Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7569,2,Mod(1,7569)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7569, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("7569.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7569 = 3^{2} \cdot 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7569.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: | \(60.4387692899\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 14x^{7} + 9x^{6} + 70x^{5} - 23x^{4} - 141x^{3} + 14x^{2} + 84x - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 87) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(2.19659\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7569.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.19659 | 1.55322 | 0.776612 | − | 0.629979i | \(-0.216937\pi\) | ||||
0.776612 | + | 0.629979i | \(0.216937\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.82501 | 1.41250 | ||||||||
\(5\) | 4.07769 | 1.82360 | 0.911798 | − | 0.410638i | \(-0.134694\pi\) | ||||
0.911798 | + | 0.410638i | \(0.134694\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.64733 | 1.37856 | 0.689281 | − | 0.724495i | \(-0.257927\pi\) | ||||
0.689281 | + | 0.724495i | \(0.257927\pi\) | |||||||
\(8\) | 1.81221 | 0.640711 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.95700 | 2.83245 | ||||||||
\(11\) | 3.52776 | 1.06366 | 0.531830 | − | 0.846851i | \(-0.321504\pi\) | ||||
0.531830 | + | 0.846851i | \(0.321504\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.926540 | 0.256976 | 0.128488 | − | 0.991711i | \(-0.458988\pi\) | ||||
0.128488 | + | 0.991711i | \(0.458988\pi\) | |||||||
\(14\) | 8.01169 | 2.14121 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.66934 | −0.417336 | ||||||||
\(17\) | −1.61861 | −0.392571 | −0.196286 | − | 0.980547i | \(-0.562888\pi\) | ||||
−0.196286 | + | 0.980547i | \(0.562888\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.98608 | −0.914470 | −0.457235 | − | 0.889346i | \(-0.651160\pi\) | ||||
−0.457235 | + | 0.889346i | \(0.651160\pi\) | |||||||
\(20\) | 11.5195 | 2.57584 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.74905 | 1.65210 | ||||||||
\(23\) | −1.54577 | −0.322315 | −0.161158 | − | 0.986929i | \(-0.551523\pi\) | ||||
−0.161158 | + | 0.986929i | \(0.551523\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.6275 | 2.32550 | ||||||||
\(26\) | 2.03523 | 0.399141 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 10.3037 | 1.94722 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.60775 | −0.288760 | −0.144380 | − | 0.989522i | \(-0.546119\pi\) | ||||
−0.144380 | + | 0.989522i | \(0.546119\pi\) | |||||||
\(32\) | −7.29128 | −1.28893 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.55543 | −0.609751 | ||||||||
\(35\) | 14.8727 | 2.51394 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.30404 | −0.871979 | −0.435990 | − | 0.899952i | \(-0.643602\pi\) | ||||
−0.435990 | + | 0.899952i | \(0.643602\pi\) | |||||||
\(38\) | −8.75579 | −1.42038 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.38960 | 1.16840 | ||||||||
\(41\) | 6.71590 | 1.04885 | 0.524423 | − | 0.851458i | \(-0.324281\pi\) | ||||
0.524423 | + | 0.851458i | \(0.324281\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.42936 | 0.675471 | 0.337736 | − | 0.941241i | \(-0.390339\pi\) | ||||
0.337736 | + | 0.941241i | \(0.390339\pi\) | |||||||
\(44\) | 9.96596 | 1.50242 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.39542 | −0.500628 | ||||||||
\(47\) | −3.33787 | −0.486879 | −0.243439 | − | 0.969916i | \(-0.578276\pi\) | ||||
−0.243439 | + | 0.969916i | \(0.578276\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.30302 | 0.900431 | ||||||||
\(50\) | 25.5409 | 3.61203 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.61748 | 0.362980 | ||||||||
\(53\) | −2.03823 | −0.279972 | −0.139986 | − | 0.990153i | \(-0.544706\pi\) | ||||
−0.139986 | + | 0.990153i | \(0.544706\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.3851 | 1.93969 | ||||||||
\(56\) | 6.60971 | 0.883260 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.29049 | −0.949141 | −0.474571 | − | 0.880217i | \(-0.657397\pi\) | ||||
−0.474571 | + | 0.880217i | \(0.657397\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00554 | −0.768930 | −0.384465 | − | 0.923139i | \(-0.625614\pi\) | ||||
−0.384465 | + | 0.923139i | \(0.625614\pi\) | |||||||
\(62\) | −3.53156 | −0.448509 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.6773 | −1.58466 | ||||||||
\(65\) | 3.77814 | 0.468620 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.48235 | 1.15845 | 0.579227 | − | 0.815167i | \(-0.303355\pi\) | ||||
0.579227 | + | 0.815167i | \(0.303355\pi\) | |||||||
\(68\) | −4.57260 | −0.554509 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 32.6692 | 3.90471 | ||||||||
\(71\) | −8.44759 | −1.00255 | −0.501273 | − | 0.865289i | \(-0.667135\pi\) | ||||
−0.501273 | + | 0.865289i | \(0.667135\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.56757 | 0.885718 | 0.442859 | − | 0.896591i | \(-0.353964\pi\) | ||||
0.442859 | + | 0.896591i | \(0.353964\pi\) | |||||||
\(74\) | −11.6508 | −1.35438 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11.2607 | −1.29169 | ||||||||
\(77\) | 12.8669 | 1.46632 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.287887 | 0.0323898 | 0.0161949 | − | 0.999869i | \(-0.494845\pi\) | ||||
0.0161949 | + | 0.999869i | \(0.494845\pi\) | |||||||
\(80\) | −6.80706 | −0.761053 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 14.7521 | 1.62909 | ||||||||
\(83\) | 6.47754 | 0.711003 | 0.355501 | − | 0.934676i | \(-0.384310\pi\) | ||||
0.355501 | + | 0.934676i | \(0.384310\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.60020 | −0.715892 | ||||||||
\(86\) | 9.72949 | 1.04916 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.39303 | 0.681499 | ||||||||
\(89\) | −16.5093 | −1.74999 | −0.874993 | − | 0.484136i | \(-0.839134\pi\) | ||||
−0.874993 | + | 0.484136i | \(0.839134\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.37940 | 0.354257 | ||||||||
\(92\) | −4.36681 | −0.455272 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.33194 | −0.756232 | ||||||||
\(95\) | −16.2540 | −1.66762 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0522 | 1.02064 | 0.510322 | − | 0.859983i | \(-0.329526\pi\) | ||||
0.510322 | + | 0.859983i | \(0.329526\pi\) | |||||||
\(98\) | 13.8451 | 1.39857 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 32.8478 | 3.28478 | ||||||||
\(101\) | −8.23922 | −0.819833 | −0.409917 | − | 0.912123i | \(-0.634442\pi\) | ||||
−0.409917 | + | 0.912123i | \(0.634442\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.62704 | 0.751515 | 0.375757 | − | 0.926718i | \(-0.377383\pi\) | ||||
0.375757 | + | 0.926718i | \(0.377383\pi\) | |||||||
\(104\) | 1.67908 | 0.164647 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.47715 | −0.434859 | ||||||||
\(107\) | 16.7576 | 1.62002 | 0.810011 | − | 0.586414i | \(-0.199461\pi\) | ||||
0.810011 | + | 0.586414i | \(0.199461\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.7116 | −1.21755 | −0.608775 | − | 0.793343i | \(-0.708339\pi\) | ||||
−0.608775 | + | 0.793343i | \(0.708339\pi\) | |||||||
\(110\) | 31.5982 | 3.01277 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.08865 | −0.575323 | ||||||||
\(113\) | 8.46482 | 0.796303 | 0.398152 | − | 0.917320i | \(-0.369652\pi\) | ||||
0.398152 | + | 0.917320i | \(0.369652\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.30316 | −0.587773 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.0142 | −1.47423 | ||||||||
\(119\) | −5.90362 | −0.541184 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.44511 | 0.131374 | ||||||||
\(122\) | −13.1917 | −1.19432 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.54190 | −0.407875 | ||||||||
\(125\) | 27.0250 | 2.41719 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.8052 | −1.57995 | −0.789977 | − | 0.613137i | \(-0.789907\pi\) | ||||
−0.789977 | + | 0.613137i | \(0.789907\pi\) | |||||||
\(128\) | −13.2642 | −1.17240 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.29902 | 0.727872 | ||||||||
\(131\) | −11.3299 | −0.989897 | −0.494949 | − | 0.868922i | \(-0.664813\pi\) | ||||
−0.494949 | + | 0.868922i | \(0.664813\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.5386 | −1.26065 | ||||||||
\(134\) | 20.8288 | 1.79934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.93326 | −0.251525 | ||||||||
\(137\) | −8.31246 | −0.710182 | −0.355091 | − | 0.934832i | \(-0.615550\pi\) | ||||
−0.355091 | + | 0.934832i | \(0.615550\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.11275 | −0.264020 | −0.132010 | − | 0.991248i | \(-0.542143\pi\) | ||||
−0.132010 | + | 0.991248i | \(0.542143\pi\) | |||||||
\(140\) | 42.0154 | 3.55095 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −18.5559 | −1.55718 | ||||||||
\(143\) | 3.26861 | 0.273335 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 16.6229 | 1.37572 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −14.9840 | −1.23167 | ||||||||
\(149\) | −15.1558 | −1.24161 | −0.620807 | − | 0.783963i | \(-0.713195\pi\) | ||||
−0.620807 | + | 0.783963i | \(0.713195\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.678890 | 0.0552473 | 0.0276237 | − | 0.999618i | \(-0.491206\pi\) | ||||
0.0276237 | + | 0.999618i | \(0.491206\pi\) | |||||||
\(152\) | −7.22360 | −0.585911 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 28.2633 | 2.27752 | ||||||||
\(155\) | −6.55589 | −0.526582 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.23584 | −0.497674 | −0.248837 | − | 0.968545i | \(-0.580048\pi\) | ||||
−0.248837 | + | 0.968545i | \(0.580048\pi\) | |||||||
\(158\) | 0.632370 | 0.0503086 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −29.7315 | −2.35048 | ||||||||
\(161\) | −5.63793 | −0.444331 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.3163 | −1.19967 | −0.599834 | − | 0.800124i | \(-0.704767\pi\) | ||||
−0.599834 | + | 0.800124i | \(0.704767\pi\) | |||||||
\(164\) | 18.9725 | 1.48150 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.2285 | 1.10435 | ||||||||
\(167\) | 15.7861 | 1.22156 | 0.610781 | − | 0.791799i | \(-0.290855\pi\) | ||||
0.610781 | + | 0.791799i | \(0.290855\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.1415 | −0.933963 | ||||||||
\(170\) | −14.4979 | −1.11194 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.5130 | 0.954106 | ||||||||
\(173\) | 3.44502 | 0.261920 | 0.130960 | − | 0.991388i | \(-0.458194\pi\) | ||||
0.130960 | + | 0.991388i | \(0.458194\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 42.4094 | 3.20585 | ||||||||
\(176\) | −5.88905 | −0.443904 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −36.2642 | −2.71812 | ||||||||
\(179\) | 12.0378 | 0.899744 | 0.449872 | − | 0.893093i | \(-0.351470\pi\) | ||||
0.449872 | + | 0.893093i | \(0.351470\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.41926 | 0.179823 | 0.0899113 | − | 0.995950i | \(-0.471342\pi\) | ||||
0.0899113 | + | 0.995950i | \(0.471342\pi\) | |||||||
\(182\) | 7.42315 | 0.550241 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.80125 | −0.206511 | ||||||||
\(185\) | −21.6282 | −1.59014 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.71008 | −0.417563 | ||||||||
\(188\) | −9.42952 | −0.687719 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −35.7034 | −2.59019 | ||||||||
\(191\) | −5.83662 | −0.422323 | −0.211162 | − | 0.977451i | \(-0.567725\pi\) | ||||
−0.211162 | + | 0.977451i | \(0.567725\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.9903 | 1.43894 | 0.719468 | − | 0.694525i | \(-0.244386\pi\) | ||||
0.719468 | + | 0.694525i | \(0.244386\pi\) | |||||||
\(194\) | 22.0805 | 1.58529 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 17.8061 | 1.27186 | ||||||||
\(197\) | 11.7126 | 0.834486 | 0.417243 | − | 0.908795i | \(-0.362996\pi\) | ||||
0.417243 | + | 0.908795i | \(0.362996\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.6484 | −1.18017 | −0.590086 | − | 0.807340i | \(-0.700906\pi\) | ||||
−0.590086 | + | 0.807340i | \(0.700906\pi\) | |||||||
\(200\) | 21.0715 | 1.48998 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −18.0982 | −1.27338 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 27.3853 | 1.91267 | ||||||||
\(206\) | 16.7535 | 1.16727 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.54671 | −0.107245 | ||||||||
\(209\) | −14.0620 | −0.972686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.2435 | −1.66899 | −0.834496 | − | 0.551014i | \(-0.814241\pi\) | ||||
−0.834496 | + | 0.551014i | \(0.814241\pi\) | |||||||
\(212\) | −5.75801 | −0.395462 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 36.8097 | 2.51626 | ||||||||
\(215\) | 18.0615 | 1.23179 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.86399 | −0.398073 | ||||||||
\(218\) | −27.9222 | −1.89113 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 40.6381 | 2.73982 | ||||||||
\(221\) | −1.49971 | −0.100881 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.3179 | 1.89631 | 0.948153 | − | 0.317814i | \(-0.102949\pi\) | ||||
0.948153 | + | 0.317814i | \(0.102949\pi\) | |||||||
\(224\) | −26.5937 | −1.77687 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.5937 | 1.23684 | ||||||||
\(227\) | −9.86418 | −0.654709 | −0.327354 | − | 0.944902i | \(-0.606157\pi\) | ||||
−0.327354 | + | 0.944902i | \(0.606157\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.6570 | 1.03464 | 0.517322 | − | 0.855791i | \(-0.326929\pi\) | ||||
0.517322 | + | 0.855791i | \(0.326929\pi\) | |||||||
\(230\) | −13.8455 | −0.912943 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.7879 | 1.29635 | 0.648176 | − | 0.761491i | \(-0.275532\pi\) | ||||
0.648176 | + | 0.761491i | \(0.275532\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.6108 | −0.887871 | ||||||||
\(236\) | −20.5957 | −1.34067 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.9678 | −0.840579 | ||||||||
\(239\) | 9.33298 | 0.603700 | 0.301850 | − | 0.953355i | \(-0.402396\pi\) | ||||
0.301850 | + | 0.953355i | \(0.402396\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.5737 | −1.58293 | −0.791464 | − | 0.611215i | \(-0.790681\pi\) | ||||
−0.791464 | + | 0.611215i | \(0.790681\pi\) | |||||||
\(242\) | 3.17432 | 0.204053 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −16.9657 | −1.08612 | ||||||||
\(245\) | 25.7017 | 1.64202 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.69327 | −0.234997 | ||||||||
\(248\) | −2.91357 | −0.185012 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 59.3627 | 3.75443 | ||||||||
\(251\) | −4.66182 | −0.294252 | −0.147126 | − | 0.989118i | \(-0.547002\pi\) | ||||
−0.147126 | + | 0.989118i | \(0.547002\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.45311 | −0.342834 | ||||||||
\(254\) | −39.1107 | −2.45402 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.78146 | −0.236341 | ||||||||
\(257\) | 28.3543 | 1.76869 | 0.884345 | − | 0.466834i | \(-0.154605\pi\) | ||||
0.884345 | + | 0.466834i | \(0.154605\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.3456 | −1.20208 | ||||||||
\(260\) | 10.6733 | 0.661928 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −24.8871 | −1.53753 | ||||||||
\(263\) | 26.7811 | 1.65139 | 0.825697 | − | 0.564114i | \(-0.190782\pi\) | ||||
0.825697 | + | 0.564114i | \(0.190782\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.31125 | −0.510556 | ||||||||
\(266\) | −31.9353 | −1.95808 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 26.7877 | 1.63632 | ||||||||
\(269\) | 0.785551 | 0.0478959 | 0.0239479 | − | 0.999713i | \(-0.492376\pi\) | ||||
0.0239479 | + | 0.999713i | \(0.492376\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.1514 | −0.738148 | −0.369074 | − | 0.929400i | \(-0.620325\pi\) | ||||
−0.369074 | + | 0.929400i | \(0.620325\pi\) | |||||||
\(272\) | 2.70202 | 0.163834 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.2591 | −1.10307 | ||||||||
\(275\) | 41.0191 | 2.47355 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.7837 | −0.948352 | −0.474176 | − | 0.880430i | \(-0.657254\pi\) | ||||
−0.474176 | + | 0.880430i | \(0.657254\pi\) | |||||||
\(278\) | −6.83744 | −0.410083 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 26.9523 | 1.61071 | ||||||||
\(281\) | −20.0723 | −1.19741 | −0.598705 | − | 0.800969i | \(-0.704318\pi\) | ||||
−0.598705 | + | 0.800969i | \(0.704318\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.95557 | −0.116246 | −0.0581232 | − | 0.998309i | \(-0.518512\pi\) | ||||
−0.0581232 | + | 0.998309i | \(0.518512\pi\) | |||||||
\(284\) | −23.8645 | −1.41610 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.17980 | 0.424551 | ||||||||
\(287\) | 24.4951 | 1.44590 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.3801 | −0.845888 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 21.3785 | 1.25108 | ||||||||
\(293\) | 2.41420 | 0.141039 | 0.0705194 | − | 0.997510i | \(-0.477534\pi\) | ||||
0.0705194 | + | 0.997510i | \(0.477534\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −29.7283 | −1.73085 | ||||||||
\(296\) | −9.61201 | −0.558687 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −33.2912 | −1.92851 | ||||||||
\(299\) | −1.43222 | −0.0828273 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.1553 | 0.931178 | ||||||||
\(302\) | 1.49124 | 0.0858114 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.65415 | 0.381641 | ||||||||
\(305\) | −24.4887 | −1.40222 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.11367 | −0.0635606 | −0.0317803 | − | 0.999495i | \(-0.510118\pi\) | ||||
−0.0317803 | + | 0.999495i | \(0.510118\pi\) | |||||||
\(308\) | 36.3491 | 2.07118 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −14.4006 | −0.817899 | ||||||||
\(311\) | −4.42989 | −0.251196 | −0.125598 | − | 0.992081i | \(-0.540085\pi\) | ||||
−0.125598 | + | 0.992081i | \(0.540085\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.1002 | −1.70136 | −0.850682 | − | 0.525680i | \(-0.823811\pi\) | ||||
−0.850682 | + | 0.525680i | \(0.823811\pi\) | |||||||
\(314\) | −13.6976 | −0.772999 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.813283 | 0.0457507 | ||||||||
\(317\) | 6.21069 | 0.348827 | 0.174414 | − | 0.984672i | \(-0.444197\pi\) | ||||
0.174414 | + | 0.984672i | \(0.444197\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −51.6939 | −2.88978 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.3842 | −0.690146 | ||||||||
\(323\) | 6.45193 | 0.358995 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.7734 | 0.597599 | ||||||||
\(326\) | −33.6437 | −1.86335 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 12.1706 | 0.672008 | ||||||||
\(329\) | −12.1743 | −0.671192 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0058 | 0.549967 | 0.274984 | − | 0.961449i | \(-0.411328\pi\) | ||||
0.274984 | + | 0.961449i | \(0.411328\pi\) | |||||||
\(332\) | 18.2991 | 1.00429 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 34.6755 | 1.89736 | ||||||||
\(335\) | 38.6660 | 2.11255 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.2955 | −1.48688 | −0.743440 | − | 0.668803i | \(-0.766807\pi\) | ||||
−0.743440 | + | 0.668803i | \(0.766807\pi\) | |||||||
\(338\) | −26.6700 | −1.45065 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −18.6456 | −1.01120 | ||||||||
\(341\) | −5.67175 | −0.307143 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.54213 | −0.137262 | ||||||||
\(344\) | 8.02691 | 0.432782 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.56729 | 0.406820 | ||||||||
\(347\) | −1.19493 | −0.0641473 | −0.0320736 | − | 0.999486i | \(-0.510211\pi\) | ||||
−0.0320736 | + | 0.999486i | \(0.510211\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.25120 | 0.388148 | 0.194074 | − | 0.980987i | \(-0.437830\pi\) | ||||
0.194074 | + | 0.980987i | \(0.437830\pi\) | |||||||
\(350\) | 93.1561 | 4.97940 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −25.7219 | −1.37098 | ||||||||
\(353\) | 5.26353 | 0.280150 | 0.140075 | − | 0.990141i | \(-0.455266\pi\) | ||||
0.140075 | + | 0.990141i | \(0.455266\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −34.4466 | −1.82824 | ||||||||
\(356\) | −46.6390 | −2.47186 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 26.4420 | 1.39750 | ||||||||
\(359\) | 14.6286 | 0.772067 | 0.386034 | − | 0.922485i | \(-0.373845\pi\) | ||||
0.386034 | + | 0.922485i | \(0.373845\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.11114 | −0.163744 | ||||||||
\(362\) | 5.31413 | 0.279305 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.54682 | 0.500390 | ||||||||
\(365\) | 30.8582 | 1.61519 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.55318 | 0.289874 | 0.144937 | − | 0.989441i | \(-0.453702\pi\) | ||||
0.144937 | + | 0.989441i | \(0.453702\pi\) | |||||||
\(368\) | 2.58042 | 0.134514 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −47.5083 | −2.46984 | ||||||||
\(371\) | −7.43409 | −0.385959 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.7459 | 1.54019 | 0.770093 | − | 0.637931i | \(-0.220210\pi\) | ||||
0.770093 | + | 0.637931i | \(0.220210\pi\) | |||||||
\(374\) | −12.5427 | −0.648568 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.04891 | −0.311949 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.96231 | −0.100797 | −0.0503986 | − | 0.998729i | \(-0.516049\pi\) | ||||
−0.0503986 | + | 0.998729i | \(0.516049\pi\) | |||||||
\(380\) | −45.9177 | −2.35553 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.8207 | −0.655962 | ||||||||
\(383\) | 11.8165 | 0.603796 | 0.301898 | − | 0.953340i | \(-0.402380\pi\) | ||||
0.301898 | + | 0.953340i | \(0.402380\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 52.4672 | 2.67398 | ||||||||
\(386\) | 43.9106 | 2.23499 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 28.3975 | 1.44166 | ||||||||
\(389\) | −11.9013 | −0.603422 | −0.301711 | − | 0.953399i | \(-0.597558\pi\) | ||||
−0.301711 | + | 0.953399i | \(0.597558\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.50200 | 0.126532 | ||||||||
\(392\) | 11.4224 | 0.576916 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 25.7277 | 1.29614 | ||||||||
\(395\) | 1.17391 | 0.0590660 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.6778 | 0.987603 | 0.493801 | − | 0.869575i | \(-0.335607\pi\) | ||||
0.493801 | + | 0.869575i | \(0.335607\pi\) | |||||||
\(398\) | −36.5697 | −1.83307 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −19.4103 | −0.970517 | ||||||||
\(401\) | 20.5264 | 1.02504 | 0.512520 | − | 0.858675i | \(-0.328712\pi\) | ||||
0.512520 | + | 0.858675i | \(0.328712\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.48964 | −0.0742044 | ||||||||
\(404\) | −23.2759 | −1.15802 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.7114 | −0.927490 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.1820 | 1.59130 | 0.795648 | − | 0.605760i | \(-0.207131\pi\) | ||||
0.795648 | + | 0.605760i | \(0.207131\pi\) | |||||||
\(410\) | 60.1543 | 2.97081 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 21.5464 | 1.06152 | ||||||||
\(413\) | −26.5908 | −1.30845 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.4134 | 1.29658 | ||||||||
\(416\) | −6.75566 | −0.331223 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −30.8884 | −1.51080 | ||||||||
\(419\) | −1.58695 | −0.0775275 | −0.0387638 | − | 0.999248i | \(-0.512342\pi\) | ||||
−0.0387638 | + | 0.999248i | \(0.512342\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.86317 | 0.285753 | 0.142877 | − | 0.989741i | \(-0.454365\pi\) | ||||
0.142877 | + | 0.989741i | \(0.454365\pi\) | |||||||
\(422\) | −53.2530 | −2.59232 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.69369 | −0.179381 | ||||||||
\(425\) | −18.8205 | −0.912926 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.9042 | −1.06002 | ||||||||
\(428\) | 47.3405 | 2.28829 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 39.6738 | 1.91324 | ||||||||
\(431\) | 8.46235 | 0.407617 | 0.203809 | − | 0.979011i | \(-0.434668\pi\) | ||||
0.203809 | + | 0.979011i | \(0.434668\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.7185 | 0.611212 | 0.305606 | − | 0.952158i | \(-0.401141\pi\) | ||||
0.305606 | + | 0.952158i | \(0.401141\pi\) | |||||||
\(434\) | −12.8808 | −0.618297 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −35.9104 | −1.71980 | ||||||||
\(437\) | 6.16157 | 0.294748 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.50539 | −0.358213 | −0.179106 | − | 0.983830i | \(-0.557321\pi\) | ||||
−0.179106 | + | 0.983830i | \(0.557321\pi\) | |||||||
\(440\) | 26.0688 | 1.24278 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.29425 | −0.156691 | ||||||||
\(443\) | 11.6583 | 0.553902 | 0.276951 | − | 0.960884i | \(-0.410676\pi\) | ||||
0.276951 | + | 0.960884i | \(0.410676\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −67.3199 | −3.19127 | ||||||||
\(446\) | 62.2028 | 2.94539 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −46.2381 | −2.18455 | ||||||||
\(449\) | 19.4512 | 0.917957 | 0.458978 | − | 0.888447i | \(-0.348216\pi\) | ||||
0.458978 | + | 0.888447i | \(0.348216\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.6921 | 1.11562 | ||||||||
\(452\) | 23.9132 | 1.12478 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −21.6676 | −1.01691 | ||||||||
\(455\) | 13.7801 | 0.646022 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.1125 | 0.800489 | 0.400245 | − | 0.916408i | \(-0.368925\pi\) | ||||
0.400245 | + | 0.916408i | \(0.368925\pi\) | |||||||
\(458\) | 34.3920 | 1.60703 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −17.8065 | −0.830232 | ||||||||
\(461\) | −8.53020 | −0.397291 | −0.198646 | − | 0.980071i | \(-0.563654\pi\) | ||||
−0.198646 | + | 0.980071i | \(0.563654\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.49772 | 0.0696050 | 0.0348025 | − | 0.999394i | \(-0.488920\pi\) | ||||
0.0348025 | + | 0.999394i | \(0.488920\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 43.4660 | 2.01352 | ||||||||
\(467\) | 21.4307 | 0.991695 | 0.495848 | − | 0.868410i | \(-0.334857\pi\) | ||||
0.495848 | + | 0.868410i | \(0.334857\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 34.5853 | 1.59700 | ||||||||
\(470\) | −29.8974 | −1.37906 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −13.2119 | −0.608126 | ||||||||
\(473\) | 15.6257 | 0.718472 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −46.3483 | −2.12660 | ||||||||
\(476\) | −16.6778 | −0.764424 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 20.5007 | 0.937682 | ||||||||
\(479\) | 28.5538 | 1.30465 | 0.652327 | − | 0.757937i | \(-0.273793\pi\) | ||||
0.652327 | + | 0.757937i | \(0.273793\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.91441 | −0.224078 | ||||||||
\(482\) | −53.9783 | −2.45864 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.08245 | 0.185566 | ||||||||
\(485\) | 40.9896 | 1.86124 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.1555 | 1.13991 | 0.569953 | − | 0.821677i | \(-0.306961\pi\) | ||||
0.569953 | + | 0.821677i | \(0.306961\pi\) | |||||||
\(488\) | −10.8833 | −0.492662 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 56.4561 | 2.55043 | ||||||||
\(491\) | 21.6846 | 0.978614 | 0.489307 | − | 0.872112i | \(-0.337250\pi\) | ||||
0.489307 | + | 0.872112i | \(0.337250\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −8.11259 | −0.365003 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.68388 | 0.120510 | ||||||||
\(497\) | −30.8112 | −1.38207 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.68927 | 0.254687 | 0.127343 | − | 0.991859i | \(-0.459355\pi\) | ||||
0.127343 | + | 0.991859i | \(0.459355\pi\) | |||||||
\(500\) | 76.3457 | 3.41428 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.2401 | −0.457039 | ||||||||
\(503\) | 9.46973 | 0.422234 | 0.211117 | − | 0.977461i | \(-0.432290\pi\) | ||||
0.211117 | + | 0.977461i | \(0.432290\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.5970 | −1.49505 | ||||||||
\(506\) | −11.9782 | −0.532498 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −50.2998 | −2.23169 | ||||||||
\(509\) | 30.5939 | 1.35605 | 0.678024 | − | 0.735039i | \(-0.262836\pi\) | ||||
0.678024 | + | 0.735039i | \(0.262836\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.6014 | 1.22102 | ||||||||
\(512\) | 18.2220 | 0.805308 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 62.2827 | 2.74717 | ||||||||
\(515\) | 31.1007 | 1.37046 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.7752 | −0.517874 | ||||||||
\(518\) | −42.4943 | −1.86709 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.84676 | 0.300250 | ||||||||
\(521\) | −8.99098 | −0.393902 | −0.196951 | − | 0.980413i | \(-0.563104\pi\) | ||||
−0.196951 | + | 0.980413i | \(0.563104\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.43930 | −0.0629362 | −0.0314681 | − | 0.999505i | \(-0.510018\pi\) | ||||
−0.0314681 | + | 0.999505i | \(0.510018\pi\) | |||||||
\(524\) | −32.0070 | −1.39823 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 58.8271 | 2.56498 | ||||||||
\(527\) | 2.60232 | 0.113359 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.6106 | −0.896113 | ||||||||
\(530\) | −18.2564 | −0.793008 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −41.0715 | −1.78068 | ||||||||
\(533\) | 6.22255 | 0.269528 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 68.3324 | 2.95427 | ||||||||
\(536\) | 17.1840 | 0.742234 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.72553 | 0.0743930 | ||||||||
\(539\) | 22.2355 | 0.957753 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.0344 | −1.16230 | −0.581150 | − | 0.813796i | \(-0.697397\pi\) | ||||
−0.581150 | + | 0.813796i | \(0.697397\pi\) | |||||||
\(542\) | −26.6917 | −1.14651 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 11.8018 | 0.505996 | ||||||||
\(545\) | −51.8339 | −2.22032 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.2739 | −1.59372 | −0.796858 | − | 0.604166i | \(-0.793506\pi\) | ||||
−0.796858 | + | 0.604166i | \(0.793506\pi\) | |||||||
\(548\) | −23.4828 | −1.00313 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 90.1022 | 3.84197 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.05002 | 0.0446513 | ||||||||
\(554\) | −34.6704 | −1.47300 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.79356 | −0.372930 | ||||||||
\(557\) | −31.7679 | −1.34605 | −0.673026 | − | 0.739619i | \(-0.735006\pi\) | ||||
−0.673026 | + | 0.739619i | \(0.735006\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.10398 | 0.173580 | ||||||||
\(560\) | −24.8276 | −1.04916 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −44.0905 | −1.85985 | ||||||||
\(563\) | −13.4735 | −0.567842 | −0.283921 | − | 0.958848i | \(-0.591635\pi\) | ||||
−0.283921 | + | 0.958848i | \(0.591635\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 34.5169 | 1.45214 | ||||||||
\(566\) | −4.29558 | −0.180557 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15.3088 | −0.642342 | ||||||||
\(569\) | 5.53839 | 0.232181 | 0.116091 | − | 0.993239i | \(-0.462964\pi\) | ||||
0.116091 | + | 0.993239i | \(0.462964\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.3036 | 1.72850 | 0.864250 | − | 0.503062i | \(-0.167793\pi\) | ||||
0.864250 | + | 0.503062i | \(0.167793\pi\) | |||||||
\(572\) | 9.23386 | 0.386087 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 53.8057 | 2.24581 | ||||||||
\(575\) | −17.9735 | −0.749546 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.7871 | −1.65636 | −0.828180 | − | 0.560463i | \(-0.810623\pi\) | ||||
−0.828180 | + | 0.560463i | \(0.810623\pi\) | |||||||
\(578\) | −31.5872 | −1.31385 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23.6257 | 0.980161 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.19039 | −0.297795 | ||||||||
\(584\) | 13.7140 | 0.567489 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.30300 | 0.219065 | ||||||||
\(587\) | −38.7105 | −1.59775 | −0.798877 | − | 0.601495i | \(-0.794572\pi\) | ||||
−0.798877 | + | 0.601495i | \(0.794572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.40861 | 0.264062 | ||||||||
\(590\) | −65.3010 | −2.68840 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.85427 | 0.363908 | ||||||||
\(593\) | 1.40712 | 0.0577833 | 0.0288916 | − | 0.999583i | \(-0.490802\pi\) | ||||
0.0288916 | + | 0.999583i | \(0.490802\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.0731 | −0.986901 | ||||||||
\(596\) | −42.8154 | −1.75379 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.14599 | −0.128649 | ||||||||
\(599\) | −30.7455 | −1.25623 | −0.628113 | − | 0.778122i | \(-0.716173\pi\) | ||||
−0.628113 | + | 0.778122i | \(0.716173\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.2534 | −0.540616 | −0.270308 | − | 0.962774i | \(-0.587125\pi\) | ||||
−0.270308 | + | 0.962774i | \(0.587125\pi\) | |||||||
\(602\) | 35.4867 | 1.44633 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.91787 | 0.0780371 | ||||||||
\(605\) | 5.89271 | 0.239573 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.85282 | 0.399914 | 0.199957 | − | 0.979805i | \(-0.435920\pi\) | ||||
0.199957 | + | 0.979805i | \(0.435920\pi\) | |||||||
\(608\) | 29.0636 | 1.17869 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −53.7916 | −2.17796 | ||||||||
\(611\) | −3.09267 | −0.125116 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.0646 | −0.931571 | −0.465785 | − | 0.884898i | \(-0.654228\pi\) | ||||
−0.465785 | + | 0.884898i | \(0.654228\pi\) | |||||||
\(614\) | −2.44628 | −0.0987238 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 23.3175 | 0.939488 | ||||||||
\(617\) | 2.14430 | 0.0863262 | 0.0431631 | − | 0.999068i | \(-0.486256\pi\) | ||||
0.0431631 | + | 0.999068i | \(0.486256\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.7463 | 1.19560 | 0.597802 | − | 0.801644i | \(-0.296041\pi\) | ||||
0.597802 | + | 0.801644i | \(0.296041\pi\) | |||||||
\(620\) | −18.5204 | −0.743799 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.73065 | −0.390163 | ||||||||
\(623\) | −60.2150 | −2.41246 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 52.0617 | 2.08247 | ||||||||
\(626\) | −66.1178 | −2.64260 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17.6163 | −0.702966 | ||||||||
\(629\) | 8.58519 | 0.342314 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.52395 | −0.180096 | −0.0900478 | − | 0.995937i | \(-0.528702\pi\) | ||||
−0.0900478 | + | 0.995937i | \(0.528702\pi\) | |||||||
\(632\) | 0.521710 | 0.0207525 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.6423 | 0.541807 | ||||||||
\(635\) | −72.6039 | −2.88120 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.84000 | 0.231389 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −54.0872 | −2.13798 | ||||||||
\(641\) | 30.7540 | 1.21471 | 0.607354 | − | 0.794431i | \(-0.292231\pi\) | ||||
0.607354 | + | 0.794431i | \(0.292231\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.8712 | 0.665337 | 0.332668 | − | 0.943044i | \(-0.392051\pi\) | ||||
0.332668 | + | 0.943044i | \(0.392051\pi\) | |||||||
\(644\) | −15.9272 | −0.627620 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14.1722 | 0.557599 | ||||||||
\(647\) | −14.1310 | −0.555548 | −0.277774 | − | 0.960646i | \(-0.589597\pi\) | ||||
−0.277774 | + | 0.960646i | \(0.589597\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.7191 | −1.00956 | ||||||||
\(650\) | 23.6647 | 0.928205 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −43.2688 | −1.69454 | ||||||||
\(653\) | 38.7238 | 1.51538 | 0.757689 | − | 0.652615i | \(-0.226328\pi\) | ||||
0.757689 | + | 0.652615i | \(0.226328\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −46.1997 | −1.80517 | ||||||||
\(656\) | −11.2111 | −0.437722 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −26.7420 | −1.04251 | ||||||||
\(659\) | −17.3822 | −0.677116 | −0.338558 | − | 0.940945i | \(-0.609939\pi\) | ||||
−0.338558 | + | 0.940945i | \(0.609939\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.959081 | 0.0373039 | 0.0186520 | − | 0.999826i | \(-0.494063\pi\) | ||||
0.0186520 | + | 0.999826i | \(0.494063\pi\) | |||||||
\(662\) | 21.9786 | 0.854222 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.7386 | 0.455547 | ||||||||
\(665\) | −59.2837 | −2.29892 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 44.5958 | 1.72546 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 84.9334 | 3.28127 | ||||||||
\(671\) | −21.1861 | −0.817881 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.1107 | −1.16068 | −0.580341 | − | 0.814374i | \(-0.697081\pi\) | ||||
−0.580341 | + | 0.814374i | \(0.697081\pi\) | |||||||
\(674\) | −59.9570 | −2.30946 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −34.2999 | −1.31923 | ||||||||
\(677\) | −41.7661 | −1.60520 | −0.802602 | − | 0.596515i | \(-0.796552\pi\) | ||||
−0.802602 | + | 0.596515i | \(0.796552\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.6636 | 1.40702 | ||||||||
\(680\) | −11.9609 | −0.458680 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.4585 | −0.477061 | ||||||||
\(683\) | −40.2674 | −1.54079 | −0.770396 | − | 0.637566i | \(-0.779941\pi\) | ||||
−0.770396 | + | 0.637566i | \(0.779941\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −33.8956 | −1.29508 | ||||||||
\(686\) | −5.58402 | −0.213199 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.39413 | −0.281899 | ||||||||
\(689\) | −1.88850 | −0.0719461 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.3791 | 1.57414 | 0.787069 | − | 0.616866i | \(-0.211598\pi\) | ||||
0.787069 | + | 0.616866i | \(0.211598\pi\) | |||||||
\(692\) | 9.73221 | 0.369963 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.62477 | −0.0996351 | ||||||||
\(695\) | −12.6928 | −0.481467 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.8704 | −0.411747 | ||||||||
\(698\) | 15.9279 | 0.602881 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 119.807 | 4.52828 | ||||||||
\(701\) | −2.28878 | −0.0864459 | −0.0432230 | − | 0.999065i | \(-0.513763\pi\) | ||||
−0.0432230 | + | 0.999065i | \(0.513763\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.1423 | 0.797399 | ||||||||
\(704\) | −44.7224 | −1.68554 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11.5618 | 0.435135 | ||||||||
\(707\) | −30.0512 | −1.13019 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.3080 | −1.02557 | −0.512786 | − | 0.858516i | \(-0.671387\pi\) | ||||
−0.512786 | + | 0.858516i | \(0.671387\pi\) | |||||||
\(710\) | −75.6651 | −2.83966 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −29.9183 | −1.12124 | ||||||||
\(713\) | 2.48521 | 0.0930717 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.3284 | 0.498453 | ||||||||
\(716\) | 34.0068 | 1.27089 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 32.1330 | 1.19919 | ||||||||
\(719\) | 19.0751 | 0.711383 | 0.355691 | − | 0.934604i | \(-0.384245\pi\) | ||||
0.355691 | + | 0.934604i | \(0.384245\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.8183 | 1.03601 | ||||||||
\(722\) | −6.83391 | −0.254332 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.83444 | 0.254000 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.2574 | −1.08510 | −0.542548 | − | 0.840024i | \(-0.682541\pi\) | ||||
−0.542548 | + | 0.840024i | \(0.682541\pi\) | |||||||
\(728\) | 6.12416 | 0.226976 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 67.7828 | 2.50875 | ||||||||
\(731\) | −7.16942 | −0.265171 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.9488 | 0.773760 | 0.386880 | − | 0.922130i | \(-0.373553\pi\) | ||||
0.386880 | + | 0.922130i | \(0.373553\pi\) | |||||||
\(734\) | 12.1981 | 0.450239 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.2706 | 0.415441 | ||||||||
\(737\) | 33.4515 | 1.23220 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.7623 | −1.24197 | −0.620983 | − | 0.783824i | \(-0.713266\pi\) | ||||
−0.620983 | + | 0.783824i | \(0.713266\pi\) | |||||||
\(740\) | −61.0999 | −2.24608 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −16.3297 | −0.599480 | ||||||||
\(743\) | 44.2943 | 1.62500 | 0.812500 | − | 0.582962i | \(-0.198106\pi\) | ||||
0.812500 | + | 0.582962i | \(0.198106\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −61.8007 | −2.26420 | ||||||||
\(746\) | 65.3396 | 2.39225 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −16.1310 | −0.589809 | ||||||||
\(749\) | 61.1207 | 2.23330 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.65239 | −0.279240 | −0.139620 | − | 0.990205i | \(-0.544588\pi\) | ||||
−0.139620 | + | 0.990205i | \(0.544588\pi\) | |||||||
\(752\) | 5.57206 | 0.203192 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.76830 | 0.100749 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.2856 | 0.591911 | 0.295955 | − | 0.955202i | \(-0.404362\pi\) | ||||
0.295955 | + | 0.955202i | \(0.404362\pi\) | |||||||
\(758\) | −4.31040 | −0.156561 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −29.4556 | −1.06847 | ||||||||
\(761\) | 28.5492 | 1.03491 | 0.517453 | − | 0.855711i | \(-0.326880\pi\) | ||||
0.517453 | + | 0.855711i | \(0.326880\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −46.3634 | −1.67847 | ||||||||
\(764\) | −16.4885 | −0.596533 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 25.9560 | 0.937830 | ||||||||
\(767\) | −6.75493 | −0.243907 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.8716 | 1.79842 | 0.899208 | − | 0.437521i | \(-0.144143\pi\) | ||||
0.899208 | + | 0.437521i | \(0.144143\pi\) | |||||||
\(770\) | 115.249 | 4.15329 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 56.4729 | 2.03250 | ||||||||
\(773\) | −4.99992 | −0.179835 | −0.0899173 | − | 0.995949i | \(-0.528660\pi\) | ||||
−0.0899173 | + | 0.995949i | \(0.528660\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.6941 | −0.671513 | ||||||||
\(776\) | 18.2166 | 0.653938 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.1424 | −0.937249 | ||||||||
\(779\) | −26.7701 | −0.959139 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.8011 | −1.06637 | ||||||||
\(782\) | 5.49588 | 0.196532 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10.5219 | −0.375782 | ||||||||
\(785\) | −25.4278 | −0.907556 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.1052 | 0.681027 | 0.340513 | − | 0.940240i | \(-0.389399\pi\) | ||||
0.340513 | + | 0.940240i | \(0.389399\pi\) | |||||||
\(788\) | 33.0881 | 1.17872 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.57860 | 0.0917426 | ||||||||
\(791\) | 30.8740 | 1.09775 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.56437 | −0.197597 | ||||||||
\(794\) | 43.2242 | 1.53397 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −47.0318 | −1.66700 | ||||||||
\(797\) | 23.2432 | 0.823318 | 0.411659 | − | 0.911338i | \(-0.364950\pi\) | ||||
0.411659 | + | 0.911338i | \(0.364950\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.40273 | 0.191135 | ||||||||
\(800\) | −84.7795 | −2.99741 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 45.0881 | 1.59212 | ||||||||
\(803\) | 26.6966 | 0.942103 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.9897 | −0.810281 | ||||||||
\(806\) | −3.27213 | −0.115256 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −14.9312 | −0.525276 | ||||||||
\(809\) | 7.53860 | 0.265043 | 0.132521 | − | 0.991180i | \(-0.457693\pi\) | ||||
0.132521 | + | 0.991180i | \(0.457693\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.2745 | −1.69515 | −0.847573 | − | 0.530679i | \(-0.821937\pi\) | ||||
−0.847573 | + | 0.530679i | \(0.821937\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −41.1013 | −1.44060 | ||||||||
\(815\) | −62.4552 | −2.18771 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.6558 | −0.617698 | ||||||||
\(818\) | 70.6906 | 2.47164 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 77.3637 | 2.70166 | ||||||||
\(821\) | −6.07390 | −0.211980 | −0.105990 | − | 0.994367i | \(-0.533801\pi\) | ||||
−0.105990 | + | 0.994367i | \(0.533801\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.0147 | 1.39483 | 0.697413 | − | 0.716670i | \(-0.254334\pi\) | ||||
0.697413 | + | 0.716670i | \(0.254334\pi\) | |||||||
\(824\) | 13.8218 | 0.481504 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −58.4092 | −2.03231 | ||||||||
\(827\) | 28.8632 | 1.00367 | 0.501837 | − | 0.864962i | \(-0.332658\pi\) | ||||
0.501837 | + | 0.864962i | \(0.332658\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −41.9301 | −1.45629 | −0.728147 | − | 0.685421i | \(-0.759618\pi\) | ||||
−0.728147 | + | 0.685421i | \(0.759618\pi\) | |||||||
\(830\) | 58.0194 | 2.01388 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −11.7460 | −0.407219 | ||||||||
\(833\) | −10.2021 | −0.353483 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 64.3706 | 2.22764 | ||||||||
\(836\) | −39.7251 | −1.37392 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.48588 | −0.120418 | ||||||||
\(839\) | 30.7540 | 1.06175 | 0.530873 | − | 0.847451i | \(-0.321864\pi\) | ||||
0.530873 | + | 0.847451i | \(0.321864\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | 12.8790 | 0.443839 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −68.4881 | −2.35746 | ||||||||
\(845\) | −49.5093 | −1.70317 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.27079 | 0.181107 | ||||||||
\(848\) | 3.40251 | 0.116843 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −41.3408 | −1.41798 | ||||||||
\(851\) | 8.19883 | 0.281052 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.3499 | −0.491330 | −0.245665 | − | 0.969355i | \(-0.579006\pi\) | ||||
−0.245665 | + | 0.969355i | \(0.579006\pi\) | |||||||
\(854\) | −48.1145 | −1.64644 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 30.3683 | 1.03797 | ||||||||
\(857\) | −12.0892 | −0.412959 | −0.206479 | − | 0.978451i | \(-0.566201\pi\) | ||||
−0.206479 | + | 0.978451i | \(0.566201\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.5722 | 0.770154 | 0.385077 | − | 0.922885i | \(-0.374175\pi\) | ||||
0.385077 | + | 0.922885i | \(0.374175\pi\) | |||||||
\(860\) | 51.0240 | 1.73990 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.5883 | 0.633121 | ||||||||
\(863\) | 20.0243 | 0.681637 | 0.340818 | − | 0.940129i | \(-0.389296\pi\) | ||||
0.340818 | + | 0.940129i | \(0.389296\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.0477 | 0.477636 | ||||||||
\(866\) | 27.9373 | 0.949348 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −16.5658 | −0.562280 | ||||||||
\(869\) | 1.01560 | 0.0344518 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.78578 | 0.297695 | ||||||||
\(872\) | −23.0360 | −0.780098 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.5344 | 0.457809 | ||||||||
\(875\) | 98.5689 | 3.33224 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42.0059 | −1.41844 | −0.709219 | − | 0.704988i | \(-0.750952\pi\) | ||||
−0.709219 | + | 0.704988i | \(0.750952\pi\) | |||||||
\(878\) | −16.4863 | −0.556384 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −24.0137 | −0.809502 | ||||||||
\(881\) | −56.1769 | −1.89265 | −0.946323 | − | 0.323221i | \(-0.895234\pi\) | ||||
−0.946323 | + | 0.323221i | \(0.895234\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −54.5727 | −1.83652 | −0.918259 | − | 0.395980i | \(-0.870405\pi\) | ||||
−0.918259 | + | 0.395980i | \(0.870405\pi\) | |||||||
\(884\) | −4.23669 | −0.142495 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.6085 | 0.860334 | ||||||||
\(887\) | −39.2007 | −1.31623 | −0.658115 | − | 0.752917i | \(-0.728646\pi\) | ||||
−0.658115 | + | 0.752917i | \(0.728646\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −64.9413 | −2.17806 | ||||||||
\(890\) | −147.874 | −4.95675 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 79.9983 | 2.67854 | ||||||||
\(893\) | 13.3050 | 0.445236 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 49.0862 | 1.64077 | ||||||||
\(896\) | −48.3789 | −1.61622 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 42.7262 | 1.42579 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.29910 | 0.109909 | ||||||||
\(902\) | 52.0418 | 1.73280 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.3400 | 0.510200 | ||||||||
\(905\) | 9.86500 | 0.327924 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.36661 | 0.111786 | 0.0558932 | − | 0.998437i | \(-0.482199\pi\) | ||||
0.0558932 | + | 0.998437i | \(0.482199\pi\) | |||||||
\(908\) | −27.8664 | −0.924779 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 30.2693 | 1.00342 | ||||||||
\(911\) | −54.9714 | −1.82128 | −0.910641 | − | 0.413198i | \(-0.864412\pi\) | ||||
−0.910641 | + | 0.413198i | \(0.864412\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.8512 | 0.756265 | ||||||||
\(914\) | 37.5892 | 1.24334 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 44.2312 | 1.46144 | ||||||||
\(917\) | −41.3238 | −1.36463 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.6983 | 0.880696 | 0.440348 | − | 0.897827i | \(-0.354855\pi\) | ||||
0.440348 | + | 0.897827i | \(0.354855\pi\) | |||||||
\(920\) | −11.4226 | −0.376593 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18.7374 | −0.617082 | ||||||||
\(923\) | −7.82703 | −0.257630 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −61.6729 | −2.02779 | ||||||||
\(926\) | 3.28988 | 0.108112 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34.4983 | −1.13185 | −0.565926 | − | 0.824456i | \(-0.691481\pi\) | ||||
−0.565926 | + | 0.824456i | \(0.691481\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.1243 | −0.823417 | ||||||||
\(932\) | 55.9011 | 1.83110 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 47.0745 | 1.54032 | ||||||||
\(935\) | −23.2839 | −0.761466 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.3860 | −1.18868 | −0.594340 | − | 0.804214i | \(-0.702587\pi\) | ||||
−0.594340 | + | 0.804214i | \(0.702587\pi\) | |||||||
\(938\) | 75.9696 | 2.48050 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −38.4506 | −1.25412 | ||||||||
\(941\) | −10.4980 | −0.342226 | −0.171113 | − | 0.985251i | \(-0.554736\pi\) | ||||
−0.171113 | + | 0.985251i | \(0.554736\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.3812 | −0.338059 | ||||||||
\(944\) | 12.1703 | 0.396111 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 34.3233 | 1.11595 | ||||||||
\(947\) | 8.01774 | 0.260542 | 0.130271 | − | 0.991478i | \(-0.458415\pi\) | ||||
0.130271 | + | 0.991478i | \(0.458415\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.01166 | 0.227608 | ||||||||
\(950\) | −101.808 | −3.30309 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.6986 | −0.346742 | ||||||||
\(953\) | 23.8505 | 0.772594 | 0.386297 | − | 0.922374i | \(-0.373754\pi\) | ||||
0.386297 | + | 0.922374i | \(0.373754\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.7999 | −0.770147 | ||||||||
\(956\) | 26.3658 | 0.852729 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 62.7209 | 2.02642 | ||||||||
\(959\) | −30.3183 | −0.979029 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.4151 | −0.916618 | ||||||||
\(962\) | −10.7949 | −0.348043 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −69.4208 | −2.23589 | ||||||||
\(965\) | 81.5143 | 2.62404 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.65641 | −0.0532667 | −0.0266333 | − | 0.999645i | \(-0.508479\pi\) | ||||
−0.0266333 | + | 0.999645i | \(0.508479\pi\) | |||||||
\(968\) | 2.61884 | 0.0841726 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 90.0374 | 2.89093 | ||||||||
\(971\) | 30.7444 | 0.986635 | 0.493317 | − | 0.869849i | \(-0.335784\pi\) | ||||
0.493317 | + | 0.869849i | \(0.335784\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.3532 | −0.363968 | ||||||||
\(974\) | 55.2564 | 1.77053 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.0253 | 0.320902 | ||||||||
\(977\) | 45.2764 | 1.44852 | 0.724260 | − | 0.689527i | \(-0.242181\pi\) | ||||
0.724260 | + | 0.689527i | \(0.242181\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −58.2410 | −1.86139 | ||||||||
\(980\) | 72.6076 | 2.31936 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 47.6323 | 1.52001 | ||||||||
\(983\) | 54.0341 | 1.72342 | 0.861711 | − | 0.507400i | \(-0.169393\pi\) | ||||
0.861711 | + | 0.507400i | \(0.169393\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 47.7602 | 1.52177 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.4335 | −0.331934 | ||||||||
\(989\) | −6.84677 | −0.217715 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.45456 | 0.0779718 | 0.0389859 | − | 0.999240i | \(-0.487587\pi\) | ||||
0.0389859 | + | 0.999240i | \(0.487587\pi\) | |||||||
\(992\) | 11.7225 | 0.372191 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −67.6795 | −2.14666 | ||||||||
\(995\) | −67.8868 | −2.15216 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.5499 | −0.587480 | −0.293740 | − | 0.955885i | \(-0.594900\pi\) | ||||
−0.293740 | + | 0.955885i | \(0.594900\pi\) | |||||||
\(998\) | 12.4970 | 0.395586 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 7569.2.a.bl.1.8 | 9 | ||
3.2 | odd | 2 | 2523.2.a.p.1.2 | 9 | |||
29.16 | even | 7 | 261.2.k.b.82.3 | 18 | |||
29.20 | even | 7 | 261.2.k.b.226.3 | 18 | |||
29.28 | even | 2 | 7569.2.a.bk.1.2 | 9 | |||
87.20 | odd | 14 | 87.2.g.b.52.1 | ✓ | 18 | ||
87.74 | odd | 14 | 87.2.g.b.82.1 | yes | 18 | ||
87.86 | odd | 2 | 2523.2.a.q.1.8 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
87.2.g.b.52.1 | ✓ | 18 | 87.20 | odd | 14 | ||
87.2.g.b.82.1 | yes | 18 | 87.74 | odd | 14 | ||
261.2.k.b.82.3 | 18 | 29.16 | even | 7 | |||
261.2.k.b.226.3 | 18 | 29.20 | even | 7 | |||
2523.2.a.p.1.2 | 9 | 3.2 | odd | 2 | |||
2523.2.a.q.1.8 | 9 | 87.86 | odd | 2 | |||
7569.2.a.bk.1.2 | 9 | 29.28 | even | 2 | |||
7569.2.a.bl.1.8 | 9 | 1.1 | even | 1 | trivial |