Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, 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("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.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: | \(64.0879326623\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 8026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −3.33028 | −1.92274 | −0.961368 | − | 0.275266i | \(-0.911234\pi\) | ||||
−0.961368 | + | 0.275266i | \(0.911234\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.81719 | −1.25989 | −0.629943 | − | 0.776641i | \(-0.716922\pi\) | ||||
−0.629943 | + | 0.776641i | \(0.716922\pi\) | |||||||
\(6\) | −3.33028 | −1.35958 | ||||||||
\(7\) | 2.39962 | 0.906971 | 0.453485 | − | 0.891264i | \(-0.350180\pi\) | ||||
0.453485 | + | 0.891264i | \(0.350180\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 8.09075 | 2.69692 | ||||||||
\(10\) | −2.81719 | −0.890874 | ||||||||
\(11\) | 2.12115 | 0.639551 | 0.319776 | − | 0.947493i | \(-0.396392\pi\) | ||||
0.319776 | + | 0.947493i | \(0.396392\pi\) | |||||||
\(12\) | −3.33028 | −0.961368 | ||||||||
\(13\) | 1.83076 | 0.507762 | 0.253881 | − | 0.967235i | \(-0.418293\pi\) | ||||
0.253881 | + | 0.967235i | \(0.418293\pi\) | |||||||
\(14\) | 2.39962 | 0.641325 | ||||||||
\(15\) | 9.38202 | 2.42243 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.43896 | −1.31914 | −0.659571 | − | 0.751643i | \(-0.729262\pi\) | ||||
−0.659571 | + | 0.751643i | \(0.729262\pi\) | |||||||
\(18\) | 8.09075 | 1.90701 | ||||||||
\(19\) | −1.66187 | −0.381259 | −0.190629 | − | 0.981662i | \(-0.561053\pi\) | ||||
−0.190629 | + | 0.981662i | \(0.561053\pi\) | |||||||
\(20\) | −2.81719 | −0.629943 | ||||||||
\(21\) | −7.99140 | −1.74387 | ||||||||
\(22\) | 2.12115 | 0.452231 | ||||||||
\(23\) | 0.107282 | 0.0223698 | 0.0111849 | − | 0.999937i | \(-0.496440\pi\) | ||||
0.0111849 | + | 0.999937i | \(0.496440\pi\) | |||||||
\(24\) | −3.33028 | −0.679790 | ||||||||
\(25\) | 2.93656 | 0.587312 | ||||||||
\(26\) | 1.83076 | 0.359042 | ||||||||
\(27\) | −16.9536 | −3.26272 | ||||||||
\(28\) | 2.39962 | 0.453485 | ||||||||
\(29\) | −1.06042 | −0.196915 | −0.0984576 | − | 0.995141i | \(-0.531391\pi\) | ||||
−0.0984576 | + | 0.995141i | \(0.531391\pi\) | |||||||
\(30\) | 9.38202 | 1.71292 | ||||||||
\(31\) | 1.63639 | 0.293904 | 0.146952 | − | 0.989144i | \(-0.453054\pi\) | ||||
0.146952 | + | 0.989144i | \(0.453054\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −7.06402 | −1.22969 | ||||||||
\(34\) | −5.43896 | −0.932774 | ||||||||
\(35\) | −6.76018 | −1.14268 | ||||||||
\(36\) | 8.09075 | 1.34846 | ||||||||
\(37\) | 3.16634 | 0.520543 | 0.260272 | − | 0.965535i | \(-0.416188\pi\) | ||||
0.260272 | + | 0.965535i | \(0.416188\pi\) | |||||||
\(38\) | −1.66187 | −0.269591 | ||||||||
\(39\) | −6.09694 | −0.976292 | ||||||||
\(40\) | −2.81719 | −0.445437 | ||||||||
\(41\) | −8.30191 | −1.29654 | −0.648270 | − | 0.761411i | \(-0.724507\pi\) | ||||
−0.648270 | + | 0.761411i | \(0.724507\pi\) | |||||||
\(42\) | −7.99140 | −1.23310 | ||||||||
\(43\) | 0.583384 | 0.0889653 | 0.0444826 | − | 0.999010i | \(-0.485836\pi\) | ||||
0.0444826 | + | 0.999010i | \(0.485836\pi\) | |||||||
\(44\) | 2.12115 | 0.319776 | ||||||||
\(45\) | −22.7932 | −3.39780 | ||||||||
\(46\) | 0.107282 | 0.0158178 | ||||||||
\(47\) | −4.59473 | −0.670210 | −0.335105 | − | 0.942181i | \(-0.608772\pi\) | ||||
−0.335105 | + | 0.942181i | \(0.608772\pi\) | |||||||
\(48\) | −3.33028 | −0.480684 | ||||||||
\(49\) | −1.24183 | −0.177404 | ||||||||
\(50\) | 2.93656 | 0.415292 | ||||||||
\(51\) | 18.1132 | 2.53636 | ||||||||
\(52\) | 1.83076 | 0.253881 | ||||||||
\(53\) | 4.37480 | 0.600924 | 0.300462 | − | 0.953794i | \(-0.402859\pi\) | ||||
0.300462 | + | 0.953794i | \(0.402859\pi\) | |||||||
\(54\) | −16.9536 | −2.30709 | ||||||||
\(55\) | −5.97569 | −0.805761 | ||||||||
\(56\) | 2.39962 | 0.320663 | ||||||||
\(57\) | 5.53448 | 0.733060 | ||||||||
\(58\) | −1.06042 | −0.139240 | ||||||||
\(59\) | −1.74148 | −0.226721 | −0.113360 | − | 0.993554i | \(-0.536161\pi\) | ||||
−0.113360 | + | 0.993554i | \(0.536161\pi\) | |||||||
\(60\) | 9.38202 | 1.21121 | ||||||||
\(61\) | 11.1464 | 1.42715 | 0.713573 | − | 0.700581i | \(-0.247076\pi\) | ||||
0.713573 | + | 0.700581i | \(0.247076\pi\) | |||||||
\(62\) | 1.63639 | 0.207822 | ||||||||
\(63\) | 19.4147 | 2.44602 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.15760 | −0.639722 | ||||||||
\(66\) | −7.06402 | −0.869521 | ||||||||
\(67\) | 3.04992 | 0.372607 | 0.186303 | − | 0.982492i | \(-0.440349\pi\) | ||||
0.186303 | + | 0.982492i | \(0.440349\pi\) | |||||||
\(68\) | −5.43896 | −0.659571 | ||||||||
\(69\) | −0.357278 | −0.0430112 | ||||||||
\(70\) | −6.76018 | −0.807997 | ||||||||
\(71\) | −13.4515 | −1.59639 | −0.798197 | − | 0.602397i | \(-0.794213\pi\) | ||||
−0.798197 | + | 0.602397i | \(0.794213\pi\) | |||||||
\(72\) | 8.09075 | 0.953504 | ||||||||
\(73\) | 9.59142 | 1.12259 | 0.561295 | − | 0.827616i | \(-0.310303\pi\) | ||||
0.561295 | + | 0.827616i | \(0.310303\pi\) | |||||||
\(74\) | 3.16634 | 0.368080 | ||||||||
\(75\) | −9.77956 | −1.12925 | ||||||||
\(76\) | −1.66187 | −0.190629 | ||||||||
\(77\) | 5.08996 | 0.580054 | ||||||||
\(78\) | −6.09694 | −0.690343 | ||||||||
\(79\) | 4.39928 | 0.494958 | 0.247479 | − | 0.968893i | \(-0.420398\pi\) | ||||
0.247479 | + | 0.968893i | \(0.420398\pi\) | |||||||
\(80\) | −2.81719 | −0.314971 | ||||||||
\(81\) | 32.1879 | 3.57644 | ||||||||
\(82\) | −8.30191 | −0.916792 | ||||||||
\(83\) | −3.04167 | −0.333866 | −0.166933 | − | 0.985968i | \(-0.553386\pi\) | ||||
−0.166933 | + | 0.985968i | \(0.553386\pi\) | |||||||
\(84\) | −7.99140 | −0.871933 | ||||||||
\(85\) | 15.3226 | 1.66197 | ||||||||
\(86\) | 0.583384 | 0.0629079 | ||||||||
\(87\) | 3.53150 | 0.378616 | ||||||||
\(88\) | 2.12115 | 0.226115 | ||||||||
\(89\) | 1.94847 | 0.206538 | 0.103269 | − | 0.994653i | \(-0.467070\pi\) | ||||
0.103269 | + | 0.994653i | \(0.467070\pi\) | |||||||
\(90\) | −22.7932 | −2.40261 | ||||||||
\(91\) | 4.39313 | 0.460525 | ||||||||
\(92\) | 0.107282 | 0.0111849 | ||||||||
\(93\) | −5.44963 | −0.565100 | ||||||||
\(94\) | −4.59473 | −0.473910 | ||||||||
\(95\) | 4.68180 | 0.480342 | ||||||||
\(96\) | −3.33028 | −0.339895 | ||||||||
\(97\) | 2.50969 | 0.254820 | 0.127410 | − | 0.991850i | \(-0.459334\pi\) | ||||
0.127410 | + | 0.991850i | \(0.459334\pi\) | |||||||
\(98\) | −1.24183 | −0.125443 | ||||||||
\(99\) | 17.1617 | 1.72482 | ||||||||
\(100\) | 2.93656 | 0.293656 | ||||||||
\(101\) | −4.29911 | −0.427778 | −0.213889 | − | 0.976858i | \(-0.568613\pi\) | ||||
−0.213889 | + | 0.976858i | \(0.568613\pi\) | |||||||
\(102\) | 18.1132 | 1.79348 | ||||||||
\(103\) | −12.3774 | −1.21958 | −0.609791 | − | 0.792563i | \(-0.708746\pi\) | ||||
−0.609791 | + | 0.792563i | \(0.708746\pi\) | |||||||
\(104\) | 1.83076 | 0.179521 | ||||||||
\(105\) | 22.5133 | 2.19707 | ||||||||
\(106\) | 4.37480 | 0.424918 | ||||||||
\(107\) | 12.2003 | 1.17945 | 0.589725 | − | 0.807604i | \(-0.299236\pi\) | ||||
0.589725 | + | 0.807604i | \(0.299236\pi\) | |||||||
\(108\) | −16.9536 | −1.63136 | ||||||||
\(109\) | 4.56595 | 0.437339 | 0.218669 | − | 0.975799i | \(-0.429828\pi\) | ||||
0.218669 | + | 0.975799i | \(0.429828\pi\) | |||||||
\(110\) | −5.97569 | −0.569759 | ||||||||
\(111\) | −10.5448 | −1.00087 | ||||||||
\(112\) | 2.39962 | 0.226743 | ||||||||
\(113\) | −11.7742 | −1.10762 | −0.553811 | − | 0.832643i | \(-0.686827\pi\) | ||||
−0.553811 | + | 0.832643i | \(0.686827\pi\) | |||||||
\(114\) | 5.53448 | 0.518352 | ||||||||
\(115\) | −0.302233 | −0.0281833 | ||||||||
\(116\) | −1.06042 | −0.0984576 | ||||||||
\(117\) | 14.8122 | 1.36939 | ||||||||
\(118\) | −1.74148 | −0.160316 | ||||||||
\(119\) | −13.0514 | −1.19642 | ||||||||
\(120\) | 9.38202 | 0.856458 | ||||||||
\(121\) | −6.50072 | −0.590974 | ||||||||
\(122\) | 11.1464 | 1.00914 | ||||||||
\(123\) | 27.6476 | 2.49290 | ||||||||
\(124\) | 1.63639 | 0.146952 | ||||||||
\(125\) | 5.81310 | 0.519940 | ||||||||
\(126\) | 19.4147 | 1.72960 | ||||||||
\(127\) | 6.13122 | 0.544058 | 0.272029 | − | 0.962289i | \(-0.412305\pi\) | ||||
0.272029 | + | 0.962289i | \(0.412305\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −1.94283 | −0.171057 | ||||||||
\(130\) | −5.15760 | −0.452352 | ||||||||
\(131\) | −7.47793 | −0.653350 | −0.326675 | − | 0.945137i | \(-0.605928\pi\) | ||||
−0.326675 | + | 0.945137i | \(0.605928\pi\) | |||||||
\(132\) | −7.06402 | −0.614844 | ||||||||
\(133\) | −3.98785 | −0.345791 | ||||||||
\(134\) | 3.04992 | 0.263473 | ||||||||
\(135\) | 47.7615 | 4.11066 | ||||||||
\(136\) | −5.43896 | −0.466387 | ||||||||
\(137\) | 11.3372 | 0.968605 | 0.484302 | − | 0.874901i | \(-0.339073\pi\) | ||||
0.484302 | + | 0.874901i | \(0.339073\pi\) | |||||||
\(138\) | −0.357278 | −0.0304135 | ||||||||
\(139\) | 15.5959 | 1.32283 | 0.661413 | − | 0.750022i | \(-0.269957\pi\) | ||||
0.661413 | + | 0.750022i | \(0.269957\pi\) | |||||||
\(140\) | −6.76018 | −0.571340 | ||||||||
\(141\) | 15.3017 | 1.28864 | ||||||||
\(142\) | −13.4515 | −1.12882 | ||||||||
\(143\) | 3.88332 | 0.324740 | ||||||||
\(144\) | 8.09075 | 0.674229 | ||||||||
\(145\) | 2.98741 | 0.248091 | ||||||||
\(146\) | 9.59142 | 0.793791 | ||||||||
\(147\) | 4.13563 | 0.341101 | ||||||||
\(148\) | 3.16634 | 0.260272 | ||||||||
\(149\) | −4.90109 | −0.401513 | −0.200756 | − | 0.979641i | \(-0.564340\pi\) | ||||
−0.200756 | + | 0.979641i | \(0.564340\pi\) | |||||||
\(150\) | −9.77956 | −0.798498 | ||||||||
\(151\) | 7.85586 | 0.639301 | 0.319650 | − | 0.947536i | \(-0.396435\pi\) | ||||
0.319650 | + | 0.947536i | \(0.396435\pi\) | |||||||
\(152\) | −1.66187 | −0.134795 | ||||||||
\(153\) | −44.0052 | −3.55761 | ||||||||
\(154\) | 5.08996 | 0.410160 | ||||||||
\(155\) | −4.61002 | −0.370286 | ||||||||
\(156\) | −6.09694 | −0.488146 | ||||||||
\(157\) | −3.77124 | −0.300977 | −0.150489 | − | 0.988612i | \(-0.548085\pi\) | ||||
−0.150489 | + | 0.988612i | \(0.548085\pi\) | |||||||
\(158\) | 4.39928 | 0.349988 | ||||||||
\(159\) | −14.5693 | −1.15542 | ||||||||
\(160\) | −2.81719 | −0.222718 | ||||||||
\(161\) | 0.257435 | 0.0202887 | ||||||||
\(162\) | 32.1879 | 2.52892 | ||||||||
\(163\) | 4.91488 | 0.384963 | 0.192482 | − | 0.981301i | \(-0.438346\pi\) | ||||
0.192482 | + | 0.981301i | \(0.438346\pi\) | |||||||
\(164\) | −8.30191 | −0.648270 | ||||||||
\(165\) | 19.9007 | 1.54927 | ||||||||
\(166\) | −3.04167 | −0.236079 | ||||||||
\(167\) | −5.12739 | −0.396770 | −0.198385 | − | 0.980124i | \(-0.563570\pi\) | ||||
−0.198385 | + | 0.980124i | \(0.563570\pi\) | |||||||
\(168\) | −7.99140 | −0.616550 | ||||||||
\(169\) | −9.64831 | −0.742178 | ||||||||
\(170\) | 15.3226 | 1.17519 | ||||||||
\(171\) | −13.4458 | −1.02822 | ||||||||
\(172\) | 0.583384 | 0.0444826 | ||||||||
\(173\) | −5.95165 | −0.452496 | −0.226248 | − | 0.974070i | \(-0.572646\pi\) | ||||
−0.226248 | + | 0.974070i | \(0.572646\pi\) | |||||||
\(174\) | 3.53150 | 0.267722 | ||||||||
\(175\) | 7.04663 | 0.532675 | ||||||||
\(176\) | 2.12115 | 0.159888 | ||||||||
\(177\) | 5.79960 | 0.435924 | ||||||||
\(178\) | 1.94847 | 0.146044 | ||||||||
\(179\) | −5.15343 | −0.385186 | −0.192593 | − | 0.981279i | \(-0.561690\pi\) | ||||
−0.192593 | + | 0.981279i | \(0.561690\pi\) | |||||||
\(180\) | −22.7932 | −1.69890 | ||||||||
\(181\) | 7.73594 | 0.575008 | 0.287504 | − | 0.957779i | \(-0.407175\pi\) | ||||
0.287504 | + | 0.957779i | \(0.407175\pi\) | |||||||
\(182\) | 4.39313 | 0.325641 | ||||||||
\(183\) | −37.1205 | −2.74402 | ||||||||
\(184\) | 0.107282 | 0.00790891 | ||||||||
\(185\) | −8.92018 | −0.655825 | ||||||||
\(186\) | −5.44963 | −0.399586 | ||||||||
\(187\) | −11.5369 | −0.843658 | ||||||||
\(188\) | −4.59473 | −0.335105 | ||||||||
\(189\) | −40.6822 | −2.95919 | ||||||||
\(190\) | 4.68180 | 0.339653 | ||||||||
\(191\) | −23.6317 | −1.70993 | −0.854967 | − | 0.518683i | \(-0.826422\pi\) | ||||
−0.854967 | + | 0.518683i | \(0.826422\pi\) | |||||||
\(192\) | −3.33028 | −0.240342 | ||||||||
\(193\) | −19.0384 | −1.37042 | −0.685208 | − | 0.728348i | \(-0.740289\pi\) | ||||
−0.685208 | + | 0.728348i | \(0.740289\pi\) | |||||||
\(194\) | 2.50969 | 0.180185 | ||||||||
\(195\) | 17.1763 | 1.23002 | ||||||||
\(196\) | −1.24183 | −0.0887019 | ||||||||
\(197\) | −1.31035 | −0.0933584 | −0.0466792 | − | 0.998910i | \(-0.514864\pi\) | ||||
−0.0466792 | + | 0.998910i | \(0.514864\pi\) | |||||||
\(198\) | 17.1617 | 1.21963 | ||||||||
\(199\) | −22.0771 | −1.56501 | −0.782503 | − | 0.622647i | \(-0.786057\pi\) | ||||
−0.782503 | + | 0.622647i | \(0.786057\pi\) | |||||||
\(200\) | 2.93656 | 0.207646 | ||||||||
\(201\) | −10.1571 | −0.716425 | ||||||||
\(202\) | −4.29911 | −0.302485 | ||||||||
\(203\) | −2.54461 | −0.178596 | ||||||||
\(204\) | 18.1132 | 1.26818 | ||||||||
\(205\) | 23.3880 | 1.63349 | ||||||||
\(206\) | −12.3774 | −0.862374 | ||||||||
\(207\) | 0.867988 | 0.0603294 | ||||||||
\(208\) | 1.83076 | 0.126941 | ||||||||
\(209\) | −3.52507 | −0.243834 | ||||||||
\(210\) | 22.5133 | 1.55356 | ||||||||
\(211\) | 20.6971 | 1.42485 | 0.712424 | − | 0.701749i | \(-0.247597\pi\) | ||||
0.712424 | + | 0.701749i | \(0.247597\pi\) | |||||||
\(212\) | 4.37480 | 0.300462 | ||||||||
\(213\) | 44.7971 | 3.06944 | ||||||||
\(214\) | 12.2003 | 0.833997 | ||||||||
\(215\) | −1.64350 | −0.112086 | ||||||||
\(216\) | −16.9536 | −1.15355 | ||||||||
\(217\) | 3.92671 | 0.266563 | ||||||||
\(218\) | 4.56595 | 0.309245 | ||||||||
\(219\) | −31.9421 | −2.15845 | ||||||||
\(220\) | −5.97569 | −0.402881 | ||||||||
\(221\) | −9.95744 | −0.669810 | ||||||||
\(222\) | −10.5448 | −0.707720 | ||||||||
\(223\) | 1.08779 | 0.0728437 | 0.0364219 | − | 0.999337i | \(-0.488404\pi\) | ||||
0.0364219 | + | 0.999337i | \(0.488404\pi\) | |||||||
\(224\) | 2.39962 | 0.160331 | ||||||||
\(225\) | 23.7590 | 1.58393 | ||||||||
\(226\) | −11.7742 | −0.783207 | ||||||||
\(227\) | 25.9393 | 1.72165 | 0.860827 | − | 0.508897i | \(-0.169947\pi\) | ||||
0.860827 | + | 0.508897i | \(0.169947\pi\) | |||||||
\(228\) | 5.53448 | 0.366530 | ||||||||
\(229\) | −5.88492 | −0.388887 | −0.194443 | − | 0.980914i | \(-0.562290\pi\) | ||||
−0.194443 | + | 0.980914i | \(0.562290\pi\) | |||||||
\(230\) | −0.302233 | −0.0199286 | ||||||||
\(231\) | −16.9510 | −1.11529 | ||||||||
\(232\) | −1.06042 | −0.0696201 | ||||||||
\(233\) | 20.1406 | 1.31945 | 0.659726 | − | 0.751506i | \(-0.270672\pi\) | ||||
0.659726 | + | 0.751506i | \(0.270672\pi\) | |||||||
\(234\) | 14.8122 | 0.968306 | ||||||||
\(235\) | 12.9442 | 0.844388 | ||||||||
\(236\) | −1.74148 | −0.113360 | ||||||||
\(237\) | −14.6508 | −0.951673 | ||||||||
\(238\) | −13.0514 | −0.845999 | ||||||||
\(239\) | −6.42727 | −0.415746 | −0.207873 | − | 0.978156i | \(-0.566654\pi\) | ||||
−0.207873 | + | 0.978156i | \(0.566654\pi\) | |||||||
\(240\) | 9.38202 | 0.605607 | ||||||||
\(241\) | −23.2804 | −1.49962 | −0.749810 | − | 0.661653i | \(-0.769855\pi\) | ||||
−0.749810 | + | 0.661653i | \(0.769855\pi\) | |||||||
\(242\) | −6.50072 | −0.417882 | ||||||||
\(243\) | −56.3339 | −3.61382 | ||||||||
\(244\) | 11.1464 | 0.713573 | ||||||||
\(245\) | 3.49846 | 0.223508 | ||||||||
\(246\) | 27.6476 | 1.76275 | ||||||||
\(247\) | −3.04248 | −0.193589 | ||||||||
\(248\) | 1.63639 | 0.103911 | ||||||||
\(249\) | 10.1296 | 0.641937 | ||||||||
\(250\) | 5.81310 | 0.367653 | ||||||||
\(251\) | −20.4566 | −1.29121 | −0.645605 | − | 0.763672i | \(-0.723395\pi\) | ||||
−0.645605 | + | 0.763672i | \(0.723395\pi\) | |||||||
\(252\) | 19.4147 | 1.22301 | ||||||||
\(253\) | 0.227561 | 0.0143066 | ||||||||
\(254\) | 6.13122 | 0.384707 | ||||||||
\(255\) | −51.0284 | −3.19553 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.6643 | −0.665221 | −0.332611 | − | 0.943064i | \(-0.607929\pi\) | ||||
−0.332611 | + | 0.943064i | \(0.607929\pi\) | |||||||
\(258\) | −1.94283 | −0.120955 | ||||||||
\(259\) | 7.59801 | 0.472117 | ||||||||
\(260\) | −5.15760 | −0.319861 | ||||||||
\(261\) | −8.57960 | −0.531064 | ||||||||
\(262\) | −7.47793 | −0.461988 | ||||||||
\(263\) | 8.64981 | 0.533370 | 0.266685 | − | 0.963784i | \(-0.414072\pi\) | ||||
0.266685 | + | 0.963784i | \(0.414072\pi\) | |||||||
\(264\) | −7.06402 | −0.434760 | ||||||||
\(265\) | −12.3246 | −0.757096 | ||||||||
\(266\) | −3.98785 | −0.244511 | ||||||||
\(267\) | −6.48895 | −0.397117 | ||||||||
\(268\) | 3.04992 | 0.186303 | ||||||||
\(269\) | −0.162261 | −0.00989325 | −0.00494662 | − | 0.999988i | \(-0.501575\pi\) | ||||
−0.00494662 | + | 0.999988i | \(0.501575\pi\) | |||||||
\(270\) | 47.7615 | 2.90667 | ||||||||
\(271\) | −7.00820 | −0.425718 | −0.212859 | − | 0.977083i | \(-0.568277\pi\) | ||||
−0.212859 | + | 0.977083i | \(0.568277\pi\) | |||||||
\(272\) | −5.43896 | −0.329785 | ||||||||
\(273\) | −14.6303 | −0.885469 | ||||||||
\(274\) | 11.3372 | 0.684907 | ||||||||
\(275\) | 6.22889 | 0.375616 | ||||||||
\(276\) | −0.357278 | −0.0215056 | ||||||||
\(277\) | −25.3290 | −1.52187 | −0.760935 | − | 0.648829i | \(-0.775259\pi\) | ||||
−0.760935 | + | 0.648829i | \(0.775259\pi\) | |||||||
\(278\) | 15.5959 | 0.935379 | ||||||||
\(279\) | 13.2396 | 0.792635 | ||||||||
\(280\) | −6.76018 | −0.403998 | ||||||||
\(281\) | −15.4832 | −0.923653 | −0.461826 | − | 0.886970i | \(-0.652806\pi\) | ||||
−0.461826 | + | 0.886970i | \(0.652806\pi\) | |||||||
\(282\) | 15.3017 | 0.911204 | ||||||||
\(283\) | −4.23467 | −0.251725 | −0.125862 | − | 0.992048i | \(-0.540170\pi\) | ||||
−0.125862 | + | 0.992048i | \(0.540170\pi\) | |||||||
\(284\) | −13.4515 | −0.798197 | ||||||||
\(285\) | −15.5917 | −0.923572 | ||||||||
\(286\) | 3.88332 | 0.229626 | ||||||||
\(287\) | −19.9214 | −1.17592 | ||||||||
\(288\) | 8.09075 | 0.476752 | ||||||||
\(289\) | 12.5823 | 0.740134 | ||||||||
\(290\) | 2.98741 | 0.175427 | ||||||||
\(291\) | −8.35795 | −0.489952 | ||||||||
\(292\) | 9.59142 | 0.561295 | ||||||||
\(293\) | 22.9981 | 1.34356 | 0.671782 | − | 0.740749i | \(-0.265529\pi\) | ||||
0.671782 | + | 0.740749i | \(0.265529\pi\) | |||||||
\(294\) | 4.13563 | 0.241195 | ||||||||
\(295\) | 4.90607 | 0.285642 | ||||||||
\(296\) | 3.16634 | 0.184040 | ||||||||
\(297\) | −35.9611 | −2.08668 | ||||||||
\(298\) | −4.90109 | −0.283912 | ||||||||
\(299\) | 0.196407 | 0.0113585 | ||||||||
\(300\) | −9.77956 | −0.564623 | ||||||||
\(301\) | 1.39990 | 0.0806889 | ||||||||
\(302\) | 7.85586 | 0.452054 | ||||||||
\(303\) | 14.3172 | 0.822504 | ||||||||
\(304\) | −1.66187 | −0.0953147 | ||||||||
\(305\) | −31.4014 | −1.79804 | ||||||||
\(306\) | −44.0052 | −2.51561 | ||||||||
\(307\) | 24.9753 | 1.42541 | 0.712707 | − | 0.701462i | \(-0.247469\pi\) | ||||
0.712707 | + | 0.701462i | \(0.247469\pi\) | |||||||
\(308\) | 5.08996 | 0.290027 | ||||||||
\(309\) | 41.2202 | 2.34493 | ||||||||
\(310\) | −4.61002 | −0.261832 | ||||||||
\(311\) | −5.44604 | −0.308816 | −0.154408 | − | 0.988007i | \(-0.549347\pi\) | ||||
−0.154408 | + | 0.988007i | \(0.549347\pi\) | |||||||
\(312\) | −6.09694 | −0.345172 | ||||||||
\(313\) | −27.5364 | −1.55645 | −0.778223 | − | 0.627987i | \(-0.783879\pi\) | ||||
−0.778223 | + | 0.627987i | \(0.783879\pi\) | |||||||
\(314\) | −3.77124 | −0.212823 | ||||||||
\(315\) | −54.6949 | −3.08171 | ||||||||
\(316\) | 4.39928 | 0.247479 | ||||||||
\(317\) | −26.2604 | −1.47493 | −0.737466 | − | 0.675384i | \(-0.763978\pi\) | ||||
−0.737466 | + | 0.675384i | \(0.763978\pi\) | |||||||
\(318\) | −14.5693 | −0.817005 | ||||||||
\(319\) | −2.24931 | −0.125937 | ||||||||
\(320\) | −2.81719 | −0.157486 | ||||||||
\(321\) | −40.6304 | −2.26777 | ||||||||
\(322\) | 0.257435 | 0.0143463 | ||||||||
\(323\) | 9.03883 | 0.502934 | ||||||||
\(324\) | 32.1879 | 1.78822 | ||||||||
\(325\) | 5.37614 | 0.298215 | ||||||||
\(326\) | 4.91488 | 0.272210 | ||||||||
\(327\) | −15.2059 | −0.840887 | ||||||||
\(328\) | −8.30191 | −0.458396 | ||||||||
\(329\) | −11.0256 | −0.607861 | ||||||||
\(330\) | 19.9007 | 1.09550 | ||||||||
\(331\) | −20.6672 | −1.13597 | −0.567986 | − | 0.823038i | \(-0.692277\pi\) | ||||
−0.567986 | + | 0.823038i | \(0.692277\pi\) | |||||||
\(332\) | −3.04167 | −0.166933 | ||||||||
\(333\) | 25.6180 | 1.40386 | ||||||||
\(334\) | −5.12739 | −0.280558 | ||||||||
\(335\) | −8.59220 | −0.469442 | ||||||||
\(336\) | −7.99140 | −0.435966 | ||||||||
\(337\) | 10.1111 | 0.550787 | 0.275394 | − | 0.961332i | \(-0.411192\pi\) | ||||
0.275394 | + | 0.961332i | \(0.411192\pi\) | |||||||
\(338\) | −9.64831 | −0.524799 | ||||||||
\(339\) | 39.2113 | 2.12966 | ||||||||
\(340\) | 15.3226 | 0.830984 | ||||||||
\(341\) | 3.47103 | 0.187967 | ||||||||
\(342\) | −13.4458 | −0.727063 | ||||||||
\(343\) | −19.7772 | −1.06787 | ||||||||
\(344\) | 0.583384 | 0.0314540 | ||||||||
\(345\) | 1.00652 | 0.0541891 | ||||||||
\(346\) | −5.95165 | −0.319963 | ||||||||
\(347\) | 23.8158 | 1.27850 | 0.639249 | − | 0.768999i | \(-0.279245\pi\) | ||||
0.639249 | + | 0.768999i | \(0.279245\pi\) | |||||||
\(348\) | 3.53150 | 0.189308 | ||||||||
\(349\) | −11.5771 | −0.619710 | −0.309855 | − | 0.950784i | \(-0.600280\pi\) | ||||
−0.309855 | + | 0.950784i | \(0.600280\pi\) | |||||||
\(350\) | 7.04663 | 0.376658 | ||||||||
\(351\) | −31.0380 | −1.65669 | ||||||||
\(352\) | 2.12115 | 0.113058 | ||||||||
\(353\) | 10.4598 | 0.556720 | 0.278360 | − | 0.960477i | \(-0.410209\pi\) | ||||
0.278360 | + | 0.960477i | \(0.410209\pi\) | |||||||
\(354\) | 5.79960 | 0.308245 | ||||||||
\(355\) | 37.8953 | 2.01127 | ||||||||
\(356\) | 1.94847 | 0.103269 | ||||||||
\(357\) | 43.4649 | 2.30041 | ||||||||
\(358\) | −5.15343 | −0.272367 | ||||||||
\(359\) | 21.2970 | 1.12401 | 0.562007 | − | 0.827133i | \(-0.310030\pi\) | ||||
0.562007 | + | 0.827133i | \(0.310030\pi\) | |||||||
\(360\) | −22.7932 | −1.20131 | ||||||||
\(361\) | −16.2382 | −0.854642 | ||||||||
\(362\) | 7.73594 | 0.406592 | ||||||||
\(363\) | 21.6492 | 1.13629 | ||||||||
\(364\) | 4.39313 | 0.230263 | ||||||||
\(365\) | −27.0208 | −1.41434 | ||||||||
\(366\) | −37.1205 | −1.94032 | ||||||||
\(367\) | 5.65006 | 0.294931 | 0.147465 | − | 0.989067i | \(-0.452888\pi\) | ||||
0.147465 | + | 0.989067i | \(0.452888\pi\) | |||||||
\(368\) | 0.107282 | 0.00559244 | ||||||||
\(369\) | −67.1686 | −3.49666 | ||||||||
\(370\) | −8.92018 | −0.463738 | ||||||||
\(371\) | 10.4978 | 0.545021 | ||||||||
\(372\) | −5.44963 | −0.282550 | ||||||||
\(373\) | −32.2999 | −1.67243 | −0.836214 | − | 0.548403i | \(-0.815236\pi\) | ||||
−0.836214 | + | 0.548403i | \(0.815236\pi\) | |||||||
\(374\) | −11.5369 | −0.596557 | ||||||||
\(375\) | −19.3592 | −0.999707 | ||||||||
\(376\) | −4.59473 | −0.236955 | ||||||||
\(377\) | −1.94138 | −0.0999861 | ||||||||
\(378\) | −40.6822 | −2.09247 | ||||||||
\(379\) | −17.0409 | −0.875334 | −0.437667 | − | 0.899137i | \(-0.644195\pi\) | ||||
−0.437667 | + | 0.899137i | \(0.644195\pi\) | |||||||
\(380\) | 4.68180 | 0.240171 | ||||||||
\(381\) | −20.4187 | −1.04608 | ||||||||
\(382\) | −23.6317 | −1.20911 | ||||||||
\(383\) | −3.21939 | −0.164503 | −0.0822515 | − | 0.996612i | \(-0.526211\pi\) | ||||
−0.0822515 | + | 0.996612i | \(0.526211\pi\) | |||||||
\(384\) | −3.33028 | −0.169947 | ||||||||
\(385\) | −14.3394 | −0.730802 | ||||||||
\(386\) | −19.0384 | −0.969030 | ||||||||
\(387\) | 4.72001 | 0.239932 | ||||||||
\(388\) | 2.50969 | 0.127410 | ||||||||
\(389\) | 3.82490 | 0.193930 | 0.0969651 | − | 0.995288i | \(-0.469086\pi\) | ||||
0.0969651 | + | 0.995288i | \(0.469086\pi\) | |||||||
\(390\) | 17.1763 | 0.869753 | ||||||||
\(391\) | −0.583500 | −0.0295089 | ||||||||
\(392\) | −1.24183 | −0.0627217 | ||||||||
\(393\) | 24.9036 | 1.25622 | ||||||||
\(394\) | −1.31035 | −0.0660143 | ||||||||
\(395\) | −12.3936 | −0.623590 | ||||||||
\(396\) | 17.1617 | 0.862408 | ||||||||
\(397\) | −7.26808 | −0.364774 | −0.182387 | − | 0.983227i | \(-0.558382\pi\) | ||||
−0.182387 | + | 0.983227i | \(0.558382\pi\) | |||||||
\(398\) | −22.0771 | −1.10663 | ||||||||
\(399\) | 13.2806 | 0.664864 | ||||||||
\(400\) | 2.93656 | 0.146828 | ||||||||
\(401\) | −32.7088 | −1.63340 | −0.816700 | − | 0.577063i | \(-0.804199\pi\) | ||||
−0.816700 | + | 0.577063i | \(0.804199\pi\) | |||||||
\(402\) | −10.1571 | −0.506589 | ||||||||
\(403\) | 2.99584 | 0.149233 | ||||||||
\(404\) | −4.29911 | −0.213889 | ||||||||
\(405\) | −90.6795 | −4.50590 | ||||||||
\(406\) | −2.54461 | −0.126287 | ||||||||
\(407\) | 6.71629 | 0.332914 | ||||||||
\(408\) | 18.1132 | 0.896739 | ||||||||
\(409\) | 14.8357 | 0.733577 | 0.366789 | − | 0.930304i | \(-0.380457\pi\) | ||||
0.366789 | + | 0.930304i | \(0.380457\pi\) | |||||||
\(410\) | 23.3880 | 1.15505 | ||||||||
\(411\) | −37.7561 | −1.86237 | ||||||||
\(412\) | −12.3774 | −0.609791 | ||||||||
\(413\) | −4.17888 | −0.205629 | ||||||||
\(414\) | 0.867988 | 0.0426593 | ||||||||
\(415\) | 8.56895 | 0.420633 | ||||||||
\(416\) | 1.83076 | 0.0897605 | ||||||||
\(417\) | −51.9386 | −2.54345 | ||||||||
\(418\) | −3.52507 | −0.172417 | ||||||||
\(419\) | −2.90261 | −0.141802 | −0.0709008 | − | 0.997483i | \(-0.522587\pi\) | ||||
−0.0709008 | + | 0.997483i | \(0.522587\pi\) | |||||||
\(420\) | 22.5133 | 1.09854 | ||||||||
\(421\) | −6.00890 | −0.292856 | −0.146428 | − | 0.989221i | \(-0.546778\pi\) | ||||
−0.146428 | + | 0.989221i | \(0.546778\pi\) | |||||||
\(422\) | 20.6971 | 1.00752 | ||||||||
\(423\) | −37.1748 | −1.80750 | ||||||||
\(424\) | 4.37480 | 0.212459 | ||||||||
\(425\) | −15.9718 | −0.774748 | ||||||||
\(426\) | 44.7971 | 2.17042 | ||||||||
\(427\) | 26.7470 | 1.29438 | ||||||||
\(428\) | 12.2003 | 0.589725 | ||||||||
\(429\) | −12.9325 | −0.624389 | ||||||||
\(430\) | −1.64350 | −0.0792568 | ||||||||
\(431\) | −1.07201 | −0.0516369 | −0.0258184 | − | 0.999667i | \(-0.508219\pi\) | ||||
−0.0258184 | + | 0.999667i | \(0.508219\pi\) | |||||||
\(432\) | −16.9536 | −0.815680 | ||||||||
\(433\) | −5.71521 | −0.274656 | −0.137328 | − | 0.990526i | \(-0.543851\pi\) | ||||
−0.137328 | + | 0.990526i | \(0.543851\pi\) | |||||||
\(434\) | 3.92671 | 0.188488 | ||||||||
\(435\) | −9.94890 | −0.477013 | ||||||||
\(436\) | 4.56595 | 0.218669 | ||||||||
\(437\) | −0.178288 | −0.00852867 | ||||||||
\(438\) | −31.9421 | −1.52625 | ||||||||
\(439\) | 22.8507 | 1.09060 | 0.545302 | − | 0.838240i | \(-0.316415\pi\) | ||||
0.545302 | + | 0.838240i | \(0.316415\pi\) | |||||||
\(440\) | −5.97569 | −0.284880 | ||||||||
\(441\) | −10.0473 | −0.478443 | ||||||||
\(442\) | −9.95744 | −0.473627 | ||||||||
\(443\) | −21.3288 | −1.01336 | −0.506680 | − | 0.862134i | \(-0.669127\pi\) | ||||
−0.506680 | + | 0.862134i | \(0.669127\pi\) | |||||||
\(444\) | −10.5448 | −0.500434 | ||||||||
\(445\) | −5.48921 | −0.260214 | ||||||||
\(446\) | 1.08779 | 0.0515083 | ||||||||
\(447\) | 16.3220 | 0.772003 | ||||||||
\(448\) | 2.39962 | 0.113371 | ||||||||
\(449\) | −5.71138 | −0.269537 | −0.134768 | − | 0.990877i | \(-0.543029\pi\) | ||||
−0.134768 | + | 0.990877i | \(0.543029\pi\) | |||||||
\(450\) | 23.7590 | 1.12001 | ||||||||
\(451\) | −17.6096 | −0.829204 | ||||||||
\(452\) | −11.7742 | −0.553811 | ||||||||
\(453\) | −26.1622 | −1.22921 | ||||||||
\(454\) | 25.9393 | 1.21739 | ||||||||
\(455\) | −12.3763 | −0.580209 | ||||||||
\(456\) | 5.53448 | 0.259176 | ||||||||
\(457\) | −12.8557 | −0.601364 | −0.300682 | − | 0.953724i | \(-0.597214\pi\) | ||||
−0.300682 | + | 0.953724i | \(0.597214\pi\) | |||||||
\(458\) | −5.88492 | −0.274984 | ||||||||
\(459\) | 92.2099 | 4.30399 | ||||||||
\(460\) | −0.302233 | −0.0140917 | ||||||||
\(461\) | 10.3980 | 0.484284 | 0.242142 | − | 0.970241i | \(-0.422150\pi\) | ||||
0.242142 | + | 0.970241i | \(0.422150\pi\) | |||||||
\(462\) | −16.9510 | −0.788630 | ||||||||
\(463\) | 34.5449 | 1.60544 | 0.802718 | − | 0.596359i | \(-0.203387\pi\) | ||||
0.802718 | + | 0.596359i | \(0.203387\pi\) | |||||||
\(464\) | −1.06042 | −0.0492288 | ||||||||
\(465\) | 15.3526 | 0.711962 | ||||||||
\(466\) | 20.1406 | 0.932993 | ||||||||
\(467\) | −28.5935 | −1.32315 | −0.661574 | − | 0.749880i | \(-0.730111\pi\) | ||||
−0.661574 | + | 0.749880i | \(0.730111\pi\) | |||||||
\(468\) | 14.8122 | 0.684696 | ||||||||
\(469\) | 7.31865 | 0.337944 | ||||||||
\(470\) | 12.9442 | 0.597072 | ||||||||
\(471\) | 12.5593 | 0.578700 | ||||||||
\(472\) | −1.74148 | −0.0801579 | ||||||||
\(473\) | 1.23745 | 0.0568978 | ||||||||
\(474\) | −14.6508 | −0.672934 | ||||||||
\(475\) | −4.88017 | −0.223918 | ||||||||
\(476\) | −13.0514 | −0.598211 | ||||||||
\(477\) | 35.3954 | 1.62064 | ||||||||
\(478\) | −6.42727 | −0.293977 | ||||||||
\(479\) | −22.0974 | −1.00966 | −0.504828 | − | 0.863220i | \(-0.668444\pi\) | ||||
−0.504828 | + | 0.863220i | \(0.668444\pi\) | |||||||
\(480\) | 9.38202 | 0.428229 | ||||||||
\(481\) | 5.79681 | 0.264312 | ||||||||
\(482\) | −23.2804 | −1.06039 | ||||||||
\(483\) | −0.857330 | −0.0390099 | ||||||||
\(484\) | −6.50072 | −0.295487 | ||||||||
\(485\) | −7.07026 | −0.321044 | ||||||||
\(486\) | −56.3339 | −2.55536 | ||||||||
\(487\) | −1.51950 | −0.0688550 | −0.0344275 | − | 0.999407i | \(-0.510961\pi\) | ||||
−0.0344275 | + | 0.999407i | \(0.510961\pi\) | |||||||
\(488\) | 11.1464 | 0.504572 | ||||||||
\(489\) | −16.3679 | −0.740183 | ||||||||
\(490\) | 3.49846 | 0.158044 | ||||||||
\(491\) | −13.3366 | −0.601870 | −0.300935 | − | 0.953645i | \(-0.597299\pi\) | ||||
−0.300935 | + | 0.953645i | \(0.597299\pi\) | |||||||
\(492\) | 27.6476 | 1.24645 | ||||||||
\(493\) | 5.76759 | 0.259759 | ||||||||
\(494\) | −3.04248 | −0.136888 | ||||||||
\(495\) | −48.3478 | −2.17307 | ||||||||
\(496\) | 1.63639 | 0.0734761 | ||||||||
\(497\) | −32.2784 | −1.44788 | ||||||||
\(498\) | 10.1296 | 0.453918 | ||||||||
\(499\) | −14.9268 | −0.668217 | −0.334108 | − | 0.942535i | \(-0.608435\pi\) | ||||
−0.334108 | + | 0.942535i | \(0.608435\pi\) | |||||||
\(500\) | 5.81310 | 0.259970 | ||||||||
\(501\) | 17.0756 | 0.762883 | ||||||||
\(502\) | −20.4566 | −0.913023 | ||||||||
\(503\) | 14.9924 | 0.668478 | 0.334239 | − | 0.942488i | \(-0.391521\pi\) | ||||
0.334239 | + | 0.942488i | \(0.391521\pi\) | |||||||
\(504\) | 19.4147 | 0.864800 | ||||||||
\(505\) | 12.1114 | 0.538951 | ||||||||
\(506\) | 0.227561 | 0.0101163 | ||||||||
\(507\) | 32.1315 | 1.42701 | ||||||||
\(508\) | 6.13122 | 0.272029 | ||||||||
\(509\) | 12.5006 | 0.554078 | 0.277039 | − | 0.960859i | \(-0.410647\pi\) | ||||
0.277039 | + | 0.960859i | \(0.410647\pi\) | |||||||
\(510\) | −51.0284 | −2.25958 | ||||||||
\(511\) | 23.0158 | 1.01816 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 28.1746 | 1.24394 | ||||||||
\(514\) | −10.6643 | −0.470383 | ||||||||
\(515\) | 34.8695 | 1.53653 | ||||||||
\(516\) | −1.94283 | −0.0855284 | ||||||||
\(517\) | −9.74611 | −0.428634 | ||||||||
\(518\) | 7.59801 | 0.333837 | ||||||||
\(519\) | 19.8206 | 0.870030 | ||||||||
\(520\) | −5.15760 | −0.226176 | ||||||||
\(521\) | 11.2046 | 0.490881 | 0.245441 | − | 0.969412i | \(-0.421067\pi\) | ||||
0.245441 | + | 0.969412i | \(0.421067\pi\) | |||||||
\(522\) | −8.57960 | −0.375519 | ||||||||
\(523\) | −7.09647 | −0.310307 | −0.155153 | − | 0.987890i | \(-0.549587\pi\) | ||||
−0.155153 | + | 0.987890i | \(0.549587\pi\) | |||||||
\(524\) | −7.47793 | −0.326675 | ||||||||
\(525\) | −23.4672 | −1.02419 | ||||||||
\(526\) | 8.64981 | 0.377150 | ||||||||
\(527\) | −8.90026 | −0.387701 | ||||||||
\(528\) | −7.06402 | −0.307422 | ||||||||
\(529\) | −22.9885 | −0.999500 | ||||||||
\(530\) | −12.3246 | −0.535348 | ||||||||
\(531\) | −14.0898 | −0.611447 | ||||||||
\(532\) | −3.98785 | −0.172895 | ||||||||
\(533\) | −15.1988 | −0.658334 | ||||||||
\(534\) | −6.48895 | −0.280804 | ||||||||
\(535\) | −34.3706 | −1.48597 | ||||||||
\(536\) | 3.04992 | 0.131736 | ||||||||
\(537\) | 17.1624 | 0.740610 | ||||||||
\(538\) | −0.162261 | −0.00699558 | ||||||||
\(539\) | −2.63410 | −0.113459 | ||||||||
\(540\) | 47.7615 | 2.05533 | ||||||||
\(541\) | 12.5010 | 0.537462 | 0.268731 | − | 0.963215i | \(-0.413396\pi\) | ||||
0.268731 | + | 0.963215i | \(0.413396\pi\) | |||||||
\(542\) | −7.00820 | −0.301028 | ||||||||
\(543\) | −25.7628 | −1.10559 | ||||||||
\(544\) | −5.43896 | −0.233193 | ||||||||
\(545\) | −12.8632 | −0.550997 | ||||||||
\(546\) | −14.6303 | −0.626121 | ||||||||
\(547\) | −8.46523 | −0.361947 | −0.180973 | − | 0.983488i | \(-0.557925\pi\) | ||||
−0.180973 | + | 0.983488i | \(0.557925\pi\) | |||||||
\(548\) | 11.3372 | 0.484302 | ||||||||
\(549\) | 90.1824 | 3.84889 | ||||||||
\(550\) | 6.22889 | 0.265601 | ||||||||
\(551\) | 1.76228 | 0.0750757 | ||||||||
\(552\) | −0.357278 | −0.0152067 | ||||||||
\(553\) | 10.5566 | 0.448912 | ||||||||
\(554\) | −25.3290 | −1.07612 | ||||||||
\(555\) | 29.7067 | 1.26098 | ||||||||
\(556\) | 15.5959 | 0.661413 | ||||||||
\(557\) | 16.0164 | 0.678636 | 0.339318 | − | 0.940672i | \(-0.389804\pi\) | ||||
0.339318 | + | 0.940672i | \(0.389804\pi\) | |||||||
\(558\) | 13.2396 | 0.560478 | ||||||||
\(559\) | 1.06804 | 0.0451732 | ||||||||
\(560\) | −6.76018 | −0.285670 | ||||||||
\(561\) | 38.4209 | 1.62213 | ||||||||
\(562\) | −15.4832 | −0.653121 | ||||||||
\(563\) | −6.27071 | −0.264279 | −0.132140 | − | 0.991231i | \(-0.542185\pi\) | ||||
−0.132140 | + | 0.991231i | \(0.542185\pi\) | |||||||
\(564\) | 15.3017 | 0.644318 | ||||||||
\(565\) | 33.1701 | 1.39548 | ||||||||
\(566\) | −4.23467 | −0.177996 | ||||||||
\(567\) | 77.2388 | 3.24372 | ||||||||
\(568\) | −13.4515 | −0.564410 | ||||||||
\(569\) | −19.2558 | −0.807243 | −0.403622 | − | 0.914926i | \(-0.632249\pi\) | ||||
−0.403622 | + | 0.914926i | \(0.632249\pi\) | |||||||
\(570\) | −15.5917 | −0.653064 | ||||||||
\(571\) | −30.6514 | −1.28272 | −0.641361 | − | 0.767239i | \(-0.721630\pi\) | ||||
−0.641361 | + | 0.767239i | \(0.721630\pi\) | |||||||
\(572\) | 3.88332 | 0.162370 | ||||||||
\(573\) | 78.7003 | 3.28775 | ||||||||
\(574\) | −19.9214 | −0.831504 | ||||||||
\(575\) | 0.315039 | 0.0131380 | ||||||||
\(576\) | 8.09075 | 0.337114 | ||||||||
\(577\) | −38.0375 | −1.58352 | −0.791761 | − | 0.610831i | \(-0.790836\pi\) | ||||
−0.791761 | + | 0.610831i | \(0.790836\pi\) | |||||||
\(578\) | 12.5823 | 0.523354 | ||||||||
\(579\) | 63.4032 | 2.63495 | ||||||||
\(580\) | 2.98741 | 0.124045 | ||||||||
\(581\) | −7.29884 | −0.302807 | ||||||||
\(582\) | −8.35795 | −0.346448 | ||||||||
\(583\) | 9.27960 | 0.384322 | ||||||||
\(584\) | 9.59142 | 0.396896 | ||||||||
\(585\) | −41.7289 | −1.72528 | ||||||||
\(586\) | 22.9981 | 0.950043 | ||||||||
\(587\) | 5.10878 | 0.210862 | 0.105431 | − | 0.994427i | \(-0.466378\pi\) | ||||
0.105431 | + | 0.994427i | \(0.466378\pi\) | |||||||
\(588\) | 4.13563 | 0.170550 | ||||||||
\(589\) | −2.71946 | −0.112054 | ||||||||
\(590\) | 4.90607 | 0.201980 | ||||||||
\(591\) | 4.36382 | 0.179504 | ||||||||
\(592\) | 3.16634 | 0.130136 | ||||||||
\(593\) | −6.74429 | −0.276955 | −0.138477 | − | 0.990366i | \(-0.544221\pi\) | ||||
−0.138477 | + | 0.990366i | \(0.544221\pi\) | |||||||
\(594\) | −35.9611 | −1.47550 | ||||||||
\(595\) | 36.7684 | 1.50736 | ||||||||
\(596\) | −4.90109 | −0.200756 | ||||||||
\(597\) | 73.5230 | 3.00909 | ||||||||
\(598\) | 0.196407 | 0.00803168 | ||||||||
\(599\) | 10.4436 | 0.426714 | 0.213357 | − | 0.976974i | \(-0.431560\pi\) | ||||
0.213357 | + | 0.976974i | \(0.431560\pi\) | |||||||
\(600\) | −9.77956 | −0.399249 | ||||||||
\(601\) | −13.7652 | −0.561494 | −0.280747 | − | 0.959782i | \(-0.590582\pi\) | ||||
−0.280747 | + | 0.959782i | \(0.590582\pi\) | |||||||
\(602\) | 1.39990 | 0.0570557 | ||||||||
\(603\) | 24.6761 | 1.00489 | ||||||||
\(604\) | 7.85586 | 0.319650 | ||||||||
\(605\) | 18.3138 | 0.744560 | ||||||||
\(606\) | 14.3172 | 0.581598 | ||||||||
\(607\) | 36.2438 | 1.47109 | 0.735546 | − | 0.677475i | \(-0.236926\pi\) | ||||
0.735546 | + | 0.677475i | \(0.236926\pi\) | |||||||
\(608\) | −1.66187 | −0.0673976 | ||||||||
\(609\) | 8.47425 | 0.343394 | ||||||||
\(610\) | −31.4014 | −1.27141 | ||||||||
\(611\) | −8.41185 | −0.340307 | ||||||||
\(612\) | −44.0052 | −1.77881 | ||||||||
\(613\) | −29.3978 | −1.18737 | −0.593684 | − | 0.804699i | \(-0.702327\pi\) | ||||
−0.593684 | + | 0.804699i | \(0.702327\pi\) | |||||||
\(614\) | 24.9753 | 1.00792 | ||||||||
\(615\) | −77.8887 | −3.14077 | ||||||||
\(616\) | 5.08996 | 0.205080 | ||||||||
\(617\) | 21.8819 | 0.880932 | 0.440466 | − | 0.897769i | \(-0.354813\pi\) | ||||
0.440466 | + | 0.897769i | \(0.354813\pi\) | |||||||
\(618\) | 41.2202 | 1.65812 | ||||||||
\(619\) | −11.7419 | −0.471948 | −0.235974 | − | 0.971759i | \(-0.575828\pi\) | ||||
−0.235974 | + | 0.971759i | \(0.575828\pi\) | |||||||
\(620\) | −4.61002 | −0.185143 | ||||||||
\(621\) | −1.81881 | −0.0729863 | ||||||||
\(622\) | −5.44604 | −0.218366 | ||||||||
\(623\) | 4.67559 | 0.187324 | ||||||||
\(624\) | −6.09694 | −0.244073 | ||||||||
\(625\) | −31.0594 | −1.24238 | ||||||||
\(626\) | −27.5364 | −1.10057 | ||||||||
\(627\) | 11.7395 | 0.468829 | ||||||||
\(628\) | −3.77124 | −0.150489 | ||||||||
\(629\) | −17.2216 | −0.686670 | ||||||||
\(630\) | −54.6949 | −2.17910 | ||||||||
\(631\) | 32.1677 | 1.28058 | 0.640289 | − | 0.768134i | \(-0.278815\pi\) | ||||
0.640289 | + | 0.768134i | \(0.278815\pi\) | |||||||
\(632\) | 4.39928 | 0.174994 | ||||||||
\(633\) | −68.9271 | −2.73961 | ||||||||
\(634\) | −26.2604 | −1.04293 | ||||||||
\(635\) | −17.2728 | −0.685450 | ||||||||
\(636\) | −14.5693 | −0.577710 | ||||||||
\(637\) | −2.27349 | −0.0900789 | ||||||||
\(638\) | −2.24931 | −0.0890512 | ||||||||
\(639\) | −108.832 | −4.30534 | ||||||||
\(640\) | −2.81719 | −0.111359 | ||||||||
\(641\) | 8.66215 | 0.342134 | 0.171067 | − | 0.985259i | \(-0.445278\pi\) | ||||
0.171067 | + | 0.985259i | \(0.445278\pi\) | |||||||
\(642\) | −40.6304 | −1.60356 | ||||||||
\(643\) | 16.9542 | 0.668608 | 0.334304 | − | 0.942465i | \(-0.391499\pi\) | ||||
0.334304 | + | 0.942465i | \(0.391499\pi\) | |||||||
\(644\) | 0.257435 | 0.0101444 | ||||||||
\(645\) | 5.47333 | 0.215512 | ||||||||
\(646\) | 9.03883 | 0.355628 | ||||||||
\(647\) | −14.0414 | −0.552026 | −0.276013 | − | 0.961154i | \(-0.589013\pi\) | ||||
−0.276013 | + | 0.961154i | \(0.589013\pi\) | |||||||
\(648\) | 32.1879 | 1.26446 | ||||||||
\(649\) | −3.69393 | −0.145000 | ||||||||
\(650\) | 5.37614 | 0.210870 | ||||||||
\(651\) | −13.0770 | −0.512530 | ||||||||
\(652\) | 4.91488 | 0.192482 | ||||||||
\(653\) | −2.56636 | −0.100429 | −0.0502147 | − | 0.998738i | \(-0.515991\pi\) | ||||
−0.0502147 | + | 0.998738i | \(0.515991\pi\) | |||||||
\(654\) | −15.2059 | −0.594597 | ||||||||
\(655\) | 21.0668 | 0.823146 | ||||||||
\(656\) | −8.30191 | −0.324135 | ||||||||
\(657\) | 77.6017 | 3.02753 | ||||||||
\(658\) | −11.0256 | −0.429823 | ||||||||
\(659\) | −6.74059 | −0.262576 | −0.131288 | − | 0.991344i | \(-0.541911\pi\) | ||||
−0.131288 | + | 0.991344i | \(0.541911\pi\) | |||||||
\(660\) | 19.9007 | 0.774633 | ||||||||
\(661\) | −8.67051 | −0.337244 | −0.168622 | − | 0.985681i | \(-0.553932\pi\) | ||||
−0.168622 | + | 0.985681i | \(0.553932\pi\) | |||||||
\(662\) | −20.6672 | −0.803254 | ||||||||
\(663\) | 33.1610 | 1.28787 | ||||||||
\(664\) | −3.04167 | −0.118040 | ||||||||
\(665\) | 11.2345 | 0.435657 | ||||||||
\(666\) | 25.6180 | 0.992679 | ||||||||
\(667\) | −0.113764 | −0.00440495 | ||||||||
\(668\) | −5.12739 | −0.198385 | ||||||||
\(669\) | −3.62264 | −0.140059 | ||||||||
\(670\) | −8.59220 | −0.331946 | ||||||||
\(671\) | 23.6431 | 0.912733 | ||||||||
\(672\) | −7.99140 | −0.308275 | ||||||||
\(673\) | −39.9558 | −1.54018 | −0.770091 | − | 0.637934i | \(-0.779789\pi\) | ||||
−0.770091 | + | 0.637934i | \(0.779789\pi\) | |||||||
\(674\) | 10.1111 | 0.389466 | ||||||||
\(675\) | −49.7852 | −1.91623 | ||||||||
\(676\) | −9.64831 | −0.371089 | ||||||||
\(677\) | −42.7582 | −1.64333 | −0.821666 | − | 0.569969i | \(-0.806955\pi\) | ||||
−0.821666 | + | 0.569969i | \(0.806955\pi\) | |||||||
\(678\) | 39.2113 | 1.50590 | ||||||||
\(679\) | 6.02229 | 0.231114 | ||||||||
\(680\) | 15.3226 | 0.587594 | ||||||||
\(681\) | −86.3852 | −3.31029 | ||||||||
\(682\) | 3.47103 | 0.132913 | ||||||||
\(683\) | 13.9559 | 0.534007 | 0.267004 | − | 0.963696i | \(-0.413966\pi\) | ||||
0.267004 | + | 0.963696i | \(0.413966\pi\) | |||||||
\(684\) | −13.4458 | −0.514111 | ||||||||
\(685\) | −31.9391 | −1.22033 | ||||||||
\(686\) | −19.7772 | −0.755099 | ||||||||
\(687\) | 19.5984 | 0.747727 | ||||||||
\(688\) | 0.583384 | 0.0222413 | ||||||||
\(689\) | 8.00921 | 0.305127 | ||||||||
\(690\) | 1.00652 | 0.0383175 | ||||||||
\(691\) | −3.78684 | −0.144058 | −0.0720290 | − | 0.997403i | \(-0.522947\pi\) | ||||
−0.0720290 | + | 0.997403i | \(0.522947\pi\) | |||||||
\(692\) | −5.95165 | −0.226248 | ||||||||
\(693\) | 41.1815 | 1.56436 | ||||||||
\(694\) | 23.8158 | 0.904035 | ||||||||
\(695\) | −43.9366 | −1.66661 | ||||||||
\(696\) | 3.53150 | 0.133861 | ||||||||
\(697\) | 45.1537 | 1.71032 | ||||||||
\(698\) | −11.5771 | −0.438201 | ||||||||
\(699\) | −67.0736 | −2.53696 | ||||||||
\(700\) | 7.04663 | 0.266337 | ||||||||
\(701\) | 14.3234 | 0.540989 | 0.270494 | − | 0.962722i | \(-0.412813\pi\) | ||||
0.270494 | + | 0.962722i | \(0.412813\pi\) | |||||||
\(702\) | −31.0380 | −1.17145 | ||||||||
\(703\) | −5.26204 | −0.198462 | ||||||||
\(704\) | 2.12115 | 0.0799439 | ||||||||
\(705\) | −43.1078 | −1.62354 | ||||||||
\(706\) | 10.4598 | 0.393661 | ||||||||
\(707\) | −10.3162 | −0.387982 | ||||||||
\(708\) | 5.79960 | 0.217962 | ||||||||
\(709\) | 30.9629 | 1.16284 | 0.581419 | − | 0.813604i | \(-0.302498\pi\) | ||||
0.581419 | + | 0.813604i | \(0.302498\pi\) | |||||||
\(710\) | 37.8953 | 1.42219 | ||||||||
\(711\) | 35.5935 | 1.33486 | ||||||||
\(712\) | 1.94847 | 0.0730220 | ||||||||
\(713\) | 0.175555 | 0.00657457 | ||||||||
\(714\) | 43.4649 | 1.62663 | ||||||||
\(715\) | −10.9401 | −0.409135 | ||||||||
\(716\) | −5.15343 | −0.192593 | ||||||||
\(717\) | 21.4046 | 0.799369 | ||||||||
\(718\) | 21.2970 | 0.794797 | ||||||||
\(719\) | −24.6366 | −0.918791 | −0.459395 | − | 0.888232i | \(-0.651934\pi\) | ||||
−0.459395 | + | 0.888232i | \(0.651934\pi\) | |||||||
\(720\) | −22.7932 | −0.849451 | ||||||||
\(721\) | −29.7010 | −1.10612 | ||||||||
\(722\) | −16.2382 | −0.604323 | ||||||||
\(723\) | 77.5301 | 2.88337 | ||||||||
\(724\) | 7.73594 | 0.287504 | ||||||||
\(725\) | −3.11399 | −0.115651 | ||||||||
\(726\) | 21.6492 | 0.803477 | ||||||||
\(727\) | 28.7483 | 1.06622 | 0.533108 | − | 0.846047i | \(-0.321024\pi\) | ||||
0.533108 | + | 0.846047i | \(0.321024\pi\) | |||||||
\(728\) | 4.39313 | 0.162820 | ||||||||
\(729\) | 91.0438 | 3.37199 | ||||||||
\(730\) | −27.0208 | −1.00009 | ||||||||
\(731\) | −3.17300 | −0.117358 | ||||||||
\(732\) | −37.1205 | −1.37201 | ||||||||
\(733\) | 12.2348 | 0.451904 | 0.225952 | − | 0.974138i | \(-0.427451\pi\) | ||||
0.225952 | + | 0.974138i | \(0.427451\pi\) | |||||||
\(734\) | 5.65006 | 0.208548 | ||||||||
\(735\) | −11.6508 | −0.429748 | ||||||||
\(736\) | 0.107282 | 0.00395445 | ||||||||
\(737\) | 6.46934 | 0.238301 | ||||||||
\(738\) | −67.1686 | −2.47251 | ||||||||
\(739\) | −51.7245 | −1.90272 | −0.951359 | − | 0.308085i | \(-0.900312\pi\) | ||||
−0.951359 | + | 0.308085i | \(0.900312\pi\) | |||||||
\(740\) | −8.92018 | −0.327912 | ||||||||
\(741\) | 10.1323 | 0.372220 | ||||||||
\(742\) | 10.4978 | 0.385388 | ||||||||
\(743\) | 9.33473 | 0.342458 | 0.171229 | − | 0.985231i | \(-0.445226\pi\) | ||||
0.171229 | + | 0.985231i | \(0.445226\pi\) | |||||||
\(744\) | −5.44963 | −0.199793 | ||||||||
\(745\) | 13.8073 | 0.505860 | ||||||||
\(746\) | −32.2999 | −1.18259 | ||||||||
\(747\) | −24.6093 | −0.900409 | ||||||||
\(748\) | −11.5369 | −0.421829 | ||||||||
\(749\) | 29.2761 | 1.06973 | ||||||||
\(750\) | −19.3592 | −0.706900 | ||||||||
\(751\) | −25.9816 | −0.948081 | −0.474040 | − | 0.880503i | \(-0.657205\pi\) | ||||
−0.474040 | + | 0.880503i | \(0.657205\pi\) | |||||||
\(752\) | −4.59473 | −0.167552 | ||||||||
\(753\) | 68.1262 | 2.48266 | ||||||||
\(754\) | −1.94138 | −0.0707009 | ||||||||
\(755\) | −22.1315 | −0.805446 | ||||||||
\(756\) | −40.6822 | −1.47960 | ||||||||
\(757\) | −5.54040 | −0.201369 | −0.100685 | − | 0.994918i | \(-0.532103\pi\) | ||||
−0.100685 | + | 0.994918i | \(0.532103\pi\) | |||||||
\(758\) | −17.0409 | −0.618955 | ||||||||
\(759\) | −0.757840 | −0.0275078 | ||||||||
\(760\) | 4.68180 | 0.169827 | ||||||||
\(761\) | 19.6930 | 0.713869 | 0.356934 | − | 0.934129i | \(-0.383822\pi\) | ||||
0.356934 | + | 0.934129i | \(0.383822\pi\) | |||||||
\(762\) | −20.4187 | −0.739690 | ||||||||
\(763\) | 10.9565 | 0.396654 | ||||||||
\(764\) | −23.6317 | −0.854967 | ||||||||
\(765\) | 123.971 | 4.48218 | ||||||||
\(766\) | −3.21939 | −0.116321 | ||||||||
\(767\) | −3.18823 | −0.115120 | ||||||||
\(768\) | −3.33028 | −0.120171 | ||||||||
\(769\) | −4.14681 | −0.149538 | −0.0747689 | − | 0.997201i | \(-0.523822\pi\) | ||||
−0.0747689 | + | 0.997201i | \(0.523822\pi\) | |||||||
\(770\) | −14.3394 | −0.516755 | ||||||||
\(771\) | 35.5151 | 1.27905 | ||||||||
\(772\) | −19.0384 | −0.685208 | ||||||||
\(773\) | −9.06029 | −0.325876 | −0.162938 | − | 0.986636i | \(-0.552097\pi\) | ||||
−0.162938 | + | 0.986636i | \(0.552097\pi\) | |||||||
\(774\) | 4.72001 | 0.169657 | ||||||||
\(775\) | 4.80536 | 0.172614 | ||||||||
\(776\) | 2.50969 | 0.0900925 | ||||||||
\(777\) | −25.3035 | −0.907757 | ||||||||
\(778\) | 3.82490 | 0.137129 | ||||||||
\(779\) | 13.7967 | 0.494317 | ||||||||
\(780\) | 17.1763 | 0.615008 | ||||||||
\(781\) | −28.5326 | −1.02098 | ||||||||
\(782\) | −0.583500 | −0.0208659 | ||||||||
\(783\) | 17.9780 | 0.642480 | ||||||||
\(784\) | −1.24183 | −0.0443509 | ||||||||
\(785\) | 10.6243 | 0.379197 | ||||||||
\(786\) | 24.9036 | 0.888281 | ||||||||
\(787\) | 13.6413 | 0.486259 | 0.243129 | − | 0.969994i | \(-0.421826\pi\) | ||||
0.243129 | + | 0.969994i | \(0.421826\pi\) | |||||||
\(788\) | −1.31035 | −0.0466792 | ||||||||
\(789\) | −28.8063 | −1.02553 | ||||||||
\(790\) | −12.3936 | −0.440945 | ||||||||
\(791\) | −28.2535 | −1.00458 | ||||||||
\(792\) | 17.1617 | 0.609814 | ||||||||
\(793\) | 20.4063 | 0.724650 | ||||||||
\(794\) | −7.26808 | −0.257934 | ||||||||
\(795\) | 41.0444 | 1.45570 | ||||||||
\(796\) | −22.0771 | −0.782503 | ||||||||
\(797\) | −3.56460 | −0.126265 | −0.0631323 | − | 0.998005i | \(-0.520109\pi\) | ||||
−0.0631323 | + | 0.998005i | \(0.520109\pi\) | |||||||
\(798\) | 13.2806 | 0.470130 | ||||||||
\(799\) | 24.9905 | 0.884102 | ||||||||
\(800\) | 2.93656 | 0.103823 | ||||||||
\(801\) | 15.7646 | 0.557014 | ||||||||
\(802\) | −32.7088 | −1.15499 | ||||||||
\(803\) | 20.3448 | 0.717954 | ||||||||
\(804\) | −10.1571 | −0.358213 | ||||||||
\(805\) | −0.725244 | −0.0255615 | ||||||||
\(806\) | 2.99584 | 0.105524 | ||||||||
\(807\) | 0.540375 | 0.0190221 | ||||||||
\(808\) | −4.29911 | −0.151242 | ||||||||
\(809\) | −35.3274 | −1.24204 | −0.621022 | − | 0.783793i | \(-0.713282\pi\) | ||||
−0.621022 | + | 0.783793i | \(0.713282\pi\) | |||||||
\(810\) | −90.6795 | −3.18615 | ||||||||
\(811\) | 27.0764 | 0.950780 | 0.475390 | − | 0.879775i | \(-0.342307\pi\) | ||||
0.475390 | + | 0.879775i | \(0.342307\pi\) | |||||||
\(812\) | −2.54461 | −0.0892982 | ||||||||
\(813\) | 23.3392 | 0.818543 | ||||||||
\(814\) | 6.71629 | 0.235406 | ||||||||
\(815\) | −13.8462 | −0.485010 | ||||||||
\(816\) | 18.1132 | 0.634090 | ||||||||
\(817\) | −0.969508 | −0.0339188 | ||||||||
\(818\) | 14.8357 | 0.518717 | ||||||||
\(819\) | 35.5437 | 1.24200 | ||||||||
\(820\) | 23.3880 | 0.816746 | ||||||||
\(821\) | 2.97788 | 0.103929 | 0.0519643 | − | 0.998649i | \(-0.483452\pi\) | ||||
0.0519643 | + | 0.998649i | \(0.483452\pi\) | |||||||
\(822\) | −37.7561 | −1.31690 | ||||||||
\(823\) | 6.28468 | 0.219070 | 0.109535 | − | 0.993983i | \(-0.465064\pi\) | ||||
0.109535 | + | 0.993983i | \(0.465064\pi\) | |||||||
\(824\) | −12.3774 | −0.431187 | ||||||||
\(825\) | −20.7439 | −0.722211 | ||||||||
\(826\) | −4.17888 | −0.145402 | ||||||||
\(827\) | −56.0991 | −1.95076 | −0.975378 | − | 0.220541i | \(-0.929218\pi\) | ||||
−0.975378 | + | 0.220541i | \(0.929218\pi\) | |||||||
\(828\) | 0.867988 | 0.0301647 | ||||||||
\(829\) | −36.0773 | −1.25302 | −0.626508 | − | 0.779415i | \(-0.715516\pi\) | ||||
−0.626508 | + | 0.779415i | \(0.715516\pi\) | |||||||
\(830\) | 8.56895 | 0.297433 | ||||||||
\(831\) | 84.3524 | 2.92615 | ||||||||
\(832\) | 1.83076 | 0.0634703 | ||||||||
\(833\) | 6.75424 | 0.234021 | ||||||||
\(834\) | −51.9386 | −1.79849 | ||||||||
\(835\) | 14.4448 | 0.499884 | ||||||||
\(836\) | −3.52507 | −0.121917 | ||||||||
\(837\) | −27.7427 | −0.958928 | ||||||||
\(838\) | −2.90261 | −0.100269 | ||||||||
\(839\) | −0.301000 | −0.0103917 | −0.00519584 | − | 0.999987i | \(-0.501654\pi\) | ||||
−0.00519584 | + | 0.999987i | \(0.501654\pi\) | |||||||
\(840\) | 22.5133 | 0.776782 | ||||||||
\(841\) | −27.8755 | −0.961224 | ||||||||
\(842\) | −6.00890 | −0.207080 | ||||||||
\(843\) | 51.5635 | 1.77594 | ||||||||
\(844\) | 20.6971 | 0.712424 | ||||||||
\(845\) | 27.1811 | 0.935059 | ||||||||
\(846\) | −37.1748 | −1.27809 | ||||||||
\(847\) | −15.5992 | −0.535996 | ||||||||
\(848\) | 4.37480 | 0.150231 | ||||||||
\(849\) | 14.1026 | 0.484001 | ||||||||
\(850\) | −15.9718 | −0.547829 | ||||||||
\(851\) | 0.339690 | 0.0116444 | ||||||||
\(852\) | 44.7971 | 1.53472 | ||||||||
\(853\) | 22.8861 | 0.783606 | 0.391803 | − | 0.920049i | \(-0.371851\pi\) | ||||
0.391803 | + | 0.920049i | \(0.371851\pi\) | |||||||
\(854\) | 26.7470 | 0.915264 | ||||||||
\(855\) | 37.8792 | 1.29544 | ||||||||
\(856\) | 12.2003 | 0.416998 | ||||||||
\(857\) | −11.1541 | −0.381018 | −0.190509 | − | 0.981685i | \(-0.561014\pi\) | ||||
−0.190509 | + | 0.981685i | \(0.561014\pi\) | |||||||
\(858\) | −12.9325 | −0.441510 | ||||||||
\(859\) | 41.7654 | 1.42502 | 0.712508 | − | 0.701664i | \(-0.247559\pi\) | ||||
0.712508 | + | 0.701664i | \(0.247559\pi\) | |||||||
\(860\) | −1.64350 | −0.0560430 | ||||||||
\(861\) | 66.3438 | 2.26099 | ||||||||
\(862\) | −1.07201 | −0.0365128 | ||||||||
\(863\) | 26.6667 | 0.907743 | 0.453872 | − | 0.891067i | \(-0.350042\pi\) | ||||
0.453872 | + | 0.891067i | \(0.350042\pi\) | |||||||
\(864\) | −16.9536 | −0.576773 | ||||||||
\(865\) | 16.7669 | 0.570093 | ||||||||
\(866\) | −5.71521 | −0.194211 | ||||||||
\(867\) | −41.9025 | −1.42308 | ||||||||
\(868\) | 3.92671 | 0.133281 | ||||||||
\(869\) | 9.33154 | 0.316551 | ||||||||
\(870\) | −9.94890 | −0.337299 | ||||||||
\(871\) | 5.58368 | 0.189196 | ||||||||
\(872\) | 4.56595 | 0.154623 | ||||||||
\(873\) | 20.3052 | 0.687228 | ||||||||
\(874\) | −0.178288 | −0.00603068 | ||||||||
\(875\) | 13.9492 | 0.471570 | ||||||||
\(876\) | −31.9421 | −1.07922 | ||||||||
\(877\) | −27.7169 | −0.935935 | −0.467967 | − | 0.883746i | \(-0.655014\pi\) | ||||
−0.467967 | + | 0.883746i | \(0.655014\pi\) | |||||||
\(878\) | 22.8507 | 0.771174 | ||||||||
\(879\) | −76.5901 | −2.58332 | ||||||||
\(880\) | −5.97569 | −0.201440 | ||||||||
\(881\) | 0.0685907 | 0.00231088 | 0.00115544 | − | 0.999999i | \(-0.499632\pi\) | ||||
0.00115544 | + | 0.999999i | \(0.499632\pi\) | |||||||
\(882\) | −10.0473 | −0.338310 | ||||||||
\(883\) | −7.30373 | −0.245790 | −0.122895 | − | 0.992420i | \(-0.539218\pi\) | ||||
−0.122895 | + | 0.992420i | \(0.539218\pi\) | |||||||
\(884\) | −9.95744 | −0.334905 | ||||||||
\(885\) | −16.3386 | −0.549215 | ||||||||
\(886\) | −21.3288 | −0.716553 | ||||||||
\(887\) | 48.1931 | 1.61817 | 0.809083 | − | 0.587694i | \(-0.199964\pi\) | ||||
0.809083 | + | 0.587694i | \(0.199964\pi\) | |||||||
\(888\) | −10.5448 | −0.353860 | ||||||||
\(889\) | 14.7126 | 0.493444 | ||||||||
\(890\) | −5.48921 | −0.183999 | ||||||||
\(891\) | 68.2755 | 2.28731 | ||||||||
\(892\) | 1.08779 | 0.0364219 | ||||||||
\(893\) | 7.63583 | 0.255523 | ||||||||
\(894\) | 16.3220 | 0.545888 | ||||||||
\(895\) | 14.5182 | 0.485290 | ||||||||
\(896\) | 2.39962 | 0.0801657 | ||||||||
\(897\) | −0.654090 | −0.0218394 | ||||||||
\(898\) | −5.71138 | −0.190591 | ||||||||
\(899\) | −1.73526 | −0.0578743 | ||||||||
\(900\) | 23.7590 | 0.791965 | ||||||||
\(901\) | −23.7943 | −0.792704 | ||||||||
\(902\) | −17.6096 | −0.586336 | ||||||||
\(903\) | −4.66206 | −0.155144 | ||||||||
\(904\) | −11.7742 | −0.391603 | ||||||||
\(905\) | −21.7936 | −0.724445 | ||||||||
\(906\) | −26.1622 | −0.869181 | ||||||||
\(907\) | 13.4155 | 0.445453 | 0.222726 | − | 0.974881i | \(-0.428504\pi\) | ||||
0.222726 | + | 0.974881i | \(0.428504\pi\) | |||||||
\(908\) | 25.9393 | 0.860827 | ||||||||
\(909\) | −34.7830 | −1.15368 | ||||||||
\(910\) | −12.3763 | −0.410270 | ||||||||
\(911\) | 51.3465 | 1.70119 | 0.850593 | − | 0.525825i | \(-0.176243\pi\) | ||||
0.850593 | + | 0.525825i | \(0.176243\pi\) | |||||||
\(912\) | 5.53448 | 0.183265 | ||||||||
\(913\) | −6.45183 | −0.213525 | ||||||||
\(914\) | −12.8557 | −0.425229 | ||||||||
\(915\) | 104.575 | 3.45716 | ||||||||
\(916\) | −5.88492 | −0.194443 | ||||||||
\(917\) | −17.9442 | −0.592569 | ||||||||
\(918\) | 92.2099 | 3.04338 | ||||||||
\(919\) | 46.9713 | 1.54944 | 0.774721 | − | 0.632304i | \(-0.217890\pi\) | ||||
0.774721 | + | 0.632304i | \(0.217890\pi\) | |||||||
\(920\) | −0.302233 | −0.00996432 | ||||||||
\(921\) | −83.1746 | −2.74069 | ||||||||
\(922\) | 10.3980 | 0.342441 | ||||||||
\(923\) | −24.6264 | −0.810588 | ||||||||
\(924\) | −16.9510 | −0.557646 | ||||||||
\(925\) | 9.29815 | 0.305721 | ||||||||
\(926\) | 34.5449 | 1.13521 | ||||||||
\(927\) | −100.142 | −3.28911 | ||||||||
\(928\) | −1.06042 | −0.0348100 | ||||||||
\(929\) | 41.3379 | 1.35625 | 0.678126 | − | 0.734946i | \(-0.262792\pi\) | ||||
0.678126 | + | 0.734946i | \(0.262792\pi\) | |||||||
\(930\) | 15.3526 | 0.503433 | ||||||||
\(931\) | 2.06375 | 0.0676367 | ||||||||
\(932\) | 20.1406 | 0.659726 | ||||||||
\(933\) | 18.1368 | 0.593773 | ||||||||
\(934\) | −28.5935 | −0.935607 | ||||||||
\(935\) | 32.5015 | 1.06291 | ||||||||
\(936\) | 14.8122 | 0.484153 | ||||||||
\(937\) | −39.1541 | −1.27911 | −0.639554 | − | 0.768746i | \(-0.720881\pi\) | ||||
−0.639554 | + | 0.768746i | \(0.720881\pi\) | |||||||
\(938\) | 7.31865 | 0.238962 | ||||||||
\(939\) | 91.7037 | 2.99264 | ||||||||
\(940\) | 12.9442 | 0.422194 | ||||||||
\(941\) | −14.0427 | −0.457780 | −0.228890 | − | 0.973452i | \(-0.573510\pi\) | ||||
−0.228890 | + | 0.973452i | \(0.573510\pi\) | |||||||
\(942\) | 12.5593 | 0.409203 | ||||||||
\(943\) | −0.890642 | −0.0290033 | ||||||||
\(944\) | −1.74148 | −0.0566802 | ||||||||
\(945\) | 114.609 | 3.72824 | ||||||||
\(946\) | 1.23745 | 0.0402329 | ||||||||
\(947\) | 25.2671 | 0.821071 | 0.410536 | − | 0.911845i | \(-0.365342\pi\) | ||||
0.410536 | + | 0.911845i | \(0.365342\pi\) | |||||||
\(948\) | −14.6508 | −0.475837 | ||||||||
\(949\) | 17.5596 | 0.570009 | ||||||||
\(950\) | −4.88017 | −0.158334 | ||||||||
\(951\) | 87.4545 | 2.83591 | ||||||||
\(952\) | −13.0514 | −0.422999 | ||||||||
\(953\) | −31.9366 | −1.03453 | −0.517264 | − | 0.855826i | \(-0.673049\pi\) | ||||
−0.517264 | + | 0.855826i | \(0.673049\pi\) | |||||||
\(954\) | 35.3954 | 1.14597 | ||||||||
\(955\) | 66.5751 | 2.15432 | ||||||||
\(956\) | −6.42727 | −0.207873 | ||||||||
\(957\) | 7.49084 | 0.242144 | ||||||||
\(958\) | −22.0974 | −0.713935 | ||||||||
\(959\) | 27.2050 | 0.878496 | ||||||||
\(960\) | 9.38202 | 0.302804 | ||||||||
\(961\) | −28.3222 | −0.913620 | ||||||||
\(962\) | 5.79681 | 0.186897 | ||||||||
\(963\) | 98.7097 | 3.18087 | ||||||||
\(964\) | −23.2804 | −0.749810 | ||||||||
\(965\) | 53.6348 | 1.72657 | ||||||||
\(966\) | −0.857330 | −0.0275841 | ||||||||
\(967\) | 29.8448 | 0.959745 | 0.479873 | − | 0.877338i | \(-0.340683\pi\) | ||||
0.479873 | + | 0.877338i | \(0.340683\pi\) | |||||||
\(968\) | −6.50072 | −0.208941 | ||||||||
\(969\) | −30.1018 | −0.967010 | ||||||||
\(970\) | −7.07026 | −0.227013 | ||||||||
\(971\) | −20.7398 | −0.665573 | −0.332787 | − | 0.943002i | \(-0.607989\pi\) | ||||
−0.332787 | + | 0.943002i | \(0.607989\pi\) | |||||||
\(972\) | −56.3339 | −1.80691 | ||||||||
\(973\) | 37.4242 | 1.19976 | ||||||||
\(974\) | −1.51950 | −0.0486878 | ||||||||
\(975\) | −17.9040 | −0.573388 | ||||||||
\(976\) | 11.1464 | 0.356786 | ||||||||
\(977\) | 2.94798 | 0.0943144 | 0.0471572 | − | 0.998887i | \(-0.484984\pi\) | ||||
0.0471572 | + | 0.998887i | \(0.484984\pi\) | |||||||
\(978\) | −16.3679 | −0.523388 | ||||||||
\(979\) | 4.13300 | 0.132091 | ||||||||
\(980\) | 3.49846 | 0.111754 | ||||||||
\(981\) | 36.9420 | 1.17947 | ||||||||
\(982\) | −13.3366 | −0.425587 | ||||||||
\(983\) | −12.5555 | −0.400457 | −0.200228 | − | 0.979749i | \(-0.564168\pi\) | ||||
−0.200228 | + | 0.979749i | \(0.564168\pi\) | |||||||
\(984\) | 27.6476 | 0.881375 | ||||||||
\(985\) | 3.69150 | 0.117621 | ||||||||
\(986\) | 5.76759 | 0.183677 | ||||||||
\(987\) | 36.7183 | 1.16876 | ||||||||
\(988\) | −3.04248 | −0.0967943 | ||||||||
\(989\) | 0.0625864 | 0.00199013 | ||||||||
\(990\) | −48.3478 | −1.53659 | ||||||||
\(991\) | 31.8321 | 1.01118 | 0.505589 | − | 0.862774i | \(-0.331275\pi\) | ||||
0.505589 | + | 0.862774i | \(0.331275\pi\) | |||||||
\(992\) | 1.63639 | 0.0519554 | ||||||||
\(993\) | 68.8275 | 2.18418 | ||||||||
\(994\) | −32.2784 | −1.02381 | ||||||||
\(995\) | 62.1955 | 1.97173 | ||||||||
\(996\) | 10.1296 | 0.320968 | ||||||||
\(997\) | −17.5521 | −0.555879 | −0.277940 | − | 0.960599i | \(-0.589651\pi\) | ||||
−0.277940 | + | 0.960599i | \(0.589651\pi\) | |||||||
\(998\) | −14.9268 | −0.472501 | ||||||||
\(999\) | −53.6808 | −1.69839 |
(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 | 8026.2.a.a.1.1 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8026.2.a.a.1.1 | ✓ | 71 | 1.1 | even | 1 | trivial |