Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(1,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, 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("441.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 147) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.414214 | −0.292893 | −0.146447 | − | 0.989219i | \(-0.546784\pi\) | ||||
−0.146447 | + | 0.989219i | \(0.546784\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.82843 | −0.914214 | ||||||||
\(5\) | 3.41421 | 1.52688 | 0.763441 | − | 0.645877i | \(-0.223508\pi\) | ||||
0.763441 | + | 0.645877i | \(0.223508\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.58579 | 0.560660 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.41421 | −0.447214 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.58579 | −0.717168 | −0.358584 | − | 0.933497i | \(-0.616740\pi\) | ||||
−0.358584 | + | 0.933497i | \(0.616740\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | −2.24264 | −0.543920 | −0.271960 | − | 0.962309i | \(-0.587672\pi\) | ||||
−0.271960 | + | 0.962309i | \(0.587672\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.82843 | 0.648886 | 0.324443 | − | 0.945905i | \(-0.394823\pi\) | ||||
0.324443 | + | 0.945905i | \(0.394823\pi\) | |||||||
\(20\) | −6.24264 | −1.39590 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.828427 | −0.176621 | ||||||||
\(23\) | 7.65685 | 1.59656 | 0.798282 | − | 0.602284i | \(-0.205742\pi\) | ||||
0.798282 | + | 0.602284i | \(0.205742\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.65685 | 1.33137 | ||||||||
\(26\) | 1.07107 | 0.210054 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.82843 | 1.26801 | 0.634004 | − | 0.773330i | \(-0.281410\pi\) | ||||
0.634004 | + | 0.773330i | \(0.281410\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.17157 | 0.210421 | 0.105210 | − | 0.994450i | \(-0.466448\pi\) | ||||
0.105210 | + | 0.994450i | \(0.466448\pi\) | |||||||
\(32\) | −4.41421 | −0.780330 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.928932 | 0.159311 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | −1.17157 | −0.190054 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.41421 | 0.856062 | ||||||||
\(41\) | 6.24264 | 0.974937 | 0.487468 | − | 0.873141i | \(-0.337920\pi\) | ||||
0.487468 | + | 0.873141i | \(0.337920\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.65685 | 0.862662 | 0.431331 | − | 0.902194i | \(-0.358044\pi\) | ||||
0.431331 | + | 0.902194i | \(0.358044\pi\) | |||||||
\(44\) | −3.65685 | −0.551292 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.17157 | −0.467623 | ||||||||
\(47\) | −2.82843 | −0.412568 | −0.206284 | − | 0.978492i | \(-0.566137\pi\) | ||||
−0.206284 | + | 0.978492i | \(0.566137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.75736 | −0.389949 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.72792 | 0.655645 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.82843 | 0.920745 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.82843 | −0.371391 | ||||||||
\(59\) | −1.17157 | −0.152526 | −0.0762629 | − | 0.997088i | \(-0.524299\pi\) | ||||
−0.0762629 | + | 0.997088i | \(0.524299\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.2426 | −1.56751 | −0.783755 | − | 0.621070i | \(-0.786698\pi\) | ||||
−0.783755 | + | 0.621070i | \(0.786698\pi\) | |||||||
\(62\) | −0.485281 | −0.0616308 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | −8.82843 | −1.09503 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.65685 | −0.691095 | −0.345547 | − | 0.938401i | \(-0.612307\pi\) | ||||
−0.345547 | + | 0.938401i | \(0.612307\pi\) | |||||||
\(68\) | 4.10051 | 0.497259 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.31371 | −1.10533 | −0.552667 | − | 0.833402i | \(-0.686390\pi\) | ||||
−0.552667 | + | 0.833402i | \(0.686390\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.8995 | −1.62681 | −0.813406 | − | 0.581696i | \(-0.802389\pi\) | ||||
−0.813406 | + | 0.581696i | \(0.802389\pi\) | |||||||
\(74\) | 1.65685 | 0.192605 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.17157 | −0.593220 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.6569 | 1.53652 | 0.768258 | − | 0.640140i | \(-0.221124\pi\) | ||||
0.768258 | + | 0.640140i | \(0.221124\pi\) | |||||||
\(80\) | 10.2426 | 1.14516 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.58579 | −0.285552 | ||||||||
\(83\) | 7.31371 | 0.802784 | 0.401392 | − | 0.915906i | \(-0.368527\pi\) | ||||
0.401392 | + | 0.915906i | \(0.368527\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.65685 | −0.830502 | ||||||||
\(86\) | −2.34315 | −0.252668 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.17157 | 0.338091 | ||||||||
\(89\) | −14.2426 | −1.50972 | −0.754858 | − | 0.655888i | \(-0.772294\pi\) | ||||
−0.754858 | + | 0.655888i | \(0.772294\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −14.0000 | −1.45960 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.17157 | 0.120839 | ||||||||
\(95\) | 9.65685 | 0.990772 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.58579 | −0.262547 | −0.131273 | − | 0.991346i | \(-0.541907\pi\) | ||||
−0.131273 | + | 0.991346i | \(0.541907\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −12.1716 | −1.21716 | ||||||||
\(101\) | 2.92893 | 0.291440 | 0.145720 | − | 0.989326i | \(-0.453450\pi\) | ||||
0.145720 | + | 0.989326i | \(0.453450\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.48528 | −0.441948 | −0.220974 | − | 0.975280i | \(-0.570924\pi\) | ||||
−0.220974 | + | 0.975280i | \(0.570924\pi\) | |||||||
\(104\) | −4.10051 | −0.402088 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.828427 | −0.0804640 | ||||||||
\(107\) | 0.343146 | 0.0331732 | 0.0165866 | − | 0.999862i | \(-0.494720\pi\) | ||||
0.0165866 | + | 0.999862i | \(0.494720\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.65685 | −0.541828 | −0.270914 | − | 0.962604i | \(-0.587326\pi\) | ||||
−0.270914 | + | 0.962604i | \(0.587326\pi\) | |||||||
\(110\) | −2.82843 | −0.269680 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.31371 | 0.499872 | 0.249936 | − | 0.968262i | \(-0.419590\pi\) | ||||
0.249936 | + | 0.968262i | \(0.419590\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 26.1421 | 2.43777 | ||||||||
\(116\) | −12.4853 | −1.15923 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.485281 | 0.0446738 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 5.07107 | 0.459113 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.14214 | −0.192369 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.65685 | −0.147022 | −0.0735110 | − | 0.997294i | \(-0.523420\pi\) | ||||
−0.0735110 | + | 0.997294i | \(0.523420\pi\) | |||||||
\(128\) | 10.5563 | 0.933058 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.65685 | 0.320727 | ||||||||
\(131\) | −15.3137 | −1.33796 | −0.668982 | − | 0.743278i | \(-0.733270\pi\) | ||||
−0.668982 | + | 0.743278i | \(0.733270\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.34315 | 0.202417 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.55635 | −0.304954 | ||||||||
\(137\) | −14.1421 | −1.20824 | −0.604122 | − | 0.796892i | \(-0.706476\pi\) | ||||
−0.604122 | + | 0.796892i | \(0.706476\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.6569 | 1.49763 | 0.748817 | − | 0.662776i | \(-0.230622\pi\) | ||||
0.748817 | + | 0.662776i | \(0.230622\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.85786 | 0.323745 | ||||||||
\(143\) | −5.17157 | −0.432469 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 23.3137 | 1.93610 | ||||||||
\(146\) | 5.75736 | 0.476482 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.31371 | 0.601183 | ||||||||
\(149\) | −17.3137 | −1.41839 | −0.709197 | − | 0.705010i | \(-0.750942\pi\) | ||||
−0.709197 | + | 0.705010i | \(0.750942\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(152\) | 4.48528 | 0.363804 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.7574 | −0.938339 | −0.469170 | − | 0.883108i | \(-0.655447\pi\) | ||||
−0.469170 | + | 0.883108i | \(0.655447\pi\) | |||||||
\(158\) | −5.65685 | −0.450035 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −15.0711 | −1.19147 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.3137 | −0.886158 | −0.443079 | − | 0.896483i | \(-0.646114\pi\) | ||||
−0.443079 | + | 0.896483i | \(0.646114\pi\) | |||||||
\(164\) | −11.4142 | −0.891300 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.02944 | −0.235130 | ||||||||
\(167\) | −19.7990 | −1.53209 | −0.766046 | − | 0.642786i | \(-0.777779\pi\) | ||||
−0.766046 | + | 0.642786i | \(0.777779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.31371 | −0.485670 | ||||||||
\(170\) | 3.17157 | 0.243249 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.3431 | −0.788657 | ||||||||
\(173\) | 21.0711 | 1.60200 | 0.801002 | − | 0.598662i | \(-0.204301\pi\) | ||||
0.801002 | + | 0.598662i | \(0.204301\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.00000 | 0.452267 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.89949 | 0.442186 | ||||||||
\(179\) | 19.6569 | 1.46922 | 0.734611 | − | 0.678488i | \(-0.237365\pi\) | ||||
0.734611 | + | 0.678488i | \(0.237365\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.58579 | 0.192200 | 0.0961000 | − | 0.995372i | \(-0.469363\pi\) | ||||
0.0961000 | + | 0.995372i | \(0.469363\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.1421 | 0.895130 | ||||||||
\(185\) | −13.6569 | −1.00407 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.48528 | −0.327996 | ||||||||
\(188\) | 5.17157 | 0.377176 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | 18.0000 | 1.30243 | 0.651217 | − | 0.758891i | \(-0.274259\pi\) | ||||
0.651217 | + | 0.758891i | \(0.274259\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.31371 | 0.382489 | 0.191245 | − | 0.981542i | \(-0.438748\pi\) | ||||
0.191245 | + | 0.981542i | \(0.438748\pi\) | |||||||
\(194\) | 1.07107 | 0.0768982 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.6569 | −1.53521 | −0.767607 | − | 0.640921i | \(-0.778553\pi\) | ||||
−0.767607 | + | 0.640921i | \(0.778553\pi\) | |||||||
\(200\) | 10.5563 | 0.746447 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.21320 | −0.0853607 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.3137 | 1.48861 | ||||||||
\(206\) | 1.85786 | 0.129444 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.75736 | −0.537876 | ||||||||
\(209\) | 5.65685 | 0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.9706 | 0.892930 | 0.446465 | − | 0.894801i | \(-0.352683\pi\) | ||||
0.446465 | + | 0.894801i | \(0.352683\pi\) | |||||||
\(212\) | −3.65685 | −0.251154 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.142136 | −0.00971619 | ||||||||
\(215\) | 19.3137 | 1.31718 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.34315 | 0.158698 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −12.4853 | −0.841757 | ||||||||
\(221\) | 5.79899 | 0.390082 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.9706 | −1.67215 | −0.836076 | − | 0.548613i | \(-0.815156\pi\) | ||||
−0.836076 | + | 0.548613i | \(0.815156\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.20101 | −0.146409 | ||||||||
\(227\) | 23.7990 | 1.57959 | 0.789797 | − | 0.613368i | \(-0.210186\pi\) | ||||
0.789797 | + | 0.613368i | \(0.210186\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.242641 | 0.0160341 | 0.00801707 | − | 0.999968i | \(-0.497448\pi\) | ||||
0.00801707 | + | 0.999968i | \(0.497448\pi\) | |||||||
\(230\) | −10.8284 | −0.714005 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.8284 | 0.710921 | ||||||||
\(233\) | 6.14214 | 0.402385 | 0.201192 | − | 0.979552i | \(-0.435518\pi\) | ||||
0.201192 | + | 0.979552i | \(0.435518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.65685 | −0.629944 | ||||||||
\(236\) | 2.14214 | 0.139441 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.6569 | 1.01276 | 0.506379 | − | 0.862311i | \(-0.330984\pi\) | ||||
0.506379 | + | 0.862311i | \(0.330984\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.2426 | 1.04628 | 0.523140 | − | 0.852247i | \(-0.324760\pi\) | ||||
0.523140 | + | 0.852247i | \(0.324760\pi\) | |||||||
\(242\) | 2.89949 | 0.186387 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 22.3848 | 1.43304 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.31371 | −0.465360 | ||||||||
\(248\) | 1.85786 | 0.117975 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.34315 | −0.148194 | ||||||||
\(251\) | −12.4853 | −0.788064 | −0.394032 | − | 0.919097i | \(-0.628920\pi\) | ||||
−0.394032 | + | 0.919097i | \(0.628920\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.3137 | 0.962765 | ||||||||
\(254\) | 0.686292 | 0.0430618 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | 23.2132 | 1.44800 | 0.724000 | − | 0.689800i | \(-0.242302\pi\) | ||||
0.724000 | + | 0.689800i | \(0.242302\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 16.1421 | 1.00109 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.34315 | 0.391881 | ||||||||
\(263\) | −5.31371 | −0.327657 | −0.163829 | − | 0.986489i | \(-0.552384\pi\) | ||||
−0.163829 | + | 0.986489i | \(0.552384\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.82843 | 0.419467 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.3431 | 0.631808 | ||||||||
\(269\) | −14.7279 | −0.897977 | −0.448989 | − | 0.893537i | \(-0.648216\pi\) | ||||
−0.448989 | + | 0.893537i | \(0.648216\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.1421 | 0.616091 | 0.308045 | − | 0.951372i | \(-0.400325\pi\) | ||||
0.308045 | + | 0.951372i | \(0.400325\pi\) | |||||||
\(272\) | −6.72792 | −0.407940 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.85786 | 0.353887 | ||||||||
\(275\) | 13.3137 | 0.802847 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.31371 | −0.559607 | −0.279803 | − | 0.960057i | \(-0.590269\pi\) | ||||
−0.279803 | + | 0.960057i | \(0.590269\pi\) | |||||||
\(278\) | −7.31371 | −0.438647 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.485281 | −0.0289495 | −0.0144747 | − | 0.999895i | \(-0.504608\pi\) | ||||
−0.0144747 | + | 0.999895i | \(0.504608\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.48528 | 0.504398 | 0.252199 | − | 0.967675i | \(-0.418846\pi\) | ||||
0.252199 | + | 0.967675i | \(0.418846\pi\) | |||||||
\(284\) | 17.0294 | 1.01051 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.14214 | 0.126667 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.9706 | −0.704151 | ||||||||
\(290\) | −9.65685 | −0.567070 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 25.4142 | 1.48725 | ||||||||
\(293\) | 16.5858 | 0.968952 | 0.484476 | − | 0.874805i | \(-0.339010\pi\) | ||||
0.484476 | + | 0.874805i | \(0.339010\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | −6.34315 | −0.368688 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.17157 | 0.415438 | ||||||||
\(299\) | −19.7990 | −1.14501 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4.97056 | −0.286024 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.48528 | 0.486664 | ||||||||
\(305\) | −41.7990 | −2.39340 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.1421 | −1.72030 | −0.860151 | − | 0.510039i | \(-0.829631\pi\) | ||||
−0.860151 | + | 0.510039i | \(0.829631\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.65685 | −0.0941030 | ||||||||
\(311\) | 6.14214 | 0.348289 | 0.174144 | − | 0.984720i | \(-0.444284\pi\) | ||||
0.174144 | + | 0.984720i | \(0.444284\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.89949 | −0.107366 | −0.0536829 | − | 0.998558i | \(-0.517096\pi\) | ||||
−0.0536829 | + | 0.998558i | \(0.517096\pi\) | |||||||
\(314\) | 4.87006 | 0.274833 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −24.9706 | −1.40470 | ||||||||
\(317\) | −10.0000 | −0.561656 | −0.280828 | − | 0.959758i | \(-0.590609\pi\) | ||||
−0.280828 | + | 0.959758i | \(0.590609\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.6569 | 0.764637 | ||||||||
\(320\) | −14.2426 | −0.796188 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.34315 | −0.352942 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.2132 | −0.954817 | ||||||||
\(326\) | 4.68629 | 0.259550 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.89949 | 0.546608 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(332\) | −13.3726 | −0.733916 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.20101 | 0.448739 | ||||||||
\(335\) | −19.3137 | −1.05522 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.6569 | −1.61551 | −0.807756 | − | 0.589517i | \(-0.799318\pi\) | ||||
−0.807756 | + | 0.589517i | \(0.799318\pi\) | |||||||
\(338\) | 2.61522 | 0.142249 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 14.0000 | 0.759257 | ||||||||
\(341\) | 2.34315 | 0.126888 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.97056 | 0.483660 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.72792 | −0.469216 | ||||||||
\(347\) | −33.3137 | −1.78837 | −0.894187 | − | 0.447694i | \(-0.852245\pi\) | ||||
−0.894187 | + | 0.447694i | \(0.852245\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.89949 | 0.529908 | 0.264954 | − | 0.964261i | \(-0.414643\pi\) | ||||
0.264954 | + | 0.964261i | \(0.414643\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8.82843 | −0.470557 | ||||||||
\(353\) | −14.7279 | −0.783888 | −0.391944 | − | 0.919989i | \(-0.628197\pi\) | ||||
−0.391944 | + | 0.919989i | \(0.628197\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −31.7990 | −1.68772 | ||||||||
\(356\) | 26.0416 | 1.38020 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.14214 | −0.430325 | ||||||||
\(359\) | 0.343146 | 0.0181105 | 0.00905527 | − | 0.999959i | \(-0.497118\pi\) | ||||
0.00905527 | + | 0.999959i | \(0.497118\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | −1.07107 | −0.0562941 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −47.4558 | −2.48395 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.31371 | 0.172974 | 0.0864871 | − | 0.996253i | \(-0.472436\pi\) | ||||
0.0864871 | + | 0.996253i | \(0.472436\pi\) | |||||||
\(368\) | 22.9706 | 1.19742 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.65685 | 0.294086 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.6863 | −0.553315 | −0.276658 | − | 0.960969i | \(-0.589227\pi\) | ||||
−0.276658 | + | 0.960969i | \(0.589227\pi\) | |||||||
\(374\) | 1.85786 | 0.0960679 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.48528 | −0.231311 | ||||||||
\(377\) | −17.6569 | −0.909374 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.68629 | 0.446185 | 0.223092 | − | 0.974797i | \(-0.428385\pi\) | ||||
0.223092 | + | 0.974797i | \(0.428385\pi\) | |||||||
\(380\) | −17.6569 | −0.905778 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.45584 | −0.381474 | ||||||||
\(383\) | −18.3431 | −0.937291 | −0.468645 | − | 0.883386i | \(-0.655258\pi\) | ||||
−0.468645 | + | 0.883386i | \(0.655258\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.20101 | −0.112028 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.72792 | 0.240024 | ||||||||
\(389\) | 18.1421 | 0.919843 | 0.459921 | − | 0.887960i | \(-0.347878\pi\) | ||||
0.459921 | + | 0.887960i | \(0.347878\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.1716 | −0.868404 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.828427 | 0.0417356 | ||||||||
\(395\) | 46.6274 | 2.34608 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.38478 | 0.119688 | 0.0598442 | − | 0.998208i | \(-0.480940\pi\) | ||||
0.0598442 | + | 0.998208i | \(0.480940\pi\) | |||||||
\(398\) | 8.97056 | 0.449654 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.9706 | 0.998528 | ||||||||
\(401\) | 6.14214 | 0.306724 | 0.153362 | − | 0.988170i | \(-0.450990\pi\) | ||||
0.153362 | + | 0.988170i | \(0.450990\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.02944 | −0.150907 | ||||||||
\(404\) | −5.35534 | −0.266438 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.4142 | 1.05886 | 0.529432 | − | 0.848352i | \(-0.322405\pi\) | ||||
0.529432 | + | 0.848352i | \(0.322405\pi\) | |||||||
\(410\) | −8.82843 | −0.436005 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.20101 | 0.404035 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.9706 | 1.22576 | ||||||||
\(416\) | 11.4142 | 0.559628 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.34315 | −0.114607 | ||||||||
\(419\) | 33.1716 | 1.62054 | 0.810269 | − | 0.586059i | \(-0.199321\pi\) | ||||
0.810269 | + | 0.586059i | \(0.199321\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.6274 | 0.810371 | 0.405185 | − | 0.914235i | \(-0.367207\pi\) | ||||
0.405185 | + | 0.914235i | \(0.367207\pi\) | |||||||
\(422\) | −5.37258 | −0.261533 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.17157 | 0.154025 | ||||||||
\(425\) | −14.9289 | −0.724160 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.627417 | −0.0303273 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.00000 | −0.385794 | ||||||||
\(431\) | 26.9706 | 1.29913 | 0.649563 | − | 0.760308i | \(-0.274952\pi\) | ||||
0.649563 | + | 0.760308i | \(0.274952\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.2426 | 0.972799 | 0.486400 | − | 0.873736i | \(-0.338310\pi\) | ||||
0.486400 | + | 0.873736i | \(0.338310\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.3431 | 0.495347 | ||||||||
\(437\) | 21.6569 | 1.03599 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.6863 | −0.605484 | −0.302742 | − | 0.953073i | \(-0.597902\pi\) | ||||
−0.302742 | + | 0.953073i | \(0.597902\pi\) | |||||||
\(440\) | 10.8284 | 0.516225 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.40202 | −0.114252 | ||||||||
\(443\) | −34.9706 | −1.66150 | −0.830751 | − | 0.556645i | \(-0.812089\pi\) | ||||
−0.830751 | + | 0.556645i | \(0.812089\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −48.6274 | −2.30516 | ||||||||
\(446\) | 10.3431 | 0.489762 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.31371 | 0.250769 | 0.125385 | − | 0.992108i | \(-0.459983\pi\) | ||||
0.125385 | + | 0.992108i | \(0.459983\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.4853 | 0.587909 | ||||||||
\(452\) | −9.71573 | −0.456989 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.85786 | −0.462652 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.0000 | −0.842004 | −0.421002 | − | 0.907060i | \(-0.638322\pi\) | ||||
−0.421002 | + | 0.907060i | \(0.638322\pi\) | |||||||
\(458\) | −0.100505 | −0.00469629 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −47.7990 | −2.22864 | ||||||||
\(461\) | −16.5858 | −0.772477 | −0.386239 | − | 0.922399i | \(-0.626226\pi\) | ||||
−0.386239 | + | 0.922399i | \(0.626226\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.6274 | −1.23748 | −0.618741 | − | 0.785595i | \(-0.712357\pi\) | ||||
−0.618741 | + | 0.785595i | \(0.712357\pi\) | |||||||
\(464\) | 20.4853 | 0.951005 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.54416 | −0.117856 | ||||||||
\(467\) | 0.201010 | 0.00930164 | 0.00465082 | − | 0.999989i | \(-0.498520\pi\) | ||||
0.00465082 | + | 0.999989i | \(0.498520\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.00000 | 0.184506 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.85786 | −0.0855151 | ||||||||
\(473\) | 11.3137 | 0.520205 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.8284 | 0.863907 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.48528 | −0.296630 | ||||||||
\(479\) | 1.85786 | 0.0848880 | 0.0424440 | − | 0.999099i | \(-0.486486\pi\) | ||||
0.0424440 | + | 0.999099i | \(0.486486\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.3431 | 0.471607 | ||||||||
\(482\) | −6.72792 | −0.306448 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.7990 | 0.581772 | ||||||||
\(485\) | −8.82843 | −0.400878 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.6274 | 1.20660 | 0.603302 | − | 0.797513i | \(-0.293851\pi\) | ||||
0.603302 | + | 0.797513i | \(0.293851\pi\) | |||||||
\(488\) | −19.4142 | −0.878840 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.02944 | −0.226975 | −0.113488 | − | 0.993539i | \(-0.536202\pi\) | ||||
−0.113488 | + | 0.993539i | \(0.536202\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.3137 | −0.689695 | ||||||||
\(494\) | 3.02944 | 0.136301 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.51472 | 0.157816 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.31371 | 0.148342 | 0.0741710 | − | 0.997246i | \(-0.476369\pi\) | ||||
0.0741710 | + | 0.997246i | \(0.476369\pi\) | |||||||
\(500\) | −10.3431 | −0.462560 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.17157 | 0.230819 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | −6.34315 | −0.281987 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.02944 | 0.134410 | ||||||||
\(509\) | 5.55635 | 0.246281 | 0.123140 | − | 0.992389i | \(-0.460703\pi\) | ||||
0.123140 | + | 0.992389i | \(0.460703\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.7574 | −1.00574 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.61522 | −0.424109 | ||||||||
\(515\) | −15.3137 | −0.674803 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.65685 | −0.248788 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −14.0000 | −0.613941 | ||||||||
\(521\) | −35.4142 | −1.55152 | −0.775762 | − | 0.631025i | \(-0.782634\pi\) | ||||
−0.775762 | + | 0.631025i | \(0.782634\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.6569 | 1.12190 | 0.560948 | − | 0.827851i | \(-0.310437\pi\) | ||||
0.560948 | + | 0.827851i | \(0.310437\pi\) | |||||||
\(524\) | 28.0000 | 1.22319 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.20101 | 0.0959686 | ||||||||
\(527\) | −2.62742 | −0.114452 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35.6274 | 1.54902 | ||||||||
\(530\) | −2.82843 | −0.122859 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.1421 | −0.699194 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.17157 | 0.0506515 | ||||||||
\(536\) | −8.97056 | −0.387469 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.10051 | 0.263011 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.3137 | 0.744374 | 0.372187 | − | 0.928158i | \(-0.378608\pi\) | ||||
0.372187 | + | 0.928158i | \(0.378608\pi\) | |||||||
\(542\) | −4.20101 | −0.180449 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.89949 | 0.424437 | ||||||||
\(545\) | −19.3137 | −0.827308 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.9706 | −1.58075 | −0.790374 | − | 0.612625i | \(-0.790114\pi\) | ||||
−0.790374 | + | 0.612625i | \(0.790114\pi\) | |||||||
\(548\) | 25.8579 | 1.10459 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.51472 | −0.235148 | ||||||||
\(551\) | 19.3137 | 0.822792 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.85786 | 0.163905 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −32.2843 | −1.36916 | ||||||||
\(557\) | −26.0000 | −1.10166 | −0.550828 | − | 0.834619i | \(-0.685688\pi\) | ||||
−0.550828 | + | 0.834619i | \(0.685688\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.6274 | −0.618674 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.201010 | 0.00847910 | ||||||||
\(563\) | −1.17157 | −0.0493759 | −0.0246880 | − | 0.999695i | \(-0.507859\pi\) | ||||
−0.0246880 | + | 0.999695i | \(0.507859\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.1421 | 0.763245 | ||||||||
\(566\) | −3.51472 | −0.147735 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.7696 | −0.619717 | ||||||||
\(569\) | 16.4853 | 0.691099 | 0.345549 | − | 0.938401i | \(-0.387693\pi\) | ||||
0.345549 | + | 0.938401i | \(0.387693\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.3431 | 0.935032 | 0.467516 | − | 0.883985i | \(-0.345149\pi\) | ||||
0.467516 | + | 0.883985i | \(0.345149\pi\) | |||||||
\(572\) | 9.45584 | 0.395369 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 50.9706 | 2.12562 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.8995 | 1.41125 | 0.705627 | − | 0.708583i | \(-0.250665\pi\) | ||||
0.705627 | + | 0.708583i | \(0.250665\pi\) | |||||||
\(578\) | 4.95837 | 0.206241 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −42.6274 | −1.77001 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.00000 | 0.165663 | ||||||||
\(584\) | −22.0416 | −0.912089 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.87006 | −0.283799 | ||||||||
\(587\) | −22.8284 | −0.942230 | −0.471115 | − | 0.882072i | \(-0.656148\pi\) | ||||
−0.471115 | + | 0.882072i | \(0.656148\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.31371 | 0.136539 | ||||||||
\(590\) | 1.65685 | 0.0682116 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.0000 | −0.493197 | ||||||||
\(593\) | −6.92893 | −0.284537 | −0.142269 | − | 0.989828i | \(-0.545440\pi\) | ||||
−0.142269 | + | 0.989828i | \(0.545440\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 31.6569 | 1.29672 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.20101 | 0.335364 | ||||||||
\(599\) | 2.00000 | 0.0817178 | 0.0408589 | − | 0.999165i | \(-0.486991\pi\) | ||||
0.0408589 | + | 0.999165i | \(0.486991\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.0711 | 0.614762 | 0.307381 | − | 0.951587i | \(-0.400547\pi\) | ||||
0.307381 | + | 0.951587i | \(0.400547\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −21.9411 | −0.892772 | ||||||||
\(605\) | −23.8995 | −0.971653 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.3431 | 0.744525 | 0.372263 | − | 0.928127i | \(-0.378582\pi\) | ||||
0.372263 | + | 0.928127i | \(0.378582\pi\) | |||||||
\(608\) | −12.4853 | −0.506345 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 17.3137 | 0.701012 | ||||||||
\(611\) | 7.31371 | 0.295881 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.68629 | 0.189278 | 0.0946388 | − | 0.995512i | \(-0.469830\pi\) | ||||
0.0946388 | + | 0.995512i | \(0.469830\pi\) | |||||||
\(614\) | 12.4853 | 0.503865 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.4853 | 0.985740 | 0.492870 | − | 0.870103i | \(-0.335948\pi\) | ||||
0.492870 | + | 0.870103i | \(0.335948\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.9706 | −1.16443 | −0.582213 | − | 0.813037i | \(-0.697813\pi\) | ||||
−0.582213 | + | 0.813037i | \(0.697813\pi\) | |||||||
\(620\) | −7.31371 | −0.293726 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.54416 | −0.102011 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | 0.786797 | 0.0314467 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21.4975 | 0.857843 | ||||||||
\(629\) | 8.97056 | 0.357680 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.3137 | 0.928104 | 0.464052 | − | 0.885808i | \(-0.346395\pi\) | ||||
0.464052 | + | 0.885808i | \(0.346395\pi\) | |||||||
\(632\) | 21.6569 | 0.861463 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.14214 | 0.164505 | ||||||||
\(635\) | −5.65685 | −0.224485 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.65685 | −0.223957 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 36.0416 | 1.42467 | ||||||||
\(641\) | 10.8284 | 0.427697 | 0.213849 | − | 0.976867i | \(-0.431400\pi\) | ||||
0.213849 | + | 0.976867i | \(0.431400\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.4264 | 1.35764 | 0.678822 | − | 0.734302i | \(-0.262491\pi\) | ||||
0.678822 | + | 0.734302i | \(0.262491\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.62742 | 0.103374 | ||||||||
\(647\) | 26.8284 | 1.05473 | 0.527367 | − | 0.849638i | \(-0.323179\pi\) | ||||
0.527367 | + | 0.849638i | \(0.323179\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.34315 | −0.0919765 | ||||||||
\(650\) | 7.12994 | 0.279659 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.6863 | 0.810138 | ||||||||
\(653\) | −36.4853 | −1.42778 | −0.713890 | − | 0.700258i | \(-0.753068\pi\) | ||||
−0.713890 | + | 0.700258i | \(0.753068\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −52.2843 | −2.04292 | ||||||||
\(656\) | 18.7279 | 0.731203 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.31371 | −0.362811 | −0.181405 | − | 0.983408i | \(-0.558065\pi\) | ||||
−0.181405 | + | 0.983408i | \(0.558065\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.5563 | 0.916236 | 0.458118 | − | 0.888891i | \(-0.348524\pi\) | ||||
0.458118 | + | 0.888891i | \(0.348524\pi\) | |||||||
\(662\) | 1.65685 | 0.0643955 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.5980 | 0.450089 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 52.2843 | 2.02446 | ||||||||
\(668\) | 36.2010 | 1.40066 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.00000 | 0.309067 | ||||||||
\(671\) | −24.4853 | −0.945244 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.3137 | 0.898677 | 0.449339 | − | 0.893361i | \(-0.351660\pi\) | ||||
0.449339 | + | 0.893361i | \(0.351660\pi\) | |||||||
\(674\) | 12.2843 | 0.473172 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.5442 | 0.444006 | ||||||||
\(677\) | 31.4142 | 1.20735 | 0.603673 | − | 0.797232i | \(-0.293703\pi\) | ||||
0.603673 | + | 0.797232i | \(0.293703\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −12.1421 | −0.465630 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.970563 | −0.0371648 | ||||||||
\(683\) | 19.6569 | 0.752149 | 0.376074 | − | 0.926590i | \(-0.377274\pi\) | ||||
0.376074 | + | 0.926590i | \(0.377274\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −48.2843 | −1.84485 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 16.9706 | 0.646997 | ||||||||
\(689\) | −5.17157 | −0.197021 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.686292 | 0.0261078 | 0.0130539 | − | 0.999915i | \(-0.495845\pi\) | ||||
0.0130539 | + | 0.999915i | \(0.495845\pi\) | |||||||
\(692\) | −38.5269 | −1.46457 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.7990 | 0.523802 | ||||||||
\(695\) | 60.2843 | 2.28671 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.0000 | −0.530288 | ||||||||
\(698\) | −4.10051 | −0.155206 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.1716 | 0.648561 | 0.324281 | − | 0.945961i | \(-0.394878\pi\) | ||||
0.324281 | + | 0.945961i | \(0.394878\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.3137 | −0.426705 | ||||||||
\(704\) | −8.34315 | −0.314444 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.10051 | 0.229596 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.2843 | −1.36268 | −0.681342 | − | 0.731965i | \(-0.738603\pi\) | ||||
−0.681342 | + | 0.731965i | \(0.738603\pi\) | |||||||
\(710\) | 13.1716 | 0.494320 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −22.5858 | −0.846438 | ||||||||
\(713\) | 8.97056 | 0.335950 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.6569 | −0.660329 | ||||||||
\(716\) | −35.9411 | −1.34318 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.142136 | −0.00530445 | ||||||||
\(719\) | 41.9411 | 1.56414 | 0.782070 | − | 0.623191i | \(-0.214164\pi\) | ||||
0.782070 | + | 0.623191i | \(0.214164\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 4.55635 | 0.169570 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.72792 | −0.175712 | ||||||||
\(725\) | 45.4558 | 1.68819 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.4853 | −0.463053 | −0.231527 | − | 0.972829i | \(-0.574372\pi\) | ||||
−0.231527 | + | 0.972829i | \(0.574372\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 19.6569 | 0.727533 | ||||||||
\(731\) | −12.6863 | −0.469219 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −49.6985 | −1.83566 | −0.917828 | − | 0.396979i | \(-0.870059\pi\) | ||||
−0.917828 | + | 0.396979i | \(0.870059\pi\) | |||||||
\(734\) | −1.37258 | −0.0506630 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −33.7990 | −1.24585 | ||||||||
\(737\) | −11.3137 | −0.416746 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.68629 | 0.172388 | 0.0861940 | − | 0.996278i | \(-0.472530\pi\) | ||||
0.0861940 | + | 0.996278i | \(0.472530\pi\) | |||||||
\(740\) | 24.9706 | 0.917936 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 50.9706 | 1.86993 | 0.934964 | − | 0.354742i | \(-0.115431\pi\) | ||||
0.934964 | + | 0.354742i | \(0.115431\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −59.1127 | −2.16572 | ||||||||
\(746\) | 4.42641 | 0.162062 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.20101 | 0.299859 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.6569 | 0.498346 | 0.249173 | − | 0.968459i | \(-0.419841\pi\) | ||||
0.249173 | + | 0.968459i | \(0.419841\pi\) | |||||||
\(752\) | −8.48528 | −0.309426 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.31371 | 0.266350 | ||||||||
\(755\) | 40.9706 | 1.49107 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.3431 | 0.957458 | 0.478729 | − | 0.877963i | \(-0.341098\pi\) | ||||
0.478729 | + | 0.877963i | \(0.341098\pi\) | |||||||
\(758\) | −3.59798 | −0.130685 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 15.3137 | 0.555487 | ||||||||
\(761\) | −18.5269 | −0.671600 | −0.335800 | − | 0.941933i | \(-0.609007\pi\) | ||||
−0.335800 | + | 0.941933i | \(0.609007\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −32.9117 | −1.19070 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.59798 | 0.274526 | ||||||||
\(767\) | 3.02944 | 0.109387 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.6985 | −1.07095 | −0.535477 | − | 0.844550i | \(-0.679868\pi\) | ||||
−0.535477 | + | 0.844550i | \(0.679868\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.71573 | −0.349677 | ||||||||
\(773\) | −9.55635 | −0.343718 | −0.171859 | − | 0.985122i | \(-0.554977\pi\) | ||||
−0.171859 | + | 0.985122i | \(0.554977\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.79899 | 0.280148 | ||||||||
\(776\) | −4.10051 | −0.147200 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.51472 | −0.269416 | ||||||||
\(779\) | 17.6569 | 0.632622 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.6274 | −0.666541 | ||||||||
\(782\) | 7.11270 | 0.254350 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −40.1421 | −1.43273 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.6863 | −0.879971 | −0.439986 | − | 0.898005i | \(-0.645016\pi\) | ||||
−0.439986 | + | 0.898005i | \(0.645016\pi\) | |||||||
\(788\) | 3.65685 | 0.130270 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −19.3137 | −0.687151 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.6569 | 1.12417 | ||||||||
\(794\) | −0.987807 | −0.0350559 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 39.5980 | 1.40351 | ||||||||
\(797\) | −8.38478 | −0.297004 | −0.148502 | − | 0.988912i | \(-0.547445\pi\) | ||||
−0.148502 | + | 0.988912i | \(0.547445\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.34315 | 0.224404 | ||||||||
\(800\) | −29.3848 | −1.03891 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.54416 | −0.0898373 | ||||||||
\(803\) | −27.7990 | −0.981005 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.25483 | 0.0441996 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.64466 | 0.163399 | ||||||||
\(809\) | −19.9411 | −0.701093 | −0.350546 | − | 0.936545i | \(-0.614004\pi\) | ||||
−0.350546 | + | 0.936545i | \(0.614004\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.6569 | 0.620016 | 0.310008 | − | 0.950734i | \(-0.399668\pi\) | ||||
0.310008 | + | 0.950734i | \(0.399668\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.31371 | 0.116145 | ||||||||
\(815\) | −38.6274 | −1.35306 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.0000 | 0.559769 | ||||||||
\(818\) | −8.87006 | −0.310134 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −38.9706 | −1.36091 | ||||||||
\(821\) | 10.6863 | 0.372954 | 0.186477 | − | 0.982459i | \(-0.440293\pi\) | ||||
0.186477 | + | 0.982459i | \(0.440293\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.97056 | 0.312694 | 0.156347 | − | 0.987702i | \(-0.450028\pi\) | ||||
0.156347 | + | 0.987702i | \(0.450028\pi\) | |||||||
\(824\) | −7.11270 | −0.247783 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.6569 | −1.65719 | −0.828596 | − | 0.559848i | \(-0.810860\pi\) | ||||
−0.828596 | + | 0.559848i | \(0.810860\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.727922 | 0.0252818 | 0.0126409 | − | 0.999920i | \(-0.495976\pi\) | ||||
0.0126409 | + | 0.999920i | \(0.495976\pi\) | |||||||
\(830\) | −10.3431 | −0.359016 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 10.7868 | 0.373965 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −67.5980 | −2.33932 | ||||||||
\(836\) | −10.3431 | −0.357725 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.7401 | −0.474644 | ||||||||
\(839\) | 50.8284 | 1.75479 | 0.877396 | − | 0.479767i | \(-0.159279\pi\) | ||||
0.877396 | + | 0.479767i | \(0.159279\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.6274 | 0.607842 | ||||||||
\(842\) | −6.88730 | −0.237352 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −23.7157 | −0.816329 | ||||||||
\(845\) | −21.5563 | −0.741561 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.18377 | 0.212101 | ||||||||
\(851\) | −30.6274 | −1.04989 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.4975 | 1.69476 | 0.847381 | − | 0.530986i | \(-0.178178\pi\) | ||||
0.847381 | + | 0.530986i | \(0.178178\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.544156 | 0.0185989 | ||||||||
\(857\) | 15.4142 | 0.526540 | 0.263270 | − | 0.964722i | \(-0.415199\pi\) | ||||
0.263270 | + | 0.964722i | \(0.415199\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −57.4558 | −1.96037 | −0.980184 | − | 0.198089i | \(-0.936527\pi\) | ||||
−0.980184 | + | 0.198089i | \(0.936527\pi\) | |||||||
\(860\) | −35.3137 | −1.20419 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.1716 | −0.380505 | ||||||||
\(863\) | −17.3137 | −0.589365 | −0.294683 | − | 0.955595i | \(-0.595214\pi\) | ||||
−0.294683 | + | 0.955595i | \(0.595214\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 71.9411 | 2.44607 | ||||||||
\(866\) | −8.38478 | −0.284926 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27.3137 | 0.926554 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.6274 | 0.495631 | ||||||||
\(872\) | −8.97056 | −0.303782 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.97056 | −0.303434 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.3137 | −0.382037 | −0.191018 | − | 0.981586i | \(-0.561179\pi\) | ||||
−0.191018 | + | 0.981586i | \(0.561179\pi\) | |||||||
\(878\) | 5.25483 | 0.177342 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 20.4853 | 0.690559 | ||||||||
\(881\) | 21.7574 | 0.733024 | 0.366512 | − | 0.930413i | \(-0.380552\pi\) | ||||
0.366512 | + | 0.930413i | \(0.380552\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.68629 | −0.157706 | −0.0788531 | − | 0.996886i | \(-0.525126\pi\) | ||||
−0.0788531 | + | 0.996886i | \(0.525126\pi\) | |||||||
\(884\) | −10.6030 | −0.356619 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.4853 | 0.486643 | ||||||||
\(887\) | −2.82843 | −0.0949693 | −0.0474846 | − | 0.998872i | \(-0.515121\pi\) | ||||
−0.0474846 | + | 0.998872i | \(0.515121\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 20.1421 | 0.675166 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 45.6569 | 1.52870 | ||||||||
\(893\) | −8.00000 | −0.267710 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 67.1127 | 2.24333 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.20101 | −0.0734487 | ||||||||
\(899\) | 8.00000 | 0.266815 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.48528 | −0.149426 | ||||||||
\(902\) | −5.17157 | −0.172195 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.42641 | 0.280258 | ||||||||
\(905\) | 8.82843 | 0.293467 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.0000 | −0.531271 | −0.265636 | − | 0.964073i | \(-0.585582\pi\) | ||||
−0.265636 | + | 0.964073i | \(0.585582\pi\) | |||||||
\(908\) | −43.5147 | −1.44409 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.02944 | 0.0341068 | 0.0170534 | − | 0.999855i | \(-0.494571\pi\) | ||||
0.0170534 | + | 0.999855i | \(0.494571\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.6274 | 0.484097 | ||||||||
\(914\) | 7.45584 | 0.246617 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.443651 | −0.0146586 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.28427 | −0.273273 | −0.136636 | − | 0.990621i | \(-0.543629\pi\) | ||||
−0.136636 | + | 0.990621i | \(0.543629\pi\) | |||||||
\(920\) | 41.4558 | 1.36676 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.87006 | 0.226253 | ||||||||
\(923\) | 24.0833 | 0.792710 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −26.6274 | −0.875504 | ||||||||
\(926\) | 11.0294 | 0.362450 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −30.1421 | −0.989464 | ||||||||
\(929\) | −39.2132 | −1.28654 | −0.643272 | − | 0.765638i | \(-0.722423\pi\) | ||||
−0.643272 | + | 0.765638i | \(0.722423\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −11.2304 | −0.367866 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.0832611 | −0.00272439 | ||||||||
\(935\) | −15.3137 | −0.500812 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.5858 | −0.999194 | −0.499597 | − | 0.866258i | \(-0.666519\pi\) | ||||
−0.499597 | + | 0.866258i | \(0.666519\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 17.6569 | 0.575903 | ||||||||
\(941\) | 35.2132 | 1.14792 | 0.573959 | − | 0.818884i | \(-0.305407\pi\) | ||||
0.573959 | + | 0.818884i | \(0.305407\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 47.7990 | 1.55655 | ||||||||
\(944\) | −3.51472 | −0.114394 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.68629 | −0.152364 | ||||||||
\(947\) | −30.6863 | −0.997170 | −0.498585 | − | 0.866841i | \(-0.666147\pi\) | ||||
−0.498585 | + | 0.866841i | \(0.666147\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35.9411 | 1.16670 | ||||||||
\(950\) | −7.79899 | −0.253033 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.00000 | −0.0647864 | −0.0323932 | − | 0.999475i | \(-0.510313\pi\) | ||||
−0.0323932 | + | 0.999475i | \(0.510313\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 61.4558 | 1.98866 | ||||||||
\(956\) | −28.6274 | −0.925877 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.769553 | −0.0248631 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6274 | −0.955723 | ||||||||
\(962\) | −4.28427 | −0.138130 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −29.6985 | −0.956524 | ||||||||
\(965\) | 18.1421 | 0.584016 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.6569 | 1.08233 | 0.541166 | − | 0.840916i | \(-0.317983\pi\) | ||||
0.541166 | + | 0.840916i | \(0.317983\pi\) | |||||||
\(968\) | −11.1005 | −0.356784 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.65685 | 0.117415 | ||||||||
\(971\) | −50.6274 | −1.62471 | −0.812356 | − | 0.583162i | \(-0.801815\pi\) | ||||
−0.812356 | + | 0.583162i | \(0.801815\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −11.0294 | −0.353406 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −36.7279 | −1.17563 | ||||||||
\(977\) | 21.1716 | 0.677339 | 0.338669 | − | 0.940905i | \(-0.390023\pi\) | ||||
0.338669 | + | 0.940905i | \(0.390023\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28.4853 | −0.910394 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.08326 | 0.0664795 | ||||||||
\(983\) | −53.2548 | −1.69857 | −0.849283 | − | 0.527938i | \(-0.822965\pi\) | ||||
−0.849283 | + | 0.527938i | \(0.822965\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.82843 | −0.217572 | ||||||||
\(986\) | 6.34315 | 0.202007 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.3726 | 0.425439 | ||||||||
\(989\) | 43.3137 | 1.37730 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.9706 | −0.412024 | −0.206012 | − | 0.978550i | \(-0.566049\pi\) | ||||
−0.206012 | + | 0.978550i | \(0.566049\pi\) | |||||||
\(992\) | −5.17157 | −0.164198 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −73.9411 | −2.34409 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.3848 | −0.835614 | −0.417807 | − | 0.908536i | \(-0.637201\pi\) | ||||
−0.417807 | + | 0.908536i | \(0.637201\pi\) | |||||||
\(998\) | −1.37258 | −0.0434484 | ||||||||
\(999\) | 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 | 441.2.a.j.1.1 | 2 | ||
3.2 | odd | 2 | 147.2.a.d.1.2 | ✓ | 2 | ||
4.3 | odd | 2 | 7056.2.a.cv.1.2 | 2 | |||
7.2 | even | 3 | 441.2.e.f.361.2 | 4 | |||
7.3 | odd | 6 | 441.2.e.g.226.2 | 4 | |||
7.4 | even | 3 | 441.2.e.f.226.2 | 4 | |||
7.5 | odd | 6 | 441.2.e.g.361.2 | 4 | |||
7.6 | odd | 2 | 441.2.a.i.1.1 | 2 | |||
12.11 | even | 2 | 2352.2.a.be.1.1 | 2 | |||
15.14 | odd | 2 | 3675.2.a.bf.1.1 | 2 | |||
21.2 | odd | 6 | 147.2.e.e.67.1 | 4 | |||
21.5 | even | 6 | 147.2.e.d.67.1 | 4 | |||
21.11 | odd | 6 | 147.2.e.e.79.1 | 4 | |||
21.17 | even | 6 | 147.2.e.d.79.1 | 4 | |||
21.20 | even | 2 | 147.2.a.e.1.2 | yes | 2 | ||
24.5 | odd | 2 | 9408.2.a.ef.1.2 | 2 | |||
24.11 | even | 2 | 9408.2.a.dq.1.2 | 2 | |||
28.27 | even | 2 | 7056.2.a.cf.1.1 | 2 | |||
84.11 | even | 6 | 2352.2.q.bb.961.2 | 4 | |||
84.23 | even | 6 | 2352.2.q.bb.1537.2 | 4 | |||
84.47 | odd | 6 | 2352.2.q.bd.1537.1 | 4 | |||
84.59 | odd | 6 | 2352.2.q.bd.961.1 | 4 | |||
84.83 | odd | 2 | 2352.2.a.bc.1.2 | 2 | |||
105.104 | even | 2 | 3675.2.a.bd.1.1 | 2 | |||
168.83 | odd | 2 | 9408.2.a.dt.1.1 | 2 | |||
168.125 | even | 2 | 9408.2.a.di.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.2.a.d.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
147.2.a.e.1.2 | yes | 2 | 21.20 | even | 2 | ||
147.2.e.d.67.1 | 4 | 21.5 | even | 6 | |||
147.2.e.d.79.1 | 4 | 21.17 | even | 6 | |||
147.2.e.e.67.1 | 4 | 21.2 | odd | 6 | |||
147.2.e.e.79.1 | 4 | 21.11 | odd | 6 | |||
441.2.a.i.1.1 | 2 | 7.6 | odd | 2 | |||
441.2.a.j.1.1 | 2 | 1.1 | even | 1 | trivial | ||
441.2.e.f.226.2 | 4 | 7.4 | even | 3 | |||
441.2.e.f.361.2 | 4 | 7.2 | even | 3 | |||
441.2.e.g.226.2 | 4 | 7.3 | odd | 6 | |||
441.2.e.g.361.2 | 4 | 7.5 | odd | 6 | |||
2352.2.a.bc.1.2 | 2 | 84.83 | odd | 2 | |||
2352.2.a.be.1.1 | 2 | 12.11 | even | 2 | |||
2352.2.q.bb.961.2 | 4 | 84.11 | even | 6 | |||
2352.2.q.bb.1537.2 | 4 | 84.23 | even | 6 | |||
2352.2.q.bd.961.1 | 4 | 84.59 | odd | 6 | |||
2352.2.q.bd.1537.1 | 4 | 84.47 | odd | 6 | |||
3675.2.a.bd.1.1 | 2 | 105.104 | even | 2 | |||
3675.2.a.bf.1.1 | 2 | 15.14 | odd | 2 | |||
7056.2.a.cf.1.1 | 2 | 28.27 | even | 2 | |||
7056.2.a.cv.1.2 | 2 | 4.3 | odd | 2 | |||
9408.2.a.di.1.1 | 2 | 168.125 | even | 2 | |||
9408.2.a.dq.1.2 | 2 | 24.11 | even | 2 | |||
9408.2.a.dt.1.1 | 2 | 168.83 | odd | 2 | |||
9408.2.a.ef.1.2 | 2 | 24.5 | odd | 2 |