Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(14.4554679514\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.1163891200.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 23x^{4} + 12x^{3} + 154x^{2} + 152x + 28 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.05886\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.644648 | 0.227917 | 0.113959 | − | 0.993485i | \(-0.463647\pi\) | ||||
0.113959 | + | 0.993485i | \(0.463647\pi\) | |||||||
\(3\) | 4.18687 | 0.805764 | 0.402882 | − | 0.915252i | \(-0.368008\pi\) | ||||
0.402882 | + | 0.915252i | \(0.368008\pi\) | |||||||
\(4\) | −7.58443 | −0.948054 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 2.69906 | 0.183648 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −10.0465 | −0.443995 | ||||||||
\(9\) | −9.47008 | −0.350744 | ||||||||
\(10\) | 3.22324 | 0.101928 | ||||||||
\(11\) | −47.7013 | −1.30750 | −0.653750 | − | 0.756711i | \(-0.726805\pi\) | ||||
−0.653750 | + | 0.756711i | \(0.726805\pi\) | |||||||
\(12\) | −31.7550 | −0.763908 | ||||||||
\(13\) | −57.2256 | −1.22089 | −0.610443 | − | 0.792060i | \(-0.709009\pi\) | ||||
−0.610443 | + | 0.792060i | \(0.709009\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 20.9344 | 0.360349 | ||||||||
\(16\) | 54.1990 | 0.846859 | ||||||||
\(17\) | 36.9686 | 0.527423 | 0.263712 | − | 0.964602i | \(-0.415053\pi\) | ||||
0.263712 | + | 0.964602i | \(0.415053\pi\) | |||||||
\(18\) | −6.10487 | −0.0799407 | ||||||||
\(19\) | −30.7659 | −0.371484 | −0.185742 | − | 0.982599i | \(-0.559469\pi\) | ||||
−0.185742 | + | 0.982599i | \(0.559469\pi\) | |||||||
\(20\) | −37.9221 | −0.423982 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −30.7506 | −0.298002 | ||||||||
\(23\) | 53.1282 | 0.481652 | 0.240826 | − | 0.970568i | \(-0.422582\pi\) | ||||
0.240826 | + | 0.970568i | \(0.422582\pi\) | |||||||
\(24\) | −42.0633 | −0.357756 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −36.8904 | −0.278261 | ||||||||
\(27\) | −152.696 | −1.08838 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −195.663 | −1.25288 | −0.626442 | − | 0.779468i | \(-0.715490\pi\) | ||||
−0.626442 | + | 0.779468i | \(0.715490\pi\) | |||||||
\(30\) | 13.4953 | 0.0821298 | ||||||||
\(31\) | −257.870 | −1.49403 | −0.747014 | − | 0.664809i | \(-0.768513\pi\) | ||||
−0.747014 | + | 0.664809i | \(0.768513\pi\) | |||||||
\(32\) | 115.311 | 0.637010 | ||||||||
\(33\) | −199.719 | −1.05354 | ||||||||
\(34\) | 23.8317 | 0.120209 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 71.8252 | 0.332524 | ||||||||
\(37\) | 346.423 | 1.53923 | 0.769616 | − | 0.638507i | \(-0.220447\pi\) | ||||
0.769616 | + | 0.638507i | \(0.220447\pi\) | |||||||
\(38\) | −19.8332 | −0.0846676 | ||||||||
\(39\) | −239.596 | −0.983747 | ||||||||
\(40\) | −50.2324 | −0.198561 | ||||||||
\(41\) | −267.050 | −1.01722 | −0.508611 | − | 0.860996i | \(-0.669841\pi\) | ||||
−0.508611 | + | 0.860996i | \(0.669841\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −176.859 | −0.627227 | −0.313614 | − | 0.949551i | \(-0.601540\pi\) | ||||
−0.313614 | + | 0.949551i | \(0.601540\pi\) | |||||||
\(44\) | 361.787 | 1.23958 | ||||||||
\(45\) | −47.3504 | −0.156857 | ||||||||
\(46\) | 34.2490 | 0.109777 | ||||||||
\(47\) | 311.598 | 0.967049 | 0.483524 | − | 0.875331i | \(-0.339356\pi\) | ||||
0.483524 | + | 0.875331i | \(0.339356\pi\) | |||||||
\(48\) | 226.924 | 0.682369 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 16.1162 | 0.0455835 | ||||||||
\(51\) | 154.783 | 0.424979 | ||||||||
\(52\) | 434.024 | 1.15747 | ||||||||
\(53\) | −492.270 | −1.27582 | −0.637910 | − | 0.770111i | \(-0.720201\pi\) | ||||
−0.637910 | + | 0.770111i | \(0.720201\pi\) | |||||||
\(54\) | −98.4349 | −0.248061 | ||||||||
\(55\) | −238.507 | −0.584731 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −128.813 | −0.299328 | ||||||||
\(58\) | −126.134 | −0.285554 | ||||||||
\(59\) | −98.7653 | −0.217935 | −0.108967 | − | 0.994045i | \(-0.534754\pi\) | ||||
−0.108967 | + | 0.994045i | \(0.534754\pi\) | |||||||
\(60\) | −158.775 | −0.341630 | ||||||||
\(61\) | −82.1682 | −0.172468 | −0.0862340 | − | 0.996275i | \(-0.527483\pi\) | ||||
−0.0862340 | + | 0.996275i | \(0.527483\pi\) | |||||||
\(62\) | −166.235 | −0.340515 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −359.257 | −0.701674 | ||||||||
\(65\) | −286.128 | −0.545997 | ||||||||
\(66\) | −128.749 | −0.240119 | ||||||||
\(67\) | 654.668 | 1.19374 | 0.596869 | − | 0.802339i | \(-0.296411\pi\) | ||||
0.596869 | + | 0.802339i | \(0.296411\pi\) | |||||||
\(68\) | −280.386 | −0.500026 | ||||||||
\(69\) | 222.441 | 0.388098 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 779.658 | 1.30322 | 0.651608 | − | 0.758556i | \(-0.274095\pi\) | ||||
0.651608 | + | 0.758556i | \(0.274095\pi\) | |||||||
\(72\) | 95.1409 | 0.155729 | ||||||||
\(73\) | 829.673 | 1.33022 | 0.665109 | − | 0.746747i | \(-0.268385\pi\) | ||||
0.665109 | + | 0.746747i | \(0.268385\pi\) | |||||||
\(74\) | 223.321 | 0.350818 | ||||||||
\(75\) | 104.672 | 0.161153 | ||||||||
\(76\) | 233.342 | 0.352186 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −154.455 | −0.224213 | ||||||||
\(79\) | −769.426 | −1.09579 | −0.547894 | − | 0.836548i | \(-0.684570\pi\) | ||||
−0.547894 | + | 0.836548i | \(0.684570\pi\) | |||||||
\(80\) | 270.995 | 0.378727 | ||||||||
\(81\) | −383.625 | −0.526235 | ||||||||
\(82\) | −172.153 | −0.231843 | ||||||||
\(83\) | −613.203 | −0.810937 | −0.405469 | − | 0.914109i | \(-0.632892\pi\) | ||||
−0.405469 | + | 0.914109i | \(0.632892\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 184.843 | 0.235871 | ||||||||
\(86\) | −114.012 | −0.142956 | ||||||||
\(87\) | −819.215 | −1.00953 | ||||||||
\(88\) | 479.230 | 0.580524 | ||||||||
\(89\) | 457.666 | 0.545084 | 0.272542 | − | 0.962144i | \(-0.412136\pi\) | ||||
0.272542 | + | 0.962144i | \(0.412136\pi\) | |||||||
\(90\) | −30.5244 | −0.0357506 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −402.947 | −0.456632 | ||||||||
\(93\) | −1079.67 | −1.20383 | ||||||||
\(94\) | 200.871 | 0.220407 | ||||||||
\(95\) | −153.830 | −0.166132 | ||||||||
\(96\) | 482.793 | 0.513280 | ||||||||
\(97\) | 1412.11 | 1.47813 | 0.739063 | − | 0.673636i | \(-0.235268\pi\) | ||||
0.739063 | + | 0.673636i | \(0.235268\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 451.736 | 0.458597 | ||||||||
\(100\) | −189.611 | −0.189611 | ||||||||
\(101\) | −1823.79 | −1.79677 | −0.898386 | − | 0.439208i | \(-0.855259\pi\) | ||||
−0.898386 | + | 0.439208i | \(0.855259\pi\) | |||||||
\(102\) | 99.7804 | 0.0968601 | ||||||||
\(103\) | −407.775 | −0.390090 | −0.195045 | − | 0.980794i | \(-0.562485\pi\) | ||||
−0.195045 | + | 0.980794i | \(0.562485\pi\) | |||||||
\(104\) | 574.915 | 0.542068 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −317.341 | −0.290782 | ||||||||
\(107\) | −370.109 | −0.334390 | −0.167195 | − | 0.985924i | \(-0.553471\pi\) | ||||
−0.167195 | + | 0.985924i | \(0.553471\pi\) | |||||||
\(108\) | 1158.11 | 1.03184 | ||||||||
\(109\) | 975.570 | 0.857272 | 0.428636 | − | 0.903477i | \(-0.358994\pi\) | ||||
0.428636 | + | 0.903477i | \(0.358994\pi\) | |||||||
\(110\) | −153.753 | −0.133270 | ||||||||
\(111\) | 1450.43 | 1.24026 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1978.85 | 1.64739 | 0.823693 | − | 0.567036i | \(-0.191910\pi\) | ||||
0.823693 | + | 0.567036i | \(0.191910\pi\) | |||||||
\(114\) | −83.0391 | −0.0682221 | ||||||||
\(115\) | 265.641 | 0.215401 | ||||||||
\(116\) | 1483.99 | 1.18780 | ||||||||
\(117\) | 541.931 | 0.428219 | ||||||||
\(118\) | −63.6689 | −0.0496711 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −210.317 | −0.159993 | ||||||||
\(121\) | 944.416 | 0.709554 | ||||||||
\(122\) | −52.9695 | −0.0393085 | ||||||||
\(123\) | −1118.10 | −0.819642 | ||||||||
\(124\) | 1955.80 | 1.41642 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1392.38 | 0.972867 | 0.486433 | − | 0.873718i | \(-0.338298\pi\) | ||||
0.486433 | + | 0.873718i | \(0.338298\pi\) | |||||||
\(128\) | −1154.08 | −0.796933 | ||||||||
\(129\) | −740.487 | −0.505397 | ||||||||
\(130\) | −184.452 | −0.124442 | ||||||||
\(131\) | 1777.02 | 1.18518 | 0.592591 | − | 0.805504i | \(-0.298105\pi\) | ||||
0.592591 | + | 0.805504i | \(0.298105\pi\) | |||||||
\(132\) | 1514.76 | 0.998809 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 422.031 | 0.272074 | ||||||||
\(135\) | −763.478 | −0.486739 | ||||||||
\(136\) | −371.404 | −0.234174 | ||||||||
\(137\) | −1980.48 | −1.23506 | −0.617532 | − | 0.786545i | \(-0.711868\pi\) | ||||
−0.617532 | + | 0.786545i | \(0.711868\pi\) | |||||||
\(138\) | 143.396 | 0.0884543 | ||||||||
\(139\) | −2182.09 | −1.33153 | −0.665763 | − | 0.746163i | \(-0.731894\pi\) | ||||
−0.665763 | + | 0.746163i | \(0.731894\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1304.62 | 0.779213 | ||||||||
\(142\) | 502.605 | 0.297026 | ||||||||
\(143\) | 2729.74 | 1.59631 | ||||||||
\(144\) | −513.269 | −0.297031 | ||||||||
\(145\) | −978.313 | −0.560307 | ||||||||
\(146\) | 534.847 | 0.303180 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2627.42 | −1.45928 | ||||||||
\(149\) | 670.154 | 0.368464 | 0.184232 | − | 0.982883i | \(-0.441020\pi\) | ||||
0.184232 | + | 0.982883i | \(0.441020\pi\) | |||||||
\(150\) | 67.4765 | 0.0367296 | ||||||||
\(151\) | 3348.84 | 1.80480 | 0.902401 | − | 0.430898i | \(-0.141803\pi\) | ||||
0.902401 | + | 0.430898i | \(0.141803\pi\) | |||||||
\(152\) | 309.089 | 0.164937 | ||||||||
\(153\) | −350.096 | −0.184990 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1289.35 | −0.668149 | ||||||||
\(156\) | 1817.20 | 0.932645 | ||||||||
\(157\) | −2408.41 | −1.22428 | −0.612140 | − | 0.790749i | \(-0.709691\pi\) | ||||
−0.612140 | + | 0.790749i | \(0.709691\pi\) | |||||||
\(158\) | −496.009 | −0.249749 | ||||||||
\(159\) | −2061.07 | −1.02801 | ||||||||
\(160\) | 576.555 | 0.284879 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −247.303 | −0.119938 | ||||||||
\(163\) | −3811.03 | −1.83131 | −0.915654 | − | 0.401968i | \(-0.868326\pi\) | ||||
−0.915654 | + | 0.401968i | \(0.868326\pi\) | |||||||
\(164\) | 2025.42 | 0.964382 | ||||||||
\(165\) | −998.597 | −0.471156 | ||||||||
\(166\) | −395.300 | −0.184827 | ||||||||
\(167\) | −1207.15 | −0.559354 | −0.279677 | − | 0.960094i | \(-0.590227\pi\) | ||||
−0.279677 | + | 0.960094i | \(0.590227\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1077.77 | 0.490564 | ||||||||
\(170\) | 119.159 | 0.0537591 | ||||||||
\(171\) | 291.356 | 0.130296 | ||||||||
\(172\) | 1341.38 | 0.594645 | ||||||||
\(173\) | −3243.28 | −1.42533 | −0.712665 | − | 0.701505i | \(-0.752512\pi\) | ||||
−0.712665 | + | 0.701505i | \(0.752512\pi\) | |||||||
\(174\) | −528.105 | −0.230089 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2585.36 | −1.10727 | ||||||||
\(177\) | −413.518 | −0.175604 | ||||||||
\(178\) | 295.034 | 0.124234 | ||||||||
\(179\) | 859.728 | 0.358989 | 0.179495 | − | 0.983759i | \(-0.442554\pi\) | ||||
0.179495 | + | 0.983759i | \(0.442554\pi\) | |||||||
\(180\) | 359.126 | 0.148709 | ||||||||
\(181\) | 290.504 | 0.119298 | 0.0596491 | − | 0.998219i | \(-0.481002\pi\) | ||||
0.0596491 | + | 0.998219i | \(0.481002\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −344.028 | −0.138969 | ||||||||
\(184\) | −533.751 | −0.213851 | ||||||||
\(185\) | 1732.12 | 0.688366 | ||||||||
\(186\) | −696.007 | −0.274375 | ||||||||
\(187\) | −1763.45 | −0.689605 | ||||||||
\(188\) | −2363.30 | −0.916814 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −99.1660 | −0.0378645 | ||||||||
\(191\) | 4895.61 | 1.85463 | 0.927315 | − | 0.374282i | \(-0.122111\pi\) | ||||
0.927315 | + | 0.374282i | \(0.122111\pi\) | |||||||
\(192\) | −1504.16 | −0.565384 | ||||||||
\(193\) | −3548.73 | −1.32354 | −0.661770 | − | 0.749707i | \(-0.730194\pi\) | ||||
−0.661770 | + | 0.749707i | \(0.730194\pi\) | |||||||
\(194\) | 910.315 | 0.336891 | ||||||||
\(195\) | −1197.98 | −0.439945 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −650.107 | −0.235118 | −0.117559 | − | 0.993066i | \(-0.537507\pi\) | ||||
−0.117559 | + | 0.993066i | \(0.537507\pi\) | |||||||
\(198\) | 291.210 | 0.104522 | ||||||||
\(199\) | −4055.09 | −1.44451 | −0.722256 | − | 0.691626i | \(-0.756895\pi\) | ||||
−0.722256 | + | 0.691626i | \(0.756895\pi\) | |||||||
\(200\) | −251.162 | −0.0887991 | ||||||||
\(201\) | 2741.01 | 0.961871 | ||||||||
\(202\) | −1175.70 | −0.409516 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1173.94 | −0.402903 | ||||||||
\(205\) | −1335.25 | −0.454916 | ||||||||
\(206\) | −262.871 | −0.0889083 | ||||||||
\(207\) | −503.128 | −0.168936 | ||||||||
\(208\) | −3101.57 | −1.03392 | ||||||||
\(209\) | 1467.58 | 0.485714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1569.67 | −0.512134 | −0.256067 | − | 0.966659i | \(-0.582427\pi\) | ||||
−0.256067 | + | 0.966659i | \(0.582427\pi\) | |||||||
\(212\) | 3733.59 | 1.20955 | ||||||||
\(213\) | 3264.33 | 1.05008 | ||||||||
\(214\) | −238.590 | −0.0762134 | ||||||||
\(215\) | −884.296 | −0.280504 | ||||||||
\(216\) | 1534.05 | 0.483236 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 628.900 | 0.195387 | ||||||||
\(219\) | 3473.74 | 1.07184 | ||||||||
\(220\) | 1808.94 | 0.554357 | ||||||||
\(221\) | −2115.55 | −0.643924 | ||||||||
\(222\) | 935.017 | 0.282677 | ||||||||
\(223\) | −4723.86 | −1.41853 | −0.709267 | − | 0.704940i | \(-0.750974\pi\) | ||||
−0.709267 | + | 0.704940i | \(0.750974\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −236.752 | −0.0701488 | ||||||||
\(226\) | 1275.66 | 0.375468 | ||||||||
\(227\) | −3685.02 | −1.07746 | −0.538730 | − | 0.842479i | \(-0.681096\pi\) | ||||
−0.538730 | + | 0.842479i | \(0.681096\pi\) | |||||||
\(228\) | 976.973 | 0.283779 | ||||||||
\(229\) | −3356.78 | −0.968656 | −0.484328 | − | 0.874887i | \(-0.660936\pi\) | ||||
−0.484328 | + | 0.874887i | \(0.660936\pi\) | |||||||
\(230\) | 171.245 | 0.0490937 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1965.72 | 0.556275 | ||||||||
\(233\) | 2314.01 | 0.650627 | 0.325314 | − | 0.945606i | \(-0.394530\pi\) | ||||
0.325314 | + | 0.945606i | \(0.394530\pi\) | |||||||
\(234\) | 349.355 | 0.0975985 | ||||||||
\(235\) | 1557.99 | 0.432477 | ||||||||
\(236\) | 749.079 | 0.206614 | ||||||||
\(237\) | −3221.49 | −0.882946 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 941.179 | 0.254727 | 0.127364 | − | 0.991856i | \(-0.459348\pi\) | ||||
0.127364 | + | 0.991856i | \(0.459348\pi\) | |||||||
\(240\) | 1134.62 | 0.305165 | ||||||||
\(241\) | −5638.24 | −1.50702 | −0.753509 | − | 0.657438i | \(-0.771640\pi\) | ||||
−0.753509 | + | 0.657438i | \(0.771640\pi\) | |||||||
\(242\) | 608.816 | 0.161720 | ||||||||
\(243\) | 2516.59 | 0.664360 | ||||||||
\(244\) | 623.199 | 0.163509 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −720.783 | −0.186811 | ||||||||
\(247\) | 1760.60 | 0.453539 | ||||||||
\(248\) | 2590.69 | 0.663341 | ||||||||
\(249\) | −2567.40 | −0.653424 | ||||||||
\(250\) | 80.5810 | 0.0203856 | ||||||||
\(251\) | −365.822 | −0.0919940 | −0.0459970 | − | 0.998942i | \(-0.514646\pi\) | ||||
−0.0459970 | + | 0.998942i | \(0.514646\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2534.28 | −0.629759 | ||||||||
\(254\) | 897.598 | 0.221733 | ||||||||
\(255\) | 773.914 | 0.190056 | ||||||||
\(256\) | 2130.08 | 0.520039 | ||||||||
\(257\) | 6276.46 | 1.52340 | 0.761702 | − | 0.647928i | \(-0.224364\pi\) | ||||
0.761702 | + | 0.647928i | \(0.224364\pi\) | |||||||
\(258\) | −477.353 | −0.115189 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2170.12 | 0.517635 | ||||||||
\(261\) | 1852.94 | 0.439442 | ||||||||
\(262\) | 1145.55 | 0.270124 | ||||||||
\(263\) | −4225.97 | −0.990817 | −0.495408 | − | 0.868660i | \(-0.664982\pi\) | ||||
−0.495408 | + | 0.868660i | \(0.664982\pi\) | |||||||
\(264\) | 2006.48 | 0.467765 | ||||||||
\(265\) | −2461.35 | −0.570564 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1916.19 | 0.439210 | ||||||||
\(268\) | −4965.28 | −1.13173 | ||||||||
\(269\) | −981.591 | −0.222486 | −0.111243 | − | 0.993793i | \(-0.535483\pi\) | ||||
−0.111243 | + | 0.993793i | \(0.535483\pi\) | |||||||
\(270\) | −492.175 | −0.110936 | ||||||||
\(271\) | −3884.42 | −0.870708 | −0.435354 | − | 0.900259i | \(-0.643377\pi\) | ||||
−0.435354 | + | 0.900259i | \(0.643377\pi\) | |||||||
\(272\) | 2003.66 | 0.446653 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1276.71 | −0.281493 | ||||||||
\(275\) | −1192.53 | −0.261500 | ||||||||
\(276\) | −1687.09 | −0.367938 | ||||||||
\(277\) | 3614.93 | 0.784116 | 0.392058 | − | 0.919941i | \(-0.371763\pi\) | ||||
0.392058 | + | 0.919941i | \(0.371763\pi\) | |||||||
\(278\) | −1406.68 | −0.303478 | ||||||||
\(279\) | 2442.05 | 0.524021 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 72.6835 | 0.0154304 | 0.00771518 | − | 0.999970i | \(-0.497544\pi\) | ||||
0.00771518 | + | 0.999970i | \(0.497544\pi\) | |||||||
\(282\) | 841.023 | 0.177596 | ||||||||
\(283\) | −1743.04 | −0.366125 | −0.183062 | − | 0.983101i | \(-0.558601\pi\) | ||||
−0.183062 | + | 0.983101i | \(0.558601\pi\) | |||||||
\(284\) | −5913.26 | −1.23552 | ||||||||
\(285\) | −644.065 | −0.133864 | ||||||||
\(286\) | 1759.72 | 0.363827 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1092.01 | −0.223427 | ||||||||
\(289\) | −3546.32 | −0.721825 | ||||||||
\(290\) | −630.668 | −0.127704 | ||||||||
\(291\) | 5912.34 | 1.19102 | ||||||||
\(292\) | −6292.59 | −1.26112 | ||||||||
\(293\) | 4989.29 | 0.994804 | 0.497402 | − | 0.867520i | \(-0.334287\pi\) | ||||
0.497402 | + | 0.867520i | \(0.334287\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −493.827 | −0.0974634 | ||||||||
\(296\) | −3480.33 | −0.683412 | ||||||||
\(297\) | 7283.78 | 1.42306 | ||||||||
\(298\) | 432.013 | 0.0839794 | ||||||||
\(299\) | −3040.29 | −0.588042 | ||||||||
\(300\) | −793.876 | −0.152782 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2158.82 | 0.411346 | ||||||||
\(303\) | −7635.98 | −1.44777 | ||||||||
\(304\) | −1667.48 | −0.314594 | ||||||||
\(305\) | −410.841 | −0.0771301 | ||||||||
\(306\) | −225.688 | −0.0421626 | ||||||||
\(307\) | −1664.61 | −0.309461 | −0.154731 | − | 0.987957i | \(-0.549451\pi\) | ||||
−0.154731 | + | 0.987957i | \(0.549451\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1707.30 | −0.314320 | ||||||||
\(310\) | −831.177 | −0.152283 | ||||||||
\(311\) | −545.623 | −0.0994838 | −0.0497419 | − | 0.998762i | \(-0.515840\pi\) | ||||
−0.0497419 | + | 0.998762i | \(0.515840\pi\) | |||||||
\(312\) | 2407.10 | 0.436779 | ||||||||
\(313\) | −213.564 | −0.0385667 | −0.0192833 | − | 0.999814i | \(-0.506138\pi\) | ||||
−0.0192833 | + | 0.999814i | \(0.506138\pi\) | |||||||
\(314\) | −1552.58 | −0.279035 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5835.66 | 1.03887 | ||||||||
\(317\) | −2683.93 | −0.475535 | −0.237767 | − | 0.971322i | \(-0.576416\pi\) | ||||
−0.237767 | + | 0.971322i | \(0.576416\pi\) | |||||||
\(318\) | −1328.67 | −0.234302 | ||||||||
\(319\) | 9333.37 | 1.63815 | ||||||||
\(320\) | −1796.28 | −0.313798 | ||||||||
\(321\) | −1549.60 | −0.269440 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1137.37 | −0.195929 | ||||||||
\(324\) | 2909.58 | 0.498899 | ||||||||
\(325\) | −1430.64 | −0.244177 | ||||||||
\(326\) | −2456.77 | −0.417387 | ||||||||
\(327\) | 4084.59 | 0.690760 | ||||||||
\(328\) | 2682.91 | 0.451642 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −643.744 | −0.107385 | ||||||||
\(331\) | −5067.52 | −0.841500 | −0.420750 | − | 0.907177i | \(-0.638233\pi\) | ||||
−0.420750 | + | 0.907177i | \(0.638233\pi\) | |||||||
\(332\) | 4650.80 | 0.768812 | ||||||||
\(333\) | −3280.66 | −0.539876 | ||||||||
\(334\) | −778.187 | −0.127487 | ||||||||
\(335\) | 3273.34 | 0.533856 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9353.21 | −1.51187 | −0.755937 | − | 0.654644i | \(-0.772818\pi\) | ||||
−0.755937 | + | 0.654644i | \(0.772818\pi\) | |||||||
\(338\) | 694.782 | 0.111808 | ||||||||
\(339\) | 8285.20 | 1.32741 | ||||||||
\(340\) | −1401.93 | −0.223618 | ||||||||
\(341\) | 12300.7 | 1.95344 | ||||||||
\(342\) | 187.822 | 0.0296966 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1776.81 | 0.278486 | ||||||||
\(345\) | 1112.21 | 0.173563 | ||||||||
\(346\) | −2090.77 | −0.324858 | ||||||||
\(347\) | 2349.34 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(348\) | 6213.28 | 0.957088 | ||||||||
\(349\) | 10472.6 | 1.60626 | 0.803128 | − | 0.595806i | \(-0.203167\pi\) | ||||
0.803128 | + | 0.595806i | \(0.203167\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8738.10 | 1.32879 | ||||||||
\(352\) | −5500.49 | −0.832889 | ||||||||
\(353\) | 7174.63 | 1.08178 | 0.540888 | − | 0.841095i | \(-0.318088\pi\) | ||||
0.540888 | + | 0.841095i | \(0.318088\pi\) | |||||||
\(354\) | −266.574 | −0.0400232 | ||||||||
\(355\) | 3898.29 | 0.582816 | ||||||||
\(356\) | −3471.14 | −0.516769 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 554.222 | 0.0818199 | ||||||||
\(359\) | −7534.13 | −1.10762 | −0.553811 | − | 0.832643i | \(-0.686827\pi\) | ||||
−0.553811 | + | 0.832643i | \(0.686827\pi\) | |||||||
\(360\) | 475.705 | 0.0696440 | ||||||||
\(361\) | −5912.46 | −0.862000 | ||||||||
\(362\) | 187.273 | 0.0271902 | ||||||||
\(363\) | 3954.15 | 0.571733 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4148.36 | 0.594891 | ||||||||
\(366\) | −221.777 | −0.0316734 | ||||||||
\(367\) | −5453.06 | −0.775606 | −0.387803 | − | 0.921742i | \(-0.626766\pi\) | ||||
−0.387803 | + | 0.921742i | \(0.626766\pi\) | |||||||
\(368\) | 2879.49 | 0.407891 | ||||||||
\(369\) | 2528.98 | 0.356785 | ||||||||
\(370\) | 1116.60 | 0.156891 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8188.68 | 1.14130 | ||||||||
\(373\) | 8231.29 | 1.14263 | 0.571314 | − | 0.820732i | \(-0.306434\pi\) | ||||
0.571314 | + | 0.820732i | \(0.306434\pi\) | |||||||
\(374\) | −1136.80 | −0.157173 | ||||||||
\(375\) | 523.359 | 0.0720698 | ||||||||
\(376\) | −3130.46 | −0.429365 | ||||||||
\(377\) | 11196.9 | 1.52963 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1670.06 | 0.226346 | 0.113173 | − | 0.993575i | \(-0.463898\pi\) | ||||
0.113173 | + | 0.993575i | \(0.463898\pi\) | |||||||
\(380\) | 1166.71 | 0.157502 | ||||||||
\(381\) | 5829.74 | 0.783901 | ||||||||
\(382\) | 3155.95 | 0.422703 | ||||||||
\(383\) | −3220.14 | −0.429612 | −0.214806 | − | 0.976657i | \(-0.568912\pi\) | ||||
−0.214806 | + | 0.976657i | \(0.568912\pi\) | |||||||
\(384\) | −4832.00 | −0.642140 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2287.68 | −0.301658 | ||||||||
\(387\) | 1674.87 | 0.219996 | ||||||||
\(388\) | −10710.1 | −1.40134 | ||||||||
\(389\) | 3522.23 | 0.459085 | 0.229543 | − | 0.973299i | \(-0.426277\pi\) | ||||
0.229543 | + | 0.973299i | \(0.426277\pi\) | |||||||
\(390\) | −772.277 | −0.100271 | ||||||||
\(391\) | 1964.07 | 0.254034 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7440.15 | 0.954977 | ||||||||
\(394\) | −419.090 | −0.0535875 | ||||||||
\(395\) | −3847.13 | −0.490051 | ||||||||
\(396\) | −3426.16 | −0.434775 | ||||||||
\(397\) | 5455.16 | 0.689639 | 0.344819 | − | 0.938669i | \(-0.387940\pi\) | ||||
0.344819 | + | 0.938669i | \(0.387940\pi\) | |||||||
\(398\) | −2614.11 | −0.329229 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1354.97 | 0.169372 | ||||||||
\(401\) | −1161.80 | −0.144682 | −0.0723409 | − | 0.997380i | \(-0.523047\pi\) | ||||
−0.0723409 | + | 0.997380i | \(0.523047\pi\) | |||||||
\(402\) | 1766.99 | 0.219227 | ||||||||
\(403\) | 14756.8 | 1.82404 | ||||||||
\(404\) | 13832.4 | 1.70344 | ||||||||
\(405\) | −1918.13 | −0.235339 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16524.8 | −2.01255 | ||||||||
\(408\) | −1555.02 | −0.188689 | ||||||||
\(409\) | 7398.65 | 0.894473 | 0.447237 | − | 0.894416i | \(-0.352408\pi\) | ||||
0.447237 | + | 0.894416i | \(0.352408\pi\) | |||||||
\(410\) | −860.765 | −0.103683 | ||||||||
\(411\) | −8292.02 | −0.995171 | ||||||||
\(412\) | 3092.74 | 0.369826 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −324.341 | −0.0385036 | ||||||||
\(415\) | −3066.02 | −0.362662 | ||||||||
\(416\) | −6598.74 | −0.777716 | ||||||||
\(417\) | −9136.12 | −1.07290 | ||||||||
\(418\) | 946.069 | 0.110703 | ||||||||
\(419\) | −2134.46 | −0.248867 | −0.124433 | − | 0.992228i | \(-0.539711\pi\) | ||||
−0.124433 | + | 0.992228i | \(0.539711\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3902.36 | −0.451756 | −0.225878 | − | 0.974156i | \(-0.572525\pi\) | ||||
−0.225878 | + | 0.974156i | \(0.572525\pi\) | |||||||
\(422\) | −1011.88 | −0.116724 | ||||||||
\(423\) | −2950.86 | −0.339186 | ||||||||
\(424\) | 4945.58 | 0.566459 | ||||||||
\(425\) | 924.214 | 0.105485 | ||||||||
\(426\) | 2104.34 | 0.239333 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2807.06 | 0.317020 | ||||||||
\(429\) | 11429.1 | 1.28625 | ||||||||
\(430\) | −570.059 | −0.0639319 | ||||||||
\(431\) | −3618.13 | −0.404360 | −0.202180 | − | 0.979348i | \(-0.564803\pi\) | ||||
−0.202180 | + | 0.979348i | \(0.564803\pi\) | |||||||
\(432\) | −8275.95 | −0.921706 | ||||||||
\(433\) | −4222.37 | −0.468624 | −0.234312 | − | 0.972161i | \(-0.575284\pi\) | ||||
−0.234312 | + | 0.972161i | \(0.575284\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4096.08 | −0.451475 | ||||||||
\(436\) | −7399.14 | −0.812740 | ||||||||
\(437\) | −1634.54 | −0.178926 | ||||||||
\(438\) | 2239.34 | 0.244291 | ||||||||
\(439\) | −13518.0 | −1.46965 | −0.734826 | − | 0.678256i | \(-0.762736\pi\) | ||||
−0.734826 | + | 0.678256i | \(0.762736\pi\) | |||||||
\(440\) | 2396.15 | 0.259618 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1363.78 | −0.146762 | ||||||||
\(443\) | 16591.2 | 1.77939 | 0.889695 | − | 0.456555i | \(-0.150917\pi\) | ||||
0.889695 | + | 0.456555i | \(0.150917\pi\) | |||||||
\(444\) | −11000.7 | −1.17583 | ||||||||
\(445\) | 2288.33 | 0.243769 | ||||||||
\(446\) | −3045.23 | −0.323309 | ||||||||
\(447\) | 2805.85 | 0.296895 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8354.32 | 0.878095 | 0.439048 | − | 0.898464i | \(-0.355316\pi\) | ||||
0.439048 | + | 0.898464i | \(0.355316\pi\) | |||||||
\(450\) | −152.622 | −0.0159881 | ||||||||
\(451\) | 12738.6 | 1.33002 | ||||||||
\(452\) | −15008.5 | −1.56181 | ||||||||
\(453\) | 14021.2 | 1.45424 | ||||||||
\(454\) | −2375.54 | −0.245572 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1294.12 | 0.132900 | ||||||||
\(457\) | −1280.34 | −0.131054 | −0.0655269 | − | 0.997851i | \(-0.520873\pi\) | ||||
−0.0655269 | + | 0.997851i | \(0.520873\pi\) | |||||||
\(458\) | −2163.94 | −0.220774 | ||||||||
\(459\) | −5644.94 | −0.574038 | ||||||||
\(460\) | −2014.73 | −0.204212 | ||||||||
\(461\) | −6986.72 | −0.705865 | −0.352932 | − | 0.935649i | \(-0.614815\pi\) | ||||
−0.352932 | + | 0.935649i | \(0.614815\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5587.32 | −0.560831 | −0.280416 | − | 0.959879i | \(-0.590472\pi\) | ||||
−0.280416 | + | 0.959879i | \(0.590472\pi\) | |||||||
\(464\) | −10604.7 | −1.06102 | ||||||||
\(465\) | −5398.35 | −0.538371 | ||||||||
\(466\) | 1491.73 | 0.148289 | ||||||||
\(467\) | −9933.83 | −0.984332 | −0.492166 | − | 0.870501i | \(-0.663795\pi\) | ||||
−0.492166 | + | 0.870501i | \(0.663795\pi\) | |||||||
\(468\) | −4110.24 | −0.405974 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1004.36 | 0.0985691 | ||||||||
\(471\) | −10083.7 | −0.986481 | ||||||||
\(472\) | 992.243 | 0.0967620 | ||||||||
\(473\) | 8436.41 | 0.820099 | ||||||||
\(474\) | −2076.73 | −0.201239 | ||||||||
\(475\) | −769.148 | −0.0742967 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4661.84 | 0.447486 | ||||||||
\(478\) | 606.729 | 0.0580568 | ||||||||
\(479\) | 5068.62 | 0.483489 | 0.241744 | − | 0.970340i | \(-0.422280\pi\) | ||||
0.241744 | + | 0.970340i | \(0.422280\pi\) | |||||||
\(480\) | 2413.96 | 0.229546 | ||||||||
\(481\) | −19824.3 | −1.87923 | ||||||||
\(482\) | −3634.68 | −0.343476 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7162.86 | −0.672695 | ||||||||
\(485\) | 7060.56 | 0.661038 | ||||||||
\(486\) | 1622.32 | 0.151419 | ||||||||
\(487\) | 264.353 | 0.0245975 | 0.0122988 | − | 0.999924i | \(-0.496085\pi\) | ||||
0.0122988 | + | 0.999924i | \(0.496085\pi\) | |||||||
\(488\) | 825.500 | 0.0765751 | ||||||||
\(489\) | −15956.3 | −1.47560 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7459.47 | −0.685623 | −0.342812 | − | 0.939404i | \(-0.611379\pi\) | ||||
−0.342812 | + | 0.939404i | \(0.611379\pi\) | |||||||
\(492\) | 8480.17 | 0.777064 | ||||||||
\(493\) | −7233.37 | −0.660800 | ||||||||
\(494\) | 1134.97 | 0.103370 | ||||||||
\(495\) | 2258.68 | 0.205091 | ||||||||
\(496\) | −13976.3 | −1.26523 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1655.07 | −0.148927 | ||||||||
\(499\) | 7206.67 | 0.646523 | 0.323261 | − | 0.946310i | \(-0.395221\pi\) | ||||
0.323261 | + | 0.946310i | \(0.395221\pi\) | |||||||
\(500\) | −948.054 | −0.0847965 | ||||||||
\(501\) | −5054.19 | −0.450707 | ||||||||
\(502\) | −235.827 | −0.0209670 | ||||||||
\(503\) | 10886.7 | 0.965037 | 0.482519 | − | 0.875886i | \(-0.339722\pi\) | ||||
0.482519 | + | 0.875886i | \(0.339722\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9118.95 | −0.803541 | ||||||||
\(506\) | −1633.72 | −0.143533 | ||||||||
\(507\) | 4512.49 | 0.395279 | ||||||||
\(508\) | −10560.4 | −0.922330 | ||||||||
\(509\) | 7504.97 | 0.653540 | 0.326770 | − | 0.945104i | \(-0.394040\pi\) | ||||
0.326770 | + | 0.945104i | \(0.394040\pi\) | |||||||
\(510\) | 498.902 | 0.0433172 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 10605.8 | 0.915459 | ||||||||
\(513\) | 4697.82 | 0.404316 | ||||||||
\(514\) | 4046.11 | 0.347210 | ||||||||
\(515\) | −2038.87 | −0.174453 | ||||||||
\(516\) | 5616.17 | 0.479144 | ||||||||
\(517\) | −14863.7 | −1.26442 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13579.2 | −1.14848 | ||||||||
\(520\) | 2874.58 | 0.242420 | ||||||||
\(521\) | 22264.8 | 1.87224 | 0.936120 | − | 0.351681i | \(-0.114390\pi\) | ||||
0.936120 | + | 0.351681i | \(0.114390\pi\) | |||||||
\(522\) | 1194.50 | 0.100156 | ||||||||
\(523\) | −11286.7 | −0.943655 | −0.471828 | − | 0.881691i | \(-0.656405\pi\) | ||||
−0.471828 | + | 0.881691i | \(0.656405\pi\) | |||||||
\(524\) | −13477.7 | −1.12362 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2724.27 | −0.225824 | ||||||||
\(527\) | −9533.09 | −0.787985 | ||||||||
\(528\) | −10824.6 | −0.892197 | ||||||||
\(529\) | −9344.40 | −0.768012 | ||||||||
\(530\) | −1586.70 | −0.130042 | ||||||||
\(531\) | 935.316 | 0.0764393 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15282.1 | 1.24191 | ||||||||
\(534\) | 1235.27 | 0.100104 | ||||||||
\(535\) | −1850.54 | −0.149544 | ||||||||
\(536\) | −6577.10 | −0.530014 | ||||||||
\(537\) | 3599.57 | 0.289261 | ||||||||
\(538\) | −632.781 | −0.0507084 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5790.55 | 0.461455 | ||||||||
\(541\) | 16406.8 | 1.30385 | 0.651924 | − | 0.758284i | \(-0.273962\pi\) | ||||
0.651924 | + | 0.758284i | \(0.273962\pi\) | |||||||
\(542\) | −2504.08 | −0.198450 | ||||||||
\(543\) | 1216.30 | 0.0961263 | ||||||||
\(544\) | 4262.88 | 0.335974 | ||||||||
\(545\) | 4877.85 | 0.383384 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8692.48 | −0.679458 | −0.339729 | − | 0.940523i | \(-0.610335\pi\) | ||||
−0.339729 | + | 0.940523i | \(0.610335\pi\) | |||||||
\(548\) | 15020.8 | 1.17091 | ||||||||
\(549\) | 778.139 | 0.0604921 | ||||||||
\(550\) | −768.764 | −0.0596004 | ||||||||
\(551\) | 6019.74 | 0.465426 | ||||||||
\(552\) | −2234.75 | −0.172314 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2330.36 | 0.178714 | ||||||||
\(555\) | 7252.15 | 0.554661 | ||||||||
\(556\) | 16549.9 | 1.26236 | ||||||||
\(557\) | −13935.7 | −1.06010 | −0.530049 | − | 0.847967i | \(-0.677826\pi\) | ||||
−0.530049 | + | 0.847967i | \(0.677826\pi\) | |||||||
\(558\) | 1574.26 | 0.119434 | ||||||||
\(559\) | 10120.9 | 0.765773 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7383.34 | −0.555659 | ||||||||
\(562\) | 46.8553 | 0.00351685 | ||||||||
\(563\) | −22263.6 | −1.66661 | −0.833304 | − | 0.552815i | \(-0.813553\pi\) | ||||
−0.833304 | + | 0.552815i | \(0.813553\pi\) | |||||||
\(564\) | −9894.82 | −0.738736 | ||||||||
\(565\) | 9894.26 | 0.736734 | ||||||||
\(566\) | −1123.65 | −0.0834462 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7832.81 | −0.578622 | ||||||||
\(569\) | 9525.66 | 0.701822 | 0.350911 | − | 0.936409i | \(-0.385872\pi\) | ||||
0.350911 | + | 0.936409i | \(0.385872\pi\) | |||||||
\(570\) | −415.195 | −0.0305099 | ||||||||
\(571\) | 7669.99 | 0.562135 | 0.281068 | − | 0.959688i | \(-0.409311\pi\) | ||||
0.281068 | + | 0.959688i | \(0.409311\pi\) | |||||||
\(572\) | −20703.5 | −1.51339 | ||||||||
\(573\) | 20497.3 | 1.49439 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1328.20 | 0.0963304 | ||||||||
\(576\) | 3402.19 | 0.246108 | ||||||||
\(577\) | 3907.15 | 0.281901 | 0.140950 | − | 0.990017i | \(-0.454984\pi\) | ||||
0.140950 | + | 0.990017i | \(0.454984\pi\) | |||||||
\(578\) | −2286.13 | −0.164516 | ||||||||
\(579\) | −14858.1 | −1.06646 | ||||||||
\(580\) | 7419.95 | 0.531201 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3811.38 | 0.271455 | ||||||||
\(583\) | 23481.9 | 1.66813 | ||||||||
\(584\) | −8335.28 | −0.590610 | ||||||||
\(585\) | 2709.66 | 0.191505 | ||||||||
\(586\) | 3216.34 | 0.226733 | ||||||||
\(587\) | −19891.6 | −1.39866 | −0.699331 | − | 0.714798i | \(-0.746519\pi\) | ||||
−0.699331 | + | 0.714798i | \(0.746519\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7933.61 | 0.555007 | ||||||||
\(590\) | −318.344 | −0.0222136 | ||||||||
\(591\) | −2721.92 | −0.189450 | ||||||||
\(592\) | 18775.8 | 1.30351 | ||||||||
\(593\) | 4780.36 | 0.331038 | 0.165519 | − | 0.986207i | \(-0.447070\pi\) | ||||
0.165519 | + | 0.986207i | \(0.447070\pi\) | |||||||
\(594\) | 4695.48 | 0.324340 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5082.74 | −0.349324 | ||||||||
\(597\) | −16978.2 | −1.16394 | ||||||||
\(598\) | −1959.92 | −0.134025 | ||||||||
\(599\) | 11085.6 | 0.756170 | 0.378085 | − | 0.925771i | \(-0.376583\pi\) | ||||
0.378085 | + | 0.925771i | \(0.376583\pi\) | |||||||
\(600\) | −1051.58 | −0.0715511 | ||||||||
\(601\) | −1573.44 | −0.106792 | −0.0533958 | − | 0.998573i | \(-0.517005\pi\) | ||||
−0.0533958 | + | 0.998573i | \(0.517005\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6199.76 | −0.418696 | ||||||||
\(604\) | −25399.1 | −1.71105 | ||||||||
\(605\) | 4722.08 | 0.317322 | ||||||||
\(606\) | −4922.52 | −0.329973 | ||||||||
\(607\) | 8542.73 | 0.571233 | 0.285617 | − | 0.958344i | \(-0.407802\pi\) | ||||
0.285617 | + | 0.958344i | \(0.407802\pi\) | |||||||
\(608\) | −3547.65 | −0.236639 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −264.848 | −0.0175793 | ||||||||
\(611\) | −17831.4 | −1.18066 | ||||||||
\(612\) | 2655.27 | 0.175381 | ||||||||
\(613\) | 15068.2 | 0.992817 | 0.496409 | − | 0.868089i | \(-0.334652\pi\) | ||||
0.496409 | + | 0.868089i | \(0.334652\pi\) | |||||||
\(614\) | −1073.09 | −0.0705316 | ||||||||
\(615\) | −5590.52 | −0.366555 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2524.58 | 0.164725 | 0.0823627 | − | 0.996602i | \(-0.473753\pi\) | ||||
0.0823627 | + | 0.996602i | \(0.473753\pi\) | |||||||
\(618\) | −1100.61 | −0.0716391 | ||||||||
\(619\) | −21238.9 | −1.37910 | −0.689551 | − | 0.724237i | \(-0.742192\pi\) | ||||
−0.689551 | + | 0.724237i | \(0.742192\pi\) | |||||||
\(620\) | 9778.99 | 0.633441 | ||||||||
\(621\) | −8112.44 | −0.524221 | ||||||||
\(622\) | −351.735 | −0.0226741 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −12985.9 | −0.833095 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −137.674 | −0.00879002 | ||||||||
\(627\) | 6144.55 | 0.391371 | ||||||||
\(628\) | 18266.4 | 1.16068 | ||||||||
\(629\) | 12806.8 | 0.811827 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8885.83 | −0.560601 | −0.280300 | − | 0.959912i | \(-0.590434\pi\) | ||||
−0.280300 | + | 0.959912i | \(0.590434\pi\) | |||||||
\(632\) | 7730.02 | 0.486525 | ||||||||
\(633\) | −6571.99 | −0.412659 | ||||||||
\(634\) | −1730.19 | −0.108383 | ||||||||
\(635\) | 6961.92 | 0.435079 | ||||||||
\(636\) | 15632.1 | 0.974609 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6016.74 | 0.373362 | ||||||||
\(639\) | −7383.42 | −0.457095 | ||||||||
\(640\) | −5770.41 | −0.356399 | ||||||||
\(641\) | 3655.63 | 0.225255 | 0.112628 | − | 0.993637i | \(-0.464073\pi\) | ||||
0.112628 | + | 0.993637i | \(0.464073\pi\) | |||||||
\(642\) | −998.946 | −0.0614100 | ||||||||
\(643\) | 4221.22 | 0.258894 | 0.129447 | − | 0.991586i | \(-0.458680\pi\) | ||||
0.129447 | + | 0.991586i | \(0.458680\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3702.43 | −0.226020 | ||||||||
\(646\) | −733.205 | −0.0446557 | ||||||||
\(647\) | 103.679 | 0.00629989 | 0.00314995 | − | 0.999995i | \(-0.498997\pi\) | ||||
0.00314995 | + | 0.999995i | \(0.498997\pi\) | |||||||
\(648\) | 3854.08 | 0.233646 | ||||||||
\(649\) | 4711.24 | 0.284949 | ||||||||
\(650\) | −922.259 | −0.0556523 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 28904.5 | 1.73618 | ||||||||
\(653\) | 4476.11 | 0.268245 | 0.134122 | − | 0.990965i | \(-0.457179\pi\) | ||||
0.134122 | + | 0.990965i | \(0.457179\pi\) | |||||||
\(654\) | 2633.12 | 0.157436 | ||||||||
\(655\) | 8885.09 | 0.530029 | ||||||||
\(656\) | −14473.8 | −0.861445 | ||||||||
\(657\) | −7857.07 | −0.466566 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12022.0 | 0.710641 | 0.355321 | − | 0.934745i | \(-0.384372\pi\) | ||||
0.355321 | + | 0.934745i | \(0.384372\pi\) | |||||||
\(660\) | 7573.79 | 0.446681 | ||||||||
\(661\) | 13451.0 | 0.791504 | 0.395752 | − | 0.918357i | \(-0.370484\pi\) | ||||
0.395752 | + | 0.918357i | \(0.370484\pi\) | |||||||
\(662\) | −3266.77 | −0.191792 | ||||||||
\(663\) | −8857.54 | −0.518851 | ||||||||
\(664\) | 6160.53 | 0.360053 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2114.87 | −0.123047 | ||||||||
\(667\) | −10395.2 | −0.603454 | ||||||||
\(668\) | 9155.55 | 0.530297 | ||||||||
\(669\) | −19778.2 | −1.14300 | ||||||||
\(670\) | 2110.15 | 0.121675 | ||||||||
\(671\) | 3919.53 | 0.225502 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9774.83 | 0.559869 | 0.279935 | − | 0.960019i | \(-0.409687\pi\) | ||||
0.279935 | + | 0.960019i | \(0.409687\pi\) | |||||||
\(674\) | −6029.53 | −0.344583 | ||||||||
\(675\) | −3817.39 | −0.217676 | ||||||||
\(676\) | −8174.27 | −0.465081 | ||||||||
\(677\) | 23857.4 | 1.35438 | 0.677190 | − | 0.735808i | \(-0.263198\pi\) | ||||
0.677190 | + | 0.735808i | \(0.263198\pi\) | |||||||
\(678\) | 5341.04 | 0.302539 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1857.02 | −0.104726 | ||||||||
\(681\) | −15428.7 | −0.868179 | ||||||||
\(682\) | 7929.65 | 0.445223 | ||||||||
\(683\) | 11919.4 | 0.667763 | 0.333881 | − | 0.942615i | \(-0.391642\pi\) | ||||
0.333881 | + | 0.942615i | \(0.391642\pi\) | |||||||
\(684\) | −2209.77 | −0.123527 | ||||||||
\(685\) | −9902.40 | −0.552338 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14054.4 | −0.780508 | ||||||||
\(688\) | −9585.59 | −0.531173 | ||||||||
\(689\) | 28170.5 | 1.55763 | ||||||||
\(690\) | 716.981 | 0.0395580 | ||||||||
\(691\) | −8203.58 | −0.451634 | −0.225817 | − | 0.974170i | \(-0.572505\pi\) | ||||
−0.225817 | + | 0.974170i | \(0.572505\pi\) | |||||||
\(692\) | 24598.4 | 1.35129 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1514.50 | 0.0828380 | ||||||||
\(695\) | −10910.4 | −0.595477 | ||||||||
\(696\) | 8230.22 | 0.448227 | ||||||||
\(697\) | −9872.44 | −0.536507 | ||||||||
\(698\) | 6751.12 | 0.366094 | ||||||||
\(699\) | 9688.49 | 0.524252 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 449.084 | 0.0241964 | 0.0120982 | − | 0.999927i | \(-0.496149\pi\) | ||||
0.0120982 | + | 0.999927i | \(0.496149\pi\) | |||||||
\(702\) | 5633.00 | 0.302855 | ||||||||
\(703\) | −10658.0 | −0.571800 | ||||||||
\(704\) | 17137.0 | 0.917438 | ||||||||
\(705\) | 6523.11 | 0.348475 | ||||||||
\(706\) | 4625.11 | 0.246556 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3136.30 | 0.166482 | ||||||||
\(709\) | 1897.64 | 0.100518 | 0.0502590 | − | 0.998736i | \(-0.483995\pi\) | ||||
0.0502590 | + | 0.998736i | \(0.483995\pi\) | |||||||
\(710\) | 2513.02 | 0.132834 | ||||||||
\(711\) | 7286.53 | 0.384341 | ||||||||
\(712\) | −4597.93 | −0.242015 | ||||||||
\(713\) | −13700.2 | −0.719601 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13648.7 | 0.713891 | ||||||||
\(716\) | −6520.54 | −0.340341 | ||||||||
\(717\) | 3940.60 | 0.205250 | ||||||||
\(718\) | −4856.86 | −0.252446 | ||||||||
\(719\) | 6494.70 | 0.336873 | 0.168436 | − | 0.985713i | \(-0.446128\pi\) | ||||
0.168436 | + | 0.985713i | \(0.446128\pi\) | |||||||
\(720\) | −2566.35 | −0.132836 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3811.45 | −0.196465 | ||||||||
\(723\) | −23606.6 | −1.21430 | ||||||||
\(724\) | −2203.31 | −0.113101 | ||||||||
\(725\) | −4891.57 | −0.250577 | ||||||||
\(726\) | 2549.04 | 0.130308 | ||||||||
\(727\) | −18311.2 | −0.934148 | −0.467074 | − | 0.884218i | \(-0.654692\pi\) | ||||
−0.467074 | + | 0.884218i | \(0.654692\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20894.5 | 1.06155 | ||||||||
\(730\) | 2674.23 | 0.135586 | ||||||||
\(731\) | −6538.23 | −0.330814 | ||||||||
\(732\) | 2609.25 | 0.131750 | ||||||||
\(733\) | 21233.3 | 1.06994 | 0.534972 | − | 0.844870i | \(-0.320322\pi\) | ||||
0.534972 | + | 0.844870i | \(0.320322\pi\) | |||||||
\(734\) | −3515.30 | −0.176774 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6126.27 | 0.306817 | ||||||||
\(737\) | −31228.5 | −1.56081 | ||||||||
\(738\) | 1630.30 | 0.0813175 | ||||||||
\(739\) | −22023.5 | −1.09628 | −0.548138 | − | 0.836388i | \(-0.684663\pi\) | ||||
−0.548138 | + | 0.836388i | \(0.684663\pi\) | |||||||
\(740\) | −13137.1 | −0.652608 | ||||||||
\(741\) | 7371.40 | 0.365446 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9436.77 | 0.465951 | 0.232975 | − | 0.972483i | \(-0.425154\pi\) | ||||
0.232975 | + | 0.972483i | \(0.425154\pi\) | |||||||
\(744\) | 10846.9 | 0.534497 | ||||||||
\(745\) | 3350.77 | 0.164782 | ||||||||
\(746\) | 5306.29 | 0.260425 | ||||||||
\(747\) | 5807.09 | 0.284431 | ||||||||
\(748\) | 13374.8 | 0.653783 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 337.383 | 0.0164260 | ||||||||
\(751\) | −39161.8 | −1.90284 | −0.951421 | − | 0.307893i | \(-0.900376\pi\) | ||||
−0.951421 | + | 0.307893i | \(0.900376\pi\) | |||||||
\(752\) | 16888.3 | 0.818954 | ||||||||
\(753\) | −1531.65 | −0.0741255 | ||||||||
\(754\) | 7218.07 | 0.348629 | ||||||||
\(755\) | 16744.2 | 0.807132 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20340.6 | 0.976607 | 0.488303 | − | 0.872674i | \(-0.337616\pi\) | ||||
0.488303 | + | 0.872674i | \(0.337616\pi\) | |||||||
\(758\) | 1076.60 | 0.0515883 | ||||||||
\(759\) | −10610.7 | −0.507438 | ||||||||
\(760\) | 1545.44 | 0.0737621 | ||||||||
\(761\) | 3307.90 | 0.157570 | 0.0787852 | − | 0.996892i | \(-0.474896\pi\) | ||||
0.0787852 | + | 0.996892i | \(0.474896\pi\) | |||||||
\(762\) | 3758.13 | 0.178665 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −37130.4 | −1.75829 | ||||||||
\(765\) | −1750.48 | −0.0827303 | ||||||||
\(766\) | −2075.85 | −0.0979160 | ||||||||
\(767\) | 5651.91 | 0.266074 | ||||||||
\(768\) | 8918.37 | 0.419029 | ||||||||
\(769\) | 17234.0 | 0.808159 | 0.404079 | − | 0.914724i | \(-0.367592\pi\) | ||||
0.404079 | + | 0.914724i | \(0.367592\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26278.7 | 1.22750 | ||||||||
\(772\) | 26915.1 | 1.25479 | ||||||||
\(773\) | −8726.33 | −0.406034 | −0.203017 | − | 0.979175i | \(-0.565075\pi\) | ||||
−0.203017 | + | 0.979175i | \(0.565075\pi\) | |||||||
\(774\) | 1079.70 | 0.0501409 | ||||||||
\(775\) | −6446.75 | −0.298806 | ||||||||
\(776\) | −14186.7 | −0.656281 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2270.60 | 0.104634 | ||||||||
\(779\) | 8216.03 | 0.377882 | ||||||||
\(780\) | 9086.01 | 0.417091 | ||||||||
\(781\) | −37190.7 | −1.70395 | ||||||||
\(782\) | 1266.14 | 0.0578989 | ||||||||
\(783\) | 29876.8 | 1.36362 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12042.0 | −0.547515 | ||||||||
\(786\) | 4796.28 | 0.217656 | ||||||||
\(787\) | −10642.1 | −0.482018 | −0.241009 | − | 0.970523i | \(-0.577478\pi\) | ||||
−0.241009 | + | 0.970523i | \(0.577478\pi\) | |||||||
\(788\) | 4930.69 | 0.222904 | ||||||||
\(789\) | −17693.6 | −0.798365 | ||||||||
\(790\) | −2480.05 | −0.111691 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4538.35 | −0.203615 | ||||||||
\(793\) | 4702.12 | 0.210564 | ||||||||
\(794\) | 3516.66 | 0.157181 | ||||||||
\(795\) | −10305.4 | −0.459740 | ||||||||
\(796\) | 30755.5 | 1.36947 | ||||||||
\(797\) | 29234.1 | 1.29928 | 0.649640 | − | 0.760242i | \(-0.274920\pi\) | ||||
0.649640 | + | 0.760242i | \(0.274920\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11519.3 | 0.510044 | ||||||||
\(800\) | 2882.78 | 0.127402 | ||||||||
\(801\) | −4334.14 | −0.191185 | ||||||||
\(802\) | −748.950 | −0.0329755 | ||||||||
\(803\) | −39576.5 | −1.73926 | ||||||||
\(804\) | −20789.0 | −0.911906 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9512.93 | 0.415730 | ||||||||
\(807\) | −4109.80 | −0.179271 | ||||||||
\(808\) | 18322.7 | 0.797758 | ||||||||
\(809\) | 36211.2 | 1.57369 | 0.786846 | − | 0.617150i | \(-0.211713\pi\) | ||||
0.786846 | + | 0.617150i | \(0.211713\pi\) | |||||||
\(810\) | −1236.52 | −0.0536380 | ||||||||
\(811\) | −27995.2 | −1.21214 | −0.606069 | − | 0.795412i | \(-0.707254\pi\) | ||||
−0.606069 | + | 0.795412i | \(0.707254\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16263.6 | −0.701585 | ||||||||
\(814\) | −10652.7 | −0.458694 | ||||||||
\(815\) | −19055.2 | −0.818985 | ||||||||
\(816\) | 8389.07 | 0.359897 | ||||||||
\(817\) | 5441.23 | 0.233005 | ||||||||
\(818\) | 4769.52 | 0.203866 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10127.1 | 0.431285 | ||||||||
\(821\) | 44805.7 | 1.90467 | 0.952333 | − | 0.305060i | \(-0.0986766\pi\) | ||||
0.952333 | + | 0.305060i | \(0.0986766\pi\) | |||||||
\(822\) | −5345.44 | −0.226817 | ||||||||
\(823\) | −15850.9 | −0.671360 | −0.335680 | − | 0.941976i | \(-0.608966\pi\) | ||||
−0.335680 | + | 0.941976i | \(0.608966\pi\) | |||||||
\(824\) | 4096.70 | 0.173198 | ||||||||
\(825\) | −4992.99 | −0.210707 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45013.9 | −1.89273 | −0.946363 | − | 0.323104i | \(-0.895274\pi\) | ||||
−0.946363 | + | 0.323104i | \(0.895274\pi\) | |||||||
\(828\) | 3815.94 | 0.160161 | ||||||||
\(829\) | 5655.83 | 0.236954 | 0.118477 | − | 0.992957i | \(-0.462199\pi\) | ||||
0.118477 | + | 0.992957i | \(0.462199\pi\) | |||||||
\(830\) | −1976.50 | −0.0826571 | ||||||||
\(831\) | 15135.3 | 0.631812 | ||||||||
\(832\) | 20558.7 | 0.856664 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −5889.58 | −0.244532 | ||||||||
\(835\) | −6035.75 | −0.250151 | ||||||||
\(836\) | −11130.7 | −0.460483 | ||||||||
\(837\) | 39375.7 | 1.62607 | ||||||||
\(838\) | −1375.97 | −0.0567211 | ||||||||
\(839\) | −22037.0 | −0.906797 | −0.453398 | − | 0.891308i | \(-0.649789\pi\) | ||||
−0.453398 | + | 0.891308i | \(0.649789\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13894.9 | 0.569719 | ||||||||
\(842\) | −2515.65 | −0.102963 | ||||||||
\(843\) | 304.317 | 0.0124332 | ||||||||
\(844\) | 11905.0 | 0.485530 | ||||||||
\(845\) | 5388.85 | 0.219387 | ||||||||
\(846\) | −1902.27 | −0.0773065 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −26680.5 | −1.08044 | ||||||||
\(849\) | −7297.91 | −0.295010 | ||||||||
\(850\) | 595.793 | 0.0240418 | ||||||||
\(851\) | 18404.8 | 0.741374 | ||||||||
\(852\) | −24758.1 | −0.995537 | ||||||||
\(853\) | −44486.7 | −1.78569 | −0.892846 | − | 0.450362i | \(-0.851295\pi\) | ||||
−0.892846 | + | 0.450362i | \(0.851295\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1456.78 | 0.0582699 | ||||||||
\(856\) | 3718.29 | 0.148468 | ||||||||
\(857\) | −38559.6 | −1.53696 | −0.768478 | − | 0.639877i | \(-0.778985\pi\) | ||||
−0.768478 | + | 0.639877i | \(0.778985\pi\) | |||||||
\(858\) | 7367.72 | 0.293158 | ||||||||
\(859\) | 8426.01 | 0.334682 | 0.167341 | − | 0.985899i | \(-0.446482\pi\) | ||||
0.167341 | + | 0.985899i | \(0.446482\pi\) | |||||||
\(860\) | 6706.88 | 0.265933 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2332.42 | −0.0921608 | ||||||||
\(863\) | −20054.3 | −0.791029 | −0.395514 | − | 0.918460i | \(-0.629434\pi\) | ||||
−0.395514 | + | 0.918460i | \(0.629434\pi\) | |||||||
\(864\) | −17607.5 | −0.693309 | ||||||||
\(865\) | −16216.4 | −0.637427 | ||||||||
\(866\) | −2721.94 | −0.106808 | ||||||||
\(867\) | −14848.0 | −0.581621 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36702.6 | 1.43274 | ||||||||
\(870\) | −2640.53 | −0.102899 | ||||||||
\(871\) | −37463.8 | −1.45742 | ||||||||
\(872\) | −9801.04 | −0.380625 | ||||||||
\(873\) | −13372.8 | −0.518444 | ||||||||
\(874\) | −1053.70 | −0.0407803 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −26346.3 | −1.01616 | ||||||||
\(877\) | 47082.1 | 1.81283 | 0.906414 | − | 0.422391i | \(-0.138809\pi\) | ||||
0.906414 | + | 0.422391i | \(0.138809\pi\) | |||||||
\(878\) | −8714.32 | −0.334959 | ||||||||
\(879\) | 20889.5 | 0.801577 | ||||||||
\(880\) | −12926.8 | −0.495185 | ||||||||
\(881\) | −9467.24 | −0.362042 | −0.181021 | − | 0.983479i | \(-0.557940\pi\) | ||||
−0.181021 | + | 0.983479i | \(0.557940\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3049.49 | −0.116221 | −0.0581106 | − | 0.998310i | \(-0.518508\pi\) | ||||
−0.0581106 | + | 0.998310i | \(0.518508\pi\) | |||||||
\(884\) | 16045.2 | 0.610475 | ||||||||
\(885\) | −2067.59 | −0.0785325 | ||||||||
\(886\) | 10695.5 | 0.405554 | ||||||||
\(887\) | −19468.6 | −0.736968 | −0.368484 | − | 0.929634i | \(-0.620123\pi\) | ||||
−0.368484 | + | 0.929634i | \(0.620123\pi\) | |||||||
\(888\) | −14571.7 | −0.550669 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1475.17 | 0.0555592 | ||||||||
\(891\) | 18299.4 | 0.688052 | ||||||||
\(892\) | 35827.8 | 1.34485 | ||||||||
\(893\) | −9586.61 | −0.359243 | ||||||||
\(894\) | 1808.79 | 0.0676676 | ||||||||
\(895\) | 4298.64 | 0.160545 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12729.3 | −0.473823 | ||||||||
\(898\) | 5385.60 | 0.200133 | ||||||||
\(899\) | 50455.6 | 1.87184 | ||||||||
\(900\) | 1795.63 | 0.0665048 | ||||||||
\(901\) | −18198.5 | −0.672898 | ||||||||
\(902\) | 8211.92 | 0.303134 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19880.5 | −0.731432 | ||||||||
\(905\) | 1452.52 | 0.0533518 | ||||||||
\(906\) | 9038.73 | 0.331448 | ||||||||
\(907\) | −32014.2 | −1.17201 | −0.586006 | − | 0.810307i | \(-0.699301\pi\) | ||||
−0.586006 | + | 0.810307i | \(0.699301\pi\) | |||||||
\(908\) | 27948.8 | 1.02149 | ||||||||
\(909\) | 17271.4 | 0.630206 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20921.1 | 0.760866 | 0.380433 | − | 0.924809i | \(-0.375775\pi\) | ||||
0.380433 | + | 0.924809i | \(0.375775\pi\) | |||||||
\(912\) | −6981.54 | −0.253489 | ||||||||
\(913\) | 29250.6 | 1.06030 | ||||||||
\(914\) | −825.366 | −0.0298694 | ||||||||
\(915\) | −1720.14 | −0.0621487 | ||||||||
\(916\) | 25459.2 | 0.918337 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3639.00 | −0.130833 | ||||||||
\(919\) | 43467.4 | 1.56024 | 0.780118 | − | 0.625632i | \(-0.215159\pi\) | ||||
0.780118 | + | 0.625632i | \(0.215159\pi\) | |||||||
\(920\) | −2668.75 | −0.0956372 | ||||||||
\(921\) | −6969.53 | −0.249353 | ||||||||
\(922\) | −4503.97 | −0.160879 | ||||||||
\(923\) | −44616.4 | −1.59108 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8660.58 | 0.307847 | ||||||||
\(926\) | −3601.85 | −0.127823 | ||||||||
\(927\) | 3861.66 | 0.136822 | ||||||||
\(928\) | −22562.1 | −0.798099 | ||||||||
\(929\) | −18542.1 | −0.654840 | −0.327420 | − | 0.944879i | \(-0.606179\pi\) | ||||
−0.327420 | + | 0.944879i | \(0.606179\pi\) | |||||||
\(930\) | −3480.04 | −0.122704 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −17550.5 | −0.616830 | ||||||||
\(933\) | −2284.46 | −0.0801605 | ||||||||
\(934\) | −6403.82 | −0.224346 | ||||||||
\(935\) | −8817.25 | −0.308401 | ||||||||
\(936\) | −5444.50 | −0.190127 | ||||||||
\(937\) | 13842.5 | 0.482619 | 0.241309 | − | 0.970448i | \(-0.422423\pi\) | ||||
0.241309 | + | 0.970448i | \(0.422423\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −894.167 | −0.0310757 | ||||||||
\(940\) | −11816.5 | −0.410012 | ||||||||
\(941\) | −53393.2 | −1.84970 | −0.924850 | − | 0.380333i | \(-0.875809\pi\) | ||||
−0.924850 | + | 0.380333i | \(0.875809\pi\) | |||||||
\(942\) | −6500.44 | −0.224836 | ||||||||
\(943\) | −14187.9 | −0.489947 | ||||||||
\(944\) | −5352.98 | −0.184560 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5438.52 | 0.186915 | ||||||||
\(947\) | 22344.2 | 0.766727 | 0.383364 | − | 0.923598i | \(-0.374766\pi\) | ||||
0.383364 | + | 0.923598i | \(0.374766\pi\) | |||||||
\(948\) | 24433.2 | 0.837081 | ||||||||
\(949\) | −47478.5 | −1.62404 | ||||||||
\(950\) | −495.830 | −0.0169335 | ||||||||
\(951\) | −11237.3 | −0.383169 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8902.63 | −0.302607 | −0.151304 | − | 0.988487i | \(-0.548347\pi\) | ||||
−0.151304 | + | 0.988487i | \(0.548347\pi\) | |||||||
\(954\) | 3005.25 | 0.101990 | ||||||||
\(955\) | 24478.1 | 0.829416 | ||||||||
\(956\) | −7138.31 | −0.241495 | ||||||||
\(957\) | 39077.6 | 1.31996 | ||||||||
\(958\) | 3267.48 | 0.110196 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −7520.82 | −0.252847 | ||||||||
\(961\) | 36706.0 | 1.23212 | ||||||||
\(962\) | −12779.7 | −0.428309 | ||||||||
\(963\) | 3504.96 | 0.117285 | ||||||||
\(964\) | 42762.8 | 1.42873 | ||||||||
\(965\) | −17743.6 | −0.591905 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2225.57 | −0.0740119 | −0.0370059 | − | 0.999315i | \(-0.511782\pi\) | ||||
−0.0370059 | + | 0.999315i | \(0.511782\pi\) | |||||||
\(968\) | −9488.05 | −0.315039 | ||||||||
\(969\) | −4762.03 | −0.157873 | ||||||||
\(970\) | 4551.58 | 0.150662 | ||||||||
\(971\) | −11324.8 | −0.374285 | −0.187143 | − | 0.982333i | \(-0.559923\pi\) | ||||
−0.187143 | + | 0.982333i | \(0.559923\pi\) | |||||||
\(972\) | −19086.9 | −0.629849 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 170.415 | 0.00560621 | ||||||||
\(975\) | −5989.91 | −0.196749 | ||||||||
\(976\) | −4453.43 | −0.146056 | ||||||||
\(977\) | −57695.9 | −1.88931 | −0.944654 | − | 0.328067i | \(-0.893603\pi\) | ||||
−0.944654 | + | 0.328067i | \(0.893603\pi\) | |||||||
\(978\) | −10286.2 | −0.336315 | ||||||||
\(979\) | −21831.3 | −0.712697 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9238.73 | −0.300683 | ||||||||
\(982\) | −4808.73 | −0.156266 | ||||||||
\(983\) | 59657.3 | 1.93568 | 0.967839 | − | 0.251570i | \(-0.0809469\pi\) | ||||
0.967839 | + | 0.251570i | \(0.0809469\pi\) | |||||||
\(984\) | 11233.0 | 0.363917 | ||||||||
\(985\) | −3250.54 | −0.105148 | ||||||||
\(986\) | −4662.98 | −0.150608 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13353.1 | −0.429980 | ||||||||
\(989\) | −9396.20 | −0.302105 | ||||||||
\(990\) | 1456.05 | 0.0467438 | ||||||||
\(991\) | 2890.60 | 0.0926568 | 0.0463284 | − | 0.998926i | \(-0.485248\pi\) | ||||
0.0463284 | + | 0.998926i | \(0.485248\pi\) | |||||||
\(992\) | −29735.3 | −0.951710 | ||||||||
\(993\) | −21217.1 | −0.678050 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20275.5 | −0.646005 | ||||||||
\(996\) | 19472.3 | 0.619481 | ||||||||
\(997\) | −10619.6 | −0.337337 | −0.168669 | − | 0.985673i | \(-0.553947\pi\) | ||||
−0.168669 | + | 0.985673i | \(0.553947\pi\) | |||||||
\(998\) | 4645.77 | 0.147354 | ||||||||
\(999\) | −52897.3 | −1.67527 |
(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 | 245.4.a.o.1.4 | ✓ | 6 | |
3.2 | odd | 2 | 2205.4.a.bz.1.3 | 6 | |||
5.4 | even | 2 | 1225.4.a.bj.1.3 | 6 | |||
7.2 | even | 3 | 245.4.e.q.116.3 | 12 | |||
7.3 | odd | 6 | 245.4.e.p.226.3 | 12 | |||
7.4 | even | 3 | 245.4.e.q.226.3 | 12 | |||
7.5 | odd | 6 | 245.4.e.p.116.3 | 12 | |||
7.6 | odd | 2 | 245.4.a.p.1.4 | yes | 6 | ||
21.20 | even | 2 | 2205.4.a.ca.1.3 | 6 | |||
35.34 | odd | 2 | 1225.4.a.bi.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.4.a.o.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial | |
245.4.a.p.1.4 | yes | 6 | 7.6 | odd | 2 | ||
245.4.e.p.116.3 | 12 | 7.5 | odd | 6 | |||
245.4.e.p.226.3 | 12 | 7.3 | odd | 6 | |||
245.4.e.q.116.3 | 12 | 7.2 | even | 3 | |||
245.4.e.q.226.3 | 12 | 7.4 | even | 3 | |||
1225.4.a.bi.1.3 | 6 | 35.34 | odd | 2 | |||
1225.4.a.bj.1.3 | 6 | 5.4 | even | 2 | |||
2205.4.a.bz.1.3 | 6 | 3.2 | odd | 2 | |||
2205.4.a.ca.1.3 | 6 | 21.20 | even | 2 |