Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5220,2,Mod(1,5220)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5220, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5220.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5220 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5220.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: | \(41.6819098551\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 580) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.51414\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5220.1 |
$q$-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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.32088 | 0.499247 | 0.249624 | − | 0.968343i | \(-0.419693\pi\) | ||||
0.249624 | + | 0.968343i | \(0.419693\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.32088 | −1.60431 | −0.802154 | − | 0.597118i | \(-0.796312\pi\) | ||||
−0.802154 | + | 0.597118i | \(0.796312\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.02827 | −1.39459 | −0.697296 | − | 0.716783i | \(-0.745614\pi\) | ||||
−0.697296 | + | 0.716783i | \(0.745614\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.34916 | 1.53990 | 0.769949 | − | 0.638106i | \(-0.220282\pi\) | ||||
0.769949 | + | 0.638106i | \(0.220282\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.34916 | −0.997765 | −0.498883 | − | 0.866670i | \(-0.666256\pi\) | ||||
−0.498883 | + | 0.866670i | \(0.666256\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.70739 | 0.356015 | 0.178008 | − | 0.984029i | \(-0.443035\pi\) | ||||
0.178008 | + | 0.984029i | \(0.443035\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.34916 | 1.49955 | 0.749777 | − | 0.661691i | \(-0.230161\pi\) | ||||
0.749777 | + | 0.661691i | \(0.230161\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.32088 | 0.223270 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.93438 | −1.14000 | −0.570002 | − | 0.821643i | \(-0.693058\pi\) | ||||
−0.570002 | + | 0.821643i | \(0.693058\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.02827 | 0.160589 | 0.0802947 | − | 0.996771i | \(-0.474414\pi\) | ||||
0.0802947 | + | 0.996771i | \(0.474414\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.7357 | 1.63717 | 0.818587 | − | 0.574383i | \(-0.194758\pi\) | ||||
0.818587 | + | 0.574383i | \(0.194758\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.679116 | 0.0990592 | 0.0495296 | − | 0.998773i | \(-0.484228\pi\) | ||||
0.0495296 | + | 0.998773i | \(0.484228\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.25526 | −0.750752 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.38650 | −0.327812 | −0.163906 | − | 0.986476i | \(-0.552409\pi\) | ||||
−0.163906 | + | 0.986476i | \(0.552409\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.32088 | −0.717468 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.4431 | −1.35957 | −0.679785 | − | 0.733412i | \(-0.737927\pi\) | ||||
−0.679785 | + | 0.733412i | \(0.737927\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.38650 | −0.817708 | −0.408854 | − | 0.912600i | \(-0.634072\pi\) | ||||
−0.408854 | + | 0.912600i | \(0.634072\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.02827 | −0.623681 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.70739 | −0.697269 | −0.348634 | − | 0.937259i | \(-0.613354\pi\) | ||||
−0.348634 | + | 0.937259i | \(0.613354\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.61350 | 0.428843 | 0.214421 | − | 0.976741i | \(-0.431213\pi\) | ||||
0.214421 | + | 0.976741i | \(0.431213\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.73566 | −0.788350 | −0.394175 | − | 0.919035i | \(-0.628970\pi\) | ||||
−0.394175 | + | 0.919035i | \(0.628970\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.02827 | −0.800946 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3774 | −1.28006 | −0.640031 | − | 0.768349i | \(-0.721078\pi\) | ||||
−0.640031 | + | 0.768349i | \(0.721078\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.96265 | 0.434958 | 0.217479 | − | 0.976065i | \(-0.430217\pi\) | ||||
0.217479 | + | 0.976065i | \(0.430217\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.34916 | 0.688663 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.58522 | −0.274033 | −0.137016 | − | 0.990569i | \(-0.543751\pi\) | ||||
−0.137016 | + | 0.990569i | \(0.543751\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.64177 | −0.696247 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.34916 | −0.446214 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.3209 | −1.55560 | −0.777800 | − | 0.628512i | \(-0.783664\pi\) | ||||
−0.777800 | + | 0.628512i | \(0.783664\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.8688 | −1.18099 | −0.590493 | − | 0.807043i | \(-0.701067\pi\) | ||||
−0.590493 | + | 0.807043i | \(0.701067\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.65084 | −0.359728 | −0.179864 | − | 0.983691i | \(-0.557566\pi\) | ||||
−0.179864 | + | 0.983691i | \(0.557566\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.32088 | 0.514389 | 0.257195 | − | 0.966360i | \(-0.417202\pi\) | ||||
0.257195 | + | 0.966360i | \(0.417202\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.3118 | −1.37082 | −0.685411 | − | 0.728156i | \(-0.740378\pi\) | ||||
−0.685411 | + | 0.728156i | \(0.740378\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.03735 | −0.191657 | −0.0958287 | − | 0.995398i | \(-0.530550\pi\) | ||||
−0.0958287 | + | 0.995398i | \(0.530550\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.70739 | 0.159215 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.38650 | 0.768790 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.3118 | 1.57380 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.26434 | −0.112192 | −0.0560959 | − | 0.998425i | \(-0.517865\pi\) | ||||
−0.0560959 | + | 0.998425i | \(0.517865\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.70739 | 0.149175 | 0.0745877 | − | 0.997214i | \(-0.476236\pi\) | ||||
0.0745877 | + | 0.997214i | \(0.476236\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.74474 | −0.498132 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −21.7639 | −1.85942 | −0.929709 | − | 0.368294i | \(-0.879942\pi\) | ||||
−0.929709 | + | 0.368294i | \(0.879942\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.6983 | −1.41633 | −0.708166 | − | 0.706046i | \(-0.750477\pi\) | ||||
−0.708166 | + | 0.706046i | \(0.750477\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 26.7549 | 2.23735 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.00000 | 0.0830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.0000 | −1.47462 | −0.737309 | − | 0.675556i | \(-0.763904\pi\) | ||||
−0.737309 | + | 0.675556i | \(0.763904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.44305 | 0.524328 | 0.262164 | − | 0.965023i | \(-0.415564\pi\) | ||||
0.262164 | + | 0.965023i | \(0.415564\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.34916 | 0.670621 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.7357 | 0.856799 | 0.428400 | − | 0.903589i | \(-0.359078\pi\) | ||||
0.428400 | + | 0.903589i | \(0.359078\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.25526 | 0.177740 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.90611 | 0.305950 | 0.152975 | − | 0.988230i | \(-0.451115\pi\) | ||||
0.152975 | + | 0.988230i | \(0.451115\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.51960 | 0.427120 | 0.213560 | − | 0.976930i | \(-0.431494\pi\) | ||||
0.213560 | + | 0.976930i | \(0.431494\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.2835 | 0.944888 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.80128 | −0.441063 | −0.220532 | − | 0.975380i | \(-0.570779\pi\) | ||||
−0.220532 | + | 0.975380i | \(0.570779\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.32088 | 0.0998495 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.0565 | −1.05064 | −0.525318 | − | 0.850906i | \(-0.676054\pi\) | ||||
−0.525318 | + | 0.850906i | \(0.676054\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.08482 | −0.526611 | −0.263305 | − | 0.964713i | \(-0.584813\pi\) | ||||
−0.263305 | + | 0.964713i | \(0.584813\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.93438 | −0.509826 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −33.7831 | −2.47047 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.547875 | 0.0396428 | 0.0198214 | − | 0.999804i | \(-0.493690\pi\) | ||||
0.0198214 | + | 0.999804i | \(0.493690\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.40571 | 0.317130 | 0.158565 | − | 0.987349i | \(-0.449313\pi\) | ||||
0.158565 | + | 0.987349i | \(0.449313\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.64177 | 0.330712 | 0.165356 | − | 0.986234i | \(-0.447123\pi\) | ||||
0.165356 | + | 0.986234i | \(0.447123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.4431 | 1.30739 | 0.653697 | − | 0.756757i | \(-0.273217\pi\) | ||||
0.653697 | + | 0.756757i | \(0.273217\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.32088 | 0.0927079 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.02827 | 0.0718178 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 23.1414 | 1.60072 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.54787 | −0.313089 | −0.156544 | − | 0.987671i | \(-0.550035\pi\) | ||||
−0.156544 | + | 0.987671i | \(0.550035\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.7357 | 0.732166 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.0283 | 0.748648 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −31.9253 | −2.14753 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.12217 | 0.0751459 | 0.0375730 | − | 0.999294i | \(-0.488037\pi\) | ||||
0.0375730 | + | 0.999294i | \(0.488037\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.63270 | −0.639345 | −0.319672 | − | 0.947528i | \(-0.603573\pi\) | ||||
−0.319672 | + | 0.947528i | \(0.603573\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.00000 | 0.132164 | 0.0660819 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660819 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.05655 | 0.527802 | 0.263901 | − | 0.964550i | \(-0.414991\pi\) | ||||
0.263901 | + | 0.964550i | \(0.414991\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.679116 | 0.0443006 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.6135 | −1.00995 | −0.504977 | − | 0.863133i | \(-0.668499\pi\) | ||||
−0.504977 | + | 0.863133i | \(0.668499\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.5105 | 1.19237 | 0.596184 | − | 0.802848i | \(-0.296683\pi\) | ||||
0.596184 | + | 0.802848i | \(0.296683\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.25526 | −0.335747 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.8688 | 1.39148 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.67912 | 0.421582 | 0.210791 | − | 0.977531i | \(-0.432396\pi\) | ||||
0.210791 | + | 0.977531i | \(0.432396\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.08482 | −0.571158 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.4249 | 1.64834 | 0.824170 | − | 0.566342i | \(-0.191642\pi\) | ||||
0.824170 | + | 0.566342i | \(0.191642\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.15951 | −0.569145 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.4340 | −1.69165 | −0.845826 | − | 0.533459i | \(-0.820892\pi\) | ||||
−0.845826 | + | 0.533459i | \(0.820892\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.38650 | −0.146602 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.9717 | 0.668958 | 0.334479 | − | 0.942403i | \(-0.391440\pi\) | ||||
0.334479 | + | 0.942403i | \(0.391440\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.1504 | 1.22405 | 0.612026 | − | 0.790838i | \(-0.290355\pi\) | ||||
0.612026 | + | 0.790838i | \(0.290355\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.32088 | −0.320861 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.15951 | 0.189837 | 0.0949184 | − | 0.995485i | \(-0.469741\pi\) | ||||
0.0949184 | + | 0.995485i | \(0.469741\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3118 | 0.615151 | 0.307576 | − | 0.951524i | \(-0.400482\pi\) | ||||
0.307576 | + | 0.951524i | \(0.400482\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.423851 | 0.0251953 | 0.0125977 | − | 0.999921i | \(-0.495990\pi\) | ||||
0.0125977 | + | 0.999921i | \(0.495990\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.35823 | 0.0801738 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.3118 | 1.37128 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.2462 | −1.12437 | −0.562187 | − | 0.827010i | \(-0.690040\pi\) | ||||
−0.562187 | + | 0.827010i | \(0.690040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.4431 | −0.608018 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.58522 | −0.496496 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.1806 | 0.817355 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.38650 | −0.365690 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.7357 | 1.29759 | 0.648796 | − | 0.760962i | \(-0.275273\pi\) | ||||
0.648796 | + | 0.760962i | \(0.275273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.8031 | −0.839409 | −0.419704 | − | 0.907661i | \(-0.637866\pi\) | ||||
−0.419704 | + | 0.907661i | \(0.637866\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.9717 | −0.846252 | −0.423126 | − | 0.906071i | \(-0.639067\pi\) | ||||
−0.423126 | + | 0.906071i | \(0.639067\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.1222 | −1.29867 | −0.649335 | − | 0.760502i | \(-0.724953\pi\) | ||||
−0.649335 | + | 0.760502i | \(0.724953\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.32088 | −0.297912 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −27.6135 | −1.53646 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.02827 | −0.278918 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.897033 | 0.0494550 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.82048 | −0.539783 | −0.269891 | − | 0.962891i | \(-0.586988\pi\) | ||||
−0.269891 | + | 0.962891i | \(0.586988\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.70739 | −0.311828 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.09389 | −0.440903 | −0.220451 | − | 0.975398i | \(-0.570753\pi\) | ||||
−0.220451 | + | 0.975398i | \(0.570753\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −44.4249 | −2.40574 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.1878 | −0.874058 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.37743 | 0.396041 | 0.198021 | − | 0.980198i | \(-0.436549\pi\) | ||||
0.198021 | + | 0.980198i | \(0.436549\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.82956 | 0.472635 | 0.236318 | − | 0.971676i | \(-0.424059\pi\) | ||||
0.236318 | + | 0.971676i | \(0.424059\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.7266 | −0.730593 | −0.365296 | − | 0.930891i | \(-0.619032\pi\) | ||||
−0.365296 | + | 0.930891i | \(0.619032\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.61350 | 0.191784 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.70739 | 0.0901126 | 0.0450563 | − | 0.998984i | \(-0.485653\pi\) | ||||
0.0450563 | + | 0.998984i | \(0.485653\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.0848216 | −0.00446429 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.73566 | −0.352561 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.9627 | −1.35524 | −0.677620 | − | 0.735412i | \(-0.736988\pi\) | ||||
−0.677620 | + | 0.735412i | \(0.736988\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.15230 | −0.163659 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.92531 | 0.513913 | 0.256956 | − | 0.966423i | \(-0.417280\pi\) | ||||
0.256956 | + | 0.966423i | \(0.417280\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.02827 | −0.258969 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.2070 | 1.75710 | 0.878548 | − | 0.477655i | \(-0.158513\pi\) | ||||
0.878548 | + | 0.477655i | \(0.158513\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.4340 | 1.09523 | 0.547613 | − | 0.836732i | \(-0.315537\pi\) | ||||
0.547613 | + | 0.836732i | \(0.315537\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.02827 | −0.358194 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 36.3684 | 1.84395 | 0.921975 | − | 0.387251i | \(-0.126575\pi\) | ||||
0.921975 | + | 0.387251i | \(0.126575\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.8405 | 0.548227 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.3774 | −0.572461 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.4713 | −1.37875 | −0.689373 | − | 0.724406i | \(-0.742114\pi\) | ||||
−0.689373 | + | 0.724406i | \(0.742114\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.3118 | −1.11420 | −0.557099 | − | 0.830446i | \(-0.688086\pi\) | ||||
−0.557099 | + | 0.830446i | \(0.688086\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −41.9819 | −2.09127 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 36.8970 | 1.82892 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.95358 | 0.244939 | 0.122469 | − | 0.992472i | \(-0.460919\pi\) | ||||
0.122469 | + | 0.992472i | \(0.460919\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.7941 | −0.678762 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.96265 | 0.194519 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.198716 | 0.00970793 | 0.00485397 | − | 0.999988i | \(-0.498455\pi\) | ||||
0.00485397 | + | 0.999988i | \(0.498455\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.4996 | 1.29151 | 0.645756 | − | 0.763544i | \(-0.276542\pi\) | ||||
0.645756 | + | 0.763544i | \(0.276542\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.34916 | 0.307979 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.43584 | −0.408239 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.2835 | 1.02519 | 0.512596 | − | 0.858630i | \(-0.328684\pi\) | ||||
0.512596 | + | 0.858630i | \(0.328684\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.8031 | −1.19196 | −0.595981 | − | 0.802998i | \(-0.703237\pi\) | ||||
−0.595981 | + | 0.802998i | \(0.703237\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.42571 | −0.355220 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.3118 | −1.54216 | −0.771079 | − | 0.636739i | \(-0.780283\pi\) | ||||
−0.771079 | + | 0.636739i | \(0.780283\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.3774 | −1.20572 | −0.602859 | − | 0.797848i | \(-0.705972\pi\) | ||||
−0.602859 | + | 0.797848i | \(0.705972\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.58522 | −0.122551 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.7266 | −0.647798 | −0.323899 | − | 0.946092i | \(-0.604994\pi\) | ||||
−0.323899 | + | 0.946092i | \(0.604994\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.47133 | −0.257635 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.64177 | −0.311371 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.0101 | −0.702144 | −0.351072 | − | 0.936348i | \(-0.614183\pi\) | ||||
−0.351072 | + | 0.936348i | \(0.614183\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.7549 | −1.52555 | −0.762773 | − | 0.646666i | \(-0.776163\pi\) | ||||
−0.762773 | + | 0.646666i | \(0.776163\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.5369 | −1.14033 | −0.570164 | − | 0.821531i | \(-0.693120\pi\) | ||||
−0.570164 | + | 0.821531i | \(0.693120\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.60442 | 0.398165 | 0.199083 | − | 0.979983i | \(-0.436204\pi\) | ||||
0.199083 | + | 0.979983i | \(0.436204\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.53880 | −0.348110 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −57.1232 | −2.62653 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.34916 | −0.199553 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.26434 | −0.149151 | −0.0745757 | − | 0.997215i | \(-0.523760\pi\) | ||||
−0.0745757 | + | 0.997215i | \(0.523760\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.8680 | 1.58984 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.3209 | −0.695686 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.2070 | 1.55007 | 0.775033 | − | 0.631920i | \(-0.217733\pi\) | ||||
0.775033 | + | 0.631920i | \(0.217733\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.93438 | 0.403203 | 0.201601 | − | 0.979468i | \(-0.435385\pi\) | ||||
0.201601 | + | 0.979468i | \(0.435385\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.34916 | 0.285952 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.77301 | 0.214099 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.6236 | 1.28137 | 0.640685 | − | 0.767804i | \(-0.278651\pi\) | ||||
0.640685 | + | 0.767804i | \(0.278651\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.0192012 | 0.000856140 0 | 0.000428070 | − | 1.00000i | \(-0.499864\pi\) | ||||
0.000428070 | 1.00000i | \(0.499864\pi\) | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.8688 | −0.528153 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.25526 | 0.365908 | 0.182954 | − | 0.983121i | \(-0.441434\pi\) | ||||
0.182954 | + | 0.983121i | \(0.441434\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.89703 | −0.393582 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.65084 | −0.160875 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.61350 | −0.158921 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.2553 | 0.887399 | 0.443700 | − | 0.896176i | \(-0.353666\pi\) | ||||
0.443700 | + | 0.896176i | \(0.353666\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.82048 | 0.0796042 | 0.0398021 | − | 0.999208i | \(-0.487327\pi\) | ||||
0.0398021 | + | 0.999208i | \(0.487327\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 53.0101 | 2.30916 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.0848 | −0.873253 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.17044 | −0.223957 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.32088 | 0.230042 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27.9627 | 1.20444 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.03920 | 0.0446788 | 0.0223394 | − | 0.999750i | \(-0.492889\pi\) | ||||
0.0223394 | + | 0.999750i | \(0.492889\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.3118 | −0.613051 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.7567 | 1.61436 | 0.807180 | − | 0.590305i | \(-0.200992\pi\) | ||||
0.807180 | + | 0.590305i | \(0.200992\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.34916 | −0.185280 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.0283 | −0.639067 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −45.8506 | −1.94275 | −0.971376 | − | 0.237545i | \(-0.923657\pi\) | ||||
−0.971376 | + | 0.237545i | \(0.923657\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −53.9819 | −2.28319 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −33.3027 | −1.40354 | −0.701772 | − | 0.712402i | \(-0.747607\pi\) | ||||
−0.701772 | + | 0.712402i | \(0.747607\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.03735 | −0.0857118 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.6700 | 0.992300 | 0.496150 | − | 0.868237i | \(-0.334747\pi\) | ||||
0.496150 | + | 0.868237i | \(0.334747\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.5671 | 0.609613 | 0.304807 | − | 0.952414i | \(-0.401408\pi\) | ||||
0.304807 | + | 0.952414i | \(0.401408\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.70739 | 0.0712031 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.7639 | −0.573000 | −0.286500 | − | 0.958080i | \(-0.592492\pi\) | ||||
−0.286500 | + | 0.958080i | \(0.592492\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.23421 | 0.217152 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.6983 | 0.525911 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.04748 | 0.0432339 | 0.0216170 | − | 0.999766i | \(-0.493119\pi\) | ||||
0.0216170 | + | 0.999766i | \(0.493119\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.3118 | −1.49620 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.3865 | −0.590783 | −0.295391 | − | 0.955376i | \(-0.595450\pi\) | ||||
−0.295391 | + | 0.955376i | \(0.595450\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.38650 | 0.343813 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.98080 | 0.244369 | 0.122184 | − | 0.992507i | \(-0.461010\pi\) | ||||
0.122184 | + | 0.992507i | \(0.461010\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.08482 | −0.288996 | −0.144498 | − | 0.989505i | \(-0.546157\pi\) | ||||
−0.144498 | + | 0.989505i | \(0.546157\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.3118 | 0.703825 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.7175 | 1.32796 | 0.663982 | − | 0.747749i | \(-0.268865\pi\) | ||||
0.663982 | + | 0.747749i | \(0.268865\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.41478 | −0.138147 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.22699 | 0.372675 | 0.186337 | − | 0.982486i | \(-0.440338\pi\) | ||||
0.186337 | + | 0.982486i | \(0.440338\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.281683 | −0.0113401 | −0.00567006 | − | 0.999984i | \(-0.501805\pi\) | ||||
−0.00567006 | + | 0.999984i | \(0.501805\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.2462 | 0.853957 | 0.426978 | − | 0.904262i | \(-0.359578\pi\) | ||||
0.426978 | + | 0.904262i | \(0.359578\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.41478 | −0.136810 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −44.0275 | −1.75549 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.8688 | 1.50753 | 0.753766 | − | 0.657143i | \(-0.228235\pi\) | ||||
0.753766 | + | 0.657143i | \(0.228235\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.26434 | −0.0501737 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.4249 | 1.04699 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.7658 | 1.45216 | 0.726081 | − | 0.687609i | \(-0.241340\pi\) | ||||
0.726081 | + | 0.687609i | \(0.241340\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.9728 | −0.984830 | −0.492415 | − | 0.870360i | \(-0.663886\pi\) | ||||
−0.492415 | + | 0.870360i | \(0.663886\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.56522 | 0.140163 | 0.0700816 | − | 0.997541i | \(-0.477674\pi\) | ||||
0.0700816 | + | 0.997541i | \(0.477674\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 55.5663 | 2.18117 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.5652 | 0.843912 | 0.421956 | − | 0.906616i | \(-0.361344\pi\) | ||||
0.421956 | + | 0.906616i | \(0.361344\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.70739 | 0.0667132 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.4623 | 1.57619 | 0.788093 | − | 0.615556i | \(-0.211069\pi\) | ||||
0.788093 | + | 0.615556i | \(0.211069\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.1987 | 1.01901 | 0.509506 | − | 0.860467i | \(-0.329828\pi\) | ||||
0.509506 | + | 0.860467i | \(0.329828\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.74474 | −0.222771 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.70739 | 0.0661104 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33.9819 | 1.31185 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.35823 | 0.129450 | 0.0647251 | − | 0.997903i | \(-0.479383\pi\) | ||||
0.0647251 | + | 0.997903i | \(0.479383\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.6965 | 0.603264 | 0.301632 | − | 0.953424i | \(-0.402469\pi\) | ||||
0.301632 | + | 0.953424i | \(0.402469\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.2371 | −0.776629 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 40.1998 | 1.53820 | 0.769101 | − | 0.639128i | \(-0.220704\pi\) | ||||
0.769101 | + | 0.639128i | \(0.220704\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.7639 | −0.831557 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.0000 | 0.457164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.7084 | 0.977995 | 0.488998 | − | 0.872285i | \(-0.337363\pi\) | ||||
0.488998 | + | 0.872285i | \(0.337363\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.6983 | −0.633403 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.52867 | 0.247291 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.51775 | 0.321711 | 0.160855 | − | 0.986978i | \(-0.448575\pi\) | ||||
0.160855 | + | 0.986978i | \(0.448575\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.1587 | 1.13746 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.6773 | −0.589604 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.0848 | 1.31764 | 0.658819 | − | 0.752301i | \(-0.271056\pi\) | ||||
0.658819 | + | 0.752301i | \(0.271056\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.2553 | 0.533864 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 26.7549 | 1.00058 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.3292 | −1.16838 | −0.584190 | − | 0.811617i | \(-0.698588\pi\) | ||||
−0.584190 | + | 0.811617i | \(0.698588\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.82234 | −0.179593 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.00000 | 0.0371391 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.9627 | −0.517846 | −0.258923 | − | 0.965898i | \(-0.583368\pi\) | ||||
−0.258923 | + | 0.965898i | \(0.583368\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 68.1624 | 2.52108 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.5761 | −1.09242 | −0.546210 | − | 0.837648i | \(-0.683930\pi\) | ||||
−0.546210 | + | 0.837648i | \(0.683930\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.3684 | 1.11863 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.66819 | −0.245293 | −0.122647 | − | 0.992450i | \(-0.539138\pi\) | ||||
−0.122647 | + | 0.992450i | \(0.539138\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.7002 | 1.23634 | 0.618170 | − | 0.786045i | \(-0.287874\pi\) | ||||
0.618170 | + | 0.786045i | \(0.287874\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0000 | −0.659469 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.02827 | 0.256808 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.3129 | −1.76296 | −0.881481 | − | 0.472220i | \(-0.843453\pi\) | ||||
−0.881481 | + | 0.472220i | \(0.843453\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.44305 | 0.234487 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.3985 | 1.54100 | 0.770500 | − | 0.637440i | \(-0.220007\pi\) | ||||
0.770500 | + | 0.637440i | \(0.220007\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.7933 | 1.62375 | 0.811877 | − | 0.583828i | \(-0.198446\pi\) | ||||
0.811877 | + | 0.583828i | \(0.198446\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.9043 | −0.684380 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 52.5105 | 1.89605 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.2080 | −1.88267 | −0.941335 | − | 0.337473i | \(-0.890428\pi\) | ||||
−0.941335 | + | 0.337473i | \(0.890428\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.2179 | 0.871058 | 0.435529 | − | 0.900175i | \(-0.356561\pi\) | ||||
0.435529 | + | 0.900175i | \(0.356561\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.34916 | 0.299911 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.47213 | −0.160231 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.2270 | −0.687996 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.7357 | 0.383172 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.43398 | −0.0511159 | −0.0255579 | − | 0.999673i | \(-0.508136\pi\) | ||||
−0.0255579 | + | 0.999673i | \(0.508136\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.69110 | −0.0956845 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.1131 | 1.14037 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.4732 | 0.512666 | 0.256333 | − | 0.966588i | \(-0.417486\pi\) | ||||
0.256333 | + | 0.966588i | \(0.417486\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.31181 | 0.152541 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35.8397 | 1.26476 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.25526 | 0.0794876 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −49.2654 | −1.73208 | −0.866039 | − | 0.499976i | \(-0.833342\pi\) | ||||
−0.866039 | + | 0.499976i | \(0.833342\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.69832 | −0.164980 | −0.0824901 | − | 0.996592i | \(-0.526287\pi\) | ||||
−0.0824901 | + | 0.996592i | \(0.526287\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.90611 | 0.136825 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −46.6911 | −1.63351 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.7730 | −1.21359 | −0.606793 | − | 0.794860i | \(-0.707544\pi\) | ||||
−0.606793 | + | 0.794860i | \(0.707544\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44.1323 | −1.53836 | −0.769178 | − | 0.639035i | \(-0.779334\pi\) | ||||
−0.769178 | + | 0.639035i | \(0.779334\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.6610 | −0.787999 | −0.394000 | − | 0.919111i | \(-0.628909\pi\) | ||||
−0.394000 | + | 0.919111i | \(0.628909\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.9144 | −1.31682 | −0.658410 | − | 0.752659i | \(-0.728771\pi\) | ||||
−0.658410 | + | 0.752659i | \(0.728771\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −33.3665 | −1.15608 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.51960 | 0.191014 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.7175 | −1.06049 | −0.530243 | − | 0.847846i | \(-0.677899\pi\) | ||||
−0.530243 | + | 0.847846i | \(0.677899\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.2835 | 0.422567 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.8669 | 0.785716 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.8397 | −0.405859 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.25341 | 0.0429159 | 0.0214579 | − | 0.999770i | \(-0.493169\pi\) | ||||
0.0214579 | + | 0.999770i | \(0.493169\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.85783 | 0.268418 | 0.134209 | − | 0.990953i | \(-0.457151\pi\) | ||||
0.134209 | + | 0.990953i | \(0.457151\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.4913 | −0.494438 | −0.247219 | − | 0.968960i | \(-0.579517\pi\) | ||||
−0.247219 | + | 0.968960i | \(0.579517\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.69646 | 0.330071 | 0.165036 | − | 0.986288i | \(-0.447226\pi\) | ||||
0.165036 | + | 0.986288i | \(0.447226\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.80128 | −0.197250 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 60.5380 | 2.05361 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.6983 | 0.972405 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.32088 | 0.0446540 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.27341 | 0.211838 | 0.105919 | − | 0.994375i | \(-0.466222\pi\) | ||||
0.105919 | + | 0.994375i | \(0.466222\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.5953 | −0.660184 | −0.330092 | − | 0.943949i | \(-0.607080\pi\) | ||||
−0.330092 | + | 0.943949i | \(0.607080\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.24619 | −0.176548 | −0.0882742 | − | 0.996096i | \(-0.528135\pi\) | ||||
−0.0882742 | + | 0.996096i | \(0.528135\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.6044 | 1.09475 | 0.547375 | − | 0.836888i | \(-0.315627\pi\) | ||||
0.547375 | + | 0.836888i | \(0.315627\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.67004 | −0.0560114 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.95358 | −0.0988378 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.0565 | −0.469859 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.34916 | 0.278460 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.1523 | −0.504796 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.08482 | −0.235507 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.96265 | −0.0651688 | −0.0325844 | − | 0.999469i | \(-0.510374\pi\) | ||||
−0.0325844 | + | 0.999469i | \(0.510374\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50.7066 | −1.67998 | −0.839992 | − | 0.542599i | \(-0.817440\pi\) | ||||
−0.839992 | + | 0.542599i | \(0.817440\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.0848 | −0.697806 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.25526 | 0.0744754 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.2371 | 1.85509 | 0.927546 | − | 0.373710i | \(-0.121914\pi\) | ||||
0.927546 | + | 0.373710i | \(0.121914\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18.1696 | −0.598061 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.93438 | −0.228001 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.34009 | 0.175203 | 0.0876013 | − | 0.996156i | \(-0.472080\pi\) | ||||
0.0876013 | + | 0.996156i | \(0.472080\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.8560 | 0.749074 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −33.7831 | −1.10483 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.01013 | −0.0983366 | −0.0491683 | − | 0.998791i | \(-0.515657\pi\) | ||||
−0.0491683 | + | 0.998791i | \(0.515657\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.829557 | 0.0270428 | 0.0135214 | − | 0.999909i | \(-0.495696\pi\) | ||||
0.0135214 | + | 0.999909i | \(0.495696\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.75566 | 0.0571723 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.3027 | −0.692246 | −0.346123 | − | 0.938189i | \(-0.612502\pi\) | ||||
−0.346123 | + | 0.938189i | \(0.612502\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.8688 | 1.09943 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.0203 | 1.29638 | 0.648192 | − | 0.761477i | \(-0.275526\pi\) | ||||
0.648192 | + | 0.761477i | \(0.275526\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.547875 | 0.0177288 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.7476 | −0.928310 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 38.7084 | 1.24866 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.40571 | 0.141825 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.0365 | −0.998068 | −0.499034 | − | 0.866582i | \(-0.666312\pi\) | ||||
−0.499034 | + | 0.866582i | \(0.666312\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.66819 | 0.0856262 | 0.0428131 | − | 0.999083i | \(-0.486368\pi\) | ||||
0.0428131 | + | 0.999083i | \(0.486368\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.0565 | −0.707100 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −45.6519 | −1.46053 | −0.730267 | − | 0.683162i | \(-0.760604\pi\) | ||||
−0.730267 | + | 0.683162i | \(0.760604\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.7557 | 0.439633 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.4521 | 0.556636 | 0.278318 | − | 0.960489i | \(-0.410223\pi\) | ||||
0.278318 | + | 0.960489i | \(0.410223\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.64177 | 0.147899 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.3300 | 0.582859 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.49960 | −0.142935 | −0.0714673 | − | 0.997443i | \(-0.522768\pi\) | ||||
−0.0714673 | + | 0.997443i | \(0.522768\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.4431 | 0.584684 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.1896 | −0.671083 | −0.335541 | − | 0.942025i | \(-0.608919\pi\) | ||||
−0.335541 | + | 0.942025i | \(0.608919\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5220.2.a.x.1.3 | 3 | ||
3.2 | odd | 2 | 580.2.a.c.1.3 | ✓ | 3 | ||
12.11 | even | 2 | 2320.2.a.m.1.1 | 3 | |||
15.2 | even | 4 | 2900.2.c.f.349.1 | 6 | |||
15.8 | even | 4 | 2900.2.c.f.349.6 | 6 | |||
15.14 | odd | 2 | 2900.2.a.g.1.1 | 3 | |||
24.5 | odd | 2 | 9280.2.a.bk.1.1 | 3 | |||
24.11 | even | 2 | 9280.2.a.bw.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
580.2.a.c.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
2320.2.a.m.1.1 | 3 | 12.11 | even | 2 | |||
2900.2.a.g.1.1 | 3 | 15.14 | odd | 2 | |||
2900.2.c.f.349.1 | 6 | 15.2 | even | 4 | |||
2900.2.c.f.349.6 | 6 | 15.8 | even | 4 | |||
5220.2.a.x.1.3 | 3 | 1.1 | even | 1 | trivial | ||
9280.2.a.bk.1.1 | 3 | 24.5 | odd | 2 | |||
9280.2.a.bw.1.3 | 3 | 24.11 | even | 2 |