Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2760,2,Mod(1,2760)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2760, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2760.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2760.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: | \(22.0387109579\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
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 | 1.1 | ||
Root | \(-2.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2760.1 |
$q$-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 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.37228 | −0.896638 | −0.448319 | − | 0.893874i | \(-0.647977\pi\) | ||||
−0.448319 | + | 0.893874i | \(0.647977\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000 | 1.20605 | 0.603023 | − | 0.797724i | \(-0.293963\pi\) | ||||
0.603023 | + | 0.797724i | \(0.293963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.74456 | −1.87061 | −0.935303 | − | 0.353849i | \(-0.884873\pi\) | ||||
−0.935303 | + | 0.353849i | \(0.884873\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.372281 | −0.0902915 | −0.0451457 | − | 0.998980i | \(-0.514375\pi\) | ||||
−0.0451457 | + | 0.998980i | \(0.514375\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.37228 | 0.517674 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.372281 | 0.0691309 | 0.0345655 | − | 0.999402i | \(-0.488995\pi\) | ||||
0.0345655 | + | 0.999402i | \(0.488995\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.37228 | −0.426074 | −0.213037 | − | 0.977044i | \(-0.568336\pi\) | ||||
−0.213037 | + | 0.977044i | \(0.568336\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | −0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.37228 | −0.400989 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.372281 | 0.0612027 | 0.0306013 | − | 0.999532i | \(-0.490258\pi\) | ||||
0.0306013 | + | 0.999532i | \(0.490258\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.74456 | 1.07999 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.11684 | 1.42381 | 0.711906 | − | 0.702275i | \(-0.247832\pi\) | ||||
0.711906 | + | 0.702275i | \(0.247832\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.74456 | 0.692066 | 0.346033 | − | 0.938222i | \(-0.387529\pi\) | ||||
0.346033 | + | 0.938222i | \(0.387529\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.37228 | −0.196040 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.372281 | 0.0521298 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.37228 | −0.600579 | −0.300290 | − | 0.953848i | \(-0.597083\pi\) | ||||
−0.300290 | + | 0.953848i | \(0.597083\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.3723 | 1.87111 | 0.935556 | − | 0.353179i | \(-0.114899\pi\) | ||||
0.935556 | + | 0.353179i | \(0.114899\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.37228 | −0.298879 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.74456 | −0.836560 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.62772 | 1.17621 | 0.588107 | − | 0.808783i | \(-0.299874\pi\) | ||||
0.588107 | + | 0.808783i | \(0.299874\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.37228 | −0.281538 | −0.140769 | − | 0.990042i | \(-0.544957\pi\) | ||||
−0.140769 | + | 0.990042i | \(0.544957\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.25544 | −0.146938 | −0.0734689 | − | 0.997298i | \(-0.523407\pi\) | ||||
−0.0734689 | + | 0.997298i | \(0.523407\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.48913 | −1.08139 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.48913 | 1.06761 | 0.533805 | − | 0.845608i | \(-0.320762\pi\) | ||||
0.533805 | + | 0.845608i | \(0.320762\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.8614 | 1.74102 | 0.870508 | − | 0.492155i | \(-0.163791\pi\) | ||||
0.870508 | + | 0.492155i | \(0.163791\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.372281 | −0.0403796 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.372281 | −0.0399127 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.74456 | 0.714922 | 0.357461 | − | 0.933928i | \(-0.383642\pi\) | ||||
0.357461 | + | 0.933928i | \(0.383642\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.0000 | 1.67726 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.37228 | 0.245994 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.48913 | −0.760405 | −0.380203 | − | 0.924903i | \(-0.624146\pi\) | ||||
−0.380203 | + | 0.924903i | \(0.624146\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.62772 | −0.758986 | −0.379493 | − | 0.925195i | \(-0.623902\pi\) | ||||
−0.379493 | + | 0.925195i | \(0.623902\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.00000 | −0.788263 | −0.394132 | − | 0.919054i | \(-0.628955\pi\) | ||||
−0.394132 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.37228 | 0.231511 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.62772 | −0.157358 | −0.0786788 | − | 0.996900i | \(-0.525070\pi\) | ||||
−0.0786788 | + | 0.996900i | \(0.525070\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.74456 | −0.646012 | −0.323006 | − | 0.946397i | \(-0.604693\pi\) | ||||
−0.323006 | + | 0.946397i | \(0.604693\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.372281 | −0.0353354 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.11684 | 0.857641 | 0.428820 | − | 0.903390i | \(-0.358929\pi\) | ||||
0.428820 | + | 0.903390i | \(0.358929\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.74456 | −0.623535 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.883156 | 0.0809588 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.11684 | −0.822038 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.7446 | 1.13090 | 0.565449 | − | 0.824784i | \(-0.308703\pi\) | ||||
0.565449 | + | 0.824784i | \(0.308703\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.48913 | −0.822812 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.4891 | 0.981582 | 0.490791 | − | 0.871277i | \(-0.336708\pi\) | ||||
0.490791 | + | 0.871277i | \(0.336708\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.3723 | 1.21904 | 0.609520 | − | 0.792770i | \(-0.291362\pi\) | ||||
0.609520 | + | 0.792770i | \(0.291362\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.74456 | −0.399564 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −26.9783 | −2.25603 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.372281 | 0.0309163 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.37228 | 0.113184 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.4891 | −1.59661 | −0.798306 | − | 0.602252i | \(-0.794270\pi\) | ||||
−0.798306 | + | 0.602252i | \(0.794270\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0000 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.372281 | −0.0300972 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.37228 | −0.190546 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.6060 | 1.80415 | 0.902076 | − | 0.431576i | \(-0.142042\pi\) | ||||
0.902076 | + | 0.431576i | \(0.142042\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.37228 | 0.346744 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.37228 | −0.186962 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.7446 | 1.31154 | 0.655768 | − | 0.754963i | \(-0.272345\pi\) | ||||
0.655768 | + | 0.754963i | \(0.272345\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.00000 | −0.311400 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.7446 | 0.986204 | 0.493102 | − | 0.869972i | \(-0.335863\pi\) | ||||
0.493102 | + | 0.869972i | \(0.335863\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.4891 | 2.49916 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000 | 0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.2337 | 1.53834 | 0.769169 | − | 0.639045i | \(-0.220670\pi\) | ||||
0.769169 | + | 0.639045i | \(0.220670\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.37228 | −0.179328 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.3723 | −1.08029 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.4891 | −1.00822 | −0.504112 | − | 0.863638i | \(-0.668180\pi\) | ||||
−0.504112 | + | 0.863638i | \(0.668180\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.2337 | 1.50396 | 0.751979 | − | 0.659187i | \(-0.229099\pi\) | ||||
0.751979 | + | 0.659187i | \(0.229099\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.372281 | 0.0273707 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.48913 | −0.108896 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.37228 | 0.172558 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.2337 | −1.02991 | −0.514957 | − | 0.857216i | \(-0.672192\pi\) | ||||
−0.514957 | + | 0.857216i | \(0.672192\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.25544 | −0.666221 | −0.333110 | − | 0.942888i | \(-0.608098\pi\) | ||||
−0.333110 | + | 0.942888i | \(0.608098\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.74456 | 0.482988 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.4891 | −0.818566 | −0.409283 | − | 0.912407i | \(-0.634221\pi\) | ||||
−0.409283 | + | 0.912407i | \(0.634221\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.7446 | 0.903438 | 0.451719 | − | 0.892160i | \(-0.350811\pi\) | ||||
0.451719 | + | 0.892160i | \(0.350811\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.62772 | −0.679087 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.883156 | −0.0619854 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.11684 | 0.636748 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0000 | 1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.86141 | −0.541202 | −0.270601 | − | 0.962692i | \(-0.587222\pi\) | ||||
−0.270601 | + | 0.962692i | \(0.587222\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.37228 | 0.162546 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.00000 | −0.272798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.62772 | 0.382034 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.25544 | 0.0848346 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.51087 | 0.168900 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.7446 | 1.92488 | 0.962439 | − | 0.271498i | \(-0.0875189\pi\) | ||||
0.962439 | + | 0.271498i | \(0.0875189\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.0000 | 0.796468 | 0.398234 | − | 0.917284i | \(-0.369623\pi\) | ||||
0.398234 | + | 0.917284i | \(0.369623\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.2554 | 1.14027 | 0.570136 | − | 0.821551i | \(-0.306891\pi\) | ||||
0.570136 | + | 0.821551i | \(0.306891\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.48913 | 0.624339 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.23369 | 0.539407 | 0.269703 | − | 0.962943i | \(-0.413074\pi\) | ||||
0.269703 | + | 0.962943i | \(0.413074\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.74456 | 0.309501 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.48913 | −0.616385 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.62772 | −0.364027 | −0.182013 | − | 0.983296i | \(-0.558261\pi\) | ||||
−0.182013 | + | 0.983296i | \(0.558261\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.7446 | −1.20744 | −0.603722 | − | 0.797195i | \(-0.706316\pi\) | ||||
−0.603722 | + | 0.797195i | \(0.706316\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.37228 | −0.0876718 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.9783 | −1.71658 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.8614 | −1.00518 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.25544 | −0.457959 | −0.228980 | − | 0.973431i | \(-0.573539\pi\) | ||||
−0.228980 | + | 0.973431i | \(0.573539\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.372281 | 0.0233132 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.4891 | 0.716672 | 0.358336 | − | 0.933593i | \(-0.383344\pi\) | ||||
0.358336 | + | 0.933593i | \(0.383344\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.883156 | −0.0548766 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.372281 | 0.0230436 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.8614 | −1.71801 | −0.859004 | − | 0.511969i | \(-0.828916\pi\) | ||||
−0.859004 | + | 0.511969i | \(0.828916\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.37228 | −0.268587 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.74456 | −0.412761 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.8614 | −0.845145 | −0.422572 | − | 0.906329i | \(-0.638873\pi\) | ||||
−0.422572 | + | 0.906329i | \(0.638873\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.1168 | −1.40425 | −0.702124 | − | 0.712055i | \(-0.747765\pi\) | ||||
−0.702124 | + | 0.712055i | \(0.747765\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.0000 | −0.968364 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.00000 | 0.241209 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.0000 | 1.32185 | 0.660926 | − | 0.750451i | \(-0.270164\pi\) | ||||
0.660926 | + | 0.750451i | \(0.270164\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.37228 | −0.142025 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.2337 | −0.729801 | −0.364900 | − | 0.931047i | \(-0.618897\pi\) | ||||
−0.364900 | + | 0.931047i | \(0.618897\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.37228 | 0.378793 | 0.189396 | − | 0.981901i | \(-0.439347\pi\) | ||||
0.189396 | + | 0.981901i | \(0.439347\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.00000 | −0.236940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.6277 | −1.27664 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8614 | −0.991847 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.48913 | 0.439020 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.86141 | 0.576110 | 0.288055 | − | 0.957614i | \(-0.406991\pi\) | ||||
0.288055 | + | 0.957614i | \(0.406991\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.3723 | 0.836787 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.00000 | −0.232104 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.74456 | −0.390048 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.48913 | 0.546944 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.62772 | 0.438201 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.00000 | −0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.00000 | −0.228292 | −0.114146 | − | 0.993464i | \(-0.536413\pi\) | ||||
−0.114146 | + | 0.993464i | \(0.536413\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.00000 | 0.453638 | 0.226819 | − | 0.973937i | \(-0.427167\pi\) | ||||
0.226819 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.8614 | −1.46177 | −0.730887 | − | 0.682499i | \(-0.760893\pi\) | ||||
−0.730887 | + | 0.682499i | \(0.760893\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.37228 | −0.133663 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 31.4891 | 1.76861 | 0.884303 | − | 0.466914i | \(-0.154634\pi\) | ||||
0.884303 | + | 0.466914i | \(0.154634\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.48913 | 0.0833750 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.62772 | 0.0908504 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.48913 | −0.0828571 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.74456 | −0.374121 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.74456 | 0.372975 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.2554 | −0.620532 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.1168 | 1.05076 | 0.525378 | − | 0.850869i | \(-0.323924\pi\) | ||||
0.525378 | + | 0.850869i | \(0.323924\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.372281 | 0.0204009 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.62772 | 0.526018 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.51087 | −0.245723 | −0.122862 | − | 0.992424i | \(-0.539207\pi\) | ||||
−0.122862 | + | 0.992424i | \(0.539207\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.11684 | −0.495159 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.48913 | −0.513865 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.8614 | 1.07242 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.00000 | −0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.00000 | 0.214731 | 0.107366 | − | 0.994220i | \(-0.465758\pi\) | ||||
0.107366 | + | 0.994220i | \(0.465758\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.1168 | 0.702129 | 0.351064 | − | 0.936351i | \(-0.385820\pi\) | ||||
0.351064 | + | 0.936351i | \(0.385820\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.74456 | 0.359998 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.0000 | −0.745145 | −0.372572 | − | 0.928003i | \(-0.621524\pi\) | ||||
−0.372572 | + | 0.928003i | \(0.621524\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.37228 | −0.125908 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.883156 | −0.0467416 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.7228 | 1.67427 | 0.837133 | − | 0.546999i | \(-0.184230\pi\) | ||||
0.837133 | + | 0.546999i | \(0.184230\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.00000 | −0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.25544 | −0.0657126 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.86141 | 0.201564 | 0.100782 | − | 0.994909i | \(-0.467866\pi\) | ||||
0.100782 | + | 0.994909i | \(0.467866\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.11684 | 0.474604 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.3723 | 0.538502 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.51087 | −0.129317 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.4891 | −0.692890 | −0.346445 | − | 0.938070i | \(-0.612611\pi\) | ||||
−0.346445 | + | 0.938070i | \(0.612611\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.7446 | −0.652924 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.883156 | −0.0451272 | −0.0225636 | − | 0.999745i | \(-0.507183\pi\) | ||||
−0.0225636 | + | 0.999745i | \(0.507183\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.48913 | −0.483611 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.00000 | −0.203331 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.4891 | −0.988138 | −0.494069 | − | 0.869423i | \(-0.664491\pi\) | ||||
−0.494069 | + | 0.869423i | \(0.664491\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.372281 | −0.0188271 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.00000 | 0.201773 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.48913 | 0.477450 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.233688 | −0.0117285 | −0.00586423 | − | 0.999983i | \(-0.501867\pi\) | ||||
−0.00586423 | + | 0.999983i | \(0.501867\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.48913 | 0.475050 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.510875 | 0.0255119 | 0.0127559 | − | 0.999919i | \(-0.495940\pi\) | ||||
0.0127559 | + | 0.999919i | \(0.495940\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.0000 | 0.797017 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.48913 | 0.0738132 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.3723 | 1.00734 | 0.503672 | − | 0.863895i | \(-0.331982\pi\) | ||||
0.503672 | + | 0.863895i | \(0.331982\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.4891 | −0.566717 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −34.0951 | −1.67771 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.8614 | 0.778606 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.3723 | −0.703814 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.7446 | −0.718606 | −0.359303 | − | 0.933221i | \(-0.616986\pi\) | ||||
−0.359303 | + | 0.933221i | \(0.616986\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.74456 | 0.230689 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.372281 | −0.0180583 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.74456 | 0.229605 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 26.9783 | 1.30252 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.0000 | −1.54139 | −0.770693 | − | 0.637207i | \(-0.780090\pi\) | ||||
−0.770693 | + | 0.637207i | \(0.780090\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.0951 | −1.54239 | −0.771196 | − | 0.636598i | \(-0.780341\pi\) | ||||
−0.771196 | + | 0.636598i | \(0.780341\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.372281 | −0.0178495 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.00000 | 0.191346 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.9783 | −0.905782 | −0.452891 | − | 0.891566i | \(-0.649607\pi\) | ||||
−0.452891 | + | 0.891566i | \(0.649607\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.37228 | −0.0653467 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.7446 | −1.55574 | −0.777871 | − | 0.628425i | \(-0.783700\pi\) | ||||
−0.777871 | + | 0.628425i | \(0.783700\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.74456 | 0.319723 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.4891 | 0.921804 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.8614 | 1.03170 | 0.515852 | − | 0.856678i | \(-0.327476\pi\) | ||||
0.515852 | + | 0.856678i | \(0.327476\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.4674 | 1.71718 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.0000 | −0.751746 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.0000 | 0.750092 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.60597 | 0.121902 | 0.0609511 | − | 0.998141i | \(-0.480587\pi\) | ||||
0.0609511 | + | 0.998141i | \(0.480587\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.372281 | 0.0173766 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.4674 | 1.60531 | 0.802653 | − | 0.596446i | \(-0.203421\pi\) | ||||
0.802653 | + | 0.596446i | \(0.203421\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.00000 | −0.371792 | −0.185896 | − | 0.982569i | \(-0.559519\pi\) | ||||
−0.185896 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.37228 | 0.110012 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.35053 | 0.432691 | 0.216346 | − | 0.976317i | \(-0.430586\pi\) | ||||
0.216346 | + | 0.976317i | \(0.430586\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.8397 | −1.05464 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.6060 | −1.04163 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.0000 | −0.735681 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.37228 | −0.200193 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.7228 | 1.08392 | 0.541962 | − | 0.840403i | \(-0.317682\pi\) | ||||
0.541962 | + | 0.840403i | \(0.317682\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.51087 | −0.114486 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.37228 | 0.107943 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.48913 | −0.340064 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.7228 | −1.07498 | −0.537492 | − | 0.843269i | \(-0.680628\pi\) | ||||
−0.537492 | + | 0.843269i | \(0.680628\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.7446 | −0.757215 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.3723 | −1.00965 | −0.504823 | − | 0.863223i | \(-0.668442\pi\) | ||||
−0.504823 | + | 0.863223i | \(0.668442\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.138593 | −0.00624193 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.00000 | 0.179787 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.62772 | 0.252438 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.39403 | 0.151938 | 0.0759688 | − | 0.997110i | \(-0.475795\pi\) | ||||
0.0759688 | + | 0.997110i | \(0.475795\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.7446 | −0.569385 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −34.3723 | −1.53258 | −0.766292 | − | 0.642492i | \(-0.777900\pi\) | ||||
−0.766292 | + | 0.642492i | \(0.777900\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.62772 | −0.339429 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −32.4891 | −1.44289 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.9783 | 1.10714 | 0.553571 | − | 0.832802i | \(-0.313265\pi\) | ||||
0.553571 | + | 0.832802i | \(0.313265\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.97825 | 0.131750 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.00000 | −0.176604 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.00000 | −0.352522 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.9783 | 0.834663 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.2337 | −0.888160 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.2337 | −0.535968 | −0.267984 | − | 0.963423i | \(-0.586357\pi\) | ||||
−0.267984 | + | 0.963423i | \(0.586357\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.97825 | −0.305138 | −0.152569 | − | 0.988293i | \(-0.548755\pi\) | ||||
−0.152569 | + | 0.988293i | \(0.548755\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.37228 | 0.103535 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.883156 | 0.0384709 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.3723 | 0.623704 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −61.4891 | −2.66339 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.62772 | −0.0703724 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.4891 | 0.582099 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.48913 | −0.236433 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.0000 | 0.601907 | 0.300954 | − | 0.953639i | \(-0.402695\pi\) | ||||
0.300954 | + | 0.953639i | \(0.402695\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.2337 | −0.868311 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.74456 | −0.288905 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.00000 | −0.171028 | −0.0855138 | − | 0.996337i | \(-0.527253\pi\) | ||||
−0.0855138 | + | 0.996337i | \(0.527253\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.48913 | 0.0634389 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.5109 | −0.957260 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.372281 | −0.0158025 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.3505 | −0.650423 | −0.325211 | − | 0.945641i | \(-0.605435\pi\) | ||||
−0.325211 | + | 0.945641i | \(0.605435\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.9783 | 1.14106 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.48913 | 0.0628709 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.62772 | 0.0686002 | 0.0343001 | − | 0.999412i | \(-0.489080\pi\) | ||||
0.0343001 | + | 0.999412i | \(0.489080\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.11684 | 0.383549 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.37228 | −0.0996265 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.4891 | −0.984715 | −0.492358 | − | 0.870393i | \(-0.663865\pi\) | ||||
−0.492358 | + | 0.870393i | \(0.663865\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.2337 | −1.43264 | −0.716318 | − | 0.697774i | \(-0.754174\pi\) | ||||
−0.716318 | + | 0.697774i | \(0.754174\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.2337 | 0.594621 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.7446 | −0.780346 | −0.390173 | − | 0.920741i | \(-0.627585\pi\) | ||||
−0.390173 | + | 0.920741i | \(0.627585\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.25544 | 0.384643 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −37.6277 | −1.56106 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.4891 | −0.724326 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.74456 | −0.278853 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.2337 | −0.422390 | −0.211195 | − | 0.977444i | \(-0.567735\pi\) | ||||
−0.211195 | + | 0.977444i | \(0.567735\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.48913 | −0.390993 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.4891 | 0.472599 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −32.9783 | −1.35425 | −0.677127 | − | 0.735866i | \(-0.736775\pi\) | ||||
−0.677127 | + | 0.735866i | \(0.736775\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.883156 | 0.0362059 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.7446 | −0.521600 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.4891 | −1.36833 | −0.684164 | − | 0.729328i | \(-0.739833\pi\) | ||||
−0.684164 | + | 0.729328i | \(0.739833\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.86141 | −0.402255 | −0.201128 | − | 0.979565i | \(-0.564461\pi\) | ||||
−0.201128 | + | 0.979565i | \(0.564461\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.62772 | 0.392071 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.00000 | 0.203279 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −44.7446 | −1.81613 | −0.908063 | − | 0.418834i | \(-0.862439\pi\) | ||||
−0.908063 | + | 0.418834i | \(0.862439\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.883156 | 0.0357873 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.0000 | −1.29458 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.5109 | −0.666868 | −0.333434 | − | 0.942773i | \(-0.608207\pi\) | ||||
−0.333434 | + | 0.942773i | \(0.608207\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.11684 | −0.367627 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.3505 | 1.26212 | 0.631062 | − | 0.775732i | \(-0.282619\pi\) | ||||
0.631062 | + | 0.775732i | \(0.282619\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.97825 | −0.280480 | −0.140240 | − | 0.990118i | \(-0.544787\pi\) | ||||
−0.140240 | + | 0.990118i | \(0.544787\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.0000 | −0.641026 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.0000 | −0.638978 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.138593 | −0.00552608 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.7446 | −1.14430 | −0.572151 | − | 0.820148i | \(-0.693891\pi\) | ||||
−0.572151 | + | 0.820148i | \(0.693891\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.86141 | 0.312463 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.7446 | 0.505753 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.25544 | 0.366714 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.37228 | −0.0938460 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.7228 | −0.542019 | −0.271009 | − | 0.962577i | \(-0.587357\pi\) | ||||
−0.271009 | + | 0.962577i | \(0.587357\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.6277 | 1.64164 | 0.820818 | − | 0.571189i | \(-0.193518\pi\) | ||||
0.820818 | + | 0.571189i | \(0.193518\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.00000 | 0.157500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.48913 | 0.0585436 | 0.0292718 | − | 0.999571i | \(-0.490681\pi\) | ||||
0.0292718 | + | 0.999571i | \(0.490681\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 57.4891 | 2.25665 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.62772 | −0.220568 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.2337 | −0.948337 | −0.474169 | − | 0.880434i | \(-0.657251\pi\) | ||||
−0.474169 | + | 0.880434i | \(0.657251\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.00000 | −0.156293 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.25544 | −0.0489793 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.9783 | −0.895106 | −0.447553 | − | 0.894258i | \(-0.647704\pi\) | ||||
−0.447553 | + | 0.894258i | \(0.647704\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000 | 0.855701 | 0.427850 | − | 0.903850i | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.51087 | −0.0975143 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.48913 | −0.367972 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.372281 | 0.0144148 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −28.7446 | −1.11133 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.00000 | −0.308837 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.4891 | −1.52219 | −0.761097 | − | 0.648638i | \(-0.775339\pi\) | ||||
−0.761097 | + | 0.648638i | \(0.775339\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.8832 | 0.879471 | 0.439736 | − | 0.898127i | \(-0.355072\pi\) | ||||
0.439736 | + | 0.898127i | \(0.355072\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.7663 | 0.681808 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.0000 | −0.459841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.23369 | 0.0854697 | 0.0427348 | − | 0.999086i | \(-0.486393\pi\) | ||||
0.0427348 | + | 0.999086i | \(0.486393\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.4891 | 0.438977 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.2554 | −0.658336 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.4891 | 1.12345 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.4891 | 0.817485 | 0.408742 | − | 0.912650i | \(-0.365967\pi\) | ||||
0.408742 | + | 0.912650i | \(0.365967\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.48913 | −0.360462 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.3723 | 0.545172 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.39403 | −0.128558 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.23369 | −0.311427 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 51.9565 | 1.96237 | 0.981185 | − | 0.193070i | \(-0.0618445\pi\) | ||||
0.981185 | + | 0.193070i | \(0.0618445\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.48913 | 0.0561634 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.74456 | −0.178691 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.0951 | 0.680536 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.9783 | 0.938078 | 0.469039 | − | 0.883177i | \(-0.344600\pi\) | ||||
0.469039 | + | 0.883177i | \(0.344600\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.48913 | 0.355870 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.37228 | −0.0888426 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26.9783 | −1.00893 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.62772 | 0.210171 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.0951 | −1.27153 | −0.635766 | − | 0.771882i | \(-0.719316\pi\) | ||||
−0.635766 | + | 0.771882i | \(0.719316\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.9783 | 0.706787 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.7446 | 0.697118 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.372281 | 0.0138262 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.37228 | 0.0879830 | 0.0439915 | − | 0.999032i | \(-0.485993\pi\) | ||||
0.0439915 | + | 0.999032i | \(0.485993\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.48913 | 0.0550773 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.1168 | −0.632225 | −0.316113 | − | 0.948722i | \(-0.602378\pi\) | ||||
−0.316113 | + | 0.948722i | \(0.602378\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.37228 | 0.0506174 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 38.5109 | 1.41857 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.6277 | 1.23702 | 0.618508 | − | 0.785779i | \(-0.287738\pi\) | ||||
0.618508 | + | 0.785779i | \(0.287738\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26.9783 | 0.991071 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.9783 | −0.402753 | −0.201376 | − | 0.979514i | \(-0.564541\pi\) | ||||
−0.201376 | + | 0.979514i | \(0.564541\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.4891 | −0.714026 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.8614 | 0.580339 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.86141 | 0.141093 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.0000 | −0.583848 | −0.291924 | − | 0.956441i | \(-0.594295\pi\) | ||||
−0.291924 | + | 0.956441i | \(0.594295\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.25544 | 0.264403 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.0000 | 0.582300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.6060 | 0.530863 | 0.265431 | − | 0.964130i | \(-0.414486\pi\) | ||||
0.265431 | + | 0.964130i | \(0.414486\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.00000 | −0.145191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.8397 | −1.04544 | −0.522718 | − | 0.852505i | \(-0.675082\pi\) | ||||
−0.522718 | + | 0.852505i | \(0.675082\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.0000 | 0.579239 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.372281 | −0.0134599 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −96.9348 | −3.50011 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.4891 | 1.56826 | 0.784129 | − | 0.620598i | \(-0.213110\pi\) | ||||
0.784129 | + | 0.620598i | \(0.213110\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.4891 | −0.413771 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.9783 | 1.47389 | 0.736943 | − | 0.675955i | \(-0.236269\pi\) | ||||
0.736943 | + | 0.675955i | \(0.236269\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.37228 | −0.0852149 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.883156 | 0.0316830 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 36.4674 | 1.30658 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.48913 | −0.339548 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.372281 | −0.0133042 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.6060 | 0.806842 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.37228 | −0.227147 | −0.113574 | − | 0.993530i | \(-0.536230\pi\) | ||||
−0.113574 | + | 0.993530i | \(0.536230\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 27.8614 | 0.991892 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.6277 | −0.768993 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.4891 | 0.479013 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.37228 | 0.155069 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.11684 | −0.0395606 | −0.0197803 | − | 0.999804i | \(-0.506297\pi\) | ||||
−0.0197803 | + | 0.999804i | \(0.506297\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.76631 | −0.0624876 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.74456 | 0.238307 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.02175 | −0.177214 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.37228 | −0.0836119 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.8614 | 0.487945 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.3723 | 1.27878 | 0.639391 | − | 0.768882i | \(-0.279187\pi\) | ||||
0.639391 | + | 0.768882i | \(0.279187\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.1168 | 1.23312 | 0.616560 | − | 0.787308i | \(-0.288526\pi\) | ||||
0.616560 | + | 0.787308i | \(0.288526\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.1168 | 0.810743 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.7446 | 0.586536 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.0000 | −0.559769 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.0000 | 0.559085 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.9783 | −1.29055 | −0.645275 | − | 0.763950i | \(-0.723257\pi\) | ||||
−0.645275 | + | 0.763950i | \(0.723257\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.9783 | 1.21927 | 0.609633 | − | 0.792684i | \(-0.291317\pi\) | ||||
0.609633 | + | 0.792684i | \(0.291317\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.00000 | −0.139262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.39403 | −0.118022 | −0.0590110 | − | 0.998257i | \(-0.518795\pi\) | ||||
−0.0590110 | + | 0.998257i | \(0.518795\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.0951 | −0.697931 | −0.348966 | − | 0.937135i | \(-0.613467\pi\) | ||||
−0.348966 | + | 0.937135i | \(0.613467\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.0000 | −0.763172 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.510875 | 0.0177008 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.7446 | 0.441044 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.37228 | 0.0819980 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.25544 | 0.112390 | 0.0561951 | − | 0.998420i | \(-0.482103\pi\) | ||||
0.0561951 | + | 0.998420i | \(0.482103\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8614 | −0.995221 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.2337 | 0.421351 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 32.4891 | 1.11766 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.8614 | −0.407563 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.37228 | −0.218696 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.372281 | 0.0127616 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.9783 | −0.444367 | −0.222183 | − | 0.975005i | \(-0.571318\pi\) | ||||
−0.222183 | + | 0.975005i | \(0.571318\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.4674 | −0.630834 | −0.315417 | − | 0.948953i | \(-0.602144\pi\) | ||||
−0.315417 | + | 0.948953i | \(0.602144\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.6060 | 0.430110 | 0.215055 | − | 0.976602i | \(-0.431007\pi\) | ||||
0.215055 | + | 0.976602i | \(0.431007\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.6277 | 0.737071 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.74456 | 0.161507 | 0.0807534 | − | 0.996734i | \(-0.474267\pi\) | ||||
0.0807534 | + | 0.996734i | \(0.474267\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.2337 | 0.687966 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.8614 | 0.572643 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37.9565 | 1.28759 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −64.9348 | −2.20023 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.48913 | −0.253468 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.37228 | −0.0801977 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43.4891 | −1.46852 | −0.734262 | − | 0.678867i | \(-0.762471\pi\) | ||||
−0.734262 | + | 0.678867i | \(0.762471\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.86141 | −0.332617 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.0000 | −0.741199 | −0.370599 | − | 0.928793i | \(-0.620848\pi\) | ||||
−0.370599 | + | 0.928793i | \(0.620848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.2119 | 0.983060 | 0.491530 | − | 0.870861i | \(-0.336438\pi\) | ||||
0.491530 | + | 0.870861i | \(0.336438\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.3723 | −0.483119 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.7228 | 1.06515 | 0.532574 | − | 0.846383i | \(-0.321225\pi\) | ||||
0.532574 | + | 0.846383i | \(0.321225\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.2337 | −1.01401 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.00000 | 0.134005 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.9783 | 0.635083 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.4891 | −0.450892 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.74456 | 0.225194 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.883156 | −0.0294549 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.62772 | 0.0542272 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.48913 | −0.315778 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.2337 | 0.672591 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.3723 | −0.477224 | −0.238612 | − | 0.971115i | \(-0.576692\pi\) | ||||
−0.238612 | + | 0.971115i | \(0.576692\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.62772 | −0.252995 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.4674 | 0.413063 | 0.206531 | − | 0.978440i | \(-0.433782\pi\) | ||||
0.206531 | + | 0.978440i | \(0.433782\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 63.4456 | 2.09974 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.00000 | 0.0661180 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.48913 | 0.313359 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.5109 | 0.478670 | 0.239335 | − | 0.970937i | \(-0.423071\pi\) | ||||
0.239335 | + | 0.970937i | \(0.423071\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.00000 | 0.131804 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.0000 | 0.526646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.372281 | 0.0122405 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.00000 | −0.262754 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.60597 | −0.216735 | −0.108367 | − | 0.994111i | \(-0.534562\pi\) | ||||
−0.108367 | + | 0.994111i | \(0.534562\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.48913 | −0.179899 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.00000 | −0.261908 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.48913 | −0.0486996 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.4674 | −1.12600 | −0.563000 | − | 0.826457i | \(-0.690353\pi\) | ||||
−0.563000 | + | 0.826457i | \(0.690353\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.8614 | 0.843955 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.9783 | 1.07506 | 0.537530 | − | 0.843245i | \(-0.319357\pi\) | ||||
0.537530 | + | 0.843245i | \(0.319357\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.11684 | 0.296885 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.37228 | 0.0771703 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.02175 | 0.293167 | 0.146584 | − | 0.989198i | \(-0.453172\pi\) | ||||
0.146584 | + | 0.989198i | \(0.453172\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.46738 | 0.274863 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31.4891 | −1.02110 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.48913 | −0.242597 | −0.121298 | − | 0.992616i | \(-0.538706\pi\) | ||||
−0.121298 | + | 0.992616i | \(0.538706\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.2337 | −0.460591 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.48913 | −0.0481366 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27.2554 | −0.880124 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.3723 | −0.818461 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.62772 | −0.0524525 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.25544 | −0.297943 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.2337 | 1.48678 | 0.743388 | − | 0.668861i | \(-0.233218\pi\) | ||||
0.743388 | + | 0.668861i | \(0.233218\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.48913 | 0.0478376 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.4891 | −0.689619 | −0.344809 | − | 0.938673i | \(-0.612056\pi\) | ||||
−0.344809 | + | 0.938673i | \(0.612056\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −34.0951 | −1.09304 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.74456 | 0.215999 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.3723 | 1.16365 | 0.581826 | − | 0.813313i | \(-0.302338\pi\) | ||||
0.581826 | + | 0.813313i | \(0.302338\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.9783 | 0.862229 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.74456 | −0.215337 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.1386 | −0.642321 | −0.321161 | − | 0.947025i | \(-0.604073\pi\) | ||||
−0.321161 | + | 0.947025i | \(0.604073\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.4891 | −0.366074 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.2554 | 0.358265 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.00000 | −0.127193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.8832 | −0.790440 | −0.395220 | − | 0.918587i | \(-0.629332\pi\) | ||||
−0.395220 | + | 0.918587i | \(0.629332\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19.1168 | −0.606655 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.7446 | 0.404030 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.7663 | −0.372643 | −0.186321 | − | 0.982489i | \(-0.559657\pi\) | ||||
−0.186321 | + | 0.982489i | \(0.559657\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.372281 | −0.0117785 |
(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 | 2760.2.a.o.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 8280.2.a.z.1.1 | 2 | |||
4.3 | odd | 2 | 5520.2.a.bq.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.2.a.o.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
5520.2.a.bq.1.2 | 2 | 4.3 | odd | 2 | |||
8280.2.a.z.1.1 | 2 | 3.2 | odd | 2 |