Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7500,2,Mod(1,7500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7500, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("7500.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7500 = 2^{2} \cdot 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7500.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: | \(59.8878015160\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{15})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 300) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.95630\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7500.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.78339 | −1.80795 | −0.903975 | − | 0.427585i | \(-0.859364\pi\) | ||||
−0.903975 | + | 0.427585i | \(0.859364\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.95630 | 0.589845 | 0.294923 | − | 0.955521i | \(-0.404706\pi\) | ||||
0.294923 | + | 0.955521i | \(0.404706\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.07985 | 0.299497 | 0.149749 | − | 0.988724i | \(-0.452154\pi\) | ||||
0.149749 | + | 0.988724i | \(0.452154\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.80573 | −0.923024 | −0.461512 | − | 0.887134i | \(-0.652693\pi\) | ||||
−0.461512 | + | 0.887134i | \(0.652693\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.25085 | 0.975212 | 0.487606 | − | 0.873064i | \(-0.337870\pi\) | ||||
0.487606 | + | 0.873064i | \(0.337870\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.78339 | −1.04382 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.86324 | −1.22257 | −0.611285 | − | 0.791411i | \(-0.709347\pi\) | ||||
−0.611285 | + | 0.791411i | \(0.709347\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.5501 | 1.95910 | 0.979550 | − | 0.201200i | \(-0.0644841\pi\) | ||||
0.979550 | + | 0.201200i | \(0.0644841\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.31592 | −0.775162 | −0.387581 | − | 0.921836i | \(-0.626689\pi\) | ||||
−0.387581 | + | 0.921836i | \(0.626689\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.95630 | 0.340547 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.65983 | 0.930470 | 0.465235 | − | 0.885187i | \(-0.345970\pi\) | ||||
0.465235 | + | 0.885187i | \(0.345970\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.07985 | 0.172915 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.858568 | 0.134086 | 0.0670429 | − | 0.997750i | \(-0.478644\pi\) | ||||
0.0670429 | + | 0.997750i | \(0.478644\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.8764 | −1.65864 | −0.829321 | − | 0.558773i | \(-0.811272\pi\) | ||||
−0.829321 | + | 0.558773i | \(0.811272\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00158 | 0.437825 | 0.218913 | − | 0.975744i | \(-0.429749\pi\) | ||||
0.218913 | + | 0.975744i | \(0.429749\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.8808 | 2.26868 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.80573 | −0.532908 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.22384 | 0.580189 | 0.290095 | − | 0.956998i | \(-0.406313\pi\) | ||||
0.290095 | + | 0.956998i | \(0.406313\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.25085 | 0.563039 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.77018 | −0.621025 | −0.310512 | − | 0.950569i | \(-0.600501\pi\) | ||||
−0.310512 | + | 0.950569i | \(0.600501\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.63184 | 0.465010 | 0.232505 | − | 0.972595i | \(-0.425308\pi\) | ||||
0.232505 | + | 0.972595i | \(0.425308\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.78339 | −0.602650 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.93046 | 0.846691 | 0.423346 | − | 0.905968i | \(-0.360856\pi\) | ||||
0.423346 | + | 0.905968i | \(0.360856\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.86324 | −0.705851 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.9971 | −1.42380 | −0.711898 | − | 0.702283i | \(-0.752164\pi\) | ||||
−0.711898 | + | 0.702283i | \(0.752164\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.9560 | −1.98455 | −0.992273 | − | 0.124075i | \(-0.960404\pi\) | ||||
−0.992273 | + | 0.124075i | \(0.960404\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.35772 | −1.06641 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.62059 | −0.744875 | −0.372437 | − | 0.928057i | \(-0.621478\pi\) | ||||
−0.372437 | + | 0.928057i | \(0.621478\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.58189 | −0.283399 | −0.141699 | − | 0.989910i | \(-0.545257\pi\) | ||||
−0.141699 | + | 0.989910i | \(0.545257\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.5501 | 1.13109 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.832738 | −0.0882700 | −0.0441350 | − | 0.999026i | \(-0.514053\pi\) | ||||
−0.0441350 | + | 0.999026i | \(0.514053\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.16535 | −0.541476 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.31592 | −0.447540 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.11698 | −0.925689 | −0.462844 | − | 0.886440i | \(-0.653171\pi\) | ||||
−0.462844 | + | 0.886440i | \(0.653171\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.95630 | 0.196615 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.49541 | 0.148799 | 0.0743994 | − | 0.997229i | \(-0.476296\pi\) | ||||
0.0743994 | + | 0.997229i | \(0.476296\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.8623 | 1.07029 | 0.535147 | − | 0.844759i | \(-0.320256\pi\) | ||||
0.535147 | + | 0.844759i | \(0.320256\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.8390 | −1.91791 | −0.958954 | − | 0.283563i | \(-0.908484\pi\) | ||||
−0.958954 | + | 0.283563i | \(0.908484\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.34391 | −0.224506 | −0.112253 | − | 0.993680i | \(-0.535807\pi\) | ||||
−0.112253 | + | 0.993680i | \(0.535807\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.65983 | 0.537207 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.22851 | −0.303713 | −0.151856 | − | 0.988403i | \(-0.548525\pi\) | ||||
−0.151856 | + | 0.988403i | \(0.548525\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.07985 | 0.0998324 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.2043 | 1.66878 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.17291 | −0.652083 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.858568 | 0.0774145 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.38631 | 0.655429 | 0.327714 | − | 0.944777i | \(-0.393722\pi\) | ||||
0.327714 | + | 0.944777i | \(0.393722\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.8764 | −0.957617 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.8839 | −1.47515 | −0.737575 | − | 0.675265i | \(-0.764029\pi\) | ||||
−0.737575 | + | 0.675265i | \(0.764029\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.3335 | −1.76313 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.839318 | 0.0717078 | 0.0358539 | − | 0.999357i | \(-0.488585\pi\) | ||||
0.0358539 | + | 0.999357i | \(0.488585\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.1580 | −0.946409 | −0.473205 | − | 0.880953i | \(-0.656903\pi\) | ||||
−0.473205 | + | 0.880953i | \(0.656903\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00158 | 0.252779 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.11251 | 0.176657 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.8808 | 1.30982 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.0277 | −1.80458 | −0.902288 | − | 0.431134i | \(-0.858114\pi\) | ||||
−0.902288 | + | 0.431134i | \(0.858114\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.7890 | 0.959378 | 0.479689 | − | 0.877439i | \(-0.340750\pi\) | ||||
0.479689 | + | 0.877439i | \(0.340750\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.80573 | −0.307675 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.2769 | 0.899994 | 0.449997 | − | 0.893030i | \(-0.351425\pi\) | ||||
0.449997 | + | 0.893030i | \(0.351425\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.22384 | 0.334972 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 28.0461 | 2.21035 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.89630 | 0.775138 | 0.387569 | − | 0.921841i | \(-0.373315\pi\) | ||||
0.387569 | + | 0.921841i | \(0.373315\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.51564 | −0.581577 | −0.290789 | − | 0.956787i | \(-0.593918\pi\) | ||||
−0.290789 | + | 0.956787i | \(0.593918\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8339 | −0.910301 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.25085 | 0.325071 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.2783 | 0.933499 | 0.466749 | − | 0.884390i | \(-0.345425\pi\) | ||||
0.466749 | + | 0.884390i | \(0.345425\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.77018 | −0.358549 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.2089 | 1.13677 | 0.568384 | − | 0.822763i | \(-0.307569\pi\) | ||||
0.568384 | + | 0.822763i | \(0.307569\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.8755 | −1.55166 | −0.775831 | − | 0.630941i | \(-0.782669\pi\) | ||||
−0.775831 | + | 0.630941i | \(0.782669\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.63184 | 0.268473 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.44512 | −0.544441 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.78339 | −0.347940 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.25085 | −0.379938 | −0.189969 | − | 0.981790i | \(-0.560839\pi\) | ||||
−0.189969 | + | 0.981790i | \(0.560839\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.94565 | 0.571940 | 0.285970 | − | 0.958239i | \(-0.407684\pi\) | ||||
0.285970 | + | 0.958239i | \(0.407684\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.0059 | −0.926633 | −0.463317 | − | 0.886193i | \(-0.653341\pi\) | ||||
−0.463317 | + | 0.886193i | \(0.653341\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.06434 | 0.0754490 | 0.0377245 | − | 0.999288i | \(-0.487989\pi\) | ||||
0.0377245 | + | 0.999288i | \(0.487989\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.93046 | 0.488837 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −50.4651 | −3.54196 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.86324 | −0.407523 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.31592 | 0.575224 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.4928 | −1.41079 | −0.705393 | − | 0.708817i | \(-0.749229\pi\) | ||||
−0.705393 | + | 0.708817i | \(0.749229\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.9971 | −0.822029 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.6447 | 1.40145 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.9560 | −1.14578 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.10962 | −0.276443 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.3121 | 0.690549 | 0.345275 | − | 0.938502i | \(-0.387786\pi\) | ||||
0.345275 | + | 0.938502i | \(0.387786\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.1409 | −1.20405 | −0.602027 | − | 0.798476i | \(-0.705640\pi\) | ||||
−0.602027 | + | 0.798476i | \(0.705640\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.71827 | −0.642202 | −0.321101 | − | 0.947045i | \(-0.604053\pi\) | ||||
−0.321101 | + | 0.947045i | \(0.604053\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.35772 | −0.615692 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.2184 | −1.45558 | −0.727788 | − | 0.685802i | \(-0.759451\pi\) | ||||
−0.727788 | + | 0.685802i | \(0.759451\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.62059 | −0.430054 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.9293 | 1.03038 | 0.515190 | − | 0.857076i | \(-0.327721\pi\) | ||||
0.515190 | + | 0.857076i | \(0.327721\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.93147 | −0.317664 | −0.158832 | − | 0.987306i | \(-0.550773\pi\) | ||||
−0.158832 | + | 0.987306i | \(0.550773\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.59029 | 0.292073 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.58189 | −0.163620 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.4351 | 0.974252 | 0.487126 | − | 0.873332i | \(-0.338045\pi\) | ||||
0.487126 | + | 0.873332i | \(0.338045\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.4702 | −0.721127 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.1828 | 1.32134 | 0.660672 | − | 0.750674i | \(-0.270271\pi\) | ||||
0.660672 | + | 0.750674i | \(0.270271\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.0731 | −1.68224 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.5501 | 0.653033 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.9264 | −1.29038 | −0.645188 | − | 0.764023i | \(-0.723221\pi\) | ||||
−0.645188 | + | 0.764023i | \(0.723221\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.832738 | −0.0509627 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.7837 | −0.840405 | −0.420202 | − | 0.907430i | \(-0.638041\pi\) | ||||
−0.420202 | + | 0.907430i | \(0.638041\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.5495 | 0.640837 | 0.320418 | − | 0.947276i | \(-0.396177\pi\) | ||||
0.320418 | + | 0.947276i | \(0.396177\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.16535 | −0.312621 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.9622 | 1.07924 | 0.539622 | − | 0.841907i | \(-0.318567\pi\) | ||||
0.539622 | + | 0.841907i | \(0.318567\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.31592 | −0.258387 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.926728 | −0.0552840 | −0.0276420 | − | 0.999618i | \(-0.508800\pi\) | ||||
−0.0276420 | + | 0.999618i | \(0.508800\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.57749 | −0.390991 | −0.195496 | − | 0.980705i | \(-0.562632\pi\) | ||||
−0.195496 | + | 0.980705i | \(0.562632\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.10686 | −0.242420 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.51644 | −0.148026 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.11698 | −0.534447 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.6208 | 1.49678 | 0.748391 | − | 0.663257i | \(-0.230827\pi\) | ||||
0.748391 | + | 0.663257i | \(0.230827\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.95630 | 0.113516 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.33143 | −0.366156 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 52.0262 | 2.99874 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.49541 | 0.0859091 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.18420 | −0.352951 | −0.176476 | − | 0.984305i | \(-0.556470\pi\) | ||||
−0.176476 | + | 0.984305i | \(0.556470\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.8623 | 0.617935 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.2382 | −1.37442 | −0.687210 | − | 0.726459i | \(-0.741165\pi\) | ||||
−0.687210 | + | 0.726459i | \(0.741165\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.9612 | −1.69351 | −0.846755 | − | 0.531984i | \(-0.821447\pi\) | ||||
−0.846755 | + | 0.531984i | \(0.821447\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.46267 | 0.138317 | 0.0691586 | − | 0.997606i | \(-0.477969\pi\) | ||||
0.0691586 | + | 0.997606i | \(0.477969\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.6391 | 1.15557 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −19.8390 | −1.10730 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.1776 | −0.900145 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.34391 | −0.129618 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.3577 | −0.791566 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.7867 | −1.47233 | −0.736166 | − | 0.676801i | \(-0.763366\pi\) | ||||
−0.736166 | + | 0.676801i | \(0.763366\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.65983 | 0.310157 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.43659 | 0.132730 | 0.0663648 | − | 0.997795i | \(-0.478860\pi\) | ||||
0.0663648 | + | 0.997795i | \(0.478860\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.22851 | −0.175349 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.44321 | −0.457226 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −42.4802 | −2.29372 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.63749 | −0.410002 | −0.205001 | − | 0.978762i | \(-0.565720\pi\) | ||||
−0.205001 | + | 0.978762i | \(0.565720\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.2283 | −1.08280 | −0.541398 | − | 0.840766i | \(-0.682105\pi\) | ||||
−0.541398 | + | 0.840766i | \(0.682105\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.07985 | 0.0576383 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.2922 | −1.50584 | −0.752922 | − | 0.658110i | \(-0.771356\pi\) | ||||
−0.752922 | + | 0.658110i | \(0.771356\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.2043 | 0.963472 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.8318 | 1.20502 | 0.602509 | − | 0.798112i | \(-0.294168\pi\) | ||||
0.602509 | + | 0.798112i | \(0.294168\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.930261 | −0.0489611 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.17291 | −0.376480 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.51795 | −0.131436 | −0.0657181 | − | 0.997838i | \(-0.520934\pi\) | ||||
−0.0657181 | + | 0.997838i | \(0.520934\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.858568 | 0.0446953 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.2043 | −1.04895 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.65398 | 0.292752 | 0.146376 | − | 0.989229i | \(-0.453239\pi\) | ||||
0.146376 | + | 0.989229i | \(0.453239\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.3925 | 0.586745 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.3917 | −0.739254 | −0.369627 | − | 0.929180i | \(-0.620515\pi\) | ||||
−0.369627 | + | 0.929180i | \(0.620515\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.38631 | 0.378412 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.19992 | −0.418996 | −0.209498 | − | 0.977809i | \(-0.567183\pi\) | ||||
−0.209498 | + | 0.977809i | \(0.567183\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.8764 | −0.552881 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.73067 | 0.239855 | 0.119927 | − | 0.992783i | \(-0.461734\pi\) | ||||
0.119927 | + | 0.992783i | \(0.461734\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.3139 | 1.12846 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.8839 | −0.851679 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.58326 | −0.380593 | −0.190297 | − | 0.981727i | \(-0.560945\pi\) | ||||
−0.190297 | + | 0.981727i | \(0.560945\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.3335 | −1.01795 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.1128 | 0.505011 | 0.252506 | − | 0.967595i | \(-0.418745\pi\) | ||||
0.252506 | + | 0.967595i | \(0.418745\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.66056 | −0.232159 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.0723 | 0.548833 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.97924 | 0.196761 | 0.0983804 | − | 0.995149i | \(-0.468634\pi\) | ||||
0.0983804 | + | 0.995149i | \(0.468634\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.839318 | 0.0414005 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.8176 | 1.12278 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.1580 | −0.546410 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.79655 | 0.0877671 | 0.0438835 | − | 0.999037i | \(-0.486027\pi\) | ||||
0.0438835 | + | 0.999037i | \(0.486027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.6701 | 0.763716 | 0.381858 | − | 0.924221i | \(-0.375284\pi\) | ||||
0.381858 | + | 0.924221i | \(0.375284\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.00158 | 0.145942 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.3725 | −0.840714 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.11251 | 0.101993 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −38.5760 | −1.85814 | −0.929071 | − | 0.369901i | \(-0.879391\pi\) | ||||
−0.929071 | + | 0.369901i | \(0.879391\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.16949 | 0.440657 | 0.220329 | − | 0.975426i | \(-0.429287\pi\) | ||||
0.220329 | + | 0.975426i | \(0.429287\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −24.9238 | −1.19227 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.6882 | 0.844212 | 0.422106 | − | 0.906546i | \(-0.361291\pi\) | ||||
0.422106 | + | 0.906546i | \(0.361291\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.8808 | 0.756228 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.6673 | −0.886912 | −0.443456 | − | 0.896296i | \(-0.646248\pi\) | ||||
−0.443456 | + | 0.896296i | \(0.646248\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22.0277 | −1.04187 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 41.2111 | 1.94487 | 0.972436 | − | 0.233171i | \(-0.0749102\pi\) | ||||
0.972436 | + | 0.233171i | \(0.0749102\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.67961 | 0.0790899 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.7890 | 0.553897 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.56092 | −0.260129 | −0.130064 | − | 0.991506i | \(-0.541518\pi\) | ||||
−0.130064 | + | 0.991506i | \(0.541518\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.80573 | −0.177636 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.1627 | 0.985646 | 0.492823 | − | 0.870130i | \(-0.335965\pi\) | ||||
0.492823 | + | 0.870130i | \(0.335965\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.74566 | −0.359971 | −0.179986 | − | 0.983669i | \(-0.557605\pi\) | ||||
−0.179986 | + | 0.983669i | \(0.557605\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.43205 | −0.112542 | −0.0562709 | − | 0.998416i | \(-0.517921\pi\) | ||||
−0.0562709 | + | 0.998416i | \(0.517921\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −33.1511 | −1.53078 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.2769 | 0.519611 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.2775 | −0.978342 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.22384 | 0.193396 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 34.1291 | 1.55940 | 0.779699 | − | 0.626155i | \(-0.215372\pi\) | ||||
0.779699 | + | 0.626155i | \(0.215372\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.11178 | 0.278673 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 28.0461 | 1.27614 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.0358 | −1.45168 | −0.725841 | − | 0.687863i | \(-0.758549\pi\) | ||||
−0.725841 | + | 0.687863i | \(0.758549\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.89630 | 0.447526 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.4011 | 1.32685 | 0.663426 | − | 0.748242i | \(-0.269102\pi\) | ||||
0.663426 | + | 0.748242i | \(0.269102\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −40.1507 | −1.80830 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 57.3868 | 2.57415 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.04298 | −0.404819 | −0.202410 | − | 0.979301i | \(-0.564877\pi\) | ||||
−0.202410 | + | 0.979301i | \(0.564877\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.51564 | −0.335774 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.07701 | 0.137197 | 0.0685985 | − | 0.997644i | \(-0.478147\pi\) | ||||
0.0685985 | + | 0.997644i | \(0.478147\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.8339 | −0.525563 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.2553 | 1.16375 | 0.581873 | − | 0.813279i | \(-0.302320\pi\) | ||||
0.581873 | + | 0.813279i | \(0.302320\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 81.1069 | 3.58796 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.25085 | 0.187680 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.87198 | 0.258249 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.2783 | 0.538956 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.7473 | 0.908956 | 0.454478 | − | 0.890758i | \(-0.349826\pi\) | ||||
0.454478 | + | 0.890758i | \(0.349826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.4498 | −0.981663 | −0.490831 | − | 0.871255i | \(-0.663307\pi\) | ||||
−0.490831 | + | 0.871255i | \(0.663307\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.4252 | 0.715494 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.3776 | 0.494677 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.77018 | −0.207008 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.927127 | 0.0401583 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.2089 | 0.656314 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 31.0675 | 1.33817 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.3337 | −1.08918 | −0.544591 | − | 0.838702i | \(-0.683315\pi\) | ||||
−0.544591 | + | 0.838702i | \(0.683315\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.8755 | −0.895852 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.8073 | −0.504844 | −0.252422 | − | 0.967617i | \(-0.581227\pi\) | ||||
−0.252422 | + | 0.967617i | \(0.581227\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.63184 | 0.155003 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 44.8468 | 1.91054 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 31.6688 | 1.34670 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.93356 | 0.251413 | 0.125706 | − | 0.992067i | \(-0.459880\pi\) | ||||
0.125706 | + | 0.992067i | \(0.459880\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.7450 | −0.496759 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.44512 | −0.314333 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.7426 | 0.579183 | 0.289592 | − | 0.957150i | \(-0.406480\pi\) | ||||
0.289592 | + | 0.957150i | \(0.406480\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.78339 | −0.200883 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.1078 | 1.38795 | 0.693975 | − | 0.719999i | \(-0.255858\pi\) | ||||
0.693975 | + | 0.719999i | \(0.255858\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.6092 | −1.07171 | −0.535855 | − | 0.844310i | \(-0.680011\pi\) | ||||
−0.535855 | + | 0.844310i | \(0.680011\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.25085 | −0.219357 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.48758 | 0.145190 | 0.0725949 | − | 0.997362i | \(-0.476872\pi\) | ||||
0.0725949 | + | 0.997362i | \(0.476872\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.94565 | 0.330210 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.3502 | 0.512371 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.26308 | 0.342222 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.4479 | 1.42182 | 0.710909 | − | 0.703284i | \(-0.248284\pi\) | ||||
0.710909 | + | 0.703284i | \(0.248284\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.3463 | −0.755948 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.0059 | −0.534992 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.7248 | 1.46704 | 0.733522 | − | 0.679666i | \(-0.237875\pi\) | ||||
0.733522 | + | 0.679666i | \(0.237875\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.06434 | 0.0435605 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.7697 | 1.62495 | 0.812473 | − | 0.582998i | \(-0.198121\pi\) | ||||
0.812473 | + | 0.582998i | \(0.198121\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.5134 | −0.632805 | −0.316402 | − | 0.948625i | \(-0.602475\pi\) | ||||
−0.316402 | + | 0.948625i | \(0.602475\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.93046 | 0.282230 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.1855 | 0.616358 | 0.308179 | − | 0.951328i | \(-0.400280\pi\) | ||||
0.308179 | + | 0.951328i | \(0.400280\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −50.4651 | −2.04495 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.24126 | 0.131128 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.1345 | −1.29790 | −0.648951 | − | 0.760831i | \(-0.724792\pi\) | ||||
−0.648951 | + | 0.760831i | \(0.724792\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.32238 | 0.174012 | 0.0870061 | − | 0.996208i | \(-0.472270\pi\) | ||||
0.0870061 | + | 0.996208i | \(0.472270\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.3967 | 1.34233 | 0.671163 | − | 0.741310i | \(-0.265795\pi\) | ||||
0.671163 | + | 0.741310i | \(0.265795\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.86324 | −0.235284 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.98331 | 0.159588 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.31592 | 0.332106 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.5398 | −0.858847 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.9937 | 0.437654 | 0.218827 | − | 0.975764i | \(-0.429777\pi\) | ||||
0.218827 | + | 0.975764i | \(0.429777\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.4928 | −0.814517 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.1489 | 0.679464 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.9971 | −0.474598 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.86056 | −0.270976 | −0.135488 | − | 0.990779i | \(-0.543260\pi\) | ||||
−0.135488 | + | 0.990779i | \(0.543260\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.1923 | 0.914615 | 0.457308 | − | 0.889309i | \(-0.348814\pi\) | ||||
0.457308 | + | 0.889309i | \(0.348814\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.7846 | −1.21027 | −0.605135 | − | 0.796123i | \(-0.706881\pi\) | ||||
−0.605135 | + | 0.796123i | \(0.706881\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.33188 | −0.366309 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.6447 | 0.809130 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.80686 | −0.305506 | −0.152753 | − | 0.988264i | \(-0.548814\pi\) | ||||
−0.152753 | + | 0.988264i | \(0.548814\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.9560 | −0.661515 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.27044 | 0.205307 | 0.102654 | − | 0.994717i | \(-0.467267\pi\) | ||||
0.102654 | + | 0.994717i | \(0.467267\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.8954 | −1.43506 | −0.717532 | − | 0.696526i | \(-0.754728\pi\) | ||||
−0.717532 | + | 0.696526i | \(0.754728\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.10962 | −0.159605 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −61.8576 | −2.39514 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.3121 | 0.398689 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.10495 | 0.274284 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −45.0209 | −1.73543 | −0.867714 | − | 0.497063i | \(-0.834412\pi\) | ||||
−0.867714 | + | 0.497063i | \(0.834412\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.5396 | 1.21217 | 0.606083 | − | 0.795402i | \(-0.292740\pi\) | ||||
0.606083 | + | 0.795402i | \(0.292740\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 43.6100 | 1.67360 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.1409 | −0.695161 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.6888 | −0.791636 | −0.395818 | − | 0.918329i | \(-0.629539\pi\) | ||||
−0.395818 | + | 0.918329i | \(0.629539\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.71827 | −0.370775 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.56113 | 0.173765 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.1801 | −1.30027 | −0.650137 | − | 0.759817i | \(-0.725288\pi\) | ||||
−0.650137 | + | 0.759817i | \(0.725288\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.35772 | −0.355470 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.26748 | −0.123764 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.2184 | −0.840377 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.6859 | −0.630216 | −0.315108 | − | 0.949056i | \(-0.602041\pi\) | ||||
−0.315108 | + | 0.949056i | \(0.602041\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.0591 | 0.907406 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.15312 | −0.269021 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 47.3162 | 1.77700 | 0.888499 | − | 0.458878i | \(-0.151749\pi\) | ||||
0.888499 | + | 0.458878i | \(0.151749\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.62059 | −0.248292 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.3053 | 0.947690 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.9293 | 0.594890 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.61236 | 0.209306 | 0.104653 | − | 0.994509i | \(-0.466627\pi\) | ||||
0.104653 | + | 0.994509i | \(0.466627\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −51.9586 | −1.93504 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.93147 | −0.183403 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.6366 | −0.542841 | −0.271420 | − | 0.962461i | \(-0.587493\pi\) | ||||
−0.271420 | + | 0.962461i | \(0.587493\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 41.3928 | 1.53097 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.2577 | 1.19147 | 0.595733 | − | 0.803183i | \(-0.296862\pi\) | ||||
0.595733 | + | 0.803183i | \(0.296862\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.5580 | 0.499417 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.8507 | −0.877361 | −0.438680 | − | 0.898643i | \(-0.644554\pi\) | ||||
−0.438680 | + | 0.898643i | \(0.644554\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.59029 | 0.168629 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.48188 | 0.274483 | 0.137242 | − | 0.990538i | \(-0.456176\pi\) | ||||
0.137242 | + | 0.990538i | \(0.456176\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.58189 | −0.0944663 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 94.8975 | 3.46748 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.3687 | −1.18115 | −0.590576 | − | 0.806982i | \(-0.701099\pi\) | ||||
−0.590576 | + | 0.806982i | \(0.701099\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.4351 | 0.562485 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.2847 | −0.373804 | −0.186902 | − | 0.982379i | \(-0.559845\pi\) | ||||
−0.186902 | + | 0.982379i | \(0.559845\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.4702 | −0.416343 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.8044 | 1.04416 | 0.522080 | − | 0.852897i | \(-0.325156\pi\) | ||||
0.522080 | + | 0.852897i | \(0.325156\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.2118 | 0.405895 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.15109 | −0.185995 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.3743 | −1.41987 | −0.709936 | − | 0.704266i | \(-0.751276\pi\) | ||||
−0.709936 | + | 0.704266i | \(0.751276\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.1828 | 0.762879 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.06407 | 0.182142 | 0.0910709 | − | 0.995844i | \(-0.470971\pi\) | ||||
0.0910709 | + | 0.995844i | \(0.470971\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −27.0731 | −0.971244 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.64965 | 0.130762 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.4699 | −0.839819 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.5501 | 0.377029 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.33151 | 0.190048 | 0.0950239 | − | 0.995475i | \(-0.469707\pi\) | ||||
0.0950239 | + | 0.995475i | \(0.469707\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.9264 | −0.744999 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.4432 | 0.549098 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.92185 | 0.139269 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.4253 | 0.794345 | 0.397172 | − | 0.917744i | \(-0.369991\pi\) | ||||
0.397172 | + | 0.917744i | \(0.369991\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.4232 | −0.404124 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.832738 | −0.0294233 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −33.1709 | −1.17057 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.7837 | −0.485208 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.0715 | 0.424411 | 0.212206 | − | 0.977225i | \(-0.431935\pi\) | ||||
0.212206 | + | 0.977225i | \(0.431935\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.5422 | 0.932024 | 0.466012 | − | 0.884778i | \(-0.345690\pi\) | ||||
0.466012 | + | 0.884778i | \(0.345690\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.5495 | 0.369987 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −46.2341 | −1.61753 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.16535 | −0.180492 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.79377 | −0.0626031 | −0.0313015 | − | 0.999510i | \(-0.509965\pi\) | ||||
−0.0313015 | + | 0.999510i | \(0.509965\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.5881 | 1.24052 | 0.620261 | − | 0.784396i | \(-0.287027\pi\) | ||||
0.620261 | + | 0.784396i | \(0.287027\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.4424 | 0.954264 | 0.477132 | − | 0.878832i | \(-0.341676\pi\) | ||||
0.477132 | + | 0.878832i | \(0.341676\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.0241 | −1.32063 | −0.660316 | − | 0.750988i | \(-0.729578\pi\) | ||||
−0.660316 | + | 0.750988i | \(0.729578\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.9622 | 0.623102 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −60.4379 | −2.09405 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.31592 | −0.149180 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.1012 | −1.24635 | −0.623175 | − | 0.782082i | \(-0.714158\pi\) | ||||
−0.623175 | + | 0.782082i | \(0.714158\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 82.3042 | 2.83807 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.926728 | −0.0319182 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34.3108 | 1.17893 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.57749 | −0.225739 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33.1849 | −1.13756 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.9489 | −1.12815 | −0.564075 | − | 0.825724i | \(-0.690767\pi\) | ||||
−0.564075 | + | 0.825724i | \(0.690767\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.9514 | −0.476572 | −0.238286 | − | 0.971195i | \(-0.576586\pi\) | ||||
−0.238286 | + | 0.971195i | \(0.576586\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.6514 | −1.31877 | −0.659384 | − | 0.751806i | \(-0.729183\pi\) | ||||
−0.659384 | + | 0.751806i | \(0.729183\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.10686 | −0.139962 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.57575 | −0.121720 | −0.0608599 | − | 0.998146i | \(-0.519384\pi\) | ||||
−0.0608599 | + | 0.998146i | \(0.519384\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.51644 | −0.0854629 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.9518 | −0.439361 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.48388 | 0.253582 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.11698 | −0.308563 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.52136 | −0.253978 | −0.126989 | − | 0.991904i | \(-0.540531\pi\) | ||||
−0.126989 | + | 0.991904i | \(0.540531\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.6208 | 0.864168 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.3654 | −0.888272 | −0.444136 | − | 0.895959i | \(-0.646489\pi\) | ||||
−0.444136 | + | 0.895959i | \(0.646489\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.411659 | −0.0138534 | −0.00692672 | − | 0.999976i | \(-0.502205\pi\) | ||||
−0.00692672 | + | 0.999976i | \(0.502205\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.8013 | 0.967054 | 0.483527 | − | 0.875329i | \(-0.339355\pi\) | ||||
0.483527 | + | 0.875329i | \(0.339355\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −35.3316 | −1.18498 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.95630 | 0.0655384 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.7593 | 0.426973 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.33143 | −0.211400 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −45.5333 | −1.51862 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.0748 | −0.535529 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 52.0262 | 1.73132 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.80122 | −0.0598085 | −0.0299042 | − | 0.999553i | \(-0.509520\pi\) | ||||
−0.0299042 | + | 0.999553i | \(0.509520\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.49541 | 0.0495996 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.33268 | 0.143548 | 0.0717741 | − | 0.997421i | \(-0.477134\pi\) | ||||
0.0717741 | + | 0.997421i | \(0.477134\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.05093 | −0.167161 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 80.7621 | 2.66700 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.79390 | −0.257097 | −0.128548 | − | 0.991703i | \(-0.541032\pi\) | ||||
−0.128548 | + | 0.991703i | \(0.541032\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.18420 | −0.203776 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.9551 | −0.426423 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.8623 | 0.356765 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.3560 | −1.09437 | −0.547187 | − | 0.837010i | \(-0.684301\pi\) | ||||
−0.547187 | + | 0.837010i | \(0.684301\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 67.5069 | 2.21245 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.2382 | −0.793522 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.0108 | 1.07842 | 0.539209 | − | 0.842172i | \(-0.318723\pi\) | ||||
0.539209 | + | 0.842172i | \(0.318723\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.9612 | −0.977748 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −51.1774 | −1.66834 | −0.834168 | − | 0.551510i | \(-0.814052\pi\) | ||||
−0.834168 | + | 0.551510i | \(0.814052\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.03399 | −0.163929 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.16556 | −0.232849 | −0.116425 | − | 0.993200i | \(-0.537143\pi\) | ||||
−0.116425 | + | 0.993200i | \(0.537143\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.3099 | −0.594366 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.46267 | 0.0798575 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.4032 | −0.434171 | −0.217085 | − | 0.976153i | \(-0.569655\pi\) | ||||
−0.217085 | + | 0.976153i | \(0.569655\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.6391 | 0.667166 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.01478 | −0.129644 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.3728 | −0.399124 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.8390 | −0.639302 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.5961 | −0.372907 | −0.186453 | − | 0.982464i | \(-0.559699\pi\) | ||||
−0.186453 | + | 0.982464i | \(0.559699\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.1776 | −0.519699 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.62019 | −0.244544 | −0.122272 | − | 0.992497i | \(-0.539018\pi\) | ||||
−0.122272 | + | 0.992497i | \(0.539018\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 53.3730 | 1.71106 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.4103 | 1.38882 | 0.694409 | − | 0.719580i | \(-0.255666\pi\) | ||||
0.694409 | + | 0.719580i | \(0.255666\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.62908 | −0.0520657 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.34391 | −0.0748352 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −54.7992 | −1.74782 | −0.873912 | − | 0.486085i | \(-0.838425\pi\) | ||||
−0.873912 | + | 0.486085i | \(0.838425\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.3577 | −0.457011 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 63.7712 | 2.02781 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.9440 | 0.697074 | 0.348537 | − | 0.937295i | \(-0.386678\pi\) | ||||
0.348537 | + | 0.937295i | \(0.386678\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.7867 | −0.850051 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.0854 | 1.23785 | 0.618924 | − | 0.785451i | \(-0.287569\pi\) | ||||
0.618924 | + | 0.785451i | \(0.287569\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.65983 | 0.179069 |
(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 | 7500.2.a.g.1.1 | 4 | ||
5.2 | odd | 4 | 7500.2.d.d.1249.1 | 8 | |||
5.3 | odd | 4 | 7500.2.d.d.1249.8 | 8 | |||
5.4 | even | 2 | 7500.2.a.d.1.4 | 4 | |||
25.3 | odd | 20 | 1500.2.o.a.49.2 | 16 | |||
25.4 | even | 10 | 1500.2.m.b.1201.2 | 8 | |||
25.6 | even | 5 | 300.2.m.a.61.1 | ✓ | 8 | ||
25.8 | odd | 20 | 1500.2.o.a.949.4 | 16 | |||
25.17 | odd | 20 | 1500.2.o.a.949.1 | 16 | |||
25.19 | even | 10 | 1500.2.m.b.301.2 | 8 | |||
25.21 | even | 5 | 300.2.m.a.241.1 | yes | 8 | ||
25.22 | odd | 20 | 1500.2.o.a.49.3 | 16 | |||
75.56 | odd | 10 | 900.2.n.a.361.2 | 8 | |||
75.71 | odd | 10 | 900.2.n.a.541.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.m.a.61.1 | ✓ | 8 | 25.6 | even | 5 | ||
300.2.m.a.241.1 | yes | 8 | 25.21 | even | 5 | ||
900.2.n.a.361.2 | 8 | 75.56 | odd | 10 | |||
900.2.n.a.541.2 | 8 | 75.71 | odd | 10 | |||
1500.2.m.b.301.2 | 8 | 25.19 | even | 10 | |||
1500.2.m.b.1201.2 | 8 | 25.4 | even | 10 | |||
1500.2.o.a.49.2 | 16 | 25.3 | odd | 20 | |||
1500.2.o.a.49.3 | 16 | 25.22 | odd | 20 | |||
1500.2.o.a.949.1 | 16 | 25.17 | odd | 20 | |||
1500.2.o.a.949.4 | 16 | 25.8 | odd | 20 | |||
7500.2.a.d.1.4 | 4 | 5.4 | even | 2 | |||
7500.2.a.g.1.1 | 4 | 1.1 | even | 1 | trivial | ||
7500.2.d.d.1249.1 | 8 | 5.2 | odd | 4 | |||
7500.2.d.d.1249.8 | 8 | 5.3 | odd | 4 |