Properties

Label 3024.2.cc.b.881.1
Level $3024$
Weight $2$
Character 3024.881
Analytic conductor $24.147$
Analytic rank $0$
Dimension $16$
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] = [3024,2,Mod(881,3024)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3024.881");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.cc (of order \(6\), 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: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{6} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 881.1
Root \(-1.62181 - 0.608059i\) of defining polynomial
Character \(\chi\) \(=\) 3024.881
Dual form 3024.2.cc.b.2897.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.94556 + 3.36980i) q^{5} +(-0.343982 - 2.62329i) q^{7} +O(q^{10})\) \(q+(-1.94556 + 3.36980i) q^{5} +(-0.343982 - 2.62329i) q^{7} +(3.41614 - 1.97231i) q^{11} +(2.46687 + 1.42425i) q^{13} -0.742117 q^{17} +1.78474i q^{19} +(-5.41535 - 3.12656i) q^{23} +(-5.07039 - 8.78217i) q^{25} +(2.50079 - 1.44383i) q^{29} +(-3.04125 - 1.75587i) q^{31} +(9.50923 + 3.94462i) q^{35} +3.00158 q^{37} +(5.24705 - 9.08816i) q^{41} +(-0.471521 - 0.816699i) q^{43} +(1.09263 + 1.89248i) q^{47} +(-6.76335 + 1.80473i) q^{49} +15.3490i q^{55} +(0.0105673 - 0.0183031i) q^{59} +(-2.13832 + 1.23456i) q^{61} +(-9.59886 + 5.54191i) q^{65} +(6.72463 - 11.6474i) q^{67} -1.94304i q^{71} +4.85486i q^{73} +(-6.34904 - 8.28311i) q^{77} +(1.81806 + 3.14898i) q^{79} +(-4.02998 - 6.98012i) q^{83} +(1.44383 - 2.50079i) q^{85} +9.26646 q^{89} +(2.88766 - 6.96124i) q^{91} +(-6.01422 - 3.47231i) q^{95} +(16.2983 - 9.40980i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{7} - 12 q^{11} - 48 q^{23} - 8 q^{25} + 12 q^{29} - 8 q^{37} - 4 q^{43} - 8 q^{49} - 84 q^{65} + 28 q^{67} - 78 q^{77} + 4 q^{79} - 12 q^{85} - 24 q^{91} + 12 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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
\(5\) −1.94556 + 3.36980i −0.870080 + 1.50702i −0.00816625 + 0.999967i \(0.502599\pi\)
−0.861913 + 0.507056i \(0.830734\pi\)
\(6\) 0 0
\(7\) −0.343982 2.62329i −0.130013 0.991512i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.41614 1.97231i 1.03001 0.594674i 0.113019 0.993593i \(-0.463948\pi\)
0.916986 + 0.398919i \(0.130615\pi\)
\(12\) 0 0
\(13\) 2.46687 + 1.42425i 0.684186 + 0.395015i 0.801430 0.598088i \(-0.204073\pi\)
−0.117244 + 0.993103i \(0.537406\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.742117 −0.179990 −0.0899949 0.995942i \(-0.528685\pi\)
−0.0899949 + 0.995942i \(0.528685\pi\)
\(18\) 0 0
\(19\) 1.78474i 0.409447i 0.978820 + 0.204723i \(0.0656295\pi\)
−0.978820 + 0.204723i \(0.934370\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −5.41535 3.12656i −1.12918 0.651932i −0.185451 0.982654i \(-0.559374\pi\)
−0.943728 + 0.330722i \(0.892708\pi\)
\(24\) 0 0
\(25\) −5.07039 8.78217i −1.01408 1.75643i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.50079 1.44383i 0.464385 0.268113i −0.249501 0.968374i \(-0.580267\pi\)
0.713886 + 0.700262i \(0.246933\pi\)
\(30\) 0 0
\(31\) −3.04125 1.75587i −0.546225 0.315363i 0.201373 0.979515i \(-0.435460\pi\)
−0.747598 + 0.664152i \(0.768793\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 9.50923 + 3.94462i 1.60735 + 0.666762i
\(36\) 0 0
\(37\) 3.00158 0.493456 0.246728 0.969085i \(-0.420645\pi\)
0.246728 + 0.969085i \(0.420645\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.24705 9.08816i 0.819452 1.41933i −0.0866345 0.996240i \(-0.527611\pi\)
0.906087 0.423092i \(-0.139055\pi\)
\(42\) 0 0
\(43\) −0.471521 0.816699i −0.0719063 0.124545i 0.827830 0.560978i \(-0.189575\pi\)
−0.899737 + 0.436433i \(0.856242\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.09263 + 1.89248i 0.159376 + 0.276047i 0.934644 0.355585i \(-0.115718\pi\)
−0.775268 + 0.631633i \(0.782385\pi\)
\(48\) 0 0
\(49\) −6.76335 + 1.80473i −0.966193 + 0.257819i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 15.3490i 2.06965i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.0105673 0.0183031i 0.00137575 0.00238286i −0.865337 0.501191i \(-0.832895\pi\)
0.866712 + 0.498808i \(0.166229\pi\)
\(60\) 0 0
\(61\) −2.13832 + 1.23456i −0.273783 + 0.158069i −0.630606 0.776103i \(-0.717193\pi\)
0.356822 + 0.934172i \(0.383860\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −9.59886 + 5.54191i −1.19059 + 0.687389i
\(66\) 0 0
\(67\) 6.72463 11.6474i 0.821544 1.42296i −0.0829874 0.996551i \(-0.526446\pi\)
0.904532 0.426406i \(-0.140221\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.94304i 0.230597i −0.993331 0.115298i \(-0.963218\pi\)
0.993331 0.115298i \(-0.0367824\pi\)
\(72\) 0 0
\(73\) 4.85486i 0.568218i 0.958792 + 0.284109i \(0.0916978\pi\)
−0.958792 + 0.284109i \(0.908302\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −6.34904 8.28311i −0.723540 0.943948i
\(78\) 0 0
\(79\) 1.81806 + 3.14898i 0.204548 + 0.354288i 0.949989 0.312284i \(-0.101094\pi\)
−0.745440 + 0.666572i \(0.767761\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.02998 6.98012i −0.442347 0.766168i 0.555516 0.831506i \(-0.312521\pi\)
−0.997863 + 0.0653378i \(0.979188\pi\)
\(84\) 0 0
\(85\) 1.44383 2.50079i 0.156605 0.271249i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 9.26646 0.982243 0.491122 0.871091i \(-0.336587\pi\)
0.491122 + 0.871091i \(0.336587\pi\)
\(90\) 0 0
\(91\) 2.88766 6.96124i 0.302709 0.729736i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −6.01422 3.47231i −0.617046 0.356251i
\(96\) 0 0
\(97\) 16.2983 9.40980i 1.65484 0.955421i 0.679794 0.733403i \(-0.262069\pi\)
0.975043 0.222018i \(-0.0712643\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.14079 7.17206i −0.412024 0.713647i 0.583087 0.812410i \(-0.301845\pi\)
−0.995111 + 0.0987631i \(0.968511\pi\)
\(102\) 0 0
\(103\) 14.7646 + 8.52435i 1.45480 + 0.839929i 0.998748 0.0500247i \(-0.0159300\pi\)
0.456051 + 0.889953i \(0.349263\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 14.3369i 1.38600i 0.720936 + 0.693001i \(0.243712\pi\)
−0.720936 + 0.693001i \(0.756288\pi\)
\(108\) 0 0
\(109\) 11.2800 1.08042 0.540212 0.841529i \(-0.318344\pi\)
0.540212 + 0.841529i \(0.318344\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 8.51501 + 4.91614i 0.801024 + 0.462472i 0.843829 0.536612i \(-0.180296\pi\)
−0.0428049 + 0.999083i \(0.513629\pi\)
\(114\) 0 0
\(115\) 21.0718 12.1658i 1.96495 1.13447i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0.255275 + 1.94679i 0.0234010 + 0.178462i
\(120\) 0 0
\(121\) 2.28001 3.94910i 0.207274 0.359009i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 20.0033 1.78915
\(126\) 0 0
\(127\) −2.94462 −0.261293 −0.130646 0.991429i \(-0.541705\pi\)
−0.130646 + 0.991429i \(0.541705\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 7.53255 13.0468i 0.658122 1.13990i −0.322979 0.946406i \(-0.604684\pi\)
0.981101 0.193495i \(-0.0619823\pi\)
\(132\) 0 0
\(133\) 4.68189 0.613917i 0.405972 0.0532334i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 13.6139 7.85997i 1.16311 0.671523i 0.211064 0.977472i \(-0.432307\pi\)
0.952048 + 0.305950i \(0.0989739\pi\)
\(138\) 0 0
\(139\) −2.86373 1.65337i −0.242898 0.140237i 0.373610 0.927586i \(-0.378120\pi\)
−0.616508 + 0.787349i \(0.711453\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 11.2362 0.939620
\(144\) 0 0
\(145\) 11.2362i 0.933118i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −9.52765 5.50079i −0.780535 0.450642i 0.0560848 0.998426i \(-0.482138\pi\)
−0.836620 + 0.547784i \(0.815472\pi\)
\(150\) 0 0
\(151\) −0.719988 1.24706i −0.0585918 0.101484i 0.835242 0.549883i \(-0.185328\pi\)
−0.893834 + 0.448399i \(0.851994\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 11.8339 6.83228i 0.950518 0.548782i
\(156\) 0 0
\(157\) 14.3822 + 8.30354i 1.14782 + 0.662695i 0.948355 0.317210i \(-0.102746\pi\)
0.199465 + 0.979905i \(0.436079\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −6.33909 + 15.2815i −0.499591 + 1.20435i
\(162\) 0 0
\(163\) 12.3955 0.970887 0.485444 0.874268i \(-0.338658\pi\)
0.485444 + 0.874268i \(0.338658\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5.86087 + 10.1513i −0.453528 + 0.785534i −0.998602 0.0528541i \(-0.983168\pi\)
0.545074 + 0.838388i \(0.316502\pi\)
\(168\) 0 0
\(169\) −2.44304 4.23147i −0.187926 0.325498i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 8.38548 + 14.5241i 0.637536 + 1.10425i 0.985972 + 0.166913i \(0.0533798\pi\)
−0.348435 + 0.937333i \(0.613287\pi\)
\(174\) 0 0
\(175\) −21.2941 + 16.3220i −1.60968 + 1.23383i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 5.77532i 0.431668i −0.976430 0.215834i \(-0.930753\pi\)
0.976430 0.215834i \(-0.0692470\pi\)
\(180\) 0 0
\(181\) 5.53310i 0.411272i 0.978629 + 0.205636i \(0.0659263\pi\)
−0.978629 + 0.205636i \(0.934074\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −5.83974 + 10.1147i −0.429346 + 0.743649i
\(186\) 0 0
\(187\) −2.53518 + 1.46368i −0.185390 + 0.107035i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −5.38124 + 3.10686i −0.389373 + 0.224805i −0.681888 0.731456i \(-0.738841\pi\)
0.292515 + 0.956261i \(0.405508\pi\)
\(192\) 0 0
\(193\) 3.90271 6.75970i 0.280923 0.486574i −0.690689 0.723152i \(-0.742693\pi\)
0.971612 + 0.236578i \(0.0760260\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 12.7737i 0.910092i −0.890468 0.455046i \(-0.849623\pi\)
0.890468 0.455046i \(-0.150377\pi\)
\(198\) 0 0
\(199\) 1.81201i 0.128450i −0.997935 0.0642250i \(-0.979542\pi\)
0.997935 0.0642250i \(-0.0204575\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −4.64782 6.06365i −0.326213 0.425585i
\(204\) 0 0
\(205\) 20.4169 + 35.3631i 1.42598 + 2.46986i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 3.52006 + 6.09692i 0.243487 + 0.421732i
\(210\) 0 0
\(211\) 1.88766 3.26953i 0.129952 0.225083i −0.793706 0.608302i \(-0.791851\pi\)
0.923658 + 0.383218i \(0.125184\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 3.66949 0.250257
\(216\) 0 0
\(217\) −3.56002 + 8.58209i −0.241670 + 0.582590i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.83070 1.05696i −0.123146 0.0710987i
\(222\) 0 0
\(223\) −11.0662 + 6.38910i −0.741051 + 0.427846i −0.822451 0.568836i \(-0.807394\pi\)
0.0814006 + 0.996681i \(0.474061\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −9.99110 17.3051i −0.663133 1.14858i −0.979788 0.200039i \(-0.935893\pi\)
0.316655 0.948541i \(-0.397440\pi\)
\(228\) 0 0
\(229\) 8.77402 + 5.06568i 0.579804 + 0.334750i 0.761055 0.648687i \(-0.224682\pi\)
−0.181252 + 0.983437i \(0.558015\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.31007i 0.478898i −0.970909 0.239449i \(-0.923033\pi\)
0.970909 0.239449i \(-0.0769669\pi\)
\(234\) 0 0
\(235\) −8.50307 −0.554679
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7.28317 + 4.20494i 0.471109 + 0.271995i 0.716704 0.697378i \(-0.245650\pi\)
−0.245595 + 0.969373i \(0.578983\pi\)
\(240\) 0 0
\(241\) −7.75277 + 4.47607i −0.499400 + 0.288329i −0.728466 0.685082i \(-0.759766\pi\)
0.229066 + 0.973411i \(0.426433\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 7.07690 26.3024i 0.452127 1.68040i
\(246\) 0 0
\(247\) −2.54191 + 4.40271i −0.161738 + 0.280138i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 12.6432 0.798033 0.399017 0.916944i \(-0.369352\pi\)
0.399017 + 0.916944i \(0.369352\pi\)
\(252\) 0 0
\(253\) −24.6661 −1.55075
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 8.15329 14.1219i 0.508588 0.880900i −0.491362 0.870955i \(-0.663501\pi\)
0.999951 0.00994523i \(-0.00316572\pi\)
\(258\) 0 0
\(259\) −1.03249 7.87402i −0.0641557 0.489268i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 20.5434 11.8608i 1.26676 0.731366i 0.292389 0.956300i \(-0.405550\pi\)
0.974374 + 0.224934i \(0.0722166\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −7.28288 −0.444045 −0.222022 0.975042i \(-0.571266\pi\)
−0.222022 + 0.975042i \(0.571266\pi\)
\(270\) 0 0
\(271\) 22.6879i 1.37819i −0.724669 0.689097i \(-0.758007\pi\)
0.724669 0.689097i \(-0.241993\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −34.6423 20.0007i −2.08901 1.20609i
\(276\) 0 0
\(277\) −12.0838 20.9298i −0.726046 1.25755i −0.958542 0.284951i \(-0.908023\pi\)
0.232496 0.972597i \(-0.425311\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4.11229 2.37423i 0.245319 0.141635i −0.372300 0.928112i \(-0.621431\pi\)
0.617619 + 0.786478i \(0.288097\pi\)
\(282\) 0 0
\(283\) 25.4484 + 14.6926i 1.51275 + 0.873387i 0.999889 + 0.0149153i \(0.00474785\pi\)
0.512861 + 0.858471i \(0.328585\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −25.6458 10.6384i −1.51382 0.627965i
\(288\) 0 0
\(289\) −16.4493 −0.967604
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −3.31206 + 5.73666i −0.193493 + 0.335139i −0.946405 0.322981i \(-0.895315\pi\)
0.752913 + 0.658121i \(0.228648\pi\)
\(294\) 0 0
\(295\) 0.0411186 + 0.0712195i 0.00239402 + 0.00414656i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −8.90597 15.4256i −0.515046 0.892085i
\(300\) 0 0
\(301\) −1.98025 + 1.51787i −0.114140 + 0.0874885i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 9.60761i 0.550130i
\(306\) 0 0
\(307\) 21.7242i 1.23987i 0.784655 + 0.619933i \(0.212840\pi\)
−0.784655 + 0.619933i \(0.787160\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 3.14900 5.45422i 0.178563 0.309281i −0.762825 0.646605i \(-0.776188\pi\)
0.941389 + 0.337324i \(0.109522\pi\)
\(312\) 0 0
\(313\) −19.2423 + 11.1095i −1.08764 + 0.627948i −0.932946 0.360015i \(-0.882771\pi\)
−0.154691 + 0.987963i \(0.549438\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −13.5632 + 7.83070i −0.761784 + 0.439816i −0.829936 0.557859i \(-0.811623\pi\)
0.0681519 + 0.997675i \(0.478290\pi\)
\(318\) 0 0
\(319\) 5.69536 9.86466i 0.318879 0.552315i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.32448i 0.0736963i
\(324\) 0 0
\(325\) 28.8859i 1.60230i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4.58870 3.51726i 0.252983 0.193913i
\(330\) 0 0
\(331\) 0.636129 + 1.10181i 0.0349648 + 0.0605608i 0.882978 0.469414i \(-0.155535\pi\)
−0.848013 + 0.529975i \(0.822201\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 26.1663 + 45.3214i 1.42962 + 2.47617i
\(336\) 0 0
\(337\) −3.78001 + 6.54717i −0.205910 + 0.356647i −0.950422 0.310962i \(-0.899349\pi\)
0.744512 + 0.667609i \(0.232682\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −13.8525 −0.750153
\(342\) 0 0
\(343\) 7.06081 + 17.1215i 0.381248 + 0.924473i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 19.1470 + 11.0545i 1.02787 + 0.593439i 0.916373 0.400326i \(-0.131103\pi\)
0.111494 + 0.993765i \(0.464436\pi\)
\(348\) 0 0
\(349\) −12.7682 + 7.37173i −0.683467 + 0.394600i −0.801160 0.598450i \(-0.795783\pi\)
0.117693 + 0.993050i \(0.462450\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −8.63881 14.9629i −0.459798 0.796393i 0.539152 0.842208i \(-0.318745\pi\)
−0.998950 + 0.0458154i \(0.985411\pi\)
\(354\) 0 0
\(355\) 6.54767 + 3.78030i 0.347514 + 0.200638i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 10.9129i 0.575963i 0.957636 + 0.287982i \(0.0929842\pi\)
−0.957636 + 0.287982i \(0.907016\pi\)
\(360\) 0 0
\(361\) 15.8147 0.832353
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −16.3599 9.44541i −0.856318 0.494395i
\(366\) 0 0
\(367\) −30.9407 + 17.8636i −1.61509 + 0.932472i −0.626923 + 0.779081i \(0.715686\pi\)
−0.988166 + 0.153391i \(0.950981\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 16.0300 27.7648i 0.830003 1.43761i −0.0680328 0.997683i \(-0.521672\pi\)
0.898035 0.439923i \(-0.144994\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.22549 0.423634
\(378\) 0 0
\(379\) −34.8891 −1.79214 −0.896068 0.443918i \(-0.853588\pi\)
−0.896068 + 0.443918i \(0.853588\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −8.76711 + 15.1851i −0.447978 + 0.775921i −0.998254 0.0590616i \(-0.981189\pi\)
0.550276 + 0.834983i \(0.314523\pi\)
\(384\) 0 0
\(385\) 40.2649 5.27976i 2.05209 0.269082i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6.60060 3.81086i 0.334664 0.193218i −0.323246 0.946315i \(-0.604774\pi\)
0.657910 + 0.753097i \(0.271441\pi\)
\(390\) 0 0
\(391\) 4.01882 + 2.32027i 0.203241 + 0.117341i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −14.1486 −0.711893
\(396\) 0 0
\(397\) 37.6469i 1.88944i −0.327873 0.944722i \(-0.606332\pi\)
0.327873 0.944722i \(-0.393668\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −18.5689 10.7207i −0.927284 0.535368i −0.0413326 0.999145i \(-0.513160\pi\)
−0.885952 + 0.463778i \(0.846494\pi\)
\(402\) 0 0
\(403\) −5.00158 8.66299i −0.249146 0.431534i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 10.2538 5.92004i 0.508262 0.293445i
\(408\) 0 0
\(409\) −25.6086 14.7851i −1.26627 0.731079i −0.291986 0.956423i \(-0.594316\pi\)
−0.974279 + 0.225344i \(0.927649\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −0.0516494 0.0214252i −0.00254150 0.00105427i
\(414\) 0 0
\(415\) 31.3622 1.53951
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3.56481 6.17443i 0.174152 0.301641i −0.765715 0.643180i \(-0.777615\pi\)
0.939868 + 0.341539i \(0.110948\pi\)
\(420\) 0 0
\(421\) −2.31007 4.00115i −0.112586 0.195004i 0.804226 0.594323i \(-0.202580\pi\)
−0.916812 + 0.399319i \(0.869247\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3.76282 + 6.51739i 0.182524 + 0.316140i
\(426\) 0 0
\(427\) 3.97415 + 5.18477i 0.192323 + 0.250908i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 4.00771i 0.193045i −0.995331 0.0965223i \(-0.969228\pi\)
0.995331 0.0965223i \(-0.0307719\pi\)
\(432\) 0 0
\(433\) 29.4125i 1.41348i 0.707475 + 0.706738i \(0.249834\pi\)
−0.707475 + 0.706738i \(0.750166\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5.58008 9.66498i 0.266931 0.462339i
\(438\) 0 0
\(439\) −18.5130 + 10.6885i −0.883575 + 0.510133i −0.871836 0.489799i \(-0.837070\pi\)
−0.0117398 + 0.999931i \(0.503737\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5.05227 2.91693i 0.240041 0.138587i −0.375155 0.926962i \(-0.622410\pi\)
0.615195 + 0.788375i \(0.289077\pi\)
\(444\) 0 0
\(445\) −18.0284 + 31.2262i −0.854630 + 1.48026i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 22.5823i 1.06573i 0.846202 + 0.532863i \(0.178884\pi\)
−0.846202 + 0.532863i \(0.821116\pi\)
\(450\) 0 0
\(451\) 41.3953i 1.94923i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 17.8399 + 23.2743i 0.836347 + 1.09112i
\(456\) 0 0
\(457\) −19.9311 34.5218i −0.932340 1.61486i −0.779310 0.626638i \(-0.784430\pi\)
−0.153029 0.988222i \(-0.548903\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −3.68254 6.37834i −0.171513 0.297069i 0.767436 0.641125i \(-0.221532\pi\)
−0.938949 + 0.344056i \(0.888199\pi\)
\(462\) 0 0
\(463\) 14.3457 24.8475i 0.666702 1.15476i −0.312119 0.950043i \(-0.601039\pi\)
0.978821 0.204718i \(-0.0656278\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 13.6704 0.632590 0.316295 0.948661i \(-0.397561\pi\)
0.316295 + 0.948661i \(0.397561\pi\)
\(468\) 0 0
\(469\) −32.8677 13.6342i −1.51769 0.629569i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3.22157 1.85997i −0.148128 0.0855216i
\(474\) 0 0
\(475\) 15.6739 9.04931i 0.719166 0.415211i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −5.20537 9.01596i −0.237839 0.411950i 0.722255 0.691627i \(-0.243106\pi\)
−0.960094 + 0.279677i \(0.909773\pi\)
\(480\) 0 0
\(481\) 7.40449 + 4.27499i 0.337616 + 0.194923i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 73.2292i 3.32517i
\(486\) 0 0
\(487\) −2.33850 −0.105968 −0.0529838 0.998595i \(-0.516873\pi\)
−0.0529838 + 0.998595i \(0.516873\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −29.3448 16.9422i −1.32431 0.764591i −0.339898 0.940462i \(-0.610392\pi\)
−0.984413 + 0.175871i \(0.943726\pi\)
\(492\) 0 0
\(493\) −1.85588 + 1.07149i −0.0835845 + 0.0482575i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.09717 + 0.668371i −0.228639 + 0.0299805i
\(498\) 0 0
\(499\) −8.30223 + 14.3799i −0.371659 + 0.643732i −0.989821 0.142319i \(-0.954544\pi\)
0.618162 + 0.786051i \(0.287877\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 35.3661 1.57690 0.788449 0.615100i \(-0.210885\pi\)
0.788449 + 0.615100i \(0.210885\pi\)
\(504\) 0 0
\(505\) 32.2246 1.43398
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −18.5291 + 32.0933i −0.821287 + 1.42251i 0.0834371 + 0.996513i \(0.473410\pi\)
−0.904724 + 0.425998i \(0.859923\pi\)
\(510\) 0 0
\(511\) 12.7357 1.66998i 0.563396 0.0738757i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −57.4507 + 33.1692i −2.53158 + 1.46161i
\(516\) 0 0
\(517\) 7.46513 + 4.30999i 0.328316 + 0.189553i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.78309 0.0781187 0.0390594 0.999237i \(-0.487564\pi\)
0.0390594 + 0.999237i \(0.487564\pi\)
\(522\) 0 0
\(523\) 24.0538i 1.05180i −0.850546 0.525901i \(-0.823728\pi\)
0.850546 0.525901i \(-0.176272\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.25696 + 1.30306i 0.0983149 + 0.0567621i
\(528\) 0 0
\(529\) 8.05069 + 13.9442i 0.350030 + 0.606270i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 25.8876 14.9462i 1.12132 0.647392i
\(534\) 0 0
\(535\) −48.3126 27.8933i −2.08874 1.20593i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −19.5451 + 19.5046i −0.841866 + 0.840124i
\(540\) 0 0
\(541\) 30.0032 1.28994 0.644968 0.764209i \(-0.276871\pi\)
0.644968 + 0.764209i \(0.276871\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −21.9458 + 38.0113i −0.940056 + 1.62822i
\(546\) 0 0
\(547\) 10.7816 + 18.6743i 0.460987 + 0.798454i 0.999010 0.0444765i \(-0.0141620\pi\)
−0.538023 + 0.842930i \(0.680829\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2.57686 + 4.46325i 0.109778 + 0.190141i
\(552\) 0 0
\(553\) 7.63532 5.85251i 0.324687 0.248874i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 36.9477i 1.56552i 0.622321 + 0.782762i \(0.286190\pi\)
−0.622321 + 0.782762i \(0.713810\pi\)
\(558\) 0 0
\(559\) 2.68625i 0.113616i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −7.58422 + 13.1363i −0.319637 + 0.553627i −0.980412 0.196957i \(-0.936894\pi\)
0.660776 + 0.750584i \(0.270228\pi\)
\(564\) 0 0
\(565\) −33.1329 + 19.1293i −1.39391 + 0.804774i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 31.8084 18.3646i 1.33348 0.769885i 0.347648 0.937625i \(-0.386980\pi\)
0.985831 + 0.167740i \(0.0536470\pi\)
\(570\) 0 0
\(571\) 5.61387 9.72351i 0.234933 0.406916i −0.724320 0.689464i \(-0.757846\pi\)
0.959253 + 0.282548i \(0.0911795\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 63.4114i 2.64444i
\(576\) 0 0
\(577\) 36.5515i 1.52166i −0.648952 0.760829i \(-0.724792\pi\)
0.648952 0.760829i \(-0.275208\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −16.9247 + 12.9729i −0.702154 + 0.538205i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −4.99738 8.65571i −0.206264 0.357259i 0.744271 0.667878i \(-0.232797\pi\)
−0.950535 + 0.310619i \(0.899464\pi\)
\(588\) 0 0
\(589\) 3.13376 5.42784i 0.129124 0.223650i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7.78223 0.319578 0.159789 0.987151i \(-0.448919\pi\)
0.159789 + 0.987151i \(0.448919\pi\)
\(594\) 0 0
\(595\) −7.05696 2.92737i −0.289307 0.120010i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 21.6614 + 12.5062i 0.885061 + 0.510990i 0.872324 0.488929i \(-0.162612\pi\)
0.0127373 + 0.999919i \(0.495945\pi\)
\(600\) 0 0
\(601\) −25.9925 + 15.0068i −1.06026 + 0.612139i −0.925503 0.378740i \(-0.876357\pi\)
−0.134753 + 0.990879i \(0.543024\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 8.87179 + 15.3664i 0.360689 + 0.624732i
\(606\) 0 0
\(607\) 3.96882 + 2.29140i 0.161089 + 0.0930050i 0.578378 0.815769i \(-0.303686\pi\)
−0.417288 + 0.908774i \(0.637019\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.22468i 0.251823i
\(612\) 0 0
\(613\) 30.5522 1.23399 0.616996 0.786966i \(-0.288349\pi\)
0.616996 + 0.786966i \(0.288349\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 28.2484 + 16.3092i 1.13724 + 0.656585i 0.945745 0.324909i \(-0.105334\pi\)
0.191493 + 0.981494i \(0.438667\pi\)
\(618\) 0 0
\(619\) −17.3244 + 10.0023i −0.696327 + 0.402024i −0.805978 0.591946i \(-0.798360\pi\)
0.109651 + 0.993970i \(0.465027\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3.18749 24.3087i −0.127704 0.973906i
\(624\) 0 0
\(625\) −13.5657 + 23.4965i −0.542628 + 0.939859i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.22752 −0.0888171
\(630\) 0 0
\(631\) −6.09634 −0.242692 −0.121346 0.992610i \(-0.538721\pi\)
−0.121346 + 0.992610i \(0.538721\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 5.72893 9.92279i 0.227345 0.393774i
\(636\) 0 0
\(637\) −19.2547 5.18065i −0.762898 0.205265i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −28.9612 + 16.7207i −1.14390 + 0.660429i −0.947393 0.320074i \(-0.896292\pi\)
−0.196504 + 0.980503i \(0.562959\pi\)
\(642\) 0 0
\(643\) −16.6022 9.58527i −0.654726 0.378006i 0.135539 0.990772i \(-0.456724\pi\)
−0.790264 + 0.612766i \(0.790057\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −44.6049 −1.75360 −0.876800 0.480854i \(-0.840327\pi\)
−0.876800 + 0.480854i \(0.840327\pi\)
\(648\) 0 0
\(649\) 0.0833680i 0.00327248i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0.564755 + 0.326061i 0.0221006 + 0.0127598i 0.511010 0.859575i \(-0.329272\pi\)
−0.488909 + 0.872335i \(0.662605\pi\)
\(654\) 0 0
\(655\) 29.3100 + 50.7664i 1.14524 + 1.98361i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 26.2738 15.1692i 1.02348 0.590908i 0.108372 0.994110i \(-0.465436\pi\)
0.915111 + 0.403202i \(0.132103\pi\)
\(660\) 0 0
\(661\) −11.1004 6.40881i −0.431755 0.249274i 0.268339 0.963325i \(-0.413525\pi\)
−0.700094 + 0.714051i \(0.746859\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −7.04011 + 16.9715i −0.273004 + 0.658126i
\(666\) 0 0
\(667\) −18.0569 −0.699165
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4.86986 + 8.43484i −0.187999 + 0.325623i
\(672\) 0 0
\(673\) 11.2246 + 19.4416i 0.432678 + 0.749420i 0.997103 0.0760644i \(-0.0242355\pi\)
−0.564425 + 0.825484i \(0.690902\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −25.5903 44.3237i −0.983516 1.70350i −0.648353 0.761340i \(-0.724542\pi\)
−0.335163 0.942160i \(-0.608791\pi\)
\(678\) 0 0
\(679\) −30.2910 39.5183i −1.16246 1.51657i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 14.5616i 0.557184i −0.960410 0.278592i \(-0.910132\pi\)
0.960410 0.278592i \(-0.0898677\pi\)
\(684\) 0 0
\(685\) 61.1681i 2.33711i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 21.1757 12.2258i 0.805560 0.465090i −0.0398517 0.999206i \(-0.512689\pi\)
0.845412 + 0.534115i \(0.179355\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 11.1431 6.43347i 0.422682 0.244035i
\(696\) 0 0
\(697\) −3.89393 + 6.74448i −0.147493 + 0.255465i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 2.21697i 0.0837337i 0.999123 + 0.0418669i \(0.0133305\pi\)
−0.999123 + 0.0418669i \(0.986669\pi\)
\(702\) 0 0
\(703\) 5.35703i 0.202044i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −17.3901 + 13.3296i −0.654021 + 0.501310i
\(708\) 0 0
\(709\) 12.1962 + 21.1244i 0.458036 + 0.793342i 0.998857 0.0477959i \(-0.0152197\pi\)
−0.540821 + 0.841138i \(0.681886\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 10.9796 + 19.0173i 0.411190 + 0.712203i
\(714\) 0 0
\(715\) −21.8607 + 37.8639i −0.817544 + 1.41603i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −2.22752 −0.0830725 −0.0415363 0.999137i \(-0.513225\pi\)
−0.0415363 + 0.999137i \(0.513225\pi\)
\(720\) 0 0
\(721\) 17.2831 41.6641i 0.643657 1.55165i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −25.3599 14.6416i −0.941844 0.543774i
\(726\) 0 0
\(727\) −10.4880 + 6.05523i −0.388977 + 0.224576i −0.681717 0.731616i \(-0.738766\pi\)
0.292740 + 0.956192i \(0.405433\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0.349924 + 0.606086i 0.0129424 + 0.0224169i
\(732\) 0 0
\(733\) 13.5673 + 7.83306i 0.501118 + 0.289321i 0.729175 0.684327i \(-0.239904\pi\)
−0.228057 + 0.973648i \(0.573237\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 53.0522i 1.95420i
\(738\) 0 0
\(739\) 8.10454 0.298130 0.149065 0.988827i \(-0.452374\pi\)
0.149065 + 0.988827i \(0.452374\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −10.5429 6.08697i −0.386783 0.223309i 0.293982 0.955811i \(-0.405019\pi\)
−0.680765 + 0.732502i \(0.738353\pi\)
\(744\) 0 0
\(745\) 37.0732 21.4042i 1.35826 0.784189i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 37.6100 4.93164i 1.37424 0.180198i
\(750\) 0 0
\(751\) 17.3062 29.9752i 0.631511 1.09381i −0.355732 0.934588i \(-0.615768\pi\)
0.987243 0.159221i \(-0.0508983\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 5.60311 0.203918
\(756\) 0 0
\(757\) −39.0553 −1.41949 −0.709744 0.704459i \(-0.751190\pi\)
−0.709744 + 0.704459i \(0.751190\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −5.11262 + 8.85532i −0.185332 + 0.321005i −0.943688 0.330835i \(-0.892670\pi\)
0.758356 + 0.651840i \(0.226003\pi\)
\(762\) 0 0
\(763\) −3.88010 29.5907i −0.140469 1.07125i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.0521363 0.0301009i 0.00188253 0.00108688i
\(768\) 0 0
\(769\) −26.6746 15.4006i −0.961910 0.555359i −0.0651494 0.997876i \(-0.520752\pi\)
−0.896760 + 0.442517i \(0.854086\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 35.7833 1.28704 0.643518 0.765431i \(-0.277474\pi\)
0.643518 + 0.765431i \(0.277474\pi\)
\(774\) 0 0
\(775\) 35.6117i 1.27921i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 16.2200 + 9.36461i 0.581141 + 0.335522i
\(780\) 0 0
\(781\) −3.83228 6.63771i −0.137130 0.237516i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −55.9626 + 32.3100i −1.99739 + 1.15319i
\(786\) 0 0
\(787\) −13.2859 7.67064i −0.473592 0.273429i 0.244150 0.969737i \(-0.421491\pi\)
−0.717742 + 0.696309i \(0.754824\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 9.96748 24.0284i 0.354403 0.854353i
\(792\) 0 0
\(793\) −7.03326 −0.249758
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 17.5200 30.3455i 0.620590 1.07489i −0.368786 0.929514i \(-0.620226\pi\)
0.989376 0.145379i \(-0.0464402\pi\)
\(798\) 0 0
\(799\) −0.810856 1.40444i −0.0286860 0.0496857i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 9.57529 + 16.5849i 0.337905 + 0.585268i
\(804\) 0 0
\(805\) −39.1627 51.0926i −1.38031 1.80078i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 27.2925i 0.959553i −0.877391 0.479777i \(-0.840718\pi\)
0.877391 0.479777i \(-0.159282\pi\)
\(810\) 0 0
\(811\) 27.7628i 0.974883i 0.873156 + 0.487442i \(0.162070\pi\)
−0.873156 + 0.487442i \(0.837930\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −24.1161 + 41.7703i −0.844749 + 1.46315i
\(816\) 0 0
\(817\) 1.45759 0.841542i 0.0509947 0.0294418i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 38.4968 22.2262i 1.34355 0.775698i 0.356223 0.934401i \(-0.384064\pi\)
0.987326 + 0.158703i \(0.0507311\pi\)
\(822\) 0 0
\(823\) −25.5577 + 44.2672i −0.890884 + 1.54306i −0.0520663 + 0.998644i \(0.516581\pi\)
−0.838818 + 0.544413i \(0.816753\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 14.5414i 0.505653i −0.967512 0.252826i \(-0.918640\pi\)
0.967512 0.252826i \(-0.0813601\pi\)
\(828\) 0 0
\(829\) 27.9681i 0.971373i 0.874133 + 0.485686i \(0.161430\pi\)
−0.874133 + 0.485686i \(0.838570\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 5.01920 1.33932i 0.173905 0.0464047i
\(834\) 0 0
\(835\) −22.8053 39.5000i −0.789211 1.36695i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −0.499354 0.864906i −0.0172396 0.0298599i 0.857277 0.514856i \(-0.172154\pi\)
−0.874517 + 0.484996i \(0.838821\pi\)
\(840\) 0 0
\(841\) −10.3307 + 17.8933i −0.356231 + 0.617011i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 19.0123 0.654044
\(846\) 0 0
\(847\) −11.1439 4.62273i −0.382910 0.158839i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −16.2546 9.38460i −0.557200 0.321700i
\(852\) 0 0
\(853\) 8.48739 4.90020i 0.290603 0.167780i −0.347611 0.937639i \(-0.613007\pi\)
0.638214 + 0.769859i \(0.279674\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −3.85002 6.66842i −0.131514 0.227789i 0.792746 0.609552i \(-0.208651\pi\)
−0.924260 + 0.381763i \(0.875317\pi\)
\(858\) 0 0
\(859\) 16.4022 + 9.46979i 0.559634 + 0.323105i 0.752999 0.658022i \(-0.228607\pi\)
−0.193364 + 0.981127i \(0.561940\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 17.4540i 0.594141i 0.954856 + 0.297070i \(0.0960096\pi\)
−0.954856 + 0.297070i \(0.903990\pi\)
\(864\) 0 0
\(865\) −65.2578 −2.21883
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 12.4215 + 7.17157i 0.421371 + 0.243279i
\(870\) 0 0
\(871\) 33.1776 19.1551i 1.12418 0.649045i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −6.88078 52.4746i −0.232613 1.77397i
\(876\) 0 0
\(877\) −0.196152 + 0.339746i −0.00662360 + 0.0114724i −0.869318 0.494253i \(-0.835442\pi\)
0.862695 + 0.505725i \(0.168775\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −37.0259 −1.24744 −0.623718 0.781650i \(-0.714378\pi\)
−0.623718 + 0.781650i \(0.714378\pi\)
\(882\) 0 0
\(883\) 29.9586 1.00819 0.504094 0.863649i \(-0.331826\pi\)
0.504094 + 0.863649i \(0.331826\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −14.4930 + 25.1026i −0.486626 + 0.842861i −0.999882 0.0153745i \(-0.995106\pi\)
0.513256 + 0.858236i \(0.328439\pi\)
\(888\) 0 0
\(889\) 1.01290 + 7.72461i 0.0339714 + 0.259075i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −3.37759 + 1.95005i −0.113027 + 0.0652560i
\(894\) 0 0
\(895\) 19.4617 + 11.2362i 0.650533 + 0.375586i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −10.1407 −0.338211
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −18.6455 10.7650i −0.619796 0.357839i
\(906\) 0 0
\(907\) −1.94773 3.37357i −0.0646733 0.112017i 0.831876 0.554962i \(-0.187267\pi\)
−0.896549 + 0.442945i \(0.853934\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.32768 0.766538i 0.0439881 0.0253966i −0.477845 0.878444i \(-0.658582\pi\)
0.521833 + 0.853048i \(0.325248\pi\)
\(912\) 0 0
\(913\) −27.5339 15.8967i −0.911240 0.526105i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −36.8166 15.2723i −1.21579 0.504334i
\(918\) 0 0
\(919\) −28.2531 −0.931984 −0.465992 0.884789i \(-0.654302\pi\)
−0.465992 + 0.884789i \(0.654302\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 2.76737 4.79323i 0.0910892 0.157771i
\(924\) 0 0
\(925\) −15.2192 26.3603i −0.500403 0.866723i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1.64363 2.84685i −0.0539257 0.0934021i 0.837802 0.545974i \(-0.183840\pi\)
−0.891728 + 0.452571i \(0.850507\pi\)
\(930\) 0 0
\(931\) −3.22097 12.0708i −0.105563 0.395605i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 11.3907i 0.372517i
\(936\) 0 0
\(937\) 35.5084i 1.16001i 0.814613 + 0.580005i \(0.196949\pi\)
−0.814613 + 0.580005i \(0.803051\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −6.24941 + 10.8243i −0.203725 + 0.352862i −0.949726 0.313083i \(-0.898638\pi\)
0.746001 + 0.665945i \(0.231972\pi\)
\(942\) 0 0
\(943\) −56.8293 + 32.8104i −1.85062 + 1.06845i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 31.2769 18.0577i 1.01636 0.586796i 0.103313 0.994649i \(-0.467056\pi\)
0.913048 + 0.407852i \(0.133722\pi\)
\(948\) 0 0
\(949\) −6.91452 + 11.9763i −0.224455 + 0.388767i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 45.2925i 1.46717i −0.679599 0.733584i \(-0.737846\pi\)
0.679599 0.733584i \(-0.262154\pi\)
\(954\) 0 0
\(955\) 24.1783i 0.782392i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −25.3019 33.0095i −0.817042 1.06593i
\(960\) 0 0
\(961\) −9.33386 16.1667i −0.301092 0.521507i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 15.1859 + 26.3028i 0.488851 + 0.846716i
\(966\) 0 0
\(967\) −12.0000 + 20.7845i −0.385893 + 0.668385i −0.991893 0.127079i \(-0.959440\pi\)
0.606000 + 0.795465i \(0.292773\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −33.3626 −1.07066 −0.535328 0.844644i \(-0.679812\pi\)
−0.535328 + 0.844644i \(0.679812\pi\)
\(972\) 0 0
\(973\) −3.35222 + 8.08113i −0.107467 + 0.259069i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 29.8846 + 17.2539i 0.956091 + 0.552000i 0.894968 0.446131i \(-0.147198\pi\)
0.0611236 + 0.998130i \(0.480532\pi\)
\(978\) 0 0
\(979\) 31.6555 18.2763i 1.01172 0.584114i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −1.20651 2.08973i −0.0384817 0.0666522i 0.846143 0.532956i \(-0.178919\pi\)
−0.884625 + 0.466304i \(0.845585\pi\)
\(984\) 0 0
\(985\) 43.0450 + 24.8521i 1.37153 + 0.791852i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 5.89695i 0.187512i
\(990\) 0 0
\(991\) −48.5982 −1.54377 −0.771887 0.635760i \(-0.780687\pi\)
−0.771887 + 0.635760i \(0.780687\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 6.10612 + 3.52537i 0.193577 + 0.111762i
\(996\) 0 0
\(997\) 38.8449 22.4271i 1.23023 0.710274i 0.263152 0.964754i \(-0.415238\pi\)
0.967078 + 0.254481i \(0.0819045\pi\)
\(998\) 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 3024.2.cc.b.881.1 16
3.2 odd 2 1008.2.cc.b.545.7 16
4.3 odd 2 378.2.m.a.125.5 16
7.6 odd 2 inner 3024.2.cc.b.881.8 16
9.2 odd 6 inner 3024.2.cc.b.2897.8 16
9.7 even 3 1008.2.cc.b.209.2 16
12.11 even 2 126.2.m.a.41.1 16
21.20 even 2 1008.2.cc.b.545.2 16
28.3 even 6 2646.2.l.b.1097.8 16
28.11 odd 6 2646.2.l.b.1097.5 16
28.19 even 6 2646.2.t.a.2285.1 16
28.23 odd 6 2646.2.t.a.2285.4 16
28.27 even 2 378.2.m.a.125.8 16
36.7 odd 6 126.2.m.a.83.4 yes 16
36.11 even 6 378.2.m.a.251.8 16
36.23 even 6 1134.2.d.a.1133.1 16
36.31 odd 6 1134.2.d.a.1133.16 16
63.20 even 6 inner 3024.2.cc.b.2897.1 16
63.34 odd 6 1008.2.cc.b.209.7 16
84.11 even 6 882.2.l.a.509.4 16
84.23 even 6 882.2.t.b.815.7 16
84.47 odd 6 882.2.t.b.815.6 16
84.59 odd 6 882.2.l.a.509.1 16
84.83 odd 2 126.2.m.a.41.4 yes 16
252.11 even 6 2646.2.t.a.1979.1 16
252.47 odd 6 2646.2.l.b.521.1 16
252.79 odd 6 882.2.l.a.227.5 16
252.83 odd 6 378.2.m.a.251.5 16
252.115 even 6 882.2.t.b.803.7 16
252.139 even 6 1134.2.d.a.1133.9 16
252.151 odd 6 882.2.t.b.803.6 16
252.167 odd 6 1134.2.d.a.1133.8 16
252.187 even 6 882.2.l.a.227.8 16
252.191 even 6 2646.2.l.b.521.4 16
252.223 even 6 126.2.m.a.83.1 yes 16
252.227 odd 6 2646.2.t.a.1979.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.m.a.41.1 16 12.11 even 2
126.2.m.a.41.4 yes 16 84.83 odd 2
126.2.m.a.83.1 yes 16 252.223 even 6
126.2.m.a.83.4 yes 16 36.7 odd 6
378.2.m.a.125.5 16 4.3 odd 2
378.2.m.a.125.8 16 28.27 even 2
378.2.m.a.251.5 16 252.83 odd 6
378.2.m.a.251.8 16 36.11 even 6
882.2.l.a.227.5 16 252.79 odd 6
882.2.l.a.227.8 16 252.187 even 6
882.2.l.a.509.1 16 84.59 odd 6
882.2.l.a.509.4 16 84.11 even 6
882.2.t.b.803.6 16 252.151 odd 6
882.2.t.b.803.7 16 252.115 even 6
882.2.t.b.815.6 16 84.47 odd 6
882.2.t.b.815.7 16 84.23 even 6
1008.2.cc.b.209.2 16 9.7 even 3
1008.2.cc.b.209.7 16 63.34 odd 6
1008.2.cc.b.545.2 16 21.20 even 2
1008.2.cc.b.545.7 16 3.2 odd 2
1134.2.d.a.1133.1 16 36.23 even 6
1134.2.d.a.1133.8 16 252.167 odd 6
1134.2.d.a.1133.9 16 252.139 even 6
1134.2.d.a.1133.16 16 36.31 odd 6
2646.2.l.b.521.1 16 252.47 odd 6
2646.2.l.b.521.4 16 252.191 even 6
2646.2.l.b.1097.5 16 28.11 odd 6
2646.2.l.b.1097.8 16 28.3 even 6
2646.2.t.a.1979.1 16 252.11 even 6
2646.2.t.a.1979.4 16 252.227 odd 6
2646.2.t.a.2285.1 16 28.19 even 6
2646.2.t.a.2285.4 16 28.23 odd 6
3024.2.cc.b.881.1 16 1.1 even 1 trivial
3024.2.cc.b.881.8 16 7.6 odd 2 inner
3024.2.cc.b.2897.1 16 63.20 even 6 inner
3024.2.cc.b.2897.8 16 9.2 odd 6 inner