LMFDB - Embedded newform 567.2.v.b.442.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(64,567)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("567.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.v (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			442.5
Character	$\chi$	$=$	567.442
Dual form			567.2.v.b.127.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.731503 + 0.613803i) q^{2} +(-0.188955 + 1.07162i) q^{4} +(3.78665 - 1.37823i) q^{5} +(0.173648 + 0.984808i) q^{7} +(-1.47445 - 2.55382i) q^{8} +O(q^{10})$	\(q+(-0.731503 + 0.613803i) q^{2} +(-0.188955 + 1.07162i) q^{4} +(3.78665 - 1.37823i) q^{5} +(0.173648 + 0.984808i) q^{7} +(-1.47445 - 2.55382i) q^{8} +(-1.92398 + 3.33244i) q^{10} +(3.90983 + 1.42306i) q^{11} +(0.402272 + 0.337546i) q^{13} +(-0.731503 - 0.613803i) q^{14} +(0.601058 + 0.218767i) q^{16} +(1.49397 - 2.58763i) q^{17} +(-1.44865 - 2.50914i) q^{19} +(0.761427 + 4.31827i) q^{20} +(-3.73353 + 1.35889i) q^{22} +(0.299868 - 1.70064i) q^{23} +(8.60901 - 7.22382i) q^{25} -0.501450 q^{26} -1.08815 q^{28} +(-0.978952 + 0.821438i) q^{29} +(-1.14367 + 6.48610i) q^{31} +(4.96817 - 1.80826i) q^{32} +(0.495454 + 2.80986i) q^{34} +(2.01484 + 3.48980i) q^{35} +(-2.51013 + 4.34766i) q^{37} +(2.59981 + 0.946255i) q^{38} +(-9.10299 - 7.63831i) q^{40} +(-7.74629 - 6.49991i) q^{41} +(5.92226 + 2.15553i) q^{43} +(-2.26376 + 3.92095i) q^{44} +(0.824503 + 1.42808i) q^{46} +(1.47781 + 8.38105i) q^{47} +(-0.939693 + 0.342020i) q^{49} +(-1.86351 + 10.5685i) q^{50} +(-0.437732 + 0.367301i) q^{52} +10.6125 q^{53} +16.7665 q^{55} +(2.25899 - 1.89552i) q^{56} +(0.211904 - 1.20177i) q^{58} +(-12.4329 + 4.52520i) q^{59} +(1.79378 + 10.1730i) q^{61} +(-3.14459 - 5.44659i) q^{62} +(-3.16394 + 5.48010i) q^{64} +(1.98848 + 0.723748i) q^{65} +(2.09084 + 1.75442i) q^{67} +(2.49066 + 2.08991i) q^{68} +(-3.61591 - 1.31608i) q^{70} +(0.743219 - 1.28729i) q^{71} +(-1.01768 - 1.76267i) q^{73} +(-0.832449 - 4.72105i) q^{74} +(2.96257 - 1.07829i) q^{76} +(-0.722508 + 4.09754i) q^{77} +(3.06523 - 2.57203i) q^{79} +2.57751 q^{80} +9.65610 q^{82} +(3.89731 - 3.27024i) q^{83} +(2.09079 - 11.8575i) q^{85} +(-5.65522 + 2.05833i) q^{86} +(-2.13060 - 12.0833i) q^{88} +(-5.12426 - 8.87547i) q^{89} +(-0.262564 + 0.454775i) q^{91} +(1.76577 + 0.642689i) q^{92} +(-6.22534 - 5.22368i) q^{94} +(-8.94372 - 7.50467i) q^{95} +(-11.3317 - 4.12439i) q^{97} +(0.477454 - 0.826975i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 3 q^{5} + 27 q^{8}+O(q^{10}) $ 54 * q + 3 * q^5 + 27 * q^8	$ 54 q + 3 q^{5} + 27 q^{8} + 6 q^{11} - 9 q^{13} + 30 q^{17} + 12 q^{20} - 9 q^{22} + 12 q^{23} + 27 q^{25} - 18 q^{26} + 54 q^{28} - 6 q^{29} - 9 q^{31} + 9 q^{32} - 9 q^{34} + 12 q^{35} - 54 q^{38} - 45 q^{40} + 15 q^{41} - 9 q^{43} + 42 q^{44} + 45 q^{47} - 18 q^{50} - 63 q^{52} - 132 q^{53} + 9 q^{56} - 27 q^{58} + 36 q^{62} - 27 q^{64} - 66 q^{65} + 45 q^{67} - 87 q^{68} + 72 q^{71} + 72 q^{74} + 54 q^{76} - 3 q^{77} - 36 q^{79} - 42 q^{80} - 24 q^{83} + 18 q^{85} + 90 q^{86} + 54 q^{88} + 42 q^{89} - 87 q^{92} - 90 q^{94} - 12 q^{95} - 18 q^{97} + 9 q^{98}+O(q^{100}) $ 54 * q + 3 * q^5 + 27 * q^8 + 6 * q^11 - 9 * q^13 + 30 * q^17 + 12 * q^20 - 9 * q^22 + 12 * q^23 + 27 * q^25 - 18 * q^26 + 54 * q^28 - 6 * q^29 - 9 * q^31 + 9 * q^32 - 9 * q^34 + 12 * q^35 - 54 * q^38 - 45 * q^40 + 15 * q^41 - 9 * q^43 + 42 * q^44 + 45 * q^47 - 18 * q^50 - 63 * q^52 - 132 * q^53 + 9 * q^56 - 27 * q^58 + 36 * q^62 - 27 * q^64 - 66 * q^65 + 45 * q^67 - 87 * q^68 + 72 * q^71 + 72 * q^74 + 54 * q^76 - 3 * q^77 - 36 * q^79 - 42 * q^80 - 24 * q^83 + 18 * q^85 + 90 * q^86 + 54 * q^88 + 42 * q^89 - 87 * q^92 - 90 * q^94 - 12 * q^95 - 18 * q^97 + 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.731503	+	0.613803i	−0.517250	+	0.434025i	−0.863672	−	0.504054i	$-0.831841\pi$
$2$	−0.731503	+	0.613803i	−0.517250	+	0.434025i	0.346422	+	0.938079i	$0.387397\pi$
$3$		0			0
$3$		0			0
$4$	−0.188955	+	1.07162i	−0.0944776	+	0.535809i
$5$	3.78665	−	1.37823i	1.69344	−	0.616363i	0.698391	−	0.715716i	$-0.253900\pi$
$5$	3.78665	−	1.37823i	1.69344	−	0.616363i	0.995052	+	0.0993536i	$0.0316775\pi$
$6$		0			0
$7$	0.173648	+	0.984808i	0.0656328	+	0.372222i
$7$	0.173648	+	0.984808i	0.0656328	+	0.372222i
$8$	−1.47445	−	2.55382i	−0.521297	−	0.902913i
$9$		0			0
$10$	−1.92398	+	3.33244i	−0.608417	+	1.05381i
$11$	3.90983	+	1.42306i	1.17886	+	0.429069i	0.855799	−	0.517309i	$-0.173066\pi$
$11$	3.90983	+	1.42306i	1.17886	+	0.429069i	0.323060	+	0.946379i	$0.395288\pi$
$12$		0			0
$13$	0.402272	+	0.337546i	0.111570	+	0.0936185i	0.696866	−	0.717201i	$-0.254577\pi$
$13$	0.402272	+	0.337546i	0.111570	+	0.0936185i	−0.585296	+	0.810820i	$0.699022\pi$
$14$	−0.731503	−	0.613803i	−0.195502	−	0.164046i
$15$		0			0
$16$	0.601058	+	0.218767i	0.150264	+	0.0546918i
$17$	1.49397	−	2.58763i	0.362340	−	0.627592i	−0.626005	−	0.779819i	$-0.715311\pi$
$17$	1.49397	−	2.58763i	0.362340	−	0.627592i	0.988346	+	0.152227i	$0.0486444\pi$
$18$		0			0
$19$	−1.44865	−	2.50914i	−0.332344	−	0.575636i	0.650627	−	0.759397i	$-0.274506\pi$
$19$	−1.44865	−	2.50914i	−0.332344	−	0.575636i	−0.982971	+	0.183761i	$0.941173\pi$
$20$	0.761427	+	4.31827i	0.170260	+	0.965594i
$21$		0			0
$22$	−3.73353	+	1.35889i	−0.795992	+	0.289717i
$23$	0.299868	−	1.70064i	0.0625269	−	0.354608i	−0.937452	−	0.348115i	$-0.886822\pi$
$23$	0.299868	−	1.70064i	0.0625269	−	0.354608i	0.999979	−	0.00649317i	$-0.00206685\pi$
$24$		0			0
$25$	8.60901	−	7.22382i	1.72180	−	1.44476i
$26$	−0.501450			−0.0983425
$27$		0			0
$28$	−1.08815			−0.205641
$29$	−0.978952	+	0.821438i	−0.181787	+	0.152537i	−0.729140	−	0.684364i	$-0.760080\pi$
$29$	−0.978952	+	0.821438i	−0.181787	+	0.152537i	0.547353	+	0.836902i	$0.315635\pi$
$30$		0			0
$31$	−1.14367	+	6.48610i	−0.205410	+	1.16494i	0.691383	+	0.722488i	$0.257002\pi$
$31$	−1.14367	+	6.48610i	−0.205410	+	1.16494i	−0.896793	+	0.442450i	$0.854109\pi$
$32$	4.96817	−	1.80826i	0.878256	−	0.319659i
$33$		0			0
$34$	0.495454	+	2.80986i	0.0849697	+	0.481887i
$35$	2.01484	+	3.48980i	0.340570	+	0.589884i
$36$		0			0
$37$	−2.51013	+	4.34766i	−0.412662	+	0.714752i	−0.995180	−	0.0980662i	$-0.968734\pi$
$37$	−2.51013	+	4.34766i	−0.412662	+	0.714752i	0.582518	+	0.812818i	$0.302068\pi$
$38$	2.59981	+	0.946255i	0.421745	+	0.153503i
$39$		0			0
$40$	−9.10299	−	7.63831i	−1.43931	−	1.20772i
$41$	−7.74629	−	6.49991i	−1.20977	−	1.01512i	−0.999296	−	0.0375159i	$-0.988056\pi$
$41$	−7.74629	−	6.49991i	−1.20977	−	1.01512i	−0.210472	−	0.977600i	$-0.567500\pi$
$42$		0			0
$43$	5.92226	+	2.15553i	0.903137	+	0.328715i	0.751509	−	0.659723i	$-0.229326\pi$
$43$	5.92226	+	2.15553i	0.903137	+	0.328715i	0.151628	+	0.988438i	$0.451549\pi$
$44$	−2.26376	+	3.92095i	−0.341275	+	0.591106i
$45$		0			0
$46$	0.824503	+	1.42808i	0.121566	+	0.210559i
$47$	1.47781	+	8.38105i	0.215560	+	1.22250i	0.879932	+	0.475100i	$0.157588\pi$
$47$	1.47781	+	8.38105i	0.215560	+	1.22250i	−0.664372	+	0.747402i	$0.731301\pi$
$48$		0			0
$49$	−0.939693	+	0.342020i	−0.134242	+	0.0488600i
$50$	−1.86351	+	10.5685i	−0.263540	+	1.49461i
$51$		0			0
$52$	−0.437732	+	0.367301i	−0.0607025	+	0.0509355i
$53$	10.6125			1.45774			0.728870	−	0.684652i	$-0.240046\pi$
$53$	10.6125			1.45774			0.728870	+	0.684652i	$0.240046\pi$
$54$		0			0
$55$	16.7665			2.26079
$56$	2.25899	−	1.89552i	0.301870	−	0.253299i
$57$		0			0
$58$	0.211904	−	1.20177i	0.0278244	−	0.157800i
$59$	−12.4329	+	4.52520i	−1.61862	+	0.589130i	−0.983119	−	0.182967i	$-0.941430\pi$
$59$	−12.4329	+	4.52520i	−1.61862	+	0.589130i	−0.635504	+	0.772098i	$0.719208\pi$
$60$		0			0
$61$	1.79378	+	10.1730i	0.229670	+	1.30253i	0.853553	+	0.521007i	$0.174443\pi$
$61$	1.79378	+	10.1730i	0.229670	+	1.30253i	−0.623882	+	0.781518i	$0.714446\pi$
$62$	−3.14459	−	5.44659i	−0.399363	−	0.691718i
$63$		0			0
$64$	−3.16394	+	5.48010i	−0.395492	+	0.685013i
$65$	1.98848	+	0.723748i	0.246641	+	0.0897699i
$66$		0			0
$67$	2.09084	+	1.75442i	0.255436	+	0.214337i	0.761509	−	0.648154i	$-0.224459\pi$
$67$	2.09084	+	1.75442i	0.255436	+	0.214337i	−0.506073	+	0.862491i	$0.668903\pi$
$68$	2.49066	+	2.08991i	0.302036	+	0.253439i
$69$		0			0
$70$	−3.61591	−	1.31608i	−0.432184	−	0.157302i
$71$	0.743219	−	1.28729i	0.0882039	−	0.152774i	−0.818548	−	0.574438i	$-0.805221\pi$
$71$	0.743219	−	1.28729i	0.0882039	−	0.152774i	0.906752	+	0.421664i	$0.138554\pi$
$72$		0			0
$73$	−1.01768	−	1.76267i	−0.119110	−	0.206305i	0.800305	−	0.599593i	$-0.204671\pi$
$73$	−1.01768	−	1.76267i	−0.119110	−	0.206305i	−0.919415	+	0.393288i	$0.871338\pi$
$74$	−0.832449	−	4.72105i	−0.0967702	−	0.548811i
$75$		0			0
$76$	2.96257	−	1.07829i	0.339830	−	0.123688i
$77$	−0.722508	+	4.09754i	−0.0823374	+	0.466959i
$78$		0			0
$79$	3.06523	−	2.57203i	0.344865	−	0.289376i	−0.453859	−	0.891073i	$-0.649953\pi$
$79$	3.06523	−	2.57203i	0.344865	−	0.289376i	0.798724	+	0.601697i	$0.205509\pi$
$80$	2.57751			0.288174
$81$		0			0
$82$	9.65610			1.06634
$83$	3.89731	−	3.27024i	0.427786	−	0.358955i	−0.403330	−	0.915055i	$-0.632147\pi$
$83$	3.89731	−	3.27024i	0.427786	−	0.358955i	0.831116	+	0.556100i	$0.187703\pi$
$84$		0			0
$85$	2.09079	−	11.8575i	0.226778	−	1.28612i
$86$	−5.65522	+	2.05833i	−0.609818	+	0.221956i
$87$		0			0
$88$	−2.13060	−	12.0833i	−0.227123	−	1.28808i
$89$	−5.12426	−	8.87547i	−0.543170	−	0.940798i	−0.998720	−	0.0505877i	$-0.983891\pi$
$89$	−5.12426	−	8.87547i	−0.543170	−	0.940798i	0.455550	−	0.890210i	$-0.349443\pi$
$90$		0			0
$91$	−0.262564	+	0.454775i	−0.0275242	+	0.0476734i
$92$	1.76577	+	0.642689i	0.184095	+	0.0670049i
$93$		0			0
$94$	−6.22534	−	5.22368i	−0.642094	−	0.538781i
$95$	−8.94372	−	7.50467i	−0.917606	−	0.769963i
$96$		0			0
$97$	−11.3317	−	4.12439i	−1.15056	−	0.418768i	−0.304841	−	0.952403i	$-0.598603\pi$
$97$	−11.3317	−	4.12439i	−1.15056	−	0.418768i	−0.845715	+	0.533635i	$0.820826\pi$
$98$	0.477454	−	0.826975i	0.0482302	−	0.0835371i
$99$		0			0
$100$	6.11446	+	10.5905i	0.611446	+	1.05905i
$101$	−1.91797	−	10.8773i	−0.190845	−	1.08233i	−0.918213	−	0.396087i	$-0.870368\pi$
$101$	−1.91797	−	10.8773i	−0.190845	−	1.08233i	0.727368	−	0.686247i	$-0.240743\pi$
$102$		0			0
$103$	−12.9847	+	4.72605i	−1.27942	+	0.465672i	−0.890241	−	0.455490i	$-0.849464\pi$
$103$	−12.9847	+	4.72605i	−1.27942	+	0.465672i	−0.389181	+	0.921161i	$0.627242\pi$
$104$	0.268903	−	1.52503i	0.0263681	−	0.149541i
$105$		0			0
$106$	−7.76308	+	6.51400i	−0.754017	+	0.632695i
$107$	−8.62687			−0.833991			−0.416996	−	0.908908i	$-0.636917\pi$
$107$	−8.62687			−0.833991			−0.416996	+	0.908908i	$0.636917\pi$
$108$		0			0
$109$	−15.8137			−1.51468			−0.757339	−	0.653022i	$-0.773501\pi$
$109$	−15.8137			−1.51468			−0.757339	+	0.653022i	$0.773501\pi$
$110$	−12.2647	+	10.2913i	−1.16940	+	0.981240i
$111$		0			0
$112$	−0.111071	+	0.629915i	−0.0104952	+	0.0595214i
$113$	7.59508	−	2.76438i	0.714485	−	0.260051i	0.0409026	−	0.999163i	$-0.486977\pi$
$113$	7.59508	−	2.76438i	0.714485	−	0.260051i	0.673583	+	0.739112i	$0.264754\pi$
$114$		0			0
$115$	−1.20837	−	6.85302i	−0.112681	−	0.639047i
$116$	−0.695290	−	1.20428i	−0.0645560	−	0.111814i
$117$		0			0
$118$	6.31710	−	10.9415i	0.581536	−	1.00725i
$119$	2.80774	+	1.02193i	0.257385	+	0.0936806i
$120$		0			0
$121$	4.83519	+	4.05720i	0.439563	+	0.368837i
$122$	−7.55641	−	6.34058i	−0.684125	−	0.574049i
$123$		0			0
$124$	−6.73452	−	2.45116i	−0.604778	−	0.220121i
$125$	12.5691	−	21.7703i	1.12421	−	1.94719i
$126$		0			0
$127$	−1.29622	−	2.24512i	−0.115021	−	0.199222i	0.802767	−	0.596293i	$-0.203360\pi$
$127$	−1.29622	−	2.24512i	−0.115021	−	0.199222i	−0.917788	+	0.397070i	$0.870027\pi$
$128$	0.786883	+	4.46263i	0.0695513	+	0.394445i
$129$		0			0
$130$	−1.89882	+	0.691113i	−0.166537	+	0.0606147i
$131$	0.180227	−	1.02212i	0.0157465	−	0.0893027i	−0.975922	−	0.218121i	$-0.930007\pi$
$131$	0.180227	−	1.02212i	0.0157465	−	0.0893027i	0.991668	+	0.128818i	$0.0411184\pi$
$132$		0			0
$133$	2.21947	−	1.86235i	0.192452	−	0.161486i
$134$	−2.60632			−0.225152
$135$		0			0
$136$	−8.81113			−0.755548
$137$	2.68053	−	2.24923i	0.229013	−	0.192165i	−0.521060	−	0.853520i	$-0.674463\pi$
$137$	2.68053	−	2.24923i	0.229013	−	0.192165i	0.750072	+	0.661356i	$0.230019\pi$
$138$		0			0
$139$	2.13974	−	12.1351i	0.181490	−	1.02928i	−0.748892	−	0.662692i	$-0.769414\pi$
$139$	2.13974	−	12.1351i	0.181490	−	1.02928i	0.930382	−	0.366590i	$-0.119475\pi$
$140$	−4.12045	+	1.49972i	−0.348241	+	0.126749i
$141$		0			0
$142$	0.246478	+	1.39785i	0.0206840	+	0.117305i
$143$	1.09247	+	1.89221i	0.0913566	+	0.158234i
$144$		0			0
$145$	−2.57482	+	4.45972i	−0.213827	+	0.370360i
$146$	1.82637	+	0.664744i	0.151151	+	0.0550146i
$147$		0			0
$148$	−4.18473	−	3.51141i	−0.343983	−	0.288636i
$149$	−9.04012	−	7.58556i	−0.740595	−	0.621433i	0.192402	−	0.981316i	$-0.438372\pi$
$149$	−9.04012	−	7.58556i	−0.740595	−	0.621433i	−0.932997	+	0.359883i	$0.882817\pi$
$150$		0			0
$151$	18.5755	+	6.76092i	1.51165	+	0.550195i	0.959046	−	0.283249i	$-0.0914123\pi$
$151$	18.5755	+	6.76092i	1.51165	+	0.550195i	0.552603	+	0.833444i	$0.313634\pi$
$152$	−4.27193	+	7.39921i	−0.346500	+	0.600155i
$153$		0			0
$154$	−1.98657	−	3.44084i	−0.160082	−	0.277271i
$155$	4.60864	+	26.1369i	0.370175	+	2.09936i
$156$		0			0
$157$	12.8719	−	4.68501i	1.02729	−	0.373904i	0.227244	−	0.973838i	$-0.427029\pi$
$157$	12.8719	−	4.68501i	1.02729	−	0.373904i	0.800050	+	0.599934i	$0.204806\pi$
$158$	−0.663500	+	3.76289i	−0.0527852	+	0.299360i
$159$		0			0
$160$	16.3205	−	13.6945i	1.29025	−	1.08265i
$161$	1.72687			0.136097
$162$		0			0
$163$	−20.4893			−1.60485			−0.802423	−	0.596755i	$-0.796456\pi$
$163$	−20.4893			−1.60485			−0.802423	+	0.596755i	$0.796456\pi$
$164$	8.42913	−	7.07288i	0.658204	−	0.552299i
$165$		0			0
$166$	−0.843614	+	4.78437i	−0.0654771	+	0.371339i
$167$	11.8892	−	4.32732i	0.920016	−	0.334858i	0.161771	−	0.986828i	$-0.448279\pi$
$167$	11.8892	−	4.32732i	0.920016	−	0.334858i	0.758245	+	0.651970i	$0.226057\pi$
$168$		0			0
$169$	−2.20954	−	12.5309i	−0.169965	−	0.963918i
$170$	5.74874	+	9.95712i	0.440909	+	0.763676i
$171$		0			0
$172$	−3.42894	+	5.93911i	−0.261455	+	0.452853i
$173$	−12.0873	−	4.39941i	−0.918979	−	0.334481i	−0.161147	−	0.986930i	$-0.551519\pi$
$173$	−12.0873	−	4.39941i	−0.918979	−	0.334481i	−0.757832	+	0.652449i	$0.773741\pi$
$174$		0			0
$175$	8.60901	+	7.22382i	0.650780	+	0.546069i
$176$	2.03872	+	1.71069i	0.153674	+	0.128948i
$177$		0			0
$178$	9.19620	+	3.34714i	0.689284	+	0.250879i
$179$	−8.24968	+	14.2889i	−0.616610	+	1.06800i	0.373489	+	0.927634i	$0.378161\pi$
$179$	−8.24968	+	14.2889i	−0.616610	+	1.06800i	−0.990100	+	0.140366i	$0.955172\pi$
$180$		0			0
$181$	−1.08979	−	1.88756i	−0.0810032	−	0.140302i	0.822678	−	0.568508i	$-0.192479\pi$
$181$	−1.08979	−	1.88756i	−0.0810032	−	0.140302i	−0.903681	+	0.428206i	$0.859146\pi$
$182$	−0.0870759	−	0.493832i	−0.00645450	−	0.0366053i
$183$		0			0
$184$	−4.78527	+	1.74170i	−0.352775	+	0.128400i
$185$	−3.51290	+	19.9226i	−0.258273	+	1.46474i
$186$		0			0
$187$	9.52352	−	7.99118i	0.696429	−	0.584373i
$188$	−9.26052			−0.675393
$189$		0			0
$190$	11.1487			0.808815
$191$	−12.0821	+	10.1381i	−0.874229	+	0.733565i	−0.964984	−	0.262308i	$-0.915516\pi$
$191$	−12.0821	+	10.1381i	−0.874229	+	0.733565i	0.0907554	+	0.995873i	$0.471072\pi$
$192$		0			0
$193$	1.52376	−	8.64167i	0.109683	−	0.622041i	−0.879564	−	0.475781i	$-0.842165\pi$
$193$	1.52376	−	8.64167i	0.109683	−	0.622041i	0.989246	−	0.146260i	$-0.0467235\pi$
$194$	10.8207	−	3.93841i	0.776881	−	0.282762i
$195$		0			0
$196$	−0.188955	−	1.07162i	−0.0134968	−	0.0765441i
$197$	−4.91970	−	8.52117i	−0.350514	−	0.607108i	0.635826	−	0.771833i	$-0.280660\pi$
$197$	−4.91970	−	8.52117i	−0.350514	−	0.607108i	−0.986340	+	0.164725i	$0.947326\pi$
$198$		0			0
$199$	9.74282	−	16.8751i	0.690650	−	1.19624i	−0.280975	−	0.959715i	$-0.590658\pi$
$199$	9.74282	−	16.8751i	0.690650	−	1.19624i	0.971625	−	0.236526i	$-0.0760089\pi$
$200$	−31.1419	−	11.3347i	−2.20207	−	0.801486i
$201$		0			0
$202$	8.07953	+	6.77953i	0.568474	+	0.477006i
$203$	−0.978952	−	0.821438i	−0.0687089	−	0.0576536i
$204$		0			0
$205$	−38.2909	−	13.9368i	−2.67435	−	0.973385i
$206$	6.59749	−	11.4272i	0.459669	−	0.796170i
$207$		0			0
$208$	0.167945	+	0.290889i	0.0116449	+	0.0201695i
$209$	−2.09333	−	11.8718i	−0.144798	−	0.821193i
$210$		0			0
$211$	−11.4983	+	4.18503i	−0.791574	+	0.288109i	−0.705990	−	0.708222i	$-0.749498\pi$
$211$	−11.4983	+	4.18503i	−0.791574	+	0.288109i	−0.0855838	+	0.996331i	$0.527276\pi$
$212$	−2.00529	+	11.3726i	−0.137724	+	0.781070i
$213$		0			0
$214$	6.31058	−	5.29521i	0.431382	−	0.361973i
$215$	25.3964			1.73202
$216$		0			0
$217$	−6.58616			−0.447098
$218$	11.5678	−	9.70651i	0.783468	−	0.657408i
$219$		0			0
$220$	−3.16811	+	17.9673i	−0.213594	+	1.21135i
$221$	1.47443	−	0.536647i	0.0991806	−	0.0360988i
$222$		0			0
$223$	3.06689	+	17.3932i	0.205374	+	1.16474i	0.896849	+	0.442336i	$0.145850\pi$
$223$	3.06689	+	17.3932i	0.205374	+	1.16474i	−0.691475	+	0.722400i	$0.743039\pi$
$224$	2.64351	+	4.57869i	0.176627	+	0.305926i
$225$		0			0
$226$	−3.85903	+	6.68404i	−0.256699	+	0.444616i
$227$	12.2133	+	4.44528i	0.810626	+	0.295044i	0.713883	−	0.700265i	$-0.246935\pi$
$227$	12.2133	+	4.44528i	0.810626	+	0.295044i	0.0967438	+	0.995309i	$0.469157\pi$
$228$		0			0
$229$	6.30393	+	5.28962i	0.416575	+	0.349548i	0.826859	−	0.562410i	$-0.190126\pi$
$229$	6.30393	+	5.28962i	0.416575	+	0.349548i	−0.410283	+	0.911958i	$0.634570\pi$
$230$	5.09033	+	4.27130i	0.335647	+	0.281641i
$231$		0			0
$232$	3.54122	+	1.28890i	0.232493	+	0.0846204i
$233$	−2.31536	+	4.01032i	−0.151684	+	0.262725i	−0.931847	−	0.362852i	$-0.881803\pi$
$233$	−2.31536	+	4.01032i	−0.151684	+	0.262725i	0.780163	+	0.625577i	$0.215136\pi$
$234$		0			0
$235$	17.1469	+	29.6994i	1.11854	+	1.93737i
$236$	−2.50003	−	14.1784i	−0.162738	−	0.922932i
$237$		0			0
$238$	−2.68114	+	0.975854i	−0.173792	+	0.0632552i
$239$	−0.763043	+	4.32743i	−0.0493571	+	0.279918i	−0.999490	−	0.0319265i	$-0.989836\pi$
$239$	−0.763043	+	4.32743i	−0.0493571	+	0.279918i	0.950133	+	0.311845i	$0.100947\pi$
$240$		0			0
$241$	−3.27879	+	2.75123i	−0.211205	+	0.177222i	−0.742253	−	0.670120i	$-0.766243\pi$
$241$	−3.27879	+	2.75123i	−0.211205	+	0.177222i	0.531048	+	0.847342i	$0.321798\pi$
$242$	−6.02728			−0.387448
$243$		0			0
$244$	−11.2406			−0.719603
$245$	−3.08691	+	2.59022i	−0.197215	+	0.165483i
$246$		0			0
$247$	0.264199	−	1.49835i	0.0168106	−	0.0953374i
$248$	18.2506	−	6.64269i	1.15892	−	0.421811i
$249$		0			0
$250$	4.16836	+	23.6400i	0.263631	+	1.49512i
$251$	−1.21897	−	2.11132i	−0.0769407	−	0.133265i	0.824988	−	0.565150i	$-0.191182\pi$
$251$	−1.21897	−	2.11132i	−0.0769407	−	0.133265i	−0.901929	+	0.431885i	$0.857849\pi$
$252$		0			0
$253$	3.59255	−	6.22248i	0.225862	−	0.391204i
$254$	2.32625	+	0.846686i	0.145962	+	0.0531258i
$255$		0			0
$256$	−13.0097	−	10.9164i	−0.813104	−	0.682275i
$257$	−4.71050	−	3.95258i	−0.293833	−	0.246555i	0.483939	−	0.875102i	$-0.339206\pi$
$257$	−4.71050	−	3.95258i	−0.293833	−	0.246555i	−0.777772	+	0.628547i	$0.783650\pi$
$258$		0			0
$259$	−4.71749	−	1.71703i	−0.293131	−	0.106691i
$260$	−1.15132	+	1.99414i	−0.0714015	+	0.123671i
$261$		0			0
$262$	0.495542	+	0.858305i	0.0306147	+	0.0530262i
$263$	−3.30355	−	18.7354i	−0.203706	−	1.15527i	−0.899463	−	0.436996i	$-0.856042\pi$
$263$	−3.30355	−	18.7354i	−0.203706	−	1.15527i	0.695757	−	0.718277i	$-0.255069\pi$
$264$		0			0
$265$	40.1859	−	14.6265i	2.46860	−	0.898497i
$266$	−0.480426	+	2.72463i	−0.0294568	+	0.167058i
$267$		0			0
$268$	−2.27514	+	1.90907i	−0.138977	+	0.116615i
$269$	−19.8948			−1.21301			−0.606505	−	0.795080i	$-0.707429\pi$
$269$	−19.8948			−1.21301			−0.606505	+	0.795080i	$0.707429\pi$
$270$		0			0
$271$	−5.49656			−0.333892			−0.166946	−	0.985966i	$-0.553391\pi$
$271$	−5.49656			−0.333892			−0.166946	+	0.985966i	$0.553391\pi$
$272$	1.46405	−	1.22848i	0.0887710	−	0.0744877i
$273$		0			0
$274$	−0.580227	+	3.29063i	−0.0350528	+	0.198794i
$275$	43.9397	−	15.9928i	2.64967	−	0.964399i
$276$		0			0
$277$	1.42916	+	8.10515i	0.0858697	+	0.486991i	0.997166	+	0.0752391i	$0.0239720\pi$
$277$	1.42916	+	8.10515i	0.0858697	+	0.486991i	−0.911296	+	0.411752i	$0.864917\pi$
$278$	5.88332	+	10.1902i	0.352858	+	0.611168i
$279$		0			0
$280$	5.94155	−	10.2911i	0.355076	−	0.615009i
$281$	19.2111	+	6.99226i	1.14604	+	0.417123i	0.844090	−	0.536201i	$-0.180141\pi$
$281$	19.2111	+	6.99226i	1.14604	+	0.417123i	0.301947	+	0.953325i	$0.402363\pi$
$282$		0			0
$283$	10.2575	+	8.60709i	0.609747	+	0.511638i	0.894562	−	0.446944i	$-0.147488\pi$
$283$	10.2575	+	8.60709i	0.609747	+	0.511638i	−0.284815	+	0.958582i	$0.591932\pi$
$284$	1.23905	+	1.03969i	0.0735242	+	0.0616941i
$285$		0			0
$286$	−1.96059	−	0.713595i	−0.115932	−	0.0421957i
$287$	5.05603	−	8.75731i	0.298448	−	0.516928i
$288$		0			0
$289$	4.03612	+	6.99076i	0.237419	+	0.411221i
$290$	−0.853904	−	4.84273i	−0.0501430	−	0.284375i
$291$		0			0
$292$	2.08121	−	0.757498i	0.121793	−	0.0443292i
$293$	−0.775443	+	4.39776i	−0.0453019	+	0.256920i	−0.999044	−	0.0437047i	$-0.986084\pi$
$293$	−0.775443	+	4.39776i	−0.0453019	+	0.256920i	0.953743	+	0.300624i	$0.0971951\pi$
$294$		0			0
$295$	−40.8422	+	34.2707i	−2.37793	+	1.99532i
$296$	14.8042			0.860478
$297$		0			0
$298$	11.2689			0.652790
$299$	0.694673	−	0.582900i	0.0401740	−	0.0337100i
$300$		0			0
$301$	−1.09439	+	6.20659i	−0.0630796	+	0.357742i
$302$	−17.7379	+	6.45606i	−1.02070	+	0.371504i
$303$		0			0
$304$	−0.321807	−	1.82506i	−0.0184569	−	0.104674i
$305$	20.8132	+	36.0496i	1.19176	+	2.06419i
$306$		0			0
$307$	2.01673	−	3.49307i	0.115101	−	0.199360i	−0.802719	−	0.596357i	$-0.796614\pi$
$307$	2.01673	−	3.49307i	0.115101	−	0.199360i	0.917820	+	0.396997i	$0.129948\pi$
$308$	−4.25448	−	1.54850i	−0.242422	−	0.0882342i
$309$		0			0
$310$	−19.4141	−	16.2904i	−1.10265	−	0.925232i
$311$	−12.6142	−	10.5846i	−0.715284	−	0.600195i	0.210792	−	0.977531i	$-0.432396\pi$
$311$	−12.6142	−	10.5846i	−0.715284	−	0.600195i	−0.926076	+	0.377336i	$0.876840\pi$
$312$		0			0
$313$	−3.97424	−	1.44651i	−0.224637	−	0.0817613i	0.227250	−	0.973837i	$-0.427027\pi$
$313$	−3.97424	−	1.44651i	−0.224637	−	0.0817613i	−0.451887	+	0.892075i	$0.649249\pi$
$314$	−6.54019	+	11.3279i	−0.369084	+	0.639273i
$315$		0			0
$316$	2.17704	+	3.77075i	0.122468	+	0.212121i
$317$	1.85839	+	10.5395i	0.104378	+	0.591956i	0.991467	+	0.130358i	$0.0416126\pi$
$317$	1.85839	+	10.5395i	0.104378	+	0.591956i	−0.887089	+	0.461598i	$0.847276\pi$
$318$		0			0
$319$	−4.99649	+	1.81857i	−0.279750	+	0.101821i
$320$	−4.42790	+	25.1119i	−0.247527	+	1.40380i
$321$		0			0
$322$	−1.26321	+	1.05996i	−0.0703961	+	0.0590693i
$323$	−8.65697			−0.481686
$324$		0			0
$325$	5.90154			0.327358
$326$	14.9880	−	12.5764i	0.830108	−	0.696543i
$327$		0			0
$328$	−5.17810	+	29.3665i	−0.285913	+	1.62149i
$329$	−7.99710	+	2.91071i	−0.440895	+	0.160473i
$330$		0			0
$331$	2.65088	+	15.0339i	0.145706	+	0.826338i	0.966798	+	0.255542i	$0.0822541\pi$
$331$	2.65088	+	15.0339i	0.145706	+	0.826338i	−0.821092	+	0.570796i	$0.806635\pi$
$332$	2.76802	+	4.79436i	0.151915	+	0.263125i
$333$		0			0
$334$	−6.04087	+	10.4631i	−0.330542	+	0.572515i
$335$	10.3353	+	3.76173i	0.564676	+	0.205525i
$336$		0			0
$337$	24.0827	+	20.2078i	1.31187	+	1.10079i	0.987961	+	0.154702i	$0.0494417\pi$
$337$	24.0827	+	20.2078i	1.31187	+	1.10079i	0.323909	+	0.946088i	$0.395003\pi$
$338$	9.30781	+	7.81018i	0.506278	+	0.424818i
$339$		0			0
$340$	12.3116	+	4.48107i	0.667692	+	0.243020i
$341$	−13.7017	+	23.7320i	−0.741989	+	1.28516i
$342$		0			0
$343$	−0.500000	−	0.866025i	−0.0269975	−	0.0467610i
$344$	−3.22725	−	18.3026i	−0.174002	−	0.986812i
$345$		0			0
$346$	11.5423	−	4.20104i	0.620515	−	0.225849i
$347$	4.98575	−	28.2756i	0.267649	−	1.51791i	−0.493735	−	0.869613i	$-0.664369\pi$
$347$	4.98575	−	28.2756i	0.267649	−	1.51791i	0.761384	−	0.648301i	$-0.224520\pi$
$348$		0			0
$349$	−26.3086	+	22.0755i	−1.40827	+	1.18168i	−0.450979	+	0.892535i	$0.648925\pi$
$349$	−26.3086	+	22.0755i	−1.40827	+	1.18168i	−0.957287	+	0.289141i	$0.906630\pi$
$350$	−10.7315			−0.573624
$351$		0			0
$352$	21.9980			1.17250
$353$	−17.0574	+	14.3129i	−0.907874	+	0.761796i	−0.971713	−	0.236164i	$-0.924110\pi$
$353$	−17.0574	+	14.3129i	−0.907874	+	0.761796i	0.0638396	+	0.997960i	$0.479665\pi$
$354$		0			0
$355$	1.04013	−	5.89886i	0.0552043	−	0.313079i
$356$	10.4794	−	3.81418i	0.555405	−	0.202151i
$357$		0			0
$358$	−2.73590	−	15.5160i	−0.144597	−	0.820048i
$359$	−0.477605	−	0.827236i	−0.0252070	−	0.0436598i	0.853147	−	0.521671i	$-0.174691\pi$
$359$	−0.477605	−	0.827236i	−0.0252070	−	0.0436598i	−0.878354	+	0.478011i	$0.841358\pi$
$360$		0			0
$361$	5.30281	−	9.18473i	0.279095	−	0.483407i
$362$	1.95577	+	0.711844i	0.102793	+	0.0374137i
$363$		0			0
$364$	−0.437732	−	0.367301i	−0.0229434	−	0.0192518i
$365$	−6.28297	−	5.27204i	−0.328866	−	0.275951i
$366$		0			0
$367$	7.54882	+	2.74755i	0.394045	+	0.143421i	0.531441	−	0.847096i	$-0.321651\pi$
$367$	7.54882	+	2.74755i	0.394045	+	0.143421i	−0.137395	+	0.990516i	$0.543873\pi$
$368$	0.552282	−	0.956581i	0.0287897	−	0.0498652i
$369$		0			0
$370$	−9.65889	−	16.7297i	−0.502142	−	0.869735i
$371$	1.84284	+	10.4513i	0.0956757	+	0.542604i
$372$		0			0
$373$	9.03262	−	3.28761i	0.467692	−	0.170226i	−0.0974148	−	0.995244i	$-0.531057\pi$
$373$	9.03262	−	3.28761i	0.467692	−	0.170226i	0.565106	+	0.825018i	$0.308835\pi$
$374$	−2.06146	+	11.6911i	−0.106596	+	0.604534i
$375$		0			0
$376$	19.2248	−	16.1315i	0.991442	−	0.831918i
$377$	−0.671078			−0.0345623
$378$		0			0
$379$	−23.3222			−1.19798			−0.598990	−	0.800757i	$-0.704431\pi$
$379$	−23.3222			−1.19798			−0.598990	+	0.800757i	$0.704431\pi$
$380$	9.73210	−	8.16620i	0.499246	−	0.418917i
$381$		0			0
$382$	2.61529	−	14.8320i	0.133810	−	0.758874i
$383$	−3.61550	+	1.31594i	−0.184744	+	0.0672412i	−0.432735	−	0.901521i	$-0.642452\pi$
$383$	−3.61550	+	1.31594i	−0.184744	+	0.0672412i	0.247992	+	0.968762i	$0.420229\pi$
$384$		0			0
$385$	2.91147	+	16.5118i	0.148382	+	0.841517i
$386$	4.18965	+	7.25669i	0.213248	+	0.369356i
$387$		0			0
$388$	6.56094	−	11.3639i	0.333081	−	0.576914i
$389$	−20.4292	−	7.43562i	−1.03580	−	0.377001i	−0.232515	−	0.972593i	$-0.574695\pi$
$389$	−20.4292	−	7.43562i	−1.03580	−	0.377001i	−0.803287	+	0.595592i	$0.796918\pi$
$390$		0			0
$391$	−3.95263	−	3.31665i	−0.199893	−	0.167730i
$392$	2.25899	+	1.89552i	0.114096	+	0.0957381i
$393$		0			0
$394$	8.82909	+	3.21353i	0.444803	+	0.161895i
$395$	8.06210	−	13.9640i	0.405649	−	0.702604i
$396$		0			0
$397$	−8.65531	−	14.9914i	−0.434398	−	0.752399i	0.562849	−	0.826560i	$-0.309705\pi$
$397$	−8.65531	−	14.9914i	−0.434398	−	0.752399i	−0.997246	+	0.0741612i	$0.976372\pi$
$398$	3.23107	+	18.3243i	0.161959	+	0.918515i
$399$		0			0
$400$	6.75485	−	2.45856i	0.337742	−	0.122928i
$401$	0.230337	−	1.30631i	0.0115025	−	0.0652339i	−0.978516	−	0.206170i	$-0.933900\pi$
$401$	0.230337	−	1.30631i	0.0115025	−	0.0652339i	0.990019	+	0.140936i	$0.0450112\pi$
$402$		0			0
$403$	−2.64943	+	2.22313i	−0.131977	+	0.110742i
$404$	12.0187			0.597955
$405$		0			0
$406$	1.22031			0.0605628
$407$	−16.0012	+	13.4266i	−0.793148	+	0.665530i
$408$		0			0
$409$	2.25387	−	12.7824i	0.111447	−	0.632047i	−0.877001	−	0.480488i	$-0.840460\pi$
$409$	2.25387	−	12.7824i	0.111447	−	0.632047i	0.988448	−	0.151559i	$-0.0484293\pi$
$410$	36.5643	−	13.3083i	1.80578	−	0.657251i
$411$		0			0
$412$	−2.61099	−	14.8077i	−0.128634	−	0.729521i
$413$	−6.61540	−	11.4582i	−0.325522	−	0.563821i
$414$		0			0
$415$	10.2506	−	17.7546i	0.503184	−	0.871541i
$416$	2.60893	+	0.949572i	0.127913	+	0.0465566i
$417$		0			0
$418$	8.81825	+	7.39939i	0.431315	+	0.361916i
$419$	−6.14231	−	5.15401i	−0.300071	−	0.251790i	0.480303	−	0.877103i	$-0.340527\pi$
$419$	−6.14231	−	5.15401i	−0.300071	−	0.251790i	−0.780374	+	0.625313i	$0.784971\pi$
$420$		0			0
$421$	29.3637	+	10.6875i	1.43110	+	0.520878i	0.937247	−	0.348667i	$-0.113366\pi$
$421$	29.3637	+	10.6875i	1.43110	+	0.520878i	0.493854	+	0.869545i	$0.335588\pi$
$422$	5.84223	−	10.1190i	0.284395	−	0.492587i
$423$		0			0
$424$	−15.6476	−	27.1025i	−0.759916	−	1.31621i
$425$	−5.83097	−	33.0691i	−0.282844	−	1.60409i
$426$		0			0
$427$	−9.70701	+	3.53306i	−0.469755	+	0.170977i
$428$	1.63009	−	9.24471i	0.0787935	−	0.446860i
$429$		0			0
$430$	−18.5775	+	15.5884i	−0.895887	+	0.751739i
$431$	−0.875234			−0.0421585			−0.0210793	−	0.999778i	$-0.506710\pi$
$431$	−0.875234			−0.0421585			−0.0210793	+	0.999778i	$0.506710\pi$
$432$		0			0
$433$	−3.75223			−0.180321			−0.0901604	−	0.995927i	$-0.528738\pi$
$433$	−3.75223			−0.180321			−0.0901604	+	0.995927i	$0.528738\pi$
$434$	4.81779	−	4.04261i	0.231261	−	0.194051i
$435$		0			0
$436$	2.98808	−	16.9462i	0.143103	−	0.811578i
$437$	−4.70155	+	1.71122i	−0.224906	+	0.0818589i
$438$		0			0
$439$	−6.59712	−	37.4142i	−0.314864	−	1.78568i	−0.572983	−	0.819567i	$-0.694214\pi$
$439$	−6.59712	−	37.4142i	−0.314864	−	1.78568i	0.258120	−	0.966113i	$-0.416897\pi$
$440$	−24.7214	−	42.8186i	−1.17854	−	2.04130i
$441$		0			0
$442$	−0.749151	+	1.29757i	−0.0356335	+	0.0617190i
$443$	7.02357	+	2.55637i	0.333700	+	0.121457i	0.503436	−	0.864033i	$-0.332069\pi$
$443$	7.02357	+	2.55637i	0.333700	+	0.121457i	−0.169736	+	0.985490i	$0.554291\pi$
$444$		0			0
$445$	−31.6362	−	26.5459i	−1.49970	−	1.25840i
$446$	−12.9195	−	10.8407i	−0.611754	−	0.513323i
$447$		0			0
$448$	−5.94626	−	2.16426i	−0.280934	−	0.102252i
$449$	−6.38762	+	11.0637i	−0.301450	+	0.522127i	−0.976465	−	0.215677i	$-0.930804\pi$
$449$	−6.38762	+	11.0637i	−0.301450	+	0.522127i	0.675014	+	0.737805i	$0.264137\pi$
$450$		0			0
$451$	−21.0369	−	36.4370i	−0.990590	−	1.71575i
$452$	1.52723	+	8.66137i	0.0718350	+	0.407397i
$453$		0			0
$454$	−11.6626	+	4.24484i	−0.547353	+	0.199220i
$455$	−0.367457	+	2.08395i	−0.0172266	+	0.0976971i
$456$		0			0
$457$	−8.38088	+	7.03239i	−0.392041	+	0.328962i	−0.817408	−	0.576060i	$-0.804590\pi$
$457$	−8.38088	+	7.03239i	−0.392041	+	0.328962i	0.425367	+	0.905021i	$0.360145\pi$
$458$	−7.85813			−0.367186
$459$		0			0
$460$	7.57215			0.353053
$461$	16.2100	−	13.6018i	0.754973	−	0.633497i	−0.181840	−	0.983328i	$-0.558205\pi$
$461$	16.2100	−	13.6018i	0.754973	−	0.633497i	0.936813	+	0.349831i	$0.113761\pi$
$462$		0			0
$463$	−4.14357	+	23.4994i	−0.192568	+	1.09211i	0.723272	+	0.690564i	$0.242638\pi$
$463$	−4.14357	+	23.4994i	−0.192568	+	1.09211i	−0.915840	+	0.401544i	$0.868474\pi$
$464$	−0.768110	+	0.279569i	−0.0356586	+	0.0129787i
$465$		0			0
$466$	−0.767857	−	4.35473i	−0.0355703	−	0.201729i
$467$	4.79553	+	8.30609i	0.221910	+	0.384360i	0.955388	−	0.295353i	$-0.0954374\pi$
$467$	4.79553	+	8.30609i	0.221910	+	0.384360i	−0.733478	+	0.679714i	$0.762104\pi$
$468$		0			0
$469$	−1.36470	+	2.36373i	−0.0630159	+	0.109147i
$470$	−30.7726	−	11.2003i	−1.41943	−	0.516632i
$471$		0			0
$472$	29.8882	+	25.0792i	1.37572	+	1.15436i
$473$	20.0876	+	16.8555i	0.923629	+	0.775017i
$474$		0			0
$475$	−30.5970	−	11.1364i	−1.40389	−	0.510974i
$476$	−1.62566	+	2.81573i	−0.0745120	+	0.129059i
$477$		0			0
$478$	−2.09802	−	3.63388i	−0.0959614	−	0.166210i
$479$	0.386092	+	2.18964i	0.0176410	+	0.100047i	0.992357	−	0.123400i	$-0.0393800\pi$
$479$	0.386092	+	2.18964i	0.0176410	+	0.100047i	−0.974716	+	0.223448i	$0.928269\pi$
$480$		0			0
$481$	−2.47729	+	0.901661i	−0.112955	+	0.0411122i
$482$	0.709727	−	4.02506i	0.0323272	−	0.183336i
$483$		0			0
$484$	−5.26141	+	4.41484i	−0.239155	+	0.200675i
$485$	−48.5934			−2.20651
$486$		0			0
$487$	12.6488			0.573172			0.286586	−	0.958054i	$-0.407480\pi$
$487$	12.6488			0.573172			0.286586	+	0.958054i	$0.407480\pi$
$488$	23.3353	−	19.5807i	1.05634	−	0.886375i
$489$		0			0
$490$	0.668193	−	3.78951i	0.0301859	−	0.171193i
$491$	18.2787	−	6.65291i	0.824908	−	0.300242i	0.105140	−	0.994457i	$-0.466471\pi$
$491$	18.2787	−	6.65291i	0.824908	−	0.300242i	0.719767	+	0.694216i	$0.244249\pi$
$492$		0			0
$493$	0.663054	+	3.76037i	0.0298624	+	0.169358i
$494$	0.726427	+	1.25821i	0.0326835	+	0.0566095i
$495$		0			0
$496$	−2.10636	+	3.64832i	−0.0945784	+	0.163815i
$497$	1.39679	+	0.508392i	0.0626548	+	0.0228045i
$498$		0			0
$499$	8.43660	+	7.07915i	0.377674	+	0.316906i	0.811789	−	0.583951i	$-0.198494\pi$
$499$	8.43660	+	7.07915i	0.377674	+	0.316906i	−0.434114	+	0.900858i	$0.642939\pi$
$500$	20.9544	+	17.5829i	0.937111	+	0.786330i
$501$		0			0
$502$	2.18761	+	0.796227i	0.0976380	+	0.0355373i
$503$	−9.36478	+	16.2203i	−0.417555	+	0.723226i	−0.995693	−	0.0927129i	$-0.970446\pi$
$503$	−9.36478	+	16.2203i	−0.417555	+	0.723226i	0.578138	+	0.815939i	$0.303779\pi$
$504$		0			0
$505$	−22.2541	−	38.5453i	−0.990295	−	1.71524i
$506$	1.19142	+	6.75688i	0.0529651	+	0.300380i
$507$		0			0
$508$	2.65084	−	0.964826i	0.117612	−	0.0428072i
$509$	3.29245	−	18.6724i	0.145935	−	0.827639i	−0.820677	−	0.571393i	$-0.806403\pi$
$509$	3.29245	−	18.6724i	0.145935	−	0.827639i	0.966612	−	0.256246i	$-0.0824857\pi$
$510$		0			0
$511$	1.55918	−	1.30830i	0.0689739	−	0.0578760i
$512$	7.15417			0.316172
$513$		0			0
$514$	5.87185			0.258996
$515$	−42.6550	+	35.7918i	−1.87961	+	1.57718i
$516$		0			0
$517$	−6.14879	+	34.8715i	−0.270423	+	1.53365i
$518$	4.50477	−	1.63960i	0.197928	−	0.0720401i
$519$		0			0
$520$	−1.08359	−	6.14536i	−0.0475187	−	0.269492i
$521$	−8.88223	−	15.3845i	−0.389138	−	0.674006i	0.603196	−	0.797593i	$-0.293894\pi$
$521$	−8.88223	−	15.3845i	−0.389138	−	0.674006i	−0.992334	+	0.123587i	$0.960560\pi$
$522$		0			0
$523$	−8.14752	+	14.1119i	−0.356266	+	0.617071i	−0.987334	−	0.158657i	$-0.949284\pi$
$523$	−8.14752	+	14.1119i	−0.356266	+	0.617071i	0.631068	+	0.775728i	$0.282617\pi$
$524$	1.06126	+	0.386268i	0.0463615	+	0.0168742i
$525$		0			0
$526$	13.9164	+	11.6772i	0.606784	+	0.509152i
$527$	15.0750	+	12.6494i	0.656678	+	0.551018i
$528$		0			0
$529$	18.8107	+	6.84653i	0.817856	+	0.297675i
$530$	−20.4183	+	35.3656i	−0.886915	+	1.53618i
$531$		0			0
$532$	1.57635	+	2.73032i	0.0683435	+	0.118374i
$533$	−0.922096	−	5.22947i	−0.0399404	−	0.226513i
$534$		0			0
$535$	−32.6670	+	11.8898i	−1.41232	+	0.514041i
$536$	1.39764	−	7.92644i	0.0603691	−	0.342370i
$537$		0			0
$538$	14.5531	−	12.2115i	0.627430	−	0.526476i
$539$	−4.16076			−0.179216
$540$		0			0
$541$	16.6054			0.713923			0.356961	−	0.934119i	$-0.383813\pi$
$541$	16.6054			0.713923			0.356961	+	0.934119i	$0.383813\pi$
$542$	4.02075	−	3.37381i	0.172706	−	0.144918i
$543$		0			0
$544$	2.74316	−	15.5573i	0.117612	−	0.667012i
$545$	−59.8810	+	21.7949i	−2.56502	+	0.933591i
$546$		0			0
$547$	−5.55686	−	31.5145i	−0.237594	−	1.34746i	−0.837081	−	0.547078i	$-0.815740\pi$
$547$	−5.55686	−	31.5145i	−0.237594	−	1.34746i	0.599487	−	0.800384i	$-0.295371\pi$
$548$	1.90381	+	3.29750i	0.0813269	+	0.140862i
$549$		0			0
$550$	−22.3256	+	38.6691i	−0.951967	+	1.64886i
$551$	3.47927	+	1.26635i	0.148222	+	0.0539483i
$552$		0			0
$553$	3.06523	+	2.57203i	0.130347	+	0.109374i
$554$	−6.02040	−	5.05172i	−0.255782	−	0.214627i
$555$		0			0
$556$	12.5998	+	4.58596i	0.534352	+	0.194488i
$557$	11.4867	−	19.8955i	0.486706	−	0.843000i	−0.513177	−	0.858283i	$-0.671532\pi$
$557$	11.4867	−	19.8955i	0.486706	−	0.843000i	0.999883	+	0.0152830i	$0.00486491\pi$
$558$		0			0
$559$	1.65477	+	2.86615i	0.0699893	+	0.121225i
$560$	0.447580	+	2.53835i	0.0189137	+	0.107265i
$561$		0			0
$562$	−18.3448	+	6.67697i	−0.773830	+	0.281651i
$563$	0.736048	−	4.17434i	0.0310207	−	0.175927i	−0.965361	−	0.260918i	$-0.915975\pi$
$563$	0.736048	−	4.17434i	0.0310207	−	0.175927i	0.996382	+	0.0849904i	$0.0270860\pi$
$564$		0			0
$565$	24.9500	−	20.9355i	1.04965	−	0.880765i
$566$	−12.7865			−0.537455
$567$		0			0
$568$	−4.38336			−0.183922
$569$	−28.1874	+	23.6520i	−1.18168	+	0.991544i	−0.181710	+	0.983352i	$0.558163\pi$
$569$	−28.1874	+	23.6520i	−1.18168	+	0.991544i	−0.999966	+	0.00819179i	$0.997392\pi$
$570$		0			0
$571$	−3.50151	+	19.8580i	−0.146533	+	0.831033i	0.819590	+	0.572951i	$0.194201\pi$
$571$	−3.50151	+	19.8580i	−0.146533	+	0.831033i	−0.966123	+	0.258082i	$0.916910\pi$
$572$	−2.23415	+	0.813164i	−0.0934145	+	0.0340001i
$573$		0			0
$574$	1.67676	+	9.50941i	0.0699868	+	0.396915i
$575$	−9.70353	−	16.8070i	−0.404665	−	0.700901i
$576$		0			0
$577$	10.6679	−	18.4773i	0.444109	−	0.769220i	−0.553881	−	0.832596i	$-0.686854\pi$
$577$	10.6679	−	18.4773i	0.444109	−	0.769220i	0.997990	+	0.0633766i	$0.0201869\pi$
$578$	−7.24339	−	2.63638i	−0.301285	−	0.109659i
$579$		0			0
$580$	−4.29259	−	3.60191i	−0.178240	−	0.149561i
$581$	3.89731	+	3.27024i	0.161688	+	0.135672i
$582$		0			0
$583$	41.4931	+	15.1023i	1.71847	+	0.625472i
$584$	−3.00104	+	5.19795i	−0.124184	+	0.215093i
$585$		0			0
$586$	−2.13212	−	3.69294i	−0.0880771	−	0.152554i
$587$	2.14277	+	12.1522i	0.0884414	+	0.501576i	0.996561	+	0.0828648i	$0.0264070\pi$
$587$	2.14277	+	12.1522i	0.0884414	+	0.501576i	−0.908119	+	0.418711i	$0.862482\pi$
$588$		0			0
$589$	17.9313	−	6.52647i	0.738848	−	0.268919i
$590$	8.84072	−	50.1382i	0.363967	−	2.06416i
$591$		0			0
$592$	−2.45986	+	2.06406i	−0.101099	+	0.0848325i
$593$	27.5842			1.13275			0.566373	−	0.824149i	$-0.308346\pi$
$593$	27.5842			1.13275			0.566373	+	0.824149i	$0.308346\pi$
$594$		0			0
$595$	12.0404			0.493608
$596$	9.83700	−	8.25422i	0.402939	−	0.338106i
$597$		0			0
$598$	−0.150369	+	0.852786i	−0.00614905	+	0.0348730i
$599$	12.9966	−	4.73037i	0.531026	−	0.193278i	−0.0625703	−	0.998041i	$-0.519930\pi$
$599$	12.9966	−	4.73037i	0.531026	−	0.193278i	0.593597	+	0.804763i	$0.297708\pi$
$600$		0			0
$601$	3.75872	+	21.3168i	0.153321	+	0.869529i	0.960304	+	0.278954i	$0.0899879\pi$
$601$	3.75872	+	21.3168i	0.153321	+	0.869529i	−0.806983	+	0.590575i	$0.798901\pi$
$602$	−3.00908	−	5.21188i	−0.122641	−	0.212420i
$603$		0			0
$604$	−10.7550	+	18.6283i	−0.437617	+	0.757974i
$605$	23.9009	+	8.69923i	0.971712	+	0.353674i
$606$		0			0
$607$	−5.59833	−	4.69756i	−0.227229	−	0.190668i	0.522064	−	0.852906i	$-0.325162\pi$
$607$	−5.59833	−	4.69756i	−0.227229	−	0.190668i	−0.749293	+	0.662238i	$0.769607\pi$
$608$	−11.7343	−	9.84628i	−0.475890	−	0.399319i
$609$		0			0
$610$	−37.3523	−	13.5951i	−1.51235	−	0.550450i
$611$	−2.23451	+	3.87029i	−0.0903987	+	0.156575i
$612$		0			0
$613$	11.2255	+	19.4432i	0.453395	+	0.785303i	0.998594	−	0.0530037i	$-0.0168795\pi$
$613$	11.2255	+	19.4432i	0.453395	+	0.785303i	−0.545200	+	0.838306i	$0.683546\pi$
$614$	0.668820	+	3.79307i	0.0269914	+	0.153076i
$615$		0			0
$616$	11.5297	−	4.19647i	0.464545	−	0.169081i
$617$	−4.60952	+	26.1419i	−0.185572	+	1.05243i	0.739645	+	0.672997i	$0.234993\pi$
$617$	−4.60952	+	26.1419i	−0.185572	+	1.05243i	−0.925218	+	0.379437i	$0.876118\pi$
$618$		0			0
$619$	−16.5534	+	13.8899i	−0.665337	+	0.558284i	−0.911681	−	0.410899i	$-0.865215\pi$
$619$	−16.5534	+	13.8899i	−0.665337	+	0.558284i	0.246344	+	0.969182i	$0.420771\pi$
$620$	−28.8796			−1.15983
$621$		0			0
$622$	15.7241			0.630480
$623$	7.85082	−	6.58762i	0.314536	−	0.263927i
$624$		0			0
$625$	7.83280	−	44.4220i	0.313312	−	1.77688i
$626$	3.79504	−	1.38128i	0.151680	−	0.0552071i
$627$		0			0
$628$	2.58831	+	14.6791i	0.103285	+	0.585758i
$629$	7.50009	+	12.9905i	0.299048	+	0.517967i
$630$		0			0
$631$	−3.79456	+	6.57237i	−0.151059	+	0.261642i	−0.931617	−	0.363441i	$-0.881602\pi$
$631$	−3.79456	+	6.57237i	−0.151059	+	0.261642i	0.780558	+	0.625083i	$0.214935\pi$
$632$	−11.0880	−	4.03571i	−0.441058	−	0.160532i
$633$		0			0
$634$	−7.82858	−	6.56896i	−0.310913	−	0.260887i
$635$	−8.00263	−	6.71500i	−0.317575	−	0.266477i
$636$		0			0
$637$	−0.493460	−	0.179605i	−0.0195516	−	0.00711620i
$638$	2.53870	−	4.39716i	0.100508	−	0.174085i
$639$		0			0
$640$	9.13018	+	15.8139i	0.360902	+	0.625101i
$641$	0.283856	+	1.60983i	0.0112117	+	0.0635844i	0.989900	−	0.141765i	$-0.0452779\pi$
$641$	0.283856	+	1.60983i	0.0112117	+	0.0635844i	−0.978689	+	0.205350i	$0.934167\pi$
$642$		0			0
$643$	25.9497	−	9.44493i	1.02336	−	0.372472i	0.224810	−	0.974403i	$-0.427824\pi$
$643$	25.9497	−	9.44493i	1.02336	−	0.372472i	0.798548	+	0.601931i	$0.205602\pi$
$644$	−0.326302	+	1.85055i	−0.0128581	+	0.0729218i
$645$		0			0
$646$	6.33259	−	5.31368i	0.249153	−	0.209064i
$647$	44.8015			1.76133			0.880663	−	0.473743i	$-0.157097\pi$
$647$	44.8015			1.76133			0.880663	+	0.473743i	$0.157097\pi$
$648$		0			0
$649$	−55.0501			−2.16091
$650$	−4.31699	+	3.62238i	−0.169326	+	0.142082i
$651$		0			0
$652$	3.87156	−	21.9567i	0.151622	−	0.859891i
$653$	3.19930	−	1.16445i	0.125198	−	0.0455685i	−0.278661	−	0.960389i	$-0.589891\pi$
$653$	3.19930	−	1.16445i	0.125198	−	0.0455685i	0.403860	+	0.914821i	$0.367668\pi$
$654$		0			0
$655$	−0.726255	−	4.11880i	−0.0283771	−	0.160935i
$656$	−3.23400	−	5.60146i	−0.126267	−	0.218700i
$657$		0			0
$658$	4.06330	−	7.03784i	0.158404	−	0.274364i
$659$	0.0175194	+	0.00637655i	0.000682460	+	0.000248395i	0.342361	−	0.939568i	$-0.388773\pi$
$659$	0.0175194	+	0.00637655i	0.000682460	+	0.000248395i	−0.341679	+	0.939817i	$0.610996\pi$
$660$		0			0
$661$	−28.5778	−	23.9796i	−1.11155	−	0.932698i	−0.113399	−	0.993549i	$-0.536174\pi$
$661$	−28.5778	−	23.9796i	−1.11155	−	0.932698i	−0.998147	+	0.0608514i	$0.980618\pi$
$662$	−11.1670	−	9.37022i	−0.434017	−	0.364184i
$663$		0			0
$664$	−14.0980	−	5.13125i	−0.547108	−	0.199131i
$665$	5.83760	−	10.1110i	0.226372	−	0.392088i
$666$		0			0
$667$	1.10341	+	1.91117i	0.0427243	+	0.0740007i
$668$	2.39071	+	13.5584i	0.0924992	+	0.524589i
$669$		0			0
$670$	−9.86924	+	3.59211i	−0.381282	+	0.138775i
$671$	−7.46349	+	42.3276i	−0.288125	+	1.63404i
$672$		0			0
$673$	24.1602	−	20.2728i	0.931307	−	0.781460i	−0.0447443	−	0.998998i	$-0.514247\pi$
$673$	24.1602	−	20.2728i	0.931307	−	0.781460i	0.976052	+	0.217539i	$0.0698029\pi$
$674$	−30.0202			−1.15634
$675$		0			0
$676$	13.8459			0.532534
$677$	−2.41097	+	2.02304i	−0.0926610	+	0.0777518i	−0.687941	−	0.725766i	$-0.741485\pi$
$677$	−2.41097	+	2.02304i	−0.0926610	+	0.0777518i	0.595280	+	0.803518i	$0.297041\pi$
$678$		0			0
$679$	2.09401	−	11.8757i	0.0803606	−	0.455748i
$680$	−33.3647	+	12.1438i	−1.27948	+	0.465692i
$681$		0			0
$682$	−4.54398	−	25.7702i	−0.173998	−	0.986792i
$683$	17.6653	+	30.5971i	0.675943	+	1.17077i	0.976192	+	0.216907i	$0.0695967\pi$
$683$	17.6653	+	30.5971i	0.675943	+	1.17077i	−0.300250	+	0.953861i	$0.597070\pi$
$684$		0			0
$685$	7.05027	−	12.2114i	0.269377	−	0.466575i
$686$	0.897321	+	0.326598i	0.0342599	+	0.0124696i
$687$		0			0
$688$	3.08806	+	2.59119i	0.117731	+	0.0987883i
$689$	4.26912	+	3.58221i	0.162640	+	0.136472i
$690$		0			0
$691$	13.1245	+	4.77694i	0.499281	+	0.181723i	0.579370	−	0.815064i	$-0.303298\pi$
$691$	13.1245	+	4.77694i	0.499281	+	0.181723i	−0.0800898	+	0.996788i	$0.525521\pi$
$692$	6.99844	−	12.1217i	0.266041	−	0.460796i
$693$		0			0
$694$	13.7086	+	23.7439i	0.520370	+	0.901308i
$695$	−8.62245	−	48.9003i	−0.327068	−	1.85489i
$696$		0			0
$697$	−28.3921	+	10.3339i	−1.07543	+	0.391423i
$698$	5.69476	−	32.2966i	0.215550	−	1.22244i
$699$		0			0
$700$	−9.36789	+	7.86059i	−0.354073	+	0.297102i
$701$	43.9837			1.66124			0.830621	−	0.556839i	$-0.187986\pi$
$701$	43.9837			1.66124			0.830621	+	0.556839i	$0.187986\pi$
$702$		0			0
$703$	14.5452			0.548583
$704$	−20.1690	+	16.9238i	−0.760148	+	0.637840i
$705$		0			0
$706$	3.69225	−	20.9398i	0.138960	−	0.788079i
$707$	10.3790	−	3.77765i	0.390343	−	0.142073i
$708$		0			0
$709$	2.98700	+	16.9401i	0.112179	+	0.636199i	0.988108	+	0.153759i	$0.0491380\pi$
$709$	2.98700	+	16.9401i	0.112179	+	0.636199i	−0.875929	+	0.482439i	$0.839751\pi$
$710$	2.85988	+	4.95346i	0.107330	+	0.185900i
$711$		0			0
$712$	−15.1109	+	26.1729i	−0.566306	+	0.980870i
$713$	10.6876	+	3.88996i	0.400252	+	0.145680i
$714$		0			0
$715$	6.74469	+	5.65947i	0.252237	+	0.211652i
$716$	−13.7534	−	11.5405i	−0.513988	−	0.431287i
$717$		0			0
$718$	0.857129	+	0.311970i	0.0319878	+	0.0116426i
$719$	−1.85884	+	3.21960i	−0.0693229	+	0.120071i	−0.898603	−	0.438762i	$-0.855417\pi$
$719$	−1.85884	+	3.21960i	−0.0693229	+	0.120071i	0.829281	+	0.558833i	$0.188751\pi$
$720$		0			0
$721$	−6.90902	−	11.9668i	−0.257305	−	0.445666i
$722$	1.75860	+	9.97354i	0.0654484	+	0.371177i
$723$		0			0
$724$	2.22867	−	0.811169i	0.0828278	−	0.0301469i
$725$	−2.49389	+	14.1435i	−0.0926206	+	0.525278i
$726$		0			0
$727$	−26.6008	+	22.3208i	−0.986571	+	0.827831i	−0.985068	−	0.172168i	$-0.944923\pi$
$727$	−26.6008	+	22.3208i	−0.986571	+	0.827831i	−0.00150311	+	0.999999i	$0.500478\pi$
$728$	1.54855			0.0573932
$729$		0			0
$730$	7.83200			0.289875
$731$	14.4254	−	12.1043i	0.533542	−	0.447695i
$732$		0			0
$733$	2.65215	−	15.0411i	0.0979595	−	0.555556i	−0.895841	−	0.444375i	$-0.853426\pi$
$733$	2.65215	−	15.0411i	0.0979595	−	0.555556i	0.993800	−	0.111181i	$-0.0354632\pi$
$734$	−7.20844	+	2.62366i	−0.266068	+	0.0968409i
$735$		0			0
$736$	−1.58541	−	8.99130i	−0.0584389	−	0.331424i
$737$	5.67817	+	9.83488i	0.209158	+	0.362273i
$738$		0			0
$739$	−13.3250	+	23.0795i	−0.490167	+	0.848995i	−0.999936	−	0.0113168i	$-0.996398\pi$
$739$	−13.3250	+	23.0795i	−0.490167	+	0.848995i	0.509769	+	0.860312i	$0.329731\pi$
$740$	−20.6857	−	7.52897i	−0.760420	−	0.276770i
$741$		0			0
$742$	−7.76308	−	6.51400i	−0.284992	−	0.239136i
$743$	−11.4662	−	9.62125i	−0.420653	−	0.352970i	0.407759	−	0.913090i	$-0.366310\pi$
$743$	−11.4662	−	9.62125i	−0.420653	−	0.352970i	−0.828411	+	0.560120i	$0.810755\pi$
$744$		0			0
$745$	−44.6864	−	16.2645i	−1.63718	−	0.595886i
$746$	−4.58944	+	7.94915i	−0.168031	+	0.291039i
$747$		0			0
$748$	6.76398	+	11.7155i	0.247315	+	0.428363i
$749$	−1.49804	−	8.49581i	−0.0547372	−	0.310430i
$750$		0			0
$751$	−5.51346	+	2.00674i	−0.201189	+	0.0732268i	−0.440649	−	0.897679i	$-0.645252\pi$
$751$	−5.51346	+	2.00674i	−0.201189	+	0.0732268i	0.239460	+	0.970906i	$0.423030\pi$
$752$	−0.945252	+	5.36079i	−0.0344698	+	0.195488i
$753$		0			0
$754$	0.490895	−	0.411910i	0.0178774	−	0.0150009i
$755$	79.6569			2.89901
$756$		0			0
$757$	35.2022			1.27944			0.639722	−	0.768606i	$-0.279049\pi$
$757$	35.2022			1.27944			0.639722	+	0.768606i	$0.279049\pi$
$758$	17.0602	−	14.3152i	0.619656	−	0.519953i
$759$		0			0
$760$	−5.97853	+	33.9059i	−0.216864	+	1.22990i
$761$	−21.4866	+	7.82050i	−0.778890	+	0.283493i	−0.700710	−	0.713446i	$-0.747133\pi$
$761$	−21.4866	+	7.82050i	−0.778890	+	0.283493i	−0.0781805	+	0.996939i	$0.524911\pi$
$762$		0			0
$763$	−2.74602	−	15.5735i	−0.0994126	−	0.563797i
$764$	−8.58117	−	14.8630i	−0.310456	−	0.537725i
$765$		0			0
$766$	1.83702	−	3.18182i	0.0663744	−	0.114964i
$767$	−6.52886	−	2.37631i	−0.235744	−	0.0858036i
$768$		0			0
$769$	−20.4868	−	17.1905i	−0.738773	−	0.619904i	0.193735	−	0.981054i	$-0.437940\pi$
$769$	−20.4868	−	17.1905i	−0.738773	−	0.619904i	−0.932508	+	0.361150i	$0.882384\pi$
$770$	−12.2647	−	10.2913i	−0.441990	−	0.370874i
$771$		0			0
$772$	8.97264	+	3.26578i	0.322933	+	0.117538i
$773$	12.1028	−	20.9627i	0.435309	−	0.753977i	−0.562012	−	0.827129i	$-0.689973\pi$
$773$	12.1028	−	20.9627i	0.435309	−	0.753977i	0.997321	+	0.0731522i	$0.0233059\pi$
$774$		0			0
$775$	37.0085	+	64.1006i	1.32938	+	2.30256i
$776$	6.17502	+	35.0203i	0.221670	+	1.25715i
$777$		0			0
$778$	19.5080	−	7.10034i	0.699397	−	0.254560i
$779$	−5.08750	+	28.8527i	−0.182279	+	1.03375i
$780$		0			0
$781$	4.73776	−	3.97545i	0.169530	−	0.142253i
$782$	4.92713			0.176194
$783$		0			0
$784$	−0.639632			−0.0228440
$785$	42.2846	−	35.4810i	1.50920	−	1.26637i
$786$		0			0
$787$	1.26486	−	7.17338i	0.0450874	−	0.255703i	−0.953930	−	0.300030i	$-0.903003\pi$
$787$	1.26486	−	7.17338i	0.0450874	−	0.255703i	0.999017	+	0.0443270i	$0.0141143\pi$
$788$	10.0610	−	3.66192i	0.358410	−	0.130450i
$789$		0			0
$790$	2.67369	+	15.1632i	0.0951255	+	0.539484i
$791$	4.04126	+	6.99967i	0.143691	+	0.248880i
$792$		0			0
$793$	−2.71229	+	4.69782i	−0.0963161	+	0.166824i
$794$	15.5332	+	5.65362i	0.551252	+	0.200639i
$795$		0			0
$796$	16.2427	+	13.6292i	0.575706	+	0.483075i
$797$	15.7226	+	13.1929i	0.556925	+	0.467315i	0.877278	−	0.479983i	$-0.159357\pi$
$797$	15.7226	+	13.1929i	0.556925	+	0.467315i	−0.320353	+	0.947298i	$0.603802\pi$
$798$		0			0
$799$	23.8948	+	8.69701i	0.845338	+	0.307678i
$800$	29.7084	−	51.4565i	1.05035	−	1.81926i
$801$		0			0
$802$	0.633324	+	1.09695i	0.0223634	+	0.0387346i
$803$	−1.47056	−	8.33998i	−0.0518950	−	0.294311i
$804$		0			0
$805$	6.53907	−	2.38003i	0.230472	−	0.0838850i
$806$	0.573496	−	3.25246i	0.0202005	−	0.114563i
$807$		0			0
$808$	−24.9508	+	20.9362i	−0.877766	+	0.736533i
$809$	−38.2426			−1.34454			−0.672269	−	0.740307i	$-0.734680\pi$
$809$	−38.2426			−1.34454			−0.672269	+	0.740307i	$0.734680\pi$
$810$		0			0
$811$	−1.70505			−0.0598725			−0.0299362	−	0.999552i	$-0.509530\pi$
$811$	−1.70505			−0.0598725			−0.0299362	+	0.999552i	$0.509530\pi$
$812$	1.06525	−	0.893847i	0.0373828	−	0.0313679i
$813$		0			0
$814$	3.46362	−	19.6431i	0.121400	−	0.688492i
$815$	−77.5859	+	28.2390i	−2.71772	+	0.989168i
$816$		0			0
$817$	−3.17078	−	17.9824i	−0.110932	−	0.629125i
$818$	6.19714	+	10.7338i	0.216678	+	0.375297i
$819$		0			0
$820$	22.1701	−	38.3998i	0.774215	−	1.34098i
$821$	−19.7561	−	7.19062i	−0.689491	−	0.250954i	−0.0265739	−	0.999647i	$-0.508460\pi$
$821$	−19.7561	−	7.19062i	−0.689491	−	0.250954i	−0.662917	+	0.748693i	$0.730682\pi$
$822$		0			0
$823$	−35.2842	−	29.6070i	−1.22993	−	1.03204i	−0.998243	−	0.0592449i	$-0.981131\pi$
$823$	−35.2842	−	29.6070i	−1.22993	−	1.03204i	−0.231688	−	0.972790i	$-0.574425\pi$
$824$	31.2148	+	26.1923i	1.08742	+	0.912453i
$825$		0			0
$826$	11.8723	+	4.32115i	0.413089	+	0.150352i
$827$	−5.75106	+	9.96113i	−0.199984	+	0.346382i	−0.948523	−	0.316708i	$-0.897422\pi$
$827$	−5.75106	+	9.96113i	−0.199984	+	0.346382i	0.748539	+	0.663091i	$0.230756\pi$
$828$		0			0
$829$	−0.313043	−	0.542206i	−0.0108724	−	0.0188316i	0.860538	−	0.509386i	$-0.170128\pi$
$829$	−0.313043	−	0.542206i	−0.0108724	−	0.0188316i	−0.871410	+	0.490555i	$0.836794\pi$
$830$	3.39949	+	19.2794i	0.117998	+	0.669199i
$831$		0			0
$832$	−3.12255	+	1.13652i	−0.108255	+	0.0394016i
$833$	−0.518850	+	2.94254i	−0.0179771	+	0.101953i
$834$		0			0
$835$	39.0563	−	32.7722i	1.35160	−	1.13413i
$836$	13.1176			0.453683
$837$		0			0
$838$	7.65666			0.264495
$839$	−4.69808	+	3.94215i	−0.162196	+	0.136098i	−0.720273	−	0.693690i	$-0.755984\pi$
$839$	−4.69808	+	3.94215i	−0.162196	+	0.136098i	0.558078	+	0.829789i	$0.311539\pi$
$840$		0			0
$841$	−4.75221	+	26.9511i	−0.163869	+	0.929349i
$842$	−28.0397	+	10.2056i	−0.966311	+	0.351709i
$843$		0			0
$844$	−2.31209	−	13.1125i	−0.0795856	−	0.451352i
$845$	−25.6373	−	44.4050i	−0.881949	−	1.52758i
$846$		0			0
$847$	−3.15594	+	5.46626i	−0.108440	+	0.187823i
$848$	6.37873	+	2.32167i	0.219047	+	0.0797264i
$849$		0			0
$850$	24.5633	+	20.6110i	0.842514	+	0.706953i
$851$	6.64110	+	5.57254i	0.227654	+	0.191024i
$852$		0			0
$853$	7.98491	+	2.90627i	0.273398	+	0.0995088i	0.475081	−	0.879942i	$-0.342419\pi$
$853$	7.98491	+	2.90627i	0.273398	+	0.0995088i	−0.201683	+	0.979451i	$0.564641\pi$
$854$	4.93209	−	8.54264i	0.168773	−	0.292323i
$855$		0			0
$856$	12.7199	+	22.0315i	0.434757	+	0.753021i
$857$	3.77946	+	21.4344i	0.129104	+	0.732184i	0.978785	+	0.204888i	$0.0656830\pi$
$857$	3.77946	+	21.4344i	0.129104	+	0.732184i	−0.849682	+	0.527296i	$0.823206\pi$
$858$		0			0
$859$	−7.59180	+	2.76319i	−0.259029	+	0.0942788i	−0.468270	−	0.883585i	$-0.655123\pi$
$859$	−7.59180	+	2.76319i	−0.259029	+	0.0942788i	0.209242	+	0.977864i	$0.432900\pi$
$860$	−4.79878	+	27.2152i	−0.163637	+	0.928031i
$861$		0			0
$862$	0.640236	−	0.537222i	0.0218065	−	0.0182978i
$863$	27.0043			0.919238			0.459619	−	0.888116i	$-0.347986\pi$
$863$	27.0043			0.919238			0.459619	+	0.888116i	$0.347986\pi$
$864$		0			0
$865$	−51.8338			−1.76240
$866$	2.74477	−	2.30313i	0.0932710	−	0.0782637i
$867$		0			0
$868$	1.24449	−	7.05785i	0.0422407	−	0.239559i
$869$	15.6447	−	5.69420i	0.530709	−	0.193162i
$870$		0			0
$871$	0.248887	+	1.41151i	0.00843322	+	0.0478272i
$872$	23.3165	+	40.3854i	0.789597	+	1.36762i
$873$		0			0
$874$	2.38884	−	4.13759i	0.0808037	−	0.139956i
$875$	23.6222	+	8.59776i	0.798574	+	0.290657i
$876$		0			0
$877$	36.9626	+	31.0153i	1.24814	+	1.04731i	0.996843	+	0.0794019i	$0.0253010\pi$
$877$	36.9626	+	31.0153i	1.24814	+	1.04731i	0.251296	+	0.967910i	$0.419143\pi$
$878$	27.7908	+	23.3192i	0.937892	+	0.786985i
$879$		0			0
$880$	10.0776	+	3.66796i	0.339717	+	0.123647i
$881$	−17.3922	+	30.1241i	−0.585957	+	1.01491i	0.408799	+	0.912625i	$0.365948\pi$
$881$	−17.3922	+	30.1241i	−0.585957	+	1.01491i	−0.994755	+	0.102282i	$0.967386\pi$
$882$		0			0
$883$	12.6838	+	21.9690i	0.426843	+	0.739315i	0.996591	−	0.0825055i	$-0.0262922\pi$
$883$	12.6838	+	21.9690i	0.426843	+	0.739315i	−0.569747	+	0.821820i	$0.692959\pi$
$884$	0.296480	+	1.68142i	0.00997171	+	0.0565524i
$885$		0			0
$886$	−6.70687	+	2.44110i	−0.225322	+	0.0820104i
$887$	−1.54005	+	8.73407i	−0.0517099	+	0.293261i	−0.999685	−	0.0250819i	$-0.992015\pi$
$887$	−1.54005	+	8.73407i	−0.0517099	+	0.293261i	0.947976	+	0.318343i	$0.103126\pi$
$888$		0			0
$889$	1.98592	−	1.66639i	0.0666058	−	0.0558889i
$890$	39.4360			1.32190
$891$		0			0
$892$	−19.2184			−0.643479
$893$	18.8884	−	15.8493i	0.632076	−	0.530375i
$894$		0			0
$895$	−11.5454	+	65.4770i	−0.385919	+	2.18865i
$896$	−4.25820	+	1.54986i	−0.142256	+	0.0517771i
$897$		0			0
$898$	−2.11837	−	12.0139i	−0.0706908	−	0.400907i
$899$	−4.20833	−	7.28904i	−0.140356	−	0.243103i
$900$		0			0
$901$	15.8548	−	27.4612i	0.528198	−	0.914866i
$902$	37.7537	+	13.7412i	1.25706	+	0.457533i
$903$		0			0
$904$	−18.2583	−	15.3206i	−0.607263	−	0.509554i
$905$	−6.72814	−	5.64558i	−0.223651	−	0.187665i
$906$		0			0
$907$	−1.41772	−	0.516006i	−0.0470745	−	0.0171337i	0.318376	−	0.947965i	$-0.396863\pi$
$907$	−1.41772	−	0.516006i	−0.0470745	−	0.0171337i	−0.365450	+	0.930831i	$0.619085\pi$
$908$	−7.07142	+	12.2481i	−0.234673	+	0.406466i
$909$		0			0
$910$	−1.01034	−	1.74996i	−0.0334924	−	0.0580106i
$911$	−0.690573	−	3.91643i	−0.0228797	−	0.129757i	0.971229	−	0.238150i	$-0.0765408\pi$
$911$	−0.690573	−	3.91643i	−0.0228797	−	0.129757i	−0.994108	+	0.108392i	$0.965430\pi$
$912$		0			0
$913$	19.8916	−	7.23995i	0.658316	−	0.239607i
$914$	1.81413	−	10.2884i	0.0600060	−	0.340311i
$915$		0			0
$916$	−6.85962	+	5.75590i	−0.226648	+	0.190180i
$917$	1.03788			0.0342740
$918$		0			0
$919$	−2.10751			−0.0695202			−0.0347601	−	0.999396i	$-0.511067\pi$
$919$	−2.10751			−0.0695202			−0.0347601	+	0.999396i	$0.511067\pi$
$920$	−15.7197	+	13.1904i	−0.518263	+	0.434875i
$921$		0			0
$922$	−3.50881	+	19.8995i	−0.115557	+	0.655354i
$923$	0.733497	−	0.266971i	0.0241434	−	0.00878746i
$924$		0			0
$925$	9.79704	+	55.5618i	0.322125	+	1.82686i
$926$	−11.3930	−	19.7332i	−0.374396	−	0.648473i
$927$		0			0
$928$	−3.37822	+	5.85124i	−0.110895	+	0.192076i
$929$	20.6143	+	7.50298i	0.676332	+	0.246165i	0.657272	−	0.753654i	$-0.271710\pi$
$929$	20.6143	+	7.50298i	0.676332	+	0.246165i	0.0190602	+	0.999818i	$0.493933\pi$
$930$		0			0
$931$	2.21947	+	1.86235i	0.0727400	+	0.0610361i
$932$	−3.86003	−	3.23895i	−0.126439	−	0.106095i
$933$		0			0
$934$	−8.60625	−	3.13242i	−0.281605	−	0.102496i
$935$	25.0486	−	43.3854i	0.819177	−	1.41886i
$936$		0			0
$937$	−1.68308	−	2.91517i	−0.0549837	−	0.0952346i	0.837223	−	0.546861i	$-0.184177\pi$
$937$	−1.68308	−	2.91517i	−0.0549837	−	0.0952346i	−0.892207	+	0.451626i	$0.850844\pi$
$938$	−0.452583	−	2.56673i	−0.0147774	−	0.0838066i
$939$		0			0
$940$	−35.0664	+	12.7631i	−1.14374	+	0.416287i
$941$	10.5413	−	59.7827i	0.343637	−	1.94886i	0.0292315	−	0.999573i	$-0.490694\pi$
$941$	10.5413	−	59.7827i	0.343637	−	1.94886i	0.314405	−	0.949289i	$-0.398195\pi$
$942$		0			0
$943$	−13.3769	+	11.2245i	−0.435611	+	0.365521i
$944$	−8.46284			−0.275442
$945$		0			0
$946$	−25.0401			−0.814124
$947$	−7.27513	+	6.10455i	−0.236410	+	0.198371i	−0.753294	−	0.657684i	$-0.771536\pi$
$947$	−7.27513	+	6.10455i	−0.236410	+	0.198371i	0.516884	+	0.856055i	$0.327092\pi$
$948$		0			0
$949$	0.185600	−	1.05259i	0.00602482	−	0.0341685i
$950$	29.2174	−	10.6343i	0.947937	−	0.345021i
$951$		0			0
$952$	−1.53004	−	8.67727i	−0.0495888	−	0.281232i
$953$	−20.2653	−	35.1006i	−0.656458	−	1.13702i	−0.981526	−	0.191328i	$-0.938721\pi$
$953$	−20.2653	−	35.1006i	−0.656458	−	1.13702i	0.325068	−	0.945691i	$-0.394613\pi$
$954$		0			0
$955$	−31.7781	+	55.0412i	−1.02831	+	1.78109i
$956$	−4.49317	−	1.63538i	−0.145320	−	0.0528920i
$957$		0			0
$958$	−1.62644	−	1.36474i	−0.0525477	−	0.0440928i
$959$	2.68053	+	2.24923i	0.0865587	+	0.0726314i
$960$		0			0
$961$	−11.6311	−	4.23336i	−0.375196	−	0.136560i
$962$	1.25870	−	2.18014i	0.0405822	−	0.0702904i
$963$		0			0
$964$	−2.32872	−	4.03346i	−0.0750031	−	0.129909i
$965$	−6.14025	−	34.8231i	−0.197662	−	1.12100i
$966$		0			0
$967$	−17.8146	+	6.48397i	−0.572877	+	0.208510i	−0.612182	−	0.790717i	$-0.709708\pi$
$967$	−17.8146	+	6.48397i	−0.572877	+	0.208510i	0.0393045	+	0.999227i	$0.487486\pi$
$968$	3.23214	−	18.3304i	0.103885	−	0.589160i
$969$		0			0
$970$	35.5462	−	29.8268i	1.14132	−	0.957681i
$971$	10.9285			0.350712			0.175356	−	0.984505i	$-0.443892\pi$
$971$	10.9285			0.350712			0.175356	+	0.984505i	$0.443892\pi$
$972$		0			0
$973$	12.3223			0.395034
$974$	−9.25263	+	7.76388i	−0.296474	+	0.248771i
$975$		0			0
$976$	−1.14736	+	6.50701i	−0.0367261	+	0.208284i
$977$	−6.15227	+	2.23924i	−0.196829	+	0.0716398i	−0.438554	−	0.898705i	$-0.644509\pi$
$977$	−6.15227	+	2.23924i	−0.196829	+	0.0716398i	0.241725	+	0.970345i	$0.422287\pi$
$978$		0			0
$979$	−7.40463	−	41.9937i	−0.236653	−	1.34213i
$980$	−2.19244	−	3.79742i	−0.0700350	−	0.121304i
$981$		0			0
$982$	−9.28736	+	16.0862i	−0.296371	+	0.513330i
$983$	−22.8534	−	8.31794i	−0.728909	−	0.265301i	−0.0492059	−	0.998789i	$-0.515669\pi$
$983$	−22.8534	−	8.31794i	−0.728909	−	0.265301i	−0.679703	+	0.733488i	$0.737891\pi$
$984$		0			0
$985$	−30.3733	−	25.4862i	−0.967774	−	0.812059i
$986$	−2.79315	−	2.34373i	−0.0889520	−	0.0746396i
$987$		0			0
$988$	1.55573	+	0.566240i	0.0494944	+	0.0180145i
$989$	5.44167	−	9.42526i	0.173035	−	0.299706i
$990$		0			0
$991$	27.1742	+	47.0671i	0.863218	+	1.49514i	0.868806	+	0.495153i	$0.164888\pi$
$991$	27.1742	+	47.0671i	0.863218	+	1.49514i	−0.00558795	+	0.999984i	$0.501779\pi$
$992$	6.04662	+	34.2921i	0.191980	+	1.08878i
$993$		0			0
$994$	−1.33381	+	0.485468i	−0.0423059	+	0.0153981i
$995$	13.6350	−	77.3279i	0.432258	−	2.45146i
$996$		0			0
$997$	35.1207	−	29.4698i	1.11228	−	0.933317i	0.114095	−	0.993470i	$-0.463603\pi$
$997$	35.1207	−	29.4698i	1.11228	−	0.933317i	0.998189	+	0.0601524i	$0.0191587\pi$
$998$	−10.5166			−0.332897
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.v.b.442.5		54
3.2	odd	2		189.2.v.a.22.5	✓	54
27.4	even	9		5103.2.a.f.1.13		27
27.11	odd	18		189.2.v.a.43.5	yes	54
27.16	even	9	inner	567.2.v.b.127.5		54
27.23	odd	18		5103.2.a.i.1.15		27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.v.a.22.5	✓	54	3.2	odd	2
189.2.v.a.43.5	yes	54	27.11	odd	18
567.2.v.b.127.5		54	27.16	even	9	inner
567.2.v.b.442.5		54	1.1	even	1	trivial
5103.2.a.f.1.13		27	27.4	even	9
5103.2.a.i.1.15		27	27.23	odd	18

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.v (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.731503 + 0.613803i) q^{2} +(-0.188955 + 1.07162i) q^{4} +(3.78665 - 1.37823i) q^{5} +(0.173648 + 0.984808i) q^{7} +(-1.47445 - 2.55382i) q^{8} +O(q^{10})\)	\(q+(-0.731503 + 0.613803i) q^{2} +(-0.188955 + 1.07162i) q^{4} +(3.78665 - 1.37823i) q^{5} +(0.173648 + 0.984808i) q^{7} +(-1.47445 - 2.55382i) q^{8} +(-1.92398 + 3.33244i) q^{10} +(3.90983 + 1.42306i) q^{11} +(0.402272 + 0.337546i) q^{13} +(-0.731503 - 0.613803i) q^{14} +(0.601058 + 0.218767i) q^{16} +(1.49397 - 2.58763i) q^{17} +(-1.44865 - 2.50914i) q^{19} +(0.761427 + 4.31827i) q^{20} +(-3.73353 + 1.35889i) q^{22} +(0.299868 - 1.70064i) q^{23} +(8.60901 - 7.22382i) q^{25} -0.501450 q^{26} -1.08815 q^{28} +(-0.978952 + 0.821438i) q^{29} +(-1.14367 + 6.48610i) q^{31} +(4.96817 - 1.80826i) q^{32} +(0.495454 + 2.80986i) q^{34} +(2.01484 + 3.48980i) q^{35} +(-2.51013 + 4.34766i) q^{37} +(2.59981 + 0.946255i) q^{38} +(-9.10299 - 7.63831i) q^{40} +(-7.74629 - 6.49991i) q^{41} +(5.92226 + 2.15553i) q^{43} +(-2.26376 + 3.92095i) q^{44} +(0.824503 + 1.42808i) q^{46} +(1.47781 + 8.38105i) q^{47} +(-0.939693 + 0.342020i) q^{49} +(-1.86351 + 10.5685i) q^{50} +(-0.437732 + 0.367301i) q^{52} +10.6125 q^{53} +16.7665 q^{55} +(2.25899 - 1.89552i) q^{56} +(0.211904 - 1.20177i) q^{58} +(-12.4329 + 4.52520i) q^{59} +(1.79378 + 10.1730i) q^{61} +(-3.14459 - 5.44659i) q^{62} +(-3.16394 + 5.48010i) q^{64} +(1.98848 + 0.723748i) q^{65} +(2.09084 + 1.75442i) q^{67} +(2.49066 + 2.08991i) q^{68} +(-3.61591 - 1.31608i) q^{70} +(0.743219 - 1.28729i) q^{71} +(-1.01768 - 1.76267i) q^{73} +(-0.832449 - 4.72105i) q^{74} +(2.96257 - 1.07829i) q^{76} +(-0.722508 + 4.09754i) q^{77} +(3.06523 - 2.57203i) q^{79} +2.57751 q^{80} +9.65610 q^{82} +(3.89731 - 3.27024i) q^{83} +(2.09079 - 11.8575i) q^{85} +(-5.65522 + 2.05833i) q^{86} +(-2.13060 - 12.0833i) q^{88} +(-5.12426 - 8.87547i) q^{89} +(-0.262564 + 0.454775i) q^{91} +(1.76577 + 0.642689i) q^{92} +(-6.22534 - 5.22368i) q^{94} +(-8.94372 - 7.50467i) q^{95} +(-11.3317 - 4.12439i) q^{97} +(0.477454 - 0.826975i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 3 q^{5} + 27 q^{8}+O(q^{10}) \) 54 * q + 3 * q^5 + 27 * q^8	\( 54 q + 3 q^{5} + 27 q^{8} + 6 q^{11} - 9 q^{13} + 30 q^{17} + 12 q^{20} - 9 q^{22} + 12 q^{23} + 27 q^{25} - 18 q^{26} + 54 q^{28} - 6 q^{29} - 9 q^{31} + 9 q^{32} - 9 q^{34} + 12 q^{35} - 54 q^{38} - 45 q^{40} + 15 q^{41} - 9 q^{43} + 42 q^{44} + 45 q^{47} - 18 q^{50} - 63 q^{52} - 132 q^{53} + 9 q^{56} - 27 q^{58} + 36 q^{62} - 27 q^{64} - 66 q^{65} + 45 q^{67} - 87 q^{68} + 72 q^{71} + 72 q^{74} + 54 q^{76} - 3 q^{77} - 36 q^{79} - 42 q^{80} - 24 q^{83} + 18 q^{85} + 90 q^{86} + 54 q^{88} + 42 q^{89} - 87 q^{92} - 90 q^{94} - 12 q^{95} - 18 q^{97} + 9 q^{98}+O(q^{100}) \) 54 * q + 3 * q^5 + 27 * q^8 + 6 * q^11 - 9 * q^13 + 30 * q^17 + 12 * q^20 - 9 * q^22 + 12 * q^23 + 27 * q^25 - 18 * q^26 + 54 * q^28 - 6 * q^29 - 9 * q^31 + 9 * q^32 - 9 * q^34 + 12 * q^35 - 54 * q^38 - 45 * q^40 + 15 * q^41 - 9 * q^43 + 42 * q^44 + 45 * q^47 - 18 * q^50 - 63 * q^52 - 132 * q^53 + 9 * q^56 - 27 * q^58 + 36 * q^62 - 27 * q^64 - 66 * q^65 + 45 * q^67 - 87 * q^68 + 72 * q^71 + 72 * q^74 + 54 * q^76 - 3 * q^77 - 36 * q^79 - 42 * q^80 - 24 * q^83 + 18 * q^85 + 90 * q^86 + 54 * q^88 + 42 * q^89 - 87 * q^92 - 90 * q^94 - 12 * q^95 - 18 * q^97 + 9 * q^98

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