Properties

Label 756.2.bq.a.25.4
Level $756$
Weight $2$
Character 756.25
Analytic conductor $6.037$
Analytic rank $0$
Dimension $144$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [756,2,Mod(25,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 10, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.bq (of order \(9\), degree \(6\), 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: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 25.4
Character \(\chi\) \(=\) 756.25
Dual form 756.2.bq.a.121.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.47274 + 0.911614i) q^{3} +(-3.21812 - 1.17130i) q^{5} +(-2.64556 + 0.0321766i) q^{7} +(1.33792 - 2.68514i) q^{9} +O(q^{10})\) \(q+(-1.47274 + 0.911614i) q^{3} +(-3.21812 - 1.17130i) q^{5} +(-2.64556 + 0.0321766i) q^{7} +(1.33792 - 2.68514i) q^{9} +(-5.42330 + 1.97392i) q^{11} +(0.660511 + 3.74594i) q^{13} +(5.80722 - 1.20866i) q^{15} +7.51635 q^{17} +3.16859 q^{19} +(3.86688 - 2.45911i) q^{21} +(-1.59042 - 9.01972i) q^{23} +(5.15413 + 4.32483i) q^{25} +(0.477401 + 5.17418i) q^{27} +(0.466529 - 2.64582i) q^{29} +(2.32322 - 1.94941i) q^{31} +(6.18765 - 7.85102i) q^{33} +(8.55140 + 2.99519i) q^{35} +(-0.552756 + 0.957402i) q^{37} +(-4.38761 - 4.91467i) q^{39} +(1.41205 + 8.00811i) q^{41} +(0.468371 + 0.393010i) q^{43} +(-7.45069 + 7.07399i) q^{45} +(-3.75927 - 3.15440i) q^{47} +(6.99793 - 0.170250i) q^{49} +(-11.0696 + 6.85200i) q^{51} +(2.19430 - 3.80063i) q^{53} +19.7649 q^{55} +(-4.66651 + 2.88853i) q^{57} +(0.616398 + 3.49577i) q^{59} +(8.01209 + 6.72295i) q^{61} +(-3.45315 + 7.14673i) q^{63} +(2.26202 - 12.8286i) q^{65} +(4.76497 + 1.73431i) q^{67} +(10.5648 + 11.8338i) q^{69} +(1.16171 + 2.01213i) q^{71} +(-3.39063 - 5.87275i) q^{73} +(-11.5333 - 1.67077i) q^{75} +(14.2841 - 5.39661i) q^{77} +(-6.56596 + 2.38981i) q^{79} +(-5.41994 - 7.18500i) q^{81} +(0.804659 - 4.56345i) q^{83} +(-24.1885 - 8.80390i) q^{85} +(1.72489 + 4.32189i) q^{87} -5.67020 q^{89} +(-1.86795 - 9.88885i) q^{91} +(-1.64438 + 4.98885i) q^{93} +(-10.1969 - 3.71137i) q^{95} +(-6.52694 - 5.47675i) q^{97} +(-1.95570 + 17.2032i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 6 q^{9} + 6 q^{11} - 12 q^{15} + 48 q^{17} + 33 q^{21} - 21 q^{23} + 6 q^{29} + 18 q^{33} - 9 q^{35} + 9 q^{39} - 12 q^{41} - 12 q^{45} + 18 q^{47} - 18 q^{49} - 9 q^{51} + 15 q^{53} + 3 q^{57} - 15 q^{59} - 36 q^{61} + 3 q^{63} + 36 q^{65} + 30 q^{69} - 12 q^{71} + 18 q^{73} - 51 q^{75} - 3 q^{77} + 18 q^{79} - 6 q^{81} - 36 q^{85} + 33 q^{87} + 144 q^{89} + 9 q^{91} + 48 q^{93} - 30 q^{95} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.47274 + 0.911614i −0.850286 + 0.526320i
\(4\) 0 0
\(5\) −3.21812 1.17130i −1.43919 0.523821i −0.499638 0.866234i \(-0.666534\pi\)
−0.939549 + 0.342413i \(0.888756\pi\)
\(6\) 0 0
\(7\) −2.64556 + 0.0321766i −0.999926 + 0.0121616i
\(8\) 0 0
\(9\) 1.33792 2.68514i 0.445974 0.895046i
\(10\) 0 0
\(11\) −5.42330 + 1.97392i −1.63519 + 0.595159i −0.986188 0.165632i \(-0.947034\pi\)
−0.648997 + 0.760791i \(0.724811\pi\)
\(12\) 0 0
\(13\) 0.660511 + 3.74594i 0.183193 + 1.03894i 0.928255 + 0.371943i \(0.121308\pi\)
−0.745063 + 0.666994i \(0.767581\pi\)
\(14\) 0 0
\(15\) 5.80722 1.20866i 1.49942 0.312076i
\(16\) 0 0
\(17\) 7.51635 1.82298 0.911491 0.411320i \(-0.134932\pi\)
0.911491 + 0.411320i \(0.134932\pi\)
\(18\) 0 0
\(19\) 3.16859 0.726924 0.363462 0.931609i \(-0.381595\pi\)
0.363462 + 0.931609i \(0.381595\pi\)
\(20\) 0 0
\(21\) 3.86688 2.45911i 0.843823 0.536622i
\(22\) 0 0
\(23\) −1.59042 9.01972i −0.331625 1.88074i −0.458301 0.888797i \(-0.651542\pi\)
0.126676 0.991944i \(-0.459569\pi\)
\(24\) 0 0
\(25\) 5.15413 + 4.32483i 1.03083 + 0.864966i
\(26\) 0 0
\(27\) 0.477401 + 5.17418i 0.0918758 + 0.995770i
\(28\) 0 0
\(29\) 0.466529 2.64582i 0.0866323 0.491316i −0.910360 0.413817i \(-0.864195\pi\)
0.996992 0.0774991i \(-0.0246935\pi\)
\(30\) 0 0
\(31\) 2.32322 1.94941i 0.417262 0.350124i −0.409858 0.912149i \(-0.634422\pi\)
0.827120 + 0.562025i \(0.189977\pi\)
\(32\) 0 0
\(33\) 6.18765 7.85102i 1.07713 1.36669i
\(34\) 0 0
\(35\) 8.55140 + 2.99519i 1.44545 + 0.506280i
\(36\) 0 0
\(37\) −0.552756 + 0.957402i −0.0908726 + 0.157396i −0.907879 0.419233i \(-0.862299\pi\)
0.817006 + 0.576629i \(0.195632\pi\)
\(38\) 0 0
\(39\) −4.38761 4.91467i −0.702580 0.786976i
\(40\) 0 0
\(41\) 1.41205 + 8.00811i 0.220524 + 1.25066i 0.871059 + 0.491179i \(0.163434\pi\)
−0.650534 + 0.759477i \(0.725455\pi\)
\(42\) 0 0
\(43\) 0.468371 + 0.393010i 0.0714259 + 0.0599335i 0.677802 0.735245i \(-0.262933\pi\)
−0.606376 + 0.795178i \(0.707377\pi\)
\(44\) 0 0
\(45\) −7.45069 + 7.07399i −1.11068 + 1.05453i
\(46\) 0 0
\(47\) −3.75927 3.15440i −0.548346 0.460117i 0.326034 0.945358i \(-0.394287\pi\)
−0.874381 + 0.485241i \(0.838732\pi\)
\(48\) 0 0
\(49\) 6.99793 0.170250i 0.999704 0.0243214i
\(50\) 0 0
\(51\) −11.0696 + 6.85200i −1.55006 + 0.959472i
\(52\) 0 0
\(53\) 2.19430 3.80063i 0.301410 0.522057i −0.675046 0.737776i \(-0.735876\pi\)
0.976456 + 0.215719i \(0.0692094\pi\)
\(54\) 0 0
\(55\) 19.7649 2.66509
\(56\) 0 0
\(57\) −4.66651 + 2.88853i −0.618094 + 0.382595i
\(58\) 0 0
\(59\) 0.616398 + 3.49577i 0.0802482 + 0.455110i 0.998281 + 0.0586062i \(0.0186656\pi\)
−0.918033 + 0.396504i \(0.870223\pi\)
\(60\) 0 0
\(61\) 8.01209 + 6.72295i 1.02584 + 0.860785i 0.990351 0.138585i \(-0.0442554\pi\)
0.0354930 + 0.999370i \(0.488700\pi\)
\(62\) 0 0
\(63\) −3.45315 + 7.14673i −0.435055 + 0.900404i
\(64\) 0 0
\(65\) 2.26202 12.8286i 0.280569 1.59119i
\(66\) 0 0
\(67\) 4.76497 + 1.73431i 0.582133 + 0.211879i 0.616266 0.787538i \(-0.288645\pi\)
−0.0341327 + 0.999417i \(0.510867\pi\)
\(68\) 0 0
\(69\) 10.5648 + 11.8338i 1.27185 + 1.42463i
\(70\) 0 0
\(71\) 1.16171 + 2.01213i 0.137869 + 0.238796i 0.926690 0.375827i \(-0.122641\pi\)
−0.788821 + 0.614623i \(0.789308\pi\)
\(72\) 0 0
\(73\) −3.39063 5.87275i −0.396844 0.687353i 0.596491 0.802620i \(-0.296561\pi\)
−0.993335 + 0.115267i \(0.963228\pi\)
\(74\) 0 0
\(75\) −11.5333 1.67077i −1.33175 0.192924i
\(76\) 0 0
\(77\) 14.2841 5.39661i 1.62783 0.615001i
\(78\) 0 0
\(79\) −6.56596 + 2.38981i −0.738728 + 0.268875i −0.683855 0.729618i \(-0.739698\pi\)
−0.0548735 + 0.998493i \(0.517476\pi\)
\(80\) 0 0
\(81\) −5.41994 7.18500i −0.602215 0.798334i
\(82\) 0 0
\(83\) 0.804659 4.56345i 0.0883228 0.500904i −0.908267 0.418391i \(-0.862594\pi\)
0.996590 0.0825129i \(-0.0262946\pi\)
\(84\) 0 0
\(85\) −24.1885 8.80390i −2.62361 0.954917i
\(86\) 0 0
\(87\) 1.72489 + 4.32189i 0.184927 + 0.463356i
\(88\) 0 0
\(89\) −5.67020 −0.601041 −0.300520 0.953775i \(-0.597160\pi\)
−0.300520 + 0.953775i \(0.597160\pi\)
\(90\) 0 0
\(91\) −1.86795 9.88885i −0.195814 1.03663i
\(92\) 0 0
\(93\) −1.64438 + 4.98885i −0.170515 + 0.517320i
\(94\) 0 0
\(95\) −10.1969 3.71137i −1.04618 0.380779i
\(96\) 0 0
\(97\) −6.52694 5.47675i −0.662710 0.556080i 0.248188 0.968712i \(-0.420165\pi\)
−0.910898 + 0.412632i \(0.864609\pi\)
\(98\) 0 0
\(99\) −1.95570 + 17.2032i −0.196555 + 1.72899i
\(100\) 0 0
\(101\) 1.21160 6.87134i 0.120559 0.683724i −0.863288 0.504712i \(-0.831599\pi\)
0.983847 0.179012i \(-0.0572902\pi\)
\(102\) 0 0
\(103\) 16.6175 + 6.04829i 1.63737 + 0.595955i 0.986577 0.163297i \(-0.0522128\pi\)
0.650797 + 0.759252i \(0.274435\pi\)
\(104\) 0 0
\(105\) −15.3244 + 3.38444i −1.49551 + 0.330288i
\(106\) 0 0
\(107\) −3.72120 6.44530i −0.359742 0.623091i 0.628176 0.778071i \(-0.283802\pi\)
−0.987918 + 0.154981i \(0.950469\pi\)
\(108\) 0 0
\(109\) −2.28310 + 3.95445i −0.218682 + 0.378768i −0.954405 0.298514i \(-0.903509\pi\)
0.735723 + 0.677282i \(0.236842\pi\)
\(110\) 0 0
\(111\) −0.0587150 1.91390i −0.00557298 0.181660i
\(112\) 0 0
\(113\) 6.54391 5.49100i 0.615600 0.516549i −0.280817 0.959761i \(-0.590606\pi\)
0.896417 + 0.443212i \(0.146161\pi\)
\(114\) 0 0
\(115\) −5.44663 + 30.8894i −0.507901 + 2.88045i
\(116\) 0 0
\(117\) 10.9421 + 3.23821i 1.01160 + 0.299373i
\(118\) 0 0
\(119\) −19.8849 + 0.241850i −1.82285 + 0.0221704i
\(120\) 0 0
\(121\) 17.0893 14.3396i 1.55357 1.30360i
\(122\) 0 0
\(123\) −9.37988 10.5066i −0.845755 0.947349i
\(124\) 0 0
\(125\) −2.95931 5.12568i −0.264689 0.458455i
\(126\) 0 0
\(127\) 0.0473743 0.0820547i 0.00420379 0.00728118i −0.863916 0.503636i \(-0.831995\pi\)
0.868120 + 0.496355i \(0.165329\pi\)
\(128\) 0 0
\(129\) −1.04806 0.151828i −0.0922767 0.0133677i
\(130\) 0 0
\(131\) 1.03526 + 5.87122i 0.0904507 + 0.512971i 0.996047 + 0.0888302i \(0.0283128\pi\)
−0.905596 + 0.424141i \(0.860576\pi\)
\(132\) 0 0
\(133\) −8.38268 + 0.101954i −0.726871 + 0.00884057i
\(134\) 0 0
\(135\) 4.52418 17.2103i 0.389379 1.48123i
\(136\) 0 0
\(137\) 10.4972 + 8.80821i 0.896837 + 0.752536i 0.969570 0.244816i \(-0.0787275\pi\)
−0.0727324 + 0.997351i \(0.523172\pi\)
\(138\) 0 0
\(139\) 8.87962 + 3.23192i 0.753160 + 0.274128i 0.689935 0.723871i \(-0.257639\pi\)
0.0632251 + 0.997999i \(0.479861\pi\)
\(140\) 0 0
\(141\) 8.41202 + 1.21861i 0.708420 + 0.102625i
\(142\) 0 0
\(143\) −10.9763 19.0116i −0.917887 1.58983i
\(144\) 0 0
\(145\) −4.60039 + 7.96811i −0.382042 + 0.661716i
\(146\) 0 0
\(147\) −10.1509 + 6.63014i −0.837234 + 0.546845i
\(148\) 0 0
\(149\) 6.94544 5.82792i 0.568993 0.477442i −0.312319 0.949977i \(-0.601106\pi\)
0.881312 + 0.472536i \(0.156661\pi\)
\(150\) 0 0
\(151\) 6.99747 2.54687i 0.569446 0.207261i −0.0412195 0.999150i \(-0.513124\pi\)
0.610665 + 0.791889i \(0.290902\pi\)
\(152\) 0 0
\(153\) 10.0563 20.1824i 0.813002 1.63165i
\(154\) 0 0
\(155\) −9.75974 + 3.55225i −0.783921 + 0.285324i
\(156\) 0 0
\(157\) −2.53840 14.3960i −0.202586 1.14892i −0.901193 0.433418i \(-0.857308\pi\)
0.698607 0.715506i \(-0.253804\pi\)
\(158\) 0 0
\(159\) 0.233083 + 7.59769i 0.0184847 + 0.602536i
\(160\) 0 0
\(161\) 4.49777 + 23.8110i 0.354474 + 1.87657i
\(162\) 0 0
\(163\) 3.03106 + 5.24995i 0.237411 + 0.411207i 0.959971 0.280101i \(-0.0903679\pi\)
−0.722560 + 0.691308i \(0.757035\pi\)
\(164\) 0 0
\(165\) −29.1085 + 18.0179i −2.26609 + 1.40269i
\(166\) 0 0
\(167\) −13.8459 + 11.6181i −1.07143 + 0.899035i −0.995181 0.0980544i \(-0.968738\pi\)
−0.0762466 + 0.997089i \(0.524294\pi\)
\(168\) 0 0
\(169\) −1.37981 + 0.502209i −0.106139 + 0.0386314i
\(170\) 0 0
\(171\) 4.23932 8.50810i 0.324189 0.650631i
\(172\) 0 0
\(173\) 2.57198 14.5864i 0.195544 1.10898i −0.716099 0.697999i \(-0.754074\pi\)
0.911642 0.410984i \(-0.134815\pi\)
\(174\) 0 0
\(175\) −13.7747 11.2757i −1.04127 0.852366i
\(176\) 0 0
\(177\) −4.09458 4.58644i −0.307768 0.344738i
\(178\) 0 0
\(179\) 14.5468 1.08728 0.543640 0.839318i \(-0.317046\pi\)
0.543640 + 0.839318i \(0.317046\pi\)
\(180\) 0 0
\(181\) 3.81925 6.61513i 0.283882 0.491699i −0.688455 0.725279i \(-0.741711\pi\)
0.972338 + 0.233580i \(0.0750441\pi\)
\(182\) 0 0
\(183\) −17.9285 2.59721i −1.32531 0.191991i
\(184\) 0 0
\(185\) 2.90024 2.43359i 0.213230 0.178921i
\(186\) 0 0
\(187\) −40.7634 + 14.8367i −2.98091 + 1.08496i
\(188\) 0 0
\(189\) −1.42948 13.6732i −0.103979 0.994579i
\(190\) 0 0
\(191\) −8.38893 + 3.05332i −0.607001 + 0.220930i −0.627191 0.778866i \(-0.715795\pi\)
0.0201892 + 0.999796i \(0.493573\pi\)
\(192\) 0 0
\(193\) −6.04659 + 5.07369i −0.435243 + 0.365212i −0.833926 0.551877i \(-0.813912\pi\)
0.398683 + 0.917089i \(0.369467\pi\)
\(194\) 0 0
\(195\) 8.36332 + 20.9552i 0.598910 + 1.50063i
\(196\) 0 0
\(197\) 9.61207 16.6486i 0.684832 1.18616i −0.288658 0.957432i \(-0.593209\pi\)
0.973490 0.228731i \(-0.0734576\pi\)
\(198\) 0 0
\(199\) 9.58364 0.679366 0.339683 0.940540i \(-0.389680\pi\)
0.339683 + 0.940540i \(0.389680\pi\)
\(200\) 0 0
\(201\) −8.59857 + 1.78963i −0.606496 + 0.126231i
\(202\) 0 0
\(203\) −1.14910 + 7.01467i −0.0806507 + 0.492333i
\(204\) 0 0
\(205\) 4.83576 27.4250i 0.337744 1.91544i
\(206\) 0 0
\(207\) −26.3470 7.79717i −1.83125 0.541941i
\(208\) 0 0
\(209\) −17.1842 + 6.25454i −1.18866 + 0.432635i
\(210\) 0 0
\(211\) 8.28493 6.95188i 0.570358 0.478587i −0.311407 0.950277i \(-0.600800\pi\)
0.881765 + 0.471689i \(0.156356\pi\)
\(212\) 0 0
\(213\) −3.54518 1.90432i −0.242912 0.130482i
\(214\) 0 0
\(215\) −1.04694 1.81336i −0.0714009 0.123670i
\(216\) 0 0
\(217\) −6.08347 + 5.23203i −0.412973 + 0.355173i
\(218\) 0 0
\(219\) 10.3472 + 5.55808i 0.699199 + 0.375580i
\(220\) 0 0
\(221\) 4.96463 + 28.1558i 0.333957 + 1.89396i
\(222\) 0 0
\(223\) 21.1785 7.70834i 1.41822 0.516188i 0.484686 0.874688i \(-0.338934\pi\)
0.933530 + 0.358500i \(0.116712\pi\)
\(224\) 0 0
\(225\) 18.5086 8.05328i 1.23391 0.536885i
\(226\) 0 0
\(227\) 8.62450 3.13906i 0.572428 0.208347i −0.0395553 0.999217i \(-0.512594\pi\)
0.611983 + 0.790871i \(0.290372\pi\)
\(228\) 0 0
\(229\) −15.2482 + 12.7947i −1.00763 + 0.845500i −0.988023 0.154308i \(-0.950685\pi\)
−0.0196049 + 0.999808i \(0.506241\pi\)
\(230\) 0 0
\(231\) −16.1171 + 20.9694i −1.06043 + 1.37969i
\(232\) 0 0
\(233\) 1.51577 2.62539i 0.0993015 0.171995i −0.812094 0.583526i \(-0.801673\pi\)
0.911396 + 0.411531i \(0.135006\pi\)
\(234\) 0 0
\(235\) 8.40304 + 14.5545i 0.548154 + 0.949430i
\(236\) 0 0
\(237\) 7.49136 9.50519i 0.486616 0.617429i
\(238\) 0 0
\(239\) 7.36486 + 2.68059i 0.476393 + 0.173393i 0.569046 0.822306i \(-0.307313\pi\)
−0.0926532 + 0.995698i \(0.529535\pi\)
\(240\) 0 0
\(241\) 12.2956 + 10.3173i 0.792032 + 0.664594i 0.946248 0.323443i \(-0.104840\pi\)
−0.154215 + 0.988037i \(0.549285\pi\)
\(242\) 0 0
\(243\) 14.5321 + 5.64075i 0.932235 + 0.361854i
\(244\) 0 0
\(245\) −22.7196 7.64879i −1.45150 0.488663i
\(246\) 0 0
\(247\) 2.09289 + 11.8694i 0.133167 + 0.755229i
\(248\) 0 0
\(249\) 2.97505 + 7.45431i 0.188536 + 0.472398i
\(250\) 0 0
\(251\) 7.17868 12.4338i 0.453114 0.784817i −0.545463 0.838135i \(-0.683646\pi\)
0.998578 + 0.0533178i \(0.0169796\pi\)
\(252\) 0 0
\(253\) 26.4295 + 45.7772i 1.66161 + 2.87799i
\(254\) 0 0
\(255\) 43.6491 9.08473i 2.73341 0.568908i
\(256\) 0 0
\(257\) −20.9282 + 17.5609i −1.30547 + 1.09542i −0.316294 + 0.948661i \(0.602439\pi\)
−0.989173 + 0.146756i \(0.953117\pi\)
\(258\) 0 0
\(259\) 1.43154 2.55065i 0.0889517 0.158489i
\(260\) 0 0
\(261\) −6.48021 4.79259i −0.401115 0.296654i
\(262\) 0 0
\(263\) −0.523469 + 2.96874i −0.0322785 + 0.183061i −0.996684 0.0813663i \(-0.974072\pi\)
0.964406 + 0.264427i \(0.0851828\pi\)
\(264\) 0 0
\(265\) −11.5132 + 9.66072i −0.707250 + 0.593453i
\(266\) 0 0
\(267\) 8.35073 5.16904i 0.511057 0.316340i
\(268\) 0 0
\(269\) −9.19714 + 15.9299i −0.560760 + 0.971264i 0.436671 + 0.899621i \(0.356157\pi\)
−0.997430 + 0.0716428i \(0.977176\pi\)
\(270\) 0 0
\(271\) −8.75087 15.1569i −0.531577 0.920719i −0.999321 0.0368545i \(-0.988266\pi\)
0.467743 0.883864i \(-0.345067\pi\)
\(272\) 0 0
\(273\) 11.7658 + 12.8608i 0.712099 + 0.778374i
\(274\) 0 0
\(275\) −36.4892 13.2810i −2.20038 0.800874i
\(276\) 0 0
\(277\) 2.36810 13.4302i 0.142285 0.806940i −0.827222 0.561876i \(-0.810080\pi\)
0.969507 0.245064i \(-0.0788090\pi\)
\(278\) 0 0
\(279\) −2.12616 8.84632i −0.127290 0.529615i
\(280\) 0 0
\(281\) 7.84240 + 6.58056i 0.467839 + 0.392563i 0.846005 0.533174i \(-0.179001\pi\)
−0.378167 + 0.925737i \(0.623445\pi\)
\(282\) 0 0
\(283\) −10.4426 3.80079i −0.620748 0.225934i 0.0124515 0.999922i \(-0.496036\pi\)
−0.633199 + 0.773989i \(0.718259\pi\)
\(284\) 0 0
\(285\) 18.4007 3.82976i 1.08996 0.226855i
\(286\) 0 0
\(287\) −3.99332 21.1405i −0.235718 1.24788i
\(288\) 0 0
\(289\) 39.4955 2.32326
\(290\) 0 0
\(291\) 14.6052 + 2.11578i 0.856170 + 0.124029i
\(292\) 0 0
\(293\) −11.0729 4.03021i −0.646886 0.235447i −0.00232167 0.999997i \(-0.500739\pi\)
−0.644564 + 0.764550i \(0.722961\pi\)
\(294\) 0 0
\(295\) 2.11095 11.9718i 0.122904 0.697025i
\(296\) 0 0
\(297\) −12.8025 27.1187i −0.742875 1.57359i
\(298\) 0 0
\(299\) 32.7369 11.9152i 1.89322 0.689076i
\(300\) 0 0
\(301\) −1.25175 1.02466i −0.0721495 0.0590604i
\(302\) 0 0
\(303\) 4.47964 + 11.2242i 0.257348 + 0.644814i
\(304\) 0 0
\(305\) −17.9093 31.0198i −1.02548 1.77619i
\(306\) 0 0
\(307\) −2.88732 5.00098i −0.164788 0.285421i 0.771792 0.635875i \(-0.219361\pi\)
−0.936580 + 0.350454i \(0.886027\pi\)
\(308\) 0 0
\(309\) −29.9870 + 6.24122i −1.70590 + 0.355051i
\(310\) 0 0
\(311\) 16.0607 + 5.84563i 0.910721 + 0.331475i 0.754541 0.656253i \(-0.227860\pi\)
0.156180 + 0.987729i \(0.450082\pi\)
\(312\) 0 0
\(313\) 0.567255 3.21706i 0.0320631 0.181839i −0.964570 0.263826i \(-0.915015\pi\)
0.996633 + 0.0819870i \(0.0261266\pi\)
\(314\) 0 0
\(315\) 19.4836 18.9544i 1.09778 1.06796i
\(316\) 0 0
\(317\) −5.14221 4.31482i −0.288815 0.242345i 0.486856 0.873482i \(-0.338144\pi\)
−0.775671 + 0.631138i \(0.782588\pi\)
\(318\) 0 0
\(319\) 2.69250 + 15.2699i 0.150751 + 0.854953i
\(320\) 0 0
\(321\) 11.3560 + 6.09995i 0.633829 + 0.340466i
\(322\) 0 0
\(323\) 23.8162 1.32517
\(324\) 0 0
\(325\) −12.7962 + 22.1637i −0.709806 + 1.22942i
\(326\) 0 0
\(327\) −0.242516 7.90518i −0.0134112 0.437158i
\(328\) 0 0
\(329\) 10.0469 + 8.22419i 0.553901 + 0.453414i
\(330\) 0 0
\(331\) 1.09302 + 0.917149i 0.0600776 + 0.0504111i 0.672332 0.740250i \(-0.265293\pi\)
−0.612254 + 0.790661i \(0.709737\pi\)
\(332\) 0 0
\(333\) 1.83121 + 2.76516i 0.100350 + 0.151530i
\(334\) 0 0
\(335\) −13.3028 11.1624i −0.726812 0.609868i
\(336\) 0 0
\(337\) −2.86833 16.2671i −0.156248 0.886127i −0.957636 0.287982i \(-0.907016\pi\)
0.801388 0.598145i \(-0.204095\pi\)
\(338\) 0 0
\(339\) −4.63181 + 14.0523i −0.251565 + 0.763218i
\(340\) 0 0
\(341\) −8.75152 + 15.1581i −0.473921 + 0.820855i
\(342\) 0 0
\(343\) −18.5079 + 0.675575i −0.999334 + 0.0364776i
\(344\) 0 0
\(345\) −20.1377 50.4572i −1.08418 2.71653i
\(346\) 0 0
\(347\) −7.54372 + 6.32993i −0.404968 + 0.339808i −0.822410 0.568895i \(-0.807371\pi\)
0.417442 + 0.908703i \(0.362927\pi\)
\(348\) 0 0
\(349\) −2.99392 + 16.9794i −0.160261 + 0.908885i 0.793556 + 0.608497i \(0.208227\pi\)
−0.953817 + 0.300388i \(0.902884\pi\)
\(350\) 0 0
\(351\) −19.0668 + 5.20591i −1.01771 + 0.277871i
\(352\) 0 0
\(353\) 4.43269 + 3.71947i 0.235928 + 0.197967i 0.753085 0.657924i \(-0.228565\pi\)
−0.517156 + 0.855891i \(0.673009\pi\)
\(354\) 0 0
\(355\) −1.38170 7.83600i −0.0733329 0.415892i
\(356\) 0 0
\(357\) 29.0648 18.4835i 1.53827 0.978253i
\(358\) 0 0
\(359\) 25.7530 1.35919 0.679596 0.733587i \(-0.262155\pi\)
0.679596 + 0.733587i \(0.262155\pi\)
\(360\) 0 0
\(361\) −8.96004 −0.471581
\(362\) 0 0
\(363\) −12.0959 + 36.6973i −0.634869 + 1.92611i
\(364\) 0 0
\(365\) 4.03271 + 22.8707i 0.211082 + 1.19710i
\(366\) 0 0
\(367\) 27.0269 9.83697i 1.41079 0.513486i 0.479429 0.877581i \(-0.340844\pi\)
0.931362 + 0.364095i \(0.118622\pi\)
\(368\) 0 0
\(369\) 23.3921 + 6.92268i 1.21774 + 0.360380i
\(370\) 0 0
\(371\) −5.68284 + 10.1254i −0.295039 + 0.525684i
\(372\) 0 0
\(373\) −33.3460 12.1370i −1.72659 0.628428i −0.728212 0.685352i \(-0.759648\pi\)
−0.998378 + 0.0569244i \(0.981871\pi\)
\(374\) 0 0
\(375\) 9.03094 + 4.85104i 0.466356 + 0.250507i
\(376\) 0 0
\(377\) 10.2192 0.526317
\(378\) 0 0
\(379\) 32.3221 1.66028 0.830138 0.557557i \(-0.188261\pi\)
0.830138 + 0.557557i \(0.188261\pi\)
\(380\) 0 0
\(381\) 0.00503220 + 0.164032i 0.000257808 + 0.00840363i
\(382\) 0 0
\(383\) 31.5447 + 11.4813i 1.61186 + 0.586668i 0.981806 0.189885i \(-0.0608115\pi\)
0.630052 + 0.776553i \(0.283034\pi\)
\(384\) 0 0
\(385\) −52.2891 + 0.635966i −2.66490 + 0.0324118i
\(386\) 0 0
\(387\) 1.68193 0.731825i 0.0854973 0.0372008i
\(388\) 0 0
\(389\) 29.3023 10.6652i 1.48568 0.540745i 0.533374 0.845879i \(-0.320924\pi\)
0.952309 + 0.305135i \(0.0987015\pi\)
\(390\) 0 0
\(391\) −11.9541 67.7953i −0.604547 3.42856i
\(392\) 0 0
\(393\) −6.87695 7.70303i −0.346896 0.388566i
\(394\) 0 0
\(395\) 23.9292 1.20401
\(396\) 0 0
\(397\) −4.66082 −0.233920 −0.116960 0.993137i \(-0.537315\pi\)
−0.116960 + 0.993137i \(0.537315\pi\)
\(398\) 0 0
\(399\) 12.2526 7.79192i 0.613395 0.390084i
\(400\) 0 0
\(401\) 0.0943919 + 0.535323i 0.00471371 + 0.0267328i 0.987074 0.160266i \(-0.0512351\pi\)
−0.982360 + 0.186999i \(0.940124\pi\)
\(402\) 0 0
\(403\) 8.83689 + 7.41503i 0.440197 + 0.369369i
\(404\) 0 0
\(405\) 9.02621 + 29.4706i 0.448516 + 1.46440i
\(406\) 0 0
\(407\) 1.10793 6.28337i 0.0549179 0.311455i
\(408\) 0 0
\(409\) 24.4687 20.5317i 1.20990 1.01523i 0.210609 0.977570i \(-0.432455\pi\)
0.999291 0.0376559i \(-0.0119891\pi\)
\(410\) 0 0
\(411\) −23.4893 3.40279i −1.15864 0.167847i
\(412\) 0 0
\(413\) −1.74320 9.22842i −0.0857772 0.454101i
\(414\) 0 0
\(415\) −7.93466 + 13.7432i −0.389497 + 0.674629i
\(416\) 0 0
\(417\) −16.0236 + 3.33501i −0.784681 + 0.163316i
\(418\) 0 0
\(419\) 3.45228 + 19.5788i 0.168655 + 0.956489i 0.945216 + 0.326447i \(0.105851\pi\)
−0.776561 + 0.630042i \(0.783037\pi\)
\(420\) 0 0
\(421\) 6.70095 + 5.62276i 0.326584 + 0.274037i 0.791306 0.611420i \(-0.209401\pi\)
−0.464722 + 0.885457i \(0.653846\pi\)
\(422\) 0 0
\(423\) −13.4996 + 5.87382i −0.656374 + 0.285595i
\(424\) 0 0
\(425\) 38.7402 + 32.5069i 1.87918 + 1.57682i
\(426\) 0 0
\(427\) −21.4128 17.5281i −1.03624 0.848245i
\(428\) 0 0
\(429\) 33.4965 + 17.9929i 1.61722 + 0.868705i
\(430\) 0 0
\(431\) 0.761083 1.31823i 0.0366601 0.0634971i −0.847113 0.531412i \(-0.821661\pi\)
0.883773 + 0.467915i \(0.154995\pi\)
\(432\) 0 0
\(433\) 11.5151 0.553382 0.276691 0.960959i \(-0.410762\pi\)
0.276691 + 0.960959i \(0.410762\pi\)
\(434\) 0 0
\(435\) −0.488664 15.9287i −0.0234296 0.763724i
\(436\) 0 0
\(437\) −5.03939 28.5798i −0.241067 1.36716i
\(438\) 0 0
\(439\) −10.0913 8.46762i −0.481632 0.404137i 0.369384 0.929277i \(-0.379569\pi\)
−0.851016 + 0.525139i \(0.824013\pi\)
\(440\) 0 0
\(441\) 8.90553 19.0182i 0.424073 0.905628i
\(442\) 0 0
\(443\) −4.05176 + 22.9787i −0.192505 + 1.09175i 0.723422 + 0.690406i \(0.242568\pi\)
−0.915927 + 0.401344i \(0.868543\pi\)
\(444\) 0 0
\(445\) 18.2474 + 6.64151i 0.865010 + 0.314838i
\(446\) 0 0
\(447\) −4.91602 + 14.9146i −0.232520 + 0.705435i
\(448\) 0 0
\(449\) 16.6509 + 28.8402i 0.785803 + 1.36105i 0.928518 + 0.371287i \(0.121083\pi\)
−0.142715 + 0.989764i \(0.545583\pi\)
\(450\) 0 0
\(451\) −23.4653 40.6431i −1.10494 1.91381i
\(452\) 0 0
\(453\) −7.98368 + 10.1299i −0.375106 + 0.475942i
\(454\) 0 0
\(455\) −5.57152 + 34.0114i −0.261197 + 1.59448i
\(456\) 0 0
\(457\) −1.09268 + 0.397705i −0.0511136 + 0.0186038i −0.367450 0.930043i \(-0.619769\pi\)
0.316337 + 0.948647i \(0.397547\pi\)
\(458\) 0 0
\(459\) 3.58831 + 38.8909i 0.167488 + 1.81527i
\(460\) 0 0
\(461\) −4.29091 + 24.3350i −0.199848 + 1.13339i 0.705496 + 0.708714i \(0.250724\pi\)
−0.905344 + 0.424679i \(0.860387\pi\)
\(462\) 0 0
\(463\) −37.5340 13.6613i −1.74435 0.634893i −0.744875 0.667204i \(-0.767491\pi\)
−0.999478 + 0.0323113i \(0.989713\pi\)
\(464\) 0 0
\(465\) 11.1353 14.1287i 0.516385 0.655201i
\(466\) 0 0
\(467\) −29.7646 −1.37734 −0.688670 0.725074i \(-0.741805\pi\)
−0.688670 + 0.725074i \(0.741805\pi\)
\(468\) 0 0
\(469\) −12.6618 4.43488i −0.584667 0.204784i
\(470\) 0 0
\(471\) 16.8620 + 18.8875i 0.776958 + 0.870288i
\(472\) 0 0
\(473\) −3.31588 1.20688i −0.152465 0.0554926i
\(474\) 0 0
\(475\) 16.3313 + 13.7036i 0.749333 + 0.628765i
\(476\) 0 0
\(477\) −7.26943 10.9769i −0.332844 0.502599i
\(478\) 0 0
\(479\) 2.81299 15.9533i 0.128529 0.728924i −0.850620 0.525781i \(-0.823773\pi\)
0.979149 0.203143i \(-0.0651157\pi\)
\(480\) 0 0
\(481\) −3.95147 1.43822i −0.180172 0.0655771i
\(482\) 0 0
\(483\) −28.3305 30.9671i −1.28908 1.40905i
\(484\) 0 0
\(485\) 14.5896 + 25.2698i 0.662477 + 1.14744i
\(486\) 0 0
\(487\) 15.5298 26.8984i 0.703721 1.21888i −0.263429 0.964679i \(-0.584854\pi\)
0.967151 0.254203i \(-0.0818130\pi\)
\(488\) 0 0
\(489\) −9.24988 4.96865i −0.418294 0.224690i
\(490\) 0 0
\(491\) −18.0069 + 15.1096i −0.812640 + 0.681886i −0.951236 0.308463i \(-0.900185\pi\)
0.138596 + 0.990349i \(0.455741\pi\)
\(492\) 0 0
\(493\) 3.50659 19.8869i 0.157929 0.895660i
\(494\) 0 0
\(495\) 26.4438 53.0714i 1.18856 2.38538i
\(496\) 0 0
\(497\) −3.13810 5.28584i −0.140763 0.237102i
\(498\) 0 0
\(499\) 3.37489 2.83187i 0.151081 0.126772i −0.564114 0.825697i \(-0.690782\pi\)
0.715195 + 0.698925i \(0.246338\pi\)
\(500\) 0 0
\(501\) 9.80019 29.7325i 0.437840 1.32835i
\(502\) 0 0
\(503\) 16.8654 + 29.2118i 0.751992 + 1.30249i 0.946856 + 0.321658i \(0.104240\pi\)
−0.194864 + 0.980830i \(0.562427\pi\)
\(504\) 0 0
\(505\) −11.9475 + 20.6937i −0.531656 + 0.920856i
\(506\) 0 0
\(507\) 1.57428 1.99747i 0.0699160 0.0887109i
\(508\) 0 0
\(509\) 5.66843 + 32.1473i 0.251249 + 1.42490i 0.805521 + 0.592567i \(0.201885\pi\)
−0.554273 + 0.832335i \(0.687003\pi\)
\(510\) 0 0
\(511\) 9.15907 + 15.4276i 0.405173 + 0.682476i
\(512\) 0 0
\(513\) 1.51269 + 16.3948i 0.0667868 + 0.723850i
\(514\) 0 0
\(515\) −46.3928 38.9282i −2.04431 1.71538i
\(516\) 0 0
\(517\) 26.6142 + 9.68677i 1.17049 + 0.426024i
\(518\) 0 0
\(519\) 9.50931 + 23.8266i 0.417412 + 1.04587i
\(520\) 0 0
\(521\) 0.0876612 + 0.151834i 0.00384051 + 0.00665195i 0.867939 0.496670i \(-0.165444\pi\)
−0.864099 + 0.503322i \(0.832111\pi\)
\(522\) 0 0
\(523\) 20.5065 35.5183i 0.896686 1.55311i 0.0649821 0.997886i \(-0.479301\pi\)
0.831704 0.555219i \(-0.187366\pi\)
\(524\) 0 0
\(525\) 30.5657 + 4.04901i 1.33399 + 0.176713i
\(526\) 0 0
\(527\) 17.4621 14.6524i 0.760661 0.638271i
\(528\) 0 0
\(529\) −57.2129 + 20.8238i −2.48752 + 0.905383i
\(530\) 0 0
\(531\) 10.2113 + 3.02195i 0.443133 + 0.131141i
\(532\) 0 0
\(533\) −29.0652 + 10.5789i −1.25896 + 0.458222i
\(534\) 0 0
\(535\) 4.42588 + 25.1004i 0.191347 + 1.08518i
\(536\) 0 0
\(537\) −21.4237 + 13.2611i −0.924500 + 0.572258i
\(538\) 0 0
\(539\) −37.6158 + 14.7367i −1.62023 + 0.634753i
\(540\) 0 0
\(541\) −15.4531 26.7655i −0.664380 1.15074i −0.979453 0.201672i \(-0.935362\pi\)
0.315073 0.949067i \(-0.397971\pi\)
\(542\) 0 0
\(543\) 0.405689 + 13.2240i 0.0174098 + 0.567498i
\(544\) 0 0
\(545\) 11.9792 10.0517i 0.513131 0.430568i
\(546\) 0 0
\(547\) −41.9716 + 15.2764i −1.79457 + 0.653172i −0.795702 + 0.605688i \(0.792898\pi\)
−0.998872 + 0.0474837i \(0.984880\pi\)
\(548\) 0 0
\(549\) 28.7716 12.5188i 1.22794 0.534290i
\(550\) 0 0
\(551\) 1.47824 8.38351i 0.0629751 0.357150i
\(552\) 0 0
\(553\) 17.2937 6.53366i 0.735404 0.277839i
\(554\) 0 0
\(555\) −2.05280 + 6.22795i −0.0871367 + 0.264362i
\(556\) 0 0
\(557\) 6.41393 0.271767 0.135883 0.990725i \(-0.456613\pi\)
0.135883 + 0.990725i \(0.456613\pi\)
\(558\) 0 0
\(559\) −1.16283 + 2.01408i −0.0491824 + 0.0851865i
\(560\) 0 0
\(561\) 46.5085 59.0110i 1.96359 2.49144i
\(562\) 0 0
\(563\) 11.3430 9.51791i 0.478051 0.401132i −0.371670 0.928365i \(-0.621215\pi\)
0.849721 + 0.527233i \(0.176770\pi\)
\(564\) 0 0
\(565\) −27.4907 + 10.0058i −1.15654 + 0.420947i
\(566\) 0 0
\(567\) 14.5699 + 18.8339i 0.611880 + 0.790951i
\(568\) 0 0
\(569\) 9.58688 3.48934i 0.401903 0.146281i −0.133157 0.991095i \(-0.542511\pi\)
0.535060 + 0.844814i \(0.320289\pi\)
\(570\) 0 0
\(571\) −28.2614 + 23.7141i −1.18270 + 0.992404i −0.182744 + 0.983160i \(0.558498\pi\)
−0.999957 + 0.00924397i \(0.997058\pi\)
\(572\) 0 0
\(573\) 9.57125 12.1442i 0.399845 0.507331i
\(574\) 0 0
\(575\) 30.8115 53.3671i 1.28493 2.22556i
\(576\) 0 0
\(577\) 21.8368 0.909078 0.454539 0.890727i \(-0.349804\pi\)
0.454539 + 0.890727i \(0.349804\pi\)
\(578\) 0 0
\(579\) 4.27980 12.9844i 0.177862 0.539612i
\(580\) 0 0
\(581\) −1.98193 + 12.0987i −0.0822245 + 0.501941i
\(582\) 0 0
\(583\) −4.39818 + 24.9433i −0.182154 + 1.03305i
\(584\) 0 0
\(585\) −31.4200 23.2374i −1.29906 0.960749i
\(586\) 0 0
\(587\) −0.574415 + 0.209070i −0.0237087 + 0.00862925i −0.353847 0.935303i \(-0.615127\pi\)
0.330139 + 0.943932i \(0.392905\pi\)
\(588\) 0 0
\(589\) 7.36132 6.17688i 0.303318 0.254514i
\(590\) 0 0
\(591\) 1.02102 + 33.2815i 0.0419990 + 1.36902i
\(592\) 0 0
\(593\) 18.6799 + 32.3545i 0.767091 + 1.32864i 0.939134 + 0.343552i \(0.111630\pi\)
−0.172043 + 0.985090i \(0.555037\pi\)
\(594\) 0 0
\(595\) 64.2753 + 22.5129i 2.63503 + 0.922939i
\(596\) 0 0
\(597\) −14.1142 + 8.73658i −0.577656 + 0.357564i
\(598\) 0 0
\(599\) −3.34928 18.9947i −0.136848 0.776102i −0.973555 0.228452i \(-0.926634\pi\)
0.836707 0.547650i \(-0.184478\pi\)
\(600\) 0 0
\(601\) −6.97144 + 2.53740i −0.284371 + 0.103503i −0.480268 0.877122i \(-0.659460\pi\)
0.195897 + 0.980625i \(0.437238\pi\)
\(602\) 0 0
\(603\) 11.0320 10.4742i 0.449258 0.426544i
\(604\) 0 0
\(605\) −71.7914 + 26.1299i −2.91873 + 1.06233i
\(606\) 0 0
\(607\) −9.72921 + 8.16378i −0.394897 + 0.331358i −0.818517 0.574482i \(-0.805203\pi\)
0.423620 + 0.905840i \(0.360759\pi\)
\(608\) 0 0
\(609\) −4.70235 11.3783i −0.190549 0.461072i
\(610\) 0 0
\(611\) 9.33318 16.1655i 0.377580 0.653987i
\(612\) 0 0
\(613\) 0.515883 + 0.893535i 0.0208363 + 0.0360895i 0.876256 0.481847i \(-0.160034\pi\)
−0.855419 + 0.517936i \(0.826700\pi\)
\(614\) 0 0
\(615\) 17.8792 + 44.7982i 0.720958 + 1.80644i
\(616\) 0 0
\(617\) 5.43837 + 1.97941i 0.218941 + 0.0796879i 0.449162 0.893450i \(-0.351723\pi\)
−0.230221 + 0.973138i \(0.573945\pi\)
\(618\) 0 0
\(619\) 8.99908 + 7.55112i 0.361703 + 0.303505i 0.805469 0.592638i \(-0.201913\pi\)
−0.443766 + 0.896143i \(0.646358\pi\)
\(620\) 0 0
\(621\) 45.9103 12.5351i 1.84232 0.503017i
\(622\) 0 0
\(623\) 15.0008 0.182448i 0.600996 0.00730962i
\(624\) 0 0
\(625\) −2.32202 13.1688i −0.0928807 0.526753i
\(626\) 0 0
\(627\) 19.6061 24.8767i 0.782993 0.993478i
\(628\) 0 0
\(629\) −4.15471 + 7.19616i −0.165659 + 0.286930i
\(630\) 0 0
\(631\) 2.87426 + 4.97837i 0.114423 + 0.198186i 0.917549 0.397623i \(-0.130165\pi\)
−0.803126 + 0.595809i \(0.796832\pi\)
\(632\) 0 0
\(633\) −5.86411 + 17.7910i −0.233077 + 0.707128i
\(634\) 0 0
\(635\) −0.248567 + 0.208572i −0.00986408 + 0.00827694i
\(636\) 0 0
\(637\) 5.25995 + 26.1014i 0.208407 + 1.03417i
\(638\) 0 0
\(639\) 6.95713 0.427266i 0.275220 0.0169024i
\(640\) 0 0
\(641\) 7.11163 40.3320i 0.280892 1.59302i −0.438707 0.898630i \(-0.644563\pi\)
0.719599 0.694389i \(-0.244325\pi\)
\(642\) 0 0
\(643\) 15.2014 12.7555i 0.599486 0.503028i −0.291795 0.956481i \(-0.594252\pi\)
0.891280 + 0.453453i \(0.149808\pi\)
\(644\) 0 0
\(645\) 3.19495 + 1.71619i 0.125801 + 0.0675751i
\(646\) 0 0
\(647\) −16.9573 + 29.3710i −0.666662 + 1.15469i 0.312170 + 0.950026i \(0.398944\pi\)
−0.978832 + 0.204666i \(0.934389\pi\)
\(648\) 0 0
\(649\) −10.2433 17.7419i −0.402084 0.696429i
\(650\) 0 0
\(651\) 4.18978 13.2512i 0.164211 0.519355i
\(652\) 0 0
\(653\) 2.58749 + 0.941769i 0.101256 + 0.0368543i 0.392152 0.919901i \(-0.371731\pi\)
−0.290895 + 0.956755i \(0.593953\pi\)
\(654\) 0 0
\(655\) 3.54539 20.1069i 0.138530 0.785642i
\(656\) 0 0
\(657\) −20.3055 + 1.24705i −0.792194 + 0.0486519i
\(658\) 0 0
\(659\) −2.71271 2.27623i −0.105672 0.0886695i 0.588421 0.808555i \(-0.299750\pi\)
−0.694093 + 0.719885i \(0.744194\pi\)
\(660\) 0 0
\(661\) −29.5490 10.7550i −1.14932 0.418319i −0.304051 0.952656i \(-0.598339\pi\)
−0.845272 + 0.534337i \(0.820562\pi\)
\(662\) 0 0
\(663\) −32.9788 36.9403i −1.28079 1.43464i
\(664\) 0 0
\(665\) 27.0959 + 9.49053i 1.05073 + 0.368027i
\(666\) 0 0
\(667\) −24.6065 −0.952768
\(668\) 0 0
\(669\) −24.1633 + 30.6590i −0.934209 + 1.18534i
\(670\) 0 0
\(671\) −56.7225 20.6453i −2.18975 0.797003i
\(672\) 0 0
\(673\) 0.446620 2.53291i 0.0172159 0.0976363i −0.974989 0.222253i \(-0.928659\pi\)
0.992205 + 0.124617i \(0.0397701\pi\)
\(674\) 0 0
\(675\) −19.9168 + 28.7331i −0.766600 + 1.10594i
\(676\) 0 0
\(677\) 9.76256 3.55328i 0.375206 0.136564i −0.147532 0.989057i \(-0.547133\pi\)
0.522738 + 0.852494i \(0.324911\pi\)
\(678\) 0 0
\(679\) 17.4436 + 14.2790i 0.669424 + 0.547979i
\(680\) 0 0
\(681\) −9.84003 + 12.4852i −0.377071 + 0.478435i
\(682\) 0 0
\(683\) 7.33259 + 12.7004i 0.280574 + 0.485968i 0.971526 0.236932i \(-0.0761419\pi\)
−0.690952 + 0.722900i \(0.742809\pi\)
\(684\) 0 0
\(685\) −23.4642 40.6412i −0.896522 1.55282i
\(686\) 0 0
\(687\) 10.7927 32.7438i 0.411768 1.24925i
\(688\) 0 0
\(689\) 15.6863 + 5.70935i 0.597601 + 0.217509i
\(690\) 0 0
\(691\) −0.640328 + 3.63148i −0.0243592 + 0.138148i −0.994562 0.104146i \(-0.966789\pi\)
0.970203 + 0.242295i \(0.0779000\pi\)
\(692\) 0 0
\(693\) 4.62036 45.5751i 0.175513 1.73125i
\(694\) 0 0
\(695\) −24.7902 20.8014i −0.940344 0.789042i
\(696\) 0 0
\(697\) 10.6134 + 60.1917i 0.402012 + 2.27992i
\(698\) 0 0
\(699\) 0.161009 + 5.24832i 0.00608991 + 0.198510i
\(700\) 0 0
\(701\) −44.4154 −1.67755 −0.838774 0.544480i \(-0.816727\pi\)
−0.838774 + 0.544480i \(0.816727\pi\)
\(702\) 0 0
\(703\) −1.75146 + 3.03361i −0.0660575 + 0.114415i
\(704\) 0 0
\(705\) −25.6435 13.7746i −0.965792 0.518783i
\(706\) 0 0
\(707\) −2.98427 + 18.2175i −0.112235 + 0.685140i
\(708\) 0 0
\(709\) 14.5183 + 12.1823i 0.545246 + 0.457516i 0.873327 0.487134i \(-0.161958\pi\)
−0.328081 + 0.944649i \(0.606402\pi\)
\(710\) 0 0
\(711\) −2.36775 + 20.8279i −0.0887977 + 0.781107i
\(712\) 0 0
\(713\) −21.2780 17.8544i −0.796868 0.668652i
\(714\) 0 0
\(715\) 13.0549 + 74.0381i 0.488226 + 2.76887i
\(716\) 0 0
\(717\) −13.2902 + 2.76610i −0.496331 + 0.103302i
\(718\) 0 0
\(719\) −7.55541 + 13.0864i −0.281769 + 0.488039i −0.971821 0.235722i \(-0.924255\pi\)
0.690051 + 0.723760i \(0.257588\pi\)
\(720\) 0 0
\(721\) −44.1572 15.4664i −1.64450 0.575998i
\(722\) 0 0
\(723\) −27.5137 3.98577i −1.02324 0.148232i
\(724\) 0 0
\(725\) 13.8473 11.6192i 0.514275 0.431528i
\(726\) 0 0
\(727\) 4.83299 27.4092i 0.179246 1.01655i −0.753883 0.657009i \(-0.771821\pi\)
0.933128 0.359543i \(-0.117067\pi\)
\(728\) 0 0
\(729\) −26.5442 + 4.94031i −0.983118 + 0.182974i
\(730\) 0 0
\(731\) 3.52044 + 2.95400i 0.130208 + 0.109258i
\(732\) 0 0
\(733\) −3.68148 20.8787i −0.135979 0.771173i −0.974173 0.225802i \(-0.927500\pi\)
0.838195 0.545371i \(-0.183611\pi\)
\(734\) 0 0
\(735\) 40.4328 9.44682i 1.49139 0.348451i
\(736\) 0 0
\(737\) −29.2652 −1.07800
\(738\) 0 0
\(739\) −27.0470 −0.994940 −0.497470 0.867481i \(-0.665738\pi\)
−0.497470 + 0.867481i \(0.665738\pi\)
\(740\) 0 0
\(741\) −13.9025 15.5726i −0.510723 0.572072i
\(742\) 0 0
\(743\) −3.65459 20.7262i −0.134074 0.760371i −0.975500 0.219999i \(-0.929395\pi\)
0.841426 0.540372i \(-0.181717\pi\)
\(744\) 0 0
\(745\) −29.1775 + 10.6197i −1.06898 + 0.389077i
\(746\) 0 0
\(747\) −11.1769 8.26615i −0.408942 0.302443i
\(748\) 0 0
\(749\) 10.0520 + 16.9317i 0.367293 + 0.618670i
\(750\) 0 0
\(751\) 3.85761 + 1.40406i 0.140766 + 0.0512348i 0.411443 0.911436i \(-0.365025\pi\)
−0.270676 + 0.962670i \(0.587247\pi\)
\(752\) 0 0
\(753\) 0.762535 + 24.8560i 0.0277883 + 0.905802i
\(754\) 0 0
\(755\) −25.5018 −0.928107
\(756\) 0 0
\(757\) −14.6566 −0.532703 −0.266352 0.963876i \(-0.585818\pi\)
−0.266352 + 0.963876i \(0.585818\pi\)
\(758\) 0 0
\(759\) −80.6549 43.3244i −2.92759 1.57258i
\(760\) 0 0
\(761\) −46.6259 16.9705i −1.69019 0.615178i −0.695539 0.718488i \(-0.744835\pi\)
−0.994649 + 0.103309i \(0.967057\pi\)
\(762\) 0 0
\(763\) 5.91284 10.5352i 0.214059 0.381399i
\(764\) 0 0
\(765\) −56.0020 + 53.1706i −2.02476 + 1.92239i
\(766\) 0 0
\(767\) −12.6878 + 4.61799i −0.458130 + 0.166746i
\(768\) 0 0
\(769\) 3.64912 + 20.6952i 0.131590 + 0.746287i 0.977174 + 0.212443i \(0.0681419\pi\)
−0.845583 + 0.533844i \(0.820747\pi\)
\(770\) 0 0
\(771\) 14.8131 44.9410i 0.533480 1.61851i
\(772\) 0 0
\(773\) −12.3099 −0.442758 −0.221379 0.975188i \(-0.571056\pi\)
−0.221379 + 0.975188i \(0.571056\pi\)
\(774\) 0 0
\(775\) 20.4050 0.732971
\(776\) 0 0
\(777\) 0.216917 + 5.06145i 0.00778184 + 0.181578i
\(778\) 0 0
\(779\) 4.47419 + 25.3744i 0.160305 + 0.909133i
\(780\) 0 0
\(781\) −10.2721 8.61929i −0.367563 0.308422i
\(782\) 0 0
\(783\) 13.9126 + 1.15079i 0.497197 + 0.0411258i
\(784\) 0 0
\(785\) −8.69313 + 49.3012i −0.310271 + 1.75963i
\(786\) 0 0
\(787\) 18.3207 15.3729i 0.653064 0.547985i −0.254935 0.966958i \(-0.582054\pi\)
0.907999 + 0.418973i \(0.137610\pi\)
\(788\) 0 0
\(789\) −1.93541 4.84939i −0.0689025 0.172643i
\(790\) 0 0
\(791\) −17.1356 + 14.7373i −0.609272 + 0.523998i
\(792\) 0 0
\(793\) −19.8917 + 34.4534i −0.706375 + 1.22348i
\(794\) 0 0
\(795\) 8.14909 24.7233i 0.289018 0.876845i
\(796\) 0 0
\(797\) −5.83496 33.0917i −0.206685 1.17217i −0.894766 0.446535i \(-0.852658\pi\)
0.688081 0.725634i \(-0.258453\pi\)
\(798\) 0 0
\(799\) −28.2560 23.7096i −0.999625 0.838785i
\(800\) 0 0
\(801\) −7.58629 + 15.2253i −0.268048 + 0.537959i
\(802\) 0 0
\(803\) 29.9807 + 25.1568i 1.05800 + 0.887765i
\(804\) 0 0
\(805\) 13.4155 81.8949i 0.472833 2.88641i
\(806\) 0 0
\(807\) −0.976941 31.8449i −0.0343899 1.12099i
\(808\) 0 0
\(809\) 10.8893 18.8608i 0.382846 0.663110i −0.608621 0.793461i \(-0.708277\pi\)
0.991468 + 0.130351i \(0.0416105\pi\)
\(810\) 0 0
\(811\) −5.09426 −0.178884 −0.0894418 0.995992i \(-0.528508\pi\)
−0.0894418 + 0.995992i \(0.528508\pi\)
\(812\) 0 0
\(813\) 26.7050 + 14.3448i 0.936586 + 0.503095i
\(814\) 0 0
\(815\) −3.60505 20.4452i −0.126279 0.716165i
\(816\) 0 0
\(817\) 1.48408 + 1.24529i 0.0519213 + 0.0435671i
\(818\) 0 0
\(819\) −29.0521 8.21479i −1.01516 0.287048i
\(820\) 0 0
\(821\) 2.32362 13.1779i 0.0810947 0.459911i −0.917036 0.398803i \(-0.869426\pi\)
0.998131 0.0611077i \(-0.0194633\pi\)
\(822\) 0 0
\(823\) 41.6365 + 15.1545i 1.45136 + 0.528251i 0.942970 0.332877i \(-0.108019\pi\)
0.508388 + 0.861128i \(0.330242\pi\)
\(824\) 0 0
\(825\) 65.8463 13.7046i 2.29247 0.477135i
\(826\) 0 0
\(827\) −23.5944 40.8667i −0.820457 1.42107i −0.905343 0.424682i \(-0.860386\pi\)
0.0848859 0.996391i \(-0.472947\pi\)
\(828\) 0 0
\(829\) 16.6222 + 28.7904i 0.577312 + 0.999933i 0.995786 + 0.0917045i \(0.0292315\pi\)
−0.418475 + 0.908228i \(0.637435\pi\)
\(830\) 0 0
\(831\) 8.75552 + 21.9379i 0.303726 + 0.761017i
\(832\) 0 0
\(833\) 52.5989 1.27966i 1.82244 0.0443375i
\(834\) 0 0
\(835\) 58.1660 21.1707i 2.01292 0.732642i
\(836\) 0 0
\(837\) 11.1957 + 11.0901i 0.386980 + 0.383329i
\(838\) 0 0
\(839\) 5.31042 30.1169i 0.183336 1.03975i −0.744738 0.667357i \(-0.767426\pi\)
0.928075 0.372395i \(-0.121463\pi\)
\(840\) 0 0
\(841\) 20.4684 + 7.44988i 0.705806 + 0.256893i
\(842\) 0 0
\(843\) −17.5487 2.54220i −0.604411 0.0875581i
\(844\) 0 0
\(845\) 5.02862 0.172990
\(846\) 0 0
\(847\) −44.7493 + 38.4861i −1.53760 + 1.32240i
\(848\) 0 0
\(849\) 18.8441 3.92204i 0.646727 0.134604i
\(850\) 0 0
\(851\) 9.51461 + 3.46303i 0.326157 + 0.118711i
\(852\) 0 0
\(853\) −21.7735 18.2701i −0.745510 0.625557i 0.188801 0.982015i \(-0.439540\pi\)
−0.934311 + 0.356458i \(0.883984\pi\)
\(854\) 0 0
\(855\) −23.6082 + 22.4146i −0.807383 + 0.766562i
\(856\) 0 0
\(857\) −6.10089 + 34.5998i −0.208402 + 1.18191i 0.683593 + 0.729863i \(0.260416\pi\)
−0.891995 + 0.452045i \(0.850695\pi\)
\(858\) 0 0
\(859\) −29.5318 10.7487i −1.00761 0.366741i −0.215097 0.976593i \(-0.569007\pi\)
−0.792516 + 0.609852i \(0.791229\pi\)
\(860\) 0 0
\(861\) 25.1530 + 27.4940i 0.857214 + 0.936994i
\(862\) 0 0
\(863\) 9.33016 + 16.1603i 0.317602 + 0.550104i 0.979987 0.199060i \(-0.0637889\pi\)
−0.662385 + 0.749164i \(0.730456\pi\)
\(864\) 0 0
\(865\) −25.3620 + 43.9282i −0.862333 + 1.49360i
\(866\) 0 0
\(867\) −58.1665 + 36.0046i −1.97544 + 1.22278i
\(868\) 0 0
\(869\) 30.8918 25.9213i 1.04793 0.879321i
\(870\) 0 0
\(871\) −3.34930 + 18.9948i −0.113487 + 0.643615i
\(872\) 0 0
\(873\) −23.4384 + 10.1983i −0.793268 + 0.345159i
\(874\) 0 0
\(875\) 7.99396 + 13.4651i 0.270245 + 0.455202i
\(876\) 0 0
\(877\) 22.7131 19.0585i 0.766967 0.643561i −0.172963 0.984928i \(-0.555334\pi\)
0.939930 + 0.341367i \(0.110890\pi\)
\(878\) 0 0
\(879\) 19.9815 4.15877i 0.673959 0.140272i
\(880\) 0 0
\(881\) −0.686405 1.18889i −0.0231256 0.0400547i 0.854231 0.519894i \(-0.174028\pi\)
−0.877357 + 0.479839i \(0.840695\pi\)
\(882\) 0 0
\(883\) 17.5910 30.4685i 0.591984 1.02535i −0.401981 0.915648i \(-0.631678\pi\)
0.993965 0.109698i \(-0.0349884\pi\)
\(884\) 0 0
\(885\) 7.80477 + 19.5557i 0.262355 + 0.657358i
\(886\) 0 0
\(887\) 3.33083 + 18.8901i 0.111838 + 0.634266i 0.988267 + 0.152735i \(0.0488081\pi\)
−0.876429 + 0.481531i \(0.840081\pi\)
\(888\) 0 0
\(889\) −0.122691 + 0.218605i −0.00411493 + 0.00733176i
\(890\) 0 0
\(891\) 43.5765 + 28.2679i 1.45987 + 0.947010i
\(892\) 0 0
\(893\) −11.9116 9.99501i −0.398606 0.334470i
\(894\) 0 0
\(895\) −46.8134 17.0387i −1.56480 0.569541i
\(896\) 0 0
\(897\) −37.3507 + 47.3914i −1.24711 + 1.58235i
\(898\) 0 0
\(899\) −4.07394 7.05627i −0.135873 0.235340i
\(900\) 0 0
\(901\) 16.4931 28.5669i 0.549465 0.951701i
\(902\) 0 0
\(903\) 2.77759 + 0.367946i 0.0924324 + 0.0122445i
\(904\) 0 0
\(905\) −20.0391 + 16.8148i −0.666122 + 0.558943i
\(906\) 0 0
\(907\) 42.5844 15.4994i 1.41399 0.514651i 0.481693 0.876340i \(-0.340022\pi\)
0.932299 + 0.361690i \(0.117800\pi\)
\(908\) 0 0
\(909\) −16.8295 12.4466i −0.558199 0.412829i
\(910\) 0 0
\(911\) −17.9489 + 6.53288i −0.594675 + 0.216444i −0.621784 0.783188i \(-0.713592\pi\)
0.0271093 + 0.999632i \(0.491370\pi\)
\(912\) 0 0
\(913\) 4.64397 + 26.3373i 0.153693 + 0.871636i
\(914\) 0 0
\(915\) 54.6538 + 29.3577i 1.80680 + 0.970537i
\(916\) 0 0
\(917\) −2.92774 15.4993i −0.0966825 0.511833i
\(918\) 0 0
\(919\) −10.4129 18.0356i −0.343489 0.594941i 0.641589 0.767049i \(-0.278276\pi\)
−0.985078 + 0.172108i \(0.944942\pi\)
\(920\) 0 0
\(921\) 8.81123 + 4.73302i 0.290340 + 0.155958i
\(922\) 0 0
\(923\) −6.77002 + 5.68072i −0.222838 + 0.186983i
\(924\) 0 0
\(925\) −6.98958 + 2.54400i −0.229816 + 0.0836462i
\(926\) 0 0
\(927\) 38.4734 36.5282i 1.26363 1.19974i
\(928\) 0 0
\(929\) −4.23922 + 24.0418i −0.139084 + 0.788786i 0.832844 + 0.553508i \(0.186711\pi\)
−0.971928 + 0.235278i \(0.924400\pi\)
\(930\) 0 0
\(931\) 22.1736 0.539452i 0.726709 0.0176798i
\(932\) 0 0
\(933\) −28.9822 + 6.03210i −0.948836 + 0.197482i
\(934\) 0 0
\(935\) 148.560 4.85842
\(936\) 0 0
\(937\) 0.331776 0.574653i 0.0108387 0.0187731i −0.860555 0.509357i \(-0.829883\pi\)
0.871394 + 0.490584i \(0.163217\pi\)
\(938\) 0 0
\(939\) 2.09730 + 5.25501i 0.0684428 + 0.171491i
\(940\) 0 0
\(941\) 34.3068 28.7868i 1.11837 0.938423i 0.119848 0.992792i \(-0.461759\pi\)
0.998521 + 0.0543689i \(0.0173147\pi\)
\(942\) 0 0
\(943\) 69.9851 25.4725i 2.27903 0.829499i
\(944\) 0 0
\(945\) −11.4152 + 45.6764i −0.371336 + 1.48585i
\(946\) 0 0
\(947\) 9.36627 3.40904i 0.304363 0.110779i −0.185324 0.982678i \(-0.559333\pi\)
0.489687 + 0.871898i \(0.337111\pi\)
\(948\) 0 0
\(949\) 19.7594 16.5801i 0.641418 0.538214i
\(950\) 0 0
\(951\) 11.5066 + 1.66690i 0.373126 + 0.0540530i
\(952\) 0 0
\(953\) 10.4619 18.1205i 0.338894 0.586981i −0.645331 0.763903i \(-0.723281\pi\)
0.984225 + 0.176922i \(0.0566139\pi\)
\(954\) 0 0
\(955\) 30.5729 0.989317
\(956\) 0 0
\(957\) −17.8856 20.0341i −0.578161 0.647611i
\(958\) 0 0
\(959\) −28.0544 22.9648i −0.905923 0.741573i
\(960\) 0 0
\(961\) −3.78596 + 21.4712i −0.122128 + 0.692620i
\(962\) 0 0
\(963\) −22.2852 + 1.36862i −0.718130 + 0.0441033i
\(964\) 0 0
\(965\) 25.4015 9.24537i 0.817702 0.297619i
\(966\) 0 0
\(967\) 27.5314 23.1016i 0.885351 0.742897i −0.0819215 0.996639i \(-0.526106\pi\)
0.967272 + 0.253741i \(0.0816612\pi\)
\(968\) 0 0
\(969\) −35.0751 + 21.7112i −1.12677 + 0.697464i
\(970\) 0 0
\(971\) −0.0313675 0.0543300i −0.00100663 0.00174353i 0.865522 0.500872i \(-0.166987\pi\)
−0.866528 + 0.499128i \(0.833654\pi\)
\(972\) 0 0
\(973\) −23.5955 8.26451i −0.756438 0.264948i
\(974\) 0 0
\(975\) −1.35924 44.3065i −0.0435306 1.41894i
\(976\) 0 0
\(977\) −6.78539 38.4819i −0.217084 1.23114i −0.877253 0.480027i \(-0.840627\pi\)
0.660170 0.751117i \(-0.270484\pi\)
\(978\) 0 0
\(979\) 30.7512 11.1925i 0.982812 0.357714i
\(980\) 0 0
\(981\) 7.56364 + 11.4212i 0.241488 + 0.364651i
\(982\) 0 0
\(983\) 15.5526 5.66068i 0.496051 0.180548i −0.0818663 0.996643i \(-0.526088\pi\)
0.577917 + 0.816096i \(0.303866\pi\)
\(984\) 0 0
\(985\) −50.4333 + 42.3186i −1.60694 + 1.34838i
\(986\) 0 0
\(987\) −22.2937 2.95323i −0.709616 0.0940023i
\(988\) 0 0
\(989\) 2.79993 4.84963i 0.0890327 0.154209i
\(990\) 0 0
\(991\) 4.21944 + 7.30828i 0.134035 + 0.232155i 0.925228 0.379411i \(-0.123873\pi\)
−0.791193 + 0.611566i \(0.790540\pi\)
\(992\) 0 0
\(993\) −2.44581 0.354313i −0.0776155 0.0112438i
\(994\) 0 0
\(995\) −30.8413 11.2253i −0.977735 0.355866i
\(996\) 0 0
\(997\) −20.1535 16.9108i −0.638269 0.535571i 0.265217 0.964189i \(-0.414556\pi\)
−0.903486 + 0.428618i \(0.859001\pi\)
\(998\) 0 0
\(999\) −5.21765 2.40299i −0.165079 0.0760274i
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 756.2.bq.a.25.4 yes 144
7.2 even 3 756.2.bp.a.457.13 yes 144
27.13 even 9 756.2.bp.a.445.13 144
189.121 even 9 inner 756.2.bq.a.121.4 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
756.2.bp.a.445.13 144 27.13 even 9
756.2.bp.a.457.13 yes 144 7.2 even 3
756.2.bq.a.25.4 yes 144 1.1 even 1 trivial
756.2.bq.a.121.4 yes 144 189.121 even 9 inner