Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3675,2,Mod(1,3675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3675.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3675.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: | \(29.3450227428\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3675.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61803 | −1.14412 | −0.572061 | − | 0.820211i | \(-0.693856\pi\) | ||||
−0.572061 | + | 0.820211i | \(0.693856\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.61803 | 0.660560 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.23607 | −0.674200 | −0.337100 | − | 0.941469i | \(-0.609446\pi\) | ||||
−0.337100 | + | 0.941469i | \(0.609446\pi\) | |||||||
\(12\) | −0.618034 | −0.178411 | ||||||||
\(13\) | 6.47214 | 1.79505 | 0.897524 | − | 0.440966i | \(-0.145364\pi\) | ||||
0.897524 | + | 0.440966i | \(0.145364\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | −2.47214 | −0.599581 | −0.299791 | − | 0.954005i | \(-0.596917\pi\) | ||||
−0.299791 | + | 0.954005i | \(0.596917\pi\) | |||||||
\(18\) | −1.61803 | −0.381374 | ||||||||
\(19\) | 2.47214 | 0.567147 | 0.283573 | − | 0.958951i | \(-0.408480\pi\) | ||||
0.283573 | + | 0.958951i | \(0.408480\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.61803 | 0.771367 | ||||||||
\(23\) | −4.23607 | −0.883281 | −0.441641 | − | 0.897192i | \(-0.645603\pi\) | ||||
−0.441641 | + | 0.897192i | \(0.645603\pi\) | |||||||
\(24\) | −2.23607 | −0.456435 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −10.4721 | −2.05375 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 3.38197 | 0.597853 | ||||||||
\(33\) | 2.23607 | 0.389249 | ||||||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.618034 | 0.103006 | ||||||||
\(37\) | 3.47214 | 0.570816 | 0.285408 | − | 0.958406i | \(-0.407871\pi\) | ||||
0.285408 | + | 0.958406i | \(0.407871\pi\) | |||||||
\(38\) | −4.00000 | −0.648886 | ||||||||
\(39\) | −6.47214 | −1.03637 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.94427 | −1.39686 | −0.698430 | − | 0.715678i | \(-0.746118\pi\) | ||||
−0.698430 | + | 0.715678i | \(0.746118\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.70820 | −0.717994 | −0.358997 | − | 0.933339i | \(-0.616881\pi\) | ||||
−0.358997 | + | 0.933339i | \(0.616881\pi\) | |||||||
\(44\) | −1.38197 | −0.208339 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.85410 | 1.01058 | ||||||||
\(47\) | 10.4721 | 1.52752 | 0.763759 | − | 0.645501i | \(-0.223352\pi\) | ||||
0.763759 | + | 0.645501i | \(0.223352\pi\) | |||||||
\(48\) | 4.85410 | 0.700629 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.47214 | 0.346168 | ||||||||
\(52\) | 4.00000 | 0.554700 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 1.61803 | 0.220187 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.47214 | −0.327442 | ||||||||
\(58\) | 4.85410 | 0.637375 | ||||||||
\(59\) | −6.47214 | −0.842600 | −0.421300 | − | 0.906921i | \(-0.638426\pi\) | ||||
−0.421300 | + | 0.906921i | \(0.638426\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0000 | −1.53644 | −0.768221 | − | 0.640184i | \(-0.778858\pi\) | ||||
−0.768221 | + | 0.640184i | \(0.778858\pi\) | |||||||
\(62\) | 6.47214 | 0.821962 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.61803 | −0.445349 | ||||||||
\(67\) | 12.7082 | 1.55255 | 0.776277 | − | 0.630392i | \(-0.217106\pi\) | ||||
0.776277 | + | 0.630392i | \(0.217106\pi\) | |||||||
\(68\) | −1.52786 | −0.185281 | ||||||||
\(69\) | 4.23607 | 0.509963 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.23607 | 0.977441 | 0.488721 | − | 0.872440i | \(-0.337464\pi\) | ||||
0.488721 | + | 0.872440i | \(0.337464\pi\) | |||||||
\(72\) | 2.23607 | 0.263523 | ||||||||
\(73\) | −14.4721 | −1.69384 | −0.846918 | − | 0.531724i | \(-0.821544\pi\) | ||||
−0.846918 | + | 0.531724i | \(0.821544\pi\) | |||||||
\(74\) | −5.61803 | −0.653083 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.52786 | 0.175258 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 10.4721 | 1.18574 | ||||||||
\(79\) | −2.70820 | −0.304697 | −0.152348 | − | 0.988327i | \(-0.548684\pi\) | ||||
−0.152348 | + | 0.988327i | \(0.548684\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 14.4721 | 1.59818 | ||||||||
\(83\) | 16.9443 | 1.85988 | 0.929938 | − | 0.367717i | \(-0.119860\pi\) | ||||
0.929938 | + | 0.367717i | \(0.119860\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.61803 | 0.821474 | ||||||||
\(87\) | 3.00000 | 0.321634 | ||||||||
\(88\) | −5.00000 | −0.533002 | ||||||||
\(89\) | −1.52786 | −0.161953 | −0.0809766 | − | 0.996716i | \(-0.525804\pi\) | ||||
−0.0809766 | + | 0.996716i | \(0.525804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.61803 | −0.272949 | ||||||||
\(93\) | 4.00000 | 0.414781 | ||||||||
\(94\) | −16.9443 | −1.74767 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.38197 | −0.345170 | ||||||||
\(97\) | −4.00000 | −0.406138 | −0.203069 | − | 0.979164i | \(-0.565092\pi\) | ||||
−0.203069 | + | 0.979164i | \(0.565092\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.23607 | −0.224733 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.52786 | −0.948058 | −0.474029 | − | 0.880509i | \(-0.657201\pi\) | ||||
−0.474029 | + | 0.880509i | \(0.657201\pi\) | |||||||
\(102\) | −4.00000 | −0.396059 | ||||||||
\(103\) | 7.41641 | 0.730760 | 0.365380 | − | 0.930858i | \(-0.380939\pi\) | ||||
0.365380 | + | 0.930858i | \(0.380939\pi\) | |||||||
\(104\) | 14.4721 | 1.41911 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.70820 | −0.942944 | ||||||||
\(107\) | −8.94427 | −0.864675 | −0.432338 | − | 0.901712i | \(-0.642311\pi\) | ||||
−0.432338 | + | 0.901712i | \(0.642311\pi\) | |||||||
\(108\) | −0.618034 | −0.0594703 | ||||||||
\(109\) | 16.4164 | 1.57241 | 0.786203 | − | 0.617968i | \(-0.212044\pi\) | ||||
0.786203 | + | 0.617968i | \(0.212044\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.47214 | −0.329561 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.5279 | −0.990378 | −0.495189 | − | 0.868785i | \(-0.664901\pi\) | ||||
−0.495189 | + | 0.868785i | \(0.664901\pi\) | |||||||
\(114\) | 4.00000 | 0.374634 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.85410 | −0.172149 | ||||||||
\(117\) | 6.47214 | 0.598349 | ||||||||
\(118\) | 10.4721 | 0.964038 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.00000 | −0.545455 | ||||||||
\(122\) | 19.4164 | 1.75788 | ||||||||
\(123\) | 8.94427 | 0.806478 | ||||||||
\(124\) | −2.47214 | −0.222004 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.1803 | 1.70198 | 0.850990 | − | 0.525182i | \(-0.176003\pi\) | ||||
0.850990 | + | 0.525182i | \(0.176003\pi\) | |||||||
\(128\) | −13.6180 | −1.20368 | ||||||||
\(129\) | 4.70820 | 0.414534 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.5279 | −1.18193 | −0.590967 | − | 0.806695i | \(-0.701254\pi\) | ||||
−0.590967 | + | 0.806695i | \(0.701254\pi\) | |||||||
\(132\) | 1.38197 | 0.120285 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −20.5623 | −1.77631 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.52786 | −0.474010 | ||||||||
\(137\) | −19.8885 | −1.69919 | −0.849596 | − | 0.527433i | \(-0.823154\pi\) | ||||
−0.849596 | + | 0.527433i | \(0.823154\pi\) | |||||||
\(138\) | −6.85410 | −0.583460 | ||||||||
\(139\) | 11.4164 | 0.968327 | 0.484164 | − | 0.874978i | \(-0.339124\pi\) | ||||
0.484164 | + | 0.874978i | \(0.339124\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.4721 | −0.881913 | ||||||||
\(142\) | −13.3262 | −1.11831 | ||||||||
\(143\) | −14.4721 | −1.21022 | ||||||||
\(144\) | −4.85410 | −0.404508 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 23.4164 | 1.93796 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.14590 | 0.176392 | ||||||||
\(149\) | 12.8885 | 1.05587 | 0.527935 | − | 0.849285i | \(-0.322966\pi\) | ||||
0.527935 | + | 0.849285i | \(0.322966\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.70820 | 0.545906 | 0.272953 | − | 0.962027i | \(-0.412000\pi\) | ||||
0.272953 | + | 0.962027i | \(0.412000\pi\) | |||||||
\(152\) | 5.52786 | 0.448369 | ||||||||
\(153\) | −2.47214 | −0.199860 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.00000 | −0.320256 | ||||||||
\(157\) | −0.944272 | −0.0753611 | −0.0376806 | − | 0.999290i | \(-0.511997\pi\) | ||||
−0.0376806 | + | 0.999290i | \(0.511997\pi\) | |||||||
\(158\) | 4.38197 | 0.348610 | ||||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.61803 | −0.127125 | ||||||||
\(163\) | 12.0000 | 0.939913 | 0.469956 | − | 0.882690i | \(-0.344270\pi\) | ||||
0.469956 | + | 0.882690i | \(0.344270\pi\) | |||||||
\(164\) | −5.52786 | −0.431654 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −27.4164 | −2.12793 | ||||||||
\(167\) | −22.4721 | −1.73895 | −0.869473 | − | 0.493980i | \(-0.835541\pi\) | ||||
−0.869473 | + | 0.493980i | \(0.835541\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.8885 | 2.22220 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.47214 | 0.189049 | ||||||||
\(172\) | −2.90983 | −0.221872 | ||||||||
\(173\) | 2.47214 | 0.187953 | 0.0939765 | − | 0.995574i | \(-0.470042\pi\) | ||||
0.0939765 | + | 0.995574i | \(0.470042\pi\) | |||||||
\(174\) | −4.85410 | −0.367989 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.8541 | 0.818159 | ||||||||
\(177\) | 6.47214 | 0.486476 | ||||||||
\(178\) | 2.47214 | 0.185294 | ||||||||
\(179\) | −0.944272 | −0.0705782 | −0.0352891 | − | 0.999377i | \(-0.511235\pi\) | ||||
−0.0352891 | + | 0.999377i | \(0.511235\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.47214 | −0.481070 | −0.240535 | − | 0.970640i | \(-0.577323\pi\) | ||||
−0.240535 | + | 0.970640i | \(0.577323\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.0000 | 0.887066 | ||||||||
\(184\) | −9.47214 | −0.698295 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.47214 | −0.474560 | ||||||||
\(187\) | 5.52786 | 0.404237 | ||||||||
\(188\) | 6.47214 | 0.472029 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.05573 | 0.221105 | 0.110552 | − | 0.993870i | \(-0.464738\pi\) | ||||
0.110552 | + | 0.993870i | \(0.464738\pi\) | |||||||
\(192\) | −4.23607 | −0.305712 | ||||||||
\(193\) | −22.8885 | −1.64755 | −0.823777 | − | 0.566914i | \(-0.808137\pi\) | ||||
−0.823777 | + | 0.566914i | \(0.808137\pi\) | |||||||
\(194\) | 6.47214 | 0.464672 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.0000 | −1.49619 | −0.748094 | − | 0.663593i | \(-0.769031\pi\) | ||||
−0.748094 | + | 0.663593i | \(0.769031\pi\) | |||||||
\(198\) | 3.61803 | 0.257122 | ||||||||
\(199\) | 21.8885 | 1.55164 | 0.775819 | − | 0.630956i | \(-0.217337\pi\) | ||||
0.775819 | + | 0.630956i | \(0.217337\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.7082 | −0.896368 | ||||||||
\(202\) | 15.4164 | 1.08469 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.52786 | 0.106972 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.0000 | −0.836080 | ||||||||
\(207\) | −4.23607 | −0.294427 | ||||||||
\(208\) | −31.4164 | −2.17834 | ||||||||
\(209\) | −5.52786 | −0.382370 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.8885 | 0.956127 | 0.478063 | − | 0.878325i | \(-0.341339\pi\) | ||||
0.478063 | + | 0.878325i | \(0.341339\pi\) | |||||||
\(212\) | 3.70820 | 0.254680 | ||||||||
\(213\) | −8.23607 | −0.564326 | ||||||||
\(214\) | 14.4721 | 0.989295 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.23607 | −0.152145 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −26.5623 | −1.79903 | ||||||||
\(219\) | 14.4721 | 0.977936 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.0000 | −1.07628 | ||||||||
\(222\) | 5.61803 | 0.377058 | ||||||||
\(223\) | −3.41641 | −0.228780 | −0.114390 | − | 0.993436i | \(-0.536491\pi\) | ||||
−0.114390 | + | 0.993436i | \(0.536491\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.0344 | 1.13311 | ||||||||
\(227\) | −7.41641 | −0.492244 | −0.246122 | − | 0.969239i | \(-0.579156\pi\) | ||||
−0.246122 | + | 0.969239i | \(0.579156\pi\) | |||||||
\(228\) | −1.52786 | −0.101185 | ||||||||
\(229\) | −28.9443 | −1.91269 | −0.956346 | − | 0.292238i | \(-0.905600\pi\) | ||||
−0.956346 | + | 0.292238i | \(0.905600\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.70820 | −0.440415 | ||||||||
\(233\) | −4.52786 | −0.296630 | −0.148315 | − | 0.988940i | \(-0.547385\pi\) | ||||
−0.148315 | + | 0.988940i | \(0.547385\pi\) | |||||||
\(234\) | −10.4721 | −0.684585 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.00000 | −0.260378 | ||||||||
\(237\) | 2.70820 | 0.175917 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.9443 | −1.35477 | −0.677386 | − | 0.735628i | \(-0.736887\pi\) | ||||
−0.677386 | + | 0.735628i | \(0.736887\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.4721 | −1.18989 | −0.594947 | − | 0.803765i | \(-0.702827\pi\) | ||||
−0.594947 | + | 0.803765i | \(0.702827\pi\) | |||||||
\(242\) | 9.70820 | 0.624067 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −7.41641 | −0.474787 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −14.4721 | −0.922710 | ||||||||
\(247\) | 16.0000 | 1.01806 | ||||||||
\(248\) | −8.94427 | −0.567962 | ||||||||
\(249\) | −16.9443 | −1.07380 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.4721 | 0.660995 | 0.330498 | − | 0.943807i | \(-0.392783\pi\) | ||||
0.330498 | + | 0.943807i | \(0.392783\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.47214 | 0.595508 | ||||||||
\(254\) | −31.0344 | −1.94727 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | −8.94427 | −0.557928 | −0.278964 | − | 0.960302i | \(-0.589991\pi\) | ||||
−0.278964 | + | 0.960302i | \(0.589991\pi\) | |||||||
\(258\) | −7.61803 | −0.474278 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | −0.185695 | ||||||||
\(262\) | 21.8885 | 1.35228 | ||||||||
\(263\) | 21.1803 | 1.30604 | 0.653018 | − | 0.757343i | \(-0.273503\pi\) | ||||
0.653018 | + | 0.757343i | \(0.273503\pi\) | |||||||
\(264\) | 5.00000 | 0.307729 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.52786 | 0.0935038 | ||||||||
\(268\) | 7.85410 | 0.479766 | ||||||||
\(269\) | 8.94427 | 0.545342 | 0.272671 | − | 0.962107i | \(-0.412093\pi\) | ||||
0.272671 | + | 0.962107i | \(0.412093\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.41641 | 0.207532 | 0.103766 | − | 0.994602i | \(-0.466911\pi\) | ||||
0.103766 | + | 0.994602i | \(0.466911\pi\) | |||||||
\(272\) | 12.0000 | 0.727607 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 32.1803 | 1.94409 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.61803 | 0.157587 | ||||||||
\(277\) | 15.8885 | 0.954650 | 0.477325 | − | 0.878727i | \(-0.341606\pi\) | ||||
0.477325 | + | 0.878727i | \(0.341606\pi\) | |||||||
\(278\) | −18.4721 | −1.10789 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.3607 | −1.15496 | −0.577481 | − | 0.816404i | \(-0.695964\pi\) | ||||
−0.577481 | + | 0.816404i | \(0.695964\pi\) | |||||||
\(282\) | 16.9443 | 1.00902 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | 5.09017 | 0.302046 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 23.4164 | 1.38464 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.38197 | 0.199284 | ||||||||
\(289\) | −10.8885 | −0.640503 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.00000 | 0.234484 | ||||||||
\(292\) | −8.94427 | −0.523424 | ||||||||
\(293\) | −16.3607 | −0.955801 | −0.477901 | − | 0.878414i | \(-0.658602\pi\) | ||||
−0.477901 | + | 0.878414i | \(0.658602\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.76393 | 0.451269 | ||||||||
\(297\) | 2.23607 | 0.129750 | ||||||||
\(298\) | −20.8541 | −1.20805 | ||||||||
\(299\) | −27.4164 | −1.58553 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −10.8541 | −0.624583 | ||||||||
\(303\) | 9.52786 | 0.547361 | ||||||||
\(304\) | −12.0000 | −0.688247 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.00000 | 0.228665 | ||||||||
\(307\) | −31.4164 | −1.79303 | −0.896515 | − | 0.443014i | \(-0.853909\pi\) | ||||
−0.896515 | + | 0.443014i | \(0.853909\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.41641 | −0.421905 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.3607 | −1.15455 | −0.577274 | − | 0.816550i | \(-0.695884\pi\) | ||||
−0.577274 | + | 0.816550i | \(0.695884\pi\) | |||||||
\(312\) | −14.4721 | −0.819323 | ||||||||
\(313\) | −7.41641 | −0.419200 | −0.209600 | − | 0.977787i | \(-0.567216\pi\) | ||||
−0.209600 | + | 0.977787i | \(0.567216\pi\) | |||||||
\(314\) | 1.52786 | 0.0862224 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.67376 | −0.0941565 | ||||||||
\(317\) | 7.94427 | 0.446195 | 0.223097 | − | 0.974796i | \(-0.428383\pi\) | ||||
0.223097 | + | 0.974796i | \(0.428383\pi\) | |||||||
\(318\) | 9.70820 | 0.544409 | ||||||||
\(319\) | 6.70820 | 0.375587 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.94427 | 0.499221 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.11146 | −0.340051 | ||||||||
\(324\) | 0.618034 | 0.0343352 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −19.4164 | −1.07538 | ||||||||
\(327\) | −16.4164 | −0.907829 | ||||||||
\(328\) | −20.0000 | −1.10432 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.1803 | −1.82376 | −0.911878 | − | 0.410461i | \(-0.865368\pi\) | ||||
−0.911878 | + | 0.410461i | \(0.865368\pi\) | |||||||
\(332\) | 10.4721 | 0.574733 | ||||||||
\(333\) | 3.47214 | 0.190272 | ||||||||
\(334\) | 36.3607 | 1.98957 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | −46.7426 | −2.54246 | ||||||||
\(339\) | 10.5279 | 0.571795 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.94427 | 0.484359 | ||||||||
\(342\) | −4.00000 | −0.216295 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −10.5279 | −0.567624 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.00000 | −0.215041 | ||||||||
\(347\) | −5.29180 | −0.284078 | −0.142039 | − | 0.989861i | \(-0.545366\pi\) | ||||
−0.142039 | + | 0.989861i | \(0.545366\pi\) | |||||||
\(348\) | 1.85410 | 0.0993903 | ||||||||
\(349\) | −23.4164 | −1.25345 | −0.626726 | − | 0.779240i | \(-0.715605\pi\) | ||||
−0.626726 | + | 0.779240i | \(0.715605\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.47214 | −0.345457 | ||||||||
\(352\) | −7.56231 | −0.403072 | ||||||||
\(353\) | 13.8885 | 0.739213 | 0.369606 | − | 0.929188i | \(-0.379493\pi\) | ||||
0.369606 | + | 0.929188i | \(0.379493\pi\) | |||||||
\(354\) | −10.4721 | −0.556588 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.944272 | −0.0500463 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.52786 | 0.0807501 | ||||||||
\(359\) | −11.7639 | −0.620877 | −0.310438 | − | 0.950594i | \(-0.600476\pi\) | ||||
−0.310438 | + | 0.950594i | \(0.600476\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.8885 | −0.678344 | ||||||||
\(362\) | 10.4721 | 0.550403 | ||||||||
\(363\) | 6.00000 | 0.314918 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −19.4164 | −1.01491 | ||||||||
\(367\) | −4.00000 | −0.208798 | −0.104399 | − | 0.994535i | \(-0.533292\pi\) | ||||
−0.104399 | + | 0.994535i | \(0.533292\pi\) | |||||||
\(368\) | 20.5623 | 1.07188 | ||||||||
\(369\) | −8.94427 | −0.465620 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.47214 | 0.128174 | ||||||||
\(373\) | 17.4721 | 0.904673 | 0.452336 | − | 0.891847i | \(-0.350591\pi\) | ||||
0.452336 | + | 0.891847i | \(0.350591\pi\) | |||||||
\(374\) | −8.94427 | −0.462497 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 23.4164 | 1.20761 | ||||||||
\(377\) | −19.4164 | −0.999996 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.70820 | 0.447310 | 0.223655 | − | 0.974668i | \(-0.428201\pi\) | ||||
0.223655 | + | 0.974668i | \(0.428201\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.1803 | −0.982639 | ||||||||
\(382\) | −4.94427 | −0.252971 | ||||||||
\(383\) | −19.4164 | −0.992132 | −0.496066 | − | 0.868285i | \(-0.665223\pi\) | ||||
−0.496066 | + | 0.868285i | \(0.665223\pi\) | |||||||
\(384\) | 13.6180 | 0.694942 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 37.0344 | 1.88500 | ||||||||
\(387\) | −4.70820 | −0.239331 | ||||||||
\(388\) | −2.47214 | −0.125504 | ||||||||
\(389\) | 12.0557 | 0.611250 | 0.305625 | − | 0.952152i | \(-0.401135\pi\) | ||||
0.305625 | + | 0.952152i | \(0.401135\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.4721 | 0.529599 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.5279 | 0.682390 | ||||||||
\(394\) | 33.9787 | 1.71182 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.38197 | −0.0694464 | ||||||||
\(397\) | 9.88854 | 0.496292 | 0.248146 | − | 0.968723i | \(-0.420179\pi\) | ||||
0.248146 | + | 0.968723i | \(0.420179\pi\) | |||||||
\(398\) | −35.4164 | −1.77526 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.4164 | 1.41905 | 0.709524 | − | 0.704681i | \(-0.248910\pi\) | ||||
0.709524 | + | 0.704681i | \(0.248910\pi\) | |||||||
\(402\) | 20.5623 | 1.02555 | ||||||||
\(403\) | −25.8885 | −1.28960 | ||||||||
\(404\) | −5.88854 | −0.292966 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.76393 | −0.384844 | ||||||||
\(408\) | 5.52786 | 0.273670 | ||||||||
\(409\) | −7.41641 | −0.366718 | −0.183359 | − | 0.983046i | \(-0.558697\pi\) | ||||
−0.183359 | + | 0.983046i | \(0.558697\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.8885 | 0.981030 | ||||||||
\(412\) | 4.58359 | 0.225817 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.85410 | 0.336861 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 21.8885 | 1.07317 | ||||||||
\(417\) | −11.4164 | −0.559064 | ||||||||
\(418\) | 8.94427 | 0.437479 | ||||||||
\(419\) | −29.8885 | −1.46015 | −0.730075 | − | 0.683367i | \(-0.760515\pi\) | ||||
−0.730075 | + | 0.683367i | \(0.760515\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.4164 | 0.507665 | 0.253832 | − | 0.967248i | \(-0.418309\pi\) | ||||
0.253832 | + | 0.967248i | \(0.418309\pi\) | |||||||
\(422\) | −22.4721 | −1.09393 | ||||||||
\(423\) | 10.4721 | 0.509173 | ||||||||
\(424\) | 13.4164 | 0.651558 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 13.3262 | 0.645658 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.52786 | −0.267199 | ||||||||
\(429\) | 14.4721 | 0.698721 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.0557 | −0.532536 | −0.266268 | − | 0.963899i | \(-0.585791\pi\) | ||||
−0.266268 | + | 0.963899i | \(0.585791\pi\) | |||||||
\(432\) | 4.85410 | 0.233543 | ||||||||
\(433\) | −12.9443 | −0.622062 | −0.311031 | − | 0.950400i | \(-0.600674\pi\) | ||||
−0.311031 | + | 0.950400i | \(0.600674\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.1459 | 0.485900 | ||||||||
\(437\) | −10.4721 | −0.500950 | ||||||||
\(438\) | −23.4164 | −1.11888 | ||||||||
\(439\) | −27.4164 | −1.30851 | −0.654257 | − | 0.756272i | \(-0.727018\pi\) | ||||
−0.654257 | + | 0.756272i | \(0.727018\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 25.8885 | 1.23139 | ||||||||
\(443\) | −15.0557 | −0.715319 | −0.357660 | − | 0.933852i | \(-0.616425\pi\) | ||||
−0.357660 | + | 0.933852i | \(0.616425\pi\) | |||||||
\(444\) | −2.14590 | −0.101840 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.52786 | 0.261752 | ||||||||
\(447\) | −12.8885 | −0.609607 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.52786 | −0.308069 | −0.154034 | − | 0.988065i | \(-0.549227\pi\) | ||||
−0.154034 | + | 0.988065i | \(0.549227\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.0000 | 0.941763 | ||||||||
\(452\) | −6.50658 | −0.306044 | ||||||||
\(453\) | −6.70820 | −0.315179 | ||||||||
\(454\) | 12.0000 | 0.563188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.52786 | −0.258866 | ||||||||
\(457\) | −25.9443 | −1.21362 | −0.606811 | − | 0.794846i | \(-0.707551\pi\) | ||||
−0.606811 | + | 0.794846i | \(0.707551\pi\) | |||||||
\(458\) | 46.8328 | 2.18835 | ||||||||
\(459\) | 2.47214 | 0.115389 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.4721 | −1.41923 | −0.709614 | − | 0.704590i | \(-0.751131\pi\) | ||||
−0.709614 | + | 0.704590i | \(0.751131\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.88854 | −0.0877681 | −0.0438840 | − | 0.999037i | \(-0.513973\pi\) | ||||
−0.0438840 | + | 0.999037i | \(0.513973\pi\) | |||||||
\(464\) | 14.5623 | 0.676038 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.32624 | 0.339381 | ||||||||
\(467\) | 1.88854 | 0.0873914 | 0.0436957 | − | 0.999045i | \(-0.486087\pi\) | ||||
0.0436957 | + | 0.999045i | \(0.486087\pi\) | |||||||
\(468\) | 4.00000 | 0.184900 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.944272 | 0.0435098 | ||||||||
\(472\) | −14.4721 | −0.666134 | ||||||||
\(473\) | 10.5279 | 0.484072 | ||||||||
\(474\) | −4.38197 | −0.201270 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.00000 | 0.274721 | ||||||||
\(478\) | 33.8885 | 1.55003 | ||||||||
\(479\) | 30.4721 | 1.39231 | 0.696154 | − | 0.717893i | \(-0.254893\pi\) | ||||
0.696154 | + | 0.717893i | \(0.254893\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.4721 | 1.02464 | ||||||||
\(482\) | 29.8885 | 1.36139 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.70820 | −0.168555 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.61803 | 0.0733955 | ||||||||
\(487\) | 14.7082 | 0.666492 | 0.333246 | − | 0.942840i | \(-0.391856\pi\) | ||||
0.333246 | + | 0.942840i | \(0.391856\pi\) | |||||||
\(488\) | −26.8328 | −1.21466 | ||||||||
\(489\) | −12.0000 | −0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.81966 | 0.217508 | 0.108754 | − | 0.994069i | \(-0.465314\pi\) | ||||
0.108754 | + | 0.994069i | \(0.465314\pi\) | |||||||
\(492\) | 5.52786 | 0.249215 | ||||||||
\(493\) | 7.41641 | 0.334018 | ||||||||
\(494\) | −25.8885 | −1.16478 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 19.4164 | 0.871822 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 27.4164 | 1.22856 | ||||||||
\(499\) | −12.0000 | −0.537194 | −0.268597 | − | 0.963253i | \(-0.586560\pi\) | ||||
−0.268597 | + | 0.963253i | \(0.586560\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.4721 | 1.00398 | ||||||||
\(502\) | −16.9443 | −0.756260 | ||||||||
\(503\) | −12.9443 | −0.577157 | −0.288578 | − | 0.957456i | \(-0.593183\pi\) | ||||
−0.288578 | + | 0.957456i | \(0.593183\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −15.3262 | −0.681334 | ||||||||
\(507\) | −28.8885 | −1.28299 | ||||||||
\(508\) | 11.8541 | 0.525941 | ||||||||
\(509\) | −9.52786 | −0.422315 | −0.211158 | − | 0.977452i | \(-0.567723\pi\) | ||||
−0.211158 | + | 0.977452i | \(0.567723\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5.29180 | 0.233867 | ||||||||
\(513\) | −2.47214 | −0.109147 | ||||||||
\(514\) | 14.4721 | 0.638339 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.90983 | 0.128098 | ||||||||
\(517\) | −23.4164 | −1.02985 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.47214 | −0.108515 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.9443 | 0.917585 | 0.458793 | − | 0.888543i | \(-0.348282\pi\) | ||||
0.458793 | + | 0.888543i | \(0.348282\pi\) | |||||||
\(522\) | 4.85410 | 0.212458 | ||||||||
\(523\) | −1.88854 | −0.0825803 | −0.0412901 | − | 0.999147i | \(-0.513147\pi\) | ||||
−0.0412901 | + | 0.999147i | \(0.513147\pi\) | |||||||
\(524\) | −8.36068 | −0.365238 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −34.2705 | −1.49427 | ||||||||
\(527\) | 9.88854 | 0.430752 | ||||||||
\(528\) | −10.8541 | −0.472364 | ||||||||
\(529\) | −5.05573 | −0.219814 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.47214 | −0.280867 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −57.8885 | −2.50743 | ||||||||
\(534\) | −2.47214 | −0.106980 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 28.4164 | 1.22740 | ||||||||
\(537\) | 0.944272 | 0.0407483 | ||||||||
\(538\) | −14.4721 | −0.623938 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.4164 | −1.22172 | −0.610858 | − | 0.791740i | \(-0.709176\pi\) | ||||
−0.610858 | + | 0.791740i | \(0.709176\pi\) | |||||||
\(542\) | −5.52786 | −0.237442 | ||||||||
\(543\) | 6.47214 | 0.277746 | ||||||||
\(544\) | −8.36068 | −0.358461 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.8197 | 0.633643 | 0.316821 | − | 0.948485i | \(-0.397384\pi\) | ||||
0.316821 | + | 0.948485i | \(0.397384\pi\) | |||||||
\(548\) | −12.2918 | −0.525080 | ||||||||
\(549\) | −12.0000 | −0.512148 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.41641 | −0.315950 | ||||||||
\(552\) | 9.47214 | 0.403161 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −25.7082 | −1.09224 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.05573 | 0.299230 | ||||||||
\(557\) | 20.8885 | 0.885076 | 0.442538 | − | 0.896750i | \(-0.354078\pi\) | ||||
0.442538 | + | 0.896750i | \(0.354078\pi\) | |||||||
\(558\) | 6.47214 | 0.273987 | ||||||||
\(559\) | −30.4721 | −1.28883 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.52786 | −0.233387 | ||||||||
\(562\) | 31.3262 | 1.32142 | ||||||||
\(563\) | −4.94427 | −0.208376 | −0.104188 | − | 0.994558i | \(-0.533224\pi\) | ||||
−0.104188 | + | 0.994558i | \(0.533224\pi\) | |||||||
\(564\) | −6.47214 | −0.272526 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 18.4164 | 0.772735 | ||||||||
\(569\) | −36.3050 | −1.52198 | −0.760991 | − | 0.648762i | \(-0.775287\pi\) | ||||
−0.760991 | + | 0.648762i | \(0.775287\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.7639 | 0.492305 | 0.246153 | − | 0.969231i | \(-0.420834\pi\) | ||||
0.246153 | + | 0.969231i | \(0.420834\pi\) | |||||||
\(572\) | −8.94427 | −0.373979 | ||||||||
\(573\) | −3.05573 | −0.127655 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.23607 | 0.176503 | ||||||||
\(577\) | 0.583592 | 0.0242953 | 0.0121476 | − | 0.999926i | \(-0.496133\pi\) | ||||
0.0121476 | + | 0.999926i | \(0.496133\pi\) | |||||||
\(578\) | 17.6180 | 0.732814 | ||||||||
\(579\) | 22.8885 | 0.951215 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.47214 | −0.268279 | ||||||||
\(583\) | −13.4164 | −0.555651 | ||||||||
\(584\) | −32.3607 | −1.33909 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26.4721 | 1.09355 | ||||||||
\(587\) | −14.4721 | −0.597329 | −0.298664 | − | 0.954358i | \(-0.596541\pi\) | ||||
−0.298664 | + | 0.954358i | \(0.596541\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.88854 | −0.407450 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.0000 | 0.863825 | ||||||||
\(592\) | −16.8541 | −0.692699 | ||||||||
\(593\) | 44.9443 | 1.84564 | 0.922820 | − | 0.385231i | \(-0.125878\pi\) | ||||
0.922820 | + | 0.385231i | \(0.125878\pi\) | |||||||
\(594\) | −3.61803 | −0.148450 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.96556 | 0.326282 | ||||||||
\(597\) | −21.8885 | −0.895838 | ||||||||
\(598\) | 44.3607 | 1.81404 | ||||||||
\(599\) | 12.7082 | 0.519243 | 0.259622 | − | 0.965710i | \(-0.416402\pi\) | ||||
0.259622 | + | 0.965710i | \(0.416402\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.9443 | −1.50699 | −0.753494 | − | 0.657455i | \(-0.771633\pi\) | ||||
−0.753494 | + | 0.657455i | \(0.771633\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.7082 | 0.517518 | ||||||||
\(604\) | 4.14590 | 0.168694 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.4164 | −0.626249 | ||||||||
\(607\) | −35.4164 | −1.43751 | −0.718754 | − | 0.695265i | \(-0.755287\pi\) | ||||
−0.718754 | + | 0.695265i | \(0.755287\pi\) | |||||||
\(608\) | 8.36068 | 0.339070 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 67.7771 | 2.74197 | ||||||||
\(612\) | −1.52786 | −0.0617602 | ||||||||
\(613\) | 35.2492 | 1.42370 | 0.711851 | − | 0.702330i | \(-0.247857\pi\) | ||||
0.711851 | + | 0.702330i | \(0.247857\pi\) | |||||||
\(614\) | 50.8328 | 2.05145 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.4164 | −1.38555 | −0.692776 | − | 0.721153i | \(-0.743613\pi\) | ||||
−0.692776 | + | 0.721153i | \(0.743613\pi\) | |||||||
\(618\) | 12.0000 | 0.482711 | ||||||||
\(619\) | 17.5279 | 0.704504 | 0.352252 | − | 0.935905i | \(-0.385416\pi\) | ||||
0.352252 | + | 0.935905i | \(0.385416\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.23607 | 0.169988 | ||||||||
\(622\) | 32.9443 | 1.32094 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 31.4164 | 1.25766 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12.0000 | 0.479616 | ||||||||
\(627\) | 5.52786 | 0.220762 | ||||||||
\(628\) | −0.583592 | −0.0232879 | ||||||||
\(629\) | −8.58359 | −0.342250 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.347524 | 0.0138347 | 0.00691736 | − | 0.999976i | \(-0.497798\pi\) | ||||
0.00691736 | + | 0.999976i | \(0.497798\pi\) | |||||||
\(632\) | −6.05573 | −0.240884 | ||||||||
\(633\) | −13.8885 | −0.552020 | ||||||||
\(634\) | −12.8541 | −0.510502 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.70820 | −0.147040 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10.8541 | −0.429718 | ||||||||
\(639\) | 8.23607 | 0.325814 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.3607 | 1.00169 | 0.500843 | − | 0.865538i | \(-0.333023\pi\) | ||||
0.500843 | + | 0.865538i | \(0.333023\pi\) | |||||||
\(642\) | −14.4721 | −0.571170 | ||||||||
\(643\) | 24.0000 | 0.946468 | 0.473234 | − | 0.880937i | \(-0.343087\pi\) | ||||
0.473234 | + | 0.880937i | \(0.343087\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.88854 | 0.389060 | ||||||||
\(647\) | 1.88854 | 0.0742463 | 0.0371232 | − | 0.999311i | \(-0.488181\pi\) | ||||
0.0371232 | + | 0.999311i | \(0.488181\pi\) | |||||||
\(648\) | 2.23607 | 0.0878410 | ||||||||
\(649\) | 14.4721 | 0.568081 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.41641 | 0.290449 | ||||||||
\(653\) | 11.8885 | 0.465235 | 0.232617 | − | 0.972568i | \(-0.425271\pi\) | ||||
0.232617 | + | 0.972568i | \(0.425271\pi\) | |||||||
\(654\) | 26.5623 | 1.03867 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 43.4164 | 1.69513 | ||||||||
\(657\) | −14.4721 | −0.564612 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.0557 | −0.586488 | −0.293244 | − | 0.956038i | \(-0.594735\pi\) | ||||
−0.293244 | + | 0.956038i | \(0.594735\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.3607 | −0.791939 | −0.395969 | − | 0.918264i | \(-0.629591\pi\) | ||||
−0.395969 | + | 0.918264i | \(0.629591\pi\) | |||||||
\(662\) | 53.6869 | 2.08660 | ||||||||
\(663\) | 16.0000 | 0.621389 | ||||||||
\(664\) | 37.8885 | 1.47036 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.61803 | −0.217694 | ||||||||
\(667\) | 12.7082 | 0.492064 | ||||||||
\(668\) | −13.8885 | −0.537364 | ||||||||
\(669\) | 3.41641 | 0.132086 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.8328 | 1.03587 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.0000 | 1.15642 | 0.578208 | − | 0.815890i | \(-0.303752\pi\) | ||||
0.578208 | + | 0.815890i | \(0.303752\pi\) | |||||||
\(674\) | 3.23607 | 0.124649 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.8541 | 0.686696 | ||||||||
\(677\) | −49.8885 | −1.91737 | −0.958686 | − | 0.284466i | \(-0.908184\pi\) | ||||
−0.958686 | + | 0.284466i | \(0.908184\pi\) | |||||||
\(678\) | −17.0344 | −0.654204 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.41641 | 0.284197 | ||||||||
\(682\) | −14.4721 | −0.554167 | ||||||||
\(683\) | −27.1803 | −1.04003 | −0.520013 | − | 0.854158i | \(-0.674073\pi\) | ||||
−0.520013 | + | 0.854158i | \(0.674073\pi\) | |||||||
\(684\) | 1.52786 | 0.0584193 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.9443 | 1.10429 | ||||||||
\(688\) | 22.8541 | 0.871304 | ||||||||
\(689\) | 38.8328 | 1.47941 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.8328 | −0.412100 | −0.206050 | − | 0.978541i | \(-0.566061\pi\) | ||||
−0.206050 | + | 0.978541i | \(0.566061\pi\) | |||||||
\(692\) | 1.52786 | 0.0580807 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.56231 | 0.325021 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.70820 | 0.254274 | ||||||||
\(697\) | 22.1115 | 0.837531 | ||||||||
\(698\) | 37.8885 | 1.43410 | ||||||||
\(699\) | 4.52786 | 0.171260 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.7771 | 1.42682 | 0.713410 | − | 0.700746i | \(-0.247150\pi\) | ||||
0.713410 | + | 0.700746i | \(0.247150\pi\) | |||||||
\(702\) | 10.4721 | 0.395245 | ||||||||
\(703\) | 8.58359 | 0.323736 | ||||||||
\(704\) | −9.47214 | −0.356995 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.4721 | −0.845750 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.00000 | 0.150329 | ||||||||
\(709\) | 26.0000 | 0.976450 | 0.488225 | − | 0.872718i | \(-0.337644\pi\) | ||||
0.488225 | + | 0.872718i | \(0.337644\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.70820 | −0.101566 | ||||||||
\(712\) | −3.41641 | −0.128035 | ||||||||
\(713\) | 16.9443 | 0.634568 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.583592 | −0.0218099 | ||||||||
\(717\) | 20.9443 | 0.782178 | ||||||||
\(718\) | 19.0344 | 0.710359 | ||||||||
\(719\) | 0.944272 | 0.0352154 | 0.0176077 | − | 0.999845i | \(-0.494395\pi\) | ||||
0.0176077 | + | 0.999845i | \(0.494395\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 20.8541 | 0.776109 | ||||||||
\(723\) | 18.4721 | 0.686986 | ||||||||
\(724\) | −4.00000 | −0.148659 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −9.70820 | −0.360305 | ||||||||
\(727\) | 17.3050 | 0.641805 | 0.320903 | − | 0.947112i | \(-0.396014\pi\) | ||||
0.320903 | + | 0.947112i | \(0.396014\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.6393 | 0.430496 | ||||||||
\(732\) | 7.41641 | 0.274118 | ||||||||
\(733\) | 32.0000 | 1.18195 | 0.590973 | − | 0.806691i | \(-0.298744\pi\) | ||||
0.590973 | + | 0.806691i | \(0.298744\pi\) | |||||||
\(734\) | 6.47214 | 0.238891 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.3262 | −0.528072 | ||||||||
\(737\) | −28.4164 | −1.04673 | ||||||||
\(738\) | 14.4721 | 0.532727 | ||||||||
\(739\) | −20.7082 | −0.761764 | −0.380882 | − | 0.924624i | \(-0.624380\pi\) | ||||
−0.380882 | + | 0.924624i | \(0.624380\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.0000 | −0.587775 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.05573 | −0.112104 | −0.0560519 | − | 0.998428i | \(-0.517851\pi\) | ||||
−0.0560519 | + | 0.998428i | \(0.517851\pi\) | |||||||
\(744\) | 8.94427 | 0.327913 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −28.2705 | −1.03506 | ||||||||
\(747\) | 16.9443 | 0.619958 | ||||||||
\(748\) | 3.41641 | 0.124916 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.7771 | −0.721676 | −0.360838 | − | 0.932628i | \(-0.617509\pi\) | ||||
−0.360838 | + | 0.932628i | \(0.617509\pi\) | |||||||
\(752\) | −50.8328 | −1.85368 | ||||||||
\(753\) | −10.4721 | −0.381626 | ||||||||
\(754\) | 31.4164 | 1.14412 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.47214 | −0.198888 | −0.0994441 | − | 0.995043i | \(-0.531706\pi\) | ||||
−0.0994441 | + | 0.995043i | \(0.531706\pi\) | |||||||
\(758\) | −14.0902 | −0.511778 | ||||||||
\(759\) | −9.47214 | −0.343817 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 52.9443 | 1.91923 | 0.959614 | − | 0.281319i | \(-0.0907720\pi\) | ||||
0.959614 | + | 0.281319i | \(0.0907720\pi\) | |||||||
\(762\) | 31.0344 | 1.12426 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.88854 | 0.0683251 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 31.4164 | 1.13512 | ||||||||
\(767\) | −41.8885 | −1.51251 | ||||||||
\(768\) | −13.5623 | −0.489388 | ||||||||
\(769\) | −20.0000 | −0.721218 | −0.360609 | − | 0.932717i | \(-0.617431\pi\) | ||||
−0.360609 | + | 0.932717i | \(0.617431\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.94427 | 0.322120 | ||||||||
\(772\) | −14.1459 | −0.509122 | ||||||||
\(773\) | −39.7771 | −1.43068 | −0.715341 | − | 0.698775i | \(-0.753729\pi\) | ||||
−0.715341 | + | 0.698775i | \(0.753729\pi\) | |||||||
\(774\) | 7.61803 | 0.273825 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.94427 | −0.321081 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19.5066 | −0.699345 | ||||||||
\(779\) | −22.1115 | −0.792225 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.4164 | −0.658991 | ||||||||
\(782\) | −16.9443 | −0.605926 | ||||||||
\(783\) | 3.00000 | 0.107211 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −21.8885 | −0.780739 | ||||||||
\(787\) | −33.5279 | −1.19514 | −0.597570 | − | 0.801817i | \(-0.703867\pi\) | ||||
−0.597570 | + | 0.801817i | \(0.703867\pi\) | |||||||
\(788\) | −12.9787 | −0.462348 | ||||||||
\(789\) | −21.1803 | −0.754040 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.00000 | −0.177667 | ||||||||
\(793\) | −77.6656 | −2.75799 | ||||||||
\(794\) | −16.0000 | −0.567819 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.5279 | 0.479482 | ||||||||
\(797\) | 34.4721 | 1.22107 | 0.610533 | − | 0.791991i | \(-0.290955\pi\) | ||||
0.610533 | + | 0.791991i | \(0.290955\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.8885 | −0.915871 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.52786 | −0.0539844 | ||||||||
\(802\) | −45.9787 | −1.62356 | ||||||||
\(803\) | 32.3607 | 1.14198 | ||||||||
\(804\) | −7.85410 | −0.276993 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 41.8885 | 1.47546 | ||||||||
\(807\) | −8.94427 | −0.314853 | ||||||||
\(808\) | −21.3050 | −0.749506 | ||||||||
\(809\) | 8.52786 | 0.299824 | 0.149912 | − | 0.988699i | \(-0.452101\pi\) | ||||
0.149912 | + | 0.988699i | \(0.452101\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.8328 | −1.36360 | −0.681802 | − | 0.731536i | \(-0.738804\pi\) | ||||
−0.681802 | + | 0.731536i | \(0.738804\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.41641 | −0.119819 | ||||||||
\(814\) | 12.5623 | 0.440309 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −12.0000 | −0.420084 | ||||||||
\(817\) | −11.6393 | −0.407208 | ||||||||
\(818\) | 12.0000 | 0.419570 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.7771 | −1.59763 | −0.798816 | − | 0.601576i | \(-0.794540\pi\) | ||||
−0.798816 | + | 0.601576i | \(0.794540\pi\) | |||||||
\(822\) | −32.1803 | −1.12242 | ||||||||
\(823\) | −17.5410 | −0.611442 | −0.305721 | − | 0.952121i | \(-0.598897\pi\) | ||||
−0.305721 | + | 0.952121i | \(0.598897\pi\) | |||||||
\(824\) | 16.5836 | 0.577717 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.2361 | −0.495037 | −0.247518 | − | 0.968883i | \(-0.579615\pi\) | ||||
−0.247518 | + | 0.968883i | \(0.579615\pi\) | |||||||
\(828\) | −2.61803 | −0.0909830 | ||||||||
\(829\) | 2.47214 | 0.0858608 | 0.0429304 | − | 0.999078i | \(-0.486331\pi\) | ||||
0.0429304 | + | 0.999078i | \(0.486331\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.8885 | −0.551167 | ||||||||
\(832\) | 27.4164 | 0.950493 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 18.4721 | 0.639638 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.41641 | −0.118159 | ||||||||
\(837\) | 4.00000 | 0.138260 | ||||||||
\(838\) | 48.3607 | 1.67059 | ||||||||
\(839\) | 55.1935 | 1.90549 | 0.952746 | − | 0.303770i | \(-0.0982453\pi\) | ||||
0.952746 | + | 0.303770i | \(0.0982453\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | −16.8541 | −0.580831 | ||||||||
\(843\) | 19.3607 | 0.666817 | ||||||||
\(844\) | 8.58359 | 0.295459 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −16.9443 | −0.582556 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −29.1246 | −1.00014 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.7082 | −0.504191 | ||||||||
\(852\) | −5.09017 | −0.174386 | ||||||||
\(853\) | 6.83282 | 0.233951 | 0.116976 | − | 0.993135i | \(-0.462680\pi\) | ||||
0.116976 | + | 0.993135i | \(0.462680\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20.0000 | −0.683586 | ||||||||
\(857\) | 37.8885 | 1.29425 | 0.647124 | − | 0.762385i | \(-0.275972\pi\) | ||||
0.647124 | + | 0.762385i | \(0.275972\pi\) | |||||||
\(858\) | −23.4164 | −0.799423 | ||||||||
\(859\) | 25.8885 | 0.883306 | 0.441653 | − | 0.897186i | \(-0.354392\pi\) | ||||
0.441653 | + | 0.897186i | \(0.354392\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.8885 | 0.609286 | ||||||||
\(863\) | 2.12461 | 0.0723226 | 0.0361613 | − | 0.999346i | \(-0.488487\pi\) | ||||
0.0361613 | + | 0.999346i | \(0.488487\pi\) | |||||||
\(864\) | −3.38197 | −0.115057 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 20.9443 | 0.711715 | ||||||||
\(867\) | 10.8885 | 0.369794 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.05573 | 0.205427 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 82.2492 | 2.78691 | ||||||||
\(872\) | 36.7082 | 1.24310 | ||||||||
\(873\) | −4.00000 | −0.135379 | ||||||||
\(874\) | 16.9443 | 0.573149 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.94427 | 0.302199 | ||||||||
\(877\) | 18.0000 | 0.607817 | 0.303908 | − | 0.952701i | \(-0.401708\pi\) | ||||
0.303908 | + | 0.952701i | \(0.401708\pi\) | |||||||
\(878\) | 44.3607 | 1.49710 | ||||||||
\(879\) | 16.3607 | 0.551832 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.9443 | −1.37945 | −0.689724 | − | 0.724073i | \(-0.742268\pi\) | ||||
−0.689724 | + | 0.724073i | \(0.742268\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.5410 | 1.46527 | 0.732636 | − | 0.680621i | \(-0.238290\pi\) | ||||
0.732636 | + | 0.680621i | \(0.238290\pi\) | |||||||
\(884\) | −9.88854 | −0.332588 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.3607 | 0.818413 | ||||||||
\(887\) | 26.8328 | 0.900958 | 0.450479 | − | 0.892787i | \(-0.351253\pi\) | ||||
0.450479 | + | 0.892787i | \(0.351253\pi\) | |||||||
\(888\) | −7.76393 | −0.260540 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.23607 | −0.0749111 | ||||||||
\(892\) | −2.11146 | −0.0706968 | ||||||||
\(893\) | 25.8885 | 0.866327 | ||||||||
\(894\) | 20.8541 | 0.697466 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27.4164 | 0.915407 | ||||||||
\(898\) | 10.5623 | 0.352469 | ||||||||
\(899\) | 12.0000 | 0.400222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.8328 | −0.494153 | ||||||||
\(902\) | −32.3607 | −1.07749 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −23.5410 | −0.782963 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 10.8541 | 0.360603 | ||||||||
\(907\) | −45.8885 | −1.52370 | −0.761852 | − | 0.647751i | \(-0.775710\pi\) | ||||
−0.761852 | + | 0.647751i | \(0.775710\pi\) | |||||||
\(908\) | −4.58359 | −0.152112 | ||||||||
\(909\) | −9.52786 | −0.316019 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −56.0132 | −1.85580 | −0.927899 | − | 0.372831i | \(-0.878387\pi\) | ||||
−0.927899 | + | 0.372831i | \(0.878387\pi\) | |||||||
\(912\) | 12.0000 | 0.397360 | ||||||||
\(913\) | −37.8885 | −1.25393 | ||||||||
\(914\) | 41.9787 | 1.38853 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.8885 | −0.591054 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.00000 | −0.132020 | ||||||||
\(919\) | 15.1803 | 0.500753 | 0.250377 | − | 0.968149i | \(-0.419446\pi\) | ||||
0.250377 | + | 0.968149i | \(0.419446\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.4164 | 1.03521 | ||||||||
\(922\) | 49.3050 | 1.62377 | ||||||||
\(923\) | 53.3050 | 1.75455 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.05573 | 0.100417 | ||||||||
\(927\) | 7.41641 | 0.243587 | ||||||||
\(928\) | −10.1459 | −0.333055 | ||||||||
\(929\) | 4.58359 | 0.150383 | 0.0751914 | − | 0.997169i | \(-0.476043\pi\) | ||||
0.0751914 | + | 0.997169i | \(0.476043\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.79837 | −0.0916638 | ||||||||
\(933\) | 20.3607 | 0.666579 | ||||||||
\(934\) | −3.05573 | −0.0999865 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 14.4721 | 0.473037 | ||||||||
\(937\) | 28.0000 | 0.914720 | 0.457360 | − | 0.889282i | \(-0.348795\pi\) | ||||
0.457360 | + | 0.889282i | \(0.348795\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.41641 | 0.242025 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.7771 | 1.03590 | 0.517952 | − | 0.855410i | \(-0.326695\pi\) | ||||
0.517952 | + | 0.855410i | \(0.326695\pi\) | |||||||
\(942\) | −1.52786 | −0.0497805 | ||||||||
\(943\) | 37.8885 | 1.23382 | ||||||||
\(944\) | 31.4164 | 1.02252 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.0344 | −0.553837 | ||||||||
\(947\) | 32.9443 | 1.07054 | 0.535272 | − | 0.844679i | \(-0.320209\pi\) | ||||
0.535272 | + | 0.844679i | \(0.320209\pi\) | |||||||
\(948\) | 1.67376 | 0.0543613 | ||||||||
\(949\) | −93.6656 | −3.04052 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.94427 | −0.257611 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.3607 | 0.368009 | 0.184004 | − | 0.982925i | \(-0.441094\pi\) | ||||
0.184004 | + | 0.982925i | \(0.441094\pi\) | |||||||
\(954\) | −9.70820 | −0.314315 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −12.9443 | −0.418648 | ||||||||
\(957\) | −6.70820 | −0.216845 | ||||||||
\(958\) | −49.3050 | −1.59297 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | −36.3607 | −1.17232 | ||||||||
\(963\) | −8.94427 | −0.288225 | ||||||||
\(964\) | −11.4164 | −0.367698 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.7771 | −1.40778 | −0.703888 | − | 0.710311i | \(-0.748554\pi\) | ||||
−0.703888 | + | 0.710311i | \(0.748554\pi\) | |||||||
\(968\) | −13.4164 | −0.431220 | ||||||||
\(969\) | 6.11146 | 0.196328 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.3050 | −1.32554 | −0.662769 | − | 0.748823i | \(-0.730619\pi\) | ||||
−0.662769 | + | 0.748823i | \(0.730619\pi\) | |||||||
\(972\) | −0.618034 | −0.0198234 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −23.7984 | −0.762549 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 58.2492 | 1.86451 | ||||||||
\(977\) | −7.58359 | −0.242621 | −0.121310 | − | 0.992615i | \(-0.538710\pi\) | ||||
−0.121310 | + | 0.992615i | \(0.538710\pi\) | |||||||
\(978\) | 19.4164 | 0.620868 | ||||||||
\(979\) | 3.41641 | 0.109189 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.4164 | 0.524136 | ||||||||
\(982\) | −7.79837 | −0.248856 | ||||||||
\(983\) | 23.0557 | 0.735364 | 0.367682 | − | 0.929952i | \(-0.380152\pi\) | ||||
0.367682 | + | 0.929952i | \(0.380152\pi\) | |||||||
\(984\) | 20.0000 | 0.637577 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −12.0000 | −0.382158 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.88854 | 0.314596 | ||||||||
\(989\) | 19.9443 | 0.634191 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.5410 | −1.82785 | −0.913925 | − | 0.405882i | \(-0.866964\pi\) | ||||
−0.913925 | + | 0.405882i | \(0.866964\pi\) | |||||||
\(992\) | −13.5279 | −0.429510 | ||||||||
\(993\) | 33.1803 | 1.05295 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −10.4721 | −0.331822 | ||||||||
\(997\) | 7.41641 | 0.234880 | 0.117440 | − | 0.993080i | \(-0.462531\pi\) | ||||
0.117440 | + | 0.993080i | \(0.462531\pi\) | |||||||
\(998\) | 19.4164 | 0.614616 | ||||||||
\(999\) | −3.47214 | −0.109854 |
(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 | 3675.2.a.u.1.1 | ✓ | 2 | |
5.4 | even | 2 | 3675.2.a.bc.1.2 | yes | 2 | ||
7.6 | odd | 2 | 3675.2.a.v.1.1 | yes | 2 | ||
35.34 | odd | 2 | 3675.2.a.ba.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3675.2.a.u.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3675.2.a.v.1.1 | yes | 2 | 7.6 | odd | 2 | ||
3675.2.a.ba.1.2 | yes | 2 | 35.34 | odd | 2 | ||
3675.2.a.bc.1.2 | yes | 2 | 5.4 | even | 2 |