Properties

Label 288.2.p.b.47.3
Level $288$
Weight $2$
Character 288.47
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 47.3
Root \(1.12063 - 0.862658i\) of defining polynomial
Character \(\chi\) \(=\) 288.47
Dual form 288.2.p.b.239.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.418594 + 1.68071i) q^{3} +(-1.60936 - 2.78750i) q^{5} +(-1.82223 - 1.05206i) q^{7} +(-2.64956 - 1.40707i) q^{9} +O(q^{10})\) \(q+(-0.418594 + 1.68071i) q^{3} +(-1.60936 - 2.78750i) q^{5} +(-1.82223 - 1.05206i) q^{7} +(-2.64956 - 1.40707i) q^{9} +(-3.47720 - 2.00756i) q^{11} +(-0.341902 + 0.197397i) q^{13} +(5.35864 - 1.53804i) q^{15} +1.20474i q^{17} +1.62474 q^{19} +(2.53098 - 2.62224i) q^{21} +(-2.74384 - 4.75248i) q^{23} +(-2.68011 + 4.64208i) q^{25} +(3.47396 - 3.86414i) q^{27} +(2.95670 - 5.12116i) q^{29} +(-3.34777 + 1.93284i) q^{31} +(4.82967 - 5.00381i) q^{33} +6.77261i q^{35} +10.8195i q^{37} +(-0.188649 - 0.657267i) q^{39} +(-1.23849 + 0.715041i) q^{41} +(1.21569 - 2.10564i) q^{43} +(0.341902 + 9.65013i) q^{45} +(-0.792576 + 1.37278i) q^{47} +(-1.28633 - 2.22799i) q^{49} +(-2.02482 - 0.504297i) q^{51} -7.07284 q^{53} +12.9236i q^{55} +(-0.680107 + 2.73072i) q^{57} +(2.29587 - 1.32552i) q^{59} +(-8.18631 - 4.72637i) q^{61} +(3.34777 + 5.35150i) q^{63} +(1.10049 + 0.635369i) q^{65} +(2.60947 + 4.51973i) q^{67} +(9.13608 - 2.62224i) q^{69} +2.69468 q^{71} +9.49652 q^{73} +(-6.68011 - 6.44762i) q^{75} +(4.22417 + 7.31647i) q^{77} +(-1.53599 - 0.886804i) q^{79} +(5.04032 + 7.45622i) q^{81} +(1.30809 + 0.755228i) q^{83} +(3.35821 - 1.93887i) q^{85} +(7.36952 + 7.11304i) q^{87} -11.2323i q^{89} +0.830698 q^{91} +(-1.84718 - 6.43570i) q^{93} +(-2.61480 - 4.52897i) q^{95} +(5.84818 - 10.1294i) q^{97} +(6.38828 + 10.2118i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 6 q^{3} - 6 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

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

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 −0.961107 0.276177i \(-0.910932\pi\)
0.241377 0.970431i \(-0.422401\pi\)
\(6\) 0 0
\(7\) −1.82223 1.05206i −0.688736 0.397642i 0.114402 0.993435i \(-0.463505\pi\)
−0.803139 + 0.595792i \(0.796838\pi\)
\(8\) 0 0
\(9\) −2.64956 1.40707i −0.883186 0.469023i
\(10\) 0 0
\(11\) −3.47720 2.00756i −1.04842 0.605303i −0.126211 0.992003i \(-0.540282\pi\)
−0.922206 + 0.386700i \(0.873615\pi\)
\(12\) 0 0
\(13\) −0.341902 + 0.197397i −0.0948267 + 0.0547482i −0.546663 0.837352i \(-0.684102\pi\)
0.451837 + 0.892101i \(0.350769\pi\)
\(14\) 0 0
\(15\) 5.35864 1.53804i 1.38360 0.397120i
\(16\) 0 0
\(17\) 1.20474i 0.292192i 0.989270 + 0.146096i \(0.0466709\pi\)
−0.989270 + 0.146096i \(0.953329\pi\)
\(18\) 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 −0.996347 0.0853986i \(-0.972784\pi\)
0.424216 0.905561i \(-0.360550\pi\)
\(24\) 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 −0.449294 0.893384i \(-0.648324\pi\)
0.998340 0.0575919i \(-0.0183422\pi\)
\(30\) 0 0
\(31\) −3.34777 + 1.93284i −0.601277 + 0.347148i −0.769544 0.638594i \(-0.779516\pi\)
0.168267 + 0.985742i \(0.446183\pi\)
\(32\) 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 −0.593582 0.804773i \(-0.702287\pi\)
0.400163 + 0.916444i \(0.368953\pi\)
\(42\) 0 0
\(43\) 1.21569 2.10564i 0.185391 0.321107i −0.758317 0.651886i \(-0.773978\pi\)
0.943708 + 0.330779i \(0.107311\pi\)
\(44\) 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 \(-0.870215\pi\)
0.802414 + 0.596768i \(0.203549\pi\)
\(48\) 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 \(-0.661459\pi\)
−0.485765 + 0.874090i \(0.661459\pi\)
\(54\) 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 −0.343050 0.939317i \(-0.611460\pi\)
0.641947 + 0.766749i \(0.278127\pi\)
\(60\) 0 0
\(61\) −8.18631 4.72637i −1.04815 0.605149i −0.126019 0.992028i \(-0.540220\pi\)
−0.922131 + 0.386879i \(0.873553\pi\)
\(62\) 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 0.980237 0.197825i \(-0.0633878\pi\)
−0.661440 + 0.749998i \(0.730054\pi\)
\(68\) 0 0
\(69\) 9.13608 2.62224i 1.09985 0.315681i
\(70\) 0 0
\(71\) 2.69468 0.319800 0.159900 0.987133i \(-0.448883\pi\)
0.159900 + 0.987133i \(0.448883\pi\)
\(72\) 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 \(-0.365145\pi\)
−0.583911 + 0.811818i \(0.698478\pi\)
\(80\) 0 0
\(81\) 5.04032 + 7.45622i 0.560036 + 0.828469i
\(82\) 0 0
\(83\) 1.30809 + 0.755228i 0.143582 + 0.0828971i 0.570070 0.821596i \(-0.306916\pi\)
−0.426488 + 0.904493i \(0.640249\pi\)
\(84\) 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 \(-0.797028\pi\)
0.803494 0.595312i \(-0.202972\pi\)
\(90\) 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 −0.399923 0.916549i \(-0.630963\pi\)
0.993716 0.111931i \(-0.0357036\pi\)
\(98\) 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 \(-0.898240\pi\)
0.746834 + 0.665010i \(0.231573\pi\)
\(102\) 0 0
\(103\) 15.6784 9.05191i 1.54484 0.891911i 0.546312 0.837582i \(-0.316031\pi\)
0.998523 0.0543294i \(-0.0173021\pi\)
\(104\) 0 0
\(105\) −11.3828 2.83497i −1.11084 0.276665i
\(106\) 0 0
\(107\) 12.3971i 1.19848i −0.800571 0.599238i \(-0.795470\pi\)
0.800571 0.599238i \(-0.204530\pi\)
\(108\) 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 −0.999869 0.0162153i \(-0.994838\pi\)
−0.485891 + 0.874019i \(0.661505\pi\)
\(114\) 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 −0.453223 0.891397i \(-0.649726\pi\)
0.545361 + 0.838201i \(0.316393\pi\)
\(132\) 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 0.741047 0.671454i \(-0.234330\pi\)
−0.210973 + 0.977492i \(0.567663\pi\)
\(138\) 0 0
\(139\) −11.0378 19.1181i −0.936217 1.62158i −0.772450 0.635076i \(-0.780969\pi\)
−0.163767 0.986499i \(-0.552365\pi\)
\(140\) 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 \(-0.168852\pi\)
−0.869438 + 0.494041i \(0.835519\pi\)
\(150\) 0 0
\(151\) −16.5201 9.53789i −1.34439 0.776182i −0.356939 0.934128i \(-0.616180\pi\)
−0.987448 + 0.157945i \(0.949513\pi\)
\(152\) 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 \(-0.455651\pi\)
0.927072 + 0.374884i \(0.122317\pi\)
\(158\) 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 0.954700 + 0.297571i \(0.0961765\pi\)
−0.219646 + 0.975580i \(0.570490\pi\)
\(168\) 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 \(-0.863959\pi\)
0.813988 + 0.580881i \(0.197292\pi\)
\(174\) 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 \(0.134803\pi\)
−0.911658 + 0.410949i \(0.865197\pi\)
\(180\) 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 \(-0.838794\pi\)
0.857321 + 0.514782i \(0.172127\pi\)
\(192\) 0 0
\(193\) −10.6703 18.4815i −0.768067 1.33033i −0.938610 0.344981i \(-0.887885\pi\)
0.170543 0.985350i \(-0.445448\pi\)
\(194\) 0 0
\(195\) −1.52853 + 1.58364i −0.109460 + 0.113407i
\(196\) 0 0
\(197\) 21.4346 1.52715 0.763575 0.645719i \(-0.223442\pi\)
0.763575 + 0.645719i \(0.223442\pi\)
\(198\) 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 0.815179 0.579209i \(-0.196638\pi\)
−0.909199 + 0.416362i \(0.863305\pi\)
\(212\) 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 \(-0.159961\pi\)
0.0210661 + 0.999778i \(0.493294\pi\)
\(224\) 0 0
\(225\) 13.6328 8.52837i 0.908855 0.568558i
\(226\) 0 0
\(227\) −13.9546 8.05671i −0.926202 0.534743i −0.0405935 0.999176i \(-0.512925\pi\)
−0.885608 + 0.464433i \(0.846258\pi\)
\(228\) 0 0
\(229\) 9.60052 5.54286i 0.634420 0.366283i −0.148042 0.988981i \(-0.547297\pi\)
0.782462 + 0.622698i \(0.213964\pi\)
\(230\) 0 0
\(231\) −14.0651 + 4.03696i −0.925413 + 0.265613i
\(232\) 0 0
\(233\) 8.96547i 0.587348i −0.955906 0.293674i \(-0.905122\pi\)
0.955906 0.293674i \(-0.0948780\pi\)
\(234\) 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 0.947096 + 0.320951i \(0.104002\pi\)
−0.195597 + 0.980684i \(0.562664\pi\)
\(240\) 0 0
\(241\) −4.27609 + 7.40641i −0.275447 + 0.477089i −0.970248 0.242114i \(-0.922159\pi\)
0.694801 + 0.719202i \(0.255493\pi\)
\(242\) 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 \(-0.857711\pi\)
0.901742 0.432275i \(-0.142289\pi\)
\(252\) 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 −0.373901 0.927469i \(-0.621980\pi\)
0.616261 + 0.787542i \(0.288647\pi\)
\(258\) 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 0.288156 + 0.957583i \(0.406958\pi\)
−0.973370 + 0.229241i \(0.926376\pi\)
\(264\) 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 \(-0.629648\pi\)
−0.396133 + 0.918193i \(0.629648\pi\)
\(270\) 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 \(-0.347637\pi\)
−0.538399 + 0.842690i \(0.680971\pi\)
\(278\) 0 0
\(279\) 11.5897 0.410623i 0.693860 0.0245833i
\(280\) 0 0
\(281\) −9.39961 5.42687i −0.560734 0.323740i 0.192706 0.981256i \(-0.438274\pi\)
−0.753440 + 0.657517i \(0.771607\pi\)
\(282\) 0 0
\(283\) 12.0627 + 20.8931i 0.717050 + 1.24197i 0.962163 + 0.272473i \(0.0878415\pi\)
−0.245113 + 0.969494i \(0.578825\pi\)
\(284\) 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 \(-0.100352\pi\)
−0.743884 + 0.668309i \(0.767019\pi\)
\(294\) 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 \(-0.314389\pi\)
−0.998229 + 0.0594804i \(0.981056\pi\)
\(312\) 0 0
\(313\) 2.06365 3.57434i 0.116644 0.202034i −0.801792 0.597604i \(-0.796120\pi\)
0.918436 + 0.395570i \(0.129453\pi\)
\(314\) 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 \(-0.973365\pi\)
0.570632 + 0.821206i \(0.306698\pi\)
\(318\) 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 −0.992455 0.122611i \(-0.960873\pi\)
0.602412 + 0.798186i \(0.294207\pi\)
\(332\) 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 −0.967243 0.253853i \(-0.918302\pi\)
0.263779 0.964583i \(-0.415031\pi\)
\(338\) 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 −0.774395 0.632702i \(-0.781946\pi\)
0.160739 + 0.986997i \(0.448612\pi\)
\(348\) 0 0
\(349\) 12.7838 + 7.38075i 0.684303 + 0.395082i 0.801474 0.598029i \(-0.204049\pi\)
−0.117171 + 0.993112i \(0.537383\pi\)
\(350\) 0 0
\(351\) −0.424983 + 2.00691i −0.0226839 + 0.107121i
\(352\) 0 0
\(353\) −1.21582 0.701955i −0.0647116 0.0373613i 0.467295 0.884101i \(-0.345229\pi\)
−0.532007 + 0.846740i \(0.678562\pi\)
\(354\) 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 \(-0.403521\pi\)
0.298477 + 0.954417i \(0.403521\pi\)
\(360\) 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 \(-0.237651\pi\)
−0.221161 + 0.975237i \(0.570985\pi\)
\(368\) 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 \(-0.881864\pi\)
−0.151873 + 0.988400i \(0.548530\pi\)
\(374\) 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 −0.933764 0.357890i \(-0.883496\pi\)
0.156940 0.987608i \(-0.449837\pi\)
\(384\) 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 −0.485873 0.874030i \(-0.661498\pi\)
0.999868 0.0162366i \(-0.00516850\pi\)
\(390\) 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 −0.974325 0.225147i \(-0.927714\pi\)
−0.292179 + 0.956364i \(0.594380\pi\)
\(402\) 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 0.943187 + 0.332263i \(0.107812\pi\)
−0.183845 + 0.982955i \(0.558855\pi\)
\(410\) 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 −0.755696 0.654923i \(-0.772701\pi\)
0.189332 + 0.981913i \(0.439368\pi\)
\(420\) 0 0
\(421\) −23.9825 13.8463i −1.16884 0.674828i −0.215431 0.976519i \(-0.569116\pi\)
−0.953406 + 0.301691i \(0.902449\pi\)
\(422\) 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 \(-0.748870\pi\)
−0.704592 + 0.709613i \(0.748870\pi\)
\(432\) 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 \(-0.0977175\pi\)
0.214920 + 0.976632i \(0.431051\pi\)
\(440\) 0 0
\(441\) 0.273275 + 7.71314i 0.0130131 + 0.367292i
\(442\) 0 0
\(443\) 23.3499 + 13.4811i 1.10939 + 0.640506i 0.938671 0.344814i \(-0.112058\pi\)
0.170718 + 0.985320i \(0.445391\pi\)
\(444\) 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 \(-0.813354\pi\)
0.832957 0.553338i \(-0.186646\pi\)
\(450\) 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 −0.990633 0.136550i \(-0.956398\pi\)
0.613573 + 0.789638i \(0.289732\pi\)
\(458\) 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 \(-0.756296\pi\)
0.960618 + 0.277874i \(0.0896297\pi\)
\(462\) 0 0
\(463\) −22.3273 + 12.8907i −1.03764 + 0.599080i −0.919163 0.393877i \(-0.871134\pi\)
−0.118474 + 0.992957i \(0.537800\pi\)
\(464\) 0 0
\(465\) −14.9667 + 15.5064i −0.694065 + 0.719091i
\(466\) 0 0
\(467\) 10.8110i 0.500271i −0.968211 0.250136i \(-0.919525\pi\)
0.968211 0.250136i \(-0.0804752\pi\)
\(468\) 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 \(-0.924176\pi\)
0.690229 + 0.723591i \(0.257510\pi\)
\(480\) 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 −0.907640 0.419749i \(-0.862118\pi\)
−0.0903072 + 0.995914i \(0.528785\pi\)
\(492\) 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 0.963574 0.267442i \(-0.0861783\pi\)
−0.713398 + 0.700759i \(0.752845\pi\)
\(500\) 0 0
\(501\) −31.6285 + 9.07802i −1.41306 + 0.405576i
\(502\) 0 0
\(503\) −22.3635 −0.997137 −0.498569 0.866850i \(-0.666141\pi\)
−0.498569 + 0.866850i \(0.666141\pi\)
\(504\) 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 \(-0.0791222\pi\)
−0.697690 + 0.716399i \(0.745789\pi\)
\(510\) 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 \(-0.722768\pi\)
0.644101 0.764940i \(-0.277232\pi\)
\(522\) 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 −0.555979 0.831196i \(-0.687657\pi\)
0.997827 + 0.0658943i \(0.0209900\pi\)
\(548\) 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 \(-0.348321\pi\)
0.458684 + 0.888600i \(0.348321\pi\)
\(558\) 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 0.549683 0.835373i \(-0.314748\pi\)
0.998296 0.0583533i \(-0.0185850\pi\)
\(564\) 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 0.846732 0.532019i \(-0.178567\pi\)
−0.0373758 + 0.999301i \(0.511900\pi\)
\(570\) 0 0
\(571\) −1.30386 2.25835i −0.0545649 0.0945091i 0.837453 0.546510i \(-0.184044\pi\)
−0.892018 + 0.452001i \(0.850711\pi\)
\(572\) 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 0.903208 0.429203i \(-0.141206\pi\)
0.0799032 + 0.996803i \(0.474539\pi\)
\(588\) 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 \(0.242261\pi\)
−0.724088 + 0.689707i \(0.757739\pi\)
\(594\) 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 \(-0.110110\pi\)
−0.764020 + 0.645193i \(0.776777\pi\)
\(600\) 0 0
\(601\) 11.3533 19.6644i 0.463109 0.802128i −0.536005 0.844215i \(-0.680067\pi\)
0.999114 + 0.0420865i \(0.0134005\pi\)
\(602\) 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 \(-0.520041\pi\)
0.832850 + 0.553498i \(0.186708\pi\)
\(608\) 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 −0.417998 0.908448i \(-0.637268\pi\)
0.577740 + 0.816221i \(0.303935\pi\)
\(618\) 0 0
\(619\) 8.24726 14.2847i 0.331486 0.574150i −0.651318 0.758805i \(-0.725784\pi\)
0.982803 + 0.184655i \(0.0591169\pi\)
\(620\) 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 0.959415 0.281998i \(-0.0909973\pi\)
0.235490 + 0.971877i \(0.424331\pi\)
\(642\) 0 0
\(643\) −18.5870 32.1936i −0.733000 1.26959i −0.955595 0.294682i \(-0.904786\pi\)
0.222596 0.974911i \(-0.428547\pi\)
\(644\) 0 0
\(645\) 3.27590 13.1531i 0.128988 0.517905i
\(646\) 0 0
\(647\) 9.36933 0.368346 0.184173 0.982894i \(-0.441039\pi\)
0.184173 + 0.982894i \(0.441039\pi\)
\(648\) 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 \(-0.0698576\pi\)
−0.676547 + 0.736400i \(0.736524\pi\)
\(654\) 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 0.123811 0.992306i \(-0.460488\pi\)
−0.797457 + 0.603376i \(0.793822\pi\)
\(660\) 0 0
\(661\) −30.6907 + 17.7193i −1.19373 + 0.689201i −0.959151 0.282896i \(-0.908705\pi\)
−0.234580 + 0.972097i \(0.575372\pi\)
\(662\) 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 −0.825869 0.563862i \(-0.809315\pi\)
0.901253 + 0.433293i \(0.142648\pi\)
\(674\) 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 \(-0.812557\pi\)
0.896794 + 0.442448i \(0.145890\pi\)
\(678\) 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 \(-0.940530\pi\)
0.982598 0.185746i \(-0.0594702\pi\)
\(684\) 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 0.201720 + 0.979443i \(0.435347\pi\)
−0.949083 + 0.315027i \(0.897986\pi\)
\(692\) 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 \(-0.426838\pi\)
0.227826 + 0.973702i \(0.426838\pi\)
\(702\) 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 \(-0.252528\pi\)
−0.266483 + 0.963840i \(0.585862\pi\)
\(710\) 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 \(-0.261969\pi\)
0.680025 + 0.733189i \(0.261969\pi\)
\(720\) 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 \(-0.360730\pi\)
−0.572596 + 0.819838i \(0.694064\pi\)
\(728\) 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 \(-0.424389\pi\)
0.959363 + 0.282175i \(0.0910557\pi\)
\(734\) 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 −0.928647 0.370964i \(-0.879027\pi\)
0.143060 0.989714i \(-0.454306\pi\)
\(744\) 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 \(-0.470905\pi\)
0.908049 + 0.418863i \(0.137571\pi\)
\(752\) 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 0.198711 0.980058i \(-0.436324\pi\)
0.948111 + 0.317940i \(0.102991\pi\)
\(762\) 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 0.829296 0.558809i \(-0.188742\pi\)
−0.898591 + 0.438787i \(0.855408\pi\)
\(770\) 0 0
\(771\) 2.14378 + 7.46909i 0.0772064 + 0.268993i
\(772\) 0 0
\(773\) −25.4969 −0.917059 −0.458529 0.888679i \(-0.651624\pi\)
−0.458529 + 0.888679i \(0.651624\pi\)
\(774\) 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 0.999471 0.0325104i \(-0.0103502\pi\)
−0.527891 + 0.849312i \(0.677017\pi\)
\(788\) 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 \(-0.213122\pi\)
−0.929532 + 0.368741i \(0.879789\pi\)
\(798\) 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 \(-0.975524\pi\)
0.997045 0.0768174i \(-0.0244759\pi\)
\(810\) 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 \(-0.735578\pi\)
0.976657 + 0.214803i \(0.0689110\pi\)
\(822\) 0 0
\(823\) 26.9923 15.5840i 0.940893 0.543225i 0.0506529 0.998716i \(-0.483870\pi\)
0.890240 + 0.455491i \(0.150536\pi\)
\(824\) 0 0
\(825\) 10.2841 + 35.8304i 0.358045 + 1.24746i
\(826\) 0 0
\(827\) 36.3732i 1.26482i −0.774634 0.632410i \(-0.782066\pi\)
0.774634 0.632410i \(-0.217934\pi\)
\(828\) 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 \(-0.782310\pi\)
0.934727 + 0.355366i \(0.115644\pi\)
\(840\) 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 \(-0.249695\pi\)
−0.257893 + 0.966174i \(0.583028\pi\)
\(854\) 0 0
\(855\) 0.555503 + 15.6790i 0.0189978 + 0.536210i
\(856\) 0 0
\(857\) −24.4191 14.0984i −0.834140 0.481591i 0.0211282 0.999777i \(-0.493274\pi\)
−0.855268 + 0.518186i \(0.826608\pi\)
\(858\) 0 0
\(859\) 3.33845 + 5.78236i 0.113906 + 0.197292i 0.917342 0.398100i \(-0.130330\pi\)
−0.803436 + 0.595392i \(0.796997\pi\)
\(860\) 0 0
\(861\) −1.25958 + 5.05737i −0.0429263 + 0.172355i
\(862\) 0 0
\(863\) −54.3136 −1.84885 −0.924427 0.381358i \(-0.875457\pi\)
−0.924427 + 0.381358i \(0.875457\pi\)
\(864\) 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 \(-0.702160\pi\)
0.400527 + 0.916285i \(0.368827\pi\)
\(878\) 0 0
\(879\) −11.7882 + 3.38346i −0.397607 + 0.114121i
\(880\) 0 0
\(881\) 15.5607i 0.524252i −0.965034 0.262126i \(-0.915576\pi\)
0.965034 0.262126i \(-0.0844236\pi\)
\(882\) 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 0.826608 + 0.562779i \(0.190268\pi\)
0.0740769 + 0.997253i \(0.476399\pi\)
\(888\) 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 −0.814542 0.580104i \(-0.803012\pi\)
0.909656 + 0.415362i \(0.136345\pi\)
\(908\) 0 0
\(909\) 10.3518 6.47585i 0.343348 0.214790i
\(910\) 0 0
\(911\) 21.2846 36.8661i 0.705192 1.22143i −0.261430 0.965222i \(-0.584194\pi\)
0.966622 0.256206i \(-0.0824725\pi\)
\(912\) 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 0.623537 0.781794i \(-0.285695\pi\)
−0.365285 + 0.930896i \(0.619028\pi\)
\(930\) 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 0.959102 + 0.283061i \(0.0913499\pi\)
−0.234413 + 0.972137i \(0.575317\pi\)
\(942\) 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 0.892841 + 0.450372i \(0.148708\pi\)
0.836454 + 0.548037i \(0.184625\pi\)
\(948\) 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 \(0.119395\pi\)
−0.930474 + 0.366358i \(0.880605\pi\)
\(954\) 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 \(-0.812760\pi\)
0.0645868 + 0.997912i \(0.479427\pi\)
\(968\) 0 0
\(969\) −3.28980 0.819352i −0.105684 0.0263214i
\(970\) 0 0
\(971\) 23.4973i 0.754064i −0.926200 0.377032i \(-0.876945\pi\)
0.926200 0.377032i \(-0.123055\pi\)
\(972\) 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 −0.0163711 0.999866i \(-0.505211\pi\)
0.857724 + 0.514111i \(0.171878\pi\)
\(978\) 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 −0.499628 0.866240i \(-0.666530\pi\)
1.00000 0.000429288i \(-0.000136646\pi\)
\(984\) 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 \(-0.631000\pi\)
−0.993729 + 0.111816i \(0.964333\pi\)
\(998\) 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.47.3 16
3.2 odd 2 864.2.p.b.143.7 16
4.3 odd 2 72.2.l.b.11.2 16
8.3 odd 2 inner 288.2.p.b.47.4 16
8.5 even 2 72.2.l.b.11.5 yes 16
9.2 odd 6 2592.2.f.b.1295.4 16
9.4 even 3 864.2.p.b.719.2 16
9.5 odd 6 inner 288.2.p.b.239.4 16
9.7 even 3 2592.2.f.b.1295.14 16
12.11 even 2 216.2.l.b.35.7 16
24.5 odd 2 216.2.l.b.35.4 16
24.11 even 2 864.2.p.b.143.2 16
36.7 odd 6 648.2.f.b.323.14 16
36.11 even 6 648.2.f.b.323.3 16
36.23 even 6 72.2.l.b.59.5 yes 16
36.31 odd 6 216.2.l.b.179.4 16
72.5 odd 6 72.2.l.b.59.2 yes 16
72.11 even 6 2592.2.f.b.1295.13 16
72.13 even 6 216.2.l.b.179.7 16
72.29 odd 6 648.2.f.b.323.13 16
72.43 odd 6 2592.2.f.b.1295.3 16
72.59 even 6 inner 288.2.p.b.239.3 16
72.61 even 6 648.2.f.b.323.4 16
72.67 odd 6 864.2.p.b.719.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.2.l.b.11.2 16 4.3 odd 2
72.2.l.b.11.5 yes 16 8.5 even 2
72.2.l.b.59.2 yes 16 72.5 odd 6
72.2.l.b.59.5 yes 16 36.23 even 6
216.2.l.b.35.4 16 24.5 odd 2
216.2.l.b.35.7 16 12.11 even 2
216.2.l.b.179.4 16 36.31 odd 6
216.2.l.b.179.7 16 72.13 even 6
288.2.p.b.47.3 16 1.1 even 1 trivial
288.2.p.b.47.4 16 8.3 odd 2 inner
288.2.p.b.239.3 16 72.59 even 6 inner
288.2.p.b.239.4 16 9.5 odd 6 inner
648.2.f.b.323.3 16 36.11 even 6
648.2.f.b.323.4 16 72.61 even 6
648.2.f.b.323.13 16 72.29 odd 6
648.2.f.b.323.14 16 36.7 odd 6
864.2.p.b.143.2 16 24.11 even 2
864.2.p.b.143.7 16 3.2 odd 2
864.2.p.b.719.2 16 9.4 even 3
864.2.p.b.719.7 16 72.67 odd 6
2592.2.f.b.1295.3 16 72.43 odd 6
2592.2.f.b.1295.4 16 9.2 odd 6
2592.2.f.b.1295.13 16 72.11 even 6
2592.2.f.b.1295.14 16 9.7 even 3