Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8712,2,Mod(1,8712)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8712, 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("8712.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8712 = 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8712.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: | \(69.5656702409\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 264) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8712.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.61803 | −1.17082 | −0.585410 | − | 0.810737i | \(-0.699067\pi\) | ||||
−0.585410 | + | 0.810737i | \(0.699067\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.236068 | −0.0892253 | −0.0446127 | − | 0.999004i | \(-0.514205\pi\) | ||||
−0.0446127 | + | 0.999004i | \(0.514205\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.23607 | 0.620174 | 0.310087 | − | 0.950708i | \(-0.399642\pi\) | ||||
0.310087 | + | 0.950708i | \(0.399642\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.85410 | 1.17729 | 0.588646 | − | 0.808391i | \(-0.299661\pi\) | ||||
0.588646 | + | 0.808391i | \(0.299661\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.61803 | −0.600618 | −0.300309 | − | 0.953842i | \(-0.597090\pi\) | ||||
−0.300309 | + | 0.953842i | \(0.597090\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.76393 | −0.367805 | −0.183903 | − | 0.982944i | \(-0.558873\pi\) | ||||
−0.183903 | + | 0.982944i | \(0.558873\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.85410 | 0.370820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.47214 | −1.57324 | −0.786618 | − | 0.617440i | \(-0.788170\pi\) | ||||
−0.786618 | + | 0.617440i | \(0.788170\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.38197 | 1.14623 | 0.573117 | − | 0.819473i | \(-0.305734\pi\) | ||||
0.573117 | + | 0.819473i | \(0.305734\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.618034 | 0.104467 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.23607 | 1.35400 | 0.677001 | − | 0.735982i | \(-0.263279\pi\) | ||||
0.677001 | + | 0.735982i | \(0.263279\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.00000 | −0.780869 | −0.390434 | − | 0.920631i | \(-0.627675\pi\) | ||||
−0.390434 | + | 0.920631i | \(0.627675\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.52786 | −0.385496 | −0.192748 | − | 0.981248i | \(-0.561740\pi\) | ||||
−0.192748 | + | 0.981248i | \(0.561740\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.85410 | −0.999774 | −0.499887 | − | 0.866091i | \(-0.666625\pi\) | ||||
−0.499887 | + | 0.866091i | \(0.666625\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.94427 | −0.992039 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.5623 | −1.45084 | −0.725422 | − | 0.688304i | \(-0.758355\pi\) | ||||
−0.725422 | + | 0.688304i | \(0.758355\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.56231 | 0.724151 | 0.362075 | − | 0.932149i | \(-0.382068\pi\) | ||||
0.362075 | + | 0.932149i | \(0.382068\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.145898 | 0.0186803 | 0.00934016 | − | 0.999956i | \(-0.497027\pi\) | ||||
0.00934016 | + | 0.999956i | \(0.497027\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.85410 | −0.726112 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.5623 | 1.90124 | 0.950619 | − | 0.310360i | \(-0.100450\pi\) | ||||
0.950619 | + | 0.310360i | \(0.100450\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.56231 | 0.897481 | 0.448740 | − | 0.893662i | \(-0.351873\pi\) | ||||
0.448740 | + | 0.893662i | \(0.351873\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.70820 | 1.13626 | 0.568130 | − | 0.822939i | \(-0.307667\pi\) | ||||
0.568130 | + | 0.822939i | \(0.307667\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.76393 | −1.09853 | −0.549264 | − | 0.835649i | \(-0.685092\pi\) | ||||
−0.549264 | + | 0.835649i | \(0.685092\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.9443 | 1.75011 | 0.875056 | − | 0.484022i | \(-0.160825\pi\) | ||||
0.875056 | + | 0.484022i | \(0.160825\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.7082 | −1.37840 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.47214 | 0.580045 | 0.290023 | − | 0.957020i | \(-0.406337\pi\) | ||||
0.290023 | + | 0.957020i | \(0.406337\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.527864 | −0.0553352 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.85410 | 0.703216 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.145898 | −0.0148137 | −0.00740685 | − | 0.999973i | \(-0.502358\pi\) | ||||
−0.00740685 | + | 0.999973i | \(0.502358\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.47214 | 0.942513 | 0.471256 | − | 0.881996i | \(-0.343801\pi\) | ||||
0.471256 | + | 0.881996i | \(0.343801\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.4721 | −1.22892 | −0.614458 | − | 0.788950i | \(-0.710625\pi\) | ||||
−0.614458 | + | 0.788950i | \(0.710625\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.94427 | −0.574654 | −0.287327 | − | 0.957832i | \(-0.592767\pi\) | ||||
−0.287327 | + | 0.957832i | \(0.592767\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.8885 | 1.71341 | 0.856706 | − | 0.515805i | \(-0.172507\pi\) | ||||
0.856706 | + | 0.515805i | \(0.172507\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.7639 | −1.29480 | −0.647401 | − | 0.762150i | \(-0.724144\pi\) | ||||
−0.647401 | + | 0.762150i | \(0.724144\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.61803 | 0.430634 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.14590 | −0.105044 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.23607 | 0.736656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.23607 | −0.464626 | −0.232313 | − | 0.972641i | \(-0.574629\pi\) | ||||
−0.232313 | + | 0.972641i | \(0.574629\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.3262 | −1.16432 | −0.582159 | − | 0.813075i | \(-0.697792\pi\) | ||||
−0.582159 | + | 0.813075i | \(0.697792\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.618034 | 0.0535903 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.47214 | 0.296645 | 0.148322 | − | 0.988939i | \(-0.452613\pi\) | ||||
0.148322 | + | 0.988939i | \(0.452613\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.3820 | 1.38950 | 0.694750 | − | 0.719251i | \(-0.255515\pi\) | ||||
0.694750 | + | 0.719251i | \(0.255515\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.1803 | 1.84198 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.47214 | −0.120602 | −0.0603010 | − | 0.998180i | \(-0.519206\pi\) | ||||
−0.0603010 | + | 0.998180i | \(0.519206\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.4164 | −1.09181 | −0.545906 | − | 0.837846i | \(-0.683814\pi\) | ||||
−0.545906 | + | 0.837846i | \(0.683814\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.7082 | −1.34204 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.18034 | −0.493245 | −0.246622 | − | 0.969112i | \(-0.579321\pi\) | ||||
−0.246622 | + | 0.969112i | \(0.579321\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.416408 | 0.0328175 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.6180 | −1.37995 | −0.689975 | − | 0.723833i | \(-0.742379\pi\) | ||||
−0.689975 | + | 0.723833i | \(0.742379\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.67376 | 0.593814 | 0.296907 | − | 0.954906i | \(-0.404045\pi\) | ||||
0.296907 | + | 0.954906i | \(0.404045\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.00000 | −0.615385 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.0344 | 0.914962 | 0.457481 | − | 0.889219i | \(-0.348752\pi\) | ||||
0.457481 | + | 0.889219i | \(0.348752\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.437694 | −0.0330866 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.41641 | −0.330098 | −0.165049 | − | 0.986285i | \(-0.552778\pi\) | ||||
−0.165049 | + | 0.986285i | \(0.552778\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.8885 | −1.55263 | −0.776317 | − | 0.630343i | \(-0.782914\pi\) | ||||
−0.776317 | + | 0.630343i | \(0.782914\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.5623 | −1.58529 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.2361 | −0.740656 | −0.370328 | − | 0.928901i | \(-0.620755\pi\) | ||||
−0.370328 | + | 0.928901i | \(0.620755\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.3262 | −1.10321 | −0.551603 | − | 0.834107i | \(-0.685984\pi\) | ||||
−0.551603 | + | 0.834107i | \(0.685984\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.8541 | −1.05831 | −0.529155 | − | 0.848525i | \(-0.677491\pi\) | ||||
−0.529155 | + | 0.848525i | \(0.677491\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.527864 | 0.0374193 | 0.0187096 | − | 0.999825i | \(-0.494044\pi\) | ||||
0.0187096 | + | 0.999825i | \(0.494044\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.00000 | 0.140372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.0902 | 0.914257 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.61803 | −0.386761 | −0.193381 | − | 0.981124i | \(-0.561945\pi\) | ||||
−0.193381 | + | 0.981124i | \(0.561945\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.61803 | 0.451346 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.50658 | −0.102273 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.8541 | 0.730126 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.4721 | −1.43788 | −0.718940 | − | 0.695072i | \(-0.755373\pi\) | ||||
−0.718940 | + | 0.695072i | \(0.755373\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 28.5967 | 1.89803 | 0.949016 | − | 0.315227i | \(-0.102081\pi\) | ||||
0.949016 | + | 0.315227i | \(0.102081\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.8885 | 1.57860 | 0.789300 | − | 0.614008i | \(-0.210444\pi\) | ||||
0.789300 | + | 0.614008i | \(0.210444\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.90983 | −0.583702 | −0.291851 | − | 0.956464i | \(-0.594271\pi\) | ||||
−0.291851 | + | 0.956464i | \(0.594271\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.9443 | 1.17056 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.0344 | −0.972497 | −0.486249 | − | 0.873821i | \(-0.661635\pi\) | ||||
−0.486249 | + | 0.873821i | \(0.661635\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.0689 | −1.80808 | −0.904038 | − | 0.427452i | \(-0.859411\pi\) | ||||
−0.904038 | + | 0.427452i | \(0.859411\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 18.1803 | 1.16150 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.85410 | −0.372488 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.85410 | −0.558866 | −0.279433 | − | 0.960165i | \(-0.590146\pi\) | ||||
−0.279433 | + | 0.960165i | \(0.590146\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.79837 | 0.424071 | 0.212035 | − | 0.977262i | \(-0.431991\pi\) | ||||
0.212035 | + | 0.977262i | \(0.431991\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.94427 | −0.120811 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.14590 | 0.255647 | 0.127824 | − | 0.991797i | \(-0.459201\pi\) | ||||
0.127824 | + | 0.991797i | \(0.459201\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.6525 | 1.69868 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.4164 | −1.54967 | −0.774833 | − | 0.632166i | \(-0.782166\pi\) | ||||
−0.774833 | + | 0.632166i | \(0.782166\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.3820 | −0.934388 | −0.467194 | − | 0.884155i | \(-0.654735\pi\) | ||||
−0.467194 | + | 0.884155i | \(0.654735\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.85410 | 0.531991 | 0.265996 | − | 0.963974i | \(-0.414299\pi\) | ||||
0.265996 | + | 0.963974i | \(0.414299\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.5967 | −1.88490 | −0.942452 | − | 0.334342i | \(-0.891486\pi\) | ||||
−0.942452 | + | 0.334342i | \(0.891486\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.29180 | 0.136233 | 0.0681166 | − | 0.997677i | \(-0.478301\pi\) | ||||
0.0681166 | + | 0.997677i | \(0.478301\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.18034 | 0.0696733 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.56231 | 0.386018 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.3607 | −1.01422 | −0.507111 | − | 0.861881i | \(-0.669287\pi\) | ||||
−0.507111 | + | 0.861881i | \(0.669287\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.5623 | −0.847850 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.94427 | −0.228103 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.596748 | 0.0343960 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.381966 | −0.0218713 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.7984 | 0.787515 | 0.393757 | − | 0.919214i | \(-0.371175\pi\) | ||||
0.393757 | + | 0.919214i | \(0.371175\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.76393 | −0.553662 | −0.276831 | − | 0.960919i | \(-0.589284\pi\) | ||||
−0.276831 | + | 0.960919i | \(0.589284\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.8885 | −1.51983 | −0.759915 | − | 0.650022i | \(-0.774760\pi\) | ||||
−0.759915 | + | 0.650022i | \(0.774760\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.9443 | −0.895520 | −0.447760 | − | 0.894154i | \(-0.647778\pi\) | ||||
−0.447760 | + | 0.894154i | \(0.647778\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.7082 | −0.707103 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.14590 | 0.229973 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.61803 | 0.0892051 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.0000 | −1.48405 | −0.742027 | − | 0.670370i | \(-0.766135\pi\) | ||||
−0.742027 | + | 0.670370i | \(0.766135\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −40.7426 | −2.22601 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.7082 | 1.29147 | 0.645734 | − | 0.763562i | \(-0.276551\pi\) | ||||
0.645734 | + | 0.763562i | \(0.276551\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.29180 | 0.177740 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.0000 | 0.858925 | 0.429463 | − | 0.903085i | \(-0.358703\pi\) | ||||
0.429463 | + | 0.903085i | \(0.358703\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.76393 | −0.415594 | −0.207797 | − | 0.978172i | \(-0.566629\pi\) | ||||
−0.207797 | + | 0.978172i | \(0.566629\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.52786 | −0.294219 | −0.147109 | − | 0.989120i | \(-0.546997\pi\) | ||||
−0.147109 | + | 0.989120i | \(0.546997\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.7984 | −1.05079 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.70820 | −0.301267 | −0.150634 | − | 0.988590i | \(-0.548131\pi\) | ||||
−0.150634 | + | 0.988590i | \(0.548131\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.1459 | −0.639258 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −25.4164 | −1.33036 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.67376 | −0.296168 | −0.148084 | − | 0.988975i | \(-0.547311\pi\) | ||||
−0.148084 | + | 0.988975i | \(0.547311\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.49342 | 0.129452 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.9443 | −0.825563 | −0.412782 | − | 0.910830i | \(-0.635443\pi\) | ||||
−0.412782 | + | 0.910830i | \(0.635443\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.9443 | −0.975680 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.1803 | −0.882495 | −0.441247 | − | 0.897386i | \(-0.645464\pi\) | ||||
−0.441247 | + | 0.897386i | \(0.645464\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.7082 | 1.67131 | 0.835656 | − | 0.549254i | \(-0.185088\pi\) | ||||
0.835656 | + | 0.549254i | \(0.185088\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.2016 | −0.517243 | −0.258621 | − | 0.965979i | \(-0.583268\pi\) | ||||
−0.258621 | + | 0.965979i | \(0.583268\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.56231 | −0.433014 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25.5623 | 1.28618 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.7082 | −1.74195 | −0.870977 | − | 0.491323i | \(-0.836513\pi\) | ||||
−0.870977 | + | 0.491323i | \(0.836513\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.4508 | −1.12114 | −0.560571 | − | 0.828106i | \(-0.689418\pi\) | ||||
−0.560571 | + | 0.828106i | \(0.689418\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.2705 | 0.710865 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.88854 | 0.0933825 | 0.0466912 | − | 0.998909i | \(-0.485132\pi\) | ||||
0.0466912 | + | 0.998909i | \(0.485132\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.31308 | −0.0646126 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −41.7426 | −2.04907 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.4508 | −1.73189 | −0.865944 | − | 0.500142i | \(-0.833281\pi\) | ||||
−0.865944 | + | 0.500142i | \(0.833281\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.7426 | −0.962198 | −0.481099 | − | 0.876666i | \(-0.659762\pi\) | ||||
−0.481099 | + | 0.876666i | \(0.659762\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.00000 | 0.436564 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0344419 | −0.00166676 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.9787 | 0.576994 | 0.288497 | − | 0.957481i | \(-0.406844\pi\) | ||||
0.288497 | + | 0.957481i | \(0.406844\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.0557 | −0.627418 | −0.313709 | − | 0.949519i | \(-0.601572\pi\) | ||||
−0.313709 | + | 0.949519i | \(0.601572\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.61803 | 0.220911 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.5279 | −0.979741 | −0.489871 | − | 0.871795i | \(-0.662956\pi\) | ||||
−0.489871 | + | 0.871795i | \(0.662956\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.81966 | −0.371523 | −0.185762 | − | 0.982595i | \(-0.559475\pi\) | ||||
−0.185762 | + | 0.982595i | \(0.559475\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.3262 | −0.679129 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.3050 | 1.28860 | 0.644300 | − | 0.764773i | \(-0.277149\pi\) | ||||
0.644300 | + | 0.764773i | \(0.277149\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.38197 | 0.0647876 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 40.7426 | 1.90586 | 0.952930 | − | 0.303189i | \(-0.0980515\pi\) | ||||
0.952930 | + | 0.303189i | \(0.0980515\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.9098 | −0.508121 | −0.254061 | − | 0.967188i | \(-0.581766\pi\) | ||||
−0.254061 | + | 0.967188i | \(0.581766\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.4508 | 1.13633 | 0.568164 | − | 0.822916i | \(-0.307654\pi\) | ||||
0.568164 | + | 0.822916i | \(0.307654\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.4164 | 0.944759 | 0.472379 | − | 0.881395i | \(-0.343395\pi\) | ||||
0.472379 | + | 0.881395i | \(0.343395\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.67376 | −0.169639 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.85410 | −0.222721 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.20163 | 0.374742 | 0.187371 | − | 0.982289i | \(-0.440003\pi\) | ||||
0.187371 | + | 0.982289i | \(0.440003\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.4164 | 0.839716 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.381966 | 0.0173442 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.05573 | −0.365040 | −0.182520 | − | 0.983202i | \(-0.558425\pi\) | ||||
−0.182520 | + | 0.983202i | \(0.558425\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.0902 | 1.71899 | 0.859493 | − | 0.511148i | \(-0.170780\pi\) | ||||
0.859493 | + | 0.511148i | \(0.170780\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −41.1246 | −1.85216 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.78522 | −0.0800780 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.0902 | 0.585996 | 0.292998 | − | 0.956113i | \(-0.405347\pi\) | ||||
0.292998 | + | 0.956113i | \(0.405347\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.23607 | −0.0551135 | −0.0275568 | − | 0.999620i | \(-0.508773\pi\) | ||||
−0.0275568 | + | 0.999620i | \(0.508773\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.7984 | −1.10351 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.14590 | 0.405385 | 0.202692 | − | 0.979242i | \(-0.435031\pi\) | ||||
0.202692 | + | 0.979242i | \(0.435031\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.29180 | −0.101383 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 32.6525 | 1.43884 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.0000 | 0.700973 | 0.350486 | − | 0.936568i | \(-0.386016\pi\) | ||||
0.350486 | + | 0.936568i | \(0.386016\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.5623 | 1.16149 | 0.580744 | − | 0.814086i | \(-0.302762\pi\) | ||||
0.580744 | + | 0.814086i | \(0.302762\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.9787 | 1.34945 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.8885 | −0.864719 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.1803 | −0.484274 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.5623 | 0.672817 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.0344 | −0.947335 | −0.473667 | − | 0.880704i | \(-0.657070\pi\) | ||||
−0.473667 | + | 0.880704i | \(0.657070\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −46.8328 | −2.00610 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.8541 | 0.977171 | 0.488585 | − | 0.872516i | \(-0.337513\pi\) | ||||
0.488585 | + | 0.872516i | \(0.337513\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.1803 | 0.944914 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.30495 | 0.0980165 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.67376 | 0.0709196 | 0.0354598 | − | 0.999371i | \(-0.488710\pi\) | ||||
0.0354598 | + | 0.999371i | \(0.488710\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.65248 | −0.239074 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.7639 | 1.08582 | 0.542910 | − | 0.839791i | \(-0.317322\pi\) | ||||
0.542910 | + | 0.839791i | \(0.317322\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 36.0344 | 1.51598 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.2918 | −0.850676 | −0.425338 | − | 0.905034i | \(-0.639845\pi\) | ||||
−0.425338 | + | 0.905034i | \(0.639845\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.8541 | 1.24936 | 0.624678 | − | 0.780883i | \(-0.285230\pi\) | ||||
0.624678 | + | 0.780883i | \(0.285230\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.27051 | −0.136390 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.81966 | −0.242276 | −0.121138 | − | 0.992636i | \(-0.538654\pi\) | ||||
−0.121138 | + | 0.992636i | \(0.538654\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.76393 | −0.156154 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.708204 | −0.0292307 | −0.0146154 | − | 0.999893i | \(-0.504652\pi\) | ||||
−0.0146154 | + | 0.999893i | \(0.504652\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.7082 | −0.688450 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.4377 | −0.757145 | −0.378573 | − | 0.925572i | \(-0.623585\pi\) | ||||
−0.378573 | + | 0.925572i | \(0.623585\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.00000 | 0.122988 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.7082 | 1.13213 | 0.566063 | − | 0.824362i | \(-0.308466\pi\) | ||||
0.566063 | + | 0.824362i | \(0.308466\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.94427 | −0.160890 | −0.0804451 | − | 0.996759i | \(-0.525634\pi\) | ||||
−0.0804451 | + | 0.996759i | \(0.525634\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.3820 | −0.421391 | −0.210696 | − | 0.977552i | \(-0.567573\pi\) | ||||
−0.210696 | + | 0.977552i | \(0.567573\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.3262 | −0.620033 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.1803 | −1.13819 | −0.569097 | − | 0.822271i | \(-0.692707\pi\) | ||||
−0.569097 | + | 0.822271i | \(0.692707\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.4721 | 0.864436 | 0.432218 | − | 0.901769i | \(-0.357731\pi\) | ||||
0.432218 | + | 0.901769i | \(0.357731\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.4721 | −1.02381 | −0.511906 | − | 0.859042i | \(-0.671060\pi\) | ||||
−0.511906 | + | 0.859042i | \(0.671060\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.29180 | −0.0517547 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.8328 | −1.23331 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 39.9787 | 1.59406 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.5066 | −0.458070 | −0.229035 | − | 0.973418i | \(-0.573557\pi\) | ||||
−0.229035 | + | 0.973418i | \(0.573557\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.7082 | 0.543993 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.5279 | −0.615236 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.79837 | 0.268520 | 0.134260 | − | 0.990946i | \(-0.457134\pi\) | ||||
0.134260 | + | 0.990946i | \(0.457134\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.0902 | −1.02890 | −0.514448 | − | 0.857522i | \(-0.672003\pi\) | ||||
−0.514448 | + | 0.857522i | \(0.672003\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.3951 | −1.31290 | −0.656449 | − | 0.754371i | \(-0.727942\pi\) | ||||
−0.656449 | + | 0.754371i | \(0.727942\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.7426 | −0.968255 | −0.484127 | − | 0.874998i | \(-0.660863\pi\) | ||||
−0.484127 | + | 0.874998i | \(0.660863\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.8885 | 1.36321 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.1246 | 0.822898 | 0.411449 | − | 0.911433i | \(-0.365023\pi\) | ||||
0.411449 | + | 0.911433i | \(0.365023\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.8541 | −0.577758 | −0.288879 | − | 0.957366i | \(-0.593282\pi\) | ||||
−0.288879 | + | 0.957366i | \(0.593282\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.61803 | −0.0627447 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.9443 | 0.578645 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.4721 | 0.673501 | 0.336751 | − | 0.941594i | \(-0.390672\pi\) | ||||
0.336751 | + | 0.941594i | \(0.390672\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.4164 | −0.592501 | −0.296250 | − | 0.955110i | \(-0.595736\pi\) | ||||
−0.296250 | + | 0.955110i | \(0.595736\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.0344419 | 0.00132176 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 50.4853 | 1.93177 | 0.965883 | − | 0.258979i | \(-0.0833860\pi\) | ||||
0.965883 | + | 0.258979i | \(0.0833860\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.09017 | −0.347318 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −23.6180 | −0.899775 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.5967 | −1.35416 | −0.677082 | − | 0.735908i | \(-0.736756\pi\) | ||||
−0.677082 | + | 0.735908i | \(0.736756\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −42.8885 | −1.62686 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.2705 | −0.919311 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.9230 | −1.20571 | −0.602857 | − | 0.797849i | \(-0.705971\pi\) | ||||
−0.602857 | + | 0.797849i | \(0.705971\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.5623 | −0.813238 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.23607 | −0.0840960 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.32624 | 0.200031 | 0.100016 | − | 0.994986i | \(-0.468111\pi\) | ||||
0.100016 | + | 0.994986i | \(0.468111\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.2574 | −0.421591 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.81966 | 0.328918 | 0.164459 | − | 0.986384i | \(-0.447412\pi\) | ||||
0.164459 | + | 0.986384i | \(0.447412\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.94427 | 0.109650 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.7082 | −0.583388 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.7426 | 0.398423 | 0.199211 | − | 0.979957i | \(-0.436162\pi\) | ||||
0.199211 | + | 0.979957i | \(0.436162\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.2705 | −0.453841 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.0689 | 0.815133 | 0.407566 | − | 0.913176i | \(-0.366377\pi\) | ||||
0.407566 | + | 0.913176i | \(0.366377\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 49.0689 | 1.80503 | 0.902514 | − | 0.430660i | \(-0.141719\pi\) | ||||
0.902514 | + | 0.430660i | \(0.141719\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.94427 | −0.364820 | −0.182410 | − | 0.983223i | \(-0.558390\pi\) | ||||
−0.182410 | + | 0.983223i | \(0.558390\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.85410 | 0.141203 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.40325 | 0.0512737 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.09017 | −0.258724 | −0.129362 | − | 0.991597i | \(-0.541293\pi\) | ||||
−0.129362 | + | 0.991597i | \(0.541293\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 35.1246 | 1.27832 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.4721 | −0.635036 | −0.317518 | − | 0.948252i | \(-0.602849\pi\) | ||||
−0.317518 | + | 0.948252i | \(0.602849\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.94427 | −0.287980 | −0.143990 | − | 0.989579i | \(-0.545993\pi\) | ||||
−0.143990 | + | 0.989579i | \(0.545993\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.22291 | −0.152880 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.4377 | 0.449099 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.43769 | −0.232149 | −0.116075 | − | 0.993240i | \(-0.537031\pi\) | ||||
−0.116075 | + | 0.993240i | \(0.537031\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 45.8328 | 1.64849 | 0.824246 | − | 0.566232i | \(-0.191599\pi\) | ||||
0.824246 | + | 0.566232i | \(0.191599\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.8328 | 0.425047 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.0902 | 0.469004 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.1803 | 0.577501 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.0132 | −1.10550 | −0.552750 | − | 0.833347i | \(-0.686421\pi\) | ||||
−0.552750 | + | 0.833347i | \(0.686421\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.24922 | 0.115529 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.326238 | 0.0115850 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.70820 | −0.273039 | −0.136519 | − | 0.990637i | \(-0.543592\pi\) | ||||
−0.136519 | + | 0.990637i | \(0.543592\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.2705 | −1.17703 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.09017 | −0.0384234 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.2705 | 0.818148 | 0.409074 | − | 0.912501i | \(-0.365852\pi\) | ||||
0.409074 | + | 0.912501i | \(0.365852\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.3262 | 0.538177 | 0.269089 | − | 0.963115i | \(-0.413278\pi\) | ||||
0.269089 | + | 0.963115i | \(0.413278\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 46.1246 | 1.61567 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.61803 | 0.231536 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.0000 | 1.08191 | 0.540954 | − | 0.841052i | \(-0.318063\pi\) | ||||
0.540954 | + | 0.841052i | \(0.318063\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.5410 | 0.890304 | 0.445152 | − | 0.895455i | \(-0.353150\pi\) | ||||
0.445152 | + | 0.895455i | \(0.353150\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.2918 | 0.357881 | 0.178940 | − | 0.983860i | \(-0.442733\pi\) | ||||
0.178940 | + | 0.983860i | \(0.442733\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.2148 | 0.945208 | 0.472604 | − | 0.881275i | \(-0.343314\pi\) | ||||
0.472604 | + | 0.881275i | \(0.343314\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −33.7082 | −1.16792 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.0902 | −0.695249 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.5279 | −1.19203 | −0.596017 | − | 0.802972i | \(-0.703251\pi\) | ||||
−0.596017 | + | 0.802972i | \(0.703251\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.7771 | 1.47507 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.9443 | 0.720505 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.5279 | −0.498009 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.4721 | −1.28302 | −0.641511 | − | 0.767114i | \(-0.721692\pi\) | ||||
−0.641511 | + | 0.767114i | \(0.721692\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.8885 | −0.440264 | −0.220132 | − | 0.975470i | \(-0.570649\pi\) | ||||
−0.220132 | + | 0.975470i | \(0.570649\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.6525 | −0.397577 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47.3050 | 1.61028 | 0.805140 | − | 0.593085i | \(-0.202090\pi\) | ||||
0.805140 | + | 0.593085i | \(0.202090\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.5066 | −1.07126 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.7984 | 1.17910 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.94427 | −0.0657284 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.8328 | −1.41259 | −0.706297 | − | 0.707916i | \(-0.749636\pi\) | ||||
−0.706297 | + | 0.707916i | \(0.749636\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.14590 | −0.0386063 | −0.0193031 | − | 0.999814i | \(-0.506145\pi\) | ||||
−0.0193031 | + | 0.999814i | \(0.506145\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.7771 | −1.27130 | −0.635650 | − | 0.771977i | \(-0.719268\pi\) | ||||
−0.635650 | + | 0.771977i | \(0.719268\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.18034 | −0.173939 | −0.0869694 | − | 0.996211i | \(-0.527718\pi\) | ||||
−0.0869694 | + | 0.996211i | \(0.527718\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.23607 | 0.0414564 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.9443 | 0.600482 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.5623 | 0.386485 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −54.0689 | −1.80330 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −51.2705 | −1.70807 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 54.6869 | 1.81785 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.5623 | 0.848782 | 0.424391 | − | 0.905479i | \(-0.360488\pi\) | ||||
0.424391 | + | 0.905479i | \(0.360488\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.708204 | −0.0234638 | −0.0117319 | − | 0.999931i | \(-0.503734\pi\) | ||||
−0.0117319 | + | 0.999931i | \(0.503734\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.14590 | 0.103887 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.8885 | 1.08489 | 0.542446 | − | 0.840090i | \(-0.317498\pi\) | ||||
0.542446 | + | 0.840090i | \(0.317498\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.9098 | 0.556594 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.2705 | 0.502091 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.9443 | −0.654350 | −0.327175 | − | 0.944964i | \(-0.606097\pi\) | ||||
−0.327175 | + | 0.944964i | \(0.606097\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.1803 | 0.595837 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.70820 | −0.284485 | −0.142242 | − | 0.989832i | \(-0.545431\pi\) | ||||
−0.142242 | + | 0.989832i | \(0.545431\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.2148 | 1.47396 | 0.736980 | − | 0.675915i | \(-0.236251\pi\) | ||||
0.736980 | + | 0.675915i | \(0.236251\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.81966 | 0.287208 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.2705 | −1.34111 | −0.670556 | − | 0.741859i | \(-0.733944\pi\) | ||||
−0.670556 | + | 0.741859i | \(0.733944\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.7082 | 0.704678 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.6525 | 0.409854 | 0.204927 | − | 0.978777i | \(-0.434304\pi\) | ||||
0.204927 | + | 0.978777i | \(0.434304\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.7984 | 0.867175 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.819660 | −0.0264682 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.72949 | 0.313855 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 40.1246 | 1.29166 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.6180 | 0.791663 | 0.395831 | − | 0.918323i | \(-0.370456\pi\) | ||||
0.395831 | + | 0.918323i | \(0.370456\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.3050 | −0.876258 | −0.438129 | − | 0.898912i | \(-0.644359\pi\) | ||||
−0.438129 | + | 0.898912i | \(0.644359\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.86726 | −0.123979 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.4164 | −0.653179 | −0.326589 | − | 0.945166i | \(-0.605899\pi\) | ||||
−0.326589 | + | 0.945166i | \(0.605899\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.7771 | −1.07732 | −0.538661 | − | 0.842523i | \(-0.681070\pi\) | ||||
−0.538661 | + | 0.842523i | \(0.681070\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.8885 | 1.23909 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.45898 | 0.141787 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.3262 | −0.455088 | −0.227544 | − | 0.973768i | \(-0.573070\pi\) | ||||
−0.227544 | + | 0.973768i | \(0.573070\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.38197 | −0.0438113 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.7984 | −1.60880 | −0.804400 | − | 0.594088i | \(-0.797513\pi\) | ||||
−0.804400 | + | 0.594088i | \(0.797513\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 8712.2.a.bc.1.1 | 2 | ||
3.2 | odd | 2 | 2904.2.a.ba.1.2 | 2 | |||
11.7 | odd | 10 | 792.2.r.d.577.1 | 4 | |||
11.8 | odd | 10 | 792.2.r.d.361.1 | 4 | |||
11.10 | odd | 2 | 8712.2.a.ba.1.1 | 2 | |||
12.11 | even | 2 | 5808.2.a.bv.1.2 | 2 | |||
33.8 | even | 10 | 264.2.q.b.97.1 | yes | 4 | ||
33.29 | even | 10 | 264.2.q.b.49.1 | ✓ | 4 | ||
33.32 | even | 2 | 2904.2.a.z.1.2 | 2 | |||
132.95 | odd | 10 | 528.2.y.h.49.1 | 4 | |||
132.107 | odd | 10 | 528.2.y.h.97.1 | 4 | |||
132.131 | odd | 2 | 5808.2.a.bw.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
264.2.q.b.49.1 | ✓ | 4 | 33.29 | even | 10 | ||
264.2.q.b.97.1 | yes | 4 | 33.8 | even | 10 | ||
528.2.y.h.49.1 | 4 | 132.95 | odd | 10 | |||
528.2.y.h.97.1 | 4 | 132.107 | odd | 10 | |||
792.2.r.d.361.1 | 4 | 11.8 | odd | 10 | |||
792.2.r.d.577.1 | 4 | 11.7 | odd | 10 | |||
2904.2.a.z.1.2 | 2 | 33.32 | even | 2 | |||
2904.2.a.ba.1.2 | 2 | 3.2 | odd | 2 | |||
5808.2.a.bv.1.2 | 2 | 12.11 | even | 2 | |||
5808.2.a.bw.1.2 | 2 | 132.131 | odd | 2 | |||
8712.2.a.ba.1.1 | 2 | 11.10 | odd | 2 | |||
8712.2.a.bc.1.1 | 2 | 1.1 | even | 1 | trivial |