Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1075,2,Mod(1,1075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1075 = 5^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1075.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: | \(8.58391821729\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.24217.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 5x^{3} - x^{2} + 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.96003\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.96003 | −1.38595 | −0.692974 | − | 0.720963i | \(-0.743700\pi\) | ||||
−0.692974 | + | 0.720963i | \(0.743700\pi\) | |||||||
\(3\) | 0.199933 | 0.115432 | 0.0577158 | − | 0.998333i | \(-0.481618\pi\) | ||||
0.0577158 | + | 0.998333i | \(0.481618\pi\) | |||||||
\(4\) | 1.84170 | 0.920852 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.391875 | −0.159982 | ||||||||
\(7\) | 3.80173 | 1.43692 | 0.718460 | − | 0.695569i | \(-0.244848\pi\) | ||||
0.718460 | + | 0.695569i | \(0.244848\pi\) | |||||||
\(8\) | 0.310264 | 0.109695 | ||||||||
\(9\) | −2.96003 | −0.986676 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.77967 | −0.536591 | −0.268296 | − | 0.963337i | \(-0.586460\pi\) | ||||
−0.268296 | + | 0.963337i | \(0.586460\pi\) | |||||||
\(12\) | 0.368218 | 0.106295 | ||||||||
\(13\) | −1.73545 | −0.481328 | −0.240664 | − | 0.970609i | \(-0.577365\pi\) | ||||
−0.240664 | + | 0.970609i | \(0.577365\pi\) | |||||||
\(14\) | −7.45149 | −1.99150 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.29153 | −1.07288 | ||||||||
\(17\) | 0.964104 | 0.233830 | 0.116915 | − | 0.993142i | \(-0.462700\pi\) | ||||
0.116915 | + | 0.993142i | \(0.462700\pi\) | |||||||
\(18\) | 5.80173 | 1.36748 | ||||||||
\(19\) | −4.34358 | −0.996485 | −0.498242 | − | 0.867038i | \(-0.666021\pi\) | ||||
−0.498242 | + | 0.867038i | \(0.666021\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.760093 | 0.165866 | ||||||||
\(22\) | 3.48820 | 0.743688 | ||||||||
\(23\) | −4.20160 | −0.876094 | −0.438047 | − | 0.898952i | \(-0.644330\pi\) | ||||
−0.438047 | + | 0.898952i | \(0.644330\pi\) | |||||||
\(24\) | 0.0620321 | 0.0126622 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.40153 | 0.667095 | ||||||||
\(27\) | −1.19161 | −0.229325 | ||||||||
\(28\) | 7.00166 | 1.32319 | ||||||||
\(29\) | −9.77008 | −1.81426 | −0.907129 | − | 0.420852i | \(-0.861731\pi\) | ||||
−0.907129 | + | 0.420852i | \(0.861731\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.61064 | 1.00770 | 0.503850 | − | 0.863791i | \(-0.331916\pi\) | ||||
0.503850 | + | 0.863791i | \(0.331916\pi\) | |||||||
\(32\) | 7.79099 | 1.37727 | ||||||||
\(33\) | −0.355816 | −0.0619396 | ||||||||
\(34\) | −1.88967 | −0.324076 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.45149 | −0.908582 | ||||||||
\(37\) | 0.837627 | 0.137705 | 0.0688525 | − | 0.997627i | \(-0.478066\pi\) | ||||
0.0688525 | + | 0.997627i | \(0.478066\pi\) | |||||||
\(38\) | 8.51353 | 1.38108 | ||||||||
\(39\) | −0.346975 | −0.0555604 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.13997 | 1.11508 | 0.557538 | − | 0.830152i | \(-0.311746\pi\) | ||||
0.557538 | + | 0.830152i | \(0.311746\pi\) | |||||||
\(42\) | −1.48980 | −0.229882 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | −3.27763 | −0.494121 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.23524 | 1.21422 | ||||||||
\(47\) | −7.86053 | −1.14658 | −0.573288 | − | 0.819354i | \(-0.694333\pi\) | ||||
−0.573288 | + | 0.819354i | \(0.694333\pi\) | |||||||
\(48\) | −0.858021 | −0.123845 | ||||||||
\(49\) | 7.45316 | 1.06474 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.192757 | 0.0269913 | ||||||||
\(52\) | −3.19619 | −0.443232 | ||||||||
\(53\) | 1.84463 | 0.253380 | 0.126690 | − | 0.991942i | \(-0.459565\pi\) | ||||
0.126690 | + | 0.991942i | \(0.459565\pi\) | |||||||
\(54\) | 2.33558 | 0.317833 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.17954 | 0.157623 | ||||||||
\(57\) | −0.868426 | −0.115026 | ||||||||
\(58\) | 19.1496 | 2.51447 | ||||||||
\(59\) | −8.35323 | −1.08750 | −0.543749 | − | 0.839248i | \(-0.682996\pi\) | ||||
−0.543749 | + | 0.839248i | \(0.682996\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.1011 | −1.42135 | −0.710674 | − | 0.703521i | \(-0.751610\pi\) | ||||
−0.710674 | + | 0.703521i | \(0.751610\pi\) | |||||||
\(62\) | −10.9970 | −1.39662 | ||||||||
\(63\) | −11.2532 | −1.41777 | ||||||||
\(64\) | −6.68749 | −0.835936 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.697409 | 0.0858451 | ||||||||
\(67\) | 2.64062 | 0.322603 | 0.161302 | − | 0.986905i | \(-0.448431\pi\) | ||||
0.161302 | + | 0.986905i | \(0.448431\pi\) | |||||||
\(68\) | 1.77559 | 0.215322 | ||||||||
\(69\) | −0.840040 | −0.101129 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.4442 | −1.23949 | −0.619747 | − | 0.784802i | \(-0.712765\pi\) | ||||
−0.619747 | + | 0.784802i | \(0.712765\pi\) | |||||||
\(72\) | −0.918389 | −0.108233 | ||||||||
\(73\) | 4.21367 | 0.493172 | 0.246586 | − | 0.969121i | \(-0.420691\pi\) | ||||
0.246586 | + | 0.969121i | \(0.420691\pi\) | |||||||
\(74\) | −1.64177 | −0.190852 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.99958 | −0.917615 | ||||||||
\(77\) | −6.76584 | −0.771038 | ||||||||
\(78\) | 0.680080 | 0.0770039 | ||||||||
\(79\) | 16.4139 | 1.84670 | 0.923352 | − | 0.383955i | \(-0.125438\pi\) | ||||
0.923352 | + | 0.383955i | \(0.125438\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.64184 | 0.960204 | ||||||||
\(82\) | −13.9945 | −1.54544 | ||||||||
\(83\) | −17.1653 | −1.88413 | −0.942067 | − | 0.335423i | \(-0.891121\pi\) | ||||
−0.942067 | + | 0.335423i | \(0.891121\pi\) | |||||||
\(84\) | 1.39987 | 0.152738 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.96003 | −0.211355 | ||||||||
\(87\) | −1.95337 | −0.209423 | ||||||||
\(88\) | −0.552168 | −0.0588613 | ||||||||
\(89\) | −11.0755 | −1.17400 | −0.586998 | − | 0.809588i | \(-0.699690\pi\) | ||||
−0.586998 | + | 0.809588i | \(0.699690\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.59772 | −0.691629 | ||||||||
\(92\) | −7.73810 | −0.806753 | ||||||||
\(93\) | 1.12175 | 0.116321 | ||||||||
\(94\) | 15.4069 | 1.58910 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.55768 | 0.158980 | ||||||||
\(97\) | 0.955297 | 0.0969957 | 0.0484979 | − | 0.998823i | \(-0.484557\pi\) | ||||
0.0484979 | + | 0.998823i | \(0.484557\pi\) | |||||||
\(98\) | −14.6084 | −1.47567 | ||||||||
\(99\) | 5.26788 | 0.529442 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.32158 | 0.231006 | 0.115503 | − | 0.993307i | \(-0.463152\pi\) | ||||
0.115503 | + | 0.993307i | \(0.463152\pi\) | |||||||
\(102\) | −0.377808 | −0.0374086 | ||||||||
\(103\) | −0.607140 | −0.0598233 | −0.0299116 | − | 0.999553i | \(-0.509523\pi\) | ||||
−0.0299116 | + | 0.999553i | \(0.509523\pi\) | |||||||
\(104\) | −0.538448 | −0.0527991 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.61553 | −0.351171 | ||||||||
\(107\) | −0.107747 | −0.0104163 | −0.00520817 | − | 0.999986i | \(-0.501658\pi\) | ||||
−0.00520817 | + | 0.999986i | \(0.501658\pi\) | |||||||
\(108\) | −2.19459 | −0.211175 | ||||||||
\(109\) | −9.60330 | −0.919829 | −0.459915 | − | 0.887963i | \(-0.652120\pi\) | ||||
−0.459915 | + | 0.887963i | \(0.652120\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.167470 | 0.0158955 | ||||||||
\(112\) | −16.3153 | −1.54165 | ||||||||
\(113\) | 5.32060 | 0.500520 | 0.250260 | − | 0.968179i | \(-0.419484\pi\) | ||||
0.250260 | + | 0.968179i | \(0.419484\pi\) | |||||||
\(114\) | 1.70214 | 0.159420 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −17.9936 | −1.67066 | ||||||||
\(117\) | 5.13698 | 0.474914 | ||||||||
\(118\) | 16.3726 | 1.50722 | ||||||||
\(119\) | 3.66526 | 0.335994 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.83277 | −0.712070 | ||||||||
\(122\) | 21.7584 | 1.96992 | ||||||||
\(123\) | 1.42752 | 0.128715 | ||||||||
\(124\) | 10.3331 | 0.927943 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 22.0566 | 1.96496 | ||||||||
\(127\) | −6.70870 | −0.595301 | −0.297651 | − | 0.954675i | \(-0.596203\pi\) | ||||
−0.297651 | + | 0.954675i | \(0.596203\pi\) | |||||||
\(128\) | −2.47434 | −0.218702 | ||||||||
\(129\) | 0.199933 | 0.0176032 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.6812 | −0.933217 | −0.466609 | − | 0.884464i | \(-0.654524\pi\) | ||||
−0.466609 | + | 0.884464i | \(0.654524\pi\) | |||||||
\(132\) | −0.655308 | −0.0570372 | ||||||||
\(133\) | −16.5131 | −1.43187 | ||||||||
\(134\) | −5.17569 | −0.447112 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.299127 | 0.0256499 | ||||||||
\(137\) | −1.64034 | −0.140144 | −0.0700720 | − | 0.997542i | \(-0.522323\pi\) | ||||
−0.0700720 | + | 0.997542i | \(0.522323\pi\) | |||||||
\(138\) | 1.64650 | 0.140159 | ||||||||
\(139\) | −5.01948 | −0.425746 | −0.212873 | − | 0.977080i | \(-0.568282\pi\) | ||||
−0.212873 | + | 0.977080i | \(0.568282\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.57158 | −0.132351 | ||||||||
\(142\) | 20.4708 | 1.71787 | ||||||||
\(143\) | 3.08854 | 0.258276 | ||||||||
\(144\) | 12.7031 | 1.05859 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.25890 | −0.683511 | ||||||||
\(147\) | 1.49014 | 0.122904 | ||||||||
\(148\) | 1.54266 | 0.126806 | ||||||||
\(149\) | −8.48755 | −0.695327 | −0.347664 | − | 0.937619i | \(-0.613025\pi\) | ||||
−0.347664 | + | 0.937619i | \(0.613025\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.2094 | −1.64462 | −0.822309 | − | 0.569041i | \(-0.807314\pi\) | ||||
−0.822309 | + | 0.569041i | \(0.807314\pi\) | |||||||
\(152\) | −1.34765 | −0.109309 | ||||||||
\(153\) | −2.85377 | −0.230714 | ||||||||
\(154\) | 13.2612 | 1.06862 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.639025 | −0.0511629 | ||||||||
\(157\) | 14.9980 | 1.19697 | 0.598485 | − | 0.801134i | \(-0.295770\pi\) | ||||
0.598485 | + | 0.801134i | \(0.295770\pi\) | |||||||
\(158\) | −32.1716 | −2.55944 | ||||||||
\(159\) | 0.368804 | 0.0292481 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.9733 | −1.25888 | ||||||||
\(162\) | −16.9382 | −1.33079 | ||||||||
\(163\) | −8.48233 | −0.664387 | −0.332194 | − | 0.943211i | \(-0.607789\pi\) | ||||
−0.332194 | + | 0.943211i | \(0.607789\pi\) | |||||||
\(164\) | 13.1497 | 1.02682 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 33.6444 | 2.61131 | ||||||||
\(167\) | −3.27586 | −0.253494 | −0.126747 | − | 0.991935i | \(-0.540454\pi\) | ||||
−0.126747 | + | 0.991935i | \(0.540454\pi\) | |||||||
\(168\) | 0.235829 | 0.0181946 | ||||||||
\(169\) | −9.98821 | −0.768324 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.8571 | 0.983207 | ||||||||
\(172\) | 1.84170 | 0.140429 | ||||||||
\(173\) | 18.7232 | 1.42350 | 0.711750 | − | 0.702432i | \(-0.247903\pi\) | ||||
0.711750 | + | 0.702432i | \(0.247903\pi\) | |||||||
\(174\) | 3.82865 | 0.290249 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.63752 | 0.575700 | ||||||||
\(177\) | −1.67009 | −0.125532 | ||||||||
\(178\) | 21.7082 | 1.62710 | ||||||||
\(179\) | −8.90541 | −0.665621 | −0.332811 | − | 0.942994i | \(-0.607997\pi\) | ||||
−0.332811 | + | 0.942994i | \(0.607997\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.61322 | −0.491557 | −0.245778 | − | 0.969326i | \(-0.579044\pi\) | ||||
−0.245778 | + | 0.969326i | \(0.579044\pi\) | |||||||
\(182\) | 12.9317 | 0.958562 | ||||||||
\(183\) | −2.21948 | −0.164069 | ||||||||
\(184\) | −1.30360 | −0.0961029 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.19867 | −0.161214 | ||||||||
\(187\) | −1.71579 | −0.125471 | ||||||||
\(188\) | −14.4768 | −1.05583 | ||||||||
\(189\) | −4.53018 | −0.329522 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.6849 | 1.78613 | 0.893067 | − | 0.449924i | \(-0.148549\pi\) | ||||
0.893067 | + | 0.449924i | \(0.148549\pi\) | |||||||
\(192\) | −1.33705 | −0.0964934 | ||||||||
\(193\) | −11.8102 | −0.850114 | −0.425057 | − | 0.905167i | \(-0.639746\pi\) | ||||
−0.425057 | + | 0.905167i | \(0.639746\pi\) | |||||||
\(194\) | −1.87241 | −0.134431 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.7265 | 0.980465 | ||||||||
\(197\) | −15.0039 | −1.06899 | −0.534493 | − | 0.845173i | \(-0.679497\pi\) | ||||
−0.534493 | + | 0.845173i | \(0.679497\pi\) | |||||||
\(198\) | −10.3252 | −0.733779 | ||||||||
\(199\) | 14.4597 | 1.02502 | 0.512511 | − | 0.858681i | \(-0.328716\pi\) | ||||
0.512511 | + | 0.858681i | \(0.328716\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.527949 | 0.0372386 | ||||||||
\(202\) | −4.55037 | −0.320163 | ||||||||
\(203\) | −37.1432 | −2.60694 | ||||||||
\(204\) | 0.355001 | 0.0248550 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.19001 | 0.0829120 | ||||||||
\(207\) | 12.4368 | 0.864420 | ||||||||
\(208\) | 7.44775 | 0.516408 | ||||||||
\(209\) | 7.73014 | 0.534705 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.2369 | 0.704738 | 0.352369 | − | 0.935861i | \(-0.385376\pi\) | ||||
0.352369 | + | 0.935861i | \(0.385376\pi\) | |||||||
\(212\) | 3.39727 | 0.233325 | ||||||||
\(213\) | −2.08814 | −0.143077 | ||||||||
\(214\) | 0.211188 | 0.0144365 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.369713 | −0.0251558 | ||||||||
\(217\) | 21.3301 | 1.44798 | ||||||||
\(218\) | 18.8227 | 1.27484 | ||||||||
\(219\) | 0.842453 | 0.0569277 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.67316 | −0.112549 | ||||||||
\(222\) | −0.328245 | −0.0220304 | ||||||||
\(223\) | 28.7779 | 1.92711 | 0.963554 | − | 0.267515i | \(-0.0862024\pi\) | ||||
0.963554 | + | 0.267515i | \(0.0862024\pi\) | |||||||
\(224\) | 29.6193 | 1.97902 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.4285 | −0.693695 | ||||||||
\(227\) | 4.24838 | 0.281975 | 0.140987 | − | 0.990011i | \(-0.454972\pi\) | ||||
0.140987 | + | 0.990011i | \(0.454972\pi\) | |||||||
\(228\) | −1.59938 | −0.105922 | ||||||||
\(229\) | 29.2506 | 1.93293 | 0.966466 | − | 0.256793i | \(-0.0826660\pi\) | ||||
0.966466 | + | 0.256793i | \(0.0826660\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.35272 | −0.0890022 | ||||||||
\(232\) | −3.03130 | −0.199015 | ||||||||
\(233\) | 15.7785 | 1.03369 | 0.516843 | − | 0.856080i | \(-0.327107\pi\) | ||||
0.516843 | + | 0.856080i | \(0.327107\pi\) | |||||||
\(234\) | −10.0686 | −0.658206 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −15.3842 | −1.00143 | ||||||||
\(237\) | 3.28168 | 0.213168 | ||||||||
\(238\) | −7.18402 | −0.465671 | ||||||||
\(239\) | 10.3196 | 0.667520 | 0.333760 | − | 0.942658i | \(-0.391682\pi\) | ||||
0.333760 | + | 0.942658i | \(0.391682\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.87891 | 0.185447 | 0.0927235 | − | 0.995692i | \(-0.470443\pi\) | ||||
0.0927235 | + | 0.995692i | \(0.470443\pi\) | |||||||
\(242\) | 15.3524 | 0.986892 | ||||||||
\(243\) | 5.30262 | 0.340163 | ||||||||
\(244\) | −20.4449 | −1.30885 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.79797 | −0.178392 | ||||||||
\(247\) | 7.53807 | 0.479636 | ||||||||
\(248\) | 1.74078 | 0.110539 | ||||||||
\(249\) | −3.43191 | −0.217489 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.4846 | −0.724903 | −0.362451 | − | 0.932003i | \(-0.618060\pi\) | ||||
−0.362451 | + | 0.932003i | \(0.618060\pi\) | |||||||
\(252\) | −20.7251 | −1.30556 | ||||||||
\(253\) | 7.47747 | 0.470104 | ||||||||
\(254\) | 13.1492 | 0.825056 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 18.2247 | 1.13905 | ||||||||
\(257\) | −9.57691 | −0.597391 | −0.298696 | − | 0.954348i | \(-0.596552\pi\) | ||||
−0.298696 | + | 0.954348i | \(0.596552\pi\) | |||||||
\(258\) | −0.391875 | −0.0243971 | ||||||||
\(259\) | 3.18443 | 0.197871 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 28.9197 | 1.79008 | ||||||||
\(262\) | 20.9354 | 1.29339 | ||||||||
\(263\) | −20.8514 | −1.28575 | −0.642875 | − | 0.765971i | \(-0.722259\pi\) | ||||
−0.642875 | + | 0.765971i | \(0.722259\pi\) | |||||||
\(264\) | −0.110397 | −0.00679445 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 32.3661 | 1.98450 | ||||||||
\(267\) | −2.21435 | −0.135516 | ||||||||
\(268\) | 4.86325 | 0.297070 | ||||||||
\(269\) | 2.09034 | 0.127450 | 0.0637250 | − | 0.997967i | \(-0.479702\pi\) | ||||
0.0637250 | + | 0.997967i | \(0.479702\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.13823 | −0.494362 | −0.247181 | − | 0.968969i | \(-0.579504\pi\) | ||||
−0.247181 | + | 0.968969i | \(0.579504\pi\) | |||||||
\(272\) | −4.13749 | −0.250872 | ||||||||
\(273\) | −1.31910 | −0.0798359 | ||||||||
\(274\) | 3.21512 | 0.194232 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.54711 | −0.0931248 | ||||||||
\(277\) | −12.1111 | −0.727688 | −0.363844 | − | 0.931460i | \(-0.618536\pi\) | ||||
−0.363844 | + | 0.931460i | \(0.618536\pi\) | |||||||
\(278\) | 9.83831 | 0.590062 | ||||||||
\(279\) | −16.6076 | −0.994273 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.1976 | 0.787306 | 0.393653 | − | 0.919259i | \(-0.371211\pi\) | ||||
0.393653 | + | 0.919259i | \(0.371211\pi\) | |||||||
\(282\) | 3.08035 | 0.183432 | ||||||||
\(283\) | −5.09205 | −0.302691 | −0.151345 | − | 0.988481i | \(-0.548361\pi\) | ||||
−0.151345 | + | 0.988481i | \(0.548361\pi\) | |||||||
\(284\) | −19.2350 | −1.14139 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.05361 | −0.357958 | ||||||||
\(287\) | 27.1442 | 1.60227 | ||||||||
\(288\) | −23.0615 | −1.35891 | ||||||||
\(289\) | −16.0705 | −0.945324 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.190996 | 0.0111964 | ||||||||
\(292\) | 7.76033 | 0.454139 | ||||||||
\(293\) | −11.1081 | −0.648943 | −0.324471 | − | 0.945895i | \(-0.605186\pi\) | ||||
−0.324471 | + | 0.945895i | \(0.605186\pi\) | |||||||
\(294\) | −2.92071 | −0.170339 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.259885 | 0.0151055 | ||||||||
\(297\) | 2.12067 | 0.123054 | ||||||||
\(298\) | 16.6358 | 0.963688 | ||||||||
\(299\) | 7.29167 | 0.421688 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.80173 | 0.219128 | ||||||||
\(302\) | 39.6110 | 2.27936 | ||||||||
\(303\) | 0.464162 | 0.0266654 | ||||||||
\(304\) | 18.6406 | 1.06911 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.59347 | 0.319758 | ||||||||
\(307\) | 27.6299 | 1.57692 | 0.788462 | − | 0.615084i | \(-0.210878\pi\) | ||||
0.788462 | + | 0.615084i | \(0.210878\pi\) | |||||||
\(308\) | −12.4607 | −0.710012 | ||||||||
\(309\) | −0.121388 | −0.00690550 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.6190 | −0.715556 | −0.357778 | − | 0.933807i | \(-0.616466\pi\) | ||||
−0.357778 | + | 0.933807i | \(0.616466\pi\) | |||||||
\(312\) | −0.107654 | −0.00609469 | ||||||||
\(313\) | −9.95430 | −0.562650 | −0.281325 | − | 0.959613i | \(-0.590774\pi\) | ||||
−0.281325 | + | 0.959613i | \(0.590774\pi\) | |||||||
\(314\) | −29.3965 | −1.65894 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 30.2295 | 1.70054 | ||||||||
\(317\) | 27.6663 | 1.55389 | 0.776947 | − | 0.629566i | \(-0.216767\pi\) | ||||
0.776947 | + | 0.629566i | \(0.216767\pi\) | |||||||
\(318\) | −0.722866 | −0.0405363 | ||||||||
\(319\) | 17.3875 | 0.973516 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.0215423 | −0.00120237 | ||||||||
\(322\) | 31.3082 | 1.74474 | ||||||||
\(323\) | −4.18766 | −0.233008 | ||||||||
\(324\) | 15.9157 | 0.884206 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.6256 | 0.920806 | ||||||||
\(327\) | −1.92002 | −0.106177 | ||||||||
\(328\) | 2.21527 | 0.122318 | ||||||||
\(329\) | −29.8836 | −1.64754 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.0556 | 0.607668 | 0.303834 | − | 0.952725i | \(-0.401733\pi\) | ||||
0.303834 | + | 0.952725i | \(0.401733\pi\) | |||||||
\(332\) | −31.6134 | −1.73501 | ||||||||
\(333\) | −2.47940 | −0.135870 | ||||||||
\(334\) | 6.42078 | 0.351329 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.26197 | −0.177955 | ||||||||
\(337\) | −11.6752 | −0.635991 | −0.317996 | − | 0.948092i | \(-0.603010\pi\) | ||||
−0.317996 | + | 0.948092i | \(0.603010\pi\) | |||||||
\(338\) | 19.5772 | 1.06486 | ||||||||
\(339\) | 1.06377 | 0.0577758 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.98510 | −0.540723 | ||||||||
\(342\) | −25.2003 | −1.36267 | ||||||||
\(343\) | 1.72279 | 0.0930217 | ||||||||
\(344\) | 0.310264 | 0.0167283 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −36.6980 | −1.97290 | ||||||||
\(347\) | 23.5556 | 1.26453 | 0.632265 | − | 0.774752i | \(-0.282125\pi\) | ||||
0.632265 | + | 0.774752i | \(0.282125\pi\) | |||||||
\(348\) | −3.59752 | −0.192847 | ||||||||
\(349\) | 19.9469 | 1.06773 | 0.533865 | − | 0.845570i | \(-0.320739\pi\) | ||||
0.533865 | + | 0.845570i | \(0.320739\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.06798 | 0.110381 | ||||||||
\(352\) | −13.8654 | −0.739029 | ||||||||
\(353\) | 30.3607 | 1.61594 | 0.807968 | − | 0.589226i | \(-0.200567\pi\) | ||||
0.807968 | + | 0.589226i | \(0.200567\pi\) | |||||||
\(354\) | 3.27342 | 0.173980 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −20.3977 | −1.08108 | ||||||||
\(357\) | 0.732809 | 0.0387844 | ||||||||
\(358\) | 17.4548 | 0.922517 | ||||||||
\(359\) | 14.6239 | 0.771822 | 0.385911 | − | 0.922536i | \(-0.373887\pi\) | ||||
0.385911 | + | 0.922536i | \(0.373887\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.133341 | −0.00701797 | ||||||||
\(362\) | 12.9621 | 0.681272 | ||||||||
\(363\) | −1.56603 | −0.0821954 | ||||||||
\(364\) | −12.1510 | −0.636888 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.35024 | 0.227391 | ||||||||
\(367\) | 3.79697 | 0.198200 | 0.0991000 | − | 0.995077i | \(-0.468404\pi\) | ||||
0.0991000 | + | 0.995077i | \(0.468404\pi\) | |||||||
\(368\) | 18.0313 | 0.939946 | ||||||||
\(369\) | −21.1345 | −1.10022 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.01280 | 0.364087 | ||||||||
\(372\) | 2.06594 | 0.107114 | ||||||||
\(373\) | −13.1551 | −0.681147 | −0.340573 | − | 0.940218i | \(-0.610621\pi\) | ||||
−0.340573 | + | 0.940218i | \(0.610621\pi\) | |||||||
\(374\) | 3.36299 | 0.173896 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.43884 | −0.125773 | ||||||||
\(377\) | 16.9555 | 0.873253 | ||||||||
\(378\) | 8.87926 | 0.456700 | ||||||||
\(379\) | −26.2492 | −1.34833 | −0.674164 | − | 0.738581i | \(-0.735496\pi\) | ||||
−0.674164 | + | 0.738581i | \(0.735496\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.34129 | −0.0687166 | ||||||||
\(382\) | −48.3830 | −2.47549 | ||||||||
\(383\) | 25.4582 | 1.30085 | 0.650426 | − | 0.759569i | \(-0.274590\pi\) | ||||
0.650426 | + | 0.759569i | \(0.274590\pi\) | |||||||
\(384\) | −0.494702 | −0.0252452 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 23.1482 | 1.17821 | ||||||||
\(387\) | −2.96003 | −0.150467 | ||||||||
\(388\) | 1.75937 | 0.0893187 | ||||||||
\(389\) | −6.70189 | −0.339799 | −0.169900 | − | 0.985461i | \(-0.554344\pi\) | ||||
−0.169900 | + | 0.985461i | \(0.554344\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.05078 | −0.204857 | ||||||||
\(392\) | 2.31244 | 0.116796 | ||||||||
\(393\) | −2.13552 | −0.107723 | ||||||||
\(394\) | 29.4081 | 1.48156 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.70187 | 0.487537 | ||||||||
\(397\) | −19.5353 | −0.980450 | −0.490225 | − | 0.871596i | \(-0.663085\pi\) | ||||
−0.490225 | + | 0.871596i | \(0.663085\pi\) | |||||||
\(398\) | −28.3414 | −1.42063 | ||||||||
\(399\) | −3.30152 | −0.165283 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −36.4161 | −1.81853 | −0.909267 | − | 0.416214i | \(-0.863357\pi\) | ||||
−0.909267 | + | 0.416214i | \(0.863357\pi\) | |||||||
\(402\) | −1.03479 | −0.0516108 | ||||||||
\(403\) | −9.73699 | −0.485034 | ||||||||
\(404\) | 4.27567 | 0.212723 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 72.8017 | 3.61309 | ||||||||
\(407\) | −1.49070 | −0.0738913 | ||||||||
\(408\) | 0.0598054 | 0.00296081 | ||||||||
\(409\) | −3.61297 | −0.178650 | −0.0893250 | − | 0.996003i | \(-0.528471\pi\) | ||||
−0.0893250 | + | 0.996003i | \(0.528471\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.327959 | −0.0161770 | ||||||||
\(412\) | −1.11817 | −0.0550884 | ||||||||
\(413\) | −31.7567 | −1.56265 | ||||||||
\(414\) | −24.3765 | −1.19804 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −13.5209 | −0.662916 | ||||||||
\(417\) | −1.00356 | −0.0491446 | ||||||||
\(418\) | −15.1513 | −0.741074 | ||||||||
\(419\) | 8.05241 | 0.393386 | 0.196693 | − | 0.980465i | \(-0.436980\pi\) | ||||
0.196693 | + | 0.980465i | \(0.436980\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.1449 | −1.81033 | −0.905165 | − | 0.425060i | \(-0.860253\pi\) | ||||
−0.905165 | + | 0.425060i | \(0.860253\pi\) | |||||||
\(422\) | −20.0646 | −0.976730 | ||||||||
\(423\) | 23.2674 | 1.13130 | ||||||||
\(424\) | 0.572323 | 0.0277945 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.09280 | 0.198297 | ||||||||
\(427\) | −42.2033 | −2.04236 | ||||||||
\(428\) | −0.198439 | −0.00959190 | ||||||||
\(429\) | 0.617501 | 0.0298133 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.3223 | −0.497209 | −0.248604 | − | 0.968605i | \(-0.579972\pi\) | ||||
−0.248604 | + | 0.968605i | \(0.579972\pi\) | |||||||
\(432\) | 5.11383 | 0.246039 | ||||||||
\(433\) | 17.4592 | 0.839036 | 0.419518 | − | 0.907747i | \(-0.362199\pi\) | ||||
0.419518 | + | 0.907747i | \(0.362199\pi\) | |||||||
\(434\) | −41.8076 | −2.00683 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.6864 | −0.847027 | ||||||||
\(437\) | 18.2500 | 0.873014 | ||||||||
\(438\) | −1.65123 | −0.0788988 | ||||||||
\(439\) | −7.85325 | −0.374815 | −0.187408 | − | 0.982282i | \(-0.560009\pi\) | ||||
−0.187408 | + | 0.982282i | \(0.560009\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −22.0615 | −1.05055 | ||||||||
\(442\) | 3.27943 | 0.155987 | ||||||||
\(443\) | 6.36246 | 0.302289 | 0.151145 | − | 0.988512i | \(-0.451704\pi\) | ||||
0.151145 | + | 0.988512i | \(0.451704\pi\) | |||||||
\(444\) | 0.308430 | 0.0146374 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −56.4054 | −2.67087 | ||||||||
\(447\) | −1.69695 | −0.0802628 | ||||||||
\(448\) | −25.4240 | −1.20117 | ||||||||
\(449\) | 14.6676 | 0.692208 | 0.346104 | − | 0.938196i | \(-0.387504\pi\) | ||||
0.346104 | + | 0.938196i | \(0.387504\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.7068 | −0.598340 | ||||||||
\(452\) | 9.79897 | 0.460905 | ||||||||
\(453\) | −4.04054 | −0.189841 | ||||||||
\(454\) | −8.32694 | −0.390803 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.269441 | −0.0126177 | ||||||||
\(457\) | −37.7674 | −1.76668 | −0.883342 | − | 0.468728i | \(-0.844712\pi\) | ||||
−0.883342 | + | 0.468728i | \(0.844712\pi\) | |||||||
\(458\) | −57.3319 | −2.67894 | ||||||||
\(459\) | −1.14883 | −0.0536230 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.2202 | −1.45407 | −0.727035 | − | 0.686601i | \(-0.759102\pi\) | ||||
−0.727035 | + | 0.686601i | \(0.759102\pi\) | |||||||
\(462\) | 2.65136 | 0.123352 | ||||||||
\(463\) | 34.5627 | 1.60627 | 0.803133 | − | 0.595799i | \(-0.203165\pi\) | ||||
0.803133 | + | 0.595799i | \(0.203165\pi\) | |||||||
\(464\) | 41.9286 | 1.94649 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −30.9263 | −1.43263 | ||||||||
\(467\) | −34.8475 | −1.61255 | −0.806274 | − | 0.591542i | \(-0.798519\pi\) | ||||
−0.806274 | + | 0.591542i | \(0.798519\pi\) | |||||||
\(468\) | 9.46080 | 0.437326 | ||||||||
\(469\) | 10.0389 | 0.463555 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.99860 | 0.138168 | ||||||||
\(472\) | −2.59171 | −0.119293 | ||||||||
\(473\) | −1.77967 | −0.0818294 | ||||||||
\(474\) | −6.43218 | −0.295440 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.75033 | 0.309401 | ||||||||
\(477\) | −5.46017 | −0.250004 | ||||||||
\(478\) | −20.2267 | −0.925149 | ||||||||
\(479\) | 27.1580 | 1.24088 | 0.620441 | − | 0.784253i | \(-0.286954\pi\) | ||||
0.620441 | + | 0.784253i | \(0.286954\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.45366 | −0.0662812 | ||||||||
\(482\) | −5.64274 | −0.257020 | ||||||||
\(483\) | −3.19361 | −0.145314 | ||||||||
\(484\) | −14.4256 | −0.655711 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −10.3933 | −0.471448 | ||||||||
\(487\) | 30.2897 | 1.37256 | 0.686279 | − | 0.727338i | \(-0.259243\pi\) | ||||
0.686279 | + | 0.727338i | \(0.259243\pi\) | |||||||
\(488\) | −3.44426 | −0.155915 | ||||||||
\(489\) | −1.69590 | −0.0766913 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.93544 | 0.448380 | 0.224190 | − | 0.974545i | \(-0.428026\pi\) | ||||
0.224190 | + | 0.974545i | \(0.428026\pi\) | |||||||
\(492\) | 2.62907 | 0.118527 | ||||||||
\(493\) | −9.41938 | −0.424227 | ||||||||
\(494\) | −14.7748 | −0.664750 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −24.0782 | −1.08115 | ||||||||
\(497\) | −39.7059 | −1.78105 | ||||||||
\(498\) | 6.72664 | 0.301428 | ||||||||
\(499\) | 28.0062 | 1.25373 | 0.626865 | − | 0.779128i | \(-0.284338\pi\) | ||||
0.626865 | + | 0.779128i | \(0.284338\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.654954 | −0.0292612 | ||||||||
\(502\) | 22.5102 | 1.00468 | ||||||||
\(503\) | −5.77091 | −0.257312 | −0.128656 | − | 0.991689i | \(-0.541066\pi\) | ||||
−0.128656 | + | 0.991689i | \(0.541066\pi\) | |||||||
\(504\) | −3.49147 | −0.155522 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −14.6560 | −0.651540 | ||||||||
\(507\) | −1.99698 | −0.0886889 | ||||||||
\(508\) | −12.3554 | −0.548184 | ||||||||
\(509\) | −37.3060 | −1.65356 | −0.826780 | − | 0.562525i | \(-0.809830\pi\) | ||||
−0.826780 | + | 0.562525i | \(0.809830\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.0192 | 0.708649 | ||||||||
\(512\) | −30.7723 | −1.35996 | ||||||||
\(513\) | 5.17584 | 0.228519 | ||||||||
\(514\) | 18.7710 | 0.827953 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.368218 | 0.0162099 | ||||||||
\(517\) | 13.9892 | 0.615243 | ||||||||
\(518\) | −6.24157 | −0.274239 | ||||||||
\(519\) | 3.74340 | 0.164317 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.0968 | −1.62524 | −0.812620 | − | 0.582794i | \(-0.801959\pi\) | ||||
−0.812620 | + | 0.582794i | \(0.801959\pi\) | |||||||
\(522\) | −56.6834 | −2.48096 | ||||||||
\(523\) | 27.8814 | 1.21917 | 0.609585 | − | 0.792721i | \(-0.291336\pi\) | ||||
0.609585 | + | 0.792721i | \(0.291336\pi\) | |||||||
\(524\) | −19.6715 | −0.859355 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 40.8692 | 1.78198 | ||||||||
\(527\) | 5.40924 | 0.235630 | ||||||||
\(528\) | 1.52700 | 0.0664540 | ||||||||
\(529\) | −5.34658 | −0.232460 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.7258 | 1.07301 | ||||||||
\(532\) | −30.4123 | −1.31854 | ||||||||
\(533\) | −12.3911 | −0.536717 | ||||||||
\(534\) | 4.34019 | 0.187818 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.819289 | 0.0353879 | ||||||||
\(537\) | −1.78049 | −0.0768338 | ||||||||
\(538\) | −4.09711 | −0.176639 | ||||||||
\(539\) | −13.2642 | −0.571329 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.5536 | 0.754689 | 0.377345 | − | 0.926073i | \(-0.376837\pi\) | ||||
0.377345 | + | 0.926073i | \(0.376837\pi\) | |||||||
\(542\) | 15.9512 | 0.685161 | ||||||||
\(543\) | −1.32220 | −0.0567412 | ||||||||
\(544\) | 7.51133 | 0.322046 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.58548 | 0.110648 | ||||||||
\(547\) | 10.0280 | 0.428768 | 0.214384 | − | 0.976749i | \(-0.431226\pi\) | ||||
0.214384 | + | 0.976749i | \(0.431226\pi\) | |||||||
\(548\) | −3.02103 | −0.129052 | ||||||||
\(549\) | 32.8595 | 1.40241 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42.4371 | 1.80788 | ||||||||
\(552\) | −0.260634 | −0.0110933 | ||||||||
\(553\) | 62.4011 | 2.65356 | ||||||||
\(554\) | 23.7382 | 1.00854 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.24439 | −0.392049 | ||||||||
\(557\) | −20.8856 | −0.884951 | −0.442475 | − | 0.896781i | \(-0.645900\pi\) | ||||
−0.442475 | + | 0.896781i | \(0.645900\pi\) | |||||||
\(558\) | 32.5514 | 1.37801 | ||||||||
\(559\) | −1.73545 | −0.0734018 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.343044 | −0.0144833 | ||||||||
\(562\) | −25.8677 | −1.09116 | ||||||||
\(563\) | 22.3621 | 0.942452 | 0.471226 | − | 0.882013i | \(-0.343812\pi\) | ||||
0.471226 | + | 0.882013i | \(0.343812\pi\) | |||||||
\(564\) | −2.89439 | −0.121876 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.98055 | 0.419514 | ||||||||
\(567\) | 32.8539 | 1.37974 | ||||||||
\(568\) | −3.24044 | −0.135966 | ||||||||
\(569\) | −0.514833 | −0.0215829 | −0.0107915 | − | 0.999942i | \(-0.503435\pi\) | ||||
−0.0107915 | + | 0.999942i | \(0.503435\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.4847 | 1.27574 | 0.637872 | − | 0.770142i | \(-0.279815\pi\) | ||||
0.637872 | + | 0.770142i | \(0.279815\pi\) | |||||||
\(572\) | 5.68817 | 0.237834 | ||||||||
\(573\) | 4.93533 | 0.206176 | ||||||||
\(574\) | −53.2034 | −2.22067 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 19.7951 | 0.824797 | ||||||||
\(577\) | −40.5019 | −1.68612 | −0.843059 | − | 0.537821i | \(-0.819248\pi\) | ||||
−0.843059 | + | 0.537821i | \(0.819248\pi\) | |||||||
\(578\) | 31.4986 | 1.31017 | ||||||||
\(579\) | −2.36125 | −0.0981300 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −65.2578 | −2.70735 | ||||||||
\(582\) | −0.374357 | −0.0155176 | ||||||||
\(583\) | −3.28284 | −0.135961 | ||||||||
\(584\) | 1.30735 | 0.0540984 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.7722 | 0.899401 | ||||||||
\(587\) | −4.75388 | −0.196214 | −0.0981068 | − | 0.995176i | \(-0.531279\pi\) | ||||
−0.0981068 | + | 0.995176i | \(0.531279\pi\) | |||||||
\(588\) | 2.74439 | 0.113177 | ||||||||
\(589\) | −24.3702 | −1.00416 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.99979 | −0.123395 | ||||||||
\(592\) | −3.59470 | −0.147741 | ||||||||
\(593\) | 44.3233 | 1.82014 | 0.910069 | − | 0.414456i | \(-0.136028\pi\) | ||||
0.910069 | + | 0.414456i | \(0.136028\pi\) | |||||||
\(594\) | −4.15658 | −0.170546 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.6316 | −0.640294 | ||||||||
\(597\) | 2.89098 | 0.118320 | ||||||||
\(598\) | −14.2919 | −0.584438 | ||||||||
\(599\) | 16.2752 | 0.664986 | 0.332493 | − | 0.943106i | \(-0.392110\pi\) | ||||
0.332493 | + | 0.943106i | \(0.392110\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.1970 | 0.905433 | 0.452716 | − | 0.891655i | \(-0.350455\pi\) | ||||
0.452716 | + | 0.891655i | \(0.350455\pi\) | |||||||
\(602\) | −7.45149 | −0.303700 | ||||||||
\(603\) | −7.81631 | −0.318305 | ||||||||
\(604\) | −37.2197 | −1.51445 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.909771 | −0.0369569 | ||||||||
\(607\) | −44.7910 | −1.81801 | −0.909005 | − | 0.416785i | \(-0.863157\pi\) | ||||
−0.909005 | + | 0.416785i | \(0.863157\pi\) | |||||||
\(608\) | −33.8408 | −1.37242 | ||||||||
\(609\) | −7.42617 | −0.300924 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.6416 | 0.551879 | ||||||||
\(612\) | −5.25581 | −0.212453 | ||||||||
\(613\) | 43.4227 | 1.75383 | 0.876914 | − | 0.480647i | \(-0.159598\pi\) | ||||
0.876914 | + | 0.480647i | \(0.159598\pi\) | |||||||
\(614\) | −54.1554 | −2.18553 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.09919 | −0.0845789 | ||||||||
\(617\) | −12.2954 | −0.494994 | −0.247497 | − | 0.968889i | \(-0.579608\pi\) | ||||
−0.247497 | + | 0.968889i | \(0.579608\pi\) | |||||||
\(618\) | 0.237923 | 0.00957066 | ||||||||
\(619\) | 39.3457 | 1.58144 | 0.790719 | − | 0.612179i | \(-0.209707\pi\) | ||||
0.790719 | + | 0.612179i | \(0.209707\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.00666 | 0.200910 | ||||||||
\(622\) | 24.7335 | 0.991723 | ||||||||
\(623\) | −42.1059 | −1.68694 | ||||||||
\(624\) | 1.48905 | 0.0596099 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 19.5107 | 0.779804 | ||||||||
\(627\) | 1.54551 | 0.0617219 | ||||||||
\(628\) | 27.6219 | 1.10223 | ||||||||
\(629\) | 0.807559 | 0.0321995 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.4877 | −1.09427 | −0.547134 | − | 0.837045i | \(-0.684281\pi\) | ||||
−0.547134 | + | 0.837045i | \(0.684281\pi\) | |||||||
\(632\) | 5.09263 | 0.202574 | ||||||||
\(633\) | 2.04670 | 0.0813490 | ||||||||
\(634\) | −54.2267 | −2.15362 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.679228 | 0.0269331 | ||||||||
\(637\) | −12.9346 | −0.512487 | ||||||||
\(638\) | −34.0800 | −1.34924 | ||||||||
\(639\) | 30.9150 | 1.22298 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.9559 | 1.14369 | 0.571845 | − | 0.820362i | \(-0.306228\pi\) | ||||
0.571845 | + | 0.820362i | \(0.306228\pi\) | |||||||
\(642\) | 0.0422235 | 0.00166643 | ||||||||
\(643\) | 20.9097 | 0.824597 | 0.412299 | − | 0.911049i | \(-0.364726\pi\) | ||||
0.412299 | + | 0.911049i | \(0.364726\pi\) | |||||||
\(644\) | −29.4182 | −1.15924 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.20793 | 0.322937 | ||||||||
\(647\) | 37.6568 | 1.48044 | 0.740221 | − | 0.672363i | \(-0.234721\pi\) | ||||
0.740221 | + | 0.672363i | \(0.234721\pi\) | |||||||
\(648\) | 2.68125 | 0.105329 | ||||||||
\(649\) | 14.8660 | 0.583542 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.26461 | 0.167143 | ||||||||
\(652\) | −15.6219 | −0.611802 | ||||||||
\(653\) | 15.3216 | 0.599579 | 0.299790 | − | 0.954005i | \(-0.403084\pi\) | ||||
0.299790 | + | 0.954005i | \(0.403084\pi\) | |||||||
\(654\) | 3.76329 | 0.147156 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −30.6414 | −1.19635 | ||||||||
\(657\) | −12.4726 | −0.486601 | ||||||||
\(658\) | 58.5727 | 2.28340 | ||||||||
\(659\) | 21.7590 | 0.847612 | 0.423806 | − | 0.905753i | \(-0.360694\pi\) | ||||
0.423806 | + | 0.905753i | \(0.360694\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.7921 | −1.43105 | −0.715524 | − | 0.698589i | \(-0.753812\pi\) | ||||
−0.715524 | + | 0.698589i | \(0.753812\pi\) | |||||||
\(662\) | −21.6692 | −0.842197 | ||||||||
\(663\) | −0.334520 | −0.0129917 | ||||||||
\(664\) | −5.32577 | −0.206680 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.85969 | 0.188309 | ||||||||
\(667\) | 41.0500 | 1.58946 | ||||||||
\(668\) | −6.03317 | −0.233430 | ||||||||
\(669\) | 5.75366 | 0.222449 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.7563 | 0.762683 | ||||||||
\(672\) | 5.92188 | 0.228442 | ||||||||
\(673\) | −38.7475 | −1.49361 | −0.746804 | − | 0.665044i | \(-0.768413\pi\) | ||||
−0.746804 | + | 0.665044i | \(0.768413\pi\) | |||||||
\(674\) | 22.8838 | 0.881451 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.3953 | −0.707513 | ||||||||
\(677\) | 44.4839 | 1.70966 | 0.854828 | − | 0.518912i | \(-0.173663\pi\) | ||||
0.854828 | + | 0.518912i | \(0.173663\pi\) | |||||||
\(678\) | −2.08501 | −0.0800743 | ||||||||
\(679\) | 3.63178 | 0.139375 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.849394 | 0.0325488 | ||||||||
\(682\) | 19.5711 | 0.749415 | ||||||||
\(683\) | −40.9070 | −1.56526 | −0.782631 | − | 0.622485i | \(-0.786123\pi\) | ||||
−0.782631 | + | 0.622485i | \(0.786123\pi\) | |||||||
\(684\) | 23.6790 | 0.905388 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.37671 | −0.128923 | ||||||||
\(687\) | 5.84817 | 0.223122 | ||||||||
\(688\) | −4.29153 | −0.163613 | ||||||||
\(689\) | −3.20127 | −0.121959 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.0512 | 0.914949 | 0.457475 | − | 0.889223i | \(-0.348754\pi\) | ||||
0.457475 | + | 0.889223i | \(0.348754\pi\) | |||||||
\(692\) | 34.4827 | 1.31083 | ||||||||
\(693\) | 20.0271 | 0.760765 | ||||||||
\(694\) | −46.1696 | −1.75257 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.606059 | −0.0229726 | ||||||||
\(697\) | 6.88367 | 0.260738 | ||||||||
\(698\) | −39.0964 | −1.47982 | ||||||||
\(699\) | 3.15465 | 0.119320 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.7283 | 1.61383 | 0.806914 | − | 0.590670i | \(-0.201136\pi\) | ||||
0.806914 | + | 0.590670i | \(0.201136\pi\) | |||||||
\(702\) | −4.05329 | −0.152982 | ||||||||
\(703\) | −3.63830 | −0.137221 | ||||||||
\(704\) | 11.9015 | 0.448556 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −59.5078 | −2.23960 | ||||||||
\(707\) | 8.82604 | 0.331937 | ||||||||
\(708\) | −3.07581 | −0.115596 | ||||||||
\(709\) | 4.99747 | 0.187684 | 0.0938420 | − | 0.995587i | \(-0.470085\pi\) | ||||
0.0938420 | + | 0.995587i | \(0.470085\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −48.5855 | −1.82210 | ||||||||
\(712\) | −3.43631 | −0.128781 | ||||||||
\(713\) | −23.5736 | −0.882840 | ||||||||
\(714\) | −1.43633 | −0.0537531 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16.4011 | −0.612939 | ||||||||
\(717\) | 2.06324 | 0.0770530 | ||||||||
\(718\) | −28.6633 | −1.06971 | ||||||||
\(719\) | −28.1008 | −1.04798 | −0.523991 | − | 0.851724i | \(-0.675558\pi\) | ||||
−0.523991 | + | 0.851724i | \(0.675558\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.30818 | −0.0859612 | ||||||||
\(722\) | 0.261353 | 0.00972654 | ||||||||
\(723\) | 0.575591 | 0.0214064 | ||||||||
\(724\) | −12.1796 | −0.452651 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.06946 | 0.113919 | ||||||||
\(727\) | −32.7169 | −1.21340 | −0.606701 | − | 0.794930i | \(-0.707508\pi\) | ||||
−0.606701 | + | 0.794930i | \(0.707508\pi\) | |||||||
\(728\) | −2.04703 | −0.0758681 | ||||||||
\(729\) | −24.8653 | −0.920939 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.964104 | 0.0356587 | ||||||||
\(732\) | −4.08762 | −0.151083 | ||||||||
\(733\) | 7.67000 | 0.283298 | 0.141649 | − | 0.989917i | \(-0.454760\pi\) | ||||
0.141649 | + | 0.989917i | \(0.454760\pi\) | |||||||
\(734\) | −7.44216 | −0.274695 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −32.7346 | −1.20661 | ||||||||
\(737\) | −4.69944 | −0.173106 | ||||||||
\(738\) | 41.4242 | 1.52484 | ||||||||
\(739\) | −3.07210 | −0.113009 | −0.0565045 | − | 0.998402i | \(-0.517996\pi\) | ||||
−0.0565045 | + | 0.998402i | \(0.517996\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.50711 | 0.0553651 | ||||||||
\(742\) | −13.7453 | −0.504605 | ||||||||
\(743\) | −1.63867 | −0.0601169 | −0.0300585 | − | 0.999548i | \(-0.509569\pi\) | ||||
−0.0300585 | + | 0.999548i | \(0.509569\pi\) | |||||||
\(744\) | 0.348040 | 0.0127598 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 25.7844 | 0.944034 | ||||||||
\(747\) | 50.8097 | 1.85903 | ||||||||
\(748\) | −3.15998 | −0.115540 | ||||||||
\(749\) | −0.409627 | −0.0149674 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.29060 | −0.0470948 | −0.0235474 | − | 0.999723i | \(-0.507496\pi\) | ||||
−0.0235474 | + | 0.999723i | \(0.507496\pi\) | |||||||
\(752\) | 33.7338 | 1.23014 | ||||||||
\(753\) | −2.29616 | −0.0836767 | ||||||||
\(754\) | −33.2332 | −1.21028 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.34324 | −0.303441 | ||||||||
\(757\) | −25.9057 | −0.941559 | −0.470780 | − | 0.882251i | \(-0.656027\pi\) | ||||
−0.470780 | + | 0.882251i | \(0.656027\pi\) | |||||||
\(758\) | 51.4490 | 1.86871 | ||||||||
\(759\) | 1.49500 | 0.0542649 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.4619 | 0.850495 | 0.425247 | − | 0.905077i | \(-0.360187\pi\) | ||||
0.425247 | + | 0.905077i | \(0.360187\pi\) | |||||||
\(762\) | 2.62897 | 0.0952376 | ||||||||
\(763\) | −36.5092 | −1.32172 | ||||||||
\(764\) | 45.4622 | 1.64477 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −49.8987 | −1.80291 | ||||||||
\(767\) | 14.4966 | 0.523443 | ||||||||
\(768\) | 3.64373 | 0.131482 | ||||||||
\(769\) | 42.1622 | 1.52041 | 0.760205 | − | 0.649684i | \(-0.225099\pi\) | ||||
0.760205 | + | 0.649684i | \(0.225099\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.91474 | −0.0689578 | ||||||||
\(772\) | −21.7508 | −0.782829 | ||||||||
\(773\) | 13.0799 | 0.470452 | 0.235226 | − | 0.971941i | \(-0.424417\pi\) | ||||
0.235226 | + | 0.971941i | \(0.424417\pi\) | |||||||
\(774\) | 5.80173 | 0.208539 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.296394 | 0.0106399 | ||||||||
\(777\) | 0.636674 | 0.0228406 | ||||||||
\(778\) | 13.1359 | 0.470944 | ||||||||
\(779\) | −31.0130 | −1.11116 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.5872 | 0.665101 | ||||||||
\(782\) | 7.93963 | 0.283921 | ||||||||
\(783\) | 11.6421 | 0.416055 | ||||||||
\(784\) | −31.9855 | −1.14234 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.18568 | 0.149298 | ||||||||
\(787\) | 18.6616 | 0.665215 | 0.332607 | − | 0.943065i | \(-0.392072\pi\) | ||||
0.332607 | + | 0.943065i | \(0.392072\pi\) | |||||||
\(788\) | −27.6328 | −0.984378 | ||||||||
\(789\) | −4.16888 | −0.148416 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.2275 | 0.719207 | ||||||||
\(792\) | 1.63443 | 0.0580770 | ||||||||
\(793\) | 19.2654 | 0.684134 | ||||||||
\(794\) | 38.2897 | 1.35885 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.6305 | 0.943893 | ||||||||
\(797\) | 17.6220 | 0.624203 | 0.312102 | − | 0.950049i | \(-0.398967\pi\) | ||||
0.312102 | + | 0.950049i | \(0.398967\pi\) | |||||||
\(798\) | 6.47107 | 0.229073 | ||||||||
\(799\) | −7.57837 | −0.268104 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32.7836 | 1.15835 | ||||||||
\(802\) | 71.3765 | 2.52039 | ||||||||
\(803\) | −7.49895 | −0.264632 | ||||||||
\(804\) | 0.972326 | 0.0342913 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 19.0848 | 0.672232 | ||||||||
\(807\) | 0.417928 | 0.0147118 | ||||||||
\(808\) | 0.720303 | 0.0253402 | ||||||||
\(809\) | 3.90127 | 0.137161 | 0.0685807 | − | 0.997646i | \(-0.478153\pi\) | ||||
0.0685807 | + | 0.997646i | \(0.478153\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.7960 | 0.765361 | 0.382681 | − | 0.923881i | \(-0.375001\pi\) | ||||
0.382681 | + | 0.923881i | \(0.375001\pi\) | |||||||
\(812\) | −68.4068 | −2.40061 | ||||||||
\(813\) | −1.62710 | −0.0570651 | ||||||||
\(814\) | 2.92181 | 0.102410 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.827222 | −0.0289586 | ||||||||
\(817\) | −4.34358 | −0.151963 | ||||||||
\(818\) | 7.08152 | 0.247600 | ||||||||
\(819\) | 19.5294 | 0.682413 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.5054 | −1.48345 | −0.741724 | − | 0.670705i | \(-0.765991\pi\) | ||||
−0.741724 | + | 0.670705i | \(0.765991\pi\) | |||||||
\(822\) | 0.642809 | 0.0224205 | ||||||||
\(823\) | −27.8169 | −0.969637 | −0.484818 | − | 0.874615i | \(-0.661114\pi\) | ||||
−0.484818 | + | 0.874615i | \(0.661114\pi\) | |||||||
\(824\) | −0.188374 | −0.00656230 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 62.2441 | 2.16575 | ||||||||
\(827\) | −34.9291 | −1.21460 | −0.607302 | − | 0.794471i | \(-0.707748\pi\) | ||||
−0.607302 | + | 0.794471i | \(0.707748\pi\) | |||||||
\(828\) | 22.9050 | 0.796003 | ||||||||
\(829\) | −31.8932 | −1.10769 | −0.553847 | − | 0.832618i | \(-0.686841\pi\) | ||||
−0.553847 | + | 0.832618i | \(0.686841\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.42142 | −0.0839982 | ||||||||
\(832\) | 11.6058 | 0.402359 | ||||||||
\(833\) | 7.18562 | 0.248967 | ||||||||
\(834\) | 1.96701 | 0.0681119 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 14.2366 | 0.492384 | ||||||||
\(837\) | −6.68569 | −0.231091 | ||||||||
\(838\) | −15.7829 | −0.545212 | ||||||||
\(839\) | −34.5556 | −1.19299 | −0.596497 | − | 0.802616i | \(-0.703441\pi\) | ||||
−0.596497 | + | 0.802616i | \(0.703441\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 66.4545 | 2.29153 | ||||||||
\(842\) | 72.8050 | 2.50902 | ||||||||
\(843\) | 2.63865 | 0.0908800 | ||||||||
\(844\) | 18.8534 | 0.648959 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −45.6047 | −1.56792 | ||||||||
\(847\) | −29.7781 | −1.02319 | ||||||||
\(848\) | −7.91631 | −0.271847 | ||||||||
\(849\) | −1.01807 | −0.0349401 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.51937 | −0.120642 | ||||||||
\(852\) | −3.84573 | −0.131752 | ||||||||
\(853\) | −49.1182 | −1.68178 | −0.840888 | − | 0.541209i | \(-0.817967\pi\) | ||||
−0.840888 | + | 0.541209i | \(0.817967\pi\) | |||||||
\(854\) | 82.7197 | 2.83061 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.0334301 | −0.00114262 | ||||||||
\(857\) | 32.0392 | 1.09444 | 0.547220 | − | 0.836989i | \(-0.315686\pi\) | ||||
0.547220 | + | 0.836989i | \(0.315686\pi\) | |||||||
\(858\) | −1.21032 | −0.0413196 | ||||||||
\(859\) | 33.2548 | 1.13464 | 0.567320 | − | 0.823498i | \(-0.307980\pi\) | ||||
0.567320 | + | 0.823498i | \(0.307980\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.42704 | 0.184953 | ||||||||
\(862\) | 20.2320 | 0.689106 | ||||||||
\(863\) | 37.0582 | 1.26147 | 0.630737 | − | 0.775996i | \(-0.282753\pi\) | ||||
0.630737 | + | 0.775996i | \(0.282753\pi\) | |||||||
\(864\) | −9.28381 | −0.315842 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −34.2205 | −1.16286 | ||||||||
\(867\) | −3.21303 | −0.109120 | ||||||||
\(868\) | 39.2838 | 1.33338 | ||||||||
\(869\) | −29.2113 | −0.990925 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.58267 | −0.155278 | ||||||||
\(872\) | −2.97956 | −0.100900 | ||||||||
\(873\) | −2.82770 | −0.0957033 | ||||||||
\(874\) | −35.7704 | −1.20995 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.55155 | 0.0524220 | ||||||||
\(877\) | −25.6636 | −0.866597 | −0.433298 | − | 0.901250i | \(-0.642650\pi\) | ||||
−0.433298 | + | 0.901250i | \(0.642650\pi\) | |||||||
\(878\) | 15.3926 | 0.519475 | ||||||||
\(879\) | −2.22088 | −0.0749085 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.09265 | 0.0705031 | 0.0352515 | − | 0.999378i | \(-0.488777\pi\) | ||||
0.0352515 | + | 0.999378i | \(0.488777\pi\) | |||||||
\(882\) | 43.2412 | 1.45601 | ||||||||
\(883\) | −55.5019 | −1.86779 | −0.933894 | − | 0.357551i | \(-0.883612\pi\) | ||||
−0.933894 | + | 0.357551i | \(0.883612\pi\) | |||||||
\(884\) | −3.08146 | −0.103641 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.4706 | −0.418957 | ||||||||
\(887\) | 4.21678 | 0.141586 | 0.0707928 | − | 0.997491i | \(-0.477447\pi\) | ||||
0.0707928 | + | 0.997491i | \(0.477447\pi\) | |||||||
\(888\) | 0.0519597 | 0.00174365 | ||||||||
\(889\) | −25.5047 | −0.855400 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.3796 | −0.515237 | ||||||||
\(892\) | 53.0003 | 1.77458 | ||||||||
\(893\) | 34.1428 | 1.14255 | ||||||||
\(894\) | 3.32606 | 0.111240 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9.40676 | −0.314258 | ||||||||
\(897\) | 1.45785 | 0.0486761 | ||||||||
\(898\) | −28.7489 | −0.959364 | ||||||||
\(899\) | −54.8164 | −1.82823 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.77842 | 0.0592477 | ||||||||
\(902\) | 24.9057 | 0.829268 | ||||||||
\(903\) | 0.760093 | 0.0252943 | ||||||||
\(904\) | 1.65079 | 0.0549044 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.91956 | 0.263110 | ||||||||
\(907\) | 35.4222 | 1.17617 | 0.588087 | − | 0.808797i | \(-0.299881\pi\) | ||||
0.588087 | + | 0.808797i | \(0.299881\pi\) | |||||||
\(908\) | 7.82426 | 0.259657 | ||||||||
\(909\) | −6.87195 | −0.227928 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.6877 | 0.354100 | 0.177050 | − | 0.984202i | \(-0.443345\pi\) | ||||
0.177050 | + | 0.984202i | \(0.443345\pi\) | |||||||
\(912\) | 3.72688 | 0.123409 | ||||||||
\(913\) | 30.5486 | 1.01101 | ||||||||
\(914\) | 74.0251 | 2.44853 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 53.8709 | 1.77995 | ||||||||
\(917\) | −40.6069 | −1.34096 | ||||||||
\(918\) | 2.25175 | 0.0743187 | ||||||||
\(919\) | −1.25334 | −0.0413437 | −0.0206719 | − | 0.999786i | \(-0.506581\pi\) | ||||
−0.0206719 | + | 0.999786i | \(0.506581\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.52415 | 0.182027 | ||||||||
\(922\) | 61.1924 | 2.01526 | ||||||||
\(923\) | 18.1253 | 0.596602 | ||||||||
\(924\) | −2.49130 | −0.0819579 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −67.7439 | −2.22620 | ||||||||
\(927\) | 1.79715 | 0.0590262 | ||||||||
\(928\) | −76.1186 | −2.49872 | ||||||||
\(929\) | −8.43820 | −0.276848 | −0.138424 | − | 0.990373i | \(-0.544204\pi\) | ||||
−0.138424 | + | 0.990373i | \(0.544204\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.3734 | −1.06099 | ||||||||
\(932\) | 29.0594 | 0.951871 | ||||||||
\(933\) | −2.52295 | −0.0825978 | ||||||||
\(934\) | 68.3020 | 2.23491 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.59382 | 0.0520956 | ||||||||
\(937\) | −41.1596 | −1.34463 | −0.672313 | − | 0.740267i | \(-0.734699\pi\) | ||||
−0.672313 | + | 0.740267i | \(0.734699\pi\) | |||||||
\(938\) | −19.6766 | −0.642463 | ||||||||
\(939\) | −1.99020 | −0.0649476 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.7706 | 1.29649 | 0.648243 | − | 0.761434i | \(-0.275504\pi\) | ||||
0.648243 | + | 0.761434i | \(0.275504\pi\) | |||||||
\(942\) | −5.87733 | −0.191494 | ||||||||
\(943\) | −29.9993 | −0.976910 | ||||||||
\(944\) | 35.8482 | 1.16676 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.48820 | 0.113411 | ||||||||
\(947\) | −5.84267 | −0.189861 | −0.0949306 | − | 0.995484i | \(-0.530263\pi\) | ||||
−0.0949306 | + | 0.995484i | \(0.530263\pi\) | |||||||
\(948\) | 6.04389 | 0.196296 | ||||||||
\(949\) | −7.31262 | −0.237378 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.53142 | 0.179368 | ||||||||
\(952\) | 1.13720 | 0.0368568 | ||||||||
\(953\) | 28.3236 | 0.917492 | 0.458746 | − | 0.888567i | \(-0.348299\pi\) | ||||
0.458746 | + | 0.888567i | \(0.348299\pi\) | |||||||
\(954\) | 10.7021 | 0.346492 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 19.0057 | 0.614688 | ||||||||
\(957\) | 3.47635 | 0.112374 | ||||||||
\(958\) | −53.2305 | −1.71980 | ||||||||
\(959\) | −6.23614 | −0.201376 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.479267 | 0.0154602 | ||||||||
\(962\) | 2.84921 | 0.0918623 | ||||||||
\(963\) | 0.318935 | 0.0102775 | ||||||||
\(964\) | 5.30210 | 0.170769 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.25955 | 0.201398 | ||||||||
\(967\) | −8.21946 | −0.264320 | −0.132160 | − | 0.991228i | \(-0.542191\pi\) | ||||
−0.132160 | + | 0.991228i | \(0.542191\pi\) | |||||||
\(968\) | −2.43022 | −0.0781103 | ||||||||
\(969\) | −0.837253 | −0.0268965 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.9899 | −1.09079 | −0.545394 | − | 0.838180i | \(-0.683620\pi\) | ||||
−0.545394 | + | 0.838180i | \(0.683620\pi\) | |||||||
\(972\) | 9.76586 | 0.313240 | ||||||||
\(973\) | −19.0827 | −0.611763 | ||||||||
\(974\) | −59.3686 | −1.90229 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 47.6407 | 1.52494 | ||||||||
\(977\) | 27.6406 | 0.884302 | 0.442151 | − | 0.896941i | \(-0.354215\pi\) | ||||
0.442151 | + | 0.896941i | \(0.354215\pi\) | |||||||
\(978\) | 3.32401 | 0.106290 | ||||||||
\(979\) | 19.7107 | 0.629956 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.4260 | 0.907573 | ||||||||
\(982\) | −19.4737 | −0.621432 | ||||||||
\(983\) | 33.7780 | 1.07735 | 0.538675 | − | 0.842513i | \(-0.318925\pi\) | ||||
0.538675 | + | 0.842513i | \(0.318925\pi\) | |||||||
\(984\) | 0.442907 | 0.0141194 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 18.4622 | 0.587957 | ||||||||
\(987\) | −5.97474 | −0.190178 | ||||||||
\(988\) | 13.8829 | 0.441674 | ||||||||
\(989\) | −4.20160 | −0.133603 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.6864 | 1.03832 | 0.519160 | − | 0.854677i | \(-0.326245\pi\) | ||||
0.519160 | + | 0.854677i | \(0.326245\pi\) | |||||||
\(992\) | 43.7124 | 1.38787 | ||||||||
\(993\) | 2.21038 | 0.0701441 | ||||||||
\(994\) | 77.8246 | 2.46844 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.32057 | −0.200275 | ||||||||
\(997\) | 24.8137 | 0.785859 | 0.392930 | − | 0.919569i | \(-0.371462\pi\) | ||||
0.392930 | + | 0.919569i | \(0.371462\pi\) | |||||||
\(998\) | −54.8929 | −1.73760 | ||||||||
\(999\) | −0.998123 | −0.0315792 |
(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 | 1075.2.a.o.1.1 | yes | 5 | |
3.2 | odd | 2 | 9675.2.a.cb.1.5 | 5 | |||
5.2 | odd | 4 | 1075.2.b.i.474.2 | 10 | |||
5.3 | odd | 4 | 1075.2.b.i.474.9 | 10 | |||
5.4 | even | 2 | 1075.2.a.n.1.5 | ✓ | 5 | ||
15.14 | odd | 2 | 9675.2.a.cc.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1075.2.a.n.1.5 | ✓ | 5 | 5.4 | even | 2 | ||
1075.2.a.o.1.1 | yes | 5 | 1.1 | even | 1 | trivial | |
1075.2.b.i.474.2 | 10 | 5.2 | odd | 4 | |||
1075.2.b.i.474.9 | 10 | 5.3 | odd | 4 | |||
9675.2.a.cb.1.5 | 5 | 3.2 | odd | 2 | |||
9675.2.a.cc.1.1 | 5 | 15.14 | odd | 2 |