Properties

Label 1440.2.bj.a.17.19
Level $1440$
Weight $2$
Character 1440.17
Analytic conductor $11.498$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1440,2,Mod(17,1440)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1440, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 2, 2, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1440.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1440.bj (of order \(4\), degree \(2\), 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: \(11.4984578911\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 360)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 17.19
Character \(\chi\) \(=\) 1440.17
Dual form 1440.2.bj.a.593.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.45381 - 1.69895i) q^{5} +(-1.53029 - 1.53029i) q^{7} +O(q^{10})\) \(q+(1.45381 - 1.69895i) q^{5} +(-1.53029 - 1.53029i) q^{7} -2.72480 q^{11} +(0.857617 + 0.857617i) q^{13} +(2.55531 - 2.55531i) q^{17} +3.54160 q^{19} +(0.626051 + 0.626051i) q^{23} +(-0.772849 - 4.93991i) q^{25} -5.12260i q^{29} -7.89544 q^{31} +(-4.82463 + 0.375125i) q^{35} +(-4.21539 + 4.21539i) q^{37} -12.4074i q^{41} +(-5.67823 - 5.67823i) q^{43} +(9.45505 - 9.45505i) q^{47} -2.31644i q^{49} +(-6.46657 + 6.46657i) q^{53} +(-3.96136 + 4.62930i) q^{55} -2.51407i q^{59} +9.49179i q^{61} +(2.70386 - 0.210231i) q^{65} +(-9.91318 + 9.91318i) q^{67} +2.19671i q^{71} +(-5.71276 + 5.71276i) q^{73} +(4.16973 + 4.16973i) q^{77} -12.7576i q^{79} +(3.58072 - 3.58072i) q^{83} +(-0.626392 - 8.05627i) q^{85} +10.2214 q^{89} -2.62480i q^{91} +(5.14884 - 6.01700i) q^{95} +(-1.29731 - 1.29731i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 32 q^{31} - 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(641\) \(901\) \(991\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(-1\) \(1\)

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
\(5\) 1.45381 1.69895i 0.650165 0.759793i
\(6\) 0 0
\(7\) −1.53029 1.53029i −0.578394 0.578394i 0.356066 0.934461i \(-0.384118\pi\)
−0.934461 + 0.356066i \(0.884118\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.72480 −0.821559 −0.410779 0.911735i \(-0.634743\pi\)
−0.410779 + 0.911735i \(0.634743\pi\)
\(12\) 0 0
\(13\) 0.857617 + 0.857617i 0.237860 + 0.237860i 0.815964 0.578103i \(-0.196207\pi\)
−0.578103 + 0.815964i \(0.696207\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.55531 2.55531i 0.619753 0.619753i −0.325715 0.945468i \(-0.605605\pi\)
0.945468 + 0.325715i \(0.105605\pi\)
\(18\) 0 0
\(19\) 3.54160 0.812500 0.406250 0.913762i \(-0.366836\pi\)
0.406250 + 0.913762i \(0.366836\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.626051 + 0.626051i 0.130541 + 0.130541i 0.769358 0.638818i \(-0.220576\pi\)
−0.638818 + 0.769358i \(0.720576\pi\)
\(24\) 0 0
\(25\) −0.772849 4.93991i −0.154570 0.987982i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5.12260i 0.951243i −0.879650 0.475622i \(-0.842223\pi\)
0.879650 0.475622i \(-0.157777\pi\)
\(30\) 0 0
\(31\) −7.89544 −1.41806 −0.709031 0.705177i \(-0.750868\pi\)
−0.709031 + 0.705177i \(0.750868\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.82463 + 0.375125i −0.815512 + 0.0634078i
\(36\) 0 0
\(37\) −4.21539 + 4.21539i −0.693005 + 0.693005i −0.962892 0.269887i \(-0.913014\pi\)
0.269887 + 0.962892i \(0.413014\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 12.4074i 1.93771i −0.247638 0.968853i \(-0.579654\pi\)
0.247638 0.968853i \(-0.420346\pi\)
\(42\) 0 0
\(43\) −5.67823 5.67823i −0.865922 0.865922i 0.126096 0.992018i \(-0.459755\pi\)
−0.992018 + 0.126096i \(0.959755\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 9.45505 9.45505i 1.37916 1.37916i 0.533124 0.846037i \(-0.321018\pi\)
0.846037 0.533124i \(-0.178982\pi\)
\(48\) 0 0
\(49\) 2.31644i 0.330920i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −6.46657 + 6.46657i −0.888252 + 0.888252i −0.994355 0.106103i \(-0.966163\pi\)
0.106103 + 0.994355i \(0.466163\pi\)
\(54\) 0 0
\(55\) −3.96136 + 4.62930i −0.534149 + 0.624214i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2.51407i 0.327304i −0.986518 0.163652i \(-0.947673\pi\)
0.986518 0.163652i \(-0.0523274\pi\)
\(60\) 0 0
\(61\) 9.49179i 1.21530i 0.794205 + 0.607649i \(0.207887\pi\)
−0.794205 + 0.607649i \(0.792113\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.70386 0.210231i 0.335373 0.0260760i
\(66\) 0 0
\(67\) −9.91318 + 9.91318i −1.21109 + 1.21109i −0.240418 + 0.970669i \(0.577285\pi\)
−0.970669 + 0.240418i \(0.922715\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.19671i 0.260702i 0.991468 + 0.130351i \(0.0416104\pi\)
−0.991468 + 0.130351i \(0.958390\pi\)
\(72\) 0 0
\(73\) −5.71276 + 5.71276i −0.668628 + 0.668628i −0.957398 0.288771i \(-0.906754\pi\)
0.288771 + 0.957398i \(0.406754\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.16973 + 4.16973i 0.475185 + 0.475185i
\(78\) 0 0
\(79\) 12.7576i 1.43534i −0.696384 0.717670i \(-0.745209\pi\)
0.696384 0.717670i \(-0.254791\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 3.58072 3.58072i 0.393035 0.393035i −0.482733 0.875768i \(-0.660356\pi\)
0.875768 + 0.482733i \(0.160356\pi\)
\(84\) 0 0
\(85\) −0.626392 8.05627i −0.0679418 0.873826i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 10.2214 1.08347 0.541734 0.840550i \(-0.317768\pi\)
0.541734 + 0.840550i \(0.317768\pi\)
\(90\) 0 0
\(91\) 2.62480i 0.275154i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 5.14884 6.01700i 0.528259 0.617331i
\(96\) 0 0
\(97\) −1.29731 1.29731i −0.131722 0.131722i 0.638172 0.769894i \(-0.279691\pi\)
−0.769894 + 0.638172i \(0.779691\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −5.82360 −0.579470 −0.289735 0.957107i \(-0.593567\pi\)
−0.289735 + 0.957107i \(0.593567\pi\)
\(102\) 0 0
\(103\) 3.08360 3.08360i 0.303836 0.303836i −0.538677 0.842513i \(-0.681076\pi\)
0.842513 + 0.538677i \(0.181076\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6.49670 6.49670i −0.628060 0.628060i 0.319520 0.947580i \(-0.396478\pi\)
−0.947580 + 0.319520i \(0.896478\pi\)
\(108\) 0 0
\(109\) 5.41031 0.518213 0.259107 0.965849i \(-0.416572\pi\)
0.259107 + 0.965849i \(0.416572\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.358788 0.358788i −0.0337519 0.0337519i 0.690029 0.723781i \(-0.257598\pi\)
−0.723781 + 0.690029i \(0.757598\pi\)
\(114\) 0 0
\(115\) 1.97379 0.153466i 0.184057 0.0143108i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −7.82071 −0.716923
\(120\) 0 0
\(121\) −3.57545 −0.325041
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −9.51623 5.86868i −0.851157 0.524911i
\(126\) 0 0
\(127\) 0.916401 + 0.916401i 0.0813174 + 0.0813174i 0.746596 0.665278i \(-0.231687\pi\)
−0.665278 + 0.746596i \(0.731687\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 19.5355 1.70683 0.853413 0.521235i \(-0.174529\pi\)
0.853413 + 0.521235i \(0.174529\pi\)
\(132\) 0 0
\(133\) −5.41968 5.41968i −0.469945 0.469945i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −7.66611 + 7.66611i −0.654960 + 0.654960i −0.954183 0.299223i \(-0.903273\pi\)
0.299223 + 0.954183i \(0.403273\pi\)
\(138\) 0 0
\(139\) 14.7210 1.24862 0.624308 0.781178i \(-0.285381\pi\)
0.624308 + 0.781178i \(0.285381\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.33684 2.33684i −0.195416 0.195416i
\(144\) 0 0
\(145\) −8.70304 7.44731i −0.722748 0.618466i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 15.6300i 1.28046i −0.768182 0.640231i \(-0.778838\pi\)
0.768182 0.640231i \(-0.221162\pi\)
\(150\) 0 0
\(151\) 17.5889 1.43136 0.715682 0.698426i \(-0.246116\pi\)
0.715682 + 0.698426i \(0.246116\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −11.4785 + 13.4139i −0.921975 + 1.07743i
\(156\) 0 0
\(157\) 7.60352 7.60352i 0.606827 0.606827i −0.335288 0.942116i \(-0.608834\pi\)
0.942116 + 0.335288i \(0.108834\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.91608i 0.151008i
\(162\) 0 0
\(163\) 8.53586 + 8.53586i 0.668580 + 0.668580i 0.957387 0.288807i \(-0.0932586\pi\)
−0.288807 + 0.957387i \(0.593259\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.11022 6.11022i 0.472823 0.472823i −0.430004 0.902827i \(-0.641488\pi\)
0.902827 + 0.430004i \(0.141488\pi\)
\(168\) 0 0
\(169\) 11.5290i 0.886845i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.593720 0.593720i 0.0451397 0.0451397i −0.684177 0.729316i \(-0.739838\pi\)
0.729316 + 0.684177i \(0.239838\pi\)
\(174\) 0 0
\(175\) −6.37680 + 8.74217i −0.482041 + 0.660846i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 11.3935i 0.851593i −0.904819 0.425796i \(-0.859994\pi\)
0.904819 0.425796i \(-0.140006\pi\)
\(180\) 0 0
\(181\) 7.31410i 0.543653i 0.962346 + 0.271827i \(0.0876277\pi\)
−0.962346 + 0.271827i \(0.912372\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.03333 + 13.2901i 0.0759722 + 0.977108i
\(186\) 0 0
\(187\) −6.96270 + 6.96270i −0.509163 + 0.509163i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.32855i 0.0961302i −0.998844 0.0480651i \(-0.984695\pi\)
0.998844 0.0480651i \(-0.0153055\pi\)
\(192\) 0 0
\(193\) −11.5366 + 11.5366i −0.830423 + 0.830423i −0.987574 0.157152i \(-0.949769\pi\)
0.157152 + 0.987574i \(0.449769\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 16.1999 + 16.1999i 1.15420 + 1.15420i 0.985703 + 0.168494i \(0.0538905\pi\)
0.168494 + 0.985703i \(0.446110\pi\)
\(198\) 0 0
\(199\) 6.09388i 0.431984i 0.976395 + 0.215992i \(0.0692985\pi\)
−0.976395 + 0.215992i \(0.930702\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −7.83906 + 7.83906i −0.550194 + 0.550194i
\(204\) 0 0
\(205\) −21.0795 18.0380i −1.47225 1.25983i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −9.65017 −0.667516
\(210\) 0 0
\(211\) 24.9318i 1.71637i 0.513338 + 0.858186i \(0.328409\pi\)
−0.513338 + 0.858186i \(0.671591\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −17.9021 + 1.39193i −1.22091 + 0.0949286i
\(216\) 0 0
\(217\) 12.0823 + 12.0823i 0.820200 + 0.820200i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 4.38295 0.294829
\(222\) 0 0
\(223\) 5.42573 5.42573i 0.363334 0.363334i −0.501705 0.865039i \(-0.667294\pi\)
0.865039 + 0.501705i \(0.167294\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 8.15485 + 8.15485i 0.541256 + 0.541256i 0.923897 0.382641i \(-0.124985\pi\)
−0.382641 + 0.923897i \(0.624985\pi\)
\(228\) 0 0
\(229\) 14.5344 0.960462 0.480231 0.877142i \(-0.340553\pi\)
0.480231 + 0.877142i \(0.340553\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2.40471 + 2.40471i 0.157538 + 0.157538i 0.781475 0.623937i \(-0.214468\pi\)
−0.623937 + 0.781475i \(0.714468\pi\)
\(234\) 0 0
\(235\) −2.31775 29.8095i −0.151194 1.94456i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6.79965 −0.439833 −0.219917 0.975519i \(-0.570578\pi\)
−0.219917 + 0.975519i \(0.570578\pi\)
\(240\) 0 0
\(241\) 16.2108 1.04423 0.522114 0.852876i \(-0.325143\pi\)
0.522114 + 0.852876i \(0.325143\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3.93551 3.36767i −0.251430 0.215153i
\(246\) 0 0
\(247\) 3.03734 + 3.03734i 0.193261 + 0.193261i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 9.56946 0.604019 0.302009 0.953305i \(-0.402343\pi\)
0.302009 + 0.953305i \(0.402343\pi\)
\(252\) 0 0
\(253\) −1.70587 1.70587i −0.107247 0.107247i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5.61999 + 5.61999i −0.350566 + 0.350566i −0.860320 0.509754i \(-0.829736\pi\)
0.509754 + 0.860320i \(0.329736\pi\)
\(258\) 0 0
\(259\) 12.9015 0.801661
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 16.0240 + 16.0240i 0.988080 + 0.988080i 0.999930 0.0118502i \(-0.00377213\pi\)
−0.0118502 + 0.999930i \(0.503772\pi\)
\(264\) 0 0
\(265\) 1.58518 + 20.3876i 0.0973766 + 1.25240i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 8.90392i 0.542882i 0.962455 + 0.271441i \(0.0875001\pi\)
−0.962455 + 0.271441i \(0.912500\pi\)
\(270\) 0 0
\(271\) 14.0162 0.851422 0.425711 0.904859i \(-0.360024\pi\)
0.425711 + 0.904859i \(0.360024\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.10586 + 13.4603i 0.126988 + 0.811685i
\(276\) 0 0
\(277\) −2.00404 + 2.00404i −0.120411 + 0.120411i −0.764745 0.644333i \(-0.777135\pi\)
0.644333 + 0.764745i \(0.277135\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 9.33618i 0.556950i 0.960444 + 0.278475i \(0.0898289\pi\)
−0.960444 + 0.278475i \(0.910171\pi\)
\(282\) 0 0
\(283\) −22.3583 22.3583i −1.32906 1.32906i −0.906187 0.422877i \(-0.861020\pi\)
−0.422877 0.906187i \(-0.638980\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −18.9868 + 18.9868i −1.12076 + 1.12076i
\(288\) 0 0
\(289\) 3.94082i 0.231813i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −5.84966 + 5.84966i −0.341741 + 0.341741i −0.857021 0.515281i \(-0.827688\pi\)
0.515281 + 0.857021i \(0.327688\pi\)
\(294\) 0 0
\(295\) −4.27127 3.65499i −0.248683 0.212802i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.07382i 0.0621009i
\(300\) 0 0
\(301\) 17.3787i 1.00169i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 16.1261 + 13.7993i 0.923375 + 0.790145i
\(306\) 0 0
\(307\) −6.13875 + 6.13875i −0.350357 + 0.350357i −0.860242 0.509886i \(-0.829688\pi\)
0.509886 + 0.860242i \(0.329688\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 13.0614i 0.740642i 0.928904 + 0.370321i \(0.120752\pi\)
−0.928904 + 0.370321i \(0.879248\pi\)
\(312\) 0 0
\(313\) 22.0110 22.0110i 1.24414 1.24414i 0.285869 0.958269i \(-0.407718\pi\)
0.958269 0.285869i \(-0.0922822\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6.28577 + 6.28577i 0.353044 + 0.353044i 0.861241 0.508197i \(-0.169688\pi\)
−0.508197 + 0.861241i \(0.669688\pi\)
\(318\) 0 0
\(319\) 13.9581i 0.781502i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 9.04989 9.04989i 0.503549 0.503549i
\(324\) 0 0
\(325\) 3.57374 4.89936i 0.198236 0.271768i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −28.9379 −1.59540
\(330\) 0 0
\(331\) 26.2733i 1.44411i −0.691836 0.722055i \(-0.743198\pi\)
0.691836 0.722055i \(-0.256802\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.43006 + 31.2539i 0.132768 + 1.70758i
\(336\) 0 0
\(337\) 16.4860 + 16.4860i 0.898047 + 0.898047i 0.995263 0.0972161i \(-0.0309938\pi\)
−0.0972161 + 0.995263i \(0.530994\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 21.5135 1.16502
\(342\) 0 0
\(343\) −14.2568 + 14.2568i −0.769797 + 0.769797i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.85611 2.85611i −0.153324 0.153324i 0.626277 0.779601i \(-0.284578\pi\)
−0.779601 + 0.626277i \(0.784578\pi\)
\(348\) 0 0
\(349\) 19.3216 1.03426 0.517130 0.855907i \(-0.327000\pi\)
0.517130 + 0.855907i \(0.327000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −17.0194 17.0194i −0.905850 0.905850i 0.0900845 0.995934i \(-0.471286\pi\)
−0.995934 + 0.0900845i \(0.971286\pi\)
\(354\) 0 0
\(355\) 3.73210 + 3.19361i 0.198079 + 0.169499i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −14.6210 −0.771665 −0.385832 0.922569i \(-0.626086\pi\)
−0.385832 + 0.922569i \(0.626086\pi\)
\(360\) 0 0
\(361\) −6.45703 −0.339844
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.40039 + 18.0110i 0.0732998 + 0.942737i
\(366\) 0 0
\(367\) 8.21722 + 8.21722i 0.428935 + 0.428935i 0.888266 0.459330i \(-0.151911\pi\)
−0.459330 + 0.888266i \(0.651911\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 19.7914 1.02752
\(372\) 0 0
\(373\) 9.54965 + 9.54965i 0.494462 + 0.494462i 0.909709 0.415247i \(-0.136305\pi\)
−0.415247 + 0.909709i \(0.636305\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.39323 4.39323i 0.226263 0.226263i
\(378\) 0 0
\(379\) 9.71237 0.498891 0.249445 0.968389i \(-0.419752\pi\)
0.249445 + 0.968389i \(0.419752\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3.97088 + 3.97088i 0.202903 + 0.202903i 0.801242 0.598340i \(-0.204173\pi\)
−0.598340 + 0.801242i \(0.704173\pi\)
\(384\) 0 0
\(385\) 13.1462 1.02214i 0.669991 0.0520932i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 15.9006i 0.806194i −0.915157 0.403097i \(-0.867934\pi\)
0.915157 0.403097i \(-0.132066\pi\)
\(390\) 0 0
\(391\) 3.19950 0.161806
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −21.6745 18.5471i −1.09056 0.933208i
\(396\) 0 0
\(397\) −17.2354 + 17.2354i −0.865019 + 0.865019i −0.991916 0.126897i \(-0.959498\pi\)
0.126897 + 0.991916i \(0.459498\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 13.1249i 0.655428i 0.944777 + 0.327714i \(0.106278\pi\)
−0.944777 + 0.327714i \(0.893722\pi\)
\(402\) 0 0
\(403\) −6.77127 6.77127i −0.337301 0.337301i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 11.4861 11.4861i 0.569345 0.569345i
\(408\) 0 0
\(409\) 11.2852i 0.558017i −0.960289 0.279008i \(-0.909994\pi\)
0.960289 0.279008i \(-0.0900058\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −3.84725 + 3.84725i −0.189311 + 0.189311i
\(414\) 0 0
\(415\) −0.877757 11.2892i −0.0430874 0.554163i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4.75266i 0.232183i −0.993239 0.116091i \(-0.962963\pi\)
0.993239 0.116091i \(-0.0370365\pi\)
\(420\) 0 0
\(421\) 0.283341i 0.0138092i −0.999976 0.00690460i \(-0.997802\pi\)
0.999976 0.00690460i \(-0.00219782\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −14.5978 10.6481i −0.708100 0.516510i
\(426\) 0 0
\(427\) 14.5252 14.5252i 0.702922 0.702922i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 10.1002i 0.486508i −0.969963 0.243254i \(-0.921785\pi\)
0.969963 0.243254i \(-0.0782149\pi\)
\(432\) 0 0
\(433\) 5.65232 5.65232i 0.271633 0.271633i −0.558124 0.829757i \(-0.688479\pi\)
0.829757 + 0.558124i \(0.188479\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.21723 + 2.21723i 0.106064 + 0.106064i
\(438\) 0 0
\(439\) 17.0307i 0.812831i −0.913688 0.406415i \(-0.866779\pi\)
0.913688 0.406415i \(-0.133221\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −10.8863 + 10.8863i −0.517226 + 0.517226i −0.916731 0.399505i \(-0.869182\pi\)
0.399505 + 0.916731i \(0.369182\pi\)
\(444\) 0 0
\(445\) 14.8600 17.3657i 0.704434 0.823211i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −10.3509 −0.488488 −0.244244 0.969714i \(-0.578540\pi\)
−0.244244 + 0.969714i \(0.578540\pi\)
\(450\) 0 0
\(451\) 33.8076i 1.59194i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −4.45940 3.81598i −0.209060 0.178896i
\(456\) 0 0
\(457\) 6.38449 + 6.38449i 0.298654 + 0.298654i 0.840486 0.541833i \(-0.182269\pi\)
−0.541833 + 0.840486i \(0.682269\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6.07751 0.283058 0.141529 0.989934i \(-0.454798\pi\)
0.141529 + 0.989934i \(0.454798\pi\)
\(462\) 0 0
\(463\) −22.2374 + 22.2374i −1.03346 + 1.03346i −0.0340371 + 0.999421i \(0.510836\pi\)
−0.999421 + 0.0340371i \(0.989164\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 17.6001 + 17.6001i 0.814434 + 0.814434i 0.985295 0.170861i \(-0.0546549\pi\)
−0.170861 + 0.985295i \(0.554655\pi\)
\(468\) 0 0
\(469\) 30.3400 1.40097
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 15.4721 + 15.4721i 0.711406 + 0.711406i
\(474\) 0 0
\(475\) −2.73713 17.4952i −0.125588 0.802735i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2.47636 −0.113148 −0.0565740 0.998398i \(-0.518018\pi\)
−0.0565740 + 0.998398i \(0.518018\pi\)
\(480\) 0 0
\(481\) −7.23038 −0.329677
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4.09012 + 0.318015i −0.185723 + 0.0144403i
\(486\) 0 0
\(487\) −12.3734 12.3734i −0.560694 0.560694i 0.368811 0.929505i \(-0.379765\pi\)
−0.929505 + 0.368811i \(0.879765\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −37.1551 −1.67679 −0.838394 0.545064i \(-0.816505\pi\)
−0.838394 + 0.545064i \(0.816505\pi\)
\(492\) 0 0
\(493\) −13.0898 13.0898i −0.589536 0.589536i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.36160 3.36160i 0.150789 0.150789i
\(498\) 0 0
\(499\) 34.8644 1.56075 0.780373 0.625315i \(-0.215029\pi\)
0.780373 + 0.625315i \(0.215029\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1.25041 1.25041i −0.0557529 0.0557529i 0.678681 0.734434i \(-0.262552\pi\)
−0.734434 + 0.678681i \(0.762552\pi\)
\(504\) 0 0
\(505\) −8.46644 + 9.89400i −0.376752 + 0.440277i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 38.4393i 1.70379i −0.523711 0.851896i \(-0.675453\pi\)
0.523711 0.851896i \(-0.324547\pi\)
\(510\) 0 0
\(511\) 17.4843 0.773461
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −0.755895 9.72185i −0.0333087 0.428396i
\(516\) 0 0
\(517\) −25.7631 + 25.7631i −1.13306 + 1.13306i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 19.1329i 0.838226i −0.907934 0.419113i \(-0.862341\pi\)
0.907934 0.419113i \(-0.137659\pi\)
\(522\) 0 0
\(523\) −0.870444 0.870444i −0.0380619 0.0380619i 0.687820 0.725882i \(-0.258568\pi\)
−0.725882 + 0.687820i \(0.758568\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −20.1753 + 20.1753i −0.878849 + 0.878849i
\(528\) 0 0
\(529\) 22.2161i 0.965918i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 10.6408 10.6408i 0.460903 0.460903i
\(534\) 0 0
\(535\) −20.4825 + 1.59256i −0.885538 + 0.0688524i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 6.31183i 0.271870i
\(540\) 0 0
\(541\) 18.7259i 0.805089i −0.915400 0.402544i \(-0.868126\pi\)
0.915400 0.402544i \(-0.131874\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 7.86558 9.19183i 0.336924 0.393735i
\(546\) 0 0
\(547\) −25.7085 + 25.7085i −1.09922 + 1.09922i −0.104713 + 0.994502i \(0.533392\pi\)
−0.994502 + 0.104713i \(0.966608\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 18.1422i 0.772885i
\(552\) 0 0
\(553\) −19.5228 + 19.5228i −0.830192 + 0.830192i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −4.85098 4.85098i −0.205543 0.205543i 0.596827 0.802370i \(-0.296428\pi\)
−0.802370 + 0.596827i \(0.796428\pi\)
\(558\) 0 0
\(559\) 9.73950i 0.411937i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −5.13320 + 5.13320i −0.216339 + 0.216339i −0.806954 0.590615i \(-0.798885\pi\)
0.590615 + 0.806954i \(0.298885\pi\)
\(564\) 0 0
\(565\) −1.13117 + 0.0879511i −0.0475888 + 0.00370013i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 27.4425 1.15045 0.575224 0.817996i \(-0.304915\pi\)
0.575224 + 0.817996i \(0.304915\pi\)
\(570\) 0 0
\(571\) 7.73020i 0.323499i −0.986832 0.161749i \(-0.948286\pi\)
0.986832 0.161749i \(-0.0517136\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.60879 3.57648i 0.108794 0.149149i
\(576\) 0 0
\(577\) −9.33858 9.33858i −0.388770 0.388770i 0.485478 0.874249i \(-0.338645\pi\)
−0.874249 + 0.485478i \(0.838645\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −10.9591 −0.454659
\(582\) 0 0
\(583\) 17.6201 17.6201i 0.729751 0.729751i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 20.5419 + 20.5419i 0.847856 + 0.847856i 0.989865 0.142010i \(-0.0453564\pi\)
−0.142010 + 0.989865i \(0.545356\pi\)
\(588\) 0 0
\(589\) −27.9625 −1.15218
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 15.8708 + 15.8708i 0.651734 + 0.651734i 0.953410 0.301676i \(-0.0975462\pi\)
−0.301676 + 0.953410i \(0.597546\pi\)
\(594\) 0 0
\(595\) −11.3699 + 13.2870i −0.466119 + 0.544713i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 31.5111 1.28751 0.643754 0.765232i \(-0.277376\pi\)
0.643754 + 0.765232i \(0.277376\pi\)
\(600\) 0 0
\(601\) 7.28520 0.297169 0.148585 0.988900i \(-0.452528\pi\)
0.148585 + 0.988900i \(0.452528\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −5.19805 + 6.07451i −0.211331 + 0.246964i
\(606\) 0 0
\(607\) 28.1836 + 28.1836i 1.14394 + 1.14394i 0.987723 + 0.156213i \(0.0499285\pi\)
0.156213 + 0.987723i \(0.450071\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 16.2176 0.656095
\(612\) 0 0
\(613\) −24.9782 24.9782i −1.00886 1.00886i −0.999960 0.00890069i \(-0.997167\pi\)
−0.00890069 0.999960i \(-0.502833\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 19.7928 19.7928i 0.796830 0.796830i −0.185764 0.982594i \(-0.559476\pi\)
0.982594 + 0.185764i \(0.0594761\pi\)
\(618\) 0 0
\(619\) −25.0717 −1.00772 −0.503859 0.863786i \(-0.668087\pi\)
−0.503859 + 0.863786i \(0.668087\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −15.6417 15.6417i −0.626672 0.626672i
\(624\) 0 0
\(625\) −23.8054 + 7.63561i −0.952216 + 0.305424i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 21.5432i 0.858984i
\(630\) 0 0
\(631\) −6.42730 −0.255867 −0.127933 0.991783i \(-0.540834\pi\)
−0.127933 + 0.991783i \(0.540834\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2.88919 0.224641i 0.114654 0.00891460i
\(636\) 0 0
\(637\) 1.98662 1.98662i 0.0787126 0.0787126i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 28.9552i 1.14366i 0.820372 + 0.571830i \(0.193766\pi\)
−0.820372 + 0.571830i \(0.806234\pi\)
\(642\) 0 0
\(643\) 20.0962 + 20.0962i 0.792517 + 0.792517i 0.981903 0.189385i \(-0.0606495\pi\)
−0.189385 + 0.981903i \(0.560650\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 27.5740 27.5740i 1.08405 1.08405i 0.0879193 0.996128i \(-0.471978\pi\)
0.996128 0.0879193i \(-0.0280218\pi\)
\(648\) 0 0
\(649\) 6.85034i 0.268899i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −17.8261 + 17.8261i −0.697590 + 0.697590i −0.963890 0.266300i \(-0.914199\pi\)
0.266300 + 0.963890i \(0.414199\pi\)
\(654\) 0 0
\(655\) 28.4010 33.1898i 1.10972 1.29683i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 37.7533i 1.47066i −0.677709 0.735331i \(-0.737027\pi\)
0.677709 0.735331i \(-0.262973\pi\)
\(660\) 0 0
\(661\) 6.03049i 0.234559i −0.993099 0.117279i \(-0.962583\pi\)
0.993099 0.117279i \(-0.0374173\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −17.0869 + 1.32855i −0.662603 + 0.0515188i
\(666\) 0 0
\(667\) 3.20701 3.20701i 0.124176 0.124176i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 25.8632i 0.998439i
\(672\) 0 0
\(673\) 3.75403 3.75403i 0.144707 0.144707i −0.631042 0.775749i \(-0.717372\pi\)
0.775749 + 0.631042i \(0.217372\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −12.0579 12.0579i −0.463421 0.463421i 0.436354 0.899775i \(-0.356270\pi\)
−0.899775 + 0.436354i \(0.856270\pi\)
\(678\) 0 0
\(679\) 3.97052i 0.152375i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −18.0083 + 18.0083i −0.689068 + 0.689068i −0.962026 0.272958i \(-0.911998\pi\)
0.272958 + 0.962026i \(0.411998\pi\)
\(684\) 0 0
\(685\) 1.87922 + 24.1694i 0.0718015 + 0.923467i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −11.0917 −0.422560
\(690\) 0 0
\(691\) 37.0052i 1.40774i 0.710327 + 0.703872i \(0.248547\pi\)
−0.710327 + 0.703872i \(0.751453\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 21.4015 25.0102i 0.811807 0.948689i
\(696\) 0 0
\(697\) −31.7046 31.7046i −1.20090 1.20090i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 10.8810 0.410968 0.205484 0.978660i \(-0.434123\pi\)
0.205484 + 0.978660i \(0.434123\pi\)
\(702\) 0 0
\(703\) −14.9292 + 14.9292i −0.563067 + 0.563067i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 8.91179 + 8.91179i 0.335162 + 0.335162i
\(708\) 0 0
\(709\) −17.9836 −0.675389 −0.337695 0.941256i \(-0.609647\pi\)
−0.337695 + 0.941256i \(0.609647\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −4.94295 4.94295i −0.185115 0.185115i
\(714\) 0 0
\(715\) −7.36749 + 0.572838i −0.275529 + 0.0214229i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 32.0959 1.19698 0.598488 0.801132i \(-0.295769\pi\)
0.598488 + 0.801132i \(0.295769\pi\)
\(720\) 0 0
\(721\) −9.43759 −0.351474
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −25.3052 + 3.95900i −0.939811 + 0.147033i
\(726\) 0 0
\(727\) −15.2813 15.2813i −0.566754 0.566754i 0.364464 0.931218i \(-0.381252\pi\)
−0.931218 + 0.364464i \(0.881252\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −29.0192 −1.07332
\(732\) 0 0
\(733\) 25.4494 + 25.4494i 0.939996 + 0.939996i 0.998299 0.0583028i \(-0.0185689\pi\)
−0.0583028 + 0.998299i \(0.518569\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 27.0115 27.0115i 0.994980 0.994980i
\(738\) 0 0
\(739\) −23.6936 −0.871584 −0.435792 0.900047i \(-0.643532\pi\)
−0.435792 + 0.900047i \(0.643532\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −10.4630 10.4630i −0.383852 0.383852i 0.488636 0.872488i \(-0.337495\pi\)
−0.872488 + 0.488636i \(0.837495\pi\)
\(744\) 0 0
\(745\) −26.5546 22.7232i −0.972886 0.832513i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 19.8836i 0.726532i
\(750\) 0 0
\(751\) −51.4858 −1.87874 −0.939372 0.342899i \(-0.888591\pi\)
−0.939372 + 0.342899i \(0.888591\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 25.5710 29.8826i 0.930623 1.08754i
\(756\) 0 0
\(757\) 20.4014 20.4014i 0.741501 0.741501i −0.231366 0.972867i \(-0.574319\pi\)
0.972867 + 0.231366i \(0.0743195\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 13.3989i 0.485709i −0.970063 0.242855i \(-0.921916\pi\)
0.970063 0.242855i \(-0.0780838\pi\)
\(762\) 0 0
\(763\) −8.27933 8.27933i −0.299732 0.299732i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.15611 2.15611i 0.0778526 0.0778526i
\(768\) 0 0
\(769\) 15.5493i 0.560721i 0.959895 + 0.280361i \(0.0904540\pi\)
−0.959895 + 0.280361i \(0.909546\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 4.70360 4.70360i 0.169177 0.169177i −0.617441 0.786617i \(-0.711830\pi\)
0.786617 + 0.617441i \(0.211830\pi\)
\(774\) 0 0
\(775\) 6.10198 + 39.0028i 0.219190 + 1.40102i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 43.9420i 1.57439i
\(780\) 0 0
\(781\) 5.98561i 0.214182i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.86388 23.9721i −0.0665248 0.855601i
\(786\) 0 0
\(787\) 7.45088 7.45088i 0.265595 0.265595i −0.561727 0.827322i \(-0.689863\pi\)
0.827322 + 0.561727i \(0.189863\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1.09810i 0.0390439i
\(792\) 0 0
\(793\) −8.14032 + 8.14032i −0.289071 + 0.289071i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −27.5898 27.5898i −0.977280 0.977280i 0.0224677 0.999748i \(-0.492848\pi\)
−0.999748 + 0.0224677i \(0.992848\pi\)
\(798\) 0 0
\(799\) 48.3211i 1.70948i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 15.5661 15.5661i 0.549317 0.549317i
\(804\) 0 0
\(805\) −3.25531 2.78562i −0.114735 0.0981802i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 9.93002 0.349121 0.174560 0.984646i \(-0.444150\pi\)
0.174560 + 0.984646i \(0.444150\pi\)
\(810\) 0 0
\(811\) 0.144213i 0.00506400i −0.999997 0.00253200i \(-0.999194\pi\)
0.999997 0.00253200i \(-0.000805962\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 26.9115 2.09243i 0.942670 0.0732946i
\(816\) 0 0
\(817\) −20.1100 20.1100i −0.703562 0.703562i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −20.3654 −0.710757 −0.355379 0.934722i \(-0.615648\pi\)
−0.355379 + 0.934722i \(0.615648\pi\)
\(822\) 0 0
\(823\) 31.7594 31.7594i 1.10706 1.10706i 0.113529 0.993535i \(-0.463784\pi\)
0.993535 0.113529i \(-0.0362156\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −28.5251 28.5251i −0.991916 0.991916i 0.00805118 0.999968i \(-0.497437\pi\)
−0.999968 + 0.00805118i \(0.997437\pi\)
\(828\) 0 0
\(829\) 54.4189 1.89005 0.945024 0.327002i \(-0.106038\pi\)
0.945024 + 0.327002i \(0.106038\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −5.91921 5.91921i −0.205088 0.205088i
\(834\) 0 0
\(835\) −1.49782 19.2641i −0.0518343 0.666661i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −47.3060 −1.63318 −0.816592 0.577215i \(-0.804139\pi\)
−0.816592 + 0.577215i \(0.804139\pi\)
\(840\) 0 0
\(841\) 2.75894 0.0951360
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −19.5871 16.7610i −0.673818 0.576596i
\(846\) 0 0
\(847\) 5.47147 + 5.47147i 0.188002 + 0.188002i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −5.27809 −0.180931
\(852\) 0 0
\(853\) −14.9083 14.9083i −0.510449 0.510449i 0.404215 0.914664i \(-0.367545\pi\)
−0.914664 + 0.404215i \(0.867545\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −6.64085 + 6.64085i −0.226847 + 0.226847i −0.811374 0.584527i \(-0.801280\pi\)
0.584527 + 0.811374i \(0.301280\pi\)
\(858\) 0 0
\(859\) 3.27984 0.111907 0.0559534 0.998433i \(-0.482180\pi\)
0.0559534 + 0.998433i \(0.482180\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −11.7285 11.7285i −0.399243 0.399243i 0.478723 0.877966i \(-0.341100\pi\)
−0.877966 + 0.478723i \(0.841100\pi\)
\(864\) 0 0
\(865\) −0.145541 1.87186i −0.00494854 0.0636451i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 34.7619i 1.17922i
\(870\) 0 0
\(871\) −17.0034 −0.576139
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 5.58180 + 23.5433i 0.188699 + 0.795910i
\(876\) 0 0
\(877\) −27.6401 + 27.6401i −0.933339 + 0.933339i −0.997913 0.0645744i \(-0.979431\pi\)
0.0645744 + 0.997913i \(0.479431\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 37.9900i 1.27991i −0.768410 0.639957i \(-0.778952\pi\)
0.768410 0.639957i \(-0.221048\pi\)
\(882\) 0 0
\(883\) 33.6777 + 33.6777i 1.13335 + 1.13335i 0.989617 + 0.143729i \(0.0459095\pi\)
0.143729 + 0.989617i \(0.454091\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.17366 + 1.17366i −0.0394078 + 0.0394078i −0.726536 0.687128i \(-0.758871\pi\)
0.687128 + 0.726536i \(0.258871\pi\)
\(888\) 0 0
\(889\) 2.80471i 0.0940671i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 33.4861 33.4861i 1.12057 1.12057i
\(894\) 0 0
\(895\) −19.3570 16.5641i −0.647034 0.553676i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 40.4452i 1.34892i
\(900\) 0 0
\(901\) 33.0482i 1.10099i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 12.4263 + 10.6333i 0.413064 + 0.353464i
\(906\) 0 0
\(907\) 16.4248 16.4248i 0.545377 0.545377i −0.379723 0.925100i \(-0.623981\pi\)
0.925100 + 0.379723i \(0.123981\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 32.3497i 1.07179i −0.844284 0.535897i \(-0.819974\pi\)
0.844284 0.535897i \(-0.180026\pi\)
\(912\) 0 0
\(913\) −9.75676 + 9.75676i −0.322902 + 0.322902i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −29.8950 29.8950i −0.987219 0.987219i
\(918\) 0 0
\(919\) 5.60588i 0.184921i −0.995716 0.0924605i \(-0.970527\pi\)
0.995716 0.0924605i \(-0.0294732\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1.88394 + 1.88394i −0.0620106 + 0.0620106i
\(924\) 0 0
\(925\) 24.0815 + 17.5658i 0.791794 + 0.577559i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 34.7413 1.13983 0.569913 0.821705i \(-0.306977\pi\)
0.569913 + 0.821705i \(0.306977\pi\)
\(930\) 0 0
\(931\) 8.20391i 0.268872i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1.70680 + 21.9518i 0.0558182 + 0.717899i
\(936\) 0 0
\(937\) 5.80471 + 5.80471i 0.189632 + 0.189632i 0.795537 0.605905i \(-0.207189\pi\)
−0.605905 + 0.795537i \(0.707189\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 23.7893 0.775510 0.387755 0.921762i \(-0.373251\pi\)
0.387755 + 0.921762i \(0.373251\pi\)
\(942\) 0 0
\(943\) 7.76765 7.76765i 0.252949 0.252949i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −12.4008 12.4008i −0.402972 0.402972i 0.476307 0.879279i \(-0.341975\pi\)
−0.879279 + 0.476307i \(0.841975\pi\)
\(948\) 0 0
\(949\) −9.79872 −0.318080
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 4.46081 + 4.46081i 0.144500 + 0.144500i 0.775656 0.631156i \(-0.217419\pi\)
−0.631156 + 0.775656i \(0.717419\pi\)
\(954\) 0 0
\(955\) −2.25713 1.93146i −0.0730390 0.0625006i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 23.4627 0.757651
\(960\) 0 0
\(961\) 31.3380 1.01090
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 2.82801 + 36.3722i 0.0910369 + 1.17086i
\(966\) 0 0
\(967\) −2.74162 2.74162i −0.0881645 0.0881645i 0.661649 0.749814i \(-0.269857\pi\)
−0.749814 + 0.661649i \(0.769857\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 10.5455 0.338421 0.169210 0.985580i \(-0.445878\pi\)
0.169210 + 0.985580i \(0.445878\pi\)
\(972\) 0 0
\(973\) −22.5273 22.5273i −0.722193 0.722193i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 13.3372 13.3372i 0.426695 0.426695i −0.460806 0.887501i \(-0.652440\pi\)
0.887501 + 0.460806i \(0.152440\pi\)
\(978\) 0 0
\(979\) −27.8513 −0.890133
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 3.84412 + 3.84412i 0.122608 + 0.122608i 0.765749 0.643140i \(-0.222369\pi\)
−0.643140 + 0.765749i \(0.722369\pi\)
\(984\) 0 0
\(985\) 51.0745 3.97115i 1.62737 0.126531i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 7.10972i 0.226076i
\(990\) 0 0
\(991\) −34.9248 −1.10942 −0.554711 0.832043i \(-0.687171\pi\)
−0.554711 + 0.832043i \(0.687171\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 10.3532 + 8.85937i 0.328218 + 0.280861i
\(996\) 0 0
\(997\) 11.0217 11.0217i 0.349062 0.349062i −0.510698 0.859760i \(-0.670613\pi\)
0.859760 + 0.510698i \(0.170613\pi\)
\(998\) 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 1440.2.bj.a.17.19 48
3.2 odd 2 inner 1440.2.bj.a.17.6 48
4.3 odd 2 360.2.x.a.197.10 yes 48
5.3 odd 4 inner 1440.2.bj.a.593.20 48
8.3 odd 2 360.2.x.a.197.22 yes 48
8.5 even 2 inner 1440.2.bj.a.17.5 48
12.11 even 2 360.2.x.a.197.15 yes 48
15.8 even 4 inner 1440.2.bj.a.593.5 48
20.3 even 4 360.2.x.a.53.3 48
24.5 odd 2 inner 1440.2.bj.a.17.20 48
24.11 even 2 360.2.x.a.197.3 yes 48
40.3 even 4 360.2.x.a.53.15 yes 48
40.13 odd 4 inner 1440.2.bj.a.593.6 48
60.23 odd 4 360.2.x.a.53.22 yes 48
120.53 even 4 inner 1440.2.bj.a.593.19 48
120.83 odd 4 360.2.x.a.53.10 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.x.a.53.3 48 20.3 even 4
360.2.x.a.53.10 yes 48 120.83 odd 4
360.2.x.a.53.15 yes 48 40.3 even 4
360.2.x.a.53.22 yes 48 60.23 odd 4
360.2.x.a.197.3 yes 48 24.11 even 2
360.2.x.a.197.10 yes 48 4.3 odd 2
360.2.x.a.197.15 yes 48 12.11 even 2
360.2.x.a.197.22 yes 48 8.3 odd 2
1440.2.bj.a.17.5 48 8.5 even 2 inner
1440.2.bj.a.17.6 48 3.2 odd 2 inner
1440.2.bj.a.17.19 48 1.1 even 1 trivial
1440.2.bj.a.17.20 48 24.5 odd 2 inner
1440.2.bj.a.593.5 48 15.8 even 4 inner
1440.2.bj.a.593.6 48 40.13 odd 4 inner
1440.2.bj.a.593.19 48 120.53 even 4 inner
1440.2.bj.a.593.20 48 5.3 odd 4 inner