Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1225,2,Mod(1,1225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1225, 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("1225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1225 = 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1225.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: | \(9.78167424761\) |
Analytic rank: | \(1\) |
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 245) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | −2.41421 | −1.39385 | −0.696923 | − | 0.717146i | \(-0.745448\pi\) | ||||
−0.696923 | + | 0.717146i | \(0.745448\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.41421 | 1.39385 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.82843 | −1.75734 | −0.878668 | − | 0.477432i | \(-0.841568\pi\) | ||||
−0.878668 | + | 0.477432i | \(0.841568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.58579 | −0.439818 | −0.219909 | − | 0.975520i | \(-0.570576\pi\) | ||||
−0.219909 | + | 0.975520i | \(0.570576\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 5.24264 | 1.27153 | 0.635764 | − | 0.771884i | \(-0.280685\pi\) | ||||
0.635764 | + | 0.771884i | \(0.280685\pi\) | |||||||
\(18\) | −4.00000 | −0.942809 | ||||||||
\(19\) | 6.00000 | 1.37649 | 0.688247 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.24264 | 1.75734 | ||||||||
\(23\) | −4.58579 | −0.956203 | −0.478101 | − | 0.878305i | \(-0.658675\pi\) | ||||
−0.478101 | + | 0.878305i | \(0.658675\pi\) | |||||||
\(24\) | −6.82843 | −1.39385 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.24264 | 0.439818 | ||||||||
\(27\) | 0.414214 | 0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.65685 | 0.493365 | 0.246683 | − | 0.969096i | \(-0.420659\pi\) | ||||
0.246683 | + | 0.969096i | \(0.420659\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.75736 | 0.315631 | 0.157816 | − | 0.987469i | \(-0.449555\pi\) | ||||
0.157816 | + | 0.987469i | \(0.449555\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 14.0711 | 2.44946 | ||||||||
\(34\) | −7.41421 | −1.27153 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.24264 | 1.02628 | 0.513142 | − | 0.858304i | \(-0.328481\pi\) | ||||
0.513142 | + | 0.858304i | \(0.328481\pi\) | |||||||
\(38\) | −8.48528 | −1.37649 | ||||||||
\(39\) | 3.82843 | 0.613039 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.24264 | 0.350242 | 0.175121 | − | 0.984547i | \(-0.443968\pi\) | ||||
0.175121 | + | 0.984547i | \(0.443968\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.48528 | 0.956203 | ||||||||
\(47\) | −1.24264 | −0.181258 | −0.0906289 | − | 0.995885i | \(-0.528888\pi\) | ||||
−0.0906289 | + | 0.995885i | \(0.528888\pi\) | |||||||
\(48\) | 9.65685 | 1.39385 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.6569 | −1.77231 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.24264 | 0.582772 | 0.291386 | − | 0.956606i | \(-0.405884\pi\) | ||||
0.291386 | + | 0.956606i | \(0.405884\pi\) | |||||||
\(54\) | −0.585786 | −0.0797154 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14.4853 | −1.91862 | ||||||||
\(58\) | −3.75736 | −0.493365 | ||||||||
\(59\) | 6.24264 | 0.812723 | 0.406361 | − | 0.913712i | \(-0.366797\pi\) | ||||
0.406361 | + | 0.913712i | \(0.366797\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.82843 | 0.362143 | 0.181071 | − | 0.983470i | \(-0.442043\pi\) | ||||
0.181071 | + | 0.983470i | \(0.442043\pi\) | |||||||
\(62\) | −2.48528 | −0.315631 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −19.8995 | −2.44946 | ||||||||
\(67\) | −0.242641 | −0.0296433 | −0.0148216 | − | 0.999890i | \(-0.504718\pi\) | ||||
−0.0148216 | + | 0.999890i | \(0.504718\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.0711 | 1.33280 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.82843 | −1.04774 | −0.523871 | − | 0.851798i | \(-0.675513\pi\) | ||||
−0.523871 | + | 0.851798i | \(0.675513\pi\) | |||||||
\(72\) | 8.00000 | 0.942809 | ||||||||
\(73\) | −8.48528 | −0.993127 | −0.496564 | − | 0.868000i | \(-0.665405\pi\) | ||||
−0.496564 | + | 0.868000i | \(0.665405\pi\) | |||||||
\(74\) | −8.82843 | −1.02628 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.41421 | −0.613039 | ||||||||
\(79\) | −15.4853 | −1.74223 | −0.871115 | − | 0.491079i | \(-0.836603\pi\) | ||||
−0.871115 | + | 0.491079i | \(0.836603\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | −3.17157 | −0.350242 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.82843 | 0.304997 | ||||||||
\(87\) | −6.41421 | −0.687676 | ||||||||
\(88\) | −16.4853 | −1.75734 | ||||||||
\(89\) | −8.00000 | −0.847998 | −0.423999 | − | 0.905663i | \(-0.639374\pi\) | ||||
−0.423999 | + | 0.905663i | \(0.639374\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.24264 | −0.439941 | ||||||||
\(94\) | 1.75736 | 0.181258 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.75736 | −0.483037 | −0.241518 | − | 0.970396i | \(-0.577645\pi\) | ||||
−0.241518 | + | 0.970396i | \(0.577645\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16.4853 | −1.65683 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.4853 | −1.44134 | −0.720670 | − | 0.693279i | \(-0.756166\pi\) | ||||
−0.720670 | + | 0.693279i | \(0.756166\pi\) | |||||||
\(102\) | 17.8995 | 1.77231 | ||||||||
\(103\) | −10.7574 | −1.05995 | −0.529977 | − | 0.848012i | \(-0.677799\pi\) | ||||
−0.529977 | + | 0.848012i | \(0.677799\pi\) | |||||||
\(104\) | −4.48528 | −0.439818 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −14.4853 | −1.40035 | −0.700173 | − | 0.713974i | \(-0.746894\pi\) | ||||
−0.700173 | + | 0.713974i | \(0.746894\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.00000 | 0.478913 | 0.239457 | − | 0.970907i | \(-0.423031\pi\) | ||||
0.239457 | + | 0.970907i | \(0.423031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.0711 | −1.43048 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.07107 | −0.100758 | −0.0503788 | − | 0.998730i | \(-0.516043\pi\) | ||||
−0.0503788 | + | 0.998730i | \(0.516043\pi\) | |||||||
\(114\) | 20.4853 | 1.91862 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.48528 | −0.414664 | ||||||||
\(118\) | −8.82843 | −0.812723 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.9706 | 2.08823 | ||||||||
\(122\) | −4.00000 | −0.362143 | ||||||||
\(123\) | −5.41421 | −0.488183 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.242641 | 0.0215309 | 0.0107654 | − | 0.999942i | \(-0.496573\pi\) | ||||
0.0107654 | + | 0.999942i | \(0.496573\pi\) | |||||||
\(128\) | −11.3137 | −1.00000 | ||||||||
\(129\) | 4.82843 | 0.425119 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.75736 | 0.328282 | 0.164141 | − | 0.986437i | \(-0.447515\pi\) | ||||
0.164141 | + | 0.986437i | \(0.447515\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.343146 | 0.0296433 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14.8284 | 1.27153 | ||||||||
\(137\) | −12.0000 | −1.02523 | −0.512615 | − | 0.858619i | \(-0.671323\pi\) | ||||
−0.512615 | + | 0.858619i | \(0.671323\pi\) | |||||||
\(138\) | −15.6569 | −1.33280 | ||||||||
\(139\) | 16.2426 | 1.37768 | 0.688841 | − | 0.724912i | \(-0.258120\pi\) | ||||
0.688841 | + | 0.724912i | \(0.258120\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | 12.4853 | 1.04774 | ||||||||
\(143\) | 9.24264 | 0.772908 | ||||||||
\(144\) | −11.3137 | −0.942809 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.0000 | 0.993127 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.8284 | −1.21479 | −0.607396 | − | 0.794399i | \(-0.707786\pi\) | ||||
−0.607396 | + | 0.794399i | \(0.707786\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.48528 | 0.771901 | 0.385951 | − | 0.922519i | \(-0.373874\pi\) | ||||
0.385951 | + | 0.922519i | \(0.373874\pi\) | |||||||
\(152\) | 16.9706 | 1.37649 | ||||||||
\(153\) | 14.8284 | 1.19881 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.8284 | 1.66229 | 0.831145 | − | 0.556056i | \(-0.187686\pi\) | ||||
0.831145 | + | 0.556056i | \(0.187686\pi\) | |||||||
\(158\) | 21.8995 | 1.74223 | ||||||||
\(159\) | −10.2426 | −0.812294 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 13.4142 | 1.05392 | ||||||||
\(163\) | 1.75736 | 0.137647 | 0.0688235 | − | 0.997629i | \(-0.478075\pi\) | ||||
0.0688235 | + | 0.997629i | \(0.478075\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.24264 | −0.715217 | −0.357609 | − | 0.933872i | \(-0.616408\pi\) | ||||
−0.357609 | + | 0.933872i | \(0.616408\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4853 | −0.806560 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.9706 | 1.29777 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.24264 | −0.0944762 | −0.0472381 | − | 0.998884i | \(-0.515042\pi\) | ||||
−0.0472381 | + | 0.998884i | \(0.515042\pi\) | |||||||
\(174\) | 9.07107 | 0.687676 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 23.3137 | 1.75734 | ||||||||
\(177\) | −15.0711 | −1.13281 | ||||||||
\(178\) | 11.3137 | 0.847998 | ||||||||
\(179\) | 2.48528 | 0.185759 | 0.0928793 | − | 0.995677i | \(-0.470393\pi\) | ||||
0.0928793 | + | 0.995677i | \(0.470393\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.72792 | 0.500083 | 0.250041 | − | 0.968235i | \(-0.419556\pi\) | ||||
0.250041 | + | 0.968235i | \(0.419556\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.82843 | −0.504772 | ||||||||
\(184\) | −12.9706 | −0.956203 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | −30.5563 | −2.23450 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.9706 | −1.44502 | −0.722510 | − | 0.691361i | \(-0.757011\pi\) | ||||
−0.722510 | + | 0.691361i | \(0.757011\pi\) | |||||||
\(192\) | −19.3137 | −1.39385 | ||||||||
\(193\) | 16.0000 | 1.15171 | 0.575853 | − | 0.817554i | \(-0.304670\pi\) | ||||
0.575853 | + | 0.817554i | \(0.304670\pi\) | |||||||
\(194\) | 6.72792 | 0.483037 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.5858 | −0.754206 | −0.377103 | − | 0.926171i | \(-0.623080\pi\) | ||||
−0.377103 | + | 0.926171i | \(0.623080\pi\) | |||||||
\(198\) | 23.3137 | 1.65683 | ||||||||
\(199\) | −4.58579 | −0.325078 | −0.162539 | − | 0.986702i | \(-0.551968\pi\) | ||||
−0.162539 | + | 0.986702i | \(0.551968\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.585786 | 0.0413182 | ||||||||
\(202\) | 20.4853 | 1.44134 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.2132 | 1.05995 | ||||||||
\(207\) | −12.9706 | −0.901516 | ||||||||
\(208\) | 6.34315 | 0.439818 | ||||||||
\(209\) | −34.9706 | −2.41896 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.00000 | 0.619586 | 0.309793 | − | 0.950804i | \(-0.399740\pi\) | ||||
0.309793 | + | 0.950804i | \(0.399740\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21.3137 | 1.46039 | ||||||||
\(214\) | 20.4853 | 1.40035 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.17157 | 0.0797154 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.07107 | −0.478913 | ||||||||
\(219\) | 20.4853 | 1.38427 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.31371 | −0.559241 | ||||||||
\(222\) | 21.3137 | 1.43048 | ||||||||
\(223\) | −18.2132 | −1.21965 | −0.609823 | − | 0.792538i | \(-0.708760\pi\) | ||||
−0.609823 | + | 0.792538i | \(0.708760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.51472 | 0.100758 | ||||||||
\(227\) | 9.72792 | 0.645665 | 0.322832 | − | 0.946456i | \(-0.395365\pi\) | ||||
0.322832 | + | 0.946456i | \(0.395365\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −30.0416 | −1.98521 | −0.992603 | − | 0.121402i | \(-0.961261\pi\) | ||||
−0.992603 | + | 0.121402i | \(0.961261\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.51472 | 0.493365 | ||||||||
\(233\) | 14.8284 | 0.971443 | 0.485721 | − | 0.874114i | \(-0.338557\pi\) | ||||
0.485721 | + | 0.874114i | \(0.338557\pi\) | |||||||
\(234\) | 6.34315 | 0.414664 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 37.3848 | 2.42840 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.514719 | −0.0332944 | −0.0166472 | − | 0.999861i | \(-0.505299\pi\) | ||||
−0.0166472 | + | 0.999861i | \(0.505299\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.7279 | 1.59287 | 0.796433 | − | 0.604727i | \(-0.206718\pi\) | ||||
0.796433 | + | 0.604727i | \(0.206718\pi\) | |||||||
\(242\) | −32.4853 | −2.08823 | ||||||||
\(243\) | 21.6569 | 1.38929 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.65685 | 0.488183 | ||||||||
\(247\) | −9.51472 | −0.605407 | ||||||||
\(248\) | 4.97056 | 0.315631 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.2132 | −1.59144 | −0.795722 | − | 0.605663i | \(-0.792908\pi\) | ||||
−0.795722 | + | 0.605663i | \(0.792908\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.7279 | 1.68037 | ||||||||
\(254\) | −0.343146 | −0.0215309 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.4853 | 1.65211 | 0.826053 | − | 0.563592i | \(-0.190581\pi\) | ||||
0.826053 | + | 0.563592i | \(0.190581\pi\) | |||||||
\(258\) | −6.82843 | −0.425119 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.51472 | 0.465149 | ||||||||
\(262\) | −5.31371 | −0.328282 | ||||||||
\(263\) | −28.6274 | −1.76524 | −0.882621 | − | 0.470085i | \(-0.844223\pi\) | ||||
−0.882621 | + | 0.470085i | \(0.844223\pi\) | |||||||
\(264\) | 39.7990 | 2.44946 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.3137 | 1.18198 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.75736 | −0.472975 | −0.236487 | − | 0.971635i | \(-0.575996\pi\) | ||||
−0.236487 | + | 0.971635i | \(0.575996\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.3137 | −1.41621 | −0.708103 | − | 0.706109i | \(-0.750449\pi\) | ||||
−0.708103 | + | 0.706109i | \(0.750449\pi\) | |||||||
\(272\) | −20.9706 | −1.27153 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.9706 | 1.02523 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.2132 | 1.63508 | 0.817541 | − | 0.575870i | \(-0.195336\pi\) | ||||
0.817541 | + | 0.575870i | \(0.195336\pi\) | |||||||
\(278\) | −22.9706 | −1.37768 | ||||||||
\(279\) | 4.97056 | 0.297580 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.3137 | −1.21181 | −0.605907 | − | 0.795535i | \(-0.707190\pi\) | ||||
−0.605907 | + | 0.795535i | \(0.707190\pi\) | |||||||
\(282\) | −4.24264 | −0.252646 | ||||||||
\(283\) | 6.55635 | 0.389735 | 0.194867 | − | 0.980830i | \(-0.437572\pi\) | ||||
0.194867 | + | 0.980830i | \(0.437572\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −13.0711 | −0.772908 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.4853 | 0.616781 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.4853 | 0.673279 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.272078 | −0.0158950 | −0.00794748 | − | 0.999968i | \(-0.502530\pi\) | ||||
−0.00794748 | + | 0.999968i | \(0.502530\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 17.6569 | 1.02628 | ||||||||
\(297\) | −2.41421 | −0.140087 | ||||||||
\(298\) | 20.9706 | 1.21479 | ||||||||
\(299\) | 7.27208 | 0.420555 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −13.4142 | −0.771901 | ||||||||
\(303\) | 34.9706 | 2.00901 | ||||||||
\(304\) | −24.0000 | −1.37649 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −20.9706 | −1.19881 | ||||||||
\(307\) | −11.1005 | −0.633539 | −0.316770 | − | 0.948503i | \(-0.602598\pi\) | ||||
−0.316770 | + | 0.948503i | \(0.602598\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 25.9706 | 1.47741 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.0000 | −0.567048 | −0.283524 | − | 0.958965i | \(-0.591504\pi\) | ||||
−0.283524 | + | 0.958965i | \(0.591504\pi\) | |||||||
\(312\) | 10.8284 | 0.613039 | ||||||||
\(313\) | −24.2132 | −1.36861 | −0.684306 | − | 0.729195i | \(-0.739895\pi\) | ||||
−0.684306 | + | 0.729195i | \(0.739895\pi\) | |||||||
\(314\) | −29.4558 | −1.66229 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.6569 | 0.654714 | 0.327357 | − | 0.944901i | \(-0.393842\pi\) | ||||
0.327357 | + | 0.944901i | \(0.393842\pi\) | |||||||
\(318\) | 14.4853 | 0.812294 | ||||||||
\(319\) | −15.4853 | −0.867009 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 34.9706 | 1.95187 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 31.4558 | 1.75025 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.48528 | −0.137647 | ||||||||
\(327\) | −12.0711 | −0.667532 | ||||||||
\(328\) | 6.34315 | 0.350242 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.4558 | 1.28925 | 0.644625 | − | 0.764499i | \(-0.277014\pi\) | ||||
0.644625 | + | 0.764499i | \(0.277014\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 17.6569 | 0.967590 | ||||||||
\(334\) | 13.0711 | 0.715217 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.7574 | −0.749411 | −0.374706 | − | 0.927144i | \(-0.622256\pi\) | ||||
−0.374706 | + | 0.927144i | \(0.622256\pi\) | |||||||
\(338\) | 14.8284 | 0.806560 | ||||||||
\(339\) | 2.58579 | 0.140441 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.2426 | −0.554670 | ||||||||
\(342\) | −24.0000 | −1.29777 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.65685 | −0.304997 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.75736 | 0.0944762 | ||||||||
\(347\) | 1.07107 | 0.0574979 | 0.0287490 | − | 0.999587i | \(-0.490848\pi\) | ||||
0.0287490 | + | 0.999587i | \(0.490848\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.9706 | 1.22959 | 0.614793 | − | 0.788688i | \(-0.289240\pi\) | ||||
0.614793 | + | 0.788688i | \(0.289240\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.656854 | −0.0350603 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −36.2132 | −1.92743 | −0.963717 | − | 0.266925i | \(-0.913992\pi\) | ||||
−0.963717 | + | 0.266925i | \(0.913992\pi\) | |||||||
\(354\) | 21.3137 | 1.13281 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.51472 | −0.185759 | ||||||||
\(359\) | 11.3137 | 0.597115 | 0.298557 | − | 0.954392i | \(-0.403495\pi\) | ||||
0.298557 | + | 0.954392i | \(0.403495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | −9.51472 | −0.500083 | ||||||||
\(363\) | −55.4558 | −2.91068 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.65685 | 0.504772 | ||||||||
\(367\) | −29.8701 | −1.55920 | −0.779602 | − | 0.626275i | \(-0.784579\pi\) | ||||
−0.779602 | + | 0.626275i | \(0.784579\pi\) | |||||||
\(368\) | 18.3431 | 0.956203 | ||||||||
\(369\) | 6.34315 | 0.330211 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.485281 | −0.0251269 | −0.0125635 | − | 0.999921i | \(-0.503999\pi\) | ||||
−0.0125635 | + | 0.999921i | \(0.503999\pi\) | |||||||
\(374\) | 43.2132 | 2.23450 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.51472 | −0.181258 | ||||||||
\(377\) | −4.21320 | −0.216991 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.00000 | 0.102733 | 0.0513665 | − | 0.998680i | \(-0.483642\pi\) | ||||
0.0513665 | + | 0.998680i | \(0.483642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.585786 | −0.0300107 | ||||||||
\(382\) | 28.2426 | 1.44502 | ||||||||
\(383\) | 12.4853 | 0.637968 | 0.318984 | − | 0.947760i | \(-0.396658\pi\) | ||||
0.318984 | + | 0.947760i | \(0.396658\pi\) | |||||||
\(384\) | 27.3137 | 1.39385 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.6274 | −1.15171 | ||||||||
\(387\) | −5.65685 | −0.287554 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.1421 | −1.78178 | −0.890889 | − | 0.454222i | \(-0.849917\pi\) | ||||
−0.890889 | + | 0.454222i | \(0.849917\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.0416 | −1.21584 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.07107 | −0.457575 | ||||||||
\(394\) | 14.9706 | 0.754206 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.41421 | −0.221543 | −0.110772 | − | 0.993846i | \(-0.535332\pi\) | ||||
−0.110772 | + | 0.993846i | \(0.535332\pi\) | |||||||
\(398\) | 6.48528 | 0.325078 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.17157 | 0.308194 | 0.154097 | − | 0.988056i | \(-0.450753\pi\) | ||||
0.154097 | + | 0.988056i | \(0.450753\pi\) | |||||||
\(402\) | −0.828427 | −0.0413182 | ||||||||
\(403\) | −2.78680 | −0.138820 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −36.3848 | −1.80353 | ||||||||
\(408\) | −35.7990 | −1.77231 | ||||||||
\(409\) | −14.4853 | −0.716251 | −0.358126 | − | 0.933673i | \(-0.616584\pi\) | ||||
−0.358126 | + | 0.933673i | \(0.616584\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.9706 | 1.42901 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 18.3431 | 0.901516 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −39.2132 | −1.92028 | ||||||||
\(418\) | 49.4558 | 2.41896 | ||||||||
\(419\) | −6.72792 | −0.328681 | −0.164340 | − | 0.986404i | \(-0.552550\pi\) | ||||
−0.164340 | + | 0.986404i | \(0.552550\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0000 | −0.926003 | −0.463002 | − | 0.886357i | \(-0.653228\pi\) | ||||
−0.463002 | + | 0.886357i | \(0.653228\pi\) | |||||||
\(422\) | −12.7279 | −0.619586 | ||||||||
\(423\) | −3.51472 | −0.170891 | ||||||||
\(424\) | 12.0000 | 0.582772 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −30.1421 | −1.46039 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −22.3137 | −1.07732 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.7990 | 0.520169 | 0.260085 | − | 0.965586i | \(-0.416250\pi\) | ||||
0.260085 | + | 0.965586i | \(0.416250\pi\) | |||||||
\(432\) | −1.65685 | −0.0797154 | ||||||||
\(433\) | 22.9706 | 1.10389 | 0.551947 | − | 0.833879i | \(-0.313885\pi\) | ||||
0.551947 | + | 0.833879i | \(0.313885\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −27.5147 | −1.31621 | ||||||||
\(438\) | −28.9706 | −1.38427 | ||||||||
\(439\) | 6.38478 | 0.304729 | 0.152364 | − | 0.988324i | \(-0.451311\pi\) | ||||
0.152364 | + | 0.988324i | \(0.451311\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.7574 | 0.559241 | ||||||||
\(443\) | −20.8284 | −0.989588 | −0.494794 | − | 0.869010i | \(-0.664757\pi\) | ||||
−0.494794 | + | 0.869010i | \(0.664757\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 25.7574 | 1.21965 | ||||||||
\(447\) | 35.7990 | 1.69323 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.8284 | −1.40769 | −0.703845 | − | 0.710353i | \(-0.748535\pi\) | ||||
−0.703845 | + | 0.710353i | \(0.748535\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.0711 | −0.615493 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.8995 | −1.07591 | ||||||||
\(454\) | −13.7574 | −0.645665 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −40.9706 | −1.91862 | ||||||||
\(457\) | 20.2426 | 0.946911 | 0.473455 | − | 0.880818i | \(-0.343007\pi\) | ||||
0.473455 | + | 0.880818i | \(0.343007\pi\) | |||||||
\(458\) | 42.4853 | 1.98521 | ||||||||
\(459\) | 2.17157 | 0.101360 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.9706 | 1.72189 | 0.860945 | − | 0.508697i | \(-0.169873\pi\) | ||||
0.860945 | + | 0.508697i | \(0.169873\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.4558 | −1.36893 | −0.684465 | − | 0.729046i | \(-0.739964\pi\) | ||||
−0.684465 | + | 0.729046i | \(0.739964\pi\) | |||||||
\(464\) | −10.6274 | −0.493365 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.9706 | −0.971443 | ||||||||
\(467\) | −19.7279 | −0.912899 | −0.456450 | − | 0.889749i | \(-0.650879\pi\) | ||||
−0.456450 | + | 0.889749i | \(0.650879\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −50.2843 | −2.31698 | ||||||||
\(472\) | 17.6569 | 0.812723 | ||||||||
\(473\) | 11.6569 | 0.535983 | ||||||||
\(474\) | −52.8701 | −2.42840 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.0000 | 0.549442 | ||||||||
\(478\) | 0.727922 | 0.0332944 | ||||||||
\(479\) | 20.2426 | 0.924910 | 0.462455 | − | 0.886643i | \(-0.346969\pi\) | ||||
0.462455 | + | 0.886643i | \(0.346969\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.89949 | −0.451378 | ||||||||
\(482\) | −34.9706 | −1.59287 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −30.6274 | −1.38929 | ||||||||
\(487\) | 31.6985 | 1.43640 | 0.718198 | − | 0.695839i | \(-0.244967\pi\) | ||||
0.718198 | + | 0.695839i | \(0.244967\pi\) | |||||||
\(488\) | 8.00000 | 0.362143 | ||||||||
\(489\) | −4.24264 | −0.191859 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.2843 | 0.870287 | 0.435143 | − | 0.900361i | \(-0.356698\pi\) | ||||
0.435143 | + | 0.900361i | \(0.356698\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.9289 | 0.627328 | ||||||||
\(494\) | 13.4558 | 0.605407 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.02944 | −0.315631 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.00000 | 0.134298 | 0.0671492 | − | 0.997743i | \(-0.478610\pi\) | ||||
0.0671492 | + | 0.997743i | \(0.478610\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.3137 | 0.996903 | ||||||||
\(502\) | 35.6569 | 1.59144 | ||||||||
\(503\) | 32.7574 | 1.46058 | 0.730289 | − | 0.683138i | \(-0.239385\pi\) | ||||
0.730289 | + | 0.683138i | \(0.239385\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −37.7990 | −1.68037 | ||||||||
\(507\) | 25.3137 | 1.12422 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.2132 | 0.762962 | 0.381481 | − | 0.924377i | \(-0.375414\pi\) | ||||
0.381481 | + | 0.924377i | \(0.375414\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | 2.48528 | 0.109728 | ||||||||
\(514\) | −37.4558 | −1.65211 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.24264 | 0.318531 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.00000 | 0.131685 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.9706 | −0.831115 | −0.415558 | − | 0.909567i | \(-0.636414\pi\) | ||||
−0.415558 | + | 0.909567i | \(0.636414\pi\) | |||||||
\(522\) | −10.6274 | −0.465149 | ||||||||
\(523\) | −15.5147 | −0.678411 | −0.339206 | − | 0.940712i | \(-0.610158\pi\) | ||||
−0.339206 | + | 0.940712i | \(0.610158\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 40.4853 | 1.76524 | ||||||||
\(527\) | 9.21320 | 0.401333 | ||||||||
\(528\) | −56.2843 | −2.44946 | ||||||||
\(529\) | −1.97056 | −0.0856766 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.6569 | 0.766242 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.55635 | −0.154043 | ||||||||
\(534\) | −27.3137 | −1.18198 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.686292 | −0.0296433 | ||||||||
\(537\) | −6.00000 | −0.258919 | ||||||||
\(538\) | 10.9706 | 0.472975 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.9706 | 0.514655 | 0.257327 | − | 0.966324i | \(-0.417158\pi\) | ||||
0.257327 | + | 0.966324i | \(0.417158\pi\) | |||||||
\(542\) | 32.9706 | 1.41621 | ||||||||
\(543\) | −16.2426 | −0.697038 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.51472 | 0.321306 | 0.160653 | − | 0.987011i | \(-0.448640\pi\) | ||||
0.160653 | + | 0.987011i | \(0.448640\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.00000 | 0.341432 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.9411 | 0.679115 | ||||||||
\(552\) | 31.3137 | 1.33280 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −38.4853 | −1.63508 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −31.7990 | −1.34737 | −0.673683 | − | 0.739020i | \(-0.735289\pi\) | ||||
−0.673683 | + | 0.739020i | \(0.735289\pi\) | |||||||
\(558\) | −7.02944 | −0.297580 | ||||||||
\(559\) | 3.17157 | 0.134143 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 73.7696 | 3.11455 | ||||||||
\(562\) | 28.7279 | 1.21181 | ||||||||
\(563\) | −35.9411 | −1.51474 | −0.757369 | − | 0.652987i | \(-0.773516\pi\) | ||||
−0.757369 | + | 0.652987i | \(0.773516\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.27208 | −0.389735 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −24.9706 | −1.04774 | ||||||||
\(569\) | −2.14214 | −0.0898030 | −0.0449015 | − | 0.998991i | \(-0.514297\pi\) | ||||
−0.0449015 | + | 0.998991i | \(0.514297\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.4853 | −1.44316 | −0.721582 | − | 0.692329i | \(-0.756585\pi\) | ||||
−0.721582 | + | 0.692329i | \(0.756585\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 48.2132 | 2.01414 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 22.6274 | 0.942809 | ||||||||
\(577\) | 9.72792 | 0.404979 | 0.202489 | − | 0.979284i | \(-0.435097\pi\) | ||||
0.202489 | + | 0.979284i | \(0.435097\pi\) | |||||||
\(578\) | −14.8284 | −0.616781 | ||||||||
\(579\) | −38.6274 | −1.60530 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −16.2426 | −0.673279 | ||||||||
\(583\) | −24.7279 | −1.02413 | ||||||||
\(584\) | −24.0000 | −0.993127 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.384776 | 0.0158950 | ||||||||
\(587\) | −13.4558 | −0.555382 | −0.277691 | − | 0.960670i | \(-0.589569\pi\) | ||||
−0.277691 | + | 0.960670i | \(0.589569\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.5442 | 0.434464 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.5563 | 1.05125 | ||||||||
\(592\) | −24.9706 | −1.02628 | ||||||||
\(593\) | −10.7574 | −0.441752 | −0.220876 | − | 0.975302i | \(-0.570892\pi\) | ||||
−0.220876 | + | 0.975302i | \(0.570892\pi\) | |||||||
\(594\) | 3.41421 | 0.140087 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.0711 | 0.453109 | ||||||||
\(598\) | −10.2843 | −0.420555 | ||||||||
\(599\) | −12.1716 | −0.497317 | −0.248658 | − | 0.968591i | \(-0.579990\pi\) | ||||
−0.248658 | + | 0.968591i | \(0.579990\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.9706 | 0.936989 | 0.468494 | − | 0.883466i | \(-0.344797\pi\) | ||||
0.468494 | + | 0.883466i | \(0.344797\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.686292 | −0.0279480 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −49.4558 | −2.00901 | ||||||||
\(607\) | 24.8995 | 1.01064 | 0.505320 | − | 0.862932i | \(-0.331375\pi\) | ||||
0.505320 | + | 0.862932i | \(0.331375\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.97056 | 0.0797204 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −43.9411 | −1.77477 | −0.887383 | − | 0.461034i | \(-0.847479\pi\) | ||||
−0.887383 | + | 0.461034i | \(0.847479\pi\) | |||||||
\(614\) | 15.6985 | 0.633539 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.41421 | −0.298485 | −0.149242 | − | 0.988801i | \(-0.547684\pi\) | ||||
−0.149242 | + | 0.988801i | \(0.547684\pi\) | |||||||
\(618\) | −36.7279 | −1.47741 | ||||||||
\(619\) | 31.0711 | 1.24885 | 0.624426 | − | 0.781084i | \(-0.285333\pi\) | ||||
0.624426 | + | 0.781084i | \(0.285333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.89949 | −0.0762241 | ||||||||
\(622\) | 14.1421 | 0.567048 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −15.3137 | −0.613039 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 34.2426 | 1.36861 | ||||||||
\(627\) | 84.4264 | 3.37167 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 32.7279 | 1.30495 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.45584 | 0.336622 | 0.168311 | − | 0.985734i | \(-0.446169\pi\) | ||||
0.168311 | + | 0.985734i | \(0.446169\pi\) | |||||||
\(632\) | −43.7990 | −1.74223 | ||||||||
\(633\) | −21.7279 | −0.863607 | ||||||||
\(634\) | −16.4853 | −0.654714 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 21.8995 | 0.867009 | ||||||||
\(639\) | −24.9706 | −0.987820 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.686292 | −0.0271069 | −0.0135534 | − | 0.999908i | \(-0.504314\pi\) | ||||
−0.0135534 | + | 0.999908i | \(0.504314\pi\) | |||||||
\(642\) | −49.4558 | −1.95187 | ||||||||
\(643\) | −27.7279 | −1.09348 | −0.546741 | − | 0.837302i | \(-0.684132\pi\) | ||||
−0.546741 | + | 0.837302i | \(0.684132\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −44.4853 | −1.75025 | ||||||||
\(647\) | 28.4853 | 1.11987 | 0.559936 | − | 0.828536i | \(-0.310826\pi\) | ||||
0.559936 | + | 0.828536i | \(0.310826\pi\) | |||||||
\(648\) | −26.8284 | −1.05392 | ||||||||
\(649\) | −36.3848 | −1.42823 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.02944 | −0.0402850 | −0.0201425 | − | 0.999797i | \(-0.506412\pi\) | ||||
−0.0201425 | + | 0.999797i | \(0.506412\pi\) | |||||||
\(654\) | 17.0711 | 0.667532 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.97056 | −0.350242 | ||||||||
\(657\) | −24.0000 | −0.936329 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.9706 | −0.544216 | −0.272108 | − | 0.962267i | \(-0.587721\pi\) | ||||
−0.272108 | + | 0.962267i | \(0.587721\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.4558 | −1.45686 | −0.728432 | − | 0.685118i | \(-0.759750\pi\) | ||||
−0.728432 | + | 0.685118i | \(0.759750\pi\) | |||||||
\(662\) | −33.1716 | −1.28925 | ||||||||
\(663\) | 20.0711 | 0.779496 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −24.9706 | −0.967590 | ||||||||
\(667\) | −12.1838 | −0.471757 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 43.9706 | 1.70000 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.4853 | −0.636407 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.4853 | −0.789650 | −0.394825 | − | 0.918756i | \(-0.629195\pi\) | ||||
−0.394825 | + | 0.918756i | \(0.629195\pi\) | |||||||
\(674\) | 19.4558 | 0.749411 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.78680 | −0.0686722 | −0.0343361 | − | 0.999410i | \(-0.510932\pi\) | ||||
−0.0343361 | + | 0.999410i | \(0.510932\pi\) | |||||||
\(678\) | −3.65685 | −0.140441 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.4853 | −0.899958 | ||||||||
\(682\) | 14.4853 | 0.554670 | ||||||||
\(683\) | 7.79899 | 0.298420 | 0.149210 | − | 0.988806i | \(-0.452327\pi\) | ||||
0.149210 | + | 0.988806i | \(0.452327\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 72.5269 | 2.76707 | ||||||||
\(688\) | 8.00000 | 0.304997 | ||||||||
\(689\) | −6.72792 | −0.256313 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.17157 | 0.348903 | 0.174452 | − | 0.984666i | \(-0.444185\pi\) | ||||
0.174452 | + | 0.984666i | \(0.444185\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.51472 | −0.0574979 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −18.1421 | −0.687676 | ||||||||
\(697\) | 11.7574 | 0.445342 | ||||||||
\(698\) | −32.4853 | −1.22959 | ||||||||
\(699\) | −35.7990 | −1.35404 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.45584 | −0.168295 | −0.0841475 | − | 0.996453i | \(-0.526817\pi\) | ||||
−0.0841475 | + | 0.996453i | \(0.526817\pi\) | |||||||
\(702\) | 0.928932 | 0.0350603 | ||||||||
\(703\) | 37.4558 | 1.41267 | ||||||||
\(704\) | −46.6274 | −1.75734 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 51.2132 | 1.92743 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.0000 | 0.638448 | 0.319224 | − | 0.947679i | \(-0.396578\pi\) | ||||
0.319224 | + | 0.947679i | \(0.396578\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −43.7990 | −1.64259 | ||||||||
\(712\) | −22.6274 | −0.847998 | ||||||||
\(713\) | −8.05887 | −0.301807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.24264 | 0.0464073 | ||||||||
\(718\) | −16.0000 | −0.597115 | ||||||||
\(719\) | 17.2132 | 0.641944 | 0.320972 | − | 0.947089i | \(-0.395990\pi\) | ||||
0.320972 | + | 0.947089i | \(0.395990\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −24.0416 | −0.894737 | ||||||||
\(723\) | −59.6985 | −2.22021 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 78.4264 | 2.91068 | ||||||||
\(727\) | 29.3137 | 1.08719 | 0.543593 | − | 0.839349i | \(-0.317064\pi\) | ||||
0.543593 | + | 0.839349i | \(0.317064\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.4853 | −0.387812 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.6985 | 1.65098 | 0.825488 | − | 0.564420i | \(-0.190900\pi\) | ||||
0.825488 | + | 0.564420i | \(0.190900\pi\) | |||||||
\(734\) | 42.2426 | 1.55920 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.41421 | 0.0520932 | ||||||||
\(738\) | −8.97056 | −0.330211 | ||||||||
\(739\) | −3.97056 | −0.146060 | −0.0730298 | − | 0.997330i | \(-0.523267\pi\) | ||||
−0.0730298 | + | 0.997330i | \(0.523267\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.9706 | 0.843845 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.7279 | −1.34742 | −0.673708 | − | 0.738997i | \(-0.735300\pi\) | ||||
−0.673708 | + | 0.738997i | \(0.735300\pi\) | |||||||
\(744\) | −12.0000 | −0.439941 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.686292 | 0.0251269 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5147 | 0.456669 | 0.228334 | − | 0.973583i | \(-0.426672\pi\) | ||||
0.228334 | + | 0.973583i | \(0.426672\pi\) | |||||||
\(752\) | 4.97056 | 0.181258 | ||||||||
\(753\) | 60.8701 | 2.21823 | ||||||||
\(754\) | 5.95837 | 0.216991 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.4853 | 0.599168 | 0.299584 | − | 0.954070i | \(-0.403152\pi\) | ||||
0.299584 | + | 0.954070i | \(0.403152\pi\) | |||||||
\(758\) | −2.82843 | −0.102733 | ||||||||
\(759\) | −64.5269 | −2.34218 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.7279 | 0.461387 | 0.230693 | − | 0.973026i | \(-0.425901\pi\) | ||||
0.230693 | + | 0.973026i | \(0.425901\pi\) | |||||||
\(762\) | 0.828427 | 0.0300107 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.6569 | −0.637968 | ||||||||
\(767\) | −9.89949 | −0.357450 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.17157 | −0.114370 | −0.0571849 | − | 0.998364i | \(-0.518212\pi\) | ||||
−0.0571849 | + | 0.998364i | \(0.518212\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −63.9411 | −2.30278 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.2132 | −1.30250 | −0.651249 | − | 0.758864i | \(-0.725755\pi\) | ||||
−0.651249 | + | 0.758864i | \(0.725755\pi\) | |||||||
\(774\) | 8.00000 | 0.287554 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13.4558 | −0.483037 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 49.6985 | 1.78178 | ||||||||
\(779\) | 13.4558 | 0.482106 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 51.4558 | 1.84123 | ||||||||
\(782\) | 34.0000 | 1.21584 | ||||||||
\(783\) | 1.10051 | 0.0393288 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12.8284 | 0.457575 | ||||||||
\(787\) | −45.7279 | −1.63002 | −0.815012 | − | 0.579444i | \(-0.803270\pi\) | ||||
−0.815012 | + | 0.579444i | \(0.803270\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 69.1127 | 2.46048 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −46.6274 | −1.65683 | ||||||||
\(793\) | −4.48528 | −0.159277 | ||||||||
\(794\) | 6.24264 | 0.221543 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −55.1838 | −1.95471 | −0.977355 | − | 0.211608i | \(-0.932130\pi\) | ||||
−0.977355 | + | 0.211608i | \(0.932130\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.51472 | −0.230474 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.6274 | −0.799500 | ||||||||
\(802\) | −8.72792 | −0.308194 | ||||||||
\(803\) | 49.4558 | 1.74526 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.94113 | 0.138820 | ||||||||
\(807\) | 18.7279 | 0.659254 | ||||||||
\(808\) | −40.9706 | −1.44134 | ||||||||
\(809\) | 30.5980 | 1.07577 | 0.537884 | − | 0.843019i | \(-0.319224\pi\) | ||||
0.537884 | + | 0.843019i | \(0.319224\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.3553 | −0.820117 | −0.410058 | − | 0.912059i | \(-0.634492\pi\) | ||||
−0.410058 | + | 0.912059i | \(0.634492\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 56.2843 | 1.97398 | ||||||||
\(814\) | 51.4558 | 1.80353 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 50.6274 | 1.77231 | ||||||||
\(817\) | −12.0000 | −0.419827 | ||||||||
\(818\) | 20.4853 | 0.716251 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.51472 | −0.227365 | −0.113683 | − | 0.993517i | \(-0.536265\pi\) | ||||
−0.113683 | + | 0.993517i | \(0.536265\pi\) | |||||||
\(822\) | −40.9706 | −1.42901 | ||||||||
\(823\) | 8.72792 | 0.304236 | 0.152118 | − | 0.988362i | \(-0.451391\pi\) | ||||
0.152118 | + | 0.988362i | \(0.451391\pi\) | |||||||
\(824\) | −30.4264 | −1.05995 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.04163 | 0.210088 | 0.105044 | − | 0.994468i | \(-0.466502\pi\) | ||||
0.105044 | + | 0.994468i | \(0.466502\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 54.0416 | 1.87694 | 0.938472 | − | 0.345356i | \(-0.112242\pi\) | ||||
0.938472 | + | 0.345356i | \(0.112242\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −65.6985 | −2.27906 | ||||||||
\(832\) | −12.6863 | −0.439818 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 55.4558 | 1.92028 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.727922 | 0.0251607 | ||||||||
\(838\) | 9.51472 | 0.328681 | ||||||||
\(839\) | −48.7279 | −1.68227 | −0.841137 | − | 0.540822i | \(-0.818113\pi\) | ||||
−0.841137 | + | 0.540822i | \(0.818113\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.9411 | −0.756591 | ||||||||
\(842\) | 26.8701 | 0.926003 | ||||||||
\(843\) | 49.0416 | 1.68908 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.97056 | 0.170891 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −16.9706 | −0.582772 | ||||||||
\(849\) | −15.8284 | −0.543230 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.6274 | −0.981335 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.9706 | 0.786497 | 0.393249 | − | 0.919432i | \(-0.371351\pi\) | ||||
0.393249 | + | 0.919432i | \(0.371351\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −40.9706 | −1.40035 | ||||||||
\(857\) | 5.51472 | 0.188379 | 0.0941896 | − | 0.995554i | \(-0.469974\pi\) | ||||
0.0941896 | + | 0.995554i | \(0.469974\pi\) | |||||||
\(858\) | 31.5563 | 1.07732 | ||||||||
\(859\) | 48.7696 | 1.66400 | 0.831998 | − | 0.554779i | \(-0.187197\pi\) | ||||
0.831998 | + | 0.554779i | \(0.187197\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.2721 | −0.520169 | ||||||||
\(863\) | 18.3848 | 0.625825 | 0.312913 | − | 0.949782i | \(-0.398695\pi\) | ||||
0.312913 | + | 0.949782i | \(0.398695\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −32.4853 | −1.10389 | ||||||||
\(867\) | −25.3137 | −0.859699 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 90.2548 | 3.06169 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.384776 | 0.0130376 | ||||||||
\(872\) | 14.1421 | 0.478913 | ||||||||
\(873\) | −13.4558 | −0.455411 | ||||||||
\(874\) | 38.9117 | 1.31621 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.9706 | −1.58608 | −0.793042 | − | 0.609167i | \(-0.791504\pi\) | ||||
−0.793042 | + | 0.609167i | \(0.791504\pi\) | |||||||
\(878\) | −9.02944 | −0.304729 | ||||||||
\(879\) | 0.656854 | 0.0221551 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.0294 | −0.641118 | −0.320559 | − | 0.947229i | \(-0.603871\pi\) | ||||
−0.320559 | + | 0.947229i | \(0.603871\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.4853 | −1.63166 | −0.815830 | − | 0.578292i | \(-0.803719\pi\) | ||||
−0.815830 | + | 0.578292i | \(0.803719\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 29.4558 | 0.989588 | ||||||||
\(887\) | 30.9706 | 1.03989 | 0.519945 | − | 0.854200i | \(-0.325952\pi\) | ||||
0.519945 | + | 0.854200i | \(0.325952\pi\) | |||||||
\(888\) | −42.6274 | −1.43048 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 55.2843 | 1.85209 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.45584 | −0.249500 | ||||||||
\(894\) | −50.6274 | −1.69323 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.5563 | −0.586189 | ||||||||
\(898\) | 42.1838 | 1.40769 | ||||||||
\(899\) | 4.66905 | 0.155721 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.2426 | 0.741010 | ||||||||
\(902\) | 18.4853 | 0.615493 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.02944 | −0.100758 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 32.3848 | 1.07591 | ||||||||
\(907\) | −32.1838 | −1.06864 | −0.534322 | − | 0.845281i | \(-0.679433\pi\) | ||||
−0.534322 | + | 0.845281i | \(0.679433\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −40.9706 | −1.35891 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.65685 | −0.187420 | −0.0937100 | − | 0.995600i | \(-0.529873\pi\) | ||||
−0.0937100 | + | 0.995600i | \(0.529873\pi\) | |||||||
\(912\) | 57.9411 | 1.91862 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −28.6274 | −0.946911 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.07107 | −0.101360 | ||||||||
\(919\) | −38.4558 | −1.26854 | −0.634271 | − | 0.773111i | \(-0.718699\pi\) | ||||
−0.634271 | + | 0.773111i | \(0.718699\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.7990 | 0.883057 | ||||||||
\(922\) | −52.2843 | −1.72189 | ||||||||
\(923\) | 14.0000 | 0.460816 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 41.6569 | 1.36893 | ||||||||
\(927\) | −30.4264 | −0.999334 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 54.7279 | 1.79556 | 0.897782 | − | 0.440439i | \(-0.145177\pi\) | ||||
0.897782 | + | 0.440439i | \(0.145177\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.1421 | 0.790378 | ||||||||
\(934\) | 27.8995 | 0.912899 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.6863 | −0.414664 | ||||||||
\(937\) | 17.4437 | 0.569859 | 0.284930 | − | 0.958548i | \(-0.408030\pi\) | ||||
0.284930 | + | 0.958548i | \(0.408030\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 58.4558 | 1.90763 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.97056 | −0.162036 | −0.0810179 | − | 0.996713i | \(-0.525817\pi\) | ||||
−0.0810179 | + | 0.996713i | \(0.525817\pi\) | |||||||
\(942\) | 71.1127 | 2.31698 | ||||||||
\(943\) | −10.2843 | −0.334902 | ||||||||
\(944\) | −24.9706 | −0.812723 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.4853 | −0.535983 | ||||||||
\(947\) | 43.7574 | 1.42192 | 0.710962 | − | 0.703231i | \(-0.248260\pi\) | ||||
0.710962 | + | 0.703231i | \(0.248260\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.4558 | 0.436795 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −28.1421 | −0.912571 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.0122 | 0.939797 | 0.469899 | − | 0.882720i | \(-0.344290\pi\) | ||||
0.469899 | + | 0.882720i | \(0.344290\pi\) | |||||||
\(954\) | −16.9706 | −0.549442 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 37.3848 | 1.20848 | ||||||||
\(958\) | −28.6274 | −0.924910 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.9117 | −0.900377 | ||||||||
\(962\) | 14.0000 | 0.451378 | ||||||||
\(963\) | −40.9706 | −1.32026 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.4264 | −0.785500 | −0.392750 | − | 0.919645i | \(-0.628476\pi\) | ||||
−0.392750 | + | 0.919645i | \(0.628476\pi\) | |||||||
\(968\) | 64.9706 | 2.08823 | ||||||||
\(969\) | −75.9411 | −2.43958 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.7279 | −1.37120 | −0.685602 | − | 0.727976i | \(-0.740461\pi\) | ||||
−0.685602 | + | 0.727976i | \(0.740461\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −44.8284 | −1.43640 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.3137 | −0.362143 | ||||||||
\(977\) | 30.7696 | 0.984405 | 0.492203 | − | 0.870481i | \(-0.336192\pi\) | ||||
0.492203 | + | 0.870481i | \(0.336192\pi\) | |||||||
\(978\) | 6.00000 | 0.191859 | ||||||||
\(979\) | 46.6274 | 1.49022 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.1421 | 0.451524 | ||||||||
\(982\) | −27.2721 | −0.870287 | ||||||||
\(983\) | 42.2132 | 1.34639 | 0.673196 | − | 0.739464i | \(-0.264921\pi\) | ||||
0.673196 | + | 0.739464i | \(0.264921\pi\) | |||||||
\(984\) | −15.3137 | −0.488183 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −19.6985 | −0.627328 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.17157 | 0.291639 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.9411 | −1.52290 | −0.761450 | − | 0.648224i | \(-0.775512\pi\) | ||||
−0.761450 | + | 0.648224i | \(0.775512\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −56.6274 | −1.79702 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.72792 | −0.118064 | −0.0590322 | − | 0.998256i | \(-0.518801\pi\) | ||||
−0.0590322 | + | 0.998256i | \(0.518801\pi\) | |||||||
\(998\) | −4.24264 | −0.134298 | ||||||||
\(999\) | 2.58579 | 0.0818107 |
(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 | 1225.2.a.p.1.1 | 2 | ||
5.2 | odd | 4 | 1225.2.b.j.99.2 | 4 | |||
5.3 | odd | 4 | 1225.2.b.j.99.3 | 4 | |||
5.4 | even | 2 | 245.2.a.f.1.2 | yes | 2 | ||
7.6 | odd | 2 | 1225.2.a.r.1.1 | 2 | |||
15.14 | odd | 2 | 2205.2.a.t.1.1 | 2 | |||
20.19 | odd | 2 | 3920.2.a.br.1.1 | 2 | |||
35.4 | even | 6 | 245.2.e.f.226.1 | 4 | |||
35.9 | even | 6 | 245.2.e.f.116.1 | 4 | |||
35.13 | even | 4 | 1225.2.b.i.99.4 | 4 | |||
35.19 | odd | 6 | 245.2.e.g.116.1 | 4 | |||
35.24 | odd | 6 | 245.2.e.g.226.1 | 4 | |||
35.27 | even | 4 | 1225.2.b.i.99.1 | 4 | |||
35.34 | odd | 2 | 245.2.a.e.1.2 | ✓ | 2 | ||
105.104 | even | 2 | 2205.2.a.v.1.1 | 2 | |||
140.139 | even | 2 | 3920.2.a.bw.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.2.a.e.1.2 | ✓ | 2 | 35.34 | odd | 2 | ||
245.2.a.f.1.2 | yes | 2 | 5.4 | even | 2 | ||
245.2.e.f.116.1 | 4 | 35.9 | even | 6 | |||
245.2.e.f.226.1 | 4 | 35.4 | even | 6 | |||
245.2.e.g.116.1 | 4 | 35.19 | odd | 6 | |||
245.2.e.g.226.1 | 4 | 35.24 | odd | 6 | |||
1225.2.a.p.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1225.2.a.r.1.1 | 2 | 7.6 | odd | 2 | |||
1225.2.b.i.99.1 | 4 | 35.27 | even | 4 | |||
1225.2.b.i.99.4 | 4 | 35.13 | even | 4 | |||
1225.2.b.j.99.2 | 4 | 5.2 | odd | 4 | |||
1225.2.b.j.99.3 | 4 | 5.3 | odd | 4 | |||
2205.2.a.t.1.1 | 2 | 15.14 | odd | 2 | |||
2205.2.a.v.1.1 | 2 | 105.104 | even | 2 | |||
3920.2.a.br.1.1 | 2 | 20.19 | odd | 2 | |||
3920.2.a.bw.1.2 | 2 | 140.139 | even | 2 |