Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3312,2,Mod(1,3312)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3312, 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("3312.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3312 = 2^{4} \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3312.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(26.4464531494\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.44688.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 2x^{3} - 5x^{2} + 6x + 2 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1656) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.277334\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3312.1 |
$q$-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 | ||||||||
\(5\) | −1.64575 | −0.736002 | −0.368001 | − | 0.929825i | \(-0.619958\pi\) | ||||
−0.368001 | + | 0.929825i | \(0.619958\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.65684 | −1.76012 | −0.880061 | − | 0.474861i | \(-0.842498\pi\) | ||||
−0.880061 | + | 0.474861i | \(0.842498\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.56576 | −1.07512 | −0.537559 | − | 0.843226i | \(-0.680653\pi\) | ||||
−0.537559 | + | 0.843226i | \(0.680653\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.554669 | −0.153837 | −0.0769187 | − | 0.997037i | \(-0.524508\pi\) | ||||
−0.0769187 | + | 0.997037i | \(0.524508\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.21151 | −1.26398 | −0.631989 | − | 0.774978i | \(-0.717761\pi\) | ||||
−0.631989 | + | 0.774978i | \(0.717761\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.20042 | −1.42247 | −0.711237 | − | 0.702952i | \(-0.751865\pi\) | ||||
−0.711237 | + | 0.702952i | \(0.751865\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.29150 | −0.458301 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.55467 | 0.845781 | 0.422890 | − | 0.906181i | \(-0.361016\pi\) | ||||
0.422890 | + | 0.906181i | \(0.361016\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.55467 | −0.818043 | −0.409021 | − | 0.912525i | \(-0.634130\pi\) | ||||
−0.409021 | + | 0.912525i | \(0.634130\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.66401 | 1.29545 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.54358 | 0.582560 | 0.291280 | − | 0.956638i | \(-0.405919\pi\) | ||||
0.291280 | + | 0.956638i | \(0.405919\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.84617 | 1.22537 | 0.612683 | − | 0.790329i | \(-0.290090\pi\) | ||||
0.612683 | + | 0.790329i | \(0.290090\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.33194 | 1.42311 | 0.711554 | − | 0.702632i | \(-0.247992\pi\) | ||||
0.711554 | + | 0.702632i | \(0.247992\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.3137 | 1.65027 | 0.825135 | − | 0.564935i | \(-0.191099\pi\) | ||||
0.825135 | + | 0.564935i | \(0.191099\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.6862 | 2.09803 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.66794 | −0.503830 | −0.251915 | − | 0.967749i | \(-0.581060\pi\) | ||||
−0.251915 | + | 0.967749i | \(0.581060\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.86836 | 0.791289 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.1599 | −1.45289 | −0.726445 | − | 0.687225i | \(-0.758829\pi\) | ||||
−0.726445 | + | 0.687225i | \(0.758829\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.56576 | −0.200475 | −0.100238 | − | 0.994964i | \(-0.531960\pi\) | ||||
−0.100238 | + | 0.994964i | \(0.531960\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.912847 | 0.113225 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.38259 | −1.02410 | −0.512048 | − | 0.858957i | \(-0.671113\pi\) | ||||
−0.512048 | + | 0.858957i | \(0.671113\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.84617 | −0.456457 | −0.228228 | − | 0.973608i | \(-0.573293\pi\) | ||||
−0.228228 | + | 0.973608i | \(0.573293\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.97769 | −1.05076 | −0.525380 | − | 0.850868i | \(-0.676077\pi\) | ||||
−0.525380 | + | 0.850868i | \(0.676077\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.6052 | 1.89234 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.76618 | −1.09878 | −0.549391 | − | 0.835566i | \(-0.685140\pi\) | ||||
−0.549391 | + | 0.835566i | \(0.685140\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.434239 | 0.0476639 | 0.0238320 | − | 0.999716i | \(-0.492413\pi\) | ||||
0.0238320 | + | 0.999716i | \(0.492413\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.57685 | 0.930290 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.02935 | 0.745109 | 0.372555 | − | 0.928010i | \(-0.378482\pi\) | ||||
0.372555 | + | 0.928010i | \(0.378482\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.58301 | 0.270773 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.2043 | 1.04694 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.02218 | 0.408391 | 0.204195 | − | 0.978930i | \(-0.434542\pi\) | ||||
0.204195 | + | 0.978930i | \(0.434542\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.8684 | 1.77797 | 0.888984 | − | 0.457938i | \(-0.151412\pi\) | ||||
0.888984 | + | 0.457938i | \(0.151412\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.7884 | −1.55567 | −0.777837 | − | 0.628466i | \(-0.783683\pi\) | ||||
−0.777837 | + | 0.628466i | \(0.783683\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.58794 | 0.926902 | 0.463451 | − | 0.886123i | \(-0.346611\pi\) | ||||
0.463451 | + | 0.886123i | \(0.346611\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.01724 | 0.863695 | 0.431848 | − | 0.901947i | \(-0.357862\pi\) | ||||
0.431848 | + | 0.901947i | \(0.357862\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.39368 | 0.319250 | 0.159625 | − | 0.987178i | \(-0.448971\pi\) | ||||
0.159625 | + | 0.987178i | \(0.448971\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.64575 | −0.153467 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 24.2692 | 2.22475 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.71465 | 0.155877 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.73068 | −0.242309 | −0.121154 | − | 0.992634i | \(-0.538660\pi\) | ||||
−0.121154 | + | 0.992634i | \(0.538660\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.97782 | 0.172803 | 0.0864013 | − | 0.996260i | \(-0.472463\pi\) | ||||
0.0864013 | + | 0.996260i | \(0.472463\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 28.8744 | 2.50373 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.7439 | −1.43053 | −0.715263 | − | 0.698856i | \(-0.753693\pi\) | ||||
−0.715263 | + | 0.698856i | \(0.753693\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.97782 | 0.165393 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.49585 | −0.622497 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.2003 | −1.24526 | −0.622628 | − | 0.782518i | \(-0.713935\pi\) | ||||
−0.622628 | + | 0.782518i | \(0.713935\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.82399 | −0.148434 | −0.0742170 | − | 0.997242i | \(-0.523646\pi\) | ||||
−0.0742170 | + | 0.997242i | \(0.523646\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.49585 | 0.602081 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.03943 | 0.561808 | 0.280904 | − | 0.959736i | \(-0.409366\pi\) | ||||
0.280904 | + | 0.959736i | \(0.409366\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.65684 | −0.367011 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.9715 | −1.17266 | −0.586331 | − | 0.810072i | \(-0.699428\pi\) | ||||
−0.586331 | + | 0.810072i | \(0.699428\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.9999 | 1.31549 | 0.657745 | − | 0.753241i | \(-0.271510\pi\) | ||||
0.657745 | + | 0.753241i | \(0.271510\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6923 | −0.976334 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 25.7084 | 1.95457 | 0.977286 | − | 0.211926i | \(-0.0679735\pi\) | ||||
0.977286 | + | 0.211926i | \(0.0679735\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.6712 | 0.806665 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.7084 | −1.17410 | −0.587050 | − | 0.809551i | \(-0.699711\pi\) | ||||
−0.587050 | + | 0.809551i | \(0.699711\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.58794 | −0.564008 | −0.282004 | − | 0.959413i | \(-0.590999\pi\) | ||||
−0.282004 | + | 0.959413i | \(0.590999\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.83185 | −0.428766 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.5830 | 1.35892 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.6052 | 1.78037 | 0.890185 | − | 0.455600i | \(-0.150575\pi\) | ||||
0.890185 | + | 0.455600i | \(0.150575\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.3785 | −1.39490 | −0.697449 | − | 0.716635i | \(-0.745681\pi\) | ||||
−0.697449 | + | 0.716635i | \(0.745681\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.46752 | 0.389544 | 0.194772 | − | 0.980849i | \(-0.437603\pi\) | ||||
0.194772 | + | 0.980849i | \(0.437603\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.5029 | 1.80785 | 0.903926 | − | 0.427689i | \(-0.140672\pi\) | ||||
0.903926 | + | 0.427689i | \(0.140672\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −21.2104 | −1.48868 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.9128 | −0.901872 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.1092 | 1.52933 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.3359 | 1.05576 | 0.527882 | − | 0.849317i | \(-0.322986\pi\) | ||||
0.527882 | + | 0.849317i | \(0.322986\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.3581 | −1.04741 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.2104 | 1.43985 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.89066 | 0.194447 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.3420 | 1.29524 | 0.647619 | − | 0.761964i | \(-0.275765\pi\) | ||||
0.647619 | + | 0.761964i | \(0.275765\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.00494 | 0.199445 | 0.0997224 | − | 0.995015i | \(-0.468205\pi\) | ||||
0.0997224 | + | 0.995015i | \(0.468205\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.01724 | −0.331549 | −0.165774 | − | 0.986164i | \(-0.553012\pi\) | ||||
−0.165774 | + | 0.986164i | \(0.553012\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.6274 | −1.74442 | −0.872209 | − | 0.489134i | \(-0.837313\pi\) | ||||
−0.872209 | + | 0.489134i | \(0.837313\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.6195 | −1.21460 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.6274 | −1.20490 | −0.602452 | − | 0.798155i | \(-0.705810\pi\) | ||||
−0.602452 | + | 0.798155i | \(0.705810\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.4959 | −1.12701 | −0.563503 | − | 0.826114i | \(-0.690547\pi\) | ||||
−0.563503 | + | 0.826114i | \(0.690547\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −24.1698 | −1.54415 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.43918 | 0.218830 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.1266 | 1.01790 | 0.508950 | − | 0.860796i | \(-0.330034\pi\) | ||||
0.508950 | + | 0.860796i | \(0.330034\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.56576 | −0.224177 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.5829 | 0.722520 | 0.361260 | − | 0.932465i | \(-0.382347\pi\) | ||||
0.361260 | + | 0.932465i | \(0.382347\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.5019 | −1.02538 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.89066 | −0.178246 | −0.0891229 | − | 0.996021i | \(-0.528406\pi\) | ||||
−0.0891229 | + | 0.996021i | \(0.528406\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.03651 | 0.370820 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.10318 | −0.0672624 | −0.0336312 | − | 0.999434i | \(-0.510707\pi\) | ||||
−0.0336312 | + | 0.999434i | \(0.510707\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.31369 | 0.565766 | 0.282883 | − | 0.959154i | \(-0.408709\pi\) | ||||
0.282883 | + | 0.959154i | \(0.408709\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.17095 | 0.492727 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.86848 | −0.412687 | −0.206343 | − | 0.978480i | \(-0.566156\pi\) | ||||
−0.206343 | + | 0.978480i | \(0.566156\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.66300 | 0.278171 | 0.139086 | − | 0.990280i | \(-0.455584\pi\) | ||||
0.139086 | + | 0.990280i | \(0.455584\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.4270 | −0.738706 | −0.369353 | − | 0.929289i | \(-0.620421\pi\) | ||||
−0.369353 | + | 0.929289i | \(0.620421\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −36.5384 | −2.15679 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.1599 | 0.597639 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.60138 | 0.327236 | 0.163618 | − | 0.986524i | \(-0.447684\pi\) | ||||
0.163618 | + | 0.986524i | \(0.447684\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.3664 | 1.06933 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.554669 | −0.0320773 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −43.4574 | −2.50484 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.57685 | 0.147550 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.5102 | 0.999359 | 0.499679 | − | 0.866210i | \(-0.333451\pi\) | ||||
0.499679 | + | 0.866210i | \(0.333451\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.6985 | −1.23041 | −0.615204 | − | 0.788368i | \(-0.710927\pi\) | ||||
−0.615204 | + | 0.788368i | \(0.710927\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.6496 | −1.50632 | −0.753161 | − | 0.657836i | \(-0.771472\pi\) | ||||
−0.753161 | + | 0.657836i | \(0.771472\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.8097 | 0.887959 | 0.443980 | − | 0.896037i | \(-0.353566\pi\) | ||||
0.443980 | + | 0.896037i | \(0.353566\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.2409 | −0.909314 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 32.3136 | 1.79797 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.27102 | 0.0705038 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −52.6861 | −2.90468 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.8745 | 1.42219 | 0.711096 | − | 0.703095i | \(-0.248199\pi\) | ||||
0.711096 | + | 0.703095i | \(0.248199\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.7957 | 0.753737 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.7811 | 1.18649 | 0.593245 | − | 0.805022i | \(-0.297846\pi\) | ||||
0.593245 | + | 0.805022i | \(0.297846\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.2409 | 0.879492 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −35.7934 | −1.93266 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.9837 | 1.39488 | 0.697440 | − | 0.716644i | \(-0.254323\pi\) | ||||
0.697440 | + | 0.716644i | \(0.254323\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.3136 | 1.19442 | 0.597209 | − | 0.802086i | \(-0.296276\pi\) | ||||
0.597209 | + | 0.802086i | \(0.296276\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.204349 | 0.0108764 | 0.00543821 | − | 0.999985i | \(-0.498269\pi\) | ||||
0.00543821 | + | 0.999985i | \(0.498269\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.32984 | 0.335953 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.7145 | −1.35716 | −0.678580 | − | 0.734526i | \(-0.737405\pi\) | ||||
−0.678580 | + | 0.734526i | \(0.737405\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.4452 | 1.02343 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.7750 | 0.773361 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.8168 | 0.669033 | 0.334516 | − | 0.942390i | \(-0.391427\pi\) | ||||
0.334516 | + | 0.942390i | \(0.391427\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.0810 | 0.886801 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.3896 | −1.46996 | −0.734980 | − | 0.678089i | \(-0.762808\pi\) | ||||
−0.734980 | + | 0.678089i | \(0.762808\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.52633 | −0.130113 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.41909 | 0.226994 | 0.113497 | − | 0.993538i | \(-0.463795\pi\) | ||||
0.113497 | + | 0.993538i | \(0.463795\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.10934 | −0.465465 | −0.232733 | − | 0.972541i | \(-0.574767\pi\) | ||||
−0.232733 | + | 0.972541i | \(0.574767\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −27.3280 | −1.39276 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.6011 | 1.19663 | 0.598313 | − | 0.801263i | \(-0.295838\pi\) | ||||
0.598313 | + | 0.801263i | \(0.295838\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.21151 | −0.263557 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.0727 | 0.808706 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.6923 | 0.687199 | 0.343599 | − | 0.939116i | \(-0.388354\pi\) | ||||
0.343599 | + | 0.939116i | \(0.388354\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.21151 | −0.260250 | −0.130125 | − | 0.991498i | \(-0.541538\pi\) | ||||
−0.130125 | + | 0.991498i | \(0.541538\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.52633 | 0.125846 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.6355 | −0.626321 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.8399 | −1.22825 | −0.614127 | − | 0.789207i | \(-0.710492\pi\) | ||||
−0.614127 | + | 0.789207i | \(0.710492\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 51.9697 | 2.55726 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.714650 | −0.0350808 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.3674 | −1.19043 | −0.595214 | − | 0.803567i | \(-0.702933\pi\) | ||||
−0.595214 | + | 0.803567i | \(0.702933\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.1710 | −1.47044 | −0.735221 | − | 0.677827i | \(-0.762922\pi\) | ||||
−0.735221 | + | 0.677827i | \(0.762922\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.9422 | 0.579281 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.29150 | 0.352861 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.8239 | 0.521367 | 0.260684 | − | 0.965424i | \(-0.416052\pi\) | ||||
0.260684 | + | 0.965424i | \(0.416052\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 40.5162 | 1.94708 | 0.973542 | − | 0.228507i | \(-0.0733843\pi\) | ||||
0.973542 | + | 0.228507i | \(0.0733843\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.20042 | −0.296606 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.04437 | −0.193027 | −0.0965136 | − | 0.995332i | \(-0.530769\pi\) | ||||
−0.0965136 | + | 0.995332i | \(0.530769\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.52633 | −0.120030 | −0.0600148 | − | 0.998197i | \(-0.519115\pi\) | ||||
−0.0600148 | + | 0.998197i | \(0.519115\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.5686 | −0.548402 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.6479 | −1.54075 | −0.770374 | − | 0.637593i | \(-0.779930\pi\) | ||||
−0.770374 | + | 0.637593i | \(0.779930\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.9776 | −1.31741 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.25098 | −0.199289 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.9778 | −1.12163 | −0.560817 | − | 0.827939i | \(-0.689513\pi\) | ||||
−0.560817 | + | 0.827939i | \(0.689513\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.32186 | −0.154714 | −0.0773572 | − | 0.997003i | \(-0.524648\pi\) | ||||
−0.0773572 | + | 0.997003i | \(0.524648\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.4087 | 0.762577 | 0.381288 | − | 0.924456i | \(-0.375480\pi\) | ||||
0.381288 | + | 0.924456i | \(0.375480\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.5131 | 1.59708 | 0.798538 | − | 0.601945i | \(-0.205607\pi\) | ||||
0.798538 | + | 0.601945i | \(0.205607\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 39.0364 | 1.80253 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −33.2755 | −1.53001 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.2083 | 0.651921 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.63567 | 0.348883 | 0.174441 | − | 0.984668i | \(-0.444188\pi\) | ||||
0.174441 | + | 0.984668i | \(0.444188\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.96551 | −0.0896196 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.61951 | −0.300577 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.53864 | 0.115037 | 0.0575183 | − | 0.998344i | \(-0.481681\pi\) | ||||
0.0575183 | + | 0.998344i | \(0.481681\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.5547 | −0.656843 | −0.328422 | − | 0.944531i | \(-0.606517\pi\) | ||||
−0.328422 | + | 0.944531i | \(0.606517\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.7367 | −1.06905 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.9110 | 0.803419 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.2913 | 1.49032 | 0.745161 | − | 0.666885i | \(-0.232373\pi\) | ||||
0.745161 | + | 0.666885i | \(0.232373\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.23281 | −0.0549682 | −0.0274841 | − | 0.999622i | \(-0.508750\pi\) | ||||
−0.0274841 | + | 0.999622i | \(0.508750\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.4069 | −1.30859 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.6113 | −1.44547 | −0.722736 | − | 0.691124i | \(-0.757116\pi\) | ||||
−0.722736 | + | 0.691124i | \(0.757116\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 41.8077 | 1.84946 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.9837 | 1.14498 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −40.3419 | −1.77423 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.7501 | −0.514783 | −0.257392 | − | 0.966307i | \(-0.582863\pi\) | ||||
−0.257392 | + | 0.966307i | \(0.582863\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.69627 | 0.0741728 | 0.0370864 | − | 0.999312i | \(-0.488192\pi\) | ||||
0.0370864 | + | 0.999312i | \(0.488192\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23.7367 | 1.03399 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.35203 | −0.188507 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.7794 | −0.682202 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −52.3674 | −2.25563 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.4879 | −1.22479 | −0.612395 | − | 0.790552i | \(-0.709794\pi\) | ||||
−0.612395 | + | 0.790552i | \(0.709794\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.8401 | −0.635682 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.2792 | 0.482264 | 0.241132 | − | 0.970492i | \(-0.422481\pi\) | ||||
0.241132 | + | 0.970492i | \(0.422481\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.2409 | −1.20310 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 45.4796 | 1.93399 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.55860 | 0.277897 | 0.138948 | − | 0.990300i | \(-0.455628\pi\) | ||||
0.138948 | + | 0.990300i | \(0.455628\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.17614 | −0.218927 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.3674 | 0.521225 | 0.260613 | − | 0.965443i | \(-0.416075\pi\) | ||||
0.260613 | + | 0.965443i | \(0.416075\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.58515 | −0.234969 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.41586 | −0.394733 | −0.197367 | − | 0.980330i | \(-0.563239\pi\) | ||||
−0.197367 | + | 0.980330i | \(0.563239\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.38259 | 0.183405 | 0.0917027 | − | 0.995786i | \(-0.470769\pi\) | ||||
0.0917027 | + | 0.995786i | \(0.470769\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.29150 | −0.0955623 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.22653 | −0.0926918 | −0.0463459 | − | 0.998925i | \(-0.514758\pi\) | ||||
−0.0463459 | + | 0.998925i | \(0.514758\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.02218 | −0.0838943 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.0790 | 0.541676 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −31.9332 | −1.31802 | −0.659012 | − | 0.752132i | \(-0.729025\pi\) | ||||
−0.659012 | + | 0.752132i | \(0.729025\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.2409 | 1.16364 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.16613 | 0.335343 | 0.167671 | − | 0.985843i | \(-0.446375\pi\) | ||||
0.167671 | + | 0.985843i | \(0.446375\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −39.9411 | −1.63742 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.4170 | −0.711639 | −0.355820 | − | 0.934555i | \(-0.615798\pi\) | ||||
−0.355820 | + | 0.934555i | \(0.615798\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.9395 | 1.09888 | 0.549442 | − | 0.835532i | \(-0.314840\pi\) | ||||
0.549442 | + | 0.835532i | \(0.314840\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.82189 | −0.114726 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.394688 | −0.0160199 | −0.00800994 | − | 0.999968i | \(-0.502550\pi\) | ||||
−0.00800994 | + | 0.999968i | \(0.502550\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.27535 | −0.253873 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.6751 | 1.07740 | 0.538699 | − | 0.842499i | \(-0.318916\pi\) | ||||
0.538699 | + | 0.842499i | \(0.318916\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.4443 | −0.903574 | −0.451787 | − | 0.892126i | \(-0.649213\pi\) | ||||
−0.451787 | + | 0.892126i | \(0.649213\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.6618 | −0.629500 | −0.314750 | − | 0.949175i | \(-0.601921\pi\) | ||||
−0.314750 | + | 0.949175i | \(0.601921\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −32.7346 | −1.31148 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.29150 | −0.331660 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.4674 | −0.736343 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.15897 | −0.284994 | −0.142497 | − | 0.989795i | \(-0.545513\pi\) | ||||
−0.142497 | + | 0.989795i | \(0.545513\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.49402 | 0.178340 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.14597 | −0.322755 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.5312 | −1.24541 | −0.622704 | − | 0.782457i | \(-0.713966\pi\) | ||||
−0.622704 | + | 0.782457i | \(0.713966\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.6681 | −0.578452 | −0.289226 | − | 0.957261i | \(-0.593398\pi\) | ||||
−0.289226 | + | 0.957261i | \(0.593398\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.7512 | 0.737184 | 0.368592 | − | 0.929591i | \(-0.379840\pi\) | ||||
0.368592 | + | 0.929591i | \(0.379840\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 39.7934 | 1.56203 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.0221 | 0.900923 | 0.450461 | − | 0.892796i | \(-0.351259\pi\) | ||||
0.450461 | + | 0.892796i | \(0.351259\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.25499 | −0.127183 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.1833 | −0.786228 | −0.393114 | − | 0.919490i | \(-0.628602\pi\) | ||||
−0.393114 | + | 0.919490i | \(0.628602\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.9381 | 1.28115 | 0.640573 | − | 0.767898i | \(-0.278697\pi\) | ||||
0.640573 | + | 0.767898i | \(0.278697\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −47.5201 | −1.84275 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.55467 | 0.176357 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.58313 | 0.215534 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.33587 | −0.282777 | −0.141389 | − | 0.989954i | \(-0.545157\pi\) | ||||
−0.141389 | + | 0.989954i | \(0.545157\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.9088 | 1.68755 | 0.843776 | − | 0.536695i | \(-0.180328\pi\) | ||||
0.843776 | + | 0.536695i | \(0.180328\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.7307 | −0.718818 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.9776 | 1.37664 | 0.688322 | − | 0.725406i | \(-0.258348\pi\) | ||||
0.688322 | + | 0.725406i | \(0.258348\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.5563 | 1.05287 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.03449 | 0.0775079 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.1376 | 1.22257 | 0.611285 | − | 0.791411i | \(-0.290653\pi\) | ||||
0.611285 | + | 0.791411i | \(0.290653\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.58301 | 0.249708 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −40.8904 | −1.54883 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.4046 | −0.430748 | −0.215374 | − | 0.976532i | \(-0.569097\pi\) | ||||
−0.215374 | + | 0.976532i | \(0.569097\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.9717 | −0.828677 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −83.2101 | −3.12944 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.30272 | 0.124036 | 0.0620181 | − | 0.998075i | \(-0.480246\pi\) | ||||
0.0620181 | + | 0.998075i | \(0.480246\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.55467 | −0.170574 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.25499 | −0.121730 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.79553 | 0.253430 | 0.126715 | − | 0.991939i | \(-0.459557\pi\) | ||||
0.126715 | + | 0.991939i | \(0.459557\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 73.5239 | 2.73817 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.4370 | −0.387622 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.5089 | −1.42822 | −0.714108 | − | 0.700035i | \(-0.753168\pi\) | ||||
−0.714108 | + | 0.700035i | \(0.753168\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −48.6335 | −1.79878 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.6970 | 1.72479 | 0.862397 | − | 0.506232i | \(-0.168962\pi\) | ||||
0.862397 | + | 0.506232i | \(0.168962\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.8903 | 1.10102 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 51.2101 | 1.88380 | 0.941898 | − | 0.335900i | \(-0.109040\pi\) | ||||
0.941898 | + | 0.335900i | \(0.109040\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −48.2751 | −1.77104 | −0.885521 | − | 0.464600i | \(-0.846198\pi\) | ||||
−0.885521 | + | 0.464600i | \(0.846198\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.0159 | 0.916512 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −44.6496 | −1.63146 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.24973 | −0.0456032 | −0.0228016 | − | 0.999740i | \(-0.507259\pi\) | ||||
−0.0228016 | + | 0.999740i | \(0.507259\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.00183 | 0.109248 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.0838 | −0.984377 | −0.492189 | − | 0.870489i | \(-0.663803\pi\) | ||||
−0.492189 | + | 0.870489i | \(0.663803\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.9411 | −1.30286 | −0.651431 | − | 0.758708i | \(-0.725831\pi\) | ||||
−0.651431 | + | 0.758708i | \(0.725831\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −41.9919 | −1.52021 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.19002 | 0.223509 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.1882 | 1.77377 | 0.886886 | − | 0.461989i | \(-0.152864\pi\) | ||||
0.886886 | + | 0.461989i | \(0.152864\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.90074 | 0.320138 | 0.160069 | − | 0.987106i | \(-0.448828\pi\) | ||||
0.160069 | + | 0.987106i | \(0.448828\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.4370 | 0.374909 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −48.6496 | −1.74305 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.7145 | 0.490744 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.5851 | −0.413492 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.88046 | 0.352200 | 0.176100 | − | 0.984372i | \(-0.443652\pi\) | ||||
0.176100 | + | 0.984372i | \(0.443652\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.8038 | −0.561919 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.868478 | 0.0308406 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 55.3013 | 1.95887 | 0.979437 | − | 0.201750i | \(-0.0646630\pi\) | ||||
0.979437 | + | 0.201750i | \(0.0646630\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −58.9614 | −2.08590 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.0123 | 1.12969 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.66401 | 0.270121 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.6863 | −1.07887 | −0.539437 | − | 0.842026i | \(-0.681363\pi\) | ||||
−0.539437 | + | 0.842026i | \(0.681363\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.25518 | 0.0791902 | 0.0395951 | − | 0.999216i | \(-0.487393\pi\) | ||||
0.0395951 | + | 0.999216i | \(0.487393\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.6394 | 0.863082 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −57.8620 | −2.02433 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.3947 | −0.711780 | −0.355890 | − | 0.934528i | \(-0.615822\pi\) | ||||
−0.355890 | + | 0.934528i | \(0.615822\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.18229 | −0.180643 | −0.0903216 | − | 0.995913i | \(-0.528789\pi\) | ||||
−0.0903216 | + | 0.995913i | \(0.528789\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.1934 | −0.563099 | −0.281550 | − | 0.959547i | \(-0.590848\pi\) | ||||
−0.281550 | + | 0.959547i | \(0.590848\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.0503 | −0.904763 | −0.452382 | − | 0.891824i | \(-0.649426\pi\) | ||||
−0.452382 | + | 0.891824i | \(0.649426\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −76.5373 | −2.65186 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −27.9776 | −0.968204 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.991950 | −0.0342459 | −0.0171230 | − | 0.999853i | \(-0.505451\pi\) | ||||
−0.0171230 | + | 0.999853i | \(0.505451\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.25499 | −0.284655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.8884 | 0.718584 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.98486 | −0.274363 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.54358 | 0.121472 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.7811 | −0.745770 | −0.372885 | − | 0.927878i | \(-0.621631\pi\) | ||||
−0.372885 | + | 0.927878i | \(0.621631\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.3197 | 1.17234 | 0.586170 | − | 0.810188i | \(-0.300635\pi\) | ||||
0.586170 | + | 0.810188i | \(0.300635\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.3280 | 0.386507 | 0.193253 | − | 0.981149i | \(-0.438096\pi\) | ||||
0.193253 | + | 0.981149i | \(0.438096\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.0059 | −1.08949 | −0.544747 | − | 0.838601i | \(-0.683374\pi\) | ||||
−0.544747 | + | 0.838601i | \(0.683374\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −42.3096 | −1.43857 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34.8239 | 1.18132 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.64956 | 0.157544 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −55.8821 | −1.88916 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.4309 | 0.824972 | 0.412486 | − | 0.910964i | \(-0.364661\pi\) | ||||
0.412486 | + | 0.910964i | \(0.364661\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.0797445 | 0.00268666 | 0.00134333 | − | 0.999999i | \(-0.499572\pi\) | ||||
0.00134333 | + | 0.999999i | \(0.499572\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.0282 | −0.505740 | −0.252870 | − | 0.967500i | \(-0.581374\pi\) | ||||
−0.252870 | + | 0.967500i | \(0.581374\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 50.7304 | 1.70336 | 0.851681 | − | 0.524061i | \(-0.175584\pi\) | ||||
0.851681 | + | 0.524061i | \(0.175584\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.7164 | 0.426493 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −70.1496 | −2.34747 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.8521 | 0.864140 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.7450 | −0.691885 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.1155 | 0.636829 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.4879 | 0.415111 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.3664 | 1.17432 | 0.587162 | − | 0.809470i | \(-0.300245\pi\) | ||||
0.587162 | + | 0.809470i | \(0.300245\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.9126 | 1.42176 | 0.710879 | − | 0.703314i | \(-0.248297\pi\) | ||||
0.710879 | + | 0.703314i | \(0.248297\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.54839 | −0.0512443 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.21038 | −0.304154 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.7278 | −1.14557 | −0.572783 | − | 0.819707i | \(-0.694136\pi\) | ||||
−0.572783 | + | 0.819707i | \(0.694136\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.13335 | 0.0702201 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.12012 | −0.266988 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.7810 | −1.20674 | −0.603372 | − | 0.797460i | \(-0.706177\pi\) | ||||
−0.603372 | + | 0.797460i | \(0.706177\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −91.0605 | −2.98439 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −30.5830 | −1.00017 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.36433 | −0.0772393 | −0.0386197 | − | 0.999254i | \(-0.512296\pi\) | ||||
−0.0386197 | + | 0.999254i | \(0.512296\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.82189 | −0.0919909 | −0.0459954 | − | 0.998942i | \(-0.514646\pi\) | ||||
−0.0459954 | + | 0.998942i | \(0.514646\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.84617 | 0.255506 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 49.8950 | 1.62137 | 0.810685 | − | 0.585483i | \(-0.199095\pi\) | ||||
0.810685 | + | 0.585483i | \(0.199095\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.97965 | 0.161646 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.6852 | 1.25314 | 0.626568 | − | 0.779367i | \(-0.284459\pi\) | ||||
0.626568 | + | 0.779367i | \(0.284459\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.4940 | −1.31036 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 77.9736 | 2.51790 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.2550 | −0.330806 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 31.8922 | 1.02665 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.918999 | 0.0295530 | 0.0147765 | − | 0.999891i | \(-0.495296\pi\) | ||||
0.0147765 | + | 0.999891i | \(0.495296\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.6083 | 1.17482 | 0.587408 | − | 0.809291i | \(-0.300148\pi\) | ||||
0.587408 | + | 0.809291i | \(0.300148\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.6274 | 0.597166 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.9502 | 0.734243 | 0.367122 | − | 0.930173i | \(-0.380343\pi\) | ||||
0.367122 | + | 0.930173i | \(0.380343\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.0650 | −0.801080 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.3058 | −0.807131 | −0.403565 | − | 0.914951i | \(-0.632229\pi\) | ||||
−0.403565 | + | 0.914951i | \(0.632229\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.99817 | −0.286706 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.33194 | 0.296738 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.65596 | −0.0843692 | −0.0421846 | − | 0.999110i | \(-0.513432\pi\) | ||||
−0.0421846 | + | 0.999110i | \(0.513432\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −41.9714 | −1.33058 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.8966 | −0.915164 | −0.457582 | − | 0.889168i | \(-0.651284\pi\) | ||||
−0.457582 | + | 0.889168i | \(0.651284\pi\) | |||||||
\(998\) | 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 | 3312.2.a.bh.1.1 | 4 | ||
3.2 | odd | 2 | 3312.2.a.bg.1.3 | 4 | |||
4.3 | odd | 2 | 1656.2.a.p.1.2 | yes | 4 | ||
12.11 | even | 2 | 1656.2.a.o.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1656.2.a.o.1.4 | ✓ | 4 | 12.11 | even | 2 | ||
1656.2.a.p.1.2 | yes | 4 | 4.3 | odd | 2 | ||
3312.2.a.bg.1.3 | 4 | 3.2 | odd | 2 | |||
3312.2.a.bh.1.1 | 4 | 1.1 | even | 1 | trivial |