Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, 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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(1\) |
Dimension: | \(114\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.75487 | −1.94799 | −0.973995 | − | 0.226568i | \(-0.927249\pi\) | ||||
−0.973995 | + | 0.226568i | \(0.927249\pi\) | |||||||
\(3\) | −1.38395 | −0.799024 | −0.399512 | − | 0.916728i | \(-0.630820\pi\) | ||||
−0.399512 | + | 0.916728i | \(0.630820\pi\) | |||||||
\(4\) | 5.58934 | 2.79467 | ||||||||
\(5\) | 1.31563 | 0.588367 | 0.294183 | − | 0.955749i | \(-0.404952\pi\) | ||||
0.294183 | + | 0.955749i | \(0.404952\pi\) | |||||||
\(6\) | 3.81261 | 1.55649 | ||||||||
\(7\) | −4.81832 | −1.82115 | −0.910577 | − | 0.413339i | \(-0.864362\pi\) | ||||
−0.910577 | + | 0.413339i | \(0.864362\pi\) | |||||||
\(8\) | −9.88817 | −3.49600 | ||||||||
\(9\) | −1.08468 | −0.361561 | ||||||||
\(10\) | −3.62439 | −1.14613 | ||||||||
\(11\) | −5.09469 | −1.53611 | −0.768054 | − | 0.640385i | \(-0.778775\pi\) | ||||
−0.768054 | + | 0.640385i | \(0.778775\pi\) | |||||||
\(12\) | −7.73536 | −2.23301 | ||||||||
\(13\) | 5.27345 | 1.46259 | 0.731295 | − | 0.682061i | \(-0.238916\pi\) | ||||
0.731295 | + | 0.682061i | \(0.238916\pi\) | |||||||
\(14\) | 13.2739 | 3.54759 | ||||||||
\(15\) | −1.82076 | −0.470119 | ||||||||
\(16\) | 16.0620 | 4.01550 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 2.98816 | 0.704317 | ||||||||
\(19\) | 6.13889 | 1.40836 | 0.704179 | − | 0.710022i | \(-0.251315\pi\) | ||||
0.704179 | + | 0.710022i | \(0.251315\pi\) | |||||||
\(20\) | 7.35348 | 1.64429 | ||||||||
\(21\) | 6.66832 | 1.45515 | ||||||||
\(22\) | 14.0352 | 2.99232 | ||||||||
\(23\) | −3.61162 | −0.753074 | −0.376537 | − | 0.926402i | \(-0.622885\pi\) | ||||
−0.376537 | + | 0.926402i | \(0.622885\pi\) | |||||||
\(24\) | 13.6847 | 2.79339 | ||||||||
\(25\) | −3.26912 | −0.653825 | ||||||||
\(26\) | −14.5277 | −2.84911 | ||||||||
\(27\) | 5.65300 | 1.08792 | ||||||||
\(28\) | −26.9312 | −5.08952 | ||||||||
\(29\) | −6.73759 | −1.25114 | −0.625569 | − | 0.780169i | \(-0.715133\pi\) | ||||
−0.625569 | + | 0.780169i | \(0.715133\pi\) | |||||||
\(30\) | 5.01598 | 0.915788 | ||||||||
\(31\) | −6.43208 | −1.15523 | −0.577617 | − | 0.816308i | \(-0.696017\pi\) | ||||
−0.577617 | + | 0.816308i | \(0.696017\pi\) | |||||||
\(32\) | −24.4725 | −4.32616 | ||||||||
\(33\) | 7.05080 | 1.22739 | ||||||||
\(34\) | −2.75487 | −0.472457 | ||||||||
\(35\) | −6.33912 | −1.07151 | ||||||||
\(36\) | −6.06265 | −1.01044 | ||||||||
\(37\) | 5.38614 | 0.885475 | 0.442738 | − | 0.896651i | \(-0.354007\pi\) | ||||
0.442738 | + | 0.896651i | \(0.354007\pi\) | |||||||
\(38\) | −16.9119 | −2.74347 | ||||||||
\(39\) | −7.29819 | −1.16865 | ||||||||
\(40\) | −13.0092 | −2.05693 | ||||||||
\(41\) | −3.59917 | −0.562096 | −0.281048 | − | 0.959694i | \(-0.590682\pi\) | ||||
−0.281048 | + | 0.959694i | \(0.590682\pi\) | |||||||
\(42\) | −18.3704 | −2.83461 | ||||||||
\(43\) | 11.4833 | 1.75118 | 0.875591 | − | 0.483053i | \(-0.160472\pi\) | ||||
0.875591 | + | 0.483053i | \(0.160472\pi\) | |||||||
\(44\) | −28.4760 | −4.29291 | ||||||||
\(45\) | −1.42704 | −0.212730 | ||||||||
\(46\) | 9.94955 | 1.46698 | ||||||||
\(47\) | −4.09995 | −0.598039 | −0.299020 | − | 0.954247i | \(-0.596660\pi\) | ||||
−0.299020 | + | 0.954247i | \(0.596660\pi\) | |||||||
\(48\) | −22.2290 | −3.20848 | ||||||||
\(49\) | 16.2162 | 2.31660 | ||||||||
\(50\) | 9.00603 | 1.27364 | ||||||||
\(51\) | −1.38395 | −0.193792 | ||||||||
\(52\) | 29.4751 | 4.08746 | ||||||||
\(53\) | 13.0616 | 1.79414 | 0.897072 | − | 0.441883i | \(-0.145690\pi\) | ||||
0.897072 | + | 0.441883i | \(0.145690\pi\) | |||||||
\(54\) | −15.5733 | −2.11926 | ||||||||
\(55\) | −6.70272 | −0.903795 | ||||||||
\(56\) | 47.6444 | 6.36675 | ||||||||
\(57\) | −8.49592 | −1.12531 | ||||||||
\(58\) | 18.5612 | 2.43721 | ||||||||
\(59\) | −10.3127 | −1.34260 | −0.671299 | − | 0.741186i | \(-0.734263\pi\) | ||||
−0.671299 | + | 0.741186i | \(0.734263\pi\) | |||||||
\(60\) | −10.1769 | −1.31383 | ||||||||
\(61\) | 1.62534 | 0.208103 | 0.104052 | − | 0.994572i | \(-0.466819\pi\) | ||||
0.104052 | + | 0.994572i | \(0.466819\pi\) | |||||||
\(62\) | 17.7196 | 2.25039 | ||||||||
\(63\) | 5.22634 | 0.658457 | ||||||||
\(64\) | 35.2946 | 4.41182 | ||||||||
\(65\) | 6.93789 | 0.860540 | ||||||||
\(66\) | −19.4241 | −2.39094 | ||||||||
\(67\) | −8.49693 | −1.03806 | −0.519032 | − | 0.854755i | \(-0.673708\pi\) | ||||
−0.519032 | + | 0.854755i | \(0.673708\pi\) | |||||||
\(68\) | 5.58934 | 0.677807 | ||||||||
\(69\) | 4.99830 | 0.601724 | ||||||||
\(70\) | 17.4635 | 2.08728 | ||||||||
\(71\) | 5.46230 | 0.648256 | 0.324128 | − | 0.946013i | \(-0.394929\pi\) | ||||
0.324128 | + | 0.946013i | \(0.394929\pi\) | |||||||
\(72\) | 10.7255 | 1.26401 | ||||||||
\(73\) | −4.51414 | −0.528340 | −0.264170 | − | 0.964476i | \(-0.585098\pi\) | ||||
−0.264170 | + | 0.964476i | \(0.585098\pi\) | |||||||
\(74\) | −14.8381 | −1.72490 | ||||||||
\(75\) | 4.52431 | 0.522422 | ||||||||
\(76\) | 34.3123 | 3.93589 | ||||||||
\(77\) | 24.5479 | 2.79749 | ||||||||
\(78\) | 20.1056 | 2.27651 | ||||||||
\(79\) | −12.2658 | −1.38001 | −0.690006 | − | 0.723804i | \(-0.742392\pi\) | ||||
−0.690006 | + | 0.723804i | \(0.742392\pi\) | |||||||
\(80\) | 21.1316 | 2.36259 | ||||||||
\(81\) | −4.56942 | −0.507713 | ||||||||
\(82\) | 9.91527 | 1.09496 | ||||||||
\(83\) | −0.164706 | −0.0180788 | −0.00903939 | − | 0.999959i | \(-0.502877\pi\) | ||||
−0.00903939 | + | 0.999959i | \(0.502877\pi\) | |||||||
\(84\) | 37.2715 | 4.06665 | ||||||||
\(85\) | 1.31563 | 0.142700 | ||||||||
\(86\) | −31.6350 | −3.41129 | ||||||||
\(87\) | 9.32448 | 0.999690 | ||||||||
\(88\) | 50.3772 | 5.37023 | ||||||||
\(89\) | 3.49655 | 0.370633 | 0.185317 | − | 0.982679i | \(-0.440669\pi\) | ||||
0.185317 | + | 0.982679i | \(0.440669\pi\) | |||||||
\(90\) | 3.93131 | 0.414396 | ||||||||
\(91\) | −25.4092 | −2.66360 | ||||||||
\(92\) | −20.1865 | −2.10459 | ||||||||
\(93\) | 8.90167 | 0.923061 | ||||||||
\(94\) | 11.2948 | 1.16497 | ||||||||
\(95\) | 8.07649 | 0.828631 | ||||||||
\(96\) | 33.8687 | 3.45671 | ||||||||
\(97\) | 14.0705 | 1.42864 | 0.714320 | − | 0.699819i | \(-0.246736\pi\) | ||||
0.714320 | + | 0.699819i | \(0.246736\pi\) | |||||||
\(98\) | −44.6736 | −4.51272 | ||||||||
\(99\) | 5.52612 | 0.555396 | ||||||||
\(100\) | −18.2722 | −1.82722 | ||||||||
\(101\) | 0.940015 | 0.0935350 | 0.0467675 | − | 0.998906i | \(-0.485108\pi\) | ||||
0.0467675 | + | 0.998906i | \(0.485108\pi\) | |||||||
\(102\) | 3.81261 | 0.377505 | ||||||||
\(103\) | 8.90741 | 0.877674 | 0.438837 | − | 0.898567i | \(-0.355391\pi\) | ||||
0.438837 | + | 0.898567i | \(0.355391\pi\) | |||||||
\(104\) | −52.1447 | −5.11321 | ||||||||
\(105\) | 8.77302 | 0.856159 | ||||||||
\(106\) | −35.9830 | −3.49498 | ||||||||
\(107\) | 19.5910 | 1.89394 | 0.946968 | − | 0.321329i | \(-0.104130\pi\) | ||||
0.946968 | + | 0.321329i | \(0.104130\pi\) | |||||||
\(108\) | 31.5965 | 3.04037 | ||||||||
\(109\) | 0.372597 | 0.0356883 | 0.0178441 | − | 0.999841i | \(-0.494320\pi\) | ||||
0.0178441 | + | 0.999841i | \(0.494320\pi\) | |||||||
\(110\) | 18.4652 | 1.76058 | ||||||||
\(111\) | −7.45414 | −0.707516 | ||||||||
\(112\) | −77.3919 | −7.31285 | ||||||||
\(113\) | 17.0229 | 1.60138 | 0.800690 | − | 0.599078i | \(-0.204466\pi\) | ||||
0.800690 | + | 0.599078i | \(0.204466\pi\) | |||||||
\(114\) | 23.4052 | 2.19210 | ||||||||
\(115\) | −4.75154 | −0.443084 | ||||||||
\(116\) | −37.6586 | −3.49652 | ||||||||
\(117\) | −5.72001 | −0.528815 | ||||||||
\(118\) | 28.4102 | 2.61537 | ||||||||
\(119\) | −4.81832 | −0.441695 | ||||||||
\(120\) | 18.0040 | 1.64353 | ||||||||
\(121\) | 14.9559 | 1.35963 | ||||||||
\(122\) | −4.47761 | −0.405384 | ||||||||
\(123\) | 4.98108 | 0.449128 | ||||||||
\(124\) | −35.9510 | −3.22850 | ||||||||
\(125\) | −10.8791 | −0.973055 | ||||||||
\(126\) | −14.3979 | −1.28267 | ||||||||
\(127\) | −8.22937 | −0.730239 | −0.365119 | − | 0.930961i | \(-0.618972\pi\) | ||||
−0.365119 | + | 0.930961i | \(0.618972\pi\) | |||||||
\(128\) | −48.2872 | −4.26803 | ||||||||
\(129\) | −15.8923 | −1.39924 | ||||||||
\(130\) | −19.1130 | −1.67632 | ||||||||
\(131\) | 6.83787 | 0.597427 | 0.298714 | − | 0.954343i | \(-0.403442\pi\) | ||||
0.298714 | + | 0.954343i | \(0.403442\pi\) | |||||||
\(132\) | 39.4093 | 3.43014 | ||||||||
\(133\) | −29.5791 | −2.56484 | ||||||||
\(134\) | 23.4080 | 2.02214 | ||||||||
\(135\) | 7.43724 | 0.640096 | ||||||||
\(136\) | −9.88817 | −0.847904 | ||||||||
\(137\) | 0.806727 | 0.0689233 | 0.0344617 | − | 0.999406i | \(-0.489028\pi\) | ||||
0.0344617 | + | 0.999406i | \(0.489028\pi\) | |||||||
\(138\) | −13.7697 | −1.17215 | ||||||||
\(139\) | 2.93234 | 0.248717 | 0.124359 | − | 0.992237i | \(-0.460313\pi\) | ||||
0.124359 | + | 0.992237i | \(0.460313\pi\) | |||||||
\(140\) | −35.4314 | −2.99450 | ||||||||
\(141\) | 5.67413 | 0.477848 | ||||||||
\(142\) | −15.0480 | −1.26280 | ||||||||
\(143\) | −26.8666 | −2.24670 | ||||||||
\(144\) | −17.4222 | −1.45185 | ||||||||
\(145\) | −8.86415 | −0.736128 | ||||||||
\(146\) | 12.4359 | 1.02920 | ||||||||
\(147\) | −22.4424 | −1.85102 | ||||||||
\(148\) | 30.1049 | 2.47461 | ||||||||
\(149\) | 10.8265 | 0.886942 | 0.443471 | − | 0.896289i | \(-0.353747\pi\) | ||||
0.443471 | + | 0.896289i | \(0.353747\pi\) | |||||||
\(150\) | −12.4639 | −1.01767 | ||||||||
\(151\) | −0.0538371 | −0.00438120 | −0.00219060 | − | 0.999998i | \(-0.500697\pi\) | ||||
−0.00219060 | + | 0.999998i | \(0.500697\pi\) | |||||||
\(152\) | −60.7024 | −4.92362 | ||||||||
\(153\) | −1.08468 | −0.0876913 | ||||||||
\(154\) | −67.6263 | −5.44948 | ||||||||
\(155\) | −8.46222 | −0.679702 | ||||||||
\(156\) | −40.7920 | −3.26598 | ||||||||
\(157\) | −7.41195 | −0.591538 | −0.295769 | − | 0.955259i | \(-0.595576\pi\) | ||||
−0.295769 | + | 0.955259i | \(0.595576\pi\) | |||||||
\(158\) | 33.7908 | 2.68825 | ||||||||
\(159\) | −18.0766 | −1.43357 | ||||||||
\(160\) | −32.1967 | −2.54537 | ||||||||
\(161\) | 17.4019 | 1.37146 | ||||||||
\(162\) | 12.5882 | 0.989021 | ||||||||
\(163\) | 10.5688 | 0.827815 | 0.413907 | − | 0.910319i | \(-0.364164\pi\) | ||||
0.413907 | + | 0.910319i | \(0.364164\pi\) | |||||||
\(164\) | −20.1170 | −1.57087 | ||||||||
\(165\) | 9.27623 | 0.722154 | ||||||||
\(166\) | 0.453743 | 0.0352173 | ||||||||
\(167\) | 8.09223 | 0.626196 | 0.313098 | − | 0.949721i | \(-0.398633\pi\) | ||||
0.313098 | + | 0.949721i | \(0.398633\pi\) | |||||||
\(168\) | −65.9375 | −5.08719 | ||||||||
\(169\) | 14.8092 | 1.13917 | ||||||||
\(170\) | −3.62439 | −0.277978 | ||||||||
\(171\) | −6.65874 | −0.509207 | ||||||||
\(172\) | 64.1839 | 4.89397 | ||||||||
\(173\) | −4.69446 | −0.356913 | −0.178457 | − | 0.983948i | \(-0.557110\pi\) | ||||
−0.178457 | + | 0.983948i | \(0.557110\pi\) | |||||||
\(174\) | −25.6878 | −1.94739 | ||||||||
\(175\) | 15.7517 | 1.19072 | ||||||||
\(176\) | −81.8310 | −6.16824 | ||||||||
\(177\) | 14.2723 | 1.07277 | ||||||||
\(178\) | −9.63255 | −0.721990 | ||||||||
\(179\) | −1.54529 | −0.115500 | −0.0577501 | − | 0.998331i | \(-0.518393\pi\) | ||||
−0.0577501 | + | 0.998331i | \(0.518393\pi\) | |||||||
\(180\) | −7.97619 | −0.594510 | ||||||||
\(181\) | 5.86638 | 0.436044 | 0.218022 | − | 0.975944i | \(-0.430039\pi\) | ||||
0.218022 | + | 0.975944i | \(0.430039\pi\) | |||||||
\(182\) | 69.9991 | 5.18867 | ||||||||
\(183\) | −2.24939 | −0.166280 | ||||||||
\(184\) | 35.7123 | 2.63274 | ||||||||
\(185\) | 7.08615 | 0.520984 | ||||||||
\(186\) | −24.5230 | −1.79811 | ||||||||
\(187\) | −5.09469 | −0.372561 | ||||||||
\(188\) | −22.9160 | −1.67132 | ||||||||
\(189\) | −27.2379 | −1.98127 | ||||||||
\(190\) | −22.2497 | −1.61417 | ||||||||
\(191\) | −24.3587 | −1.76253 | −0.881266 | − | 0.472621i | \(-0.843308\pi\) | ||||
−0.881266 | + | 0.472621i | \(0.843308\pi\) | |||||||
\(192\) | −48.8460 | −3.52515 | ||||||||
\(193\) | 7.18898 | 0.517474 | 0.258737 | − | 0.965948i | \(-0.416694\pi\) | ||||
0.258737 | + | 0.965948i | \(0.416694\pi\) | |||||||
\(194\) | −38.7624 | −2.78298 | ||||||||
\(195\) | −9.60170 | −0.687592 | ||||||||
\(196\) | 90.6379 | 6.47413 | ||||||||
\(197\) | −18.1768 | −1.29505 | −0.647523 | − | 0.762046i | \(-0.724195\pi\) | ||||
−0.647523 | + | 0.762046i | \(0.724195\pi\) | |||||||
\(198\) | −15.2238 | −1.08191 | ||||||||
\(199\) | −9.60114 | −0.680607 | −0.340304 | − | 0.940316i | \(-0.610530\pi\) | ||||
−0.340304 | + | 0.940316i | \(0.610530\pi\) | |||||||
\(200\) | 32.3257 | 2.28577 | ||||||||
\(201\) | 11.7593 | 0.829439 | ||||||||
\(202\) | −2.58962 | −0.182205 | ||||||||
\(203\) | 32.4638 | 2.27852 | ||||||||
\(204\) | −7.73536 | −0.541584 | ||||||||
\(205\) | −4.73517 | −0.330719 | ||||||||
\(206\) | −24.5388 | −1.70970 | ||||||||
\(207\) | 3.91745 | 0.272282 | ||||||||
\(208\) | 84.7021 | 5.87304 | ||||||||
\(209\) | −31.2758 | −2.16339 | ||||||||
\(210\) | −24.1686 | −1.66779 | ||||||||
\(211\) | 16.9496 | 1.16686 | 0.583429 | − | 0.812164i | \(-0.301711\pi\) | ||||
0.583429 | + | 0.812164i | \(0.301711\pi\) | |||||||
\(212\) | 73.0055 | 5.01404 | ||||||||
\(213\) | −7.55956 | −0.517972 | ||||||||
\(214\) | −53.9708 | −3.68937 | ||||||||
\(215\) | 15.1077 | 1.03034 | ||||||||
\(216\) | −55.8978 | −3.80336 | ||||||||
\(217\) | 30.9918 | 2.10386 | ||||||||
\(218\) | −1.02646 | −0.0695205 | ||||||||
\(219\) | 6.24734 | 0.422156 | ||||||||
\(220\) | −37.4638 | −2.52581 | ||||||||
\(221\) | 5.27345 | 0.354730 | ||||||||
\(222\) | 20.5352 | 1.37823 | ||||||||
\(223\) | 10.8772 | 0.728391 | 0.364196 | − | 0.931322i | \(-0.381344\pi\) | ||||
0.364196 | + | 0.931322i | \(0.381344\pi\) | |||||||
\(224\) | 117.916 | 7.87861 | ||||||||
\(225\) | 3.54596 | 0.236397 | ||||||||
\(226\) | −46.8960 | −3.11947 | ||||||||
\(227\) | −16.7208 | −1.10980 | −0.554899 | − | 0.831918i | \(-0.687243\pi\) | ||||
−0.554899 | + | 0.831918i | \(0.687243\pi\) | |||||||
\(228\) | −47.4866 | −3.14487 | ||||||||
\(229\) | −5.12306 | −0.338541 | −0.169271 | − | 0.985570i | \(-0.554141\pi\) | ||||
−0.169271 | + | 0.985570i | \(0.554141\pi\) | |||||||
\(230\) | 13.0899 | 0.863123 | ||||||||
\(231\) | −33.9730 | −2.23526 | ||||||||
\(232\) | 66.6224 | 4.37397 | ||||||||
\(233\) | 17.1101 | 1.12092 | 0.560461 | − | 0.828181i | \(-0.310624\pi\) | ||||
0.560461 | + | 0.828181i | \(0.310624\pi\) | |||||||
\(234\) | 15.7579 | 1.03013 | ||||||||
\(235\) | −5.39401 | −0.351866 | ||||||||
\(236\) | −57.6411 | −3.75212 | ||||||||
\(237\) | 16.9753 | 1.10266 | ||||||||
\(238\) | 13.2739 | 0.860417 | ||||||||
\(239\) | −10.8259 | −0.700269 | −0.350135 | − | 0.936699i | \(-0.613864\pi\) | ||||
−0.350135 | + | 0.936699i | \(0.613864\pi\) | |||||||
\(240\) | −29.2451 | −1.88776 | ||||||||
\(241\) | 8.02923 | 0.517208 | 0.258604 | − | 0.965983i | \(-0.416738\pi\) | ||||
0.258604 | + | 0.965983i | \(0.416738\pi\) | |||||||
\(242\) | −41.2017 | −2.64854 | ||||||||
\(243\) | −10.6351 | −0.682244 | ||||||||
\(244\) | 9.08457 | 0.581580 | ||||||||
\(245\) | 21.3345 | 1.36301 | ||||||||
\(246\) | −13.7222 | −0.874898 | ||||||||
\(247\) | 32.3731 | 2.05985 | ||||||||
\(248\) | 63.6015 | 4.03870 | ||||||||
\(249\) | 0.227944 | 0.0144454 | ||||||||
\(250\) | 29.9705 | 1.89550 | ||||||||
\(251\) | 27.3790 | 1.72815 | 0.864074 | − | 0.503365i | \(-0.167905\pi\) | ||||
0.864074 | + | 0.503365i | \(0.167905\pi\) | |||||||
\(252\) | 29.2118 | 1.84017 | ||||||||
\(253\) | 18.4001 | 1.15680 | ||||||||
\(254\) | 22.6709 | 1.42250 | ||||||||
\(255\) | −1.82076 | −0.114021 | ||||||||
\(256\) | 62.4361 | 3.90226 | ||||||||
\(257\) | −13.4438 | −0.838604 | −0.419302 | − | 0.907847i | \(-0.637725\pi\) | ||||
−0.419302 | + | 0.907847i | \(0.637725\pi\) | |||||||
\(258\) | 43.7812 | 2.72570 | ||||||||
\(259\) | −25.9521 | −1.61259 | ||||||||
\(260\) | 38.7782 | 2.40492 | ||||||||
\(261\) | 7.30813 | 0.452362 | ||||||||
\(262\) | −18.8375 | −1.16378 | ||||||||
\(263\) | 17.1270 | 1.05610 | 0.528048 | − | 0.849214i | \(-0.322924\pi\) | ||||
0.528048 | + | 0.849214i | \(0.322924\pi\) | |||||||
\(264\) | −69.7196 | −4.29094 | ||||||||
\(265\) | 17.1842 | 1.05561 | ||||||||
\(266\) | 81.4868 | 4.99628 | ||||||||
\(267\) | −4.83905 | −0.296145 | ||||||||
\(268\) | −47.4922 | −2.90105 | ||||||||
\(269\) | −2.30480 | −0.140526 | −0.0702630 | − | 0.997529i | \(-0.522384\pi\) | ||||
−0.0702630 | + | 0.997529i | \(0.522384\pi\) | |||||||
\(270\) | −20.4887 | −1.24690 | ||||||||
\(271\) | −2.55742 | −0.155352 | −0.0776762 | − | 0.996979i | \(-0.524750\pi\) | ||||
−0.0776762 | + | 0.996979i | \(0.524750\pi\) | |||||||
\(272\) | 16.0620 | 0.973902 | ||||||||
\(273\) | 35.1650 | 2.12828 | ||||||||
\(274\) | −2.22243 | −0.134262 | ||||||||
\(275\) | 16.6552 | 1.00435 | ||||||||
\(276\) | 27.9372 | 1.68162 | ||||||||
\(277\) | −11.1856 | −0.672078 | −0.336039 | − | 0.941848i | \(-0.609087\pi\) | ||||
−0.336039 | + | 0.941848i | \(0.609087\pi\) | |||||||
\(278\) | −8.07822 | −0.484499 | ||||||||
\(279\) | 6.97675 | 0.417687 | ||||||||
\(280\) | 62.6823 | 3.74598 | ||||||||
\(281\) | 6.12385 | 0.365318 | 0.182659 | − | 0.983176i | \(-0.441530\pi\) | ||||
0.182659 | + | 0.983176i | \(0.441530\pi\) | |||||||
\(282\) | −15.6315 | −0.930843 | ||||||||
\(283\) | −25.8471 | −1.53645 | −0.768226 | − | 0.640178i | \(-0.778860\pi\) | ||||
−0.768226 | + | 0.640178i | \(0.778860\pi\) | |||||||
\(284\) | 30.5306 | 1.81166 | ||||||||
\(285\) | −11.1775 | −0.662096 | ||||||||
\(286\) | 74.0141 | 4.37655 | ||||||||
\(287\) | 17.3420 | 1.02366 | ||||||||
\(288\) | 26.5448 | 1.56417 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 24.4196 | 1.43397 | ||||||||
\(291\) | −19.4728 | −1.14152 | ||||||||
\(292\) | −25.2310 | −1.47653 | ||||||||
\(293\) | 11.4962 | 0.671617 | 0.335808 | − | 0.941930i | \(-0.390991\pi\) | ||||
0.335808 | + | 0.941930i | \(0.390991\pi\) | |||||||
\(294\) | 61.8261 | 3.60577 | ||||||||
\(295\) | −13.5677 | −0.789940 | ||||||||
\(296\) | −53.2590 | −3.09562 | ||||||||
\(297\) | −28.8003 | −1.67116 | ||||||||
\(298\) | −29.8257 | −1.72775 | ||||||||
\(299\) | −19.0457 | −1.10144 | ||||||||
\(300\) | 25.2879 | 1.46000 | ||||||||
\(301\) | −55.3301 | −3.18917 | ||||||||
\(302\) | 0.148314 | 0.00853454 | ||||||||
\(303\) | −1.30093 | −0.0747367 | ||||||||
\(304\) | 98.6029 | 5.65526 | ||||||||
\(305\) | 2.13834 | 0.122441 | ||||||||
\(306\) | 2.98816 | 0.170822 | ||||||||
\(307\) | 6.71400 | 0.383188 | 0.191594 | − | 0.981474i | \(-0.438634\pi\) | ||||
0.191594 | + | 0.981474i | \(0.438634\pi\) | |||||||
\(308\) | 137.206 | 7.81805 | ||||||||
\(309\) | −12.3274 | −0.701282 | ||||||||
\(310\) | 23.3123 | 1.32405 | ||||||||
\(311\) | 0.693118 | 0.0393031 | 0.0196515 | − | 0.999807i | \(-0.493744\pi\) | ||||
0.0196515 | + | 0.999807i | \(0.493744\pi\) | |||||||
\(312\) | 72.1657 | 4.08558 | ||||||||
\(313\) | −0.300505 | −0.0169855 | −0.00849277 | − | 0.999964i | \(-0.502703\pi\) | ||||
−0.00849277 | + | 0.999964i | \(0.502703\pi\) | |||||||
\(314\) | 20.4190 | 1.15231 | ||||||||
\(315\) | 6.87592 | 0.387414 | ||||||||
\(316\) | −68.5577 | −3.85667 | ||||||||
\(317\) | −27.9780 | −1.57140 | −0.785701 | − | 0.618606i | \(-0.787698\pi\) | ||||
−0.785701 | + | 0.618606i | \(0.787698\pi\) | |||||||
\(318\) | 49.7987 | 2.79257 | ||||||||
\(319\) | 34.3259 | 1.92188 | ||||||||
\(320\) | 46.4345 | 2.59577 | ||||||||
\(321\) | −27.1130 | −1.51330 | ||||||||
\(322\) | −47.9401 | −2.67160 | ||||||||
\(323\) | 6.13889 | 0.341577 | ||||||||
\(324\) | −25.5400 | −1.41889 | ||||||||
\(325\) | −17.2396 | −0.956278 | ||||||||
\(326\) | −29.1158 | −1.61258 | ||||||||
\(327\) | −0.515655 | −0.0285158 | ||||||||
\(328\) | 35.5892 | 1.96509 | ||||||||
\(329\) | 19.7549 | 1.08912 | ||||||||
\(330\) | −25.5549 | −1.40675 | ||||||||
\(331\) | −3.91937 | −0.215428 | −0.107714 | − | 0.994182i | \(-0.534353\pi\) | ||||
−0.107714 | + | 0.994182i | \(0.534353\pi\) | |||||||
\(332\) | −0.920594 | −0.0505242 | ||||||||
\(333\) | −5.84224 | −0.320153 | ||||||||
\(334\) | −22.2931 | −1.21982 | ||||||||
\(335\) | −11.1788 | −0.610763 | ||||||||
\(336\) | 107.107 | 5.84314 | ||||||||
\(337\) | −27.8817 | −1.51881 | −0.759405 | − | 0.650618i | \(-0.774510\pi\) | ||||
−0.759405 | + | 0.650618i | \(0.774510\pi\) | |||||||
\(338\) | −40.7976 | −2.21910 | ||||||||
\(339\) | −23.5589 | −1.27954 | ||||||||
\(340\) | 7.35348 | 0.398799 | ||||||||
\(341\) | 32.7695 | 1.77457 | ||||||||
\(342\) | 18.3440 | 0.991930 | ||||||||
\(343\) | −44.4067 | −2.39774 | ||||||||
\(344\) | −113.549 | −6.12213 | ||||||||
\(345\) | 6.57590 | 0.354034 | ||||||||
\(346\) | 12.9326 | 0.695264 | ||||||||
\(347\) | −5.18556 | −0.278376 | −0.139188 | − | 0.990266i | \(-0.544449\pi\) | ||||
−0.139188 | + | 0.990266i | \(0.544449\pi\) | |||||||
\(348\) | 52.1177 | 2.79380 | ||||||||
\(349\) | −12.9154 | −0.691346 | −0.345673 | − | 0.938355i | \(-0.612349\pi\) | ||||
−0.345673 | + | 0.938355i | \(0.612349\pi\) | |||||||
\(350\) | −43.3939 | −2.31950 | ||||||||
\(351\) | 29.8108 | 1.59118 | ||||||||
\(352\) | 124.680 | 6.64545 | ||||||||
\(353\) | 1.00000 | 0.0532246 | ||||||||
\(354\) | −39.3183 | −2.08974 | ||||||||
\(355\) | 7.18636 | 0.381412 | ||||||||
\(356\) | 19.5434 | 1.03580 | ||||||||
\(357\) | 6.66832 | 0.352925 | ||||||||
\(358\) | 4.25707 | 0.224993 | ||||||||
\(359\) | −27.8674 | −1.47079 | −0.735393 | − | 0.677641i | \(-0.763002\pi\) | ||||
−0.735393 | + | 0.677641i | \(0.763002\pi\) | |||||||
\(360\) | 14.1108 | 0.743704 | ||||||||
\(361\) | 18.6860 | 0.983473 | ||||||||
\(362\) | −16.1611 | −0.849410 | ||||||||
\(363\) | −20.6982 | −1.08638 | ||||||||
\(364\) | −142.020 | −7.44389 | ||||||||
\(365\) | −5.93892 | −0.310857 | ||||||||
\(366\) | 6.19679 | 0.323911 | ||||||||
\(367\) | 6.50514 | 0.339565 | 0.169783 | − | 0.985482i | \(-0.445693\pi\) | ||||
0.169783 | + | 0.985482i | \(0.445693\pi\) | |||||||
\(368\) | −58.0098 | −3.02397 | ||||||||
\(369\) | 3.90396 | 0.203232 | ||||||||
\(370\) | −19.5215 | −1.01487 | ||||||||
\(371\) | −62.9348 | −3.26741 | ||||||||
\(372\) | 49.7544 | 2.57965 | ||||||||
\(373\) | 27.7373 | 1.43618 | 0.718092 | − | 0.695948i | \(-0.245016\pi\) | ||||
0.718092 | + | 0.695948i | \(0.245016\pi\) | |||||||
\(374\) | 14.0352 | 0.725745 | ||||||||
\(375\) | 15.0561 | 0.777495 | ||||||||
\(376\) | 40.5410 | 2.09074 | ||||||||
\(377\) | −35.5303 | −1.82990 | ||||||||
\(378\) | 75.0371 | 3.85949 | ||||||||
\(379\) | −15.4252 | −0.792341 | −0.396171 | − | 0.918177i | \(-0.629661\pi\) | ||||
−0.396171 | + | 0.918177i | \(0.629661\pi\) | |||||||
\(380\) | 45.1422 | 2.31575 | ||||||||
\(381\) | 11.3890 | 0.583479 | ||||||||
\(382\) | 67.1051 | 3.43339 | ||||||||
\(383\) | 8.25417 | 0.421768 | 0.210884 | − | 0.977511i | \(-0.432366\pi\) | ||||
0.210884 | + | 0.977511i | \(0.432366\pi\) | |||||||
\(384\) | 66.8271 | 3.41026 | ||||||||
\(385\) | 32.2959 | 1.64595 | ||||||||
\(386\) | −19.8047 | −1.00803 | ||||||||
\(387\) | −12.4557 | −0.633158 | ||||||||
\(388\) | 78.6446 | 3.99257 | ||||||||
\(389\) | −22.3600 | −1.13370 | −0.566848 | − | 0.823823i | \(-0.691837\pi\) | ||||
−0.566848 | + | 0.823823i | \(0.691837\pi\) | |||||||
\(390\) | 26.4515 | 1.33942 | ||||||||
\(391\) | −3.61162 | −0.182647 | ||||||||
\(392\) | −160.349 | −8.09883 | ||||||||
\(393\) | −9.46327 | −0.477359 | ||||||||
\(394\) | 50.0749 | 2.52274 | ||||||||
\(395\) | −16.1372 | −0.811953 | ||||||||
\(396\) | 30.8873 | 1.55215 | ||||||||
\(397\) | −24.5964 | −1.23446 | −0.617228 | − | 0.786784i | \(-0.711745\pi\) | ||||
−0.617228 | + | 0.786784i | \(0.711745\pi\) | |||||||
\(398\) | 26.4500 | 1.32582 | ||||||||
\(399\) | 40.9361 | 2.04937 | ||||||||
\(400\) | −52.5087 | −2.62543 | ||||||||
\(401\) | 17.0749 | 0.852681 | 0.426341 | − | 0.904563i | \(-0.359802\pi\) | ||||
0.426341 | + | 0.904563i | \(0.359802\pi\) | |||||||
\(402\) | −32.3955 | −1.61574 | ||||||||
\(403\) | −33.9192 | −1.68964 | ||||||||
\(404\) | 5.25406 | 0.261399 | ||||||||
\(405\) | −6.01166 | −0.298722 | ||||||||
\(406\) | −89.4338 | −4.43853 | ||||||||
\(407\) | −27.4407 | −1.36019 | ||||||||
\(408\) | 13.6847 | 0.677496 | ||||||||
\(409\) | 32.9225 | 1.62791 | 0.813956 | − | 0.580927i | \(-0.197310\pi\) | ||||
0.813956 | + | 0.580927i | \(0.197310\pi\) | |||||||
\(410\) | 13.0448 | 0.644237 | ||||||||
\(411\) | −1.11647 | −0.0550714 | ||||||||
\(412\) | 49.7865 | 2.45281 | ||||||||
\(413\) | 49.6899 | 2.44508 | ||||||||
\(414\) | −10.7921 | −0.530402 | ||||||||
\(415\) | −0.216691 | −0.0106369 | ||||||||
\(416\) | −129.054 | −6.32741 | ||||||||
\(417\) | −4.05821 | −0.198731 | ||||||||
\(418\) | 86.1608 | 4.21426 | ||||||||
\(419\) | 26.0108 | 1.27071 | 0.635355 | − | 0.772220i | \(-0.280854\pi\) | ||||
0.635355 | + | 0.772220i | \(0.280854\pi\) | |||||||
\(420\) | 49.0354 | 2.39268 | ||||||||
\(421\) | −6.62047 | −0.322662 | −0.161331 | − | 0.986900i | \(-0.551579\pi\) | ||||
−0.161331 | + | 0.986900i | \(0.551579\pi\) | |||||||
\(422\) | −46.6940 | −2.27303 | ||||||||
\(423\) | 4.44714 | 0.216227 | ||||||||
\(424\) | −129.155 | −6.27232 | ||||||||
\(425\) | −3.26912 | −0.158576 | ||||||||
\(426\) | 20.8256 | 1.00901 | ||||||||
\(427\) | −7.83141 | −0.378988 | ||||||||
\(428\) | 109.501 | 5.29292 | ||||||||
\(429\) | 37.1820 | 1.79517 | ||||||||
\(430\) | −41.6199 | −2.00709 | ||||||||
\(431\) | 28.2510 | 1.36080 | 0.680401 | − | 0.732840i | \(-0.261806\pi\) | ||||
0.680401 | + | 0.732840i | \(0.261806\pi\) | |||||||
\(432\) | 90.7985 | 4.36854 | ||||||||
\(433\) | −12.4363 | −0.597651 | −0.298825 | − | 0.954308i | \(-0.596595\pi\) | ||||
−0.298825 | + | 0.954308i | \(0.596595\pi\) | |||||||
\(434\) | −85.3785 | −4.09830 | ||||||||
\(435\) | 12.2675 | 0.588184 | ||||||||
\(436\) | 2.08257 | 0.0997369 | ||||||||
\(437\) | −22.1713 | −1.06060 | ||||||||
\(438\) | −17.2106 | −0.822356 | ||||||||
\(439\) | 32.0340 | 1.52890 | 0.764450 | − | 0.644683i | \(-0.223011\pi\) | ||||
0.764450 | + | 0.644683i | \(0.223011\pi\) | |||||||
\(440\) | 66.2777 | 3.15966 | ||||||||
\(441\) | −17.5894 | −0.837592 | ||||||||
\(442\) | −14.5277 | −0.691012 | ||||||||
\(443\) | −33.6093 | −1.59683 | −0.798414 | − | 0.602109i | \(-0.794327\pi\) | ||||
−0.798414 | + | 0.602109i | \(0.794327\pi\) | |||||||
\(444\) | −41.6637 | −1.97727 | ||||||||
\(445\) | 4.60015 | 0.218068 | ||||||||
\(446\) | −29.9653 | −1.41890 | ||||||||
\(447\) | −14.9833 | −0.708688 | ||||||||
\(448\) | −170.061 | −8.03461 | ||||||||
\(449\) | −13.2498 | −0.625295 | −0.312648 | − | 0.949869i | \(-0.601216\pi\) | ||||
−0.312648 | + | 0.949869i | \(0.601216\pi\) | |||||||
\(450\) | −9.76867 | −0.460500 | ||||||||
\(451\) | 18.3367 | 0.863441 | ||||||||
\(452\) | 95.1468 | 4.47533 | ||||||||
\(453\) | 0.0745079 | 0.00350068 | ||||||||
\(454\) | 46.0637 | 2.16188 | ||||||||
\(455\) | −33.4290 | −1.56718 | ||||||||
\(456\) | 84.0091 | 3.93409 | ||||||||
\(457\) | −25.2382 | −1.18059 | −0.590297 | − | 0.807186i | \(-0.700989\pi\) | ||||
−0.590297 | + | 0.807186i | \(0.700989\pi\) | |||||||
\(458\) | 14.1134 | 0.659475 | ||||||||
\(459\) | 5.65300 | 0.263859 | ||||||||
\(460\) | −26.5580 | −1.23827 | ||||||||
\(461\) | −0.317499 | −0.0147874 | −0.00739369 | − | 0.999973i | \(-0.502354\pi\) | ||||
−0.00739369 | + | 0.999973i | \(0.502354\pi\) | |||||||
\(462\) | 93.5915 | 4.35427 | ||||||||
\(463\) | 32.0904 | 1.49137 | 0.745684 | − | 0.666300i | \(-0.232123\pi\) | ||||
0.745684 | + | 0.666300i | \(0.232123\pi\) | |||||||
\(464\) | −108.219 | −5.02395 | ||||||||
\(465\) | 11.7113 | 0.543098 | ||||||||
\(466\) | −47.1362 | −2.18354 | ||||||||
\(467\) | 3.11978 | 0.144366 | 0.0721832 | − | 0.997391i | \(-0.477003\pi\) | ||||
0.0721832 | + | 0.997391i | \(0.477003\pi\) | |||||||
\(468\) | −31.9711 | −1.47786 | ||||||||
\(469\) | 40.9409 | 1.89048 | ||||||||
\(470\) | 14.8598 | 0.685432 | ||||||||
\(471\) | 10.2578 | 0.472653 | ||||||||
\(472\) | 101.974 | 4.69372 | ||||||||
\(473\) | −58.5038 | −2.69001 | ||||||||
\(474\) | −46.7647 | −2.14798 | ||||||||
\(475\) | −20.0688 | −0.920819 | ||||||||
\(476\) | −26.9312 | −1.23439 | ||||||||
\(477\) | −14.1676 | −0.648692 | ||||||||
\(478\) | 29.8240 | 1.36412 | ||||||||
\(479\) | −1.51347 | −0.0691524 | −0.0345762 | − | 0.999402i | \(-0.511008\pi\) | ||||
−0.0345762 | + | 0.999402i | \(0.511008\pi\) | |||||||
\(480\) | 44.5586 | 2.03381 | ||||||||
\(481\) | 28.4035 | 1.29509 | ||||||||
\(482\) | −22.1195 | −1.00752 | ||||||||
\(483\) | −24.0834 | −1.09583 | ||||||||
\(484\) | 83.5936 | 3.79971 | ||||||||
\(485\) | 18.5115 | 0.840564 | ||||||||
\(486\) | 29.2985 | 1.32901 | ||||||||
\(487\) | −9.89872 | −0.448554 | −0.224277 | − | 0.974525i | \(-0.572002\pi\) | ||||
−0.224277 | + | 0.974525i | \(0.572002\pi\) | |||||||
\(488\) | −16.0716 | −0.727529 | ||||||||
\(489\) | −14.6267 | −0.661444 | ||||||||
\(490\) | −58.7739 | −2.65513 | ||||||||
\(491\) | −13.7986 | −0.622721 | −0.311360 | − | 0.950292i | \(-0.600785\pi\) | ||||
−0.311360 | + | 0.950292i | \(0.600785\pi\) | |||||||
\(492\) | 27.8409 | 1.25516 | ||||||||
\(493\) | −6.73759 | −0.303446 | ||||||||
\(494\) | −89.1839 | −4.01257 | ||||||||
\(495\) | 7.27032 | 0.326776 | ||||||||
\(496\) | −103.312 | −4.63885 | ||||||||
\(497\) | −26.3191 | −1.18057 | ||||||||
\(498\) | −0.627958 | −0.0281395 | ||||||||
\(499\) | −37.5978 | −1.68311 | −0.841555 | − | 0.540172i | \(-0.818359\pi\) | ||||
−0.841555 | + | 0.540172i | \(0.818359\pi\) | |||||||
\(500\) | −60.8069 | −2.71937 | ||||||||
\(501\) | −11.1992 | −0.500345 | ||||||||
\(502\) | −75.4258 | −3.36642 | ||||||||
\(503\) | −13.3935 | −0.597187 | −0.298593 | − | 0.954380i | \(-0.596517\pi\) | ||||
−0.298593 | + | 0.954380i | \(0.596517\pi\) | |||||||
\(504\) | −51.6790 | −2.30196 | ||||||||
\(505\) | 1.23671 | 0.0550329 | ||||||||
\(506\) | −50.6899 | −2.25344 | ||||||||
\(507\) | −20.4953 | −0.910226 | ||||||||
\(508\) | −45.9967 | −2.04078 | ||||||||
\(509\) | −28.7976 | −1.27643 | −0.638216 | − | 0.769858i | \(-0.720327\pi\) | ||||
−0.638216 | + | 0.769858i | \(0.720327\pi\) | |||||||
\(510\) | 5.01598 | 0.222111 | ||||||||
\(511\) | 21.7506 | 0.962188 | ||||||||
\(512\) | −75.4292 | −3.33353 | ||||||||
\(513\) | 34.7031 | 1.53218 | ||||||||
\(514\) | 37.0361 | 1.63359 | ||||||||
\(515\) | 11.7188 | 0.516394 | ||||||||
\(516\) | −88.8273 | −3.91040 | ||||||||
\(517\) | 20.8880 | 0.918653 | ||||||||
\(518\) | 71.4949 | 3.14130 | ||||||||
\(519\) | 6.49690 | 0.285182 | ||||||||
\(520\) | −68.6031 | −3.00844 | ||||||||
\(521\) | −2.06407 | −0.0904285 | −0.0452143 | − | 0.998977i | \(-0.514397\pi\) | ||||
−0.0452143 | + | 0.998977i | \(0.514397\pi\) | |||||||
\(522\) | −20.1330 | −0.881197 | ||||||||
\(523\) | 20.3347 | 0.889175 | 0.444587 | − | 0.895736i | \(-0.353350\pi\) | ||||
0.444587 | + | 0.895736i | \(0.353350\pi\) | |||||||
\(524\) | 38.2191 | 1.66961 | ||||||||
\(525\) | −21.7996 | −0.951411 | ||||||||
\(526\) | −47.1827 | −2.05727 | ||||||||
\(527\) | −6.43208 | −0.280186 | ||||||||
\(528\) | 113.250 | 4.92858 | ||||||||
\(529\) | −9.95623 | −0.432880 | ||||||||
\(530\) | −47.3402 | −2.05633 | ||||||||
\(531\) | 11.1860 | 0.485431 | ||||||||
\(532\) | −165.328 | −7.16787 | ||||||||
\(533\) | −18.9800 | −0.822117 | ||||||||
\(534\) | 13.3310 | 0.576887 | ||||||||
\(535\) | 25.7745 | 1.11433 | ||||||||
\(536\) | 84.0191 | 3.62907 | ||||||||
\(537\) | 2.13860 | 0.0922874 | ||||||||
\(538\) | 6.34943 | 0.273743 | ||||||||
\(539\) | −82.6167 | −3.55855 | ||||||||
\(540\) | 41.5692 | 1.78885 | ||||||||
\(541\) | 31.0928 | 1.33679 | 0.668393 | − | 0.743809i | \(-0.266983\pi\) | ||||
0.668393 | + | 0.743809i | \(0.266983\pi\) | |||||||
\(542\) | 7.04539 | 0.302625 | ||||||||
\(543\) | −8.11877 | −0.348410 | ||||||||
\(544\) | −24.4725 | −1.04925 | ||||||||
\(545\) | 0.490199 | 0.0209978 | ||||||||
\(546\) | −96.8752 | −4.14588 | ||||||||
\(547\) | 16.3923 | 0.700884 | 0.350442 | − | 0.936584i | \(-0.386031\pi\) | ||||
0.350442 | + | 0.936584i | \(0.386031\pi\) | |||||||
\(548\) | 4.50907 | 0.192618 | ||||||||
\(549\) | −1.76298 | −0.0752420 | ||||||||
\(550\) | −45.8830 | −1.95646 | ||||||||
\(551\) | −41.3613 | −1.76205 | ||||||||
\(552\) | −49.4240 | −2.10363 | ||||||||
\(553\) | 59.1006 | 2.51321 | ||||||||
\(554\) | 30.8149 | 1.30920 | ||||||||
\(555\) | −9.80688 | −0.416279 | ||||||||
\(556\) | 16.3898 | 0.695083 | ||||||||
\(557\) | −31.0733 | −1.31662 | −0.658310 | − | 0.752747i | \(-0.728728\pi\) | ||||
−0.658310 | + | 0.752747i | \(0.728728\pi\) | |||||||
\(558\) | −19.2201 | −0.813651 | ||||||||
\(559\) | 60.5564 | 2.56126 | ||||||||
\(560\) | −101.819 | −4.30263 | ||||||||
\(561\) | 7.05080 | 0.297685 | ||||||||
\(562\) | −16.8704 | −0.711637 | ||||||||
\(563\) | 7.46822 | 0.314748 | 0.157374 | − | 0.987539i | \(-0.449697\pi\) | ||||
0.157374 | + | 0.987539i | \(0.449697\pi\) | |||||||
\(564\) | 31.7146 | 1.33543 | ||||||||
\(565\) | 22.3958 | 0.942199 | ||||||||
\(566\) | 71.2056 | 2.99300 | ||||||||
\(567\) | 22.0169 | 0.924624 | ||||||||
\(568\) | −54.0122 | −2.26630 | ||||||||
\(569\) | −4.01374 | −0.168265 | −0.0841324 | − | 0.996455i | \(-0.526812\pi\) | ||||
−0.0841324 | + | 0.996455i | \(0.526812\pi\) | |||||||
\(570\) | 30.7925 | 1.28976 | ||||||||
\(571\) | −12.6101 | −0.527718 | −0.263859 | − | 0.964561i | \(-0.584995\pi\) | ||||
−0.263859 | + | 0.964561i | \(0.584995\pi\) | |||||||
\(572\) | −150.166 | −6.27877 | ||||||||
\(573\) | 33.7112 | 1.40831 | ||||||||
\(574\) | −47.7749 | −1.99409 | ||||||||
\(575\) | 11.8068 | 0.492378 | ||||||||
\(576\) | −38.2834 | −1.59514 | ||||||||
\(577\) | −8.66150 | −0.360583 | −0.180291 | − | 0.983613i | \(-0.557704\pi\) | ||||
−0.180291 | + | 0.983613i | \(0.557704\pi\) | |||||||
\(578\) | −2.75487 | −0.114588 | ||||||||
\(579\) | −9.94919 | −0.413474 | ||||||||
\(580\) | −49.5447 | −2.05723 | ||||||||
\(581\) | 0.793604 | 0.0329242 | ||||||||
\(582\) | 53.6452 | 2.22367 | ||||||||
\(583\) | −66.5447 | −2.75600 | ||||||||
\(584\) | 44.6365 | 1.84707 | ||||||||
\(585\) | −7.52540 | −0.311137 | ||||||||
\(586\) | −31.6707 | −1.30830 | ||||||||
\(587\) | 21.6722 | 0.894508 | 0.447254 | − | 0.894407i | \(-0.352402\pi\) | ||||
0.447254 | + | 0.894407i | \(0.352402\pi\) | |||||||
\(588\) | −125.438 | −5.17299 | ||||||||
\(589\) | −39.4858 | −1.62698 | ||||||||
\(590\) | 37.3772 | 1.53880 | ||||||||
\(591\) | 25.1558 | 1.03477 | ||||||||
\(592\) | 86.5121 | 3.55563 | ||||||||
\(593\) | 41.3352 | 1.69743 | 0.848716 | − | 0.528849i | \(-0.177376\pi\) | ||||
0.848716 | + | 0.528849i | \(0.177376\pi\) | |||||||
\(594\) | 79.3412 | 3.25541 | ||||||||
\(595\) | −6.33912 | −0.259878 | ||||||||
\(596\) | 60.5130 | 2.47871 | ||||||||
\(597\) | 13.2875 | 0.543821 | ||||||||
\(598\) | 52.4684 | 2.14559 | ||||||||
\(599\) | −32.4854 | −1.32732 | −0.663659 | − | 0.748035i | \(-0.730998\pi\) | ||||
−0.663659 | + | 0.748035i | \(0.730998\pi\) | |||||||
\(600\) | −44.7371 | −1.82638 | ||||||||
\(601\) | −4.99245 | −0.203646 | −0.101823 | − | 0.994803i | \(-0.532468\pi\) | ||||
−0.101823 | + | 0.994803i | \(0.532468\pi\) | |||||||
\(602\) | 152.427 | 6.21248 | ||||||||
\(603\) | 9.21646 | 0.375323 | ||||||||
\(604\) | −0.300914 | −0.0122440 | ||||||||
\(605\) | 19.6764 | 0.799960 | ||||||||
\(606\) | 3.58391 | 0.145586 | ||||||||
\(607\) | 11.7942 | 0.478711 | 0.239355 | − | 0.970932i | \(-0.423064\pi\) | ||||
0.239355 | + | 0.970932i | \(0.423064\pi\) | |||||||
\(608\) | −150.234 | −6.09279 | ||||||||
\(609\) | −44.9284 | −1.82059 | ||||||||
\(610\) | −5.89087 | −0.238514 | ||||||||
\(611\) | −21.6209 | −0.874687 | ||||||||
\(612\) | −6.06265 | −0.245068 | ||||||||
\(613\) | 27.9795 | 1.13008 | 0.565042 | − | 0.825062i | \(-0.308860\pi\) | ||||
0.565042 | + | 0.825062i | \(0.308860\pi\) | |||||||
\(614\) | −18.4962 | −0.746447 | ||||||||
\(615\) | 6.55324 | 0.264252 | ||||||||
\(616\) | −242.734 | −9.78001 | ||||||||
\(617\) | −7.29682 | −0.293759 | −0.146879 | − | 0.989154i | \(-0.546923\pi\) | ||||
−0.146879 | + | 0.989154i | \(0.546923\pi\) | |||||||
\(618\) | 33.9605 | 1.36609 | ||||||||
\(619\) | 25.9805 | 1.04425 | 0.522123 | − | 0.852870i | \(-0.325140\pi\) | ||||
0.522123 | + | 0.852870i | \(0.325140\pi\) | |||||||
\(620\) | −47.2982 | −1.89954 | ||||||||
\(621\) | −20.4164 | −0.819284 | ||||||||
\(622\) | −1.90945 | −0.0765621 | ||||||||
\(623\) | −16.8475 | −0.674980 | ||||||||
\(624\) | −117.224 | −4.69270 | ||||||||
\(625\) | 2.03279 | 0.0813117 | ||||||||
\(626\) | 0.827853 | 0.0330877 | ||||||||
\(627\) | 43.2841 | 1.72860 | ||||||||
\(628\) | −41.4279 | −1.65315 | ||||||||
\(629\) | 5.38614 | 0.214759 | ||||||||
\(630\) | −18.9423 | −0.754679 | ||||||||
\(631\) | −28.4391 | −1.13214 | −0.566071 | − | 0.824357i | \(-0.691537\pi\) | ||||
−0.566071 | + | 0.824357i | \(0.691537\pi\) | |||||||
\(632\) | 121.286 | 4.82452 | ||||||||
\(633\) | −23.4574 | −0.932348 | ||||||||
\(634\) | 77.0760 | 3.06108 | ||||||||
\(635\) | −10.8268 | −0.429648 | ||||||||
\(636\) | −101.036 | −4.00634 | ||||||||
\(637\) | 85.5153 | 3.38824 | ||||||||
\(638\) | −94.5637 | −3.74381 | ||||||||
\(639\) | −5.92486 | −0.234384 | ||||||||
\(640\) | −63.5280 | −2.51117 | ||||||||
\(641\) | −16.9746 | −0.670458 | −0.335229 | − | 0.942137i | \(-0.608814\pi\) | ||||
−0.335229 | + | 0.942137i | \(0.608814\pi\) | |||||||
\(642\) | 74.6929 | 2.94789 | ||||||||
\(643\) | −25.3326 | −0.999019 | −0.499509 | − | 0.866308i | \(-0.666486\pi\) | ||||
−0.499509 | + | 0.866308i | \(0.666486\pi\) | |||||||
\(644\) | 97.2652 | 3.83279 | ||||||||
\(645\) | −20.9083 | −0.823264 | ||||||||
\(646\) | −16.9119 | −0.665389 | ||||||||
\(647\) | −36.8206 | −1.44757 | −0.723784 | − | 0.690026i | \(-0.757599\pi\) | ||||
−0.723784 | + | 0.690026i | \(0.757599\pi\) | |||||||
\(648\) | 45.1832 | 1.77496 | ||||||||
\(649\) | 52.5400 | 2.06238 | ||||||||
\(650\) | 47.4928 | 1.86282 | ||||||||
\(651\) | −42.8911 | −1.68104 | ||||||||
\(652\) | 59.0728 | 2.31347 | ||||||||
\(653\) | 38.8027 | 1.51847 | 0.759234 | − | 0.650818i | \(-0.225574\pi\) | ||||
0.759234 | + | 0.650818i | \(0.225574\pi\) | |||||||
\(654\) | 1.42057 | 0.0555485 | ||||||||
\(655\) | 8.99608 | 0.351506 | ||||||||
\(656\) | −57.8099 | −2.25710 | ||||||||
\(657\) | 4.89640 | 0.191027 | ||||||||
\(658\) | −54.4222 | −2.12160 | ||||||||
\(659\) | 24.4183 | 0.951201 | 0.475601 | − | 0.879661i | \(-0.342231\pi\) | ||||
0.475601 | + | 0.879661i | \(0.342231\pi\) | |||||||
\(660\) | 51.8480 | 2.01818 | ||||||||
\(661\) | 41.5089 | 1.61451 | 0.807254 | − | 0.590204i | \(-0.200953\pi\) | ||||
0.807254 | + | 0.590204i | \(0.200953\pi\) | |||||||
\(662\) | 10.7974 | 0.419652 | ||||||||
\(663\) | −7.29819 | −0.283438 | ||||||||
\(664\) | 1.62864 | 0.0632033 | ||||||||
\(665\) | −38.9151 | −1.50906 | ||||||||
\(666\) | 16.0946 | 0.623655 | ||||||||
\(667\) | 24.3336 | 0.942200 | ||||||||
\(668\) | 45.2302 | 1.75001 | ||||||||
\(669\) | −15.0535 | −0.582002 | ||||||||
\(670\) | 30.7962 | 1.18976 | ||||||||
\(671\) | −8.28061 | −0.319669 | ||||||||
\(672\) | −163.190 | −6.29520 | ||||||||
\(673\) | −25.8865 | −0.997850 | −0.498925 | − | 0.866645i | \(-0.666272\pi\) | ||||
−0.498925 | + | 0.866645i | \(0.666272\pi\) | |||||||
\(674\) | 76.8105 | 2.95863 | ||||||||
\(675\) | −18.4803 | −0.711309 | ||||||||
\(676\) | 82.7738 | 3.18361 | ||||||||
\(677\) | −23.7726 | −0.913657 | −0.456828 | − | 0.889555i | \(-0.651015\pi\) | ||||
−0.456828 | + | 0.889555i | \(0.651015\pi\) | |||||||
\(678\) | 64.9017 | 2.49254 | ||||||||
\(679\) | −67.7960 | −2.60177 | ||||||||
\(680\) | −13.0092 | −0.498878 | ||||||||
\(681\) | 23.1407 | 0.886755 | ||||||||
\(682\) | −90.2758 | −3.45684 | ||||||||
\(683\) | −9.56096 | −0.365840 | −0.182920 | − | 0.983128i | \(-0.558555\pi\) | ||||
−0.182920 | + | 0.983128i | \(0.558555\pi\) | |||||||
\(684\) | −37.2179 | −1.42306 | ||||||||
\(685\) | 1.06135 | 0.0405522 | ||||||||
\(686\) | 122.335 | 4.67077 | ||||||||
\(687\) | 7.09006 | 0.270503 | ||||||||
\(688\) | 184.444 | 7.03188 | ||||||||
\(689\) | 68.8795 | 2.62410 | ||||||||
\(690\) | −18.1158 | −0.689656 | ||||||||
\(691\) | −48.4330 | −1.84248 | −0.921239 | − | 0.388997i | \(-0.872822\pi\) | ||||
−0.921239 | + | 0.388997i | \(0.872822\pi\) | |||||||
\(692\) | −26.2389 | −0.997454 | ||||||||
\(693\) | −26.6266 | −1.01146 | ||||||||
\(694\) | 14.2856 | 0.542273 | ||||||||
\(695\) | 3.85786 | 0.146337 | ||||||||
\(696\) | −92.2021 | −3.49491 | ||||||||
\(697\) | −3.59917 | −0.136328 | ||||||||
\(698\) | 35.5803 | 1.34674 | ||||||||
\(699\) | −23.6796 | −0.895643 | ||||||||
\(700\) | 88.0415 | 3.32766 | ||||||||
\(701\) | −11.6295 | −0.439239 | −0.219620 | − | 0.975586i | \(-0.570482\pi\) | ||||
−0.219620 | + | 0.975586i | \(0.570482\pi\) | |||||||
\(702\) | −82.1250 | −3.09961 | ||||||||
\(703\) | 33.0649 | 1.24707 | ||||||||
\(704\) | −179.815 | −6.77704 | ||||||||
\(705\) | 7.46504 | 0.281150 | ||||||||
\(706\) | −2.75487 | −0.103681 | ||||||||
\(707\) | −4.52929 | −0.170342 | ||||||||
\(708\) | 79.7724 | 2.99803 | ||||||||
\(709\) | −24.1336 | −0.906356 | −0.453178 | − | 0.891420i | \(-0.649710\pi\) | ||||
−0.453178 | + | 0.891420i | \(0.649710\pi\) | |||||||
\(710\) | −19.7975 | −0.742987 | ||||||||
\(711\) | 13.3045 | 0.498958 | ||||||||
\(712\) | −34.5745 | −1.29573 | ||||||||
\(713\) | 23.2302 | 0.869977 | ||||||||
\(714\) | −18.3704 | −0.687494 | ||||||||
\(715\) | −35.3464 | −1.32188 | ||||||||
\(716\) | −8.63713 | −0.322785 | ||||||||
\(717\) | 14.9825 | 0.559532 | ||||||||
\(718\) | 76.7712 | 2.86508 | ||||||||
\(719\) | −48.0895 | −1.79344 | −0.896718 | − | 0.442603i | \(-0.854055\pi\) | ||||
−0.896718 | + | 0.442603i | \(0.854055\pi\) | |||||||
\(720\) | −22.9211 | −0.854218 | ||||||||
\(721\) | −42.9188 | −1.59838 | ||||||||
\(722\) | −51.4775 | −1.91580 | ||||||||
\(723\) | −11.1121 | −0.413262 | ||||||||
\(724\) | 32.7891 | 1.21860 | ||||||||
\(725\) | 22.0260 | 0.818025 | ||||||||
\(726\) | 57.0211 | 2.11625 | ||||||||
\(727\) | 34.4811 | 1.27883 | 0.639417 | − | 0.768861i | \(-0.279176\pi\) | ||||
0.639417 | + | 0.768861i | \(0.279176\pi\) | |||||||
\(728\) | 251.250 | 9.31195 | ||||||||
\(729\) | 28.4268 | 1.05284 | ||||||||
\(730\) | 16.3610 | 0.605547 | ||||||||
\(731\) | 11.4833 | 0.424724 | ||||||||
\(732\) | −12.5726 | −0.464697 | ||||||||
\(733\) | −35.4817 | −1.31055 | −0.655273 | − | 0.755392i | \(-0.727446\pi\) | ||||
−0.655273 | + | 0.755392i | \(0.727446\pi\) | |||||||
\(734\) | −17.9208 | −0.661470 | ||||||||
\(735\) | −29.5259 | −1.08908 | ||||||||
\(736\) | 88.3852 | 3.25792 | ||||||||
\(737\) | 43.2892 | 1.59458 | ||||||||
\(738\) | −10.7549 | −0.395894 | ||||||||
\(739\) | 8.06191 | 0.296562 | 0.148281 | − | 0.988945i | \(-0.452626\pi\) | ||||
0.148281 | + | 0.988945i | \(0.452626\pi\) | |||||||
\(740\) | 39.6069 | 1.45598 | ||||||||
\(741\) | −44.8028 | −1.64587 | ||||||||
\(742\) | 173.378 | 6.36489 | ||||||||
\(743\) | −19.3678 | −0.710536 | −0.355268 | − | 0.934765i | \(-0.615610\pi\) | ||||
−0.355268 | + | 0.934765i | \(0.615610\pi\) | |||||||
\(744\) | −88.0213 | −3.22702 | ||||||||
\(745\) | 14.2437 | 0.521847 | ||||||||
\(746\) | −76.4129 | −2.79767 | ||||||||
\(747\) | 0.178653 | 0.00653657 | ||||||||
\(748\) | −28.4760 | −1.04118 | ||||||||
\(749\) | −94.3958 | −3.44915 | ||||||||
\(750\) | −41.4777 | −1.51455 | ||||||||
\(751\) | −7.95756 | −0.290375 | −0.145188 | − | 0.989404i | \(-0.546379\pi\) | ||||
−0.145188 | + | 0.989404i | \(0.546379\pi\) | |||||||
\(752\) | −65.8534 | −2.40143 | ||||||||
\(753\) | −37.8912 | −1.38083 | ||||||||
\(754\) | 97.8815 | 3.56463 | ||||||||
\(755\) | −0.0708296 | −0.00257775 | ||||||||
\(756\) | −152.242 | −5.53699 | ||||||||
\(757\) | −47.5578 | −1.72852 | −0.864260 | − | 0.503046i | \(-0.832213\pi\) | ||||
−0.864260 | + | 0.503046i | \(0.832213\pi\) | |||||||
\(758\) | 42.4946 | 1.54347 | ||||||||
\(759\) | −25.4648 | −0.924313 | ||||||||
\(760\) | −79.8618 | −2.89689 | ||||||||
\(761\) | 3.39134 | 0.122936 | 0.0614680 | − | 0.998109i | \(-0.480422\pi\) | ||||
0.0614680 | + | 0.998109i | \(0.480422\pi\) | |||||||
\(762\) | −31.3754 | −1.13661 | ||||||||
\(763\) | −1.79529 | −0.0649939 | ||||||||
\(764\) | −136.149 | −4.92569 | ||||||||
\(765\) | −1.42704 | −0.0515946 | ||||||||
\(766\) | −22.7392 | −0.821601 | ||||||||
\(767\) | −54.3834 | −1.96367 | ||||||||
\(768\) | −86.4085 | −3.11800 | ||||||||
\(769\) | 16.0805 | 0.579877 | 0.289939 | − | 0.957045i | \(-0.406365\pi\) | ||||
0.289939 | + | 0.957045i | \(0.406365\pi\) | |||||||
\(770\) | −88.9711 | −3.20629 | ||||||||
\(771\) | 18.6056 | 0.670065 | ||||||||
\(772\) | 40.1816 | 1.44617 | ||||||||
\(773\) | −48.9441 | −1.76040 | −0.880198 | − | 0.474607i | \(-0.842590\pi\) | ||||
−0.880198 | + | 0.474607i | \(0.842590\pi\) | |||||||
\(774\) | 34.3139 | 1.23339 | ||||||||
\(775\) | 21.0273 | 0.755321 | ||||||||
\(776\) | −139.131 | −4.99452 | ||||||||
\(777\) | 35.9165 | 1.28850 | ||||||||
\(778\) | 61.5989 | 2.20843 | ||||||||
\(779\) | −22.0949 | −0.791633 | ||||||||
\(780\) | −53.6671 | −1.92159 | ||||||||
\(781\) | −27.8288 | −0.995792 | ||||||||
\(782\) | 9.94955 | 0.355795 | ||||||||
\(783\) | −38.0875 | −1.36114 | ||||||||
\(784\) | 260.465 | 9.30232 | ||||||||
\(785\) | −9.75137 | −0.348041 | ||||||||
\(786\) | 26.0701 | 0.929890 | ||||||||
\(787\) | −32.7361 | −1.16692 | −0.583459 | − | 0.812143i | \(-0.698301\pi\) | ||||
−0.583459 | + | 0.812143i | \(0.698301\pi\) | |||||||
\(788\) | −101.596 | −3.61922 | ||||||||
\(789\) | −23.7029 | −0.843846 | ||||||||
\(790\) | 44.4561 | 1.58168 | ||||||||
\(791\) | −82.0218 | −2.91636 | ||||||||
\(792\) | −54.6432 | −1.94166 | ||||||||
\(793\) | 8.57114 | 0.304370 | ||||||||
\(794\) | 67.7599 | 2.40471 | ||||||||
\(795\) | −23.7820 | −0.843462 | ||||||||
\(796\) | −53.6640 | −1.90207 | ||||||||
\(797\) | −6.87112 | −0.243387 | −0.121694 | − | 0.992568i | \(-0.538833\pi\) | ||||
−0.121694 | + | 0.992568i | \(0.538833\pi\) | |||||||
\(798\) | −112.774 | −3.99215 | ||||||||
\(799\) | −4.09995 | −0.145046 | ||||||||
\(800\) | 80.0035 | 2.82855 | ||||||||
\(801\) | −3.79264 | −0.134006 | ||||||||
\(802\) | −47.0393 | −1.66102 | ||||||||
\(803\) | 22.9981 | 0.811587 | ||||||||
\(804\) | 65.7268 | 2.31801 | ||||||||
\(805\) | 22.8944 | 0.806923 | ||||||||
\(806\) | 93.4432 | 3.29140 | ||||||||
\(807\) | 3.18972 | 0.112284 | ||||||||
\(808\) | −9.29503 | −0.326998 | ||||||||
\(809\) | 16.0637 | 0.564770 | 0.282385 | − | 0.959301i | \(-0.408874\pi\) | ||||
0.282385 | + | 0.959301i | \(0.408874\pi\) | |||||||
\(810\) | 16.5614 | 0.581907 | ||||||||
\(811\) | −43.7462 | −1.53614 | −0.768068 | − | 0.640369i | \(-0.778782\pi\) | ||||
−0.768068 | + | 0.640369i | \(0.778782\pi\) | |||||||
\(812\) | 181.451 | 6.36769 | ||||||||
\(813\) | 3.53935 | 0.124130 | ||||||||
\(814\) | 75.5957 | 2.64963 | ||||||||
\(815\) | 13.9046 | 0.487059 | ||||||||
\(816\) | −22.2290 | −0.778171 | ||||||||
\(817\) | 70.4946 | 2.46629 | ||||||||
\(818\) | −90.6973 | −3.17116 | ||||||||
\(819\) | 27.5608 | 0.963054 | ||||||||
\(820\) | −26.4665 | −0.924249 | ||||||||
\(821\) | 32.7099 | 1.14158 | 0.570791 | − | 0.821095i | \(-0.306637\pi\) | ||||
0.570791 | + | 0.821095i | \(0.306637\pi\) | |||||||
\(822\) | 3.07574 | 0.107279 | ||||||||
\(823\) | 51.9900 | 1.81226 | 0.906129 | − | 0.423000i | \(-0.139023\pi\) | ||||
0.906129 | + | 0.423000i | \(0.139023\pi\) | |||||||
\(824\) | −88.0780 | −3.06834 | ||||||||
\(825\) | −23.0500 | −0.802496 | ||||||||
\(826\) | −136.889 | −4.76299 | ||||||||
\(827\) | −3.56395 | −0.123931 | −0.0619654 | − | 0.998078i | \(-0.519737\pi\) | ||||
−0.0619654 | + | 0.998078i | \(0.519737\pi\) | |||||||
\(828\) | 21.8960 | 0.760937 | ||||||||
\(829\) | 43.5030 | 1.51092 | 0.755460 | − | 0.655194i | \(-0.227413\pi\) | ||||
0.755460 | + | 0.655194i | \(0.227413\pi\) | |||||||
\(830\) | 0.596957 | 0.0207207 | ||||||||
\(831\) | 15.4803 | 0.537006 | ||||||||
\(832\) | 186.124 | 6.45269 | ||||||||
\(833\) | 16.2162 | 0.561859 | ||||||||
\(834\) | 11.1799 | 0.387127 | ||||||||
\(835\) | 10.6464 | 0.368433 | ||||||||
\(836\) | −174.811 | −6.04596 | ||||||||
\(837\) | −36.3605 | −1.25680 | ||||||||
\(838\) | −71.6565 | −2.47533 | ||||||||
\(839\) | −47.9142 | −1.65418 | −0.827091 | − | 0.562068i | \(-0.810006\pi\) | ||||
−0.827091 | + | 0.562068i | \(0.810006\pi\) | |||||||
\(840\) | −86.7491 | −2.99313 | ||||||||
\(841\) | 16.3951 | 0.565347 | ||||||||
\(842\) | 18.2386 | 0.628543 | ||||||||
\(843\) | −8.47511 | −0.291898 | ||||||||
\(844\) | 94.7370 | 3.26098 | ||||||||
\(845\) | 19.4834 | 0.670251 | ||||||||
\(846\) | −12.2513 | −0.421209 | ||||||||
\(847\) | −72.0624 | −2.47609 | ||||||||
\(848\) | 209.795 | 7.20439 | ||||||||
\(849\) | 35.7712 | 1.22766 | ||||||||
\(850\) | 9.00603 | 0.308904 | ||||||||
\(851\) | −19.4527 | −0.666828 | ||||||||
\(852\) | −42.2529 | −1.44756 | ||||||||
\(853\) | −11.7507 | −0.402337 | −0.201168 | − | 0.979557i | \(-0.564474\pi\) | ||||
−0.201168 | + | 0.979557i | \(0.564474\pi\) | |||||||
\(854\) | 21.5746 | 0.738266 | ||||||||
\(855\) | −8.76042 | −0.299600 | ||||||||
\(856\) | −193.719 | −6.62119 | ||||||||
\(857\) | 39.3138 | 1.34293 | 0.671467 | − | 0.741035i | \(-0.265665\pi\) | ||||
0.671467 | + | 0.741035i | \(0.265665\pi\) | |||||||
\(858\) | −102.432 | −3.49697 | ||||||||
\(859\) | −50.7875 | −1.73285 | −0.866424 | − | 0.499309i | \(-0.833587\pi\) | ||||
−0.866424 | + | 0.499309i | \(0.833587\pi\) | |||||||
\(860\) | 84.4421 | 2.87945 | ||||||||
\(861\) | −24.0004 | −0.817932 | ||||||||
\(862\) | −77.8280 | −2.65083 | ||||||||
\(863\) | 33.5353 | 1.14155 | 0.570777 | − | 0.821105i | \(-0.306642\pi\) | ||||
0.570777 | + | 0.821105i | \(0.306642\pi\) | |||||||
\(864\) | −138.343 | −4.70652 | ||||||||
\(865\) | −6.17616 | −0.209996 | ||||||||
\(866\) | 34.2605 | 1.16422 | ||||||||
\(867\) | −1.38395 | −0.0470014 | ||||||||
\(868\) | 173.224 | 5.87959 | ||||||||
\(869\) | 62.4906 | 2.11985 | ||||||||
\(870\) | −33.7956 | −1.14578 | ||||||||
\(871\) | −44.8081 | −1.51826 | ||||||||
\(872\) | −3.68430 | −0.124766 | ||||||||
\(873\) | −15.2620 | −0.516540 | ||||||||
\(874\) | 61.0792 | 2.06603 | ||||||||
\(875\) | 52.4189 | 1.77208 | ||||||||
\(876\) | 34.9185 | 1.17979 | ||||||||
\(877\) | −3.59414 | −0.121366 | −0.0606828 | − | 0.998157i | \(-0.519328\pi\) | ||||
−0.0606828 | + | 0.998157i | \(0.519328\pi\) | |||||||
\(878\) | −88.2497 | −2.97828 | ||||||||
\(879\) | −15.9102 | −0.536638 | ||||||||
\(880\) | −107.659 | −3.62919 | ||||||||
\(881\) | −41.9150 | −1.41215 | −0.706076 | − | 0.708136i | \(-0.749536\pi\) | ||||
−0.706076 | + | 0.708136i | \(0.749536\pi\) | |||||||
\(882\) | 48.4567 | 1.63162 | ||||||||
\(883\) | −6.93214 | −0.233285 | −0.116643 | − | 0.993174i | \(-0.537213\pi\) | ||||
−0.116643 | + | 0.993174i | \(0.537213\pi\) | |||||||
\(884\) | 29.4751 | 0.991354 | ||||||||
\(885\) | 18.7770 | 0.631181 | ||||||||
\(886\) | 92.5896 | 3.11061 | ||||||||
\(887\) | −10.9871 | −0.368911 | −0.184455 | − | 0.982841i | \(-0.559052\pi\) | ||||
−0.184455 | + | 0.982841i | \(0.559052\pi\) | |||||||
\(888\) | 73.7079 | 2.47347 | ||||||||
\(889\) | 39.6518 | 1.32988 | ||||||||
\(890\) | −12.6728 | −0.424795 | ||||||||
\(891\) | 23.2798 | 0.779903 | ||||||||
\(892\) | 60.7963 | 2.03561 | ||||||||
\(893\) | −25.1691 | −0.842253 | ||||||||
\(894\) | 41.2773 | 1.38052 | ||||||||
\(895\) | −2.03302 | −0.0679564 | ||||||||
\(896\) | 232.663 | 7.77274 | ||||||||
\(897\) | 26.3582 | 0.880076 | ||||||||
\(898\) | 36.5015 | 1.21807 | ||||||||
\(899\) | 43.3367 | 1.44536 | ||||||||
\(900\) | 19.8196 | 0.660652 | ||||||||
\(901\) | 13.0616 | 0.435144 | ||||||||
\(902\) | −50.5153 | −1.68197 | ||||||||
\(903\) | 76.5741 | 2.54823 | ||||||||
\(904\) | −168.325 | −5.59842 | ||||||||
\(905\) | 7.71797 | 0.256554 | ||||||||
\(906\) | −0.205260 | −0.00681930 | ||||||||
\(907\) | 2.94876 | 0.0979119 | 0.0489560 | − | 0.998801i | \(-0.484411\pi\) | ||||
0.0489560 | + | 0.998801i | \(0.484411\pi\) | |||||||
\(908\) | −93.4581 | −3.10152 | ||||||||
\(909\) | −1.01962 | −0.0338186 | ||||||||
\(910\) | 92.0927 | 3.05284 | ||||||||
\(911\) | −9.70709 | −0.321610 | −0.160805 | − | 0.986986i | \(-0.551409\pi\) | ||||
−0.160805 | + | 0.986986i | \(0.551409\pi\) | |||||||
\(912\) | −136.462 | −4.51869 | ||||||||
\(913\) | 0.839124 | 0.0277710 | ||||||||
\(914\) | 69.5282 | 2.29979 | ||||||||
\(915\) | −2.95936 | −0.0978334 | ||||||||
\(916\) | −28.6345 | −0.946110 | ||||||||
\(917\) | −32.9470 | −1.08801 | ||||||||
\(918\) | −15.5733 | −0.513995 | ||||||||
\(919\) | −34.8141 | −1.14841 | −0.574206 | − | 0.818711i | \(-0.694689\pi\) | ||||
−0.574206 | + | 0.818711i | \(0.694689\pi\) | |||||||
\(920\) | 46.9841 | 1.54902 | ||||||||
\(921\) | −9.29184 | −0.306176 | ||||||||
\(922\) | 0.874669 | 0.0288057 | ||||||||
\(923\) | 28.8052 | 0.948133 | ||||||||
\(924\) | −189.887 | −6.24681 | ||||||||
\(925\) | −17.6079 | −0.578946 | ||||||||
\(926\) | −88.4050 | −2.90517 | ||||||||
\(927\) | −9.66171 | −0.317332 | ||||||||
\(928\) | 164.885 | 5.41263 | ||||||||
\(929\) | 11.6150 | 0.381074 | 0.190537 | − | 0.981680i | \(-0.438977\pi\) | ||||
0.190537 | + | 0.981680i | \(0.438977\pi\) | |||||||
\(930\) | −32.2631 | −1.05795 | ||||||||
\(931\) | 99.5496 | 3.26261 | ||||||||
\(932\) | 95.6342 | 3.13260 | ||||||||
\(933\) | −0.959240 | −0.0314041 | ||||||||
\(934\) | −8.59461 | −0.281224 | ||||||||
\(935\) | −6.70272 | −0.219202 | ||||||||
\(936\) | 56.5604 | 1.84874 | ||||||||
\(937\) | 18.2768 | 0.597078 | 0.298539 | − | 0.954397i | \(-0.403501\pi\) | ||||
0.298539 | + | 0.954397i | \(0.403501\pi\) | |||||||
\(938\) | −112.787 | −3.68263 | ||||||||
\(939\) | 0.415884 | 0.0135719 | ||||||||
\(940\) | −30.1489 | −0.983349 | ||||||||
\(941\) | −7.46183 | −0.243249 | −0.121624 | − | 0.992576i | \(-0.538810\pi\) | ||||
−0.121624 | + | 0.992576i | \(0.538810\pi\) | |||||||
\(942\) | −28.2589 | −0.920724 | ||||||||
\(943\) | 12.9988 | 0.423300 | ||||||||
\(944\) | −165.643 | −5.39121 | ||||||||
\(945\) | −35.8350 | −1.16571 | ||||||||
\(946\) | 161.171 | 5.24011 | ||||||||
\(947\) | −10.5432 | −0.342607 | −0.171303 | − | 0.985218i | \(-0.554798\pi\) | ||||
−0.171303 | + | 0.985218i | \(0.554798\pi\) | |||||||
\(948\) | 94.8805 | 3.08158 | ||||||||
\(949\) | −23.8051 | −0.772745 | ||||||||
\(950\) | 55.2870 | 1.79375 | ||||||||
\(951\) | 38.7202 | 1.25559 | ||||||||
\(952\) | 47.6444 | 1.54416 | ||||||||
\(953\) | 25.0948 | 0.812900 | 0.406450 | − | 0.913673i | \(-0.366767\pi\) | ||||
0.406450 | + | 0.913673i | \(0.366767\pi\) | |||||||
\(954\) | 39.0301 | 1.26365 | ||||||||
\(955\) | −32.0469 | −1.03701 | ||||||||
\(956\) | −60.5096 | −1.95702 | ||||||||
\(957\) | −47.5054 | −1.53563 | ||||||||
\(958\) | 4.16943 | 0.134708 | ||||||||
\(959\) | −3.88707 | −0.125520 | ||||||||
\(960\) | −64.2631 | −2.07408 | ||||||||
\(961\) | 10.3716 | 0.334568 | ||||||||
\(962\) | −78.2481 | −2.52282 | ||||||||
\(963\) | −21.2500 | −0.684772 | ||||||||
\(964\) | 44.8781 | 1.44542 | ||||||||
\(965\) | 9.45802 | 0.304464 | ||||||||
\(966\) | 66.3467 | 2.13467 | ||||||||
\(967\) | −23.1106 | −0.743187 | −0.371594 | − | 0.928395i | \(-0.621189\pi\) | ||||
−0.371594 | + | 0.928395i | \(0.621189\pi\) | |||||||
\(968\) | −147.887 | −4.75326 | ||||||||
\(969\) | −8.49592 | −0.272928 | ||||||||
\(970\) | −50.9969 | −1.63741 | ||||||||
\(971\) | −13.6255 | −0.437264 | −0.218632 | − | 0.975807i | \(-0.570159\pi\) | ||||
−0.218632 | + | 0.975807i | \(0.570159\pi\) | |||||||
\(972\) | −59.4434 | −1.90665 | ||||||||
\(973\) | −14.1289 | −0.452953 | ||||||||
\(974\) | 27.2697 | 0.873778 | ||||||||
\(975\) | 23.8587 | 0.764089 | ||||||||
\(976\) | 26.1062 | 0.835640 | ||||||||
\(977\) | −55.4372 | −1.77359 | −0.886797 | − | 0.462159i | \(-0.847075\pi\) | ||||
−0.886797 | + | 0.462159i | \(0.847075\pi\) | |||||||
\(978\) | 40.2948 | 1.28849 | ||||||||
\(979\) | −17.8138 | −0.569333 | ||||||||
\(980\) | 119.246 | 3.80916 | ||||||||
\(981\) | −0.404149 | −0.0129035 | ||||||||
\(982\) | 38.0133 | 1.21305 | ||||||||
\(983\) | −28.6291 | −0.913128 | −0.456564 | − | 0.889691i | \(-0.650920\pi\) | ||||
−0.456564 | + | 0.889691i | \(0.650920\pi\) | |||||||
\(984\) | −49.2537 | −1.57015 | ||||||||
\(985\) | −23.9139 | −0.761961 | ||||||||
\(986\) | 18.5612 | 0.591109 | ||||||||
\(987\) | −27.3398 | −0.870234 | ||||||||
\(988\) | 180.944 | 5.75660 | ||||||||
\(989\) | −41.4732 | −1.31877 | ||||||||
\(990\) | −20.0288 | −0.636558 | ||||||||
\(991\) | −15.6685 | −0.497726 | −0.248863 | − | 0.968539i | \(-0.580057\pi\) | ||||
−0.248863 | + | 0.968539i | \(0.580057\pi\) | |||||||
\(992\) | 157.409 | 4.99773 | ||||||||
\(993\) | 5.42422 | 0.172132 | ||||||||
\(994\) | 72.5059 | 2.29975 | ||||||||
\(995\) | −12.6315 | −0.400446 | ||||||||
\(996\) | 1.27406 | 0.0403700 | ||||||||
\(997\) | 1.25717 | 0.0398150 | 0.0199075 | − | 0.999802i | \(-0.493663\pi\) | ||||
0.0199075 | + | 0.999802i | \(0.493663\pi\) | |||||||
\(998\) | 103.577 | 3.27868 | ||||||||
\(999\) | 30.4478 | 0.963326 |
(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 | 6001.2.a.b.1.3 | ✓ | 114 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.b.1.3 | ✓ | 114 | 1.1 | even | 1 | trivial |