Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4001,2,Mod(1,4001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4001, 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("4001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4001.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: | \(31.9481458487\) |
Analytic rank: | \(0\) |
Dimension: | \(184\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 4001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.68105 | −1.89579 | −0.947894 | − | 0.318586i | \(-0.896792\pi\) | ||||
−0.947894 | + | 0.318586i | \(0.896792\pi\) | |||||||
\(3\) | −2.59933 | −1.50072 | −0.750361 | − | 0.661028i | \(-0.770120\pi\) | ||||
−0.750361 | + | 0.661028i | \(0.770120\pi\) | |||||||
\(4\) | 5.18802 | 2.59401 | ||||||||
\(5\) | −3.48579 | −1.55889 | −0.779446 | − | 0.626470i | \(-0.784499\pi\) | ||||
−0.779446 | + | 0.626470i | \(0.784499\pi\) | |||||||
\(6\) | 6.96892 | 2.84505 | ||||||||
\(7\) | −5.16960 | −1.95393 | −0.976963 | − | 0.213408i | \(-0.931544\pi\) | ||||
−0.976963 | + | 0.213408i | \(0.931544\pi\) | |||||||
\(8\) | −8.54725 | −3.02191 | ||||||||
\(9\) | 3.75650 | 1.25217 | ||||||||
\(10\) | 9.34557 | 2.95533 | ||||||||
\(11\) | 0.876427 | 0.264253 | 0.132126 | − | 0.991233i | \(-0.457820\pi\) | ||||
0.132126 | + | 0.991233i | \(0.457820\pi\) | |||||||
\(12\) | −13.4854 | −3.89289 | ||||||||
\(13\) | 0.747353 | 0.207278 | 0.103639 | − | 0.994615i | \(-0.466951\pi\) | ||||
0.103639 | + | 0.994615i | \(0.466951\pi\) | |||||||
\(14\) | 13.8600 | 3.70423 | ||||||||
\(15\) | 9.06070 | 2.33946 | ||||||||
\(16\) | 12.5395 | 3.13488 | ||||||||
\(17\) | 4.37103 | 1.06013 | 0.530065 | − | 0.847957i | \(-0.322167\pi\) | ||||
0.530065 | + | 0.847957i | \(0.322167\pi\) | |||||||
\(18\) | −10.0714 | −2.37384 | ||||||||
\(19\) | 3.62648 | 0.831971 | 0.415985 | − | 0.909371i | \(-0.363437\pi\) | ||||
0.415985 | + | 0.909371i | \(0.363437\pi\) | |||||||
\(20\) | −18.0843 | −4.04378 | ||||||||
\(21\) | 13.4375 | 2.93230 | ||||||||
\(22\) | −2.34974 | −0.500967 | ||||||||
\(23\) | 4.16300 | 0.868046 | 0.434023 | − | 0.900902i | \(-0.357094\pi\) | ||||
0.434023 | + | 0.900902i | \(0.357094\pi\) | |||||||
\(24\) | 22.2171 | 4.53504 | ||||||||
\(25\) | 7.15071 | 1.43014 | ||||||||
\(26\) | −2.00369 | −0.392956 | ||||||||
\(27\) | −1.96639 | −0.378432 | ||||||||
\(28\) | −26.8200 | −5.06851 | ||||||||
\(29\) | 6.77142 | 1.25742 | 0.628711 | − | 0.777639i | \(-0.283583\pi\) | ||||
0.628711 | + | 0.777639i | \(0.283583\pi\) | |||||||
\(30\) | −24.2922 | −4.43512 | ||||||||
\(31\) | 8.64457 | 1.55261 | 0.776305 | − | 0.630357i | \(-0.217092\pi\) | ||||
0.776305 | + | 0.630357i | \(0.217092\pi\) | |||||||
\(32\) | −16.5246 | −2.92117 | ||||||||
\(33\) | −2.27812 | −0.396570 | ||||||||
\(34\) | −11.7189 | −2.00978 | ||||||||
\(35\) | 18.0201 | 3.04596 | ||||||||
\(36\) | 19.4888 | 3.24813 | ||||||||
\(37\) | 0.671547 | 0.110402 | 0.0552008 | − | 0.998475i | \(-0.482420\pi\) | ||||
0.0552008 | + | 0.998475i | \(0.482420\pi\) | |||||||
\(38\) | −9.72276 | −1.57724 | ||||||||
\(39\) | −1.94261 | −0.311067 | ||||||||
\(40\) | 29.7939 | 4.71083 | ||||||||
\(41\) | −12.1738 | −1.90122 | −0.950611 | − | 0.310385i | \(-0.899542\pi\) | ||||
−0.950611 | + | 0.310385i | \(0.899542\pi\) | |||||||
\(42\) | −36.0266 | −5.55902 | ||||||||
\(43\) | −2.88411 | −0.439822 | −0.219911 | − | 0.975520i | \(-0.570577\pi\) | ||||
−0.219911 | + | 0.975520i | \(0.570577\pi\) | |||||||
\(44\) | 4.54692 | 0.685474 | ||||||||
\(45\) | −13.0944 | −1.95199 | ||||||||
\(46\) | −11.1612 | −1.64563 | ||||||||
\(47\) | 4.06999 | 0.593670 | 0.296835 | − | 0.954929i | \(-0.404069\pi\) | ||||
0.296835 | + | 0.954929i | \(0.404069\pi\) | |||||||
\(48\) | −32.5944 | −4.70459 | ||||||||
\(49\) | 19.7248 | 2.81783 | ||||||||
\(50\) | −19.1714 | −2.71125 | ||||||||
\(51\) | −11.3617 | −1.59096 | ||||||||
\(52\) | 3.87728 | 0.537683 | ||||||||
\(53\) | −10.3253 | −1.41829 | −0.709146 | − | 0.705062i | \(-0.750919\pi\) | ||||
−0.709146 | + | 0.705062i | \(0.750919\pi\) | |||||||
\(54\) | 5.27199 | 0.717427 | ||||||||
\(55\) | −3.05504 | −0.411941 | ||||||||
\(56\) | 44.1859 | 5.90459 | ||||||||
\(57\) | −9.42640 | −1.24856 | ||||||||
\(58\) | −18.1545 | −2.38380 | ||||||||
\(59\) | −7.85472 | −1.02260 | −0.511299 | − | 0.859403i | \(-0.670835\pi\) | ||||
−0.511299 | + | 0.859403i | \(0.670835\pi\) | |||||||
\(60\) | 47.0071 | 6.06859 | ||||||||
\(61\) | 1.75285 | 0.224429 | 0.112214 | − | 0.993684i | \(-0.464206\pi\) | ||||
0.112214 | + | 0.993684i | \(0.464206\pi\) | |||||||
\(62\) | −23.1765 | −2.94342 | ||||||||
\(63\) | −19.4196 | −2.44664 | ||||||||
\(64\) | 19.2242 | 2.40303 | ||||||||
\(65\) | −2.60511 | −0.323125 | ||||||||
\(66\) | 6.10775 | 0.751812 | ||||||||
\(67\) | 10.2935 | 1.25755 | 0.628776 | − | 0.777586i | \(-0.283556\pi\) | ||||
0.628776 | + | 0.777586i | \(0.283556\pi\) | |||||||
\(68\) | 22.6770 | 2.74999 | ||||||||
\(69\) | −10.8210 | −1.30270 | ||||||||
\(70\) | −48.3129 | −5.77449 | ||||||||
\(71\) | −13.3355 | −1.58263 | −0.791315 | − | 0.611409i | \(-0.790603\pi\) | ||||
−0.791315 | + | 0.611409i | \(0.790603\pi\) | |||||||
\(72\) | −32.1077 | −3.78393 | ||||||||
\(73\) | 4.52167 | 0.529221 | 0.264611 | − | 0.964355i | \(-0.414757\pi\) | ||||
0.264611 | + | 0.964355i | \(0.414757\pi\) | |||||||
\(74\) | −1.80045 | −0.209298 | ||||||||
\(75\) | −18.5870 | −2.14625 | ||||||||
\(76\) | 18.8142 | 2.15814 | ||||||||
\(77\) | −4.53078 | −0.516330 | ||||||||
\(78\) | 5.20824 | 0.589718 | ||||||||
\(79\) | 14.6471 | 1.64793 | 0.823966 | − | 0.566640i | \(-0.191757\pi\) | ||||
0.823966 | + | 0.566640i | \(0.191757\pi\) | |||||||
\(80\) | −43.7102 | −4.88694 | ||||||||
\(81\) | −6.15821 | −0.684245 | ||||||||
\(82\) | 32.6385 | 3.60431 | ||||||||
\(83\) | 7.13638 | 0.783320 | 0.391660 | − | 0.920110i | \(-0.371901\pi\) | ||||
0.391660 | + | 0.920110i | \(0.371901\pi\) | |||||||
\(84\) | 69.7140 | 7.60642 | ||||||||
\(85\) | −15.2365 | −1.65263 | ||||||||
\(86\) | 7.73244 | 0.833810 | ||||||||
\(87\) | −17.6011 | −1.88704 | ||||||||
\(88\) | −7.49103 | −0.798547 | ||||||||
\(89\) | 11.2472 | 1.19220 | 0.596100 | − | 0.802910i | \(-0.296716\pi\) | ||||
0.596100 | + | 0.802910i | \(0.296716\pi\) | |||||||
\(90\) | 35.1066 | 3.70056 | ||||||||
\(91\) | −3.86352 | −0.405007 | ||||||||
\(92\) | 21.5978 | 2.25172 | ||||||||
\(93\) | −22.4701 | −2.33004 | ||||||||
\(94\) | −10.9119 | −1.12547 | ||||||||
\(95\) | −12.6411 | −1.29695 | ||||||||
\(96\) | 42.9529 | 4.38386 | ||||||||
\(97\) | 0.565715 | 0.0574396 | 0.0287198 | − | 0.999588i | \(-0.490857\pi\) | ||||
0.0287198 | + | 0.999588i | \(0.490857\pi\) | |||||||
\(98\) | −52.8831 | −5.34200 | ||||||||
\(99\) | 3.29230 | 0.330888 | ||||||||
\(100\) | 37.0981 | 3.70981 | ||||||||
\(101\) | −0.915682 | −0.0911138 | −0.0455569 | − | 0.998962i | \(-0.514506\pi\) | ||||
−0.0455569 | + | 0.998962i | \(0.514506\pi\) | |||||||
\(102\) | 30.4614 | 3.01612 | ||||||||
\(103\) | −5.97154 | −0.588393 | −0.294197 | − | 0.955745i | \(-0.595052\pi\) | ||||
−0.294197 | + | 0.955745i | \(0.595052\pi\) | |||||||
\(104\) | −6.38781 | −0.626376 | ||||||||
\(105\) | −46.8402 | −4.57114 | ||||||||
\(106\) | 27.6827 | 2.68878 | ||||||||
\(107\) | 2.56650 | 0.248113 | 0.124057 | − | 0.992275i | \(-0.460410\pi\) | ||||
0.124057 | + | 0.992275i | \(0.460410\pi\) | |||||||
\(108\) | −10.2017 | −0.981657 | ||||||||
\(109\) | 5.89465 | 0.564605 | 0.282303 | − | 0.959325i | \(-0.408902\pi\) | ||||
0.282303 | + | 0.959325i | \(0.408902\pi\) | |||||||
\(110\) | 8.19070 | 0.780953 | ||||||||
\(111\) | −1.74557 | −0.165682 | ||||||||
\(112\) | −64.8244 | −6.12533 | ||||||||
\(113\) | 13.6703 | 1.28600 | 0.642998 | − | 0.765868i | \(-0.277690\pi\) | ||||
0.642998 | + | 0.765868i | \(0.277690\pi\) | |||||||
\(114\) | 25.2726 | 2.36700 | ||||||||
\(115\) | −14.5113 | −1.35319 | ||||||||
\(116\) | 35.1303 | 3.26176 | ||||||||
\(117\) | 2.80743 | 0.259547 | ||||||||
\(118\) | 21.0589 | 1.93863 | ||||||||
\(119\) | −22.5965 | −2.07142 | ||||||||
\(120\) | −77.4440 | −7.06964 | ||||||||
\(121\) | −10.2319 | −0.930171 | ||||||||
\(122\) | −4.69947 | −0.425470 | ||||||||
\(123\) | 31.6436 | 2.85321 | ||||||||
\(124\) | 44.8482 | 4.02749 | ||||||||
\(125\) | −7.49692 | −0.670545 | ||||||||
\(126\) | 52.0649 | 4.63831 | ||||||||
\(127\) | 13.7879 | 1.22348 | 0.611738 | − | 0.791060i | \(-0.290471\pi\) | ||||
0.611738 | + | 0.791060i | \(0.290471\pi\) | |||||||
\(128\) | −18.4919 | −1.63447 | ||||||||
\(129\) | 7.49674 | 0.660051 | ||||||||
\(130\) | 6.98444 | 0.612576 | ||||||||
\(131\) | 2.16019 | 0.188736 | 0.0943682 | − | 0.995537i | \(-0.469917\pi\) | ||||
0.0943682 | + | 0.995537i | \(0.469917\pi\) | |||||||
\(132\) | −11.8189 | −1.02871 | ||||||||
\(133\) | −18.7474 | −1.62561 | ||||||||
\(134\) | −27.5974 | −2.38405 | ||||||||
\(135\) | 6.85442 | 0.589934 | ||||||||
\(136\) | −37.3603 | −3.20362 | ||||||||
\(137\) | −3.67996 | −0.314400 | −0.157200 | − | 0.987567i | \(-0.550247\pi\) | ||||
−0.157200 | + | 0.987567i | \(0.550247\pi\) | |||||||
\(138\) | 29.0116 | 2.46964 | ||||||||
\(139\) | 21.3708 | 1.81264 | 0.906322 | − | 0.422588i | \(-0.138878\pi\) | ||||
0.906322 | + | 0.422588i | \(0.138878\pi\) | |||||||
\(140\) | 93.4889 | 7.90125 | ||||||||
\(141\) | −10.5792 | −0.890933 | ||||||||
\(142\) | 35.7531 | 3.00033 | ||||||||
\(143\) | 0.655000 | 0.0547738 | ||||||||
\(144\) | 47.1048 | 3.92540 | ||||||||
\(145\) | −23.6037 | −1.96018 | ||||||||
\(146\) | −12.1228 | −1.00329 | ||||||||
\(147\) | −51.2712 | −4.22878 | ||||||||
\(148\) | 3.48400 | 0.286383 | ||||||||
\(149\) | 2.39933 | 0.196561 | 0.0982804 | − | 0.995159i | \(-0.468666\pi\) | ||||
0.0982804 | + | 0.995159i | \(0.468666\pi\) | |||||||
\(150\) | 49.8328 | 4.06883 | ||||||||
\(151\) | 12.0064 | 0.977065 | 0.488533 | − | 0.872546i | \(-0.337532\pi\) | ||||
0.488533 | + | 0.872546i | \(0.337532\pi\) | |||||||
\(152\) | −30.9964 | −2.51414 | ||||||||
\(153\) | 16.4198 | 1.32746 | ||||||||
\(154\) | 12.1472 | 0.978852 | ||||||||
\(155\) | −30.1331 | −2.42035 | ||||||||
\(156\) | −10.0783 | −0.806912 | ||||||||
\(157\) | −12.9825 | −1.03612 | −0.518060 | − | 0.855344i | \(-0.673346\pi\) | ||||
−0.518060 | + | 0.855344i | \(0.673346\pi\) | |||||||
\(158\) | −39.2697 | −3.12413 | ||||||||
\(159\) | 26.8389 | 2.12846 | ||||||||
\(160\) | 57.6013 | 4.55378 | ||||||||
\(161\) | −21.5211 | −1.69610 | ||||||||
\(162\) | 16.5105 | 1.29718 | ||||||||
\(163\) | −14.6077 | −1.14416 | −0.572082 | − | 0.820196i | \(-0.693864\pi\) | ||||
−0.572082 | + | 0.820196i | \(0.693864\pi\) | |||||||
\(164\) | −63.1578 | −4.93179 | ||||||||
\(165\) | 7.94104 | 0.618209 | ||||||||
\(166\) | −19.1330 | −1.48501 | ||||||||
\(167\) | 12.4688 | 0.964867 | 0.482434 | − | 0.875933i | \(-0.339753\pi\) | ||||
0.482434 | + | 0.875933i | \(0.339753\pi\) | |||||||
\(168\) | −114.854 | −8.86114 | ||||||||
\(169\) | −12.4415 | −0.957036 | ||||||||
\(170\) | 40.8497 | 3.13303 | ||||||||
\(171\) | 13.6229 | 1.04177 | ||||||||
\(172\) | −14.9628 | −1.14090 | ||||||||
\(173\) | 14.8043 | 1.12555 | 0.562774 | − | 0.826611i | \(-0.309734\pi\) | ||||
0.562774 | + | 0.826611i | \(0.309734\pi\) | |||||||
\(174\) | 47.1895 | 3.57743 | ||||||||
\(175\) | −36.9663 | −2.79439 | ||||||||
\(176\) | 10.9900 | 0.828401 | ||||||||
\(177\) | 20.4170 | 1.53463 | ||||||||
\(178\) | −30.1543 | −2.26016 | ||||||||
\(179\) | −16.2288 | −1.21299 | −0.606497 | − | 0.795086i | \(-0.707426\pi\) | ||||
−0.606497 | + | 0.795086i | \(0.707426\pi\) | |||||||
\(180\) | −67.9338 | −5.06349 | ||||||||
\(181\) | −5.72393 | −0.425456 | −0.212728 | − | 0.977111i | \(-0.568235\pi\) | ||||
−0.212728 | + | 0.977111i | \(0.568235\pi\) | |||||||
\(182\) | 10.3583 | 0.767807 | ||||||||
\(183\) | −4.55622 | −0.336805 | ||||||||
\(184\) | −35.5822 | −2.62316 | ||||||||
\(185\) | −2.34087 | −0.172104 | ||||||||
\(186\) | 60.2433 | 4.41725 | ||||||||
\(187\) | 3.83089 | 0.280142 | ||||||||
\(188\) | 21.1152 | 1.53999 | ||||||||
\(189\) | 10.1655 | 0.739428 | ||||||||
\(190\) | 33.8915 | 2.45875 | ||||||||
\(191\) | 14.4684 | 1.04689 | 0.523447 | − | 0.852058i | \(-0.324646\pi\) | ||||
0.523447 | + | 0.852058i | \(0.324646\pi\) | |||||||
\(192\) | −49.9701 | −3.60628 | ||||||||
\(193\) | −2.82574 | −0.203401 | −0.101701 | − | 0.994815i | \(-0.532428\pi\) | ||||
−0.101701 | + | 0.994815i | \(0.532428\pi\) | |||||||
\(194\) | −1.51671 | −0.108893 | ||||||||
\(195\) | 6.77154 | 0.484920 | ||||||||
\(196\) | 102.333 | 7.30948 | ||||||||
\(197\) | −11.3114 | −0.805904 | −0.402952 | − | 0.915221i | \(-0.632016\pi\) | ||||
−0.402952 | + | 0.915221i | \(0.632016\pi\) | |||||||
\(198\) | −8.82681 | −0.627294 | ||||||||
\(199\) | 25.2559 | 1.79034 | 0.895170 | − | 0.445724i | \(-0.147054\pi\) | ||||
0.895170 | + | 0.445724i | \(0.147054\pi\) | |||||||
\(200\) | −61.1189 | −4.32176 | ||||||||
\(201\) | −26.7562 | −1.88724 | ||||||||
\(202\) | 2.45499 | 0.172732 | ||||||||
\(203\) | −35.0055 | −2.45691 | ||||||||
\(204\) | −58.9449 | −4.12697 | ||||||||
\(205\) | 42.4351 | 2.96380 | ||||||||
\(206\) | 16.0100 | 1.11547 | ||||||||
\(207\) | 15.6383 | 1.08694 | ||||||||
\(208\) | 9.37146 | 0.649794 | ||||||||
\(209\) | 3.17834 | 0.219850 | ||||||||
\(210\) | 125.581 | 8.66591 | ||||||||
\(211\) | 9.06987 | 0.624396 | 0.312198 | − | 0.950017i | \(-0.398935\pi\) | ||||
0.312198 | + | 0.950017i | \(0.398935\pi\) | |||||||
\(212\) | −53.5680 | −3.67906 | ||||||||
\(213\) | 34.6632 | 2.37509 | ||||||||
\(214\) | −6.88092 | −0.470370 | ||||||||
\(215\) | 10.0534 | 0.685635 | ||||||||
\(216\) | 16.8072 | 1.14359 | ||||||||
\(217\) | −44.6890 | −3.03369 | ||||||||
\(218\) | −15.8039 | −1.07037 | ||||||||
\(219\) | −11.7533 | −0.794214 | ||||||||
\(220\) | −15.8496 | −1.06858 | ||||||||
\(221\) | 3.26670 | 0.219742 | ||||||||
\(222\) | 4.67996 | 0.314098 | ||||||||
\(223\) | 16.2622 | 1.08900 | 0.544499 | − | 0.838761i | \(-0.316720\pi\) | ||||
0.544499 | + | 0.838761i | \(0.316720\pi\) | |||||||
\(224\) | 85.4257 | 5.70775 | ||||||||
\(225\) | 26.8616 | 1.79078 | ||||||||
\(226\) | −36.6508 | −2.43798 | ||||||||
\(227\) | −20.0618 | −1.33155 | −0.665775 | − | 0.746153i | \(-0.731899\pi\) | ||||
−0.665775 | + | 0.746153i | \(0.731899\pi\) | |||||||
\(228\) | −48.9044 | −3.23877 | ||||||||
\(229\) | 21.7895 | 1.43989 | 0.719946 | − | 0.694031i | \(-0.244167\pi\) | ||||
0.719946 | + | 0.694031i | \(0.244167\pi\) | |||||||
\(230\) | 38.9056 | 2.56536 | ||||||||
\(231\) | 11.7770 | 0.774868 | ||||||||
\(232\) | −57.8770 | −3.79981 | ||||||||
\(233\) | −21.4003 | −1.40198 | −0.700992 | − | 0.713169i | \(-0.747259\pi\) | ||||
−0.700992 | + | 0.713169i | \(0.747259\pi\) | |||||||
\(234\) | −7.52686 | −0.492046 | ||||||||
\(235\) | −14.1871 | −0.925467 | ||||||||
\(236\) | −40.7505 | −2.65263 | ||||||||
\(237\) | −38.0727 | −2.47309 | ||||||||
\(238\) | 60.5823 | 3.92697 | ||||||||
\(239\) | −25.7485 | −1.66553 | −0.832765 | − | 0.553627i | \(-0.813243\pi\) | ||||
−0.832765 | + | 0.553627i | \(0.813243\pi\) | |||||||
\(240\) | 113.617 | 7.33395 | ||||||||
\(241\) | −8.58061 | −0.552726 | −0.276363 | − | 0.961053i | \(-0.589129\pi\) | ||||
−0.276363 | + | 0.961053i | \(0.589129\pi\) | |||||||
\(242\) | 27.4322 | 1.76341 | ||||||||
\(243\) | 21.9064 | 1.40529 | ||||||||
\(244\) | 9.09381 | 0.582171 | ||||||||
\(245\) | −68.7564 | −4.39269 | ||||||||
\(246\) | −84.8380 | −5.40907 | ||||||||
\(247\) | 2.71026 | 0.172450 | ||||||||
\(248\) | −73.8873 | −4.69185 | ||||||||
\(249\) | −18.5498 | −1.17554 | ||||||||
\(250\) | 20.0996 | 1.27121 | ||||||||
\(251\) | 1.61960 | 0.102228 | 0.0511142 | − | 0.998693i | \(-0.483723\pi\) | ||||
0.0511142 | + | 0.998693i | \(0.483723\pi\) | |||||||
\(252\) | −100.749 | −6.34662 | ||||||||
\(253\) | 3.64857 | 0.229383 | ||||||||
\(254\) | −36.9660 | −2.31945 | ||||||||
\(255\) | 39.6046 | 2.48014 | ||||||||
\(256\) | 11.1292 | 0.695575 | ||||||||
\(257\) | −26.2702 | −1.63869 | −0.819345 | − | 0.573301i | \(-0.805662\pi\) | ||||
−0.819345 | + | 0.573301i | \(0.805662\pi\) | |||||||
\(258\) | −20.0991 | −1.25132 | ||||||||
\(259\) | −3.47163 | −0.215717 | ||||||||
\(260\) | −13.5154 | −0.838189 | ||||||||
\(261\) | 25.4368 | 1.57450 | ||||||||
\(262\) | −5.79157 | −0.357804 | ||||||||
\(263\) | 7.18538 | 0.443070 | 0.221535 | − | 0.975152i | \(-0.428893\pi\) | ||||
0.221535 | + | 0.975152i | \(0.428893\pi\) | |||||||
\(264\) | 19.4716 | 1.19840 | ||||||||
\(265\) | 35.9919 | 2.21096 | ||||||||
\(266\) | 50.2628 | 3.08181 | ||||||||
\(267\) | −29.2351 | −1.78916 | ||||||||
\(268\) | 53.4030 | 3.26211 | ||||||||
\(269\) | 17.6646 | 1.07703 | 0.538516 | − | 0.842615i | \(-0.318985\pi\) | ||||
0.538516 | + | 0.842615i | \(0.318985\pi\) | |||||||
\(270\) | −18.3770 | −1.11839 | ||||||||
\(271\) | −16.6755 | −1.01297 | −0.506483 | − | 0.862250i | \(-0.669055\pi\) | ||||
−0.506483 | + | 0.862250i | \(0.669055\pi\) | |||||||
\(272\) | 54.8107 | 3.32339 | ||||||||
\(273\) | 10.0425 | 0.607803 | ||||||||
\(274\) | 9.86616 | 0.596036 | ||||||||
\(275\) | 6.26707 | 0.377919 | ||||||||
\(276\) | −56.1396 | −3.37921 | ||||||||
\(277\) | −2.85615 | −0.171609 | −0.0858047 | − | 0.996312i | \(-0.527346\pi\) | ||||
−0.0858047 | + | 0.996312i | \(0.527346\pi\) | |||||||
\(278\) | −57.2961 | −3.43639 | ||||||||
\(279\) | 32.4733 | 1.94413 | ||||||||
\(280\) | −154.023 | −9.20461 | ||||||||
\(281\) | 8.28079 | 0.493991 | 0.246995 | − | 0.969017i | \(-0.420557\pi\) | ||||
0.246995 | + | 0.969017i | \(0.420557\pi\) | |||||||
\(282\) | 28.3635 | 1.68902 | ||||||||
\(283\) | −20.5986 | −1.22446 | −0.612229 | − | 0.790680i | \(-0.709727\pi\) | ||||
−0.612229 | + | 0.790680i | \(0.709727\pi\) | |||||||
\(284\) | −69.1847 | −4.10536 | ||||||||
\(285\) | 32.8584 | 1.94636 | ||||||||
\(286\) | −1.75609 | −0.103840 | ||||||||
\(287\) | 62.9335 | 3.71485 | ||||||||
\(288\) | −62.0748 | −3.65779 | ||||||||
\(289\) | 2.10590 | 0.123876 | ||||||||
\(290\) | 63.2827 | 3.71609 | ||||||||
\(291\) | −1.47048 | −0.0862009 | ||||||||
\(292\) | 23.4585 | 1.37281 | ||||||||
\(293\) | −15.4501 | −0.902603 | −0.451301 | − | 0.892372i | \(-0.649040\pi\) | ||||
−0.451301 | + | 0.892372i | \(0.649040\pi\) | |||||||
\(294\) | 137.461 | 8.01686 | ||||||||
\(295\) | 27.3799 | 1.59412 | ||||||||
\(296\) | −5.73988 | −0.333624 | ||||||||
\(297\) | −1.72340 | −0.100002 | ||||||||
\(298\) | −6.43272 | −0.372637 | ||||||||
\(299\) | 3.11123 | 0.179927 | ||||||||
\(300\) | −96.4300 | −5.56739 | ||||||||
\(301\) | 14.9097 | 0.859381 | ||||||||
\(302\) | −32.1897 | −1.85231 | ||||||||
\(303\) | 2.38016 | 0.136736 | ||||||||
\(304\) | 45.4743 | 2.60813 | ||||||||
\(305\) | −6.11005 | −0.349860 | ||||||||
\(306\) | −44.0222 | −2.51658 | ||||||||
\(307\) | 17.3595 | 0.990759 | 0.495380 | − | 0.868677i | \(-0.335029\pi\) | ||||
0.495380 | + | 0.868677i | \(0.335029\pi\) | |||||||
\(308\) | −23.5058 | −1.33937 | ||||||||
\(309\) | 15.5220 | 0.883015 | ||||||||
\(310\) | 80.7884 | 4.58847 | ||||||||
\(311\) | −6.00112 | −0.340292 | −0.170146 | − | 0.985419i | \(-0.554424\pi\) | ||||
−0.170146 | + | 0.985419i | \(0.554424\pi\) | |||||||
\(312\) | 16.6040 | 0.940017 | ||||||||
\(313\) | 32.5860 | 1.84187 | 0.920936 | − | 0.389715i | \(-0.127426\pi\) | ||||
0.920936 | + | 0.389715i | \(0.127426\pi\) | |||||||
\(314\) | 34.8068 | 1.96426 | ||||||||
\(315\) | 67.6926 | 3.81405 | ||||||||
\(316\) | 75.9897 | 4.27475 | ||||||||
\(317\) | 15.3550 | 0.862421 | 0.431210 | − | 0.902251i | \(-0.358087\pi\) | ||||
0.431210 | + | 0.902251i | \(0.358087\pi\) | |||||||
\(318\) | −71.9563 | −4.03511 | ||||||||
\(319\) | 5.93465 | 0.332277 | ||||||||
\(320\) | −67.0116 | −3.74606 | ||||||||
\(321\) | −6.67118 | −0.372349 | ||||||||
\(322\) | 57.6991 | 3.21544 | ||||||||
\(323\) | 15.8514 | 0.881997 | ||||||||
\(324\) | −31.9489 | −1.77494 | ||||||||
\(325\) | 5.34411 | 0.296438 | ||||||||
\(326\) | 39.1640 | 2.16909 | ||||||||
\(327\) | −15.3221 | −0.847316 | ||||||||
\(328\) | 104.052 | 5.74532 | ||||||||
\(329\) | −21.0403 | −1.15999 | ||||||||
\(330\) | −21.2903 | −1.17199 | ||||||||
\(331\) | −1.18210 | −0.0649743 | −0.0324872 | − | 0.999472i | \(-0.510343\pi\) | ||||
−0.0324872 | + | 0.999472i | \(0.510343\pi\) | |||||||
\(332\) | 37.0237 | 2.03194 | ||||||||
\(333\) | 2.52267 | 0.138241 | ||||||||
\(334\) | −33.4296 | −1.82918 | ||||||||
\(335\) | −35.8810 | −1.96039 | ||||||||
\(336\) | 168.500 | 9.19242 | ||||||||
\(337\) | 5.30255 | 0.288848 | 0.144424 | − | 0.989516i | \(-0.453867\pi\) | ||||
0.144424 | + | 0.989516i | \(0.453867\pi\) | |||||||
\(338\) | 33.3562 | 1.81434 | ||||||||
\(339\) | −35.5336 | −1.92992 | ||||||||
\(340\) | −79.0472 | −4.28694 | ||||||||
\(341\) | 7.57633 | 0.410281 | ||||||||
\(342\) | −36.5235 | −1.97497 | ||||||||
\(343\) | −65.7821 | −3.55190 | ||||||||
\(344\) | 24.6512 | 1.32910 | ||||||||
\(345\) | 37.7197 | 2.03076 | ||||||||
\(346\) | −39.6910 | −2.13380 | ||||||||
\(347\) | 9.90287 | 0.531614 | 0.265807 | − | 0.964026i | \(-0.414362\pi\) | ||||
0.265807 | + | 0.964026i | \(0.414362\pi\) | |||||||
\(348\) | −91.3151 | −4.89500 | ||||||||
\(349\) | 5.73195 | 0.306824 | 0.153412 | − | 0.988162i | \(-0.450974\pi\) | ||||
0.153412 | + | 0.988162i | \(0.450974\pi\) | |||||||
\(350\) | 99.1086 | 5.29758 | ||||||||
\(351\) | −1.46959 | −0.0784408 | ||||||||
\(352\) | −14.4826 | −0.771926 | ||||||||
\(353\) | 7.84835 | 0.417725 | 0.208863 | − | 0.977945i | \(-0.433024\pi\) | ||||
0.208863 | + | 0.977945i | \(0.433024\pi\) | |||||||
\(354\) | −54.7389 | −2.90934 | ||||||||
\(355\) | 46.4846 | 2.46715 | ||||||||
\(356\) | 58.3507 | 3.09258 | ||||||||
\(357\) | 58.7356 | 3.10862 | ||||||||
\(358\) | 43.5101 | 2.29958 | ||||||||
\(359\) | 2.98498 | 0.157541 | 0.0787707 | − | 0.996893i | \(-0.474901\pi\) | ||||
0.0787707 | + | 0.996893i | \(0.474901\pi\) | |||||||
\(360\) | 111.921 | 5.89874 | ||||||||
\(361\) | −5.84867 | −0.307825 | ||||||||
\(362\) | 15.3461 | 0.806575 | ||||||||
\(363\) | 26.5960 | 1.39593 | ||||||||
\(364\) | −20.0440 | −1.05059 | ||||||||
\(365\) | −15.7616 | −0.824998 | ||||||||
\(366\) | 12.2154 | 0.638512 | ||||||||
\(367\) | 21.2046 | 1.10687 | 0.553434 | − | 0.832893i | \(-0.313317\pi\) | ||||
0.553434 | + | 0.832893i | \(0.313317\pi\) | |||||||
\(368\) | 52.2021 | 2.72122 | ||||||||
\(369\) | −45.7307 | −2.38065 | ||||||||
\(370\) | 6.27599 | 0.326273 | ||||||||
\(371\) | 53.3778 | 2.77124 | ||||||||
\(372\) | −116.575 | −6.04414 | ||||||||
\(373\) | −17.1844 | −0.889775 | −0.444887 | − | 0.895587i | \(-0.646756\pi\) | ||||
−0.444887 | + | 0.895587i | \(0.646756\pi\) | |||||||
\(374\) | −10.2708 | −0.531090 | ||||||||
\(375\) | 19.4870 | 1.00630 | ||||||||
\(376\) | −34.7872 | −1.79402 | ||||||||
\(377\) | 5.06064 | 0.260636 | ||||||||
\(378\) | −27.2541 | −1.40180 | ||||||||
\(379\) | 8.96136 | 0.460314 | 0.230157 | − | 0.973154i | \(-0.426076\pi\) | ||||
0.230157 | + | 0.973154i | \(0.426076\pi\) | |||||||
\(380\) | −65.5824 | −3.36431 | ||||||||
\(381\) | −35.8392 | −1.83610 | ||||||||
\(382\) | −38.7904 | −1.98469 | ||||||||
\(383\) | 13.7675 | 0.703486 | 0.351743 | − | 0.936097i | \(-0.385589\pi\) | ||||
0.351743 | + | 0.936097i | \(0.385589\pi\) | |||||||
\(384\) | 48.0665 | 2.45288 | ||||||||
\(385\) | 15.7933 | 0.804902 | ||||||||
\(386\) | 7.57594 | 0.385605 | ||||||||
\(387\) | −10.8342 | −0.550731 | ||||||||
\(388\) | 2.93494 | 0.148999 | ||||||||
\(389\) | −18.3355 | −0.929647 | −0.464823 | − | 0.885403i | \(-0.653882\pi\) | ||||
−0.464823 | + | 0.885403i | \(0.653882\pi\) | |||||||
\(390\) | −18.1548 | −0.919306 | ||||||||
\(391\) | 18.1966 | 0.920242 | ||||||||
\(392\) | −168.593 | −8.51522 | ||||||||
\(393\) | −5.61503 | −0.283241 | ||||||||
\(394\) | 30.3264 | 1.52782 | ||||||||
\(395\) | −51.0568 | −2.56895 | ||||||||
\(396\) | 17.0805 | 0.858328 | ||||||||
\(397\) | 20.4665 | 1.02719 | 0.513593 | − | 0.858034i | \(-0.328314\pi\) | ||||
0.513593 | + | 0.858034i | \(0.328314\pi\) | |||||||
\(398\) | −67.7122 | −3.39411 | ||||||||
\(399\) | 48.7307 | 2.43959 | ||||||||
\(400\) | 89.6666 | 4.48333 | ||||||||
\(401\) | 20.4937 | 1.02341 | 0.511703 | − | 0.859163i | \(-0.329015\pi\) | ||||
0.511703 | + | 0.859163i | \(0.329015\pi\) | |||||||
\(402\) | 71.7347 | 3.57780 | ||||||||
\(403\) | 6.46054 | 0.321823 | ||||||||
\(404\) | −4.75058 | −0.236350 | ||||||||
\(405\) | 21.4662 | 1.06666 | ||||||||
\(406\) | 93.8516 | 4.65778 | ||||||||
\(407\) | 0.588562 | 0.0291739 | ||||||||
\(408\) | 97.1115 | 4.80774 | ||||||||
\(409\) | −24.7995 | −1.22626 | −0.613129 | − | 0.789983i | \(-0.710089\pi\) | ||||
−0.613129 | + | 0.789983i | \(0.710089\pi\) | |||||||
\(410\) | −113.771 | −5.61873 | ||||||||
\(411\) | 9.56542 | 0.471828 | ||||||||
\(412\) | −30.9805 | −1.52630 | ||||||||
\(413\) | 40.6058 | 1.99808 | ||||||||
\(414\) | −41.9271 | −2.06060 | ||||||||
\(415\) | −24.8759 | −1.22111 | ||||||||
\(416\) | −12.3497 | −0.605495 | ||||||||
\(417\) | −55.5496 | −2.72028 | ||||||||
\(418\) | −8.52128 | −0.416790 | ||||||||
\(419\) | 2.55337 | 0.124740 | 0.0623702 | − | 0.998053i | \(-0.480134\pi\) | ||||
0.0623702 | + | 0.998053i | \(0.480134\pi\) | |||||||
\(420\) | −243.008 | −11.8576 | ||||||||
\(421\) | 3.17201 | 0.154594 | 0.0772972 | − | 0.997008i | \(-0.475371\pi\) | ||||
0.0772972 | + | 0.997008i | \(0.475371\pi\) | |||||||
\(422\) | −24.3168 | −1.18372 | ||||||||
\(423\) | 15.2889 | 0.743373 | ||||||||
\(424\) | 88.2530 | 4.28595 | ||||||||
\(425\) | 31.2560 | 1.51614 | ||||||||
\(426\) | −92.9339 | −4.50266 | ||||||||
\(427\) | −9.06152 | −0.438518 | ||||||||
\(428\) | 13.3151 | 0.643609 | ||||||||
\(429\) | −1.70256 | −0.0822003 | ||||||||
\(430\) | −26.9536 | −1.29982 | ||||||||
\(431\) | −5.48399 | −0.264154 | −0.132077 | − | 0.991239i | \(-0.542165\pi\) | ||||
−0.132077 | + | 0.991239i | \(0.542165\pi\) | |||||||
\(432\) | −24.6576 | −1.18634 | ||||||||
\(433\) | 1.03307 | 0.0496462 | 0.0248231 | − | 0.999692i | \(-0.492098\pi\) | ||||
0.0248231 | + | 0.999692i | \(0.492098\pi\) | |||||||
\(434\) | 119.813 | 5.75122 | ||||||||
\(435\) | 61.3538 | 2.94169 | ||||||||
\(436\) | 30.5816 | 1.46459 | ||||||||
\(437\) | 15.0970 | 0.722189 | ||||||||
\(438\) | 31.5111 | 1.50566 | ||||||||
\(439\) | −27.3336 | −1.30456 | −0.652280 | − | 0.757978i | \(-0.726187\pi\) | ||||
−0.652280 | + | 0.757978i | \(0.726187\pi\) | |||||||
\(440\) | 26.1121 | 1.24485 | ||||||||
\(441\) | 74.0962 | 3.52839 | ||||||||
\(442\) | −8.75819 | −0.416584 | ||||||||
\(443\) | 23.2589 | 1.10507 | 0.552533 | − | 0.833491i | \(-0.313662\pi\) | ||||
0.552533 | + | 0.833491i | \(0.313662\pi\) | |||||||
\(444\) | −9.05606 | −0.429782 | ||||||||
\(445\) | −39.2053 | −1.85851 | ||||||||
\(446\) | −43.5998 | −2.06451 | ||||||||
\(447\) | −6.23664 | −0.294983 | ||||||||
\(448\) | −99.3817 | −4.69535 | ||||||||
\(449\) | −21.4726 | −1.01336 | −0.506678 | − | 0.862135i | \(-0.669127\pi\) | ||||
−0.506678 | + | 0.862135i | \(0.669127\pi\) | |||||||
\(450\) | −72.0174 | −3.39493 | ||||||||
\(451\) | −10.6694 | −0.502403 | ||||||||
\(452\) | 70.9220 | 3.33589 | ||||||||
\(453\) | −31.2085 | −1.46630 | ||||||||
\(454\) | 53.7867 | 2.52434 | ||||||||
\(455\) | 13.4674 | 0.631361 | ||||||||
\(456\) | 80.5697 | 3.77302 | ||||||||
\(457\) | −30.9583 | −1.44817 | −0.724084 | − | 0.689711i | \(-0.757737\pi\) | ||||
−0.724084 | + | 0.689711i | \(0.757737\pi\) | |||||||
\(458\) | −58.4187 | −2.72973 | ||||||||
\(459\) | −8.59515 | −0.401187 | ||||||||
\(460\) | −75.2852 | −3.51019 | ||||||||
\(461\) | 8.38181 | 0.390380 | 0.195190 | − | 0.980765i | \(-0.437468\pi\) | ||||
0.195190 | + | 0.980765i | \(0.437468\pi\) | |||||||
\(462\) | −31.5746 | −1.46898 | ||||||||
\(463\) | 37.7697 | 1.75531 | 0.877653 | − | 0.479297i | \(-0.159108\pi\) | ||||
0.877653 | + | 0.479297i | \(0.159108\pi\) | |||||||
\(464\) | 84.9105 | 3.94187 | ||||||||
\(465\) | 78.3258 | 3.63227 | ||||||||
\(466\) | 57.3754 | 2.65786 | ||||||||
\(467\) | 15.1792 | 0.702411 | 0.351205 | − | 0.936298i | \(-0.385772\pi\) | ||||
0.351205 | + | 0.936298i | \(0.385772\pi\) | |||||||
\(468\) | 14.5650 | 0.673268 | ||||||||
\(469\) | −53.2134 | −2.45717 | ||||||||
\(470\) | 38.0364 | 1.75449 | ||||||||
\(471\) | 33.7459 | 1.55493 | ||||||||
\(472\) | 67.1362 | 3.09020 | ||||||||
\(473\) | −2.52771 | −0.116224 | ||||||||
\(474\) | 102.075 | 4.68845 | ||||||||
\(475\) | 25.9319 | 1.18984 | ||||||||
\(476\) | −117.231 | −5.37328 | ||||||||
\(477\) | −38.7871 | −1.77594 | ||||||||
\(478\) | 69.0329 | 3.15749 | ||||||||
\(479\) | 24.6932 | 1.12826 | 0.564131 | − | 0.825685i | \(-0.309211\pi\) | ||||
0.564131 | + | 0.825685i | \(0.309211\pi\) | |||||||
\(480\) | −149.725 | −6.83396 | ||||||||
\(481\) | 0.501883 | 0.0228839 | ||||||||
\(482\) | 23.0050 | 1.04785 | ||||||||
\(483\) | 55.9403 | 2.54537 | ||||||||
\(484\) | −53.0832 | −2.41287 | ||||||||
\(485\) | −1.97196 | −0.0895422 | ||||||||
\(486\) | −58.7320 | −2.66414 | ||||||||
\(487\) | 23.2653 | 1.05425 | 0.527125 | − | 0.849787i | \(-0.323270\pi\) | ||||
0.527125 | + | 0.849787i | \(0.323270\pi\) | |||||||
\(488\) | −14.9820 | −0.678204 | ||||||||
\(489\) | 37.9702 | 1.71707 | ||||||||
\(490\) | 184.339 | 8.32760 | ||||||||
\(491\) | −24.0510 | −1.08541 | −0.542704 | − | 0.839924i | \(-0.682600\pi\) | ||||
−0.542704 | + | 0.839924i | \(0.682600\pi\) | |||||||
\(492\) | 164.168 | 7.40125 | ||||||||
\(493\) | 29.5981 | 1.33303 | ||||||||
\(494\) | −7.26633 | −0.326928 | ||||||||
\(495\) | −11.4762 | −0.515819 | ||||||||
\(496\) | 108.399 | 4.86725 | ||||||||
\(497\) | 68.9391 | 3.09234 | ||||||||
\(498\) | 49.7329 | 2.22858 | ||||||||
\(499\) | −32.8536 | −1.47073 | −0.735365 | − | 0.677671i | \(-0.762989\pi\) | ||||
−0.735365 | + | 0.677671i | \(0.762989\pi\) | |||||||
\(500\) | −38.8942 | −1.73940 | ||||||||
\(501\) | −32.4106 | −1.44800 | ||||||||
\(502\) | −4.34224 | −0.193804 | ||||||||
\(503\) | 37.9490 | 1.69206 | 0.846030 | − | 0.533135i | \(-0.178986\pi\) | ||||
0.846030 | + | 0.533135i | \(0.178986\pi\) | |||||||
\(504\) | 165.984 | 7.39352 | ||||||||
\(505\) | 3.19187 | 0.142036 | ||||||||
\(506\) | −9.78199 | −0.434862 | ||||||||
\(507\) | 32.3394 | 1.43624 | ||||||||
\(508\) | 71.5318 | 3.17371 | ||||||||
\(509\) | −17.0253 | −0.754635 | −0.377317 | − | 0.926084i | \(-0.623153\pi\) | ||||
−0.377317 | + | 0.926084i | \(0.623153\pi\) | |||||||
\(510\) | −106.182 | −4.70181 | ||||||||
\(511\) | −23.3752 | −1.03406 | ||||||||
\(512\) | 7.14588 | 0.315806 | ||||||||
\(513\) | −7.13107 | −0.314844 | ||||||||
\(514\) | 70.4317 | 3.10661 | ||||||||
\(515\) | 20.8155 | 0.917241 | ||||||||
\(516\) | 38.8933 | 1.71218 | ||||||||
\(517\) | 3.56705 | 0.156879 | ||||||||
\(518\) | 9.30761 | 0.408953 | ||||||||
\(519\) | −38.4811 | −1.68913 | ||||||||
\(520\) | 22.2665 | 0.976453 | ||||||||
\(521\) | −16.4070 | −0.718804 | −0.359402 | − | 0.933183i | \(-0.617019\pi\) | ||||
−0.359402 | + | 0.933183i | \(0.617019\pi\) | |||||||
\(522\) | −68.1974 | −2.98492 | ||||||||
\(523\) | −38.4907 | −1.68308 | −0.841540 | − | 0.540194i | \(-0.818351\pi\) | ||||
−0.841540 | + | 0.540194i | \(0.818351\pi\) | |||||||
\(524\) | 11.2071 | 0.489584 | ||||||||
\(525\) | 96.0876 | 4.19361 | ||||||||
\(526\) | −19.2644 | −0.839966 | ||||||||
\(527\) | 37.7857 | 1.64597 | ||||||||
\(528\) | −28.5666 | −1.24320 | ||||||||
\(529\) | −5.66940 | −0.246496 | ||||||||
\(530\) | −96.4959 | −4.19152 | ||||||||
\(531\) | −29.5063 | −1.28046 | ||||||||
\(532\) | −97.2622 | −4.21685 | ||||||||
\(533\) | −9.09810 | −0.394082 | ||||||||
\(534\) | 78.3808 | 3.39187 | ||||||||
\(535\) | −8.94629 | −0.386782 | ||||||||
\(536\) | −87.9812 | −3.80021 | ||||||||
\(537\) | 42.1839 | 1.82037 | ||||||||
\(538\) | −47.3598 | −2.04183 | ||||||||
\(539\) | 17.2873 | 0.744618 | ||||||||
\(540\) | 35.5609 | 1.53030 | ||||||||
\(541\) | −29.8843 | −1.28483 | −0.642414 | − | 0.766358i | \(-0.722067\pi\) | ||||
−0.642414 | + | 0.766358i | \(0.722067\pi\) | |||||||
\(542\) | 44.7079 | 1.92037 | ||||||||
\(543\) | 14.8784 | 0.638492 | ||||||||
\(544\) | −72.2296 | −3.09682 | ||||||||
\(545\) | −20.5475 | −0.880159 | ||||||||
\(546\) | −26.9246 | −1.15226 | ||||||||
\(547\) | 20.3017 | 0.868038 | 0.434019 | − | 0.900904i | \(-0.357095\pi\) | ||||
0.434019 | + | 0.900904i | \(0.357095\pi\) | |||||||
\(548\) | −19.0917 | −0.815558 | ||||||||
\(549\) | 6.58457 | 0.281022 | ||||||||
\(550\) | −16.8023 | −0.716454 | ||||||||
\(551\) | 24.5564 | 1.04614 | ||||||||
\(552\) | 92.4898 | 3.93663 | ||||||||
\(553\) | −75.7199 | −3.21994 | ||||||||
\(554\) | 7.65748 | 0.325335 | ||||||||
\(555\) | 6.08469 | 0.258281 | ||||||||
\(556\) | 110.872 | 4.70202 | ||||||||
\(557\) | 5.33868 | 0.226207 | 0.113104 | − | 0.993583i | \(-0.463921\pi\) | ||||
0.113104 | + | 0.993583i | \(0.463921\pi\) | |||||||
\(558\) | −87.0626 | −3.68565 | ||||||||
\(559\) | −2.15545 | −0.0911657 | ||||||||
\(560\) | 225.964 | 9.54873 | ||||||||
\(561\) | −9.95772 | −0.420415 | ||||||||
\(562\) | −22.2012 | −0.936502 | ||||||||
\(563\) | −1.04621 | −0.0440925 | −0.0220463 | − | 0.999757i | \(-0.507018\pi\) | ||||
−0.0220463 | + | 0.999757i | \(0.507018\pi\) | |||||||
\(564\) | −54.8854 | −2.31109 | ||||||||
\(565\) | −47.6519 | −2.00473 | ||||||||
\(566\) | 55.2258 | 2.32131 | ||||||||
\(567\) | 31.8355 | 1.33696 | ||||||||
\(568\) | 113.982 | 4.78256 | ||||||||
\(569\) | −27.6822 | −1.16050 | −0.580249 | − | 0.814439i | \(-0.697045\pi\) | ||||
−0.580249 | + | 0.814439i | \(0.697045\pi\) | |||||||
\(570\) | −88.0950 | −3.68989 | ||||||||
\(571\) | −14.0987 | −0.590012 | −0.295006 | − | 0.955495i | \(-0.595322\pi\) | ||||
−0.295006 | + | 0.955495i | \(0.595322\pi\) | |||||||
\(572\) | 3.39815 | 0.142084 | ||||||||
\(573\) | −37.6080 | −1.57110 | ||||||||
\(574\) | −168.728 | −7.04256 | ||||||||
\(575\) | 29.7684 | 1.24143 | ||||||||
\(576\) | 72.2159 | 3.00900 | ||||||||
\(577\) | 7.17715 | 0.298789 | 0.149394 | − | 0.988778i | \(-0.452268\pi\) | ||||
0.149394 | + | 0.988778i | \(0.452268\pi\) | |||||||
\(578\) | −5.64601 | −0.234843 | ||||||||
\(579\) | 7.34502 | 0.305249 | ||||||||
\(580\) | −122.457 | −5.08474 | ||||||||
\(581\) | −36.8923 | −1.53055 | ||||||||
\(582\) | 3.94242 | 0.163419 | ||||||||
\(583\) | −9.04938 | −0.374787 | ||||||||
\(584\) | −38.6478 | −1.59926 | ||||||||
\(585\) | −9.78611 | −0.404606 | ||||||||
\(586\) | 41.4224 | 1.71114 | ||||||||
\(587\) | −19.8595 | −0.819690 | −0.409845 | − | 0.912155i | \(-0.634417\pi\) | ||||
−0.409845 | + | 0.912155i | \(0.634417\pi\) | |||||||
\(588\) | −265.996 | −10.9695 | ||||||||
\(589\) | 31.3493 | 1.29173 | ||||||||
\(590\) | −73.4068 | −3.02211 | ||||||||
\(591\) | 29.4020 | 1.20944 | ||||||||
\(592\) | 8.42089 | 0.346096 | ||||||||
\(593\) | 10.8390 | 0.445105 | 0.222553 | − | 0.974921i | \(-0.428561\pi\) | ||||
0.222553 | + | 0.974921i | \(0.428561\pi\) | |||||||
\(594\) | 4.62051 | 0.189582 | ||||||||
\(595\) | 78.7665 | 3.22911 | ||||||||
\(596\) | 12.4478 | 0.509881 | ||||||||
\(597\) | −65.6482 | −2.68680 | ||||||||
\(598\) | −8.34137 | −0.341104 | ||||||||
\(599\) | 3.82319 | 0.156211 | 0.0781056 | − | 0.996945i | \(-0.475113\pi\) | ||||
0.0781056 | + | 0.996945i | \(0.475113\pi\) | |||||||
\(600\) | 158.868 | 6.48576 | ||||||||
\(601\) | 46.1006 | 1.88048 | 0.940241 | − | 0.340511i | \(-0.110600\pi\) | ||||
0.940241 | + | 0.340511i | \(0.110600\pi\) | |||||||
\(602\) | −39.9736 | −1.62920 | ||||||||
\(603\) | 38.6676 | 1.57467 | ||||||||
\(604\) | 62.2894 | 2.53452 | ||||||||
\(605\) | 35.6661 | 1.45003 | ||||||||
\(606\) | −6.38132 | −0.259223 | ||||||||
\(607\) | 8.72839 | 0.354274 | 0.177137 | − | 0.984186i | \(-0.443316\pi\) | ||||
0.177137 | + | 0.984186i | \(0.443316\pi\) | |||||||
\(608\) | −59.9262 | −2.43033 | ||||||||
\(609\) | 90.9909 | 3.68714 | ||||||||
\(610\) | 16.3813 | 0.663261 | ||||||||
\(611\) | 3.04172 | 0.123055 | ||||||||
\(612\) | 85.1862 | 3.44345 | ||||||||
\(613\) | −23.1545 | −0.935200 | −0.467600 | − | 0.883940i | \(-0.654881\pi\) | ||||
−0.467600 | + | 0.883940i | \(0.654881\pi\) | |||||||
\(614\) | −46.5417 | −1.87827 | ||||||||
\(615\) | −110.303 | −4.44784 | ||||||||
\(616\) | 38.7257 | 1.56030 | ||||||||
\(617\) | −22.5030 | −0.905938 | −0.452969 | − | 0.891526i | \(-0.649635\pi\) | ||||
−0.452969 | + | 0.891526i | \(0.649635\pi\) | |||||||
\(618\) | −41.6152 | −1.67401 | ||||||||
\(619\) | 16.3434 | 0.656897 | 0.328448 | − | 0.944522i | \(-0.393474\pi\) | ||||
0.328448 | + | 0.944522i | \(0.393474\pi\) | |||||||
\(620\) | −156.331 | −6.27842 | ||||||||
\(621\) | −8.18609 | −0.328497 | ||||||||
\(622\) | 16.0893 | 0.645122 | ||||||||
\(623\) | −58.1435 | −2.32947 | ||||||||
\(624\) | −24.3595 | −0.975160 | ||||||||
\(625\) | −9.62088 | −0.384835 | ||||||||
\(626\) | −87.3647 | −3.49180 | ||||||||
\(627\) | −8.26154 | −0.329934 | ||||||||
\(628\) | −67.3537 | −2.68771 | ||||||||
\(629\) | 2.93535 | 0.117040 | ||||||||
\(630\) | −181.487 | −7.23063 | ||||||||
\(631\) | 19.9320 | 0.793482 | 0.396741 | − | 0.917931i | \(-0.370141\pi\) | ||||
0.396741 | + | 0.917931i | \(0.370141\pi\) | |||||||
\(632\) | −125.193 | −4.97990 | ||||||||
\(633\) | −23.5756 | −0.937044 | ||||||||
\(634\) | −41.1674 | −1.63497 | ||||||||
\(635\) | −48.0616 | −1.90727 | ||||||||
\(636\) | 139.241 | 5.52125 | ||||||||
\(637\) | 14.7414 | 0.584075 | ||||||||
\(638\) | −15.9111 | −0.629926 | ||||||||
\(639\) | −50.0947 | −1.98172 | ||||||||
\(640\) | 64.4588 | 2.54796 | ||||||||
\(641\) | 2.36150 | 0.0932737 | 0.0466368 | − | 0.998912i | \(-0.485150\pi\) | ||||
0.0466368 | + | 0.998912i | \(0.485150\pi\) | |||||||
\(642\) | 17.8858 | 0.705895 | ||||||||
\(643\) | 15.3925 | 0.607019 | 0.303510 | − | 0.952828i | \(-0.401842\pi\) | ||||
0.303510 | + | 0.952828i | \(0.401842\pi\) | |||||||
\(644\) | −111.652 | −4.39970 | ||||||||
\(645\) | −26.1320 | −1.02895 | ||||||||
\(646\) | −42.4985 | −1.67208 | ||||||||
\(647\) | 18.7879 | 0.738627 | 0.369313 | − | 0.929305i | \(-0.379593\pi\) | ||||
0.369313 | + | 0.929305i | \(0.379593\pi\) | |||||||
\(648\) | 52.6357 | 2.06773 | ||||||||
\(649\) | −6.88409 | −0.270224 | ||||||||
\(650\) | −14.3278 | −0.561983 | ||||||||
\(651\) | 116.161 | 4.55272 | ||||||||
\(652\) | −75.7852 | −2.96798 | ||||||||
\(653\) | 14.6954 | 0.575075 | 0.287538 | − | 0.957769i | \(-0.407163\pi\) | ||||
0.287538 | + | 0.957769i | \(0.407163\pi\) | |||||||
\(654\) | 41.0794 | 1.60633 | ||||||||
\(655\) | −7.52995 | −0.294220 | ||||||||
\(656\) | −152.653 | −5.96011 | ||||||||
\(657\) | 16.9856 | 0.662673 | ||||||||
\(658\) | 56.4100 | 2.19909 | ||||||||
\(659\) | −8.89957 | −0.346678 | −0.173339 | − | 0.984862i | \(-0.555456\pi\) | ||||
−0.173339 | + | 0.984862i | \(0.555456\pi\) | |||||||
\(660\) | 41.1983 | 1.60364 | ||||||||
\(661\) | −49.6246 | −1.93017 | −0.965086 | − | 0.261933i | \(-0.915640\pi\) | ||||
−0.965086 | + | 0.261933i | \(0.915640\pi\) | |||||||
\(662\) | 3.16928 | 0.123178 | ||||||||
\(663\) | −8.49122 | −0.329772 | ||||||||
\(664\) | −60.9964 | −2.36712 | ||||||||
\(665\) | 65.3496 | 2.53415 | ||||||||
\(666\) | −6.76339 | −0.262076 | ||||||||
\(667\) | 28.1894 | 1.09150 | ||||||||
\(668\) | 64.6886 | 2.50288 | ||||||||
\(669\) | −42.2708 | −1.63428 | ||||||||
\(670\) | 96.1987 | 3.71648 | ||||||||
\(671\) | 1.53624 | 0.0593059 | ||||||||
\(672\) | −222.049 | −8.56574 | ||||||||
\(673\) | 8.50990 | 0.328033 | 0.164016 | − | 0.986458i | \(-0.447555\pi\) | ||||
0.164016 | + | 0.986458i | \(0.447555\pi\) | |||||||
\(674\) | −14.2164 | −0.547595 | ||||||||
\(675\) | −14.0611 | −0.541212 | ||||||||
\(676\) | −64.5466 | −2.48256 | ||||||||
\(677\) | 12.5579 | 0.482639 | 0.241319 | − | 0.970446i | \(-0.422420\pi\) | ||||
0.241319 | + | 0.970446i | \(0.422420\pi\) | |||||||
\(678\) | 95.2675 | 3.65872 | ||||||||
\(679\) | −2.92452 | −0.112233 | ||||||||
\(680\) | 130.230 | 4.99409 | ||||||||
\(681\) | 52.1472 | 1.99829 | ||||||||
\(682\) | −20.3125 | −0.777806 | ||||||||
\(683\) | −28.8857 | −1.10528 | −0.552639 | − | 0.833420i | \(-0.686379\pi\) | ||||
−0.552639 | + | 0.833420i | \(0.686379\pi\) | |||||||
\(684\) | 70.6757 | 2.70235 | ||||||||
\(685\) | 12.8276 | 0.490116 | ||||||||
\(686\) | 176.365 | 6.73365 | ||||||||
\(687\) | −56.6380 | −2.16088 | ||||||||
\(688\) | −36.1654 | −1.37879 | ||||||||
\(689\) | −7.71666 | −0.293981 | ||||||||
\(690\) | −101.128 | −3.84989 | ||||||||
\(691\) | −21.6329 | −0.822953 | −0.411476 | − | 0.911420i | \(-0.634987\pi\) | ||||
−0.411476 | + | 0.911420i | \(0.634987\pi\) | |||||||
\(692\) | 76.8049 | 2.91968 | ||||||||
\(693\) | −17.0199 | −0.646531 | ||||||||
\(694\) | −26.5501 | −1.00783 | ||||||||
\(695\) | −74.4939 | −2.82572 | ||||||||
\(696\) | 150.441 | 5.70246 | ||||||||
\(697\) | −53.2119 | −2.01554 | ||||||||
\(698\) | −15.3676 | −0.581674 | ||||||||
\(699\) | 55.6265 | 2.10399 | ||||||||
\(700\) | −191.782 | −7.24869 | ||||||||
\(701\) | 16.4987 | 0.623148 | 0.311574 | − | 0.950222i | \(-0.399144\pi\) | ||||
0.311574 | + | 0.950222i | \(0.399144\pi\) | |||||||
\(702\) | 3.94004 | 0.148707 | ||||||||
\(703\) | 2.43535 | 0.0918509 | ||||||||
\(704\) | 16.8486 | 0.635007 | ||||||||
\(705\) | 36.8770 | 1.38887 | ||||||||
\(706\) | −21.0418 | −0.791919 | ||||||||
\(707\) | 4.73371 | 0.178030 | ||||||||
\(708\) | 105.924 | 3.98086 | ||||||||
\(709\) | 17.8019 | 0.668565 | 0.334282 | − | 0.942473i | \(-0.391506\pi\) | ||||
0.334282 | + | 0.942473i | \(0.391506\pi\) | |||||||
\(710\) | −124.628 | −4.67719 | ||||||||
\(711\) | 55.0219 | 2.06348 | ||||||||
\(712\) | −96.1326 | −3.60272 | ||||||||
\(713\) | 35.9874 | 1.34774 | ||||||||
\(714\) | −157.473 | −5.89328 | ||||||||
\(715\) | −2.28319 | −0.0853865 | ||||||||
\(716\) | −84.1952 | −3.14652 | ||||||||
\(717\) | 66.9287 | 2.49950 | ||||||||
\(718\) | −8.00288 | −0.298665 | ||||||||
\(719\) | 5.51006 | 0.205491 | 0.102745 | − | 0.994708i | \(-0.467237\pi\) | ||||
0.102745 | + | 0.994708i | \(0.467237\pi\) | |||||||
\(720\) | −164.197 | −6.11927 | ||||||||
\(721\) | 30.8705 | 1.14968 | ||||||||
\(722\) | 15.6806 | 0.583570 | ||||||||
\(723\) | 22.3038 | 0.829488 | ||||||||
\(724\) | −29.6959 | −1.10364 | ||||||||
\(725\) | 48.4205 | 1.79829 | ||||||||
\(726\) | −71.3052 | −2.64638 | ||||||||
\(727\) | −50.0027 | −1.85450 | −0.927248 | − | 0.374447i | \(-0.877833\pi\) | ||||
−0.927248 | + | 0.374447i | \(0.877833\pi\) | |||||||
\(728\) | 33.0224 | 1.22389 | ||||||||
\(729\) | −38.4672 | −1.42471 | ||||||||
\(730\) | 42.2575 | 1.56402 | ||||||||
\(731\) | −12.6065 | −0.466269 | ||||||||
\(732\) | −23.6378 | −0.873677 | ||||||||
\(733\) | −17.1710 | −0.634224 | −0.317112 | − | 0.948388i | \(-0.602713\pi\) | ||||
−0.317112 | + | 0.948388i | \(0.602713\pi\) | |||||||
\(734\) | −56.8504 | −2.09839 | ||||||||
\(735\) | 178.720 | 6.59220 | ||||||||
\(736\) | −68.7921 | −2.53571 | ||||||||
\(737\) | 9.02151 | 0.332311 | ||||||||
\(738\) | 122.606 | 4.51320 | ||||||||
\(739\) | −24.8717 | −0.914920 | −0.457460 | − | 0.889230i | \(-0.651241\pi\) | ||||
−0.457460 | + | 0.889230i | \(0.651241\pi\) | |||||||
\(740\) | −12.1445 | −0.446440 | ||||||||
\(741\) | −7.04485 | −0.258799 | ||||||||
\(742\) | −143.108 | −5.25368 | ||||||||
\(743\) | 6.44568 | 0.236469 | 0.118234 | − | 0.992986i | \(-0.462277\pi\) | ||||
0.118234 | + | 0.992986i | \(0.462277\pi\) | |||||||
\(744\) | 192.057 | 7.04116 | ||||||||
\(745\) | −8.36355 | −0.306417 | ||||||||
\(746\) | 46.0722 | 1.68682 | ||||||||
\(747\) | 26.8078 | 0.980847 | ||||||||
\(748\) | 19.8747 | 0.726692 | ||||||||
\(749\) | −13.2678 | −0.484795 | ||||||||
\(750\) | −52.2455 | −1.90773 | ||||||||
\(751\) | 43.9422 | 1.60348 | 0.801738 | − | 0.597676i | \(-0.203909\pi\) | ||||
0.801738 | + | 0.597676i | \(0.203909\pi\) | |||||||
\(752\) | 51.0359 | 1.86109 | ||||||||
\(753\) | −4.20988 | −0.153417 | ||||||||
\(754\) | −13.5678 | −0.494111 | ||||||||
\(755\) | −41.8517 | −1.52314 | ||||||||
\(756\) | 52.7386 | 1.91809 | ||||||||
\(757\) | −11.0556 | −0.401823 | −0.200912 | − | 0.979609i | \(-0.564390\pi\) | ||||
−0.200912 | + | 0.979609i | \(0.564390\pi\) | |||||||
\(758\) | −24.0258 | −0.872658 | ||||||||
\(759\) | −9.48382 | −0.344241 | ||||||||
\(760\) | 108.047 | 3.91927 | ||||||||
\(761\) | 17.5540 | 0.636332 | 0.318166 | − | 0.948035i | \(-0.396933\pi\) | ||||
0.318166 | + | 0.948035i | \(0.396933\pi\) | |||||||
\(762\) | 96.0866 | 3.48085 | ||||||||
\(763\) | −30.4730 | −1.10320 | ||||||||
\(764\) | 75.0622 | 2.71565 | ||||||||
\(765\) | −57.2358 | −2.06937 | ||||||||
\(766\) | −36.9113 | −1.33366 | ||||||||
\(767\) | −5.87025 | −0.211962 | ||||||||
\(768\) | −28.9284 | −1.04386 | ||||||||
\(769\) | −25.6853 | −0.926236 | −0.463118 | − | 0.886297i | \(-0.653269\pi\) | ||||
−0.463118 | + | 0.886297i | \(0.653269\pi\) | |||||||
\(770\) | −42.3427 | −1.52592 | ||||||||
\(771\) | 68.2848 | 2.45922 | ||||||||
\(772\) | −14.6600 | −0.527625 | ||||||||
\(773\) | −8.40534 | −0.302319 | −0.151160 | − | 0.988509i | \(-0.548301\pi\) | ||||
−0.151160 | + | 0.988509i | \(0.548301\pi\) | |||||||
\(774\) | 29.0469 | 1.04407 | ||||||||
\(775\) | 61.8148 | 2.22045 | ||||||||
\(776\) | −4.83530 | −0.173577 | ||||||||
\(777\) | 9.02390 | 0.323731 | ||||||||
\(778\) | 49.1584 | 1.76241 | ||||||||
\(779\) | −44.1479 | −1.58176 | ||||||||
\(780\) | 35.1309 | 1.25789 | ||||||||
\(781\) | −11.6876 | −0.418214 | ||||||||
\(782\) | −48.7860 | −1.74458 | ||||||||
\(783\) | −13.3153 | −0.475848 | ||||||||
\(784\) | 247.340 | 8.83357 | ||||||||
\(785\) | 45.2544 | 1.61520 | ||||||||
\(786\) | 15.0542 | 0.536965 | ||||||||
\(787\) | −42.4076 | −1.51167 | −0.755834 | − | 0.654764i | \(-0.772768\pi\) | ||||
−0.755834 | + | 0.654764i | \(0.772768\pi\) | |||||||
\(788\) | −58.6838 | −2.09052 | ||||||||
\(789\) | −18.6772 | −0.664924 | ||||||||
\(790\) | 136.886 | 4.87018 | ||||||||
\(791\) | −70.6702 | −2.51274 | ||||||||
\(792\) | −28.1401 | −0.999914 | ||||||||
\(793\) | 1.30999 | 0.0465193 | ||||||||
\(794\) | −54.8718 | −1.94733 | ||||||||
\(795\) | −93.5546 | −3.31804 | ||||||||
\(796\) | 131.028 | 4.64416 | ||||||||
\(797\) | 36.6030 | 1.29655 | 0.648273 | − | 0.761408i | \(-0.275492\pi\) | ||||
0.648273 | + | 0.761408i | \(0.275492\pi\) | |||||||
\(798\) | −130.649 | −4.62494 | ||||||||
\(799\) | 17.7901 | 0.629367 | ||||||||
\(800\) | −118.163 | −4.17769 | ||||||||
\(801\) | 42.2501 | 1.49283 | ||||||||
\(802\) | −54.9445 | −1.94016 | ||||||||
\(803\) | 3.96291 | 0.139848 | ||||||||
\(804\) | −138.812 | −4.89551 | ||||||||
\(805\) | 75.0179 | 2.64403 | ||||||||
\(806\) | −17.3210 | −0.610107 | ||||||||
\(807\) | −45.9162 | −1.61633 | ||||||||
\(808\) | 7.82656 | 0.275337 | ||||||||
\(809\) | 40.1918 | 1.41307 | 0.706535 | − | 0.707678i | \(-0.250257\pi\) | ||||
0.706535 | + | 0.707678i | \(0.250257\pi\) | |||||||
\(810\) | −57.5519 | −2.02217 | ||||||||
\(811\) | −35.0857 | −1.23203 | −0.616013 | − | 0.787736i | \(-0.711253\pi\) | ||||
−0.616013 | + | 0.787736i | \(0.711253\pi\) | |||||||
\(812\) | −181.610 | −6.37325 | ||||||||
\(813\) | 43.3452 | 1.52018 | ||||||||
\(814\) | −1.57796 | −0.0553076 | ||||||||
\(815\) | 50.9194 | 1.78363 | ||||||||
\(816\) | −142.471 | −4.98748 | ||||||||
\(817\) | −10.4592 | −0.365919 | ||||||||
\(818\) | 66.4888 | 2.32472 | ||||||||
\(819\) | −14.5133 | −0.507136 | ||||||||
\(820\) | 220.155 | 7.68813 | ||||||||
\(821\) | 32.3118 | 1.12769 | 0.563844 | − | 0.825881i | \(-0.309322\pi\) | ||||
0.563844 | + | 0.825881i | \(0.309322\pi\) | |||||||
\(822\) | −25.6454 | −0.894485 | ||||||||
\(823\) | −17.0148 | −0.593100 | −0.296550 | − | 0.955017i | \(-0.595836\pi\) | ||||
−0.296550 | + | 0.955017i | \(0.595836\pi\) | |||||||
\(824\) | 51.0402 | 1.77807 | ||||||||
\(825\) | −16.2902 | −0.567151 | ||||||||
\(826\) | −108.866 | −3.78794 | ||||||||
\(827\) | 1.15823 | 0.0402756 | 0.0201378 | − | 0.999797i | \(-0.493590\pi\) | ||||
0.0201378 | + | 0.999797i | \(0.493590\pi\) | |||||||
\(828\) | 81.1320 | 2.81953 | ||||||||
\(829\) | 7.70413 | 0.267576 | 0.133788 | − | 0.991010i | \(-0.457286\pi\) | ||||
0.133788 | + | 0.991010i | \(0.457286\pi\) | |||||||
\(830\) | 66.6935 | 2.31497 | ||||||||
\(831\) | 7.42407 | 0.257538 | ||||||||
\(832\) | 14.3673 | 0.498096 | ||||||||
\(833\) | 86.2176 | 2.98726 | ||||||||
\(834\) | 148.931 | 5.15706 | ||||||||
\(835\) | −43.4637 | −1.50412 | ||||||||
\(836\) | 16.4893 | 0.570294 | ||||||||
\(837\) | −16.9986 | −0.587557 | ||||||||
\(838\) | −6.84572 | −0.236482 | ||||||||
\(839\) | −45.8973 | −1.58455 | −0.792276 | − | 0.610163i | \(-0.791104\pi\) | ||||
−0.792276 | + | 0.610163i | \(0.791104\pi\) | |||||||
\(840\) | 400.355 | 13.8136 | ||||||||
\(841\) | 16.8521 | 0.581108 | ||||||||
\(842\) | −8.50432 | −0.293078 | ||||||||
\(843\) | −21.5245 | −0.741343 | ||||||||
\(844\) | 47.0547 | 1.61969 | ||||||||
\(845\) | 43.3683 | 1.49191 | ||||||||
\(846\) | −40.9904 | −1.40928 | ||||||||
\(847\) | 52.8947 | 1.81748 | ||||||||
\(848\) | −129.475 | −4.44618 | ||||||||
\(849\) | 53.5424 | 1.83757 | ||||||||
\(850\) | −83.7988 | −2.87427 | ||||||||
\(851\) | 2.79565 | 0.0958337 | ||||||||
\(852\) | 179.834 | 6.16100 | ||||||||
\(853\) | 15.9270 | 0.545328 | 0.272664 | − | 0.962109i | \(-0.412095\pi\) | ||||
0.272664 | + | 0.962109i | \(0.412095\pi\) | |||||||
\(854\) | 24.2944 | 0.831336 | ||||||||
\(855\) | −47.4864 | −1.62400 | ||||||||
\(856\) | −21.9365 | −0.749776 | ||||||||
\(857\) | −16.3697 | −0.559179 | −0.279590 | − | 0.960120i | \(-0.590198\pi\) | ||||
−0.279590 | + | 0.960120i | \(0.590198\pi\) | |||||||
\(858\) | 4.56464 | 0.155834 | ||||||||
\(859\) | 35.9599 | 1.22694 | 0.613468 | − | 0.789720i | \(-0.289774\pi\) | ||||
0.613468 | + | 0.789720i | \(0.289774\pi\) | |||||||
\(860\) | 52.1572 | 1.77855 | ||||||||
\(861\) | −163.585 | −5.57495 | ||||||||
\(862\) | 14.7028 | 0.500781 | ||||||||
\(863\) | −23.3613 | −0.795228 | −0.397614 | − | 0.917553i | \(-0.630162\pi\) | ||||
−0.397614 | + | 0.917553i | \(0.630162\pi\) | |||||||
\(864\) | 32.4939 | 1.10546 | ||||||||
\(865\) | −51.6045 | −1.75461 | ||||||||
\(866\) | −2.76971 | −0.0941186 | ||||||||
\(867\) | −5.47391 | −0.185904 | ||||||||
\(868\) | −231.847 | −7.86942 | ||||||||
\(869\) | 12.8371 | 0.435470 | ||||||||
\(870\) | −164.493 | −5.57682 | ||||||||
\(871\) | 7.69289 | 0.260664 | ||||||||
\(872\) | −50.3831 | −1.70619 | ||||||||
\(873\) | 2.12511 | 0.0719240 | ||||||||
\(874\) | −40.4759 | −1.36912 | ||||||||
\(875\) | 38.7561 | 1.31020 | ||||||||
\(876\) | −60.9763 | −2.06020 | ||||||||
\(877\) | −11.0060 | −0.371646 | −0.185823 | − | 0.982583i | \(-0.559495\pi\) | ||||
−0.185823 | + | 0.982583i | \(0.559495\pi\) | |||||||
\(878\) | 73.2826 | 2.47317 | ||||||||
\(879\) | 40.1598 | 1.35456 | ||||||||
\(880\) | −38.3087 | −1.29139 | ||||||||
\(881\) | 30.4744 | 1.02671 | 0.513354 | − | 0.858177i | \(-0.328403\pi\) | ||||
0.513354 | + | 0.858177i | \(0.328403\pi\) | |||||||
\(882\) | −198.656 | −6.68908 | ||||||||
\(883\) | 2.53253 | 0.0852266 | 0.0426133 | − | 0.999092i | \(-0.486432\pi\) | ||||
0.0426133 | + | 0.999092i | \(0.486432\pi\) | |||||||
\(884\) | 16.9477 | 0.570014 | ||||||||
\(885\) | −71.1693 | −2.39233 | ||||||||
\(886\) | −62.3583 | −2.09497 | ||||||||
\(887\) | 38.8851 | 1.30563 | 0.652817 | − | 0.757516i | \(-0.273587\pi\) | ||||
0.652817 | + | 0.757516i | \(0.273587\pi\) | |||||||
\(888\) | 14.9198 | 0.500676 | ||||||||
\(889\) | −71.2778 | −2.39058 | ||||||||
\(890\) | 105.111 | 3.52334 | ||||||||
\(891\) | −5.39722 | −0.180814 | ||||||||
\(892\) | 84.3688 | 2.82488 | ||||||||
\(893\) | 14.7597 | 0.493916 | ||||||||
\(894\) | 16.7207 | 0.559225 | ||||||||
\(895\) | 56.5700 | 1.89093 | ||||||||
\(896\) | 95.5958 | 3.19363 | ||||||||
\(897\) | −8.08711 | −0.270021 | ||||||||
\(898\) | 57.5692 | 1.92111 | ||||||||
\(899\) | 58.5360 | 1.95228 | ||||||||
\(900\) | 139.359 | 4.64530 | ||||||||
\(901\) | −45.1323 | −1.50357 | ||||||||
\(902\) | 28.6052 | 0.952449 | ||||||||
\(903\) | −38.7552 | −1.28969 | ||||||||
\(904\) | −116.844 | −3.88616 | ||||||||
\(905\) | 19.9524 | 0.663240 | ||||||||
\(906\) | 83.6715 | 2.77980 | ||||||||
\(907\) | −20.5975 | −0.683930 | −0.341965 | − | 0.939713i | \(-0.611092\pi\) | ||||
−0.341965 | + | 0.939713i | \(0.611092\pi\) | |||||||
\(908\) | −104.081 | −3.45405 | ||||||||
\(909\) | −3.43976 | −0.114090 | ||||||||
\(910\) | −36.1068 | −1.19693 | ||||||||
\(911\) | −47.3267 | −1.56800 | −0.784001 | − | 0.620759i | \(-0.786824\pi\) | ||||
−0.784001 | + | 0.620759i | \(0.786824\pi\) | |||||||
\(912\) | −118.203 | −3.91408 | ||||||||
\(913\) | 6.25451 | 0.206994 | ||||||||
\(914\) | 83.0007 | 2.74542 | ||||||||
\(915\) | 15.8820 | 0.525043 | ||||||||
\(916\) | 113.044 | 3.73509 | ||||||||
\(917\) | −11.1673 | −0.368777 | ||||||||
\(918\) | 23.0440 | 0.760566 | ||||||||
\(919\) | −44.2802 | −1.46067 | −0.730335 | − | 0.683089i | \(-0.760636\pi\) | ||||
−0.730335 | + | 0.683089i | \(0.760636\pi\) | |||||||
\(920\) | 124.032 | 4.08921 | ||||||||
\(921\) | −45.1230 | −1.48685 | ||||||||
\(922\) | −22.4720 | −0.740077 | ||||||||
\(923\) | −9.96630 | −0.328045 | ||||||||
\(924\) | 61.0992 | 2.01002 | ||||||||
\(925\) | 4.80204 | 0.157890 | ||||||||
\(926\) | −101.262 | −3.32769 | ||||||||
\(927\) | −22.4321 | −0.736766 | ||||||||
\(928\) | −111.895 | −3.67314 | ||||||||
\(929\) | −42.2540 | −1.38631 | −0.693155 | − | 0.720788i | \(-0.743780\pi\) | ||||
−0.693155 | + | 0.720788i | \(0.743780\pi\) | |||||||
\(930\) | −209.995 | −6.88602 | ||||||||
\(931\) | 71.5315 | 2.34435 | ||||||||
\(932\) | −111.026 | −3.63676 | ||||||||
\(933\) | 15.5989 | 0.510684 | ||||||||
\(934\) | −40.6962 | −1.33162 | ||||||||
\(935\) | −13.3537 | −0.436711 | ||||||||
\(936\) | −23.9958 | −0.784327 | ||||||||
\(937\) | −19.0600 | −0.622665 | −0.311332 | − | 0.950301i | \(-0.600775\pi\) | ||||
−0.311332 | + | 0.950301i | \(0.600775\pi\) | |||||||
\(938\) | 142.668 | 4.65826 | ||||||||
\(939\) | −84.7017 | −2.76414 | ||||||||
\(940\) | −73.6032 | −2.40067 | ||||||||
\(941\) | −28.9026 | −0.942197 | −0.471098 | − | 0.882081i | \(-0.656142\pi\) | ||||
−0.471098 | + | 0.882081i | \(0.656142\pi\) | |||||||
\(942\) | −90.4743 | −2.94781 | ||||||||
\(943\) | −50.6794 | −1.65035 | ||||||||
\(944\) | −98.4946 | −3.20573 | ||||||||
\(945\) | −35.4346 | −1.15269 | ||||||||
\(946\) | 6.77691 | 0.220336 | ||||||||
\(947\) | 48.2970 | 1.56944 | 0.784721 | − | 0.619849i | \(-0.212806\pi\) | ||||
0.784721 | + | 0.619849i | \(0.212806\pi\) | |||||||
\(948\) | −197.522 | −6.41522 | ||||||||
\(949\) | 3.37928 | 0.109696 | ||||||||
\(950\) | −69.5247 | −2.25568 | ||||||||
\(951\) | −39.9126 | −1.29425 | ||||||||
\(952\) | 193.138 | 6.25963 | ||||||||
\(953\) | 38.9193 | 1.26072 | 0.630360 | − | 0.776303i | \(-0.282907\pi\) | ||||
0.630360 | + | 0.776303i | \(0.282907\pi\) | |||||||
\(954\) | 103.990 | 3.36680 | ||||||||
\(955\) | −50.4336 | −1.63199 | ||||||||
\(956\) | −133.584 | −4.32040 | ||||||||
\(957\) | −15.4261 | −0.498655 | ||||||||
\(958\) | −66.2038 | −2.13895 | ||||||||
\(959\) | 19.0239 | 0.614315 | ||||||||
\(960\) | 174.185 | 5.62180 | ||||||||
\(961\) | 43.7286 | 1.41060 | ||||||||
\(962\) | −1.34557 | −0.0433830 | ||||||||
\(963\) | 9.64108 | 0.310679 | ||||||||
\(964\) | −44.5164 | −1.43378 | ||||||||
\(965\) | 9.84992 | 0.317080 | ||||||||
\(966\) | −149.979 | −4.82549 | ||||||||
\(967\) | 17.9995 | 0.578823 | 0.289412 | − | 0.957205i | \(-0.406540\pi\) | ||||
0.289412 | + | 0.957205i | \(0.406540\pi\) | |||||||
\(968\) | 87.4544 | 2.81089 | ||||||||
\(969\) | −41.2031 | −1.32363 | ||||||||
\(970\) | 5.28693 | 0.169753 | ||||||||
\(971\) | 51.1998 | 1.64308 | 0.821540 | − | 0.570150i | \(-0.193115\pi\) | ||||
0.821540 | + | 0.570150i | \(0.193115\pi\) | |||||||
\(972\) | 113.651 | 3.64535 | ||||||||
\(973\) | −110.478 | −3.54177 | ||||||||
\(974\) | −62.3754 | −1.99864 | ||||||||
\(975\) | −13.8911 | −0.444870 | ||||||||
\(976\) | 21.9799 | 0.703559 | ||||||||
\(977\) | −29.4243 | −0.941366 | −0.470683 | − | 0.882302i | \(-0.655992\pi\) | ||||
−0.470683 | + | 0.882302i | \(0.655992\pi\) | |||||||
\(978\) | −101.800 | −3.25521 | ||||||||
\(979\) | 9.85734 | 0.315042 | ||||||||
\(980\) | −356.710 | −11.3947 | ||||||||
\(981\) | 22.1433 | 0.706980 | ||||||||
\(982\) | 64.4820 | 2.05770 | ||||||||
\(983\) | 7.77916 | 0.248117 | 0.124058 | − | 0.992275i | \(-0.460409\pi\) | ||||
0.124058 | + | 0.992275i | \(0.460409\pi\) | |||||||
\(984\) | −270.466 | −8.62213 | ||||||||
\(985\) | 39.4291 | 1.25632 | ||||||||
\(986\) | −79.3539 | −2.52714 | ||||||||
\(987\) | 54.6905 | 1.74082 | ||||||||
\(988\) | 14.0609 | 0.447336 | ||||||||
\(989\) | −12.0066 | −0.381786 | ||||||||
\(990\) | 30.7684 | 0.977883 | ||||||||
\(991\) | 49.1705 | 1.56195 | 0.780976 | − | 0.624561i | \(-0.214722\pi\) | ||||
0.780976 | + | 0.624561i | \(0.214722\pi\) | |||||||
\(992\) | −142.848 | −4.53544 | ||||||||
\(993\) | 3.07268 | 0.0975084 | ||||||||
\(994\) | −184.829 | −5.86242 | ||||||||
\(995\) | −88.0366 | −2.79095 | ||||||||
\(996\) | −96.2367 | −3.04938 | ||||||||
\(997\) | −22.6434 | −0.717124 | −0.358562 | − | 0.933506i | \(-0.616733\pi\) | ||||
−0.358562 | + | 0.933506i | \(0.616733\pi\) | |||||||
\(998\) | 88.0821 | 2.78819 | ||||||||
\(999\) | −1.32052 | −0.0417795 |
(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 | 4001.2.a.b.1.8 | ✓ | 184 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4001.2.a.b.1.8 | ✓ | 184 | 1.1 | even | 1 | trivial |