Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6040,2,Mod(1,6040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6040, 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("6040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6040 = 2^{3} \cdot 5 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6040.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: | \(48.2296428209\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 11x^{7} + 9x^{6} + 32x^{5} - 17x^{4} - 27x^{3} + 10x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.10984\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6040.1 |
$q$-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 | ||||||||
\(3\) | −1.57672 | −0.910320 | −0.455160 | − | 0.890410i | \(-0.650418\pi\) | ||||
−0.455160 | + | 0.890410i | \(0.650418\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.208807 | −0.0789215 | −0.0394608 | − | 0.999221i | \(-0.512564\pi\) | ||||
−0.0394608 | + | 0.999221i | \(0.512564\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.513952 | −0.171317 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.616299 | −0.185821 | −0.0929106 | − | 0.995674i | \(-0.529617\pi\) | ||||
−0.0929106 | + | 0.995674i | \(0.529617\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.24227 | −0.899244 | −0.449622 | − | 0.893219i | \(-0.648441\pi\) | ||||
−0.449622 | + | 0.893219i | \(0.648441\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.57672 | −0.407107 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.94776 | 0.472401 | 0.236201 | − | 0.971704i | \(-0.424098\pi\) | ||||
0.236201 | + | 0.971704i | \(0.424098\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.81681 | 0.416805 | 0.208402 | − | 0.978043i | \(-0.433174\pi\) | ||||
0.208402 | + | 0.978043i | \(0.433174\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.329230 | 0.0718438 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.42747 | −0.297647 | −0.148824 | − | 0.988864i | \(-0.547549\pi\) | ||||
−0.148824 | + | 0.988864i | \(0.547549\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.54052 | 1.06627 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.26518 | −0.792023 | −0.396012 | − | 0.918245i | \(-0.629606\pi\) | ||||
−0.396012 | + | 0.918245i | \(0.629606\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.21450 | 1.11616 | 0.558079 | − | 0.829788i | \(-0.311539\pi\) | ||||
0.558079 | + | 0.829788i | \(0.311539\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.971732 | 0.169157 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.208807 | −0.0352948 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.31510 | 0.709397 | 0.354699 | − | 0.934981i | \(-0.384583\pi\) | ||||
0.354699 | + | 0.934981i | \(0.384583\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.11215 | 0.818600 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.53452 | 0.239652 | 0.119826 | − | 0.992795i | \(-0.461766\pi\) | ||||
0.119826 | + | 0.992795i | \(0.461766\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.84534 | −0.281412 | −0.140706 | − | 0.990051i | \(-0.544937\pi\) | ||||
−0.140706 | + | 0.990051i | \(0.544937\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.513952 | −0.0766155 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.09784 | −0.597732 | −0.298866 | − | 0.954295i | \(-0.596608\pi\) | ||||
−0.298866 | + | 0.954295i | \(0.596608\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.95640 | −0.993771 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.07107 | −0.430036 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.8297 | 1.48757 | 0.743785 | − | 0.668419i | \(-0.233029\pi\) | ||||
0.743785 | + | 0.668419i | \(0.233029\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.616299 | −0.0831018 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.86460 | −0.379426 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.06057 | 1.04940 | 0.524699 | − | 0.851288i | \(-0.324178\pi\) | ||||
0.524699 | + | 0.851288i | \(0.324178\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.1832 | −1.43187 | −0.715933 | − | 0.698169i | \(-0.753998\pi\) | ||||
−0.715933 | + | 0.698169i | \(0.753998\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.107317 | 0.0135206 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.24227 | −0.402154 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.24700 | 0.641023 | 0.320511 | − | 0.947245i | \(-0.396145\pi\) | ||||
0.320511 | + | 0.947245i | \(0.396145\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.25071 | 0.270954 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.10268 | 0.961611 | 0.480805 | − | 0.876827i | \(-0.340344\pi\) | ||||
0.480805 | + | 0.876827i | \(0.340344\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.11838 | −0.130896 | −0.0654480 | − | 0.997856i | \(-0.520848\pi\) | ||||
−0.0654480 | + | 0.997856i | \(0.520848\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.57672 | −0.182064 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.128687 | 0.0146653 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.47039 | −0.840484 | −0.420242 | − | 0.907412i | \(-0.638055\pi\) | ||||
−0.420242 | + | 0.907412i | \(0.638055\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.19400 | −0.799333 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.6712 | −1.50061 | −0.750305 | − | 0.661092i | \(-0.770093\pi\) | ||||
−0.750305 | + | 0.661092i | \(0.770093\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.94776 | 0.211264 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.72499 | 0.720995 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.1975 | −1.39893 | −0.699467 | − | 0.714665i | \(-0.746579\pi\) | ||||
−0.699467 | + | 0.714665i | \(0.746579\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.677008 | 0.0709697 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.79853 | −1.01606 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.81681 | 0.186401 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.40168 | 0.954596 | 0.477298 | − | 0.878741i | \(-0.341616\pi\) | ||||
0.477298 | + | 0.878741i | \(0.341616\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.316748 | 0.0318344 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.2614 | −1.31956 | −0.659781 | − | 0.751458i | \(-0.729351\pi\) | ||||
−0.659781 | + | 0.751458i | \(0.729351\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.44604 | 0.142483 | 0.0712415 | − | 0.997459i | \(-0.477304\pi\) | ||||
0.0712415 | + | 0.997459i | \(0.477304\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.329230 | 0.0321295 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.7757 | 1.04173 | 0.520865 | − | 0.853639i | \(-0.325610\pi\) | ||||
0.520865 | + | 0.853639i | \(0.325610\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.75641 | 0.551364 | 0.275682 | − | 0.961249i | \(-0.411096\pi\) | ||||
0.275682 | + | 0.961249i | \(0.411096\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.80370 | −0.645779 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.46809 | −0.514394 | −0.257197 | − | 0.966359i | \(-0.582799\pi\) | ||||
−0.257197 | + | 0.966359i | \(0.582799\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.42747 | −0.133112 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.66637 | 0.154056 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.406705 | −0.0372826 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6202 | −0.965470 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.41951 | −0.218160 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.43210 | −0.659492 | −0.329746 | − | 0.944070i | \(-0.606963\pi\) | ||||
−0.329746 | + | 0.944070i | \(0.606963\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.90958 | 0.256175 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.40484 | 0.646964 | 0.323482 | − | 0.946234i | \(-0.395146\pi\) | ||||
0.323482 | + | 0.946234i | \(0.395146\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.379362 | −0.0328949 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.54052 | 0.476852 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.9623 | −1.53462 | −0.767312 | − | 0.641273i | \(-0.778406\pi\) | ||||
−0.767312 | + | 0.641273i | \(0.778406\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.74094 | −0.232483 | −0.116242 | − | 0.993221i | \(-0.537085\pi\) | ||||
−0.116242 | + | 0.993221i | \(0.537085\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.46115 | 0.544127 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.99821 | 0.167099 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.26518 | −0.354204 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.9683 | 0.904650 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.6431 | −1.44538 | −0.722689 | − | 0.691174i | \(-0.757094\pi\) | ||||
−0.722689 | + | 0.691174i | \(0.757094\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.00000 | −0.0813788 | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.00106 | −0.0809305 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.21450 | 0.499161 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.25706 | −0.259942 | −0.129971 | − | 0.991518i | \(-0.541488\pi\) | ||||
−0.129971 | + | 0.991518i | \(0.541488\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −17.0754 | −1.35416 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.298064 | 0.0234908 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.69472 | −0.602697 | −0.301348 | − | 0.953514i | \(-0.597437\pi\) | ||||
−0.301348 | + | 0.953514i | \(0.597437\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.971732 | 0.0756492 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.9172 | 1.61862 | 0.809311 | − | 0.587381i | \(-0.199841\pi\) | ||||
0.809311 | + | 0.587381i | \(0.199841\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.48769 | −0.191361 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.933754 | −0.0714060 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.4578 | −1.09921 | −0.549605 | − | 0.835425i | \(-0.685222\pi\) | ||||
−0.549605 | + | 0.835425i | \(0.685222\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.208807 | −0.0157843 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.7093 | −0.955287 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.11436 | −0.606496 | −0.303248 | − | 0.952912i | \(-0.598071\pi\) | ||||
−0.303248 | + | 0.952912i | \(0.598071\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.6472 | 1.68335 | 0.841676 | − | 0.539983i | \(-0.181569\pi\) | ||||
0.841676 | + | 0.539983i | \(0.181569\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17.6328 | 1.30346 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.31510 | 0.317252 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.20040 | −0.0877822 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.15690 | −0.0841519 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.36141 | 0.243223 | 0.121611 | − | 0.992578i | \(-0.461194\pi\) | ||||
0.121611 | + | 0.992578i | \(0.461194\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.99457 | 0.287535 | 0.143768 | − | 0.989611i | \(-0.454078\pi\) | ||||
0.143768 | + | 0.989611i | \(0.454078\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.11215 | 0.366089 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.4145 | 1.09823 | 0.549117 | − | 0.835745i | \(-0.314964\pi\) | ||||
0.549117 | + | 0.835745i | \(0.314964\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.61808 | 0.327367 | 0.163683 | − | 0.986513i | \(-0.447662\pi\) | ||||
0.163683 | + | 0.986513i | \(0.447662\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.27305 | −0.583536 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.890597 | 0.0625077 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.53452 | 0.107175 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.733649 | 0.0509921 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.11970 | −0.0774512 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.713130 | −0.0490939 | −0.0245470 | − | 0.999699i | \(-0.507814\pi\) | ||||
−0.0245470 | + | 0.999699i | \(0.507814\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.7757 | −0.875374 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.84534 | −0.125851 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.29763 | −0.0880888 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.76337 | 0.119157 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.31516 | −0.424804 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.64969 | 0.244401 | 0.122201 | − | 0.992505i | \(-0.461005\pi\) | ||||
0.122201 | + | 0.992505i | \(0.461005\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.513952 | −0.0342635 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.20840 | 0.345694 | 0.172847 | − | 0.984949i | \(-0.444703\pi\) | ||||
0.172847 | + | 0.984949i | \(0.444703\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.13516 | 0.339341 | 0.169670 | − | 0.985501i | \(-0.445730\pi\) | ||||
0.169670 | + | 0.985501i | \(0.445730\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.202904 | −0.0133501 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.78606 | 0.182521 | 0.0912605 | − | 0.995827i | \(-0.470910\pi\) | ||||
0.0912605 | + | 0.995827i | \(0.470910\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.09784 | −0.267314 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.7787 | 0.765110 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.6225 | −0.881167 | −0.440584 | − | 0.897712i | \(-0.645229\pi\) | ||||
−0.440584 | + | 0.897712i | \(0.645229\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.6786 | −1.84735 | −0.923677 | − | 0.383173i | \(-0.874831\pi\) | ||||
−0.923677 | + | 0.383173i | \(0.874831\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.27864 | −0.338625 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.95640 | −0.444428 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.89059 | −0.374809 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21.5557 | 1.36604 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.32430 | −0.399186 | −0.199593 | − | 0.979879i | \(-0.563962\pi\) | ||||
−0.199593 | + | 0.979879i | \(0.563962\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.879746 | 0.0553092 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.07107 | −0.192318 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.1344 | −1.38071 | −0.690354 | − | 0.723472i | \(-0.742545\pi\) | ||||
−0.690354 | + | 0.723472i | \(0.742545\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.901021 | −0.0559867 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.19210 | 0.135687 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.72503 | −0.599671 | −0.299836 | − | 0.953991i | \(-0.596932\pi\) | ||||
−0.299836 | + | 0.953991i | \(0.596932\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.8297 | 0.665261 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.8088 | 1.27348 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.848837 | −0.0517545 | −0.0258773 | − | 0.999665i | \(-0.508238\pi\) | ||||
−0.0258773 | + | 0.999665i | \(0.508238\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.31253 | −0.201222 | −0.100611 | − | 0.994926i | \(-0.532080\pi\) | ||||
−0.100611 | + | 0.994926i | \(0.532080\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.06745 | −0.0646051 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.616299 | −0.0371643 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.1085 | −1.26829 | −0.634144 | − | 0.773215i | \(-0.718647\pi\) | ||||
−0.634144 | + | 0.773215i | \(0.718647\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.19396 | −0.191217 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.31579 | −0.376768 | −0.188384 | − | 0.982095i | \(-0.560325\pi\) | ||||
−0.188384 | + | 0.982095i | \(0.560325\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.7968 | 0.820134 | 0.410067 | − | 0.912055i | \(-0.365505\pi\) | ||||
0.410067 | + | 0.912055i | \(0.365505\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.86460 | −0.169684 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.320418 | −0.0189137 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.2062 | −0.776837 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.8238 | −0.868988 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.0503915 | −0.00294390 | −0.00147195 | − | 0.999999i | \(-0.500469\pi\) | ||||
−0.00147195 | + | 0.999999i | \(0.500469\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.06057 | 0.469305 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.41462 | −0.198136 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.62823 | 0.267657 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.385319 | 0.0222094 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.9096 | 1.20122 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.1832 | −0.640350 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.5064 | −1.68402 | −0.842008 | − | 0.539464i | \(-0.818627\pi\) | ||||
−0.842008 | + | 0.539464i | \(0.818627\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.28001 | −0.129705 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.6955 | −0.890012 | −0.445006 | − | 0.895528i | \(-0.646798\pi\) | ||||
−0.445006 | + | 0.895528i | \(0.646798\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.2491 | 1.08803 | 0.544013 | − | 0.839077i | \(-0.316904\pi\) | ||||
0.544013 | + | 0.839077i | \(0.316904\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.107317 | 0.00604661 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.23495 | −0.462521 | −0.231260 | − | 0.972892i | \(-0.574285\pi\) | ||||
−0.231260 | + | 0.972892i | \(0.574285\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.62863 | 0.147175 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.9903 | −0.948307 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.53871 | 0.196899 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.24227 | −0.179849 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.07625 | −0.501918 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.855657 | 0.0471739 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.87968 | 0.488072 | 0.244036 | − | 0.969766i | \(-0.421529\pi\) | ||||
0.244036 | + | 0.969766i | \(0.421529\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.21775 | −0.121532 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.24700 | 0.286674 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.6349 | 0.906159 | 0.453080 | − | 0.891470i | \(-0.350325\pi\) | ||||
0.453080 | + | 0.891470i | \(0.350325\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.62165 | 0.468264 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.82999 | −0.207406 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.91419 | 0.157351 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.25071 | 0.121174 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.2974 | 1.30435 | 0.652176 | − | 0.758068i | \(-0.273856\pi\) | ||||
0.652176 | + | 0.758068i | \(0.273856\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.5363 | −0.671051 | −0.335525 | − | 0.942031i | \(-0.608914\pi\) | ||||
−0.335525 | + | 0.942031i | \(0.608914\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.9639 | −0.958840 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.4445 | −0.981703 | −0.490852 | − | 0.871243i | \(-0.663314\pi\) | ||||
−0.490852 | + | 0.871243i | \(0.663314\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.10268 | 0.430045 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.641260 | 0.0339391 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.0751 | 0.637300 | 0.318650 | − | 0.947873i | \(-0.396771\pi\) | ||||
0.318650 | + | 0.947873i | \(0.396771\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6992 | −0.826274 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.7450 | 0.878887 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.11838 | −0.0585385 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.7726 | −0.614523 | −0.307262 | − | 0.951625i | \(-0.599413\pi\) | ||||
−0.307262 | + | 0.951625i | \(0.599413\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.788669 | −0.0410565 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.26131 | −0.117401 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.70761 | −0.0884168 | −0.0442084 | − | 0.999022i | \(-0.514077\pi\) | ||||
−0.0442084 | + | 0.999022i | \(0.514077\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.57672 | −0.0814215 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.8289 | 0.712222 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.29129 | 0.374528 | 0.187264 | − | 0.982310i | \(-0.440038\pi\) | ||||
0.187264 | + | 0.982310i | \(0.440038\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.7183 | 0.600349 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.6210 | 0.696002 | 0.348001 | − | 0.937494i | \(-0.386861\pi\) | ||||
0.348001 | + | 0.937494i | \(0.386861\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.128687 | 0.00655852 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.948416 | 0.0482107 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.8664 | −1.15937 | −0.579685 | − | 0.814841i | \(-0.696824\pi\) | ||||
−0.579685 | + | 0.814841i | \(0.696824\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.78036 | −0.140609 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.6754 | −0.588944 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.47039 | −0.375876 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.92578 | −0.197029 | −0.0985146 | − | 0.995136i | \(-0.531409\pi\) | ||||
−0.0985146 | + | 0.995136i | \(0.531409\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.598148 | 0.0299449 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.5785 | 1.17745 | 0.588727 | − | 0.808332i | \(-0.299629\pi\) | ||||
0.588727 | + | 0.808332i | \(0.299629\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.1491 | −1.00370 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.19400 | −0.357473 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.65939 | −0.131821 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.4830 | −1.55673 | −0.778367 | − | 0.627810i | \(-0.783952\pi\) | ||||
−0.778367 | + | 0.627810i | \(0.783952\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.3216 | 1.39700 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.68310 | −0.0828200 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.6712 | −0.671093 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.32169 | 0.211634 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.50972 | 0.220314 | 0.110157 | − | 0.993914i | \(-0.464865\pi\) | ||||
0.110157 | + | 0.993914i | \(0.464865\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.7864 | −1.35423 | −0.677113 | − | 0.735879i | \(-0.736769\pi\) | ||||
−0.677113 | + | 0.735879i | \(0.736769\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.10609 | 0.102402 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.94776 | 0.0944802 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.33513 | 0.113005 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.15062 | −0.152113 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.0231 | −1.30166 | −0.650829 | − | 0.759225i | \(-0.725578\pi\) | ||||
−0.650829 | + | 0.759225i | \(0.725578\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.9410 | −1.48693 | −0.743464 | − | 0.668775i | \(-0.766819\pi\) | ||||
−0.743464 | + | 0.668775i | \(0.766819\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.72499 | 0.322439 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.59343 | −0.124061 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.2431 | −1.72979 | −0.864895 | − | 0.501952i | \(-0.832615\pi\) | ||||
−0.864895 | + | 0.501952i | \(0.832615\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.57526 | 0.170250 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.3711 | −1.20542 | −0.602709 | − | 0.797961i | \(-0.705912\pi\) | ||||
−0.602709 | + | 0.797961i | \(0.705912\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.1975 | −0.625622 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 27.8182 | 1.31576 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.9558 | 0.894580 | 0.447290 | − | 0.894389i | \(-0.352389\pi\) | ||||
0.447290 | + | 0.894389i | \(0.352389\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.945723 | −0.0445323 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.57672 | 0.0740808 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.677008 | 0.0317386 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.2217 | −0.665265 | −0.332632 | − | 0.943057i | \(-0.607937\pi\) | ||||
−0.332632 | + | 0.943057i | \(0.607937\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.7916 | 0.503709 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.0031 | −1.11794 | −0.558969 | − | 0.829189i | \(-0.688803\pi\) | ||||
−0.558969 | + | 0.829189i | \(0.688803\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.8075 | −0.548743 | −0.274372 | − | 0.961624i | \(-0.588470\pi\) | ||||
−0.274372 | + | 0.961624i | \(0.588470\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.79853 | −0.454396 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.03966 | −0.186933 | −0.0934667 | − | 0.995622i | \(-0.529795\pi\) | ||||
−0.0934667 | + | 0.995622i | \(0.529795\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.09561 | −0.0505905 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.13547 | 0.236630 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.13728 | 0.0522923 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.81681 | 0.0833610 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.56593 | −0.254847 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.1312 | −1.10258 | −0.551291 | − | 0.834313i | \(-0.685864\pi\) | ||||
−0.551291 | + | 0.834313i | \(0.685864\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.9907 | −0.637921 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.469964 | −0.0213841 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.40168 | 0.426908 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.0591 | 0.818334 | 0.409167 | − | 0.912460i | \(-0.365819\pi\) | ||||
0.409167 | + | 0.912460i | \(0.365819\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.1324 | 0.548647 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.3288 | −0.872295 | −0.436148 | − | 0.899875i | \(-0.643657\pi\) | ||||
−0.436148 | + | 0.899875i | \(0.643657\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.30754 | −0.374153 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.316748 | 0.0142368 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.69189 | −0.0758918 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.06467 | 0.226726 | 0.113363 | − | 0.993554i | \(-0.463838\pi\) | ||||
0.113363 | + | 0.993554i | \(0.463838\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −32.9806 | −1.47346 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.2555 | −1.25985 | −0.629925 | − | 0.776656i | \(-0.716915\pi\) | ||||
−0.629925 | + | 0.776656i | \(0.716915\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.2614 | −0.590126 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.92239 | 0.174199 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.2474 | 1.38502 | 0.692508 | − | 0.721410i | \(-0.256506\pi\) | ||||
0.692508 | + | 0.721410i | \(0.256506\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.233524 | 0.0103305 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.0661 | 0.444428 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.44604 | 0.0637203 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.52550 | 0.111071 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.7960 | 1.00063 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.0452 | 0.702954 | 0.351477 | − | 0.936196i | \(-0.385679\pi\) | ||||
0.351477 | + | 0.936196i | \(0.385679\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.44740 | −0.150744 | −0.0753722 | − | 0.997155i | \(-0.524015\pi\) | ||||
−0.0753722 | + | 0.997155i | \(0.524015\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.329230 | 0.0143688 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.1044 | 0.527274 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.9623 | −0.911406 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.14275 | −0.179780 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.97532 | −0.215505 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.7757 | 0.465876 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.7941 | 0.552106 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.28723 | 0.184664 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.3423 | −0.917578 | −0.458789 | − | 0.888545i | \(-0.651717\pi\) | ||||
−0.458789 | + | 0.888545i | \(0.651717\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −35.7083 | −1.53239 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.75641 | 0.246578 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.9664 | 1.36679 | 0.683393 | − | 0.730050i | \(-0.260503\pi\) | ||||
0.683393 | + | 0.730050i | \(0.260503\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.74764 | 0.245303 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.74902 | −0.330119 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.55987 | 0.0663323 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.80370 | −0.288801 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.5091 | 1.25034 | 0.625171 | − | 0.780488i | \(-0.285029\pi\) | ||||
0.625171 | + | 0.780488i | \(0.285029\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.98309 | 0.253058 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.89270 | 0.0799099 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −47.0845 | −1.98438 | −0.992188 | − | 0.124748i | \(-0.960188\pi\) | ||||
−0.992188 | + | 0.124748i | \(0.960188\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.46809 | −0.230044 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.50215 | 0.0630846 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.8848 | −0.540158 | −0.270079 | − | 0.962838i | \(-0.587050\pi\) | ||||
−0.270079 | + | 0.962838i | \(0.587050\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.7747 | −1.70637 | −0.853183 | − | 0.521611i | \(-0.825331\pi\) | ||||
−0.853183 | + | 0.521611i | \(0.825331\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.30000 | −0.221411 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.42747 | −0.0595294 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.8273 | 1.86618 | 0.933091 | − | 0.359639i | \(-0.117100\pi\) | ||||
0.933091 | + | 0.359639i | \(0.117100\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.29832 | −0.261749 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.85464 | 0.118430 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.67432 | −0.276422 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.66637 | 0.0688960 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.2724 | 0.795455 | 0.397728 | − | 0.917504i | \(-0.369799\pi\) | ||||
0.397728 | + | 0.917504i | \(0.369799\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.2906 | 0.465220 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.3043 | −0.999745 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.6610 | 0.602055 | 0.301027 | − | 0.953616i | \(-0.402670\pi\) | ||||
0.301027 | + | 0.953616i | \(0.402670\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.406705 | −0.0166733 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.28142 | −0.298009 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0961 | 0.494232 | 0.247116 | − | 0.968986i | \(-0.420517\pi\) | ||||
0.247116 | + | 0.968986i | \(0.420517\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.0154 | 0.490117 | 0.245059 | − | 0.969508i | \(-0.421193\pi\) | ||||
0.245059 | + | 0.969508i | \(0.421193\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.69671 | −0.109818 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.6202 | −0.431772 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.7414 | −0.923047 | −0.461523 | − | 0.887128i | \(-0.652697\pi\) | ||||
−0.461523 | + | 0.887128i | \(0.652697\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.40422 | −0.0569020 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.2863 | 0.537506 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.0718 | 0.689522 | 0.344761 | − | 0.938690i | \(-0.387960\pi\) | ||||
0.344761 | + | 0.938690i | \(0.387960\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.41951 | −0.0975639 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.6057 | −1.39317 | −0.696587 | − | 0.717473i | \(-0.745299\pi\) | ||||
−0.696587 | + | 0.717473i | \(0.745299\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.1899 | −1.21344 | −0.606718 | − | 0.794917i | \(-0.707514\pi\) | ||||
−0.606718 | + | 0.794917i | \(0.707514\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.90890 | −0.317373 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.75573 | 0.110406 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.76545 | 0.0705054 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.40477 | 0.335120 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.2735 | −1.76250 | −0.881251 | − | 0.472649i | \(-0.843298\pi\) | ||||
−0.881251 | + | 0.472649i | \(0.843298\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.12441 | 0.0446912 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.43210 | −0.294934 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.5545 | 0.893643 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.16439 | −0.164741 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.3085 | 1.27611 | 0.638055 | − | 0.769991i | \(-0.279739\pi\) | ||||
0.638055 | + | 0.769991i | \(0.279739\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.498956 | −0.0196769 | −0.00983845 | − | 0.999952i | \(-0.503132\pi\) | ||||
−0.00983845 | + | 0.999952i | \(0.503132\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.90958 | 0.114565 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.2668 | 1.54374 | 0.771869 | − | 0.635781i | \(-0.219322\pi\) | ||||
0.771869 | + | 0.635781i | \(0.219322\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.96773 | −0.195000 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.04600 | 0.0801890 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.0748 | 0.902987 | 0.451493 | − | 0.892274i | \(-0.350891\pi\) | ||||
0.451493 | + | 0.892274i | \(0.350891\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.40484 | 0.289331 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.574792 | 0.0224248 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.2100 | 1.41054 | 0.705271 | − | 0.708938i | \(-0.250825\pi\) | ||||
0.705271 | + | 0.708938i | \(0.250825\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.4735 | 1.53534 | 0.767670 | − | 0.640846i | \(-0.221416\pi\) | ||||
0.767670 | + | 0.640846i | \(0.221416\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.95725 | 0.386707 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.379362 | −0.0147110 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.08839 | 0.235743 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.75454 | −0.222483 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.89222 | 0.266071 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.5574 | 0.522598 | 0.261299 | − | 0.965258i | \(-0.415849\pi\) | ||||
0.261299 | + | 0.965258i | \(0.415849\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.54052 | 0.213255 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.1325 | −1.58085 | −0.790426 | − | 0.612558i | \(-0.790141\pi\) | ||||
−0.790426 | + | 0.612558i | \(0.790141\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.96313 | −0.0753382 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.21219 | −0.314692 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.1400 | 0.732371 | 0.366186 | − | 0.930542i | \(-0.380664\pi\) | ||||
0.366186 | + | 0.930542i | \(0.380664\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.9623 | −0.686305 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.09671 | −0.308909 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −35.1127 | −1.33769 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.34560 | 0.279440 | 0.139720 | − | 0.990191i | \(-0.455380\pi\) | ||||
0.139720 | + | 0.990191i | \(0.455380\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.0661392 | −0.00251242 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.74094 | −0.103970 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.98887 | 0.113212 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.39284 | −0.166153 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.2689 | −1.02993 | −0.514966 | − | 0.857210i | \(-0.672196\pi\) | ||||
−0.514966 | + | 0.857210i | \(0.672196\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.83971 | 0.295680 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.46115 | 0.243341 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.76908 | 0.104142 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.89231 | 0.333958 | 0.166979 | − | 0.985960i | \(-0.446599\pi\) | ||||
0.166979 | + | 0.985960i | \(0.446599\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.83942 | 0.143990 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.87098 | −0.332221 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.99821 | 0.0747288 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.4789 | 0.802144 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.7533 | −0.811260 | −0.405630 | − | 0.914037i | \(-0.632948\pi\) | ||||
−0.405630 | + | 0.914037i | \(0.632948\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.301944 | −0.0112450 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 45.2182 | 1.68168 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.26518 | −0.158405 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.99766 | 0.370793 | 0.185396 | − | 0.982664i | \(-0.440643\pi\) | ||||
0.185396 | + | 0.982664i | \(0.440643\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9049 | 1.10759 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.59428 | −0.132939 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.6425 | 0.984061 | 0.492031 | − | 0.870578i | \(-0.336255\pi\) | ||||
0.492031 | + | 0.870578i | \(0.336255\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.9683 | 0.404572 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.23372 | −0.119116 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.9446 | 1.76367 | 0.881835 | − | 0.471558i | \(-0.156308\pi\) | ||||
0.881835 | + | 0.471558i | \(0.156308\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.28782 | 0.341196 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.8792 | −0.765983 | −0.382992 | − | 0.923752i | \(-0.625106\pi\) | ||||
−0.382992 | + | 0.923752i | \(0.625106\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.6431 | −0.646392 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.02635 | 0.257081 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.25004 | −0.0822148 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.44860 | 0.125841 | 0.0629207 | − | 0.998019i | \(-0.479958\pi\) | ||||
0.0629207 | + | 0.998019i | \(0.479958\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.97166 | 0.363387 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.00000 | −0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.99315 | 0.108788 | 0.0543940 | − | 0.998520i | \(-0.482677\pi\) | ||||
0.0543940 | + | 0.998520i | \(0.482677\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.38711 | −0.0503490 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.5750 | −0.890844 | −0.445422 | − | 0.895321i | \(-0.646946\pi\) | ||||
−0.445422 | + | 0.895321i | \(0.646946\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.20198 | −0.0435145 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.00106 | −0.0361932 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.1345 | −0.943664 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.2537 | −1.34340 | −0.671702 | − | 0.740822i | \(-0.734436\pi\) | ||||
−0.671702 | + | 0.740822i | \(0.734436\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 34.8998 | 1.25689 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.3887 | 0.769299 | 0.384649 | − | 0.923063i | \(-0.374322\pi\) | ||||
0.384649 | + | 0.923063i | \(0.374322\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.21450 | 0.223231 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.42066 | 0.0509658 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.78793 | 0.0998879 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.99368 | −0.178688 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −23.6313 | −0.844514 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.25706 | −0.116249 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.1181 | 1.07359 | 0.536797 | − | 0.843711i | \(-0.319634\pi\) | ||||
0.536797 | + | 0.843711i | \(0.319634\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.3337 | 0.545893 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.14177 | 0.0405968 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.2590 | 1.28760 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −17.0754 | −0.605601 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.1673 | −0.608099 | −0.304049 | − | 0.952656i | \(-0.598339\pi\) | ||||
−0.304049 | + | 0.952656i | \(0.598339\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.98161 | −0.282369 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.78289 | 0.239662 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.689255 | 0.0243233 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.298064 | 0.0105054 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.33838 | 0.0471132 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.1584 | −0.497784 | −0.248892 | − | 0.968531i | \(-0.580066\pi\) | ||||
−0.248892 | + | 0.968531i | \(0.580066\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.0139 | 0.737897 | 0.368948 | − | 0.929450i | \(-0.379718\pi\) | ||||
0.368948 | + | 0.929450i | \(0.379718\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.22294 | 0.183176 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.69472 | −0.269534 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.35263 | −0.117294 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.347950 | −0.0121583 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.3762 | −1.19974 | −0.599869 | − | 0.800098i | \(-0.704781\pi\) | ||||
−0.599869 | + | 0.800098i | \(0.704781\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.5373 | 0.994749 | 0.497375 | − | 0.867536i | \(-0.334297\pi\) | ||||
0.497375 | + | 0.867536i | \(0.334297\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.971732 | 0.0338314 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.2311 | −1.08601 | −0.543005 | − | 0.839729i | \(-0.682714\pi\) | ||||
−0.543005 | + | 0.839729i | \(0.682714\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.1885 | 0.458056 | 0.229028 | − | 0.973420i | \(-0.426445\pi\) | ||||
0.229028 | + | 0.973420i | \(0.426445\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.2822 | 1.15455 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.5494 | −0.469459 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.9172 | 0.723870 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34.4316 | 1.19013 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.03792 | 0.242976 | 0.121488 | − | 0.992593i | \(-0.461233\pi\) | ||||
0.121488 | + | 0.992593i | \(0.461233\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.8083 | −0.372699 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.95823 | 0.342980 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.48769 | −0.0855791 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.21756 | 0.0761964 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.7537 | −0.746584 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.15965 | −0.211150 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.21589 | 0.0758705 | 0.0379353 | − | 0.999280i | \(-0.487922\pi\) | ||||
0.0379353 | + | 0.999280i | \(0.487922\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.933754 | −0.0319337 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.678188 | −0.0231665 | −0.0115832 | − | 0.999933i | \(-0.503687\pi\) | ||||
−0.0115832 | + | 0.999933i | \(0.503687\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.2532 | 0.418073 | 0.209036 | − | 0.977908i | \(-0.432967\pi\) | ||||
0.209036 | + | 0.977908i | \(0.432967\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.505209 | 0.0172175 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.7632 | −1.59184 | −0.795920 | − | 0.605402i | \(-0.793012\pi\) | ||||
−0.795920 | + | 0.605402i | \(0.793012\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.4578 | −0.491582 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20.8225 | 0.707170 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.60400 | 0.156180 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.0122 | −0.576436 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.83202 | −0.163539 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.208807 | −0.00705895 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.3470 | 0.720838 | 0.360419 | − | 0.932791i | \(-0.382634\pi\) | ||||
0.360419 | + | 0.932791i | \(0.382634\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.0794533 | 0.00267989 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.7670 | −1.37348 | −0.686738 | − | 0.726905i | \(-0.740958\pi\) | ||||
−0.686738 | + | 0.726905i | \(0.740958\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.0744 | 1.14669 | 0.573347 | − | 0.819313i | \(-0.305645\pi\) | ||||
0.573347 | + | 0.819313i | \(0.305645\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.7093 | −0.427217 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.3868 | −1.12102 | −0.560510 | − | 0.828148i | \(-0.689395\pi\) | ||||
−0.560510 | + | 0.828148i | \(0.689395\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.55187 | 0.0520481 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.43366 | 0.148533 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.44500 | −0.249137 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.11436 | −0.271233 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.29742 | −0.243654 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26.5059 | −0.884023 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.0936 | 0.702729 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.607541 | −0.0202177 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.6472 | 0.752818 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.3554 | 1.00794 | 0.503968 | − | 0.863723i | \(-0.331873\pi\) | ||||
0.503968 | + | 0.863723i | \(0.331873\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.81574 | 0.226064 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.3403 | 1.56845 | 0.784227 | − | 0.620474i | \(-0.213060\pi\) | ||||
0.784227 | + | 0.620474i | \(0.213060\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.42556 | 0.278845 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17.6328 | 0.582923 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.54618 | −0.0510594 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.15031 | 0.202880 | 0.101440 | − | 0.994842i | \(-0.467655\pi\) | ||||
0.101440 | + | 0.994842i | \(0.467655\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 46.5233 | 1.53299 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −26.2711 | −0.864723 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.31510 | 0.141879 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.743198 | −0.0244098 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.7758 | 1.17377 | 0.586883 | − | 0.809672i | \(-0.300355\pi\) | ||||
0.586883 | + | 0.809672i | \(0.300355\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.6385 | −0.414209 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.7475 | 0.810196 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.20040 | −0.0392574 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.49148 | 0.212067 | 0.106034 | − | 0.994363i | \(-0.466185\pi\) | ||||
0.106034 | + | 0.994363i | \(0.466185\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.3505 | −0.990452 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48.9031 | 1.59420 | 0.797098 | − | 0.603850i | \(-0.206367\pi\) | ||||
0.797098 | + | 0.603850i | \(0.206367\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.19047 | −0.0713316 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.15690 | −0.0376339 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.8981 | 0.776585 | 0.388292 | − | 0.921536i | \(-0.373065\pi\) | ||||
0.388292 | + | 0.921536i | \(0.373065\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.62608 | 0.117707 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.9842 | 0.421042 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.3409 | −1.43634 | −0.718172 | − | 0.695866i | \(-0.755021\pi\) | ||||
−0.718172 | + | 0.695866i | \(0.755021\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.36141 | 0.108773 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.14461 | −0.133976 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.75065 | 0.121115 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.62001 | 0.245807 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.53821 | −0.178466 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.99457 | 0.128590 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.2516 | 1.39088 | 0.695440 | − | 0.718585i | \(-0.255210\pi\) | ||||
0.695440 | + | 0.718585i | \(0.255210\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.57956 | −0.179241 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.3956 | −1.55309 | −0.776544 | − | 0.630062i | \(-0.783029\pi\) | ||||
−0.776544 | + | 0.630062i | \(0.783029\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.572326 | 0.0183479 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.11215 | 0.163720 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.81703 | −0.154110 | −0.0770552 | − | 0.997027i | \(-0.524552\pi\) | ||||
−0.0770552 | + | 0.997027i | \(0.524552\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.13362 | 0.259952 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.95852 | −0.0944583 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.128226 | −0.00408979 | −0.00204490 | − | 0.999998i | \(-0.500651\pi\) | ||||
−0.00204490 | + | 0.999998i | \(0.500651\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.4145 | 0.491146 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.34913 | −0.0429433 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.63416 | 0.0837614 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.3265 | 0.328033 | 0.164016 | − | 0.986458i | \(-0.447555\pi\) | ||||
0.164016 | + | 0.986458i | \(0.447555\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.0008 | −0.444301 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.61808 | 0.146403 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.1178 | 1.55558 | 0.777789 | − | 0.628526i | \(-0.216341\pi\) | ||||
0.777789 | + | 0.628526i | \(0.216341\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 23.9079 | 0.756412 |
(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 | 6040.2.a.l.1.3 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6040.2.a.l.1.3 | ✓ | 9 | 1.1 | even | 1 | trivial |