Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3800,2,Mod(1,3800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3800, 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("3800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3800.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: | \(30.3431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 10x^{4} + 16x^{3} + 15x^{2} - 14x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.848258\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3800.1 |
$q$-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 | ||||||||
\(3\) | 0.848258 | 0.489742 | 0.244871 | − | 0.969556i | \(-0.421254\pi\) | ||||
0.244871 | + | 0.969556i | \(0.421254\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.74484 | 0.659486 | 0.329743 | − | 0.944071i | \(-0.393038\pi\) | ||||
0.329743 | + | 0.944071i | \(0.393038\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.28046 | −0.760153 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.92425 | 1.78623 | 0.893115 | − | 0.449829i | \(-0.148515\pi\) | ||||
0.893115 | + | 0.449829i | \(0.148515\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.78582 | 1.88205 | 0.941024 | − | 0.338339i | \(-0.109865\pi\) | ||||
0.941024 | + | 0.338339i | \(0.109865\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.86024 | 0.451174 | 0.225587 | − | 0.974223i | \(-0.427570\pi\) | ||||
0.225587 | + | 0.974223i | \(0.427570\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.48007 | 0.322978 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.94357 | 1.23932 | 0.619660 | − | 0.784871i | \(-0.287271\pi\) | ||||
0.619660 | + | 0.784871i | \(0.287271\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.47919 | −0.862021 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.29977 | 0.612752 | 0.306376 | − | 0.951911i | \(-0.400883\pi\) | ||||
0.306376 | + | 0.951911i | \(0.400883\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.75242 | −1.03316 | −0.516582 | − | 0.856238i | \(-0.672796\pi\) | ||||
−0.516582 | + | 0.856238i | \(0.672796\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.02529 | 0.874791 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.36379 | −0.717402 | −0.358701 | − | 0.933453i | \(-0.616780\pi\) | ||||
−0.358701 | + | 0.933453i | \(0.616780\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.75613 | 0.921718 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.12500 | 1.11274 | 0.556369 | − | 0.830935i | \(-0.312194\pi\) | ||||
0.556369 | + | 0.830935i | \(0.312194\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.98455 | −1.06513 | −0.532567 | − | 0.846388i | \(-0.678773\pi\) | ||||
−0.532567 | + | 0.846388i | \(0.678773\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.02529 | −0.587149 | −0.293575 | − | 0.955936i | \(-0.594845\pi\) | ||||
−0.293575 | + | 0.955936i | \(0.594845\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.95555 | −0.565078 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.57796 | 0.220959 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.19015 | −1.26236 | −0.631182 | − | 0.775635i | \(-0.717430\pi\) | ||||
−0.631182 | + | 0.775635i | \(0.717430\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.848258 | −0.112354 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.51553 | 0.327494 | 0.163747 | − | 0.986502i | \(-0.447642\pi\) | ||||
0.163747 | + | 0.986502i | \(0.447642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.49621 | −0.319607 | −0.159804 | − | 0.987149i | \(-0.551086\pi\) | ||||
−0.159804 | + | 0.987149i | \(0.551086\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.97903 | −0.501310 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.90485 | 0.843561 | 0.421781 | − | 0.906698i | \(-0.361405\pi\) | ||||
0.421781 | + | 0.906698i | \(0.361405\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.04168 | 0.606947 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.27288 | 0.151063 | 0.0755314 | − | 0.997143i | \(-0.475935\pi\) | ||||
0.0755314 | + | 0.997143i | \(0.475935\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.1217 | 1.41874 | 0.709371 | − | 0.704836i | \(-0.248979\pi\) | ||||
0.709371 | + | 0.704836i | \(0.248979\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.3368 | 1.17799 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.8376 | −1.55685 | −0.778424 | − | 0.627739i | \(-0.783980\pi\) | ||||
−0.778424 | + | 0.627739i | \(0.783980\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.04187 | 0.337985 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.94955 | −0.543283 | −0.271642 | − | 0.962398i | \(-0.587567\pi\) | ||||
−0.271642 | + | 0.962398i | \(0.587567\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.79906 | 0.300091 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.6067 | 1.65430 | 0.827151 | − | 0.561980i | \(-0.189960\pi\) | ||||
0.827151 | + | 0.561980i | \(0.189960\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.8401 | 1.24118 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.87953 | −0.505984 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.7764 | −1.60185 | −0.800924 | − | 0.598766i | \(-0.795658\pi\) | ||||
−0.800924 | + | 0.598766i | \(0.795658\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.5100 | −1.35781 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.81483 | −0.678101 | −0.339050 | − | 0.940768i | \(-0.610106\pi\) | ||||
−0.339050 | + | 0.940768i | \(0.610106\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.3177 | 1.31224 | 0.656118 | − | 0.754659i | \(-0.272197\pi\) | ||||
0.656118 | + | 0.754659i | \(0.272197\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.69935 | 0.357629 | 0.178815 | − | 0.983883i | \(-0.442774\pi\) | ||||
0.178815 | + | 0.983883i | \(0.442774\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.7753 | 1.22366 | 0.611828 | − | 0.790991i | \(-0.290434\pi\) | ||||
0.611828 | + | 0.790991i | \(0.290434\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.70162 | −0.351342 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.81845 | −0.829570 | −0.414785 | − | 0.909919i | \(-0.636143\pi\) | ||||
−0.414785 | + | 0.909919i | \(0.636143\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.4748 | −1.43064 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.24581 | 0.297543 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24.0968 | 2.19062 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.04384 | 0.544955 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.39650 | 0.390127 | 0.195063 | − | 0.980791i | \(-0.437509\pi\) | ||||
0.195063 | + | 0.980791i | \(0.437509\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.92470 | −0.521641 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.0076 | 1.83544 | 0.917719 | − | 0.397229i | \(-0.130028\pi\) | ||||
0.917719 | + | 0.397229i | \(0.130028\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.74484 | −0.151296 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.3766 | −0.971973 | −0.485986 | − | 0.873966i | \(-0.661540\pi\) | ||||
−0.485986 | + | 0.873966i | \(0.661540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.18664 | 0.439925 | 0.219962 | − | 0.975508i | \(-0.429407\pi\) | ||||
0.219962 | + | 0.975508i | \(0.429407\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.41449 | −0.287552 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 40.2009 | 3.36177 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.35533 | −0.276743 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.474871 | 0.0389030 | 0.0194515 | − | 0.999811i | \(-0.493808\pi\) | ||||
0.0194515 | + | 0.999811i | \(0.493808\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.6164 | 1.35222 | 0.676110 | − | 0.736800i | \(-0.263664\pi\) | ||||
0.676110 | + | 0.736800i | \(0.263664\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.24220 | −0.342962 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.83889 | 0.545803 | 0.272901 | − | 0.962042i | \(-0.412017\pi\) | ||||
0.272901 | + | 0.962042i | \(0.412017\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.79561 | −0.618232 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.3705 | 0.817314 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.42620 | 0.190035 | 0.0950173 | − | 0.995476i | \(-0.469709\pi\) | ||||
0.0950173 | + | 0.995476i | \(0.469709\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.02699 | 0.0794705 | 0.0397353 | − | 0.999210i | \(-0.487349\pi\) | ||||
0.0397353 | + | 0.999210i | \(0.487349\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.0474 | 2.54211 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.28046 | 0.174391 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.2443 | −1.00694 | −0.503472 | − | 0.864012i | \(-0.667944\pi\) | ||||
−0.503472 | + | 0.864012i | \(0.667944\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.13382 | 0.160387 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.8025 | −1.40536 | −0.702681 | − | 0.711505i | \(-0.748014\pi\) | ||||
−0.702681 | + | 0.711505i | \(0.748014\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.01073 | −0.595433 | −0.297716 | − | 0.954654i | \(-0.596225\pi\) | ||||
−0.297716 | + | 0.954654i | \(0.596225\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.11743 | −0.156525 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.0205 | 0.805901 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.81545 | −0.568490 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.3198 | 1.68736 | 0.843682 | − | 0.536844i | \(-0.180384\pi\) | ||||
0.843682 | + | 0.536844i | \(0.180384\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.55652 | 0.543930 | 0.271965 | − | 0.962307i | \(-0.412327\pi\) | ||||
0.271965 | + | 0.962307i | \(0.412327\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.5405 | −1.46345 | −0.731726 | − | 0.681599i | \(-0.761285\pi\) | ||||
−0.731726 | + | 0.681599i | \(0.761285\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.93624 | −0.349920 | −0.174960 | − | 0.984576i | \(-0.555980\pi\) | ||||
−0.174960 | + | 0.984576i | \(0.555980\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.85709 | 0.413127 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.75756 | 0.404102 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.5541 | −0.942072 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.92425 | −0.409789 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.6716 | −1.01003 | −0.505017 | − | 0.863109i | \(-0.668514\pi\) | ||||
−0.505017 | + | 0.863109i | \(0.668514\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.07973 | 0.0739818 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.0370 | −0.681357 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.2824 | 0.694817 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.6233 | 0.849132 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.8357 | 1.26133 | 0.630667 | − | 0.776054i | \(-0.282782\pi\) | ||||
0.630667 | + | 0.776054i | \(0.282782\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.8621 | −1.65015 | −0.825076 | − | 0.565021i | \(-0.808868\pi\) | ||||
−0.825076 | + | 0.565021i | \(0.808868\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.2743 | 1.33976 | 0.669880 | − | 0.742469i | \(-0.266345\pi\) | ||||
0.669880 | + | 0.742469i | \(0.266345\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.76831 | 0.576913 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.9597 | −1.76619 | −0.883095 | − | 0.469194i | \(-0.844545\pi\) | ||||
−0.883095 | + | 0.469194i | \(0.844545\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.7378 | −0.762453 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.1013 | 0.782767 | 0.391384 | − | 0.920228i | \(-0.371997\pi\) | ||||
0.391384 | + | 0.920228i | \(0.371997\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.2563 | −1.17599 | −0.587997 | − | 0.808863i | \(-0.700083\pi\) | ||||
−0.587997 | + | 0.808863i | \(0.700083\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0179 | 1.02755 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.78582 | −0.431772 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.19849 | −0.266069 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.65623 | −0.357018 | −0.178509 | − | 0.983938i | \(-0.557127\pi\) | ||||
−0.178509 | + | 0.983938i | \(0.557127\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 35.2112 | 2.21371 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.04957 | −0.502119 | −0.251059 | − | 0.967972i | \(-0.580779\pi\) | ||||
−0.251059 | + | 0.967972i | \(0.580779\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.61409 | −0.473116 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.52500 | −0.465786 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.24808 | −0.508598 | −0.254299 | − | 0.967126i | \(-0.581845\pi\) | ||||
−0.254299 | + | 0.967126i | \(0.581845\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.2385 | 0.810181 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.48032 | −0.517054 | −0.258527 | − | 0.966004i | \(-0.583237\pi\) | ||||
−0.258527 | + | 0.966004i | \(0.583237\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.2291 | 1.83629 | 0.918145 | − | 0.396244i | \(-0.129687\pi\) | ||||
0.918145 | + | 0.396244i | \(0.129687\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.0435 | 0.607860 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.42364 | 0.145622 | 0.0728111 | − | 0.997346i | \(-0.476803\pi\) | ||||
0.0728111 | + | 0.997346i | \(0.476803\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.1181 | 0.785363 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.6355 | −1.23101 | −0.615504 | − | 0.788133i | \(-0.711048\pi\) | ||||
−0.615504 | + | 0.788133i | \(0.711048\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −30.1197 | −1.79043 | −0.895215 | − | 0.445635i | \(-0.852978\pi\) | ||||
−0.895215 | + | 0.445635i | \(0.852978\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.4320 | 0.733835 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.5395 | −0.796442 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.3824 | −0.784492 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.8274 | 0.690963 | 0.345481 | − | 0.938426i | \(-0.387716\pi\) | ||||
0.345481 | + | 0.938426i | \(0.387716\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −26.5359 | −1.53977 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 40.3320 | 2.33246 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.1869 | −0.702441 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.78073 | −0.332094 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.22041 | 0.412091 | 0.206045 | − | 0.978542i | \(-0.433941\pi\) | ||||
0.206045 | + | 0.978542i | \(0.433941\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.2969 | 0.642657 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.1574 | −0.575975 | −0.287987 | − | 0.957634i | \(-0.592986\pi\) | ||||
−0.287987 | + | 0.957634i | \(0.592986\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.03525 | −0.341132 | −0.170566 | − | 0.985346i | \(-0.554560\pi\) | ||||
−0.170566 | + | 0.985346i | \(0.554560\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −30.5978 | −1.71854 | −0.859271 | − | 0.511520i | \(-0.829083\pi\) | ||||
−0.859271 | + | 0.511520i | \(0.829083\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.5487 | 1.09452 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.13800 | 0.175146 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.86024 | −0.103507 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.8368 | 0.599276 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.02348 | −0.387217 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.1478 | 1.05246 | 0.526228 | − | 0.850343i | \(-0.323606\pi\) | ||||
0.526228 | + | 0.850343i | \(0.323606\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.95143 | 0.545335 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.8090 | 0.588804 | 0.294402 | − | 0.955682i | \(-0.404880\pi\) | ||||
0.294402 | + | 0.955682i | \(0.404880\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.48032 | −0.406275 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −34.0788 | −1.84547 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.1156 | −1.03215 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.0847 | 1.02452 | 0.512261 | − | 0.858830i | \(-0.328808\pi\) | ||||
0.512261 | + | 0.858830i | \(0.328808\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.18421 | 0.277504 | 0.138752 | − | 0.990327i | \(-0.455691\pi\) | ||||
0.138752 | + | 0.990327i | \(0.455691\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −30.3950 | −1.62236 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.6398 | −0.832423 | −0.416212 | − | 0.909268i | \(-0.636642\pi\) | ||||
−0.416212 | + | 0.909268i | \(0.636642\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.75329 | 0.145719 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.4768 | −0.922392 | −0.461196 | − | 0.887298i | \(-0.652580\pi\) | ||||
−0.461196 | + | 0.887298i | \(0.652580\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 20.4403 | 1.07284 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.99560 | −0.156369 | −0.0781845 | − | 0.996939i | \(-0.524912\pi\) | ||||
−0.0781845 | + | 0.996939i | \(0.524912\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.2483 | −0.845852 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.0353 | −0.832511 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.76504 | −0.194946 | −0.0974731 | − | 0.995238i | \(-0.531076\pi\) | ||||
−0.0974731 | + | 0.995238i | \(0.531076\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.3917 | 1.15323 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.5503 | −0.541933 | −0.270967 | − | 0.962589i | \(-0.587343\pi\) | ||||
−0.270967 | + | 0.962589i | \(0.587343\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.72937 | 0.191061 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.25532 | −0.319632 | −0.159816 | − | 0.987147i | \(-0.551090\pi\) | ||||
−0.159816 | + | 0.987147i | \(0.551090\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15.9280 | 0.809665 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.8669 | 0.652379 | 0.326190 | − | 0.945304i | \(-0.394235\pi\) | ||||
0.326190 | + | 0.945304i | \(0.394235\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.0565 | 0.559149 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.8198 | 0.898891 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.4649 | 1.42861 | 0.714306 | − | 0.699834i | \(-0.246743\pi\) | ||||
0.714306 | + | 0.699834i | \(0.246743\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.48007 | −0.0740962 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.2837 | 0.863106 | 0.431553 | − | 0.902088i | \(-0.357966\pi\) | ||||
0.431553 | + | 0.902088i | \(0.357966\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −39.0349 | −1.94447 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.8522 | −1.28144 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.3677 | −1.40269 | −0.701346 | − | 0.712821i | \(-0.747417\pi\) | ||||
−0.701346 | + | 0.712821i | \(0.747417\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.65033 | −0.476016 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.38918 | 0.215978 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.39961 | 0.215450 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.0821 | −0.492542 | −0.246271 | − | 0.969201i | \(-0.579205\pi\) | ||||
−0.246271 | + | 0.969201i | \(0.579205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.3802 | 0.993269 | 0.496635 | − | 0.867960i | \(-0.334569\pi\) | ||||
0.496635 | + | 0.867960i | \(0.334569\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.17952 | 0.446323 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.35548 | −0.210777 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 34.1008 | 1.64640 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.1090 | 0.872280 | 0.436140 | − | 0.899879i | \(-0.356345\pi\) | ||||
0.436140 | + | 0.899879i | \(0.356345\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.8792 | −1.62813 | −0.814066 | − | 0.580772i | \(-0.802751\pi\) | ||||
−0.814066 | + | 0.580772i | \(0.802751\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.94357 | −0.284319 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.7440 | 1.03779 | 0.518893 | − | 0.854839i | \(-0.326344\pi\) | ||||
0.518893 | + | 0.854839i | \(0.326344\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.02047 | 0.429546 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.6461 | 0.980924 | 0.490462 | − | 0.871463i | \(-0.336828\pi\) | ||||
0.490462 | + | 0.871463i | \(0.336828\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.402813 | 0.0190524 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.4288 | 0.775322 | 0.387661 | − | 0.921802i | \(-0.373283\pi\) | ||||
0.387661 | + | 0.921802i | \(0.373283\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 42.2103 | 1.98761 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.0950 | 0.662239 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.5543 | −0.914711 | −0.457355 | − | 0.889284i | \(-0.651203\pi\) | ||||
−0.457355 | + | 0.889284i | \(0.651203\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.33237 | −0.388922 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.4065 | 0.717554 | 0.358777 | − | 0.933423i | \(-0.383194\pi\) | ||||
0.358777 | + | 0.933423i | \(0.383194\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.44151 | 0.206414 | 0.103207 | − | 0.994660i | \(-0.467090\pi\) | ||||
0.103207 | + | 0.994660i | \(0.467090\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.1240 | 0.561030 | 0.280515 | − | 0.959850i | \(-0.409495\pi\) | ||||
0.280515 | + | 0.959850i | \(0.409495\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.0478 | 0.556317 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.80114 | 0.267303 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −41.3783 | −1.90257 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 20.9577 | 0.959589 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −42.5961 | −1.94626 | −0.973132 | − | 0.230249i | \(-0.926046\pi\) | ||||
−0.973132 | + | 0.230249i | \(0.926046\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −29.6119 | −1.35019 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.79690 | 0.400273 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.3424 | 0.876489 | 0.438245 | − | 0.898856i | \(-0.355600\pi\) | ||||
0.438245 | + | 0.898856i | \(0.355600\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.05804 | 0.0930679 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.2941 | 0.554823 | 0.277412 | − | 0.960751i | \(-0.410523\pi\) | ||||
0.277412 | + | 0.960751i | \(0.410523\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.13837 | 0.276458 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.22096 | 0.0996238 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.75085 | 0.0783789 | 0.0391894 | − | 0.999232i | \(-0.487522\pi\) | ||||
0.0391894 | + | 0.999232i | \(0.487522\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.871149 | 0.0389201 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.13252 | 0.0950843 | 0.0475422 | − | 0.998869i | \(-0.484861\pi\) | ||||
0.0475422 | + | 0.998869i | \(0.484861\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28.0327 | 1.24498 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −35.0078 | −1.55169 | −0.775846 | − | 0.630923i | \(-0.782676\pi\) | ||||
−0.775846 | + | 0.630923i | \(0.782676\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.1504 | 0.935640 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.47919 | 0.197761 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23.8469 | −1.04878 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.2346 | −0.493143 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.5581 | −0.681613 | −0.340807 | − | 0.940133i | \(-0.610700\pi\) | ||||
−0.340807 | + | 0.940133i | \(0.610700\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.91872 | 0.433715 | 0.216858 | − | 0.976203i | \(-0.430419\pi\) | ||||
0.216858 | + | 0.976203i | \(0.430419\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.7009 | −0.466137 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.3260 | 0.535913 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.73656 | −0.248945 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 48.3490 | 2.09423 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.9493 | −0.688264 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.4337 | −1.00936 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.7150 | 1.79347 | 0.896734 | − | 0.442569i | \(-0.145933\pi\) | ||||
0.896734 | + | 0.442569i | \(0.145933\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.79516 | −0.291608 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.9230 | −0.809089 | −0.404545 | − | 0.914518i | \(-0.632570\pi\) | ||||
−0.404545 | + | 0.914518i | \(0.632570\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.69251 | 0.242951 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.29977 | −0.140575 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.1443 | −1.02672 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.02768 | −0.0859157 | −0.0429579 | − | 0.999077i | \(-0.513678\pi\) | ||||
−0.0429579 | + | 0.999077i | \(0.513678\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −47.3960 | −2.00464 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.34825 | 0.394684 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.7497 | 0.874497 | 0.437248 | − | 0.899341i | \(-0.355953\pi\) | ||||
0.437248 | + | 0.899341i | \(0.355953\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.30756 | 0.222897 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.2161 | 0.763659 | 0.381830 | − | 0.924233i | \(-0.375294\pi\) | ||||
0.381830 | + | 0.924233i | \(0.375294\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.0512 | −1.46685 | −0.733424 | − | 0.679771i | \(-0.762079\pi\) | ||||
−0.733424 | + | 0.679771i | \(0.762079\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.7812 | 0.826372 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.6181 | 0.899973 | 0.449987 | − | 0.893035i | \(-0.351429\pi\) | ||||
0.449987 | + | 0.893035i | \(0.351429\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.40987 | 0.266385 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.63615 | −0.358288 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −54.4448 | −2.25487 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.3305 | 0.839130 | 0.419565 | − | 0.907725i | \(-0.362183\pi\) | ||||
0.419565 | + | 0.907725i | \(0.362183\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.75242 | 0.237024 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.4237 | −0.716714 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.11878 | −0.0870077 | −0.0435039 | − | 0.999053i | \(-0.513852\pi\) | ||||
−0.0435039 | + | 0.999053i | \(0.513852\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.18720 | −0.171371 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.08633 | −0.166963 | −0.0834814 | − | 0.996509i | \(-0.526604\pi\) | ||||
−0.0834814 | + | 0.996509i | \(0.526604\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.7445 | −0.968557 | −0.484279 | − | 0.874914i | \(-0.660918\pi\) | ||||
−0.484279 | + | 0.874914i | \(0.660918\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.7462 | −0.641236 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.5940 | 0.957653 | 0.478826 | − | 0.877910i | \(-0.341062\pi\) | ||||
0.478826 | + | 0.877910i | \(0.341062\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.88390 | 0.197905 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.3149 | −1.10504 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −48.4877 | −1.95840 | −0.979200 | − | 0.202897i | \(-0.934964\pi\) | ||||
−0.979200 | + | 0.202897i | \(0.934964\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.1353 | −1.25346 | −0.626730 | − | 0.779236i | \(-0.715607\pi\) | ||||
−0.626730 | + | 0.779236i | \(0.715607\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.1220 | 1.21071 | 0.605353 | − | 0.795957i | \(-0.293032\pi\) | ||||
0.605353 | + | 0.795957i | \(0.293032\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −26.6224 | −1.06832 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.2310 | 1.09099 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.02529 | −0.200691 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.11769 | −0.323673 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.15070 | −0.244855 | −0.122428 | − | 0.992477i | \(-0.539068\pi\) | ||||
−0.122428 | + | 0.992477i | \(0.539068\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.4453 | −0.494656 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.8417 | −1.06351 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.90275 | −0.114831 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.9554 | −0.827690 | −0.413845 | − | 0.910347i | \(-0.635814\pi\) | ||||
−0.413845 | + | 0.910347i | \(0.635814\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.6309 | −0.971349 | −0.485675 | − | 0.874140i | \(-0.661426\pi\) | ||||
−0.485675 | + | 0.874140i | \(0.661426\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.1496 | 0.634906 | 0.317453 | − | 0.948274i | \(-0.397172\pi\) | ||||
0.317453 | + | 0.948274i | \(0.397172\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.9026 | 0.584979 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.51398 | −0.333689 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.3511 | 1.30513 | 0.652565 | − | 0.757733i | \(-0.273693\pi\) | ||||
0.652565 | + | 0.757733i | \(0.273693\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −27.6431 | −1.07846 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.1727 | −0.435226 | −0.217613 | − | 0.976035i | \(-0.569827\pi\) | ||||
−0.217613 | + | 0.976035i | \(0.569827\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.5484 | −1.30488 | −0.652440 | − | 0.757840i | \(-0.726255\pi\) | ||||
−0.652440 | + | 0.757840i | \(0.726255\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.7078 | 0.415856 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.6124 | 0.759396 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.9775 | 0.617728 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.7882 | −0.570892 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.13528 | 0.159403 | 0.0797017 | − | 0.996819i | \(-0.474603\pi\) | ||||
0.0797017 | + | 0.996819i | \(0.474603\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.7150 | −0.680842 | −0.340421 | − | 0.940273i | \(-0.610570\pi\) | ||||
−0.340421 | + | 0.940273i | \(0.610570\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.5272 | −1.05640 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.0894 | −0.808149 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.1004 | 0.501273 | 0.250637 | − | 0.968081i | \(-0.419360\pi\) | ||||
0.250637 | + | 0.968081i | \(0.419360\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.1978 | 0.656137 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −62.3627 | −2.37583 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.6952 | −0.711200 | −0.355600 | − | 0.934638i | \(-0.615724\pi\) | ||||
−0.355600 | + | 0.934638i | \(0.615724\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −23.5728 | −0.895455 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.2542 | 0.502039 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.8688 | −0.864977 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.3160 | −1.25833 | −0.629164 | − | 0.777273i | \(-0.716603\pi\) | ||||
−0.629164 | + | 0.777273i | \(0.716603\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.36379 | 0.164583 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.8908 | −0.447198 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.1888 | 0.420206 | 0.210103 | − | 0.977679i | \(-0.432620\pi\) | ||||
0.210103 | + | 0.977679i | \(0.432620\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.5560 | 1.18344 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −34.1899 | −1.28042 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.2650 | 0.383354 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.3734 | 0.685212 | 0.342606 | − | 0.939479i | \(-0.388690\pi\) | ||||
0.342606 | + | 0.939479i | \(0.388690\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.2373 | 0.865401 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.4861 | −0.575934 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.69538 | 0.322494 | 0.161247 | − | 0.986914i | \(-0.448448\pi\) | ||||
0.161247 | + | 0.986914i | \(0.448448\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.46167 | 0.165247 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.9929 | −0.480562 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.9016 | −1.54767 | −0.773836 | − | 0.633386i | \(-0.781665\pi\) | ||||
−0.773836 | + | 0.633386i | \(0.781665\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 40.9061 | 1.50679 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 49.4636 | 1.81955 | 0.909774 | − | 0.415104i | \(-0.136255\pi\) | ||||
0.909774 | + | 0.415104i | \(0.136255\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.75613 | −0.211457 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.1266 | −1.14192 | −0.570962 | − | 0.820977i | \(-0.693430\pi\) | ||||
−0.570962 | + | 0.820977i | \(0.693430\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.2872 | 0.412978 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.45475 | 0.235852 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.27888 | 0.229119 | 0.114560 | − | 0.993416i | \(-0.463454\pi\) | ||||
0.114560 | + | 0.993416i | \(0.463454\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.79794 | −0.174847 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.1507 | 1.38661 | 0.693304 | − | 0.720645i | \(-0.256154\pi\) | ||||
0.693304 | + | 0.720645i | \(0.256154\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 29.8682 | 1.08415 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.59360 | −0.0940180 | −0.0470090 | − | 0.998894i | \(-0.514969\pi\) | ||||
−0.0470090 | + | 0.998894i | \(0.514969\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.2909 | 0.806984 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.0699 | 0.616359 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.8561 | −1.90604 | −0.953020 | − | 0.302908i | \(-0.902043\pi\) | ||||
−0.953020 | + | 0.302908i | \(0.902043\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.82811 | −0.245908 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.1684 | 0.761374 | 0.380687 | − | 0.924704i | \(-0.375688\pi\) | ||||
0.380687 | + | 0.924704i | \(0.375688\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.45871 | −0.231705 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.12500 | −0.255280 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.54085 | 0.269833 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14.7803 | −0.528205 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 48.1097 | 1.71492 | 0.857462 | − | 0.514547i | \(-0.172040\pi\) | ||||
0.857462 | + | 0.514547i | \(0.172040\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.99650 | −0.249082 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.3867 | −0.547090 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.9389 | −0.601517 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.3510 | 0.508338 | 0.254169 | − | 0.967160i | \(-0.418198\pi\) | ||||
0.254169 | + | 0.967160i | \(0.418198\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.48801 | −0.264907 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −35.5903 | −1.25752 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 71.8122 | 2.53420 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.19350 | −0.253223 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.2263 | −0.992384 | −0.496192 | − | 0.868213i | \(-0.665269\pi\) | ||||
−0.496192 | + | 0.868213i | \(0.665269\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.7490 | −0.623250 | −0.311625 | − | 0.950205i | \(-0.600873\pi\) | ||||
−0.311625 | + | 0.950205i | \(0.600873\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.6421 | 0.899308 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.98455 | 0.244359 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −27.0010 | −0.943490 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.2066 | −1.12402 | −0.562010 | − | 0.827130i | \(-0.689972\pi\) | ||||
−0.562010 | + | 0.827130i | \(0.689972\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.0278 | −0.942130 | −0.471065 | − | 0.882099i | \(-0.656130\pi\) | ||||
−0.471065 | + | 0.882099i | \(0.656130\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41.2334 | 1.43383 | 0.716913 | − | 0.697163i | \(-0.245555\pi\) | ||||
0.716913 | + | 0.697163i | \(0.245555\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.0919 | −0.767285 | −0.383642 | − | 0.923482i | \(-0.625330\pi\) | ||||
−0.383642 | + | 0.923482i | \(0.625330\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.05587 | 0.0713173 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.35827 | −0.254949 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25.7662 | 0.890609 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.1096 | 0.763310 | 0.381655 | − | 0.924305i | \(-0.375354\pi\) | ||||
0.381655 | + | 0.924305i | \(0.375354\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.1115 | −0.624534 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.5042 | −0.602877 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 42.0449 | 1.44468 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.5493 | −0.876848 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.9365 | −0.889090 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.0868 | 0.824717 | 0.412359 | − | 0.911022i | \(-0.364705\pi\) | ||||
0.412359 | + | 0.911022i | \(0.364705\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.7836 | −1.22235 | −0.611173 | − | 0.791497i | \(-0.709302\pi\) | ||||
−0.611173 | + | 0.791497i | \(0.709302\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.4286 | −0.560538 | −0.280269 | − | 0.959922i | \(-0.590424\pi\) | ||||
−0.280269 | + | 0.959922i | \(0.590424\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.5455 | 0.359390 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.2841 | −0.554319 | −0.277159 | − | 0.960824i | \(-0.589393\pi\) | ||||
−0.277159 | + | 0.960824i | \(0.589393\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.4850 | −0.390051 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −81.9772 | −2.78089 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.8551 | 1.58762 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 35.9774 | 1.21765 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 57.3960 | 1.93813 | 0.969063 | − | 0.246814i | \(-0.0793835\pi\) | ||||
0.969063 | + | 0.246814i | \(0.0793835\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.0327 | 0.338393 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.6832 | 1.74125 | 0.870625 | − | 0.491947i | \(-0.163715\pi\) | ||||
0.870625 | + | 0.491947i | \(0.163715\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.8329 | −1.10492 | −0.552458 | − | 0.833541i | \(-0.686310\pi\) | ||||
−0.552458 | + | 0.833541i | \(0.686310\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.04248 | −0.236463 | −0.118232 | − | 0.992986i | \(-0.537723\pi\) | ||||
−0.118232 | + | 0.992986i | \(0.537723\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.67118 | 0.257283 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.0208 | 0.603719 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.02529 | 0.134701 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 34.2119 | 1.14230 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.9817 | −0.633074 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.0959 | −0.569546 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.3376 | −0.344015 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.94068 | 0.0644391 | 0.0322195 | − | 0.999481i | \(-0.489742\pi\) | ||||
0.0322195 | + | 0.999481i | \(0.489742\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.5409 | 0.515460 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −57.4852 | −1.90457 | −0.952284 | − | 0.305212i | \(-0.901273\pi\) | ||||
−0.952284 | + | 0.305212i | \(0.901273\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29.3224 | −0.970429 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36.6547 | 1.21045 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.4475 | 1.63112 | 0.815561 | − | 0.578672i | \(-0.196429\pi\) | ||||
0.815561 | + | 0.578672i | \(0.196429\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.12477 | 0.201818 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.63753 | 0.284308 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30.3705 | −0.997500 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43.8092 | 1.43733 | 0.718667 | − | 0.695354i | \(-0.244753\pi\) | ||||
0.718667 | + | 0.695354i | \(0.244753\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.95555 | 0.129638 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.61612 | −0.282079 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.4692 | −0.864712 | −0.432356 | − | 0.901703i | \(-0.642318\pi\) | ||||
−0.432356 | + | 0.901703i | \(0.642318\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.11945 | −0.167067 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.38141 | −0.0450327 | −0.0225164 | − | 0.999746i | \(-0.507168\pi\) | ||||
−0.0225164 | + | 0.999746i | \(0.507168\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42.3479 | 1.37904 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.40723 | −0.0457289 | −0.0228645 | − | 0.999739i | \(-0.507279\pi\) | ||||
−0.0228645 | + | 0.999739i | \(0.507279\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 82.2559 | 2.67014 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.9548 | −0.841642 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.5899 | −0.731760 | −0.365880 | − | 0.930662i | \(-0.619232\pi\) | ||||
−0.365880 | + | 0.930662i | \(0.619232\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.5823 | 0.536031 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.8504 | −0.641002 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.09029 | 0.0674287 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.43621 | −0.271853 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.8866 | −1.08972 | −0.544860 | − | 0.838527i | \(-0.683417\pi\) | ||||
−0.544860 | + | 0.838527i | \(0.683417\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.57796 | −0.0506915 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.0982 | 0.612890 | 0.306445 | − | 0.951888i | \(-0.400860\pi\) | ||||
0.306445 | + | 0.951888i | \(0.400860\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.04983 | 0.290124 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35.4149 | −1.13302 | −0.566511 | − | 0.824054i | \(-0.691707\pi\) | ||||
−0.566511 | + | 0.824054i | \(0.691707\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 92.4578 | 2.95496 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.1336 | −0.930166 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.3537 | −1.19140 | −0.595700 | − | 0.803207i | \(-0.703125\pi\) | ||||
−0.595700 | + | 0.803207i | \(0.703125\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.95772 | −0.189636 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −41.5132 | −1.32004 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.4720 | 0.682082 | 0.341041 | − | 0.940048i | \(-0.389221\pi\) | ||||
0.341041 | + | 0.940048i | \(0.389221\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.2422 | 0.515432 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.3410 | 0.644204 | 0.322102 | − | 0.946705i | \(-0.395611\pi\) | ||||
0.322102 | + | 0.946705i | \(0.395611\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 19.5462 | 0.618415 |
(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 | 3800.2.a.bc.1.4 | yes | 6 | |
4.3 | odd | 2 | 7600.2.a.ch.1.3 | 6 | |||
5.2 | odd | 4 | 3800.2.d.q.3649.5 | 12 | |||
5.3 | odd | 4 | 3800.2.d.q.3649.8 | 12 | |||
5.4 | even | 2 | 3800.2.a.ba.1.3 | ✓ | 6 | ||
20.19 | odd | 2 | 7600.2.a.cl.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3800.2.a.ba.1.3 | ✓ | 6 | 5.4 | even | 2 | ||
3800.2.a.bc.1.4 | yes | 6 | 1.1 | even | 1 | trivial | |
3800.2.d.q.3649.5 | 12 | 5.2 | odd | 4 | |||
3800.2.d.q.3649.8 | 12 | 5.3 | odd | 4 | |||
7600.2.a.ch.1.3 | 6 | 4.3 | odd | 2 | |||
7600.2.a.cl.1.4 | 6 | 20.19 | odd | 2 |