Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2960,2,Mod(1,2960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2960.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2960 = 2^{4} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2960.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(23.6357189983\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.935504.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 8x^{3} + 4x^{2} + 8x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1480) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.43118\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2960.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.43118 | 0.826290 | 0.413145 | − | 0.910665i | \(-0.364430\pi\) | ||||
0.413145 | + | 0.910665i | \(0.364430\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.96628 | 0.743183 | 0.371591 | − | 0.928396i | \(-0.378812\pi\) | ||||
0.371591 | + | 0.928396i | \(0.378812\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.951735 | −0.317245 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.12053 | −1.54390 | −0.771949 | − | 0.635685i | \(-0.780718\pi\) | ||||
−0.771949 | + | 0.635685i | \(0.780718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.62611 | 0.451002 | 0.225501 | − | 0.974243i | \(-0.427598\pi\) | ||||
0.225501 | + | 0.974243i | \(0.427598\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.43118 | −0.369528 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.16879 | 1.25362 | 0.626808 | − | 0.779174i | \(-0.284361\pi\) | ||||
0.626808 | + | 0.779174i | \(0.284361\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.46621 | 1.48345 | 0.741725 | − | 0.670704i | \(-0.234008\pi\) | ||||
0.741725 | + | 0.670704i | \(0.234008\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.81409 | 0.614084 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.862352 | −0.179813 | −0.0899064 | − | 0.995950i | \(-0.528657\pi\) | ||||
−0.0899064 | + | 0.995950i | \(0.528657\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65563 | −1.08843 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.93255 | 0.358866 | 0.179433 | − | 0.983770i | \(-0.442574\pi\) | ||||
0.179433 | + | 0.983770i | \(0.442574\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.62962 | 1.37032 | 0.685160 | − | 0.728393i | \(-0.259732\pi\) | ||||
0.685160 | + | 0.728393i | \(0.259732\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.32838 | −1.27571 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.96628 | −0.332361 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.32725 | 0.372659 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.1907 | −1.59152 | −0.795762 | − | 0.605609i | \(-0.792930\pi\) | ||||
−0.795762 | + | 0.605609i | \(0.792930\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.83602 | 1.49998 | 0.749990 | − | 0.661449i | \(-0.230058\pi\) | ||||
0.749990 | + | 0.661449i | \(0.230058\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.951735 | 0.141876 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.66465 | −1.26387 | −0.631935 | − | 0.775022i | \(-0.717739\pi\) | ||||
−0.631935 | + | 0.775022i | \(0.717739\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.13376 | −0.447680 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.39745 | 1.03585 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.89752 | −0.398005 | −0.199002 | − | 0.979999i | \(-0.563770\pi\) | ||||
−0.199002 | + | 0.979999i | \(0.563770\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.12053 | 0.690452 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.25429 | 1.22576 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.4920 | 1.88669 | 0.943347 | − | 0.331808i | \(-0.107659\pi\) | ||||
0.943347 | + | 0.331808i | \(0.107659\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.24119 | 0.927139 | 0.463569 | − | 0.886061i | \(-0.346568\pi\) | ||||
0.463569 | + | 0.886061i | \(0.346568\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.87137 | −0.235771 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.62611 | −0.201694 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3286 | 1.38400 | 0.692002 | − | 0.721895i | \(-0.256729\pi\) | ||||
0.692002 | + | 0.721895i | \(0.256729\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.23418 | −0.148577 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.89739 | 1.17460 | 0.587302 | − | 0.809368i | \(-0.300190\pi\) | ||||
0.587302 | + | 0.809368i | \(0.300190\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.03504 | 1.05747 | 0.528735 | − | 0.848787i | \(-0.322666\pi\) | ||||
0.528735 | + | 0.848787i | \(0.322666\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.43118 | 0.165258 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.0684 | −1.14740 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.9492 | 1.34439 | 0.672193 | − | 0.740376i | \(-0.265353\pi\) | ||||
0.672193 | + | 0.740376i | \(0.265353\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.23899 | −0.582110 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.24915 | 0.795698 | 0.397849 | − | 0.917451i | \(-0.369757\pi\) | ||||
0.397849 | + | 0.917451i | \(0.369757\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.16879 | −0.560634 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.76582 | 0.296527 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.85407 | 0.832530 | 0.416265 | − | 0.909243i | \(-0.363339\pi\) | ||||
0.416265 | + | 0.909243i | \(0.363339\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.19738 | 0.335177 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.9193 | 1.13228 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.46621 | −0.663419 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.24947 | 0.228399 | 0.114200 | − | 0.993458i | \(-0.463570\pi\) | ||||
0.114200 | + | 0.993458i | \(0.463570\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.87339 | 0.489794 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0218 | 0.997207 | 0.498603 | − | 0.866830i | \(-0.333846\pi\) | ||||
0.498603 | + | 0.866830i | \(0.333846\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.0207 | −1.77563 | −0.887815 | − | 0.460201i | \(-0.847777\pi\) | ||||
−0.887815 | + | 0.460201i | \(0.847777\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.81409 | −0.274627 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.76451 | 0.170582 | 0.0852909 | − | 0.996356i | \(-0.472818\pi\) | ||||
0.0852909 | + | 0.996356i | \(0.472818\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.7839 | −1.41604 | −0.708019 | − | 0.706194i | \(-0.750411\pi\) | ||||
−0.708019 | + | 0.706194i | \(0.750411\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.43118 | 0.135841 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.1687 | −1.33288 | −0.666438 | − | 0.745561i | \(-0.732182\pi\) | ||||
−0.666438 | + | 0.745561i | \(0.732182\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.862352 | 0.0804147 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.54763 | −0.143078 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.1633 | 0.931666 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.2198 | 1.38362 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.5847 | −1.31506 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.7134 | −1.12813 | −0.564064 | − | 0.825731i | \(-0.690763\pi\) | ||||
−0.564064 | + | 0.825731i | \(0.690763\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.0771 | 1.23942 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.9569 | 1.21942 | 0.609709 | − | 0.792626i | \(-0.291286\pi\) | ||||
0.609709 | + | 0.792626i | \(0.291286\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.7144 | 1.10247 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.65563 | 0.486759 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.38974 | −0.289605 | −0.144803 | − | 0.989461i | \(-0.546255\pi\) | ||||
−0.144803 | + | 0.989461i | \(0.546255\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.6982 | −0.992232 | −0.496116 | − | 0.868256i | \(-0.665241\pi\) | ||||
−0.496116 | + | 0.868256i | \(0.665241\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.4006 | −1.04432 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.32655 | −0.696301 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.93255 | −0.160490 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.48496 | −0.369913 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.6610 | −1.11915 | −0.559577 | − | 0.828778i | \(-0.689036\pi\) | ||||
−0.559577 | + | 0.828778i | \(0.689036\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.31954 | 0.351519 | 0.175760 | − | 0.984433i | \(-0.443762\pi\) | ||||
0.175760 | + | 0.984433i | \(0.443762\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.91932 | −0.397704 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.62962 | −0.612826 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.27609 | −0.580695 | −0.290348 | − | 0.956921i | \(-0.593771\pi\) | ||||
−0.290348 | + | 0.956921i | \(0.593771\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.14686 | −0.328867 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.69562 | −0.133634 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.0800 | 1.88609 | 0.943044 | − | 0.332668i | \(-0.107949\pi\) | ||||
0.943044 | + | 0.332668i | \(0.107949\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.32838 | 0.570513 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.8045 | 1.76467 | 0.882334 | − | 0.470624i | \(-0.155971\pi\) | ||||
0.882334 | + | 0.470624i | \(0.155971\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.3558 | −0.796597 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.15412 | −0.470617 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.38804 | −0.561703 | −0.280851 | − | 0.959751i | \(-0.590617\pi\) | ||||
−0.280851 | + | 0.959751i | \(0.590617\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.96628 | 0.148637 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 20.7406 | 1.55896 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.08751 | 0.230771 | 0.115386 | − | 0.993321i | \(-0.463190\pi\) | ||||
0.115386 | + | 0.993321i | \(0.463190\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.8320 | 1.32544 | 0.662721 | − | 0.748866i | \(-0.269401\pi\) | ||||
0.662721 | + | 0.748866i | \(0.269401\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.3634 | 0.766085 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.00000 | −0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.4670 | −1.93546 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.1205 | −0.808899 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.7442 | −1.28392 | −0.641962 | − | 0.766736i | \(-0.721879\pi\) | ||||
−0.641962 | + | 0.766736i | \(0.721879\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.4702 | −1.47348 | −0.736739 | − | 0.676177i | \(-0.763635\pi\) | ||||
−0.736739 | + | 0.676177i | \(0.763635\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.32725 | −0.166658 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.85627 | −0.203501 | −0.101750 | − | 0.994810i | \(-0.532444\pi\) | ||||
−0.101750 | + | 0.994810i | \(0.532444\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.00902 | −0.355080 | −0.177540 | − | 0.984114i | \(-0.556814\pi\) | ||||
−0.177540 | + | 0.984114i | \(0.556814\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.2132 | 1.14359 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.79993 | 0.266703 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.1907 | 0.711751 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.820731 | 0.0570447 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −33.1104 | −2.29030 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.45224 | 0.650719 | 0.325359 | − | 0.945590i | \(-0.394515\pi\) | ||||
0.325359 | + | 0.945590i | \(0.394515\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.1649 | 0.970563 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.83602 | −0.670811 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.0019 | 1.01840 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.9307 | 0.873777 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.40503 | 0.565384 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.04681 | 0.471889 | 0.235945 | − | 0.971766i | \(-0.424182\pi\) | ||||
0.235945 | + | 0.971766i | \(0.424182\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.951735 | −0.0634490 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.65437 | 0.242549 | 0.121275 | − | 0.992619i | \(-0.461302\pi\) | ||||
0.121275 | + | 0.992619i | \(0.461302\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.48132 | 0.626543 | 0.313272 | − | 0.949664i | \(-0.398575\pi\) | ||||
0.313272 | + | 0.949664i | \(0.398575\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.4096 | −0.948083 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.4379 | 1.33893 | 0.669465 | − | 0.742844i | \(-0.266524\pi\) | ||||
0.669465 | + | 0.742844i | \(0.266524\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.66465 | 0.565220 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 17.1013 | 1.11085 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.6661 | −1.53084 | −0.765418 | − | 0.643533i | \(-0.777468\pi\) | ||||
−0.765418 | + | 0.643533i | \(0.777468\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.5265 | 1.77314 | 0.886568 | − | 0.462597i | \(-0.153082\pi\) | ||||
0.886568 | + | 0.462597i | \(0.153082\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.46896 | 0.607434 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.13376 | 0.200208 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.5148 | 0.669039 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.3748 | 0.657477 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.9382 | 1.13225 | 0.566124 | − | 0.824320i | \(-0.308442\pi\) | ||||
0.566124 | + | 0.824320i | \(0.308442\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.41570 | 0.277613 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.39745 | −0.463246 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.3166 | 1.20493 | 0.602467 | − | 0.798143i | \(-0.294184\pi\) | ||||
0.602467 | + | 0.798143i | \(0.294184\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.96628 | 0.122178 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.83928 | −0.113848 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.13733 | −0.131794 | −0.0658968 | − | 0.997826i | \(-0.520991\pi\) | ||||
−0.0658968 | + | 0.997826i | \(0.520991\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.89752 | 0.177993 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.2406 | 0.687911 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.0542 | −0.917872 | −0.458936 | − | 0.888469i | \(-0.651769\pi\) | ||||
−0.458936 | + | 0.888469i | \(0.651769\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.6188 | −0.705794 | −0.352897 | − | 0.935662i | \(-0.614803\pi\) | ||||
−0.352897 | + | 0.935662i | \(0.614803\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.57602 | 0.276953 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.12053 | −0.308779 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.8551 | −0.892558 | −0.446279 | − | 0.894894i | \(-0.647251\pi\) | ||||
−0.446279 | + | 0.894894i | \(0.647251\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.26138 | −0.434727 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.5081 | −1.28306 | −0.641532 | − | 0.767096i | \(-0.721701\pi\) | ||||
−0.641532 | + | 0.767096i | \(0.721701\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −31.5556 | −1.87578 | −0.937892 | − | 0.346928i | \(-0.887225\pi\) | ||||
−0.937892 | + | 0.346928i | \(0.887225\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.25429 | −0.548177 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.0378 | −1.18279 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.71642 | 0.571554 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.21939 | 0.188724 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.70954 | −0.567237 | −0.283619 | − | 0.958937i | \(-0.591535\pi\) | ||||
−0.283619 | + | 0.958937i | \(0.591535\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.4920 | −0.843755 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 28.9598 | 1.68042 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.40228 | −0.0810960 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.3403 | 1.11476 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.3430 | 0.823982 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.24119 | −0.414629 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.28306 | −0.0732283 | −0.0366142 | − | 0.999329i | \(-0.511657\pi\) | ||||
−0.0366142 | + | 0.999329i | \(0.511657\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.7907 | −1.46718 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.93386 | 0.393183 | 0.196592 | − | 0.980485i | \(-0.437013\pi\) | ||||
0.196592 | + | 0.980485i | \(0.437013\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.0619 | 1.36006 | 0.680030 | − | 0.733184i | \(-0.261967\pi\) | ||||
0.680030 | + | 0.733184i | \(0.261967\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.87137 | 0.105440 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.8481 | 0.609288 | 0.304644 | − | 0.952466i | \(-0.401463\pi\) | ||||
0.304644 | + | 0.952466i | \(0.401463\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.89569 | −0.554052 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.52533 | 0.140950 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 33.4225 | 1.85968 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.62611 | 0.0902004 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.1583 | −1.17006 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.0371 | −0.939286 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.14379 | 0.117833 | 0.0589166 | − | 0.998263i | \(-0.481235\pi\) | ||||
0.0589166 | + | 0.998263i | \(0.481235\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.951735 | −0.0521548 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.3286 | −0.618946 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.2817 | 1.10482 | 0.552408 | − | 0.833574i | \(-0.313709\pi\) | ||||
0.552408 | + | 0.833574i | \(0.313709\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.2778 | −1.10134 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −39.0677 | −2.11563 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9258 | −1.07589 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.23418 | 0.0664459 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.7426 | −1.22089 | −0.610444 | − | 0.792060i | \(-0.709009\pi\) | ||||
−0.610444 | + | 0.792060i | \(0.709009\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.3742 | −1.73295 | −0.866477 | − | 0.499218i | \(-0.833621\pi\) | ||||
−0.866477 | + | 0.499218i | \(0.833621\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.19668 | −0.490883 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.0358 | 1.06640 | 0.533200 | − | 0.845989i | \(-0.320989\pi\) | ||||
0.533200 | + | 0.845989i | \(0.320989\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.89739 | −0.525299 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.5454 | 0.769826 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −35.2849 | −1.86226 | −0.931132 | − | 0.364683i | \(-0.881177\pi\) | ||||
−0.931132 | + | 0.364683i | \(0.881177\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.8119 | 1.20063 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.7822 | 1.14327 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.03504 | −0.472915 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.45843 | 0.337127 | 0.168564 | − | 0.985691i | \(-0.446087\pi\) | ||||
0.168564 | + | 0.985691i | \(0.446087\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.69888 | 0.504903 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.69732 | −0.295790 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.6727 | −1.53639 | −0.768197 | − | 0.640213i | \(-0.778846\pi\) | ||||
−0.768197 | + | 0.640213i | \(0.778846\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.43118 | −0.0739056 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.14255 | 0.161849 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.66321 | −0.444999 | −0.222500 | − | 0.974933i | \(-0.571422\pi\) | ||||
−0.222500 | + | 0.974933i | \(0.571422\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.1950 | −0.932160 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.7713 | 0.754780 | 0.377390 | − | 0.926054i | \(-0.376822\pi\) | ||||
0.377390 | + | 0.926054i | \(0.376822\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.0684 | 0.513132 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.36129 | −0.475861 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.4077 | 0.527689 | 0.263845 | − | 0.964565i | \(-0.415009\pi\) | ||||
0.263845 | + | 0.964565i | \(0.415009\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.45732 | −0.225416 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.9747 | 1.00759 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.9492 | −0.601227 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.6548 | −0.936257 | −0.468129 | − | 0.883660i | \(-0.655072\pi\) | ||||
−0.468129 | + | 0.883660i | \(0.655072\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18.1965 | 0.910964 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.4491 | −1.37075 | −0.685373 | − | 0.728193i | \(-0.740361\pi\) | ||||
−0.685373 | + | 0.728193i | \(0.740361\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.4066 | 0.618017 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.23899 | 0.260328 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.12053 | −0.253815 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.0540 | −1.23884 | −0.619420 | − | 0.785059i | \(-0.712632\pi\) | ||||
−0.619420 | + | 0.785059i | \(0.712632\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.85132 | −0.239298 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.4952 | 1.40216 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.24915 | −0.355847 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.7422 | −0.819871 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.0041 | 0.537583 | 0.268792 | − | 0.963198i | \(-0.413376\pi\) | ||||
0.268792 | + | 0.963198i | \(0.413376\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.32255 | −0.259405 | −0.129703 | − | 0.991553i | \(-0.541402\pi\) | ||||
−0.129703 | + | 0.991553i | \(0.541402\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.24646 | 0.400956 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.16879 | 0.250723 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.2382 | 0.689034 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.9168 | −0.575346 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.75785 | 0.277346 | 0.138673 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138673 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −35.0962 | −1.68661 | −0.843307 | − | 0.537431i | \(-0.819395\pi\) | ||||
−0.843307 | + | 0.537431i | \(0.819395\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.76582 | −0.132611 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.57615 | −0.266743 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.2085 | 1.29859 | 0.649294 | − | 0.760537i | \(-0.275064\pi\) | ||||
0.649294 | + | 0.760537i | \(0.275064\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.98251 | 0.142024 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.64372 | 0.125607 | 0.0628035 | − | 0.998026i | \(-0.479996\pi\) | ||||
0.0628035 | + | 0.998026i | \(0.479996\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.85407 | −0.372319 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.5513 | −0.924746 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.7067 | −0.835629 | −0.417814 | − | 0.908532i | \(-0.637204\pi\) | ||||
−0.417814 | + | 0.908532i | \(0.637204\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 52.1819 | 2.45715 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.18202 | 0.290457 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.19738 | −0.149896 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.5575 | 1.00842 | 0.504208 | − | 0.863582i | \(-0.331784\pi\) | ||||
0.504208 | + | 0.863582i | \(0.331784\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −29.2328 | −1.36447 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.7163 | 0.918279 | 0.459140 | − | 0.888364i | \(-0.348158\pi\) | ||||
0.459140 | + | 0.888364i | \(0.348158\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.8570 | −0.922831 | −0.461415 | − | 0.887184i | \(-0.652658\pi\) | ||||
−0.461415 | + | 0.887184i | \(0.652658\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.9193 | −0.506371 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.4068 | 0.481569 | 0.240784 | − | 0.970579i | \(-0.422595\pi\) | ||||
0.240784 | + | 0.970579i | \(0.422595\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.2751 | 1.02857 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.4134 | −0.479823 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −50.3656 | −2.31581 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.46621 | 0.296690 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.75767 | 0.126265 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.4266 | 1.34453 | 0.672267 | − | 0.740309i | \(-0.265321\pi\) | ||||
0.672267 | + | 0.740309i | \(0.265321\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.62611 | 0.0741443 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.42673 | −0.110420 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.24947 | −0.102143 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.5370 | −1.38376 | −0.691882 | − | 0.722010i | \(-0.743218\pi\) | ||||
−0.691882 | + | 0.722010i | \(0.743218\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 34.4627 | 1.55846 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.73261 | 0.123321 | 0.0616606 | − | 0.998097i | \(-0.480360\pi\) | ||||
0.0616606 | + | 0.998097i | \(0.480360\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.98896 | 0.449880 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.87339 | −0.219043 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.4610 | 0.872945 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.3826 | −1.09152 | −0.545758 | − | 0.837943i | \(-0.683758\pi\) | ||||
−0.545758 | + | 0.837943i | \(0.683758\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 32.6373 | 1.45813 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.3183 | −0.772183 | −0.386092 | − | 0.922460i | \(-0.626175\pi\) | ||||
−0.386092 | + | 0.922460i | \(0.626175\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.0218 | −0.445965 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.8209 | −0.658220 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.4419 | 1.39364 | 0.696819 | − | 0.717247i | \(-0.254598\pi\) | ||||
0.696819 | + | 0.717247i | \(0.254598\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.7654 | 0.785894 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −36.5705 | −1.61463 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.0207 | 0.794086 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.3676 | 1.95128 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.5736 | −0.464129 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.3564 | −0.453722 | −0.226861 | − | 0.973927i | \(-0.572846\pi\) | ||||
−0.226861 | + | 0.973927i | \(0.572846\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.7283 | −0.556571 | −0.278285 | − | 0.960498i | \(-0.589766\pi\) | ||||
−0.278285 | + | 0.960498i | \(0.589766\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.81409 | 0.122817 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39.4359 | 1.71786 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.2563 | −0.967667 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.7925 | −0.598544 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.5713 | −0.717781 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.76451 | −0.0762865 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.41876 | 0.190684 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.0465 | 0.691171 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.9313 | −0.727933 | −0.363966 | − | 0.931412i | \(-0.618578\pi\) | ||||
−0.363966 | + | 0.931412i | \(0.618578\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25.5207 | 1.09520 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.7839 | 0.633271 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.2625 | 1.25117 | 0.625587 | − | 0.780155i | \(-0.284860\pi\) | ||||
0.625587 | + | 0.780155i | \(0.284860\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.89169 | −0.294130 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.4963 | 0.532360 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.4953 | 0.999124 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.43118 | −0.0607500 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.254156 | 0.0107689 | 0.00538447 | − | 0.999986i | \(-0.498286\pi\) | ||||
0.00538447 | + | 0.999986i | \(0.498286\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.9945 | 0.676494 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −37.8789 | −1.59925 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.8152 | 0.455807 | 0.227904 | − | 0.973684i | \(-0.426813\pi\) | ||||
0.227904 | + | 0.973684i | \(0.426813\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.1687 | 0.596080 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.3013 | −0.432614 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.5266 | −1.44743 | −0.723716 | − | 0.690098i | \(-0.757567\pi\) | ||||
−0.723716 | + | 0.690098i | \(0.757567\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.9437 | 0.457978 | 0.228989 | − | 0.973429i | \(-0.426458\pi\) | ||||
0.228989 | + | 0.973429i | \(0.426458\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.3951 | −1.06089 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.862352 | −0.0359626 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.82017 | −0.367189 | −0.183594 | − | 0.983002i | \(-0.558773\pi\) | ||||
−0.183594 | + | 0.983002i | \(0.558773\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −29.2965 | −1.21752 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.2538 | 0.591349 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.8368 | 0.614478 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.54763 | 0.0639865 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.95988 | 0.328539 | 0.164270 | − | 0.986415i | \(-0.447473\pi\) | ||||
0.164270 | + | 0.986415i | \(0.447473\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49.3347 | 2.03280 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.08782 | −0.168151 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.27685 | −0.339890 | −0.169945 | − | 0.985454i | \(-0.554359\pi\) | ||||
−0.169945 | + | 0.985454i | \(0.554359\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.1633 | −0.416654 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.16879 | −0.293399 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.8285 | −1.54563 | −0.772816 | − | 0.634630i | \(-0.781152\pi\) | ||||
−0.772816 | + | 0.634630i | \(0.781152\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.98714 | 0.285012 | 0.142506 | − | 0.989794i | \(-0.454484\pi\) | ||||
0.142506 | + | 0.989794i | \(0.454484\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.7818 | −0.439069 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.2198 | −0.618773 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.1934 | −1.14434 | −0.572168 | − | 0.820137i | \(-0.693897\pi\) | ||||
−0.572168 | + | 0.820137i | \(0.693897\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.43837 | 0.220374 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.0897 | −0.570008 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.45523 | −0.220335 | −0.110167 | − | 0.993913i | \(-0.535139\pi\) | ||||
−0.110167 | + | 0.993913i | \(0.535139\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14.5847 | 0.588113 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.8893 | −1.28382 | −0.641908 | − | 0.766781i | \(-0.721857\pi\) | ||||
−0.641908 | + | 0.766781i | \(0.721857\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.6809 | 1.51452 | 0.757261 | − | 0.653112i | \(-0.226537\pi\) | ||||
0.757261 | + | 0.653112i | \(0.226537\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.87714 | 0.195713 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.4433 | 0.618722 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −47.3868 | −1.89245 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.16879 | 0.206093 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.7753 | −0.428960 | −0.214480 | − | 0.976728i | \(-0.568806\pi\) | ||||
−0.214480 | + | 0.976728i | \(0.568806\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.5278 | 0.537682 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.7134 | 0.504514 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.09584 | −0.201905 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.41969 | −0.372637 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.9725 | 0.433389 | 0.216695 | − | 0.976239i | \(-0.430472\pi\) | ||||
0.216695 | + | 0.976239i | \(0.430472\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.5820 | −0.693368 | −0.346684 | − | 0.937982i | \(-0.612692\pi\) | ||||
−0.346684 | + | 0.937982i | \(0.612692\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.0771 | −0.554284 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.1582 | 1.10701 | 0.553506 | − | 0.832845i | \(-0.313289\pi\) | ||||
0.553506 | + | 0.832845i | \(0.313289\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −74.2065 | −2.91286 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.4704 | 0.841492 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.7639 | 0.499491 | 0.249745 | − | 0.968312i | \(-0.419653\pi\) | ||||
0.249745 | + | 0.968312i | \(0.419653\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.9569 | −0.545340 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.59896 | −0.335477 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.64289 | −0.102952 | −0.0514762 | − | 0.998674i | \(-0.516393\pi\) | ||||
−0.0514762 | + | 0.998674i | \(0.516393\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.1897 | −0.435228 | −0.217614 | − | 0.976035i | \(-0.569827\pi\) | ||||
−0.217614 | + | 0.976035i | \(0.569827\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.0291 | 0.467171 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.7144 | −0.493042 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.66654 | −0.0645287 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.0852 | 0.389917 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −37.0787 | −1.43141 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.2846 | 0.550632 | 0.275316 | − | 0.961354i | \(-0.411217\pi\) | ||||
0.275316 | + | 0.961354i | \(0.411217\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.65563 | −0.217685 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.0898 | 0.503082 | 0.251541 | − | 0.967847i | \(-0.419063\pi\) | ||||
0.251541 | + | 0.967847i | \(0.419063\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.42308 | 0.169742 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.23005 | 0.200416 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.0870 | 1.38083 | 0.690415 | − | 0.723414i | \(-0.257428\pi\) | ||||
0.690415 | + | 0.723414i | \(0.257428\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.38974 | 0.129515 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.5694 | 0.517706 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.71169 | −0.179501 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.0837 | 0.459687 | 0.229844 | − | 0.973228i | \(-0.426179\pi\) | ||||
0.229844 | + | 0.973228i | \(0.426179\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.58243 | 0.364006 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.6982 | 0.443740 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −52.6738 | −1.99516 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.2502 | 1.10634 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.45578 | 0.281601 | 0.140801 | − | 0.990038i | \(-0.455032\pi\) | ||||
0.140801 | + | 0.990038i | \(0.455032\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.46621 | 0.243878 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.4006 | 0.467035 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.7056 | 0.741107 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.69787 | −0.213988 | −0.106994 | − | 0.994260i | \(-0.534123\pi\) | ||||
−0.106994 | + | 0.994260i | \(0.534123\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.3724 | −0.426500 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.57941 | −0.246401 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.32655 | 0.311395 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −33.8704 | −1.26491 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.1129 | −0.824671 | −0.412336 | − | 0.911032i | \(-0.635287\pi\) | ||||
−0.412336 | + | 0.911032i | \(0.635287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35.4336 | −1.31962 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 39.3952 | 1.46513 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.93255 | 0.0717732 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.34486 | 0.0869659 | 0.0434829 | − | 0.999054i | \(-0.486155\pi\) | ||||
0.0434829 | + | 0.999054i | \(0.486155\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.2687 | 1.08403 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 50.8404 | 1.88040 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.9071 | 1.06771 | 0.533855 | − | 0.845576i | \(-0.320743\pi\) | ||||
0.533855 | + | 0.845576i | \(0.320743\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.48496 | 0.165430 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −58.0082 | −2.13676 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.5736 | −1.38217 | −0.691083 | − | 0.722776i | \(-0.742866\pi\) | ||||
−0.691083 | + | 0.722776i | \(0.742866\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.0485 | 0.552820 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.1665 | 0.923268 | 0.461634 | − | 0.887070i | \(-0.347263\pi\) | ||||
0.461634 | + | 0.887070i | \(0.347263\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.6610 | 0.500501 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.89928 | −0.252431 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.46952 | 0.126773 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.3267 | −0.924186 | −0.462093 | − | 0.886832i | \(-0.652901\pi\) | ||||
−0.462093 | + | 0.886832i | \(0.652901\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25.6727 | 0.935565 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.31954 | −0.157204 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.67645 | 0.133623 | 0.0668113 | − | 0.997766i | \(-0.478717\pi\) | ||||
0.0668113 | + | 0.997766i | \(0.478717\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.31964 | 0.229388 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.1461 | 0.911545 | 0.455773 | − | 0.890096i | \(-0.349363\pi\) | ||||
0.455773 | + | 0.890096i | \(0.349363\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.0692 | −1.05237 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.91932 | 0.177859 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.5656 | 0.850903 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.5928 | −1.21139 | −0.605694 | − | 0.795698i | \(-0.707104\pi\) | ||||
−0.605694 | + | 0.795698i | \(0.707104\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.6454 | 0.995625 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.23222 | 0.0443199 | 0.0221599 | − | 0.999754i | \(-0.492946\pi\) | ||||
0.0221599 | + | 0.999754i | \(0.492946\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.62962 | 0.274064 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.81409 | 0.100955 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −65.8954 | −2.36095 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −50.6799 | −1.81347 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.9298 | −0.390599 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.27609 | 0.259695 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.09991 | 0.181792 | 0.0908961 | − | 0.995860i | \(-0.471027\pi\) | ||||
0.0908961 | + | 0.995860i | \(0.471027\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.05890 | −0.108900 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −27.8595 | −0.990570 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.7750 | 0.418142 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.14686 | 0.147074 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.94742 | −0.210668 | −0.105334 | − | 0.994437i | \(-0.533591\pi\) | ||||
−0.105334 | + | 0.994437i | \(0.533591\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.7858 | −1.58441 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.47500 | −0.264116 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −46.2642 | −1.63263 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.69562 | 0.0597628 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.5452 | −0.758428 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.8869 | −0.488238 | −0.244119 | − | 0.969745i | \(-0.578499\pi\) | ||||
−0.244119 | + | 0.969745i | \(0.578499\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.71735 | −0.235878 | −0.117939 | − | 0.993021i | \(-0.537629\pi\) | ||||
−0.117939 | + | 0.993021i | \(0.537629\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.6286 | −0.583190 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.0800 | −0.843484 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 63.6018 | 2.22515 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.04306 | −0.106333 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.3600 | −0.431365 | −0.215683 | − | 0.976464i | \(-0.569198\pi\) | ||||
−0.215683 | + | 0.976464i | \(0.569198\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.75674 | −0.165810 | −0.0829048 | − | 0.996557i | \(-0.526420\pi\) | ||||
−0.0829048 | + | 0.996557i | \(0.526420\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.32838 | −0.255141 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.29371 | −0.218854 | −0.109427 | − | 0.993995i | \(-0.534902\pi\) | ||||
−0.109427 | + | 0.993995i | \(0.534902\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.9655 | 1.11021 | 0.555104 | − | 0.831781i | \(-0.312679\pi\) | ||||
0.555104 | + | 0.831781i | \(0.312679\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.2603 | −0.737512 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.1977 | −0.561219 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.8045 | −0.789184 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −43.1503 | −1.49149 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.6992 | −0.507474 | −0.253737 | − | 0.967273i | \(-0.581660\pi\) | ||||
−0.253737 | + | 0.967273i | \(0.581660\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.2652 | −0.871215 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −30.7818 | −1.06018 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.3558 | 0.356249 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.9264 | 1.02828 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −45.1616 | −1.54994 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.862352 | −0.0295610 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 54.5264 | 1.86695 | 0.933473 | − | 0.358646i | \(-0.116762\pi\) | ||||
0.933473 | + | 0.358646i | \(0.116762\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.15412 | 0.210467 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.2996 | 1.30829 | 0.654144 | − | 0.756370i | \(-0.273029\pi\) | ||||
0.654144 | + | 0.756370i | \(0.273029\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.2599 | 0.964216 | 0.482108 | − | 0.876112i | \(-0.339871\pi\) | ||||
0.482108 | + | 0.876112i | \(0.339871\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −28.6776 | −0.977330 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.8707 | −0.540246 | −0.270123 | − | 0.962826i | \(-0.587064\pi\) | ||||
−0.270123 | + | 0.962826i | \(0.587064\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.38804 | 0.251201 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.9059 | 0.472269 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −61.1860 | −2.07559 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.4215 | 0.624189 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.14090 | −0.0724585 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.96628 | −0.0664723 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.0036 | −1.35083 | −0.675413 | − | 0.737440i | \(-0.736035\pi\) | ||||
−0.675413 | + | 0.737440i | \(0.736035\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.8961 | −0.468703 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 52.3990 | 1.76537 | 0.882684 | − | 0.469967i | \(-0.155734\pi\) | ||||
0.882684 | + | 0.469967i | \(0.155734\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.8804 | 0.635376 | 0.317688 | − | 0.948195i | \(-0.397094\pi\) | ||||
0.317688 | + | 0.948195i | \(0.397094\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20.7406 | −0.697186 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.60874 | −0.322630 | −0.161315 | − | 0.986903i | \(-0.551574\pi\) | ||||
−0.161315 | + | 0.986903i | \(0.551574\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.9980 | −0.838405 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26.8264 | 0.898719 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −56.0275 | −1.87489 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.08751 | −0.103204 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.00691 | −0.0670088 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.7446 | 0.491761 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.9767 | −0.498945 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27.6794 | 0.921114 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.8320 | −0.592756 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −52.8613 | −1.75523 | −0.877616 | − | 0.479365i | \(-0.840867\pi\) | ||||
−0.877616 | + | 0.479365i | \(0.840867\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.53811 | −0.316359 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.2226 | −1.39890 | −0.699448 | − | 0.714684i | \(-0.746571\pi\) | ||||
−0.699448 | + | 0.714684i | \(0.746571\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −37.1195 | −1.22848 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.3634 | −0.342604 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27.4431 | 0.906250 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.11038 | 0.102602 | 0.0513010 | − | 0.998683i | \(-0.483663\pi\) | ||||
0.0513010 | + | 0.998683i | \(0.483663\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.83629 | −0.0605078 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.0943 | 0.529749 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00000 | 0.0328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.1509 | 0.563310 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −55.6513 | −1.82586 | −0.912930 | − | 0.408115i | \(-0.866186\pi\) | ||||
−0.912930 | + | 0.408115i | \(0.866186\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.2635 | −0.664111 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.92358 | 0.324883 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 26.4670 | 0.865562 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.1645 | 0.397398 | 0.198699 | − | 0.980061i | \(-0.436328\pi\) | ||||
0.198699 | + | 0.980061i | \(0.436328\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 34.4368 | 1.12380 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48.8595 | −1.59277 | −0.796387 | − | 0.604787i | \(-0.793258\pi\) | ||||
−0.796387 | + | 0.604787i | \(0.793258\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.78799 | 0.286176 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.1205 | 0.361751 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.8474 | 0.514972 | 0.257486 | − | 0.966282i | \(-0.417106\pi\) | ||||
0.257486 | + | 0.966282i | \(0.417106\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.6920 | 0.476922 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.5255 | 0.503448 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.5946 | −0.407980 | −0.203990 | − | 0.978973i | \(-0.565391\pi\) | ||||
−0.203990 | + | 0.978973i | \(0.565391\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.7442 | 0.574189 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −14.1625 | −0.457808 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.66517 | −0.215229 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.2110 | 0.877776 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.67935 | −0.0541162 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.4702 | 0.658959 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.89371 | 0.286002 | 0.143001 | − | 0.989723i | \(-0.454325\pi\) | ||||
0.143001 | + | 0.989723i | \(0.454325\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 47.8335 | 1.53663 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.1917 | −0.647981 | −0.323991 | − | 0.946060i | \(-0.605025\pi\) | ||||
−0.323991 | + | 0.946060i | \(0.605025\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.0020 | −0.737410 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.32725 | 0.0745317 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.5456 | −0.369375 | −0.184688 | − | 0.982797i | \(-0.559127\pi\) | ||||
−0.184688 | + | 0.982797i | \(0.559127\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40.2170 | −1.28534 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.0703 | 0.449231 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.5253 | −0.973606 | −0.486803 | − | 0.873512i | \(-0.661837\pi\) | ||||
−0.486803 | + | 0.873512i | \(0.661837\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.85627 | 0.0910083 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −24.3831 | −0.776122 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.48211 | −0.269716 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.9540 | 1.20565 | 0.602824 | − | 0.797874i | \(-0.294042\pi\) | ||||
0.602824 | + | 0.797874i | \(0.294042\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.06814 | 0.0973644 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.00902 | 0.158797 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.2156 | −1.05195 | −0.525974 | − | 0.850500i | \(-0.676299\pi\) | ||||
−0.525974 | + | 0.850500i | \(0.676299\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.65563 | −0.178936 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2960.2.a.z.1.4 | 5 | ||
4.3 | odd | 2 | 1480.2.a.h.1.2 | ✓ | 5 | ||
20.19 | odd | 2 | 7400.2.a.q.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1480.2.a.h.1.2 | ✓ | 5 | 4.3 | odd | 2 | ||
2960.2.a.z.1.4 | 5 | 1.1 | even | 1 | trivial | ||
7400.2.a.q.1.4 | 5 | 20.19 | odd | 2 |