Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.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: | \(64.2236783457\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.33165 | −1.64873 | −0.824364 | − | 0.566059i | \(-0.808467\pi\) | ||||
−0.824364 | + | 0.566059i | \(0.808467\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.43661 | 1.71831 | ||||||||
\(5\) | −1.59780 | −0.714557 | −0.357278 | − | 0.933998i | \(-0.616295\pi\) | ||||
−0.357278 | + | 0.933998i | \(0.616295\pi\) | |||||||
\(6\) | 2.33165 | 0.951894 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −3.34969 | −1.18429 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.72551 | 1.17811 | ||||||||
\(11\) | −5.81283 | −1.75264 | −0.876318 | − | 0.481734i | \(-0.840007\pi\) | ||||
−0.876318 | + | 0.481734i | \(0.840007\pi\) | |||||||
\(12\) | −3.43661 | −0.992065 | ||||||||
\(13\) | −0.402462 | −0.111623 | −0.0558114 | − | 0.998441i | \(-0.517775\pi\) | ||||
−0.0558114 | + | 0.998441i | \(0.517775\pi\) | |||||||
\(14\) | 2.33165 | 0.623161 | ||||||||
\(15\) | 1.59780 | 0.412549 | ||||||||
\(16\) | 0.937085 | 0.234271 | ||||||||
\(17\) | 0.289318 | 0.0701700 | 0.0350850 | − | 0.999384i | \(-0.488830\pi\) | ||||
0.0350850 | + | 0.999384i | \(0.488830\pi\) | |||||||
\(18\) | −2.33165 | −0.549576 | ||||||||
\(19\) | 4.51626 | 1.03610 | 0.518050 | − | 0.855350i | \(-0.326658\pi\) | ||||
0.518050 | + | 0.855350i | \(0.326658\pi\) | |||||||
\(20\) | −5.49101 | −1.22783 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 13.5535 | 2.88962 | ||||||||
\(23\) | 7.54020 | 1.57224 | 0.786120 | − | 0.618074i | \(-0.212087\pi\) | ||||
0.786120 | + | 0.618074i | \(0.212087\pi\) | |||||||
\(24\) | 3.34969 | 0.683752 | ||||||||
\(25\) | −2.44704 | −0.489409 | ||||||||
\(26\) | 0.938402 | 0.184036 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.43661 | −0.649459 | ||||||||
\(29\) | 7.97204 | 1.48037 | 0.740185 | − | 0.672403i | \(-0.234738\pi\) | ||||
0.740185 | + | 0.672403i | \(0.234738\pi\) | |||||||
\(30\) | −3.72551 | −0.680182 | ||||||||
\(31\) | 5.94230 | 1.06727 | 0.533635 | − | 0.845715i | \(-0.320826\pi\) | ||||
0.533635 | + | 0.845715i | \(0.320826\pi\) | |||||||
\(32\) | 4.51441 | 0.798043 | ||||||||
\(33\) | 5.81283 | 1.01188 | ||||||||
\(34\) | −0.674591 | −0.115691 | ||||||||
\(35\) | 1.59780 | 0.270077 | ||||||||
\(36\) | 3.43661 | 0.572769 | ||||||||
\(37\) | −0.443031 | −0.0728339 | −0.0364169 | − | 0.999337i | \(-0.511594\pi\) | ||||
−0.0364169 | + | 0.999337i | \(0.511594\pi\) | |||||||
\(38\) | −10.5303 | −1.70825 | ||||||||
\(39\) | 0.402462 | 0.0644455 | ||||||||
\(40\) | 5.35212 | 0.846244 | ||||||||
\(41\) | −5.28630 | −0.825581 | −0.412790 | − | 0.910826i | \(-0.635446\pi\) | ||||
−0.412790 | + | 0.910826i | \(0.635446\pi\) | |||||||
\(42\) | −2.33165 | −0.359782 | ||||||||
\(43\) | 9.72378 | 1.48286 | 0.741431 | − | 0.671029i | \(-0.234147\pi\) | ||||
0.741431 | + | 0.671029i | \(0.234147\pi\) | |||||||
\(44\) | −19.9765 | −3.01156 | ||||||||
\(45\) | −1.59780 | −0.238186 | ||||||||
\(46\) | −17.5811 | −2.59220 | ||||||||
\(47\) | 3.02531 | 0.441287 | 0.220643 | − | 0.975355i | \(-0.429184\pi\) | ||||
0.220643 | + | 0.975355i | \(0.429184\pi\) | |||||||
\(48\) | −0.937085 | −0.135257 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 5.70566 | 0.806903 | ||||||||
\(51\) | −0.289318 | −0.0405127 | ||||||||
\(52\) | −1.38311 | −0.191802 | ||||||||
\(53\) | −10.7576 | −1.47767 | −0.738836 | − | 0.673885i | \(-0.764624\pi\) | ||||
−0.738836 | + | 0.673885i | \(0.764624\pi\) | |||||||
\(54\) | 2.33165 | 0.317298 | ||||||||
\(55\) | 9.28773 | 1.25236 | ||||||||
\(56\) | 3.34969 | 0.447621 | ||||||||
\(57\) | −4.51626 | −0.598193 | ||||||||
\(58\) | −18.5880 | −2.44073 | ||||||||
\(59\) | −2.00386 | −0.260881 | −0.130440 | − | 0.991456i | \(-0.541639\pi\) | ||||
−0.130440 | + | 0.991456i | \(0.541639\pi\) | |||||||
\(60\) | 5.49101 | 0.708886 | ||||||||
\(61\) | 6.76064 | 0.865612 | 0.432806 | − | 0.901487i | \(-0.357524\pi\) | ||||
0.432806 | + | 0.901487i | \(0.357524\pi\) | |||||||
\(62\) | −13.8554 | −1.75964 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −12.4002 | −1.55003 | ||||||||
\(65\) | 0.643052 | 0.0797608 | ||||||||
\(66\) | −13.5535 | −1.66832 | ||||||||
\(67\) | −4.93512 | −0.602920 | −0.301460 | − | 0.953479i | \(-0.597474\pi\) | ||||
−0.301460 | + | 0.953479i | \(0.597474\pi\) | |||||||
\(68\) | 0.994276 | 0.120574 | ||||||||
\(69\) | −7.54020 | −0.907734 | ||||||||
\(70\) | −3.72551 | −0.445284 | ||||||||
\(71\) | −12.7643 | −1.51485 | −0.757424 | − | 0.652923i | \(-0.773543\pi\) | ||||
−0.757424 | + | 0.652923i | \(0.773543\pi\) | |||||||
\(72\) | −3.34969 | −0.394764 | ||||||||
\(73\) | 10.1541 | 1.18844 | 0.594221 | − | 0.804302i | \(-0.297460\pi\) | ||||
0.594221 | + | 0.804302i | \(0.297460\pi\) | |||||||
\(74\) | 1.03300 | 0.120083 | ||||||||
\(75\) | 2.44704 | 0.282560 | ||||||||
\(76\) | 15.5206 | 1.78034 | ||||||||
\(77\) | 5.81283 | 0.662434 | ||||||||
\(78\) | −0.938402 | −0.106253 | ||||||||
\(79\) | 2.61238 | 0.293916 | 0.146958 | − | 0.989143i | \(-0.453052\pi\) | ||||
0.146958 | + | 0.989143i | \(0.453052\pi\) | |||||||
\(80\) | −1.49727 | −0.167400 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 12.3258 | 1.36116 | ||||||||
\(83\) | −16.0045 | −1.75672 | −0.878362 | − | 0.477995i | \(-0.841364\pi\) | ||||
−0.878362 | + | 0.477995i | \(0.841364\pi\) | |||||||
\(84\) | 3.43661 | 0.374965 | ||||||||
\(85\) | −0.462272 | −0.0501405 | ||||||||
\(86\) | −22.6725 | −2.44484 | ||||||||
\(87\) | −7.97204 | −0.854692 | ||||||||
\(88\) | 19.4712 | 2.07563 | ||||||||
\(89\) | −7.22871 | −0.766241 | −0.383121 | − | 0.923698i | \(-0.625151\pi\) | ||||
−0.383121 | + | 0.923698i | \(0.625151\pi\) | |||||||
\(90\) | 3.72551 | 0.392703 | ||||||||
\(91\) | 0.402462 | 0.0421895 | ||||||||
\(92\) | 25.9128 | 2.70159 | ||||||||
\(93\) | −5.94230 | −0.616188 | ||||||||
\(94\) | −7.05398 | −0.727562 | ||||||||
\(95\) | −7.21606 | −0.740352 | ||||||||
\(96\) | −4.51441 | −0.460750 | ||||||||
\(97\) | −16.6173 | −1.68723 | −0.843617 | − | 0.536946i | \(-0.819578\pi\) | ||||
−0.843617 | + | 0.536946i | \(0.819578\pi\) | |||||||
\(98\) | −2.33165 | −0.235533 | ||||||||
\(99\) | −5.81283 | −0.584212 | ||||||||
\(100\) | −8.40955 | −0.840955 | ||||||||
\(101\) | −14.3690 | −1.42977 | −0.714886 | − | 0.699241i | \(-0.753521\pi\) | ||||
−0.714886 | + | 0.699241i | \(0.753521\pi\) | |||||||
\(102\) | 0.674591 | 0.0667944 | ||||||||
\(103\) | −0.298231 | −0.0293856 | −0.0146928 | − | 0.999892i | \(-0.504677\pi\) | ||||
−0.0146928 | + | 0.999892i | \(0.504677\pi\) | |||||||
\(104\) | 1.34812 | 0.132194 | ||||||||
\(105\) | −1.59780 | −0.155929 | ||||||||
\(106\) | 25.0830 | 2.43628 | ||||||||
\(107\) | 14.1875 | 1.37156 | 0.685779 | − | 0.727809i | \(-0.259461\pi\) | ||||
0.685779 | + | 0.727809i | \(0.259461\pi\) | |||||||
\(108\) | −3.43661 | −0.330688 | ||||||||
\(109\) | 4.30479 | 0.412324 | 0.206162 | − | 0.978518i | \(-0.433903\pi\) | ||||
0.206162 | + | 0.978518i | \(0.433903\pi\) | |||||||
\(110\) | −21.6558 | −2.06480 | ||||||||
\(111\) | 0.443031 | 0.0420506 | ||||||||
\(112\) | −0.937085 | −0.0885462 | ||||||||
\(113\) | −2.54672 | −0.239575 | −0.119788 | − | 0.992800i | \(-0.538221\pi\) | ||||
−0.119788 | + | 0.992800i | \(0.538221\pi\) | |||||||
\(114\) | 10.5303 | 0.986257 | ||||||||
\(115\) | −12.0477 | −1.12345 | ||||||||
\(116\) | 27.3968 | 2.54373 | ||||||||
\(117\) | −0.402462 | −0.0372076 | ||||||||
\(118\) | 4.67232 | 0.430122 | ||||||||
\(119\) | −0.289318 | −0.0265218 | ||||||||
\(120\) | −5.35212 | −0.488579 | ||||||||
\(121\) | 22.7890 | 2.07173 | ||||||||
\(122\) | −15.7635 | −1.42716 | ||||||||
\(123\) | 5.28630 | 0.476649 | ||||||||
\(124\) | 20.4214 | 1.83390 | ||||||||
\(125\) | 11.8989 | 1.06427 | ||||||||
\(126\) | 2.33165 | 0.207720 | ||||||||
\(127\) | 1.10147 | 0.0977397 | 0.0488699 | − | 0.998805i | \(-0.484438\pi\) | ||||
0.0488699 | + | 0.998805i | \(0.484438\pi\) | |||||||
\(128\) | 19.8842 | 1.75753 | ||||||||
\(129\) | −9.72378 | −0.856131 | ||||||||
\(130\) | −1.49938 | −0.131504 | ||||||||
\(131\) | 5.65688 | 0.494244 | 0.247122 | − | 0.968984i | \(-0.420515\pi\) | ||||
0.247122 | + | 0.968984i | \(0.420515\pi\) | |||||||
\(132\) | 19.9765 | 1.73873 | ||||||||
\(133\) | −4.51626 | −0.391609 | ||||||||
\(134\) | 11.5070 | 0.994052 | ||||||||
\(135\) | 1.59780 | 0.137516 | ||||||||
\(136\) | −0.969126 | −0.0831019 | ||||||||
\(137\) | −15.7632 | −1.34674 | −0.673372 | − | 0.739304i | \(-0.735155\pi\) | ||||
−0.673372 | + | 0.739304i | \(0.735155\pi\) | |||||||
\(138\) | 17.5811 | 1.49661 | ||||||||
\(139\) | −2.20020 | −0.186618 | −0.0933091 | − | 0.995637i | \(-0.529744\pi\) | ||||
−0.0933091 | + | 0.995637i | \(0.529744\pi\) | |||||||
\(140\) | 5.49101 | 0.464075 | ||||||||
\(141\) | −3.02531 | −0.254777 | ||||||||
\(142\) | 29.7620 | 2.49758 | ||||||||
\(143\) | 2.33944 | 0.195634 | ||||||||
\(144\) | 0.937085 | 0.0780904 | ||||||||
\(145\) | −12.7377 | −1.05781 | ||||||||
\(146\) | −23.6757 | −1.95942 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −1.52253 | −0.125151 | ||||||||
\(149\) | 2.52281 | 0.206677 | 0.103338 | − | 0.994646i | \(-0.467048\pi\) | ||||
0.103338 | + | 0.994646i | \(0.467048\pi\) | |||||||
\(150\) | −5.70566 | −0.465865 | ||||||||
\(151\) | 15.6399 | 1.27276 | 0.636379 | − | 0.771376i | \(-0.280431\pi\) | ||||
0.636379 | + | 0.771376i | \(0.280431\pi\) | |||||||
\(152\) | −15.1280 | −1.22705 | ||||||||
\(153\) | 0.289318 | 0.0233900 | ||||||||
\(154\) | −13.5535 | −1.09217 | ||||||||
\(155\) | −9.49459 | −0.762624 | ||||||||
\(156\) | 1.38311 | 0.110737 | ||||||||
\(157\) | 5.94452 | 0.474424 | 0.237212 | − | 0.971458i | \(-0.423766\pi\) | ||||
0.237212 | + | 0.971458i | \(0.423766\pi\) | |||||||
\(158\) | −6.09117 | −0.484587 | ||||||||
\(159\) | 10.7576 | 0.853135 | ||||||||
\(160\) | −7.21312 | −0.570247 | ||||||||
\(161\) | −7.54020 | −0.594251 | ||||||||
\(162\) | −2.33165 | −0.183192 | ||||||||
\(163\) | −22.3137 | −1.74774 | −0.873870 | − | 0.486159i | \(-0.838398\pi\) | ||||
−0.873870 | + | 0.486159i | \(0.838398\pi\) | |||||||
\(164\) | −18.1670 | −1.41860 | ||||||||
\(165\) | −9.28773 | −0.723049 | ||||||||
\(166\) | 37.3170 | 2.89636 | ||||||||
\(167\) | −3.15606 | −0.244223 | −0.122112 | − | 0.992516i | \(-0.538967\pi\) | ||||
−0.122112 | + | 0.992516i | \(0.538967\pi\) | |||||||
\(168\) | −3.34969 | −0.258434 | ||||||||
\(169\) | −12.8380 | −0.987540 | ||||||||
\(170\) | 1.07786 | 0.0826680 | ||||||||
\(171\) | 4.51626 | 0.345367 | ||||||||
\(172\) | 33.4169 | 2.54801 | ||||||||
\(173\) | 6.29175 | 0.478353 | 0.239176 | − | 0.970976i | \(-0.423123\pi\) | ||||
0.239176 | + | 0.970976i | \(0.423123\pi\) | |||||||
\(174\) | 18.5880 | 1.40916 | ||||||||
\(175\) | 2.44704 | 0.184979 | ||||||||
\(176\) | −5.44712 | −0.410592 | ||||||||
\(177\) | 2.00386 | 0.150620 | ||||||||
\(178\) | 16.8548 | 1.26332 | ||||||||
\(179\) | 5.45653 | 0.407840 | 0.203920 | − | 0.978988i | \(-0.434632\pi\) | ||||
0.203920 | + | 0.978988i | \(0.434632\pi\) | |||||||
\(180\) | −5.49101 | −0.409276 | ||||||||
\(181\) | 8.75810 | 0.650985 | 0.325492 | − | 0.945545i | \(-0.394470\pi\) | ||||
0.325492 | + | 0.945545i | \(0.394470\pi\) | |||||||
\(182\) | −0.938402 | −0.0695590 | ||||||||
\(183\) | −6.76064 | −0.499761 | ||||||||
\(184\) | −25.2573 | −1.86199 | ||||||||
\(185\) | 0.707874 | 0.0520439 | ||||||||
\(186\) | 13.8554 | 1.01593 | ||||||||
\(187\) | −1.68176 | −0.122982 | ||||||||
\(188\) | 10.3968 | 0.758266 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 16.8254 | 1.22064 | ||||||||
\(191\) | −17.9071 | −1.29571 | −0.647855 | − | 0.761764i | \(-0.724334\pi\) | ||||
−0.647855 | + | 0.761764i | \(0.724334\pi\) | |||||||
\(192\) | 12.4002 | 0.894909 | ||||||||
\(193\) | 19.3215 | 1.39079 | 0.695397 | − | 0.718625i | \(-0.255228\pi\) | ||||
0.695397 | + | 0.718625i | \(0.255228\pi\) | |||||||
\(194\) | 38.7459 | 2.78179 | ||||||||
\(195\) | −0.643052 | −0.0460499 | ||||||||
\(196\) | 3.43661 | 0.245472 | ||||||||
\(197\) | −17.5692 | −1.25175 | −0.625875 | − | 0.779923i | \(-0.715258\pi\) | ||||
−0.625875 | + | 0.779923i | \(0.715258\pi\) | |||||||
\(198\) | 13.5535 | 0.963207 | ||||||||
\(199\) | 23.8610 | 1.69146 | 0.845731 | − | 0.533609i | \(-0.179165\pi\) | ||||
0.845731 | + | 0.533609i | \(0.179165\pi\) | |||||||
\(200\) | 8.19683 | 0.579604 | ||||||||
\(201\) | 4.93512 | 0.348096 | ||||||||
\(202\) | 33.5036 | 2.35730 | ||||||||
\(203\) | −7.97204 | −0.559527 | ||||||||
\(204\) | −0.994276 | −0.0696132 | ||||||||
\(205\) | 8.44643 | 0.589924 | ||||||||
\(206\) | 0.695371 | 0.0484488 | ||||||||
\(207\) | 7.54020 | 0.524080 | ||||||||
\(208\) | −0.377141 | −0.0261500 | ||||||||
\(209\) | −26.2522 | −1.81591 | ||||||||
\(210\) | 3.72551 | 0.257085 | ||||||||
\(211\) | 7.01306 | 0.482799 | 0.241399 | − | 0.970426i | \(-0.422394\pi\) | ||||
0.241399 | + | 0.970426i | \(0.422394\pi\) | |||||||
\(212\) | −36.9698 | −2.53909 | ||||||||
\(213\) | 12.7643 | 0.874598 | ||||||||
\(214\) | −33.0804 | −2.26133 | ||||||||
\(215\) | −15.5366 | −1.05959 | ||||||||
\(216\) | 3.34969 | 0.227917 | ||||||||
\(217\) | −5.94230 | −0.403390 | ||||||||
\(218\) | −10.0373 | −0.679811 | ||||||||
\(219\) | −10.1541 | −0.686147 | ||||||||
\(220\) | 31.9183 | 2.15193 | ||||||||
\(221\) | −0.116440 | −0.00783258 | ||||||||
\(222\) | −1.03300 | −0.0693301 | ||||||||
\(223\) | −23.9297 | −1.60245 | −0.801224 | − | 0.598364i | \(-0.795818\pi\) | ||||
−0.801224 | + | 0.598364i | \(0.795818\pi\) | |||||||
\(224\) | −4.51441 | −0.301632 | ||||||||
\(225\) | −2.44704 | −0.163136 | ||||||||
\(226\) | 5.93807 | 0.394995 | ||||||||
\(227\) | 25.0959 | 1.66567 | 0.832836 | − | 0.553520i | \(-0.186716\pi\) | ||||
0.832836 | + | 0.553520i | \(0.186716\pi\) | |||||||
\(228\) | −15.5206 | −1.02788 | ||||||||
\(229\) | −21.0074 | −1.38821 | −0.694103 | − | 0.719876i | \(-0.744199\pi\) | ||||
−0.694103 | + | 0.719876i | \(0.744199\pi\) | |||||||
\(230\) | 28.0911 | 1.85227 | ||||||||
\(231\) | −5.81283 | −0.382456 | ||||||||
\(232\) | −26.7038 | −1.75319 | ||||||||
\(233\) | 17.9336 | 1.17487 | 0.587436 | − | 0.809271i | \(-0.300137\pi\) | ||||
0.587436 | + | 0.809271i | \(0.300137\pi\) | |||||||
\(234\) | 0.938402 | 0.0613453 | ||||||||
\(235\) | −4.83383 | −0.315324 | ||||||||
\(236\) | −6.88651 | −0.448274 | ||||||||
\(237\) | −2.61238 | −0.169692 | ||||||||
\(238\) | 0.674591 | 0.0437272 | ||||||||
\(239\) | −26.3324 | −1.70330 | −0.851651 | − | 0.524109i | \(-0.824399\pi\) | ||||
−0.851651 | + | 0.524109i | \(0.824399\pi\) | |||||||
\(240\) | 1.49727 | 0.0966485 | ||||||||
\(241\) | 11.6061 | 0.747616 | 0.373808 | − | 0.927506i | \(-0.378052\pi\) | ||||
0.373808 | + | 0.927506i | \(0.378052\pi\) | |||||||
\(242\) | −53.1361 | −3.41572 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 23.2337 | 1.48739 | ||||||||
\(245\) | −1.59780 | −0.102080 | ||||||||
\(246\) | −12.3258 | −0.785865 | ||||||||
\(247\) | −1.81762 | −0.115652 | ||||||||
\(248\) | −19.9049 | −1.26396 | ||||||||
\(249\) | 16.0045 | 1.01425 | ||||||||
\(250\) | −27.7440 | −1.75469 | ||||||||
\(251\) | 15.5574 | 0.981973 | 0.490987 | − | 0.871167i | \(-0.336636\pi\) | ||||
0.490987 | + | 0.871167i | \(0.336636\pi\) | |||||||
\(252\) | −3.43661 | −0.216486 | ||||||||
\(253\) | −43.8299 | −2.75556 | ||||||||
\(254\) | −2.56825 | −0.161146 | ||||||||
\(255\) | 0.462272 | 0.0289486 | ||||||||
\(256\) | −21.5627 | −1.34767 | ||||||||
\(257\) | 10.4359 | 0.650976 | 0.325488 | − | 0.945546i | \(-0.394471\pi\) | ||||
0.325488 | + | 0.945546i | \(0.394471\pi\) | |||||||
\(258\) | 22.6725 | 1.41153 | ||||||||
\(259\) | 0.443031 | 0.0275286 | ||||||||
\(260\) | 2.20992 | 0.137054 | ||||||||
\(261\) | 7.97204 | 0.493457 | ||||||||
\(262\) | −13.1899 | −0.814875 | ||||||||
\(263\) | −14.7946 | −0.912274 | −0.456137 | − | 0.889909i | \(-0.650767\pi\) | ||||
−0.456137 | + | 0.889909i | \(0.650767\pi\) | |||||||
\(264\) | −19.4712 | −1.19837 | ||||||||
\(265\) | 17.1885 | 1.05588 | ||||||||
\(266\) | 10.5303 | 0.645657 | ||||||||
\(267\) | 7.22871 | 0.442390 | ||||||||
\(268\) | −16.9601 | −1.03600 | ||||||||
\(269\) | −21.5132 | −1.31168 | −0.655840 | − | 0.754900i | \(-0.727686\pi\) | ||||
−0.655840 | + | 0.754900i | \(0.727686\pi\) | |||||||
\(270\) | −3.72551 | −0.226727 | ||||||||
\(271\) | −20.9775 | −1.27429 | −0.637145 | − | 0.770744i | \(-0.719885\pi\) | ||||
−0.637145 | + | 0.770744i | \(0.719885\pi\) | |||||||
\(272\) | 0.271116 | 0.0164388 | ||||||||
\(273\) | −0.402462 | −0.0243581 | ||||||||
\(274\) | 36.7544 | 2.22041 | ||||||||
\(275\) | 14.2243 | 0.857755 | ||||||||
\(276\) | −25.9128 | −1.55976 | ||||||||
\(277\) | 9.97176 | 0.599145 | 0.299572 | − | 0.954074i | \(-0.403156\pi\) | ||||
0.299572 | + | 0.954074i | \(0.403156\pi\) | |||||||
\(278\) | 5.13010 | 0.307683 | ||||||||
\(279\) | 5.94230 | 0.355756 | ||||||||
\(280\) | −5.35212 | −0.319850 | ||||||||
\(281\) | −22.6902 | −1.35358 | −0.676792 | − | 0.736174i | \(-0.736630\pi\) | ||||
−0.676792 | + | 0.736174i | \(0.736630\pi\) | |||||||
\(282\) | 7.05398 | 0.420058 | ||||||||
\(283\) | 6.26616 | 0.372485 | 0.186242 | − | 0.982504i | \(-0.440369\pi\) | ||||
0.186242 | + | 0.982504i | \(0.440369\pi\) | |||||||
\(284\) | −43.8661 | −2.60298 | ||||||||
\(285\) | 7.21606 | 0.427442 | ||||||||
\(286\) | −5.45477 | −0.322548 | ||||||||
\(287\) | 5.28630 | 0.312040 | ||||||||
\(288\) | 4.51441 | 0.266014 | ||||||||
\(289\) | −16.9163 | −0.995076 | ||||||||
\(290\) | 29.6999 | 1.74404 | ||||||||
\(291\) | 16.6173 | 0.974125 | ||||||||
\(292\) | 34.8956 | 2.04211 | ||||||||
\(293\) | 23.3443 | 1.36379 | 0.681893 | − | 0.731452i | \(-0.261157\pi\) | ||||
0.681893 | + | 0.731452i | \(0.261157\pi\) | |||||||
\(294\) | 2.33165 | 0.135985 | ||||||||
\(295\) | 3.20177 | 0.186414 | ||||||||
\(296\) | 1.48402 | 0.0862566 | ||||||||
\(297\) | 5.81283 | 0.337295 | ||||||||
\(298\) | −5.88232 | −0.340754 | ||||||||
\(299\) | −3.03464 | −0.175498 | ||||||||
\(300\) | 8.40955 | 0.485525 | ||||||||
\(301\) | −9.72378 | −0.560469 | ||||||||
\(302\) | −36.4669 | −2.09843 | ||||||||
\(303\) | 14.3690 | 0.825479 | ||||||||
\(304\) | 4.23212 | 0.242729 | ||||||||
\(305\) | −10.8021 | −0.618528 | ||||||||
\(306\) | −0.674591 | −0.0385638 | ||||||||
\(307\) | 4.85883 | 0.277308 | 0.138654 | − | 0.990341i | \(-0.455722\pi\) | ||||
0.138654 | + | 0.990341i | \(0.455722\pi\) | |||||||
\(308\) | 19.9765 | 1.13826 | ||||||||
\(309\) | 0.298231 | 0.0169658 | ||||||||
\(310\) | 22.1381 | 1.25736 | ||||||||
\(311\) | −9.25092 | −0.524571 | −0.262286 | − | 0.964990i | \(-0.584476\pi\) | ||||
−0.262286 | + | 0.964990i | \(0.584476\pi\) | |||||||
\(312\) | −1.34812 | −0.0763223 | ||||||||
\(313\) | 11.2008 | 0.633107 | 0.316554 | − | 0.948575i | \(-0.397474\pi\) | ||||
0.316554 | + | 0.948575i | \(0.397474\pi\) | |||||||
\(314\) | −13.8606 | −0.782197 | ||||||||
\(315\) | 1.59780 | 0.0900257 | ||||||||
\(316\) | 8.97774 | 0.505037 | ||||||||
\(317\) | 11.4783 | 0.644687 | 0.322343 | − | 0.946623i | \(-0.395529\pi\) | ||||
0.322343 | + | 0.946623i | \(0.395529\pi\) | |||||||
\(318\) | −25.0830 | −1.40659 | ||||||||
\(319\) | −46.3401 | −2.59455 | ||||||||
\(320\) | 19.8130 | 1.10758 | ||||||||
\(321\) | −14.1875 | −0.791870 | ||||||||
\(322\) | 17.5811 | 0.979759 | ||||||||
\(323\) | 1.30664 | 0.0727032 | ||||||||
\(324\) | 3.43661 | 0.190923 | ||||||||
\(325\) | 0.984842 | 0.0546292 | ||||||||
\(326\) | 52.0278 | 2.88155 | ||||||||
\(327\) | −4.30479 | −0.238055 | ||||||||
\(328\) | 17.7074 | 0.977730 | ||||||||
\(329\) | −3.02531 | −0.166791 | ||||||||
\(330\) | 21.6558 | 1.19211 | ||||||||
\(331\) | 15.6860 | 0.862180 | 0.431090 | − | 0.902309i | \(-0.358129\pi\) | ||||
0.431090 | + | 0.902309i | \(0.358129\pi\) | |||||||
\(332\) | −55.0014 | −3.01859 | ||||||||
\(333\) | −0.443031 | −0.0242780 | ||||||||
\(334\) | 7.35884 | 0.402658 | ||||||||
\(335\) | 7.88531 | 0.430821 | ||||||||
\(336\) | 0.937085 | 0.0511222 | ||||||||
\(337\) | 18.9502 | 1.03228 | 0.516141 | − | 0.856504i | \(-0.327368\pi\) | ||||
0.516141 | + | 0.856504i | \(0.327368\pi\) | |||||||
\(338\) | 29.9338 | 1.62819 | ||||||||
\(339\) | 2.54672 | 0.138319 | ||||||||
\(340\) | −1.58865 | −0.0861567 | ||||||||
\(341\) | −34.5416 | −1.87053 | ||||||||
\(342\) | −10.5303 | −0.569416 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −32.5716 | −1.75614 | ||||||||
\(345\) | 12.0477 | 0.648627 | ||||||||
\(346\) | −14.6702 | −0.788674 | ||||||||
\(347\) | 31.9769 | 1.71661 | 0.858305 | − | 0.513140i | \(-0.171518\pi\) | ||||
0.858305 | + | 0.513140i | \(0.171518\pi\) | |||||||
\(348\) | −27.3968 | −1.46862 | ||||||||
\(349\) | −17.5204 | −0.937846 | −0.468923 | − | 0.883239i | \(-0.655358\pi\) | ||||
−0.468923 | + | 0.883239i | \(0.655358\pi\) | |||||||
\(350\) | −5.70566 | −0.304981 | ||||||||
\(351\) | 0.402462 | 0.0214818 | ||||||||
\(352\) | −26.2415 | −1.39868 | ||||||||
\(353\) | 33.8568 | 1.80202 | 0.901008 | − | 0.433802i | \(-0.142828\pi\) | ||||
0.901008 | + | 0.433802i | \(0.142828\pi\) | |||||||
\(354\) | −4.67232 | −0.248331 | ||||||||
\(355\) | 20.3948 | 1.08245 | ||||||||
\(356\) | −24.8423 | −1.31664 | ||||||||
\(357\) | 0.289318 | 0.0153124 | ||||||||
\(358\) | −12.7227 | −0.672418 | ||||||||
\(359\) | 25.5548 | 1.34873 | 0.674366 | − | 0.738398i | \(-0.264417\pi\) | ||||
0.674366 | + | 0.738398i | \(0.264417\pi\) | |||||||
\(360\) | 5.35212 | 0.282081 | ||||||||
\(361\) | 1.39656 | 0.0735034 | ||||||||
\(362\) | −20.4209 | −1.07330 | ||||||||
\(363\) | −22.7890 | −1.19611 | ||||||||
\(364\) | 1.38311 | 0.0724944 | ||||||||
\(365\) | −16.2241 | −0.849209 | ||||||||
\(366\) | 15.7635 | 0.823970 | ||||||||
\(367\) | −31.6113 | −1.65010 | −0.825049 | − | 0.565061i | \(-0.808853\pi\) | ||||
−0.825049 | + | 0.565061i | \(0.808853\pi\) | |||||||
\(368\) | 7.06581 | 0.368331 | ||||||||
\(369\) | −5.28630 | −0.275194 | ||||||||
\(370\) | −1.65052 | −0.0858063 | ||||||||
\(371\) | 10.7576 | 0.558508 | ||||||||
\(372\) | −20.4214 | −1.05880 | ||||||||
\(373\) | 6.60783 | 0.342141 | 0.171070 | − | 0.985259i | \(-0.445277\pi\) | ||||
0.171070 | + | 0.985259i | \(0.445277\pi\) | |||||||
\(374\) | 3.92128 | 0.202765 | ||||||||
\(375\) | −11.8989 | −0.614455 | ||||||||
\(376\) | −10.1338 | −0.522613 | ||||||||
\(377\) | −3.20844 | −0.165243 | ||||||||
\(378\) | −2.33165 | −0.119927 | ||||||||
\(379\) | −15.7343 | −0.808216 | −0.404108 | − | 0.914711i | \(-0.632418\pi\) | ||||
−0.404108 | + | 0.914711i | \(0.632418\pi\) | |||||||
\(380\) | −24.7988 | −1.27215 | ||||||||
\(381\) | −1.10147 | −0.0564301 | ||||||||
\(382\) | 41.7531 | 2.13627 | ||||||||
\(383\) | 1.00000 | 0.0510976 | ||||||||
\(384\) | −19.8842 | −1.01471 | ||||||||
\(385\) | −9.28773 | −0.473346 | ||||||||
\(386\) | −45.0512 | −2.29304 | ||||||||
\(387\) | 9.72378 | 0.494287 | ||||||||
\(388\) | −57.1073 | −2.89918 | ||||||||
\(389\) | 28.7760 | 1.45900 | 0.729500 | − | 0.683981i | \(-0.239753\pi\) | ||||
0.729500 | + | 0.683981i | \(0.239753\pi\) | |||||||
\(390\) | 1.49938 | 0.0759238 | ||||||||
\(391\) | 2.18152 | 0.110324 | ||||||||
\(392\) | −3.34969 | −0.169185 | ||||||||
\(393\) | −5.65688 | −0.285352 | ||||||||
\(394\) | 40.9652 | 2.06380 | ||||||||
\(395\) | −4.17405 | −0.210019 | ||||||||
\(396\) | −19.9765 | −1.00385 | ||||||||
\(397\) | 5.37667 | 0.269847 | 0.134924 | − | 0.990856i | \(-0.456921\pi\) | ||||
0.134924 | + | 0.990856i | \(0.456921\pi\) | |||||||
\(398\) | −55.6357 | −2.78876 | ||||||||
\(399\) | 4.51626 | 0.226096 | ||||||||
\(400\) | −2.29309 | −0.114654 | ||||||||
\(401\) | 22.1980 | 1.10852 | 0.554258 | − | 0.832345i | \(-0.313002\pi\) | ||||
0.554258 | + | 0.832345i | \(0.313002\pi\) | |||||||
\(402\) | −11.5070 | −0.573916 | ||||||||
\(403\) | −2.39155 | −0.119132 | ||||||||
\(404\) | −49.3808 | −2.45679 | ||||||||
\(405\) | −1.59780 | −0.0793952 | ||||||||
\(406\) | 18.5880 | 0.922509 | ||||||||
\(407\) | 2.57527 | 0.127651 | ||||||||
\(408\) | 0.969126 | 0.0479789 | ||||||||
\(409\) | 20.9907 | 1.03792 | 0.518961 | − | 0.854798i | \(-0.326319\pi\) | ||||
0.518961 | + | 0.854798i | \(0.326319\pi\) | |||||||
\(410\) | −19.6942 | −0.972625 | ||||||||
\(411\) | 15.7632 | 0.777542 | ||||||||
\(412\) | −1.02490 | −0.0504934 | ||||||||
\(413\) | 2.00386 | 0.0986037 | ||||||||
\(414\) | −17.5811 | −0.864066 | ||||||||
\(415\) | 25.5720 | 1.25528 | ||||||||
\(416\) | −1.81688 | −0.0890798 | ||||||||
\(417\) | 2.20020 | 0.107744 | ||||||||
\(418\) | 61.2112 | 2.99394 | ||||||||
\(419\) | −6.88529 | −0.336368 | −0.168184 | − | 0.985756i | \(-0.553790\pi\) | ||||
−0.168184 | + | 0.985756i | \(0.553790\pi\) | |||||||
\(420\) | −5.49101 | −0.267934 | ||||||||
\(421\) | 23.7414 | 1.15709 | 0.578543 | − | 0.815652i | \(-0.303621\pi\) | ||||
0.578543 | + | 0.815652i | \(0.303621\pi\) | |||||||
\(422\) | −16.3520 | −0.796004 | ||||||||
\(423\) | 3.02531 | 0.147096 | ||||||||
\(424\) | 36.0346 | 1.75000 | ||||||||
\(425\) | −0.707975 | −0.0343418 | ||||||||
\(426\) | −29.7620 | −1.44198 | ||||||||
\(427\) | −6.76064 | −0.327170 | ||||||||
\(428\) | 48.7570 | 2.35676 | ||||||||
\(429\) | −2.33944 | −0.112949 | ||||||||
\(430\) | 36.2260 | 1.74697 | ||||||||
\(431\) | −30.9196 | −1.48934 | −0.744671 | − | 0.667431i | \(-0.767394\pi\) | ||||
−0.744671 | + | 0.667431i | \(0.767394\pi\) | |||||||
\(432\) | −0.937085 | −0.0450855 | ||||||||
\(433\) | −39.3270 | −1.88994 | −0.944968 | − | 0.327164i | \(-0.893907\pi\) | ||||
−0.944968 | + | 0.327164i | \(0.893907\pi\) | |||||||
\(434\) | 13.8554 | 0.665080 | ||||||||
\(435\) | 12.7377 | 0.610726 | ||||||||
\(436\) | 14.7939 | 0.708499 | ||||||||
\(437\) | 34.0535 | 1.62900 | ||||||||
\(438\) | 23.6757 | 1.13127 | ||||||||
\(439\) | −32.2271 | −1.53812 | −0.769058 | − | 0.639179i | \(-0.779274\pi\) | ||||
−0.769058 | + | 0.639179i | \(0.779274\pi\) | |||||||
\(440\) | −31.1110 | −1.48316 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0.271497 | 0.0129138 | ||||||||
\(443\) | −4.09684 | −0.194647 | −0.0973233 | − | 0.995253i | \(-0.531028\pi\) | ||||
−0.0973233 | + | 0.995253i | \(0.531028\pi\) | |||||||
\(444\) | 1.52253 | 0.0722559 | ||||||||
\(445\) | 11.5500 | 0.547523 | ||||||||
\(446\) | 55.7957 | 2.64200 | ||||||||
\(447\) | −2.52281 | −0.119325 | ||||||||
\(448\) | 12.4002 | 0.585856 | ||||||||
\(449\) | −17.5330 | −0.827434 | −0.413717 | − | 0.910406i | \(-0.635770\pi\) | ||||
−0.413717 | + | 0.910406i | \(0.635770\pi\) | |||||||
\(450\) | 5.70566 | 0.268968 | ||||||||
\(451\) | 30.7284 | 1.44694 | ||||||||
\(452\) | −8.75209 | −0.411664 | ||||||||
\(453\) | −15.6399 | −0.734827 | ||||||||
\(454\) | −58.5149 | −2.74624 | ||||||||
\(455\) | −0.643052 | −0.0301468 | ||||||||
\(456\) | 15.1280 | 0.708435 | ||||||||
\(457\) | 39.3588 | 1.84113 | 0.920564 | − | 0.390593i | \(-0.127730\pi\) | ||||
0.920564 | + | 0.390593i | \(0.127730\pi\) | |||||||
\(458\) | 48.9819 | 2.28878 | ||||||||
\(459\) | −0.289318 | −0.0135042 | ||||||||
\(460\) | −41.4033 | −1.93044 | ||||||||
\(461\) | 22.5425 | 1.04991 | 0.524954 | − | 0.851130i | \(-0.324082\pi\) | ||||
0.524954 | + | 0.851130i | \(0.324082\pi\) | |||||||
\(462\) | 13.5535 | 0.630567 | ||||||||
\(463\) | 5.00587 | 0.232643 | 0.116321 | − | 0.993212i | \(-0.462890\pi\) | ||||
0.116321 | + | 0.993212i | \(0.462890\pi\) | |||||||
\(464\) | 7.47048 | 0.346808 | ||||||||
\(465\) | 9.49459 | 0.440301 | ||||||||
\(466\) | −41.8151 | −1.93705 | ||||||||
\(467\) | 38.8405 | 1.79733 | 0.898663 | − | 0.438640i | \(-0.144540\pi\) | ||||
0.898663 | + | 0.438640i | \(0.144540\pi\) | |||||||
\(468\) | −1.38311 | −0.0639341 | ||||||||
\(469\) | 4.93512 | 0.227883 | ||||||||
\(470\) | 11.2708 | 0.519884 | ||||||||
\(471\) | −5.94452 | −0.273909 | ||||||||
\(472\) | 6.71232 | 0.308960 | ||||||||
\(473\) | −56.5227 | −2.59892 | ||||||||
\(474\) | 6.09117 | 0.279777 | ||||||||
\(475\) | −11.0515 | −0.507077 | ||||||||
\(476\) | −0.994276 | −0.0455726 | ||||||||
\(477\) | −10.7576 | −0.492557 | ||||||||
\(478\) | 61.3981 | 2.80828 | ||||||||
\(479\) | −18.8144 | −0.859651 | −0.429826 | − | 0.902912i | \(-0.641425\pi\) | ||||
−0.429826 | + | 0.902912i | \(0.641425\pi\) | |||||||
\(480\) | 7.21312 | 0.329232 | ||||||||
\(481\) | 0.178303 | 0.00812992 | ||||||||
\(482\) | −27.0615 | −1.23262 | ||||||||
\(483\) | 7.54020 | 0.343091 | ||||||||
\(484\) | 78.3171 | 3.55987 | ||||||||
\(485\) | 26.5511 | 1.20562 | ||||||||
\(486\) | 2.33165 | 0.105766 | ||||||||
\(487\) | −19.6799 | −0.891780 | −0.445890 | − | 0.895088i | \(-0.647113\pi\) | ||||
−0.445890 | + | 0.895088i | \(0.647113\pi\) | |||||||
\(488\) | −22.6460 | −1.02514 | ||||||||
\(489\) | 22.3137 | 1.00906 | ||||||||
\(490\) | 3.72551 | 0.168301 | ||||||||
\(491\) | −29.4916 | −1.33094 | −0.665469 | − | 0.746425i | \(-0.731769\pi\) | ||||
−0.665469 | + | 0.746425i | \(0.731769\pi\) | |||||||
\(492\) | 18.1670 | 0.819030 | ||||||||
\(493\) | 2.30646 | 0.103878 | ||||||||
\(494\) | 4.23806 | 0.190679 | ||||||||
\(495\) | 9.28773 | 0.417452 | ||||||||
\(496\) | 5.56844 | 0.250031 | ||||||||
\(497\) | 12.7643 | 0.572559 | ||||||||
\(498\) | −37.3170 | −1.67222 | ||||||||
\(499\) | −36.4429 | −1.63141 | −0.815705 | − | 0.578469i | \(-0.803650\pi\) | ||||
−0.815705 | + | 0.578469i | \(0.803650\pi\) | |||||||
\(500\) | 40.8918 | 1.82874 | ||||||||
\(501\) | 3.15606 | 0.141002 | ||||||||
\(502\) | −36.2745 | −1.61901 | ||||||||
\(503\) | 7.29510 | 0.325272 | 0.162636 | − | 0.986686i | \(-0.448000\pi\) | ||||
0.162636 | + | 0.986686i | \(0.448000\pi\) | |||||||
\(504\) | 3.34969 | 0.149207 | ||||||||
\(505\) | 22.9588 | 1.02165 | ||||||||
\(506\) | 102.196 | 4.54318 | ||||||||
\(507\) | 12.8380 | 0.570157 | ||||||||
\(508\) | 3.78533 | 0.167947 | ||||||||
\(509\) | 1.85074 | 0.0820328 | 0.0410164 | − | 0.999158i | \(-0.486940\pi\) | ||||
0.0410164 | + | 0.999158i | \(0.486940\pi\) | |||||||
\(510\) | −1.07786 | −0.0477284 | ||||||||
\(511\) | −10.1541 | −0.449189 | ||||||||
\(512\) | 10.5083 | 0.464404 | ||||||||
\(513\) | −4.51626 | −0.199398 | ||||||||
\(514\) | −24.3330 | −1.07328 | ||||||||
\(515\) | 0.476512 | 0.0209976 | ||||||||
\(516\) | −33.4169 | −1.47110 | ||||||||
\(517\) | −17.5856 | −0.773415 | ||||||||
\(518\) | −1.03300 | −0.0453872 | ||||||||
\(519\) | −6.29175 | −0.276177 | ||||||||
\(520\) | −2.15402 | −0.0944602 | ||||||||
\(521\) | −19.8621 | −0.870175 | −0.435087 | − | 0.900388i | \(-0.643283\pi\) | ||||
−0.435087 | + | 0.900388i | \(0.643283\pi\) | |||||||
\(522\) | −18.5880 | −0.813576 | ||||||||
\(523\) | −17.2257 | −0.753228 | −0.376614 | − | 0.926370i | \(-0.622912\pi\) | ||||
−0.376614 | + | 0.926370i | \(0.622912\pi\) | |||||||
\(524\) | 19.4405 | 0.849263 | ||||||||
\(525\) | −2.44704 | −0.106798 | ||||||||
\(526\) | 34.4959 | 1.50409 | ||||||||
\(527\) | 1.71922 | 0.0748903 | ||||||||
\(528\) | 5.44712 | 0.237055 | ||||||||
\(529\) | 33.8546 | 1.47194 | ||||||||
\(530\) | −40.0776 | −1.74086 | ||||||||
\(531\) | −2.00386 | −0.0869603 | ||||||||
\(532\) | −15.5206 | −0.672904 | ||||||||
\(533\) | 2.12753 | 0.0921537 | ||||||||
\(534\) | −16.8548 | −0.729381 | ||||||||
\(535\) | −22.6688 | −0.980056 | ||||||||
\(536\) | 16.5311 | 0.714035 | ||||||||
\(537\) | −5.45653 | −0.235467 | ||||||||
\(538\) | 50.1613 | 2.16261 | ||||||||
\(539\) | −5.81283 | −0.250376 | ||||||||
\(540\) | 5.49101 | 0.236295 | ||||||||
\(541\) | −20.5841 | −0.884979 | −0.442489 | − | 0.896774i | \(-0.645905\pi\) | ||||
−0.442489 | + | 0.896774i | \(0.645905\pi\) | |||||||
\(542\) | 48.9122 | 2.10096 | ||||||||
\(543\) | −8.75810 | −0.375846 | ||||||||
\(544\) | 1.30610 | 0.0559987 | ||||||||
\(545\) | −6.87818 | −0.294629 | ||||||||
\(546\) | 0.938402 | 0.0401599 | ||||||||
\(547\) | −7.29507 | −0.311915 | −0.155957 | − | 0.987764i | \(-0.549846\pi\) | ||||
−0.155957 | + | 0.987764i | \(0.549846\pi\) | |||||||
\(548\) | −54.1721 | −2.31412 | ||||||||
\(549\) | 6.76064 | 0.288537 | ||||||||
\(550\) | −33.1661 | −1.41421 | ||||||||
\(551\) | 36.0038 | 1.53381 | ||||||||
\(552\) | 25.2573 | 1.07502 | ||||||||
\(553\) | −2.61238 | −0.111090 | ||||||||
\(554\) | −23.2507 | −0.987827 | ||||||||
\(555\) | −0.707874 | −0.0300476 | ||||||||
\(556\) | −7.56122 | −0.320667 | ||||||||
\(557\) | 1.15446 | 0.0489158 | 0.0244579 | − | 0.999701i | \(-0.492214\pi\) | ||||
0.0244579 | + | 0.999701i | \(0.492214\pi\) | |||||||
\(558\) | −13.8554 | −0.586546 | ||||||||
\(559\) | −3.91345 | −0.165521 | ||||||||
\(560\) | 1.49727 | 0.0632713 | ||||||||
\(561\) | 1.68176 | 0.0710040 | ||||||||
\(562\) | 52.9057 | 2.23169 | ||||||||
\(563\) | −13.8671 | −0.584427 | −0.292213 | − | 0.956353i | \(-0.594392\pi\) | ||||
−0.292213 | + | 0.956353i | \(0.594392\pi\) | |||||||
\(564\) | −10.3968 | −0.437785 | ||||||||
\(565\) | 4.06914 | 0.171190 | ||||||||
\(566\) | −14.6105 | −0.614126 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 42.7566 | 1.79403 | ||||||||
\(569\) | −30.8539 | −1.29346 | −0.646731 | − | 0.762719i | \(-0.723864\pi\) | ||||
−0.646731 | + | 0.762719i | \(0.723864\pi\) | |||||||
\(570\) | −16.8254 | −0.704737 | ||||||||
\(571\) | 11.0429 | 0.462132 | 0.231066 | − | 0.972938i | \(-0.425779\pi\) | ||||
0.231066 | + | 0.972938i | \(0.425779\pi\) | |||||||
\(572\) | 8.03976 | 0.336159 | ||||||||
\(573\) | 17.9071 | 0.748078 | ||||||||
\(574\) | −12.3258 | −0.514470 | ||||||||
\(575\) | −18.4512 | −0.769469 | ||||||||
\(576\) | −12.4002 | −0.516676 | ||||||||
\(577\) | −18.0509 | −0.751471 | −0.375735 | − | 0.926727i | \(-0.622610\pi\) | ||||
−0.375735 | + | 0.926727i | \(0.622610\pi\) | |||||||
\(578\) | 39.4430 | 1.64061 | ||||||||
\(579\) | −19.3215 | −0.802976 | ||||||||
\(580\) | −43.7745 | −1.81764 | ||||||||
\(581\) | 16.0045 | 0.663980 | ||||||||
\(582\) | −38.7459 | −1.60607 | ||||||||
\(583\) | 62.5322 | 2.58982 | ||||||||
\(584\) | −34.0129 | −1.40746 | ||||||||
\(585\) | 0.643052 | 0.0265869 | ||||||||
\(586\) | −54.4308 | −2.24851 | ||||||||
\(587\) | 27.2619 | 1.12522 | 0.562610 | − | 0.826723i | \(-0.309797\pi\) | ||||
0.562610 | + | 0.826723i | \(0.309797\pi\) | |||||||
\(588\) | −3.43661 | −0.141724 | ||||||||
\(589\) | 26.8370 | 1.10580 | ||||||||
\(590\) | −7.46542 | −0.307346 | ||||||||
\(591\) | 17.5692 | 0.722699 | ||||||||
\(592\) | −0.415158 | −0.0170629 | ||||||||
\(593\) | 39.4390 | 1.61956 | 0.809782 | − | 0.586731i | \(-0.199585\pi\) | ||||
0.809782 | + | 0.586731i | \(0.199585\pi\) | |||||||
\(594\) | −13.5535 | −0.556108 | ||||||||
\(595\) | 0.462272 | 0.0189513 | ||||||||
\(596\) | 8.66992 | 0.355134 | ||||||||
\(597\) | −23.8610 | −0.976566 | ||||||||
\(598\) | 7.07574 | 0.289348 | ||||||||
\(599\) | −3.94542 | −0.161206 | −0.0806028 | − | 0.996746i | \(-0.525685\pi\) | ||||
−0.0806028 | + | 0.996746i | \(0.525685\pi\) | |||||||
\(600\) | −8.19683 | −0.334634 | ||||||||
\(601\) | −12.3453 | −0.503573 | −0.251787 | − | 0.967783i | \(-0.581018\pi\) | ||||
−0.251787 | + | 0.967783i | \(0.581018\pi\) | |||||||
\(602\) | 22.6725 | 0.924062 | ||||||||
\(603\) | −4.93512 | −0.200973 | ||||||||
\(604\) | 53.7484 | 2.18699 | ||||||||
\(605\) | −36.4122 | −1.48037 | ||||||||
\(606\) | −33.5036 | −1.36099 | ||||||||
\(607\) | 19.8208 | 0.804502 | 0.402251 | − | 0.915529i | \(-0.368228\pi\) | ||||
0.402251 | + | 0.915529i | \(0.368228\pi\) | |||||||
\(608\) | 20.3882 | 0.826853 | ||||||||
\(609\) | 7.97204 | 0.323043 | ||||||||
\(610\) | 25.1868 | 1.01979 | ||||||||
\(611\) | −1.21757 | −0.0492577 | ||||||||
\(612\) | 0.994276 | 0.0401912 | ||||||||
\(613\) | −24.7199 | −0.998426 | −0.499213 | − | 0.866479i | \(-0.666377\pi\) | ||||
−0.499213 | + | 0.866479i | \(0.666377\pi\) | |||||||
\(614\) | −11.3291 | −0.457206 | ||||||||
\(615\) | −8.44643 | −0.340593 | ||||||||
\(616\) | −19.4712 | −0.784516 | ||||||||
\(617\) | 22.0279 | 0.886810 | 0.443405 | − | 0.896321i | \(-0.353770\pi\) | ||||
0.443405 | + | 0.896321i | \(0.353770\pi\) | |||||||
\(618\) | −0.695371 | −0.0279719 | ||||||||
\(619\) | 21.0470 | 0.845950 | 0.422975 | − | 0.906141i | \(-0.360986\pi\) | ||||
0.422975 | + | 0.906141i | \(0.360986\pi\) | |||||||
\(620\) | −32.6292 | −1.31042 | ||||||||
\(621\) | −7.54020 | −0.302578 | ||||||||
\(622\) | 21.5699 | 0.864876 | ||||||||
\(623\) | 7.22871 | 0.289612 | ||||||||
\(624\) | 0.377141 | 0.0150977 | ||||||||
\(625\) | −6.77675 | −0.271070 | ||||||||
\(626\) | −26.1164 | −1.04382 | ||||||||
\(627\) | 26.2522 | 1.04841 | ||||||||
\(628\) | 20.4290 | 0.815206 | ||||||||
\(629\) | −0.128177 | −0.00511075 | ||||||||
\(630\) | −3.72551 | −0.148428 | ||||||||
\(631\) | 17.7033 | 0.704758 | 0.352379 | − | 0.935857i | \(-0.385373\pi\) | ||||
0.352379 | + | 0.935857i | \(0.385373\pi\) | |||||||
\(632\) | −8.75065 | −0.348082 | ||||||||
\(633\) | −7.01306 | −0.278744 | ||||||||
\(634\) | −26.7635 | −1.06291 | ||||||||
\(635\) | −1.75993 | −0.0698406 | ||||||||
\(636\) | 36.9698 | 1.46595 | ||||||||
\(637\) | −0.402462 | −0.0159461 | ||||||||
\(638\) | 108.049 | 4.27771 | ||||||||
\(639\) | −12.7643 | −0.504950 | ||||||||
\(640\) | −31.7709 | −1.25586 | ||||||||
\(641\) | 24.5713 | 0.970509 | 0.485254 | − | 0.874373i | \(-0.338727\pi\) | ||||
0.485254 | + | 0.874373i | \(0.338727\pi\) | |||||||
\(642\) | 33.0804 | 1.30558 | ||||||||
\(643\) | 12.7318 | 0.502092 | 0.251046 | − | 0.967975i | \(-0.419225\pi\) | ||||
0.251046 | + | 0.967975i | \(0.419225\pi\) | |||||||
\(644\) | −25.9128 | −1.02111 | ||||||||
\(645\) | 15.5366 | 0.611754 | ||||||||
\(646\) | −3.04662 | −0.119868 | ||||||||
\(647\) | 22.9617 | 0.902719 | 0.451359 | − | 0.892342i | \(-0.350939\pi\) | ||||
0.451359 | + | 0.892342i | \(0.350939\pi\) | |||||||
\(648\) | −3.34969 | −0.131588 | ||||||||
\(649\) | 11.6481 | 0.457229 | ||||||||
\(650\) | −2.29631 | −0.0900687 | ||||||||
\(651\) | 5.94230 | 0.232897 | ||||||||
\(652\) | −76.6834 | −3.00316 | ||||||||
\(653\) | 9.76257 | 0.382039 | 0.191019 | − | 0.981586i | \(-0.438821\pi\) | ||||
0.191019 | + | 0.981586i | \(0.438821\pi\) | |||||||
\(654\) | 10.0373 | 0.392489 | ||||||||
\(655\) | −9.03855 | −0.353165 | ||||||||
\(656\) | −4.95371 | −0.193410 | ||||||||
\(657\) | 10.1541 | 0.396147 | ||||||||
\(658\) | 7.05398 | 0.274993 | ||||||||
\(659\) | −18.5259 | −0.721666 | −0.360833 | − | 0.932630i | \(-0.617508\pi\) | ||||
−0.360833 | + | 0.932630i | \(0.617508\pi\) | |||||||
\(660\) | −31.9183 | −1.24242 | ||||||||
\(661\) | −13.2466 | −0.515231 | −0.257616 | − | 0.966247i | \(-0.582937\pi\) | ||||
−0.257616 | + | 0.966247i | \(0.582937\pi\) | |||||||
\(662\) | −36.5743 | −1.42150 | ||||||||
\(663\) | 0.116440 | 0.00452214 | ||||||||
\(664\) | 53.6101 | 2.08048 | ||||||||
\(665\) | 7.21606 | 0.279827 | ||||||||
\(666\) | 1.03300 | 0.0400278 | ||||||||
\(667\) | 60.1108 | 2.32750 | ||||||||
\(668\) | −10.8462 | −0.419650 | ||||||||
\(669\) | 23.9297 | 0.925174 | ||||||||
\(670\) | −18.3858 | −0.710307 | ||||||||
\(671\) | −39.2985 | −1.51710 | ||||||||
\(672\) | 4.51441 | 0.174147 | ||||||||
\(673\) | 45.7730 | 1.76442 | 0.882210 | − | 0.470856i | \(-0.156055\pi\) | ||||
0.882210 | + | 0.470856i | \(0.156055\pi\) | |||||||
\(674\) | −44.1853 | −1.70195 | ||||||||
\(675\) | 2.44704 | 0.0941868 | ||||||||
\(676\) | −44.1193 | −1.69690 | ||||||||
\(677\) | −16.7208 | −0.642632 | −0.321316 | − | 0.946972i | \(-0.604125\pi\) | ||||
−0.321316 | + | 0.946972i | \(0.604125\pi\) | |||||||
\(678\) | −5.93807 | −0.228050 | ||||||||
\(679\) | 16.6173 | 0.637714 | ||||||||
\(680\) | 1.54847 | 0.0593810 | ||||||||
\(681\) | −25.0959 | −0.961676 | ||||||||
\(682\) | 80.5391 | 3.08400 | ||||||||
\(683\) | 26.0426 | 0.996493 | 0.498246 | − | 0.867035i | \(-0.333978\pi\) | ||||
0.498246 | + | 0.867035i | \(0.333978\pi\) | |||||||
\(684\) | 15.5206 | 0.593446 | ||||||||
\(685\) | 25.1864 | 0.962324 | ||||||||
\(686\) | 2.33165 | 0.0890230 | ||||||||
\(687\) | 21.0074 | 0.801481 | ||||||||
\(688\) | 9.11201 | 0.347392 | ||||||||
\(689\) | 4.32953 | 0.164942 | ||||||||
\(690\) | −28.0911 | −1.06941 | ||||||||
\(691\) | −17.1943 | −0.654102 | −0.327051 | − | 0.945007i | \(-0.606055\pi\) | ||||
−0.327051 | + | 0.945007i | \(0.606055\pi\) | |||||||
\(692\) | 21.6223 | 0.821957 | ||||||||
\(693\) | 5.81283 | 0.220811 | ||||||||
\(694\) | −74.5591 | −2.83022 | ||||||||
\(695\) | 3.51547 | 0.133349 | ||||||||
\(696\) | 26.7038 | 1.01221 | ||||||||
\(697\) | −1.52942 | −0.0579310 | ||||||||
\(698\) | 40.8515 | 1.54625 | ||||||||
\(699\) | −17.9336 | −0.678313 | ||||||||
\(700\) | 8.40955 | 0.317851 | ||||||||
\(701\) | 24.0669 | 0.908992 | 0.454496 | − | 0.890749i | \(-0.349819\pi\) | ||||
0.454496 | + | 0.890749i | \(0.349819\pi\) | |||||||
\(702\) | −0.938402 | −0.0354177 | ||||||||
\(703\) | −2.00084 | −0.0754632 | ||||||||
\(704\) | 72.0804 | 2.71663 | ||||||||
\(705\) | 4.83383 | 0.182053 | ||||||||
\(706\) | −78.9424 | −2.97104 | ||||||||
\(707\) | 14.3690 | 0.540403 | ||||||||
\(708\) | 6.88651 | 0.258811 | ||||||||
\(709\) | 19.6823 | 0.739183 | 0.369591 | − | 0.929194i | \(-0.379498\pi\) | ||||
0.369591 | + | 0.929194i | \(0.379498\pi\) | |||||||
\(710\) | −47.5537 | −1.78466 | ||||||||
\(711\) | 2.61238 | 0.0979719 | ||||||||
\(712\) | 24.2139 | 0.907454 | ||||||||
\(713\) | 44.8062 | 1.67800 | ||||||||
\(714\) | −0.674591 | −0.0252459 | ||||||||
\(715\) | −3.73796 | −0.139792 | ||||||||
\(716\) | 18.7520 | 0.700794 | ||||||||
\(717\) | 26.3324 | 0.983402 | ||||||||
\(718\) | −59.5850 | −2.22369 | ||||||||
\(719\) | −32.5767 | −1.21491 | −0.607454 | − | 0.794355i | \(-0.707809\pi\) | ||||
−0.607454 | + | 0.794355i | \(0.707809\pi\) | |||||||
\(720\) | −1.49727 | −0.0558000 | ||||||||
\(721\) | 0.298231 | 0.0111067 | ||||||||
\(722\) | −3.25630 | −0.121187 | ||||||||
\(723\) | −11.6061 | −0.431636 | ||||||||
\(724\) | 30.0982 | 1.11859 | ||||||||
\(725\) | −19.5079 | −0.724506 | ||||||||
\(726\) | 53.1361 | 1.97207 | ||||||||
\(727\) | 13.6078 | 0.504684 | 0.252342 | − | 0.967638i | \(-0.418799\pi\) | ||||
0.252342 | + | 0.967638i | \(0.418799\pi\) | |||||||
\(728\) | −1.34812 | −0.0499647 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 37.8290 | 1.40012 | ||||||||
\(731\) | 2.81327 | 0.104052 | ||||||||
\(732\) | −23.2337 | −0.858743 | ||||||||
\(733\) | 44.3774 | 1.63912 | 0.819558 | − | 0.572996i | \(-0.194219\pi\) | ||||
0.819558 | + | 0.572996i | \(0.194219\pi\) | |||||||
\(734\) | 73.7067 | 2.72057 | ||||||||
\(735\) | 1.59780 | 0.0589356 | ||||||||
\(736\) | 34.0396 | 1.25472 | ||||||||
\(737\) | 28.6870 | 1.05670 | ||||||||
\(738\) | 12.3258 | 0.453720 | ||||||||
\(739\) | −21.6585 | −0.796720 | −0.398360 | − | 0.917229i | \(-0.630420\pi\) | ||||
−0.398360 | + | 0.917229i | \(0.630420\pi\) | |||||||
\(740\) | 2.43269 | 0.0894274 | ||||||||
\(741\) | 1.81762 | 0.0667719 | ||||||||
\(742\) | −25.0830 | −0.920828 | ||||||||
\(743\) | −13.6760 | −0.501726 | −0.250863 | − | 0.968023i | \(-0.580714\pi\) | ||||
−0.250863 | + | 0.968023i | \(0.580714\pi\) | |||||||
\(744\) | 19.9049 | 0.729747 | ||||||||
\(745\) | −4.03094 | −0.147682 | ||||||||
\(746\) | −15.4072 | −0.564097 | ||||||||
\(747\) | −16.0045 | −0.585575 | ||||||||
\(748\) | −5.77956 | −0.211322 | ||||||||
\(749\) | −14.1875 | −0.518401 | ||||||||
\(750\) | 27.7440 | 1.01307 | ||||||||
\(751\) | 26.2599 | 0.958239 | 0.479119 | − | 0.877750i | \(-0.340956\pi\) | ||||
0.479119 | + | 0.877750i | \(0.340956\pi\) | |||||||
\(752\) | 2.83497 | 0.103381 | ||||||||
\(753\) | −15.5574 | −0.566943 | ||||||||
\(754\) | 7.48097 | 0.272441 | ||||||||
\(755\) | −24.9894 | −0.909458 | ||||||||
\(756\) | 3.43661 | 0.124988 | ||||||||
\(757\) | 14.9365 | 0.542876 | 0.271438 | − | 0.962456i | \(-0.412501\pi\) | ||||
0.271438 | + | 0.962456i | \(0.412501\pi\) | |||||||
\(758\) | 36.6869 | 1.33253 | ||||||||
\(759\) | 43.8299 | 1.59093 | ||||||||
\(760\) | 24.1715 | 0.876794 | ||||||||
\(761\) | 44.1733 | 1.60128 | 0.800641 | − | 0.599144i | \(-0.204492\pi\) | ||||
0.800641 | + | 0.599144i | \(0.204492\pi\) | |||||||
\(762\) | 2.56825 | 0.0930379 | ||||||||
\(763\) | −4.30479 | −0.155844 | ||||||||
\(764\) | −61.5396 | −2.22643 | ||||||||
\(765\) | −0.462272 | −0.0167135 | ||||||||
\(766\) | −2.33165 | −0.0842461 | ||||||||
\(767\) | 0.806479 | 0.0291203 | ||||||||
\(768\) | 21.5627 | 0.778076 | ||||||||
\(769\) | −5.04610 | −0.181967 | −0.0909836 | − | 0.995852i | \(-0.529001\pi\) | ||||
−0.0909836 | + | 0.995852i | \(0.529001\pi\) | |||||||
\(770\) | 21.6558 | 0.780420 | ||||||||
\(771\) | −10.4359 | −0.375841 | ||||||||
\(772\) | 66.4007 | 2.38981 | ||||||||
\(773\) | −8.47679 | −0.304889 | −0.152444 | − | 0.988312i | \(-0.548714\pi\) | ||||
−0.152444 | + | 0.988312i | \(0.548714\pi\) | |||||||
\(774\) | −22.6725 | −0.814946 | ||||||||
\(775\) | −14.5411 | −0.522331 | ||||||||
\(776\) | 55.6628 | 1.99818 | ||||||||
\(777\) | −0.443031 | −0.0158936 | ||||||||
\(778\) | −67.0957 | −2.40550 | ||||||||
\(779\) | −23.8743 | −0.855384 | ||||||||
\(780\) | −2.20992 | −0.0791279 | ||||||||
\(781\) | 74.1970 | 2.65498 | ||||||||
\(782\) | −5.08655 | −0.181895 | ||||||||
\(783\) | −7.97204 | −0.284897 | ||||||||
\(784\) | 0.937085 | 0.0334673 | ||||||||
\(785\) | −9.49814 | −0.339003 | ||||||||
\(786\) | 13.1899 | 0.470468 | ||||||||
\(787\) | 13.5247 | 0.482103 | 0.241051 | − | 0.970512i | \(-0.422508\pi\) | ||||
0.241051 | + | 0.970512i | \(0.422508\pi\) | |||||||
\(788\) | −60.3784 | −2.15089 | ||||||||
\(789\) | 14.7946 | 0.526702 | ||||||||
\(790\) | 9.73245 | 0.346265 | ||||||||
\(791\) | 2.54672 | 0.0905509 | ||||||||
\(792\) | 19.4712 | 0.691878 | ||||||||
\(793\) | −2.72090 | −0.0966220 | ||||||||
\(794\) | −12.5365 | −0.444905 | ||||||||
\(795\) | −17.1885 | −0.609613 | ||||||||
\(796\) | 82.0011 | 2.90645 | ||||||||
\(797\) | 50.0068 | 1.77133 | 0.885666 | − | 0.464324i | \(-0.153703\pi\) | ||||
0.885666 | + | 0.464324i | \(0.153703\pi\) | |||||||
\(798\) | −10.5303 | −0.372770 | ||||||||
\(799\) | 0.875278 | 0.0309651 | ||||||||
\(800\) | −11.0470 | −0.390569 | ||||||||
\(801\) | −7.22871 | −0.255414 | ||||||||
\(802\) | −51.7582 | −1.82764 | ||||||||
\(803\) | −59.0238 | −2.08291 | ||||||||
\(804\) | 16.9601 | 0.598136 | ||||||||
\(805\) | 12.0477 | 0.424626 | ||||||||
\(806\) | 5.57627 | 0.196416 | ||||||||
\(807\) | 21.5132 | 0.757299 | ||||||||
\(808\) | 48.1317 | 1.69327 | ||||||||
\(809\) | −39.4153 | −1.38577 | −0.692883 | − | 0.721050i | \(-0.743660\pi\) | ||||
−0.692883 | + | 0.721050i | \(0.743660\pi\) | |||||||
\(810\) | 3.72551 | 0.130901 | ||||||||
\(811\) | −43.3030 | −1.52057 | −0.760286 | − | 0.649588i | \(-0.774941\pi\) | ||||
−0.760286 | + | 0.649588i | \(0.774941\pi\) | |||||||
\(812\) | −27.3968 | −0.961440 | ||||||||
\(813\) | 20.9775 | 0.735711 | ||||||||
\(814\) | −6.00463 | −0.210462 | ||||||||
\(815\) | 35.6527 | 1.24886 | ||||||||
\(816\) | −0.271116 | −0.00949096 | ||||||||
\(817\) | 43.9151 | 1.53639 | ||||||||
\(818\) | −48.9430 | −1.71125 | ||||||||
\(819\) | 0.402462 | 0.0140632 | ||||||||
\(820\) | 29.0271 | 1.01367 | ||||||||
\(821\) | 13.5554 | 0.473085 | 0.236543 | − | 0.971621i | \(-0.423986\pi\) | ||||
0.236543 | + | 0.971621i | \(0.423986\pi\) | |||||||
\(822\) | −36.7544 | −1.28196 | ||||||||
\(823\) | −15.7731 | −0.549815 | −0.274907 | − | 0.961471i | \(-0.588647\pi\) | ||||
−0.274907 | + | 0.961471i | \(0.588647\pi\) | |||||||
\(824\) | 0.998980 | 0.0348011 | ||||||||
\(825\) | −14.2243 | −0.495225 | ||||||||
\(826\) | −4.67232 | −0.162571 | ||||||||
\(827\) | 22.8042 | 0.792980 | 0.396490 | − | 0.918039i | \(-0.370228\pi\) | ||||
0.396490 | + | 0.918039i | \(0.370228\pi\) | |||||||
\(828\) | 25.9128 | 0.900531 | ||||||||
\(829\) | 43.8904 | 1.52438 | 0.762188 | − | 0.647356i | \(-0.224125\pi\) | ||||
0.762188 | + | 0.647356i | \(0.224125\pi\) | |||||||
\(830\) | −59.6250 | −2.06962 | ||||||||
\(831\) | −9.97176 | −0.345916 | ||||||||
\(832\) | 4.99062 | 0.173018 | ||||||||
\(833\) | 0.289318 | 0.0100243 | ||||||||
\(834\) | −5.13010 | −0.177641 | ||||||||
\(835\) | 5.04274 | 0.174511 | ||||||||
\(836\) | −90.2188 | −3.12028 | ||||||||
\(837\) | −5.94230 | −0.205396 | ||||||||
\(838\) | 16.0541 | 0.554580 | ||||||||
\(839\) | −32.3666 | −1.11742 | −0.558710 | − | 0.829363i | \(-0.688703\pi\) | ||||
−0.558710 | + | 0.829363i | \(0.688703\pi\) | |||||||
\(840\) | 5.35212 | 0.184666 | ||||||||
\(841\) | 34.5534 | 1.19150 | ||||||||
\(842\) | −55.3568 | −1.90772 | ||||||||
\(843\) | 22.6902 | 0.781492 | ||||||||
\(844\) | 24.1012 | 0.829596 | ||||||||
\(845\) | 20.5126 | 0.705653 | ||||||||
\(846\) | −7.05398 | −0.242521 | ||||||||
\(847\) | −22.7890 | −0.783040 | ||||||||
\(848\) | −10.0808 | −0.346176 | ||||||||
\(849\) | −6.26616 | −0.215054 | ||||||||
\(850\) | 1.65075 | 0.0566204 | ||||||||
\(851\) | −3.34054 | −0.114512 | ||||||||
\(852\) | 43.8661 | 1.50283 | ||||||||
\(853\) | 53.9608 | 1.84758 | 0.923791 | − | 0.382898i | \(-0.125074\pi\) | ||||
0.923791 | + | 0.382898i | \(0.125074\pi\) | |||||||
\(854\) | 15.7635 | 0.539415 | ||||||||
\(855\) | −7.21606 | −0.246784 | ||||||||
\(856\) | −47.5237 | −1.62433 | ||||||||
\(857\) | −6.64829 | −0.227101 | −0.113551 | − | 0.993532i | \(-0.536222\pi\) | ||||
−0.113551 | + | 0.993532i | \(0.536222\pi\) | |||||||
\(858\) | 5.45477 | 0.186223 | ||||||||
\(859\) | 17.0555 | 0.581926 | 0.290963 | − | 0.956734i | \(-0.406024\pi\) | ||||
0.290963 | + | 0.956734i | \(0.406024\pi\) | |||||||
\(860\) | −53.3934 | −1.82070 | ||||||||
\(861\) | −5.28630 | −0.180156 | ||||||||
\(862\) | 72.0937 | 2.45552 | ||||||||
\(863\) | 29.0399 | 0.988530 | 0.494265 | − | 0.869311i | \(-0.335437\pi\) | ||||
0.494265 | + | 0.869311i | \(0.335437\pi\) | |||||||
\(864\) | −4.51441 | −0.153583 | ||||||||
\(865\) | −10.0529 | −0.341810 | ||||||||
\(866\) | 91.6970 | 3.11599 | ||||||||
\(867\) | 16.9163 | 0.574507 | ||||||||
\(868\) | −20.4214 | −0.693147 | ||||||||
\(869\) | −15.1853 | −0.515127 | ||||||||
\(870\) | −29.6999 | −1.00692 | ||||||||
\(871\) | 1.98620 | 0.0672997 | ||||||||
\(872\) | −14.4197 | −0.488313 | ||||||||
\(873\) | −16.6173 | −0.562411 | ||||||||
\(874\) | −79.4009 | −2.68578 | ||||||||
\(875\) | −11.8989 | −0.402255 | ||||||||
\(876\) | −34.8956 | −1.17901 | ||||||||
\(877\) | 8.85278 | 0.298937 | 0.149469 | − | 0.988766i | \(-0.452244\pi\) | ||||
0.149469 | + | 0.988766i | \(0.452244\pi\) | |||||||
\(878\) | 75.1425 | 2.53594 | ||||||||
\(879\) | −23.3443 | −0.787382 | ||||||||
\(880\) | 8.70339 | 0.293391 | ||||||||
\(881\) | −44.5240 | −1.50005 | −0.750026 | − | 0.661409i | \(-0.769959\pi\) | ||||
−0.750026 | + | 0.661409i | \(0.769959\pi\) | |||||||
\(882\) | −2.33165 | −0.0785109 | ||||||||
\(883\) | 4.16684 | 0.140225 | 0.0701127 | − | 0.997539i | \(-0.477664\pi\) | ||||
0.0701127 | + | 0.997539i | \(0.477664\pi\) | |||||||
\(884\) | −0.400158 | −0.0134588 | ||||||||
\(885\) | −3.20177 | −0.107626 | ||||||||
\(886\) | 9.55241 | 0.320919 | ||||||||
\(887\) | 14.1528 | 0.475205 | 0.237602 | − | 0.971363i | \(-0.423639\pi\) | ||||
0.237602 | + | 0.971363i | \(0.423639\pi\) | |||||||
\(888\) | −1.48402 | −0.0498003 | ||||||||
\(889\) | −1.10147 | −0.0369421 | ||||||||
\(890\) | −26.9306 | −0.902717 | ||||||||
\(891\) | −5.81283 | −0.194737 | ||||||||
\(892\) | −82.2370 | −2.75350 | ||||||||
\(893\) | 13.6631 | 0.457217 | ||||||||
\(894\) | 5.88232 | 0.196734 | ||||||||
\(895\) | −8.71842 | −0.291425 | ||||||||
\(896\) | −19.8842 | −0.664285 | ||||||||
\(897\) | 3.03464 | 0.101324 | ||||||||
\(898\) | 40.8809 | 1.36421 | ||||||||
\(899\) | 47.3723 | 1.57995 | ||||||||
\(900\) | −8.40955 | −0.280318 | ||||||||
\(901\) | −3.11238 | −0.103688 | ||||||||
\(902\) | −71.6479 | −2.38561 | ||||||||
\(903\) | 9.72378 | 0.323587 | ||||||||
\(904\) | 8.53071 | 0.283727 | ||||||||
\(905\) | −13.9937 | −0.465165 | ||||||||
\(906\) | 36.4669 | 1.21153 | ||||||||
\(907\) | −17.2412 | −0.572483 | −0.286242 | − | 0.958157i | \(-0.592406\pi\) | ||||
−0.286242 | + | 0.958157i | \(0.592406\pi\) | |||||||
\(908\) | 86.2448 | 2.86213 | ||||||||
\(909\) | −14.3690 | −0.476590 | ||||||||
\(910\) | 1.49938 | 0.0497038 | ||||||||
\(911\) | 10.6056 | 0.351380 | 0.175690 | − | 0.984446i | \(-0.443784\pi\) | ||||
0.175690 | + | 0.984446i | \(0.443784\pi\) | |||||||
\(912\) | −4.23212 | −0.140139 | ||||||||
\(913\) | 93.0316 | 3.07890 | ||||||||
\(914\) | −91.7711 | −3.03552 | ||||||||
\(915\) | 10.8021 | 0.357108 | ||||||||
\(916\) | −72.1942 | −2.38536 | ||||||||
\(917\) | −5.65688 | −0.186807 | ||||||||
\(918\) | 0.674591 | 0.0222648 | ||||||||
\(919\) | −27.1277 | −0.894861 | −0.447431 | − | 0.894319i | \(-0.647661\pi\) | ||||
−0.447431 | + | 0.894319i | \(0.647661\pi\) | |||||||
\(920\) | 40.3561 | 1.33050 | ||||||||
\(921\) | −4.85883 | −0.160104 | ||||||||
\(922\) | −52.5613 | −1.73101 | ||||||||
\(923\) | 5.13716 | 0.169092 | ||||||||
\(924\) | −19.9765 | −0.657177 | ||||||||
\(925\) | 1.08412 | 0.0356455 | ||||||||
\(926\) | −11.6720 | −0.383565 | ||||||||
\(927\) | −0.298231 | −0.00979518 | ||||||||
\(928\) | 35.9891 | 1.18140 | ||||||||
\(929\) | 23.0252 | 0.755431 | 0.377715 | − | 0.925922i | \(-0.376710\pi\) | ||||
0.377715 | + | 0.925922i | \(0.376710\pi\) | |||||||
\(930\) | −22.1381 | −0.725937 | ||||||||
\(931\) | 4.51626 | 0.148014 | ||||||||
\(932\) | 61.6310 | 2.01879 | ||||||||
\(933\) | 9.25092 | 0.302861 | ||||||||
\(934\) | −90.5627 | −2.96330 | ||||||||
\(935\) | 2.68711 | 0.0878779 | ||||||||
\(936\) | 1.34812 | 0.0440647 | ||||||||
\(937\) | 33.7275 | 1.10183 | 0.550915 | − | 0.834561i | \(-0.314279\pi\) | ||||
0.550915 | + | 0.834561i | \(0.314279\pi\) | |||||||
\(938\) | −11.5070 | −0.375716 | ||||||||
\(939\) | −11.2008 | −0.365525 | ||||||||
\(940\) | −16.6120 | −0.541824 | ||||||||
\(941\) | −50.9437 | −1.66072 | −0.830359 | − | 0.557228i | \(-0.811865\pi\) | ||||
−0.830359 | + | 0.557228i | \(0.811865\pi\) | |||||||
\(942\) | 13.8606 | 0.451602 | ||||||||
\(943\) | −39.8597 | −1.29801 | ||||||||
\(944\) | −1.87779 | −0.0611169 | ||||||||
\(945\) | −1.59780 | −0.0519763 | ||||||||
\(946\) | 131.791 | 4.28491 | ||||||||
\(947\) | −59.5145 | −1.93396 | −0.966980 | − | 0.254853i | \(-0.917973\pi\) | ||||
−0.966980 | + | 0.254853i | \(0.917973\pi\) | |||||||
\(948\) | −8.97774 | −0.291583 | ||||||||
\(949\) | −4.08662 | −0.132657 | ||||||||
\(950\) | 25.7682 | 0.836032 | ||||||||
\(951\) | −11.4783 | −0.372210 | ||||||||
\(952\) | 0.969126 | 0.0314096 | ||||||||
\(953\) | −21.4127 | −0.693625 | −0.346812 | − | 0.937935i | \(-0.612736\pi\) | ||||
−0.346812 | + | 0.937935i | \(0.612736\pi\) | |||||||
\(954\) | 25.0830 | 0.812094 | ||||||||
\(955\) | 28.6118 | 0.925858 | ||||||||
\(956\) | −90.4944 | −2.92680 | ||||||||
\(957\) | 46.3401 | 1.49796 | ||||||||
\(958\) | 43.8686 | 1.41733 | ||||||||
\(959\) | 15.7632 | 0.509021 | ||||||||
\(960\) | −19.8130 | −0.639463 | ||||||||
\(961\) | 4.31096 | 0.139063 | ||||||||
\(962\) | −0.415741 | −0.0134040 | ||||||||
\(963\) | 14.1875 | 0.457186 | ||||||||
\(964\) | 39.8858 | 1.28463 | ||||||||
\(965\) | −30.8719 | −0.993802 | ||||||||
\(966\) | −17.5811 | −0.565664 | ||||||||
\(967\) | −35.8832 | −1.15392 | −0.576962 | − | 0.816771i | \(-0.695762\pi\) | ||||
−0.576962 | + | 0.816771i | \(0.695762\pi\) | |||||||
\(968\) | −76.3361 | −2.45353 | ||||||||
\(969\) | −1.30664 | −0.0419752 | ||||||||
\(970\) | −61.9080 | −1.98775 | ||||||||
\(971\) | 51.9947 | 1.66859 | 0.834295 | − | 0.551319i | \(-0.185875\pi\) | ||||
0.834295 | + | 0.551319i | \(0.185875\pi\) | |||||||
\(972\) | −3.43661 | −0.110229 | ||||||||
\(973\) | 2.20020 | 0.0705350 | ||||||||
\(974\) | 45.8867 | 1.47030 | ||||||||
\(975\) | −0.984842 | −0.0315402 | ||||||||
\(976\) | 6.33530 | 0.202788 | ||||||||
\(977\) | 24.4196 | 0.781252 | 0.390626 | − | 0.920550i | \(-0.372259\pi\) | ||||
0.390626 | + | 0.920550i | \(0.372259\pi\) | |||||||
\(978\) | −52.0278 | −1.66366 | ||||||||
\(979\) | 42.0193 | 1.34294 | ||||||||
\(980\) | −5.49101 | −0.175404 | ||||||||
\(981\) | 4.30479 | 0.137441 | ||||||||
\(982\) | 68.7643 | 2.19436 | ||||||||
\(983\) | 25.3920 | 0.809880 | 0.404940 | − | 0.914343i | \(-0.367292\pi\) | ||||
0.404940 | + | 0.914343i | \(0.367292\pi\) | |||||||
\(984\) | −17.7074 | −0.564492 | ||||||||
\(985\) | 28.0720 | 0.894447 | ||||||||
\(986\) | −5.37786 | −0.171266 | ||||||||
\(987\) | 3.02531 | 0.0962967 | ||||||||
\(988\) | −6.24646 | −0.198726 | ||||||||
\(989\) | 73.3192 | 2.33142 | ||||||||
\(990\) | −21.6558 | −0.688266 | ||||||||
\(991\) | 11.2458 | 0.357236 | 0.178618 | − | 0.983918i | \(-0.442837\pi\) | ||||
0.178618 | + | 0.983918i | \(0.442837\pi\) | |||||||
\(992\) | 26.8260 | 0.851727 | ||||||||
\(993\) | −15.6860 | −0.497780 | ||||||||
\(994\) | −29.7620 | −0.943995 | ||||||||
\(995\) | −38.1251 | −1.20865 | ||||||||
\(996\) | 55.0014 | 1.74279 | ||||||||
\(997\) | 36.4242 | 1.15357 | 0.576783 | − | 0.816898i | \(-0.304308\pi\) | ||||
0.576783 | + | 0.816898i | \(0.304308\pi\) | |||||||
\(998\) | 84.9723 | 2.68975 | ||||||||
\(999\) | 0.443031 | 0.0140169 |
(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 | 8043.2.a.s.1.7 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.s.1.7 | ✓ | 50 | 1.1 | even | 1 | trivial |