Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.36108 | −1.66954 | −0.834769 | − | 0.550601i | \(-0.814399\pi\) | ||||
−0.834769 | + | 0.550601i | \(0.814399\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.57471 | 1.78735 | ||||||||
\(5\) | 4.34691 | 1.94400 | 0.971998 | − | 0.234991i | \(-0.0755060\pi\) | ||||
0.971998 | + | 0.234991i | \(0.0755060\pi\) | |||||||
\(6\) | 2.36108 | 0.963908 | ||||||||
\(7\) | −0.239132 | −0.0903835 | −0.0451918 | − | 0.998978i | \(-0.514390\pi\) | ||||
−0.0451918 | + | 0.998978i | \(0.514390\pi\) | |||||||
\(8\) | −3.71802 | −1.31452 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −10.2634 | −3.24557 | ||||||||
\(11\) | −4.29376 | −1.29462 | −0.647309 | − | 0.762228i | \(-0.724106\pi\) | ||||
−0.647309 | + | 0.762228i | \(0.724106\pi\) | |||||||
\(12\) | −3.57471 | −1.03193 | ||||||||
\(13\) | −2.72772 | −0.756533 | −0.378266 | − | 0.925697i | \(-0.623480\pi\) | ||||
−0.378266 | + | 0.925697i | \(0.623480\pi\) | |||||||
\(14\) | 0.564611 | 0.150899 | ||||||||
\(15\) | −4.34691 | −1.12237 | ||||||||
\(16\) | 1.62912 | 0.407281 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −2.36108 | −0.556512 | ||||||||
\(19\) | −0.558873 | −0.128214 | −0.0641071 | − | 0.997943i | \(-0.520420\pi\) | ||||
−0.0641071 | + | 0.997943i | \(0.520420\pi\) | |||||||
\(20\) | 15.5389 | 3.47461 | ||||||||
\(21\) | 0.239132 | 0.0521830 | ||||||||
\(22\) | 10.1379 | 2.16141 | ||||||||
\(23\) | 2.65463 | 0.553529 | 0.276764 | − | 0.960938i | \(-0.410738\pi\) | ||||
0.276764 | + | 0.960938i | \(0.410738\pi\) | |||||||
\(24\) | 3.71802 | 0.758937 | ||||||||
\(25\) | 13.8956 | 2.77912 | ||||||||
\(26\) | 6.44036 | 1.26306 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.854829 | −0.161547 | ||||||||
\(29\) | 5.97258 | 1.10908 | 0.554540 | − | 0.832157i | \(-0.312894\pi\) | ||||
0.554540 | + | 0.832157i | \(0.312894\pi\) | |||||||
\(30\) | 10.2634 | 1.87383 | ||||||||
\(31\) | 4.82570 | 0.866721 | 0.433361 | − | 0.901221i | \(-0.357328\pi\) | ||||
0.433361 | + | 0.901221i | \(0.357328\pi\) | |||||||
\(32\) | 3.58954 | 0.634547 | ||||||||
\(33\) | 4.29376 | 0.747448 | ||||||||
\(34\) | 2.36108 | 0.404922 | ||||||||
\(35\) | −1.03949 | −0.175705 | ||||||||
\(36\) | 3.57471 | 0.595785 | ||||||||
\(37\) | 10.0820 | 1.65747 | 0.828737 | − | 0.559638i | \(-0.189060\pi\) | ||||
0.828737 | + | 0.559638i | \(0.189060\pi\) | |||||||
\(38\) | 1.31954 | 0.214058 | ||||||||
\(39\) | 2.72772 | 0.436784 | ||||||||
\(40\) | −16.1619 | −2.55541 | ||||||||
\(41\) | 3.97167 | 0.620271 | 0.310136 | − | 0.950692i | \(-0.399626\pi\) | ||||
0.310136 | + | 0.950692i | \(0.399626\pi\) | |||||||
\(42\) | −0.564611 | −0.0871214 | ||||||||
\(43\) | −7.12244 | −1.08616 | −0.543081 | − | 0.839680i | \(-0.682742\pi\) | ||||
−0.543081 | + | 0.839680i | \(0.682742\pi\) | |||||||
\(44\) | −15.3489 | −2.31394 | ||||||||
\(45\) | 4.34691 | 0.647998 | ||||||||
\(46\) | −6.26780 | −0.924137 | ||||||||
\(47\) | −2.80084 | −0.408545 | −0.204273 | − | 0.978914i | \(-0.565483\pi\) | ||||
−0.204273 | + | 0.978914i | \(0.565483\pi\) | |||||||
\(48\) | −1.62912 | −0.235144 | ||||||||
\(49\) | −6.94282 | −0.991831 | ||||||||
\(50\) | −32.8086 | −4.63984 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −9.75079 | −1.35219 | ||||||||
\(53\) | 1.71862 | 0.236070 | 0.118035 | − | 0.993009i | \(-0.462340\pi\) | ||||
0.118035 | + | 0.993009i | \(0.462340\pi\) | |||||||
\(54\) | 2.36108 | 0.321303 | ||||||||
\(55\) | −18.6646 | −2.51673 | ||||||||
\(56\) | 0.889098 | 0.118811 | ||||||||
\(57\) | 0.558873 | 0.0740245 | ||||||||
\(58\) | −14.1017 | −1.85165 | ||||||||
\(59\) | −2.11577 | −0.275449 | −0.137725 | − | 0.990471i | \(-0.543979\pi\) | ||||
−0.137725 | + | 0.990471i | \(0.543979\pi\) | |||||||
\(60\) | −15.5389 | −2.00607 | ||||||||
\(61\) | −1.44266 | −0.184714 | −0.0923569 | − | 0.995726i | \(-0.529440\pi\) | ||||
−0.0923569 | + | 0.995726i | \(0.529440\pi\) | |||||||
\(62\) | −11.3939 | −1.44702 | ||||||||
\(63\) | −0.239132 | −0.0301278 | ||||||||
\(64\) | −11.7334 | −1.46668 | ||||||||
\(65\) | −11.8571 | −1.47070 | ||||||||
\(66\) | −10.1379 | −1.24789 | ||||||||
\(67\) | 10.5560 | 1.28963 | 0.644813 | − | 0.764340i | \(-0.276935\pi\) | ||||
0.644813 | + | 0.764340i | \(0.276935\pi\) | |||||||
\(68\) | −3.57471 | −0.433497 | ||||||||
\(69\) | −2.65463 | −0.319580 | ||||||||
\(70\) | 2.45431 | 0.293346 | ||||||||
\(71\) | 15.0221 | 1.78280 | 0.891401 | − | 0.453216i | \(-0.149724\pi\) | ||||
0.891401 | + | 0.453216i | \(0.149724\pi\) | |||||||
\(72\) | −3.71802 | −0.438172 | ||||||||
\(73\) | 13.2860 | 1.55501 | 0.777507 | − | 0.628874i | \(-0.216484\pi\) | ||||
0.777507 | + | 0.628874i | \(0.216484\pi\) | |||||||
\(74\) | −23.8045 | −2.76722 | ||||||||
\(75\) | −13.8956 | −1.60452 | ||||||||
\(76\) | −1.99781 | −0.229164 | ||||||||
\(77\) | 1.02678 | 0.117012 | ||||||||
\(78\) | −6.44036 | −0.729228 | ||||||||
\(79\) | −17.3773 | −1.95510 | −0.977549 | − | 0.210709i | \(-0.932423\pi\) | ||||
−0.977549 | + | 0.210709i | \(0.932423\pi\) | |||||||
\(80\) | 7.08164 | 0.791752 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.37745 | −1.03557 | ||||||||
\(83\) | −15.7988 | −1.73414 | −0.867072 | − | 0.498182i | \(-0.834001\pi\) | ||||
−0.867072 | + | 0.498182i | \(0.834001\pi\) | |||||||
\(84\) | 0.854829 | 0.0932694 | ||||||||
\(85\) | −4.34691 | −0.471488 | ||||||||
\(86\) | 16.8167 | 1.81339 | ||||||||
\(87\) | −5.97258 | −0.640327 | ||||||||
\(88\) | 15.9643 | 1.70180 | ||||||||
\(89\) | −3.58085 | −0.379569 | −0.189785 | − | 0.981826i | \(-0.560779\pi\) | ||||
−0.189785 | + | 0.981826i | \(0.560779\pi\) | |||||||
\(90\) | −10.2634 | −1.08186 | ||||||||
\(91\) | 0.652286 | 0.0683781 | ||||||||
\(92\) | 9.48953 | 0.989352 | ||||||||
\(93\) | −4.82570 | −0.500402 | ||||||||
\(94\) | 6.61302 | 0.682081 | ||||||||
\(95\) | −2.42937 | −0.249248 | ||||||||
\(96\) | −3.58954 | −0.366356 | ||||||||
\(97\) | 9.93045 | 1.00828 | 0.504142 | − | 0.863621i | \(-0.331809\pi\) | ||||
0.504142 | + | 0.863621i | \(0.331809\pi\) | |||||||
\(98\) | 16.3926 | 1.65590 | ||||||||
\(99\) | −4.29376 | −0.431539 | ||||||||
\(100\) | 49.6727 | 4.96727 | ||||||||
\(101\) | 13.2773 | 1.32114 | 0.660570 | − | 0.750764i | \(-0.270315\pi\) | ||||
0.660570 | + | 0.750764i | \(0.270315\pi\) | |||||||
\(102\) | −2.36108 | −0.233782 | ||||||||
\(103\) | 5.88732 | 0.580095 | 0.290047 | − | 0.957012i | \(-0.406329\pi\) | ||||
0.290047 | + | 0.957012i | \(0.406329\pi\) | |||||||
\(104\) | 10.1417 | 0.994475 | ||||||||
\(105\) | 1.03949 | 0.101443 | ||||||||
\(106\) | −4.05780 | −0.394128 | ||||||||
\(107\) | −8.75477 | −0.846356 | −0.423178 | − | 0.906047i | \(-0.639085\pi\) | ||||
−0.423178 | + | 0.906047i | \(0.639085\pi\) | |||||||
\(108\) | −3.57471 | −0.343976 | ||||||||
\(109\) | −18.7043 | −1.79154 | −0.895771 | − | 0.444515i | \(-0.853376\pi\) | ||||
−0.895771 | + | 0.444515i | \(0.853376\pi\) | |||||||
\(110\) | 44.0686 | 4.20177 | ||||||||
\(111\) | −10.0820 | −0.956944 | ||||||||
\(112\) | −0.389576 | −0.0368115 | ||||||||
\(113\) | −17.0792 | −1.60668 | −0.803340 | − | 0.595521i | \(-0.796946\pi\) | ||||
−0.803340 | + | 0.595521i | \(0.796946\pi\) | |||||||
\(114\) | −1.31954 | −0.123587 | ||||||||
\(115\) | 11.5394 | 1.07606 | ||||||||
\(116\) | 21.3502 | 1.98232 | ||||||||
\(117\) | −2.72772 | −0.252178 | ||||||||
\(118\) | 4.99549 | 0.459873 | ||||||||
\(119\) | 0.239132 | 0.0219212 | ||||||||
\(120\) | 16.1619 | 1.47537 | ||||||||
\(121\) | 7.43637 | 0.676034 | ||||||||
\(122\) | 3.40624 | 0.308387 | ||||||||
\(123\) | −3.97167 | −0.358114 | ||||||||
\(124\) | 17.2505 | 1.54914 | ||||||||
\(125\) | 38.6683 | 3.45860 | ||||||||
\(126\) | 0.564611 | 0.0502996 | ||||||||
\(127\) | 5.59833 | 0.496772 | 0.248386 | − | 0.968661i | \(-0.420100\pi\) | ||||
0.248386 | + | 0.968661i | \(0.420100\pi\) | |||||||
\(128\) | 20.5245 | 1.81413 | ||||||||
\(129\) | 7.12244 | 0.627096 | ||||||||
\(130\) | 27.9957 | 2.45538 | ||||||||
\(131\) | −0.225417 | −0.0196948 | −0.00984741 | − | 0.999952i | \(-0.503135\pi\) | ||||
−0.00984741 | + | 0.999952i | \(0.503135\pi\) | |||||||
\(132\) | 15.3489 | 1.33595 | ||||||||
\(133\) | 0.133645 | 0.0115885 | ||||||||
\(134\) | −24.9237 | −2.15308 | ||||||||
\(135\) | −4.34691 | −0.374122 | ||||||||
\(136\) | 3.71802 | 0.318817 | ||||||||
\(137\) | 12.1855 | 1.04108 | 0.520540 | − | 0.853838i | \(-0.325731\pi\) | ||||
0.520540 | + | 0.853838i | \(0.325731\pi\) | |||||||
\(138\) | 6.26780 | 0.533551 | ||||||||
\(139\) | 12.2898 | 1.04241 | 0.521204 | − | 0.853432i | \(-0.325483\pi\) | ||||
0.521204 | + | 0.853432i | \(0.325483\pi\) | |||||||
\(140\) | −3.71586 | −0.314047 | ||||||||
\(141\) | 2.80084 | 0.235874 | ||||||||
\(142\) | −35.4685 | −2.97645 | ||||||||
\(143\) | 11.7122 | 0.979420 | ||||||||
\(144\) | 1.62912 | 0.135760 | ||||||||
\(145\) | 25.9622 | 2.15605 | ||||||||
\(146\) | −31.3694 | −2.59615 | ||||||||
\(147\) | 6.94282 | 0.572634 | ||||||||
\(148\) | 36.0403 | 2.96249 | ||||||||
\(149\) | −6.45616 | −0.528910 | −0.264455 | − | 0.964398i | \(-0.585192\pi\) | ||||
−0.264455 | + | 0.964398i | \(0.585192\pi\) | |||||||
\(150\) | 32.8086 | 2.67881 | ||||||||
\(151\) | −6.83320 | −0.556078 | −0.278039 | − | 0.960570i | \(-0.589684\pi\) | ||||
−0.278039 | + | 0.960570i | \(0.589684\pi\) | |||||||
\(152\) | 2.07790 | 0.168540 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −2.42430 | −0.195356 | ||||||||
\(155\) | 20.9769 | 1.68490 | ||||||||
\(156\) | 9.75079 | 0.780688 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | 41.0292 | 3.26411 | ||||||||
\(159\) | −1.71862 | −0.136295 | ||||||||
\(160\) | 15.6034 | 1.23356 | ||||||||
\(161\) | −0.634808 | −0.0500299 | ||||||||
\(162\) | −2.36108 | −0.185504 | ||||||||
\(163\) | 10.9751 | 0.859633 | 0.429816 | − | 0.902916i | \(-0.358578\pi\) | ||||
0.429816 | + | 0.902916i | \(0.358578\pi\) | |||||||
\(164\) | 14.1976 | 1.10864 | ||||||||
\(165\) | 18.6646 | 1.45303 | ||||||||
\(166\) | 37.3023 | 2.89522 | ||||||||
\(167\) | −18.9833 | −1.46897 | −0.734487 | − | 0.678623i | \(-0.762577\pi\) | ||||
−0.734487 | + | 0.678623i | \(0.762577\pi\) | |||||||
\(168\) | −0.889098 | −0.0685954 | ||||||||
\(169\) | −5.55956 | −0.427658 | ||||||||
\(170\) | 10.2634 | 0.787167 | ||||||||
\(171\) | −0.558873 | −0.0427381 | ||||||||
\(172\) | −25.4607 | −1.94136 | ||||||||
\(173\) | −8.69719 | −0.661235 | −0.330617 | − | 0.943765i | \(-0.607257\pi\) | ||||
−0.330617 | + | 0.943765i | \(0.607257\pi\) | |||||||
\(174\) | 14.1017 | 1.06905 | ||||||||
\(175\) | −3.32288 | −0.251186 | ||||||||
\(176\) | −6.99506 | −0.527273 | ||||||||
\(177\) | 2.11577 | 0.159031 | ||||||||
\(178\) | 8.45467 | 0.633705 | ||||||||
\(179\) | −13.0370 | −0.974434 | −0.487217 | − | 0.873281i | \(-0.661988\pi\) | ||||
−0.487217 | + | 0.873281i | \(0.661988\pi\) | |||||||
\(180\) | 15.5389 | 1.15820 | ||||||||
\(181\) | 5.90900 | 0.439212 | 0.219606 | − | 0.975589i | \(-0.429523\pi\) | ||||
0.219606 | + | 0.975589i | \(0.429523\pi\) | |||||||
\(182\) | −1.54010 | −0.114160 | ||||||||
\(183\) | 1.44266 | 0.106645 | ||||||||
\(184\) | −9.86996 | −0.727623 | ||||||||
\(185\) | 43.8256 | 3.22212 | ||||||||
\(186\) | 11.3939 | 0.835439 | ||||||||
\(187\) | 4.29376 | 0.313991 | ||||||||
\(188\) | −10.0122 | −0.730215 | ||||||||
\(189\) | 0.239132 | 0.0173943 | ||||||||
\(190\) | 5.73594 | 0.416129 | ||||||||
\(191\) | −19.2275 | −1.39125 | −0.695627 | − | 0.718403i | \(-0.744873\pi\) | ||||
−0.695627 | + | 0.718403i | \(0.744873\pi\) | |||||||
\(192\) | 11.7334 | 0.846788 | ||||||||
\(193\) | 2.61911 | 0.188528 | 0.0942640 | − | 0.995547i | \(-0.469950\pi\) | ||||
0.0942640 | + | 0.995547i | \(0.469950\pi\) | |||||||
\(194\) | −23.4466 | −1.68337 | ||||||||
\(195\) | 11.8571 | 0.849107 | ||||||||
\(196\) | −24.8185 | −1.77275 | ||||||||
\(197\) | −18.7336 | −1.33471 | −0.667356 | − | 0.744739i | \(-0.732574\pi\) | ||||
−0.667356 | + | 0.744739i | \(0.732574\pi\) | |||||||
\(198\) | 10.1379 | 0.720471 | ||||||||
\(199\) | −5.84406 | −0.414275 | −0.207137 | − | 0.978312i | \(-0.566415\pi\) | ||||
−0.207137 | + | 0.978312i | \(0.566415\pi\) | |||||||
\(200\) | −51.6640 | −3.65320 | ||||||||
\(201\) | −10.5560 | −0.744566 | ||||||||
\(202\) | −31.3488 | −2.20569 | ||||||||
\(203\) | −1.42824 | −0.100243 | ||||||||
\(204\) | 3.57471 | 0.250280 | ||||||||
\(205\) | 17.2645 | 1.20580 | ||||||||
\(206\) | −13.9004 | −0.968490 | ||||||||
\(207\) | 2.65463 | 0.184510 | ||||||||
\(208\) | −4.44379 | −0.308121 | ||||||||
\(209\) | 2.39967 | 0.165988 | ||||||||
\(210\) | −2.45431 | −0.169364 | ||||||||
\(211\) | 8.18565 | 0.563523 | 0.281762 | − | 0.959484i | \(-0.409081\pi\) | ||||
0.281762 | + | 0.959484i | \(0.409081\pi\) | |||||||
\(212\) | 6.14356 | 0.421941 | ||||||||
\(213\) | −15.0221 | −1.02930 | ||||||||
\(214\) | 20.6707 | 1.41302 | ||||||||
\(215\) | −30.9606 | −2.11149 | ||||||||
\(216\) | 3.71802 | 0.252979 | ||||||||
\(217\) | −1.15398 | −0.0783373 | ||||||||
\(218\) | 44.1623 | 2.99105 | ||||||||
\(219\) | −13.2860 | −0.897788 | ||||||||
\(220\) | −66.7204 | −4.49829 | ||||||||
\(221\) | 2.72772 | 0.183486 | ||||||||
\(222\) | 23.8045 | 1.59765 | ||||||||
\(223\) | 8.53078 | 0.571263 | 0.285632 | − | 0.958339i | \(-0.407797\pi\) | ||||
0.285632 | + | 0.958339i | \(0.407797\pi\) | |||||||
\(224\) | −0.858375 | −0.0573526 | ||||||||
\(225\) | 13.8956 | 0.926372 | ||||||||
\(226\) | 40.3255 | 2.68241 | ||||||||
\(227\) | 20.5611 | 1.36469 | 0.682345 | − | 0.731030i | \(-0.260960\pi\) | ||||
0.682345 | + | 0.731030i | \(0.260960\pi\) | |||||||
\(228\) | 1.99781 | 0.132308 | ||||||||
\(229\) | 21.5999 | 1.42736 | 0.713679 | − | 0.700472i | \(-0.247027\pi\) | ||||
0.713679 | + | 0.700472i | \(0.247027\pi\) | |||||||
\(230\) | −27.2455 | −1.79652 | ||||||||
\(231\) | −1.02678 | −0.0675570 | ||||||||
\(232\) | −22.2061 | −1.45790 | ||||||||
\(233\) | −14.9035 | −0.976362 | −0.488181 | − | 0.872742i | \(-0.662339\pi\) | ||||
−0.488181 | + | 0.872742i | \(0.662339\pi\) | |||||||
\(234\) | 6.44036 | 0.421020 | ||||||||
\(235\) | −12.1750 | −0.794210 | ||||||||
\(236\) | −7.56324 | −0.492325 | ||||||||
\(237\) | 17.3773 | 1.12878 | ||||||||
\(238\) | −0.564611 | −0.0365983 | ||||||||
\(239\) | 29.1491 | 1.88550 | 0.942750 | − | 0.333500i | \(-0.108230\pi\) | ||||
0.942750 | + | 0.333500i | \(0.108230\pi\) | |||||||
\(240\) | −7.08164 | −0.457118 | ||||||||
\(241\) | 23.2353 | 1.49672 | 0.748358 | − | 0.663295i | \(-0.230842\pi\) | ||||
0.748358 | + | 0.663295i | \(0.230842\pi\) | |||||||
\(242\) | −17.5579 | −1.12866 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −5.15709 | −0.330149 | ||||||||
\(245\) | −30.1798 | −1.92811 | ||||||||
\(246\) | 9.37745 | 0.597884 | ||||||||
\(247\) | 1.52445 | 0.0969983 | ||||||||
\(248\) | −17.9420 | −1.13932 | ||||||||
\(249\) | 15.7988 | 1.00121 | ||||||||
\(250\) | −91.2990 | −5.77425 | ||||||||
\(251\) | −21.3881 | −1.35000 | −0.675002 | − | 0.737816i | \(-0.735857\pi\) | ||||
−0.675002 | + | 0.737816i | \(0.735857\pi\) | |||||||
\(252\) | −0.854829 | −0.0538491 | ||||||||
\(253\) | −11.3983 | −0.716608 | ||||||||
\(254\) | −13.2181 | −0.829379 | ||||||||
\(255\) | 4.34691 | 0.272214 | ||||||||
\(256\) | −24.9932 | −1.56208 | ||||||||
\(257\) | −17.8369 | −1.11264 | −0.556319 | − | 0.830969i | \(-0.687787\pi\) | ||||
−0.556319 | + | 0.830969i | \(0.687787\pi\) | |||||||
\(258\) | −16.8167 | −1.04696 | ||||||||
\(259\) | −2.41094 | −0.149808 | ||||||||
\(260\) | −42.3858 | −2.62865 | ||||||||
\(261\) | 5.97258 | 0.369693 | ||||||||
\(262\) | 0.532229 | 0.0328812 | ||||||||
\(263\) | 30.6048 | 1.88718 | 0.943588 | − | 0.331122i | \(-0.107427\pi\) | ||||
0.943588 | + | 0.331122i | \(0.107427\pi\) | |||||||
\(264\) | −15.9643 | −0.982533 | ||||||||
\(265\) | 7.47067 | 0.458920 | ||||||||
\(266\) | −0.315546 | −0.0193474 | ||||||||
\(267\) | 3.58085 | 0.219144 | ||||||||
\(268\) | 37.7348 | 2.30502 | ||||||||
\(269\) | −4.17373 | −0.254477 | −0.127238 | − | 0.991872i | \(-0.540611\pi\) | ||||
−0.127238 | + | 0.991872i | \(0.540611\pi\) | |||||||
\(270\) | 10.2634 | 0.624611 | ||||||||
\(271\) | 8.22291 | 0.499506 | 0.249753 | − | 0.968310i | \(-0.419651\pi\) | ||||
0.249753 | + | 0.968310i | \(0.419651\pi\) | |||||||
\(272\) | −1.62912 | −0.0987801 | ||||||||
\(273\) | −0.652286 | −0.0394781 | ||||||||
\(274\) | −28.7710 | −1.73812 | ||||||||
\(275\) | −59.6643 | −3.59789 | ||||||||
\(276\) | −9.48953 | −0.571203 | ||||||||
\(277\) | 2.24584 | 0.134940 | 0.0674698 | − | 0.997721i | \(-0.478507\pi\) | ||||
0.0674698 | + | 0.997721i | \(0.478507\pi\) | |||||||
\(278\) | −29.0173 | −1.74034 | ||||||||
\(279\) | 4.82570 | 0.288907 | ||||||||
\(280\) | 3.86482 | 0.230967 | ||||||||
\(281\) | 26.9942 | 1.61034 | 0.805169 | − | 0.593046i | \(-0.202075\pi\) | ||||
0.805169 | + | 0.593046i | \(0.202075\pi\) | |||||||
\(282\) | −6.61302 | −0.393800 | ||||||||
\(283\) | −11.0508 | −0.656902 | −0.328451 | − | 0.944521i | \(-0.606527\pi\) | ||||
−0.328451 | + | 0.944521i | \(0.606527\pi\) | |||||||
\(284\) | 53.6998 | 3.18650 | ||||||||
\(285\) | 2.42937 | 0.143903 | ||||||||
\(286\) | −27.6534 | −1.63518 | ||||||||
\(287\) | −0.949756 | −0.0560623 | ||||||||
\(288\) | 3.58954 | 0.211516 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −61.2989 | −3.59960 | ||||||||
\(291\) | −9.93045 | −0.582133 | ||||||||
\(292\) | 47.4937 | 2.77936 | ||||||||
\(293\) | 12.5607 | 0.733806 | 0.366903 | − | 0.930259i | \(-0.380418\pi\) | ||||
0.366903 | + | 0.930259i | \(0.380418\pi\) | |||||||
\(294\) | −16.3926 | −0.956033 | ||||||||
\(295\) | −9.19703 | −0.535472 | ||||||||
\(296\) | −37.4851 | −2.17878 | ||||||||
\(297\) | 4.29376 | 0.249149 | ||||||||
\(298\) | 15.2435 | 0.883034 | ||||||||
\(299\) | −7.24108 | −0.418763 | ||||||||
\(300\) | −49.6727 | −2.86785 | ||||||||
\(301\) | 1.70321 | 0.0981712 | ||||||||
\(302\) | 16.1337 | 0.928392 | ||||||||
\(303\) | −13.2773 | −0.762761 | ||||||||
\(304\) | −0.910472 | −0.0522192 | ||||||||
\(305\) | −6.27111 | −0.359083 | ||||||||
\(306\) | 2.36108 | 0.134974 | ||||||||
\(307\) | 25.1925 | 1.43781 | 0.718906 | − | 0.695107i | \(-0.244643\pi\) | ||||
0.718906 | + | 0.695107i | \(0.244643\pi\) | |||||||
\(308\) | 3.67043 | 0.209142 | ||||||||
\(309\) | −5.88732 | −0.334918 | ||||||||
\(310\) | −49.5281 | −2.81301 | ||||||||
\(311\) | −24.5619 | −1.39278 | −0.696390 | − | 0.717663i | \(-0.745212\pi\) | ||||
−0.696390 | + | 0.717663i | \(0.745212\pi\) | |||||||
\(312\) | −10.1417 | −0.574160 | ||||||||
\(313\) | 13.1599 | 0.743843 | 0.371921 | − | 0.928264i | \(-0.378699\pi\) | ||||
0.371921 | + | 0.928264i | \(0.378699\pi\) | |||||||
\(314\) | −2.36108 | −0.133244 | ||||||||
\(315\) | −1.03949 | −0.0585684 | ||||||||
\(316\) | −62.1187 | −3.49445 | ||||||||
\(317\) | 12.5489 | 0.704815 | 0.352408 | − | 0.935847i | \(-0.385363\pi\) | ||||
0.352408 | + | 0.935847i | \(0.385363\pi\) | |||||||
\(318\) | 4.05780 | 0.227550 | ||||||||
\(319\) | −25.6448 | −1.43583 | ||||||||
\(320\) | −51.0042 | −2.85122 | ||||||||
\(321\) | 8.75477 | 0.488644 | ||||||||
\(322\) | 1.49883 | 0.0835268 | ||||||||
\(323\) | 0.558873 | 0.0310965 | ||||||||
\(324\) | 3.57471 | 0.198595 | ||||||||
\(325\) | −37.9032 | −2.10249 | ||||||||
\(326\) | −25.9130 | −1.43519 | ||||||||
\(327\) | 18.7043 | 1.03435 | ||||||||
\(328\) | −14.7667 | −0.815357 | ||||||||
\(329\) | 0.669773 | 0.0369258 | ||||||||
\(330\) | −44.0686 | −2.42590 | ||||||||
\(331\) | 23.8446 | 1.31062 | 0.655310 | − | 0.755360i | \(-0.272538\pi\) | ||||
0.655310 | + | 0.755360i | \(0.272538\pi\) | |||||||
\(332\) | −56.4761 | −3.09953 | ||||||||
\(333\) | 10.0820 | 0.552492 | ||||||||
\(334\) | 44.8212 | 2.45250 | ||||||||
\(335\) | 45.8861 | 2.50703 | ||||||||
\(336\) | 0.389576 | 0.0212531 | ||||||||
\(337\) | −5.79654 | −0.315758 | −0.157879 | − | 0.987458i | \(-0.550466\pi\) | ||||
−0.157879 | + | 0.987458i | \(0.550466\pi\) | |||||||
\(338\) | 13.1266 | 0.713991 | ||||||||
\(339\) | 17.0792 | 0.927617 | ||||||||
\(340\) | −15.5389 | −0.842716 | ||||||||
\(341\) | −20.7204 | −1.12207 | ||||||||
\(342\) | 1.31954 | 0.0713528 | ||||||||
\(343\) | 3.33418 | 0.180029 | ||||||||
\(344\) | 26.4814 | 1.42778 | ||||||||
\(345\) | −11.5394 | −0.621262 | ||||||||
\(346\) | 20.5348 | 1.10396 | ||||||||
\(347\) | −9.82793 | −0.527591 | −0.263795 | − | 0.964579i | \(-0.584974\pi\) | ||||
−0.263795 | + | 0.964579i | \(0.584974\pi\) | |||||||
\(348\) | −21.3502 | −1.14449 | ||||||||
\(349\) | −4.59284 | −0.245849 | −0.122925 | − | 0.992416i | \(-0.539227\pi\) | ||||
−0.122925 | + | 0.992416i | \(0.539227\pi\) | |||||||
\(350\) | 7.84560 | 0.419365 | ||||||||
\(351\) | 2.72772 | 0.145595 | ||||||||
\(352\) | −15.4126 | −0.821495 | ||||||||
\(353\) | 27.1082 | 1.44282 | 0.721412 | − | 0.692506i | \(-0.243494\pi\) | ||||
0.721412 | + | 0.692506i | \(0.243494\pi\) | |||||||
\(354\) | −4.99549 | −0.265508 | ||||||||
\(355\) | 65.2999 | 3.46576 | ||||||||
\(356\) | −12.8005 | −0.678424 | ||||||||
\(357\) | −0.239132 | −0.0126562 | ||||||||
\(358\) | 30.7815 | 1.62685 | ||||||||
\(359\) | 32.1725 | 1.69800 | 0.849000 | − | 0.528393i | \(-0.177205\pi\) | ||||
0.849000 | + | 0.528393i | \(0.177205\pi\) | |||||||
\(360\) | −16.1619 | −0.851805 | ||||||||
\(361\) | −18.6877 | −0.983561 | ||||||||
\(362\) | −13.9516 | −0.733281 | ||||||||
\(363\) | −7.43637 | −0.390308 | ||||||||
\(364\) | 2.33173 | 0.122216 | ||||||||
\(365\) | 57.7532 | 3.02294 | ||||||||
\(366\) | −3.40624 | −0.178047 | ||||||||
\(367\) | 29.1230 | 1.52021 | 0.760103 | − | 0.649803i | \(-0.225148\pi\) | ||||
0.760103 | + | 0.649803i | \(0.225148\pi\) | |||||||
\(368\) | 4.32472 | 0.225442 | ||||||||
\(369\) | 3.97167 | 0.206757 | ||||||||
\(370\) | −103.476 | −5.37945 | ||||||||
\(371\) | −0.410977 | −0.0213369 | ||||||||
\(372\) | −17.2505 | −0.894395 | ||||||||
\(373\) | 3.10973 | 0.161016 | 0.0805078 | − | 0.996754i | \(-0.474346\pi\) | ||||
0.0805078 | + | 0.996754i | \(0.474346\pi\) | |||||||
\(374\) | −10.1379 | −0.524219 | ||||||||
\(375\) | −38.6683 | −1.99682 | ||||||||
\(376\) | 10.4136 | 0.537040 | ||||||||
\(377\) | −16.2915 | −0.839055 | ||||||||
\(378\) | −0.564611 | −0.0290405 | ||||||||
\(379\) | −29.7419 | −1.52774 | −0.763868 | − | 0.645372i | \(-0.776702\pi\) | ||||
−0.763868 | + | 0.645372i | \(0.776702\pi\) | |||||||
\(380\) | −8.68428 | −0.445494 | ||||||||
\(381\) | −5.59833 | −0.286811 | ||||||||
\(382\) | 45.3977 | 2.32275 | ||||||||
\(383\) | 15.7433 | 0.804443 | 0.402222 | − | 0.915542i | \(-0.368238\pi\) | ||||
0.402222 | + | 0.915542i | \(0.368238\pi\) | |||||||
\(384\) | −20.5245 | −1.04739 | ||||||||
\(385\) | 4.46330 | 0.227471 | ||||||||
\(386\) | −6.18394 | −0.314754 | ||||||||
\(387\) | −7.12244 | −0.362054 | ||||||||
\(388\) | 35.4984 | 1.80216 | ||||||||
\(389\) | 8.68107 | 0.440148 | 0.220074 | − | 0.975483i | \(-0.429370\pi\) | ||||
0.220074 | + | 0.975483i | \(0.429370\pi\) | |||||||
\(390\) | −27.9957 | −1.41762 | ||||||||
\(391\) | −2.65463 | −0.134250 | ||||||||
\(392\) | 25.8135 | 1.30378 | ||||||||
\(393\) | 0.225417 | 0.0113708 | ||||||||
\(394\) | 44.2315 | 2.22835 | ||||||||
\(395\) | −75.5374 | −3.80070 | ||||||||
\(396\) | −15.3489 | −0.771313 | ||||||||
\(397\) | 38.9186 | 1.95327 | 0.976633 | − | 0.214914i | \(-0.0689470\pi\) | ||||
0.976633 | + | 0.214914i | \(0.0689470\pi\) | |||||||
\(398\) | 13.7983 | 0.691647 | ||||||||
\(399\) | −0.133645 | −0.00669060 | ||||||||
\(400\) | 22.6376 | 1.13188 | ||||||||
\(401\) | −29.3930 | −1.46782 | −0.733908 | − | 0.679249i | \(-0.762306\pi\) | ||||
−0.733908 | + | 0.679249i | \(0.762306\pi\) | |||||||
\(402\) | 24.9237 | 1.24308 | ||||||||
\(403\) | −13.1631 | −0.655703 | ||||||||
\(404\) | 47.4625 | 2.36135 | ||||||||
\(405\) | 4.34691 | 0.215999 | ||||||||
\(406\) | 3.37218 | 0.167359 | ||||||||
\(407\) | −43.2898 | −2.14580 | ||||||||
\(408\) | −3.71802 | −0.184069 | ||||||||
\(409\) | 29.4105 | 1.45426 | 0.727128 | − | 0.686502i | \(-0.240855\pi\) | ||||
0.727128 | + | 0.686502i | \(0.240855\pi\) | |||||||
\(410\) | −40.7629 | −2.01314 | ||||||||
\(411\) | −12.1855 | −0.601067 | ||||||||
\(412\) | 21.0454 | 1.03683 | ||||||||
\(413\) | 0.505948 | 0.0248961 | ||||||||
\(414\) | −6.26780 | −0.308046 | ||||||||
\(415\) | −68.6759 | −3.37117 | ||||||||
\(416\) | −9.79125 | −0.480055 | ||||||||
\(417\) | −12.2898 | −0.601835 | ||||||||
\(418\) | −5.66581 | −0.277124 | ||||||||
\(419\) | −2.08284 | −0.101753 | −0.0508766 | − | 0.998705i | \(-0.516202\pi\) | ||||
−0.0508766 | + | 0.998705i | \(0.516202\pi\) | |||||||
\(420\) | 3.71586 | 0.181315 | ||||||||
\(421\) | 33.1287 | 1.61459 | 0.807296 | − | 0.590146i | \(-0.200930\pi\) | ||||
0.807296 | + | 0.590146i | \(0.200930\pi\) | |||||||
\(422\) | −19.3270 | −0.940823 | ||||||||
\(423\) | −2.80084 | −0.136182 | ||||||||
\(424\) | −6.38985 | −0.310318 | ||||||||
\(425\) | −13.8956 | −0.674035 | ||||||||
\(426\) | 35.4685 | 1.71846 | ||||||||
\(427\) | 0.344987 | 0.0166951 | ||||||||
\(428\) | −31.2958 | −1.51274 | ||||||||
\(429\) | −11.7122 | −0.565469 | ||||||||
\(430\) | 73.1005 | 3.52522 | ||||||||
\(431\) | −32.0274 | −1.54271 | −0.771353 | − | 0.636407i | \(-0.780420\pi\) | ||||
−0.771353 | + | 0.636407i | \(0.780420\pi\) | |||||||
\(432\) | −1.62912 | −0.0783812 | ||||||||
\(433\) | 11.5441 | 0.554773 | 0.277387 | − | 0.960758i | \(-0.410532\pi\) | ||||
0.277387 | + | 0.960758i | \(0.410532\pi\) | |||||||
\(434\) | 2.72464 | 0.130787 | ||||||||
\(435\) | −25.9622 | −1.24479 | ||||||||
\(436\) | −66.8623 | −3.20212 | ||||||||
\(437\) | −1.48360 | −0.0709703 | ||||||||
\(438\) | 31.3694 | 1.49889 | ||||||||
\(439\) | 34.2145 | 1.63297 | 0.816486 | − | 0.577366i | \(-0.195919\pi\) | ||||
0.816486 | + | 0.577366i | \(0.195919\pi\) | |||||||
\(440\) | 69.3952 | 3.30828 | ||||||||
\(441\) | −6.94282 | −0.330610 | ||||||||
\(442\) | −6.44036 | −0.306337 | ||||||||
\(443\) | 14.3421 | 0.681413 | 0.340707 | − | 0.940170i | \(-0.389334\pi\) | ||||
0.340707 | + | 0.940170i | \(0.389334\pi\) | |||||||
\(444\) | −36.0403 | −1.71040 | ||||||||
\(445\) | −15.5656 | −0.737880 | ||||||||
\(446\) | −20.1419 | −0.953745 | ||||||||
\(447\) | 6.45616 | 0.305366 | ||||||||
\(448\) | 2.80585 | 0.132564 | ||||||||
\(449\) | −40.6583 | −1.91878 | −0.959392 | − | 0.282076i | \(-0.908977\pi\) | ||||
−0.959392 | + | 0.282076i | \(0.908977\pi\) | |||||||
\(450\) | −32.8086 | −1.54661 | ||||||||
\(451\) | −17.0534 | −0.803014 | ||||||||
\(452\) | −61.0533 | −2.87171 | ||||||||
\(453\) | 6.83320 | 0.321052 | ||||||||
\(454\) | −48.5465 | −2.27840 | ||||||||
\(455\) | 2.83542 | 0.132927 | ||||||||
\(456\) | −2.07790 | −0.0973065 | ||||||||
\(457\) | 14.6616 | 0.685839 | 0.342919 | − | 0.939365i | \(-0.388584\pi\) | ||||
0.342919 | + | 0.939365i | \(0.388584\pi\) | |||||||
\(458\) | −50.9990 | −2.38303 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 41.2501 | 1.92330 | ||||||||
\(461\) | 32.9775 | 1.53591 | 0.767957 | − | 0.640501i | \(-0.221273\pi\) | ||||
0.767957 | + | 0.640501i | \(0.221273\pi\) | |||||||
\(462\) | 2.42430 | 0.112789 | ||||||||
\(463\) | 32.8403 | 1.52622 | 0.763108 | − | 0.646270i | \(-0.223672\pi\) | ||||
0.763108 | + | 0.646270i | \(0.223672\pi\) | |||||||
\(464\) | 9.73006 | 0.451707 | ||||||||
\(465\) | −20.9769 | −0.972778 | ||||||||
\(466\) | 35.1884 | 1.63007 | ||||||||
\(467\) | 42.2274 | 1.95405 | 0.977025 | − | 0.213124i | \(-0.0683639\pi\) | ||||
0.977025 | + | 0.213124i | \(0.0683639\pi\) | |||||||
\(468\) | −9.75079 | −0.450731 | ||||||||
\(469\) | −2.52429 | −0.116561 | ||||||||
\(470\) | 28.7462 | 1.32596 | ||||||||
\(471\) | −1.00000 | −0.0460776 | ||||||||
\(472\) | 7.86645 | 0.362083 | ||||||||
\(473\) | 30.5821 | 1.40616 | ||||||||
\(474\) | −41.0292 | −1.88453 | ||||||||
\(475\) | −7.76587 | −0.356322 | ||||||||
\(476\) | 0.854829 | 0.0391810 | ||||||||
\(477\) | 1.71862 | 0.0786901 | ||||||||
\(478\) | −68.8235 | −3.14791 | ||||||||
\(479\) | −39.5310 | −1.80622 | −0.903108 | − | 0.429413i | \(-0.858721\pi\) | ||||
−0.903108 | + | 0.429413i | \(0.858721\pi\) | |||||||
\(480\) | −15.6034 | −0.712194 | ||||||||
\(481\) | −27.5009 | −1.25393 | ||||||||
\(482\) | −54.8604 | −2.49882 | ||||||||
\(483\) | 0.634808 | 0.0288848 | ||||||||
\(484\) | 26.5829 | 1.20831 | ||||||||
\(485\) | 43.1667 | 1.96010 | ||||||||
\(486\) | 2.36108 | 0.107101 | ||||||||
\(487\) | 18.4553 | 0.836287 | 0.418144 | − | 0.908381i | \(-0.362681\pi\) | ||||
0.418144 | + | 0.908381i | \(0.362681\pi\) | |||||||
\(488\) | 5.36384 | 0.242809 | ||||||||
\(489\) | −10.9751 | −0.496309 | ||||||||
\(490\) | 71.2569 | 3.21906 | ||||||||
\(491\) | −28.6553 | −1.29320 | −0.646599 | − | 0.762830i | \(-0.723809\pi\) | ||||
−0.646599 | + | 0.762830i | \(0.723809\pi\) | |||||||
\(492\) | −14.1976 | −0.640076 | ||||||||
\(493\) | −5.97258 | −0.268991 | ||||||||
\(494\) | −3.59934 | −0.161942 | ||||||||
\(495\) | −18.6646 | −0.838910 | ||||||||
\(496\) | 7.86165 | 0.352999 | ||||||||
\(497\) | −3.59228 | −0.161136 | ||||||||
\(498\) | −37.3023 | −1.67156 | ||||||||
\(499\) | 12.2309 | 0.547531 | 0.273766 | − | 0.961796i | \(-0.411731\pi\) | ||||
0.273766 | + | 0.961796i | \(0.411731\pi\) | |||||||
\(500\) | 138.228 | 6.18174 | ||||||||
\(501\) | 18.9833 | 0.848112 | ||||||||
\(502\) | 50.4990 | 2.25388 | ||||||||
\(503\) | −2.53088 | −0.112846 | −0.0564231 | − | 0.998407i | \(-0.517970\pi\) | ||||
−0.0564231 | + | 0.998407i | \(0.517970\pi\) | |||||||
\(504\) | 0.889098 | 0.0396036 | ||||||||
\(505\) | 57.7152 | 2.56829 | ||||||||
\(506\) | 26.9124 | 1.19640 | ||||||||
\(507\) | 5.55956 | 0.246909 | ||||||||
\(508\) | 20.0124 | 0.887907 | ||||||||
\(509\) | −1.71224 | −0.0758938 | −0.0379469 | − | 0.999280i | \(-0.512082\pi\) | ||||
−0.0379469 | + | 0.999280i | \(0.512082\pi\) | |||||||
\(510\) | −10.2634 | −0.454471 | ||||||||
\(511\) | −3.17712 | −0.140548 | ||||||||
\(512\) | 17.9620 | 0.793816 | ||||||||
\(513\) | 0.558873 | 0.0246748 | ||||||||
\(514\) | 42.1145 | 1.85759 | ||||||||
\(515\) | 25.5916 | 1.12770 | ||||||||
\(516\) | 25.4607 | 1.12084 | ||||||||
\(517\) | 12.0262 | 0.528910 | ||||||||
\(518\) | 5.69242 | 0.250111 | ||||||||
\(519\) | 8.69719 | 0.381764 | ||||||||
\(520\) | 44.0850 | 1.93325 | ||||||||
\(521\) | −1.78373 | −0.0781465 | −0.0390733 | − | 0.999236i | \(-0.512441\pi\) | ||||
−0.0390733 | + | 0.999236i | \(0.512441\pi\) | |||||||
\(522\) | −14.1017 | −0.617217 | ||||||||
\(523\) | −20.9715 | −0.917020 | −0.458510 | − | 0.888689i | \(-0.651617\pi\) | ||||
−0.458510 | + | 0.888689i | \(0.651617\pi\) | |||||||
\(524\) | −0.805802 | −0.0352016 | ||||||||
\(525\) | 3.32288 | 0.145023 | ||||||||
\(526\) | −72.2606 | −3.15071 | ||||||||
\(527\) | −4.82570 | −0.210211 | ||||||||
\(528\) | 6.99506 | 0.304421 | ||||||||
\(529\) | −15.9529 | −0.693606 | ||||||||
\(530\) | −17.6389 | −0.766183 | ||||||||
\(531\) | −2.11577 | −0.0918164 | ||||||||
\(532\) | 0.477740 | 0.0207127 | ||||||||
\(533\) | −10.8336 | −0.469256 | ||||||||
\(534\) | −8.45467 | −0.365869 | ||||||||
\(535\) | −38.0562 | −1.64531 | ||||||||
\(536\) | −39.2475 | −1.69524 | ||||||||
\(537\) | 13.0370 | 0.562590 | ||||||||
\(538\) | 9.85451 | 0.424858 | ||||||||
\(539\) | 29.8108 | 1.28404 | ||||||||
\(540\) | −15.5389 | −0.668689 | ||||||||
\(541\) | −36.2603 | −1.55895 | −0.779476 | − | 0.626433i | \(-0.784514\pi\) | ||||
−0.779476 | + | 0.626433i | \(0.784514\pi\) | |||||||
\(542\) | −19.4150 | −0.833944 | ||||||||
\(543\) | −5.90900 | −0.253579 | ||||||||
\(544\) | −3.58954 | −0.153900 | ||||||||
\(545\) | −81.3056 | −3.48275 | ||||||||
\(546\) | 1.54010 | 0.0659102 | ||||||||
\(547\) | 15.5266 | 0.663869 | 0.331935 | − | 0.943302i | \(-0.392299\pi\) | ||||
0.331935 | + | 0.943302i | \(0.392299\pi\) | |||||||
\(548\) | 43.5597 | 1.86078 | ||||||||
\(549\) | −1.44266 | −0.0615713 | ||||||||
\(550\) | 140.872 | 6.00682 | ||||||||
\(551\) | −3.33791 | −0.142200 | ||||||||
\(552\) | 9.86996 | 0.420093 | ||||||||
\(553\) | 4.15547 | 0.176709 | ||||||||
\(554\) | −5.30262 | −0.225287 | ||||||||
\(555\) | −43.8256 | −1.86029 | ||||||||
\(556\) | 43.9325 | 1.86315 | ||||||||
\(557\) | −15.5911 | −0.660615 | −0.330307 | − | 0.943873i | \(-0.607152\pi\) | ||||
−0.330307 | + | 0.943873i | \(0.607152\pi\) | |||||||
\(558\) | −11.3939 | −0.482341 | ||||||||
\(559\) | 19.4280 | 0.821718 | ||||||||
\(560\) | −1.69345 | −0.0715613 | ||||||||
\(561\) | −4.29376 | −0.181283 | ||||||||
\(562\) | −63.7355 | −2.68852 | ||||||||
\(563\) | −10.2620 | −0.432492 | −0.216246 | − | 0.976339i | \(-0.569381\pi\) | ||||
−0.216246 | + | 0.976339i | \(0.569381\pi\) | |||||||
\(564\) | 10.0122 | 0.421590 | ||||||||
\(565\) | −74.2418 | −3.12338 | ||||||||
\(566\) | 26.0918 | 1.09672 | ||||||||
\(567\) | −0.239132 | −0.0100426 | ||||||||
\(568\) | −55.8526 | −2.34352 | ||||||||
\(569\) | −19.4921 | −0.817152 | −0.408576 | − | 0.912724i | \(-0.633975\pi\) | ||||
−0.408576 | + | 0.912724i | \(0.633975\pi\) | |||||||
\(570\) | −5.73594 | −0.240252 | ||||||||
\(571\) | 27.7876 | 1.16287 | 0.581437 | − | 0.813592i | \(-0.302491\pi\) | ||||
0.581437 | + | 0.813592i | \(0.302491\pi\) | |||||||
\(572\) | 41.8676 | 1.75057 | ||||||||
\(573\) | 19.2275 | 0.803240 | ||||||||
\(574\) | 2.24245 | 0.0935981 | ||||||||
\(575\) | 36.8877 | 1.53832 | ||||||||
\(576\) | −11.7334 | −0.488893 | ||||||||
\(577\) | 17.4527 | 0.726565 | 0.363283 | − | 0.931679i | \(-0.381656\pi\) | ||||
0.363283 | + | 0.931679i | \(0.381656\pi\) | |||||||
\(578\) | −2.36108 | −0.0982081 | ||||||||
\(579\) | −2.61911 | −0.108847 | ||||||||
\(580\) | 92.8074 | 3.85362 | ||||||||
\(581\) | 3.77801 | 0.156738 | ||||||||
\(582\) | 23.4466 | 0.971893 | ||||||||
\(583\) | −7.37933 | −0.305621 | ||||||||
\(584\) | −49.3977 | −2.04409 | ||||||||
\(585\) | −11.8571 | −0.490232 | ||||||||
\(586\) | −29.6569 | −1.22512 | ||||||||
\(587\) | −8.29956 | −0.342559 | −0.171280 | − | 0.985222i | \(-0.554790\pi\) | ||||
−0.171280 | + | 0.985222i | \(0.554790\pi\) | |||||||
\(588\) | 24.8185 | 1.02350 | ||||||||
\(589\) | −2.69695 | −0.111126 | ||||||||
\(590\) | 21.7149 | 0.893990 | ||||||||
\(591\) | 18.7336 | 0.770597 | ||||||||
\(592\) | 16.4249 | 0.675057 | ||||||||
\(593\) | −13.1422 | −0.539686 | −0.269843 | − | 0.962904i | \(-0.586972\pi\) | ||||
−0.269843 | + | 0.962904i | \(0.586972\pi\) | |||||||
\(594\) | −10.1379 | −0.415964 | ||||||||
\(595\) | 1.03949 | 0.0426148 | ||||||||
\(596\) | −23.0789 | −0.945349 | ||||||||
\(597\) | 5.84406 | 0.239182 | ||||||||
\(598\) | 17.0968 | 0.699140 | ||||||||
\(599\) | 4.90358 | 0.200355 | 0.100177 | − | 0.994970i | \(-0.468059\pi\) | ||||
0.100177 | + | 0.994970i | \(0.468059\pi\) | |||||||
\(600\) | 51.6640 | 2.10917 | ||||||||
\(601\) | −18.4545 | −0.752776 | −0.376388 | − | 0.926462i | \(-0.622834\pi\) | ||||
−0.376388 | + | 0.926462i | \(0.622834\pi\) | |||||||
\(602\) | −4.02141 | −0.163901 | ||||||||
\(603\) | 10.5560 | 0.429875 | ||||||||
\(604\) | −24.4267 | −0.993908 | ||||||||
\(605\) | 32.3252 | 1.31421 | ||||||||
\(606\) | 31.3488 | 1.27346 | ||||||||
\(607\) | 4.69772 | 0.190675 | 0.0953373 | − | 0.995445i | \(-0.469607\pi\) | ||||
0.0953373 | + | 0.995445i | \(0.469607\pi\) | |||||||
\(608\) | −2.00610 | −0.0813579 | ||||||||
\(609\) | 1.42824 | 0.0578751 | ||||||||
\(610\) | 14.8066 | 0.599502 | ||||||||
\(611\) | 7.63991 | 0.309078 | ||||||||
\(612\) | −3.57471 | −0.144499 | ||||||||
\(613\) | 36.5863 | 1.47771 | 0.738853 | − | 0.673867i | \(-0.235368\pi\) | ||||
0.738853 | + | 0.673867i | \(0.235368\pi\) | |||||||
\(614\) | −59.4816 | −2.40048 | ||||||||
\(615\) | −17.2645 | −0.696172 | ||||||||
\(616\) | −3.81757 | −0.153814 | ||||||||
\(617\) | 48.5686 | 1.95530 | 0.977649 | − | 0.210243i | \(-0.0674256\pi\) | ||||
0.977649 | + | 0.210243i | \(0.0674256\pi\) | |||||||
\(618\) | 13.9004 | 0.559158 | ||||||||
\(619\) | 8.26092 | 0.332034 | 0.166017 | − | 0.986123i | \(-0.446909\pi\) | ||||
0.166017 | + | 0.986123i | \(0.446909\pi\) | |||||||
\(620\) | 74.9861 | 3.01152 | ||||||||
\(621\) | −2.65463 | −0.106527 | ||||||||
\(622\) | 57.9928 | 2.32530 | ||||||||
\(623\) | 0.856296 | 0.0343068 | ||||||||
\(624\) | 4.44379 | 0.177894 | ||||||||
\(625\) | 98.6094 | 3.94438 | ||||||||
\(626\) | −31.0717 | −1.24187 | ||||||||
\(627\) | −2.39967 | −0.0958334 | ||||||||
\(628\) | 3.57471 | 0.142646 | ||||||||
\(629\) | −10.0820 | −0.401997 | ||||||||
\(630\) | 2.45431 | 0.0977821 | ||||||||
\(631\) | 23.8988 | 0.951397 | 0.475698 | − | 0.879608i | \(-0.342195\pi\) | ||||
0.475698 | + | 0.879608i | \(0.342195\pi\) | |||||||
\(632\) | 64.6090 | 2.57001 | ||||||||
\(633\) | −8.18565 | −0.325350 | ||||||||
\(634\) | −29.6289 | −1.17672 | ||||||||
\(635\) | 24.3354 | 0.965722 | ||||||||
\(636\) | −6.14356 | −0.243608 | ||||||||
\(637\) | 18.9380 | 0.750352 | ||||||||
\(638\) | 60.5495 | 2.39718 | ||||||||
\(639\) | 15.0221 | 0.594267 | ||||||||
\(640\) | 89.2182 | 3.52666 | ||||||||
\(641\) | 41.8633 | 1.65350 | 0.826750 | − | 0.562569i | \(-0.190187\pi\) | ||||
0.826750 | + | 0.562569i | \(0.190187\pi\) | |||||||
\(642\) | −20.6707 | −0.815809 | ||||||||
\(643\) | 20.7153 | 0.816932 | 0.408466 | − | 0.912774i | \(-0.366064\pi\) | ||||
0.408466 | + | 0.912774i | \(0.366064\pi\) | |||||||
\(644\) | −2.26925 | −0.0894211 | ||||||||
\(645\) | 30.9606 | 1.21907 | ||||||||
\(646\) | −1.31954 | −0.0519168 | ||||||||
\(647\) | −24.2501 | −0.953369 | −0.476685 | − | 0.879074i | \(-0.658162\pi\) | ||||
−0.476685 | + | 0.879074i | \(0.658162\pi\) | |||||||
\(648\) | −3.71802 | −0.146057 | ||||||||
\(649\) | 9.08459 | 0.356601 | ||||||||
\(650\) | 89.4926 | 3.51019 | ||||||||
\(651\) | 1.15398 | 0.0452281 | ||||||||
\(652\) | 39.2326 | 1.53647 | ||||||||
\(653\) | 23.9540 | 0.937393 | 0.468697 | − | 0.883359i | \(-0.344724\pi\) | ||||
0.468697 | + | 0.883359i | \(0.344724\pi\) | |||||||
\(654\) | −44.1623 | −1.72688 | ||||||||
\(655\) | −0.979868 | −0.0382866 | ||||||||
\(656\) | 6.47034 | 0.252625 | ||||||||
\(657\) | 13.2860 | 0.518338 | ||||||||
\(658\) | −1.58139 | −0.0616489 | ||||||||
\(659\) | 20.9300 | 0.815317 | 0.407659 | − | 0.913134i | \(-0.366345\pi\) | ||||
0.407659 | + | 0.913134i | \(0.366345\pi\) | |||||||
\(660\) | 66.7204 | 2.59709 | ||||||||
\(661\) | −24.2094 | −0.941637 | −0.470819 | − | 0.882230i | \(-0.656041\pi\) | ||||
−0.470819 | + | 0.882230i | \(0.656041\pi\) | |||||||
\(662\) | −56.2992 | −2.18813 | ||||||||
\(663\) | −2.72772 | −0.105936 | ||||||||
\(664\) | 58.7402 | 2.27956 | ||||||||
\(665\) | 0.580940 | 0.0225279 | ||||||||
\(666\) | −23.8045 | −0.922405 | ||||||||
\(667\) | 15.8550 | 0.613907 | ||||||||
\(668\) | −67.8598 | −2.62558 | ||||||||
\(669\) | −8.53078 | −0.329819 | ||||||||
\(670\) | −108.341 | −4.18558 | ||||||||
\(671\) | 6.19444 | 0.239134 | ||||||||
\(672\) | 0.858375 | 0.0331125 | ||||||||
\(673\) | 1.53716 | 0.0592533 | 0.0296266 | − | 0.999561i | \(-0.490568\pi\) | ||||
0.0296266 | + | 0.999561i | \(0.490568\pi\) | |||||||
\(674\) | 13.6861 | 0.527169 | ||||||||
\(675\) | −13.8956 | −0.534841 | ||||||||
\(676\) | −19.8738 | −0.764377 | ||||||||
\(677\) | −0.606449 | −0.0233077 | −0.0116539 | − | 0.999932i | \(-0.503710\pi\) | ||||
−0.0116539 | + | 0.999932i | \(0.503710\pi\) | |||||||
\(678\) | −40.3255 | −1.54869 | ||||||||
\(679\) | −2.37469 | −0.0911323 | ||||||||
\(680\) | 16.1619 | 0.619779 | ||||||||
\(681\) | −20.5611 | −0.787905 | ||||||||
\(682\) | 48.9225 | 1.87334 | ||||||||
\(683\) | −8.56732 | −0.327819 | −0.163910 | − | 0.986475i | \(-0.552411\pi\) | ||||
−0.163910 | + | 0.986475i | \(0.552411\pi\) | |||||||
\(684\) | −1.99781 | −0.0763881 | ||||||||
\(685\) | 52.9693 | 2.02385 | ||||||||
\(686\) | −7.87227 | −0.300565 | ||||||||
\(687\) | −21.5999 | −0.824086 | ||||||||
\(688\) | −11.6033 | −0.442373 | ||||||||
\(689\) | −4.68790 | −0.178595 | ||||||||
\(690\) | 27.2455 | 1.03722 | ||||||||
\(691\) | −0.187920 | −0.00714880 | −0.00357440 | − | 0.999994i | \(-0.501138\pi\) | ||||
−0.00357440 | + | 0.999994i | \(0.501138\pi\) | |||||||
\(692\) | −31.0899 | −1.18186 | ||||||||
\(693\) | 1.02678 | 0.0390040 | ||||||||
\(694\) | 23.2045 | 0.880833 | ||||||||
\(695\) | 53.4227 | 2.02644 | ||||||||
\(696\) | 22.2061 | 0.841721 | ||||||||
\(697\) | −3.97167 | −0.150438 | ||||||||
\(698\) | 10.8441 | 0.410454 | ||||||||
\(699\) | 14.9035 | 0.563703 | ||||||||
\(700\) | −11.8783 | −0.448959 | ||||||||
\(701\) | 22.0960 | 0.834555 | 0.417277 | − | 0.908779i | \(-0.362984\pi\) | ||||
0.417277 | + | 0.908779i | \(0.362984\pi\) | |||||||
\(702\) | −6.44036 | −0.243076 | ||||||||
\(703\) | −5.63457 | −0.212512 | ||||||||
\(704\) | 50.3806 | 1.89879 | ||||||||
\(705\) | 12.1750 | 0.458537 | ||||||||
\(706\) | −64.0047 | −2.40885 | ||||||||
\(707\) | −3.17503 | −0.119409 | ||||||||
\(708\) | 7.56324 | 0.284244 | ||||||||
\(709\) | −15.1413 | −0.568642 | −0.284321 | − | 0.958729i | \(-0.591768\pi\) | ||||
−0.284321 | + | 0.958729i | \(0.591768\pi\) | |||||||
\(710\) | −154.178 | −5.78621 | ||||||||
\(711\) | −17.3773 | −0.651699 | ||||||||
\(712\) | 13.3136 | 0.498950 | ||||||||
\(713\) | 12.8104 | 0.479755 | ||||||||
\(714\) | 0.564611 | 0.0211300 | ||||||||
\(715\) | 50.9117 | 1.90399 | ||||||||
\(716\) | −46.6036 | −1.74166 | ||||||||
\(717\) | −29.1491 | −1.08859 | ||||||||
\(718\) | −75.9619 | −2.83487 | ||||||||
\(719\) | 51.5149 | 1.92118 | 0.960591 | − | 0.277964i | \(-0.0896597\pi\) | ||||
0.960591 | + | 0.277964i | \(0.0896597\pi\) | |||||||
\(720\) | 7.08164 | 0.263917 | ||||||||
\(721\) | −1.40785 | −0.0524310 | ||||||||
\(722\) | 44.1231 | 1.64209 | ||||||||
\(723\) | −23.2353 | −0.864130 | ||||||||
\(724\) | 21.1229 | 0.785028 | ||||||||
\(725\) | 82.9925 | 3.08226 | ||||||||
\(726\) | 17.5579 | 0.651634 | ||||||||
\(727\) | 34.2647 | 1.27081 | 0.635403 | − | 0.772180i | \(-0.280834\pi\) | ||||
0.635403 | + | 0.772180i | \(0.280834\pi\) | |||||||
\(728\) | −2.42521 | −0.0898842 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −136.360 | −5.04691 | ||||||||
\(731\) | 7.12244 | 0.263433 | ||||||||
\(732\) | 5.15709 | 0.190612 | ||||||||
\(733\) | 48.5082 | 1.79169 | 0.895845 | − | 0.444366i | \(-0.146571\pi\) | ||||
0.895845 | + | 0.444366i | \(0.146571\pi\) | |||||||
\(734\) | −68.7617 | −2.53804 | ||||||||
\(735\) | 30.1798 | 1.11320 | ||||||||
\(736\) | 9.52890 | 0.351240 | ||||||||
\(737\) | −45.3251 | −1.66957 | ||||||||
\(738\) | −9.37745 | −0.345189 | ||||||||
\(739\) | −23.4148 | −0.861327 | −0.430664 | − | 0.902512i | \(-0.641720\pi\) | ||||
−0.430664 | + | 0.902512i | \(0.641720\pi\) | |||||||
\(740\) | 156.664 | 5.75908 | ||||||||
\(741\) | −1.52445 | −0.0560020 | ||||||||
\(742\) | 0.970351 | 0.0356227 | ||||||||
\(743\) | −2.03363 | −0.0746066 | −0.0373033 | − | 0.999304i | \(-0.511877\pi\) | ||||
−0.0373033 | + | 0.999304i | \(0.511877\pi\) | |||||||
\(744\) | 17.9420 | 0.657786 | ||||||||
\(745\) | −28.0643 | −1.02820 | ||||||||
\(746\) | −7.34232 | −0.268821 | ||||||||
\(747\) | −15.7988 | −0.578048 | ||||||||
\(748\) | 15.3489 | 0.561213 | ||||||||
\(749\) | 2.09355 | 0.0764966 | ||||||||
\(750\) | 91.2990 | 3.33377 | ||||||||
\(751\) | 2.89574 | 0.105667 | 0.0528335 | − | 0.998603i | \(-0.483175\pi\) | ||||
0.0528335 | + | 0.998603i | \(0.483175\pi\) | |||||||
\(752\) | −4.56292 | −0.166393 | ||||||||
\(753\) | 21.3881 | 0.779426 | ||||||||
\(754\) | 38.4656 | 1.40083 | ||||||||
\(755\) | −29.7033 | −1.08101 | ||||||||
\(756\) | 0.854829 | 0.0310898 | ||||||||
\(757\) | 3.24190 | 0.117829 | 0.0589145 | − | 0.998263i | \(-0.481236\pi\) | ||||
0.0589145 | + | 0.998263i | \(0.481236\pi\) | |||||||
\(758\) | 70.2230 | 2.55061 | ||||||||
\(759\) | 11.3983 | 0.413734 | ||||||||
\(760\) | 9.03243 | 0.327641 | ||||||||
\(761\) | 18.9431 | 0.686686 | 0.343343 | − | 0.939210i | \(-0.388441\pi\) | ||||
0.343343 | + | 0.939210i | \(0.388441\pi\) | |||||||
\(762\) | 13.2181 | 0.478842 | ||||||||
\(763\) | 4.47279 | 0.161926 | ||||||||
\(764\) | −68.7327 | −2.48666 | ||||||||
\(765\) | −4.34691 | −0.157163 | ||||||||
\(766\) | −37.1711 | −1.34305 | ||||||||
\(767\) | 5.77121 | 0.208386 | ||||||||
\(768\) | 24.9932 | 0.901866 | ||||||||
\(769\) | −25.5068 | −0.919800 | −0.459900 | − | 0.887971i | \(-0.652115\pi\) | ||||
−0.459900 | + | 0.887971i | \(0.652115\pi\) | |||||||
\(770\) | −10.5382 | −0.379771 | ||||||||
\(771\) | 17.8369 | 0.642382 | ||||||||
\(772\) | 9.36257 | 0.336966 | ||||||||
\(773\) | −39.6111 | −1.42471 | −0.712356 | − | 0.701818i | \(-0.752372\pi\) | ||||
−0.712356 | + | 0.701818i | \(0.752372\pi\) | |||||||
\(774\) | 16.8167 | 0.604463 | ||||||||
\(775\) | 67.0559 | 2.40872 | ||||||||
\(776\) | −36.9216 | −1.32541 | ||||||||
\(777\) | 2.41094 | 0.0864920 | ||||||||
\(778\) | −20.4967 | −0.734843 | ||||||||
\(779\) | −2.21966 | −0.0795276 | ||||||||
\(780\) | 42.3858 | 1.51765 | ||||||||
\(781\) | −64.5015 | −2.30805 | ||||||||
\(782\) | 6.26780 | 0.224136 | ||||||||
\(783\) | −5.97258 | −0.213442 | ||||||||
\(784\) | −11.3107 | −0.403953 | ||||||||
\(785\) | 4.34691 | 0.155148 | ||||||||
\(786\) | −0.532229 | −0.0189840 | ||||||||
\(787\) | −14.8884 | −0.530713 | −0.265356 | − | 0.964150i | \(-0.585490\pi\) | ||||
−0.265356 | + | 0.964150i | \(0.585490\pi\) | |||||||
\(788\) | −66.9671 | −2.38560 | ||||||||
\(789\) | −30.6048 | −1.08956 | ||||||||
\(790\) | 178.350 | 6.34541 | ||||||||
\(791\) | 4.08420 | 0.145217 | ||||||||
\(792\) | 15.9643 | 0.567265 | ||||||||
\(793\) | 3.93517 | 0.139742 | ||||||||
\(794\) | −91.8899 | −3.26105 | ||||||||
\(795\) | −7.47067 | −0.264957 | ||||||||
\(796\) | −20.8908 | −0.740456 | ||||||||
\(797\) | 30.4304 | 1.07790 | 0.538951 | − | 0.842337i | \(-0.318821\pi\) | ||||
0.538951 | + | 0.842337i | \(0.318821\pi\) | |||||||
\(798\) | 0.315546 | 0.0111702 | ||||||||
\(799\) | 2.80084 | 0.0990868 | ||||||||
\(800\) | 49.8787 | 1.76348 | ||||||||
\(801\) | −3.58085 | −0.126523 | ||||||||
\(802\) | 69.3993 | 2.45057 | ||||||||
\(803\) | −57.0471 | −2.01315 | ||||||||
\(804\) | −37.7348 | −1.33080 | ||||||||
\(805\) | −2.75945 | −0.0972579 | ||||||||
\(806\) | 31.0793 | 1.09472 | ||||||||
\(807\) | 4.17373 | 0.146922 | ||||||||
\(808\) | −49.3652 | −1.73666 | ||||||||
\(809\) | 16.3888 | 0.576200 | 0.288100 | − | 0.957600i | \(-0.406976\pi\) | ||||
0.288100 | + | 0.957600i | \(0.406976\pi\) | |||||||
\(810\) | −10.2634 | −0.360619 | ||||||||
\(811\) | −36.9386 | −1.29709 | −0.648545 | − | 0.761176i | \(-0.724622\pi\) | ||||
−0.648545 | + | 0.761176i | \(0.724622\pi\) | |||||||
\(812\) | −5.10553 | −0.179169 | ||||||||
\(813\) | −8.22291 | −0.288390 | ||||||||
\(814\) | 102.211 | 3.58249 | ||||||||
\(815\) | 47.7075 | 1.67112 | ||||||||
\(816\) | 1.62912 | 0.0570307 | ||||||||
\(817\) | 3.98054 | 0.139262 | ||||||||
\(818\) | −69.4406 | −2.42793 | ||||||||
\(819\) | 0.652286 | 0.0227927 | ||||||||
\(820\) | 61.7155 | 2.15520 | ||||||||
\(821\) | 9.54259 | 0.333039 | 0.166519 | − | 0.986038i | \(-0.446747\pi\) | ||||
0.166519 | + | 0.986038i | \(0.446747\pi\) | |||||||
\(822\) | 28.7710 | 1.00350 | ||||||||
\(823\) | −16.1476 | −0.562870 | −0.281435 | − | 0.959580i | \(-0.590810\pi\) | ||||
−0.281435 | + | 0.959580i | \(0.590810\pi\) | |||||||
\(824\) | −21.8891 | −0.762544 | ||||||||
\(825\) | 59.6643 | 2.07724 | ||||||||
\(826\) | −1.19458 | −0.0415649 | ||||||||
\(827\) | −11.8462 | −0.411934 | −0.205967 | − | 0.978559i | \(-0.566034\pi\) | ||||
−0.205967 | + | 0.978559i | \(0.566034\pi\) | |||||||
\(828\) | 9.48953 | 0.329784 | ||||||||
\(829\) | −24.2450 | −0.842063 | −0.421031 | − | 0.907046i | \(-0.638332\pi\) | ||||
−0.421031 | + | 0.907046i | \(0.638332\pi\) | |||||||
\(830\) | 162.149 | 5.62829 | ||||||||
\(831\) | −2.24584 | −0.0779074 | ||||||||
\(832\) | 32.0055 | 1.10959 | ||||||||
\(833\) | 6.94282 | 0.240554 | ||||||||
\(834\) | 29.0173 | 1.00479 | ||||||||
\(835\) | −82.5187 | −2.85568 | ||||||||
\(836\) | 8.57811 | 0.296680 | ||||||||
\(837\) | −4.82570 | −0.166801 | ||||||||
\(838\) | 4.91775 | 0.169881 | ||||||||
\(839\) | 24.4650 | 0.844627 | 0.422314 | − | 0.906450i | \(-0.361218\pi\) | ||||
0.422314 | + | 0.906450i | \(0.361218\pi\) | |||||||
\(840\) | −3.86482 | −0.133349 | ||||||||
\(841\) | 6.67167 | 0.230058 | ||||||||
\(842\) | −78.2195 | −2.69562 | ||||||||
\(843\) | −26.9942 | −0.929729 | ||||||||
\(844\) | 29.2613 | 1.00722 | ||||||||
\(845\) | −24.1669 | −0.831366 | ||||||||
\(846\) | 6.61302 | 0.227360 | ||||||||
\(847\) | −1.77828 | −0.0611023 | ||||||||
\(848\) | 2.79984 | 0.0961469 | ||||||||
\(849\) | 11.0508 | 0.379262 | ||||||||
\(850\) | 32.8086 | 1.12533 | ||||||||
\(851\) | 26.7641 | 0.917460 | ||||||||
\(852\) | −53.6998 | −1.83972 | ||||||||
\(853\) | 19.7630 | 0.676672 | 0.338336 | − | 0.941025i | \(-0.390136\pi\) | ||||
0.338336 | + | 0.941025i | \(0.390136\pi\) | |||||||
\(854\) | −0.814543 | −0.0278731 | ||||||||
\(855\) | −2.42937 | −0.0830826 | ||||||||
\(856\) | 32.5504 | 1.11255 | ||||||||
\(857\) | 14.6229 | 0.499509 | 0.249754 | − | 0.968309i | \(-0.419650\pi\) | ||||
0.249754 | + | 0.968309i | \(0.419650\pi\) | |||||||
\(858\) | 27.6534 | 0.944071 | ||||||||
\(859\) | 34.8977 | 1.19069 | 0.595347 | − | 0.803468i | \(-0.297014\pi\) | ||||
0.595347 | + | 0.803468i | \(0.297014\pi\) | |||||||
\(860\) | −110.675 | −3.77399 | ||||||||
\(861\) | 0.949756 | 0.0323676 | ||||||||
\(862\) | 75.6194 | 2.57561 | ||||||||
\(863\) | −19.4256 | −0.661254 | −0.330627 | − | 0.943761i | \(-0.607260\pi\) | ||||
−0.330627 | + | 0.943761i | \(0.607260\pi\) | |||||||
\(864\) | −3.58954 | −0.122119 | ||||||||
\(865\) | −37.8059 | −1.28544 | ||||||||
\(866\) | −27.2565 | −0.926215 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −4.12514 | −0.140017 | ||||||||
\(869\) | 74.6139 | 2.53110 | ||||||||
\(870\) | 61.2989 | 2.07823 | ||||||||
\(871\) | −28.7939 | −0.975644 | ||||||||
\(872\) | 69.5427 | 2.35501 | ||||||||
\(873\) | 9.93045 | 0.336095 | ||||||||
\(874\) | 3.50290 | 0.118487 | ||||||||
\(875\) | −9.24684 | −0.312600 | ||||||||
\(876\) | −47.4937 | −1.60466 | ||||||||
\(877\) | −30.9996 | −1.04678 | −0.523391 | − | 0.852092i | \(-0.675333\pi\) | ||||
−0.523391 | + | 0.852092i | \(0.675333\pi\) | |||||||
\(878\) | −80.7833 | −2.72631 | ||||||||
\(879\) | −12.5607 | −0.423663 | ||||||||
\(880\) | −30.4069 | −1.02502 | ||||||||
\(881\) | −30.6950 | −1.03414 | −0.517070 | − | 0.855943i | \(-0.672977\pi\) | ||||
−0.517070 | + | 0.855943i | \(0.672977\pi\) | |||||||
\(882\) | 16.3926 | 0.551966 | ||||||||
\(883\) | −41.4471 | −1.39481 | −0.697403 | − | 0.716679i | \(-0.745661\pi\) | ||||
−0.697403 | + | 0.716679i | \(0.745661\pi\) | |||||||
\(884\) | 9.75079 | 0.327955 | ||||||||
\(885\) | 9.19703 | 0.309155 | ||||||||
\(886\) | −33.8628 | −1.13764 | ||||||||
\(887\) | −0.357051 | −0.0119886 | −0.00599429 | − | 0.999982i | \(-0.501908\pi\) | ||||
−0.00599429 | + | 0.999982i | \(0.501908\pi\) | |||||||
\(888\) | 37.4851 | 1.25792 | ||||||||
\(889\) | −1.33874 | −0.0449000 | ||||||||
\(890\) | 36.7517 | 1.23192 | ||||||||
\(891\) | −4.29376 | −0.143846 | ||||||||
\(892\) | 30.4950 | 1.02105 | ||||||||
\(893\) | 1.56532 | 0.0523813 | ||||||||
\(894\) | −15.2435 | −0.509820 | ||||||||
\(895\) | −56.6708 | −1.89430 | ||||||||
\(896\) | −4.90808 | −0.163967 | ||||||||
\(897\) | 7.24108 | 0.241773 | ||||||||
\(898\) | 95.9976 | 3.20348 | ||||||||
\(899\) | 28.8219 | 0.961263 | ||||||||
\(900\) | 49.6727 | 1.65576 | ||||||||
\(901\) | −1.71862 | −0.0572555 | ||||||||
\(902\) | 40.2645 | 1.34066 | ||||||||
\(903\) | −1.70321 | −0.0566792 | ||||||||
\(904\) | 63.5009 | 2.11201 | ||||||||
\(905\) | 25.6859 | 0.853827 | ||||||||
\(906\) | −16.1337 | −0.536008 | ||||||||
\(907\) | −11.2127 | −0.372311 | −0.186155 | − | 0.982520i | \(-0.559603\pi\) | ||||
−0.186155 | + | 0.982520i | \(0.559603\pi\) | |||||||
\(908\) | 73.5001 | 2.43919 | ||||||||
\(909\) | 13.2773 | 0.440380 | ||||||||
\(910\) | −6.69467 | −0.221926 | ||||||||
\(911\) | 53.7265 | 1.78004 | 0.890019 | − | 0.455923i | \(-0.150691\pi\) | ||||
0.890019 | + | 0.455923i | \(0.150691\pi\) | |||||||
\(912\) | 0.910472 | 0.0301488 | ||||||||
\(913\) | 67.8363 | 2.24505 | ||||||||
\(914\) | −34.6171 | −1.14503 | ||||||||
\(915\) | 6.27111 | 0.207317 | ||||||||
\(916\) | 77.2132 | 2.55120 | ||||||||
\(917\) | 0.0539046 | 0.00178009 | ||||||||
\(918\) | −2.36108 | −0.0779273 | ||||||||
\(919\) | −11.2400 | −0.370773 | −0.185386 | − | 0.982666i | \(-0.559354\pi\) | ||||
−0.185386 | + | 0.982666i | \(0.559354\pi\) | |||||||
\(920\) | −42.9038 | −1.41450 | ||||||||
\(921\) | −25.1925 | −0.830121 | ||||||||
\(922\) | −77.8625 | −2.56427 | ||||||||
\(923\) | −40.9762 | −1.34875 | ||||||||
\(924\) | −3.67043 | −0.120748 | ||||||||
\(925\) | 140.096 | 4.60632 | ||||||||
\(926\) | −77.5386 | −2.54808 | ||||||||
\(927\) | 5.88732 | 0.193365 | ||||||||
\(928\) | 21.4388 | 0.703763 | ||||||||
\(929\) | 44.8261 | 1.47070 | 0.735348 | − | 0.677689i | \(-0.237019\pi\) | ||||
0.735348 | + | 0.677689i | \(0.237019\pi\) | |||||||
\(930\) | 49.5281 | 1.62409 | ||||||||
\(931\) | 3.88015 | 0.127167 | ||||||||
\(932\) | −53.2758 | −1.74511 | ||||||||
\(933\) | 24.5619 | 0.804122 | ||||||||
\(934\) | −99.7023 | −3.26236 | ||||||||
\(935\) | 18.6646 | 0.610397 | ||||||||
\(936\) | 10.1417 | 0.331492 | ||||||||
\(937\) | −45.6902 | −1.49263 | −0.746316 | − | 0.665592i | \(-0.768179\pi\) | ||||
−0.746316 | + | 0.665592i | \(0.768179\pi\) | |||||||
\(938\) | 5.96006 | 0.194603 | ||||||||
\(939\) | −13.1599 | −0.429458 | ||||||||
\(940\) | −43.5221 | −1.41953 | ||||||||
\(941\) | 3.87350 | 0.126273 | 0.0631363 | − | 0.998005i | \(-0.479890\pi\) | ||||
0.0631363 | + | 0.998005i | \(0.479890\pi\) | |||||||
\(942\) | 2.36108 | 0.0769282 | ||||||||
\(943\) | 10.5433 | 0.343338 | ||||||||
\(944\) | −3.44684 | −0.112185 | ||||||||
\(945\) | 1.03949 | 0.0338145 | ||||||||
\(946\) | −72.2068 | −2.34764 | ||||||||
\(947\) | −2.49828 | −0.0811831 | −0.0405916 | − | 0.999176i | \(-0.512924\pi\) | ||||
−0.0405916 | + | 0.999176i | \(0.512924\pi\) | |||||||
\(948\) | 62.1187 | 2.01752 | ||||||||
\(949\) | −36.2406 | −1.17642 | ||||||||
\(950\) | 18.3358 | 0.594893 | ||||||||
\(951\) | −12.5489 | −0.406925 | ||||||||
\(952\) | −0.889098 | −0.0288158 | ||||||||
\(953\) | 15.5421 | 0.503457 | 0.251729 | − | 0.967798i | \(-0.419001\pi\) | ||||
0.251729 | + | 0.967798i | \(0.419001\pi\) | |||||||
\(954\) | −4.05780 | −0.131376 | ||||||||
\(955\) | −83.5801 | −2.70459 | ||||||||
\(956\) | 104.200 | 3.37006 | ||||||||
\(957\) | 25.6448 | 0.828979 | ||||||||
\(958\) | 93.3359 | 3.01555 | ||||||||
\(959\) | −2.91395 | −0.0940964 | ||||||||
\(960\) | 51.0042 | 1.64615 | ||||||||
\(961\) | −7.71263 | −0.248795 | ||||||||
\(962\) | 64.9319 | 2.09349 | ||||||||
\(963\) | −8.75477 | −0.282119 | ||||||||
\(964\) | 83.0594 | 2.67516 | ||||||||
\(965\) | 11.3850 | 0.366498 | ||||||||
\(966\) | −1.49883 | −0.0482242 | ||||||||
\(967\) | 41.2896 | 1.32779 | 0.663893 | − | 0.747828i | \(-0.268903\pi\) | ||||
0.663893 | + | 0.747828i | \(0.268903\pi\) | |||||||
\(968\) | −27.6486 | −0.888658 | ||||||||
\(969\) | −0.558873 | −0.0179536 | ||||||||
\(970\) | −101.920 | −3.27246 | ||||||||
\(971\) | 22.7317 | 0.729495 | 0.364747 | − | 0.931106i | \(-0.381155\pi\) | ||||
0.364747 | + | 0.931106i | \(0.381155\pi\) | |||||||
\(972\) | −3.57471 | −0.114659 | ||||||||
\(973\) | −2.93889 | −0.0942166 | ||||||||
\(974\) | −43.5744 | −1.39621 | ||||||||
\(975\) | 37.9032 | 1.21388 | ||||||||
\(976\) | −2.35027 | −0.0752304 | ||||||||
\(977\) | −55.9454 | −1.78985 | −0.894926 | − | 0.446215i | \(-0.852772\pi\) | ||||
−0.894926 | + | 0.446215i | \(0.852772\pi\) | |||||||
\(978\) | 25.9130 | 0.828607 | ||||||||
\(979\) | 15.3753 | 0.491397 | ||||||||
\(980\) | −107.884 | −3.44622 | ||||||||
\(981\) | −18.7043 | −0.597181 | ||||||||
\(982\) | 67.6576 | 2.15904 | ||||||||
\(983\) | −4.20101 | −0.133992 | −0.0669958 | − | 0.997753i | \(-0.521341\pi\) | ||||
−0.0669958 | + | 0.997753i | \(0.521341\pi\) | |||||||
\(984\) | 14.7667 | 0.470747 | ||||||||
\(985\) | −81.4331 | −2.59468 | ||||||||
\(986\) | 14.1017 | 0.449091 | ||||||||
\(987\) | −0.669773 | −0.0213191 | ||||||||
\(988\) | 5.44945 | 0.173370 | ||||||||
\(989\) | −18.9075 | −0.601222 | ||||||||
\(990\) | 44.0686 | 1.40059 | ||||||||
\(991\) | 21.1070 | 0.670485 | 0.335242 | − | 0.942132i | \(-0.391182\pi\) | ||||
0.335242 | + | 0.942132i | \(0.391182\pi\) | |||||||
\(992\) | 17.3220 | 0.549975 | ||||||||
\(993\) | −23.8446 | −0.756687 | ||||||||
\(994\) | 8.48167 | 0.269022 | ||||||||
\(995\) | −25.4036 | −0.805348 | ||||||||
\(996\) | 56.4761 | 1.78951 | ||||||||
\(997\) | −18.4564 | −0.584519 | −0.292259 | − | 0.956339i | \(-0.594407\pi\) | ||||
−0.292259 | + | 0.956339i | \(0.594407\pi\) | |||||||
\(998\) | −28.8782 | −0.914124 | ||||||||
\(999\) | −10.0820 | −0.318981 |
(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 | 8007.2.a.g.1.7 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.g.1.7 | ✓ | 56 | 1.1 | even | 1 | trivial |