Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4624,2,Mod(1,4624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4624, 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("4624.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4624 = 2^{4} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4624.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: | \(36.9228258946\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{16})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 136) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.765367\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4624.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.765367 | −0.441885 | −0.220942 | − | 0.975287i | \(-0.570913\pi\) | ||||
−0.220942 | + | 0.975287i | \(0.570913\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.84776 | −0.826343 | −0.413171 | − | 0.910653i | \(-0.635579\pi\) | ||||
−0.413171 | + | 0.910653i | \(0.635579\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.317025 | −0.119824 | −0.0599122 | − | 0.998204i | \(-0.519082\pi\) | ||||
−0.0599122 | + | 0.998204i | \(0.519082\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.41421 | −0.804738 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.765367 | −0.230767 | −0.115383 | − | 0.993321i | \(-0.536810\pi\) | ||||
−0.115383 | + | 0.993321i | \(0.536810\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.41421 | 0.365148 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.24264 | −0.514497 | −0.257249 | − | 0.966345i | \(-0.582816\pi\) | ||||
−0.257249 | + | 0.966345i | \(0.582816\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.242641 | 0.0529485 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.62567 | −1.38155 | −0.690774 | − | 0.723071i | \(-0.742730\pi\) | ||||
−0.690774 | + | 0.723071i | \(0.742730\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.58579 | −0.317157 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.14386 | 0.797486 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.54328 | −1.02936 | −0.514680 | − | 0.857382i | \(-0.672089\pi\) | ||||
−0.514680 | + | 0.857382i | \(0.672089\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.29610 | −0.412392 | −0.206196 | − | 0.978511i | \(-0.566108\pi\) | ||||
−0.206196 | + | 0.978511i | \(0.566108\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.585786 | 0.101972 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.585786 | 0.0990160 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.765367 | −0.125826 | −0.0629128 | − | 0.998019i | \(-0.520039\pi\) | ||||
−0.0629128 | + | 0.998019i | \(0.520039\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.48181 | 0.387594 | 0.193797 | − | 0.981042i | \(-0.437920\pi\) | ||||
0.193797 | + | 0.981042i | \(0.437920\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.2426 | 1.56199 | 0.780994 | − | 0.624538i | \(-0.214713\pi\) | ||||
0.780994 | + | 0.624538i | \(0.214713\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.46088 | 0.664989 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.8284 | 1.87122 | 0.935609 | − | 0.353037i | \(-0.114851\pi\) | ||||
0.935609 | + | 0.353037i | \(0.114851\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.89949 | −0.985642 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.07107 | −0.421844 | −0.210922 | − | 0.977503i | \(-0.567647\pi\) | ||||
−0.210922 | + | 0.977503i | \(0.567647\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.41421 | 0.190693 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.71644 | 0.227348 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.89949 | −1.02843 | −0.514213 | − | 0.857662i | \(-0.671916\pi\) | ||||
−0.514213 | + | 0.857662i | \(0.671916\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.87285 | −1.26409 | −0.632044 | − | 0.774932i | \(-0.717784\pi\) | ||||
−0.632044 | + | 0.774932i | \(0.717784\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.765367 | 0.0964272 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.65685 | 1.17977 | 0.589886 | − | 0.807486i | \(-0.299173\pi\) | ||||
0.589886 | + | 0.807486i | \(0.299173\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.07107 | 0.610485 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.68714 | 1.14965 | 0.574826 | − | 0.818276i | \(-0.305070\pi\) | ||||
0.574826 | + | 0.818276i | \(0.305070\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.97069 | −0.932899 | −0.466450 | − | 0.884548i | \(-0.654467\pi\) | ||||
−0.466450 | + | 0.884548i | \(0.654467\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.21371 | 0.140147 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.242641 | 0.0276515 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.2793 | −1.60655 | −0.803276 | − | 0.595608i | \(-0.796911\pi\) | ||||
−0.803276 | + | 0.595608i | \(0.796911\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.07107 | 0.452341 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.2426 | 1.12428 | 0.562138 | − | 0.827043i | \(-0.309979\pi\) | ||||
0.562138 | + | 0.827043i | \(0.309979\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.24264 | 0.454859 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.65685 | 0.175626 | 0.0878131 | − | 0.996137i | \(-0.472012\pi\) | ||||
0.0878131 | + | 0.996137i | \(0.472012\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.75736 | 0.182230 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.14386 | 0.425151 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.9958 | −1.62413 | −0.812063 | − | 0.583570i | \(-0.801655\pi\) | ||||
−0.812063 | + | 0.583570i | \(0.801655\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.84776 | 0.185707 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.0000 | −0.995037 | −0.497519 | − | 0.867453i | \(-0.665755\pi\) | ||||
−0.497519 | + | 0.867453i | \(0.665755\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.34315 | 0.230877 | 0.115439 | − | 0.993315i | \(-0.463173\pi\) | ||||
0.115439 | + | 0.993315i | \(0.463173\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.448342 | −0.0437537 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.4650 | −1.39839 | −0.699194 | − | 0.714932i | \(-0.746458\pi\) | ||||
−0.699194 | + | 0.714932i | \(0.746458\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.6662 | 1.11742 | 0.558710 | − | 0.829363i | \(-0.311296\pi\) | ||||
0.558710 | + | 0.829363i | \(0.311296\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.585786 | 0.0556004 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.15640 | 0.767290 | 0.383645 | − | 0.923481i | \(-0.374669\pi\) | ||||
0.383645 | + | 0.923481i | \(0.374669\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.2426 | 1.14163 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4142 | −0.946747 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.89949 | −0.171272 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1689 | 1.08842 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.75736 | 0.155940 | 0.0779702 | − | 0.996956i | \(-0.475156\pi\) | ||||
0.0779702 | + | 0.996956i | \(0.475156\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.83938 | −0.690219 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.4650 | 1.26382 | 0.631909 | − | 0.775043i | \(-0.282272\pi\) | ||||
0.631909 | + | 0.775043i | \(0.282272\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.710974 | 0.0616493 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.65685 | −0.658997 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.0000 | 1.19610 | 0.598050 | − | 0.801459i | \(-0.295942\pi\) | ||||
0.598050 | + | 0.801459i | \(0.295942\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.502734 | 0.0426414 | 0.0213207 | − | 0.999773i | \(-0.493213\pi\) | ||||
0.0213207 | + | 0.999773i | \(0.493213\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.81845 | −0.826863 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.2426 | 0.850605 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.28064 | 0.435540 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.34315 | 0.519651 | 0.259825 | − | 0.965656i | \(-0.416335\pi\) | ||||
0.259825 | + | 0.965656i | \(0.416335\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.8995 | 1.61940 | 0.809699 | − | 0.586845i | \(-0.199630\pi\) | ||||
0.809699 | + | 0.586845i | \(0.199630\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.24264 | 0.340777 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.3137 | 1.22217 | 0.611083 | − | 0.791566i | \(-0.290734\pi\) | ||||
0.611083 | + | 0.791566i | \(0.290734\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.35049 | 0.186406 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.10051 | 0.165543 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.64659 | 0.363949 | 0.181975 | − | 0.983303i | \(-0.441751\pi\) | ||||
0.181975 | + | 0.983303i | \(0.441751\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.08239 | −0.0842641 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.765367 | 0.0592259 | 0.0296129 | − | 0.999561i | \(-0.490573\pi\) | ||||
0.0296129 | + | 0.999561i | \(0.490573\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.41421 | 0.414035 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.8715 | 1.43478 | 0.717388 | − | 0.696674i | \(-0.245337\pi\) | ||||
0.717388 | + | 0.696674i | \(0.245337\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.502734 | 0.0380032 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.04601 | 0.454446 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.2426 | 1.36352 | 0.681759 | − | 0.731576i | \(-0.261215\pi\) | ||||
0.681759 | + | 0.731576i | \(0.261215\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.15640 | 0.606261 | 0.303130 | − | 0.952949i | \(-0.401968\pi\) | ||||
0.303130 | + | 0.952949i | \(0.401968\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.55635 | 0.558581 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.41421 | 0.103975 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.31371 | −0.0955582 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.82843 | 0.638803 | 0.319401 | − | 0.947620i | \(-0.396518\pi\) | ||||
0.319401 | + | 0.947620i | \(0.396518\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.765367 | −0.0550923 | −0.0275462 | − | 0.999621i | \(-0.508769\pi\) | ||||
−0.0275462 | + | 0.999621i | \(0.508769\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.3003 | 0.876357 | 0.438179 | − | 0.898888i | \(-0.355624\pi\) | ||||
0.438179 | + | 0.898888i | \(0.355624\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.4901 | −1.59428 | −0.797142 | − | 0.603792i | \(-0.793656\pi\) | ||||
−0.797142 | + | 0.603792i | \(0.793656\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.39104 | −0.521324 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.75736 | 0.123342 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.58579 | −0.320285 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.9958 | 1.11178 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.71644 | 0.118729 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.1857 | 1.80269 | 0.901347 | − | 0.433097i | \(-0.142579\pi\) | ||||
0.901347 | + | 0.433097i | \(0.142579\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.41421 | −0.508014 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −18.9259 | −1.29074 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.727922 | 0.0494146 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.10051 | 0.412234 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.5563 | −1.17566 | −0.587830 | − | 0.808984i | \(-0.700018\pi\) | ||||
−0.587830 | + | 0.808984i | \(0.700018\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.82843 | 0.255228 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.56420 | −0.236564 | −0.118282 | − | 0.992980i | \(-0.537739\pi\) | ||||
−0.118282 | + | 0.992980i | \(0.537739\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.89949 | −0.654177 | −0.327089 | − | 0.944994i | \(-0.606068\pi\) | ||||
−0.327089 | + | 0.944994i | \(0.606068\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.185709 | −0.0122188 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.579658 | 0.0379746 | 0.0189873 | − | 0.999820i | \(-0.493956\pi\) | ||||
0.0189873 | + | 0.999820i | \(0.493956\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −23.7038 | −1.54627 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.9289 | 0.709910 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.3137 | −0.731823 | −0.365911 | − | 0.930650i | \(-0.619243\pi\) | ||||
−0.365911 | + | 0.930650i | \(0.619243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0167 | 0.902895 | 0.451448 | − | 0.892298i | \(-0.350908\pi\) | ||||
0.451448 | + | 0.892298i | \(0.350908\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5474 | −0.997369 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.7486 | 0.814478 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.83938 | −0.496800 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.828427 | 0.0522899 | 0.0261449 | − | 0.999658i | \(-0.491677\pi\) | ||||
0.0261449 | + | 0.999658i | \(0.491677\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.07107 | 0.318815 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.24264 | 0.514162 | 0.257081 | − | 0.966390i | \(-0.417239\pi\) | ||||
0.257081 | + | 0.966390i | \(0.417239\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.242641 | 0.0150770 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.3827 | 0.828366 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.89949 | −0.240453 | −0.120227 | − | 0.992746i | \(-0.538362\pi\) | ||||
−0.120227 | + | 0.992746i | \(0.538362\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.67459 | 0.348588 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.26810 | −0.0776065 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.0167 | −0.854614 | −0.427307 | − | 0.904107i | \(-0.640538\pi\) | ||||
−0.427307 | + | 0.904107i | \(0.640538\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.3137 | −0.687259 | −0.343629 | − | 0.939105i | \(-0.611656\pi\) | ||||
−0.343629 | + | 0.939105i | \(0.611656\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.21371 | 0.0731894 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.23880 | −0.555105 | −0.277553 | − | 0.960710i | \(-0.589523\pi\) | ||||
−0.277553 | + | 0.960710i | \(0.589523\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.54328 | 0.331867 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.27208 | 0.195196 | 0.0975979 | − | 0.995226i | \(-0.468884\pi\) | ||||
0.0975979 | + | 0.995226i | \(0.468884\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.2626 | 1.56115 | 0.780574 | − | 0.625063i | \(-0.214927\pi\) | ||||
0.780574 | + | 0.625063i | \(0.214927\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.17157 | −0.187868 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.786797 | −0.0464431 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.2426 | 0.717676 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.31371 | −0.427271 | −0.213636 | − | 0.976913i | \(-0.568531\pi\) | ||||
−0.213636 | + | 0.976913i | \(0.568531\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.5964 | 0.849833 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.17157 | −0.184033 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.24718 | −0.187164 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.65367 | 0.439692 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.2426 | 1.04457 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.6274 | 1.51971 | 0.759853 | − | 0.650094i | \(-0.225271\pi\) | ||||
0.759853 | + | 0.650094i | \(0.225271\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.79337 | −0.102021 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.01254 | −0.227530 | −0.113765 | − | 0.993508i | \(-0.536291\pi\) | ||||
−0.113765 | + | 0.993508i | \(0.536291\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.27518 | 0.241647 | 0.120824 | − | 0.992674i | \(-0.461446\pi\) | ||||
0.120824 | + | 0.992674i | \(0.461446\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.41421 | −0.0796819 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.8101 | −0.887982 | −0.443991 | − | 0.896031i | \(-0.646438\pi\) | ||||
−0.443991 | + | 0.896031i | \(0.646438\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.24264 | 0.237542 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.0711 | 0.617927 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.92893 | −0.493771 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.06694 | −0.224217 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.7574 | 0.756173 | 0.378086 | − | 0.925770i | \(-0.376582\pi\) | ||||
0.378086 | + | 0.925770i | \(0.376582\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.84776 | 0.101257 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.8435 | −0.974897 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.5474 | 0.846923 | 0.423461 | − | 0.905914i | \(-0.360815\pi\) | ||||
0.423461 | + | 0.905914i | \(0.360815\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.24264 | −0.339054 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.75736 | 0.0951663 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.40649 | 0.237928 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.37011 | −0.504470 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.80591 | 0.311678 | 0.155839 | − | 0.987783i | \(-0.450192\pi\) | ||||
0.155839 | + | 0.987783i | \(0.450192\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.8995 | 1.17225 | 0.586127 | − | 0.810220i | \(-0.300652\pi\) | ||||
0.586127 | + | 0.810220i | \(0.300652\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.9706 | 1.32905 | 0.664524 | − | 0.747266i | \(-0.268634\pi\) | ||||
0.664524 | + | 0.747266i | \(0.268634\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17.8995 | −0.950007 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.2426 | −1.17392 | −0.586961 | − | 0.809615i | \(-0.699676\pi\) | ||||
−0.586961 | + | 0.809615i | \(0.699676\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.9706 | −0.735293 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.97069 | 0.418353 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.7279 | 0.770895 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.11039 | 0.110162 | 0.0550808 | − | 0.998482i | \(-0.482458\pi\) | ||||
0.0550808 | + | 0.998482i | \(0.482458\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.99162 | −0.311911 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.973606 | 0.0505471 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.9411 | −1.86096 | −0.930480 | − | 0.366342i | \(-0.880610\pi\) | ||||
−0.930480 | + | 0.366342i | \(0.880610\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.31371 | −0.480958 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.0991 | 0.775589 | 0.387794 | − | 0.921746i | \(-0.373237\pi\) | ||||
0.387794 | + | 0.921746i | \(0.373237\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.34502 | −0.0689077 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.7279 | −0.548171 | −0.274086 | − | 0.961705i | \(-0.588375\pi\) | ||||
−0.274086 | + | 0.961705i | \(0.588375\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.448342 | −0.0228496 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −24.7279 | −1.25699 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.7279 | 1.45656 | 0.728282 | − | 0.685278i | \(-0.240319\pi\) | ||||
0.728282 | + | 0.685278i | \(0.240319\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.0711 | −0.558461 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 26.3848 | 1.32756 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.0614 | −1.45855 | −0.729275 | − | 0.684221i | \(-0.760143\pi\) | ||||
−0.729275 | + | 0.684221i | \(0.760143\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.544156 | −0.0272419 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.0823 | 1.35243 | 0.676214 | − | 0.736706i | \(-0.263620\pi\) | ||||
0.676214 | + | 0.736706i | \(0.263620\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.52235 | −0.373789 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.585786 | 0.0290364 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.0000 | 0.890043 | 0.445021 | − | 0.895520i | \(-0.353196\pi\) | ||||
0.445021 | + | 0.895520i | \(0.353196\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.7151 | −0.528539 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.50434 | 0.123231 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.9259 | −0.929037 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.384776 | −0.0188426 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.62567 | 0.323685 | 0.161843 | − | 0.986817i | \(-0.448256\pi\) | ||||
0.161843 | + | 0.986817i | \(0.448256\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.3137 | 0.551396 | 0.275698 | − | 0.961244i | \(-0.411091\pi\) | ||||
0.275698 | + | 0.961244i | \(0.411091\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −30.9706 | −1.50584 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.12994 | 0.151469 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.29610 | −0.110599 | −0.0552996 | − | 0.998470i | \(-0.517611\pi\) | ||||
−0.0552996 | + | 0.998470i | \(0.517611\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.41421 | 0.260190 | 0.130095 | − | 0.991502i | \(-0.458472\pi\) | ||||
0.130095 | + | 0.991502i | \(0.458472\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.83938 | −0.375869 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.8590 | 0.710802 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.42450 | 0.449807 | 0.224904 | − | 0.974381i | \(-0.427793\pi\) | ||||
0.224904 | + | 0.974381i | \(0.427793\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.6569 | 0.793184 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 40.2843 | 1.91396 | 0.956982 | − | 0.290148i | \(-0.0937046\pi\) | ||||
0.956982 | + | 0.290148i | \(0.0937046\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.06147 | −0.145127 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.85483 | −0.229626 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.8979 | −0.844656 | −0.422328 | − | 0.906443i | \(-0.638787\pi\) | ||||
−0.422328 | + | 0.906443i | \(0.638787\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.89949 | −0.0894437 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.2304 | −0.715587 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.92893 | −0.230566 | −0.115283 | − | 0.993333i | \(-0.536777\pi\) | ||||
−0.115283 | + | 0.993333i | \(0.536777\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.55635 | 0.165636 | 0.0828178 | − | 0.996565i | \(-0.473608\pi\) | ||||
0.0828178 | + | 0.996565i | \(0.473608\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.1421 | −1.12198 | −0.560990 | − | 0.827823i | \(-0.689579\pi\) | ||||
−0.560990 | + | 0.827823i | \(0.689579\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.24718 | −0.150584 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.5563 | −0.627313 | −0.313657 | − | 0.949537i | \(-0.601554\pi\) | ||||
−0.313657 | + | 0.949537i | \(0.601554\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.06147 | −0.141365 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.7206 | −0.540057 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.83938 | −0.360455 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.55635 | 0.163176 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.41421 | 0.339474 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.9832 | 1.73550 | 0.867748 | − | 0.497005i | \(-0.165567\pi\) | ||||
0.867748 | + | 0.497005i | \(0.165567\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.60766 | −0.0731509 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 29.5563 | 1.34208 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.6034 | 0.797688 | 0.398844 | − | 0.917019i | \(-0.369412\pi\) | ||||
0.398844 | + | 0.917019i | \(0.369412\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.55635 | −0.160824 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.3848 | −0.919952 | −0.459976 | − | 0.887931i | \(-0.652142\pi\) | ||||
−0.459976 | + | 0.887931i | \(0.652142\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.41421 | −0.153457 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.07107 | −0.137756 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.8155 | 0.752767 | 0.376383 | − | 0.926464i | \(-0.377168\pi\) | ||||
0.376383 | + | 0.926464i | \(0.377168\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.585786 | −0.0261710 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.317025 | 0.0141355 | 0.00706773 | − | 0.999975i | \(-0.497750\pi\) | ||||
0.00706773 | + | 0.999975i | \(0.497750\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.4776 | 0.822242 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.94977 | 0.441885 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 38.2843 | 1.69692 | 0.848460 | − | 0.529259i | \(-0.177530\pi\) | ||||
0.848460 | + | 0.529259i | \(0.177530\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.52691 | 0.111784 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.29319 | −0.410304 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.32957 | −0.190784 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.81845 | −0.431815 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.4437 | −0.634006 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.2513 | −1.71963 | −0.859815 | − | 0.510606i | \(-0.829421\pi\) | ||||
−0.859815 | + | 0.510606i | \(0.829421\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.14214 | 0.181123 | 0.0905615 | − | 0.995891i | \(-0.471134\pi\) | ||||
0.0905615 | + | 0.995891i | \(0.471134\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.384776 | −0.0167930 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.8995 | 0.908674 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.0711 | 0.827614 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.7279 | 1.15555 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.9623 | −0.602518 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.28064 | 0.227453 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.9999 | 1.11782 | 0.558912 | − | 0.829227i | \(-0.311219\pi\) | ||||
0.558912 | + | 0.829227i | \(0.311219\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.24264 | −0.267897 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21.5563 | −0.923373 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −45.1116 | −1.92883 | −0.964416 | − | 0.264389i | \(-0.914830\pi\) | ||||
−0.964416 | + | 0.264389i | \(0.914830\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 23.8352 | 1.01726 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.4316 | 0.529603 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.52691 | 0.192504 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.08239 | −0.0459450 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.0000 | 0.677942 | 0.338971 | − | 0.940797i | \(-0.389921\pi\) | ||||
0.338971 | + | 0.940797i | \(0.389921\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.0416 | 1.09752 | 0.548762 | − | 0.835979i | \(-0.315099\pi\) | ||||
0.548762 | + | 0.835979i | \(0.315099\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.0711 | −0.634045 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.29063 | −0.0542014 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.1838 | −1.26537 | −0.632685 | − | 0.774410i | \(-0.718047\pi\) | ||||
−0.632685 | + | 0.774410i | \(0.718047\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.3086 | −1.35207 | −0.676036 | − | 0.736868i | \(-0.736304\pi\) | ||||
−0.676036 | + | 0.736868i | \(0.736304\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.75699 | −0.282277 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.5069 | 0.438168 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.0000 | −0.582828 | −0.291414 | − | 0.956597i | \(-0.594126\pi\) | ||||
−0.291414 | + | 0.956597i | \(0.594126\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.585786 | 0.0243445 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.24718 | −0.134716 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.35049 | 0.0973475 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.87006 | 0.366106 | 0.183053 | − | 0.983103i | \(-0.441402\pi\) | ||||
0.183053 | + | 0.983103i | \(0.441402\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.14933 | 0.212174 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.41421 | −0.387249 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.6985 | 0.891050 | 0.445525 | − | 0.895270i | \(-0.353017\pi\) | ||||
0.445525 | + | 0.895270i | \(0.353017\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.2132 | 0.704490 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.8284 | −1.83164 | −0.915820 | − | 0.401589i | \(-0.868458\pi\) | ||||
−0.915820 | + | 0.401589i | \(0.868458\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.3295 | −1.23717 | −0.618583 | − | 0.785719i | \(-0.712293\pi\) | ||||
−0.618583 | + | 0.785719i | \(0.712293\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −23.3137 | −0.949408 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19.2430 | 0.782337 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −39.0656 | −1.58562 | −0.792811 | − | 0.609467i | \(-0.791383\pi\) | ||||
−0.792811 | + | 0.609467i | \(0.791383\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.34502 | −0.0545031 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.3137 | −1.18397 | −0.591985 | − | 0.805949i | \(-0.701655\pi\) | ||||
−0.591985 | + | 0.805949i | \(0.701655\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.50981 | 0.141529 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.6549 | 0.992570 | 0.496285 | − | 0.868160i | \(-0.334697\pi\) | ||||
0.496285 | + | 0.868160i | \(0.334697\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.11039 | −0.0848238 | −0.0424119 | − | 0.999100i | \(-0.513504\pi\) | ||||
−0.0424119 | + | 0.999100i | \(0.513504\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.4558 | −1.10177 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.525265 | −0.0210443 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.5563 | −0.582254 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.31371 | −0.0524645 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.5858 | −0.978745 | −0.489372 | − | 0.872075i | \(-0.662774\pi\) | ||||
−0.489372 | + | 0.872075i | \(0.662774\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.0416 | −0.796583 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.24718 | −0.128860 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.3868 | −0.925168 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.7750 | 0.465084 | 0.232542 | − | 0.972586i | \(-0.425296\pi\) | ||||
0.232542 | + | 0.972586i | \(0.425296\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.2513 | −1.54792 | −0.773960 | − | 0.633235i | \(-0.781727\pi\) | ||||
−0.773960 | + | 0.633235i | \(0.781727\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.4853 | 0.570357 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −45.2548 | −1.77915 | −0.889576 | − | 0.456788i | \(-0.849000\pi\) | ||||
−0.889576 | + | 0.456788i | \(0.849000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.04601 | 0.237327 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.557127 | −0.0218355 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.2890 | −0.989634 | −0.494817 | − | 0.868997i | \(-0.664765\pi\) | ||||
−0.494817 | + | 0.868997i | \(0.664765\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.7279 | −1.04435 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19.2430 | 0.750739 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.7696 | −0.886976 | −0.443488 | − | 0.896280i | \(-0.646259\pi\) | ||||
−0.443488 | + | 0.896280i | \(0.646259\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.5858 | −1.03407 | −0.517034 | − | 0.855965i | \(-0.672964\pi\) | ||||
−0.517034 | + | 0.855965i | \(0.672964\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.31371 | −0.0509434 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.7279 | 1.42211 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.4370 | 0.519506 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.55635 | 0.291710 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.3617 | 0.592151 | 0.296076 | − | 0.955165i | \(-0.404322\pi\) | ||||
0.296076 | + | 0.955165i | \(0.404322\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.57128 | −0.252929 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.2124 | −0.392494 | −0.196247 | − | 0.980554i | \(-0.562876\pi\) | ||||
−0.196247 | + | 0.980554i | \(0.562876\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.07107 | 0.194610 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.72792 | 0.104534 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.9162 | −1.29777 | −0.648885 | − | 0.760887i | \(-0.724764\pi\) | ||||
−0.648885 | + | 0.760887i | \(0.724764\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.8686 | −0.988389 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.57675 | 0.289071 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.3855 | 1.23200 | 0.616001 | − | 0.787745i | \(-0.288752\pi\) | ||||
0.616001 | + | 0.787745i | \(0.288752\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.585786 | −0.0222522 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.928932 | −0.0352364 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.443651 | −0.0167804 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.6863 | 1.08347 | 0.541733 | − | 0.840551i | \(-0.317768\pi\) | ||||
0.541733 | + | 0.840551i | \(0.317768\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.71644 | 0.0647369 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.1421 | 0.683272 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.17025 | 0.119230 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.0096 | 1.38992 | 0.694962 | − | 0.719047i | \(-0.255421\pi\) | ||||
0.694962 | + | 0.719047i | \(0.255421\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 34.4734 | 1.29285 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.2132 | 0.569739 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.65914 | 0.323381 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.4287 | 0.724567 | 0.362284 | − | 0.932068i | \(-0.381997\pi\) | ||||
0.362284 | + | 0.932068i | \(0.381997\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.742837 | −0.0276647 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.7279 | −0.398976 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.79045 | 0.326469 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.7990 | −0.660128 | −0.330064 | − | 0.943959i | \(-0.607070\pi\) | ||||
−0.330064 | + | 0.943959i | \(0.607070\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.313708 | −0.0116188 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.7279 | −0.913347 | −0.456673 | − | 0.889634i | \(-0.650959\pi\) | ||||
−0.456673 | + | 0.889634i | \(0.650959\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.75736 | −0.359906 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.39104 | −0.272252 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.07107 | 0.333685 | 0.166842 | − | 0.985984i | \(-0.446643\pi\) | ||||
0.166842 | + | 0.985984i | \(0.446643\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.3086 | 1.18529 | 0.592644 | − | 0.805465i | \(-0.298084\pi\) | ||||
0.592644 | + | 0.805465i | \(0.298084\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.7206 | −0.429410 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −24.7279 | −0.904747 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.58579 | 0.167561 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.2066 | −0.883311 | −0.441655 | − | 0.897185i | \(-0.645609\pi\) | ||||
−0.441655 | + | 0.897185i | \(0.645609\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.634051 | −0.0231061 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −36.7695 | −1.33818 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.1005 | −0.512492 | −0.256246 | − | 0.966612i | \(-0.582486\pi\) | ||||
−0.256246 | + | 0.966612i | \(0.582486\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.88123 | −0.140880 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.02944 | 0.109817 | 0.0549085 | − | 0.998491i | \(-0.482513\pi\) | ||||
0.0549085 | + | 0.998491i | \(0.482513\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.69848 | −0.133894 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.5980 | 1.57218 | 0.786092 | − | 0.618110i | \(-0.212101\pi\) | ||||
0.786092 | + | 0.618110i | \(0.212101\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.30864 | −0.227200 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.9289 | −1.18437 | −0.592186 | − | 0.805802i | \(-0.701735\pi\) | ||||
−0.592186 | + | 0.805802i | \(0.701735\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.64113 | 0.130793 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.185709 | −0.00666228 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.56581 | −0.199416 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.41421 | −0.265301 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22.9706 | −0.820901 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −28.2960 | −1.00993 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.2948 | 0.402616 | 0.201308 | − | 0.979528i | \(-0.435481\pi\) | ||||
0.201308 | + | 0.979528i | \(0.435481\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.98454 | 0.106253 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.58579 | −0.0919400 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.34315 | −0.154036 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.4142 | 0.475156 | 0.237578 | − | 0.971368i | \(-0.423646\pi\) | ||||
0.237578 | + | 0.971368i | \(0.423646\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.00000 | −0.141333 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.10051 | 0.215282 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.88123 | −0.136795 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.7279 | 0.377641 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.9958 | −0.562382 | −0.281191 | − | 0.959652i | \(-0.590729\pi\) | ||||
−0.281191 | + | 0.959652i | \(0.590729\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.7611 | 1.50154 | 0.750772 | − | 0.660561i | \(-0.229681\pi\) | ||||
0.750772 | + | 0.660561i | \(0.229681\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.65914 | 0.303689 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.58579 | −0.300747 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.9706 | −0.803638 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 48.0961 | 1.67857 | 0.839283 | − | 0.543694i | \(-0.182975\pi\) | ||||
0.839283 | + | 0.543694i | \(0.182975\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.50143 | −0.331199 | −0.165599 | − | 0.986193i | \(-0.552956\pi\) | ||||
−0.165599 | + | 0.986193i | \(0.552956\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.928932 | −0.0323413 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.15640 | −0.283626 | −0.141813 | − | 0.989893i | \(-0.545293\pi\) | ||||
−0.141813 | + | 0.989893i | \(0.545293\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −53.9411 | −1.87345 | −0.936726 | − | 0.350062i | \(-0.886160\pi\) | ||||
−0.936726 | + | 0.350062i | \(0.886160\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.07107 | 0.245293 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.41421 | −0.0489409 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.51472 | −0.328877 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.9217 | −1.20563 | −0.602816 | − | 0.797880i | \(-0.705955\pi\) | ||||
−0.602816 | + | 0.797880i | \(0.705955\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.72792 | 0.0595835 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.50434 | −0.0862541 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24.0209 | 0.826343 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.30157 | 0.113443 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.1005 | −0.689848 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.07107 | 0.173834 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.8101 | 0.541327 | 0.270663 | − | 0.962674i | \(-0.412757\pi\) | ||||
0.270663 | + | 0.962674i | \(0.412757\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.0042 | −0.342135 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.97069 | −0.272274 | −0.136137 | − | 0.990690i | \(-0.543469\pi\) | ||||
−0.136137 | + | 0.990690i | \(0.543469\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.0416 | −1.43444 | −0.717221 | − | 0.696846i | \(-0.754586\pi\) | ||||
−0.717221 | + | 0.696846i | \(0.754586\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.602188 | 0.0205225 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.8579 | −0.539808 | −0.269904 | − | 0.962887i | \(-0.586992\pi\) | ||||
−0.269904 | + | 0.962887i | \(0.586992\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34.8701 | −1.18562 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.9289 | 0.370739 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 38.6172 | 1.30700 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.85786 | −0.130420 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.33664 | −0.247741 | −0.123870 | − | 0.992298i | \(-0.539531\pi\) | ||||
−0.123870 | + | 0.992298i | \(0.539531\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.59767 | 0.188805 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.2066 | 0.815540 | 0.407770 | − | 0.913085i | \(-0.366306\pi\) | ||||
0.407770 | + | 0.913085i | \(0.366306\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.2548 | 1.38834 | 0.694168 | − | 0.719813i | \(-0.255773\pi\) | ||||
0.694168 | + | 0.719813i | \(0.255773\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.1716 | −0.375528 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.2848 | 0.513214 | 0.256607 | − | 0.966516i | \(-0.417395\pi\) | ||||
0.256607 | + | 0.966516i | \(0.417395\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.557127 | −0.0186855 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.11586 | −0.104385 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.7696 | −0.962736 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.7080 | −1.12673 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.7279 | 0.424500 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.48528 | 0.0827050 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.0711 | −0.500979 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.4637 | 0.779101 | 0.389550 | − | 0.921005i | \(-0.372630\pi\) | ||||
0.389550 | + | 0.921005i | \(0.372630\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 24.1421 | 0.800744 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.1383 | 0.965396 | 0.482698 | − | 0.875787i | \(-0.339657\pi\) | ||||
0.482698 | + | 0.875787i | \(0.339657\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.83938 | −0.259446 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.9623 | −0.461580 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.58579 | −0.151436 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.2843 | −1.46080 | −0.730402 | − | 0.683018i | \(-0.760667\pi\) | ||||
−0.730402 | + | 0.683018i | \(0.760667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.3797 | −0.671535 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.21371 | 0.0399065 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.65685 | −0.185795 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.7933 | 0.911869 | 0.455934 | − | 0.890013i | \(-0.349305\pi\) | ||||
0.455934 | + | 0.890013i | \(0.349305\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.4731 | 0.507110 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.07107 | 0.100542 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.443651 | −0.0144934 | −0.00724672 | − | 0.999974i | \(-0.502307\pi\) | ||||
−0.00724672 | + | 0.999974i | \(0.502307\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.27208 | −0.106780 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.9886 | −1.27099 | −0.635497 | − | 0.772103i | \(-0.719205\pi\) | ||||
−0.635497 | + | 0.772103i | \(0.719205\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.4437 | −0.535479 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.42742 | 0.0789639 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.4202 | 1.67093 | 0.835466 | − | 0.549541i | \(-0.185198\pi\) | ||||
0.835466 | + | 0.549541i | \(0.185198\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.1005 | 0.392386 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −50.0000 | −1.61966 | −0.809829 | − | 0.586665i | \(-0.800440\pi\) | ||||
−0.809829 | + | 0.586665i | \(0.800440\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.3128 | −0.527870 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.24718 | −0.104966 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.43835 | −0.143322 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.7279 | −0.829933 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 34.9217 | 1.12534 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.41421 | 0.0455251 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.5269 | 1.11031 | 0.555155 | − | 0.831747i | \(-0.312659\pi\) | ||||
0.555155 | + | 0.831747i | \(0.312659\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 54.7279 | 1.75630 | 0.878151 | − | 0.478383i | \(-0.158777\pi\) | ||||
0.878151 | + | 0.478383i | \(0.158777\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.159380 | −0.00510947 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34.3848 | 1.10007 | 0.550033 | − | 0.835143i | \(-0.314615\pi\) | ||||
0.550033 | + | 0.835143i | \(0.314615\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.26810 | −0.0405287 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −28.1647 | −0.899231 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38.9886 | 1.24354 | 0.621772 | − | 0.783198i | \(-0.286413\pi\) | ||||
0.621772 | + | 0.783198i | \(0.286413\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.7279 | −0.724172 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.11270 | 0.0990783 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −67.8644 | −2.15796 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.7862 | 1.61328 | 0.806638 | − | 0.591046i | \(-0.201285\pi\) | ||||
0.806638 | + | 0.591046i | \(0.201285\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.5294 | −0.334141 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 41.5563 | 1.31742 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.68167 | 0.274951 | 0.137476 | − | 0.990505i | \(-0.456101\pi\) | ||||
0.137476 | + | 0.990505i | \(0.456101\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.17157 | −0.100344 |
(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 | 4624.2.a.bm.1.2 | 4 | ||
4.3 | odd | 2 | 2312.2.a.s.1.3 | 4 | |||
17.5 | odd | 16 | 272.2.v.e.161.1 | 4 | |||
17.7 | odd | 16 | 272.2.v.e.49.1 | 4 | |||
17.16 | even | 2 | inner | 4624.2.a.bm.1.3 | 4 | ||
68.7 | even | 16 | 136.2.n.a.49.1 | yes | 4 | ||
68.39 | even | 16 | 136.2.n.a.25.1 | ✓ | 4 | ||
68.47 | odd | 4 | 2312.2.b.j.577.3 | 4 | |||
68.55 | odd | 4 | 2312.2.b.j.577.2 | 4 | |||
68.67 | odd | 2 | 2312.2.a.s.1.2 | 4 | |||
204.107 | odd | 16 | 1224.2.bq.a.433.1 | 4 | |||
204.143 | odd | 16 | 1224.2.bq.a.865.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.2.n.a.25.1 | ✓ | 4 | 68.39 | even | 16 | ||
136.2.n.a.49.1 | yes | 4 | 68.7 | even | 16 | ||
272.2.v.e.49.1 | 4 | 17.7 | odd | 16 | |||
272.2.v.e.161.1 | 4 | 17.5 | odd | 16 | |||
1224.2.bq.a.433.1 | 4 | 204.107 | odd | 16 | |||
1224.2.bq.a.865.1 | 4 | 204.143 | odd | 16 | |||
2312.2.a.s.1.2 | 4 | 68.67 | odd | 2 | |||
2312.2.a.s.1.3 | 4 | 4.3 | odd | 2 | |||
2312.2.b.j.577.2 | 4 | 68.55 | odd | 4 | |||
2312.2.b.j.577.3 | 4 | 68.47 | odd | 4 | |||
4624.2.a.bm.1.2 | 4 | 1.1 | even | 1 | trivial | ||
4624.2.a.bm.1.3 | 4 | 17.16 | even | 2 | inner |