Properties

Label 288.2.p.b.239.5
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: \( x^{16} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 16 x^{12} - 12 x^{11} - 8 x^{10} + 36 x^{9} - 68 x^{8} + 72 x^{7} - 32 x^{6} - 96 x^{5} + 256 x^{4} - 384 x^{3} + 448 x^{2} - 384 x + 256 \) 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 239.5
Root \(-0.409484 + 1.35363i\) of defining polynomial
Character \(\chi\) \(=\) 288.239
Dual form 288.2.p.b.47.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.12774 + 1.31461i) q^{3} +(-0.565188 + 0.978934i) q^{5} +(-3.71499 + 2.14485i) q^{7} +(-0.456412 + 2.96508i) q^{9} +O(q^{10})\) \(q+(1.12774 + 1.31461i) q^{3} +(-0.565188 + 0.978934i) q^{5} +(-3.71499 + 2.14485i) q^{7} +(-0.456412 + 2.96508i) q^{9} +(-1.00953 + 0.582853i) q^{11} +(2.64466 + 1.52689i) q^{13} +(-1.92430 + 0.360979i) q^{15} -1.49654i q^{17} +3.42378 q^{19} +(-7.00918 - 2.46494i) q^{21} +(3.85938 - 6.68464i) q^{23} +(1.86113 + 3.22356i) q^{25} +(-4.41264 + 2.74383i) q^{27} +(-0.709580 - 1.22903i) q^{29} +(4.66408 + 2.69281i) q^{31} +(-1.90471 - 0.669837i) q^{33} -4.84897i q^{35} +2.97201i q^{37} +(0.975209 + 5.19864i) q^{39} +(-4.23339 - 2.44415i) q^{41} +(1.74292 + 3.01882i) q^{43} +(-2.64466 - 2.12262i) q^{45} +(1.77991 + 3.08289i) q^{47} +(5.70075 - 9.87399i) q^{49} +(1.96737 - 1.68770i) q^{51} +11.2786 q^{53} -1.31769i q^{55} +(3.86113 + 4.50094i) q^{57} +(-7.50935 - 4.33553i) q^{59} +(-3.16057 + 1.82476i) q^{61} +(-4.66408 - 11.9942i) q^{63} +(-2.98946 + 1.72596i) q^{65} +(5.58255 - 9.66925i) q^{67} +(13.1401 - 2.46494i) q^{69} -2.54954 q^{71} -7.06491 q^{73} +(-2.13887 + 6.08200i) q^{75} +(2.50026 - 4.33059i) q^{77} +(2.24998 - 1.29902i) q^{79} +(-8.58338 - 2.70659i) q^{81} +(3.98482 - 2.30064i) q^{83} +(1.46501 + 0.845824i) q^{85} +(0.815476 - 2.31885i) q^{87} -8.63803i q^{89} -13.0998 q^{91} +(1.71986 + 9.16824i) q^{93} +(-1.93508 + 3.35165i) q^{95} +(3.35869 + 5.81742i) q^{97} +(-1.26744 - 3.25936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 6 q^{3} - 6 q^{9}+O(q^{10}) \) 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
\(3\) 1.12774 + 1.31461i 0.651100 + 0.758992i
\(4\) 0 0
\(5\) −0.565188 + 0.978934i −0.252760 + 0.437793i −0.964285 0.264868i \(-0.914672\pi\)
0.711525 + 0.702661i \(0.248005\pi\)
\(6\) 0 0
\(7\) −3.71499 + 2.14485i −1.40413 + 0.810677i −0.994814 0.101714i \(-0.967567\pi\)
−0.409320 + 0.912391i \(0.634234\pi\)
\(8\) 0 0
\(9\) −0.456412 + 2.96508i −0.152137 + 0.988359i
\(10\) 0 0
\(11\) −1.00953 + 0.582853i −0.304385 + 0.175737i −0.644411 0.764679i \(-0.722897\pi\)
0.340026 + 0.940416i \(0.389564\pi\)
\(12\) 0 0
\(13\) 2.64466 + 1.52689i 0.733496 + 0.423484i 0.819700 0.572793i \(-0.194140\pi\)
−0.0862038 + 0.996278i \(0.527474\pi\)
\(14\) 0 0
\(15\) −1.92430 + 0.360979i −0.496853 + 0.0932043i
\(16\) 0 0
\(17\) 1.49654i 0.362963i −0.983394 0.181482i \(-0.941911\pi\)
0.983394 0.181482i \(-0.0580893\pi\)
\(18\) 0 0
\(19\) 3.42378 0.785468 0.392734 0.919652i \(-0.371529\pi\)
0.392734 + 0.919652i \(0.371529\pi\)
\(20\) 0 0
\(21\) −7.00918 2.46494i −1.52953 0.537894i
\(22\) 0 0
\(23\) 3.85938 6.68464i 0.804736 1.39384i −0.111733 0.993738i \(-0.535640\pi\)
0.916469 0.400106i \(-0.131027\pi\)
\(24\) 0 0
\(25\) 1.86113 + 3.22356i 0.372225 + 0.644713i
\(26\) 0 0
\(27\) −4.41264 + 2.74383i −0.849213 + 0.528050i
\(28\) 0 0
\(29\) −0.709580 1.22903i −0.131766 0.228225i 0.792592 0.609753i \(-0.208731\pi\)
−0.924357 + 0.381528i \(0.875398\pi\)
\(30\) 0 0
\(31\) 4.66408 + 2.69281i 0.837694 + 0.483643i 0.856480 0.516181i \(-0.172647\pi\)
−0.0187859 + 0.999824i \(0.505980\pi\)
\(32\) 0 0
\(33\) −1.90471 0.669837i −0.331568 0.116604i
\(34\) 0 0
\(35\) 4.84897i 0.819625i
\(36\) 0 0
\(37\) 2.97201i 0.488596i 0.969700 + 0.244298i \(0.0785575\pi\)
−0.969700 + 0.244298i \(0.921443\pi\)
\(38\) 0 0
\(39\) 0.975209 + 5.19864i 0.156158 + 0.832448i
\(40\) 0 0
\(41\) −4.23339 2.44415i −0.661144 0.381712i 0.131569 0.991307i \(-0.457999\pi\)
−0.792713 + 0.609595i \(0.791332\pi\)
\(42\) 0 0
\(43\) 1.74292 + 3.01882i 0.265793 + 0.460366i 0.967771 0.251832i \(-0.0810330\pi\)
−0.701978 + 0.712198i \(0.747700\pi\)
\(44\) 0 0
\(45\) −2.64466 2.12262i −0.394242 0.316422i
\(46\) 0 0
\(47\) 1.77991 + 3.08289i 0.259627 + 0.449686i 0.966142 0.258011i \(-0.0830672\pi\)
−0.706515 + 0.707698i \(0.749734\pi\)
\(48\) 0 0
\(49\) 5.70075 9.87399i 0.814393 1.41057i
\(50\) 0 0
\(51\) 1.96737 1.68770i 0.275486 0.236326i
\(52\) 0 0
\(53\) 11.2786 1.54923 0.774616 0.632432i \(-0.217943\pi\)
0.774616 + 0.632432i \(0.217943\pi\)
\(54\) 0 0
\(55\) 1.31769i 0.177677i
\(56\) 0 0
\(57\) 3.86113 + 4.50094i 0.511419 + 0.596164i
\(58\) 0 0
\(59\) −7.50935 4.33553i −0.977634 0.564437i −0.0760791 0.997102i \(-0.524240\pi\)
−0.901555 + 0.432664i \(0.857573\pi\)
\(60\) 0 0
\(61\) −3.16057 + 1.82476i −0.404670 + 0.233636i −0.688497 0.725239i \(-0.741729\pi\)
0.283827 + 0.958875i \(0.408396\pi\)
\(62\) 0 0
\(63\) −4.66408 11.9942i −0.587619 1.51112i
\(64\) 0 0
\(65\) −2.98946 + 1.72596i −0.370796 + 0.214079i
\(66\) 0 0
\(67\) 5.58255 9.66925i 0.682017 1.18129i −0.292348 0.956312i \(-0.594437\pi\)
0.974364 0.224975i \(-0.0722301\pi\)
\(68\) 0 0
\(69\) 13.1401 2.46494i 1.58188 0.296744i
\(70\) 0 0
\(71\) −2.54954 −0.302574 −0.151287 0.988490i \(-0.548342\pi\)
−0.151287 + 0.988490i \(0.548342\pi\)
\(72\) 0 0
\(73\) −7.06491 −0.826885 −0.413442 0.910530i \(-0.635674\pi\)
−0.413442 + 0.910530i \(0.635674\pi\)
\(74\) 0 0
\(75\) −2.13887 + 6.08200i −0.246976 + 0.702288i
\(76\) 0 0
\(77\) 2.50026 4.33059i 0.284932 0.493516i
\(78\) 0 0
\(79\) 2.24998 1.29902i 0.253142 0.146152i −0.368060 0.929802i \(-0.619978\pi\)
0.621202 + 0.783650i \(0.286645\pi\)
\(80\) 0 0
\(81\) −8.58338 2.70659i −0.953709 0.300732i
\(82\) 0 0
\(83\) 3.98482 2.30064i 0.437391 0.252528i −0.265099 0.964221i \(-0.585405\pi\)
0.702490 + 0.711693i \(0.252071\pi\)
\(84\) 0 0
\(85\) 1.46501 + 0.845824i 0.158903 + 0.0917425i
\(86\) 0 0
\(87\) 0.815476 2.31885i 0.0874282 0.248606i
\(88\) 0 0
\(89\) 8.63803i 0.915630i −0.889048 0.457815i \(-0.848632\pi\)
0.889048 0.457815i \(-0.151368\pi\)
\(90\) 0 0
\(91\) −13.0998 −1.37323
\(92\) 0 0
\(93\) 1.71986 + 9.16824i 0.178342 + 0.950702i
\(94\) 0 0
\(95\) −1.93508 + 3.35165i −0.198535 + 0.343872i
\(96\) 0 0
\(97\) 3.35869 + 5.81742i 0.341023 + 0.590670i 0.984623 0.174693i \(-0.0558931\pi\)
−0.643600 + 0.765362i \(0.722560\pi\)
\(98\) 0 0
\(99\) −1.26744 3.25936i −0.127383 0.327578i
\(100\) 0 0
\(101\) −6.86479 11.8902i −0.683072 1.18312i −0.974039 0.226382i \(-0.927310\pi\)
0.290967 0.956733i \(-0.406023\pi\)
\(102\) 0 0
\(103\) 5.48137 + 3.16467i 0.540095 + 0.311824i 0.745118 0.666933i \(-0.232393\pi\)
−0.205022 + 0.978757i \(0.565727\pi\)
\(104\) 0 0
\(105\) 6.37451 5.46837i 0.622089 0.533658i
\(106\) 0 0
\(107\) 10.4483i 1.01007i 0.863097 + 0.505037i \(0.168521\pi\)
−0.863097 + 0.505037i \(0.831479\pi\)
\(108\) 0 0
\(109\) 9.67531i 0.926727i −0.886168 0.463364i \(-0.846642\pi\)
0.886168 0.463364i \(-0.153358\pi\)
\(110\) 0 0
\(111\) −3.90704 + 3.35165i −0.370840 + 0.318125i
\(112\) 0 0
\(113\) 7.15149 + 4.12891i 0.672756 + 0.388416i 0.797120 0.603821i \(-0.206356\pi\)
−0.124364 + 0.992237i \(0.539689\pi\)
\(114\) 0 0
\(115\) 4.36255 + 7.55615i 0.406810 + 0.704615i
\(116\) 0 0
\(117\) −5.73441 + 7.14472i −0.530146 + 0.660530i
\(118\) 0 0
\(119\) 3.20984 + 5.55961i 0.294246 + 0.509649i
\(120\) 0 0
\(121\) −4.82056 + 8.34946i −0.438233 + 0.759042i
\(122\) 0 0
\(123\) −1.56105 8.32162i −0.140755 0.750335i
\(124\) 0 0
\(125\) −9.85942 −0.881853
\(126\) 0 0
\(127\) 2.78757i 0.247357i −0.992322 0.123678i \(-0.960531\pi\)
0.992322 0.123678i \(-0.0394691\pi\)
\(128\) 0 0
\(129\) −2.00303 + 5.69571i −0.176357 + 0.501479i
\(130\) 0 0
\(131\) 13.0529 + 7.53612i 1.14044 + 0.658434i 0.946540 0.322587i \(-0.104553\pi\)
0.193901 + 0.981021i \(0.437886\pi\)
\(132\) 0 0
\(133\) −12.7193 + 7.34348i −1.10290 + 0.636761i
\(134\) 0 0
\(135\) −0.192056 5.87046i −0.0165295 0.505249i
\(136\) 0 0
\(137\) 7.55211 4.36021i 0.645220 0.372518i −0.141402 0.989952i \(-0.545161\pi\)
0.786623 + 0.617434i \(0.211828\pi\)
\(138\) 0 0
\(139\) −1.18897 + 2.05935i −0.100847 + 0.174672i −0.912034 0.410115i \(-0.865489\pi\)
0.811187 + 0.584787i \(0.198822\pi\)
\(140\) 0 0
\(141\) −2.04554 + 5.81659i −0.172265 + 0.489845i
\(142\) 0 0
\(143\) −3.55982 −0.297687
\(144\) 0 0
\(145\) 1.60418 0.133220
\(146\) 0 0
\(147\) 19.4094 3.64100i 1.60086 0.300305i
\(148\) 0 0
\(149\) −8.94426 + 15.4919i −0.732742 + 1.26915i 0.222965 + 0.974826i \(0.428426\pi\)
−0.955707 + 0.294320i \(0.904907\pi\)
\(150\) 0 0
\(151\) −2.39162 + 1.38080i −0.194627 + 0.112368i −0.594147 0.804357i \(-0.702510\pi\)
0.399520 + 0.916725i \(0.369177\pi\)
\(152\) 0 0
\(153\) 4.43735 + 0.683037i 0.358738 + 0.0552202i
\(154\) 0 0
\(155\) −5.27216 + 3.04388i −0.423470 + 0.244491i
\(156\) 0 0
\(157\) 2.21148 + 1.27680i 0.176495 + 0.101900i 0.585645 0.810568i \(-0.300841\pi\)
−0.409150 + 0.912467i \(0.634175\pi\)
\(158\) 0 0
\(159\) 12.7193 + 14.8270i 1.00871 + 1.17585i
\(160\) 0 0
\(161\) 33.1111i 2.60952i
\(162\) 0 0
\(163\) −6.93355 −0.543077 −0.271539 0.962428i \(-0.587532\pi\)
−0.271539 + 0.962428i \(0.587532\pi\)
\(164\) 0 0
\(165\) 1.73225 1.48601i 0.134855 0.115685i
\(166\) 0 0
\(167\) −8.36829 + 14.4943i −0.647558 + 1.12160i 0.336146 + 0.941810i \(0.390876\pi\)
−0.983704 + 0.179794i \(0.942457\pi\)
\(168\) 0 0
\(169\) −1.83719 3.18211i −0.141322 0.244778i
\(170\) 0 0
\(171\) −1.56265 + 10.1518i −0.119499 + 0.776325i
\(172\) 0 0
\(173\) 10.2190 + 17.6999i 0.776938 + 1.34570i 0.933699 + 0.358059i \(0.116562\pi\)
−0.156761 + 0.987637i \(0.550105\pi\)
\(174\) 0 0
\(175\) −13.8281 7.98367i −1.04531 0.603508i
\(176\) 0 0
\(177\) −2.76905 14.7612i −0.208134 1.10952i
\(178\) 0 0
\(179\) 4.07982i 0.304940i −0.988308 0.152470i \(-0.951277\pi\)
0.988308 0.152470i \(-0.0487227\pi\)
\(180\) 0 0
\(181\) 22.3226i 1.65923i −0.558337 0.829614i \(-0.688560\pi\)
0.558337 0.829614i \(-0.311440\pi\)
\(182\) 0 0
\(183\) −5.96315 2.09708i −0.440809 0.155021i
\(184\) 0 0
\(185\) −2.90940 1.67974i −0.213904 0.123497i
\(186\) 0 0
\(187\) 0.872261 + 1.51080i 0.0637861 + 0.110481i
\(188\) 0 0
\(189\) 10.5078 19.6577i 0.764331 1.42989i
\(190\) 0 0
\(191\) −7.27481 12.6003i −0.526387 0.911728i −0.999527 0.0307415i \(-0.990213\pi\)
0.473141 0.880987i \(-0.343120\pi\)
\(192\) 0 0
\(193\) 2.19526 3.80230i 0.158018 0.273696i −0.776136 0.630566i \(-0.782823\pi\)
0.934154 + 0.356870i \(0.116156\pi\)
\(194\) 0 0
\(195\) −5.64030 1.98354i −0.403910 0.142044i
\(196\) 0 0
\(197\) −7.69721 −0.548404 −0.274202 0.961672i \(-0.588414\pi\)
−0.274202 + 0.961672i \(0.588414\pi\)
\(198\) 0 0
\(199\) 20.9790i 1.48716i −0.668646 0.743580i \(-0.733126\pi\)
0.668646 0.743580i \(-0.266874\pi\)
\(200\) 0 0
\(201\) 19.0070 3.56551i 1.34065 0.251491i
\(202\) 0 0
\(203\) 5.27216 + 3.04388i 0.370033 + 0.213639i
\(204\) 0 0
\(205\) 4.78532 2.76280i 0.334221 0.192963i
\(206\) 0 0
\(207\) 18.0590 + 14.4943i 1.25519 + 1.00742i
\(208\) 0 0
\(209\) −3.45641 + 1.99556i −0.239085 + 0.138036i
\(210\) 0 0
\(211\) −2.38482 + 4.13063i −0.164178 + 0.284364i −0.936363 0.351033i \(-0.885830\pi\)
0.772185 + 0.635397i \(0.219164\pi\)
\(212\) 0 0
\(213\) −2.87521 3.35165i −0.197006 0.229651i
\(214\) 0 0
\(215\) −3.94031 −0.268727
\(216\) 0 0
\(217\) −23.1027 −1.56831
\(218\) 0 0
\(219\) −7.96737 9.28761i −0.538385 0.627599i
\(220\) 0 0
\(221\) 2.28505 3.95783i 0.153709 0.266232i
\(222\) 0 0
\(223\) −12.5272 + 7.23260i −0.838886 + 0.484331i −0.856885 0.515507i \(-0.827604\pi\)
0.0179997 + 0.999838i \(0.494270\pi\)
\(224\) 0 0
\(225\) −10.4076 + 4.04711i −0.693837 + 0.269807i
\(226\) 0 0
\(227\) −0.561821 + 0.324367i −0.0372894 + 0.0215290i −0.518529 0.855060i \(-0.673520\pi\)
0.481239 + 0.876589i \(0.340187\pi\)
\(228\) 0 0
\(229\) 12.0007 + 6.92863i 0.793032 + 0.457857i 0.841029 0.540990i \(-0.181950\pi\)
−0.0479971 + 0.998847i \(0.515284\pi\)
\(230\) 0 0
\(231\) 8.51269 1.59689i 0.560094 0.105068i
\(232\) 0 0
\(233\) 23.1276i 1.51514i −0.652755 0.757569i \(-0.726387\pi\)
0.652755 0.757569i \(-0.273613\pi\)
\(234\) 0 0
\(235\) −4.02393 −0.262492
\(236\) 0 0
\(237\) 4.24510 + 1.49289i 0.275749 + 0.0969734i
\(238\) 0 0
\(239\) 7.44075 12.8878i 0.481302 0.833640i −0.518468 0.855097i \(-0.673497\pi\)
0.999770 + 0.0214576i \(0.00683070\pi\)
\(240\) 0 0
\(241\) −5.87960 10.1838i −0.378738 0.655994i 0.612141 0.790749i \(-0.290309\pi\)
−0.990879 + 0.134755i \(0.956975\pi\)
\(242\) 0 0
\(243\) −6.12169 14.3361i −0.392706 0.919664i
\(244\) 0 0
\(245\) 6.44399 + 11.1613i 0.411691 + 0.713071i
\(246\) 0 0
\(247\) 9.05472 + 5.22774i 0.576138 + 0.332633i
\(248\) 0 0
\(249\) 7.51829 + 2.64398i 0.476452 + 0.167555i
\(250\) 0 0
\(251\) 5.51619i 0.348179i 0.984730 + 0.174089i \(0.0556981\pi\)
−0.984730 + 0.174089i \(0.944302\pi\)
\(252\) 0 0
\(253\) 8.99781i 0.565687i
\(254\) 0 0
\(255\) 0.540218 + 2.87979i 0.0338298 + 0.180339i
\(256\) 0 0
\(257\) 16.9194 + 9.76841i 1.05540 + 0.609337i 0.924157 0.382013i \(-0.124769\pi\)
0.131245 + 0.991350i \(0.458102\pi\)
\(258\) 0 0
\(259\) −6.37451 11.0410i −0.396093 0.686053i
\(260\) 0 0
\(261\) 3.96803 1.54302i 0.245615 0.0955104i
\(262\) 0 0
\(263\) −5.62576 9.74411i −0.346899 0.600847i 0.638798 0.769375i \(-0.279432\pi\)
−0.985697 + 0.168527i \(0.946099\pi\)
\(264\) 0 0
\(265\) −6.37451 + 11.0410i −0.391583 + 0.678242i
\(266\) 0 0
\(267\) 11.3557 9.74144i 0.694955 0.596167i
\(268\) 0 0
\(269\) −14.1600 −0.863350 −0.431675 0.902029i \(-0.642077\pi\)
−0.431675 + 0.902029i \(0.642077\pi\)
\(270\) 0 0
\(271\) 3.91574i 0.237864i 0.992902 + 0.118932i \(0.0379471\pi\)
−0.992902 + 0.118932i \(0.962053\pi\)
\(272\) 0 0
\(273\) −14.7732 17.2212i −0.894113 1.04227i
\(274\) 0 0
\(275\) −3.75773 2.16953i −0.226600 0.130827i
\(276\) 0 0
\(277\) 22.9537 13.2523i 1.37915 0.796253i 0.387094 0.922040i \(-0.373479\pi\)
0.992057 + 0.125787i \(0.0401455\pi\)
\(278\) 0 0
\(279\) −10.1131 + 12.6003i −0.605457 + 0.754362i
\(280\) 0 0
\(281\) −0.923368 + 0.533106i −0.0550835 + 0.0318025i −0.527289 0.849686i \(-0.676791\pi\)
0.472205 + 0.881489i \(0.343458\pi\)
\(282\) 0 0
\(283\) −1.77840 + 3.08028i −0.105715 + 0.183103i −0.914030 0.405647i \(-0.867046\pi\)
0.808315 + 0.588750i \(0.200380\pi\)
\(284\) 0 0
\(285\) −6.58838 + 1.23591i −0.390262 + 0.0732090i
\(286\) 0 0
\(287\) 20.9693 1.23778
\(288\) 0 0
\(289\) 14.7604 0.868258
\(290\) 0 0
\(291\) −3.85993 + 10.9759i −0.226273 + 0.643419i
\(292\) 0 0
\(293\) 7.78958 13.4919i 0.455072 0.788208i −0.543620 0.839331i \(-0.682947\pi\)
0.998692 + 0.0511233i \(0.0162802\pi\)
\(294\) 0 0
\(295\) 8.48839 4.90077i 0.494213 0.285334i
\(296\) 0 0
\(297\) 2.85545 5.34190i 0.165690 0.309969i
\(298\) 0 0
\(299\) 20.4135 11.7857i 1.18054 0.681586i
\(300\) 0 0
\(301\) −12.9498 7.47659i −0.746416 0.430944i
\(302\) 0 0
\(303\) 7.88927 22.4335i 0.453227 1.28877i
\(304\) 0 0
\(305\) 4.12532i 0.236215i
\(306\) 0 0
\(307\) 0.960690 0.0548295 0.0274147 0.999624i \(-0.491273\pi\)
0.0274147 + 0.999624i \(0.491273\pi\)
\(308\) 0 0
\(309\) 2.02124 + 10.7748i 0.114984 + 0.612957i
\(310\) 0 0
\(311\) −4.49539 + 7.78624i −0.254910 + 0.441517i −0.964871 0.262724i \(-0.915379\pi\)
0.709961 + 0.704241i \(0.248713\pi\)
\(312\) 0 0
\(313\) 8.55885 + 14.8244i 0.483775 + 0.837923i 0.999826 0.0186349i \(-0.00593201\pi\)
−0.516051 + 0.856558i \(0.672599\pi\)
\(314\) 0 0
\(315\) 14.3776 + 2.21313i 0.810084 + 0.124696i
\(316\) 0 0
\(317\) −3.96528 6.86806i −0.222712 0.385749i 0.732919 0.680316i \(-0.238158\pi\)
−0.955631 + 0.294568i \(0.904824\pi\)
\(318\) 0 0
\(319\) 1.43269 + 0.827162i 0.0802151 + 0.0463122i
\(320\) 0 0
\(321\) −13.7355 + 11.7829i −0.766639 + 0.657660i
\(322\) 0 0
\(323\) 5.12381i 0.285096i
\(324\) 0 0
\(325\) 11.3670i 0.630526i
\(326\) 0 0
\(327\) 12.7193 10.9112i 0.703378 0.603392i
\(328\) 0 0
\(329\) −13.2247 7.63528i −0.729101 0.420946i
\(330\) 0 0
\(331\) −4.78348 8.28523i −0.262924 0.455397i 0.704094 0.710107i \(-0.251353\pi\)
−0.967018 + 0.254710i \(0.918020\pi\)
\(332\) 0 0
\(333\) −8.81225 1.35646i −0.482908 0.0743336i
\(334\) 0 0
\(335\) 6.31037 + 10.9299i 0.344773 + 0.597164i
\(336\) 0 0
\(337\) 17.0727 29.5707i 0.930007 1.61082i 0.146702 0.989181i \(-0.453134\pi\)
0.783305 0.621638i \(-0.213532\pi\)
\(338\) 0 0
\(339\) 2.63709 + 14.0578i 0.143227 + 0.763514i
\(340\) 0 0
\(341\) −6.27805 −0.339975
\(342\) 0 0
\(343\) 18.8811i 1.01949i
\(344\) 0 0
\(345\) −5.01360 + 14.2564i −0.269923 + 0.767540i
\(346\) 0 0
\(347\) −20.9431 12.0915i −1.12428 0.649105i −0.181792 0.983337i \(-0.558190\pi\)
−0.942491 + 0.334232i \(0.891523\pi\)
\(348\) 0 0
\(349\) −9.71845 + 5.61095i −0.520217 + 0.300347i −0.737023 0.675867i \(-0.763769\pi\)
0.216807 + 0.976215i \(0.430436\pi\)
\(350\) 0 0
\(351\) −15.8595 + 0.518852i −0.846515 + 0.0276943i
\(352\) 0 0
\(353\) −5.85176 + 3.37852i −0.311458 + 0.179820i −0.647579 0.761999i \(-0.724218\pi\)
0.336121 + 0.941819i \(0.390885\pi\)
\(354\) 0 0
\(355\) 1.44097 2.49583i 0.0764786 0.132465i
\(356\) 0 0
\(357\) −3.68887 + 10.4895i −0.195236 + 0.555163i
\(358\) 0 0
\(359\) 20.3395 1.07348 0.536739 0.843748i \(-0.319656\pi\)
0.536739 + 0.843748i \(0.319656\pi\)
\(360\) 0 0
\(361\) −7.27775 −0.383039
\(362\) 0 0
\(363\) −16.4126 + 3.07884i −0.861440 + 0.161597i
\(364\) 0 0
\(365\) 3.99300 6.91608i 0.209003 0.362004i
\(366\) 0 0
\(367\) 11.7198 6.76642i 0.611767 0.353204i −0.161889 0.986809i \(-0.551759\pi\)
0.773657 + 0.633605i \(0.218425\pi\)
\(368\) 0 0
\(369\) 9.17925 11.4368i 0.477853 0.595375i
\(370\) 0 0
\(371\) −41.8998 + 24.1908i −2.17533 + 1.25593i
\(372\) 0 0
\(373\) −23.0364 13.3001i −1.19278 0.688651i −0.233843 0.972274i \(-0.575130\pi\)
−0.958936 + 0.283623i \(0.908464\pi\)
\(374\) 0 0
\(375\) −11.1188 12.9613i −0.574175 0.669319i
\(376\) 0 0
\(377\) 4.33381i 0.223203i
\(378\) 0 0
\(379\) 28.5030 1.46410 0.732050 0.681251i \(-0.238564\pi\)
0.732050 + 0.681251i \(0.238564\pi\)
\(380\) 0 0
\(381\) 3.66457 3.14365i 0.187742 0.161054i
\(382\) 0 0
\(383\) −10.0515 + 17.4097i −0.513606 + 0.889592i 0.486269 + 0.873809i \(0.338357\pi\)
−0.999875 + 0.0157832i \(0.994976\pi\)
\(384\) 0 0
\(385\) 2.82624 + 4.89519i 0.144038 + 0.249482i
\(386\) 0 0
\(387\) −9.74654 + 3.79006i −0.495444 + 0.192660i
\(388\) 0 0
\(389\) 1.08110 + 1.87253i 0.0548142 + 0.0949409i 0.892130 0.451778i \(-0.149210\pi\)
−0.837316 + 0.546719i \(0.815877\pi\)
\(390\) 0 0
\(391\) −10.0038 5.77570i −0.505914 0.292090i
\(392\) 0 0
\(393\) 4.81323 + 25.6583i 0.242795 + 1.29429i
\(394\) 0 0
\(395\) 2.93677i 0.147765i
\(396\) 0 0
\(397\) 18.8504i 0.946076i 0.881042 + 0.473038i \(0.156843\pi\)
−0.881042 + 0.473038i \(0.843157\pi\)
\(398\) 0 0
\(399\) −23.9979 8.43940i −1.20140 0.422499i
\(400\) 0 0
\(401\) −15.0668 8.69883i −0.752401 0.434399i 0.0741601 0.997246i \(-0.476372\pi\)
−0.826561 + 0.562848i \(0.809706\pi\)
\(402\) 0 0
\(403\) 8.22326 + 14.2431i 0.409630 + 0.709500i
\(404\) 0 0
\(405\) 7.50079 6.87283i 0.372717 0.341513i
\(406\) 0 0
\(407\) −1.73225 3.00034i −0.0858643 0.148721i
\(408\) 0 0
\(409\) −10.2872 + 17.8179i −0.508667 + 0.881037i 0.491282 + 0.871000i \(0.336528\pi\)
−0.999950 + 0.0100370i \(0.996805\pi\)
\(410\) 0 0
\(411\) 14.2488 + 5.01092i 0.702841 + 0.247170i
\(412\) 0 0
\(413\) 37.1962 1.83030
\(414\) 0 0
\(415\) 5.20117i 0.255316i
\(416\) 0 0
\(417\) −4.04810 + 0.759379i −0.198236 + 0.0371870i
\(418\) 0 0
\(419\) 24.1959 + 13.9695i 1.18205 + 0.682455i 0.956487 0.291774i \(-0.0942454\pi\)
0.225560 + 0.974229i \(0.427579\pi\)
\(420\) 0 0
\(421\) −6.27826 + 3.62475i −0.305983 + 0.176660i −0.645128 0.764075i \(-0.723196\pi\)
0.339144 + 0.940734i \(0.389863\pi\)
\(422\) 0 0
\(423\) −9.95340 + 3.87050i −0.483951 + 0.188190i
\(424\) 0 0
\(425\) 4.82418 2.78524i 0.234007 0.135104i
\(426\) 0 0
\(427\) 7.82766 13.5579i 0.378807 0.656113i
\(428\) 0 0
\(429\) −4.01455 4.67978i −0.193824 0.225942i
\(430\) 0 0
\(431\) −37.7004 −1.81596 −0.907982 0.419009i \(-0.862377\pi\)
−0.907982 + 0.419009i \(0.862377\pi\)
\(432\) 0 0
\(433\) 36.1185 1.73575 0.867873 0.496787i \(-0.165487\pi\)
0.867873 + 0.496787i \(0.165487\pi\)
\(434\) 0 0
\(435\) 1.80910 + 2.10888i 0.0867397 + 0.101113i
\(436\) 0 0
\(437\) 13.2137 22.8867i 0.632095 1.09482i
\(438\) 0 0
\(439\) −9.02239 + 5.20908i −0.430615 + 0.248616i −0.699609 0.714526i \(-0.746642\pi\)
0.268993 + 0.963142i \(0.413309\pi\)
\(440\) 0 0
\(441\) 26.6753 + 21.4098i 1.27025 + 1.01951i
\(442\) 0 0
\(443\) 30.7905 17.7769i 1.46290 0.844606i 0.463756 0.885963i \(-0.346502\pi\)
0.999144 + 0.0413574i \(0.0131682\pi\)
\(444\) 0 0
\(445\) 8.45606 + 4.88211i 0.400856 + 0.231434i
\(446\) 0 0
\(447\) −30.4526 + 5.71259i −1.44036 + 0.270196i
\(448\) 0 0
\(449\) 16.7750i 0.791662i 0.918323 + 0.395831i \(0.129543\pi\)
−0.918323 + 0.395831i \(0.870457\pi\)
\(450\) 0 0
\(451\) 5.69832 0.268323
\(452\) 0 0
\(453\) −4.51234 1.58687i −0.212008 0.0745575i
\(454\) 0 0
\(455\) 7.40386 12.8239i 0.347098 0.601192i
\(456\) 0 0
\(457\) −0.679436 1.17682i −0.0317827 0.0550492i 0.849697 0.527272i \(-0.176785\pi\)
−0.881479 + 0.472223i \(0.843452\pi\)
\(458\) 0 0
\(459\) 4.10624 + 6.60368i 0.191663 + 0.308233i
\(460\) 0 0
\(461\) −5.07410 8.78860i −0.236324 0.409326i 0.723332 0.690500i \(-0.242609\pi\)
−0.959657 + 0.281174i \(0.909276\pi\)
\(462\) 0 0
\(463\) 23.2656 + 13.4324i 1.08124 + 0.624256i 0.931232 0.364428i \(-0.118735\pi\)
0.150012 + 0.988684i \(0.452069\pi\)
\(464\) 0 0
\(465\) −9.94715 3.49814i −0.461288 0.162223i
\(466\) 0 0
\(467\) 31.4118i 1.45356i −0.686868 0.726782i \(-0.741015\pi\)
0.686868 0.726782i \(-0.258985\pi\)
\(468\) 0 0
\(469\) 47.8949i 2.21158i
\(470\) 0 0
\(471\) 0.815476 + 4.34713i 0.0375751 + 0.200305i
\(472\) 0 0
\(473\) −3.51906 2.03173i −0.161807 0.0934191i
\(474\) 0 0
\(475\) 6.37208 + 11.0368i 0.292371 + 0.506402i
\(476\) 0 0
\(477\) −5.14767 + 33.4419i −0.235696 + 1.53120i
\(478\) 0 0
\(479\) −2.42488 4.20001i −0.110796 0.191904i 0.805296 0.592873i \(-0.202007\pi\)
−0.916091 + 0.400970i \(0.868673\pi\)
\(480\) 0 0
\(481\) −4.53794 + 7.85995i −0.206912 + 0.358383i
\(482\) 0 0
\(483\) −43.5283 + 37.3407i −1.98061 + 1.69906i
\(484\) 0 0
\(485\) −7.59316 −0.344788
\(486\) 0 0
\(487\) 23.2664i 1.05430i 0.849772 + 0.527150i \(0.176739\pi\)
−0.849772 + 0.527150i \(0.823261\pi\)
\(488\) 0 0
\(489\) −7.81923 9.11493i −0.353598 0.412191i
\(490\) 0 0
\(491\) −9.48139 5.47408i −0.427889 0.247042i 0.270558 0.962704i \(-0.412792\pi\)
−0.698447 + 0.715662i \(0.746125\pi\)
\(492\) 0 0
\(493\) −1.83929 + 1.06191i −0.0828373 + 0.0478262i
\(494\) 0 0
\(495\) 3.90704 + 0.601407i 0.175609 + 0.0270312i
\(496\) 0 0
\(497\) 9.47149 5.46837i 0.424855 0.245290i
\(498\) 0 0
\(499\) −19.4409 + 33.6726i −0.870293 + 1.50739i −0.00859924 + 0.999963i \(0.502737\pi\)
−0.861694 + 0.507429i \(0.830596\pi\)
\(500\) 0 0
\(501\) −28.4916 + 5.34473i −1.27291 + 0.238785i
\(502\) 0 0
\(503\) 9.97588 0.444803 0.222401 0.974955i \(-0.428610\pi\)
0.222401 + 0.974955i \(0.428610\pi\)
\(504\) 0 0
\(505\) 15.5196 0.690612
\(506\) 0 0
\(507\) 2.11137 6.00378i 0.0937692 0.266637i
\(508\) 0 0
\(509\) −7.82922 + 13.5606i −0.347024 + 0.601063i −0.985719 0.168396i \(-0.946141\pi\)
0.638695 + 0.769460i \(0.279474\pi\)
\(510\) 0 0
\(511\) 26.2460 15.1532i 1.16106 0.670336i
\(512\) 0 0
\(513\) −15.1079 + 9.39426i −0.667030 + 0.414767i
\(514\) 0 0
\(515\) −6.19601 + 3.57727i −0.273029 + 0.157633i
\(516\) 0 0
\(517\) −3.59375 2.07485i −0.158053 0.0912519i
\(518\) 0 0
\(519\) −11.7441 + 33.3949i −0.515508 + 1.46587i
\(520\) 0 0
\(521\) 9.78813i 0.428826i −0.976743 0.214413i \(-0.931216\pi\)
0.976743 0.214413i \(-0.0687838\pi\)
\(522\) 0 0
\(523\) 32.9015 1.43868 0.719342 0.694656i \(-0.244443\pi\)
0.719342 + 0.694656i \(0.244443\pi\)
\(524\) 0 0
\(525\) −5.09907 27.1821i −0.222542 1.18632i
\(526\) 0 0
\(527\) 4.02989 6.97997i 0.175545 0.304052i
\(528\) 0 0
\(529\) −18.2896 31.6786i −0.795201 1.37733i
\(530\) 0 0
\(531\) 16.2825 20.2870i 0.706601 0.880382i
\(532\) 0 0
\(533\) −7.46391 12.9279i −0.323298 0.559968i
\(534\) 0 0
\(535\) −10.2282 5.90525i −0.442203 0.255306i
\(536\) 0 0
\(537\) 5.36338 4.60097i 0.231447 0.198546i
\(538\) 0 0
\(539\) 13.2908i 0.572476i
\(540\) 0 0
\(541\) 26.4228i 1.13601i −0.823027 0.568003i \(-0.807716\pi\)
0.823027 0.568003i \(-0.192284\pi\)
\(542\) 0 0
\(543\) 29.3456 25.1741i 1.25934 1.08032i
\(544\) 0 0
\(545\) 9.47149 + 5.46837i 0.405714 + 0.234239i
\(546\) 0 0
\(547\) −17.7776 30.7917i −0.760116 1.31656i −0.942790 0.333387i \(-0.891809\pi\)
0.182674 0.983174i \(-0.441525\pi\)
\(548\) 0 0
\(549\) −3.96803 10.2042i −0.169351 0.435504i
\(550\) 0 0
\(551\) −2.42944 4.20792i −0.103498 0.179263i
\(552\) 0 0
\(553\) −5.57242 + 9.65172i −0.236964 + 0.410433i
\(554\) 0 0
\(555\) −1.07283 5.71905i −0.0455392 0.242760i
\(556\) 0 0
\(557\) 18.4413 0.781384 0.390692 0.920522i \(-0.372236\pi\)
0.390692 + 0.920522i \(0.372236\pi\)
\(558\) 0 0
\(559\) 10.6450i 0.450236i
\(560\) 0 0
\(561\) −1.00244 + 2.85047i −0.0423228 + 0.120347i
\(562\) 0 0
\(563\) −35.4943 20.4926i −1.49591 0.863661i −0.495917 0.868370i \(-0.665168\pi\)
−0.999989 + 0.00470871i \(0.998501\pi\)
\(564\) 0 0
\(565\) −8.08387 + 4.66722i −0.340091 + 0.196352i
\(566\) 0 0
\(567\) 37.6924 8.35509i 1.58293 0.350881i
\(568\) 0 0
\(569\) −3.72340 + 2.14971i −0.156093 + 0.0901205i −0.576012 0.817441i \(-0.695392\pi\)
0.419919 + 0.907562i \(0.362059\pi\)
\(570\) 0 0
\(571\) 2.17462 3.76656i 0.0910052 0.157626i −0.816929 0.576738i \(-0.804325\pi\)
0.907934 + 0.419112i \(0.137659\pi\)
\(572\) 0 0
\(573\) 8.36048 23.7734i 0.349264 0.993150i
\(574\) 0 0
\(575\) 28.7312 1.19817
\(576\) 0 0
\(577\) 12.5475 0.522361 0.261180 0.965290i \(-0.415888\pi\)
0.261180 + 0.965290i \(0.415888\pi\)
\(578\) 0 0
\(579\) 7.47423 1.40209i 0.310619 0.0582687i
\(580\) 0 0
\(581\) −9.86905 + 17.0937i −0.409437 + 0.709166i
\(582\) 0 0
\(583\) −11.3861 + 6.57376i −0.471563 + 0.272257i
\(584\) 0 0
\(585\) −3.75319 9.65172i −0.155175 0.399049i
\(586\) 0 0
\(587\) 8.02388 4.63259i 0.331181 0.191207i −0.325184 0.945651i \(-0.605426\pi\)
0.656365 + 0.754443i \(0.272093\pi\)
\(588\) 0 0
\(589\) 15.9688 + 9.21958i 0.657982 + 0.379886i
\(590\) 0 0
\(591\) −8.68044 10.1188i −0.357066 0.416234i
\(592\) 0 0
\(593\) 11.1342i 0.457228i −0.973517 0.228614i \(-0.926581\pi\)
0.973517 0.228614i \(-0.0734193\pi\)
\(594\) 0 0
\(595\) −7.25666 −0.297494
\(596\) 0 0
\(597\) 27.5792 23.6588i 1.12874 0.968291i
\(598\) 0 0
\(599\) 22.8693 39.6108i 0.934415 1.61845i 0.158740 0.987320i \(-0.449257\pi\)
0.775675 0.631133i \(-0.217410\pi\)
\(600\) 0 0
\(601\) −11.2521 19.4892i −0.458982 0.794980i 0.539925 0.841713i \(-0.318453\pi\)
−0.998907 + 0.0467325i \(0.985119\pi\)
\(602\) 0 0
\(603\) 26.1222 + 20.9658i 1.06378 + 0.853795i
\(604\) 0 0
\(605\) −5.44905 9.43803i −0.221535 0.383710i
\(606\) 0 0
\(607\) −24.7306 14.2782i −1.00378 0.579535i −0.0944185 0.995533i \(-0.530099\pi\)
−0.909366 + 0.415997i \(0.863433\pi\)
\(608\) 0 0
\(609\) 1.94409 + 10.3636i 0.0787786 + 0.419953i
\(610\) 0 0
\(611\) 10.8709i 0.439791i
\(612\) 0 0
\(613\) 40.4574i 1.63406i −0.576596 0.817030i \(-0.695619\pi\)
0.576596 0.817030i \(-0.304381\pi\)
\(614\) 0 0
\(615\) 9.02860 + 3.17512i 0.364068 + 0.128033i
\(616\) 0 0
\(617\) −31.6715 18.2855i −1.27505 0.736148i −0.299112 0.954218i \(-0.596691\pi\)
−0.975933 + 0.218070i \(0.930024\pi\)
\(618\) 0 0
\(619\) −20.3697 35.2814i −0.818727 1.41808i −0.906620 0.421948i \(-0.861347\pi\)
0.0878927 0.996130i \(-0.471987\pi\)
\(620\) 0 0
\(621\) 1.31145 + 40.0864i 0.0526267 + 1.60861i
\(622\) 0 0
\(623\) 18.5273 + 32.0902i 0.742279 + 1.28567i
\(624\) 0 0
\(625\) −3.73321 + 6.46610i −0.149328 + 0.258644i
\(626\) 0 0
\(627\) −6.52132 2.29337i −0.260436 0.0915884i
\(628\) 0 0
\(629\) 4.44772 0.177342
\(630\) 0 0
\(631\) 15.0916i 0.600788i −0.953815 0.300394i \(-0.902882\pi\)
0.953815 0.300394i \(-0.0971182\pi\)
\(632\) 0 0
\(633\) −8.11963 + 1.52316i −0.322726 + 0.0605400i
\(634\) 0 0
\(635\) 2.72884 + 1.57550i 0.108291 + 0.0625218i
\(636\) 0 0
\(637\) 30.1531 17.4089i 1.19471 0.689765i
\(638\) 0 0
\(639\) 1.16364 7.55957i 0.0460328 0.299052i
\(640\) 0 0
\(641\) −26.9377 + 15.5525i −1.06398 + 0.614287i −0.926529 0.376222i \(-0.877223\pi\)
−0.137447 + 0.990509i \(0.543890\pi\)
\(642\) 0 0
\(643\) 1.93125 3.34503i 0.0761612 0.131915i −0.825429 0.564505i \(-0.809067\pi\)
0.901591 + 0.432590i \(0.142400\pi\)
\(644\) 0 0
\(645\) −4.44363 5.17997i −0.174968 0.203961i
\(646\) 0 0
\(647\) −24.1359 −0.948879 −0.474440 0.880288i \(-0.657349\pi\)
−0.474440 + 0.880288i \(0.657349\pi\)
\(648\) 0 0
\(649\) 10.1079 0.396770
\(650\) 0 0
\(651\) −26.0538 30.3711i −1.02113 1.19034i
\(652\) 0 0
\(653\) −16.2083 + 28.0736i −0.634279 + 1.09860i 0.352388 + 0.935854i \(0.385370\pi\)
−0.986667 + 0.162750i \(0.947964\pi\)
\(654\) 0 0
\(655\) −14.7547 + 8.51864i −0.576515 + 0.332851i
\(656\) 0 0
\(657\) 3.22450 20.9480i 0.125800 0.817259i
\(658\) 0 0
\(659\) −19.7202 + 11.3855i −0.768191 + 0.443515i −0.832229 0.554432i \(-0.812936\pi\)
0.0640377 + 0.997947i \(0.479602\pi\)
\(660\) 0 0
\(661\) 25.6004 + 14.7804i 0.995740 + 0.574891i 0.906985 0.421163i \(-0.138378\pi\)
0.0887549 + 0.996053i \(0.471711\pi\)
\(662\) 0 0
\(663\) 7.77995 1.45944i 0.302148 0.0566798i
\(664\) 0 0
\(665\) 16.6018i 0.643790i
\(666\) 0 0
\(667\) −10.9542 −0.424147
\(668\) 0 0
\(669\) −23.6355 8.31197i −0.913802 0.321359i
\(670\) 0 0
\(671\) 2.12713 3.68430i 0.0821171 0.142231i
\(672\) 0 0
\(673\) 8.89907 + 15.4136i 0.343034 + 0.594152i 0.984995 0.172585i \(-0.0552121\pi\)
−0.641961 + 0.766738i \(0.721879\pi\)
\(674\) 0 0
\(675\) −17.0574 9.11782i −0.656539 0.350945i
\(676\) 0 0
\(677\) 22.9383 + 39.7303i 0.881591 + 1.52696i 0.849572 + 0.527473i \(0.176860\pi\)
0.0320192 + 0.999487i \(0.489806\pi\)
\(678\) 0 0
\(679\) −24.9550 14.4078i −0.957684 0.552919i
\(680\) 0 0
\(681\) −1.06000 0.372775i −0.0406195 0.0142848i
\(682\) 0 0
\(683\) 2.20513i 0.0843769i 0.999110 + 0.0421884i \(0.0134330\pi\)
−0.999110 + 0.0421884i \(0.986567\pi\)
\(684\) 0 0
\(685\) 9.85735i 0.376630i
\(686\) 0 0
\(687\) 4.42524 + 23.5900i 0.168833 + 0.900015i
\(688\) 0 0
\(689\) 29.8280 + 17.2212i 1.13636 + 0.656075i
\(690\) 0 0
\(691\) 10.2512 + 17.7556i 0.389975 + 0.675457i 0.992446 0.122684i \(-0.0391503\pi\)
−0.602471 + 0.798141i \(0.705817\pi\)
\(692\) 0 0
\(693\) 11.6994 + 9.39001i 0.444422 + 0.356697i
\(694\) 0 0
\(695\) −1.34398 2.32784i −0.0509801 0.0883001i
\(696\) 0 0
\(697\) −3.65776 + 6.33542i −0.138547 + 0.239971i
\(698\) 0 0
\(699\) 30.4038 26.0819i 1.14998 0.986506i
\(700\) 0 0
\(701\) −26.6854 −1.00789 −0.503947 0.863734i \(-0.668119\pi\)
−0.503947 + 0.863734i \(0.668119\pi\)
\(702\) 0 0
\(703\) 10.1755i 0.383776i
\(704\) 0 0
\(705\) −4.53794 5.28991i −0.170909 0.199230i
\(706\) 0 0
\(707\) 51.0052 + 29.4479i 1.91825 + 1.10750i
\(708\) 0 0
\(709\) 37.8684 21.8633i 1.42218 0.821095i 0.425693 0.904868i \(-0.360030\pi\)
0.996485 + 0.0837727i \(0.0266970\pi\)
\(710\) 0 0
\(711\) 2.82479 + 7.26425i 0.105938 + 0.272431i
\(712\) 0 0
\(713\) 36.0009 20.7851i 1.34825 0.778410i
\(714\) 0 0
\(715\) 2.01197 3.48483i 0.0752433 0.130325i
\(716\) 0 0
\(717\) 25.3336 4.75232i 0.946101 0.177479i
\(718\) 0 0
\(719\) −13.9253 −0.519327 −0.259663 0.965699i \(-0.583612\pi\)
−0.259663 + 0.965699i \(0.583612\pi\)
\(720\) 0 0
\(721\) −27.1510 −1.01115
\(722\) 0 0
\(723\) 6.75705 19.2140i 0.251297 0.714577i
\(724\) 0 0
\(725\) 2.64124 4.57475i 0.0980930 0.169902i
\(726\) 0 0
\(727\) 30.9380 17.8621i 1.14743 0.662468i 0.199169 0.979965i \(-0.436176\pi\)
0.948259 + 0.317497i \(0.102842\pi\)
\(728\) 0 0
\(729\) 11.9428 24.2151i 0.442326 0.896854i
\(730\) 0 0
\(731\) 4.51778 2.60834i 0.167096 0.0964730i
\(732\) 0 0
\(733\) −30.2141 17.4441i −1.11598 0.644312i −0.175610 0.984460i \(-0.556190\pi\)
−0.940372 + 0.340148i \(0.889523\pi\)
\(734\) 0 0
\(735\) −7.40567 + 21.0584i −0.273162 + 0.776751i
\(736\) 0 0
\(737\) 13.0152i 0.479422i
\(738\) 0 0
\(739\) −13.1128 −0.482361 −0.241181 0.970480i \(-0.577535\pi\)
−0.241181 + 0.970480i \(0.577535\pi\)
\(740\) 0 0
\(741\) 3.33890 + 17.7990i 0.122657 + 0.653862i
\(742\) 0 0
\(743\) −11.1665 + 19.3410i −0.409660 + 0.709551i −0.994851 0.101344i \(-0.967686\pi\)
0.585192 + 0.810895i \(0.301019\pi\)
\(744\) 0 0
\(745\) −10.1104 17.5117i −0.370415 0.641578i
\(746\) 0 0
\(747\) 5.00286 + 12.8654i 0.183045 + 0.470719i
\(748\) 0 0
\(749\) −22.4100 38.8153i −0.818844 1.41828i
\(750\) 0 0
\(751\) −6.99545 4.03882i −0.255267 0.147379i 0.366906 0.930258i \(-0.380417\pi\)
−0.622174 + 0.782879i \(0.713750\pi\)
\(752\) 0 0
\(753\) −7.25165 + 6.22082i −0.264265 + 0.226699i
\(754\) 0 0
\(755\) 3.12165i 0.113608i
\(756\) 0 0
\(757\) 12.7751i 0.464319i 0.972678 + 0.232160i \(0.0745792\pi\)
−0.972678 + 0.232160i \(0.925421\pi\)
\(758\) 0 0
\(759\) −11.8286 + 10.1472i −0.429352 + 0.368319i
\(760\) 0 0
\(761\) 43.2325 + 24.9603i 1.56718 + 0.904809i 0.996496 + 0.0836361i \(0.0266533\pi\)
0.570679 + 0.821173i \(0.306680\pi\)
\(762\) 0 0
\(763\) 20.7521 + 35.9437i 0.751276 + 1.30125i
\(764\) 0 0
\(765\) −3.17658 + 3.95783i −0.114850 + 0.143096i
\(766\) 0 0
\(767\) −13.2398 22.9320i −0.478060 0.828025i
\(768\) 0 0
\(769\) −14.2517 + 24.6846i −0.513929 + 0.890150i 0.485941 + 0.873992i \(0.338477\pi\)
−0.999869 + 0.0161588i \(0.994856\pi\)
\(770\) 0 0
\(771\) 6.23897 + 33.2586i 0.224691 + 1.19778i
\(772\) 0 0
\(773\) 20.8254 0.749037 0.374518 0.927220i \(-0.377808\pi\)
0.374518 + 0.927220i \(0.377808\pi\)
\(774\) 0 0
\(775\) 20.0466i 0.720096i
\(776\) 0 0
\(777\) 7.32583 20.8314i 0.262813 0.747321i
\(778\) 0 0
\(779\) −14.4942 8.36822i −0.519308 0.299822i
\(780\) 0 0
\(781\) 2.57384 1.48601i 0.0920991 0.0531735i
\(782\) 0 0
\(783\) 6.50337 + 3.47630i 0.232411 + 0.124233i
\(784\) 0 0
\(785\) −2.49980 + 1.44326i −0.0892218 + 0.0515122i
\(786\) 0 0
\(787\) −10.4386 + 18.0802i −0.372096 + 0.644488i −0.989888 0.141853i \(-0.954694\pi\)
0.617792 + 0.786341i \(0.288027\pi\)
\(788\) 0 0
\(789\) 6.46533 18.3845i 0.230172 0.654506i
\(790\) 0 0
\(791\) −35.4236 −1.25952
\(792\) 0 0
\(793\) −11.1448 −0.395765
\(794\) 0 0
\(795\) −21.7034 + 4.07133i −0.769740 + 0.144395i
\(796\) 0 0
\(797\) −14.4238 + 24.9828i −0.510918 + 0.884935i 0.489002 + 0.872283i \(0.337361\pi\)
−0.999920 + 0.0126529i \(0.995972\pi\)
\(798\) 0 0
\(799\) 4.61367 2.66370i 0.163220 0.0942350i
\(800\) 0 0
\(801\) 25.6124 + 3.94250i 0.904971 + 0.139301i
\(802\) 0 0
\(803\) 7.13225 4.11780i 0.251691 0.145314i
\(804\) 0 0
\(805\) −32.4136 18.7140i −1.14243 0.659582i
\(806\) 0 0
\(807\) −15.9688 18.6149i −0.562128 0.655276i
\(808\) 0 0
\(809\) 43.6746i 1.53552i 0.640739 + 0.767759i \(0.278628\pi\)
−0.640739 + 0.767759i \(0.721372\pi\)
\(810\) 0 0
\(811\) −42.3445 −1.48692 −0.743458 0.668782i \(-0.766816\pi\)
−0.743458 + 0.668782i \(0.766816\pi\)
\(812\) 0 0
\(813\) −5.14767 + 4.41593i −0.180537 + 0.154873i
\(814\) 0 0
\(815\) 3.91876 6.78749i 0.137268 0.237755i
\(816\) 0 0
\(817\) 5.96737 + 10.3358i 0.208772 + 0.361603i
\(818\) 0 0
\(819\) 5.97891 38.8420i 0.208920 1.35725i
\(820\) 0 0
\(821\) −1.40953 2.44138i −0.0491930 0.0852047i 0.840380 0.541997i \(-0.182332\pi\)
−0.889573 + 0.456792i \(0.848998\pi\)
\(822\) 0 0
\(823\) −4.46763 2.57939i −0.155732 0.0899118i 0.420109 0.907474i \(-0.361992\pi\)
−0.575841 + 0.817562i \(0.695325\pi\)
\(824\) 0 0
\(825\) −1.38565 7.38662i −0.0482422 0.257169i
\(826\) 0 0
\(827\) 21.8630i 0.760251i 0.924935 + 0.380125i \(0.124119\pi\)
−0.924935 + 0.380125i \(0.875881\pi\)
\(828\) 0 0
\(829\) 22.0815i 0.766924i 0.923557 + 0.383462i \(0.125268\pi\)
−0.923557 + 0.383462i \(0.874732\pi\)
\(830\) 0 0
\(831\) 43.3074 + 15.2300i 1.50232 + 0.528324i
\(832\) 0 0
\(833\) −14.7768 8.53139i −0.511986 0.295595i
\(834\) 0 0
\(835\) −9.45931 16.3840i −0.327353 0.566992i
\(836\) 0 0
\(837\) −27.9695 + 0.915040i −0.966768 + 0.0316284i
\(838\) 0 0
\(839\) 25.4035 + 44.0002i 0.877026 + 1.51905i 0.854588 + 0.519306i \(0.173809\pi\)
0.0224378 + 0.999748i \(0.492857\pi\)
\(840\) 0 0
\(841\) 13.4930 23.3705i 0.465276 0.805881i
\(842\) 0 0
\(843\) −1.74215 0.612666i −0.0600027 0.0211013i
\(844\) 0 0
\(845\) 4.15343 0.142882
\(846\) 0 0
\(847\) 41.3575i 1.42106i
\(848\) 0 0
\(849\) −6.05494 + 1.13584i −0.207805 + 0.0389820i
\(850\) 0 0
\(851\) 19.8668 + 11.4701i 0.681026 + 0.393191i
\(852\) 0 0
\(853\) −45.4891 + 26.2631i −1.55752 + 0.899233i −0.560023 + 0.828477i \(0.689208\pi\)
−0.997494 + 0.0707558i \(0.977459\pi\)
\(854\) 0 0
\(855\) −9.05472 7.26739i −0.309665 0.248539i
\(856\) 0 0
\(857\) −48.4564 + 27.9763i −1.65524 + 0.955653i −0.680372 + 0.732867i \(0.738182\pi\)
−0.974867 + 0.222786i \(0.928485\pi\)
\(858\) 0 0
\(859\) −15.4078 + 26.6871i −0.525708 + 0.910554i 0.473843 + 0.880609i \(0.342866\pi\)
−0.999552 + 0.0299443i \(0.990467\pi\)
\(860\) 0 0
\(861\) 23.6479 + 27.5665i 0.805918 + 0.939464i
\(862\) 0 0
\(863\) −25.1750 −0.856966 −0.428483 0.903550i \(-0.640952\pi\)
−0.428483 + 0.903550i \(0.640952\pi\)
\(864\) 0 0
\(865\) −23.1027 −0.785514
\(866\) 0 0
\(867\) 16.6458 + 19.4042i 0.565323 + 0.659000i
\(868\) 0 0
\(869\) −1.51428 + 2.62281i −0.0513685 + 0.0889728i
\(870\) 0 0
\(871\) 29.5278 17.0479i 1.00051 0.577646i
\(872\) 0 0
\(873\) −18.7821 + 7.30364i −0.635676 + 0.247191i
\(874\) 0 0
\(875\) 36.6276 21.1470i 1.23824 0.714898i
\(876\) 0 0
\(877\) −31.8486 18.3878i −1.07545 0.620913i −0.145786 0.989316i \(-0.546571\pi\)
−0.929666 + 0.368404i \(0.879904\pi\)
\(878\) 0 0
\(879\) 26.5213 4.97511i 0.894541 0.167806i
\(880\) 0 0
\(881\) 8.15439i 0.274728i 0.990521 + 0.137364i \(0.0438631\pi\)
−0.990521 + 0.137364i \(0.956137\pi\)
\(882\) 0 0
\(883\) 20.3792 0.685814 0.342907 0.939369i \(-0.388588\pi\)
0.342907 + 0.939369i \(0.388588\pi\)
\(884\) 0 0
\(885\) 16.0153 + 5.63215i 0.538348 + 0.189323i
\(886\) 0 0
\(887\) −22.3561 + 38.7220i −0.750646 + 1.30016i 0.196864 + 0.980431i \(0.436924\pi\)
−0.947510 + 0.319726i \(0.896409\pi\)
\(888\) 0 0
\(889\) 5.97891 + 10.3558i 0.200526 + 0.347322i
\(890\) 0 0
\(891\) 10.2427 2.27046i 0.343145 0.0760633i
\(892\) 0 0
\(893\) 6.09402 + 10.5551i 0.203928 + 0.353214i
\(894\) 0 0
\(895\) 3.99387 + 2.30586i 0.133500 + 0.0770765i
\(896\) 0 0
\(897\) 38.5147 + 13.5446i 1.28597 + 0.452241i
\(898\) 0 0
\(899\) 7.64305i 0.254910i
\(900\) 0 0
\(901\) 16.8788i 0.562315i
\(902\) 0 0
\(903\) −4.77521 25.4557i −0.158909 0.847112i
\(904\) 0 0
\(905\) 21.8524 + 12.6165i 0.726398 + 0.419386i
\(906\) 0 0
\(907\) −7.99519 13.8481i −0.265476 0.459818i 0.702212 0.711968i \(-0.252196\pi\)
−0.967688 + 0.252150i \(0.918862\pi\)
\(908\) 0 0
\(909\) 38.3884 14.9278i 1.27326 0.495125i
\(910\) 0 0
\(911\) −14.1609 24.5275i −0.469173 0.812631i 0.530206 0.847869i \(-0.322115\pi\)
−0.999379 + 0.0352377i \(0.988781\pi\)
\(912\) 0 0
\(913\) −2.68187 + 4.64514i −0.0887570 + 0.153732i
\(914\) 0 0
\(915\) 5.42320 4.65229i 0.179286 0.153800i
\(916\) 0 0
\(917\) −64.6553 −2.13511
\(918\) 0 0
\(919\) 17.1474i 0.565642i −0.959173 0.282821i \(-0.908730\pi\)
0.959173 0.282821i \(-0.0912702\pi\)
\(920\) 0 0
\(921\) 1.08341 + 1.26294i 0.0356995 + 0.0416151i
\(922\) 0 0
\(923\) −6.74265 3.89287i −0.221937 0.128135i
\(924\) 0 0
\(925\) −9.58047 + 5.53129i −0.315004 + 0.181868i
\(926\) 0 0
\(927\) −11.8853 + 14.8083i −0.390363 + 0.486368i
\(928\) 0 0
\(929\) 38.0670 21.9780i 1.24894 0.721075i 0.278040 0.960569i \(-0.410315\pi\)
0.970898 + 0.239495i \(0.0769818\pi\)
\(930\) 0 0
\(931\) 19.5181 33.8064i 0.639680 1.10796i
\(932\) 0 0
\(933\) −15.3055 + 2.87115i −0.501080 + 0.0939972i
\(934\) 0 0
\(935\) −1.97197 −0.0644902
\(936\) 0 0
\(937\) −13.5845 −0.443786 −0.221893 0.975071i \(-0.571223\pi\)
−0.221893 + 0.975071i \(0.571223\pi\)
\(938\) 0 0
\(939\) −9.83615 + 27.9696i −0.320991 + 0.912753i
\(940\) 0 0
\(941\) 13.5116 23.4028i 0.440466 0.762909i −0.557258 0.830339i \(-0.688147\pi\)
0.997724 + 0.0674301i \(0.0214800\pi\)
\(942\) 0 0
\(943\) −32.6765 + 18.8658i −1.06409 + 0.614354i
\(944\) 0 0
\(945\) 13.3047 + 21.3968i 0.432803 + 0.696037i
\(946\) 0 0
\(947\) −34.5376 + 19.9403i −1.12232 + 0.647972i −0.941992 0.335634i \(-0.891049\pi\)
−0.180328 + 0.983607i \(0.557716\pi\)
\(948\) 0 0
\(949\) −18.6843 10.7874i −0.606516 0.350172i
\(950\) 0 0
\(951\) 4.55704 12.9582i 0.147772 0.420198i
\(952\) 0 0
\(953\) 14.0999i 0.456741i −0.973574 0.228371i \(-0.926660\pi\)
0.973574 0.228371i \(-0.0733398\pi\)
\(954\) 0 0
\(955\) 16.4465 0.532197
\(956\) 0 0
\(957\) 0.528299 + 2.81625i 0.0170775 + 0.0910365i
\(958\) 0 0
\(959\) −18.7040 + 32.3963i −0.603983 + 1.04613i
\(960\) 0 0
\(961\) −0.997565 1.72783i −0.0321795 0.0557366i
\(962\) 0 0
\(963\) −30.9800 4.76872i −0.998317 0.153670i
\(964\) 0 0
\(965\) 2.48147 + 4.29803i 0.0798813 + 0.138358i
\(966\) 0 0
\(967\) 45.4687 + 26.2514i 1.46217 + 0.844187i 0.999112 0.0421387i \(-0.0134171\pi\)
0.463063 + 0.886326i \(0.346750\pi\)
\(968\) 0 0
\(969\) 6.73582 5.77832i 0.216386 0.185626i
\(970\) 0 0
\(971\) 61.3864i 1.96998i 0.172599 + 0.984992i \(0.444784\pi\)
−0.172599 + 0.984992i \(0.555216\pi\)
\(972\) 0 0
\(973\) 10.2006i 0.327017i
\(974\) 0 0
\(975\) −14.9432 + 12.8190i −0.478564 + 0.410535i
\(976\) 0 0
\(977\) −25.9568 14.9862i −0.830431 0.479450i 0.0235691 0.999722i \(-0.492497\pi\)
−0.854000 + 0.520273i \(0.825830\pi\)
\(978\) 0 0
\(979\) 5.03471 + 8.72037i 0.160910 + 0.278704i
\(980\) 0 0
\(981\) 28.6881 + 4.41593i 0.915939 + 0.140990i
\(982\) 0 0
\(983\) 21.1703 + 36.6681i 0.675228 + 1.16953i 0.976402 + 0.215961i \(0.0692883\pi\)
−0.301174 + 0.953569i \(0.597378\pi\)
\(984\) 0 0
\(985\) 4.35037 7.53506i 0.138614 0.240087i
\(986\) 0 0
\(987\) −4.87656 25.9959i −0.155223 0.827460i
\(988\) 0 0
\(989\) 26.9063 0.855572
\(990\) 0 0
\(991\) 12.3787i 0.393222i −0.980482 0.196611i \(-0.937006\pi\)
0.980482 0.196611i \(-0.0629937\pi\)
\(992\) 0 0
\(993\) 5.49735 15.6320i 0.174453 0.496066i
\(994\) 0 0
\(995\) 20.5370 + 11.8571i 0.651068 + 0.375894i
\(996\) 0 0
\(997\) −6.20535 + 3.58266i −0.196525 + 0.113464i −0.595034 0.803701i \(-0.702861\pi\)
0.398508 + 0.917165i \(0.369528\pi\)
\(998\) 0 0
\(999\) −8.15469 13.1144i −0.258003 0.414922i
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.239.5 16
3.2 odd 2 864.2.p.b.719.5 16
4.3 odd 2 72.2.l.b.59.6 yes 16
8.3 odd 2 inner 288.2.p.b.239.6 16
8.5 even 2 72.2.l.b.59.8 yes 16
9.2 odd 6 inner 288.2.p.b.47.6 16
9.4 even 3 2592.2.f.b.1295.9 16
9.5 odd 6 2592.2.f.b.1295.7 16
9.7 even 3 864.2.p.b.143.4 16
12.11 even 2 216.2.l.b.179.3 16
24.5 odd 2 216.2.l.b.179.1 16
24.11 even 2 864.2.p.b.719.4 16
36.7 odd 6 216.2.l.b.35.1 16
36.11 even 6 72.2.l.b.11.8 yes 16
36.23 even 6 648.2.f.b.323.5 16
36.31 odd 6 648.2.f.b.323.12 16
72.5 odd 6 648.2.f.b.323.11 16
72.11 even 6 inner 288.2.p.b.47.5 16
72.13 even 6 648.2.f.b.323.6 16
72.29 odd 6 72.2.l.b.11.6 16
72.43 odd 6 864.2.p.b.143.5 16
72.59 even 6 2592.2.f.b.1295.10 16
72.61 even 6 216.2.l.b.35.3 16
72.67 odd 6 2592.2.f.b.1295.8 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.2.l.b.11.6 16 72.29 odd 6
72.2.l.b.11.8 yes 16 36.11 even 6
72.2.l.b.59.6 yes 16 4.3 odd 2
72.2.l.b.59.8 yes 16 8.5 even 2
216.2.l.b.35.1 16 36.7 odd 6
216.2.l.b.35.3 16 72.61 even 6
216.2.l.b.179.1 16 24.5 odd 2
216.2.l.b.179.3 16 12.11 even 2
288.2.p.b.47.5 16 72.11 even 6 inner
288.2.p.b.47.6 16 9.2 odd 6 inner
288.2.p.b.239.5 16 1.1 even 1 trivial
288.2.p.b.239.6 16 8.3 odd 2 inner
648.2.f.b.323.5 16 36.23 even 6
648.2.f.b.323.6 16 72.13 even 6
648.2.f.b.323.11 16 72.5 odd 6
648.2.f.b.323.12 16 36.31 odd 6
864.2.p.b.143.4 16 9.7 even 3
864.2.p.b.143.5 16 72.43 odd 6
864.2.p.b.719.4 16 24.11 even 2
864.2.p.b.719.5 16 3.2 odd 2
2592.2.f.b.1295.7 16 9.5 odd 6
2592.2.f.b.1295.8 16 72.67 odd 6
2592.2.f.b.1295.9 16 9.4 even 3
2592.2.f.b.1295.10 16 72.59 even 6