Properties

Label 2646.2.t.a.2285.1
Level $2646$
Weight $2$
Character 2646.2285
Analytic conductor $21.128$
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] = [2646,2,Mod(1979,2646)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2646.1979");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.t (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: \(21.1284163748\)
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: \( x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 2285.1
Root \(-1.62181 - 0.608059i\) of defining polynomial
Character \(\chi\) \(=\) 2646.2285
Dual form 2646.2.t.a.1979.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -3.89111 q^{5} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -3.89111 q^{5} -1.00000i q^{8} +(3.36980 + 1.94556i) q^{10} -3.94462i q^{11} +(-2.46687 - 1.42425i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(-0.371058 + 0.642692i) q^{17} +(1.54563 - 0.892369i) q^{19} +(-1.94556 - 3.36980i) q^{20} +(-1.97231 + 3.41614i) q^{22} -6.25311i q^{23} +10.1408 q^{25} +(1.42425 + 2.46687i) q^{26} +(2.50079 - 1.44383i) q^{29} +(3.04125 - 1.75587i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.642692 - 0.371058i) q^{34} +(-1.50079 - 2.59944i) q^{37} -1.78474 q^{38} +3.89111i q^{40} +(-5.24705 + 9.08816i) q^{41} +(0.471521 + 0.816699i) q^{43} +(3.41614 - 1.97231i) q^{44} +(-3.12656 + 5.41535i) q^{46} +(1.09263 - 1.89248i) q^{47} +(-8.78217 - 5.07039i) q^{50} -2.84849i q^{52} +15.3490i q^{55} -2.88766 q^{58} +(0.0105673 + 0.0183031i) q^{59} +(-2.13832 - 1.23456i) q^{61} -3.51174 q^{62} -1.00000 q^{64} +(9.59886 + 5.54191i) q^{65} +(-6.72463 - 11.6474i) q^{67} -0.742117 q^{68} +1.94304i q^{71} +(4.20443 + 2.42743i) q^{73} +3.00158i q^{74} +(1.54563 + 0.892369i) q^{76} +(-1.81806 + 3.14898i) q^{79} +(1.94556 - 3.36980i) q^{80} +(9.08816 - 5.24705i) q^{82} +(-4.02998 - 6.98012i) q^{83} +(1.44383 - 2.50079i) q^{85} -0.943042i q^{86} -3.94462 q^{88} +(4.63323 + 8.02499i) q^{89} +(5.41535 - 3.12656i) q^{92} +(-1.89248 + 1.09263i) q^{94} +(-6.01422 + 3.47231i) q^{95} +(-16.2983 + 9.40980i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} - 8 q^{16} + 16 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} - 60 q^{50} + 24 q^{58} - 16 q^{64} + 84 q^{65} - 28 q^{67} - 4 q^{79} - 12 q^{85} + 48 q^{92} + 12 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −3.89111 −1.74016 −0.870080 0.492911i \(-0.835933\pi\)
−0.870080 + 0.492911i \(0.835933\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 3.36980 + 1.94556i 1.06563 + 0.615239i
\(11\) 3.94462i 1.18935i −0.803967 0.594674i \(-0.797281\pi\)
0.803967 0.594674i \(-0.202719\pi\)
\(12\) 0 0
\(13\) −2.46687 1.42425i −0.684186 0.395015i 0.117244 0.993103i \(-0.462594\pi\)
−0.801430 + 0.598088i \(0.795927\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.371058 + 0.642692i −0.0899949 + 0.155876i −0.907509 0.420033i \(-0.862018\pi\)
0.817514 + 0.575909i \(0.195352\pi\)
\(18\) 0 0
\(19\) 1.54563 0.892369i 0.354591 0.204723i −0.312114 0.950045i \(-0.601037\pi\)
0.666706 + 0.745321i \(0.267704\pi\)
\(20\) −1.94556 3.36980i −0.435040 0.753511i
\(21\) 0 0
\(22\) −1.97231 + 3.41614i −0.420498 + 0.728324i
\(23\) 6.25311i 1.30386i −0.758278 0.651932i \(-0.773959\pi\)
0.758278 0.651932i \(-0.226041\pi\)
\(24\) 0 0
\(25\) 10.1408 2.02815
\(26\) 1.42425 + 2.46687i 0.279318 + 0.483793i
\(27\) 0 0
\(28\) 0 0
\(29\) 2.50079 1.44383i 0.464385 0.268113i −0.249501 0.968374i \(-0.580267\pi\)
0.713886 + 0.700262i \(0.246933\pi\)
\(30\) 0 0
\(31\) 3.04125 1.75587i 0.546225 0.315363i −0.201373 0.979515i \(-0.564540\pi\)
0.747598 + 0.664152i \(0.231207\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 0.642692 0.371058i 0.110221 0.0636360i
\(35\) 0 0
\(36\) 0 0
\(37\) −1.50079 2.59944i −0.246728 0.427346i 0.715888 0.698215i \(-0.246022\pi\)
−0.962616 + 0.270870i \(0.912689\pi\)
\(38\) −1.78474 −0.289523
\(39\) 0 0
\(40\) 3.89111i 0.615239i
\(41\) −5.24705 + 9.08816i −0.819452 + 1.41933i 0.0866345 + 0.996240i \(0.472389\pi\)
−0.906087 + 0.423092i \(0.860945\pi\)
\(42\) 0 0
\(43\) 0.471521 + 0.816699i 0.0719063 + 0.124545i 0.899737 0.436433i \(-0.143758\pi\)
−0.827830 + 0.560978i \(0.810425\pi\)
\(44\) 3.41614 1.97231i 0.515003 0.297337i
\(45\) 0 0
\(46\) −3.12656 + 5.41535i −0.460985 + 0.798450i
\(47\) 1.09263 1.89248i 0.159376 0.276047i −0.775268 0.631633i \(-0.782385\pi\)
0.934644 + 0.355585i \(0.115718\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −8.78217 5.07039i −1.24199 0.717061i
\(51\) 0 0
\(52\) 2.84849i 0.395015i
\(53\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) 0 0
\(55\) 15.3490i 2.06965i
\(56\) 0 0
\(57\) 0 0
\(58\) −2.88766 −0.379169
\(59\) 0.0105673 + 0.0183031i 0.00137575 + 0.00238286i 0.866712 0.498808i \(-0.166229\pi\)
−0.865337 + 0.501191i \(0.832895\pi\)
\(60\) 0 0
\(61\) −2.13832 1.23456i −0.273783 0.158069i 0.356822 0.934172i \(-0.383860\pi\)
−0.630606 + 0.776103i \(0.717193\pi\)
\(62\) −3.51174 −0.445991
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 9.59886 + 5.54191i 1.19059 + 0.687389i
\(66\) 0 0
\(67\) −6.72463 11.6474i −0.821544 1.42296i −0.904532 0.426406i \(-0.859779\pi\)
0.0829874 0.996551i \(-0.473554\pi\)
\(68\) −0.742117 −0.0899949
\(69\) 0 0
\(70\) 0 0
\(71\) 1.94304i 0.230597i 0.993331 + 0.115298i \(0.0367824\pi\)
−0.993331 + 0.115298i \(0.963218\pi\)
\(72\) 0 0
\(73\) 4.20443 + 2.42743i 0.492092 + 0.284109i 0.725442 0.688284i \(-0.241636\pi\)
−0.233350 + 0.972393i \(0.574969\pi\)
\(74\) 3.00158i 0.348926i
\(75\) 0 0
\(76\) 1.54563 + 0.892369i 0.177296 + 0.102362i
\(77\) 0 0
\(78\) 0 0
\(79\) −1.81806 + 3.14898i −0.204548 + 0.354288i −0.949989 0.312284i \(-0.898906\pi\)
0.745440 + 0.666572i \(0.232239\pi\)
\(80\) 1.94556 3.36980i 0.217520 0.376756i
\(81\) 0 0
\(82\) 9.08816 5.24705i 1.00362 0.579440i
\(83\) −4.02998 6.98012i −0.442347 0.766168i 0.555516 0.831506i \(-0.312521\pi\)
−0.997863 + 0.0653378i \(0.979188\pi\)
\(84\) 0 0
\(85\) 1.44383 2.50079i 0.156605 0.271249i
\(86\) 0.943042i 0.101691i
\(87\) 0 0
\(88\) −3.94462 −0.420498
\(89\) 4.63323 + 8.02499i 0.491122 + 0.850647i 0.999948 0.0102218i \(-0.00325375\pi\)
−0.508826 + 0.860869i \(0.669920\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 5.41535 3.12656i 0.564589 0.325966i
\(93\) 0 0
\(94\) −1.89248 + 1.09263i −0.195195 + 0.112696i
\(95\) −6.01422 + 3.47231i −0.617046 + 0.356251i
\(96\) 0 0
\(97\) −16.2983 + 9.40980i −1.65484 + 0.955421i −0.679794 + 0.733403i \(0.737931\pi\)
−0.975043 + 0.222018i \(0.928736\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 5.07039 + 8.78217i 0.507039 + 0.878217i
\(101\) −8.28158 −0.824048 −0.412024 0.911173i \(-0.635178\pi\)
−0.412024 + 0.911173i \(0.635178\pi\)
\(102\) 0 0
\(103\) 17.0487i 1.67986i −0.542697 0.839929i \(-0.682597\pi\)
0.542697 0.839929i \(-0.317403\pi\)
\(104\) −1.42425 + 2.46687i −0.139659 + 0.241896i
\(105\) 0 0
\(106\) 0 0
\(107\) −12.4161 + 7.16846i −1.20031 + 0.693001i −0.960625 0.277848i \(-0.910379\pi\)
−0.239689 + 0.970850i \(0.577045\pi\)
\(108\) 0 0
\(109\) −5.63998 + 9.76874i −0.540212 + 0.935675i 0.458679 + 0.888602i \(0.348323\pi\)
−0.998891 + 0.0470733i \(0.985011\pi\)
\(110\) 7.67448 13.2926i 0.731733 1.26740i
\(111\) 0 0
\(112\) 0 0
\(113\) 8.51501 + 4.91614i 0.801024 + 0.462472i 0.843829 0.536612i \(-0.180296\pi\)
−0.0428049 + 0.999083i \(0.513629\pi\)
\(114\) 0 0
\(115\) 24.3316i 2.26893i
\(116\) 2.50079 + 1.44383i 0.232192 + 0.134056i
\(117\) 0 0
\(118\) 0.0211346i 0.00194560i
\(119\) 0 0
\(120\) 0 0
\(121\) −4.56002 −0.414548
\(122\) 1.23456 + 2.13832i 0.111772 + 0.193594i
\(123\) 0 0
\(124\) 3.04125 + 1.75587i 0.273112 + 0.157682i
\(125\) −20.0033 −1.78915
\(126\) 0 0
\(127\) 2.94462 0.261293 0.130646 0.991429i \(-0.458295\pi\)
0.130646 + 0.991429i \(0.458295\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −5.54191 9.59886i −0.486057 0.841876i
\(131\) −15.0651 −1.31624 −0.658122 0.752911i \(-0.728649\pi\)
−0.658122 + 0.752911i \(0.728649\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 13.4493i 1.16184i
\(135\) 0 0
\(136\) 0.642692 + 0.371058i 0.0551104 + 0.0318180i
\(137\) 15.7199i 1.34305i 0.740984 + 0.671523i \(0.234359\pi\)
−0.740984 + 0.671523i \(0.765641\pi\)
\(138\) 0 0
\(139\) −2.86373 1.65337i −0.242898 0.140237i 0.373610 0.927586i \(-0.378120\pi\)
−0.616508 + 0.787349i \(0.711453\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0.971521 1.68272i 0.0815282 0.141211i
\(143\) −5.61811 + 9.73085i −0.469810 + 0.813735i
\(144\) 0 0
\(145\) −9.73085 + 5.61811i −0.808103 + 0.466559i
\(146\) −2.42743 4.20443i −0.200896 0.347961i
\(147\) 0 0
\(148\) 1.50079 2.59944i 0.123364 0.213673i
\(149\) 11.0016i 0.901284i 0.892705 + 0.450642i \(0.148805\pi\)
−0.892705 + 0.450642i \(0.851195\pi\)
\(150\) 0 0
\(151\) −1.43998 −0.117184 −0.0585918 0.998282i \(-0.518661\pi\)
−0.0585918 + 0.998282i \(0.518661\pi\)
\(152\) −0.892369 1.54563i −0.0723807 0.125367i
\(153\) 0 0
\(154\) 0 0
\(155\) −11.8339 + 6.83228i −0.950518 + 0.548782i
\(156\) 0 0
\(157\) 14.3822 8.30354i 1.14782 0.662695i 0.199465 0.979905i \(-0.436079\pi\)
0.948355 + 0.317210i \(0.102746\pi\)
\(158\) 3.14898 1.81806i 0.250519 0.144637i
\(159\) 0 0
\(160\) −3.36980 + 1.94556i −0.266406 + 0.153810i
\(161\) 0 0
\(162\) 0 0
\(163\) 6.19773 + 10.7348i 0.485444 + 0.840813i 0.999860 0.0167274i \(-0.00532476\pi\)
−0.514416 + 0.857541i \(0.671991\pi\)
\(164\) −10.4941 −0.819452
\(165\) 0 0
\(166\) 8.05995i 0.625574i
\(167\) −5.86087 + 10.1513i −0.453528 + 0.785534i −0.998602 0.0528541i \(-0.983168\pi\)
0.545074 + 0.838388i \(0.316502\pi\)
\(168\) 0 0
\(169\) −2.44304 4.23147i −0.187926 0.325498i
\(170\) −2.50079 + 1.44383i −0.191802 + 0.110737i
\(171\) 0 0
\(172\) −0.471521 + 0.816699i −0.0359532 + 0.0622727i
\(173\) −8.38548 + 14.5241i −0.637536 + 1.10425i 0.348435 + 0.937333i \(0.386713\pi\)
−0.985972 + 0.166913i \(0.946620\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3.41614 + 1.97231i 0.257501 + 0.148668i
\(177\) 0 0
\(178\) 9.26646i 0.694551i
\(179\) −5.00158 2.88766i −0.373835 0.215834i 0.301297 0.953530i \(-0.402580\pi\)
−0.675133 + 0.737696i \(0.735914\pi\)
\(180\) 0 0
\(181\) 5.53310i 0.411272i −0.978629 0.205636i \(-0.934074\pi\)
0.978629 0.205636i \(-0.0659263\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −6.25311 −0.460985
\(185\) 5.83974 + 10.1147i 0.429346 + 0.743649i
\(186\) 0 0
\(187\) 2.53518 + 1.46368i 0.185390 + 0.107035i
\(188\) 2.18525 0.159376
\(189\) 0 0
\(190\) 6.94462 0.503816
\(191\) −5.38124 3.10686i −0.389373 0.224805i 0.292515 0.956261i \(-0.405508\pi\)
−0.681888 + 0.731456i \(0.738841\pi\)
\(192\) 0 0
\(193\) 3.90271 + 6.75970i 0.280923 + 0.486574i 0.971612 0.236578i \(-0.0760260\pi\)
−0.690689 + 0.723152i \(0.742693\pi\)
\(194\) 18.8196 1.35117
\(195\) 0 0
\(196\) 0 0
\(197\) 12.7737i 0.910092i −0.890468 0.455046i \(-0.849623\pi\)
0.890468 0.455046i \(-0.150377\pi\)
\(198\) 0 0
\(199\) 1.56925 + 0.906005i 0.111241 + 0.0642250i 0.554588 0.832125i \(-0.312876\pi\)
−0.443347 + 0.896350i \(0.646209\pi\)
\(200\) 10.1408i 0.717061i
\(201\) 0 0
\(202\) 7.17206 + 4.14079i 0.504624 + 0.291345i
\(203\) 0 0
\(204\) 0 0
\(205\) 20.4169 35.3631i 1.42598 2.46986i
\(206\) −8.52435 + 14.7646i −0.593919 + 1.02870i
\(207\) 0 0
\(208\) 2.46687 1.42425i 0.171047 0.0987537i
\(209\) −3.52006 6.09692i −0.243487 0.421732i
\(210\) 0 0
\(211\) −1.88766 + 3.26953i −0.129952 + 0.225083i −0.923658 0.383218i \(-0.874816\pi\)
0.793706 + 0.608302i \(0.208149\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 14.3369 0.980052
\(215\) −1.83474 3.17787i −0.125128 0.216729i
\(216\) 0 0
\(217\) 0 0
\(218\) 9.76874 5.63998i 0.661622 0.381988i
\(219\) 0 0
\(220\) −13.2926 + 7.67448i −0.896187 + 0.517414i
\(221\) 1.83070 1.05696i 0.123146 0.0710987i
\(222\) 0 0
\(223\) −11.0662 + 6.38910i −0.741051 + 0.427846i −0.822451 0.568836i \(-0.807394\pi\)
0.0814006 + 0.996681i \(0.474061\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −4.91614 8.51501i −0.327017 0.566410i
\(227\) 19.9822 1.32627 0.663133 0.748502i \(-0.269227\pi\)
0.663133 + 0.748502i \(0.269227\pi\)
\(228\) 0 0
\(229\) 10.1314i 0.669500i 0.942307 + 0.334750i \(0.108652\pi\)
−0.942307 + 0.334750i \(0.891348\pi\)
\(230\) 12.1658 21.0718i 0.802188 1.38943i
\(231\) 0 0
\(232\) −1.44383 2.50079i −0.0947921 0.164185i
\(233\) −6.33070 + 3.65503i −0.414738 + 0.239449i −0.692824 0.721107i \(-0.743634\pi\)
0.278085 + 0.960556i \(0.410300\pi\)
\(234\) 0 0
\(235\) −4.25153 + 7.36387i −0.277339 + 0.480366i
\(236\) −0.0105673 + 0.0183031i −0.000687873 + 0.00119143i
\(237\) 0 0
\(238\) 0 0
\(239\) −7.28317 4.20494i −0.471109 0.271995i 0.245595 0.969373i \(-0.421017\pi\)
−0.716704 + 0.697378i \(0.754350\pi\)
\(240\) 0 0
\(241\) 8.95213i 0.576657i 0.957531 + 0.288329i \(0.0930996\pi\)
−0.957531 + 0.288329i \(0.906900\pi\)
\(242\) 3.94910 + 2.28001i 0.253858 + 0.146565i
\(243\) 0 0
\(244\) 2.46911i 0.158069i
\(245\) 0 0
\(246\) 0 0
\(247\) −5.08381 −0.323475
\(248\) −1.75587 3.04125i −0.111498 0.193120i
\(249\) 0 0
\(250\) 17.3234 + 10.0017i 1.09563 + 0.632561i
\(251\) 12.6432 0.798033 0.399017 0.916944i \(-0.369352\pi\)
0.399017 + 0.916944i \(0.369352\pi\)
\(252\) 0 0
\(253\) −24.6661 −1.55075
\(254\) −2.55012 1.47231i −0.160008 0.0923809i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 16.3066 1.01718 0.508588 0.861010i \(-0.330168\pi\)
0.508588 + 0.861010i \(0.330168\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 11.0838i 0.687389i
\(261\) 0 0
\(262\) 13.0468 + 7.53255i 0.806032 + 0.465363i
\(263\) 23.7215i 1.46273i −0.681985 0.731366i \(-0.738883\pi\)
0.681985 0.731366i \(-0.261117\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 6.72463 11.6474i 0.410772 0.711478i
\(269\) −3.64144 + 6.30716i −0.222022 + 0.384554i −0.955422 0.295244i \(-0.904599\pi\)
0.733400 + 0.679798i \(0.237932\pi\)
\(270\) 0 0
\(271\) −19.6483 + 11.3440i −1.19355 + 0.689097i −0.959110 0.283033i \(-0.908659\pi\)
−0.234441 + 0.972130i \(0.575326\pi\)
\(272\) −0.371058 0.642692i −0.0224987 0.0389689i
\(273\) 0 0
\(274\) 7.85997 13.6139i 0.474838 0.822444i
\(275\) 40.0015i 2.41218i
\(276\) 0 0
\(277\) 24.1676 1.45209 0.726046 0.687646i \(-0.241356\pi\)
0.726046 + 0.687646i \(0.241356\pi\)
\(278\) 1.65337 + 2.86373i 0.0991628 + 0.171755i
\(279\) 0 0
\(280\) 0 0
\(281\) 4.11229 2.37423i 0.245319 0.141635i −0.372300 0.928112i \(-0.621431\pi\)
0.617619 + 0.786478i \(0.288097\pi\)
\(282\) 0 0
\(283\) −25.4484 + 14.6926i −1.51275 + 0.873387i −0.512861 + 0.858471i \(0.671415\pi\)
−0.999889 + 0.0149153i \(0.995252\pi\)
\(284\) −1.68272 + 0.971521i −0.0998513 + 0.0576492i
\(285\) 0 0
\(286\) 9.73085 5.61811i 0.575398 0.332206i
\(287\) 0 0
\(288\) 0 0
\(289\) 8.22463 + 14.2455i 0.483802 + 0.837969i
\(290\) 11.2362 0.659814
\(291\) 0 0
\(292\) 4.85486i 0.284109i
\(293\) 3.31206 5.73666i 0.193493 0.335139i −0.752913 0.658121i \(-0.771352\pi\)
0.946405 + 0.322981i \(0.104685\pi\)
\(294\) 0 0
\(295\) −0.0411186 0.0712195i −0.00239402 0.00414656i
\(296\) −2.59944 + 1.50079i −0.151090 + 0.0872316i
\(297\) 0 0
\(298\) 5.50079 9.52765i 0.318652 0.551922i
\(299\) −8.90597 + 15.4256i −0.515046 + 0.892085i
\(300\) 0 0
\(301\) 0 0
\(302\) 1.24706 + 0.719988i 0.0717600 + 0.0414307i
\(303\) 0 0
\(304\) 1.78474i 0.102362i
\(305\) 8.32043 + 4.80380i 0.476426 + 0.275065i
\(306\) 0 0
\(307\) 21.7242i 1.23987i 0.784655 + 0.619933i \(0.212840\pi\)
−0.784655 + 0.619933i \(0.787160\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 13.6646 0.776095
\(311\) 3.14900 + 5.45422i 0.178563 + 0.309281i 0.941389 0.337324i \(-0.109522\pi\)
−0.762825 + 0.646605i \(0.776188\pi\)
\(312\) 0 0
\(313\) −19.2423 11.1095i −1.08764 0.627948i −0.154691 0.987963i \(-0.549438\pi\)
−0.932946 + 0.360015i \(0.882771\pi\)
\(314\) −16.6071 −0.937192
\(315\) 0 0
\(316\) −3.63613 −0.204548
\(317\) 13.5632 + 7.83070i 0.761784 + 0.439816i 0.829936 0.557859i \(-0.188377\pi\)
−0.0681519 + 0.997675i \(0.521710\pi\)
\(318\) 0 0
\(319\) −5.69536 9.86466i −0.318879 0.552315i
\(320\) 3.89111 0.217520
\(321\) 0 0
\(322\) 0 0
\(323\) 1.32448i 0.0736963i
\(324\) 0 0
\(325\) −25.0159 14.4430i −1.38763 0.801151i
\(326\) 12.3955i 0.686521i
\(327\) 0 0
\(328\) 9.08816 + 5.24705i 0.501810 + 0.289720i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.636129 + 1.10181i −0.0349648 + 0.0605608i −0.882978 0.469414i \(-0.844465\pi\)
0.848013 + 0.529975i \(0.177799\pi\)
\(332\) 4.02998 6.98012i 0.221174 0.383084i
\(333\) 0 0
\(334\) 10.1513 5.86087i 0.555456 0.320693i
\(335\) 26.1663 + 45.3214i 1.42962 + 2.47617i
\(336\) 0 0
\(337\) −3.78001 + 6.54717i −0.205910 + 0.356647i −0.950422 0.310962i \(-0.899349\pi\)
0.744512 + 0.667609i \(0.232682\pi\)
\(338\) 4.88608i 0.265768i
\(339\) 0 0
\(340\) 2.88766 0.156605
\(341\) −6.92623 11.9966i −0.375076 0.649651i
\(342\) 0 0
\(343\) 0 0
\(344\) 0.816699 0.471521i 0.0440334 0.0254227i
\(345\) 0 0
\(346\) 14.5241 8.38548i 0.780820 0.450806i
\(347\) 19.1470 11.0545i 1.02787 0.593439i 0.111494 0.993765i \(-0.464436\pi\)
0.916373 + 0.400326i \(0.131103\pi\)
\(348\) 0 0
\(349\) 12.7682 7.37173i 0.683467 0.394600i −0.117693 0.993050i \(-0.537550\pi\)
0.801160 + 0.598450i \(0.204217\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.97231 3.41614i −0.105124 0.182081i
\(353\) −17.2776 −0.919595 −0.459798 0.888024i \(-0.652078\pi\)
−0.459798 + 0.888024i \(0.652078\pi\)
\(354\) 0 0
\(355\) 7.56060i 0.401275i
\(356\) −4.63323 + 8.02499i −0.245561 + 0.425324i
\(357\) 0 0
\(358\) 2.88766 + 5.00158i 0.152618 + 0.264342i
\(359\) −9.45088 + 5.45647i −0.498799 + 0.287982i −0.728217 0.685346i \(-0.759651\pi\)
0.229419 + 0.973328i \(0.426318\pi\)
\(360\) 0 0
\(361\) −7.90736 + 13.6959i −0.416177 + 0.720839i
\(362\) −2.76655 + 4.79180i −0.145407 + 0.251852i
\(363\) 0 0
\(364\) 0 0
\(365\) −16.3599 9.44541i −0.856318 0.494395i
\(366\) 0 0
\(367\) 35.7272i 1.86494i −0.361242 0.932472i \(-0.617647\pi\)
0.361242 0.932472i \(-0.382353\pi\)
\(368\) 5.41535 + 3.12656i 0.282295 + 0.162983i
\(369\) 0 0
\(370\) 11.6795i 0.607187i
\(371\) 0 0
\(372\) 0 0
\(373\) −32.0600 −1.66001 −0.830003 0.557760i \(-0.811661\pi\)
−0.830003 + 0.557760i \(0.811661\pi\)
\(374\) −1.46368 2.53518i −0.0756853 0.131091i
\(375\) 0 0
\(376\) −1.89248 1.09263i −0.0975974 0.0563479i
\(377\) −8.22549 −0.423634
\(378\) 0 0
\(379\) 34.8891 1.79214 0.896068 0.443918i \(-0.146412\pi\)
0.896068 + 0.443918i \(0.146412\pi\)
\(380\) −6.01422 3.47231i −0.308523 0.178126i
\(381\) 0 0
\(382\) 3.10686 + 5.38124i 0.158961 + 0.275328i
\(383\) 17.5342 0.895957 0.447978 0.894044i \(-0.352144\pi\)
0.447978 + 0.894044i \(0.352144\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 7.80542i 0.397286i
\(387\) 0 0
\(388\) −16.2983 9.40980i −0.827418 0.477710i
\(389\) 7.62171i 0.386436i 0.981156 + 0.193218i \(0.0618925\pi\)
−0.981156 + 0.193218i \(0.938108\pi\)
\(390\) 0 0
\(391\) 4.01882 + 2.32027i 0.203241 + 0.117341i
\(392\) 0 0
\(393\) 0 0
\(394\) −6.38687 + 11.0624i −0.321766 + 0.557315i
\(395\) 7.07430 12.2530i 0.355947 0.616517i
\(396\) 0 0
\(397\) 32.6032 18.8234i 1.63631 0.944722i 0.654216 0.756307i \(-0.272999\pi\)
0.982090 0.188414i \(-0.0603348\pi\)
\(398\) −0.906005 1.56925i −0.0454139 0.0786592i
\(399\) 0 0
\(400\) −5.07039 + 8.78217i −0.253519 + 0.439108i
\(401\) 21.4415i 1.07074i 0.844619 + 0.535368i \(0.179827\pi\)
−0.844619 + 0.535368i \(0.820173\pi\)
\(402\) 0 0
\(403\) −10.0032 −0.498293
\(404\) −4.14079 7.17206i −0.206012 0.356823i
\(405\) 0 0
\(406\) 0 0
\(407\) −10.2538 + 5.92004i −0.508262 + 0.293445i
\(408\) 0 0
\(409\) −25.6086 + 14.7851i −1.26627 + 0.731079i −0.974279 0.225344i \(-0.927649\pi\)
−0.291986 + 0.956423i \(0.594316\pi\)
\(410\) −35.3631 + 20.4169i −1.74646 + 1.00832i
\(411\) 0 0
\(412\) 14.7646 8.52435i 0.727400 0.419964i
\(413\) 0 0
\(414\) 0 0
\(415\) 15.6811 + 27.1605i 0.769755 + 1.33325i
\(416\) −2.84849 −0.139659
\(417\) 0 0
\(418\) 7.04011i 0.344343i
\(419\) 3.56481 6.17443i 0.174152 0.301641i −0.765715 0.643180i \(-0.777615\pi\)
0.939868 + 0.341539i \(0.110948\pi\)
\(420\) 0 0
\(421\) −2.31007 4.00115i −0.112586 0.195004i 0.804226 0.594323i \(-0.202580\pi\)
−0.916812 + 0.399319i \(0.869247\pi\)
\(422\) 3.26953 1.88766i 0.159158 0.0918899i
\(423\) 0 0
\(424\) 0 0
\(425\) −3.76282 + 6.51739i −0.182524 + 0.316140i
\(426\) 0 0
\(427\) 0 0
\(428\) −12.4161 7.16846i −0.600157 0.346501i
\(429\) 0 0
\(430\) 3.66949i 0.176958i
\(431\) −3.47078 2.00385i −0.167181 0.0965223i 0.414075 0.910243i \(-0.364105\pi\)
−0.581256 + 0.813721i \(0.697439\pi\)
\(432\) 0 0
\(433\) 29.4125i 1.41348i −0.707475 0.706738i \(-0.750166\pi\)
0.707475 0.706738i \(-0.249834\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −11.2800 −0.540212
\(437\) −5.58008 9.66498i −0.266931 0.462339i
\(438\) 0 0
\(439\) 18.5130 + 10.6885i 0.883575 + 0.510133i 0.871836 0.489799i \(-0.162930\pi\)
0.0117398 + 0.999931i \(0.496263\pi\)
\(440\) 15.3490 0.731733
\(441\) 0 0
\(442\) −2.11392 −0.100549
\(443\) 5.05227 + 2.91693i 0.240041 + 0.138587i 0.615195 0.788375i \(-0.289077\pi\)
−0.375155 + 0.926962i \(0.622410\pi\)
\(444\) 0 0
\(445\) −18.0284 31.2262i −0.854630 1.48026i
\(446\) 12.7782 0.605065
\(447\) 0 0
\(448\) 0 0
\(449\) 22.5823i 1.06573i 0.846202 + 0.532863i \(0.178884\pi\)
−0.846202 + 0.532863i \(0.821116\pi\)
\(450\) 0 0
\(451\) 35.8493 + 20.6976i 1.68808 + 0.974613i
\(452\) 9.83228i 0.462472i
\(453\) 0 0
\(454\) −17.3051 9.99110i −0.812168 0.468906i
\(455\) 0 0
\(456\) 0 0
\(457\) −19.9311 + 34.5218i −0.932340 + 1.61486i −0.153029 + 0.988222i \(0.548903\pi\)
−0.779310 + 0.626638i \(0.784430\pi\)
\(458\) 5.06568 8.77402i 0.236704 0.409983i
\(459\) 0 0
\(460\) −21.0718 + 12.1658i −0.982476 + 0.567233i
\(461\) 3.68254 + 6.37834i 0.171513 + 0.297069i 0.938949 0.344056i \(-0.111801\pi\)
−0.767436 + 0.641125i \(0.778468\pi\)
\(462\) 0 0
\(463\) −14.3457 + 24.8475i −0.666702 + 1.15476i 0.312119 + 0.950043i \(0.398961\pi\)
−0.978821 + 0.204718i \(0.934372\pi\)
\(464\) 2.88766i 0.134056i
\(465\) 0 0
\(466\) 7.31007 0.338632
\(467\) −6.83519 11.8389i −0.316295 0.547839i 0.663417 0.748250i \(-0.269106\pi\)
−0.979712 + 0.200411i \(0.935772\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 7.36387 4.25153i 0.339670 0.196109i
\(471\) 0 0
\(472\) 0.0183031 0.0105673i 0.000842469 0.000486400i
\(473\) 3.22157 1.85997i 0.148128 0.0855216i
\(474\) 0 0
\(475\) 15.6739 9.04931i 0.719166 0.415211i
\(476\) 0 0
\(477\) 0 0
\(478\) 4.20494 + 7.28317i 0.192329 + 0.333124i
\(479\) 10.4107 0.475679 0.237839 0.971304i \(-0.423561\pi\)
0.237839 + 0.971304i \(0.423561\pi\)
\(480\) 0 0
\(481\) 8.54997i 0.389845i
\(482\) 4.47607 7.75277i 0.203879 0.353129i
\(483\) 0 0
\(484\) −2.28001 3.94910i −0.103637 0.179504i
\(485\) 63.4184 36.6146i 2.87968 1.66258i
\(486\) 0 0
\(487\) −1.16925 + 2.02520i −0.0529838 + 0.0917707i −0.891301 0.453412i \(-0.850207\pi\)
0.838317 + 0.545183i \(0.183540\pi\)
\(488\) −1.23456 + 2.13832i −0.0558858 + 0.0967970i
\(489\) 0 0
\(490\) 0 0
\(491\) 29.3448 + 16.9422i 1.32431 + 0.764591i 0.984413 0.175871i \(-0.0562742\pi\)
0.339898 + 0.940462i \(0.389608\pi\)
\(492\) 0 0
\(493\) 2.14298i 0.0965151i
\(494\) 4.40271 + 2.54191i 0.198087 + 0.114366i
\(495\) 0 0
\(496\) 3.51174i 0.157682i
\(497\) 0 0
\(498\) 0 0
\(499\) −16.6045 −0.743317 −0.371659 0.928369i \(-0.621211\pi\)
−0.371659 + 0.928369i \(0.621211\pi\)
\(500\) −10.0017 17.3234i −0.447288 0.774726i
\(501\) 0 0
\(502\) −10.9494 6.32161i −0.488694 0.282147i
\(503\) 35.3661 1.57690 0.788449 0.615100i \(-0.210885\pi\)
0.788449 + 0.615100i \(0.210885\pi\)
\(504\) 0 0
\(505\) 32.2246 1.43398
\(506\) 21.3615 + 12.3331i 0.949635 + 0.548272i
\(507\) 0 0
\(508\) 1.47231 + 2.55012i 0.0653232 + 0.113143i
\(509\) −37.0582 −1.64257 −0.821287 0.570515i \(-0.806744\pi\)
−0.821287 + 0.570515i \(0.806744\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −14.1219 8.15329i −0.622891 0.359626i
\(515\) 66.3384i 2.92322i
\(516\) 0 0
\(517\) −7.46513 4.30999i −0.328316 0.189553i
\(518\) 0 0
\(519\) 0 0
\(520\) 5.54191 9.59886i 0.243029 0.420938i
\(521\) 0.891547 1.54420i 0.0390594 0.0676528i −0.845835 0.533445i \(-0.820897\pi\)
0.884894 + 0.465792i \(0.154231\pi\)
\(522\) 0 0
\(523\) −20.8312 + 12.0269i −0.910886 + 0.525901i −0.880716 0.473644i \(-0.842938\pi\)
−0.0301702 + 0.999545i \(0.509605\pi\)
\(524\) −7.53255 13.0468i −0.329061 0.569950i
\(525\) 0 0
\(526\) −11.8608 + 20.5434i −0.517154 + 0.895737i
\(527\) 2.60612i 0.113524i
\(528\) 0 0
\(529\) −16.1014 −0.700060
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 25.8876 14.9462i 1.12132 0.647392i
\(534\) 0 0
\(535\) 48.3126 27.8933i 2.08874 1.20593i
\(536\) −11.6474 + 6.72463i −0.503091 + 0.290460i
\(537\) 0 0
\(538\) 6.30716 3.64144i 0.271921 0.156994i
\(539\) 0 0
\(540\) 0 0
\(541\) −15.0016 25.9835i −0.644968 1.11712i −0.984309 0.176454i \(-0.943537\pi\)
0.339341 0.940664i \(-0.389796\pi\)
\(542\) 22.6879 0.974530
\(543\) 0 0
\(544\) 0.742117i 0.0318180i
\(545\) 21.9458 38.0113i 0.940056 1.62822i
\(546\) 0 0
\(547\) −10.7816 18.6743i −0.460987 0.798454i 0.538023 0.842930i \(-0.319171\pi\)
−0.999010 + 0.0444765i \(0.985838\pi\)
\(548\) −13.6139 + 7.85997i −0.581556 + 0.335761i
\(549\) 0 0
\(550\) −20.0007 + 34.6423i −0.852835 + 1.47715i
\(551\) 2.57686 4.46325i 0.109778 0.190141i
\(552\) 0 0
\(553\) 0 0
\(554\) −20.9298 12.0838i −0.889221 0.513392i
\(555\) 0 0
\(556\) 3.30675i 0.140237i
\(557\) −31.9976 18.4738i −1.35578 0.782762i −0.366731 0.930327i \(-0.619523\pi\)
−0.989052 + 0.147565i \(0.952856\pi\)
\(558\) 0 0
\(559\) 2.68625i 0.113616i
\(560\) 0 0
\(561\) 0 0
\(562\) −4.74847 −0.200302
\(563\) −7.58422 13.1363i −0.319637 0.553627i 0.660776 0.750584i \(-0.270228\pi\)
−0.980412 + 0.196957i \(0.936894\pi\)
\(564\) 0 0
\(565\) −33.1329 19.1293i −1.39391 0.804774i
\(566\) 29.3853 1.23516
\(567\) 0 0
\(568\) 1.94304 0.0815282
\(569\) −31.8084 18.3646i −1.33348 0.769885i −0.347648 0.937625i \(-0.613020\pi\)
−0.985831 + 0.167740i \(0.946353\pi\)
\(570\) 0 0
\(571\) −5.61387 9.72351i −0.234933 0.406916i 0.724320 0.689464i \(-0.242154\pi\)
−0.959253 + 0.282548i \(0.908820\pi\)
\(572\) −11.2362 −0.469810
\(573\) 0 0
\(574\) 0 0
\(575\) 63.4114i 2.64444i
\(576\) 0 0
\(577\) −31.6545 18.2757i −1.31780 0.760829i −0.334422 0.942424i \(-0.608541\pi\)
−0.983374 + 0.181594i \(0.941874\pi\)
\(578\) 16.4493i 0.684199i
\(579\) 0 0
\(580\) −9.73085 5.61811i −0.404052 0.233279i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 2.42743 4.20443i 0.100448 0.173981i
\(585\) 0 0
\(586\) −5.73666 + 3.31206i −0.236979 + 0.136820i
\(587\) −4.99738 8.65571i −0.206264 0.357259i 0.744271 0.667878i \(-0.232797\pi\)
−0.950535 + 0.310619i \(0.899464\pi\)
\(588\) 0 0
\(589\) 3.13376 5.42784i 0.129124 0.223650i
\(590\) 0.0822372i 0.00338565i
\(591\) 0 0
\(592\) 3.00158 0.123364
\(593\) 3.89111 + 6.73961i 0.159789 + 0.276763i 0.934792 0.355194i \(-0.115585\pi\)
−0.775004 + 0.631957i \(0.782252\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −9.52765 + 5.50079i −0.390268 + 0.225321i
\(597\) 0 0
\(598\) 15.4256 8.90597i 0.630800 0.364192i
\(599\) 21.6614 12.5062i 0.885061 0.510990i 0.0127373 0.999919i \(-0.495945\pi\)
0.872324 + 0.488929i \(0.162612\pi\)
\(600\) 0 0
\(601\) 25.9925 15.0068i 1.06026 0.612139i 0.134753 0.990879i \(-0.456976\pi\)
0.925503 + 0.378740i \(0.123643\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −0.719988 1.24706i −0.0292959 0.0507420i
\(605\) 17.7436 0.721379
\(606\) 0 0
\(607\) 4.58280i 0.186010i −0.995666 0.0930050i \(-0.970353\pi\)
0.995666 0.0930050i \(-0.0296473\pi\)
\(608\) 0.892369 1.54563i 0.0361903 0.0626835i
\(609\) 0 0
\(610\) −4.80380 8.32043i −0.194500 0.336884i
\(611\) −5.39073 + 3.11234i −0.218085 + 0.125912i
\(612\) 0 0
\(613\) −15.2761 + 26.4590i −0.616996 + 1.06867i 0.373034 + 0.927818i \(0.378317\pi\)
−0.990031 + 0.140852i \(0.955016\pi\)
\(614\) 10.8621 18.8137i 0.438359 0.759259i
\(615\) 0 0
\(616\) 0 0
\(617\) 28.2484 + 16.3092i 1.13724 + 0.656585i 0.945745 0.324909i \(-0.105334\pi\)
0.191493 + 0.981494i \(0.438667\pi\)
\(618\) 0 0
\(619\) 20.0045i 0.804049i −0.915629 0.402024i \(-0.868307\pi\)
0.915629 0.402024i \(-0.131693\pi\)
\(620\) −11.8339 6.83228i −0.475259 0.274391i
\(621\) 0 0
\(622\) 6.29800i 0.252527i
\(623\) 0 0
\(624\) 0 0
\(625\) 27.1314 1.08526
\(626\) 11.1095 + 19.2423i 0.444026 + 0.769076i
\(627\) 0 0
\(628\) 14.3822 + 8.30354i 0.573910 + 0.331347i
\(629\) 2.22752 0.0888171
\(630\) 0 0
\(631\) 6.09634 0.242692 0.121346 0.992610i \(-0.461279\pi\)
0.121346 + 0.992610i \(0.461279\pi\)
\(632\) 3.14898 + 1.81806i 0.125260 + 0.0723187i
\(633\) 0 0
\(634\) −7.83070 13.5632i −0.310997 0.538663i
\(635\) −11.4579 −0.454691
\(636\) 0 0
\(637\) 0 0
\(638\) 11.3907i 0.450963i
\(639\) 0 0
\(640\) −3.36980 1.94556i −0.133203 0.0769049i
\(641\) 33.4415i 1.32086i −0.750888 0.660429i \(-0.770374\pi\)
0.750888 0.660429i \(-0.229626\pi\)
\(642\) 0 0
\(643\) −16.6022 9.58527i −0.654726 0.378006i 0.135539 0.990772i \(-0.456724\pi\)
−0.790264 + 0.612766i \(0.790057\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.662242 1.14704i 0.0260556 0.0451296i
\(647\) 22.3025 38.6290i 0.876800 1.51866i 0.0219681 0.999759i \(-0.493007\pi\)
0.854832 0.518904i \(-0.173660\pi\)
\(648\) 0 0
\(649\) 0.0721988 0.0416840i 0.00283405 0.00163624i
\(650\) 14.4430 + 25.0159i 0.566500 + 0.981206i
\(651\) 0 0
\(652\) −6.19773 + 10.7348i −0.242722 + 0.420407i
\(653\) 0.652123i 0.0255195i −0.999919 0.0127598i \(-0.995938\pi\)
0.999919 0.0127598i \(-0.00406167\pi\)
\(654\) 0 0
\(655\) 58.6200 2.29047
\(656\) −5.24705 9.08816i −0.204863 0.354833i
\(657\) 0 0
\(658\) 0 0
\(659\) −26.2738 + 15.1692i −1.02348 + 0.590908i −0.915111 0.403202i \(-0.867897\pi\)
−0.108372 + 0.994110i \(0.534564\pi\)
\(660\) 0 0
\(661\) −11.1004 + 6.40881i −0.431755 + 0.249274i −0.700094 0.714051i \(-0.746859\pi\)
0.268339 + 0.963325i \(0.413525\pi\)
\(662\) 1.10181 0.636129i 0.0428230 0.0247239i
\(663\) 0 0
\(664\) −6.98012 + 4.02998i −0.270881 + 0.156393i
\(665\) 0 0
\(666\) 0 0
\(667\) −9.02843 15.6377i −0.349582 0.605494i
\(668\) −11.7217 −0.453528
\(669\) 0 0
\(670\) 52.3326i 2.02179i
\(671\) −4.86986 + 8.43484i −0.187999 + 0.325623i
\(672\) 0 0
\(673\) 11.2246 + 19.4416i 0.432678 + 0.749420i 0.997103 0.0760644i \(-0.0242355\pi\)
−0.564425 + 0.825484i \(0.690902\pi\)
\(674\) 6.54717 3.78001i 0.252188 0.145601i
\(675\) 0 0
\(676\) 2.44304 4.23147i 0.0939632 0.162749i
\(677\) 25.5903 44.3237i 0.983516 1.70350i 0.335163 0.942160i \(-0.391209\pi\)
0.648353 0.761340i \(-0.275458\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −2.50079 1.44383i −0.0959009 0.0553684i
\(681\) 0 0
\(682\) 13.8525i 0.530438i
\(683\) −12.6107 7.28080i −0.482536 0.278592i 0.238937 0.971035i \(-0.423201\pi\)
−0.721473 + 0.692443i \(0.756534\pi\)
\(684\) 0 0
\(685\) 61.1681i 2.33711i
\(686\) 0 0
\(687\) 0 0
\(688\) −0.943042 −0.0359532
\(689\) 0 0
\(690\) 0 0
\(691\) −21.1757 12.2258i −0.805560 0.465090i 0.0398517 0.999206i \(-0.487311\pi\)
−0.845412 + 0.534115i \(0.820645\pi\)
\(692\) −16.7710 −0.637536
\(693\) 0 0
\(694\) −22.1091 −0.839250
\(695\) 11.1431 + 6.43347i 0.422682 + 0.244035i
\(696\) 0 0
\(697\) −3.89393 6.74448i −0.147493 0.255465i
\(698\) −14.7435 −0.558048
\(699\) 0 0
\(700\) 0 0
\(701\) 2.21697i 0.0837337i 0.999123 + 0.0418669i \(0.0133305\pi\)
−0.999123 + 0.0418669i \(0.986669\pi\)
\(702\) 0 0
\(703\) −4.63932 2.67851i −0.174975 0.101022i
\(704\) 3.94462i 0.148668i
\(705\) 0 0
\(706\) 14.9629 + 8.63881i 0.563135 + 0.325126i
\(707\) 0 0
\(708\) 0 0
\(709\) 12.1962 21.1244i 0.458036 0.793342i −0.540821 0.841138i \(-0.681886\pi\)
0.998857 + 0.0477959i \(0.0152197\pi\)
\(710\) −3.78030 + 6.54767i −0.141872 + 0.245730i
\(711\) 0 0
\(712\) 8.02499 4.63323i 0.300749 0.173638i
\(713\) −10.9796 19.0173i −0.411190 0.712203i
\(714\) 0 0
\(715\) 21.8607 37.8639i 0.817544 1.41603i
\(716\) 5.77532i 0.215834i
\(717\) 0 0
\(718\) 10.9129 0.407267
\(719\) 1.11376 + 1.92909i 0.0415363 + 0.0719429i 0.886046 0.463597i \(-0.153441\pi\)
−0.844510 + 0.535540i \(0.820108\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 13.6959 7.90736i 0.509710 0.294281i
\(723\) 0 0
\(724\) 4.79180 2.76655i 0.178086 0.102818i
\(725\) 25.3599 14.6416i 0.941844 0.543774i
\(726\) 0 0
\(727\) −10.4880 + 6.05523i −0.388977 + 0.224576i −0.681717 0.731616i \(-0.738766\pi\)
0.292740 + 0.956192i \(0.405433\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 9.44541 + 16.3599i 0.349590 + 0.605508i
\(731\) −0.699848 −0.0258848
\(732\) 0 0
\(733\) 15.6661i 0.578641i 0.957232 + 0.289321i \(0.0934293\pi\)
−0.957232 + 0.289321i \(0.906571\pi\)
\(734\) −17.8636 + 30.9407i −0.659357 + 1.14204i
\(735\) 0 0
\(736\) −3.12656 5.41535i −0.115246 0.199613i
\(737\) −45.9446 + 26.5261i −1.69239 + 0.977102i
\(738\) 0 0
\(739\) 4.05227 7.01874i 0.149065 0.258188i −0.781817 0.623508i \(-0.785707\pi\)
0.930882 + 0.365319i \(0.119040\pi\)
\(740\) −5.83974 + 10.1147i −0.214673 + 0.371825i
\(741\) 0 0
\(742\) 0 0
\(743\) 10.5429 + 6.08697i 0.386783 + 0.223309i 0.680765 0.732502i \(-0.261647\pi\)
−0.293982 + 0.955811i \(0.594981\pi\)
\(744\) 0 0
\(745\) 42.8084i 1.56838i
\(746\) 27.7648 + 16.0300i 1.01654 + 0.586900i
\(747\) 0 0
\(748\) 2.92737i 0.107035i
\(749\) 0 0
\(750\) 0 0
\(751\) 34.6123 1.26302 0.631511 0.775367i \(-0.282435\pi\)
0.631511 + 0.775367i \(0.282435\pi\)
\(752\) 1.09263 + 1.89248i 0.0398440 + 0.0690118i
\(753\) 0 0
\(754\) 7.12348 + 4.11274i 0.259422 + 0.149777i
\(755\) 5.60311 0.203918
\(756\) 0 0
\(757\) −39.0553 −1.41949 −0.709744 0.704459i \(-0.751190\pi\)
−0.709744 + 0.704459i \(0.751190\pi\)
\(758\) −30.2149 17.4446i −1.09745 0.633615i
\(759\) 0 0
\(760\) 3.47231 + 6.01422i 0.125954 + 0.218159i
\(761\) −10.2252 −0.370665 −0.185332 0.982676i \(-0.559336\pi\)
−0.185332 + 0.982676i \(0.559336\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 6.21372i 0.224805i
\(765\) 0 0
\(766\) −15.1851 8.76711i −0.548659 0.316769i
\(767\) 0.0602018i 0.00217376i
\(768\) 0 0
\(769\) 26.6746 + 15.4006i 0.961910 + 0.555359i 0.896760 0.442517i \(-0.145914\pi\)
0.0651494 + 0.997876i \(0.479248\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −3.90271 + 6.75970i −0.140462 + 0.243287i
\(773\) 17.8916 30.9892i 0.643518 1.11461i −0.341124 0.940018i \(-0.610808\pi\)
0.984642 0.174587i \(-0.0558590\pi\)
\(774\) 0 0
\(775\) 30.8406 17.8059i 1.10783 0.639605i
\(776\) 9.40980 + 16.2983i 0.337792 + 0.585073i
\(777\) 0 0
\(778\) 3.81086 6.60060i 0.136626 0.236643i
\(779\) 18.7292i 0.671044i
\(780\) 0 0
\(781\) 7.66456 0.274260
\(782\) −2.32027 4.01882i −0.0829727 0.143713i
\(783\) 0 0
\(784\) 0 0
\(785\) −55.9626 + 32.3100i −1.99739 + 1.15319i
\(786\) 0 0
\(787\) 13.2859 7.67064i 0.473592 0.273429i −0.244150 0.969737i \(-0.578509\pi\)
0.717742 + 0.696309i \(0.245176\pi\)
\(788\) 11.0624 6.38687i 0.394081 0.227523i
\(789\) 0 0
\(790\) −12.2530 + 7.07430i −0.435944 + 0.251692i
\(791\) 0 0
\(792\) 0 0
\(793\) 3.51663 + 6.09098i 0.124879 + 0.216297i
\(794\) −37.6469 −1.33604
\(795\) 0 0
\(796\) 1.81201i 0.0642250i
\(797\) −17.5200 + 30.3455i −0.620590 + 1.07489i 0.368786 + 0.929514i \(0.379774\pi\)
−0.989376 + 0.145379i \(0.953560\pi\)
\(798\) 0 0
\(799\) 0.810856 + 1.40444i 0.0286860 + 0.0496857i
\(800\) 8.78217 5.07039i 0.310496 0.179265i
\(801\) 0 0
\(802\) 10.7207 18.5689i 0.378562 0.655689i
\(803\) 9.57529 16.5849i 0.337905 0.585268i
\(804\) 0 0
\(805\) 0 0
\(806\) 8.66299 + 5.00158i 0.305141 + 0.176173i
\(807\) 0 0
\(808\) 8.28158i 0.291345i
\(809\) 23.6360 + 13.6462i 0.830997 + 0.479777i 0.854194 0.519954i \(-0.174051\pi\)
−0.0231967 + 0.999731i \(0.507384\pi\)
\(810\) 0 0
\(811\) 27.7628i 0.974883i 0.873156 + 0.487442i \(0.162070\pi\)
−0.873156 + 0.487442i \(0.837930\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 11.8401 0.414995
\(815\) −24.1161 41.7703i −0.844749 1.46315i
\(816\) 0 0
\(817\) 1.45759 + 0.841542i 0.0509947 + 0.0294418i
\(818\) 29.5703 1.03390
\(819\) 0 0
\(820\) 40.8338 1.42598
\(821\) −38.4968 22.2262i −1.34355 0.775698i −0.356223 0.934401i \(-0.615936\pi\)
−0.987326 + 0.158703i \(0.949269\pi\)
\(822\) 0 0
\(823\) 25.5577 + 44.2672i 0.890884 + 1.54306i 0.838818 + 0.544413i \(0.183247\pi\)
0.0520663 + 0.998644i \(0.483419\pi\)
\(824\) −17.0487 −0.593919
\(825\) 0 0
\(826\) 0 0
\(827\) 14.5414i 0.505653i 0.967512 + 0.252826i \(0.0813601\pi\)
−0.967512 + 0.252826i \(0.918640\pi\)
\(828\) 0 0
\(829\) 24.2211 + 13.9841i 0.841234 + 0.485686i 0.857683 0.514178i \(-0.171903\pi\)
−0.0164497 + 0.999865i \(0.505236\pi\)
\(830\) 31.3622i 1.08860i
\(831\) 0 0
\(832\) 2.46687 + 1.42425i 0.0855233 + 0.0493769i
\(833\) 0 0
\(834\) 0 0
\(835\) 22.8053 39.5000i 0.789211 1.36695i
\(836\) 3.52006 6.09692i 0.121744 0.210866i
\(837\) 0 0
\(838\) −6.17443 + 3.56481i −0.213292 + 0.123144i
\(839\) −0.499354 0.864906i −0.0172396 0.0298599i 0.857277 0.514856i \(-0.172154\pi\)
−0.874517 + 0.484996i \(0.838821\pi\)
\(840\) 0 0
\(841\) −10.3307 + 17.8933i −0.356231 + 0.617011i
\(842\) 4.62014i 0.159220i
\(843\) 0 0
\(844\) −3.77532 −0.129952
\(845\) 9.50616 + 16.4651i 0.327022 + 0.566418i
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 6.51739 3.76282i 0.223545 0.129064i
\(851\) −16.2546 + 9.38460i −0.557200 + 0.321700i
\(852\) 0 0
\(853\) −8.48739 + 4.90020i −0.290603 + 0.167780i −0.638214 0.769859i \(-0.720326\pi\)
0.347611 + 0.937639i \(0.386993\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 7.16846 + 12.4161i 0.245013 + 0.424375i
\(857\) −7.70003 −0.263028 −0.131514 0.991314i \(-0.541984\pi\)
−0.131514 + 0.991314i \(0.541984\pi\)
\(858\) 0 0
\(859\) 18.9396i 0.646210i −0.946363 0.323105i \(-0.895273\pi\)
0.946363 0.323105i \(-0.104727\pi\)
\(860\) 1.83474 3.17787i 0.0625642 0.108364i
\(861\) 0 0
\(862\) 2.00385 + 3.47078i 0.0682515 + 0.118215i
\(863\) −15.1156 + 8.72700i −0.514541 + 0.297070i −0.734698 0.678394i \(-0.762676\pi\)
0.220157 + 0.975464i \(0.429343\pi\)
\(864\) 0 0
\(865\) 32.6289 56.5149i 1.10942 1.92156i
\(866\) −14.7063 + 25.4720i −0.499740 + 0.865574i
\(867\) 0 0
\(868\) 0 0
\(869\) 12.4215 + 7.17157i 0.421371 + 0.243279i
\(870\) 0 0
\(871\) 38.3101i 1.29809i
\(872\) 9.76874 + 5.63998i 0.330811 + 0.190994i
\(873\) 0 0
\(874\) 11.1602i 0.377498i
\(875\) 0 0
\(876\) 0 0
\(877\) 0.392305 0.0132472 0.00662360 0.999978i \(-0.497892\pi\)
0.00662360 + 0.999978i \(0.497892\pi\)
\(878\) −10.6885 18.5130i −0.360718 0.624782i
\(879\) 0 0
\(880\) −13.2926 7.67448i −0.448093 0.258707i
\(881\) 37.0259 1.24744 0.623718 0.781650i \(-0.285622\pi\)
0.623718 + 0.781650i \(0.285622\pi\)
\(882\) 0 0
\(883\) −29.9586 −1.00819 −0.504094 0.863649i \(-0.668174\pi\)
−0.504094 + 0.863649i \(0.668174\pi\)
\(884\) 1.83070 + 1.05696i 0.0615732 + 0.0355493i
\(885\) 0 0
\(886\) −2.91693 5.05227i −0.0979962 0.169734i
\(887\) 28.9859 0.973252 0.486626 0.873610i \(-0.338227\pi\)
0.486626 + 0.873610i \(0.338227\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 36.0569i 1.20863i
\(891\) 0 0
\(892\) −11.0662 6.38910i −0.370525 0.213923i
\(893\) 3.90010i 0.130512i
\(894\) 0 0
\(895\) 19.4617 + 11.2362i 0.650533 + 0.375586i
\(896\) 0 0
\(897\) 0 0
\(898\) 11.2912 19.5569i 0.376791 0.652621i
\(899\) 5.07035 8.78211i 0.169106 0.292900i
\(900\) 0 0
\(901\) 0 0
\(902\) −20.6976 35.8493i −0.689156 1.19365i
\(903\) 0 0
\(904\) 4.91614 8.51501i 0.163508 0.283205i
\(905\) 21.5299i 0.715679i
\(906\) 0 0
\(907\) −3.89546 −0.129347 −0.0646733 0.997906i \(-0.520601\pi\)
−0.0646733 + 0.997906i \(0.520601\pi\)
\(908\) 9.99110 + 17.3051i 0.331566 + 0.574290i
\(909\) 0 0
\(910\) 0 0
\(911\) −1.32768 + 0.766538i −0.0439881 + 0.0253966i −0.521833 0.853048i \(-0.674752\pi\)
0.477845 + 0.878444i \(0.341418\pi\)
\(912\) 0 0
\(913\) −27.5339 + 15.8967i −0.911240 + 0.526105i
\(914\) 34.5218 19.9311i 1.14188 0.659264i
\(915\) 0 0
\(916\) −8.77402 + 5.06568i −0.289902 + 0.167375i
\(917\) 0 0
\(918\) 0 0
\(919\) −14.1266 24.4679i −0.465992 0.807122i 0.533254 0.845955i \(-0.320969\pi\)
−0.999246 + 0.0388335i \(0.987636\pi\)
\(920\) 24.3316 0.802188
\(921\) 0 0
\(922\) 7.36507i 0.242556i
\(923\) 2.76737 4.79323i 0.0910892 0.157771i
\(924\) 0 0
\(925\) −15.2192 26.3603i −0.500403 0.866723i
\(926\) 24.8475 14.3457i 0.816539 0.471429i
\(927\) 0 0
\(928\) 1.44383 2.50079i 0.0473961 0.0820924i
\(929\) 1.64363 2.84685i 0.0539257 0.0934021i −0.837802 0.545974i \(-0.816160\pi\)
0.891728 + 0.452571i \(0.149493\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −6.33070 3.65503i −0.207369 0.119725i
\(933\) 0 0
\(934\) 13.6704i 0.447308i
\(935\) −9.86466 5.69536i −0.322609 0.186258i
\(936\) 0 0
\(937\) 35.5084i 1.16001i −0.814613 0.580005i \(-0.803051\pi\)
0.814613 0.580005i \(-0.196949\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −8.50307 −0.277339
\(941\) 6.24941 + 10.8243i 0.203725 + 0.352862i 0.949726 0.313083i \(-0.101362\pi\)
−0.746001 + 0.665945i \(0.768028\pi\)
\(942\) 0 0
\(943\) 56.8293 + 32.8104i 1.85062 + 1.06845i
\(944\) −0.0211346 −0.000687873
\(945\) 0 0
\(946\) −3.71994 −0.120946
\(947\) 31.2769 + 18.0577i 1.01636 + 0.586796i 0.913048 0.407852i \(-0.133722\pi\)
0.103313 + 0.994649i \(0.467056\pi\)
\(948\) 0 0
\(949\) −6.91452 11.9763i −0.224455 0.388767i
\(950\) −18.0986 −0.587197
\(951\) 0 0
\(952\) 0 0
\(953\) 45.2925i 1.46717i −0.679599 0.733584i \(-0.737846\pi\)
0.679599 0.733584i \(-0.262154\pi\)
\(954\) 0 0
\(955\) 20.9390 + 12.0892i 0.677571 + 0.391196i
\(956\) 8.40988i 0.271995i
\(957\) 0 0
\(958\) −9.01596 5.20537i −0.291293 0.168178i
\(959\) 0 0
\(960\) 0 0
\(961\) −9.33386 + 16.1667i −0.301092 + 0.521507i
\(962\) 4.27499 7.40449i 0.137831 0.238730i
\(963\) 0 0
\(964\) −7.75277 + 4.47607i −0.249700 + 0.144164i
\(965\) −15.1859 26.3028i −0.488851 0.846716i
\(966\) 0 0
\(967\) 12.0000 20.7845i 0.385893 0.668385i −0.606000 0.795465i \(-0.707227\pi\)
0.991893 + 0.127079i \(0.0405602\pi\)
\(968\) 4.56002i 0.146565i
\(969\) 0 0
\(970\) −73.2292 −2.35125
\(971\) 16.6813 + 28.8928i 0.535328 + 0.927215i 0.999147 + 0.0412855i \(0.0131453\pi\)
−0.463819 + 0.885930i \(0.653521\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 2.02520 1.16925i 0.0648917 0.0374652i
\(975\) 0 0
\(976\) 2.13832 1.23456i 0.0684458 0.0395172i
\(977\) −29.8846 + 17.2539i −0.956091 + 0.552000i −0.894968 0.446131i \(-0.852802\pi\)
−0.0611236 + 0.998130i \(0.519468\pi\)
\(978\) 0 0
\(979\) 31.6555 18.2763i 1.01172 0.584114i
\(980\) 0 0
\(981\) 0 0
\(982\) −16.9422 29.3448i −0.540648 0.936429i
\(983\) 2.41302 0.0769633 0.0384817 0.999259i \(-0.487748\pi\)
0.0384817 + 0.999259i \(0.487748\pi\)
\(984\) 0 0
\(985\) 49.7041i 1.58370i
\(986\) 1.07149 1.85588i 0.0341232 0.0591032i
\(987\) 0 0
\(988\) −2.54191 4.40271i −0.0808688 0.140069i
\(989\) 5.10691 2.94847i 0.162390 0.0937560i
\(990\) 0 0
\(991\) −24.2991 + 42.0873i −0.771887 + 1.33695i 0.164641 + 0.986354i \(0.447353\pi\)
−0.936528 + 0.350594i \(0.885980\pi\)
\(992\) 1.75587 3.04125i 0.0557488 0.0965598i
\(993\) 0 0
\(994\) 0 0
\(995\) −6.10612 3.52537i −0.193577 0.111762i
\(996\) 0 0
\(997\) 44.8542i 1.42055i −0.703926 0.710274i \(-0.748571\pi\)
0.703926 0.710274i \(-0.251429\pi\)
\(998\) 14.3799 + 8.30223i 0.455187 + 0.262802i
\(999\) 0 0
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 2646.2.t.a.2285.1 16
3.2 odd 2 882.2.t.b.815.6 16
7.2 even 3 2646.2.l.b.1097.8 16
7.3 odd 6 378.2.m.a.125.5 16
7.4 even 3 378.2.m.a.125.8 16
7.5 odd 6 2646.2.l.b.1097.5 16
7.6 odd 2 inner 2646.2.t.a.2285.4 16
9.2 odd 6 2646.2.l.b.521.1 16
9.7 even 3 882.2.l.a.227.8 16
21.2 odd 6 882.2.l.a.509.1 16
21.5 even 6 882.2.l.a.509.4 16
21.11 odd 6 126.2.m.a.41.4 yes 16
21.17 even 6 126.2.m.a.41.1 16
21.20 even 2 882.2.t.b.815.7 16
28.3 even 6 3024.2.cc.b.881.1 16
28.11 odd 6 3024.2.cc.b.881.8 16
63.2 odd 6 inner 2646.2.t.a.1979.4 16
63.4 even 3 1134.2.d.a.1133.9 16
63.11 odd 6 378.2.m.a.251.5 16
63.16 even 3 882.2.t.b.803.7 16
63.20 even 6 2646.2.l.b.521.4 16
63.25 even 3 126.2.m.a.83.1 yes 16
63.31 odd 6 1134.2.d.a.1133.16 16
63.32 odd 6 1134.2.d.a.1133.8 16
63.34 odd 6 882.2.l.a.227.5 16
63.38 even 6 378.2.m.a.251.8 16
63.47 even 6 inner 2646.2.t.a.1979.1 16
63.52 odd 6 126.2.m.a.83.4 yes 16
63.59 even 6 1134.2.d.a.1133.1 16
63.61 odd 6 882.2.t.b.803.6 16
84.11 even 6 1008.2.cc.b.545.2 16
84.59 odd 6 1008.2.cc.b.545.7 16
252.11 even 6 3024.2.cc.b.2897.1 16
252.115 even 6 1008.2.cc.b.209.2 16
252.151 odd 6 1008.2.cc.b.209.7 16
252.227 odd 6 3024.2.cc.b.2897.8 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.m.a.41.1 16 21.17 even 6
126.2.m.a.41.4 yes 16 21.11 odd 6
126.2.m.a.83.1 yes 16 63.25 even 3
126.2.m.a.83.4 yes 16 63.52 odd 6
378.2.m.a.125.5 16 7.3 odd 6
378.2.m.a.125.8 16 7.4 even 3
378.2.m.a.251.5 16 63.11 odd 6
378.2.m.a.251.8 16 63.38 even 6
882.2.l.a.227.5 16 63.34 odd 6
882.2.l.a.227.8 16 9.7 even 3
882.2.l.a.509.1 16 21.2 odd 6
882.2.l.a.509.4 16 21.5 even 6
882.2.t.b.803.6 16 63.61 odd 6
882.2.t.b.803.7 16 63.16 even 3
882.2.t.b.815.6 16 3.2 odd 2
882.2.t.b.815.7 16 21.20 even 2
1008.2.cc.b.209.2 16 252.115 even 6
1008.2.cc.b.209.7 16 252.151 odd 6
1008.2.cc.b.545.2 16 84.11 even 6
1008.2.cc.b.545.7 16 84.59 odd 6
1134.2.d.a.1133.1 16 63.59 even 6
1134.2.d.a.1133.8 16 63.32 odd 6
1134.2.d.a.1133.9 16 63.4 even 3
1134.2.d.a.1133.16 16 63.31 odd 6
2646.2.l.b.521.1 16 9.2 odd 6
2646.2.l.b.521.4 16 63.20 even 6
2646.2.l.b.1097.5 16 7.5 odd 6
2646.2.l.b.1097.8 16 7.2 even 3
2646.2.t.a.1979.1 16 63.47 even 6 inner
2646.2.t.a.1979.4 16 63.2 odd 6 inner
2646.2.t.a.2285.1 16 1.1 even 1 trivial
2646.2.t.a.2285.4 16 7.6 odd 2 inner
3024.2.cc.b.881.1 16 28.3 even 6
3024.2.cc.b.881.8 16 28.11 odd 6
3024.2.cc.b.2897.1 16 252.11 even 6
3024.2.cc.b.2897.8 16 252.227 odd 6