Properties

Label 864.2.bf.a.49.8
Level $864$
Weight $2$
Character 864.49
Analytic conductor $6.899$
Analytic rank $0$
Dimension $204$
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] = [864,2,Mod(49,864)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(864, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 9, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("864.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.bf (of order \(18\), degree \(6\), 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: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(204\)
Relative dimension: \(34\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 216)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 49.8
Character \(\chi\) \(=\) 864.49
Dual form 864.2.bf.a.529.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.34903 + 1.08633i) q^{3} +(1.01754 + 2.79566i) q^{5} +(-0.349397 - 1.98153i) q^{7} +(0.639780 - 2.93099i) q^{9} +O(q^{10})\) \(q+(-1.34903 + 1.08633i) q^{3} +(1.01754 + 2.79566i) q^{5} +(-0.349397 - 1.98153i) q^{7} +(0.639780 - 2.93099i) q^{9} +(1.51659 - 4.16680i) q^{11} +(0.650169 - 0.774841i) q^{13} +(-4.40969 - 2.66606i) q^{15} +(3.27371 - 5.67024i) q^{17} +(0.916008 - 0.528857i) q^{19} +(2.62394 + 2.29359i) q^{21} +(0.627609 - 3.55935i) q^{23} +(-2.95010 + 2.47543i) q^{25} +(2.32093 + 4.64901i) q^{27} +(1.96383 + 2.34041i) q^{29} +(-1.42354 + 8.07327i) q^{31} +(2.48058 + 7.26866i) q^{33} +(5.18415 - 2.99307i) q^{35} +(3.07033 + 1.77266i) q^{37} +(-0.0353672 + 1.75158i) q^{39} +(-7.68484 - 6.44835i) q^{41} +(1.32782 - 3.64816i) q^{43} +(8.84504 - 1.19378i) q^{45} +(1.19526 + 6.77867i) q^{47} +(2.77348 - 1.00946i) q^{49} +(1.74339 + 11.2057i) q^{51} -7.11001i q^{53} +13.1921 q^{55} +(-0.661212 + 1.70853i) q^{57} +(4.18952 + 11.5106i) q^{59} +(-6.57705 + 1.15971i) q^{61} +(-6.03136 - 0.243665i) q^{63} +(2.82776 + 1.02922i) q^{65} +(0.910019 - 1.08452i) q^{67} +(3.01995 + 5.48346i) q^{69} +(6.98248 - 12.0940i) q^{71} +(5.31517 + 9.20614i) q^{73} +(1.29066 - 6.54422i) q^{75} +(-8.78651 - 1.54930i) q^{77} +(9.12725 - 7.65867i) q^{79} +(-8.18136 - 3.75037i) q^{81} +(-4.79613 - 5.71581i) q^{83} +(19.1832 + 3.38251i) q^{85} +(-5.19173 - 1.02392i) q^{87} +(-3.19380 - 5.53182i) q^{89} +(-1.76254 - 1.01760i) q^{91} +(-6.84983 - 12.4375i) q^{93} +(2.41058 + 2.02271i) q^{95} +(7.73985 + 2.81708i) q^{97} +(-11.2425 - 7.11094i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 204 q + 12 q^{7} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73} + 12 q^{79} - 12 q^{81} + 48 q^{87} - 6 q^{89} + 42 q^{95} - 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{9}\right)\) \(1\)

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
\(3\) −1.34903 + 1.08633i −0.778865 + 0.627192i
\(4\) 0 0
\(5\) 1.01754 + 2.79566i 0.455056 + 1.25026i 0.929124 + 0.369768i \(0.120563\pi\)
−0.474068 + 0.880488i \(0.657215\pi\)
\(6\) 0 0
\(7\) −0.349397 1.98153i −0.132060 0.748947i −0.976862 0.213869i \(-0.931393\pi\)
0.844803 0.535078i \(-0.179718\pi\)
\(8\) 0 0
\(9\) 0.639780 2.93099i 0.213260 0.976995i
\(10\) 0 0
\(11\) 1.51659 4.16680i 0.457269 1.25634i −0.470241 0.882538i \(-0.655833\pi\)
0.927510 0.373798i \(-0.121945\pi\)
\(12\) 0 0
\(13\) 0.650169 0.774841i 0.180324 0.214902i −0.668309 0.743884i \(-0.732982\pi\)
0.848633 + 0.528982i \(0.177426\pi\)
\(14\) 0 0
\(15\) −4.40969 2.66606i −1.13858 0.688373i
\(16\) 0 0
\(17\) 3.27371 5.67024i 0.793992 1.37523i −0.129486 0.991581i \(-0.541333\pi\)
0.923477 0.383653i \(-0.125334\pi\)
\(18\) 0 0
\(19\) 0.916008 0.528857i 0.210147 0.121328i −0.391233 0.920292i \(-0.627951\pi\)
0.601380 + 0.798963i \(0.294618\pi\)
\(20\) 0 0
\(21\) 2.62394 + 2.29359i 0.572590 + 0.500501i
\(22\) 0 0
\(23\) 0.627609 3.55935i 0.130865 0.742175i −0.846785 0.531936i \(-0.821465\pi\)
0.977650 0.210239i \(-0.0674242\pi\)
\(24\) 0 0
\(25\) −2.95010 + 2.47543i −0.590021 + 0.495086i
\(26\) 0 0
\(27\) 2.32093 + 4.64901i 0.446663 + 0.894702i
\(28\) 0 0
\(29\) 1.96383 + 2.34041i 0.364675 + 0.434603i 0.916915 0.399082i \(-0.130671\pi\)
−0.552240 + 0.833685i \(0.686227\pi\)
\(30\) 0 0
\(31\) −1.42354 + 8.07327i −0.255675 + 1.45000i 0.538661 + 0.842523i \(0.318930\pi\)
−0.794335 + 0.607480i \(0.792181\pi\)
\(32\) 0 0
\(33\) 2.48058 + 7.26866i 0.431814 + 1.26531i
\(34\) 0 0
\(35\) 5.18415 2.99307i 0.876281 0.505921i
\(36\) 0 0
\(37\) 3.07033 + 1.77266i 0.504759 + 0.291423i 0.730677 0.682724i \(-0.239205\pi\)
−0.225918 + 0.974146i \(0.572538\pi\)
\(38\) 0 0
\(39\) −0.0353672 + 1.75158i −0.00566329 + 0.280478i
\(40\) 0 0
\(41\) −7.68484 6.44835i −1.20017 1.00706i −0.999625 0.0273783i \(-0.991284\pi\)
−0.200545 0.979684i \(-0.564271\pi\)
\(42\) 0 0
\(43\) 1.32782 3.64816i 0.202491 0.556339i −0.796331 0.604861i \(-0.793229\pi\)
0.998822 + 0.0485216i \(0.0154510\pi\)
\(44\) 0 0
\(45\) 8.84504 1.19378i 1.31854 0.177958i
\(46\) 0 0
\(47\) 1.19526 + 6.77867i 0.174347 + 0.988771i 0.938895 + 0.344204i \(0.111851\pi\)
−0.764548 + 0.644567i \(0.777038\pi\)
\(48\) 0 0
\(49\) 2.77348 1.00946i 0.396211 0.144209i
\(50\) 0 0
\(51\) 1.74339 + 11.2057i 0.244124 + 1.56911i
\(52\) 0 0
\(53\) 7.11001i 0.976635i −0.872666 0.488317i \(-0.837611\pi\)
0.872666 0.488317i \(-0.162389\pi\)
\(54\) 0 0
\(55\) 13.1921 1.77883
\(56\) 0 0
\(57\) −0.661212 + 1.70853i −0.0875797 + 0.226301i
\(58\) 0 0
\(59\) 4.18952 + 11.5106i 0.545429 + 1.49855i 0.839818 + 0.542868i \(0.182662\pi\)
−0.294389 + 0.955686i \(0.595116\pi\)
\(60\) 0 0
\(61\) −6.57705 + 1.15971i −0.842105 + 0.148486i −0.578029 0.816016i \(-0.696178\pi\)
−0.264076 + 0.964502i \(0.585067\pi\)
\(62\) 0 0
\(63\) −6.03136 0.243665i −0.759881 0.0306989i
\(64\) 0 0
\(65\) 2.82776 + 1.02922i 0.350741 + 0.127659i
\(66\) 0 0
\(67\) 0.910019 1.08452i 0.111177 0.132495i −0.707586 0.706627i \(-0.750216\pi\)
0.818763 + 0.574132i \(0.194660\pi\)
\(68\) 0 0
\(69\) 3.01995 + 5.48346i 0.363560 + 0.660132i
\(70\) 0 0
\(71\) 6.98248 12.0940i 0.828668 1.43529i −0.0704159 0.997518i \(-0.522433\pi\)
0.899084 0.437777i \(-0.144234\pi\)
\(72\) 0 0
\(73\) 5.31517 + 9.20614i 0.622093 + 1.07750i 0.989095 + 0.147277i \(0.0470508\pi\)
−0.367002 + 0.930220i \(0.619616\pi\)
\(74\) 0 0
\(75\) 1.29066 6.54422i 0.149032 0.755661i
\(76\) 0 0
\(77\) −8.78651 1.54930i −1.00132 0.176559i
\(78\) 0 0
\(79\) 9.12725 7.65867i 1.02690 0.861668i 0.0364172 0.999337i \(-0.488405\pi\)
0.990478 + 0.137669i \(0.0439610\pi\)
\(80\) 0 0
\(81\) −8.18136 3.75037i −0.909040 0.416708i
\(82\) 0 0
\(83\) −4.79613 5.71581i −0.526444 0.627392i 0.435648 0.900117i \(-0.356519\pi\)
−0.962092 + 0.272726i \(0.912075\pi\)
\(84\) 0 0
\(85\) 19.1832 + 3.38251i 2.08071 + 0.366885i
\(86\) 0 0
\(87\) −5.19173 1.02392i −0.556612 0.109775i
\(88\) 0 0
\(89\) −3.19380 5.53182i −0.338542 0.586371i 0.645617 0.763661i \(-0.276600\pi\)
−0.984159 + 0.177290i \(0.943267\pi\)
\(90\) 0 0
\(91\) −1.76254 1.01760i −0.184764 0.106674i
\(92\) 0 0
\(93\) −6.84983 12.4375i −0.710294 1.28971i
\(94\) 0 0
\(95\) 2.41058 + 2.02271i 0.247320 + 0.207526i
\(96\) 0 0
\(97\) 7.73985 + 2.81708i 0.785863 + 0.286031i 0.703615 0.710581i \(-0.251568\pi\)
0.0822478 + 0.996612i \(0.473790\pi\)
\(98\) 0 0
\(99\) −11.2425 7.11094i −1.12992 0.714676i
\(100\) 0 0
\(101\) −14.4452 + 2.54709i −1.43736 + 0.253445i −0.837401 0.546589i \(-0.815926\pi\)
−0.599955 + 0.800034i \(0.704815\pi\)
\(102\) 0 0
\(103\) 2.22120 0.808450i 0.218861 0.0796589i −0.230263 0.973129i \(-0.573958\pi\)
0.449124 + 0.893470i \(0.351736\pi\)
\(104\) 0 0
\(105\) −3.74213 + 9.66944i −0.365194 + 0.943640i
\(106\) 0 0
\(107\) 8.59548i 0.830956i 0.909603 + 0.415478i \(0.136386\pi\)
−0.909603 + 0.415478i \(0.863614\pi\)
\(108\) 0 0
\(109\) 8.57665i 0.821494i −0.911749 0.410747i \(-0.865268\pi\)
0.911749 0.410747i \(-0.134732\pi\)
\(110\) 0 0
\(111\) −6.06766 + 0.944016i −0.575917 + 0.0896020i
\(112\) 0 0
\(113\) 6.60462 2.40389i 0.621310 0.226139i −0.0121343 0.999926i \(-0.503863\pi\)
0.633445 + 0.773788i \(0.281640\pi\)
\(114\) 0 0
\(115\) 10.5893 1.86718i 0.987460 0.174116i
\(116\) 0 0
\(117\) −1.85508 2.40136i −0.171503 0.222006i
\(118\) 0 0
\(119\) −12.3795 4.50579i −1.13483 0.413045i
\(120\) 0 0
\(121\) −6.63566 5.56798i −0.603242 0.506180i
\(122\) 0 0
\(123\) 17.3721 + 0.350771i 1.56639 + 0.0316279i
\(124\) 0 0
\(125\) 2.96017 + 1.70905i 0.264766 + 0.152862i
\(126\) 0 0
\(127\) 1.55918 + 2.70057i 0.138355 + 0.239637i 0.926874 0.375373i \(-0.122485\pi\)
−0.788519 + 0.615010i \(0.789152\pi\)
\(128\) 0 0
\(129\) 2.17183 + 6.36394i 0.191219 + 0.560314i
\(130\) 0 0
\(131\) −6.90861 1.21817i −0.603608 0.106432i −0.136511 0.990639i \(-0.543589\pi\)
−0.467097 + 0.884206i \(0.654700\pi\)
\(132\) 0 0
\(133\) −1.36800 1.63031i −0.118620 0.141366i
\(134\) 0 0
\(135\) −10.6354 + 11.2191i −0.915350 + 0.965583i
\(136\) 0 0
\(137\) 13.7097 11.5038i 1.17130 0.982839i 0.171305 0.985218i \(-0.445202\pi\)
0.999997 + 0.00237903i \(0.000757270\pi\)
\(138\) 0 0
\(139\) −1.43645 0.253285i −0.121838 0.0214834i 0.112397 0.993663i \(-0.464147\pi\)
−0.234235 + 0.972180i \(0.575258\pi\)
\(140\) 0 0
\(141\) −8.97632 7.84621i −0.755942 0.660770i
\(142\) 0 0
\(143\) −2.24257 3.88424i −0.187533 0.324816i
\(144\) 0 0
\(145\) −4.54470 + 7.87166i −0.377417 + 0.653706i
\(146\) 0 0
\(147\) −2.64490 + 4.37471i −0.218148 + 0.360820i
\(148\) 0 0
\(149\) −10.0991 + 12.0356i −0.827350 + 0.985998i 0.172649 + 0.984983i \(0.444767\pi\)
−0.999999 + 0.00101449i \(0.999677\pi\)
\(150\) 0 0
\(151\) −7.63579 2.77920i −0.621392 0.226168i 0.0120883 0.999927i \(-0.496152\pi\)
−0.633480 + 0.773759i \(0.718374\pi\)
\(152\) 0 0
\(153\) −14.5249 13.2229i −1.17427 1.06901i
\(154\) 0 0
\(155\) −24.0186 + 4.23513i −1.92922 + 0.340174i
\(156\) 0 0
\(157\) 3.71655 + 10.2111i 0.296613 + 0.814938i 0.995060 + 0.0992761i \(0.0316527\pi\)
−0.698447 + 0.715662i \(0.746125\pi\)
\(158\) 0 0
\(159\) 7.72380 + 9.59163i 0.612537 + 0.760666i
\(160\) 0 0
\(161\) −7.27222 −0.573131
\(162\) 0 0
\(163\) 13.5578i 1.06193i 0.847395 + 0.530963i \(0.178170\pi\)
−0.847395 + 0.530963i \(0.821830\pi\)
\(164\) 0 0
\(165\) −17.7966 + 14.3310i −1.38546 + 1.11567i
\(166\) 0 0
\(167\) 5.51744 2.00819i 0.426953 0.155398i −0.119601 0.992822i \(-0.538162\pi\)
0.546554 + 0.837424i \(0.315939\pi\)
\(168\) 0 0
\(169\) 2.07977 + 11.7949i 0.159982 + 0.907303i
\(170\) 0 0
\(171\) −0.964030 3.02316i −0.0737212 0.231187i
\(172\) 0 0
\(173\) 5.91383 16.2481i 0.449620 1.23532i −0.483369 0.875417i \(-0.660587\pi\)
0.932989 0.359905i \(-0.117191\pi\)
\(174\) 0 0
\(175\) 5.93589 + 4.98080i 0.448711 + 0.376513i
\(176\) 0 0
\(177\) −18.1561 10.9770i −1.36470 0.825081i
\(178\) 0 0
\(179\) −5.18882 2.99577i −0.387831 0.223914i 0.293389 0.955993i \(-0.405217\pi\)
−0.681220 + 0.732079i \(0.738550\pi\)
\(180\) 0 0
\(181\) −19.3375 + 11.1645i −1.43734 + 0.829850i −0.997664 0.0683064i \(-0.978240\pi\)
−0.439677 + 0.898156i \(0.644907\pi\)
\(182\) 0 0
\(183\) 7.61283 8.70933i 0.562757 0.643812i
\(184\) 0 0
\(185\) −1.83157 + 10.3873i −0.134659 + 0.763692i
\(186\) 0 0
\(187\) −18.6618 22.2403i −1.36469 1.62637i
\(188\) 0 0
\(189\) 8.40121 6.22333i 0.611098 0.452681i
\(190\) 0 0
\(191\) −7.79513 + 6.54089i −0.564036 + 0.473282i −0.879661 0.475602i \(-0.842230\pi\)
0.315625 + 0.948884i \(0.397786\pi\)
\(192\) 0 0
\(193\) 0.500646 2.83931i 0.0360373 0.204378i −0.961473 0.274900i \(-0.911355\pi\)
0.997510 + 0.0705220i \(0.0224665\pi\)
\(194\) 0 0
\(195\) −4.93282 + 1.68343i −0.353246 + 0.120553i
\(196\) 0 0
\(197\) 9.17911 5.29956i 0.653984 0.377578i −0.135997 0.990709i \(-0.543424\pi\)
0.789981 + 0.613131i \(0.210090\pi\)
\(198\) 0 0
\(199\) −11.6904 + 20.2483i −0.828708 + 1.43537i 0.0703434 + 0.997523i \(0.477590\pi\)
−0.899052 + 0.437842i \(0.855743\pi\)
\(200\) 0 0
\(201\) −0.0495023 + 2.45163i −0.00349162 + 0.172925i
\(202\) 0 0
\(203\) 3.95142 4.70912i 0.277335 0.330515i
\(204\) 0 0
\(205\) 10.2078 28.0456i 0.712942 1.95879i
\(206\) 0 0
\(207\) −10.0309 4.11671i −0.697193 0.286131i
\(208\) 0 0
\(209\) −0.814433 4.61888i −0.0563355 0.319495i
\(210\) 0 0
\(211\) 0.0791638 + 0.217501i 0.00544986 + 0.0149734i 0.942388 0.334523i \(-0.108575\pi\)
−0.936938 + 0.349496i \(0.886353\pi\)
\(212\) 0 0
\(213\) 3.71847 + 23.9005i 0.254786 + 1.63763i
\(214\) 0 0
\(215\) 11.5501 0.787711
\(216\) 0 0
\(217\) 16.4948 1.11974
\(218\) 0 0
\(219\) −17.1712 6.64537i −1.16032 0.449052i
\(220\) 0 0
\(221\) −2.26507 6.22322i −0.152365 0.418619i
\(222\) 0 0
\(223\) 1.23427 + 6.99987i 0.0826526 + 0.468746i 0.997838 + 0.0657141i \(0.0209325\pi\)
−0.915186 + 0.403032i \(0.867956\pi\)
\(224\) 0 0
\(225\) 5.36803 + 10.2304i 0.357869 + 0.682030i
\(226\) 0 0
\(227\) 8.64915 23.7633i 0.574064 1.57723i −0.223957 0.974599i \(-0.571898\pi\)
0.798021 0.602629i \(-0.205880\pi\)
\(228\) 0 0
\(229\) 3.59262 4.28151i 0.237407 0.282930i −0.634166 0.773197i \(-0.718656\pi\)
0.871572 + 0.490267i \(0.163101\pi\)
\(230\) 0 0
\(231\) 13.5363 7.45498i 0.890626 0.490502i
\(232\) 0 0
\(233\) −6.23001 + 10.7907i −0.408141 + 0.706921i −0.994681 0.102999i \(-0.967156\pi\)
0.586540 + 0.809920i \(0.300490\pi\)
\(234\) 0 0
\(235\) −17.7346 + 10.2391i −1.15688 + 0.667925i
\(236\) 0 0
\(237\) −3.99313 + 20.2470i −0.259381 + 1.31518i
\(238\) 0 0
\(239\) 3.84127 21.7849i 0.248471 1.40915i −0.563820 0.825897i \(-0.690669\pi\)
0.812291 0.583252i \(-0.198220\pi\)
\(240\) 0 0
\(241\) −1.87526 + 1.57353i −0.120796 + 0.101360i −0.701185 0.712980i \(-0.747345\pi\)
0.580388 + 0.814340i \(0.302901\pi\)
\(242\) 0 0
\(243\) 15.1111 3.82827i 0.969375 0.245584i
\(244\) 0 0
\(245\) 5.64423 + 6.72653i 0.360597 + 0.429742i
\(246\) 0 0
\(247\) 0.185779 1.05361i 0.0118209 0.0670394i
\(248\) 0 0
\(249\) 12.6794 + 2.50064i 0.803524 + 0.158472i
\(250\) 0 0
\(251\) −0.113257 + 0.0653892i −0.00714874 + 0.00412733i −0.503570 0.863954i \(-0.667980\pi\)
0.496421 + 0.868082i \(0.334647\pi\)
\(252\) 0 0
\(253\) −13.8792 8.01319i −0.872581 0.503785i
\(254\) 0 0
\(255\) −29.5532 + 16.2761i −1.85070 + 1.01925i
\(256\) 0 0
\(257\) 17.8423 + 14.9715i 1.11297 + 0.933894i 0.998228 0.0595012i \(-0.0189510\pi\)
0.114743 + 0.993395i \(0.463395\pi\)
\(258\) 0 0
\(259\) 2.43980 6.70330i 0.151602 0.416523i
\(260\) 0 0
\(261\) 8.11612 4.25863i 0.502375 0.263602i
\(262\) 0 0
\(263\) −2.21695 12.5730i −0.136703 0.775282i −0.973659 0.228011i \(-0.926778\pi\)
0.836955 0.547271i \(-0.184333\pi\)
\(264\) 0 0
\(265\) 19.8771 7.23469i 1.22104 0.444424i
\(266\) 0 0
\(267\) 10.3179 + 3.99309i 0.631446 + 0.244373i
\(268\) 0 0
\(269\) 17.0793i 1.04134i −0.853757 0.520671i \(-0.825682\pi\)
0.853757 0.520671i \(-0.174318\pi\)
\(270\) 0 0
\(271\) 8.33081 0.506061 0.253030 0.967458i \(-0.418573\pi\)
0.253030 + 0.967458i \(0.418573\pi\)
\(272\) 0 0
\(273\) 3.48317 0.541916i 0.210811 0.0327983i
\(274\) 0 0
\(275\) 5.84052 + 16.0467i 0.352197 + 0.967652i
\(276\) 0 0
\(277\) −18.3112 + 3.22875i −1.10021 + 0.193997i −0.694137 0.719843i \(-0.744214\pi\)
−0.406075 + 0.913840i \(0.633103\pi\)
\(278\) 0 0
\(279\) 22.7519 + 9.33748i 1.36212 + 0.559020i
\(280\) 0 0
\(281\) −6.82507 2.48412i −0.407150 0.148190i 0.130323 0.991472i \(-0.458399\pi\)
−0.537473 + 0.843281i \(0.680621\pi\)
\(282\) 0 0
\(283\) −2.81006 + 3.34889i −0.167041 + 0.199071i −0.843071 0.537803i \(-0.819254\pi\)
0.676030 + 0.736874i \(0.263699\pi\)
\(284\) 0 0
\(285\) −5.44928 0.110030i −0.322787 0.00651759i
\(286\) 0 0
\(287\) −10.0925 + 17.4807i −0.595742 + 1.03186i
\(288\) 0 0
\(289\) −12.9344 22.4030i −0.760846 1.31782i
\(290\) 0 0
\(291\) −13.5016 + 4.60770i −0.791477 + 0.270108i
\(292\) 0 0
\(293\) 15.1582 + 2.67279i 0.885550 + 0.156146i 0.597882 0.801584i \(-0.296009\pi\)
0.287668 + 0.957730i \(0.407120\pi\)
\(294\) 0 0
\(295\) −27.9167 + 23.4249i −1.62538 + 1.36385i
\(296\) 0 0
\(297\) 22.8914 2.62020i 1.32829 0.152040i
\(298\) 0 0
\(299\) −2.34988 2.80047i −0.135897 0.161956i
\(300\) 0 0
\(301\) −7.69286 1.35646i −0.443409 0.0781850i
\(302\) 0 0
\(303\) 16.7201 19.1284i 0.960547 1.09890i
\(304\) 0 0
\(305\) −9.93455 17.2071i −0.568851 0.985278i
\(306\) 0 0
\(307\) 1.19235 + 0.688405i 0.0680511 + 0.0392893i 0.533639 0.845712i \(-0.320824\pi\)
−0.465588 + 0.885001i \(0.654157\pi\)
\(308\) 0 0
\(309\) −2.11823 + 3.50358i −0.120502 + 0.199311i
\(310\) 0 0
\(311\) 1.18602 + 0.995190i 0.0672531 + 0.0564320i 0.675795 0.737090i \(-0.263801\pi\)
−0.608541 + 0.793522i \(0.708245\pi\)
\(312\) 0 0
\(313\) −3.87251 1.40948i −0.218887 0.0796684i 0.230249 0.973132i \(-0.426046\pi\)
−0.449136 + 0.893463i \(0.648268\pi\)
\(314\) 0 0
\(315\) −5.45593 17.1096i −0.307407 0.964015i
\(316\) 0 0
\(317\) −5.88959 + 1.03849i −0.330792 + 0.0583276i −0.336578 0.941656i \(-0.609269\pi\)
0.00578564 + 0.999983i \(0.498158\pi\)
\(318\) 0 0
\(319\) 12.7303 4.63346i 0.712762 0.259424i
\(320\) 0 0
\(321\) −9.33752 11.5956i −0.521169 0.647203i
\(322\) 0 0
\(323\) 6.92531i 0.385334i
\(324\) 0 0
\(325\) 3.89531i 0.216073i
\(326\) 0 0
\(327\) 9.31706 + 11.5702i 0.515234 + 0.639832i
\(328\) 0 0
\(329\) 13.0145 4.73689i 0.717513 0.261153i
\(330\) 0 0
\(331\) 29.6474 5.22764i 1.62957 0.287337i 0.717250 0.696816i \(-0.245400\pi\)
0.912320 + 0.409478i \(0.134289\pi\)
\(332\) 0 0
\(333\) 7.15997 7.86498i 0.392364 0.430998i
\(334\) 0 0
\(335\) 3.95792 + 1.44057i 0.216244 + 0.0787065i
\(336\) 0 0
\(337\) 13.6718 + 11.4720i 0.744750 + 0.624919i 0.934109 0.356989i \(-0.116197\pi\)
−0.189359 + 0.981908i \(0.560641\pi\)
\(338\) 0 0
\(339\) −6.29844 + 10.4177i −0.342084 + 0.565812i
\(340\) 0 0
\(341\) 31.4808 + 18.1754i 1.70478 + 0.984255i
\(342\) 0 0
\(343\) −10.0117 17.3407i −0.540579 0.936310i
\(344\) 0 0
\(345\) −12.2570 + 14.0224i −0.659894 + 0.754940i
\(346\) 0 0
\(347\) −3.08430 0.543845i −0.165574 0.0291951i 0.0902466 0.995919i \(-0.471234\pi\)
−0.255820 + 0.966724i \(0.582346\pi\)
\(348\) 0 0
\(349\) −3.33211 3.97105i −0.178364 0.212565i 0.669454 0.742854i \(-0.266528\pi\)
−0.847817 + 0.530288i \(0.822084\pi\)
\(350\) 0 0
\(351\) 5.11124 + 1.22429i 0.272818 + 0.0653477i
\(352\) 0 0
\(353\) −21.0874 + 17.6945i −1.12237 + 0.941781i −0.998722 0.0505449i \(-0.983904\pi\)
−0.123649 + 0.992326i \(0.539460\pi\)
\(354\) 0 0
\(355\) 40.9156 + 7.21453i 2.17158 + 0.382908i
\(356\) 0 0
\(357\) 21.5952 7.36980i 1.14294 0.390051i
\(358\) 0 0
\(359\) −0.214812 0.372066i −0.0113374 0.0196369i 0.860301 0.509786i \(-0.170276\pi\)
−0.871638 + 0.490149i \(0.836942\pi\)
\(360\) 0 0
\(361\) −8.94062 + 15.4856i −0.470559 + 0.815032i
\(362\) 0 0
\(363\) 15.0004 + 0.302881i 0.787316 + 0.0158972i
\(364\) 0 0
\(365\) −20.3288 + 24.2270i −1.06406 + 1.26810i
\(366\) 0 0
\(367\) −8.09024 2.94460i −0.422307 0.153707i 0.122120 0.992515i \(-0.461031\pi\)
−0.544427 + 0.838808i \(0.683253\pi\)
\(368\) 0 0
\(369\) −23.8166 + 18.3986i −1.23984 + 0.957795i
\(370\) 0 0
\(371\) −14.0887 + 2.48421i −0.731447 + 0.128974i
\(372\) 0 0
\(373\) 2.53886 + 6.97545i 0.131457 + 0.361175i 0.987905 0.155057i \(-0.0495563\pi\)
−0.856449 + 0.516232i \(0.827334\pi\)
\(374\) 0 0
\(375\) −5.84996 + 0.910146i −0.302091 + 0.0469997i
\(376\) 0 0
\(377\) 3.09027 0.159157
\(378\) 0 0
\(379\) 9.22435i 0.473823i 0.971531 + 0.236911i \(0.0761351\pi\)
−0.971531 + 0.236911i \(0.923865\pi\)
\(380\) 0 0
\(381\) −5.03709 1.94938i −0.258058 0.0998699i
\(382\) 0 0
\(383\) −12.3981 + 4.51256i −0.633516 + 0.230581i −0.638761 0.769405i \(-0.720553\pi\)
0.00524510 + 0.999986i \(0.498330\pi\)
\(384\) 0 0
\(385\) −4.60928 26.1405i −0.234911 1.33225i
\(386\) 0 0
\(387\) −9.84319 6.22585i −0.500358 0.316478i
\(388\) 0 0
\(389\) −3.89331 + 10.6968i −0.197399 + 0.542348i −0.998414 0.0562953i \(-0.982071\pi\)
0.801016 + 0.598644i \(0.204293\pi\)
\(390\) 0 0
\(391\) −18.1277 15.2110i −0.916758 0.769251i
\(392\) 0 0
\(393\) 10.6433 5.86166i 0.536882 0.295682i
\(394\) 0 0
\(395\) 30.6983 + 17.7237i 1.54460 + 0.891776i
\(396\) 0 0
\(397\) 0.689201 0.397910i 0.0345900 0.0199705i −0.482605 0.875838i \(-0.660309\pi\)
0.517195 + 0.855867i \(0.326976\pi\)
\(398\) 0 0
\(399\) 3.61653 + 0.713254i 0.181053 + 0.0357074i
\(400\) 0 0
\(401\) −3.96800 + 22.5036i −0.198152 + 1.12378i 0.709705 + 0.704499i \(0.248828\pi\)
−0.907858 + 0.419279i \(0.862283\pi\)
\(402\) 0 0
\(403\) 5.32997 + 6.35201i 0.265504 + 0.316416i
\(404\) 0 0
\(405\) 2.15993 26.6884i 0.107328 1.32616i
\(406\) 0 0
\(407\) 12.0427 10.1050i 0.596936 0.500889i
\(408\) 0 0
\(409\) 4.08287 23.1551i 0.201885 1.14494i −0.700383 0.713768i \(-0.746987\pi\)
0.902267 0.431177i \(-0.141902\pi\)
\(410\) 0 0
\(411\) −5.99794 + 30.4123i −0.295857 + 1.50013i
\(412\) 0 0
\(413\) 21.3448 12.3234i 1.05031 0.606395i
\(414\) 0 0
\(415\) 11.0992 19.2244i 0.544839 0.943689i
\(416\) 0 0
\(417\) 2.21297 1.21877i 0.108370 0.0596833i
\(418\) 0 0
\(419\) −6.80387 + 8.10854i −0.332391 + 0.396128i −0.906192 0.422867i \(-0.861024\pi\)
0.573801 + 0.818995i \(0.305468\pi\)
\(420\) 0 0
\(421\) −2.48899 + 6.83843i −0.121306 + 0.333285i −0.985452 0.169957i \(-0.945637\pi\)
0.864146 + 0.503242i \(0.167859\pi\)
\(422\) 0 0
\(423\) 20.6329 + 0.833562i 1.00321 + 0.0405292i
\(424\) 0 0
\(425\) 4.37848 + 24.8316i 0.212388 + 1.20451i
\(426\) 0 0
\(427\) 4.59600 + 12.6274i 0.222416 + 0.611083i
\(428\) 0 0
\(429\) 7.24486 + 2.80380i 0.349785 + 0.135369i
\(430\) 0 0
\(431\) −14.0983 −0.679093 −0.339546 0.940589i \(-0.610274\pi\)
−0.339546 + 0.940589i \(0.610274\pi\)
\(432\) 0 0
\(433\) −15.4760 −0.743729 −0.371864 0.928287i \(-0.621281\pi\)
−0.371864 + 0.928287i \(0.621281\pi\)
\(434\) 0 0
\(435\) −2.42025 15.5562i −0.116042 0.745861i
\(436\) 0 0
\(437\) −1.30749 3.59231i −0.0625458 0.171843i
\(438\) 0 0
\(439\) 1.66041 + 9.41668i 0.0792473 + 0.449433i 0.998450 + 0.0556497i \(0.0177230\pi\)
−0.919203 + 0.393784i \(0.871166\pi\)
\(440\) 0 0
\(441\) −1.18431 8.77486i −0.0563956 0.417851i
\(442\) 0 0
\(443\) −0.155479 + 0.427176i −0.00738705 + 0.0202957i −0.943331 0.331852i \(-0.892326\pi\)
0.935944 + 0.352148i \(0.114549\pi\)
\(444\) 0 0
\(445\) 12.2153 14.5576i 0.579059 0.690096i
\(446\) 0 0
\(447\) 0.549361 27.2074i 0.0259839 1.28687i
\(448\) 0 0
\(449\) 5.88563 10.1942i 0.277760 0.481094i −0.693068 0.720872i \(-0.743741\pi\)
0.970828 + 0.239778i \(0.0770747\pi\)
\(450\) 0 0
\(451\) −38.5237 + 22.2417i −1.81401 + 1.04732i
\(452\) 0 0
\(453\) 13.3201 4.54575i 0.625831 0.213578i
\(454\) 0 0
\(455\) 1.05142 5.96289i 0.0492913 0.279545i
\(456\) 0 0
\(457\) −15.3541 + 12.8836i −0.718232 + 0.602669i −0.926896 0.375319i \(-0.877533\pi\)
0.208663 + 0.977988i \(0.433089\pi\)
\(458\) 0 0
\(459\) 33.9590 + 2.05930i 1.58507 + 0.0961198i
\(460\) 0 0
\(461\) −20.1626 24.0288i −0.939064 1.11913i −0.992705 0.120573i \(-0.961527\pi\)
0.0536406 0.998560i \(-0.482917\pi\)
\(462\) 0 0
\(463\) 4.55213 25.8164i 0.211555 1.19979i −0.675230 0.737607i \(-0.735956\pi\)
0.886785 0.462182i \(-0.152933\pi\)
\(464\) 0 0
\(465\) 27.8012 31.8054i 1.28925 1.47494i
\(466\) 0 0
\(467\) 10.9748 6.33628i 0.507851 0.293208i −0.224099 0.974566i \(-0.571944\pi\)
0.731950 + 0.681358i \(0.238610\pi\)
\(468\) 0 0
\(469\) −2.46696 1.42430i −0.113914 0.0657680i
\(470\) 0 0
\(471\) −16.1064 9.73778i −0.742144 0.448693i
\(472\) 0 0
\(473\) −13.1874 11.0655i −0.606356 0.508793i
\(474\) 0 0
\(475\) −1.39317 + 3.82770i −0.0639229 + 0.175627i
\(476\) 0 0
\(477\) −20.8393 4.54884i −0.954168 0.208277i
\(478\) 0 0
\(479\) 4.27041 + 24.2187i 0.195120 + 1.10658i 0.912248 + 0.409639i \(0.134345\pi\)
−0.717128 + 0.696942i \(0.754544\pi\)
\(480\) 0 0
\(481\) 3.36976 1.22649i 0.153648 0.0559232i
\(482\) 0 0
\(483\) 9.81047 7.90002i 0.446392 0.359464i
\(484\) 0 0
\(485\) 24.5045i 1.11269i
\(486\) 0 0
\(487\) 20.5101 0.929400 0.464700 0.885468i \(-0.346162\pi\)
0.464700 + 0.885468i \(0.346162\pi\)
\(488\) 0 0
\(489\) −14.7282 18.2899i −0.666032 0.827097i
\(490\) 0 0
\(491\) 0.320432 + 0.880380i 0.0144609 + 0.0397310i 0.946713 0.322078i \(-0.104381\pi\)
−0.932252 + 0.361809i \(0.882159\pi\)
\(492\) 0 0
\(493\) 19.6997 3.47359i 0.887229 0.156442i
\(494\) 0 0
\(495\) 8.44006 38.6659i 0.379353 1.73790i
\(496\) 0 0
\(497\) −26.4043 9.61036i −1.18439 0.431084i
\(498\) 0 0
\(499\) 7.03395 8.38274i 0.314883 0.375263i −0.585269 0.810839i \(-0.699011\pi\)
0.900152 + 0.435576i \(0.143455\pi\)
\(500\) 0 0
\(501\) −5.26166 + 8.70287i −0.235074 + 0.388815i
\(502\) 0 0
\(503\) −3.13866 + 5.43632i −0.139946 + 0.242394i −0.927476 0.373883i \(-0.878026\pi\)
0.787530 + 0.616276i \(0.211360\pi\)
\(504\) 0 0
\(505\) −21.8193 37.7922i −0.970948 1.68173i
\(506\) 0 0
\(507\) −15.6189 13.6525i −0.693658 0.606327i
\(508\) 0 0
\(509\) 37.6835 + 6.64461i 1.67029 + 0.294517i 0.927170 0.374641i \(-0.122234\pi\)
0.743120 + 0.669158i \(0.233345\pi\)
\(510\) 0 0
\(511\) 16.3851 13.7487i 0.724834 0.608208i
\(512\) 0 0
\(513\) 4.58465 + 3.03109i 0.202417 + 0.133826i
\(514\) 0 0
\(515\) 4.52030 + 5.38708i 0.199188 + 0.237383i
\(516\) 0 0
\(517\) 30.0581 + 5.30005i 1.32195 + 0.233096i
\(518\) 0 0
\(519\) 9.67284 + 28.3436i 0.424591 + 1.24415i
\(520\) 0 0
\(521\) 13.4720 + 23.3341i 0.590217 + 1.02229i 0.994203 + 0.107521i \(0.0342912\pi\)
−0.403986 + 0.914765i \(0.632375\pi\)
\(522\) 0 0
\(523\) 28.7103 + 16.5759i 1.25541 + 0.724813i 0.972179 0.234237i \(-0.0752593\pi\)
0.283234 + 0.959051i \(0.408593\pi\)
\(524\) 0 0
\(525\) −13.4185 0.270941i −0.585631 0.0118248i
\(526\) 0 0
\(527\) 41.1171 + 34.5013i 1.79109 + 1.50290i
\(528\) 0 0
\(529\) 9.33788 + 3.39871i 0.405995 + 0.147770i
\(530\) 0 0
\(531\) 36.4178 4.91516i 1.58040 0.213300i
\(532\) 0 0
\(533\) −9.99289 + 1.76202i −0.432840 + 0.0763214i
\(534\) 0 0
\(535\) −24.0300 + 8.74621i −1.03891 + 0.378132i
\(536\) 0 0
\(537\) 10.2543 1.59538i 0.442505 0.0688456i
\(538\) 0 0
\(539\) 13.0875i 0.563717i
\(540\) 0 0
\(541\) 32.6539i 1.40390i 0.712227 + 0.701949i \(0.247687\pi\)
−0.712227 + 0.701949i \(0.752313\pi\)
\(542\) 0 0
\(543\) 13.9586 36.0681i 0.599019 1.54783i
\(544\) 0 0
\(545\) 23.9774 8.72705i 1.02708 0.373826i
\(546\) 0 0
\(547\) −41.4271 + 7.30472i −1.77130 + 0.312327i −0.961586 0.274504i \(-0.911486\pi\)
−0.809709 + 0.586831i \(0.800375\pi\)
\(548\) 0 0
\(549\) −0.808769 + 20.0192i −0.0345174 + 0.854399i
\(550\) 0 0
\(551\) 3.03663 + 1.10524i 0.129365 + 0.0470849i
\(552\) 0 0
\(553\) −18.3649 15.4100i −0.780954 0.655299i
\(554\) 0 0
\(555\) −8.81321 16.0025i −0.374100 0.679270i
\(556\) 0 0
\(557\) −29.8243 17.2191i −1.26370 0.729596i −0.289909 0.957054i \(-0.593625\pi\)
−0.973788 + 0.227459i \(0.926958\pi\)
\(558\) 0 0
\(559\) −1.96344 3.40077i −0.0830445 0.143837i
\(560\) 0 0
\(561\) 49.3357 + 9.73003i 2.08296 + 0.410802i
\(562\) 0 0
\(563\) 8.29224 + 1.46215i 0.349476 + 0.0616221i 0.345631 0.938371i \(-0.387665\pi\)
0.00384529 + 0.999993i \(0.498776\pi\)
\(564\) 0 0
\(565\) 13.4409 + 16.0182i 0.565462 + 0.673892i
\(566\) 0 0
\(567\) −4.57293 + 17.5220i −0.192045 + 0.735853i
\(568\) 0 0
\(569\) 0.141118 0.118412i 0.00591598 0.00496410i −0.639825 0.768521i \(-0.720993\pi\)
0.645741 + 0.763557i \(0.276549\pi\)
\(570\) 0 0
\(571\) −15.1765 2.67603i −0.635119 0.111989i −0.153187 0.988197i \(-0.548954\pi\)
−0.481932 + 0.876209i \(0.660065\pi\)
\(572\) 0 0
\(573\) 3.41033 17.2920i 0.142469 0.722382i
\(574\) 0 0
\(575\) 6.95940 + 12.0540i 0.290227 + 0.502688i
\(576\) 0 0
\(577\) −18.1357 + 31.4120i −0.755001 + 1.30770i 0.190373 + 0.981712i \(0.439030\pi\)
−0.945374 + 0.325988i \(0.894303\pi\)
\(578\) 0 0
\(579\) 2.40903 + 4.37418i 0.100116 + 0.181785i
\(580\) 0 0
\(581\) −9.65028 + 11.5008i −0.400361 + 0.477132i
\(582\) 0 0
\(583\) −29.6260 10.7830i −1.22698 0.446585i
\(584\) 0 0
\(585\) 4.82578 7.62966i 0.199521 0.315448i
\(586\) 0 0
\(587\) 15.7563 2.77827i 0.650334 0.114671i 0.161257 0.986912i \(-0.448445\pi\)
0.489076 + 0.872241i \(0.337334\pi\)
\(588\) 0 0
\(589\) 2.96564 + 8.14803i 0.122197 + 0.335734i
\(590\) 0 0
\(591\) −6.62585 + 17.1208i −0.272551 + 0.704256i
\(592\) 0 0
\(593\) 7.18736 0.295150 0.147575 0.989051i \(-0.452853\pi\)
0.147575 + 0.989051i \(0.452853\pi\)
\(594\) 0 0
\(595\) 39.1938i 1.60679i
\(596\) 0 0
\(597\) −6.22563 40.0152i −0.254798 1.63771i
\(598\) 0 0
\(599\) −27.3895 + 9.96896i −1.11910 + 0.407320i −0.834325 0.551273i \(-0.814142\pi\)
−0.284779 + 0.958593i \(0.591920\pi\)
\(600\) 0 0
\(601\) −0.344316 1.95271i −0.0140449 0.0796528i 0.976980 0.213333i \(-0.0684318\pi\)
−0.991025 + 0.133680i \(0.957321\pi\)
\(602\) 0 0
\(603\) −2.59650 3.36111i −0.105737 0.136875i
\(604\) 0 0
\(605\) 8.81415 24.2167i 0.358346 0.984548i
\(606\) 0 0
\(607\) −2.10496 1.76628i −0.0854379 0.0716909i 0.599068 0.800698i \(-0.295538\pi\)
−0.684506 + 0.729007i \(0.739982\pi\)
\(608\) 0 0
\(609\) −0.214945 + 10.6453i −0.00871003 + 0.431369i
\(610\) 0 0
\(611\) 6.02952 + 3.48115i 0.243928 + 0.140832i
\(612\) 0 0
\(613\) −8.19090 + 4.72902i −0.330827 + 0.191003i −0.656208 0.754580i \(-0.727841\pi\)
0.325381 + 0.945583i \(0.394507\pi\)
\(614\) 0 0
\(615\) 16.6961 + 48.9235i 0.673253 + 1.97278i
\(616\) 0 0
\(617\) −1.23039 + 6.97788i −0.0495336 + 0.280919i −0.999506 0.0314135i \(-0.989999\pi\)
0.949973 + 0.312332i \(0.101110\pi\)
\(618\) 0 0
\(619\) −23.0376 27.4551i −0.925959 1.10351i −0.994381 0.105858i \(-0.966241\pi\)
0.0684224 0.997656i \(-0.478203\pi\)
\(620\) 0 0
\(621\) 18.0041 5.34323i 0.722478 0.214417i
\(622\) 0 0
\(623\) −9.84554 + 8.26139i −0.394453 + 0.330986i
\(624\) 0 0
\(625\) −5.10952 + 28.9775i −0.204381 + 1.15910i
\(626\) 0 0
\(627\) 6.11632 + 5.34628i 0.244262 + 0.213510i
\(628\) 0 0
\(629\) 20.1027 11.6063i 0.801549 0.462775i
\(630\) 0 0
\(631\) −23.5980 + 40.8729i −0.939422 + 1.62713i −0.172869 + 0.984945i \(0.555304\pi\)
−0.766553 + 0.642181i \(0.778030\pi\)
\(632\) 0 0
\(633\) −0.343072 0.207418i −0.0136359 0.00824412i
\(634\) 0 0
\(635\) −5.96336 + 7.10685i −0.236649 + 0.282027i
\(636\) 0 0
\(637\) 1.02106 2.80533i 0.0404557 0.111151i
\(638\) 0 0
\(639\) −30.9801 28.2031i −1.22555 1.11570i
\(640\) 0 0
\(641\) 2.99885 + 17.0073i 0.118448 + 0.671749i 0.984985 + 0.172638i \(0.0552291\pi\)
−0.866538 + 0.499111i \(0.833660\pi\)
\(642\) 0 0
\(643\) 2.53686 + 6.96996i 0.100044 + 0.274868i 0.979610 0.200908i \(-0.0643893\pi\)
−0.879566 + 0.475777i \(0.842167\pi\)
\(644\) 0 0
\(645\) −15.5815 + 12.5472i −0.613521 + 0.494046i
\(646\) 0 0
\(647\) −27.6670 −1.08770 −0.543852 0.839181i \(-0.683035\pi\)
−0.543852 + 0.839181i \(0.683035\pi\)
\(648\) 0 0
\(649\) 54.3161 2.13209
\(650\) 0 0
\(651\) −22.2520 + 17.9188i −0.872125 + 0.702291i
\(652\) 0 0
\(653\) 7.93819 + 21.8100i 0.310645 + 0.853491i 0.992527 + 0.122028i \(0.0389399\pi\)
−0.681881 + 0.731463i \(0.738838\pi\)
\(654\) 0 0
\(655\) −3.62416 20.5536i −0.141608 0.803097i
\(656\) 0 0
\(657\) 30.3836 9.68877i 1.18538 0.377995i
\(658\) 0 0
\(659\) −12.1258 + 33.3152i −0.472352 + 1.29778i 0.443504 + 0.896272i \(0.353735\pi\)
−0.915857 + 0.401505i \(0.868487\pi\)
\(660\) 0 0
\(661\) −32.3094 + 38.5048i −1.25669 + 1.49766i −0.466868 + 0.884327i \(0.654618\pi\)
−0.789821 + 0.613337i \(0.789827\pi\)
\(662\) 0 0
\(663\) 9.81611 + 5.93472i 0.381226 + 0.230485i
\(664\) 0 0
\(665\) 3.16581 5.48335i 0.122765 0.212635i
\(666\) 0 0
\(667\) 9.56284 5.52111i 0.370275 0.213778i
\(668\) 0 0
\(669\) −9.26923 8.10224i −0.358369 0.313251i
\(670\) 0 0
\(671\) −5.14241 + 29.1640i −0.198520 + 1.12587i
\(672\) 0 0
\(673\) 12.4003 10.4051i 0.477998 0.401088i −0.371704 0.928351i \(-0.621226\pi\)
0.849702 + 0.527264i \(0.176782\pi\)
\(674\) 0 0
\(675\) −18.3553 7.96976i −0.706495 0.306756i
\(676\) 0 0
\(677\) −17.5329 20.8949i −0.673844 0.803057i 0.315457 0.948940i \(-0.397842\pi\)
−0.989302 + 0.145883i \(0.953398\pi\)
\(678\) 0 0
\(679\) 2.87783 16.3210i 0.110441 0.626343i
\(680\) 0 0
\(681\) 14.1468 + 41.4533i 0.542107 + 1.58850i
\(682\) 0 0
\(683\) 24.2989 14.0290i 0.929770 0.536803i 0.0430314 0.999074i \(-0.486298\pi\)
0.886739 + 0.462271i \(0.152965\pi\)
\(684\) 0 0
\(685\) 46.1110 + 26.6222i 1.76181 + 1.01718i
\(686\) 0 0
\(687\) −0.195428 + 9.67867i −0.00745602 + 0.369264i
\(688\) 0 0
\(689\) −5.50913 4.62271i −0.209881 0.176111i
\(690\) 0 0
\(691\) 5.89760 16.2035i 0.224355 0.616411i −0.775534 0.631306i \(-0.782519\pi\)
0.999889 + 0.0148951i \(0.00474145\pi\)
\(692\) 0 0
\(693\) −10.1624 + 24.7619i −0.386038 + 0.940628i
\(694\) 0 0
\(695\) −0.753543 4.27355i −0.0285835 0.162105i
\(696\) 0 0
\(697\) −61.7216 + 22.4648i −2.33787 + 0.850916i
\(698\) 0 0
\(699\) −3.31775 21.3248i −0.125489 0.806579i
\(700\) 0 0
\(701\) 13.0471i 0.492781i 0.969171 + 0.246391i \(0.0792447\pi\)
−0.969171 + 0.246391i \(0.920755\pi\)
\(702\) 0 0
\(703\) 3.74993 0.141431
\(704\) 0 0
\(705\) 12.8016 33.0785i 0.482136 1.24581i
\(706\) 0 0
\(707\) 10.0942 + 27.7337i 0.379633 + 1.04303i
\(708\) 0 0
\(709\) 9.97070 1.75810i 0.374457 0.0660269i 0.0167476 0.999860i \(-0.494669\pi\)
0.357710 + 0.933833i \(0.383558\pi\)
\(710\) 0 0
\(711\) −16.6080 31.6517i −0.622850 1.18703i
\(712\) 0 0
\(713\) 27.8421 + 10.1337i 1.04270 + 0.379510i
\(714\) 0 0
\(715\) 8.57711 10.2218i 0.320766 0.382274i
\(716\) 0 0
\(717\) 18.4836 + 33.5615i 0.690282 + 1.25338i
\(718\) 0 0
\(719\) −4.51073 + 7.81281i −0.168222 + 0.291369i −0.937795 0.347190i \(-0.887136\pi\)
0.769573 + 0.638559i \(0.220469\pi\)
\(720\) 0 0
\(721\) −2.37804 4.11889i −0.0885630 0.153396i
\(722\) 0 0
\(723\) 0.820418 4.15990i 0.0305117 0.154708i
\(724\) 0 0
\(725\) −11.5870 2.04311i −0.430331 0.0758790i
\(726\) 0 0
\(727\) 20.0185 16.7975i 0.742446 0.622986i −0.191047 0.981581i \(-0.561188\pi\)
0.933493 + 0.358595i \(0.116744\pi\)
\(728\) 0 0
\(729\) −16.2266 + 21.5800i −0.600984 + 0.799261i
\(730\) 0 0
\(731\) −16.3390 19.4721i −0.604321 0.720201i
\(732\) 0 0
\(733\) −38.9827 6.87370i −1.43986 0.253886i −0.601442 0.798916i \(-0.705407\pi\)
−0.838416 + 0.545030i \(0.816518\pi\)
\(734\) 0 0
\(735\) −14.9215 2.94282i −0.550387 0.108548i
\(736\) 0 0
\(737\) −3.13884 5.43663i −0.115621 0.200261i
\(738\) 0 0
\(739\) −22.3748 12.9181i −0.823069 0.475199i 0.0284045 0.999597i \(-0.490957\pi\)
−0.851474 + 0.524397i \(0.824291\pi\)
\(740\) 0 0
\(741\) 0.893941 + 1.62317i 0.0328398 + 0.0596286i
\(742\) 0 0
\(743\) 11.7136 + 9.82885i 0.429729 + 0.360585i 0.831849 0.555001i \(-0.187282\pi\)
−0.402120 + 0.915587i \(0.631727\pi\)
\(744\) 0 0
\(745\) −43.9237 15.9869i −1.60924 0.585716i
\(746\) 0 0
\(747\) −19.8214 + 10.4005i −0.725228 + 0.380536i
\(748\) 0 0
\(749\) 17.0322 3.00323i 0.622342 0.109736i
\(750\) 0 0
\(751\) 10.8628 3.95373i 0.396389 0.144274i −0.136132 0.990691i \(-0.543467\pi\)
0.532521 + 0.846417i \(0.321245\pi\)
\(752\) 0 0
\(753\) 0.0817538 0.211247i 0.00297927 0.00769826i
\(754\) 0 0
\(755\) 24.1750i 0.879819i
\(756\) 0 0
\(757\) 25.7483i 0.935840i −0.883771 0.467920i \(-0.845004\pi\)
0.883771 0.467920i \(-0.154996\pi\)
\(758\) 0 0
\(759\) 27.4285 4.26737i 0.995592 0.154896i
\(760\) 0 0
\(761\) 0.635064 0.231144i 0.0230211 0.00837898i −0.330484 0.943812i \(-0.607212\pi\)
0.353505 + 0.935433i \(0.384990\pi\)
\(762\) 0 0
\(763\) −16.9949 + 2.99665i −0.615255 + 0.108486i
\(764\) 0 0
\(765\) 22.1871 54.0615i 0.802176 1.95460i
\(766\) 0 0
\(767\) 11.6428 + 4.23763i 0.420397 + 0.153012i
\(768\) 0 0
\(769\) −0.808949 0.678789i −0.0291714 0.0244777i 0.628085 0.778144i \(-0.283839\pi\)
−0.657257 + 0.753667i \(0.728283\pi\)
\(770\) 0 0
\(771\) −40.3338 0.814402i −1.45259 0.0293300i
\(772\) 0 0
\(773\) −2.76890 1.59862i −0.0995903 0.0574985i 0.449378 0.893342i \(-0.351646\pi\)
−0.548968 + 0.835843i \(0.684979\pi\)
\(774\) 0 0
\(775\) −15.7852 27.3408i −0.567023 0.982112i
\(776\) 0 0
\(777\) 3.99061 + 11.6934i 0.143162 + 0.419498i
\(778\) 0 0
\(779\) −10.4496 1.84255i −0.374397 0.0660163i
\(780\) 0 0
\(781\) −39.8037 47.4362i −1.42429 1.69740i
\(782\) 0 0
\(783\) −6.32265 + 14.5618i −0.225953 + 0.520396i
\(784\) 0 0
\(785\) −24.7651 + 20.7804i −0.883906 + 0.741685i
\(786\) 0 0
\(787\) −41.9180 7.39128i −1.49422 0.263471i −0.633974 0.773355i \(-0.718577\pi\)
−0.860243 + 0.509884i \(0.829688\pi\)
\(788\) 0 0
\(789\) 16.6491 + 14.5530i 0.592724 + 0.518101i
\(790\) 0 0
\(791\) −7.07100 12.2473i −0.251416 0.435465i
\(792\) 0 0
\(793\) −3.37760 + 5.85018i −0.119942 + 0.207746i
\(794\) 0 0
\(795\) −18.9557 + 31.3530i −0.672289 + 1.11197i
\(796\) 0 0
\(797\) −4.57093 + 5.44743i −0.161911 + 0.192958i −0.840900 0.541190i \(-0.817974\pi\)
0.678989 + 0.734148i \(0.262418\pi\)
\(798\) 0 0
\(799\) 42.3496 + 15.4140i 1.49822 + 0.545308i
\(800\) 0 0
\(801\) −18.2570 + 5.82182i −0.645080 + 0.205704i
\(802\) 0 0
\(803\) 46.4210 8.18528i 1.63816 0.288852i
\(804\) 0 0
\(805\) −7.39975 20.3307i −0.260807 0.716561i
\(806\) 0 0
\(807\) 18.5537 + 23.0405i 0.653122 + 0.811065i
\(808\) 0 0
\(809\) −32.9358 −1.15796 −0.578981 0.815341i \(-0.696550\pi\)
−0.578981 + 0.815341i \(0.696550\pi\)
\(810\) 0 0
\(811\) 12.6751i 0.445084i −0.974923 0.222542i \(-0.928565\pi\)
0.974923 0.222542i \(-0.0714354\pi\)
\(812\) 0 0
\(813\) −11.2385 + 9.05000i −0.394153 + 0.317397i
\(814\) 0 0
\(815\) −37.9029 + 13.7955i −1.32768 + 0.483236i
\(816\) 0 0
\(817\) −0.713061 4.04397i −0.0249469 0.141481i
\(818\) 0 0
\(819\) −4.11021 + 4.51493i −0.143622 + 0.157764i
\(820\) 0 0
\(821\) −3.89007 + 10.6879i −0.135764 + 0.373009i −0.988881 0.148711i \(-0.952487\pi\)
0.853116 + 0.521721i \(0.174710\pi\)
\(822\) 0 0
\(823\) 11.0019 + 9.23172i 0.383503 + 0.321798i 0.814076 0.580758i \(-0.197244\pi\)
−0.430573 + 0.902556i \(0.641688\pi\)
\(824\) 0 0
\(825\) −25.3110 15.3028i −0.881217 0.532775i
\(826\) 0 0
\(827\) −22.7649 13.1433i −0.791614 0.457039i 0.0489165 0.998803i \(-0.484423\pi\)
−0.840530 + 0.541764i \(0.817757\pi\)
\(828\) 0 0
\(829\) −35.0559 + 20.2396i −1.21754 + 0.702949i −0.964392 0.264478i \(-0.914800\pi\)
−0.253151 + 0.967427i \(0.581467\pi\)
\(830\) 0 0
\(831\) 21.1949 24.2476i 0.735242 0.841141i
\(832\) 0 0
\(833\) 3.35567 19.0310i 0.116267 0.659384i
\(834\) 0 0
\(835\) 11.2284 + 13.3815i 0.388575 + 0.463085i
\(836\) 0 0
\(837\) −40.8366 + 12.1195i −1.41152 + 0.418910i
\(838\) 0 0
\(839\) −20.1199 + 16.8826i −0.694615 + 0.582851i −0.920236 0.391364i \(-0.872003\pi\)
0.225621 + 0.974215i \(0.427559\pi\)
\(840\) 0 0
\(841\) 3.41494 19.3671i 0.117757 0.667830i
\(842\) 0 0
\(843\) 11.9058 4.06311i 0.410058 0.139941i
\(844\) 0 0
\(845\) −30.8584 + 17.8161i −1.06156 + 0.612893i
\(846\) 0 0
\(847\) −8.71463 + 15.0942i −0.299438 + 0.518642i
\(848\) 0 0
\(849\) 0.152859 7.57041i 0.00524609 0.259816i
\(850\) 0 0
\(851\) 8.23646 9.81583i 0.282342 0.336482i
\(852\) 0 0
\(853\) 4.25849 11.7001i 0.145808 0.400604i −0.845193 0.534462i \(-0.820514\pi\)
0.991001 + 0.133858i \(0.0427366\pi\)
\(854\) 0 0
\(855\) 7.47079 5.77127i 0.255495 0.197373i
\(856\) 0 0
\(857\) −7.86174 44.5861i −0.268552 1.52303i −0.758727 0.651409i \(-0.774178\pi\)
0.490175 0.871624i \(-0.336933\pi\)
\(858\) 0 0
\(859\) 5.63070 + 15.4702i 0.192117 + 0.527837i 0.997928 0.0643355i \(-0.0204928\pi\)
−0.805811 + 0.592172i \(0.798271\pi\)
\(860\) 0 0
\(861\) −5.37470 34.5459i −0.183169 1.17732i
\(862\) 0 0
\(863\) 31.6950 1.07891 0.539455 0.842014i \(-0.318630\pi\)
0.539455 + 0.842014i \(0.318630\pi\)
\(864\) 0 0
\(865\) 51.4417 1.74907
\(866\) 0 0
\(867\) 41.7859 + 16.1714i 1.41912 + 0.549210i
\(868\) 0 0
\(869\) −18.0698 49.6464i −0.612977 1.68414i
\(870\) 0 0
\(871\) −0.248663 1.41024i −0.00842564 0.0477842i
\(872\) 0 0
\(873\) 13.2086 20.8831i 0.447044 0.706786i
\(874\) 0 0
\(875\) 2.35226 6.46279i 0.0795210 0.218482i
\(876\) 0 0
\(877\) 7.22447 8.60978i 0.243953 0.290732i −0.630149 0.776474i \(-0.717006\pi\)
0.874102 + 0.485742i \(0.161451\pi\)
\(878\) 0 0
\(879\) −23.3524 + 12.8611i −0.787657 + 0.433793i
\(880\) 0 0
\(881\) 2.85195 4.93971i 0.0960845 0.166423i −0.813976 0.580898i \(-0.802701\pi\)
0.910061 + 0.414475i \(0.136035\pi\)
\(882\) 0 0
\(883\) 5.76147 3.32639i 0.193889 0.111942i −0.399913 0.916553i \(-0.630960\pi\)
0.593802 + 0.804611i \(0.297626\pi\)
\(884\) 0 0
\(885\) 12.2134 61.9277i 0.410550 2.08168i
\(886\) 0 0
\(887\) 5.28016 29.9453i 0.177291 1.00546i −0.758176 0.652050i \(-0.773909\pi\)
0.935467 0.353415i \(-0.114980\pi\)
\(888\) 0 0
\(889\) 4.80648 4.03312i 0.161204 0.135266i
\(890\) 0 0
\(891\) −28.0348 + 28.4023i −0.939202 + 0.951513i
\(892\) 0 0
\(893\) 4.67982 + 5.57720i 0.156604 + 0.186634i
\(894\) 0 0
\(895\) 3.09533 17.5545i 0.103465 0.586782i
\(896\) 0 0
\(897\) 6.21230 + 1.22519i 0.207423 + 0.0409080i
\(898\) 0 0
\(899\) −21.6903 + 12.5229i −0.723413 + 0.417663i
\(900\) 0 0
\(901\) −40.3154 23.2761i −1.34310 0.775440i
\(902\) 0 0
\(903\) 11.8515 6.52707i 0.394393 0.217207i
\(904\) 0 0
\(905\) −50.8886 42.7006i −1.69160 1.41942i
\(906\) 0 0
\(907\) −19.4374 + 53.4037i −0.645407 + 1.77324i −0.0113732 + 0.999935i \(0.503620\pi\)
−0.634034 + 0.773305i \(0.718602\pi\)
\(908\) 0 0
\(909\) −1.77631 + 43.9684i −0.0589164 + 1.45834i
\(910\) 0 0
\(911\) 2.73844 + 15.5304i 0.0907284 + 0.514547i 0.995973 + 0.0896553i \(0.0285766\pi\)
−0.905244 + 0.424891i \(0.860312\pi\)
\(912\) 0 0
\(913\) −31.0904 + 11.3160i −1.02894 + 0.374504i
\(914\) 0 0
\(915\) 32.0946 + 12.4208i 1.06102 + 0.410620i
\(916\) 0 0
\(917\) 14.1152i 0.466125i
\(918\) 0 0
\(919\) −14.9150 −0.492002 −0.246001 0.969270i \(-0.579117\pi\)
−0.246001 + 0.969270i \(0.579117\pi\)
\(920\) 0 0
\(921\) −2.35636 + 0.366605i −0.0776446 + 0.0120801i
\(922\) 0 0
\(923\) −4.83115 13.2735i −0.159019 0.436901i
\(924\) 0 0
\(925\) −13.4459 + 2.37087i −0.442098 + 0.0779537i
\(926\) 0 0
\(927\) −0.948477 7.02753i −0.0311521 0.230814i
\(928\) 0 0
\(929\) 26.9926 + 9.82451i 0.885599 + 0.322332i 0.744467 0.667659i \(-0.232704\pi\)
0.141132 + 0.989991i \(0.454926\pi\)
\(930\) 0 0
\(931\) 2.00667 2.39145i 0.0657658 0.0783767i
\(932\) 0 0
\(933\) −2.68109 0.0541353i −0.0877748 0.00177231i
\(934\) 0 0
\(935\) 43.1872 74.8025i 1.41237 2.44630i
\(936\) 0 0
\(937\) 18.4509 + 31.9578i 0.602763 + 1.04402i 0.992401 + 0.123048i \(0.0392670\pi\)
−0.389637 + 0.920968i \(0.627400\pi\)
\(938\) 0 0
\(939\) 6.75530 2.30539i 0.220451 0.0752334i
\(940\) 0 0
\(941\) 12.0405 + 2.12306i 0.392509 + 0.0692098i 0.366419 0.930450i \(-0.380584\pi\)
0.0260891 + 0.999660i \(0.491695\pi\)
\(942\) 0 0
\(943\) −27.7750 + 23.3060i −0.904478 + 0.758947i
\(944\) 0 0
\(945\) 25.9468 + 17.1544i 0.844051 + 0.558034i
\(946\) 0 0
\(947\) −0.998881 1.19042i −0.0324593 0.0386835i 0.749571 0.661924i \(-0.230260\pi\)
−0.782030 + 0.623241i \(0.785816\pi\)
\(948\) 0 0
\(949\) 10.5891 + 1.86714i 0.343735 + 0.0606098i
\(950\) 0 0
\(951\) 6.81710 7.79899i 0.221060 0.252899i
\(952\) 0 0
\(953\) 22.6088 + 39.1596i 0.732371 + 1.26850i 0.955867 + 0.293799i \(0.0949198\pi\)
−0.223496 + 0.974705i \(0.571747\pi\)
\(954\) 0 0
\(955\) −26.2179 15.1369i −0.848392 0.489820i
\(956\) 0 0
\(957\) −12.1402 + 20.0800i −0.392436 + 0.649095i
\(958\) 0 0
\(959\) −27.5853 23.1468i −0.890776 0.747449i
\(960\) 0 0
\(961\) −34.0208 12.3826i −1.09744 0.399437i
\(962\) 0 0
\(963\) 25.1932 + 5.49922i 0.811841 + 0.177210i
\(964\) 0 0
\(965\) 8.44715 1.48946i 0.271923 0.0479474i
\(966\) 0 0
\(967\) −13.8966 + 5.05794i −0.446884 + 0.162652i −0.555652 0.831415i \(-0.687531\pi\)
0.108769 + 0.994067i \(0.465309\pi\)
\(968\) 0 0
\(969\) 7.52316 + 9.34247i 0.241679 + 0.300123i
\(970\) 0 0
\(971\) 9.29617i 0.298328i −0.988812 0.149164i \(-0.952342\pi\)
0.988812 0.149164i \(-0.0476583\pi\)
\(972\) 0 0
\(973\) 2.93486i 0.0940874i
\(974\) 0 0
\(975\) −4.23159 5.25490i −0.135519 0.168292i
\(976\) 0 0
\(977\) −40.3617 + 14.6904i −1.29128 + 0.469989i −0.894148 0.447771i \(-0.852218\pi\)
−0.397135 + 0.917760i \(0.629996\pi\)
\(978\) 0 0
\(979\) −27.8936 + 4.91840i −0.891484 + 0.157193i
\(980\) 0 0
\(981\) −25.1380 5.48717i −0.802596 0.175192i
\(982\) 0 0
\(983\) 32.6478 + 11.8828i 1.04130 + 0.379003i 0.805374 0.592767i \(-0.201964\pi\)
0.235929 + 0.971770i \(0.424187\pi\)
\(984\) 0 0
\(985\) 24.1558 + 20.2692i 0.769669 + 0.645829i
\(986\) 0 0
\(987\) −12.4112 + 20.5283i −0.395052 + 0.653421i
\(988\) 0 0
\(989\) −12.1517 7.01579i −0.386402 0.223089i
\(990\) 0 0
\(991\) −5.69720 9.86784i −0.180977 0.313462i 0.761236 0.648475i \(-0.224593\pi\)
−0.942214 + 0.335013i \(0.891259\pi\)
\(992\) 0 0
\(993\) −34.3164 + 39.2591i −1.08900 + 1.24585i
\(994\) 0 0
\(995\) −68.5028 12.0789i −2.17168 0.382926i
\(996\) 0 0
\(997\) 20.8999 + 24.9075i 0.661906 + 0.788829i 0.987658 0.156626i \(-0.0500619\pi\)
−0.325752 + 0.945455i \(0.605617\pi\)
\(998\) 0 0
\(999\) −1.11507 + 18.3882i −0.0352793 + 0.581777i
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 864.2.bf.a.49.8 204
4.3 odd 2 216.2.t.a.157.5 204
8.3 odd 2 216.2.t.a.157.11 yes 204
8.5 even 2 inner 864.2.bf.a.49.27 204
12.11 even 2 648.2.t.a.37.30 204
24.11 even 2 648.2.t.a.37.24 204
27.16 even 9 inner 864.2.bf.a.529.27 204
108.11 even 18 648.2.t.a.613.24 204
108.43 odd 18 216.2.t.a.205.11 yes 204
216.11 even 18 648.2.t.a.613.30 204
216.43 odd 18 216.2.t.a.205.5 yes 204
216.205 even 18 inner 864.2.bf.a.529.8 204
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.2.t.a.157.5 204 4.3 odd 2
216.2.t.a.157.11 yes 204 8.3 odd 2
216.2.t.a.205.5 yes 204 216.43 odd 18
216.2.t.a.205.11 yes 204 108.43 odd 18
648.2.t.a.37.24 204 24.11 even 2
648.2.t.a.37.30 204 12.11 even 2
648.2.t.a.613.24 204 108.11 even 18
648.2.t.a.613.30 204 216.11 even 18
864.2.bf.a.49.8 204 1.1 even 1 trivial
864.2.bf.a.49.27 204 8.5 even 2 inner
864.2.bf.a.529.8 204 216.205 even 18 inner
864.2.bf.a.529.27 204 27.16 even 9 inner