) | −17.7912 | −0.637845 | ||||||||
\(779\) | −0.447347 | −0.0160279 | ||||||||
\(780\) | 10.1447 | 0.363237 | ||||||||
\(781\) | −27.2488 | −0.975038 | ||||||||
\(782\) | 27.1411 | 0.970565 | ||||||||
\(783\) | 10.0289 | 0.358403 | ||||||||
\(784\) | 68.1544 | 2.43409 | ||||||||
\(785\) | −10.6840 | −0.381328 | ||||||||
\(786\) | 0.239705 | 0.00855000 | ||||||||
\(787\) | −8.01053 | −0.285545 | −0.142772 | − | 0.989756i | \(-0.545602\pi\) | ||||
−0.142772 | + | 0.989756i | \(0.545602\pi\) | |||||||
\(788\) | 21.8194 | 0.777285 | ||||||||
\(789\) | −1.43967 | −0.0512537 | ||||||||
\(790\) | −47.5389 | −1.69136 | ||||||||
\(791\) | −48.9401 | −1.74011 | ||||||||
\(792\) | 59.4846 | 2.11369 | ||||||||
\(793\) | 25.9450 | 0.921335 | ||||||||
\(794\) | 68.2898 | 2.42351 | ||||||||
\(795\) | −4.83328 | −0.171419 | ||||||||
\(796\) | −111.852 | −3.96450 | ||||||||
\(797\) | 17.7909 | 0.630185 | 0.315093 | − | 0.949061i | \(-0.397964\pi\) | ||||
0.315093 | + | 0.949061i | \(0.397964\pi\) | |||||||
\(798\) | 0.724525 | 0.0256479 | ||||||||
\(799\) | −3.71979 | −0.131597 | ||||||||
\(800\) | 0.531770 | 0.0188009 | ||||||||
\(801\) | −30.6558 | −1.08317 | ||||||||
\(802\) | 48.7387 | 1.72102 | ||||||||
\(803\) | −3.71144 | −0.130974 | ||||||||
\(804\) | −0.130747 | −0.00461109 | ||||||||
\(805\) | −20.7054 | −0.729770 | ||||||||
\(806\) | −123.584 | −4.35305 | ||||||||
\(807\) | 2.21927 | 0.0781220 | ||||||||
\(808\) | 76.1022 | 2.67727 | ||||||||
\(809\) | 16.4208 | 0.577325 | 0.288663 | − | 0.957431i | \(-0.406789\pi\) | ||||
0.288663 | + | 0.957431i | \(0.406789\pi\) | |||||||
\(810\) | 51.4570 | 1.80801 | ||||||||
\(811\) | −41.4014 | −1.45380 | −0.726900 | − | 0.686743i | \(-0.759040\pi\) | ||||
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(812\) | 204.306 | 7.16972 | ||||||||
\(813\) | 1.12686 | 0.0395207 | ||||||||
\(814\) | 56.3001 | 1.97332 | ||||||||
\(815\) | 38.8234 | 1.35992 | ||||||||
\(816\) | 4.22029 | 0.147740 | ||||||||
\(817\) | −1.25813 | −0.0440163 | ||||||||
\(818\) | −8.36401 | −0.292441 | ||||||||
\(819\) | 92.7787 | 3.24195 | ||||||||
\(820\) | 10.9820 | 0.383507 | ||||||||
\(821\) | 3.47859 | 0.121404 | 0.0607018 | − | 0.998156i | \(-0.480666\pi\) | ||||
0.0607018 | + | 0.998156i | \(0.480666\pi\) | |||||||
\(822\) | −1.29888 | −0.0453038 | ||||||||
\(823\) | −32.2803 | −1.12522 | −0.562610 | − | 0.826723i | \(-0.690203\pi\) | ||||
−0.562610 | + | 0.826723i | \(0.690203\pi\) | |||||||
\(824\) | −16.9488 | −0.590438 | ||||||||
\(825\) | 0.401813 | 0.0139893 | ||||||||
\(826\) | −1.64485 | −0.0572315 | ||||||||
\(827\) | −32.1878 | −1.11928 | −0.559641 | − | 0.828735i | \(-0.689061\pi\) | ||||
−0.559641 | + | 0.828735i | \(0.689061\pi\) | |||||||
\(828\) | 22.4533 | 0.780307 | ||||||||
\(829\) | 25.5266 | 0.886576 | 0.443288 | − | 0.896379i | \(-0.353812\pi\) | ||||
0.443288 | + | 0.896379i | \(0.353812\pi\) | |||||||
\(830\) | 55.4922 | 1.92616 | ||||||||
\(831\) | 0.733607 | 0.0254485 | ||||||||
\(832\) | 46.2030 | 1.60180 | ||||||||
\(833\) | −90.2983 | −3.12865 | ||||||||
\(834\) | 0.977637 | 0.0338528 | ||||||||
\(835\) | −51.9413 | −1.79750 | ||||||||
\(836\) | 6.28486 | 0.217366 | ||||||||
\(837\) | 7.13794 | 0.246723 | ||||||||
\(838\) | 86.0014 | 2.97087 | ||||||||
\(839\) | 22.3785 | 0.772592 | 0.386296 | − | 0.922375i | \(-0.373754\pi\) | ||||
0.386296 | + | 0.922375i | \(0.373754\pi\) | |||||||
\(840\) | −9.06952 | −0.312928 | ||||||||
\(841\) | 84.0399 | 2.89793 | ||||||||
\(842\) | −48.2945 | −1.66434 | ||||||||
\(843\) | 3.85740 | 0.132856 | ||||||||
\(844\) | −3.87043 | −0.133226 | ||||||||
\(845\) | 73.3775 | 2.52426 | ||||||||
\(846\) | −4.58546 | −0.157651 | ||||||||
\(847\) | 19.6948 | 0.676720 | ||||||||
\(848\) | 57.8406 | 1.98626 | ||||||||
\(849\) | 0.870426 | 0.0298729 | ||||||||
\(850\) | −9.58649 | −0.328814 | ||||||||
\(851\) | 10.8363 | 0.371462 | ||||||||
\(852\) | −4.50529 | −0.154349 | ||||||||
\(853\) | 1.03212 | 0.0353391 | 0.0176696 | − | 0.999844i | \(-0.494375\pi\) | ||||
0.0176696 | + | 0.999844i | \(0.494375\pi\) | |||||||
\(854\) | −45.4890 | −1.55660 | ||||||||
\(855\) | 2.79585 | 0.0956161 | ||||||||
\(856\) | −11.7897 | −0.402964 | ||||||||
\(857\) | 10.9674 | 0.374639 | 0.187320 | − | 0.982299i | \(-0.440020\pi\) | ||||
0.187320 | + | 0.982299i | \(0.440020\pi\) | |||||||
\(858\) | −10.0459 | −0.342963 | ||||||||
\(859\) | 2.06472 | 0.0704474 | 0.0352237 | − | 0.999379i | \(-0.488786\pi\) | ||||
0.0352237 | + | 0.999379i | \(0.488786\pi\) | |||||||
\(860\) | 30.8859 | 1.05320 | ||||||||
\(861\) | −0.841354 | −0.0286733 | ||||||||
\(862\) | 94.8133 | 3.22935 | ||||||||
\(863\) | 33.9733 | 1.15647 | 0.578233 | − | 0.815872i | \(-0.303742\pi\) | ||||
0.578233 | + | 0.815872i | \(0.303742\pi\) | |||||||
\(864\) | 0.767895 | 0.0261243 | ||||||||
\(865\) | −6.98542 | −0.237512 | ||||||||
\(866\) | 30.7495 | 1.04491 | ||||||||
\(867\) | −2.90774 | −0.0987521 | ||||||||
\(868\) | 145.412 | 4.93561 | ||||||||
\(869\) | 31.5929 | 1.07172 | ||||||||
\(870\) | −9.84103 | −0.333642 | ||||||||
\(871\) | −1.34408 | −0.0455423 | ||||||||
\(872\) | 48.4506 | 1.64075 | ||||||||
\(873\) | 36.4359 | 1.23317 | ||||||||
\(874\) | 1.80251 | 0.0609709 | ||||||||
\(875\) | −48.6659 | −1.64521 | ||||||||
\(876\) | −0.613647 | −0.0207332 | ||||||||
\(877\) | 13.8165 | 0.466549 | 0.233274 | − | 0.972411i | \(-0.425056\pi\) | ||||
0.233274 | + | 0.972411i | \(0.425056\pi\) | |||||||
\(878\) | −50.3623 | −1.69964 | ||||||||
\(879\) | 0.146077 | 0.00492707 | ||||||||
\(880\) | −41.6152 | −1.40285 | ||||||||
\(881\) | −28.9080 | −0.973937 | −0.486968 | − | 0.873420i | \(-0.661897\pi\) | ||||
−0.486968 | + | 0.873420i | \(0.661897\pi\) | |||||||
\(882\) | −111.313 | −3.74809 | ||||||||
\(883\) | −27.2983 | −0.918662 | −0.459331 | − | 0.888265i | \(-0.651911\pi\) | ||||
−0.459331 | + | 0.888265i | \(0.651911\pi\) | |||||||
\(884\) | 160.847 | 5.40988 | ||||||||
\(885\) | 0.0531708 | 0.00178732 | ||||||||
\(886\) | 81.0154 | 2.72177 | ||||||||
\(887\) | 7.67238 | 0.257613 | 0.128807 | − | 0.991670i | \(-0.458885\pi\) | ||||
0.128807 | + | 0.991670i | \(0.458885\pi\) | |||||||
\(888\) | 4.74657 | 0.159284 | ||||||||
\(889\) | −16.3702 | −0.549039 | ||||||||
\(890\) | 60.4152 | 2.02512 | ||||||||
\(891\) | −34.1968 | −1.14563 | ||||||||
\(892\) | −96.4852 | −3.23056 | ||||||||
\(893\) | −0.247041 | −0.00826690 | ||||||||
\(894\) | −1.03252 | −0.0345326 | ||||||||
\(895\) | 3.26625 | 0.109179 | ||||||||
\(896\) | −88.6736 | −2.96238 | ||||||||
\(897\) | −1.93357 | −0.0645602 | ||||||||
\(898\) | 44.3748 | 1.48081 | ||||||||
\(899\) | 80.4548 | 2.68332 | ||||||||
\(900\) | −7.93072 | −0.264357 | ||||||||
\(901\) | −76.6335 | −2.55303 | ||||||||
\(902\) | −10.8751 | −0.362101 | ||||||||
\(903\) | −2.36624 | −0.0787435 | ||||||||
\(904\) | −53.3323 | −1.77380 | ||||||||
\(905\) | −29.3287 | −0.974919 | ||||||||
\(906\) | 2.97525 | 0.0988459 | ||||||||
\(907\) | 12.5770 | 0.417612 | 0.208806 | − | 0.977957i | \(-0.433042\pi\) | ||||
0.208806 | + | 0.977957i | \(0.433042\pi\) | |||||||
\(908\) | 0.425200 | 0.0141108 | ||||||||
\(909\) | −44.1227 | −1.46346 | ||||||||
\(910\) | −182.844 | −6.06123 | ||||||||
\(911\) | −45.3692 | −1.50315 | −0.751574 | − | 0.659649i | \(-0.770705\pi\) | ||||
−0.751574 | + | 0.659649i | \(0.770705\pi\) | |||||||
\(912\) | 0.280280 | 0.00928101 | ||||||||
\(913\) | −36.8784 | −1.22050 | ||||||||
\(914\) | 92.1254 | 3.04724 | ||||||||
\(915\) | 1.47046 | 0.0486120 | ||||||||
\(916\) | 64.8395 | 2.14236 | ||||||||
\(917\) | −2.89941 | −0.0957470 | ||||||||
\(918\) | −13.8432 | −0.456895 | ||||||||
\(919\) | −7.95324 | −0.262353 | −0.131177 | − | 0.991359i | \(-0.541875\pi\) | ||||
−0.131177 | + | 0.991359i | \(0.541875\pi\) | |||||||
\(920\) | −22.5636 | −0.743901 | ||||||||
\(921\) | 4.33047 | 0.142694 | ||||||||
\(922\) | 23.2121 | 0.764451 | ||||||||
\(923\) | −46.3144 | −1.52446 | ||||||||
\(924\) | 11.8203 | 0.388861 | ||||||||
\(925\) | −3.82747 | −0.125846 | ||||||||
\(926\) | −72.7762 | −2.39157 | ||||||||
\(927\) | 9.82657 | 0.322747 | ||||||||
\(928\) | 8.65528 | 0.284123 | ||||||||
\(929\) | 45.9188 | 1.50655 | 0.753273 | − | 0.657708i | \(-0.228474\pi\) | ||||
0.753273 | + | 0.657708i | \(0.228474\pi\) | |||||||
\(930\) | −7.00424 | −0.229678 | ||||||||
\(931\) | −5.99694 | −0.196542 | ||||||||
\(932\) | 113.120 | 3.70536 | ||||||||
\(933\) | 3.48821 | 0.114199 | ||||||||
\(934\) | 38.7783 | 1.26886 | ||||||||
\(935\) | 55.1363 | 1.80315 | ||||||||
\(936\) | 101.105 | 3.30473 | ||||||||
\(937\) | −22.0280 | −0.719623 | −0.359812 | − | 0.933025i | \(-0.617159\pi\) | ||||
−0.359812 | + | 0.933025i | \(0.617159\pi\) | |||||||
\(938\) | 2.35654 | 0.0769439 | ||||||||
\(939\) | 1.90167 | 0.0620588 | ||||||||
\(940\) | 6.06463 | 0.197806 | ||||||||
\(941\) | 25.0867 | 0.817804 | 0.408902 | − | 0.912578i | \(-0.365912\pi\) | ||||
0.408902 | + | 0.912578i | \(0.365912\pi\) | |||||||
\(942\) | 1.74929 | 0.0569950 | ||||||||
\(943\) | −2.09317 | −0.0681628 | ||||||||
\(944\) | −0.636303 | −0.0207099 | ||||||||
\(945\) | 10.5607 | 0.343540 | ||||||||
\(946\) | −30.5853 | −0.994414 | ||||||||
\(947\) | −44.2883 | −1.43918 | −0.719588 | − | 0.694401i | \(-0.755669\pi\) | ||||
−0.719588 | + | 0.694401i | \(0.755669\pi\) | |||||||
\(948\) | 5.22355 | 0.169653 | ||||||||
\(949\) | −6.30828 | −0.204776 | ||||||||
\(950\) | −0.636664 | −0.0206561 | ||||||||
\(951\) | −1.20898 | −0.0392037 | ||||||||
\(952\) | −143.801 | −4.66060 | ||||||||
\(953\) | 5.30431 | 0.171824 | 0.0859118 | − | 0.996303i | \(-0.472620\pi\) | ||||
0.0859118 | + | 0.996303i | \(0.472620\pi\) | |||||||
\(954\) | −94.4677 | −3.05850 | ||||||||
\(955\) | −32.0491 | −1.03708 | ||||||||
\(956\) | 12.0360 | 0.389273 | ||||||||
\(957\) | 6.54006 | 0.211410 | ||||||||
\(958\) | −48.2076 | −1.55752 | ||||||||
\(959\) | 15.7109 | 0.507333 | ||||||||
\(960\) | 2.61861 | 0.0845152 | ||||||||
\(961\) | 26.2627 | 0.847184 | ||||||||
\(962\) | 95.6924 | 3.08525 | ||||||||
\(963\) | 6.83546 | 0.220270 | ||||||||
\(964\) | −46.4832 | −1.49712 | ||||||||
\(965\) | 30.0084 | 0.966006 | ||||||||
\(966\) | 3.39010 | 0.109075 | ||||||||
\(967\) | −4.04692 | −0.130140 | −0.0650701 | − | 0.997881i | \(-0.520727\pi\) | ||||
−0.0650701 | + | 0.997881i | \(0.520727\pi\) | |||||||
\(968\) | 21.4623 | 0.689824 | ||||||||
\(969\) | −0.371345 | −0.0119293 | ||||||||
\(970\) | −71.8064 | −2.30556 | ||||||||
\(971\) | 38.9428 | 1.24973 | 0.624867 | − | 0.780732i | \(-0.285153\pi\) | ||||
0.624867 | + | 0.780732i | \(0.285153\pi\) | |||||||
\(972\) | −17.2022 | −0.551762 | ||||||||
\(973\) | −11.8252 | −0.379100 | ||||||||
\(974\) | −39.8361 | −1.27643 | ||||||||
\(975\) | 0.682956 | 0.0218721 | ||||||||
\(976\) | −17.5973 | −0.563275 | ||||||||
\(977\) | 46.3245 | 1.48205 | 0.741026 | − | 0.671476i | \(-0.234339\pi\) | ||||
0.741026 | + | 0.671476i | \(0.234339\pi\) | |||||||
\(978\) | −6.35656 | −0.203260 | ||||||||
\(979\) | −40.1501 | −1.28320 | ||||||||
\(980\) | 147.220 | 4.70276 | ||||||||
\(981\) | −28.0908 | −0.896870 | ||||||||
\(982\) | 71.2242 | 2.27285 | ||||||||
\(983\) | 1.07524 | 0.0342949 | 0.0171475 | − | 0.999853i | \(-0.494542\pi\) | ||||
0.0171475 | + | 0.999853i | \(0.494542\pi\) | |||||||
\(984\) | −0.916862 | −0.0292285 | ||||||||
\(985\) | 12.7126 | 0.405058 | ||||||||
\(986\) | −156.033 | −4.96911 | ||||||||
\(987\) | −0.464626 | −0.0147892 | ||||||||
\(988\) | 10.6823 | 0.339849 | ||||||||
\(989\) | −5.88686 | −0.187191 | ||||||||
\(990\) | 67.9677 | 2.16015 | ||||||||
\(991\) | 30.8827 | 0.981020 | 0.490510 | − | 0.871436i | \(-0.336811\pi\) | ||||
0.490510 | + | 0.871436i | \(0.336811\pi\) | |||||||
\(992\) | 6.16029 | 0.195589 | ||||||||
\(993\) | −2.67275 | −0.0848171 | ||||||||
\(994\) | 81.2021 | 2.57558 | ||||||||
\(995\) | −65.1685 | −2.06598 | ||||||||
\(996\) | −6.09746 | −0.193205 | ||||||||
\(997\) | 40.1301 | 1.27093 | 0.635466 | − | 0.772129i | \(-0.280808\pi\) | ||||
0.635466 | + | 0.772129i | \(0.280808\pi\) | |||||||
\(998\) | −4.64287 | −0.146967 | ||||||||
\(999\) | −5.52700 | −0.174867 |
(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 | 619.2.a.b.1.27 | ✓ | 30 | |
3.2 | odd | 2 | 5571.2.a.g.1.4 | 30 | |||
4.3 | odd | 2 | 9904.2.a.n.1.16 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
619.2.a.b.1.27 | ✓ | 30 | 1.1 | even | 1 | trivial | |
5571.2.a.g.1.4 | 30 | 3.2 | odd | 2 | |||
9904.2.a.n.1.16 | 30 | 4.3 | odd | 2 |