Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5292,2,Mod(1,5292)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5292, 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("5292.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5292.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: | \(42.2568327497\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.321.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 756) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.239123\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5292.1 |
$q$-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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.42107 | 1.08273 | 0.541367 | − | 0.840786i | \(-0.317907\pi\) | ||||
0.541367 | + | 0.840786i | \(0.317907\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.70370 | −1.41822 | −0.709109 | − | 0.705099i | \(-0.750903\pi\) | ||||
−0.709109 | + | 0.705099i | \(0.750903\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.42107 | −0.948833 | −0.474417 | − | 0.880300i | \(-0.657341\pi\) | ||||
−0.474417 | + | 0.880300i | \(0.657341\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.70370 | −0.413207 | −0.206604 | − | 0.978425i | \(-0.566241\pi\) | ||||
−0.206604 | + | 0.978425i | \(0.566241\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.28263 | 0.294256 | 0.147128 | − | 0.989117i | \(-0.452997\pi\) | ||||
0.147128 | + | 0.989117i | \(0.452997\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.12476 | 0.234529 | 0.117265 | − | 0.993101i | \(-0.462587\pi\) | ||||
0.117265 | + | 0.993101i | \(0.462587\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.861564 | 0.172313 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.70370 | 0.873455 | 0.436727 | − | 0.899594i | \(-0.356137\pi\) | ||||
0.436727 | + | 0.899594i | \(0.356137\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.42107 | −0.614442 | −0.307221 | − | 0.951638i | \(-0.599399\pi\) | ||||
−0.307221 | + | 0.951638i | \(0.599399\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.54583 | 1.40493 | 0.702463 | − | 0.711720i | \(-0.252084\pi\) | ||||
0.702463 | + | 0.711720i | \(0.252084\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.71737 | −0.580556 | −0.290278 | − | 0.956942i | \(-0.593748\pi\) | ||||
−0.290278 | + | 0.956942i | \(0.593748\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.54583 | 0.845731 | 0.422866 | − | 0.906192i | \(-0.361024\pi\) | ||||
0.422866 | + | 0.906192i | \(0.361024\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.8285 | 1.72536 | 0.862679 | − | 0.505752i | \(-0.168785\pi\) | ||||
0.862679 | + | 0.505752i | \(0.168785\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.2632 | −1.40976 | −0.704879 | − | 0.709327i | \(-0.748999\pi\) | ||||
−0.704879 | + | 0.709327i | \(0.748999\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.3880 | −1.53555 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.12476 | −0.536998 | −0.268499 | − | 0.963280i | \(-0.586528\pi\) | ||||
−0.268499 | + | 0.963280i | \(0.586528\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.24953 | −1.18428 | −0.592140 | − | 0.805835i | \(-0.701717\pi\) | ||||
−0.592140 | + | 0.805835i | \(0.701717\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.28263 | −1.02733 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.1248 | −1.35911 | −0.679553 | − | 0.733626i | \(-0.737826\pi\) | ||||
−0.679553 | + | 0.733626i | \(0.737826\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.9669 | −1.77624 | −0.888122 | − | 0.459608i | \(-0.847990\pi\) | ||||
−0.888122 | + | 0.459608i | \(0.847990\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.13844 | 0.250285 | 0.125143 | − | 0.992139i | \(-0.460061\pi\) | ||||
0.125143 | + | 0.992139i | \(0.460061\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.5322 | −1.63500 | −0.817498 | − | 0.575932i | \(-0.804639\pi\) | ||||
−0.817498 | + | 0.575932i | \(0.804639\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.42107 | −0.924332 | −0.462166 | − | 0.886793i | \(-0.652928\pi\) | ||||
−0.462166 | + | 0.886793i | \(0.652928\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.12476 | −0.447393 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.0917 | −1.70571 | −0.852856 | − | 0.522146i | \(-0.825132\pi\) | ||||
−0.852856 | + | 0.522146i | \(0.825132\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.10533 | 0.318600 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.2495 | 1.64989 | 0.824945 | − | 0.565213i | \(-0.191206\pi\) | ||||
0.824945 | + | 0.565213i | \(0.191206\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.9863 | 1.29219 | 0.646094 | − | 0.763258i | \(-0.276401\pi\) | ||||
0.646094 | + | 0.763258i | \(0.276401\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.00000 | −0.689730 | −0.344865 | − | 0.938652i | \(-0.612075\pi\) | ||||
−0.344865 | + | 0.938652i | \(0.612075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.7174 | −1.22943 | −0.614717 | − | 0.788748i | \(-0.710730\pi\) | ||||
−0.614717 | + | 0.788748i | \(0.710730\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.40739 | −0.709500 | −0.354750 | − | 0.934961i | \(-0.615434\pi\) | ||||
−0.354750 | + | 0.934961i | \(0.615434\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.68427 | 0.628803 | 0.314401 | − | 0.949290i | \(-0.398196\pi\) | ||||
0.314401 | + | 0.949290i | \(0.398196\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.72313 | 0.253933 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.1248 | 1.01134 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.0194 | −0.896165 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.5322 | −1.02331 | −0.511657 | − | 0.859190i | \(-0.670968\pi\) | ||||
−0.511657 | + | 0.859190i | \(0.670968\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.13844 | 0.798429 | 0.399214 | − | 0.916858i | \(-0.369283\pi\) | ||||
0.399214 | + | 0.916858i | \(0.369283\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.24953 | 0.192190 | 0.0960950 | − | 0.995372i | \(-0.469365\pi\) | ||||
0.0960950 | + | 0.995372i | \(0.469365\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.5789 | −0.897293 | −0.448647 | − | 0.893709i | \(-0.648094\pi\) | ||||
−0.448647 | + | 0.893709i | \(0.648094\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.0917 | 1.34565 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.3880 | 0.945719 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −24.3743 | −1.99682 | −0.998410 | − | 0.0563721i | \(-0.982047\pi\) | ||||
−0.998410 | + | 0.0563721i | \(0.982047\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.1384 | 0.906433 | 0.453217 | − | 0.891400i | \(-0.350276\pi\) | ||||
0.453217 | + | 0.891400i | \(0.350276\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.28263 | −0.665277 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.26320 | 0.260432 | 0.130216 | − | 0.991486i | \(-0.458433\pi\) | ||||
0.130216 | + | 0.991486i | \(0.458433\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.152110 | −0.0119141 | −0.00595707 | − | 0.999982i | \(-0.501896\pi\) | ||||
−0.00595707 | + | 0.999982i | \(0.501896\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.2359 | −1.87543 | −0.937713 | − | 0.347410i | \(-0.887061\pi\) | ||||
−0.937713 | + | 0.347410i | \(0.887061\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.29630 | −0.0997156 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.95322 | −0.528644 | −0.264322 | − | 0.964435i | \(-0.585148\pi\) | ||||
−0.264322 | + | 0.964435i | \(0.585148\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.6979 | −1.09858 | −0.549288 | − | 0.835633i | \(-0.685101\pi\) | ||||
−0.549288 | + | 0.835633i | \(0.685101\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.1053 | 1.27143 | 0.635715 | − | 0.771924i | \(-0.280705\pi\) | ||||
0.635715 | + | 0.771924i | \(0.280705\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.6900 | 1.52116 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.01367 | 0.586018 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.9806 | −1.66282 | −0.831408 | − | 0.555663i | \(-0.812465\pi\) | ||||
−0.831408 | + | 0.555663i | \(0.812465\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.37429 | 0.386850 | 0.193425 | − | 0.981115i | \(-0.438040\pi\) | ||||
0.193425 | + | 0.981115i | \(0.438040\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.57893 | 0.254988 | 0.127494 | − | 0.991839i | \(-0.459307\pi\) | ||||
0.127494 | + | 0.991839i | \(0.459307\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.00000 | −0.496217 | −0.248108 | − | 0.968732i | \(-0.579809\pi\) | ||||
−0.248108 | + | 0.968732i | \(0.579809\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.00000 | −0.628587 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.03310 | −0.417318 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.1111 | 1.31566 | 0.657831 | − | 0.753166i | \(-0.271474\pi\) | ||||
0.657831 | + | 0.753166i | \(0.271474\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.4268 | 0.915702 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.82846 | 0.392065 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.2632 | 1.62478 | 0.812392 | − | 0.583112i | \(-0.198165\pi\) | ||||
0.812392 | + | 0.583112i | \(0.198165\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.84789 | −0.255393 | −0.127697 | − | 0.991813i | \(-0.540758\pi\) | ||||
−0.127697 | + | 0.991813i | \(0.540758\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.53216 | 0.233412 | 0.116706 | − | 0.993167i | \(-0.462767\pi\) | ||||
0.116706 | + | 0.993167i | \(0.462767\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.2495 | −1.52313 | −0.761564 | − | 0.648090i | \(-0.775568\pi\) | ||||
−0.761564 | + | 0.648090i | \(0.775568\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28.6375 | 1.86810 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.28263 | −0.535759 | −0.267879 | − | 0.963452i | \(-0.586323\pi\) | ||||
−0.267879 | + | 0.963452i | \(0.586323\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.5264 | 0.871312 | 0.435656 | − | 0.900113i | \(-0.356516\pi\) | ||||
0.435656 | + | 0.900113i | \(0.356516\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.38796 | −0.279199 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.11109 | 0.322609 | 0.161305 | − | 0.986905i | \(-0.448430\pi\) | ||||
0.161305 | + | 0.986905i | \(0.448430\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.29055 | −0.332614 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.0917 | 1.00377 | 0.501885 | − | 0.864934i | \(-0.332640\pi\) | ||||
0.501885 | + | 0.864934i | \(0.332640\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.7174 | −0.784187 | −0.392093 | − | 0.919925i | \(-0.628249\pi\) | ||||
−0.392093 | + | 0.919925i | \(0.628249\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.8479 | −1.52639 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.7037 | 1.38427 | 0.692134 | − | 0.721769i | \(-0.256671\pi\) | ||||
0.692134 | + | 0.721769i | \(0.256671\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.1248 | 0.918764 | 0.459382 | − | 0.888239i | \(-0.348071\pi\) | ||||
0.459382 | + | 0.888239i | \(0.348071\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.05253 | −0.244377 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.5458 | 1.41473 | 0.707366 | − | 0.706848i | \(-0.249883\pi\) | ||||
0.707366 | + | 0.706848i | \(0.249883\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.55950 | 0.331652 | 0.165826 | − | 0.986155i | \(-0.446971\pi\) | ||||
0.165826 | + | 0.986155i | \(0.446971\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.9532 | −0.829433 | −0.414717 | − | 0.909951i | \(-0.636119\pi\) | ||||
−0.414717 | + | 0.909951i | \(0.636119\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0974 | −0.829260 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.15211 | −0.476251 | −0.238126 | − | 0.971234i | \(-0.576533\pi\) | ||||
−0.238126 | + | 0.971234i | \(0.576533\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.98633 | −0.581426 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.84789 | −0.222529 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.3937 | −1.28226 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.13844 | 0.122047 | 0.0610235 | − | 0.998136i | \(-0.480564\pi\) | ||||
0.0610235 | + | 0.998136i | \(0.480564\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.8421 | −0.614801 | −0.307400 | − | 0.951580i | \(-0.599459\pi\) | ||||
−0.307400 | + | 0.951580i | \(0.599459\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.3412 | 1.82803 | 0.914016 | − | 0.405678i | \(-0.132965\pi\) | ||||
0.914016 | + | 0.405678i | \(0.132965\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.9201 | 1.23116 | 0.615578 | − | 0.788076i | \(-0.288922\pi\) | ||||
0.615578 | + | 0.788076i | \(0.288922\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.1248 | −1.23875 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.18521 | −0.121588 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.94747 | −0.163496 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.3937 | 0.681220 | 0.340610 | − | 0.940205i | \(-0.389366\pi\) | ||||
0.340610 | + | 0.940205i | \(0.389366\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −26.9338 | −1.47155 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.73104 | 0.421137 | 0.210568 | − | 0.977579i | \(-0.432469\pi\) | ||||
0.210568 | + | 0.977579i | \(0.432469\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0917 | 0.871412 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.2222 | −1.51505 | −0.757523 | − | 0.652808i | \(-0.773591\pi\) | ||||
−0.757523 | + | 0.652808i | \(0.773591\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.23585 | −0.0661537 | −0.0330769 | − | 0.999453i | \(-0.510531\pi\) | ||||
−0.0330769 | + | 0.999453i | \(0.510531\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.9201 | −1.00702 | −0.503508 | − | 0.863990i | \(-0.667958\pi\) | ||||
−0.503508 | + | 0.863990i | \(0.667958\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −36.2359 | −1.92320 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.8616 | −0.626029 | −0.313015 | − | 0.949748i | \(-0.601339\pi\) | ||||
−0.313015 | + | 0.949748i | \(0.601339\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.3549 | −0.913414 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.17730 | 0.270992 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.2222 | −0.742392 | −0.371196 | − | 0.928555i | \(-0.621052\pi\) | ||||
−0.371196 | + | 0.928555i | \(0.621052\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.6843 | 1.22632 | 0.613162 | − | 0.789957i | \(-0.289897\pi\) | ||||
0.613162 | + | 0.789957i | \(0.289897\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.0917 | −0.828763 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.42107 | 0.227095 | 0.113547 | − | 0.993533i | \(-0.463779\pi\) | ||||
0.113547 | + | 0.993533i | \(0.463779\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.40164 | −0.224913 | −0.112457 | − | 0.993657i | \(-0.535872\pi\) | ||||
−0.112457 | + | 0.993657i | \(0.535872\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.30998 | 0.167822 | 0.0839112 | − | 0.996473i | \(-0.473259\pi\) | ||||
0.0839112 | + | 0.996473i | \(0.473259\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.91626 | −0.0969092 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −35.1833 | −1.77026 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −31.1696 | −1.56436 | −0.782180 | − | 0.623053i | \(-0.785892\pi\) | ||||
−0.782180 | + | 0.623053i | \(0.785892\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.586849 | −0.0293058 | −0.0146529 | − | 0.999893i | \(-0.504664\pi\) | ||||
−0.0146529 | + | 0.999893i | \(0.504664\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.7037 | 0.583003 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −40.1970 | −1.99249 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.0312 | 1.43550 | 0.717750 | − | 0.696300i | \(-0.245172\pi\) | ||||
0.717750 | + | 0.696300i | \(0.245172\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.3880 | −1.00081 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.1833 | 1.13258 | 0.566290 | − | 0.824206i | \(-0.308378\pi\) | ||||
0.566290 | + | 0.824206i | \(0.308378\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.0586 | −1.41623 | −0.708114 | − | 0.706098i | \(-0.750454\pi\) | ||||
−0.708114 | + | 0.706098i | \(0.750454\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.46784 | −0.0712008 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.98057 | 0.0954007 | 0.0477003 | − | 0.998862i | \(-0.484811\pi\) | ||||
0.0477003 | + | 0.998862i | \(0.484811\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.5048 | 1.41791 | 0.708955 | − | 0.705253i | \(-0.249167\pi\) | ||||
0.708955 | + | 0.705253i | \(0.249167\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.44266 | 0.0690116 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.9727 | 0.905515 | 0.452758 | − | 0.891634i | \(-0.350440\pi\) | ||||
0.452758 | + | 0.891634i | \(0.350440\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.2690 | −1.01052 | −0.505259 | − | 0.862968i | \(-0.668603\pi\) | ||||
−0.505259 | + | 0.862968i | \(0.668603\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −38.9590 | −1.84683 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.2690 | 1.00374 | 0.501872 | − | 0.864942i | \(-0.332645\pi\) | ||||
0.501872 | + | 0.864942i | \(0.332645\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.4854 | 0.823354 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.4678 | −0.536443 | −0.268222 | − | 0.963357i | \(-0.586436\pi\) | ||||
−0.268222 | + | 0.963357i | \(0.586436\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.40164 | 0.344729 | 0.172364 | − | 0.985033i | \(-0.444859\pi\) | ||||
0.172364 | + | 0.985033i | \(0.444859\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.68427 | 0.264170 | 0.132085 | − | 0.991238i | \(-0.457833\pi\) | ||||
0.132085 | + | 0.991238i | \(0.457833\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.2301 | 1.16751 | 0.583755 | − | 0.811930i | \(-0.301583\pi\) | ||||
0.583755 | + | 0.811930i | \(0.301583\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −26.0859 | −1.19943 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.10507 | 0.0507040 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.2359 | 0.559070 | 0.279535 | − | 0.960135i | \(-0.409820\pi\) | ||||
0.279535 | + | 0.960135i | \(0.409820\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −29.2359 | −1.33304 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 39.3412 | 1.78639 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.98057 | −0.271005 | −0.135503 | − | 0.990777i | \(-0.543265\pi\) | ||||
−0.135503 | + | 0.990777i | \(0.543265\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.20275 | 0.415314 | 0.207657 | − | 0.978202i | \(-0.433416\pi\) | ||||
0.207657 | + | 0.978202i | \(0.433416\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.01367 | −0.360918 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.6648 | 0.880319 | 0.440159 | − | 0.897920i | \(-0.354922\pi\) | ||||
0.440159 | + | 0.897920i | \(0.354922\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.54583 | −0.425628 | −0.212814 | − | 0.977093i | \(-0.568263\pi\) | ||||
−0.212814 | + | 0.977093i | \(0.568263\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 31.4408 | 1.39910 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.54583 | −0.157166 | −0.0785831 | − | 0.996908i | \(-0.525040\pi\) | ||||
−0.0785831 | + | 0.996908i | \(0.525040\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.9475 | −0.746795 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −55.6375 | −2.44693 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.5458 | 0.681075 | 0.340538 | − | 0.940231i | \(-0.389391\pi\) | ||||
0.340538 | + | 0.940231i | \(0.389391\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.3743 | −1.37190 | −0.685951 | − | 0.727648i | \(-0.740614\pi\) | ||||
−0.685951 | + | 0.727648i | \(0.740614\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.82846 | 0.253892 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.7349 | −0.944996 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.7174 | 0.550850 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.7896 | −1.33115 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.26896 | −0.183537 | −0.0917684 | − | 0.995780i | \(-0.529252\pi\) | ||||
−0.0917684 | + | 0.995780i | \(0.529252\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.9338 | −0.768199 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.4016 | −0.872311 | −0.436155 | − | 0.899871i | \(-0.643660\pi\) | ||||
−0.436155 | + | 0.899871i | \(0.643660\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.03310 | 0.257019 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.4933 | 1.50390 | 0.751950 | − | 0.659221i | \(-0.229114\pi\) | ||||
0.751950 | + | 0.659221i | \(0.229114\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.9727 | −0.802458 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.29055 | −0.222970 | −0.111485 | − | 0.993766i | \(-0.535561\pi\) | ||||
−0.111485 | + | 0.993766i | \(0.535561\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.1831 | 0.680826 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.06045 | 0.0444564 | 0.0222282 | − | 0.999753i | \(-0.492924\pi\) | ||||
0.0222282 | + | 0.999753i | \(0.492924\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.0996 | −1.21778 | −0.608890 | − | 0.793255i | \(-0.708385\pi\) | ||||
−0.608890 | + | 0.793255i | \(0.708385\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.969055 | 0.0404124 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.23585 | −0.0514493 | −0.0257246 | − | 0.999669i | \(-0.508189\pi\) | ||||
−0.0257246 | + | 0.999669i | \(0.508189\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 48.2750 | 1.99935 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.9727 | 1.07201 | 0.536003 | − | 0.844216i | \(-0.319934\pi\) | ||||
0.536003 | + | 0.844216i | \(0.319934\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.38796 | −0.180803 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.3021 | −0.505185 | −0.252593 | − | 0.967573i | \(-0.581283\pi\) | ||||
−0.252593 | + | 0.967573i | \(0.581283\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.7874 | 0.971928 | 0.485964 | − | 0.873979i | \(-0.338469\pi\) | ||||
0.485964 | + | 0.873979i | \(0.338469\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.92012 | −0.323068 | −0.161534 | − | 0.986867i | \(-0.551644\pi\) | ||||
−0.161534 | + | 0.986867i | \(0.551644\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 26.9338 | 1.09501 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.0467764 | −0.00189860 | −0.000949298 | − | 1.00000i | \(-0.500302\pi\) | ||||
−0.000949298 | 1.00000i | \(0.500302\pi\) | ||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −40.4660 | −1.63708 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.8205 | 0.800544 | 0.400272 | − | 0.916396i | \(-0.368916\pi\) | ||||
0.400272 | + | 0.916396i | \(0.368916\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.4328 | −1.38621 | −0.693107 | − | 0.720835i | \(-0.743759\pi\) | ||||
−0.693107 | + | 0.720835i | \(0.743759\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.5127 | 1.90970 | 0.954849 | − | 0.297092i | \(-0.0960168\pi\) | ||||
0.954849 | + | 0.297092i | \(0.0960168\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.5655 | −1.14262 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.5595 | −0.580525 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.26320 | 0.368762 | 0.184381 | − | 0.982855i | \(-0.440972\pi\) | ||||
0.184381 | + | 0.982855i | \(0.440972\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −27.9201 | −1.10798 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.10533 | 0.122653 | 0.0613266 | − | 0.998118i | \(-0.480467\pi\) | ||||
0.0613266 | + | 0.998118i | \(0.480467\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.7368 | −0.699471 | −0.349736 | − | 0.936848i | \(-0.613729\pi\) | ||||
−0.349736 | + | 0.936848i | \(0.613729\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.920120 | 0.0361737 | 0.0180868 | − | 0.999836i | \(-0.494242\pi\) | ||||
0.0180868 | + | 0.999836i | \(0.494242\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.4016 | 0.761581 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.20275 | −0.360131 | −0.180066 | − | 0.983655i | \(-0.557631\pi\) | ||||
−0.180066 | + | 0.983655i | \(0.557631\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.1248 | 0.864486 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 49.3997 | 1.92434 | 0.962170 | − | 0.272448i | \(-0.0878334\pi\) | ||||
0.962170 | + | 0.272448i | \(0.0878334\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −49.9844 | −1.94417 | −0.972085 | − | 0.234631i | \(-0.924612\pi\) | ||||
−0.972085 | + | 0.234631i | \(0.924612\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.29055 | 0.204851 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 43.5070 | 1.67957 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.43474 | 0.363682 | 0.181841 | − | 0.983328i | \(-0.441794\pi\) | ||||
0.181841 | + | 0.983328i | \(0.441794\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.7874 | 0.914226 | 0.457113 | − | 0.889409i | \(-0.348884\pi\) | ||||
0.457113 | + | 0.889409i | \(0.348884\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.6375 | 1.32537 | 0.662683 | − | 0.748900i | \(-0.269418\pi\) | ||||
0.662683 | + | 0.748900i | \(0.269418\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.44625 | 0.208091 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 35.1111 | 1.33763 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.9201 | 1.36647 | 0.683233 | − | 0.730201i | \(-0.260573\pi\) | ||||
0.683233 | + | 0.730201i | \(0.260573\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25.6123 | −0.971530 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.33327 | 0.239890 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.72529 | 0.367319 | 0.183659 | − | 0.982990i | \(-0.441206\pi\) | ||||
0.183659 | + | 0.982990i | \(0.441206\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.9611 | 0.413407 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.1111 | −0.905511 | −0.452756 | − | 0.891635i | \(-0.649559\pi\) | ||||
−0.452756 | + | 0.891635i | \(0.649559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.84789 | −0.144105 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 38.9590 | 1.45698 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.3527 | −0.945496 | −0.472748 | − | 0.881198i | \(-0.656738\pi\) | ||||
−0.472748 | + | 0.881198i | \(0.656738\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.05253 | 0.150507 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.5127 | 1.76215 | 0.881075 | − | 0.472977i | \(-0.156821\pi\) | ||||
0.881075 | + | 0.472977i | \(0.156821\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.44841 | −0.349462 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.8364 | −1.13897 | −0.569484 | − | 0.822003i | \(-0.692857\pi\) | ||||
−0.569484 | + | 0.822003i | \(0.692857\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 52.3275 | 1.92751 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.9942 | 0.772286 | 0.386143 | − | 0.922439i | \(-0.373807\pi\) | ||||
0.386143 | + | 0.922439i | \(0.373807\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.3743 | −1.66462 | −0.832311 | − | 0.554309i | \(-0.812982\pi\) | ||||
−0.832311 | + | 0.554309i | \(0.812982\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −59.0118 | −2.16202 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.8421 | 0.468616 | 0.234308 | − | 0.972162i | \(-0.424718\pi\) | ||||
0.234308 | + | 0.972162i | \(0.424718\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26.9669 | 0.981426 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.9727 | 0.471499 | 0.235750 | − | 0.971814i | \(-0.424245\pi\) | ||||
0.235750 | + | 0.971814i | \(0.424245\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.4933 | −1.50413 | −0.752065 | − | 0.659088i | \(-0.770942\pi\) | ||||
−0.752065 | + | 0.659088i | \(0.770942\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.1111 | 0.509522 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.6900 | −0.890345 | −0.445173 | − | 0.895445i | \(-0.646858\pi\) | ||||
−0.445173 | + | 0.895445i | \(0.646858\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −39.6512 | −1.42615 | −0.713077 | − | 0.701086i | \(-0.752699\pi\) | ||||
−0.713077 | + | 0.701086i | \(0.752699\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.94747 | −0.105876 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.76801 | −0.170832 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 70.3997 | 2.51910 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.90042 | 0.281978 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.0255 | 0.642538 | 0.321269 | − | 0.946988i | \(-0.395891\pi\) | ||||
0.321269 | + | 0.946988i | \(0.395891\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.6432 | 1.12368 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39.8791 | −1.41259 | −0.706295 | − | 0.707918i | \(-0.749635\pi\) | ||||
−0.706295 | + | 0.707918i | \(0.749635\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.1521 | −0.712930 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.0586 | −0.354959 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.1696 | 1.58808 | 0.794040 | − | 0.607865i | \(-0.207974\pi\) | ||||
0.794040 | + | 0.607865i | \(0.207974\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.70945 | −0.0600271 | −0.0300135 | − | 0.999549i | \(-0.509555\pi\) | ||||
−0.0300135 | + | 0.999549i | \(0.509555\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.368267 | −0.0128998 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.11325 | 0.248861 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 52.9144 | 1.84672 | 0.923362 | − | 0.383930i | \(-0.125430\pi\) | ||||
0.923362 | + | 0.383930i | \(0.125430\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.2359 | −1.08881 | −0.544407 | − | 0.838821i | \(-0.683245\pi\) | ||||
−0.544407 | + | 0.838821i | \(0.683245\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.2243 | −1.22487 | −0.612435 | − | 0.790521i | \(-0.709810\pi\) | ||||
−0.612435 | + | 0.790521i | \(0.709810\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.1168 | 0.629224 | 0.314612 | − | 0.949220i | \(-0.398126\pi\) | ||||
0.314612 | + | 0.949220i | \(0.398126\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −58.6766 | −2.03059 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.5401 | 0.674598 | 0.337299 | − | 0.941398i | \(-0.390487\pi\) | ||||
0.337299 | + | 0.941398i | \(0.390487\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.87524 | −0.237077 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.13844 | −0.107965 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.61204 | 0.329496 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.3743 | 0.594884 | 0.297442 | − | 0.954740i | \(-0.403866\pi\) | ||||
0.297442 | + | 0.954740i | \(0.403866\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.5458 | 0.735992 | 0.367996 | − | 0.929827i | \(-0.380044\pi\) | ||||
0.367996 | + | 0.929827i | \(0.380044\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.3743 | 0.592803 | 0.296402 | − | 0.955063i | \(-0.404213\pi\) | ||||
0.296402 | + | 0.955063i | \(0.404213\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.4211 | 0.593020 | 0.296510 | − | 0.955030i | \(-0.404177\pi\) | ||||
0.296510 | + | 0.955030i | \(0.404177\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.8342 | −0.572381 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 68.3549 | 2.31878 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.0586 | 1.28956 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.9981 | 1.58701 | 0.793507 | − | 0.608562i | \(-0.208253\pi\) | ||||
0.793507 | + | 0.608562i | \(0.208253\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.1715 | 0.511142 | 0.255571 | − | 0.966790i | \(-0.417737\pi\) | ||||
0.255571 | + | 0.966790i | \(0.417737\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.4660 | −1.09257 | −0.546283 | − | 0.837601i | \(-0.683958\pi\) | ||||
−0.546283 | + | 0.837601i | \(0.683958\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.86948 | −0.0963477 | −0.0481738 | − | 0.998839i | \(-0.515340\pi\) | ||||
−0.0481738 | + | 0.998839i | \(0.515340\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.1715 | 0.507696 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −35.5847 | −1.18947 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.0917 | −0.536687 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.4854 | 0.582522 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 41.4132 | 1.37662 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.4328 | −1.07692 | −0.538458 | − | 0.842653i | \(-0.680993\pi\) | ||||
−0.538458 | + | 0.842653i | \(0.680993\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.2438 | −1.10142 | −0.550708 | − | 0.834698i | \(-0.685642\pi\) | ||||
−0.550708 | + | 0.834698i | \(0.685642\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.6101 | 1.31090 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.7505 | −0.948391 | −0.474195 | − | 0.880420i | \(-0.657261\pi\) | ||||
−0.474195 | + | 0.880420i | \(0.657261\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 51.2028 | 1.68536 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.36278 | 0.242087 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −54.5458 | −1.78959 | −0.894795 | − | 0.446477i | \(-0.852679\pi\) | ||||
−0.894795 | + | 0.446477i | \(0.852679\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.4016 | 0.634501 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.6979 | 0.937521 | 0.468760 | − | 0.883325i | \(-0.344701\pi\) | ||||
0.468760 | + | 0.883325i | \(0.344701\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.2963 | −0.629042 | −0.314521 | − | 0.949251i | \(-0.601844\pi\) | ||||
−0.314521 | + | 0.949251i | \(0.601844\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.18116 | −0.136157 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.5322 | 0.342249 | 0.171125 | − | 0.985249i | \(-0.445260\pi\) | ||||
0.171125 | + | 0.985249i | \(0.445260\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.31573 | −0.237479 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.1970 | 0.621852 | 0.310926 | − | 0.950434i | \(-0.399361\pi\) | ||||
0.310926 | + | 0.950434i | \(0.399361\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −55.6375 | −1.80039 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.2963 | −0.622461 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.0115 | 0.418855 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.4854 | −0.497976 | −0.248988 | − | 0.968507i | \(-0.580098\pi\) | ||||
−0.248988 | + | 0.968507i | \(0.580098\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.80903 | 0.0580545 | 0.0290273 | − | 0.999579i | \(-0.490759\pi\) | ||||
0.0290273 | + | 0.999579i | \(0.490759\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.8985 | −1.21248 | −0.606241 | − | 0.795281i | \(-0.707323\pi\) | ||||
−0.606241 | + | 0.795281i | \(0.707323\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 75.6903 | 2.41907 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38.1111 | −1.21556 | −0.607778 | − | 0.794107i | \(-0.707939\pi\) | ||||
−0.607778 | + | 0.794107i | \(0.707939\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.66484 | 0.276085 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.23775 | 0.198349 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.7896 | 0.374509 | 0.187254 | − | 0.982311i | \(-0.440041\pi\) | ||||
0.187254 | + | 0.982311i | \(0.440041\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.9475 | −0.537271 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.8069 | 0.468938 | 0.234469 | − | 0.972124i | \(-0.424665\pi\) | ||||
0.234469 | + | 0.972124i | \(0.424665\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 5292.2.a.u.1.3 | 3 | ||
3.2 | odd | 2 | 5292.2.a.x.1.1 | 3 | |||
7.2 | even | 3 | 756.2.k.f.109.1 | yes | 6 | ||
7.4 | even | 3 | 756.2.k.f.541.1 | yes | 6 | ||
7.6 | odd | 2 | 5292.2.a.w.1.1 | 3 | |||
21.2 | odd | 6 | 756.2.k.e.109.3 | ✓ | 6 | ||
21.11 | odd | 6 | 756.2.k.e.541.3 | yes | 6 | ||
21.20 | even | 2 | 5292.2.a.v.1.3 | 3 | |||
63.2 | odd | 6 | 2268.2.l.k.109.1 | 6 | |||
63.4 | even | 3 | 2268.2.l.j.541.3 | 6 | |||
63.11 | odd | 6 | 2268.2.i.j.2053.3 | 6 | |||
63.16 | even | 3 | 2268.2.l.j.109.3 | 6 | |||
63.23 | odd | 6 | 2268.2.i.j.865.3 | 6 | |||
63.25 | even | 3 | 2268.2.i.k.2053.1 | 6 | |||
63.32 | odd | 6 | 2268.2.l.k.541.1 | 6 | |||
63.58 | even | 3 | 2268.2.i.k.865.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.k.e.109.3 | ✓ | 6 | 21.2 | odd | 6 | ||
756.2.k.e.541.3 | yes | 6 | 21.11 | odd | 6 | ||
756.2.k.f.109.1 | yes | 6 | 7.2 | even | 3 | ||
756.2.k.f.541.1 | yes | 6 | 7.4 | even | 3 | ||
2268.2.i.j.865.3 | 6 | 63.23 | odd | 6 | |||
2268.2.i.j.2053.3 | 6 | 63.11 | odd | 6 | |||
2268.2.i.k.865.1 | 6 | 63.58 | even | 3 | |||
2268.2.i.k.2053.1 | 6 | 63.25 | even | 3 | |||
2268.2.l.j.109.3 | 6 | 63.16 | even | 3 | |||
2268.2.l.j.541.3 | 6 | 63.4 | even | 3 | |||
2268.2.l.k.109.1 | 6 | 63.2 | odd | 6 | |||
2268.2.l.k.541.1 | 6 | 63.32 | odd | 6 | |||
5292.2.a.u.1.3 | 3 | 1.1 | even | 1 | trivial | ||
5292.2.a.v.1.3 | 3 | 21.20 | even | 2 | |||
5292.2.a.w.1.1 | 3 | 7.6 | odd | 2 | |||
5292.2.a.x.1.1 | 3 | 3.2 | odd | 2 |