Properties

Label 1728.4.f.d.863.6
Level $1728$
Weight $4$
Character 1728.863
Analytic conductor $101.955$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1728,4,Mod(863,1728)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1728.863");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1728 = 2^{6} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1728.f (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(101.955300490\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.58594980096.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 21x^{6} + 341x^{4} - 2100x^{2} + 10000 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{12}\cdot 3^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 863.6
Root \(-3.20565 + 1.85078i\) of defining polynomial
Character \(\chi\) \(=\) 1728.863
Dual form 1728.4.f.d.863.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.73205 q^{5} -13.0000i q^{7} +O(q^{10})\) \(q+1.73205 q^{5} -13.0000i q^{7} -22.5167i q^{11} +66.5432i q^{13} +115.256i q^{17} +66.5432 q^{19} +115.256 q^{23} -122.000 q^{25} -207.846 q^{29} +13.0000i q^{31} -22.5167i q^{35} -332.716i q^{37} -345.769i q^{41} -266.173 q^{43} -230.512 q^{47} +174.000 q^{49} -112.583 q^{53} -39.0000i q^{55} -135.100i q^{59} +399.259i q^{61} +115.256i q^{65} -345.769 q^{71} +85.0000 q^{73} -292.717 q^{77} +844.000i q^{79} +1259.20i q^{83} +199.630i q^{85} -230.512i q^{89} +865.062 q^{91} +115.256 q^{95} -481.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 976 q^{25} + 1392 q^{49} + 680 q^{73} - 3848 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(703\) \(1217\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 1.73205 0.154919 0.0774597 0.996995i \(-0.475319\pi\)
0.0774597 + 0.996995i \(0.475319\pi\)
\(6\) 0 0
\(7\) − 13.0000i − 0.701934i −0.936388 0.350967i \(-0.885853\pi\)
0.936388 0.350967i \(-0.114147\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) − 22.5167i − 0.617184i −0.951194 0.308592i \(-0.900142\pi\)
0.951194 0.308592i \(-0.0998578\pi\)
\(12\) 0 0
\(13\) 66.5432i 1.41967i 0.704366 + 0.709837i \(0.251232\pi\)
−0.704366 + 0.709837i \(0.748768\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 115.256i 1.64434i 0.569244 + 0.822169i \(0.307236\pi\)
−0.569244 + 0.822169i \(0.692764\pi\)
\(18\) 0 0
\(19\) 66.5432 0.803477 0.401738 0.915754i \(-0.368406\pi\)
0.401738 + 0.915754i \(0.368406\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 115.256 1.04490 0.522448 0.852671i \(-0.325019\pi\)
0.522448 + 0.852671i \(0.325019\pi\)
\(24\) 0 0
\(25\) −122.000 −0.976000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −207.846 −1.33090 −0.665449 0.746443i \(-0.731760\pi\)
−0.665449 + 0.746443i \(0.731760\pi\)
\(30\) 0 0
\(31\) 13.0000i 0.0753184i 0.999291 + 0.0376592i \(0.0119901\pi\)
−0.999291 + 0.0376592i \(0.988010\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) − 22.5167i − 0.108743i
\(36\) 0 0
\(37\) − 332.716i − 1.47833i −0.673525 0.739165i \(-0.735220\pi\)
0.673525 0.739165i \(-0.264780\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 345.769i − 1.31707i −0.752549 0.658537i \(-0.771176\pi\)
0.752549 0.658537i \(-0.228824\pi\)
\(42\) 0 0
\(43\) −266.173 −0.943976 −0.471988 0.881605i \(-0.656464\pi\)
−0.471988 + 0.881605i \(0.656464\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −230.512 −0.715398 −0.357699 0.933837i \(-0.616439\pi\)
−0.357699 + 0.933837i \(0.616439\pi\)
\(48\) 0 0
\(49\) 174.000 0.507289
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −112.583 −0.291783 −0.145892 0.989301i \(-0.546605\pi\)
−0.145892 + 0.989301i \(0.546605\pi\)
\(54\) 0 0
\(55\) − 39.0000i − 0.0956138i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) − 135.100i − 0.298110i −0.988829 0.149055i \(-0.952377\pi\)
0.988829 0.149055i \(-0.0476232\pi\)
\(60\) 0 0
\(61\) 399.259i 0.838031i 0.907979 + 0.419016i \(0.137625\pi\)
−0.907979 + 0.419016i \(0.862375\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 115.256i 0.219935i
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −345.769 −0.577961 −0.288980 0.957335i \(-0.593316\pi\)
−0.288980 + 0.957335i \(0.593316\pi\)
\(72\) 0 0
\(73\) 85.0000 0.136281 0.0681404 0.997676i \(-0.478293\pi\)
0.0681404 + 0.997676i \(0.478293\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −292.717 −0.433223
\(78\) 0 0
\(79\) 844.000i 1.20199i 0.799252 + 0.600996i \(0.205229\pi\)
−0.799252 + 0.600996i \(0.794771\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1259.20i 1.66524i 0.553842 + 0.832622i \(0.313161\pi\)
−0.553842 + 0.832622i \(0.686839\pi\)
\(84\) 0 0
\(85\) 199.630i 0.254740i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) − 230.512i − 0.274542i −0.990534 0.137271i \(-0.956167\pi\)
0.990534 0.137271i \(-0.0438332\pi\)
\(90\) 0 0
\(91\) 865.062 0.996518
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 115.256 0.124474
\(96\) 0 0
\(97\) −481.000 −0.503486 −0.251743 0.967794i \(-0.581004\pi\)
−0.251743 + 0.967794i \(0.581004\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −694.552 −0.684263 −0.342131 0.939652i \(-0.611149\pi\)
−0.342131 + 0.939652i \(0.611149\pi\)
\(102\) 0 0
\(103\) − 632.000i − 0.604590i −0.953214 0.302295i \(-0.902247\pi\)
0.953214 0.302295i \(-0.0977528\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1311.16i 1.18462i 0.805708 + 0.592312i \(0.201785\pi\)
−0.805708 + 0.592312i \(0.798215\pi\)
\(108\) 0 0
\(109\) 66.5432i 0.0584742i 0.999573 + 0.0292371i \(0.00930778\pi\)
−0.999573 + 0.0292371i \(0.990692\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1498.33i 1.24736i 0.781682 + 0.623678i \(0.214362\pi\)
−0.781682 + 0.623678i \(0.785638\pi\)
\(114\) 0 0
\(115\) 199.630 0.161874
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1498.33 1.15422
\(120\) 0 0
\(121\) 824.000 0.619083
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −427.817 −0.306121
\(126\) 0 0
\(127\) − 1201.00i − 0.839146i −0.907722 0.419573i \(-0.862180\pi\)
0.907722 0.419573i \(-0.137820\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2274.18i 1.51677i 0.651810 + 0.758383i \(0.274010\pi\)
−0.651810 + 0.758383i \(0.725990\pi\)
\(132\) 0 0
\(133\) − 865.062i − 0.563988i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 230.512i − 0.143752i −0.997414 0.0718759i \(-0.977101\pi\)
0.997414 0.0718759i \(-0.0228986\pi\)
\(138\) 0 0
\(139\) −1330.86 −0.812104 −0.406052 0.913850i \(-0.633095\pi\)
−0.406052 + 0.913850i \(0.633095\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1498.33 0.876201
\(144\) 0 0
\(145\) −360.000 −0.206182
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1352.73 −0.743759 −0.371880 0.928281i \(-0.621287\pi\)
−0.371880 + 0.928281i \(0.621287\pi\)
\(150\) 0 0
\(151\) − 319.000i − 0.171920i −0.996299 0.0859598i \(-0.972604\pi\)
0.996299 0.0859598i \(-0.0273957\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 22.5167i 0.0116683i
\(156\) 0 0
\(157\) − 1730.12i − 0.879483i −0.898124 0.439742i \(-0.855070\pi\)
0.898124 0.439742i \(-0.144930\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) − 1498.33i − 0.733447i
\(162\) 0 0
\(163\) −3127.53 −1.50287 −0.751433 0.659809i \(-0.770637\pi\)
−0.751433 + 0.659809i \(0.770637\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3227.17 −1.49537 −0.747683 0.664055i \(-0.768834\pi\)
−0.747683 + 0.664055i \(0.768834\pi\)
\(168\) 0 0
\(169\) −2231.00 −1.01548
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3628.65 −1.59469 −0.797344 0.603526i \(-0.793762\pi\)
−0.797344 + 0.603526i \(0.793762\pi\)
\(174\) 0 0
\(175\) 1586.00i 0.685088i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3576.68i 1.49349i 0.665113 + 0.746743i \(0.268383\pi\)
−0.665113 + 0.746743i \(0.731617\pi\)
\(180\) 0 0
\(181\) 3460.25i 1.42098i 0.703705 + 0.710492i \(0.251528\pi\)
−0.703705 + 0.710492i \(0.748472\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) − 576.281i − 0.229022i
\(186\) 0 0
\(187\) 2595.19 1.01486
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3572.94 −1.35356 −0.676778 0.736187i \(-0.736624\pi\)
−0.676778 + 0.736187i \(0.736624\pi\)
\(192\) 0 0
\(193\) 3101.00 1.15655 0.578277 0.815841i \(-0.303725\pi\)
0.578277 + 0.815841i \(0.303725\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −4480.82 −1.62053 −0.810266 0.586062i \(-0.800677\pi\)
−0.810266 + 0.586062i \(0.800677\pi\)
\(198\) 0 0
\(199\) − 5.00000i − 0.00178111i −1.00000 0.000890554i \(-0.999717\pi\)
1.00000 0.000890554i \(-0.000283472\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2702.00i 0.934203i
\(204\) 0 0
\(205\) − 598.889i − 0.204040i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) − 1498.33i − 0.495893i
\(210\) 0 0
\(211\) 6055.43 1.97570 0.987851 0.155403i \(-0.0496676\pi\)
0.987851 + 0.155403i \(0.0496676\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −461.025 −0.146240
\(216\) 0 0
\(217\) 169.000 0.0528685
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −7669.52 −2.33442
\(222\) 0 0
\(223\) − 2032.00i − 0.610192i −0.952322 0.305096i \(-0.901311\pi\)
0.952322 0.305096i \(-0.0986885\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2546.11i 0.744456i 0.928141 + 0.372228i \(0.121406\pi\)
−0.928141 + 0.372228i \(0.878594\pi\)
\(228\) 0 0
\(229\) 1730.12i 0.499257i 0.968342 + 0.249628i \(0.0803085\pi\)
−0.968342 + 0.249628i \(0.919692\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4610.25i 1.29626i 0.761532 + 0.648128i \(0.224448\pi\)
−0.761532 + 0.648128i \(0.775552\pi\)
\(234\) 0 0
\(235\) −399.259 −0.110829
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6339.09 1.71566 0.857828 0.513937i \(-0.171813\pi\)
0.857828 + 0.513937i \(0.171813\pi\)
\(240\) 0 0
\(241\) 2626.00 0.701890 0.350945 0.936396i \(-0.385860\pi\)
0.350945 + 0.936396i \(0.385860\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 301.377 0.0785888
\(246\) 0 0
\(247\) 4428.00i 1.14068i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1714.73i 0.431206i 0.976481 + 0.215603i \(0.0691718\pi\)
−0.976481 + 0.215603i \(0.930828\pi\)
\(252\) 0 0
\(253\) − 2595.19i − 0.644893i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 4494.99i − 1.09101i −0.838107 0.545506i \(-0.816338\pi\)
0.838107 0.545506i \(-0.183662\pi\)
\(258\) 0 0
\(259\) −4325.31 −1.03769
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3572.94 0.837708 0.418854 0.908054i \(-0.362432\pi\)
0.418854 + 0.908054i \(0.362432\pi\)
\(264\) 0 0
\(265\) −195.000 −0.0452028
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −5133.80 −1.16362 −0.581809 0.813325i \(-0.697655\pi\)
−0.581809 + 0.813325i \(0.697655\pi\)
\(270\) 0 0
\(271\) − 1723.00i − 0.386217i −0.981177 0.193108i \(-0.938143\pi\)
0.981177 0.193108i \(-0.0618569\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2747.03i 0.602372i
\(276\) 0 0
\(277\) − 1463.95i − 0.317546i −0.987315 0.158773i \(-0.949246\pi\)
0.987315 0.158773i \(-0.0507538\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4264.48i 0.905330i 0.891681 + 0.452665i \(0.149527\pi\)
−0.891681 + 0.452665i \(0.850473\pi\)
\(282\) 0 0
\(283\) −7519.38 −1.57944 −0.789719 0.613469i \(-0.789774\pi\)
−0.789719 + 0.613469i \(0.789774\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4494.99 −0.924498
\(288\) 0 0
\(289\) −8371.00 −1.70385
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1621.20 −0.323247 −0.161624 0.986852i \(-0.551673\pi\)
−0.161624 + 0.986852i \(0.551673\pi\)
\(294\) 0 0
\(295\) − 234.000i − 0.0461831i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 7669.52i 1.48341i
\(300\) 0 0
\(301\) 3460.25i 0.662609i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 691.537i 0.129827i
\(306\) 0 0
\(307\) 3792.96 0.705133 0.352567 0.935787i \(-0.385309\pi\)
0.352567 + 0.935787i \(0.385309\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 3111.92 0.567398 0.283699 0.958913i \(-0.408438\pi\)
0.283699 + 0.958913i \(0.408438\pi\)
\(312\) 0 0
\(313\) 625.000 0.112866 0.0564330 0.998406i \(-0.482027\pi\)
0.0564330 + 0.998406i \(0.482027\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7588.11 −1.34445 −0.672226 0.740346i \(-0.734661\pi\)
−0.672226 + 0.740346i \(0.734661\pi\)
\(318\) 0 0
\(319\) 4680.00i 0.821410i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 7669.52i 1.32119i
\(324\) 0 0
\(325\) − 8118.27i − 1.38560i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2996.66i 0.502162i
\(330\) 0 0
\(331\) 931.605 0.154700 0.0773499 0.997004i \(-0.475354\pi\)
0.0773499 + 0.997004i \(0.475354\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 2738.00 0.442577 0.221288 0.975208i \(-0.428974\pi\)
0.221288 + 0.975208i \(0.428974\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 292.717 0.0464853
\(342\) 0 0
\(343\) − 6721.00i − 1.05802i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 9614.61i 1.48743i 0.668495 + 0.743717i \(0.266939\pi\)
−0.668495 + 0.743717i \(0.733061\pi\)
\(348\) 0 0
\(349\) 7253.21i 1.11248i 0.831022 + 0.556240i \(0.187756\pi\)
−0.831022 + 0.556240i \(0.812244\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2189.87i 0.330184i 0.986278 + 0.165092i \(0.0527921\pi\)
−0.986278 + 0.165092i \(0.947208\pi\)
\(354\) 0 0
\(355\) −598.889 −0.0895373
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −2431.00 −0.354425
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 147.224 0.0211125
\(366\) 0 0
\(367\) − 10895.0i − 1.54963i −0.632188 0.774815i \(-0.717843\pi\)
0.632188 0.774815i \(-0.282157\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1463.58i 0.204813i
\(372\) 0 0
\(373\) − 6055.43i − 0.840586i −0.907389 0.420293i \(-0.861927\pi\)
0.907389 0.420293i \(-0.138073\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 13830.7i − 1.88944i
\(378\) 0 0
\(379\) 10247.7 1.38888 0.694442 0.719549i \(-0.255651\pi\)
0.694442 + 0.719549i \(0.255651\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −13485.0 −1.79909 −0.899543 0.436831i \(-0.856101\pi\)
−0.899543 + 0.436831i \(0.856101\pi\)
\(384\) 0 0
\(385\) −507.000 −0.0671146
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2682.95 −0.349694 −0.174847 0.984596i \(-0.555943\pi\)
−0.174847 + 0.984596i \(0.555943\pi\)
\(390\) 0 0
\(391\) 13284.0i 1.71816i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1461.85i 0.186212i
\(396\) 0 0
\(397\) 7253.21i 0.916948i 0.888708 + 0.458474i \(0.151604\pi\)
−0.888708 + 0.458474i \(0.848396\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2996.66i 0.373182i 0.982438 + 0.186591i \(0.0597440\pi\)
−0.982438 + 0.186591i \(0.940256\pi\)
\(402\) 0 0
\(403\) −865.062 −0.106928
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −7491.66 −0.912402
\(408\) 0 0
\(409\) 10435.0 1.26156 0.630779 0.775962i \(-0.282735\pi\)
0.630779 + 0.775962i \(0.282735\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1756.30 −0.209254
\(414\) 0 0
\(415\) 2181.00i 0.257979i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 4250.45i − 0.495580i −0.968814 0.247790i \(-0.920296\pi\)
0.968814 0.247790i \(-0.0797044\pi\)
\(420\) 0 0
\(421\) 7719.01i 0.893591i 0.894636 + 0.446795i \(0.147435\pi\)
−0.894636 + 0.446795i \(0.852565\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) − 14061.3i − 1.60487i
\(426\) 0 0
\(427\) 5190.37 0.588243
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 10834.1 1.21081 0.605406 0.795917i \(-0.293011\pi\)
0.605406 + 0.795917i \(0.293011\pi\)
\(432\) 0 0
\(433\) −7493.00 −0.831618 −0.415809 0.909452i \(-0.636502\pi\)
−0.415809 + 0.909452i \(0.636502\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7669.52 0.839549
\(438\) 0 0
\(439\) − 4217.00i − 0.458466i −0.973372 0.229233i \(-0.926378\pi\)
0.973372 0.229233i \(-0.0736217\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6765.39i 0.725583i 0.931870 + 0.362792i \(0.118176\pi\)
−0.931870 + 0.362792i \(0.881824\pi\)
\(444\) 0 0
\(445\) − 399.259i − 0.0425319i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 10488.3i 1.10239i 0.834376 + 0.551196i \(0.185828\pi\)
−0.834376 + 0.551196i \(0.814172\pi\)
\(450\) 0 0
\(451\) −7785.56 −0.812877
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1498.33 0.154380
\(456\) 0 0
\(457\) −10049.0 −1.02860 −0.514302 0.857609i \(-0.671949\pi\)
−0.514302 + 0.857609i \(0.671949\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −8509.57 −0.859718 −0.429859 0.902896i \(-0.641437\pi\)
−0.429859 + 0.902896i \(0.641437\pi\)
\(462\) 0 0
\(463\) 16061.0i 1.61213i 0.591824 + 0.806067i \(0.298408\pi\)
−0.591824 + 0.806067i \(0.701592\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 9881.35i − 0.979131i −0.871966 0.489566i \(-0.837155\pi\)
0.871966 0.489566i \(-0.162845\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 5993.32i 0.582607i
\(474\) 0 0
\(475\) −8118.27 −0.784193
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 17518.9 1.67111 0.835554 0.549408i \(-0.185147\pi\)
0.835554 + 0.549408i \(0.185147\pi\)
\(480\) 0 0
\(481\) 22140.0 2.09875
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −833.116 −0.0779997
\(486\) 0 0
\(487\) − 13984.0i − 1.30118i −0.759428 0.650591i \(-0.774521\pi\)
0.759428 0.650591i \(-0.225479\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) − 6060.45i − 0.557035i −0.960431 0.278517i \(-0.910157\pi\)
0.960431 0.278517i \(-0.0898430\pi\)
\(492\) 0 0
\(493\) − 23955.6i − 2.18845i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4494.99i 0.405690i
\(498\) 0 0
\(499\) −10380.7 −0.931274 −0.465637 0.884976i \(-0.654175\pi\)
−0.465637 + 0.884976i \(0.654175\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4494.99 0.398453 0.199226 0.979953i \(-0.436157\pi\)
0.199226 + 0.979953i \(0.436157\pi\)
\(504\) 0 0
\(505\) −1203.00 −0.106006
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16189.5 −1.40980 −0.704898 0.709309i \(-0.749007\pi\)
−0.704898 + 0.709309i \(0.749007\pi\)
\(510\) 0 0
\(511\) − 1105.00i − 0.0956601i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 1094.66i − 0.0936627i
\(516\) 0 0
\(517\) 5190.37i 0.441532i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 8413.71i 0.707507i 0.935339 + 0.353753i \(0.115095\pi\)
−0.935339 + 0.353753i \(0.884905\pi\)
\(522\) 0 0
\(523\) −12576.7 −1.05151 −0.525755 0.850636i \(-0.676217\pi\)
−0.525755 + 0.850636i \(0.676217\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1498.33 −0.123849
\(528\) 0 0
\(529\) 1117.00 0.0918057
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 23008.6 1.86982
\(534\) 0 0
\(535\) 2271.00i 0.183521i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) − 3917.90i − 0.313091i
\(540\) 0 0
\(541\) − 3460.25i − 0.274986i −0.990503 0.137493i \(-0.956095\pi\)
0.990503 0.137493i \(-0.0439045\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 115.256i 0.00905878i
\(546\) 0 0
\(547\) 22957.4 1.79449 0.897247 0.441529i \(-0.145564\pi\)
0.897247 + 0.441529i \(0.145564\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −13830.7 −1.06935
\(552\) 0 0
\(553\) 10972.0 0.843720
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −10380.2 −0.789627 −0.394814 0.918761i \(-0.629191\pi\)
−0.394814 + 0.918761i \(0.629191\pi\)
\(558\) 0 0
\(559\) − 17712.0i − 1.34014i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 10331.7i − 0.773408i −0.922204 0.386704i \(-0.873614\pi\)
0.922204 0.386704i \(-0.126386\pi\)
\(564\) 0 0
\(565\) 2595.19i 0.193239i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 11986.6i 0.883140i 0.897227 + 0.441570i \(0.145578\pi\)
−0.897227 + 0.441570i \(0.854422\pi\)
\(570\) 0 0
\(571\) 16702.3 1.22412 0.612059 0.790812i \(-0.290341\pi\)
0.612059 + 0.790812i \(0.290341\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −14061.3 −1.01982
\(576\) 0 0
\(577\) −24518.0 −1.76897 −0.884487 0.466565i \(-0.845491\pi\)
−0.884487 + 0.466565i \(0.845491\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 16369.6 1.16889
\(582\) 0 0
\(583\) 2535.00i 0.180084i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 19161.7i − 1.34734i −0.739033 0.673669i \(-0.764717\pi\)
0.739033 0.673669i \(-0.235283\pi\)
\(588\) 0 0
\(589\) 865.062i 0.0605166i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 11986.6i − 0.830072i −0.909805 0.415036i \(-0.863769\pi\)
0.909805 0.415036i \(-0.136231\pi\)
\(594\) 0 0
\(595\) 2595.19 0.178810
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 12908.7 0.880526 0.440263 0.897869i \(-0.354885\pi\)
0.440263 + 0.897869i \(0.354885\pi\)
\(600\) 0 0
\(601\) −15835.0 −1.07475 −0.537374 0.843344i \(-0.680583\pi\)
−0.537374 + 0.843344i \(0.680583\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1427.21 0.0959080
\(606\) 0 0
\(607\) 18344.0i 1.22662i 0.789841 + 0.613311i \(0.210163\pi\)
−0.789841 + 0.613311i \(0.789837\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) − 15339.0i − 1.01563i
\(612\) 0 0
\(613\) 21560.0i 1.42056i 0.703922 + 0.710278i \(0.251431\pi\)
−0.703922 + 0.710278i \(0.748569\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 21322.4i − 1.39126i −0.718400 0.695630i \(-0.755125\pi\)
0.718400 0.695630i \(-0.244875\pi\)
\(618\) 0 0
\(619\) 1397.41 0.0907376 0.0453688 0.998970i \(-0.485554\pi\)
0.0453688 + 0.998970i \(0.485554\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2996.66 −0.192711
\(624\) 0 0
\(625\) 14509.0 0.928576
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 38347.6 2.43087
\(630\) 0 0
\(631\) − 11245.0i − 0.709440i −0.934973 0.354720i \(-0.884576\pi\)
0.934973 0.354720i \(-0.115424\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 2080.19i − 0.130000i
\(636\) 0 0
\(637\) 11578.5i 0.720185i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) − 4494.99i − 0.276976i −0.990364 0.138488i \(-0.955776\pi\)
0.990364 0.138488i \(-0.0442242\pi\)
\(642\) 0 0
\(643\) 5988.89 0.367308 0.183654 0.982991i \(-0.441207\pi\)
0.183654 + 0.982991i \(0.441207\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −5993.32 −0.364176 −0.182088 0.983282i \(-0.558286\pi\)
−0.182088 + 0.983282i \(0.558286\pi\)
\(648\) 0 0
\(649\) −3042.00 −0.183989
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 10858.2 0.650712 0.325356 0.945592i \(-0.394516\pi\)
0.325356 + 0.945592i \(0.394516\pi\)
\(654\) 0 0
\(655\) 3939.00i 0.234976i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) − 13217.3i − 0.781293i −0.920541 0.390647i \(-0.872251\pi\)
0.920541 0.390647i \(-0.127749\pi\)
\(660\) 0 0
\(661\) − 3792.96i − 0.223191i −0.993754 0.111595i \(-0.964404\pi\)
0.993754 0.111595i \(-0.0355961\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) − 1498.33i − 0.0873726i
\(666\) 0 0
\(667\) −23955.6 −1.39065
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 8989.99 0.517220
\(672\) 0 0
\(673\) −21965.0 −1.25808 −0.629041 0.777373i \(-0.716552\pi\)
−0.629041 + 0.777373i \(0.716552\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 17292.8 0.981708 0.490854 0.871242i \(-0.336685\pi\)
0.490854 + 0.871242i \(0.336685\pi\)
\(678\) 0 0
\(679\) 6253.00i 0.353414i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 5372.82i 0.301003i 0.988610 + 0.150502i \(0.0480889\pi\)
−0.988610 + 0.150502i \(0.951911\pi\)
\(684\) 0 0
\(685\) − 399.259i − 0.0222699i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) − 7491.66i − 0.414237i
\(690\) 0 0
\(691\) −19031.4 −1.04774 −0.523869 0.851799i \(-0.675512\pi\)
−0.523869 + 0.851799i \(0.675512\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2305.12 −0.125811
\(696\) 0 0
\(697\) 39852.0 2.16571
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −7272.88 −0.391859 −0.195929 0.980618i \(-0.562772\pi\)
−0.195929 + 0.980618i \(0.562772\pi\)
\(702\) 0 0
\(703\) − 22140.0i − 1.18780i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 9029.18i 0.480307i
\(708\) 0 0
\(709\) − 16103.5i − 0.853002i −0.904487 0.426501i \(-0.859746\pi\)
0.904487 0.426501i \(-0.140254\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1498.33i 0.0786998i
\(714\) 0 0
\(715\) 2595.19 0.135740
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −19593.6 −1.01630 −0.508148 0.861270i \(-0.669670\pi\)
−0.508148 + 0.861270i \(0.669670\pi\)
\(720\) 0 0
\(721\) −8216.00 −0.424383
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 25357.2 1.29896
\(726\) 0 0
\(727\) − 949.000i − 0.0484133i −0.999707 0.0242066i \(-0.992294\pi\)
0.999707 0.0242066i \(-0.00770597\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) − 30678.1i − 1.55222i
\(732\) 0 0
\(733\) − 10314.2i − 0.519732i −0.965645 0.259866i \(-0.916322\pi\)
0.965645 0.259866i \(-0.0836784\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 28014.7 1.39450 0.697251 0.716827i \(-0.254406\pi\)
0.697251 + 0.716827i \(0.254406\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1498.33 0.0739817 0.0369909 0.999316i \(-0.488223\pi\)
0.0369909 + 0.999316i \(0.488223\pi\)
\(744\) 0 0
\(745\) −2343.00 −0.115223
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 17045.1 0.831528
\(750\) 0 0
\(751\) 40261.0i 1.95625i 0.208015 + 0.978126i \(0.433300\pi\)
−0.208015 + 0.978126i \(0.566700\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) − 552.524i − 0.0266337i
\(756\) 0 0
\(757\) − 20761.5i − 0.996815i −0.866943 0.498408i \(-0.833918\pi\)
0.866943 0.498408i \(-0.166082\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 14752.8i 0.702744i 0.936236 + 0.351372i \(0.114285\pi\)
−0.936236 + 0.351372i \(0.885715\pi\)
\(762\) 0 0
\(763\) 865.062 0.0410450
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 8989.99 0.423220
\(768\) 0 0
\(769\) 28877.0 1.35414 0.677068 0.735920i \(-0.263250\pi\)
0.677068 + 0.735920i \(0.263250\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 38119.0 1.77367 0.886833 0.462090i \(-0.152900\pi\)
0.886833 + 0.462090i \(0.152900\pi\)
\(774\) 0 0
\(775\) − 1586.00i − 0.0735107i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 23008.6i − 1.05824i
\(780\) 0 0
\(781\) 7785.56i 0.356708i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) − 2996.66i − 0.136249i
\(786\) 0 0
\(787\) −40325.2 −1.82648 −0.913239 0.407425i \(-0.866427\pi\)
−0.913239 + 0.407425i \(0.866427\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 19478.3 0.875561
\(792\) 0 0
\(793\) −26568.0 −1.18973
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2315.75 0.102921 0.0514606 0.998675i \(-0.483612\pi\)
0.0514606 + 0.998675i \(0.483612\pi\)
\(798\) 0 0
\(799\) − 26568.0i − 1.17636i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) − 1913.92i − 0.0841104i
\(804\) 0 0
\(805\) − 2595.19i − 0.113625i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 38956.6i 1.69301i 0.532384 + 0.846503i \(0.321296\pi\)
−0.532384 + 0.846503i \(0.678704\pi\)
\(810\) 0 0
\(811\) 25086.8 1.08621 0.543105 0.839665i \(-0.317249\pi\)
0.543105 + 0.839665i \(0.317249\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −5417.04 −0.232823
\(816\) 0 0
\(817\) −17712.0 −0.758463
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 32424.0 1.37833 0.689163 0.724607i \(-0.257979\pi\)
0.689163 + 0.724607i \(0.257979\pi\)
\(822\) 0 0
\(823\) 43277.0i 1.83298i 0.400059 + 0.916489i \(0.368990\pi\)
−0.400059 + 0.916489i \(0.631010\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 42660.4i − 1.79377i −0.442264 0.896885i \(-0.645824\pi\)
0.442264 0.896885i \(-0.354176\pi\)
\(828\) 0 0
\(829\) − 13841.0i − 0.579876i −0.957045 0.289938i \(-0.906365\pi\)
0.957045 0.289938i \(-0.0936347\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 20054.6i 0.834154i
\(834\) 0 0
\(835\) −5589.63 −0.231661
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 25702.1 1.05761 0.528806 0.848743i \(-0.322640\pi\)
0.528806 + 0.848743i \(0.322640\pi\)
\(840\) 0 0
\(841\) 18811.0 0.771290
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −3864.21 −0.157317
\(846\) 0 0
\(847\) − 10712.0i − 0.434556i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) − 38347.6i − 1.54470i
\(852\) 0 0
\(853\) 23157.0i 0.929522i 0.885436 + 0.464761i \(0.153860\pi\)
−0.885436 + 0.464761i \(0.846140\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 11871.4i 0.473184i 0.971609 + 0.236592i \(0.0760305\pi\)
−0.971609 + 0.236592i \(0.923969\pi\)
\(858\) 0 0
\(859\) −3060.99 −0.121583 −0.0607914 0.998150i \(-0.519362\pi\)
−0.0607914 + 0.998150i \(0.519362\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 42644.8 1.68209 0.841046 0.540963i \(-0.181940\pi\)
0.841046 + 0.540963i \(0.181940\pi\)
\(864\) 0 0
\(865\) −6285.00 −0.247048
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 19004.1 0.741851
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 5561.62i 0.214876i
\(876\) 0 0
\(877\) 34602.5i 1.33232i 0.745810 + 0.666159i \(0.232063\pi\)
−0.745810 + 0.666159i \(0.767937\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 32848.0i − 1.25616i −0.778148 0.628081i \(-0.783841\pi\)
0.778148 0.628081i \(-0.216159\pi\)
\(882\) 0 0
\(883\) 23090.5 0.880019 0.440010 0.897993i \(-0.354975\pi\)
0.440010 + 0.897993i \(0.354975\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −48522.9 −1.83680 −0.918398 0.395657i \(-0.870517\pi\)
−0.918398 + 0.395657i \(0.870517\pi\)
\(888\) 0 0
\(889\) −15613.0 −0.589025
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −15339.0 −0.574806
\(894\) 0 0
\(895\) 6195.00i 0.231370i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) − 2702.00i − 0.100241i
\(900\) 0 0
\(901\) − 12975.9i − 0.479790i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 5993.32i 0.220138i
\(906\) 0 0
\(907\) 7519.38 0.275278 0.137639 0.990482i \(-0.456049\pi\)
0.137639 + 0.990482i \(0.456049\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −44027.9 −1.60122 −0.800609 0.599188i \(-0.795490\pi\)
−0.800609 + 0.599188i \(0.795490\pi\)
\(912\) 0 0
\(913\) 28353.0 1.02776
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 29564.4 1.06467
\(918\) 0 0
\(919\) − 35671.0i − 1.28039i −0.768213 0.640195i \(-0.778854\pi\)
0.768213 0.640195i \(-0.221146\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) − 23008.6i − 0.820516i
\(924\) 0 0
\(925\) 40591.4i 1.44285i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) − 38956.6i − 1.37581i −0.725802 0.687904i \(-0.758531\pi\)
0.725802 0.687904i \(-0.241469\pi\)
\(930\) 0 0
\(931\) 11578.5 0.407595
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 4494.99 0.157221
\(936\) 0 0
\(937\) −21605.0 −0.753260 −0.376630 0.926364i \(-0.622917\pi\)
−0.376630 + 0.926364i \(0.622917\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −31476.6 −1.09044 −0.545221 0.838292i \(-0.683554\pi\)
−0.545221 + 0.838292i \(0.683554\pi\)
\(942\) 0 0
\(943\) − 39852.0i − 1.37620i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 10349.0i − 0.355119i −0.984110 0.177559i \(-0.943180\pi\)
0.984110 0.177559i \(-0.0568202\pi\)
\(948\) 0 0
\(949\) 5656.17i 0.193474i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 50943.3i − 1.73160i −0.500391 0.865800i \(-0.666810\pi\)
0.500391 0.865800i \(-0.333190\pi\)
\(954\) 0 0
\(955\) −6188.52 −0.209692
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −2996.66 −0.100904
\(960\) 0 0
\(961\) 29622.0 0.994327
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 5371.09 0.179173
\(966\) 0 0
\(967\) 5629.00i 0.187194i 0.995610 + 0.0935969i \(0.0298365\pi\)
−0.995610 + 0.0935969i \(0.970164\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) − 22241.3i − 0.735073i −0.930009 0.367537i \(-0.880201\pi\)
0.930009 0.367537i \(-0.119799\pi\)
\(972\) 0 0
\(973\) 17301.2i 0.570043i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1844.10i 0.0603869i 0.999544 + 0.0301934i \(0.00961233\pi\)
−0.999544 + 0.0301934i \(0.990388\pi\)
\(978\) 0 0
\(979\) −5190.37 −0.169443
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 5762.81 0.186984 0.0934919 0.995620i \(-0.470197\pi\)
0.0934919 + 0.995620i \(0.470197\pi\)
\(984\) 0 0
\(985\) −7761.00 −0.251052
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −30678.1 −0.986356
\(990\) 0 0
\(991\) − 9293.00i − 0.297883i −0.988846 0.148941i \(-0.952413\pi\)
0.988846 0.148941i \(-0.0475866\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) − 8.66025i 0 0.000275928i
\(996\) 0 0
\(997\) − 54498.9i − 1.73119i −0.500744 0.865595i \(-0.666940\pi\)
0.500744 0.865595i \(-0.333060\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 1728.4.f.d.863.6 yes 8
3.2 odd 2 inner 1728.4.f.d.863.2 yes 8
4.3 odd 2 inner 1728.4.f.d.863.8 yes 8
8.3 odd 2 inner 1728.4.f.d.863.3 yes 8
8.5 even 2 inner 1728.4.f.d.863.1 8
12.11 even 2 inner 1728.4.f.d.863.4 yes 8
24.5 odd 2 inner 1728.4.f.d.863.5 yes 8
24.11 even 2 inner 1728.4.f.d.863.7 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1728.4.f.d.863.1 8 8.5 even 2 inner
1728.4.f.d.863.2 yes 8 3.2 odd 2 inner
1728.4.f.d.863.3 yes 8 8.3 odd 2 inner
1728.4.f.d.863.4 yes 8 12.11 even 2 inner
1728.4.f.d.863.5 yes 8 24.5 odd 2 inner
1728.4.f.d.863.6 yes 8 1.1 even 1 trivial
1728.4.f.d.863.7 yes 8 24.11 even 2 inner
1728.4.f.d.863.8 yes 8 4.3 odd 2 inner