Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [495,2,Mod(1,495)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(495, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("495.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 495 = 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 495.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(3.95259490005\) |
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 55) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 495.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.414214 | 0.292893 | 0.146447 | − | 0.989219i | \(-0.453216\pi\) | ||||
0.146447 | + | 0.989219i | \(0.453216\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.82843 | −0.914214 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | −1.58579 | −0.560660 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.414214 | 0.130986 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.82843 | −1.89386 | −0.946932 | − | 0.321433i | \(-0.895836\pi\) | ||||
−0.946932 | + | 0.321433i | \(0.895836\pi\) | |||||||
\(14\) | −0.828427 | −0.221406 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | −1.17157 | −0.284148 | −0.142074 | − | 0.989856i | \(-0.545377\pi\) | ||||
−0.142074 | + | 0.989856i | \(0.545377\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | −1.82843 | −0.408849 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.414214 | −0.0883106 | ||||||||
\(23\) | −2.82843 | −0.589768 | −0.294884 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294884 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.82843 | −0.554700 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.65685 | 0.691080 | ||||||||
\(29\) | −7.65685 | −1.42184 | −0.710921 | − | 0.703272i | \(-0.751722\pi\) | ||||
−0.710921 | + | 0.703272i | \(0.751722\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 4.41421 | 0.780330 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.485281 | −0.0832251 | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.65685 | 0.601183 | 0.300592 | − | 0.953753i | \(-0.402816\pi\) | ||||
0.300592 | + | 0.953753i | \(0.402816\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.58579 | −0.250735 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.00000 | −0.914991 | −0.457496 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457496 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(44\) | 1.82843 | 0.275646 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.17157 | −0.172739 | ||||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0.414214 | 0.0585786 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 12.4853 | 1.73140 | ||||||||
\(53\) | −0.343146 | −0.0471347 | −0.0235673 | − | 0.999722i | \(-0.507502\pi\) | ||||
−0.0235673 | + | 0.999722i | \(0.507502\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 3.17157 | 0.423819 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.17157 | −0.416448 | ||||||||
\(59\) | 9.65685 | 1.25722 | 0.628608 | − | 0.777723i | \(-0.283625\pi\) | ||||
0.628608 | + | 0.777723i | \(0.283625\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.3137 | 1.70465 | 0.852323 | − | 0.523016i | \(-0.175193\pi\) | ||||
0.852323 | + | 0.523016i | \(0.175193\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | −6.82843 | −0.846962 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.48528 | −0.547964 | −0.273982 | − | 0.961735i | \(-0.588341\pi\) | ||||
−0.273982 | + | 0.961735i | \(0.588341\pi\) | |||||||
\(68\) | 2.14214 | 0.259772 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.828427 | −0.0990160 | ||||||||
\(71\) | 11.3137 | 1.34269 | 0.671345 | − | 0.741145i | \(-0.265717\pi\) | ||||
0.671345 | + | 0.741145i | \(0.265717\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.82843 | −0.799207 | −0.399603 | − | 0.916688i | \(-0.630852\pi\) | ||||
−0.399603 | + | 0.916688i | \(0.630852\pi\) | |||||||
\(74\) | 1.51472 | 0.176082 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00000 | 0.227921 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.48528 | −0.274453 | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.17157 | −0.127075 | ||||||||
\(86\) | −2.48528 | −0.267995 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.58579 | 0.169045 | ||||||||
\(89\) | −9.31371 | −0.987251 | −0.493626 | − | 0.869675i | \(-0.664329\pi\) | ||||
−0.493626 | + | 0.869675i | \(0.664329\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.6569 | 1.43163 | ||||||||
\(92\) | 5.17157 | 0.539174 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.17157 | 0.120839 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.65685 | −0.777436 | −0.388718 | − | 0.921357i | \(-0.627082\pi\) | ||||
−0.388718 | + | 0.921357i | \(0.627082\pi\) | |||||||
\(98\) | −1.24264 | −0.125526 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.82843 | −0.182843 | ||||||||
\(101\) | 13.3137 | 1.32476 | 0.662382 | − | 0.749166i | \(-0.269546\pi\) | ||||
0.662382 | + | 0.749166i | \(0.269546\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.17157 | 0.115439 | 0.0577193 | − | 0.998333i | \(-0.481617\pi\) | ||||
0.0577193 | + | 0.998333i | \(0.481617\pi\) | |||||||
\(104\) | 10.8284 | 1.06181 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.142136 | −0.0138054 | ||||||||
\(107\) | 3.65685 | 0.353521 | 0.176761 | − | 0.984254i | \(-0.443438\pi\) | ||||
0.176761 | + | 0.984254i | \(0.443438\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.65685 | 0.350263 | 0.175132 | − | 0.984545i | \(-0.443965\pi\) | ||||
0.175132 | + | 0.984545i | \(0.443965\pi\) | |||||||
\(110\) | −0.414214 | −0.0394937 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.00000 | −0.566947 | ||||||||
\(113\) | −8.34315 | −0.784857 | −0.392429 | − | 0.919782i | \(-0.628365\pi\) | ||||
−0.392429 | + | 0.919782i | \(0.628365\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.82843 | −0.263752 | ||||||||
\(116\) | 14.0000 | 1.29987 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.00000 | 0.368230 | ||||||||
\(119\) | 2.34315 | 0.214796 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 5.51472 | 0.499279 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.6569 | 1.38932 | 0.694661 | − | 0.719338i | \(-0.255555\pi\) | ||||
0.694661 | + | 0.719338i | \(0.255555\pi\) | |||||||
\(128\) | −10.5563 | −0.933058 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.82843 | −0.248069 | ||||||||
\(131\) | −11.3137 | −0.988483 | −0.494242 | − | 0.869325i | \(-0.664554\pi\) | ||||
−0.494242 | + | 0.869325i | \(0.664554\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.85786 | −0.160495 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.85786 | 0.159311 | ||||||||
\(137\) | −22.9706 | −1.96251 | −0.981254 | − | 0.192720i | \(-0.938269\pi\) | ||||
−0.981254 | + | 0.192720i | \(0.938269\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 3.65685 | 0.309061 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.68629 | 0.393265 | ||||||||
\(143\) | 6.82843 | 0.571022 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.65685 | −0.635867 | ||||||||
\(146\) | −2.82843 | −0.234082 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.68629 | −0.549610 | ||||||||
\(149\) | −11.6569 | −0.954967 | −0.477483 | − | 0.878641i | \(-0.658451\pi\) | ||||
−0.477483 | + | 0.878641i | \(0.658451\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.828427 | 0.0667566 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.0000 | −1.11732 | −0.558661 | − | 0.829396i | \(-0.688685\pi\) | ||||
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | 1.65685 | 0.131812 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.41421 | 0.348974 | ||||||||
\(161\) | 5.65685 | 0.445823 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.485281 | −0.0380102 | −0.0190051 | − | 0.999819i | \(-0.506050\pi\) | ||||
−0.0190051 | + | 0.999819i | \(0.506050\pi\) | |||||||
\(164\) | 10.9706 | 0.856657 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.48528 | 0.192895 | ||||||||
\(167\) | −10.9706 | −0.848928 | −0.424464 | − | 0.905445i | \(-0.639537\pi\) | ||||
−0.424464 | + | 0.905445i | \(0.639537\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.6274 | 2.58672 | ||||||||
\(170\) | −0.485281 | −0.0372194 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.9706 | 0.836498 | ||||||||
\(173\) | −6.14214 | −0.466978 | −0.233489 | − | 0.972359i | \(-0.575014\pi\) | ||||
−0.233489 | + | 0.972359i | \(0.575014\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | −0.151186 | ||||||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.85786 | −0.289159 | ||||||||
\(179\) | 1.65685 | 0.123839 | 0.0619196 | − | 0.998081i | \(-0.480278\pi\) | ||||
0.0619196 | + | 0.998081i | \(0.480278\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.31371 | −0.0976472 | −0.0488236 | − | 0.998807i | \(-0.515547\pi\) | ||||
−0.0488236 | + | 0.998807i | \(0.515547\pi\) | |||||||
\(182\) | 5.65685 | 0.419314 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.48528 | 0.330659 | ||||||||
\(185\) | 3.65685 | 0.268857 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.17157 | 0.0856739 | ||||||||
\(188\) | −5.17157 | −0.377176 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.3137 | 1.39749 | 0.698745 | − | 0.715370i | \(-0.253742\pi\) | ||||
0.698745 | + | 0.715370i | \(0.253742\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.82843 | −0.491521 | −0.245760 | − | 0.969331i | \(-0.579038\pi\) | ||||
−0.245760 | + | 0.969331i | \(0.579038\pi\) | |||||||
\(194\) | −3.17157 | −0.227706 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.48528 | 0.391806 | ||||||||
\(197\) | 5.17157 | 0.368459 | 0.184230 | − | 0.982883i | \(-0.441021\pi\) | ||||
0.184230 | + | 0.982883i | \(0.441021\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.6569 | 1.53521 | 0.767607 | − | 0.640921i | \(-0.221447\pi\) | ||||
0.767607 | + | 0.640921i | \(0.221447\pi\) | |||||||
\(200\) | −1.58579 | −0.112132 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.51472 | 0.388014 | ||||||||
\(203\) | 15.3137 | 1.07481 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | −0.419058 | ||||||||
\(206\) | 0.485281 | 0.0338112 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −20.4853 | −1.42040 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 0.627417 | 0.0430912 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.51472 | 0.103544 | ||||||||
\(215\) | −6.00000 | −0.409197 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.51472 | 0.102590 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.82843 | 0.123273 | ||||||||
\(221\) | 8.00000 | 0.538138 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.17157 | −0.346314 | −0.173157 | − | 0.984894i | \(-0.555397\pi\) | ||||
−0.173157 | + | 0.984894i | \(0.555397\pi\) | |||||||
\(224\) | −8.82843 | −0.589874 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.45584 | −0.229879 | ||||||||
\(227\) | −2.68629 | −0.178295 | −0.0891477 | − | 0.996018i | \(-0.528414\pi\) | ||||
−0.0891477 | + | 0.996018i | \(0.528414\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.3137 | −1.40845 | −0.704225 | − | 0.709977i | \(-0.748705\pi\) | ||||
−0.704225 | + | 0.709977i | \(0.748705\pi\) | |||||||
\(230\) | −1.17157 | −0.0772512 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.1421 | 0.797170 | ||||||||
\(233\) | −22.1421 | −1.45058 | −0.725290 | − | 0.688444i | \(-0.758294\pi\) | ||||
−0.725290 | + | 0.688444i | \(0.758294\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.82843 | 0.184506 | ||||||||
\(236\) | −17.6569 | −1.14936 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.970563 | 0.0629122 | ||||||||
\(239\) | 0.686292 | 0.0443925 | 0.0221963 | − | 0.999754i | \(-0.492934\pi\) | ||||
0.0221963 | + | 0.999754i | \(0.492934\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.00000 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(242\) | 0.414214 | 0.0266267 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −24.3431 | −1.55841 | ||||||||
\(245\) | −3.00000 | −0.191663 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.414214 | 0.0261972 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.82843 | 0.177822 | ||||||||
\(254\) | 6.48528 | 0.406923 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | −13.3137 | −0.830486 | −0.415243 | − | 0.909710i | \(-0.636304\pi\) | ||||
−0.415243 | + | 0.909710i | \(0.636304\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.31371 | −0.454452 | ||||||||
\(260\) | 12.4853 | 0.774304 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.68629 | −0.289520 | ||||||||
\(263\) | −22.9706 | −1.41643 | −0.708213 | − | 0.705999i | \(-0.750498\pi\) | ||||
−0.708213 | + | 0.705999i | \(0.750498\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.343146 | −0.0210793 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.20101 | 0.500956 | ||||||||
\(269\) | 5.31371 | 0.323983 | 0.161991 | − | 0.986792i | \(-0.448208\pi\) | ||||
0.161991 | + | 0.986792i | \(0.448208\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.3137 | −0.930242 | −0.465121 | − | 0.885247i | \(-0.653989\pi\) | ||||
−0.465121 | + | 0.885247i | \(0.653989\pi\) | |||||||
\(272\) | −3.51472 | −0.213111 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.51472 | −0.574805 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.17157 | 0.0703930 | 0.0351965 | − | 0.999380i | \(-0.488794\pi\) | ||||
0.0351965 | + | 0.999380i | \(0.488794\pi\) | |||||||
\(278\) | −1.65685 | −0.0993715 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.17157 | 0.189538 | ||||||||
\(281\) | 5.31371 | 0.316989 | 0.158495 | − | 0.987360i | \(-0.449336\pi\) | ||||
0.158495 | + | 0.987360i | \(0.449336\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.6274 | −0.750622 | −0.375311 | − | 0.926899i | \(-0.622464\pi\) | ||||
−0.375311 | + | 0.926899i | \(0.622464\pi\) | |||||||
\(284\) | −20.6863 | −1.22751 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.82843 | 0.167248 | ||||||||
\(287\) | 12.0000 | 0.708338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6274 | −0.919260 | ||||||||
\(290\) | −3.17157 | −0.186241 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.4853 | 0.730646 | ||||||||
\(293\) | 14.8284 | 0.866286 | 0.433143 | − | 0.901325i | \(-0.357405\pi\) | ||||
0.433143 | + | 0.901325i | \(0.357405\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.65685 | 0.562244 | ||||||||
\(296\) | −5.79899 | −0.337059 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.82843 | −0.279703 | ||||||||
\(299\) | 19.3137 | 1.11694 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0000 | 0.691669 | ||||||||
\(302\) | −4.97056 | −0.286024 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.3137 | 0.762341 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.6569 | −1.57846 | −0.789230 | − | 0.614098i | \(-0.789520\pi\) | ||||
−0.789230 | + | 0.614098i | \(0.789520\pi\) | |||||||
\(308\) | −3.65685 | −0.208369 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.3137 | −1.54882 | −0.774409 | − | 0.632685i | \(-0.781953\pi\) | ||||
−0.774409 | + | 0.632685i | \(0.781953\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.3137 | 1.20472 | 0.602361 | − | 0.798224i | \(-0.294227\pi\) | ||||
0.602361 | + | 0.798224i | \(0.294227\pi\) | |||||||
\(314\) | −5.79899 | −0.327256 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.31371 | −0.411428 | ||||||||
\(317\) | −21.3137 | −1.19710 | −0.598549 | − | 0.801087i | \(-0.704256\pi\) | ||||
−0.598549 | + | 0.801087i | \(0.704256\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.65685 | 0.428702 | ||||||||
\(320\) | −4.17157 | −0.233198 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.34315 | 0.130578 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.82843 | −0.378773 | ||||||||
\(326\) | −0.201010 | −0.0111329 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.51472 | 0.525362 | ||||||||
\(329\) | −5.65685 | −0.311872 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.3137 | 0.841718 | 0.420859 | − | 0.907126i | \(-0.361729\pi\) | ||||
0.420859 | + | 0.907126i | \(0.361729\pi\) | |||||||
\(332\) | −10.9706 | −0.602088 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.54416 | −0.248645 | ||||||||
\(335\) | −4.48528 | −0.245057 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.51472 | −0.191459 | −0.0957295 | − | 0.995407i | \(-0.530518\pi\) | ||||
−0.0957295 | + | 0.995407i | \(0.530518\pi\) | |||||||
\(338\) | 13.9289 | 0.757634 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.14214 | 0.116174 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 9.51472 | 0.512999 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.54416 | −0.136775 | ||||||||
\(347\) | 22.9706 | 1.23312 | 0.616562 | − | 0.787306i | \(-0.288525\pi\) | ||||
0.616562 | + | 0.787306i | \(0.288525\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.97056 | −0.373126 | −0.186563 | − | 0.982443i | \(-0.559735\pi\) | ||||
−0.186563 | + | 0.982443i | \(0.559735\pi\) | |||||||
\(350\) | −0.828427 | −0.0442813 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.41421 | −0.235278 | ||||||||
\(353\) | 1.31371 | 0.0699216 | 0.0349608 | − | 0.999389i | \(-0.488869\pi\) | ||||
0.0349608 | + | 0.999389i | \(0.488869\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.3137 | 0.600469 | ||||||||
\(356\) | 17.0294 | 0.902558 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.686292 | 0.0362716 | ||||||||
\(359\) | −23.3137 | −1.23045 | −0.615225 | − | 0.788351i | \(-0.710935\pi\) | ||||
−0.615225 | + | 0.788351i | \(0.710935\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | −0.544156 | −0.0286002 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −24.9706 | −1.30881 | ||||||||
\(365\) | −6.82843 | −0.357416 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.48528 | 0.442928 | 0.221464 | − | 0.975169i | \(-0.428916\pi\) | ||||
0.221464 | + | 0.975169i | \(0.428916\pi\) | |||||||
\(368\) | −8.48528 | −0.442326 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.51472 | 0.0787465 | ||||||||
\(371\) | 0.686292 | 0.0356305 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.79899 | −0.196704 | −0.0983521 | − | 0.995152i | \(-0.531357\pi\) | ||||
−0.0983521 | + | 0.995152i | \(0.531357\pi\) | |||||||
\(374\) | 0.485281 | 0.0250933 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.48528 | −0.231311 | ||||||||
\(377\) | 52.2843 | 2.69278 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.3431 | 1.14769 | 0.573845 | − | 0.818964i | \(-0.305451\pi\) | ||||
0.573845 | + | 0.818964i | \(0.305451\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.00000 | 0.409316 | ||||||||
\(383\) | 34.1421 | 1.74458 | 0.872291 | − | 0.488987i | \(-0.162634\pi\) | ||||
0.872291 | + | 0.488987i | \(0.162634\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.00000 | 0.101929 | ||||||||
\(386\) | −2.82843 | −0.143963 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.0000 | 0.710742 | ||||||||
\(389\) | 24.6274 | 1.24866 | 0.624330 | − | 0.781161i | \(-0.285372\pi\) | ||||
0.624330 | + | 0.781161i | \(0.285372\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.31371 | 0.167581 | ||||||||
\(392\) | 4.75736 | 0.240283 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.14214 | 0.107919 | ||||||||
\(395\) | 4.00000 | 0.201262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.3137 | 0.668196 | 0.334098 | − | 0.942538i | \(-0.391568\pi\) | ||||
0.334098 | + | 0.942538i | \(0.391568\pi\) | |||||||
\(398\) | 8.97056 | 0.449654 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | −17.3137 | −0.864605 | −0.432303 | − | 0.901729i | \(-0.642299\pi\) | ||||
−0.432303 | + | 0.901729i | \(0.642299\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −24.3431 | −1.21112 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.34315 | 0.314805 | ||||||||
\(407\) | −3.65685 | −0.181264 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.9706 | 1.72918 | 0.864592 | − | 0.502475i | \(-0.167577\pi\) | ||||
0.864592 | + | 0.502475i | \(0.167577\pi\) | |||||||
\(410\) | −2.48528 | −0.122739 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.14214 | −0.105535 | ||||||||
\(413\) | −19.3137 | −0.950365 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | −30.1421 | −1.47784 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.3431 | 0.700709 | 0.350354 | − | 0.936617i | \(-0.386061\pi\) | ||||
0.350354 | + | 0.936617i | \(0.386061\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | −6.62742 | −0.322618 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.544156 | 0.0264265 | ||||||||
\(425\) | −1.17157 | −0.0568296 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −26.6274 | −1.28859 | ||||||||
\(428\) | −6.68629 | −0.323194 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.48528 | −0.119851 | ||||||||
\(431\) | −11.3137 | −0.544962 | −0.272481 | − | 0.962161i | \(-0.587844\pi\) | ||||
−0.272481 | + | 0.962161i | \(0.587844\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.65685 | 0.175737 | 0.0878686 | − | 0.996132i | \(-0.471994\pi\) | ||||
0.0878686 | + | 0.996132i | \(0.471994\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.68629 | −0.320215 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.0000 | −0.763638 | −0.381819 | − | 0.924237i | \(-0.624702\pi\) | ||||
−0.381819 | + | 0.924237i | \(0.624702\pi\) | |||||||
\(440\) | 1.58579 | 0.0755994 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.31371 | 0.157617 | ||||||||
\(443\) | 21.1716 | 1.00589 | 0.502946 | − | 0.864318i | \(-0.332249\pi\) | ||||
0.502946 | + | 0.864318i | \(0.332249\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.31371 | −0.441512 | ||||||||
\(446\) | −2.14214 | −0.101433 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.34315 | 0.394177 | ||||||||
\(449\) | 16.6274 | 0.784696 | 0.392348 | − | 0.919817i | \(-0.371663\pi\) | ||||
0.392348 | + | 0.919817i | \(0.371663\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.00000 | 0.282529 | ||||||||
\(452\) | 15.2548 | 0.717527 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.11270 | −0.0522215 | ||||||||
\(455\) | 13.6569 | 0.640243 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.4853 | −0.771149 | −0.385574 | − | 0.922677i | \(-0.625997\pi\) | ||||
−0.385574 | + | 0.922677i | \(0.625997\pi\) | |||||||
\(458\) | −8.82843 | −0.412525 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.17157 | 0.241126 | ||||||||
\(461\) | 32.6274 | 1.51961 | 0.759805 | − | 0.650151i | \(-0.225294\pi\) | ||||
0.759805 | + | 0.650151i | \(0.225294\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.1421 | 1.02903 | 0.514516 | − | 0.857481i | \(-0.327972\pi\) | ||||
0.514516 | + | 0.857481i | \(0.327972\pi\) | |||||||
\(464\) | −22.9706 | −1.06638 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.17157 | −0.424865 | ||||||||
\(467\) | 9.17157 | 0.424410 | 0.212205 | − | 0.977225i | \(-0.431936\pi\) | ||||
0.212205 | + | 0.977225i | \(0.431936\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.97056 | 0.414222 | ||||||||
\(470\) | 1.17157 | 0.0540406 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15.3137 | −0.704871 | ||||||||
\(473\) | 6.00000 | 0.275880 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.28427 | −0.196369 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.284271 | 0.0130023 | ||||||||
\(479\) | 36.0000 | 1.64488 | 0.822441 | − | 0.568850i | \(-0.192612\pi\) | ||||
0.822441 | + | 0.568850i | \(0.192612\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.9706 | −1.13856 | ||||||||
\(482\) | 2.48528 | 0.113201 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.82843 | −0.0831103 | ||||||||
\(485\) | −7.65685 | −0.347680 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.51472 | −0.340524 | −0.170262 | − | 0.985399i | \(-0.554461\pi\) | ||||
−0.170262 | + | 0.985399i | \(0.554461\pi\) | |||||||
\(488\) | −21.1127 | −0.955727 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.24264 | −0.0561368 | ||||||||
\(491\) | 23.3137 | 1.05213 | 0.526066 | − | 0.850443i | \(-0.323666\pi\) | ||||
0.526066 | + | 0.850443i | \(0.323666\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.97056 | 0.404014 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.6274 | −1.01498 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.65685 | −0.0741710 | −0.0370855 | − | 0.999312i | \(-0.511807\pi\) | ||||
−0.0370855 | + | 0.999312i | \(0.511807\pi\) | |||||||
\(500\) | −1.82843 | −0.0817697 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.97056 | −0.221847 | ||||||||
\(503\) | 28.6274 | 1.27643 | 0.638217 | − | 0.769857i | \(-0.279672\pi\) | ||||
0.638217 | + | 0.769857i | \(0.279672\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.3137 | 0.592452 | ||||||||
\(506\) | 1.17157 | 0.0520828 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −28.6274 | −1.27014 | ||||||||
\(509\) | −9.31371 | −0.412823 | −0.206411 | − | 0.978465i | \(-0.566179\pi\) | ||||
−0.206411 | + | 0.978465i | \(0.566179\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.6569 | 0.604144 | ||||||||
\(512\) | 22.7574 | 1.00574 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.51472 | −0.243244 | ||||||||
\(515\) | 1.17157 | 0.0516257 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.82843 | −0.124394 | ||||||||
\(518\) | −3.02944 | −0.133106 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.8284 | 0.474858 | ||||||||
\(521\) | −2.68629 | −0.117689 | −0.0588443 | − | 0.998267i | \(-0.518742\pi\) | ||||
−0.0588443 | + | 0.998267i | \(0.518742\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.5980 | 1.64404 | 0.822022 | − | 0.569455i | \(-0.192846\pi\) | ||||
0.822022 | + | 0.569455i | \(0.192846\pi\) | |||||||
\(524\) | 20.6863 | 0.903685 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.51472 | −0.414861 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | −0.142136 | −0.00617398 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.9706 | 1.77463 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.65685 | 0.158100 | ||||||||
\(536\) | 7.11270 | 0.307222 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.20101 | 0.0948923 | ||||||||
\(539\) | 3.00000 | 0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.00000 | 0.257960 | 0.128980 | − | 0.991647i | \(-0.458830\pi\) | ||||
0.128980 | + | 0.991647i | \(0.458830\pi\) | |||||||
\(542\) | −6.34315 | −0.272461 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.17157 | −0.221729 | ||||||||
\(545\) | 3.65685 | 0.156642 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.0000 | −1.45374 | −0.726868 | − | 0.686778i | \(-0.759025\pi\) | ||||
−0.726868 | + | 0.686778i | \(0.759025\pi\) | |||||||
\(548\) | 42.0000 | 1.79415 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.414214 | −0.0176621 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.00000 | −0.340195 | ||||||||
\(554\) | 0.485281 | 0.0206176 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.31371 | 0.310170 | ||||||||
\(557\) | −38.1421 | −1.61613 | −0.808067 | − | 0.589090i | \(-0.799486\pi\) | ||||
−0.808067 | + | 0.589090i | \(0.799486\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.9706 | 1.73287 | ||||||||
\(560\) | −6.00000 | −0.253546 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.20101 | 0.0928440 | ||||||||
\(563\) | −11.6569 | −0.491278 | −0.245639 | − | 0.969361i | \(-0.578998\pi\) | ||||
−0.245639 | + | 0.969361i | \(0.578998\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.34315 | −0.350999 | ||||||||
\(566\) | −5.23045 | −0.219852 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −17.9411 | −0.752793 | ||||||||
\(569\) | −20.3431 | −0.852829 | −0.426415 | − | 0.904528i | \(-0.640224\pi\) | ||||
−0.426415 | + | 0.904528i | \(0.640224\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.9411 | 1.92258 | 0.961288 | − | 0.275545i | \(-0.0888584\pi\) | ||||
0.961288 | + | 0.275545i | \(0.0888584\pi\) | |||||||
\(572\) | −12.4853 | −0.522036 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.97056 | 0.207467 | ||||||||
\(575\) | −2.82843 | −0.117954 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.97056 | 0.290188 | 0.145094 | − | 0.989418i | \(-0.453651\pi\) | ||||
0.145094 | + | 0.989418i | \(0.453651\pi\) | |||||||
\(578\) | −6.47309 | −0.269245 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 14.0000 | 0.581318 | ||||||||
\(581\) | −12.0000 | −0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.343146 | 0.0142116 | ||||||||
\(584\) | 10.8284 | 0.448084 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.14214 | 0.253729 | ||||||||
\(587\) | −26.1421 | −1.07900 | −0.539501 | − | 0.841985i | \(-0.681387\pi\) | ||||
−0.539501 | + | 0.841985i | \(0.681387\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 4.00000 | 0.164677 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.9706 | 0.450887 | ||||||||
\(593\) | −20.4853 | −0.841230 | −0.420615 | − | 0.907239i | \(-0.638186\pi\) | ||||
−0.420615 | + | 0.907239i | \(0.638186\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.34315 | 0.0960596 | ||||||||
\(596\) | 21.3137 | 0.873044 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.00000 | 0.327144 | ||||||||
\(599\) | −5.65685 | −0.231133 | −0.115566 | − | 0.993300i | \(-0.536868\pi\) | ||||
−0.115566 | + | 0.993300i | \(0.536868\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −43.9411 | −1.79240 | −0.896198 | − | 0.443654i | \(-0.853682\pi\) | ||||
−0.896198 | + | 0.443654i | \(0.853682\pi\) | |||||||
\(602\) | 4.97056 | 0.202585 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 21.9411 | 0.892772 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.2843 | −0.742136 | −0.371068 | − | 0.928606i | \(-0.621008\pi\) | ||||
−0.371068 | + | 0.928606i | \(0.621008\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.51472 | 0.223284 | ||||||||
\(611\) | −19.3137 | −0.781349 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.4558 | 1.02815 | 0.514076 | − | 0.857745i | \(-0.328135\pi\) | ||||
0.514076 | + | 0.857745i | \(0.328135\pi\) | |||||||
\(614\) | −11.4558 | −0.462320 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.17157 | −0.127786 | ||||||||
\(617\) | −11.6569 | −0.469287 | −0.234644 | − | 0.972081i | \(-0.575392\pi\) | ||||
−0.234644 | + | 0.972081i | \(0.575392\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.6569 | −1.03124 | −0.515618 | − | 0.856819i | \(-0.672438\pi\) | ||||
−0.515618 | + | 0.856819i | \(0.672438\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.3137 | −0.453638 | ||||||||
\(623\) | 18.6274 | 0.746292 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 8.82843 | 0.352855 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 25.5980 | 1.02147 | ||||||||
\(629\) | −4.28427 | −0.170825 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | −6.34315 | −0.252317 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.82843 | −0.350622 | ||||||||
\(635\) | 15.6569 | 0.621323 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.4853 | 0.811656 | ||||||||
\(638\) | 3.17157 | 0.125564 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.5563 | −0.417276 | ||||||||
\(641\) | −30.0000 | −1.18493 | −0.592464 | − | 0.805597i | \(-0.701845\pi\) | ||||
−0.592464 | + | 0.805597i | \(0.701845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 49.4558 | 1.95035 | 0.975174 | − | 0.221440i | \(-0.0710756\pi\) | ||||
0.975174 | + | 0.221440i | \(0.0710756\pi\) | |||||||
\(644\) | −10.3431 | −0.407577 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 35.1127 | 1.38042 | 0.690211 | − | 0.723608i | \(-0.257518\pi\) | ||||
0.690211 | + | 0.723608i | \(0.257518\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.65685 | −0.379065 | ||||||||
\(650\) | −2.82843 | −0.110940 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.887302 | 0.0347494 | ||||||||
\(653\) | −0.343146 | −0.0134283 | −0.00671417 | − | 0.999977i | \(-0.502137\pi\) | ||||
−0.00671417 | + | 0.999977i | \(0.502137\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.3137 | −0.442063 | ||||||||
\(656\) | −18.0000 | −0.702782 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.34315 | −0.0913453 | ||||||||
\(659\) | 21.9411 | 0.854705 | 0.427352 | − | 0.904085i | \(-0.359446\pi\) | ||||
0.427352 | + | 0.904085i | \(0.359446\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.627417 | −0.0244037 | −0.0122018 | − | 0.999926i | \(-0.503884\pi\) | ||||
−0.0122018 | + | 0.999926i | \(0.503884\pi\) | |||||||
\(662\) | 6.34315 | 0.246533 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.51472 | −0.369243 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.6569 | 0.838557 | ||||||||
\(668\) | 20.0589 | 0.776101 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.85786 | −0.0717756 | ||||||||
\(671\) | −13.3137 | −0.513970 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.48528 | 0.172895 | 0.0864474 | − | 0.996256i | \(-0.472449\pi\) | ||||
0.0864474 | + | 0.996256i | \(0.472449\pi\) | |||||||
\(674\) | −1.45584 | −0.0560770 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −61.4853 | −2.36482 | ||||||||
\(677\) | −17.1716 | −0.659957 | −0.329979 | − | 0.943988i | \(-0.607042\pi\) | ||||
−0.329979 | + | 0.943988i | \(0.607042\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.3137 | 0.587686 | ||||||||
\(680\) | 1.85786 | 0.0712458 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.7990 | −1.21675 | −0.608377 | − | 0.793648i | \(-0.708179\pi\) | ||||
−0.608377 | + | 0.793648i | \(0.708179\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.9706 | −0.877660 | ||||||||
\(686\) | 8.28427 | 0.316295 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18.0000 | −0.686244 | ||||||||
\(689\) | 2.34315 | 0.0892667 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.6863 | −0.634776 | −0.317388 | − | 0.948296i | \(-0.602806\pi\) | ||||
−0.317388 | + | 0.948296i | \(0.602806\pi\) | |||||||
\(692\) | 11.2304 | 0.426918 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.51472 | 0.361174 | ||||||||
\(695\) | −4.00000 | −0.151729 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.02944 | 0.266259 | ||||||||
\(698\) | −2.88730 | −0.109286 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.65685 | 0.138216 | ||||||||
\(701\) | −32.6274 | −1.23232 | −0.616160 | − | 0.787621i | \(-0.711313\pi\) | ||||
−0.616160 | + | 0.787621i | \(0.711313\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 4.17157 | 0.157222 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.544156 | 0.0204796 | ||||||||
\(707\) | −26.6274 | −1.00143 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.6274 | −0.774679 | −0.387339 | − | 0.921937i | \(-0.626606\pi\) | ||||
−0.387339 | + | 0.921937i | \(0.626606\pi\) | |||||||
\(710\) | 4.68629 | 0.175873 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.7696 | 0.553512 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.82843 | 0.255369 | ||||||||
\(716\) | −3.02944 | −0.113215 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.65685 | −0.360391 | ||||||||
\(719\) | −29.6569 | −1.10601 | −0.553007 | − | 0.833177i | \(-0.686520\pi\) | ||||
−0.553007 | + | 0.833177i | \(0.686520\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.34315 | −0.0872633 | ||||||||
\(722\) | −7.87006 | −0.292893 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.40202 | 0.0892704 | ||||||||
\(725\) | −7.65685 | −0.284368 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.4853 | −1.35316 | −0.676582 | − | 0.736367i | \(-0.736540\pi\) | ||||
−0.676582 | + | 0.736367i | \(0.736540\pi\) | |||||||
\(728\) | −21.6569 | −0.802656 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.82843 | −0.104685 | ||||||||
\(731\) | 7.02944 | 0.259993 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.4558 | 1.23572 | 0.617860 | − | 0.786288i | \(-0.288000\pi\) | ||||
0.617860 | + | 0.786288i | \(0.288000\pi\) | |||||||
\(734\) | 3.51472 | 0.129731 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.4853 | −0.460214 | ||||||||
\(737\) | 4.48528 | 0.165217 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.9411 | −1.39569 | −0.697843 | − | 0.716250i | \(-0.745857\pi\) | ||||
−0.697843 | + | 0.716250i | \(0.745857\pi\) | |||||||
\(740\) | −6.68629 | −0.245793 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.284271 | 0.0104359 | ||||||||
\(743\) | −29.5980 | −1.08584 | −0.542922 | − | 0.839783i | \(-0.682682\pi\) | ||||
−0.542922 | + | 0.839783i | \(0.682682\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.6569 | −0.427074 | ||||||||
\(746\) | −1.57359 | −0.0576133 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.14214 | −0.0783242 | ||||||||
\(749\) | −7.31371 | −0.267237 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.0000 | −0.583848 | −0.291924 | − | 0.956441i | \(-0.594295\pi\) | ||||
−0.291924 | + | 0.956441i | \(0.594295\pi\) | |||||||
\(752\) | 8.48528 | 0.309426 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 21.6569 | 0.788696 | ||||||||
\(755\) | −12.0000 | −0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.31371 | −0.338512 | −0.169256 | − | 0.985572i | \(-0.554137\pi\) | ||||
−0.169256 | + | 0.985572i | \(0.554137\pi\) | |||||||
\(758\) | 9.25483 | 0.336151 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.0000 | 1.08750 | 0.543750 | − | 0.839248i | \(-0.317004\pi\) | ||||
0.543750 | + | 0.839248i | \(0.317004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.31371 | −0.264774 | ||||||||
\(764\) | −35.3137 | −1.27761 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 14.1421 | 0.510976 | ||||||||
\(767\) | −65.9411 | −2.38100 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.9706 | 0.539852 | 0.269926 | − | 0.962881i | \(-0.413001\pi\) | ||||
0.269926 | + | 0.962881i | \(0.413001\pi\) | |||||||
\(770\) | 0.828427 | 0.0298544 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12.4853 | 0.449355 | ||||||||
\(773\) | 30.2843 | 1.08925 | 0.544625 | − | 0.838680i | \(-0.316672\pi\) | ||||
0.544625 | + | 0.838680i | \(0.316672\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 12.1421 | 0.435877 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.2010 | 0.365724 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.3137 | −0.404836 | ||||||||
\(782\) | 1.37258 | 0.0490835 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.00000 | −0.321429 | ||||||||
\(785\) | −14.0000 | −0.499681 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.9706 | 0.676228 | 0.338114 | − | 0.941105i | \(-0.390211\pi\) | ||||
0.338114 | + | 0.941105i | \(0.390211\pi\) | |||||||
\(788\) | −9.45584 | −0.336850 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.65685 | 0.0589482 | ||||||||
\(791\) | 16.6863 | 0.593296 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −90.9117 | −3.22837 | ||||||||
\(794\) | 5.51472 | 0.195710 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −39.5980 | −1.40351 | ||||||||
\(797\) | 12.6274 | 0.447286 | 0.223643 | − | 0.974671i | \(-0.428205\pi\) | ||||
0.223643 | + | 0.974671i | \(0.428205\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.31371 | −0.117231 | ||||||||
\(800\) | 4.41421 | 0.156066 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.17157 | −0.253237 | ||||||||
\(803\) | 6.82843 | 0.240970 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.65685 | 0.199378 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −21.1127 | −0.742742 | ||||||||
\(809\) | −22.9706 | −0.807602 | −0.403801 | − | 0.914847i | \(-0.632311\pi\) | ||||
−0.403801 | + | 0.914847i | \(0.632311\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.9411 | −0.489539 | −0.244770 | − | 0.969581i | \(-0.578712\pi\) | ||||
−0.244770 | + | 0.969581i | \(0.578712\pi\) | |||||||
\(812\) | −28.0000 | −0.982607 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.51472 | −0.0530909 | ||||||||
\(815\) | −0.485281 | −0.0169987 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 14.4853 | 0.506466 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.9706 | 0.383109 | ||||||||
\(821\) | 18.6863 | 0.652156 | 0.326078 | − | 0.945343i | \(-0.394273\pi\) | ||||
0.326078 | + | 0.945343i | \(0.394273\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.4853 | 1.27180 | 0.635898 | − | 0.771773i | \(-0.280630\pi\) | ||||
0.635898 | + | 0.771773i | \(0.280630\pi\) | |||||||
\(824\) | −1.85786 | −0.0647218 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | −0.278356 | ||||||||
\(827\) | 34.2843 | 1.19218 | 0.596090 | − | 0.802917i | \(-0.296720\pi\) | ||||
0.596090 | + | 0.802917i | \(0.296720\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.0000 | 0.625166 | 0.312583 | − | 0.949890i | \(-0.398806\pi\) | ||||
0.312583 | + | 0.949890i | \(0.398806\pi\) | |||||||
\(830\) | 2.48528 | 0.0862654 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 28.4853 | 0.987549 | ||||||||
\(833\) | 3.51472 | 0.121778 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.9706 | −0.379652 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.94113 | 0.205233 | ||||||||
\(839\) | −37.6569 | −1.30006 | −0.650029 | − | 0.759909i | \(-0.725243\pi\) | ||||
−0.650029 | + | 0.759909i | \(0.725243\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.6274 | 1.02164 | ||||||||
\(842\) | −2.48528 | −0.0856485 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 29.2548 | 1.00699 | ||||||||
\(845\) | 33.6274 | 1.15682 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.00000 | −0.0687208 | ||||||||
\(848\) | −1.02944 | −0.0353510 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.485281 | −0.0166450 | ||||||||
\(851\) | −10.3431 | −0.354558 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.4853 | −1.11227 | −0.556137 | − | 0.831090i | \(-0.687717\pi\) | ||||
−0.556137 | + | 0.831090i | \(0.687717\pi\) | |||||||
\(854\) | −11.0294 | −0.377420 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.79899 | −0.198205 | ||||||||
\(857\) | 48.7696 | 1.66594 | 0.832968 | − | 0.553321i | \(-0.186640\pi\) | ||||
0.832968 | + | 0.553321i | \(0.186640\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.2843 | −1.10153 | −0.550763 | − | 0.834662i | \(-0.685663\pi\) | ||||
−0.550763 | + | 0.834662i | \(0.685663\pi\) | |||||||
\(860\) | 10.9706 | 0.374093 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.68629 | −0.159616 | ||||||||
\(863\) | 14.8284 | 0.504766 | 0.252383 | − | 0.967627i | \(-0.418786\pi\) | ||||
0.252383 | + | 0.967627i | \(0.418786\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.14214 | −0.208839 | ||||||||
\(866\) | 1.51472 | 0.0514722 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.00000 | −0.135691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.6274 | 1.03777 | ||||||||
\(872\) | −5.79899 | −0.196379 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.00000 | −0.0676123 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.45584 | 0.0491604 | 0.0245802 | − | 0.999698i | \(-0.492175\pi\) | ||||
0.0245802 | + | 0.999698i | \(0.492175\pi\) | |||||||
\(878\) | −6.62742 | −0.223664 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.00000 | −0.101130 | ||||||||
\(881\) | 52.6274 | 1.77306 | 0.886531 | − | 0.462668i | \(-0.153108\pi\) | ||||
0.886531 | + | 0.462668i | \(0.153108\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.8284 | 1.44129 | 0.720646 | − | 0.693304i | \(-0.243845\pi\) | ||||
0.720646 | + | 0.693304i | \(0.243845\pi\) | |||||||
\(884\) | −14.6274 | −0.491973 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.76955 | 0.294619 | ||||||||
\(887\) | 18.2843 | 0.613926 | 0.306963 | − | 0.951721i | \(-0.400687\pi\) | ||||
0.306963 | + | 0.951721i | \(0.400687\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.3137 | −1.05023 | ||||||||
\(890\) | −3.85786 | −0.129316 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.45584 | 0.316605 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.65685 | 0.0553825 | ||||||||
\(896\) | 21.1127 | 0.705326 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.88730 | 0.229832 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.402020 | 0.0133932 | ||||||||
\(902\) | 2.48528 | 0.0827508 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.2304 | 0.440038 | ||||||||
\(905\) | −1.31371 | −0.0436691 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.4853 | −1.47711 | −0.738555 | − | 0.674193i | \(-0.764491\pi\) | ||||
−0.738555 | + | 0.674193i | \(0.764491\pi\) | |||||||
\(908\) | 4.91169 | 0.163000 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.65685 | 0.187523 | ||||||||
\(911\) | −57.9411 | −1.91968 | −0.959838 | − | 0.280556i | \(-0.909481\pi\) | ||||
−0.959838 | + | 0.280556i | \(0.909481\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.00000 | −0.198571 | ||||||||
\(914\) | −6.82843 | −0.225864 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 38.9706 | 1.28762 | ||||||||
\(917\) | 22.6274 | 0.747223 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.0000 | −1.05558 | −0.527791 | − | 0.849374i | \(-0.676980\pi\) | ||||
−0.527791 | + | 0.849374i | \(0.676980\pi\) | |||||||
\(920\) | 4.48528 | 0.147875 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.5147 | 0.445084 | ||||||||
\(923\) | −77.2548 | −2.54287 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.65685 | 0.120237 | ||||||||
\(926\) | 9.17157 | 0.301397 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −33.7990 | −1.10951 | ||||||||
\(929\) | 17.3137 | 0.568044 | 0.284022 | − | 0.958818i | \(-0.408331\pi\) | ||||
0.284022 | + | 0.958818i | \(0.408331\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 40.4853 | 1.32614 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.79899 | 0.124307 | ||||||||
\(935\) | 1.17157 | 0.0383145 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.4558 | 1.61565 | 0.807826 | − | 0.589421i | \(-0.200644\pi\) | ||||
0.807826 | + | 0.589421i | \(0.200644\pi\) | |||||||
\(938\) | 3.71573 | 0.121323 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.17157 | −0.168678 | ||||||||
\(941\) | 29.3137 | 0.955600 | 0.477800 | − | 0.878469i | \(-0.341434\pi\) | ||||
0.477800 | + | 0.878469i | \(0.341434\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.9706 | 0.552638 | ||||||||
\(944\) | 28.9706 | 0.942912 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.48528 | 0.0808035 | ||||||||
\(947\) | −46.8284 | −1.52172 | −0.760860 | − | 0.648916i | \(-0.775222\pi\) | ||||
−0.760860 | + | 0.648916i | \(0.775222\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 46.6274 | 1.51359 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.71573 | −0.120427 | ||||||||
\(953\) | −58.8284 | −1.90564 | −0.952820 | − | 0.303536i | \(-0.901833\pi\) | ||||
−0.952820 | + | 0.303536i | \(0.901833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.3137 | 0.624977 | ||||||||
\(956\) | −1.25483 | −0.0405842 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.9117 | 0.481775 | ||||||||
\(959\) | 45.9411 | 1.48352 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | −10.3431 | −0.333476 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.9706 | −0.353338 | ||||||||
\(965\) | −6.82843 | −0.219815 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.9706 | 0.610052 | 0.305026 | − | 0.952344i | \(-0.401335\pi\) | ||||
0.305026 | + | 0.952344i | \(0.401335\pi\) | |||||||
\(968\) | −1.58579 | −0.0509691 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.17157 | −0.101833 | ||||||||
\(971\) | 31.3137 | 1.00490 | 0.502452 | − | 0.864605i | \(-0.332431\pi\) | ||||
0.502452 | + | 0.864605i | \(0.332431\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.00000 | 0.256468 | ||||||||
\(974\) | −3.11270 | −0.0997373 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 39.9411 | 1.27848 | ||||||||
\(977\) | −43.6569 | −1.39671 | −0.698353 | − | 0.715753i | \(-0.746084\pi\) | ||||
−0.698353 | + | 0.715753i | \(0.746084\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.31371 | 0.297667 | ||||||||
\(980\) | 5.48528 | 0.175221 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.65685 | 0.308163 | ||||||||
\(983\) | 50.1421 | 1.59929 | 0.799643 | − | 0.600476i | \(-0.205022\pi\) | ||||
0.799643 | + | 0.600476i | \(0.205022\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.17157 | 0.164780 | ||||||||
\(986\) | 3.71573 | 0.118333 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.9706 | 0.539633 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.94113 | 0.315790 | 0.157895 | − | 0.987456i | \(-0.449529\pi\) | ||||
0.157895 | + | 0.987456i | \(0.449529\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.37258 | −0.297280 | ||||||||
\(995\) | 21.6569 | 0.686568 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.45584 | 0.299470 | 0.149735 | − | 0.988726i | \(-0.452158\pi\) | ||||
0.149735 | + | 0.988726i | \(0.452158\pi\) | |||||||
\(998\) | −0.686292 | −0.0217242 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 495.2.a.b.1.2 | 2 | ||
3.2 | odd | 2 | 55.2.a.b.1.1 | ✓ | 2 | ||
4.3 | odd | 2 | 7920.2.a.ch.1.1 | 2 | |||
5.2 | odd | 4 | 2475.2.c.l.199.3 | 4 | |||
5.3 | odd | 4 | 2475.2.c.l.199.2 | 4 | |||
5.4 | even | 2 | 2475.2.a.x.1.1 | 2 | |||
11.10 | odd | 2 | 5445.2.a.y.1.1 | 2 | |||
12.11 | even | 2 | 880.2.a.m.1.1 | 2 | |||
15.2 | even | 4 | 275.2.b.d.199.2 | 4 | |||
15.8 | even | 4 | 275.2.b.d.199.3 | 4 | |||
15.14 | odd | 2 | 275.2.a.c.1.2 | 2 | |||
21.20 | even | 2 | 2695.2.a.f.1.1 | 2 | |||
24.5 | odd | 2 | 3520.2.a.bn.1.1 | 2 | |||
24.11 | even | 2 | 3520.2.a.bo.1.2 | 2 | |||
33.2 | even | 10 | 605.2.g.l.81.1 | 8 | |||
33.5 | odd | 10 | 605.2.g.f.366.2 | 8 | |||
33.8 | even | 10 | 605.2.g.l.251.2 | 8 | |||
33.14 | odd | 10 | 605.2.g.f.251.1 | 8 | |||
33.17 | even | 10 | 605.2.g.l.366.1 | 8 | |||
33.20 | odd | 10 | 605.2.g.f.81.2 | 8 | |||
33.26 | odd | 10 | 605.2.g.f.511.1 | 8 | |||
33.29 | even | 10 | 605.2.g.l.511.2 | 8 | |||
33.32 | even | 2 | 605.2.a.d.1.2 | 2 | |||
39.38 | odd | 2 | 9295.2.a.g.1.2 | 2 | |||
60.23 | odd | 4 | 4400.2.b.q.4049.1 | 4 | |||
60.47 | odd | 4 | 4400.2.b.q.4049.4 | 4 | |||
60.59 | even | 2 | 4400.2.a.bn.1.2 | 2 | |||
132.131 | odd | 2 | 9680.2.a.bn.1.1 | 2 | |||
165.164 | even | 2 | 3025.2.a.o.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.a.b.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
275.2.a.c.1.2 | 2 | 15.14 | odd | 2 | |||
275.2.b.d.199.2 | 4 | 15.2 | even | 4 | |||
275.2.b.d.199.3 | 4 | 15.8 | even | 4 | |||
495.2.a.b.1.2 | 2 | 1.1 | even | 1 | trivial | ||
605.2.a.d.1.2 | 2 | 33.32 | even | 2 | |||
605.2.g.f.81.2 | 8 | 33.20 | odd | 10 | |||
605.2.g.f.251.1 | 8 | 33.14 | odd | 10 | |||
605.2.g.f.366.2 | 8 | 33.5 | odd | 10 | |||
605.2.g.f.511.1 | 8 | 33.26 | odd | 10 | |||
605.2.g.l.81.1 | 8 | 33.2 | even | 10 | |||
605.2.g.l.251.2 | 8 | 33.8 | even | 10 | |||
605.2.g.l.366.1 | 8 | 33.17 | even | 10 | |||
605.2.g.l.511.2 | 8 | 33.29 | even | 10 | |||
880.2.a.m.1.1 | 2 | 12.11 | even | 2 | |||
2475.2.a.x.1.1 | 2 | 5.4 | even | 2 | |||
2475.2.c.l.199.2 | 4 | 5.3 | odd | 4 | |||
2475.2.c.l.199.3 | 4 | 5.2 | odd | 4 | |||
2695.2.a.f.1.1 | 2 | 21.20 | even | 2 | |||
3025.2.a.o.1.1 | 2 | 165.164 | even | 2 | |||
3520.2.a.bn.1.1 | 2 | 24.5 | odd | 2 | |||
3520.2.a.bo.1.2 | 2 | 24.11 | even | 2 | |||
4400.2.a.bn.1.2 | 2 | 60.59 | even | 2 | |||
4400.2.b.q.4049.1 | 4 | 60.23 | odd | 4 | |||
4400.2.b.q.4049.4 | 4 | 60.47 | odd | 4 | |||
5445.2.a.y.1.1 | 2 | 11.10 | odd | 2 | |||
7920.2.a.ch.1.1 | 2 | 4.3 | odd | 2 | |||
9295.2.a.g.1.2 | 2 | 39.38 | odd | 2 | |||
9680.2.a.bn.1.1 | 2 | 132.131 | odd | 2 |