Properties

Label 288.2.p.b.239.4
Level $288$
Weight $2$
Character 288.239
Analytic conductor $2.300$
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] = [288,2,Mod(47,288)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(288, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("288.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.p (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: \(2.29969157821\)
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: \( x^{16} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 16 x^{12} - 12 x^{11} - 8 x^{10} + 36 x^{9} - 68 x^{8} + \cdots + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: no (minimal twist has level 72)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 239.4
Root \(-0.186766 - 1.40183i\) of defining polynomial
Character \(\chi\) \(=\) 288.239
Dual form 288.2.p.b.47.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.418594 - 1.68071i) q^{3} +(1.60936 - 2.78750i) q^{5} +(1.82223 - 1.05206i) q^{7} +(-2.64956 + 1.40707i) q^{9} +O(q^{10})\) \(q+(-0.418594 - 1.68071i) q^{3} +(1.60936 - 2.78750i) q^{5} +(1.82223 - 1.05206i) q^{7} +(-2.64956 + 1.40707i) q^{9} +(-3.47720 + 2.00756i) q^{11} +(0.341902 + 0.197397i) q^{13} +(-5.35864 - 1.53804i) q^{15} -1.20474i q^{17} +1.62474 q^{19} +(-2.53098 - 2.62224i) q^{21} +(2.74384 - 4.75248i) q^{23} +(-2.68011 - 4.64208i) q^{25} +(3.47396 + 3.86414i) q^{27} +(-2.95670 - 5.12116i) q^{29} +(3.34777 + 1.93284i) q^{31} +(4.82967 + 5.00381i) q^{33} -6.77261i q^{35} +10.8195i q^{37} +(0.188649 - 0.657267i) q^{39} +(-1.23849 - 0.715041i) q^{41} +(1.21569 + 2.10564i) q^{43} +(-0.341902 + 9.65013i) q^{45} +(0.792576 + 1.37278i) q^{47} +(-1.28633 + 2.22799i) q^{49} +(-2.02482 + 0.504297i) q^{51} +7.07284 q^{53} +12.9236i q^{55} +(-0.680107 - 2.73072i) q^{57} +(2.29587 + 1.32552i) q^{59} +(8.18631 - 4.72637i) q^{61} +(-3.34777 + 5.35150i) q^{63} +(1.10049 - 0.635369i) q^{65} +(2.60947 - 4.51973i) q^{67} +(-9.13608 - 2.62224i) q^{69} -2.69468 q^{71} +9.49652 q^{73} +(-6.68011 + 6.44762i) q^{75} +(-4.22417 + 7.31647i) q^{77} +(1.53599 - 0.886804i) q^{79} +(5.04032 - 7.45622i) q^{81} +(1.30809 - 0.755228i) q^{83} +(-3.35821 - 1.93887i) q^{85} +(-7.36952 + 7.11304i) q^{87} +11.2323i q^{89} +0.830698 q^{91} +(1.84718 - 6.43570i) q^{93} +(2.61480 - 4.52897i) q^{95} +(5.84818 + 10.1294i) q^{97} +(6.38828 - 10.2118i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 6 q^{3} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 6 q^{3} - 6 q^{9} - 12 q^{11} + 4 q^{19} - 14 q^{25} + 36 q^{27} + 12 q^{33} - 36 q^{41} - 8 q^{43} + 10 q^{49} - 18 q^{51} + 18 q^{57} - 12 q^{59} - 6 q^{65} + 16 q^{67} - 4 q^{73} - 78 q^{75} - 6 q^{81} - 54 q^{83} + 36 q^{91} + 8 q^{97} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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
\(3\) −0.418594 1.68071i −0.241675 0.970357i
\(4\) 0 0
\(5\) 1.60936 2.78750i 0.719730 1.24661i −0.241377 0.970431i \(-0.577599\pi\)
0.961107 0.276177i \(-0.0890676\pi\)
\(6\) 0 0
\(7\) 1.82223 1.05206i 0.688736 0.397642i −0.114402 0.993435i \(-0.536495\pi\)
0.803139 + 0.595792i \(0.203162\pi\)
\(8\) 0 0
\(9\) −2.64956 + 1.40707i −0.883186 + 0.469023i
\(10\) 0 0
\(11\) −3.47720 + 2.00756i −1.04842 + 0.605303i −0.922206 0.386700i \(-0.873615\pi\)
−0.126211 + 0.992003i \(0.540282\pi\)
\(12\) 0 0
\(13\) 0.341902 + 0.197397i 0.0948267 + 0.0547482i 0.546663 0.837352i \(-0.315898\pi\)
−0.451837 + 0.892101i \(0.649231\pi\)
\(14\) 0 0
\(15\) −5.35864 1.53804i −1.38360 0.397120i
\(16\) 0 0
\(17\) 1.20474i 0.292192i −0.989270 0.146096i \(-0.953329\pi\)
0.989270 0.146096i \(-0.0466709\pi\)
\(18\) 0 0
\(19\) 1.62474 0.372741 0.186371 0.982480i \(-0.440327\pi\)
0.186371 + 0.982480i \(0.440327\pi\)
\(20\) 0 0
\(21\) −2.53098 2.62224i −0.552306 0.572220i
\(22\) 0 0
\(23\) 2.74384 4.75248i 0.572131 0.990960i −0.424216 0.905561i \(-0.639450\pi\)
0.996347 0.0853986i \(-0.0272164\pi\)
\(24\) 0 0
\(25\) −2.68011 4.64208i −0.536021 0.928416i
\(26\) 0 0
\(27\) 3.47396 + 3.86414i 0.668564 + 0.743655i
\(28\) 0 0
\(29\) −2.95670 5.12116i −0.549046 0.950976i −0.998340 0.0575919i \(-0.981658\pi\)
0.449294 0.893384i \(-0.351676\pi\)
\(30\) 0 0
\(31\) 3.34777 + 1.93284i 0.601277 + 0.347148i 0.769544 0.638594i \(-0.220484\pi\)
−0.168267 + 0.985742i \(0.553817\pi\)
\(32\) 0 0
\(33\) 4.82967 + 5.00381i 0.840737 + 0.871051i
\(34\) 0 0
\(35\) 6.77261i 1.14478i
\(36\) 0 0
\(37\) 10.8195i 1.77871i 0.457215 + 0.889356i \(0.348847\pi\)
−0.457215 + 0.889356i \(0.651153\pi\)
\(38\) 0 0
\(39\) 0.188649 0.657267i 0.0302081 0.105247i
\(40\) 0 0
\(41\) −1.23849 0.715041i −0.193419 0.111671i 0.400163 0.916444i \(-0.368953\pi\)
−0.593582 + 0.804773i \(0.702287\pi\)
\(42\) 0 0
\(43\) 1.21569 + 2.10564i 0.185391 + 0.321107i 0.943708 0.330779i \(-0.107311\pi\)
−0.758317 + 0.651886i \(0.773978\pi\)
\(44\) 0 0
\(45\) −0.341902 + 9.65013i −0.0509678 + 1.43856i
\(46\) 0 0
\(47\) 0.792576 + 1.37278i 0.115609 + 0.200241i 0.918023 0.396527i \(-0.129785\pi\)
−0.802414 + 0.596768i \(0.796451\pi\)
\(48\) 0 0
\(49\) −1.28633 + 2.22799i −0.183761 + 0.318284i
\(50\) 0 0
\(51\) −2.02482 + 0.504297i −0.283531 + 0.0706157i
\(52\) 0 0
\(53\) 7.07284 0.971529 0.485765 0.874090i \(-0.338541\pi\)
0.485765 + 0.874090i \(0.338541\pi\)
\(54\) 0 0
\(55\) 12.9236i 1.74262i
\(56\) 0 0
\(57\) −0.680107 2.73072i −0.0900824 0.361692i
\(58\) 0 0
\(59\) 2.29587 + 1.32552i 0.298897 + 0.172568i 0.641947 0.766749i \(-0.278127\pi\)
−0.343050 + 0.939317i \(0.611460\pi\)
\(60\) 0 0
\(61\) 8.18631 4.72637i 1.04815 0.605149i 0.126019 0.992028i \(-0.459780\pi\)
0.922131 + 0.386879i \(0.126447\pi\)
\(62\) 0 0
\(63\) −3.34777 + 5.35150i −0.421779 + 0.674225i
\(64\) 0 0
\(65\) 1.10049 0.635369i 0.136499 0.0788078i
\(66\) 0 0
\(67\) 2.60947 4.51973i 0.318797 0.552173i −0.661440 0.749998i \(-0.730054\pi\)
0.980237 + 0.197825i \(0.0633878\pi\)
\(68\) 0 0
\(69\) −9.13608 2.62224i −1.09985 0.315681i
\(70\) 0 0
\(71\) −2.69468 −0.319800 −0.159900 0.987133i \(-0.551117\pi\)
−0.159900 + 0.987133i \(0.551117\pi\)
\(72\) 0 0
\(73\) 9.49652 1.11148 0.555742 0.831355i \(-0.312434\pi\)
0.555742 + 0.831355i \(0.312434\pi\)
\(74\) 0 0
\(75\) −6.68011 + 6.44762i −0.771352 + 0.744507i
\(76\) 0 0
\(77\) −4.22417 + 7.31647i −0.481388 + 0.833789i
\(78\) 0 0
\(79\) 1.53599 0.886804i 0.172812 0.0997732i −0.411099 0.911591i \(-0.634855\pi\)
0.583911 + 0.811818i \(0.301522\pi\)
\(80\) 0 0
\(81\) 5.04032 7.45622i 0.560036 0.828469i
\(82\) 0 0
\(83\) 1.30809 0.755228i 0.143582 0.0828971i −0.426488 0.904493i \(-0.640249\pi\)
0.570070 + 0.821596i \(0.306916\pi\)
\(84\) 0 0
\(85\) −3.35821 1.93887i −0.364249 0.210300i
\(86\) 0 0
\(87\) −7.36952 + 7.11304i −0.790095 + 0.762598i
\(88\) 0 0
\(89\) 11.2323i 1.19062i 0.803494 + 0.595312i \(0.202972\pi\)
−0.803494 + 0.595312i \(0.797028\pi\)
\(90\) 0 0
\(91\) 0.830698 0.0870808
\(92\) 0 0
\(93\) 1.84718 6.43570i 0.191543 0.667351i
\(94\) 0 0
\(95\) 2.61480 4.52897i 0.268273 0.464662i
\(96\) 0 0
\(97\) 5.84818 + 10.1294i 0.593793 + 1.02848i 0.993716 + 0.111931i \(0.0357036\pi\)
−0.399923 + 0.916549i \(0.630963\pi\)
\(98\) 0 0
\(99\) 6.38828 10.2118i 0.642046 1.02633i
\(100\) 0 0
\(101\) 2.03509 + 3.52487i 0.202499 + 0.350738i 0.949333 0.314272i \(-0.101760\pi\)
−0.746834 + 0.665010i \(0.768427\pi\)
\(102\) 0 0
\(103\) −15.6784 9.05191i −1.54484 0.891911i −0.998523 0.0543294i \(-0.982698\pi\)
−0.546312 0.837582i \(-0.683969\pi\)
\(104\) 0 0
\(105\) −11.3828 + 2.83497i −1.11084 + 0.276665i
\(106\) 0 0
\(107\) 12.3971i 1.19848i 0.800571 + 0.599238i \(0.204530\pi\)
−0.800571 + 0.599238i \(0.795470\pi\)
\(108\) 0 0
\(109\) 1.76155i 0.168726i −0.996435 0.0843628i \(-0.973115\pi\)
0.996435 0.0843628i \(-0.0268855\pi\)
\(110\) 0 0
\(111\) 18.1844 4.52897i 1.72599 0.429871i
\(112\) 0 0
\(113\) −15.7938 9.11858i −1.48576 0.857804i −0.485891 0.874019i \(-0.661505\pi\)
−0.999869 + 0.0162153i \(0.994838\pi\)
\(114\) 0 0
\(115\) −8.83169 15.2969i −0.823559 1.42645i
\(116\) 0 0
\(117\) −1.18364 0.0419362i −0.109428 0.00387701i
\(118\) 0 0
\(119\) −1.26746 2.19531i −0.116188 0.201244i
\(120\) 0 0
\(121\) 2.56063 4.43514i 0.232785 0.403195i
\(122\) 0 0
\(123\) −0.683352 + 2.38085i −0.0616158 + 0.214674i
\(124\) 0 0
\(125\) −1.15943 −0.103703
\(126\) 0 0
\(127\) 2.09206i 0.185641i −0.995683 0.0928203i \(-0.970412\pi\)
0.995683 0.0928203i \(-0.0295882\pi\)
\(128\) 0 0
\(129\) 3.03008 2.92463i 0.266784 0.257499i
\(130\) 0 0
\(131\) 1.05457 + 0.608856i 0.0921382 + 0.0531960i 0.545361 0.838201i \(-0.316393\pi\)
−0.453223 + 0.891397i \(0.649726\pi\)
\(132\) 0 0
\(133\) 2.96065 1.70933i 0.256721 0.148218i
\(134\) 0 0
\(135\) 16.3622 3.46485i 1.40823 0.298207i
\(136\) 0 0
\(137\) 6.20436 3.58209i 0.530074 0.306038i −0.210973 0.977492i \(-0.567663\pi\)
0.741047 + 0.671454i \(0.234330\pi\)
\(138\) 0 0
\(139\) −11.0378 + 19.1181i −0.936217 + 1.62158i −0.163767 + 0.986499i \(0.552365\pi\)
−0.772450 + 0.635076i \(0.780969\pi\)
\(140\) 0 0
\(141\) 1.97548 1.90673i 0.166365 0.160575i
\(142\) 0 0
\(143\) −1.58515 −0.132557
\(144\) 0 0
\(145\) −19.0337 −1.58066
\(146\) 0 0
\(147\) 4.28305 + 1.22932i 0.353260 + 0.101393i
\(148\) 0 0
\(149\) 0.0838199 0.145180i 0.00686679 0.0118936i −0.862572 0.505935i \(-0.831148\pi\)
0.869438 + 0.494041i \(0.164481\pi\)
\(150\) 0 0
\(151\) 16.5201 9.53789i 1.34439 0.776182i 0.356939 0.934128i \(-0.383820\pi\)
0.987448 + 0.157945i \(0.0504870\pi\)
\(152\) 0 0
\(153\) 1.69515 + 3.19203i 0.137045 + 0.258060i
\(154\) 0 0
\(155\) 10.7756 6.22127i 0.865514 0.499705i
\(156\) 0 0
\(157\) −13.3563 7.71126i −1.06595 0.615426i −0.138877 0.990310i \(-0.544349\pi\)
−0.927072 + 0.374884i \(0.877683\pi\)
\(158\) 0 0
\(159\) −2.96065 11.8874i −0.234795 0.942730i
\(160\) 0 0
\(161\) 11.5468i 0.910013i
\(162\) 0 0
\(163\) 5.04605 0.395237 0.197619 0.980279i \(-0.436679\pi\)
0.197619 + 0.980279i \(0.436679\pi\)
\(164\) 0 0
\(165\) 21.7208 5.40974i 1.69096 0.421148i
\(166\) 0 0
\(167\) −9.49899 + 16.4527i −0.735054 + 1.27315i 0.219646 + 0.975580i \(0.429510\pi\)
−0.954700 + 0.297571i \(0.903823\pi\)
\(168\) 0 0
\(169\) −6.42207 11.1233i −0.494005 0.855642i
\(170\) 0 0
\(171\) −4.30485 + 2.28612i −0.329200 + 0.174824i
\(172\) 0 0
\(173\) 1.26352 + 2.18848i 0.0960636 + 0.166387i 0.910052 0.414494i \(-0.136041\pi\)
−0.813988 + 0.580881i \(0.802708\pi\)
\(174\) 0 0
\(175\) −9.76752 5.63928i −0.738355 0.426289i
\(176\) 0 0
\(177\) 1.26678 4.41355i 0.0952169 0.331742i
\(178\) 0 0
\(179\) 10.9962i 0.821898i −0.911658 0.410949i \(-0.865197\pi\)
0.911658 0.410949i \(-0.134803\pi\)
\(180\) 0 0
\(181\) 14.3426i 1.06608i −0.846091 0.533038i \(-0.821050\pi\)
0.846091 0.533038i \(-0.178950\pi\)
\(182\) 0 0
\(183\) −11.3704 11.7804i −0.840523 0.870830i
\(184\) 0 0
\(185\) 30.1593 + 17.4125i 2.21736 + 1.28019i
\(186\) 0 0
\(187\) 2.41859 + 4.18913i 0.176865 + 0.306339i
\(188\) 0 0
\(189\) 10.3957 + 3.38652i 0.756173 + 0.246333i
\(190\) 0 0
\(191\) 0.237073 + 0.410623i 0.0171540 + 0.0297116i 0.874475 0.485071i \(-0.161206\pi\)
−0.857321 + 0.514782i \(0.827873\pi\)
\(192\) 0 0
\(193\) −10.6703 + 18.4815i −0.768067 + 1.33033i 0.170543 + 0.985350i \(0.445448\pi\)
−0.938610 + 0.344981i \(0.887885\pi\)
\(194\) 0 0
\(195\) −1.52853 1.58364i −0.109460 0.113407i
\(196\) 0 0
\(197\) −21.4346 −1.52715 −0.763575 0.645719i \(-0.776558\pi\)
−0.763575 + 0.645719i \(0.776558\pi\)
\(198\) 0 0
\(199\) 6.09835i 0.432301i −0.976360 0.216150i \(-0.930650\pi\)
0.976360 0.216150i \(-0.0693501\pi\)
\(200\) 0 0
\(201\) −8.68865 2.49382i −0.612850 0.175901i
\(202\) 0 0
\(203\) −10.7756 6.22127i −0.756296 0.436648i
\(204\) 0 0
\(205\) −3.98635 + 2.30152i −0.278419 + 0.160745i
\(206\) 0 0
\(207\) −0.582917 + 16.4527i −0.0405156 + 1.14354i
\(208\) 0 0
\(209\) −5.64956 + 3.26177i −0.390788 + 0.225622i
\(210\) 0 0
\(211\) −1.36572 + 2.36549i −0.0940197 + 0.162847i −0.909199 0.416362i \(-0.863305\pi\)
0.815179 + 0.579209i \(0.196638\pi\)
\(212\) 0 0
\(213\) 1.12798 + 4.52897i 0.0772876 + 0.310320i
\(214\) 0 0
\(215\) 7.82596 0.533726
\(216\) 0 0
\(217\) 8.13386 0.552162
\(218\) 0 0
\(219\) −3.97518 15.9609i −0.268618 1.07854i
\(220\) 0 0
\(221\) 0.237813 0.411904i 0.0159970 0.0277076i
\(222\) 0 0
\(223\) −13.4015 + 7.73737i −0.897432 + 0.518133i −0.876366 0.481645i \(-0.840039\pi\)
−0.0210661 + 0.999778i \(0.506706\pi\)
\(224\) 0 0
\(225\) 13.6328 + 8.52837i 0.908855 + 0.568558i
\(226\) 0 0
\(227\) −13.9546 + 8.05671i −0.926202 + 0.534743i −0.885608 0.464433i \(-0.846258\pi\)
−0.0405935 + 0.999176i \(0.512925\pi\)
\(228\) 0 0
\(229\) −9.60052 5.54286i −0.634420 0.366283i 0.148042 0.988981i \(-0.452703\pi\)
−0.782462 + 0.622698i \(0.786036\pi\)
\(230\) 0 0
\(231\) 14.0651 + 4.03696i 0.925413 + 0.265613i
\(232\) 0 0
\(233\) 8.96547i 0.587348i 0.955906 + 0.293674i \(0.0948780\pi\)
−0.955906 + 0.293674i \(0.905122\pi\)
\(234\) 0 0
\(235\) 5.10218 0.332829
\(236\) 0 0
\(237\) −2.13341 2.21034i −0.138580 0.143577i
\(238\) 0 0
\(239\) −11.6179 + 20.1228i −0.751499 + 1.30163i 0.195597 + 0.980684i \(0.437336\pi\)
−0.947096 + 0.320951i \(0.895998\pi\)
\(240\) 0 0
\(241\) −4.27609 7.40641i −0.275447 0.477089i 0.694801 0.719202i \(-0.255493\pi\)
−0.970248 + 0.242114i \(0.922159\pi\)
\(242\) 0 0
\(243\) −14.6416 5.35018i −0.939257 0.343214i
\(244\) 0 0
\(245\) 4.14035 + 7.17129i 0.264517 + 0.458157i
\(246\) 0 0
\(247\) 0.555503 + 0.320720i 0.0353458 + 0.0204069i
\(248\) 0 0
\(249\) −1.81688 1.88239i −0.115140 0.119292i
\(250\) 0 0
\(251\) 13.6971i 0.864551i 0.901742 + 0.432275i \(0.142289\pi\)
−0.901742 + 0.432275i \(0.857711\pi\)
\(252\) 0 0
\(253\) 22.0338i 1.38525i
\(254\) 0 0
\(255\) −1.85294 + 6.45577i −0.116036 + 0.404276i
\(256\) 0 0
\(257\) 3.88533 + 2.24320i 0.242360 + 0.139927i 0.616261 0.787542i \(-0.288647\pi\)
−0.373901 + 0.927469i \(0.621980\pi\)
\(258\) 0 0
\(259\) 11.3828 + 19.7155i 0.707291 + 1.22506i
\(260\) 0 0
\(261\) 15.0398 + 9.40853i 0.930939 + 0.582374i
\(262\) 0 0
\(263\) 11.1123 + 19.2471i 0.685214 + 1.18682i 0.973370 + 0.229241i \(0.0736245\pi\)
−0.288156 + 0.957583i \(0.593042\pi\)
\(264\) 0 0
\(265\) 11.3828 19.7155i 0.699238 1.21112i
\(266\) 0 0
\(267\) 18.8783 4.70178i 1.15533 0.287744i
\(268\) 0 0
\(269\) 12.9941 0.792266 0.396133 0.918193i \(-0.370352\pi\)
0.396133 + 0.918193i \(0.370352\pi\)
\(270\) 0 0
\(271\) 11.1500i 0.677314i −0.940910 0.338657i \(-0.890027\pi\)
0.940910 0.338657i \(-0.109973\pi\)
\(272\) 0 0
\(273\) −0.347725 1.39616i −0.0210453 0.0844995i
\(274\) 0 0
\(275\) 18.6386 + 10.7610i 1.12395 + 0.648911i
\(276\) 0 0
\(277\) 1.29497 0.747654i 0.0778074 0.0449221i −0.460592 0.887612i \(-0.652363\pi\)
0.538399 + 0.842690i \(0.319029\pi\)
\(278\) 0 0
\(279\) −11.5897 0.410623i −0.693860 0.0245833i
\(280\) 0 0
\(281\) −9.39961 + 5.42687i −0.560734 + 0.323740i −0.753440 0.657517i \(-0.771607\pi\)
0.192706 + 0.981256i \(0.438274\pi\)
\(282\) 0 0
\(283\) 12.0627 20.8931i 0.717050 1.24197i −0.245113 0.969494i \(-0.578825\pi\)
0.962163 0.272473i \(-0.0878415\pi\)
\(284\) 0 0
\(285\) −8.70641 2.49892i −0.515723 0.148023i
\(286\) 0 0
\(287\) −3.00907 −0.177620
\(288\) 0 0
\(289\) 15.5486 0.914624
\(290\) 0 0
\(291\) 14.5765 14.0692i 0.854488 0.824750i
\(292\) 0 0
\(293\) −3.54036 + 6.13209i −0.206830 + 0.358240i −0.950714 0.310068i \(-0.899648\pi\)
0.743884 + 0.668309i \(0.232981\pi\)
\(294\) 0 0
\(295\) 7.38979 4.26650i 0.430250 0.248405i
\(296\) 0 0
\(297\) −19.8372 6.46222i −1.15107 0.374976i
\(298\) 0 0
\(299\) 1.87625 1.08326i 0.108507 0.0626463i
\(300\) 0 0
\(301\) 4.43052 + 2.55796i 0.255371 + 0.147439i
\(302\) 0 0
\(303\) 5.07241 4.89588i 0.291402 0.281261i
\(304\) 0 0
\(305\) 30.4258i 1.74218i
\(306\) 0 0
\(307\) −12.9052 −0.736541 −0.368270 0.929719i \(-0.620050\pi\)
−0.368270 + 0.929719i \(0.620050\pi\)
\(308\) 0 0
\(309\) −8.65075 + 30.1398i −0.492124 + 1.71459i
\(310\) 0 0
\(311\) 7.89357 13.6721i 0.447603 0.775271i −0.550626 0.834752i \(-0.685611\pi\)
0.998229 + 0.0594804i \(0.0189444\pi\)
\(312\) 0 0
\(313\) 2.06365 + 3.57434i 0.116644 + 0.202034i 0.918436 0.395570i \(-0.129453\pi\)
−0.801792 + 0.597604i \(0.796120\pi\)
\(314\) 0 0
\(315\) 9.52952 + 17.9444i 0.536927 + 1.01105i
\(316\) 0 0
\(317\) 7.58238 + 13.1331i 0.425869 + 0.737627i 0.996501 0.0835791i \(-0.0266351\pi\)
−0.570632 + 0.821206i \(0.693302\pi\)
\(318\) 0 0
\(319\) 20.5621 + 11.8715i 1.15126 + 0.664679i
\(320\) 0 0
\(321\) 20.8360 5.18936i 1.16295 0.289642i
\(322\) 0 0
\(323\) 1.95739i 0.108912i
\(324\) 0 0
\(325\) 2.11619i 0.117385i
\(326\) 0 0
\(327\) −2.96065 + 0.737373i −0.163724 + 0.0407768i
\(328\) 0 0
\(329\) 2.88851 + 1.66768i 0.159248 + 0.0919421i
\(330\) 0 0
\(331\) −7.09621 12.2910i −0.390043 0.675575i 0.602412 0.798186i \(-0.294207\pi\)
−0.992455 + 0.122611i \(0.960873\pi\)
\(332\) 0 0
\(333\) −15.2237 28.6669i −0.834256 1.57093i
\(334\) 0 0
\(335\) −8.39917 14.5478i −0.458896 0.794830i
\(336\) 0 0
\(337\) −12.9139 + 22.3675i −0.703464 + 1.21844i 0.263779 + 0.964583i \(0.415031\pi\)
−0.967243 + 0.253853i \(0.918302\pi\)
\(338\) 0 0
\(339\) −8.71447 + 30.3618i −0.473305 + 1.64903i
\(340\) 0 0
\(341\) −15.5212 −0.840518
\(342\) 0 0
\(343\) 20.1421i 1.08757i
\(344\) 0 0
\(345\) −22.0128 + 21.2467i −1.18513 + 1.14388i
\(346\) 0 0
\(347\) −11.4312 6.59978i −0.613656 0.354295i 0.160739 0.986997i \(-0.448612\pi\)
−0.774395 + 0.632702i \(0.781946\pi\)
\(348\) 0 0
\(349\) −12.7838 + 7.38075i −0.684303 + 0.395082i −0.801474 0.598029i \(-0.795951\pi\)
0.117171 + 0.993112i \(0.462617\pi\)
\(350\) 0 0
\(351\) 0.424983 + 2.00691i 0.0226839 + 0.107121i
\(352\) 0 0
\(353\) −1.21582 + 0.701955i −0.0647116 + 0.0373613i −0.532007 0.846740i \(-0.678562\pi\)
0.467295 + 0.884101i \(0.345229\pi\)
\(354\) 0 0
\(355\) −4.33672 + 7.51142i −0.230169 + 0.398665i
\(356\) 0 0
\(357\) −3.15912 + 3.04918i −0.167198 + 0.161379i
\(358\) 0 0
\(359\) −11.3107 −0.596953 −0.298477 0.954417i \(-0.596479\pi\)
−0.298477 + 0.954417i \(0.596479\pi\)
\(360\) 0 0
\(361\) −16.3602 −0.861064
\(362\) 0 0
\(363\) −8.52604 2.44715i −0.447501 0.128442i
\(364\) 0 0
\(365\) 15.2834 26.4716i 0.799967 1.38558i
\(366\) 0 0
\(367\) −9.82457 + 5.67222i −0.512838 + 0.296087i −0.734000 0.679150i \(-0.762349\pi\)
0.221161 + 0.975237i \(0.429015\pi\)
\(368\) 0 0
\(369\) 4.28755 + 0.151907i 0.223201 + 0.00790798i
\(370\) 0 0
\(371\) 12.8883 7.44107i 0.669127 0.386321i
\(372\) 0 0
\(373\) 20.9314 + 12.0848i 1.08379 + 0.625726i 0.931916 0.362674i \(-0.118136\pi\)
0.151873 + 0.988400i \(0.451470\pi\)
\(374\) 0 0
\(375\) 0.485330 + 1.94866i 0.0250623 + 0.100629i
\(376\) 0 0
\(377\) 2.33458i 0.120237i
\(378\) 0 0
\(379\) −20.7029 −1.06344 −0.531719 0.846921i \(-0.678454\pi\)
−0.531719 + 0.846921i \(0.678454\pi\)
\(380\) 0 0
\(381\) −3.51615 + 0.875725i −0.180138 + 0.0448648i
\(382\) 0 0
\(383\) 15.2027 26.3319i 0.776824 1.34550i −0.156940 0.987608i \(-0.550163\pi\)
0.933764 0.357890i \(-0.116504\pi\)
\(384\) 0 0
\(385\) 13.5964 + 23.5497i 0.692939 + 1.20021i
\(386\) 0 0
\(387\) −6.18382 3.86845i −0.314341 0.196644i
\(388\) 0 0
\(389\) −10.1376 17.5588i −0.513995 0.890266i −0.999868 0.0162366i \(-0.994831\pi\)
0.485873 0.874030i \(-0.338502\pi\)
\(390\) 0 0
\(391\) −5.72550 3.30562i −0.289551 0.167172i
\(392\) 0 0
\(393\) 0.581873 2.02729i 0.0293516 0.102263i
\(394\) 0 0
\(395\) 5.70876i 0.287239i
\(396\) 0 0
\(397\) 12.2942i 0.617030i −0.951220 0.308515i \(-0.900168\pi\)
0.951220 0.308515i \(-0.0998320\pi\)
\(398\) 0 0
\(399\) −4.11219 4.26047i −0.205867 0.213290i
\(400\) 0 0
\(401\) −25.3617 14.6426i −1.26650 0.731216i −0.292179 0.956364i \(-0.594380\pi\)
−0.974325 + 0.225147i \(0.927714\pi\)
\(402\) 0 0
\(403\) 0.763074 + 1.32168i 0.0380114 + 0.0658377i
\(404\) 0 0
\(405\) −12.6725 26.0497i −0.629701 1.29442i
\(406\) 0 0
\(407\) −21.7208 37.6216i −1.07666 1.86483i
\(408\) 0 0
\(409\) 15.3567 26.5986i 0.759342 1.31522i −0.183845 0.982955i \(-0.558855\pi\)
0.943187 0.332263i \(-0.107812\pi\)
\(410\) 0 0
\(411\) −8.61755 8.92827i −0.425072 0.440399i
\(412\) 0 0
\(413\) 5.57813 0.274482
\(414\) 0 0
\(415\) 4.86175i 0.238654i
\(416\) 0 0
\(417\) 36.7523 + 10.5487i 1.79977 + 0.516570i
\(418\) 0 0
\(419\) −11.5932 6.69333i −0.566364 0.326991i 0.189332 0.981913i \(-0.439368\pi\)
−0.755696 + 0.654923i \(0.772701\pi\)
\(420\) 0 0
\(421\) 23.9825 13.8463i 1.16884 0.674828i 0.215431 0.976519i \(-0.430884\pi\)
0.953406 + 0.301691i \(0.0975510\pi\)
\(422\) 0 0
\(423\) −4.03157 2.52206i −0.196022 0.122627i
\(424\) 0 0
\(425\) −5.59250 + 3.22883i −0.271276 + 0.156621i
\(426\) 0 0
\(427\) 9.94486 17.2250i 0.481266 0.833577i
\(428\) 0 0
\(429\) 0.663535 + 2.66418i 0.0320358 + 0.128628i
\(430\) 0 0
\(431\) 29.2554 1.40918 0.704592 0.709613i \(-0.251130\pi\)
0.704592 + 0.709613i \(0.251130\pi\)
\(432\) 0 0
\(433\) 2.57756 0.123870 0.0619348 0.998080i \(-0.480273\pi\)
0.0619348 + 0.998080i \(0.480273\pi\)
\(434\) 0 0
\(435\) 7.96737 + 31.9900i 0.382006 + 1.53380i
\(436\) 0 0
\(437\) 4.45804 7.72155i 0.213257 0.369372i
\(438\) 0 0
\(439\) −24.4758 + 14.1311i −1.16817 + 0.674442i −0.953248 0.302189i \(-0.902283\pi\)
−0.214920 + 0.976632i \(0.568949\pi\)
\(440\) 0 0
\(441\) 0.273275 7.71314i 0.0130131 0.367292i
\(442\) 0 0
\(443\) 23.3499 13.4811i 1.10939 0.640506i 0.170718 0.985320i \(-0.445391\pi\)
0.938671 + 0.344814i \(0.112058\pi\)
\(444\) 0 0
\(445\) 31.3101 + 18.0769i 1.48424 + 0.856928i
\(446\) 0 0
\(447\) −0.279092 0.0801052i −0.0132006 0.00378884i
\(448\) 0 0
\(449\) 23.4500i 1.10668i 0.832957 + 0.553338i \(0.186646\pi\)
−0.832957 + 0.553338i \(0.813354\pi\)
\(450\) 0 0
\(451\) 5.74196 0.270378
\(452\) 0 0
\(453\) −22.9456 23.7730i −1.07808 1.11695i
\(454\) 0 0
\(455\) 1.33690 2.31557i 0.0626746 0.108556i
\(456\) 0 0
\(457\) −8.06063 13.9614i −0.377060 0.653088i 0.613573 0.789638i \(-0.289732\pi\)
−0.990633 + 0.136550i \(0.956398\pi\)
\(458\) 0 0
\(459\) 4.65529 4.18522i 0.217290 0.195349i
\(460\) 0 0
\(461\) −5.14578 8.91276i −0.239663 0.415109i 0.720955 0.692982i \(-0.243704\pi\)
−0.960618 + 0.277874i \(0.910370\pi\)
\(462\) 0 0
\(463\) 22.3273 + 12.8907i 1.03764 + 0.599080i 0.919163 0.393877i \(-0.128866\pi\)
0.118474 + 0.992957i \(0.462200\pi\)
\(464\) 0 0
\(465\) −14.9667 15.5064i −0.694065 0.719091i
\(466\) 0 0
\(467\) 10.8110i 0.500271i 0.968211 + 0.250136i \(0.0804752\pi\)
−0.968211 + 0.250136i \(0.919525\pi\)
\(468\) 0 0
\(469\) 10.9813i 0.507069i
\(470\) 0 0
\(471\) −7.36952 + 25.6759i −0.339570 + 1.18308i
\(472\) 0 0
\(473\) −8.45441 4.88115i −0.388734 0.224436i
\(474\) 0 0
\(475\) −4.35448 7.54218i −0.199797 0.346059i
\(476\) 0 0
\(477\) −18.7399 + 9.95196i −0.858041 + 0.455669i
\(478\) 0 0
\(479\) 6.16167 + 10.6723i 0.281534 + 0.487631i 0.971763 0.235960i \(-0.0758236\pi\)
−0.690229 + 0.723591i \(0.742490\pi\)
\(480\) 0 0
\(481\) −2.13574 + 3.69921i −0.0973813 + 0.168669i
\(482\) 0 0
\(483\) −19.4068 + 4.83341i −0.883038 + 0.219928i
\(484\) 0 0
\(485\) 37.6474 1.70948
\(486\) 0 0
\(487\) 7.62691i 0.345608i −0.984956 0.172804i \(-0.944717\pi\)
0.984956 0.172804i \(-0.0552828\pi\)
\(488\) 0 0
\(489\) −2.11225 8.48094i −0.0955191 0.383521i
\(490\) 0 0
\(491\) −22.1130 12.7670i −0.997948 0.576165i −0.0903072 0.995914i \(-0.528785\pi\)
−0.907640 + 0.419749i \(0.862118\pi\)
\(492\) 0 0
\(493\) −6.16967 + 3.56206i −0.277868 + 0.160427i
\(494\) 0 0
\(495\) −18.1844 34.2419i −0.817328 1.53906i
\(496\) 0 0
\(497\) −4.91031 + 2.83497i −0.220258 + 0.127166i
\(498\) 0 0
\(499\) 5.58850 9.67956i 0.250176 0.433317i −0.713398 0.700759i \(-0.752845\pi\)
0.963574 + 0.267442i \(0.0861783\pi\)
\(500\) 0 0
\(501\) 31.6285 + 9.07802i 1.41306 + 0.405576i
\(502\) 0 0
\(503\) 22.3635 0.997137 0.498569 0.866850i \(-0.333859\pi\)
0.498569 + 0.866850i \(0.333859\pi\)
\(504\) 0 0
\(505\) 13.1008 0.582977
\(506\) 0 0
\(507\) −16.0069 + 15.4498i −0.710890 + 0.686149i
\(508\) 0 0
\(509\) −6.12701 + 10.6123i −0.271575 + 0.470382i −0.969265 0.246018i \(-0.920878\pi\)
0.697690 + 0.716399i \(0.254211\pi\)
\(510\) 0 0
\(511\) 17.3048 9.99093i 0.765519 0.441973i
\(512\) 0 0
\(513\) 5.64429 + 6.27824i 0.249201 + 0.277191i
\(514\) 0 0
\(515\) −50.4644 + 29.1356i −2.22373 + 1.28387i
\(516\) 0 0
\(517\) −5.51190 3.18230i −0.242413 0.139957i
\(518\) 0 0
\(519\) 3.14930 3.03969i 0.138239 0.133428i
\(520\) 0 0
\(521\) 34.9202i 1.52988i 0.644101 + 0.764940i \(0.277232\pi\)
−0.644101 + 0.764940i \(0.722768\pi\)
\(522\) 0 0
\(523\) 36.8697 1.61220 0.806100 0.591779i \(-0.201574\pi\)
0.806100 + 0.591779i \(0.201574\pi\)
\(524\) 0 0
\(525\) −5.38936 + 18.7769i −0.235211 + 0.819492i
\(526\) 0 0
\(527\) 2.32857 4.03319i 0.101434 0.175689i
\(528\) 0 0
\(529\) −3.55735 6.16151i −0.154667 0.267892i
\(530\) 0 0
\(531\) −7.94815 0.281601i −0.344920 0.0122205i
\(532\) 0 0
\(533\) −0.282294 0.488948i −0.0122275 0.0211787i
\(534\) 0 0
\(535\) 34.5570 + 19.9515i 1.49403 + 0.862579i
\(536\) 0 0
\(537\) −18.4815 + 4.60296i −0.797534 + 0.198632i
\(538\) 0 0
\(539\) 10.3296i 0.444926i
\(540\) 0 0
\(541\) 11.9200i 0.512481i −0.966613 0.256240i \(-0.917516\pi\)
0.966613 0.256240i \(-0.0824839\pi\)
\(542\) 0 0
\(543\) −24.1057 + 6.00371i −1.03447 + 0.257644i
\(544\) 0 0
\(545\) −4.91031 2.83497i −0.210335 0.121437i
\(546\) 0 0
\(547\) 10.3339 + 17.8989i 0.441847 + 0.765302i 0.997827 0.0658943i \(-0.0209900\pi\)
−0.555979 + 0.831196i \(0.687657\pi\)
\(548\) 0 0
\(549\) −15.0398 + 24.0415i −0.641882 + 1.02607i
\(550\) 0 0
\(551\) −4.80388 8.32057i −0.204652 0.354468i
\(552\) 0 0
\(553\) 1.86595 3.23191i 0.0793481 0.137435i
\(554\) 0 0
\(555\) 16.6408 57.9778i 0.706363 2.46102i
\(556\) 0 0
\(557\) −21.6506 −0.917367 −0.458684 0.888600i \(-0.651679\pi\)
−0.458684 + 0.888600i \(0.651679\pi\)
\(558\) 0 0
\(559\) 0.959897i 0.0405993i
\(560\) 0 0
\(561\) 6.02829 5.81849i 0.254515 0.245657i
\(562\) 0 0
\(563\) 36.7299 + 21.2060i 1.54798 + 0.893726i 0.998296 + 0.0583533i \(0.0185850\pi\)
0.549683 + 0.835373i \(0.314748\pi\)
\(564\) 0 0
\(565\) −50.8361 + 29.3502i −2.13869 + 1.23477i
\(566\) 0 0
\(567\) 1.34020 18.8896i 0.0562829 0.793290i
\(568\) 0 0
\(569\) 19.3062 11.1464i 0.809357 0.467282i −0.0373758 0.999301i \(-0.511900\pi\)
0.846732 + 0.532019i \(0.178567\pi\)
\(570\) 0 0
\(571\) −1.30386 + 2.25835i −0.0545649 + 0.0945091i −0.892018 0.452001i \(-0.850711\pi\)
0.837453 + 0.546510i \(0.184044\pi\)
\(572\) 0 0
\(573\) 0.590899 0.570335i 0.0246852 0.0238261i
\(574\) 0 0
\(575\) −29.4152 −1.22670
\(576\) 0 0
\(577\) −12.3081 −0.512394 −0.256197 0.966625i \(-0.582470\pi\)
−0.256197 + 0.966625i \(0.582470\pi\)
\(578\) 0 0
\(579\) 35.5286 + 10.1974i 1.47652 + 0.423791i
\(580\) 0 0
\(581\) 1.58909 2.75239i 0.0659267 0.114188i
\(582\) 0 0
\(583\) −24.5937 + 14.1992i −1.01857 + 0.588070i
\(584\) 0 0
\(585\) −2.02181 + 3.23191i −0.0835915 + 0.133623i
\(586\) 0 0
\(587\) 23.8189 13.7518i 0.983111 0.567599i 0.0799032 0.996803i \(-0.474539\pi\)
0.903208 + 0.429203i \(0.141206\pi\)
\(588\) 0 0
\(589\) 5.43926 + 3.14036i 0.224121 + 0.129396i
\(590\) 0 0
\(591\) 8.97238 + 36.0253i 0.369074 + 1.48188i
\(592\) 0 0
\(593\) 33.5909i 1.37941i −0.724088 0.689707i \(-0.757739\pi\)
0.724088 0.689707i \(-0.242261\pi\)
\(594\) 0 0
\(595\) −8.15923 −0.334496
\(596\) 0 0
\(597\) −10.2495 + 2.55273i −0.419486 + 0.104476i
\(598\) 0 0
\(599\) −4.32570 + 7.49232i −0.176743 + 0.306128i −0.940763 0.339064i \(-0.889890\pi\)
0.764020 + 0.645193i \(0.223223\pi\)
\(600\) 0 0
\(601\) 11.3533 + 19.6644i 0.463109 + 0.802128i 0.999114 0.0420865i \(-0.0134005\pi\)
−0.536005 + 0.844215i \(0.680067\pi\)
\(602\) 0 0
\(603\) −0.554370 + 15.6470i −0.0225757 + 0.637195i
\(604\) 0 0
\(605\) −8.24197 14.2755i −0.335084 0.580382i
\(606\) 0 0
\(607\) −18.9691 10.9518i −0.769932 0.444520i 0.0629187 0.998019i \(-0.479959\pi\)
−0.832850 + 0.553498i \(0.813292\pi\)
\(608\) 0 0
\(609\) −5.94556 + 20.7148i −0.240926 + 0.839404i
\(610\) 0 0
\(611\) 0.625810i 0.0253176i
\(612\) 0 0
\(613\) 35.2553i 1.42395i 0.702206 + 0.711973i \(0.252198\pi\)
−0.702206 + 0.711973i \(0.747802\pi\)
\(614\) 0 0
\(615\) 5.53685 + 5.73649i 0.223267 + 0.231318i
\(616\) 0 0
\(617\) 3.96793 + 2.29088i 0.159743 + 0.0922275i 0.577740 0.816221i \(-0.303935\pi\)
−0.417998 + 0.908448i \(0.637268\pi\)
\(618\) 0 0
\(619\) 8.24726 + 14.2847i 0.331486 + 0.574150i 0.982803 0.184655i \(-0.0591169\pi\)
−0.651318 + 0.758805i \(0.725784\pi\)
\(620\) 0 0
\(621\) 27.8962 5.90730i 1.11944 0.237052i
\(622\) 0 0
\(623\) 11.8171 + 20.4678i 0.473443 + 0.820027i
\(624\) 0 0
\(625\) 11.5346 19.9785i 0.461384 0.799140i
\(626\) 0 0
\(627\) 7.84696 + 8.12990i 0.313377 + 0.324677i
\(628\) 0 0
\(629\) 13.0347 0.519726
\(630\) 0 0
\(631\) 38.0635i 1.51528i −0.652670 0.757642i \(-0.726351\pi\)
0.652670 0.757642i \(-0.273649\pi\)
\(632\) 0 0
\(633\) 4.54738 + 1.30519i 0.180742 + 0.0518767i
\(634\) 0 0
\(635\) −5.83163 3.36689i −0.231421 0.133611i
\(636\) 0 0
\(637\) −0.879598 + 0.507836i −0.0348510 + 0.0201212i
\(638\) 0 0
\(639\) 7.13971 3.79160i 0.282443 0.149993i
\(640\) 0 0
\(641\) 30.2526 17.4663i 1.19490 0.689878i 0.235490 0.971877i \(-0.424331\pi\)
0.959415 + 0.281998i \(0.0909973\pi\)
\(642\) 0 0
\(643\) −18.5870 + 32.1936i −0.733000 + 1.26959i 0.222596 + 0.974911i \(0.428547\pi\)
−0.955595 + 0.294682i \(0.904786\pi\)
\(644\) 0 0
\(645\) −3.27590 13.1531i −0.128988 0.517905i
\(646\) 0 0
\(647\) −9.36933 −0.368346 −0.184173 0.982894i \(-0.558961\pi\)
−0.184173 + 0.982894i \(0.558961\pi\)
\(648\) 0 0
\(649\) −10.6443 −0.417825
\(650\) 0 0
\(651\) −3.40478 13.6706i −0.133444 0.535794i
\(652\) 0 0
\(653\) −7.65255 + 13.2546i −0.299468 + 0.518693i −0.976014 0.217707i \(-0.930142\pi\)
0.676547 + 0.736400i \(0.263476\pi\)
\(654\) 0 0
\(655\) 3.39437 1.95974i 0.132629 0.0765735i
\(656\) 0 0
\(657\) −25.1616 + 13.3622i −0.981647 + 0.521311i
\(658\) 0 0
\(659\) −17.2932 + 9.98421i −0.673646 + 0.388930i −0.797457 0.603376i \(-0.793822\pi\)
0.123811 + 0.992306i \(0.460488\pi\)
\(660\) 0 0
\(661\) 30.6907 + 17.7193i 1.19373 + 0.689201i 0.959151 0.282896i \(-0.0912950\pi\)
0.234580 + 0.972097i \(0.424628\pi\)
\(662\) 0 0
\(663\) −0.791837 0.227273i −0.0307524 0.00882657i
\(664\) 0 0
\(665\) 11.0037i 0.426707i
\(666\) 0 0
\(667\) −32.4509 −1.25650
\(668\) 0 0
\(669\) 18.6141 + 19.2852i 0.719661 + 0.745610i
\(670\) 0 0
\(671\) −18.9770 + 32.8691i −0.732598 + 1.26890i
\(672\) 0 0
\(673\) 1.95563 + 3.38725i 0.0753841 + 0.130569i 0.901253 0.433293i \(-0.142648\pi\)
−0.825869 + 0.563862i \(0.809315\pi\)
\(674\) 0 0
\(675\) 8.62709 26.4827i 0.332057 1.01932i
\(676\) 0 0
\(677\) −1.69713 2.93951i −0.0652259 0.112974i 0.831568 0.555423i \(-0.187443\pi\)
−0.896794 + 0.442448i \(0.854110\pi\)
\(678\) 0 0
\(679\) 21.3134 + 12.3053i 0.817934 + 0.472234i
\(680\) 0 0
\(681\) 19.3823 + 20.0812i 0.742732 + 0.769512i
\(682\) 0 0
\(683\) 9.70867i 0.371492i 0.982598 + 0.185746i \(0.0594702\pi\)
−0.982598 + 0.185746i \(0.940530\pi\)
\(684\) 0 0
\(685\) 23.0595i 0.881060i
\(686\) 0 0
\(687\) −5.29722 + 18.4559i −0.202101 + 0.704136i
\(688\) 0 0
\(689\) 2.41822 + 1.39616i 0.0921269 + 0.0531895i
\(690\) 0 0
\(691\) −19.6458 34.0276i −0.747363 1.29447i −0.949083 0.315027i \(-0.897986\pi\)
0.201720 0.979443i \(-0.435347\pi\)
\(692\) 0 0
\(693\) 0.897406 25.3291i 0.0340896 0.962173i
\(694\) 0 0
\(695\) 35.5278 + 61.5359i 1.34765 + 2.33419i
\(696\) 0 0
\(697\) −0.861438 + 1.49206i −0.0326293 + 0.0565156i
\(698\) 0 0
\(699\) 15.0683 3.75289i 0.569937 0.141947i
\(700\) 0 0
\(701\) −12.0640 −0.455651 −0.227826 0.973702i \(-0.573162\pi\)
−0.227826 + 0.973702i \(0.573162\pi\)
\(702\) 0 0
\(703\) 17.5789i 0.663000i
\(704\) 0 0
\(705\) −2.13574 8.57527i −0.0804366 0.322963i
\(706\) 0 0
\(707\) 7.41677 + 4.28208i 0.278936 + 0.161044i
\(708\) 0 0
\(709\) −11.5824 + 6.68709i −0.434985 + 0.251139i −0.701468 0.712701i \(-0.747472\pi\)
0.266483 + 0.963840i \(0.414138\pi\)
\(710\) 0 0
\(711\) −2.82190 + 4.51088i −0.105830 + 0.169171i
\(712\) 0 0
\(713\) 18.3715 10.6068i 0.688018 0.397228i
\(714\) 0 0
\(715\) −2.55109 + 4.41861i −0.0954053 + 0.165247i
\(716\) 0 0
\(717\) 38.6837 + 11.1030i 1.44467 + 0.414650i
\(718\) 0 0
\(719\) −36.4686 −1.36005 −0.680025 0.733189i \(-0.738031\pi\)
−0.680025 + 0.733189i \(0.738031\pi\)
\(720\) 0 0
\(721\) −38.0927 −1.41865
\(722\) 0 0
\(723\) −10.6581 + 10.2871i −0.396378 + 0.382583i
\(724\) 0 0
\(725\) −15.8486 + 27.4505i −0.588601 + 1.01949i
\(726\) 0 0
\(727\) 4.01460 2.31783i 0.148893 0.0859637i −0.423702 0.905801i \(-0.639270\pi\)
0.572596 + 0.819838i \(0.305936\pi\)
\(728\) 0 0
\(729\) −2.86322 + 26.8478i −0.106045 + 0.994361i
\(730\) 0 0
\(731\) 2.53675 1.46459i 0.0938250 0.0541699i
\(732\) 0 0
\(733\) −32.3446 18.6742i −1.19467 0.689746i −0.235311 0.971920i \(-0.575611\pi\)
−0.959363 + 0.282175i \(0.908944\pi\)
\(734\) 0 0
\(735\) 10.3197 9.96057i 0.380649 0.367401i
\(736\) 0 0
\(737\) 20.9547i 0.771876i
\(738\) 0 0
\(739\) 21.7009 0.798279 0.399140 0.916890i \(-0.369309\pi\)
0.399140 + 0.916890i \(0.369309\pi\)
\(740\) 0 0
\(741\) 0.306506 1.06789i 0.0112598 0.0392299i
\(742\) 0 0
\(743\) 21.4136 37.0894i 0.785588 1.36068i −0.143060 0.989714i \(-0.545694\pi\)
0.928647 0.370964i \(-0.120973\pi\)
\(744\) 0 0
\(745\) −0.269793 0.467296i −0.00988446 0.0171204i
\(746\) 0 0
\(747\) −2.40321 + 3.84160i −0.0879290 + 0.140557i
\(748\) 0 0
\(749\) 13.0426 + 22.5904i 0.476565 + 0.825434i
\(750\) 0 0
\(751\) −27.3860 15.8113i −0.999328 0.576962i −0.0912787 0.995825i \(-0.529095\pi\)
−0.908049 + 0.418863i \(0.862429\pi\)
\(752\) 0 0
\(753\) 23.0208 5.73351i 0.838923 0.208941i
\(754\) 0 0
\(755\) 61.3997i 2.23457i
\(756\) 0 0
\(757\) 32.2957i 1.17381i −0.809657 0.586903i \(-0.800347\pi\)
0.809657 0.586903i \(-0.199653\pi\)
\(758\) 0 0
\(759\) 37.0323 9.22320i 1.34419 0.334781i
\(760\) 0 0
\(761\) 31.6365 + 18.2653i 1.14682 + 0.662118i 0.948111 0.317940i \(-0.102991\pi\)
0.198711 + 0.980058i \(0.436324\pi\)
\(762\) 0 0
\(763\) −1.85326 3.20994i −0.0670924 0.116207i
\(764\) 0 0
\(765\) 11.6259 + 0.411904i 0.420335 + 0.0148924i
\(766\) 0 0
\(767\) 0.523309 + 0.906399i 0.0188956 + 0.0327282i
\(768\) 0 0
\(769\) −1.92161 + 3.32832i −0.0692950 + 0.120022i −0.898591 0.438787i \(-0.855408\pi\)
0.829296 + 0.558809i \(0.188742\pi\)
\(770\) 0 0
\(771\) 2.14378 7.46909i 0.0772064 0.268993i
\(772\) 0 0
\(773\) 25.4969 0.917059 0.458529 0.888679i \(-0.348376\pi\)
0.458529 + 0.888679i \(0.348376\pi\)
\(774\) 0 0
\(775\) 20.7208i 0.744314i
\(776\) 0 0
\(777\) 28.3713 27.3839i 1.01782 0.982393i
\(778\) 0 0
\(779\) −2.01222 1.16176i −0.0720953 0.0416243i
\(780\) 0 0
\(781\) 9.36995 5.40974i 0.335283 0.193576i
\(782\) 0 0
\(783\) 9.51744 29.2158i 0.340126 1.04409i
\(784\) 0 0
\(785\) −42.9903 + 24.8205i −1.53439 + 0.885881i
\(786\) 0 0
\(787\) 13.2295 22.9142i 0.471581 0.816802i −0.527891 0.849312i \(-0.677017\pi\)
0.999471 + 0.0325104i \(0.0103502\pi\)
\(788\) 0 0
\(789\) 27.6972 26.7332i 0.986045 0.951728i
\(790\) 0 0
\(791\) −38.3733 −1.36440
\(792\) 0 0
\(793\) 3.73189 0.132523
\(794\) 0 0
\(795\) −37.9008 10.8783i −1.34420 0.385814i
\(796\) 0 0
\(797\) 4.10557 7.11105i 0.145427 0.251886i −0.784105 0.620628i \(-0.786878\pi\)
0.929532 + 0.368741i \(0.120211\pi\)
\(798\) 0 0
\(799\) 1.65385 0.954848i 0.0585089 0.0337801i
\(800\) 0 0
\(801\) −15.8046 29.7607i −0.558430 1.05154i
\(802\) 0 0
\(803\) −33.0213 + 19.0649i −1.16530 + 0.672785i
\(804\) 0 0
\(805\) −32.1866 18.5830i −1.13443 0.654964i
\(806\) 0 0
\(807\) −5.43926 21.8393i −0.191471 0.768781i
\(808\) 0 0
\(809\) 4.36982i 0.153635i 0.997045 + 0.0768174i \(0.0244759\pi\)
−0.997045 + 0.0768174i \(0.975524\pi\)
\(810\) 0 0
\(811\) 0.393286 0.0138101 0.00690507 0.999976i \(-0.497802\pi\)
0.00690507 + 0.999976i \(0.497802\pi\)
\(812\) 0 0
\(813\) −18.7399 + 4.66732i −0.657237 + 0.163690i
\(814\) 0 0
\(815\) 8.12094 14.0659i 0.284464 0.492706i
\(816\) 0 0
\(817\) 1.97518 + 3.42112i 0.0691029 + 0.119690i
\(818\) 0 0
\(819\) −2.20098 + 1.16885i −0.0769085 + 0.0408429i
\(820\) 0 0
\(821\) −8.66193 15.0029i −0.302304 0.523605i 0.674354 0.738408i \(-0.264422\pi\)
−0.976657 + 0.214803i \(0.931089\pi\)
\(822\) 0 0
\(823\) −26.9923 15.5840i −0.940893 0.543225i −0.0506529 0.998716i \(-0.516130\pi\)
−0.890240 + 0.455491i \(0.849464\pi\)
\(824\) 0 0
\(825\) 10.2841 35.8304i 0.358045 1.24746i
\(826\) 0 0
\(827\) 36.3732i 1.26482i 0.774634 + 0.632410i \(0.217934\pi\)
−0.774634 + 0.632410i \(0.782066\pi\)
\(828\) 0 0
\(829\) 47.9890i 1.66673i −0.552726 0.833363i \(-0.686412\pi\)
0.552726 0.833363i \(-0.313588\pi\)
\(830\) 0 0
\(831\) −1.79866 1.86351i −0.0623947 0.0646444i
\(832\) 0 0
\(833\) 2.68415 + 1.54969i 0.0930002 + 0.0536937i
\(834\) 0 0
\(835\) 30.5747 + 52.9569i 1.05808 + 1.83265i
\(836\) 0 0
\(837\) 4.16126 + 19.6509i 0.143834 + 0.679233i
\(838\) 0 0
\(839\) −4.62312 8.00747i −0.159608 0.276449i 0.775120 0.631815i \(-0.217690\pi\)
−0.934727 + 0.355366i \(0.884356\pi\)
\(840\) 0 0
\(841\) −2.98420 + 5.16878i −0.102903 + 0.178234i
\(842\) 0 0
\(843\) 13.0556 + 13.5263i 0.449659 + 0.465872i
\(844\) 0 0
\(845\) −41.3418 −1.42220
\(846\) 0 0
\(847\) 10.7758i 0.370260i
\(848\) 0 0
\(849\) −40.1646 11.5281i −1.37845 0.395642i
\(850\) 0 0
\(851\) 51.4193 + 29.6870i 1.76263 + 1.01766i
\(852\) 0 0
\(853\) −13.1396 + 7.58616i −0.449892 + 0.259745i −0.707785 0.706428i \(-0.750305\pi\)
0.257893 + 0.966174i \(0.416972\pi\)
\(854\) 0 0
\(855\) −0.555503 + 15.6790i −0.0189978 + 0.536210i
\(856\) 0 0
\(857\) −24.4191 + 14.0984i −0.834140 + 0.481591i −0.855268 0.518186i \(-0.826608\pi\)
0.0211282 + 0.999777i \(0.493274\pi\)
\(858\) 0 0
\(859\) 3.33845 5.78236i 0.113906 0.197292i −0.803436 0.595392i \(-0.796997\pi\)
0.917342 + 0.398100i \(0.130330\pi\)
\(860\) 0 0
\(861\) 1.25958 + 5.05737i 0.0429263 + 0.172355i
\(862\) 0 0
\(863\) 54.3136 1.84885 0.924427 0.381358i \(-0.124543\pi\)
0.924427 + 0.381358i \(0.124543\pi\)
\(864\) 0 0
\(865\) 8.13386 0.276559
\(866\) 0 0
\(867\) −6.50855 26.1327i −0.221042 0.887512i
\(868\) 0 0
\(869\) −3.56063 + 6.16719i −0.120786 + 0.209208i
\(870\) 0 0
\(871\) 1.78437 1.03020i 0.0604610 0.0349071i
\(872\) 0 0
\(873\) −29.7478 18.6095i −1.00681 0.629837i
\(874\) 0 0
\(875\) −2.11274 + 1.21979i −0.0714238 + 0.0412365i
\(876\) 0 0
\(877\) 5.70769 + 3.29534i 0.192735 + 0.111276i 0.593262 0.805009i \(-0.297840\pi\)
−0.400527 + 0.916285i \(0.631173\pi\)
\(878\) 0 0
\(879\) 11.7882 + 3.38346i 0.397607 + 0.114121i
\(880\) 0 0
\(881\) 15.5607i 0.524252i 0.965034 + 0.262126i \(0.0844236\pi\)
−0.965034 + 0.262126i \(0.915576\pi\)
\(882\) 0 0
\(883\) −41.6548 −1.40180 −0.700898 0.713262i \(-0.747217\pi\)
−0.700898 + 0.713262i \(0.747217\pi\)
\(884\) 0 0
\(885\) −10.2641 10.6341i −0.345022 0.357463i
\(886\) 0 0
\(887\) −26.8247 + 46.4617i −0.900684 + 1.56003i −0.0740769 + 0.997253i \(0.523601\pi\)
−0.826608 + 0.562779i \(0.809732\pi\)
\(888\) 0 0
\(889\) −2.20098 3.81221i −0.0738186 0.127858i
\(890\) 0 0
\(891\) −2.55739 + 36.0456i −0.0856756 + 1.20757i
\(892\) 0 0
\(893\) 1.28773 + 2.23042i 0.0430923 + 0.0746381i
\(894\) 0 0
\(895\) −30.6520 17.6970i −1.02458 0.591544i
\(896\) 0 0
\(897\) −2.60602 2.69999i −0.0870126 0.0901500i
\(898\) 0 0
\(899\) 22.8593i 0.762400i
\(900\) 0 0
\(901\) 8.52093i 0.283873i
\(902\) 0 0
\(903\) 2.44460 8.51717i 0.0813512 0.283434i
\(904\) 0 0
\(905\) −39.9800 23.0824i −1.32898 0.767286i
\(906\) 0 0
\(907\) 2.86449 + 4.96144i 0.0951139 + 0.164742i 0.909656 0.415362i \(-0.136345\pi\)
−0.814542 + 0.580104i \(0.803012\pi\)
\(908\) 0 0
\(909\) −10.3518 6.47585i −0.343348 0.214790i
\(910\) 0 0
\(911\) −21.2846 36.8661i −0.705192 1.22143i −0.966622 0.256206i \(-0.917528\pi\)
0.261430 0.965222i \(-0.415806\pi\)
\(912\) 0 0
\(913\) −3.03234 + 5.25216i −0.100356 + 0.173821i
\(914\) 0 0
\(915\) −51.1369 + 12.7360i −1.69053 + 0.421041i
\(916\) 0 0
\(917\) 2.56222 0.0846119
\(918\) 0 0
\(919\) 40.3722i 1.33175i −0.746061 0.665877i \(-0.768057\pi\)
0.746061 0.665877i \(-0.231943\pi\)
\(920\) 0 0
\(921\) 5.40205 + 21.6899i 0.178004 + 0.714707i
\(922\) 0 0
\(923\) −0.921317 0.531923i −0.0303255 0.0175085i
\(924\) 0 0
\(925\) 50.2249 28.9974i 1.65139 0.953428i
\(926\) 0 0
\(927\) 54.2774 + 1.92304i 1.78270 + 0.0631609i
\(928\) 0 0
\(929\) 7.87141 4.54456i 0.258253 0.149102i −0.365285 0.930896i \(-0.619028\pi\)
0.623537 + 0.781794i \(0.285695\pi\)
\(930\) 0 0
\(931\) −2.08995 + 3.61991i −0.0684955 + 0.118638i
\(932\) 0 0
\(933\) −26.2829 7.54374i −0.860465 0.246971i
\(934\) 0 0
\(935\) 15.5696 0.509180
\(936\) 0 0
\(937\) 5.39574 0.176271 0.0881355 0.996108i \(-0.471909\pi\)
0.0881355 + 0.996108i \(0.471909\pi\)
\(938\) 0 0
\(939\) 5.14359 4.96458i 0.167855 0.162013i
\(940\) 0 0
\(941\) −22.2304 + 38.5041i −0.724689 + 1.25520i 0.234413 + 0.972137i \(0.424683\pi\)
−0.959102 + 0.283061i \(0.908650\pi\)
\(942\) 0 0
\(943\) −6.79643 + 3.92392i −0.221322 + 0.127780i
\(944\) 0 0
\(945\) 26.1703 23.5278i 0.851321 0.765358i
\(946\) 0 0
\(947\) 53.2162 30.7244i 1.72930 0.998409i 0.836454 0.548037i \(-0.184625\pi\)
0.892841 0.450372i \(-0.148708\pi\)
\(948\) 0 0
\(949\) 3.24688 + 1.87459i 0.105398 + 0.0608517i
\(950\) 0 0
\(951\) 18.8989 18.2412i 0.612839 0.591511i
\(952\) 0 0
\(953\) 22.6195i 0.732716i −0.930474 0.366358i \(-0.880605\pi\)
0.930474 0.366358i \(-0.119395\pi\)
\(954\) 0 0
\(955\) 1.52615 0.0493850
\(956\) 0 0
\(957\) 11.3454 39.5283i 0.366746 1.27777i
\(958\) 0 0
\(959\) 7.53716 13.0547i 0.243388 0.421560i
\(960\) 0 0
\(961\) −8.02829 13.9054i −0.258977 0.448562i
\(962\) 0 0
\(963\) −17.4436 32.8469i −0.562112 1.05848i
\(964\) 0 0
\(965\) 34.3449 + 59.4871i 1.10560 + 1.91496i
\(966\) 0 0
\(967\) 23.8616 + 13.7765i 0.767337 + 0.443022i 0.831924 0.554890i \(-0.187240\pi\)
−0.0645868 + 0.997912i \(0.520573\pi\)
\(968\) 0 0
\(969\) −3.28980 + 0.819352i −0.105684 + 0.0263214i
\(970\) 0 0
\(971\) 23.4973i 0.754064i 0.926200 + 0.377032i \(0.123055\pi\)
−0.926200 + 0.377032i \(0.876945\pi\)
\(972\) 0 0
\(973\) 46.4500i 1.48912i
\(974\) 0 0
\(975\) −3.55669 + 0.885822i −0.113905 + 0.0283690i
\(976\) 0 0
\(977\) 26.2982 + 15.1832i 0.841353 + 0.485755i 0.857724 0.514111i \(-0.171878\pi\)
−0.0163711 + 0.999866i \(0.505211\pi\)
\(978\) 0 0
\(979\) −22.5496 39.0571i −0.720689 1.24827i
\(980\) 0 0
\(981\) 2.47862 + 4.66732i 0.0791361 + 0.149016i
\(982\) 0 0
\(983\) −15.6881 27.1725i −0.500372 0.866669i −1.00000 0.000429288i \(-0.999863\pi\)
0.499628 0.866240i \(-0.333470\pi\)
\(984\) 0 0
\(985\) −34.4960 + 59.7489i −1.09914 + 1.90376i
\(986\) 0 0
\(987\) 1.59377 5.55281i 0.0507303 0.176748i
\(988\) 0 0
\(989\) 13.3427 0.424272
\(990\) 0 0
\(991\) 19.2702i 0.612138i 0.952009 + 0.306069i \(0.0990138\pi\)
−0.952009 + 0.306069i \(0.900986\pi\)
\(992\) 0 0
\(993\) −17.6872 + 17.0716i −0.561285 + 0.541751i
\(994\) 0 0
\(995\) −16.9992 9.81447i −0.538910 0.311140i
\(996\) 0 0
\(997\) 44.0083 25.4082i 1.39376 0.804687i 0.400029 0.916502i \(-0.369000\pi\)
0.993729 + 0.111816i \(0.0356667\pi\)
\(998\) 0 0
\(999\) −41.8081 + 37.5864i −1.32275 + 1.18918i
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 288.2.p.b.239.4 16
3.2 odd 2 864.2.p.b.719.2 16
4.3 odd 2 72.2.l.b.59.5 yes 16
8.3 odd 2 inner 288.2.p.b.239.3 16
8.5 even 2 72.2.l.b.59.2 yes 16
9.2 odd 6 inner 288.2.p.b.47.3 16
9.4 even 3 2592.2.f.b.1295.4 16
9.5 odd 6 2592.2.f.b.1295.14 16
9.7 even 3 864.2.p.b.143.7 16
12.11 even 2 216.2.l.b.179.4 16
24.5 odd 2 216.2.l.b.179.7 16
24.11 even 2 864.2.p.b.719.7 16
36.7 odd 6 216.2.l.b.35.7 16
36.11 even 6 72.2.l.b.11.2 16
36.23 even 6 648.2.f.b.323.14 16
36.31 odd 6 648.2.f.b.323.3 16
72.5 odd 6 648.2.f.b.323.4 16
72.11 even 6 inner 288.2.p.b.47.4 16
72.13 even 6 648.2.f.b.323.13 16
72.29 odd 6 72.2.l.b.11.5 yes 16
72.43 odd 6 864.2.p.b.143.2 16
72.59 even 6 2592.2.f.b.1295.3 16
72.61 even 6 216.2.l.b.35.4 16
72.67 odd 6 2592.2.f.b.1295.13 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.2.l.b.11.2 16 36.11 even 6
72.2.l.b.11.5 yes 16 72.29 odd 6
72.2.l.b.59.2 yes 16 8.5 even 2
72.2.l.b.59.5 yes 16 4.3 odd 2
216.2.l.b.35.4 16 72.61 even 6
216.2.l.b.35.7 16 36.7 odd 6
216.2.l.b.179.4 16 12.11 even 2
216.2.l.b.179.7 16 24.5 odd 2
288.2.p.b.47.3 16 9.2 odd 6 inner
288.2.p.b.47.4 16 72.11 even 6 inner
288.2.p.b.239.3 16 8.3 odd 2 inner
288.2.p.b.239.4 16 1.1 even 1 trivial
648.2.f.b.323.3 16 36.31 odd 6
648.2.f.b.323.4 16 72.5 odd 6
648.2.f.b.323.13 16 72.13 even 6
648.2.f.b.323.14 16 36.23 even 6
864.2.p.b.143.2 16 72.43 odd 6
864.2.p.b.143.7 16 9.7 even 3
864.2.p.b.719.2 16 3.2 odd 2
864.2.p.b.719.7 16 24.11 even 2
2592.2.f.b.1295.3 16 72.59 even 6
2592.2.f.b.1295.4 16 9.4 even 3
2592.2.f.b.1295.13 16 72.67 odd 6
2592.2.f.b.1295.14 16 9.5 odd 6