Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.460717 | −0.325776 | −0.162888 | − | 0.986645i | \(-0.552081\pi\) | ||||
−0.162888 | + | 0.986645i | \(0.552081\pi\) | |||||||
\(3\) | 3.13691 | 1.81110 | 0.905548 | − | 0.424245i | \(-0.139460\pi\) | ||||
0.905548 | + | 0.424245i | \(0.139460\pi\) | |||||||
\(4\) | −1.78774 | −0.893870 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.44523 | −0.590011 | ||||||||
\(7\) | 1.56377 | 0.591051 | 0.295525 | − | 0.955335i | \(-0.404505\pi\) | ||||
0.295525 | + | 0.955335i | \(0.404505\pi\) | |||||||
\(8\) | 1.74508 | 0.616977 | ||||||||
\(9\) | 6.84020 | 2.28007 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.23889 | −1.88110 | −0.940548 | − | 0.339661i | \(-0.889688\pi\) | ||||
−0.940548 | + | 0.339661i | \(0.889688\pi\) | |||||||
\(12\) | −5.60798 | −1.61888 | ||||||||
\(13\) | −1.64617 | −0.456566 | −0.228283 | − | 0.973595i | \(-0.573311\pi\) | ||||
−0.228283 | + | 0.973595i | \(0.573311\pi\) | |||||||
\(14\) | −0.720457 | −0.192550 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.77149 | 0.692874 | ||||||||
\(17\) | 5.60674 | 1.35983 | 0.679917 | − | 0.733289i | \(-0.262016\pi\) | ||||
0.679917 | + | 0.733289i | \(0.262016\pi\) | |||||||
\(18\) | −3.15139 | −0.742791 | ||||||||
\(19\) | 3.84868 | 0.882947 | 0.441474 | − | 0.897274i | \(-0.354456\pi\) | ||||
0.441474 | + | 0.897274i | \(0.354456\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.90541 | 1.07045 | ||||||||
\(22\) | 2.87436 | 0.612816 | ||||||||
\(23\) | 1.97859 | 0.412565 | 0.206283 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206283 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(24\) | 5.47414 | 1.11740 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.758419 | 0.148738 | ||||||||
\(27\) | 12.0463 | 2.31832 | ||||||||
\(28\) | −2.79562 | −0.528323 | ||||||||
\(29\) | −3.28774 | −0.610519 | −0.305259 | − | 0.952269i | \(-0.598743\pi\) | ||||
−0.305259 | + | 0.952269i | \(0.598743\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.165861 | 0.0297896 | 0.0148948 | − | 0.999889i | \(-0.495259\pi\) | ||||
0.0148948 | + | 0.999889i | \(0.495259\pi\) | |||||||
\(32\) | −4.76703 | −0.842699 | ||||||||
\(33\) | −19.5708 | −3.40684 | ||||||||
\(34\) | −2.58312 | −0.443001 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −12.2285 | −2.03808 | ||||||||
\(37\) | 0.397154 | 0.0652917 | 0.0326458 | − | 0.999467i | \(-0.489607\pi\) | ||||
0.0326458 | + | 0.999467i | \(0.489607\pi\) | |||||||
\(38\) | −1.77315 | −0.287643 | ||||||||
\(39\) | −5.16389 | −0.826884 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.4703 | 1.79136 | 0.895680 | − | 0.444699i | \(-0.146689\pi\) | ||||
0.895680 | + | 0.444699i | \(0.146689\pi\) | |||||||
\(42\) | −2.26001 | −0.348727 | ||||||||
\(43\) | 0.935446 | 0.142654 | 0.0713271 | − | 0.997453i | \(-0.477277\pi\) | ||||
0.0713271 | + | 0.997453i | \(0.477277\pi\) | |||||||
\(44\) | 11.1535 | 1.68145 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.911571 | −0.134404 | ||||||||
\(47\) | 8.85389 | 1.29147 | 0.645736 | − | 0.763561i | \(-0.276551\pi\) | ||||
0.645736 | + | 0.763561i | \(0.276551\pi\) | |||||||
\(48\) | 8.69392 | 1.25486 | ||||||||
\(49\) | −4.55461 | −0.650659 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 17.5878 | 2.46279 | ||||||||
\(52\) | 2.94293 | 0.408111 | ||||||||
\(53\) | −12.1915 | −1.67463 | −0.837313 | − | 0.546723i | \(-0.815875\pi\) | ||||
−0.837313 | + | 0.546723i | \(0.815875\pi\) | |||||||
\(54\) | −5.54995 | −0.755253 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.72890 | 0.364665 | ||||||||
\(57\) | 12.0729 | 1.59910 | ||||||||
\(58\) | 1.51472 | 0.198892 | ||||||||
\(59\) | −0.836116 | −0.108853 | −0.0544265 | − | 0.998518i | \(-0.517333\pi\) | ||||
−0.0544265 | + | 0.998518i | \(0.517333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.1724 | 1.43047 | 0.715237 | − | 0.698882i | \(-0.246319\pi\) | ||||
0.715237 | + | 0.698882i | \(0.246319\pi\) | |||||||
\(62\) | −0.0764151 | −0.00970473 | ||||||||
\(63\) | 10.6965 | 1.34763 | ||||||||
\(64\) | −3.34674 | −0.418342 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 9.01661 | 1.10987 | ||||||||
\(67\) | −9.21225 | −1.12546 | −0.562728 | − | 0.826642i | \(-0.690248\pi\) | ||||
−0.562728 | + | 0.826642i | \(0.690248\pi\) | |||||||
\(68\) | −10.0234 | −1.21551 | ||||||||
\(69\) | 6.20666 | 0.747194 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.539173 | 0.0639880 | 0.0319940 | − | 0.999488i | \(-0.489814\pi\) | ||||
0.0319940 | + | 0.999488i | \(0.489814\pi\) | |||||||
\(72\) | 11.9367 | 1.40675 | ||||||||
\(73\) | −0.619847 | −0.0725476 | −0.0362738 | − | 0.999342i | \(-0.511549\pi\) | ||||
−0.0362738 | + | 0.999342i | \(0.511549\pi\) | |||||||
\(74\) | −0.182975 | −0.0212705 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.88043 | −0.789240 | ||||||||
\(77\) | −9.75621 | −1.11182 | ||||||||
\(78\) | 2.37909 | 0.269379 | ||||||||
\(79\) | 11.0121 | 1.23895 | 0.619477 | − | 0.785015i | \(-0.287345\pi\) | ||||
0.619477 | + | 0.785015i | \(0.287345\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 17.2677 | 1.91863 | ||||||||
\(82\) | −5.28456 | −0.583582 | ||||||||
\(83\) | −2.18586 | −0.239929 | −0.119965 | − | 0.992778i | \(-0.538278\pi\) | ||||
−0.119965 | + | 0.992778i | \(0.538278\pi\) | |||||||
\(84\) | −8.76961 | −0.956842 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.430976 | −0.0464733 | ||||||||
\(87\) | −10.3134 | −1.10571 | ||||||||
\(88\) | −10.8873 | −1.16059 | ||||||||
\(89\) | 2.25777 | 0.239323 | 0.119662 | − | 0.992815i | \(-0.461819\pi\) | ||||
0.119662 | + | 0.992815i | \(0.461819\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.57424 | −0.269854 | ||||||||
\(92\) | −3.53721 | −0.368779 | ||||||||
\(93\) | 0.520292 | 0.0539518 | ||||||||
\(94\) | −4.07913 | −0.420731 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −14.9537 | −1.52621 | ||||||||
\(97\) | −7.24352 | −0.735468 | −0.367734 | − | 0.929931i | \(-0.619866\pi\) | ||||
−0.367734 | + | 0.929931i | \(0.619866\pi\) | |||||||
\(98\) | 2.09839 | 0.211969 | ||||||||
\(99\) | −42.6752 | −4.28902 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.71147 | −0.269802 | −0.134901 | − | 0.990859i | \(-0.543072\pi\) | ||||
−0.134901 | + | 0.990859i | \(0.543072\pi\) | |||||||
\(102\) | −8.10301 | −0.802317 | ||||||||
\(103\) | 0.177602 | 0.0174996 | 0.00874980 | − | 0.999962i | \(-0.497215\pi\) | ||||
0.00874980 | + | 0.999962i | \(0.497215\pi\) | |||||||
\(104\) | −2.87269 | −0.281691 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.61681 | 0.545553 | ||||||||
\(107\) | 16.3490 | 1.58052 | 0.790258 | − | 0.612774i | \(-0.209947\pi\) | ||||
0.790258 | + | 0.612774i | \(0.209947\pi\) | |||||||
\(108\) | −21.5357 | −2.07228 | ||||||||
\(109\) | 18.3591 | 1.75848 | 0.879242 | − | 0.476376i | \(-0.158050\pi\) | ||||
0.879242 | + | 0.476376i | \(0.158050\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.24584 | 0.118249 | ||||||||
\(112\) | 4.33399 | 0.409523 | ||||||||
\(113\) | 7.57102 | 0.712221 | 0.356111 | − | 0.934444i | \(-0.384103\pi\) | ||||
0.356111 | + | 0.934444i | \(0.384103\pi\) | |||||||
\(114\) | −5.56221 | −0.520949 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.87763 | 0.545724 | ||||||||
\(117\) | −11.2601 | −1.04100 | ||||||||
\(118\) | 0.385213 | 0.0354617 | ||||||||
\(119\) | 8.76767 | 0.803731 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.9237 | 2.53852 | ||||||||
\(122\) | −5.14729 | −0.466014 | ||||||||
\(123\) | 35.9813 | 3.24432 | ||||||||
\(124\) | −0.296517 | −0.0266280 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.92807 | −0.439027 | ||||||||
\(127\) | −7.81978 | −0.693893 | −0.346947 | − | 0.937885i | \(-0.612782\pi\) | ||||
−0.346947 | + | 0.937885i | \(0.612782\pi\) | |||||||
\(128\) | 11.0759 | 0.978985 | ||||||||
\(129\) | 2.93441 | 0.258360 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.96702 | 0.608711 | 0.304356 | − | 0.952558i | \(-0.401559\pi\) | ||||
0.304356 | + | 0.952558i | \(0.401559\pi\) | |||||||
\(132\) | 34.9875 | 3.04527 | ||||||||
\(133\) | 6.01846 | 0.521867 | ||||||||
\(134\) | 4.24424 | 0.366646 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.78418 | 0.838987 | ||||||||
\(137\) | 5.17568 | 0.442188 | 0.221094 | − | 0.975252i | \(-0.429037\pi\) | ||||
0.221094 | + | 0.975252i | \(0.429037\pi\) | |||||||
\(138\) | −2.85951 | −0.243418 | ||||||||
\(139\) | −10.6546 | −0.903714 | −0.451857 | − | 0.892090i | \(-0.649238\pi\) | ||||
−0.451857 | + | 0.892090i | \(0.649238\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 27.7738 | 2.33898 | ||||||||
\(142\) | −0.248406 | −0.0208458 | ||||||||
\(143\) | 10.2703 | 0.858844 | ||||||||
\(144\) | 18.9576 | 1.57980 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.285574 | 0.0236343 | ||||||||
\(147\) | −14.2874 | −1.17841 | ||||||||
\(148\) | −0.710008 | −0.0583623 | ||||||||
\(149\) | 8.67506 | 0.710689 | 0.355344 | − | 0.934735i | \(-0.384364\pi\) | ||||
0.355344 | + | 0.934735i | \(0.384364\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.36349 | 0.436474 | 0.218237 | − | 0.975896i | \(-0.429969\pi\) | ||||
0.218237 | + | 0.975896i | \(0.429969\pi\) | |||||||
\(152\) | 6.71623 | 0.544758 | ||||||||
\(153\) | 38.3512 | 3.10051 | ||||||||
\(154\) | 4.49485 | 0.362205 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 9.23170 | 0.739127 | ||||||||
\(157\) | 19.1465 | 1.52806 | 0.764030 | − | 0.645180i | \(-0.223218\pi\) | ||||
0.764030 | + | 0.645180i | \(0.223218\pi\) | |||||||
\(158\) | −5.07344 | −0.403621 | ||||||||
\(159\) | −38.2435 | −3.03291 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.09407 | 0.243847 | ||||||||
\(162\) | −7.95552 | −0.625045 | ||||||||
\(163\) | 1.64100 | 0.128533 | 0.0642666 | − | 0.997933i | \(-0.479529\pi\) | ||||
0.0642666 | + | 0.997933i | \(0.479529\pi\) | |||||||
\(164\) | −20.5059 | −1.60124 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.00706 | 0.0781632 | ||||||||
\(167\) | 7.75478 | 0.600083 | 0.300041 | − | 0.953926i | \(-0.403000\pi\) | ||||
0.300041 | + | 0.953926i | \(0.403000\pi\) | |||||||
\(168\) | 8.56032 | 0.660443 | ||||||||
\(169\) | −10.2901 | −0.791547 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 26.3257 | 2.01318 | ||||||||
\(172\) | −1.67233 | −0.127514 | ||||||||
\(173\) | −24.0284 | −1.82685 | −0.913423 | − | 0.407013i | \(-0.866571\pi\) | ||||
−0.913423 | + | 0.407013i | \(0.866571\pi\) | |||||||
\(174\) | 4.75153 | 0.360213 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −17.2910 | −1.30336 | ||||||||
\(177\) | −2.62282 | −0.197143 | ||||||||
\(178\) | −1.04019 | −0.0779658 | ||||||||
\(179\) | −1.14342 | −0.0854629 | −0.0427314 | − | 0.999087i | \(-0.513606\pi\) | ||||
−0.0427314 | + | 0.999087i | \(0.513606\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.84022 | 0.434100 | 0.217050 | − | 0.976160i | \(-0.430356\pi\) | ||||
0.217050 | + | 0.976160i | \(0.430356\pi\) | |||||||
\(182\) | 1.18600 | 0.0879118 | ||||||||
\(183\) | 35.0466 | 2.59072 | ||||||||
\(184\) | 3.45279 | 0.254543 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.239707 | −0.0175762 | ||||||||
\(187\) | −34.9798 | −2.55798 | ||||||||
\(188\) | −15.8284 | −1.15441 | ||||||||
\(189\) | 18.8378 | 1.37024 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.6293 | 1.78211 | 0.891057 | − | 0.453891i | \(-0.149964\pi\) | ||||
0.891057 | + | 0.453891i | \(0.149964\pi\) | |||||||
\(192\) | −10.4984 | −0.757658 | ||||||||
\(193\) | −8.15947 | −0.587332 | −0.293666 | − | 0.955908i | \(-0.594875\pi\) | ||||
−0.293666 | + | 0.955908i | \(0.594875\pi\) | |||||||
\(194\) | 3.33721 | 0.239598 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.14246 | 0.581605 | ||||||||
\(197\) | 20.3690 | 1.45123 | 0.725617 | − | 0.688098i | \(-0.241554\pi\) | ||||
0.725617 | + | 0.688098i | \(0.241554\pi\) | |||||||
\(198\) | 19.6612 | 1.39726 | ||||||||
\(199\) | −4.91440 | −0.348372 | −0.174186 | − | 0.984713i | \(-0.555729\pi\) | ||||
−0.174186 | + | 0.984713i | \(0.555729\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −28.8980 | −2.03831 | ||||||||
\(202\) | 1.24922 | 0.0878949 | ||||||||
\(203\) | −5.14129 | −0.360848 | ||||||||
\(204\) | −31.4425 | −2.20141 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.0818241 | −0.00570095 | ||||||||
\(207\) | 13.5340 | 0.940675 | ||||||||
\(208\) | −4.56236 | −0.316343 | ||||||||
\(209\) | −24.0115 | −1.66091 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.5510 | −1.69016 | −0.845082 | − | 0.534637i | \(-0.820448\pi\) | ||||
−0.845082 | + | 0.534637i | \(0.820448\pi\) | |||||||
\(212\) | 21.7952 | 1.49690 | ||||||||
\(213\) | 1.69134 | 0.115888 | ||||||||
\(214\) | −7.53225 | −0.514894 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 21.0218 | 1.43035 | ||||||||
\(217\) | 0.259370 | 0.0176072 | ||||||||
\(218\) | −8.45835 | −0.572872 | ||||||||
\(219\) | −1.94440 | −0.131391 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.22966 | −0.620854 | ||||||||
\(222\) | −0.573977 | −0.0385228 | ||||||||
\(223\) | −7.15892 | −0.479397 | −0.239699 | − | 0.970847i | \(-0.577049\pi\) | ||||
−0.239699 | + | 0.970847i | \(0.577049\pi\) | |||||||
\(224\) | −7.45455 | −0.498078 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.48810 | −0.232025 | ||||||||
\(227\) | 26.1878 | 1.73815 | 0.869073 | − | 0.494683i | \(-0.164716\pi\) | ||||
0.869073 | + | 0.494683i | \(0.164716\pi\) | |||||||
\(228\) | −21.5833 | −1.42939 | ||||||||
\(229\) | 4.52449 | 0.298987 | 0.149494 | − | 0.988763i | \(-0.452236\pi\) | ||||
0.149494 | + | 0.988763i | \(0.452236\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −30.6043 | −2.01362 | ||||||||
\(232\) | −5.73736 | −0.376676 | ||||||||
\(233\) | 21.3515 | 1.39878 | 0.699391 | − | 0.714739i | \(-0.253454\pi\) | ||||
0.699391 | + | 0.714739i | \(0.253454\pi\) | |||||||
\(234\) | 5.18774 | 0.339133 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.49476 | 0.0973004 | ||||||||
\(237\) | 34.5438 | 2.24386 | ||||||||
\(238\) | −4.03941 | −0.261836 | ||||||||
\(239\) | 25.4300 | 1.64493 | 0.822466 | − | 0.568814i | \(-0.192598\pi\) | ||||
0.822466 | + | 0.568814i | \(0.192598\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | −12.8649 | −0.826989 | ||||||||
\(243\) | 18.0282 | 1.15651 | ||||||||
\(244\) | −19.9733 | −1.27866 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −16.5772 | −1.05692 | ||||||||
\(247\) | −6.33558 | −0.403124 | ||||||||
\(248\) | 0.289441 | 0.0183795 | ||||||||
\(249\) | −6.85684 | −0.434535 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.3573 | −1.85302 | −0.926508 | − | 0.376274i | \(-0.877205\pi\) | ||||
−0.926508 | + | 0.376274i | \(0.877205\pi\) | |||||||
\(252\) | −19.1226 | −1.20461 | ||||||||
\(253\) | −12.3442 | −0.776074 | ||||||||
\(254\) | 3.60271 | 0.226054 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.59060 | 0.0994127 | ||||||||
\(257\) | 22.1494 | 1.38164 | 0.690820 | − | 0.723027i | \(-0.257250\pi\) | ||||
0.690820 | + | 0.723027i | \(0.257250\pi\) | |||||||
\(258\) | −1.35193 | −0.0841676 | ||||||||
\(259\) | 0.621059 | 0.0385907 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.4888 | −1.39202 | ||||||||
\(262\) | −3.20982 | −0.198304 | ||||||||
\(263\) | −17.3292 | −1.06856 | −0.534282 | − | 0.845306i | \(-0.679418\pi\) | ||||
−0.534282 | + | 0.845306i | \(0.679418\pi\) | |||||||
\(264\) | −34.1526 | −2.10195 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.77281 | −0.170012 | ||||||||
\(267\) | 7.08242 | 0.433437 | ||||||||
\(268\) | 16.4691 | 1.00601 | ||||||||
\(269\) | −15.9261 | −0.971032 | −0.485516 | − | 0.874228i | \(-0.661368\pi\) | ||||
−0.485516 | + | 0.874228i | \(0.661368\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.3504 | 1.23620 | 0.618099 | − | 0.786100i | \(-0.287903\pi\) | ||||
0.618099 | + | 0.786100i | \(0.287903\pi\) | |||||||
\(272\) | 15.5390 | 0.942193 | ||||||||
\(273\) | −8.07516 | −0.488731 | ||||||||
\(274\) | −2.38452 | −0.144054 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −11.0959 | −0.667895 | ||||||||
\(277\) | −27.6708 | −1.66258 | −0.831289 | − | 0.555841i | \(-0.812396\pi\) | ||||
−0.831289 | + | 0.555841i | \(0.812396\pi\) | |||||||
\(278\) | 4.90877 | 0.294408 | ||||||||
\(279\) | 1.13452 | 0.0679222 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.8732 | −1.18554 | −0.592769 | − | 0.805373i | \(-0.701965\pi\) | ||||
−0.592769 | + | 0.805373i | \(0.701965\pi\) | |||||||
\(282\) | −12.7959 | −0.761983 | ||||||||
\(283\) | 10.4690 | 0.622319 | 0.311160 | − | 0.950358i | \(-0.399283\pi\) | ||||
0.311160 | + | 0.950358i | \(0.399283\pi\) | |||||||
\(284\) | −0.963900 | −0.0571970 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.73169 | −0.279791 | ||||||||
\(287\) | 17.9369 | 1.05878 | ||||||||
\(288\) | −32.6074 | −1.92141 | ||||||||
\(289\) | 14.4355 | 0.849148 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.7223 | −1.33200 | ||||||||
\(292\) | 1.10813 | 0.0648481 | ||||||||
\(293\) | 10.2693 | 0.599940 | 0.299970 | − | 0.953949i | \(-0.403023\pi\) | ||||
0.299970 | + | 0.953949i | \(0.403023\pi\) | |||||||
\(294\) | 6.58245 | 0.383896 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.693063 | 0.0402835 | ||||||||
\(297\) | −75.1558 | −4.36098 | ||||||||
\(298\) | −3.99675 | −0.231525 | ||||||||
\(299\) | −3.25710 | −0.188363 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.46283 | 0.0843158 | ||||||||
\(302\) | −2.47105 | −0.142193 | ||||||||
\(303\) | −8.50564 | −0.488636 | ||||||||
\(304\) | 10.6666 | 0.611771 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −17.6690 | −1.01007 | ||||||||
\(307\) | −18.7089 | −1.06777 | −0.533887 | − | 0.845556i | \(-0.679269\pi\) | ||||
−0.533887 | + | 0.845556i | \(0.679269\pi\) | |||||||
\(308\) | 17.4416 | 0.993825 | ||||||||
\(309\) | 0.557120 | 0.0316935 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.38262 | −0.475335 | −0.237667 | − | 0.971347i | \(-0.576383\pi\) | ||||
−0.237667 | + | 0.971347i | \(0.576383\pi\) | |||||||
\(312\) | −9.01138 | −0.510169 | ||||||||
\(313\) | −11.9859 | −0.677485 | −0.338742 | − | 0.940879i | \(-0.610002\pi\) | ||||
−0.338742 | + | 0.940879i | \(0.610002\pi\) | |||||||
\(314\) | −8.82114 | −0.497806 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.6867 | −1.10746 | ||||||||
\(317\) | 10.6885 | 0.600327 | 0.300163 | − | 0.953888i | \(-0.402959\pi\) | ||||
0.300163 | + | 0.953888i | \(0.402959\pi\) | |||||||
\(318\) | 17.6194 | 0.988049 | ||||||||
\(319\) | 20.5119 | 1.14844 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 51.2853 | 2.86246 | ||||||||
\(322\) | −1.42549 | −0.0794395 | ||||||||
\(323\) | 21.5785 | 1.20066 | ||||||||
\(324\) | −30.8702 | −1.71501 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.756037 | −0.0418730 | ||||||||
\(327\) | 57.5909 | 3.18478 | ||||||||
\(328\) | 20.0165 | 1.10523 | ||||||||
\(329\) | 13.8455 | 0.763325 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.55229 | −0.0853217 | −0.0426608 | − | 0.999090i | \(-0.513583\pi\) | ||||
−0.0426608 | + | 0.999090i | \(0.513583\pi\) | |||||||
\(332\) | 3.90775 | 0.214466 | ||||||||
\(333\) | 2.71661 | 0.148869 | ||||||||
\(334\) | −3.57276 | −0.195493 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 13.5953 | 0.741686 | ||||||||
\(337\) | 32.7770 | 1.78548 | 0.892738 | − | 0.450576i | \(-0.148781\pi\) | ||||
0.892738 | + | 0.450576i | \(0.148781\pi\) | |||||||
\(338\) | 4.74083 | 0.257867 | ||||||||
\(339\) | 23.7496 | 1.28990 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.03479 | −0.0560371 | ||||||||
\(342\) | −12.1287 | −0.655845 | ||||||||
\(343\) | −18.0688 | −0.975623 | ||||||||
\(344\) | 1.63242 | 0.0880144 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.0703 | 0.595142 | ||||||||
\(347\) | −0.133187 | −0.00714987 | −0.00357494 | − | 0.999994i | \(-0.501138\pi\) | ||||
−0.00357494 | + | 0.999994i | \(0.501138\pi\) | |||||||
\(348\) | 18.4376 | 0.988359 | ||||||||
\(349\) | −17.7031 | −0.947623 | −0.473811 | − | 0.880626i | \(-0.657122\pi\) | ||||
−0.473811 | + | 0.880626i | \(0.657122\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.8304 | −1.05847 | ||||||||
\(352\) | 29.7409 | 1.58520 | ||||||||
\(353\) | −36.7532 | −1.95618 | −0.978089 | − | 0.208189i | \(-0.933243\pi\) | ||||
−0.978089 | + | 0.208189i | \(0.933243\pi\) | |||||||
\(354\) | 1.20838 | 0.0642245 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.03631 | −0.213924 | ||||||||
\(357\) | 27.5034 | 1.45563 | ||||||||
\(358\) | 0.526791 | 0.0278417 | ||||||||
\(359\) | 1.20900 | 0.0638087 | 0.0319043 | − | 0.999491i | \(-0.489843\pi\) | ||||
0.0319043 | + | 0.999491i | \(0.489843\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.18769 | −0.220405 | ||||||||
\(362\) | −2.69069 | −0.141420 | ||||||||
\(363\) | 87.5942 | 4.59750 | ||||||||
\(364\) | 4.60207 | 0.241214 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −16.1466 | −0.843995 | ||||||||
\(367\) | 26.4811 | 1.38230 | 0.691151 | − | 0.722710i | \(-0.257104\pi\) | ||||
0.691151 | + | 0.722710i | \(0.257104\pi\) | |||||||
\(368\) | 5.48366 | 0.285855 | ||||||||
\(369\) | 78.4591 | 4.08442 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.0647 | −0.989789 | ||||||||
\(372\) | −0.930147 | −0.0482259 | ||||||||
\(373\) | 1.46114 | 0.0756550 | 0.0378275 | − | 0.999284i | \(-0.487956\pi\) | ||||
0.0378275 | + | 0.999284i | \(0.487956\pi\) | |||||||
\(374\) | 16.1158 | 0.833328 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.4507 | 0.796809 | ||||||||
\(377\) | 5.41219 | 0.278742 | ||||||||
\(378\) | −8.67887 | −0.446393 | ||||||||
\(379\) | −22.8502 | −1.17374 | −0.586868 | − | 0.809683i | \(-0.699639\pi\) | ||||
−0.586868 | + | 0.809683i | \(0.699639\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.5299 | −1.25671 | ||||||||
\(382\) | −11.3471 | −0.580570 | ||||||||
\(383\) | 1.62018 | 0.0827873 | 0.0413936 | − | 0.999143i | \(-0.486820\pi\) | ||||
0.0413936 | + | 0.999143i | \(0.486820\pi\) | |||||||
\(384\) | 34.7442 | 1.77303 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.75921 | 0.191339 | ||||||||
\(387\) | 6.39863 | 0.325261 | ||||||||
\(388\) | 12.9495 | 0.657413 | ||||||||
\(389\) | −26.5358 | −1.34542 | −0.672708 | − | 0.739908i | \(-0.734869\pi\) | ||||
−0.672708 | + | 0.739908i | \(0.734869\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.0934 | 0.561020 | ||||||||
\(392\) | −7.94814 | −0.401442 | ||||||||
\(393\) | 21.8549 | 1.10243 | ||||||||
\(394\) | −9.38436 | −0.472777 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 76.2922 | 3.83383 | ||||||||
\(397\) | 12.4792 | 0.626315 | 0.313157 | − | 0.949701i | \(-0.398613\pi\) | ||||
0.313157 | + | 0.949701i | \(0.398613\pi\) | |||||||
\(398\) | 2.26414 | 0.113491 | ||||||||
\(399\) | 18.8794 | 0.945150 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.3699 | −0.817476 | −0.408738 | − | 0.912652i | \(-0.634031\pi\) | ||||
−0.408738 | + | 0.912652i | \(0.634031\pi\) | |||||||
\(402\) | 13.3138 | 0.664032 | ||||||||
\(403\) | −0.273036 | −0.0136009 | ||||||||
\(404\) | 4.84741 | 0.241167 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.36868 | 0.117555 | ||||||||
\(407\) | −2.47780 | −0.122820 | ||||||||
\(408\) | 30.6921 | 1.51948 | ||||||||
\(409\) | 1.14611 | 0.0566715 | 0.0283357 | − | 0.999598i | \(-0.490979\pi\) | ||||
0.0283357 | + | 0.999598i | \(0.490979\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.2356 | 0.800845 | ||||||||
\(412\) | −0.317506 | −0.0156424 | ||||||||
\(413\) | −1.30750 | −0.0643377 | ||||||||
\(414\) | −6.23532 | −0.306449 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7.84734 | 0.384748 | ||||||||
\(417\) | −33.4226 | −1.63671 | ||||||||
\(418\) | 11.0625 | 0.541084 | ||||||||
\(419\) | 34.6674 | 1.69361 | 0.846807 | − | 0.531901i | \(-0.178522\pi\) | ||||
0.846807 | + | 0.531901i | \(0.178522\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.98107 | 0.145289 | 0.0726443 | − | 0.997358i | \(-0.476856\pi\) | ||||
0.0726443 | + | 0.997358i | \(0.476856\pi\) | |||||||
\(422\) | 11.3111 | 0.550615 | ||||||||
\(423\) | 60.5623 | 2.94464 | ||||||||
\(424\) | −21.2750 | −1.03321 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.779227 | −0.0377537 | ||||||||
\(427\) | 17.4710 | 0.845482 | ||||||||
\(428\) | −29.2277 | −1.41278 | ||||||||
\(429\) | 32.2169 | 1.55545 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.7519 | −0.517898 | −0.258949 | − | 0.965891i | \(-0.583376\pi\) | ||||
−0.258949 | + | 0.965891i | \(0.583376\pi\) | |||||||
\(432\) | 33.3864 | 1.60630 | ||||||||
\(433\) | −28.1073 | −1.35075 | −0.675376 | − | 0.737474i | \(-0.736018\pi\) | ||||
−0.675376 | + | 0.737474i | \(0.736018\pi\) | |||||||
\(434\) | −0.119496 | −0.00573599 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −32.8213 | −1.57186 | ||||||||
\(437\) | 7.61496 | 0.364273 | ||||||||
\(438\) | 0.895819 | 0.0428039 | ||||||||
\(439\) | −19.4634 | −0.928938 | −0.464469 | − | 0.885589i | \(-0.653755\pi\) | ||||
−0.464469 | + | 0.885589i | \(0.653755\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −31.1544 | −1.48355 | ||||||||
\(442\) | 4.25226 | 0.202259 | ||||||||
\(443\) | −13.2766 | −0.630792 | −0.315396 | − | 0.948960i | \(-0.602137\pi\) | ||||
−0.315396 | + | 0.948960i | \(0.602137\pi\) | |||||||
\(444\) | −2.22723 | −0.105700 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.29824 | 0.156176 | ||||||||
\(447\) | 27.2129 | 1.28712 | ||||||||
\(448\) | −5.23354 | −0.247262 | ||||||||
\(449\) | 9.13708 | 0.431206 | 0.215603 | − | 0.976481i | \(-0.430828\pi\) | ||||
0.215603 | + | 0.976481i | \(0.430828\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −71.5619 | −3.36972 | ||||||||
\(452\) | −13.5350 | −0.636633 | ||||||||
\(453\) | 16.8248 | 0.790496 | ||||||||
\(454\) | −12.0652 | −0.566246 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 21.0682 | 0.986609 | ||||||||
\(457\) | −19.9016 | −0.930959 | −0.465479 | − | 0.885059i | \(-0.654118\pi\) | ||||
−0.465479 | + | 0.885059i | \(0.654118\pi\) | |||||||
\(458\) | −2.08451 | −0.0974028 | ||||||||
\(459\) | 67.5407 | 3.15253 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.8467 | 0.598330 | 0.299165 | − | 0.954201i | \(-0.403292\pi\) | ||||
0.299165 | + | 0.954201i | \(0.403292\pi\) | |||||||
\(462\) | 14.0999 | 0.655988 | ||||||||
\(463\) | 14.1128 | 0.655879 | 0.327940 | − | 0.944699i | \(-0.393646\pi\) | ||||
0.327940 | + | 0.944699i | \(0.393646\pi\) | |||||||
\(464\) | −9.11196 | −0.423012 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.83699 | −0.455690 | ||||||||
\(467\) | 12.3901 | 0.573345 | 0.286672 | − | 0.958029i | \(-0.407451\pi\) | ||||
0.286672 | + | 0.958029i | \(0.407451\pi\) | |||||||
\(468\) | 20.1302 | 0.930519 | ||||||||
\(469\) | −14.4059 | −0.665201 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 60.0610 | 2.76746 | ||||||||
\(472\) | −1.45909 | −0.0671598 | ||||||||
\(473\) | −5.83614 | −0.268346 | ||||||||
\(474\) | −15.9149 | −0.730997 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −15.6743 | −0.718431 | ||||||||
\(477\) | −83.3920 | −3.81826 | ||||||||
\(478\) | −11.7160 | −0.535879 | ||||||||
\(479\) | −28.9441 | −1.32249 | −0.661245 | − | 0.750170i | \(-0.729972\pi\) | ||||
−0.661245 | + | 0.750170i | \(0.729972\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.653784 | −0.0298100 | ||||||||
\(482\) | −0.460717 | −0.0209851 | ||||||||
\(483\) | 9.70581 | 0.441630 | ||||||||
\(484\) | −49.9204 | −2.26911 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8.30587 | −0.376762 | ||||||||
\(487\) | 12.8942 | 0.584292 | 0.292146 | − | 0.956374i | \(-0.405631\pi\) | ||||
0.292146 | + | 0.956374i | \(0.405631\pi\) | |||||||
\(488\) | 19.4966 | 0.882570 | ||||||||
\(489\) | 5.14768 | 0.232786 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.9396 | 0.719344 | 0.359672 | − | 0.933079i | \(-0.382889\pi\) | ||||
0.359672 | + | 0.933079i | \(0.382889\pi\) | |||||||
\(492\) | −64.3252 | −2.90000 | ||||||||
\(493\) | −18.4335 | −0.830204 | ||||||||
\(494\) | 2.91891 | 0.131328 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.459684 | 0.0206404 | ||||||||
\(497\) | 0.843144 | 0.0378202 | ||||||||
\(498\) | 3.15906 | 0.141561 | ||||||||
\(499\) | 3.02622 | 0.135472 | 0.0677362 | − | 0.997703i | \(-0.478422\pi\) | ||||
0.0677362 | + | 0.997703i | \(0.478422\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.3260 | 1.08681 | ||||||||
\(502\) | 13.5254 | 0.603668 | ||||||||
\(503\) | 26.4629 | 1.17992 | 0.589961 | − | 0.807432i | \(-0.299143\pi\) | ||||
0.589961 | + | 0.807432i | \(0.299143\pi\) | |||||||
\(504\) | 18.6662 | 0.831460 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.68719 | 0.252826 | ||||||||
\(507\) | −32.2792 | −1.43357 | ||||||||
\(508\) | 13.9797 | 0.620251 | ||||||||
\(509\) | 16.8536 | 0.747024 | 0.373512 | − | 0.927625i | \(-0.378154\pi\) | ||||
0.373512 | + | 0.927625i | \(0.378154\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.969300 | −0.0428793 | ||||||||
\(512\) | −22.8847 | −1.01137 | ||||||||
\(513\) | 46.3625 | 2.04695 | ||||||||
\(514\) | −10.2046 | −0.450105 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.24596 | −0.230940 | ||||||||
\(517\) | −55.2384 | −2.42938 | ||||||||
\(518\) | −0.286132 | −0.0125719 | ||||||||
\(519\) | −75.3749 | −3.30859 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.4237 | −0.938591 | −0.469295 | − | 0.883041i | \(-0.655492\pi\) | ||||
−0.469295 | + | 0.883041i | \(0.655492\pi\) | |||||||
\(522\) | 10.3610 | 0.453488 | ||||||||
\(523\) | 2.10170 | 0.0919007 | 0.0459504 | − | 0.998944i | \(-0.485368\pi\) | ||||
0.0459504 | + | 0.998944i | \(0.485368\pi\) | |||||||
\(524\) | −12.4552 | −0.544109 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.98385 | 0.348112 | ||||||||
\(527\) | 0.929941 | 0.0405089 | ||||||||
\(528\) | −54.2404 | −2.36051 | ||||||||
\(529\) | −19.0852 | −0.829790 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.71920 | −0.248192 | ||||||||
\(532\) | −10.7594 | −0.466481 | ||||||||
\(533\) | −18.8821 | −0.817874 | ||||||||
\(534\) | −3.26299 | −0.141203 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −16.0761 | −0.694381 | ||||||||
\(537\) | −3.58679 | −0.154781 | ||||||||
\(538\) | 7.33742 | 0.316339 | ||||||||
\(539\) | 28.4157 | 1.22395 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.1902 | 1.55594 | 0.777968 | − | 0.628304i | \(-0.216251\pi\) | ||||
0.777968 | + | 0.628304i | \(0.216251\pi\) | |||||||
\(542\) | −9.37577 | −0.402724 | ||||||||
\(543\) | 18.3203 | 0.786197 | ||||||||
\(544\) | −26.7275 | −1.14593 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.72036 | 0.159217 | ||||||||
\(547\) | 4.54148 | 0.194180 | 0.0970898 | − | 0.995276i | \(-0.469047\pi\) | ||||
0.0970898 | + | 0.995276i | \(0.469047\pi\) | |||||||
\(548\) | −9.25277 | −0.395259 | ||||||||
\(549\) | 76.4211 | 3.26157 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.6535 | −0.539056 | ||||||||
\(552\) | 10.8311 | 0.461002 | ||||||||
\(553\) | 17.2204 | 0.732284 | ||||||||
\(554\) | 12.7484 | 0.541628 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.0477 | 0.807803 | ||||||||
\(557\) | −24.9534 | −1.05731 | −0.528654 | − | 0.848837i | \(-0.677303\pi\) | ||||
−0.528654 | + | 0.848837i | \(0.677303\pi\) | |||||||
\(558\) | −0.522695 | −0.0221274 | ||||||||
\(559\) | −1.53990 | −0.0651310 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −109.728 | −4.63274 | ||||||||
\(562\) | 9.15593 | 0.386220 | ||||||||
\(563\) | −32.2026 | −1.35718 | −0.678589 | − | 0.734518i | \(-0.737408\pi\) | ||||
−0.678589 | + | 0.734518i | \(0.737408\pi\) | |||||||
\(564\) | −49.6524 | −2.09074 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.82326 | −0.202737 | ||||||||
\(567\) | 27.0028 | 1.13401 | ||||||||
\(568\) | 0.940897 | 0.0394792 | ||||||||
\(569\) | −36.2971 | −1.52166 | −0.760828 | − | 0.648954i | \(-0.775207\pi\) | ||||
−0.760828 | + | 0.648954i | \(0.775207\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.6923 | 0.740401 | 0.370200 | − | 0.928952i | \(-0.379289\pi\) | ||||
0.370200 | + | 0.928952i | \(0.379289\pi\) | |||||||
\(572\) | −18.3606 | −0.767695 | ||||||||
\(573\) | 77.2599 | 3.22758 | ||||||||
\(574\) | −8.26385 | −0.344927 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −22.8924 | −0.953848 | ||||||||
\(577\) | −2.04206 | −0.0850121 | −0.0425060 | − | 0.999096i | \(-0.513534\pi\) | ||||
−0.0425060 | + | 0.999096i | \(0.513534\pi\) | |||||||
\(578\) | −6.65068 | −0.276632 | ||||||||
\(579\) | −25.5955 | −1.06371 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.41819 | −0.141810 | ||||||||
\(582\) | 10.4685 | 0.433934 | ||||||||
\(583\) | 76.0612 | 3.15013 | ||||||||
\(584\) | −1.08168 | −0.0447602 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.73125 | −0.195446 | ||||||||
\(587\) | −27.7310 | −1.14458 | −0.572291 | − | 0.820050i | \(-0.693945\pi\) | ||||
−0.572291 | + | 0.820050i | \(0.693945\pi\) | |||||||
\(588\) | 25.5422 | 1.05334 | ||||||||
\(589\) | 0.638347 | 0.0263026 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 63.8958 | 2.62832 | ||||||||
\(592\) | 1.10071 | 0.0452389 | ||||||||
\(593\) | 29.7831 | 1.22305 | 0.611524 | − | 0.791226i | \(-0.290557\pi\) | ||||
0.611524 | + | 0.791226i | \(0.290557\pi\) | |||||||
\(594\) | 34.6255 | 1.42070 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.5088 | −0.635263 | ||||||||
\(597\) | −15.4160 | −0.630935 | ||||||||
\(598\) | 1.50060 | 0.0613642 | ||||||||
\(599\) | 20.2828 | 0.828733 | 0.414367 | − | 0.910110i | \(-0.364003\pi\) | ||||
0.414367 | + | 0.910110i | \(0.364003\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.0237662 | 0.000969445 0 | 0.000484722 | − | 1.00000i | \(-0.499846\pi\) | ||||
0.000484722 | 1.00000i | \(0.499846\pi\) | ||||||||
\(602\) | −0.673948 | −0.0274681 | ||||||||
\(603\) | −63.0136 | −2.56611 | ||||||||
\(604\) | −9.58852 | −0.390151 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.91869 | 0.159186 | ||||||||
\(607\) | −26.3346 | −1.06889 | −0.534444 | − | 0.845204i | \(-0.679479\pi\) | ||||
−0.534444 | + | 0.845204i | \(0.679479\pi\) | |||||||
\(608\) | −18.3467 | −0.744059 | ||||||||
\(609\) | −16.1277 | −0.653529 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.5750 | −0.589642 | ||||||||
\(612\) | −68.5620 | −2.77145 | ||||||||
\(613\) | 28.6550 | 1.15737 | 0.578683 | − | 0.815553i | \(-0.303567\pi\) | ||||
0.578683 | + | 0.815553i | \(0.303567\pi\) | |||||||
\(614\) | 8.61951 | 0.347855 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −17.0253 | −0.685970 | ||||||||
\(617\) | −39.0568 | −1.57237 | −0.786183 | − | 0.617994i | \(-0.787946\pi\) | ||||
−0.786183 | + | 0.617994i | \(0.787946\pi\) | |||||||
\(618\) | −0.256675 | −0.0103250 | ||||||||
\(619\) | 31.5865 | 1.26957 | 0.634785 | − | 0.772689i | \(-0.281089\pi\) | ||||
0.634785 | + | 0.772689i | \(0.281089\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 23.8348 | 0.956458 | ||||||||
\(622\) | 3.86201 | 0.154853 | ||||||||
\(623\) | 3.53064 | 0.141452 | ||||||||
\(624\) | −14.3117 | −0.572926 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.52212 | 0.220708 | ||||||||
\(627\) | −75.3218 | −3.00806 | ||||||||
\(628\) | −34.2290 | −1.36589 | ||||||||
\(629\) | 2.22674 | 0.0887858 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.0013 | −1.23414 | −0.617070 | − | 0.786908i | \(-0.711681\pi\) | ||||
−0.617070 | + | 0.786908i | \(0.711681\pi\) | |||||||
\(632\) | 19.2169 | 0.764406 | ||||||||
\(633\) | −77.0144 | −3.06105 | ||||||||
\(634\) | −4.92438 | −0.195572 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 68.3695 | 2.71103 | ||||||||
\(637\) | 7.49768 | 0.297069 | ||||||||
\(638\) | −9.45016 | −0.374135 | ||||||||
\(639\) | 3.68805 | 0.145897 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.0027 | 1.58001 | 0.790006 | − | 0.613099i | \(-0.210077\pi\) | ||||
0.790006 | + | 0.613099i | \(0.210077\pi\) | |||||||
\(642\) | −23.6280 | −0.932522 | ||||||||
\(643\) | 22.3354 | 0.880824 | 0.440412 | − | 0.897796i | \(-0.354832\pi\) | ||||
0.440412 | + | 0.897796i | \(0.354832\pi\) | |||||||
\(644\) | −5.53139 | −0.217967 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.94159 | −0.391147 | ||||||||
\(647\) | 18.8557 | 0.741295 | 0.370647 | − | 0.928774i | \(-0.379136\pi\) | ||||
0.370647 | + | 0.928774i | \(0.379136\pi\) | |||||||
\(648\) | 30.1334 | 1.18375 | ||||||||
\(649\) | 5.21643 | 0.204763 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.813619 | 0.0318882 | ||||||||
\(652\) | −2.93369 | −0.114892 | ||||||||
\(653\) | −35.9274 | −1.40595 | −0.702974 | − | 0.711215i | \(-0.748145\pi\) | ||||
−0.702974 | + | 0.711215i | \(0.748145\pi\) | |||||||
\(654\) | −26.5331 | −1.03753 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 31.7899 | 1.24119 | ||||||||
\(657\) | −4.23987 | −0.165413 | ||||||||
\(658\) | −6.37884 | −0.248673 | ||||||||
\(659\) | 11.5076 | 0.448274 | 0.224137 | − | 0.974558i | \(-0.428044\pi\) | ||||
0.224137 | + | 0.974558i | \(0.428044\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.26981 | 0.0882852 | 0.0441426 | − | 0.999025i | \(-0.485944\pi\) | ||||
0.0441426 | + | 0.999025i | \(0.485944\pi\) | |||||||
\(662\) | 0.715167 | 0.0277957 | ||||||||
\(663\) | −28.9526 | −1.12443 | ||||||||
\(664\) | −3.81449 | −0.148031 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.25159 | −0.0484980 | ||||||||
\(667\) | −6.50510 | −0.251879 | ||||||||
\(668\) | −13.8635 | −0.536396 | ||||||||
\(669\) | −22.4569 | −0.868234 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −69.7031 | −2.69086 | ||||||||
\(672\) | −23.3842 | −0.902066 | ||||||||
\(673\) | −24.3712 | −0.939441 | −0.469720 | − | 0.882815i | \(-0.655645\pi\) | ||||
−0.469720 | + | 0.882815i | \(0.655645\pi\) | |||||||
\(674\) | −15.1009 | −0.581665 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.3961 | 0.707541 | ||||||||
\(677\) | 2.60623 | 0.100166 | 0.0500829 | − | 0.998745i | \(-0.484051\pi\) | ||||
0.0500829 | + | 0.998745i | \(0.484051\pi\) | |||||||
\(678\) | −10.9418 | −0.420219 | ||||||||
\(679\) | −11.3272 | −0.434699 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 82.1488 | 3.14795 | ||||||||
\(682\) | 0.476746 | 0.0182555 | ||||||||
\(683\) | −6.93762 | −0.265461 | −0.132730 | − | 0.991152i | \(-0.542374\pi\) | ||||
−0.132730 | + | 0.991152i | \(0.542374\pi\) | |||||||
\(684\) | −47.0635 | −1.79952 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.32460 | 0.317835 | ||||||||
\(687\) | 14.1929 | 0.541494 | ||||||||
\(688\) | 2.59258 | 0.0988413 | ||||||||
\(689\) | 20.0693 | 0.764578 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.69414 | −0.178574 | −0.0892868 | − | 0.996006i | \(-0.528459\pi\) | ||||
−0.0892868 | + | 0.996006i | \(0.528459\pi\) | |||||||
\(692\) | 42.9565 | 1.63296 | ||||||||
\(693\) | −66.7344 | −2.53503 | ||||||||
\(694\) | 0.0613617 | 0.00232926 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −17.9976 | −0.682196 | ||||||||
\(697\) | 64.3110 | 2.43595 | ||||||||
\(698\) | 8.15610 | 0.308713 | ||||||||
\(699\) | 66.9777 | 2.53333 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.76392 | −0.0666223 | −0.0333112 | − | 0.999445i | \(-0.510605\pi\) | ||||
−0.0333112 | + | 0.999445i | \(0.510605\pi\) | |||||||
\(702\) | 9.13618 | 0.344823 | ||||||||
\(703\) | 1.52852 | 0.0576491 | ||||||||
\(704\) | 20.8799 | 0.786942 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.9328 | 0.637276 | ||||||||
\(707\) | −4.24013 | −0.159466 | ||||||||
\(708\) | 4.68892 | 0.176220 | ||||||||
\(709\) | −26.5409 | −0.996766 | −0.498383 | − | 0.866957i | \(-0.666073\pi\) | ||||
−0.498383 | + | 0.866957i | \(0.666073\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 75.3246 | 2.82489 | ||||||||
\(712\) | 3.93998 | 0.147657 | ||||||||
\(713\) | 0.328172 | 0.0122901 | ||||||||
\(714\) | −12.6713 | −0.474210 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.04413 | 0.0763927 | ||||||||
\(717\) | 79.7717 | 2.97913 | ||||||||
\(718\) | −0.557007 | −0.0207873 | ||||||||
\(719\) | 19.6415 | 0.732503 | 0.366252 | − | 0.930516i | \(-0.380641\pi\) | ||||
0.366252 | + | 0.930516i | \(0.380641\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.277729 | 0.0103432 | ||||||||
\(722\) | 1.92934 | 0.0718025 | ||||||||
\(723\) | 3.13691 | 0.116663 | ||||||||
\(724\) | −10.4408 | −0.388029 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −40.3561 | −1.49776 | ||||||||
\(727\) | 22.6724 | 0.840874 | 0.420437 | − | 0.907322i | \(-0.361877\pi\) | ||||
0.420437 | + | 0.907322i | \(0.361877\pi\) | |||||||
\(728\) | −4.49224 | −0.166494 | ||||||||
\(729\) | 4.74958 | 0.175910 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.24480 | 0.193986 | ||||||||
\(732\) | −62.6543 | −2.31577 | ||||||||
\(733\) | 19.0027 | 0.701881 | 0.350941 | − | 0.936398i | \(-0.385862\pi\) | ||||
0.350941 | + | 0.936398i | \(0.385862\pi\) | |||||||
\(734\) | −12.2003 | −0.450321 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.43200 | −0.347668 | ||||||||
\(737\) | 57.4742 | 2.11709 | ||||||||
\(738\) | −36.1474 | −1.33061 | ||||||||
\(739\) | −0.100236 | −0.00368725 | −0.00184362 | − | 0.999998i | \(-0.500587\pi\) | ||||
−0.00184362 | + | 0.999998i | \(0.500587\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.8742 | −0.730095 | ||||||||
\(742\) | 8.78342 | 0.322450 | ||||||||
\(743\) | 11.6994 | 0.429211 | 0.214606 | − | 0.976701i | \(-0.431153\pi\) | ||||
0.214606 | + | 0.976701i | \(0.431153\pi\) | |||||||
\(744\) | 0.907949 | 0.0332870 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.673172 | −0.0246466 | ||||||||
\(747\) | −14.9517 | −0.547055 | ||||||||
\(748\) | 62.5348 | 2.28650 | ||||||||
\(749\) | 25.5661 | 0.934165 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.8880 | −0.944667 | −0.472334 | − | 0.881420i | \(-0.656588\pi\) | ||||
−0.472334 | + | 0.881420i | \(0.656588\pi\) | |||||||
\(752\) | 24.5385 | 0.894827 | ||||||||
\(753\) | −92.0912 | −3.35599 | ||||||||
\(754\) | −2.49349 | −0.0908075 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −33.6770 | −1.22482 | ||||||||
\(757\) | −31.9067 | −1.15967 | −0.579834 | − | 0.814735i | \(-0.696882\pi\) | ||||
−0.579834 | + | 0.814735i | \(0.696882\pi\) | |||||||
\(758\) | 10.5275 | 0.382375 | ||||||||
\(759\) | −38.7227 | −1.40554 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.1311 | −1.63600 | −0.818000 | − | 0.575218i | \(-0.804917\pi\) | ||||
−0.818000 | + | 0.575218i | \(0.804917\pi\) | |||||||
\(762\) | 11.3014 | 0.409405 | ||||||||
\(763\) | 28.7095 | 1.03935 | ||||||||
\(764\) | −44.0308 | −1.59298 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.746444 | −0.0269701 | ||||||||
\(767\) | 1.37639 | 0.0496986 | ||||||||
\(768\) | 4.98958 | 0.180046 | ||||||||
\(769\) | −0.386985 | −0.0139550 | −0.00697751 | − | 0.999976i | \(-0.502221\pi\) | ||||
−0.00697751 | + | 0.999976i | \(0.502221\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 69.4805 | 2.50228 | ||||||||
\(772\) | 14.5870 | 0.524998 | ||||||||
\(773\) | −33.7397 | −1.21353 | −0.606767 | − | 0.794880i | \(-0.707534\pi\) | ||||
−0.606767 | + | 0.794880i | \(0.707534\pi\) | |||||||
\(774\) | −2.94796 | −0.105962 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12.6405 | −0.453767 | ||||||||
\(777\) | 1.94820 | 0.0698914 | ||||||||
\(778\) | 12.2255 | 0.438304 | ||||||||
\(779\) | 44.1455 | 1.58168 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.36384 | −0.120368 | ||||||||
\(782\) | −5.11094 | −0.182767 | ||||||||
\(783\) | −39.6053 | −1.41538 | ||||||||
\(784\) | −12.6231 | −0.450824 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −10.0689 | −0.359147 | ||||||||
\(787\) | −8.95234 | −0.319116 | −0.159558 | − | 0.987189i | \(-0.551007\pi\) | ||||
−0.159558 | + | 0.987189i | \(0.551007\pi\) | |||||||
\(788\) | −36.4146 | −1.29722 | ||||||||
\(789\) | −54.3601 | −1.93527 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.8394 | 0.420959 | ||||||||
\(792\) | −74.4715 | −2.64623 | ||||||||
\(793\) | −18.3916 | −0.653105 | ||||||||
\(794\) | −5.74939 | −0.204038 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.78566 | 0.311400 | ||||||||
\(797\) | −37.3700 | −1.32371 | −0.661856 | − | 0.749631i | \(-0.730231\pi\) | ||||
−0.661856 | + | 0.749631i | \(0.730231\pi\) | |||||||
\(798\) | −8.69804 | −0.307907 | ||||||||
\(799\) | 49.6414 | 1.75619 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.4436 | 0.545673 | ||||||||
\(802\) | 7.54191 | 0.266314 | ||||||||
\(803\) | 3.86716 | 0.136469 | ||||||||
\(804\) | 51.6621 | 1.82198 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.125792 | 0.00443085 | ||||||||
\(807\) | −49.9587 | −1.75863 | ||||||||
\(808\) | −4.73172 | −0.166461 | ||||||||
\(809\) | −36.3719 | −1.27877 | −0.639385 | − | 0.768887i | \(-0.720811\pi\) | ||||
−0.639385 | + | 0.768887i | \(0.720811\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −53.9078 | −1.89296 | −0.946479 | − | 0.322766i | \(-0.895387\pi\) | ||||
−0.946479 | + | 0.322766i | \(0.895387\pi\) | |||||||
\(812\) | 9.19128 | 0.322551 | ||||||||
\(813\) | 63.8374 | 2.23887 | ||||||||
\(814\) | 1.14156 | 0.0400118 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 48.7446 | 1.70640 | ||||||||
\(817\) | 3.60023 | 0.125956 | ||||||||
\(818\) | −0.528032 | −0.0184622 | ||||||||
\(819\) | −17.6083 | −0.615284 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.76390 | −0.340762 | −0.170381 | − | 0.985378i | \(-0.554500\pi\) | ||||
−0.170381 | + | 0.985378i | \(0.554500\pi\) | |||||||
\(822\) | −7.48003 | −0.260896 | ||||||||
\(823\) | −27.2909 | −0.951301 | −0.475650 | − | 0.879634i | \(-0.657787\pi\) | ||||
−0.475650 | + | 0.879634i | \(0.657787\pi\) | |||||||
\(824\) | 0.309928 | 0.0107969 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.602385 | 0.0209597 | ||||||||
\(827\) | −50.2553 | −1.74755 | −0.873773 | − | 0.486334i | \(-0.838334\pi\) | ||||
−0.873773 | + | 0.486334i | \(0.838334\pi\) | |||||||
\(828\) | −24.1952 | −0.840841 | ||||||||
\(829\) | 46.7978 | 1.62535 | 0.812677 | − | 0.582714i | \(-0.198009\pi\) | ||||
0.812677 | + | 0.582714i | \(0.198009\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −86.8008 | −3.01109 | ||||||||
\(832\) | 5.50931 | 0.191001 | ||||||||
\(833\) | −25.5365 | −0.884788 | ||||||||
\(834\) | 15.3984 | 0.533202 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 42.9263 | 1.48464 | ||||||||
\(837\) | 1.99802 | 0.0690618 | ||||||||
\(838\) | −15.9719 | −0.551739 | ||||||||
\(839\) | −31.0781 | −1.07294 | −0.536468 | − | 0.843921i | \(-0.680242\pi\) | ||||
−0.536468 | + | 0.843921i | \(0.680242\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.1907 | −0.627267 | ||||||||
\(842\) | −1.37343 | −0.0473315 | ||||||||
\(843\) | −62.3405 | −2.14712 | ||||||||
\(844\) | 43.8909 | 1.51079 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −27.9021 | −0.959293 | ||||||||
\(847\) | 43.6664 | 1.50039 | ||||||||
\(848\) | −33.7886 | −1.16030 | ||||||||
\(849\) | 32.8404 | 1.12708 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.785805 | 0.0269371 | ||||||||
\(852\) | −3.02367 | −0.103589 | ||||||||
\(853\) | −13.0908 | −0.448220 | −0.224110 | − | 0.974564i | \(-0.571948\pi\) | ||||
−0.224110 | + | 0.974564i | \(0.571948\pi\) | |||||||
\(854\) | −8.04920 | −0.275438 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 28.5302 | 0.975142 | ||||||||
\(857\) | −10.7419 | −0.366937 | −0.183468 | − | 0.983026i | \(-0.558733\pi\) | ||||
−0.183468 | + | 0.983026i | \(0.558733\pi\) | |||||||
\(858\) | −14.8429 | −0.506728 | ||||||||
\(859\) | 32.5982 | 1.11224 | 0.556119 | − | 0.831103i | \(-0.312290\pi\) | ||||
0.556119 | + | 0.831103i | \(0.312290\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 56.2666 | 1.91756 | ||||||||
\(862\) | 4.95356 | 0.168719 | ||||||||
\(863\) | 32.3524 | 1.10129 | 0.550644 | − | 0.834740i | \(-0.314382\pi\) | ||||
0.550644 | + | 0.834740i | \(0.314382\pi\) | |||||||
\(864\) | −57.4252 | −1.95365 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.9495 | 0.440042 | ||||||||
\(867\) | 45.2829 | 1.53789 | ||||||||
\(868\) | −0.463685 | −0.0157385 | ||||||||
\(869\) | −68.7030 | −2.33059 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.1650 | 0.513845 | ||||||||
\(872\) | 32.0380 | 1.08494 | ||||||||
\(873\) | −49.5471 | −1.67692 | ||||||||
\(874\) | −3.50834 | −0.118671 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.47609 | 0.117446 | ||||||||
\(877\) | −21.9696 | −0.741859 | −0.370930 | − | 0.928661i | \(-0.620961\pi\) | ||||
−0.370930 | + | 0.928661i | \(0.620961\pi\) | |||||||
\(878\) | 8.96712 | 0.302626 | ||||||||
\(879\) | 32.2139 | 1.08655 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.0958 | 1.72146 | 0.860730 | − | 0.509062i | \(-0.170008\pi\) | ||||
0.860730 | + | 0.509062i | \(0.170008\pi\) | |||||||
\(882\) | 14.3534 | 0.483303 | ||||||||
\(883\) | −40.1088 | −1.34977 | −0.674885 | − | 0.737923i | \(-0.735807\pi\) | ||||
−0.674885 | + | 0.737923i | \(0.735807\pi\) | |||||||
\(884\) | 16.5002 | 0.554963 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.11677 | 0.205497 | ||||||||
\(887\) | −8.96502 | −0.301016 | −0.150508 | − | 0.988609i | \(-0.548091\pi\) | ||||
−0.150508 | + | 0.988609i | \(0.548091\pi\) | |||||||
\(888\) | 2.17408 | 0.0729572 | ||||||||
\(889\) | −12.2284 | −0.410126 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −107.731 | −3.60913 | ||||||||
\(892\) | 12.7983 | 0.428519 | ||||||||
\(893\) | 34.0757 | 1.14030 | ||||||||
\(894\) | −12.5374 | −0.419314 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 17.3203 | 0.578630 | ||||||||
\(897\) | −10.2172 | −0.341144 | ||||||||
\(898\) | −4.20961 | −0.140476 | ||||||||
\(899\) | −0.545310 | −0.0181871 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −68.3544 | −2.27721 | ||||||||
\(902\) | 32.9698 | 1.09777 | ||||||||
\(903\) | 4.58875 | 0.152704 | ||||||||
\(904\) | 13.2120 | 0.439425 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7.75145 | −0.257525 | ||||||||
\(907\) | 36.3979 | 1.20857 | 0.604287 | − | 0.796767i | \(-0.293458\pi\) | ||||
0.604287 | + | 0.796767i | \(0.293458\pi\) | |||||||
\(908\) | −46.8170 | −1.55368 | ||||||||
\(909\) | −18.5470 | −0.615165 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.2020 | −0.569928 | −0.284964 | − | 0.958538i | \(-0.591982\pi\) | ||||
−0.284964 | + | 0.958538i | \(0.591982\pi\) | |||||||
\(912\) | 33.4601 | 1.10797 | ||||||||
\(913\) | 13.6373 | 0.451330 | ||||||||
\(914\) | 9.16902 | 0.303284 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.08862 | −0.267256 | ||||||||
\(917\) | 10.8948 | 0.359779 | ||||||||
\(918\) | −31.1171 | −1.02702 | ||||||||
\(919\) | −33.0226 | −1.08931 | −0.544657 | − | 0.838659i | \(-0.683340\pi\) | ||||
−0.544657 | + | 0.838659i | \(0.683340\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −58.6882 | −1.93384 | ||||||||
\(922\) | −5.91868 | −0.194921 | ||||||||
\(923\) | −0.887571 | −0.0292148 | ||||||||
\(924\) | 54.7126 | 1.79991 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6.50202 | −0.213670 | ||||||||
\(927\) | 1.21483 | 0.0399003 | ||||||||
\(928\) | 15.6728 | 0.514483 | ||||||||
\(929\) | 11.9266 | 0.391299 | 0.195650 | − | 0.980674i | \(-0.437318\pi\) | ||||
0.195650 | + | 0.980674i | \(0.437318\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.5292 | −0.574497 | ||||||||
\(932\) | −38.1709 | −1.25033 | ||||||||
\(933\) | −26.2955 | −0.860876 | ||||||||
\(934\) | −5.70832 | −0.186782 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −19.6498 | −0.642274 | ||||||||
\(937\) | 3.61452 | 0.118081 | 0.0590406 | − | 0.998256i | \(-0.481196\pi\) | ||||
0.0590406 | + | 0.998256i | \(0.481196\pi\) | |||||||
\(938\) | 6.63703 | 0.216707 | ||||||||
\(939\) | −37.5988 | −1.22699 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.5409 | 1.38679 | 0.693397 | − | 0.720556i | \(-0.256113\pi\) | ||||
0.693397 | + | 0.720556i | \(0.256113\pi\) | |||||||
\(942\) | −27.6711 | −0.901573 | ||||||||
\(943\) | 22.6950 | 0.739052 | ||||||||
\(944\) | −2.31729 | −0.0754214 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.68881 | 0.0874207 | ||||||||
\(947\) | 27.2502 | 0.885511 | 0.442756 | − | 0.896642i | \(-0.354001\pi\) | ||||
0.442756 | + | 0.896642i | \(0.354001\pi\) | |||||||
\(948\) | −61.7554 | −2.00572 | ||||||||
\(949\) | 1.02037 | 0.0331228 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.5289 | 1.08725 | ||||||||
\(952\) | 15.3002 | 0.495884 | ||||||||
\(953\) | 51.7919 | 1.67770 | 0.838852 | − | 0.544359i | \(-0.183227\pi\) | ||||
0.838852 | + | 0.544359i | \(0.183227\pi\) | |||||||
\(954\) | 38.4201 | 1.24390 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −45.4623 | −1.47036 | ||||||||
\(957\) | 64.3439 | 2.07994 | ||||||||
\(958\) | 13.3350 | 0.430835 | ||||||||
\(959\) | 8.09359 | 0.261356 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9725 | −0.999113 | ||||||||
\(962\) | 0.301209 | 0.00971137 | ||||||||
\(963\) | 111.830 | 3.60368 | ||||||||
\(964\) | −1.78774 | −0.0575792 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.47163 | −0.143872 | ||||||||
\(967\) | 19.5691 | 0.629299 | 0.314650 | − | 0.949208i | \(-0.398113\pi\) | ||||
0.314650 | + | 0.949208i | \(0.398113\pi\) | |||||||
\(968\) | 48.7290 | 1.56621 | ||||||||
\(969\) | 67.6899 | 2.17451 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.00517 | −0.160623 | −0.0803117 | − | 0.996770i | \(-0.525592\pi\) | ||||
−0.0803117 | + | 0.996770i | \(0.525592\pi\) | |||||||
\(972\) | −32.2296 | −1.03377 | ||||||||
\(973\) | −16.6614 | −0.534141 | ||||||||
\(974\) | −5.94058 | −0.190348 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30.9641 | 0.991137 | ||||||||
\(977\) | 42.5568 | 1.36151 | 0.680757 | − | 0.732510i | \(-0.261651\pi\) | ||||
0.680757 | + | 0.732510i | \(0.261651\pi\) | |||||||
\(978\) | −2.37162 | −0.0758361 | ||||||||
\(979\) | −14.0860 | −0.450190 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 125.580 | 4.00946 | ||||||||
\(982\) | −7.34364 | −0.234345 | ||||||||
\(983\) | −29.2524 | −0.933008 | −0.466504 | − | 0.884519i | \(-0.654487\pi\) | ||||
−0.466504 | + | 0.884519i | \(0.654487\pi\) | |||||||
\(984\) | 62.7901 | 2.00167 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8.49263 | 0.270460 | ||||||||
\(987\) | 43.4320 | 1.38245 | ||||||||
\(988\) | 11.3264 | 0.360340 | ||||||||
\(989\) | 1.85087 | 0.0588541 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.7307 | −0.467935 | −0.233967 | − | 0.972244i | \(-0.575171\pi\) | ||||
−0.233967 | + | 0.972244i | \(0.575171\pi\) | |||||||
\(992\) | −0.790666 | −0.0251037 | ||||||||
\(993\) | −4.86940 | −0.154526 | ||||||||
\(994\) | −0.388451 | −0.0123209 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 12.2583 | 0.388418 | ||||||||
\(997\) | −57.7565 | −1.82917 | −0.914584 | − | 0.404396i | \(-0.867482\pi\) | ||||
−0.914584 | + | 0.404396i | \(0.867482\pi\) | |||||||
\(998\) | −1.39423 | −0.0441336 | ||||||||
\(999\) | 4.78425 | 0.151367 |
(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 | 6025.2.a.n.1.15 | yes | 40 | |
5.4 | even | 2 | 6025.2.a.m.1.26 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6025.2.a.m.1.26 | ✓ | 40 | 5.4 | even | 2 | ||
6025.2.a.n.1.15 | yes | 40 | 1.1 | even | 1 | trivial |