Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6016,2,Mod(1,6016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6016, 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("6016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6016 = 2^{7} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6016.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: | \(48.0380018560\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 22 x^{11} + 96 x^{10} + 163 x^{9} - 840 x^{8} - 438 x^{7} + 3358 x^{6} + 5 x^{5} - 6230 x^{4} + 1488 x^{3} + 4720 x^{2} - 1440 x - 832 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.18016\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.18016 | 0.681365 | 0.340682 | − | 0.940178i | \(-0.389342\pi\) | ||||
0.340682 | + | 0.940178i | \(0.389342\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.06312 | 0.922657 | 0.461328 | − | 0.887230i | \(-0.347373\pi\) | ||||
0.461328 | + | 0.887230i | \(0.347373\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.279748 | 0.105735 | 0.0528673 | − | 0.998602i | \(-0.483164\pi\) | ||||
0.0528673 | + | 0.998602i | \(0.483164\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.60723 | −0.535742 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.49808 | 1.05471 | 0.527356 | − | 0.849645i | \(-0.323184\pi\) | ||||
0.527356 | + | 0.849645i | \(0.323184\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.50765 | 0.972847 | 0.486424 | − | 0.873723i | \(-0.338301\pi\) | ||||
0.486424 | + | 0.873723i | \(0.338301\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.43481 | 0.628666 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.93033 | −0.710709 | −0.355355 | − | 0.934732i | \(-0.615640\pi\) | ||||
−0.355355 | + | 0.934732i | \(0.615640\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.42881 | 0.557206 | 0.278603 | − | 0.960406i | \(-0.410129\pi\) | ||||
0.278603 | + | 0.960406i | \(0.410129\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.330146 | 0.0720439 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.39220 | −0.498808 | −0.249404 | − | 0.968400i | \(-0.580235\pi\) | ||||
−0.249404 | + | 0.968400i | \(0.580235\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.743524 | −0.148705 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.43726 | −1.04640 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.15996 | 0.586790 | 0.293395 | − | 0.955991i | \(-0.405215\pi\) | ||||
0.293395 | + | 0.955991i | \(0.405215\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.46282 | −0.801545 | −0.400773 | − | 0.916178i | \(-0.631258\pi\) | ||||
−0.400773 | + | 0.916178i | \(0.631258\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.12829 | 0.718643 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.577153 | 0.0975567 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.97509 | 1.14670 | 0.573348 | − | 0.819312i | \(-0.305644\pi\) | ||||
0.573348 | + | 0.819312i | \(0.305644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.13959 | 0.662864 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.78599 | 1.37214 | 0.686071 | − | 0.727535i | \(-0.259334\pi\) | ||||
0.686071 | + | 0.727535i | \(0.259334\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.9727 | 1.97833 | 0.989163 | − | 0.146822i | \(-0.0469045\pi\) | ||||
0.989163 | + | 0.146822i | \(0.0469045\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.31590 | −0.494306 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.00000 | −0.145865 | ||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.92174 | −0.988820 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.45825 | −0.484252 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.29816 | 0.590398 | 0.295199 | − | 0.955436i | \(-0.404614\pi\) | ||||
0.295199 | + | 0.955436i | \(0.404614\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.21697 | 0.973136 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.86638 | 0.379661 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.39738 | 0.181923 | 0.0909614 | − | 0.995854i | \(-0.471006\pi\) | ||||
0.0909614 | + | 0.995854i | \(0.471006\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.74584 | −0.479606 | −0.239803 | − | 0.970822i | \(-0.577083\pi\) | ||||
−0.239803 | + | 0.970822i | \(0.577083\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.449617 | −0.0566465 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.23672 | 0.897604 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.66539 | 0.936476 | 0.468238 | − | 0.883602i | \(-0.344889\pi\) | ||||
0.468238 | + | 0.883602i | \(0.344889\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.82317 | −0.339870 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.67409 | −0.198677 | −0.0993387 | − | 0.995054i | \(-0.531673\pi\) | ||||
−0.0993387 | + | 0.995054i | \(0.531673\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.21968 | 0.844999 | 0.422500 | − | 0.906363i | \(-0.361153\pi\) | ||||
0.422500 | + | 0.906363i | \(0.361153\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.877477 | −0.101322 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.978579 | 0.111519 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.44688 | 0.275296 | 0.137648 | − | 0.990481i | \(-0.456046\pi\) | ||||
0.137648 | + | 0.990481i | \(0.456046\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.59515 | −0.177239 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.4732 | 1.58864 | 0.794321 | − | 0.607499i | \(-0.207827\pi\) | ||||
0.794321 | + | 0.607499i | \(0.207827\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.04563 | −0.655740 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.72926 | 0.399818 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.63757 | −0.491581 | −0.245791 | − | 0.969323i | \(-0.579048\pi\) | ||||
−0.245791 | + | 0.969323i | \(0.579048\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.981257 | 0.102864 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.26683 | −0.546145 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.01092 | 0.514110 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.16215 | 0.321068 | 0.160534 | − | 0.987030i | \(-0.448678\pi\) | ||||
0.160534 | + | 0.987030i | \(0.448678\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.62220 | −0.565053 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.46764 | 0.743058 | 0.371529 | − | 0.928421i | \(-0.378834\pi\) | ||||
0.371529 | + | 0.928421i | \(0.378834\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.99761 | 0.492429 | 0.246215 | − | 0.969215i | \(-0.420813\pi\) | ||||
0.246215 | + | 0.969215i | \(0.420813\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.681133 | 0.0664717 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.44704 | 0.429912 | 0.214956 | − | 0.976624i | \(-0.431039\pi\) | ||||
0.214956 | + | 0.976624i | \(0.431039\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −20.5089 | −1.96439 | −0.982197 | − | 0.187852i | \(-0.939847\pi\) | ||||
−0.982197 | + | 0.187852i | \(0.939847\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.23171 | 0.781319 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.31188 | −0.687844 | −0.343922 | − | 0.938998i | \(-0.611756\pi\) | ||||
−0.343922 | + | 0.938998i | \(0.611756\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.93540 | −0.460228 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.63759 | −0.521195 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.819752 | −0.0751466 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.23657 | 0.112415 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.3689 | 0.934929 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.8496 | −1.05986 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.55329 | −0.404039 | −0.202020 | − | 0.979381i | \(-0.564750\pi\) | ||||
−0.202020 | + | 0.979381i | \(0.564750\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.3099 | 1.34796 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.1327 | 1.58426 | 0.792132 | − | 0.610350i | \(-0.208971\pi\) | ||||
0.792132 | + | 0.610350i | \(0.208971\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.679452 | 0.0589160 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.2177 | −0.965468 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.06635 | −0.603719 | −0.301860 | − | 0.953352i | \(-0.597607\pi\) | ||||
−0.301860 | + | 0.953352i | \(0.597607\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.88583 | −0.329592 | −0.164796 | − | 0.986328i | \(-0.552697\pi\) | ||||
−0.164796 | + | 0.986328i | \(0.552697\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.18016 | −0.0993873 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.2700 | 1.02607 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.51939 | 0.541406 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.16875 | −0.673747 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.46359 | −0.365672 | −0.182836 | − | 0.983143i | \(-0.558528\pi\) | ||||
−0.182836 | + | 0.983143i | \(0.558528\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.81966 | −0.473598 | −0.236799 | − | 0.971559i | \(-0.576098\pi\) | ||||
−0.236799 | + | 0.971559i | \(0.576098\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.70970 | 0.380757 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.20734 | −0.739551 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.881406 | −0.0703438 | −0.0351719 | − | 0.999381i | \(-0.511198\pi\) | ||||
−0.0351719 | + | 0.999381i | \(0.511198\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.07251 | 0.402277 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.669211 | −0.0527412 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.22097 | 0.330612 | 0.165306 | − | 0.986242i | \(-0.447139\pi\) | ||||
0.165306 | + | 0.986242i | \(0.447139\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.51717 | 0.663061 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.27379 | 0.717628 | 0.358814 | − | 0.933409i | \(-0.383181\pi\) | ||||
0.358814 | + | 0.933409i | \(0.383181\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.696382 | −0.0535679 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.90364 | −0.298519 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −25.3560 | −1.92778 | −0.963892 | − | 0.266295i | \(-0.914200\pi\) | ||||
−0.963892 | + | 0.266295i | \(0.914200\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.207999 | −0.0157233 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.64912 | 0.123956 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.59962 | −0.568022 | −0.284011 | − | 0.958821i | \(-0.591665\pi\) | ||||
−0.284011 | + | 0.958821i | \(0.591665\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.6388 | 1.23675 | 0.618374 | − | 0.785884i | \(-0.287792\pi\) | ||||
0.618374 | + | 0.785884i | \(0.287792\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.42069 | −0.326786 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.3905 | 1.05801 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.2505 | −0.749593 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.52106 | −0.110641 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.9636 | −0.793299 | −0.396650 | − | 0.917970i | \(-0.629827\pi\) | ||||
−0.396650 | + | 0.917970i | \(0.629827\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.68560 | 0.553221 | 0.276611 | − | 0.960982i | \(-0.410789\pi\) | ||||
0.276611 | + | 0.960982i | \(0.410789\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.54047 | 0.611596 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.1032 | 0.933567 | 0.466783 | − | 0.884372i | \(-0.345413\pi\) | ||||
0.466783 | + | 0.884372i | \(0.345413\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.51169 | 0.107161 | 0.0535806 | − | 0.998564i | \(-0.482937\pi\) | ||||
0.0535806 | + | 0.998564i | \(0.482937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.04638 | 0.638082 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.883991 | 0.0620440 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.1266 | 1.26601 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.84480 | 0.267232 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.49616 | 0.587692 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.3271 | 1.19285 | 0.596424 | − | 0.802669i | \(-0.296588\pi\) | ||||
0.596424 | + | 0.802669i | \(0.296588\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.97569 | −0.135372 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 26.7644 | 1.82532 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.24846 | −0.0847511 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.52037 | 0.575753 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.2786 | −0.691411 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.7548 | −1.32288 | −0.661439 | − | 0.749999i | \(-0.730054\pi\) | ||||
−0.661439 | + | 0.749999i | \(0.730054\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.19501 | 0.0796674 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 28.0461 | 1.86149 | 0.930743 | − | 0.365673i | \(-0.119161\pi\) | ||||
0.930743 | + | 0.365673i | \(0.119161\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.24499 | −0.0822714 | −0.0411357 | − | 0.999154i | \(-0.513098\pi\) | ||||
−0.0411357 | + | 0.999154i | \(0.513098\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.15488 | 0.0759855 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.9085 | 1.69732 | 0.848660 | − | 0.528938i | \(-0.177410\pi\) | ||||
0.848660 | + | 0.528938i | \(0.177410\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.06312 | −0.134583 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.88771 | 0.187577 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.89745 | −0.640213 | −0.320106 | − | 0.947382i | \(-0.603719\pi\) | ||||
−0.320106 | + | 0.947382i | \(0.603719\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.78140 | 0.179166 | 0.0895829 | − | 0.995979i | \(-0.471447\pi\) | ||||
0.0895829 | + | 0.995979i | \(0.471447\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.4292 | 0.925636 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.2804 | −0.912341 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.51940 | 0.542077 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.0807 | 1.08244 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.89038 | −0.561156 | −0.280578 | − | 0.959831i | \(-0.590526\pi\) | ||||
−0.280578 | + | 0.959831i | \(0.590526\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.36810 | −0.526098 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.13480 | −0.446799 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.1651 | −1.38262 | −0.691310 | − | 0.722558i | \(-0.742966\pi\) | ||||
−0.691310 | + | 0.722558i | \(0.742966\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.95126 | 0.121246 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.07877 | −0.314368 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 31.6693 | 1.95282 | 0.976408 | − | 0.215936i | \(-0.0692802\pi\) | ||||
0.976408 | + | 0.215936i | \(0.0692802\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.86764 | 0.544735 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.47307 | −0.334946 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.5301 | −1.61757 | −0.808785 | − | 0.588105i | \(-0.799874\pi\) | ||||
−0.808785 | + | 0.588105i | \(0.799874\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.48366 | −0.211617 | −0.105809 | − | 0.994387i | \(-0.533743\pi\) | ||||
−0.105809 | + | 0.994387i | \(0.533743\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.15804 | 0.0700877 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.60091 | −0.156841 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.2766 | 0.977965 | 0.488983 | − | 0.872294i | \(-0.337368\pi\) | ||||
0.488983 | + | 0.872294i | \(0.337368\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.17275 | 0.429421 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.8688 | 1.60286 | 0.801429 | − | 0.598090i | \(-0.204073\pi\) | ||||
0.801429 | + | 0.598090i | \(0.204073\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.99091 | 0.415567 | 0.207783 | − | 0.978175i | \(-0.433375\pi\) | ||||
0.207783 | + | 0.978175i | \(0.433375\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.91369 | 0.350297 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.45786 | 0.145083 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.41317 | −0.494893 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.73184 | 0.218764 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.9302 | −1.45644 | −0.728220 | − | 0.685343i | \(-0.759652\pi\) | ||||
−0.728220 | + | 0.685343i | \(0.759652\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.88296 | 0.167852 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −19.0200 | −1.10365 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.39099 | −0.485264 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.62909 | 0.209178 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.81301 | 0.506294 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.72813 | −0.442511 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.38854 | −0.535832 | −0.267916 | − | 0.963442i | \(-0.586335\pi\) | ||||
−0.267916 | + | 0.963442i | \(0.586335\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.89797 | 0.335524 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.0444 | 1.13661 | 0.568306 | − | 0.822817i | \(-0.307599\pi\) | ||||
0.568306 | + | 0.822817i | \(0.307599\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.1356 | −1.59032 | −0.795160 | − | 0.606400i | \(-0.792613\pi\) | ||||
−0.795160 | + | 0.606400i | \(0.792613\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.927616 | −0.0522652 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.4954 | −1.09497 | −0.547484 | − | 0.836816i | \(-0.684414\pi\) | ||||
−0.547484 | + | 0.836816i | \(0.684414\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.0538 | 0.618894 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.24822 | 0.292927 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.11720 | −0.396012 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.60802 | −0.144667 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −24.2037 | −1.33847 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.279748 | −0.0154230 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.1069 | 1.27007 | 0.635035 | − | 0.772484i | \(-0.280986\pi\) | ||||
0.635035 | + | 0.772484i | \(0.280986\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.2105 | −0.614333 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.8146 | 0.864046 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.4810 | 1.11567 | 0.557835 | − | 0.829952i | \(-0.311632\pi\) | ||||
0.557835 | + | 0.829952i | \(0.311632\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.62918 | −0.468673 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.6113 | −0.845399 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.89457 | −0.210287 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.82455 | −0.313583 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.0707 | −1.07745 | −0.538726 | − | 0.842481i | \(-0.681094\pi\) | ||||
−0.538726 | + | 0.842481i | \(0.681094\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.97410 | −0.266258 | −0.133129 | − | 0.991099i | \(-0.542502\pi\) | ||||
−0.133129 | + | 0.991099i | \(0.542502\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.0720 | −1.01799 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.00102 | 0.0532788 | 0.0266394 | − | 0.999645i | \(-0.491519\pi\) | ||||
0.0266394 | + | 0.999645i | \(0.491519\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.45384 | −0.183311 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.967438 | −0.0512022 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.7311 | −0.883036 | −0.441518 | − | 0.897252i | \(-0.645560\pi\) | ||||
−0.441518 | + | 0.897252i | \(0.645560\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.1009 | −0.689521 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.45935 | 0.0765959 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.8951 | 0.779644 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.525038 | 0.0274067 | 0.0137034 | − | 0.999906i | \(-0.495638\pi\) | ||||
0.0137034 | + | 0.999906i | \(0.495638\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −14.1211 | −0.735113 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.20240 | 0.0624255 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.43021 | −0.0740534 | −0.0370267 | − | 0.999314i | \(-0.511789\pi\) | ||||
−0.0370267 | + | 0.999314i | \(0.511789\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.9844 | −0.722152 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.0840 | 0.570857 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.0852 | 0.980342 | 0.490171 | − | 0.871626i | \(-0.336934\pi\) | ||||
0.490171 | + | 0.871626i | \(0.336934\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.37360 | −0.275298 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.6095 | −0.950904 | −0.475452 | − | 0.879742i | \(-0.657715\pi\) | ||||
−0.475452 | + | 0.879742i | \(0.657715\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.01893 | 0.102894 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.8501 | −1.05987 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.96907 | −0.454750 | −0.227375 | − | 0.973807i | \(-0.573014\pi\) | ||||
−0.227375 | + | 0.973807i | \(0.573014\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.00992 | 0.354507 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.3995 | 1.07946 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.04822 | 0.254004 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.64572 | −0.333539 | −0.166770 | − | 0.985996i | \(-0.553334\pi\) | ||||
−0.166770 | + | 0.985996i | \(0.553334\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.801862 | 0.0401433 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.85295 | 0.0925320 | 0.0462660 | − | 0.998929i | \(-0.485268\pi\) | ||||
0.0462660 | + | 0.998929i | \(0.485268\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.6540 | −0.779781 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.29099 | −0.163531 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.3994 | 1.20943 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.0196 | 1.48437 | 0.742187 | − | 0.670192i | \(-0.233788\pi\) | ||||
0.742187 | + | 0.670192i | \(0.233788\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.33942 | −0.411353 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.390912 | 0.0192355 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29.8600 | 1.46577 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.58590 | −0.224572 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.42035 | −0.118242 | −0.0591209 | − | 0.998251i | \(-0.518830\pi\) | ||||
−0.0591209 | + | 0.998251i | \(0.518830\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.7969 | −1.01358 | −0.506789 | − | 0.862070i | \(-0.669168\pi\) | ||||
−0.506789 | + | 0.862070i | \(0.669168\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.60723 | 0.0781460 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.17877 | 0.105686 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.04789 | −0.0507109 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.4806 | 0.699130 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.73175 | 0.276089 | 0.138044 | − | 0.990426i | \(-0.455918\pi\) | ||||
0.138044 | + | 0.990426i | \(0.455918\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.2943 | −1.60002 | −0.800012 | − | 0.599984i | \(-0.795174\pi\) | ||||
−0.800012 | + | 0.599984i | \(0.795174\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.69391 | 0.368895 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.81018 | −0.277939 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.2471 | −1.20498 | −0.602489 | − | 0.798127i | \(-0.705824\pi\) | ||||
−0.602489 | + | 0.798127i | \(0.705824\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.1248 | 0.529752 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.8718 | 0.754094 | 0.377047 | − | 0.926194i | \(-0.376940\pi\) | ||||
0.377047 | + | 0.926194i | \(0.376940\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.56787 | −0.453561 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.26775 | −0.249156 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.61052 | 0.264777 | 0.132388 | − | 0.991198i | \(-0.457735\pi\) | ||||
0.132388 | + | 0.991198i | \(0.457735\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.7341 | 1.44721 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.86813 | −0.322693 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.02445 | 0.0949078 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.6225 | −1.10502 | −0.552508 | − | 0.833508i | \(-0.686329\pi\) | ||||
−0.552508 | + | 0.833508i | \(0.686329\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 15.9330 | 0.743686 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.96173 | −0.324240 | −0.162120 | − | 0.986771i | \(-0.551833\pi\) | ||||
−0.162120 | + | 0.986771i | \(0.551833\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.69193 | 0.171578 | 0.0857892 | − | 0.996313i | \(-0.472659\pi\) | ||||
0.0857892 | + | 0.996313i | \(0.472659\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.8661 | −0.503904 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.7477 | −0.821267 | −0.410634 | − | 0.911800i | \(-0.634692\pi\) | ||||
−0.410634 | + | 0.911800i | \(0.634692\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.14437 | 0.0990180 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.04020 | −0.0479298 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 45.3797 | 2.08656 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.80588 | −0.0828593 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.90812 | −0.316301 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.3638 | 1.25028 | 0.625142 | − | 0.780511i | \(-0.285041\pi\) | ||||
0.625142 | + | 0.780511i | \(0.285041\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.4662 | 1.11556 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.789775 | −0.0359360 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.52390 | 0.296235 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 43.9223 | 1.99031 | 0.995155 | − | 0.0983196i | \(-0.0313467\pi\) | ||||
0.995155 | + | 0.0983196i | \(0.0313467\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.98142 | 0.225268 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.0950 | 0.636097 | 0.318048 | − | 0.948074i | \(-0.396973\pi\) | ||||
0.318048 | + | 0.948074i | \(0.396973\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.25973 | −0.417037 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.5993 | −0.521350 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.468321 | −0.0210071 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.6023 | −0.787987 | −0.393993 | − | 0.919113i | \(-0.628907\pi\) | ||||
−0.393993 | + | 0.919113i | \(0.628907\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.9445 | 0.488966 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.94532 | −0.398852 | −0.199426 | − | 0.979913i | \(-0.563908\pi\) | ||||
−0.199426 | + | 0.979913i | \(0.563908\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.4067 | 0.685588 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.821842 | −0.0364993 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.4504 | 0.862123 | 0.431061 | − | 0.902323i | \(-0.358139\pi\) | ||||
0.431061 | + | 0.902323i | \(0.358139\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.01969 | 0.0893457 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13.2060 | −0.583061 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.3107 | 0.454343 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.49808 | −0.153845 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −29.9241 | −1.31352 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.8725 | −0.958253 | −0.479126 | − | 0.877746i | \(-0.659046\pi\) | ||||
−0.479126 | + | 0.877746i | \(0.659046\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.5279 | −0.722714 | −0.361357 | − | 0.932427i | \(-0.617687\pi\) | ||||
−0.361357 | + | 0.932427i | \(0.617687\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.245472 | −0.0107133 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.0775 | 0.569666 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.2774 | −0.751191 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.24590 | −0.0974636 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.8182 | 1.33488 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.17480 | 0.396661 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.96876 | −0.387031 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24.2128 | −1.04292 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.56928 | 0.325429 | 0.162714 | − | 0.986673i | \(-0.447975\pi\) | ||||
0.162714 | + | 0.986673i | \(0.447975\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.6364 | 0.842677 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −42.3123 | −1.81246 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.2004 | −1.16301 | −0.581503 | − | 0.813544i | \(-0.697535\pi\) | ||||
−0.581503 | + | 0.813544i | \(0.697535\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.02041 | 0.256945 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.67493 | 0.326963 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.684510 | 0.0291083 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16.9830 | 0.720889 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.7806 | −1.17710 | −0.588551 | − | 0.808460i | \(-0.700301\pi\) | ||||
−0.588551 | + | 0.808460i | \(0.700301\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 45.5039 | 1.92461 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.0972 | −0.510746 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.709879 | −0.0299178 | −0.0149589 | − | 0.999888i | \(-0.504762\pi\) | ||||
−0.0149589 | + | 0.999888i | \(0.504762\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.0853 | −0.634644 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.446240 | −0.0187403 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.1083 | 1.38797 | 0.693986 | − | 0.719988i | \(-0.255853\pi\) | ||||
0.693986 | + | 0.719988i | \(0.255853\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.640242 | −0.0267933 | −0.0133966 | − | 0.999910i | \(-0.504264\pi\) | ||||
−0.0133966 | + | 0.999910i | \(0.504264\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.9388 | −0.540526 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.77866 | 0.0741751 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.5999 | −0.649431 | −0.324715 | − | 0.945812i | \(-0.605269\pi\) | ||||
−0.324715 | + | 0.945812i | \(0.605269\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.07022 | 0.376946 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.04884 | 0.167974 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.0353 | 0.622699 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11.6310 | −0.480884 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.178942 | −0.00738572 | −0.00369286 | − | 0.999993i | \(-0.501175\pi\) | ||||
−0.00369286 | + | 0.999993i | \(0.501175\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.8393 | −0.446626 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.4639 | 0.636100 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −47.7952 | −1.96272 | −0.981358 | − | 0.192190i | \(-0.938441\pi\) | ||||
−0.981358 | + | 0.192190i | \(0.938441\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.69125 | −0.0693345 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.78404 | 0.0730159 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.5227 | −0.470806 | −0.235403 | − | 0.971898i | \(-0.575641\pi\) | ||||
−0.235403 | + | 0.971898i | \(0.575641\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.30751 | −0.0941253 | −0.0470627 | − | 0.998892i | \(-0.514986\pi\) | ||||
−0.0470627 | + | 0.998892i | \(0.514986\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.3200 | −0.501710 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.55119 | 0.103721 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.4093 | −1.23427 | −0.617137 | − | 0.786855i | \(-0.711708\pi\) | ||||
−0.617137 | + | 0.786855i | \(0.711708\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.04325 | 0.0422746 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.50765 | −0.141904 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.1057 | 1.09479 | 0.547394 | − | 0.836875i | \(-0.315620\pi\) | ||||
0.547394 | + | 0.836875i | \(0.315620\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 21.3922 | 0.862618 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.8852 | 0.639513 | 0.319756 | − | 0.947500i | \(-0.396399\pi\) | ||||
0.319756 | + | 0.947500i | \(0.396399\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.2692 | 0.935269 | 0.467635 | − | 0.883922i | \(-0.345106\pi\) | ||||
0.467635 | + | 0.883922i | \(0.345106\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.0070 | 0.521952 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.29735 | −0.0519772 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.7296 | −0.829182 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.0268 | 0.400432 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.4393 | −0.814968 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.4704 | −0.536248 | −0.268124 | − | 0.963384i | \(-0.586404\pi\) | ||||
−0.268124 | + | 0.963384i | \(0.586404\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.4488 | 0.812765 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.39399 | −0.372789 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.2791 | −0.961971 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.69063 | 0.106440 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.2199 | −0.877634 | −0.438817 | − | 0.898577i | \(-0.644602\pi\) | ||||
−0.438817 | + | 0.898577i | \(0.644602\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.57458 | −0.338148 | −0.169074 | − | 0.985603i | \(-0.554078\pi\) | ||||
−0.169074 | + | 0.985603i | \(0.554078\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 31.5862 | 1.24371 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0914 | 0.475360 | 0.237680 | − | 0.971343i | \(-0.423613\pi\) | ||||
0.237680 | + | 0.971343i | \(0.423613\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.88813 | 0.191876 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.47338 | −0.0577464 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.0993 | 1.06048 | 0.530239 | − | 0.847848i | \(-0.322102\pi\) | ||||
0.530239 | + | 0.847848i | \(0.322102\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 37.4100 | 1.46173 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.6037 | −0.452702 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.2447 | 0.438032 | 0.219016 | − | 0.975721i | \(-0.429715\pi\) | ||||
0.219016 | + | 0.975721i | \(0.429715\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.6805 | 1.58229 | 0.791143 | − | 0.611631i | \(-0.209486\pi\) | ||||
0.791143 | + | 0.611631i | \(0.209486\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.1303 | −0.471104 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.40179 | 0.0543592 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.55925 | −0.292695 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23.3138 | −0.901363 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.1032 | −0.505845 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.11190 | −0.119955 | −0.0599774 | − | 0.998200i | \(-0.519103\pi\) | ||||
−0.0599774 | + | 0.998200i | \(0.519103\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.04273 | 0.155605 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.3779 | −1.47498 | −0.737491 | − | 0.675357i | \(-0.763989\pi\) | ||||
−0.737491 | + | 0.675357i | \(0.763989\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.884603 | 0.0339480 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 33.0989 | 1.26835 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.3628 | 1.00874 | 0.504372 | − | 0.863487i | \(-0.331724\pi\) | ||||
0.504372 | + | 0.863487i | \(0.331724\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.5788 | −0.557025 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.46929 | −0.0560568 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.0765 | 0.574367 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.2289 | 1.26409 | 0.632044 | − | 0.774932i | \(-0.282216\pi\) | ||||
0.632044 | + | 0.774932i | \(0.282216\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.57280 | −0.0597456 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.01695 | −0.304100 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.7458 | −0.975193 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 30.5761 | 1.15650 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.59061 | −0.286693 | −0.143347 | − | 0.989673i | \(-0.545786\pi\) | ||||
−0.143347 | + | 0.989673i | \(0.545786\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.9411 | 0.638947 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.43481 | −0.0917003 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.08906 | 0.0785670 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.5138 | 0.582633 | 0.291316 | − | 0.956627i | \(-0.405907\pi\) | ||||
0.291316 | + | 0.956627i | \(0.405907\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.93269 | −0.147488 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.6759 | 0.399817 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 25.3146 | 0.946713 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.6806 | −0.436218 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.6361 | −1.03065 | −0.515325 | − | 0.856995i | \(-0.672329\pi\) | ||||
−0.515325 | + | 0.856995i | \(0.672329\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.39807 | 0.0520668 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.28249 | 0.122077 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.34951 | −0.0872585 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.6442 | −0.914003 | −0.457002 | − | 0.889466i | \(-0.651077\pi\) | ||||
−0.457002 | + | 0.889466i | \(0.651077\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.8142 | 0.807935 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −38.0144 | −1.40601 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 52.3115 | 1.93217 | 0.966084 | − | 0.258226i | \(-0.0831380\pi\) | ||||
0.966084 | + | 0.258226i | \(0.0831380\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.8531 | −0.621638 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.8142 | 0.987712 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.43918 | −0.236869 | −0.118435 | − | 0.992962i | \(-0.537788\pi\) | ||||
−0.118435 | + | 0.992962i | \(0.537788\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.0542 | 0.369352 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.2625 | 0.926792 | 0.463396 | − | 0.886151i | \(-0.346631\pi\) | ||||
0.463396 | + | 0.886151i | \(0.346631\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.20893 | −0.337389 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −23.2617 | −0.851101 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.24405 | 0.0454566 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.3072 | 1.32487 | 0.662435 | − | 0.749120i | \(-0.269523\pi\) | ||||
0.662435 | + | 0.749120i | \(0.269523\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.4921 | −0.382352 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.0067 | −0.436968 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.29994 | 0.0835929 | 0.0417964 | − | 0.999126i | \(-0.486692\pi\) | ||||
0.0417964 | + | 0.999126i | \(0.486692\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.87568 | −0.358465 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.44599 | 0.124917 | 0.0624584 | − | 0.998048i | \(-0.480106\pi\) | ||||
0.0624584 | + | 0.998048i | \(0.480106\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.73731 | −0.207705 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.71669 | 0.351308 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.90151 | 0.176983 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.47883 | −0.197572 | −0.0987858 | − | 0.995109i | \(-0.531496\pi\) | ||||
−0.0987858 | + | 0.995109i | \(0.531496\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.1583 | −0.942069 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.2329 | 0.368052 | 0.184026 | − | 0.982921i | \(-0.441087\pi\) | ||||
0.184026 | + | 0.982921i | \(0.441087\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.31821 | 0.119194 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.30280 | 0.0826125 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21.3395 | 0.764566 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.85608 | −0.209547 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.1815 | −0.614018 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.81845 | −0.0649032 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.82336 | −0.207580 | −0.103790 | − | 0.994599i | \(-0.533097\pi\) | ||||
−0.103790 | + | 0.994599i | \(0.533097\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 37.3748 | 1.33058 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.04548 | −0.0727289 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.1391 | −0.466583 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.4652 | 0.371163 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.9127 | 1.37836 | 0.689179 | − | 0.724591i | \(-0.257971\pi\) | ||||
0.689179 | + | 0.724591i | \(0.257971\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.93033 | 0.103668 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.45362 | 0.263361 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.2550 | 0.891230 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.38066 | −0.0486620 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −31.3097 | −1.10216 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.6415 | −0.479608 | −0.239804 | − | 0.970821i | \(-0.577083\pi\) | ||||
−0.239804 | + | 0.970821i | \(0.577083\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.3721 | 1.10162 | 0.550812 | − | 0.834629i | \(-0.314318\pi\) | ||||
0.550812 | + | 0.834629i | \(0.314318\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.11127 | −0.144189 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.70839 | 0.305042 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.5083 | 1.10234 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.57710 | −0.0551084 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.7420 | −1.10781 | −0.553903 | − | 0.832581i | \(-0.686862\pi\) | ||||
−0.553903 | + | 0.832581i | \(0.686862\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.0929 | −0.456388 | −0.228194 | − | 0.973616i | \(-0.573282\pi\) | ||||
−0.228194 | + | 0.973616i | \(0.573282\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.06948 | −0.106866 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.7565 | 1.41724 | 0.708621 | − | 0.705589i | \(-0.249317\pi\) | ||||
0.708621 | + | 0.705589i | \(0.249317\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.8485 | −0.446246 | −0.223123 | − | 0.974790i | \(-0.571625\pi\) | ||||
−0.223123 | + | 0.974790i | \(0.571625\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.2090 | 0.666351 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.2830 | 0.702763 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.1330 | 0.662124 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 24.2655 | 0.838738 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.8858 | 0.548440 | 0.274220 | − | 0.961667i | \(-0.411580\pi\) | ||||
0.274220 | + | 0.961667i | \(0.411580\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.0146 | −0.655677 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.7094 | 1.09213 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.43672 | −0.0494247 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.345927 | 0.0118862 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.25039 | 0.283153 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.6858 | −0.571981 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.8272 | 1.02126 | 0.510631 | − | 0.859800i | \(-0.329412\pi\) | ||||
0.510631 | + | 0.859800i | \(0.329412\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.05368 | −0.275430 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.1512 | −0.995786 | −0.497893 | − | 0.867238i | \(-0.665893\pi\) | ||||
−0.497893 | + | 0.867238i | \(0.665893\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.3351 | −0.454987 | −0.227494 | − | 0.973780i | \(-0.573053\pi\) | ||||
−0.227494 | + | 0.973780i | \(0.573053\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.90066 | 0.0988543 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.2707 | −0.519821 | −0.259910 | − | 0.965633i | \(-0.583693\pi\) | ||||
−0.259910 | + | 0.965633i | \(0.583693\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −52.3126 | −1.77868 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.92888 | −0.337203 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.55940 | 0.290358 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.8875 | 0.911049 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.08229 | −0.172009 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.31489 | −0.112064 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.7918 | −0.668322 | −0.334161 | − | 0.942516i | \(-0.608453\pi\) | ||||
−0.334161 | + | 0.942516i | \(0.608453\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −29.4216 | −0.992367 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.9189 | −0.906920 | −0.453460 | − | 0.891277i | \(-0.649811\pi\) | ||||
−0.453460 | + | 0.891277i | \(0.649811\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.6624 | −0.560733 | −0.280367 | − | 0.959893i | \(-0.590456\pi\) | ||||
−0.280367 | + | 0.959893i | \(0.590456\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.40235 | 0.114369 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.7724 | −1.50331 | −0.751654 | − | 0.659557i | \(-0.770744\pi\) | ||||
−0.751654 | + | 0.659557i | \(0.770744\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.27377 | −0.0427209 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.57997 | −0.186936 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.42881 | −0.0812769 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.6790 | −0.524090 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.90270 | −0.330642 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.1023 | −0.470339 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.5950 | −0.419601 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.28291 | 0.142526 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 34.3278 | 1.14109 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.9720 | −1.02841 | −0.514205 | − | 0.857667i | \(-0.671913\pi\) | ||||
−0.514205 | + | 0.857667i | \(0.671913\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.0022 | −0.398087 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.4237 | −1.77000 | −0.885002 | − | 0.465586i | \(-0.845843\pi\) | ||||
−0.885002 | + | 0.465586i | \(0.845843\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 50.6285 | 1.67556 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.12042 | −0.301512 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.07259 | 0.167512 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.0113 | −0.924009 | −0.462004 | − | 0.886878i | \(-0.652870\pi\) | ||||
−0.462004 | + | 0.886878i | \(0.652870\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.0800 | −0.365097 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.87211 | −0.193283 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.18614 | −0.170519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.03228 | −0.263815 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.0405 | 0.329419 | 0.164709 | − | 0.986342i | \(-0.447331\pi\) | ||||
0.164709 | + | 0.986342i | \(0.447331\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.8116 | −0.550977 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.6555 | 0.774447 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −21.1481 | −0.691617 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.2383 | −1.02051 | −0.510255 | − | 0.860023i | \(-0.670449\pi\) | ||||
−0.510255 | + | 0.860023i | \(0.670449\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −33.2045 | −1.08359 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.8715 | −0.941184 | −0.470592 | − | 0.882351i | \(-0.655960\pi\) | ||||
−0.470592 | + | 0.882351i | \(0.655960\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.0178 | −0.684434 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.13813 | −0.102083 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.1273 | 1.14148 | 0.570742 | − | 0.821130i | \(-0.306656\pi\) | ||||
0.570742 | + | 0.821130i | \(0.306656\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.3241 | 0.822056 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.0076 | −0.746073 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.72292 | 0.282563 | 0.141282 | − | 0.989969i | \(-0.454878\pi\) | ||||
0.141282 | + | 0.989969i | \(0.454878\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.6193 | −0.731943 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.0452 | 0.421693 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.97679 | −0.0638340 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.0833 | −0.357525 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.14740 | −0.230322 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.8563 | 0.510433 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.5185 | −1.52809 | −0.764047 | − | 0.645161i | \(-0.776790\pi\) | ||||
−0.764047 | + | 0.645161i | \(0.776790\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.39942 | −0.269828 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.6662 | 0.502754 | 0.251377 | − | 0.967889i | \(-0.419117\pi\) | ||||
0.251377 | + | 0.967889i | \(0.419117\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.08705 | −0.0348493 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.07788 | −0.0985711 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.0680 | 0.610041 | 0.305020 | − | 0.952346i | \(-0.401337\pi\) | ||||
0.305020 | + | 0.952346i | \(0.401337\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.2226 | −0.518476 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 32.9624 | 1.05241 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.59597 | 0.210379 | 0.105189 | − | 0.994452i | \(-0.466455\pi\) | ||||
0.105189 | + | 0.994452i | \(0.466455\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.0336 | 0.861361 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.330146 | −0.0105087 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −31.0334 | −0.986804 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.7341 | −1.73868 | −0.869342 | − | 0.494210i | \(-0.835457\pi\) | ||||
−0.869342 | + | 0.494210i | \(0.835457\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.2698 | 0.865381 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.11881 | 0.0988730 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.7121 | 1.47939 | 0.739694 | − | 0.672943i | \(-0.234970\pi\) | ||||
0.739694 | + | 0.672943i | \(0.234970\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −37.9253 | −1.19990 |
(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 | 6016.2.a.o.1.8 | yes | 13 | |
4.3 | odd | 2 | 6016.2.a.m.1.6 | ✓ | 13 | ||
8.3 | odd | 2 | 6016.2.a.p.1.8 | yes | 13 | ||
8.5 | even | 2 | 6016.2.a.n.1.6 | yes | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6016.2.a.m.1.6 | ✓ | 13 | 4.3 | odd | 2 | ||
6016.2.a.n.1.6 | yes | 13 | 8.5 | even | 2 | ||
6016.2.a.o.1.8 | yes | 13 | 1.1 | even | 1 | trivial | |
6016.2.a.p.1.8 | yes | 13 | 8.3 | odd | 2 |