Properties

Label 3024.2.cc.a.881.2
Level $3024$
Weight $2$
Character 3024.881
Analytic conductor $24.147$
Analytic rank $0$
Dimension $12$
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: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 881.2
Root \(-0.474636 - 0.274031i\) of defining polynomial
Character \(\chi\) \(=\) 3024.881
Dual form 3024.2.cc.a.2897.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.10552 + 1.91482i) q^{5} +(0.906161 - 2.48573i) q^{7} +O(q^{10})\) \(q+(-1.10552 + 1.91482i) q^{5} +(0.906161 - 2.48573i) q^{7} +(-2.93818 + 1.69636i) q^{11} +(-1.56060 - 0.901012i) q^{13} +5.96901 q^{17} +1.64419i q^{19} +(2.05563 + 1.18682i) q^{23} +(0.0556321 + 0.0963576i) q^{25} +(-2.44437 + 1.41126i) q^{29} +(-9.28558 - 5.36103i) q^{31} +(3.75796 + 4.48318i) q^{35} +1.69963 q^{37} +(0.455074 - 0.788211i) q^{41} +(1.96108 + 3.39669i) q^{43} +(0.123005 + 0.213051i) q^{47} +(-5.35774 - 4.50495i) q^{49} +7.87589i q^{53} -7.50146i q^{55} +(-5.39093 + 9.33736i) q^{59} +(1.22853 - 0.709292i) q^{61} +(3.45056 - 1.99218i) q^{65} +(-3.99381 + 6.91748i) q^{67} +12.1743i q^{71} +0.426103i q^{73} +(1.55423 + 8.84070i) q^{77} +(-2.49381 - 4.31941i) q^{79} +(-4.28541 - 7.42254i) q^{83} +(-6.59888 + 11.4296i) q^{85} -10.5358 q^{89} +(-3.65383 + 3.06277i) q^{91} +(-3.14833 - 1.81769i) q^{95} +(-6.30108 + 3.63793i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{7} + 24 q^{23} - 30 q^{29} - 4 q^{37} + 10 q^{43} + 6 q^{49} + 78 q^{65} - 12 q^{67} + 24 q^{77} + 6 q^{79} - 6 q^{85} + 24 q^{91} + 72 q^{95}+O(q^{100}) \) 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
\(5\) −1.10552 + 1.91482i −0.494405 + 0.856335i −0.999979 0.00644798i \(-0.997948\pi\)
0.505574 + 0.862783i \(0.331281\pi\)
\(6\) 0 0
\(7\) 0.906161 2.48573i 0.342497 0.939519i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.93818 + 1.69636i −0.885894 + 0.511471i −0.872597 0.488440i \(-0.837566\pi\)
−0.0132968 + 0.999912i \(0.504233\pi\)
\(12\) 0 0
\(13\) −1.56060 0.901012i −0.432832 0.249896i 0.267720 0.963497i \(-0.413730\pi\)
−0.700552 + 0.713601i \(0.747063\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.96901 1.44770 0.723849 0.689959i \(-0.242371\pi\)
0.723849 + 0.689959i \(0.242371\pi\)
\(18\) 0 0
\(19\) 1.64419i 0.377202i 0.982054 + 0.188601i \(0.0603953\pi\)
−0.982054 + 0.188601i \(0.939605\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.05563 + 1.18682i 0.428629 + 0.247469i 0.698762 0.715354i \(-0.253734\pi\)
−0.270133 + 0.962823i \(0.587068\pi\)
\(24\) 0 0
\(25\) 0.0556321 + 0.0963576i 0.0111264 + 0.0192715i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.44437 + 1.41126i −0.453908 + 0.262064i −0.709479 0.704726i \(-0.751070\pi\)
0.255571 + 0.966790i \(0.417736\pi\)
\(30\) 0 0
\(31\) −9.28558 5.36103i −1.66774 0.962870i −0.968853 0.247638i \(-0.920346\pi\)
−0.698887 0.715232i \(-0.746321\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.75796 + 4.48318i 0.635211 + 0.757795i
\(36\) 0 0
\(37\) 1.69963 0.279417 0.139709 0.990193i \(-0.455383\pi\)
0.139709 + 0.990193i \(0.455383\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.455074 0.788211i 0.0710706 0.123098i −0.828300 0.560285i \(-0.810692\pi\)
0.899371 + 0.437187i \(0.144025\pi\)
\(42\) 0 0
\(43\) 1.96108 + 3.39669i 0.299062 + 0.517990i 0.975922 0.218122i \(-0.0699931\pi\)
−0.676860 + 0.736112i \(0.736660\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.123005 + 0.213051i 0.0179422 + 0.0310767i 0.874857 0.484381i \(-0.160955\pi\)
−0.856915 + 0.515458i \(0.827622\pi\)
\(48\) 0 0
\(49\) −5.35774 4.50495i −0.765392 0.643564i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 7.87589i 1.08184i 0.841075 + 0.540919i \(0.181923\pi\)
−0.841075 + 0.540919i \(0.818077\pi\)
\(54\) 0 0
\(55\) 7.50146i 1.01150i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −5.39093 + 9.33736i −0.701839 + 1.21562i 0.265981 + 0.963978i \(0.414304\pi\)
−0.967820 + 0.251643i \(0.919029\pi\)
\(60\) 0 0
\(61\) 1.22853 0.709292i 0.157297 0.0908155i −0.419285 0.907855i \(-0.637719\pi\)
0.576582 + 0.817039i \(0.304386\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.45056 1.99218i 0.427989 0.247100i
\(66\) 0 0
\(67\) −3.99381 + 6.91748i −0.487922 + 0.845105i −0.999904 0.0138913i \(-0.995578\pi\)
0.511982 + 0.858996i \(0.328911\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 12.1743i 1.44482i 0.691463 + 0.722412i \(0.256966\pi\)
−0.691463 + 0.722412i \(0.743034\pi\)
\(72\) 0 0
\(73\) 0.426103i 0.0498715i 0.999689 + 0.0249358i \(0.00793812\pi\)
−0.999689 + 0.0249358i \(0.992062\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.55423 + 8.84070i 0.177121 + 1.00749i
\(78\) 0 0
\(79\) −2.49381 4.31941i −0.280576 0.485971i 0.690951 0.722902i \(-0.257192\pi\)
−0.971527 + 0.236930i \(0.923859\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.28541 7.42254i −0.470384 0.814730i 0.529042 0.848596i \(-0.322551\pi\)
−0.999426 + 0.0338660i \(0.989218\pi\)
\(84\) 0 0
\(85\) −6.59888 + 11.4296i −0.715750 + 1.23971i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −10.5358 −1.11680 −0.558399 0.829573i \(-0.688584\pi\)
−0.558399 + 0.829573i \(0.688584\pi\)
\(90\) 0 0
\(91\) −3.65383 + 3.06277i −0.383025 + 0.321065i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.14833 1.81769i −0.323012 0.186491i
\(96\) 0 0
\(97\) −6.30108 + 3.63793i −0.639777 + 0.369376i −0.784529 0.620092i \(-0.787095\pi\)
0.144751 + 0.989468i \(0.453762\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 2.33405 + 4.04270i 0.232247 + 0.402264i 0.958469 0.285197i \(-0.0920589\pi\)
−0.726222 + 0.687460i \(0.758726\pi\)
\(102\) 0 0
\(103\) 5.40462 + 3.12036i 0.532533 + 0.307458i 0.742047 0.670348i \(-0.233855\pi\)
−0.209515 + 0.977806i \(0.567188\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.48939i 0.143985i −0.997405 0.0719925i \(-0.977064\pi\)
0.997405 0.0719925i \(-0.0229358\pi\)
\(108\) 0 0
\(109\) −4.38688 −0.420187 −0.210093 0.977681i \(-0.567377\pi\)
−0.210093 + 0.977681i \(0.567377\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 14.8764 + 8.58887i 1.39945 + 0.807973i 0.994335 0.106293i \(-0.0338981\pi\)
0.405115 + 0.914266i \(0.367231\pi\)
\(114\) 0 0
\(115\) −4.54510 + 2.62412i −0.423833 + 0.244700i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 5.40888 14.8374i 0.495831 1.36014i
\(120\) 0 0
\(121\) 0.255260 0.442124i 0.0232055 0.0401931i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −11.3013 −1.01081
\(126\) 0 0
\(127\) −6.32141 −0.560935 −0.280467 0.959864i \(-0.590489\pi\)
−0.280467 + 0.959864i \(0.590489\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −8.51213 + 14.7434i −0.743708 + 1.28814i 0.207088 + 0.978322i \(0.433601\pi\)
−0.950796 + 0.309818i \(0.899732\pi\)
\(132\) 0 0
\(133\) 4.08701 + 1.48990i 0.354389 + 0.129190i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −5.42580 + 3.13259i −0.463557 + 0.267635i −0.713539 0.700616i \(-0.752909\pi\)
0.249982 + 0.968251i \(0.419575\pi\)
\(138\) 0 0
\(139\) −6.65488 3.84220i −0.564460 0.325891i 0.190474 0.981692i \(-0.438998\pi\)
−0.754934 + 0.655801i \(0.772331\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 6.11375 0.511258
\(144\) 0 0
\(145\) 6.24071i 0.518263i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −13.3695 7.71887i −1.09527 0.632355i −0.160296 0.987069i \(-0.551245\pi\)
−0.934975 + 0.354714i \(0.884578\pi\)
\(150\) 0 0
\(151\) 5.84362 + 10.1215i 0.475547 + 0.823672i 0.999608 0.0280089i \(-0.00891668\pi\)
−0.524060 + 0.851681i \(0.675583\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 20.5309 11.8535i 1.64908 0.952096i
\(156\) 0 0
\(157\) −4.93586 2.84972i −0.393924 0.227432i 0.289935 0.957046i \(-0.406366\pi\)
−0.683859 + 0.729614i \(0.739700\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 4.81285 4.03430i 0.379306 0.317948i
\(162\) 0 0
\(163\) 10.2101 0.799721 0.399860 0.916576i \(-0.369059\pi\)
0.399860 + 0.916576i \(0.369059\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.80661 3.12914i 0.139800 0.242140i −0.787621 0.616160i \(-0.788688\pi\)
0.927421 + 0.374020i \(0.122021\pi\)
\(168\) 0 0
\(169\) −4.87636 8.44610i −0.375104 0.649700i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −9.03957 15.6570i −0.687266 1.19038i −0.972719 0.231987i \(-0.925477\pi\)
0.285453 0.958393i \(-0.407856\pi\)
\(174\) 0 0
\(175\) 0.289931 0.0509711i 0.0219167 0.00385305i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 5.03194i 0.376105i 0.982159 + 0.188052i \(0.0602175\pi\)
−0.982159 + 0.188052i \(0.939783\pi\)
\(180\) 0 0
\(181\) 13.5592i 1.00785i −0.863747 0.503925i \(-0.831889\pi\)
0.863747 0.503925i \(-0.168111\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.87898 + 3.25449i −0.138145 + 0.239275i
\(186\) 0 0
\(187\) −17.5380 + 10.1256i −1.28251 + 0.740455i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −8.86948 + 5.12080i −0.641773 + 0.370528i −0.785297 0.619119i \(-0.787490\pi\)
0.143524 + 0.989647i \(0.454156\pi\)
\(192\) 0 0
\(193\) −8.06615 + 13.9710i −0.580614 + 1.00565i 0.414792 + 0.909916i \(0.363854\pi\)
−0.995407 + 0.0957374i \(0.969479\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3.86303i 0.275230i −0.990486 0.137615i \(-0.956056\pi\)
0.990486 0.137615i \(-0.0439436\pi\)
\(198\) 0 0
\(199\) 15.2034i 1.07774i 0.842388 + 0.538871i \(0.181149\pi\)
−0.842388 + 0.538871i \(0.818851\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.29302 + 7.35487i 0.0907520 + 0.516211i
\(204\) 0 0
\(205\) 1.00619 + 1.74277i 0.0702753 + 0.121720i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.78913 4.83091i −0.192928 0.334161i
\(210\) 0 0
\(211\) −11.9523 + 20.7021i −0.822833 + 1.42519i 0.0807311 + 0.996736i \(0.474274\pi\)
−0.903564 + 0.428453i \(0.859059\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −8.67208 −0.591431
\(216\) 0 0
\(217\) −21.7403 + 18.2235i −1.47583 + 1.23709i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −9.31522 5.37815i −0.626610 0.361773i
\(222\) 0 0
\(223\) 16.6198 9.59545i 1.11294 0.642559i 0.173354 0.984860i \(-0.444539\pi\)
0.939591 + 0.342300i \(0.111206\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4.33604 + 7.51024i 0.287793 + 0.498472i 0.973283 0.229610i \(-0.0737451\pi\)
−0.685490 + 0.728082i \(0.740412\pi\)
\(228\) 0 0
\(229\) 12.4437 + 7.18439i 0.822304 + 0.474758i 0.851211 0.524824i \(-0.175869\pi\)
−0.0289060 + 0.999582i \(0.509202\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 29.7160i 1.94676i 0.229194 + 0.973381i \(0.426391\pi\)
−0.229194 + 0.973381i \(0.573609\pi\)
\(234\) 0 0
\(235\) −0.543941 −0.0354828
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −13.7101 7.91556i −0.886836 0.512015i −0.0139296 0.999903i \(-0.504434\pi\)
−0.872906 + 0.487888i \(0.837767\pi\)
\(240\) 0 0
\(241\) −4.34973 + 2.51132i −0.280190 + 0.161768i −0.633510 0.773735i \(-0.718386\pi\)
0.353319 + 0.935503i \(0.385053\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 14.5493 5.27881i 0.929521 0.337251i
\(246\) 0 0
\(247\) 1.48143 2.56591i 0.0942612 0.163265i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −7.29728 −0.460600 −0.230300 0.973120i \(-0.573971\pi\)
−0.230300 + 0.973120i \(0.573971\pi\)
\(252\) 0 0
\(253\) −8.05308 −0.506293
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.00397 6.93508i 0.249761 0.432598i −0.713699 0.700453i \(-0.752981\pi\)
0.963459 + 0.267855i \(0.0863147\pi\)
\(258\) 0 0
\(259\) 1.54014 4.22482i 0.0956994 0.262518i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −13.6051 + 7.85489i −0.838925 + 0.484353i −0.856899 0.515485i \(-0.827612\pi\)
0.0179738 + 0.999838i \(0.494278\pi\)
\(264\) 0 0
\(265\) −15.0810 8.70699i −0.926416 0.534866i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −10.4924 −0.639731 −0.319866 0.947463i \(-0.603638\pi\)
−0.319866 + 0.947463i \(0.603638\pi\)
\(270\) 0 0
\(271\) 22.2537i 1.35181i −0.736987 0.675907i \(-0.763752\pi\)
0.736987 0.675907i \(-0.236248\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.326914 0.188744i −0.0197137 0.0113817i
\(276\) 0 0
\(277\) 11.4251 + 19.7889i 0.686468 + 1.18900i 0.972973 + 0.230919i \(0.0741733\pi\)
−0.286505 + 0.958079i \(0.592493\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −0.796041 + 0.459595i −0.0474878 + 0.0274171i −0.523556 0.851991i \(-0.675395\pi\)
0.476068 + 0.879408i \(0.342062\pi\)
\(282\) 0 0
\(283\) 19.1573 + 11.0605i 1.13878 + 0.657477i 0.946129 0.323790i \(-0.104957\pi\)
0.192654 + 0.981267i \(0.438290\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.54691 1.84544i −0.0913113 0.108933i
\(288\) 0 0
\(289\) 18.6291 1.09583
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −14.6259 + 25.3328i −0.854453 + 1.47996i 0.0226986 + 0.999742i \(0.492774\pi\)
−0.877152 + 0.480214i \(0.840559\pi\)
\(294\) 0 0
\(295\) −11.9196 20.6454i −0.693986 1.20202i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.13868 3.70430i −0.123683 0.214225i
\(300\) 0 0
\(301\) 10.2203 1.79677i 0.589089 0.103564i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 3.13656i 0.179599i
\(306\) 0 0
\(307\) 14.8451i 0.847254i −0.905837 0.423627i \(-0.860757\pi\)
0.905837 0.423627i \(-0.139243\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 9.69002 16.7836i 0.549471 0.951711i −0.448840 0.893612i \(-0.648163\pi\)
0.998311 0.0580991i \(-0.0185040\pi\)
\(312\) 0 0
\(313\) 12.6608 7.30974i 0.715633 0.413171i −0.0975102 0.995235i \(-0.531088\pi\)
0.813143 + 0.582064i \(0.197755\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 14.7046 8.48973i 0.825895 0.476831i −0.0265499 0.999647i \(-0.508452\pi\)
0.852445 + 0.522817i \(0.175119\pi\)
\(318\) 0 0
\(319\) 4.78799 8.29305i 0.268076 0.464321i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 9.81416i 0.546074i
\(324\) 0 0
\(325\) 0.200501i 0.0111218i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0.641051 0.112699i 0.0353423 0.00621332i
\(330\) 0 0
\(331\) 9.94801 + 17.2305i 0.546792 + 0.947072i 0.998492 + 0.0549016i \(0.0174845\pi\)
−0.451700 + 0.892170i \(0.649182\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −8.83051 15.2949i −0.482462 0.835649i
\(336\) 0 0
\(337\) 0.490168 0.848996i 0.0267012 0.0462478i −0.852366 0.522946i \(-0.824833\pi\)
0.879067 + 0.476698i \(0.158166\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 36.3769 1.96992
\(342\) 0 0
\(343\) −16.0531 + 9.23572i −0.866785 + 0.498682i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 18.3702 + 10.6060i 0.986162 + 0.569361i 0.904125 0.427268i \(-0.140524\pi\)
0.0820373 + 0.996629i \(0.473857\pi\)
\(348\) 0 0
\(349\) 8.69945 5.02263i 0.465671 0.268855i −0.248755 0.968566i \(-0.580021\pi\)
0.714426 + 0.699711i \(0.246688\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.37327 2.37858i −0.0730920 0.126599i 0.827163 0.561962i \(-0.189953\pi\)
−0.900255 + 0.435363i \(0.856620\pi\)
\(354\) 0 0
\(355\) −23.3116 13.4590i −1.23725 0.714329i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 10.0013i 0.527849i 0.964543 + 0.263925i \(0.0850170\pi\)
−0.964543 + 0.263925i \(0.914983\pi\)
\(360\) 0 0
\(361\) 16.2967 0.857719
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −0.815912 0.471067i −0.0427068 0.0246568i
\(366\) 0 0
\(367\) 5.03560 2.90731i 0.262856 0.151760i −0.362781 0.931875i \(-0.618173\pi\)
0.625637 + 0.780114i \(0.284839\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 19.5774 + 7.13683i 1.01641 + 0.370526i
\(372\) 0 0
\(373\) 7.75959 13.4400i 0.401776 0.695897i −0.592164 0.805817i \(-0.701726\pi\)
0.993940 + 0.109920i \(0.0350596\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5.08623 0.261954
\(378\) 0 0
\(379\) −2.79714 −0.143679 −0.0718396 0.997416i \(-0.522887\pi\)
−0.0718396 + 0.997416i \(0.522887\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.74229 + 3.01773i −0.0890268 + 0.154199i −0.907100 0.420915i \(-0.861709\pi\)
0.818073 + 0.575114i \(0.195042\pi\)
\(384\) 0 0
\(385\) −18.6466 6.79753i −0.950320 0.346434i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6.37017 3.67782i 0.322980 0.186473i −0.329740 0.944072i \(-0.606961\pi\)
0.652720 + 0.757599i \(0.273628\pi\)
\(390\) 0 0
\(391\) 12.2701 + 7.08414i 0.620525 + 0.358260i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 11.0279 0.554872
\(396\) 0 0
\(397\) 19.2838i 0.967825i −0.875116 0.483912i \(-0.839215\pi\)
0.875116 0.483912i \(-0.160785\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.60576 5.54589i −0.479689 0.276949i 0.240598 0.970625i \(-0.422656\pi\)
−0.720287 + 0.693676i \(0.755990\pi\)
\(402\) 0 0
\(403\) 9.66071 + 16.7328i 0.481234 + 0.833522i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.99381 + 2.88318i −0.247534 + 0.142914i
\(408\) 0 0
\(409\) 17.5597 + 10.1381i 0.868274 + 0.501298i 0.866774 0.498701i \(-0.166189\pi\)
0.00149954 + 0.999999i \(0.499523\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 18.3252 + 21.8616i 0.901722 + 1.07574i
\(414\) 0 0
\(415\) 18.9505 0.930243
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −5.54936 + 9.61177i −0.271104 + 0.469566i −0.969145 0.246492i \(-0.920722\pi\)
0.698041 + 0.716058i \(0.254055\pi\)
\(420\) 0 0
\(421\) 4.59269 + 7.95478i 0.223834 + 0.387692i 0.955969 0.293467i \(-0.0948092\pi\)
−0.732135 + 0.681160i \(0.761476\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.332068 + 0.575159i 0.0161077 + 0.0278993i
\(426\) 0 0
\(427\) −0.649865 3.69653i −0.0314492 0.178888i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 15.1102i 0.727833i −0.931432 0.363916i \(-0.881439\pi\)
0.931432 0.363916i \(-0.118561\pi\)
\(432\) 0 0
\(433\) 3.33578i 0.160307i 0.996783 + 0.0801537i \(0.0255411\pi\)
−0.996783 + 0.0801537i \(0.974459\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.95135 + 3.37984i −0.0933458 + 0.161680i
\(438\) 0 0
\(439\) −5.91032 + 3.41233i −0.282084 + 0.162861i −0.634367 0.773032i \(-0.718739\pi\)
0.352282 + 0.935894i \(0.385406\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 9.77747 5.64503i 0.464542 0.268203i −0.249410 0.968398i \(-0.580237\pi\)
0.713952 + 0.700195i \(0.246903\pi\)
\(444\) 0 0
\(445\) 11.6476 20.1743i 0.552151 0.956354i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 24.8554i 1.17300i −0.809950 0.586498i \(-0.800506\pi\)
0.809950 0.586498i \(-0.199494\pi\)
\(450\) 0 0
\(451\) 3.08787i 0.145402i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.82527 10.3824i −0.0855700 0.486735i
\(456\) 0 0
\(457\) 6.30470 + 10.9201i 0.294922 + 0.510819i 0.974967 0.222351i \(-0.0713732\pi\)
−0.680045 + 0.733170i \(0.738040\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −14.4031 24.9470i −0.670821 1.16190i −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951758i \(-0.400725\pi\)
\(462\) 0 0
\(463\) 12.5858 21.7993i 0.584912 1.01310i −0.409974 0.912097i \(-0.634462\pi\)
0.994886 0.101001i \(-0.0322045\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 25.5951 1.18440 0.592199 0.805792i \(-0.298260\pi\)
0.592199 + 0.805792i \(0.298260\pi\)
\(468\) 0 0
\(469\) 13.5760 + 16.1959i 0.626881 + 0.747857i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −11.5240 6.65338i −0.529874 0.305923i
\(474\) 0 0
\(475\) −0.158430 + 0.0914695i −0.00726926 + 0.00419691i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −0.267749 0.463755i −0.0122338 0.0211895i 0.859844 0.510557i \(-0.170561\pi\)
−0.872077 + 0.489368i \(0.837228\pi\)
\(480\) 0 0
\(481\) −2.65244 1.53138i −0.120941 0.0698251i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 16.0873i 0.730485i
\(486\) 0 0
\(487\) −34.1323 −1.54668 −0.773341 0.633990i \(-0.781416\pi\)
−0.773341 + 0.633990i \(0.781416\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5.86948 + 3.38874i 0.264886 + 0.152932i 0.626561 0.779372i \(-0.284462\pi\)
−0.361675 + 0.932304i \(0.617795\pi\)
\(492\) 0 0
\(493\) −14.5905 + 8.42380i −0.657121 + 0.379389i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 30.2621 + 11.0319i 1.35744 + 0.494847i
\(498\) 0 0
\(499\) 4.30037 7.44846i 0.192511 0.333439i −0.753571 0.657367i \(-0.771670\pi\)
0.946082 + 0.323928i \(0.105004\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2.96518 −0.132211 −0.0661055 0.997813i \(-0.521057\pi\)
−0.0661055 + 0.997813i \(0.521057\pi\)
\(504\) 0 0
\(505\) −10.3214 −0.459297
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 3.04882 5.28072i 0.135137 0.234064i −0.790513 0.612445i \(-0.790186\pi\)
0.925650 + 0.378382i \(0.123519\pi\)
\(510\) 0 0
\(511\) 1.05918 + 0.386118i 0.0468553 + 0.0170808i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −11.9499 + 6.89926i −0.526574 + 0.304018i
\(516\) 0 0
\(517\) −0.722823 0.417322i −0.0317897 0.0183538i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 32.6929 1.43230 0.716150 0.697946i \(-0.245903\pi\)
0.716150 + 0.697946i \(0.245903\pi\)
\(522\) 0 0
\(523\) 2.00252i 0.0875643i 0.999041 + 0.0437821i \(0.0139407\pi\)
−0.999041 + 0.0437821i \(0.986059\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −55.4257 32.0001i −2.41438 1.39394i
\(528\) 0 0
\(529\) −8.68292 15.0393i −0.377518 0.653881i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.42037 + 0.820053i −0.0615232 + 0.0355204i
\(534\) 0 0
\(535\) 2.85192 + 1.64656i 0.123299 + 0.0711870i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 23.3840 + 4.14769i 1.00722 + 0.178654i
\(540\) 0 0
\(541\) −11.4451 −0.492061 −0.246031 0.969262i \(-0.579126\pi\)
−0.246031 + 0.969262i \(0.579126\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.84980 8.40010i 0.207743 0.359821i
\(546\) 0 0
\(547\) 3.91961 + 6.78896i 0.167590 + 0.290275i 0.937572 0.347791i \(-0.113068\pi\)
−0.769982 + 0.638066i \(0.779735\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2.32037 4.01899i −0.0988510 0.171215i
\(552\) 0 0
\(553\) −12.9967 + 2.28487i −0.552675 + 0.0971626i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.0134996i 0.000571997i −1.00000 0.000285998i \(-0.999909\pi\)
1.00000 0.000285998i \(-9.10361e-5\pi\)
\(558\) 0 0
\(559\) 7.06782i 0.298937i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −9.54528 + 16.5329i −0.402286 + 0.696779i −0.994001 0.109368i \(-0.965117\pi\)
0.591716 + 0.806147i \(0.298451\pi\)
\(564\) 0 0
\(565\) −32.8923 + 18.9904i −1.38379 + 0.798932i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −32.3406 + 18.6719i −1.35579 + 0.782765i −0.989053 0.147561i \(-0.952858\pi\)
−0.366735 + 0.930325i \(0.619525\pi\)
\(570\) 0 0
\(571\) 22.6421 39.2173i 0.947544 1.64119i 0.196968 0.980410i \(-0.436890\pi\)
0.750576 0.660784i \(-0.229776\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.264101i 0.0110138i
\(576\) 0 0
\(577\) 37.0988i 1.54444i 0.635354 + 0.772221i \(0.280854\pi\)
−0.635354 + 0.772221i \(0.719146\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −22.3337 + 3.92636i −0.926559 + 0.162893i
\(582\) 0 0
\(583\) −13.3603 23.1408i −0.553329 0.958393i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −17.0612 29.5509i −0.704191 1.21969i −0.966983 0.254842i \(-0.917977\pi\)
0.262792 0.964853i \(-0.415357\pi\)
\(588\) 0 0
\(589\) 8.81453 15.2672i 0.363197 0.629075i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −19.6999 −0.808980 −0.404490 0.914542i \(-0.632551\pi\)
−0.404490 + 0.914542i \(0.632551\pi\)
\(594\) 0 0
\(595\) 22.4313 + 26.7601i 0.919594 + 1.09706i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −9.74033 5.62358i −0.397979 0.229773i 0.287632 0.957741i \(-0.407132\pi\)
−0.685612 + 0.727967i \(0.740465\pi\)
\(600\) 0 0
\(601\) 29.7646 17.1846i 1.21412 0.700975i 0.250469 0.968125i \(-0.419415\pi\)
0.963655 + 0.267150i \(0.0860818\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.564393 + 0.977557i 0.0229458 + 0.0397433i
\(606\) 0 0
\(607\) 33.7888 + 19.5080i 1.37145 + 0.791804i 0.991110 0.133044i \(-0.0424753\pi\)
0.380335 + 0.924849i \(0.375809\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0.443317i 0.0179347i
\(612\) 0 0
\(613\) −16.1099 −0.650672 −0.325336 0.945598i \(-0.605477\pi\)
−0.325336 + 0.945598i \(0.605477\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −7.03569 4.06205i −0.283246 0.163532i 0.351646 0.936133i \(-0.385622\pi\)
−0.634892 + 0.772601i \(0.718955\pi\)
\(618\) 0 0
\(619\) −32.4018 + 18.7072i −1.30234 + 0.751906i −0.980805 0.194991i \(-0.937532\pi\)
−0.321535 + 0.946898i \(0.604199\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −9.54718 + 26.1893i −0.382499 + 1.04925i
\(624\) 0 0
\(625\) 12.2156 21.1581i 0.488626 0.846325i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 10.1451 0.404511
\(630\) 0 0
\(631\) 19.8268 0.789294 0.394647 0.918833i \(-0.370867\pi\)
0.394647 + 0.918833i \(0.370867\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 6.98848 12.1044i 0.277329 0.480348i
\(636\) 0 0
\(637\) 4.30227 + 11.8578i 0.170462 + 0.469823i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 8.01849 4.62948i 0.316711 0.182853i −0.333214 0.942851i \(-0.608133\pi\)
0.649926 + 0.759998i \(0.274800\pi\)
\(642\) 0 0
\(643\) −36.3456 20.9841i −1.43333 0.827534i −0.435958 0.899967i \(-0.643590\pi\)
−0.997373 + 0.0724332i \(0.976924\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6.28587 0.247123 0.123561 0.992337i \(-0.460568\pi\)
0.123561 + 0.992337i \(0.460568\pi\)
\(648\) 0 0
\(649\) 36.5798i 1.43588i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −20.1668 11.6433i −0.789189 0.455638i 0.0504882 0.998725i \(-0.483922\pi\)
−0.839677 + 0.543086i \(0.817256\pi\)
\(654\) 0 0
\(655\) −18.8207 32.5985i −0.735387 1.27373i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 25.8880 14.9464i 1.00845 0.582230i 0.0977141 0.995215i \(-0.468847\pi\)
0.910738 + 0.412984i \(0.135514\pi\)
\(660\) 0 0
\(661\) 17.6184 + 10.1720i 0.685278 + 0.395645i 0.801841 0.597538i \(-0.203854\pi\)
−0.116563 + 0.993183i \(0.537188\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −7.37118 + 6.17878i −0.285842 + 0.239603i
\(666\) 0 0
\(667\) −6.69963 −0.259411
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2.40643 + 4.16805i −0.0928990 + 0.160906i
\(672\) 0 0
\(673\) −8.55996 14.8263i −0.329962 0.571511i 0.652542 0.757753i \(-0.273703\pi\)
−0.982504 + 0.186241i \(0.940369\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −14.2078 24.6085i −0.546048 0.945783i −0.998540 0.0540148i \(-0.982798\pi\)
0.452492 0.891769i \(-0.350535\pi\)
\(678\) 0 0
\(679\) 3.33313 + 18.9593i 0.127914 + 0.727593i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 20.9274i 0.800764i −0.916348 0.400382i \(-0.868877\pi\)
0.916348 0.400382i \(-0.131123\pi\)
\(684\) 0 0
\(685\) 13.8526i 0.529281i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 7.09627 12.2911i 0.270346 0.468254i
\(690\) 0 0
\(691\) 20.7918 12.0041i 0.790957 0.456659i −0.0493424 0.998782i \(-0.515713\pi\)
0.840299 + 0.542123i \(0.182379\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 14.7143 8.49529i 0.558144 0.322245i
\(696\) 0 0
\(697\) 2.71634 4.70484i 0.102889 0.178208i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 42.0117i 1.58676i 0.608728 + 0.793379i \(0.291680\pi\)
−0.608728 + 0.793379i \(0.708320\pi\)
\(702\) 0 0
\(703\) 2.79450i 0.105397i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 12.1641 2.13850i 0.457478 0.0804266i
\(708\) 0 0
\(709\) −18.6094 32.2324i −0.698891 1.21051i −0.968851 0.247643i \(-0.920344\pi\)
0.269960 0.962871i \(-0.412989\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −12.7252 22.0406i −0.476561 0.825428i
\(714\) 0 0
\(715\) −6.75890 + 11.7068i −0.252769 + 0.437808i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 18.2978 0.682392 0.341196 0.939992i \(-0.389168\pi\)
0.341196 + 0.939992i \(0.389168\pi\)
\(720\) 0 0
\(721\) 12.6538 10.6069i 0.471253 0.395021i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −0.271971 0.157022i −0.0101007 0.00583166i
\(726\) 0 0
\(727\) 28.3214 16.3514i 1.05038 0.606439i 0.127626 0.991822i \(-0.459264\pi\)
0.922756 + 0.385384i \(0.125931\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 11.7057 + 20.2749i 0.432951 + 0.749893i
\(732\) 0 0
\(733\) 0.431812 + 0.249307i 0.0159494 + 0.00920836i 0.507953 0.861385i \(-0.330402\pi\)
−0.492004 + 0.870593i \(0.663736\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 27.0997i 0.998231i
\(738\) 0 0
\(739\) 47.7046 1.75484 0.877421 0.479722i \(-0.159263\pi\)
0.877421 + 0.479722i \(0.159263\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 9.20534 + 5.31470i 0.337711 + 0.194978i 0.659259 0.751916i \(-0.270870\pi\)
−0.321548 + 0.946893i \(0.604203\pi\)
\(744\) 0 0
\(745\) 29.5606 17.0668i 1.08302 0.625279i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.70223 1.34963i −0.135277 0.0493144i
\(750\) 0 0
\(751\) 9.55927 16.5571i 0.348823 0.604179i −0.637218 0.770684i \(-0.719915\pi\)
0.986041 + 0.166505i \(0.0532482\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −25.8411 −0.940453
\(756\) 0 0
\(757\) 28.5388 1.03726 0.518631 0.854998i \(-0.326442\pi\)
0.518631 + 0.854998i \(0.326442\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −21.6650 + 37.5249i −0.785355 + 1.36028i 0.143431 + 0.989660i \(0.454186\pi\)
−0.928787 + 0.370615i \(0.879147\pi\)
\(762\) 0 0
\(763\) −3.97522 + 10.9046i −0.143912 + 0.394773i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 16.8261 9.71458i 0.607557 0.350773i
\(768\) 0 0
\(769\) 5.75189 + 3.32086i 0.207419 + 0.119753i 0.600111 0.799917i \(-0.295123\pi\)
−0.392693 + 0.919670i \(0.628456\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 44.4831 1.59995 0.799973 0.600036i \(-0.204847\pi\)
0.799973 + 0.600036i \(0.204847\pi\)
\(774\) 0 0
\(775\) 1.19298i 0.0428532i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.29596 + 0.748226i 0.0464328 + 0.0268080i
\(780\) 0 0
\(781\) −20.6520 35.7703i −0.738986 1.27996i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 10.9134 6.30087i 0.389517 0.224888i
\(786\) 0 0
\(787\) 19.0399 + 10.9927i 0.678700 + 0.391848i 0.799365 0.600846i \(-0.205169\pi\)
−0.120665 + 0.992693i \(0.538503\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 34.8300 29.1958i 1.23841 1.03808i
\(792\) 0 0
\(793\) −2.55632 −0.0907776
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 9.71892 16.8337i 0.344262 0.596279i −0.640958 0.767576i \(-0.721463\pi\)
0.985219 + 0.171297i \(0.0547959\pi\)
\(798\) 0 0
\(799\) 0.734219 + 1.27171i 0.0259748 + 0.0449897i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −0.722823 1.25197i −0.0255079 0.0441809i
\(804\) 0 0
\(805\) 2.40426 + 13.6758i 0.0847390 + 0.482008i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 21.0058i 0.738526i −0.929325 0.369263i \(-0.879610\pi\)
0.929325 0.369263i \(-0.120390\pi\)
\(810\) 0 0
\(811\) 37.3291i 1.31080i 0.755281 + 0.655401i \(0.227500\pi\)
−0.755281 + 0.655401i \(0.772500\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −11.2876 + 19.5506i −0.395386 + 0.684829i
\(816\) 0 0
\(817\) −5.58478 + 3.22438i −0.195387 + 0.112807i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 10.9017 6.29412i 0.380473 0.219666i −0.297551 0.954706i \(-0.596170\pi\)
0.678024 + 0.735040i \(0.262837\pi\)
\(822\) 0 0
\(823\) −22.4189 + 38.8307i −0.781474 + 1.35355i 0.149608 + 0.988745i \(0.452199\pi\)
−0.931083 + 0.364808i \(0.881135\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 25.7293i 0.894695i −0.894360 0.447347i \(-0.852369\pi\)
0.894360 0.447347i \(-0.147631\pi\)
\(828\) 0 0
\(829\) 16.9628i 0.589142i 0.955630 + 0.294571i \(0.0951767\pi\)
−0.955630 + 0.294571i \(0.904823\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −31.9804 26.8901i −1.10806 0.931686i
\(834\) 0 0
\(835\) 3.99450 + 6.91867i 0.138235 + 0.239431i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −13.3539 23.1296i −0.461027 0.798522i 0.537986 0.842954i \(-0.319185\pi\)
−0.999012 + 0.0444321i \(0.985852\pi\)
\(840\) 0 0
\(841\) −10.5167 + 18.2155i −0.362645 + 0.628120i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 21.5637 0.741815
\(846\) 0 0
\(847\) −0.867695 1.03514i −0.0298144 0.0355680i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 3.49381 + 2.01715i 0.119766 + 0.0691471i
\(852\) 0 0
\(853\) 37.6287 21.7249i 1.28838 0.743848i 0.310017 0.950731i \(-0.399665\pi\)
0.978366 + 0.206883i \(0.0663319\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 7.83430 + 13.5694i 0.267615 + 0.463522i 0.968245 0.250002i \(-0.0804312\pi\)
−0.700631 + 0.713524i \(0.747098\pi\)
\(858\) 0 0
\(859\) 17.3578 + 10.0216i 0.592242 + 0.341931i 0.765984 0.642860i \(-0.222252\pi\)
−0.173742 + 0.984791i \(0.555586\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 40.0219i 1.36236i 0.732115 + 0.681181i \(0.238533\pi\)
−0.732115 + 0.681181i \(0.761467\pi\)
\(864\) 0 0
\(865\) 39.9739 1.35915
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 14.6545 + 8.46079i 0.497120 + 0.287013i
\(870\) 0 0
\(871\) 12.4655 7.19694i 0.422376 0.243859i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −10.2408 + 28.0919i −0.346201 + 0.949680i
\(876\) 0 0
\(877\) −22.6353 + 39.2054i −0.764338 + 1.32387i 0.176257 + 0.984344i \(0.443601\pi\)
−0.940596 + 0.339529i \(0.889732\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −45.3385 −1.52749 −0.763746 0.645517i \(-0.776642\pi\)
−0.763746 + 0.645517i \(0.776642\pi\)
\(882\) 0 0
\(883\) −12.5650 −0.422845 −0.211423 0.977395i \(-0.567810\pi\)
−0.211423 + 0.977395i \(0.567810\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 17.8620 30.9379i 0.599748 1.03879i −0.393110 0.919492i \(-0.628601\pi\)
0.992858 0.119303i \(-0.0380659\pi\)
\(888\) 0 0
\(889\) −5.72822 + 15.7133i −0.192118 + 0.527009i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −0.350296 + 0.202243i −0.0117222 + 0.00676782i
\(894\) 0 0
\(895\) −9.63528 5.56293i −0.322072 0.185948i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 30.2632 1.00933
\(900\) 0 0
\(901\) 47.0113i 1.56617i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 25.9635 + 14.9901i 0.863058 + 0.498287i
\(906\) 0 0
\(907\) −4.52104 7.83067i −0.150119 0.260013i 0.781152 0.624341i \(-0.214632\pi\)
−0.931271 + 0.364327i \(0.881299\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −35.5171 + 20.5058i −1.17673 + 0.679388i −0.955257 0.295777i \(-0.904421\pi\)
−0.221478 + 0.975165i \(0.571088\pi\)
\(912\) 0 0
\(913\) 25.1826 + 14.5392i 0.833421 + 0.481176i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 28.9349 + 34.5188i 0.955515 + 1.13991i
\(918\) 0 0
\(919\) −10.2326 −0.337541 −0.168771 0.985655i \(-0.553980\pi\)
−0.168771 + 0.985655i \(0.553980\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 10.9692 18.9992i 0.361055 0.625366i
\(924\) 0 0
\(925\) 0.0945538 + 0.163772i 0.00310891 + 0.00538479i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 12.8330 + 22.2273i 0.421036 + 0.729255i 0.996041 0.0888945i \(-0.0283334\pi\)
−0.575005 + 0.818150i \(0.695000\pi\)
\(930\) 0 0
\(931\) 7.40697 8.80913i 0.242754 0.288707i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 44.7763i 1.46434i
\(936\) 0 0
\(937\) 15.9276i 0.520333i −0.965564 0.260167i \(-0.916223\pi\)
0.965564 0.260167i \(-0.0837775\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −19.6767 + 34.0810i −0.641442 + 1.11101i 0.343669 + 0.939091i \(0.388330\pi\)
−0.985111 + 0.171919i \(0.945003\pi\)
\(942\) 0 0
\(943\) 1.87093 1.08018i 0.0609258 0.0351755i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 28.9086 16.6904i 0.939403 0.542365i 0.0496302 0.998768i \(-0.484196\pi\)
0.889773 + 0.456403i \(0.150862\pi\)
\(948\) 0 0
\(949\) 0.383923 0.664975i 0.0124627 0.0215860i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 44.4622i 1.44027i −0.693832 0.720137i \(-0.744079\pi\)
0.693832 0.720137i \(-0.255921\pi\)
\(954\) 0 0
\(955\) 22.6447i 0.732764i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 2.87013 + 16.3257i 0.0926813 + 0.527185i
\(960\) 0 0
\(961\) 41.9814 + 72.7138i 1.35424 + 2.34561i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −17.8347 30.8905i −0.574118 0.994401i
\(966\) 0 0
\(967\) 20.0556 34.7372i 0.644943 1.11707i −0.339371 0.940652i \(-0.610214\pi\)
0.984315 0.176422i \(-0.0564523\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −46.0026 −1.47629 −0.738147 0.674640i \(-0.764299\pi\)
−0.738147 + 0.674640i \(0.764299\pi\)
\(972\) 0 0
\(973\) −15.5811 + 13.0606i −0.499506 + 0.418704i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 46.8323 + 27.0386i 1.49830 + 0.865042i 0.999998 0.00196335i \(-0.000624955\pi\)
0.498299 + 0.867005i \(0.333958\pi\)
\(978\) 0 0
\(979\) 30.9562 17.8726i 0.989365 0.571210i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −6.97890 12.0878i −0.222592 0.385541i 0.733002 0.680226i \(-0.238119\pi\)
−0.955594 + 0.294685i \(0.904785\pi\)
\(984\) 0 0
\(985\) 7.39703 + 4.27068i 0.235689 + 0.136075i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 9.30979i 0.296034i
\(990\) 0 0
\(991\) 37.0297 1.17629 0.588144 0.808756i \(-0.299859\pi\)
0.588144 + 0.808756i \(0.299859\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −29.1119 16.8077i −0.922909 0.532841i
\(996\) 0 0
\(997\) −43.4282 + 25.0733i −1.37538 + 0.794079i −0.991600 0.129344i \(-0.958713\pi\)
−0.383785 + 0.923422i \(0.625380\pi\)
\(998\) 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.a.881.2 12
3.2 odd 2 1008.2.cc.a.545.1 12
4.3 odd 2 189.2.o.a.125.3 12
7.6 odd 2 inner 3024.2.cc.a.881.5 12
9.2 odd 6 inner 3024.2.cc.a.2897.5 12
9.7 even 3 1008.2.cc.a.209.6 12
12.11 even 2 63.2.o.a.41.4 yes 12
21.20 even 2 1008.2.cc.a.545.6 12
28.3 even 6 1323.2.i.c.1097.4 12
28.11 odd 6 1323.2.i.c.1097.3 12
28.19 even 6 1323.2.s.c.962.3 12
28.23 odd 6 1323.2.s.c.962.4 12
28.27 even 2 189.2.o.a.125.4 12
36.7 odd 6 63.2.o.a.20.3 12
36.11 even 6 189.2.o.a.62.4 12
36.23 even 6 567.2.c.c.566.5 12
36.31 odd 6 567.2.c.c.566.8 12
63.20 even 6 inner 3024.2.cc.a.2897.2 12
63.34 odd 6 1008.2.cc.a.209.1 12
84.11 even 6 441.2.i.c.68.3 12
84.23 even 6 441.2.s.c.374.3 12
84.47 odd 6 441.2.s.c.374.4 12
84.59 odd 6 441.2.i.c.68.4 12
84.83 odd 2 63.2.o.a.41.3 yes 12
252.11 even 6 1323.2.s.c.656.3 12
252.47 odd 6 1323.2.i.c.521.3 12
252.79 odd 6 441.2.i.c.227.4 12
252.83 odd 6 189.2.o.a.62.3 12
252.115 even 6 441.2.s.c.362.3 12
252.139 even 6 567.2.c.c.566.7 12
252.151 odd 6 441.2.s.c.362.4 12
252.167 odd 6 567.2.c.c.566.6 12
252.187 even 6 441.2.i.c.227.3 12
252.191 even 6 1323.2.i.c.521.4 12
252.223 even 6 63.2.o.a.20.4 yes 12
252.227 odd 6 1323.2.s.c.656.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.o.a.20.3 12 36.7 odd 6
63.2.o.a.20.4 yes 12 252.223 even 6
63.2.o.a.41.3 yes 12 84.83 odd 2
63.2.o.a.41.4 yes 12 12.11 even 2
189.2.o.a.62.3 12 252.83 odd 6
189.2.o.a.62.4 12 36.11 even 6
189.2.o.a.125.3 12 4.3 odd 2
189.2.o.a.125.4 12 28.27 even 2
441.2.i.c.68.3 12 84.11 even 6
441.2.i.c.68.4 12 84.59 odd 6
441.2.i.c.227.3 12 252.187 even 6
441.2.i.c.227.4 12 252.79 odd 6
441.2.s.c.362.3 12 252.115 even 6
441.2.s.c.362.4 12 252.151 odd 6
441.2.s.c.374.3 12 84.23 even 6
441.2.s.c.374.4 12 84.47 odd 6
567.2.c.c.566.5 12 36.23 even 6
567.2.c.c.566.6 12 252.167 odd 6
567.2.c.c.566.7 12 252.139 even 6
567.2.c.c.566.8 12 36.31 odd 6
1008.2.cc.a.209.1 12 63.34 odd 6
1008.2.cc.a.209.6 12 9.7 even 3
1008.2.cc.a.545.1 12 3.2 odd 2
1008.2.cc.a.545.6 12 21.20 even 2
1323.2.i.c.521.3 12 252.47 odd 6
1323.2.i.c.521.4 12 252.191 even 6
1323.2.i.c.1097.3 12 28.11 odd 6
1323.2.i.c.1097.4 12 28.3 even 6
1323.2.s.c.656.3 12 252.11 even 6
1323.2.s.c.656.4 12 252.227 odd 6
1323.2.s.c.962.3 12 28.19 even 6
1323.2.s.c.962.4 12 28.23 odd 6
3024.2.cc.a.881.2 12 1.1 even 1 trivial
3024.2.cc.a.881.5 12 7.6 odd 2 inner
3024.2.cc.a.2897.2 12 63.20 even 6 inner
3024.2.cc.a.2897.5 12 9.2 odd 6 inner