Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(1,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, 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("1148.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(9.16682615204\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{18})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.87939\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1148.1 |
$q$-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 | 0 | ||||||||
\(3\) | 0.879385 | 0.507713 | 0.253857 | − | 0.967242i | \(-0.418301\pi\) | ||||
0.253857 | + | 0.967242i | \(0.418301\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.694593 | −0.310631 | −0.155316 | − | 0.987865i | \(-0.549639\pi\) | ||||
−0.155316 | + | 0.987865i | \(0.549639\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.22668 | −0.742227 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.36959 | −1.31748 | −0.658740 | − | 0.752371i | \(-0.728910\pi\) | ||||
−0.658740 | + | 0.752371i | \(0.728910\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.71688 | −1.03088 | −0.515439 | − | 0.856926i | \(-0.672371\pi\) | ||||
−0.515439 | + | 0.856926i | \(0.672371\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.610815 | −0.157712 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.53209 | 0.614122 | 0.307061 | − | 0.951690i | \(-0.400654\pi\) | ||||
0.307061 | + | 0.951690i | \(0.400654\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.29086 | 0.525559 | 0.262780 | − | 0.964856i | \(-0.415361\pi\) | ||||
0.262780 | + | 0.964856i | \(0.415361\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.879385 | 0.191898 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.94356 | −0.822290 | −0.411145 | − | 0.911570i | \(-0.634871\pi\) | ||||
−0.411145 | + | 0.911570i | \(0.634871\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.51754 | −0.903508 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.59627 | −0.884552 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.241230 | −0.0447952 | −0.0223976 | − | 0.999749i | \(-0.507130\pi\) | ||||
−0.0223976 | + | 0.999749i | \(0.507130\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.38919 | −0.967926 | −0.483963 | − | 0.875088i | \(-0.660803\pi\) | ||||
−0.483963 | + | 0.875088i | \(0.660803\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.84255 | −0.668902 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.694593 | −0.117408 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.1061 | −1.82583 | −0.912913 | − | 0.408154i | \(-0.866173\pi\) | ||||
−0.912913 | + | 0.408154i | \(0.866173\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.26857 | −0.523390 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.98545 | 0.760274 | 0.380137 | − | 0.924930i | \(-0.375877\pi\) | ||||
0.380137 | + | 0.924930i | \(0.375877\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.54664 | 0.230559 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.92902 | 1.44830 | 0.724148 | − | 0.689645i | \(-0.242233\pi\) | ||||
0.724148 | + | 0.689645i | \(0.242233\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.22668 | 0.311798 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.8229 | 1.76137 | 0.880684 | − | 0.473705i | \(-0.157084\pi\) | ||||
0.880684 | + | 0.473705i | \(0.157084\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.03508 | 0.409250 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.01455 | 0.266833 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.38919 | −0.441234 | −0.220617 | − | 0.975360i | \(-0.570807\pi\) | ||||
−0.220617 | + | 0.975360i | \(0.570807\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.24123 | −0.799108 | −0.399554 | − | 0.916710i | \(-0.630835\pi\) | ||||
−0.399554 | + | 0.916710i | \(0.630835\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.22668 | −0.280536 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.58172 | 0.320223 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.38919 | −0.902733 | −0.451366 | − | 0.892339i | \(-0.649063\pi\) | ||||
−0.451366 | + | 0.892339i | \(0.649063\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.46791 | −0.417487 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.43376 | −0.170156 | −0.0850782 | − | 0.996374i | \(-0.527114\pi\) | ||||
−0.0850782 | + | 0.996374i | \(0.527114\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.61081 | −0.305573 | −0.152786 | − | 0.988259i | \(-0.548825\pi\) | ||||
−0.152786 | + | 0.988259i | \(0.548825\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.97266 | −0.458723 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.36959 | −0.497960 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.91622 | 0.215592 | 0.107796 | − | 0.994173i | \(-0.465621\pi\) | ||||
0.107796 | + | 0.994173i | \(0.465621\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.63816 | 0.293128 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.51754 | 0.166572 | 0.0832859 | − | 0.996526i | \(-0.473459\pi\) | ||||
0.0832859 | + | 0.996526i | \(0.473459\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.75877 | −0.190765 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.212134 | −0.0227431 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.32770 | −0.246735 | −0.123368 | − | 0.992361i | \(-0.539369\pi\) | ||||
−0.123368 | + | 0.992361i | \(0.539369\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.71688 | −0.389635 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.73917 | −0.491429 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.59121 | −0.163255 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.26857 | 0.433408 | 0.216704 | − | 0.976237i | \(-0.430469\pi\) | ||||
0.216704 | + | 0.976237i | \(0.430469\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.72967 | 0.977869 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.638156 | −0.0634989 | −0.0317494 | − | 0.999496i | \(-0.510108\pi\) | ||||
−0.0317494 | + | 0.999496i | \(0.510108\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.7297 | −1.74696 | −0.873478 | − | 0.486863i | \(-0.838141\pi\) | ||||
−0.873478 | + | 0.486863i | \(0.838141\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.610815 | −0.0596094 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.0496 | −1.74492 | −0.872462 | − | 0.488682i | \(-0.837478\pi\) | ||||
−0.872462 | + | 0.488682i | \(0.837478\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.51754 | −0.528485 | −0.264242 | − | 0.964456i | \(-0.585122\pi\) | ||||
−0.264242 | + | 0.964456i | \(0.585122\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.76651 | −0.926996 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.8307 | 1.67737 | 0.838685 | − | 0.544617i | \(-0.183325\pi\) | ||||
0.838685 | + | 0.544617i | \(0.183325\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.73917 | 0.255429 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.27631 | 0.765145 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.53209 | 0.232116 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.09327 | 0.735752 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.879385 | −0.0792915 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.61081 | 0.591289 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.76558 | −0.245405 | −0.122703 | − | 0.992443i | \(-0.539156\pi\) | ||||
−0.122703 | + | 0.992443i | \(0.539156\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.38413 | 0.386001 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.0000 | −1.22319 | −0.611593 | − | 0.791173i | \(-0.709471\pi\) | ||||
−0.611593 | + | 0.791173i | \(0.709471\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.29086 | 0.198643 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.19253 | 0.274770 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.14796 | 0.610691 | 0.305346 | − | 0.952242i | \(-0.401228\pi\) | ||||
0.305346 | + | 0.952242i | \(0.401228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0155 | 1.01914 | 0.509570 | − | 0.860429i | \(-0.329805\pi\) | ||||
0.509570 | + | 0.860429i | \(0.329805\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.73143 | 0.735319 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.2412 | 1.35816 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.167556 | 0.0139148 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.879385 | 0.0725305 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.85204 | 0.397495 | 0.198747 | − | 0.980051i | \(-0.436313\pi\) | ||||
0.198747 | + | 0.980051i | \(0.436313\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.5526 | 1.67255 | 0.836274 | − | 0.548311i | \(-0.184729\pi\) | ||||
0.836274 | + | 0.548311i | \(0.184729\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.63816 | −0.455818 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.74329 | 0.300668 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.5963 | −1.24472 | −0.622359 | − | 0.782732i | \(-0.713826\pi\) | ||||
−0.622359 | + | 0.782732i | \(0.713826\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.2763 | 0.894270 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.94356 | −0.310796 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.963163 | −0.0754408 | −0.0377204 | − | 0.999288i | \(-0.512010\pi\) | ||||
−0.0377204 | + | 0.999288i | \(0.512010\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.66901 | 0.207782 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.03415 | −0.157407 | −0.0787036 | − | 0.996898i | \(-0.525078\pi\) | ||||
−0.0787036 | + | 0.996898i | \(0.525078\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.815207 | 0.0627083 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.10101 | −0.390084 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.9513 | 0.984669 | 0.492335 | − | 0.870406i | \(-0.336144\pi\) | ||||
0.492335 | + | 0.870406i | \(0.336144\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.51754 | −0.341494 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.98040 | −0.224021 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.9864 | −1.64334 | −0.821670 | − | 0.569964i | \(-0.806957\pi\) | ||||
−0.821670 | + | 0.569964i | \(0.806957\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.85978 | −0.435554 | −0.217777 | − | 0.975999i | \(-0.569881\pi\) | ||||
−0.217777 | + | 0.975999i | \(0.569881\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.48845 | −0.405718 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.71419 | 0.567159 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.0642 | −0.809093 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.59627 | −0.334329 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.45336 | 0.177519 | 0.0887596 | − | 0.996053i | \(-0.471710\pi\) | ||||
0.0887596 | + | 0.996053i | \(0.471710\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.0547 | 1.58753 | 0.793765 | − | 0.608224i | \(-0.208118\pi\) | ||||
0.793765 | + | 0.608224i | \(0.208118\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.27033 | 0.162581 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.0942 | 1.43165 | 0.715826 | − | 0.698278i | \(-0.246050\pi\) | ||||
0.715826 | + | 0.698278i | \(0.246050\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.8357 | −1.33523 | −0.667615 | − | 0.744507i | \(-0.732685\pi\) | ||||
−0.667615 | + | 0.744507i | \(0.732685\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.49794 | −0.458329 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.241230 | −0.0169310 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.694593 | 0.0485125 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.78106 | 0.610326 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.0101 | −0.692413 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.48246 | 0.170900 | 0.0854498 | − | 0.996342i | \(-0.472767\pi\) | ||||
0.0854498 | + | 0.996342i | \(0.472767\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.26083 | −0.0863906 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.46286 | −0.236165 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.38919 | −0.365842 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.29591 | −0.155143 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.41147 | −0.633084 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.4534 | −0.700009 | −0.350004 | − | 0.936748i | \(-0.613820\pi\) | ||||
−0.350004 | + | 0.936748i | \(0.613820\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.0591 | 0.670608 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 26.5526 | 1.76236 | 0.881180 | − | 0.472781i | \(-0.156750\pi\) | ||||
0.881180 | + | 0.472781i | \(0.156750\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.22937 | 0.147321 | 0.0736605 | − | 0.997283i | \(-0.476532\pi\) | ||||
0.0736605 | + | 0.997283i | \(0.476532\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.84255 | −0.252821 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.4534 | 0.946871 | 0.473436 | − | 0.880828i | \(-0.343014\pi\) | ||||
0.473436 | + | 0.880828i | \(0.343014\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.89662 | −0.449886 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.68510 | 0.109459 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.56212 | −0.359784 | −0.179892 | − | 0.983686i | \(-0.557575\pi\) | ||||
−0.179892 | + | 0.983686i | \(0.557575\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.1830 | 1.81543 | 0.907715 | − | 0.419588i | \(-0.137826\pi\) | ||||
0.907715 | + | 0.419588i | \(0.137826\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.1088 | 1.03338 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.694593 | −0.0443759 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.51485 | −0.541787 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.33450 | 0.0845707 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.95130 | 0.312524 | 0.156262 | − | 0.987716i | \(-0.450056\pi\) | ||||
0.156262 | + | 0.987716i | \(0.450056\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.2317 | 1.08335 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.54664 | −0.0968542 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.14022 | 0.133503 | 0.0667515 | − | 0.997770i | \(-0.478737\pi\) | ||||
0.0667515 | + | 0.997770i | \(0.478737\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.1061 | −0.690097 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.537141 | 0.0332482 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.8135 | −1.71505 | −0.857525 | − | 0.514441i | \(-0.827999\pi\) | ||||
−0.857525 | + | 0.514441i | \(0.827999\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.90673 | −0.547136 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.04694 | −0.125271 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.5972 | −1.01195 | −0.505975 | − | 0.862548i | \(-0.668867\pi\) | ||||
−0.505975 | + | 0.862548i | \(0.668867\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.40467 | −0.449801 | −0.224901 | − | 0.974382i | \(-0.572206\pi\) | ||||
−0.224901 | + | 0.974382i | \(0.572206\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.26857 | −0.197823 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.7398 | 1.19035 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.1807 | 1.51296 | 0.756480 | − | 0.654017i | \(-0.226917\pi\) | ||||
0.756480 | + | 0.654017i | \(0.226917\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.0000 | 0.718421 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.8871 | 1.54430 | 0.772148 | − | 0.635442i | \(-0.219182\pi\) | ||||
0.772148 | + | 0.635442i | \(0.219182\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.59121 | −0.213476 | −0.106738 | − | 0.994287i | \(-0.534041\pi\) | ||||
−0.106738 | + | 0.994287i | \(0.534041\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.39929 | −0.0828868 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.00000 | −0.0590281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.5885 | −0.622854 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.75372 | 0.220047 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.55674 | −0.441470 | −0.220735 | − | 0.975334i | \(-0.570846\pi\) | ||||
−0.220735 | + | 0.975334i | \(0.570846\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.35410 | 0.137061 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 20.0838 | 1.16538 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.6578 | 0.847680 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.98545 | 0.287357 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.561185 | −0.0322392 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.33511 | 0.248228 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.167556 | 0.00956294 | 0.00478147 | − | 0.999989i | \(-0.498478\pi\) | ||||
0.00478147 | + | 0.999989i | \(0.498478\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.5912 | −0.886953 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.99495 | 0.453352 | 0.226676 | − | 0.973970i | \(-0.427214\pi\) | ||||
0.226676 | + | 0.973970i | \(0.427214\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.2713 | −0.637089 | −0.318545 | − | 0.947908i | \(-0.603194\pi\) | ||||
−0.318545 | + | 0.947908i | \(0.603194\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.54664 | 0.0871431 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.9905 | −0.954282 | −0.477141 | − | 0.878827i | \(-0.658327\pi\) | ||||
−0.477141 | + | 0.878827i | \(0.658327\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.05407 | 0.0590168 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.8726 | −0.885921 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.80066 | 0.322757 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.7912 | 0.931406 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.85204 | −0.268319 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.92902 | 0.547404 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.53714 | −0.139454 | −0.0697269 | − | 0.997566i | \(-0.522213\pi\) | ||||
−0.0697269 | + | 0.997566i | \(0.522213\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 24.7297 | 1.35518 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.13247 | 0.280417 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.9941 | 1.68836 | 0.844179 | − | 0.536062i | \(-0.180089\pi\) | ||||
0.844179 | + | 0.536062i | \(0.180089\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.6800 | 0.851623 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.5485 | 1.27522 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.40879 | 0.129685 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.65951 | −0.0890872 | −0.0445436 | − | 0.999007i | \(-0.514183\pi\) | ||||
−0.0445436 | + | 0.999007i | \(0.514183\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.9959 | −1.87329 | −0.936643 | − | 0.350285i | \(-0.886085\pi\) | ||||
−0.936643 | + | 0.350285i | \(0.886085\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.0838 | 0.911865 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.58172 | 0.137411 | 0.0687055 | − | 0.997637i | \(-0.478113\pi\) | ||||
0.0687055 | + | 0.997637i | \(0.478113\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.995881 | 0.0528559 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.22668 | 0.117848 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.6236 | −0.982916 | −0.491458 | − | 0.870901i | \(-0.663536\pi\) | ||||
−0.491458 | + | 0.870901i | \(0.663536\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.7520 | −0.723788 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.11711 | 0.373551 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.81345 | 0.0949205 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.16756 | 0.426343 | 0.213171 | − | 0.977015i | \(-0.431621\pi\) | ||||
0.213171 | + | 0.977015i | \(0.431621\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.22668 | 0.115916 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.8229 | 0.665734 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.68004 | 0.190545 | 0.0952727 | − | 0.995451i | \(-0.469628\pi\) | ||||
0.0952727 | + | 0.995451i | \(0.469628\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.81345 | 0.300205 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.896622 | 0.0461784 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.20027 | −0.215754 | −0.107877 | − | 0.994164i | \(-0.534405\pi\) | ||||
−0.107877 | + | 0.994164i | \(0.534405\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.43201 | −0.124596 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −37.4475 | −1.91348 | −0.956739 | − | 0.290949i | \(-0.906029\pi\) | ||||
−0.956739 | + | 0.290949i | \(0.906029\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.03508 | 0.154682 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.1010 | −0.564296 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.28312 | 0.318567 | 0.159283 | − | 0.987233i | \(-0.449082\pi\) | ||||
0.159283 | + | 0.987233i | \(0.449082\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.98545 | −0.504986 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.3114 | −0.621028 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.33099 | −0.0669696 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −35.6459 | −1.78902 | −0.894508 | − | 0.447052i | \(-0.852474\pi\) | ||||
−0.894508 | + | 0.447052i | \(0.852474\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.01455 | 0.100854 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.8494 | 0.741541 | 0.370771 | − | 0.928724i | \(-0.379094\pi\) | ||||
0.370771 | + | 0.928724i | \(0.379094\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.0310 | 0.997813 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.83244 | −0.0910549 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 48.5289 | 2.40549 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.4979 | 0.716877 | 0.358439 | − | 0.933553i | \(-0.383309\pi\) | ||||
0.358439 | + | 0.933553i | \(0.383309\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.28581 | 0.310056 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.38919 | −0.166771 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.05407 | −0.0517424 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.5662 | 0.517431 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.06418 | −0.345108 | −0.172554 | − | 0.985000i | \(-0.555202\pi\) | ||||
−0.172554 | + | 0.985000i | \(0.555202\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.47834 | 0.266998 | 0.133499 | − | 0.991049i | \(-0.457379\pi\) | ||||
0.133499 | + | 0.991049i | \(0.457379\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.1088 | −1.07496 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.4388 | −0.554864 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.24123 | −0.302034 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.2823 | 0.689556 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.34998 | 0.354036 | 0.177018 | − | 0.984208i | \(-0.443355\pi\) | ||||
0.177018 | + | 0.984208i | \(0.443355\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.6108 | 0.606037 | 0.303019 | − | 0.952985i | \(-0.402006\pi\) | ||||
0.303019 | + | 0.952985i | \(0.402006\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.147347 | 0.00706472 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.03415 | −0.432162 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −37.2799 | −1.77927 | −0.889637 | − | 0.456668i | \(-0.849043\pi\) | ||||
−0.889637 | + | 0.456668i | \(0.849043\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.22668 | −0.106032 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.3628 | −0.729908 | −0.364954 | − | 0.931026i | \(-0.618915\pi\) | ||||
−0.364954 | + | 0.931026i | \(0.618915\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.61680 | 0.0766437 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.26682 | 0.201813 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.1070 | −1.09049 | −0.545243 | − | 0.838278i | \(-0.683563\pi\) | ||||
−0.545243 | + | 0.838278i | \(0.683563\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.36959 | 0.205756 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.0737 | 0.849175 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.58172 | 0.121033 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.9026 | −0.743893 | −0.371946 | − | 0.928254i | \(-0.621309\pi\) | ||||
−0.371946 | + | 0.928254i | \(0.621309\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.6382 | −0.543223 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.6655 | −0.496742 | −0.248371 | − | 0.968665i | \(-0.579895\pi\) | ||||
−0.248371 | + | 0.968665i | \(0.579895\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.7547 | −1.05750 | −0.528749 | − | 0.848778i | \(-0.677339\pi\) | ||||
−0.528749 | + | 0.848778i | \(0.677339\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.29179 | 0.152653 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.38919 | −0.249382 | −0.124691 | − | 0.992196i | \(-0.539794\pi\) | ||||
−0.124691 | + | 0.992196i | \(0.539794\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.38919 | −0.341201 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.7151 | −0.631960 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.7844 | −1.00165 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.3491 | −0.474847 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −28.5526 | −1.30733 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.9495 | 1.04859 | 0.524296 | − | 0.851536i | \(-0.324329\pi\) | ||||
0.524296 | + | 0.851536i | \(0.324329\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 41.2799 | 1.88220 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.46791 | −0.157795 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.96492 | −0.134630 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.0888 | −0.547797 | −0.273899 | − | 0.961759i | \(-0.588313\pi\) | ||||
−0.273899 | + | 0.961759i | \(0.588313\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.846992 | −0.0383023 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.92396 | 0.312474 | 0.156237 | − | 0.987720i | \(-0.450064\pi\) | ||||
0.156237 | + | 0.987720i | \(0.450064\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.610815 | −0.0275097 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.75816 | −0.303757 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.43376 | −0.0643131 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.0155 | 1.43321 | 0.716605 | − | 0.697479i | \(-0.245695\pi\) | ||||
0.716605 | + | 0.697479i | \(0.245695\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.78880 | −0.0799177 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.3429 | −0.862455 | −0.431228 | − | 0.902243i | \(-0.641919\pi\) | ||||
−0.431228 | + | 0.902243i | \(0.641919\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.443258 | 0.0197247 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.716881 | 0.0318378 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.8708 | −1.14670 | −0.573352 | − | 0.819309i | \(-0.694357\pi\) | ||||
−0.573352 | + | 0.819309i | \(0.694357\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.61081 | −0.115496 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.5294 | −0.464884 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.3149 | 0.542659 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −43.3857 | −1.90810 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.3892 | 0.499930 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.8316 | 1.56981 | 0.784906 | − | 0.619615i | \(-0.212711\pi\) | ||||
0.784906 | + | 0.619615i | \(0.212711\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −42.3168 | −1.85038 | −0.925192 | − | 0.379500i | \(-0.876096\pi\) | ||||
−0.925192 | + | 0.379500i | \(0.876096\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.97266 | −0.173381 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.6459 | −0.594425 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.44831 | −0.323840 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.54664 | 0.327496 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.71688 | 0.160996 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.5371 | 0.542028 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.3345 | −0.834345 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.36959 | −0.188211 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.67593 | 0.373007 | 0.186504 | − | 0.982454i | \(-0.440284\pi\) | ||||
0.186504 | + | 0.982454i | \(0.440284\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.15301 | −0.221137 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.83244 | 0.164164 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.7392 | 0.544688 | 0.272344 | − | 0.962200i | \(-0.412201\pi\) | ||||
0.272344 | + | 0.962200i | \(0.412201\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.8972 | 0.593119 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.552623 | −0.0235425 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.91622 | 0.0814860 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.78375 | 0.287954 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.0547 | −0.680259 | −0.340129 | − | 0.940379i | \(-0.610471\pi\) | ||||
−0.340129 | + | 0.940379i | \(0.610471\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.5303 | −0.783750 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.72967 | −0.410787 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.5749 | −0.824984 | −0.412492 | − | 0.910961i | \(-0.635342\pi\) | ||||
−0.412492 | + | 0.910961i | \(0.635342\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.3851 | −0.521044 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.63816 | 0.110792 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.6450 | −0.530104 | −0.265052 | − | 0.964234i | \(-0.585389\pi\) | ||||
−0.265052 | + | 0.964234i | \(0.585389\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.3797 | −1.02026 | −0.510129 | − | 0.860098i | \(-0.670402\pi\) | ||||
−0.510129 | + | 0.860098i | \(0.670402\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.15745 | 0.0901288 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.8152 | 0.742946 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.3191 | −1.05405 | −0.527025 | − | 0.849850i | \(-0.676692\pi\) | ||||
−0.527025 | + | 0.849850i | \(0.676692\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.3946 | 0.806010 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.51754 | 0.0629582 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −56.0310 | −2.32057 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.74867 | −0.237678 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.6509 | 1.22383 | 0.611913 | − | 0.790925i | \(-0.290400\pi\) | ||||
0.611913 | + | 0.790925i | \(0.290400\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.3459 | −0.508703 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.6705 | 0.726869 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.0574 | −0.495137 | −0.247568 | − | 0.968870i | \(-0.579632\pi\) | ||||
−0.247568 | + | 0.968870i | \(0.579632\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.75877 | −0.0721026 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.5639 | −0.677914 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.0087 | 0.694956 | 0.347478 | − | 0.937688i | \(-0.387038\pi\) | ||||
0.347478 | + | 0.937688i | \(0.387038\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.7948 | 1.78643 | 0.893213 | − | 0.449633i | \(-0.148445\pi\) | ||||
0.893213 | + | 0.449633i | \(0.148445\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.4534 | 0.670033 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.62153 | −0.228548 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.5175 | −1.52279 | −0.761395 | − | 0.648288i | \(-0.775485\pi\) | ||||
−0.761395 | + | 0.648288i | \(0.775485\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.212134 | −0.00859609 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −36.9050 | −1.49302 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.9085 | −0.602148 | −0.301074 | − | 0.953601i | \(-0.597345\pi\) | ||||
−0.301074 | + | 0.953601i | \(0.597345\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.610815 | 0.0246304 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.22256 | −0.250511 | −0.125255 | − | 0.992125i | \(-0.539975\pi\) | ||||
−0.125255 | + | 0.992125i | \(0.539975\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.9554 | −0.882463 | −0.441231 | − | 0.897393i | \(-0.645458\pi\) | ||||
−0.441231 | + | 0.897393i | \(0.645458\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.1257 | 0.727358 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.32770 | −0.0932572 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.9959 | 0.719835 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.80274 | −0.351548 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −28.1215 | −1.12128 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.22493 | 0.247810 | 0.123905 | − | 0.992294i | \(-0.460458\pi\) | ||||
0.123905 | + | 0.992294i | \(0.460458\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.18304 | 0.0867680 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.92095 | 0.0762306 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.71688 | −0.147268 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.19253 | 0.126295 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.2121 | 1.43029 | 0.715147 | − | 0.698974i | \(-0.246360\pi\) | ||||
0.715147 | + | 0.698974i | \(0.246360\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.92364 | 0.391350 | 0.195675 | − | 0.980669i | \(-0.437310\pi\) | ||||
0.195675 | + | 0.980669i | \(0.437310\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.04519 | −0.119904 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 45.6769 | 1.79574 | 0.897871 | − | 0.440258i | \(-0.145113\pi\) | ||||
0.897871 | + | 0.440258i | \(0.145113\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.8093 | 0.581317 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.73917 | −0.185743 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.6209 | 0.572161 | 0.286080 | − | 0.958206i | \(-0.407648\pi\) | ||||
0.286080 | + | 0.958206i | \(0.407648\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.72430 | 0.379960 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.81345 | 0.226804 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.990505 | 0.0385846 | 0.0192923 | − | 0.999814i | \(-0.493859\pi\) | ||||
0.0192923 | + | 0.999814i | \(0.493859\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −47.1397 | −1.83352 | −0.916761 | − | 0.399436i | \(-0.869206\pi\) | ||||
−0.916761 | + | 0.399436i | \(0.869206\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.27631 | −0.321425 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.59121 | −0.0617046 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.951304 | 0.0368346 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.19253 | −0.355404 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.2716 | 1.05281 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.4338 | −0.517834 | −0.258917 | − | 0.965900i | \(-0.583366\pi\) | ||||
−0.258917 | + | 0.965900i | \(0.583366\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20.7638 | 0.799200 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.5039 | −1.28766 | −0.643830 | − | 0.765168i | \(-0.722656\pi\) | ||||
−0.643830 | + | 0.765168i | \(0.722656\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.26857 | 0.163813 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.3500 | 0.894773 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.4047 | 0.742499 | 0.371249 | − | 0.928533i | \(-0.378929\pi\) | ||||
0.371249 | + | 0.928533i | \(0.378929\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.96492 | −0.189700 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.96048 | 0.0747968 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −47.6614 | −1.81575 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.0574 | −1.52385 | −0.761927 | − | 0.647663i | \(-0.775747\pi\) | ||||
−0.761927 | + | 0.647663i | \(0.775747\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.72967 | 0.369600 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.34587 | −0.316577 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.53209 | −0.0959097 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.7101 | 0.480739 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.2885 | −0.690747 | −0.345373 | − | 0.938465i | \(-0.612248\pi\) | ||||
−0.345373 | + | 0.938465i | \(0.612248\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.4424 | −0.959580 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.06479 | −0.228413 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.638156 | −0.0240003 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.1147 | 1.73188 | 0.865938 | − | 0.500152i | \(-0.166722\pi\) | ||||
0.865938 | + | 0.500152i | \(0.166722\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.26682 | −0.160018 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.2526 | 0.795916 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.2810 | −0.421887 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.89124 | −0.182667 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.0392 | −0.523574 | −0.261787 | − | 0.965126i | \(-0.584312\pi\) | ||||
−0.261787 | + | 0.965126i | \(0.584312\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.7297 | −0.660288 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24.7837 | 0.921717 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.08976 | 0.0404728 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.4834 | −0.648423 | −0.324212 | − | 0.945985i | \(-0.605099\pi\) | ||||
−0.324212 | + | 0.945985i | \(0.605099\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.25133 | 0.231531 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.6236 | 0.466901 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.97502 | −0.109885 | −0.0549425 | − | 0.998490i | \(-0.517498\pi\) | ||||
−0.0549425 | + | 0.998490i | \(0.517498\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.610815 | −0.0225302 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.2877 | 1.18933 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.2439 | −0.597542 | −0.298771 | − | 0.954325i | \(-0.596577\pi\) | ||||
−0.298771 | + | 0.954325i | \(0.596577\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.48784 | −0.275073 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.1138 | 1.28820 | 0.644100 | − | 0.764941i | \(-0.277232\pi\) | ||||
0.644100 | + | 0.764941i | \(0.277232\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.37019 | −0.123474 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.37908 | −0.123634 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.0496 | −0.659519 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.95130 | 0.180676 | 0.0903378 | − | 0.995911i | \(-0.471205\pi\) | ||||
0.0903378 | + | 0.995911i | \(0.471205\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.35410 | 0.158672 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.2757 | −0.519546 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.2020 | −0.443490 | −0.221745 | − | 0.975105i | \(-0.571175\pi\) | ||||
−0.221745 | + | 0.975105i | \(0.571175\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.1533 | 0.550031 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.3696 | 0.738397 | 0.369198 | − | 0.929351i | \(-0.379632\pi\) | ||||
0.369198 | + | 0.929351i | \(0.379632\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.51754 | −0.199748 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.91622 | 0.141591 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.5972 | 0.454859 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.34049 | −0.228644 | −0.114322 | − | 0.993444i | \(-0.536470\pi\) | ||||
−0.114322 | + | 0.993444i | \(0.536470\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.88207 | 0.0677812 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −52.0205 | −1.87105 | −0.935524 | − | 0.353262i | \(-0.885072\pi\) | ||||
−0.935524 | + | 0.353262i | \(0.885072\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.3459 | 0.874529 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.76651 | −0.350372 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.29086 | −0.0820786 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.26495 | 0.224177 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.10876 | 0.0396237 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.8331 | 0.386648 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.1539 | −1.57392 | −0.786959 | − | 0.617005i | \(-0.788346\pi\) | ||||
−0.786959 | + | 0.617005i | \(0.788346\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.4587 | −0.870754 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.8307 | 0.633986 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.1979 | 0.823782 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.83244 | −0.277788 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.9162 | −0.563782 | −0.281891 | − | 0.959447i | \(-0.590962\pi\) | ||||
−0.281891 | + | 0.959447i | \(0.590962\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.1411 | 0.889430 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.18304 | 0.183134 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.4082 | 0.402586 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.73917 | 0.0965431 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.5953 | −0.513780 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.8331 | 0.943400 | 0.471700 | − | 0.881759i | \(-0.343641\pi\) | ||||
0.471700 | + | 0.881759i | \(0.343641\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.0196 | 1.15947 | 0.579737 | − | 0.814803i | \(-0.303155\pi\) | ||||
0.579737 | + | 0.814803i | \(0.303155\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.51155 | −0.228370 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.669006 | 0.0234343 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.4210 | 0.399569 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.27631 | 0.289198 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.2327 | −0.636324 | −0.318162 | − | 0.948036i | \(-0.603066\pi\) | ||||
−0.318162 | + | 0.948036i | \(0.603066\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.77238 | −0.270928 | −0.135464 | − | 0.990782i | \(-0.543253\pi\) | ||||
−0.135464 | + | 0.990782i | \(0.543253\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17.3589 | 0.604358 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.00599 | −0.313169 | −0.156584 | − | 0.987665i | \(-0.550048\pi\) | ||||
−0.156584 | + | 0.987665i | \(0.550048\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.0702 | −0.835991 | −0.417996 | − | 0.908449i | \(-0.637267\pi\) | ||||
−0.417996 | + | 0.908449i | \(0.637267\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.1435 | 0.768150 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.53209 | 0.0877317 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.41290 | 0.0488956 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 24.7701 | 0.856181 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −51.3191 | −1.77173 | −0.885867 | − | 0.463940i | \(-0.846435\pi\) | ||||
−0.885867 | + | 0.463940i | \(0.846435\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9418 | −0.997993 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.7648 | 0.784060 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.566237 | −0.0194792 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.09327 | 0.278088 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.15806 | −0.108384 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 43.7975 | 1.50136 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.0114 | −0.993330 | −0.496665 | − | 0.867942i | \(-0.665442\pi\) | ||||
−0.496665 | + | 0.867942i | \(0.665442\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.54313 | 0.121172 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.1385 | 0.551279 | 0.275640 | − | 0.961261i | \(-0.411110\pi\) | ||||
0.275640 | + | 0.961261i | \(0.411110\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.1492 | 1.50635 | 0.753176 | − | 0.657819i | \(-0.228521\pi\) | ||||
0.753176 | + | 0.657819i | \(0.228521\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.879385 | −0.0299694 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36.2567 | 1.23419 | 0.617096 | − | 0.786888i | \(-0.288309\pi\) | ||||
0.617096 | + | 0.786888i | \(0.288309\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.99588 | −0.305869 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.31139 | −0.316231 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.37309 | −0.284038 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.4647 | 0.930607 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.50475 | −0.321687 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.61081 | 0.223486 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.578097 | 0.0195209 | 0.00976047 | − | 0.999952i | \(-0.496893\pi\) | ||||
0.00976047 | + | 0.999952i | \(0.496893\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.64529 | −0.224140 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.1046 | −1.48592 | −0.742961 | − | 0.669334i | \(-0.766579\pi\) | ||||
−0.742961 | + | 0.669334i | \(0.766579\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.9959 | −1.31232 | −0.656158 | − | 0.754624i | \(-0.727819\pi\) | ||||
−0.656158 | + | 0.754624i | \(0.727819\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.07016 | 0.0695878 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.36278 | −0.314371 | −0.157186 | − | 0.987569i | \(-0.550242\pi\) | ||||
−0.157186 | + | 0.987569i | \(0.550242\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.76558 | −0.0927545 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.5276 | −0.386191 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.7460 | 0.761165 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.2716 | 0.510473 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.8898 | 0.430378 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.30003 | 0.0433584 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.4688 | 1.08169 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.38413 | 0.145895 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.07016 | 0.135297 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.2844 | −1.03878 | −0.519390 | − | 0.854537i | \(-0.673841\pi\) | ||||
−0.519390 | + | 0.854537i | \(0.673841\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.42097 | 0.0471306 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.6355 | 0.716815 | 0.358408 | − | 0.933565i | \(-0.383320\pi\) | ||||
0.358408 | + | 0.933565i | \(0.383320\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.63102 | −0.219455 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.81223 | 0.126029 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.0000 | −0.462321 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.4296 | 0.475990 | 0.237995 | − | 0.971266i | \(-0.423510\pi\) | ||||
0.237995 | + | 0.971266i | \(0.423510\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.147347 | 0.00485523 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.32913 | 0.175410 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 50.1721 | 1.64965 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 39.4783 | 1.29664 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.2145 | 0.630407 | 0.315204 | − | 0.949024i | \(-0.397927\pi\) | ||||
0.315204 | + | 0.949024i | \(0.397927\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.29086 | 0.0750799 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.03064 | 0.230173 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.68510 | 0.251330 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.0627 | −0.786096 | −0.393048 | − | 0.919518i | \(-0.628579\pi\) | ||||
−0.393048 | + | 0.919518i | \(0.628579\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.91178 | −0.323459 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −50.3424 | −1.64111 | −0.820557 | − | 0.571565i | \(-0.806337\pi\) | ||||
−0.820557 | + | 0.571565i | \(0.806337\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.94356 | 0.128420 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.19253 | 0.103853 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39.1807 | −1.27320 | −0.636600 | − | 0.771194i | \(-0.719660\pi\) | ||||
−0.636600 | + | 0.771194i | \(0.719660\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.70409 | 0.315008 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.9412 | −0.484502 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.3533 | −1.30717 | −0.653586 | − | 0.756853i | \(-0.726736\pi\) | ||||
−0.653586 | + | 0.756853i | \(0.726736\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.70409 | −0.0551430 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.926936 | 0.0299636 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.14796 | 0.230820 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.95668 | −0.0631187 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 40.1908 | 1.29513 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.3190 | −0.493137 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.62630 | 0.0844560 | 0.0422280 | − | 0.999108i | \(-0.486554\pi\) | ||||
0.0422280 | + | 0.999108i | \(0.486554\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.10101 | 0.163868 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.5577 | 1.36574 | 0.682870 | − | 0.730540i | \(-0.260731\pi\) | ||||
0.682870 | + | 0.730540i | \(0.260731\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0155 | 0.385199 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.7659 | 0.472887 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.0101 | −1.21605 | −0.608025 | − | 0.793917i | \(-0.708038\pi\) | ||||
−0.608025 | + | 0.793917i | \(0.708038\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.1711 | 0.325069 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.2858 | 0.392256 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.5276 | 0.367675 | 0.183837 | − | 0.982957i | \(-0.441148\pi\) | ||||
0.183837 | + | 0.982957i | \(0.441148\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.9573 | −0.444716 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.73143 | 0.277924 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.6604 | −0.625166 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.9750 | 0.348633 | 0.174317 | − | 0.984690i | \(-0.444228\pi\) | ||||
0.174317 | + | 0.984690i | \(0.444228\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.23112 | −0.0708026 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.0832 | 0.414764 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.7279 | 1.13151 | 0.565757 | − | 0.824572i | \(-0.308584\pi\) | ||||
0.565757 | + | 0.824572i | \(0.308584\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 51.0464 | 1.61504 |
(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 | 1148.2.a.b.1.3 | ✓ | 3 | |
4.3 | odd | 2 | 4592.2.a.v.1.1 | 3 | |||
7.6 | odd | 2 | 8036.2.a.h.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.a.b.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
4592.2.a.v.1.1 | 3 | 4.3 | odd | 2 | |||
8036.2.a.h.1.1 | 3 | 7.6 | odd | 2 |