Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, 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("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.3979184.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 9x^{3} + 18x^{2} + 5x - 12 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1672) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.915789\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-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 | ||||||||
\(3\) | 2.85680 | 1.64938 | 0.824688 | − | 0.565587i | \(-0.191351\pi\) | ||||
0.824688 | + | 0.565587i | \(0.191351\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.91579 | 0.856767 | 0.428383 | − | 0.903597i | \(-0.359083\pi\) | ||||
0.428383 | + | 0.903597i | \(0.359083\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.08421 | −0.409793 | −0.204897 | − | 0.978784i | \(-0.565686\pi\) | ||||
−0.204897 | + | 0.978784i | \(0.565686\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.16133 | 1.72044 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.31769 | 1.47486 | 0.737431 | − | 0.675422i | \(-0.236038\pi\) | ||||
0.737431 | + | 0.675422i | \(0.236038\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.47303 | 1.41313 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.09738 | −0.675903 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.07712 | 0.641624 | 0.320812 | − | 0.947143i | \(-0.396044\pi\) | ||||
0.320812 | + | 0.947143i | \(0.396044\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.32975 | −0.265950 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 6.17450 | 1.18828 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.29854 | 0.241132 | 0.120566 | − | 0.992705i | \(-0.461529\pi\) | ||||
0.120566 | + | 0.992705i | \(0.461529\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.99189 | −0.896569 | −0.448285 | − | 0.893891i | \(-0.647965\pi\) | ||||
−0.448285 | + | 0.893891i | \(0.647965\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.85680 | 0.497306 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.07712 | −0.351097 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.24554 | −0.533564 | −0.266782 | − | 0.963757i | \(-0.585960\pi\) | ||||
−0.266782 | + | 0.963757i | \(0.585960\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 15.1916 | 2.43260 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.99503 | 0.467746 | 0.233873 | − | 0.972267i | \(-0.424860\pi\) | ||||
0.233873 | + | 0.972267i | \(0.424860\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.87494 | 1.35342 | 0.676708 | − | 0.736252i | \(-0.263406\pi\) | ||||
0.676708 | + | 0.736252i | \(0.263406\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.88802 | 1.47402 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.32266 | −0.922255 | −0.461127 | − | 0.887334i | \(-0.652555\pi\) | ||||
−0.461127 | + | 0.887334i | \(0.652555\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.82449 | −0.832070 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.71361 | 0.800065 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.91579 | 0.258325 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.85680 | −0.378393 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.72669 | −0.485174 | −0.242587 | − | 0.970130i | \(-0.577996\pi\) | ||||
−0.242587 | + | 0.970130i | \(0.577996\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.3731 | −1.84029 | −0.920144 | − | 0.391579i | \(-0.871929\pi\) | ||||
−0.920144 | + | 0.391579i | \(0.871929\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.59597 | −0.705026 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.1876 | 1.26361 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.78576 | −0.706843 | −0.353422 | − | 0.935464i | \(-0.614982\pi\) | ||||
−0.353422 | + | 0.935464i | \(0.614982\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.79073 | 1.05828 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.3102 | −1.46095 | −0.730475 | − | 0.682939i | \(-0.760701\pi\) | ||||
−0.730475 | + | 0.682939i | \(0.760701\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.9461 | 1.51522 | 0.757611 | − | 0.652706i | \(-0.226366\pi\) | ||||
0.757611 | + | 0.652706i | \(0.226366\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.79884 | −0.438653 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.08421 | −0.123557 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.168422 | −0.0189489 | −0.00947447 | − | 0.999955i | \(-0.503016\pi\) | ||||
−0.00947447 | + | 0.999955i | \(0.503016\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.15534 | 0.239482 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.58998 | −0.174523 | −0.0872616 | − | 0.996185i | \(-0.527812\pi\) | ||||
−0.0872616 | + | 0.996185i | \(0.527812\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.83158 | 0.415593 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.70966 | 0.397718 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.32376 | 0.670317 | 0.335159 | − | 0.942162i | \(-0.391210\pi\) | ||||
0.335159 | + | 0.942162i | \(0.391210\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.76550 | −0.604389 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.2608 | −1.47878 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.91579 | −0.196556 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.5305 | 1.47535 | 0.737674 | − | 0.675157i | \(-0.235924\pi\) | ||||
0.737674 | + | 0.675157i | \(0.235924\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.16133 | 0.518733 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.1407 | 1.10854 | 0.554268 | − | 0.832338i | \(-0.312998\pi\) | ||||
0.554268 | + | 0.832338i | \(0.312998\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.18057 | −0.707522 | −0.353761 | − | 0.935336i | \(-0.615097\pi\) | ||||
−0.353761 | + | 0.935336i | \(0.615097\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.93392 | −0.579092 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.49108 | 0.240822 | 0.120411 | − | 0.992724i | \(-0.461579\pi\) | ||||
0.120411 | + | 0.992724i | \(0.461579\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.48115 | 0.429216 | 0.214608 | − | 0.976700i | \(-0.431153\pi\) | ||||
0.214608 | + | 0.976700i | \(0.431153\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.27188 | −0.880048 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.7510 | 1.48173 | 0.740864 | − | 0.671655i | \(-0.234416\pi\) | ||||
0.740864 | + | 0.671655i | \(0.234416\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.89511 | 0.549722 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 27.4464 | 2.53742 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.16842 | −0.198779 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.55622 | 0.771489 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1265 | −1.08462 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.62341 | 0.232790 | 0.116395 | − | 0.993203i | \(-0.462866\pi\) | ||||
0.116395 | + | 0.993203i | \(0.462866\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 25.3540 | 2.23229 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.4987 | 1.00464 | 0.502322 | − | 0.864681i | \(-0.332479\pi\) | ||||
0.502322 | + | 0.864681i | \(0.332479\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.08421 | 0.0940130 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.8290 | 1.01808 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.161330 | 0.0137834 | 0.00689169 | − | 0.999976i | \(-0.497806\pi\) | ||||
0.00689169 | + | 0.999976i | \(0.497806\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.3697 | −1.21882 | −0.609410 | − | 0.792855i | \(-0.708594\pi\) | ||||
−0.609410 | + | 0.792855i | \(0.708594\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.0626 | −1.52115 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.31769 | 0.444688 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.48772 | 0.206594 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.6394 | −1.37240 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.09020 | 0.253159 | 0.126580 | − | 0.991956i | \(-0.459600\pi\) | ||||
0.126580 | + | 0.991956i | \(0.459600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.09020 | 0.251477 | 0.125738 | − | 0.992063i | \(-0.459870\pi\) | ||||
0.125738 | + | 0.992063i | \(0.459870\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.3227 | 0.834538 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.56340 | −0.768151 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.03232 | 0.561241 | 0.280620 | − | 0.959819i | \(-0.409460\pi\) | ||||
0.280620 | + | 0.959819i | \(0.409460\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.71361 | 0.453119 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.33625 | −0.262933 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.36318 | −0.341751 | −0.170875 | − | 0.985293i | \(-0.554660\pi\) | ||||
−0.170875 | + | 0.985293i | \(0.554660\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.47303 | 0.426075 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.75131 | −0.212903 | −0.106451 | − | 0.994318i | \(-0.533949\pi\) | ||||
−0.106451 | + | 0.994318i | \(0.533949\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.2779 | 1.17522 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.16133 | −0.394697 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.20690 | −0.699988 | −0.349994 | − | 0.936752i | \(-0.613816\pi\) | ||||
−0.349994 | + | 0.936752i | \(0.613816\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.44173 | 0.108985 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.6464 | −0.800234 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.18647 | 0.0886810 | 0.0443405 | − | 0.999016i | \(-0.485881\pi\) | ||||
0.0443405 | + | 0.999016i | \(0.485881\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.9593 | −1.85521 | −0.927606 | − | 0.373560i | \(-0.878137\pi\) | ||||
−0.927606 | + | 0.373560i | \(0.878137\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −41.0612 | −3.03533 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.21777 | −0.457140 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.00000 | 0.146254 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.69446 | −0.486950 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.3096 | 0.745975 | 0.372987 | − | 0.927836i | \(-0.378333\pi\) | ||||
0.372987 | + | 0.927836i | \(0.378333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.1125 | 1.87962 | 0.939808 | − | 0.341704i | \(-0.111004\pi\) | ||||
0.939808 | + | 0.341704i | \(0.111004\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 29.1039 | 2.08417 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.0768 | −0.717941 | −0.358971 | − | 0.933349i | \(-0.616872\pi\) | ||||
−0.358971 | + | 0.933349i | \(0.616872\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0002 | −0.708893 | −0.354447 | − | 0.935076i | \(-0.615331\pi\) | ||||
−0.354447 | + | 0.935076i | \(0.615331\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.5288 | −1.16585 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.40789 | −0.0988143 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.73785 | 0.400749 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.8820 | 1.10388 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.10438 | 0.213715 | 0.106857 | − | 0.994274i | \(-0.465921\pi\) | ||||
0.106857 | + | 0.994274i | \(0.465921\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −35.1678 | −2.40966 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.0025 | 1.15956 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.41226 | 0.367408 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 36.9844 | 2.49917 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.6354 | 0.715414 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.4097 | 1.03191 | 0.515955 | − | 0.856615i | \(-0.327437\pi\) | ||||
0.515955 | + | 0.856615i | \(0.327437\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.86329 | −0.457553 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.9183 | −0.923790 | −0.461895 | − | 0.886935i | \(-0.652830\pi\) | ||||
−0.461895 | + | 0.886935i | \(0.652830\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.4742 | −1.22081 | −0.610406 | − | 0.792089i | \(-0.708994\pi\) | ||||
−0.610406 | + | 0.792089i | \(0.708994\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.09738 | −0.203793 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.7221 | 1.88165 | 0.940824 | − | 0.338896i | \(-0.110053\pi\) | ||||
0.940824 | + | 0.338896i | \(0.110053\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.1129 | −0.790157 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.481148 | −0.0312540 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.9274 | −1.22431 | −0.612157 | − | 0.790736i | \(-0.709698\pi\) | ||||
−0.612157 | + | 0.790736i | \(0.709698\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.5821 | −1.51905 | −0.759527 | − | 0.650476i | \(-0.774570\pi\) | ||||
−0.759527 | + | 0.650476i | \(0.774570\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.3661 | −0.793286 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.1585 | −0.712890 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.31769 | −0.338357 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.54226 | −0.287854 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.7745 | −0.932558 | −0.466279 | − | 0.884638i | \(-0.654406\pi\) | ||||
−0.466279 | + | 0.884638i | \(0.654406\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.07712 | 0.193457 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.9461 | 0.685469 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.53160 | −0.532187 | −0.266093 | − | 0.963947i | \(-0.585733\pi\) | ||||
−0.266093 | + | 0.963947i | \(0.585733\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.51885 | 0.218651 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.70217 | 0.414854 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.8573 | −1.47110 | −0.735551 | − | 0.677469i | \(-0.763077\pi\) | ||||
−0.735551 | + | 0.677469i | \(0.763077\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.83158 | 0.235372 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.0658 | 1.10561 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.7534 | 0.899528 | 0.449764 | − | 0.893147i | \(-0.351508\pi\) | ||||
0.449764 | + | 0.893147i | \(0.351508\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.61665 | −0.219696 | −0.109848 | − | 0.993948i | \(-0.535036\pi\) | ||||
−0.109848 | + | 0.993948i | \(0.535036\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.4709 | −0.996865 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.32975 | −0.0801871 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.871327 | −0.0523529 | −0.0261765 | − | 0.999657i | \(-0.508333\pi\) | ||||
−0.0261765 | + | 0.999657i | \(0.508333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −25.7648 | −1.54250 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.5658 | −1.52513 | −0.762565 | − | 0.646912i | \(-0.776060\pi\) | ||||
−0.762565 | + | 0.646912i | \(0.776060\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.5513 | 1.28109 | 0.640547 | − | 0.767919i | \(-0.278708\pi\) | ||||
0.640547 | + | 0.767919i | \(0.278708\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.47303 | −0.324195 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.24725 | −0.191679 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 41.5108 | 2.43341 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.07530 | 0.121240 | 0.0606201 | − | 0.998161i | \(-0.480692\pi\) | ||||
0.0606201 | + | 0.998161i | \(0.480692\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.13955 | −0.415681 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.17450 | 0.358281 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.3632 | 0.946307 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.62231 | −0.554620 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 31.8267 | 1.82839 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −27.5359 | −1.57670 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.47971 | −0.541036 | −0.270518 | − | 0.962715i | \(-0.587195\pi\) | ||||
−0.270518 | + | 0.962715i | \(0.587195\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20.5135 | −1.16697 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.49108 | −0.481485 | −0.240743 | − | 0.970589i | \(-0.577391\pi\) | ||||
−0.240743 | + | 0.970589i | \(0.577391\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.21577 | −0.520906 | −0.260453 | − | 0.965487i | \(-0.583872\pi\) | ||||
−0.260453 | + | 0.965487i | \(0.583872\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.7207 | −0.604043 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −28.2279 | −1.58544 | −0.792718 | − | 0.609589i | \(-0.791335\pi\) | ||||
−0.792718 | + | 0.609589i | \(0.791335\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.29854 | 0.0727041 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.11654 | 0.397206 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.00000 | −0.111283 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.07122 | −0.392240 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.8018 | 0.707939 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.85510 | 0.377934 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.72813 | 0.0949867 | 0.0474933 | − | 0.998872i | \(-0.484877\pi\) | ||||
0.0474933 | + | 0.998872i | \(0.484877\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.7513 | −0.917966 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.0843 | −0.605600 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.2502 | 0.721783 | 0.360892 | − | 0.932608i | \(-0.382472\pi\) | ||||
0.360892 | + | 0.932608i | \(0.382472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 44.9975 | 2.44393 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.99189 | −0.270326 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.9044 | 0.750770 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16.8412 | 0.906699 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.88126 | −0.476771 | −0.238386 | − | 0.971171i | \(-0.576618\pi\) | ||||
−0.238386 | + | 0.971171i | \(0.576618\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.0464 | −1.28717 | −0.643586 | − | 0.765373i | \(-0.722554\pi\) | ||||
−0.643586 | + | 0.765373i | \(0.722554\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 32.8341 | 1.75255 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.90522 | 0.527202 | 0.263601 | − | 0.964632i | \(-0.415090\pi\) | ||||
0.263601 | + | 0.964632i | \(0.415090\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.5837 | −1.25169 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.19476 | −0.327861 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.9158 | 0.681669 | 0.340835 | − | 0.940123i | \(-0.389290\pi\) | ||||
0.340835 | + | 0.940123i | \(0.389290\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.85680 | 0.149943 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.8019 | 1.29819 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.7858 | 1.60701 | 0.803503 | − | 0.595300i | \(-0.202967\pi\) | ||||
0.803503 | + | 0.595300i | \(0.202967\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.4584 | 0.804730 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.16842 | −0.112579 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.4250 | −1.16112 | −0.580561 | − | 0.814216i | \(-0.697167\pi\) | ||||
−0.580561 | + | 0.814216i | \(0.697167\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −34.6430 | −1.78895 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.90522 | 0.355637 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.51924 | −0.386237 | −0.193119 | − | 0.981175i | \(-0.561860\pi\) | ||||
−0.193119 | + | 0.981175i | \(0.561860\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.49456 | 0.383958 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.5491 | 0.845617 | 0.422809 | − | 0.906219i | \(-0.361044\pi\) | ||||
0.422809 | + | 0.906219i | \(0.361044\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.07712 | −0.105860 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 45.8065 | 2.32847 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.5840 | 1.80418 | 0.902089 | − | 0.431549i | \(-0.142033\pi\) | ||||
0.902089 | + | 0.431549i | \(0.142033\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.15424 | 0.311233 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 32.8495 | 1.65704 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.322661 | −0.0162348 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.3529 | 0.619976 | 0.309988 | − | 0.950740i | \(-0.399675\pi\) | ||||
0.309988 | + | 0.950740i | \(0.399675\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.09738 | 0.155063 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.9049 | −1.64319 | −0.821596 | − | 0.570070i | \(-0.806916\pi\) | ||||
−0.821596 | + | 0.570070i | \(0.806916\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.5453 | −1.32232 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.12918 | 0.205180 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.24554 | −0.160876 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.8018 | −1.27582 | −0.637908 | − | 0.770113i | \(-0.720200\pi\) | ||||
−0.637908 | + | 0.770113i | \(0.720200\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.460889 | 0.0227340 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.04052 | 0.198821 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.04607 | −0.149526 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −41.0513 | −2.01029 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.2971 | −1.04043 | −0.520216 | − | 0.854035i | \(-0.674149\pi\) | ||||
−0.520216 | + | 0.854035i | \(0.674149\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.4734 | 1.43645 | 0.718223 | − | 0.695813i | \(-0.244956\pi\) | ||||
0.718223 | + | 0.695813i | \(0.244956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −32.6333 | −1.58669 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.65950 | −0.129005 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.5835 | 0.754138 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 15.1916 | 0.733458 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.7861 | 1.04940 | 0.524701 | − | 0.851287i | \(-0.324177\pi\) | ||||
0.524701 | + | 0.851287i | \(0.324177\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.3657 | 1.02677 | 0.513386 | − | 0.858158i | \(-0.328391\pi\) | ||||
0.513386 | + | 0.858158i | \(0.328391\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.10693 | 0.340751 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.07712 | −0.147199 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.81816 | −0.420868 | −0.210434 | − | 0.977608i | \(-0.567488\pi\) | ||||
−0.210434 | + | 0.977608i | \(0.567488\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −30.0621 | −1.43153 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.5521 | 1.30904 | 0.654521 | − | 0.756044i | \(-0.272870\pi\) | ||||
0.654521 | + | 0.756044i | \(0.272870\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.1150 | 0.574306 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.82810 | 0.417555 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.16732 | 0.385440 | 0.192720 | − | 0.981254i | \(-0.438269\pi\) | ||||
0.192720 | + | 0.981254i | \(0.438269\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.99503 | 0.141031 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.82810 | 0.414780 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.0455 | −0.517820 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.97240 | −0.232599 | −0.116300 | − | 0.993214i | \(-0.537103\pi\) | ||||
−0.116300 | + | 0.993214i | \(0.537103\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.3490 | 0.576402 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.9039 | −0.740721 | −0.370360 | − | 0.928888i | \(-0.620766\pi\) | ||||
−0.370360 | + | 0.928888i | \(0.620766\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.24715 | −0.197382 | −0.0986908 | − | 0.995118i | \(-0.531465\pi\) | ||||
−0.0986908 | + | 0.995118i | \(0.531465\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −27.3208 | −1.26697 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.2216 | −1.25967 | −0.629833 | − | 0.776731i | \(-0.716877\pi\) | ||||
−0.629833 | + | 0.776731i | \(0.716877\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.27299 | 0.289660 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.0900 | 0.925697 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.87494 | 0.408070 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.32975 | 0.0610132 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.3227 | 0.472642 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.08201 | −0.414968 | −0.207484 | − | 0.978238i | \(-0.566527\pi\) | ||||
−0.207484 | + | 0.978238i | \(0.566527\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.2588 | −0.786933 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.53100 | −0.433676 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 27.8374 | 1.26403 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.6203 | −0.798451 | −0.399225 | − | 0.916853i | \(-0.630721\pi\) | ||||
−0.399225 | + | 0.916853i | \(0.630721\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.4647 | −0.563675 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.7082 | −1.02481 | −0.512404 | − | 0.858744i | \(-0.671245\pi\) | ||||
−0.512404 | + | 0.858744i | \(0.671245\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.59707 | 0.116966 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.88802 | 0.444433 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.3468 | 0.598687 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.11592 | 0.184254 | 0.0921270 | − | 0.995747i | \(-0.470633\pi\) | ||||
0.0921270 | + | 0.995747i | \(0.470633\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.85996 | −0.351157 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.1716 | −1.74658 | −0.873288 | − | 0.487205i | \(-0.838017\pi\) | ||||
−0.873288 | + | 0.487205i | \(0.838017\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.3431 | 0.949757 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 43.6459 | 1.93838 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.4018 | −0.771322 | −0.385661 | − | 0.922640i | \(-0.626027\pi\) | ||||
−0.385661 | + | 0.922640i | \(0.626027\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.0363 | −0.620928 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.17450 | −0.272611 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.7565 | −0.606182 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.32266 | −0.278070 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −26.3023 | −1.15454 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.2691 | 0.888004 | 0.444002 | − | 0.896026i | \(-0.353558\pi\) | ||||
0.444002 | + | 0.896026i | \(0.353558\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.23875 | 0.316529 | 0.158264 | − | 0.987397i | \(-0.449410\pi\) | ||||
0.158264 | + | 0.987397i | \(0.449410\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.11875 | 0.179757 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.98377 | −0.434900 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.5313 | −0.588319 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −19.2347 | −0.834714 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.9267 | 0.689861 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.77239 | 0.206328 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.38951 | 0.146268 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.82449 | −0.250878 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.1394 | 1.63974 | 0.819870 | − | 0.572549i | \(-0.194046\pi\) | ||||
0.819870 | + | 0.572549i | \(0.194046\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −71.3039 | −3.05994 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.58494 | 0.367738 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.50161 | −0.0642044 | −0.0321022 | − | 0.999485i | \(-0.510220\pi\) | ||||
−0.0321022 | + | 0.999485i | \(0.510220\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −74.1844 | −3.16611 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.29854 | −0.0553195 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.182605 | 0.00776515 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −17.7630 | −0.753996 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.0847 | 1.10524 | 0.552622 | − | 0.833432i | \(-0.313627\pi\) | ||||
0.552622 | + | 0.833432i | \(0.313627\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 47.1942 | 1.99610 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.71361 | 0.241229 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.9759 | −1.17904 | −0.589521 | − | 0.807753i | \(-0.700684\pi\) | ||||
−0.589521 | + | 0.807753i | \(0.700684\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.1756 | 1.26950 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.33684 | −0.0981382 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.2097 | 0.889155 | 0.444578 | − | 0.895740i | \(-0.353354\pi\) | ||||
0.444578 | + | 0.895740i | \(0.353354\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.1347 | 0.800761 | 0.400380 | − | 0.916349i | \(-0.368878\pi\) | ||||
0.400380 | + | 0.916349i | \(0.368878\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 29.4525 | 1.23039 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.09181 | −0.170640 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.9979 | −1.91492 | −0.957459 | − | 0.288568i | \(-0.906821\pi\) | ||||
−0.957459 | + | 0.288568i | \(0.906821\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 74.5982 | 3.10019 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.72387 | 0.0715184 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.00000 | 0.0828315 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 52.5815 | 2.17398 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 46.3398 | 1.91265 | 0.956325 | − | 0.292306i | \(-0.0944226\pi\) | ||||
0.956325 | + | 0.292306i | \(0.0944226\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.99189 | 0.205687 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −28.7874 | −1.18416 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.8898 | 0.734644 | 0.367322 | − | 0.930094i | \(-0.380275\pi\) | ||||
0.367322 | + | 0.930094i | \(0.380275\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.15424 | −0.170307 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −28.5685 | −1.16923 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.8508 | 0.770222 | 0.385111 | − | 0.922870i | \(-0.374163\pi\) | ||||
0.385111 | + | 0.922870i | \(0.374163\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.16363 | −0.373792 | −0.186896 | − | 0.982380i | \(-0.559843\pi\) | ||||
−0.186896 | + | 0.982380i | \(0.559843\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −29.8622 | −1.21608 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.91579 | 0.0778879 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.11636 | −0.0453118 | −0.0226559 | − | 0.999743i | \(-0.507212\pi\) | ||||
−0.0226559 | + | 0.999743i | \(0.507212\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.02206 | −0.162982 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −33.6220 | −1.36020 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.64609 | 0.389602 | 0.194801 | − | 0.980843i | \(-0.437594\pi\) | ||||
0.194801 | + | 0.980843i | \(0.437594\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.3919 | 0.660986 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −38.4415 | −1.54760 | −0.773799 | − | 0.633431i | \(-0.781646\pi\) | ||||
−0.773799 | + | 0.633431i | \(0.781646\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.2599 | 1.57799 | 0.788995 | − | 0.614400i | \(-0.210602\pi\) | ||||
0.788995 | + | 0.614400i | \(0.210602\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.9997 | 0.762430 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.85629 | −0.274692 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.5830 | −0.663320 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.85680 | −0.114090 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.49108 | −0.258816 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.9952 | −0.596951 | −0.298476 | − | 0.954417i | \(-0.596478\pi\) | ||||
−0.298476 | + | 0.954417i | \(0.596478\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.86862 | 0.352496 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.02590 | 0.199447 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −30.9728 | −1.22719 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −63.5369 | −2.51348 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.3586 | 0.606628 | 0.303314 | − | 0.952891i | \(-0.401907\pi\) | ||||
0.303314 | + | 0.952891i | \(0.401907\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.0013 | −1.41975 | −0.709876 | − | 0.704327i | \(-0.751249\pi\) | ||||
−0.709876 | + | 0.704327i | \(0.751249\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 48.5728 | 1.91255 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.30041 | 0.208381 | 0.104190 | − | 0.994557i | \(-0.466775\pi\) | ||||
0.104190 | + | 0.994557i | \(0.466775\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.72669 | −0.146285 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.4618 | 0.605994 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.0255 | 0.979325 | 0.489662 | − | 0.871912i | \(-0.337120\pi\) | ||||
0.489662 | + | 0.871912i | \(0.337120\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.0290 | 0.860746 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 66.8189 | 2.60686 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.7896 | 1.12148 | 0.560742 | − | 0.827990i | \(-0.310516\pi\) | ||||
0.560742 | + | 0.827990i | \(0.310516\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.8286 | −0.615661 | −0.307831 | − | 0.951441i | \(-0.599603\pi\) | ||||
−0.307831 | + | 0.951441i | \(0.599603\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 30.3832 | 1.17999 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.07712 | 0.0805472 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.99575 | 0.154716 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 44.0225 | 1.70201 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.3731 | −0.554868 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.5104 | 0.752071 | 0.376035 | − | 0.926605i | \(-0.377287\pi\) | ||||
0.376035 | + | 0.926605i | \(0.377287\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.21055 | −0.316024 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.3832 | 0.744957 | 0.372479 | − | 0.928041i | \(-0.378508\pi\) | ||||
0.372479 | + | 0.928041i | \(0.378508\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.7541 | −0.604588 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −39.7619 | −1.52368 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.67657 | −0.178944 | −0.0894720 | − | 0.995989i | \(-0.528518\pi\) | ||||
−0.0894720 | + | 0.995989i | \(0.528518\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.309075 | 0.0118092 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −52.7773 | −2.01358 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.6354 | 0.405176 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.7096 | −0.521539 | −0.260769 | − | 0.965401i | \(-0.583976\pi\) | ||||
−0.260769 | + | 0.965401i | \(0.583976\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.59597 | −0.212573 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27.5293 | −1.04424 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.99007 | 0.226890 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 82.0534 | 3.10355 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −40.8786 | −1.54396 | −0.771981 | − | 0.635646i | \(-0.780734\pi\) | ||||
−0.771981 | + | 0.635646i | \(0.780734\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.24554 | 0.122408 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −34.6041 | −1.30327 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.0788 | −0.454271 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.3293 | −1.25171 | −0.625855 | − | 0.779940i | \(-0.715250\pi\) | ||||
−0.625855 | + | 0.779940i | \(0.715250\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.869281 | −0.0326006 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.3606 | −0.575260 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.1876 | 0.380994 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −54.0720 | −2.01936 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.5647 | 0.916110 | 0.458055 | − | 0.888924i | \(-0.348546\pi\) | ||||
0.458055 | + | 0.888924i | \(0.348546\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.78525 | 0.289938 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −67.3693 | −2.50549 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.72673 | −0.0641292 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.42755 | −0.312560 | −0.156280 | − | 0.987713i | \(-0.549950\pi\) | ||||
−0.156280 | + | 0.987713i | \(0.549950\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.7936 | −1.54791 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.7499 | 0.656503 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.3192 | −0.418084 | −0.209042 | − | 0.977907i | \(-0.567034\pi\) | ||||
−0.209042 | + | 0.977907i | \(0.567034\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −31.8776 | −1.17582 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.78576 | −0.213121 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.8757 | 1.76114 | 0.880568 | − | 0.473919i | \(-0.157161\pi\) | ||||
0.880568 | + | 0.473919i | \(0.157161\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.1916 | −0.558078 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −49.9347 | −1.83193 | −0.915963 | − | 0.401262i | \(-0.868572\pi\) | ||||
−0.915963 | + | 0.401262i | \(0.868572\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.92017 | 0.216898 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.20642 | −0.300257 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.70086 | −0.0986872 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.9473 | 0.618417 | 0.309209 | − | 0.950994i | \(-0.399936\pi\) | ||||
0.309209 | + | 0.950994i | \(0.399936\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −42.2079 | −1.53814 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.92017 | 0.215457 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.939402 | 0.0341431 | 0.0170716 | − | 0.999854i | \(-0.494566\pi\) | ||||
0.0170716 | + | 0.999854i | \(0.494566\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.79073 | 0.319083 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.1954 | 0.369584 | 0.184792 | − | 0.982778i | \(-0.440839\pi\) | ||||
0.184792 | + | 0.982778i | \(0.440839\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.85851 | −0.175890 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 19.7760 | 0.715004 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.8174 | −0.715565 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.22600 | −0.0802718 | −0.0401359 | − | 0.999194i | \(-0.512779\pi\) | ||||
−0.0401359 | + | 0.999194i | \(0.512779\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.3731 | −0.877776 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.2189 | −0.871092 | −0.435546 | − | 0.900166i | \(-0.643445\pi\) | ||||
−0.435546 | + | 0.900166i | \(0.643445\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.63797 | 0.238443 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.0527 | 0.360638 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.99503 | −0.107308 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.3102 | −0.440493 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.01781 | 0.286533 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.4725 | 0.480852 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.7756 | 1.31091 | 0.655454 | − | 0.755235i | \(-0.272477\pi\) | ||||
0.655454 | + | 0.755235i | \(0.272477\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −68.1556 | −2.42640 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.0774 | −0.607202 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −76.4318 | −2.71417 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.9461 | 0.388217 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.1391 | 1.49264 | 0.746322 | − | 0.665585i | \(-0.231818\pi\) | ||||
0.746322 | + | 0.665585i | \(0.231818\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.6453 | −0.447359 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32.6390 | 1.15324 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.9461 | 0.456857 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.39154 | −0.225272 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 42.1475 | 1.48366 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.6056 | −0.408030 | −0.204015 | − | 0.978968i | \(-0.565399\pi\) | ||||
−0.204015 | + | 0.978968i | \(0.565399\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.3945 | 1.83982 | 0.919910 | − | 0.392128i | \(-0.128261\pi\) | ||||
0.919910 | + | 0.392128i | \(0.128261\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.3321 | −0.362361 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.35893 | −0.292801 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.87494 | −0.310495 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −29.7577 | −1.03982 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −49.2156 | −1.71764 | −0.858818 | − | 0.512281i | \(-0.828801\pi\) | ||||
−0.858818 | + | 0.512281i | \(0.828801\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.6059 | −0.718277 | −0.359138 | − | 0.933284i | \(-0.616929\pi\) | ||||
−0.359138 | + | 0.933284i | \(0.616929\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.79884 | −0.132259 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.6595 | −0.996589 | −0.498295 | − | 0.867008i | \(-0.666040\pi\) | ||||
−0.498295 | + | 0.867008i | \(0.666040\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.1774 | −0.353476 | −0.176738 | − | 0.984258i | \(-0.556555\pi\) | ||||
−0.176738 | + | 0.984258i | \(0.556555\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.48921 | −0.0863497 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.6490 | −0.403613 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.27093 | −0.182408 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30.8224 | −1.06538 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.4526 | 0.637055 | 0.318528 | − | 0.947914i | \(-0.396812\pi\) | ||||
0.318528 | + | 0.947914i | \(0.396812\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.3138 | −0.941855 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −73.0366 | −2.51551 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 29.2692 | 1.00689 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.08421 | −0.0372539 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 61.5680 | 2.11301 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.98692 | −0.342347 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.8680 | 1.09114 | 0.545570 | − | 0.838065i | \(-0.316313\pi\) | ||||
0.545570 | + | 0.838065i | \(0.316313\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.88802 | −0.338163 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.31725 | −0.0791559 | −0.0395779 | − | 0.999216i | \(-0.512601\pi\) | ||||
−0.0395779 | + | 0.999216i | \(0.512601\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.0900 | 1.50433 | 0.752166 | − | 0.658973i | \(-0.229009\pi\) | ||||
0.752166 | + | 0.658973i | \(0.229009\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.27675 | −0.316151 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.09373 | 0.173393 | 0.0866964 | − | 0.996235i | \(-0.472369\pi\) | ||||
0.0866964 | + | 0.996235i | \(0.472369\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.6385 | −0.599726 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −37.1385 | −1.26129 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.168422 | −0.00571332 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.7669 | −1.04250 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 74.9967 | 2.53825 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.1477 | 0.444472 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.8573 | 0.467928 | 0.233964 | − | 0.972245i | \(-0.424830\pi\) | ||||
0.233964 | + | 0.972245i | \(0.424830\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.92872 | 0.199971 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.6376 | −1.09959 | −0.549794 | − | 0.835300i | \(-0.685294\pi\) | ||||
−0.549794 | + | 0.835300i | \(0.685294\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.3091 | 1.05363 | 0.526817 | − | 0.849979i | \(-0.323385\pi\) | ||||
0.526817 | + | 0.849979i | \(0.323385\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20.3963 | −0.685614 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.6199 | 1.19600 | 0.598000 | − | 0.801496i | \(-0.295962\pi\) | ||||
0.598000 | + | 0.801496i | \(0.295962\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.84433 | −0.0953957 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.15534 | 0.0722066 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.32266 | 0.211580 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.27303 | 0.0759789 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 46.7464 | 1.56082 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.48214 | −0.216192 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.00000 | 0.133259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −27.4890 | −0.914778 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −47.8168 | −1.58948 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.1629 | 1.36679 | 0.683396 | − | 0.730048i | \(-0.260502\pi\) | ||||
0.683396 | + | 0.730048i | \(0.260502\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 57.5006 | 1.90717 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.30560 | 0.275177 | 0.137588 | − | 0.990490i | \(-0.456065\pi\) | ||||
0.137588 | + | 0.990490i | \(0.456065\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.58998 | −0.0526207 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −78.6645 | −2.60057 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.4670 | −0.411696 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.5343 | 0.578402 | 0.289201 | − | 0.957268i | \(-0.406610\pi\) | ||||
0.289201 | + | 0.957268i | \(0.406610\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.0817 | −0.892372 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −65.4618 | −2.15470 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.31577 | 0.141902 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −37.0613 | −1.21725 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.8335 | −0.585097 | −0.292549 | − | 0.956251i | \(-0.594503\pi\) | ||||
−0.292549 | + | 0.956251i | \(0.594503\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.82449 | 0.190890 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.2574 | −0.794150 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.83158 | 0.125306 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.8865 | 0.518988 | 0.259494 | − | 0.965745i | \(-0.416444\pi\) | ||||
0.259494 | + | 0.965745i | \(0.416444\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.3276 | −0.859170 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.0364 | −0.457575 | −0.228787 | − | 0.973476i | \(-0.573476\pi\) | ||||
−0.228787 | + | 0.973476i | \(0.573476\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.21607 | 0.300117 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.8252 | −0.417203 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.1959 | 0.981234 | 0.490617 | − | 0.871375i | \(-0.336771\pi\) | ||||
0.490617 | + | 0.871375i | \(0.336771\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 68.8432 | 2.23475 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −80.6415 | −2.61498 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.71300 | 0.282242 | 0.141121 | − | 0.989992i | \(-0.454929\pi\) | ||||
0.141121 | + | 0.989992i | \(0.454929\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.7510 | 0.639127 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.70966 | 0.119916 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.174916 | −0.00564834 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.08108 | −0.196164 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.8573 | 0.414321 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 50.0259 | 1.61039 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.1106 | −1.38634 | −0.693171 | − | 0.720773i | \(-0.743787\pi\) | ||||
−0.693171 | + | 0.720773i | \(0.743787\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.71361 | −0.183548 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.2824 | −0.682985 | −0.341493 | − | 0.939884i | \(-0.610932\pi\) | ||||
−0.341493 | + | 0.939884i | \(0.610932\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.5798 | 0.499464 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −20.2011 | −0.646952 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.2820 | −0.424928 | −0.212464 | − | 0.977169i | \(-0.568149\pi\) | ||||
−0.212464 | + | 0.977169i | \(0.568149\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.32376 | 0.202108 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.1287 | 0.738442 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −59.4823 | −1.89719 | −0.948596 | − | 0.316491i | \(-0.897495\pi\) | ||||
−0.948596 | + | 0.316491i | \(0.897495\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.3050 | −0.615108 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19.5837 | 0.623355 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.3092 | 0.868384 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.0005 | −1.77891 | −0.889457 | − | 0.457019i | \(-0.848917\pi\) | ||||
−0.889457 | + | 0.457019i | \(0.848917\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.93693 | 0.156669 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.1582 | −0.607356 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.3839 | 0.518883 | 0.259441 | − | 0.965759i | \(-0.416462\pi\) | ||||
0.259441 | + | 0.965759i | \(0.416462\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20.0396 | −0.634025 |
(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 | 3344.2.a.u.1.5 | 5 | ||
4.3 | odd | 2 | 1672.2.a.g.1.1 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1672.2.a.g.1.1 | ✓ | 5 | 4.3 | odd | 2 | ||
3344.2.a.u.1.5 | 5 | 1.1 | even | 1 | trivial |