Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.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: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(29\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.630217 | −0.445631 | −0.222815 | − | 0.974861i | \(-0.571525\pi\) | ||||
−0.222815 | + | 0.974861i | \(0.571525\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.60283 | −0.801413 | ||||||||
\(5\) | −2.79883 | −1.25168 | −0.625838 | − | 0.779953i | \(-0.715243\pi\) | ||||
−0.625838 | + | 0.779953i | \(0.715243\pi\) | |||||||
\(6\) | −0.630217 | −0.257285 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.27056 | 0.802765 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.76387 | 0.557785 | ||||||||
\(11\) | 1.05357 | 0.317662 | 0.158831 | − | 0.987306i | \(-0.449227\pi\) | ||||
0.158831 | + | 0.987306i | \(0.449227\pi\) | |||||||
\(12\) | −1.60283 | −0.462696 | ||||||||
\(13\) | −2.76000 | −0.765487 | −0.382744 | − | 0.923855i | \(-0.625021\pi\) | ||||
−0.382744 | + | 0.923855i | \(0.625021\pi\) | |||||||
\(14\) | 0.630217 | 0.168433 | ||||||||
\(15\) | −2.79883 | −0.722655 | ||||||||
\(16\) | 1.77470 | 0.443676 | ||||||||
\(17\) | −0.136595 | −0.0331290 | −0.0165645 | − | 0.999863i | \(-0.505273\pi\) | ||||
−0.0165645 | + | 0.999863i | \(0.505273\pi\) | |||||||
\(18\) | −0.630217 | −0.148544 | ||||||||
\(19\) | −0.161750 | −0.0371079 | −0.0185540 | − | 0.999828i | \(-0.505906\pi\) | ||||
−0.0185540 | + | 0.999828i | \(0.505906\pi\) | |||||||
\(20\) | 4.48604 | 1.00311 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −0.663975 | −0.141560 | ||||||||
\(23\) | −0.925481 | −0.192976 | −0.0964880 | − | 0.995334i | \(-0.530761\pi\) | ||||
−0.0964880 | + | 0.995334i | \(0.530761\pi\) | |||||||
\(24\) | 2.27056 | 0.463477 | ||||||||
\(25\) | 2.83346 | 0.566693 | ||||||||
\(26\) | 1.73940 | 0.341125 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.60283 | 0.302906 | ||||||||
\(29\) | −0.490039 | −0.0909980 | −0.0454990 | − | 0.998964i | \(-0.514488\pi\) | ||||
−0.0454990 | + | 0.998964i | \(0.514488\pi\) | |||||||
\(30\) | 1.76387 | 0.322038 | ||||||||
\(31\) | 5.37505 | 0.965387 | 0.482694 | − | 0.875789i | \(-0.339658\pi\) | ||||
0.482694 | + | 0.875789i | \(0.339658\pi\) | |||||||
\(32\) | −5.65958 | −1.00048 | ||||||||
\(33\) | 1.05357 | 0.183402 | ||||||||
\(34\) | 0.0860842 | 0.0147633 | ||||||||
\(35\) | 2.79883 | 0.473089 | ||||||||
\(36\) | −1.60283 | −0.267138 | ||||||||
\(37\) | −7.86861 | −1.29359 | −0.646796 | − | 0.762663i | \(-0.723892\pi\) | ||||
−0.646796 | + | 0.762663i | \(0.723892\pi\) | |||||||
\(38\) | 0.101937 | 0.0165364 | ||||||||
\(39\) | −2.76000 | −0.441954 | ||||||||
\(40\) | −6.35493 | −1.00480 | ||||||||
\(41\) | −10.3578 | −1.61761 | −0.808807 | − | 0.588074i | \(-0.799886\pi\) | ||||
−0.808807 | + | 0.588074i | \(0.799886\pi\) | |||||||
\(42\) | 0.630217 | 0.0972446 | ||||||||
\(43\) | −8.97705 | −1.36899 | −0.684493 | − | 0.729019i | \(-0.739977\pi\) | ||||
−0.684493 | + | 0.729019i | \(0.739977\pi\) | |||||||
\(44\) | −1.68868 | −0.254579 | ||||||||
\(45\) | −2.79883 | −0.417225 | ||||||||
\(46\) | 0.583254 | 0.0859961 | ||||||||
\(47\) | 3.64355 | 0.531466 | 0.265733 | − | 0.964047i | \(-0.414386\pi\) | ||||
0.265733 | + | 0.964047i | \(0.414386\pi\) | |||||||
\(48\) | 1.77470 | 0.256157 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.78570 | −0.252536 | ||||||||
\(51\) | −0.136595 | −0.0191271 | ||||||||
\(52\) | 4.42381 | 0.613472 | ||||||||
\(53\) | −9.32669 | −1.28112 | −0.640560 | − | 0.767908i | \(-0.721298\pi\) | ||||
−0.640560 | + | 0.767908i | \(0.721298\pi\) | |||||||
\(54\) | −0.630217 | −0.0857617 | ||||||||
\(55\) | −2.94875 | −0.397610 | ||||||||
\(56\) | −2.27056 | −0.303417 | ||||||||
\(57\) | −0.161750 | −0.0214243 | ||||||||
\(58\) | 0.308831 | 0.0405515 | ||||||||
\(59\) | −2.93568 | −0.382193 | −0.191096 | − | 0.981571i | \(-0.561204\pi\) | ||||
−0.191096 | + | 0.981571i | \(0.561204\pi\) | |||||||
\(60\) | 4.48604 | 0.579146 | ||||||||
\(61\) | 12.4971 | 1.60008 | 0.800042 | − | 0.599944i | \(-0.204810\pi\) | ||||
0.800042 | + | 0.599944i | \(0.204810\pi\) | |||||||
\(62\) | −3.38745 | −0.430206 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0.0173536 | 0.00216920 | ||||||||
\(65\) | 7.72479 | 0.958142 | ||||||||
\(66\) | −0.663975 | −0.0817297 | ||||||||
\(67\) | −11.3408 | −1.38550 | −0.692752 | − | 0.721176i | \(-0.743602\pi\) | ||||
−0.692752 | + | 0.721176i | \(0.743602\pi\) | |||||||
\(68\) | 0.218937 | 0.0265500 | ||||||||
\(69\) | −0.925481 | −0.111415 | ||||||||
\(70\) | −1.76387 | −0.210823 | ||||||||
\(71\) | 5.60512 | 0.665205 | 0.332603 | − | 0.943067i | \(-0.392073\pi\) | ||||
0.332603 | + | 0.943067i | \(0.392073\pi\) | |||||||
\(72\) | 2.27056 | 0.267588 | ||||||||
\(73\) | 11.1905 | 1.30975 | 0.654873 | − | 0.755739i | \(-0.272722\pi\) | ||||
0.654873 | + | 0.755739i | \(0.272722\pi\) | |||||||
\(74\) | 4.95894 | 0.576465 | ||||||||
\(75\) | 2.83346 | 0.327180 | ||||||||
\(76\) | 0.259257 | 0.0297388 | ||||||||
\(77\) | −1.05357 | −0.120065 | ||||||||
\(78\) | 1.73940 | 0.196948 | ||||||||
\(79\) | 10.3167 | 1.16072 | 0.580359 | − | 0.814361i | \(-0.302912\pi\) | ||||
0.580359 | + | 0.814361i | \(0.302912\pi\) | |||||||
\(80\) | −4.96710 | −0.555339 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.52765 | 0.720859 | ||||||||
\(83\) | 11.9571 | 1.31247 | 0.656233 | − | 0.754558i | \(-0.272149\pi\) | ||||
0.656233 | + | 0.754558i | \(0.272149\pi\) | |||||||
\(84\) | 1.60283 | 0.174883 | ||||||||
\(85\) | 0.382305 | 0.0414668 | ||||||||
\(86\) | 5.65749 | 0.610063 | ||||||||
\(87\) | −0.490039 | −0.0525377 | ||||||||
\(88\) | 2.39219 | 0.255008 | ||||||||
\(89\) | 1.58305 | 0.167803 | 0.0839017 | − | 0.996474i | \(-0.473262\pi\) | ||||
0.0839017 | + | 0.996474i | \(0.473262\pi\) | |||||||
\(90\) | 1.76387 | 0.185928 | ||||||||
\(91\) | 2.76000 | 0.289327 | ||||||||
\(92\) | 1.48338 | 0.154654 | ||||||||
\(93\) | 5.37505 | 0.557367 | ||||||||
\(94\) | −2.29623 | −0.236838 | ||||||||
\(95\) | 0.452710 | 0.0464471 | ||||||||
\(96\) | −5.65958 | −0.577628 | ||||||||
\(97\) | −12.4149 | −1.26055 | −0.630273 | − | 0.776373i | \(-0.717057\pi\) | ||||
−0.630273 | + | 0.776373i | \(0.717057\pi\) | |||||||
\(98\) | −0.630217 | −0.0636616 | ||||||||
\(99\) | 1.05357 | 0.105887 | ||||||||
\(100\) | −4.54155 | −0.454155 | ||||||||
\(101\) | 4.96651 | 0.494187 | 0.247093 | − | 0.968992i | \(-0.420525\pi\) | ||||
0.247093 | + | 0.968992i | \(0.420525\pi\) | |||||||
\(102\) | 0.0860842 | 0.00852361 | ||||||||
\(103\) | −6.79070 | −0.669107 | −0.334554 | − | 0.942377i | \(-0.608586\pi\) | ||||
−0.334554 | + | 0.942377i | \(0.608586\pi\) | |||||||
\(104\) | −6.26676 | −0.614507 | ||||||||
\(105\) | 2.79883 | 0.273138 | ||||||||
\(106\) | 5.87784 | 0.570906 | ||||||||
\(107\) | 18.7427 | 1.81192 | 0.905961 | − | 0.423361i | \(-0.139150\pi\) | ||||
0.905961 | + | 0.423361i | \(0.139150\pi\) | |||||||
\(108\) | −1.60283 | −0.154232 | ||||||||
\(109\) | 2.36857 | 0.226868 | 0.113434 | − | 0.993546i | \(-0.463815\pi\) | ||||
0.113434 | + | 0.993546i | \(0.463815\pi\) | |||||||
\(110\) | 1.85836 | 0.177187 | ||||||||
\(111\) | −7.86861 | −0.746856 | ||||||||
\(112\) | −1.77470 | −0.167694 | ||||||||
\(113\) | 10.3546 | 0.974082 | 0.487041 | − | 0.873379i | \(-0.338076\pi\) | ||||
0.487041 | + | 0.873379i | \(0.338076\pi\) | |||||||
\(114\) | 0.101937 | 0.00954731 | ||||||||
\(115\) | 2.59026 | 0.241543 | ||||||||
\(116\) | 0.785448 | 0.0729270 | ||||||||
\(117\) | −2.76000 | −0.255162 | ||||||||
\(118\) | 1.85012 | 0.170317 | ||||||||
\(119\) | 0.136595 | 0.0125216 | ||||||||
\(120\) | −6.35493 | −0.580123 | ||||||||
\(121\) | −9.89000 | −0.899091 | ||||||||
\(122\) | −7.87586 | −0.713047 | ||||||||
\(123\) | −10.3578 | −0.933930 | ||||||||
\(124\) | −8.61527 | −0.773674 | ||||||||
\(125\) | 6.06377 | 0.542360 | ||||||||
\(126\) | 0.630217 | 0.0561442 | ||||||||
\(127\) | 12.9282 | 1.14720 | 0.573598 | − | 0.819137i | \(-0.305547\pi\) | ||||
0.573598 | + | 0.819137i | \(0.305547\pi\) | |||||||
\(128\) | 11.3082 | 0.999514 | ||||||||
\(129\) | −8.97705 | −0.790385 | ||||||||
\(130\) | −4.86829 | −0.426978 | ||||||||
\(131\) | 15.4387 | 1.34888 | 0.674441 | − | 0.738329i | \(-0.264385\pi\) | ||||
0.674441 | + | 0.738329i | \(0.264385\pi\) | |||||||
\(132\) | −1.68868 | −0.146981 | ||||||||
\(133\) | 0.161750 | 0.0140255 | ||||||||
\(134\) | 7.14719 | 0.617424 | ||||||||
\(135\) | −2.79883 | −0.240885 | ||||||||
\(136\) | −0.310147 | −0.0265948 | ||||||||
\(137\) | −13.0607 | −1.11585 | −0.557924 | − | 0.829892i | \(-0.688402\pi\) | ||||
−0.557924 | + | 0.829892i | \(0.688402\pi\) | |||||||
\(138\) | 0.583254 | 0.0496499 | ||||||||
\(139\) | −11.8431 | −1.00452 | −0.502261 | − | 0.864716i | \(-0.667498\pi\) | ||||
−0.502261 | + | 0.864716i | \(0.667498\pi\) | |||||||
\(140\) | −4.48604 | −0.379140 | ||||||||
\(141\) | 3.64355 | 0.306842 | ||||||||
\(142\) | −3.53244 | −0.296436 | ||||||||
\(143\) | −2.90785 | −0.243166 | ||||||||
\(144\) | 1.77470 | 0.147892 | ||||||||
\(145\) | 1.37154 | 0.113900 | ||||||||
\(146\) | −7.05243 | −0.583663 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 12.6120 | 1.03670 | ||||||||
\(149\) | 20.8541 | 1.70844 | 0.854218 | − | 0.519915i | \(-0.174036\pi\) | ||||
0.854218 | + | 0.519915i | \(0.174036\pi\) | |||||||
\(150\) | −1.78570 | −0.145802 | ||||||||
\(151\) | 19.0122 | 1.54719 | 0.773595 | − | 0.633680i | \(-0.218456\pi\) | ||||
0.773595 | + | 0.633680i | \(0.218456\pi\) | |||||||
\(152\) | −0.367263 | −0.0297889 | ||||||||
\(153\) | −0.136595 | −0.0110430 | ||||||||
\(154\) | 0.663975 | 0.0535047 | ||||||||
\(155\) | −15.0439 | −1.20835 | ||||||||
\(156\) | 4.42381 | 0.354188 | ||||||||
\(157\) | −15.6456 | −1.24865 | −0.624326 | − | 0.781164i | \(-0.714626\pi\) | ||||
−0.624326 | + | 0.781164i | \(0.714626\pi\) | |||||||
\(158\) | −6.50176 | −0.517252 | ||||||||
\(159\) | −9.32669 | −0.739655 | ||||||||
\(160\) | 15.8402 | 1.25228 | ||||||||
\(161\) | 0.925481 | 0.0729381 | ||||||||
\(162\) | −0.630217 | −0.0495145 | ||||||||
\(163\) | 12.5969 | 0.986669 | 0.493334 | − | 0.869840i | \(-0.335778\pi\) | ||||
0.493334 | + | 0.869840i | \(0.335778\pi\) | |||||||
\(164\) | 16.6017 | 1.29638 | ||||||||
\(165\) | −2.94875 | −0.229560 | ||||||||
\(166\) | −7.53559 | −0.584875 | ||||||||
\(167\) | −0.0346152 | −0.00267860 | −0.00133930 | − | 0.999999i | \(-0.500426\pi\) | ||||
−0.00133930 | + | 0.999999i | \(0.500426\pi\) | |||||||
\(168\) | −2.27056 | −0.175178 | ||||||||
\(169\) | −5.38238 | −0.414029 | ||||||||
\(170\) | −0.240935 | −0.0184789 | ||||||||
\(171\) | −0.161750 | −0.0123693 | ||||||||
\(172\) | 14.3886 | 1.09712 | ||||||||
\(173\) | −19.6553 | −1.49436 | −0.747181 | − | 0.664621i | \(-0.768593\pi\) | ||||
−0.747181 | + | 0.664621i | \(0.768593\pi\) | |||||||
\(174\) | 0.308831 | 0.0234124 | ||||||||
\(175\) | −2.83346 | −0.214190 | ||||||||
\(176\) | 1.86977 | 0.140939 | ||||||||
\(177\) | −2.93568 | −0.220659 | ||||||||
\(178\) | −0.997668 | −0.0747783 | ||||||||
\(179\) | 14.4193 | 1.07775 | 0.538874 | − | 0.842387i | \(-0.318850\pi\) | ||||
0.538874 | + | 0.842387i | \(0.318850\pi\) | |||||||
\(180\) | 4.48604 | 0.334370 | ||||||||
\(181\) | 25.7574 | 1.91453 | 0.957266 | − | 0.289209i | \(-0.0933923\pi\) | ||||
0.957266 | + | 0.289209i | \(0.0933923\pi\) | |||||||
\(182\) | −1.73940 | −0.128933 | ||||||||
\(183\) | 12.4971 | 0.923809 | ||||||||
\(184\) | −2.10136 | −0.154914 | ||||||||
\(185\) | 22.0229 | 1.61916 | ||||||||
\(186\) | −3.38745 | −0.248380 | ||||||||
\(187\) | −0.143911 | −0.0105238 | ||||||||
\(188\) | −5.83997 | −0.425924 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −0.285306 | −0.0206983 | ||||||||
\(191\) | −1.00000 | −0.0723575 | ||||||||
\(192\) | 0.0173536 | 0.00125239 | ||||||||
\(193\) | −22.2471 | −1.60138 | −0.800691 | − | 0.599078i | \(-0.795534\pi\) | ||||
−0.800691 | + | 0.599078i | \(0.795534\pi\) | |||||||
\(194\) | 7.82411 | 0.561738 | ||||||||
\(195\) | 7.72479 | 0.553184 | ||||||||
\(196\) | −1.60283 | −0.114488 | ||||||||
\(197\) | 14.1243 | 1.00631 | 0.503156 | − | 0.864195i | \(-0.332172\pi\) | ||||
0.503156 | + | 0.864195i | \(0.332172\pi\) | |||||||
\(198\) | −0.663975 | −0.0471867 | ||||||||
\(199\) | 2.88412 | 0.204450 | 0.102225 | − | 0.994761i | \(-0.467404\pi\) | ||||
0.102225 | + | 0.994761i | \(0.467404\pi\) | |||||||
\(200\) | 6.43356 | 0.454921 | ||||||||
\(201\) | −11.3408 | −0.799921 | ||||||||
\(202\) | −3.12998 | −0.220225 | ||||||||
\(203\) | 0.490039 | 0.0343940 | ||||||||
\(204\) | 0.218937 | 0.0153287 | ||||||||
\(205\) | 28.9897 | 2.02473 | ||||||||
\(206\) | 4.27961 | 0.298175 | ||||||||
\(207\) | −0.925481 | −0.0643253 | ||||||||
\(208\) | −4.89819 | −0.339628 | ||||||||
\(209\) | −0.170414 | −0.0117878 | ||||||||
\(210\) | −1.76387 | −0.121719 | ||||||||
\(211\) | 3.75758 | 0.258683 | 0.129341 | − | 0.991600i | \(-0.458714\pi\) | ||||
0.129341 | + | 0.991600i | \(0.458714\pi\) | |||||||
\(212\) | 14.9491 | 1.02671 | ||||||||
\(213\) | 5.60512 | 0.384056 | ||||||||
\(214\) | −11.8120 | −0.807449 | ||||||||
\(215\) | 25.1253 | 1.71353 | ||||||||
\(216\) | 2.27056 | 0.154492 | ||||||||
\(217\) | −5.37505 | −0.364882 | ||||||||
\(218\) | −1.49272 | −0.101099 | ||||||||
\(219\) | 11.1905 | 0.756182 | ||||||||
\(220\) | 4.72634 | 0.318650 | ||||||||
\(221\) | 0.377001 | 0.0253599 | ||||||||
\(222\) | 4.95894 | 0.332822 | ||||||||
\(223\) | −14.4001 | −0.964303 | −0.482152 | − | 0.876088i | \(-0.660145\pi\) | ||||
−0.482152 | + | 0.876088i | \(0.660145\pi\) | |||||||
\(224\) | 5.65958 | 0.378146 | ||||||||
\(225\) | 2.83346 | 0.188898 | ||||||||
\(226\) | −6.52567 | −0.434081 | ||||||||
\(227\) | 17.6252 | 1.16982 | 0.584912 | − | 0.811097i | \(-0.301129\pi\) | ||||
0.584912 | + | 0.811097i | \(0.301129\pi\) | |||||||
\(228\) | 0.259257 | 0.0171697 | ||||||||
\(229\) | 24.4011 | 1.61247 | 0.806236 | − | 0.591594i | \(-0.201501\pi\) | ||||
0.806236 | + | 0.591594i | \(0.201501\pi\) | |||||||
\(230\) | −1.63243 | −0.107639 | ||||||||
\(231\) | −1.05357 | −0.0693195 | ||||||||
\(232\) | −1.11267 | −0.0730501 | ||||||||
\(233\) | 13.8079 | 0.904586 | 0.452293 | − | 0.891869i | \(-0.350606\pi\) | ||||
0.452293 | + | 0.891869i | \(0.350606\pi\) | |||||||
\(234\) | 1.73940 | 0.113708 | ||||||||
\(235\) | −10.1977 | −0.665223 | ||||||||
\(236\) | 4.70538 | 0.306294 | ||||||||
\(237\) | 10.3167 | 0.670141 | ||||||||
\(238\) | −0.0860842 | −0.00558001 | ||||||||
\(239\) | 10.4988 | 0.679113 | 0.339557 | − | 0.940586i | \(-0.389723\pi\) | ||||
0.339557 | + | 0.940586i | \(0.389723\pi\) | |||||||
\(240\) | −4.96710 | −0.320625 | ||||||||
\(241\) | 4.39472 | 0.283089 | 0.141544 | − | 0.989932i | \(-0.454793\pi\) | ||||
0.141544 | + | 0.989932i | \(0.454793\pi\) | |||||||
\(242\) | 6.23285 | 0.400663 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −20.0306 | −1.28233 | ||||||||
\(245\) | −2.79883 | −0.178811 | ||||||||
\(246\) | 6.52765 | 0.416188 | ||||||||
\(247\) | 0.446429 | 0.0284056 | ||||||||
\(248\) | 12.2044 | 0.774980 | ||||||||
\(249\) | 11.9571 | 0.757752 | ||||||||
\(250\) | −3.82149 | −0.241693 | ||||||||
\(251\) | 9.09002 | 0.573757 | 0.286878 | − | 0.957967i | \(-0.407382\pi\) | ||||
0.286878 | + | 0.957967i | \(0.407382\pi\) | |||||||
\(252\) | 1.60283 | 0.100969 | ||||||||
\(253\) | −0.975055 | −0.0613012 | ||||||||
\(254\) | −8.14760 | −0.511226 | ||||||||
\(255\) | 0.382305 | 0.0239409 | ||||||||
\(256\) | −7.16134 | −0.447584 | ||||||||
\(257\) | −18.7230 | −1.16791 | −0.583955 | − | 0.811786i | \(-0.698495\pi\) | ||||
−0.583955 | + | 0.811786i | \(0.698495\pi\) | |||||||
\(258\) | 5.65749 | 0.352220 | ||||||||
\(259\) | 7.86861 | 0.488932 | ||||||||
\(260\) | −12.3815 | −0.767868 | ||||||||
\(261\) | −0.490039 | −0.0303327 | ||||||||
\(262\) | −9.72970 | −0.601103 | ||||||||
\(263\) | 23.3921 | 1.44242 | 0.721210 | − | 0.692717i | \(-0.243586\pi\) | ||||
0.721210 | + | 0.692717i | \(0.243586\pi\) | |||||||
\(264\) | 2.39219 | 0.147229 | ||||||||
\(265\) | 26.1038 | 1.60355 | ||||||||
\(266\) | −0.101937 | −0.00625018 | ||||||||
\(267\) | 1.58305 | 0.0968813 | ||||||||
\(268\) | 18.1774 | 1.11036 | ||||||||
\(269\) | −21.5915 | −1.31646 | −0.658228 | − | 0.752819i | \(-0.728694\pi\) | ||||
−0.658228 | + | 0.752819i | \(0.728694\pi\) | |||||||
\(270\) | 1.76387 | 0.107346 | ||||||||
\(271\) | −12.2493 | −0.744095 | −0.372047 | − | 0.928214i | \(-0.621344\pi\) | ||||
−0.372047 | + | 0.928214i | \(0.621344\pi\) | |||||||
\(272\) | −0.242415 | −0.0146986 | ||||||||
\(273\) | 2.76000 | 0.167043 | ||||||||
\(274\) | 8.23106 | 0.497257 | ||||||||
\(275\) | 2.98524 | 0.180017 | ||||||||
\(276\) | 1.48338 | 0.0892893 | ||||||||
\(277\) | 4.71527 | 0.283313 | 0.141657 | − | 0.989916i | \(-0.454757\pi\) | ||||
0.141657 | + | 0.989916i | \(0.454757\pi\) | |||||||
\(278\) | 7.46374 | 0.447646 | ||||||||
\(279\) | 5.37505 | 0.321796 | ||||||||
\(280\) | 6.35493 | 0.379779 | ||||||||
\(281\) | 17.4265 | 1.03958 | 0.519788 | − | 0.854295i | \(-0.326011\pi\) | ||||
0.519788 | + | 0.854295i | \(0.326011\pi\) | |||||||
\(282\) | −2.29623 | −0.136738 | ||||||||
\(283\) | −15.2066 | −0.903937 | −0.451968 | − | 0.892034i | \(-0.649278\pi\) | ||||
−0.451968 | + | 0.892034i | \(0.649278\pi\) | |||||||
\(284\) | −8.98403 | −0.533104 | ||||||||
\(285\) | 0.452710 | 0.0268162 | ||||||||
\(286\) | 1.83257 | 0.108362 | ||||||||
\(287\) | 10.3578 | 0.611400 | ||||||||
\(288\) | −5.65958 | −0.333494 | ||||||||
\(289\) | −16.9813 | −0.998902 | ||||||||
\(290\) | −0.864367 | −0.0507574 | ||||||||
\(291\) | −12.4149 | −0.727777 | ||||||||
\(292\) | −17.9364 | −1.04965 | ||||||||
\(293\) | −3.78217 | −0.220957 | −0.110478 | − | 0.993879i | \(-0.535238\pi\) | ||||
−0.110478 | + | 0.993879i | \(0.535238\pi\) | |||||||
\(294\) | −0.630217 | −0.0367550 | ||||||||
\(295\) | 8.21647 | 0.478381 | ||||||||
\(296\) | −17.8662 | −1.03845 | ||||||||
\(297\) | 1.05357 | 0.0611341 | ||||||||
\(298\) | −13.1426 | −0.761332 | ||||||||
\(299\) | 2.55433 | 0.147721 | ||||||||
\(300\) | −4.54155 | −0.262207 | ||||||||
\(301\) | 8.97705 | 0.517428 | ||||||||
\(302\) | −11.9818 | −0.689476 | ||||||||
\(303\) | 4.96651 | 0.285319 | ||||||||
\(304\) | −0.287058 | −0.0164639 | ||||||||
\(305\) | −34.9772 | −2.00279 | ||||||||
\(306\) | 0.0860842 | 0.00492111 | ||||||||
\(307\) | −16.0020 | −0.913280 | −0.456640 | − | 0.889652i | \(-0.650947\pi\) | ||||
−0.456640 | + | 0.889652i | \(0.650947\pi\) | |||||||
\(308\) | 1.68868 | 0.0962216 | ||||||||
\(309\) | −6.79070 | −0.386309 | ||||||||
\(310\) | 9.48090 | 0.538479 | ||||||||
\(311\) | −14.9728 | −0.849029 | −0.424514 | − | 0.905421i | \(-0.639555\pi\) | ||||
−0.424514 | + | 0.905421i | \(0.639555\pi\) | |||||||
\(312\) | −6.26676 | −0.354786 | ||||||||
\(313\) | −16.6362 | −0.940335 | −0.470168 | − | 0.882577i | \(-0.655807\pi\) | ||||
−0.470168 | + | 0.882577i | \(0.655807\pi\) | |||||||
\(314\) | 9.86011 | 0.556438 | ||||||||
\(315\) | 2.79883 | 0.157696 | ||||||||
\(316\) | −16.5359 | −0.930215 | ||||||||
\(317\) | 34.7996 | 1.95454 | 0.977269 | − | 0.212002i | \(-0.0679983\pi\) | ||||
0.977269 | + | 0.212002i | \(0.0679983\pi\) | |||||||
\(318\) | 5.87784 | 0.329613 | ||||||||
\(319\) | −0.516289 | −0.0289066 | ||||||||
\(320\) | −0.0485698 | −0.00271514 | ||||||||
\(321\) | 18.7427 | 1.04611 | ||||||||
\(322\) | −0.583254 | −0.0325035 | ||||||||
\(323\) | 0.0220941 | 0.00122935 | ||||||||
\(324\) | −1.60283 | −0.0890459 | ||||||||
\(325\) | −7.82037 | −0.433796 | ||||||||
\(326\) | −7.93881 | −0.439690 | ||||||||
\(327\) | 2.36857 | 0.130982 | ||||||||
\(328\) | −23.5180 | −1.29856 | ||||||||
\(329\) | −3.64355 | −0.200875 | ||||||||
\(330\) | 1.85836 | 0.102299 | ||||||||
\(331\) | 24.8449 | 1.36560 | 0.682800 | − | 0.730605i | \(-0.260762\pi\) | ||||
0.682800 | + | 0.730605i | \(0.260762\pi\) | |||||||
\(332\) | −19.1652 | −1.05183 | ||||||||
\(333\) | −7.86861 | −0.431197 | ||||||||
\(334\) | 0.0218151 | 0.00119367 | ||||||||
\(335\) | 31.7411 | 1.73420 | ||||||||
\(336\) | −1.77470 | −0.0968181 | ||||||||
\(337\) | −19.6563 | −1.07074 | −0.535372 | − | 0.844616i | \(-0.679829\pi\) | ||||
−0.535372 | + | 0.844616i | \(0.679829\pi\) | |||||||
\(338\) | 3.39207 | 0.184504 | ||||||||
\(339\) | 10.3546 | 0.562387 | ||||||||
\(340\) | −0.612769 | −0.0332321 | ||||||||
\(341\) | 5.66297 | 0.306667 | ||||||||
\(342\) | 0.101937 | 0.00551214 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −20.3830 | −1.09898 | ||||||||
\(345\) | 2.59026 | 0.139455 | ||||||||
\(346\) | 12.3871 | 0.665934 | ||||||||
\(347\) | 19.7723 | 1.06143 | 0.530716 | − | 0.847549i | \(-0.321923\pi\) | ||||
0.530716 | + | 0.847549i | \(0.321923\pi\) | |||||||
\(348\) | 0.785448 | 0.0421044 | ||||||||
\(349\) | 7.50169 | 0.401556 | 0.200778 | − | 0.979637i | \(-0.435653\pi\) | ||||
0.200778 | + | 0.979637i | \(0.435653\pi\) | |||||||
\(350\) | 1.78570 | 0.0954496 | ||||||||
\(351\) | −2.76000 | −0.147318 | ||||||||
\(352\) | −5.96274 | −0.317815 | ||||||||
\(353\) | 16.2391 | 0.864318 | 0.432159 | − | 0.901797i | \(-0.357752\pi\) | ||||
0.432159 | + | 0.901797i | \(0.357752\pi\) | |||||||
\(354\) | 1.85012 | 0.0983325 | ||||||||
\(355\) | −15.6878 | −0.832621 | ||||||||
\(356\) | −2.53736 | −0.134480 | ||||||||
\(357\) | 0.136595 | 0.00722935 | ||||||||
\(358\) | −9.08728 | −0.480278 | ||||||||
\(359\) | 3.52732 | 0.186165 | 0.0930825 | − | 0.995658i | \(-0.470328\pi\) | ||||
0.0930825 | + | 0.995658i | \(0.470328\pi\) | |||||||
\(360\) | −6.35493 | −0.334934 | ||||||||
\(361\) | −18.9738 | −0.998623 | ||||||||
\(362\) | −16.2328 | −0.853175 | ||||||||
\(363\) | −9.89000 | −0.519090 | ||||||||
\(364\) | −4.42381 | −0.231870 | ||||||||
\(365\) | −31.3203 | −1.63938 | ||||||||
\(366\) | −7.87586 | −0.411678 | ||||||||
\(367\) | −19.8507 | −1.03620 | −0.518100 | − | 0.855320i | \(-0.673360\pi\) | ||||
−0.518100 | + | 0.855320i | \(0.673360\pi\) | |||||||
\(368\) | −1.64245 | −0.0856188 | ||||||||
\(369\) | −10.3578 | −0.539205 | ||||||||
\(370\) | −13.8792 | −0.721547 | ||||||||
\(371\) | 9.32669 | 0.484218 | ||||||||
\(372\) | −8.61527 | −0.446681 | ||||||||
\(373\) | 36.8570 | 1.90838 | 0.954192 | − | 0.299195i | \(-0.0967180\pi\) | ||||
0.954192 | + | 0.299195i | \(0.0967180\pi\) | |||||||
\(374\) | 0.0906954 | 0.00468975 | ||||||||
\(375\) | 6.06377 | 0.313132 | ||||||||
\(376\) | 8.27290 | 0.426642 | ||||||||
\(377\) | 1.35251 | 0.0696578 | ||||||||
\(378\) | 0.630217 | 0.0324149 | ||||||||
\(379\) | 28.5680 | 1.46744 | 0.733720 | − | 0.679452i | \(-0.237782\pi\) | ||||
0.733720 | + | 0.679452i | \(0.237782\pi\) | |||||||
\(380\) | −0.725616 | −0.0372233 | ||||||||
\(381\) | 12.9282 | 0.662334 | ||||||||
\(382\) | 0.630217 | 0.0322447 | ||||||||
\(383\) | 4.46037 | 0.227914 | 0.113957 | − | 0.993486i | \(-0.463647\pi\) | ||||
0.113957 | + | 0.993486i | \(0.463647\pi\) | |||||||
\(384\) | 11.3082 | 0.577070 | ||||||||
\(385\) | 2.94875 | 0.150282 | ||||||||
\(386\) | 14.0205 | 0.713625 | ||||||||
\(387\) | −8.97705 | −0.456329 | ||||||||
\(388\) | 19.8990 | 1.01022 | ||||||||
\(389\) | 16.3109 | 0.826995 | 0.413497 | − | 0.910505i | \(-0.364307\pi\) | ||||
0.413497 | + | 0.910505i | \(0.364307\pi\) | |||||||
\(390\) | −4.86829 | −0.246516 | ||||||||
\(391\) | 0.126416 | 0.00639311 | ||||||||
\(392\) | 2.27056 | 0.114681 | ||||||||
\(393\) | 15.4387 | 0.778777 | ||||||||
\(394\) | −8.90136 | −0.448444 | ||||||||
\(395\) | −28.8747 | −1.45284 | ||||||||
\(396\) | −1.68868 | −0.0848595 | ||||||||
\(397\) | 11.0036 | 0.552256 | 0.276128 | − | 0.961121i | \(-0.410949\pi\) | ||||
0.276128 | + | 0.961121i | \(0.410949\pi\) | |||||||
\(398\) | −1.81762 | −0.0911090 | ||||||||
\(399\) | 0.161750 | 0.00809761 | ||||||||
\(400\) | 5.02856 | 0.251428 | ||||||||
\(401\) | 33.8060 | 1.68819 | 0.844096 | − | 0.536192i | \(-0.180138\pi\) | ||||
0.844096 | + | 0.536192i | \(0.180138\pi\) | |||||||
\(402\) | 7.14719 | 0.356470 | ||||||||
\(403\) | −14.8352 | −0.738992 | ||||||||
\(404\) | −7.96046 | −0.396048 | ||||||||
\(405\) | −2.79883 | −0.139075 | ||||||||
\(406\) | −0.308831 | −0.0153270 | ||||||||
\(407\) | −8.29010 | −0.410925 | ||||||||
\(408\) | −0.310147 | −0.0153545 | ||||||||
\(409\) | 10.5452 | 0.521426 | 0.260713 | − | 0.965416i | \(-0.416042\pi\) | ||||
0.260713 | + | 0.965416i | \(0.416042\pi\) | |||||||
\(410\) | −18.2698 | −0.902281 | ||||||||
\(411\) | −13.0607 | −0.644235 | ||||||||
\(412\) | 10.8843 | 0.536231 | ||||||||
\(413\) | 2.93568 | 0.144455 | ||||||||
\(414\) | 0.583254 | 0.0286654 | ||||||||
\(415\) | −33.4660 | −1.64278 | ||||||||
\(416\) | 15.6204 | 0.765856 | ||||||||
\(417\) | −11.8431 | −0.579961 | ||||||||
\(418\) | 0.107398 | 0.00525300 | ||||||||
\(419\) | −14.4031 | −0.703637 | −0.351819 | − | 0.936068i | \(-0.614437\pi\) | ||||
−0.351819 | + | 0.936068i | \(0.614437\pi\) | |||||||
\(420\) | −4.48604 | −0.218896 | ||||||||
\(421\) | 2.81960 | 0.137419 | 0.0687095 | − | 0.997637i | \(-0.478112\pi\) | ||||
0.0687095 | + | 0.997637i | \(0.478112\pi\) | |||||||
\(422\) | −2.36809 | −0.115277 | ||||||||
\(423\) | 3.64355 | 0.177155 | ||||||||
\(424\) | −21.1768 | −1.02844 | ||||||||
\(425\) | −0.387036 | −0.0187740 | ||||||||
\(426\) | −3.53244 | −0.171147 | ||||||||
\(427\) | −12.4971 | −0.604775 | ||||||||
\(428\) | −30.0412 | −1.45210 | ||||||||
\(429\) | −2.90785 | −0.140392 | ||||||||
\(430\) | −15.8344 | −0.763601 | ||||||||
\(431\) | −18.1076 | −0.872211 | −0.436105 | − | 0.899896i | \(-0.643642\pi\) | ||||
−0.436105 | + | 0.899896i | \(0.643642\pi\) | |||||||
\(432\) | 1.77470 | 0.0853855 | ||||||||
\(433\) | −24.3620 | −1.17076 | −0.585382 | − | 0.810758i | \(-0.699055\pi\) | ||||
−0.585382 | + | 0.810758i | \(0.699055\pi\) | |||||||
\(434\) | 3.38745 | 0.162603 | ||||||||
\(435\) | 1.37154 | 0.0657602 | ||||||||
\(436\) | −3.79641 | −0.181815 | ||||||||
\(437\) | 0.149696 | 0.00716094 | ||||||||
\(438\) | −7.05243 | −0.336978 | ||||||||
\(439\) | −1.86612 | −0.0890648 | −0.0445324 | − | 0.999008i | \(-0.514180\pi\) | ||||
−0.0445324 | + | 0.999008i | \(0.514180\pi\) | |||||||
\(440\) | −6.69533 | −0.319187 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −0.237593 | −0.0113011 | ||||||||
\(443\) | 27.9040 | 1.32576 | 0.662879 | − | 0.748727i | \(-0.269335\pi\) | ||||
0.662879 | + | 0.748727i | \(0.269335\pi\) | |||||||
\(444\) | 12.6120 | 0.598540 | ||||||||
\(445\) | −4.43070 | −0.210035 | ||||||||
\(446\) | 9.07520 | 0.429723 | ||||||||
\(447\) | 20.8541 | 0.986366 | ||||||||
\(448\) | −0.0173536 | −0.000819880 0 | ||||||||
\(449\) | −39.4282 | −1.86073 | −0.930366 | − | 0.366632i | \(-0.880511\pi\) | ||||
−0.930366 | + | 0.366632i | \(0.880511\pi\) | |||||||
\(450\) | −1.78570 | −0.0841786 | ||||||||
\(451\) | −10.9126 | −0.513854 | ||||||||
\(452\) | −16.5967 | −0.780642 | ||||||||
\(453\) | 19.0122 | 0.893271 | ||||||||
\(454\) | −11.1077 | −0.521310 | ||||||||
\(455\) | −7.72479 | −0.362144 | ||||||||
\(456\) | −0.367263 | −0.0171987 | ||||||||
\(457\) | −12.1071 | −0.566348 | −0.283174 | − | 0.959069i | \(-0.591387\pi\) | ||||
−0.283174 | + | 0.959069i | \(0.591387\pi\) | |||||||
\(458\) | −15.3780 | −0.718567 | ||||||||
\(459\) | −0.136595 | −0.00637569 | ||||||||
\(460\) | −4.15174 | −0.193576 | ||||||||
\(461\) | −13.0305 | −0.606893 | −0.303446 | − | 0.952849i | \(-0.598137\pi\) | ||||
−0.303446 | + | 0.952849i | \(0.598137\pi\) | |||||||
\(462\) | 0.663975 | 0.0308909 | ||||||||
\(463\) | 34.8486 | 1.61955 | 0.809777 | − | 0.586738i | \(-0.199588\pi\) | ||||
0.809777 | + | 0.586738i | \(0.199588\pi\) | |||||||
\(464\) | −0.869675 | −0.0403736 | ||||||||
\(465\) | −15.0439 | −0.697643 | ||||||||
\(466\) | −8.70198 | −0.403111 | ||||||||
\(467\) | −4.22272 | −0.195404 | −0.0977020 | − | 0.995216i | \(-0.531149\pi\) | ||||
−0.0977020 | + | 0.995216i | \(0.531149\pi\) | |||||||
\(468\) | 4.42381 | 0.204491 | ||||||||
\(469\) | 11.3408 | 0.523671 | ||||||||
\(470\) | 6.42675 | 0.296444 | ||||||||
\(471\) | −15.6456 | −0.720910 | ||||||||
\(472\) | −6.66564 | −0.306811 | ||||||||
\(473\) | −9.45791 | −0.434875 | ||||||||
\(474\) | −6.50176 | −0.298636 | ||||||||
\(475\) | −0.458312 | −0.0210288 | ||||||||
\(476\) | −0.218937 | −0.0100350 | ||||||||
\(477\) | −9.32669 | −0.427040 | ||||||||
\(478\) | −6.61655 | −0.302634 | ||||||||
\(479\) | −25.7175 | −1.17506 | −0.587531 | − | 0.809202i | \(-0.699900\pi\) | ||||
−0.587531 | + | 0.809202i | \(0.699900\pi\) | |||||||
\(480\) | 15.8402 | 0.723003 | ||||||||
\(481\) | 21.7174 | 0.990228 | ||||||||
\(482\) | −2.76963 | −0.126153 | ||||||||
\(483\) | 0.925481 | 0.0421108 | ||||||||
\(484\) | 15.8519 | 0.720543 | ||||||||
\(485\) | 34.7473 | 1.57780 | ||||||||
\(486\) | −0.630217 | −0.0285872 | ||||||||
\(487\) | −15.3784 | −0.696864 | −0.348432 | − | 0.937334i | \(-0.613286\pi\) | ||||
−0.348432 | + | 0.937334i | \(0.613286\pi\) | |||||||
\(488\) | 28.3754 | 1.28449 | ||||||||
\(489\) | 12.5969 | 0.569654 | ||||||||
\(490\) | 1.76387 | 0.0796836 | ||||||||
\(491\) | 12.6021 | 0.568726 | 0.284363 | − | 0.958717i | \(-0.408218\pi\) | ||||
0.284363 | + | 0.958717i | \(0.408218\pi\) | |||||||
\(492\) | 16.6017 | 0.748463 | ||||||||
\(493\) | 0.0669367 | 0.00301468 | ||||||||
\(494\) | −0.281348 | −0.0126584 | ||||||||
\(495\) | −2.94875 | −0.132537 | ||||||||
\(496\) | 9.53912 | 0.428319 | ||||||||
\(497\) | −5.60512 | −0.251424 | ||||||||
\(498\) | −7.53559 | −0.337678 | ||||||||
\(499\) | −33.3896 | −1.49472 | −0.747362 | − | 0.664417i | \(-0.768680\pi\) | ||||
−0.747362 | + | 0.664417i | \(0.768680\pi\) | |||||||
\(500\) | −9.71917 | −0.434655 | ||||||||
\(501\) | −0.0346152 | −0.00154649 | ||||||||
\(502\) | −5.72868 | −0.255684 | ||||||||
\(503\) | −10.0887 | −0.449835 | −0.224917 | − | 0.974378i | \(-0.572211\pi\) | ||||
−0.224917 | + | 0.974378i | \(0.572211\pi\) | |||||||
\(504\) | −2.27056 | −0.101139 | ||||||||
\(505\) | −13.9004 | −0.618562 | ||||||||
\(506\) | 0.614496 | 0.0273177 | ||||||||
\(507\) | −5.38238 | −0.239040 | ||||||||
\(508\) | −20.7217 | −0.919378 | ||||||||
\(509\) | −11.3443 | −0.502826 | −0.251413 | − | 0.967880i | \(-0.580895\pi\) | ||||
−0.251413 | + | 0.967880i | \(0.580895\pi\) | |||||||
\(510\) | −0.240935 | −0.0106688 | ||||||||
\(511\) | −11.1905 | −0.495037 | ||||||||
\(512\) | −18.1032 | −0.800057 | ||||||||
\(513\) | −0.161750 | −0.00714142 | ||||||||
\(514\) | 11.7996 | 0.520456 | ||||||||
\(515\) | 19.0060 | 0.837506 | ||||||||
\(516\) | 14.3886 | 0.633425 | ||||||||
\(517\) | 3.83872 | 0.168827 | ||||||||
\(518\) | −4.95894 | −0.217883 | ||||||||
\(519\) | −19.6553 | −0.862770 | ||||||||
\(520\) | 17.5396 | 0.769163 | ||||||||
\(521\) | −1.59553 | −0.0699014 | −0.0349507 | − | 0.999389i | \(-0.511127\pi\) | ||||
−0.0349507 | + | 0.999389i | \(0.511127\pi\) | |||||||
\(522\) | 0.308831 | 0.0135172 | ||||||||
\(523\) | 34.3878 | 1.50367 | 0.751836 | − | 0.659351i | \(-0.229169\pi\) | ||||
0.751836 | + | 0.659351i | \(0.229169\pi\) | |||||||
\(524\) | −24.7455 | −1.08101 | ||||||||
\(525\) | −2.83346 | −0.123662 | ||||||||
\(526\) | −14.7421 | −0.642787 | ||||||||
\(527\) | −0.734202 | −0.0319824 | ||||||||
\(528\) | 1.86977 | 0.0813712 | ||||||||
\(529\) | −22.1435 | −0.962760 | ||||||||
\(530\) | −16.4511 | −0.714590 | ||||||||
\(531\) | −2.93568 | −0.127398 | ||||||||
\(532\) | −0.259257 | −0.0112402 | ||||||||
\(533\) | 28.5875 | 1.23826 | ||||||||
\(534\) | −0.997668 | −0.0431733 | ||||||||
\(535\) | −52.4576 | −2.26794 | ||||||||
\(536\) | −25.7501 | −1.11223 | ||||||||
\(537\) | 14.4193 | 0.622238 | ||||||||
\(538\) | 13.6073 | 0.586653 | ||||||||
\(539\) | 1.05357 | 0.0453803 | ||||||||
\(540\) | 4.48604 | 0.193049 | ||||||||
\(541\) | 8.66011 | 0.372327 | 0.186164 | − | 0.982519i | \(-0.440395\pi\) | ||||
0.186164 | + | 0.982519i | \(0.440395\pi\) | |||||||
\(542\) | 7.71975 | 0.331592 | ||||||||
\(543\) | 25.7574 | 1.10536 | ||||||||
\(544\) | 0.773067 | 0.0331450 | ||||||||
\(545\) | −6.62924 | −0.283965 | ||||||||
\(546\) | −1.73940 | −0.0744395 | ||||||||
\(547\) | 13.8428 | 0.591876 | 0.295938 | − | 0.955207i | \(-0.404368\pi\) | ||||
0.295938 | + | 0.955207i | \(0.404368\pi\) | |||||||
\(548\) | 20.9340 | 0.894256 | ||||||||
\(549\) | 12.4971 | 0.533362 | ||||||||
\(550\) | −1.88135 | −0.0802210 | ||||||||
\(551\) | 0.0792637 | 0.00337675 | ||||||||
\(552\) | −2.10136 | −0.0894399 | ||||||||
\(553\) | −10.3167 | −0.438710 | ||||||||
\(554\) | −2.97165 | −0.126253 | ||||||||
\(555\) | 22.0229 | 0.934822 | ||||||||
\(556\) | 18.9825 | 0.805036 | ||||||||
\(557\) | 22.7232 | 0.962811 | 0.481406 | − | 0.876498i | \(-0.340126\pi\) | ||||
0.481406 | + | 0.876498i | \(0.340126\pi\) | |||||||
\(558\) | −3.38745 | −0.143402 | ||||||||
\(559\) | 24.7767 | 1.04794 | ||||||||
\(560\) | 4.96710 | 0.209898 | ||||||||
\(561\) | −0.143911 | −0.00607594 | ||||||||
\(562\) | −10.9825 | −0.463267 | ||||||||
\(563\) | −20.2508 | −0.853471 | −0.426736 | − | 0.904376i | \(-0.640337\pi\) | ||||
−0.426736 | + | 0.904376i | \(0.640337\pi\) | |||||||
\(564\) | −5.83997 | −0.245907 | ||||||||
\(565\) | −28.9809 | −1.21924 | ||||||||
\(566\) | 9.58344 | 0.402822 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 12.7268 | 0.534004 | ||||||||
\(569\) | −32.2811 | −1.35329 | −0.676647 | − | 0.736308i | \(-0.736567\pi\) | ||||
−0.676647 | + | 0.736308i | \(0.736567\pi\) | |||||||
\(570\) | −0.285306 | −0.0119501 | ||||||||
\(571\) | −7.72882 | −0.323441 | −0.161721 | − | 0.986837i | \(-0.551704\pi\) | ||||
−0.161721 | + | 0.986837i | \(0.551704\pi\) | |||||||
\(572\) | 4.66077 | 0.194877 | ||||||||
\(573\) | −1.00000 | −0.0417756 | ||||||||
\(574\) | −6.52765 | −0.272459 | ||||||||
\(575\) | −2.62232 | −0.109358 | ||||||||
\(576\) | 0.0173536 | 0.000723067 0 | ||||||||
\(577\) | −33.8600 | −1.40961 | −0.704805 | − | 0.709401i | \(-0.748965\pi\) | ||||
−0.704805 | + | 0.709401i | \(0.748965\pi\) | |||||||
\(578\) | 10.7019 | 0.445142 | ||||||||
\(579\) | −22.2471 | −0.924558 | ||||||||
\(580\) | −2.19834 | −0.0912810 | ||||||||
\(581\) | −11.9571 | −0.496065 | ||||||||
\(582\) | 7.82411 | 0.324320 | ||||||||
\(583\) | −9.82628 | −0.406963 | ||||||||
\(584\) | 25.4087 | 1.05142 | ||||||||
\(585\) | 7.72479 | 0.319381 | ||||||||
\(586\) | 2.38359 | 0.0984652 | ||||||||
\(587\) | 28.5033 | 1.17646 | 0.588228 | − | 0.808695i | \(-0.299826\pi\) | ||||
0.588228 | + | 0.808695i | \(0.299826\pi\) | |||||||
\(588\) | −1.60283 | −0.0660994 | ||||||||
\(589\) | −0.869412 | −0.0358235 | ||||||||
\(590\) | −5.17816 | −0.213182 | ||||||||
\(591\) | 14.1243 | 0.580995 | ||||||||
\(592\) | −13.9645 | −0.573936 | ||||||||
\(593\) | 11.7239 | 0.481443 | 0.240722 | − | 0.970594i | \(-0.422616\pi\) | ||||
0.240722 | + | 0.970594i | \(0.422616\pi\) | |||||||
\(594\) | −0.663975 | −0.0272432 | ||||||||
\(595\) | −0.382305 | −0.0156730 | ||||||||
\(596\) | −33.4255 | −1.36916 | ||||||||
\(597\) | 2.88412 | 0.118039 | ||||||||
\(598\) | −1.60978 | −0.0658289 | ||||||||
\(599\) | 44.7437 | 1.82818 | 0.914090 | − | 0.405512i | \(-0.132907\pi\) | ||||
0.914090 | + | 0.405512i | \(0.132907\pi\) | |||||||
\(600\) | 6.43356 | 0.262649 | ||||||||
\(601\) | 5.87076 | 0.239473 | 0.119737 | − | 0.992806i | \(-0.461795\pi\) | ||||
0.119737 | + | 0.992806i | \(0.461795\pi\) | |||||||
\(602\) | −5.65749 | −0.230582 | ||||||||
\(603\) | −11.3408 | −0.461835 | ||||||||
\(604\) | −30.4733 | −1.23994 | ||||||||
\(605\) | 27.6805 | 1.12537 | ||||||||
\(606\) | −3.12998 | −0.127147 | ||||||||
\(607\) | 14.3774 | 0.583559 | 0.291779 | − | 0.956486i | \(-0.405753\pi\) | ||||
0.291779 | + | 0.956486i | \(0.405753\pi\) | |||||||
\(608\) | 0.915434 | 0.0371258 | ||||||||
\(609\) | 0.490039 | 0.0198574 | ||||||||
\(610\) | 22.0432 | 0.892504 | ||||||||
\(611\) | −10.0562 | −0.406830 | ||||||||
\(612\) | 0.218937 | 0.00885002 | ||||||||
\(613\) | −20.6085 | −0.832371 | −0.416186 | − | 0.909280i | \(-0.636633\pi\) | ||||
−0.416186 | + | 0.909280i | \(0.636633\pi\) | |||||||
\(614\) | 10.0847 | 0.406986 | ||||||||
\(615\) | 28.9897 | 1.16898 | ||||||||
\(616\) | −2.39219 | −0.0963840 | ||||||||
\(617\) | 20.5442 | 0.827079 | 0.413539 | − | 0.910486i | \(-0.364292\pi\) | ||||
0.413539 | + | 0.910486i | \(0.364292\pi\) | |||||||
\(618\) | 4.27961 | 0.172151 | ||||||||
\(619\) | 44.6946 | 1.79643 | 0.898215 | − | 0.439557i | \(-0.144865\pi\) | ||||
0.898215 | + | 0.439557i | \(0.144865\pi\) | |||||||
\(620\) | 24.1127 | 0.968389 | ||||||||
\(621\) | −0.925481 | −0.0371383 | ||||||||
\(622\) | 9.43611 | 0.378353 | ||||||||
\(623\) | −1.58305 | −0.0634237 | ||||||||
\(624\) | −4.89819 | −0.196085 | ||||||||
\(625\) | −31.1388 | −1.24555 | ||||||||
\(626\) | 10.4844 | 0.419043 | ||||||||
\(627\) | −0.170414 | −0.00680567 | ||||||||
\(628\) | 25.0771 | 1.00069 | ||||||||
\(629\) | 1.07481 | 0.0428555 | ||||||||
\(630\) | −1.76387 | −0.0702744 | ||||||||
\(631\) | 32.7954 | 1.30556 | 0.652782 | − | 0.757546i | \(-0.273602\pi\) | ||||
0.652782 | + | 0.757546i | \(0.273602\pi\) | |||||||
\(632\) | 23.4247 | 0.931785 | ||||||||
\(633\) | 3.75758 | 0.149350 | ||||||||
\(634\) | −21.9313 | −0.871003 | ||||||||
\(635\) | −36.1840 | −1.43592 | ||||||||
\(636\) | 14.9491 | 0.592769 | ||||||||
\(637\) | −2.76000 | −0.109355 | ||||||||
\(638\) | 0.325374 | 0.0128817 | ||||||||
\(639\) | 5.60512 | 0.221735 | ||||||||
\(640\) | −31.6498 | −1.25107 | ||||||||
\(641\) | 30.6688 | 1.21134 | 0.605672 | − | 0.795714i | \(-0.292904\pi\) | ||||
0.605672 | + | 0.795714i | \(0.292904\pi\) | |||||||
\(642\) | −11.8120 | −0.466181 | ||||||||
\(643\) | 40.6256 | 1.60212 | 0.801058 | − | 0.598587i | \(-0.204271\pi\) | ||||
0.801058 | + | 0.598587i | \(0.204271\pi\) | |||||||
\(644\) | −1.48338 | −0.0584535 | ||||||||
\(645\) | 25.1253 | 0.989306 | ||||||||
\(646\) | −0.0139241 | −0.000547836 0 | ||||||||
\(647\) | −13.2387 | −0.520465 | −0.260233 | − | 0.965546i | \(-0.583799\pi\) | ||||
−0.260233 | + | 0.965546i | \(0.583799\pi\) | |||||||
\(648\) | 2.27056 | 0.0891961 | ||||||||
\(649\) | −3.09293 | −0.121408 | ||||||||
\(650\) | 4.92853 | 0.193313 | ||||||||
\(651\) | −5.37505 | −0.210665 | ||||||||
\(652\) | −20.1907 | −0.790729 | ||||||||
\(653\) | 30.4110 | 1.19008 | 0.595038 | − | 0.803698i | \(-0.297137\pi\) | ||||
0.595038 | + | 0.803698i | \(0.297137\pi\) | |||||||
\(654\) | −1.49272 | −0.0583698 | ||||||||
\(655\) | −43.2102 | −1.68836 | ||||||||
\(656\) | −18.3820 | −0.717696 | ||||||||
\(657\) | 11.1905 | 0.436582 | ||||||||
\(658\) | 2.29623 | 0.0895162 | ||||||||
\(659\) | −24.8780 | −0.969109 | −0.484555 | − | 0.874761i | \(-0.661018\pi\) | ||||
−0.484555 | + | 0.874761i | \(0.661018\pi\) | |||||||
\(660\) | 4.72634 | 0.183973 | ||||||||
\(661\) | 26.7177 | 1.03920 | 0.519599 | − | 0.854410i | \(-0.326081\pi\) | ||||
0.519599 | + | 0.854410i | \(0.326081\pi\) | |||||||
\(662\) | −15.6577 | −0.608554 | ||||||||
\(663\) | 0.377001 | 0.0146415 | ||||||||
\(664\) | 27.1494 | 1.05360 | ||||||||
\(665\) | −0.452710 | −0.0175553 | ||||||||
\(666\) | 4.95894 | 0.192155 | ||||||||
\(667\) | 0.453522 | 0.0175604 | ||||||||
\(668\) | 0.0554821 | 0.00214667 | ||||||||
\(669\) | −14.4001 | −0.556741 | ||||||||
\(670\) | −20.0038 | −0.772814 | ||||||||
\(671\) | 13.1665 | 0.508286 | ||||||||
\(672\) | 5.65958 | 0.218323 | ||||||||
\(673\) | 6.60622 | 0.254651 | 0.127325 | − | 0.991861i | \(-0.459361\pi\) | ||||
0.127325 | + | 0.991861i | \(0.459361\pi\) | |||||||
\(674\) | 12.3877 | 0.477157 | ||||||||
\(675\) | 2.83346 | 0.109060 | ||||||||
\(676\) | 8.62702 | 0.331808 | ||||||||
\(677\) | 2.80381 | 0.107759 | 0.0538797 | − | 0.998547i | \(-0.482841\pi\) | ||||
0.0538797 | + | 0.998547i | \(0.482841\pi\) | |||||||
\(678\) | −6.52567 | −0.250617 | ||||||||
\(679\) | 12.4149 | 0.476442 | ||||||||
\(680\) | 0.868048 | 0.0332881 | ||||||||
\(681\) | 17.6252 | 0.675398 | ||||||||
\(682\) | −3.56890 | −0.136660 | ||||||||
\(683\) | 1.41732 | 0.0542322 | 0.0271161 | − | 0.999632i | \(-0.491368\pi\) | ||||
0.0271161 | + | 0.999632i | \(0.491368\pi\) | |||||||
\(684\) | 0.259257 | 0.00991292 | ||||||||
\(685\) | 36.5546 | 1.39668 | ||||||||
\(686\) | 0.630217 | 0.0240618 | ||||||||
\(687\) | 24.4011 | 0.930961 | ||||||||
\(688\) | −15.9316 | −0.607387 | ||||||||
\(689\) | 25.7417 | 0.980681 | ||||||||
\(690\) | −1.63243 | −0.0621455 | ||||||||
\(691\) | −15.8855 | −0.604314 | −0.302157 | − | 0.953258i | \(-0.597707\pi\) | ||||
−0.302157 | + | 0.953258i | \(0.597707\pi\) | |||||||
\(692\) | 31.5040 | 1.19760 | ||||||||
\(693\) | −1.05357 | −0.0400217 | ||||||||
\(694\) | −12.4608 | −0.473007 | ||||||||
\(695\) | 33.1469 | 1.25733 | ||||||||
\(696\) | −1.11267 | −0.0421755 | ||||||||
\(697\) | 1.41482 | 0.0535900 | ||||||||
\(698\) | −4.72769 | −0.178946 | ||||||||
\(699\) | 13.8079 | 0.522263 | ||||||||
\(700\) | 4.54155 | 0.171654 | ||||||||
\(701\) | −42.2541 | −1.59591 | −0.797957 | − | 0.602714i | \(-0.794086\pi\) | ||||
−0.797957 | + | 0.602714i | \(0.794086\pi\) | |||||||
\(702\) | 1.73940 | 0.0656495 | ||||||||
\(703\) | 1.27275 | 0.0480025 | ||||||||
\(704\) | 0.0182832 | 0.000689072 0 | ||||||||
\(705\) | −10.1977 | −0.384067 | ||||||||
\(706\) | −10.2341 | −0.385167 | ||||||||
\(707\) | −4.96651 | −0.186785 | ||||||||
\(708\) | 4.70538 | 0.176839 | ||||||||
\(709\) | −42.1888 | −1.58443 | −0.792217 | − | 0.610240i | \(-0.791073\pi\) | ||||
−0.792217 | + | 0.610240i | \(0.791073\pi\) | |||||||
\(710\) | 9.88672 | 0.371042 | ||||||||
\(711\) | 10.3167 | 0.386906 | ||||||||
\(712\) | 3.59442 | 0.134707 | ||||||||
\(713\) | −4.97450 | −0.186297 | ||||||||
\(714\) | −0.0860842 | −0.00322162 | ||||||||
\(715\) | 8.13857 | 0.304365 | ||||||||
\(716\) | −23.1116 | −0.863721 | ||||||||
\(717\) | 10.4988 | 0.392086 | ||||||||
\(718\) | −2.22298 | −0.0829609 | ||||||||
\(719\) | 33.8749 | 1.26332 | 0.631660 | − | 0.775245i | \(-0.282374\pi\) | ||||
0.631660 | + | 0.775245i | \(0.282374\pi\) | |||||||
\(720\) | −4.96710 | −0.185113 | ||||||||
\(721\) | 6.79070 | 0.252899 | ||||||||
\(722\) | 11.9576 | 0.445017 | ||||||||
\(723\) | 4.39472 | 0.163441 | ||||||||
\(724\) | −41.2846 | −1.53433 | ||||||||
\(725\) | −1.38851 | −0.0515679 | ||||||||
\(726\) | 6.23285 | 0.231323 | ||||||||
\(727\) | −36.7976 | −1.36475 | −0.682374 | − | 0.731003i | \(-0.739052\pi\) | ||||
−0.682374 | + | 0.731003i | \(0.739052\pi\) | |||||||
\(728\) | 6.26676 | 0.232262 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 19.7386 | 0.730557 | ||||||||
\(731\) | 1.22622 | 0.0453532 | ||||||||
\(732\) | −20.0306 | −0.740353 | ||||||||
\(733\) | 1.68998 | 0.0624210 | 0.0312105 | − | 0.999513i | \(-0.490064\pi\) | ||||
0.0312105 | + | 0.999513i | \(0.490064\pi\) | |||||||
\(734\) | 12.5103 | 0.461762 | ||||||||
\(735\) | −2.79883 | −0.103236 | ||||||||
\(736\) | 5.23783 | 0.193069 | ||||||||
\(737\) | −11.9483 | −0.440122 | ||||||||
\(738\) | 6.52765 | 0.240286 | ||||||||
\(739\) | −17.0080 | −0.625649 | −0.312824 | − | 0.949811i | \(-0.601275\pi\) | ||||
−0.312824 | + | 0.949811i | \(0.601275\pi\) | |||||||
\(740\) | −35.2989 | −1.29761 | ||||||||
\(741\) | 0.446429 | 0.0164000 | ||||||||
\(742\) | −5.87784 | −0.215782 | ||||||||
\(743\) | 18.8028 | 0.689807 | 0.344904 | − | 0.938638i | \(-0.387912\pi\) | ||||
0.344904 | + | 0.938638i | \(0.387912\pi\) | |||||||
\(744\) | 12.2044 | 0.447435 | ||||||||
\(745\) | −58.3672 | −2.13841 | ||||||||
\(746\) | −23.2279 | −0.850435 | ||||||||
\(747\) | 11.9571 | 0.437489 | ||||||||
\(748\) | 0.230665 | 0.00843394 | ||||||||
\(749\) | −18.7427 | −0.684842 | ||||||||
\(750\) | −3.82149 | −0.139541 | ||||||||
\(751\) | 43.6044 | 1.59115 | 0.795574 | − | 0.605856i | \(-0.207169\pi\) | ||||
0.795574 | + | 0.605856i | \(0.207169\pi\) | |||||||
\(752\) | 6.46622 | 0.235799 | ||||||||
\(753\) | 9.09002 | 0.331259 | ||||||||
\(754\) | −0.852375 | −0.0310417 | ||||||||
\(755\) | −53.2120 | −1.93658 | ||||||||
\(756\) | 1.60283 | 0.0582942 | ||||||||
\(757\) | −21.8607 | −0.794539 | −0.397270 | − | 0.917702i | \(-0.630042\pi\) | ||||
−0.397270 | + | 0.917702i | \(0.630042\pi\) | |||||||
\(758\) | −18.0041 | −0.653937 | ||||||||
\(759\) | −0.975055 | −0.0353922 | ||||||||
\(760\) | 1.02791 | 0.0372861 | ||||||||
\(761\) | 45.8129 | 1.66072 | 0.830358 | − | 0.557231i | \(-0.188136\pi\) | ||||
0.830358 | + | 0.557231i | \(0.188136\pi\) | |||||||
\(762\) | −8.14760 | −0.295156 | ||||||||
\(763\) | −2.36857 | −0.0857481 | ||||||||
\(764\) | 1.60283 | 0.0579882 | ||||||||
\(765\) | 0.382305 | 0.0138223 | ||||||||
\(766\) | −2.81100 | −0.101566 | ||||||||
\(767\) | 8.10248 | 0.292564 | ||||||||
\(768\) | −7.16134 | −0.258413 | ||||||||
\(769\) | 38.5576 | 1.39042 | 0.695211 | − | 0.718805i | \(-0.255311\pi\) | ||||
0.695211 | + | 0.718805i | \(0.255311\pi\) | |||||||
\(770\) | −1.85836 | −0.0669705 | ||||||||
\(771\) | −18.7230 | −0.674293 | ||||||||
\(772\) | 35.6582 | 1.28337 | ||||||||
\(773\) | −30.5446 | −1.09861 | −0.549306 | − | 0.835621i | \(-0.685108\pi\) | ||||
−0.549306 | + | 0.835621i | \(0.685108\pi\) | |||||||
\(774\) | 5.65749 | 0.203354 | ||||||||
\(775\) | 15.2300 | 0.547078 | ||||||||
\(776\) | −28.1889 | −1.01192 | ||||||||
\(777\) | 7.86861 | 0.282285 | ||||||||
\(778\) | −10.2794 | −0.368534 | ||||||||
\(779\) | 1.67537 | 0.0600263 | ||||||||
\(780\) | −12.3815 | −0.443329 | ||||||||
\(781\) | 5.90536 | 0.211310 | ||||||||
\(782\) | −0.0796693 | −0.00284897 | ||||||||
\(783\) | −0.490039 | −0.0175126 | ||||||||
\(784\) | 1.77470 | 0.0633823 | ||||||||
\(785\) | 43.7893 | 1.56291 | ||||||||
\(786\) | −9.72970 | −0.347047 | ||||||||
\(787\) | −17.3830 | −0.619637 | −0.309818 | − | 0.950796i | \(-0.600268\pi\) | ||||
−0.309818 | + | 0.950796i | \(0.600268\pi\) | |||||||
\(788\) | −22.6388 | −0.806472 | ||||||||
\(789\) | 23.3921 | 0.832781 | ||||||||
\(790\) | 18.1973 | 0.647432 | ||||||||
\(791\) | −10.3546 | −0.368169 | ||||||||
\(792\) | 2.39219 | 0.0850027 | ||||||||
\(793\) | −34.4919 | −1.22484 | ||||||||
\(794\) | −6.93467 | −0.246102 | ||||||||
\(795\) | 26.1038 | 0.925808 | ||||||||
\(796\) | −4.62274 | −0.163849 | ||||||||
\(797\) | −40.1037 | −1.42055 | −0.710273 | − | 0.703926i | \(-0.751428\pi\) | ||||
−0.710273 | + | 0.703926i | \(0.751428\pi\) | |||||||
\(798\) | −0.101937 | −0.00360854 | ||||||||
\(799\) | −0.497689 | −0.0176070 | ||||||||
\(800\) | −16.0362 | −0.566965 | ||||||||
\(801\) | 1.58305 | 0.0559344 | ||||||||
\(802\) | −21.3051 | −0.752310 | ||||||||
\(803\) | 11.7899 | 0.416057 | ||||||||
\(804\) | 18.1774 | 0.641067 | ||||||||
\(805\) | −2.59026 | −0.0912948 | ||||||||
\(806\) | 9.34937 | 0.329318 | ||||||||
\(807\) | −21.5915 | −0.760056 | ||||||||
\(808\) | 11.2768 | 0.396716 | ||||||||
\(809\) | 17.1149 | 0.601726 | 0.300863 | − | 0.953667i | \(-0.402725\pi\) | ||||
0.300863 | + | 0.953667i | \(0.402725\pi\) | |||||||
\(810\) | 1.76387 | 0.0619762 | ||||||||
\(811\) | −29.9348 | −1.05115 | −0.525576 | − | 0.850746i | \(-0.676150\pi\) | ||||
−0.525576 | + | 0.850746i | \(0.676150\pi\) | |||||||
\(812\) | −0.785448 | −0.0275638 | ||||||||
\(813\) | −12.2493 | −0.429603 | ||||||||
\(814\) | 5.22457 | 0.183121 | ||||||||
\(815\) | −35.2567 | −1.23499 | ||||||||
\(816\) | −0.242415 | −0.00848622 | ||||||||
\(817\) | 1.45203 | 0.0508002 | ||||||||
\(818\) | −6.64576 | −0.232363 | ||||||||
\(819\) | 2.76000 | 0.0964423 | ||||||||
\(820\) | −46.4654 | −1.62264 | ||||||||
\(821\) | 37.4553 | 1.30720 | 0.653599 | − | 0.756841i | \(-0.273258\pi\) | ||||
0.653599 | + | 0.756841i | \(0.273258\pi\) | |||||||
\(822\) | 8.23106 | 0.287091 | ||||||||
\(823\) | 39.6390 | 1.38173 | 0.690864 | − | 0.722985i | \(-0.257230\pi\) | ||||
0.690864 | + | 0.722985i | \(0.257230\pi\) | |||||||
\(824\) | −15.4187 | −0.537136 | ||||||||
\(825\) | 2.98524 | 0.103933 | ||||||||
\(826\) | −1.85012 | −0.0643737 | ||||||||
\(827\) | −17.1286 | −0.595619 | −0.297809 | − | 0.954625i | \(-0.596256\pi\) | ||||
−0.297809 | + | 0.954625i | \(0.596256\pi\) | |||||||
\(828\) | 1.48338 | 0.0515512 | ||||||||
\(829\) | −23.2860 | −0.808757 | −0.404378 | − | 0.914592i | \(-0.632512\pi\) | ||||
−0.404378 | + | 0.914592i | \(0.632512\pi\) | |||||||
\(830\) | 21.0909 | 0.732074 | ||||||||
\(831\) | 4.71527 | 0.163571 | ||||||||
\(832\) | −0.0478960 | −0.00166049 | ||||||||
\(833\) | −0.136595 | −0.00473272 | ||||||||
\(834\) | 7.46374 | 0.258448 | ||||||||
\(835\) | 0.0968821 | 0.00335274 | ||||||||
\(836\) | 0.273144 | 0.00944688 | ||||||||
\(837\) | 5.37505 | 0.185789 | ||||||||
\(838\) | 9.07708 | 0.313563 | ||||||||
\(839\) | 30.4584 | 1.05154 | 0.525770 | − | 0.850627i | \(-0.323777\pi\) | ||||
0.525770 | + | 0.850627i | \(0.323777\pi\) | |||||||
\(840\) | 6.35493 | 0.219266 | ||||||||
\(841\) | −28.7599 | −0.991719 | ||||||||
\(842\) | −1.77696 | −0.0612381 | ||||||||
\(843\) | 17.4265 | 0.600199 | ||||||||
\(844\) | −6.02275 | −0.207312 | ||||||||
\(845\) | 15.0644 | 0.518230 | ||||||||
\(846\) | −2.29623 | −0.0789459 | ||||||||
\(847\) | 9.89000 | 0.339824 | ||||||||
\(848\) | −16.5521 | −0.568402 | ||||||||
\(849\) | −15.2066 | −0.521888 | ||||||||
\(850\) | 0.243917 | 0.00836627 | ||||||||
\(851\) | 7.28225 | 0.249632 | ||||||||
\(852\) | −8.98403 | −0.307788 | ||||||||
\(853\) | 10.8946 | 0.373024 | 0.186512 | − | 0.982453i | \(-0.440282\pi\) | ||||
0.186512 | + | 0.982453i | \(0.440282\pi\) | |||||||
\(854\) | 7.87586 | 0.269507 | ||||||||
\(855\) | 0.452710 | 0.0154824 | ||||||||
\(856\) | 42.5564 | 1.45455 | ||||||||
\(857\) | 3.14257 | 0.107348 | 0.0536741 | − | 0.998559i | \(-0.482907\pi\) | ||||
0.0536741 | + | 0.998559i | \(0.482907\pi\) | |||||||
\(858\) | 1.83257 | 0.0625631 | ||||||||
\(859\) | 35.1275 | 1.19854 | 0.599268 | − | 0.800549i | \(-0.295458\pi\) | ||||
0.599268 | + | 0.800549i | \(0.295458\pi\) | |||||||
\(860\) | −40.2714 | −1.37324 | ||||||||
\(861\) | 10.3578 | 0.352992 | ||||||||
\(862\) | 11.4117 | 0.388684 | ||||||||
\(863\) | −27.2388 | −0.927220 | −0.463610 | − | 0.886039i | \(-0.653446\pi\) | ||||
−0.463610 | + | 0.886039i | \(0.653446\pi\) | |||||||
\(864\) | −5.65958 | −0.192543 | ||||||||
\(865\) | 55.0118 | 1.87046 | ||||||||
\(866\) | 15.3534 | 0.521729 | ||||||||
\(867\) | −16.9813 | −0.576717 | ||||||||
\(868\) | 8.61527 | 0.292421 | ||||||||
\(869\) | 10.8693 | 0.368716 | ||||||||
\(870\) | −0.864367 | −0.0293048 | ||||||||
\(871\) | 31.3008 | 1.06059 | ||||||||
\(872\) | 5.37799 | 0.182122 | ||||||||
\(873\) | −12.4149 | −0.420182 | ||||||||
\(874\) | −0.0943411 | −0.00319113 | ||||||||
\(875\) | −6.06377 | −0.204993 | ||||||||
\(876\) | −17.9364 | −0.606014 | ||||||||
\(877\) | −15.2811 | −0.516006 | −0.258003 | − | 0.966144i | \(-0.583064\pi\) | ||||
−0.258003 | + | 0.966144i | \(0.583064\pi\) | |||||||
\(878\) | 1.17606 | 0.0396900 | ||||||||
\(879\) | −3.78217 | −0.127569 | ||||||||
\(880\) | −5.23317 | −0.176410 | ||||||||
\(881\) | 24.6078 | 0.829060 | 0.414530 | − | 0.910036i | \(-0.363946\pi\) | ||||
0.414530 | + | 0.910036i | \(0.363946\pi\) | |||||||
\(882\) | −0.630217 | −0.0212205 | ||||||||
\(883\) | 0.103313 | 0.00347676 | 0.00173838 | − | 0.999998i | \(-0.499447\pi\) | ||||
0.00173838 | + | 0.999998i | \(0.499447\pi\) | |||||||
\(884\) | −0.604268 | −0.0203237 | ||||||||
\(885\) | 8.21647 | 0.276194 | ||||||||
\(886\) | −17.5856 | −0.590798 | ||||||||
\(887\) | 6.99559 | 0.234889 | 0.117444 | − | 0.993079i | \(-0.462530\pi\) | ||||
0.117444 | + | 0.993079i | \(0.462530\pi\) | |||||||
\(888\) | −17.8662 | −0.599550 | ||||||||
\(889\) | −12.9282 | −0.433599 | ||||||||
\(890\) | 2.79230 | 0.0935983 | ||||||||
\(891\) | 1.05357 | 0.0352958 | ||||||||
\(892\) | 23.0809 | 0.772805 | ||||||||
\(893\) | −0.589342 | −0.0197216 | ||||||||
\(894\) | −13.1426 | −0.439555 | ||||||||
\(895\) | −40.3571 | −1.34899 | ||||||||
\(896\) | −11.3082 | −0.377781 | ||||||||
\(897\) | 2.55433 | 0.0852866 | ||||||||
\(898\) | 24.8483 | 0.829200 | ||||||||
\(899\) | −2.63399 | −0.0878484 | ||||||||
\(900\) | −4.54155 | −0.151385 | ||||||||
\(901\) | 1.27398 | 0.0424423 | ||||||||
\(902\) | 6.87731 | 0.228989 | ||||||||
\(903\) | 8.97705 | 0.298737 | ||||||||
\(904\) | 23.5109 | 0.781960 | ||||||||
\(905\) | −72.0906 | −2.39637 | ||||||||
\(906\) | −11.9818 | −0.398069 | ||||||||
\(907\) | 26.6735 | 0.885679 | 0.442839 | − | 0.896601i | \(-0.353971\pi\) | ||||
0.442839 | + | 0.896601i | \(0.353971\pi\) | |||||||
\(908\) | −28.2501 | −0.937513 | ||||||||
\(909\) | 4.96651 | 0.164729 | ||||||||
\(910\) | 4.86829 | 0.161382 | ||||||||
\(911\) | 28.7475 | 0.952447 | 0.476223 | − | 0.879324i | \(-0.342005\pi\) | ||||
0.476223 | + | 0.879324i | \(0.342005\pi\) | |||||||
\(912\) | −0.287058 | −0.00950543 | ||||||||
\(913\) | 12.5976 | 0.416920 | ||||||||
\(914\) | 7.63013 | 0.252382 | ||||||||
\(915\) | −34.9772 | −1.15631 | ||||||||
\(916\) | −39.1108 | −1.29226 | ||||||||
\(917\) | −15.4387 | −0.509829 | ||||||||
\(918\) | 0.0860842 | 0.00284120 | ||||||||
\(919\) | −3.57141 | −0.117810 | −0.0589049 | − | 0.998264i | \(-0.518761\pi\) | ||||
−0.0589049 | + | 0.998264i | \(0.518761\pi\) | |||||||
\(920\) | 5.88136 | 0.193903 | ||||||||
\(921\) | −16.0020 | −0.527283 | ||||||||
\(922\) | 8.21207 | 0.270450 | ||||||||
\(923\) | −15.4701 | −0.509206 | ||||||||
\(924\) | 1.68868 | 0.0555536 | ||||||||
\(925\) | −22.2954 | −0.733069 | ||||||||
\(926\) | −21.9622 | −0.721723 | ||||||||
\(927\) | −6.79070 | −0.223036 | ||||||||
\(928\) | 2.77341 | 0.0910418 | ||||||||
\(929\) | −46.0524 | −1.51093 | −0.755464 | − | 0.655190i | \(-0.772589\pi\) | ||||
−0.755464 | + | 0.655190i | \(0.772589\pi\) | |||||||
\(930\) | 9.48090 | 0.310891 | ||||||||
\(931\) | −0.161750 | −0.00530113 | ||||||||
\(932\) | −22.1317 | −0.724947 | ||||||||
\(933\) | −14.9728 | −0.490187 | ||||||||
\(934\) | 2.66123 | 0.0870781 | ||||||||
\(935\) | 0.402784 | 0.0131724 | ||||||||
\(936\) | −6.26676 | −0.204836 | ||||||||
\(937\) | −36.2809 | −1.18525 | −0.592623 | − | 0.805480i | \(-0.701907\pi\) | ||||
−0.592623 | + | 0.805480i | \(0.701907\pi\) | |||||||
\(938\) | −7.14719 | −0.233364 | ||||||||
\(939\) | −16.6362 | −0.542903 | ||||||||
\(940\) | 16.3451 | 0.533118 | ||||||||
\(941\) | −51.6167 | −1.68266 | −0.841328 | − | 0.540524i | \(-0.818226\pi\) | ||||
−0.841328 | + | 0.540524i | \(0.818226\pi\) | |||||||
\(942\) | 9.86011 | 0.321260 | ||||||||
\(943\) | 9.58592 | 0.312161 | ||||||||
\(944\) | −5.20996 | −0.169570 | ||||||||
\(945\) | 2.79883 | 0.0910460 | ||||||||
\(946\) | 5.96054 | 0.193794 | ||||||||
\(947\) | −5.47498 | −0.177913 | −0.0889565 | − | 0.996036i | \(-0.528353\pi\) | ||||
−0.0889565 | + | 0.996036i | \(0.528353\pi\) | |||||||
\(948\) | −16.5359 | −0.537060 | ||||||||
\(949\) | −30.8858 | −1.00259 | ||||||||
\(950\) | 0.288836 | 0.00937107 | ||||||||
\(951\) | 34.7996 | 1.12845 | ||||||||
\(952\) | 0.310147 | 0.0100519 | ||||||||
\(953\) | −5.78476 | −0.187387 | −0.0936934 | − | 0.995601i | \(-0.529867\pi\) | ||||
−0.0936934 | + | 0.995601i | \(0.529867\pi\) | |||||||
\(954\) | 5.87784 | 0.190302 | ||||||||
\(955\) | 2.79883 | 0.0905681 | ||||||||
\(956\) | −16.8278 | −0.544250 | ||||||||
\(957\) | −0.516289 | −0.0166892 | ||||||||
\(958\) | 16.2076 | 0.523644 | ||||||||
\(959\) | 13.0607 | 0.421751 | ||||||||
\(960\) | −0.0485698 | −0.00156758 | ||||||||
\(961\) | −2.10884 | −0.0680270 | ||||||||
\(962\) | −13.6867 | −0.441276 | ||||||||
\(963\) | 18.7427 | 0.603974 | ||||||||
\(964\) | −7.04397 | −0.226871 | ||||||||
\(965\) | 62.2659 | 2.00441 | ||||||||
\(966\) | −0.583254 | −0.0187659 | ||||||||
\(967\) | −7.45410 | −0.239708 | −0.119854 | − | 0.992792i | \(-0.538243\pi\) | ||||
−0.119854 | + | 0.992792i | \(0.538243\pi\) | |||||||
\(968\) | −22.4559 | −0.721759 | ||||||||
\(969\) | 0.0220941 | 0.000709765 0 | ||||||||
\(970\) | −21.8984 | −0.703114 | ||||||||
\(971\) | 4.23396 | 0.135874 | 0.0679371 | − | 0.997690i | \(-0.478358\pi\) | ||||
0.0679371 | + | 0.997690i | \(0.478358\pi\) | |||||||
\(972\) | −1.60283 | −0.0514107 | ||||||||
\(973\) | 11.8431 | 0.379673 | ||||||||
\(974\) | 9.69176 | 0.310544 | ||||||||
\(975\) | −7.82037 | −0.250452 | ||||||||
\(976\) | 22.1786 | 0.709919 | ||||||||
\(977\) | −31.4322 | −1.00561 | −0.502803 | − | 0.864401i | \(-0.667698\pi\) | ||||
−0.502803 | + | 0.864401i | \(0.667698\pi\) | |||||||
\(978\) | −7.93881 | −0.253855 | ||||||||
\(979\) | 1.66785 | 0.0533047 | ||||||||
\(980\) | 4.48604 | 0.143301 | ||||||||
\(981\) | 2.36857 | 0.0756227 | ||||||||
\(982\) | −7.94208 | −0.253442 | ||||||||
\(983\) | 54.4740 | 1.73745 | 0.868725 | − | 0.495295i | \(-0.164940\pi\) | ||||
0.868725 | + | 0.495295i | \(0.164940\pi\) | |||||||
\(984\) | −23.5180 | −0.749726 | ||||||||
\(985\) | −39.5315 | −1.25958 | ||||||||
\(986\) | −0.0421847 | −0.00134343 | ||||||||
\(987\) | −3.64355 | −0.115975 | ||||||||
\(988\) | −0.715549 | −0.0227646 | ||||||||
\(989\) | 8.30808 | 0.264182 | ||||||||
\(990\) | 1.85836 | 0.0590624 | ||||||||
\(991\) | −18.3507 | −0.582930 | −0.291465 | − | 0.956581i | \(-0.594143\pi\) | ||||
−0.291465 | + | 0.956581i | \(0.594143\pi\) | |||||||
\(992\) | −30.4205 | −0.965852 | ||||||||
\(993\) | 24.8449 | 0.788430 | ||||||||
\(994\) | 3.53244 | 0.112042 | ||||||||
\(995\) | −8.07216 | −0.255905 | ||||||||
\(996\) | −19.1652 | −0.607273 | ||||||||
\(997\) | 8.20240 | 0.259773 | 0.129886 | − | 0.991529i | \(-0.458539\pi\) | ||||
0.129886 | + | 0.991529i | \(0.458539\pi\) | |||||||
\(998\) | 21.0427 | 0.666095 | ||||||||
\(999\) | −7.86861 | −0.248952 |
(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 | 4011.2.a.m.1.11 | ✓ | 29 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.m.1.11 | ✓ | 29 | 1.1 | even | 1 | trivial |