Properties

Label 288.2.r.b.49.4
Level $288$
Weight $2$
Character 288.49
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(49,288)]
 
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([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("288.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.r (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: \( x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 72)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.4
Root \(1.41411 + 0.0174668i\) of defining polynomial
Character \(\chi\) \(=\) 288.49
Dual form 288.2.r.b.241.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.294546 + 1.70682i) q^{3} +(3.17262 + 1.83171i) q^{5} +(0.191926 + 0.332426i) q^{7} +(-2.82649 - 1.00547i) q^{9} +O(q^{10})\) \(q+(-0.294546 + 1.70682i) q^{3} +(3.17262 + 1.83171i) q^{5} +(0.191926 + 0.332426i) q^{7} +(-2.82649 - 1.00547i) q^{9} +(1.73849 - 1.00372i) q^{11} +(-0.397799 - 0.229669i) q^{13} +(-4.06089 + 4.87557i) q^{15} -4.08495 q^{17} +4.72398i q^{19} +(-0.623923 + 0.229669i) q^{21} +(2.97594 - 5.15447i) q^{23} +(4.21034 + 7.29252i) q^{25} +(2.54870 - 4.52815i) q^{27} +(-2.03783 + 1.17654i) q^{29} +(-0.592083 + 1.02552i) q^{31} +(1.20110 + 3.26293i) q^{33} +1.40621i q^{35} +5.74432i q^{37} +(0.509175 - 0.611324i) q^{39} +(4.75281 - 8.23212i) q^{41} +(-1.03633 + 0.598327i) q^{43} +(-7.12562 - 8.36729i) q^{45} +(-3.27688 - 5.67572i) q^{47} +(3.42633 - 5.93458i) q^{49} +(1.20321 - 6.97229i) q^{51} -7.63807i q^{53} +7.35407 q^{55} +(-8.06300 - 1.39143i) q^{57} +(-0.603703 - 0.348548i) q^{59} +(4.23774 - 2.44666i) q^{61} +(-0.208231 - 1.13257i) q^{63} +(-0.841376 - 1.45731i) q^{65} +(-8.87932 - 5.12648i) q^{67} +(7.92122 + 6.59762i) q^{69} +3.73792 q^{71} -2.68275 q^{73} +(-13.6872 + 5.03832i) q^{75} +(0.667322 + 0.385279i) q^{77} +(5.35979 + 9.28342i) q^{79} +(6.97804 + 5.68392i) q^{81} +(5.49039 - 3.16988i) q^{83} +(-12.9600 - 7.48246i) q^{85} +(-1.40792 - 3.82477i) q^{87} +7.56802 q^{89} -0.176318i q^{91} +(-1.57598 - 1.31264i) q^{93} +(-8.65297 + 14.9874i) q^{95} +(-2.98511 - 5.17036i) q^{97} +(-5.92302 + 1.08898i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 6 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 6 q^{7} + 2 q^{9} + 10 q^{15} - 28 q^{17} + 10 q^{23} + 2 q^{25} + 10 q^{31} - 2 q^{39} - 8 q^{41} - 6 q^{47} + 18 q^{49} + 4 q^{55} + 10 q^{57} - 2 q^{63} - 14 q^{65} - 72 q^{71} - 44 q^{73} + 30 q^{79} + 10 q^{81} - 42 q^{87} + 64 q^{89} - 44 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) −0.294546 + 1.70682i −0.170056 + 0.985434i
\(4\) 0 0
\(5\) 3.17262 + 1.83171i 1.41884 + 0.819167i 0.996197 0.0871306i \(-0.0277697\pi\)
0.422641 + 0.906297i \(0.361103\pi\)
\(6\) 0 0
\(7\) 0.191926 + 0.332426i 0.0725413 + 0.125645i 0.900014 0.435860i \(-0.143556\pi\)
−0.827473 + 0.561505i \(0.810222\pi\)
\(8\) 0 0
\(9\) −2.82649 1.00547i −0.942162 0.335158i
\(10\) 0 0
\(11\) 1.73849 1.00372i 0.524173 0.302632i −0.214467 0.976731i \(-0.568801\pi\)
0.738640 + 0.674100i \(0.235468\pi\)
\(12\) 0 0
\(13\) −0.397799 0.229669i −0.110330 0.0636988i 0.443820 0.896116i \(-0.353623\pi\)
−0.554149 + 0.832417i \(0.686956\pi\)
\(14\) 0 0
\(15\) −4.06089 + 4.87557i −1.04852 + 1.25887i
\(16\) 0 0
\(17\) −4.08495 −0.990747 −0.495373 0.868680i \(-0.664969\pi\)
−0.495373 + 0.868680i \(0.664969\pi\)
\(18\) 0 0
\(19\) 4.72398i 1.08376i 0.840457 + 0.541878i \(0.182286\pi\)
−0.840457 + 0.541878i \(0.817714\pi\)
\(20\) 0 0
\(21\) −0.623923 + 0.229669i −0.136151 + 0.0501179i
\(22\) 0 0
\(23\) 2.97594 5.15447i 0.620525 1.07478i −0.368863 0.929484i \(-0.620253\pi\)
0.989388 0.145298i \(-0.0464140\pi\)
\(24\) 0 0
\(25\) 4.21034 + 7.29252i 0.842068 + 1.45850i
\(26\) 0 0
\(27\) 2.54870 4.52815i 0.490497 0.871443i
\(28\) 0 0
\(29\) −2.03783 + 1.17654i −0.378416 + 0.218479i −0.677129 0.735864i \(-0.736776\pi\)
0.298713 + 0.954343i \(0.403443\pi\)
\(30\) 0 0
\(31\) −0.592083 + 1.02552i −0.106341 + 0.184188i −0.914285 0.405071i \(-0.867247\pi\)
0.807944 + 0.589259i \(0.200580\pi\)
\(32\) 0 0
\(33\) 1.20110 + 3.26293i 0.209085 + 0.568003i
\(34\) 0 0
\(35\) 1.40621i 0.237693i
\(36\) 0 0
\(37\) 5.74432i 0.944360i 0.881502 + 0.472180i \(0.156533\pi\)
−0.881502 + 0.472180i \(0.843467\pi\)
\(38\) 0 0
\(39\) 0.509175 0.611324i 0.0815332 0.0978902i
\(40\) 0 0
\(41\) 4.75281 8.23212i 0.742265 1.28564i −0.209197 0.977874i \(-0.567085\pi\)
0.951462 0.307767i \(-0.0995817\pi\)
\(42\) 0 0
\(43\) −1.03633 + 0.598327i −0.158039 + 0.0912440i −0.576934 0.816791i \(-0.695751\pi\)
0.418895 + 0.908035i \(0.362418\pi\)
\(44\) 0 0
\(45\) −7.12562 8.36729i −1.06222 1.24732i
\(46\) 0 0
\(47\) −3.27688 5.67572i −0.477982 0.827889i 0.521699 0.853129i \(-0.325298\pi\)
−0.999681 + 0.0252403i \(0.991965\pi\)
\(48\) 0 0
\(49\) 3.42633 5.93458i 0.489476 0.847796i
\(50\) 0 0
\(51\) 1.20321 6.97229i 0.168482 0.976316i
\(52\) 0 0
\(53\) 7.63807i 1.04917i −0.851358 0.524585i \(-0.824221\pi\)
0.851358 0.524585i \(-0.175779\pi\)
\(54\) 0 0
\(55\) 7.35407 0.991623
\(56\) 0 0
\(57\) −8.06300 1.39143i −1.06797 0.184299i
\(58\) 0 0
\(59\) −0.603703 0.348548i −0.0785954 0.0453771i 0.460187 0.887822i \(-0.347782\pi\)
−0.538783 + 0.842445i \(0.681116\pi\)
\(60\) 0 0
\(61\) 4.23774 2.44666i 0.542587 0.313263i −0.203540 0.979067i \(-0.565245\pi\)
0.746127 + 0.665804i \(0.231911\pi\)
\(62\) 0 0
\(63\) −0.208231 1.13257i −0.0262346 0.142691i
\(64\) 0 0
\(65\) −0.841376 1.45731i −0.104360 0.180757i
\(66\) 0 0
\(67\) −8.87932 5.12648i −1.08478 0.626299i −0.152599 0.988288i \(-0.548764\pi\)
−0.932182 + 0.361989i \(0.882098\pi\)
\(68\) 0 0
\(69\) 7.92122 + 6.59762i 0.953603 + 0.794260i
\(70\) 0 0
\(71\) 3.73792 0.443610 0.221805 0.975091i \(-0.428805\pi\)
0.221805 + 0.975091i \(0.428805\pi\)
\(72\) 0 0
\(73\) −2.68275 −0.313992 −0.156996 0.987599i \(-0.550181\pi\)
−0.156996 + 0.987599i \(0.550181\pi\)
\(74\) 0 0
\(75\) −13.6872 + 5.03832i −1.58046 + 0.581775i
\(76\) 0 0
\(77\) 0.667322 + 0.385279i 0.0760484 + 0.0439066i
\(78\) 0 0
\(79\) 5.35979 + 9.28342i 0.603023 + 1.04447i 0.992361 + 0.123372i \(0.0393707\pi\)
−0.389337 + 0.921095i \(0.627296\pi\)
\(80\) 0 0
\(81\) 6.97804 + 5.68392i 0.775338 + 0.631546i
\(82\) 0 0
\(83\) 5.49039 3.16988i 0.602648 0.347939i −0.167434 0.985883i \(-0.553548\pi\)
0.770083 + 0.637944i \(0.220215\pi\)
\(84\) 0 0
\(85\) −12.9600 7.48246i −1.40571 0.811586i
\(86\) 0 0
\(87\) −1.40792 3.82477i −0.150945 0.410058i
\(88\) 0 0
\(89\) 7.56802 0.802208 0.401104 0.916032i \(-0.368627\pi\)
0.401104 + 0.916032i \(0.368627\pi\)
\(90\) 0 0
\(91\) 0.176318i 0.0184832i
\(92\) 0 0
\(93\) −1.57598 1.31264i −0.163422 0.136115i
\(94\) 0 0
\(95\) −8.65297 + 14.9874i −0.887776 + 1.53767i
\(96\) 0 0
\(97\) −2.98511 5.17036i −0.303092 0.524971i 0.673743 0.738966i \(-0.264686\pi\)
−0.976835 + 0.213995i \(0.931352\pi\)
\(98\) 0 0
\(99\) −5.92302 + 1.08898i −0.595286 + 0.109447i
\(100\) 0 0
\(101\) 4.81265 2.77859i 0.478877 0.276480i −0.241071 0.970507i \(-0.577499\pi\)
0.719948 + 0.694028i \(0.244165\pi\)
\(102\) 0 0
\(103\) 6.14380 10.6414i 0.605366 1.04853i −0.386627 0.922236i \(-0.626360\pi\)
0.991993 0.126289i \(-0.0403067\pi\)
\(104\) 0 0
\(105\) −2.40016 0.414194i −0.234231 0.0404212i
\(106\) 0 0
\(107\) 6.61773i 0.639760i 0.947458 + 0.319880i \(0.103643\pi\)
−0.947458 + 0.319880i \(0.896357\pi\)
\(108\) 0 0
\(109\) 7.01563i 0.671975i 0.941866 + 0.335988i \(0.109070\pi\)
−0.941866 + 0.335988i \(0.890930\pi\)
\(110\) 0 0
\(111\) −9.80453 1.69196i −0.930605 0.160594i
\(112\) 0 0
\(113\) −4.09419 + 7.09135i −0.385149 + 0.667098i −0.991790 0.127878i \(-0.959183\pi\)
0.606641 + 0.794976i \(0.292517\pi\)
\(114\) 0 0
\(115\) 18.8830 10.9021i 1.76085 1.01663i
\(116\) 0 0
\(117\) 0.893446 + 1.04913i 0.0825991 + 0.0969924i
\(118\) 0 0
\(119\) −0.784009 1.35794i −0.0718700 0.124483i
\(120\) 0 0
\(121\) −3.48511 + 6.03639i −0.316828 + 0.548762i
\(122\) 0 0
\(123\) 12.6508 + 10.5369i 1.14069 + 0.950084i
\(124\) 0 0
\(125\) 12.5314i 1.12084i
\(126\) 0 0
\(127\) −21.0113 −1.86445 −0.932224 0.361882i \(-0.882134\pi\)
−0.932224 + 0.361882i \(0.882134\pi\)
\(128\) 0 0
\(129\) −0.715991 1.94507i −0.0630395 0.171254i
\(130\) 0 0
\(131\) −5.49039 3.16988i −0.479697 0.276953i 0.240593 0.970626i \(-0.422658\pi\)
−0.720290 + 0.693673i \(0.755991\pi\)
\(132\) 0 0
\(133\) −1.57037 + 0.906655i −0.136169 + 0.0786170i
\(134\) 0 0
\(135\) 16.3803 9.69762i 1.40979 0.834638i
\(136\) 0 0
\(137\) 0.483695 + 0.837785i 0.0413249 + 0.0715768i 0.885948 0.463784i \(-0.153509\pi\)
−0.844623 + 0.535361i \(0.820175\pi\)
\(138\) 0 0
\(139\) 5.18167 + 2.99164i 0.439503 + 0.253747i 0.703387 0.710807i \(-0.251670\pi\)
−0.263884 + 0.964554i \(0.585004\pi\)
\(140\) 0 0
\(141\) 10.6526 3.92129i 0.897114 0.330232i
\(142\) 0 0
\(143\) −0.922090 −0.0771091
\(144\) 0 0
\(145\) −8.62036 −0.715882
\(146\) 0 0
\(147\) 9.12006 + 7.59614i 0.752210 + 0.626519i
\(148\) 0 0
\(149\) −6.43764 3.71678i −0.527392 0.304490i 0.212562 0.977148i \(-0.431819\pi\)
−0.739954 + 0.672658i \(0.765153\pi\)
\(150\) 0 0
\(151\) 0.492870 + 0.853676i 0.0401092 + 0.0694711i 0.885383 0.464862i \(-0.153896\pi\)
−0.845274 + 0.534333i \(0.820563\pi\)
\(152\) 0 0
\(153\) 11.5461 + 4.10732i 0.933444 + 0.332057i
\(154\) 0 0
\(155\) −3.75691 + 2.16905i −0.301762 + 0.174222i
\(156\) 0 0
\(157\) 15.2336 + 8.79510i 1.21577 + 0.701925i 0.964010 0.265864i \(-0.0856573\pi\)
0.251760 + 0.967790i \(0.418991\pi\)
\(158\) 0 0
\(159\) 13.0368 + 2.24976i 1.03389 + 0.178418i
\(160\) 0 0
\(161\) 2.28464 0.180055
\(162\) 0 0
\(163\) 17.8852i 1.40088i 0.713711 + 0.700440i \(0.247013\pi\)
−0.713711 + 0.700440i \(0.752987\pi\)
\(164\) 0 0
\(165\) −2.16611 + 12.5521i −0.168631 + 0.977179i
\(166\) 0 0
\(167\) 1.04037 1.80197i 0.0805062 0.139441i −0.822961 0.568097i \(-0.807680\pi\)
0.903467 + 0.428657i \(0.141013\pi\)
\(168\) 0 0
\(169\) −6.39450 11.0756i −0.491885 0.851970i
\(170\) 0 0
\(171\) 4.74984 13.3523i 0.363229 1.02107i
\(172\) 0 0
\(173\) −16.4718 + 9.51000i −1.25233 + 0.723032i −0.971571 0.236747i \(-0.923919\pi\)
−0.280757 + 0.959779i \(0.590585\pi\)
\(174\) 0 0
\(175\) −1.61615 + 2.79925i −0.122169 + 0.211603i
\(176\) 0 0
\(177\) 0.772728 0.927750i 0.0580818 0.0697340i
\(178\) 0 0
\(179\) 2.12111i 0.158539i 0.996853 + 0.0792697i \(0.0252588\pi\)
−0.996853 + 0.0792697i \(0.974741\pi\)
\(180\) 0 0
\(181\) 1.66297i 0.123608i −0.998088 0.0618039i \(-0.980315\pi\)
0.998088 0.0618039i \(-0.0196853\pi\)
\(182\) 0 0
\(183\) 2.92781 + 7.95372i 0.216430 + 0.587956i
\(184\) 0 0
\(185\) −10.5219 + 18.2245i −0.773588 + 1.33989i
\(186\) 0 0
\(187\) −7.10164 + 4.10013i −0.519323 + 0.299831i
\(188\) 0 0
\(189\) 1.99444 0.0218184i 0.145074 0.00158705i
\(190\) 0 0
\(191\) 8.69755 + 15.0646i 0.629333 + 1.09004i 0.987686 + 0.156450i \(0.0500052\pi\)
−0.358353 + 0.933586i \(0.616662\pi\)
\(192\) 0 0
\(193\) −1.41709 + 2.45447i −0.102004 + 0.176677i −0.912510 0.409054i \(-0.865859\pi\)
0.810506 + 0.585730i \(0.199192\pi\)
\(194\) 0 0
\(195\) 2.73519 1.00684i 0.195871 0.0721010i
\(196\) 0 0
\(197\) 12.5991i 0.897646i −0.893621 0.448823i \(-0.851843\pi\)
0.893621 0.448823i \(-0.148157\pi\)
\(198\) 0 0
\(199\) −17.2733 −1.22447 −0.612237 0.790674i \(-0.709730\pi\)
−0.612237 + 0.790674i \(0.709730\pi\)
\(200\) 0 0
\(201\) 11.3654 13.6454i 0.801650 0.962475i
\(202\) 0 0
\(203\) −0.782227 0.451619i −0.0549016 0.0316975i
\(204\) 0 0
\(205\) 30.1577 17.4116i 2.10631 1.21608i
\(206\) 0 0
\(207\) −13.5941 + 11.5768i −0.944857 + 0.804644i
\(208\) 0 0
\(209\) 4.74153 + 8.21258i 0.327979 + 0.568076i
\(210\) 0 0
\(211\) −15.2192 8.78678i −1.04773 0.604907i −0.125717 0.992066i \(-0.540123\pi\)
−0.922013 + 0.387159i \(0.873456\pi\)
\(212\) 0 0
\(213\) −1.10099 + 6.37997i −0.0754386 + 0.437149i
\(214\) 0 0
\(215\) −4.38385 −0.298976
\(216\) 0 0
\(217\) −0.454545 −0.0308565
\(218\) 0 0
\(219\) 0.790193 4.57898i 0.0533963 0.309419i
\(220\) 0 0
\(221\) 1.62499 + 0.938188i 0.109309 + 0.0631094i
\(222\) 0 0
\(223\) −12.3137 21.3280i −0.824587 1.42823i −0.902235 0.431245i \(-0.858074\pi\)
0.0776484 0.996981i \(-0.475259\pi\)
\(224\) 0 0
\(225\) −4.56802 24.8456i −0.304535 1.65637i
\(226\) 0 0
\(227\) −16.9918 + 9.81024i −1.12779 + 0.651128i −0.943378 0.331721i \(-0.892371\pi\)
−0.184410 + 0.982849i \(0.559037\pi\)
\(228\) 0 0
\(229\) −21.3431 12.3224i −1.41039 0.814289i −0.414965 0.909837i \(-0.636206\pi\)
−0.995425 + 0.0955486i \(0.969539\pi\)
\(230\) 0 0
\(231\) −0.854159 + 1.02552i −0.0561995 + 0.0674741i
\(232\) 0 0
\(233\) −20.9222 −1.37066 −0.685330 0.728233i \(-0.740342\pi\)
−0.685330 + 0.728233i \(0.740342\pi\)
\(234\) 0 0
\(235\) 24.0092i 1.56619i
\(236\) 0 0
\(237\) −17.4239 + 6.41381i −1.13180 + 0.416622i
\(238\) 0 0
\(239\) 5.14584 8.91286i 0.332857 0.576525i −0.650214 0.759751i \(-0.725321\pi\)
0.983071 + 0.183226i \(0.0586541\pi\)
\(240\) 0 0
\(241\) 10.2379 + 17.7326i 0.659483 + 1.14226i 0.980750 + 0.195269i \(0.0625579\pi\)
−0.321267 + 0.946989i \(0.604109\pi\)
\(242\) 0 0
\(243\) −11.7568 + 10.2361i −0.754199 + 0.656646i
\(244\) 0 0
\(245\) 21.7409 12.5521i 1.38897 0.801924i
\(246\) 0 0
\(247\) 1.08495 1.87919i 0.0690339 0.119570i
\(248\) 0 0
\(249\) 3.79325 + 10.3048i 0.240387 + 0.653040i
\(250\) 0 0
\(251\) 28.0987i 1.77358i −0.462177 0.886788i \(-0.652932\pi\)
0.462177 0.886788i \(-0.347068\pi\)
\(252\) 0 0
\(253\) 11.9480i 0.751163i
\(254\) 0 0
\(255\) 16.5885 19.9165i 1.03881 1.24722i
\(256\) 0 0
\(257\) 5.53682 9.59006i 0.345378 0.598211i −0.640045 0.768338i \(-0.721084\pi\)
0.985422 + 0.170126i \(0.0544175\pi\)
\(258\) 0 0
\(259\) −1.90956 + 1.10248i −0.118654 + 0.0685050i
\(260\) 0 0
\(261\) 6.94290 1.27650i 0.429754 0.0790131i
\(262\) 0 0
\(263\) 12.7620 + 22.1044i 0.786938 + 1.36302i 0.927834 + 0.372992i \(0.121668\pi\)
−0.140897 + 0.990024i \(0.544998\pi\)
\(264\) 0 0
\(265\) 13.9907 24.2327i 0.859444 1.48860i
\(266\) 0 0
\(267\) −2.22913 + 12.9173i −0.136420 + 0.790524i
\(268\) 0 0
\(269\) 18.3998i 1.12185i 0.827865 + 0.560927i \(0.189555\pi\)
−0.827865 + 0.560927i \(0.810445\pi\)
\(270\) 0 0
\(271\) 22.4135 1.36152 0.680760 0.732506i \(-0.261650\pi\)
0.680760 + 0.732506i \(0.261650\pi\)
\(272\) 0 0
\(273\) 0.300944 + 0.0519337i 0.0182139 + 0.00314317i
\(274\) 0 0
\(275\) 14.6392 + 8.45196i 0.882779 + 0.509673i
\(276\) 0 0
\(277\) −20.2421 + 11.6868i −1.21623 + 0.702190i −0.964109 0.265506i \(-0.914461\pi\)
−0.252119 + 0.967696i \(0.581128\pi\)
\(278\) 0 0
\(279\) 2.70465 2.30329i 0.161923 0.137894i
\(280\) 0 0
\(281\) 5.29466 + 9.17062i 0.315853 + 0.547073i 0.979618 0.200867i \(-0.0643760\pi\)
−0.663765 + 0.747941i \(0.731043\pi\)
\(282\) 0 0
\(283\) 7.69029 + 4.43999i 0.457140 + 0.263930i 0.710841 0.703353i \(-0.248314\pi\)
−0.253701 + 0.967283i \(0.581648\pi\)
\(284\) 0 0
\(285\) −23.0321 19.1836i −1.36430 1.13634i
\(286\) 0 0
\(287\) 3.64876 0.215379
\(288\) 0 0
\(289\) −0.313160 −0.0184212
\(290\) 0 0
\(291\) 9.70414 3.57214i 0.568867 0.209403i
\(292\) 0 0
\(293\) −9.82117 5.67026i −0.573759 0.331260i 0.184890 0.982759i \(-0.440807\pi\)
−0.758649 + 0.651499i \(0.774140\pi\)
\(294\) 0 0
\(295\) −1.27688 2.21162i −0.0743428 0.128765i
\(296\) 0 0
\(297\) −0.114103 10.4303i −0.00662095 0.605227i
\(298\) 0 0
\(299\) −2.36765 + 1.36696i −0.136925 + 0.0790534i
\(300\) 0 0
\(301\) −0.397799 0.229669i −0.0229287 0.0132379i
\(302\) 0 0
\(303\) 3.32501 + 9.03277i 0.191017 + 0.518919i
\(304\) 0 0
\(305\) 17.9263 1.02646
\(306\) 0 0
\(307\) 0.628678i 0.0358805i −0.999839 0.0179403i \(-0.994289\pi\)
0.999839 0.0179403i \(-0.00571087\pi\)
\(308\) 0 0
\(309\) 16.3533 + 13.6207i 0.930307 + 0.774857i
\(310\) 0 0
\(311\) 9.64443 16.7046i 0.546885 0.947233i −0.451600 0.892220i \(-0.649147\pi\)
0.998486 0.0550127i \(-0.0175199\pi\)
\(312\) 0 0
\(313\) −2.86959 4.97028i −0.162199 0.280937i 0.773458 0.633847i \(-0.218525\pi\)
−0.935657 + 0.352911i \(0.885192\pi\)
\(314\) 0 0
\(315\) 1.41391 3.97464i 0.0796649 0.223946i
\(316\) 0 0
\(317\) −10.8187 + 6.24618i −0.607639 + 0.350821i −0.772041 0.635573i \(-0.780764\pi\)
0.164402 + 0.986393i \(0.447431\pi\)
\(318\) 0 0
\(319\) −2.36183 + 4.09081i −0.132237 + 0.229042i
\(320\) 0 0
\(321\) −11.2953 1.94922i −0.630442 0.108795i
\(322\) 0 0
\(323\) 19.2972i 1.07373i
\(324\) 0 0
\(325\) 3.86794i 0.214555i
\(326\) 0 0
\(327\) −11.9744 2.06642i −0.662188 0.114273i
\(328\) 0 0
\(329\) 1.25784 2.17864i 0.0693468 0.120112i
\(330\) 0 0
\(331\) 3.00014 1.73213i 0.164902 0.0952065i −0.415278 0.909695i \(-0.636316\pi\)
0.580180 + 0.814488i \(0.302982\pi\)
\(332\) 0 0
\(333\) 5.77576 16.2362i 0.316510 0.889740i
\(334\) 0 0
\(335\) −18.7805 32.5287i −1.02609 1.77723i
\(336\) 0 0
\(337\) −9.30453 + 16.1159i −0.506850 + 0.877890i 0.493119 + 0.869962i \(0.335857\pi\)
−0.999969 + 0.00792778i \(0.997476\pi\)
\(338\) 0 0
\(339\) −10.8977 9.07678i −0.591884 0.492983i
\(340\) 0 0
\(341\) 2.37713i 0.128729i
\(342\) 0 0
\(343\) 5.31737 0.287111
\(344\) 0 0
\(345\) 13.0461 + 35.4411i 0.702376 + 1.90809i
\(346\) 0 0
\(347\) 0.0408752 + 0.0235993i 0.00219430 + 0.00126688i 0.501097 0.865391i \(-0.332930\pi\)
−0.498902 + 0.866658i \(0.666263\pi\)
\(348\) 0 0
\(349\) −12.8884 + 7.44113i −0.689901 + 0.398314i −0.803575 0.595204i \(-0.797071\pi\)
0.113674 + 0.993518i \(0.463738\pi\)
\(350\) 0 0
\(351\) −2.05384 + 1.21594i −0.109626 + 0.0649019i
\(352\) 0 0
\(353\) −9.25423 16.0288i −0.492553 0.853127i 0.507410 0.861705i \(-0.330603\pi\)
−0.999963 + 0.00857792i \(0.997270\pi\)
\(354\) 0 0
\(355\) 11.8590 + 6.84680i 0.629411 + 0.363390i
\(356\) 0 0
\(357\) 2.54870 0.938188i 0.134891 0.0496542i
\(358\) 0 0
\(359\) −31.3426 −1.65420 −0.827101 0.562054i \(-0.810011\pi\)
−0.827101 + 0.562054i \(0.810011\pi\)
\(360\) 0 0
\(361\) −3.31599 −0.174526
\(362\) 0 0
\(363\) −9.27652 7.72646i −0.486891 0.405534i
\(364\) 0 0
\(365\) −8.51135 4.91403i −0.445504 0.257212i
\(366\) 0 0
\(367\) 10.2308 + 17.7203i 0.534043 + 0.924990i 0.999209 + 0.0397663i \(0.0126613\pi\)
−0.465166 + 0.885224i \(0.654005\pi\)
\(368\) 0 0
\(369\) −21.7109 + 18.4891i −1.13023 + 0.962505i
\(370\) 0 0
\(371\) 2.53909 1.46594i 0.131823 0.0761081i
\(372\) 0 0
\(373\) 20.6021 + 11.8946i 1.06674 + 0.615880i 0.927288 0.374349i \(-0.122134\pi\)
0.139448 + 0.990229i \(0.455467\pi\)
\(374\) 0 0
\(375\) −21.3889 3.69107i −1.10452 0.190606i
\(376\) 0 0
\(377\) 1.08086 0.0556673
\(378\) 0 0
\(379\) 24.0988i 1.23787i 0.785441 + 0.618937i \(0.212436\pi\)
−0.785441 + 0.618937i \(0.787564\pi\)
\(380\) 0 0
\(381\) 6.18878 35.8625i 0.317061 1.83729i
\(382\) 0 0
\(383\) −9.39161 + 16.2667i −0.479889 + 0.831192i −0.999734 0.0230686i \(-0.992656\pi\)
0.519845 + 0.854261i \(0.325990\pi\)
\(384\) 0 0
\(385\) 1.41144 + 2.44468i 0.0719336 + 0.124593i
\(386\) 0 0
\(387\) 3.53078 0.649157i 0.179480 0.0329985i
\(388\) 0 0
\(389\) 15.0467 8.68720i 0.762897 0.440459i −0.0674382 0.997723i \(-0.521483\pi\)
0.830335 + 0.557265i \(0.188149\pi\)
\(390\) 0 0
\(391\) −12.1566 + 21.0558i −0.614783 + 1.06484i
\(392\) 0 0
\(393\) 7.02759 8.43744i 0.354495 0.425613i
\(394\) 0 0
\(395\) 39.2703i 1.97591i
\(396\) 0 0
\(397\) 26.2401i 1.31696i 0.752600 + 0.658478i \(0.228799\pi\)
−0.752600 + 0.658478i \(0.771201\pi\)
\(398\) 0 0
\(399\) −1.08495 2.94740i −0.0543156 0.147555i
\(400\) 0 0
\(401\) 10.8194 18.7398i 0.540296 0.935820i −0.458591 0.888648i \(-0.651646\pi\)
0.998887 0.0471725i \(-0.0150210\pi\)
\(402\) 0 0
\(403\) 0.471060 0.271967i 0.0234652 0.0135476i
\(404\) 0 0
\(405\) 11.7274 + 30.8147i 0.582737 + 1.53119i
\(406\) 0 0
\(407\) 5.76566 + 9.98642i 0.285793 + 0.495008i
\(408\) 0 0
\(409\) −6.00563 + 10.4021i −0.296959 + 0.514348i −0.975439 0.220271i \(-0.929306\pi\)
0.678480 + 0.734619i \(0.262639\pi\)
\(410\) 0 0
\(411\) −1.57242 + 0.578816i −0.0775618 + 0.0285509i
\(412\) 0 0
\(413\) 0.267582i 0.0131668i
\(414\) 0 0
\(415\) 23.2252 1.14008
\(416\) 0 0
\(417\) −6.63243 + 7.96301i −0.324791 + 0.389950i
\(418\) 0 0
\(419\) 1.38092 + 0.797277i 0.0674625 + 0.0389495i 0.533352 0.845893i \(-0.320932\pi\)
−0.465889 + 0.884843i \(0.654266\pi\)
\(420\) 0 0
\(421\) −15.6612 + 9.04197i −0.763278 + 0.440679i −0.830471 0.557061i \(-0.811929\pi\)
0.0671934 + 0.997740i \(0.478596\pi\)
\(422\) 0 0
\(423\) 3.55526 + 19.3372i 0.172863 + 0.940205i
\(424\) 0 0
\(425\) −17.1990 29.7896i −0.834276 1.44501i
\(426\) 0 0
\(427\) 1.62667 + 0.939156i 0.0787199 + 0.0454489i
\(428\) 0 0
\(429\) 0.271598 1.57384i 0.0131129 0.0759859i
\(430\) 0 0
\(431\) 34.7451 1.67361 0.836806 0.547499i \(-0.184420\pi\)
0.836806 + 0.547499i \(0.184420\pi\)
\(432\) 0 0
\(433\) 12.7197 0.611270 0.305635 0.952149i \(-0.401131\pi\)
0.305635 + 0.952149i \(0.401131\pi\)
\(434\) 0 0
\(435\) 2.53909 14.7134i 0.121740 0.705455i
\(436\) 0 0
\(437\) 24.3496 + 14.0583i 1.16480 + 0.672498i
\(438\) 0 0
\(439\) 7.45900 + 12.9194i 0.355999 + 0.616608i 0.987288 0.158939i \(-0.0508074\pi\)
−0.631290 + 0.775547i \(0.717474\pi\)
\(440\) 0 0
\(441\) −15.6515 + 13.3289i −0.745311 + 0.634710i
\(442\) 0 0
\(443\) 3.48405 2.01152i 0.165532 0.0955702i −0.414945 0.909846i \(-0.636199\pi\)
0.580478 + 0.814276i \(0.302866\pi\)
\(444\) 0 0
\(445\) 24.0104 + 13.8624i 1.13820 + 0.657142i
\(446\) 0 0
\(447\) 8.24006 9.89315i 0.389741 0.467930i
\(448\) 0 0
\(449\) 10.9179 0.515246 0.257623 0.966245i \(-0.417061\pi\)
0.257623 + 0.966245i \(0.417061\pi\)
\(450\) 0 0
\(451\) 19.0819i 0.898531i
\(452\) 0 0
\(453\) −1.60225 + 0.589795i −0.0752801 + 0.0277110i
\(454\) 0 0
\(455\) 0.322964 0.559390i 0.0151408 0.0262246i
\(456\) 0 0
\(457\) −0.815204 1.41197i −0.0381336 0.0660494i 0.846329 0.532661i \(-0.178808\pi\)
−0.884462 + 0.466612i \(0.845475\pi\)
\(458\) 0 0
\(459\) −10.4113 + 18.4973i −0.485958 + 0.863379i
\(460\) 0 0
\(461\) 10.1812 5.87811i 0.474185 0.273771i −0.243805 0.969824i \(-0.578396\pi\)
0.717990 + 0.696054i \(0.245062\pi\)
\(462\) 0 0
\(463\) 10.6473 18.4416i 0.494820 0.857053i −0.505162 0.863024i \(-0.668567\pi\)
0.999982 + 0.00597113i \(0.00190068\pi\)
\(464\) 0 0
\(465\) −2.59560 7.05126i −0.120368 0.326994i
\(466\) 0 0
\(467\) 18.9230i 0.875650i 0.899060 + 0.437825i \(0.144251\pi\)
−0.899060 + 0.437825i \(0.855749\pi\)
\(468\) 0 0
\(469\) 3.93562i 0.181730i
\(470\) 0 0
\(471\) −19.4987 + 23.4104i −0.898451 + 1.07870i
\(472\) 0 0
\(473\) −1.20110 + 2.08037i −0.0552267 + 0.0956554i
\(474\) 0 0
\(475\) −34.4497 + 19.8896i −1.58066 + 0.912595i
\(476\) 0 0
\(477\) −7.67988 + 21.5889i −0.351638 + 0.988487i
\(478\) 0 0
\(479\) −14.9759 25.9391i −0.684268 1.18519i −0.973666 0.227978i \(-0.926789\pi\)
0.289398 0.957209i \(-0.406545\pi\)
\(480\) 0 0
\(481\) 1.31929 2.28508i 0.0601546 0.104191i
\(482\) 0 0
\(483\) −0.672931 + 3.89947i −0.0306194 + 0.177432i
\(484\) 0 0
\(485\) 21.8714i 0.993131i
\(486\) 0 0
\(487\) 17.3370 0.785614 0.392807 0.919621i \(-0.371504\pi\)
0.392807 + 0.919621i \(0.371504\pi\)
\(488\) 0 0
\(489\) −30.5269 5.26802i −1.38048 0.238228i
\(490\) 0 0
\(491\) 31.1204 + 17.9674i 1.40444 + 0.810856i 0.994845 0.101409i \(-0.0323351\pi\)
0.409599 + 0.912265i \(0.365668\pi\)
\(492\) 0 0
\(493\) 8.32446 4.80613i 0.374915 0.216457i
\(494\) 0 0
\(495\) −20.7862 7.39433i −0.934269 0.332350i
\(496\) 0 0
\(497\) 0.717405 + 1.24258i 0.0321800 + 0.0557374i
\(498\) 0 0
\(499\) 10.4956 + 6.05962i 0.469846 + 0.271266i 0.716175 0.697920i \(-0.245891\pi\)
−0.246329 + 0.969186i \(0.579224\pi\)
\(500\) 0 0
\(501\) 2.76921 + 2.30649i 0.123719 + 0.103046i
\(502\) 0 0
\(503\) −32.3442 −1.44215 −0.721077 0.692855i \(-0.756353\pi\)
−0.721077 + 0.692855i \(0.756353\pi\)
\(504\) 0 0
\(505\) 20.3583 0.905932
\(506\) 0 0
\(507\) 20.7876 7.65201i 0.923208 0.339838i
\(508\) 0 0
\(509\) −2.90310 1.67610i −0.128677 0.0742919i 0.434280 0.900778i \(-0.357003\pi\)
−0.562957 + 0.826486i \(0.690336\pi\)
\(510\) 0 0
\(511\) −0.514890 0.891816i −0.0227774 0.0394516i
\(512\) 0 0
\(513\) 21.3909 + 12.0400i 0.944431 + 0.531578i
\(514\) 0 0
\(515\) 38.9838 22.5073i 1.71783 0.991792i
\(516\) 0 0
\(517\) −11.3936 6.57811i −0.501091 0.289305i
\(518\) 0 0
\(519\) −11.3802 30.9156i −0.499535 1.35704i
\(520\) 0 0
\(521\) 21.5651 0.944786 0.472393 0.881388i \(-0.343390\pi\)
0.472393 + 0.881388i \(0.343390\pi\)
\(522\) 0 0
\(523\) 24.9549i 1.09120i −0.838046 0.545600i \(-0.816302\pi\)
0.838046 0.545600i \(-0.183698\pi\)
\(524\) 0 0
\(525\) −4.30179 3.58298i −0.187746 0.156374i
\(526\) 0 0
\(527\) 2.41863 4.18919i 0.105357 0.182484i
\(528\) 0 0
\(529\) −6.21238 10.7602i −0.270104 0.467833i
\(530\) 0 0
\(531\) 1.35590 + 1.59217i 0.0588411 + 0.0690944i
\(532\) 0 0
\(533\) −3.78133 + 2.18315i −0.163787 + 0.0945627i
\(534\) 0 0
\(535\) −12.1218 + 20.9955i −0.524070 + 0.907716i
\(536\) 0 0
\(537\) −3.62036 0.624764i −0.156230 0.0269606i
\(538\) 0 0
\(539\) 13.7562i 0.592523i
\(540\) 0 0
\(541\) 41.9065i 1.80170i −0.434131 0.900850i \(-0.642945\pi\)
0.434131 0.900850i \(-0.357055\pi\)
\(542\) 0 0
\(543\) 2.83840 + 0.489821i 0.121807 + 0.0210202i
\(544\) 0 0
\(545\) −12.8506 + 22.2579i −0.550460 + 0.953424i
\(546\) 0 0
\(547\) −25.7251 + 14.8524i −1.09993 + 0.635043i −0.936202 0.351462i \(-0.885684\pi\)
−0.163726 + 0.986506i \(0.552351\pi\)
\(548\) 0 0
\(549\) −14.4380 + 2.65451i −0.616197 + 0.113292i
\(550\) 0 0
\(551\) −5.55797 9.62669i −0.236778 0.410111i
\(552\) 0 0
\(553\) −2.05737 + 3.56346i −0.0874881 + 0.151534i
\(554\) 0 0
\(555\) −28.0068 23.3270i −1.18882 0.990177i
\(556\) 0 0
\(557\) 21.9632i 0.930609i 0.885151 + 0.465305i \(0.154055\pi\)
−0.885151 + 0.465305i \(0.845945\pi\)
\(558\) 0 0
\(559\) 0.549669 0.0232485
\(560\) 0 0
\(561\) −4.90644 13.3289i −0.207150 0.562747i
\(562\) 0 0
\(563\) −23.8394 13.7637i −1.00471 0.580069i −0.0950710 0.995470i \(-0.530308\pi\)
−0.909638 + 0.415401i \(0.863641\pi\)
\(564\) 0 0
\(565\) −25.9786 + 14.9988i −1.09293 + 0.631002i
\(566\) 0 0
\(567\) −0.550212 + 3.41057i −0.0231067 + 0.143231i
\(568\) 0 0
\(569\) 8.83572 + 15.3039i 0.370413 + 0.641574i 0.989629 0.143647i \(-0.0458829\pi\)
−0.619216 + 0.785221i \(0.712550\pi\)
\(570\) 0 0
\(571\) 3.92630 + 2.26685i 0.164311 + 0.0948648i 0.579900 0.814687i \(-0.303091\pi\)
−0.415590 + 0.909552i \(0.636425\pi\)
\(572\) 0 0
\(573\) −28.2744 + 10.4080i −1.18118 + 0.434799i
\(574\) 0 0
\(575\) 50.1188 2.09010
\(576\) 0 0
\(577\) 23.3909 0.973776 0.486888 0.873464i \(-0.338132\pi\)
0.486888 + 0.873464i \(0.338132\pi\)
\(578\) 0 0
\(579\) −3.77195 3.14168i −0.156757 0.130564i
\(580\) 0 0
\(581\) 2.10750 + 1.21676i 0.0874337 + 0.0504799i
\(582\) 0 0
\(583\) −7.66645 13.2787i −0.317512 0.549947i
\(584\) 0 0
\(585\) 0.912853 + 4.96504i 0.0377418 + 0.205279i
\(586\) 0 0
\(587\) 7.18259 4.14687i 0.296457 0.171160i −0.344393 0.938826i \(-0.611915\pi\)
0.640850 + 0.767666i \(0.278582\pi\)
\(588\) 0 0
\(589\) −4.84453 2.79699i −0.199615 0.115248i
\(590\) 0 0
\(591\) 21.5044 + 3.71100i 0.884572 + 0.152650i
\(592\) 0 0
\(593\) −43.5169 −1.78702 −0.893512 0.449039i \(-0.851766\pi\)
−0.893512 + 0.449039i \(0.851766\pi\)
\(594\) 0 0
\(595\) 5.74432i 0.235494i
\(596\) 0 0
\(597\) 5.08779 29.4825i 0.208229 1.20664i
\(598\) 0 0
\(599\) −0.527649 + 0.913915i −0.0215592 + 0.0373416i −0.876604 0.481213i \(-0.840196\pi\)
0.855045 + 0.518555i \(0.173530\pi\)
\(600\) 0 0
\(601\) 17.9922 + 31.1633i 0.733915 + 1.27118i 0.955198 + 0.295969i \(0.0956424\pi\)
−0.221282 + 0.975210i \(0.571024\pi\)
\(602\) 0 0
\(603\) 19.9427 + 23.4178i 0.812131 + 0.953648i
\(604\) 0 0
\(605\) −22.1138 + 12.7674i −0.899056 + 0.519070i
\(606\) 0 0
\(607\) 9.81512 17.0003i 0.398383 0.690020i −0.595143 0.803620i \(-0.702905\pi\)
0.993527 + 0.113599i \(0.0362381\pi\)
\(608\) 0 0
\(609\) 1.00124 1.20210i 0.0405721 0.0487116i
\(610\) 0 0
\(611\) 3.01039i 0.121787i
\(612\) 0 0
\(613\) 0.0630655i 0.00254719i −0.999999 0.00127360i \(-0.999595\pi\)
0.999999 0.00127360i \(-0.000405399\pi\)
\(614\) 0 0
\(615\) 20.8356 + 56.6024i 0.840174 + 2.28243i
\(616\) 0 0
\(617\) 15.0926 26.1412i 0.607606 1.05240i −0.384028 0.923322i \(-0.625463\pi\)
0.991634 0.129083i \(-0.0412034\pi\)
\(618\) 0 0
\(619\) 38.2663 22.0930i 1.53805 0.887994i 0.539099 0.842243i \(-0.318765\pi\)
0.998953 0.0457517i \(-0.0145683\pi\)
\(620\) 0 0
\(621\) −15.7555 26.6127i −0.632245 1.06793i
\(622\) 0 0
\(623\) 1.45250 + 2.51580i 0.0581932 + 0.100794i
\(624\) 0 0
\(625\) −1.90220 + 3.29471i −0.0760881 + 0.131788i
\(626\) 0 0
\(627\) −15.4140 + 5.67398i −0.615576 + 0.226597i
\(628\) 0 0
\(629\) 23.4653i 0.935621i
\(630\) 0 0
\(631\) −19.6743 −0.783221 −0.391610 0.920131i \(-0.628082\pi\)
−0.391610 + 0.920131i \(0.628082\pi\)
\(632\) 0 0
\(633\) 19.4802 23.3883i 0.774269 0.929601i
\(634\) 0 0
\(635\) −66.6607 38.4866i −2.64535 1.52729i
\(636\) 0 0
\(637\) −2.72598 + 1.57384i −0.108007 + 0.0623580i
\(638\) 0 0
\(639\) −10.5652 3.75839i −0.417952 0.148679i
\(640\) 0 0
\(641\) −0.994371 1.72230i −0.0392753 0.0680268i 0.845720 0.533628i \(-0.179172\pi\)
−0.884995 + 0.465601i \(0.845838\pi\)
\(642\) 0 0
\(643\) 12.9370 + 7.46917i 0.510185 + 0.294555i 0.732910 0.680326i \(-0.238162\pi\)
−0.222725 + 0.974881i \(0.571495\pi\)
\(644\) 0 0
\(645\) 1.29124 7.48246i 0.0508427 0.294621i
\(646\) 0 0
\(647\) 8.81283 0.346468 0.173234 0.984881i \(-0.444578\pi\)
0.173234 + 0.984881i \(0.444578\pi\)
\(648\) 0 0
\(649\) −1.39937 −0.0549302
\(650\) 0 0
\(651\) 0.133884 0.775827i 0.00524734 0.0304071i
\(652\) 0 0
\(653\) 18.1802 + 10.4964i 0.711447 + 0.410754i 0.811597 0.584218i \(-0.198599\pi\)
−0.100150 + 0.994972i \(0.531932\pi\)
\(654\) 0 0
\(655\) −11.6126 20.1136i −0.453742 0.785904i
\(656\) 0 0
\(657\) 7.58276 + 2.69744i 0.295832 + 0.105237i
\(658\) 0 0
\(659\) −40.6209 + 23.4525i −1.58237 + 0.913580i −0.587853 + 0.808968i \(0.700027\pi\)
−0.994513 + 0.104612i \(0.966640\pi\)
\(660\) 0 0
\(661\) −0.736985 0.425498i −0.0286654 0.0165500i 0.485599 0.874182i \(-0.338602\pi\)
−0.514264 + 0.857632i \(0.671935\pi\)
\(662\) 0 0
\(663\) −2.07995 + 2.49723i −0.0807787 + 0.0969843i
\(664\) 0 0
\(665\) −6.64293 −0.257602
\(666\) 0 0
\(667\) 14.0053i 0.542287i
\(668\) 0 0
\(669\) 40.0300 14.7352i 1.54765 0.569698i
\(670\) 0 0
\(671\) 4.91150 8.50697i 0.189606 0.328408i
\(672\) 0 0
\(673\) −22.4873 38.9491i −0.866820 1.50138i −0.865229 0.501378i \(-0.832827\pi\)
−0.00159139 0.999999i \(-0.500507\pi\)
\(674\) 0 0
\(675\) 43.7525 0.478635i 1.68403 0.0184227i
\(676\) 0 0
\(677\) −7.29713 + 4.21300i −0.280451 + 0.161919i −0.633628 0.773638i \(-0.718435\pi\)
0.353176 + 0.935557i \(0.385102\pi\)
\(678\) 0 0
\(679\) 1.14584 1.98466i 0.0439733 0.0761641i
\(680\) 0 0
\(681\) −11.7395 31.8916i −0.449857 1.22209i
\(682\) 0 0
\(683\) 23.3602i 0.893853i −0.894571 0.446926i \(-0.852519\pi\)
0.894571 0.446926i \(-0.147481\pi\)
\(684\) 0 0
\(685\) 3.54396i 0.135408i
\(686\) 0 0
\(687\) 27.3187 32.7993i 1.04227 1.25137i
\(688\) 0 0
\(689\) −1.75423 + 3.03841i −0.0668308 + 0.115754i
\(690\) 0 0
\(691\) −25.9304 + 14.9709i −0.986439 + 0.569521i −0.904208 0.427092i \(-0.859538\pi\)
−0.0822311 + 0.996613i \(0.526205\pi\)
\(692\) 0 0
\(693\) −1.49879 1.75996i −0.0569343 0.0668553i
\(694\) 0 0
\(695\) 10.9596 + 18.9826i 0.415722 + 0.720052i
\(696\) 0 0
\(697\) −19.4150 + 33.6278i −0.735396 + 1.27374i
\(698\) 0 0
\(699\) 6.16255 35.7105i 0.233089 1.35070i
\(700\) 0 0
\(701\) 0.718775i 0.0271478i −0.999908 0.0135739i \(-0.995679\pi\)
0.999908 0.0135739i \(-0.00432083\pi\)
\(702\) 0 0
\(703\) −27.1360 −1.02346
\(704\) 0 0
\(705\) 40.9794 + 7.07181i 1.54337 + 0.266340i
\(706\) 0 0
\(707\) 1.84735 + 1.06657i 0.0694767 + 0.0401124i
\(708\) 0 0
\(709\) 10.9918 6.34613i 0.412807 0.238334i −0.279188 0.960236i \(-0.590065\pi\)
0.691995 + 0.721902i \(0.256732\pi\)
\(710\) 0 0
\(711\) −5.81512 31.6286i −0.218084 1.18616i
\(712\) 0 0
\(713\) 3.52400 + 6.10375i 0.131975 + 0.228587i
\(714\) 0 0
\(715\) −2.92544 1.68900i −0.109405 0.0631652i
\(716\) 0 0
\(717\) 13.6970 + 11.4083i 0.511523 + 0.426050i
\(718\) 0 0
\(719\) −7.74226 −0.288738 −0.144369 0.989524i \(-0.546115\pi\)
−0.144369 + 0.989524i \(0.546115\pi\)
\(720\) 0 0
\(721\) 4.71662 0.175656
\(722\) 0 0
\(723\) −33.2819 + 12.2513i −1.23777 + 0.455629i
\(724\) 0 0
\(725\) −17.1599 9.90730i −0.637304 0.367948i
\(726\) 0 0
\(727\) −9.91355 17.1708i −0.367673 0.636828i 0.621528 0.783392i \(-0.286512\pi\)
−0.989201 + 0.146563i \(0.953179\pi\)
\(728\) 0 0
\(729\) −14.0083 23.0818i −0.518826 0.854880i
\(730\) 0 0
\(731\) 4.23337 2.44414i 0.156577 0.0903997i
\(732\) 0 0
\(733\) 32.7535 + 18.9102i 1.20978 + 0.698466i 0.962711 0.270532i \(-0.0871997\pi\)
0.247068 + 0.968998i \(0.420533\pi\)
\(734\) 0 0
\(735\) 15.0205 + 40.8050i 0.554040 + 1.50511i
\(736\) 0 0
\(737\) −20.5821 −0.758152
\(738\) 0 0
\(739\) 6.61431i 0.243311i −0.992572 0.121656i \(-0.961180\pi\)
0.992572 0.121656i \(-0.0388204\pi\)
\(740\) 0 0
\(741\) 2.88788 + 2.40533i 0.106089 + 0.0883620i
\(742\) 0 0
\(743\) 3.30245 5.72000i 0.121155 0.209847i −0.799068 0.601240i \(-0.794674\pi\)
0.920223 + 0.391394i \(0.128007\pi\)
\(744\) 0 0
\(745\) −13.6161 23.5838i −0.498856 0.864044i
\(746\) 0 0
\(747\) −18.7057 + 3.43917i −0.684407 + 0.125833i
\(748\) 0 0
\(749\) −2.19990 + 1.27012i −0.0803828 + 0.0464090i
\(750\) 0 0
\(751\) −12.8675 + 22.2871i −0.469540 + 0.813268i −0.999394 0.0348217i \(-0.988914\pi\)
0.529853 + 0.848089i \(0.322247\pi\)
\(752\) 0 0
\(753\) 47.9595 + 8.27636i 1.74774 + 0.301607i
\(754\) 0 0
\(755\) 3.61118i 0.131424i
\(756\) 0 0
\(757\) 48.0424i 1.74613i −0.487602 0.873066i \(-0.662128\pi\)
0.487602 0.873066i \(-0.337872\pi\)
\(758\) 0 0
\(759\) 20.3931 + 3.51922i 0.740221 + 0.127740i
\(760\) 0 0
\(761\) −1.20688 + 2.09038i −0.0437493 + 0.0757761i −0.887071 0.461633i \(-0.847264\pi\)
0.843322 + 0.537409i \(0.180597\pi\)
\(762\) 0 0
\(763\) −2.33218 + 1.34648i −0.0844305 + 0.0487459i
\(764\) 0 0
\(765\) 29.1078 + 34.1800i 1.05240 + 1.23578i
\(766\) 0 0
\(767\) 0.160101 + 0.277304i 0.00578093 + 0.0100129i
\(768\) 0 0
\(769\) 16.8464 29.1788i 0.607496 1.05221i −0.384156 0.923268i \(-0.625507\pi\)
0.991652 0.128945i \(-0.0411592\pi\)
\(770\) 0 0
\(771\) 14.7377 + 12.2751i 0.530765 + 0.442076i
\(772\) 0 0
\(773\) 18.8545i 0.678149i 0.940759 + 0.339075i \(0.110114\pi\)
−0.940759 + 0.339075i \(0.889886\pi\)
\(774\) 0 0
\(775\) −9.97148 −0.358186
\(776\) 0 0
\(777\) −1.31929 3.58401i −0.0473294 0.128576i
\(778\) 0 0
\(779\) 38.8884 + 22.4522i 1.39332 + 0.804434i
\(780\) 0 0
\(781\) 6.49833 3.75181i 0.232529 0.134250i
\(782\) 0 0
\(783\) 0.133751 + 12.2263i 0.00477986 + 0.436931i
\(784\) 0 0
\(785\) 32.2202 + 55.8070i 1.14999 + 1.99184i
\(786\) 0 0
\(787\) 14.8124 + 8.55193i 0.528004 + 0.304843i 0.740203 0.672383i \(-0.234729\pi\)
−0.212199 + 0.977226i \(0.568063\pi\)
\(788\) 0 0
\(789\) −41.4873 + 15.2717i −1.47699 + 0.543687i
\(790\) 0 0
\(791\) −3.14313 −0.111757
\(792\) 0 0
\(793\) −2.24769 −0.0798178
\(794\) 0 0
\(795\) 37.2400 + 31.0173i 1.32077 + 1.10007i
\(796\) 0 0
\(797\) 3.11800 + 1.80018i 0.110445 + 0.0637656i 0.554205 0.832380i \(-0.313022\pi\)
−0.443760 + 0.896146i \(0.646356\pi\)
\(798\) 0 0
\(799\) 13.3859 + 23.1851i 0.473559 + 0.820228i
\(800\) 0 0
\(801\) −21.3909 7.60945i −0.755810 0.268867i
\(802\) 0 0
\(803\) −4.66393 + 2.69272i −0.164586 + 0.0950240i
\(804\) 0 0
\(805\) 7.24829 + 4.18480i 0.255469 + 0.147495i
\(806\) 0 0
\(807\) −31.4052 5.41958i −1.10551 0.190778i
\(808\) 0 0
\(809\) 13.5918 0.477864 0.238932 0.971036i \(-0.423203\pi\)
0.238932 + 0.971036i \(0.423203\pi\)
\(810\) 0 0
\(811\) 10.0627i 0.353349i −0.984269 0.176674i \(-0.943466\pi\)
0.984269 0.176674i \(-0.0565339\pi\)
\(812\) 0 0
\(813\) −6.60179 + 38.2558i −0.231535 + 1.34169i
\(814\) 0 0
\(815\) −32.7606 + 56.7430i −1.14755 + 1.98762i
\(816\) 0 0
\(817\) −2.82649 4.89562i −0.0988862 0.171276i
\(818\) 0 0
\(819\) −0.177283 + 0.498361i −0.00619478 + 0.0174141i
\(820\) 0 0
\(821\) −33.4098 + 19.2891i −1.16601 + 0.673196i −0.952737 0.303797i \(-0.901746\pi\)
−0.213273 + 0.976993i \(0.568412\pi\)
\(822\) 0 0
\(823\) 16.1120 27.9068i 0.561628 0.972768i −0.435727 0.900079i \(-0.643509\pi\)
0.997355 0.0726892i \(-0.0231581\pi\)
\(824\) 0 0
\(825\) −18.7379 + 22.4971i −0.652371 + 0.783248i
\(826\) 0 0
\(827\) 27.7190i 0.963886i 0.876203 + 0.481943i \(0.160069\pi\)
−0.876203 + 0.481943i \(0.839931\pi\)
\(828\) 0 0
\(829\) 10.3137i 0.358208i 0.983830 + 0.179104i \(0.0573199\pi\)
−0.983830 + 0.179104i \(0.942680\pi\)
\(830\) 0 0
\(831\) −13.9850 37.9919i −0.485135 1.31793i
\(832\) 0 0
\(833\) −13.9964 + 24.2425i −0.484946 + 0.839951i
\(834\) 0 0
\(835\) 6.60139 3.81131i 0.228451 0.131896i
\(836\) 0 0
\(837\) 3.13466 + 5.29477i 0.108350 + 0.183014i
\(838\) 0 0
\(839\) 19.1961 + 33.2487i 0.662724 + 1.14787i 0.979897 + 0.199504i \(0.0639332\pi\)
−0.317173 + 0.948368i \(0.602733\pi\)
\(840\) 0 0
\(841\) −11.7315 + 20.3195i −0.404534 + 0.700673i
\(842\) 0 0
\(843\) −17.2121 + 6.33588i −0.592818 + 0.218219i
\(844\) 0 0
\(845\) 46.8516i 1.61174i
\(846\) 0 0
\(847\) −2.67553 −0.0919325
\(848\) 0 0
\(849\) −9.84342 + 11.8182i −0.337825 + 0.405599i
\(850\) 0 0
\(851\) 29.6089 + 17.0947i 1.01498 + 0.585999i
\(852\) 0 0
\(853\) 24.4212 14.0996i 0.836166 0.482761i −0.0197931 0.999804i \(-0.506301\pi\)
0.855959 + 0.517043i \(0.172967\pi\)
\(854\) 0 0
\(855\) 39.5269 33.6613i 1.35179 1.15119i
\(856\) 0 0
\(857\) 15.7011 + 27.1951i 0.536339 + 0.928966i 0.999097 + 0.0424814i \(0.0135263\pi\)
−0.462759 + 0.886484i \(0.653140\pi\)
\(858\) 0 0
\(859\) −41.6368 24.0390i −1.42063 0.820201i −0.424278 0.905532i \(-0.639472\pi\)
−0.996353 + 0.0853309i \(0.972805\pi\)
\(860\) 0 0
\(861\) −1.07473 + 6.22778i −0.0366266 + 0.212242i
\(862\) 0 0
\(863\) −37.6968 −1.28321 −0.641607 0.767034i \(-0.721732\pi\)
−0.641607 + 0.767034i \(0.721732\pi\)
\(864\) 0 0
\(865\) −69.6783 −2.36913
\(866\) 0 0
\(867\) 0.0922398 0.534508i 0.00313263 0.0181528i
\(868\) 0 0
\(869\) 18.6358 + 10.7594i 0.632177 + 0.364988i
\(870\) 0 0
\(871\) 2.35479 + 4.07861i 0.0797890 + 0.138199i
\(872\) 0 0
\(873\) 3.23870 + 17.6154i 0.109614 + 0.596191i
\(874\) 0 0
\(875\) −4.16576 + 2.40510i −0.140828 + 0.0813072i
\(876\) 0 0
\(877\) −21.6823 12.5183i −0.732158 0.422711i 0.0870533 0.996204i \(-0.472255\pi\)
−0.819211 + 0.573492i \(0.805588\pi\)
\(878\) 0 0
\(879\) 12.5709 15.0928i 0.424006 0.509069i
\(880\) 0 0
\(881\) −21.0382 −0.708795 −0.354398 0.935095i \(-0.615314\pi\)
−0.354398 + 0.935095i \(0.615314\pi\)
\(882\) 0 0
\(883\) 55.5904i 1.87077i −0.353636 0.935383i \(-0.615055\pi\)
0.353636 0.935383i \(-0.384945\pi\)
\(884\) 0 0
\(885\) 4.15094 1.52798i 0.139532 0.0513626i
\(886\) 0 0
\(887\) −0.695385 + 1.20444i −0.0233487 + 0.0404412i −0.877464 0.479643i \(-0.840766\pi\)
0.854115 + 0.520084i \(0.174099\pi\)
\(888\) 0 0
\(889\) −4.03261 6.98468i −0.135249 0.234259i
\(890\) 0 0
\(891\) 17.8363 + 2.87744i 0.597538 + 0.0963980i
\(892\) 0 0
\(893\) 26.8120 15.4799i 0.897229 0.518015i
\(894\) 0 0
\(895\) −3.88527 + 6.72948i −0.129870 + 0.224942i
\(896\) 0 0
\(897\) −1.63578 4.44379i −0.0546171 0.148374i
\(898\) 0 0
\(899\) 2.78645i 0.0929332i
\(900\) 0 0
\(901\) 31.2011i 1.03946i
\(902\) 0 0
\(903\) 0.509175 0.611324i 0.0169443 0.0203436i
\(904\) 0 0
\(905\) 3.04608 5.27597i 0.101255 0.175379i
\(906\) 0 0
\(907\) 37.3197 21.5465i 1.23918 0.715440i 0.270252 0.962789i \(-0.412893\pi\)
0.968926 + 0.247349i \(0.0795595\pi\)
\(908\) 0 0
\(909\) −16.3967 + 3.01464i −0.543844 + 0.0999892i
\(910\) 0 0
\(911\) 3.96463 + 6.86694i 0.131354 + 0.227512i 0.924199 0.381912i \(-0.124734\pi\)
−0.792845 + 0.609424i \(0.791401\pi\)
\(912\) 0 0
\(913\) 6.36331 11.0216i 0.210595 0.364761i
\(914\) 0 0
\(915\) −5.28012 + 30.5970i −0.174555 + 1.01151i
\(916\) 0 0
\(917\) 2.43353i 0.0803622i
\(918\) 0 0
\(919\) −1.66862 −0.0550426 −0.0275213 0.999621i \(-0.508761\pi\)
−0.0275213 + 0.999621i \(0.508761\pi\)
\(920\) 0 0
\(921\) 1.07304 + 0.185174i 0.0353579 + 0.00610170i
\(922\) 0 0
\(923\) −1.48694 0.858486i −0.0489433 0.0282574i
\(924\) 0 0
\(925\) −41.8905 + 24.1855i −1.37735 + 0.795215i
\(926\) 0 0
\(927\) −28.0650 + 23.9002i −0.921775 + 0.784987i
\(928\) 0 0
\(929\) −23.3838 40.5020i −0.767199 1.32883i −0.939076 0.343709i \(-0.888317\pi\)
0.171878 0.985118i \(-0.445017\pi\)
\(930\) 0 0
\(931\) 28.0348 + 16.1859i 0.918804 + 0.530472i
\(932\) 0 0
\(933\) 25.6711 + 21.3816i 0.840435 + 0.700002i
\(934\) 0 0
\(935\) −30.0410 −0.982447
\(936\) 0 0
\(937\) −9.30185 −0.303878 −0.151939 0.988390i \(-0.548552\pi\)
−0.151939 + 0.988390i \(0.548552\pi\)
\(938\) 0 0
\(939\) 9.32861 3.43391i 0.304428 0.112061i
\(940\) 0 0
\(941\) −5.42009 3.12929i −0.176690 0.102012i 0.409047 0.912513i \(-0.365861\pi\)
−0.585736 + 0.810502i \(0.699195\pi\)
\(942\) 0 0
\(943\) −28.2881 48.9965i −0.921188 1.59555i
\(944\) 0 0
\(945\) 6.36755 + 3.58401i 0.207136 + 0.116588i
\(946\) 0 0
\(947\) 38.4243 22.1843i 1.24862 0.720893i 0.277789 0.960642i \(-0.410399\pi\)
0.970835 + 0.239749i \(0.0770652\pi\)
\(948\) 0 0
\(949\) 1.06720 + 0.616146i 0.0346426 + 0.0200009i
\(950\) 0 0
\(951\) −7.47452 20.3054i −0.242378 0.658448i
\(952\) 0 0
\(953\) 6.11599 0.198116 0.0990582 0.995082i \(-0.468417\pi\)
0.0990582 + 0.995082i \(0.468417\pi\)
\(954\) 0 0
\(955\) 63.7257i 2.06211i
\(956\) 0 0
\(957\) −6.28662 5.23616i −0.203218 0.169261i
\(958\) 0 0
\(959\) −0.185668 + 0.321586i −0.00599552 + 0.0103845i
\(960\) 0 0
\(961\) 14.7989 + 25.6324i 0.477383 + 0.826852i
\(962\) 0 0
\(963\) 6.65396 18.7049i 0.214421 0.602758i
\(964\) 0 0
\(965\) −8.99178 + 5.19141i −0.289456 + 0.167117i
\(966\) 0 0
\(967\) −16.9985 + 29.4423i −0.546635 + 0.946799i 0.451867 + 0.892085i \(0.350758\pi\)
−0.998502 + 0.0547141i \(0.982575\pi\)
\(968\) 0 0
\(969\) 32.9370 + 5.68392i 1.05809 + 0.182594i
\(970\) 0 0
\(971\) 42.4798i 1.36324i 0.731706 + 0.681621i \(0.238725\pi\)
−0.731706 + 0.681621i \(0.761275\pi\)
\(972\) 0 0
\(973\) 2.29669i 0.0736286i
\(974\) 0 0
\(975\) 6.60189 + 1.13929i 0.211430 + 0.0364863i
\(976\) 0 0
\(977\) 7.66569 13.2774i 0.245247 0.424781i −0.716954 0.697121i \(-0.754464\pi\)
0.962201 + 0.272340i \(0.0877975\pi\)
\(978\) 0 0
\(979\) 13.1569 7.59614i 0.420496 0.242774i
\(980\) 0 0
\(981\) 7.05404 19.8296i 0.225218 0.633110i
\(982\) 0 0
\(983\) 14.8653 + 25.7474i 0.474129 + 0.821216i 0.999561 0.0296198i \(-0.00942964\pi\)
−0.525432 + 0.850836i \(0.676096\pi\)
\(984\) 0 0
\(985\) 23.0779 39.9720i 0.735322 1.27361i
\(986\) 0 0
\(987\) 3.34806 + 2.78861i 0.106570 + 0.0887626i
\(988\) 0 0
\(989\) 7.12233i 0.226477i
\(990\) 0 0
\(991\) 49.5495 1.57399 0.786996 0.616958i \(-0.211635\pi\)
0.786996 + 0.616958i \(0.211635\pi\)
\(992\) 0 0
\(993\) 2.07276 + 5.63089i 0.0657771 + 0.178691i
\(994\) 0 0
\(995\) −54.8017 31.6398i −1.73733 1.00305i
\(996\) 0 0
\(997\) 34.4541 19.8921i 1.09117 0.629988i 0.157284 0.987553i \(-0.449726\pi\)
0.933888 + 0.357565i \(0.116393\pi\)
\(998\) 0 0
\(999\) 26.0111 + 14.6405i 0.822956 + 0.463205i
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.r.b.49.4 16
3.2 odd 2 864.2.r.b.145.1 16
4.3 odd 2 72.2.n.b.13.3 16
8.3 odd 2 72.2.n.b.13.8 yes 16
8.5 even 2 inner 288.2.r.b.49.5 16
9.2 odd 6 864.2.r.b.721.8 16
9.4 even 3 2592.2.d.j.1297.1 8
9.5 odd 6 2592.2.d.k.1297.8 8
9.7 even 3 inner 288.2.r.b.241.5 16
12.11 even 2 216.2.n.b.37.6 16
24.5 odd 2 864.2.r.b.145.8 16
24.11 even 2 216.2.n.b.37.1 16
36.7 odd 6 72.2.n.b.61.8 yes 16
36.11 even 6 216.2.n.b.181.1 16
36.23 even 6 648.2.d.k.325.6 8
36.31 odd 6 648.2.d.j.325.3 8
72.5 odd 6 2592.2.d.k.1297.1 8
72.11 even 6 216.2.n.b.181.6 16
72.13 even 6 2592.2.d.j.1297.8 8
72.29 odd 6 864.2.r.b.721.1 16
72.43 odd 6 72.2.n.b.61.3 yes 16
72.59 even 6 648.2.d.k.325.5 8
72.61 even 6 inner 288.2.r.b.241.4 16
72.67 odd 6 648.2.d.j.325.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.2.n.b.13.3 16 4.3 odd 2
72.2.n.b.13.8 yes 16 8.3 odd 2
72.2.n.b.61.3 yes 16 72.43 odd 6
72.2.n.b.61.8 yes 16 36.7 odd 6
216.2.n.b.37.1 16 24.11 even 2
216.2.n.b.37.6 16 12.11 even 2
216.2.n.b.181.1 16 36.11 even 6
216.2.n.b.181.6 16 72.11 even 6
288.2.r.b.49.4 16 1.1 even 1 trivial
288.2.r.b.49.5 16 8.5 even 2 inner
288.2.r.b.241.4 16 72.61 even 6 inner
288.2.r.b.241.5 16 9.7 even 3 inner
648.2.d.j.325.3 8 36.31 odd 6
648.2.d.j.325.4 8 72.67 odd 6
648.2.d.k.325.5 8 72.59 even 6
648.2.d.k.325.6 8 36.23 even 6
864.2.r.b.145.1 16 3.2 odd 2
864.2.r.b.145.8 16 24.5 odd 2
864.2.r.b.721.1 16 72.29 odd 6
864.2.r.b.721.8 16 9.2 odd 6
2592.2.d.j.1297.1 8 9.4 even 3
2592.2.d.j.1297.8 8 72.13 even 6
2592.2.d.k.1297.1 8 72.5 odd 6
2592.2.d.k.1297.8 8 9.5 odd 6