Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4014,2,Mod(1,4014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4014 = 2 \cdot 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4014.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0519513713\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 14x^{5} + 12x^{4} + 50x^{3} - 36x^{2} - 38x + 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 446) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-2.90898\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4014.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.52361 | 1.57581 | 0.787903 | − | 0.615800i | \(-0.211167\pi\) | ||||
0.787903 | + | 0.615800i | \(0.211167\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.552246 | −0.208729 | −0.104365 | − | 0.994539i | \(-0.533281\pi\) | ||||
−0.104365 | + | 0.994539i | \(0.533281\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.52361 | −1.11426 | ||||||||
\(11\) | −4.67688 | −1.41013 | −0.705066 | − | 0.709142i | \(-0.749082\pi\) | ||||
−0.705066 | + | 0.709142i | \(0.749082\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.98313 | 1.38207 | 0.691036 | − | 0.722821i | \(-0.257155\pi\) | ||||
0.691036 | + | 0.722821i | \(0.257155\pi\) | |||||||
\(14\) | 0.552246 | 0.147594 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.42398 | 1.31551 | 0.657754 | − | 0.753233i | \(-0.271507\pi\) | ||||
0.657754 | + | 0.753233i | \(0.271507\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.81795 | 1.33473 | 0.667365 | − | 0.744731i | \(-0.267422\pi\) | ||||
0.667365 | + | 0.744731i | \(0.267422\pi\) | |||||||
\(20\) | 3.52361 | 0.787903 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.67688 | 0.997113 | ||||||||
\(23\) | −1.00816 | −0.210216 | −0.105108 | − | 0.994461i | \(-0.533519\pi\) | ||||
−0.105108 | + | 0.994461i | \(0.533519\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.41582 | 1.48316 | ||||||||
\(26\) | −4.98313 | −0.977272 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.552246 | −0.104365 | ||||||||
\(29\) | −1.30022 | −0.241444 | −0.120722 | − | 0.992686i | \(-0.538521\pi\) | ||||
−0.120722 | + | 0.992686i | \(0.538521\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.55507 | −0.458904 | −0.229452 | − | 0.973320i | \(-0.573693\pi\) | ||||
−0.229452 | + | 0.973320i | \(0.573693\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.42398 | −0.930205 | ||||||||
\(35\) | −1.94590 | −0.328917 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.51958 | 1.07181 | 0.535906 | − | 0.844278i | \(-0.319970\pi\) | ||||
0.535906 | + | 0.844278i | \(0.319970\pi\) | |||||||
\(38\) | −5.81795 | −0.943797 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.52361 | −0.557131 | ||||||||
\(41\) | 1.43947 | 0.224807 | 0.112404 | − | 0.993663i | \(-0.464145\pi\) | ||||
0.112404 | + | 0.993663i | \(0.464145\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.12633 | −0.324263 | −0.162131 | − | 0.986769i | \(-0.551837\pi\) | ||||
−0.162131 | + | 0.986769i | \(0.551837\pi\) | |||||||
\(44\) | −4.67688 | −0.705066 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00816 | 0.148645 | ||||||||
\(47\) | −9.21193 | −1.34370 | −0.671849 | − | 0.740688i | \(-0.734500\pi\) | ||||
−0.671849 | + | 0.740688i | \(0.734500\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.69502 | −0.956432 | ||||||||
\(50\) | −7.41582 | −1.04876 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.98313 | 0.691036 | ||||||||
\(53\) | 11.7307 | 1.61133 | 0.805666 | − | 0.592370i | \(-0.201808\pi\) | ||||
0.805666 | + | 0.592370i | \(0.201808\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.4795 | −2.22209 | ||||||||
\(56\) | 0.552246 | 0.0737970 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.30022 | 0.170727 | ||||||||
\(59\) | −10.2734 | −1.33748 | −0.668741 | − | 0.743495i | \(-0.733166\pi\) | ||||
−0.668741 | + | 0.743495i | \(0.733166\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.3437 | 1.32438 | 0.662190 | − | 0.749336i | \(-0.269627\pi\) | ||||
0.662190 | + | 0.749336i | \(0.269627\pi\) | |||||||
\(62\) | 2.55507 | 0.324494 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 17.5586 | 2.17788 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.7510 | 1.80212 | 0.901058 | − | 0.433699i | \(-0.142792\pi\) | ||||
0.901058 | + | 0.433699i | \(0.142792\pi\) | |||||||
\(68\) | 5.42398 | 0.657754 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.94590 | 0.232579 | ||||||||
\(71\) | −13.2562 | −1.57322 | −0.786611 | − | 0.617449i | \(-0.788166\pi\) | ||||
−0.786611 | + | 0.617449i | \(0.788166\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.22665 | −0.143569 | −0.0717844 | − | 0.997420i | \(-0.522869\pi\) | ||||
−0.0717844 | + | 0.997420i | \(0.522869\pi\) | |||||||
\(74\) | −6.51958 | −0.757886 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.81795 | 0.667365 | ||||||||
\(77\) | 2.58279 | 0.294336 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.86075 | 0.884403 | 0.442202 | − | 0.896916i | \(-0.354198\pi\) | ||||
0.442202 | + | 0.896916i | \(0.354198\pi\) | |||||||
\(80\) | 3.52361 | 0.393951 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.43947 | −0.158963 | ||||||||
\(83\) | 1.03632 | 0.113751 | 0.0568755 | − | 0.998381i | \(-0.481886\pi\) | ||||
0.0568755 | + | 0.998381i | \(0.481886\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.1120 | 2.07299 | ||||||||
\(86\) | 2.12633 | 0.229288 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.67688 | 0.498557 | ||||||||
\(89\) | −6.94988 | −0.736686 | −0.368343 | − | 0.929690i | \(-0.620075\pi\) | ||||
−0.368343 | + | 0.929690i | \(0.620075\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.75191 | −0.288479 | ||||||||
\(92\) | −1.00816 | −0.105108 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.21193 | 0.950138 | ||||||||
\(95\) | 20.5002 | 2.10328 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.1636 | −1.53964 | −0.769818 | − | 0.638264i | \(-0.779653\pi\) | ||||
−0.769818 | + | 0.638264i | \(0.779653\pi\) | |||||||
\(98\) | 6.69502 | 0.676300 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.41582 | 0.741582 | ||||||||
\(101\) | 5.37759 | 0.535090 | 0.267545 | − | 0.963545i | \(-0.413788\pi\) | ||||
0.267545 | + | 0.963545i | \(0.413788\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.48947 | 0.343828 | 0.171914 | − | 0.985112i | \(-0.445005\pi\) | ||||
0.171914 | + | 0.985112i | \(0.445005\pi\) | |||||||
\(104\) | −4.98313 | −0.488636 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.7307 | −1.13938 | ||||||||
\(107\) | 19.0825 | 1.84478 | 0.922389 | − | 0.386263i | \(-0.126234\pi\) | ||||
0.922389 | + | 0.386263i | \(0.126234\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.42944 | −0.328481 | −0.164240 | − | 0.986420i | \(-0.552517\pi\) | ||||
−0.164240 | + | 0.986420i | \(0.552517\pi\) | |||||||
\(110\) | 16.4795 | 1.57126 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.552246 | −0.0521823 | ||||||||
\(113\) | 11.2528 | 1.05857 | 0.529287 | − | 0.848443i | \(-0.322459\pi\) | ||||
0.529287 | + | 0.848443i | \(0.322459\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.55237 | −0.331260 | ||||||||
\(116\) | −1.30022 | −0.120722 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.2734 | 0.945743 | ||||||||
\(119\) | −2.99537 | −0.274585 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.8732 | 0.988470 | ||||||||
\(122\) | −10.3437 | −0.936478 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.55507 | −0.229452 | ||||||||
\(125\) | 8.51240 | 0.761372 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.66213 | −0.147490 | −0.0737452 | − | 0.997277i | \(-0.523495\pi\) | ||||
−0.0737452 | + | 0.997277i | \(0.523495\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −17.5586 | −1.53999 | ||||||||
\(131\) | 17.8952 | 1.56351 | 0.781754 | − | 0.623586i | \(-0.214325\pi\) | ||||
0.781754 | + | 0.623586i | \(0.214325\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.21294 | −0.278597 | ||||||||
\(134\) | −14.7510 | −1.27429 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.42398 | −0.465102 | ||||||||
\(137\) | −8.80332 | −0.752118 | −0.376059 | − | 0.926596i | \(-0.622721\pi\) | ||||
−0.376059 | + | 0.926596i | \(0.622721\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.48773 | 0.719920 | 0.359960 | − | 0.932968i | \(-0.382790\pi\) | ||||
0.359960 | + | 0.932968i | \(0.382790\pi\) | |||||||
\(140\) | −1.94590 | −0.164458 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13.2562 | 1.11244 | ||||||||
\(143\) | −23.3055 | −1.94890 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.58146 | −0.380469 | ||||||||
\(146\) | 1.22665 | 0.101518 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.51958 | 0.535906 | ||||||||
\(149\) | −19.1172 | −1.56614 | −0.783069 | − | 0.621934i | \(-0.786347\pi\) | ||||
−0.783069 | + | 0.621934i | \(0.786347\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.99709 | −0.406657 | −0.203329 | − | 0.979111i | \(-0.565176\pi\) | ||||
−0.203329 | + | 0.979111i | \(0.565176\pi\) | |||||||
\(152\) | −5.81795 | −0.471898 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.58279 | −0.208127 | ||||||||
\(155\) | −9.00307 | −0.723144 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.2136 | 1.37380 | 0.686898 | − | 0.726754i | \(-0.258972\pi\) | ||||
0.686898 | + | 0.726754i | \(0.258972\pi\) | |||||||
\(158\) | −7.86075 | −0.625367 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.52361 | −0.278566 | ||||||||
\(161\) | 0.556753 | 0.0438783 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.92931 | 0.386093 | 0.193047 | − | 0.981190i | \(-0.438163\pi\) | ||||
0.193047 | + | 0.981190i | \(0.438163\pi\) | |||||||
\(164\) | 1.43947 | 0.112404 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.03632 | −0.0804341 | ||||||||
\(167\) | 6.43760 | 0.498157 | 0.249078 | − | 0.968483i | \(-0.419872\pi\) | ||||
0.249078 | + | 0.968483i | \(0.419872\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8316 | 0.910121 | ||||||||
\(170\) | −19.1120 | −1.46582 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.12633 | −0.162131 | ||||||||
\(173\) | 0.967478 | 0.0735560 | 0.0367780 | − | 0.999323i | \(-0.488291\pi\) | ||||
0.0367780 | + | 0.999323i | \(0.488291\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.09535 | −0.309580 | ||||||||
\(176\) | −4.67688 | −0.352533 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.94988 | 0.520915 | ||||||||
\(179\) | 22.2380 | 1.66215 | 0.831073 | − | 0.556163i | \(-0.187727\pi\) | ||||
0.831073 | + | 0.556163i | \(0.187727\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.64066 | −0.493597 | −0.246798 | − | 0.969067i | \(-0.579379\pi\) | ||||
−0.246798 | + | 0.969067i | \(0.579379\pi\) | |||||||
\(182\) | 2.75191 | 0.203985 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.00816 | 0.0743227 | ||||||||
\(185\) | 22.9724 | 1.68897 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.3673 | −1.85504 | ||||||||
\(188\) | −9.21193 | −0.671849 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −20.5002 | −1.48724 | ||||||||
\(191\) | −16.0979 | −1.16480 | −0.582400 | − | 0.812902i | \(-0.697886\pi\) | ||||
−0.582400 | + | 0.812902i | \(0.697886\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.49577 | −0.683520 | −0.341760 | − | 0.939787i | \(-0.611023\pi\) | ||||
−0.341760 | + | 0.939787i | \(0.611023\pi\) | |||||||
\(194\) | 15.1636 | 1.08869 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.69502 | −0.478216 | ||||||||
\(197\) | −18.2762 | −1.30213 | −0.651063 | − | 0.759024i | \(-0.725676\pi\) | ||||
−0.651063 | + | 0.759024i | \(0.725676\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.57295 | 0.607721 | 0.303860 | − | 0.952717i | \(-0.401724\pi\) | ||||
0.303860 | + | 0.952717i | \(0.401724\pi\) | |||||||
\(200\) | −7.41582 | −0.524378 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.37759 | −0.378366 | ||||||||
\(203\) | 0.718040 | 0.0503965 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.07213 | 0.354253 | ||||||||
\(206\) | −3.48947 | −0.243123 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.98313 | 0.345518 | ||||||||
\(209\) | −27.2098 | −1.88214 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.80449 | −0.468441 | −0.234220 | − | 0.972184i | \(-0.575254\pi\) | ||||
−0.234220 | + | 0.972184i | \(0.575254\pi\) | |||||||
\(212\) | 11.7307 | 0.805666 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −19.0825 | −1.30445 | ||||||||
\(215\) | −7.49236 | −0.510975 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.41103 | 0.0957867 | ||||||||
\(218\) | 3.42944 | 0.232271 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −16.4795 | −1.11105 | ||||||||
\(221\) | 27.0284 | 1.81813 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | −0.0669650 | ||||||||
\(224\) | 0.552246 | 0.0368985 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.2528 | −0.748525 | ||||||||
\(227\) | −27.8830 | −1.85066 | −0.925330 | − | 0.379163i | \(-0.876212\pi\) | ||||
−0.925330 | + | 0.379163i | \(0.876212\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.6798 | 0.705739 | 0.352869 | − | 0.935673i | \(-0.385206\pi\) | ||||
0.352869 | + | 0.935673i | \(0.385206\pi\) | |||||||
\(230\) | 3.55237 | 0.234236 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.30022 | 0.0853634 | ||||||||
\(233\) | 26.2101 | 1.71708 | 0.858541 | − | 0.512745i | \(-0.171371\pi\) | ||||
0.858541 | + | 0.512745i | \(0.171371\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −32.4592 | −2.11741 | ||||||||
\(236\) | −10.2734 | −0.668741 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.99537 | 0.194161 | ||||||||
\(239\) | 8.82406 | 0.570781 | 0.285390 | − | 0.958411i | \(-0.407877\pi\) | ||||
0.285390 | + | 0.958411i | \(0.407877\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.7867 | −0.952497 | −0.476248 | − | 0.879311i | \(-0.658004\pi\) | ||||
−0.476248 | + | 0.879311i | \(0.658004\pi\) | |||||||
\(242\) | −10.8732 | −0.698954 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.3437 | 0.662190 | ||||||||
\(245\) | −23.5906 | −1.50715 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 28.9916 | 1.84469 | ||||||||
\(248\) | 2.55507 | 0.162247 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.51240 | −0.538371 | ||||||||
\(251\) | −5.31532 | −0.335500 | −0.167750 | − | 0.985830i | \(-0.553650\pi\) | ||||
−0.167750 | + | 0.985830i | \(0.553650\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.71505 | 0.296433 | ||||||||
\(254\) | 1.66213 | 0.104291 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −25.7340 | −1.60524 | −0.802620 | − | 0.596491i | \(-0.796561\pi\) | ||||
−0.802620 | + | 0.596491i | \(0.796561\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.60041 | −0.223719 | ||||||||
\(260\) | 17.5586 | 1.08894 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −17.8952 | −1.10557 | ||||||||
\(263\) | 17.6294 | 1.08708 | 0.543539 | − | 0.839384i | \(-0.317084\pi\) | ||||
0.543539 | + | 0.839384i | \(0.317084\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 41.3343 | 2.53915 | ||||||||
\(266\) | 3.21294 | 0.196998 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.7510 | 0.901058 | ||||||||
\(269\) | 21.5522 | 1.31406 | 0.657030 | − | 0.753864i | \(-0.271812\pi\) | ||||
0.657030 | + | 0.753864i | \(0.271812\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.1455 | −0.980768 | −0.490384 | − | 0.871506i | \(-0.663144\pi\) | ||||
−0.490384 | + | 0.871506i | \(0.663144\pi\) | |||||||
\(272\) | 5.42398 | 0.328877 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.80332 | 0.531828 | ||||||||
\(275\) | −34.6829 | −2.09146 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.90050 | −0.174274 | −0.0871369 | − | 0.996196i | \(-0.527772\pi\) | ||||
−0.0871369 | + | 0.996196i | \(0.527772\pi\) | |||||||
\(278\) | −8.48773 | −0.509060 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.94590 | 0.116290 | ||||||||
\(281\) | 27.2079 | 1.62309 | 0.811543 | − | 0.584293i | \(-0.198628\pi\) | ||||
0.811543 | + | 0.584293i | \(0.198628\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.6305 | 0.929139 | 0.464570 | − | 0.885537i | \(-0.346209\pi\) | ||||
0.464570 | + | 0.885537i | \(0.346209\pi\) | |||||||
\(284\) | −13.2562 | −0.786611 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 23.3055 | 1.37808 | ||||||||
\(287\) | −0.794941 | −0.0469239 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.4196 | 0.730562 | ||||||||
\(290\) | 4.58146 | 0.269032 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.22665 | −0.0717844 | ||||||||
\(293\) | 5.47540 | 0.319876 | 0.159938 | − | 0.987127i | \(-0.448871\pi\) | ||||
0.159938 | + | 0.987127i | \(0.448871\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −36.1994 | −2.10761 | ||||||||
\(296\) | −6.51958 | −0.378943 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 19.1172 | 1.10743 | ||||||||
\(299\) | −5.02380 | −0.290534 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.17426 | 0.0676831 | ||||||||
\(302\) | 4.99709 | 0.287550 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.81795 | 0.333682 | ||||||||
\(305\) | 36.4473 | 2.08697 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.4616 | −1.05366 | −0.526829 | − | 0.849971i | \(-0.676619\pi\) | ||||
−0.526829 | + | 0.849971i | \(0.676619\pi\) | |||||||
\(308\) | 2.58279 | 0.147168 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.00307 | 0.511340 | ||||||||
\(311\) | 17.6340 | 0.999931 | 0.499965 | − | 0.866045i | \(-0.333346\pi\) | ||||
0.499965 | + | 0.866045i | \(0.333346\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.93775 | 0.561715 | 0.280857 | − | 0.959750i | \(-0.409381\pi\) | ||||
0.280857 | + | 0.959750i | \(0.409381\pi\) | |||||||
\(314\) | −17.2136 | −0.971421 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.86075 | 0.442202 | ||||||||
\(317\) | −8.14935 | −0.457713 | −0.228857 | − | 0.973460i | \(-0.573499\pi\) | ||||
−0.228857 | + | 0.973460i | \(0.573499\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.08096 | 0.340468 | ||||||||
\(320\) | 3.52361 | 0.196976 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.556753 | −0.0310266 | ||||||||
\(323\) | 31.5565 | 1.75585 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 36.9540 | 2.04984 | ||||||||
\(326\) | −4.92931 | −0.273009 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.43947 | −0.0794814 | ||||||||
\(329\) | 5.08725 | 0.280469 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.0504 | 0.992138 | 0.496069 | − | 0.868283i | \(-0.334776\pi\) | ||||
0.496069 | + | 0.868283i | \(0.334776\pi\) | |||||||
\(332\) | 1.03632 | 0.0568755 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.43760 | −0.352250 | ||||||||
\(335\) | 51.9766 | 2.83978 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.3184 | 1.32471 | 0.662355 | − | 0.749191i | \(-0.269557\pi\) | ||||
0.662355 | + | 0.749191i | \(0.269557\pi\) | |||||||
\(338\) | −11.8316 | −0.643553 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 19.1120 | 1.03649 | ||||||||
\(341\) | 11.9497 | 0.647115 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.56302 | 0.408365 | ||||||||
\(344\) | 2.12633 | 0.114644 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.967478 | −0.0520119 | ||||||||
\(347\) | 20.6234 | 1.10712 | 0.553560 | − | 0.832809i | \(-0.313269\pi\) | ||||
0.553560 | + | 0.832809i | \(0.313269\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.4414 | 0.826557 | 0.413278 | − | 0.910605i | \(-0.364384\pi\) | ||||
0.413278 | + | 0.910605i | \(0.364384\pi\) | |||||||
\(350\) | 4.09535 | 0.218906 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.67688 | 0.249278 | ||||||||
\(353\) | −8.29029 | −0.441247 | −0.220624 | − | 0.975359i | \(-0.570809\pi\) | ||||
−0.220624 | + | 0.975359i | \(0.570809\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −46.7097 | −2.47909 | ||||||||
\(356\) | −6.94988 | −0.368343 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −22.2380 | −1.17532 | ||||||||
\(359\) | −5.43143 | −0.286660 | −0.143330 | − | 0.989675i | \(-0.545781\pi\) | ||||
−0.143330 | + | 0.989675i | \(0.545781\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.8486 | 0.781504 | ||||||||
\(362\) | 6.64066 | 0.349026 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.75191 | −0.144239 | ||||||||
\(365\) | −4.32224 | −0.226236 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.7690 | −1.55393 | −0.776965 | − | 0.629543i | \(-0.783242\pi\) | ||||
−0.776965 | + | 0.629543i | \(0.783242\pi\) | |||||||
\(368\) | −1.00816 | −0.0525541 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −22.9724 | −1.19428 | ||||||||
\(371\) | −6.47822 | −0.336332 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.2795 | −1.10181 | −0.550906 | − | 0.834567i | \(-0.685718\pi\) | ||||
−0.550906 | + | 0.834567i | \(0.685718\pi\) | |||||||
\(374\) | 25.3673 | 1.31171 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.21193 | 0.475069 | ||||||||
\(377\) | −6.47915 | −0.333693 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.9952 | 1.12982 | 0.564910 | − | 0.825153i | \(-0.308911\pi\) | ||||
0.564910 | + | 0.825153i | \(0.308911\pi\) | |||||||
\(380\) | 20.5002 | 1.05164 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.0979 | 0.823638 | ||||||||
\(383\) | 6.33678 | 0.323794 | 0.161897 | − | 0.986808i | \(-0.448239\pi\) | ||||
0.161897 | + | 0.986808i | \(0.448239\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.10072 | 0.463816 | ||||||||
\(386\) | 9.49577 | 0.483322 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −15.1636 | −0.769818 | ||||||||
\(389\) | 15.1173 | 0.766479 | 0.383239 | − | 0.923649i | \(-0.374808\pi\) | ||||
0.383239 | + | 0.923649i | \(0.374808\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.46825 | −0.276541 | ||||||||
\(392\) | 6.69502 | 0.338150 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.2762 | 0.920742 | ||||||||
\(395\) | 27.6982 | 1.39365 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.598725 | 0.0300492 | 0.0150246 | − | 0.999887i | \(-0.495217\pi\) | ||||
0.0150246 | + | 0.999887i | \(0.495217\pi\) | |||||||
\(398\) | −8.57295 | −0.429723 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.41582 | 0.370791 | ||||||||
\(401\) | −5.71303 | −0.285295 | −0.142648 | − | 0.989774i | \(-0.545562\pi\) | ||||
−0.142648 | + | 0.989774i | \(0.545562\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.7322 | −0.634238 | ||||||||
\(404\) | 5.37759 | 0.267545 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.718040 | −0.0356357 | ||||||||
\(407\) | −30.4913 | −1.51140 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.4094 | −0.910285 | −0.455142 | − | 0.890419i | \(-0.650412\pi\) | ||||
−0.455142 | + | 0.890419i | \(0.650412\pi\) | |||||||
\(410\) | −5.07213 | −0.250495 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.48947 | 0.171914 | ||||||||
\(413\) | 5.67344 | 0.279172 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.65159 | 0.179249 | ||||||||
\(416\) | −4.98313 | −0.244318 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 27.2098 | 1.33088 | ||||||||
\(419\) | 2.26470 | 0.110638 | 0.0553189 | − | 0.998469i | \(-0.482382\pi\) | ||||
0.0553189 | + | 0.998469i | \(0.482382\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.936904 | 0.0456619 | 0.0228309 | − | 0.999739i | \(-0.492732\pi\) | ||||
0.0228309 | + | 0.999739i | \(0.492732\pi\) | |||||||
\(422\) | 6.80449 | 0.331237 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.7307 | −0.569692 | ||||||||
\(425\) | 40.2232 | 1.95111 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.71229 | −0.276437 | ||||||||
\(428\) | 19.0825 | 0.922389 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.49236 | 0.361314 | ||||||||
\(431\) | −3.93486 | −0.189536 | −0.0947678 | − | 0.995499i | \(-0.530211\pi\) | ||||
−0.0947678 | + | 0.995499i | \(0.530211\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.0634 | −1.34864 | −0.674320 | − | 0.738439i | \(-0.735563\pi\) | ||||
−0.674320 | + | 0.738439i | \(0.735563\pi\) | |||||||
\(434\) | −1.41103 | −0.0677315 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.42944 | −0.164240 | ||||||||
\(437\) | −5.86544 | −0.280582 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.19677 | 0.248028 | 0.124014 | − | 0.992280i | \(-0.460423\pi\) | ||||
0.124014 | + | 0.992280i | \(0.460423\pi\) | |||||||
\(440\) | 16.4795 | 0.785628 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −27.0284 | −1.28561 | ||||||||
\(443\) | 40.3997 | 1.91945 | 0.959724 | − | 0.280945i | \(-0.0906480\pi\) | ||||
0.959724 | + | 0.280945i | \(0.0906480\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.4886 | −1.16087 | ||||||||
\(446\) | 1.00000 | 0.0473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.552246 | −0.0260912 | ||||||||
\(449\) | −21.0560 | −0.993693 | −0.496847 | − | 0.867838i | \(-0.665509\pi\) | ||||
−0.496847 | + | 0.867838i | \(0.665509\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.73222 | −0.317008 | ||||||||
\(452\) | 11.2528 | 0.529287 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 27.8830 | 1.30861 | ||||||||
\(455\) | −9.69666 | −0.454587 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.4763 | −1.05140 | −0.525698 | − | 0.850671i | \(-0.676196\pi\) | ||||
−0.525698 | + | 0.850671i | \(0.676196\pi\) | |||||||
\(458\) | −10.6798 | −0.499033 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.55237 | −0.165630 | ||||||||
\(461\) | 40.9480 | 1.90714 | 0.953570 | − | 0.301173i | \(-0.0973781\pi\) | ||||
0.953570 | + | 0.301173i | \(0.0973781\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.1771 | 1.54187 | 0.770935 | − | 0.636914i | \(-0.219789\pi\) | ||||
0.770935 | + | 0.636914i | \(0.219789\pi\) | |||||||
\(464\) | −1.30022 | −0.0603611 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −26.2101 | −1.21416 | ||||||||
\(467\) | 5.18020 | 0.239711 | 0.119856 | − | 0.992791i | \(-0.461757\pi\) | ||||
0.119856 | + | 0.992791i | \(0.461757\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.14615 | −0.376154 | ||||||||
\(470\) | 32.4592 | 1.49723 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.2734 | 0.472871 | ||||||||
\(473\) | 9.94459 | 0.457253 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 43.1449 | 1.97962 | ||||||||
\(476\) | −2.99537 | −0.137293 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.82406 | −0.403603 | ||||||||
\(479\) | 22.1006 | 1.00980 | 0.504902 | − | 0.863177i | \(-0.331529\pi\) | ||||
0.504902 | + | 0.863177i | \(0.331529\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.4879 | 1.48132 | ||||||||
\(482\) | 14.7867 | 0.673517 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.8732 | 0.494235 | ||||||||
\(485\) | −53.4308 | −2.42617 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.33737 | −0.332488 | −0.166244 | − | 0.986085i | \(-0.553164\pi\) | ||||
−0.166244 | + | 0.986085i | \(0.553164\pi\) | |||||||
\(488\) | −10.3437 | −0.468239 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 23.5906 | 1.06572 | ||||||||
\(491\) | −23.5057 | −1.06080 | −0.530399 | − | 0.847748i | \(-0.677958\pi\) | ||||
−0.530399 | + | 0.847748i | \(0.677958\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.05235 | −0.317622 | ||||||||
\(494\) | −28.9916 | −1.30439 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.55507 | −0.114726 | ||||||||
\(497\) | 7.32068 | 0.328377 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.0215 | 0.896284 | 0.448142 | − | 0.893962i | \(-0.352086\pi\) | ||||
0.448142 | + | 0.893962i | \(0.352086\pi\) | |||||||
\(500\) | 8.51240 | 0.380686 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.31532 | 0.237234 | ||||||||
\(503\) | −21.7880 | −0.971480 | −0.485740 | − | 0.874103i | \(-0.661450\pi\) | ||||
−0.485740 | + | 0.874103i | \(0.661450\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.9485 | 0.843199 | ||||||||
\(506\) | −4.71505 | −0.209609 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.66213 | −0.0737452 | ||||||||
\(509\) | −39.6437 | −1.75718 | −0.878588 | − | 0.477580i | \(-0.841514\pi\) | ||||
−0.878588 | + | 0.477580i | \(0.841514\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.677413 | 0.0299670 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 25.7340 | 1.13508 | ||||||||
\(515\) | 12.2955 | 0.541806 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 43.0831 | 1.89479 | ||||||||
\(518\) | 3.60041 | 0.158193 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −17.5586 | −0.769995 | ||||||||
\(521\) | −13.2341 | −0.579796 | −0.289898 | − | 0.957058i | \(-0.593621\pi\) | ||||
−0.289898 | + | 0.957058i | \(0.593621\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.619536 | −0.0270904 | −0.0135452 | − | 0.999908i | \(-0.504312\pi\) | ||||
−0.0135452 | + | 0.999908i | \(0.504312\pi\) | |||||||
\(524\) | 17.8952 | 0.781754 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.6294 | −0.768680 | ||||||||
\(527\) | −13.8586 | −0.603692 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.9836 | −0.955809 | ||||||||
\(530\) | −41.3343 | −1.79545 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.21294 | −0.139299 | ||||||||
\(533\) | 7.17306 | 0.310700 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 67.2394 | 2.90701 | ||||||||
\(536\) | −14.7510 | −0.637144 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −21.5522 | −0.929181 | ||||||||
\(539\) | 31.3118 | 1.34869 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.9524 | −1.24476 | −0.622380 | − | 0.782715i | \(-0.713834\pi\) | ||||
−0.622380 | + | 0.782715i | \(0.713834\pi\) | |||||||
\(542\) | 16.1455 | 0.693508 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.42398 | −0.232551 | ||||||||
\(545\) | −12.0840 | −0.517622 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −40.8559 | −1.74687 | −0.873436 | − | 0.486938i | \(-0.838114\pi\) | ||||
−0.873436 | + | 0.486938i | \(0.838114\pi\) | |||||||
\(548\) | −8.80332 | −0.376059 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 34.6829 | 1.47888 | ||||||||
\(551\) | −7.56460 | −0.322263 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.34106 | −0.184601 | ||||||||
\(554\) | 2.90050 | 0.123230 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.48773 | 0.359960 | ||||||||
\(557\) | −20.5129 | −0.869161 | −0.434580 | − | 0.900633i | \(-0.643103\pi\) | ||||
−0.434580 | + | 0.900633i | \(0.643103\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.5958 | −0.448154 | ||||||||
\(560\) | −1.94590 | −0.0822292 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −27.2079 | −1.14770 | ||||||||
\(563\) | −6.76288 | −0.285021 | −0.142511 | − | 0.989793i | \(-0.545518\pi\) | ||||
−0.142511 | + | 0.989793i | \(0.545518\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 39.6505 | 1.66811 | ||||||||
\(566\) | −15.6305 | −0.657001 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.2562 | 0.556218 | ||||||||
\(569\) | −29.3112 | −1.22879 | −0.614394 | − | 0.788999i | \(-0.710600\pi\) | ||||
−0.614394 | + | 0.788999i | \(0.710600\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.1295 | −0.633148 | −0.316574 | − | 0.948568i | \(-0.602533\pi\) | ||||
−0.316574 | + | 0.948568i | \(0.602533\pi\) | |||||||
\(572\) | −23.3055 | −0.974451 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.794941 | 0.0331802 | ||||||||
\(575\) | −7.47635 | −0.311785 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.0457 | 0.792883 | 0.396441 | − | 0.918060i | \(-0.370245\pi\) | ||||
0.396441 | + | 0.918060i | \(0.370245\pi\) | |||||||
\(578\) | −12.4196 | −0.516585 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.58146 | −0.190235 | ||||||||
\(581\) | −0.572304 | −0.0237432 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −54.8629 | −2.27219 | ||||||||
\(584\) | 1.22665 | 0.0507592 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.47540 | −0.226187 | ||||||||
\(587\) | 21.9243 | 0.904915 | 0.452457 | − | 0.891786i | \(-0.350547\pi\) | ||||
0.452457 | + | 0.891786i | \(0.350547\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.8653 | −0.612513 | ||||||||
\(590\) | 36.1994 | 1.49031 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.51958 | 0.267953 | ||||||||
\(593\) | −36.3422 | −1.49240 | −0.746198 | − | 0.665725i | \(-0.768123\pi\) | ||||
−0.746198 | + | 0.665725i | \(0.768123\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.5545 | −0.432693 | ||||||||
\(596\) | −19.1172 | −0.783069 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.02380 | 0.205439 | ||||||||
\(599\) | −4.75160 | −0.194145 | −0.0970725 | − | 0.995277i | \(-0.530948\pi\) | ||||
−0.0970725 | + | 0.995277i | \(0.530948\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.5124 | 0.469600 | 0.234800 | − | 0.972044i | \(-0.424557\pi\) | ||||
0.234800 | + | 0.972044i | \(0.424557\pi\) | |||||||
\(602\) | −1.17426 | −0.0478592 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.99709 | −0.203329 | ||||||||
\(605\) | 38.3128 | 1.55764 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.3437 | 0.785137 | 0.392569 | − | 0.919723i | \(-0.371587\pi\) | ||||
0.392569 | + | 0.919723i | \(0.371587\pi\) | |||||||
\(608\) | −5.81795 | −0.235949 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −36.4473 | −1.47571 | ||||||||
\(611\) | −45.9042 | −1.85709 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.72707 | −0.110145 | −0.0550727 | − | 0.998482i | \(-0.517539\pi\) | ||||
−0.0550727 | + | 0.998482i | \(0.517539\pi\) | |||||||
\(614\) | 18.4616 | 0.745049 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.58279 | −0.104063 | ||||||||
\(617\) | 19.4135 | 0.781557 | 0.390779 | − | 0.920485i | \(-0.372206\pi\) | ||||
0.390779 | + | 0.920485i | \(0.372206\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.0336 | 0.885605 | 0.442803 | − | 0.896619i | \(-0.353984\pi\) | ||||
0.442803 | + | 0.896619i | \(0.353984\pi\) | |||||||
\(620\) | −9.00307 | −0.361572 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17.6340 | −0.707058 | ||||||||
\(623\) | 3.83804 | 0.153768 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.08474 | −0.283389 | ||||||||
\(626\) | −9.93775 | −0.397192 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.2136 | 0.686898 | ||||||||
\(629\) | 35.3621 | 1.40998 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.0832 | 1.11798 | 0.558988 | − | 0.829176i | \(-0.311190\pi\) | ||||
0.558988 | + | 0.829176i | \(0.311190\pi\) | |||||||
\(632\) | −7.86075 | −0.312684 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.14935 | 0.323652 | ||||||||
\(635\) | −5.85670 | −0.232416 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.3622 | −1.32186 | ||||||||
\(638\) | −6.08096 | −0.240747 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.52361 | −0.139283 | ||||||||
\(641\) | −38.4899 | −1.52026 | −0.760129 | − | 0.649772i | \(-0.774864\pi\) | ||||
−0.760129 | + | 0.649772i | \(0.774864\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.7998 | −1.09632 | −0.548158 | − | 0.836375i | \(-0.684671\pi\) | ||||
−0.548158 | + | 0.836375i | \(0.684671\pi\) | |||||||
\(644\) | 0.556753 | 0.0219392 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −31.5565 | −1.24157 | ||||||||
\(647\) | 39.2430 | 1.54280 | 0.771401 | − | 0.636349i | \(-0.219556\pi\) | ||||
0.771401 | + | 0.636349i | \(0.219556\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 48.0474 | 1.88603 | ||||||||
\(650\) | −36.9540 | −1.44945 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.92931 | 0.193047 | ||||||||
\(653\) | 26.8999 | 1.05268 | 0.526338 | − | 0.850276i | \(-0.323565\pi\) | ||||
0.526338 | + | 0.850276i | \(0.323565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 63.0556 | 2.46379 | ||||||||
\(656\) | 1.43947 | 0.0562019 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.08725 | −0.198322 | ||||||||
\(659\) | 4.28280 | 0.166834 | 0.0834170 | − | 0.996515i | \(-0.473417\pi\) | ||||
0.0834170 | + | 0.996515i | \(0.473417\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.991244 | −0.0385549 | −0.0192775 | − | 0.999814i | \(-0.506137\pi\) | ||||
−0.0192775 | + | 0.999814i | \(0.506137\pi\) | |||||||
\(662\) | −18.0504 | −0.701548 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.03632 | −0.0402170 | ||||||||
\(665\) | −11.3211 | −0.439015 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.31083 | 0.0507555 | ||||||||
\(668\) | 6.43760 | 0.249078 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −51.9766 | −2.00803 | ||||||||
\(671\) | −48.3764 | −1.86755 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.1899 | −1.70339 | −0.851697 | − | 0.524035i | \(-0.824426\pi\) | ||||
−0.851697 | + | 0.524035i | \(0.824426\pi\) | |||||||
\(674\) | −24.3184 | −0.936711 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.8316 | 0.455061 | ||||||||
\(677\) | −15.0897 | −0.579945 | −0.289973 | − | 0.957035i | \(-0.593646\pi\) | ||||
−0.289973 | + | 0.957035i | \(0.593646\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.37406 | 0.321367 | ||||||||
\(680\) | −19.1120 | −0.732911 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −11.9497 | −0.457579 | ||||||||
\(683\) | 10.1984 | 0.390230 | 0.195115 | − | 0.980780i | \(-0.437492\pi\) | ||||
0.195115 | + | 0.980780i | \(0.437492\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.0195 | −1.18519 | ||||||||
\(686\) | −7.56302 | −0.288757 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.12633 | −0.0810657 | ||||||||
\(689\) | 58.4555 | 2.22698 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.7250 | −1.28296 | −0.641479 | − | 0.767140i | \(-0.721679\pi\) | ||||
−0.641479 | + | 0.767140i | \(0.721679\pi\) | |||||||
\(692\) | 0.967478 | 0.0367780 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.6234 | −0.782852 | ||||||||
\(695\) | 29.9074 | 1.13445 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.80765 | 0.295736 | ||||||||
\(698\) | −15.4414 | −0.584464 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.09535 | −0.154790 | ||||||||
\(701\) | −5.58673 | −0.211008 | −0.105504 | − | 0.994419i | \(-0.533646\pi\) | ||||
−0.105504 | + | 0.994419i | \(0.533646\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37.9306 | 1.43058 | ||||||||
\(704\) | −4.67688 | −0.176266 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.29029 | 0.312009 | ||||||||
\(707\) | −2.96975 | −0.111689 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.63305 | −0.173998 | −0.0869989 | − | 0.996208i | \(-0.527728\pi\) | ||||
−0.0869989 | + | 0.996208i | \(0.527728\pi\) | |||||||
\(710\) | 46.7097 | 1.75298 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.94988 | 0.260458 | ||||||||
\(713\) | 2.57592 | 0.0964691 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −82.1194 | −3.07109 | ||||||||
\(716\) | 22.2380 | 0.831073 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.43143 | 0.202699 | ||||||||
\(719\) | −23.8702 | −0.890207 | −0.445103 | − | 0.895479i | \(-0.646833\pi\) | ||||
−0.445103 | + | 0.895479i | \(0.646833\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.92705 | −0.0717670 | ||||||||
\(722\) | −14.8486 | −0.552607 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.64066 | −0.246798 | ||||||||
\(725\) | −9.64217 | −0.358101 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.4145 | 1.12801 | 0.564005 | − | 0.825771i | \(-0.309260\pi\) | ||||
0.564005 | + | 0.825771i | \(0.309260\pi\) | |||||||
\(728\) | 2.75191 | 0.101993 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.32224 | 0.159973 | ||||||||
\(731\) | −11.5332 | −0.426570 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.9252 | 0.477404 | 0.238702 | − | 0.971093i | \(-0.423278\pi\) | ||||
0.238702 | + | 0.971093i | \(0.423278\pi\) | |||||||
\(734\) | 29.7690 | 1.09879 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00816 | 0.0371613 | ||||||||
\(737\) | −68.9884 | −2.54122 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.4826 | −1.26846 | −0.634231 | − | 0.773144i | \(-0.718683\pi\) | ||||
−0.634231 | + | 0.773144i | \(0.718683\pi\) | |||||||
\(740\) | 22.9724 | 0.844484 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.47822 | 0.237823 | ||||||||
\(743\) | −43.0222 | −1.57833 | −0.789166 | − | 0.614180i | \(-0.789487\pi\) | ||||
−0.789166 | + | 0.614180i | \(0.789487\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −67.3614 | −2.46793 | ||||||||
\(746\) | 21.2795 | 0.779099 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −25.3673 | −0.927520 | ||||||||
\(749\) | −10.5382 | −0.385059 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.0251921 | 0.000919274 0 | 0.000459637 | − | 1.00000i | \(-0.499854\pi\) | ||||
0.000459637 | 1.00000i | \(0.499854\pi\) | ||||||||
\(752\) | −9.21193 | −0.335925 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.47915 | 0.235957 | ||||||||
\(755\) | −17.6078 | −0.640813 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.9990 | 1.05399 | 0.526994 | − | 0.849869i | \(-0.323319\pi\) | ||||
0.526994 | + | 0.849869i | \(0.323319\pi\) | |||||||
\(758\) | −21.9952 | −0.798903 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −20.5002 | −0.743620 | ||||||||
\(761\) | −4.62723 | −0.167737 | −0.0838686 | − | 0.996477i | \(-0.526728\pi\) | ||||
−0.0838686 | + | 0.996477i | \(0.526728\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.89389 | 0.0685636 | ||||||||
\(764\) | −16.0979 | −0.582400 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.33678 | −0.228957 | ||||||||
\(767\) | −51.1936 | −1.84850 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.41324 | −0.339450 | −0.169725 | − | 0.985491i | \(-0.554288\pi\) | ||||
−0.169725 | + | 0.985491i | \(0.554288\pi\) | |||||||
\(770\) | −9.10072 | −0.327967 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.49577 | −0.341760 | ||||||||
\(773\) | 46.4250 | 1.66979 | 0.834895 | − | 0.550409i | \(-0.185528\pi\) | ||||
0.834895 | + | 0.550409i | \(0.185528\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.9479 | −0.680630 | ||||||||
\(776\) | 15.1636 | 0.544343 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.1173 | −0.541982 | ||||||||
\(779\) | 8.37477 | 0.300057 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 61.9976 | 2.21845 | ||||||||
\(782\) | 5.46825 | 0.195544 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.69502 | −0.239108 | ||||||||
\(785\) | 60.6540 | 2.16484 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.0666 | 0.608360 | 0.304180 | − | 0.952615i | \(-0.401618\pi\) | ||||
0.304180 | + | 0.952615i | \(0.401618\pi\) | |||||||
\(788\) | −18.2762 | −0.651063 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −27.6982 | −0.985458 | ||||||||
\(791\) | −6.21431 | −0.220955 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 51.5442 | 1.83039 | ||||||||
\(794\) | −0.598725 | −0.0212480 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.57295 | 0.303860 | ||||||||
\(797\) | −45.2805 | −1.60392 | −0.801959 | − | 0.597380i | \(-0.796209\pi\) | ||||
−0.801959 | + | 0.597380i | \(0.796209\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −49.9653 | −1.76765 | ||||||||
\(800\) | −7.41582 | −0.262189 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.71303 | 0.201734 | ||||||||
\(803\) | 5.73690 | 0.202451 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.96178 | 0.0691437 | ||||||||
\(806\) | 12.7322 | 0.448474 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.37759 | −0.189183 | ||||||||
\(809\) | 1.67580 | 0.0589181 | 0.0294590 | − | 0.999566i | \(-0.490622\pi\) | ||||
0.0294590 | + | 0.999566i | \(0.490622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.23025 | 0.0783146 | 0.0391573 | − | 0.999233i | \(-0.487533\pi\) | ||||
0.0391573 | + | 0.999233i | \(0.487533\pi\) | |||||||
\(812\) | 0.718040 | 0.0251982 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 30.4913 | 1.06872 | ||||||||
\(815\) | 17.3690 | 0.608408 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.3709 | −0.432803 | ||||||||
\(818\) | 18.4094 | 0.643669 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.07213 | 0.177126 | ||||||||
\(821\) | −6.28415 | −0.219318 | −0.109659 | − | 0.993969i | \(-0.534976\pi\) | ||||
−0.109659 | + | 0.993969i | \(0.534976\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.4870 | −0.644415 | −0.322207 | − | 0.946669i | \(-0.604425\pi\) | ||||
−0.322207 | + | 0.946669i | \(0.604425\pi\) | |||||||
\(824\) | −3.48947 | −0.121562 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.67344 | −0.197404 | ||||||||
\(827\) | −16.2279 | −0.564299 | −0.282150 | − | 0.959370i | \(-0.591047\pi\) | ||||
−0.282150 | + | 0.959370i | \(0.591047\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.7274 | 0.615698 | 0.307849 | − | 0.951435i | \(-0.400391\pi\) | ||||
0.307849 | + | 0.951435i | \(0.400391\pi\) | |||||||
\(830\) | −3.65159 | −0.126748 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.98313 | 0.172759 | ||||||||
\(833\) | −36.3137 | −1.25819 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.6836 | 0.784998 | ||||||||
\(836\) | −27.2098 | −0.941072 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.26470 | −0.0782327 | ||||||||
\(839\) | 27.7284 | 0.957291 | 0.478646 | − | 0.878008i | \(-0.341128\pi\) | ||||
0.478646 | + | 0.878008i | \(0.341128\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.3094 | −0.941705 | ||||||||
\(842\) | −0.936904 | −0.0322878 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.80449 | −0.234220 | ||||||||
\(845\) | 41.6898 | 1.43417 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.00466 | −0.206323 | ||||||||
\(848\) | 11.7307 | 0.402833 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −40.2232 | −1.37965 | ||||||||
\(851\) | −6.57279 | −0.225312 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.1483 | −0.655625 | −0.327812 | − | 0.944743i | \(-0.606311\pi\) | ||||
−0.327812 | + | 0.944743i | \(0.606311\pi\) | |||||||
\(854\) | 5.71229 | 0.195470 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −19.0825 | −0.652227 | ||||||||
\(857\) | −29.8037 | −1.01807 | −0.509037 | − | 0.860745i | \(-0.669998\pi\) | ||||
−0.509037 | + | 0.860745i | \(0.669998\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.4840 | −0.357709 | −0.178855 | − | 0.983876i | \(-0.557239\pi\) | ||||
−0.178855 | + | 0.983876i | \(0.557239\pi\) | |||||||
\(860\) | −7.49236 | −0.255487 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.93486 | 0.134022 | ||||||||
\(863\) | −8.13754 | −0.277005 | −0.138502 | − | 0.990362i | \(-0.544229\pi\) | ||||
−0.138502 | + | 0.990362i | \(0.544229\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.40901 | 0.115910 | ||||||||
\(866\) | 28.0634 | 0.953633 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.41103 | 0.0478934 | ||||||||
\(869\) | −36.7637 | −1.24712 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 73.5059 | 2.49065 | ||||||||
\(872\) | 3.42944 | 0.116135 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.86544 | 0.198401 | ||||||||
\(875\) | −4.70094 | −0.158921 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.5659 | 1.50488 | 0.752442 | − | 0.658659i | \(-0.228876\pi\) | ||||
0.752442 | + | 0.658659i | \(0.228876\pi\) | |||||||
\(878\) | −5.19677 | −0.175382 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −16.4795 | −0.555523 | ||||||||
\(881\) | 7.17323 | 0.241672 | 0.120836 | − | 0.992672i | \(-0.461442\pi\) | ||||
0.120836 | + | 0.992672i | \(0.461442\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.5763 | −1.12993 | −0.564967 | − | 0.825114i | \(-0.691111\pi\) | ||||
−0.564967 | + | 0.825114i | \(0.691111\pi\) | |||||||
\(884\) | 27.0284 | 0.909063 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −40.3997 | −1.35725 | ||||||||
\(887\) | −21.7630 | −0.730730 | −0.365365 | − | 0.930864i | \(-0.619056\pi\) | ||||
−0.365365 | + | 0.930864i | \(0.619056\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.917905 | 0.0307856 | ||||||||
\(890\) | 24.4886 | 0.820861 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.00000 | −0.0334825 | ||||||||
\(893\) | −53.5946 | −1.79347 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 78.3580 | 2.61922 | ||||||||
\(896\) | 0.552246 | 0.0184492 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.0560 | 0.702647 | ||||||||
\(899\) | 3.32215 | 0.110800 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 63.6269 | 2.11972 | ||||||||
\(902\) | 6.73222 | 0.224158 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.2528 | −0.374262 | ||||||||
\(905\) | −23.3991 | −0.777812 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.9243 | 0.894008 | 0.447004 | − | 0.894532i | \(-0.352491\pi\) | ||||
0.447004 | + | 0.894532i | \(0.352491\pi\) | |||||||
\(908\) | −27.8830 | −0.925330 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 9.69666 | 0.321441 | ||||||||
\(911\) | 24.3104 | 0.805439 | 0.402719 | − | 0.915323i | \(-0.368065\pi\) | ||||
0.402719 | + | 0.915323i | \(0.368065\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.84674 | −0.160404 | ||||||||
\(914\) | 22.4763 | 0.743449 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.6798 | 0.352869 | ||||||||
\(917\) | −9.88254 | −0.326350 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.1810 | −1.35844 | −0.679219 | − | 0.733936i | \(-0.737681\pi\) | ||||
−0.679219 | + | 0.733936i | \(0.737681\pi\) | |||||||
\(920\) | 3.55237 | 0.117118 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −40.9480 | −1.34855 | ||||||||
\(923\) | −66.0574 | −2.17430 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48.3480 | 1.58967 | ||||||||
\(926\) | −33.1771 | −1.09027 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.30022 | 0.0426817 | ||||||||
\(929\) | 0.772006 | 0.0253287 | 0.0126643 | − | 0.999920i | \(-0.495969\pi\) | ||||
0.0126643 | + | 0.999920i | \(0.495969\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −38.9513 | −1.27658 | ||||||||
\(932\) | 26.2101 | 0.858541 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.18020 | −0.169501 | ||||||||
\(935\) | −89.3844 | −2.92318 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.1568 | −0.527819 | −0.263909 | − | 0.964547i | \(-0.585012\pi\) | ||||
−0.263909 | + | 0.964547i | \(0.585012\pi\) | |||||||
\(938\) | 8.14615 | 0.265981 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −32.4592 | −1.05870 | ||||||||
\(941\) | 42.1770 | 1.37493 | 0.687465 | − | 0.726218i | \(-0.258724\pi\) | ||||
0.687465 | + | 0.726218i | \(0.258724\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.45122 | −0.0472582 | ||||||||
\(944\) | −10.2734 | −0.334371 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.94459 | −0.323327 | ||||||||
\(947\) | 6.20082 | 0.201499 | 0.100750 | − | 0.994912i | \(-0.467876\pi\) | ||||
0.100750 | + | 0.994912i | \(0.467876\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.11256 | −0.198422 | ||||||||
\(950\) | −43.1449 | −1.39980 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.99537 | 0.0970805 | ||||||||
\(953\) | 2.34293 | 0.0758950 | 0.0379475 | − | 0.999280i | \(-0.487918\pi\) | ||||
0.0379475 | + | 0.999280i | \(0.487918\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −56.7226 | −1.83550 | ||||||||
\(956\) | 8.82406 | 0.285390 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22.1006 | −0.714040 | ||||||||
\(959\) | 4.86160 | 0.156989 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.4716 | −0.789407 | ||||||||
\(962\) | −32.4879 | −1.04745 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.7867 | −0.476248 | ||||||||
\(965\) | −33.4594 | −1.07710 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.0757963 | 0.00243744 | 0.00121872 | − | 0.999999i | \(-0.499612\pi\) | ||||
0.00121872 | + | 0.999999i | \(0.499612\pi\) | |||||||
\(968\) | −10.8732 | −0.349477 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 53.4308 | 1.71556 | ||||||||
\(971\) | 29.9768 | 0.962001 | 0.481001 | − | 0.876720i | \(-0.340273\pi\) | ||||
0.481001 | + | 0.876720i | \(0.340273\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.68732 | −0.150268 | ||||||||
\(974\) | 7.33737 | 0.235104 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.3437 | 0.331095 | ||||||||
\(977\) | 3.26298 | 0.104392 | 0.0521960 | − | 0.998637i | \(-0.483378\pi\) | ||||
0.0521960 | + | 0.998637i | \(0.483378\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.5037 | 1.03882 | ||||||||
\(980\) | −23.5906 | −0.753576 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 23.5057 | 0.750098 | ||||||||
\(983\) | 26.6268 | 0.849264 | 0.424632 | − | 0.905366i | \(-0.360403\pi\) | ||||
0.424632 | + | 0.905366i | \(0.360403\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −64.3982 | −2.05190 | ||||||||
\(986\) | 7.05235 | 0.224593 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 28.9916 | 0.922346 | ||||||||
\(989\) | 2.14369 | 0.0681653 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.34679 | 0.0745482 | 0.0372741 | − | 0.999305i | \(-0.488133\pi\) | ||||
0.0372741 | + | 0.999305i | \(0.488133\pi\) | |||||||
\(992\) | 2.55507 | 0.0811236 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.32068 | −0.232198 | ||||||||
\(995\) | 30.2077 | 0.957650 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.39888 | −0.107644 | −0.0538218 | − | 0.998551i | \(-0.517140\pi\) | ||||
−0.0538218 | + | 0.998551i | \(0.517140\pi\) | |||||||
\(998\) | −20.0215 | −0.633769 | ||||||||
\(999\) | 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 | 4014.2.a.w.1.7 | 7 | ||
3.2 | odd | 2 | 446.2.a.e.1.1 | ✓ | 7 | ||
12.11 | even | 2 | 3568.2.a.l.1.7 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
446.2.a.e.1.1 | ✓ | 7 | 3.2 | odd | 2 | ||
3568.2.a.l.1.7 | 7 | 12.11 | even | 2 | |||
4014.2.a.w.1.7 | 7 | 1.1 | even | 1 | trivial |