Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6044,2,Mod(1,6044)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6044, 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("6044.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6044 = 2^{2} \cdot 1511 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6044.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2615829817\) |
Analytic rank: | \(1\) |
Dimension: | \(63\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6044.1 |
$q$-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 | 0 | ||||||||
\(3\) | −1.69210 | −0.976932 | −0.488466 | − | 0.872583i | \(-0.662443\pi\) | ||||
−0.488466 | + | 0.872583i | \(0.662443\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.14690 | −1.40734 | −0.703668 | − | 0.710529i | \(-0.748456\pi\) | ||||
−0.703668 | + | 0.710529i | \(0.748456\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.59556 | −1.73696 | −0.868479 | − | 0.495726i | \(-0.834902\pi\) | ||||
−0.868479 | + | 0.495726i | \(0.834902\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.136814 | −0.0456048 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.69483 | −1.71706 | −0.858528 | − | 0.512767i | \(-0.828620\pi\) | ||||
−0.858528 | + | 0.512767i | \(0.828620\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.92959 | 1.08987 | 0.544937 | − | 0.838477i | \(-0.316554\pi\) | ||||
0.544937 | + | 0.838477i | \(0.316554\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.32485 | 1.37487 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.33507 | −0.566338 | −0.283169 | − | 0.959070i | \(-0.591386\pi\) | ||||
−0.283169 | + | 0.959070i | \(0.591386\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.08583 | 0.249107 | 0.124553 | − | 0.992213i | \(-0.460250\pi\) | ||||
0.124553 | + | 0.992213i | \(0.460250\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.77612 | 1.69689 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.85256 | 1.01183 | 0.505914 | − | 0.862584i | \(-0.331155\pi\) | ||||
0.505914 | + | 0.862584i | \(0.331155\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.90297 | 0.980595 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.30779 | 1.02148 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.08338 | 0.758265 | 0.379132 | − | 0.925342i | \(-0.376223\pi\) | ||||
0.379132 | + | 0.925342i | \(0.376223\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.61535 | −1.72697 | −0.863484 | − | 0.504377i | \(-0.831722\pi\) | ||||
−0.863484 | + | 0.504377i | \(0.831722\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.63619 | 1.67745 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 14.4618 | 2.44448 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.31752 | 0.545397 | 0.272699 | − | 0.962100i | \(-0.412084\pi\) | ||||
0.272699 | + | 0.962100i | \(0.412084\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.64925 | −1.06473 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.45302 | 1.00779 | 0.503896 | − | 0.863764i | \(-0.331899\pi\) | ||||
0.503896 | + | 0.863764i | \(0.331899\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.23341 | −1.40808 | −0.704041 | − | 0.710159i | \(-0.748623\pi\) | ||||
−0.704041 | + | 0.710159i | \(0.748623\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.430541 | 0.0641813 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.80366 | 0.263091 | 0.131545 | − | 0.991310i | \(-0.458006\pi\) | ||||
0.131545 | + | 0.991310i | \(0.458006\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.1192 | 2.01702 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.95117 | 0.553274 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.50944 | −1.16886 | −0.584431 | − | 0.811444i | \(-0.698682\pi\) | ||||
−0.584431 | + | 0.811444i | \(0.698682\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.9210 | 2.41647 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.83733 | −0.243360 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.592149 | 0.0770912 | 0.0385456 | − | 0.999257i | \(-0.487728\pi\) | ||||
0.0385456 | + | 0.999257i | \(0.487728\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.40726 | 1.07644 | 0.538220 | − | 0.842805i | \(-0.319097\pi\) | ||||
0.538220 | + | 0.842805i | \(0.319097\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.628739 | 0.0792136 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.3660 | −1.53382 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.92906 | 0.968688 | 0.484344 | − | 0.874878i | \(-0.339058\pi\) | ||||
0.484344 | + | 0.874878i | \(0.339058\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.21099 | −0.988487 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.6221 | 1.49797 | 0.748987 | − | 0.662585i | \(-0.230541\pi\) | ||||
0.748987 | + | 0.662585i | \(0.230541\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.92521 | 0.693493 | 0.346746 | − | 0.937959i | \(-0.387286\pi\) | ||||
0.346746 | + | 0.937959i | \(0.387286\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.29630 | −0.957974 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 26.1709 | 2.98245 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.779830 | −0.0877377 | −0.0438688 | − | 0.999037i | \(-0.513968\pi\) | ||||
−0.0438688 | + | 0.999037i | \(0.513968\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.57084 | −0.952315 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.12808 | 0.123823 | 0.0619114 | − | 0.998082i | \(-0.480280\pi\) | ||||
0.0619114 | + | 0.998082i | \(0.480280\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.34824 | 0.797028 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.90947 | −0.740773 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.30578 | −0.562411 | −0.281206 | − | 0.959648i | \(-0.590734\pi\) | ||||
−0.281206 | + | 0.959648i | \(0.590734\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.0587 | −1.89306 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 16.2701 | 1.68713 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.41700 | −0.350577 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.82457 | −0.692930 | −0.346465 | − | 0.938063i | \(-0.612618\pi\) | ||||
−0.346465 | + | 0.938063i | \(0.612618\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.779134 | 0.0783059 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.83229 | 0.978349 | 0.489175 | − | 0.872186i | \(-0.337298\pi\) | ||||
0.489175 | + | 0.872186i | \(0.337298\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.3958 | −1.22140 | −0.610699 | − | 0.791863i | \(-0.709112\pi\) | ||||
−0.610699 | + | 0.791863i | \(0.709112\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −24.4707 | −2.38809 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.92440 | 0.476060 | 0.238030 | − | 0.971258i | \(-0.423498\pi\) | ||||
0.238030 | + | 0.971258i | \(0.423498\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.00736550 | −0.000705487 0 | −0.000352744 | − | 1.00000i | \(-0.500112\pi\) | ||||
−0.000352744 | 1.00000i | \(0.500112\pi\) | ||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.61356 | −0.532816 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.04716 | 0.192580 | 0.0962901 | − | 0.995353i | \(-0.469302\pi\) | ||||
0.0962901 | + | 0.995353i | \(0.469302\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.2705 | −1.42398 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.537625 | −0.0497034 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.7310 | 0.983706 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.4311 | 1.94828 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.9191 | −0.984545 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.305333 | 0.0273098 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.4190 | −1.45695 | −0.728477 | − | 0.685071i | \(-0.759771\pi\) | ||||
−0.728477 | + | 0.685071i | \(0.759771\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.6238 | 1.37560 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.34708 | −0.117695 | −0.0588476 | − | 0.998267i | \(-0.518743\pi\) | ||||
−0.0588476 | + | 0.998267i | \(0.518743\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.99000 | −0.432688 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −16.7031 | −1.43757 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.3729 | −1.14253 | −0.571263 | − | 0.820767i | \(-0.693546\pi\) | ||||
−0.571263 | + | 0.820767i | \(0.693546\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.1789 | −1.62673 | −0.813367 | − | 0.581750i | \(-0.802368\pi\) | ||||
−0.813367 | + | 0.581750i | \(0.802368\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.05196 | −0.257021 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −22.3784 | −1.87137 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.8500 | −1.06713 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −23.8910 | −1.97049 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.953182 | 0.0780877 | 0.0390439 | − | 0.999237i | \(-0.487569\pi\) | ||||
0.0390439 | + | 0.999237i | \(0.487569\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.91434 | 0.806817 | 0.403409 | − | 0.915020i | \(-0.367825\pi\) | ||||
0.403409 | + | 0.915020i | \(0.367825\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.319471 | 0.0258277 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 30.2585 | 2.43042 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.4114 | −1.54920 | −0.774598 | − | 0.632454i | \(-0.782048\pi\) | ||||
−0.774598 | + | 0.632454i | \(0.782048\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.3988 | 1.14190 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.3002 | −1.75750 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.0599 | 1.57122 | 0.785608 | − | 0.618725i | \(-0.212351\pi\) | ||||
0.785608 | + | 0.618725i | \(0.212351\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −30.3241 | −2.36073 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.03069 | 0.389287 | 0.194643 | − | 0.980874i | \(-0.437645\pi\) | ||||
0.194643 | + | 0.980874i | \(0.437645\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.44171 | 0.187824 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.148557 | −0.0113605 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.7174 | 1.57512 | 0.787558 | − | 0.616241i | \(-0.211345\pi\) | ||||
0.787558 | + | 0.616241i | \(0.211345\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −22.5319 | −1.70325 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.00197 | −0.0753128 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.2961 | −1.66649 | −0.833245 | − | 0.552904i | \(-0.813520\pi\) | ||||
−0.833245 | + | 0.552904i | \(0.813520\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.185538 | 0.0137909 | 0.00689547 | − | 0.999976i | \(-0.497805\pi\) | ||||
0.00689547 | + | 0.999976i | \(0.497805\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.2259 | −1.05161 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.4399 | −0.767557 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.2978 | 0.972434 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −24.3923 | −1.77428 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.76061 | 0.561538 | 0.280769 | − | 0.959775i | \(-0.409411\pi\) | ||||
0.280769 | + | 0.959775i | \(0.409411\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.8010 | 1.85719 | 0.928597 | − | 0.371090i | \(-0.121016\pi\) | ||||
0.928597 | + | 0.371090i | \(0.121016\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 20.9245 | 1.49843 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.1393 | −1.00738 | −0.503692 | − | 0.863884i | \(-0.668025\pi\) | ||||
−0.503692 | + | 0.863884i | \(0.668025\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.50667 | 0.177693 | 0.0888467 | − | 0.996045i | \(-0.471682\pi\) | ||||
0.0888467 | + | 0.996045i | \(0.471682\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.4167 | −0.946342 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.7654 | −1.31707 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.3070 | −1.41830 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.663900 | −0.0461442 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.18362 | −0.427730 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.118771 | −0.00817653 | −0.00408827 | − | 0.999992i | \(-0.501301\pi\) | ||||
−0.00408827 | + | 0.999992i | \(0.501301\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −21.3579 | −1.46342 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 29.0566 | 1.98164 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 44.1879 | 2.99967 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.0260 | −0.677495 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.17589 | −0.617237 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.30992 | −0.355578 | −0.177789 | − | 0.984069i | \(-0.556894\pi\) | ||||
−0.177789 | + | 0.984069i | \(0.556894\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.670797 | −0.0447198 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.4601 | 1.35798 | 0.678992 | − | 0.734146i | \(-0.262417\pi\) | ||||
0.678992 | + | 0.734146i | \(0.262417\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.0178 | −1.58714 | −0.793571 | − | 0.608477i | \(-0.791781\pi\) | ||||
−0.793571 | + | 0.608477i | \(0.791781\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −44.2837 | −2.91365 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.8085 | 1.62526 | 0.812631 | − | 0.582779i | \(-0.198035\pi\) | ||||
0.812631 | + | 0.582779i | \(0.198035\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.67593 | −0.370257 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.31955 | 0.0857137 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.7778 | 1.47337 | 0.736685 | − | 0.676236i | \(-0.236390\pi\) | ||||
0.736685 | + | 0.676236i | \(0.236390\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.8617 | 0.892913 | 0.446456 | − | 0.894805i | \(-0.352686\pi\) | ||||
0.446456 | + | 0.894805i | \(0.352686\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.42069 | −0.0911373 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −44.4316 | −2.83863 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.26687 | 0.271495 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.90882 | −0.120966 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.4608 | −1.85955 | −0.929776 | − | 0.368126i | \(-0.880000\pi\) | ||||
−0.929776 | + | 0.368126i | \(0.880000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.6345 | −1.73737 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.4339 | −0.778642 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.96323 | 0.559111 | 0.279555 | − | 0.960130i | \(-0.409813\pi\) | ||||
0.279555 | + | 0.960130i | \(0.409813\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.2459 | −0.947332 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.558665 | −0.0345805 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.43491 | 0.581781 | 0.290891 | − | 0.956756i | \(-0.406048\pi\) | ||||
0.290891 | + | 0.956756i | \(0.406048\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 26.7783 | 1.64498 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.97788 | 0.549437 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.4934 | 1.00562 | 0.502809 | − | 0.864398i | \(-0.332300\pi\) | ||||
0.502809 | + | 0.864398i | \(0.332300\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.5270 | −1.24693 | −0.623463 | − | 0.781853i | \(-0.714275\pi\) | ||||
−0.623463 | + | 0.781853i | \(0.714275\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 30.5570 | 1.84939 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −27.9216 | −1.68374 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −32.1996 | −1.93469 | −0.967343 | − | 0.253471i | \(-0.918428\pi\) | ||||
−0.967343 | + | 0.253471i | \(0.918428\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.31552 | 0.0787580 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.99197 | 0.357451 | 0.178725 | − | 0.983899i | \(-0.442803\pi\) | ||||
0.178725 | + | 0.983899i | \(0.442803\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.41773 | −0.262607 | −0.131303 | − | 0.991342i | \(-0.541916\pi\) | ||||
−0.131303 | + | 0.991342i | \(0.541916\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.78189 | 0.342490 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −29.6553 | −1.75049 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.5474 | −0.679261 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.5478 | 0.676945 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.5419 | 1.08323 | 0.541613 | − | 0.840628i | \(-0.317814\pi\) | ||||
0.541613 | + | 0.840628i | \(0.317814\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.86343 | −0.108493 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −30.2269 | −1.75395 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 19.0686 | 1.10276 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 42.4327 | 2.44578 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.6372 | −0.955780 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −26.4568 | −1.51491 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.87316 | −0.106907 | −0.0534533 | − | 0.998570i | \(-0.517023\pi\) | ||||
−0.0534533 | + | 0.998570i | \(0.517023\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.9749 | 1.19322 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.9051 | 1.01530 | 0.507652 | − | 0.861562i | \(-0.330513\pi\) | ||||
0.507652 | + | 0.861562i | \(0.330513\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.974340 | 0.0550730 | 0.0275365 | − | 0.999621i | \(-0.491234\pi\) | ||||
0.0275365 | + | 0.999621i | \(0.491234\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.97858 | −0.111480 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.932531 | 0.0523761 | 0.0261881 | − | 0.999657i | \(-0.491663\pi\) | ||||
0.0261881 | + | 0.999657i | \(0.491663\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.2541 | −1.30198 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.33255 | −0.465078 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.53549 | −0.141079 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.2667 | 1.06872 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.0124631 | 0.000689213 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.28882 | −0.456977 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.783393 | 0.0430592 | 0.0215296 | − | 0.999768i | \(-0.493146\pi\) | ||||
0.0215296 | + | 0.999768i | \(0.493146\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.453884 | −0.0248727 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −24.9519 | −1.36327 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.7470 | 1.18463 | 0.592317 | − | 0.805705i | \(-0.298213\pi\) | ||||
0.592317 | + | 0.805705i | \(0.298213\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.46398 | −0.188138 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 54.7578 | 2.96530 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −32.7166 | −1.76653 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 25.8392 | 1.39113 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.59377 | 0.0855580 | 0.0427790 | − | 0.999085i | \(-0.486379\pi\) | ||||
0.0427790 | + | 0.999085i | \(0.486379\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.66352 | 0.463748 | 0.231874 | − | 0.972746i | \(-0.425514\pi\) | ||||
0.231874 | + | 0.972746i | \(0.425514\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.8575 | 1.11329 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.2226 | −1.50214 | −0.751069 | − | 0.660224i | \(-0.770461\pi\) | ||||
−0.751069 | + | 0.660224i | \(0.770461\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −39.7206 | −2.10815 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.1578 | −0.961014 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.57586 | 0.347061 | 0.173530 | − | 0.984829i | \(-0.444483\pi\) | ||||
0.173530 | + | 0.984829i | \(0.444483\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.8210 | −0.937946 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −36.2634 | −1.90334 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.6460 | −0.975977 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.1926 | 0.584250 | 0.292125 | − | 0.956380i | \(-0.405638\pi\) | ||||
0.292125 | + | 0.956380i | \(0.405638\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.882866 | −0.0459602 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 39.1056 | 2.03026 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.0435 | −1.34848 | −0.674240 | − | 0.738513i | \(-0.735529\pi\) | ||||
−0.674240 | + | 0.738513i | \(0.735529\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.516652 | −0.0266798 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.0460 | 0.826412 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.9379 | −0.921407 | −0.460704 | − | 0.887554i | \(-0.652403\pi\) | ||||
−0.460704 | + | 0.887554i | \(0.652403\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 27.7826 | 1.42334 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.9563 | 0.968621 | 0.484310 | − | 0.874896i | \(-0.339071\pi\) | ||||
0.484310 | + | 0.874896i | \(0.339071\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −82.3573 | −4.19731 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.26326 | 0.0642153 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.46208 | −0.327640 | −0.163820 | − | 0.986490i | \(-0.552382\pi\) | ||||
−0.163820 | + | 0.986490i | \(0.552382\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.3311 | −0.573037 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.27939 | 0.114980 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.45405 | 0.123476 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.23140 | 0.362933 | 0.181467 | − | 0.983397i | \(-0.441916\pi\) | ||||
0.181467 | + | 0.983397i | \(0.441916\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.44356 | 0.422707 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.59144 | −0.379098 | −0.189549 | − | 0.981871i | \(-0.560703\pi\) | ||||
−0.189549 | + | 0.981871i | \(0.560703\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −37.7844 | −1.88218 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 26.9716 | 1.34023 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.8927 | −0.936477 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.09486 | 0.202478 | 0.101239 | − | 0.994862i | \(-0.467719\pi\) | ||||
0.101239 | + | 0.994862i | \(0.467719\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.6283 | 1.11617 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.72126 | −0.133904 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.54995 | −0.174260 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 32.4526 | 1.58921 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.2867 | −0.942219 | −0.471109 | − | 0.882075i | \(-0.656146\pi\) | ||||
−0.471109 | + | 0.882075i | \(0.656146\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.7625 | 1.49927 | 0.749637 | − | 0.661849i | \(-0.230228\pi\) | ||||
0.749637 | + | 0.661849i | \(0.230228\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.246766 | −0.0119982 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.4488 | −0.555348 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −38.6361 | −1.86973 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 37.8663 | 1.82820 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.7863 | 0.856737 | 0.428369 | − | 0.903604i | \(-0.359088\pi\) | ||||
0.428369 | + | 0.903604i | \(0.359088\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.3098 | 0.591573 | 0.295786 | − | 0.955254i | \(-0.404418\pi\) | ||||
0.295786 | + | 0.955254i | \(0.404418\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 21.7434 | 1.04252 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.26906 | 0.252053 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.0190 | 0.525909 | 0.262954 | − | 0.964808i | \(-0.415303\pi\) | ||||
0.262954 | + | 0.964808i | \(0.415303\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.93170 | −0.0919860 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.1366 | 0.766674 | 0.383337 | − | 0.923609i | \(-0.374775\pi\) | ||||
0.383337 | + | 0.923609i | \(0.374775\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.6967 | 0.791502 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.61287 | −0.0762863 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.39561 | 0.207442 | 0.103721 | − | 0.994606i | \(-0.466925\pi\) | ||||
0.103721 | + | 0.994606i | \(0.466925\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.7489 | −1.73044 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.7760 | −0.788205 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 56.8289 | 2.66418 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.60279 | −0.402421 | −0.201211 | − | 0.979548i | \(-0.564488\pi\) | ||||
−0.201211 | + | 0.979548i | \(0.564488\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.3941 | −0.578506 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.2090 | 1.50012 | 0.750062 | − | 0.661367i | \(-0.230024\pi\) | ||||
0.750062 | + | 0.661367i | \(0.230024\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.4715 | 1.74145 | 0.870724 | − | 0.491772i | \(-0.163651\pi\) | ||||
0.870724 | + | 0.491772i | \(0.163651\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −51.2003 | −2.37436 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.02962 | −0.417841 | −0.208920 | − | 0.977933i | \(-0.566995\pi\) | ||||
−0.208920 | + | 0.977933i | \(0.566995\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −36.4385 | −1.68257 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 32.8459 | 1.51346 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 52.5827 | 2.41775 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.32380 | 0.244273 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.16421 | 0.0533057 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.7722 | −1.04049 | −0.520244 | − | 0.854018i | \(-0.674159\pi\) | ||||
−0.520244 | + | 0.854018i | \(0.674159\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.0365 | 0.594414 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 37.7341 | 1.71696 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.4762 | 0.975185 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.1539 | −0.913260 | −0.456630 | − | 0.889657i | \(-0.650944\pi\) | ||||
−0.456630 | + | 0.889657i | \(0.650944\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −33.9433 | −1.53497 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.37481 | −0.0620444 | −0.0310222 | − | 0.999519i | \(-0.509876\pi\) | ||||
−0.0310222 | + | 0.999519i | \(0.509876\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.53499 | −0.429434 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.45186 | −0.110203 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −58.0058 | −2.60192 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.1920 | 1.53064 | 0.765321 | − | 0.643648i | \(-0.222580\pi\) | ||||
0.765321 | + | 0.643648i | \(0.222580\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.51241 | −0.380307 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.7273 | −1.14712 | −0.573562 | − | 0.819162i | \(-0.694439\pi\) | ||||
−0.573562 | + | 0.819162i | \(0.694439\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.9412 | −1.37687 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.13160 | −0.183491 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.8511 | −0.702589 | −0.351295 | − | 0.936265i | \(-0.614258\pi\) | ||||
−0.351295 | + | 0.936265i | \(0.614258\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.2296 | −1.20457 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.76336 | 0.254459 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 39.0085 | 1.71892 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.2715 | −0.451741 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −35.0558 | −1.53878 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.8557 | −1.13276 | −0.566380 | − | 0.824145i | \(-0.691656\pi\) | ||||
−0.566380 | + | 0.824145i | \(0.691656\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.7520 | 0.819968 | 0.409984 | − | 0.912093i | \(-0.365534\pi\) | ||||
0.409984 | + | 0.912093i | \(0.365534\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 38.1261 | 1.66396 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.4525 | 0.978048 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.547319 | 0.0237965 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.0810145 | −0.00351573 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.3578 | 1.09837 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.4966 | −0.669976 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 37.7272 | 1.62805 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −80.4062 | −3.46334 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.9779 | −1.15987 | −0.579935 | − | 0.814663i | \(-0.696922\pi\) | ||||
−0.579935 | + | 0.814663i | \(0.696922\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.313948 | −0.0134728 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.0231785 | 0.000992857 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.3083 | −0.526265 | −0.263132 | − | 0.964760i | \(-0.584756\pi\) | ||||
−0.263132 | + | 0.964760i | \(0.584756\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.15023 | −0.0490908 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.43386 | 0.188889 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.58375 | 0.152397 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.6653 | 0.749851 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.3883 | 0.524908 | 0.262454 | − | 0.964945i | \(-0.415468\pi\) | ||||
0.262454 | + | 0.964945i | \(0.415468\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.2835 | −1.53463 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.5012 | −0.950002 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.6637 | 1.58733 | 0.793667 | − | 0.608352i | \(-0.208169\pi\) | ||||
0.793667 | + | 0.608352i | \(0.208169\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.44219 | −0.271025 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 39.3878 | 1.65413 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.4760 | 1.27762 | 0.638810 | − | 0.769365i | \(-0.279427\pi\) | ||||
0.638810 | + | 0.769365i | \(0.279427\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.0572 | −1.25785 | −0.628927 | − | 0.777464i | \(-0.716506\pi\) | ||||
−0.628927 | + | 0.777464i | \(0.716506\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.1317 | −0.548584 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.7920 | 0.992193 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.5982 | −1.10730 | −0.553648 | − | 0.832751i | \(-0.686765\pi\) | ||||
−0.553648 | + | 0.832751i | \(0.686765\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −43.6577 | −1.81435 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.18415 | −0.215075 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 48.4598 | 2.00700 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.69185 | 0.0699494 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.0950 | 0.870682 | 0.435341 | − | 0.900266i | \(-0.356628\pi\) | ||||
0.435341 | + | 0.900266i | \(0.356628\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.4406 | −0.430199 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.9250 | 0.984144 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.903545 | 0.0371042 | 0.0185521 | − | 0.999828i | \(-0.494094\pi\) | ||||
0.0185521 | + | 0.999828i | \(0.494094\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −33.7693 | −1.38441 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.24153 | −0.173594 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.4974 | −0.919219 | −0.459609 | − | 0.888121i | \(-0.652011\pi\) | ||||
−0.459609 | + | 0.888121i | \(0.652011\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.2701 | 0.867624 | 0.433812 | − | 0.901003i | \(-0.357168\pi\) | ||||
0.433812 | + | 0.901003i | \(0.357168\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.08481 | −0.0441768 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −67.4414 | −2.74188 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.4773 | 1.39939 | 0.699694 | − | 0.714442i | \(-0.253320\pi\) | ||||
0.699694 | + | 0.714442i | \(0.253320\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 31.7529 | 1.28669 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.08764 | 0.286735 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.8354 | −0.962703 | −0.481352 | − | 0.876528i | \(-0.659854\pi\) | ||||
−0.481352 | + | 0.876528i | \(0.659854\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 34.3614 | 1.38559 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.7763 | 0.433838 | 0.216919 | − | 0.976190i | \(-0.430399\pi\) | ||||
0.216919 | + | 0.976190i | \(0.430399\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.40006 | −0.377820 | −0.188910 | − | 0.981994i | \(-0.560496\pi\) | ||||
−0.188910 | + | 0.981994i | \(0.560496\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 25.7563 | 1.03357 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24.3830 | 0.976885 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.4757 | −1.01903 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.4633 | 0.417863 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.74665 | −0.308879 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.9393 | −0.515107 | −0.257554 | − | 0.966264i | \(-0.582916\pi\) | ||||
−0.257554 | + | 0.966264i | \(0.582916\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.200972 | 0.00798791 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 51.6690 | 2.05042 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 55.4826 | 2.19830 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.72689 | −0.0683147 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.0587 | 1.30574 | 0.652870 | − | 0.757470i | \(-0.273565\pi\) | ||||
0.652870 | + | 0.757470i | \(0.273565\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.0151 | 0.552702 | 0.276351 | − | 0.961057i | \(-0.410875\pi\) | ||||
0.276351 | + | 0.961057i | \(0.410875\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −49.1665 | −1.93593 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.5787 | −0.730406 | −0.365203 | − | 0.930928i | \(-0.619000\pi\) | ||||
−0.365203 | + | 0.930928i | \(0.619000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.37219 | −0.132370 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −74.7701 | −2.93047 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.9360 | −1.13235 | −0.566176 | − | 0.824285i | \(-0.691578\pi\) | ||||
−0.566176 | + | 0.824285i | \(0.691578\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.23914 | 0.165637 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.810653 | −0.0316266 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −39.6658 | −1.54516 | −0.772580 | − | 0.634918i | \(-0.781034\pi\) | ||||
−0.772580 | + | 0.634918i | \(0.781034\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.2335 | 1.21484 | 0.607422 | − | 0.794380i | \(-0.292204\pi\) | ||||
0.607422 | + | 0.794380i | \(0.292204\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.5265 | 0.602998 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.7030 | 0.608937 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.8148 | 0.767234 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.98488 | 0.347376 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −47.8779 | −1.84831 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.7035 | 1.22208 | 0.611041 | − | 0.791599i | \(-0.290751\pi\) | ||||
0.611041 | + | 0.791599i | \(0.290751\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 26.0239 | 1.00166 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.6884 | −0.948851 | −0.474425 | − | 0.880296i | \(-0.657344\pi\) | ||||
−0.474425 | + | 0.880296i | \(0.657344\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.3627 | 1.20359 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −34.6204 | −1.32666 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.2114 | −0.888160 | −0.444080 | − | 0.895987i | \(-0.646469\pi\) | ||||
−0.444080 | + | 0.895987i | \(0.646469\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 42.0832 | 1.60792 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 40.6405 | 1.55053 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −33.4386 | −1.27391 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.6128 | 1.27869 | 0.639345 | − | 0.768920i | \(-0.279205\pi\) | ||||
0.639345 | + | 0.768920i | \(0.279205\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.58056 | −0.136014 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 60.3541 | 2.28936 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.0683 | −0.570752 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −41.9784 | −1.58777 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.6502 | −1.19541 | −0.597706 | − | 0.801715i | \(-0.703921\pi\) | ||||
−0.597706 | + | 0.801715i | \(0.703921\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.60227 | 0.135862 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.60421 | 0.361716 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −45.1849 | −1.69935 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.7600 | −0.479211 | −0.239605 | − | 0.970870i | \(-0.577018\pi\) | ||||
−0.239605 | + | 0.970870i | \(0.577018\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.106692 | 0.00400126 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −46.6590 | −1.74739 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 70.4224 | 2.63365 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −38.5421 | −1.43938 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.6344 | 0.583066 | 0.291533 | − | 0.956561i | \(-0.405835\pi\) | ||||
0.291533 | + | 0.956561i | \(0.405835\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 56.9658 | 2.12152 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −23.4554 | −0.872315 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20.0207 | 0.743550 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.5645 | 0.725607 | 0.362804 | − | 0.931866i | \(-0.381820\pi\) | ||||
0.362804 | + | 0.931866i | \(0.381820\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.1165 | 1.04135 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.5607 | 0.797451 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.2321 | −1.19052 | −0.595260 | − | 0.803533i | \(-0.702951\pi\) | ||||
−0.595260 | + | 0.803533i | \(0.702951\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 75.1825 | 2.77315 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −45.1546 | −1.66329 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.3566 | −1.26383 | −0.631914 | − | 0.775039i | \(-0.717730\pi\) | ||||
−0.631914 | + | 0.775039i | \(0.717730\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.21996 | −0.265232 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.52763 | −0.239475 | −0.119738 | − | 0.992806i | \(-0.538205\pi\) | ||||
−0.119738 | + | 0.992806i | \(0.538205\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.99957 | −0.109896 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.154337 | −0.00564691 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.6304 | −0.826896 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.5317 | −1.44253 | −0.721266 | − | 0.692658i | \(-0.756439\pi\) | ||||
−0.721266 | + | 0.692658i | \(0.756439\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 49.8505 | 1.81665 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −31.1994 | −1.13546 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.4056 | 1.65030 | 0.825148 | − | 0.564917i | \(-0.191092\pi\) | ||||
0.825148 | + | 0.564917i | \(0.191092\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 46.7602 | 1.69729 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.34636 | 0.338805 | 0.169403 | − | 0.985547i | \(-0.445816\pi\) | ||||
0.169403 | + | 0.985547i | \(0.445816\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.0338486 | 0.00122540 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.00534 | −0.0363483 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.32690 | 0.0840197 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.58409 | 0.345611 | 0.172805 | − | 0.984956i | \(-0.444717\pi\) | ||||
0.172805 | + | 0.984956i | \(0.444717\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.1666 | −0.546213 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 42.3846 | 1.52447 | 0.762235 | − | 0.647301i | \(-0.224102\pi\) | ||||
0.762235 | + | 0.647301i | \(0.224102\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −47.1438 | −1.69345 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 25.7975 | 0.925478 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.00689 | 0.251048 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −71.8810 | −2.57210 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.6737 | 0.774555 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 61.0856 | 2.18024 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.5259 | 1.33766 | 0.668828 | − | 0.743417i | \(-0.266796\pi\) | ||||
0.668828 | + | 0.743417i | \(0.266796\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.9648 | −0.568361 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.40782 | −0.334504 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 33.0371 | 1.17318 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −45.3115 | −1.60703 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.67031 | 0.342540 | 0.171270 | − | 0.985224i | \(-0.445213\pi\) | ||||
0.171270 | + | 0.985224i | \(0.445213\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.21167 | −0.148998 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.725906 | 0.0256486 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −33.7430 | −1.19077 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 70.1765 | 2.47340 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.9083 | −0.982420 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.30000 | −0.221496 | −0.110748 | − | 0.993849i | \(-0.535325\pi\) | ||||
−0.110748 | + | 0.993849i | \(0.535325\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.0930 | −0.354413 | −0.177207 | − | 0.984174i | \(-0.556706\pi\) | ||||
−0.177207 | + | 0.984174i | \(0.556706\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 34.7336 | 1.21816 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −63.1266 | −2.21123 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.0259 | −0.350763 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.47069 | 0.0863328 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.9742 | −0.557505 | −0.278752 | − | 0.960363i | \(-0.589921\pi\) | ||||
−0.278752 | + | 0.960363i | \(0.589921\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.46196 | 0.329823 | 0.164912 | − | 0.986308i | \(-0.447266\pi\) | ||||
0.164912 | + | 0.986308i | \(0.447266\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 47.2460 | 1.64489 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.9899 | 0.764663 | 0.382331 | − | 0.924025i | \(-0.375121\pi\) | ||||
0.382331 | + | 0.924025i | \(0.375121\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.3581 | −0.811259 | −0.405629 | − | 0.914038i | \(-0.632948\pi\) | ||||
−0.405629 | + | 0.914038i | \(0.632948\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 54.4848 | 1.89006 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −32.9693 | −1.14232 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.8311 | −0.547857 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −51.0362 | −1.76407 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.1584 | −1.45547 | −0.727734 | − | 0.685859i | \(-0.759427\pi\) | ||||
−0.727734 | + | 0.685859i | \(0.759427\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.3260 | −0.425035 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.1390 | −0.349205 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.68380 | −0.264331 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −98.4878 | −3.38408 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.47521 | 0.256549 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.0985 | 0.551848 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.3356 | 0.970193 | 0.485097 | − | 0.874461i | \(-0.338784\pi\) | ||||
0.485097 | + | 0.874461i | \(0.338784\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.467495 | 0.0159880 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.6407 | −0.431800 | −0.215900 | − | 0.976416i | \(-0.569268\pi\) | ||||
−0.215900 | + | 0.976416i | \(0.569268\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.49113 | −0.289714 | −0.144857 | − | 0.989453i | \(-0.546272\pi\) | ||||
−0.144857 | + | 0.989453i | \(0.546272\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 50.1795 | 1.71011 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −58.2820 | −1.98394 | −0.991971 | − | 0.126464i | \(-0.959637\pi\) | ||||
−0.991971 | + | 0.126464i | \(0.959637\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −65.1956 | −2.21672 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.5394 | 0.663591 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.44100 | 0.150650 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.1580 | 1.05575 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.933699 | 0.0316009 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.40317 | −0.0474359 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.7129 | −0.766961 | −0.383480 | − | 0.923549i | \(-0.625275\pi\) | ||||
−0.383480 | + | 0.923549i | \(0.625275\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −31.3746 | −1.05824 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.0766 | −0.912233 | −0.456117 | − | 0.889920i | \(-0.650760\pi\) | ||||
−0.456117 | + | 0.889920i | \(0.650760\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.9690 | −1.17680 | −0.588400 | − | 0.808570i | \(-0.700242\pi\) | ||||
−0.588400 | + | 0.808570i | \(0.700242\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.15311 | 0.105990 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.5367 | −0.655979 | −0.327990 | − | 0.944681i | \(-0.606371\pi\) | ||||
−0.327990 | + | 0.944681i | \(0.606371\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 75.4546 | 2.53067 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 48.8095 | 1.63518 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.95847 | 0.0655376 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 70.1636 | 2.34531 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −32.2659 | −1.07733 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −39.2631 | −1.30950 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.8702 | 0.661971 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −71.8001 | −2.38936 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.583870 | −0.0194085 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.2224 | −0.937108 | −0.468554 | − | 0.883435i | \(-0.655225\pi\) | ||||
−0.468554 | + | 0.883435i | \(0.655225\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.34520 | −0.0446174 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.0715 | 1.16197 | 0.580986 | − | 0.813914i | \(-0.302667\pi\) | ||||
0.580986 | + | 0.813914i | \(0.302667\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.42422 | −0.212611 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 44.7674 | 1.47996 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.19061 | 0.204432 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.03558 | −0.199095 | −0.0995477 | − | 0.995033i | \(-0.531740\pi\) | ||||
−0.0995477 | + | 0.995033i | \(0.531740\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.16956 | 0.104440 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 49.5999 | 1.63260 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.2657 | 0.534813 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.69593 | 0.0557016 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.3941 | 1.16124 | 0.580622 | − | 0.814173i | \(-0.302810\pi\) | ||||
0.580622 | + | 0.814173i | \(0.302810\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.3310 | 0.502454 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −30.2971 | −0.991883 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −41.8470 | −1.36854 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.3352 | 1.41570 | 0.707849 | − | 0.706364i | \(-0.249666\pi\) | ||||
0.707849 | + | 0.706364i | \(0.249666\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.64868 | −0.0538025 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.3659 | 1.21809 | 0.609047 | − | 0.793134i | \(-0.291552\pi\) | ||||
0.609047 | + | 0.793134i | \(0.291552\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.3137 | 1.01971 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 76.7600 | 2.49700 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.93807 | −0.160466 | −0.0802329 | − | 0.996776i | \(-0.525566\pi\) | ||||
−0.0802329 | + | 0.996776i | \(0.525566\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.2837 | 0.755819 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.57793 | −0.0511679 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.9905 | 0.615163 | 0.307581 | − | 0.951522i | \(-0.400480\pi\) | ||||
0.307581 | + | 0.951522i | \(0.400480\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.4219 | −0.790273 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 39.3482 | 1.27195 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 61.4561 | 1.98452 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 61.4549 | 1.98242 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.673729 | −0.0217106 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −81.1930 | −2.61370 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.62083 | 0.116438 | 0.0582190 | − | 0.998304i | \(-0.481458\pi\) | ||||
0.0582190 | + | 0.998304i | \(0.481458\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.29030 | 0.137824 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.0623 | 0.547557 | 0.273778 | − | 0.961793i | \(-0.411727\pi\) | ||||
0.273778 | + | 0.961793i | \(0.411727\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 88.1379 | 2.82557 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −32.6011 | −1.04407 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 61.1954 | 1.95782 | 0.978908 | − | 0.204303i | \(-0.0654928\pi\) | ||||
0.978908 | + | 0.204303i | \(0.0654928\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.2155 | 0.965691 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.00100771 | 3.21736e−5 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −48.5723 | −1.54922 | −0.774608 | − | 0.632442i | \(-0.782053\pi\) | ||||
−0.774608 | + | 0.632442i | \(0.782053\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 44.4949 | 1.41773 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.0255 | 0.446436 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.8057 | −1.42474 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.5476 | −0.620950 | −0.310475 | − | 0.950581i | \(-0.600488\pi\) | ||||
−0.310475 | + | 0.950581i | \(0.600488\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.32558 | −0.0420659 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.88825 | −0.250074 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52.6915 | 1.66876 | 0.834378 | − | 0.551193i | \(-0.185827\pi\) | ||||
0.834378 | + | 0.551193i | \(0.185827\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 17.6087 | 0.557115 |
(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 | 6044.2.a.a.1.16 | ✓ | 63 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6044.2.a.a.1.16 | ✓ | 63 | 1.1 | even | 1 | trivial |