Properties

Label 6048.2.j.d.5615.9
Level $6048$
Weight $2$
Character 6048.5615
Analytic conductor $48.294$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6048,2,Mod(5615,6048)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6048.5615");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6048.j (of order \(2\), degree \(1\), not 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: \(48.2935231425\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: no (minimal twist has level 1512)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5615.9
Character \(\chi\) \(=\) 6048.5615
Dual form 6048.2.j.d.5615.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.85878 q^{5} -1.00000i q^{7} +O(q^{10})\) \(q-2.85878 q^{5} -1.00000i q^{7} +4.98479i q^{11} +2.35304i q^{13} +8.19706i q^{17} -5.90589 q^{19} +4.43848 q^{23} +3.17265 q^{25} -6.41440 q^{29} +3.31678i q^{31} +2.85878i q^{35} -5.51080i q^{37} -3.41549i q^{41} -1.37638 q^{43} +2.60102 q^{47} -1.00000 q^{49} +13.3184 q^{53} -14.2505i q^{55} +10.6485i q^{59} -1.41211i q^{61} -6.72683i q^{65} -0.221252 q^{67} -0.398786 q^{71} -10.7893 q^{73} +4.98479 q^{77} +9.76133i q^{79} -2.06831i q^{83} -23.4336i q^{85} -17.6684i q^{89} +2.35304 q^{91} +16.8837 q^{95} -3.62651 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 16 q^{19} + 48 q^{25} - 64 q^{43} - 48 q^{49} - 32 q^{67}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).

\(n\) \(2593\) \(3781\) \(3809\) \(4159\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

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
\(5\) −2.85878 −1.27849 −0.639244 0.769004i \(-0.720753\pi\)
−0.639244 + 0.769004i \(0.720753\pi\)
\(6\) 0 0
\(7\) − 1.00000i − 0.377964i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.98479i 1.50297i 0.659749 + 0.751486i \(0.270663\pi\)
−0.659749 + 0.751486i \(0.729337\pi\)
\(12\) 0 0
\(13\) 2.35304i 0.652615i 0.945264 + 0.326308i \(0.105805\pi\)
−0.945264 + 0.326308i \(0.894195\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 8.19706i 1.98808i 0.109021 + 0.994039i \(0.465228\pi\)
−0.109021 + 0.994039i \(0.534772\pi\)
\(18\) 0 0
\(19\) −5.90589 −1.35491 −0.677453 0.735566i \(-0.736916\pi\)
−0.677453 + 0.735566i \(0.736916\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.43848 0.925487 0.462744 0.886492i \(-0.346865\pi\)
0.462744 + 0.886492i \(0.346865\pi\)
\(24\) 0 0
\(25\) 3.17265 0.634530
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6.41440 −1.19112 −0.595562 0.803309i \(-0.703071\pi\)
−0.595562 + 0.803309i \(0.703071\pi\)
\(30\) 0 0
\(31\) 3.31678i 0.595710i 0.954611 + 0.297855i \(0.0962713\pi\)
−0.954611 + 0.297855i \(0.903729\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.85878i 0.483223i
\(36\) 0 0
\(37\) − 5.51080i − 0.905970i −0.891518 0.452985i \(-0.850359\pi\)
0.891518 0.452985i \(-0.149641\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 3.41549i − 0.533410i −0.963778 0.266705i \(-0.914065\pi\)
0.963778 0.266705i \(-0.0859349\pi\)
\(42\) 0 0
\(43\) −1.37638 −0.209895 −0.104948 0.994478i \(-0.533468\pi\)
−0.104948 + 0.994478i \(0.533468\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.60102 0.379398 0.189699 0.981842i \(-0.439249\pi\)
0.189699 + 0.981842i \(0.439249\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 13.3184 1.82942 0.914710 0.404110i \(-0.132419\pi\)
0.914710 + 0.404110i \(0.132419\pi\)
\(54\) 0 0
\(55\) − 14.2505i − 1.92153i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 10.6485i 1.38631i 0.720788 + 0.693156i \(0.243780\pi\)
−0.720788 + 0.693156i \(0.756220\pi\)
\(60\) 0 0
\(61\) − 1.41211i − 0.180802i −0.995905 0.0904011i \(-0.971185\pi\)
0.995905 0.0904011i \(-0.0288149\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) − 6.72683i − 0.834361i
\(66\) 0 0
\(67\) −0.221252 −0.0270303 −0.0135151 0.999909i \(-0.504302\pi\)
−0.0135151 + 0.999909i \(0.504302\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −0.398786 −0.0473271 −0.0236636 0.999720i \(-0.507533\pi\)
−0.0236636 + 0.999720i \(0.507533\pi\)
\(72\) 0 0
\(73\) −10.7893 −1.26279 −0.631397 0.775460i \(-0.717518\pi\)
−0.631397 + 0.775460i \(0.717518\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.98479 0.568070
\(78\) 0 0
\(79\) 9.76133i 1.09824i 0.835745 + 0.549118i \(0.185036\pi\)
−0.835745 + 0.549118i \(0.814964\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) − 2.06831i − 0.227027i −0.993536 0.113513i \(-0.963789\pi\)
0.993536 0.113513i \(-0.0362105\pi\)
\(84\) 0 0
\(85\) − 23.4336i − 2.54173i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) − 17.6684i − 1.87284i −0.350875 0.936422i \(-0.614116\pi\)
0.350875 0.936422i \(-0.385884\pi\)
\(90\) 0 0
\(91\) 2.35304 0.246665
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 16.8837 1.73223
\(96\) 0 0
\(97\) −3.62651 −0.368217 −0.184108 0.982906i \(-0.558940\pi\)
−0.184108 + 0.982906i \(0.558940\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 10.4729 1.04209 0.521047 0.853528i \(-0.325541\pi\)
0.521047 + 0.853528i \(0.325541\pi\)
\(102\) 0 0
\(103\) 4.50892i 0.444277i 0.975015 + 0.222139i \(0.0713037\pi\)
−0.975015 + 0.222139i \(0.928696\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.82640i 0.659933i 0.943993 + 0.329966i \(0.107037\pi\)
−0.943993 + 0.329966i \(0.892963\pi\)
\(108\) 0 0
\(109\) − 13.1273i − 1.25737i −0.777660 0.628685i \(-0.783593\pi\)
0.777660 0.628685i \(-0.216407\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 5.30759i − 0.499297i −0.968337 0.249648i \(-0.919685\pi\)
0.968337 0.249648i \(-0.0803150\pi\)
\(114\) 0 0
\(115\) −12.6887 −1.18322
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 8.19706 0.751423
\(120\) 0 0
\(121\) −13.8482 −1.25892
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 5.22400 0.467248
\(126\) 0 0
\(127\) 1.80347i 0.160032i 0.996794 + 0.0800160i \(0.0254972\pi\)
−0.996794 + 0.0800160i \(0.974503\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 9.93535i 0.868056i 0.900899 + 0.434028i \(0.142908\pi\)
−0.900899 + 0.434028i \(0.857092\pi\)
\(132\) 0 0
\(133\) 5.90589i 0.512106i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 1.16258i − 0.0993261i −0.998766 0.0496630i \(-0.984185\pi\)
0.998766 0.0496630i \(-0.0158147\pi\)
\(138\) 0 0
\(139\) −17.0996 −1.45037 −0.725186 0.688553i \(-0.758246\pi\)
−0.725186 + 0.688553i \(0.758246\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −11.7294 −0.980863
\(144\) 0 0
\(145\) 18.3374 1.52284
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −23.1689 −1.89807 −0.949034 0.315173i \(-0.897937\pi\)
−0.949034 + 0.315173i \(0.897937\pi\)
\(150\) 0 0
\(151\) − 1.67795i − 0.136549i −0.997667 0.0682747i \(-0.978251\pi\)
0.997667 0.0682747i \(-0.0217494\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) − 9.48195i − 0.761608i
\(156\) 0 0
\(157\) 2.22459i 0.177542i 0.996052 + 0.0887710i \(0.0282939\pi\)
−0.996052 + 0.0887710i \(0.971706\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) − 4.43848i − 0.349801i
\(162\) 0 0
\(163\) 17.3358 1.35785 0.678924 0.734209i \(-0.262447\pi\)
0.678924 + 0.734209i \(0.262447\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −21.4429 −1.65930 −0.829650 0.558284i \(-0.811460\pi\)
−0.829650 + 0.558284i \(0.811460\pi\)
\(168\) 0 0
\(169\) 7.46321 0.574093
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −9.70545 −0.737892 −0.368946 0.929451i \(-0.620281\pi\)
−0.368946 + 0.929451i \(0.620281\pi\)
\(174\) 0 0
\(175\) − 3.17265i − 0.239830i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) − 14.7350i − 1.10134i −0.834722 0.550671i \(-0.814372\pi\)
0.834722 0.550671i \(-0.185628\pi\)
\(180\) 0 0
\(181\) − 17.7055i − 1.31604i −0.753001 0.658019i \(-0.771395\pi\)
0.753001 0.658019i \(-0.228605\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 15.7542i 1.15827i
\(186\) 0 0
\(187\) −40.8606 −2.98803
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −17.9941 −1.30201 −0.651003 0.759075i \(-0.725652\pi\)
−0.651003 + 0.759075i \(0.725652\pi\)
\(192\) 0 0
\(193\) −24.8594 −1.78942 −0.894709 0.446649i \(-0.852617\pi\)
−0.894709 + 0.446649i \(0.852617\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 17.4145 1.24073 0.620367 0.784312i \(-0.286984\pi\)
0.620367 + 0.784312i \(0.286984\pi\)
\(198\) 0 0
\(199\) − 20.0065i − 1.41823i −0.705095 0.709113i \(-0.749096\pi\)
0.705095 0.709113i \(-0.250904\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 6.41440i 0.450203i
\(204\) 0 0
\(205\) 9.76415i 0.681958i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) − 29.4397i − 2.03638i
\(210\) 0 0
\(211\) 15.0542 1.03637 0.518186 0.855268i \(-0.326608\pi\)
0.518186 + 0.855268i \(0.326608\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 3.93476 0.268349
\(216\) 0 0
\(217\) 3.31678 0.225157
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −19.2880 −1.29745
\(222\) 0 0
\(223\) 12.7615i 0.854570i 0.904117 + 0.427285i \(0.140530\pi\)
−0.904117 + 0.427285i \(0.859470\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 25.7167i 1.70688i 0.521194 + 0.853438i \(0.325487\pi\)
−0.521194 + 0.853438i \(0.674513\pi\)
\(228\) 0 0
\(229\) 10.7033i 0.707293i 0.935379 + 0.353647i \(0.115058\pi\)
−0.935379 + 0.353647i \(0.884942\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 5.55917i − 0.364194i −0.983281 0.182097i \(-0.941712\pi\)
0.983281 0.182097i \(-0.0582884\pi\)
\(234\) 0 0
\(235\) −7.43577 −0.485056
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −20.7187 −1.34018 −0.670092 0.742278i \(-0.733745\pi\)
−0.670092 + 0.742278i \(0.733745\pi\)
\(240\) 0 0
\(241\) 6.03091 0.388485 0.194242 0.980954i \(-0.437775\pi\)
0.194242 + 0.980954i \(0.437775\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.85878 0.182641
\(246\) 0 0
\(247\) − 13.8968i − 0.884232i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 8.01117i 0.505660i 0.967511 + 0.252830i \(0.0813614\pi\)
−0.967511 + 0.252830i \(0.918639\pi\)
\(252\) 0 0
\(253\) 22.1249i 1.39098i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 14.1009i 0.879590i 0.898098 + 0.439795i \(0.144949\pi\)
−0.898098 + 0.439795i \(0.855051\pi\)
\(258\) 0 0
\(259\) −5.51080 −0.342424
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 24.6348 1.51905 0.759524 0.650479i \(-0.225432\pi\)
0.759524 + 0.650479i \(0.225432\pi\)
\(264\) 0 0
\(265\) −38.0744 −2.33889
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −9.64498 −0.588065 −0.294032 0.955795i \(-0.594997\pi\)
−0.294032 + 0.955795i \(0.594997\pi\)
\(270\) 0 0
\(271\) − 13.3466i − 0.810751i −0.914150 0.405375i \(-0.867141\pi\)
0.914150 0.405375i \(-0.132859\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 15.8150i 0.953681i
\(276\) 0 0
\(277\) − 18.5217i − 1.11286i −0.830895 0.556429i \(-0.812171\pi\)
0.830895 0.556429i \(-0.187829\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) − 18.7455i − 1.11826i −0.829079 0.559131i \(-0.811135\pi\)
0.829079 0.559131i \(-0.188865\pi\)
\(282\) 0 0
\(283\) 2.32063 0.137947 0.0689736 0.997618i \(-0.478028\pi\)
0.0689736 + 0.997618i \(0.478028\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.41549 −0.201610
\(288\) 0 0
\(289\) −50.1918 −2.95246
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −3.61125 −0.210972 −0.105486 0.994421i \(-0.533640\pi\)
−0.105486 + 0.994421i \(0.533640\pi\)
\(294\) 0 0
\(295\) − 30.4417i − 1.77238i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 10.4439i 0.603987i
\(300\) 0 0
\(301\) 1.37638i 0.0793330i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4.03692i 0.231153i
\(306\) 0 0
\(307\) 19.9273 1.13731 0.568656 0.822576i \(-0.307464\pi\)
0.568656 + 0.822576i \(0.307464\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −4.68722 −0.265788 −0.132894 0.991130i \(-0.542427\pi\)
−0.132894 + 0.991130i \(0.542427\pi\)
\(312\) 0 0
\(313\) −13.2179 −0.747118 −0.373559 0.927606i \(-0.621863\pi\)
−0.373559 + 0.927606i \(0.621863\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −13.8162 −0.775995 −0.387997 0.921660i \(-0.626833\pi\)
−0.387997 + 0.921660i \(0.626833\pi\)
\(318\) 0 0
\(319\) − 31.9745i − 1.79023i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) − 48.4110i − 2.69366i
\(324\) 0 0
\(325\) 7.46537i 0.414104i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) − 2.60102i − 0.143399i
\(330\) 0 0
\(331\) −9.70429 −0.533396 −0.266698 0.963780i \(-0.585933\pi\)
−0.266698 + 0.963780i \(0.585933\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0.632513 0.0345579
\(336\) 0 0
\(337\) 5.04484 0.274810 0.137405 0.990515i \(-0.456124\pi\)
0.137405 + 0.990515i \(0.456124\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −16.5334 −0.895336
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 2.01718i − 0.108288i −0.998533 0.0541440i \(-0.982757\pi\)
0.998533 0.0541440i \(-0.0172430\pi\)
\(348\) 0 0
\(349\) 0.528557i 0.0282930i 0.999900 + 0.0141465i \(0.00450312\pi\)
−0.999900 + 0.0141465i \(0.995497\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 10.3448i 0.550600i 0.961358 + 0.275300i \(0.0887772\pi\)
−0.961358 + 0.275300i \(0.911223\pi\)
\(354\) 0 0
\(355\) 1.14004 0.0605072
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.62306 −0.0856618 −0.0428309 0.999082i \(-0.513638\pi\)
−0.0428309 + 0.999082i \(0.513638\pi\)
\(360\) 0 0
\(361\) 15.8796 0.835768
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 30.8443 1.61447
\(366\) 0 0
\(367\) − 33.5635i − 1.75200i −0.482312 0.875999i \(-0.660203\pi\)
0.482312 0.875999i \(-0.339797\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) − 13.3184i − 0.691456i
\(372\) 0 0
\(373\) − 20.4199i − 1.05730i −0.848840 0.528650i \(-0.822698\pi\)
0.848840 0.528650i \(-0.177302\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 15.0933i − 0.777346i
\(378\) 0 0
\(379\) −29.6529 −1.52317 −0.761583 0.648068i \(-0.775577\pi\)
−0.761583 + 0.648068i \(0.775577\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −4.82347 −0.246468 −0.123234 0.992378i \(-0.539327\pi\)
−0.123234 + 0.992378i \(0.539327\pi\)
\(384\) 0 0
\(385\) −14.2505 −0.726270
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −18.5242 −0.939214 −0.469607 0.882876i \(-0.655604\pi\)
−0.469607 + 0.882876i \(0.655604\pi\)
\(390\) 0 0
\(391\) 36.3825i 1.83994i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) − 27.9056i − 1.40408i
\(396\) 0 0
\(397\) − 2.91585i − 0.146342i −0.997319 0.0731712i \(-0.976688\pi\)
0.997319 0.0731712i \(-0.0233119\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) − 2.62856i − 0.131264i −0.997844 0.0656319i \(-0.979094\pi\)
0.997844 0.0656319i \(-0.0209063\pi\)
\(402\) 0 0
\(403\) −7.80450 −0.388770
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 27.4702 1.36165
\(408\) 0 0
\(409\) 26.0556 1.28836 0.644182 0.764872i \(-0.277198\pi\)
0.644182 + 0.764872i \(0.277198\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 10.6485 0.523977
\(414\) 0 0
\(415\) 5.91286i 0.290251i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 9.43185i − 0.460776i −0.973099 0.230388i \(-0.926000\pi\)
0.973099 0.230388i \(-0.0739995\pi\)
\(420\) 0 0
\(421\) − 22.3767i − 1.09057i −0.838249 0.545287i \(-0.816421\pi\)
0.838249 0.545287i \(-0.183579\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 26.0064i 1.26150i
\(426\) 0 0
\(427\) −1.41211 −0.0683368
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 14.1600 0.682061 0.341030 0.940052i \(-0.389224\pi\)
0.341030 + 0.940052i \(0.389224\pi\)
\(432\) 0 0
\(433\) 9.47617 0.455396 0.227698 0.973732i \(-0.426880\pi\)
0.227698 + 0.973732i \(0.426880\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −26.2132 −1.25395
\(438\) 0 0
\(439\) − 5.40493i − 0.257963i −0.991647 0.128982i \(-0.958829\pi\)
0.991647 0.128982i \(-0.0411709\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 28.2417i − 1.34180i −0.741546 0.670902i \(-0.765907\pi\)
0.741546 0.670902i \(-0.234093\pi\)
\(444\) 0 0
\(445\) 50.5101i 2.39441i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 31.0885i 1.46716i 0.679605 + 0.733578i \(0.262151\pi\)
−0.679605 + 0.733578i \(0.737849\pi\)
\(450\) 0 0
\(451\) 17.0255 0.801700
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −6.72683 −0.315359
\(456\) 0 0
\(457\) 15.4214 0.721383 0.360691 0.932685i \(-0.382541\pi\)
0.360691 + 0.932685i \(0.382541\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 21.7699 1.01392 0.506962 0.861968i \(-0.330768\pi\)
0.506962 + 0.861968i \(0.330768\pi\)
\(462\) 0 0
\(463\) − 33.1540i − 1.54080i −0.637563 0.770398i \(-0.720057\pi\)
0.637563 0.770398i \(-0.279943\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 23.3233i 1.07927i 0.841898 + 0.539637i \(0.181439\pi\)
−0.841898 + 0.539637i \(0.818561\pi\)
\(468\) 0 0
\(469\) 0.221252i 0.0102165i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) − 6.86095i − 0.315467i
\(474\) 0 0
\(475\) −18.7373 −0.859728
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −29.7837 −1.36085 −0.680426 0.732817i \(-0.738205\pi\)
−0.680426 + 0.732817i \(0.738205\pi\)
\(480\) 0 0
\(481\) 12.9671 0.591250
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 10.3674 0.470761
\(486\) 0 0
\(487\) 7.61251i 0.344956i 0.985013 + 0.172478i \(0.0551773\pi\)
−0.985013 + 0.172478i \(0.944823\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 10.4249i 0.470471i 0.971938 + 0.235236i \(0.0755862\pi\)
−0.971938 + 0.235236i \(0.924414\pi\)
\(492\) 0 0
\(493\) − 52.5792i − 2.36805i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.398786i 0.0178880i
\(498\) 0 0
\(499\) 24.3685 1.09088 0.545441 0.838149i \(-0.316362\pi\)
0.545441 + 0.838149i \(0.316362\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 38.3668 1.71069 0.855345 0.518058i \(-0.173345\pi\)
0.855345 + 0.518058i \(0.173345\pi\)
\(504\) 0 0
\(505\) −29.9398 −1.33231
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 11.6708 0.517298 0.258649 0.965971i \(-0.416723\pi\)
0.258649 + 0.965971i \(0.416723\pi\)
\(510\) 0 0
\(511\) 10.7893i 0.477291i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 12.8900i − 0.568003i
\(516\) 0 0
\(517\) 12.9656i 0.570225i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) − 8.09319i − 0.354569i −0.984160 0.177284i \(-0.943269\pi\)
0.984160 0.177284i \(-0.0567313\pi\)
\(522\) 0 0
\(523\) 12.5864 0.550363 0.275181 0.961392i \(-0.411262\pi\)
0.275181 + 0.961392i \(0.411262\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −27.1878 −1.18432
\(528\) 0 0
\(529\) −3.29989 −0.143473
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 8.03678 0.348112
\(534\) 0 0
\(535\) − 19.5152i − 0.843716i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) − 4.98479i − 0.214710i
\(540\) 0 0
\(541\) − 33.6824i − 1.44812i −0.689738 0.724059i \(-0.742274\pi\)
0.689738 0.724059i \(-0.257726\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 37.5282i 1.60753i
\(546\) 0 0
\(547\) 31.7087 1.35576 0.677882 0.735170i \(-0.262898\pi\)
0.677882 + 0.735170i \(0.262898\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 37.8828 1.61386
\(552\) 0 0
\(553\) 9.76133 0.415094
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −29.0418 −1.23054 −0.615270 0.788316i \(-0.710953\pi\)
−0.615270 + 0.788316i \(0.710953\pi\)
\(558\) 0 0
\(559\) − 3.23867i − 0.136981i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 34.5955i 1.45803i 0.684499 + 0.729013i \(0.260021\pi\)
−0.684499 + 0.729013i \(0.739979\pi\)
\(564\) 0 0
\(565\) 15.1733i 0.638344i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 44.7913i 1.87775i 0.344258 + 0.938875i \(0.388131\pi\)
−0.344258 + 0.938875i \(0.611869\pi\)
\(570\) 0 0
\(571\) 13.8182 0.578276 0.289138 0.957287i \(-0.406631\pi\)
0.289138 + 0.957287i \(0.406631\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 14.0818 0.587250
\(576\) 0 0
\(577\) −2.53927 −0.105711 −0.0528557 0.998602i \(-0.516832\pi\)
−0.0528557 + 0.998602i \(0.516832\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −2.06831 −0.0858081
\(582\) 0 0
\(583\) 66.3894i 2.74957i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.23636i 0.0510300i 0.999674 + 0.0255150i \(0.00812256\pi\)
−0.999674 + 0.0255150i \(0.991877\pi\)
\(588\) 0 0
\(589\) − 19.5885i − 0.807131i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 2.47202i − 0.101514i −0.998711 0.0507568i \(-0.983837\pi\)
0.998711 0.0507568i \(-0.0161633\pi\)
\(594\) 0 0
\(595\) −23.4336 −0.960685
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 6.80798 0.278166 0.139083 0.990281i \(-0.455584\pi\)
0.139083 + 0.990281i \(0.455584\pi\)
\(600\) 0 0
\(601\) −0.857050 −0.0349598 −0.0174799 0.999847i \(-0.505564\pi\)
−0.0174799 + 0.999847i \(0.505564\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 39.5889 1.60952
\(606\) 0 0
\(607\) 22.9929i 0.933252i 0.884455 + 0.466626i \(0.154531\pi\)
−0.884455 + 0.466626i \(0.845469\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.12031i 0.247601i
\(612\) 0 0
\(613\) 10.9605i 0.442691i 0.975195 + 0.221346i \(0.0710449\pi\)
−0.975195 + 0.221346i \(0.928955\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 15.9140i 0.640675i 0.947304 + 0.320337i \(0.103796\pi\)
−0.947304 + 0.320337i \(0.896204\pi\)
\(618\) 0 0
\(619\) −24.1115 −0.969124 −0.484562 0.874757i \(-0.661021\pi\)
−0.484562 + 0.874757i \(0.661021\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −17.6684 −0.707869
\(624\) 0 0
\(625\) −30.7975 −1.23190
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 45.1723 1.80114
\(630\) 0 0
\(631\) 19.0647i 0.758955i 0.925201 + 0.379477i \(0.123896\pi\)
−0.925201 + 0.379477i \(0.876104\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 5.15573i − 0.204599i
\(636\) 0 0
\(637\) − 2.35304i − 0.0932308i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) − 16.6996i − 0.659595i −0.944052 0.329797i \(-0.893020\pi\)
0.944052 0.329797i \(-0.106980\pi\)
\(642\) 0 0
\(643\) −15.2897 −0.602966 −0.301483 0.953472i \(-0.597482\pi\)
−0.301483 + 0.953472i \(0.597482\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −42.6300 −1.67596 −0.837979 0.545702i \(-0.816263\pi\)
−0.837979 + 0.545702i \(0.816263\pi\)
\(648\) 0 0
\(649\) −53.0804 −2.08359
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 5.14973 0.201524 0.100762 0.994911i \(-0.467872\pi\)
0.100762 + 0.994911i \(0.467872\pi\)
\(654\) 0 0
\(655\) − 28.4030i − 1.10980i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) − 0.965465i − 0.0376092i −0.999823 0.0188046i \(-0.994014\pi\)
0.999823 0.0188046i \(-0.00598604\pi\)
\(660\) 0 0
\(661\) 8.54386i 0.332318i 0.986099 + 0.166159i \(0.0531365\pi\)
−0.986099 + 0.166159i \(0.946864\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) − 16.8837i − 0.654721i
\(666\) 0 0
\(667\) −28.4702 −1.10237
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 7.03908 0.271741
\(672\) 0 0
\(673\) 35.8364 1.38139 0.690695 0.723146i \(-0.257305\pi\)
0.690695 + 0.723146i \(0.257305\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 15.3770 0.590985 0.295493 0.955345i \(-0.404516\pi\)
0.295493 + 0.955345i \(0.404516\pi\)
\(678\) 0 0
\(679\) 3.62651i 0.139173i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 31.3038i − 1.19781i −0.800822 0.598903i \(-0.795604\pi\)
0.800822 0.598903i \(-0.204396\pi\)
\(684\) 0 0
\(685\) 3.32357i 0.126987i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 31.3387i 1.19391i
\(690\) 0 0
\(691\) −38.1921 −1.45289 −0.726447 0.687222i \(-0.758830\pi\)
−0.726447 + 0.687222i \(0.758830\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 48.8842 1.85428
\(696\) 0 0
\(697\) 27.9970 1.06046
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 45.5040 1.71866 0.859331 0.511419i \(-0.170880\pi\)
0.859331 + 0.511419i \(0.170880\pi\)
\(702\) 0 0
\(703\) 32.5462i 1.22750i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 10.4729i − 0.393875i
\(708\) 0 0
\(709\) 17.7256i 0.665698i 0.942980 + 0.332849i \(0.108010\pi\)
−0.942980 + 0.332849i \(0.891990\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 14.7214i 0.551322i
\(714\) 0 0
\(715\) 33.5319 1.25402
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 31.0561 1.15820 0.579098 0.815258i \(-0.303405\pi\)
0.579098 + 0.815258i \(0.303405\pi\)
\(720\) 0 0
\(721\) 4.50892 0.167921
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −20.3507 −0.755804
\(726\) 0 0
\(727\) − 7.88096i − 0.292289i −0.989263 0.146144i \(-0.953314\pi\)
0.989263 0.146144i \(-0.0466864\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) − 11.2822i − 0.417288i
\(732\) 0 0
\(733\) − 31.2981i − 1.15602i −0.816029 0.578011i \(-0.803829\pi\)
0.816029 0.578011i \(-0.196171\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 1.10290i − 0.0406257i
\(738\) 0 0
\(739\) −9.91989 −0.364909 −0.182455 0.983214i \(-0.558404\pi\)
−0.182455 + 0.983214i \(0.558404\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −21.2085 −0.778065 −0.389032 0.921224i \(-0.627191\pi\)
−0.389032 + 0.921224i \(0.627191\pi\)
\(744\) 0 0
\(745\) 66.2348 2.42666
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 6.82640 0.249431
\(750\) 0 0
\(751\) − 31.2986i − 1.14210i −0.820915 0.571051i \(-0.806536\pi\)
0.820915 0.571051i \(-0.193464\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 4.79689i 0.174577i
\(756\) 0 0
\(757\) − 50.1185i − 1.82159i −0.412863 0.910793i \(-0.635471\pi\)
0.412863 0.910793i \(-0.364529\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 33.4522i 1.21264i 0.795220 + 0.606321i \(0.207355\pi\)
−0.795220 + 0.606321i \(0.792645\pi\)
\(762\) 0 0
\(763\) −13.1273 −0.475241
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −25.0562 −0.904728
\(768\) 0 0
\(769\) −34.8586 −1.25703 −0.628516 0.777797i \(-0.716337\pi\)
−0.628516 + 0.777797i \(0.716337\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −0.819156 −0.0294630 −0.0147315 0.999891i \(-0.504689\pi\)
−0.0147315 + 0.999891i \(0.504689\pi\)
\(774\) 0 0
\(775\) 10.5230i 0.377996i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 20.1715i 0.722720i
\(780\) 0 0
\(781\) − 1.98786i − 0.0711314i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) − 6.35964i − 0.226985i
\(786\) 0 0
\(787\) −21.1948 −0.755514 −0.377757 0.925905i \(-0.623305\pi\)
−0.377757 + 0.925905i \(0.623305\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −5.30759 −0.188716
\(792\) 0 0
\(793\) 3.32275 0.117994
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −10.4236 −0.369221 −0.184611 0.982812i \(-0.559102\pi\)
−0.184611 + 0.982812i \(0.559102\pi\)
\(798\) 0 0
\(799\) 21.3207i 0.754274i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) − 53.7825i − 1.89794i
\(804\) 0 0
\(805\) 12.6887i 0.447217i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) − 6.79289i − 0.238825i −0.992845 0.119413i \(-0.961899\pi\)
0.992845 0.119413i \(-0.0381012\pi\)
\(810\) 0 0
\(811\) −15.6600 −0.549897 −0.274949 0.961459i \(-0.588661\pi\)
−0.274949 + 0.961459i \(0.588661\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −49.5594 −1.73599
\(816\) 0 0
\(817\) 8.12873 0.284388
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −9.83489 −0.343240 −0.171620 0.985163i \(-0.554900\pi\)
−0.171620 + 0.985163i \(0.554900\pi\)
\(822\) 0 0
\(823\) 16.9492i 0.590811i 0.955372 + 0.295406i \(0.0954548\pi\)
−0.955372 + 0.295406i \(0.904545\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 54.3499i 1.88993i 0.327169 + 0.944966i \(0.393905\pi\)
−0.327169 + 0.944966i \(0.606095\pi\)
\(828\) 0 0
\(829\) 0.679562i 0.0236022i 0.999930 + 0.0118011i \(0.00375649\pi\)
−0.999930 + 0.0118011i \(0.996244\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) − 8.19706i − 0.284011i
\(834\) 0 0
\(835\) 61.3006 2.12139
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −46.0696 −1.59050 −0.795249 0.606283i \(-0.792660\pi\)
−0.795249 + 0.606283i \(0.792660\pi\)
\(840\) 0 0
\(841\) 12.1445 0.418777
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −21.3357 −0.733971
\(846\) 0 0
\(847\) 13.8482i 0.475828i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) − 24.4596i − 0.838463i
\(852\) 0 0
\(853\) 35.6910i 1.22204i 0.791617 + 0.611018i \(0.209240\pi\)
−0.791617 + 0.611018i \(0.790760\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 27.4542i − 0.937818i −0.883247 0.468909i \(-0.844647\pi\)
0.883247 0.468909i \(-0.155353\pi\)
\(858\) 0 0
\(859\) 20.8392 0.711025 0.355512 0.934672i \(-0.384306\pi\)
0.355512 + 0.934672i \(0.384306\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 25.8505 0.879960 0.439980 0.898008i \(-0.354986\pi\)
0.439980 + 0.898008i \(0.354986\pi\)
\(864\) 0 0
\(865\) 27.7458 0.943385
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −48.6582 −1.65062
\(870\) 0 0
\(871\) − 0.520615i − 0.0176404i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) − 5.22400i − 0.176603i
\(876\) 0 0
\(877\) − 12.7819i − 0.431613i −0.976436 0.215806i \(-0.930762\pi\)
0.976436 0.215806i \(-0.0692380\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 9.54473i − 0.321570i −0.986989 0.160785i \(-0.948597\pi\)
0.986989 0.160785i \(-0.0514026\pi\)
\(882\) 0 0
\(883\) 18.8835 0.635479 0.317740 0.948178i \(-0.397076\pi\)
0.317740 + 0.948178i \(0.397076\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −19.9738 −0.670654 −0.335327 0.942102i \(-0.608847\pi\)
−0.335327 + 0.942102i \(0.608847\pi\)
\(888\) 0 0
\(889\) 1.80347 0.0604864
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −15.3614 −0.514049
\(894\) 0 0
\(895\) 42.1241i 1.40805i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) − 21.2751i − 0.709565i
\(900\) 0 0
\(901\) 109.172i 3.63703i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 50.6162i 1.68254i
\(906\) 0 0
\(907\) −7.50951 −0.249349 −0.124675 0.992198i \(-0.539789\pi\)
−0.124675 + 0.992198i \(0.539789\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −33.1774 −1.09922 −0.549609 0.835422i \(-0.685223\pi\)
−0.549609 + 0.835422i \(0.685223\pi\)
\(912\) 0 0
\(913\) 10.3101 0.341215
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 9.93535 0.328094
\(918\) 0 0
\(919\) 13.2043i 0.435568i 0.975997 + 0.217784i \(0.0698829\pi\)
−0.975997 + 0.217784i \(0.930117\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) − 0.938358i − 0.0308864i
\(924\) 0 0
\(925\) − 17.4838i − 0.574865i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0.175426i 0.00575553i 0.999996 + 0.00287776i \(0.000916022\pi\)
−0.999996 + 0.00287776i \(0.999084\pi\)
\(930\) 0 0
\(931\) 5.90589 0.193558
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 116.812 3.82015
\(936\) 0 0
\(937\) −10.2203 −0.333884 −0.166942 0.985967i \(-0.553389\pi\)
−0.166942 + 0.985967i \(0.553389\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −18.9676 −0.618327 −0.309163 0.951009i \(-0.600049\pi\)
−0.309163 + 0.951009i \(0.600049\pi\)
\(942\) 0 0
\(943\) − 15.1596i − 0.493664i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 6.01612i 0.195497i 0.995211 + 0.0977487i \(0.0311642\pi\)
−0.995211 + 0.0977487i \(0.968836\pi\)
\(948\) 0 0
\(949\) − 25.3877i − 0.824119i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 18.9690i − 0.614468i −0.951634 0.307234i \(-0.900597\pi\)
0.951634 0.307234i \(-0.0994034\pi\)
\(954\) 0 0
\(955\) 51.4412 1.66460
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.16258 −0.0375417
\(960\) 0 0
\(961\) 19.9990 0.645129
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 71.0677 2.28775
\(966\) 0 0
\(967\) − 28.6527i − 0.921408i −0.887554 0.460704i \(-0.847597\pi\)
0.887554 0.460704i \(-0.152403\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) − 47.4986i − 1.52430i −0.647399 0.762151i \(-0.724143\pi\)
0.647399 0.762151i \(-0.275857\pi\)
\(972\) 0 0
\(973\) 17.0996i 0.548189i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 40.0015i 1.27976i 0.768474 + 0.639881i \(0.221016\pi\)
−0.768474 + 0.639881i \(0.778984\pi\)
\(978\) 0 0
\(979\) 88.0732 2.81483
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 22.0829 0.704334 0.352167 0.935937i \(-0.385445\pi\)
0.352167 + 0.935937i \(0.385445\pi\)
\(984\) 0 0
\(985\) −49.7844 −1.58626
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −6.10902 −0.194255
\(990\) 0 0
\(991\) 17.2351i 0.547490i 0.961802 + 0.273745i \(0.0882625\pi\)
−0.961802 + 0.273745i \(0.911738\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 57.1944i 1.81318i
\(996\) 0 0
\(997\) 21.9872i 0.696342i 0.937431 + 0.348171i \(0.113197\pi\)
−0.937431 + 0.348171i \(0.886803\pi\)
\(998\) 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 6048.2.j.d.5615.9 48
3.2 odd 2 inner 6048.2.j.d.5615.40 48
4.3 odd 2 1512.2.j.d.323.10 yes 48
8.3 odd 2 inner 6048.2.j.d.5615.39 48
8.5 even 2 1512.2.j.d.323.40 yes 48
12.11 even 2 1512.2.j.d.323.39 yes 48
24.5 odd 2 1512.2.j.d.323.9 48
24.11 even 2 inner 6048.2.j.d.5615.10 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1512.2.j.d.323.9 48 24.5 odd 2
1512.2.j.d.323.10 yes 48 4.3 odd 2
1512.2.j.d.323.39 yes 48 12.11 even 2
1512.2.j.d.323.40 yes 48 8.5 even 2
6048.2.j.d.5615.9 48 1.1 even 1 trivial
6048.2.j.d.5615.10 48 24.11 even 2 inner
6048.2.j.d.5615.39 48 8.3 odd 2 inner
6048.2.j.d.5615.40 48 3.2 odd 2 inner