Properties

Label 576.2.p.c.95.3
Level $576$
Weight $2$
Character 576.95
Analytic conductor $4.599$
Analytic rank $0$
Dimension $16$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [576,2,Mod(95,576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(576, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("576.95");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.p (of order \(6\), degree \(2\), 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: \(4.59938315643\)
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: \( x^{16} + 11x^{14} + 85x^{12} + 332x^{10} + 940x^{8} + 1064x^{6} + 880x^{4} + 128x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 95.3
Root \(-1.03144 - 1.78651i\) of defining polynomial
Character \(\chi\) \(=\) 576.95
Dual form 576.2.p.c.479.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.31461 + 1.12774i) q^{3} +(-1.21189 + 2.09905i) q^{5} +(3.96035 - 2.28651i) q^{7} +(0.456412 - 2.96508i) q^{9} +O(q^{10})\) \(q+(-1.31461 + 1.12774i) q^{3} +(-1.21189 + 2.09905i) q^{5} +(3.96035 - 2.28651i) q^{7} +(0.456412 - 2.96508i) q^{9} +(3.73910 - 2.15877i) q^{11} +(-1.88322 - 1.08728i) q^{13} +(-0.774019 - 4.12613i) q^{15} +3.90660i q^{17} +5.93016 q^{19} +(-2.62774 + 7.47211i) q^{21} +(-2.94857 + 5.10707i) q^{23} +(-0.437348 - 0.757509i) q^{25} +(2.74383 + 4.41264i) q^{27} +(-0.776975 - 1.34576i) q^{29} +(0.925013 + 0.534057i) q^{31} +(-2.48094 + 7.05467i) q^{33} +11.0840i q^{35} +2.02356i q^{37} +(3.70186 - 0.694430i) q^{39} +(10.4666 + 6.04289i) q^{41} +(-0.995268 - 1.72386i) q^{43} +(5.67074 + 4.55138i) q^{45} +(-3.70186 - 6.41181i) q^{47} +(6.95623 - 12.0485i) q^{49} +(-4.40562 - 5.13567i) q^{51} +3.97773 q^{53} +10.4647i q^{55} +(-7.79586 + 6.68767i) q^{57} +(-0.294283 - 0.169904i) q^{59} +(-8.33093 + 4.80986i) q^{61} +(-4.97212 - 12.7863i) q^{63} +(4.56450 - 2.63531i) q^{65} +(1.71554 - 2.97141i) q^{67} +(-1.88322 - 10.0390i) q^{69} -2.32554 q^{71} -2.37960 q^{73} +(1.42922 + 0.502617i) q^{75} +(9.87208 - 17.0989i) q^{77} +(5.38160 - 3.10707i) q^{79} +(-8.58338 - 2.70659i) q^{81} +(5.40089 - 3.11821i) q^{83} +(-8.20016 - 4.73437i) q^{85} +(2.53909 + 0.892929i) q^{87} +4.90465i q^{89} -9.94425 q^{91} +(-1.81831 + 0.341096i) q^{93} +(-7.18669 + 12.4477i) q^{95} +(-1.32056 - 2.28728i) q^{97} +(-4.69435 - 12.0720i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 6 q^{5} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 6 q^{5} + 6 q^{9} + 6 q^{13} - 30 q^{21} - 14 q^{25} + 18 q^{29} - 48 q^{33} + 66 q^{45} + 6 q^{49} - 48 q^{53} + 18 q^{57} - 42 q^{61} + 54 q^{65} + 6 q^{69} + 28 q^{73} + 66 q^{77} - 6 q^{81} - 36 q^{85} - 102 q^{93} + 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\)

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
\(3\) −1.31461 + 1.12774i −0.758992 + 0.651100i
\(4\) 0 0
\(5\) −1.21189 + 2.09905i −0.541973 + 0.938725i 0.456818 + 0.889560i \(0.348989\pi\)
−0.998791 + 0.0491645i \(0.984344\pi\)
\(6\) 0 0
\(7\) 3.96035 2.28651i 1.49687 0.864218i 0.496877 0.867821i \(-0.334480\pi\)
0.999994 + 0.00360263i \(0.00114675\pi\)
\(8\) 0 0
\(9\) 0.456412 2.96508i 0.152137 0.988359i
\(10\) 0 0
\(11\) 3.73910 2.15877i 1.12738 0.650893i 0.184105 0.982907i \(-0.441061\pi\)
0.943275 + 0.332013i \(0.107728\pi\)
\(12\) 0 0
\(13\) −1.88322 1.08728i −0.522310 0.301556i 0.215569 0.976489i \(-0.430839\pi\)
−0.737879 + 0.674933i \(0.764173\pi\)
\(14\) 0 0
\(15\) −0.774019 4.12613i −0.199851 1.06536i
\(16\) 0 0
\(17\) 3.90660i 0.947490i 0.880662 + 0.473745i \(0.157098\pi\)
−0.880662 + 0.473745i \(0.842902\pi\)
\(18\) 0 0
\(19\) 5.93016 1.36047 0.680236 0.732994i \(-0.261877\pi\)
0.680236 + 0.732994i \(0.261877\pi\)
\(20\) 0 0
\(21\) −2.62774 + 7.47211i −0.573420 + 1.63055i
\(22\) 0 0
\(23\) −2.94857 + 5.10707i −0.614819 + 1.06490i 0.375597 + 0.926783i \(0.377438\pi\)
−0.990416 + 0.138115i \(0.955896\pi\)
\(24\) 0 0
\(25\) −0.437348 0.757509i −0.0874697 0.151502i
\(26\) 0 0
\(27\) 2.74383 + 4.41264i 0.528050 + 0.849213i
\(28\) 0 0
\(29\) −0.776975 1.34576i −0.144281 0.249902i 0.784824 0.619719i \(-0.212753\pi\)
−0.929104 + 0.369818i \(0.879420\pi\)
\(30\) 0 0
\(31\) 0.925013 + 0.534057i 0.166137 + 0.0959194i 0.580763 0.814073i \(-0.302754\pi\)
−0.414626 + 0.909992i \(0.636088\pi\)
\(32\) 0 0
\(33\) −2.48094 + 7.05467i −0.431876 + 1.22806i
\(34\) 0 0
\(35\) 11.0840i 1.87353i
\(36\) 0 0
\(37\) 2.02356i 0.332670i 0.986069 + 0.166335i \(0.0531934\pi\)
−0.986069 + 0.166335i \(0.946807\pi\)
\(38\) 0 0
\(39\) 3.70186 0.694430i 0.592772 0.111198i
\(40\) 0 0
\(41\) 10.4666 + 6.04289i 1.63461 + 0.943741i 0.982647 + 0.185488i \(0.0593866\pi\)
0.651961 + 0.758253i \(0.273947\pi\)
\(42\) 0 0
\(43\) −0.995268 1.72386i −0.151777 0.262885i 0.780104 0.625650i \(-0.215166\pi\)
−0.931881 + 0.362765i \(0.881833\pi\)
\(44\) 0 0
\(45\) 5.67074 + 4.55138i 0.845343 + 0.678479i
\(46\) 0 0
\(47\) −3.70186 6.41181i −0.539972 0.935259i −0.998905 0.0467878i \(-0.985102\pi\)
0.458933 0.888471i \(-0.348232\pi\)
\(48\) 0 0
\(49\) 6.95623 12.0485i 0.993747 1.72122i
\(50\) 0 0
\(51\) −4.40562 5.13567i −0.616911 0.719137i
\(52\) 0 0
\(53\) 3.97773 0.546383 0.273192 0.961960i \(-0.411921\pi\)
0.273192 + 0.961960i \(0.411921\pi\)
\(54\) 0 0
\(55\) 10.4647i 1.41107i
\(56\) 0 0
\(57\) −7.79586 + 6.68767i −1.03259 + 0.885803i
\(58\) 0 0
\(59\) −0.294283 0.169904i −0.0383124 0.0221197i 0.480721 0.876873i \(-0.340375\pi\)
−0.519034 + 0.854754i \(0.673708\pi\)
\(60\) 0 0
\(61\) −8.33093 + 4.80986i −1.06667 + 0.615840i −0.927269 0.374397i \(-0.877850\pi\)
−0.139397 + 0.990237i \(0.544516\pi\)
\(62\) 0 0
\(63\) −4.97212 12.7863i −0.626429 1.61093i
\(64\) 0 0
\(65\) 4.56450 2.63531i 0.566156 0.326870i
\(66\) 0 0
\(67\) 1.71554 2.97141i 0.209587 0.363015i −0.741998 0.670402i \(-0.766121\pi\)
0.951584 + 0.307388i \(0.0994548\pi\)
\(68\) 0 0
\(69\) −1.88322 10.0390i −0.226713 1.20856i
\(70\) 0 0
\(71\) −2.32554 −0.275991 −0.137996 0.990433i \(-0.544066\pi\)
−0.137996 + 0.990433i \(0.544066\pi\)
\(72\) 0 0
\(73\) −2.37960 −0.278511 −0.139255 0.990256i \(-0.544471\pi\)
−0.139255 + 0.990256i \(0.544471\pi\)
\(74\) 0 0
\(75\) 1.42922 + 0.502617i 0.165032 + 0.0580372i
\(76\) 0 0
\(77\) 9.87208 17.0989i 1.12503 1.94861i
\(78\) 0 0
\(79\) 5.38160 3.10707i 0.605478 0.349573i −0.165716 0.986174i \(-0.552993\pi\)
0.771194 + 0.636601i \(0.219660\pi\)
\(80\) 0 0
\(81\) −8.58338 2.70659i −0.953709 0.300732i
\(82\) 0 0
\(83\) 5.40089 3.11821i 0.592825 0.342268i −0.173389 0.984853i \(-0.555472\pi\)
0.766214 + 0.642586i \(0.222138\pi\)
\(84\) 0 0
\(85\) −8.20016 4.73437i −0.889432 0.513514i
\(86\) 0 0
\(87\) 2.53909 + 0.892929i 0.272219 + 0.0957320i
\(88\) 0 0
\(89\) 4.90465i 0.519892i 0.965623 + 0.259946i \(0.0837047\pi\)
−0.965623 + 0.259946i \(0.916295\pi\)
\(90\) 0 0
\(91\) −9.94425 −1.04244
\(92\) 0 0
\(93\) −1.81831 + 0.341096i −0.188550 + 0.0353700i
\(94\) 0 0
\(95\) −7.18669 + 12.4477i −0.737339 + 1.27711i
\(96\) 0 0
\(97\) −1.32056 2.28728i −0.134083 0.232238i 0.791164 0.611604i \(-0.209476\pi\)
−0.925247 + 0.379366i \(0.876142\pi\)
\(98\) 0 0
\(99\) −4.69435 12.0720i −0.471800 1.21328i
\(100\) 0 0
\(101\) 7.44830 + 12.9008i 0.741134 + 1.28368i 0.951979 + 0.306162i \(0.0990449\pi\)
−0.210846 + 0.977519i \(0.567622\pi\)
\(102\) 0 0
\(103\) 15.3451 + 8.85952i 1.51200 + 0.872955i 0.999902 + 0.0140288i \(0.00446566\pi\)
0.512100 + 0.858926i \(0.328868\pi\)
\(104\) 0 0
\(105\) −12.4998 14.5711i −1.21986 1.42200i
\(106\) 0 0
\(107\) 6.57622i 0.635747i 0.948133 + 0.317874i \(0.102969\pi\)
−0.948133 + 0.317874i \(0.897031\pi\)
\(108\) 0 0
\(109\) 1.50658i 0.144305i −0.997394 0.0721523i \(-0.977013\pi\)
0.997394 0.0721523i \(-0.0229868\pi\)
\(110\) 0 0
\(111\) −2.28204 2.66019i −0.216602 0.252494i
\(112\) 0 0
\(113\) −13.1406 7.58671i −1.23616 0.713698i −0.267853 0.963460i \(-0.586314\pi\)
−0.968307 + 0.249762i \(0.919648\pi\)
\(114\) 0 0
\(115\) −7.14667 12.3784i −0.666431 1.15429i
\(116\) 0 0
\(117\) −4.08338 + 5.08764i −0.377508 + 0.470352i
\(118\) 0 0
\(119\) 8.93247 + 15.4715i 0.818838 + 1.41827i
\(120\) 0 0
\(121\) 3.82056 6.61741i 0.347324 0.601583i
\(122\) 0 0
\(123\) −20.5743 + 3.85952i −1.85512 + 0.348001i
\(124\) 0 0
\(125\) −9.99882 −0.894321
\(126\) 0 0
\(127\) 9.14603i 0.811579i −0.913967 0.405789i \(-0.866997\pi\)
0.913967 0.405789i \(-0.133003\pi\)
\(128\) 0 0
\(129\) 3.25245 + 1.14380i 0.286362 + 0.100706i
\(130\) 0 0
\(131\) −6.90748 3.98803i −0.603509 0.348436i 0.166912 0.985972i \(-0.446620\pi\)
−0.770421 + 0.637536i \(0.779954\pi\)
\(132\) 0 0
\(133\) 23.4855 13.5593i 2.03645 1.17574i
\(134\) 0 0
\(135\) −12.5876 + 0.411811i −1.08337 + 0.0354430i
\(136\) 0 0
\(137\) −0.252450 + 0.145752i −0.0215683 + 0.0124525i −0.510745 0.859732i \(-0.670631\pi\)
0.489177 + 0.872184i \(0.337297\pi\)
\(138\) 0 0
\(139\) 7.36792 12.7616i 0.624939 1.08243i −0.363613 0.931550i \(-0.618457\pi\)
0.988553 0.150876i \(-0.0482096\pi\)
\(140\) 0 0
\(141\) 12.0974 + 4.25431i 1.01878 + 0.358278i
\(142\) 0 0
\(143\) −9.38870 −0.785123
\(144\) 0 0
\(145\) 3.76643 0.312785
\(146\) 0 0
\(147\) 4.44286 + 23.6840i 0.366441 + 1.95342i
\(148\) 0 0
\(149\) 7.85810 13.6106i 0.643761 1.11503i −0.340826 0.940126i \(-0.610707\pi\)
0.984586 0.174899i \(-0.0559601\pi\)
\(150\) 0 0
\(151\) −5.59864 + 3.23237i −0.455611 + 0.263047i −0.710197 0.704003i \(-0.751394\pi\)
0.254586 + 0.967050i \(0.418061\pi\)
\(152\) 0 0
\(153\) 11.5834 + 1.78302i 0.936461 + 0.144148i
\(154\) 0 0
\(155\) −2.24203 + 1.29443i −0.180084 + 0.103971i
\(156\) 0 0
\(157\) 0.316946 + 0.182989i 0.0252950 + 0.0146041i 0.512594 0.858631i \(-0.328685\pi\)
−0.487299 + 0.873235i \(0.662018\pi\)
\(158\) 0 0
\(159\) −5.22917 + 4.48584i −0.414700 + 0.355750i
\(160\) 0 0
\(161\) 26.9677i 2.12535i
\(162\) 0 0
\(163\) 0.884999 0.0693184 0.0346592 0.999399i \(-0.488965\pi\)
0.0346592 + 0.999399i \(0.488965\pi\)
\(164\) 0 0
\(165\) −11.8015 13.7571i −0.918746 1.07099i
\(166\) 0 0
\(167\) −2.41231 + 4.17824i −0.186670 + 0.323322i −0.944138 0.329550i \(-0.893103\pi\)
0.757468 + 0.652872i \(0.226436\pi\)
\(168\) 0 0
\(169\) −4.13567 7.16318i −0.318128 0.551014i
\(170\) 0 0
\(171\) 2.70659 17.5834i 0.206978 1.34463i
\(172\) 0 0
\(173\) −0.342062 0.592469i −0.0260065 0.0450446i 0.852729 0.522353i \(-0.174946\pi\)
−0.878736 + 0.477309i \(0.841612\pi\)
\(174\) 0 0
\(175\) −3.46410 2.00000i −0.261861 0.151186i
\(176\) 0 0
\(177\) 0.578476 0.108516i 0.0434809 0.00815656i
\(178\) 0 0
\(179\) 12.8030i 0.956942i −0.878103 0.478471i \(-0.841191\pi\)
0.878103 0.478471i \(-0.158809\pi\)
\(180\) 0 0
\(181\) 22.7310i 1.68958i −0.535096 0.844791i \(-0.679724\pi\)
0.535096 0.844791i \(-0.320276\pi\)
\(182\) 0 0
\(183\) 5.52767 15.7182i 0.408617 1.16192i
\(184\) 0 0
\(185\) −4.24755 2.45232i −0.312286 0.180298i
\(186\) 0 0
\(187\) 8.43345 + 14.6072i 0.616715 + 1.06818i
\(188\) 0 0
\(189\) 20.9560 + 11.2018i 1.52433 + 0.814811i
\(190\) 0 0
\(191\) −10.8885 18.8595i −0.787868 1.36463i −0.927271 0.374391i \(-0.877852\pi\)
0.139403 0.990236i \(-0.455482\pi\)
\(192\) 0 0
\(193\) −11.5919 + 20.0778i −0.834403 + 1.44523i 0.0601127 + 0.998192i \(0.480854\pi\)
−0.894516 + 0.447037i \(0.852479\pi\)
\(194\) 0 0
\(195\) −3.02860 + 8.61197i −0.216882 + 0.616716i
\(196\) 0 0
\(197\) −23.9076 −1.70335 −0.851673 0.524074i \(-0.824411\pi\)
−0.851673 + 0.524074i \(0.824411\pi\)
\(198\) 0 0
\(199\) 1.89173i 0.134102i −0.997750 0.0670508i \(-0.978641\pi\)
0.997750 0.0670508i \(-0.0213589\pi\)
\(200\) 0 0
\(201\) 1.09570 + 5.84093i 0.0772844 + 0.411987i
\(202\) 0 0
\(203\) −6.15418 3.55312i −0.431939 0.249380i
\(204\) 0 0
\(205\) −25.3687 + 14.6466i −1.77183 + 1.02296i
\(206\) 0 0
\(207\) 13.7971 + 11.0737i 0.958965 + 0.769673i
\(208\) 0 0
\(209\) 22.1734 12.8018i 1.53377 0.885521i
\(210\) 0 0
\(211\) −12.6013 + 21.8261i −0.867510 + 1.50257i −0.00297716 + 0.999996i \(0.500948\pi\)
−0.864533 + 0.502576i \(0.832386\pi\)
\(212\) 0 0
\(213\) 3.05719 2.62261i 0.209475 0.179698i
\(214\) 0 0
\(215\) 4.82462 0.329036
\(216\) 0 0
\(217\) 4.88450 0.331581
\(218\) 0 0
\(219\) 3.12825 2.68356i 0.211387 0.181338i
\(220\) 0 0
\(221\) 4.24755 7.35697i 0.285721 0.494883i
\(222\) 0 0
\(223\) −8.41694 + 4.85952i −0.563640 + 0.325418i −0.754605 0.656179i \(-0.772172\pi\)
0.190965 + 0.981597i \(0.438838\pi\)
\(224\) 0 0
\(225\) −2.44569 + 0.951036i −0.163046 + 0.0634024i
\(226\) 0 0
\(227\) 8.52577 4.92235i 0.565875 0.326708i −0.189625 0.981857i \(-0.560727\pi\)
0.755500 + 0.655148i \(0.227394\pi\)
\(228\) 0 0
\(229\) 19.4021 + 11.2018i 1.28213 + 0.740236i 0.977237 0.212151i \(-0.0680470\pi\)
0.304890 + 0.952388i \(0.401380\pi\)
\(230\) 0 0
\(231\) 6.30518 + 33.6116i 0.414850 + 2.21148i
\(232\) 0 0
\(233\) 13.3753i 0.876247i −0.898915 0.438124i \(-0.855643\pi\)
0.898915 0.438124i \(-0.144357\pi\)
\(234\) 0 0
\(235\) 17.9450 1.17060
\(236\) 0 0
\(237\) −3.57076 + 10.1536i −0.231946 + 0.659550i
\(238\) 0 0
\(239\) 3.94106 6.82611i 0.254926 0.441545i −0.709949 0.704253i \(-0.751282\pi\)
0.964875 + 0.262708i \(0.0846156\pi\)
\(240\) 0 0
\(241\) −7.00490 12.1328i −0.451225 0.781545i 0.547237 0.836978i \(-0.315680\pi\)
−0.998462 + 0.0554324i \(0.982346\pi\)
\(242\) 0 0
\(243\) 14.3361 6.12169i 0.919664 0.392706i
\(244\) 0 0
\(245\) 16.8604 + 29.2030i 1.07717 + 1.86571i
\(246\) 0 0
\(247\) −11.1678 6.44771i −0.710588 0.410258i
\(248\) 0 0
\(249\) −3.58356 + 10.1900i −0.227099 + 0.645767i
\(250\) 0 0
\(251\) 16.2713i 1.02704i 0.858078 + 0.513519i \(0.171658\pi\)
−0.858078 + 0.513519i \(0.828342\pi\)
\(252\) 0 0
\(253\) 25.4611i 1.60073i
\(254\) 0 0
\(255\) 16.1192 3.02378i 1.00942 0.189357i
\(256\) 0 0
\(257\) 2.06209 + 1.19055i 0.128630 + 0.0742644i 0.562934 0.826502i \(-0.309672\pi\)
−0.434304 + 0.900766i \(0.643006\pi\)
\(258\) 0 0
\(259\) 4.62687 + 8.01398i 0.287500 + 0.497965i
\(260\) 0 0
\(261\) −4.34491 + 1.68957i −0.268943 + 0.104582i
\(262\) 0 0
\(263\) −9.42872 16.3310i −0.581400 1.00701i −0.995314 0.0966976i \(-0.969172\pi\)
0.413914 0.910316i \(-0.364161\pi\)
\(264\) 0 0
\(265\) −4.82056 + 8.34946i −0.296125 + 0.512903i
\(266\) 0 0
\(267\) −5.53116 6.44771i −0.338502 0.394593i
\(268\) 0 0
\(269\) −11.6030 −0.707447 −0.353724 0.935350i \(-0.615085\pi\)
−0.353724 + 0.935350i \(0.615085\pi\)
\(270\) 0 0
\(271\) 3.74939i 0.227759i 0.993495 + 0.113880i \(0.0363278\pi\)
−0.993495 + 0.113880i \(0.963672\pi\)
\(272\) 0 0
\(273\) 13.0728 11.2145i 0.791204 0.678733i
\(274\) 0 0
\(275\) −3.27058 1.88827i −0.197223 0.113867i
\(276\) 0 0
\(277\) −10.1978 + 5.88768i −0.612724 + 0.353756i −0.774031 0.633148i \(-0.781762\pi\)
0.161307 + 0.986904i \(0.448429\pi\)
\(278\) 0 0
\(279\) 2.00571 2.49899i 0.120079 0.149610i
\(280\) 0 0
\(281\) −7.36869 + 4.25431i −0.439579 + 0.253791i −0.703419 0.710775i \(-0.748344\pi\)
0.263840 + 0.964566i \(0.415011\pi\)
\(282\) 0 0
\(283\) 5.28292 9.15028i 0.314037 0.543928i −0.665195 0.746669i \(-0.731652\pi\)
0.979232 + 0.202742i \(0.0649851\pi\)
\(284\) 0 0
\(285\) −4.59005 24.4686i −0.271891 1.44940i
\(286\) 0 0
\(287\) 55.2684 3.26239
\(288\) 0 0
\(289\) 1.73847 0.102263
\(290\) 0 0
\(291\) 4.31549 + 1.51764i 0.252978 + 0.0889657i
\(292\) 0 0
\(293\) −13.8498 + 23.9886i −0.809114 + 1.40143i 0.104364 + 0.994539i \(0.466719\pi\)
−0.913478 + 0.406888i \(0.866614\pi\)
\(294\) 0 0
\(295\) 0.713277 0.411811i 0.0415286 0.0239765i
\(296\) 0 0
\(297\) 19.7853 + 10.5760i 1.14806 + 0.613682i
\(298\) 0 0
\(299\) 11.1056 6.41181i 0.642252 0.370805i
\(300\) 0 0
\(301\) −7.88322 4.55138i −0.454381 0.262337i
\(302\) 0 0
\(303\) −24.3404 8.55986i −1.39832 0.491751i
\(304\) 0 0
\(305\) 23.3161i 1.33507i
\(306\) 0 0
\(307\) −18.0264 −1.02882 −0.514411 0.857544i \(-0.671989\pi\)
−0.514411 + 0.857544i \(0.671989\pi\)
\(308\) 0 0
\(309\) −30.1641 + 5.65847i −1.71598 + 0.321899i
\(310\) 0 0
\(311\) 14.9599 25.9113i 0.848297 1.46929i −0.0344304 0.999407i \(-0.510962\pi\)
0.882727 0.469886i \(-0.155705\pi\)
\(312\) 0 0
\(313\) 12.5207 + 21.6865i 0.707713 + 1.22580i 0.965703 + 0.259648i \(0.0836064\pi\)
−0.257990 + 0.966148i \(0.583060\pi\)
\(314\) 0 0
\(315\) 32.8648 + 5.05885i 1.85172 + 0.285034i
\(316\) 0 0
\(317\) −9.62738 16.6751i −0.540727 0.936567i −0.998862 0.0476846i \(-0.984816\pi\)
0.458135 0.888883i \(-0.348518\pi\)
\(318\) 0 0
\(319\) −5.81037 3.35462i −0.325318 0.187823i
\(320\) 0 0
\(321\) −7.41626 8.64518i −0.413935 0.482527i
\(322\) 0 0
\(323\) 23.1668i 1.28903i
\(324\) 0 0
\(325\) 1.90207i 0.105508i
\(326\) 0 0
\(327\) 1.69903 + 1.98057i 0.0939567 + 0.109526i
\(328\) 0 0
\(329\) −29.3213 16.9287i −1.61654 0.933307i
\(330\) 0 0
\(331\) 3.13258 + 5.42579i 0.172182 + 0.298228i 0.939183 0.343418i \(-0.111585\pi\)
−0.767000 + 0.641647i \(0.778252\pi\)
\(332\) 0 0
\(333\) 6.00000 + 0.923574i 0.328798 + 0.0506116i
\(334\) 0 0
\(335\) 4.15809 + 7.20202i 0.227181 + 0.393489i
\(336\) 0 0
\(337\) −6.71414 + 11.6292i −0.365743 + 0.633485i −0.988895 0.148616i \(-0.952518\pi\)
0.623152 + 0.782100i \(0.285852\pi\)
\(338\) 0 0
\(339\) 25.8306 4.84554i 1.40292 0.263174i
\(340\) 0 0
\(341\) 4.61162 0.249733
\(342\) 0 0
\(343\) 31.6108i 1.70682i
\(344\) 0 0
\(345\) 23.3547 + 8.21322i 1.25738 + 0.442185i
\(346\) 0 0
\(347\) −17.2324 9.94913i −0.925084 0.534097i −0.0398305 0.999206i \(-0.512682\pi\)
−0.885253 + 0.465109i \(0.846015\pi\)
\(348\) 0 0
\(349\) 15.8218 9.13475i 0.846924 0.488972i −0.0126878 0.999920i \(-0.504039\pi\)
0.859612 + 0.510948i \(0.170705\pi\)
\(350\) 0 0
\(351\) −0.369466 11.2933i −0.0197206 0.602789i
\(352\) 0 0
\(353\) −13.9143 + 8.03343i −0.740584 + 0.427576i −0.822281 0.569081i \(-0.807299\pi\)
0.0816978 + 0.996657i \(0.473966\pi\)
\(354\) 0 0
\(355\) 2.81830 4.88144i 0.149580 0.259080i
\(356\) 0 0
\(357\) −29.1905 10.2655i −1.54493 0.543309i
\(358\) 0 0
\(359\) −7.57725 −0.399912 −0.199956 0.979805i \(-0.564080\pi\)
−0.199956 + 0.979805i \(0.564080\pi\)
\(360\) 0 0
\(361\) 16.1668 0.850882
\(362\) 0 0
\(363\) 2.44015 + 13.0079i 0.128075 + 0.682739i
\(364\) 0 0
\(365\) 2.88381 4.99490i 0.150945 0.261445i
\(366\) 0 0
\(367\) −1.70047 + 0.981768i −0.0887639 + 0.0512479i −0.543725 0.839263i \(-0.682987\pi\)
0.454961 + 0.890511i \(0.349653\pi\)
\(368\) 0 0
\(369\) 22.6947 28.2762i 1.18144 1.47200i
\(370\) 0 0
\(371\) 15.7532 9.09510i 0.817864 0.472194i
\(372\) 0 0
\(373\) 26.6400 + 15.3806i 1.37937 + 0.796379i 0.992083 0.125582i \(-0.0400797\pi\)
0.387285 + 0.921960i \(0.373413\pi\)
\(374\) 0 0
\(375\) 13.1446 11.2761i 0.678783 0.582293i
\(376\) 0 0
\(377\) 3.37914i 0.174035i
\(378\) 0 0
\(379\) −33.6044 −1.72614 −0.863071 0.505083i \(-0.831462\pi\)
−0.863071 + 0.505083i \(0.831462\pi\)
\(380\) 0 0
\(381\) 10.3143 + 12.0235i 0.528419 + 0.615982i
\(382\) 0 0
\(383\) −13.3876 + 23.1880i −0.684076 + 1.18485i 0.289651 + 0.957132i \(0.406461\pi\)
−0.973726 + 0.227721i \(0.926872\pi\)
\(384\) 0 0
\(385\) 23.9277 + 41.4440i 1.21947 + 2.11218i
\(386\) 0 0
\(387\) −5.56562 + 2.16426i −0.282916 + 0.110016i
\(388\) 0 0
\(389\) 11.4260 + 19.7905i 0.579323 + 1.00342i 0.995557 + 0.0941591i \(0.0300162\pi\)
−0.416234 + 0.909257i \(0.636650\pi\)
\(390\) 0 0
\(391\) −19.9513 11.5189i −1.00898 0.582535i
\(392\) 0 0
\(393\) 13.5781 2.54711i 0.684925 0.128485i
\(394\) 0 0
\(395\) 15.0617i 0.757836i
\(396\) 0 0
\(397\) 19.2780i 0.967536i 0.875196 + 0.483768i \(0.160732\pi\)
−0.875196 + 0.483768i \(0.839268\pi\)
\(398\) 0 0
\(399\) −15.5829 + 44.3108i −0.780121 + 2.21831i
\(400\) 0 0
\(401\) −1.98112 1.14380i −0.0989323 0.0571186i 0.449718 0.893171i \(-0.351525\pi\)
−0.548650 + 0.836052i \(0.684858\pi\)
\(402\) 0 0
\(403\) −1.16133 2.01149i −0.0578501 0.100199i
\(404\) 0 0
\(405\) 16.0834 14.7369i 0.799189 0.732281i
\(406\) 0 0
\(407\) 4.36839 + 7.56627i 0.216533 + 0.375046i
\(408\) 0 0
\(409\) −7.14113 + 12.3688i −0.353106 + 0.611598i −0.986792 0.161993i \(-0.948208\pi\)
0.633686 + 0.773590i \(0.281541\pi\)
\(410\) 0 0
\(411\) 0.167504 0.476306i 0.00826236 0.0234944i
\(412\) 0 0
\(413\) −1.55395 −0.0764649
\(414\) 0 0
\(415\) 15.1157i 0.741999i
\(416\) 0 0
\(417\) 4.70580 + 25.0857i 0.230444 + 1.22845i
\(418\) 0 0
\(419\) −18.7485 10.8245i −0.915924 0.528809i −0.0335917 0.999436i \(-0.510695\pi\)
−0.882333 + 0.470627i \(0.844028\pi\)
\(420\) 0 0
\(421\) 17.1351 9.89297i 0.835115 0.482154i −0.0204860 0.999790i \(-0.506521\pi\)
0.855601 + 0.517636i \(0.173188\pi\)
\(422\) 0 0
\(423\) −20.7011 + 8.04988i −1.00652 + 0.391399i
\(424\) 0 0
\(425\) 2.95929 1.70855i 0.143547 0.0828766i
\(426\) 0 0
\(427\) −21.9956 + 38.0974i −1.06444 + 1.84366i
\(428\) 0 0
\(429\) 12.3425 10.5880i 0.595902 0.511193i
\(430\) 0 0
\(431\) 17.3865 0.837480 0.418740 0.908106i \(-0.362472\pi\)
0.418740 + 0.908106i \(0.362472\pi\)
\(432\) 0 0
\(433\) −34.9223 −1.67826 −0.839128 0.543933i \(-0.816934\pi\)
−0.839128 + 0.543933i \(0.816934\pi\)
\(434\) 0 0
\(435\) −4.95140 + 4.24755i −0.237401 + 0.203654i
\(436\) 0 0
\(437\) −17.4855 + 30.2857i −0.836444 + 1.44876i
\(438\) 0 0
\(439\) −18.1634 + 10.4867i −0.866894 + 0.500501i −0.866315 0.499498i \(-0.833518\pi\)
−0.000579038 1.00000i \(0.500184\pi\)
\(440\) 0 0
\(441\) −32.5500 26.1249i −1.55000 1.24404i
\(442\) 0 0
\(443\) 27.2999 15.7616i 1.29706 0.748857i 0.317164 0.948371i \(-0.397270\pi\)
0.979895 + 0.199514i \(0.0639363\pi\)
\(444\) 0 0
\(445\) −10.2951 5.94389i −0.488035 0.281767i
\(446\) 0 0
\(447\) 5.01887 + 26.7546i 0.237385 + 1.26545i
\(448\) 0 0
\(449\) 7.30467i 0.344728i −0.985033 0.172364i \(-0.944859\pi\)
0.985033 0.172364i \(-0.0551406\pi\)
\(450\) 0 0
\(451\) 52.1808 2.45710
\(452\) 0 0
\(453\) 3.71476 10.5631i 0.174535 0.496299i
\(454\) 0 0
\(455\) 12.0513 20.8735i 0.564975 0.978565i
\(456\) 0 0
\(457\) −8.44587 14.6287i −0.395081 0.684300i 0.598031 0.801473i \(-0.295950\pi\)
−0.993112 + 0.117173i \(0.962617\pi\)
\(458\) 0 0
\(459\) −17.2384 + 10.7190i −0.804621 + 0.500322i
\(460\) 0 0
\(461\) −9.41205 16.3021i −0.438363 0.759267i 0.559201 0.829032i \(-0.311108\pi\)
−0.997563 + 0.0697657i \(0.977775\pi\)
\(462\) 0 0
\(463\) 2.94364 + 1.69951i 0.136803 + 0.0789830i 0.566839 0.823828i \(-0.308166\pi\)
−0.430037 + 0.902811i \(0.641499\pi\)
\(464\) 0 0
\(465\) 1.48761 4.23010i 0.0689864 0.196166i
\(466\) 0 0
\(467\) 12.8423i 0.594269i −0.954836 0.297134i \(-0.903969\pi\)
0.954836 0.297134i \(-0.0960310\pi\)
\(468\) 0 0
\(469\) 15.6904i 0.724515i
\(470\) 0 0
\(471\) −0.623024 + 0.116873i −0.0287074 + 0.00538521i
\(472\) 0 0
\(473\) −7.44281 4.29711i −0.342221 0.197581i
\(474\) 0 0
\(475\) −2.59354 4.49215i −0.119000 0.206114i
\(476\) 0 0
\(477\) 1.81548 11.7943i 0.0831252 0.540023i
\(478\) 0 0
\(479\) −14.3334 24.8261i −0.654908 1.13433i −0.981917 0.189313i \(-0.939374\pi\)
0.327009 0.945021i \(-0.393959\pi\)
\(480\) 0 0
\(481\) 2.20016 3.81079i 0.100319 0.173757i
\(482\) 0 0
\(483\) −30.4125 35.4521i −1.38382 1.61312i
\(484\) 0 0
\(485\) 6.40151 0.290677
\(486\) 0 0
\(487\) 3.53286i 0.160089i −0.996791 0.0800446i \(-0.974494\pi\)
0.996791 0.0800446i \(-0.0255063\pi\)
\(488\) 0 0
\(489\) −1.16343 + 0.998047i −0.0526121 + 0.0451332i
\(490\) 0 0
\(491\) −20.4103 11.7839i −0.921104 0.531800i −0.0371168 0.999311i \(-0.511817\pi\)
−0.883987 + 0.467511i \(0.845151\pi\)
\(492\) 0 0
\(493\) 5.25735 3.03533i 0.236779 0.136705i
\(494\) 0 0
\(495\) 31.0288 + 4.77623i 1.39464 + 0.214676i
\(496\) 0 0
\(497\) −9.20996 + 5.31737i −0.413123 + 0.238517i
\(498\) 0 0
\(499\) 4.12641 7.14715i 0.184724 0.319951i −0.758760 0.651371i \(-0.774194\pi\)
0.943483 + 0.331420i \(0.107528\pi\)
\(500\) 0 0
\(501\) −1.54071 8.21322i −0.0688340 0.366940i
\(502\) 0 0
\(503\) −18.4591 −0.823049 −0.411525 0.911399i \(-0.635004\pi\)
−0.411525 + 0.911399i \(0.635004\pi\)
\(504\) 0 0
\(505\) −36.1061 −1.60670
\(506\) 0 0
\(507\) 13.5150 + 4.75286i 0.600222 + 0.211082i
\(508\) 0 0
\(509\) 12.7057 22.0068i 0.563168 0.975436i −0.434049 0.900889i \(-0.642916\pi\)
0.997218 0.0745468i \(-0.0237510\pi\)
\(510\) 0 0
\(511\) −9.42403 + 5.44097i −0.416895 + 0.240694i
\(512\) 0 0
\(513\) 16.2713 + 26.1677i 0.718397 + 1.15533i
\(514\) 0 0
\(515\) −37.1932 + 21.4735i −1.63893 + 0.946236i
\(516\) 0 0
\(517\) −27.6832 15.9829i −1.21751 0.702928i
\(518\) 0 0
\(519\) 1.11783 + 0.393111i 0.0490673 + 0.0172556i
\(520\) 0 0
\(521\) 9.82832i 0.430587i −0.976549 0.215293i \(-0.930929\pi\)
0.976549 0.215293i \(-0.0690707\pi\)
\(522\) 0 0
\(523\) 3.21054 0.140387 0.0701936 0.997533i \(-0.477638\pi\)
0.0701936 + 0.997533i \(0.477638\pi\)
\(524\) 0 0
\(525\) 6.80943 1.27738i 0.297188 0.0557493i
\(526\) 0 0
\(527\) −2.08635 + 3.61366i −0.0908827 + 0.157413i
\(528\) 0 0
\(529\) −5.88812 10.1985i −0.256005 0.443414i
\(530\) 0 0
\(531\) −0.638094 + 0.795026i −0.0276909 + 0.0345012i
\(532\) 0 0
\(533\) −13.1406 22.7601i −0.569181 0.985851i
\(534\) 0 0
\(535\) −13.8038 7.96965i −0.596792 0.344558i
\(536\) 0 0
\(537\) 14.4384 + 16.8310i 0.623065 + 0.726311i
\(538\) 0 0
\(539\) 60.0676i 2.58729i
\(540\) 0 0
\(541\) 13.3394i 0.573507i −0.958004 0.286754i \(-0.907424\pi\)
0.958004 0.286754i \(-0.0925761\pi\)
\(542\) 0 0
\(543\) 25.6346 + 29.8825i 1.10009 + 1.28238i
\(544\) 0 0
\(545\) 3.16240 + 1.82581i 0.135462 + 0.0782092i
\(546\) 0 0
\(547\) 5.21266 + 9.02859i 0.222877 + 0.386035i 0.955680 0.294406i \(-0.0951217\pi\)
−0.732803 + 0.680441i \(0.761788\pi\)
\(548\) 0 0
\(549\) 10.4593 + 26.8971i 0.446391 + 1.14794i
\(550\) 0 0
\(551\) −4.60759 7.98057i −0.196290 0.339984i
\(552\) 0 0
\(553\) 14.2087 24.6102i 0.604215 1.04653i
\(554\) 0 0
\(555\) 8.34946 1.56627i 0.354415 0.0664845i
\(556\) 0 0
\(557\) −21.2479 −0.900301 −0.450151 0.892953i \(-0.648630\pi\)
−0.450151 + 0.892953i \(0.648630\pi\)
\(558\) 0 0
\(559\) 4.32852i 0.183077i
\(560\) 0 0
\(561\) −27.5598 9.69203i −1.16357 0.409198i
\(562\) 0 0
\(563\) −7.30513 4.21762i −0.307875 0.177752i 0.338100 0.941110i \(-0.390216\pi\)
−0.645975 + 0.763359i \(0.723549\pi\)
\(564\) 0 0
\(565\) 31.8498 18.3885i 1.33993 0.773610i
\(566\) 0 0
\(567\) −40.1818 + 8.90691i −1.68748 + 0.374055i
\(568\) 0 0
\(569\) 32.1996 18.5905i 1.34988 0.779353i 0.361646 0.932315i \(-0.382215\pi\)
0.988232 + 0.152963i \(0.0488815\pi\)
\(570\) 0 0
\(571\) −1.30606 + 2.26216i −0.0546569 + 0.0946686i −0.892059 0.451918i \(-0.850740\pi\)
0.837402 + 0.546587i \(0.184073\pi\)
\(572\) 0 0
\(573\) 35.5828 + 12.5135i 1.48649 + 0.522760i
\(574\) 0 0
\(575\) 5.15821 0.215112
\(576\) 0 0
\(577\) −10.2993 −0.428765 −0.214383 0.976750i \(-0.568774\pi\)
−0.214383 + 0.976750i \(0.568774\pi\)
\(578\) 0 0
\(579\) −7.40361 39.4671i −0.307683 1.64020i
\(580\) 0 0
\(581\) 14.2596 24.6984i 0.591588 1.02466i
\(582\) 0 0
\(583\) 14.8731 8.58700i 0.615981 0.355637i
\(584\) 0 0
\(585\) −5.73062 14.7369i −0.236932 0.609295i
\(586\) 0 0
\(587\) −33.0046 + 19.0552i −1.36225 + 0.786493i −0.989923 0.141610i \(-0.954772\pi\)
−0.372324 + 0.928103i \(0.621439\pi\)
\(588\) 0 0
\(589\) 5.48547 + 3.16704i 0.226025 + 0.130496i
\(590\) 0 0
\(591\) 31.4292 26.9615i 1.29283 1.10905i
\(592\) 0 0
\(593\) 20.4440i 0.839536i −0.907631 0.419768i \(-0.862111\pi\)
0.907631 0.419768i \(-0.137889\pi\)
\(594\) 0 0
\(595\) −43.3006 −1.77515
\(596\) 0 0
\(597\) 2.13338 + 2.48690i 0.0873135 + 0.101782i
\(598\) 0 0
\(599\) 2.49234 4.31686i 0.101834 0.176382i −0.810606 0.585592i \(-0.800862\pi\)
0.912440 + 0.409210i \(0.134196\pi\)
\(600\) 0 0
\(601\) −1.00184 1.73524i −0.0408661 0.0707821i 0.844869 0.534973i \(-0.179678\pi\)
−0.885735 + 0.464191i \(0.846345\pi\)
\(602\) 0 0
\(603\) −8.02746 6.44290i −0.326903 0.262375i
\(604\) 0 0
\(605\) 9.26020 + 16.0391i 0.376481 + 0.652083i
\(606\) 0 0
\(607\) −2.75082 1.58819i −0.111653 0.0644626i 0.443134 0.896455i \(-0.353867\pi\)
−0.554786 + 0.831993i \(0.687200\pi\)
\(608\) 0 0
\(609\) 12.0974 2.26934i 0.490210 0.0919581i
\(610\) 0 0
\(611\) 16.0998i 0.651327i
\(612\) 0 0
\(613\) 4.38768i 0.177217i 0.996067 + 0.0886083i \(0.0282419\pi\)
−0.996067 + 0.0886083i \(0.971758\pi\)
\(614\) 0 0
\(615\) 16.8324 47.8639i 0.678749 1.93006i
\(616\) 0 0
\(617\) 5.29984 + 3.05986i 0.213363 + 0.123185i 0.602874 0.797837i \(-0.294022\pi\)
−0.389510 + 0.921022i \(0.627356\pi\)
\(618\) 0 0
\(619\) −18.1785 31.4861i −0.730656 1.26553i −0.956603 0.291394i \(-0.905881\pi\)
0.225947 0.974140i \(-0.427452\pi\)
\(620\) 0 0
\(621\) −30.6260 + 1.00195i −1.22898 + 0.0402069i
\(622\) 0 0
\(623\) 11.2145 + 19.4241i 0.449300 + 0.778210i
\(624\) 0 0
\(625\) 14.3042 24.7756i 0.572168 0.991024i
\(626\) 0 0
\(627\) −14.7123 + 41.8353i −0.587554 + 1.67074i
\(628\) 0 0
\(629\) −7.90522 −0.315202
\(630\) 0 0
\(631\) 37.8249i 1.50579i 0.658143 + 0.752893i \(0.271342\pi\)
−0.658143 + 0.752893i \(0.728658\pi\)
\(632\) 0 0
\(633\) −8.04831 42.9039i −0.319892 1.70528i
\(634\) 0 0
\(635\) 19.1980 + 11.0840i 0.761849 + 0.439854i
\(636\) 0 0
\(637\) −26.2002 + 15.1267i −1.03809 + 0.599340i
\(638\) 0 0
\(639\) −1.06141 + 6.89542i −0.0419886 + 0.272779i
\(640\) 0 0
\(641\) −24.7993 + 14.3179i −0.979513 + 0.565522i −0.902123 0.431479i \(-0.857992\pi\)
−0.0773901 + 0.997001i \(0.524659\pi\)
\(642\) 0 0
\(643\) 9.04767 15.6710i 0.356805 0.618005i −0.630620 0.776092i \(-0.717199\pi\)
0.987425 + 0.158087i \(0.0505327\pi\)
\(644\) 0 0
\(645\) −6.34250 + 5.44091i −0.249736 + 0.214236i
\(646\) 0 0
\(647\) −0.594123 −0.0233574 −0.0116787 0.999932i \(-0.503718\pi\)
−0.0116787 + 0.999932i \(0.503718\pi\)
\(648\) 0 0
\(649\) −1.46714 −0.0575902
\(650\) 0 0
\(651\) −6.42122 + 5.50844i −0.251668 + 0.215893i
\(652\) 0 0
\(653\) 2.76584 4.79057i 0.108236 0.187470i −0.806820 0.590797i \(-0.798813\pi\)
0.915056 + 0.403328i \(0.132147\pi\)
\(654\) 0 0
\(655\) 16.7422 9.66610i 0.654171 0.377686i
\(656\) 0 0
\(657\) −1.08608 + 7.05569i −0.0423719 + 0.275269i
\(658\) 0 0
\(659\) 2.32903 1.34467i 0.0907262 0.0523808i −0.453950 0.891027i \(-0.649986\pi\)
0.544677 + 0.838646i \(0.316652\pi\)
\(660\) 0 0
\(661\) 31.9642 + 18.4545i 1.24326 + 0.717798i 0.969757 0.244072i \(-0.0784834\pi\)
0.273506 + 0.961870i \(0.411817\pi\)
\(662\) 0 0
\(663\) 2.71286 + 14.4617i 0.105359 + 0.561646i
\(664\) 0 0
\(665\) 65.7297i 2.54889i
\(666\) 0 0
\(667\) 9.16386 0.354826
\(668\) 0 0
\(669\) 5.58474 15.8805i 0.215919 0.613975i
\(670\) 0 0
\(671\) −20.7668 + 35.9691i −0.801692 + 1.38857i
\(672\) 0 0
\(673\) −10.5243 18.2287i −0.405684 0.702665i 0.588717 0.808339i \(-0.299633\pi\)
−0.994401 + 0.105674i \(0.966300\pi\)
\(674\) 0 0
\(675\) 2.14261 4.00834i 0.0824691 0.154281i
\(676\) 0 0
\(677\) −1.23701 2.14256i −0.0475420 0.0823451i 0.841275 0.540607i \(-0.181805\pi\)
−0.888817 + 0.458262i \(0.848472\pi\)
\(678\) 0 0
\(679\) −10.4598 6.03896i −0.401410 0.231754i
\(680\) 0 0
\(681\) −5.65695 + 16.0858i −0.216775 + 0.616410i
\(682\) 0 0
\(683\) 1.37923i 0.0527749i 0.999652 + 0.0263875i \(0.00840036\pi\)
−0.999652 + 0.0263875i \(0.991600\pi\)
\(684\) 0 0
\(685\) 0.706542i 0.0269956i
\(686\) 0 0
\(687\) −38.1389 + 7.15446i −1.45509 + 0.272960i
\(688\) 0 0
\(689\) −7.49092 4.32488i −0.285381 0.164765i
\(690\) 0 0
\(691\) 1.71132 + 2.96410i 0.0651018 + 0.112760i 0.896739 0.442559i \(-0.145929\pi\)
−0.831637 + 0.555319i \(0.812596\pi\)
\(692\) 0 0
\(693\) −46.1940 37.0756i −1.75476 1.40839i
\(694\) 0 0
\(695\) 17.8582 + 30.9313i 0.677400 + 1.17329i
\(696\) 0 0
\(697\) −23.6072 + 40.8888i −0.894185 + 1.54877i
\(698\) 0 0
\(699\) 15.0839 + 17.5834i 0.570525 + 0.665064i
\(700\) 0 0
\(701\) 21.2981 0.804419 0.402209 0.915548i \(-0.368242\pi\)
0.402209 + 0.915548i \(0.368242\pi\)
\(702\) 0 0
\(703\) 12.0000i 0.452589i
\(704\) 0 0
\(705\) −23.5907 + 20.2372i −0.888476 + 0.762178i
\(706\) 0 0
\(707\) 58.9957 + 34.0612i 2.21876 + 1.28100i
\(708\) 0 0
\(709\) −15.5213 + 8.96122i −0.582914 + 0.336546i −0.762291 0.647235i \(-0.775925\pi\)
0.179377 + 0.983780i \(0.442592\pi\)
\(710\) 0 0
\(711\) −6.75648 17.3750i −0.253388 0.651613i
\(712\) 0 0
\(713\) −5.45493 + 3.14941i −0.204289 + 0.117946i
\(714\) 0 0
\(715\) 11.3781 19.7074i 0.425515 0.737014i
\(716\) 0 0
\(717\) 2.51711 + 13.4182i 0.0940031 + 0.501111i
\(718\) 0 0
\(719\) −24.7546 −0.923190 −0.461595 0.887091i \(-0.652723\pi\)
−0.461595 + 0.887091i \(0.652723\pi\)
\(720\) 0 0
\(721\) 81.0294 3.01769
\(722\) 0 0
\(723\) 22.8914 + 8.05029i 0.851341 + 0.299394i
\(724\) 0 0
\(725\) −0.679618 + 1.17713i −0.0252404 + 0.0437176i
\(726\) 0 0
\(727\) 24.6871 14.2531i 0.915594 0.528618i 0.0333669 0.999443i \(-0.489377\pi\)
0.882227 + 0.470825i \(0.156044\pi\)
\(728\) 0 0
\(729\) −11.9428 + 24.2151i −0.442326 + 0.896854i
\(730\) 0 0
\(731\) 6.73442 3.88812i 0.249081 0.143807i
\(732\) 0 0
\(733\) −10.8260 6.25041i −0.399868 0.230864i 0.286559 0.958063i \(-0.407489\pi\)
−0.686427 + 0.727199i \(0.740822\pi\)
\(734\) 0 0
\(735\) −55.0982 19.3765i −2.03233 0.714714i
\(736\) 0 0
\(737\) 14.8138i 0.545674i
\(738\) 0 0
\(739\) 6.72166 0.247260 0.123630 0.992328i \(-0.460546\pi\)
0.123630 + 0.992328i \(0.460546\pi\)
\(740\) 0 0
\(741\) 21.9526 4.11808i 0.806449 0.151281i
\(742\) 0 0
\(743\) 12.3951 21.4690i 0.454733 0.787621i −0.543939 0.839124i \(-0.683068\pi\)
0.998673 + 0.0515032i \(0.0164012\pi\)
\(744\) 0 0
\(745\) 19.0463 + 32.9891i 0.697802 + 1.20863i
\(746\) 0 0
\(747\) −6.78070 17.4373i −0.248093 0.637996i
\(748\) 0 0
\(749\) 15.0366 + 26.0441i 0.549425 + 0.951631i
\(750\) 0 0
\(751\) 34.6991 + 20.0335i 1.26619 + 0.731033i 0.974264 0.225409i \(-0.0723718\pi\)
0.291922 + 0.956442i \(0.405705\pi\)
\(752\) 0 0
\(753\) −18.3498 21.3905i −0.668704 0.779513i
\(754\) 0 0
\(755\) 15.6691i 0.570257i
\(756\) 0 0
\(757\) 14.5925i 0.530372i −0.964197 0.265186i \(-0.914567\pi\)
0.964197 0.265186i \(-0.0854334\pi\)
\(758\) 0 0
\(759\) −28.7135 33.4715i −1.04223 1.21494i
\(760\) 0 0
\(761\) 1.95502 + 1.12873i 0.0708693 + 0.0409164i 0.535016 0.844842i \(-0.320306\pi\)
−0.464147 + 0.885758i \(0.653639\pi\)
\(762\) 0 0
\(763\) −3.44481 5.96659i −0.124711 0.216005i
\(764\) 0 0
\(765\) −17.7804 + 22.1533i −0.642852 + 0.800954i
\(766\) 0 0
\(767\) 0.369466 + 0.639933i 0.0133406 + 0.0231067i
\(768\) 0 0
\(769\) 4.55775 7.89426i 0.164357 0.284674i −0.772070 0.635538i \(-0.780779\pi\)
0.936427 + 0.350863i \(0.114112\pi\)
\(770\) 0 0
\(771\) −4.05348 + 0.760389i −0.145982 + 0.0273847i
\(772\) 0 0
\(773\) 49.6226 1.78480 0.892401 0.451244i \(-0.149020\pi\)
0.892401 + 0.451244i \(0.149020\pi\)
\(774\) 0 0
\(775\) 0.934275i 0.0335602i
\(776\) 0 0
\(777\) −15.1202 5.31737i −0.542435 0.190760i
\(778\) 0 0
\(779\) 62.0685 + 35.8353i 2.22384 + 1.28393i
\(780\) 0 0
\(781\) −8.69544 + 5.02031i −0.311147 + 0.179641i
\(782\) 0 0
\(783\) 3.80647 7.12105i 0.136032 0.254486i
\(784\) 0 0
\(785\) −0.768206 + 0.443524i −0.0274184 + 0.0158300i
\(786\) 0 0
\(787\) −17.1621 + 29.7257i −0.611765 + 1.05961i 0.379178 + 0.925324i \(0.376207\pi\)
−0.990943 + 0.134284i \(0.957127\pi\)
\(788\) 0 0
\(789\) 30.8122 + 10.8358i 1.09694 + 0.385766i
\(790\) 0 0
\(791\) −69.3883 −2.46716
\(792\) 0 0
\(793\) 20.9186 0.742840
\(794\) 0 0
\(795\) −3.07884 16.4126i −0.109195 0.582096i
\(796\) 0 0
\(797\) −14.9392 + 25.8755i −0.529174 + 0.916557i 0.470247 + 0.882535i \(0.344165\pi\)
−0.999421 + 0.0340219i \(0.989168\pi\)
\(798\) 0 0
\(799\) 25.0484 14.4617i 0.886148 0.511618i
\(800\) 0 0
\(801\) 14.5427 + 2.23854i 0.513840 + 0.0790949i
\(802\) 0 0
\(803\) −8.89755 + 5.13700i −0.313988 + 0.181281i
\(804\) 0 0
\(805\) −56.6066 32.6818i −1.99512 1.15188i
\(806\) 0 0
\(807\) 15.2534 13.0852i 0.536947 0.460619i
\(808\) 0 0
\(809\) 3.31248i 0.116461i 0.998303 + 0.0582303i \(0.0185458\pi\)
−0.998303 + 0.0582303i \(0.981454\pi\)
\(810\) 0 0
\(811\) 31.5697 1.10856 0.554281 0.832329i \(-0.312993\pi\)
0.554281 + 0.832329i \(0.312993\pi\)
\(812\) 0 0
\(813\) −4.22834 4.92900i −0.148294 0.172868i
\(814\) 0 0
\(815\) −1.07252 + 1.85766i −0.0375687 + 0.0650709i
\(816\) 0 0
\(817\) −5.90210 10.2227i −0.206488 0.357648i
\(818\) 0 0
\(819\) −4.53867 + 29.4855i −0.158594 + 1.03031i
\(820\) 0 0
\(821\) 4.94041 + 8.55703i 0.172421 + 0.298643i 0.939266 0.343190i \(-0.111508\pi\)
−0.766845 + 0.641833i \(0.778174\pi\)
\(822\) 0 0
\(823\) 25.4921 + 14.7178i 0.888597 + 0.513032i 0.873483 0.486854i \(-0.161856\pi\)
0.0151139 + 0.999886i \(0.495189\pi\)
\(824\) 0 0
\(825\) 6.42901 1.20601i 0.223829 0.0419880i
\(826\) 0 0
\(827\) 25.9774i 0.903324i 0.892189 + 0.451662i \(0.149169\pi\)
−0.892189 + 0.451662i \(0.850831\pi\)
\(828\) 0 0
\(829\) 35.0365i 1.21687i 0.793604 + 0.608434i \(0.208202\pi\)
−0.793604 + 0.608434i \(0.791798\pi\)
\(830\) 0 0
\(831\) 6.76634 19.2404i 0.234722 0.667443i
\(832\) 0 0
\(833\) 47.0689 + 27.1752i 1.63084 + 0.941565i
\(834\) 0 0
\(835\) −5.84690 10.1271i −0.202340 0.350464i
\(836\) 0 0
\(837\) 0.181477 + 5.54711i 0.00627277 + 0.191736i
\(838\) 0 0
\(839\) 23.9724 + 41.5214i 0.827618 + 1.43348i 0.899902 + 0.436093i \(0.143638\pi\)
−0.0722833 + 0.997384i \(0.523029\pi\)
\(840\) 0 0
\(841\) 13.2926 23.0235i 0.458366 0.793913i
\(842\) 0 0
\(843\) 4.88922 13.9027i 0.168394 0.478835i
\(844\) 0 0
\(845\) 20.0479 0.689668
\(846\) 0 0
\(847\) 34.9430i 1.20066i
\(848\) 0 0
\(849\) 3.37414 + 17.9868i 0.115800 + 0.617306i
\(850\) 0 0
\(851\) −10.3344 5.96659i −0.354260 0.204532i
\(852\) 0 0
\(853\) −42.4065 + 24.4834i −1.45197 + 0.838295i −0.998593 0.0530245i \(-0.983114\pi\)
−0.453376 + 0.891319i \(0.649781\pi\)
\(854\) 0 0
\(855\) 33.6283 + 26.9904i 1.15007 + 0.923051i
\(856\) 0 0
\(857\) 41.0598 23.7059i 1.40258 0.809777i 0.407919 0.913018i \(-0.366255\pi\)
0.994656 + 0.103241i \(0.0329213\pi\)
\(858\) 0 0
\(859\) −1.42404 + 2.46650i −0.0485875 + 0.0841560i −0.889296 0.457331i \(-0.848805\pi\)
0.840709 + 0.541487i \(0.182139\pi\)
\(860\) 0 0
\(861\) −72.6566 + 62.3284i −2.47613 + 2.12414i
\(862\) 0 0
\(863\) 23.5015 0.800002 0.400001 0.916515i \(-0.369010\pi\)
0.400001 + 0.916515i \(0.369010\pi\)
\(864\) 0 0
\(865\) 1.65817 0.0563793
\(866\) 0 0
\(867\) −2.28541 + 1.96054i −0.0776167 + 0.0665834i
\(868\) 0 0
\(869\) 13.4149 23.2353i 0.455069 0.788203i
\(870\) 0 0
\(871\) −6.46147 + 3.73053i −0.218939 + 0.126404i
\(872\) 0 0
\(873\) −7.38470 + 2.87163i −0.249934 + 0.0971900i
\(874\) 0 0
\(875\) −39.5988 + 22.8624i −1.33868 + 0.772889i
\(876\) 0 0
\(877\) 35.5743 + 20.5388i 1.20126 + 0.693547i 0.960835 0.277121i \(-0.0893803\pi\)
0.240424 + 0.970668i \(0.422714\pi\)
\(878\) 0 0
\(879\) −8.84571 47.1546i −0.298358 1.59049i
\(880\) 0 0
\(881\) 28.4932i 0.959960i 0.877279 + 0.479980i \(0.159356\pi\)
−0.877279 + 0.479980i \(0.840644\pi\)
\(882\) 0 0
\(883\) −25.6755 −0.864048 −0.432024 0.901862i \(-0.642200\pi\)
−0.432024 + 0.901862i \(0.642200\pi\)
\(884\) 0 0
\(885\) −0.473268 + 1.34576i −0.0159087 + 0.0452373i
\(886\) 0 0
\(887\) 15.2134 26.3504i 0.510817 0.884761i −0.489104 0.872225i \(-0.662676\pi\)
0.999921 0.0125359i \(-0.00399041\pi\)
\(888\) 0 0
\(889\) −20.9125 36.2214i −0.701381 1.21483i
\(890\) 0 0
\(891\) −37.9370 + 8.40931i −1.27094 + 0.281723i
\(892\) 0 0
\(893\) −21.9526 38.0230i −0.734616 1.27239i
\(894\) 0 0
\(895\) 26.8742 + 15.5158i 0.898305 + 0.518637i
\(896\) 0 0
\(897\) −7.36869 + 20.9532i −0.246033 + 0.699608i
\(898\) 0 0
\(899\) 1.65980i 0.0553573i
\(900\) 0 0
\(901\) 15.5394i 0.517692i
\(902\) 0 0
\(903\) 15.4961 2.90691i 0.515679 0.0967359i
\(904\) 0 0
\(905\) 47.7136 + 27.5475i 1.58605 + 0.915708i
\(906\) 0 0
\(907\) 18.9318 + 32.7908i 0.628620 + 1.08880i 0.987829 + 0.155545i \(0.0497133\pi\)
−0.359209 + 0.933257i \(0.616953\pi\)
\(908\) 0 0
\(909\) 41.6515 16.1967i 1.38149 0.537211i
\(910\) 0 0
\(911\) −13.5579 23.4830i −0.449193 0.778026i 0.549140 0.835730i \(-0.314955\pi\)
−0.998334 + 0.0577043i \(0.981622\pi\)
\(912\) 0 0
\(913\) 13.4630 23.3186i 0.445559 0.771732i
\(914\) 0 0
\(915\) 26.2944 + 30.6516i 0.869267 + 1.01331i
\(916\) 0 0
\(917\) −36.4747 −1.20450
\(918\) 0 0
\(919\) 20.1170i 0.663598i −0.943350 0.331799i \(-0.892344\pi\)
0.943350 0.331799i \(-0.107656\pi\)
\(920\) 0 0
\(921\) 23.6978 20.3291i 0.780868 0.669866i
\(922\) 0 0
\(923\) 4.37950 + 2.52851i 0.144153 + 0.0832268i
\(924\) 0 0
\(925\) 1.53286 0.884999i 0.0504002 0.0290986i
\(926\) 0 0
\(927\) 33.2729 41.4560i 1.09282 1.36159i
\(928\) 0 0
\(929\) −17.3881 + 10.0390i −0.570486 + 0.329370i −0.757343 0.653017i \(-0.773503\pi\)
0.186858 + 0.982387i \(0.440170\pi\)
\(930\) 0 0
\(931\) 41.2515 71.4497i 1.35196 2.34167i
\(932\) 0 0
\(933\) 9.55469 + 50.9341i 0.312807 + 1.66751i
\(934\) 0 0
\(935\) −40.8816 −1.33697
\(936\) 0 0
\(937\) −20.9648 −0.684891 −0.342446 0.939538i \(-0.611255\pi\)
−0.342446 + 0.939538i \(0.611255\pi\)
\(938\) 0 0
\(939\) −40.9166 14.3893i −1.33526 0.469576i
\(940\) 0 0
\(941\) −20.4621 + 35.4415i −0.667046 + 1.15536i 0.311680 + 0.950187i \(0.399108\pi\)
−0.978726 + 0.205171i \(0.934225\pi\)
\(942\) 0 0
\(943\) −61.7229 + 35.6358i −2.00998 + 1.16046i
\(944\) 0 0
\(945\) −48.9096 + 30.4125i −1.59103 + 0.989319i
\(946\) 0 0
\(947\) 50.7982 29.3284i 1.65072 0.953044i 0.673944 0.738782i \(-0.264599\pi\)
0.976776 0.214262i \(-0.0687345\pi\)
\(948\) 0 0
\(949\) 4.48129 + 2.58728i 0.145469 + 0.0839866i
\(950\) 0 0
\(951\) 31.4614 + 11.0641i 1.02021 + 0.358779i
\(952\) 0 0
\(953\) 8.47068i 0.274392i −0.990544 0.137196i \(-0.956191\pi\)
0.990544 0.137196i \(-0.0438091\pi\)
\(954\) 0 0
\(955\) 52.7828 1.70801
\(956\) 0 0
\(957\) 11.4215 2.14256i 0.369205 0.0692590i
\(958\) 0 0
\(959\) −0.666527 + 1.15446i −0.0215233 + 0.0372794i
\(960\) 0 0
\(961\) −14.9296 25.8588i −0.481599 0.834154i
\(962\) 0 0
\(963\) 19.4990 + 3.00146i 0.628347 + 0.0967208i
\(964\) 0 0
\(965\) −28.0962 48.6640i −0.904448 1.56655i
\(966\) 0 0
\(967\) 46.1228 + 26.6290i 1.48321 + 0.856331i 0.999818 0.0190733i \(-0.00607158\pi\)
0.483391 + 0.875404i \(0.339405\pi\)
\(968\) 0 0
\(969\) −26.1260 30.4553i −0.839289 0.978365i
\(970\) 0 0
\(971\) 30.2916i 0.972105i 0.873930 + 0.486052i \(0.161564\pi\)
−0.873930 + 0.486052i \(0.838436\pi\)
\(972\) 0 0
\(973\) 67.3872i 2.16034i
\(974\) 0 0
\(975\) −2.14504 2.50049i −0.0686962 0.0800797i
\(976\) 0 0
\(977\) 38.7617 + 22.3791i 1.24010 + 0.715970i 0.969114 0.246614i \(-0.0793179\pi\)
0.270983 + 0.962584i \(0.412651\pi\)
\(978\) 0 0
\(979\) 10.5880 + 18.3390i 0.338394 + 0.586115i
\(980\) 0 0
\(981\) −4.46714 0.687622i −0.142625 0.0219541i
\(982\) 0 0
\(983\) −6.22310 10.7787i −0.198486 0.343788i 0.749552 0.661946i \(-0.230269\pi\)
−0.948038 + 0.318158i \(0.896936\pi\)
\(984\) 0 0
\(985\) 28.9733 50.1833i 0.923167 1.59897i
\(986\) 0 0
\(987\) 57.6373 10.8121i 1.83461 0.344154i
\(988\) 0 0
\(989\) 11.7385 0.373262
\(990\) 0 0
\(991\) 8.02185i 0.254822i 0.991850 + 0.127411i \(0.0406668\pi\)
−0.991850 + 0.127411i \(0.959333\pi\)
\(992\) 0 0
\(993\) −10.2370 3.60008i −0.324862 0.114245i
\(994\) 0 0
\(995\) 3.97085 + 2.29257i 0.125884 + 0.0726794i
\(996\) 0 0
\(997\) −7.14910 + 4.12754i −0.226414 + 0.130720i −0.608917 0.793234i \(-0.708396\pi\)
0.382502 + 0.923954i \(0.375062\pi\)
\(998\) 0 0
\(999\) −8.92922 + 5.55229i −0.282508 + 0.175667i
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 576.2.p.c.95.3 yes 16
3.2 odd 2 1728.2.p.a.287.8 16
4.3 odd 2 inner 576.2.p.c.95.6 yes 16
8.3 odd 2 576.2.p.a.95.3 16
8.5 even 2 576.2.p.a.95.6 yes 16
9.2 odd 6 576.2.p.a.479.3 yes 16
9.4 even 3 5184.2.f.a.2591.16 16
9.5 odd 6 5184.2.f.f.2591.4 16
9.7 even 3 1728.2.p.c.1439.1 16
12.11 even 2 1728.2.p.a.287.7 16
24.5 odd 2 1728.2.p.c.287.2 16
24.11 even 2 1728.2.p.c.287.1 16
36.7 odd 6 1728.2.p.c.1439.2 16
36.11 even 6 576.2.p.a.479.6 yes 16
36.23 even 6 5184.2.f.f.2591.2 16
36.31 odd 6 5184.2.f.a.2591.14 16
72.5 odd 6 5184.2.f.a.2591.15 16
72.11 even 6 inner 576.2.p.c.479.3 yes 16
72.13 even 6 5184.2.f.f.2591.3 16
72.29 odd 6 inner 576.2.p.c.479.6 yes 16
72.43 odd 6 1728.2.p.a.1439.8 16
72.59 even 6 5184.2.f.a.2591.13 16
72.61 even 6 1728.2.p.a.1439.7 16
72.67 odd 6 5184.2.f.f.2591.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
576.2.p.a.95.3 16 8.3 odd 2
576.2.p.a.95.6 yes 16 8.5 even 2
576.2.p.a.479.3 yes 16 9.2 odd 6
576.2.p.a.479.6 yes 16 36.11 even 6
576.2.p.c.95.3 yes 16 1.1 even 1 trivial
576.2.p.c.95.6 yes 16 4.3 odd 2 inner
576.2.p.c.479.3 yes 16 72.11 even 6 inner
576.2.p.c.479.6 yes 16 72.29 odd 6 inner
1728.2.p.a.287.7 16 12.11 even 2
1728.2.p.a.287.8 16 3.2 odd 2
1728.2.p.a.1439.7 16 72.61 even 6
1728.2.p.a.1439.8 16 72.43 odd 6
1728.2.p.c.287.1 16 24.11 even 2
1728.2.p.c.287.2 16 24.5 odd 2
1728.2.p.c.1439.1 16 9.7 even 3
1728.2.p.c.1439.2 16 36.7 odd 6
5184.2.f.a.2591.13 16 72.59 even 6
5184.2.f.a.2591.14 16 36.31 odd 6
5184.2.f.a.2591.15 16 72.5 odd 6
5184.2.f.a.2591.16 16 9.4 even 3
5184.2.f.f.2591.1 16 72.67 odd 6
5184.2.f.f.2591.2 16 36.23 even 6
5184.2.f.f.2591.3 16 72.13 even 6
5184.2.f.f.2591.4 16 9.5 odd 6