Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2420,2,Mod(1,2420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2420, 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("2420.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2420 = 2^{2} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2420.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: | \(19.3237972891\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2525.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 5x + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 220) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.777484\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2420.1 |
$q$-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 | ||||||||
\(3\) | 2.39552 | 1.38305 | 0.691527 | − | 0.722351i | \(-0.256938\pi\) | ||||
0.691527 | + | 0.722351i | \(0.256938\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.65351 | 1.75886 | 0.879432 | − | 0.476025i | \(-0.157923\pi\) | ||||
0.879432 | + | 0.476025i | \(0.157923\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.73851 | 0.912836 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.03548 | 1.67394 | 0.836971 | − | 0.547248i | \(-0.184325\pi\) | ||||
0.836971 | + | 0.547248i | \(0.184325\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.39552 | 0.618520 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.32106 | 0.805476 | 0.402738 | − | 0.915315i | \(-0.368059\pi\) | ||||
0.402738 | + | 0.915315i | \(0.368059\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.73851 | −0.628257 | −0.314128 | − | 0.949381i | \(-0.601712\pi\) | ||||
−0.314128 | + | 0.949381i | \(0.601712\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.1476 | 2.43260 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.97807 | −0.412457 | −0.206228 | − | 0.978504i | \(-0.566119\pi\) | ||||
−0.206228 | + | 0.978504i | \(0.566119\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.626410 | −0.120553 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.29348 | −0.425888 | −0.212944 | − | 0.977064i | \(-0.568305\pi\) | ||||
−0.212944 | + | 0.977064i | \(0.568305\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.95265 | −1.24873 | −0.624366 | − | 0.781132i | \(-0.714643\pi\) | ||||
−0.624366 | + | 0.781132i | \(0.714643\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.65351 | 0.786587 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.83705 | −0.630808 | −0.315404 | − | 0.948958i | \(-0.602140\pi\) | ||||
−0.315404 | + | 0.948958i | \(0.602140\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.4581 | 2.31515 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.79320 | −0.592398 | −0.296199 | − | 0.955126i | \(-0.595719\pi\) | ||||
−0.296199 | + | 0.955126i | \(0.595719\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.98463 | −1.21764 | −0.608822 | − | 0.793307i | \(-0.708358\pi\) | ||||
−0.608822 | + | 0.793307i | \(0.708358\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.73851 | 0.408233 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.1590 | −1.77357 | −0.886784 | − | 0.462184i | \(-0.847066\pi\) | ||||
−0.886784 | + | 0.462184i | \(0.847066\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.6552 | 2.09360 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.95566 | 1.11402 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.5020 | −1.57992 | −0.789958 | − | 0.613161i | \(-0.789898\pi\) | ||||
−0.789958 | + | 0.613161i | \(0.789898\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.56014 | −0.868912 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.09855 | 0.924152 | 0.462076 | − | 0.886840i | \(-0.347105\pi\) | ||||
0.462076 | + | 0.886840i | \(0.347105\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.33811 | 0.171327 | 0.0856637 | − | 0.996324i | \(-0.472699\pi\) | ||||
0.0856637 | + | 0.996324i | \(0.472699\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.7437 | 1.60555 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.03548 | 0.748609 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.18872 | −0.878241 | −0.439121 | − | 0.898428i | \(-0.644710\pi\) | ||||
−0.439121 | + | 0.898428i | \(0.644710\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.73851 | −0.570449 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.74368 | 0.800328 | 0.400164 | − | 0.916444i | \(-0.368953\pi\) | ||||
0.400164 | + | 0.916444i | \(0.368953\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.71658 | 1.02020 | 0.510099 | − | 0.860116i | \(-0.329609\pi\) | ||||
0.510099 | + | 0.860116i | \(0.329609\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.39552 | 0.276611 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.48569 | −0.617188 | −0.308594 | − | 0.951194i | \(-0.599858\pi\) | ||||
−0.308594 | + | 0.951194i | \(0.599858\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.71610 | −1.07957 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.21414 | 0.901619 | 0.450809 | − | 0.892620i | \(-0.351135\pi\) | ||||
0.450809 | + | 0.892620i | \(0.351135\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.32106 | 0.360220 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.49406 | −0.589025 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.4213 | −1.21065 | −0.605327 | − | 0.795977i | \(-0.706958\pi\) | ||||
−0.605327 | + | 0.795977i | \(0.706958\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 28.0862 | 2.94423 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16.6552 | −1.72706 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.73851 | −0.280965 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.54798 | 0.664846 | 0.332423 | − | 0.943130i | \(-0.392134\pi\) | ||||
0.332423 | + | 0.943130i | \(0.392134\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.272884 | 0.0271529 | 0.0135765 | − | 0.999908i | \(-0.495678\pi\) | ||||
0.0135765 | + | 0.999908i | \(0.495678\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.19221 | 0.807203 | 0.403601 | − | 0.914935i | \(-0.367758\pi\) | ||||
0.403601 | + | 0.914935i | \(0.367758\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.1476 | 1.08789 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.58773 | −0.636860 | −0.318430 | − | 0.947946i | \(-0.603156\pi\) | ||||
−0.318430 | + | 0.947946i | \(0.603156\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.06258 | −0.293342 | −0.146671 | − | 0.989185i | \(-0.546856\pi\) | ||||
−0.146671 | + | 0.989185i | \(0.546856\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.19173 | −0.872441 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.78586 | −0.544288 | −0.272144 | − | 0.962257i | \(-0.587733\pi\) | ||||
−0.272144 | + | 0.962257i | \(0.587733\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.97807 | −0.184456 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.5282 | 1.52803 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.4546 | 1.41672 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.08667 | −0.819318 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.75340 | −0.155589 | −0.0777943 | − | 0.996969i | \(-0.524788\pi\) | ||||
−0.0777943 | + | 0.996969i | \(0.524788\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −19.1273 | −1.68407 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.7047 | 1.11002 | 0.555008 | − | 0.831845i | \(-0.312715\pi\) | ||||
0.555008 | + | 0.831845i | \(0.312715\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.7437 | −1.10502 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.626410 | −0.0539128 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.73635 | −0.148346 | −0.0741731 | − | 0.997245i | \(-0.523632\pi\) | ||||
−0.0741731 | + | 0.997245i | \(0.523632\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.46998 | −0.548776 | −0.274388 | − | 0.961619i | \(-0.588475\pi\) | ||||
−0.274388 | + | 0.961619i | \(0.588475\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −29.1270 | −2.45294 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.29348 | −0.190463 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 35.1068 | 2.89556 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.30836 | −0.107185 | −0.0535927 | − | 0.998563i | \(-0.517067\pi\) | ||||
−0.0535927 | + | 0.998563i | \(0.517067\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.0578 | 1.63228 | 0.816138 | − | 0.577857i | \(-0.196111\pi\) | ||||
0.816138 | + | 0.577857i | \(0.196111\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.09475 | 0.735267 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.95265 | −0.558450 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.6614 | 1.40953 | 0.704767 | − | 0.709439i | \(-0.251052\pi\) | ||||
0.704767 | + | 0.709439i | \(0.251052\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −27.5532 | −2.18511 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.20499 | −0.725455 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.62425 | 0.362199 | 0.181100 | − | 0.983465i | \(-0.442034\pi\) | ||||
0.181100 | + | 0.983465i | \(0.442034\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.4278 | −1.73552 | −0.867758 | − | 0.496988i | \(-0.834439\pi\) | ||||
−0.867758 | + | 0.496988i | \(0.834439\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.4270 | 1.80208 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.49942 | −0.573495 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.11042 | 0.540595 | 0.270298 | − | 0.962777i | \(-0.412878\pi\) | ||||
0.270298 | + | 0.962777i | \(0.412878\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.65351 | 0.351773 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.0047 | 1.27815 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.00000 | 0.373718 | 0.186859 | − | 0.982387i | \(-0.440169\pi\) | ||||
0.186859 | + | 0.982387i | \(0.440169\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.9841 | 1.26242 | 0.631208 | − | 0.775613i | \(-0.282559\pi\) | ||||
0.631208 | + | 0.775613i | \(0.282559\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.20547 | 0.236955 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.83705 | −0.282106 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.91501 | −0.212036 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.59045 | 0.332153 | 0.166077 | − | 0.986113i | \(-0.446890\pi\) | ||||
0.166077 | + | 0.986113i | \(0.446890\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.75388 | 0.630118 | 0.315059 | − | 0.949072i | \(-0.397976\pi\) | ||||
0.315059 | + | 0.949072i | \(0.397976\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.4581 | 1.03537 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.4511 | −0.958352 | −0.479176 | − | 0.877719i | \(-0.659064\pi\) | ||||
−0.479176 | + | 0.877719i | \(0.659064\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.55665 | 0.323012 | 0.161506 | − | 0.986872i | \(-0.448365\pi\) | ||||
0.161506 | + | 0.986872i | \(0.448365\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.2207 | −1.21465 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.6727 | −0.749078 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.79320 | −0.264928 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.41697 | −0.376505 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.206025 | 0.0141833 | 0.00709166 | − | 0.999975i | \(-0.497743\pi\) | ||||
0.00709166 | + | 0.999975i | \(0.497743\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.1546 | 1.10690 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.98463 | −0.544547 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −32.3542 | −2.19635 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 20.8807 | 1.41099 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.0442 | 1.34832 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.9806 | 1.60586 | 0.802929 | − | 0.596075i | \(-0.203274\pi\) | ||||
0.802929 | + | 0.596075i | \(0.203274\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.73851 | 0.182567 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.4113 | −1.55386 | −0.776932 | − | 0.629585i | \(-0.783225\pi\) | ||||
−0.776932 | + | 0.629585i | \(0.783225\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.9592 | −1.31894 | −0.659471 | − | 0.751730i | \(-0.729220\pi\) | ||||
−0.659471 | + | 0.751730i | \(0.729220\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.30695 | 0.0856213 | 0.0428106 | − | 0.999083i | \(-0.486369\pi\) | ||||
0.0428106 | + | 0.999083i | \(0.486369\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.1590 | −0.793164 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.1411 | −0.853604 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.1243 | 0.784257 | 0.392128 | − | 0.919911i | \(-0.371739\pi\) | ||||
0.392128 | + | 0.919911i | \(0.371739\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.3095 | 1.17942 | 0.589709 | − | 0.807616i | \(-0.299242\pi\) | ||||
0.589709 | + | 0.807616i | \(0.299242\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.3959 | −1.37255 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.6552 | 0.936286 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.5282 | −1.05166 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.6771 | 1.24699 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.7897 | −1.69095 | −0.845475 | − | 0.534014i | \(-0.820683\pi\) | ||||
−0.845475 | + | 0.534014i | \(0.820683\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.95566 | 0.498203 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.20227 | −0.449265 | −0.224633 | − | 0.974444i | \(-0.572118\pi\) | ||||
−0.224633 | + | 0.974444i | \(0.572118\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.8558 | −1.10950 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.28070 | −0.388766 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.7870 | −0.726816 | −0.363408 | − | 0.931630i | \(-0.618387\pi\) | ||||
−0.363408 | + | 0.931630i | \(0.618387\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.5020 | −0.706560 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.3599 | −1.67440 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.7994 | 0.902336 | 0.451168 | − | 0.892439i | \(-0.351008\pi\) | ||||
0.451168 | + | 0.892439i | \(0.351008\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.2838 | −1.41439 | −0.707194 | − | 0.707020i | \(-0.750039\pi\) | ||||
−0.707194 | + | 0.707020i | \(0.750039\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 67.2810 | 4.07203 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.4870 | 0.930525 | 0.465263 | − | 0.885173i | \(-0.345960\pi\) | ||||
0.465263 | + | 0.885173i | \(0.345960\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −19.0399 | −1.13989 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.0218 | 0.896125 | 0.448062 | − | 0.894002i | \(-0.352114\pi\) | ||||
0.448062 | + | 0.894002i | \(0.352114\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.4830 | 0.860923 | 0.430462 | − | 0.902609i | \(-0.358351\pi\) | ||||
0.430462 | + | 0.902609i | \(0.358351\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.56014 | −0.388589 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.6517 | −1.04195 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.97055 | −0.351209 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.6858 | 0.919518 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.6763 | 0.974240 | 0.487120 | − | 0.873335i | \(-0.338047\pi\) | ||||
0.487120 | + | 0.873335i | \(0.338047\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.09855 | 0.413293 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.9386 | −0.690428 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −37.1566 | −2.14167 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.653698 | 0.0375540 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.33811 | 0.0766200 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.537575 | −0.0306810 | −0.0153405 | − | 0.999882i | \(-0.504883\pi\) | ||||
−0.0153405 | + | 0.999882i | \(0.504883\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.6246 | 1.11640 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.4946 | 0.708505 | 0.354252 | − | 0.935150i | \(-0.384735\pi\) | ||||
0.354252 | + | 0.935150i | \(0.384735\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.8371 | 1.06474 | 0.532369 | − | 0.846513i | \(-0.321302\pi\) | ||||
0.532369 | + | 0.846513i | \(0.321302\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.7437 | 0.718025 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.06090 | −0.396580 | −0.198290 | − | 0.980143i | \(-0.563539\pi\) | ||||
−0.198290 | + | 0.980143i | \(0.563539\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.7810 | −0.880811 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.09475 | −0.506046 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.03548 | 0.334788 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.33648 | −0.405708 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −56.5819 | −3.11946 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.83433 | 0.430614 | 0.215307 | − | 0.976546i | \(-0.430925\pi\) | ||||
0.215307 | + | 0.976546i | \(0.430925\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.5078 | −0.575824 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.18872 | −0.392761 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.30949 | −0.398173 | −0.199087 | − | 0.979982i | \(-0.563797\pi\) | ||||
−0.199087 | + | 0.979982i | \(0.563797\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.8601 | −0.752779 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 35.6236 | 1.92349 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.73851 | −0.255113 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.5746 | 0.943454 | 0.471727 | − | 0.881745i | \(-0.343631\pi\) | ||||
0.471727 | + | 0.881745i | \(0.343631\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.3794 | 1.14441 | 0.572206 | − | 0.820110i | \(-0.306088\pi\) | ||||
0.572206 | + | 0.820110i | \(0.306088\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.78068 | −0.201798 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.59779 | 0.404389 | 0.202195 | − | 0.979345i | \(-0.435193\pi\) | ||||
0.202195 | + | 0.979345i | \(0.435193\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.74368 | 0.357918 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 37.0218 | 1.95940 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 34.6662 | 1.82961 | 0.914805 | − | 0.403896i | \(-0.132344\pi\) | ||||
0.914805 | + | 0.403896i | \(0.132344\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.5006 | −0.605293 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.71658 | 0.456247 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.0303 | −0.784575 | −0.392288 | − | 0.919843i | \(-0.628316\pi\) | ||||
−0.392288 | + | 0.919843i | \(0.628316\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.3877 | −0.540762 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −53.5245 | −2.77886 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.5055 | 0.699286 | 0.349643 | − | 0.936883i | \(-0.386303\pi\) | ||||
0.349643 | + | 0.936883i | \(0.386303\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.39552 | 0.123704 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.8422 | −0.712911 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.1937 | −1.19138 | −0.595689 | − | 0.803215i | \(-0.703121\pi\) | ||||
−0.595689 | + | 0.803215i | \(0.703121\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.20029 | −0.215187 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 35.1392 | 1.79553 | 0.897765 | − | 0.440475i | \(-0.145190\pi\) | ||||
0.897765 | + | 0.440475i | \(0.145190\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −21.8660 | −1.11151 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.7603 | −1.81312 | −0.906560 | − | 0.422078i | \(-0.861301\pi\) | ||||
−0.906560 | + | 0.422078i | \(0.861301\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.56930 | −0.332224 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 30.4344 | 1.53521 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.48569 | −0.276015 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.62347 | −0.181857 | −0.0909284 | − | 0.995857i | \(-0.528983\pi\) | ||||
−0.0909284 | + | 0.995857i | \(0.528983\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −30.5277 | −1.52830 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.05301 | 0.0525848 | 0.0262924 | − | 0.999654i | \(-0.491630\pi\) | ||||
0.0262924 | + | 0.999654i | \(0.491630\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −41.9626 | −2.09030 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.71610 | −0.482797 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.4892 | 0.568106 | 0.284053 | − | 0.958809i | \(-0.408321\pi\) | ||||
0.284053 | + | 0.958809i | \(0.408321\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.15945 | −0.205171 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 33.0332 | 1.62546 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.21414 | 0.403216 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.4989 | −0.758987 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.12829 | 0.445946 | 0.222973 | − | 0.974825i | \(-0.428424\pi\) | ||||
0.222973 | + | 0.974825i | \(0.428424\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.1610 | −1.22627 | −0.613136 | − | 0.789977i | \(-0.710092\pi\) | ||||
−0.613136 | + | 0.789977i | \(0.710092\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −33.2974 | −1.61898 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.32106 | 0.161095 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.22691 | 0.301342 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.8014 | 0.761128 | 0.380564 | − | 0.924754i | \(-0.375730\pi\) | ||||
0.380564 | + | 0.924754i | \(0.375730\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.68676 | −0.129117 | −0.0645586 | − | 0.997914i | \(-0.520564\pi\) | ||||
−0.0645586 | + | 0.997914i | \(0.520564\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.49406 | −0.263420 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.41697 | 0.259129 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.0888 | 0.863333 | 0.431666 | − | 0.902033i | \(-0.357926\pi\) | ||||
0.431666 | + | 0.902033i | \(0.357926\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 40.1334 | 1.91111 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.6959 | −1.55343 | −0.776713 | − | 0.629854i | \(-0.783115\pi\) | ||||
−0.776713 | + | 0.629854i | \(0.783115\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.4213 | −0.541421 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.13421 | −0.148243 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.06419 | 0.427765 | 0.213883 | − | 0.976859i | \(-0.431389\pi\) | ||||
0.213883 | + | 0.976859i | \(0.431389\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 48.0487 | 2.25753 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 28.0862 | 1.31670 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.7502 | −0.736763 | −0.368382 | − | 0.929675i | \(-0.620088\pi\) | ||||
−0.368382 | + | 0.929675i | \(0.620088\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.08035 | −0.0971022 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.2263 | 1.54750 | 0.773751 | − | 0.633489i | \(-0.218378\pi\) | ||||
0.773751 | + | 0.633489i | \(0.218378\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.68368 | 0.310617 | 0.155309 | − | 0.987866i | \(-0.450363\pi\) | ||||
0.155309 | + | 0.987866i | \(0.450363\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −16.6552 | −0.772366 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.3345 | 0.987242 | 0.493621 | − | 0.869677i | \(-0.335673\pi\) | ||||
0.493621 | + | 0.869677i | \(0.335673\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −33.4528 | −1.54471 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 42.3082 | 1.94946 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.73851 | −0.125651 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −31.4982 | −1.44220 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −39.2657 | −1.79409 | −0.897047 | − | 0.441935i | \(-0.854292\pi\) | ||||
−0.897047 | + | 0.441935i | \(0.854292\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.1585 | −1.05593 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −22.0507 | −1.00334 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.54798 | 0.297328 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.7297 | 0.576836 | 0.288418 | − | 0.957505i | \(-0.406871\pi\) | ||||
0.288418 | + | 0.957505i | \(0.406871\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.0775 | 0.500941 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.40592 | 0.243966 | 0.121983 | − | 0.992532i | \(-0.461075\pi\) | ||||
0.121983 | + | 0.992532i | \(0.461075\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.61678 | −0.343042 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31.3818 | 1.40767 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.76471 | −0.213298 | −0.106649 | − | 0.994297i | \(-0.534012\pi\) | ||||
−0.106649 | + | 0.994297i | \(0.534012\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −53.7262 | −2.40031 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.4005 | −0.731261 | −0.365631 | − | 0.930760i | \(-0.619147\pi\) | ||||
−0.365631 | + | 0.930760i | \(0.619147\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.272884 | 0.0121432 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 56.1199 | 2.49237 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 41.0717 | 1.82047 | 0.910236 | − | 0.414090i | \(-0.135900\pi\) | ||||
0.910236 | + | 0.414090i | \(0.135900\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 40.5627 | 1.79439 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.71543 | 0.0757380 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.19221 | 0.360992 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.0331 | 0.747672 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.3976 | 1.72604 | 0.863021 | − | 0.505169i | \(-0.168570\pi\) | ||||
0.863021 | + | 0.505169i | \(0.168570\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.7391 | 0.731948 | 0.365974 | − | 0.930625i | \(-0.380736\pi\) | ||||
0.365974 | + | 0.930625i | \(0.380736\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.1476 | 0.486520 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −23.0902 | −1.00582 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0872 | −0.829880 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.4394 | 0.843599 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.8938 | −0.991639 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.58773 | −0.284812 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.9776 | 0.516871 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.98943 | 0.386486 | 0.193243 | − | 0.981151i | \(-0.438099\pi\) | ||||
0.193243 | + | 0.981151i | \(0.438099\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 40.6857 | 1.74599 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.06258 | −0.131187 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.9605 | −0.896206 | −0.448103 | − | 0.893982i | \(-0.647900\pi\) | ||||
−0.448103 | + | 0.893982i | \(0.647900\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.66442 | 0.156394 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.28070 | 0.267567 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.5277 | −1.08555 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.19173 | −0.390167 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.2334 | 0.645461 | 0.322730 | − | 0.946491i | \(-0.395399\pi\) | ||||
0.322730 | + | 0.946491i | \(0.395399\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −48.1911 | −2.03827 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.2106 | −0.641052 | −0.320526 | − | 0.947240i | \(-0.603860\pi\) | ||||
−0.320526 | + | 0.947240i | \(0.603860\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.78586 | −0.243413 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −45.2140 | −1.89881 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −38.4882 | −1.61351 | −0.806755 | − | 0.590886i | \(-0.798778\pi\) | ||||
−0.806755 | + | 0.590886i | \(0.798778\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.3549 | −0.726282 | −0.363141 | − | 0.931734i | \(-0.618296\pi\) | ||||
−0.363141 | + | 0.931734i | \(0.618296\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.9965 | 0.459386 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.97807 | −0.0824913 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.98019 | 0.207328 | 0.103664 | − | 0.994612i | \(-0.466943\pi\) | ||||
0.103664 | + | 0.994612i | \(0.466943\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.9701 | 0.871486 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.2246 | 1.58582 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16.5282 | 0.683357 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.1518 | −1.61597 | −0.807985 | − | 0.589203i | \(-0.799442\pi\) | ||||
−0.807985 | + | 0.589203i | \(0.799442\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.0399 | 0.784525 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −32.2224 | −1.32545 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.2454 | −1.48842 | −0.744211 | − | 0.667945i | \(-0.767174\pi\) | ||||
−0.744211 | + | 0.667945i | \(0.767174\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.4546 | 0.633577 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.9155 | 0.446743 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0593 | 0.492732 | 0.246366 | − | 0.969177i | \(-0.420764\pi\) | ||||
0.246366 | + | 0.969177i | \(0.420764\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.8585 | 1.13637 | 0.568186 | − | 0.822900i | \(-0.307645\pi\) | ||||
0.568186 | + | 0.822900i | \(0.307645\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.6864 | −0.801690 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −41.5181 | −1.68517 | −0.842584 | − | 0.538565i | \(-0.818966\pi\) | ||||
−0.842584 | + | 0.538565i | \(0.818966\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −25.5667 | −1.03602 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −73.3852 | −2.96885 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 43.4438 | 1.75468 | 0.877339 | − | 0.479870i | \(-0.159316\pi\) | ||||
0.877339 | + | 0.479870i | \(0.159316\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.08667 | −0.366410 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.9692 | −0.763672 | −0.381836 | − | 0.924230i | \(-0.624708\pi\) | ||||
−0.381836 | + | 0.924230i | \(0.624708\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.80636 | 0.112797 | 0.0563985 | − | 0.998408i | \(-0.482038\pi\) | ||||
0.0563985 | + | 0.998408i | \(0.482038\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.23908 | 0.0497227 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −53.1491 | −2.12937 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.7431 | −0.508100 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.6412 | −0.941140 | −0.470570 | − | 0.882363i | \(-0.655952\pi\) | ||||
−0.470570 | + | 0.882363i | \(0.655952\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.493536 | 0.0196163 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.75340 | −0.0695814 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 88.4511 | 3.50456 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.4676 | 0.730568 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.43527 | −0.214680 | −0.107340 | − | 0.994222i | \(-0.534233\pi\) | ||||
−0.107340 | + | 0.994222i | \(0.534233\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.5956 | 0.575595 | 0.287798 | − | 0.957691i | \(-0.407077\pi\) | ||||
0.287798 | + | 0.957691i | \(0.407077\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.1273 | −0.753138 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.4578 | −0.450453 | −0.225226 | − | 0.974306i | \(-0.572312\pi\) | ||||
−0.225226 | + | 0.974306i | \(0.572312\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −77.5052 | −3.03767 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.08857 | −0.277397 | −0.138699 | − | 0.990335i | \(-0.544292\pi\) | ||||
−0.138699 | + | 0.990335i | \(0.544292\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.7047 | 0.496414 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.8704 | 0.931274 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.2209 | −0.398150 | −0.199075 | − | 0.979984i | \(-0.563794\pi\) | ||||
−0.199075 | + | 0.979984i | \(0.563794\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.7641 | −0.613151 | −0.306575 | − | 0.951846i | \(-0.599183\pi\) | ||||
−0.306575 | + | 0.951846i | \(0.599183\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 48.0162 | 1.86480 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.7437 | −0.494179 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.53666 | 0.175660 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 57.4459 | 2.22099 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.8914 | 0.458380 | 0.229190 | − | 0.973382i | \(-0.426392\pi\) | ||||
0.229190 | + | 0.973382i | \(0.426392\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.626410 | −0.0241105 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.6643 | 0.794195 | 0.397098 | − | 0.917776i | \(-0.370017\pi\) | ||||
0.397098 | + | 0.917776i | \(0.370017\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 30.4711 | 1.16937 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −56.0822 | −2.14908 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.8239 | −0.873331 | −0.436666 | − | 0.899624i | \(-0.643841\pi\) | ||||
−0.436666 | + | 0.899624i | \(0.643841\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.73635 | −0.0663424 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −47.8126 | −1.82417 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −69.4198 | −2.64469 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.9712 | −1.55862 | −0.779309 | − | 0.626640i | \(-0.784430\pi\) | ||||
−0.779309 | + | 0.626640i | \(0.784430\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.46998 | −0.245420 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.5974 | −0.477162 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.13083 | 0.118419 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.3585 | −1.25993 | −0.629967 | − | 0.776622i | \(-0.716932\pi\) | ||||
−0.629967 | + | 0.776622i | \(0.716932\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.5078 | 0.396309 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −29.1270 | −1.09699 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.26987 | 0.0477583 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.0315 | −0.602074 | −0.301037 | − | 0.953612i | \(-0.597333\pi\) | ||||
−0.301037 | + | 0.953612i | \(0.597333\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.0226 | −0.563391 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.7528 | 0.515048 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 29.0440 | 1.08467 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.2094 | 0.492626 | 0.246313 | − | 0.969190i | \(-0.420781\pi\) | ||||
0.246313 | + | 0.969190i | \(0.420781\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38.1226 | 1.41976 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 43.8607 | 1.63120 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.29348 | −0.0851776 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.9855 | 0.815395 | 0.407698 | − | 0.913117i | \(-0.366332\pi\) | ||||
0.407698 | + | 0.913117i | \(0.366332\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.1059 | −0.818736 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.5175 | −0.980783 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.7989 | 1.24839 | 0.624196 | − | 0.781268i | \(-0.285427\pi\) | ||||
0.624196 | + | 0.781268i | \(0.285427\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 35.1068 | 1.29493 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.7537 | −0.542725 | −0.271363 | − | 0.962477i | \(-0.587474\pi\) | ||||
−0.271363 | + | 0.962477i | \(0.587474\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −39.5936 | −1.45451 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.3494 | −0.893292 | −0.446646 | − | 0.894711i | \(-0.647382\pi\) | ||||
−0.446646 | + | 0.894711i | \(0.647382\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.30836 | −0.0479347 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.4945 | 0.823030 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −30.6561 | −1.12015 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.6302 | −1.37315 | −0.686573 | − | 0.727061i | \(-0.740886\pi\) | ||||
−0.686573 | + | 0.727061i | \(0.740886\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −64.1752 | −2.33867 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.0578 | 0.729976 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.9401 | −1.59703 | −0.798515 | − | 0.601975i | \(-0.794381\pi\) | ||||
−0.798515 | + | 0.601975i | \(0.794381\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.2126 | −1.49396 | −0.746978 | − | 0.664849i | \(-0.768496\pi\) | ||||
−0.746978 | + | 0.664849i | \(0.768496\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.2518 | −0.515949 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.09475 | 0.328821 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 42.8431 | 1.54698 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.4283 | 0.772724 | 0.386362 | − | 0.922347i | \(-0.373732\pi\) | ||||
0.386362 | + | 0.922347i | \(0.373732\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.2532 | −0.621358 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.79976 | 0.208603 | 0.104301 | − | 0.994546i | \(-0.466739\pi\) | ||||
0.104301 | + | 0.994546i | \(0.466739\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.95265 | −0.249746 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −42.7739 | −1.53450 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.3877 | 0.372178 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.43666 | 0.0513419 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.6614 | 0.630363 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.2120 | −0.898710 | −0.449355 | − | 0.893353i | \(-0.648346\pi\) | ||||
−0.449355 | + | 0.893353i | \(0.648346\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −28.2359 | −1.00523 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.9246 | −0.957328 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.07614 | 0.286792 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −27.5532 | −0.977210 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.4471 | 0.653428 | 0.326714 | − | 0.945123i | \(-0.394059\pi\) | ||||
0.326714 | + | 0.945123i | \(0.394059\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.3807 | −1.42857 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −31.2773 | −1.10513 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.20499 | −0.324433 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 35.4523 | 1.24798 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.20841 | −0.183118 | −0.0915589 | − | 0.995800i | \(-0.529185\pi\) | ||||
−0.0915589 | + | 0.995800i | \(0.529185\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.79012 | 0.273548 | 0.136774 | − | 0.990602i | \(-0.456327\pi\) | ||||
0.136774 | + | 0.990602i | \(0.456327\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −55.7767 | −1.95617 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.62425 | 0.161980 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.8660 | 0.764994 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 76.9143 | 2.68760 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.56369 | 0.333775 | 0.166888 | − | 0.985976i | \(-0.446628\pi\) | ||||
0.166888 | + | 0.985976i | \(0.446628\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.4877 | −0.470152 | −0.235076 | − | 0.971977i | \(-0.575534\pi\) | ||||
−0.235076 | + | 0.971977i | \(0.575534\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.8316 | −0.654839 | −0.327420 | − | 0.944879i | \(-0.606179\pi\) | ||||
−0.327420 | + | 0.944879i | \(0.606179\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.2659 | 1.01645 | 0.508223 | − | 0.861225i | \(-0.330302\pi\) | ||||
0.508223 | + | 0.861225i | \(0.330302\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 37.0994 | 1.28697 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 48.6708 | 1.68634 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.4278 | −0.776146 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.35521 | 0.150538 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.4646 | 0.430326 | 0.215163 | − | 0.976578i | \(-0.430972\pi\) | ||||
0.215163 | + | 0.976578i | \(0.430972\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.7400 | −0.818620 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 35.9850 | 1.23939 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.4270 | 0.805914 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 34.6942 | 1.19070 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.58997 | 0.260181 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.3608 | −1.17649 | −0.588246 | − | 0.808682i | \(-0.700181\pi\) | ||||
−0.588246 | + | 0.808682i | \(0.700181\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.49942 | −0.256475 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.9439 | 0.510474 | 0.255237 | − | 0.966879i | \(-0.417847\pi\) | ||||
0.255237 | + | 0.966879i | \(0.417847\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.2500 | 0.895640 | 0.447820 | − | 0.894124i | \(-0.352201\pi\) | ||||
0.447820 | + | 0.894124i | \(0.352201\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −42.2850 | −1.44107 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.0675 | 0.683107 | 0.341554 | − | 0.939862i | \(-0.389047\pi\) | ||||
0.341554 | + | 0.939862i | \(0.389047\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.11042 | 0.241761 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.3026 | −0.485741 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −43.3874 | −1.47012 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.9317 | 0.606895 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.65351 | 0.157317 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.2903 | 1.22544 | 0.612718 | − | 0.790302i | \(-0.290076\pi\) | ||||
0.612718 | + | 0.790302i | \(0.290076\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 39.9484 | 1.34743 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.3513 | 0.887796 | 0.443898 | − | 0.896077i | \(-0.353595\pi\) | ||||
0.443898 | + | 0.896077i | \(0.353595\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 54.0051 | 1.81742 | 0.908708 | − | 0.417432i | \(-0.137070\pi\) | ||||
0.908708 | + | 0.417432i | \(0.137070\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.0047 | 0.571607 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.7946 | 0.429601 | 0.214801 | − | 0.976658i | \(-0.431090\pi\) | ||||
0.214801 | + | 0.976658i | \(0.431090\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.15945 | −0.273659 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 33.2974 | 1.11426 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.00000 | 0.167132 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.5992 | −0.954898 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.9457 | 0.531820 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38.1987 | −1.27258 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −89.0093 | −2.96204 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.9841 | 0.564570 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.0096 | 1.69375 | 0.846873 | − | 0.531795i | \(-0.178482\pi\) | ||||
0.846873 | + | 0.531795i | \(0.178482\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.747294 | 0.0247862 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.54632 | −0.0512320 | −0.0256160 | − | 0.999672i | \(-0.508155\pi\) | ||||
−0.0256160 | + | 0.999672i | \(0.508155\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.20547 | 0.105969 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 59.1215 | 1.95237 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.3314 | 0.835605 | 0.417802 | − | 0.908538i | \(-0.362800\pi\) | ||||
0.417802 | + | 0.908538i | \(0.362800\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.28777 | −0.0424335 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 40.7014 | 1.33970 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.83705 | −0.126162 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.4344 | 0.736844 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −54.7970 | −1.79783 | −0.898915 | − | 0.438122i | \(-0.855644\pi\) | ||||
−0.898915 | + | 0.438122i | \(0.855644\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −40.1334 | −1.31532 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 29.9311 | 0.979900 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.3128 | 1.05561 | 0.527806 | − | 0.849365i | \(-0.323015\pi\) | ||||
0.527806 | + | 0.849365i | \(0.323015\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 45.1247 | 1.47259 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.5783 | −0.638234 | −0.319117 | − | 0.947715i | \(-0.603386\pi\) | ||||
−0.319117 | + | 0.947715i | \(0.603386\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.50322 | 0.244338 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.91501 | −0.0948252 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.1674 | −0.720345 | −0.360172 | − | 0.932886i | \(-0.617282\pi\) | ||||
−0.360172 | + | 0.932886i | \(0.617282\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 52.6087 | 1.70775 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.9145 | −0.548491 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.4293 | 1.69835 | 0.849177 | − | 0.528109i | \(-0.177099\pi\) | ||||
0.849177 | + | 0.528109i | \(0.177099\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.59045 | 0.148543 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.08011 | −0.260920 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.3393 | 0.559333 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.0405 | −0.581349 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.75388 | 0.281797 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.72125 | −0.312614 | −0.156307 | − | 0.987709i | \(-0.549959\pi\) | ||||
−0.156307 | + | 0.987709i | \(0.549959\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −21.7866 | −0.699888 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.2487 | −1.51628 | −0.758142 | − | 0.652090i | \(-0.773892\pi\) | ||||
−0.758142 | + | 0.652090i | \(0.773892\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −30.1081 | −0.965222 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.4581 | 0.463030 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −41.8556 | −1.33908 | −0.669540 | − | 0.742776i | \(-0.733509\pi\) | ||||
−0.669540 | + | 0.742776i | \(0.733509\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.38691 | −0.267773 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35.9902 | −1.14791 | −0.573954 | − | 0.818887i | \(-0.694591\pi\) | ||||
−0.573954 | + | 0.818887i | \(0.694591\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.4511 | −0.428588 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −135.543 | −4.31438 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.7942 | 0.502226 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.548830 | 0.0174342 | 0.00871709 | − | 0.999962i | \(-0.497225\pi\) | ||||
0.00871709 | + | 0.999962i | \(0.497225\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.7673 | 0.595562 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.55665 | 0.144455 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.25013 | 0.292955 | 0.146477 | − | 0.989214i | \(-0.453206\pi\) | ||||
0.146477 | + | 0.989214i | \(0.453206\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.40357 | 0.0760455 |
(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 | 2420.2.a.l.1.4 | 4 | ||
4.3 | odd | 2 | 9680.2.a.co.1.1 | 4 | |||
11.2 | odd | 10 | 220.2.m.b.81.2 | ✓ | 8 | ||
11.6 | odd | 10 | 220.2.m.b.201.2 | yes | 8 | ||
11.10 | odd | 2 | 2420.2.a.k.1.4 | 4 | |||
33.2 | even | 10 | 1980.2.z.d.1621.1 | 8 | |||
33.17 | even | 10 | 1980.2.z.d.1081.1 | 8 | |||
44.35 | even | 10 | 880.2.bo.c.81.1 | 8 | |||
44.39 | even | 10 | 880.2.bo.c.641.1 | 8 | |||
44.43 | even | 2 | 9680.2.a.cp.1.1 | 4 | |||
55.2 | even | 20 | 1100.2.cb.b.1049.1 | 16 | |||
55.13 | even | 20 | 1100.2.cb.b.1049.4 | 16 | |||
55.17 | even | 20 | 1100.2.cb.b.949.4 | 16 | |||
55.24 | odd | 10 | 1100.2.n.b.301.1 | 8 | |||
55.28 | even | 20 | 1100.2.cb.b.949.1 | 16 | |||
55.39 | odd | 10 | 1100.2.n.b.201.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
220.2.m.b.81.2 | ✓ | 8 | 11.2 | odd | 10 | ||
220.2.m.b.201.2 | yes | 8 | 11.6 | odd | 10 | ||
880.2.bo.c.81.1 | 8 | 44.35 | even | 10 | |||
880.2.bo.c.641.1 | 8 | 44.39 | even | 10 | |||
1100.2.n.b.201.1 | 8 | 55.39 | odd | 10 | |||
1100.2.n.b.301.1 | 8 | 55.24 | odd | 10 | |||
1100.2.cb.b.949.1 | 16 | 55.28 | even | 20 | |||
1100.2.cb.b.949.4 | 16 | 55.17 | even | 20 | |||
1100.2.cb.b.1049.1 | 16 | 55.2 | even | 20 | |||
1100.2.cb.b.1049.4 | 16 | 55.13 | even | 20 | |||
1980.2.z.d.1081.1 | 8 | 33.17 | even | 10 | |||
1980.2.z.d.1621.1 | 8 | 33.2 | even | 10 | |||
2420.2.a.k.1.4 | 4 | 11.10 | odd | 2 | |||
2420.2.a.l.1.4 | 4 | 1.1 | even | 1 | trivial | ||
9680.2.a.co.1.1 | 4 | 4.3 | odd | 2 | |||
9680.2.a.cp.1.1 | 4 | 44.43 | even | 2 |