Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, 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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.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: | \(64.1677830643\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 37 x^{13} + 39 x^{12} + 537 x^{11} - 616 x^{10} - 3853 x^{9} + 4929 x^{8} + \cdots + 3381 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1148) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-0.741382\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-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 | ||||||||
\(3\) | 0.741382 | 0.428037 | 0.214019 | − | 0.976830i | \(-0.431345\pi\) | ||||
0.214019 | + | 0.976830i | \(0.431345\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.48663 | −1.11205 | −0.556026 | − | 0.831165i | \(-0.687675\pi\) | ||||
−0.556026 | + | 0.831165i | \(0.687675\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.45035 | −0.816784 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.32934 | −1.60686 | −0.803428 | − | 0.595401i | \(-0.796993\pi\) | ||||
−0.803428 | + | 0.595401i | \(0.796993\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.45475 | 1.23553 | 0.617763 | − | 0.786364i | \(-0.288039\pi\) | ||||
0.617763 | + | 0.786364i | \(0.288039\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.84354 | −0.476000 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.22789 | −1.26795 | −0.633975 | − | 0.773354i | \(-0.718578\pi\) | ||||
−0.633975 | + | 0.773354i | \(0.718578\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.97370 | 0.452798 | 0.226399 | − | 0.974035i | \(-0.427305\pi\) | ||||
0.226399 | + | 0.974035i | \(0.427305\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.97574 | −1.45454 | −0.727271 | − | 0.686351i | \(-0.759212\pi\) | ||||
−0.727271 | + | 0.686351i | \(0.759212\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.18331 | 0.236662 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.04079 | −0.777651 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.94874 | 0.733262 | 0.366631 | − | 0.930366i | \(-0.380511\pi\) | ||||
0.366631 | + | 0.930366i | \(0.380511\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.03917 | 0.725456 | 0.362728 | − | 0.931895i | \(-0.381845\pi\) | ||||
0.362728 | + | 0.931895i | \(0.381845\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.95108 | −0.687794 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.44085 | 1.38767 | 0.693833 | − | 0.720136i | \(-0.255920\pi\) | ||||
0.693833 | + | 0.720136i | \(0.255920\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.30267 | 0.528851 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.5890 | −1.61481 | −0.807406 | − | 0.589996i | \(-0.799129\pi\) | ||||
−0.807406 | + | 0.589996i | \(0.799129\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.09311 | 0.908307 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.67102 | −0.681338 | −0.340669 | − | 0.940183i | \(-0.610654\pi\) | ||||
−0.340669 | + | 0.940183i | \(0.610654\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.87586 | −0.542729 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.15249 | 0.295667 | 0.147833 | − | 0.989012i | \(-0.452770\pi\) | ||||
0.147833 | + | 0.989012i | \(0.452770\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.2521 | 1.78691 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.46327 | 0.193814 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.06901 | 0.399551 | 0.199775 | − | 0.979842i | \(-0.435979\pi\) | ||||
0.199775 | + | 0.979842i | \(0.435979\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0271 | −1.53992 | −0.769958 | − | 0.638094i | \(-0.779723\pi\) | ||||
−0.769958 | + | 0.638094i | \(0.779723\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.0773 | −1.37397 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.6266 | −1.90909 | −0.954546 | − | 0.298065i | \(-0.903659\pi\) | ||||
−0.954546 | + | 0.298065i | \(0.903659\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.17169 | −0.622598 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.549015 | −0.0651560 | −0.0325780 | − | 0.999469i | \(-0.510372\pi\) | ||||
−0.0325780 | + | 0.999469i | \(0.510372\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.10132 | −0.714106 | −0.357053 | − | 0.934084i | \(-0.616218\pi\) | ||||
−0.357053 | + | 0.934084i | \(0.616218\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.877284 | 0.101300 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.5674 | 1.63896 | 0.819478 | − | 0.573110i | \(-0.194263\pi\) | ||||
0.819478 | + | 0.573110i | \(0.194263\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.35529 | 0.483921 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.2369 | −1.78223 | −0.891116 | − | 0.453776i | \(-0.850077\pi\) | ||||
−0.891116 | + | 0.453776i | \(0.850077\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.9998 | 1.41003 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.92752 | 0.313863 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.02391 | 0.320534 | 0.160267 | − | 0.987074i | \(-0.448764\pi\) | ||||
0.160267 | + | 0.987074i | \(0.448764\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.99457 | 0.310522 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.90786 | −0.503535 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.3079 | 1.14814 | 0.574070 | − | 0.818806i | \(-0.305364\pi\) | ||||
0.574070 | + | 0.818806i | \(0.305364\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.0588 | 1.31246 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.36685 | 0.932037 | 0.466018 | − | 0.884775i | \(-0.345688\pi\) | ||||
0.466018 | + | 0.884775i | \(0.345688\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.128628 | 0.0126741 | 0.00633703 | − | 0.999980i | \(-0.497983\pi\) | ||||
0.00633703 | + | 0.999980i | \(0.497983\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.7155 | 1.80930 | 0.904649 | − | 0.426157i | \(-0.140133\pi\) | ||||
0.904649 | + | 0.426157i | \(0.140133\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.5776 | 1.01315 | 0.506577 | − | 0.862194i | \(-0.330910\pi\) | ||||
0.506577 | + | 0.862194i | \(0.330910\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.25789 | 0.593973 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.86842 | −0.552054 | −0.276027 | − | 0.961150i | \(-0.589018\pi\) | ||||
−0.276027 | + | 0.961150i | \(0.589018\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.3460 | 1.61753 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.9157 | −1.00916 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.4019 | 1.58199 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.741382 | −0.0668482 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.49068 | 0.848873 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.77348 | 0.157371 | 0.0786856 | − | 0.996899i | \(-0.474928\pi\) | ||||
0.0786856 | + | 0.996899i | \(0.474928\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.85051 | −0.691199 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.95356 | −0.520165 | −0.260083 | − | 0.965586i | \(-0.583750\pi\) | ||||
−0.260083 | + | 0.965586i | \(0.583750\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.0479 | 0.864789 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22.2147 | 1.89793 | 0.948965 | − | 0.315380i | \(-0.102132\pi\) | ||||
0.948965 | + | 0.315380i | \(0.102132\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.81730 | −0.747873 | −0.373937 | − | 0.927454i | \(-0.621992\pi\) | ||||
−0.373937 | + | 0.927454i | \(0.621992\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.46301 | −0.291638 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.7409 | −1.98531 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.81903 | −0.815426 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.1559 | 0.995853 | 0.497926 | − | 0.867219i | \(-0.334095\pi\) | ||||
0.497926 | + | 0.867219i | \(0.334095\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.8222 | 1.61311 | 0.806553 | − | 0.591161i | \(-0.201330\pi\) | ||||
0.806553 | + | 0.591161i | \(0.201330\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.8102 | 1.03564 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.0439 | −0.806746 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.1217 | −1.12704 | −0.563519 | − | 0.826103i | \(-0.690553\pi\) | ||||
−0.563519 | + | 0.826103i | \(0.690553\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.59581 | 0.126556 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.03291 | −0.315882 | −0.157941 | − | 0.987449i | \(-0.550486\pi\) | ||||
−0.157941 | + | 0.987449i | \(0.550486\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.82485 | 0.764864 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.4677 | −1.50646 | −0.753229 | − | 0.657758i | \(-0.771505\pi\) | ||||
−0.753229 | + | 0.657758i | \(0.771505\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.84483 | 0.526525 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.83626 | −0.369838 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.03063 | −0.230415 | −0.115207 | − | 0.993341i | \(-0.536753\pi\) | ||||
−0.115207 | + | 0.993341i | \(0.536753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.27531 | 0.171022 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.73289 | −0.353753 | −0.176876 | − | 0.984233i | \(-0.556599\pi\) | ||||
−0.176876 | + | 0.984233i | \(0.556599\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.6349 | 1.75677 | 0.878383 | − | 0.477957i | \(-0.158623\pi\) | ||||
0.878383 | + | 0.477957i | \(0.158623\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.91670 | −0.659141 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −20.9892 | −1.54316 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.8612 | 2.03741 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.6528 | 1.42203 | 0.711014 | − | 0.703178i | \(-0.248236\pi\) | ||||
0.711014 | + | 0.703178i | \(0.248236\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.7887 | −1.56839 | −0.784193 | − | 0.620517i | \(-0.786923\pi\) | ||||
−0.784193 | + | 0.620517i | \(0.786923\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.21251 | −0.588110 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.4791 | −1.17409 | −0.587044 | − | 0.809555i | \(-0.699709\pi\) | ||||
−0.587044 | + | 0.809555i | \(0.699709\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.5780 | 1.03341 | 0.516705 | − | 0.856164i | \(-0.327158\pi\) | ||||
0.516705 | + | 0.856164i | \(0.327158\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.5853 | −0.817162 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.48663 | 0.173673 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 17.0930 | 1.18805 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.5185 | −0.727582 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.7405 | 1.29015 | 0.645075 | − | 0.764119i | \(-0.276826\pi\) | ||||
0.645075 | + | 0.764119i | \(0.276826\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.407029 | −0.0278892 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 26.3310 | 1.79576 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.52341 | −0.305664 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.2890 | −1.56659 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.6617 | 1.51754 | 0.758770 | − | 0.651359i | \(-0.225801\pi\) | ||||
0.758770 | + | 0.651359i | \(0.225801\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.89952 | −0.193302 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.4497 | −1.09180 | −0.545901 | − | 0.837850i | \(-0.683813\pi\) | ||||
−0.545901 | + | 0.837850i | \(0.683813\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.3549 | 1.34509 | 0.672546 | − | 0.740055i | \(-0.265201\pi\) | ||||
0.672546 | + | 0.740055i | \(0.265201\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.08432 | 0.136548 | 0.0682740 | − | 0.997667i | \(-0.478251\pi\) | ||||
0.0682740 | + | 0.997667i | \(0.478251\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.6151 | 0.757684 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.8000 | 0.701534 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.18128 | −0.0764108 | −0.0382054 | − | 0.999270i | \(-0.512164\pi\) | ||||
−0.0382054 | + | 0.999270i | \(0.512164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.25967 | −0.274390 | −0.137195 | − | 0.990544i | \(-0.543809\pi\) | ||||
−0.137195 | + | 0.990544i | \(0.543809\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.3513 | 0.984787 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.79235 | 0.559444 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.0377 | −0.762861 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.1506 | 1.58749 | 0.793745 | − | 0.608251i | \(-0.208128\pi\) | ||||
0.793745 | + | 0.608251i | \(0.208128\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37.1761 | 2.33724 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.63782 | 0.603544 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.04026 | −0.127268 | −0.0636338 | − | 0.997973i | \(-0.520269\pi\) | ||||
−0.0636338 | + | 0.997973i | \(0.520269\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.67580 | −0.598917 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.76783 | 0.417322 | 0.208661 | − | 0.977988i | \(-0.433089\pi\) | ||||
0.208661 | + | 0.977988i | \(0.433089\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.35243 | −0.328797 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.24188 | 0.137201 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.32017 | −0.568261 | −0.284130 | − | 0.958786i | \(-0.591705\pi\) | ||||
−0.284130 | + | 0.958786i | \(0.591705\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.55575 | 0.519724 | 0.259862 | − | 0.965646i | \(-0.416323\pi\) | ||||
0.259862 | + | 0.965646i | \(0.416323\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.30626 | −0.380282 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.8689 | 1.43414 | 0.717071 | − | 0.697000i | \(-0.245482\pi\) | ||||
0.717071 | + | 0.697000i | \(0.245482\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.89739 | −0.592541 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.77742 | −0.344652 | −0.172326 | − | 0.985040i | \(-0.555128\pi\) | ||||
−0.172326 | + | 0.985040i | \(0.555128\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.9250 | −0.768311 | −0.384156 | − | 0.923268i | \(-0.625507\pi\) | ||||
−0.384156 | + | 0.923268i | \(0.625507\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.63860 | −0.215532 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.3308 | 0.607696 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.38345 | 0.491447 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.1943 | −1.06292 | −0.531460 | − | 0.847083i | \(-0.678357\pi\) | ||||
−0.531460 | + | 0.847083i | \(0.678357\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.63147 | −0.444321 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 21.5348 | 1.24957 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −31.0752 | −1.79712 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.94442 | 0.398946 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 29.9070 | 1.71247 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.8287 | −1.01754 | −0.508769 | − | 0.860903i | \(-0.669899\pi\) | ||||
−0.508769 | + | 0.860903i | \(0.669899\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0953623 | 0.00542497 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.8260 | 1.40775 | 0.703877 | − | 0.710322i | \(-0.251451\pi\) | ||||
0.703877 | + | 0.710322i | \(0.251451\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.38319 | 0.304276 | 0.152138 | − | 0.988359i | \(-0.451384\pi\) | ||||
0.152138 | + | 0.988359i | \(0.451384\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.6539 | 1.16004 | 0.580019 | − | 0.814603i | \(-0.303045\pi\) | ||||
0.580019 | + | 0.814603i | \(0.303045\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.0442 | −1.17825 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.8754 | 0.774447 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.3183 | −0.574125 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.27135 | 0.292402 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.84208 | 0.433668 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.2209 | −1.11144 | −0.555721 | − | 0.831369i | \(-0.687558\pi\) | ||||
−0.555721 | + | 0.831369i | \(0.687558\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −20.6831 | −1.13342 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 38.8575 | 2.12301 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.9748 | 0.652308 | 0.326154 | − | 0.945317i | \(-0.394247\pi\) | ||||
0.326154 | + | 0.945317i | \(0.394247\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.35074 | −0.236300 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.5261 | −1.16570 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.8600 | 0.692362 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.01201 | −0.108011 | −0.0540053 | − | 0.998541i | \(-0.517199\pi\) | ||||
−0.0540053 | + | 0.998541i | \(0.517199\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.51102 | −0.348527 | −0.174264 | − | 0.984699i | \(-0.555754\pi\) | ||||
−0.174264 | + | 0.984699i | \(0.555754\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.0007 | −0.960808 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.0590 | 1.06763 | 0.533816 | − | 0.845601i | \(-0.320757\pi\) | ||||
0.533816 | + | 0.845601i | \(0.320757\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.36519 | 0.0724570 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.73717 | 0.0916843 | 0.0458422 | − | 0.998949i | \(-0.485403\pi\) | ||||
0.0458422 | + | 0.998949i | \(0.485403\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.1045 | −0.794974 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.9014 | 0.677150 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.1717 | 0.794124 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.24439 | −0.482553 | −0.241276 | − | 0.970456i | \(-0.577566\pi\) | ||||
−0.241276 | + | 0.970456i | \(0.577566\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.45035 | 0.127560 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.407031 | −0.0210753 | −0.0105376 | − | 0.999944i | \(-0.503354\pi\) | ||||
−0.0105376 | + | 0.999944i | \(0.503354\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.03622 | 0.363349 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.5907 | 0.905965 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.4222 | 0.946284 | 0.473142 | − | 0.880986i | \(-0.343120\pi\) | ||||
0.473142 | + | 0.880986i | \(0.343120\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.31483 | 0.0673607 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.29414 | −0.117225 | −0.0586124 | − | 0.998281i | \(-0.518668\pi\) | ||||
−0.0586124 | + | 0.998281i | \(0.518668\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 25.9469 | 1.31895 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.05178 | −0.357540 | −0.178770 | − | 0.983891i | \(-0.557212\pi\) | ||||
−0.178770 | + | 0.983891i | \(0.557212\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.4684 | 1.84429 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.41386 | −0.222650 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −36.2236 | −1.82261 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.9163 | −0.949383 | −0.474691 | − | 0.880152i | \(-0.657440\pi\) | ||||
−0.474691 | + | 0.880152i | \(0.657440\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.7668 | −1.43655 | −0.718274 | − | 0.695761i | \(-0.755067\pi\) | ||||
−0.718274 | + | 0.695761i | \(0.755067\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.9935 | 0.896321 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.8300 | −0.538146 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −44.9842 | −2.22978 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.08393 | −0.251384 | −0.125692 | − | 0.992069i | \(-0.540115\pi\) | ||||
−0.125692 | + | 0.992069i | \(0.540115\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.4696 | 0.812385 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 40.3751 | 1.98194 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.53699 | −0.320118 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.5598 | 1.54180 | 0.770899 | − | 0.636958i | \(-0.219807\pi\) | ||||
0.770899 | + | 0.636958i | \(0.219807\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.7675 | 1.54825 | 0.774127 | − | 0.633031i | \(-0.218189\pi\) | ||||
0.774127 | + | 0.633031i | \(0.218189\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.4456 | 0.556506 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.18621 | −0.300075 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17.6011 | −0.849788 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.89423 | −0.235747 | −0.117873 | − | 0.993029i | \(-0.537608\pi\) | ||||
−0.117873 | + | 0.993029i | \(0.537608\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.3722 | 0.738739 | 0.369369 | − | 0.929283i | \(-0.379574\pi\) | ||||
0.369369 | + | 0.929283i | \(0.379574\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.27965 | −0.349033 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.7680 | −0.658614 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.49024 | −0.357490 | −0.178745 | − | 0.983895i | \(-0.557204\pi\) | ||||
−0.178745 | + | 0.983895i | \(0.557204\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.33920 | −0.206162 | −0.103081 | − | 0.994673i | \(-0.532870\pi\) | ||||
−0.103081 | + | 0.994673i | \(0.532870\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.51935 | −0.356451 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.01219 | 0.426262 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.4206 | −0.869324 | −0.434662 | − | 0.900594i | \(-0.643132\pi\) | ||||
−0.434662 | + | 0.900594i | \(0.643132\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.32934 | 0.250949 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.6958 | 0.690469 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.3293 | 1.60586 | 0.802929 | − | 0.596075i | \(-0.203274\pi\) | ||||
0.802929 | + | 0.596075i | \(0.203274\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 21.1248 | 0.986022 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.11137 | 0.144911 | 0.0724556 | − | 0.997372i | \(-0.476916\pi\) | ||||
0.0724556 | + | 0.997372i | \(0.476916\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.1968 | −0.752730 | −0.376365 | − | 0.926471i | \(-0.622826\pi\) | ||||
−0.376365 | + | 0.926471i | \(0.622826\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.44637 | −0.345317 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.3607 | −1.26610 | −0.633052 | − | 0.774110i | \(-0.718198\pi\) | ||||
−0.633052 | + | 0.774110i | \(0.718198\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.4696 | −0.482414 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 56.4325 | 2.59477 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.33550 | 0.107160 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.27435 | −0.241496 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.3553 | 0.473147 | 0.236573 | − | 0.971614i | \(-0.423976\pi\) | ||||
0.236573 | + | 0.971614i | \(0.423976\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 37.6019 | 1.71450 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −28.1185 | −1.27679 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.5693 | 0.524255 | 0.262128 | − | 0.965033i | \(-0.415576\pi\) | ||||
0.262128 | + | 0.965033i | \(0.415576\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.98993 | −0.135209 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.18896 | −0.0536571 | −0.0268286 | − | 0.999640i | \(-0.508541\pi\) | ||||
−0.0268286 | + | 0.999640i | \(0.508541\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.6436 | −0.929740 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −32.4723 | −1.45952 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.5433 | 0.695812 | 0.347906 | − | 0.937529i | \(-0.386893\pi\) | ||||
0.347906 | + | 0.937529i | \(0.386893\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.4330 | −0.644820 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.661991 | 0.0295167 | 0.0147584 | − | 0.999891i | \(-0.495302\pi\) | ||||
0.0147584 | + | 0.999891i | \(0.495302\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.2919 | −1.03647 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.07463 | 0.225372 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −42.2412 | −1.87231 | −0.936154 | − | 0.351590i | \(-0.885641\pi\) | ||||
−0.936154 | + | 0.351590i | \(0.885641\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.97532 | −0.352119 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.319849 | −0.0140942 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.8934 | 1.09481 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.24685 | −0.0986260 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.19485 | −0.139969 | −0.0699844 | − | 0.997548i | \(-0.522295\pi\) | ||||
−0.0699844 | + | 0.997548i | \(0.522295\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.6853 | 0.991960 | 0.495980 | − | 0.868334i | \(-0.334809\pi\) | ||||
0.495980 | + | 0.868334i | \(0.334809\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.1163 | −0.919842 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.6609 | 1.11569 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.52015 | −0.326347 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.45475 | −0.192957 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −46.5385 | −2.01204 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.50888 | −0.151419 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.75666 | 0.419472 | 0.209736 | − | 0.977758i | \(-0.432740\pi\) | ||||
0.209736 | + | 0.977758i | \(0.432740\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.5225 | 0.751961 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.3027 | −1.12668 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.2506 | −1.20791 | −0.603954 | − | 0.797020i | \(-0.706409\pi\) | ||||
−0.603954 | + | 0.797020i | \(0.706409\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 29.4707 | 1.25778 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.79363 | 0.332020 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.5610 | −0.660529 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.14602 | 0.133301 | 0.0666505 | − | 0.997776i | \(-0.478769\pi\) | ||||
0.0666505 | + | 0.997776i | \(0.478769\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −47.1715 | −1.99514 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.6558 | 0.872088 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.0597 | 0.676835 | 0.338418 | − | 0.940996i | \(-0.390108\pi\) | ||||
0.338418 | + | 0.940996i | \(0.390108\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.5926 | 0.613913 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.87323 | 0.371985 | 0.185993 | − | 0.982551i | \(-0.440450\pi\) | ||||
0.185993 | + | 0.982551i | \(0.440450\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.5143 | −0.900343 | −0.450172 | − | 0.892942i | \(-0.648637\pi\) | ||||
−0.450172 | + | 0.892942i | \(0.648637\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.5702 | 0.608681 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.25445 | −0.344234 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.1462 | −0.505654 | −0.252827 | − | 0.967512i | \(-0.581360\pi\) | ||||
−0.252827 | + | 0.967512i | \(0.581360\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.1538 | −0.671327 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.4713 | −0.475094 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 27.1433 | 1.12224 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.2739 | 1.45591 | 0.727955 | − | 0.685625i | \(-0.240471\pi\) | ||||
0.727955 | + | 0.685625i | \(0.240471\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.97211 | 0.328485 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.2173 | −0.502553 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.7141 | −0.645302 | −0.322651 | − | 0.946518i | \(-0.604574\pi\) | ||||
−0.322651 | + | 0.946518i | \(0.604574\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.8079 | 0.442338 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.99253 | −0.203989 | −0.101995 | − | 0.994785i | \(-0.532522\pi\) | ||||
−0.101995 | + | 0.994785i | \(0.532522\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.58505 | −0.187028 | −0.0935140 | − | 0.995618i | \(-0.529810\pi\) | ||||
−0.0935140 | + | 0.995618i | \(0.529810\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 38.2906 | 1.55932 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −43.2720 | −1.75926 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.5291 | −0.833249 | −0.416624 | − | 0.909079i | \(-0.636787\pi\) | ||||
−0.416624 | + | 0.909079i | \(0.636787\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.8082 | −0.841811 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.8528 | −1.52886 | −0.764430 | − | 0.644707i | \(-0.776980\pi\) | ||||
−0.764430 | + | 0.644707i | \(0.776980\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.84354 | 0.0743387 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.91820 | 0.318775 | 0.159387 | − | 0.987216i | \(-0.449048\pi\) | ||||
0.159387 | + | 0.987216i | \(0.449048\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.12484 | −0.366758 | −0.183379 | − | 0.983042i | \(-0.558704\pi\) | ||||
−0.183379 | + | 0.983042i | \(0.558704\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.1875 | 1.13113 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.5163 | −1.18065 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.79824 | −0.311432 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −44.1278 | −1.75949 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.35091 | −0.0537790 | −0.0268895 | − | 0.999638i | \(-0.508560\pi\) | ||||
−0.0268895 | + | 0.999638i | \(0.508560\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.8939 | 0.552232 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.40999 | −0.175005 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.34528 | 0.0532184 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.5152 | 1.16578 | 0.582890 | − | 0.812551i | \(-0.301922\pi\) | ||||
0.582890 | + | 0.812551i | \(0.301922\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.8306 | 0.505988 | 0.252994 | − | 0.967468i | \(-0.418585\pi\) | ||||
0.252994 | + | 0.967468i | \(0.418585\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.5213 | 0.768650 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.2023 | −1.50189 | −0.750943 | − | 0.660367i | \(-0.770401\pi\) | ||||
−0.750943 | + | 0.660367i | \(0.770401\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.3558 | −0.642021 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.5985 | 0.414750 | 0.207375 | − | 0.978261i | \(-0.433508\pi\) | ||||
0.207375 | + | 0.978261i | \(0.433508\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.8043 | 0.578451 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.9504 | 0.583271 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.7450 | 0.847065 | 0.423533 | − | 0.905881i | \(-0.360790\pi\) | ||||
0.423533 | + | 0.905881i | \(0.360790\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.5702 | 0.800089 | 0.400045 | − | 0.916496i | \(-0.368995\pi\) | ||||
0.400045 | + | 0.916496i | \(0.368995\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.2660 | −0.670557 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −27.5454 | −1.06656 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.8010 | 0.649563 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 64.0967 | 2.47443 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.627387 | 0.0241840 | 0.0120920 | − | 0.999927i | \(-0.496151\pi\) | ||||
0.0120920 | + | 0.999927i | \(0.496151\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.78151 | −0.184040 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.8225 | −1.29990 | −0.649951 | − | 0.759976i | \(-0.725211\pi\) | ||||
−0.649951 | + | 0.759976i | \(0.725211\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.1955 | −0.467332 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 47.8189 | 1.82974 | 0.914869 | − | 0.403751i | \(-0.132294\pi\) | ||||
0.914869 | + | 0.403751i | \(0.132294\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −55.2397 | −2.11060 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.0908 | 0.575749 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.58880 | 0.365304 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.8561 | −1.32599 | −0.662995 | − | 0.748624i | \(-0.730715\pi\) | ||||
−0.662995 | + | 0.748624i | \(0.730715\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.9253 | 0.831675 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.22789 | 0.198020 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.54527 | 0.0584476 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.9927 | 1.47274 | 0.736368 | − | 0.676582i | \(-0.236539\pi\) | ||||
0.736368 | + | 0.676582i | \(0.236539\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.6597 | 0.628333 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.61120 | 0.324317 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.8075 | 1.38233 | 0.691167 | − | 0.722695i | \(-0.257097\pi\) | ||||
0.691167 | + | 0.722695i | \(0.257097\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −35.6952 | −1.33867 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28.1762 | −1.05521 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 59.0347 | 2.20777 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.875782 | −0.0327067 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.14550 | 0.191895 | 0.0959474 | − | 0.995386i | \(-0.469412\pi\) | ||||
0.0959474 | + | 0.995386i | \(0.469412\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.15804 | −0.117449 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.67258 | 0.173535 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.7881 | −0.770987 | −0.385493 | − | 0.922711i | \(-0.625969\pi\) | ||||
−0.385493 | + | 0.922711i | \(0.625969\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.68468 | −0.0623955 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 55.3583 | 2.04750 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.34880 | 0.0498191 | 0.0249096 | − | 0.999690i | \(-0.492070\pi\) | ||||
0.0249096 | + | 0.999690i | \(0.492070\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 83.2794 | 3.06764 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.1004 | 0.445119 | 0.222559 | − | 0.974919i | \(-0.428559\pi\) | ||||
0.222559 | + | 0.974919i | \(0.428559\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.51849 | 0.239463 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.927403 | 0.0340231 | 0.0170116 | − | 0.999855i | \(-0.494585\pi\) | ||||
0.0170116 | + | 0.999855i | \(0.494585\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.2273 | −1.10744 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 39.7861 | 1.45570 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.82085 | −0.139425 | −0.0697124 | − | 0.997567i | \(-0.522208\pi\) | ||||
−0.0697124 | + | 0.997567i | \(0.522208\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.6462 | 0.679505 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −49.2904 | −1.79386 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.5073 | 0.418240 | 0.209120 | − | 0.977890i | \(-0.432940\pi\) | ||||
0.209120 | + | 0.977890i | \(0.432940\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 27.5617 | 1.00043 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.9439 | −0.614215 | −0.307108 | − | 0.951675i | \(-0.599361\pi\) | ||||
−0.307108 | + | 0.951675i | \(0.599361\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −31.8541 | −1.15169 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.6717 | 0.493655 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.5516 | −0.957476 | −0.478738 | − | 0.877958i | \(-0.658906\pi\) | ||||
−0.478738 | + | 0.877958i | \(0.658906\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.51261 | −0.0544753 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.1372 | −0.616382 | −0.308191 | − | 0.951325i | \(-0.599724\pi\) | ||||
−0.308191 | + | 0.951325i | \(0.599724\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.77959 | 0.171688 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.97370 | −0.0707152 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.92589 | 0.104696 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.9560 | −0.570222 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 35.1155 | 1.25333 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.2517 | −0.508017 | −0.254008 | − | 0.967202i | \(-0.581749\pi\) | ||||
−0.254008 | + | 0.967202i | \(0.581749\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.01755 | 0.178629 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −53.5779 | −1.90261 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.96819 | −0.140737 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.5237 | −0.762409 | −0.381205 | − | 0.924491i | \(-0.624491\pi\) | ||||
−0.381205 | + | 0.924491i | \(0.624491\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.4196 | 0.863902 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.40966 | −0.261807 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.5160 | 1.14747 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.90981 | −0.243237 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.97942 | −0.104751 | −0.0523755 | − | 0.998627i | \(-0.516679\pi\) | ||||
−0.0523755 | + | 0.998627i | \(0.516679\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.2556 | 0.500582 | 0.250291 | − | 0.968171i | \(-0.419474\pi\) | ||||
0.250291 | + | 0.968171i | \(0.419474\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.34307 | 0.222461 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.0283 | 0.351277 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.8996 | −0.731183 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.5905 | 1.06762 | 0.533808 | − | 0.845606i | \(-0.320760\pi\) | ||||
0.533808 | + | 0.845606i | \(0.320760\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.42460 | −0.0496586 | −0.0248293 | − | 0.999692i | \(-0.507904\pi\) | ||||
−0.0248293 | + | 0.999692i | \(0.507904\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.67534 | −0.162775 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −52.6818 | −1.83193 | −0.915963 | − | 0.401263i | \(-0.868571\pi\) | ||||
−0.915963 | + | 0.401263i | \(0.868571\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.57709 | 0.0547746 | 0.0273873 | − | 0.999625i | \(-0.491281\pi\) | ||||
0.0273873 | + | 0.999625i | \(0.491281\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.6960 | 0.613866 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 48.4090 | 1.67526 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.3215 | −0.564152 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.1309 | 0.936662 | 0.468331 | − | 0.883553i | \(-0.344856\pi\) | ||||
0.468331 | + | 0.883553i | \(0.344856\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.4075 | −0.462326 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.28327 | −0.147524 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.0205 | −0.585524 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.58236 | −0.328866 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −58.8811 | −2.01842 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.8997 | 0.886788 | 0.443394 | − | 0.896327i | \(-0.353774\pi\) | ||||
0.443394 | + | 0.896327i | \(0.353774\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.0260 | 0.411280 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.3188 | 1.03567 | 0.517836 | − | 0.855480i | \(-0.326738\pi\) | ||||
0.517836 | + | 0.855480i | \(0.326738\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.94984 | 0.305365 | 0.152682 | − | 0.988275i | \(-0.451209\pi\) | ||||
0.152682 | + | 0.988275i | \(0.451209\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.3881 | 0.728059 | 0.364029 | − | 0.931387i | \(-0.381401\pi\) | ||||
0.364029 | + | 0.931387i | \(0.381401\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.53604 | 0.256233 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.65910 | 0.260117 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −77.6345 | −2.63357 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −69.6126 | −2.35873 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −27.7083 | −0.937783 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.4718 | 1.67055 | 0.835273 | − | 0.549836i | \(-0.185310\pi\) | ||||
0.835273 | + | 0.549836i | \(0.185310\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.4889 | −0.454969 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.6776 | −1.60630 | −0.803149 | − | 0.595778i | \(-0.796844\pi\) | ||||
−0.803149 | + | 0.595778i | \(0.796844\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.47242 | 0.184162 | 0.0920809 | − | 0.995752i | \(-0.470648\pi\) | ||||
0.0920809 | + | 0.995752i | \(0.470648\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.65783 | −0.190186 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31.9348 | −1.07226 | −0.536132 | − | 0.844134i | \(-0.680115\pi\) | ||||
−0.536132 | + | 0.844134i | \(0.680115\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.2108 | −0.777591 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.21919 | −0.308508 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.7689 | 0.393392 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23.0386 | −0.769236 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.9496 | 0.531950 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.2530 | −0.374891 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −58.7711 | −1.95362 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.3838 | −0.577220 | −0.288610 | − | 0.957447i | \(-0.593193\pi\) | ||||
−0.288610 | + | 0.957447i | \(0.593193\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −22.9521 | −0.761273 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.20564 | 0.172471 | 0.0862353 | − | 0.996275i | \(-0.472516\pi\) | ||||
0.0862353 | + | 0.996275i | \(0.472516\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 86.5320 | 2.86379 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22.1725 | 0.733000 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.9641 | −1.08738 | −0.543692 | − | 0.839285i | \(-0.682974\pi\) | ||||
−0.543692 | + | 0.839285i | \(0.682974\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.2179 | −0.435544 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.44572 | −0.0805020 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.98813 | 0.328408 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.315183 | −0.0103520 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.5028 | 0.836720 | 0.418360 | − | 0.908281i | \(-0.362605\pi\) | ||||
0.418360 | + | 0.908281i | \(0.362605\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.4056 | 0.602571 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −69.2804 | −2.26571 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47.1388 | −1.53996 | −0.769979 | − | 0.638070i | \(-0.779733\pi\) | ||||
−0.769979 | + | 0.638070i | \(0.779733\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.99100 | 0.130241 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.2555 | 0.758108 | 0.379054 | − | 0.925374i | \(-0.376249\pi\) | ||||
0.379054 | + | 0.925374i | \(0.376249\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.97574 | 0.227161 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.1710 | −0.785453 | −0.392727 | − | 0.919655i | \(-0.628468\pi\) | ||||
−0.392727 | + | 0.919655i | \(0.628468\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.1799 | −0.882297 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.3124 | 0.496540 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.9082 | 0.774464 | 0.387232 | − | 0.921982i | \(-0.373431\pi\) | ||||
0.387232 | + | 0.921982i | \(0.373431\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −48.8692 | −1.58137 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15.6018 | −0.504334 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.6851 | −0.473713 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −45.8597 | −1.47781 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 54.1804 | 1.74413 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.7841 | −0.764846 | −0.382423 | − | 0.923987i | \(-0.624910\pi\) | ||||
−0.382423 | + | 0.923987i | \(0.624910\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.64979 | −0.245747 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.88609 | 0.188894 | 0.0944468 | − | 0.995530i | \(-0.469892\pi\) | ||||
0.0944468 | + | 0.995530i | \(0.469892\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.90808 | 0.125159 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.8602 | 1.27524 | 0.637620 | − | 0.770351i | \(-0.279919\pi\) | ||||
0.637620 | + | 0.770351i | \(0.279919\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.1155 | −0.515053 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.9190 | −0.827529 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.6127 | −0.402282 | −0.201141 | − | 0.979562i | \(-0.564465\pi\) | ||||
−0.201141 | + | 0.979562i | \(0.564465\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 40.9774 | 1.30565 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 73.8663 | 2.34881 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.60602 | −0.146315 | −0.0731575 | − | 0.997320i | \(-0.523308\pi\) | ||||
−0.0731575 | + | 0.997320i | \(0.523308\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.9914 | −0.475738 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −36.2501 | −1.14921 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 57.7765 | 1.82980 | 0.914900 | − | 0.403680i | \(-0.132269\pi\) | ||||
0.914900 | + | 0.403680i | \(0.132269\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −34.1077 | −1.07912 |
(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 | 8036.2.a.q.1.10 | 15 | ||
7.2 | even | 3 | 1148.2.i.e.165.6 | ✓ | 30 | ||
7.4 | even | 3 | 1148.2.i.e.821.6 | yes | 30 | ||
7.6 | odd | 2 | 8036.2.a.r.1.6 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.i.e.165.6 | ✓ | 30 | 7.2 | even | 3 | ||
1148.2.i.e.821.6 | yes | 30 | 7.4 | even | 3 | ||
8036.2.a.q.1.10 | 15 | 1.1 | even | 1 | trivial | ||
8036.2.a.r.1.6 | 15 | 7.6 | odd | 2 |