Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3920,2,Mod(1,3920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3920, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3920.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3920.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: | \(31.3013575923\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1944.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 9x - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.705720\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3920.1 |
$q$-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 | ||||||||
\(3\) | 0.705720 | 0.407447 | 0.203724 | − | 0.979028i | \(-0.434696\pi\) | ||||
0.203724 | + | 0.979028i | \(0.434696\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.50196 | −0.833987 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.50196 | 1.35739 | 0.678696 | − | 0.734419i | \(-0.262545\pi\) | ||||
0.678696 | + | 0.734419i | \(0.262545\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.09052 | −1.41186 | −0.705928 | − | 0.708283i | \(-0.749470\pi\) | ||||
−0.705928 | + | 0.708283i | \(0.749470\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.705720 | −0.182216 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.09052 | −0.709014 | −0.354507 | − | 0.935053i | \(-0.615351\pi\) | ||||
−0.354507 | + | 0.935053i | \(0.615351\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.79624 | −1.20860 | −0.604300 | − | 0.796757i | \(-0.706547\pi\) | ||||
−0.604300 | + | 0.796757i | \(0.706547\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.88284 | −0.747253 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.50196 | 1.76447 | 0.882235 | − | 0.470810i | \(-0.156038\pi\) | ||||
0.882235 | + | 0.470810i | \(0.156038\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.41144 | 0.971923 | 0.485962 | − | 0.873980i | \(-0.338469\pi\) | ||||
0.485962 | + | 0.873980i | \(0.338469\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.17712 | 0.553066 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.09052 | 1.16567 | 0.582837 | − | 0.812589i | \(-0.301943\pi\) | ||||
0.582837 | + | 0.812589i | \(0.301943\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.59248 | −0.575257 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.59248 | 1.02957 | 0.514786 | − | 0.857319i | \(-0.327871\pi\) | ||||
0.514786 | + | 0.857319i | \(0.327871\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.70572 | −0.717616 | −0.358808 | − | 0.933411i | \(-0.616817\pi\) | ||||
−0.358808 | + | 0.933411i | \(0.616817\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.50196 | 0.372970 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.0944 | 1.47243 | 0.736213 | − | 0.676750i | \(-0.236612\pi\) | ||||
0.736213 | + | 0.676750i | \(0.236612\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.41144 | −0.197641 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.91340 | 1.36171 | 0.680855 | − | 0.732418i | \(-0.261608\pi\) | ||||
0.680855 | + | 0.732418i | \(0.261608\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.50196 | −0.607044 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.18104 | −0.288886 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.00000 | 1.04151 | 0.520756 | − | 0.853706i | \(-0.325650\pi\) | ||||
0.520756 | + | 0.853706i | \(0.325650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.91340 | 1.14124 | 0.570622 | − | 0.821213i | \(-0.306702\pi\) | ||||
0.570622 | + | 0.821213i | \(0.306702\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.09052 | 0.631401 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.117159 | 0.0143132 | 0.00715662 | − | 0.999974i | \(-0.497722\pi\) | ||||
0.00715662 | + | 0.999974i | \(0.497722\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.09052 | −0.492441 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.18104 | −0.957518 | −0.478759 | − | 0.877946i | \(-0.658913\pi\) | ||||
−0.478759 | + | 0.877946i | \(0.658913\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.705720 | 0.0814895 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.1810 | 1.59549 | 0.797746 | − | 0.602994i | \(-0.206026\pi\) | ||||
0.797746 | + | 0.602994i | \(0.206026\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.76568 | 0.529520 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.7057 | −1.17511 | −0.587553 | − | 0.809186i | \(-0.699909\pi\) | ||||
−0.587553 | + | 0.809186i | \(0.699909\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | 0.216930 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.70572 | 0.718929 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.09052 | −0.433594 | −0.216797 | − | 0.976217i | \(-0.569561\pi\) | ||||
−0.216797 | + | 0.976217i | \(0.569561\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.81896 | 0.396008 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.09052 | 0.317081 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.2637 | −1.13205 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.32092 | 0.330444 | 0.165222 | − | 0.986256i | \(-0.447166\pi\) | ||||
0.165222 | + | 0.986256i | \(0.447166\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.8868 | −1.07270 | −0.536352 | − | 0.843994i | \(-0.680198\pi\) | ||||
−0.536352 | + | 0.843994i | \(0.680198\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.88284 | −0.375368 | −0.187684 | − | 0.982229i | \(-0.560098\pi\) | ||||
−0.187684 | + | 0.982229i | \(0.560098\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.2716 | −0.983837 | −0.491919 | − | 0.870641i | \(-0.663704\pi\) | ||||
−0.491919 | + | 0.870641i | \(0.663704\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.00392 | 0.474951 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.82288 | 0.265554 | 0.132777 | − | 0.991146i | \(-0.457611\pi\) | ||||
0.132777 | + | 0.991146i | \(0.457611\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.79624 | 0.540502 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.7363 | 1.17747 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.26764 | 0.842513 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.65244 | 0.419497 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.73236 | 0.153722 | 0.0768610 | − | 0.997042i | \(-0.475510\pi\) | ||||
0.0768610 | + | 0.997042i | \(0.475510\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.32092 | −0.292391 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.7363 | −1.11277 | −0.556387 | − | 0.830923i | \(-0.687813\pi\) | ||||
−0.556387 | + | 0.830923i | \(0.687813\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.88284 | 0.334182 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.00000 | 0.341743 | 0.170872 | − | 0.985293i | \(-0.445342\pi\) | ||||
0.170872 | + | 0.985293i | \(0.445342\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.41144 | −0.119717 | −0.0598584 | − | 0.998207i | \(-0.519065\pi\) | ||||
−0.0598584 | + | 0.998207i | \(0.519065\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.12384 | 0.599936 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −22.9173 | −1.91644 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.50196 | −0.789095 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.0944 | 1.89197 | 0.945985 | − | 0.324210i | \(-0.105098\pi\) | ||||
0.945985 | + | 0.324210i | \(0.105098\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.407520 | 0.0331635 | 0.0165817 | − | 0.999863i | \(-0.494722\pi\) | ||||
0.0165817 | + | 0.999863i | \(0.494722\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.00392 | 0.404543 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.41144 | −0.434657 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0944 | 1.12486 | 0.562429 | − | 0.826845i | \(-0.309867\pi\) | ||||
0.562429 | + | 0.826845i | \(0.309867\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.99608 | 0.554825 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.1810 | 1.26740 | 0.633698 | − | 0.773580i | \(-0.281536\pi\) | ||||
0.633698 | + | 0.773580i | \(0.281536\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.17712 | −0.247339 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.79624 | 0.603291 | 0.301646 | − | 0.953420i | \(-0.402464\pi\) | ||||
0.301646 | + | 0.953420i | \(0.402464\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9134 | 0.993338 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.73236 | 0.591308 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.90948 | 0.677375 | 0.338688 | − | 0.940899i | \(-0.390017\pi\) | ||||
0.338688 | + | 0.940899i | \(0.390017\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.64576 | 0.424361 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.67908 | −0.125500 | −0.0627502 | − | 0.998029i | \(-0.519987\pi\) | ||||
−0.0627502 | + | 0.998029i | \(0.519987\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.5059 | −0.929555 | −0.464777 | − | 0.885428i | \(-0.653866\pi\) | ||||
−0.464777 | + | 0.885428i | \(0.653866\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.29036 | 0.464997 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.09052 | −0.521305 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.00392 | −0.658432 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.58856 | −0.476732 | −0.238366 | − | 0.971175i | \(-0.576612\pi\) | ||||
−0.238366 | + | 0.971175i | \(0.576612\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.8268 | 1.28320 | 0.641601 | − | 0.767039i | \(-0.278271\pi\) | ||||
0.641601 | + | 0.767039i | \(0.278271\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.59248 | 0.257263 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.09052 | 0.362685 | 0.181342 | − | 0.983420i | \(-0.441956\pi\) | ||||
0.181342 | + | 0.983420i | \(0.441956\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.3621 | 1.72698 | 0.863491 | − | 0.504364i | \(-0.168273\pi\) | ||||
0.863491 | + | 0.504364i | \(0.168273\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.0826814 | 0.00583189 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.59248 | −0.460439 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.5020 | 1.00796 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.9134 | −0.962410 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.26764 | 0.569168 | 0.284584 | − | 0.958651i | \(-0.408145\pi\) | ||||
0.284584 | + | 0.958651i | \(0.408145\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.70572 | 0.320927 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.77352 | −0.390138 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.1810 | 0.684851 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.8268 | −1.19377 | −0.596885 | − | 0.802327i | \(-0.703595\pi\) | ||||
−0.596885 | + | 0.802327i | \(0.703595\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.50196 | −0.166797 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.35816 | 0.355634 | 0.177817 | − | 0.984064i | \(-0.443097\pi\) | ||||
0.177817 | + | 0.984064i | \(0.443097\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.1810 | −1.59793 | −0.798964 | − | 0.601379i | \(-0.794618\pi\) | ||||
−0.798964 | + | 0.601379i | \(0.794618\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.0944 | −0.658489 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.0078 | 0.650079 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.7696 | 0.825997 | 0.412998 | − | 0.910732i | \(-0.364481\pi\) | ||||
0.412998 | + | 0.910732i | \(0.364481\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.0944 | 1.42323 | 0.711614 | − | 0.702571i | \(-0.247965\pi\) | ||||
0.711614 | + | 0.702571i | \(0.247965\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.0118 | 0.963005 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.7324 | 1.00103 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.55524 | −0.478794 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.5059 | −0.852484 | −0.426242 | − | 0.904609i | \(-0.640163\pi\) | ||||
−0.426242 | + | 0.904609i | \(0.640163\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26.0944 | −1.64054 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.41144 | 0.0883878 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.3621 | 1.02064 | 0.510319 | − | 0.859985i | \(-0.329527\pi\) | ||||
0.510319 | + | 0.859985i | \(0.329527\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −23.7735 | −1.47154 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.11324 | −0.561946 | −0.280973 | − | 0.959716i | \(-0.590657\pi\) | ||||
−0.280973 | + | 0.959716i | \(0.590657\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.91340 | −0.608975 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.88676 | −0.176667 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.91340 | −0.543460 | −0.271730 | − | 0.962374i | \(-0.587596\pi\) | ||||
−0.271730 | + | 0.962374i | \(0.587596\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.3621 | 0.993926 | 0.496963 | − | 0.867772i | \(-0.334449\pi\) | ||||
0.496963 | + | 0.867772i | \(0.334449\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.50196 | 0.271478 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.1771 | 0.671568 | 0.335784 | − | 0.941939i | \(-0.390999\pi\) | ||||
0.335784 | + | 0.941939i | \(0.390999\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.5392 | −0.810571 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.2755 | −1.68677 | −0.843387 | − | 0.537307i | \(-0.819442\pi\) | ||||
−0.843387 | + | 0.537307i | \(0.819442\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.8229 | −0.762241 | −0.381121 | − | 0.924525i | \(-0.624462\pi\) | ||||
−0.381121 | + | 0.924525i | \(0.624462\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.18104 | 0.129194 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.41144 | 0.0827400 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.90948 | −0.520497 | −0.260249 | − | 0.965542i | \(-0.583805\pi\) | ||||
−0.260249 | + | 0.965542i | \(0.583805\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.00000 | −0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −17.4804 | −1.01432 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 29.5059 | 1.70637 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.34364 | 0.134638 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.91340 | −0.510380 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.12108 | −0.520567 | −0.260284 | − | 0.965532i | \(-0.583816\pi\) | ||||
−0.260284 | + | 0.965532i | \(0.583816\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.68300 | −0.437071 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.1771 | −0.747206 | −0.373603 | − | 0.927589i | \(-0.621878\pi\) | ||||
−0.373603 | + | 0.927589i | \(0.621878\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.5392 | 0.991374 | 0.495687 | − | 0.868501i | \(-0.334916\pi\) | ||||
0.495687 | + | 0.868501i | \(0.334916\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.1850 | −0.740541 | −0.370271 | − | 0.928924i | \(-0.620735\pi\) | ||||
−0.370271 | + | 0.928924i | \(0.620735\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 42.7774 | 2.39508 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.74020 | −0.152943 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.18104 | 0.343922 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.09052 | −0.282371 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.24884 | −0.400862 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.50196 | −0.467310 | −0.233655 | − | 0.972320i | \(-0.575069\pi\) | ||||
−0.233655 | + | 0.972320i | \(0.575069\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −17.7402 | −0.972157 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.117159 | −0.00640108 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.1889 | 1.53555 | 0.767773 | − | 0.640722i | \(-0.221365\pi\) | ||||
0.767773 | + | 0.640722i | \(0.221365\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.99216 | 0.108199 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.3621 | 1.31928 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.09052 | 0.220226 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.70572 | −0.145251 | −0.0726253 | − | 0.997359i | \(-0.523138\pi\) | ||||
−0.0726253 | + | 0.997359i | \(0.523138\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.6830 | 0.732434 | 0.366217 | − | 0.930529i | \(-0.380653\pi\) | ||||
0.366217 | + | 0.930529i | \(0.380653\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.7657 | 1.05501 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.3621 | 1.08376 | 0.541882 | − | 0.840454i | \(-0.317712\pi\) | ||||
0.541882 | + | 0.840454i | \(0.317712\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.4154 | 0.971925 | 0.485963 | − | 0.873980i | \(-0.338469\pi\) | ||||
0.485963 | + | 0.873980i | \(0.338469\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.44868 | −0.497299 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.54036 | 0.343280 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.18104 | 0.428215 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.6230 | −1.33751 | −0.668756 | − | 0.743482i | \(-0.733173\pi\) | ||||
−0.668756 | + | 0.743482i | \(0.733173\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.4941 | −0.858650 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.1889 | 1.45956 | 0.729782 | − | 0.683679i | \(-0.239621\pi\) | ||||
0.729782 | + | 0.683679i | \(0.239621\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.705720 | −0.0364432 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −48.3699 | −2.49118 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.7402 | −1.11672 | −0.558359 | − | 0.829599i | \(-0.688569\pi\) | ||||
−0.558359 | + | 0.829599i | \(0.688569\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.22256 | 0.0626336 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.2116 | −1.03276 | −0.516382 | − | 0.856358i | \(-0.672722\pi\) | ||||
−0.516382 | + | 0.856358i | \(0.672722\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.7735 | 0.598482 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.8268 | 0.701046 | 0.350523 | − | 0.936554i | \(-0.386004\pi\) | ||||
0.350523 | + | 0.936554i | \(0.386004\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.5925 | 0.586257 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.98824 | −0.453397 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.1810 | −0.713526 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −36.3699 | −1.82535 | −0.912677 | − | 0.408682i | \(-0.865989\pi\) | ||||
−0.912677 | + | 0.408682i | \(0.865989\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.81896 | −0.340523 | −0.170261 | − | 0.985399i | \(-0.554461\pi\) | ||||
−0.170261 | + | 0.985399i | \(0.554461\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −27.5470 | −1.37222 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.76568 | −0.236809 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 31.9212 | 1.58228 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.8640 | 0.883320 | 0.441660 | − | 0.897182i | \(-0.354390\pi\) | ||||
0.441660 | + | 0.897182i | \(0.354390\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.82288 | 0.139242 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.7057 | 0.525523 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.996080 | −0.0487783 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.4487 | 0.901277 | 0.450639 | − | 0.892706i | \(-0.351196\pi\) | ||||
0.450639 | + | 0.892706i | \(0.351196\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.7324 | −0.523063 | −0.261532 | − | 0.965195i | \(-0.584228\pi\) | ||||
−0.261532 | + | 0.965195i | \(0.584228\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −25.2559 | −1.22798 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.00000 | −0.0970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16.1732 | −0.780850 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.58856 | −0.317360 | −0.158680 | − | 0.987330i | \(-0.550724\pi\) | ||||
−0.158680 | + | 0.987330i | \(0.550724\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.17712 | −0.248797 | −0.124398 | − | 0.992232i | \(-0.539700\pi\) | ||||
−0.124398 | + | 0.992232i | \(0.539700\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.70572 | −0.321515 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.9134 | 0.856914 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.0118 | 1.48011 | 0.740055 | − | 0.672546i | \(-0.234799\pi\) | ||||
0.740055 | + | 0.672546i | \(0.234799\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.87892 | −0.231805 | −0.115902 | − | 0.993261i | \(-0.536976\pi\) | ||||
−0.115902 | + | 0.993261i | \(0.536976\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.09052 | 0.193909 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.2982 | 0.770878 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.7696 | 1.31053 | 0.655264 | − | 0.755400i | \(-0.272557\pi\) | ||||
0.655264 | + | 0.755400i | \(0.272557\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.6791 | 1.39753 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.287595 | 0.0135124 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.0039 | −1.16963 | −0.584817 | − | 0.811165i | \(-0.698834\pi\) | ||||
−0.584817 | + | 0.811165i | \(0.698834\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.76568 | 0.362471 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.00784 | 0.186664 | 0.0933318 | − | 0.995635i | \(-0.470248\pi\) | ||||
0.0933318 | + | 0.995635i | \(0.470248\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.8002 | 1.71025 | 0.855124 | − | 0.518423i | \(-0.173481\pi\) | ||||
0.855124 | + | 0.518423i | \(0.173481\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.81896 | −0.177100 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.4753 | −1.08631 | −0.543154 | − | 0.839633i | \(-0.682770\pi\) | ||||
−0.543154 | + | 0.839633i | \(0.682770\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.94672 | 0.458321 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.1850 | −0.974086 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.09052 | −0.141803 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.8029 | −1.13565 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −37.7735 | −1.72592 | −0.862958 | − | 0.505275i | \(-0.831391\pi\) | ||||
−0.862958 | + | 0.505275i | \(0.831391\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36.0944 | −1.64576 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.00000 | −0.0908153 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.17320 | 0.279734 | 0.139867 | − | 0.990170i | \(-0.455332\pi\) | ||||
0.139867 | + | 0.990170i | \(0.455332\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.4193 | 0.516398 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.7814 | −1.79531 | −0.897654 | − | 0.440701i | \(-0.854730\pi\) | ||||
−0.897654 | + | 0.440701i | \(0.854730\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.0039 | −0.855893 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.2637 | 0.506267 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.76568 | −0.168575 | −0.0842875 | − | 0.996441i | \(-0.526861\pi\) | ||||
−0.0842875 | + | 0.996441i | \(0.526861\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.50196 | 0.245809 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.7057 | 0.834047 | 0.417023 | − | 0.908896i | \(-0.363073\pi\) | ||||
0.417023 | + | 0.908896i | \(0.363073\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.32092 | −0.147779 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.11324 | 0.404733 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.3248 | −0.546289 | −0.273144 | − | 0.961973i | \(-0.588064\pi\) | ||||
−0.273144 | + | 0.961973i | \(0.588064\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.0000 | 0.529813 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.8868 | 0.479728 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 45.4448 | 1.99866 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.28759 | 0.275995 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.5592 | 1.29501 | 0.647505 | − | 0.762061i | \(-0.275812\pi\) | ||||
0.647505 | + | 0.762061i | \(0.275812\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −43.0039 | −1.88043 | −0.940215 | − | 0.340581i | \(-0.889376\pi\) | ||||
−0.940215 | + | 0.340581i | \(0.889376\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.8229 | −0.471452 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.5964 | 0.460713 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.0157 | −0.868606 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.5592 | −1.45361 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.88284 | 0.167870 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.18496 | −0.0511348 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.96668 | −0.213534 | −0.106767 | − | 0.994284i | \(-0.534050\pi\) | ||||
−0.106767 | + | 0.994284i | \(0.534050\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.82564 | −0.378745 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.2716 | 0.439985 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.1250 | 0.945997 | 0.472998 | − | 0.881063i | \(-0.343172\pi\) | ||||
0.472998 | + | 0.881063i | \(0.343172\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −22.3010 | −0.951782 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.3660 | −1.25103 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.00392 | −0.212405 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.55916 | 0.235549 | 0.117775 | − | 0.993040i | \(-0.462424\pi\) | ||||
0.117775 | + | 0.993040i | \(0.462424\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.9546 | 1.01317 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.35424 | −0.268276 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.48316 | 0.399668 | 0.199834 | − | 0.979830i | \(-0.435960\pi\) | ||||
0.199834 | + | 0.979830i | \(0.435960\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.82288 | −0.118759 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.2833 | −1.43723 | −0.718616 | − | 0.695407i | \(-0.755224\pi\) | ||||
−0.718616 | + | 0.695407i | \(0.755224\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.5470 | 1.32020 | 0.660101 | − | 0.751177i | \(-0.270513\pi\) | ||||
0.660101 | + | 0.751177i | \(0.270513\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.64968 | −0.194243 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.79624 | −0.241720 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.6418 | 0.443025 | 0.221513 | − | 0.975157i | \(-0.428901\pi\) | ||||
0.221513 | + | 0.975157i | \(0.428901\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.5807 | 0.522837 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 44.6297 | 1.84837 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.7363 | −0.526580 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.64184 | 0.274138 | 0.137069 | − | 0.990562i | \(-0.456232\pi\) | ||||
0.137069 | + | 0.990562i | \(0.456232\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.7242 | −0.689107 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.59248 | 0.147775 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.5392 | −0.555988 | −0.277994 | − | 0.960583i | \(-0.589670\pi\) | ||||
−0.277994 | + | 0.960583i | \(0.589670\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.1928 | 0.703654 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.1810 | −1.06973 | −0.534864 | − | 0.844938i | \(-0.679637\pi\) | ||||
−0.534864 | + | 0.844938i | \(0.679637\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.0078 | 1.46879 | 0.734395 | − | 0.678722i | \(-0.237466\pi\) | ||||
0.734395 | + | 0.678722i | \(0.237466\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.293127 | −0.0119371 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.26764 | −0.376783 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.7430 | 0.963697 | 0.481849 | − | 0.876255i | \(-0.339966\pi\) | ||||
0.481849 | + | 0.876255i | \(0.339966\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −51.3860 | −2.07885 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.55916 | −0.386091 | −0.193045 | − | 0.981190i | \(-0.561836\pi\) | ||||
−0.193045 | + | 0.981190i | \(0.561836\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.65244 | −0.187605 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.8268 | −0.798197 | −0.399098 | − | 0.916908i | \(-0.630677\pi\) | ||||
−0.399098 | + | 0.916908i | \(0.630677\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.1516 | 1.09132 | 0.545658 | − | 0.838008i | \(-0.316280\pi\) | ||||
0.545658 | + | 0.838008i | \(0.316280\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.5059 | 0.903130 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.81896 | −0.392131 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.1810 | −0.565435 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 49.7735 | 1.98145 | 0.990726 | − | 0.135873i | \(-0.0433838\pi\) | ||||
0.990726 | + | 0.135873i | \(0.0433838\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.83464 | 0.231906 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.73236 | −0.0687465 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.2304 | 0.799053 | 0.399526 | − | 0.916722i | \(-0.369175\pi\) | ||||
0.399526 | + | 0.916722i | \(0.369175\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.1850 | −0.993198 | −0.496599 | − | 0.867980i | \(-0.665418\pi\) | ||||
−0.496599 | + | 0.867980i | \(0.665418\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.32092 | 0.130761 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.5698 | 0.769367 | 0.384683 | − | 0.923049i | \(-0.374311\pi\) | ||||
0.384683 | + | 0.923049i | \(0.374311\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.0157 | 1.41374 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.2676 | 0.714868 | 0.357434 | − | 0.933938i | \(-0.383652\pi\) | ||||
0.357434 | + | 0.933938i | \(0.383652\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.7363 | 0.497648 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20.4686 | 0.798558 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −46.0078 | −1.79221 | −0.896105 | − | 0.443841i | \(-0.853615\pi\) | ||||
−0.896105 | + | 0.443841i | \(0.853615\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 48.4604 | 1.88489 | 0.942446 | − | 0.334357i | \(-0.108519\pi\) | ||||
0.942446 | + | 0.334357i | \(0.108519\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.18496 | 0.279041 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −55.0756 | −2.13254 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.5807 | −0.486399 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 40.1278 | 1.54912 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.0118 | −0.578661 | −0.289330 | − | 0.957229i | \(-0.593433\pi\) | ||||
−0.289330 | + | 0.957229i | \(0.593433\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.88284 | −0.149451 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.91340 | −0.304137 | −0.152068 | − | 0.988370i | \(-0.548593\pi\) | ||||
−0.152068 | + | 0.988370i | \(0.548593\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.78136 | 0.144902 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.7096 | −1.13681 | −0.568404 | − | 0.822750i | \(-0.692439\pi\) | ||||
−0.568404 | + | 0.822750i | \(0.692439\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.00000 | −0.152832 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.0650 | −0.651072 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −50.4644 | −1.92254 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.7735 | −0.828304 | −0.414152 | − | 0.910208i | \(-0.635922\pi\) | ||||
−0.414152 | + | 0.910208i | \(0.635922\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.41144 | 0.0535389 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.1850 | −0.499416 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.7030 | 0.480470 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.0905 | 0.909886 | 0.454943 | − | 0.890520i | \(-0.349660\pi\) | ||||
0.454943 | + | 0.890520i | \(0.349660\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.9134 | −0.826479 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.12384 | −0.268300 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.0372 | −0.902738 | −0.451369 | − | 0.892337i | \(-0.649064\pi\) | ||||
−0.451369 | + | 0.892337i | \(0.649064\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −35.4804 | −1.33062 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31.3660 | −1.17467 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.9173 | 0.857059 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.01176 | 0.336550 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.234318 | −0.00873858 | −0.00436929 | − | 0.999990i | \(-0.501391\pi\) | ||||
−0.00436929 | + | 0.999990i | \(0.501391\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.5925 | 0.579891 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.50196 | 0.352894 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.44200 | 0.350184 | 0.175092 | − | 0.984552i | \(-0.443978\pi\) | ||||
0.175092 | + | 0.984552i | \(0.443978\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.70295 | −0.137146 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.41144 | 0.348095 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.7441 | 1.06169 | 0.530844 | − | 0.847469i | \(-0.321875\pi\) | ||||
0.530844 | + | 0.847469i | \(0.321875\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.527445 | 0.0194287 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.1477 | 0.961859 | 0.480930 | − | 0.876759i | \(-0.340299\pi\) | ||||
0.480930 | + | 0.876759i | \(0.340299\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.1026 | 0.407865 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.7547 | −1.20165 | −0.600827 | − | 0.799379i | \(-0.705162\pi\) | ||||
−0.600827 | + | 0.799379i | \(0.705162\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.0944 | −0.846115 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 26.7853 | 0.980022 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.1810 | −0.955360 | −0.477680 | − | 0.878534i | \(-0.658522\pi\) | ||||
−0.477680 | + | 0.878534i | \(0.658522\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.53136 | −0.347342 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.407520 | −0.0148312 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.8229 | 0.611438 | 0.305719 | − | 0.952122i | \(-0.401103\pi\) | ||||
0.305719 | + | 0.952122i | \(0.401103\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.4154 | −0.668435 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.90556 | 0.214076 | 0.107038 | − | 0.994255i | \(-0.465863\pi\) | ||||
0.107038 | + | 0.994255i | \(0.465863\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.00392 | −0.180917 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −40.7242 | −1.47046 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.275481 | −0.00993410 | −0.00496705 | − | 0.999988i | \(-0.501581\pi\) | ||||
−0.00496705 | + | 0.999988i | \(0.501581\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.5470 | 0.415857 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.37812 | −0.265372 | −0.132686 | − | 0.991158i | \(-0.542360\pi\) | ||||
−0.132686 | + | 0.991158i | \(0.542360\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.41144 | 0.194385 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.3742 | −0.729981 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −36.8946 | −1.31851 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.0944 | −0.503052 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.6603 | −0.665167 | −0.332584 | − | 0.943074i | \(-0.607920\pi\) | ||||
−0.332584 | + | 0.943074i | \(0.607920\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.43139 | −0.228964 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −45.3738 | −1.61127 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.99608 | −0.248125 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.81896 | −0.347805 | −0.173903 | − | 0.984763i | \(-0.555638\pi\) | ||||
−0.173903 | + | 0.984763i | \(0.555638\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.1889 | −0.714231 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.2343 | 0.361612 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −36.8307 | −1.29973 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.29036 | −0.221431 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32.0039 | −1.12520 | −0.562599 | − | 0.826730i | \(-0.690198\pi\) | ||||
−0.562599 | + | 0.826730i | \(0.690198\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.5137 | 1.52797 | 0.763987 | − | 0.645232i | \(-0.223239\pi\) | ||||
0.763987 | + | 0.645232i | \(0.223239\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.5470 | 0.404972 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.1810 | −0.566797 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.5431 | 0.508799 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.7242 | −1.21188 | −0.605941 | − | 0.795510i | \(-0.707203\pi\) | ||||
−0.605941 | + | 0.795510i | \(0.707203\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.3021 | 0.812261 | 0.406130 | − | 0.913815i | \(-0.366878\pi\) | ||||
0.406130 | + | 0.913815i | \(0.366878\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.17712 | 0.110613 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.2943 | −0.392741 | −0.196370 | − | 0.980530i | \(-0.562915\pi\) | ||||
−0.196370 | + | 0.980530i | \(0.562915\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.0078 | −0.694901 | −0.347450 | − | 0.937698i | \(-0.612953\pi\) | ||||
−0.347450 | + | 0.937698i | \(0.612953\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.88791 | 0.273629 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.79624 | −0.269800 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21.0118 | −0.726273 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.5846 | 0.468994 | 0.234497 | − | 0.972117i | \(-0.424656\pi\) | ||||
0.234497 | + | 0.972117i | \(0.424656\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 61.2872 | 2.11335 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.9546 | −0.687272 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.9134 | −0.444234 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.04936 | −0.310573 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −41.0984 | −1.40883 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.6336 | 1.01464 | 0.507318 | − | 0.861759i | \(-0.330637\pi\) | ||||
0.507318 | + | 0.861759i | \(0.330637\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.73236 | −0.264441 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.8307 | 0.643245 | 0.321623 | − | 0.946868i | \(-0.395772\pi\) | ||||
0.321623 | + | 0.946868i | \(0.395772\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.00000 | 0.272956 | 0.136478 | − | 0.990643i | \(-0.456422\pi\) | ||||
0.136478 | + | 0.990643i | \(0.456422\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.8574 | −0.675952 | −0.337976 | − | 0.941155i | \(-0.609742\pi\) | ||||
−0.337976 | + | 0.941155i | \(0.609742\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.90948 | −0.302931 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.17436 | −0.311577 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 63.8425 | 2.16571 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.596400 | −0.0202082 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.00392 | −0.169357 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.5513 | −0.457595 | −0.228798 | − | 0.973474i | \(-0.573479\pi\) | ||||
−0.228798 | + | 0.973474i | \(0.573479\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.28759 | −0.212075 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.5964 | 1.60356 | 0.801782 | − | 0.597617i | \(-0.203886\pi\) | ||||
0.801782 | + | 0.597617i | \(0.203886\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.6497 | −1.23336 | −0.616680 | − | 0.787214i | \(-0.711523\pi\) | ||||
−0.616680 | + | 0.787214i | \(0.711523\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.64576 | −0.189780 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46.1250 | 1.54873 | 0.774363 | − | 0.632742i | \(-0.218071\pi\) | ||||
0.774363 | + | 0.632742i | \(0.218071\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.4549 | 0.718767 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −31.1971 | −1.04397 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.67908 | 0.0561255 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.8229 | 0.695256 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 51.4193 | 1.71493 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.8268 | −0.660526 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.5059 | 0.415709 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.06780 | 0.168274 | 0.0841368 | − | 0.996454i | \(-0.473187\pi\) | ||||
0.0841368 | + | 0.996454i | \(0.473187\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.30881 | −0.275586 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.41536 | 0.0800244 | 0.0400122 | − | 0.999199i | \(-0.487260\pi\) | ||||
0.0400122 | + | 0.999199i | \(0.487260\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −48.1967 | −1.59508 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.29036 | −0.207953 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.5510 | −1.20570 | −0.602852 | − | 0.797853i | \(-0.705969\pi\) | ||||
−0.602852 | + | 0.797853i | \(0.705969\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.43692 | −0.212104 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.09052 | 0.233135 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 27.2382 | 0.894621 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.2304 | 0.532502 | 0.266251 | − | 0.963904i | \(-0.414215\pi\) | ||||
0.266251 | + | 0.963904i | \(0.414215\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.29935 | −0.304447 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.00392 | 0.294460 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.1889 | 1.44359 | 0.721794 | − | 0.692108i | \(-0.243318\pi\) | ||||
0.721794 | + | 0.692108i | \(0.243318\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.3778 | 0.403933 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.4726 | −0.765183 | −0.382592 | − | 0.923918i | \(-0.624968\pi\) | ||||
−0.382592 | + | 0.923918i | \(0.624968\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −38.2116 | −1.24434 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −56.0717 | −1.82209 | −0.911043 | − | 0.412311i | \(-0.864722\pi\) | ||||
−0.911043 | + | 0.412311i | \(0.864722\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41.6458 | 1.35188 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.30489 | −0.301732 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.7163 | −0.735854 | −0.367927 | − | 0.929855i | \(-0.619932\pi\) | ||||
−0.367927 | + | 0.929855i | \(0.619932\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.58856 | 0.213201 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 30.1889 | 0.975868 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.71632 | −0.0553653 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.71471 | 0.313052 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.8268 | −0.573865 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.9400 | −0.351808 | −0.175904 | − | 0.984407i | \(-0.556285\pi\) | ||||
−0.175904 | + | 0.984407i | \(0.556285\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.36208 | 0.140130 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.7402 | 0.826042 | 0.413021 | − | 0.910721i | \(-0.364474\pi\) | ||||
0.413021 | + | 0.910721i | \(0.364474\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.59248 | −0.115051 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.8229 | 0.538212 | 0.269106 | − | 0.963111i | \(-0.413272\pi\) | ||||
0.269106 | + | 0.963111i | \(0.413272\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.4154 | −0.588557 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25.6990 | 0.820507 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −43.9851 | −1.40291 | −0.701454 | − | 0.712715i | \(-0.747465\pi\) | ||||
−0.701454 | + | 0.712715i | \(0.747465\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.09052 | −0.162197 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.2755 | 0.867310 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.2343 | 1.40515 | 0.702575 | − | 0.711610i | \(-0.252034\pi\) | ||||
0.702575 | + | 0.711610i | \(0.252034\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.00000 | −0.190404 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.3621 | −0.772330 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.1967 | −1.08302 | −0.541510 | − | 0.840694i | \(-0.682147\pi\) | ||||
−0.541510 | + | 0.840694i | \(0.682147\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −27.5314 | −0.871054 |
(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 | 3920.2.a.cb.1.2 | 3 | ||
4.3 | odd | 2 | 1960.2.a.v.1.2 | 3 | |||
7.3 | odd | 6 | 560.2.q.l.401.2 | 6 | |||
7.5 | odd | 6 | 560.2.q.l.81.2 | 6 | |||
7.6 | odd | 2 | 3920.2.a.cc.1.2 | 3 | |||
20.19 | odd | 2 | 9800.2.a.cf.1.2 | 3 | |||
28.3 | even | 6 | 280.2.q.e.121.2 | yes | 6 | ||
28.11 | odd | 6 | 1960.2.q.w.961.2 | 6 | |||
28.19 | even | 6 | 280.2.q.e.81.2 | ✓ | 6 | ||
28.23 | odd | 6 | 1960.2.q.w.361.2 | 6 | |||
28.27 | even | 2 | 1960.2.a.w.1.2 | 3 | |||
84.47 | odd | 6 | 2520.2.bi.q.361.2 | 6 | |||
84.59 | odd | 6 | 2520.2.bi.q.1801.2 | 6 | |||
140.3 | odd | 12 | 1400.2.bh.i.849.4 | 12 | |||
140.19 | even | 6 | 1400.2.q.j.1201.2 | 6 | |||
140.47 | odd | 12 | 1400.2.bh.i.249.4 | 12 | |||
140.59 | even | 6 | 1400.2.q.j.401.2 | 6 | |||
140.87 | odd | 12 | 1400.2.bh.i.849.3 | 12 | |||
140.103 | odd | 12 | 1400.2.bh.i.249.3 | 12 | |||
140.139 | even | 2 | 9800.2.a.ce.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.q.e.81.2 | ✓ | 6 | 28.19 | even | 6 | ||
280.2.q.e.121.2 | yes | 6 | 28.3 | even | 6 | ||
560.2.q.l.81.2 | 6 | 7.5 | odd | 6 | |||
560.2.q.l.401.2 | 6 | 7.3 | odd | 6 | |||
1400.2.q.j.401.2 | 6 | 140.59 | even | 6 | |||
1400.2.q.j.1201.2 | 6 | 140.19 | even | 6 | |||
1400.2.bh.i.249.3 | 12 | 140.103 | odd | 12 | |||
1400.2.bh.i.249.4 | 12 | 140.47 | odd | 12 | |||
1400.2.bh.i.849.3 | 12 | 140.87 | odd | 12 | |||
1400.2.bh.i.849.4 | 12 | 140.3 | odd | 12 | |||
1960.2.a.v.1.2 | 3 | 4.3 | odd | 2 | |||
1960.2.a.w.1.2 | 3 | 28.27 | even | 2 | |||
1960.2.q.w.361.2 | 6 | 28.23 | odd | 6 | |||
1960.2.q.w.961.2 | 6 | 28.11 | odd | 6 | |||
2520.2.bi.q.361.2 | 6 | 84.47 | odd | 6 | |||
2520.2.bi.q.1801.2 | 6 | 84.59 | odd | 6 | |||
3920.2.a.cb.1.2 | 3 | 1.1 | even | 1 | trivial | ||
3920.2.a.cc.1.2 | 3 | 7.6 | odd | 2 | |||
9800.2.a.ce.1.2 | 3 | 140.139 | even | 2 | |||
9800.2.a.cf.1.2 | 3 | 20.19 | odd | 2 |