Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,4,Mod(1,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("38.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.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: | \(2.24207258022\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{73}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 18 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.77200\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 8.77200 | 1.68817 | 0.844086 | − | 0.536207i | \(-0.180144\pi\) | ||||
0.844086 | + | 0.536207i | \(0.180144\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −17.3160 | −1.54879 | −0.774395 | − | 0.632702i | \(-0.781946\pi\) | ||||
−0.774395 | + | 0.632702i | \(0.781946\pi\) | |||||||
\(6\) | 17.5440 | 1.19372 | ||||||||
\(7\) | −26.0880 | −1.40862 | −0.704310 | − | 0.709893i | \(-0.748743\pi\) | ||||
−0.704310 | + | 0.709893i | \(0.748743\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 49.9480 | 1.84993 | ||||||||
\(10\) | −34.6320 | −1.09516 | ||||||||
\(11\) | −4.22800 | −0.115890 | −0.0579450 | − | 0.998320i | \(-0.518455\pi\) | ||||
−0.0579450 | + | 0.998320i | \(0.518455\pi\) | |||||||
\(12\) | 35.0880 | 0.844086 | ||||||||
\(13\) | 64.0360 | 1.36618 | 0.683092 | − | 0.730332i | \(-0.260635\pi\) | ||||
0.683092 | + | 0.730332i | \(0.260635\pi\) | |||||||
\(14\) | −52.1760 | −0.996045 | ||||||||
\(15\) | −151.896 | −2.61463 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −48.5440 | −0.692568 | −0.346284 | − | 0.938130i | \(-0.612557\pi\) | ||||
−0.346284 | + | 0.938130i | \(0.612557\pi\) | |||||||
\(18\) | 99.8960 | 1.30810 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | −69.2640 | −0.774395 | ||||||||
\(21\) | −228.844 | −2.37799 | ||||||||
\(22\) | −8.45600 | −0.0819466 | ||||||||
\(23\) | 92.0360 | 0.834384 | 0.417192 | − | 0.908818i | \(-0.363014\pi\) | ||||
0.417192 | + | 0.908818i | \(0.363014\pi\) | |||||||
\(24\) | 70.1760 | 0.596859 | ||||||||
\(25\) | 174.844 | 1.39875 | ||||||||
\(26\) | 128.072 | 0.966038 | ||||||||
\(27\) | 201.300 | 1.43482 | ||||||||
\(28\) | −104.352 | −0.704310 | ||||||||
\(29\) | −88.2120 | −0.564847 | −0.282424 | − | 0.959290i | \(-0.591138\pi\) | ||||
−0.282424 | + | 0.959290i | \(0.591138\pi\) | |||||||
\(30\) | −303.792 | −1.84882 | ||||||||
\(31\) | −81.9681 | −0.474900 | −0.237450 | − | 0.971400i | \(-0.576312\pi\) | ||||
−0.237450 | + | 0.971400i | \(0.576312\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | −37.0880 | −0.195642 | ||||||||
\(34\) | −97.0880 | −0.489719 | ||||||||
\(35\) | 451.740 | 2.18166 | ||||||||
\(36\) | 199.792 | 0.924963 | ||||||||
\(37\) | −23.6161 | −0.104931 | −0.0524656 | − | 0.998623i | \(-0.516708\pi\) | ||||
−0.0524656 | + | 0.998623i | \(0.516708\pi\) | |||||||
\(38\) | 38.0000 | 0.162221 | ||||||||
\(39\) | 561.724 | 2.30636 | ||||||||
\(40\) | −138.528 | −0.547580 | ||||||||
\(41\) | 17.7200 | 0.0674976 | 0.0337488 | − | 0.999430i | \(-0.489255\pi\) | ||||
0.0337488 | + | 0.999430i | \(0.489255\pi\) | |||||||
\(42\) | −457.688 | −1.68150 | ||||||||
\(43\) | 368.404 | 1.30654 | 0.653268 | − | 0.757126i | \(-0.273397\pi\) | ||||
0.653268 | + | 0.757126i | \(0.273397\pi\) | |||||||
\(44\) | −16.9120 | −0.0579450 | ||||||||
\(45\) | −864.900 | −2.86515 | ||||||||
\(46\) | 184.072 | 0.589999 | ||||||||
\(47\) | −497.812 | −1.54497 | −0.772483 | − | 0.635036i | \(-0.780985\pi\) | ||||
−0.772483 | + | 0.635036i | \(0.780985\pi\) | |||||||
\(48\) | 140.352 | 0.422043 | ||||||||
\(49\) | 337.584 | 0.984210 | ||||||||
\(50\) | 349.688 | 0.989067 | ||||||||
\(51\) | −425.828 | −1.16917 | ||||||||
\(52\) | 256.144 | 0.683092 | ||||||||
\(53\) | −536.876 | −1.39143 | −0.695713 | − | 0.718320i | \(-0.744911\pi\) | ||||
−0.695713 | + | 0.718320i | \(0.744911\pi\) | |||||||
\(54\) | 402.600 | 1.01457 | ||||||||
\(55\) | 73.2120 | 0.179489 | ||||||||
\(56\) | −208.704 | −0.498022 | ||||||||
\(57\) | 166.668 | 0.387293 | ||||||||
\(58\) | −176.424 | −0.399407 | ||||||||
\(59\) | −36.7000 | −0.0809818 | −0.0404909 | − | 0.999180i | \(-0.512892\pi\) | ||||
−0.0404909 | + | 0.999180i | \(0.512892\pi\) | |||||||
\(60\) | −607.584 | −1.30731 | ||||||||
\(61\) | 630.692 | 1.32380 | 0.661901 | − | 0.749592i | \(-0.269750\pi\) | ||||
0.661901 | + | 0.749592i | \(0.269750\pi\) | |||||||
\(62\) | −163.936 | −0.335805 | ||||||||
\(63\) | −1303.04 | −2.60584 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −1108.85 | −2.11593 | ||||||||
\(66\) | −74.1760 | −0.138340 | ||||||||
\(67\) | 282.556 | 0.515219 | 0.257610 | − | 0.966249i | \(-0.417065\pi\) | ||||
0.257610 | + | 0.966249i | \(0.417065\pi\) | |||||||
\(68\) | −194.176 | −0.346284 | ||||||||
\(69\) | 807.340 | 1.40858 | ||||||||
\(70\) | 903.480 | 1.54266 | ||||||||
\(71\) | 595.552 | 0.995480 | 0.497740 | − | 0.867326i | \(-0.334163\pi\) | ||||
0.497740 | + | 0.867326i | \(0.334163\pi\) | |||||||
\(72\) | 399.584 | 0.654048 | ||||||||
\(73\) | −597.048 | −0.957250 | −0.478625 | − | 0.878020i | \(-0.658865\pi\) | ||||
−0.478625 | + | 0.878020i | \(0.658865\pi\) | |||||||
\(74\) | −47.2321 | −0.0741976 | ||||||||
\(75\) | 1533.73 | 2.36134 | ||||||||
\(76\) | 76.0000 | 0.114708 | ||||||||
\(77\) | 110.300 | 0.163245 | ||||||||
\(78\) | 1123.45 | 1.63084 | ||||||||
\(79\) | 427.224 | 0.608436 | 0.304218 | − | 0.952602i | \(-0.401605\pi\) | ||||
0.304218 | + | 0.952602i | \(0.401605\pi\) | |||||||
\(80\) | −277.056 | −0.387198 | ||||||||
\(81\) | 417.208 | 0.572302 | ||||||||
\(82\) | 35.4400 | 0.0477280 | ||||||||
\(83\) | 493.768 | 0.652989 | 0.326495 | − | 0.945199i | \(-0.394132\pi\) | ||||
0.326495 | + | 0.945199i | \(0.394132\pi\) | |||||||
\(84\) | −915.376 | −1.18900 | ||||||||
\(85\) | 840.588 | 1.07264 | ||||||||
\(86\) | 736.808 | 0.923861 | ||||||||
\(87\) | −773.796 | −0.953559 | ||||||||
\(88\) | −33.8240 | −0.0409733 | ||||||||
\(89\) | −921.136 | −1.09708 | −0.548541 | − | 0.836124i | \(-0.684816\pi\) | ||||
−0.548541 | + | 0.836124i | \(0.684816\pi\) | |||||||
\(90\) | −1729.80 | −2.02597 | ||||||||
\(91\) | −1670.57 | −1.92443 | ||||||||
\(92\) | 368.144 | 0.417192 | ||||||||
\(93\) | −719.024 | −0.801713 | ||||||||
\(94\) | −995.624 | −1.09246 | ||||||||
\(95\) | −329.004 | −0.355317 | ||||||||
\(96\) | 280.704 | 0.298430 | ||||||||
\(97\) | 1082.74 | 1.13336 | 0.566680 | − | 0.823938i | \(-0.308227\pi\) | ||||
0.566680 | + | 0.823938i | \(0.308227\pi\) | |||||||
\(98\) | 675.168 | 0.695942 | ||||||||
\(99\) | −211.180 | −0.214388 | ||||||||
\(100\) | 699.376 | 0.699376 | ||||||||
\(101\) | −712.448 | −0.701893 | −0.350947 | − | 0.936395i | \(-0.614140\pi\) | ||||
−0.350947 | + | 0.936395i | \(0.614140\pi\) | |||||||
\(102\) | −851.656 | −0.826731 | ||||||||
\(103\) | −26.4797 | −0.0253313 | −0.0126656 | − | 0.999920i | \(-0.504032\pi\) | ||||
−0.0126656 | + | 0.999920i | \(0.504032\pi\) | |||||||
\(104\) | 512.288 | 0.483019 | ||||||||
\(105\) | 3962.66 | 3.68301 | ||||||||
\(106\) | −1073.75 | −0.983887 | ||||||||
\(107\) | −740.996 | −0.669484 | −0.334742 | − | 0.942310i | \(-0.608649\pi\) | ||||
−0.334742 | + | 0.942310i | \(0.608649\pi\) | |||||||
\(108\) | 805.200 | 0.717411 | ||||||||
\(109\) | −1983.08 | −1.74261 | −0.871304 | − | 0.490744i | \(-0.836725\pi\) | ||||
−0.871304 | + | 0.490744i | \(0.836725\pi\) | |||||||
\(110\) | 146.424 | 0.126918 | ||||||||
\(111\) | −207.160 | −0.177142 | ||||||||
\(112\) | −417.408 | −0.352155 | ||||||||
\(113\) | −718.720 | −0.598332 | −0.299166 | − | 0.954201i | \(-0.596708\pi\) | ||||
−0.299166 | + | 0.954201i | \(0.596708\pi\) | |||||||
\(114\) | 333.336 | 0.273858 | ||||||||
\(115\) | −1593.70 | −1.29229 | ||||||||
\(116\) | −352.848 | −0.282424 | ||||||||
\(117\) | 3198.47 | 2.52734 | ||||||||
\(118\) | −73.3999 | −0.0572628 | ||||||||
\(119\) | 1266.42 | 0.975565 | ||||||||
\(120\) | −1215.17 | −0.924410 | ||||||||
\(121\) | −1313.12 | −0.986570 | ||||||||
\(122\) | 1261.38 | 0.936069 | ||||||||
\(123\) | 155.440 | 0.113948 | ||||||||
\(124\) | −327.872 | −0.237450 | ||||||||
\(125\) | −863.100 | −0.617584 | ||||||||
\(126\) | −2606.09 | −1.84261 | ||||||||
\(127\) | 2610.72 | 1.82413 | 0.912063 | − | 0.410050i | \(-0.134489\pi\) | ||||
0.912063 | + | 0.410050i | \(0.134489\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 3231.64 | 2.20566 | ||||||||
\(130\) | −2217.70 | −1.49619 | ||||||||
\(131\) | −1216.69 | −0.811472 | −0.405736 | − | 0.913990i | \(-0.632985\pi\) | ||||
−0.405736 | + | 0.913990i | \(0.632985\pi\) | |||||||
\(132\) | −148.352 | −0.0978211 | ||||||||
\(133\) | −495.672 | −0.323160 | ||||||||
\(134\) | 565.112 | 0.364315 | ||||||||
\(135\) | −3485.71 | −2.22224 | ||||||||
\(136\) | −388.352 | −0.244860 | ||||||||
\(137\) | 1170.67 | 0.730053 | 0.365026 | − | 0.930997i | \(-0.381060\pi\) | ||||
0.365026 | + | 0.930997i | \(0.381060\pi\) | |||||||
\(138\) | 1614.68 | 0.996020 | ||||||||
\(139\) | −271.083 | −0.165417 | −0.0827086 | − | 0.996574i | \(-0.526357\pi\) | ||||
−0.0827086 | + | 0.996574i | \(0.526357\pi\) | |||||||
\(140\) | 1806.96 | 1.09083 | ||||||||
\(141\) | −4366.81 | −2.60817 | ||||||||
\(142\) | 1191.10 | 0.703910 | ||||||||
\(143\) | −270.744 | −0.158327 | ||||||||
\(144\) | 799.168 | 0.462482 | ||||||||
\(145\) | 1527.48 | 0.874830 | ||||||||
\(146\) | −1194.10 | −0.676878 | ||||||||
\(147\) | 2961.29 | 1.66152 | ||||||||
\(148\) | −94.4642 | −0.0524656 | ||||||||
\(149\) | 1841.19 | 1.01232 | 0.506161 | − | 0.862439i | \(-0.331064\pi\) | ||||
0.506161 | + | 0.862439i | \(0.331064\pi\) | |||||||
\(150\) | 3067.46 | 1.66972 | ||||||||
\(151\) | 3322.32 | 1.79051 | 0.895254 | − | 0.445557i | \(-0.146994\pi\) | ||||
0.895254 | + | 0.445557i | \(0.146994\pi\) | |||||||
\(152\) | 152.000 | 0.0811107 | ||||||||
\(153\) | −2424.68 | −1.28120 | ||||||||
\(154\) | 220.600 | 0.115432 | ||||||||
\(155\) | 1419.36 | 0.735521 | ||||||||
\(156\) | 2246.90 | 1.15318 | ||||||||
\(157\) | 243.616 | 0.123839 | 0.0619194 | − | 0.998081i | \(-0.480278\pi\) | ||||
0.0619194 | + | 0.998081i | \(0.480278\pi\) | |||||||
\(158\) | 854.448 | 0.430229 | ||||||||
\(159\) | −4709.48 | −2.34897 | ||||||||
\(160\) | −554.112 | −0.273790 | ||||||||
\(161\) | −2401.04 | −1.17533 | ||||||||
\(162\) | 834.416 | 0.404678 | ||||||||
\(163\) | −2598.11 | −1.24847 | −0.624233 | − | 0.781238i | \(-0.714588\pi\) | ||||
−0.624233 | + | 0.781238i | \(0.714588\pi\) | |||||||
\(164\) | 70.8801 | 0.0337488 | ||||||||
\(165\) | 642.216 | 0.303009 | ||||||||
\(166\) | 987.537 | 0.461733 | ||||||||
\(167\) | −491.064 | −0.227543 | −0.113772 | − | 0.993507i | \(-0.536293\pi\) | ||||
−0.113772 | + | 0.993507i | \(0.536293\pi\) | |||||||
\(168\) | −1830.75 | −0.840748 | ||||||||
\(169\) | 1903.61 | 0.866460 | ||||||||
\(170\) | 1681.18 | 0.758473 | ||||||||
\(171\) | 949.012 | 0.424402 | ||||||||
\(172\) | 1473.62 | 0.653268 | ||||||||
\(173\) | 1648.56 | 0.724496 | 0.362248 | − | 0.932082i | \(-0.382009\pi\) | ||||
0.362248 | + | 0.932082i | \(0.382009\pi\) | |||||||
\(174\) | −1547.59 | −0.674268 | ||||||||
\(175\) | −4561.33 | −1.97031 | ||||||||
\(176\) | −67.6480 | −0.0289725 | ||||||||
\(177\) | −321.932 | −0.136711 | ||||||||
\(178\) | −1842.27 | −0.775754 | ||||||||
\(179\) | 2326.81 | 0.971586 | 0.485793 | − | 0.874074i | \(-0.338531\pi\) | ||||
0.485793 | + | 0.874074i | \(0.338531\pi\) | |||||||
\(180\) | −3459.60 | −1.43257 | ||||||||
\(181\) | −4637.46 | −1.90442 | −0.952208 | − | 0.305449i | \(-0.901193\pi\) | ||||
−0.952208 | + | 0.305449i | \(0.901193\pi\) | |||||||
\(182\) | −3341.14 | −1.36078 | ||||||||
\(183\) | 5532.43 | 2.23480 | ||||||||
\(184\) | 736.288 | 0.294999 | ||||||||
\(185\) | 408.936 | 0.162516 | ||||||||
\(186\) | −1438.05 | −0.566897 | ||||||||
\(187\) | 205.244 | 0.0802616 | ||||||||
\(188\) | −1991.25 | −0.772483 | ||||||||
\(189\) | −5251.52 | −2.02112 | ||||||||
\(190\) | −658.008 | −0.251247 | ||||||||
\(191\) | 5260.38 | 1.99281 | 0.996407 | − | 0.0846903i | \(-0.0269901\pi\) | ||||
0.996407 | + | 0.0846903i | \(0.0269901\pi\) | |||||||
\(192\) | 561.408 | 0.211022 | ||||||||
\(193\) | 16.1833 | 0.00603575 | 0.00301787 | − | 0.999995i | \(-0.499039\pi\) | ||||
0.00301787 | + | 0.999995i | \(0.499039\pi\) | |||||||
\(194\) | 2165.49 | 0.801407 | ||||||||
\(195\) | −9726.82 | −3.57206 | ||||||||
\(196\) | 1350.34 | 0.492105 | ||||||||
\(197\) | 3784.71 | 1.36878 | 0.684390 | − | 0.729116i | \(-0.260069\pi\) | ||||
0.684390 | + | 0.729116i | \(0.260069\pi\) | |||||||
\(198\) | −422.360 | −0.151595 | ||||||||
\(199\) | 73.2079 | 0.0260783 | 0.0130391 | − | 0.999915i | \(-0.495849\pi\) | ||||
0.0130391 | + | 0.999915i | \(0.495849\pi\) | |||||||
\(200\) | 1398.75 | 0.494534 | ||||||||
\(201\) | 2478.58 | 0.869779 | ||||||||
\(202\) | −1424.90 | −0.496313 | ||||||||
\(203\) | 2301.28 | 0.795655 | ||||||||
\(204\) | −1703.31 | −0.584587 | ||||||||
\(205\) | −306.840 | −0.104540 | ||||||||
\(206\) | −52.9594 | −0.0179119 | ||||||||
\(207\) | 4597.02 | 1.54355 | ||||||||
\(208\) | 1024.58 | 0.341546 | ||||||||
\(209\) | −80.3320 | −0.0265870 | ||||||||
\(210\) | 7925.33 | 2.60428 | ||||||||
\(211\) | −2945.44 | −0.961006 | −0.480503 | − | 0.876993i | \(-0.659546\pi\) | ||||
−0.480503 | + | 0.876993i | \(0.659546\pi\) | |||||||
\(212\) | −2147.50 | −0.695713 | ||||||||
\(213\) | 5224.19 | 1.68054 | ||||||||
\(214\) | −1481.99 | −0.473397 | ||||||||
\(215\) | −6379.29 | −2.02355 | ||||||||
\(216\) | 1610.40 | 0.507286 | ||||||||
\(217\) | 2138.38 | 0.668954 | ||||||||
\(218\) | −3966.15 | −1.23221 | ||||||||
\(219\) | −5237.31 | −1.61600 | ||||||||
\(220\) | 292.848 | 0.0897446 | ||||||||
\(221\) | −3108.57 | −0.946175 | ||||||||
\(222\) | −414.320 | −0.125258 | ||||||||
\(223\) | 3125.30 | 0.938499 | 0.469250 | − | 0.883066i | \(-0.344524\pi\) | ||||
0.469250 | + | 0.883066i | \(0.344524\pi\) | |||||||
\(224\) | −834.816 | −0.249011 | ||||||||
\(225\) | 8733.11 | 2.58759 | ||||||||
\(226\) | −1437.44 | −0.423085 | ||||||||
\(227\) | −3577.80 | −1.04611 | −0.523055 | − | 0.852299i | \(-0.675208\pi\) | ||||
−0.523055 | + | 0.852299i | \(0.675208\pi\) | |||||||
\(228\) | 666.672 | 0.193647 | ||||||||
\(229\) | −4802.00 | −1.38570 | −0.692850 | − | 0.721082i | \(-0.743645\pi\) | ||||
−0.692850 | + | 0.721082i | \(0.743645\pi\) | |||||||
\(230\) | −3187.39 | −0.913785 | ||||||||
\(231\) | 967.552 | 0.275586 | ||||||||
\(232\) | −705.696 | −0.199704 | ||||||||
\(233\) | 5829.49 | 1.63907 | 0.819534 | − | 0.573031i | \(-0.194232\pi\) | ||||
0.819534 | + | 0.573031i | \(0.194232\pi\) | |||||||
\(234\) | 6396.94 | 1.78710 | ||||||||
\(235\) | 8620.12 | 2.39283 | ||||||||
\(236\) | −146.800 | −0.0404909 | ||||||||
\(237\) | 3747.61 | 1.02714 | ||||||||
\(238\) | 2532.83 | 0.689828 | ||||||||
\(239\) | 1364.33 | 0.369251 | 0.184625 | − | 0.982809i | \(-0.440893\pi\) | ||||
0.184625 | + | 0.982809i | \(0.440893\pi\) | |||||||
\(240\) | −2430.34 | −0.653656 | ||||||||
\(241\) | −2647.22 | −0.707563 | −0.353782 | − | 0.935328i | \(-0.615104\pi\) | ||||
−0.353782 | + | 0.935328i | \(0.615104\pi\) | |||||||
\(242\) | −2626.25 | −0.697610 | ||||||||
\(243\) | −1775.35 | −0.468679 | ||||||||
\(244\) | 2522.77 | 0.661901 | ||||||||
\(245\) | −5845.61 | −1.52434 | ||||||||
\(246\) | 310.880 | 0.0805731 | ||||||||
\(247\) | 1216.68 | 0.313424 | ||||||||
\(248\) | −655.745 | −0.167903 | ||||||||
\(249\) | 4331.34 | 1.10236 | ||||||||
\(250\) | −1726.20 | −0.436698 | ||||||||
\(251\) | 1970.73 | 0.495582 | 0.247791 | − | 0.968814i | \(-0.420295\pi\) | ||||
0.247791 | + | 0.968814i | \(0.420295\pi\) | |||||||
\(252\) | −5212.18 | −1.30292 | ||||||||
\(253\) | −389.128 | −0.0966967 | ||||||||
\(254\) | 5221.44 | 1.28985 | ||||||||
\(255\) | 7373.64 | 1.81081 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −7915.82 | −1.92131 | −0.960653 | − | 0.277752i | \(-0.910411\pi\) | ||||
−0.960653 | + | 0.277752i | \(0.910411\pi\) | |||||||
\(258\) | 6463.28 | 1.55964 | ||||||||
\(259\) | 616.096 | 0.147808 | ||||||||
\(260\) | −4435.39 | −1.05797 | ||||||||
\(261\) | −4406.02 | −1.04493 | ||||||||
\(262\) | −2433.38 | −0.573798 | ||||||||
\(263\) | 3287.96 | 0.770892 | 0.385446 | − | 0.922730i | \(-0.374048\pi\) | ||||
0.385446 | + | 0.922730i | \(0.374048\pi\) | |||||||
\(264\) | −296.704 | −0.0691700 | ||||||||
\(265\) | 9296.55 | 2.15503 | ||||||||
\(266\) | −991.344 | −0.228508 | ||||||||
\(267\) | −8080.21 | −1.85206 | ||||||||
\(268\) | 1130.22 | 0.257610 | ||||||||
\(269\) | −4749.61 | −1.07654 | −0.538269 | − | 0.842773i | \(-0.680922\pi\) | ||||
−0.538269 | + | 0.842773i | \(0.680922\pi\) | |||||||
\(270\) | −6971.43 | −1.57136 | ||||||||
\(271\) | 242.661 | 0.0543933 | 0.0271967 | − | 0.999630i | \(-0.491342\pi\) | ||||
0.0271967 | + | 0.999630i | \(0.491342\pi\) | |||||||
\(272\) | −776.704 | −0.173142 | ||||||||
\(273\) | −14654.3 | −3.24878 | ||||||||
\(274\) | 2341.34 | 0.516225 | ||||||||
\(275\) | −739.240 | −0.162101 | ||||||||
\(276\) | 3229.36 | 0.704292 | ||||||||
\(277\) | −4131.13 | −0.896086 | −0.448043 | − | 0.894012i | \(-0.647879\pi\) | ||||
−0.448043 | + | 0.894012i | \(0.647879\pi\) | |||||||
\(278\) | −542.167 | −0.116968 | ||||||||
\(279\) | −4094.14 | −0.878530 | ||||||||
\(280\) | 3613.92 | 0.771332 | ||||||||
\(281\) | 1007.19 | 0.213822 | 0.106911 | − | 0.994269i | \(-0.465904\pi\) | ||||
0.106911 | + | 0.994269i | \(0.465904\pi\) | |||||||
\(282\) | −8733.62 | −1.84425 | ||||||||
\(283\) | 2333.63 | 0.490176 | 0.245088 | − | 0.969501i | \(-0.421183\pi\) | ||||
0.245088 | + | 0.969501i | \(0.421183\pi\) | |||||||
\(284\) | 2382.21 | 0.497740 | ||||||||
\(285\) | −2886.02 | −0.599836 | ||||||||
\(286\) | −541.488 | −0.111954 | ||||||||
\(287\) | −462.280 | −0.0950785 | ||||||||
\(288\) | 1598.34 | 0.327024 | ||||||||
\(289\) | −2556.48 | −0.520350 | ||||||||
\(290\) | 3054.96 | 0.618598 | ||||||||
\(291\) | 9497.83 | 1.91331 | ||||||||
\(292\) | −2388.19 | −0.478625 | ||||||||
\(293\) | −1588.68 | −0.316763 | −0.158381 | − | 0.987378i | \(-0.550628\pi\) | ||||
−0.158381 | + | 0.987378i | \(0.550628\pi\) | |||||||
\(294\) | 5922.58 | 1.17487 | ||||||||
\(295\) | 635.497 | 0.125424 | ||||||||
\(296\) | −188.928 | −0.0370988 | ||||||||
\(297\) | −851.096 | −0.166282 | ||||||||
\(298\) | 3682.38 | 0.715820 | ||||||||
\(299\) | 5893.62 | 1.13992 | ||||||||
\(300\) | 6134.93 | 1.18067 | ||||||||
\(301\) | −9610.93 | −1.84041 | ||||||||
\(302\) | 6644.64 | 1.26608 | ||||||||
\(303\) | −6249.59 | −1.18492 | ||||||||
\(304\) | 304.000 | 0.0573539 | ||||||||
\(305\) | −10921.1 | −2.05029 | ||||||||
\(306\) | −4849.35 | −0.905945 | ||||||||
\(307\) | 4057.46 | 0.754304 | 0.377152 | − | 0.926151i | \(-0.376903\pi\) | ||||
0.377152 | + | 0.926151i | \(0.376903\pi\) | |||||||
\(308\) | 441.200 | 0.0816224 | ||||||||
\(309\) | −232.280 | −0.0427636 | ||||||||
\(310\) | 2838.72 | 0.520092 | ||||||||
\(311\) | 2871.92 | 0.523638 | 0.261819 | − | 0.965117i | \(-0.415678\pi\) | ||||
0.261819 | + | 0.965117i | \(0.415678\pi\) | |||||||
\(312\) | 4493.79 | 0.815420 | ||||||||
\(313\) | 4322.67 | 0.780612 | 0.390306 | − | 0.920685i | \(-0.372369\pi\) | ||||
0.390306 | + | 0.920685i | \(0.372369\pi\) | |||||||
\(314\) | 487.232 | 0.0875672 | ||||||||
\(315\) | 22563.5 | 4.03591 | ||||||||
\(316\) | 1708.90 | 0.304218 | ||||||||
\(317\) | 2513.56 | 0.445349 | 0.222674 | − | 0.974893i | \(-0.428521\pi\) | ||||
0.222674 | + | 0.974893i | \(0.428521\pi\) | |||||||
\(318\) | −9418.95 | −1.66097 | ||||||||
\(319\) | 372.960 | 0.0654601 | ||||||||
\(320\) | −1108.22 | −0.193599 | ||||||||
\(321\) | −6500.02 | −1.13021 | ||||||||
\(322\) | −4802.07 | −0.831084 | ||||||||
\(323\) | −922.336 | −0.158886 | ||||||||
\(324\) | 1668.83 | 0.286151 | ||||||||
\(325\) | 11196.3 | 1.91095 | ||||||||
\(326\) | −5196.22 | −0.882798 | ||||||||
\(327\) | −17395.6 | −2.94182 | ||||||||
\(328\) | 141.760 | 0.0238640 | ||||||||
\(329\) | 12986.9 | 2.17627 | ||||||||
\(330\) | 1284.43 | 0.214260 | ||||||||
\(331\) | −4573.78 | −0.759509 | −0.379754 | − | 0.925087i | \(-0.623992\pi\) | ||||
−0.379754 | + | 0.925087i | \(0.623992\pi\) | |||||||
\(332\) | 1975.07 | 0.326495 | ||||||||
\(333\) | −1179.57 | −0.194115 | ||||||||
\(334\) | −982.129 | −0.160897 | ||||||||
\(335\) | −4892.74 | −0.797967 | ||||||||
\(336\) | −3661.50 | −0.594498 | ||||||||
\(337\) | 9001.71 | 1.45506 | 0.727529 | − | 0.686077i | \(-0.240669\pi\) | ||||
0.727529 | + | 0.686077i | \(0.240669\pi\) | |||||||
\(338\) | 3807.22 | 0.612680 | ||||||||
\(339\) | −6304.62 | −1.01009 | ||||||||
\(340\) | 3362.35 | 0.536321 | ||||||||
\(341\) | 346.561 | 0.0550361 | ||||||||
\(342\) | 1898.02 | 0.300098 | ||||||||
\(343\) | 141.289 | 0.0222417 | ||||||||
\(344\) | 2947.23 | 0.461931 | ||||||||
\(345\) | −13979.9 | −2.18160 | ||||||||
\(346\) | 3297.12 | 0.512296 | ||||||||
\(347\) | 9358.68 | 1.44784 | 0.723920 | − | 0.689884i | \(-0.242339\pi\) | ||||
0.723920 | + | 0.689884i | \(0.242339\pi\) | |||||||
\(348\) | −3095.18 | −0.476780 | ||||||||
\(349\) | 5787.76 | 0.887712 | 0.443856 | − | 0.896098i | \(-0.353610\pi\) | ||||
0.443856 | + | 0.896098i | \(0.353610\pi\) | |||||||
\(350\) | −9122.67 | −1.39322 | ||||||||
\(351\) | 12890.5 | 1.96023 | ||||||||
\(352\) | −135.296 | −0.0204866 | ||||||||
\(353\) | 5784.59 | 0.872188 | 0.436094 | − | 0.899901i | \(-0.356361\pi\) | ||||
0.436094 | + | 0.899901i | \(0.356361\pi\) | |||||||
\(354\) | −643.864 | −0.0966695 | ||||||||
\(355\) | −10312.6 | −1.54179 | ||||||||
\(356\) | −3684.55 | −0.548541 | ||||||||
\(357\) | 11109.0 | 1.64692 | ||||||||
\(358\) | 4653.62 | 0.687015 | ||||||||
\(359\) | −10132.3 | −1.48959 | −0.744796 | − | 0.667292i | \(-0.767453\pi\) | ||||
−0.744796 | + | 0.667292i | \(0.767453\pi\) | |||||||
\(360\) | −6919.20 | −1.01298 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | −9274.91 | −1.34663 | ||||||||
\(363\) | −11518.7 | −1.66550 | ||||||||
\(364\) | −6682.29 | −0.962217 | ||||||||
\(365\) | 10338.5 | 1.48258 | ||||||||
\(366\) | 11064.9 | 1.58025 | ||||||||
\(367\) | −6993.81 | −0.994752 | −0.497376 | − | 0.867535i | \(-0.665703\pi\) | ||||
−0.497376 | + | 0.867535i | \(0.665703\pi\) | |||||||
\(368\) | 1472.58 | 0.208596 | ||||||||
\(369\) | 885.080 | 0.124866 | ||||||||
\(370\) | 817.871 | 0.114917 | ||||||||
\(371\) | 14006.0 | 1.95999 | ||||||||
\(372\) | −2876.10 | −0.400857 | ||||||||
\(373\) | 6523.15 | 0.905512 | 0.452756 | − | 0.891634i | \(-0.350441\pi\) | ||||
0.452756 | + | 0.891634i | \(0.350441\pi\) | |||||||
\(374\) | 410.488 | 0.0567535 | ||||||||
\(375\) | −7571.11 | −1.04259 | ||||||||
\(376\) | −3982.50 | −0.546228 | ||||||||
\(377\) | −5648.75 | −0.771685 | ||||||||
\(378\) | −10503.0 | −1.42915 | ||||||||
\(379\) | −9782.00 | −1.32577 | −0.662886 | − | 0.748720i | \(-0.730669\pi\) | ||||
−0.662886 | + | 0.748720i | \(0.730669\pi\) | |||||||
\(380\) | −1316.02 | −0.177658 | ||||||||
\(381\) | 22901.2 | 3.07944 | ||||||||
\(382\) | 10520.8 | 1.40913 | ||||||||
\(383\) | 9878.11 | 1.31788 | 0.658940 | − | 0.752196i | \(-0.271005\pi\) | ||||
0.658940 | + | 0.752196i | \(0.271005\pi\) | |||||||
\(384\) | 1122.82 | 0.149215 | ||||||||
\(385\) | −1909.96 | −0.252832 | ||||||||
\(386\) | 32.3666 | 0.00426792 | ||||||||
\(387\) | 18401.0 | 2.41700 | ||||||||
\(388\) | 4330.98 | 0.566680 | ||||||||
\(389\) | −7891.25 | −1.02854 | −0.514270 | − | 0.857628i | \(-0.671937\pi\) | ||||
−0.514270 | + | 0.857628i | \(0.671937\pi\) | |||||||
\(390\) | −19453.6 | −2.52583 | ||||||||
\(391\) | −4467.80 | −0.577868 | ||||||||
\(392\) | 2700.67 | 0.347971 | ||||||||
\(393\) | −10672.8 | −1.36991 | ||||||||
\(394\) | 7569.43 | 0.967874 | ||||||||
\(395\) | −7397.81 | −0.942340 | ||||||||
\(396\) | −844.720 | −0.107194 | ||||||||
\(397\) | −2787.84 | −0.352437 | −0.176219 | − | 0.984351i | \(-0.556387\pi\) | ||||
−0.176219 | + | 0.984351i | \(0.556387\pi\) | |||||||
\(398\) | 146.416 | 0.0184401 | ||||||||
\(399\) | −4348.04 | −0.545549 | ||||||||
\(400\) | 2797.50 | 0.349688 | ||||||||
\(401\) | 1264.42 | 0.157461 | 0.0787306 | − | 0.996896i | \(-0.474913\pi\) | ||||
0.0787306 | + | 0.996896i | \(0.474913\pi\) | |||||||
\(402\) | 4957.16 | 0.615027 | ||||||||
\(403\) | −5248.91 | −0.648801 | ||||||||
\(404\) | −2849.79 | −0.350947 | ||||||||
\(405\) | −7224.37 | −0.886375 | ||||||||
\(406\) | 4602.55 | 0.562613 | ||||||||
\(407\) | 99.8486 | 0.0121605 | ||||||||
\(408\) | −3406.62 | −0.413365 | ||||||||
\(409\) | −8140.55 | −0.984166 | −0.492083 | − | 0.870548i | \(-0.663764\pi\) | ||||
−0.492083 | + | 0.870548i | \(0.663764\pi\) | |||||||
\(410\) | −613.680 | −0.0739207 | ||||||||
\(411\) | 10269.1 | 1.23246 | ||||||||
\(412\) | −105.919 | −0.0126656 | ||||||||
\(413\) | 957.429 | 0.114073 | ||||||||
\(414\) | 9194.03 | 1.09145 | ||||||||
\(415\) | −8550.10 | −1.01134 | ||||||||
\(416\) | 2049.15 | 0.241510 | ||||||||
\(417\) | −2377.94 | −0.279253 | ||||||||
\(418\) | −160.664 | −0.0187998 | ||||||||
\(419\) | −9601.15 | −1.11944 | −0.559722 | − | 0.828680i | \(-0.689092\pi\) | ||||
−0.559722 | + | 0.828680i | \(0.689092\pi\) | |||||||
\(420\) | 15850.7 | 1.84151 | ||||||||
\(421\) | 5702.48 | 0.660147 | 0.330074 | − | 0.943955i | \(-0.392926\pi\) | ||||
0.330074 | + | 0.943955i | \(0.392926\pi\) | |||||||
\(422\) | −5890.87 | −0.679534 | ||||||||
\(423\) | −24864.7 | −2.85807 | ||||||||
\(424\) | −4295.01 | −0.491943 | ||||||||
\(425\) | −8487.63 | −0.968731 | ||||||||
\(426\) | 10448.4 | 1.18832 | ||||||||
\(427\) | −16453.5 | −1.86473 | ||||||||
\(428\) | −2963.99 | −0.334742 | ||||||||
\(429\) | −2374.97 | −0.267283 | ||||||||
\(430\) | −12758.6 | −1.43087 | ||||||||
\(431\) | −4025.72 | −0.449912 | −0.224956 | − | 0.974369i | \(-0.572224\pi\) | ||||
−0.224956 | + | 0.974369i | \(0.572224\pi\) | |||||||
\(432\) | 3220.80 | 0.358706 | ||||||||
\(433\) | −1347.10 | −0.149510 | −0.0747548 | − | 0.997202i | \(-0.523817\pi\) | ||||
−0.0747548 | + | 0.997202i | \(0.523817\pi\) | |||||||
\(434\) | 4276.77 | 0.473022 | ||||||||
\(435\) | 13399.1 | 1.47686 | ||||||||
\(436\) | −7932.31 | −0.871304 | ||||||||
\(437\) | 1748.68 | 0.191421 | ||||||||
\(438\) | −10474.6 | −1.14269 | ||||||||
\(439\) | 4109.36 | 0.446763 | 0.223381 | − | 0.974731i | \(-0.428290\pi\) | ||||
0.223381 | + | 0.974731i | \(0.428290\pi\) | |||||||
\(440\) | 585.696 | 0.0634590 | ||||||||
\(441\) | 16861.7 | 1.82072 | ||||||||
\(442\) | −6217.13 | −0.669047 | ||||||||
\(443\) | 6964.84 | 0.746974 | 0.373487 | − | 0.927635i | \(-0.378162\pi\) | ||||
0.373487 | + | 0.927635i | \(0.378162\pi\) | |||||||
\(444\) | −828.640 | −0.0885710 | ||||||||
\(445\) | 15950.4 | 1.69915 | ||||||||
\(446\) | 6250.59 | 0.663619 | ||||||||
\(447\) | 16150.9 | 1.70897 | ||||||||
\(448\) | −1669.63 | −0.176078 | ||||||||
\(449\) | 3041.21 | 0.319652 | 0.159826 | − | 0.987145i | \(-0.448907\pi\) | ||||
0.159826 | + | 0.987145i | \(0.448907\pi\) | |||||||
\(450\) | 17466.2 | 1.82970 | ||||||||
\(451\) | −74.9202 | −0.00782229 | ||||||||
\(452\) | −2874.88 | −0.299166 | ||||||||
\(453\) | 29143.4 | 3.02269 | ||||||||
\(454\) | −7155.60 | −0.739711 | ||||||||
\(455\) | 28927.6 | 2.98055 | ||||||||
\(456\) | 1333.34 | 0.136929 | ||||||||
\(457\) | 11984.3 | 1.22670 | 0.613352 | − | 0.789810i | \(-0.289821\pi\) | ||||
0.613352 | + | 0.789810i | \(0.289821\pi\) | |||||||
\(458\) | −9604.01 | −0.979838 | ||||||||
\(459\) | −9771.91 | −0.993712 | ||||||||
\(460\) | −6374.79 | −0.646143 | ||||||||
\(461\) | −12126.7 | −1.22515 | −0.612577 | − | 0.790411i | \(-0.709867\pi\) | ||||
−0.612577 | + | 0.790411i | \(0.709867\pi\) | |||||||
\(462\) | 1935.10 | 0.194868 | ||||||||
\(463\) | −6399.19 | −0.642323 | −0.321162 | − | 0.947024i | \(-0.604073\pi\) | ||||
−0.321162 | + | 0.947024i | \(0.604073\pi\) | |||||||
\(464\) | −1411.39 | −0.141212 | ||||||||
\(465\) | 12450.6 | 1.24169 | ||||||||
\(466\) | 11659.0 | 1.15900 | ||||||||
\(467\) | 993.366 | 0.0984315 | 0.0492157 | − | 0.998788i | \(-0.484328\pi\) | ||||
0.0492157 | + | 0.998788i | \(0.484328\pi\) | |||||||
\(468\) | 12793.9 | 1.26367 | ||||||||
\(469\) | −7371.32 | −0.725748 | ||||||||
\(470\) | 17240.2 | 1.69198 | ||||||||
\(471\) | 2137.00 | 0.209061 | ||||||||
\(472\) | −293.600 | −0.0286314 | ||||||||
\(473\) | −1557.61 | −0.151414 | ||||||||
\(474\) | 7495.22 | 0.726301 | ||||||||
\(475\) | 3322.04 | 0.320896 | ||||||||
\(476\) | 5065.67 | 0.487782 | ||||||||
\(477\) | −26815.9 | −2.57404 | ||||||||
\(478\) | 2728.65 | 0.261100 | ||||||||
\(479\) | 6639.36 | 0.633320 | 0.316660 | − | 0.948539i | \(-0.397439\pi\) | ||||
0.316660 | + | 0.948539i | \(0.397439\pi\) | |||||||
\(480\) | −4860.67 | −0.462205 | ||||||||
\(481\) | −1512.28 | −0.143355 | ||||||||
\(482\) | −5294.45 | −0.500323 | ||||||||
\(483\) | −21061.9 | −1.98416 | ||||||||
\(484\) | −5252.50 | −0.493285 | ||||||||
\(485\) | −18748.8 | −1.75534 | ||||||||
\(486\) | −3550.70 | −0.331406 | ||||||||
\(487\) | −11088.8 | −1.03179 | −0.515894 | − | 0.856652i | \(-0.672540\pi\) | ||||
−0.515894 | + | 0.856652i | \(0.672540\pi\) | |||||||
\(488\) | 5045.54 | 0.468034 | ||||||||
\(489\) | −22790.6 | −2.10762 | ||||||||
\(490\) | −11691.2 | −1.07787 | ||||||||
\(491\) | −13215.2 | −1.21465 | −0.607324 | − | 0.794454i | \(-0.707757\pi\) | ||||
−0.607324 | + | 0.794454i | \(0.707757\pi\) | |||||||
\(492\) | 621.760 | 0.0569738 | ||||||||
\(493\) | 4282.17 | 0.391195 | ||||||||
\(494\) | 2433.37 | 0.221624 | ||||||||
\(495\) | 3656.80 | 0.332042 | ||||||||
\(496\) | −1311.49 | −0.118725 | ||||||||
\(497\) | −15536.8 | −1.40225 | ||||||||
\(498\) | 8662.67 | 0.779485 | ||||||||
\(499\) | 410.640 | 0.0368393 | 0.0184196 | − | 0.999830i | \(-0.494137\pi\) | ||||
0.0184196 | + | 0.999830i | \(0.494137\pi\) | |||||||
\(500\) | −3452.40 | −0.308792 | ||||||||
\(501\) | −4307.62 | −0.384132 | ||||||||
\(502\) | 3941.45 | 0.350429 | ||||||||
\(503\) | −9407.88 | −0.833950 | −0.416975 | − | 0.908918i | \(-0.636910\pi\) | ||||
−0.416975 | + | 0.908918i | \(0.636910\pi\) | |||||||
\(504\) | −10424.4 | −0.921305 | ||||||||
\(505\) | 12336.7 | 1.08709 | ||||||||
\(506\) | −778.256 | −0.0683749 | ||||||||
\(507\) | 16698.5 | 1.46273 | ||||||||
\(508\) | 10442.9 | 0.912063 | ||||||||
\(509\) | 10482.2 | 0.912803 | 0.456402 | − | 0.889774i | \(-0.349138\pi\) | ||||
0.456402 | + | 0.889774i | \(0.349138\pi\) | |||||||
\(510\) | 14747.3 | 1.28043 | ||||||||
\(511\) | 15575.8 | 1.34840 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 3824.70 | 0.329171 | ||||||||
\(514\) | −15831.6 | −1.35857 | ||||||||
\(515\) | 458.523 | 0.0392329 | ||||||||
\(516\) | 12926.6 | 1.10283 | ||||||||
\(517\) | 2104.75 | 0.179046 | ||||||||
\(518\) | 1232.19 | 0.104516 | ||||||||
\(519\) | 14461.2 | 1.22307 | ||||||||
\(520\) | −8870.79 | −0.748096 | ||||||||
\(521\) | −3181.02 | −0.267492 | −0.133746 | − | 0.991016i | \(-0.542701\pi\) | ||||
−0.133746 | + | 0.991016i | \(0.542701\pi\) | |||||||
\(522\) | −8812.03 | −0.738874 | ||||||||
\(523\) | −4360.12 | −0.364541 | −0.182270 | − | 0.983248i | \(-0.558345\pi\) | ||||
−0.182270 | + | 0.983248i | \(0.558345\pi\) | |||||||
\(524\) | −4866.77 | −0.405736 | ||||||||
\(525\) | −40012.0 | −3.32622 | ||||||||
\(526\) | 6575.93 | 0.545103 | ||||||||
\(527\) | 3979.06 | 0.328900 | ||||||||
\(528\) | −593.408 | −0.0489106 | ||||||||
\(529\) | −3696.37 | −0.303803 | ||||||||
\(530\) | 18593.1 | 1.52383 | ||||||||
\(531\) | −1833.09 | −0.149810 | ||||||||
\(532\) | −1982.69 | −0.161580 | ||||||||
\(533\) | 1134.72 | 0.0922142 | ||||||||
\(534\) | −16160.4 | −1.30961 | ||||||||
\(535\) | 12831.1 | 1.03689 | ||||||||
\(536\) | 2260.45 | 0.182158 | ||||||||
\(537\) | 20410.8 | 1.64020 | ||||||||
\(538\) | −9499.22 | −0.761227 | ||||||||
\(539\) | −1427.31 | −0.114060 | ||||||||
\(540\) | −13942.9 | −1.11112 | ||||||||
\(541\) | −23681.2 | −1.88195 | −0.940973 | − | 0.338481i | \(-0.890087\pi\) | ||||
−0.940973 | + | 0.338481i | \(0.890087\pi\) | |||||||
\(542\) | 485.322 | 0.0384619 | ||||||||
\(543\) | −40679.8 | −3.21498 | ||||||||
\(544\) | −1553.41 | −0.122430 | ||||||||
\(545\) | 34339.0 | 2.69894 | ||||||||
\(546\) | −29308.5 | −2.29723 | ||||||||
\(547\) | −7373.25 | −0.576339 | −0.288169 | − | 0.957579i | \(-0.593047\pi\) | ||||
−0.288169 | + | 0.957579i | \(0.593047\pi\) | |||||||
\(548\) | 4682.69 | 0.365026 | ||||||||
\(549\) | 31501.8 | 2.44893 | ||||||||
\(550\) | −1478.48 | −0.114623 | ||||||||
\(551\) | −1676.03 | −0.129585 | ||||||||
\(552\) | 6458.72 | 0.498010 | ||||||||
\(553\) | −11145.4 | −0.857055 | ||||||||
\(554\) | −8262.27 | −0.633628 | ||||||||
\(555\) | 3587.18 | 0.274356 | ||||||||
\(556\) | −1084.33 | −0.0827086 | ||||||||
\(557\) | 4772.14 | 0.363020 | 0.181510 | − | 0.983389i | \(-0.441902\pi\) | ||||
0.181510 | + | 0.983389i | \(0.441902\pi\) | |||||||
\(558\) | −8188.29 | −0.621215 | ||||||||
\(559\) | 23591.1 | 1.78497 | ||||||||
\(560\) | 7227.84 | 0.545414 | ||||||||
\(561\) | 1800.40 | 0.135495 | ||||||||
\(562\) | 2014.38 | 0.151195 | ||||||||
\(563\) | 7276.49 | 0.544702 | 0.272351 | − | 0.962198i | \(-0.412199\pi\) | ||||
0.272351 | + | 0.962198i | \(0.412199\pi\) | |||||||
\(564\) | −17467.2 | −1.30408 | ||||||||
\(565\) | 12445.4 | 0.926691 | ||||||||
\(566\) | 4667.26 | 0.346607 | ||||||||
\(567\) | −10884.1 | −0.806156 | ||||||||
\(568\) | 4764.42 | 0.351955 | ||||||||
\(569\) | −10685.1 | −0.787245 | −0.393622 | − | 0.919272i | \(-0.628778\pi\) | ||||
−0.393622 | + | 0.919272i | \(0.628778\pi\) | |||||||
\(570\) | −5772.05 | −0.424148 | ||||||||
\(571\) | 14856.1 | 1.08881 | 0.544404 | − | 0.838823i | \(-0.316756\pi\) | ||||
0.544404 | + | 0.838823i | \(0.316756\pi\) | |||||||
\(572\) | −1082.98 | −0.0791635 | ||||||||
\(573\) | 46144.0 | 3.36421 | ||||||||
\(574\) | −924.560 | −0.0672306 | ||||||||
\(575\) | 16092.0 | 1.16710 | ||||||||
\(576\) | 3196.67 | 0.231241 | ||||||||
\(577\) | 3212.67 | 0.231794 | 0.115897 | − | 0.993261i | \(-0.463026\pi\) | ||||
0.115897 | + | 0.993261i | \(0.463026\pi\) | |||||||
\(578\) | −5112.96 | −0.367943 | ||||||||
\(579\) | 141.960 | 0.0101894 | ||||||||
\(580\) | 6109.92 | 0.437415 | ||||||||
\(581\) | −12881.4 | −0.919814 | ||||||||
\(582\) | 18995.7 | 1.35291 | ||||||||
\(583\) | 2269.91 | 0.161252 | ||||||||
\(584\) | −4776.39 | −0.338439 | ||||||||
\(585\) | −55384.8 | −3.91432 | ||||||||
\(586\) | −3177.35 | −0.223985 | ||||||||
\(587\) | −22321.1 | −1.56949 | −0.784745 | − | 0.619818i | \(-0.787206\pi\) | ||||
−0.784745 | + | 0.619818i | \(0.787206\pi\) | |||||||
\(588\) | 11845.2 | 0.830758 | ||||||||
\(589\) | −1557.39 | −0.108950 | ||||||||
\(590\) | 1270.99 | 0.0886881 | ||||||||
\(591\) | 33199.5 | 2.31074 | ||||||||
\(592\) | −377.857 | −0.0262328 | ||||||||
\(593\) | −8202.50 | −0.568021 | −0.284010 | − | 0.958821i | \(-0.591665\pi\) | ||||
−0.284010 | + | 0.958821i | \(0.591665\pi\) | |||||||
\(594\) | −1702.19 | −0.117579 | ||||||||
\(595\) | −21929.3 | −1.51095 | ||||||||
\(596\) | 7364.75 | 0.506161 | ||||||||
\(597\) | 642.180 | 0.0440246 | ||||||||
\(598\) | 11787.2 | 0.806047 | ||||||||
\(599\) | 10583.3 | 0.721906 | 0.360953 | − | 0.932584i | \(-0.382452\pi\) | ||||
0.360953 | + | 0.932584i | \(0.382452\pi\) | |||||||
\(600\) | 12269.9 | 0.834858 | ||||||||
\(601\) | −9051.94 | −0.614370 | −0.307185 | − | 0.951650i | \(-0.599387\pi\) | ||||
−0.307185 | + | 0.951650i | \(0.599387\pi\) | |||||||
\(602\) | −19221.9 | −1.30137 | ||||||||
\(603\) | 14113.1 | 0.953118 | ||||||||
\(604\) | 13289.3 | 0.895254 | ||||||||
\(605\) | 22738.1 | 1.52799 | ||||||||
\(606\) | −12499.2 | −0.837863 | ||||||||
\(607\) | 8123.48 | 0.543199 | 0.271599 | − | 0.962410i | \(-0.412447\pi\) | ||||
0.271599 | + | 0.962410i | \(0.412447\pi\) | |||||||
\(608\) | 608.000 | 0.0405554 | ||||||||
\(609\) | 20186.8 | 1.34320 | ||||||||
\(610\) | −21842.1 | −1.44977 | ||||||||
\(611\) | −31877.9 | −2.11071 | ||||||||
\(612\) | −9698.71 | −0.640600 | ||||||||
\(613\) | 22384.7 | 1.47490 | 0.737448 | − | 0.675404i | \(-0.236031\pi\) | ||||
0.737448 | + | 0.675404i | \(0.236031\pi\) | |||||||
\(614\) | 8114.91 | 0.533373 | ||||||||
\(615\) | −2691.60 | −0.176481 | ||||||||
\(616\) | 882.400 | 0.0577158 | ||||||||
\(617\) | 11349.1 | 0.740517 | 0.370259 | − | 0.928929i | \(-0.379269\pi\) | ||||
0.370259 | + | 0.928929i | \(0.379269\pi\) | |||||||
\(618\) | −464.560 | −0.0302384 | ||||||||
\(619\) | −9106.25 | −0.591294 | −0.295647 | − | 0.955297i | \(-0.595535\pi\) | ||||
−0.295647 | + | 0.955297i | \(0.595535\pi\) | |||||||
\(620\) | 5677.44 | 0.367760 | ||||||||
\(621\) | 18526.9 | 1.19719 | ||||||||
\(622\) | 5743.84 | 0.370268 | ||||||||
\(623\) | 24030.6 | 1.54537 | ||||||||
\(624\) | 8987.59 | 0.576589 | ||||||||
\(625\) | −6910.06 | −0.442244 | ||||||||
\(626\) | 8645.34 | 0.551976 | ||||||||
\(627\) | −704.672 | −0.0448834 | ||||||||
\(628\) | 974.464 | 0.0619194 | ||||||||
\(629\) | 1146.42 | 0.0726720 | ||||||||
\(630\) | 45127.0 | 2.85382 | ||||||||
\(631\) | −27784.2 | −1.75289 | −0.876444 | − | 0.481505i | \(-0.840090\pi\) | ||||
−0.876444 | + | 0.481505i | \(0.840090\pi\) | |||||||
\(632\) | 3417.79 | 0.215115 | ||||||||
\(633\) | −25837.4 | −1.62234 | ||||||||
\(634\) | 5027.12 | 0.314909 | ||||||||
\(635\) | −45207.3 | −2.82519 | ||||||||
\(636\) | −18837.9 | −1.17448 | ||||||||
\(637\) | 21617.5 | 1.34461 | ||||||||
\(638\) | 745.921 | 0.0462873 | ||||||||
\(639\) | 29746.7 | 1.84156 | ||||||||
\(640\) | −2216.45 | −0.136895 | ||||||||
\(641\) | −16958.3 | −1.04495 | −0.522476 | − | 0.852654i | \(-0.674992\pi\) | ||||
−0.522476 | + | 0.852654i | \(0.674992\pi\) | |||||||
\(642\) | −13000.0 | −0.799176 | ||||||||
\(643\) | 4754.37 | 0.291592 | 0.145796 | − | 0.989315i | \(-0.453426\pi\) | ||||
0.145796 | + | 0.989315i | \(0.453426\pi\) | |||||||
\(644\) | −9604.15 | −0.587665 | ||||||||
\(645\) | −55959.1 | −3.41611 | ||||||||
\(646\) | −1844.67 | −0.112349 | ||||||||
\(647\) | −11254.0 | −0.683831 | −0.341916 | − | 0.939731i | \(-0.611076\pi\) | ||||
−0.341916 | + | 0.939731i | \(0.611076\pi\) | |||||||
\(648\) | 3337.66 | 0.202339 | ||||||||
\(649\) | 155.167 | 0.00938498 | ||||||||
\(650\) | 22392.6 | 1.35125 | ||||||||
\(651\) | 18757.9 | 1.12931 | ||||||||
\(652\) | −10392.4 | −0.624233 | ||||||||
\(653\) | −15515.1 | −0.929793 | −0.464896 | − | 0.885365i | \(-0.653908\pi\) | ||||
−0.464896 | + | 0.885365i | \(0.653908\pi\) | |||||||
\(654\) | −34791.1 | −2.08018 | ||||||||
\(655\) | 21068.2 | 1.25680 | ||||||||
\(656\) | 283.520 | 0.0168744 | ||||||||
\(657\) | −29821.4 | −1.77084 | ||||||||
\(658\) | 25973.9 | 1.53885 | ||||||||
\(659\) | 17203.2 | 1.01691 | 0.508453 | − | 0.861090i | \(-0.330217\pi\) | ||||
0.508453 | + | 0.861090i | \(0.330217\pi\) | |||||||
\(660\) | 2568.86 | 0.151504 | ||||||||
\(661\) | 2305.65 | 0.135672 | 0.0678361 | − | 0.997696i | \(-0.478390\pi\) | ||||
0.0678361 | + | 0.997696i | \(0.478390\pi\) | |||||||
\(662\) | −9147.55 | −0.537054 | ||||||||
\(663\) | −27268.3 | −1.59731 | ||||||||
\(664\) | 3950.15 | 0.230867 | ||||||||
\(665\) | 8583.06 | 0.500507 | ||||||||
\(666\) | −2359.15 | −0.137260 | ||||||||
\(667\) | −8118.69 | −0.471299 | ||||||||
\(668\) | −1964.26 | −0.113772 | ||||||||
\(669\) | 27415.1 | 1.58435 | ||||||||
\(670\) | −9785.48 | −0.564248 | ||||||||
\(671\) | −2666.57 | −0.153415 | ||||||||
\(672\) | −7323.01 | −0.420374 | ||||||||
\(673\) | −14242.8 | −0.815782 | −0.407891 | − | 0.913031i | \(-0.633736\pi\) | ||||
−0.407891 | + | 0.913031i | \(0.633736\pi\) | |||||||
\(674\) | 18003.4 | 1.02888 | ||||||||
\(675\) | 35196.1 | 2.00696 | ||||||||
\(676\) | 7614.45 | 0.433230 | ||||||||
\(677\) | −13480.0 | −0.765256 | −0.382628 | − | 0.923902i | \(-0.624981\pi\) | ||||
−0.382628 | + | 0.923902i | \(0.624981\pi\) | |||||||
\(678\) | −12609.2 | −0.714240 | ||||||||
\(679\) | −28246.6 | −1.59647 | ||||||||
\(680\) | 6724.71 | 0.379236 | ||||||||
\(681\) | −31384.5 | −1.76601 | ||||||||
\(682\) | 693.122 | 0.0389164 | ||||||||
\(683\) | 27626.1 | 1.54771 | 0.773854 | − | 0.633365i | \(-0.218327\pi\) | ||||
0.773854 | + | 0.633365i | \(0.218327\pi\) | |||||||
\(684\) | 3796.05 | 0.212201 | ||||||||
\(685\) | −20271.4 | −1.13070 | ||||||||
\(686\) | 282.578 | 0.0157272 | ||||||||
\(687\) | −42123.2 | −2.33930 | ||||||||
\(688\) | 5894.46 | 0.326634 | ||||||||
\(689\) | −34379.4 | −1.90094 | ||||||||
\(690\) | −27959.8 | −1.54263 | ||||||||
\(691\) | 17419.7 | 0.959009 | 0.479505 | − | 0.877539i | \(-0.340816\pi\) | ||||
0.479505 | + | 0.877539i | \(0.340816\pi\) | |||||||
\(692\) | 6594.24 | 0.362248 | ||||||||
\(693\) | 5509.27 | 0.301991 | ||||||||
\(694\) | 18717.4 | 1.02378 | ||||||||
\(695\) | 4694.08 | 0.256197 | ||||||||
\(696\) | −6190.37 | −0.337134 | ||||||||
\(697\) | −860.201 | −0.0467467 | ||||||||
\(698\) | 11575.5 | 0.627707 | ||||||||
\(699\) | 51136.3 | 2.76703 | ||||||||
\(700\) | −18245.3 | −0.985155 | ||||||||
\(701\) | 5069.39 | 0.273136 | 0.136568 | − | 0.990631i | \(-0.456393\pi\) | ||||
0.136568 | + | 0.990631i | \(0.456393\pi\) | |||||||
\(702\) | 25780.9 | 1.38609 | ||||||||
\(703\) | −448.705 | −0.0240729 | ||||||||
\(704\) | −270.592 | −0.0144862 | ||||||||
\(705\) | 75615.7 | 4.03951 | ||||||||
\(706\) | 11569.2 | 0.616730 | ||||||||
\(707\) | 18586.3 | 0.988701 | ||||||||
\(708\) | −1287.73 | −0.0683556 | ||||||||
\(709\) | −16758.9 | −0.887719 | −0.443860 | − | 0.896096i | \(-0.646391\pi\) | ||||
−0.443860 | + | 0.896096i | \(0.646391\pi\) | |||||||
\(710\) | −20625.2 | −1.09021 | ||||||||
\(711\) | 21339.0 | 1.12556 | ||||||||
\(712\) | −7369.09 | −0.387877 | ||||||||
\(713\) | −7544.02 | −0.396249 | ||||||||
\(714\) | 22218.0 | 1.16455 | ||||||||
\(715\) | 4688.21 | 0.245215 | ||||||||
\(716\) | 9307.24 | 0.485793 | ||||||||
\(717\) | 11967.9 | 0.623359 | ||||||||
\(718\) | −20264.6 | −1.05330 | ||||||||
\(719\) | −3885.84 | −0.201554 | −0.100777 | − | 0.994909i | \(-0.532133\pi\) | ||||
−0.100777 | + | 0.994909i | \(0.532133\pi\) | |||||||
\(720\) | −13838.4 | −0.716287 | ||||||||
\(721\) | 690.803 | 0.0356822 | ||||||||
\(722\) | 722.000 | 0.0372161 | ||||||||
\(723\) | −23221.5 | −1.19449 | ||||||||
\(724\) | −18549.8 | −0.952208 | ||||||||
\(725\) | −15423.4 | −0.790081 | ||||||||
\(726\) | −23037.5 | −1.17769 | ||||||||
\(727\) | 6468.37 | 0.329984 | 0.164992 | − | 0.986295i | \(-0.447240\pi\) | ||||
0.164992 | + | 0.986295i | \(0.447240\pi\) | |||||||
\(728\) | −13364.6 | −0.680390 | ||||||||
\(729\) | −26838.0 | −1.36351 | ||||||||
\(730\) | 20677.0 | 1.04834 | ||||||||
\(731\) | −17883.8 | −0.904865 | ||||||||
\(732\) | 22129.7 | 1.11740 | ||||||||
\(733\) | 25245.5 | 1.27212 | 0.636059 | − | 0.771640i | \(-0.280563\pi\) | ||||
0.636059 | + | 0.771640i | \(0.280563\pi\) | |||||||
\(734\) | −13987.6 | −0.703396 | ||||||||
\(735\) | −51277.7 | −2.57334 | ||||||||
\(736\) | 2945.15 | 0.147500 | ||||||||
\(737\) | −1194.65 | −0.0597087 | ||||||||
\(738\) | 1770.16 | 0.0882933 | ||||||||
\(739\) | 3229.28 | 0.160746 | 0.0803728 | − | 0.996765i | \(-0.474389\pi\) | ||||
0.0803728 | + | 0.996765i | \(0.474389\pi\) | |||||||
\(740\) | 1635.74 | 0.0812582 | ||||||||
\(741\) | 10672.8 | 0.529114 | ||||||||
\(742\) | 28012.0 | 1.38592 | ||||||||
\(743\) | 18876.2 | 0.932033 | 0.466016 | − | 0.884776i | \(-0.345689\pi\) | ||||
0.466016 | + | 0.884776i | \(0.345689\pi\) | |||||||
\(744\) | −5752.19 | −0.283448 | ||||||||
\(745\) | −31882.0 | −1.56788 | ||||||||
\(746\) | 13046.3 | 0.640294 | ||||||||
\(747\) | 24662.8 | 1.20798 | ||||||||
\(748\) | 820.976 | 0.0401308 | ||||||||
\(749\) | 19331.1 | 0.943049 | ||||||||
\(750\) | −15142.2 | −0.737221 | ||||||||
\(751\) | 24895.8 | 1.20967 | 0.604833 | − | 0.796352i | \(-0.293240\pi\) | ||||
0.604833 | + | 0.796352i | \(0.293240\pi\) | |||||||
\(752\) | −7964.99 | −0.386241 | ||||||||
\(753\) | 17287.2 | 0.836628 | ||||||||
\(754\) | −11297.5 | −0.545664 | ||||||||
\(755\) | −57529.3 | −2.77312 | ||||||||
\(756\) | −21006.1 | −1.01056 | ||||||||
\(757\) | −36203.2 | −1.73821 | −0.869107 | − | 0.494624i | \(-0.835306\pi\) | ||||
−0.869107 | + | 0.494624i | \(0.835306\pi\) | |||||||
\(758\) | −19564.0 | −0.937462 | ||||||||
\(759\) | −3413.43 | −0.163241 | ||||||||
\(760\) | −2632.03 | −0.125624 | ||||||||
\(761\) | 11417.5 | 0.543868 | 0.271934 | − | 0.962316i | \(-0.412337\pi\) | ||||
0.271934 | + | 0.962316i | \(0.412337\pi\) | |||||||
\(762\) | 45802.5 | 2.17749 | ||||||||
\(763\) | 51734.5 | 2.45467 | ||||||||
\(764\) | 21041.5 | 0.996407 | ||||||||
\(765\) | 41985.7 | 1.98431 | ||||||||
\(766\) | 19756.2 | 0.931881 | ||||||||
\(767\) | −2350.12 | −0.110636 | ||||||||
\(768\) | 2245.63 | 0.105511 | ||||||||
\(769\) | 39414.5 | 1.84828 | 0.924138 | − | 0.382058i | \(-0.124785\pi\) | ||||
0.924138 | + | 0.382058i | \(0.124785\pi\) | |||||||
\(770\) | −3819.91 | −0.178779 | ||||||||
\(771\) | −69437.6 | −3.24350 | ||||||||
\(772\) | 64.7332 | 0.00301787 | ||||||||
\(773\) | −14268.5 | −0.663910 | −0.331955 | − | 0.943295i | \(-0.607708\pi\) | ||||
−0.331955 | + | 0.943295i | \(0.607708\pi\) | |||||||
\(774\) | 36802.1 | 1.70908 | ||||||||
\(775\) | −14331.6 | −0.664268 | ||||||||
\(776\) | 8661.95 | 0.400704 | ||||||||
\(777\) | 5404.39 | 0.249526 | ||||||||
\(778\) | −15782.5 | −0.727288 | ||||||||
\(779\) | 336.680 | 0.0154850 | ||||||||
\(780\) | −38907.3 | −1.78603 | ||||||||
\(781\) | −2517.99 | −0.115366 | ||||||||
\(782\) | −8935.59 | −0.408614 | ||||||||
\(783\) | −17757.1 | −0.810455 | ||||||||
\(784\) | 5401.35 | 0.246053 | ||||||||
\(785\) | −4218.46 | −0.191800 | ||||||||
\(786\) | −21345.7 | −0.968669 | ||||||||
\(787\) | −2922.28 | −0.132361 | −0.0661804 | − | 0.997808i | \(-0.521081\pi\) | ||||
−0.0661804 | + | 0.997808i | \(0.521081\pi\) | |||||||
\(788\) | 15138.9 | 0.684390 | ||||||||
\(789\) | 28842.0 | 1.30140 | ||||||||
\(790\) | −14795.6 | −0.666335 | ||||||||
\(791\) | 18750.0 | 0.842823 | ||||||||
\(792\) | −1689.44 | −0.0757976 | ||||||||
\(793\) | 40387.0 | 1.80856 | ||||||||
\(794\) | −5575.67 | −0.249211 | ||||||||
\(795\) | 81549.3 | 3.63806 | ||||||||
\(796\) | 292.832 | 0.0130391 | ||||||||
\(797\) | −7724.25 | −0.343296 | −0.171648 | − | 0.985158i | \(-0.554909\pi\) | ||||
−0.171648 | + | 0.985158i | \(0.554909\pi\) | |||||||
\(798\) | −8696.07 | −0.385762 | ||||||||
\(799\) | 24165.8 | 1.06999 | ||||||||
\(800\) | 5595.01 | 0.247267 | ||||||||
\(801\) | −46008.9 | −2.02952 | ||||||||
\(802\) | 2528.83 | 0.111342 | ||||||||
\(803\) | 2524.32 | 0.110936 | ||||||||
\(804\) | 9914.32 | 0.434890 | ||||||||
\(805\) | 41576.4 | 1.82034 | ||||||||
\(806\) | −10497.8 | −0.458772 | ||||||||
\(807\) | −41663.6 | −1.81738 | ||||||||
\(808\) | −5699.58 | −0.248157 | ||||||||
\(809\) | 42980.8 | 1.86789 | 0.933947 | − | 0.357412i | \(-0.116341\pi\) | ||||
0.933947 | + | 0.357412i | \(0.116341\pi\) | |||||||
\(810\) | −14448.7 | −0.626762 | ||||||||
\(811\) | 28749.5 | 1.24480 | 0.622398 | − | 0.782701i | \(-0.286158\pi\) | ||||
0.622398 | + | 0.782701i | \(0.286158\pi\) | |||||||
\(812\) | 9205.11 | 0.397827 | ||||||||
\(813\) | 2128.62 | 0.0918253 | ||||||||
\(814\) | 199.697 | 0.00859875 | ||||||||
\(815\) | 44988.9 | 1.93361 | ||||||||
\(816\) | −6813.25 | −0.292293 | ||||||||
\(817\) | 6999.68 | 0.299740 | ||||||||
\(818\) | −16281.1 | −0.695911 | ||||||||
\(819\) | −83441.8 | −3.56006 | ||||||||
\(820\) | −1227.36 | −0.0522698 | ||||||||
\(821\) | −30274.8 | −1.28696 | −0.643482 | − | 0.765461i | \(-0.722511\pi\) | ||||
−0.643482 | + | 0.765461i | \(0.722511\pi\) | |||||||
\(822\) | 20538.3 | 0.871477 | ||||||||
\(823\) | 17296.1 | 0.732568 | 0.366284 | − | 0.930503i | \(-0.380630\pi\) | ||||
0.366284 | + | 0.930503i | \(0.380630\pi\) | |||||||
\(824\) | −211.838 | −0.00895596 | ||||||||
\(825\) | −6484.62 | −0.273655 | ||||||||
\(826\) | 1914.86 | 0.0806615 | ||||||||
\(827\) | −2022.80 | −0.0850541 | −0.0425271 | − | 0.999095i | \(-0.513541\pi\) | ||||
−0.0425271 | + | 0.999095i | \(0.513541\pi\) | |||||||
\(828\) | 18388.1 | 0.771775 | ||||||||
\(829\) | −43239.0 | −1.81152 | −0.905762 | − | 0.423786i | \(-0.860701\pi\) | ||||
−0.905762 | + | 0.423786i | \(0.860701\pi\) | |||||||
\(830\) | −17100.2 | −0.715128 | ||||||||
\(831\) | −36238.3 | −1.51275 | ||||||||
\(832\) | 4098.31 | 0.170773 | ||||||||
\(833\) | −16387.7 | −0.681632 | ||||||||
\(834\) | −4755.89 | −0.197462 | ||||||||
\(835\) | 8503.27 | 0.352417 | ||||||||
\(836\) | −321.328 | −0.0132935 | ||||||||
\(837\) | −16500.2 | −0.681397 | ||||||||
\(838\) | −19202.3 | −0.791567 | ||||||||
\(839\) | 27435.9 | 1.12895 | 0.564477 | − | 0.825449i | \(-0.309078\pi\) | ||||
0.564477 | + | 0.825449i | \(0.309078\pi\) | |||||||
\(840\) | 31701.3 | 1.30214 | ||||||||
\(841\) | −16607.6 | −0.680948 | ||||||||
\(842\) | 11405.0 | 0.466795 | ||||||||
\(843\) | 8835.09 | 0.360969 | ||||||||
\(844\) | −11781.7 | −0.480503 | ||||||||
\(845\) | −32963.0 | −1.34196 | ||||||||
\(846\) | −49729.5 | −2.02096 | ||||||||
\(847\) | 34256.8 | 1.38970 | ||||||||
\(848\) | −8590.02 | −0.347857 | ||||||||
\(849\) | 20470.6 | 0.827502 | ||||||||
\(850\) | −16975.3 | −0.684996 | ||||||||
\(851\) | −2173.53 | −0.0875530 | ||||||||
\(852\) | 20896.7 | 0.840271 | ||||||||
\(853\) | −20978.4 | −0.842071 | −0.421035 | − | 0.907044i | \(-0.638333\pi\) | ||||
−0.421035 | + | 0.907044i | \(0.638333\pi\) | |||||||
\(854\) | −32907.0 | −1.31857 | ||||||||
\(855\) | −16433.1 | −0.657310 | ||||||||
\(856\) | −5927.97 | −0.236698 | ||||||||
\(857\) | −30822.4 | −1.22856 | −0.614279 | − | 0.789089i | \(-0.710553\pi\) | ||||
−0.614279 | + | 0.789089i | \(0.710553\pi\) | |||||||
\(858\) | −4749.94 | −0.188998 | ||||||||
\(859\) | −39267.6 | −1.55971 | −0.779856 | − | 0.625959i | \(-0.784708\pi\) | ||||
−0.779856 | + | 0.625959i | \(0.784708\pi\) | |||||||
\(860\) | −25517.1 | −1.01178 | ||||||||
\(861\) | −4055.12 | −0.160509 | ||||||||
\(862\) | −8051.45 | −0.318136 | ||||||||
\(863\) | −24131.3 | −0.951842 | −0.475921 | − | 0.879488i | \(-0.657885\pi\) | ||||
−0.475921 | + | 0.879488i | \(0.657885\pi\) | |||||||
\(864\) | 6441.60 | 0.253643 | ||||||||
\(865\) | −28546.5 | −1.12209 | ||||||||
\(866\) | −2694.21 | −0.105719 | ||||||||
\(867\) | −22425.4 | −0.878441 | ||||||||
\(868\) | 8553.54 | 0.334477 | ||||||||
\(869\) | −1806.30 | −0.0705116 | ||||||||
\(870\) | 26798.1 | 1.04430 | ||||||||
\(871\) | 18093.8 | 0.703885 | ||||||||
\(872\) | −15864.6 | −0.616105 | ||||||||
\(873\) | 54080.9 | 2.09663 | ||||||||
\(874\) | 3497.37 | 0.135355 | ||||||||
\(875\) | 22516.6 | 0.869941 | ||||||||
\(876\) | −20949.2 | −0.808001 | ||||||||
\(877\) | 39380.6 | 1.51629 | 0.758147 | − | 0.652084i | \(-0.226105\pi\) | ||||
0.758147 | + | 0.652084i | \(0.226105\pi\) | |||||||
\(878\) | 8218.71 | 0.315909 | ||||||||
\(879\) | −13935.9 | −0.534750 | ||||||||
\(880\) | 1171.39 | 0.0448723 | ||||||||
\(881\) | 30887.5 | 1.18119 | 0.590595 | − | 0.806968i | \(-0.298893\pi\) | ||||
0.590595 | + | 0.806968i | \(0.298893\pi\) | |||||||
\(882\) | 33723.3 | 1.28744 | ||||||||
\(883\) | 28191.9 | 1.07444 | 0.537221 | − | 0.843441i | \(-0.319474\pi\) | ||||
0.537221 | + | 0.843441i | \(0.319474\pi\) | |||||||
\(884\) | −12434.3 | −0.473088 | ||||||||
\(885\) | 5574.58 | 0.211737 | ||||||||
\(886\) | 13929.7 | 0.528190 | ||||||||
\(887\) | 2760.58 | 0.104500 | 0.0522498 | − | 0.998634i | \(-0.483361\pi\) | ||||
0.0522498 | + | 0.998634i | \(0.483361\pi\) | |||||||
\(888\) | −1657.28 | −0.0626292 | ||||||||
\(889\) | −68108.5 | −2.56950 | ||||||||
\(890\) | 31900.8 | 1.20148 | ||||||||
\(891\) | −1763.95 | −0.0663240 | ||||||||
\(892\) | 12501.2 | 0.469250 | ||||||||
\(893\) | −9458.43 | −0.354439 | ||||||||
\(894\) | 32301.8 | 1.20843 | ||||||||
\(895\) | −40291.0 | −1.50478 | ||||||||
\(896\) | −3339.26 | −0.124506 | ||||||||
\(897\) | 51698.9 | 1.92439 | ||||||||
\(898\) | 6082.42 | 0.226028 | ||||||||
\(899\) | 7230.57 | 0.268246 | ||||||||
\(900\) | 34932.5 | 1.29379 | ||||||||
\(901\) | 26062.1 | 0.963657 | ||||||||
\(902\) | −149.840 | −0.00553120 | ||||||||
\(903\) | −84307.1 | −3.10694 | ||||||||
\(904\) | −5749.76 | −0.211542 | ||||||||
\(905\) | 80302.2 | 2.94954 | ||||||||
\(906\) | 58286.8 | 2.13736 | ||||||||
\(907\) | −18969.1 | −0.694443 | −0.347222 | − | 0.937783i | \(-0.612875\pi\) | ||||
−0.347222 | + | 0.937783i | \(0.612875\pi\) | |||||||
\(908\) | −14311.2 | −0.523055 | ||||||||
\(909\) | −35585.4 | −1.29845 | ||||||||
\(910\) | 57855.3 | 2.10756 | ||||||||
\(911\) | −48732.9 | −1.77233 | −0.886164 | − | 0.463371i | \(-0.846640\pi\) | ||||
−0.886164 | + | 0.463371i | \(0.846640\pi\) | |||||||
\(912\) | 2666.69 | 0.0968233 | ||||||||
\(913\) | −2087.65 | −0.0756749 | ||||||||
\(914\) | 23968.7 | 0.867411 | ||||||||
\(915\) | −95799.6 | −3.46124 | ||||||||
\(916\) | −19208.0 | −0.692850 | ||||||||
\(917\) | 31741.1 | 1.14306 | ||||||||
\(918\) | −19543.8 | −0.702660 | ||||||||
\(919\) | −35850.4 | −1.28683 | −0.643414 | − | 0.765518i | \(-0.722483\pi\) | ||||
−0.643414 | + | 0.765518i | \(0.722483\pi\) | |||||||
\(920\) | −12749.6 | −0.456892 | ||||||||
\(921\) | 35592.0 | 1.27340 | ||||||||
\(922\) | −24253.4 | −0.866315 | ||||||||
\(923\) | 38136.8 | 1.36001 | ||||||||
\(924\) | 3870.21 | 0.137793 | ||||||||
\(925\) | −4129.13 | −0.146773 | ||||||||
\(926\) | −12798.4 | −0.454191 | ||||||||
\(927\) | −1322.61 | −0.0468610 | ||||||||
\(928\) | −2822.79 | −0.0998518 | ||||||||
\(929\) | 22936.8 | 0.810044 | 0.405022 | − | 0.914307i | \(-0.367264\pi\) | ||||
0.405022 | + | 0.914307i | \(0.367264\pi\) | |||||||
\(930\) | 24901.3 | 0.878005 | ||||||||
\(931\) | 6414.10 | 0.225793 | ||||||||
\(932\) | 23318.0 | 0.819534 | ||||||||
\(933\) | 25192.5 | 0.883992 | ||||||||
\(934\) | 1986.73 | 0.0696016 | ||||||||
\(935\) | −3554.01 | −0.124308 | ||||||||
\(936\) | 25587.8 | 0.893550 | ||||||||
\(937\) | 47925.4 | 1.67092 | 0.835462 | − | 0.549548i | \(-0.185200\pi\) | ||||
0.835462 | + | 0.549548i | \(0.185200\pi\) | |||||||
\(938\) | −14742.6 | −0.513181 | ||||||||
\(939\) | 37918.5 | 1.31781 | ||||||||
\(940\) | 34480.5 | 1.19641 | ||||||||
\(941\) | −25842.2 | −0.895251 | −0.447626 | − | 0.894221i | \(-0.647730\pi\) | ||||
−0.447626 | + | 0.894221i | \(0.647730\pi\) | |||||||
\(942\) | 4274.00 | 0.147829 | ||||||||
\(943\) | 1630.88 | 0.0563189 | ||||||||
\(944\) | −587.199 | −0.0202455 | ||||||||
\(945\) | 90935.3 | 3.13029 | ||||||||
\(946\) | −3115.22 | −0.107066 | ||||||||
\(947\) | 36562.8 | 1.25463 | 0.627314 | − | 0.778766i | \(-0.284154\pi\) | ||||
0.627314 | + | 0.778766i | \(0.284154\pi\) | |||||||
\(948\) | 14990.4 | 0.513572 | ||||||||
\(949\) | −38232.6 | −1.30778 | ||||||||
\(950\) | 6644.07 | 0.226908 | ||||||||
\(951\) | 22048.9 | 0.751825 | ||||||||
\(952\) | 10131.3 | 0.344914 | ||||||||
\(953\) | 29813.1 | 1.01337 | 0.506684 | − | 0.862132i | \(-0.330871\pi\) | ||||
0.506684 | + | 0.862132i | \(0.330871\pi\) | |||||||
\(954\) | −53631.8 | −1.82012 | ||||||||
\(955\) | −91088.7 | −3.08645 | ||||||||
\(956\) | 5457.31 | 0.184625 | ||||||||
\(957\) | 3271.61 | 0.110508 | ||||||||
\(958\) | 13278.7 | 0.447825 | ||||||||
\(959\) | −30540.5 | −1.02837 | ||||||||
\(960\) | −9721.35 | −0.326828 | ||||||||
\(961\) | −23072.2 | −0.774470 | ||||||||
\(962\) | −3024.56 | −0.101368 | ||||||||
\(963\) | −37011.3 | −1.23850 | ||||||||
\(964\) | −10588.9 | −0.353782 | ||||||||
\(965\) | −280.230 | −0.00934811 | ||||||||
\(966\) | −42123.8 | −1.40301 | ||||||||
\(967\) | 30315.5 | 1.00815 | 0.504075 | − | 0.863660i | \(-0.331833\pi\) | ||||
0.504075 | + | 0.863660i | \(0.331833\pi\) | |||||||
\(968\) | −10505.0 | −0.348805 | ||||||||
\(969\) | −8090.73 | −0.268227 | ||||||||
\(970\) | −37497.6 | −1.24121 | ||||||||
\(971\) | 26455.6 | 0.874357 | 0.437178 | − | 0.899375i | \(-0.355978\pi\) | ||||
0.437178 | + | 0.899375i | \(0.355978\pi\) | |||||||
\(972\) | −7101.41 | −0.234339 | ||||||||
\(973\) | 7072.03 | 0.233010 | ||||||||
\(974\) | −22177.6 | −0.729584 | ||||||||
\(975\) | 98214.1 | 3.22602 | ||||||||
\(976\) | 10091.1 | 0.330950 | ||||||||
\(977\) | 30207.7 | 0.989183 | 0.494591 | − | 0.869126i | \(-0.335318\pi\) | ||||
0.494591 | + | 0.869126i | \(0.335318\pi\) | |||||||
\(978\) | −45581.3 | −1.49032 | ||||||||
\(979\) | 3894.56 | 0.127141 | ||||||||
\(980\) | −23382.4 | −0.762168 | ||||||||
\(981\) | −99050.7 | −3.22370 | ||||||||
\(982\) | −26430.3 | −0.858886 | ||||||||
\(983\) | −5878.48 | −0.190737 | −0.0953685 | − | 0.995442i | \(-0.530403\pi\) | ||||
−0.0953685 | + | 0.995442i | \(0.530403\pi\) | |||||||
\(984\) | 1243.52 | 0.0402866 | ||||||||
\(985\) | −65536.1 | −2.11995 | ||||||||
\(986\) | 8564.33 | 0.276616 | ||||||||
\(987\) | 113921. | 3.67392 | ||||||||
\(988\) | 4866.74 | 0.156712 | ||||||||
\(989\) | 33906.4 | 1.09015 | ||||||||
\(990\) | 7313.59 | 0.234789 | ||||||||
\(991\) | −42532.3 | −1.36335 | −0.681676 | − | 0.731654i | \(-0.738749\pi\) | ||||
−0.681676 | + | 0.731654i | \(0.738749\pi\) | |||||||
\(992\) | −2622.98 | −0.0839513 | ||||||||
\(993\) | −40121.2 | −1.28218 | ||||||||
\(994\) | −31073.5 | −0.991542 | ||||||||
\(995\) | −1267.67 | −0.0403898 | ||||||||
\(996\) | 17325.3 | 0.551179 | ||||||||
\(997\) | 6320.28 | 0.200767 | 0.100384 | − | 0.994949i | \(-0.467993\pi\) | ||||
0.100384 | + | 0.994949i | \(0.467993\pi\) | |||||||
\(998\) | 821.281 | 0.0260493 | ||||||||
\(999\) | −4753.91 | −0.150558 |
(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 | 38.4.a.c.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 342.4.a.h.1.2 | 2 | |||
4.3 | odd | 2 | 304.4.a.c.1.1 | 2 | |||
5.2 | odd | 4 | 950.4.b.i.799.3 | 4 | |||
5.3 | odd | 4 | 950.4.b.i.799.2 | 4 | |||
5.4 | even | 2 | 950.4.a.e.1.1 | 2 | |||
7.6 | odd | 2 | 1862.4.a.e.1.1 | 2 | |||
8.3 | odd | 2 | 1216.4.a.p.1.2 | 2 | |||
8.5 | even | 2 | 1216.4.a.g.1.1 | 2 | |||
19.18 | odd | 2 | 722.4.a.f.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.4.a.c.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
304.4.a.c.1.1 | 2 | 4.3 | odd | 2 | |||
342.4.a.h.1.2 | 2 | 3.2 | odd | 2 | |||
722.4.a.f.1.1 | 2 | 19.18 | odd | 2 | |||
950.4.a.e.1.1 | 2 | 5.4 | even | 2 | |||
950.4.b.i.799.2 | 4 | 5.3 | odd | 4 | |||
950.4.b.i.799.3 | 4 | 5.2 | odd | 4 | |||
1216.4.a.g.1.1 | 2 | 8.5 | even | 2 | |||
1216.4.a.p.1.2 | 2 | 8.3 | odd | 2 | |||
1862.4.a.e.1.1 | 2 | 7.6 | odd | 2 |