Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3703,2,Mod(1,3703)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3703, 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("3703.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3703 = 7 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3703.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: | \(29.5686038685\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.2147108.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 9x^{3} + 17x^{2} + 16x - 27 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 161) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.50216\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3703.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50216 | −1.06219 | −0.531093 | − | 0.847313i | \(-0.678219\pi\) | ||||
−0.531093 | + | 0.847313i | \(0.678219\pi\) | |||||||
\(3\) | −3.04067 | −1.75553 | −0.877766 | − | 0.479090i | \(-0.840967\pi\) | ||||
−0.877766 | + | 0.479090i | \(0.840967\pi\) | |||||||
\(4\) | 0.256481 | 0.128240 | ||||||||
\(5\) | 3.82405 | 1.71017 | 0.855084 | − | 0.518490i | \(-0.173506\pi\) | ||||
0.855084 | + | 0.518490i | \(0.173506\pi\) | |||||||
\(6\) | 4.56757 | 1.86470 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.61904 | 0.925971 | ||||||||
\(9\) | 6.24568 | 2.08189 | ||||||||
\(10\) | −5.74433 | −1.81652 | ||||||||
\(11\) | 0.542019 | 0.163425 | 0.0817124 | − | 0.996656i | \(-0.473961\pi\) | ||||
0.0817124 | + | 0.996656i | \(0.473961\pi\) | |||||||
\(12\) | −0.779873 | −0.225130 | ||||||||
\(13\) | −1.21662 | −0.337430 | −0.168715 | − | 0.985665i | \(-0.553962\pi\) | ||||
−0.168715 | + | 0.985665i | \(0.553962\pi\) | |||||||
\(14\) | 1.50216 | 0.401469 | ||||||||
\(15\) | −11.6277 | −3.00225 | ||||||||
\(16\) | −4.44718 | −1.11179 | ||||||||
\(17\) | 3.66299 | 0.888405 | 0.444203 | − | 0.895926i | \(-0.353487\pi\) | ||||
0.444203 | + | 0.895926i | \(0.353487\pi\) | |||||||
\(18\) | −9.38200 | −2.21136 | ||||||||
\(19\) | −5.00432 | −1.14807 | −0.574035 | − | 0.818831i | \(-0.694622\pi\) | ||||
−0.574035 | + | 0.818831i | \(0.694622\pi\) | |||||||
\(20\) | 0.980794 | 0.219312 | ||||||||
\(21\) | 3.04067 | 0.663529 | ||||||||
\(22\) | −0.814198 | −0.173588 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | −7.96365 | −1.62557 | ||||||||
\(25\) | 9.62336 | 1.92467 | ||||||||
\(26\) | 1.82756 | 0.358413 | ||||||||
\(27\) | −9.86904 | −1.89930 | ||||||||
\(28\) | −0.256481 | −0.0484703 | ||||||||
\(29\) | 3.72840 | 0.692346 | 0.346173 | − | 0.938171i | \(-0.387481\pi\) | ||||
0.346173 | + | 0.938171i | \(0.387481\pi\) | |||||||
\(30\) | 17.4666 | 3.18895 | ||||||||
\(31\) | 9.04067 | 1.62375 | 0.811876 | − | 0.583830i | \(-0.198446\pi\) | ||||
0.811876 | + | 0.583830i | \(0.198446\pi\) | |||||||
\(32\) | 1.44228 | 0.254962 | ||||||||
\(33\) | −1.64810 | −0.286897 | ||||||||
\(34\) | −5.50239 | −0.943652 | ||||||||
\(35\) | −3.82405 | −0.646382 | ||||||||
\(36\) | 1.60189 | 0.266982 | ||||||||
\(37\) | 9.08566 | 1.49367 | 0.746837 | − | 0.665008i | \(-0.231572\pi\) | ||||
0.746837 | + | 0.665008i | \(0.231572\pi\) | |||||||
\(38\) | 7.51728 | 1.21946 | ||||||||
\(39\) | 3.69934 | 0.592369 | ||||||||
\(40\) | 10.0154 | 1.58357 | ||||||||
\(41\) | −4.86472 | −0.759742 | −0.379871 | − | 0.925040i | \(-0.624032\pi\) | ||||
−0.379871 | + | 0.925040i | \(0.624032\pi\) | |||||||
\(42\) | −4.56757 | −0.704791 | ||||||||
\(43\) | −3.64810 | −0.556330 | −0.278165 | − | 0.960533i | \(-0.589726\pi\) | ||||
−0.278165 | + | 0.960533i | \(0.589726\pi\) | |||||||
\(44\) | 0.139017 | 0.0209576 | ||||||||
\(45\) | 23.8838 | 3.56038 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.6393 | 1.55190 | 0.775950 | − | 0.630794i | \(-0.217271\pi\) | ||||
0.775950 | + | 0.630794i | \(0.217271\pi\) | |||||||
\(48\) | 13.5224 | 1.95179 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −14.4558 | −2.04436 | ||||||||
\(51\) | −11.1379 | −1.55962 | ||||||||
\(52\) | −0.312039 | −0.0432721 | ||||||||
\(53\) | −7.48704 | −1.02842 | −0.514212 | − | 0.857663i | \(-0.671916\pi\) | ||||
−0.514212 | + | 0.857663i | \(0.671916\pi\) | |||||||
\(54\) | 14.8249 | 2.01741 | ||||||||
\(55\) | 2.07271 | 0.279484 | ||||||||
\(56\) | −2.61904 | −0.349984 | ||||||||
\(57\) | 15.2165 | 2.01547 | ||||||||
\(58\) | −5.60065 | −0.735401 | ||||||||
\(59\) | 5.18027 | 0.674413 | 0.337207 | − | 0.941431i | \(-0.390518\pi\) | ||||
0.337207 | + | 0.941431i | \(0.390518\pi\) | |||||||
\(60\) | −2.98227 | −0.385010 | ||||||||
\(61\) | −3.26161 | −0.417606 | −0.208803 | − | 0.977958i | \(-0.566957\pi\) | ||||
−0.208803 | + | 0.977958i | \(0.566957\pi\) | |||||||
\(62\) | −13.5805 | −1.72473 | ||||||||
\(63\) | −6.24568 | −0.786881 | ||||||||
\(64\) | 6.72782 | 0.840978 | ||||||||
\(65\) | −4.65242 | −0.577061 | ||||||||
\(66\) | 2.47571 | 0.304739 | ||||||||
\(67\) | 12.0377 | 1.47064 | 0.735319 | − | 0.677721i | \(-0.237032\pi\) | ||||
0.735319 | + | 0.677721i | \(0.237032\pi\) | |||||||
\(68\) | 0.939485 | 0.113929 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.74433 | 0.686579 | ||||||||
\(71\) | −5.29796 | −0.628752 | −0.314376 | − | 0.949298i | \(-0.601795\pi\) | ||||
−0.314376 | + | 0.949298i | \(0.601795\pi\) | |||||||
\(72\) | 16.3577 | 1.92777 | ||||||||
\(73\) | 8.19070 | 0.958649 | 0.479324 | − | 0.877638i | \(-0.340882\pi\) | ||||
0.479324 | + | 0.877638i | \(0.340882\pi\) | |||||||
\(74\) | −13.6481 | −1.58656 | ||||||||
\(75\) | −29.2615 | −3.37882 | ||||||||
\(76\) | −1.28351 | −0.147229 | ||||||||
\(77\) | −0.542019 | −0.0617688 | ||||||||
\(78\) | −5.55700 | −0.629206 | ||||||||
\(79\) | −10.0291 | −1.12836 | −0.564179 | − | 0.825653i | \(-0.690807\pi\) | ||||
−0.564179 | + | 0.825653i | \(0.690807\pi\) | |||||||
\(80\) | −17.0062 | −1.90135 | ||||||||
\(81\) | 11.2715 | 1.25238 | ||||||||
\(82\) | 7.30758 | 0.806987 | ||||||||
\(83\) | −7.64810 | −0.839488 | −0.419744 | − | 0.907643i | \(-0.637880\pi\) | ||||
−0.419744 | + | 0.907643i | \(0.637880\pi\) | |||||||
\(84\) | 0.779873 | 0.0850911 | ||||||||
\(85\) | 14.0075 | 1.51932 | ||||||||
\(86\) | 5.48003 | 0.590926 | ||||||||
\(87\) | −11.3368 | −1.21544 | ||||||||
\(88\) | 1.41957 | 0.151327 | ||||||||
\(89\) | 4.74703 | 0.503184 | 0.251592 | − | 0.967833i | \(-0.419046\pi\) | ||||
0.251592 | + | 0.967833i | \(0.419046\pi\) | |||||||
\(90\) | −35.8772 | −3.78179 | ||||||||
\(91\) | 1.21662 | 0.127536 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −27.4897 | −2.85055 | ||||||||
\(94\) | −15.9819 | −1.64841 | ||||||||
\(95\) | −19.1368 | −1.96339 | ||||||||
\(96\) | −4.38551 | −0.447594 | ||||||||
\(97\) | 10.9894 | 1.11581 | 0.557904 | − | 0.829906i | \(-0.311606\pi\) | ||||
0.557904 | + | 0.829906i | \(0.311606\pi\) | |||||||
\(98\) | −1.50216 | −0.151741 | ||||||||
\(99\) | 3.38527 | 0.340233 | ||||||||
\(100\) | 2.46820 | 0.246820 | ||||||||
\(101\) | 3.59862 | 0.358076 | 0.179038 | − | 0.983842i | \(-0.442701\pi\) | ||||
0.179038 | + | 0.983842i | \(0.442701\pi\) | |||||||
\(102\) | 16.7310 | 1.65661 | ||||||||
\(103\) | −9.48704 | −0.934786 | −0.467393 | − | 0.884050i | \(-0.654807\pi\) | ||||
−0.467393 | + | 0.884050i | \(0.654807\pi\) | |||||||
\(104\) | −3.18638 | −0.312450 | ||||||||
\(105\) | 11.6277 | 1.13475 | ||||||||
\(106\) | 11.2467 | 1.09238 | ||||||||
\(107\) | −6.60294 | −0.638330 | −0.319165 | − | 0.947699i | \(-0.603402\pi\) | ||||
−0.319165 | + | 0.947699i | \(0.603402\pi\) | |||||||
\(108\) | −2.53122 | −0.243566 | ||||||||
\(109\) | −1.10726 | −0.106057 | −0.0530283 | − | 0.998593i | \(-0.516887\pi\) | ||||
−0.0530283 | + | 0.998593i | \(0.516887\pi\) | |||||||
\(110\) | −3.11353 | −0.296864 | ||||||||
\(111\) | −27.6265 | −2.62219 | ||||||||
\(112\) | 4.44718 | 0.420219 | ||||||||
\(113\) | −0.433241 | −0.0407559 | −0.0203779 | − | 0.999792i | \(-0.506487\pi\) | ||||
−0.0203779 | + | 0.999792i | \(0.506487\pi\) | |||||||
\(114\) | −22.8576 | −2.14081 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.956262 | 0.0887867 | ||||||||
\(117\) | −7.59862 | −0.702493 | ||||||||
\(118\) | −7.78158 | −0.716353 | ||||||||
\(119\) | −3.66299 | −0.335786 | ||||||||
\(120\) | −30.4534 | −2.78000 | ||||||||
\(121\) | −10.7062 | −0.973292 | ||||||||
\(122\) | 4.89945 | 0.443576 | ||||||||
\(123\) | 14.7920 | 1.33375 | ||||||||
\(124\) | 2.31876 | 0.208230 | ||||||||
\(125\) | 17.6800 | 1.58134 | ||||||||
\(126\) | 9.38200 | 0.835815 | ||||||||
\(127\) | 8.84149 | 0.784556 | 0.392278 | − | 0.919847i | \(-0.371687\pi\) | ||||
0.392278 | + | 0.919847i | \(0.371687\pi\) | |||||||
\(128\) | −12.9908 | −1.14824 | ||||||||
\(129\) | 11.0927 | 0.976655 | ||||||||
\(130\) | 6.98867 | 0.612947 | ||||||||
\(131\) | −2.54931 | −0.222735 | −0.111367 | − | 0.993779i | \(-0.535523\pi\) | ||||
−0.111367 | + | 0.993779i | \(0.535523\pi\) | |||||||
\(132\) | −0.422706 | −0.0367918 | ||||||||
\(133\) | 5.00432 | 0.433929 | ||||||||
\(134\) | −18.0825 | −1.56209 | ||||||||
\(135\) | −37.7397 | −3.24812 | ||||||||
\(136\) | 9.59352 | 0.822638 | ||||||||
\(137\) | −13.6265 | −1.16419 | −0.582095 | − | 0.813121i | \(-0.697767\pi\) | ||||
−0.582095 | + | 0.813121i | \(0.697767\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.0466 | −1.53069 | −0.765347 | − | 0.643618i | \(-0.777432\pi\) | ||||
−0.765347 | + | 0.643618i | \(0.777432\pi\) | |||||||
\(140\) | −0.980794 | −0.0828923 | ||||||||
\(141\) | −32.3506 | −2.72441 | ||||||||
\(142\) | 7.95838 | 0.667852 | ||||||||
\(143\) | −0.659431 | −0.0551444 | ||||||||
\(144\) | −27.7756 | −2.31464 | ||||||||
\(145\) | 14.2576 | 1.18403 | ||||||||
\(146\) | −12.3037 | −1.01826 | ||||||||
\(147\) | −3.04067 | −0.250790 | ||||||||
\(148\) | 2.33029 | 0.191549 | ||||||||
\(149\) | −13.8178 | −1.13200 | −0.565999 | − | 0.824406i | \(-0.691509\pi\) | ||||
−0.565999 | + | 0.824406i | \(0.691509\pi\) | |||||||
\(150\) | 43.9554 | 3.58894 | ||||||||
\(151\) | 16.1412 | 1.31355 | 0.656777 | − | 0.754085i | \(-0.271919\pi\) | ||||
0.656777 | + | 0.754085i | \(0.271919\pi\) | |||||||
\(152\) | −13.1065 | −1.06308 | ||||||||
\(153\) | 22.8778 | 1.84956 | ||||||||
\(154\) | 0.814198 | 0.0656100 | ||||||||
\(155\) | 34.5720 | 2.77689 | ||||||||
\(156\) | 0.948809 | 0.0759655 | ||||||||
\(157\) | 15.3111 | 1.22196 | 0.610979 | − | 0.791647i | \(-0.290776\pi\) | ||||
0.610979 | + | 0.791647i | \(0.290776\pi\) | |||||||
\(158\) | 15.0652 | 1.19853 | ||||||||
\(159\) | 22.7656 | 1.80543 | ||||||||
\(160\) | 5.51536 | 0.436028 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −16.9315 | −1.33027 | ||||||||
\(163\) | −3.94876 | −0.309291 | −0.154645 | − | 0.987970i | \(-0.549423\pi\) | ||||
−0.154645 | + | 0.987970i | \(0.549423\pi\) | |||||||
\(164\) | −1.24771 | −0.0974295 | ||||||||
\(165\) | −6.30242 | −0.490643 | ||||||||
\(166\) | 11.4887 | 0.891693 | ||||||||
\(167\) | 1.87752 | 0.145287 | 0.0726433 | − | 0.997358i | \(-0.476857\pi\) | ||||
0.0726433 | + | 0.997358i | \(0.476857\pi\) | |||||||
\(168\) | 7.96365 | 0.614409 | ||||||||
\(169\) | −11.5198 | −0.886141 | ||||||||
\(170\) | −21.0414 | −1.61380 | ||||||||
\(171\) | −31.2554 | −2.39016 | ||||||||
\(172\) | −0.935667 | −0.0713439 | ||||||||
\(173\) | 10.9246 | 0.830582 | 0.415291 | − | 0.909689i | \(-0.363680\pi\) | ||||
0.415291 | + | 0.909689i | \(0.363680\pi\) | |||||||
\(174\) | 17.0297 | 1.29102 | ||||||||
\(175\) | −9.62336 | −0.727458 | ||||||||
\(176\) | −2.41045 | −0.181695 | ||||||||
\(177\) | −15.7515 | −1.18395 | ||||||||
\(178\) | −7.13079 | −0.534475 | ||||||||
\(179\) | 4.74253 | 0.354474 | 0.177237 | − | 0.984168i | \(-0.443284\pi\) | ||||
0.177237 | + | 0.984168i | \(0.443284\pi\) | |||||||
\(180\) | 6.12573 | 0.456585 | ||||||||
\(181\) | −2.82837 | −0.210231 | −0.105115 | − | 0.994460i | \(-0.533521\pi\) | ||||
−0.105115 | + | 0.994460i | \(0.533521\pi\) | |||||||
\(182\) | −1.82756 | −0.135468 | ||||||||
\(183\) | 9.91748 | 0.733121 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 34.7440 | 2.55443 | ||||||||
\(186\) | 41.2939 | 3.02782 | ||||||||
\(187\) | 1.98541 | 0.145187 | ||||||||
\(188\) | 2.72877 | 0.199016 | ||||||||
\(189\) | 9.86904 | 0.717867 | ||||||||
\(190\) | 28.7464 | 2.08549 | ||||||||
\(191\) | 3.56838 | 0.258199 | 0.129099 | − | 0.991632i | \(-0.458791\pi\) | ||||
0.129099 | + | 0.991632i | \(0.458791\pi\) | |||||||
\(192\) | −20.4571 | −1.47636 | ||||||||
\(193\) | 20.9158 | 1.50555 | 0.752777 | − | 0.658276i | \(-0.228714\pi\) | ||||
0.752777 | + | 0.658276i | \(0.228714\pi\) | |||||||
\(194\) | −16.5079 | −1.18520 | ||||||||
\(195\) | 14.1465 | 1.01305 | ||||||||
\(196\) | 0.256481 | 0.0183200 | ||||||||
\(197\) | 5.54576 | 0.395119 | 0.197559 | − | 0.980291i | \(-0.436698\pi\) | ||||
0.197559 | + | 0.980291i | \(0.436698\pi\) | |||||||
\(198\) | −5.08522 | −0.361391 | ||||||||
\(199\) | 7.73808 | 0.548538 | 0.274269 | − | 0.961653i | \(-0.411564\pi\) | ||||
0.274269 | + | 0.961653i | \(0.411564\pi\) | |||||||
\(200\) | 25.2040 | 1.78219 | ||||||||
\(201\) | −36.6027 | −2.58175 | ||||||||
\(202\) | −5.40570 | −0.380344 | ||||||||
\(203\) | −3.72840 | −0.261682 | ||||||||
\(204\) | −2.85667 | −0.200007 | ||||||||
\(205\) | −18.6029 | −1.29929 | ||||||||
\(206\) | 14.2510 | 0.992917 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.41053 | 0.375153 | ||||||||
\(209\) | −2.71243 | −0.187623 | ||||||||
\(210\) | −17.4666 | −1.20531 | ||||||||
\(211\) | 9.43918 | 0.649820 | 0.324910 | − | 0.945745i | \(-0.394666\pi\) | ||||
0.324910 | + | 0.945745i | \(0.394666\pi\) | |||||||
\(212\) | −1.92028 | −0.131885 | ||||||||
\(213\) | 16.1094 | 1.10379 | ||||||||
\(214\) | 9.91866 | 0.678026 | ||||||||
\(215\) | −13.9505 | −0.951418 | ||||||||
\(216\) | −25.8474 | −1.75870 | ||||||||
\(217\) | −9.04067 | −0.613721 | ||||||||
\(218\) | 1.66329 | 0.112652 | ||||||||
\(219\) | −24.9052 | −1.68294 | ||||||||
\(220\) | 0.531609 | 0.0358411 | ||||||||
\(221\) | −4.45647 | −0.299774 | ||||||||
\(222\) | 41.4994 | 2.78526 | ||||||||
\(223\) | 11.1010 | 0.743379 | 0.371689 | − | 0.928357i | \(-0.378779\pi\) | ||||
0.371689 | + | 0.928357i | \(0.378779\pi\) | |||||||
\(224\) | −1.44228 | −0.0963665 | ||||||||
\(225\) | 60.1044 | 4.00696 | ||||||||
\(226\) | 0.650797 | 0.0432903 | ||||||||
\(227\) | −20.9827 | −1.39267 | −0.696336 | − | 0.717716i | \(-0.745188\pi\) | ||||
−0.696336 | + | 0.717716i | \(0.745188\pi\) | |||||||
\(228\) | 3.90273 | 0.258465 | ||||||||
\(229\) | −4.63545 | −0.306319 | −0.153159 | − | 0.988201i | \(-0.548945\pi\) | ||||
−0.153159 | + | 0.988201i | \(0.548945\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.64810 | 0.108437 | ||||||||
\(232\) | 9.76484 | 0.641093 | ||||||||
\(233\) | 16.1703 | 1.05935 | 0.529675 | − | 0.848201i | \(-0.322314\pi\) | ||||
0.529675 | + | 0.848201i | \(0.322314\pi\) | |||||||
\(234\) | 11.4143 | 0.746178 | ||||||||
\(235\) | 40.6852 | 2.65401 | ||||||||
\(236\) | 1.32864 | 0.0864869 | ||||||||
\(237\) | 30.4951 | 1.98087 | ||||||||
\(238\) | 5.50239 | 0.356667 | ||||||||
\(239\) | 1.26610 | 0.0818973 | 0.0409486 | − | 0.999161i | \(-0.486962\pi\) | ||||
0.0409486 | + | 0.999161i | \(0.486962\pi\) | |||||||
\(240\) | 51.7104 | 3.33789 | ||||||||
\(241\) | 2.09623 | 0.135030 | 0.0675150 | − | 0.997718i | \(-0.478493\pi\) | ||||
0.0675150 | + | 0.997718i | \(0.478493\pi\) | |||||||
\(242\) | 16.0824 | 1.03382 | ||||||||
\(243\) | −4.66568 | −0.299304 | ||||||||
\(244\) | −0.836539 | −0.0535539 | ||||||||
\(245\) | 3.82405 | 0.244310 | ||||||||
\(246\) | −22.2200 | −1.41669 | ||||||||
\(247\) | 6.08835 | 0.387393 | ||||||||
\(248\) | 23.6779 | 1.50355 | ||||||||
\(249\) | 23.2554 | 1.47375 | ||||||||
\(250\) | −26.5581 | −1.67968 | ||||||||
\(251\) | −11.5365 | −0.728179 | −0.364089 | − | 0.931364i | \(-0.618620\pi\) | ||||
−0.364089 | + | 0.931364i | \(0.618620\pi\) | |||||||
\(252\) | −1.60189 | −0.100910 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −13.2813 | −0.833345 | ||||||||
\(255\) | −42.5921 | −2.66722 | ||||||||
\(256\) | 6.05863 | 0.378664 | ||||||||
\(257\) | 14.6546 | 0.914131 | 0.457066 | − | 0.889433i | \(-0.348900\pi\) | ||||
0.457066 | + | 0.889433i | \(0.348900\pi\) | |||||||
\(258\) | −16.6630 | −1.03739 | ||||||||
\(259\) | −9.08566 | −0.564555 | ||||||||
\(260\) | −1.19325 | −0.0740025 | ||||||||
\(261\) | 23.2864 | 1.44139 | ||||||||
\(262\) | 3.82947 | 0.236586 | ||||||||
\(263\) | 22.7133 | 1.40056 | 0.700282 | − | 0.713866i | \(-0.253058\pi\) | ||||
0.700282 | + | 0.713866i | \(0.253058\pi\) | |||||||
\(264\) | −4.31645 | −0.265659 | ||||||||
\(265\) | −28.6308 | −1.75878 | ||||||||
\(266\) | −7.51728 | −0.460914 | ||||||||
\(267\) | −14.4341 | −0.883355 | ||||||||
\(268\) | 3.08743 | 0.188595 | ||||||||
\(269\) | 25.0855 | 1.52949 | 0.764746 | − | 0.644332i | \(-0.222865\pi\) | ||||
0.764746 | + | 0.644332i | \(0.222865\pi\) | |||||||
\(270\) | 56.6910 | 3.45011 | ||||||||
\(271\) | −28.0232 | −1.70229 | −0.851145 | − | 0.524930i | \(-0.824091\pi\) | ||||
−0.851145 | + | 0.524930i | \(0.824091\pi\) | |||||||
\(272\) | −16.2900 | −0.987724 | ||||||||
\(273\) | −3.69934 | −0.223894 | ||||||||
\(274\) | 20.4692 | 1.23659 | ||||||||
\(275\) | 5.21604 | 0.314539 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.2692 | −0.977524 | −0.488762 | − | 0.872417i | \(-0.662551\pi\) | ||||
−0.488762 | + | 0.872417i | \(0.662551\pi\) | |||||||
\(278\) | 27.1089 | 1.62588 | ||||||||
\(279\) | 56.4651 | 3.38048 | ||||||||
\(280\) | −10.0154 | −0.598532 | ||||||||
\(281\) | 13.4694 | 0.803518 | 0.401759 | − | 0.915745i | \(-0.368399\pi\) | ||||
0.401759 | + | 0.915745i | \(0.368399\pi\) | |||||||
\(282\) | 48.5957 | 2.89383 | ||||||||
\(283\) | −18.0516 | −1.07305 | −0.536527 | − | 0.843883i | \(-0.680264\pi\) | ||||
−0.536527 | + | 0.843883i | \(0.680264\pi\) | |||||||
\(284\) | −1.35882 | −0.0806314 | ||||||||
\(285\) | 58.1886 | 3.44679 | ||||||||
\(286\) | 0.990570 | 0.0585736 | ||||||||
\(287\) | 4.86472 | 0.287155 | ||||||||
\(288\) | 9.00803 | 0.530803 | ||||||||
\(289\) | −3.58251 | −0.210736 | ||||||||
\(290\) | −21.4172 | −1.25766 | ||||||||
\(291\) | −33.4152 | −1.95884 | ||||||||
\(292\) | 2.10075 | 0.122937 | ||||||||
\(293\) | −23.1521 | −1.35256 | −0.676280 | − | 0.736644i | \(-0.736409\pi\) | ||||
−0.676280 | + | 0.736644i | \(0.736409\pi\) | |||||||
\(294\) | 4.56757 | 0.266386 | ||||||||
\(295\) | 19.8096 | 1.15336 | ||||||||
\(296\) | 23.7957 | 1.38310 | ||||||||
\(297\) | −5.34920 | −0.310392 | ||||||||
\(298\) | 20.7565 | 1.20239 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −7.50500 | −0.433301 | ||||||||
\(301\) | 3.64810 | 0.210273 | ||||||||
\(302\) | −24.2467 | −1.39524 | ||||||||
\(303\) | −10.9422 | −0.628614 | ||||||||
\(304\) | 22.2551 | 1.27642 | ||||||||
\(305\) | −12.4726 | −0.714176 | ||||||||
\(306\) | −34.3662 | −1.96458 | ||||||||
\(307\) | −1.14301 | −0.0652353 | −0.0326176 | − | 0.999468i | \(-0.510384\pi\) | ||||
−0.0326176 | + | 0.999468i | \(0.510384\pi\) | |||||||
\(308\) | −0.139017 | −0.00792124 | ||||||||
\(309\) | 28.8470 | 1.64105 | ||||||||
\(310\) | −51.9326 | −2.94957 | ||||||||
\(311\) | −19.3196 | −1.09551 | −0.547757 | − | 0.836638i | \(-0.684518\pi\) | ||||
−0.547757 | + | 0.836638i | \(0.684518\pi\) | |||||||
\(312\) | 9.68874 | 0.548517 | ||||||||
\(313\) | 17.4140 | 0.984299 | 0.492150 | − | 0.870511i | \(-0.336211\pi\) | ||||
0.492150 | + | 0.870511i | \(0.336211\pi\) | |||||||
\(314\) | −22.9997 | −1.29795 | ||||||||
\(315\) | −23.8838 | −1.34570 | ||||||||
\(316\) | −2.57226 | −0.144701 | ||||||||
\(317\) | 1.42612 | 0.0800989 | 0.0400495 | − | 0.999198i | \(-0.487248\pi\) | ||||
0.0400495 | + | 0.999198i | \(0.487248\pi\) | |||||||
\(318\) | −34.1976 | −1.91770 | ||||||||
\(319\) | 2.02086 | 0.113147 | ||||||||
\(320\) | 25.7275 | 1.43821 | ||||||||
\(321\) | 20.0774 | 1.12061 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.3308 | −1.01995 | ||||||||
\(324\) | 2.89091 | 0.160606 | ||||||||
\(325\) | −11.7080 | −0.649442 | ||||||||
\(326\) | 5.93166 | 0.328524 | ||||||||
\(327\) | 3.36682 | 0.186186 | ||||||||
\(328\) | −12.7409 | −0.703499 | ||||||||
\(329\) | −10.6393 | −0.586563 | ||||||||
\(330\) | 9.46723 | 0.521154 | ||||||||
\(331\) | 3.91690 | 0.215292 | 0.107646 | − | 0.994189i | \(-0.465669\pi\) | ||||
0.107646 | + | 0.994189i | \(0.465669\pi\) | |||||||
\(332\) | −1.96159 | −0.107656 | ||||||||
\(333\) | 56.7461 | 3.10967 | ||||||||
\(334\) | −2.82033 | −0.154321 | ||||||||
\(335\) | 46.0327 | 2.51504 | ||||||||
\(336\) | −13.5224 | −0.737708 | ||||||||
\(337\) | −7.73646 | −0.421432 | −0.210716 | − | 0.977547i | \(-0.567579\pi\) | ||||
−0.210716 | + | 0.977547i | \(0.567579\pi\) | |||||||
\(338\) | 17.3046 | 0.941247 | ||||||||
\(339\) | 1.31734 | 0.0715482 | ||||||||
\(340\) | 3.59264 | 0.194838 | ||||||||
\(341\) | 4.90021 | 0.265361 | ||||||||
\(342\) | 46.9505 | 2.53879 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −9.55453 | −0.515146 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.4105 | −0.882233 | ||||||||
\(347\) | −32.0316 | −1.71955 | −0.859773 | − | 0.510677i | \(-0.829395\pi\) | ||||
−0.859773 | + | 0.510677i | \(0.829395\pi\) | |||||||
\(348\) | −2.90768 | −0.155868 | ||||||||
\(349\) | 29.0447 | 1.55473 | 0.777363 | − | 0.629052i | \(-0.216557\pi\) | ||||
0.777363 | + | 0.629052i | \(0.216557\pi\) | |||||||
\(350\) | 14.4558 | 0.772696 | ||||||||
\(351\) | 12.0069 | 0.640880 | ||||||||
\(352\) | 0.781744 | 0.0416671 | ||||||||
\(353\) | 14.1412 | 0.752661 | 0.376331 | − | 0.926485i | \(-0.377186\pi\) | ||||
0.376331 | + | 0.926485i | \(0.377186\pi\) | |||||||
\(354\) | 23.6612 | 1.25758 | ||||||||
\(355\) | −20.2597 | −1.07527 | ||||||||
\(356\) | 1.21752 | 0.0645284 | ||||||||
\(357\) | 11.1379 | 0.589482 | ||||||||
\(358\) | −7.12404 | −0.376517 | ||||||||
\(359\) | −7.25851 | −0.383089 | −0.191545 | − | 0.981484i | \(-0.561350\pi\) | ||||
−0.191545 | + | 0.981484i | \(0.561350\pi\) | |||||||
\(360\) | 62.5527 | 3.29681 | ||||||||
\(361\) | 6.04319 | 0.318063 | ||||||||
\(362\) | 4.24866 | 0.223304 | ||||||||
\(363\) | 32.5541 | 1.70865 | ||||||||
\(364\) | 0.312039 | 0.0163553 | ||||||||
\(365\) | 31.3216 | 1.63945 | ||||||||
\(366\) | −14.8976 | −0.778711 | ||||||||
\(367\) | 15.7667 | 0.823015 | 0.411507 | − | 0.911406i | \(-0.365002\pi\) | ||||
0.411507 | + | 0.911406i | \(0.365002\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −30.3835 | −1.58170 | ||||||||
\(370\) | −52.1910 | −2.71328 | ||||||||
\(371\) | 7.48704 | 0.388708 | ||||||||
\(372\) | −7.05057 | −0.365555 | ||||||||
\(373\) | −4.16807 | −0.215815 | −0.107907 | − | 0.994161i | \(-0.534415\pi\) | ||||
−0.107907 | + | 0.994161i | \(0.534415\pi\) | |||||||
\(374\) | −2.98240 | −0.154216 | ||||||||
\(375\) | −53.7589 | −2.77610 | ||||||||
\(376\) | 27.8648 | 1.43702 | ||||||||
\(377\) | −4.53605 | −0.233618 | ||||||||
\(378\) | −14.8249 | −0.762509 | ||||||||
\(379\) | −18.6572 | −0.958356 | −0.479178 | − | 0.877718i | \(-0.659065\pi\) | ||||
−0.479178 | + | 0.877718i | \(0.659065\pi\) | |||||||
\(380\) | −4.90821 | −0.251786 | ||||||||
\(381\) | −26.8841 | −1.37731 | ||||||||
\(382\) | −5.36027 | −0.274255 | ||||||||
\(383\) | 30.2829 | 1.54738 | 0.773692 | − | 0.633562i | \(-0.218408\pi\) | ||||
0.773692 | + | 0.633562i | \(0.218408\pi\) | |||||||
\(384\) | 39.5008 | 2.01577 | ||||||||
\(385\) | −2.07271 | −0.105635 | ||||||||
\(386\) | −31.4189 | −1.59918 | ||||||||
\(387\) | −22.7849 | −1.15822 | ||||||||
\(388\) | 2.81857 | 0.143091 | ||||||||
\(389\) | 14.0727 | 0.713515 | 0.356757 | − | 0.934197i | \(-0.383882\pi\) | ||||
0.356757 | + | 0.934197i | \(0.383882\pi\) | |||||||
\(390\) | −21.2502 | −1.07605 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 2.61904 | 0.132282 | ||||||||
\(393\) | 7.75163 | 0.391018 | ||||||||
\(394\) | −8.33061 | −0.419690 | ||||||||
\(395\) | −38.3516 | −1.92968 | ||||||||
\(396\) | 0.868257 | 0.0436316 | ||||||||
\(397\) | 30.2423 | 1.51782 | 0.758908 | − | 0.651198i | \(-0.225733\pi\) | ||||
0.758908 | + | 0.651198i | \(0.225733\pi\) | |||||||
\(398\) | −11.6238 | −0.582649 | ||||||||
\(399\) | −15.2165 | −0.761777 | ||||||||
\(400\) | −42.7968 | −2.13984 | ||||||||
\(401\) | 0.668630 | 0.0333898 | 0.0166949 | − | 0.999861i | \(-0.494686\pi\) | ||||
0.0166949 | + | 0.999861i | \(0.494686\pi\) | |||||||
\(402\) | 54.9830 | 2.74230 | ||||||||
\(403\) | −10.9991 | −0.547902 | ||||||||
\(404\) | 0.922976 | 0.0459198 | ||||||||
\(405\) | 43.1026 | 2.14179 | ||||||||
\(406\) | 5.60065 | 0.277955 | ||||||||
\(407\) | 4.92460 | 0.244103 | ||||||||
\(408\) | −29.1707 | −1.44417 | ||||||||
\(409\) | −9.05602 | −0.447791 | −0.223896 | − | 0.974613i | \(-0.571878\pi\) | ||||
−0.223896 | + | 0.974613i | \(0.571878\pi\) | |||||||
\(410\) | 27.9446 | 1.38008 | ||||||||
\(411\) | 41.4337 | 2.04377 | ||||||||
\(412\) | −2.43324 | −0.119877 | ||||||||
\(413\) | −5.18027 | −0.254904 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −29.2467 | −1.43567 | ||||||||
\(416\) | −1.75471 | −0.0860318 | ||||||||
\(417\) | 54.8738 | 2.68718 | ||||||||
\(418\) | 4.07451 | 0.199291 | ||||||||
\(419\) | 19.9592 | 0.975068 | 0.487534 | − | 0.873104i | \(-0.337896\pi\) | ||||
0.487534 | + | 0.873104i | \(0.337896\pi\) | |||||||
\(420\) | 2.98227 | 0.145520 | ||||||||
\(421\) | 6.86296 | 0.334480 | 0.167240 | − | 0.985916i | \(-0.446514\pi\) | ||||
0.167240 | + | 0.985916i | \(0.446514\pi\) | |||||||
\(422\) | −14.1791 | −0.690230 | ||||||||
\(423\) | 66.4496 | 3.23089 | ||||||||
\(424\) | −19.6089 | −0.952291 | ||||||||
\(425\) | 35.2503 | 1.70989 | ||||||||
\(426\) | −24.1988 | −1.17244 | ||||||||
\(427\) | 3.26161 | 0.157840 | ||||||||
\(428\) | −1.69352 | −0.0818596 | ||||||||
\(429\) | 2.00511 | 0.0968078 | ||||||||
\(430\) | 20.9559 | 1.01058 | ||||||||
\(431\) | −4.52160 | −0.217798 | −0.108899 | − | 0.994053i | \(-0.534732\pi\) | ||||
−0.108899 | + | 0.994053i | \(0.534732\pi\) | |||||||
\(432\) | 43.8894 | 2.11163 | ||||||||
\(433\) | −14.5170 | −0.697641 | −0.348820 | − | 0.937190i | \(-0.613418\pi\) | ||||
−0.348820 | + | 0.937190i | \(0.613418\pi\) | |||||||
\(434\) | 13.5805 | 0.651886 | ||||||||
\(435\) | −43.3526 | −2.07860 | ||||||||
\(436\) | −0.283992 | −0.0136007 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 37.4116 | 1.78759 | ||||||||
\(439\) | 25.5058 | 1.21732 | 0.608662 | − | 0.793430i | \(-0.291707\pi\) | ||||
0.608662 | + | 0.793430i | \(0.291707\pi\) | |||||||
\(440\) | 5.42851 | 0.258794 | ||||||||
\(441\) | 6.24568 | 0.297413 | ||||||||
\(442\) | 6.69432 | 0.318416 | ||||||||
\(443\) | 13.9434 | 0.662469 | 0.331235 | − | 0.943548i | \(-0.392535\pi\) | ||||
0.331235 | + | 0.943548i | \(0.392535\pi\) | |||||||
\(444\) | −7.08566 | −0.336270 | ||||||||
\(445\) | 18.1529 | 0.860528 | ||||||||
\(446\) | −16.6755 | −0.789607 | ||||||||
\(447\) | 42.0154 | 1.98726 | ||||||||
\(448\) | −6.72782 | −0.317860 | ||||||||
\(449\) | −22.5307 | −1.06329 | −0.531644 | − | 0.846968i | \(-0.678426\pi\) | ||||
−0.531644 | + | 0.846968i | \(0.678426\pi\) | |||||||
\(450\) | −90.2864 | −4.25614 | ||||||||
\(451\) | −2.63677 | −0.124161 | ||||||||
\(452\) | −0.111118 | −0.00522654 | ||||||||
\(453\) | −49.0801 | −2.30599 | ||||||||
\(454\) | 31.5194 | 1.47928 | ||||||||
\(455\) | 4.65242 | 0.218109 | ||||||||
\(456\) | 39.8526 | 1.86627 | ||||||||
\(457\) | 12.9589 | 0.606191 | 0.303096 | − | 0.952960i | \(-0.401980\pi\) | ||||
0.303096 | + | 0.952960i | \(0.401980\pi\) | |||||||
\(458\) | 6.96317 | 0.325368 | ||||||||
\(459\) | −36.1502 | −1.68735 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.9315 | 0.695428 | 0.347714 | − | 0.937601i | \(-0.386958\pi\) | ||||
0.347714 | + | 0.937601i | \(0.386958\pi\) | |||||||
\(462\) | −2.47571 | −0.115180 | ||||||||
\(463\) | 17.4941 | 0.813018 | 0.406509 | − | 0.913647i | \(-0.366746\pi\) | ||||
0.406509 | + | 0.913647i | \(0.366746\pi\) | |||||||
\(464\) | −16.5809 | −0.769747 | ||||||||
\(465\) | −105.122 | −4.87492 | ||||||||
\(466\) | −24.2903 | −1.12523 | ||||||||
\(467\) | 17.6281 | 0.815732 | 0.407866 | − | 0.913042i | \(-0.366273\pi\) | ||||
0.407866 | + | 0.913042i | \(0.366273\pi\) | |||||||
\(468\) | −1.94890 | −0.0900878 | ||||||||
\(469\) | −12.0377 | −0.555849 | ||||||||
\(470\) | −61.1156 | −2.81905 | ||||||||
\(471\) | −46.5560 | −2.14519 | ||||||||
\(472\) | 13.5673 | 0.624487 | ||||||||
\(473\) | −1.97734 | −0.0909181 | ||||||||
\(474\) | −45.8084 | −2.10405 | ||||||||
\(475\) | −48.1583 | −2.20966 | ||||||||
\(476\) | −0.939485 | −0.0430612 | ||||||||
\(477\) | −46.7616 | −2.14107 | ||||||||
\(478\) | −1.90188 | −0.0869902 | ||||||||
\(479\) | 11.7457 | 0.536673 | 0.268336 | − | 0.963325i | \(-0.413526\pi\) | ||||
0.268336 | + | 0.963325i | \(0.413526\pi\) | |||||||
\(480\) | −16.7704 | −0.765460 | ||||||||
\(481\) | −11.0538 | −0.504010 | ||||||||
\(482\) | −3.14887 | −0.143427 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.74594 | −0.124815 | ||||||||
\(485\) | 42.0241 | 1.90822 | ||||||||
\(486\) | 7.00860 | 0.317916 | ||||||||
\(487\) | 22.9380 | 1.03942 | 0.519710 | − | 0.854342i | \(-0.326040\pi\) | ||||
0.519710 | + | 0.854342i | \(0.326040\pi\) | |||||||
\(488\) | −8.54229 | −0.386691 | ||||||||
\(489\) | 12.0069 | 0.542970 | ||||||||
\(490\) | −5.74433 | −0.259502 | ||||||||
\(491\) | 11.5682 | 0.522067 | 0.261034 | − | 0.965330i | \(-0.415937\pi\) | ||||
0.261034 | + | 0.965330i | \(0.415937\pi\) | |||||||
\(492\) | 3.79386 | 0.171041 | ||||||||
\(493\) | 13.6571 | 0.615084 | ||||||||
\(494\) | −9.14567 | −0.411483 | ||||||||
\(495\) | 12.9455 | 0.581855 | ||||||||
\(496\) | −40.2055 | −1.80528 | ||||||||
\(497\) | 5.29796 | 0.237646 | ||||||||
\(498\) | −34.9332 | −1.56540 | ||||||||
\(499\) | 25.0063 | 1.11943 | 0.559717 | − | 0.828684i | \(-0.310910\pi\) | ||||
0.559717 | + | 0.828684i | \(0.310910\pi\) | |||||||
\(500\) | 4.53457 | 0.202792 | ||||||||
\(501\) | −5.70891 | −0.255055 | ||||||||
\(502\) | 17.3297 | 0.773462 | ||||||||
\(503\) | −16.1238 | −0.718925 | −0.359463 | − | 0.933160i | \(-0.617040\pi\) | ||||
−0.359463 | + | 0.933160i | \(0.617040\pi\) | |||||||
\(504\) | −16.3577 | −0.728630 | ||||||||
\(505\) | 13.7613 | 0.612370 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 35.0280 | 1.55565 | ||||||||
\(508\) | 2.26767 | 0.100612 | ||||||||
\(509\) | −1.46604 | −0.0649809 | −0.0324905 | − | 0.999472i | \(-0.510344\pi\) | ||||
−0.0324905 | + | 0.999472i | \(0.510344\pi\) | |||||||
\(510\) | 63.9800 | 2.83308 | ||||||||
\(511\) | −8.19070 | −0.362335 | ||||||||
\(512\) | 16.8806 | 0.746025 | ||||||||
\(513\) | 49.3878 | 2.18052 | ||||||||
\(514\) | −22.0136 | −0.970978 | ||||||||
\(515\) | −36.2789 | −1.59864 | ||||||||
\(516\) | 2.84505 | 0.125247 | ||||||||
\(517\) | 5.76669 | 0.253619 | ||||||||
\(518\) | 13.6481 | 0.599663 | ||||||||
\(519\) | −33.2181 | −1.45811 | ||||||||
\(520\) | −12.1849 | −0.534342 | ||||||||
\(521\) | 31.1921 | 1.36655 | 0.683276 | − | 0.730160i | \(-0.260554\pi\) | ||||
0.683276 | + | 0.730160i | \(0.260554\pi\) | |||||||
\(522\) | −34.9798 | −1.53103 | ||||||||
\(523\) | 25.0064 | 1.09345 | 0.546727 | − | 0.837311i | \(-0.315874\pi\) | ||||
0.546727 | + | 0.837311i | \(0.315874\pi\) | |||||||
\(524\) | −0.653850 | −0.0285636 | ||||||||
\(525\) | 29.2615 | 1.27708 | ||||||||
\(526\) | −34.1190 | −1.48766 | ||||||||
\(527\) | 33.1159 | 1.44255 | ||||||||
\(528\) | 7.32940 | 0.318971 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 43.0080 | 1.86815 | ||||||||
\(531\) | 32.3543 | 1.40406 | ||||||||
\(532\) | 1.28351 | 0.0556472 | ||||||||
\(533\) | 5.91852 | 0.256360 | ||||||||
\(534\) | 21.6824 | 0.938288 | ||||||||
\(535\) | −25.2500 | −1.09165 | ||||||||
\(536\) | 31.5272 | 1.36177 | ||||||||
\(537\) | −14.4205 | −0.622290 | ||||||||
\(538\) | −37.6824 | −1.62460 | ||||||||
\(539\) | 0.542019 | 0.0233464 | ||||||||
\(540\) | −9.67950 | −0.416539 | ||||||||
\(541\) | −29.8577 | −1.28368 | −0.641842 | − | 0.766837i | \(-0.721829\pi\) | ||||
−0.641842 | + | 0.766837i | \(0.721829\pi\) | |||||||
\(542\) | 42.0954 | 1.80815 | ||||||||
\(543\) | 8.60013 | 0.369067 | ||||||||
\(544\) | 5.28306 | 0.226510 | ||||||||
\(545\) | −4.23423 | −0.181375 | ||||||||
\(546\) | 5.55700 | 0.237818 | ||||||||
\(547\) | 29.1669 | 1.24708 | 0.623542 | − | 0.781789i | \(-0.285693\pi\) | ||||
0.623542 | + | 0.781789i | \(0.285693\pi\) | |||||||
\(548\) | −3.49493 | −0.149296 | ||||||||
\(549\) | −20.3710 | −0.869411 | ||||||||
\(550\) | −7.83532 | −0.334099 | ||||||||
\(551\) | −18.6581 | −0.794862 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.0291 | 0.426479 | ||||||||
\(554\) | 24.4390 | 1.03831 | ||||||||
\(555\) | −105.645 | −4.48439 | ||||||||
\(556\) | −4.62860 | −0.196297 | ||||||||
\(557\) | −40.2543 | −1.70563 | −0.852814 | − | 0.522214i | \(-0.825106\pi\) | ||||
−0.852814 | + | 0.522214i | \(0.825106\pi\) | |||||||
\(558\) | −84.8196 | −3.59070 | ||||||||
\(559\) | 4.43835 | 0.187722 | ||||||||
\(560\) | 17.0062 | 0.718645 | ||||||||
\(561\) | −6.03697 | −0.254881 | ||||||||
\(562\) | −20.2332 | −0.853486 | ||||||||
\(563\) | 22.5130 | 0.948808 | 0.474404 | − | 0.880307i | \(-0.342664\pi\) | ||||
0.474404 | + | 0.880307i | \(0.342664\pi\) | |||||||
\(564\) | −8.29729 | −0.349379 | ||||||||
\(565\) | −1.65673 | −0.0696994 | ||||||||
\(566\) | 27.1163 | 1.13978 | ||||||||
\(567\) | −11.2715 | −0.473357 | ||||||||
\(568\) | −13.8756 | −0.582207 | ||||||||
\(569\) | −6.81862 | −0.285852 | −0.142926 | − | 0.989733i | \(-0.545651\pi\) | ||||
−0.142926 | + | 0.989733i | \(0.545651\pi\) | |||||||
\(570\) | −87.4085 | −3.66114 | ||||||||
\(571\) | 0.873495 | 0.0365546 | 0.0182773 | − | 0.999833i | \(-0.494182\pi\) | ||||
0.0182773 | + | 0.999833i | \(0.494182\pi\) | |||||||
\(572\) | −0.169131 | −0.00707173 | ||||||||
\(573\) | −10.8503 | −0.453276 | ||||||||
\(574\) | −7.30758 | −0.305013 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 42.0198 | 1.75083 | ||||||||
\(577\) | −16.4150 | −0.683366 | −0.341683 | − | 0.939815i | \(-0.610997\pi\) | ||||
−0.341683 | + | 0.939815i | \(0.610997\pi\) | |||||||
\(578\) | 5.38150 | 0.223841 | ||||||||
\(579\) | −63.5981 | −2.64305 | ||||||||
\(580\) | 3.65679 | 0.151840 | ||||||||
\(581\) | 7.64810 | 0.317297 | ||||||||
\(582\) | 50.1950 | 2.08065 | ||||||||
\(583\) | −4.05812 | −0.168070 | ||||||||
\(584\) | 21.4518 | 0.887681 | ||||||||
\(585\) | −29.0575 | −1.20138 | ||||||||
\(586\) | 34.7781 | 1.43667 | ||||||||
\(587\) | −9.97331 | −0.411643 | −0.205821 | − | 0.978590i | \(-0.565987\pi\) | ||||
−0.205821 | + | 0.978590i | \(0.565987\pi\) | |||||||
\(588\) | −0.779873 | −0.0321614 | ||||||||
\(589\) | −45.2424 | −1.86418 | ||||||||
\(590\) | −29.7572 | −1.22508 | ||||||||
\(591\) | −16.8628 | −0.693644 | ||||||||
\(592\) | −40.4055 | −1.66066 | ||||||||
\(593\) | −20.5516 | −0.843951 | −0.421976 | − | 0.906607i | \(-0.638663\pi\) | ||||
−0.421976 | + | 0.906607i | \(0.638663\pi\) | |||||||
\(594\) | 8.03535 | 0.329694 | ||||||||
\(595\) | −14.0075 | −0.574250 | ||||||||
\(596\) | −3.54400 | −0.145168 | ||||||||
\(597\) | −23.5289 | −0.962975 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.5468 | 0.635224 | 0.317612 | − | 0.948221i | \(-0.397119\pi\) | ||||
0.317612 | + | 0.948221i | \(0.397119\pi\) | |||||||
\(600\) | −76.6370 | −3.12869 | ||||||||
\(601\) | −29.3814 | −1.19849 | −0.599246 | − | 0.800565i | \(-0.704533\pi\) | ||||
−0.599246 | + | 0.800565i | \(0.704533\pi\) | |||||||
\(602\) | −5.48003 | −0.223349 | ||||||||
\(603\) | 75.1836 | 3.06171 | ||||||||
\(604\) | 4.13991 | 0.168450 | ||||||||
\(605\) | −40.9411 | −1.66449 | ||||||||
\(606\) | 16.4369 | 0.667705 | ||||||||
\(607\) | 31.1108 | 1.26275 | 0.631374 | − | 0.775478i | \(-0.282491\pi\) | ||||
0.631374 | + | 0.775478i | \(0.282491\pi\) | |||||||
\(608\) | −7.21764 | −0.292714 | ||||||||
\(609\) | 11.3368 | 0.459392 | ||||||||
\(610\) | 18.7358 | 0.758589 | ||||||||
\(611\) | −12.9440 | −0.523657 | ||||||||
\(612\) | 5.86772 | 0.237189 | ||||||||
\(613\) | 27.7365 | 1.12026 | 0.560132 | − | 0.828403i | \(-0.310750\pi\) | ||||
0.560132 | + | 0.828403i | \(0.310750\pi\) | |||||||
\(614\) | 1.71699 | 0.0692920 | ||||||||
\(615\) | 56.5654 | 2.28094 | ||||||||
\(616\) | −1.41957 | −0.0571961 | ||||||||
\(617\) | 20.6041 | 0.829490 | 0.414745 | − | 0.909938i | \(-0.363871\pi\) | ||||
0.414745 | + | 0.909938i | \(0.363871\pi\) | |||||||
\(618\) | −43.3327 | −1.74310 | ||||||||
\(619\) | 9.83894 | 0.395460 | 0.197730 | − | 0.980256i | \(-0.436643\pi\) | ||||
0.197730 | + | 0.980256i | \(0.436643\pi\) | |||||||
\(620\) | 8.86704 | 0.356109 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 29.0211 | 1.16364 | ||||||||
\(623\) | −4.74703 | −0.190186 | ||||||||
\(624\) | −16.4516 | −0.658593 | ||||||||
\(625\) | 19.4923 | 0.779690 | ||||||||
\(626\) | −26.1586 | −1.04551 | ||||||||
\(627\) | 8.24762 | 0.329378 | ||||||||
\(628\) | 3.92700 | 0.156704 | ||||||||
\(629\) | 33.2807 | 1.32699 | ||||||||
\(630\) | 35.8772 | 1.42938 | ||||||||
\(631\) | −2.65314 | −0.105620 | −0.0528098 | − | 0.998605i | \(-0.516818\pi\) | ||||
−0.0528098 | + | 0.998605i | \(0.516818\pi\) | |||||||
\(632\) | −26.2665 | −1.04483 | ||||||||
\(633\) | −28.7014 | −1.14078 | ||||||||
\(634\) | −2.14226 | −0.0850800 | ||||||||
\(635\) | 33.8103 | 1.34172 | ||||||||
\(636\) | 5.83894 | 0.231529 | ||||||||
\(637\) | −1.21662 | −0.0482043 | ||||||||
\(638\) | −3.03566 | −0.120183 | ||||||||
\(639\) | −33.0894 | −1.30899 | ||||||||
\(640\) | −49.6775 | −1.96368 | ||||||||
\(641\) | 46.9550 | 1.85461 | 0.927306 | − | 0.374304i | \(-0.122118\pi\) | ||||
0.927306 | + | 0.374304i | \(0.122118\pi\) | |||||||
\(642\) | −30.1594 | −1.19030 | ||||||||
\(643\) | 8.01924 | 0.316248 | 0.158124 | − | 0.987419i | \(-0.449455\pi\) | ||||
0.158124 | + | 0.987419i | \(0.449455\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 42.4189 | 1.67024 | ||||||||
\(646\) | 27.5357 | 1.08338 | ||||||||
\(647\) | 20.3950 | 0.801810 | 0.400905 | − | 0.916120i | \(-0.368696\pi\) | ||||
0.400905 | + | 0.916120i | \(0.368696\pi\) | |||||||
\(648\) | 29.5204 | 1.15967 | ||||||||
\(649\) | 2.80780 | 0.110216 | ||||||||
\(650\) | 17.5872 | 0.689828 | ||||||||
\(651\) | 27.4897 | 1.07741 | ||||||||
\(652\) | −1.01278 | −0.0396635 | ||||||||
\(653\) | −30.9134 | −1.20973 | −0.604867 | − | 0.796326i | \(-0.706774\pi\) | ||||
−0.604867 | + | 0.796326i | \(0.706774\pi\) | |||||||
\(654\) | −5.05750 | −0.197764 | ||||||||
\(655\) | −9.74871 | −0.380913 | ||||||||
\(656\) | 21.6343 | 0.844677 | ||||||||
\(657\) | 51.1565 | 1.99580 | ||||||||
\(658\) | 15.9819 | 0.623039 | ||||||||
\(659\) | −8.74476 | −0.340647 | −0.170324 | − | 0.985388i | \(-0.554481\pi\) | ||||
−0.170324 | + | 0.985388i | \(0.554481\pi\) | |||||||
\(660\) | −1.61645 | −0.0629201 | ||||||||
\(661\) | −36.1030 | −1.40424 | −0.702121 | − | 0.712057i | \(-0.747764\pi\) | ||||
−0.702121 | + | 0.712057i | \(0.747764\pi\) | |||||||
\(662\) | −5.88380 | −0.228680 | ||||||||
\(663\) | 13.5506 | 0.526264 | ||||||||
\(664\) | −20.0307 | −0.777342 | ||||||||
\(665\) | 19.1368 | 0.742092 | ||||||||
\(666\) | −85.2416 | −3.30305 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0.481546 | 0.0186316 | ||||||||
\(669\) | −33.7545 | −1.30502 | ||||||||
\(670\) | −69.1485 | −2.67144 | ||||||||
\(671\) | −1.76785 | −0.0682472 | ||||||||
\(672\) | 4.38551 | 0.169175 | ||||||||
\(673\) | −37.5762 | −1.44845 | −0.724227 | − | 0.689561i | \(-0.757803\pi\) | ||||
−0.724227 | + | 0.689561i | \(0.757803\pi\) | |||||||
\(674\) | 11.6214 | 0.447639 | ||||||||
\(675\) | −94.9733 | −3.65552 | ||||||||
\(676\) | −2.95461 | −0.113639 | ||||||||
\(677\) | 21.5389 | 0.827807 | 0.413904 | − | 0.910321i | \(-0.364165\pi\) | ||||
0.413904 | + | 0.910321i | \(0.364165\pi\) | |||||||
\(678\) | −1.97886 | −0.0759976 | ||||||||
\(679\) | −10.9894 | −0.421736 | ||||||||
\(680\) | 36.6861 | 1.40685 | ||||||||
\(681\) | 63.8015 | 2.44488 | ||||||||
\(682\) | −7.36090 | −0.281863 | ||||||||
\(683\) | 20.0545 | 0.767364 | 0.383682 | − | 0.923465i | \(-0.374656\pi\) | ||||
0.383682 | + | 0.923465i | \(0.374656\pi\) | |||||||
\(684\) | −8.01639 | −0.306514 | ||||||||
\(685\) | −52.1084 | −1.99096 | ||||||||
\(686\) | 1.50216 | 0.0573527 | ||||||||
\(687\) | 14.0949 | 0.537753 | ||||||||
\(688\) | 16.2238 | 0.618525 | ||||||||
\(689\) | 9.10888 | 0.347021 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.3245 | 1.38185 | 0.690925 | − | 0.722927i | \(-0.257204\pi\) | ||||
0.690925 | + | 0.722927i | \(0.257204\pi\) | |||||||
\(692\) | 2.80195 | 0.106514 | ||||||||
\(693\) | −3.38527 | −0.128596 | ||||||||
\(694\) | 48.1165 | 1.82648 | ||||||||
\(695\) | −69.0111 | −2.61774 | ||||||||
\(696\) | −29.6917 | −1.12546 | ||||||||
\(697\) | −17.8194 | −0.674959 | ||||||||
\(698\) | −43.6297 | −1.65141 | ||||||||
\(699\) | −49.1685 | −1.85972 | ||||||||
\(700\) | −2.46820 | −0.0932894 | ||||||||
\(701\) | −28.3217 | −1.06969 | −0.534847 | − | 0.844949i | \(-0.679631\pi\) | ||||
−0.534847 | + | 0.844949i | \(0.679631\pi\) | |||||||
\(702\) | −18.0362 | −0.680734 | ||||||||
\(703\) | −45.4675 | −1.71484 | ||||||||
\(704\) | 3.64660 | 0.137437 | ||||||||
\(705\) | −123.710 | −4.65920 | ||||||||
\(706\) | −21.2424 | −0.799466 | ||||||||
\(707\) | −3.59862 | −0.135340 | ||||||||
\(708\) | −4.03995 | −0.151831 | ||||||||
\(709\) | −21.4326 | −0.804919 | −0.402460 | − | 0.915438i | \(-0.631845\pi\) | ||||
−0.402460 | + | 0.915438i | \(0.631845\pi\) | |||||||
\(710\) | 30.4332 | 1.14214 | ||||||||
\(711\) | −62.6383 | −2.34912 | ||||||||
\(712\) | 12.4327 | 0.465934 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −16.7310 | −0.626140 | ||||||||
\(715\) | −2.52170 | −0.0943061 | ||||||||
\(716\) | 1.21637 | 0.0454578 | ||||||||
\(717\) | −3.84980 | −0.143773 | ||||||||
\(718\) | 10.9034 | 0.406912 | ||||||||
\(719\) | 46.7125 | 1.74208 | 0.871040 | − | 0.491212i | \(-0.163446\pi\) | ||||
0.871040 | + | 0.491212i | \(0.163446\pi\) | |||||||
\(720\) | −106.215 | −3.95842 | ||||||||
\(721\) | 9.48704 | 0.353316 | ||||||||
\(722\) | −9.07783 | −0.337842 | ||||||||
\(723\) | −6.37394 | −0.237050 | ||||||||
\(724\) | −0.725421 | −0.0269601 | ||||||||
\(725\) | 35.8797 | 1.33254 | ||||||||
\(726\) | −48.9014 | −1.81490 | ||||||||
\(727\) | −17.3705 | −0.644237 | −0.322119 | − | 0.946699i | \(-0.604395\pi\) | ||||
−0.322119 | + | 0.946699i | \(0.604395\pi\) | |||||||
\(728\) | 3.18638 | 0.118095 | ||||||||
\(729\) | −19.6276 | −0.726947 | ||||||||
\(730\) | −47.0501 | −1.74140 | ||||||||
\(731\) | −13.3630 | −0.494247 | ||||||||
\(732\) | 2.54364 | 0.0940156 | ||||||||
\(733\) | −15.4702 | −0.571404 | −0.285702 | − | 0.958318i | \(-0.592227\pi\) | ||||
−0.285702 | + | 0.958318i | \(0.592227\pi\) | |||||||
\(734\) | −23.6841 | −0.874195 | ||||||||
\(735\) | −11.6277 | −0.428893 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.52465 | 0.240339 | ||||||||
\(738\) | 45.6408 | 1.68006 | ||||||||
\(739\) | −17.5944 | −0.647221 | −0.323611 | − | 0.946190i | \(-0.604897\pi\) | ||||
−0.323611 | + | 0.946190i | \(0.604897\pi\) | |||||||
\(740\) | 8.91116 | 0.327581 | ||||||||
\(741\) | −18.5127 | −0.680080 | ||||||||
\(742\) | −11.2467 | −0.412880 | ||||||||
\(743\) | 32.0161 | 1.17456 | 0.587278 | − | 0.809385i | \(-0.300199\pi\) | ||||
0.587278 | + | 0.809385i | \(0.300199\pi\) | |||||||
\(744\) | −71.9967 | −2.63953 | ||||||||
\(745\) | −52.8399 | −1.93591 | ||||||||
\(746\) | 6.26111 | 0.229236 | ||||||||
\(747\) | −47.7676 | −1.74772 | ||||||||
\(748\) | 0.509219 | 0.0186189 | ||||||||
\(749\) | 6.60294 | 0.241266 | ||||||||
\(750\) | 80.7545 | 2.94874 | ||||||||
\(751\) | −38.1097 | −1.39064 | −0.695321 | − | 0.718700i | \(-0.744738\pi\) | ||||
−0.695321 | + | 0.718700i | \(0.744738\pi\) | |||||||
\(752\) | −47.3148 | −1.72539 | ||||||||
\(753\) | 35.0788 | 1.27834 | ||||||||
\(754\) | 6.81386 | 0.248146 | ||||||||
\(755\) | 61.7248 | 2.24640 | ||||||||
\(756\) | 2.53122 | 0.0920594 | ||||||||
\(757\) | −19.5846 | −0.711814 | −0.355907 | − | 0.934521i | \(-0.615828\pi\) | ||||
−0.355907 | + | 0.934521i | \(0.615828\pi\) | |||||||
\(758\) | 28.0261 | 1.01795 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −50.1200 | −1.81804 | ||||||||
\(761\) | −1.99465 | −0.0723058 | −0.0361529 | − | 0.999346i | \(-0.511510\pi\) | ||||
−0.0361529 | + | 0.999346i | \(0.511510\pi\) | |||||||
\(762\) | 40.3841 | 1.46296 | ||||||||
\(763\) | 1.10726 | 0.0400856 | ||||||||
\(764\) | 0.915220 | 0.0331115 | ||||||||
\(765\) | 87.4860 | 3.16306 | ||||||||
\(766\) | −45.4897 | −1.64361 | ||||||||
\(767\) | −6.30242 | −0.227567 | ||||||||
\(768\) | −18.4223 | −0.664757 | ||||||||
\(769\) | −11.5731 | −0.417338 | −0.208669 | − | 0.977986i | \(-0.566913\pi\) | ||||
−0.208669 | + | 0.977986i | \(0.566913\pi\) | |||||||
\(770\) | 3.11353 | 0.112204 | ||||||||
\(771\) | −44.5599 | −1.60479 | ||||||||
\(772\) | 5.36450 | 0.193073 | ||||||||
\(773\) | 47.3961 | 1.70472 | 0.852360 | − | 0.522955i | \(-0.175170\pi\) | ||||
0.852360 | + | 0.522955i | \(0.175170\pi\) | |||||||
\(774\) | 34.2265 | 1.23025 | ||||||||
\(775\) | 87.0016 | 3.12519 | ||||||||
\(776\) | 28.7818 | 1.03321 | ||||||||
\(777\) | 27.6265 | 0.991095 | ||||||||
\(778\) | −21.1394 | −0.757886 | ||||||||
\(779\) | 24.3446 | 0.872236 | ||||||||
\(780\) | 3.62829 | 0.129914 | ||||||||
\(781\) | −2.87159 | −0.102754 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −36.7957 | −1.31497 | ||||||||
\(784\) | −4.44718 | −0.158828 | ||||||||
\(785\) | 58.5504 | 2.08975 | ||||||||
\(786\) | −11.6442 | −0.415334 | ||||||||
\(787\) | 30.1964 | 1.07639 | 0.538193 | − | 0.842822i | \(-0.319107\pi\) | ||||
0.538193 | + | 0.842822i | \(0.319107\pi\) | |||||||
\(788\) | 1.42238 | 0.0506701 | ||||||||
\(789\) | −69.0638 | −2.45874 | ||||||||
\(790\) | 57.6102 | 2.04968 | ||||||||
\(791\) | 0.433241 | 0.0154043 | ||||||||
\(792\) | 8.86618 | 0.315046 | ||||||||
\(793\) | 3.96814 | 0.140913 | ||||||||
\(794\) | −45.4287 | −1.61220 | ||||||||
\(795\) | 87.0569 | 3.08759 | ||||||||
\(796\) | 1.98467 | 0.0703446 | ||||||||
\(797\) | 41.0916 | 1.45554 | 0.727770 | − | 0.685821i | \(-0.240557\pi\) | ||||
0.727770 | + | 0.685821i | \(0.240557\pi\) | |||||||
\(798\) | 22.8576 | 0.809149 | ||||||||
\(799\) | 38.9716 | 1.37872 | ||||||||
\(800\) | 13.8796 | 0.490718 | ||||||||
\(801\) | 29.6484 | 1.04757 | ||||||||
\(802\) | −1.00439 | −0.0354662 | ||||||||
\(803\) | 4.43951 | 0.156667 | ||||||||
\(804\) | −9.38787 | −0.331085 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16.5223 | 0.581975 | ||||||||
\(807\) | −76.2768 | −2.68507 | ||||||||
\(808\) | 9.42494 | 0.331568 | ||||||||
\(809\) | 17.9154 | 0.629870 | 0.314935 | − | 0.949113i | \(-0.398017\pi\) | ||||
0.314935 | + | 0.949113i | \(0.398017\pi\) | |||||||
\(810\) | −64.7470 | −2.27498 | ||||||||
\(811\) | 10.1577 | 0.356686 | 0.178343 | − | 0.983968i | \(-0.442926\pi\) | ||||
0.178343 | + | 0.983968i | \(0.442926\pi\) | |||||||
\(812\) | −0.956262 | −0.0335582 | ||||||||
\(813\) | 85.2095 | 2.98843 | ||||||||
\(814\) | −7.39753 | −0.259283 | ||||||||
\(815\) | −15.1003 | −0.528939 | ||||||||
\(816\) | 49.5324 | 1.73398 | ||||||||
\(817\) | 18.2563 | 0.638705 | ||||||||
\(818\) | 13.6036 | 0.475638 | ||||||||
\(819\) | 7.59862 | 0.265517 | ||||||||
\(820\) | −4.77129 | −0.166621 | ||||||||
\(821\) | −15.2289 | −0.531491 | −0.265745 | − | 0.964043i | \(-0.585618\pi\) | ||||
−0.265745 | + | 0.964043i | \(0.585618\pi\) | |||||||
\(822\) | −62.2400 | −2.17087 | ||||||||
\(823\) | −20.0090 | −0.697468 | −0.348734 | − | 0.937222i | \(-0.613388\pi\) | ||||
−0.348734 | + | 0.937222i | \(0.613388\pi\) | |||||||
\(824\) | −24.8470 | −0.865585 | ||||||||
\(825\) | −15.8603 | −0.552184 | ||||||||
\(826\) | 7.78158 | 0.270756 | ||||||||
\(827\) | −18.0259 | −0.626822 | −0.313411 | − | 0.949618i | \(-0.601472\pi\) | ||||
−0.313411 | + | 0.949618i | \(0.601472\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.2616 | 0.495327 | 0.247664 | − | 0.968846i | \(-0.420337\pi\) | ||||
0.247664 | + | 0.968846i | \(0.420337\pi\) | |||||||
\(830\) | 43.9332 | 1.52494 | ||||||||
\(831\) | 49.4694 | 1.71607 | ||||||||
\(832\) | −8.18520 | −0.283771 | ||||||||
\(833\) | 3.66299 | 0.126915 | ||||||||
\(834\) | −82.4291 | −2.85429 | ||||||||
\(835\) | 7.17971 | 0.248464 | ||||||||
\(836\) | −0.695686 | −0.0240608 | ||||||||
\(837\) | −89.2227 | −3.08399 | ||||||||
\(838\) | −29.9818 | −1.03570 | ||||||||
\(839\) | −51.5877 | −1.78101 | −0.890503 | − | 0.454977i | \(-0.849647\pi\) | ||||
−0.890503 | + | 0.454977i | \(0.849647\pi\) | |||||||
\(840\) | 30.4534 | 1.05074 | ||||||||
\(841\) | −15.0990 | −0.520656 | ||||||||
\(842\) | −10.3093 | −0.355280 | ||||||||
\(843\) | −40.9561 | −1.41060 | ||||||||
\(844\) | 2.42097 | 0.0833331 | ||||||||
\(845\) | −44.0524 | −1.51545 | ||||||||
\(846\) | −99.8178 | −3.43181 | ||||||||
\(847\) | 10.7062 | 0.367870 | ||||||||
\(848\) | 33.2962 | 1.14340 | ||||||||
\(849\) | 54.8889 | 1.88378 | ||||||||
\(850\) | −52.9515 | −1.81622 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 4.13174 | 0.141551 | ||||||||
\(853\) | 48.2610 | 1.65243 | 0.826213 | − | 0.563358i | \(-0.190491\pi\) | ||||
0.826213 | + | 0.563358i | \(0.190491\pi\) | |||||||
\(854\) | −4.89945 | −0.167656 | ||||||||
\(855\) | −119.522 | −4.08757 | ||||||||
\(856\) | −17.2934 | −0.591075 | ||||||||
\(857\) | −1.37665 | −0.0470256 | −0.0235128 | − | 0.999724i | \(-0.507485\pi\) | ||||
−0.0235128 | + | 0.999724i | \(0.507485\pi\) | |||||||
\(858\) | −3.01200 | −0.102828 | ||||||||
\(859\) | −36.3622 | −1.24066 | −0.620331 | − | 0.784340i | \(-0.713002\pi\) | ||||
−0.620331 | + | 0.784340i | \(0.713002\pi\) | |||||||
\(860\) | −3.57804 | −0.122010 | ||||||||
\(861\) | −14.7920 | −0.504110 | ||||||||
\(862\) | 6.79215 | 0.231342 | ||||||||
\(863\) | 44.8731 | 1.52750 | 0.763749 | − | 0.645514i | \(-0.223357\pi\) | ||||
0.763749 | + | 0.645514i | \(0.223357\pi\) | |||||||
\(864\) | −14.2339 | −0.484248 | ||||||||
\(865\) | 41.7762 | 1.42043 | ||||||||
\(866\) | 21.8068 | 0.741025 | ||||||||
\(867\) | 10.8932 | 0.369954 | ||||||||
\(868\) | −2.31876 | −0.0787037 | ||||||||
\(869\) | −5.43594 | −0.184402 | ||||||||
\(870\) | 65.1225 | 2.20786 | ||||||||
\(871\) | −14.6453 | −0.496237 | ||||||||
\(872\) | −2.89997 | −0.0982054 | ||||||||
\(873\) | 68.6364 | 2.32299 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −17.6800 | −0.597692 | ||||||||
\(876\) | −6.38770 | −0.215820 | ||||||||
\(877\) | 42.2559 | 1.42688 | 0.713441 | − | 0.700716i | \(-0.247136\pi\) | ||||
0.713441 | + | 0.700716i | \(0.247136\pi\) | |||||||
\(878\) | −38.3137 | −1.29303 | ||||||||
\(879\) | 70.3979 | 2.37446 | ||||||||
\(880\) | −9.21770 | −0.310729 | ||||||||
\(881\) | −51.1432 | −1.72306 | −0.861529 | − | 0.507708i | \(-0.830493\pi\) | ||||
−0.861529 | + | 0.507708i | \(0.830493\pi\) | |||||||
\(882\) | −9.38200 | −0.315908 | ||||||||
\(883\) | 52.6889 | 1.77312 | 0.886562 | − | 0.462610i | \(-0.153087\pi\) | ||||
0.886562 | + | 0.462610i | \(0.153087\pi\) | |||||||
\(884\) | −1.14300 | −0.0384432 | ||||||||
\(885\) | −60.2345 | −2.02476 | ||||||||
\(886\) | −20.9451 | −0.703666 | ||||||||
\(887\) | −42.9102 | −1.44078 | −0.720391 | − | 0.693568i | \(-0.756038\pi\) | ||||
−0.720391 | + | 0.693568i | \(0.756038\pi\) | |||||||
\(888\) | −72.3550 | −2.42807 | ||||||||
\(889\) | −8.84149 | −0.296534 | ||||||||
\(890\) | −27.2685 | −0.914042 | ||||||||
\(891\) | 6.10934 | 0.204671 | ||||||||
\(892\) | 2.84719 | 0.0953311 | ||||||||
\(893\) | −53.2424 | −1.78169 | ||||||||
\(894\) | −63.1137 | −2.11084 | ||||||||
\(895\) | 18.1357 | 0.606209 | ||||||||
\(896\) | 12.9908 | 0.433993 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 33.8446 | 1.12941 | ||||||||
\(899\) | 33.7072 | 1.12420 | ||||||||
\(900\) | 15.4156 | 0.513854 | ||||||||
\(901\) | −27.4249 | −0.913657 | ||||||||
\(902\) | 3.96085 | 0.131882 | ||||||||
\(903\) | −11.0927 | −0.369141 | ||||||||
\(904\) | −1.13468 | −0.0377388 | ||||||||
\(905\) | −10.8158 | −0.359530 | ||||||||
\(906\) | 73.7261 | 2.44939 | ||||||||
\(907\) | 24.5213 | 0.814217 | 0.407108 | − | 0.913380i | \(-0.366537\pi\) | ||||
0.407108 | + | 0.913380i | \(0.366537\pi\) | |||||||
\(908\) | −5.38166 | −0.178597 | ||||||||
\(909\) | 22.4758 | 0.745476 | ||||||||
\(910\) | −6.98867 | −0.231672 | ||||||||
\(911\) | 31.6347 | 1.04810 | 0.524052 | − | 0.851686i | \(-0.324420\pi\) | ||||
0.524052 | + | 0.851686i | \(0.324420\pi\) | |||||||
\(912\) | −67.6704 | −2.24079 | ||||||||
\(913\) | −4.14541 | −0.137193 | ||||||||
\(914\) | −19.4663 | −0.643888 | ||||||||
\(915\) | 37.9249 | 1.25376 | ||||||||
\(916\) | −1.18890 | −0.0392824 | ||||||||
\(917\) | 2.54931 | 0.0841858 | ||||||||
\(918\) | 54.3033 | 1.79228 | ||||||||
\(919\) | 43.7293 | 1.44250 | 0.721249 | − | 0.692676i | \(-0.243569\pi\) | ||||
0.721249 | + | 0.692676i | \(0.243569\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.47553 | 0.114523 | ||||||||
\(922\) | −22.4294 | −0.738674 | ||||||||
\(923\) | 6.44561 | 0.212160 | ||||||||
\(924\) | 0.422706 | 0.0139060 | ||||||||
\(925\) | 87.4346 | 2.87483 | ||||||||
\(926\) | −26.2788 | −0.863576 | ||||||||
\(927\) | −59.2530 | −1.94612 | ||||||||
\(928\) | 5.37741 | 0.176522 | ||||||||
\(929\) | 3.63411 | 0.119231 | 0.0596157 | − | 0.998221i | \(-0.481012\pi\) | ||||
0.0596157 | + | 0.998221i | \(0.481012\pi\) | |||||||
\(930\) | 157.910 | 5.17807 | ||||||||
\(931\) | −5.00432 | −0.164010 | ||||||||
\(932\) | 4.14736 | 0.135851 | ||||||||
\(933\) | 58.7445 | 1.92321 | ||||||||
\(934\) | −26.4802 | −0.866460 | ||||||||
\(935\) | 7.59230 | 0.248295 | ||||||||
\(936\) | −19.9011 | −0.650488 | ||||||||
\(937\) | 10.3649 | 0.338606 | 0.169303 | − | 0.985564i | \(-0.445848\pi\) | ||||
0.169303 | + | 0.985564i | \(0.445848\pi\) | |||||||
\(938\) | 18.0825 | 0.590415 | ||||||||
\(939\) | −52.9503 | −1.72797 | ||||||||
\(940\) | 10.4350 | 0.340351 | ||||||||
\(941\) | 29.8720 | 0.973800 | 0.486900 | − | 0.873458i | \(-0.338128\pi\) | ||||
0.486900 | + | 0.873458i | \(0.338128\pi\) | |||||||
\(942\) | 69.9345 | 2.27859 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −23.0376 | −0.749809 | ||||||||
\(945\) | 37.7397 | 1.22767 | ||||||||
\(946\) | 2.97028 | 0.0965720 | ||||||||
\(947\) | 7.17017 | 0.232999 | 0.116500 | − | 0.993191i | \(-0.462833\pi\) | ||||
0.116500 | + | 0.993191i | \(0.462833\pi\) | |||||||
\(948\) | 7.82139 | 0.254027 | ||||||||
\(949\) | −9.96497 | −0.323477 | ||||||||
\(950\) | 72.3415 | 2.34707 | ||||||||
\(951\) | −4.33636 | −0.140616 | ||||||||
\(952\) | −9.59352 | −0.310928 | ||||||||
\(953\) | −16.0495 | −0.519894 | −0.259947 | − | 0.965623i | \(-0.583705\pi\) | ||||
−0.259947 | + | 0.965623i | \(0.583705\pi\) | |||||||
\(954\) | 70.2434 | 2.27421 | ||||||||
\(955\) | 13.6457 | 0.441563 | ||||||||
\(956\) | 0.324730 | 0.0105025 | ||||||||
\(957\) | −6.14478 | −0.198632 | ||||||||
\(958\) | −17.6438 | −0.570046 | ||||||||
\(959\) | 13.6265 | 0.440022 | ||||||||
\(960\) | −78.2289 | −2.52483 | ||||||||
\(961\) | 50.7337 | 1.63657 | ||||||||
\(962\) | 16.6046 | 0.535352 | ||||||||
\(963\) | −41.2398 | −1.32893 | ||||||||
\(964\) | 0.537642 | 0.0173163 | ||||||||
\(965\) | 79.9832 | 2.57475 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.5360 | 1.07845 | 0.539223 | − | 0.842163i | \(-0.318718\pi\) | ||||
0.539223 | + | 0.842163i | \(0.318718\pi\) | |||||||
\(968\) | −28.0400 | −0.901241 | ||||||||
\(969\) | 55.7378 | 1.79056 | ||||||||
\(970\) | −63.1269 | −2.02688 | ||||||||
\(971\) | 17.5189 | 0.562208 | 0.281104 | − | 0.959677i | \(-0.409299\pi\) | ||||
0.281104 | + | 0.959677i | \(0.409299\pi\) | |||||||
\(972\) | −1.19666 | −0.0383828 | ||||||||
\(973\) | 18.0466 | 0.578548 | ||||||||
\(974\) | −34.4565 | −1.10406 | ||||||||
\(975\) | 35.6001 | 1.14012 | ||||||||
\(976\) | 14.5050 | 0.464292 | ||||||||
\(977\) | −50.1902 | −1.60573 | −0.802863 | − | 0.596163i | \(-0.796691\pi\) | ||||
−0.802863 | + | 0.596163i | \(0.796691\pi\) | |||||||
\(978\) | −18.0362 | −0.576735 | ||||||||
\(979\) | 2.57298 | 0.0822327 | ||||||||
\(980\) | 0.980794 | 0.0313303 | ||||||||
\(981\) | −6.91561 | −0.220798 | ||||||||
\(982\) | −17.3773 | −0.554533 | ||||||||
\(983\) | 22.7924 | 0.726966 | 0.363483 | − | 0.931601i | \(-0.381587\pi\) | ||||
0.363483 | + | 0.931601i | \(0.381587\pi\) | |||||||
\(984\) | 38.7409 | 1.23502 | ||||||||
\(985\) | 21.2073 | 0.675719 | ||||||||
\(986\) | −20.5151 | −0.653334 | ||||||||
\(987\) | 32.3506 | 1.02973 | ||||||||
\(988\) | 1.56154 | 0.0496793 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −19.4461 | −0.618039 | ||||||||
\(991\) | −0.965443 | −0.0306683 | −0.0153342 | − | 0.999882i | \(-0.504881\pi\) | ||||
−0.0153342 | + | 0.999882i | \(0.504881\pi\) | |||||||
\(992\) | 13.0392 | 0.413995 | ||||||||
\(993\) | −11.9100 | −0.377952 | ||||||||
\(994\) | −7.95838 | −0.252424 | ||||||||
\(995\) | 29.5908 | 0.938091 | ||||||||
\(996\) | 5.96455 | 0.188994 | ||||||||
\(997\) | −4.22619 | −0.133845 | −0.0669224 | − | 0.997758i | \(-0.521318\pi\) | ||||
−0.0669224 | + | 0.997758i | \(0.521318\pi\) | |||||||
\(998\) | −37.5634 | −1.18905 | ||||||||
\(999\) | −89.6667 | −2.83693 |
(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 | 3703.2.a.j.1.2 | 5 | ||
23.22 | odd | 2 | 161.2.a.d.1.2 | ✓ | 5 | ||
69.68 | even | 2 | 1449.2.a.r.1.4 | 5 | |||
92.91 | even | 2 | 2576.2.a.bd.1.5 | 5 | |||
115.114 | odd | 2 | 4025.2.a.p.1.4 | 5 | |||
161.160 | even | 2 | 1127.2.a.h.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
161.2.a.d.1.2 | ✓ | 5 | 23.22 | odd | 2 | ||
1127.2.a.h.1.2 | 5 | 161.160 | even | 2 | |||
1449.2.a.r.1.4 | 5 | 69.68 | even | 2 | |||
2576.2.a.bd.1.5 | 5 | 92.91 | even | 2 | |||
3703.2.a.j.1.2 | 5 | 1.1 | even | 1 | trivial | ||
4025.2.a.p.1.4 | 5 | 115.114 | odd | 2 |