Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4013,2,Mod(1,4013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4013.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: | \(32.0439663311\) |
Analytic rank: | \(0\) |
Dimension: | \(176\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 4013.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.63729 | −1.86485 | −0.932423 | − | 0.361368i | \(-0.882310\pi\) | ||||
−0.932423 | + | 0.361368i | \(0.882310\pi\) | |||||||
\(3\) | 1.99604 | 1.15241 | 0.576206 | − | 0.817304i | \(-0.304533\pi\) | ||||
0.576206 | + | 0.817304i | \(0.304533\pi\) | |||||||
\(4\) | 4.95530 | 2.47765 | ||||||||
\(5\) | −2.90741 | −1.30023 | −0.650117 | − | 0.759834i | \(-0.725280\pi\) | ||||
−0.650117 | + | 0.759834i | \(0.725280\pi\) | |||||||
\(6\) | −5.26413 | −2.14907 | ||||||||
\(7\) | 3.48548 | 1.31739 | 0.658694 | − | 0.752411i | \(-0.271109\pi\) | ||||
0.658694 | + | 0.752411i | \(0.271109\pi\) | |||||||
\(8\) | −7.79400 | −2.75559 | ||||||||
\(9\) | 0.984162 | 0.328054 | ||||||||
\(10\) | 7.66769 | 2.42474 | ||||||||
\(11\) | −4.95478 | −1.49392 | −0.746961 | − | 0.664867i | \(-0.768488\pi\) | ||||
−0.746961 | + | 0.664867i | \(0.768488\pi\) | |||||||
\(12\) | 9.89097 | 2.85528 | ||||||||
\(13\) | −4.04969 | −1.12318 | −0.561591 | − | 0.827415i | \(-0.689811\pi\) | ||||
−0.561591 | + | 0.827415i | \(0.689811\pi\) | |||||||
\(14\) | −9.19222 | −2.45673 | ||||||||
\(15\) | −5.80330 | −1.49841 | ||||||||
\(16\) | 10.6444 | 2.66111 | ||||||||
\(17\) | 0.154371 | 0.0374404 | 0.0187202 | − | 0.999825i | \(-0.494041\pi\) | ||||
0.0187202 | + | 0.999825i | \(0.494041\pi\) | |||||||
\(18\) | −2.59552 | −0.611771 | ||||||||
\(19\) | 0.682953 | 0.156680 | 0.0783401 | − | 0.996927i | \(-0.475038\pi\) | ||||
0.0783401 | + | 0.996927i | \(0.475038\pi\) | |||||||
\(20\) | −14.4071 | −3.22153 | ||||||||
\(21\) | 6.95715 | 1.51817 | ||||||||
\(22\) | 13.0672 | 2.78594 | ||||||||
\(23\) | 0.607940 | 0.126764 | 0.0633822 | − | 0.997989i | \(-0.479811\pi\) | ||||
0.0633822 | + | 0.997989i | \(0.479811\pi\) | |||||||
\(24\) | −15.5571 | −3.17558 | ||||||||
\(25\) | 3.45304 | 0.690607 | ||||||||
\(26\) | 10.6802 | 2.09456 | ||||||||
\(27\) | −4.02369 | −0.774359 | ||||||||
\(28\) | 17.2716 | 3.26403 | ||||||||
\(29\) | 0.135779 | 0.0252135 | 0.0126067 | − | 0.999921i | \(-0.495987\pi\) | ||||
0.0126067 | + | 0.999921i | \(0.495987\pi\) | |||||||
\(30\) | 15.3050 | 2.79430 | ||||||||
\(31\) | 3.48959 | 0.626750 | 0.313375 | − | 0.949630i | \(-0.398540\pi\) | ||||
0.313375 | + | 0.949630i | \(0.398540\pi\) | |||||||
\(32\) | −12.4845 | −2.20696 | ||||||||
\(33\) | −9.88993 | −1.72162 | ||||||||
\(34\) | −0.407121 | −0.0698206 | ||||||||
\(35\) | −10.1337 | −1.71291 | ||||||||
\(36\) | 4.87682 | 0.812804 | ||||||||
\(37\) | −3.57078 | −0.587033 | −0.293516 | − | 0.955954i | \(-0.594826\pi\) | ||||
−0.293516 | + | 0.955954i | \(0.594826\pi\) | |||||||
\(38\) | −1.80115 | −0.292185 | ||||||||
\(39\) | −8.08333 | −1.29437 | ||||||||
\(40\) | 22.6604 | 3.58292 | ||||||||
\(41\) | −2.02330 | −0.315987 | −0.157993 | − | 0.987440i | \(-0.550502\pi\) | ||||
−0.157993 | + | 0.987440i | \(0.550502\pi\) | |||||||
\(42\) | −18.3480 | −2.83116 | ||||||||
\(43\) | −1.01463 | −0.154729 | −0.0773647 | − | 0.997003i | \(-0.524651\pi\) | ||||
−0.0773647 | + | 0.997003i | \(0.524651\pi\) | |||||||
\(44\) | −24.5525 | −3.70142 | ||||||||
\(45\) | −2.86136 | −0.426547 | ||||||||
\(46\) | −1.60332 | −0.236396 | ||||||||
\(47\) | −0.259199 | −0.0378081 | −0.0189040 | − | 0.999821i | \(-0.506018\pi\) | ||||
−0.0189040 | + | 0.999821i | \(0.506018\pi\) | |||||||
\(48\) | 21.2467 | 3.06669 | ||||||||
\(49\) | 5.14857 | 0.735510 | ||||||||
\(50\) | −9.10666 | −1.28788 | ||||||||
\(51\) | 0.308130 | 0.0431468 | ||||||||
\(52\) | −20.0674 | −2.78285 | ||||||||
\(53\) | 9.03516 | 1.24108 | 0.620538 | − | 0.784177i | \(-0.286914\pi\) | ||||
0.620538 | + | 0.784177i | \(0.286914\pi\) | |||||||
\(54\) | 10.6116 | 1.44406 | ||||||||
\(55\) | 14.4056 | 1.94245 | ||||||||
\(56\) | −27.1658 | −3.63019 | ||||||||
\(57\) | 1.36320 | 0.180560 | ||||||||
\(58\) | −0.358088 | −0.0470193 | ||||||||
\(59\) | 6.98583 | 0.909477 | 0.454739 | − | 0.890625i | \(-0.349733\pi\) | ||||
0.454739 | + | 0.890625i | \(0.349733\pi\) | |||||||
\(60\) | −28.7571 | −3.71253 | ||||||||
\(61\) | 8.08766 | 1.03552 | 0.517759 | − | 0.855526i | \(-0.326766\pi\) | ||||
0.517759 | + | 0.855526i | \(0.326766\pi\) | |||||||
\(62\) | −9.20307 | −1.16879 | ||||||||
\(63\) | 3.43028 | 0.432174 | ||||||||
\(64\) | 11.6363 | 1.45454 | ||||||||
\(65\) | 11.7741 | 1.46040 | ||||||||
\(66\) | 26.0826 | 3.21055 | ||||||||
\(67\) | 13.0891 | 1.59909 | 0.799545 | − | 0.600607i | \(-0.205074\pi\) | ||||
0.799545 | + | 0.600607i | \(0.205074\pi\) | |||||||
\(68\) | 0.764954 | 0.0927643 | ||||||||
\(69\) | 1.21347 | 0.146085 | ||||||||
\(70\) | 26.7256 | 3.19432 | ||||||||
\(71\) | −11.1324 | −1.32118 | −0.660589 | − | 0.750748i | \(-0.729693\pi\) | ||||
−0.660589 | + | 0.750748i | \(0.729693\pi\) | |||||||
\(72\) | −7.67056 | −0.903984 | ||||||||
\(73\) | −8.45075 | −0.989086 | −0.494543 | − | 0.869153i | \(-0.664664\pi\) | ||||
−0.494543 | + | 0.869153i | \(0.664664\pi\) | |||||||
\(74\) | 9.41719 | 1.09473 | ||||||||
\(75\) | 6.89238 | 0.795864 | ||||||||
\(76\) | 3.38424 | 0.388199 | ||||||||
\(77\) | −17.2698 | −1.96808 | ||||||||
\(78\) | 21.3181 | 2.41380 | ||||||||
\(79\) | −0.383966 | −0.0431996 | −0.0215998 | − | 0.999767i | \(-0.506876\pi\) | ||||
−0.0215998 | + | 0.999767i | \(0.506876\pi\) | |||||||
\(80\) | −30.9477 | −3.46006 | ||||||||
\(81\) | −10.9839 | −1.22043 | ||||||||
\(82\) | 5.33604 | 0.589267 | ||||||||
\(83\) | 9.61858 | 1.05578 | 0.527888 | − | 0.849314i | \(-0.322984\pi\) | ||||
0.527888 | + | 0.849314i | \(0.322984\pi\) | |||||||
\(84\) | 34.4748 | 3.76151 | ||||||||
\(85\) | −0.448819 | −0.0486813 | ||||||||
\(86\) | 2.67587 | 0.288547 | ||||||||
\(87\) | 0.271020 | 0.0290563 | ||||||||
\(88\) | 38.6176 | 4.11665 | ||||||||
\(89\) | 5.16555 | 0.547547 | 0.273774 | − | 0.961794i | \(-0.411728\pi\) | ||||
0.273774 | + | 0.961794i | \(0.411728\pi\) | |||||||
\(90\) | 7.54625 | 0.795445 | ||||||||
\(91\) | −14.1151 | −1.47967 | ||||||||
\(92\) | 3.01253 | 0.314078 | ||||||||
\(93\) | 6.96536 | 0.722274 | ||||||||
\(94\) | 0.683583 | 0.0705062 | ||||||||
\(95\) | −1.98563 | −0.203721 | ||||||||
\(96\) | −24.9195 | −2.54333 | ||||||||
\(97\) | −2.46812 | −0.250599 | −0.125300 | − | 0.992119i | \(-0.539989\pi\) | ||||
−0.125300 | + | 0.992119i | \(0.539989\pi\) | |||||||
\(98\) | −13.5783 | −1.37161 | ||||||||
\(99\) | −4.87631 | −0.490088 | ||||||||
\(100\) | 17.1108 | 1.71108 | ||||||||
\(101\) | −0.186225 | −0.0185301 | −0.00926504 | − | 0.999957i | \(-0.502949\pi\) | ||||
−0.00926504 | + | 0.999957i | \(0.502949\pi\) | |||||||
\(102\) | −0.812628 | −0.0804621 | ||||||||
\(103\) | 4.51502 | 0.444878 | 0.222439 | − | 0.974947i | \(-0.428598\pi\) | ||||
0.222439 | + | 0.974947i | \(0.428598\pi\) | |||||||
\(104\) | 31.5633 | 3.09503 | ||||||||
\(105\) | −20.2273 | −1.97398 | ||||||||
\(106\) | −23.8284 | −2.31441 | ||||||||
\(107\) | 16.2234 | 1.56838 | 0.784189 | − | 0.620522i | \(-0.213079\pi\) | ||||
0.784189 | + | 0.620522i | \(0.213079\pi\) | |||||||
\(108\) | −19.9386 | −1.91859 | ||||||||
\(109\) | 7.92634 | 0.759206 | 0.379603 | − | 0.925150i | \(-0.376061\pi\) | ||||
0.379603 | + | 0.925150i | \(0.376061\pi\) | |||||||
\(110\) | −37.9917 | −3.62237 | ||||||||
\(111\) | −7.12741 | −0.676504 | ||||||||
\(112\) | 37.1010 | 3.50571 | ||||||||
\(113\) | 7.51012 | 0.706493 | 0.353246 | − | 0.935530i | \(-0.385078\pi\) | ||||
0.353246 | + | 0.935530i | \(0.385078\pi\) | |||||||
\(114\) | −3.59515 | −0.336717 | ||||||||
\(115\) | −1.76753 | −0.164823 | ||||||||
\(116\) | 0.672825 | 0.0624703 | ||||||||
\(117\) | −3.98555 | −0.368465 | ||||||||
\(118\) | −18.4237 | −1.69604 | ||||||||
\(119\) | 0.538056 | 0.0493235 | ||||||||
\(120\) | 45.2309 | 4.12900 | ||||||||
\(121\) | 13.5499 | 1.23181 | ||||||||
\(122\) | −21.3295 | −1.93108 | ||||||||
\(123\) | −4.03859 | −0.364147 | ||||||||
\(124\) | 17.2920 | 1.55287 | ||||||||
\(125\) | 4.49766 | 0.402283 | ||||||||
\(126\) | −9.04664 | −0.805939 | ||||||||
\(127\) | 9.47810 | 0.841045 | 0.420523 | − | 0.907282i | \(-0.361847\pi\) | ||||
0.420523 | + | 0.907282i | \(0.361847\pi\) | |||||||
\(128\) | −5.71942 | −0.505530 | ||||||||
\(129\) | −2.02524 | −0.178312 | ||||||||
\(130\) | −31.0518 | −2.72342 | ||||||||
\(131\) | 10.2774 | 0.897937 | 0.448969 | − | 0.893547i | \(-0.351791\pi\) | ||||
0.448969 | + | 0.893547i | \(0.351791\pi\) | |||||||
\(132\) | −49.0076 | −4.26556 | ||||||||
\(133\) | 2.38042 | 0.206409 | ||||||||
\(134\) | −34.5198 | −2.98206 | ||||||||
\(135\) | 11.6985 | 1.00685 | ||||||||
\(136\) | −1.20317 | −0.103171 | ||||||||
\(137\) | −20.7474 | −1.77257 | −0.886285 | − | 0.463140i | \(-0.846723\pi\) | ||||
−0.886285 | + | 0.463140i | \(0.846723\pi\) | |||||||
\(138\) | −3.20028 | −0.272426 | ||||||||
\(139\) | 16.5124 | 1.40056 | 0.700281 | − | 0.713868i | \(-0.253058\pi\) | ||||
0.700281 | + | 0.713868i | \(0.253058\pi\) | |||||||
\(140\) | −50.2157 | −4.24400 | ||||||||
\(141\) | −0.517371 | −0.0435705 | ||||||||
\(142\) | 29.3595 | 2.46379 | ||||||||
\(143\) | 20.0653 | 1.67795 | ||||||||
\(144\) | 10.4759 | 0.872988 | ||||||||
\(145\) | −0.394765 | −0.0327834 | ||||||||
\(146\) | 22.2871 | 1.84449 | ||||||||
\(147\) | 10.2767 | 0.847611 | ||||||||
\(148\) | −17.6943 | −1.45446 | ||||||||
\(149\) | 17.8509 | 1.46240 | 0.731200 | − | 0.682163i | \(-0.238960\pi\) | ||||
0.731200 | + | 0.682163i | \(0.238960\pi\) | |||||||
\(150\) | −18.1772 | −1.48416 | ||||||||
\(151\) | −12.2871 | −0.999911 | −0.499955 | − | 0.866051i | \(-0.666650\pi\) | ||||
−0.499955 | + | 0.866051i | \(0.666650\pi\) | |||||||
\(152\) | −5.32294 | −0.431747 | ||||||||
\(153\) | 0.151926 | 0.0122825 | ||||||||
\(154\) | 45.5455 | 3.67016 | ||||||||
\(155\) | −10.1457 | −0.814921 | ||||||||
\(156\) | −40.0554 | −3.20700 | ||||||||
\(157\) | 9.71208 | 0.775108 | 0.387554 | − | 0.921847i | \(-0.373320\pi\) | ||||
0.387554 | + | 0.921847i | \(0.373320\pi\) | |||||||
\(158\) | 1.01263 | 0.0805606 | ||||||||
\(159\) | 18.0345 | 1.43023 | ||||||||
\(160\) | 36.2975 | 2.86957 | ||||||||
\(161\) | 2.11896 | 0.166998 | ||||||||
\(162\) | 28.9678 | 2.27592 | ||||||||
\(163\) | −3.91059 | −0.306301 | −0.153151 | − | 0.988203i | \(-0.548942\pi\) | ||||
−0.153151 | + | 0.988203i | \(0.548942\pi\) | |||||||
\(164\) | −10.0261 | −0.782906 | ||||||||
\(165\) | 28.7541 | 2.23850 | ||||||||
\(166\) | −25.3670 | −1.96886 | ||||||||
\(167\) | −1.22763 | −0.0949971 | −0.0474986 | − | 0.998871i | \(-0.515125\pi\) | ||||
−0.0474986 | + | 0.998871i | \(0.515125\pi\) | |||||||
\(168\) | −54.2240 | −4.18347 | ||||||||
\(169\) | 3.39999 | 0.261538 | ||||||||
\(170\) | 1.18367 | 0.0907831 | ||||||||
\(171\) | 0.672137 | 0.0513996 | ||||||||
\(172\) | −5.02779 | −0.383366 | ||||||||
\(173\) | −17.0253 | −1.29441 | −0.647205 | − | 0.762316i | \(-0.724062\pi\) | ||||
−0.647205 | + | 0.762316i | \(0.724062\pi\) | |||||||
\(174\) | −0.714757 | −0.0541856 | ||||||||
\(175\) | 12.0355 | 0.909797 | ||||||||
\(176\) | −52.7408 | −3.97549 | ||||||||
\(177\) | 13.9440 | 1.04809 | ||||||||
\(178\) | −13.6231 | −1.02109 | ||||||||
\(179\) | −3.36050 | −0.251175 | −0.125588 | − | 0.992083i | \(-0.540082\pi\) | ||||
−0.125588 | + | 0.992083i | \(0.540082\pi\) | |||||||
\(180\) | −14.1789 | −1.05684 | ||||||||
\(181\) | 16.0099 | 1.19001 | 0.595004 | − | 0.803723i | \(-0.297150\pi\) | ||||
0.595004 | + | 0.803723i | \(0.297150\pi\) | |||||||
\(182\) | 37.2257 | 2.75935 | ||||||||
\(183\) | 16.1433 | 1.19334 | ||||||||
\(184\) | −4.73829 | −0.349311 | ||||||||
\(185\) | 10.3817 | 0.763280 | ||||||||
\(186\) | −18.3697 | −1.34693 | ||||||||
\(187\) | −0.764873 | −0.0559331 | ||||||||
\(188\) | −1.28441 | −0.0936753 | ||||||||
\(189\) | −14.0245 | −1.02013 | ||||||||
\(190\) | 5.23667 | 0.379908 | ||||||||
\(191\) | 15.5762 | 1.12706 | 0.563528 | − | 0.826097i | \(-0.309444\pi\) | ||||
0.563528 | + | 0.826097i | \(0.309444\pi\) | |||||||
\(192\) | 23.2265 | 1.67623 | ||||||||
\(193\) | 4.79230 | 0.344957 | 0.172479 | − | 0.985013i | \(-0.444822\pi\) | ||||
0.172479 | + | 0.985013i | \(0.444822\pi\) | |||||||
\(194\) | 6.50914 | 0.467329 | ||||||||
\(195\) | 23.5016 | 1.68298 | ||||||||
\(196\) | 25.5127 | 1.82234 | ||||||||
\(197\) | −12.5379 | −0.893287 | −0.446643 | − | 0.894712i | \(-0.647381\pi\) | ||||
−0.446643 | + | 0.894712i | \(0.647381\pi\) | |||||||
\(198\) | 12.8602 | 0.913938 | ||||||||
\(199\) | 23.6326 | 1.67527 | 0.837636 | − | 0.546229i | \(-0.183937\pi\) | ||||
0.837636 | + | 0.546229i | \(0.183937\pi\) | |||||||
\(200\) | −26.9129 | −1.90303 | ||||||||
\(201\) | 26.1263 | 1.84281 | ||||||||
\(202\) | 0.491130 | 0.0345558 | ||||||||
\(203\) | 0.473254 | 0.0332159 | ||||||||
\(204\) | 1.52688 | 0.106903 | ||||||||
\(205\) | 5.88257 | 0.410857 | ||||||||
\(206\) | −11.9074 | −0.829629 | ||||||||
\(207\) | 0.598312 | 0.0415856 | ||||||||
\(208\) | −43.1067 | −2.98891 | ||||||||
\(209\) | −3.38388 | −0.234068 | ||||||||
\(210\) | 53.3452 | 3.68117 | ||||||||
\(211\) | −18.1762 | −1.25130 | −0.625649 | − | 0.780105i | \(-0.715166\pi\) | ||||
−0.625649 | + | 0.780105i | \(0.715166\pi\) | |||||||
\(212\) | 44.7720 | 3.07495 | ||||||||
\(213\) | −22.2208 | −1.52254 | ||||||||
\(214\) | −42.7859 | −2.92478 | ||||||||
\(215\) | 2.94994 | 0.201184 | ||||||||
\(216\) | 31.3606 | 2.13382 | ||||||||
\(217\) | 12.1629 | 0.825672 | ||||||||
\(218\) | −20.9041 | −1.41580 | ||||||||
\(219\) | −16.8680 | −1.13983 | ||||||||
\(220\) | 71.3841 | 4.81271 | ||||||||
\(221\) | −0.625154 | −0.0420524 | ||||||||
\(222\) | 18.7971 | 1.26158 | ||||||||
\(223\) | −17.6894 | −1.18457 | −0.592284 | − | 0.805729i | \(-0.701774\pi\) | ||||
−0.592284 | + | 0.805729i | \(0.701774\pi\) | |||||||
\(224\) | −43.5144 | −2.90743 | ||||||||
\(225\) | 3.39835 | 0.226557 | ||||||||
\(226\) | −19.8064 | −1.31750 | ||||||||
\(227\) | 10.0811 | 0.669104 | 0.334552 | − | 0.942377i | \(-0.391415\pi\) | ||||
0.334552 | + | 0.942377i | \(0.391415\pi\) | |||||||
\(228\) | 6.75507 | 0.447365 | ||||||||
\(229\) | 5.42671 | 0.358607 | 0.179304 | − | 0.983794i | \(-0.442616\pi\) | ||||
0.179304 | + | 0.983794i | \(0.442616\pi\) | |||||||
\(230\) | 4.66150 | 0.307370 | ||||||||
\(231\) | −34.4711 | −2.26803 | ||||||||
\(232\) | −1.05826 | −0.0694782 | ||||||||
\(233\) | 12.1459 | 0.795702 | 0.397851 | − | 0.917450i | \(-0.369756\pi\) | ||||
0.397851 | + | 0.917450i | \(0.369756\pi\) | |||||||
\(234\) | 10.5111 | 0.687130 | ||||||||
\(235\) | 0.753598 | 0.0491593 | ||||||||
\(236\) | 34.6169 | 2.25337 | ||||||||
\(237\) | −0.766411 | −0.0497837 | ||||||||
\(238\) | −1.41901 | −0.0919808 | ||||||||
\(239\) | −0.0139699 | −0.000903636 0 | −0.000451818 | − | 1.00000i | \(-0.500144\pi\) | ||||
−0.000451818 | 1.00000i | \(0.500144\pi\) | ||||||||
\(240\) | −61.7728 | −3.98742 | ||||||||
\(241\) | −16.0391 | −1.03317 | −0.516586 | − | 0.856236i | \(-0.672797\pi\) | ||||
−0.516586 | + | 0.856236i | \(0.672797\pi\) | |||||||
\(242\) | −35.7349 | −2.29713 | ||||||||
\(243\) | −9.85323 | −0.632085 | ||||||||
\(244\) | 40.0768 | 2.56565 | ||||||||
\(245\) | −14.9690 | −0.956335 | ||||||||
\(246\) | 10.6509 | 0.679079 | ||||||||
\(247\) | −2.76575 | −0.175980 | ||||||||
\(248\) | −27.1979 | −1.72707 | ||||||||
\(249\) | 19.1990 | 1.21669 | ||||||||
\(250\) | −11.8616 | −0.750196 | ||||||||
\(251\) | −4.43737 | −0.280085 | −0.140042 | − | 0.990146i | \(-0.544724\pi\) | ||||
−0.140042 | + | 0.990146i | \(0.544724\pi\) | |||||||
\(252\) | 16.9981 | 1.07078 | ||||||||
\(253\) | −3.01221 | −0.189376 | ||||||||
\(254\) | −24.9965 | −1.56842 | ||||||||
\(255\) | −0.895859 | −0.0561009 | ||||||||
\(256\) | −8.18886 | −0.511804 | ||||||||
\(257\) | 7.19000 | 0.448500 | 0.224250 | − | 0.974532i | \(-0.428007\pi\) | ||||
0.224250 | + | 0.974532i | \(0.428007\pi\) | |||||||
\(258\) | 5.34114 | 0.332525 | ||||||||
\(259\) | −12.4459 | −0.773350 | ||||||||
\(260\) | 58.3443 | 3.61836 | ||||||||
\(261\) | 0.133628 | 0.00827139 | ||||||||
\(262\) | −27.1044 | −1.67452 | ||||||||
\(263\) | 15.3493 | 0.946476 | 0.473238 | − | 0.880935i | \(-0.343085\pi\) | ||||
0.473238 | + | 0.880935i | \(0.343085\pi\) | |||||||
\(264\) | 77.0821 | 4.74407 | ||||||||
\(265\) | −26.2689 | −1.61369 | ||||||||
\(266\) | −6.27786 | −0.384920 | ||||||||
\(267\) | 10.3106 | 0.631000 | ||||||||
\(268\) | 64.8605 | 3.96199 | ||||||||
\(269\) | −4.98255 | −0.303792 | −0.151896 | − | 0.988397i | \(-0.548538\pi\) | ||||
−0.151896 | + | 0.988397i | \(0.548538\pi\) | |||||||
\(270\) | −30.8524 | −1.87762 | ||||||||
\(271\) | −4.94942 | −0.300656 | −0.150328 | − | 0.988636i | \(-0.548033\pi\) | ||||
−0.150328 | + | 0.988636i | \(0.548033\pi\) | |||||||
\(272\) | 1.64319 | 0.0996330 | ||||||||
\(273\) | −28.1743 | −1.70519 | ||||||||
\(274\) | 54.7169 | 3.30557 | ||||||||
\(275\) | −17.1090 | −1.03171 | ||||||||
\(276\) | 6.01312 | 0.361947 | ||||||||
\(277\) | 18.9701 | 1.13980 | 0.569902 | − | 0.821713i | \(-0.306981\pi\) | ||||
0.569902 | + | 0.821713i | \(0.306981\pi\) | |||||||
\(278\) | −43.5479 | −2.61183 | ||||||||
\(279\) | 3.43433 | 0.205608 | ||||||||
\(280\) | 78.9822 | 4.72009 | ||||||||
\(281\) | 21.2273 | 1.26632 | 0.633158 | − | 0.774022i | \(-0.281758\pi\) | ||||
0.633158 | + | 0.774022i | \(0.281758\pi\) | |||||||
\(282\) | 1.36446 | 0.0812523 | ||||||||
\(283\) | −24.0345 | −1.42870 | −0.714351 | − | 0.699788i | \(-0.753278\pi\) | ||||
−0.714351 | + | 0.699788i | \(0.753278\pi\) | |||||||
\(284\) | −55.1646 | −3.27342 | ||||||||
\(285\) | −3.96338 | −0.234770 | ||||||||
\(286\) | −52.9181 | −3.12911 | ||||||||
\(287\) | −7.05218 | −0.416277 | ||||||||
\(288\) | −12.2867 | −0.724004 | ||||||||
\(289\) | −16.9762 | −0.998598 | ||||||||
\(290\) | 1.04111 | 0.0611361 | ||||||||
\(291\) | −4.92645 | −0.288794 | ||||||||
\(292\) | −41.8760 | −2.45061 | ||||||||
\(293\) | −17.1490 | −1.00185 | −0.500927 | − | 0.865489i | \(-0.667008\pi\) | ||||
−0.500927 | + | 0.865489i | \(0.667008\pi\) | |||||||
\(294\) | −27.1027 | −1.58066 | ||||||||
\(295\) | −20.3107 | −1.18253 | ||||||||
\(296\) | 27.8307 | 1.61762 | ||||||||
\(297\) | 19.9365 | 1.15683 | ||||||||
\(298\) | −47.0780 | −2.72715 | ||||||||
\(299\) | −2.46197 | −0.142379 | ||||||||
\(300\) | 34.1539 | 1.97187 | ||||||||
\(301\) | −3.53647 | −0.203839 | ||||||||
\(302\) | 32.4047 | 1.86468 | ||||||||
\(303\) | −0.371712 | −0.0213543 | ||||||||
\(304\) | 7.26965 | 0.416943 | ||||||||
\(305\) | −23.5141 | −1.34642 | ||||||||
\(306\) | −0.400673 | −0.0229049 | ||||||||
\(307\) | 5.06111 | 0.288853 | 0.144426 | − | 0.989516i | \(-0.453866\pi\) | ||||
0.144426 | + | 0.989516i | \(0.453866\pi\) | |||||||
\(308\) | −85.5771 | −4.87621 | ||||||||
\(309\) | 9.01214 | 0.512683 | ||||||||
\(310\) | 26.7571 | 1.51970 | ||||||||
\(311\) | −25.1255 | −1.42474 | −0.712369 | − | 0.701805i | \(-0.752378\pi\) | ||||
−0.712369 | + | 0.701805i | \(0.752378\pi\) | |||||||
\(312\) | 63.0015 | 3.56676 | ||||||||
\(313\) | −11.9658 | −0.676349 | −0.338175 | − | 0.941083i | \(-0.609809\pi\) | ||||
−0.338175 | + | 0.941083i | \(0.609809\pi\) | |||||||
\(314\) | −25.6136 | −1.44546 | ||||||||
\(315\) | −9.97323 | −0.561928 | ||||||||
\(316\) | −1.90267 | −0.107034 | ||||||||
\(317\) | 11.5993 | 0.651481 | 0.325741 | − | 0.945459i | \(-0.394386\pi\) | ||||
0.325741 | + | 0.945459i | \(0.394386\pi\) | |||||||
\(318\) | −47.5623 | −2.66716 | ||||||||
\(319\) | −0.672754 | −0.0376670 | ||||||||
\(320\) | −33.8316 | −1.89124 | ||||||||
\(321\) | 32.3826 | 1.80742 | ||||||||
\(322\) | −5.58833 | −0.311425 | ||||||||
\(323\) | 0.105428 | 0.00586617 | ||||||||
\(324\) | −54.4286 | −3.02381 | ||||||||
\(325\) | −13.9837 | −0.775677 | ||||||||
\(326\) | 10.3134 | 0.571205 | ||||||||
\(327\) | 15.8213 | 0.874918 | ||||||||
\(328\) | 15.7696 | 0.870732 | ||||||||
\(329\) | −0.903433 | −0.0498079 | ||||||||
\(330\) | −75.8329 | −4.17446 | ||||||||
\(331\) | 9.61198 | 0.528322 | 0.264161 | − | 0.964479i | \(-0.414905\pi\) | ||||
0.264161 | + | 0.964479i | \(0.414905\pi\) | |||||||
\(332\) | 47.6630 | 2.61585 | ||||||||
\(333\) | −3.51423 | −0.192579 | ||||||||
\(334\) | 3.23763 | 0.177155 | ||||||||
\(335\) | −38.0554 | −2.07919 | ||||||||
\(336\) | 74.0549 | 4.04002 | ||||||||
\(337\) | −20.0283 | −1.09101 | −0.545504 | − | 0.838108i | \(-0.683662\pi\) | ||||
−0.545504 | + | 0.838108i | \(0.683662\pi\) | |||||||
\(338\) | −8.96677 | −0.487728 | ||||||||
\(339\) | 14.9905 | 0.814171 | ||||||||
\(340\) | −2.22404 | −0.120615 | ||||||||
\(341\) | −17.2902 | −0.936315 | ||||||||
\(342\) | −1.77262 | −0.0958524 | ||||||||
\(343\) | −6.45312 | −0.348436 | ||||||||
\(344\) | 7.90801 | 0.426371 | ||||||||
\(345\) | −3.52806 | −0.189944 | ||||||||
\(346\) | 44.9007 | 2.41388 | ||||||||
\(347\) | −19.3733 | −1.04001 | −0.520006 | − | 0.854163i | \(-0.674070\pi\) | ||||
−0.520006 | + | 0.854163i | \(0.674070\pi\) | |||||||
\(348\) | 1.34298 | 0.0719915 | ||||||||
\(349\) | −5.30816 | −0.284140 | −0.142070 | − | 0.989857i | \(-0.545376\pi\) | ||||
−0.142070 | + | 0.989857i | \(0.545376\pi\) | |||||||
\(350\) | −31.7411 | −1.69663 | ||||||||
\(351\) | 16.2947 | 0.869746 | ||||||||
\(352\) | 61.8578 | 3.29703 | ||||||||
\(353\) | 2.98686 | 0.158975 | 0.0794874 | − | 0.996836i | \(-0.474672\pi\) | ||||
0.0794874 | + | 0.996836i | \(0.474672\pi\) | |||||||
\(354\) | −36.7743 | −1.95453 | ||||||||
\(355\) | 32.3666 | 1.71784 | ||||||||
\(356\) | 25.5969 | 1.35663 | ||||||||
\(357\) | 1.07398 | 0.0568410 | ||||||||
\(358\) | 8.86261 | 0.468403 | ||||||||
\(359\) | −13.5515 | −0.715219 | −0.357610 | − | 0.933871i | \(-0.616408\pi\) | ||||
−0.357610 | + | 0.933871i | \(0.616408\pi\) | |||||||
\(360\) | 22.3015 | 1.17539 | ||||||||
\(361\) | −18.5336 | −0.975451 | ||||||||
\(362\) | −42.2228 | −2.21918 | ||||||||
\(363\) | 27.0460 | 1.41955 | ||||||||
\(364\) | −69.9447 | −3.66610 | ||||||||
\(365\) | 24.5698 | 1.28604 | ||||||||
\(366\) | −42.5745 | −2.22540 | ||||||||
\(367\) | 25.0725 | 1.30878 | 0.654388 | − | 0.756159i | \(-0.272926\pi\) | ||||
0.654388 | + | 0.756159i | \(0.272926\pi\) | |||||||
\(368\) | 6.47118 | 0.337334 | ||||||||
\(369\) | −1.99126 | −0.103661 | ||||||||
\(370\) | −27.3796 | −1.42340 | ||||||||
\(371\) | 31.4919 | 1.63498 | ||||||||
\(372\) | 34.5155 | 1.78954 | ||||||||
\(373\) | 26.1180 | 1.35234 | 0.676169 | − | 0.736747i | \(-0.263639\pi\) | ||||
0.676169 | + | 0.736747i | \(0.263639\pi\) | |||||||
\(374\) | 2.01719 | 0.104307 | ||||||||
\(375\) | 8.97750 | 0.463596 | ||||||||
\(376\) | 2.02020 | 0.104184 | ||||||||
\(377\) | −0.549862 | −0.0283193 | ||||||||
\(378\) | 36.9866 | 1.90239 | ||||||||
\(379\) | 7.20275 | 0.369981 | 0.184990 | − | 0.982740i | \(-0.440775\pi\) | ||||
0.184990 | + | 0.982740i | \(0.440775\pi\) | |||||||
\(380\) | −9.83938 | −0.504749 | ||||||||
\(381\) | 18.9186 | 0.969231 | ||||||||
\(382\) | −41.0790 | −2.10179 | ||||||||
\(383\) | −38.4884 | −1.96666 | −0.983332 | − | 0.181818i | \(-0.941802\pi\) | ||||
−0.983332 | + | 0.181818i | \(0.941802\pi\) | |||||||
\(384\) | −11.4162 | −0.582579 | ||||||||
\(385\) | 50.2104 | 2.55896 | ||||||||
\(386\) | −12.6387 | −0.643293 | ||||||||
\(387\) | −0.998559 | −0.0507596 | ||||||||
\(388\) | −12.2303 | −0.620898 | ||||||||
\(389\) | 32.8888 | 1.66753 | 0.833764 | − | 0.552121i | \(-0.186181\pi\) | ||||
0.833764 | + | 0.552121i | \(0.186181\pi\) | |||||||
\(390\) | −61.9805 | −3.13850 | ||||||||
\(391\) | 0.0938482 | 0.00474611 | ||||||||
\(392\) | −40.1279 | −2.02677 | ||||||||
\(393\) | 20.5140 | 1.03479 | ||||||||
\(394\) | 33.0660 | 1.66584 | ||||||||
\(395\) | 1.11635 | 0.0561695 | ||||||||
\(396\) | −24.1636 | −1.21427 | ||||||||
\(397\) | −26.1246 | −1.31116 | −0.655578 | − | 0.755127i | \(-0.727575\pi\) | ||||
−0.655578 | + | 0.755127i | \(0.727575\pi\) | |||||||
\(398\) | −62.3261 | −3.12412 | ||||||||
\(399\) | 4.75140 | 0.237868 | ||||||||
\(400\) | 36.7556 | 1.83778 | ||||||||
\(401\) | 22.1022 | 1.10373 | 0.551865 | − | 0.833934i | \(-0.313916\pi\) | ||||
0.551865 | + | 0.833934i | \(0.313916\pi\) | |||||||
\(402\) | −68.9028 | −3.43656 | ||||||||
\(403\) | −14.1318 | −0.703954 | ||||||||
\(404\) | −0.922802 | −0.0459111 | ||||||||
\(405\) | 31.9347 | 1.58685 | ||||||||
\(406\) | −1.24811 | −0.0619426 | ||||||||
\(407\) | 17.6924 | 0.876982 | ||||||||
\(408\) | −2.40156 | −0.118895 | ||||||||
\(409\) | 19.8717 | 0.982590 | 0.491295 | − | 0.870993i | \(-0.336524\pi\) | ||||
0.491295 | + | 0.870993i | \(0.336524\pi\) | |||||||
\(410\) | −15.5141 | −0.766185 | ||||||||
\(411\) | −41.4126 | −2.04273 | ||||||||
\(412\) | 22.3733 | 1.10225 | ||||||||
\(413\) | 24.3490 | 1.19813 | ||||||||
\(414\) | −1.57792 | −0.0775507 | ||||||||
\(415\) | −27.9651 | −1.37276 | ||||||||
\(416\) | 50.5582 | 2.47882 | ||||||||
\(417\) | 32.9593 | 1.61402 | ||||||||
\(418\) | 8.92429 | 0.436501 | ||||||||
\(419\) | 12.7274 | 0.621774 | 0.310887 | − | 0.950447i | \(-0.399374\pi\) | ||||
0.310887 | + | 0.950447i | \(0.399374\pi\) | |||||||
\(420\) | −100.232 | −4.89084 | ||||||||
\(421\) | 26.9931 | 1.31556 | 0.657781 | − | 0.753209i | \(-0.271495\pi\) | ||||
0.657781 | + | 0.753209i | \(0.271495\pi\) | |||||||
\(422\) | 47.9358 | 2.33348 | ||||||||
\(423\) | −0.255094 | −0.0124031 | ||||||||
\(424\) | −70.4201 | −3.41990 | ||||||||
\(425\) | 0.533048 | 0.0258566 | ||||||||
\(426\) | 58.6026 | 2.83931 | ||||||||
\(427\) | 28.1894 | 1.36418 | ||||||||
\(428\) | 80.3920 | 3.88589 | ||||||||
\(429\) | 40.0511 | 1.93369 | ||||||||
\(430\) | −7.77985 | −0.375178 | ||||||||
\(431\) | −22.4294 | −1.08038 | −0.540192 | − | 0.841542i | \(-0.681648\pi\) | ||||
−0.540192 | + | 0.841542i | \(0.681648\pi\) | |||||||
\(432\) | −42.8299 | −2.06065 | ||||||||
\(433\) | 12.3006 | 0.591131 | 0.295565 | − | 0.955322i | \(-0.404492\pi\) | ||||
0.295565 | + | 0.955322i | \(0.404492\pi\) | |||||||
\(434\) | −32.0771 | −1.53975 | ||||||||
\(435\) | −0.787965 | −0.0377800 | ||||||||
\(436\) | 39.2774 | 1.88105 | ||||||||
\(437\) | 0.415195 | 0.0198615 | ||||||||
\(438\) | 44.4858 | 2.12562 | ||||||||
\(439\) | 16.9150 | 0.807310 | 0.403655 | − | 0.914911i | \(-0.367740\pi\) | ||||
0.403655 | + | 0.914911i | \(0.367740\pi\) | |||||||
\(440\) | −112.277 | −5.35260 | ||||||||
\(441\) | 5.06703 | 0.241287 | ||||||||
\(442\) | 1.64871 | 0.0784212 | ||||||||
\(443\) | 34.1708 | 1.62350 | 0.811752 | − | 0.584003i | \(-0.198514\pi\) | ||||
0.811752 | + | 0.584003i | \(0.198514\pi\) | |||||||
\(444\) | −35.3185 | −1.67614 | ||||||||
\(445\) | −15.0184 | −0.711939 | ||||||||
\(446\) | 46.6520 | 2.20904 | ||||||||
\(447\) | 35.6310 | 1.68529 | ||||||||
\(448\) | 40.5582 | 1.91619 | ||||||||
\(449\) | −1.75466 | −0.0828078 | −0.0414039 | − | 0.999142i | \(-0.513183\pi\) | ||||
−0.0414039 | + | 0.999142i | \(0.513183\pi\) | |||||||
\(450\) | −8.96243 | −0.422493 | ||||||||
\(451\) | 10.0250 | 0.472060 | ||||||||
\(452\) | 37.2149 | 1.75044 | ||||||||
\(453\) | −24.5255 | −1.15231 | ||||||||
\(454\) | −26.5867 | −1.24778 | ||||||||
\(455\) | 41.0384 | 1.92391 | ||||||||
\(456\) | −10.6248 | −0.497551 | ||||||||
\(457\) | 39.2354 | 1.83535 | 0.917677 | − | 0.397326i | \(-0.130062\pi\) | ||||
0.917677 | + | 0.397326i | \(0.130062\pi\) | |||||||
\(458\) | −14.3118 | −0.668748 | ||||||||
\(459\) | −0.621139 | −0.0289923 | ||||||||
\(460\) | −8.75866 | −0.408375 | ||||||||
\(461\) | 21.9984 | 1.02457 | 0.512284 | − | 0.858816i | \(-0.328799\pi\) | ||||
0.512284 | + | 0.858816i | \(0.328799\pi\) | |||||||
\(462\) | 90.9104 | 4.22954 | ||||||||
\(463\) | 27.0710 | 1.25809 | 0.629047 | − | 0.777367i | \(-0.283445\pi\) | ||||
0.629047 | + | 0.777367i | \(0.283445\pi\) | |||||||
\(464\) | 1.44529 | 0.0670958 | ||||||||
\(465\) | −20.2512 | −0.939125 | ||||||||
\(466\) | −32.0322 | −1.48386 | ||||||||
\(467\) | 27.6910 | 1.28139 | 0.640694 | − | 0.767796i | \(-0.278647\pi\) | ||||
0.640694 | + | 0.767796i | \(0.278647\pi\) | |||||||
\(468\) | −19.7496 | −0.912927 | ||||||||
\(469\) | 45.6218 | 2.10662 | ||||||||
\(470\) | −1.98746 | −0.0916746 | ||||||||
\(471\) | 19.3857 | 0.893244 | ||||||||
\(472\) | −54.4475 | −2.50615 | ||||||||
\(473\) | 5.02726 | 0.231154 | ||||||||
\(474\) | 2.02125 | 0.0928390 | ||||||||
\(475\) | 2.35826 | 0.108204 | ||||||||
\(476\) | 2.66623 | 0.122207 | ||||||||
\(477\) | 8.89207 | 0.407140 | ||||||||
\(478\) | 0.0368426 | 0.00168514 | ||||||||
\(479\) | 27.8490 | 1.27245 | 0.636226 | − | 0.771502i | \(-0.280494\pi\) | ||||
0.636226 | + | 0.771502i | \(0.280494\pi\) | |||||||
\(480\) | 72.4511 | 3.30693 | ||||||||
\(481\) | 14.4606 | 0.659345 | ||||||||
\(482\) | 42.2998 | 1.92671 | ||||||||
\(483\) | 4.22953 | 0.192450 | ||||||||
\(484\) | 67.1437 | 3.05199 | ||||||||
\(485\) | 7.17583 | 0.325838 | ||||||||
\(486\) | 25.9858 | 1.17874 | ||||||||
\(487\) | 9.46325 | 0.428821 | 0.214410 | − | 0.976744i | \(-0.431217\pi\) | ||||
0.214410 | + | 0.976744i | \(0.431217\pi\) | |||||||
\(488\) | −63.0352 | −2.85347 | ||||||||
\(489\) | −7.80569 | −0.352986 | ||||||||
\(490\) | 39.4776 | 1.78342 | ||||||||
\(491\) | 25.5374 | 1.15249 | 0.576243 | − | 0.817279i | \(-0.304518\pi\) | ||||
0.576243 | + | 0.817279i | \(0.304518\pi\) | |||||||
\(492\) | −20.0124 | −0.902230 | ||||||||
\(493\) | 0.0209603 | 0.000944004 0 | ||||||||
\(494\) | 7.29409 | 0.328176 | ||||||||
\(495\) | 14.1774 | 0.637228 | ||||||||
\(496\) | 37.1447 | 1.66785 | ||||||||
\(497\) | −38.8019 | −1.74050 | ||||||||
\(498\) | −50.6334 | −2.26894 | ||||||||
\(499\) | −26.6371 | −1.19244 | −0.596220 | − | 0.802821i | \(-0.703331\pi\) | ||||
−0.596220 | + | 0.802821i | \(0.703331\pi\) | |||||||
\(500\) | 22.2873 | 0.996718 | ||||||||
\(501\) | −2.45040 | −0.109476 | ||||||||
\(502\) | 11.7026 | 0.522315 | ||||||||
\(503\) | −10.4117 | −0.464236 | −0.232118 | − | 0.972688i | \(-0.574566\pi\) | ||||
−0.232118 | + | 0.972688i | \(0.574566\pi\) | |||||||
\(504\) | −26.7356 | −1.19090 | ||||||||
\(505\) | 0.541433 | 0.0240934 | ||||||||
\(506\) | 7.94408 | 0.353157 | ||||||||
\(507\) | 6.78651 | 0.301399 | ||||||||
\(508\) | 46.9669 | 2.08382 | ||||||||
\(509\) | −28.1055 | −1.24576 | −0.622878 | − | 0.782319i | \(-0.714037\pi\) | ||||
−0.622878 | + | 0.782319i | \(0.714037\pi\) | |||||||
\(510\) | 2.36264 | 0.104620 | ||||||||
\(511\) | −29.4549 | −1.30301 | ||||||||
\(512\) | 33.0353 | 1.45997 | ||||||||
\(513\) | −2.74799 | −0.121327 | ||||||||
\(514\) | −18.9621 | −0.836384 | ||||||||
\(515\) | −13.1270 | −0.578445 | ||||||||
\(516\) | −10.0357 | −0.441795 | ||||||||
\(517\) | 1.28427 | 0.0564823 | ||||||||
\(518\) | 32.8234 | 1.44218 | ||||||||
\(519\) | −33.9831 | −1.49169 | ||||||||
\(520\) | −91.7674 | −4.02427 | ||||||||
\(521\) | −23.0015 | −1.00772 | −0.503858 | − | 0.863787i | \(-0.668086\pi\) | ||||
−0.503858 | + | 0.863787i | \(0.668086\pi\) | |||||||
\(522\) | −0.352417 | −0.0154249 | ||||||||
\(523\) | −7.80221 | −0.341167 | −0.170583 | − | 0.985343i | \(-0.554565\pi\) | ||||
−0.170583 | + | 0.985343i | \(0.554565\pi\) | |||||||
\(524\) | 50.9275 | 2.22478 | ||||||||
\(525\) | 24.0233 | 1.04846 | ||||||||
\(526\) | −40.4805 | −1.76503 | ||||||||
\(527\) | 0.538691 | 0.0234658 | ||||||||
\(528\) | −105.273 | −4.58140 | ||||||||
\(529\) | −22.6304 | −0.983931 | ||||||||
\(530\) | 69.2788 | 3.00928 | ||||||||
\(531\) | 6.87519 | 0.298358 | ||||||||
\(532\) | 11.7957 | 0.511409 | ||||||||
\(533\) | 8.19375 | 0.354911 | ||||||||
\(534\) | −27.1921 | −1.17672 | ||||||||
\(535\) | −47.1682 | −2.03926 | ||||||||
\(536\) | −102.016 | −4.40644 | ||||||||
\(537\) | −6.70767 | −0.289457 | ||||||||
\(538\) | 13.1404 | 0.566525 | ||||||||
\(539\) | −25.5100 | −1.09880 | ||||||||
\(540\) | 57.9697 | 2.49462 | ||||||||
\(541\) | 22.3560 | 0.961159 | 0.480580 | − | 0.876951i | \(-0.340426\pi\) | ||||
0.480580 | + | 0.876951i | \(0.340426\pi\) | |||||||
\(542\) | 13.0531 | 0.560677 | ||||||||
\(543\) | 31.9564 | 1.37138 | ||||||||
\(544\) | −1.92724 | −0.0826296 | ||||||||
\(545\) | −23.0451 | −0.987144 | ||||||||
\(546\) | 74.3038 | 3.17991 | ||||||||
\(547\) | −21.5007 | −0.919304 | −0.459652 | − | 0.888099i | \(-0.652026\pi\) | ||||
−0.459652 | + | 0.888099i | \(0.652026\pi\) | |||||||
\(548\) | −102.810 | −4.39181 | ||||||||
\(549\) | 7.95957 | 0.339706 | ||||||||
\(550\) | 45.1215 | 1.92399 | ||||||||
\(551\) | 0.0927306 | 0.00395046 | ||||||||
\(552\) | −9.45779 | −0.402550 | ||||||||
\(553\) | −1.33831 | −0.0569106 | ||||||||
\(554\) | −50.0297 | −2.12556 | ||||||||
\(555\) | 20.7223 | 0.879613 | ||||||||
\(556\) | 81.8238 | 3.47010 | ||||||||
\(557\) | −31.5554 | −1.33705 | −0.668523 | − | 0.743691i | \(-0.733073\pi\) | ||||
−0.668523 | + | 0.743691i | \(0.733073\pi\) | |||||||
\(558\) | −9.05732 | −0.383427 | ||||||||
\(559\) | 4.10893 | 0.173789 | ||||||||
\(560\) | −107.868 | −4.55824 | ||||||||
\(561\) | −1.52672 | −0.0644580 | ||||||||
\(562\) | −55.9827 | −2.36149 | ||||||||
\(563\) | 15.2317 | 0.641941 | 0.320971 | − | 0.947089i | \(-0.395991\pi\) | ||||
0.320971 | + | 0.947089i | \(0.395991\pi\) | |||||||
\(564\) | −2.56373 | −0.107953 | ||||||||
\(565\) | −21.8350 | −0.918606 | ||||||||
\(566\) | 63.3859 | 2.66431 | ||||||||
\(567\) | −38.2842 | −1.60779 | ||||||||
\(568\) | 86.7662 | 3.64063 | ||||||||
\(569\) | 25.8001 | 1.08160 | 0.540799 | − | 0.841152i | \(-0.318122\pi\) | ||||
0.540799 | + | 0.841152i | \(0.318122\pi\) | |||||||
\(570\) | 10.4526 | 0.437811 | ||||||||
\(571\) | −20.4726 | −0.856750 | −0.428375 | − | 0.903601i | \(-0.640914\pi\) | ||||
−0.428375 | + | 0.903601i | \(0.640914\pi\) | |||||||
\(572\) | 99.4298 | 4.15737 | ||||||||
\(573\) | 31.0907 | 1.29883 | ||||||||
\(574\) | 18.5987 | 0.776293 | ||||||||
\(575\) | 2.09924 | 0.0875444 | ||||||||
\(576\) | 11.4520 | 0.477168 | ||||||||
\(577\) | 36.6337 | 1.52508 | 0.762540 | − | 0.646942i | \(-0.223952\pi\) | ||||
0.762540 | + | 0.646942i | \(0.223952\pi\) | |||||||
\(578\) | 44.7711 | 1.86223 | ||||||||
\(579\) | 9.56561 | 0.397533 | ||||||||
\(580\) | −1.95618 | −0.0812259 | ||||||||
\(581\) | 33.5254 | 1.39087 | ||||||||
\(582\) | 12.9925 | 0.538556 | ||||||||
\(583\) | −44.7673 | −1.85407 | ||||||||
\(584\) | 65.8651 | 2.72552 | ||||||||
\(585\) | 11.5876 | 0.479090 | ||||||||
\(586\) | 45.2269 | 1.86831 | ||||||||
\(587\) | −0.928581 | −0.0383267 | −0.0191633 | − | 0.999816i | \(-0.506100\pi\) | ||||
−0.0191633 | + | 0.999816i | \(0.506100\pi\) | |||||||
\(588\) | 50.9243 | 2.10008 | ||||||||
\(589\) | 2.38323 | 0.0981992 | ||||||||
\(590\) | 53.5651 | 2.20524 | ||||||||
\(591\) | −25.0261 | −1.02943 | ||||||||
\(592\) | −38.0089 | −1.56216 | ||||||||
\(593\) | 42.8223 | 1.75850 | 0.879251 | − | 0.476359i | \(-0.158044\pi\) | ||||
0.879251 | + | 0.476359i | \(0.158044\pi\) | |||||||
\(594\) | −52.5783 | −2.15731 | ||||||||
\(595\) | −1.56435 | −0.0641321 | ||||||||
\(596\) | 88.4565 | 3.62332 | ||||||||
\(597\) | 47.1716 | 1.93060 | ||||||||
\(598\) | 6.49293 | 0.265516 | ||||||||
\(599\) | −33.8960 | −1.38495 | −0.692476 | − | 0.721441i | \(-0.743480\pi\) | ||||
−0.692476 | + | 0.721441i | \(0.743480\pi\) | |||||||
\(600\) | −53.7192 | −2.19308 | ||||||||
\(601\) | 27.3368 | 1.11509 | 0.557545 | − | 0.830147i | \(-0.311743\pi\) | ||||
0.557545 | + | 0.830147i | \(0.311743\pi\) | |||||||
\(602\) | 9.32669 | 0.380128 | ||||||||
\(603\) | 12.8818 | 0.524588 | ||||||||
\(604\) | −60.8864 | −2.47743 | ||||||||
\(605\) | −39.3950 | −1.60163 | ||||||||
\(606\) | 0.980313 | 0.0398225 | ||||||||
\(607\) | −34.3409 | −1.39385 | −0.696926 | − | 0.717143i | \(-0.745450\pi\) | ||||
−0.696926 | + | 0.717143i | \(0.745450\pi\) | |||||||
\(608\) | −8.52631 | −0.345788 | ||||||||
\(609\) | 0.944633 | 0.0382785 | ||||||||
\(610\) | 62.0136 | 2.51086 | ||||||||
\(611\) | 1.04968 | 0.0424653 | ||||||||
\(612\) | 0.752839 | 0.0304317 | ||||||||
\(613\) | 31.8122 | 1.28488 | 0.642442 | − | 0.766334i | \(-0.277921\pi\) | ||||
0.642442 | + | 0.766334i | \(0.277921\pi\) | |||||||
\(614\) | −13.3476 | −0.538666 | ||||||||
\(615\) | 11.7418 | 0.473476 | ||||||||
\(616\) | 134.601 | 5.42322 | ||||||||
\(617\) | 27.3971 | 1.10297 | 0.551483 | − | 0.834186i | \(-0.314062\pi\) | ||||
0.551483 | + | 0.834186i | \(0.314062\pi\) | |||||||
\(618\) | −23.7676 | −0.956074 | ||||||||
\(619\) | 20.4135 | 0.820486 | 0.410243 | − | 0.911976i | \(-0.365444\pi\) | ||||
0.410243 | + | 0.911976i | \(0.365444\pi\) | |||||||
\(620\) | −50.2749 | −2.01909 | ||||||||
\(621\) | −2.44616 | −0.0981611 | ||||||||
\(622\) | 66.2633 | 2.65692 | ||||||||
\(623\) | 18.0044 | 0.721332 | ||||||||
\(624\) | −86.0425 | −3.44446 | ||||||||
\(625\) | −30.3417 | −1.21367 | ||||||||
\(626\) | 31.5574 | 1.26129 | ||||||||
\(627\) | −6.75436 | −0.269743 | ||||||||
\(628\) | 48.1263 | 1.92045 | ||||||||
\(629\) | −0.551224 | −0.0219787 | ||||||||
\(630\) | 26.3023 | 1.04791 | ||||||||
\(631\) | −28.0587 | −1.11700 | −0.558499 | − | 0.829505i | \(-0.688623\pi\) | ||||
−0.558499 | + | 0.829505i | \(0.688623\pi\) | |||||||
\(632\) | 2.99263 | 0.119041 | ||||||||
\(633\) | −36.2803 | −1.44201 | ||||||||
\(634\) | −30.5907 | −1.21491 | ||||||||
\(635\) | −27.5567 | −1.09356 | ||||||||
\(636\) | 89.3665 | 3.54361 | ||||||||
\(637\) | −20.8501 | −0.826112 | ||||||||
\(638\) | 1.77425 | 0.0702432 | ||||||||
\(639\) | −10.9561 | −0.433418 | ||||||||
\(640\) | 16.6287 | 0.657308 | ||||||||
\(641\) | 24.8337 | 0.980874 | 0.490437 | − | 0.871477i | \(-0.336837\pi\) | ||||
0.490437 | + | 0.871477i | \(0.336837\pi\) | |||||||
\(642\) | −85.4022 | −3.37056 | ||||||||
\(643\) | 19.5294 | 0.770163 | 0.385081 | − | 0.922883i | \(-0.374173\pi\) | ||||
0.385081 | + | 0.922883i | \(0.374173\pi\) | |||||||
\(644\) | 10.5001 | 0.413762 | ||||||||
\(645\) | 5.88819 | 0.231847 | ||||||||
\(646\) | −0.278044 | −0.0109395 | ||||||||
\(647\) | 16.2936 | 0.640566 | 0.320283 | − | 0.947322i | \(-0.396222\pi\) | ||||
0.320283 | + | 0.947322i | \(0.396222\pi\) | |||||||
\(648\) | 85.6086 | 3.36302 | ||||||||
\(649\) | −34.6132 | −1.35869 | ||||||||
\(650\) | 36.8791 | 1.44652 | ||||||||
\(651\) | 24.2776 | 0.951515 | ||||||||
\(652\) | −19.3782 | −0.758908 | ||||||||
\(653\) | −6.85713 | −0.268340 | −0.134170 | − | 0.990958i | \(-0.542837\pi\) | ||||
−0.134170 | + | 0.990958i | \(0.542837\pi\) | |||||||
\(654\) | −41.7253 | −1.63159 | ||||||||
\(655\) | −29.8805 | −1.16753 | ||||||||
\(656\) | −21.5369 | −0.840875 | ||||||||
\(657\) | −8.31691 | −0.324474 | ||||||||
\(658\) | 2.38262 | 0.0928841 | ||||||||
\(659\) | 20.8861 | 0.813609 | 0.406804 | − | 0.913515i | \(-0.366643\pi\) | ||||
0.406804 | + | 0.913515i | \(0.366643\pi\) | |||||||
\(660\) | 142.485 | 5.54623 | ||||||||
\(661\) | −24.6725 | −0.959648 | −0.479824 | − | 0.877365i | \(-0.659299\pi\) | ||||
−0.479824 | + | 0.877365i | \(0.659299\pi\) | |||||||
\(662\) | −25.3496 | −0.985240 | ||||||||
\(663\) | −1.24783 | −0.0484617 | ||||||||
\(664\) | −74.9672 | −2.90929 | ||||||||
\(665\) | −6.92086 | −0.268379 | ||||||||
\(666\) | 9.26804 | 0.359129 | ||||||||
\(667\) | 0.0825455 | 0.00319617 | ||||||||
\(668\) | −6.08330 | −0.235370 | ||||||||
\(669\) | −35.3086 | −1.36511 | ||||||||
\(670\) | 100.363 | 3.87737 | ||||||||
\(671\) | −40.0726 | −1.54698 | ||||||||
\(672\) | −86.8563 | −3.35055 | ||||||||
\(673\) | 6.51326 | 0.251068 | 0.125534 | − | 0.992089i | \(-0.459936\pi\) | ||||
0.125534 | + | 0.992089i | \(0.459936\pi\) | |||||||
\(674\) | 52.8203 | 2.03456 | ||||||||
\(675\) | −13.8939 | −0.534778 | ||||||||
\(676\) | 16.8480 | 0.648000 | ||||||||
\(677\) | 22.8151 | 0.876856 | 0.438428 | − | 0.898766i | \(-0.355535\pi\) | ||||
0.438428 | + | 0.898766i | \(0.355535\pi\) | |||||||
\(678\) | −39.5343 | −1.51830 | ||||||||
\(679\) | −8.60257 | −0.330136 | ||||||||
\(680\) | 3.49810 | 0.134146 | ||||||||
\(681\) | 20.1222 | 0.771084 | ||||||||
\(682\) | 45.5992 | 1.74608 | ||||||||
\(683\) | 27.9282 | 1.06864 | 0.534321 | − | 0.845282i | \(-0.320567\pi\) | ||||
0.534321 | + | 0.845282i | \(0.320567\pi\) | |||||||
\(684\) | 3.33064 | 0.127350 | ||||||||
\(685\) | 60.3212 | 2.30475 | ||||||||
\(686\) | 17.0188 | 0.649779 | ||||||||
\(687\) | 10.8319 | 0.413263 | ||||||||
\(688\) | −10.8001 | −0.411752 | ||||||||
\(689\) | −36.5896 | −1.39395 | ||||||||
\(690\) | 9.30452 | 0.354217 | ||||||||
\(691\) | −15.0130 | −0.571122 | −0.285561 | − | 0.958361i | \(-0.592180\pi\) | ||||
−0.285561 | + | 0.958361i | \(0.592180\pi\) | |||||||
\(692\) | −84.3656 | −3.20710 | ||||||||
\(693\) | −16.9963 | −0.645635 | ||||||||
\(694\) | 51.0929 | 1.93946 | ||||||||
\(695\) | −48.0082 | −1.82106 | ||||||||
\(696\) | −2.11233 | −0.0800675 | ||||||||
\(697\) | −0.312339 | −0.0118307 | ||||||||
\(698\) | 13.9992 | 0.529877 | ||||||||
\(699\) | 24.2436 | 0.916977 | ||||||||
\(700\) | 59.6395 | 2.25416 | ||||||||
\(701\) | 29.6151 | 1.11855 | 0.559273 | − | 0.828983i | \(-0.311080\pi\) | ||||
0.559273 | + | 0.828983i | \(0.311080\pi\) | |||||||
\(702\) | −42.9738 | −1.62194 | ||||||||
\(703\) | −2.43868 | −0.0919764 | ||||||||
\(704\) | −57.6554 | −2.17297 | ||||||||
\(705\) | 1.50421 | 0.0566518 | ||||||||
\(706\) | −7.87723 | −0.296464 | ||||||||
\(707\) | −0.649084 | −0.0244113 | ||||||||
\(708\) | 69.0966 | 2.59681 | ||||||||
\(709\) | −37.7070 | −1.41612 | −0.708058 | − | 0.706154i | \(-0.750429\pi\) | ||||
−0.708058 | + | 0.706154i | \(0.750429\pi\) | |||||||
\(710\) | −85.3601 | −3.20351 | ||||||||
\(711\) | −0.377885 | −0.0141718 | ||||||||
\(712\) | −40.2603 | −1.50882 | ||||||||
\(713\) | 2.12147 | 0.0794495 | ||||||||
\(714\) | −2.83240 | −0.106000 | ||||||||
\(715\) | −58.3382 | −2.18172 | ||||||||
\(716\) | −16.6523 | −0.622325 | ||||||||
\(717\) | −0.0278844 | −0.00104136 | ||||||||
\(718\) | 35.7392 | 1.33377 | ||||||||
\(719\) | −14.2728 | −0.532286 | −0.266143 | − | 0.963933i | \(-0.585749\pi\) | ||||
−0.266143 | + | 0.963933i | \(0.585749\pi\) | |||||||
\(720\) | −30.4576 | −1.13509 | ||||||||
\(721\) | 15.7370 | 0.586076 | ||||||||
\(722\) | 48.8784 | 1.81907 | ||||||||
\(723\) | −32.0147 | −1.19064 | ||||||||
\(724\) | 79.3341 | 2.94843 | ||||||||
\(725\) | 0.468849 | 0.0174126 | ||||||||
\(726\) | −71.3282 | −2.64724 | ||||||||
\(727\) | 30.5702 | 1.13379 | 0.566894 | − | 0.823791i | \(-0.308145\pi\) | ||||
0.566894 | + | 0.823791i | \(0.308145\pi\) | |||||||
\(728\) | 110.013 | 4.07736 | ||||||||
\(729\) | 13.2843 | 0.492012 | ||||||||
\(730\) | −64.7977 | −2.39827 | ||||||||
\(731\) | −0.156629 | −0.00579313 | ||||||||
\(732\) | 79.9948 | 2.95669 | ||||||||
\(733\) | 4.84002 | 0.178770 | 0.0893851 | − | 0.995997i | \(-0.471510\pi\) | ||||
0.0893851 | + | 0.995997i | \(0.471510\pi\) | |||||||
\(734\) | −66.1236 | −2.44067 | ||||||||
\(735\) | −29.8787 | −1.10209 | ||||||||
\(736\) | −7.58982 | −0.279764 | ||||||||
\(737\) | −64.8537 | −2.38892 | ||||||||
\(738\) | 5.25153 | 0.193312 | ||||||||
\(739\) | −25.8870 | −0.952267 | −0.476134 | − | 0.879373i | \(-0.657962\pi\) | ||||
−0.476134 | + | 0.879373i | \(0.657962\pi\) | |||||||
\(740\) | 51.4446 | 1.89114 | ||||||||
\(741\) | −5.52054 | −0.202802 | ||||||||
\(742\) | −83.0533 | −3.04898 | ||||||||
\(743\) | 10.4101 | 0.381910 | 0.190955 | − | 0.981599i | \(-0.438842\pi\) | ||||
0.190955 | + | 0.981599i | \(0.438842\pi\) | |||||||
\(744\) | −54.2880 | −1.99029 | ||||||||
\(745\) | −51.8998 | −1.90146 | ||||||||
\(746\) | −68.8807 | −2.52190 | ||||||||
\(747\) | 9.46624 | 0.346352 | ||||||||
\(748\) | −3.79018 | −0.138583 | ||||||||
\(749\) | 56.5464 | 2.06616 | ||||||||
\(750\) | −23.6763 | −0.864535 | ||||||||
\(751\) | −2.90026 | −0.105832 | −0.0529160 | − | 0.998599i | \(-0.516852\pi\) | ||||
−0.0529160 | + | 0.998599i | \(0.516852\pi\) | |||||||
\(752\) | −2.75903 | −0.100611 | ||||||||
\(753\) | −8.85716 | −0.322773 | ||||||||
\(754\) | 1.45015 | 0.0528112 | ||||||||
\(755\) | 35.7237 | 1.30012 | ||||||||
\(756\) | −69.4955 | −2.52753 | ||||||||
\(757\) | −20.0209 | −0.727672 | −0.363836 | − | 0.931463i | \(-0.618533\pi\) | ||||
−0.363836 | + | 0.931463i | \(0.618533\pi\) | |||||||
\(758\) | −18.9958 | −0.689957 | ||||||||
\(759\) | −6.01249 | −0.218239 | ||||||||
\(760\) | 15.4760 | 0.561372 | ||||||||
\(761\) | −3.24170 | −0.117512 | −0.0587558 | − | 0.998272i | \(-0.518713\pi\) | ||||
−0.0587558 | + | 0.998272i | \(0.518713\pi\) | |||||||
\(762\) | −49.8939 | −1.80747 | ||||||||
\(763\) | 27.6271 | 1.00017 | ||||||||
\(764\) | 77.1849 | 2.79245 | ||||||||
\(765\) | −0.441711 | −0.0159701 | ||||||||
\(766\) | 101.505 | 3.66753 | ||||||||
\(767\) | −28.2904 | −1.02151 | ||||||||
\(768\) | −16.3453 | −0.589809 | ||||||||
\(769\) | 19.0249 | 0.686056 | 0.343028 | − | 0.939325i | \(-0.388547\pi\) | ||||
0.343028 | + | 0.939325i | \(0.388547\pi\) | |||||||
\(770\) | −132.419 | −4.77206 | ||||||||
\(771\) | 14.3515 | 0.516857 | ||||||||
\(772\) | 23.7473 | 0.854684 | ||||||||
\(773\) | −30.5793 | −1.09986 | −0.549931 | − | 0.835210i | \(-0.685346\pi\) | ||||
−0.549931 | + | 0.835210i | \(0.685346\pi\) | |||||||
\(774\) | 2.63349 | 0.0946589 | ||||||||
\(775\) | 12.0497 | 0.432838 | ||||||||
\(776\) | 19.2365 | 0.690550 | ||||||||
\(777\) | −24.8424 | −0.891218 | ||||||||
\(778\) | −86.7373 | −3.10968 | ||||||||
\(779\) | −1.38182 | −0.0495089 | ||||||||
\(780\) | 116.457 | 4.16984 | ||||||||
\(781\) | 55.1588 | 1.97374 | ||||||||
\(782\) | −0.247505 | −0.00885076 | ||||||||
\(783\) | −0.546331 | −0.0195243 | ||||||||
\(784\) | 54.8036 | 1.95727 | ||||||||
\(785\) | −28.2370 | −1.00782 | ||||||||
\(786\) | −54.1014 | −1.92973 | ||||||||
\(787\) | −33.3331 | −1.18820 | −0.594098 | − | 0.804393i | \(-0.702491\pi\) | ||||
−0.594098 | + | 0.804393i | \(0.702491\pi\) | |||||||
\(788\) | −62.1290 | −2.21325 | ||||||||
\(789\) | 30.6377 | 1.09073 | ||||||||
\(790\) | −2.94413 | −0.104748 | ||||||||
\(791\) | 26.1764 | 0.930725 | ||||||||
\(792\) | 38.0060 | 1.35048 | ||||||||
\(793\) | −32.7525 | −1.16308 | ||||||||
\(794\) | 68.8982 | 2.44511 | ||||||||
\(795\) | −52.4337 | −1.85963 | ||||||||
\(796\) | 117.107 | 4.15074 | ||||||||
\(797\) | 41.0279 | 1.45328 | 0.726642 | − | 0.687017i | \(-0.241080\pi\) | ||||
0.726642 | + | 0.687017i | \(0.241080\pi\) | |||||||
\(798\) | −12.5308 | −0.443587 | ||||||||
\(799\) | −0.0400128 | −0.00141555 | ||||||||
\(800\) | −43.1093 | −1.52414 | ||||||||
\(801\) | 5.08374 | 0.179625 | ||||||||
\(802\) | −58.2899 | −2.05829 | ||||||||
\(803\) | 41.8716 | 1.47762 | ||||||||
\(804\) | 129.464 | 4.56584 | ||||||||
\(805\) | −6.16070 | −0.217136 | ||||||||
\(806\) | 37.2696 | 1.31277 | ||||||||
\(807\) | −9.94536 | −0.350093 | ||||||||
\(808\) | 1.45144 | 0.0510614 | ||||||||
\(809\) | 17.6275 | 0.619750 | 0.309875 | − | 0.950777i | \(-0.399713\pi\) | ||||
0.309875 | + | 0.950777i | \(0.399713\pi\) | |||||||
\(810\) | −84.2212 | −2.95923 | ||||||||
\(811\) | −21.6049 | −0.758652 | −0.379326 | − | 0.925263i | \(-0.623844\pi\) | ||||
−0.379326 | + | 0.925263i | \(0.623844\pi\) | |||||||
\(812\) | 2.34512 | 0.0822976 | ||||||||
\(813\) | −9.87923 | −0.346480 | ||||||||
\(814\) | −46.6601 | −1.63544 | ||||||||
\(815\) | 11.3697 | 0.398263 | ||||||||
\(816\) | 3.27987 | 0.114818 | ||||||||
\(817\) | −0.692944 | −0.0242430 | ||||||||
\(818\) | −52.4073 | −1.83238 | ||||||||
\(819\) | −13.8916 | −0.485411 | ||||||||
\(820\) | 29.1499 | 1.01796 | ||||||||
\(821\) | −54.7645 | −1.91130 | −0.955648 | − | 0.294513i | \(-0.904843\pi\) | ||||
−0.955648 | + | 0.294513i | \(0.904843\pi\) | |||||||
\(822\) | 109.217 | 3.80938 | ||||||||
\(823\) | −9.10628 | −0.317425 | −0.158712 | − | 0.987325i | \(-0.550734\pi\) | ||||
−0.158712 | + | 0.987325i | \(0.550734\pi\) | |||||||
\(824\) | −35.1900 | −1.22590 | ||||||||
\(825\) | −34.1503 | −1.18896 | ||||||||
\(826\) | −64.2153 | −2.23434 | ||||||||
\(827\) | −16.1228 | −0.560644 | −0.280322 | − | 0.959906i | \(-0.590441\pi\) | ||||
−0.280322 | + | 0.959906i | \(0.590441\pi\) | |||||||
\(828\) | 2.96482 | 0.103035 | ||||||||
\(829\) | −5.95725 | −0.206904 | −0.103452 | − | 0.994634i | \(-0.532989\pi\) | ||||
−0.103452 | + | 0.994634i | \(0.532989\pi\) | |||||||
\(830\) | 73.7522 | 2.55998 | ||||||||
\(831\) | 37.8650 | 1.31352 | ||||||||
\(832\) | −47.1235 | −1.63371 | ||||||||
\(833\) | 0.794789 | 0.0275378 | ||||||||
\(834\) | −86.9233 | −3.00991 | ||||||||
\(835\) | 3.56923 | 0.123518 | ||||||||
\(836\) | −16.7682 | −0.579939 | ||||||||
\(837\) | −14.0410 | −0.485329 | ||||||||
\(838\) | −33.5659 | −1.15951 | ||||||||
\(839\) | 1.66229 | 0.0573887 | 0.0286944 | − | 0.999588i | \(-0.490865\pi\) | ||||
0.0286944 | + | 0.999588i | \(0.490865\pi\) | |||||||
\(840\) | 157.651 | 5.43949 | ||||||||
\(841\) | −28.9816 | −0.999364 | ||||||||
\(842\) | −71.1886 | −2.45332 | ||||||||
\(843\) | 42.3705 | 1.45932 | ||||||||
\(844\) | −90.0684 | −3.10028 | ||||||||
\(845\) | −9.88517 | −0.340060 | ||||||||
\(846\) | 0.672757 | 0.0231299 | ||||||||
\(847\) | 47.2278 | 1.62277 | ||||||||
\(848\) | 96.1742 | 3.30264 | ||||||||
\(849\) | −47.9737 | −1.64645 | ||||||||
\(850\) | −1.40580 | −0.0482186 | ||||||||
\(851\) | −2.17082 | −0.0744148 | ||||||||
\(852\) | −110.111 | −3.77233 | ||||||||
\(853\) | 46.6355 | 1.59677 | 0.798384 | − | 0.602148i | \(-0.205688\pi\) | ||||
0.798384 | + | 0.602148i | \(0.205688\pi\) | |||||||
\(854\) | −74.3436 | −2.54398 | ||||||||
\(855\) | −1.95418 | −0.0668315 | ||||||||
\(856\) | −126.445 | −4.32181 | ||||||||
\(857\) | −35.3101 | −1.20617 | −0.603085 | − | 0.797677i | \(-0.706062\pi\) | ||||
−0.603085 | + | 0.797677i | \(0.706062\pi\) | |||||||
\(858\) | −105.627 | −3.60603 | ||||||||
\(859\) | −48.4098 | −1.65172 | −0.825861 | − | 0.563873i | \(-0.809311\pi\) | ||||
−0.825861 | + | 0.563873i | \(0.809311\pi\) | |||||||
\(860\) | 14.6179 | 0.498465 | ||||||||
\(861\) | −14.0764 | −0.479723 | ||||||||
\(862\) | 59.1527 | 2.01475 | ||||||||
\(863\) | 3.82206 | 0.130104 | 0.0650522 | − | 0.997882i | \(-0.479279\pi\) | ||||
0.0650522 | + | 0.997882i | \(0.479279\pi\) | |||||||
\(864\) | 50.2336 | 1.70898 | ||||||||
\(865\) | 49.4995 | 1.68304 | ||||||||
\(866\) | −32.4404 | −1.10237 | ||||||||
\(867\) | −33.8851 | −1.15080 | ||||||||
\(868\) | 60.2709 | 2.04573 | ||||||||
\(869\) | 1.90247 | 0.0645369 | ||||||||
\(870\) | 2.07809 | 0.0704540 | ||||||||
\(871\) | −53.0068 | −1.79607 | ||||||||
\(872\) | −61.7779 | −2.09206 | ||||||||
\(873\) | −2.42903 | −0.0822101 | ||||||||
\(874\) | −1.09499 | −0.0370386 | ||||||||
\(875\) | 15.6765 | 0.529963 | ||||||||
\(876\) | −83.5861 | −2.82411 | ||||||||
\(877\) | 31.2125 | 1.05397 | 0.526985 | − | 0.849874i | \(-0.323322\pi\) | ||||
0.526985 | + | 0.849874i | \(0.323322\pi\) | |||||||
\(878\) | −44.6098 | −1.50551 | ||||||||
\(879\) | −34.2300 | −1.15455 | ||||||||
\(880\) | 153.339 | 5.16907 | ||||||||
\(881\) | 22.0770 | 0.743791 | 0.371896 | − | 0.928275i | \(-0.378708\pi\) | ||||
0.371896 | + | 0.928275i | \(0.378708\pi\) | |||||||
\(882\) | −13.3632 | −0.449963 | ||||||||
\(883\) | 13.1851 | 0.443714 | 0.221857 | − | 0.975079i | \(-0.428788\pi\) | ||||
0.221857 | + | 0.975079i | \(0.428788\pi\) | |||||||
\(884\) | −3.09783 | −0.104191 | ||||||||
\(885\) | −40.5408 | −1.36277 | ||||||||
\(886\) | −90.1183 | −3.02758 | ||||||||
\(887\) | 44.4006 | 1.49082 | 0.745412 | − | 0.666604i | \(-0.232253\pi\) | ||||
0.745412 | + | 0.666604i | \(0.232253\pi\) | |||||||
\(888\) | 55.5510 | 1.86417 | ||||||||
\(889\) | 33.0357 | 1.10798 | ||||||||
\(890\) | 39.6078 | 1.32766 | ||||||||
\(891\) | 54.4229 | 1.82324 | ||||||||
\(892\) | −87.6562 | −2.93495 | ||||||||
\(893\) | −0.177021 | −0.00592378 | ||||||||
\(894\) | −93.9693 | −3.14280 | ||||||||
\(895\) | 9.77034 | 0.326586 | ||||||||
\(896\) | −19.9349 | −0.665979 | ||||||||
\(897\) | −4.91418 | −0.164080 | ||||||||
\(898\) | 4.62756 | 0.154424 | ||||||||
\(899\) | 0.473813 | 0.0158025 | ||||||||
\(900\) | 16.8398 | 0.561328 | ||||||||
\(901\) | 1.39477 | 0.0464664 | ||||||||
\(902\) | −26.4389 | −0.880320 | ||||||||
\(903\) | −7.05892 | −0.234906 | ||||||||
\(904\) | −58.5339 | −1.94681 | ||||||||
\(905\) | −46.5474 | −1.54729 | ||||||||
\(906\) | 64.6809 | 2.14888 | ||||||||
\(907\) | −0.0574867 | −0.00190881 | −0.000954407 | − | 1.00000i | \(-0.500304\pi\) | ||||
−0.000954407 | 1.00000i | \(0.500304\pi\) | ||||||||
\(908\) | 49.9548 | 1.65781 | ||||||||
\(909\) | −0.183276 | −0.00607887 | ||||||||
\(910\) | −108.230 | −3.58780 | ||||||||
\(911\) | −33.5536 | −1.11168 | −0.555841 | − | 0.831289i | \(-0.687604\pi\) | ||||
−0.555841 | + | 0.831289i | \(0.687604\pi\) | |||||||
\(912\) | 14.5105 | 0.480490 | ||||||||
\(913\) | −47.6579 | −1.57725 | ||||||||
\(914\) | −103.475 | −3.42265 | ||||||||
\(915\) | −46.9351 | −1.55163 | ||||||||
\(916\) | 26.8910 | 0.888504 | ||||||||
\(917\) | 35.8215 | 1.18293 | ||||||||
\(918\) | 1.63813 | 0.0540662 | ||||||||
\(919\) | −39.7205 | −1.31026 | −0.655129 | − | 0.755517i | \(-0.727386\pi\) | ||||
−0.655129 | + | 0.755517i | \(0.727386\pi\) | |||||||
\(920\) | 13.7761 | 0.454186 | ||||||||
\(921\) | 10.1022 | 0.332878 | ||||||||
\(922\) | −58.0162 | −1.91066 | ||||||||
\(923\) | 45.0829 | 1.48392 | ||||||||
\(924\) | −170.815 | −5.61940 | ||||||||
\(925\) | −12.3300 | −0.405409 | ||||||||
\(926\) | −71.3940 | −2.34615 | ||||||||
\(927\) | 4.44351 | 0.145944 | ||||||||
\(928\) | −1.69513 | −0.0556453 | ||||||||
\(929\) | −34.3982 | −1.12857 | −0.564284 | − | 0.825581i | \(-0.690848\pi\) | ||||
−0.564284 | + | 0.825581i | \(0.690848\pi\) | |||||||
\(930\) | 53.4082 | 1.75132 | ||||||||
\(931\) | 3.51623 | 0.115240 | ||||||||
\(932\) | 60.1865 | 1.97147 | ||||||||
\(933\) | −50.1515 | −1.64189 | ||||||||
\(934\) | −73.0293 | −2.38959 | ||||||||
\(935\) | 2.22380 | 0.0727261 | ||||||||
\(936\) | 31.0634 | 1.01534 | ||||||||
\(937\) | 14.9917 | 0.489757 | 0.244879 | − | 0.969554i | \(-0.421252\pi\) | ||||
0.244879 | + | 0.969554i | \(0.421252\pi\) | |||||||
\(938\) | −120.318 | −3.92852 | ||||||||
\(939\) | −23.8842 | −0.779433 | ||||||||
\(940\) | 3.73431 | 0.121800 | ||||||||
\(941\) | 36.5885 | 1.19275 | 0.596375 | − | 0.802706i | \(-0.296607\pi\) | ||||
0.596375 | + | 0.802706i | \(0.296607\pi\) | |||||||
\(942\) | −51.1256 | −1.66576 | ||||||||
\(943\) | −1.23005 | −0.0400559 | ||||||||
\(944\) | 74.3602 | 2.42022 | ||||||||
\(945\) | 40.7749 | 1.32641 | ||||||||
\(946\) | −13.2584 | −0.431066 | ||||||||
\(947\) | 22.8767 | 0.743392 | 0.371696 | − | 0.928355i | \(-0.378776\pi\) | ||||
0.371696 | + | 0.928355i | \(0.378776\pi\) | |||||||
\(948\) | −3.79780 | −0.123347 | ||||||||
\(949\) | 34.2229 | 1.11092 | ||||||||
\(950\) | −6.21942 | −0.201785 | ||||||||
\(951\) | 23.1526 | 0.750775 | ||||||||
\(952\) | −4.19361 | −0.135916 | ||||||||
\(953\) | 41.6773 | 1.35006 | 0.675031 | − | 0.737790i | \(-0.264130\pi\) | ||||
0.675031 | + | 0.737790i | \(0.264130\pi\) | |||||||
\(954\) | −23.4510 | −0.759253 | ||||||||
\(955\) | −45.2865 | −1.46544 | ||||||||
\(956\) | −0.0692250 | −0.00223890 | ||||||||
\(957\) | −1.34284 | −0.0434079 | ||||||||
\(958\) | −73.4459 | −2.37293 | ||||||||
\(959\) | −72.3146 | −2.33516 | ||||||||
\(960\) | −67.5290 | −2.17949 | ||||||||
\(961\) | −18.8227 | −0.607185 | ||||||||
\(962\) | −38.1367 | −1.22958 | ||||||||
\(963\) | 15.9665 | 0.514513 | ||||||||
\(964\) | −79.4788 | −2.55984 | ||||||||
\(965\) | −13.9332 | −0.448525 | ||||||||
\(966\) | −11.1545 | −0.358890 | ||||||||
\(967\) | −28.7176 | −0.923495 | −0.461747 | − | 0.887012i | \(-0.652777\pi\) | ||||
−0.461747 | + | 0.887012i | \(0.652777\pi\) | |||||||
\(968\) | −105.608 | −3.39436 | ||||||||
\(969\) | 0.210438 | 0.00676025 | ||||||||
\(970\) | −18.9247 | −0.607637 | ||||||||
\(971\) | −22.2210 | −0.713105 | −0.356552 | − | 0.934275i | \(-0.616048\pi\) | ||||
−0.356552 | + | 0.934275i | \(0.616048\pi\) | |||||||
\(972\) | −48.8258 | −1.56609 | ||||||||
\(973\) | 57.5535 | 1.84508 | ||||||||
\(974\) | −24.9573 | −0.799685 | ||||||||
\(975\) | −27.9120 | −0.893900 | ||||||||
\(976\) | 86.0885 | 2.75563 | ||||||||
\(977\) | 0.0112943 | 0.000361336 0 | 0.000180668 | − | 1.00000i | \(-0.499942\pi\) | ||||
0.000180668 | 1.00000i | \(0.499942\pi\) | ||||||||
\(978\) | 20.5859 | 0.658264 | ||||||||
\(979\) | −25.5942 | −0.817993 | ||||||||
\(980\) | −74.1760 | −2.36946 | ||||||||
\(981\) | 7.80081 | 0.249061 | ||||||||
\(982\) | −67.3495 | −2.14921 | ||||||||
\(983\) | 31.3987 | 1.00146 | 0.500732 | − | 0.865603i | \(-0.333064\pi\) | ||||
0.500732 | + | 0.865603i | \(0.333064\pi\) | |||||||
\(984\) | 31.4767 | 1.00344 | ||||||||
\(985\) | 36.4527 | 1.16148 | ||||||||
\(986\) | −0.0552784 | −0.00176042 | ||||||||
\(987\) | −1.80329 | −0.0573992 | ||||||||
\(988\) | −13.7051 | −0.436018 | ||||||||
\(989\) | −0.616834 | −0.0196142 | ||||||||
\(990\) | −37.3900 | −1.18833 | ||||||||
\(991\) | 22.6112 | 0.718270 | 0.359135 | − | 0.933286i | \(-0.383072\pi\) | ||||
0.359135 | + | 0.933286i | \(0.383072\pi\) | |||||||
\(992\) | −43.5657 | −1.38321 | ||||||||
\(993\) | 19.1859 | 0.608845 | ||||||||
\(994\) | 102.332 | 3.24577 | ||||||||
\(995\) | −68.7097 | −2.17824 | ||||||||
\(996\) | 95.1370 | 3.01453 | ||||||||
\(997\) | 59.1186 | 1.87230 | 0.936152 | − | 0.351595i | \(-0.114361\pi\) | ||||
0.936152 | + | 0.351595i | \(0.114361\pi\) | |||||||
\(998\) | 70.2497 | 2.22372 | ||||||||
\(999\) | 14.3677 | 0.454574 |
(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 | 4013.2.a.c.1.7 | ✓ | 176 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4013.2.a.c.1.7 | ✓ | 176 | 1.1 | even | 1 | trivial |