Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(1,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, 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("567.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.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: | \(4.52751779461\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.621.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.14510\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.14510 | −1.51682 | −0.758408 | − | 0.651780i | \(-0.774023\pi\) | ||||
−0.758408 | + | 0.651780i | \(0.774023\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.60147 | 1.30073 | ||||||||
\(5\) | −3.74657 | −1.67552 | −0.837758 | − | 0.546041i | \(-0.816134\pi\) | ||||
−0.837758 | + | 0.546041i | \(0.816134\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.29021 | −0.456156 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.03677 | 2.54145 | ||||||||
\(11\) | 0.746568 | 0.225099 | 0.112549 | − | 0.993646i | \(-0.464098\pi\) | ||||
0.112549 | + | 0.993646i | \(0.464098\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.03677 | −1.67430 | −0.837150 | − | 0.546974i | \(-0.815780\pi\) | ||||
−0.837150 | + | 0.546974i | \(0.815780\pi\) | |||||||
\(14\) | −2.14510 | −0.573303 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.43531 | −0.608827 | ||||||||
\(17\) | 0.543637 | 0.131851 | 0.0659257 | − | 0.997825i | \(-0.479000\pi\) | ||||
0.0659257 | + | 0.997825i | \(0.479000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.20293 | −0.275971 | −0.137986 | − | 0.990434i | \(-0.544063\pi\) | ||||
−0.137986 | + | 0.990434i | \(0.544063\pi\) | |||||||
\(20\) | −9.74657 | −2.17940 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.60147 | −0.341434 | ||||||||
\(23\) | 7.49314 | 1.56243 | 0.781213 | − | 0.624264i | \(-0.214601\pi\) | ||||
0.781213 | + | 0.624264i | \(0.214601\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.03677 | 1.80735 | ||||||||
\(26\) | 12.9495 | 2.53961 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.60147 | 0.491631 | ||||||||
\(29\) | −8.03677 | −1.49239 | −0.746196 | − | 0.665727i | \(-0.768122\pi\) | ||||
−0.746196 | + | 0.665727i | \(0.768122\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 7.80440 | 1.37964 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.16616 | −0.199994 | ||||||||
\(35\) | −3.74657 | −0.633286 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00000 | 0.821995 | 0.410997 | − | 0.911636i | \(-0.365181\pi\) | ||||
0.410997 | + | 0.911636i | \(0.365181\pi\) | |||||||
\(38\) | 2.58041 | 0.418598 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.83384 | 0.764298 | ||||||||
\(41\) | 2.79707 | 0.436829 | 0.218414 | − | 0.975856i | \(-0.429912\pi\) | ||||
0.218414 | + | 0.975856i | \(0.429912\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.83384 | 1.49965 | 0.749823 | − | 0.661638i | \(-0.230138\pi\) | ||||
0.749823 | + | 0.661638i | \(0.230138\pi\) | |||||||
\(44\) | 1.94217 | 0.292793 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −16.0735 | −2.36992 | ||||||||
\(47\) | 4.29021 | 0.625791 | 0.312895 | − | 0.949788i | \(-0.398701\pi\) | ||||
0.312895 | + | 0.949788i | \(0.398701\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −19.3848 | −2.74143 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −15.7045 | −2.17782 | ||||||||
\(53\) | −2.45636 | −0.337407 | −0.168704 | − | 0.985667i | \(-0.553958\pi\) | ||||
−0.168704 | + | 0.985667i | \(0.553958\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.79707 | −0.377157 | ||||||||
\(56\) | −1.29021 | −0.172411 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 17.2397 | 2.26368 | ||||||||
\(59\) | 14.5804 | 1.89821 | 0.949104 | − | 0.314963i | \(-0.101992\pi\) | ||||
0.949104 | + | 0.314963i | \(0.101992\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.23970 | −1.18302 | −0.591511 | − | 0.806297i | \(-0.701469\pi\) | ||||
−0.591511 | + | 0.806297i | \(0.701469\pi\) | |||||||
\(62\) | −4.29021 | −0.544857 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.8706 | −1.48383 | ||||||||
\(65\) | 22.6172 | 2.80532 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.2397 | 1.25098 | 0.625490 | − | 0.780233i | \(-0.284899\pi\) | ||||
0.625490 | + | 0.780233i | \(0.284899\pi\) | |||||||
\(68\) | 1.41425 | 0.171503 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.03677 | 0.960578 | ||||||||
\(71\) | 8.23970 | 0.977873 | 0.488937 | − | 0.872319i | \(-0.337385\pi\) | ||||
0.488937 | + | 0.872319i | \(0.337385\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0368 | 1.17472 | 0.587358 | − | 0.809327i | \(-0.300168\pi\) | ||||
0.587358 | + | 0.809327i | \(0.300168\pi\) | |||||||
\(74\) | −10.7255 | −1.24682 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.12938 | −0.358965 | ||||||||
\(77\) | 0.746568 | 0.0850793 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.2397 | 1.15206 | 0.576028 | − | 0.817430i | \(-0.304602\pi\) | ||||
0.576028 | + | 0.817430i | \(0.304602\pi\) | |||||||
\(80\) | 9.12405 | 1.02010 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.00000 | −0.662589 | ||||||||
\(83\) | −2.79707 | −0.307018 | −0.153509 | − | 0.988147i | \(-0.549057\pi\) | ||||
−0.153509 | + | 0.988147i | \(0.549057\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.03677 | −0.220919 | ||||||||
\(86\) | −21.0946 | −2.27469 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.963226 | −0.102680 | ||||||||
\(89\) | −6.54364 | −0.693624 | −0.346812 | − | 0.937935i | \(-0.612736\pi\) | ||||
−0.346812 | + | 0.937935i | \(0.612736\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.03677 | −0.632826 | ||||||||
\(92\) | 19.4931 | 2.03230 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.20293 | −0.949210 | ||||||||
\(95\) | 4.50686 | 0.462394 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.20293 | 0.528278 | 0.264139 | − | 0.964485i | \(-0.414912\pi\) | ||||
0.264139 | + | 0.964485i | \(0.414912\pi\) | |||||||
\(98\) | −2.14510 | −0.216688 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 23.5089 | 2.35089 | ||||||||
\(101\) | 4.50686 | 0.448450 | 0.224225 | − | 0.974537i | \(-0.428015\pi\) | ||||
0.224225 | + | 0.974537i | \(0.428015\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.8706 | −1.07111 | −0.535557 | − | 0.844499i | \(-0.679898\pi\) | ||||
−0.535557 | + | 0.844499i | \(0.679898\pi\) | |||||||
\(104\) | 7.78868 | 0.763743 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.26915 | 0.511785 | ||||||||
\(107\) | 3.32698 | 0.321631 | 0.160816 | − | 0.986984i | \(-0.448588\pi\) | ||||
0.160816 | + | 0.986984i | \(0.448588\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.63091 | −0.539343 | −0.269672 | − | 0.962952i | \(-0.586915\pi\) | ||||
−0.269672 | + | 0.962952i | \(0.586915\pi\) | |||||||
\(110\) | 6.00000 | 0.572078 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.43531 | −0.230115 | ||||||||
\(113\) | −2.59414 | −0.244036 | −0.122018 | − | 0.992528i | \(-0.538937\pi\) | ||||
−0.122018 | + | 0.992528i | \(0.538937\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −28.0735 | −2.61787 | ||||||||
\(116\) | −20.9074 | −1.94120 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −31.2765 | −2.87923 | ||||||||
\(119\) | 0.543637 | 0.0498351 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4426 | −0.949331 | ||||||||
\(122\) | 19.8201 | 1.79443 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.20293 | 0.467237 | ||||||||
\(125\) | −15.1240 | −1.35274 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.83384 | 0.872612 | 0.436306 | − | 0.899798i | \(-0.356286\pi\) | ||||
0.436306 | + | 0.899798i | \(0.356286\pi\) | |||||||
\(128\) | 9.85490 | 0.871058 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −48.5162 | −4.25515 | ||||||||
\(131\) | −5.37748 | −0.469833 | −0.234916 | − | 0.972016i | \(-0.575482\pi\) | ||||
−0.234916 | + | 0.972016i | \(0.575482\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.20293 | −0.104307 | ||||||||
\(134\) | −21.9652 | −1.89751 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.701404 | −0.0601449 | ||||||||
\(137\) | −10.4931 | −0.896489 | −0.448245 | − | 0.893911i | \(-0.647951\pi\) | ||||
−0.448245 | + | 0.893911i | \(0.647951\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.79707 | −0.576520 | −0.288260 | − | 0.957552i | \(-0.593077\pi\) | ||||
−0.288260 | + | 0.957552i | \(0.593077\pi\) | |||||||
\(140\) | −9.74657 | −0.823735 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −17.6750 | −1.48325 | ||||||||
\(143\) | −4.50686 | −0.376883 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 30.1103 | 2.50053 | ||||||||
\(146\) | −21.5299 | −1.78183 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 13.0073 | 1.06920 | ||||||||
\(149\) | −1.50686 | −0.123447 | −0.0617235 | − | 0.998093i | \(-0.519660\pi\) | ||||
−0.0617235 | + | 0.998093i | \(0.519660\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.23970 | −0.507780 | −0.253890 | − | 0.967233i | \(-0.581710\pi\) | ||||
−0.253890 | + | 0.967233i | \(0.581710\pi\) | |||||||
\(152\) | 1.55203 | 0.125886 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.60147 | −0.129050 | ||||||||
\(155\) | −7.49314 | −0.601863 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.5162 | 1.63737 | 0.818685 | − | 0.574243i | \(-0.194704\pi\) | ||||
0.818685 | + | 0.574243i | \(0.194704\pi\) | |||||||
\(158\) | −21.9652 | −1.74746 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −29.2397 | −2.31160 | ||||||||
\(161\) | 7.49314 | 0.590542 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.2397 | −0.958688 | −0.479344 | − | 0.877627i | \(-0.659125\pi\) | ||||
−0.479344 | + | 0.877627i | \(0.659125\pi\) | |||||||
\(164\) | 7.27648 | 0.568198 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | 0.465690 | ||||||||
\(167\) | 14.7971 | 1.14503 | 0.572516 | − | 0.819894i | \(-0.305968\pi\) | ||||
0.572516 | + | 0.819894i | \(0.305968\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.4426 | 1.80328 | ||||||||
\(170\) | 4.36909 | 0.335094 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 25.5824 | 1.95064 | ||||||||
\(173\) | −1.82012 | −0.138381 | −0.0691904 | − | 0.997603i | \(-0.522042\pi\) | ||||
−0.0691904 | + | 0.997603i | \(0.522042\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.03677 | 0.683116 | ||||||||
\(176\) | −1.81812 | −0.137046 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.0368 | 1.05210 | ||||||||
\(179\) | −1.08727 | −0.0812667 | −0.0406333 | − | 0.999174i | \(-0.512938\pi\) | ||||
−0.0406333 | + | 0.999174i | \(0.512938\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 12.9495 | 0.959881 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.66769 | −0.712711 | ||||||||
\(185\) | −18.7328 | −1.37727 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.405862 | 0.0296796 | ||||||||
\(188\) | 11.1608 | 0.813987 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.66769 | −0.701368 | ||||||||
\(191\) | −10.8201 | −0.782916 | −0.391458 | − | 0.920196i | \(-0.628029\pi\) | ||||
−0.391458 | + | 0.920196i | \(0.628029\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.63091 | 0.693248 | 0.346624 | − | 0.938004i | \(-0.387328\pi\) | ||||
0.346624 | + | 0.938004i | \(0.387328\pi\) | |||||||
\(194\) | −11.1608 | −0.801300 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.60147 | 0.185819 | ||||||||
\(197\) | −19.4794 | −1.38785 | −0.693925 | − | 0.720047i | \(-0.744120\pi\) | ||||
−0.693925 | + | 0.720047i | \(0.744120\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.8706 | −1.19593 | −0.597963 | − | 0.801524i | \(-0.704023\pi\) | ||||
−0.597963 | + | 0.801524i | \(0.704023\pi\) | |||||||
\(200\) | −11.6593 | −0.824437 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.66769 | −0.680216 | ||||||||
\(203\) | −8.03677 | −0.564071 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.4794 | −0.731914 | ||||||||
\(206\) | 23.3186 | 1.62468 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 14.7014 | 1.01936 | ||||||||
\(209\) | −0.898070 | −0.0621208 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.83384 | 0.263933 | 0.131966 | − | 0.991254i | \(-0.457871\pi\) | ||||
0.131966 | + | 0.991254i | \(0.457871\pi\) | |||||||
\(212\) | −6.39014 | −0.438877 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.13671 | −0.487856 | ||||||||
\(215\) | −36.8432 | −2.51268 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | 12.0789 | 0.818085 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.27648 | −0.490580 | ||||||||
\(221\) | −3.28181 | −0.220759 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.4794 | 0.835683 | 0.417842 | − | 0.908520i | \(-0.362787\pi\) | ||||
0.417842 | + | 0.908520i | \(0.362787\pi\) | |||||||
\(224\) | 7.80440 | 0.521453 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.56469 | 0.370158 | ||||||||
\(227\) | 21.8569 | 1.45069 | 0.725346 | − | 0.688384i | \(-0.241680\pi\) | ||||
0.725346 | + | 0.688384i | \(0.241680\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.2397 | 1.27140 | 0.635698 | − | 0.771938i | \(-0.280712\pi\) | ||||
0.635698 | + | 0.771938i | \(0.280712\pi\) | |||||||
\(230\) | 60.2206 | 3.97083 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.3691 | 0.680764 | ||||||||
\(233\) | 11.4564 | 0.750531 | 0.375266 | − | 0.926917i | \(-0.377551\pi\) | ||||
0.375266 | + | 0.926917i | \(0.377551\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.0735 | −1.04852 | ||||||||
\(236\) | 37.9304 | 2.46906 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.16616 | −0.0755908 | ||||||||
\(239\) | 4.16616 | 0.269486 | 0.134743 | − | 0.990881i | \(-0.456979\pi\) | ||||
0.134743 | + | 0.990881i | \(0.456979\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.2397 | 0.852844 | 0.426422 | − | 0.904524i | \(-0.359774\pi\) | ||||
0.426422 | + | 0.904524i | \(0.359774\pi\) | |||||||
\(242\) | 22.4005 | 1.43996 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −24.0368 | −1.53880 | ||||||||
\(245\) | −3.74657 | −0.239359 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.26182 | 0.462059 | ||||||||
\(248\) | −2.58041 | −0.163856 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 32.4426 | 2.05185 | ||||||||
\(251\) | 12.8706 | 0.812386 | 0.406193 | − | 0.913787i | \(-0.366856\pi\) | ||||
0.406193 | + | 0.913787i | \(0.366856\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.59414 | 0.351700 | ||||||||
\(254\) | −21.0946 | −1.32359 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.60147 | 0.162592 | ||||||||
\(257\) | −0.137775 | −0.00859416 | −0.00429708 | − | 0.999991i | \(-0.501368\pi\) | ||||
−0.00429708 | + | 0.999991i | \(0.501368\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.00000 | 0.310685 | ||||||||
\(260\) | 58.8378 | 3.64897 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.5352 | 0.712650 | ||||||||
\(263\) | −11.2534 | −0.693916 | −0.346958 | − | 0.937881i | \(-0.612785\pi\) | ||||
−0.346958 | + | 0.937881i | \(0.612785\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.20293 | 0.565332 | ||||||||
\(266\) | 2.58041 | 0.158215 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 26.6382 | 1.62719 | ||||||||
\(269\) | −5.45636 | −0.332680 | −0.166340 | − | 0.986068i | \(-0.553195\pi\) | ||||
−0.166340 | + | 0.986068i | \(0.553195\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.12938 | −0.190097 | −0.0950483 | − | 0.995473i | \(-0.530301\pi\) | ||||
−0.0950483 | + | 0.995473i | \(0.530301\pi\) | |||||||
\(272\) | −1.32392 | −0.0802747 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.5089 | 1.35981 | ||||||||
\(275\) | 6.74657 | 0.406833 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.63091 | −0.518581 | −0.259291 | − | 0.965799i | \(-0.583489\pi\) | ||||
−0.259291 | + | 0.965799i | \(0.583489\pi\) | |||||||
\(278\) | 14.5804 | 0.874475 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.83384 | 0.288877 | ||||||||
\(281\) | 13.0735 | 0.779902 | 0.389951 | − | 0.920836i | \(-0.372492\pi\) | ||||
0.389951 | + | 0.920836i | \(0.372492\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.6088 | −0.808959 | −0.404479 | − | 0.914547i | \(-0.632547\pi\) | ||||
−0.404479 | + | 0.914547i | \(0.632547\pi\) | |||||||
\(284\) | 21.4353 | 1.27195 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.66769 | 0.571662 | ||||||||
\(287\) | 2.79707 | 0.165106 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7045 | −0.982615 | ||||||||
\(290\) | −64.5897 | −3.79284 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 26.1103 | 1.52799 | ||||||||
\(293\) | −10.8338 | −0.632920 | −0.316460 | − | 0.948606i | \(-0.602494\pi\) | ||||
−0.316460 | + | 0.948606i | \(0.602494\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −54.6265 | −3.18048 | ||||||||
\(296\) | −6.45103 | −0.374958 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.23238 | 0.187247 | ||||||||
\(299\) | −45.2344 | −2.61597 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.83384 | 0.566813 | ||||||||
\(302\) | 13.3848 | 0.770209 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.92951 | 0.168019 | ||||||||
\(305\) | 34.6172 | 1.98217 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0735 | 1.03151 | 0.515756 | − | 0.856736i | \(-0.327511\pi\) | ||||
0.515756 | + | 0.856736i | \(0.327511\pi\) | |||||||
\(308\) | 1.94217 | 0.110665 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 16.0735 | 0.912916 | ||||||||
\(311\) | −4.29021 | −0.243275 | −0.121638 | − | 0.992575i | \(-0.538815\pi\) | ||||
−0.121638 | + | 0.992575i | \(0.538815\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.55736 | 0.314121 | 0.157060 | − | 0.987589i | \(-0.449798\pi\) | ||||
0.157060 | + | 0.987589i | \(0.449798\pi\) | |||||||
\(314\) | −44.0093 | −2.48359 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 26.6382 | 1.49852 | ||||||||
\(317\) | 27.5299 | 1.54623 | 0.773117 | − | 0.634264i | \(-0.218697\pi\) | ||||
0.773117 | + | 0.634264i | \(0.218697\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.00000 | −0.335936 | ||||||||
\(320\) | 44.4741 | 2.48618 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −16.0735 | −0.895744 | ||||||||
\(323\) | −0.653958 | −0.0363872 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −54.5530 | −3.02605 | ||||||||
\(326\) | 26.2554 | 1.45415 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.60879 | −0.199262 | ||||||||
\(329\) | 4.29021 | 0.236527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.1471 | 0.887525 | 0.443762 | − | 0.896145i | \(-0.353643\pi\) | ||||
0.443762 | + | 0.896145i | \(0.353643\pi\) | |||||||
\(332\) | −7.27648 | −0.399349 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −31.7412 | −1.73680 | ||||||||
\(335\) | −38.3638 | −2.09604 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.11032 | −0.0604830 | −0.0302415 | − | 0.999543i | \(-0.509628\pi\) | ||||
−0.0302415 | + | 0.999543i | \(0.509628\pi\) | |||||||
\(338\) | −50.2869 | −2.73524 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.29860 | −0.287357 | ||||||||
\(341\) | 1.49314 | 0.0808579 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −12.6877 | −0.684074 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.90433 | 0.209898 | ||||||||
\(347\) | 28.8201 | 1.54714 | 0.773572 | − | 0.633708i | \(-0.218468\pi\) | ||||
0.773572 | + | 0.633708i | \(0.218468\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.2765 | −1.24596 | −0.622981 | − | 0.782237i | \(-0.714078\pi\) | ||||
−0.622981 | + | 0.782237i | \(0.714078\pi\) | |||||||
\(350\) | −19.3848 | −1.03616 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.82651 | 0.310554 | ||||||||
\(353\) | −2.36375 | −0.125810 | −0.0629049 | − | 0.998020i | \(-0.520036\pi\) | ||||
−0.0629049 | + | 0.998020i | \(0.520036\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −30.8706 | −1.63844 | ||||||||
\(356\) | −17.0230 | −0.902220 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.33231 | 0.123267 | ||||||||
\(359\) | 3.32698 | 0.175591 | 0.0877956 | − | 0.996139i | \(-0.472018\pi\) | ||||
0.0877956 | + | 0.996139i | \(0.472018\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.5530 | −0.923840 | ||||||||
\(362\) | −4.29021 | −0.225488 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −15.7045 | −0.823137 | ||||||||
\(365\) | −37.6035 | −1.96825 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.66769 | 0.295851 | 0.147925 | − | 0.988999i | \(-0.452740\pi\) | ||||
0.147925 | + | 0.988999i | \(0.452740\pi\) | |||||||
\(368\) | −18.2481 | −0.951248 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 40.1839 | 2.08906 | ||||||||
\(371\) | −2.45636 | −0.127528 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.5162 | 1.21762 | 0.608811 | − | 0.793315i | \(-0.291647\pi\) | ||||
0.608811 | + | 0.793315i | \(0.291647\pi\) | |||||||
\(374\) | −0.870616 | −0.0450185 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.53525 | −0.285459 | ||||||||
\(377\) | 48.5162 | 2.49871 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.7927 | 1.88991 | 0.944956 | − | 0.327197i | \(-0.106104\pi\) | ||||
0.944956 | + | 0.327197i | \(0.106104\pi\) | |||||||
\(380\) | 11.7245 | 0.601452 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 23.2103 | 1.18754 | ||||||||
\(383\) | −26.9863 | −1.37893 | −0.689467 | − | 0.724317i | \(-0.742155\pi\) | ||||
−0.689467 | + | 0.724317i | \(0.742155\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.79707 | −0.142552 | ||||||||
\(386\) | −20.6593 | −1.05153 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.5352 | 0.687148 | ||||||||
\(389\) | 8.98627 | 0.455622 | 0.227811 | − | 0.973705i | \(-0.426843\pi\) | ||||
0.227811 | + | 0.973705i | \(0.426843\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.07355 | 0.206008 | ||||||||
\(392\) | −1.29021 | −0.0651652 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 41.7853 | 2.10511 | ||||||||
\(395\) | −38.3638 | −1.93029 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.5015 | 1.43045 | 0.715225 | − | 0.698894i | \(-0.246324\pi\) | ||||
0.715225 | + | 0.698894i | \(0.246324\pi\) | |||||||
\(398\) | 36.1892 | 1.81400 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −22.0073 | −1.10037 | ||||||||
\(401\) | −7.50686 | −0.374875 | −0.187437 | − | 0.982277i | \(-0.560018\pi\) | ||||
−0.187437 | + | 0.982277i | \(0.560018\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.0735 | −0.601426 | ||||||||
\(404\) | 11.7245 | 0.583313 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 17.2397 | 0.855592 | ||||||||
\(407\) | 3.73284 | 0.185030 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.2397 | −1.34692 | −0.673458 | − | 0.739225i | \(-0.735192\pi\) | ||||
−0.673458 | + | 0.739225i | \(0.735192\pi\) | |||||||
\(410\) | 22.4794 | 1.11018 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −28.2795 | −1.39323 | ||||||||
\(413\) | 14.5804 | 0.717455 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.4794 | 0.514414 | ||||||||
\(416\) | −47.1134 | −2.30992 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.92645 | 0.0942259 | ||||||||
\(419\) | −19.6823 | −0.961545 | −0.480773 | − | 0.876845i | \(-0.659644\pi\) | ||||
−0.480773 | + | 0.876845i | \(0.659644\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.4794 | 1.04684 | 0.523421 | − | 0.852074i | \(-0.324655\pi\) | ||||
0.523421 | + | 0.852074i | \(0.324655\pi\) | |||||||
\(422\) | −8.22399 | −0.400337 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.16921 | 0.153911 | ||||||||
\(425\) | 4.91273 | 0.238302 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.23970 | −0.447141 | ||||||||
\(428\) | 8.65502 | 0.418356 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 79.0324 | 3.81128 | ||||||||
\(431\) | 2.17455 | 0.104744 | 0.0523722 | − | 0.998628i | \(-0.483322\pi\) | ||||
0.0523722 | + | 0.998628i | \(0.483322\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.3133 | 1.69705 | 0.848523 | − | 0.529158i | \(-0.177492\pi\) | ||||
0.848523 | + | 0.529158i | \(0.177492\pi\) | |||||||
\(434\) | −4.29021 | −0.205936 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.6486 | −0.701542 | ||||||||
\(437\) | −9.01373 | −0.431185 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.2029 | −0.916506 | −0.458253 | − | 0.888822i | \(-0.651525\pi\) | ||||
−0.458253 | + | 0.888822i | \(0.651525\pi\) | |||||||
\(440\) | 3.60879 | 0.172042 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.03983 | 0.334851 | ||||||||
\(443\) | −5.31859 | −0.252694 | −0.126347 | − | 0.991986i | \(-0.540325\pi\) | ||||
−0.126347 | + | 0.991986i | \(0.540325\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.5162 | 1.16218 | ||||||||
\(446\) | −26.7696 | −1.26758 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −11.8706 | −0.560834 | ||||||||
\(449\) | 7.36909 | 0.347769 | 0.173884 | − | 0.984766i | \(-0.444368\pi\) | ||||
0.173884 | + | 0.984766i | \(0.444368\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.08820 | 0.0983296 | ||||||||
\(452\) | −6.74856 | −0.317426 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −46.8853 | −2.20043 | ||||||||
\(455\) | 22.6172 | 1.06031 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | −0.0467780 | −0.0233890 | − | 0.999726i | \(-0.507446\pi\) | ||||
−0.0233890 | + | 0.999726i | \(0.507446\pi\) | |||||||
\(458\) | −41.2711 | −1.92847 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −73.0324 | −3.40515 | ||||||||
\(461\) | 30.4648 | 1.41889 | 0.709443 | − | 0.704763i | \(-0.248947\pi\) | ||||
0.709443 | + | 0.704763i | \(0.248947\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.5015 | −1.27810 | −0.639052 | − | 0.769163i | \(-0.720673\pi\) | ||||
−0.639052 | + | 0.769163i | \(0.720673\pi\) | |||||||
\(464\) | 19.5720 | 0.908608 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.5751 | −1.13842 | ||||||||
\(467\) | 39.1755 | 1.81282 | 0.906412 | − | 0.422394i | \(-0.138810\pi\) | ||||
0.906412 | + | 0.422394i | \(0.138810\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.2397 | 0.472826 | ||||||||
\(470\) | 34.4794 | 1.59042 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −18.8117 | −0.865880 | ||||||||
\(473\) | 7.34163 | 0.337569 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.8706 | −0.498778 | ||||||||
\(476\) | 1.41425 | 0.0648222 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.93684 | −0.408761 | ||||||||
\(479\) | 20.9863 | 0.958887 | 0.479444 | − | 0.877573i | \(-0.340838\pi\) | ||||
0.479444 | + | 0.877573i | \(0.340838\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.1839 | −1.37627 | ||||||||
\(482\) | −28.4005 | −1.29361 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −27.1662 | −1.23483 | ||||||||
\(485\) | −19.4931 | −0.885138 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.6456 | 1.29805 | 0.649027 | − | 0.760765i | \(-0.275176\pi\) | ||||
0.649027 | + | 0.760765i | \(0.275176\pi\) | |||||||
\(488\) | 11.9211 | 0.539644 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.03677 | 0.363064 | ||||||||
\(491\) | 32.1471 | 1.45078 | 0.725389 | − | 0.688339i | \(-0.241660\pi\) | ||||
0.725389 | + | 0.688339i | \(0.241660\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.36909 | −0.196774 | ||||||||
\(494\) | −15.5774 | −0.700858 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.87062 | −0.218697 | ||||||||
\(497\) | 8.23970 | 0.369601 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.2618 | −0.862278 | −0.431139 | − | 0.902286i | \(-0.641888\pi\) | ||||
−0.431139 | + | 0.902286i | \(0.641888\pi\) | |||||||
\(500\) | −39.3447 | −1.75955 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −27.6088 | −1.23224 | ||||||||
\(503\) | −36.2206 | −1.61500 | −0.807499 | − | 0.589869i | \(-0.799180\pi\) | ||||
−0.807499 | + | 0.589869i | \(0.799180\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.8853 | −0.751385 | ||||||||
\(506\) | −12.0000 | −0.533465 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 25.5824 | 1.13504 | ||||||||
\(509\) | −8.98627 | −0.398310 | −0.199155 | − | 0.979968i | \(-0.563820\pi\) | ||||
−0.199155 | + | 0.979968i | \(0.563820\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.0368 | 0.444001 | ||||||||
\(512\) | −25.2902 | −1.11768 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.295541 | 0.0130358 | ||||||||
\(515\) | 40.7275 | 1.79467 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.20293 | 0.140865 | ||||||||
\(518\) | −10.7255 | −0.471252 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −29.1808 | −1.27966 | ||||||||
\(521\) | −17.5667 | −0.769610 | −0.384805 | − | 0.922998i | \(-0.625731\pi\) | ||||
−0.384805 | + | 0.922998i | \(0.625731\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.6088 | −1.11979 | −0.559897 | − | 0.828562i | \(-0.689159\pi\) | ||||
−0.559897 | + | 0.828562i | \(0.689159\pi\) | |||||||
\(524\) | −13.9893 | −0.611127 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.1398 | 1.05254 | ||||||||
\(527\) | 1.08727 | 0.0473624 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 33.1471 | 1.44118 | ||||||||
\(530\) | −19.7412 | −0.857504 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.12938 | −0.135676 | ||||||||
\(533\) | −16.8853 | −0.731382 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.4648 | −0.538898 | ||||||||
\(536\) | −13.2113 | −0.570642 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11.7045 | 0.504615 | ||||||||
\(539\) | 0.746568 | 0.0321570 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.0735 | −1.76589 | −0.882945 | − | 0.469477i | \(-0.844443\pi\) | ||||
−0.882945 | + | 0.469477i | \(0.844443\pi\) | |||||||
\(542\) | 6.71285 | 0.288342 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.24276 | 0.181907 | ||||||||
\(545\) | 21.0966 | 0.903679 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.6456 | −1.56685 | −0.783426 | − | 0.621486i | \(-0.786529\pi\) | ||||
−0.783426 | + | 0.621486i | \(0.786529\pi\) | |||||||
\(548\) | −27.2975 | −1.16609 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −14.4721 | −0.617092 | ||||||||
\(551\) | 9.66769 | 0.411857 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.2397 | 0.435437 | ||||||||
\(554\) | 18.5142 | 0.786593 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.6823 | −0.749898 | ||||||||
\(557\) | 13.9127 | 0.589501 | 0.294751 | − | 0.955574i | \(-0.404763\pi\) | ||||
0.294751 | + | 0.955574i | \(0.404763\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −59.3647 | −2.51086 | ||||||||
\(560\) | 9.12405 | 0.385561 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −28.0441 | −1.18297 | ||||||||
\(563\) | −0.681412 | −0.0287181 | −0.0143590 | − | 0.999897i | \(-0.504571\pi\) | ||||
−0.0143590 | + | 0.999897i | \(0.504571\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.71911 | 0.408886 | ||||||||
\(566\) | 29.1923 | 1.22704 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.6309 | −0.446063 | ||||||||
\(569\) | −34.0598 | −1.42786 | −0.713931 | − | 0.700216i | \(-0.753087\pi\) | ||||
−0.713931 | + | 0.700216i | \(0.753087\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.6677 | 0.739370 | 0.369685 | − | 0.929157i | \(-0.379466\pi\) | ||||
0.369685 | + | 0.929157i | \(0.379466\pi\) | |||||||
\(572\) | −11.7245 | −0.490224 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.00000 | −0.250435 | ||||||||
\(575\) | 67.7138 | 2.82386 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.5015 | −0.520445 | −0.260223 | − | 0.965549i | \(-0.583796\pi\) | ||||
−0.260223 | + | 0.965549i | \(0.583796\pi\) | |||||||
\(578\) | 35.8328 | 1.49045 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 78.3310 | 3.25252 | ||||||||
\(581\) | −2.79707 | −0.116042 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.83384 | −0.0759500 | ||||||||
\(584\) | −12.9495 | −0.535854 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23.2397 | 0.960023 | ||||||||
\(587\) | −45.3647 | −1.87240 | −0.936200 | − | 0.351467i | \(-0.885683\pi\) | ||||
−0.936200 | + | 0.351467i | \(0.885683\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.40586 | −0.0991318 | ||||||||
\(590\) | 117.179 | 4.82420 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.1765 | −0.500453 | ||||||||
\(593\) | 9.93577 | 0.408013 | 0.204007 | − | 0.978970i | \(-0.434604\pi\) | ||||
0.204007 | + | 0.978970i | \(0.434604\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.03677 | −0.0834996 | ||||||||
\(596\) | −3.92005 | −0.160572 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 97.0324 | 3.96795 | ||||||||
\(599\) | 18.3407 | 0.749381 | 0.374690 | − | 0.927150i | \(-0.377749\pi\) | ||||
0.374690 | + | 0.927150i | \(0.377749\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.35443 | 0.0960393 | 0.0480197 | − | 0.998846i | \(-0.484709\pi\) | ||||
0.0480197 | + | 0.998846i | \(0.484709\pi\) | |||||||
\(602\) | −21.0946 | −0.859752 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −16.2324 | −0.660486 | ||||||||
\(605\) | 39.1240 | 1.59062 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −41.6823 | −1.69183 | −0.845917 | − | 0.533315i | \(-0.820946\pi\) | ||||
−0.845917 | + | 0.533315i | \(0.820946\pi\) | |||||||
\(608\) | −9.38815 | −0.380740 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −74.2574 | −3.00659 | ||||||||
\(611\) | −25.8990 | −1.04776 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.5897 | 0.872001 | 0.436000 | − | 0.899946i | \(-0.356395\pi\) | ||||
0.436000 | + | 0.899946i | \(0.356395\pi\) | |||||||
\(614\) | −38.7696 | −1.56461 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.963226 | −0.0388095 | ||||||||
\(617\) | 0.819187 | 0.0329792 | 0.0164896 | − | 0.999864i | \(-0.494751\pi\) | ||||
0.0164896 | + | 0.999864i | \(0.494751\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.3500 | 1.26006 | 0.630032 | − | 0.776569i | \(-0.283042\pi\) | ||||
0.630032 | + | 0.776569i | \(0.283042\pi\) | |||||||
\(620\) | −19.4931 | −0.782863 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9.20293 | 0.369004 | ||||||||
\(623\) | −6.54364 | −0.262165 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.4794 | 0.459176 | ||||||||
\(626\) | −11.9211 | −0.476464 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 53.3721 | 2.12978 | ||||||||
\(629\) | 2.71819 | 0.108381 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.66769 | −0.0663895 | −0.0331947 | − | 0.999449i | \(-0.510568\pi\) | ||||
−0.0331947 | + | 0.999449i | \(0.510568\pi\) | |||||||
\(632\) | −13.2113 | −0.525518 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −59.0545 | −2.34535 | ||||||||
\(635\) | −36.8432 | −1.46208 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.03677 | −0.239186 | ||||||||
\(638\) | 12.8706 | 0.509553 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −36.9220 | −1.45947 | ||||||||
\(641\) | 15.2481 | 0.602264 | 0.301132 | − | 0.953583i | \(-0.402636\pi\) | ||||
0.301132 | + | 0.953583i | \(0.402636\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.6265 | −0.892302 | −0.446151 | − | 0.894958i | \(-0.647206\pi\) | ||||
−0.446151 | + | 0.894958i | \(0.647206\pi\) | |||||||
\(644\) | 19.4931 | 0.768137 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.40281 | 0.0551927 | ||||||||
\(647\) | 42.0040 | 1.65135 | 0.825673 | − | 0.564148i | \(-0.190795\pi\) | ||||
0.825673 | + | 0.564148i | \(0.190795\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.8853 | 0.427284 | ||||||||
\(650\) | 117.022 | 4.58997 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −31.8412 | −1.24700 | ||||||||
\(653\) | −22.3554 | −0.874833 | −0.437416 | − | 0.899259i | \(-0.644106\pi\) | ||||
−0.437416 | + | 0.899259i | \(0.644106\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.1471 | 0.787212 | ||||||||
\(656\) | −6.81172 | −0.265953 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −9.20293 | −0.358768 | ||||||||
\(659\) | −31.4280 | −1.22426 | −0.612130 | − | 0.790757i | \(-0.709687\pi\) | ||||
−0.612130 | + | 0.790757i | \(0.709687\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.4426 | −0.950708 | −0.475354 | − | 0.879795i | \(-0.657680\pi\) | ||||
−0.475354 | + | 0.879795i | \(0.657680\pi\) | |||||||
\(662\) | −34.6372 | −1.34621 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.60879 | 0.140048 | ||||||||
\(665\) | 4.50686 | 0.174769 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −60.2206 | −2.33175 | ||||||||
\(668\) | 38.4941 | 1.48938 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 82.2942 | 3.17930 | ||||||||
\(671\) | −6.89807 | −0.266297 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.4794 | 1.52182 | 0.760910 | − | 0.648858i | \(-0.224753\pi\) | ||||
0.760910 | + | 0.648858i | \(0.224753\pi\) | |||||||
\(674\) | 2.38175 | 0.0917417 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 60.9852 | 2.34558 | ||||||||
\(677\) | 42.3784 | 1.62873 | 0.814367 | − | 0.580350i | \(-0.197084\pi\) | ||||
0.814367 | + | 0.580350i | \(0.197084\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.20293 | 0.199670 | ||||||||
\(680\) | 2.62786 | 0.100774 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.20293 | −0.122647 | ||||||||
\(683\) | 22.4143 | 0.857658 | 0.428829 | − | 0.903386i | \(-0.358926\pi\) | ||||
0.428829 | + | 0.903386i | \(0.358926\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39.3133 | 1.50208 | ||||||||
\(686\) | −2.14510 | −0.0819004 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −23.9484 | −0.913026 | ||||||||
\(689\) | 14.8285 | 0.564921 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.4794 | 0.474739 | 0.237370 | − | 0.971419i | \(-0.423715\pi\) | ||||
0.237370 | + | 0.971419i | \(0.423715\pi\) | |||||||
\(692\) | −4.73497 | −0.179996 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −61.8221 | −2.34674 | ||||||||
\(695\) | 25.4657 | 0.965968 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.52059 | 0.0575965 | ||||||||
\(698\) | 49.9304 | 1.88989 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 23.5089 | 0.888551 | ||||||||
\(701\) | −15.0000 | −0.566542 | −0.283271 | − | 0.959040i | \(-0.591420\pi\) | ||||
−0.283271 | + | 0.959040i | \(0.591420\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.01466 | −0.226847 | ||||||||
\(704\) | −8.86223 | −0.334008 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.07049 | 0.190830 | ||||||||
\(707\) | 4.50686 | 0.169498 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.0000 | −1.16423 | −0.582115 | − | 0.813107i | \(-0.697775\pi\) | ||||
−0.582115 | + | 0.813107i | \(0.697775\pi\) | |||||||
\(710\) | 66.2206 | 2.48522 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.44264 | 0.316401 | ||||||||
\(713\) | 14.9863 | 0.561240 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.8853 | 0.631473 | ||||||||
\(716\) | −2.82851 | −0.105706 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.13671 | −0.266340 | ||||||||
\(719\) | −6.65396 | −0.248151 | −0.124075 | − | 0.992273i | \(-0.539596\pi\) | ||||
−0.124075 | + | 0.992273i | \(0.539596\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.8706 | −0.404843 | ||||||||
\(722\) | 37.6529 | 1.40130 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.20293 | 0.193365 | ||||||||
\(725\) | −72.6265 | −2.69728 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.9442 | 1.37018 | 0.685092 | − | 0.728457i | \(-0.259762\pi\) | ||||
0.685092 | + | 0.728457i | \(0.259762\pi\) | |||||||
\(728\) | 7.78868 | 0.288668 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 80.6633 | 2.98548 | ||||||||
\(731\) | 5.34604 | 0.197731 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.1324 | −1.40845 | −0.704227 | − | 0.709975i | \(-0.748706\pi\) | ||||
−0.704227 | + | 0.709975i | \(0.748706\pi\) | |||||||
\(734\) | −12.1578 | −0.448751 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 58.4794 | 2.15558 | ||||||||
\(737\) | 7.64464 | 0.281594 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.23970 | −0.229531 | −0.114766 | − | 0.993393i | \(-0.536612\pi\) | ||||
−0.114766 | + | 0.993393i | \(0.536612\pi\) | |||||||
\(740\) | −48.7328 | −1.79145 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.26915 | 0.193437 | ||||||||
\(743\) | −11.0957 | −0.407060 | −0.203530 | − | 0.979069i | \(-0.565242\pi\) | ||||
−0.203530 | + | 0.979069i | \(0.565242\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.64557 | 0.206838 | ||||||||
\(746\) | −50.4446 | −1.84691 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.05584 | 0.0386052 | ||||||||
\(749\) | 3.32698 | 0.121565 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.3868 | 1.32777 | 0.663887 | − | 0.747833i | \(-0.268906\pi\) | ||||
0.663887 | + | 0.747833i | \(0.268906\pi\) | |||||||
\(752\) | −10.4480 | −0.380998 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −104.072 | −3.79009 | ||||||||
\(755\) | 23.3775 | 0.850794 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.40586 | −0.160134 | −0.0800669 | − | 0.996789i | \(-0.525513\pi\) | ||||
−0.0800669 | + | 0.996789i | \(0.525513\pi\) | |||||||
\(758\) | −78.9240 | −2.86665 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.81478 | −0.210924 | ||||||||
\(761\) | 47.2123 | 1.71144 | 0.855721 | − | 0.517437i | \(-0.173114\pi\) | ||||
0.855721 | + | 0.517437i | \(0.173114\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.63091 | −0.203853 | ||||||||
\(764\) | −28.1482 | −1.01836 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 57.8883 | 2.09159 | ||||||||
\(767\) | −88.0186 | −3.17817 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.7603 | 0.748635 | 0.374318 | − | 0.927301i | \(-0.377877\pi\) | ||||
0.374318 | + | 0.927301i | \(0.377877\pi\) | |||||||
\(770\) | 6.00000 | 0.216225 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 25.0545 | 0.901731 | ||||||||
\(773\) | −0.976953 | −0.0351386 | −0.0175693 | − | 0.999846i | \(-0.505593\pi\) | ||||
−0.0175693 | + | 0.999846i | \(0.505593\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.0735 | 0.649221 | ||||||||
\(776\) | −6.71285 | −0.240977 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19.2765 | −0.691095 | ||||||||
\(779\) | −3.36468 | −0.120552 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.15150 | 0.220118 | ||||||||
\(782\) | −8.73818 | −0.312477 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.43531 | −0.0869753 | ||||||||
\(785\) | −76.8653 | −2.74344 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.87062 | 0.102326 | 0.0511632 | − | 0.998690i | \(-0.483707\pi\) | ||||
0.0511632 | + | 0.998690i | \(0.483707\pi\) | |||||||
\(788\) | −50.6750 | −1.80522 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 82.2942 | 2.92790 | ||||||||
\(791\) | −2.59414 | −0.0922369 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 55.7780 | 1.98074 | ||||||||
\(794\) | −61.1387 | −2.16973 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −43.8883 | −1.55558 | ||||||||
\(797\) | −1.22505 | −0.0433935 | −0.0216967 | − | 0.999765i | \(-0.506907\pi\) | ||||
−0.0216967 | + | 0.999765i | \(0.506907\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.33231 | 0.0825114 | ||||||||
\(800\) | 70.5266 | 2.49349 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16.1030 | 0.568616 | ||||||||
\(803\) | 7.49314 | 0.264427 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28.0735 | −0.989463 | ||||||||
\(806\) | 25.8990 | 0.912253 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.81478 | −0.204563 | ||||||||
\(809\) | 15.4333 | 0.542607 | 0.271303 | − | 0.962494i | \(-0.412545\pi\) | ||||
0.271303 | + | 0.962494i | \(0.412545\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.47941 | −0.0870638 | −0.0435319 | − | 0.999052i | \(-0.513861\pi\) | ||||
−0.0435319 | + | 0.999052i | \(0.513861\pi\) | |||||||
\(812\) | −20.9074 | −0.733706 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.00733 | −0.280657 | ||||||||
\(815\) | 45.8569 | 1.60630 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.8294 | −0.413860 | ||||||||
\(818\) | 58.4320 | 2.04303 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −27.2618 | −0.952024 | ||||||||
\(821\) | 28.8990 | 1.00858 | 0.504291 | − | 0.863534i | \(-0.331754\pi\) | ||||
0.504291 | + | 0.863534i | \(0.331754\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.9588 | −0.870010 | −0.435005 | − | 0.900428i | \(-0.643253\pi\) | ||||
−0.435005 | + | 0.900428i | \(0.643253\pi\) | |||||||
\(824\) | 14.0253 | 0.488595 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −31.2765 | −1.08825 | ||||||||
\(827\) | −12.7191 | −0.442287 | −0.221143 | − | 0.975241i | \(-0.570979\pi\) | ||||
−0.221143 | + | 0.975241i | \(0.570979\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.33231 | −0.219930 | −0.109965 | − | 0.993935i | \(-0.535074\pi\) | ||||
−0.109965 | + | 0.993935i | \(0.535074\pi\) | |||||||
\(830\) | −22.4794 | −0.780272 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 71.6602 | 2.48437 | ||||||||
\(833\) | 0.543637 | 0.0188359 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −55.4382 | −1.91852 | ||||||||
\(836\) | −2.33630 | −0.0808026 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 42.2206 | 1.45849 | ||||||||
\(839\) | 45.4236 | 1.56820 | 0.784098 | − | 0.620637i | \(-0.213126\pi\) | ||||
0.784098 | + | 0.620637i | \(0.213126\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.5897 | 1.22723 | ||||||||
\(842\) | −46.0755 | −1.58787 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.97361 | 0.343306 | ||||||||
\(845\) | −87.8294 | −3.02142 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.4426 | −0.358813 | ||||||||
\(848\) | 5.98200 | 0.205423 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10.5383 | −0.361461 | ||||||||
\(851\) | 37.4657 | 1.28431 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.0882 | −0.824764 | −0.412382 | − | 0.911011i | \(-0.635303\pi\) | ||||
−0.412382 | + | 0.911011i | \(0.635303\pi\) | |||||||
\(854\) | 19.8201 | 0.678230 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.29249 | −0.146714 | ||||||||
\(857\) | −17.8622 | −0.610162 | −0.305081 | − | 0.952326i | \(-0.598684\pi\) | ||||
−0.305081 | + | 0.952326i | \(0.598684\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.7412 | 1.15124 | 0.575618 | − | 0.817719i | \(-0.304762\pi\) | ||||
0.575618 | + | 0.817719i | \(0.304762\pi\) | |||||||
\(860\) | −95.8462 | −3.26833 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.66463 | −0.158878 | ||||||||
\(863\) | −54.1555 | −1.84347 | −0.921737 | − | 0.387815i | \(-0.873230\pi\) | ||||
−0.921737 | + | 0.387815i | \(0.873230\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.81919 | 0.231859 | ||||||||
\(866\) | −75.7506 | −2.57411 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.20293 | 0.176599 | ||||||||
\(869\) | 7.64464 | 0.259327 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −61.8148 | −2.09451 | ||||||||
\(872\) | 7.26503 | 0.246025 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19.3354 | 0.654029 | ||||||||
\(875\) | −15.1240 | −0.511286 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.0000 | −0.641584 | −0.320792 | − | 0.947150i | \(-0.603949\pi\) | ||||
−0.320792 | + | 0.947150i | \(0.603949\pi\) | |||||||
\(878\) | 41.1923 | 1.39017 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.81172 | 0.229623 | ||||||||
\(881\) | −41.3500 | −1.39312 | −0.696559 | − | 0.717500i | \(-0.745287\pi\) | ||||
−0.696559 | + | 0.717500i | \(0.745287\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.4603 | 1.76543 | 0.882716 | − | 0.469908i | \(-0.155713\pi\) | ||||
0.882716 | + | 0.469908i | \(0.155713\pi\) | |||||||
\(884\) | −8.53753 | −0.287148 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.4089 | 0.383290 | ||||||||
\(887\) | 21.2344 | 0.712980 | 0.356490 | − | 0.934299i | \(-0.383973\pi\) | ||||
0.356490 | + | 0.934299i | \(0.383973\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.83384 | 0.329816 | ||||||||
\(890\) | −52.5897 | −1.76281 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 32.4648 | 1.08700 | ||||||||
\(893\) | −5.16082 | −0.172700 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.07355 | 0.136164 | ||||||||
\(896\) | 9.85490 | 0.329229 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.8075 | −0.527501 | ||||||||
\(899\) | −16.0735 | −0.536083 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.33537 | −0.0444876 | ||||||||
\(902\) | −4.47941 | −0.149148 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.34697 | 0.111319 | ||||||||
\(905\) | −7.49314 | −0.249080 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.2397 | 1.33614 | 0.668069 | − | 0.744100i | \(-0.267121\pi\) | ||||
0.668069 | + | 0.744100i | \(0.267121\pi\) | |||||||
\(908\) | 56.8599 | 1.88696 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −48.5162 | −1.60830 | ||||||||
\(911\) | 0.811724 | 0.0268936 | 0.0134468 | − | 0.999910i | \(-0.495720\pi\) | ||||
0.0134468 | + | 0.999910i | \(0.495720\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.08820 | −0.0691094 | ||||||||
\(914\) | 2.14510 | 0.0709537 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 50.0514 | 1.65375 | ||||||||
\(917\) | −5.37748 | −0.177580 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.7603 | 0.585858 | 0.292929 | − | 0.956134i | \(-0.405370\pi\) | ||||
0.292929 | + | 0.956134i | \(0.405370\pi\) | |||||||
\(920\) | 36.2206 | 1.19416 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −65.3500 | −2.15219 | ||||||||
\(923\) | −49.7412 | −1.63725 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 45.1839 | 1.48564 | ||||||||
\(926\) | 58.9936 | 1.93865 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −62.7222 | −2.05896 | ||||||||
\(929\) | −1.59947 | −0.0524770 | −0.0262385 | − | 0.999656i | \(-0.508353\pi\) | ||||
−0.0262385 | + | 0.999656i | \(0.508353\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.20293 | −0.0394245 | ||||||||
\(932\) | 29.8033 | 0.976241 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −84.0354 | −2.74972 | ||||||||
\(935\) | −1.52059 | −0.0497286 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.70140 | 0.0882510 | 0.0441255 | − | 0.999026i | \(-0.485950\pi\) | ||||
0.0441255 | + | 0.999026i | \(0.485950\pi\) | |||||||
\(938\) | −21.9652 | −0.717190 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −41.8148 | −1.36385 | ||||||||
\(941\) | −36.7917 | −1.19938 | −0.599688 | − | 0.800234i | \(-0.704709\pi\) | ||||
−0.599688 | + | 0.800234i | \(0.704709\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.9588 | 0.682513 | ||||||||
\(944\) | −35.5078 | −1.15568 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.7486 | −0.512030 | ||||||||
\(947\) | 24.3784 | 0.792192 | 0.396096 | − | 0.918209i | \(-0.370365\pi\) | ||||
0.396096 | + | 0.918209i | \(0.370365\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −60.5897 | −1.96683 | ||||||||
\(950\) | 23.3186 | 0.756555 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.701404 | −0.0227326 | ||||||||
\(953\) | 1.63091 | 0.0528304 | 0.0264152 | − | 0.999651i | \(-0.491591\pi\) | ||||
0.0264152 | + | 0.999651i | \(0.491591\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40.5383 | 1.31179 | ||||||||
\(956\) | 10.8381 | 0.350530 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −45.0177 | −1.45446 | ||||||||
\(959\) | −10.4931 | −0.338841 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 64.7475 | 2.08754 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 34.4426 | 1.10932 | ||||||||
\(965\) | −36.0829 | −1.16155 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.0735 | 1.54594 | 0.772971 | − | 0.634442i | \(-0.218770\pi\) | ||||
0.772971 | + | 0.634442i | \(0.218770\pi\) | |||||||
\(968\) | 13.4731 | 0.433043 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 41.8148 | 1.34259 | ||||||||
\(971\) | 10.3491 | 0.332118 | 0.166059 | − | 0.986116i | \(-0.446896\pi\) | ||||
0.166059 | + | 0.986116i | \(0.446896\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.79707 | −0.217904 | ||||||||
\(974\) | −61.4477 | −1.96891 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.5015 | 0.720256 | ||||||||
\(977\) | −11.1608 | −0.357066 | −0.178533 | − | 0.983934i | \(-0.557135\pi\) | ||||
−0.178533 | + | 0.983934i | \(0.557135\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.88527 | −0.156134 | ||||||||
\(980\) | −9.74657 | −0.311343 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −68.9588 | −2.20056 | ||||||||
\(983\) | 41.3775 | 1.31974 | 0.659868 | − | 0.751381i | \(-0.270612\pi\) | ||||
0.659868 | + | 0.751381i | \(0.270612\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 72.9809 | 2.32537 | ||||||||
\(986\) | 9.37214 | 0.298470 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.8914 | 0.601015 | ||||||||
\(989\) | 73.6863 | 2.34309 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.977882 | 0.0310634 | 0.0155317 | − | 0.999879i | \(-0.495056\pi\) | ||||
0.0155317 | + | 0.999879i | \(0.495056\pi\) | |||||||
\(992\) | 15.6088 | 0.495580 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −17.6750 | −0.560617 | ||||||||
\(995\) | 63.2069 | 2.00379 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.1103 | −0.890263 | −0.445131 | − | 0.895465i | \(-0.646843\pi\) | ||||
−0.445131 | + | 0.895465i | \(0.646843\pi\) | |||||||
\(998\) | 41.3186 | 1.30792 | ||||||||
\(999\) | 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 | 567.2.a.e.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 567.2.a.f.1.3 | yes | 3 | ||
4.3 | odd | 2 | 9072.2.a.bu.1.1 | 3 | |||
7.6 | odd | 2 | 3969.2.a.o.1.1 | 3 | |||
9.2 | odd | 6 | 567.2.f.l.190.1 | 6 | |||
9.4 | even | 3 | 567.2.f.m.379.3 | 6 | |||
9.5 | odd | 6 | 567.2.f.l.379.1 | 6 | |||
9.7 | even | 3 | 567.2.f.m.190.3 | 6 | |||
12.11 | even | 2 | 9072.2.a.cb.1.3 | 3 | |||
21.20 | even | 2 | 3969.2.a.n.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
567.2.a.e.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
567.2.a.f.1.3 | yes | 3 | 3.2 | odd | 2 | ||
567.2.f.l.190.1 | 6 | 9.2 | odd | 6 | |||
567.2.f.l.379.1 | 6 | 9.5 | odd | 6 | |||
567.2.f.m.190.3 | 6 | 9.7 | even | 3 | |||
567.2.f.m.379.3 | 6 | 9.4 | even | 3 | |||
3969.2.a.n.1.3 | 3 | 21.20 | even | 2 | |||
3969.2.a.o.1.1 | 3 | 7.6 | odd | 2 | |||
9072.2.a.bu.1.1 | 3 | 4.3 | odd | 2 | |||
9072.2.a.cb.1.3 | 3 | 12.11 | even | 2 |