Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6010,2,Mod(1,6010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6010, 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("6010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6010 = 2 \cdot 5 \cdot 601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6010.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: | \(47.9900916148\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + 164 x^{7} + 2332 x^{6} - 440 x^{5} - 1344 x^{4} + 244 x^{3} + 295 x^{2} + \cdots - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(3.28691\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6010.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.28691 | 1.32035 | 0.660175 | − | 0.751112i | \(-0.270482\pi\) | ||||
0.660175 | + | 0.751112i | \(0.270482\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.28691 | 0.933629 | ||||||||
\(7\) | −3.46813 | −1.31083 | −0.655415 | − | 0.755269i | \(-0.727506\pi\) | ||||
−0.655415 | + | 0.755269i | \(0.727506\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.22998 | 0.743325 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −3.41913 | −1.03091 | −0.515453 | − | 0.856918i | \(-0.672376\pi\) | ||||
−0.515453 | + | 0.856918i | \(0.672376\pi\) | |||||||
\(12\) | 2.28691 | 0.660175 | ||||||||
\(13\) | −2.63900 | −0.731927 | −0.365964 | − | 0.930629i | \(-0.619261\pi\) | ||||
−0.365964 | + | 0.930629i | \(0.619261\pi\) | |||||||
\(14\) | −3.46813 | −0.926897 | ||||||||
\(15\) | 2.28691 | 0.590479 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.45967 | −0.839092 | −0.419546 | − | 0.907734i | \(-0.637811\pi\) | ||||
−0.419546 | + | 0.907734i | \(0.637811\pi\) | |||||||
\(18\) | 2.22998 | 0.525610 | ||||||||
\(19\) | 1.07603 | 0.246859 | 0.123429 | − | 0.992353i | \(-0.460611\pi\) | ||||
0.123429 | + | 0.992353i | \(0.460611\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −7.93132 | −1.73076 | ||||||||
\(22\) | −3.41913 | −0.728961 | ||||||||
\(23\) | −6.75440 | −1.40839 | −0.704195 | − | 0.710007i | \(-0.748692\pi\) | ||||
−0.704195 | + | 0.710007i | \(0.748692\pi\) | |||||||
\(24\) | 2.28691 | 0.466814 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.63900 | −0.517551 | ||||||||
\(27\) | −1.76098 | −0.338901 | ||||||||
\(28\) | −3.46813 | −0.655415 | ||||||||
\(29\) | −1.95342 | −0.362742 | −0.181371 | − | 0.983415i | \(-0.558053\pi\) | ||||
−0.181371 | + | 0.983415i | \(0.558053\pi\) | |||||||
\(30\) | 2.28691 | 0.417531 | ||||||||
\(31\) | 4.65022 | 0.835204 | 0.417602 | − | 0.908630i | \(-0.362871\pi\) | ||||
0.417602 | + | 0.908630i | \(0.362871\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −7.81926 | −1.36116 | ||||||||
\(34\) | −3.45967 | −0.593328 | ||||||||
\(35\) | −3.46813 | −0.586221 | ||||||||
\(36\) | 2.22998 | 0.371663 | ||||||||
\(37\) | −6.85159 | −1.12639 | −0.563197 | − | 0.826322i | \(-0.690429\pi\) | ||||
−0.563197 | + | 0.826322i | \(0.690429\pi\) | |||||||
\(38\) | 1.07603 | 0.174555 | ||||||||
\(39\) | −6.03517 | −0.966400 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 0.892755 | 0.139425 | 0.0697125 | − | 0.997567i | \(-0.477792\pi\) | ||||
0.0697125 | + | 0.997567i | \(0.477792\pi\) | |||||||
\(42\) | −7.93132 | −1.22383 | ||||||||
\(43\) | 10.1922 | 1.55429 | 0.777145 | − | 0.629321i | \(-0.216667\pi\) | ||||
0.777145 | + | 0.629321i | \(0.216667\pi\) | |||||||
\(44\) | −3.41913 | −0.515453 | ||||||||
\(45\) | 2.22998 | 0.332425 | ||||||||
\(46\) | −6.75440 | −0.995882 | ||||||||
\(47\) | 2.60823 | 0.380449 | 0.190224 | − | 0.981741i | \(-0.439078\pi\) | ||||
0.190224 | + | 0.981741i | \(0.439078\pi\) | |||||||
\(48\) | 2.28691 | 0.330088 | ||||||||
\(49\) | 5.02795 | 0.718278 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −7.91196 | −1.10790 | ||||||||
\(52\) | −2.63900 | −0.365964 | ||||||||
\(53\) | −14.2976 | −1.96393 | −0.981964 | − | 0.189068i | \(-0.939453\pi\) | ||||
−0.981964 | + | 0.189068i | \(0.939453\pi\) | |||||||
\(54\) | −1.76098 | −0.239639 | ||||||||
\(55\) | −3.41913 | −0.461035 | ||||||||
\(56\) | −3.46813 | −0.463449 | ||||||||
\(57\) | 2.46079 | 0.325940 | ||||||||
\(58\) | −1.95342 | −0.256497 | ||||||||
\(59\) | −9.44473 | −1.22960 | −0.614800 | − | 0.788683i | \(-0.710763\pi\) | ||||
−0.614800 | + | 0.788683i | \(0.710763\pi\) | |||||||
\(60\) | 2.28691 | 0.295239 | ||||||||
\(61\) | 9.42299 | 1.20649 | 0.603245 | − | 0.797556i | \(-0.293874\pi\) | ||||
0.603245 | + | 0.797556i | \(0.293874\pi\) | |||||||
\(62\) | 4.65022 | 0.590579 | ||||||||
\(63\) | −7.73385 | −0.974374 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.63900 | −0.327328 | ||||||||
\(66\) | −7.81926 | −0.962484 | ||||||||
\(67\) | 9.09482 | 1.11111 | 0.555554 | − | 0.831480i | \(-0.312506\pi\) | ||||
0.555554 | + | 0.831480i | \(0.312506\pi\) | |||||||
\(68\) | −3.45967 | −0.419546 | ||||||||
\(69\) | −15.4467 | −1.85957 | ||||||||
\(70\) | −3.46813 | −0.414521 | ||||||||
\(71\) | −11.7865 | −1.39880 | −0.699398 | − | 0.714732i | \(-0.746549\pi\) | ||||
−0.699398 | + | 0.714732i | \(0.746549\pi\) | |||||||
\(72\) | 2.22998 | 0.262805 | ||||||||
\(73\) | 3.96524 | 0.464097 | 0.232048 | − | 0.972704i | \(-0.425457\pi\) | ||||
0.232048 | + | 0.972704i | \(0.425457\pi\) | |||||||
\(74\) | −6.85159 | −0.796481 | ||||||||
\(75\) | 2.28691 | 0.264070 | ||||||||
\(76\) | 1.07603 | 0.123429 | ||||||||
\(77\) | 11.8580 | 1.35134 | ||||||||
\(78\) | −6.03517 | −0.683348 | ||||||||
\(79\) | −12.9753 | −1.45983 | −0.729917 | − | 0.683536i | \(-0.760441\pi\) | ||||
−0.729917 | + | 0.683536i | \(0.760441\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −10.7171 | −1.19079 | ||||||||
\(82\) | 0.892755 | 0.0985883 | ||||||||
\(83\) | −10.1444 | −1.11349 | −0.556746 | − | 0.830683i | \(-0.687950\pi\) | ||||
−0.556746 | + | 0.830683i | \(0.687950\pi\) | |||||||
\(84\) | −7.93132 | −0.865378 | ||||||||
\(85\) | −3.45967 | −0.375253 | ||||||||
\(86\) | 10.1922 | 1.09905 | ||||||||
\(87\) | −4.46731 | −0.478946 | ||||||||
\(88\) | −3.41913 | −0.364480 | ||||||||
\(89\) | 0.456762 | 0.0484167 | 0.0242084 | − | 0.999707i | \(-0.492293\pi\) | ||||
0.0242084 | + | 0.999707i | \(0.492293\pi\) | |||||||
\(90\) | 2.22998 | 0.235060 | ||||||||
\(91\) | 9.15240 | 0.959433 | ||||||||
\(92\) | −6.75440 | −0.704195 | ||||||||
\(93\) | 10.6347 | 1.10276 | ||||||||
\(94\) | 2.60823 | 0.269018 | ||||||||
\(95\) | 1.07603 | 0.110399 | ||||||||
\(96\) | 2.28691 | 0.233407 | ||||||||
\(97\) | 16.6254 | 1.68806 | 0.844029 | − | 0.536298i | \(-0.180178\pi\) | ||||
0.844029 | + | 0.536298i | \(0.180178\pi\) | |||||||
\(98\) | 5.02795 | 0.507899 | ||||||||
\(99\) | −7.62458 | −0.766299 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −12.3402 | −1.22790 | −0.613949 | − | 0.789346i | \(-0.710420\pi\) | ||||
−0.613949 | + | 0.789346i | \(0.710420\pi\) | |||||||
\(102\) | −7.91196 | −0.783401 | ||||||||
\(103\) | 8.99878 | 0.886677 | 0.443338 | − | 0.896354i | \(-0.353794\pi\) | ||||
0.443338 | + | 0.896354i | \(0.353794\pi\) | |||||||
\(104\) | −2.63900 | −0.258775 | ||||||||
\(105\) | −7.93132 | −0.774018 | ||||||||
\(106\) | −14.2976 | −1.38871 | ||||||||
\(107\) | −3.18238 | −0.307652 | −0.153826 | − | 0.988098i | \(-0.549160\pi\) | ||||
−0.153826 | + | 0.988098i | \(0.549160\pi\) | |||||||
\(108\) | −1.76098 | −0.169450 | ||||||||
\(109\) | 1.47514 | 0.141293 | 0.0706465 | − | 0.997501i | \(-0.477494\pi\) | ||||
0.0706465 | + | 0.997501i | \(0.477494\pi\) | |||||||
\(110\) | −3.41913 | −0.326001 | ||||||||
\(111\) | −15.6690 | −1.48724 | ||||||||
\(112\) | −3.46813 | −0.327708 | ||||||||
\(113\) | −5.35901 | −0.504133 | −0.252067 | − | 0.967710i | \(-0.581110\pi\) | ||||
−0.252067 | + | 0.967710i | \(0.581110\pi\) | |||||||
\(114\) | 2.46079 | 0.230474 | ||||||||
\(115\) | −6.75440 | −0.629851 | ||||||||
\(116\) | −1.95342 | −0.181371 | ||||||||
\(117\) | −5.88491 | −0.544060 | ||||||||
\(118\) | −9.44473 | −0.869458 | ||||||||
\(119\) | 11.9986 | 1.09991 | ||||||||
\(120\) | 2.28691 | 0.208766 | ||||||||
\(121\) | 0.690448 | 0.0627680 | ||||||||
\(122\) | 9.42299 | 0.853118 | ||||||||
\(123\) | 2.04165 | 0.184090 | ||||||||
\(124\) | 4.65022 | 0.417602 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −7.73385 | −0.688986 | ||||||||
\(127\) | 13.4391 | 1.19253 | 0.596263 | − | 0.802789i | \(-0.296651\pi\) | ||||
0.596263 | + | 0.802789i | \(0.296651\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 23.3086 | 2.05221 | ||||||||
\(130\) | −2.63900 | −0.231456 | ||||||||
\(131\) | 6.82635 | 0.596421 | 0.298211 | − | 0.954500i | \(-0.403610\pi\) | ||||
0.298211 | + | 0.954500i | \(0.403610\pi\) | |||||||
\(132\) | −7.81926 | −0.680579 | ||||||||
\(133\) | −3.73182 | −0.323590 | ||||||||
\(134\) | 9.09482 | 0.785672 | ||||||||
\(135\) | −1.76098 | −0.151561 | ||||||||
\(136\) | −3.45967 | −0.296664 | ||||||||
\(137\) | −1.49274 | −0.127534 | −0.0637668 | − | 0.997965i | \(-0.520311\pi\) | ||||
−0.0637668 | + | 0.997965i | \(0.520311\pi\) | |||||||
\(138\) | −15.4467 | −1.31491 | ||||||||
\(139\) | 3.60693 | 0.305935 | 0.152968 | − | 0.988231i | \(-0.451117\pi\) | ||||
0.152968 | + | 0.988231i | \(0.451117\pi\) | |||||||
\(140\) | −3.46813 | −0.293111 | ||||||||
\(141\) | 5.96479 | 0.502326 | ||||||||
\(142\) | −11.7865 | −0.989098 | ||||||||
\(143\) | 9.02309 | 0.754548 | ||||||||
\(144\) | 2.22998 | 0.185831 | ||||||||
\(145\) | −1.95342 | −0.162223 | ||||||||
\(146\) | 3.96524 | 0.328166 | ||||||||
\(147\) | 11.4985 | 0.948378 | ||||||||
\(148\) | −6.85159 | −0.563197 | ||||||||
\(149\) | −2.87791 | −0.235767 | −0.117884 | − | 0.993027i | \(-0.537611\pi\) | ||||
−0.117884 | + | 0.993027i | \(0.537611\pi\) | |||||||
\(150\) | 2.28691 | 0.186726 | ||||||||
\(151\) | −16.4331 | −1.33731 | −0.668655 | − | 0.743573i | \(-0.733130\pi\) | ||||
−0.668655 | + | 0.743573i | \(0.733130\pi\) | |||||||
\(152\) | 1.07603 | 0.0872777 | ||||||||
\(153\) | −7.71497 | −0.623718 | ||||||||
\(154\) | 11.8580 | 0.955545 | ||||||||
\(155\) | 4.65022 | 0.373515 | ||||||||
\(156\) | −6.03517 | −0.483200 | ||||||||
\(157\) | 12.2295 | 0.976021 | 0.488011 | − | 0.872838i | \(-0.337723\pi\) | ||||
0.488011 | + | 0.872838i | \(0.337723\pi\) | |||||||
\(158\) | −12.9753 | −1.03226 | ||||||||
\(159\) | −32.6974 | −2.59307 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 23.4252 | 1.84616 | ||||||||
\(162\) | −10.7171 | −0.842018 | ||||||||
\(163\) | −1.53692 | −0.120381 | −0.0601906 | − | 0.998187i | \(-0.519171\pi\) | ||||
−0.0601906 | + | 0.998187i | \(0.519171\pi\) | |||||||
\(164\) | 0.892755 | 0.0697125 | ||||||||
\(165\) | −7.81926 | −0.608728 | ||||||||
\(166\) | −10.1444 | −0.787357 | ||||||||
\(167\) | 5.13478 | 0.397341 | 0.198671 | − | 0.980066i | \(-0.436338\pi\) | ||||
0.198671 | + | 0.980066i | \(0.436338\pi\) | |||||||
\(168\) | −7.93132 | −0.611915 | ||||||||
\(169\) | −6.03568 | −0.464283 | ||||||||
\(170\) | −3.45967 | −0.265344 | ||||||||
\(171\) | 2.39952 | 0.183496 | ||||||||
\(172\) | 10.1922 | 0.777145 | ||||||||
\(173\) | −0.0718874 | −0.00546550 | −0.00273275 | − | 0.999996i | \(-0.500870\pi\) | ||||
−0.00273275 | + | 0.999996i | \(0.500870\pi\) | |||||||
\(174\) | −4.46731 | −0.338666 | ||||||||
\(175\) | −3.46813 | −0.262166 | ||||||||
\(176\) | −3.41913 | −0.257727 | ||||||||
\(177\) | −21.5993 | −1.62350 | ||||||||
\(178\) | 0.456762 | 0.0342358 | ||||||||
\(179\) | −5.16654 | −0.386166 | −0.193083 | − | 0.981182i | \(-0.561849\pi\) | ||||
−0.193083 | + | 0.981182i | \(0.561849\pi\) | |||||||
\(180\) | 2.22998 | 0.166213 | ||||||||
\(181\) | 1.51191 | 0.112380 | 0.0561898 | − | 0.998420i | \(-0.482105\pi\) | ||||
0.0561898 | + | 0.998420i | \(0.482105\pi\) | |||||||
\(182\) | 9.15240 | 0.678421 | ||||||||
\(183\) | 21.5496 | 1.59299 | ||||||||
\(184\) | −6.75440 | −0.497941 | ||||||||
\(185\) | −6.85159 | −0.503739 | ||||||||
\(186\) | 10.6347 | 0.779771 | ||||||||
\(187\) | 11.8290 | 0.865025 | ||||||||
\(188\) | 2.60823 | 0.190224 | ||||||||
\(189\) | 6.10731 | 0.444241 | ||||||||
\(190\) | 1.07603 | 0.0780635 | ||||||||
\(191\) | 13.0731 | 0.945936 | 0.472968 | − | 0.881080i | \(-0.343183\pi\) | ||||
0.472968 | + | 0.881080i | \(0.343183\pi\) | |||||||
\(192\) | 2.28691 | 0.165044 | ||||||||
\(193\) | −1.07841 | −0.0776260 | −0.0388130 | − | 0.999246i | \(-0.512358\pi\) | ||||
−0.0388130 | + | 0.999246i | \(0.512358\pi\) | |||||||
\(194\) | 16.6254 | 1.19364 | ||||||||
\(195\) | −6.03517 | −0.432187 | ||||||||
\(196\) | 5.02795 | 0.359139 | ||||||||
\(197\) | 13.5161 | 0.962981 | 0.481490 | − | 0.876451i | \(-0.340096\pi\) | ||||
0.481490 | + | 0.876451i | \(0.340096\pi\) | |||||||
\(198\) | −7.62458 | −0.541855 | ||||||||
\(199\) | −20.3859 | −1.44512 | −0.722558 | − | 0.691310i | \(-0.757034\pi\) | ||||
−0.722558 | + | 0.691310i | \(0.757034\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 20.7991 | 1.46705 | ||||||||
\(202\) | −12.3402 | −0.868255 | ||||||||
\(203\) | 6.77473 | 0.475493 | ||||||||
\(204\) | −7.91196 | −0.553948 | ||||||||
\(205\) | 0.892755 | 0.0623527 | ||||||||
\(206\) | 8.99878 | 0.626975 | ||||||||
\(207\) | −15.0621 | −1.04689 | ||||||||
\(208\) | −2.63900 | −0.182982 | ||||||||
\(209\) | −3.67909 | −0.254488 | ||||||||
\(210\) | −7.93132 | −0.547313 | ||||||||
\(211\) | −14.3190 | −0.985761 | −0.492880 | − | 0.870097i | \(-0.664056\pi\) | ||||
−0.492880 | + | 0.870097i | \(0.664056\pi\) | |||||||
\(212\) | −14.2976 | −0.981964 | ||||||||
\(213\) | −26.9546 | −1.84690 | ||||||||
\(214\) | −3.18238 | −0.217543 | ||||||||
\(215\) | 10.1922 | 0.695100 | ||||||||
\(216\) | −1.76098 | −0.119819 | ||||||||
\(217\) | −16.1276 | −1.09481 | ||||||||
\(218\) | 1.47514 | 0.0999092 | ||||||||
\(219\) | 9.06817 | 0.612770 | ||||||||
\(220\) | −3.41913 | −0.230518 | ||||||||
\(221\) | 9.13006 | 0.614154 | ||||||||
\(222\) | −15.6690 | −1.05163 | ||||||||
\(223\) | 12.1093 | 0.810899 | 0.405450 | − | 0.914117i | \(-0.367115\pi\) | ||||
0.405450 | + | 0.914117i | \(0.367115\pi\) | |||||||
\(224\) | −3.46813 | −0.231724 | ||||||||
\(225\) | 2.22998 | 0.148665 | ||||||||
\(226\) | −5.35901 | −0.356476 | ||||||||
\(227\) | 0.00202746 | 0.000134567 0 | 6.72835e−5 | − | 1.00000i | \(-0.499979\pi\) | ||||
6.72835e−5 | 1.00000i | \(0.499979\pi\) | ||||||||
\(228\) | 2.46079 | 0.162970 | ||||||||
\(229\) | −4.08309 | −0.269818 | −0.134909 | − | 0.990858i | \(-0.543074\pi\) | ||||
−0.134909 | + | 0.990858i | \(0.543074\pi\) | |||||||
\(230\) | −6.75440 | −0.445372 | ||||||||
\(231\) | 27.1182 | 1.78425 | ||||||||
\(232\) | −1.95342 | −0.128249 | ||||||||
\(233\) | −25.4843 | −1.66953 | −0.834764 | − | 0.550607i | \(-0.814396\pi\) | ||||
−0.834764 | + | 0.550607i | \(0.814396\pi\) | |||||||
\(234\) | −5.88491 | −0.384708 | ||||||||
\(235\) | 2.60823 | 0.170142 | ||||||||
\(236\) | −9.44473 | −0.614800 | ||||||||
\(237\) | −29.6734 | −1.92749 | ||||||||
\(238\) | 11.9986 | 0.777752 | ||||||||
\(239\) | −11.3288 | −0.732801 | −0.366400 | − | 0.930457i | \(-0.619410\pi\) | ||||
−0.366400 | + | 0.930457i | \(0.619410\pi\) | |||||||
\(240\) | 2.28691 | 0.147620 | ||||||||
\(241\) | 17.6302 | 1.13566 | 0.567829 | − | 0.823146i | \(-0.307783\pi\) | ||||
0.567829 | + | 0.823146i | \(0.307783\pi\) | |||||||
\(242\) | 0.690448 | 0.0443837 | ||||||||
\(243\) | −19.2262 | −1.23336 | ||||||||
\(244\) | 9.42299 | 0.603245 | ||||||||
\(245\) | 5.02795 | 0.321224 | ||||||||
\(246\) | 2.04165 | 0.130171 | ||||||||
\(247\) | −2.83965 | −0.180682 | ||||||||
\(248\) | 4.65022 | 0.295289 | ||||||||
\(249\) | −23.1993 | −1.47020 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 20.1405 | 1.27126 | 0.635629 | − | 0.771995i | \(-0.280741\pi\) | ||||
0.635629 | + | 0.771995i | \(0.280741\pi\) | |||||||
\(252\) | −7.73385 | −0.487187 | ||||||||
\(253\) | 23.0942 | 1.45192 | ||||||||
\(254\) | 13.4391 | 0.843244 | ||||||||
\(255\) | −7.91196 | −0.495466 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.8286 | 1.42401 | 0.712005 | − | 0.702175i | \(-0.247787\pi\) | ||||
0.712005 | + | 0.702175i | \(0.247787\pi\) | |||||||
\(258\) | 23.3086 | 1.45113 | ||||||||
\(259\) | 23.7622 | 1.47651 | ||||||||
\(260\) | −2.63900 | −0.163664 | ||||||||
\(261\) | −4.35609 | −0.269635 | ||||||||
\(262\) | 6.82635 | 0.421733 | ||||||||
\(263\) | −0.616108 | −0.0379909 | −0.0189954 | − | 0.999820i | \(-0.506047\pi\) | ||||
−0.0189954 | + | 0.999820i | \(0.506047\pi\) | |||||||
\(264\) | −7.81926 | −0.481242 | ||||||||
\(265\) | −14.2976 | −0.878295 | ||||||||
\(266\) | −3.73182 | −0.228813 | ||||||||
\(267\) | 1.04458 | 0.0639270 | ||||||||
\(268\) | 9.09482 | 0.555554 | ||||||||
\(269\) | −12.1415 | −0.740281 | −0.370141 | − | 0.928976i | \(-0.620691\pi\) | ||||
−0.370141 | + | 0.928976i | \(0.620691\pi\) | |||||||
\(270\) | −1.76098 | −0.107170 | ||||||||
\(271\) | −2.61919 | −0.159104 | −0.0795521 | − | 0.996831i | \(-0.525349\pi\) | ||||
−0.0795521 | + | 0.996831i | \(0.525349\pi\) | |||||||
\(272\) | −3.45967 | −0.209773 | ||||||||
\(273\) | 20.9308 | 1.26679 | ||||||||
\(274\) | −1.49274 | −0.0901798 | ||||||||
\(275\) | −3.41913 | −0.206181 | ||||||||
\(276\) | −15.4467 | −0.929784 | ||||||||
\(277\) | 12.2159 | 0.733985 | 0.366993 | − | 0.930224i | \(-0.380387\pi\) | ||||
0.366993 | + | 0.930224i | \(0.380387\pi\) | |||||||
\(278\) | 3.60693 | 0.216329 | ||||||||
\(279\) | 10.3699 | 0.620828 | ||||||||
\(280\) | −3.46813 | −0.207261 | ||||||||
\(281\) | 10.2239 | 0.609904 | 0.304952 | − | 0.952368i | \(-0.401360\pi\) | ||||
0.304952 | + | 0.952368i | \(0.401360\pi\) | |||||||
\(282\) | 5.96479 | 0.355198 | ||||||||
\(283\) | 20.7073 | 1.23092 | 0.615462 | − | 0.788167i | \(-0.288970\pi\) | ||||
0.615462 | + | 0.788167i | \(0.288970\pi\) | |||||||
\(284\) | −11.7865 | −0.699398 | ||||||||
\(285\) | 2.46079 | 0.145765 | ||||||||
\(286\) | 9.02309 | 0.533546 | ||||||||
\(287\) | −3.09619 | −0.182763 | ||||||||
\(288\) | 2.22998 | 0.131403 | ||||||||
\(289\) | −5.03071 | −0.295924 | ||||||||
\(290\) | −1.95342 | −0.114709 | ||||||||
\(291\) | 38.0209 | 2.22883 | ||||||||
\(292\) | 3.96524 | 0.232048 | ||||||||
\(293\) | −24.4481 | −1.42827 | −0.714136 | − | 0.700007i | \(-0.753180\pi\) | ||||
−0.714136 | + | 0.700007i | \(0.753180\pi\) | |||||||
\(294\) | 11.4985 | 0.670605 | ||||||||
\(295\) | −9.44473 | −0.549893 | ||||||||
\(296\) | −6.85159 | −0.398241 | ||||||||
\(297\) | 6.02102 | 0.349375 | ||||||||
\(298\) | −2.87791 | −0.166713 | ||||||||
\(299\) | 17.8249 | 1.03084 | ||||||||
\(300\) | 2.28691 | 0.132035 | ||||||||
\(301\) | −35.3478 | −2.03741 | ||||||||
\(302\) | −16.4331 | −0.945621 | ||||||||
\(303\) | −28.2210 | −1.62126 | ||||||||
\(304\) | 1.07603 | 0.0617146 | ||||||||
\(305\) | 9.42299 | 0.539559 | ||||||||
\(306\) | −7.71497 | −0.441035 | ||||||||
\(307\) | −0.655961 | −0.0374376 | −0.0187188 | − | 0.999825i | \(-0.505959\pi\) | ||||
−0.0187188 | + | 0.999825i | \(0.505959\pi\) | |||||||
\(308\) | 11.8580 | 0.675672 | ||||||||
\(309\) | 20.5794 | 1.17072 | ||||||||
\(310\) | 4.65022 | 0.264115 | ||||||||
\(311\) | −7.06795 | −0.400787 | −0.200393 | − | 0.979716i | \(-0.564222\pi\) | ||||
−0.200393 | + | 0.979716i | \(0.564222\pi\) | |||||||
\(312\) | −6.03517 | −0.341674 | ||||||||
\(313\) | 22.6761 | 1.28173 | 0.640863 | − | 0.767655i | \(-0.278577\pi\) | ||||
0.640863 | + | 0.767655i | \(0.278577\pi\) | |||||||
\(314\) | 12.2295 | 0.690151 | ||||||||
\(315\) | −7.73385 | −0.435753 | ||||||||
\(316\) | −12.9753 | −0.729917 | ||||||||
\(317\) | 9.20507 | 0.517008 | 0.258504 | − | 0.966010i | \(-0.416770\pi\) | ||||
0.258504 | + | 0.966010i | \(0.416770\pi\) | |||||||
\(318\) | −32.6974 | −1.83358 | ||||||||
\(319\) | 6.67901 | 0.373953 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −7.27783 | −0.406209 | ||||||||
\(322\) | 23.4252 | 1.30543 | ||||||||
\(323\) | −3.72271 | −0.207137 | ||||||||
\(324\) | −10.7171 | −0.595396 | ||||||||
\(325\) | −2.63900 | −0.146385 | ||||||||
\(326\) | −1.53692 | −0.0851223 | ||||||||
\(327\) | 3.37352 | 0.186556 | ||||||||
\(328\) | 0.892755 | 0.0492942 | ||||||||
\(329\) | −9.04567 | −0.498704 | ||||||||
\(330\) | −7.81926 | −0.430436 | ||||||||
\(331\) | 9.28864 | 0.510550 | 0.255275 | − | 0.966869i | \(-0.417834\pi\) | ||||
0.255275 | + | 0.966869i | \(0.417834\pi\) | |||||||
\(332\) | −10.1444 | −0.556746 | ||||||||
\(333\) | −15.2789 | −0.837278 | ||||||||
\(334\) | 5.13478 | 0.280963 | ||||||||
\(335\) | 9.09482 | 0.496903 | ||||||||
\(336\) | −7.93132 | −0.432689 | ||||||||
\(337\) | 3.36720 | 0.183423 | 0.0917115 | − | 0.995786i | \(-0.470766\pi\) | ||||
0.0917115 | + | 0.995786i | \(0.470766\pi\) | |||||||
\(338\) | −6.03568 | −0.328298 | ||||||||
\(339\) | −12.2556 | −0.665633 | ||||||||
\(340\) | −3.45967 | −0.187627 | ||||||||
\(341\) | −15.8997 | −0.861017 | ||||||||
\(342\) | 2.39952 | 0.129751 | ||||||||
\(343\) | 6.83935 | 0.369290 | ||||||||
\(344\) | 10.1922 | 0.549525 | ||||||||
\(345\) | −15.4467 | −0.831624 | ||||||||
\(346\) | −0.0718874 | −0.00386469 | ||||||||
\(347\) | 7.07999 | 0.380074 | 0.190037 | − | 0.981777i | \(-0.439139\pi\) | ||||
0.190037 | + | 0.981777i | \(0.439139\pi\) | |||||||
\(348\) | −4.46731 | −0.239473 | ||||||||
\(349\) | −30.8890 | −1.65345 | −0.826724 | − | 0.562607i | \(-0.809798\pi\) | ||||
−0.826724 | + | 0.562607i | \(0.809798\pi\) | |||||||
\(350\) | −3.46813 | −0.185379 | ||||||||
\(351\) | 4.64722 | 0.248051 | ||||||||
\(352\) | −3.41913 | −0.182240 | ||||||||
\(353\) | −10.2224 | −0.544082 | −0.272041 | − | 0.962286i | \(-0.587699\pi\) | ||||
−0.272041 | + | 0.962286i | \(0.587699\pi\) | |||||||
\(354\) | −21.5993 | −1.14799 | ||||||||
\(355\) | −11.7865 | −0.625561 | ||||||||
\(356\) | 0.456762 | 0.0242084 | ||||||||
\(357\) | 27.4397 | 1.45226 | ||||||||
\(358\) | −5.16654 | −0.273060 | ||||||||
\(359\) | −7.35821 | −0.388351 | −0.194176 | − | 0.980967i | \(-0.562203\pi\) | ||||
−0.194176 | + | 0.980967i | \(0.562203\pi\) | |||||||
\(360\) | 2.22998 | 0.117530 | ||||||||
\(361\) | −17.8422 | −0.939061 | ||||||||
\(362\) | 1.51191 | 0.0794644 | ||||||||
\(363\) | 1.57900 | 0.0828758 | ||||||||
\(364\) | 9.15240 | 0.479716 | ||||||||
\(365\) | 3.96524 | 0.207550 | ||||||||
\(366\) | 21.5496 | 1.12641 | ||||||||
\(367\) | 24.7672 | 1.29284 | 0.646420 | − | 0.762982i | \(-0.276266\pi\) | ||||
0.646420 | + | 0.762982i | \(0.276266\pi\) | |||||||
\(368\) | −6.75440 | −0.352097 | ||||||||
\(369\) | 1.99082 | 0.103638 | ||||||||
\(370\) | −6.85159 | −0.356197 | ||||||||
\(371\) | 49.5860 | 2.57438 | ||||||||
\(372\) | 10.6347 | 0.551381 | ||||||||
\(373\) | 0.888462 | 0.0460028 | 0.0230014 | − | 0.999735i | \(-0.492678\pi\) | ||||
0.0230014 | + | 0.999735i | \(0.492678\pi\) | |||||||
\(374\) | 11.8290 | 0.611665 | ||||||||
\(375\) | 2.28691 | 0.118096 | ||||||||
\(376\) | 2.60823 | 0.134509 | ||||||||
\(377\) | 5.15509 | 0.265500 | ||||||||
\(378\) | 6.10731 | 0.314126 | ||||||||
\(379\) | −7.54193 | −0.387403 | −0.193701 | − | 0.981061i | \(-0.562049\pi\) | ||||
−0.193701 | + | 0.981061i | \(0.562049\pi\) | |||||||
\(380\) | 1.07603 | 0.0551993 | ||||||||
\(381\) | 30.7340 | 1.57455 | ||||||||
\(382\) | 13.0731 | 0.668878 | ||||||||
\(383\) | 16.9073 | 0.863924 | 0.431962 | − | 0.901892i | \(-0.357821\pi\) | ||||
0.431962 | + | 0.901892i | \(0.357821\pi\) | |||||||
\(384\) | 2.28691 | 0.116704 | ||||||||
\(385\) | 11.8580 | 0.604339 | ||||||||
\(386\) | −1.07841 | −0.0548898 | ||||||||
\(387\) | 22.7283 | 1.15534 | ||||||||
\(388\) | 16.6254 | 0.844029 | ||||||||
\(389\) | −10.4172 | −0.528175 | −0.264088 | − | 0.964499i | \(-0.585071\pi\) | ||||
−0.264088 | + | 0.964499i | \(0.585071\pi\) | |||||||
\(390\) | −6.03517 | −0.305603 | ||||||||
\(391\) | 23.3680 | 1.18177 | ||||||||
\(392\) | 5.02795 | 0.253950 | ||||||||
\(393\) | 15.6113 | 0.787485 | ||||||||
\(394\) | 13.5161 | 0.680930 | ||||||||
\(395\) | −12.9753 | −0.652857 | ||||||||
\(396\) | −7.62458 | −0.383149 | ||||||||
\(397\) | 19.4309 | 0.975208 | 0.487604 | − | 0.873065i | \(-0.337871\pi\) | ||||
0.487604 | + | 0.873065i | \(0.337871\pi\) | |||||||
\(398\) | −20.3859 | −1.02185 | ||||||||
\(399\) | −8.53435 | −0.427252 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −9.96824 | −0.497790 | −0.248895 | − | 0.968530i | \(-0.580067\pi\) | ||||
−0.248895 | + | 0.968530i | \(0.580067\pi\) | |||||||
\(402\) | 20.7991 | 1.03736 | ||||||||
\(403\) | −12.2719 | −0.611309 | ||||||||
\(404\) | −12.3402 | −0.613949 | ||||||||
\(405\) | −10.7171 | −0.532539 | ||||||||
\(406\) | 6.77473 | 0.336224 | ||||||||
\(407\) | 23.4265 | 1.16121 | ||||||||
\(408\) | −7.91196 | −0.391700 | ||||||||
\(409\) | −24.5937 | −1.21608 | −0.608039 | − | 0.793907i | \(-0.708044\pi\) | ||||
−0.608039 | + | 0.793907i | \(0.708044\pi\) | |||||||
\(410\) | 0.892755 | 0.0440900 | ||||||||
\(411\) | −3.41377 | −0.168389 | ||||||||
\(412\) | 8.99878 | 0.443338 | ||||||||
\(413\) | 32.7556 | 1.61180 | ||||||||
\(414\) | −15.0621 | −0.740264 | ||||||||
\(415\) | −10.1444 | −0.497968 | ||||||||
\(416\) | −2.63900 | −0.129388 | ||||||||
\(417\) | 8.24873 | 0.403942 | ||||||||
\(418\) | −3.67909 | −0.179950 | ||||||||
\(419\) | 26.5545 | 1.29727 | 0.648636 | − | 0.761099i | \(-0.275340\pi\) | ||||
0.648636 | + | 0.761099i | \(0.275340\pi\) | |||||||
\(420\) | −7.93132 | −0.387009 | ||||||||
\(421\) | −9.27013 | −0.451798 | −0.225899 | − | 0.974151i | \(-0.572532\pi\) | ||||
−0.225899 | + | 0.974151i | \(0.572532\pi\) | |||||||
\(422\) | −14.3190 | −0.697038 | ||||||||
\(423\) | 5.81628 | 0.282797 | ||||||||
\(424\) | −14.2976 | −0.694353 | ||||||||
\(425\) | −3.45967 | −0.167818 | ||||||||
\(426\) | −26.9546 | −1.30596 | ||||||||
\(427\) | −32.6802 | −1.58151 | ||||||||
\(428\) | −3.18238 | −0.153826 | ||||||||
\(429\) | 20.6350 | 0.996268 | ||||||||
\(430\) | 10.1922 | 0.491510 | ||||||||
\(431\) | 10.0647 | 0.484802 | 0.242401 | − | 0.970176i | \(-0.422065\pi\) | ||||
0.242401 | + | 0.970176i | \(0.422065\pi\) | |||||||
\(432\) | −1.76098 | −0.0847251 | ||||||||
\(433\) | 17.6499 | 0.848198 | 0.424099 | − | 0.905616i | \(-0.360591\pi\) | ||||
0.424099 | + | 0.905616i | \(0.360591\pi\) | |||||||
\(434\) | −16.1276 | −0.774149 | ||||||||
\(435\) | −4.46731 | −0.214191 | ||||||||
\(436\) | 1.47514 | 0.0706465 | ||||||||
\(437\) | −7.26795 | −0.347673 | ||||||||
\(438\) | 9.06817 | 0.433294 | ||||||||
\(439\) | 24.8537 | 1.18620 | 0.593102 | − | 0.805127i | \(-0.297903\pi\) | ||||
0.593102 | + | 0.805127i | \(0.297903\pi\) | |||||||
\(440\) | −3.41913 | −0.163001 | ||||||||
\(441\) | 11.2122 | 0.533914 | ||||||||
\(442\) | 9.13006 | 0.434273 | ||||||||
\(443\) | 21.0429 | 0.999777 | 0.499888 | − | 0.866090i | \(-0.333374\pi\) | ||||
0.499888 | + | 0.866090i | \(0.333374\pi\) | |||||||
\(444\) | −15.6690 | −0.743618 | ||||||||
\(445\) | 0.456762 | 0.0216526 | ||||||||
\(446\) | 12.1093 | 0.573392 | ||||||||
\(447\) | −6.58152 | −0.311295 | ||||||||
\(448\) | −3.46813 | −0.163854 | ||||||||
\(449\) | −6.39622 | −0.301856 | −0.150928 | − | 0.988545i | \(-0.548226\pi\) | ||||
−0.150928 | + | 0.988545i | \(0.548226\pi\) | |||||||
\(450\) | 2.22998 | 0.105122 | ||||||||
\(451\) | −3.05245 | −0.143734 | ||||||||
\(452\) | −5.35901 | −0.252067 | ||||||||
\(453\) | −37.5812 | −1.76572 | ||||||||
\(454\) | 0.00202746 | 9.51532e−5 0 | ||||||||
\(455\) | 9.15240 | 0.429071 | ||||||||
\(456\) | 2.46079 | 0.115237 | ||||||||
\(457\) | −20.1485 | −0.942508 | −0.471254 | − | 0.881998i | \(-0.656198\pi\) | ||||
−0.471254 | + | 0.881998i | \(0.656198\pi\) | |||||||
\(458\) | −4.08309 | −0.190790 | ||||||||
\(459\) | 6.09240 | 0.284369 | ||||||||
\(460\) | −6.75440 | −0.314926 | ||||||||
\(461\) | −4.34495 | −0.202365 | −0.101182 | − | 0.994868i | \(-0.532263\pi\) | ||||
−0.101182 | + | 0.994868i | \(0.532263\pi\) | |||||||
\(462\) | 27.1182 | 1.26165 | ||||||||
\(463\) | 2.35773 | 0.109573 | 0.0547864 | − | 0.998498i | \(-0.482552\pi\) | ||||
0.0547864 | + | 0.998498i | \(0.482552\pi\) | |||||||
\(464\) | −1.95342 | −0.0906854 | ||||||||
\(465\) | 10.6347 | 0.493170 | ||||||||
\(466\) | −25.4843 | −1.18054 | ||||||||
\(467\) | −6.22229 | −0.287933 | −0.143967 | − | 0.989583i | \(-0.545986\pi\) | ||||
−0.143967 | + | 0.989583i | \(0.545986\pi\) | |||||||
\(468\) | −5.88491 | −0.272030 | ||||||||
\(469\) | −31.5420 | −1.45648 | ||||||||
\(470\) | 2.60823 | 0.120308 | ||||||||
\(471\) | 27.9678 | 1.28869 | ||||||||
\(472\) | −9.44473 | −0.434729 | ||||||||
\(473\) | −34.8483 | −1.60233 | ||||||||
\(474\) | −29.6734 | −1.36294 | ||||||||
\(475\) | 1.07603 | 0.0493717 | ||||||||
\(476\) | 11.9986 | 0.549954 | ||||||||
\(477\) | −31.8833 | −1.45984 | ||||||||
\(478\) | −11.3288 | −0.518169 | ||||||||
\(479\) | −20.8295 | −0.951725 | −0.475862 | − | 0.879520i | \(-0.657864\pi\) | ||||
−0.475862 | + | 0.879520i | \(0.657864\pi\) | |||||||
\(480\) | 2.28691 | 0.104383 | ||||||||
\(481\) | 18.0814 | 0.824439 | ||||||||
\(482\) | 17.6302 | 0.803032 | ||||||||
\(483\) | 53.5713 | 2.43758 | ||||||||
\(484\) | 0.690448 | 0.0313840 | ||||||||
\(485\) | 16.6254 | 0.754922 | ||||||||
\(486\) | −19.2262 | −0.872119 | ||||||||
\(487\) | −3.26784 | −0.148080 | −0.0740401 | − | 0.997255i | \(-0.523589\pi\) | ||||
−0.0740401 | + | 0.997255i | \(0.523589\pi\) | |||||||
\(488\) | 9.42299 | 0.426559 | ||||||||
\(489\) | −3.51481 | −0.158945 | ||||||||
\(490\) | 5.02795 | 0.227139 | ||||||||
\(491\) | 24.0782 | 1.08663 | 0.543317 | − | 0.839528i | \(-0.317168\pi\) | ||||
0.543317 | + | 0.839528i | \(0.317168\pi\) | |||||||
\(492\) | 2.04165 | 0.0920449 | ||||||||
\(493\) | 6.75819 | 0.304374 | ||||||||
\(494\) | −2.83965 | −0.127762 | ||||||||
\(495\) | −7.62458 | −0.342699 | ||||||||
\(496\) | 4.65022 | 0.208801 | ||||||||
\(497\) | 40.8770 | 1.83359 | ||||||||
\(498\) | −23.1993 | −1.03959 | ||||||||
\(499\) | 18.8538 | 0.844012 | 0.422006 | − | 0.906593i | \(-0.361326\pi\) | ||||
0.422006 | + | 0.906593i | \(0.361326\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 11.7428 | 0.524629 | ||||||||
\(502\) | 20.1405 | 0.898915 | ||||||||
\(503\) | −38.9095 | −1.73489 | −0.867444 | − | 0.497534i | \(-0.834239\pi\) | ||||
−0.867444 | + | 0.497534i | \(0.834239\pi\) | |||||||
\(504\) | −7.73385 | −0.344493 | ||||||||
\(505\) | −12.3402 | −0.549133 | ||||||||
\(506\) | 23.0942 | 1.02666 | ||||||||
\(507\) | −13.8031 | −0.613016 | ||||||||
\(508\) | 13.4391 | 0.596263 | ||||||||
\(509\) | −3.71681 | −0.164745 | −0.0823724 | − | 0.996602i | \(-0.526250\pi\) | ||||
−0.0823724 | + | 0.996602i | \(0.526250\pi\) | |||||||
\(510\) | −7.91196 | −0.350347 | ||||||||
\(511\) | −13.7520 | −0.608352 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.89487 | −0.0836605 | ||||||||
\(514\) | 22.8286 | 1.00693 | ||||||||
\(515\) | 8.99878 | 0.396534 | ||||||||
\(516\) | 23.3086 | 1.02610 | ||||||||
\(517\) | −8.91786 | −0.392207 | ||||||||
\(518\) | 23.7622 | 1.04405 | ||||||||
\(519\) | −0.164400 | −0.00721637 | ||||||||
\(520\) | −2.63900 | −0.115728 | ||||||||
\(521\) | −15.6307 | −0.684793 | −0.342396 | − | 0.939556i | \(-0.611239\pi\) | ||||
−0.342396 | + | 0.939556i | \(0.611239\pi\) | |||||||
\(522\) | −4.35609 | −0.190661 | ||||||||
\(523\) | −15.6826 | −0.685753 | −0.342877 | − | 0.939380i | \(-0.611401\pi\) | ||||
−0.342877 | + | 0.939380i | \(0.611401\pi\) | |||||||
\(524\) | 6.82635 | 0.298211 | ||||||||
\(525\) | −7.93132 | −0.346151 | ||||||||
\(526\) | −0.616108 | −0.0268636 | ||||||||
\(527\) | −16.0882 | −0.700813 | ||||||||
\(528\) | −7.81926 | −0.340289 | ||||||||
\(529\) | 22.6219 | 0.983562 | ||||||||
\(530\) | −14.2976 | −0.621049 | ||||||||
\(531\) | −21.0615 | −0.913992 | ||||||||
\(532\) | −3.73182 | −0.161795 | ||||||||
\(533\) | −2.35598 | −0.102049 | ||||||||
\(534\) | 1.04458 | 0.0452032 | ||||||||
\(535\) | −3.18238 | −0.137586 | ||||||||
\(536\) | 9.09482 | 0.392836 | ||||||||
\(537\) | −11.8154 | −0.509874 | ||||||||
\(538\) | −12.1415 | −0.523458 | ||||||||
\(539\) | −17.1912 | −0.740477 | ||||||||
\(540\) | −1.76098 | −0.0757805 | ||||||||
\(541\) | 31.4126 | 1.35053 | 0.675266 | − | 0.737575i | \(-0.264029\pi\) | ||||
0.675266 | + | 0.737575i | \(0.264029\pi\) | |||||||
\(542\) | −2.61919 | −0.112504 | ||||||||
\(543\) | 3.45762 | 0.148381 | ||||||||
\(544\) | −3.45967 | −0.148332 | ||||||||
\(545\) | 1.47514 | 0.0631881 | ||||||||
\(546\) | 20.9308 | 0.895754 | ||||||||
\(547\) | −36.9988 | −1.58195 | −0.790977 | − | 0.611846i | \(-0.790427\pi\) | ||||
−0.790977 | + | 0.611846i | \(0.790427\pi\) | |||||||
\(548\) | −1.49274 | −0.0637668 | ||||||||
\(549\) | 21.0130 | 0.896815 | ||||||||
\(550\) | −3.41913 | −0.145792 | ||||||||
\(551\) | −2.10195 | −0.0895459 | ||||||||
\(552\) | −15.4467 | −0.657457 | ||||||||
\(553\) | 45.0000 | 1.91360 | ||||||||
\(554\) | 12.2159 | 0.519006 | ||||||||
\(555\) | −15.6690 | −0.665112 | ||||||||
\(556\) | 3.60693 | 0.152968 | ||||||||
\(557\) | −26.4800 | −1.12199 | −0.560996 | − | 0.827818i | \(-0.689582\pi\) | ||||
−0.560996 | + | 0.827818i | \(0.689582\pi\) | |||||||
\(558\) | 10.3699 | 0.438992 | ||||||||
\(559\) | −26.8971 | −1.13763 | ||||||||
\(560\) | −3.46813 | −0.146555 | ||||||||
\(561\) | 27.0520 | 1.14214 | ||||||||
\(562\) | 10.2239 | 0.431268 | ||||||||
\(563\) | 35.0804 | 1.47846 | 0.739230 | − | 0.673453i | \(-0.235189\pi\) | ||||
0.739230 | + | 0.673453i | \(0.235189\pi\) | |||||||
\(564\) | 5.96479 | 0.251163 | ||||||||
\(565\) | −5.35901 | −0.225455 | ||||||||
\(566\) | 20.7073 | 0.870394 | ||||||||
\(567\) | 37.1684 | 1.56093 | ||||||||
\(568\) | −11.7865 | −0.494549 | ||||||||
\(569\) | −10.0633 | −0.421876 | −0.210938 | − | 0.977499i | \(-0.567652\pi\) | ||||
−0.210938 | + | 0.977499i | \(0.567652\pi\) | |||||||
\(570\) | 2.46079 | 0.103071 | ||||||||
\(571\) | 4.19294 | 0.175469 | 0.0877346 | − | 0.996144i | \(-0.472037\pi\) | ||||
0.0877346 | + | 0.996144i | \(0.472037\pi\) | |||||||
\(572\) | 9.02309 | 0.377274 | ||||||||
\(573\) | 29.8970 | 1.24897 | ||||||||
\(574\) | −3.09619 | −0.129233 | ||||||||
\(575\) | −6.75440 | −0.281678 | ||||||||
\(576\) | 2.22998 | 0.0929157 | ||||||||
\(577\) | −12.6805 | −0.527897 | −0.263949 | − | 0.964537i | \(-0.585025\pi\) | ||||
−0.263949 | + | 0.964537i | \(0.585025\pi\) | |||||||
\(578\) | −5.03071 | −0.209250 | ||||||||
\(579\) | −2.46624 | −0.102493 | ||||||||
\(580\) | −1.95342 | −0.0811115 | ||||||||
\(581\) | 35.1821 | 1.45960 | ||||||||
\(582\) | 38.0209 | 1.57602 | ||||||||
\(583\) | 48.8854 | 2.02463 | ||||||||
\(584\) | 3.96524 | 0.164083 | ||||||||
\(585\) | −5.88491 | −0.243311 | ||||||||
\(586\) | −24.4481 | −1.00994 | ||||||||
\(587\) | 14.4013 | 0.594404 | 0.297202 | − | 0.954815i | \(-0.403947\pi\) | ||||
0.297202 | + | 0.954815i | \(0.403947\pi\) | |||||||
\(588\) | 11.4985 | 0.474189 | ||||||||
\(589\) | 5.00378 | 0.206177 | ||||||||
\(590\) | −9.44473 | −0.388833 | ||||||||
\(591\) | 30.9101 | 1.27147 | ||||||||
\(592\) | −6.85159 | −0.281599 | ||||||||
\(593\) | −18.3748 | −0.754563 | −0.377282 | − | 0.926099i | \(-0.623141\pi\) | ||||
−0.377282 | + | 0.926099i | \(0.623141\pi\) | |||||||
\(594\) | 6.02102 | 0.247045 | ||||||||
\(595\) | 11.9986 | 0.491894 | ||||||||
\(596\) | −2.87791 | −0.117884 | ||||||||
\(597\) | −46.6207 | −1.90806 | ||||||||
\(598\) | 17.8249 | 0.728913 | ||||||||
\(599\) | −25.4849 | −1.04129 | −0.520643 | − | 0.853774i | \(-0.674308\pi\) | ||||
−0.520643 | + | 0.853774i | \(0.674308\pi\) | |||||||
\(600\) | 2.28691 | 0.0933629 | ||||||||
\(601\) | −1.00000 | −0.0407909 | ||||||||
\(602\) | −35.3478 | −1.44067 | ||||||||
\(603\) | 20.2812 | 0.825915 | ||||||||
\(604\) | −16.4331 | −0.668655 | ||||||||
\(605\) | 0.690448 | 0.0280707 | ||||||||
\(606\) | −28.2210 | −1.14640 | ||||||||
\(607\) | −12.5100 | −0.507764 | −0.253882 | − | 0.967235i | \(-0.581708\pi\) | ||||
−0.253882 | + | 0.967235i | \(0.581708\pi\) | |||||||
\(608\) | 1.07603 | 0.0436388 | ||||||||
\(609\) | 15.4932 | 0.627817 | ||||||||
\(610\) | 9.42299 | 0.381526 | ||||||||
\(611\) | −6.88311 | −0.278461 | ||||||||
\(612\) | −7.71497 | −0.311859 | ||||||||
\(613\) | −38.2008 | −1.54292 | −0.771458 | − | 0.636280i | \(-0.780472\pi\) | ||||
−0.771458 | + | 0.636280i | \(0.780472\pi\) | |||||||
\(614\) | −0.655961 | −0.0264724 | ||||||||
\(615\) | 2.04165 | 0.0823275 | ||||||||
\(616\) | 11.8580 | 0.477772 | ||||||||
\(617\) | −40.2974 | −1.62231 | −0.811156 | − | 0.584829i | \(-0.801161\pi\) | ||||
−0.811156 | + | 0.584829i | \(0.801161\pi\) | |||||||
\(618\) | 20.5794 | 0.827827 | ||||||||
\(619\) | −22.1722 | −0.891174 | −0.445587 | − | 0.895239i | \(-0.647005\pi\) | ||||
−0.445587 | + | 0.895239i | \(0.647005\pi\) | |||||||
\(620\) | 4.65022 | 0.186757 | ||||||||
\(621\) | 11.8944 | 0.477304 | ||||||||
\(622\) | −7.06795 | −0.283399 | ||||||||
\(623\) | −1.58411 | −0.0634661 | ||||||||
\(624\) | −6.03517 | −0.241600 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 22.6761 | 0.906317 | ||||||||
\(627\) | −8.41377 | −0.336013 | ||||||||
\(628\) | 12.2295 | 0.488011 | ||||||||
\(629\) | 23.7042 | 0.945149 | ||||||||
\(630\) | −7.73385 | −0.308124 | ||||||||
\(631\) | −47.0690 | −1.87379 | −0.936893 | − | 0.349615i | \(-0.886312\pi\) | ||||
−0.936893 | + | 0.349615i | \(0.886312\pi\) | |||||||
\(632\) | −12.9753 | −0.516129 | ||||||||
\(633\) | −32.7463 | −1.30155 | ||||||||
\(634\) | 9.20507 | 0.365580 | ||||||||
\(635\) | 13.4391 | 0.533314 | ||||||||
\(636\) | −32.6974 | −1.29654 | ||||||||
\(637\) | −13.2687 | −0.525727 | ||||||||
\(638\) | 6.67901 | 0.264424 | ||||||||
\(639\) | −26.2835 | −1.03976 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −11.6058 | −0.458402 | −0.229201 | − | 0.973379i | \(-0.573611\pi\) | ||||
−0.229201 | + | 0.973379i | \(0.573611\pi\) | |||||||
\(642\) | −7.27783 | −0.287233 | ||||||||
\(643\) | 16.3522 | 0.644867 | 0.322433 | − | 0.946592i | \(-0.395499\pi\) | ||||
0.322433 | + | 0.946592i | \(0.395499\pi\) | |||||||
\(644\) | 23.4252 | 0.923080 | ||||||||
\(645\) | 23.3086 | 0.917776 | ||||||||
\(646\) | −3.72271 | −0.146468 | ||||||||
\(647\) | 43.5027 | 1.71027 | 0.855134 | − | 0.518407i | \(-0.173475\pi\) | ||||
0.855134 | + | 0.518407i | \(0.173475\pi\) | |||||||
\(648\) | −10.7171 | −0.421009 | ||||||||
\(649\) | 32.2928 | 1.26760 | ||||||||
\(650\) | −2.63900 | −0.103510 | ||||||||
\(651\) | −36.8824 | −1.44553 | ||||||||
\(652\) | −1.53692 | −0.0601906 | ||||||||
\(653\) | 18.4089 | 0.720397 | 0.360199 | − | 0.932876i | \(-0.382709\pi\) | ||||
0.360199 | + | 0.932876i | \(0.382709\pi\) | |||||||
\(654\) | 3.37352 | 0.131915 | ||||||||
\(655\) | 6.82635 | 0.266728 | ||||||||
\(656\) | 0.892755 | 0.0348562 | ||||||||
\(657\) | 8.84240 | 0.344975 | ||||||||
\(658\) | −9.04567 | −0.352637 | ||||||||
\(659\) | −32.7240 | −1.27475 | −0.637373 | − | 0.770556i | \(-0.719979\pi\) | ||||
−0.637373 | + | 0.770556i | \(0.719979\pi\) | |||||||
\(660\) | −7.81926 | −0.304364 | ||||||||
\(661\) | −19.1635 | −0.745374 | −0.372687 | − | 0.927957i | \(-0.621563\pi\) | ||||
−0.372687 | + | 0.927957i | \(0.621563\pi\) | |||||||
\(662\) | 9.28864 | 0.361013 | ||||||||
\(663\) | 20.8797 | 0.810899 | ||||||||
\(664\) | −10.1444 | −0.393679 | ||||||||
\(665\) | −3.73182 | −0.144714 | ||||||||
\(666\) | −15.2789 | −0.592045 | ||||||||
\(667\) | 13.1942 | 0.510882 | ||||||||
\(668\) | 5.13478 | 0.198671 | ||||||||
\(669\) | 27.6929 | 1.07067 | ||||||||
\(670\) | 9.09482 | 0.351363 | ||||||||
\(671\) | −32.2184 | −1.24378 | ||||||||
\(672\) | −7.93132 | −0.305957 | ||||||||
\(673\) | 41.2479 | 1.58999 | 0.794995 | − | 0.606616i | \(-0.207473\pi\) | ||||
0.794995 | + | 0.606616i | \(0.207473\pi\) | |||||||
\(674\) | 3.36720 | 0.129700 | ||||||||
\(675\) | −1.76098 | −0.0677801 | ||||||||
\(676\) | −6.03568 | −0.232141 | ||||||||
\(677\) | −13.4359 | −0.516382 | −0.258191 | − | 0.966094i | \(-0.583126\pi\) | ||||
−0.258191 | + | 0.966094i | \(0.583126\pi\) | |||||||
\(678\) | −12.2556 | −0.470673 | ||||||||
\(679\) | −57.6592 | −2.21276 | ||||||||
\(680\) | −3.45967 | −0.132672 | ||||||||
\(681\) | 0.00463662 | 0.000177676 0 | ||||||||
\(682\) | −15.8997 | −0.608831 | ||||||||
\(683\) | −5.40108 | −0.206667 | −0.103333 | − | 0.994647i | \(-0.532951\pi\) | ||||
−0.103333 | + | 0.994647i | \(0.532951\pi\) | |||||||
\(684\) | 2.39952 | 0.0917481 | ||||||||
\(685\) | −1.49274 | −0.0570347 | ||||||||
\(686\) | 6.83935 | 0.261128 | ||||||||
\(687\) | −9.33768 | −0.356255 | ||||||||
\(688\) | 10.1922 | 0.388573 | ||||||||
\(689\) | 37.7314 | 1.43745 | ||||||||
\(690\) | −15.4467 | −0.588047 | ||||||||
\(691\) | 6.15996 | 0.234336 | 0.117168 | − | 0.993112i | \(-0.462618\pi\) | ||||
0.117168 | + | 0.993112i | \(0.462618\pi\) | |||||||
\(692\) | −0.0718874 | −0.00273275 | ||||||||
\(693\) | 26.4430 | 1.00449 | ||||||||
\(694\) | 7.07999 | 0.268753 | ||||||||
\(695\) | 3.60693 | 0.136819 | ||||||||
\(696\) | −4.46731 | −0.169333 | ||||||||
\(697\) | −3.08863 | −0.116990 | ||||||||
\(698\) | −30.8890 | −1.16916 | ||||||||
\(699\) | −58.2803 | −2.20436 | ||||||||
\(700\) | −3.46813 | −0.131083 | ||||||||
\(701\) | 9.14301 | 0.345327 | 0.172663 | − | 0.984981i | \(-0.444763\pi\) | ||||
0.172663 | + | 0.984981i | \(0.444763\pi\) | |||||||
\(702\) | 4.64722 | 0.175398 | ||||||||
\(703\) | −7.37253 | −0.278060 | ||||||||
\(704\) | −3.41913 | −0.128863 | ||||||||
\(705\) | 5.96479 | 0.224647 | ||||||||
\(706\) | −10.2224 | −0.384724 | ||||||||
\(707\) | 42.7975 | 1.60957 | ||||||||
\(708\) | −21.5993 | −0.811751 | ||||||||
\(709\) | −14.8939 | −0.559350 | −0.279675 | − | 0.960095i | \(-0.590227\pi\) | ||||
−0.279675 | + | 0.960095i | \(0.590227\pi\) | |||||||
\(710\) | −11.7865 | −0.442338 | ||||||||
\(711\) | −28.9346 | −1.08513 | ||||||||
\(712\) | 0.456762 | 0.0171179 | ||||||||
\(713\) | −31.4094 | −1.17629 | ||||||||
\(714\) | 27.4397 | 1.02691 | ||||||||
\(715\) | 9.02309 | 0.337444 | ||||||||
\(716\) | −5.16654 | −0.193083 | ||||||||
\(717\) | −25.9081 | −0.967554 | ||||||||
\(718\) | −7.35821 | −0.274606 | ||||||||
\(719\) | 50.8962 | 1.89811 | 0.949053 | − | 0.315116i | \(-0.102043\pi\) | ||||
0.949053 | + | 0.315116i | \(0.102043\pi\) | |||||||
\(720\) | 2.22998 | 0.0831063 | ||||||||
\(721\) | −31.2090 | −1.16228 | ||||||||
\(722\) | −17.8422 | −0.664016 | ||||||||
\(723\) | 40.3187 | 1.49947 | ||||||||
\(724\) | 1.51191 | 0.0561898 | ||||||||
\(725\) | −1.95342 | −0.0725483 | ||||||||
\(726\) | 1.57900 | 0.0586020 | ||||||||
\(727\) | −28.3480 | −1.05137 | −0.525684 | − | 0.850680i | \(-0.676190\pi\) | ||||
−0.525684 | + | 0.850680i | \(0.676190\pi\) | |||||||
\(728\) | 9.15240 | 0.339211 | ||||||||
\(729\) | −11.8173 | −0.437679 | ||||||||
\(730\) | 3.96524 | 0.146760 | ||||||||
\(731\) | −35.2615 | −1.30419 | ||||||||
\(732\) | 21.5496 | 0.796495 | ||||||||
\(733\) | −22.1043 | −0.816442 | −0.408221 | − | 0.912883i | \(-0.633851\pi\) | ||||
−0.408221 | + | 0.912883i | \(0.633851\pi\) | |||||||
\(734\) | 24.7672 | 0.914175 | ||||||||
\(735\) | 11.4985 | 0.424128 | ||||||||
\(736\) | −6.75440 | −0.248970 | ||||||||
\(737\) | −31.0964 | −1.14545 | ||||||||
\(738\) | 1.99082 | 0.0732832 | ||||||||
\(739\) | 43.4697 | 1.59906 | 0.799529 | − | 0.600627i | \(-0.205082\pi\) | ||||
0.799529 | + | 0.600627i | \(0.205082\pi\) | |||||||
\(740\) | −6.85159 | −0.251870 | ||||||||
\(741\) | −6.49403 | −0.238564 | ||||||||
\(742\) | 49.5860 | 1.82036 | ||||||||
\(743\) | −11.3533 | −0.416514 | −0.208257 | − | 0.978074i | \(-0.566779\pi\) | ||||
−0.208257 | + | 0.978074i | \(0.566779\pi\) | |||||||
\(744\) | 10.6347 | 0.389885 | ||||||||
\(745\) | −2.87791 | −0.105438 | ||||||||
\(746\) | 0.888462 | 0.0325289 | ||||||||
\(747\) | −22.6217 | −0.827686 | ||||||||
\(748\) | 11.8290 | 0.432513 | ||||||||
\(749\) | 11.0369 | 0.403280 | ||||||||
\(750\) | 2.28691 | 0.0835063 | ||||||||
\(751\) | 35.7866 | 1.30587 | 0.652935 | − | 0.757414i | \(-0.273537\pi\) | ||||
0.652935 | + | 0.757414i | \(0.273537\pi\) | |||||||
\(752\) | 2.60823 | 0.0951122 | ||||||||
\(753\) | 46.0596 | 1.67851 | ||||||||
\(754\) | 5.15509 | 0.187737 | ||||||||
\(755\) | −16.4331 | −0.598063 | ||||||||
\(756\) | 6.10731 | 0.222121 | ||||||||
\(757\) | 28.1509 | 1.02316 | 0.511581 | − | 0.859235i | \(-0.329060\pi\) | ||||
0.511581 | + | 0.859235i | \(0.329060\pi\) | |||||||
\(758\) | −7.54193 | −0.273935 | ||||||||
\(759\) | 52.8144 | 1.91704 | ||||||||
\(760\) | 1.07603 | 0.0390318 | ||||||||
\(761\) | −11.7505 | −0.425956 | −0.212978 | − | 0.977057i | \(-0.568316\pi\) | ||||
−0.212978 | + | 0.977057i | \(0.568316\pi\) | |||||||
\(762\) | 30.7340 | 1.11338 | ||||||||
\(763\) | −5.11599 | −0.185211 | ||||||||
\(764\) | 13.0731 | 0.472968 | ||||||||
\(765\) | −7.71497 | −0.278935 | ||||||||
\(766\) | 16.9073 | 0.610886 | ||||||||
\(767\) | 24.9246 | 0.899977 | ||||||||
\(768\) | 2.28691 | 0.0825219 | ||||||||
\(769\) | −31.9995 | −1.15393 | −0.576966 | − | 0.816768i | \(-0.695764\pi\) | ||||
−0.576966 | + | 0.816768i | \(0.695764\pi\) | |||||||
\(770\) | 11.8580 | 0.427333 | ||||||||
\(771\) | 52.2071 | 1.88019 | ||||||||
\(772\) | −1.07841 | −0.0388130 | ||||||||
\(773\) | 42.9219 | 1.54379 | 0.771897 | − | 0.635747i | \(-0.219308\pi\) | ||||
0.771897 | + | 0.635747i | \(0.219308\pi\) | |||||||
\(774\) | 22.7283 | 0.816951 | ||||||||
\(775\) | 4.65022 | 0.167041 | ||||||||
\(776\) | 16.6254 | 0.596818 | ||||||||
\(777\) | 54.3422 | 1.94951 | ||||||||
\(778\) | −10.4172 | −0.373476 | ||||||||
\(779\) | 0.960633 | 0.0344182 | ||||||||
\(780\) | −6.03517 | −0.216094 | ||||||||
\(781\) | 40.2995 | 1.44203 | ||||||||
\(782\) | 23.3680 | 0.835637 | ||||||||
\(783\) | 3.43994 | 0.122933 | ||||||||
\(784\) | 5.02795 | 0.179569 | ||||||||
\(785\) | 12.2295 | 0.436490 | ||||||||
\(786\) | 15.6113 | 0.556836 | ||||||||
\(787\) | −30.2128 | −1.07697 | −0.538484 | − | 0.842636i | \(-0.681003\pi\) | ||||
−0.538484 | + | 0.842636i | \(0.681003\pi\) | |||||||
\(788\) | 13.5161 | 0.481490 | ||||||||
\(789\) | −1.40899 | −0.0501612 | ||||||||
\(790\) | −12.9753 | −0.461640 | ||||||||
\(791\) | 18.5858 | 0.660833 | ||||||||
\(792\) | −7.62458 | −0.270928 | ||||||||
\(793\) | −24.8673 | −0.883063 | ||||||||
\(794\) | 19.4309 | 0.689576 | ||||||||
\(795\) | −32.6974 | −1.15966 | ||||||||
\(796\) | −20.3859 | −0.722558 | ||||||||
\(797\) | 32.9373 | 1.16670 | 0.583349 | − | 0.812222i | \(-0.301742\pi\) | ||||
0.583349 | + | 0.812222i | \(0.301742\pi\) | |||||||
\(798\) | −8.53435 | −0.302113 | ||||||||
\(799\) | −9.02359 | −0.319232 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 1.01857 | 0.0359894 | ||||||||
\(802\) | −9.96824 | −0.351991 | ||||||||
\(803\) | −13.5577 | −0.478440 | ||||||||
\(804\) | 20.7991 | 0.733526 | ||||||||
\(805\) | 23.4252 | 0.825628 | ||||||||
\(806\) | −12.2719 | −0.432260 | ||||||||
\(807\) | −27.7666 | −0.977431 | ||||||||
\(808\) | −12.3402 | −0.434127 | ||||||||
\(809\) | 11.9501 | 0.420143 | 0.210071 | − | 0.977686i | \(-0.432630\pi\) | ||||
0.210071 | + | 0.977686i | \(0.432630\pi\) | |||||||
\(810\) | −10.7171 | −0.376562 | ||||||||
\(811\) | −26.2408 | −0.921439 | −0.460719 | − | 0.887546i | \(-0.652409\pi\) | ||||
−0.460719 | + | 0.887546i | \(0.652409\pi\) | |||||||
\(812\) | 6.77473 | 0.237746 | ||||||||
\(813\) | −5.98985 | −0.210073 | ||||||||
\(814\) | 23.4265 | 0.821098 | ||||||||
\(815\) | −1.53692 | −0.0538361 | ||||||||
\(816\) | −7.91196 | −0.276974 | ||||||||
\(817\) | 10.9671 | 0.383690 | ||||||||
\(818\) | −24.5937 | −0.859897 | ||||||||
\(819\) | 20.4096 | 0.713171 | ||||||||
\(820\) | 0.892755 | 0.0311764 | ||||||||
\(821\) | −27.9055 | −0.973909 | −0.486954 | − | 0.873427i | \(-0.661892\pi\) | ||||
−0.486954 | + | 0.873427i | \(0.661892\pi\) | |||||||
\(822\) | −3.41377 | −0.119069 | ||||||||
\(823\) | 16.9874 | 0.592144 | 0.296072 | − | 0.955166i | \(-0.404323\pi\) | ||||
0.296072 | + | 0.955166i | \(0.404323\pi\) | |||||||
\(824\) | 8.99878 | 0.313487 | ||||||||
\(825\) | −7.81926 | −0.272232 | ||||||||
\(826\) | 32.7556 | 1.13971 | ||||||||
\(827\) | −36.8601 | −1.28175 | −0.640876 | − | 0.767645i | \(-0.721429\pi\) | ||||
−0.640876 | + | 0.767645i | \(0.721429\pi\) | |||||||
\(828\) | −15.0621 | −0.523446 | ||||||||
\(829\) | −17.1133 | −0.594369 | −0.297184 | − | 0.954820i | \(-0.596048\pi\) | ||||
−0.297184 | + | 0.954820i | \(0.596048\pi\) | |||||||
\(830\) | −10.1444 | −0.352117 | ||||||||
\(831\) | 27.9368 | 0.969118 | ||||||||
\(832\) | −2.63900 | −0.0914909 | ||||||||
\(833\) | −17.3950 | −0.602701 | ||||||||
\(834\) | 8.24873 | 0.285630 | ||||||||
\(835\) | 5.13478 | 0.177696 | ||||||||
\(836\) | −3.67909 | −0.127244 | ||||||||
\(837\) | −8.18894 | −0.283051 | ||||||||
\(838\) | 26.5545 | 0.917310 | ||||||||
\(839\) | 26.2070 | 0.904765 | 0.452383 | − | 0.891824i | \(-0.350574\pi\) | ||||
0.452383 | + | 0.891824i | \(0.350574\pi\) | |||||||
\(840\) | −7.93132 | −0.273657 | ||||||||
\(841\) | −25.1841 | −0.868419 | ||||||||
\(842\) | −9.27013 | −0.319470 | ||||||||
\(843\) | 23.3811 | 0.805287 | ||||||||
\(844\) | −14.3190 | −0.492880 | ||||||||
\(845\) | −6.03568 | −0.207634 | ||||||||
\(846\) | 5.81628 | 0.199968 | ||||||||
\(847\) | −2.39457 | −0.0822783 | ||||||||
\(848\) | −14.2976 | −0.490982 | ||||||||
\(849\) | 47.3559 | 1.62525 | ||||||||
\(850\) | −3.45967 | −0.118666 | ||||||||
\(851\) | 46.2784 | 1.58640 | ||||||||
\(852\) | −26.9546 | −0.923451 | ||||||||
\(853\) | −46.6720 | −1.59802 | −0.799010 | − | 0.601318i | \(-0.794642\pi\) | ||||
−0.799010 | + | 0.601318i | \(0.794642\pi\) | |||||||
\(854\) | −32.6802 | −1.11829 | ||||||||
\(855\) | 2.39952 | 0.0820620 | ||||||||
\(856\) | −3.18238 | −0.108772 | ||||||||
\(857\) | −51.6221 | −1.76338 | −0.881689 | − | 0.471831i | \(-0.843593\pi\) | ||||
−0.881689 | + | 0.471831i | \(0.843593\pi\) | |||||||
\(858\) | 20.6350 | 0.704468 | ||||||||
\(859\) | −0.0411982 | −0.00140567 | −0.000702833 | − | 1.00000i | \(-0.500224\pi\) | ||||
−0.000702833 | 1.00000i | \(0.500224\pi\) | ||||||||
\(860\) | 10.1922 | 0.347550 | ||||||||
\(861\) | −7.08073 | −0.241311 | ||||||||
\(862\) | 10.0647 | 0.342806 | ||||||||
\(863\) | 10.3915 | 0.353731 | 0.176866 | − | 0.984235i | \(-0.443404\pi\) | ||||
0.176866 | + | 0.984235i | \(0.443404\pi\) | |||||||
\(864\) | −1.76098 | −0.0599097 | ||||||||
\(865\) | −0.0718874 | −0.00244424 | ||||||||
\(866\) | 17.6499 | 0.599766 | ||||||||
\(867\) | −11.5048 | −0.390724 | ||||||||
\(868\) | −16.1276 | −0.547406 | ||||||||
\(869\) | 44.3642 | 1.50495 | ||||||||
\(870\) | −4.46731 | −0.151456 | ||||||||
\(871\) | −24.0012 | −0.813250 | ||||||||
\(872\) | 1.47514 | 0.0499546 | ||||||||
\(873\) | 37.0743 | 1.25478 | ||||||||
\(874\) | −7.26795 | −0.245842 | ||||||||
\(875\) | −3.46813 | −0.117244 | ||||||||
\(876\) | 9.06817 | 0.306385 | ||||||||
\(877\) | −39.5376 | −1.33509 | −0.667544 | − | 0.744570i | \(-0.732655\pi\) | ||||
−0.667544 | + | 0.744570i | \(0.732655\pi\) | |||||||
\(878\) | 24.8537 | 0.838773 | ||||||||
\(879\) | −55.9106 | −1.88582 | ||||||||
\(880\) | −3.41913 | −0.115259 | ||||||||
\(881\) | 9.99559 | 0.336760 | 0.168380 | − | 0.985722i | \(-0.446146\pi\) | ||||
0.168380 | + | 0.985722i | \(0.446146\pi\) | |||||||
\(882\) | 11.2122 | 0.377534 | ||||||||
\(883\) | −28.9383 | −0.973850 | −0.486925 | − | 0.873444i | \(-0.661882\pi\) | ||||
−0.486925 | + | 0.873444i | \(0.661882\pi\) | |||||||
\(884\) | 9.13006 | 0.307077 | ||||||||
\(885\) | −21.5993 | −0.726052 | ||||||||
\(886\) | 21.0429 | 0.706949 | ||||||||
\(887\) | −16.9411 | −0.568827 | −0.284413 | − | 0.958702i | \(-0.591799\pi\) | ||||
−0.284413 | + | 0.958702i | \(0.591799\pi\) | |||||||
\(888\) | −15.6690 | −0.525817 | ||||||||
\(889\) | −46.6086 | −1.56320 | ||||||||
\(890\) | 0.456762 | 0.0153107 | ||||||||
\(891\) | 36.6433 | 1.22760 | ||||||||
\(892\) | 12.1093 | 0.405450 | ||||||||
\(893\) | 2.80653 | 0.0939170 | ||||||||
\(894\) | −6.58152 | −0.220119 | ||||||||
\(895\) | −5.16654 | −0.172699 | ||||||||
\(896\) | −3.46813 | −0.115862 | ||||||||
\(897\) | 40.7639 | 1.36107 | ||||||||
\(898\) | −6.39622 | −0.213445 | ||||||||
\(899\) | −9.08385 | −0.302963 | ||||||||
\(900\) | 2.22998 | 0.0743325 | ||||||||
\(901\) | 49.4650 | 1.64792 | ||||||||
\(902\) | −3.05245 | −0.101635 | ||||||||
\(903\) | −80.8373 | −2.69010 | ||||||||
\(904\) | −5.35901 | −0.178238 | ||||||||
\(905\) | 1.51191 | 0.0502577 | ||||||||
\(906\) | −37.5812 | −1.24855 | ||||||||
\(907\) | −35.1477 | −1.16706 | −0.583531 | − | 0.812091i | \(-0.698329\pi\) | ||||
−0.583531 | + | 0.812091i | \(0.698329\pi\) | |||||||
\(908\) | 0.00202746 | 6.72835e−5 0 | ||||||||
\(909\) | −27.5184 | −0.912727 | ||||||||
\(910\) | 9.15240 | 0.303399 | ||||||||
\(911\) | 7.21548 | 0.239059 | 0.119530 | − | 0.992831i | \(-0.461861\pi\) | ||||
0.119530 | + | 0.992831i | \(0.461861\pi\) | |||||||
\(912\) | 2.46079 | 0.0814850 | ||||||||
\(913\) | 34.6850 | 1.14791 | ||||||||
\(914\) | −20.1485 | −0.666454 | ||||||||
\(915\) | 21.5496 | 0.712407 | ||||||||
\(916\) | −4.08309 | −0.134909 | ||||||||
\(917\) | −23.6747 | −0.781807 | ||||||||
\(918\) | 6.09240 | 0.201079 | ||||||||
\(919\) | −36.6000 | −1.20732 | −0.603662 | − | 0.797241i | \(-0.706292\pi\) | ||||
−0.603662 | + | 0.797241i | \(0.706292\pi\) | |||||||
\(920\) | −6.75440 | −0.222686 | ||||||||
\(921\) | −1.50013 | −0.0494308 | ||||||||
\(922\) | −4.34495 | −0.143093 | ||||||||
\(923\) | 31.1045 | 1.02382 | ||||||||
\(924\) | 27.1182 | 0.892124 | ||||||||
\(925\) | −6.85159 | −0.225279 | ||||||||
\(926\) | 2.35773 | 0.0774797 | ||||||||
\(927\) | 20.0671 | 0.659089 | ||||||||
\(928\) | −1.95342 | −0.0641243 | ||||||||
\(929\) | −7.88078 | −0.258560 | −0.129280 | − | 0.991608i | \(-0.541267\pi\) | ||||
−0.129280 | + | 0.991608i | \(0.541267\pi\) | |||||||
\(930\) | 10.6347 | 0.348724 | ||||||||
\(931\) | 5.41023 | 0.177313 | ||||||||
\(932\) | −25.4843 | −0.834764 | ||||||||
\(933\) | −16.1638 | −0.529179 | ||||||||
\(934\) | −6.22229 | −0.203599 | ||||||||
\(935\) | 11.8290 | 0.386851 | ||||||||
\(936\) | −5.88491 | −0.192354 | ||||||||
\(937\) | 46.9540 | 1.53392 | 0.766960 | − | 0.641695i | \(-0.221768\pi\) | ||||
0.766960 | + | 0.641695i | \(0.221768\pi\) | |||||||
\(938\) | −31.5420 | −1.02988 | ||||||||
\(939\) | 51.8582 | 1.69233 | ||||||||
\(940\) | 2.60823 | 0.0850709 | ||||||||
\(941\) | 8.86863 | 0.289109 | 0.144555 | − | 0.989497i | \(-0.453825\pi\) | ||||
0.144555 | + | 0.989497i | \(0.453825\pi\) | |||||||
\(942\) | 27.9678 | 0.911241 | ||||||||
\(943\) | −6.03003 | −0.196365 | ||||||||
\(944\) | −9.44473 | −0.307400 | ||||||||
\(945\) | 6.10731 | 0.198671 | ||||||||
\(946\) | −34.8483 | −1.13302 | ||||||||
\(947\) | −2.59018 | −0.0841695 | −0.0420848 | − | 0.999114i | \(-0.513400\pi\) | ||||
−0.0420848 | + | 0.999114i | \(0.513400\pi\) | |||||||
\(948\) | −29.6734 | −0.963746 | ||||||||
\(949\) | −10.4643 | −0.339685 | ||||||||
\(950\) | 1.07603 | 0.0349111 | ||||||||
\(951\) | 21.0512 | 0.682632 | ||||||||
\(952\) | 11.9986 | 0.388876 | ||||||||
\(953\) | −49.6993 | −1.60992 | −0.804959 | − | 0.593331i | \(-0.797813\pi\) | ||||
−0.804959 | + | 0.593331i | \(0.797813\pi\) | |||||||
\(954\) | −31.8833 | −1.03226 | ||||||||
\(955\) | 13.0731 | 0.423035 | ||||||||
\(956\) | −11.3288 | −0.366400 | ||||||||
\(957\) | 15.2743 | 0.493749 | ||||||||
\(958\) | −20.8295 | −0.672971 | ||||||||
\(959\) | 5.17703 | 0.167175 | ||||||||
\(960\) | 2.28691 | 0.0738098 | ||||||||
\(961\) | −9.37545 | −0.302434 | ||||||||
\(962\) | 18.0814 | 0.582966 | ||||||||
\(963\) | −7.09663 | −0.228686 | ||||||||
\(964\) | 17.6302 | 0.567829 | ||||||||
\(965\) | −1.07841 | −0.0347154 | ||||||||
\(966\) | 53.5713 | 1.72363 | ||||||||
\(967\) | 33.0048 | 1.06136 | 0.530682 | − | 0.847571i | \(-0.321936\pi\) | ||||
0.530682 | + | 0.847571i | \(0.321936\pi\) | |||||||
\(968\) | 0.690448 | 0.0221918 | ||||||||
\(969\) | −8.51352 | −0.273494 | ||||||||
\(970\) | 16.6254 | 0.533810 | ||||||||
\(971\) | 16.3480 | 0.524633 | 0.262316 | − | 0.964982i | \(-0.415514\pi\) | ||||
0.262316 | + | 0.964982i | \(0.415514\pi\) | |||||||
\(972\) | −19.2262 | −0.616682 | ||||||||
\(973\) | −12.5093 | −0.401030 | ||||||||
\(974\) | −3.26784 | −0.104708 | ||||||||
\(975\) | −6.03517 | −0.193280 | ||||||||
\(976\) | 9.42299 | 0.301623 | ||||||||
\(977\) | −21.0197 | −0.672481 | −0.336241 | − | 0.941776i | \(-0.609156\pi\) | ||||
−0.336241 | + | 0.941776i | \(0.609156\pi\) | |||||||
\(978\) | −3.51481 | −0.112391 | ||||||||
\(979\) | −1.56173 | −0.0499131 | ||||||||
\(980\) | 5.02795 | 0.160612 | ||||||||
\(981\) | 3.28953 | 0.105027 | ||||||||
\(982\) | 24.0782 | 0.768366 | ||||||||
\(983\) | 23.8635 | 0.761127 | 0.380564 | − | 0.924755i | \(-0.375730\pi\) | ||||
0.380564 | + | 0.924755i | \(0.375730\pi\) | |||||||
\(984\) | 2.04165 | 0.0650856 | ||||||||
\(985\) | 13.5161 | 0.430658 | ||||||||
\(986\) | 6.75819 | 0.215225 | ||||||||
\(987\) | −20.6867 | −0.658464 | ||||||||
\(988\) | −2.83965 | −0.0903412 | ||||||||
\(989\) | −68.8420 | −2.18905 | ||||||||
\(990\) | −7.62458 | −0.242325 | ||||||||
\(991\) | −26.1375 | −0.830285 | −0.415142 | − | 0.909757i | \(-0.636268\pi\) | ||||
−0.415142 | + | 0.909757i | \(0.636268\pi\) | |||||||
\(992\) | 4.65022 | 0.147645 | ||||||||
\(993\) | 21.2423 | 0.674105 | ||||||||
\(994\) | 40.8770 | 1.29654 | ||||||||
\(995\) | −20.3859 | −0.646275 | ||||||||
\(996\) | −23.1993 | −0.735099 | ||||||||
\(997\) | −37.3032 | −1.18140 | −0.590702 | − | 0.806890i | \(-0.701149\pi\) | ||||
−0.590702 | + | 0.806890i | \(0.701149\pi\) | |||||||
\(998\) | 18.8538 | 0.596807 | ||||||||
\(999\) | 12.0655 | 0.381736 |
(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 | 6010.2.a.c.1.16 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6010.2.a.c.1.16 | ✓ | 16 | 1.1 | even | 1 | trivial |