Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1225,2,Mod(99,1225)]
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([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1225.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1225 = 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1225.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(9.78167424761\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 245) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.3 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1225.99 |
Dual form | 1225.2.b.j.99.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | − 2.41421i | − 1.39385i | −0.717146 | − | 0.696923i | \(-0.754552\pi\) | ||||
0.717146 | − | 0.696923i | \(-0.245448\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.41421 | 1.39385 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843i | 1.00000i | ||||||||
\(9\) | −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 | ||||||||
\(13\) | − 1.58579i | − 0.439818i | −0.975520 | − | 0.219909i | \(-0.929424\pi\) | ||||
0.975520 | − | 0.219909i | \(-0.0705760\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | − 5.24264i | − 1.27153i | −0.771884 | − | 0.635764i | \(-0.780685\pi\) | ||||
0.771884 | − | 0.635764i | \(-0.219315\pi\) | |||||||
\(18\) | − 4.00000i | − 0.942809i | ||||||||
\(19\) | −6.00000 | −1.37649 | −0.688247 | − | 0.725476i | \(-0.741620\pi\) | ||||
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 8.24264i | − 1.75734i | ||||||||
\(23\) | − 4.58579i | − 0.956203i | −0.878305 | − | 0.478101i | \(-0.841325\pi\) | ||||
0.878305 | − | 0.478101i | \(-0.158675\pi\) | |||||||
\(24\) | 6.82843 | 1.39385 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.24264 | 0.439818 | ||||||||
\(27\) | − 0.414214i | − 0.0797154i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.65685 | −0.493365 | −0.246683 | − | 0.969096i | \(-0.579341\pi\) | ||||
−0.246683 | + | 0.969096i | \(0.579341\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.75736 | 0.315631 | 0.157816 | − | 0.987469i | \(-0.449555\pi\) | ||||
0.157816 | + | 0.987469i | \(0.449555\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 14.0711i | 2.44946i | ||||||||
\(34\) | 7.41421 | 1.27153 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 6.24264i | − 1.02628i | −0.858304 | − | 0.513142i | \(-0.828481\pi\) | ||||
0.858304 | − | 0.513142i | \(-0.171519\pi\) | |||||||
\(38\) | − 8.48528i | − 1.37649i | ||||||||
\(39\) | −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 | ||||||||
\(43\) | − 2.00000i | − 0.304997i | −0.988304 | − | 0.152499i | \(-0.951268\pi\) | ||||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.48528 | 0.956203 | ||||||||
\(47\) | 1.24264i | 0.181258i | 0.995885 | + | 0.0906289i | \(0.0288877\pi\) | ||||
−0.995885 | + | 0.0906289i | \(0.971112\pi\) | |||||||
\(48\) | 9.65685i | 1.39385i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.6569 | −1.77231 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.24264i | 0.582772i | 0.956606 | + | 0.291386i | \(0.0941163\pi\) | ||||
−0.956606 | + | 0.291386i | \(0.905884\pi\) | |||||||
\(54\) | 0.585786 | 0.0797154 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.4853i | 1.91862i | ||||||||
\(58\) | − 3.75736i | − 0.493365i | ||||||||
\(59\) | −6.24264 | −0.812723 | −0.406361 | − | 0.913712i | \(-0.633203\pi\) | ||||
−0.406361 | + | 0.913712i | \(0.633203\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.82843 | 0.362143 | 0.181071 | − | 0.983470i | \(-0.442043\pi\) | ||||
0.181071 | + | 0.983470i | \(0.442043\pi\) | |||||||
\(62\) | 2.48528i | 0.315631i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −19.8995 | −2.44946 | ||||||||
\(67\) | 0.242641i | 0.0296433i | 0.999890 | + | 0.0148216i | \(0.00471805\pi\) | ||||
−0.999890 | + | 0.0148216i | \(0.995282\pi\) | |||||||
\(68\) | 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 | \(0.675513\pi\) | |||||||
\(72\) | − 8.00000i | − 0.942809i | ||||||||
\(73\) | − 8.48528i | − 0.993127i | −0.868000 | − | 0.496564i | \(-0.834595\pi\) | ||||
0.868000 | − | 0.496564i | \(-0.165405\pi\) | |||||||
\(74\) | 8.82843 | 1.02628 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − 5.41421i | − 0.613039i | ||||||||
\(79\) | 15.4853 | 1.74223 | 0.871115 | − | 0.491079i | \(-0.163397\pi\) | ||||
0.871115 | + | 0.491079i | \(0.163397\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 3.17157i | 0.350242i | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.82843 | 0.304997 | ||||||||
\(87\) | 6.41421i | 0.687676i | ||||||||
\(88\) | − 16.4853i | − 1.75734i | ||||||||
\(89\) | 8.00000 | 0.847998 | 0.423999 | − | 0.905663i | \(-0.360626\pi\) | ||||
0.423999 | + | 0.905663i | \(0.360626\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 4.24264i | − 0.439941i | ||||||||
\(94\) | −1.75736 | −0.181258 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.75736i | 0.483037i | 0.970396 | + | 0.241518i | \(0.0776454\pi\) | ||||
−0.970396 | + | 0.241518i | \(0.922355\pi\) | |||||||
\(98\) | 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 | \(0.756166\pi\) | |||||||
\(102\) | − 17.8995i | − 1.77231i | ||||||||
\(103\) | − 10.7574i | − 1.05995i | −0.848012 | − | 0.529977i | \(-0.822201\pi\) | ||||
0.848012 | − | 0.529977i | \(-0.177799\pi\) | |||||||
\(104\) | 4.48528 | 0.439818 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 14.4853i | 1.40035i | 0.713974 | + | 0.700173i | \(0.246894\pi\) | ||||
−0.713974 | + | 0.700173i | \(0.753106\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.00000 | −0.478913 | −0.239457 | − | 0.970907i | \(-0.576969\pi\) | ||||
−0.239457 | + | 0.970907i | \(0.576969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.0711 | −1.43048 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 1.07107i | − 0.100758i | −0.998730 | − | 0.0503788i | \(-0.983957\pi\) | ||||
0.998730 | − | 0.0503788i | \(-0.0160429\pi\) | |||||||
\(114\) | −20.4853 | −1.91862 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.48528i | 0.414664i | ||||||||
\(118\) | − 8.82843i | − 0.812723i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.9706 | 2.08823 | ||||||||
\(122\) | 4.00000i | 0.362143i | ||||||||
\(123\) | − 5.41421i | − 0.488183i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 0.242641i | − 0.0215309i | −0.999942 | − | 0.0107654i | \(-0.996573\pi\) | ||||
0.999942 | − | 0.0107654i | \(-0.00342681\pi\) | |||||||
\(128\) | − 11.3137i | − 1.00000i | ||||||||
\(129\) | −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 | ||||||||
\(137\) | 12.0000i | 1.02523i | 0.858619 | + | 0.512615i | \(0.171323\pi\) | ||||
−0.858619 | + | 0.512615i | \(0.828677\pi\) | |||||||
\(138\) | − 15.6569i | − 1.33280i | ||||||||
\(139\) | −16.2426 | −1.37768 | −0.688841 | − | 0.724912i | \(-0.741880\pi\) | ||||
−0.688841 | + | 0.724912i | \(0.741880\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | − 12.4853i | − 1.04774i | ||||||||
\(143\) | 9.24264i | 0.772908i | ||||||||
\(144\) | 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 | \(-0.292214\pi\) | ||||
0.607396 | + | 0.794399i | \(0.292214\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.48528 | 0.771901 | 0.385951 | − | 0.922519i | \(-0.373874\pi\) | ||||
0.385951 | + | 0.922519i | \(0.373874\pi\) | |||||||
\(152\) | − 16.9706i | − 1.37649i | ||||||||
\(153\) | 14.8284i | 1.19881i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 20.8284i | − 1.66229i | −0.556056 | − | 0.831145i | \(-0.687686\pi\) | ||||
0.556056 | − | 0.831145i | \(-0.312314\pi\) | |||||||
\(158\) | 21.8995i | 1.74223i | ||||||||
\(159\) | 10.2426 | 0.812294 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − 13.4142i | − 1.05392i | ||||||||
\(163\) | 1.75736i | 0.137647i | 0.997629 | + | 0.0688235i | \(0.0219245\pi\) | ||||
−0.997629 | + | 0.0688235i | \(0.978075\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.24264i | 0.715217i | 0.933872 | + | 0.357609i | \(0.116408\pi\) | ||||
−0.933872 | + | 0.357609i | \(0.883592\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4853 | 0.806560 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.9706 | 1.29777 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.24264i | − 0.0944762i | −0.998884 | − | 0.0472381i | \(-0.984958\pi\) | ||||
0.998884 | − | 0.0472381i | \(-0.0150420\pi\) | |||||||
\(174\) | −9.07107 | −0.687676 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 23.3137 | 1.75734 | ||||||||
\(177\) | 15.0711i | 1.13281i | ||||||||
\(178\) | 11.3137i | 0.847998i | ||||||||
\(179\) | −2.48528 | −0.185759 | −0.0928793 | − | 0.995677i | \(-0.529607\pi\) | ||||
−0.0928793 | + | 0.995677i | \(0.529607\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.72792 | 0.500083 | 0.250041 | − | 0.968235i | \(-0.419556\pi\) | ||||
0.250041 | + | 0.968235i | \(0.419556\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 6.82843i | − 0.504772i | ||||||||
\(184\) | 12.9706 | 0.956203 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | 30.5563i | 2.23450i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.9706 | −1.44502 | −0.722510 | − | 0.691361i | \(-0.757011\pi\) | ||||
−0.722510 | + | 0.691361i | \(0.757011\pi\) | |||||||
\(192\) | 19.3137i | 1.39385i | ||||||||
\(193\) | 16.0000i | 1.15171i | 0.817554 | + | 0.575853i | \(0.195330\pi\) | ||||
−0.817554 | + | 0.575853i | \(0.804670\pi\) | |||||||
\(194\) | −6.72792 | −0.483037 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.5858i | 0.754206i | 0.926171 | + | 0.377103i | \(0.123080\pi\) | ||||
−0.926171 | + | 0.377103i | \(0.876920\pi\) | |||||||
\(198\) | 23.3137i | 1.65683i | ||||||||
\(199\) | 4.58579 | 0.325078 | 0.162539 | − | 0.986702i | \(-0.448032\pi\) | ||||
0.162539 | + | 0.986702i | \(0.448032\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.585786 | 0.0413182 | ||||||||
\(202\) | − 20.4853i | − 1.44134i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.2132 | 1.05995 | ||||||||
\(207\) | 12.9706i | 0.901516i | ||||||||
\(208\) | 6.34315i | 0.439818i | ||||||||
\(209\) | 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 | ||||||||
\(213\) | 21.3137i | 1.46039i | ||||||||
\(214\) | −20.4853 | −1.40035 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.17157 | 0.0797154 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 7.07107i | − 0.478913i | ||||||||
\(219\) | −20.4853 | −1.38427 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.31371 | −0.559241 | ||||||||
\(222\) | − 21.3137i | − 1.43048i | ||||||||
\(223\) | − 18.2132i | − 1.21965i | −0.792538 | − | 0.609823i | \(-0.791240\pi\) | ||||
0.792538 | − | 0.609823i | \(-0.208760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.51472 | 0.100758 | ||||||||
\(227\) | − 9.72792i | − 0.645665i | −0.946456 | − | 0.322832i | \(-0.895365\pi\) | ||||
0.946456 | − | 0.322832i | \(-0.104635\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 30.0416 | 1.98521 | 0.992603 | − | 0.121402i | \(-0.0387390\pi\) | ||||
0.992603 | + | 0.121402i | \(0.0387390\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 7.51472i | − 0.493365i | ||||||||
\(233\) | 14.8284i | 0.971443i | 0.874114 | + | 0.485721i | \(0.161443\pi\) | ||||
−0.874114 | + | 0.485721i | \(0.838557\pi\) | |||||||
\(234\) | −6.34315 | −0.414664 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 37.3848i | − 2.42840i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.514719 | 0.0332944 | 0.0166472 | − | 0.999861i | \(-0.494701\pi\) | ||||
0.0166472 | + | 0.999861i | \(0.494701\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.7279 | 1.59287 | 0.796433 | − | 0.604727i | \(-0.206718\pi\) | ||||
0.796433 | + | 0.604727i | \(0.206718\pi\) | |||||||
\(242\) | 32.4853i | 2.08823i | ||||||||
\(243\) | 21.6569i | 1.38929i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.65685 | 0.488183 | ||||||||
\(247\) | 9.51472i | 0.605407i | ||||||||
\(248\) | 4.97056i | 0.315631i | ||||||||
\(249\) | 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 | ||||||||
\(253\) | 26.7279i | 1.68037i | ||||||||
\(254\) | 0.343146 | 0.0215309 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 26.4853i | − 1.65211i | −0.563592 | − | 0.826053i | \(-0.690581\pi\) | ||||
0.563592 | − | 0.826053i | \(-0.309419\pi\) | |||||||
\(258\) | − 6.82843i | − 0.425119i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.51472 | 0.465149 | ||||||||
\(262\) | 5.31371i | 0.328282i | ||||||||
\(263\) | − 28.6274i | − 1.76524i | −0.470085 | − | 0.882621i | \(-0.655777\pi\) | ||||
0.470085 | − | 0.882621i | \(-0.344223\pi\) | |||||||
\(264\) | −39.7990 | −2.44946 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 19.3137i | − 1.18198i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.75736 | 0.472975 | 0.236487 | − | 0.971635i | \(-0.424004\pi\) | ||||
0.236487 | + | 0.971635i | \(0.424004\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.3137 | −1.41621 | −0.708103 | − | 0.706109i | \(-0.750449\pi\) | ||||
−0.708103 | + | 0.706109i | \(0.750449\pi\) | |||||||
\(272\) | 20.9706i | 1.27153i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.9706 | −1.02523 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 27.2132i | − 1.63508i | −0.575870 | − | 0.817541i | \(-0.695336\pi\) | ||||
0.575870 | − | 0.817541i | \(-0.304664\pi\) | |||||||
\(278\) | − 22.9706i | − 1.37768i | ||||||||
\(279\) | −4.97056 | −0.297580 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.3137 | −1.21181 | −0.605907 | − | 0.795535i | \(-0.707190\pi\) | ||||
−0.605907 | + | 0.795535i | \(0.707190\pi\) | |||||||
\(282\) | 4.24264i | 0.252646i | ||||||||
\(283\) | 6.55635i | 0.389735i | 0.980830 | + | 0.194867i | \(0.0624276\pi\) | ||||
−0.980830 | + | 0.194867i | \(0.937572\pi\) | |||||||
\(284\) | 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 | ||||||||
\(293\) | − 0.272078i | − 0.0158950i | −0.999968 | − | 0.00794748i | \(-0.997470\pi\) | ||||
0.999968 | − | 0.00794748i | \(-0.00252979\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 17.6569 | 1.02628 | ||||||||
\(297\) | 2.41421i | 0.140087i | ||||||||
\(298\) | 20.9706i | 1.21479i | ||||||||
\(299\) | −7.27208 | −0.420555 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 13.4142i | 0.771901i | ||||||||
\(303\) | 34.9706i | 2.00901i | ||||||||
\(304\) | 24.0000 | 1.37649 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −20.9706 | −1.19881 | ||||||||
\(307\) | 11.1005i | 0.633539i | 0.948503 | + | 0.316770i | \(0.102598\pi\) | ||||
−0.948503 | + | 0.316770i | \(0.897402\pi\) | |||||||
\(308\) | 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 | \(0.591504\pi\) | |||||||
\(312\) | − 10.8284i | − 0.613039i | ||||||||
\(313\) | − 24.2132i | − 1.36861i | −0.729195 | − | 0.684306i | \(-0.760105\pi\) | ||||
0.729195 | − | 0.684306i | \(-0.239895\pi\) | |||||||
\(314\) | 29.4558 | 1.66229 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 11.6569i | − 0.654714i | −0.944901 | − | 0.327357i | \(-0.893842\pi\) | ||||
0.944901 | − | 0.327357i | \(-0.106158\pi\) | |||||||
\(318\) | 14.4853i | 0.812294i | ||||||||
\(319\) | 15.4853 | 0.867009 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 34.9706 | 1.95187 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 31.4558i | 1.75025i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.48528 | −0.137647 | ||||||||
\(327\) | 12.0711i | 0.667532i | ||||||||
\(328\) | 6.34315i | 0.350242i | ||||||||
\(329\) | 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 | ||||||||
\(333\) | 17.6569i | 0.967590i | ||||||||
\(334\) | −13.0711 | −0.715217 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.7574i | 0.749411i | 0.927144 | + | 0.374706i | \(0.122256\pi\) | ||||
−0.927144 | + | 0.374706i | \(0.877744\pi\) | |||||||
\(338\) | 14.8284i | 0.806560i | ||||||||
\(339\) | −2.58579 | −0.140441 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.2426 | −0.554670 | ||||||||
\(342\) | 24.0000i | 1.29777i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.65685 | 0.304997 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.75736 | 0.0944762 | ||||||||
\(347\) | − 1.07107i | − 0.0574979i | −0.999587 | − | 0.0287490i | \(-0.990848\pi\) | ||||
0.999587 | − | 0.0287490i | \(-0.00915234\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.9706 | −1.22959 | −0.614793 | − | 0.788688i | \(-0.710760\pi\) | ||||
−0.614793 | + | 0.788688i | \(0.710760\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.656854 | −0.0350603 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 36.2132i | − 1.92743i | −0.266925 | − | 0.963717i | \(-0.586008\pi\) | ||||
0.266925 | − | 0.963717i | \(-0.413992\pi\) | |||||||
\(354\) | −21.3137 | −1.13281 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 3.51472i | − 0.185759i | ||||||||
\(359\) | −11.3137 | −0.597115 | −0.298557 | − | 0.954392i | \(-0.596505\pi\) | ||||
−0.298557 | + | 0.954392i | \(0.596505\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 9.51472i | 0.500083i | ||||||||
\(363\) | − 55.4558i | − 2.91068i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.65685 | 0.504772 | ||||||||
\(367\) | 29.8701i | 1.55920i | 0.626275 | + | 0.779602i | \(0.284579\pi\) | ||||
−0.626275 | + | 0.779602i | \(0.715421\pi\) | |||||||
\(368\) | 18.3431i | 0.956203i | ||||||||
\(369\) | −6.34315 | −0.330211 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 0.485281i | − 0.0251269i | −0.999921 | − | 0.0125635i | \(-0.996001\pi\) | ||||
0.999921 | − | 0.0125635i | \(-0.00399918\pi\) | |||||||
\(374\) | −43.2132 | −2.23450 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.51472 | −0.181258 | ||||||||
\(377\) | 4.21320i | 0.216991i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.00000 | −0.102733 | −0.0513665 | − | 0.998680i | \(-0.516358\pi\) | ||||
−0.0513665 | + | 0.998680i | \(0.516358\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.585786 | −0.0300107 | ||||||||
\(382\) | − 28.2426i | − 1.44502i | ||||||||
\(383\) | 12.4853i | 0.637968i | 0.947760 | + | 0.318984i | \(0.103342\pi\) | ||||
−0.947760 | + | 0.318984i | \(0.896658\pi\) | |||||||
\(384\) | −27.3137 | −1.39385 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.6274 | −1.15171 | ||||||||
\(387\) | 5.65685i | 0.287554i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.1421 | 1.78178 | 0.890889 | − | 0.454222i | \(-0.150083\pi\) | ||||
0.890889 | + | 0.454222i | \(0.150083\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.0416 | −1.21584 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 9.07107i | − 0.457575i | ||||||||
\(394\) | −14.9706 | −0.754206 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.41421i | 0.221543i | 0.993846 | + | 0.110772i | \(0.0353322\pi\) | ||||
−0.993846 | + | 0.110772i | \(0.964668\pi\) | |||||||
\(398\) | 6.48528i | 0.325078i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.17157 | 0.308194 | 0.154097 | − | 0.988056i | \(-0.450753\pi\) | ||||
0.154097 | + | 0.988056i | \(0.450753\pi\) | |||||||
\(402\) | 0.828427i | 0.0413182i | ||||||||
\(403\) | − 2.78680i | − 0.138820i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 36.3848i | 1.80353i | ||||||||
\(408\) | − 35.7990i | − 1.77231i | ||||||||
\(409\) | 14.4853 | 0.716251 | 0.358126 | − | 0.933673i | \(-0.383416\pi\) | ||||
0.358126 | + | 0.933673i | \(0.383416\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.9706 | 1.42901 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −18.3431 | −0.901516 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 39.2132i | 1.92028i | ||||||||
\(418\) | 49.4558i | 2.41896i | ||||||||
\(419\) | 6.72792 | 0.328681 | 0.164340 | − | 0.986404i | \(-0.447450\pi\) | ||||
0.164340 | + | 0.986404i | \(0.447450\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0000 | −0.926003 | −0.463002 | − | 0.886357i | \(-0.653228\pi\) | ||||
−0.463002 | + | 0.886357i | \(0.653228\pi\) | |||||||
\(422\) | 12.7279i | 0.619586i | ||||||||
\(423\) | − 3.51472i | − 0.170891i | ||||||||
\(424\) | −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 | \(0.416250\pi\) | |||||||
\(432\) | 1.65685i | 0.0797154i | ||||||||
\(433\) | 22.9706i | 1.10389i | 0.833879 | + | 0.551947i | \(0.186115\pi\) | ||||
−0.833879 | + | 0.551947i | \(0.813885\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27.5147i | 1.31621i | ||||||||
\(438\) | − 28.9706i | − 1.38427i | ||||||||
\(439\) | −6.38478 | −0.304729 | −0.152364 | − | 0.988324i | \(-0.548689\pi\) | ||||
−0.152364 | + | 0.988324i | \(0.548689\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 11.7574i | − 0.559241i | ||||||||
\(443\) | − 20.8284i | − 0.989588i | −0.869010 | − | 0.494794i | \(-0.835243\pi\) | ||||
0.869010 | − | 0.494794i | \(-0.164757\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 25.7574 | 1.21965 | ||||||||
\(447\) | − 35.7990i | − 1.69323i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.8284 | 1.40769 | 0.703845 | − | 0.710353i | \(-0.251465\pi\) | ||||
0.703845 | + | 0.710353i | \(0.251465\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.0711 | −0.615493 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 22.8995i | − 1.07591i | ||||||||
\(454\) | 13.7574 | 0.645665 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −40.9706 | −1.91862 | ||||||||
\(457\) | − 20.2426i | − 0.946911i | −0.880818 | − | 0.473455i | \(-0.843007\pi\) | ||||
0.880818 | − | 0.473455i | \(-0.156993\pi\) | |||||||
\(458\) | 42.4853i | 1.98521i | ||||||||
\(459\) | −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 | ||||||||
\(463\) | − 29.4558i | − 1.36893i | −0.729046 | − | 0.684465i | \(-0.760036\pi\) | ||||
0.729046 | − | 0.684465i | \(-0.239964\pi\) | |||||||
\(464\) | 10.6274 | 0.493365 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.9706 | −0.971443 | ||||||||
\(467\) | 19.7279i | 0.912899i | 0.889749 | + | 0.456450i | \(0.150879\pi\) | ||||
−0.889749 | + | 0.456450i | \(0.849121\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −50.2843 | −2.31698 | ||||||||
\(472\) | − 17.6569i | − 0.812723i | ||||||||
\(473\) | 11.6569i | 0.535983i | ||||||||
\(474\) | 52.8701 | 2.42840 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 12.0000i | − 0.549442i | ||||||||
\(478\) | 0.727922i | 0.0332944i | ||||||||
\(479\) | −20.2426 | −0.924910 | −0.462455 | − | 0.886643i | \(-0.653031\pi\) | ||||
−0.462455 | + | 0.886643i | \(0.653031\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.89949 | −0.451378 | ||||||||
\(482\) | 34.9706i | 1.59287i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −30.6274 | −1.38929 | ||||||||
\(487\) | − 31.6985i | − 1.43640i | −0.695839 | − | 0.718198i | \(-0.744967\pi\) | ||||
0.695839 | − | 0.718198i | \(-0.255033\pi\) | |||||||
\(488\) | 8.00000i | 0.362143i | ||||||||
\(489\) | 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 | ||||||||
\(493\) | 13.9289i | 0.627328i | ||||||||
\(494\) | −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 | \(-0.521390\pi\) | ||||
−0.0671492 | + | 0.997743i | \(0.521390\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.3137 | 0.996903 | ||||||||
\(502\) | − 35.6569i | − 1.59144i | ||||||||
\(503\) | 32.7574i | 1.46058i | 0.683138 | + | 0.730289i | \(0.260615\pi\) | ||||
−0.683138 | + | 0.730289i | \(0.739385\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −37.7990 | −1.68037 | ||||||||
\(507\) | − 25.3137i | − 1.12422i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.2132 | −0.762962 | −0.381481 | − | 0.924377i | \(-0.624586\pi\) | ||||
−0.381481 | + | 0.924377i | \(0.624586\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 22.6274i | − 1.00000i | ||||||||
\(513\) | 2.48528i | 0.109728i | ||||||||
\(514\) | 37.4558 | 1.65211 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 7.24264i | − 0.318531i | ||||||||
\(518\) | 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 | \(0.636414\pi\) | |||||||
\(522\) | 10.6274i | 0.465149i | ||||||||
\(523\) | − 15.5147i | − 0.678411i | −0.940712 | − | 0.339206i | \(-0.889842\pi\) | ||||
0.940712 | − | 0.339206i | \(-0.110158\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 40.4853 | 1.76524 | ||||||||
\(527\) | − 9.21320i | − 0.401333i | ||||||||
\(528\) | − 56.2843i | − 2.44946i | ||||||||
\(529\) | 1.97056 | 0.0856766 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.6569 | 0.766242 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 3.55635i | − 0.154043i | ||||||||
\(534\) | 27.3137 | 1.18198 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.686292 | −0.0296433 | ||||||||
\(537\) | 6.00000i | 0.258919i | ||||||||
\(538\) | 10.9706i | 0.472975i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.9706 | 0.514655 | 0.257327 | − | 0.966324i | \(-0.417158\pi\) | ||||
0.257327 | + | 0.966324i | \(0.417158\pi\) | |||||||
\(542\) | − 32.9706i | − 1.41621i | ||||||||
\(543\) | − 16.2426i | − 0.697038i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 7.51472i | − 0.321306i | −0.987011 | − | 0.160653i | \(-0.948640\pi\) | ||||
0.987011 | − | 0.160653i | \(-0.0513600\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.00000 | −0.341432 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.9411 | 0.679115 | ||||||||
\(552\) | − 31.3137i | − 1.33280i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 38.4853 | 1.63508 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.7990i | 1.34737i | 0.739020 | + | 0.673683i | \(0.235289\pi\) | ||||
−0.739020 | + | 0.673683i | \(0.764711\pi\) | |||||||
\(558\) | − 7.02944i | − 0.297580i | ||||||||
\(559\) | −3.17157 | −0.134143 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 73.7696 | 3.11455 | ||||||||
\(562\) | − 28.7279i | − 1.21181i | ||||||||
\(563\) | − 35.9411i | − 1.51474i | −0.652987 | − | 0.757369i | \(-0.726484\pi\) | ||||
0.652987 | − | 0.757369i | \(-0.273516\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.27208 | −0.389735 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 24.9706i | − 1.04774i | ||||||||
\(569\) | 2.14214 | 0.0898030 | 0.0449015 | − | 0.998991i | \(-0.485703\pi\) | ||||
0.0449015 | + | 0.998991i | \(0.485703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.4853 | −1.44316 | −0.721582 | − | 0.692329i | \(-0.756585\pi\) | ||||
−0.721582 | + | 0.692329i | \(0.756585\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 48.2132i | 2.01414i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 22.6274 | 0.942809 | ||||||||
\(577\) | − 9.72792i | − 0.404979i | −0.979284 | − | 0.202489i | \(-0.935097\pi\) | ||||
0.979284 | − | 0.202489i | \(-0.0649032\pi\) | |||||||
\(578\) | − 14.8284i | − 0.616781i | ||||||||
\(579\) | 38.6274 | 1.60530 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 16.2426i | 0.673279i | ||||||||
\(583\) | − 24.7279i | − 1.02413i | ||||||||
\(584\) | 24.0000 | 0.993127 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.384776 | 0.0158950 | ||||||||
\(587\) | 13.4558i | 0.555382i | 0.960670 | + | 0.277691i | \(0.0895692\pi\) | ||||
−0.960670 | + | 0.277691i | \(0.910431\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.5442 | −0.434464 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.5563 | 1.05125 | ||||||||
\(592\) | 24.9706i | 1.02628i | ||||||||
\(593\) | − 10.7574i | − 0.441752i | −0.975302 | − | 0.220876i | \(-0.929108\pi\) | ||||
0.975302 | − | 0.220876i | \(-0.0708916\pi\) | |||||||
\(594\) | −3.41421 | −0.140087 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 11.0711i | − 0.453109i | ||||||||
\(598\) | − 10.2843i | − 0.420555i | ||||||||
\(599\) | 12.1716 | 0.497317 | 0.248658 | − | 0.968591i | \(-0.420010\pi\) | ||||
0.248658 | + | 0.968591i | \(0.420010\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.9706 | 0.936989 | 0.468494 | − | 0.883466i | \(-0.344797\pi\) | ||||
0.468494 | + | 0.883466i | \(0.344797\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 0.686292i | − 0.0279480i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −49.4558 | −2.00901 | ||||||||
\(607\) | − 24.8995i | − 1.01064i | −0.862932 | − | 0.505320i | \(-0.831375\pi\) | ||||
0.862932 | − | 0.505320i | \(-0.168625\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.97056 | 0.0797204 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 43.9411i | − 1.77477i | −0.461034 | − | 0.887383i | \(-0.652521\pi\) | ||||
0.461034 | − | 0.887383i | \(-0.347479\pi\) | |||||||
\(614\) | −15.6985 | −0.633539 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.41421i | 0.298485i | 0.988801 | + | 0.149242i | \(0.0476835\pi\) | ||||
−0.988801 | + | 0.149242i | \(0.952316\pi\) | |||||||
\(618\) | − 36.7279i | − 1.47741i | ||||||||
\(619\) | −31.0711 | −1.24885 | −0.624426 | − | 0.781084i | \(-0.714667\pi\) | ||||
−0.624426 | + | 0.781084i | \(0.714667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.89949 | −0.0762241 | ||||||||
\(622\) | − 14.1421i | − 0.567048i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 15.3137 | 0.613039 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 34.2426 | 1.36861 | ||||||||
\(627\) | − 84.4264i | − 3.37167i | ||||||||
\(628\) | 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 | \(0.446169\pi\) | |||||||
\(632\) | 43.7990i | 1.74223i | ||||||||
\(633\) | − 21.7279i | − 0.863607i | ||||||||
\(634\) | 16.4853 | 0.654714 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 21.8995i | 0.867009i | ||||||||
\(639\) | 24.9706 | 0.987820 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.686292 | −0.0271069 | −0.0135534 | − | 0.999908i | \(-0.504314\pi\) | ||||
−0.0135534 | + | 0.999908i | \(0.504314\pi\) | |||||||
\(642\) | 49.4558i | 1.95187i | ||||||||
\(643\) | − 27.7279i | − 1.09348i | −0.837302 | − | 0.546741i | \(-0.815868\pi\) | ||||
0.837302 | − | 0.546741i | \(-0.184132\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −44.4853 | −1.75025 | ||||||||
\(647\) | − 28.4853i | − 1.11987i | −0.828536 | − | 0.559936i | \(-0.810826\pi\) | ||||
0.828536 | − | 0.559936i | \(-0.189174\pi\) | |||||||
\(648\) | − 26.8284i | − 1.05392i | ||||||||
\(649\) | 36.3848 | 1.42823 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 1.02944i | − 0.0402850i | −0.999797 | − | 0.0201425i | \(-0.993588\pi\) | ||||
0.999797 | − | 0.0201425i | \(-0.00641199\pi\) | |||||||
\(654\) | −17.0711 | −0.667532 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.97056 | −0.350242 | ||||||||
\(657\) | 24.0000i | 0.936329i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.9706 | 0.544216 | 0.272108 | − | 0.962267i | \(-0.412279\pi\) | ||||
0.272108 | + | 0.962267i | \(0.412279\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.4558 | −1.45686 | −0.728432 | − | 0.685118i | \(-0.759750\pi\) | ||||
−0.728432 | + | 0.685118i | \(0.759750\pi\) | |||||||
\(662\) | 33.1716i | 1.28925i | ||||||||
\(663\) | 20.0711i | 0.779496i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −24.9706 | −0.967590 | ||||||||
\(667\) | 12.1838i | 0.471757i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −43.9706 | −1.70000 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.4853 | −0.636407 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 20.4853i | − 0.789650i | −0.918756 | − | 0.394825i | \(-0.870805\pi\) | ||||
0.918756 | − | 0.394825i | \(-0.129195\pi\) | |||||||
\(674\) | −19.4558 | −0.749411 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.78680i | 0.0686722i | 0.999410 | + | 0.0343361i | \(0.0109317\pi\) | ||||
−0.999410 | + | 0.0343361i | \(0.989068\pi\) | |||||||
\(678\) | − 3.65685i | − 0.140441i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.4853 | −0.899958 | ||||||||
\(682\) | − 14.4853i | − 0.554670i | ||||||||
\(683\) | 7.79899i | 0.298420i | 0.988806 | + | 0.149210i | \(0.0476731\pi\) | ||||
−0.988806 | + | 0.149210i | \(0.952327\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 72.5269i | − 2.76707i | ||||||||
\(688\) | 8.00000i | 0.304997i | ||||||||
\(689\) | 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 | ||||||||
\(697\) | − 11.7574i | − 0.445342i | ||||||||
\(698\) | − 32.4853i | − 1.22959i | ||||||||
\(699\) | 35.7990 | 1.35404 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.45584 | −0.168295 | −0.0841475 | − | 0.996453i | \(-0.526817\pi\) | ||||
−0.0841475 | + | 0.996453i | \(0.526817\pi\) | |||||||
\(702\) | − 0.928932i | − 0.0350603i | ||||||||
\(703\) | 37.4558i | 1.41267i | ||||||||
\(704\) | 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 | \(-0.603422\pi\) | ||||
−0.319224 | + | 0.947679i | \(0.603422\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −43.7990 | −1.64259 | ||||||||
\(712\) | 22.6274i | 0.847998i | ||||||||
\(713\) | − 8.05887i | − 0.301807i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1.24264i | − 0.0464073i | ||||||||
\(718\) | − 16.0000i | − 0.597115i | ||||||||
\(719\) | −17.2132 | −0.641944 | −0.320972 | − | 0.947089i | \(-0.604010\pi\) | ||||
−0.320972 | + | 0.947089i | \(0.604010\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 24.0416i | 0.894737i | ||||||||
\(723\) | − 59.6985i | − 2.22021i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 78.4264 | 2.91068 | ||||||||
\(727\) | − 29.3137i | − 1.08719i | −0.839349 | − | 0.543593i | \(-0.817064\pi\) | ||||
0.839349 | − | 0.543593i | \(-0.182936\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.8284 | 0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.4853 | −0.387812 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.6985i | 1.65098i | 0.564420 | + | 0.825488i | \(0.309100\pi\) | ||||
−0.564420 | + | 0.825488i | \(0.690900\pi\) | |||||||
\(734\) | −42.2426 | −1.55920 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 1.41421i | − 0.0520932i | ||||||||
\(738\) | − 8.97056i | − 0.330211i | ||||||||
\(739\) | 3.97056 | 0.146060 | 0.0730298 | − | 0.997330i | \(-0.476733\pi\) | ||||
0.0730298 | + | 0.997330i | \(0.476733\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.9706 | 0.843845 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 36.7279i | − 1.34742i | −0.738997 | − | 0.673708i | \(-0.764700\pi\) | ||||
0.738997 | − | 0.673708i | \(-0.235300\pi\) | |||||||
\(744\) | 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 | \(0.426672\pi\) | |||||||
\(752\) | − 4.97056i | − 0.181258i | ||||||||
\(753\) | 60.8701i | 2.21823i | ||||||||
\(754\) | −5.95837 | −0.216991 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 16.4853i | − 0.599168i | −0.954070 | − | 0.299584i | \(-0.903152\pi\) | ||||
0.954070 | − | 0.299584i | \(-0.0968478\pi\) | |||||||
\(758\) | − 2.82843i | − 0.102733i | ||||||||
\(759\) | 64.5269 | 2.34218 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.7279 | 0.461387 | 0.230693 | − | 0.973026i | \(-0.425901\pi\) | ||||
0.230693 | + | 0.973026i | \(0.425901\pi\) | |||||||
\(762\) | − 0.828427i | − 0.0300107i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.6569 | −0.637968 | ||||||||
\(767\) | 9.89949i | 0.357450i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.17157 | 0.114370 | 0.0571849 | − | 0.998364i | \(-0.481788\pi\) | ||||
0.0571849 | + | 0.998364i | \(0.481788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −63.9411 | −2.30278 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 36.2132i | − 1.30250i | −0.758864 | − | 0.651249i | \(-0.774245\pi\) | ||||
0.758864 | − | 0.651249i | \(-0.225755\pi\) | |||||||
\(774\) | −8.00000 | −0.287554 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13.4558 | −0.483037 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 49.6985i | 1.78178i | ||||||||
\(779\) | −13.4558 | −0.482106 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 51.4558 | 1.84123 | ||||||||
\(782\) | − 34.0000i | − 1.21584i | ||||||||
\(783\) | 1.10051i | 0.0393288i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12.8284 | 0.457575 | ||||||||
\(787\) | 45.7279i | 1.63002i | 0.579444 | + | 0.815012i | \(0.303270\pi\) | ||||
−0.579444 | + | 0.815012i | \(0.696730\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −69.1127 | −2.46048 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 46.6274i | 1.65683i | ||||||||
\(793\) | − 4.48528i | − 0.159277i | ||||||||
\(794\) | −6.24264 | −0.221543 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 55.1838i | 1.95471i | 0.211608 | + | 0.977355i | \(0.432130\pi\) | ||||
−0.211608 | + | 0.977355i | \(0.567870\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.51472 | 0.230474 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.6274 | −0.799500 | ||||||||
\(802\) | 8.72792i | 0.308194i | ||||||||
\(803\) | 49.4558i | 1.74526i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.94113 | 0.138820 | ||||||||
\(807\) | − 18.7279i | − 0.659254i | ||||||||
\(808\) | − 40.9706i | − 1.44134i | ||||||||
\(809\) | −30.5980 | −1.07577 | −0.537884 | − | 0.843019i | \(-0.680776\pi\) | ||||
−0.537884 | + | 0.843019i | \(0.680776\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.3553 | −0.820117 | −0.410058 | − | 0.912059i | \(-0.634492\pi\) | ||||
−0.410058 | + | 0.912059i | \(0.634492\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 56.2843i | 1.97398i | ||||||||
\(814\) | −51.4558 | −1.80353 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 50.6274 | 1.77231 | ||||||||
\(817\) | 12.0000i | 0.419827i | ||||||||
\(818\) | 20.4853i | 0.716251i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.51472 | −0.227365 | −0.113683 | − | 0.993517i | \(-0.536265\pi\) | ||||
−0.113683 | + | 0.993517i | \(0.536265\pi\) | |||||||
\(822\) | 40.9706i | 1.42901i | ||||||||
\(823\) | 8.72792i | 0.304236i | 0.988362 | + | 0.152118i | \(0.0486094\pi\) | ||||
−0.988362 | + | 0.152118i | \(0.951391\pi\) | |||||||
\(824\) | 30.4264 | 1.05995 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 6.04163i | − 0.210088i | −0.994468 | − | 0.105044i | \(-0.966502\pi\) | ||||
0.994468 | − | 0.105044i | \(-0.0334984\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −54.0416 | −1.87694 | −0.938472 | − | 0.345356i | \(-0.887758\pi\) | ||||
−0.938472 | + | 0.345356i | \(0.887758\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −65.6985 | −2.27906 | ||||||||
\(832\) | 12.6863i | 0.439818i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −55.4558 | −1.92028 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 0.727922i | − 0.0251607i | ||||||||
\(838\) | 9.51472i | 0.328681i | ||||||||
\(839\) | 48.7279 | 1.68227 | 0.841137 | − | 0.540822i | \(-0.181887\pi\) | ||||
0.841137 | + | 0.540822i | \(0.181887\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.9411 | −0.756591 | ||||||||
\(842\) | − 26.8701i | − 0.926003i | ||||||||
\(843\) | 49.0416i | 1.68908i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.97056 | 0.170891 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 16.9706i | − 0.582772i | ||||||||
\(849\) | 15.8284 | 0.543230 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.6274 | −0.981335 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.9706i | 0.786497i | 0.919432 | + | 0.393249i | \(0.128649\pi\) | ||||
−0.919432 | + | 0.393249i | \(0.871351\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −40.9706 | −1.40035 | ||||||||
\(857\) | − 5.51472i | − 0.188379i | −0.995554 | − | 0.0941896i | \(-0.969974\pi\) | ||||
0.995554 | − | 0.0941896i | \(-0.0300260\pi\) | |||||||
\(858\) | 31.5563i | 1.07732i | ||||||||
\(859\) | −48.7696 | −1.66400 | −0.831998 | − | 0.554779i | \(-0.812803\pi\) | ||||
−0.831998 | + | 0.554779i | \(0.812803\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.2721i | 0.520169i | ||||||||
\(863\) | 18.3848i | 0.625825i | 0.949782 | + | 0.312913i | \(0.101305\pi\) | ||||
−0.949782 | + | 0.312913i | \(0.898695\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −32.4853 | −1.10389 | ||||||||
\(867\) | 25.3137i | 0.859699i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −90.2548 | −3.06169 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.384776 | 0.0130376 | ||||||||
\(872\) | − 14.1421i | − 0.478913i | ||||||||
\(873\) | − 13.4558i | − 0.455411i | ||||||||
\(874\) | −38.9117 | −1.31621 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.9706i | 1.58608i | 0.609167 | + | 0.793042i | \(0.291504\pi\) | ||||
−0.609167 | + | 0.793042i | \(0.708496\pi\) | |||||||
\(878\) | − 9.02944i | − 0.304729i | ||||||||
\(879\) | −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 | ||||||||
\(883\) | − 48.4853i | − 1.63166i | −0.578292 | − | 0.815830i | \(-0.696281\pi\) | ||||
0.578292 | − | 0.815830i | \(-0.303719\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 29.4558 | 0.989588 | ||||||||
\(887\) | − 30.9706i | − 1.03989i | −0.854200 | − | 0.519945i | \(-0.825952\pi\) | ||||
0.854200 | − | 0.519945i | \(-0.174048\pi\) | |||||||
\(888\) | − 42.6274i | − 1.43048i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 55.2843 | 1.85209 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 7.45584i | − 0.249500i | ||||||||
\(894\) | 50.6274 | 1.69323 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.5563i | 0.586189i | ||||||||
\(898\) | 42.1838i | 1.40769i | ||||||||
\(899\) | −4.66905 | −0.155721 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.2426 | 0.741010 | ||||||||
\(902\) | − 18.4853i | − 0.615493i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.02944 | 0.100758 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 32.3848 | 1.07591 | ||||||||
\(907\) | 32.1838i | 1.06864i | 0.845281 | + | 0.534322i | \(0.179433\pi\) | ||||
−0.845281 | + | 0.534322i | \(0.820567\pi\) | |||||||
\(908\) | 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 | \(0.529873\pi\) | |||||||
\(912\) | − 57.9411i | − 1.91862i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 28.6274 | 0.946911 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − 3.07107i | − 0.101360i | ||||||||
\(919\) | 38.4558 | 1.26854 | 0.634271 | − | 0.773111i | \(-0.281301\pi\) | ||||
0.634271 | + | 0.773111i | \(0.281301\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.7990 | 0.883057 | ||||||||
\(922\) | 52.2843i | 1.72189i | ||||||||
\(923\) | 14.0000i | 0.460816i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 41.6569 | 1.36893 | ||||||||
\(927\) | 30.4264i | 0.999334i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −54.7279 | −1.79556 | −0.897782 | − | 0.440439i | \(-0.854823\pi\) | ||||
−0.897782 | + | 0.440439i | \(0.854823\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.1421i | 0.790378i | ||||||||
\(934\) | −27.8995 | −0.912899 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.6863 | −0.414664 | ||||||||
\(937\) | − 17.4437i | − 0.569859i | −0.958548 | − | 0.284930i | \(-0.908030\pi\) | ||||
0.958548 | − | 0.284930i | \(-0.0919702\pi\) | |||||||
\(938\) | 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 | \(0.525817\pi\) | |||||||
\(942\) | − 71.1127i | − 2.31698i | ||||||||
\(943\) | − 10.2843i | − 0.334902i | ||||||||
\(944\) | 24.9706 | 0.812723 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.4853 | −0.535983 | ||||||||
\(947\) | − 43.7574i | − 1.42192i | −0.703231 | − | 0.710962i | \(-0.748260\pi\) | ||||
0.703231 | − | 0.710962i | \(-0.251740\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.4558 | −0.436795 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −28.1421 | −0.912571 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.0122i | 0.939797i | 0.882720 | + | 0.469899i | \(0.155710\pi\) | ||||
−0.882720 | + | 0.469899i | \(0.844290\pi\) | |||||||
\(954\) | 16.9706 | 0.549442 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 37.3848i | − 1.20848i | ||||||||
\(958\) | − 28.6274i | − 0.924910i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.9117 | −0.900377 | ||||||||
\(962\) | − 14.0000i | − 0.451378i | ||||||||
\(963\) | − 40.9706i | − 1.32026i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.4264i | 0.785500i | 0.919645 | + | 0.392750i | \(0.128476\pi\) | ||||
−0.919645 | + | 0.392750i | \(0.871524\pi\) | |||||||
\(968\) | 64.9706i | 2.08823i | ||||||||
\(969\) | 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 | ||||||||
\(977\) | − 30.7696i | − 0.984405i | −0.870481 | − | 0.492203i | \(-0.836192\pi\) | ||||
0.870481 | − | 0.492203i | \(-0.163808\pi\) | |||||||
\(978\) | 6.00000i | 0.191859i | ||||||||
\(979\) | −46.6274 | −1.49022 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.1421 | 0.451524 | ||||||||
\(982\) | 27.2721i | 0.870287i | ||||||||
\(983\) | 42.2132i | 1.34639i | 0.739464 | + | 0.673196i | \(0.235079\pi\) | ||||
−0.739464 | + | 0.673196i | \(0.764921\pi\) | |||||||
\(984\) | 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 | ||||||||
\(993\) | − 56.6274i | − 1.79702i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.72792i | 0.118064i | 0.998256 | + | 0.0590322i | \(0.0188015\pi\) | ||||
−0.998256 | + | 0.0590322i | \(0.981199\pi\) | |||||||
\(998\) | − 4.24264i | − 0.134298i | ||||||||
\(999\) | −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.b.j.99.3 | 4 | ||
5.2 | odd | 4 | 1225.2.a.p.1.1 | 2 | |||
5.3 | odd | 4 | 245.2.a.f.1.2 | yes | 2 | ||
5.4 | even | 2 | inner | 1225.2.b.j.99.2 | 4 | ||
7.6 | odd | 2 | 1225.2.b.i.99.4 | 4 | |||
15.8 | even | 4 | 2205.2.a.t.1.1 | 2 | |||
20.3 | even | 4 | 3920.2.a.br.1.1 | 2 | |||
35.3 | even | 12 | 245.2.e.g.226.1 | 4 | |||
35.13 | even | 4 | 245.2.a.e.1.2 | ✓ | 2 | ||
35.18 | odd | 12 | 245.2.e.f.226.1 | 4 | |||
35.23 | odd | 12 | 245.2.e.f.116.1 | 4 | |||
35.27 | even | 4 | 1225.2.a.r.1.1 | 2 | |||
35.33 | even | 12 | 245.2.e.g.116.1 | 4 | |||
35.34 | odd | 2 | 1225.2.b.i.99.1 | 4 | |||
105.83 | odd | 4 | 2205.2.a.v.1.1 | 2 | |||
140.83 | odd | 4 | 3920.2.a.bw.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.2.a.e.1.2 | ✓ | 2 | 35.13 | even | 4 | ||
245.2.a.f.1.2 | yes | 2 | 5.3 | odd | 4 | ||
245.2.e.f.116.1 | 4 | 35.23 | odd | 12 | |||
245.2.e.f.226.1 | 4 | 35.18 | odd | 12 | |||
245.2.e.g.116.1 | 4 | 35.33 | even | 12 | |||
245.2.e.g.226.1 | 4 | 35.3 | even | 12 | |||
1225.2.a.p.1.1 | 2 | 5.2 | odd | 4 | |||
1225.2.a.r.1.1 | 2 | 35.27 | even | 4 | |||
1225.2.b.i.99.1 | 4 | 35.34 | odd | 2 | |||
1225.2.b.i.99.4 | 4 | 7.6 | odd | 2 | |||
1225.2.b.j.99.2 | 4 | 5.4 | even | 2 | inner | ||
1225.2.b.j.99.3 | 4 | 1.1 | even | 1 | trivial | ||
2205.2.a.t.1.1 | 2 | 15.8 | even | 4 | |||
2205.2.a.v.1.1 | 2 | 105.83 | odd | 4 | |||
3920.2.a.br.1.1 | 2 | 20.3 | even | 4 | |||
3920.2.a.bw.1.2 | 2 | 140.83 | odd | 4 |