Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2475,2,Mod(1,2475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2475, 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("2475.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2475.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: | \(19.7629745003\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{24})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 495) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.517638\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2475.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.517638 | −0.366025 | −0.183013 | − | 0.983111i | \(-0.558585\pi\) | ||||
−0.183013 | + | 0.983111i | \(0.558585\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.73205 | −0.866025 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.44949 | −0.925820 | −0.462910 | − | 0.886405i | \(-0.653195\pi\) | ||||
−0.462910 | + | 0.886405i | \(0.653195\pi\) | |||||||
\(8\) | 1.93185 | 0.683013 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.24264 | 1.17670 | 0.588348 | − | 0.808608i | \(-0.299778\pi\) | ||||
0.588348 | + | 0.808608i | \(0.299778\pi\) | |||||||
\(14\) | 1.26795 | 0.338874 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.46410 | 0.616025 | ||||||||
\(17\) | 0.378937 | 0.0919058 | 0.0459529 | − | 0.998944i | \(-0.485368\pi\) | ||||
0.0459529 | + | 0.998944i | \(0.485368\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.517638 | 0.110361 | ||||||||
\(23\) | −7.72741 | −1.61128 | −0.805638 | − | 0.592408i | \(-0.798177\pi\) | ||||
−0.805638 | + | 0.592408i | \(0.798177\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.19615 | −0.430701 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.24264 | 0.801784 | ||||||||
\(29\) | 2.53590 | 0.470905 | 0.235452 | − | 0.971886i | \(-0.424343\pi\) | ||||
0.235452 | + | 0.971886i | \(0.424343\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.535898 | −0.0962502 | −0.0481251 | − | 0.998841i | \(-0.515325\pi\) | ||||
−0.0481251 | + | 0.998841i | \(0.515325\pi\) | |||||||
\(32\) | −5.13922 | −0.908494 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.196152 | −0.0336399 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.89898 | −0.805387 | −0.402694 | − | 0.915335i | \(-0.631926\pi\) | ||||
−0.402694 | + | 0.915335i | \(0.631926\pi\) | |||||||
\(38\) | 1.03528 | 0.167944 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.53590 | 0.396041 | 0.198020 | − | 0.980198i | \(-0.436549\pi\) | ||||
0.198020 | + | 0.980198i | \(0.436549\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.9348 | −1.66754 | −0.833768 | − | 0.552114i | \(-0.813821\pi\) | ||||
−0.833768 | + | 0.552114i | \(0.813821\pi\) | |||||||
\(44\) | 1.73205 | 0.261116 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.00000 | 0.589768 | ||||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.34847 | −1.01905 | ||||||||
\(53\) | 10.5558 | 1.44996 | 0.724978 | − | 0.688772i | \(-0.241850\pi\) | ||||
0.724978 | + | 0.688772i | \(0.241850\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.73205 | −0.632347 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.31268 | −0.172363 | ||||||||
\(59\) | 12.9282 | 1.68311 | 0.841554 | − | 0.540172i | \(-0.181641\pi\) | ||||
0.841554 | + | 0.540172i | \(0.181641\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.92820 | −0.630992 | −0.315496 | − | 0.948927i | \(-0.602171\pi\) | ||||
−0.315496 | + | 0.948927i | \(0.602171\pi\) | |||||||
\(62\) | 0.277401 | 0.0352300 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.26795 | −0.283494 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.58630 | 0.438137 | 0.219068 | − | 0.975710i | \(-0.429698\pi\) | ||||
0.219068 | + | 0.975710i | \(0.429698\pi\) | |||||||
\(68\) | −0.656339 | −0.0795928 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.656339 | 0.0768186 | 0.0384093 | − | 0.999262i | \(-0.487771\pi\) | ||||
0.0384093 | + | 0.999262i | \(0.487771\pi\) | |||||||
\(74\) | 2.53590 | 0.294792 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.46410 | 0.397360 | ||||||||
\(77\) | 2.44949 | 0.279145 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.8564 | 1.33395 | 0.666975 | − | 0.745080i | \(-0.267589\pi\) | ||||
0.666975 | + | 0.745080i | \(0.267589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.31268 | −0.144961 | ||||||||
\(83\) | −7.07107 | −0.776151 | −0.388075 | − | 0.921628i | \(-0.626860\pi\) | ||||
−0.388075 | + | 0.921628i | \(0.626860\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.66025 | 0.610361 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.93185 | −0.205936 | ||||||||
\(89\) | 15.4641 | 1.63919 | 0.819596 | − | 0.572942i | \(-0.194198\pi\) | ||||
0.819596 | + | 0.572942i | \(0.194198\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.3923 | −1.08941 | ||||||||
\(92\) | 13.3843 | 1.39541 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.46410 | −0.151011 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.3843 | 1.35897 | 0.679483 | − | 0.733691i | \(-0.262204\pi\) | ||||
0.679483 | + | 0.733691i | \(0.262204\pi\) | |||||||
\(98\) | 0.517638 | 0.0522893 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.3923 | 1.63110 | 0.815548 | − | 0.578690i | \(-0.196436\pi\) | ||||
0.815548 | + | 0.578690i | \(0.196436\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.48528 | −0.836080 | −0.418040 | − | 0.908429i | \(-0.637283\pi\) | ||||
−0.418040 | + | 0.908429i | \(0.637283\pi\) | |||||||
\(104\) | 8.19615 | 0.803699 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.46410 | −0.530720 | ||||||||
\(107\) | −1.41421 | −0.136717 | −0.0683586 | − | 0.997661i | \(-0.521776\pi\) | ||||
−0.0683586 | + | 0.997661i | \(0.521776\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.03579 | −0.570329 | ||||||||
\(113\) | 5.65685 | 0.532152 | 0.266076 | − | 0.963952i | \(-0.414273\pi\) | ||||
0.266076 | + | 0.963952i | \(0.414273\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.39230 | −0.407815 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.69213 | −0.616061 | ||||||||
\(119\) | −0.928203 | −0.0850883 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.55103 | 0.230959 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.928203 | 0.0833551 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.1464 | 1.52150 | 0.760750 | − | 0.649045i | \(-0.224831\pi\) | ||||
0.760750 | + | 0.649045i | \(0.224831\pi\) | |||||||
\(128\) | 11.4524 | 1.01226 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.8564 | 1.21064 | 0.605320 | − | 0.795982i | \(-0.293045\pi\) | ||||
0.605320 | + | 0.795982i | \(0.293045\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.89898 | 0.424795 | ||||||||
\(134\) | −1.85641 | −0.160369 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.732051 | 0.0627728 | ||||||||
\(137\) | −6.96953 | −0.595447 | −0.297724 | − | 0.954652i | \(-0.596227\pi\) | ||||
−0.297724 | + | 0.954652i | \(0.596227\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.00000 | −0.169638 | −0.0848189 | − | 0.996396i | \(-0.527031\pi\) | ||||
−0.0848189 | + | 0.996396i | \(0.527031\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.10583 | −0.260635 | ||||||||
\(143\) | −4.24264 | −0.354787 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.339746 | −0.0281176 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.48528 | 0.697486 | ||||||||
\(149\) | 23.3205 | 1.91049 | 0.955245 | − | 0.295815i | \(-0.0955912\pi\) | ||||
0.955245 | + | 0.295815i | \(0.0955912\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.7846 | −1.52867 | −0.764335 | − | 0.644819i | \(-0.776933\pi\) | ||||
−0.764335 | + | 0.644819i | \(0.776933\pi\) | |||||||
\(152\) | −3.86370 | −0.313388 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.26795 | −0.102174 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.2832 | −1.45916 | −0.729581 | − | 0.683895i | \(-0.760285\pi\) | ||||
−0.729581 | + | 0.683895i | \(0.760285\pi\) | |||||||
\(158\) | −6.13733 | −0.488260 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.9282 | 1.49175 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.31268 | 0.102817 | 0.0514084 | − | 0.998678i | \(-0.483629\pi\) | ||||
0.0514084 | + | 0.998678i | \(0.483629\pi\) | |||||||
\(164\) | −4.39230 | −0.342981 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.66025 | 0.284091 | ||||||||
\(167\) | −23.2838 | −1.80175 | −0.900876 | − | 0.434077i | \(-0.857074\pi\) | ||||
−0.900876 | + | 0.434077i | \(0.857074\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 18.9396 | 1.44413 | ||||||||
\(173\) | −18.6622 | −1.41886 | −0.709430 | − | 0.704776i | \(-0.751047\pi\) | ||||
−0.709430 | + | 0.704776i | \(0.751047\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.46410 | −0.185739 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.00481 | −0.599986 | ||||||||
\(179\) | 6.92820 | 0.517838 | 0.258919 | − | 0.965899i | \(-0.416634\pi\) | ||||
0.258919 | + | 0.965899i | \(0.416634\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.7846 | 1.24759 | 0.623795 | − | 0.781588i | \(-0.285590\pi\) | ||||
0.623795 | + | 0.781588i | \(0.285590\pi\) | |||||||
\(182\) | 5.37945 | 0.398752 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −14.9282 | −1.10052 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.378937 | −0.0277106 | ||||||||
\(188\) | −4.89898 | −0.357295 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.8564 | −1.00261 | −0.501307 | − | 0.865269i | \(-0.667147\pi\) | ||||
−0.501307 | + | 0.865269i | \(0.667147\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.14162 | 0.658028 | 0.329014 | − | 0.944325i | \(-0.393284\pi\) | ||||
0.329014 | + | 0.944325i | \(0.393284\pi\) | |||||||
\(194\) | −6.92820 | −0.497416 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.73205 | 0.123718 | ||||||||
\(197\) | 16.3886 | 1.16764 | 0.583818 | − | 0.811885i | \(-0.301558\pi\) | ||||
0.583818 | + | 0.811885i | \(0.301558\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.00000 | 0.283552 | 0.141776 | − | 0.989899i | \(-0.454719\pi\) | ||||
0.141776 | + | 0.989899i | \(0.454719\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.48528 | −0.597022 | ||||||||
\(203\) | −6.21166 | −0.435973 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.39230 | 0.306026 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.4543 | 0.724875 | ||||||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.8564 | 1.09160 | 0.545800 | − | 0.837915i | \(-0.316226\pi\) | ||||
0.545800 | + | 0.837915i | \(0.316226\pi\) | |||||||
\(212\) | −18.2832 | −1.25570 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.732051 | 0.0500420 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.31268 | 0.0891104 | ||||||||
\(218\) | −5.17638 | −0.350589 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.60770 | 0.108145 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.6969 | 0.984180 | 0.492090 | − | 0.870544i | \(-0.336233\pi\) | ||||
0.492090 | + | 0.870544i | \(0.336233\pi\) | |||||||
\(224\) | 12.5885 | 0.841102 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.92820 | −0.194781 | ||||||||
\(227\) | −11.2122 | −0.744178 | −0.372089 | − | 0.928197i | \(-0.621358\pi\) | ||||
−0.372089 | + | 0.928197i | \(0.621358\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.8564 | −1.84080 | −0.920402 | − | 0.390974i | \(-0.872138\pi\) | ||||
−0.920402 | + | 0.390974i | \(0.872138\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.89898 | 0.321634 | ||||||||
\(233\) | 21.4906 | 1.40790 | 0.703948 | − | 0.710251i | \(-0.251419\pi\) | ||||
0.703948 | + | 0.710251i | \(0.251419\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −22.3923 | −1.45761 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.480473 | 0.0311445 | ||||||||
\(239\) | 13.8564 | 0.896296 | 0.448148 | − | 0.893959i | \(-0.352084\pi\) | ||||
0.448148 | + | 0.893959i | \(0.352084\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.92820 | 0.575116 | 0.287558 | − | 0.957763i | \(-0.407157\pi\) | ||||
0.287558 | + | 0.957763i | \(0.407157\pi\) | |||||||
\(242\) | −0.517638 | −0.0332750 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.53590 | 0.546455 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.48528 | −0.539906 | ||||||||
\(248\) | −1.03528 | −0.0657401 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.0000 | 1.13615 | 0.568075 | − | 0.822977i | \(-0.307688\pi\) | ||||
0.568075 | + | 0.822977i | \(0.307688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.72741 | 0.485818 | ||||||||
\(254\) | −8.87564 | −0.556907 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.39230 | −0.0870191 | ||||||||
\(257\) | 27.3233 | 1.70438 | 0.852191 | − | 0.523231i | \(-0.175273\pi\) | ||||
0.852191 | + | 0.523231i | \(0.175273\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.0000 | 0.745644 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.17260 | −0.443125 | ||||||||
\(263\) | 24.5964 | 1.51668 | 0.758341 | − | 0.651859i | \(-0.226010\pi\) | ||||
0.758341 | + | 0.651859i | \(0.226010\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.53590 | −0.155486 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.21166 | −0.379437 | ||||||||
\(269\) | −1.85641 | −0.113187 | −0.0565935 | − | 0.998397i | \(-0.518024\pi\) | ||||
−0.0565935 | + | 0.998397i | \(0.518024\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.92820 | −0.299367 | −0.149684 | − | 0.988734i | \(-0.547825\pi\) | ||||
−0.149684 | + | 0.988734i | \(0.547825\pi\) | |||||||
\(272\) | 0.933740 | 0.0566163 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.60770 | 0.217949 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.3533 | 0.922489 | 0.461245 | − | 0.887273i | \(-0.347403\pi\) | ||||
0.461245 | + | 0.887273i | \(0.347403\pi\) | |||||||
\(278\) | 1.03528 | 0.0620917 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.3205 | −1.39118 | −0.695592 | − | 0.718437i | \(-0.744858\pi\) | ||||
−0.695592 | + | 0.718437i | \(0.744858\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.13681 | 0.0675765 | 0.0337882 | − | 0.999429i | \(-0.489243\pi\) | ||||
0.0337882 | + | 0.999429i | \(0.489243\pi\) | |||||||
\(284\) | −10.3923 | −0.616670 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.19615 | 0.129861 | ||||||||
\(287\) | −6.21166 | −0.366663 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8564 | −0.991553 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.13681 | −0.0665269 | ||||||||
\(293\) | 8.10634 | 0.473578 | 0.236789 | − | 0.971561i | \(-0.423905\pi\) | ||||
0.236789 | + | 0.971561i | \(0.423905\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.46410 | −0.550090 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.0716 | −0.699288 | ||||||||
\(299\) | −32.7846 | −1.89598 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.7846 | 1.54384 | ||||||||
\(302\) | 9.72363 | 0.559532 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.92820 | −0.282652 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.03579 | −0.344481 | −0.172240 | − | 0.985055i | \(-0.555101\pi\) | ||||
−0.172240 | + | 0.985055i | \(0.555101\pi\) | |||||||
\(308\) | −4.24264 | −0.241747 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.0718 | 0.627824 | 0.313912 | − | 0.949452i | \(-0.398360\pi\) | ||||
0.313912 | + | 0.949452i | \(0.398360\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.8695 | −1.23614 | −0.618070 | − | 0.786123i | \(-0.712085\pi\) | ||||
−0.618070 | + | 0.786123i | \(0.712085\pi\) | |||||||
\(314\) | 9.46410 | 0.534090 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.5359 | −1.15523 | ||||||||
\(317\) | −12.8295 | −0.720574 | −0.360287 | − | 0.932841i | \(-0.617321\pi\) | ||||
−0.360287 | + | 0.932841i | \(0.617321\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.53590 | −0.141983 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.79796 | −0.546019 | ||||||||
\(323\) | −0.757875 | −0.0421693 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.679492 | −0.0376336 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.89898 | 0.270501 | ||||||||
\(329\) | −6.92820 | −0.381964 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.39230 | −0.131493 | −0.0657465 | − | 0.997836i | \(-0.520943\pi\) | ||||
−0.0657465 | + | 0.997836i | \(0.520943\pi\) | |||||||
\(332\) | 12.2474 | 0.672166 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.0526 | 0.659487 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.82894 | −0.426470 | −0.213235 | − | 0.977001i | \(-0.568400\pi\) | ||||
−0.213235 | + | 0.977001i | \(0.568400\pi\) | |||||||
\(338\) | −2.58819 | −0.140779 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.535898 | 0.0290205 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5959 | 1.05808 | ||||||||
\(344\) | −21.1244 | −1.13895 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.66025 | 0.519338 | ||||||||
\(347\) | 24.0416 | 1.29062 | 0.645311 | − | 0.763920i | \(-0.276728\pi\) | ||||
0.645311 | + | 0.763920i | \(0.276728\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.9282 | −1.76261 | −0.881303 | − | 0.472551i | \(-0.843333\pi\) | ||||
−0.881303 | + | 0.472551i | \(0.843333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.13922 | 0.273921 | ||||||||
\(353\) | 3.38323 | 0.180071 | 0.0900356 | − | 0.995939i | \(-0.471302\pi\) | ||||
0.0900356 | + | 0.995939i | \(0.471302\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −26.7846 | −1.41958 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.58630 | −0.189542 | ||||||||
\(359\) | −18.9282 | −0.998992 | −0.499496 | − | 0.866316i | \(-0.666482\pi\) | ||||
−0.499496 | + | 0.866316i | \(0.666482\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | −8.68835 | −0.456650 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 18.0000 | 0.943456 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.8695 | 1.14158 | 0.570790 | − | 0.821096i | \(-0.306637\pi\) | ||||
0.570790 | + | 0.821096i | \(0.306637\pi\) | |||||||
\(368\) | −19.0411 | −0.992587 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −25.8564 | −1.34240 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.4152 | 0.591059 | 0.295529 | − | 0.955334i | \(-0.404504\pi\) | ||||
0.295529 | + | 0.955334i | \(0.404504\pi\) | |||||||
\(374\) | 0.196152 | 0.0101428 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.46410 | 0.281790 | ||||||||
\(377\) | 10.7589 | 0.554112 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.14359 | −0.315575 | −0.157788 | − | 0.987473i | \(-0.550436\pi\) | ||||
−0.157788 | + | 0.987473i | \(0.550436\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.17260 | 0.366982 | ||||||||
\(383\) | 3.38323 | 0.172875 | 0.0864375 | − | 0.996257i | \(-0.472452\pi\) | ||||
0.0864375 | + | 0.996257i | \(0.472452\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.73205 | −0.240855 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −23.1822 | −1.17690 | ||||||||
\(389\) | 6.92820 | 0.351274 | 0.175637 | − | 0.984455i | \(-0.443802\pi\) | ||||
0.175637 | + | 0.984455i | \(0.443802\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.92820 | −0.148086 | ||||||||
\(392\) | −1.93185 | −0.0975732 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.48334 | −0.427384 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.5569 | −1.03172 | −0.515860 | − | 0.856673i | \(-0.672527\pi\) | ||||
−0.515860 | + | 0.856673i | \(0.672527\pi\) | |||||||
\(398\) | −2.07055 | −0.103787 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.3205 | 0.864945 | 0.432472 | − | 0.901647i | \(-0.357641\pi\) | ||||
0.432472 | + | 0.901647i | \(0.357641\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.27362 | −0.113257 | ||||||||
\(404\) | −28.3923 | −1.41257 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.21539 | 0.159577 | ||||||||
\(407\) | 4.89898 | 0.242833 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.0718 | 0.745252 | 0.372626 | − | 0.927982i | \(-0.378457\pi\) | ||||
0.372626 | + | 0.927982i | \(0.378457\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.6969 | 0.724066 | ||||||||
\(413\) | −31.6675 | −1.55826 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −21.8038 | −1.06902 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.03528 | −0.0506370 | ||||||||
\(419\) | −6.92820 | −0.338465 | −0.169232 | − | 0.985576i | \(-0.554129\pi\) | ||||
−0.169232 | + | 0.985576i | \(0.554129\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.07180 | −0.442132 | −0.221066 | − | 0.975259i | \(-0.570954\pi\) | ||||
−0.221066 | + | 0.975259i | \(0.570954\pi\) | |||||||
\(422\) | −8.20788 | −0.399553 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 20.3923 | 0.990338 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.0716 | 0.584185 | ||||||||
\(428\) | 2.44949 | 0.118401 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.7128 | 1.33488 | 0.667440 | − | 0.744664i | \(-0.267390\pi\) | ||||
0.667440 | + | 0.744664i | \(0.267390\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.9802 | 1.58493 | 0.792463 | − | 0.609920i | \(-0.208798\pi\) | ||||
0.792463 | + | 0.609920i | \(0.208798\pi\) | |||||||
\(434\) | −0.679492 | −0.0326167 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.3205 | −0.829502 | ||||||||
\(437\) | 15.4548 | 0.739304 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.8564 | 1.71133 | 0.855666 | − | 0.517528i | \(-0.173148\pi\) | ||||
0.855666 | + | 0.517528i | \(0.173148\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.832204 | −0.0395839 | ||||||||
\(443\) | −9.04008 | −0.429507 | −0.214754 | − | 0.976668i | \(-0.568895\pi\) | ||||
−0.214754 | + | 0.976668i | \(0.568895\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.60770 | −0.360235 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.55532 | 0.262464 | ||||||||
\(449\) | −15.4641 | −0.729796 | −0.364898 | − | 0.931047i | \(-0.618896\pi\) | ||||
−0.364898 | + | 0.931047i | \(0.618896\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.53590 | −0.119411 | ||||||||
\(452\) | −9.79796 | −0.460857 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.80385 | 0.272388 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.4543 | −0.489031 | −0.244516 | − | 0.969645i | \(-0.578629\pi\) | ||||
−0.244516 | + | 0.969645i | \(0.578629\pi\) | |||||||
\(458\) | 14.4195 | 0.673781 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.60770 | 0.354326 | 0.177163 | − | 0.984182i | \(-0.443308\pi\) | ||||
0.177163 | + | 0.984182i | \(0.443308\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.52433 | −0.349685 | −0.174843 | − | 0.984596i | \(-0.555942\pi\) | ||||
−0.174843 | + | 0.984596i | \(0.555942\pi\) | |||||||
\(464\) | 6.24871 | 0.290089 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.1244 | −0.515326 | ||||||||
\(467\) | −31.4644 | −1.45600 | −0.728000 | − | 0.685577i | \(-0.759550\pi\) | ||||
−0.728000 | + | 0.685577i | \(0.759550\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.78461 | −0.405636 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 24.9754 | 1.14958 | ||||||||
\(473\) | 10.9348 | 0.502781 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.60770 | 0.0736886 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.17260 | −0.328067 | ||||||||
\(479\) | −17.0718 | −0.780030 | −0.390015 | − | 0.920808i | \(-0.627530\pi\) | ||||
−0.390015 | + | 0.920808i | \(0.627530\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.7846 | −0.947697 | ||||||||
\(482\) | −4.62158 | −0.210507 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.73205 | −0.0787296 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.1528 | 1.81950 | 0.909748 | − | 0.415161i | \(-0.136275\pi\) | ||||
0.909748 | + | 0.415161i | \(0.136275\pi\) | |||||||
\(488\) | −9.52056 | −0.430975 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.8564 | −0.625331 | −0.312665 | − | 0.949863i | \(-0.601222\pi\) | ||||
−0.312665 | + | 0.949863i | \(0.601222\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.960947 | 0.0432789 | ||||||||
\(494\) | 4.39230 | 0.197619 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.32051 | −0.0592926 | ||||||||
\(497\) | −14.6969 | −0.659248 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.0000 | 0.716258 | 0.358129 | − | 0.933672i | \(-0.383415\pi\) | ||||
0.358129 | + | 0.933672i | \(0.383415\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.31749 | −0.415860 | ||||||||
\(503\) | 25.9091 | 1.15523 | 0.577615 | − | 0.816309i | \(-0.303983\pi\) | ||||
0.577615 | + | 0.816309i | \(0.303983\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.00000 | −0.177822 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −29.6985 | −1.31766 | ||||||||
\(509\) | −1.85641 | −0.0822838 | −0.0411419 | − | 0.999153i | \(-0.513100\pi\) | ||||
−0.0411419 | + | 0.999153i | \(0.513100\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.60770 | −0.0711202 | ||||||||
\(512\) | −22.1841 | −0.980408 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.1436 | −0.623847 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.82843 | −0.124394 | ||||||||
\(518\) | −6.21166 | −0.272925 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.3205 | 0.758825 | 0.379413 | − | 0.925228i | \(-0.376126\pi\) | ||||
0.379413 | + | 0.925228i | \(0.376126\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.9053 | −1.22022 | −0.610108 | − | 0.792319i | \(-0.708874\pi\) | ||||
−0.610108 | + | 0.792319i | \(0.708874\pi\) | |||||||
\(524\) | −24.0000 | −1.04844 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.7321 | −0.555144 | ||||||||
\(527\) | −0.203072 | −0.00884595 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 36.7128 | 1.59621 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.48528 | −0.367884 | ||||||||
\(533\) | 10.7589 | 0.466020 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.92820 | 0.299253 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.960947 | 0.0414294 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.7846 | 1.49551 | 0.747754 | − | 0.663976i | \(-0.231132\pi\) | ||||
0.747754 | + | 0.663976i | \(0.231132\pi\) | |||||||
\(542\) | 2.55103 | 0.109576 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.94744 | −0.0834958 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.7327 | −0.886468 | −0.443234 | − | 0.896406i | \(-0.646169\pi\) | ||||
−0.443234 | + | 0.896406i | \(0.646169\pi\) | |||||||
\(548\) | 12.0716 | 0.515672 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.07180 | −0.216066 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −29.0421 | −1.23500 | ||||||||
\(554\) | −7.94744 | −0.337654 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.46410 | 0.146911 | ||||||||
\(557\) | 1.69161 | 0.0716760 | 0.0358380 | − | 0.999358i | \(-0.488590\pi\) | ||||
0.0358380 | + | 0.999358i | \(0.488590\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −46.3923 | −1.96219 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.0716 | 0.509209 | ||||||||
\(563\) | 1.41421 | 0.0596020 | 0.0298010 | − | 0.999556i | \(-0.490513\pi\) | ||||
0.0298010 | + | 0.999556i | \(0.490513\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.588457 | −0.0247347 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.5911 | 0.486352 | ||||||||
\(569\) | 2.53590 | 0.106310 | 0.0531552 | − | 0.998586i | \(-0.483072\pi\) | ||||
0.0531552 | + | 0.998586i | \(0.483072\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.92820 | −0.206239 | −0.103119 | − | 0.994669i | \(-0.532882\pi\) | ||||
−0.103119 | + | 0.994669i | \(0.532882\pi\) | |||||||
\(572\) | 7.34847 | 0.307255 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.21539 | 0.134208 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.2538 | −1.46764 | −0.733818 | − | 0.679347i | \(-0.762263\pi\) | ||||
−0.733818 | + | 0.679347i | \(0.762263\pi\) | |||||||
\(578\) | 8.72552 | 0.362934 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.3205 | 0.718576 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.5558 | −0.437178 | ||||||||
\(584\) | 1.26795 | 0.0524681 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.19615 | −0.173341 | ||||||||
\(587\) | 10.3528 | 0.427304 | 0.213652 | − | 0.976910i | \(-0.431464\pi\) | ||||
0.213652 | + | 0.976910i | \(0.431464\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.07180 | 0.0441626 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.0716 | −0.496139 | ||||||||
\(593\) | −27.1475 | −1.11481 | −0.557406 | − | 0.830240i | \(-0.688203\pi\) | ||||
−0.557406 | + | 0.830240i | \(0.688203\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −40.3923 | −1.65453 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16.9706 | 0.693978 | ||||||||
\(599\) | −29.0718 | −1.18784 | −0.593921 | − | 0.804524i | \(-0.702421\pi\) | ||||
−0.593921 | + | 0.804524i | \(0.702421\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0000 | 0.571072 | 0.285536 | − | 0.958368i | \(-0.407828\pi\) | ||||
0.285536 | + | 0.958368i | \(0.407828\pi\) | |||||||
\(602\) | −13.8647 | −0.565084 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 32.5359 | 1.32387 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.8728 | −0.603668 | −0.301834 | − | 0.953360i | \(-0.597599\pi\) | ||||
−0.301834 | + | 0.953360i | \(0.597599\pi\) | |||||||
\(608\) | 10.2784 | 0.416845 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.0000 | 0.485468 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.5259 | 0.909812 | 0.454906 | − | 0.890540i | \(-0.349673\pi\) | ||||
0.454906 | + | 0.890540i | \(0.349673\pi\) | |||||||
\(614\) | 3.12436 | 0.126089 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.73205 | 0.190660 | ||||||||
\(617\) | 11.3137 | 0.455473 | 0.227736 | − | 0.973723i | \(-0.426868\pi\) | ||||
0.227736 | + | 0.973723i | \(0.426868\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.3923 | −0.739249 | −0.369625 | − | 0.929181i | \(-0.620514\pi\) | ||||
−0.369625 | + | 0.929181i | \(0.620514\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.73118 | −0.229800 | ||||||||
\(623\) | −37.8792 | −1.51760 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 11.3205 | 0.452459 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 31.6675 | 1.26367 | ||||||||
\(629\) | −1.85641 | −0.0740198 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.85641 | 0.392377 | 0.196189 | − | 0.980566i | \(-0.437143\pi\) | ||||
0.196189 | + | 0.980566i | \(0.437143\pi\) | |||||||
\(632\) | 22.9048 | 0.911105 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.64102 | 0.263748 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.24264 | −0.168100 | ||||||||
\(638\) | 1.31268 | 0.0519694 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.4641 | −0.610795 | −0.305398 | − | 0.952225i | \(-0.598789\pi\) | ||||
−0.305398 | + | 0.952225i | \(0.598789\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.85993 | 0.231093 | 0.115546 | − | 0.993302i | \(-0.463138\pi\) | ||||
0.115546 | + | 0.993302i | \(0.463138\pi\) | |||||||
\(644\) | −32.7846 | −1.29189 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.392305 | 0.0154350 | ||||||||
\(647\) | 23.3853 | 0.919371 | 0.459685 | − | 0.888082i | \(-0.347962\pi\) | ||||
0.459685 | + | 0.888082i | \(0.347962\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.9282 | −0.507476 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.27362 | −0.0890420 | ||||||||
\(653\) | −5.10205 | −0.199659 | −0.0998294 | − | 0.995005i | \(-0.531830\pi\) | ||||
−0.0998294 | + | 0.995005i | \(0.531830\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.24871 | 0.243971 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.58630 | 0.139809 | ||||||||
\(659\) | −30.9282 | −1.20479 | −0.602396 | − | 0.798197i | \(-0.705787\pi\) | ||||
−0.602396 | + | 0.798197i | \(0.705787\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0000 | 0.544537 | 0.272268 | − | 0.962221i | \(-0.412226\pi\) | ||||
0.272268 | + | 0.962221i | \(0.412226\pi\) | |||||||
\(662\) | 1.23835 | 0.0481298 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.6603 | −0.530121 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.5959 | −0.758757 | ||||||||
\(668\) | 40.3286 | 1.56036 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.92820 | 0.190251 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.656339 | 0.0253000 | 0.0126500 | − | 0.999920i | \(-0.495973\pi\) | ||||
0.0126500 | + | 0.999920i | \(0.495973\pi\) | |||||||
\(674\) | 4.05256 | 0.156099 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.66025 | −0.333087 | ||||||||
\(677\) | −42.3992 | −1.62953 | −0.814767 | − | 0.579789i | \(-0.803135\pi\) | ||||
−0.814767 | + | 0.579789i | \(0.803135\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −32.7846 | −1.25816 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.277401 | −0.0106222 | ||||||||
\(683\) | −15.2517 | −0.583592 | −0.291796 | − | 0.956481i | \(-0.594253\pi\) | ||||
−0.291796 | + | 0.956481i | \(0.594253\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10.1436 | −0.387284 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −26.9444 | −1.02725 | ||||||||
\(689\) | 44.7846 | 1.70616 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.8564 | −0.679290 | −0.339645 | − | 0.940554i | \(-0.610307\pi\) | ||||
−0.339645 | + | 0.940554i | \(0.610307\pi\) | |||||||
\(692\) | 32.3238 | 1.22877 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.4449 | −0.472401 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.960947 | 0.0363985 | ||||||||
\(698\) | 17.0449 | 0.645159 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.4641 | 1.26392 | 0.631961 | − | 0.775000i | \(-0.282250\pi\) | ||||
0.631961 | + | 0.775000i | \(0.282250\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.79796 | 0.369537 | ||||||||
\(704\) | 2.26795 | 0.0854766 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.75129 | −0.0659106 | ||||||||
\(707\) | −40.1528 | −1.51010 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.7846 | −1.08103 | −0.540514 | − | 0.841335i | \(-0.681770\pi\) | ||||
−0.540514 | + | 0.841335i | \(0.681770\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 29.8744 | 1.11959 | ||||||||
\(713\) | 4.14110 | 0.155086 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.79796 | 0.365657 | ||||||||
\(719\) | −41.5692 | −1.55027 | −0.775135 | − | 0.631795i | \(-0.782318\pi\) | ||||
−0.775135 | + | 0.631795i | \(0.782318\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.7846 | 0.774059 | ||||||||
\(722\) | 7.76457 | 0.288967 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −29.0718 | −1.08044 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.17260 | −0.266017 | −0.133009 | − | 0.991115i | \(-0.542464\pi\) | ||||
−0.133009 | + | 0.991115i | \(0.542464\pi\) | |||||||
\(728\) | −20.0764 | −0.744081 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.14359 | −0.153256 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.18067 | −0.302160 | −0.151080 | − | 0.988522i | \(-0.548275\pi\) | ||||
−0.151080 | + | 0.988522i | \(0.548275\pi\) | |||||||
\(734\) | −11.3205 | −0.417848 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 39.7128 | 1.46383 | ||||||||
\(737\) | −3.58630 | −0.132103 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.8564 | 1.31900 | 0.659500 | − | 0.751705i | \(-0.270768\pi\) | ||||
0.659500 | + | 0.751705i | \(0.270768\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.3843 | 0.491352 | ||||||||
\(743\) | 24.5964 | 0.902356 | 0.451178 | − | 0.892434i | \(-0.351004\pi\) | ||||
0.451178 | + | 0.892434i | \(0.351004\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.90897 | −0.216343 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.656339 | 0.0239981 | ||||||||
\(749\) | 3.46410 | 0.126576 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.1436 | −0.516107 | −0.258054 | − | 0.966131i | \(-0.583081\pi\) | ||||
−0.258054 | + | 0.966131i | \(0.583081\pi\) | |||||||
\(752\) | 6.96953 | 0.254153 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.56922 | −0.202819 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.8792 | −1.37674 | −0.688371 | − | 0.725359i | \(-0.741674\pi\) | ||||
−0.688371 | + | 0.725359i | \(0.741674\pi\) | |||||||
\(758\) | 3.18016 | 0.115509 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.24871 | −0.226516 | −0.113258 | − | 0.993566i | \(-0.536129\pi\) | ||||
−0.113258 | + | 0.993566i | \(0.536129\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.4949 | −0.886775 | ||||||||
\(764\) | 24.0000 | 0.868290 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.75129 | −0.0632766 | ||||||||
\(767\) | 54.8497 | 1.98051 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.7128 | 1.35996 | 0.679979 | − | 0.733231i | \(-0.261989\pi\) | ||||
0.679979 | + | 0.733231i | \(0.261989\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15.8338 | −0.569869 | ||||||||
\(773\) | −41.6685 | −1.49871 | −0.749356 | − | 0.662167i | \(-0.769637\pi\) | ||||
−0.749356 | + | 0.662167i | \(0.769637\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 25.8564 | 0.928191 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.58630 | −0.128575 | ||||||||
\(779\) | −5.07180 | −0.181716 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.00000 | −0.214697 | ||||||||
\(782\) | 1.51575 | 0.0542031 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.46410 | −0.0880036 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.5307 | −1.08830 | −0.544151 | − | 0.838987i | \(-0.683148\pi\) | ||||
−0.544151 | + | 0.838987i | \(0.683148\pi\) | |||||||
\(788\) | −28.3858 | −1.01120 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.8564 | −0.492677 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.9086 | −0.742486 | ||||||||
\(794\) | 10.6410 | 0.377636 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.92820 | −0.245564 | ||||||||
\(797\) | −52.0213 | −1.84269 | −0.921344 | − | 0.388747i | \(-0.872908\pi\) | ||||
−0.921344 | + | 0.388747i | \(0.872908\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.07180 | 0.0379174 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.96575 | −0.316592 | ||||||||
\(803\) | −0.656339 | −0.0231617 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.17691 | 0.0414550 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 31.6675 | 1.11406 | ||||||||
\(809\) | 9.46410 | 0.332740 | 0.166370 | − | 0.986063i | \(-0.446795\pi\) | ||||
0.166370 | + | 0.986063i | \(0.446795\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.0000 | 0.491606 | 0.245803 | − | 0.969320i | \(-0.420948\pi\) | ||||
0.245803 | + | 0.969320i | \(0.420948\pi\) | |||||||
\(812\) | 10.7589 | 0.377564 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.53590 | −0.0888832 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.8695 | 0.765118 | ||||||||
\(818\) | −7.80174 | −0.272781 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.1769 | −1.29748 | −0.648742 | − | 0.761009i | \(-0.724704\pi\) | ||||
−0.648742 | + | 0.761009i | \(0.724704\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.2538 | −1.22887 | −0.614435 | − | 0.788967i | \(-0.710616\pi\) | ||||
−0.614435 | + | 0.788967i | \(0.710616\pi\) | |||||||
\(824\) | −16.3923 | −0.571053 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.3923 | 0.570361 | ||||||||
\(827\) | 19.4944 | 0.677886 | 0.338943 | − | 0.940807i | \(-0.389931\pi\) | ||||
0.338943 | + | 0.940807i | \(0.389931\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.7846 | −0.582954 | −0.291477 | − | 0.956578i | \(-0.594147\pi\) | ||||
−0.291477 | + | 0.956578i | \(0.594147\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9.62209 | −0.333586 | ||||||||
\(833\) | −0.378937 | −0.0131294 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.46410 | −0.119808 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.58630 | 0.123887 | ||||||||
\(839\) | 14.7846 | 0.510421 | 0.255211 | − | 0.966885i | \(-0.417855\pi\) | ||||
0.255211 | + | 0.966885i | \(0.417855\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.5692 | −0.778249 | ||||||||
\(842\) | 4.69591 | 0.161832 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −27.4641 | −0.945353 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.44949 | −0.0841655 | ||||||||
\(848\) | 26.0106 | 0.893209 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 37.8564 | 1.29770 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.6071 | 1.73275 | 0.866377 | − | 0.499391i | \(-0.166443\pi\) | ||||
0.866377 | + | 0.499391i | \(0.166443\pi\) | |||||||
\(854\) | −6.24871 | −0.213826 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.73205 | −0.0933796 | ||||||||
\(857\) | 15.0759 | 0.514982 | 0.257491 | − | 0.966281i | \(-0.417104\pi\) | ||||
0.257491 | + | 0.966281i | \(0.417104\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.1769 | 1.60966 | 0.804828 | − | 0.593508i | \(-0.202258\pi\) | ||||
0.804828 | + | 0.593508i | \(0.202258\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.3452 | −0.488600 | ||||||||
\(863\) | 24.9010 | 0.847641 | 0.423821 | − | 0.905746i | \(-0.360689\pi\) | ||||
0.423821 | + | 0.905746i | \(0.360689\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17.0718 | −0.580123 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.27362 | −0.0771718 | ||||||||
\(869\) | −11.8564 | −0.402201 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.2154 | 0.515554 | ||||||||
\(872\) | 19.3185 | 0.654208 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.00000 | −0.270604 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.1512 | 0.849297 | 0.424648 | − | 0.905358i | \(-0.360398\pi\) | ||||
0.424648 | + | 0.905358i | \(0.360398\pi\) | |||||||
\(878\) | −18.5606 | −0.626391 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.07180 | 0.170873 | 0.0854366 | − | 0.996344i | \(-0.472771\pi\) | ||||
0.0854366 | + | 0.996344i | \(0.472771\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.5370 | 1.80166 | 0.900832 | − | 0.434167i | \(-0.142957\pi\) | ||||
0.900832 | + | 0.434167i | \(0.142957\pi\) | |||||||
\(884\) | −2.78461 | −0.0936566 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.67949 | 0.157211 | ||||||||
\(887\) | 38.7386 | 1.30071 | 0.650357 | − | 0.759629i | \(-0.274619\pi\) | ||||
0.650357 | + | 0.759629i | \(0.274619\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −42.0000 | −1.40863 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −25.4558 | −0.852325 | ||||||||
\(893\) | −5.65685 | −0.189299 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −28.0526 | −0.937170 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.00481 | 0.267124 | ||||||||
\(899\) | −1.35898 | −0.0453246 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.00000 | 0.133259 | ||||||||
\(902\) | 1.31268 | 0.0437074 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.9282 | 0.363467 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.6381 | 1.61500 | 0.807500 | − | 0.589867i | \(-0.200820\pi\) | ||||
0.807500 | + | 0.589867i | \(0.200820\pi\) | |||||||
\(908\) | 19.4201 | 0.644477 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.8564 | −1.25424 | −0.627119 | − | 0.778923i | \(-0.715766\pi\) | ||||
−0.627119 | + | 0.778923i | \(0.715766\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.07107 | 0.234018 | ||||||||
\(914\) | 5.41154 | 0.178998 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 48.2487 | 1.59418 | ||||||||
\(917\) | −33.9411 | −1.12083 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.7846 | 1.80718 | 0.903589 | − | 0.428401i | \(-0.140923\pi\) | ||||
0.903589 | + | 0.428401i | \(0.140923\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.93803 | −0.129692 | ||||||||
\(923\) | 25.4558 | 0.837889 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.89488 | 0.127994 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −13.0325 | −0.427814 | ||||||||
\(929\) | −22.6410 | −0.742828 | −0.371414 | − | 0.928467i | \(-0.621127\pi\) | ||||
−0.371414 | + | 0.928467i | \(0.621127\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | 0.0655474 | ||||||||
\(932\) | −37.2228 | −1.21927 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16.2872 | 0.532933 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.0208 | 1.53610 | 0.768051 | − | 0.640389i | \(-0.221227\pi\) | ||||
0.768051 | + | 0.640389i | \(0.221227\pi\) | |||||||
\(938\) | 4.54725 | 0.148473 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.6077 | 0.639193 | 0.319596 | − | 0.947554i | \(-0.396453\pi\) | ||||
0.319596 | + | 0.947554i | \(0.396453\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.5959 | −0.638131 | ||||||||
\(944\) | 31.8564 | 1.03684 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.66025 | −0.184031 | ||||||||
\(947\) | −16.7675 | −0.544870 | −0.272435 | − | 0.962174i | \(-0.587829\pi\) | ||||
−0.272435 | + | 0.962174i | \(0.587829\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.78461 | 0.0903923 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.79315 | −0.0581164 | ||||||||
\(953\) | 6.79367 | 0.220068 | 0.110034 | − | 0.993928i | \(-0.464904\pi\) | ||||
0.110034 | + | 0.993928i | \(0.464904\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −24.0000 | −0.776215 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.83701 | 0.285511 | ||||||||
\(959\) | 17.0718 | 0.551277 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7128 | −0.990736 | ||||||||
\(962\) | 10.7589 | 0.346881 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15.4641 | −0.498065 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.0454 | −0.708933 | −0.354466 | − | 0.935069i | \(-0.615337\pi\) | ||||
−0.354466 | + | 0.935069i | \(0.615337\pi\) | |||||||
\(968\) | 1.93185 | 0.0620921 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.7128 | −1.27444 | −0.637222 | − | 0.770680i | \(-0.719917\pi\) | ||||
−0.637222 | + | 0.770680i | \(0.719917\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.89898 | 0.157054 | ||||||||
\(974\) | −20.7846 | −0.665982 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.1436 | −0.388707 | ||||||||
\(977\) | −14.1421 | −0.452447 | −0.226224 | − | 0.974075i | \(-0.572638\pi\) | ||||
−0.226224 | + | 0.974075i | \(0.572638\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.4641 | −0.494235 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.17260 | 0.228887 | ||||||||
\(983\) | 47.1223 | 1.50297 | 0.751484 | − | 0.659751i | \(-0.229338\pi\) | ||||
0.751484 | + | 0.659751i | \(0.229338\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.497423 | −0.0158412 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.6969 | 0.467572 | ||||||||
\(989\) | 84.4974 | 2.68686 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.46410 | −0.237105 | −0.118553 | − | 0.992948i | \(-0.537825\pi\) | ||||
−0.118553 | + | 0.992948i | \(0.537825\pi\) | |||||||
\(992\) | 2.75410 | 0.0874427 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.60770 | 0.241301 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.4964 | 1.25086 | 0.625432 | − | 0.780278i | \(-0.284923\pi\) | ||||
0.625432 | + | 0.780278i | \(0.284923\pi\) | |||||||
\(998\) | −8.28221 | −0.262169 | ||||||||
\(999\) | 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 | 2475.2.a.bg.1.2 | 4 | ||
3.2 | odd | 2 | 2475.2.a.bh.1.3 | 4 | |||
5.2 | odd | 4 | 495.2.c.b.199.2 | ✓ | 4 | ||
5.3 | odd | 4 | 495.2.c.b.199.3 | yes | 4 | ||
5.4 | even | 2 | inner | 2475.2.a.bg.1.3 | 4 | ||
15.2 | even | 4 | 495.2.c.c.199.3 | yes | 4 | ||
15.8 | even | 4 | 495.2.c.c.199.2 | yes | 4 | ||
15.14 | odd | 2 | 2475.2.a.bh.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
495.2.c.b.199.2 | ✓ | 4 | 5.2 | odd | 4 | ||
495.2.c.b.199.3 | yes | 4 | 5.3 | odd | 4 | ||
495.2.c.c.199.2 | yes | 4 | 15.8 | even | 4 | ||
495.2.c.c.199.3 | yes | 4 | 15.2 | even | 4 | ||
2475.2.a.bg.1.2 | 4 | 1.1 | even | 1 | trivial | ||
2475.2.a.bg.1.3 | 4 | 5.4 | even | 2 | inner | ||
2475.2.a.bh.1.2 | 4 | 15.14 | odd | 2 | |||
2475.2.a.bh.1.3 | 4 | 3.2 | odd | 2 |