Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4056,2,Mod(1,4056)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4056, 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("4056.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4056 = 2^{3} \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4056.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: | \(32.3873230598\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.27700337.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 19x^{4} + 17x^{3} + 103x^{2} - 71x - 127 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(3.16419\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4056.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.71914 | 1.21604 | 0.608019 | − | 0.793922i | \(-0.291964\pi\) | ||||
0.608019 | + | 0.793922i | \(0.291964\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.735542 | −0.278009 | −0.139004 | − | 0.990292i | \(-0.544390\pi\) | ||||
−0.139004 | + | 0.990292i | \(0.544390\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.14374 | −0.344850 | −0.172425 | − | 0.985023i | \(-0.555160\pi\) | ||||
−0.172425 | + | 0.985023i | \(0.555160\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.71914 | 0.702080 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.96612 | 1.44700 | 0.723499 | − | 0.690326i | \(-0.242533\pi\) | ||||
0.723499 | + | 0.690326i | \(0.242533\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.07604 | 0.705692 | 0.352846 | − | 0.935681i | \(-0.385214\pi\) | ||||
0.352846 | + | 0.935681i | \(0.385214\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.735542 | −0.160508 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.31230 | 1.10769 | 0.553845 | − | 0.832620i | \(-0.313160\pi\) | ||||
0.553845 | + | 0.832620i | \(0.313160\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.39374 | 0.478749 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.12923 | −1.50956 | −0.754780 | − | 0.655978i | \(-0.772256\pi\) | ||||
−0.754780 | + | 0.655978i | \(0.772256\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.67023 | 0.299982 | 0.149991 | − | 0.988687i | \(-0.452076\pi\) | ||||
0.149991 | + | 0.988687i | \(0.452076\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.14374 | −0.199099 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00004 | −0.338069 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.90945 | 0.313912 | 0.156956 | − | 0.987606i | \(-0.449832\pi\) | ||||
0.156956 | + | 0.987606i | \(0.449832\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.69257 | −1.35755 | −0.678775 | − | 0.734346i | \(-0.737489\pi\) | ||||
−0.678775 | + | 0.734346i | \(0.737489\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.7282 | 1.78853 | 0.894266 | − | 0.447536i | \(-0.147698\pi\) | ||||
0.894266 | + | 0.447536i | \(0.147698\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.71914 | 0.405346 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.53981 | 1.09979 | 0.549897 | − | 0.835233i | \(-0.314667\pi\) | ||||
0.549897 | + | 0.835233i | \(0.314667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.45898 | −0.922711 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.96612 | 0.835424 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.86294 | 0.255894 | 0.127947 | − | 0.991781i | \(-0.459161\pi\) | ||||
0.127947 | + | 0.991781i | \(0.459161\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.10999 | −0.419350 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.07604 | 0.407431 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.28323 | 0.557629 | 0.278814 | − | 0.960345i | \(-0.410059\pi\) | ||||
0.278814 | + | 0.960345i | \(0.410059\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.91045 | −0.372645 | −0.186323 | − | 0.982489i | \(-0.559657\pi\) | ||||
−0.186323 | + | 0.982489i | \(0.559657\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.735542 | −0.0926696 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.596077 | 0.0728224 | 0.0364112 | − | 0.999337i | \(-0.488407\pi\) | ||||
0.0364112 | + | 0.999337i | \(0.488407\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.31230 | 0.639525 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.30363 | −0.273391 | −0.136695 | − | 0.990613i | \(-0.543648\pi\) | ||||
−0.136695 | + | 0.990613i | \(0.543648\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.1830 | −1.54295 | −0.771477 | − | 0.636258i | \(-0.780482\pi\) | ||||
−0.771477 | + | 0.636258i | \(0.780482\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.39374 | 0.276406 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.841267 | 0.0958713 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.6413 | 1.42226 | 0.711129 | − | 0.703061i | \(-0.248184\pi\) | ||||
0.711129 | + | 0.703061i | \(0.248184\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.10421 | −0.999317 | −0.499658 | − | 0.866222i | \(-0.666541\pi\) | ||||
−0.499658 | + | 0.866222i | \(0.666541\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.2227 | 1.75960 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.12923 | −0.871545 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.77241 | −0.929873 | −0.464937 | − | 0.885344i | \(-0.653923\pi\) | ||||
−0.464937 | + | 0.885344i | \(0.653923\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.67023 | 0.173194 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.36419 | 0.858148 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.86954 | 0.697496 | 0.348748 | − | 0.937216i | \(-0.386607\pi\) | ||||
0.348748 | + | 0.937216i | \(0.386607\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.14374 | −0.114950 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.11227 | 0.707697 | 0.353849 | − | 0.935303i | \(-0.384873\pi\) | ||||
0.353849 | + | 0.935303i | \(0.384873\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.16550 | 0.903103 | 0.451552 | − | 0.892245i | \(-0.350871\pi\) | ||||
0.451552 | + | 0.892245i | \(0.350871\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00004 | −0.195184 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.98925 | 0.482329 | 0.241165 | − | 0.970484i | \(-0.422471\pi\) | ||||
0.241165 | + | 0.970484i | \(0.422471\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.6880 | 1.50264 | 0.751318 | − | 0.659940i | \(-0.229418\pi\) | ||||
0.751318 | + | 0.659940i | \(0.229418\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.90945 | 0.181237 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.7801 | 1.39039 | 0.695197 | − | 0.718819i | \(-0.255317\pi\) | ||||
0.695197 | + | 0.718819i | \(0.255317\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.4449 | 1.34699 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.38833 | −0.402278 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.69187 | −0.881079 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.69257 | −0.783782 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.08679 | −0.633862 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.9211 | 1.67898 | 0.839490 | − | 0.543375i | \(-0.182854\pi\) | ||||
0.839490 | + | 0.543375i | \(0.182854\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.7282 | 1.03261 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.4920 | 1.44091 | 0.720456 | − | 0.693500i | \(-0.243932\pi\) | ||||
0.720456 | + | 0.693500i | \(0.243932\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.26256 | −0.196189 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.71914 | 0.234027 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0062 | 0.854888 | 0.427444 | − | 0.904042i | \(-0.359414\pi\) | ||||
0.427444 | + | 0.904042i | \(0.359414\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.1940 | −0.949464 | −0.474732 | − | 0.880130i | \(-0.657455\pi\) | ||||
−0.474732 | + | 0.880130i | \(0.657455\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.53981 | 0.634966 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22.1045 | −1.83568 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.45898 | −0.532728 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.0579 | −1.23359 | −0.616795 | − | 0.787124i | \(-0.711569\pi\) | ||||
−0.616795 | + | 0.787124i | \(0.711569\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.1086 | −1.47365 | −0.736827 | − | 0.676081i | \(-0.763677\pi\) | ||||
−0.736827 | + | 0.676081i | \(0.763677\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.96612 | 0.482332 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.54159 | 0.364789 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.72080 | −0.296952 | −0.148476 | − | 0.988916i | \(-0.547437\pi\) | ||||
−0.148476 | + | 0.988916i | \(0.547437\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.86294 | 0.147740 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.90742 | −0.307948 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.0780 | 1.25932 | 0.629661 | − | 0.776870i | \(-0.283194\pi\) | ||||
0.629661 | + | 0.776870i | \(0.283194\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.10999 | −0.242112 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.0746 | −1.01174 | −0.505871 | − | 0.862609i | \(-0.668829\pi\) | ||||
−0.505871 | + | 0.862609i | \(0.668829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.07604 | 0.235231 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.0060 | 1.29294 | 0.646470 | − | 0.762940i | \(-0.276245\pi\) | ||||
0.646470 | + | 0.762940i | \(0.276245\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.76070 | −0.133096 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.28323 | 0.321947 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.9269 | 0.891458 | 0.445729 | − | 0.895168i | \(-0.352945\pi\) | ||||
0.445729 | + | 0.895168i | \(0.352945\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.248257 | 0.0184528 | 0.00922639 | − | 0.999957i | \(-0.497063\pi\) | ||||
0.00922639 | + | 0.999957i | \(0.497063\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.91045 | −0.215147 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.19208 | 0.381729 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.82368 | −0.498997 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.735542 | −0.0535028 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.1792 | −1.24304 | −0.621522 | − | 0.783397i | \(-0.713485\pi\) | ||||
−0.621522 | + | 0.783397i | \(0.713485\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.6570 | −1.63088 | −0.815442 | − | 0.578839i | \(-0.803506\pi\) | ||||
−0.815442 | + | 0.578839i | \(0.803506\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.47161 | −0.318589 | −0.159294 | − | 0.987231i | \(-0.550922\pi\) | ||||
−0.159294 | + | 0.987231i | \(0.550922\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.1993 | −1.50278 | −0.751389 | − | 0.659859i | \(-0.770616\pi\) | ||||
−0.751389 | + | 0.659859i | \(0.770616\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.596077 | 0.0420440 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.97939 | 0.419671 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −23.6363 | −1.65083 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.31230 | 0.369230 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.51818 | −0.243358 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.4474 | −1.61419 | −0.807093 | − | 0.590424i | \(-0.798960\pi\) | ||||
−0.807093 | + | 0.590424i | \(0.798960\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.30363 | −0.157842 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 31.8906 | 2.17492 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.22852 | −0.0833975 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.1830 | −0.890825 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.25181 | 0.284722 | 0.142361 | − | 0.989815i | \(-0.454531\pi\) | ||||
0.142361 | + | 0.989815i | \(0.454531\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.39374 | 0.159583 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.3153 | −0.883768 | −0.441884 | − | 0.897072i | \(-0.645690\pi\) | ||||
−0.441884 | + | 0.897072i | \(0.645690\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.6238 | −0.768123 | −0.384062 | − | 0.923307i | \(-0.625475\pi\) | ||||
−0.384062 | + | 0.923307i | \(0.625475\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.841267 | 0.0553513 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 29.4566 | 1.92977 | 0.964883 | − | 0.262682i | \(-0.0846069\pi\) | ||||
0.964883 | + | 0.262682i | \(0.0846069\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.5018 | 1.33739 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.6413 | 0.821141 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.36845 | −0.411941 | −0.205971 | − | 0.978558i | \(-0.566035\pi\) | ||||
−0.205971 | + | 0.978558i | \(0.566035\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.2290 | 0.980984 | 0.490492 | − | 0.871446i | \(-0.336817\pi\) | ||||
0.490492 | + | 0.871446i | \(0.336817\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.5629 | −1.12205 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.10421 | −0.576956 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.57425 | −0.0993655 | −0.0496828 | − | 0.998765i | \(-0.515821\pi\) | ||||
−0.0496828 | + | 0.998765i | \(0.515821\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.07587 | −0.381987 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.2227 | 1.01591 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.1261 | 0.818782 | 0.409391 | − | 0.912359i | \(-0.365741\pi\) | ||||
0.409391 | + | 0.912359i | \(0.365741\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.40448 | −0.0872703 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.12923 | −0.503187 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.1263 | 0.624412 | 0.312206 | − | 0.950014i | \(-0.398932\pi\) | ||||
0.312206 | + | 0.950014i | \(0.398932\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.06559 | 0.311177 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.77241 | −0.536863 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.1811 | −1.04755 | −0.523774 | − | 0.851857i | \(-0.675476\pi\) | ||||
−0.523774 | + | 0.851857i | \(0.675476\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.5460 | 1.00510 | 0.502550 | − | 0.864548i | \(-0.332395\pi\) | ||||
0.502550 | + | 0.864548i | \(0.332395\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.73781 | −0.165096 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.6891 | 1.72376 | 0.861882 | − | 0.507110i | \(-0.169286\pi\) | ||||
0.861882 | + | 0.507110i | \(0.169286\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.67023 | 0.0999938 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.08857 | −0.542179 | −0.271089 | − | 0.962554i | \(-0.587384\pi\) | ||||
−0.271089 | + | 0.962554i | \(0.587384\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.3186 | −1.32671 | −0.663353 | − | 0.748307i | \(-0.730867\pi\) | ||||
−0.663353 | + | 0.748307i | \(0.730867\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.36419 | 0.495452 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.39375 | 0.377411 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.5946 | 1.09380 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.86954 | 0.402700 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.5171 | −1.31546 | −0.657731 | − | 0.753253i | \(-0.728484\pi\) | ||||
−0.657731 | + | 0.753253i | \(0.728484\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.6467 | 0.678098 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.14374 | −0.0663664 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.62658 | −0.497228 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.11227 | 0.408589 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.91394 | −0.453151 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.1371 | −1.14928 | −0.574641 | − | 0.818405i | \(-0.694858\pi\) | ||||
−0.574641 | + | 0.818405i | \(0.694858\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.16550 | 0.521407 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.9556 | −0.734645 | −0.367322 | − | 0.930094i | \(-0.619725\pi\) | ||||
−0.367322 | + | 0.930094i | \(0.619725\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.8936 | 0.728789 | 0.364394 | − | 0.931245i | \(-0.381276\pi\) | ||||
0.364394 | + | 0.931245i | \(0.381276\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.00004 | −0.112690 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.2814 | 1.53228 | 0.766138 | − | 0.642676i | \(-0.222176\pi\) | ||||
0.766138 | + | 0.642676i | \(0.222176\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.29770 | 0.520571 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.98925 | 0.278473 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.3520 | 1.02113 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.6880 | 0.867547 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.54584 | −0.305752 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.4726 | 0.795484 | 0.397742 | − | 0.917497i | \(-0.369794\pi\) | ||||
0.397742 | + | 0.917497i | \(0.369794\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.90945 | 0.104637 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.62082 | 0.0885548 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.27680 | −0.505339 | −0.252670 | − | 0.967553i | \(-0.581309\pi\) | ||||
−0.252670 | + | 0.967553i | \(0.581309\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.7801 | 0.802744 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.91030 | −0.103449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.89964 | 0.534531 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14.4449 | 0.777687 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.9968 | −1.34190 | −0.670951 | − | 0.741502i | \(-0.734114\pi\) | ||||
−0.670951 | + | 0.741502i | \(0.734114\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.8625 | −1.00969 | −0.504844 | − | 0.863211i | \(-0.668450\pi\) | ||||
−0.504844 | + | 0.863211i | \(0.668450\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.99213 | 0.372154 | 0.186077 | − | 0.982535i | \(-0.440423\pi\) | ||||
0.186077 | + | 0.982535i | \(0.440423\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.26390 | −0.332453 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.38833 | −0.232255 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.5257 | 1.39997 | 0.699987 | − | 0.714156i | \(-0.253189\pi\) | ||||
0.699987 | + | 0.714156i | \(0.253189\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.53798 | −0.501999 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.69187 | −0.508691 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −35.8465 | −1.87629 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.6137 | −1.70242 | −0.851211 | − | 0.524824i | \(-0.824131\pi\) | ||||
−0.851211 | + | 0.524824i | \(0.824131\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.69257 | −0.452517 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.37027 | −0.0711408 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.4172 | −0.539384 | −0.269692 | − | 0.962947i | \(-0.586922\pi\) | ||||
−0.269692 | + | 0.962947i | \(0.586922\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.08679 | −0.365960 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.4662 | −1.05128 | −0.525640 | − | 0.850707i | \(-0.676174\pi\) | ||||
−0.525640 | + | 0.850707i | \(0.676174\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.9211 | 0.969360 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 35.4182 | 1.80979 | 0.904894 | − | 0.425637i | \(-0.139950\pi\) | ||||
0.904894 | + | 0.425637i | \(0.139950\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.28753 | 0.116583 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.7282 | 0.596177 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.20097 | 0.314402 | 0.157201 | − | 0.987567i | \(-0.449753\pi\) | ||||
0.157201 | + | 0.987567i | \(0.449753\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.6938 | 1.60282 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.4920 | 0.831911 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 34.3735 | 1.72952 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.93338 | −0.197410 | −0.0987052 | − | 0.995117i | \(-0.531470\pi\) | ||||
−0.0987052 | + | 0.995117i | \(0.531470\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.26256 | −0.113270 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.6651 | −0.982027 | −0.491013 | − | 0.871152i | \(-0.663373\pi\) | ||||
−0.491013 | + | 0.871152i | \(0.663373\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.71914 | 0.135115 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.18391 | −0.108252 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.2584 | 0.705033 | 0.352516 | − | 0.935806i | \(-0.385326\pi\) | ||||
0.352516 | + | 0.935806i | \(0.385326\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.0062 | 0.493570 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.15049 | −0.155026 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.7557 | −1.21521 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.1940 | −0.548174 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.3494 | 0.505603 | 0.252802 | − | 0.967518i | \(-0.418648\pi\) | ||||
0.252802 | + | 0.967518i | \(0.418648\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.5629 | 1.73323 | 0.866614 | − | 0.498979i | \(-0.166291\pi\) | ||||
0.866614 | + | 0.498979i | \(0.166291\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.53981 | 0.366598 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.2814 | 0.692748 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.14076 | 0.103599 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.9667 | 0.817257 | 0.408629 | − | 0.912701i | \(-0.366007\pi\) | ||||
0.408629 | + | 0.912701i | \(0.366007\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.2275 | −0.875958 | −0.437979 | − | 0.898985i | \(-0.644306\pi\) | ||||
−0.437979 | + | 0.898985i | \(0.644306\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.1045 | −1.05983 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.3408 | 0.781688 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.98284 | −0.476455 | −0.238228 | − | 0.971209i | \(-0.576566\pi\) | ||||
−0.238228 | + | 0.971209i | \(0.576566\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.45898 | −0.307570 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.8110 | 0.561156 | 0.280578 | − | 0.959831i | \(-0.409474\pi\) | ||||
0.280578 | + | 0.959831i | \(0.409474\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −23.8534 | −1.13076 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.0579 | −0.712213 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.3334 | −1.47872 | −0.739358 | − | 0.673313i | \(-0.764871\pi\) | ||||
−0.739358 | + | 0.673313i | \(0.764871\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.94201 | 0.468151 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.1086 | −0.850815 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.275381 | −0.0128818 | −0.00644089 | − | 0.999979i | \(-0.502050\pi\) | ||||
−0.00644089 | + | 0.999979i | \(0.502050\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.96612 | 0.278475 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.7955 | 0.642519 | 0.321260 | − | 0.946991i | \(-0.395894\pi\) | ||||
0.321260 | + | 0.946991i | \(0.395894\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.6326 | −0.865929 | −0.432965 | − | 0.901411i | \(-0.642533\pi\) | ||||
−0.432965 | + | 0.901411i | \(0.642533\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.54159 | 0.210611 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.1171 | 0.930909 | 0.465454 | − | 0.885072i | \(-0.345891\pi\) | ||||
0.465454 | + | 0.885072i | \(0.345891\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.438440 | −0.0202453 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.72080 | −0.171446 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.4140 | −0.616775 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.36325 | 0.337849 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.86294 | 0.0852980 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.7364 | 1.49576 | 0.747882 | − | 0.663832i | \(-0.231071\pi\) | ||||
0.747882 | + | 0.663832i | \(0.231071\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.90742 | −0.177794 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.6793 | 0.848182 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.2763 | −0.828177 | −0.414089 | − | 0.910237i | \(-0.635900\pi\) | ||||
−0.414089 | + | 0.910237i | \(0.635900\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.0780 | 0.727070 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.2495 | −1.13949 | −0.569747 | − | 0.821820i | \(-0.692959\pi\) | ||||
−0.569747 | + | 0.821820i | \(0.692959\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −48.5000 | −2.18433 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.10999 | −0.139783 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.69442 | 0.0760050 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.3791 | −1.71808 | −0.859042 | − | 0.511906i | \(-0.828940\pi\) | ||||
−0.859042 | + | 0.511906i | \(0.828940\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.0746 | −0.584129 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.196327 | −0.00875380 | −0.00437690 | − | 0.999990i | \(-0.501393\pi\) | ||||
−0.00437690 | + | 0.999990i | \(0.501393\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.3393 | 0.860587 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.7356 | 1.14071 | 0.570355 | − | 0.821399i | \(-0.306806\pi\) | ||||
0.570355 | + | 0.821399i | \(0.306806\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.69665 | 0.428955 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.07604 | 0.135810 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.9223 | 1.09821 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.62356 | −0.379264 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.0060 | 0.746479 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.0712 | 0.485040 | 0.242520 | − | 0.970146i | \(-0.422026\pi\) | ||||
0.242520 | + | 0.970146i | \(0.422026\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.2974 | −1.06245 | −0.531227 | − | 0.847230i | \(-0.678269\pi\) | ||||
−0.531227 | + | 0.847230i | \(0.678269\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.76070 | −0.0768432 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.96478 | 0.434072 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.22048 | 0.226977 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.28323 | 0.185876 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.5665 | 0.586531 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.9269 | 0.514683 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.38737 | 0.318197 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.5652 | −1.35710 | −0.678548 | − | 0.734556i | \(-0.737390\pi\) | ||||
−0.678548 | + | 0.734556i | \(0.737390\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.248257 | 0.0106537 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 42.6579 | 1.82726 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.79582 | −0.0767838 | −0.0383919 | − | 0.999263i | \(-0.512224\pi\) | ||||
−0.0383919 | + | 0.999263i | \(0.512224\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.91045 | −0.124215 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.0058 | −1.06528 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.29822 | −0.395400 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.19208 | 0.220391 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.1019 | −0.555146 | −0.277573 | − | 0.960705i | \(-0.589530\pi\) | ||||
−0.277573 | + | 0.960705i | \(0.589530\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.82368 | −0.288096 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.44099 | −0.229310 | −0.114655 | − | 0.993405i | \(-0.536576\pi\) | ||||
−0.114655 | + | 0.993405i | \(0.536576\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 40.1892 | 1.69077 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.735542 | −0.0308899 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.65863 | 0.362989 | 0.181494 | − | 0.983392i | \(-0.441907\pi\) | ||||
0.181494 | + | 0.983392i | \(0.441907\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0718 | −0.672585 | −0.336293 | − | 0.941758i | \(-0.609173\pi\) | ||||
−0.336293 | + | 0.941758i | \(0.609173\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.1792 | −0.717672 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.7163 | 0.530305 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.8157 | −1.49103 | −0.745513 | − | 0.666491i | \(-0.767796\pi\) | ||||
−0.745513 | + | 0.666491i | \(0.767796\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.6570 | −0.941591 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.69653 | 0.277819 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.13071 | −0.0882450 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.0888 | 0.994250 | 0.497125 | − | 0.867679i | \(-0.334389\pi\) | ||||
0.497125 | + | 0.867679i | \(0.334389\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.13768 | 0.211695 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.47161 | −0.183937 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −32.7042 | −1.34300 | −0.671501 | − | 0.741004i | \(-0.734350\pi\) | ||||
−0.671501 | + | 0.741004i | \(0.734350\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.9325 | −0.489185 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.1993 | −0.867630 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.2139 | −1.23451 | −0.617254 | − | 0.786764i | \(-0.711755\pi\) | ||||
−0.617254 | + | 0.786764i | \(0.711755\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.78275 | 0.0727200 | 0.0363600 | − | 0.999339i | \(-0.488424\pi\) | ||||
0.0363600 | + | 0.999339i | \(0.488424\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.596077 | 0.0242741 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −26.3536 | −1.07143 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.5806 | 0.957109 | 0.478554 | − | 0.878058i | \(-0.341161\pi\) | ||||
0.478554 | + | 0.878058i | \(0.341161\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.97939 | 0.242297 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.4093 | −0.703156 | −0.351578 | − | 0.936159i | \(-0.614355\pi\) | ||||
−0.351578 | + | 0.936159i | \(0.614355\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −23.6363 | −0.953109 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.9193 | −1.24476 | −0.622382 | − | 0.782714i | \(-0.713835\pi\) | ||||
−0.622382 | + | 0.782714i | \(0.713835\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.6808 | 1.31355 | 0.656777 | − | 0.754085i | \(-0.271919\pi\) | ||||
0.656777 | + | 0.754085i | \(0.271919\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.31230 | 0.213175 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.45248 | 0.258513 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2387 | −1.24955 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.51818 | −0.140503 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.3920 | 0.454230 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.7322 | −0.467053 | −0.233527 | − | 0.972350i | \(-0.575027\pi\) | ||||
−0.233527 | + | 0.972350i | \(0.575027\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.4474 | −0.931951 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 51.4493 | 2.04170 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.30363 | −0.0911302 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.0086 | −1.50125 | −0.750624 | − | 0.660729i | \(-0.770247\pi\) | ||||
−0.750624 | + | 0.660729i | \(0.770247\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.53115 | −0.139255 | −0.0696275 | − | 0.997573i | \(-0.522181\pi\) | ||||
−0.0696275 | + | 0.997573i | \(0.522181\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 31.8906 | 1.25569 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.2407 | 1.03163 | 0.515814 | − | 0.856701i | \(-0.327490\pi\) | ||||
0.515814 | + | 0.856701i | \(0.327490\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.89889 | −0.192298 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.22852 | −0.0481496 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.79758 | 0.109478 | 0.0547389 | − | 0.998501i | \(-0.482567\pi\) | ||||
0.0547389 | + | 0.998501i | \(0.482567\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 44.8441 | 1.75220 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.1830 | −0.514318 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.5249 | 0.409991 | 0.204996 | − | 0.978763i | \(-0.434282\pi\) | ||||
0.204996 | + | 0.978763i | \(0.434282\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.8706 | 1.35631 | 0.678155 | − | 0.734919i | \(-0.262780\pi\) | ||||
0.678155 | + | 0.734919i | \(0.262780\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.15222 | −0.238573 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −43.1849 | −1.67212 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.25181 | 0.164385 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.32879 | 0.128507 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.3696 | −0.399718 | −0.199859 | − | 0.979825i | \(-0.564048\pi\) | ||||
−0.199859 | + | 0.979825i | \(0.564048\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.39374 | 0.0921352 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.0671 | 0.463778 | 0.231889 | − | 0.972742i | \(-0.425509\pi\) | ||||
0.231889 | + | 0.972742i | \(0.425509\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.05284 | −0.193910 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.3153 | −0.510244 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.35234 | 0.357857 | 0.178929 | − | 0.983862i | \(-0.442737\pi\) | ||||
0.178929 | + | 0.983862i | \(0.442737\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.2083 | 1.03958 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.6238 | −0.443476 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.8063 | 0.411092 | 0.205546 | − | 0.978647i | \(-0.434103\pi\) | ||||
0.205546 | + | 0.978647i | \(0.434103\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.841267 | 0.0319571 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −30.4382 | −1.15458 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −51.8609 | −1.96437 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.4566 | 1.11415 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.25030 | 0.198301 | 0.0991505 | − | 0.995072i | \(-0.468387\pi\) | ||||
0.0991505 | + | 0.995072i | \(0.468387\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.87355 | 0.221525 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 20.5018 | 0.772143 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.23137 | −0.196746 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.6495 | −0.625284 | −0.312642 | − | 0.949871i | \(-0.601214\pi\) | ||||
−0.312642 | + | 0.949871i | \(0.601214\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.6413 | 0.474086 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.87274 | 0.332287 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.36845 | −0.237834 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.0141 | 0.410756 | 0.205378 | − | 0.978683i | \(-0.434158\pi\) | ||||
0.205378 | + | 0.978683i | \(0.434158\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.74161 | −0.251071 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.2290 | 0.566371 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −19.4593 | −0.722700 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.3243 | −1.23593 | −0.617965 | − | 0.786205i | \(-0.712043\pi\) | ||||
−0.617965 | + | 0.786205i | \(0.712043\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 69.9718 | 2.58800 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.4717 | −1.16243 | −0.581216 | − | 0.813749i | \(-0.697423\pi\) | ||||
−0.581216 | + | 0.813749i | \(0.697423\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −17.5629 | −0.647817 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.681755 | −0.0251128 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.78683 | −0.286443 | −0.143222 | − | 0.989691i | \(-0.545746\pi\) | ||||
−0.143222 | + | 0.989691i | \(0.545746\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.4688 | 0.457437 | 0.228718 | − | 0.973493i | \(-0.426546\pi\) | ||||
0.228718 | + | 0.973493i | \(0.426546\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −40.9445 | −1.50009 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.10421 | −0.333106 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.66980 | −0.134092 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.0652 | 0.695699 | 0.347849 | − | 0.937550i | \(-0.386912\pi\) | ||||
0.347849 | + | 0.937550i | \(0.386912\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.57425 | −0.0573687 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −49.2398 | −1.79202 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.1165 | 0.404037 | 0.202018 | − | 0.979382i | \(-0.435250\pi\) | ||||
0.202018 | + | 0.979382i | \(0.435250\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.07587 | −0.220540 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.9184 | −0.939542 | −0.469771 | − | 0.882788i | \(-0.655664\pi\) | ||||
−0.469771 | + | 0.882788i | \(0.655664\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.5392 | −0.417746 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.2227 | 0.586535 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −51.8255 | −1.86888 | −0.934438 | − | 0.356125i | \(-0.884098\pi\) | ||||
−0.934438 | + | 0.356125i | \(0.884098\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.1261 | 0.472724 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.0857906 | −0.00308567 | −0.00154284 | − | 0.999999i | \(-0.500491\pi\) | ||||
−0.00154284 | + | 0.999999i | \(0.500491\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.99809 | 0.143616 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.40448 | −0.0503855 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −26.7387 | −0.958012 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.63475 | 0.0942787 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.12923 | −0.290515 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.1174 | −0.361105 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.76170 | −0.312321 | −0.156160 | − | 0.987732i | \(-0.549912\pi\) | ||||
−0.156160 | + | 0.987732i | \(0.549912\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.1263 | 0.360504 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.8714 | −0.386542 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.06559 | 0.179658 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.288970 | 0.0102358 | 0.00511792 | − | 0.999987i | \(-0.498371\pi\) | ||||
0.00511792 | + | 0.999987i | \(0.498371\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44.9834 | 1.59140 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.77241 | −0.309958 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.0779 | 0.532087 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.6248 | −0.374476 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.1811 | −0.604802 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.0782 | −0.354330 | −0.177165 | − | 0.984181i | \(-0.556693\pi\) | ||||
−0.177165 | + | 0.984181i | \(0.556693\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.3498 | −1.69779 | −0.848896 | − | 0.528559i | \(-0.822732\pi\) | ||||
−0.848896 | + | 0.528559i | \(0.822732\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.5460 | 0.580295 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 43.7183 | 1.53138 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.0764 | 1.26215 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.6203 | 1.41766 | 0.708829 | − | 0.705381i | \(-0.249224\pi\) | ||||
0.708829 | + | 0.705381i | \(0.249224\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.6609 | −1.20820 | −0.604101 | − | 0.796908i | \(-0.706468\pi\) | ||||
−0.604101 | + | 0.796908i | \(0.706468\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.73781 | −0.0953184 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.13065 | −0.0393164 | −0.0196582 | − | 0.999807i | \(-0.506258\pi\) | ||||
−0.0196582 | + | 0.999807i | \(0.506258\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.5479 | −0.366342 | −0.183171 | − | 0.983081i | \(-0.558636\pi\) | ||||
−0.183171 | + | 0.983081i | \(0.558636\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.6891 | 0.995215 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −38.5351 | −1.33516 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.5517 | −1.23032 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.67023 | 0.0577315 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.0198 | −0.794732 | −0.397366 | − | 0.917660i | \(-0.630076\pi\) | ||||
−0.397366 | + | 0.917660i | \(0.630076\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.0844 | 1.27877 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.08857 | −0.313027 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.12877 | 0.244948 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.3186 | −0.765974 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.1436 | 0.347717 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.9208 | 0.545119 | 0.272560 | − | 0.962139i | \(-0.412130\pi\) | ||||
0.272560 | + | 0.962139i | \(0.412130\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.36419 | 0.286049 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −42.0212 | −1.43542 | −0.717708 | − | 0.696344i | \(-0.754809\pi\) | ||||
−0.717708 | + | 0.696344i | \(0.754809\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.6037 | −0.430033 | −0.215017 | − | 0.976610i | \(-0.568981\pi\) | ||||
−0.215017 | + | 0.976610i | \(0.568981\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.39375 | 0.217898 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −53.7003 | −1.82798 | −0.913990 | − | 0.405737i | \(-0.867015\pi\) | ||||
−0.913990 | + | 0.405737i | \(0.867015\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 46.2417 | 1.57226 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.5946 | 0.631507 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.4583 | −0.490465 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.86954 | 0.232499 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.21263 | 0.176219 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.3597 | 0.822569 | 0.411284 | − | 0.911507i | \(-0.365080\pi\) | ||||
0.411284 | + | 0.911507i | \(0.365080\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.5171 | −0.759482 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.00559 | 0.101261 | 0.0506305 | − | 0.998717i | \(-0.483877\pi\) | ||||
0.0506305 | + | 0.998717i | \(0.483877\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8422 | 0.667745 | 0.333872 | − | 0.942618i | \(-0.391645\pi\) | ||||
0.333872 | + | 0.942618i | \(0.391645\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.6467 | 0.391500 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.19535 | −0.308750 | −0.154375 | − | 0.988012i | \(-0.549336\pi\) | ||||
−0.154375 | + | 0.988012i | \(0.549336\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.9173 | −0.466771 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.14374 | −0.0383166 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23.1927 | 0.776116 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.4309 | 1.08405 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.5777 | −0.452840 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.1145 | 0.370278 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.62658 | −0.287074 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.675046 | 0.0224393 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −55.1117 | −1.82995 | −0.914977 | − | 0.403507i | \(-0.867791\pi\) | ||||
−0.914977 | + | 0.403507i | \(0.867791\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.11227 | 0.235899 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.1678 | −1.43021 | −0.715107 | − | 0.699015i | \(-0.753622\pi\) | ||||
−0.715107 | + | 0.699015i | \(0.753622\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.4128 | 0.344614 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.91394 | −0.261627 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.1306 | −0.400586 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.83265 | −0.258375 | −0.129188 | − | 0.991620i | \(-0.541237\pi\) | ||||
−0.129188 | + | 0.991620i | \(0.541237\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.1371 | −0.663539 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.57074 | 0.150285 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.16550 | 0.301034 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.9070 | 0.357847 | 0.178923 | − | 0.983863i | \(-0.442739\pi\) | ||||
0.178923 | + | 0.983863i | \(0.442739\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.8681 | −0.651150 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.9556 | −0.424147 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18.5546 | −0.606799 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −53.4124 | −1.74491 | −0.872453 | − | 0.488697i | \(-0.837472\pi\) | ||||
−0.872453 | + | 0.488697i | \(0.837472\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.8936 | 0.420766 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.56819 | 0.0837207 | 0.0418604 | − | 0.999123i | \(-0.486672\pi\) | ||||
0.0418604 | + | 0.999123i | \(0.486672\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −46.1775 | −1.50375 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.00004 | −0.0650615 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.6747 | 0.736827 | 0.368414 | − | 0.929662i | \(-0.379901\pi\) | ||||
0.368414 | + | 0.929662i | \(0.379901\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.2814 | 0.884660 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.2443 | −1.14168 | −0.570838 | − | 0.821063i | \(-0.693382\pi\) | ||||
−0.570838 | + | 0.821063i | \(0.693382\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −46.7128 | −1.51159 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.29770 | 0.300552 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.35999 | −0.237666 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.2103 | −0.910011 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.98925 | 0.160776 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −61.6075 | −1.98322 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.6851 | 1.56561 | 0.782804 | − | 0.622268i | \(-0.213789\pi\) | ||||
0.782804 | + | 0.622268i | \(0.213789\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.3520 | 0.589552 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.7782 | −0.987718 | −0.493859 | − | 0.869542i | \(-0.664414\pi\) | ||||
−0.493859 | + | 0.869542i | \(0.664414\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.23367 | 0.263959 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.9491 | 0.606234 | 0.303117 | − | 0.952953i | \(-0.401973\pi\) | ||||
0.303117 | + | 0.952953i | \(0.401973\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.0333 | 0.320667 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.6880 | 0.500879 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53.9304 | 1.72011 | 0.860056 | − | 0.510200i | \(-0.170429\pi\) | ||||
0.860056 | + | 0.510200i | \(0.170429\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.1589 | −0.387416 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.54584 | −0.176526 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 62.3036 | 1.98114 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 58.1777 | 1.84807 | 0.924037 | − | 0.382303i | \(-0.124869\pi\) | ||||
0.924037 | + | 0.382303i | \(0.124869\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.4726 | 0.459273 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −57.6440 | −1.82744 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.3857 | −1.18402 | −0.592009 | − | 0.805931i | \(-0.701665\pi\) | ||||
−0.592009 | + | 0.805931i | \(0.701665\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.90945 | 0.0604124 |
(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 | 4056.2.a.bh.1.5 | ✓ | 6 | |
4.3 | odd | 2 | 8112.2.a.ct.1.5 | 6 | |||
13.5 | odd | 4 | 4056.2.c.r.337.4 | 12 | |||
13.8 | odd | 4 | 4056.2.c.r.337.9 | 12 | |||
13.12 | even | 2 | 4056.2.a.bi.1.2 | yes | 6 | ||
52.51 | odd | 2 | 8112.2.a.cu.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4056.2.a.bh.1.5 | ✓ | 6 | 1.1 | even | 1 | trivial | |
4056.2.a.bi.1.2 | yes | 6 | 13.12 | even | 2 | ||
4056.2.c.r.337.4 | 12 | 13.5 | odd | 4 | |||
4056.2.c.r.337.9 | 12 | 13.8 | odd | 4 | |||
8112.2.a.ct.1.5 | 6 | 4.3 | odd | 2 | |||
8112.2.a.cu.1.2 | 6 | 52.51 | odd | 2 |