Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2401,4,Mod(1,2401)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2401, 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("2401.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2401 = 7^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2401.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: | \(141.663585924\) |
Analytic rank: | \(1\) |
Dimension: | \(39\) |
Twist minimal: | no (minimal twist has level 49) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 2401.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.11024 | −0.746082 | −0.373041 | − | 0.927815i | \(-0.621685\pi\) | ||||
−0.373041 | + | 0.927815i | \(0.621685\pi\) | |||||||
\(3\) | 5.68890 | 1.09483 | 0.547415 | − | 0.836861i | \(-0.315612\pi\) | ||||
0.547415 | + | 0.836861i | \(0.315612\pi\) | |||||||
\(4\) | −3.54689 | −0.443361 | ||||||||
\(5\) | 12.6417 | 1.13070 | 0.565352 | − | 0.824850i | \(-0.308740\pi\) | ||||
0.565352 | + | 0.824850i | \(0.308740\pi\) | |||||||
\(6\) | −12.0050 | −0.816834 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 24.3667 | 1.07687 | ||||||||
\(9\) | 5.36363 | 0.198653 | ||||||||
\(10\) | −26.6769 | −0.843598 | ||||||||
\(11\) | −10.0089 | −0.274344 | −0.137172 | − | 0.990547i | \(-0.543801\pi\) | ||||
−0.137172 | + | 0.990547i | \(0.543801\pi\) | |||||||
\(12\) | −20.1779 | −0.485405 | ||||||||
\(13\) | −12.8371 | −0.273875 | −0.136938 | − | 0.990580i | \(-0.543726\pi\) | ||||
−0.136938 | + | 0.990580i | \(0.543726\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 71.9172 | 1.23793 | ||||||||
\(16\) | −23.0445 | −0.360070 | ||||||||
\(17\) | 50.2235 | 0.716529 | 0.358265 | − | 0.933620i | \(-0.383369\pi\) | ||||
0.358265 | + | 0.933620i | \(0.383369\pi\) | |||||||
\(18\) | −11.3185 | −0.148212 | ||||||||
\(19\) | 42.4412 | 0.512457 | 0.256228 | − | 0.966616i | \(-0.417520\pi\) | ||||
0.256228 | + | 0.966616i | \(0.417520\pi\) | |||||||
\(20\) | −44.8385 | −0.501310 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 21.1211 | 0.204683 | ||||||||
\(23\) | 50.9366 | 0.461783 | 0.230891 | − | 0.972980i | \(-0.425836\pi\) | ||||
0.230891 | + | 0.972980i | \(0.425836\pi\) | |||||||
\(24\) | 138.620 | 1.17899 | ||||||||
\(25\) | 34.8114 | 0.278492 | ||||||||
\(26\) | 27.0894 | 0.204334 | ||||||||
\(27\) | −123.087 | −0.877339 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −177.055 | −1.13374 | −0.566868 | − | 0.823809i | \(-0.691845\pi\) | ||||
−0.566868 | + | 0.823809i | \(0.691845\pi\) | |||||||
\(30\) | −151.762 | −0.923597 | ||||||||
\(31\) | −261.107 | −1.51278 | −0.756392 | − | 0.654119i | \(-0.773040\pi\) | ||||
−0.756392 | + | 0.654119i | \(0.773040\pi\) | |||||||
\(32\) | −146.304 | −0.808224 | ||||||||
\(33\) | −56.9395 | −0.300360 | ||||||||
\(34\) | −105.984 | −0.534590 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −19.0242 | −0.0880750 | ||||||||
\(37\) | −88.0904 | −0.391404 | −0.195702 | − | 0.980663i | \(-0.562699\pi\) | ||||
−0.195702 | + | 0.980663i | \(0.562699\pi\) | |||||||
\(38\) | −89.5611 | −0.382335 | ||||||||
\(39\) | −73.0292 | −0.299847 | ||||||||
\(40\) | 308.035 | 1.21762 | ||||||||
\(41\) | −408.680 | −1.55671 | −0.778354 | − | 0.627826i | \(-0.783945\pi\) | ||||
−0.778354 | + | 0.627826i | \(0.783945\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 479.476 | 1.70045 | 0.850225 | − | 0.526419i | \(-0.176466\pi\) | ||||
0.850225 | + | 0.526419i | \(0.176466\pi\) | |||||||
\(44\) | 35.5003 | 0.121634 | ||||||||
\(45\) | 67.8052 | 0.224618 | ||||||||
\(46\) | −107.488 | −0.344528 | ||||||||
\(47\) | −424.333 | −1.31692 | −0.658461 | − | 0.752615i | \(-0.728792\pi\) | ||||
−0.658461 | + | 0.752615i | \(0.728792\pi\) | |||||||
\(48\) | −131.098 | −0.394215 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −73.4605 | −0.207778 | ||||||||
\(51\) | 285.717 | 0.784478 | ||||||||
\(52\) | 45.5319 | 0.121426 | ||||||||
\(53\) | 336.898 | 0.873141 | 0.436570 | − | 0.899670i | \(-0.356193\pi\) | ||||
0.436570 | + | 0.899670i | \(0.356193\pi\) | |||||||
\(54\) | 259.744 | 0.654567 | ||||||||
\(55\) | −126.529 | −0.310202 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 241.444 | 0.561053 | ||||||||
\(58\) | 373.629 | 0.845860 | ||||||||
\(59\) | 642.691 | 1.41816 | 0.709078 | − | 0.705130i | \(-0.249111\pi\) | ||||
0.709078 | + | 0.705130i | \(0.249111\pi\) | |||||||
\(60\) | −255.082 | −0.548849 | ||||||||
\(61\) | 500.725 | 1.05100 | 0.525502 | − | 0.850792i | \(-0.323878\pi\) | ||||
0.525502 | + | 0.850792i | \(0.323878\pi\) | |||||||
\(62\) | 550.999 | 1.12866 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 493.093 | 0.963072 | ||||||||
\(65\) | −162.283 | −0.309672 | ||||||||
\(66\) | 120.156 | 0.224094 | ||||||||
\(67\) | −1028.35 | −1.87512 | −0.937560 | − | 0.347824i | \(-0.886921\pi\) | ||||
−0.937560 | + | 0.347824i | \(0.886921\pi\) | |||||||
\(68\) | −178.137 | −0.317681 | ||||||||
\(69\) | 289.773 | 0.505574 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −796.583 | −1.33151 | −0.665753 | − | 0.746172i | \(-0.731890\pi\) | ||||
−0.665753 | + | 0.746172i | \(0.731890\pi\) | |||||||
\(72\) | 130.694 | 0.213923 | ||||||||
\(73\) | 296.735 | 0.475756 | 0.237878 | − | 0.971295i | \(-0.423548\pi\) | ||||
0.237878 | + | 0.971295i | \(0.423548\pi\) | |||||||
\(74\) | 185.892 | 0.292020 | ||||||||
\(75\) | 198.039 | 0.304901 | ||||||||
\(76\) | −150.534 | −0.227203 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 154.109 | 0.223711 | ||||||||
\(79\) | −1173.27 | −1.67093 | −0.835463 | − | 0.549547i | \(-0.814801\pi\) | ||||
−0.835463 | + | 0.549547i | \(0.814801\pi\) | |||||||
\(80\) | −291.320 | −0.407133 | ||||||||
\(81\) | −845.050 | −1.15919 | ||||||||
\(82\) | 862.412 | 1.16143 | ||||||||
\(83\) | 508.597 | 0.672600 | 0.336300 | − | 0.941755i | \(-0.390824\pi\) | ||||
0.336300 | + | 0.941755i | \(0.390824\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 634.909 | 0.810183 | ||||||||
\(86\) | −1011.81 | −1.26868 | ||||||||
\(87\) | −1007.25 | −1.24125 | ||||||||
\(88\) | −243.883 | −0.295432 | ||||||||
\(89\) | −897.274 | −1.06866 | −0.534331 | − | 0.845276i | \(-0.679436\pi\) | ||||
−0.534331 | + | 0.845276i | \(0.679436\pi\) | |||||||
\(90\) | −143.085 | −0.167583 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −180.666 | −0.204737 | ||||||||
\(93\) | −1485.42 | −1.65624 | ||||||||
\(94\) | 895.445 | 0.982533 | ||||||||
\(95\) | 536.527 | 0.579437 | ||||||||
\(96\) | −832.311 | −0.884868 | ||||||||
\(97\) | −185.840 | −0.194528 | −0.0972639 | − | 0.995259i | \(-0.531009\pi\) | ||||
−0.0972639 | + | 0.995259i | \(0.531009\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −53.6839 | −0.0544993 | ||||||||
\(100\) | −123.472 | −0.123472 | ||||||||
\(101\) | 310.730 | 0.306127 | 0.153063 | − | 0.988216i | \(-0.451086\pi\) | ||||
0.153063 | + | 0.988216i | \(0.451086\pi\) | |||||||
\(102\) | −602.931 | −0.585285 | ||||||||
\(103\) | −147.361 | −0.140970 | −0.0704849 | − | 0.997513i | \(-0.522455\pi\) | ||||
−0.0704849 | + | 0.997513i | \(0.522455\pi\) | |||||||
\(104\) | −312.799 | −0.294927 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −710.935 | −0.651435 | ||||||||
\(107\) | −1194.18 | −1.07894 | −0.539468 | − | 0.842006i | \(-0.681375\pi\) | ||||
−0.539468 | + | 0.842006i | \(0.681375\pi\) | |||||||
\(108\) | 436.577 | 0.388978 | ||||||||
\(109\) | −416.520 | −0.366012 | −0.183006 | − | 0.983112i | \(-0.558583\pi\) | ||||
−0.183006 | + | 0.983112i | \(0.558583\pi\) | |||||||
\(110\) | 267.006 | 0.231436 | ||||||||
\(111\) | −501.138 | −0.428521 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 908.912 | 0.756666 | 0.378333 | − | 0.925670i | \(-0.376497\pi\) | ||||
0.378333 | + | 0.925670i | \(0.376497\pi\) | |||||||
\(114\) | −509.504 | −0.418592 | ||||||||
\(115\) | 643.922 | 0.522140 | ||||||||
\(116\) | 627.995 | 0.502654 | ||||||||
\(117\) | −68.8537 | −0.0544062 | ||||||||
\(118\) | −1356.23 | −1.05806 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1752.38 | 1.33308 | ||||||||
\(121\) | −1230.82 | −0.924735 | ||||||||
\(122\) | −1056.65 | −0.784136 | ||||||||
\(123\) | −2324.94 | −1.70433 | ||||||||
\(124\) | 926.119 | 0.670709 | ||||||||
\(125\) | −1140.13 | −0.815813 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2710.31 | −1.89371 | −0.946853 | − | 0.321666i | \(-0.895757\pi\) | ||||
−0.946853 | + | 0.321666i | \(0.895757\pi\) | |||||||
\(128\) | 129.890 | 0.0896933 | ||||||||
\(129\) | 2727.69 | 1.86170 | ||||||||
\(130\) | 342.455 | 0.231041 | ||||||||
\(131\) | 2675.67 | 1.78454 | 0.892269 | − | 0.451505i | \(-0.149113\pi\) | ||||
0.892269 | + | 0.451505i | \(0.149113\pi\) | |||||||
\(132\) | 201.958 | 0.133168 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2170.07 | 1.39899 | ||||||||
\(135\) | −1556.03 | −0.992010 | ||||||||
\(136\) | 1223.78 | 0.771606 | ||||||||
\(137\) | 1006.12 | 0.627432 | 0.313716 | − | 0.949517i | \(-0.398426\pi\) | ||||
0.313716 | + | 0.949517i | \(0.398426\pi\) | |||||||
\(138\) | −611.491 | −0.377200 | ||||||||
\(139\) | 1228.73 | 0.749779 | 0.374889 | − | 0.927070i | \(-0.377681\pi\) | ||||
0.374889 | + | 0.927070i | \(0.377681\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2413.99 | −1.44181 | ||||||||
\(142\) | 1680.98 | 0.993414 | ||||||||
\(143\) | 128.485 | 0.0751361 | ||||||||
\(144\) | −123.602 | −0.0715290 | ||||||||
\(145\) | −2238.27 | −1.28192 | ||||||||
\(146\) | −626.182 | −0.354954 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 312.447 | 0.173533 | ||||||||
\(149\) | −1509.91 | −0.830177 | −0.415089 | − | 0.909781i | \(-0.636249\pi\) | ||||
−0.415089 | + | 0.909781i | \(0.636249\pi\) | |||||||
\(150\) | −417.910 | −0.227481 | ||||||||
\(151\) | 1507.32 | 0.812344 | 0.406172 | − | 0.913797i | \(-0.366863\pi\) | ||||
0.406172 | + | 0.913797i | \(0.366863\pi\) | |||||||
\(152\) | 1034.15 | 0.551847 | ||||||||
\(153\) | 269.381 | 0.142341 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3300.83 | −1.71051 | ||||||||
\(156\) | 259.027 | 0.132941 | ||||||||
\(157\) | 1504.47 | 0.764775 | 0.382387 | − | 0.924002i | \(-0.375102\pi\) | ||||
0.382387 | + | 0.924002i | \(0.375102\pi\) | |||||||
\(158\) | 2475.88 | 1.24665 | ||||||||
\(159\) | 1916.58 | 0.955941 | ||||||||
\(160\) | −1849.53 | −0.913863 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1783.26 | 0.864851 | ||||||||
\(163\) | 300.373 | 0.144338 | 0.0721688 | − | 0.997392i | \(-0.477008\pi\) | ||||
0.0721688 | + | 0.997392i | \(0.477008\pi\) | |||||||
\(164\) | 1449.54 | 0.690184 | ||||||||
\(165\) | −719.809 | −0.339619 | ||||||||
\(166\) | −1073.26 | −0.501815 | ||||||||
\(167\) | −292.022 | −0.135313 | −0.0676566 | − | 0.997709i | \(-0.521552\pi\) | ||||
−0.0676566 | + | 0.997709i | \(0.521552\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2032.21 | −0.924992 | ||||||||
\(170\) | −1339.81 | −0.604463 | ||||||||
\(171\) | 227.639 | 0.101801 | ||||||||
\(172\) | −1700.65 | −0.753914 | ||||||||
\(173\) | −469.067 | −0.206142 | −0.103071 | − | 0.994674i | \(-0.532867\pi\) | ||||
−0.103071 | + | 0.994674i | \(0.532867\pi\) | |||||||
\(174\) | 2125.54 | 0.926073 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 230.649 | 0.0987831 | ||||||||
\(177\) | 3656.21 | 1.55264 | ||||||||
\(178\) | 1893.46 | 0.797309 | ||||||||
\(179\) | 1454.08 | 0.607169 | 0.303585 | − | 0.952805i | \(-0.401817\pi\) | ||||
0.303585 | + | 0.952805i | \(0.401817\pi\) | |||||||
\(180\) | −240.497 | −0.0995868 | ||||||||
\(181\) | −2755.70 | −1.13165 | −0.565827 | − | 0.824524i | \(-0.691443\pi\) | ||||
−0.565827 | + | 0.824524i | \(0.691443\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2848.58 | 1.15067 | ||||||||
\(184\) | 1241.16 | 0.497278 | ||||||||
\(185\) | −1113.61 | −0.442563 | ||||||||
\(186\) | 3134.58 | 1.23569 | ||||||||
\(187\) | −502.681 | −0.196576 | ||||||||
\(188\) | 1505.06 | 0.583872 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1132.20 | −0.432308 | ||||||||
\(191\) | 583.799 | 0.221164 | 0.110582 | − | 0.993867i | \(-0.464729\pi\) | ||||
0.110582 | + | 0.993867i | \(0.464729\pi\) | |||||||
\(192\) | 2805.16 | 1.05440 | ||||||||
\(193\) | 3955.96 | 1.47542 | 0.737711 | − | 0.675116i | \(-0.235907\pi\) | ||||
0.737711 | + | 0.675116i | \(0.235907\pi\) | |||||||
\(194\) | 392.167 | 0.145134 | ||||||||
\(195\) | −923.210 | −0.339038 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1611.23 | −0.582718 | −0.291359 | − | 0.956614i | \(-0.594107\pi\) | ||||
−0.291359 | + | 0.956614i | \(0.594107\pi\) | |||||||
\(198\) | 113.286 | 0.0406610 | ||||||||
\(199\) | −2468.03 | −0.879167 | −0.439584 | − | 0.898202i | \(-0.644874\pi\) | ||||
−0.439584 | + | 0.898202i | \(0.644874\pi\) | |||||||
\(200\) | 848.240 | 0.299898 | ||||||||
\(201\) | −5850.19 | −2.05294 | ||||||||
\(202\) | −655.715 | −0.228396 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1013.41 | −0.347807 | ||||||||
\(205\) | −5166.39 | −1.76018 | ||||||||
\(206\) | 310.967 | 0.105175 | ||||||||
\(207\) | 273.205 | 0.0917346 | ||||||||
\(208\) | 295.825 | 0.0986143 | ||||||||
\(209\) | −424.788 | −0.140590 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 717.224 | 0.234008 | 0.117004 | − | 0.993131i | \(-0.462671\pi\) | ||||
0.117004 | + | 0.993131i | \(0.462671\pi\) | |||||||
\(212\) | −1194.94 | −0.387117 | ||||||||
\(213\) | −4531.68 | −1.45777 | ||||||||
\(214\) | 2520.02 | 0.804976 | ||||||||
\(215\) | 6061.37 | 1.92271 | ||||||||
\(216\) | −2999.23 | −0.944777 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 878.956 | 0.273075 | ||||||||
\(219\) | 1688.10 | 0.520873 | ||||||||
\(220\) | 448.783 | 0.137532 | ||||||||
\(221\) | −644.726 | −0.196240 | ||||||||
\(222\) | 1057.52 | 0.319712 | ||||||||
\(223\) | −2606.20 | −0.782618 | −0.391309 | − | 0.920259i | \(-0.627978\pi\) | ||||
−0.391309 | + | 0.920259i | \(0.627978\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 186.716 | 0.0553232 | ||||||||
\(226\) | −1918.02 | −0.564535 | ||||||||
\(227\) | 3734.91 | 1.09205 | 0.546024 | − | 0.837770i | \(-0.316141\pi\) | ||||
0.546024 | + | 0.837770i | \(0.316141\pi\) | |||||||
\(228\) | −856.374 | −0.248749 | ||||||||
\(229\) | −1482.24 | −0.427725 | −0.213862 | − | 0.976864i | \(-0.568604\pi\) | ||||
−0.213862 | + | 0.976864i | \(0.568604\pi\) | |||||||
\(230\) | −1358.83 | −0.389559 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4314.25 | −1.22088 | ||||||||
\(233\) | 4548.93 | 1.27902 | 0.639508 | − | 0.768785i | \(-0.279138\pi\) | ||||
0.639508 | + | 0.768785i | \(0.279138\pi\) | |||||||
\(234\) | 145.298 | 0.0405915 | ||||||||
\(235\) | −5364.27 | −1.48905 | ||||||||
\(236\) | −2279.55 | −0.628755 | ||||||||
\(237\) | −6674.62 | −1.82938 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 170.647 | 0.0461852 | 0.0230926 | − | 0.999733i | \(-0.492649\pi\) | ||||
0.0230926 | + | 0.999733i | \(0.492649\pi\) | |||||||
\(240\) | −1657.29 | −0.445741 | ||||||||
\(241\) | 5551.66 | 1.48388 | 0.741938 | − | 0.670469i | \(-0.233907\pi\) | ||||
0.741938 | + | 0.670469i | \(0.233907\pi\) | |||||||
\(242\) | 2597.33 | 0.689929 | ||||||||
\(243\) | −1484.05 | −0.391777 | ||||||||
\(244\) | −1776.02 | −0.465974 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4906.18 | 1.27157 | ||||||||
\(247\) | −544.823 | −0.140349 | ||||||||
\(248\) | −6362.33 | −1.62907 | ||||||||
\(249\) | 2893.36 | 0.736383 | ||||||||
\(250\) | 2405.95 | 0.608663 | ||||||||
\(251\) | −3414.09 | −0.858546 | −0.429273 | − | 0.903175i | \(-0.641230\pi\) | ||||
−0.429273 | + | 0.903175i | \(0.641230\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −509.817 | −0.126687 | ||||||||
\(254\) | 5719.39 | 1.41286 | ||||||||
\(255\) | 3611.94 | 0.887012 | ||||||||
\(256\) | −4218.84 | −1.02999 | ||||||||
\(257\) | −2872.39 | −0.697177 | −0.348589 | − | 0.937276i | \(-0.613339\pi\) | ||||
−0.348589 | + | 0.937276i | \(0.613339\pi\) | |||||||
\(258\) | −5756.08 | −1.38899 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 575.598 | 0.137297 | ||||||||
\(261\) | −949.659 | −0.225220 | ||||||||
\(262\) | −5646.31 | −1.33141 | ||||||||
\(263\) | −3715.72 | −0.871182 | −0.435591 | − | 0.900145i | \(-0.643461\pi\) | ||||
−0.435591 | + | 0.900145i | \(0.643461\pi\) | |||||||
\(264\) | −1387.43 | −0.323448 | ||||||||
\(265\) | 4258.94 | 0.987264 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5104.50 | −1.17000 | ||||||||
\(268\) | 3647.44 | 0.831355 | ||||||||
\(269\) | 6037.35 | 1.36842 | 0.684208 | − | 0.729287i | \(-0.260148\pi\) | ||||
0.684208 | + | 0.729287i | \(0.260148\pi\) | |||||||
\(270\) | 3283.59 | 0.740122 | ||||||||
\(271\) | 11.8979 | 0.00266696 | 0.00133348 | − | 0.999999i | \(-0.499576\pi\) | ||||
0.00133348 | + | 0.999999i | \(0.499576\pi\) | |||||||
\(272\) | −1157.38 | −0.258001 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2123.14 | −0.468116 | ||||||||
\(275\) | −348.423 | −0.0764025 | ||||||||
\(276\) | −1027.79 | −0.224152 | ||||||||
\(277\) | −1100.81 | −0.238778 | −0.119389 | − | 0.992848i | \(-0.538094\pi\) | ||||
−0.119389 | + | 0.992848i | \(0.538094\pi\) | |||||||
\(278\) | −2592.91 | −0.559397 | ||||||||
\(279\) | −1400.48 | −0.300519 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2894.16 | 0.614417 | 0.307208 | − | 0.951642i | \(-0.400605\pi\) | ||||
0.307208 | + | 0.951642i | \(0.400605\pi\) | |||||||
\(282\) | 5094.10 | 1.07571 | ||||||||
\(283\) | −1872.66 | −0.393350 | −0.196675 | − | 0.980469i | \(-0.563014\pi\) | ||||
−0.196675 | + | 0.980469i | \(0.563014\pi\) | |||||||
\(284\) | 2825.39 | 0.590338 | ||||||||
\(285\) | 3052.25 | 0.634385 | ||||||||
\(286\) | −271.134 | −0.0560577 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −784.722 | −0.160556 | ||||||||
\(289\) | −2390.60 | −0.486586 | ||||||||
\(290\) | 4723.29 | 0.956418 | ||||||||
\(291\) | −1057.23 | −0.212975 | ||||||||
\(292\) | −1052.49 | −0.210932 | ||||||||
\(293\) | −2375.66 | −0.473677 | −0.236839 | − | 0.971549i | \(-0.576111\pi\) | ||||
−0.236839 | + | 0.971549i | \(0.576111\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8124.67 | 1.60351 | ||||||||
\(296\) | −2146.47 | −0.421490 | ||||||||
\(297\) | 1231.96 | 0.240693 | ||||||||
\(298\) | 3186.27 | 0.619381 | ||||||||
\(299\) | −653.879 | −0.126471 | ||||||||
\(300\) | −702.422 | −0.135181 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3180.81 | −0.606076 | ||||||||
\(303\) | 1767.71 | 0.335157 | ||||||||
\(304\) | −978.035 | −0.184520 | ||||||||
\(305\) | 6329.99 | 1.18837 | ||||||||
\(306\) | −568.458 | −0.106198 | ||||||||
\(307\) | 3387.12 | 0.629685 | 0.314843 | − | 0.949144i | \(-0.398048\pi\) | ||||
0.314843 | + | 0.949144i | \(0.398048\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −838.321 | −0.154338 | ||||||||
\(310\) | 6965.54 | 1.27618 | ||||||||
\(311\) | 7430.10 | 1.35473 | 0.677367 | − | 0.735645i | \(-0.263121\pi\) | ||||
0.677367 | + | 0.735645i | \(0.263121\pi\) | |||||||
\(312\) | −1779.48 | −0.322895 | ||||||||
\(313\) | −3669.26 | −0.662616 | −0.331308 | − | 0.943523i | \(-0.607490\pi\) | ||||
−0.331308 | + | 0.943523i | \(0.607490\pi\) | |||||||
\(314\) | −3174.79 | −0.570585 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4161.46 | 0.740824 | ||||||||
\(317\) | −36.1403 | −0.00640328 | −0.00320164 | − | 0.999995i | \(-0.501019\pi\) | ||||
−0.00320164 | + | 0.999995i | \(0.501019\pi\) | |||||||
\(318\) | −4044.44 | −0.713211 | ||||||||
\(319\) | 1772.12 | 0.311034 | ||||||||
\(320\) | 6233.51 | 1.08895 | ||||||||
\(321\) | −6793.60 | −1.18125 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2131.55 | 0.367190 | ||||||||
\(324\) | 2997.30 | 0.513940 | ||||||||
\(325\) | −446.879 | −0.0762720 | ||||||||
\(326\) | −633.859 | −0.107688 | ||||||||
\(327\) | −2369.54 | −0.400721 | ||||||||
\(328\) | −9958.17 | −1.67637 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1518.97 | 0.253383 | ||||||||
\(331\) | −4932.92 | −0.819148 | −0.409574 | − | 0.912277i | \(-0.634323\pi\) | ||||
−0.409574 | + | 0.912277i | \(0.634323\pi\) | |||||||
\(332\) | −1803.94 | −0.298205 | ||||||||
\(333\) | −472.484 | −0.0777537 | ||||||||
\(334\) | 616.236 | 0.100955 | ||||||||
\(335\) | −13000.1 | −2.12021 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12305.8 | −1.98914 | −0.994570 | − | 0.104074i | \(-0.966812\pi\) | ||||
−0.994570 | + | 0.104074i | \(0.966812\pi\) | |||||||
\(338\) | 4288.45 | 0.690120 | ||||||||
\(339\) | 5170.72 | 0.828421 | ||||||||
\(340\) | −2251.95 | −0.359203 | ||||||||
\(341\) | 2613.39 | 0.415023 | ||||||||
\(342\) | −480.373 | −0.0759520 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 11683.2 | 1.83116 | ||||||||
\(345\) | 3663.21 | 0.571654 | ||||||||
\(346\) | 989.843 | 0.153799 | ||||||||
\(347\) | −5498.02 | −0.850573 | −0.425287 | − | 0.905059i | \(-0.639827\pi\) | ||||
−0.425287 | + | 0.905059i | \(0.639827\pi\) | |||||||
\(348\) | 3572.60 | 0.550321 | ||||||||
\(349\) | −7661.39 | −1.17509 | −0.587543 | − | 0.809193i | \(-0.699905\pi\) | ||||
−0.587543 | + | 0.809193i | \(0.699905\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1580.09 | 0.240282 | ||||||||
\(352\) | 1464.34 | 0.221732 | ||||||||
\(353\) | 620.074 | 0.0934935 | 0.0467468 | − | 0.998907i | \(-0.485115\pi\) | ||||
0.0467468 | + | 0.998907i | \(0.485115\pi\) | |||||||
\(354\) | −7715.47 | −1.15840 | ||||||||
\(355\) | −10070.1 | −1.50554 | ||||||||
\(356\) | 3182.53 | 0.473803 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3068.46 | −0.452998 | ||||||||
\(359\) | −8298.50 | −1.21999 | −0.609997 | − | 0.792403i | \(-0.708830\pi\) | ||||
−0.609997 | + | 0.792403i | \(0.708830\pi\) | |||||||
\(360\) | 1652.19 | 0.241883 | ||||||||
\(361\) | −5057.75 | −0.737388 | ||||||||
\(362\) | 5815.18 | 0.844307 | ||||||||
\(363\) | −7002.03 | −1.01243 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3751.22 | 0.537940 | ||||||||
\(366\) | −6011.18 | −0.858495 | ||||||||
\(367\) | −3561.51 | −0.506565 | −0.253282 | − | 0.967392i | \(-0.581510\pi\) | ||||
−0.253282 | + | 0.967392i | \(0.581510\pi\) | |||||||
\(368\) | −1173.81 | −0.166274 | ||||||||
\(369\) | −2192.01 | −0.309245 | ||||||||
\(370\) | 2349.98 | 0.330188 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5268.60 | 0.734313 | ||||||||
\(373\) | −5272.91 | −0.731959 | −0.365979 | − | 0.930623i | \(-0.619266\pi\) | ||||
−0.365979 | + | 0.930623i | \(0.619266\pi\) | |||||||
\(374\) | 1060.78 | 0.146662 | ||||||||
\(375\) | −6486.11 | −0.893176 | ||||||||
\(376\) | −10339.6 | −1.41815 | ||||||||
\(377\) | 2272.88 | 0.310502 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4074.65 | 0.552244 | 0.276122 | − | 0.961123i | \(-0.410951\pi\) | ||||
0.276122 | + | 0.961123i | \(0.410951\pi\) | |||||||
\(380\) | −1903.00 | −0.256900 | ||||||||
\(381\) | −15418.7 | −2.07329 | ||||||||
\(382\) | −1231.96 | −0.165006 | ||||||||
\(383\) | −248.518 | −0.0331558 | −0.0165779 | − | 0.999863i | \(-0.505277\pi\) | ||||
−0.0165779 | + | 0.999863i | \(0.505277\pi\) | |||||||
\(384\) | 738.931 | 0.0981989 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8348.03 | −1.10079 | ||||||||
\(387\) | 2571.73 | 0.337800 | ||||||||
\(388\) | 659.154 | 0.0862460 | ||||||||
\(389\) | −8731.10 | −1.13801 | −0.569003 | − | 0.822335i | \(-0.692671\pi\) | ||||
−0.569003 | + | 0.822335i | \(0.692671\pi\) | |||||||
\(390\) | 1948.20 | 0.252950 | ||||||||
\(391\) | 2558.21 | 0.330881 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15221.6 | 1.95377 | ||||||||
\(394\) | 3400.08 | 0.434756 | ||||||||
\(395\) | −14832.1 | −1.88932 | ||||||||
\(396\) | 190.411 | 0.0241629 | ||||||||
\(397\) | −8208.17 | −1.03767 | −0.518836 | − | 0.854873i | \(-0.673635\pi\) | ||||
−0.518836 | + | 0.854873i | \(0.673635\pi\) | |||||||
\(398\) | 5208.14 | 0.655931 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −802.211 | −0.100276 | ||||||||
\(401\) | 8255.65 | 1.02810 | 0.514049 | − | 0.857761i | \(-0.328145\pi\) | ||||
0.514049 | + | 0.857761i | \(0.328145\pi\) | |||||||
\(402\) | 12345.3 | 1.53166 | ||||||||
\(403\) | 3351.87 | 0.414314 | ||||||||
\(404\) | −1102.12 | −0.135725 | ||||||||
\(405\) | −10682.8 | −1.31070 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 881.684 | 0.107380 | ||||||||
\(408\) | 6961.98 | 0.844778 | ||||||||
\(409\) | −2289.15 | −0.276751 | −0.138375 | − | 0.990380i | \(-0.544188\pi\) | ||||
−0.138375 | + | 0.990380i | \(0.544188\pi\) | |||||||
\(410\) | 10902.3 | 1.31324 | ||||||||
\(411\) | 5723.69 | 0.686932 | ||||||||
\(412\) | 522.672 | 0.0625005 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −576.528 | −0.0684416 | ||||||||
\(415\) | 6429.51 | 0.760512 | ||||||||
\(416\) | 1878.13 | 0.221353 | ||||||||
\(417\) | 6990.11 | 0.820880 | ||||||||
\(418\) | 896.405 | 0.104891 | ||||||||
\(419\) | −5890.09 | −0.686753 | −0.343377 | − | 0.939198i | \(-0.611571\pi\) | ||||
−0.343377 | + | 0.939198i | \(0.611571\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7601.77 | −0.880018 | −0.440009 | − | 0.897993i | \(-0.645025\pi\) | ||||
−0.440009 | + | 0.897993i | \(0.645025\pi\) | |||||||
\(422\) | −1513.52 | −0.174590 | ||||||||
\(423\) | −2275.97 | −0.261611 | ||||||||
\(424\) | 8209.09 | 0.940256 | ||||||||
\(425\) | 1748.35 | 0.199547 | ||||||||
\(426\) | 9562.94 | 1.08762 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4235.64 | 0.478358 | ||||||||
\(429\) | 730.940 | 0.0822613 | ||||||||
\(430\) | −12790.9 | −1.43450 | ||||||||
\(431\) | 8456.60 | 0.945105 | 0.472552 | − | 0.881303i | \(-0.343333\pi\) | ||||
0.472552 | + | 0.881303i | \(0.343333\pi\) | |||||||
\(432\) | 2836.48 | 0.315903 | ||||||||
\(433\) | 15308.9 | 1.69907 | 0.849536 | − | 0.527531i | \(-0.176882\pi\) | ||||
0.849536 | + | 0.527531i | \(0.176882\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12733.3 | −1.40348 | ||||||||
\(436\) | 1477.35 | 0.162276 | ||||||||
\(437\) | 2161.81 | 0.236644 | ||||||||
\(438\) | −3562.29 | −0.388614 | ||||||||
\(439\) | 12467.3 | 1.35542 | 0.677712 | − | 0.735327i | \(-0.262971\pi\) | ||||
0.677712 | + | 0.735327i | \(0.262971\pi\) | |||||||
\(440\) | −3083.09 | −0.334046 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1360.53 | 0.146411 | ||||||||
\(443\) | 6760.71 | 0.725081 | 0.362541 | − | 0.931968i | \(-0.381909\pi\) | ||||
0.362541 | + | 0.931968i | \(0.381909\pi\) | |||||||
\(444\) | 1777.48 | 0.189990 | ||||||||
\(445\) | −11343.0 | −1.20834 | ||||||||
\(446\) | 5499.70 | 0.583898 | ||||||||
\(447\) | −8589.72 | −0.908903 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13211.5 | −1.38861 | −0.694306 | − | 0.719680i | \(-0.744289\pi\) | ||||
−0.694306 | + | 0.719680i | \(0.744289\pi\) | |||||||
\(450\) | −394.015 | −0.0412757 | ||||||||
\(451\) | 4090.42 | 0.427074 | ||||||||
\(452\) | −3223.81 | −0.335476 | ||||||||
\(453\) | 8575.00 | 0.889379 | ||||||||
\(454\) | −7881.56 | −0.814757 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5883.19 | 0.604179 | ||||||||
\(457\) | 11863.1 | 1.21430 | 0.607148 | − | 0.794589i | \(-0.292313\pi\) | ||||
0.607148 | + | 0.794589i | \(0.292313\pi\) | |||||||
\(458\) | 3127.87 | 0.319118 | ||||||||
\(459\) | −6181.88 | −0.628639 | ||||||||
\(460\) | −2283.92 | −0.231496 | ||||||||
\(461\) | 1832.05 | 0.185091 | 0.0925456 | − | 0.995708i | \(-0.470500\pi\) | ||||
0.0925456 | + | 0.995708i | \(0.470500\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2277.23 | −0.228579 | −0.114289 | − | 0.993448i | \(-0.536459\pi\) | ||||
−0.114289 | + | 0.993448i | \(0.536459\pi\) | |||||||
\(464\) | 4080.15 | 0.408224 | ||||||||
\(465\) | −18778.1 | −1.87272 | ||||||||
\(466\) | −9599.34 | −0.954251 | ||||||||
\(467\) | −12037.0 | −1.19274 | −0.596368 | − | 0.802711i | \(-0.703390\pi\) | ||||
−0.596368 | + | 0.802711i | \(0.703390\pi\) | |||||||
\(468\) | 244.216 | 0.0241216 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 11319.9 | 1.11095 | ||||||||
\(471\) | 8558.78 | 0.837298 | ||||||||
\(472\) | 15660.2 | 1.52716 | ||||||||
\(473\) | −4799.01 | −0.466509 | ||||||||
\(474\) | 14085.0 | 1.36487 | ||||||||
\(475\) | 1477.44 | 0.142715 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1807.00 | 0.173452 | ||||||||
\(478\) | −360.107 | −0.0344580 | ||||||||
\(479\) | −7092.00 | −0.676496 | −0.338248 | − | 0.941057i | \(-0.609834\pi\) | ||||
−0.338248 | + | 0.941057i | \(0.609834\pi\) | |||||||
\(480\) | −10521.8 | −1.00052 | ||||||||
\(481\) | 1130.83 | 0.107196 | ||||||||
\(482\) | −11715.3 | −1.10709 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4365.59 | 0.409992 | ||||||||
\(485\) | −2349.32 | −0.219953 | ||||||||
\(486\) | 3131.70 | 0.292298 | ||||||||
\(487\) | 12604.1 | 1.17279 | 0.586394 | − | 0.810026i | \(-0.300547\pi\) | ||||
0.586394 | + | 0.810026i | \(0.300547\pi\) | |||||||
\(488\) | 12201.0 | 1.13179 | ||||||||
\(489\) | 1708.79 | 0.158025 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13353.9 | −1.22740 | −0.613699 | − | 0.789540i | \(-0.710319\pi\) | ||||
−0.613699 | + | 0.789540i | \(0.710319\pi\) | |||||||
\(492\) | 8246.30 | 0.755634 | ||||||||
\(493\) | −8892.34 | −0.812355 | ||||||||
\(494\) | 1149.71 | 0.104712 | ||||||||
\(495\) | −678.653 | −0.0616226 | ||||||||
\(496\) | 6017.09 | 0.544708 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6105.69 | −0.549402 | ||||||||
\(499\) | −2844.01 | −0.255141 | −0.127570 | − | 0.991830i | \(-0.540718\pi\) | ||||
−0.127570 | + | 0.991830i | \(0.540718\pi\) | |||||||
\(500\) | 4043.92 | 0.361699 | ||||||||
\(501\) | −1661.28 | −0.148145 | ||||||||
\(502\) | 7204.54 | 0.640546 | ||||||||
\(503\) | 10539.7 | 0.934276 | 0.467138 | − | 0.884184i | \(-0.345285\pi\) | ||||
0.467138 | + | 0.884184i | \(0.345285\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3928.14 | 0.346139 | ||||||||
\(506\) | 1075.84 | 0.0945193 | ||||||||
\(507\) | −11561.0 | −1.01271 | ||||||||
\(508\) | 9613.15 | 0.839596 | ||||||||
\(509\) | −10661.0 | −0.928367 | −0.464184 | − | 0.885739i | \(-0.653652\pi\) | ||||
−0.464184 | + | 0.885739i | \(0.653652\pi\) | |||||||
\(510\) | −7622.05 | −0.661784 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 7863.65 | 0.678765 | ||||||||
\(513\) | −5223.97 | −0.449598 | ||||||||
\(514\) | 6061.42 | 0.520152 | ||||||||
\(515\) | −1862.88 | −0.159395 | ||||||||
\(516\) | −9674.82 | −0.825407 | ||||||||
\(517\) | 4247.09 | 0.361290 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2668.48 | −0.225690 | ||||||||
\(520\) | −3954.29 | −0.333475 | ||||||||
\(521\) | 259.834 | 0.0218494 | 0.0109247 | − | 0.999940i | \(-0.496522\pi\) | ||||
0.0109247 | + | 0.999940i | \(0.496522\pi\) | |||||||
\(522\) | 2004.01 | 0.168033 | ||||||||
\(523\) | −8262.04 | −0.690772 | −0.345386 | − | 0.938461i | \(-0.612252\pi\) | ||||
−0.345386 | + | 0.938461i | \(0.612252\pi\) | |||||||
\(524\) | −9490.30 | −0.791194 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7841.05 | 0.649974 | ||||||||
\(527\) | −13113.7 | −1.08395 | ||||||||
\(528\) | 1312.14 | 0.108151 | ||||||||
\(529\) | −9572.47 | −0.786757 | ||||||||
\(530\) | −8987.39 | −0.736580 | ||||||||
\(531\) | 3447.16 | 0.281721 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5246.27 | 0.426344 | ||||||||
\(534\) | 10771.7 | 0.872918 | ||||||||
\(535\) | −15096.5 | −1.21996 | ||||||||
\(536\) | −25057.5 | −2.01925 | ||||||||
\(537\) | 8272.14 | 0.664747 | ||||||||
\(538\) | −12740.3 | −1.02095 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5519.05 | 0.439819 | ||||||||
\(541\) | −1510.93 | −0.120074 | −0.0600369 | − | 0.998196i | \(-0.519122\pi\) | ||||
−0.0600369 | + | 0.998196i | \(0.519122\pi\) | |||||||
\(542\) | −25.1074 | −0.00198977 | ||||||||
\(543\) | −15676.9 | −1.23897 | ||||||||
\(544\) | −7347.92 | −0.579117 | ||||||||
\(545\) | −5265.50 | −0.413852 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24353.1 | −1.90359 | −0.951795 | − | 0.306734i | \(-0.900764\pi\) | ||||
−0.951795 | + | 0.306734i | \(0.900764\pi\) | |||||||
\(548\) | −3568.58 | −0.278179 | ||||||||
\(549\) | 2685.70 | 0.208785 | ||||||||
\(550\) | 735.256 | 0.0570026 | ||||||||
\(551\) | −7514.44 | −0.580991 | ||||||||
\(552\) | 7060.82 | 0.544435 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2322.98 | 0.178148 | ||||||||
\(555\) | −6335.21 | −0.484531 | ||||||||
\(556\) | −4358.16 | −0.332423 | ||||||||
\(557\) | 3899.76 | 0.296658 | 0.148329 | − | 0.988938i | \(-0.452611\pi\) | ||||
0.148329 | + | 0.988938i | \(0.452611\pi\) | |||||||
\(558\) | 2955.36 | 0.224212 | ||||||||
\(559\) | −6155.10 | −0.465712 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2859.70 | −0.215217 | ||||||||
\(562\) | −6107.37 | −0.458406 | ||||||||
\(563\) | −8850.81 | −0.662553 | −0.331276 | − | 0.943534i | \(-0.607479\pi\) | ||||
−0.331276 | + | 0.943534i | \(0.607479\pi\) | |||||||
\(564\) | 8562.16 | 0.639241 | ||||||||
\(565\) | 11490.2 | 0.855565 | ||||||||
\(566\) | 3951.76 | 0.293471 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −19410.1 | −1.43385 | ||||||||
\(569\) | 4961.33 | 0.365536 | 0.182768 | − | 0.983156i | \(-0.441494\pi\) | ||||
0.182768 | + | 0.983156i | \(0.441494\pi\) | |||||||
\(570\) | −6440.98 | −0.473303 | ||||||||
\(571\) | 15405.7 | 1.12909 | 0.564544 | − | 0.825403i | \(-0.309052\pi\) | ||||
0.564544 | + | 0.825403i | \(0.309052\pi\) | |||||||
\(572\) | −455.722 | −0.0333124 | ||||||||
\(573\) | 3321.18 | 0.242137 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1773.17 | 0.128603 | ||||||||
\(576\) | 2644.77 | 0.191317 | ||||||||
\(577\) | 8507.85 | 0.613841 | 0.306921 | − | 0.951735i | \(-0.400701\pi\) | ||||
0.306921 | + | 0.951735i | \(0.400701\pi\) | |||||||
\(578\) | 5044.73 | 0.363033 | ||||||||
\(579\) | 22505.1 | 1.61534 | ||||||||
\(580\) | 7938.90 | 0.568353 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2231.00 | 0.158897 | ||||||||
\(583\) | −3371.96 | −0.239541 | ||||||||
\(584\) | 7230.46 | 0.512326 | ||||||||
\(585\) | −870.424 | −0.0615173 | ||||||||
\(586\) | 5013.21 | 0.353402 | ||||||||
\(587\) | −15021.4 | −1.05622 | −0.528109 | − | 0.849177i | \(-0.677099\pi\) | ||||
−0.528109 | + | 0.849177i | \(0.677099\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11081.7 | −0.775236 | ||||||||
\(590\) | −17145.0 | −1.19635 | ||||||||
\(591\) | −9166.14 | −0.637977 | ||||||||
\(592\) | 2030.00 | 0.140933 | ||||||||
\(593\) | 15336.5 | 1.06205 | 0.531023 | − | 0.847358i | \(-0.321808\pi\) | ||||
0.531023 | + | 0.847358i | \(0.321808\pi\) | |||||||
\(594\) | −2599.74 | −0.179577 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5355.47 | 0.368068 | ||||||||
\(597\) | −14040.4 | −0.962539 | ||||||||
\(598\) | 1379.84 | 0.0943578 | ||||||||
\(599\) | 24938.9 | 1.70113 | 0.850564 | − | 0.525871i | \(-0.176261\pi\) | ||||
0.850564 | + | 0.525871i | \(0.176261\pi\) | |||||||
\(600\) | 4825.56 | 0.328338 | ||||||||
\(601\) | −29218.2 | −1.98309 | −0.991545 | − | 0.129766i | \(-0.958577\pi\) | ||||
−0.991545 | + | 0.129766i | \(0.958577\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5515.69 | −0.372498 | ||||||||
\(604\) | −5346.30 | −0.360162 | ||||||||
\(605\) | −15559.6 | −1.04560 | ||||||||
\(606\) | −3730.30 | −0.250054 | ||||||||
\(607\) | −19730.9 | −1.31936 | −0.659682 | − | 0.751545i | \(-0.729309\pi\) | ||||
−0.659682 | + | 0.751545i | \(0.729309\pi\) | |||||||
\(608\) | −6209.33 | −0.414180 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13357.8 | −0.886625 | ||||||||
\(611\) | 5447.22 | 0.360673 | ||||||||
\(612\) | −955.463 | −0.0631083 | ||||||||
\(613\) | 5601.87 | 0.369098 | 0.184549 | − | 0.982823i | \(-0.440918\pi\) | ||||
0.184549 | + | 0.982823i | \(0.440918\pi\) | |||||||
\(614\) | −7147.64 | −0.469797 | ||||||||
\(615\) | −29391.1 | −1.92709 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6214.02 | −0.405457 | −0.202729 | − | 0.979235i | \(-0.564981\pi\) | ||||
−0.202729 | + | 0.979235i | \(0.564981\pi\) | |||||||
\(618\) | 1769.06 | 0.115149 | ||||||||
\(619\) | −15396.6 | −0.999745 | −0.499873 | − | 0.866099i | \(-0.666620\pi\) | ||||
−0.499873 | + | 0.866099i | \(0.666620\pi\) | |||||||
\(620\) | 11707.7 | 0.758374 | ||||||||
\(621\) | −6269.64 | −0.405140 | ||||||||
\(622\) | −15679.3 | −1.01074 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1682.92 | 0.107966 | ||||||||
\(625\) | −18764.6 | −1.20093 | ||||||||
\(626\) | 7743.02 | 0.494366 | ||||||||
\(627\) | −2416.58 | −0.153922 | ||||||||
\(628\) | −5336.18 | −0.339071 | ||||||||
\(629\) | −4424.21 | −0.280453 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16725.6 | −1.05521 | −0.527604 | − | 0.849490i | \(-0.676909\pi\) | ||||
−0.527604 | + | 0.849490i | \(0.676909\pi\) | |||||||
\(632\) | −28588.7 | −1.79936 | ||||||||
\(633\) | 4080.22 | 0.256199 | ||||||||
\(634\) | 76.2646 | 0.00477737 | ||||||||
\(635\) | −34262.7 | −2.14122 | ||||||||
\(636\) | −6797.89 | −0.423827 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3739.60 | −0.232057 | ||||||||
\(639\) | −4272.58 | −0.264508 | ||||||||
\(640\) | 1642.02 | 0.101417 | ||||||||
\(641\) | 14477.0 | 0.892057 | 0.446028 | − | 0.895019i | \(-0.352838\pi\) | ||||
0.446028 | + | 0.895019i | \(0.352838\pi\) | |||||||
\(642\) | 14336.1 | 0.881312 | ||||||||
\(643\) | 3953.95 | 0.242502 | 0.121251 | − | 0.992622i | \(-0.461309\pi\) | ||||
0.121251 | + | 0.992622i | \(0.461309\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 34482.5 | 2.10504 | ||||||||
\(646\) | −4498.08 | −0.273954 | ||||||||
\(647\) | −24134.3 | −1.46649 | −0.733244 | − | 0.679966i | \(-0.761995\pi\) | ||||
−0.733244 | + | 0.679966i | \(0.761995\pi\) | |||||||
\(648\) | −20591.1 | −1.24829 | ||||||||
\(649\) | −6432.60 | −0.389063 | ||||||||
\(650\) | 943.022 | 0.0569052 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1065.39 | −0.0639937 | ||||||||
\(653\) | −23338.9 | −1.39865 | −0.699326 | − | 0.714803i | \(-0.746517\pi\) | ||||
−0.699326 | + | 0.714803i | \(0.746517\pi\) | |||||||
\(654\) | 5000.30 | 0.298971 | ||||||||
\(655\) | 33824.9 | 2.01778 | ||||||||
\(656\) | 9417.81 | 0.560524 | ||||||||
\(657\) | 1591.58 | 0.0945105 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1319.35 | −0.0779885 | −0.0389943 | − | 0.999239i | \(-0.512415\pi\) | ||||
−0.0389943 | + | 0.999239i | \(0.512415\pi\) | |||||||
\(660\) | 2553.08 | 0.150574 | ||||||||
\(661\) | 13576.1 | 0.798862 | 0.399431 | − | 0.916763i | \(-0.369208\pi\) | ||||
0.399431 | + | 0.916763i | \(0.369208\pi\) | |||||||
\(662\) | 10409.6 | 0.611152 | ||||||||
\(663\) | −3667.79 | −0.214849 | ||||||||
\(664\) | 12392.8 | 0.724301 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 997.055 | 0.0580107 | ||||||||
\(667\) | −9018.59 | −0.523540 | ||||||||
\(668\) | 1035.77 | 0.0599926 | ||||||||
\(669\) | −14826.4 | −0.856834 | ||||||||
\(670\) | 27433.2 | 1.58185 | ||||||||
\(671\) | −5011.69 | −0.288337 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19574.5 | −1.12116 | −0.560580 | − | 0.828101i | \(-0.689422\pi\) | ||||
−0.560580 | + | 0.828101i | \(0.689422\pi\) | |||||||
\(674\) | 25968.2 | 1.48406 | ||||||||
\(675\) | −4284.84 | −0.244331 | ||||||||
\(676\) | 7208.01 | 0.410106 | ||||||||
\(677\) | −5326.66 | −0.302393 | −0.151196 | − | 0.988504i | \(-0.548313\pi\) | ||||
−0.151196 | + | 0.988504i | \(0.548313\pi\) | |||||||
\(678\) | −10911.4 | −0.618070 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 15470.6 | 0.872458 | ||||||||
\(681\) | 21247.6 | 1.19561 | ||||||||
\(682\) | −5514.88 | −0.309642 | ||||||||
\(683\) | 29615.4 | 1.65915 | 0.829575 | − | 0.558395i | \(-0.188583\pi\) | ||||
0.829575 | + | 0.558395i | \(0.188583\pi\) | |||||||
\(684\) | −807.410 | −0.0451346 | ||||||||
\(685\) | 12719.0 | 0.709440 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8432.30 | −0.468286 | ||||||||
\(688\) | −11049.3 | −0.612281 | ||||||||
\(689\) | −4324.80 | −0.239132 | ||||||||
\(690\) | −7730.26 | −0.426501 | ||||||||
\(691\) | 22053.0 | 1.21409 | 0.607045 | − | 0.794667i | \(-0.292355\pi\) | ||||
0.607045 | + | 0.794667i | \(0.292355\pi\) | |||||||
\(692\) | 1663.73 | 0.0913951 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11602.1 | 0.634598 | ||||||||
\(695\) | 15533.1 | 0.847778 | ||||||||
\(696\) | −24543.4 | −1.33666 | ||||||||
\(697\) | −20525.3 | −1.11543 | ||||||||
\(698\) | 16167.4 | 0.876711 | ||||||||
\(699\) | 25878.4 | 1.40030 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28160.5 | 1.51727 | 0.758635 | − | 0.651516i | \(-0.225867\pi\) | ||||
0.758635 | + | 0.651516i | \(0.225867\pi\) | |||||||
\(702\) | −3334.36 | −0.179270 | ||||||||
\(703\) | −3738.66 | −0.200578 | ||||||||
\(704\) | −4935.30 | −0.264213 | ||||||||
\(705\) | −30516.8 | −1.63026 | ||||||||
\(706\) | −1308.50 | −0.0697539 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −12968.2 | −0.688380 | ||||||||
\(709\) | −5639.27 | −0.298713 | −0.149356 | − | 0.988783i | \(-0.547720\pi\) | ||||
−0.149356 | + | 0.988783i | \(0.547720\pi\) | |||||||
\(710\) | 21250.4 | 1.12326 | ||||||||
\(711\) | −6292.99 | −0.331935 | ||||||||
\(712\) | −21863.6 | −1.15081 | ||||||||
\(713\) | −13299.9 | −0.698577 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1624.26 | 0.0849567 | ||||||||
\(716\) | −5157.47 | −0.269195 | ||||||||
\(717\) | 970.797 | 0.0505649 | ||||||||
\(718\) | 17511.8 | 0.910217 | ||||||||
\(719\) | 14592.5 | 0.756898 | 0.378449 | − | 0.925622i | \(-0.376457\pi\) | ||||
0.378449 | + | 0.925622i | \(0.376457\pi\) | |||||||
\(720\) | −1562.54 | −0.0808781 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 10673.1 | 0.550152 | ||||||||
\(723\) | 31582.9 | 1.62459 | ||||||||
\(724\) | 9774.14 | 0.501731 | ||||||||
\(725\) | −6163.55 | −0.315736 | ||||||||
\(726\) | 14776.0 | 0.755355 | ||||||||
\(727\) | 4920.88 | 0.251039 | 0.125520 | − | 0.992091i | \(-0.459940\pi\) | ||||
0.125520 | + | 0.992091i | \(0.459940\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14373.7 | 0.730260 | ||||||||
\(730\) | −7915.98 | −0.401347 | ||||||||
\(731\) | 24081.0 | 1.21842 | ||||||||
\(732\) | −10103.6 | −0.510163 | ||||||||
\(733\) | −20148.1 | −1.01526 | −0.507630 | − | 0.861575i | \(-0.669478\pi\) | ||||
−0.507630 | + | 0.861575i | \(0.669478\pi\) | |||||||
\(734\) | 7515.64 | 0.377939 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7452.23 | −0.373224 | ||||||||
\(737\) | 10292.6 | 0.514428 | ||||||||
\(738\) | 4625.66 | 0.230722 | ||||||||
\(739\) | 7469.08 | 0.371793 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(740\) | 3949.84 | 0.196215 | ||||||||
\(741\) | −3099.45 | −0.153659 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9936.10 | −0.490606 | −0.245303 | − | 0.969447i | \(-0.578887\pi\) | ||||
−0.245303 | + | 0.969447i | \(0.578887\pi\) | |||||||
\(744\) | −36194.7 | −1.78355 | ||||||||
\(745\) | −19087.7 | −0.938685 | ||||||||
\(746\) | 11127.1 | 0.546102 | ||||||||
\(747\) | 2727.93 | 0.133614 | ||||||||
\(748\) | 1782.95 | 0.0871540 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 13687.2 | 0.666383 | ||||||||
\(751\) | −7257.79 | −0.352651 | −0.176325 | − | 0.984332i | \(-0.556421\pi\) | ||||
−0.176325 | + | 0.984332i | \(0.556421\pi\) | |||||||
\(752\) | 9778.54 | 0.474184 | ||||||||
\(753\) | −19422.4 | −0.939963 | ||||||||
\(754\) | −4796.33 | −0.231660 | ||||||||
\(755\) | 19055.0 | 0.918521 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10026.2 | 0.481386 | 0.240693 | − | 0.970601i | \(-0.422625\pi\) | ||||
0.240693 | + | 0.970601i | \(0.422625\pi\) | |||||||
\(758\) | −8598.48 | −0.412020 | ||||||||
\(759\) | −2900.30 | −0.138701 | ||||||||
\(760\) | 13073.4 | 0.623976 | ||||||||
\(761\) | 6355.38 | 0.302736 | 0.151368 | − | 0.988477i | \(-0.451632\pi\) | ||||
0.151368 | + | 0.988477i | \(0.451632\pi\) | |||||||
\(762\) | 32537.1 | 1.54684 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2070.67 | −0.0980553 | ||||||||
\(765\) | 3405.42 | 0.160945 | ||||||||
\(766\) | 524.433 | 0.0247370 | ||||||||
\(767\) | −8250.31 | −0.388398 | ||||||||
\(768\) | −24000.6 | −1.12766 | ||||||||
\(769\) | 26720.1 | 1.25299 | 0.626496 | − | 0.779424i | \(-0.284488\pi\) | ||||
0.626496 | + | 0.779424i | \(0.284488\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16340.7 | −0.763291 | ||||||||
\(772\) | −14031.4 | −0.654145 | ||||||||
\(773\) | 13231.3 | 0.615650 | 0.307825 | − | 0.951443i | \(-0.400399\pi\) | ||||
0.307825 | + | 0.951443i | \(0.400399\pi\) | |||||||
\(774\) | −5426.97 | −0.252026 | ||||||||
\(775\) | −9089.53 | −0.421297 | ||||||||
\(776\) | −4528.31 | −0.209480 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18424.7 | 0.849047 | ||||||||
\(779\) | −17344.8 | −0.797745 | ||||||||
\(780\) | 3274.52 | 0.150316 | ||||||||
\(781\) | 7972.89 | 0.365291 | ||||||||
\(782\) | −5398.45 | −0.246864 | ||||||||
\(783\) | 21793.2 | 0.994670 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19019.0 | 0.864734 | ||||||||
\(786\) | −32121.3 | −1.45767 | ||||||||
\(787\) | −5816.34 | −0.263444 | −0.131722 | − | 0.991287i | \(-0.542051\pi\) | ||||
−0.131722 | + | 0.991287i | \(0.542051\pi\) | |||||||
\(788\) | 5714.86 | 0.258355 | ||||||||
\(789\) | −21138.4 | −0.953797 | ||||||||
\(790\) | 31299.2 | 1.40959 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1308.10 | −0.0586885 | ||||||||
\(793\) | −6427.87 | −0.287844 | ||||||||
\(794\) | 17321.2 | 0.774190 | ||||||||
\(795\) | 24228.7 | 1.08089 | ||||||||
\(796\) | 8753.84 | 0.389788 | ||||||||
\(797\) | 9903.73 | 0.440161 | 0.220080 | − | 0.975482i | \(-0.429368\pi\) | ||||
0.220080 | + | 0.975482i | \(0.429368\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21311.5 | −0.943614 | ||||||||
\(800\) | −5093.06 | −0.225084 | ||||||||
\(801\) | −4812.65 | −0.212293 | ||||||||
\(802\) | −17421.4 | −0.767046 | ||||||||
\(803\) | −2969.98 | −0.130521 | ||||||||
\(804\) | 20750.0 | 0.910192 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7073.25 | −0.309113 | ||||||||
\(807\) | 34345.9 | 1.49818 | ||||||||
\(808\) | 7571.46 | 0.329657 | ||||||||
\(809\) | 29403.4 | 1.27784 | 0.638918 | − | 0.769274i | \(-0.279382\pi\) | ||||
0.638918 | + | 0.769274i | \(0.279382\pi\) | |||||||
\(810\) | 22543.3 | 0.977891 | ||||||||
\(811\) | 27551.5 | 1.19293 | 0.596464 | − | 0.802640i | \(-0.296572\pi\) | ||||
0.596464 | + | 0.802640i | \(0.296572\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 67.6860 | 0.00291987 | ||||||||
\(814\) | −1860.57 | −0.0801140 | ||||||||
\(815\) | 3797.21 | 0.163203 | ||||||||
\(816\) | −6584.20 | −0.282467 | ||||||||
\(817\) | 20349.5 | 0.871407 | ||||||||
\(818\) | 4830.65 | 0.206479 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 18324.6 | 0.780393 | ||||||||
\(821\) | −28990.6 | −1.23237 | −0.616187 | − | 0.787600i | \(-0.711323\pi\) | ||||
−0.616187 | + | 0.787600i | \(0.711323\pi\) | |||||||
\(822\) | −12078.4 | −0.512508 | ||||||||
\(823\) | 20510.6 | 0.868718 | 0.434359 | − | 0.900740i | \(-0.356975\pi\) | ||||
0.434359 | + | 0.900740i | \(0.356975\pi\) | |||||||
\(824\) | −3590.70 | −0.151806 | ||||||||
\(825\) | −1982.14 | −0.0836478 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37073.4 | 1.55885 | 0.779425 | − | 0.626495i | \(-0.215511\pi\) | ||||
0.779425 | + | 0.626495i | \(0.215511\pi\) | |||||||
\(828\) | −969.027 | −0.0406715 | ||||||||
\(829\) | −37891.3 | −1.58748 | −0.793739 | − | 0.608258i | \(-0.791869\pi\) | ||||
−0.793739 | + | 0.608258i | \(0.791869\pi\) | |||||||
\(830\) | −13567.8 | −0.567405 | ||||||||
\(831\) | −6262.42 | −0.261421 | ||||||||
\(832\) | −6329.90 | −0.263762 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −14750.8 | −0.612444 | ||||||||
\(835\) | −3691.64 | −0.152999 | ||||||||
\(836\) | 1506.68 | 0.0623319 | ||||||||
\(837\) | 32139.0 | 1.32722 | ||||||||
\(838\) | 12429.5 | 0.512374 | ||||||||
\(839\) | −15467.0 | −0.636449 | −0.318224 | − | 0.948015i | \(-0.603087\pi\) | ||||
−0.318224 | + | 0.948015i | \(0.603087\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6959.57 | 0.285357 | ||||||||
\(842\) | 16041.6 | 0.656566 | ||||||||
\(843\) | 16464.6 | 0.672682 | ||||||||
\(844\) | −2543.91 | −0.103750 | ||||||||
\(845\) | −25690.5 | −1.04589 | ||||||||
\(846\) | 4802.84 | 0.195183 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7763.63 | −0.314392 | ||||||||
\(849\) | −10653.4 | −0.430651 | ||||||||
\(850\) | −3689.45 | −0.148879 | ||||||||
\(851\) | −4487.02 | −0.180744 | ||||||||
\(852\) | 16073.4 | 0.646320 | ||||||||
\(853\) | 28436.9 | 1.14146 | 0.570728 | − | 0.821139i | \(-0.306661\pi\) | ||||
0.570728 | + | 0.821139i | \(0.306661\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2877.73 | 0.115107 | ||||||||
\(856\) | −29098.4 | −1.16187 | ||||||||
\(857\) | −26186.6 | −1.04378 | −0.521889 | − | 0.853013i | \(-0.674772\pi\) | ||||
−0.521889 | + | 0.853013i | \(0.674772\pi\) | |||||||
\(858\) | −1542.46 | −0.0613737 | ||||||||
\(859\) | 13765.8 | 0.546777 | 0.273388 | − | 0.961904i | \(-0.411856\pi\) | ||||
0.273388 | + | 0.961904i | \(0.411856\pi\) | |||||||
\(860\) | −21499.0 | −0.852453 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −17845.5 | −0.705126 | ||||||||
\(863\) | −21052.9 | −0.830414 | −0.415207 | − | 0.909727i | \(-0.636291\pi\) | ||||
−0.415207 | + | 0.909727i | \(0.636291\pi\) | |||||||
\(864\) | 18008.2 | 0.709087 | ||||||||
\(865\) | −5929.78 | −0.233085 | ||||||||
\(866\) | −32305.4 | −1.26765 | ||||||||
\(867\) | −13599.9 | −0.532729 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11743.1 | 0.458409 | ||||||||
\(870\) | 26870.3 | 1.04711 | ||||||||
\(871\) | 13201.1 | 0.513549 | ||||||||
\(872\) | −10149.2 | −0.394146 | ||||||||
\(873\) | −996.777 | −0.0386435 | ||||||||
\(874\) | −4561.93 | −0.176556 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5987.49 | −0.230935 | ||||||||
\(877\) | 8478.36 | 0.326447 | 0.163224 | − | 0.986589i | \(-0.447811\pi\) | ||||
0.163224 | + | 0.986589i | \(0.447811\pi\) | |||||||
\(878\) | −26309.0 | −1.01126 | ||||||||
\(879\) | −13514.9 | −0.518596 | ||||||||
\(880\) | 2915.79 | 0.111694 | ||||||||
\(881\) | 19901.7 | 0.761072 | 0.380536 | − | 0.924766i | \(-0.375740\pi\) | ||||
0.380536 | + | 0.924766i | \(0.375740\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35898.3 | −1.36815 | −0.684073 | − | 0.729413i | \(-0.739793\pi\) | ||||
−0.684073 | + | 0.729413i | \(0.739793\pi\) | |||||||
\(884\) | 2286.77 | 0.0870051 | ||||||||
\(885\) | 46220.5 | 1.75558 | ||||||||
\(886\) | −14266.7 | −0.540971 | ||||||||
\(887\) | −41970.1 | −1.58875 | −0.794373 | − | 0.607430i | \(-0.792200\pi\) | ||||
−0.794373 | + | 0.607430i | \(0.792200\pi\) | |||||||
\(888\) | −12211.1 | −0.461460 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 23936.5 | 0.901521 | ||||||||
\(891\) | 8457.99 | 0.318017 | ||||||||
\(892\) | 9243.89 | 0.346982 | ||||||||
\(893\) | −18009.2 | −0.674866 | ||||||||
\(894\) | 18126.4 | 0.678117 | ||||||||
\(895\) | 18382.0 | 0.686528 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3719.86 | −0.138464 | ||||||||
\(898\) | 27879.3 | 1.03602 | ||||||||
\(899\) | 46230.5 | 1.71510 | ||||||||
\(900\) | −662.260 | −0.0245281 | ||||||||
\(901\) | 16920.2 | 0.625631 | ||||||||
\(902\) | −8631.76 | −0.318632 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22147.2 | 0.814828 | ||||||||
\(905\) | −34836.6 | −1.27956 | ||||||||
\(906\) | −18095.3 | −0.663550 | ||||||||
\(907\) | −44174.7 | −1.61719 | −0.808597 | − | 0.588363i | \(-0.799773\pi\) | ||||
−0.808597 | + | 0.588363i | \(0.799773\pi\) | |||||||
\(908\) | −13247.3 | −0.484171 | ||||||||
\(909\) | 1666.64 | 0.0608130 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1001.93 | 0.0364383 | 0.0182192 | − | 0.999834i | \(-0.494200\pi\) | ||||
0.0182192 | + | 0.999834i | \(0.494200\pi\) | |||||||
\(912\) | −5563.95 | −0.202018 | ||||||||
\(913\) | −5090.48 | −0.184524 | ||||||||
\(914\) | −25034.0 | −0.905965 | ||||||||
\(915\) | 36010.7 | 1.30107 | ||||||||
\(916\) | 5257.33 | 0.189636 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 13045.2 | 0.469017 | ||||||||
\(919\) | 2062.63 | 0.0740367 | 0.0370184 | − | 0.999315i | \(-0.488214\pi\) | ||||
0.0370184 | + | 0.999315i | \(0.488214\pi\) | |||||||
\(920\) | 15690.3 | 0.562275 | ||||||||
\(921\) | 19269.0 | 0.689398 | ||||||||
\(922\) | −3866.06 | −0.138093 | ||||||||
\(923\) | 10225.8 | 0.364667 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3066.55 | −0.109003 | ||||||||
\(926\) | 4805.50 | 0.170539 | ||||||||
\(927\) | −790.389 | −0.0280041 | ||||||||
\(928\) | 25903.9 | 0.916313 | ||||||||
\(929\) | 16067.2 | 0.567436 | 0.283718 | − | 0.958908i | \(-0.408432\pi\) | ||||
0.283718 | + | 0.958908i | \(0.408432\pi\) | |||||||
\(930\) | 39626.3 | 1.39720 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −16134.6 | −0.567065 | ||||||||
\(933\) | 42269.1 | 1.48320 | ||||||||
\(934\) | 25401.1 | 0.889880 | ||||||||
\(935\) | −6354.72 | −0.222269 | ||||||||
\(936\) | −1677.74 | −0.0585882 | ||||||||
\(937\) | 11043.2 | 0.385021 | 0.192510 | − | 0.981295i | \(-0.438337\pi\) | ||||
0.192510 | + | 0.981295i | \(0.438337\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20874.1 | −0.725452 | ||||||||
\(940\) | 19026.5 | 0.660186 | ||||||||
\(941\) | −33595.2 | −1.16384 | −0.581920 | − | 0.813246i | \(-0.697698\pi\) | ||||
−0.581920 | + | 0.813246i | \(0.697698\pi\) | |||||||
\(942\) | −18061.1 | −0.624694 | ||||||||
\(943\) | −20816.7 | −0.718861 | ||||||||
\(944\) | −14810.5 | −0.510635 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10127.1 | 0.348054 | ||||||||
\(947\) | 56186.7 | 1.92801 | 0.964003 | − | 0.265892i | \(-0.0856663\pi\) | ||||
0.964003 | + | 0.265892i | \(0.0856663\pi\) | |||||||
\(948\) | 23674.1 | 0.811076 | ||||||||
\(949\) | −3809.23 | −0.130298 | ||||||||
\(950\) | −3117.75 | −0.106477 | ||||||||
\(951\) | −205.598 | −0.00701050 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5829.81 | 0.198160 | 0.0990798 | − | 0.995079i | \(-0.468410\pi\) | ||||
0.0990798 | + | 0.995079i | \(0.468410\pi\) | |||||||
\(954\) | −3813.19 | −0.129410 | ||||||||
\(955\) | 7380.19 | 0.250071 | ||||||||
\(956\) | −605.267 | −0.0204767 | ||||||||
\(957\) | 10081.4 | 0.340529 | ||||||||
\(958\) | 14965.8 | 0.504722 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 35461.8 | 1.19221 | ||||||||
\(961\) | 38386.1 | 1.28851 | ||||||||
\(962\) | −2386.32 | −0.0799771 | ||||||||
\(963\) | −6405.17 | −0.214334 | ||||||||
\(964\) | −19691.1 | −0.657893 | ||||||||
\(965\) | 50009.9 | 1.66827 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −535.705 | −0.0178150 | −0.00890751 | − | 0.999960i | \(-0.502835\pi\) | ||||
−0.00890751 | + | 0.999960i | \(0.502835\pi\) | |||||||
\(968\) | −29991.1 | −0.995816 | ||||||||
\(969\) | 12126.2 | 0.402011 | ||||||||
\(970\) | 4957.64 | 0.164103 | ||||||||
\(971\) | −33903.8 | −1.12052 | −0.560260 | − | 0.828317i | \(-0.689299\pi\) | ||||
−0.560260 | + | 0.828317i | \(0.689299\pi\) | |||||||
\(972\) | 5263.76 | 0.173699 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −26597.8 | −0.874997 | ||||||||
\(975\) | −2542.25 | −0.0835049 | ||||||||
\(976\) | −11538.9 | −0.378435 | ||||||||
\(977\) | −12648.8 | −0.414199 | −0.207099 | − | 0.978320i | \(-0.566402\pi\) | ||||
−0.207099 | + | 0.978320i | \(0.566402\pi\) | |||||||
\(978\) | −3605.96 | −0.117900 | ||||||||
\(979\) | 8980.69 | 0.293181 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2234.06 | −0.0727094 | ||||||||
\(982\) | 28179.9 | 0.915740 | ||||||||
\(983\) | 35544.3 | 1.15329 | 0.576647 | − | 0.816993i | \(-0.304361\pi\) | ||||
0.576647 | + | 0.816993i | \(0.304361\pi\) | |||||||
\(984\) | −56651.1 | −1.83534 | ||||||||
\(985\) | −20368.6 | −0.658882 | ||||||||
\(986\) | 18765.0 | 0.606084 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1932.43 | 0.0622254 | ||||||||
\(989\) | 24422.8 | 0.785239 | ||||||||
\(990\) | 1432.12 | 0.0459755 | ||||||||
\(991\) | 41025.1 | 1.31504 | 0.657520 | − | 0.753437i | \(-0.271605\pi\) | ||||
0.657520 | + | 0.753437i | \(0.271605\pi\) | |||||||
\(992\) | 38201.1 | 1.22267 | ||||||||
\(993\) | −28062.9 | −0.896828 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −31200.0 | −0.994078 | ||||||||
\(996\) | −10262.4 | −0.326484 | ||||||||
\(997\) | −9309.43 | −0.295720 | −0.147860 | − | 0.989008i | \(-0.547238\pi\) | ||||
−0.147860 | + | 0.989008i | \(0.547238\pi\) | |||||||
\(998\) | 6001.53 | 0.190356 | ||||||||
\(999\) | 10842.8 | 0.343394 |
(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 | 2401.4.a.c.1.13 | 39 | ||
7.6 | odd | 2 | 2401.4.a.d.1.13 | 39 | |||
49.6 | odd | 14 | 49.4.e.a.36.9 | yes | 78 | ||
49.41 | odd | 14 | 49.4.e.a.15.9 | ✓ | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.4.e.a.15.9 | ✓ | 78 | 49.41 | odd | 14 | ||
49.4.e.a.36.9 | yes | 78 | 49.6 | odd | 14 | ||
2401.4.a.c.1.13 | 39 | 1.1 | even | 1 | trivial | ||
2401.4.a.d.1.13 | 39 | 7.6 | odd | 2 |