Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2960,2,Mod(1,2960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("2960.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2960 = 2^{4} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2960.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: | \(23.6357189983\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.583504.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 8x^{3} - 2x^{2} + 15x + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1480) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.34794\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2960.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.34794 | −0.778234 | −0.389117 | − | 0.921188i | \(-0.627220\pi\) | ||||
−0.389117 | + | 0.921188i | \(0.627220\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.75056 | 1.03961 | 0.519807 | − | 0.854284i | \(-0.326004\pi\) | ||||
0.519807 | + | 0.854284i | \(0.326004\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.18306 | −0.394352 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.31429 | 1.30081 | 0.650404 | − | 0.759589i | \(-0.274600\pi\) | ||||
0.650404 | + | 0.759589i | \(0.274600\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.72307 | −0.477893 | −0.238947 | − | 0.971033i | \(-0.576802\pi\) | ||||
−0.238947 | + | 0.971033i | \(0.576802\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.34794 | −0.348037 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.15688 | 1.25073 | 0.625364 | − | 0.780333i | \(-0.284950\pi\) | ||||
0.625364 | + | 0.780333i | \(0.284950\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.66223 | 1.75784 | 0.878918 | − | 0.476973i | \(-0.158266\pi\) | ||||
0.878918 | + | 0.476973i | \(0.158266\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.70759 | −0.809062 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.12970 | −1.69516 | −0.847580 | − | 0.530668i | \(-0.821941\pi\) | ||||
−0.847580 | + | 0.530668i | \(0.821941\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.63851 | 1.08513 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.12970 | −1.50965 | −0.754823 | − | 0.655928i | \(-0.772277\pi\) | ||||
−0.754823 | + | 0.655928i | \(0.772277\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.73508 | 1.20966 | 0.604828 | − | 0.796356i | \(-0.293242\pi\) | ||||
0.604828 | + | 0.796356i | \(0.293242\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.81541 | −1.01233 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.75056 | 0.464929 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.32259 | 0.371913 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.31429 | 0.673779 | 0.336889 | − | 0.941544i | \(-0.390625\pi\) | ||||
0.336889 | + | 0.941544i | \(0.390625\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.32977 | 0.660284 | 0.330142 | − | 0.943931i | \(-0.392903\pi\) | ||||
0.330142 | + | 0.943931i | \(0.392903\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.18306 | −0.176360 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.42079 | 0.644838 | 0.322419 | − | 0.946597i | \(-0.395504\pi\) | ||||
0.322419 | + | 0.946597i | \(0.395504\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.565572 | 0.0807960 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.95117 | −0.973359 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.82650 | −1.34977 | −0.674887 | − | 0.737921i | \(-0.735808\pi\) | ||||
−0.674887 | + | 0.737921i | \(0.735808\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.31429 | 0.581739 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.3282 | −1.36801 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.54032 | −0.200532 | −0.100266 | − | 0.994961i | \(-0.531969\pi\) | ||||
−0.100266 | + | 0.994961i | \(0.531969\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.61748 | 0.591208 | 0.295604 | − | 0.955311i | \(-0.404479\pi\) | ||||
0.295604 | + | 0.955311i | \(0.404479\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.25406 | −0.409974 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.72307 | −0.213720 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.17935 | 0.388419 | 0.194210 | − | 0.980960i | \(-0.437786\pi\) | ||||
0.194210 | + | 0.980960i | \(0.437786\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.9584 | 1.31923 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.39492 | −0.877616 | −0.438808 | − | 0.898581i | \(-0.644599\pi\) | ||||
−0.438808 | + | 0.898581i | \(0.644599\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.08857 | 0.595572 | 0.297786 | − | 0.954633i | \(-0.403752\pi\) | ||||
0.297786 | + | 0.954633i | \(0.403752\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.34794 | −0.155647 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.8667 | 1.35234 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.14325 | −0.578660 | −0.289330 | − | 0.957229i | \(-0.593433\pi\) | ||||
−0.289330 | + | 0.957229i | \(0.593433\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.05121 | −0.450134 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.99108 | −0.986899 | −0.493449 | − | 0.869775i | \(-0.664264\pi\) | ||||
−0.493449 | + | 0.869775i | \(0.664264\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.15688 | 0.559343 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.9584 | 1.17486 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.83089 | −0.194074 | −0.0970368 | − | 0.995281i | \(-0.530936\pi\) | ||||
−0.0970368 | + | 0.995281i | \(0.530936\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.73940 | −0.496824 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.07849 | −0.941395 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.66223 | 0.786128 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.3922 | −1.46130 | −0.730652 | − | 0.682751i | \(-0.760784\pi\) | ||||
−0.730652 | + | 0.682751i | \(0.760784\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.10405 | −0.512976 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.8629 | 1.47892 | 0.739459 | − | 0.673202i | \(-0.235081\pi\) | ||||
0.739459 | + | 0.673202i | \(0.235081\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.86763 | 0.873754 | 0.436877 | − | 0.899521i | \(-0.356085\pi\) | ||||
0.436877 | + | 0.899521i | \(0.356085\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.70759 | −0.361824 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.9559 | 1.92921 | 0.964605 | − | 0.263700i | \(-0.0849429\pi\) | ||||
0.964605 | + | 0.263700i | \(0.0849429\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.36611 | 0.609763 | 0.304881 | − | 0.952390i | \(-0.401383\pi\) | ||||
0.304881 | + | 0.952390i | \(0.401383\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.34794 | 0.127941 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.14457 | 0.860248 | 0.430124 | − | 0.902770i | \(-0.358470\pi\) | ||||
0.430124 | + | 0.902770i | \(0.358470\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.12970 | −0.758098 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.03849 | 0.188458 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.1843 | 1.30027 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.61310 | 0.692100 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.81541 | −0.524358 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.8185 | −1.04872 | −0.524361 | − | 0.851496i | \(-0.675696\pi\) | ||||
−0.524361 | + | 0.851496i | \(0.675696\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.83627 | −0.513855 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.0053 | 1.31102 | 0.655511 | − | 0.755186i | \(-0.272453\pi\) | ||||
0.655511 | + | 0.755186i | \(0.272453\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.0754 | 1.82747 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.63851 | 0.485286 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.13500 | −0.609585 | −0.304792 | − | 0.952419i | \(-0.598587\pi\) | ||||
−0.304792 | + | 0.952419i | \(0.598587\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.12706 | 0.180415 | 0.0902074 | − | 0.995923i | \(-0.471247\pi\) | ||||
0.0902074 | + | 0.995923i | \(0.471247\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.95896 | −0.501835 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.43382 | −0.621647 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.12970 | −0.675135 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.762357 | −0.0628782 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.4035 | 1.17998 | 0.589989 | − | 0.807411i | \(-0.299132\pi\) | ||||
0.589989 | + | 0.807411i | \(0.299132\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.3811 | −1.00756 | −0.503779 | − | 0.863833i | \(-0.668057\pi\) | ||||
−0.503779 | + | 0.863833i | \(0.668057\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.10088 | −0.493227 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.73508 | 0.540975 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.88271 | 0.150256 | 0.0751282 | − | 0.997174i | \(-0.476063\pi\) | ||||
0.0751282 | + | 0.997174i | \(0.476063\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.2455 | 1.05044 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.3612 | −1.76231 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.84900 | −0.379803 | −0.189901 | − | 0.981803i | \(-0.560817\pi\) | ||||
−0.189901 | + | 0.981803i | \(0.560817\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.81541 | −0.452729 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.89328 | −0.765565 | −0.382783 | − | 0.923838i | \(-0.625034\pi\) | ||||
−0.382783 | + | 0.923838i | \(0.625034\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.0310 | −0.771618 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.06485 | −0.693206 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.57676 | 0.500022 | 0.250011 | − | 0.968243i | \(-0.419566\pi\) | ||||
0.250011 | + | 0.968243i | \(0.419566\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.75056 | 0.207923 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.07625 | 0.156061 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.2526 | 1.81273 | 0.906363 | − | 0.422500i | \(-0.138847\pi\) | ||||
0.906363 | + | 0.422500i | \(0.138847\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.7696 | 1.09781 | 0.548907 | − | 0.835883i | \(-0.315044\pi\) | ||||
0.548907 | + | 0.835883i | \(0.315044\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.22409 | −0.460098 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.00000 | −0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.2483 | 1.62696 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 15.5091 | 1.12812 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.4859 | 1.12052 | 0.560262 | − | 0.828316i | \(-0.310701\pi\) | ||||
0.560262 | + | 0.828316i | \(0.310701\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.61047 | 0.259887 | 0.129944 | − | 0.991521i | \(-0.458520\pi\) | ||||
0.129944 | + | 0.991521i | \(0.458520\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.32259 | 0.166324 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.1142 | −1.29058 | −0.645292 | − | 0.763936i | \(-0.723264\pi\) | ||||
−0.645292 | + | 0.763936i | \(0.723264\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.86932 | −0.628729 | −0.314365 | − | 0.949302i | \(-0.601791\pi\) | ||||
−0.314365 | + | 0.949302i | \(0.601791\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.28557 | −0.302281 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −22.3612 | −1.56945 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.31429 | 0.301323 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.61789 | 0.668489 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 33.0571 | 2.28661 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.43820 | 0.236695 | 0.118348 | − | 0.992972i | \(-0.462240\pi\) | ||||
0.118348 | + | 0.992972i | \(0.462240\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.96792 | 0.682990 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.32977 | 0.295288 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.5252 | 1.25757 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.85909 | −0.463494 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.88566 | −0.597714 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 27.4184 | 1.83607 | 0.918035 | − | 0.396500i | \(-0.129775\pi\) | ||||
0.918035 | + | 0.396500i | \(0.129775\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.18306 | −0.0788704 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.1660 | 1.20572 | 0.602861 | − | 0.797846i | \(-0.294027\pi\) | ||||
0.602861 | + | 0.797846i | \(0.294027\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.6592 | 1.69561 | 0.847804 | − | 0.530309i | \(-0.177924\pi\) | ||||
0.847804 | + | 0.530309i | \(0.177924\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.9956 | −1.05243 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0129 | 0.655969 | 0.327984 | − | 0.944683i | \(-0.393631\pi\) | ||||
0.327984 | + | 0.944683i | \(0.393631\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.42079 | 0.288380 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.93279 | 0.450333 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.9610 | −0.903065 | −0.451532 | − | 0.892255i | \(-0.649122\pi\) | ||||
−0.451532 | + | 0.892255i | \(0.649122\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.864995 | 0.0557192 | 0.0278596 | − | 0.999612i | \(-0.491131\pi\) | ||||
0.0278596 | + | 0.999612i | \(0.491131\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.4547 | −0.734822 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.565572 | 0.0361331 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.2025 | −0.840058 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.1194 | 0.768038 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.6608 | 0.672903 | 0.336451 | − | 0.941701i | \(-0.390773\pi\) | ||||
0.336451 | + | 0.941701i | \(0.390773\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −35.0739 | −2.20508 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.95117 | −0.435299 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.1158 | 1.00528 | 0.502639 | − | 0.864496i | \(-0.332362\pi\) | ||||
0.502639 | + | 0.864496i | \(0.332362\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.75056 | −0.170911 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.61789 | 0.595332 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.0572 | −1.29844 | −0.649220 | − | 0.760601i | \(-0.724904\pi\) | ||||
−0.649220 | + | 0.760601i | \(0.724904\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.82650 | −0.603637 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.46793 | 0.151035 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.0096 | −0.732236 | −0.366118 | − | 0.930568i | \(-0.619313\pi\) | ||||
−0.366118 | + | 0.930568i | \(0.619313\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.8450 | 1.69146 | 0.845732 | − | 0.533609i | \(-0.179164\pi\) | ||||
0.845732 | + | 0.533609i | \(0.179164\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.38843 | 0.386645 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.31429 | 0.260162 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.94879 | 0.417512 | 0.208756 | − | 0.977968i | \(-0.433059\pi\) | ||||
0.208756 | + | 0.977968i | \(0.433059\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.96798 | −0.477030 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.52862 | −0.389465 | −0.194732 | − | 0.980856i | \(-0.562384\pi\) | ||||
−0.194732 | + | 0.980856i | \(0.562384\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.8724 | 0.884073 | 0.442037 | − | 0.896997i | \(-0.354256\pi\) | ||||
0.442037 | + | 0.896997i | \(0.354256\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.3282 | −0.611792 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.8667 | 0.700470 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.59346 | 0.564321 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.3998 | 1.13724 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.85654 | −0.166881 | −0.0834403 | − | 0.996513i | \(-0.526591\pi\) | ||||
−0.0834403 | + | 0.996513i | \(0.526591\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.54032 | −0.0896806 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.3262 | 1.41155 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.0080 | 0.810105 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.9093 | 0.686440 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −20.0344 | −1.15094 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.61748 | 0.264396 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.93300 | −0.224468 | −0.112234 | − | 0.993682i | \(-0.535801\pi\) | ||||
−0.112234 | + | 0.993682i | \(0.535801\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.9530 | −0.679985 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.14548 | −0.235069 | −0.117534 | − | 0.993069i | \(-0.537499\pi\) | ||||
−0.117534 | + | 0.993069i | \(0.537499\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.94502 | 0.109939 | 0.0549695 | − | 0.998488i | \(-0.482494\pi\) | ||||
0.0549695 | + | 0.998488i | \(0.482494\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.25406 | −0.183346 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.9543 | −1.57007 | −0.785034 | − | 0.619453i | \(-0.787355\pi\) | ||||
−0.785034 | + | 0.619453i | \(0.787355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −35.0739 | −1.96376 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −26.8994 | −1.50138 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 39.5132 | 2.19858 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.72307 | −0.0955786 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.58114 | −0.474538 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.1596 | 0.670383 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.64991 | 0.200617 | 0.100309 | − | 0.994956i | \(-0.468017\pi\) | ||||
0.100309 | + | 0.994956i | \(0.468017\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.18306 | 0.0648311 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.17935 | 0.173706 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.0764 | −0.821265 | −0.410633 | − | 0.911801i | \(-0.634692\pi\) | ||||
−0.410633 | + | 0.911801i | \(0.634692\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.3263 | −0.669474 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.0571 | 1.57353 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.6983 | −0.955617 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.9584 | 0.589978 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −32.4761 | −1.74341 | −0.871705 | − | 0.490031i | \(-0.836985\pi\) | ||||
−0.871705 | + | 0.490031i | \(0.836985\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 36.8006 | 1.96989 | 0.984946 | − | 0.172861i | \(-0.0553012\pi\) | ||||
0.984946 | + | 0.172861i | \(0.0553012\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.71554 | −0.518577 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.10364 | −0.324864 | −0.162432 | − | 0.986720i | \(-0.551934\pi\) | ||||
−0.162432 | + | 0.986720i | \(0.551934\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.39492 | −0.392482 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −19.1196 | −1.01192 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.1491 | −1.11621 | −0.558104 | − | 0.829771i | \(-0.688471\pi\) | ||||
−0.558104 | + | 0.829771i | \(0.688471\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.7098 | 2.08999 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.2620 | −0.538616 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.08857 | 0.266348 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.8689 | 0.567351 | 0.283675 | − | 0.958920i | \(-0.408446\pi\) | ||||
0.283675 | + | 0.958920i | \(0.408446\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.10405 | −0.265706 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −27.0284 | −1.40324 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.6046 | −0.963312 | −0.481656 | − | 0.876360i | \(-0.659965\pi\) | ||||
−0.481656 | + | 0.876360i | \(0.659965\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.34794 | −0.0696074 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.0080 | 0.721450 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.4846 | 1.41179 | 0.705894 | − | 0.708317i | \(-0.250545\pi\) | ||||
0.705894 | + | 0.708317i | \(0.250545\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.9306 | 0.816152 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.9963 | −0.919569 | −0.459785 | − | 0.888031i | \(-0.652073\pi\) | ||||
−0.459785 | + | 0.888031i | \(0.652073\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.8667 | 0.604783 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.12236 | −0.260384 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.62327 | 0.386515 | 0.193258 | − | 0.981148i | \(-0.438095\pi\) | ||||
0.193258 | + | 0.981148i | \(0.438095\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −41.9239 | −2.12018 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.2263 | −1.02028 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.14325 | −0.258785 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.3599 | −1.22259 | −0.611294 | − | 0.791404i | \(-0.709351\pi\) | ||||
−0.611294 | + | 0.791404i | \(0.709351\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −28.4084 | −1.42220 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.3427 | −0.616365 | −0.308182 | − | 0.951327i | \(-0.599721\pi\) | ||||
−0.308182 | + | 0.951327i | \(0.599721\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.6050 | −0.578086 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.05121 | −0.201306 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.31429 | −0.213851 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.7263 | −1.42042 | −0.710212 | − | 0.703988i | \(-0.751401\pi\) | ||||
−0.710212 | + | 0.703988i | \(0.751401\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.61756 | 0.474399 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.23673 | −0.208476 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.99108 | −0.441355 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.86715 | −0.140405 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.4021 | 0.605880 | 0.302940 | − | 0.953010i | \(-0.402032\pi\) | ||||
0.302940 | + | 0.953010i | \(0.402032\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.1603 | 0.738865 | 0.369433 | − | 0.929257i | \(-0.379552\pi\) | ||||
0.369433 | + | 0.929257i | \(0.379552\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.23004 | −0.254293 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.15688 | 0.250146 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.7007 | 0.614628 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.0203 | 0.483787 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37.2804 | 1.79573 | 0.897866 | − | 0.440269i | \(-0.145117\pi\) | ||||
0.897866 | + | 0.440269i | \(0.145117\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.57676 | 0.123831 | 0.0619156 | − | 0.998081i | \(-0.480279\pi\) | ||||
0.0619156 | + | 0.998081i | \(0.480279\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.9584 | 0.525413 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −62.2916 | −2.97981 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.03202 | −0.383348 | −0.191674 | − | 0.981459i | \(-0.561392\pi\) | ||||
−0.191674 | + | 0.981459i | \(0.561392\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.669103 | −0.0318621 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.3158 | −1.63039 | −0.815196 | − | 0.579185i | \(-0.803371\pi\) | ||||
−0.815196 | + | 0.579185i | \(0.803371\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.83089 | −0.0867923 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.4150 | −0.918299 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.9062 | −1.03382 | −0.516909 | − | 0.856040i | \(-0.672917\pi\) | ||||
−0.516909 | + | 0.856040i | \(0.672917\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.6131 | 0.876457 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.6889 | 0.784115 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.73940 | −0.222186 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.01851 | 0.187978 | 0.0939891 | − | 0.995573i | \(-0.470038\pi\) | ||||
0.0939891 | + | 0.995573i | \(0.470038\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 29.0772 | 1.35721 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.0129 | −0.838946 | −0.419473 | − | 0.907768i | \(-0.637785\pi\) | ||||
−0.419473 | + | 0.907768i | \(0.637785\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.9141 | 0.553693 | 0.276847 | − | 0.960914i | \(-0.410711\pi\) | ||||
0.276847 | + | 0.960914i | \(0.410711\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.07849 | −0.421005 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.63266 | 0.353198 | 0.176599 | − | 0.984283i | \(-0.443490\pi\) | ||||
0.176599 | + | 0.984283i | \(0.443490\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.74498 | 0.403806 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.53778 | −0.116935 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.6799 | 0.858902 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.66223 | 0.351567 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.6253 | 0.532286 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.90659 | 0.406953 | 0.203476 | − | 0.979080i | \(-0.434776\pi\) | ||||
0.203476 | + | 0.979080i | \(0.434776\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.72307 | 0.0785651 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 30.1416 | 1.37149 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.3922 | −0.653515 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.44411 | −0.0654386 | −0.0327193 | − | 0.999465i | \(-0.510417\pi\) | ||||
−0.0327193 | + | 0.999465i | \(0.510417\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.53616 | 0.295575 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.7679 | −1.79470 | −0.897351 | − | 0.441318i | \(-0.854511\pi\) | ||||
−0.897351 | + | 0.441318i | \(0.854511\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −41.9239 | −1.88816 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.10405 | −0.229410 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.3402 | −0.912381 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.7811 | −0.975055 | −0.487527 | − | 0.873108i | \(-0.662101\pi\) | ||||
−0.487527 | + | 0.873108i | \(0.662101\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.3356 | 0.595789 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.05275 | −0.0469397 | −0.0234698 | − | 0.999725i | \(-0.507471\pi\) | ||||
−0.0234698 | + | 0.999725i | \(0.507471\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.8629 | 0.661392 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.5212 | 0.600499 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.7721 | −1.23098 | −0.615489 | − | 0.788145i | \(-0.711041\pi\) | ||||
−0.615489 | + | 0.788145i | \(0.711041\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.9964 | 0.619165 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 43.2036 | 1.90748 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.86763 | 0.390755 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.0726 | 0.838811 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.86508 | −0.389134 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.4835 | −0.765966 | −0.382983 | − | 0.923755i | \(-0.625103\pi\) | ||||
−0.382983 | + | 0.923755i | \(0.625103\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.74840 | 0.207633 | 0.103817 | − | 0.994596i | \(-0.466894\pi\) | ||||
0.103817 | + | 0.994596i | \(0.466894\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.70759 | −0.161812 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 34.7320 | 1.51295 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 43.0920 | 1.87356 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.82228 | 0.0790802 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.43382 | −0.321994 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.9559 | 0.862769 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −32.6911 | −1.41072 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.44004 | 0.105100 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.8878 | 1.71491 | 0.857454 | − | 0.514560i | \(-0.172045\pi\) | ||||
0.857454 | + | 0.514560i | \(0.172045\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.9085 | −0.854356 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.36611 | 0.272694 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.5673 | −1.60626 | −0.803130 | − | 0.595804i | \(-0.796833\pi\) | ||||
−0.803130 | + | 0.595804i | \(0.796833\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.46274 | −0.233144 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −62.2916 | −2.65371 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.1468 | −0.601583 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.34794 | 0.0572169 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.3652 | −1.62558 | −0.812792 | − | 0.582553i | \(-0.802054\pi\) | ||||
−0.812792 | + | 0.582553i | \(0.802054\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.46049 | −0.315545 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −29.9894 | −1.26615 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −45.9437 | −1.93629 | −0.968147 | − | 0.250382i | \(-0.919444\pi\) | ||||
−0.968147 | + | 0.250382i | \(0.919444\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.14457 | 0.384715 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.1431 | −0.467966 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.4312 | 0.563064 | 0.281532 | − | 0.959552i | \(-0.409157\pi\) | ||||
0.281532 | + | 0.959552i | \(0.409157\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.7210 | −0.741601 | −0.370801 | − | 0.928712i | \(-0.620917\pi\) | ||||
−0.370801 | + | 0.928712i | \(0.620917\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.8741 | −0.872029 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.12970 | −0.339032 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.17860 | −0.0490656 | −0.0245328 | − | 0.999699i | \(-0.507810\pi\) | ||||
−0.0245328 | + | 0.999699i | \(0.507810\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.86670 | −0.202253 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.7305 | −1.02599 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −42.3944 | −1.75580 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.03849 | 0.0842810 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.8110 | 0.982785 | 0.491393 | − | 0.870938i | \(-0.336488\pi\) | ||||
0.491393 | + | 0.870938i | \(0.336488\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 51.6057 | 2.12638 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.4169 | 1.00438 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −47.3367 | −1.94389 | −0.971944 | − | 0.235214i | \(-0.924421\pi\) | ||||
−0.971944 | + | 0.235214i | \(0.924421\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.1843 | 0.581500 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.9553 | 0.489298 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.1889 | 0.824898 | 0.412449 | − | 0.910981i | \(-0.364674\pi\) | ||||
0.412449 | + | 0.910981i | \(0.364674\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.6771 | −0.761856 | −0.380928 | − | 0.924605i | \(-0.624395\pi\) | ||||
−0.380928 | + | 0.924605i | \(0.624395\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.76135 | −0.153174 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.61310 | 0.309517 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.2797 | −0.701360 | −0.350680 | − | 0.936495i | \(-0.614049\pi\) | ||||
−0.350680 | + | 0.936495i | \(0.614049\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 30.1416 | 1.22140 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.61732 | −0.308164 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 43.6926 | 1.76473 | 0.882363 | − | 0.470569i | \(-0.155951\pi\) | ||||
0.882363 | + | 0.470569i | \(0.155951\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.81541 | −0.234500 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −38.0451 | −1.53164 | −0.765818 | − | 0.643057i | \(-0.777666\pi\) | ||||
−0.765818 | + | 0.643057i | \(0.777666\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.23864 | 0.250752 | 0.125376 | − | 0.992109i | \(-0.459986\pi\) | ||||
0.125376 | + | 0.992109i | \(0.459986\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −45.8394 | −1.83947 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.03596 | −0.201761 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −44.5590 | −1.77951 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.15688 | −0.205618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.71843 | 0.148029 | 0.0740143 | − | 0.997257i | \(-0.476419\pi\) | ||||
0.0740143 | + | 0.997257i | \(0.476419\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.63449 | −0.184204 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.8185 | −0.469003 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.974519 | −0.0386118 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.74861 | 0.346090 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.3123 | −1.15777 | −0.578884 | − | 0.815410i | \(-0.696512\pi\) | ||||
−0.578884 | + | 0.815410i | \(0.696512\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.1939 | 1.19073 | 0.595366 | − | 0.803455i | \(-0.297007\pi\) | ||||
0.595366 | + | 0.803455i | \(0.297007\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.83627 | −0.229803 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.13074 | −0.162396 | −0.0811981 | − | 0.996698i | \(-0.525875\pi\) | ||||
−0.0811981 | + | 0.996698i | \(0.525875\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.64537 | −0.260854 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.9709 | −0.978687 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.4367 | −0.995417 | −0.497708 | − | 0.867344i | \(-0.665825\pi\) | ||||
−0.497708 | + | 0.867344i | \(0.665825\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.0053 | 0.586307 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.02006 | −0.234865 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.3373 | 0.675365 | 0.337683 | − | 0.941260i | \(-0.390357\pi\) | ||||
0.337683 | + | 0.941260i | \(0.390357\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −51.2968 | −1.99521 | −0.997607 | − | 0.0691355i | \(-0.977976\pi\) | ||||
−0.997607 | + | 0.0691355i | \(0.977976\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.9773 | 0.465162 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 21.0754 | 0.817270 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 66.0920 | 2.55909 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −36.9583 | −1.42889 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.9212 | 0.769048 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.9495 | −1.03883 | −0.519413 | − | 0.854523i | \(-0.673849\pi\) | ||||
−0.519413 | + | 0.854523i | \(0.673849\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.63851 | 0.217026 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −45.3779 | −1.74401 | −0.872007 | − | 0.489494i | \(-0.837182\pi\) | ||||
−0.872007 | + | 0.489494i | \(0.837182\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −39.5865 | −1.51919 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.4867 | −0.938334 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.88140 | 0.225045 | 0.112523 | − | 0.993649i | \(-0.464107\pi\) | ||||
0.112523 | + | 0.993649i | \(0.464107\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.13500 | −0.272615 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −34.5871 | −1.31958 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.9317 | 0.645048 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.6836 | −1.16726 | −0.583629 | − | 0.812021i | \(-0.698368\pi\) | ||||
−0.583629 | + | 0.812021i | \(0.698368\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.0390 | −0.533297 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.12706 | 0.0806840 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.2483 | 0.842714 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.4968 | −0.510497 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.1117 | 0.457451 | 0.228726 | − | 0.973491i | \(-0.426544\pi\) | ||||
0.228726 | + | 0.973491i | \(0.426544\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.66223 | −0.288987 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.95896 | −0.224427 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 40.8814 | 1.53750 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.2904 | 1.25025 | 0.625124 | − | 0.780525i | \(-0.285048\pi\) | ||||
0.625124 | + | 0.780525i | \(0.285048\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.08475 | 0.228196 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −54.7542 | −2.05056 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.43382 | −0.278009 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.8187 | 0.702796 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.7261 | 0.400017 | 0.200008 | − | 0.979794i | \(-0.435903\pi\) | ||||
0.200008 | + | 0.979794i | \(0.435903\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.3909 | 0.908366 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.16596 | −0.0433626 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.12970 | −0.301929 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.8826 | −0.477789 | −0.238894 | − | 0.971046i | \(-0.576785\pi\) | ||||
−0.238894 | + | 0.971046i | \(0.576785\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.5939 | 1.02200 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.3281 | 0.825835 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.9729 | 1.40256 | 0.701280 | − | 0.712886i | \(-0.252612\pi\) | ||||
0.701280 | + | 0.712886i | \(0.252612\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.762357 | −0.0281200 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.7166 | 0.505259 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.3682 | 1.55854 | 0.779270 | − | 0.626688i | \(-0.215590\pi\) | ||||
0.779270 | + | 0.626688i | \(0.215590\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.7962 | 0.653762 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.3869 | 0.968043 | 0.484021 | − | 0.875056i | \(-0.339176\pi\) | ||||
0.484021 | + | 0.875056i | \(0.339176\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.4035 | 0.527702 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.6369 | 0.389186 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 54.8899 | 2.00563 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.2028 | −0.810192 | −0.405096 | − | 0.914274i | \(-0.632762\pi\) | ||||
−0.405096 | + | 0.914274i | \(0.632762\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.3701 | −0.523676 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.3811 | −0.450593 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.1775 | −0.915093 | −0.457546 | − | 0.889186i | \(-0.651272\pi\) | ||||
−0.457546 | + | 0.889186i | \(0.651272\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 47.2775 | 1.71606 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46.5088 | −1.68594 | −0.842972 | − | 0.537958i | \(-0.819196\pi\) | ||||
−0.842972 | + | 0.537958i | \(0.819196\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.5104 | 0.633918 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.10088 | −0.220578 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.65407 | 0.0958329 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.1946 | 0.944600 | 0.472300 | − | 0.881438i | \(-0.343424\pi\) | ||||
0.472300 | + | 0.881438i | \(0.343424\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.7232 | −0.782342 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.2957 | −0.658049 | −0.329024 | − | 0.944321i | \(-0.606720\pi\) | ||||
−0.329024 | + | 0.944321i | \(0.606720\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.73508 | 0.241931 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.70759 | 0.133009 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33.0571 | 1.18439 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.9038 | −1.14161 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −45.8394 | −1.63817 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.88271 | 0.0671967 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.40992 | 0.192843 | 0.0964213 | − | 0.995341i | \(-0.469260\pi\) | ||||
0.0964213 | + | 0.995341i | \(0.469260\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28.3838 | 1.01049 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.1527 | 0.894326 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.95624 | −0.282534 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.2455 | 0.469771 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.16219 | −0.289120 | −0.144560 | − | 0.989496i | \(-0.546177\pi\) | ||||
−0.144560 | + | 0.989496i | \(0.546177\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.7975 | 0.806518 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.16604 | 0.0765333 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21.9536 | 0.774724 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.3612 | −0.788129 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.1882 | 0.569851 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.2261 | 0.851745 | 0.425872 | − | 0.904783i | \(-0.359967\pi\) | ||||
0.425872 | + | 0.904783i | \(0.359967\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.36927 | −0.0831964 | −0.0415982 | − | 0.999134i | \(-0.513245\pi\) | ||||
−0.0415982 | + | 0.999134i | \(0.513245\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −37.5334 | −1.31635 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.84900 | −0.169853 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.1757 | 1.16067 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.60698 | 0.195924 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.7721 | −0.410850 | −0.205425 | − | 0.978673i | \(-0.565858\pi\) | ||||
−0.205425 | + | 0.978673i | \(0.565858\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.6452 | −0.510499 | −0.255249 | − | 0.966875i | \(-0.582158\pi\) | ||||
−0.255249 | + | 0.966875i | \(0.582158\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.81541 | −0.202466 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.2646 | 1.57400 | 0.787001 | − | 0.616951i | \(-0.211632\pi\) | ||||
0.787001 | + | 0.616951i | \(0.211632\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.0248 | −1.18173 | −0.590865 | − | 0.806770i | \(-0.701214\pi\) | ||||
−0.590865 | + | 0.806770i | \(0.701214\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.36656 | −0.324922 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.91659 | 0.101054 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.89328 | −0.342371 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 37.9758 | 1.31264 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.8847 | 1.30793 | 0.653963 | − | 0.756527i | \(-0.273105\pi\) | ||||
0.653963 | + | 0.756527i | \(0.273105\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.0920 | 1.27903 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.80019 | 0.303095 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.0310 | −0.345078 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.9403 | 0.719517 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.0471 | −0.688016 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.12970 | 0.278682 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.38585 | −0.218647 | −0.109324 | − | 0.994006i | \(-0.534868\pi\) | ||||
−0.109324 | + | 0.994006i | \(0.534868\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.06485 | −0.310011 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.5675 | 0.770890 | 0.385445 | − | 0.922731i | \(-0.374048\pi\) | ||||
0.385445 | + | 0.922731i | \(0.374048\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.9293 | 0.441143 | 0.220572 | − | 0.975371i | \(-0.429208\pi\) | ||||
0.220572 | + | 0.975371i | \(0.429208\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.9956 | −0.545129 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 56.6075 | 1.92694 | 0.963471 | − | 0.267813i | \(-0.0863008\pi\) | ||||
0.963471 | + | 0.267813i | \(0.0863008\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.57676 | 0.223617 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.9314 | −0.439174 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.1895 | −0.752726 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.47823 | −0.185623 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.0267 | 0.576268 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.75056 | 0.0929858 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.8870 | −1.54949 | −0.774747 | − | 0.632271i | \(-0.782123\pi\) | ||||
−0.774747 | + | 0.632271i | \(0.782123\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.85044 | 0.129872 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.7211 | 1.64145 | 0.820727 | − | 0.571320i | \(-0.193569\pi\) | ||||
0.820727 | + | 0.571320i | \(0.193569\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.5541 | 0.658049 | 0.329025 | − | 0.944321i | \(-0.393280\pi\) | ||||
0.329025 | + | 0.944321i | \(0.393280\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.07625 | 0.0697925 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.99614 | −0.0670238 | −0.0335119 | − | 0.999438i | \(-0.510669\pi\) | ||||
−0.0335119 | + | 0.999438i | \(0.510669\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.5075 | −1.09027 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.4781 | −0.585538 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 33.8731 | 1.13352 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.2526 | 0.810676 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.8820 | −0.630451 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −54.7542 | −1.82615 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −50.6742 | −1.68820 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.0530 | −0.534211 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.7696 | 0.490958 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.3162 | 1.27227 | 0.636134 | − | 0.771578i | \(-0.280532\pi\) | ||||
0.636134 | + | 0.771578i | \(0.280532\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.5837 | −0.583214 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.6766 | −1.08262 | −0.541312 | − | 0.840822i | \(-0.682072\pi\) | ||||
−0.541312 | + | 0.840822i | \(0.682072\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −38.7901 | −1.28377 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.22409 | −0.205762 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 41.2730 | 1.36296 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.4614 | 1.49963 | 0.749816 | − | 0.661646i | \(-0.230142\pi\) | ||||
0.749816 | + | 0.661646i | \(0.230142\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.30145 | 0.174689 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.7420 | 0.419407 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.00000 | −0.0328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.4909 | −0.344567 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.1627 | −1.48174 | −0.740871 | − | 0.671648i | \(-0.765587\pi\) | ||||
−0.740871 | + | 0.671648i | \(0.765587\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.33354 | 0.142026 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.58786 | 0.182938 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 22.2483 | 0.727597 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.8750 | −0.877967 | −0.438983 | − | 0.898495i | \(-0.644661\pi\) | ||||
−0.438983 | + | 0.898495i | \(0.644661\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.62177 | −0.0855583 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.1286 | −0.395381 | −0.197690 | − | 0.980264i | \(-0.563344\pi\) | ||||
−0.197690 | + | 0.980264i | \(0.563344\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35.0739 | −1.14216 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 15.5091 | 0.504510 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39.4063 | −1.28053 | −0.640266 | − | 0.768153i | \(-0.721176\pi\) | ||||
−0.640266 | + | 0.768153i | \(0.721176\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.76795 | −0.284620 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 37.6807 | 1.22188 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.36823 | 0.141501 | 0.0707504 | − | 0.997494i | \(-0.477461\pi\) | ||||
0.0707504 | + | 0.997494i | \(0.477461\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.4859 | 0.501113 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 47.2775 | 1.52826 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.6252 | −0.633732 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.3613 | 0.463268 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −23.6089 | −0.760788 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.61047 | 0.116225 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.1859 | −0.649135 | −0.324567 | − | 0.945863i | \(-0.605219\pi\) | ||||
−0.324567 | + | 0.945863i | \(0.605219\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −53.2615 | −1.71101 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.9791 | −1.34717 | −0.673587 | − | 0.739108i | \(-0.735247\pi\) | ||||
−0.673587 | + | 0.739108i | \(0.735247\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.85060 | 0.187562 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.32259 | 0.0743825 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.0938 | 0.898801 | 0.449400 | − | 0.893330i | \(-0.351638\pi\) | ||||
0.449400 | + | 0.893330i | \(0.351638\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.89897 | −0.252452 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.53147 | −0.240461 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.8210 | 1.39767 | 0.698837 | − | 0.715281i | \(-0.253701\pi\) | ||||
0.698837 | + | 0.715281i | \(0.253701\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.1142 | −0.577167 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.3905 | −0.521714 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.1997 | −1.11929 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.04515 | −0.192031 | −0.0960153 | − | 0.995380i | \(-0.530610\pi\) | ||||
−0.0960153 | + | 0.995380i | \(0.530610\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.91986 | −0.156127 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.86932 | −0.281176 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.4559 | 0.964548 | 0.482274 | − | 0.876020i | \(-0.339811\pi\) | ||||
0.482274 | + | 0.876020i | \(0.339811\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.63851 | −0.178395 |
(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 | 2960.2.a.bb.1.1 | 5 | ||
4.3 | odd | 2 | 1480.2.a.g.1.5 | ✓ | 5 | ||
20.19 | odd | 2 | 7400.2.a.r.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1480.2.a.g.1.5 | ✓ | 5 | 4.3 | odd | 2 | ||
2960.2.a.bb.1.1 | 5 | 1.1 | even | 1 | trivial | ||
7400.2.a.r.1.1 | 5 | 20.19 | odd | 2 |