LMFDB - Embedded newform 819.2.fm.g.496.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(370,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("819.370");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fm (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			496.2
Character	$\chi$	$=$	819.496
Dual form			819.2.fm.g.748.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61897 - 0.433802i) q^{2} +(0.700831 + 0.404625i) q^{4} +(1.42145 + 1.42145i) q^{5} +(0.234216 + 2.63536i) q^{7} +(1.41124 + 1.41124i) q^{8} +O(q^{10})$	\(q+(-1.61897 - 0.433802i) q^{2} +(0.700831 + 0.404625i) q^{4} +(1.42145 + 1.42145i) q^{5} +(0.234216 + 2.63536i) q^{7} +(1.41124 + 1.41124i) q^{8} +(-1.68466 - 2.91792i) q^{10} +(-0.254101 + 0.948318i) q^{11} +(-1.60977 + 3.22624i) q^{13} +(0.764036 - 4.36818i) q^{14} +(-2.48181 - 4.29862i) q^{16} +(-2.99281 + 5.18370i) q^{17} +(2.71200 - 0.726678i) q^{19} +(0.421043 + 1.57135i) q^{20} +(0.822765 - 1.42507i) q^{22} +(-2.58851 + 1.49448i) q^{23} -0.958941i q^{25} +(4.00573 - 4.52487i) q^{26} +(-0.902188 + 1.94172i) q^{28} +(-3.65708 - 6.33425i) q^{29} +(-6.11048 - 6.11048i) q^{31} +(1.12013 + 4.18037i) q^{32} +(7.09397 - 7.09397i) q^{34} +(-3.41312 + 4.07897i) q^{35} +(-1.24143 + 4.63309i) q^{37} -4.70588 q^{38} +4.01202i q^{40} +(0.886060 - 3.30682i) q^{41} +(-0.748633 - 0.432224i) q^{43} +(-0.561795 + 0.561795i) q^{44} +(4.83903 - 1.29661i) q^{46} +(2.17001 - 2.17001i) q^{47} +(-6.89029 + 1.23449i) q^{49} +(-0.415990 + 1.55250i) q^{50} +(-2.43360 + 1.60970i) q^{52} -6.32446 q^{53} +(-1.70918 + 0.986797i) q^{55} +(-3.38859 + 4.04966i) q^{56} +(3.17290 + 11.8414i) q^{58} +(0.131692 + 0.491481i) q^{59} +(11.2829 + 6.51419i) q^{61} +(7.24196 + 12.5434i) q^{62} +2.67342i q^{64} +(-6.87417 + 2.29773i) q^{65} +(-0.827827 - 0.221815i) q^{67} +(-4.19491 + 2.42193i) q^{68} +(7.29521 - 5.12312i) q^{70} +(3.01121 + 11.2380i) q^{71} +(-1.03002 + 1.03002i) q^{73} +(4.01968 - 6.96230i) q^{74} +(2.19469 + 0.588064i) q^{76} +(-2.55868 - 0.447537i) q^{77} -11.6027 q^{79} +(2.58251 - 9.63806i) q^{80} +(-2.86901 + 4.96927i) q^{82} +(1.23779 + 1.23779i) q^{83} +(-11.6225 + 3.11424i) q^{85} +(1.02452 + 1.02452i) q^{86} +(-1.69690 + 0.979707i) q^{88} +(7.75255 + 2.07729i) q^{89} +(-8.87935 - 3.48670i) q^{91} -2.41881 q^{92} +(-4.45454 + 2.57183i) q^{94} +(4.88792 + 2.82204i) q^{95} +(-12.0756 + 3.23566i) q^{97} +(11.6907 + 0.990414i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8}+O(q^{10}) $ 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8	$ 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8} + 4 q^{11} + 32 q^{14} + 12 q^{16} + 4 q^{22} + 12 q^{23} + 24 q^{28} - 4 q^{29} - 4 q^{32} + 20 q^{35} + 4 q^{37} - 48 q^{43} - 24 q^{44} + 84 q^{46} + 24 q^{49} + 44 q^{50} - 72 q^{53} - 60 q^{56} - 16 q^{58} - 4 q^{65} - 56 q^{67} + 56 q^{70} - 84 q^{71} + 24 q^{74} - 80 q^{79} + 36 q^{85} + 48 q^{86} - 228 q^{88} - 48 q^{91} - 24 q^{92} + 84 q^{95} + 32 q^{98}+O(q^{100}) $ 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8 + 4 * q^11 + 32 * q^14 + 12 * q^16 + 4 * q^22 + 12 * q^23 + 24 * q^28 - 4 * q^29 - 4 * q^32 + 20 * q^35 + 4 * q^37 - 48 * q^43 - 24 * q^44 + 84 * q^46 + 24 * q^49 + 44 * q^50 - 72 * q^53 - 60 * q^56 - 16 * q^58 - 4 * q^65 - 56 * q^67 + 56 * q^70 - 84 * q^71 + 24 * q^74 - 80 * q^79 + 36 * q^85 + 48 * q^86 - 228 * q^88 - 48 * q^91 - 24 * q^92 + 84 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$

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 $a_p$)

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

$2$	−1.61897	−	0.433802i	−1.14479	−	0.306744i	−0.363912	−	0.931433i	$-0.618559\pi$
$2$	−1.61897	−	0.433802i	−1.14479	−	0.306744i	−0.780873	+	0.624689i	$0.785226\pi$
$3$		0			0
$3$		0			0
$4$	0.700831	+	0.404625i	0.350416	+	0.202313i
$5$	1.42145	+	1.42145i	0.635693	+	0.635693i	0.949490	−	0.313797i	$-0.101601\pi$
$5$	1.42145	+	1.42145i	0.635693	+	0.635693i	−0.313797	+	0.949490i	$0.601601\pi$
$6$		0			0
$7$	0.234216	+	2.63536i	0.0885255	+	0.996074i
$7$	0.234216	+	2.63536i	0.0885255	+	0.996074i
$8$	1.41124	+	1.41124i	0.498948	+	0.498948i
$9$		0			0
$10$	−1.68466	−	2.91792i	−0.532737	−	0.922727i
$11$	−0.254101	+	0.948318i	−0.0766144	+	0.285929i	−0.993595	−	0.113004i	$-0.963953\pi$
$11$	−0.254101	+	0.948318i	−0.0766144	+	0.285929i	0.916980	+	0.398933i	$0.130619\pi$
$12$		0			0
$13$	−1.60977	+	3.22624i	−0.446471	+	0.894798i
$13$	−1.60977	+	3.22624i	−0.446471	+	0.894798i
$14$	0.764036	−	4.36818i	0.204197	−	1.16745i
$15$		0			0
$16$	−2.48181	−	4.29862i	−0.620452	−	1.07465i
$17$	−2.99281	+	5.18370i	−0.725863	+	1.25723i	0.232755	+	0.972535i	$0.425226\pi$
$17$	−2.99281	+	5.18370i	−0.725863	+	1.25723i	−0.958618	+	0.284696i	$0.908107\pi$
$18$		0			0
$19$	2.71200	−	0.726678i	0.622175	−	0.166711i	0.0660587	−	0.997816i	$-0.478958\pi$
$19$	2.71200	−	0.726678i	0.622175	−	0.166711i	0.556116	+	0.831104i	$0.312291\pi$
$20$	0.421043	+	1.57135i	0.0941481	+	0.351366i
$21$		0			0
$22$	0.822765	−	1.42507i	0.175414	−	0.303826i
$23$	−2.58851	+	1.49448i	−0.539742	+	0.311620i	−0.744974	−	0.667093i	$-0.767538\pi$
$23$	−2.58851	+	1.49448i	−0.539742	+	0.311620i	0.205233	+	0.978713i	$0.434205\pi$
$24$		0			0
$25$		−	0.958941i		−	0.191788i
$26$	4.00573	−	4.52487i	0.785588	−	0.887399i
$27$		0			0
$28$	−0.902188	+	1.94172i	−0.170498	+	0.366950i
$29$	−3.65708	−	6.33425i	−0.679103	−	1.17624i	−0.975251	−	0.221099i	$-0.929036\pi$
$29$	−3.65708	−	6.33425i	−0.679103	−	1.17624i	0.296148	−	0.955142i	$-0.404298\pi$
$30$		0			0
$31$	−6.11048	−	6.11048i	−1.09748	−	1.09748i	−0.994705	−	0.102770i	$-0.967229\pi$
$31$	−6.11048	−	6.11048i	−1.09748	−	1.09748i	−0.102770	−	0.994705i	$-0.532771\pi$
$32$	1.12013	+	4.18037i	0.198012	+	0.738992i
$33$		0			0
$34$	7.09397	−	7.09397i	1.21661	−	1.21661i
$35$	−3.41312	+	4.07897i	−0.576922	+	0.689472i
$36$		0			0
$37$	−1.24143	+	4.63309i	−0.204090	+	0.761675i	0.785635	+	0.618690i	$0.212336\pi$
$37$	−1.24143	+	4.63309i	−0.204090	+	0.761675i	−0.989725	+	0.142984i	$0.954330\pi$
$38$	−4.70588			−0.763395
$39$		0			0
$40$			4.01202i			0.634356i
$41$	0.886060	−	3.30682i	0.138379	−	0.516439i	−0.861582	−	0.507619i	$-0.830526\pi$
$41$	0.886060	−	3.30682i	0.138379	−	0.516439i	0.999961	−	0.00881984i	$-0.00280748\pi$
$42$		0			0
$43$	−0.748633	−	0.432224i	−0.114165	−	0.0659135i	0.441830	−	0.897099i	$-0.354329\pi$
$43$	−0.748633	−	0.432224i	−0.114165	−	0.0659135i	−0.555995	+	0.831185i	$0.687663\pi$
$44$	−0.561795	+	0.561795i	−0.0846939	+	0.0846939i
$45$		0			0
$46$	4.83903	−	1.29661i	0.713476	−	0.191175i
$47$	2.17001	−	2.17001i	0.316529	−	0.316529i	−0.530903	−	0.847432i	$-0.678147\pi$
$47$	2.17001	−	2.17001i	0.316529	−	0.316529i	0.847432	+	0.530903i	$0.178147\pi$
$48$		0			0
$49$	−6.89029	+	1.23449i	−0.984326	+	0.176356i
$50$	−0.415990	+	1.55250i	−0.0588299	+	0.219556i
$51$		0			0
$52$	−2.43360	+	1.60970i	−0.337479	+	0.223225i
$53$	−6.32446			−0.868732			−0.434366	−	0.900737i	$-0.643028\pi$
$53$	−6.32446			−0.868732			−0.434366	+	0.900737i	$0.643028\pi$
$54$		0			0
$55$	−1.70918	+	0.986797i	−0.230466	+	0.133060i
$56$	−3.38859	+	4.04966i	−0.452820	+	0.541159i
$57$		0			0
$58$	3.17290	+	11.8414i	0.416622	+	1.55485i
$59$	0.131692	+	0.491481i	0.0171448	+	0.0639854i	0.973968	−	0.226684i	$-0.0727886\pi$
$59$	0.131692	+	0.491481i	0.0171448	+	0.0639854i	−0.956823	+	0.290670i	$0.906122\pi$
$60$		0			0
$61$	11.2829	+	6.51419i	1.44463	+	0.834057i	0.998154	−	0.0607392i	$-0.0193458\pi$
$61$	11.2829	+	6.51419i	1.44463	+	0.834057i	0.446475	+	0.894796i	$0.352679\pi$
$62$	7.24196	+	12.5434i	0.919729	+	1.59302i
$63$		0			0
$64$			2.67342i			0.334178i
$65$	−6.87417	+	2.29773i	−0.852636	+	0.284998i
$66$		0			0
$67$	−0.827827	−	0.221815i	−0.101135	−	0.0270991i	0.207897	−	0.978151i	$-0.433338\pi$
$67$	−0.827827	−	0.221815i	−0.101135	−	0.0270991i	−0.309032	+	0.951052i	$0.600005\pi$
$68$	−4.19491	+	2.42193i	−0.508707	+	0.293702i
$69$		0			0
$70$	7.29521	−	5.12312i	0.871944	−	0.612330i
$71$	3.01121	+	11.2380i	0.357365	+	1.33370i	0.877482	+	0.479609i	$0.159222\pi$
$71$	3.01121	+	11.2380i	0.357365	+	1.33370i	−0.520117	+	0.854095i	$0.674112\pi$
$72$		0			0
$73$	−1.03002	+	1.03002i	−0.120555	+	0.120555i	−0.764810	−	0.644255i	$-0.777167\pi$
$73$	−1.03002	+	1.03002i	−0.120555	+	0.120555i	0.644255	+	0.764810i	$0.277167\pi$
$74$	4.01968	−	6.96230i	0.467279	−	0.809350i
$75$		0			0
$76$	2.19469	+	0.588064i	0.251748	+	0.0674556i
$77$	−2.55868	−	0.447537i	−0.291588	−	0.0510016i
$78$		0			0
$79$	−11.6027			−1.30541			−0.652705	−	0.757612i	$-0.726366\pi$
$79$	−11.6027			−1.30541			−0.652705	+	0.757612i	$0.726366\pi$
$80$	2.58251	−	9.63806i	0.288733	−	1.07757i
$81$		0			0
$82$	−2.86901	+	4.96927i	−0.316829	+	0.548764i
$83$	1.23779	+	1.23779i	0.135865	+	0.135865i	0.771768	−	0.635904i	$-0.219372\pi$
$83$	1.23779	+	1.23779i	0.135865	+	0.135865i	−0.635904	+	0.771768i	$0.719372\pi$
$84$		0			0
$85$	−11.6225	+	3.11424i	−1.26064	+	0.337787i
$86$	1.02452	+	1.02452i	0.110476	+	0.110476i
$87$		0			0
$88$	−1.69690	+	0.979707i	−0.180890	+	0.104437i
$89$	7.75255	+	2.07729i	0.821769	+	0.220192i	0.645120	−	0.764082i	$-0.276807\pi$
$89$	7.75255	+	2.07729i	0.821769	+	0.220192i	0.176649	+	0.984274i	$0.443474\pi$
$90$		0			0
$91$	−8.87935	−	3.48670i	−0.930809	−	0.365506i
$92$	−2.41881			−0.252179
$93$		0			0
$94$	−4.45454	+	2.57183i	−0.459451	+	0.265264i
$95$	4.88792	+	2.82204i	0.501490	+	0.289535i
$96$		0			0
$97$	−12.0756	+	3.23566i	−1.22609	+	0.328531i	−0.813058	−	0.582183i	$-0.802199\pi$
$97$	−12.0756	+	3.23566i	−1.22609	+	0.328531i	−0.413037	+	0.910714i	$0.635532\pi$
$98$	11.6907	+	0.990414i	1.18094	+	0.100047i
$99$		0			0
$100$	0.388012	−	0.672056i	0.0388012	−	0.0672056i
$101$	−3.99818	−	6.92504i	−0.397833	−	0.689068i	0.595625	−	0.803263i	$-0.296904\pi$
$101$	−3.99818	−	6.92504i	−0.397833	−	0.689068i	−0.993458	+	0.114195i	$0.963571\pi$
$102$		0			0
$103$	10.3386			1.01869			0.509344	−	0.860563i	$-0.329888\pi$
$103$	10.3386			1.01869			0.509344	+	0.860563i	$0.329888\pi$
$104$	−6.82477	+	2.28122i	−0.669224	+	0.223692i
$105$		0			0
$106$	10.2391	+	2.74356i	0.994511	+	0.266479i
$107$	6.52593	+	11.3032i	0.630885	+	1.09273i	0.987371	+	0.158425i	$0.0506415\pi$
$107$	6.52593	+	11.3032i	0.630885	+	1.09273i	−0.356486	+	0.934301i	$0.616025\pi$
$108$		0			0
$109$	−8.28013	+	8.28013i	−0.793093	+	0.793093i	−0.981996	−	0.188903i	$-0.939507\pi$
$109$	−8.28013	+	8.28013i	−0.793093	+	0.793093i	0.188903	+	0.981996i	$0.439507\pi$
$110$	3.19519	−	0.856149i	0.304650	−	0.0816306i
$111$		0			0
$112$	10.7471	−	7.54727i	1.01551	−	0.713150i
$113$	−4.05748	+	7.02777i	−0.381696	+	0.661117i	−0.991305	−	0.131586i	$-0.957993\pi$
$113$	−4.05748	+	7.02777i	−0.381696	+	0.661117i	0.609609	+	0.792702i	$0.291326\pi$
$114$		0			0
$115$	−5.80377	−	1.55512i	−0.541205	−	0.145015i
$116$		−	5.91899i		−	0.549565i
$117$		0			0
$118$		−	0.852822i		−	0.0785086i
$119$	−14.3619	−	6.67303i	−1.31655	−	0.611716i
$120$		0			0
$121$	8.69154	+	5.01806i	0.790140	+	0.456188i
$122$	−15.4408	−	15.4408i	−1.39795	−	1.39795i
$123$		0			0
$124$	−1.80996	−	6.75488i	−0.162540	−	0.606606i
$125$	8.47036	−	8.47036i	0.757612	−	0.757612i
$126$		0			0
$127$	6.81853	−	3.93668i	0.605047	−	0.349324i	−0.165977	−	0.986130i	$-0.553078\pi$
$127$	6.81853	−	3.93668i	0.605047	−	0.349324i	0.771024	+	0.636805i	$0.219745\pi$
$128$	3.39999	−	12.6889i	0.300519	−	1.12155i
$129$		0			0
$130$	12.1258	−	0.737931i	1.06351	−	0.0647208i
$131$			19.9597i			1.74389i	0.489604	+	0.871945i	$0.337141\pi$
$131$			19.9597i			1.74389i	−0.489604	+	0.871945i	$0.662859\pi$
$132$		0			0
$133$	2.55025	+	6.97690i	0.221135	+	0.604974i
$134$	1.24400	+	0.718226i	0.107466	+	0.0620452i
$135$		0			0
$136$	−11.5390	+	3.09187i	−0.989461	+	0.265125i
$137$	−10.3872	+	2.78324i	−0.887437	+	0.237788i	−0.673613	−	0.739084i	$-0.735259\pi$
$137$	−10.3872	+	2.78324i	−0.887437	+	0.237788i	−0.213824	+	0.976872i	$0.568592\pi$
$138$		0			0
$139$	14.1096	+	8.14616i	1.19676	+	0.690949i	0.959831	−	0.280579i	$-0.0905264\pi$
$139$	14.1096	+	8.14616i	1.19676	+	0.690949i	0.236927	+	0.971527i	$0.423860\pi$
$140$	−4.04248	+	1.47764i	−0.341652	+	0.124883i
$141$		0			0
$142$		−	19.5002i		−	1.63642i
$143$	−2.65046	−	2.34637i	−0.221642	−	0.196213i
$144$		0			0
$145$	3.80547	−	14.2022i	0.316027	−	1.17943i
$146$	2.11440	−	1.22075i	0.174989	−	0.101030i
$147$		0			0
$148$	−2.74470	+	2.74470i	−0.225613	+	0.225613i
$149$	−4.84157	−	18.0690i	−0.396637	−	1.48027i	−0.818975	−	0.573829i	$-0.805457\pi$
$149$	−4.84157	−	18.0690i	−0.396637	−	1.48027i	0.422338	−	0.906438i	$-0.361209\pi$
$150$		0			0
$151$	−0.0257634	−	0.0257634i	−0.00209659	−	0.00209659i	0.706058	−	0.708154i	$-0.250472\pi$
$151$	−0.0257634	−	0.0257634i	−0.00209659	−	0.00209659i	−0.708154	+	0.706058i	$0.750472\pi$
$152$	4.85280	+	2.80176i	0.393614	+	0.227253i
$153$		0			0
$154$	3.94828	+	1.83451i	0.318162	+	0.147829i
$155$		−	17.3715i		−	1.39532i
$156$		0			0
$157$		−	7.18863i		−	0.573716i	−0.957973	−	0.286858i	$-0.907389\pi$
$157$		−	7.18863i		−	0.573716i	0.957973	−	0.286858i	$-0.0926107\pi$
$158$	18.7845	+	5.03329i	1.49442	+	0.400427i
$159$		0			0
$160$	−4.34999	+	7.53441i	−0.343897	+	0.595647i
$161$	−4.54476	−	6.47163i	−0.358177	−	0.510036i
$162$		0			0
$163$	15.8950	−	4.25905i	1.24499	−	0.333594i	0.424592	−	0.905385i	$-0.360418\pi$
$163$	15.8950	−	4.25905i	1.24499	−	0.333594i	0.820400	+	0.571791i	$0.193751\pi$
$164$	1.95900	−	1.95900i	0.152972	−	0.152972i
$165$		0			0
$166$	−1.46699	−	2.54090i	−0.113860	−	0.197212i
$167$	6.49344	+	1.73991i	0.502478	+	0.134638i	0.501150	−	0.865361i	$-0.332911\pi$
$167$	6.49344	+	1.73991i	0.502478	+	0.134638i	0.00132801	+	0.999999i	$0.499577\pi$
$168$		0			0
$169$	−7.81725	−	10.3870i	−0.601327	−	0.799003i
$170$	20.1675			1.54678
$171$		0			0
$172$	−0.349777	−	0.605832i	−0.0266702	−	0.0461942i
$173$	−4.75865	+	8.24223i	−0.361794	+	0.626645i	−0.988256	−	0.152807i	$-0.951169\pi$
$173$	−4.75865	+	8.24223i	−0.361794	+	0.626645i	0.626462	+	0.779452i	$0.284502\pi$
$174$		0			0
$175$	2.52716	−	0.224600i	0.191035	−	0.0169781i
$176$	4.70709	−	1.26126i	0.354810	−	0.0950711i
$177$		0			0
$178$	−11.6500	−	6.72614i	−0.873206	−	0.504146i
$179$	5.20227	−	3.00353i	0.388836	−	0.224495i	−0.292820	−	0.956168i	$-0.594594\pi$
$179$	5.20227	−	3.00353i	0.388836	−	0.224495i	0.681656	+	0.731673i	$0.261260\pi$
$180$		0			0
$181$	−6.05960			−0.450407			−0.225203	−	0.974312i	$-0.572305\pi$
$181$	−6.05960			−0.450407			−0.225203	+	0.974312i	$0.572305\pi$
$182$	12.8629	+	9.49675i	0.953460	+	0.703946i
$183$		0			0
$184$	−5.76207	−	1.54394i	−0.424786	−	0.113821i
$185$	−8.35035	+	4.82108i	−0.613930	+	0.354453i
$186$		0			0
$187$	−4.15532	−	4.15532i	−0.303867	−	0.303867i
$188$	2.39886	−	0.642771i	0.174955	−	0.0468789i
$189$		0			0
$190$	−6.68919	−	6.68919i	−0.485285	−	0.485285i
$191$	10.8137	−	18.7298i	0.782449	−	1.35524i	−0.148062	−	0.988978i	$-0.547304\pi$
$191$	10.8137	−	18.7298i	0.782449	−	1.35524i	0.930511	−	0.366263i	$-0.119363\pi$
$192$		0			0
$193$	2.50822	−	9.36080i	0.180546	−	0.673805i	−0.814995	−	0.579468i	$-0.803260\pi$
$193$	2.50822	−	9.36080i	0.180546	−	0.673805i	0.995540	−	0.0943368i	$-0.0300731\pi$
$194$	20.9537			1.50439
$195$		0			0
$196$	−5.32843	−	1.92281i	−0.380602	−	0.137344i
$197$	4.47322	+	1.19859i	0.318704	+	0.0853964i	0.414624	−	0.909993i	$-0.363913\pi$
$197$	4.47322	+	1.19859i	0.318704	+	0.0853964i	−0.0959210	+	0.995389i	$0.530580\pi$
$198$		0			0
$199$	−10.7801	+	18.6717i	−0.764182	+	1.32360i	0.176496	+	0.984301i	$0.443524\pi$
$199$	−10.7801	+	18.6717i	−0.764182	+	1.32360i	−0.940678	+	0.339300i	$0.889810\pi$
$200$	1.35330	−	1.35330i	0.0956924	−	0.0956924i
$201$		0			0
$202$	3.46883	+	12.9459i	0.244066	+	0.910868i
$203$	15.8365	−	11.1213i	1.11151	−	0.780564i
$204$		0			0
$205$	5.95998	−	3.44100i	0.416263	−	0.240330i
$206$	−16.7378	−	4.48489i	−1.16618	−	0.312477i
$207$		0			0
$208$	17.8635	−	1.08710i	1.23861	−	0.0753771i
$209$			2.75649i			0.190670i
$210$		0			0
$211$	7.39505	+	12.8086i	0.509096	+	0.881780i	0.999945	+	0.0105352i	$0.00335353\pi$
$211$	7.39505	+	12.8086i	0.509096	+	0.881780i	−0.490848	+	0.871245i	$0.663313\pi$
$212$	−4.43238	−	2.55904i	−0.304417	−	0.175755i
$213$		0			0
$214$	−5.66192	−	21.1306i	−0.387041	−	1.44446i
$215$	−0.449761	−	1.67853i	−0.0306735	−	0.114475i
$216$		0			0
$217$	14.6722	−	17.5345i	0.996012	−	1.19032i
$218$	16.9972	−	9.81336i	1.15120	−	0.664644i
$219$		0			0
$220$	−1.59713			−0.107679
$221$	−11.9061	−	18.0001i	−0.800891	−	1.21082i
$222$		0			0
$223$	5.52568	−	20.6221i	0.370027	−	1.38096i	−0.490450	−	0.871469i	$-0.663168\pi$
$223$	5.52568	−	20.6221i	0.370027	−	1.38096i	0.860477	−	0.509490i	$-0.170166\pi$
$224$	−10.7544	+	3.93105i	−0.718561	+	0.262654i
$225$		0			0
$226$	9.61760	−	9.61760i	0.639753	−	0.639753i
$227$	−13.0566	+	3.49849i	−0.866594	+	0.232203i	−0.664615	−	0.747186i	$-0.731404\pi$
$227$	−13.0566	+	3.49849i	−0.866594	+	0.232203i	−0.201980	+	0.979390i	$0.564738\pi$
$228$		0			0
$229$	−5.08550	+	5.08550i	−0.336059	+	0.336059i	−0.854882	−	0.518823i	$-0.826371\pi$
$229$	−5.08550	+	5.08550i	−0.336059	+	0.336059i	0.518823	+	0.854882i	$0.326371\pi$
$230$	8.72153	+	5.03538i	0.575081	+	0.332023i
$231$		0			0
$232$	3.77813	−	14.1002i	0.248046	−	0.925721i
$233$			23.2048i			1.52019i	0.649809	+	0.760097i	$0.274849\pi$
$233$			23.2048i			1.52019i	−0.649809	+	0.760097i	$0.725151\pi$
$234$		0			0
$235$	6.16915			0.402431
$236$	−0.106572	+	0.397731i	−0.00693723	+	0.0258901i
$237$		0			0
$238$	20.3567	+	17.0337i	1.31953	+	1.10413i
$239$	2.77302	−	2.77302i	0.179372	−	0.179372i	−0.611710	−	0.791082i	$-0.709518\pi$
$239$	2.77302	−	2.77302i	0.179372	−	0.179372i	0.791082	+	0.611710i	$0.209518\pi$
$240$		0			0
$241$	0.825382	+	3.08037i	0.0531675	+	0.198424i	0.987401	−	0.158238i	$-0.0505814\pi$
$241$	0.825382	+	3.08037i	0.0531675	+	0.198424i	−0.934233	+	0.356662i	$0.883915\pi$
$242$	−11.8945	−	11.8945i	−0.764608	−	0.764608i
$243$		0			0
$244$	5.27161	+	9.13070i	0.337480	+	0.584533i
$245$	−11.5490	−	8.03945i	−0.737838	−	0.513621i
$246$		0			0
$247$	−2.02127	+	9.91935i	−0.128610	+	0.631153i
$248$		−	17.2467i		−	1.09517i
$249$		0			0
$250$	−17.3877	+	10.0388i	−1.09970	+	0.634910i
$251$	−5.89697	+	10.2138i	−0.372213	+	0.644692i	−0.989906	−	0.141727i	$-0.954734\pi$
$251$	−5.89697	+	10.2138i	−0.372213	+	0.644692i	0.617692	+	0.786420i	$0.288068\pi$
$252$		0			0
$253$	−0.759496	−	2.83448i	−0.0477491	−	0.178202i
$254$	−12.7467	+	3.41548i	−0.799802	+	0.214306i
$255$		0			0
$256$	−8.33554	+	14.4376i	−0.520971	+	0.902349i
$257$	−8.34519	−	14.4543i	−0.520559	−	0.901634i	−0.999714	−	0.0239041i	$-0.992390\pi$
$257$	−8.34519	−	14.4543i	−0.520559	−	0.901634i	0.479156	−	0.877730i	$-0.340943\pi$
$258$		0			0
$259$	−12.5006	−	2.18648i	−0.776751	−	0.135861i
$260$	−5.74735	−	1.17114i	−0.356436	−	0.0726310i
$261$		0			0
$262$	8.65857	−	32.3142i	0.534928	−	1.99638i
$263$	4.75769	+	8.24055i	0.293371	+	0.508134i	0.974605	−	0.223932i	$-0.0718894\pi$
$263$	4.75769	+	8.24055i	0.293371	+	0.508134i	−0.681233	+	0.732066i	$0.738556\pi$
$264$		0			0
$265$	−8.98993	−	8.98993i	−0.552247	−	0.552247i
$266$	−1.10219	−	12.4017i	−0.0675799	−	0.760397i
$267$		0			0
$268$	−0.490415	−	0.490415i	−0.0299569	−	0.0299569i
$269$	−0.275945	−	0.159317i	−0.0168247	−	0.00971373i	0.491564	−	0.870841i	$-0.336425\pi$
$269$	−0.275945	−	0.159317i	−0.0168247	−	0.00971373i	−0.508389	+	0.861128i	$0.669759\pi$
$270$		0			0
$271$	25.9248	+	6.94654i	1.57482	+	0.421972i	0.937318	−	0.348475i	$-0.113300\pi$
$271$	25.9248	+	6.94654i	1.57482	+	0.421972i	0.637504	+	0.770447i	$0.279967\pi$
$272$	29.7103			1.80145
$273$		0			0
$274$	18.0239			1.08886
$275$	0.909381	+	0.243668i	0.0548378	+	0.0146937i
$276$		0			0
$277$	−13.1218	−	7.57587i	−0.788412	−	0.455190i	0.0509909	−	0.998699i	$-0.483762\pi$
$277$	−13.1218	−	7.57587i	−0.788412	−	0.455190i	−0.839403	+	0.543509i	$0.817095\pi$
$278$	−19.3092	−	19.3092i	−1.15809	−	1.15809i
$279$		0			0
$280$	−10.5731	+	0.939681i	−0.631866	+	0.0561567i
$281$	−5.40600	−	5.40600i	−0.322495	−	0.322495i	0.527228	−	0.849724i	$-0.323231\pi$
$281$	−5.40600	−	5.40600i	−0.322495	−	0.322495i	−0.849724	+	0.527228i	$0.823231\pi$
$282$		0			0
$283$	−0.896218	−	1.55229i	−0.0532746	−	0.0922743i	0.838158	−	0.545427i	$-0.183633\pi$
$283$	−0.896218	−	1.55229i	−0.0532746	−	0.0922743i	−0.891433	+	0.453153i	$0.850299\pi$
$284$	−2.43682	+	9.09435i	−0.144599	+	0.539650i
$285$		0			0
$286$	3.27315	+	4.94848i	0.193546	+	0.292610i
$287$	8.92220	+	1.56058i	0.526661	+	0.0921180i
$288$		0			0
$289$	−9.41380	−	16.3052i	−0.553753	−	0.959128i
$290$	−12.3219	+	21.3422i	−0.723567	+	1.25325i
$291$		0			0
$292$	−1.13864	+	0.305099i	−0.0666341	+	0.0178546i
$293$	6.85691	+	25.5903i	0.400585	+	1.49500i	0.812055	+	0.583580i	$0.198349\pi$
$293$	6.85691	+	25.5903i	0.400585	+	1.49500i	−0.411471	+	0.911423i	$0.634985\pi$
$294$		0			0
$295$	−0.511424	+	0.885812i	−0.0297762	+	0.0515739i
$296$	−8.29035	+	4.78644i	−0.481867	+	0.278206i
$297$		0			0
$298$			31.3534i			1.81625i
$299$	−0.654624	−	10.7569i	−0.0378579	−	0.622089i
$300$		0			0
$301$	0.963724	−	2.07415i	0.0555481	−	0.119552i
$302$	0.0305339	+	0.0528863i	0.00175703	+	0.00304327i
$303$		0			0
$304$	−9.85437	−	9.85437i	−0.565187	−	0.565187i
$305$	6.77851	+	25.2978i	0.388136	+	1.44855i
$306$		0			0
$307$	1.54710	−	1.54710i	0.0882978	−	0.0882978i	−0.661578	−	0.749876i	$-0.730113\pi$
$307$	1.54710	−	1.54710i	0.0882978	−	0.0882978i	0.749876	+	0.661578i	$0.230113\pi$
$308$	−1.61212	−	1.34895i	−0.0918589	−	0.0768638i
$309$		0			0
$310$	−7.53581	+	28.1240i	−0.428005	+	1.59734i
$311$	29.3344			1.66340			0.831699	−	0.555226i	$-0.187368\pi$
$311$	29.3344			1.66340			0.831699	+	0.555226i	$0.187368\pi$
$312$		0			0
$313$			27.9847i			1.58179i	0.611954	+	0.790893i	$0.290384\pi$
$313$			27.9847i			1.58179i	−0.611954	+	0.790893i	$0.709616\pi$
$314$	−3.11844	+	11.6382i	−0.175984	+	0.656781i
$315$		0			0
$316$	−8.13157	−	4.69476i	−0.457436	−	0.264101i
$317$	−5.56105	+	5.56105i	−0.312340	+	0.312340i	−0.845815	−	0.533476i	$-0.820886\pi$
$317$	−5.56105	+	5.56105i	−0.312340	+	0.312340i	0.533476	+	0.845815i	$0.320886\pi$
$318$		0			0
$319$	6.93616	−	1.85854i	0.388350	−	0.104058i
$320$	−3.80014	+	3.80014i	−0.212434	+	0.212434i
$321$		0			0
$322$	4.55043	+	12.4489i	0.253585	+	0.693751i
$323$	−4.34961	+	16.2330i	−0.242019	+	0.903227i
$324$		0			0
$325$	3.09377	+	1.54368i	0.171612	+	0.0856279i
$326$	−27.5811			−1.52758
$327$		0			0
$328$	5.91716	−	3.41627i	0.326720	−	0.188632i
$329$	6.22703	+	5.21052i	0.343307	+	0.287265i
$330$		0			0
$331$	4.21415	+	15.7274i	0.231630	+	0.864457i	0.979639	+	0.200767i	$0.0643436\pi$
$331$	4.21415	+	15.7274i	0.231630	+	0.864457i	−0.748008	+	0.663689i	$0.768990\pi$
$332$	0.366640	+	1.36832i	0.0201220	+	0.0750963i
$333$		0			0
$334$	−9.75792	−	5.63374i	−0.533929	−	0.308264i
$335$	−0.861417	−	1.49202i	−0.0470642	−	0.0815176i
$336$		0			0
$337$			11.0114i			0.599827i	0.953966	+	0.299913i	$0.0969578\pi$
$337$			11.0114i			0.599827i	−0.953966	+	0.299913i	$0.903042\pi$
$338$	8.14999	+	20.2075i	0.443301	+	1.09914i
$339$		0			0
$340$	−9.40553	−	2.52020i	−0.510086	−	0.136677i
$341$	7.34737	−	4.24200i	0.397882	−	0.229717i
$342$		0			0
$343$	−4.86715	−	17.8693i	−0.262801	−	0.964850i
$344$	−0.446530	−	1.66647i	−0.0240753	−	0.0898501i
$345$		0			0
$346$	11.2796	−	11.2796i	0.606396	−	0.606396i
$347$	2.36362	−	4.09391i	0.126886	−	0.219772i	−0.795583	−	0.605845i	$-0.792835\pi$
$347$	2.36362	−	4.09391i	0.126886	−	0.219772i	0.922468	+	0.386073i	$0.126169\pi$
$348$		0			0
$349$	22.4353	+	6.01151i	1.20093	+	0.321789i	0.803198	−	0.595712i	$-0.203130\pi$
$349$	22.4353	+	6.01151i	1.20093	+	0.321789i	0.397734	+	0.917501i	$0.369797\pi$
$350$	−4.18883	−	0.732666i	−0.223902	−	0.0391626i
$351$		0			0
$352$	−4.24895			−0.226470
$353$	−3.40370	+	12.7028i	−0.181161	+	0.676101i	0.814259	+	0.580501i	$0.197143\pi$
$353$	−3.40370	+	12.7028i	−0.181161	+	0.676101i	−0.995420	+	0.0955993i	$0.969523\pi$
$354$		0			0
$355$	−11.6940	+	20.2546i	−0.620652	+	1.07500i
$356$	4.59271	+	4.59271i	0.243413	+	0.243413i
$357$		0			0
$358$	−9.72526	+	2.60588i	−0.513996	+	0.137725i
$359$	−6.64709	−	6.64709i	−0.350820	−	0.350820i	0.509594	−	0.860415i	$-0.329795\pi$
$359$	−6.64709	−	6.64709i	−0.350820	−	0.350820i	−0.860415	+	0.509594i	$0.829795\pi$
$360$		0			0
$361$	−9.62761	+	5.55850i	−0.506716	+	0.292553i
$362$	9.81032	+	2.62867i	0.515619	+	0.138160i
$363$		0			0
$364$	−4.81212	−	6.03640i	−0.252224	−	0.316393i
$365$	−2.92826			−0.153272
$366$		0			0
$367$	6.33897	−	3.65981i	0.330892	−	0.191040i	−0.325345	−	0.945595i	$-0.605481\pi$
$367$	6.33897	−	3.65981i	0.330892	−	0.191040i	0.656237	+	0.754555i	$0.272147\pi$
$368$	12.8484	+	7.41801i	0.669767	+	0.386690i
$369$		0			0
$370$	15.6104	−	4.18279i	0.811544	−	0.217453i
$371$	−1.48129	−	16.6673i	−0.0769049	−	0.865321i
$372$		0			0
$373$	0.542562	−	0.939745i	0.0280928	−	0.0486582i	−0.851637	−	0.524132i	$-0.824390\pi$
$373$	0.542562	−	0.939745i	0.0280928	−	0.0486582i	0.879730	+	0.475474i	$0.157723\pi$
$374$	4.92475	+	8.52992i	0.254653	+	0.441072i
$375$		0			0
$376$	6.12482			0.315863
$377$	26.3229	−	1.60191i	1.35570	−	0.0825025i
$378$		0			0
$379$	−25.1695	−	6.74414i	−1.29287	−	0.346423i	−0.454119	−	0.890941i	$-0.650046\pi$
$379$	−25.1695	−	6.74414i	−1.29287	−	0.346423i	−0.838749	+	0.544518i	$0.816713\pi$
$380$	2.28374	+	3.95555i	0.117153	+	0.202915i
$381$		0			0
$382$	−25.6320	+	25.6320i	−1.31145	+	1.31145i
$383$	−5.14879	+	1.37961i	−0.263091	+	0.0704950i	−0.387953	−	0.921679i	$-0.626818\pi$
$383$	−5.14879	+	1.37961i	−0.263091	+	0.0704950i	0.124862	+	0.992174i	$0.460151\pi$
$384$		0			0
$385$	−3.00089	−	4.27320i	−0.152939	−	0.217782i
$386$	−8.12146	+	14.0668i	−0.413372	+	0.715981i
$387$		0			0
$388$	−9.77221	−	2.61846i	−0.496109	−	0.132932i
$389$		−	3.43917i		−	0.174373i	−0.996192	−	0.0871864i	$-0.972212\pi$
$389$		−	3.43917i		−	0.174373i	0.996192	−	0.0871864i	$-0.0277876\pi$
$390$		0			0
$391$		−	17.8907i		−	0.904773i
$392$	−11.4660	−	7.98168i	−0.579121	−	0.403136i
$393$		0			0
$394$	−6.72205	−	3.88098i	−0.338652	−	0.195521i
$395$	−16.4928	−	16.4928i	−0.829841	−	0.829841i
$396$		0			0
$397$	−0.155514	−	0.580386i	−0.00780502	−	0.0291287i	0.961914	−	0.273354i	$-0.0881330\pi$
$397$	−0.155514	−	0.580386i	−0.00780502	−	0.0291287i	−0.969719	+	0.244225i	$0.921466\pi$
$398$	25.5525	−	25.5525i	1.28083	−	1.28083i
$399$		0			0
$400$	−4.12212	+	2.37991i	−0.206106	+	0.118995i
$401$	−3.10377	+	11.5834i	−0.154995	+	0.578448i	0.844111	+	0.536168i	$0.180129\pi$
$401$	−3.10377	+	11.5834i	−0.154995	+	0.578448i	−0.999106	+	0.0422800i	$0.986538\pi$
$402$		0			0
$403$	29.5504	−	9.87739i	1.47201	−	0.492028i
$404$		−	6.47105i		−	0.321947i
$405$		0			0
$406$	−30.4633	+	11.1352i	−1.51187	+	0.552631i
$407$	−4.07819	−	2.35454i	−0.202148	−	0.116710i
$408$		0			0
$409$	−11.2120	+	3.00424i	−0.554396	+	0.148550i	−0.525131	−	0.851022i	$-0.675984\pi$
$409$	−11.2120	+	3.00424i	−0.554396	+	0.148550i	−0.0292657	+	0.999572i	$0.509317\pi$
$410$	−11.1418	+	2.98542i	−0.550252	+	0.147440i
$411$		0			0
$412$	7.24558	+	4.18324i	0.356964	+	0.206093i
$413$	−1.26439	+	0.462169i	−0.0622164	+	0.0227419i
$414$		0			0
$415$			3.51891i			0.172737i
$416$	−15.2900	−	3.11565i	−0.749655	−	0.152758i
$417$		0			0
$418$	1.19577	−	4.46267i	0.0584870	−	0.218276i
$419$	−30.9881	+	17.8910i	−1.51387	+	0.874032i	−0.513999	+	0.857791i	$0.671836\pi$
$419$	−30.9881	+	17.8910i	−1.51387	+	0.874032i	−0.999868	+	0.0162408i	$0.994830\pi$
$420$		0			0
$421$	−3.47255	+	3.47255i	−0.169242	+	0.169242i	−0.786646	−	0.617404i	$-0.788184\pi$
$421$	−3.47255	+	3.47255i	−0.169242	+	0.169242i	0.617404	+	0.786646i	$0.288184\pi$
$422$	−6.41597	−	23.9447i	−0.312325	−	1.16561i
$423$		0			0
$424$	−8.92533	−	8.92533i	−0.433452	−	0.433452i
$425$	4.97086	+	2.86993i	0.241122	+	0.139212i
$426$		0			0
$427$	−14.5246	+	31.2603i	−0.702896	+	1.51279i
$428$			10.5622i			0.510544i
$429$		0			0
$430$			2.91260i			0.140458i
$431$	0.474207	+	0.127063i	0.0228418	+	0.00612043i	0.270222	−	0.962798i	$-0.412903\pi$
$431$	0.474207	+	0.127063i	0.0228418	+	0.00612043i	−0.247380	+	0.968919i	$0.579570\pi$
$432$		0			0
$433$	−8.89347	+	15.4039i	−0.427393	+	0.740266i	−0.996641	−	0.0818999i	$-0.973901\pi$
$433$	−8.89347	+	15.4039i	−0.427393	+	0.740266i	0.569248	+	0.822166i	$0.307235\pi$
$434$	−31.3603	+	22.0231i	−1.50534	+	1.05714i
$435$		0			0
$436$	−9.15333	+	2.45263i	−0.438365	+	0.117460i
$437$	−5.93403	+	5.93403i	−0.283863	+	0.283863i
$438$		0			0
$439$	−14.3012	−	24.7704i	−0.682559	−	1.18223i	−0.974197	−	0.225698i	$-0.927534\pi$
$439$	−14.3012	−	24.7704i	−0.682559	−	1.18223i	0.291639	−	0.956529i	$-0.405800\pi$
$440$	−3.80467	−	1.01946i	−0.181381	−	0.0486008i
$441$		0			0
$442$	11.4672	+	34.3065i	0.545437	+	1.63179i
$443$	7.37150			0.350231			0.175115	−	0.984548i	$-0.443970\pi$
$443$	7.37150			0.350231			0.175115	+	0.984548i	$0.443970\pi$
$444$		0			0
$445$	8.06712	+	13.9727i	0.382418	+	0.662368i
$446$	−17.8918	+	30.9896i	−0.847203	+	1.46740i
$447$		0			0
$448$	−7.04544	+	0.626159i	−0.332866	+	0.0295832i
$449$	−22.5220	+	6.03476i	−1.06288	+	0.284798i	−0.747565	−	0.664189i	$-0.768777\pi$
$449$	−22.5220	+	6.03476i	−1.06288	+	0.284798i	−0.315315	+	0.948987i	$0.602110\pi$
$450$		0			0
$451$	2.91077	+	1.68053i	0.137063	+	0.0791332i
$452$	−5.68722	+	3.28352i	−0.267504	+	0.154444i
$453$		0			0
$454$	22.6558			1.06329
$455$	−7.66540	−	17.5778i	−0.359359	−	0.824059i
$456$		0			0
$457$	4.35841	+	1.16783i	0.203878	+	0.0546289i	0.359313	−	0.933217i	$-0.383011\pi$
$457$	4.35841	+	1.16783i	0.203878	+	0.0546289i	−0.155435	+	0.987846i	$0.549678\pi$
$458$	10.4394	−	6.02718i	0.487800	−	0.281631i
$459$		0			0
$460$	−3.43823	−	3.43823i	−0.160308	−	0.160308i
$461$	32.1809	−	8.62285i	1.49882	−	0.401606i	0.586112	−	0.810230i	$-0.300658\pi$
$461$	32.1809	−	8.62285i	1.49882	−	0.401606i	0.912703	+	0.408623i	$0.133991\pi$
$462$		0			0
$463$	29.0991	+	29.0991i	1.35235	+	1.35235i	0.883028	+	0.469321i	$0.155501\pi$
$463$	29.0991	+	29.0991i	1.35235	+	1.35235i	0.469321	+	0.883028i	$0.344499\pi$
$464$	−18.1524	+	31.4408i	−0.842702	+	1.45960i
$465$		0			0
$466$	10.0663	−	37.5678i	0.466311	−	1.74030i
$467$	5.71733			0.264566			0.132283	−	0.991212i	$-0.457769\pi$
$467$	5.71733			0.264566			0.132283	+	0.991212i	$0.457769\pi$
$468$		0			0
$469$	0.390674	−	2.23358i	0.0180396	−	0.103137i
$470$	−9.98767	−	2.67619i	−0.460697	−	0.123443i
$471$		0			0
$472$	−0.507749	+	0.879447i	−0.0233710	+	0.0404798i
$473$	0.600114	−	0.600114i	0.0275933	−	0.0275933i
$474$		0			0
$475$	−0.696841	−	2.60065i	−0.0319733	−	0.119326i
$476$	−7.36519	−	10.4879i	−0.337583	−	0.480710i
$477$		0			0
$478$	−5.69239	+	3.28650i	−0.260364	+	0.150321i
$479$	32.1894	+	8.62513i	1.47077	+	0.394092i	0.903196	−	0.429229i	$-0.141215\pi$
$479$	32.1894	+	8.62513i	1.47077	+	0.394092i	0.567576	+	0.823321i	$0.307881\pi$
$480$		0			0
$481$	−12.9490	−	11.4634i	−0.590425	−	0.522685i
$482$		−	5.34507i		−	0.243461i
$483$		0			0
$484$	4.06087	+	7.03363i	0.184585	+	0.319711i
$485$	−21.7643	−	12.5656i	−0.988265	−	0.570575i
$486$		0			0
$487$	−3.91309	−	14.6038i	−0.177319	−	0.661763i	−0.996145	−	0.0877214i	$-0.972041\pi$
$487$	−3.91309	−	14.6038i	−0.177319	−	0.661763i	0.818826	−	0.574041i	$-0.194625\pi$
$488$	6.72980	+	25.1160i	0.304644	+	1.13695i
$489$		0			0
$490$	15.2099	+	18.0256i	0.687115	+	0.814314i
$491$	3.79911	−	2.19342i	0.171451	−	0.0989875i	−0.411819	−	0.911266i	$-0.635106\pi$
$491$	3.79911	−	2.19342i	0.171451	−	0.0989875i	0.583270	+	0.812278i	$0.301773\pi$
$492$		0			0
$493$	43.7798			1.97174
$494$	7.57541	−	15.1823i	0.340834	−	0.683084i
$495$		0			0
$496$	−11.1016	+	41.4317i	−0.498476	+	1.86034i
$497$	−28.9109	+	10.5678i	−1.29683	+	0.474029i
$498$		0			0
$499$	14.1707	−	14.1707i	0.634366	−	0.634366i	−0.314794	−	0.949160i	$-0.601936\pi$
$499$	14.1707	−	14.1707i	0.634366	−	0.634366i	0.949160	+	0.314794i	$0.101936\pi$
$500$	9.36361	−	2.50897i	0.418753	−	0.112205i
$501$		0			0
$502$	13.9778	−	13.9778i	0.623860	−	0.623860i
$503$	−0.917016	−	0.529439i	−0.0408877	−	0.0236065i	0.479417	−	0.877587i	$-0.340848\pi$
$503$	−0.917016	−	0.529439i	−0.0408877	−	0.0236065i	−0.520305	+	0.853981i	$0.674182\pi$
$504$		0			0
$505$	4.16041	−	15.5268i	0.185136	−	0.690936i
$506$			4.91841i			0.218650i
$507$		0			0
$508$	6.37152			0.282691
$509$	2.91008	−	10.8606i	0.128987	−	0.481387i	−0.870963	−	0.491348i	$-0.836504\pi$
$509$	2.91008	−	10.8606i	0.128987	−	0.481387i	0.999950	+	0.00996149i	$0.00317089\pi$
$510$		0			0
$511$	−2.95573	−	2.47323i	−0.130754	−	0.109409i
$512$	1.18017	−	1.18017i	0.0521565	−	0.0521565i
$513$		0			0
$514$	7.24032	+	27.0212i	0.319357	+	1.19186i
$515$	14.6958	+	14.6958i	0.647573	+	0.647573i
$516$		0			0
$517$	1.50646	+	2.60927i	0.0662541	+	0.114755i
$518$	19.2897	+	8.96264i	0.847539	+	0.393796i
$519$		0			0
$520$	−12.9437	−	6.45845i	−0.567621	−	0.283222i
$521$			16.9175i			0.741168i	0.928799	+	0.370584i	$0.120843\pi$
$521$			16.9175i			0.741168i	−0.928799	+	0.370584i	$0.879157\pi$
$522$		0			0
$523$	0.268849	−	0.155220i	0.0117560	−	0.00678731i	−0.494111	−	0.869399i	$-0.664506\pi$
$523$	0.268849	−	0.155220i	0.0117560	−	0.00678731i	0.505866	+	0.862612i	$0.331173\pi$
$524$	−8.07621	+	13.9884i	−0.352811	+	0.611086i
$525$		0			0
$526$	−4.12779	−	15.4051i	−0.179980	−	0.671695i
$527$	49.9624	−	13.3874i	2.17640	−	0.583164i
$528$		0			0
$529$	−7.03308	+	12.1816i	−0.305786	+	0.529637i
$530$	10.6546	+	18.4543i	0.462806	+	0.801603i
$531$		0			0
$532$	−1.03573	+	5.92153i	−0.0449047	+	0.256731i
$533$	9.24224	+	8.18188i	0.400326	+	0.354396i
$534$		0			0
$535$	−6.79073	+	25.3433i	−0.293589	+	1.09569i
$536$	−0.855227	−	1.48130i	−0.0369402	−	0.0639823i
$537$		0			0
$538$	0.377635	+	0.377635i	0.0162810	+	0.0162810i
$539$	0.580139	−	6.84787i	0.0249884	−	0.294959i
$540$		0			0
$541$	−22.0115	−	22.0115i	−0.946347	−	0.946347i	0.0522854	−	0.998632i	$-0.483349\pi$
$541$	−22.0115	−	22.0115i	−0.946347	−	0.946347i	−0.998632	+	0.0522854i	$0.983349\pi$
$542$	−38.9581	−	22.4925i	−1.67340	−	0.966135i
$543$		0			0
$544$	−25.0221	−	6.70465i	−1.07281	−	0.287459i
$545$	−23.5396			−1.00833
$546$		0			0
$547$	−13.8672			−0.592920			−0.296460	−	0.955045i	$-0.595806\pi$
$547$	−13.8672			−0.592920			−0.296460	+	0.955045i	$0.595806\pi$
$548$	−8.40583	−	2.25234i	−0.359079	−	0.0962150i
$549$		0			0
$550$	−1.36656	−	0.788983i	−0.0582702	−	0.0336423i
$551$	−14.5210	−	14.5210i	−0.618614	−	0.618614i
$552$		0			0
$553$	−2.71755	−	30.5775i	−0.115562	−	1.30029i
$554$	17.9574	+	17.9574i	0.762936	+	0.762936i
$555$		0			0
$556$	6.59229	+	11.4182i	0.279575	+	0.484238i
$557$	5.87298	−	21.9183i	0.248846	−	0.928706i	−0.722565	−	0.691303i	$-0.757037\pi$
$557$	5.87298	−	21.9183i	0.248846	−	0.928706i	0.971411	−	0.237403i	$-0.0762963\pi$
$558$		0			0
$559$	2.59959	−	1.71949i	0.109951	−	0.0727266i
$560$	26.0046	+	4.54846i	1.09890	+	0.192208i
$561$		0			0
$562$	6.40703	+	11.0973i	0.270264	+	0.468111i
$563$	11.2217	−	19.4366i	0.472940	−	0.819156i	−0.526580	−	0.850125i	$-0.676526\pi$
$563$	11.2217	−	19.4366i	0.472940	−	0.819156i	0.999520	+	0.0309690i	$0.00985932\pi$
$564$		0			0
$565$	−15.7572	+	4.22212i	−0.662909	+	0.177626i
$566$	0.777562	+	2.90190i	0.0326834	+	0.121976i
$567$		0			0
$568$	−11.6100	+	20.1090i	−0.487143	+	0.843756i
$569$	11.1921	−	6.46175i	0.469196	−	0.270891i	−0.246707	−	0.969090i	$-0.579349\pi$
$569$	11.1921	−	6.46175i	0.469196	−	0.270891i	0.715903	+	0.698200i	$0.246015\pi$
$570$		0			0
$571$		−	17.4421i		−	0.729930i	−0.931021	−	0.364965i	$-0.881081\pi$
$571$		−	17.4421i		−	0.729930i	0.931021	−	0.364965i	$-0.118919\pi$
$572$	−0.908123	−	2.71685i	−0.0379705	−	0.113597i
$573$		0			0
$574$	−13.7678	−	6.39700i	−0.574657	−	0.267006i
$575$	1.43312	+	2.48223i	0.0597650	+	0.103516i
$576$		0			0
$577$	10.2002	+	10.2002i	0.424642	+	0.424642i	0.886798	−	0.462157i	$-0.152924\pi$
$577$	10.2002	+	10.2002i	0.424642	+	0.424642i	−0.462157	+	0.886798i	$0.652924\pi$
$578$	8.16745	+	30.4813i	0.339721	+	1.26786i
$579$		0			0
$580$	8.41357	−	8.41357i	0.349354	−	0.349354i
$581$	−2.97211	+	3.55193i	−0.123304	+	0.147359i
$582$		0			0
$583$	1.60705	−	5.99760i	0.0665573	−	0.248395i
$584$	−2.90721			−0.120301
$585$		0			0
$586$		−	44.4045i		−	1.83433i
$587$	4.97130	−	18.5532i	0.205188	−	0.765771i	−0.784205	−	0.620502i	$-0.786929\pi$
$587$	4.97130	−	18.5532i	0.205188	−	0.765771i	0.989392	−	0.145268i	$-0.0464046\pi$
$588$		0			0
$589$	−21.0120	−	12.1313i	−0.865783	−	0.499860i
$590$	1.21225	−	1.21225i	0.0499074	−	0.0499074i
$591$		0			0
$592$	22.9969	−	6.16199i	0.945165	−	0.253256i
$593$	1.84156	−	1.84156i	0.0756236	−	0.0756236i	−0.668283	−	0.743907i	$-0.732971\pi$
$593$	1.84156	−	1.84156i	0.0756236	−	0.0756236i	0.743907	+	0.668283i	$0.232971\pi$
$594$		0			0
$595$	−10.9294	−	29.9002i	−0.448060	−	1.22579i
$596$	3.91804	−	14.6223i	0.160489	−	0.598954i
$597$		0			0
$598$	−3.60656	+	17.6991i	−0.147483	+	0.723771i
$599$	−24.8100			−1.01371			−0.506855	−	0.862031i	$-0.669192\pi$
$599$	−24.8100			−1.01371			−0.506855	+	0.862031i	$0.669192\pi$
$600$		0			0
$601$	−15.2889	+	8.82708i	−0.623649	+	0.360064i	−0.778288	−	0.627907i	$-0.783912\pi$
$601$	−15.2889	+	8.82708i	−0.623649	+	0.360064i	0.154639	+	0.987971i	$0.450578\pi$
$602$	−2.46001	+	2.93993i	−0.100263	+	0.119823i
$603$		0			0
$604$	−0.00763126	−	0.0284803i	−0.000310512	−	0.00115885i
$605$	5.22168	+	19.4876i	0.212291	+	0.792282i
$606$		0			0
$607$	13.0545	+	7.53700i	0.529864	+	0.305917i	0.740961	−	0.671548i	$-0.234370\pi$
$607$	13.0545	+	7.53700i	0.529864	+	0.305917i	−0.211097	+	0.977465i	$0.567704\pi$
$608$	6.07556	+	10.5232i	0.246397	+	0.426771i
$609$		0			0
$610$		−	43.8969i		−	1.77733i
$611$	3.50775	+	10.4942i	0.141908	+	0.424551i
$612$		0			0
$613$	33.8842	+	9.07924i	1.36857	+	0.366707i	0.866956	−	0.498384i	$-0.166073\pi$
$613$	33.8842	+	9.07924i	1.36857	+	0.366707i	0.501614	+	0.865092i	$0.332740\pi$
$614$	−3.17585	+	1.83358i	−0.128167	+	0.0739972i
$615$		0			0
$616$	−2.97933	−	4.24249i	−0.120040	−	0.170935i
$617$	−9.01921	−	33.6601i	−0.363100	−	1.35511i	−0.869979	−	0.493089i	$-0.835868\pi$
$617$	−9.01921	−	33.6601i	−0.363100	−	1.35511i	0.506879	−	0.862017i	$-0.330799\pi$
$618$		0			0
$619$	5.61860	−	5.61860i	0.225830	−	0.225830i	−0.585118	−	0.810948i	$-0.698952\pi$
$619$	5.61860	−	5.61860i	0.225830	−	0.225830i	0.810948	+	0.585118i	$0.198952\pi$
$620$	7.02896	−	12.1745i	0.282290	−	0.488940i
$621$		0			0
$622$	−47.4915	−	12.7253i	−1.90423	−	0.510238i
$623$	−3.65864	+	20.9173i	−0.146580	+	0.838035i
$624$		0			0
$625$	19.2857			0.771429
$626$	12.1398	−	45.3063i	0.485204	−	1.81081i
$627$		0			0
$628$	2.90870	−	5.03802i	0.116070	−	0.201039i
$629$	−20.3011	−	20.3011i	−0.809460	−	0.809460i
$630$		0			0
$631$	40.9973	−	10.9852i	1.63208	−	0.437314i	0.677559	−	0.735469i	$-0.263038\pi$
$631$	40.9973	−	10.9852i	1.63208	−	0.437314i	0.954517	+	0.298155i	$0.0963713\pi$
$632$	−16.3743	−	16.3743i	−0.651333	−	0.651333i
$633$		0			0
$634$	11.4156	−	6.59079i	0.453370	−	0.261754i
$635$	15.2880	+	4.09642i	0.606687	+	0.162561i
$636$		0			0
$637$	7.10904	−	24.2170i	0.281670	−	0.959511i
$638$	−12.0357			−0.476497
$639$		0			0
$640$	22.8696	−	13.2038i	0.904002	−	0.521926i
$641$	17.7415	+	10.2431i	0.700748	+	0.404577i	0.807626	−	0.589695i	$-0.200752\pi$
$641$	17.7415	+	10.2431i	0.700748	+	0.404577i	−0.106878	+	0.994272i	$0.534085\pi$
$642$		0			0
$643$	20.9593	−	5.61604i	0.826556	−	0.221475i	0.179345	−	0.983786i	$-0.442602\pi$
$643$	20.9593	−	5.61604i	0.826556	−	0.221475i	0.647211	+	0.762311i	$0.275935\pi$
$644$	−0.566525	−	6.37445i	−0.0223242	−	0.251188i
$645$		0			0
$646$	14.0838	−	24.3939i	0.554120	−	0.959763i
$647$	19.5669	+	33.8908i	0.769252	+	1.33238i	0.937969	+	0.346720i	$0.112704\pi$
$647$	19.5669	+	33.8908i	0.769252	+	1.33238i	−0.168716	+	0.985665i	$0.553962\pi$
$648$		0			0
$649$	−0.499544			−0.0196088
$650$	−4.33908	−	3.84126i	−0.170193	−	0.150666i
$651$		0			0
$652$	12.8630	+	3.44664i	0.503755	+	0.134981i
$653$	−14.8092	−	25.6503i	−0.579528	−	1.00377i	−0.995533	−	0.0944103i	$-0.969903\pi$
$653$	−14.8092	−	25.6503i	−0.579528	−	1.00377i	0.416005	−	0.909362i	$-0.363430\pi$
$654$		0			0
$655$	−28.3718	+	28.3718i	−1.10858	+	1.10858i
$656$	−16.4138	+	4.39806i	−0.640851	+	0.171715i
$657$		0			0
$658$	−7.82104	−	11.1370i	−0.304896	−	0.434165i
$659$	−1.87682	+	3.25074i	−0.0731104	+	0.126631i	−0.900263	−	0.435346i	$-0.856626\pi$
$659$	−1.87682	+	3.25074i	−0.0731104	+	0.126631i	0.827153	+	0.561977i	$0.189959\pi$
$660$		0			0
$661$	41.9725	+	11.2465i	1.63254	+	0.437438i	0.954651	−	0.297726i	$-0.0962282\pi$
$661$	41.9725	+	11.2465i	1.63254	+	0.437438i	0.677889	+	0.735164i	$0.262895\pi$
$662$		−	27.2903i		−	1.06067i
$663$		0			0
$664$			3.49363i			0.135579i
$665$	−6.29227	+	13.5424i	−0.244004	+	0.525152i
$666$		0			0
$667$	18.9328	+	10.9309i	0.733081	+	0.423244i
$668$	3.84680	+	3.84680i	0.148837	+	0.148837i
$669$		0			0
$670$	0.747368	+	2.78922i	0.0288734	+	0.107757i
$671$	−9.04453	+	9.04453i	−0.349160	+	0.349160i
$672$		0			0
$673$	23.1880	−	13.3876i	0.893833	−	0.516055i	0.0186390	−	0.999826i	$-0.494067\pi$
$673$	23.1880	−	13.3876i	0.893833	−	0.516055i	0.875194	+	0.483771i	$0.160733\pi$
$674$	4.77675	−	17.8271i	0.183993	−	0.686673i
$675$		0			0
$676$	−1.27572	−	10.4426i	−0.0490661	−	0.401639i
$677$		−	20.8667i		−	0.801971i	−0.916084	−	0.400985i	$-0.868668\pi$
$677$		−	20.8667i		−	0.801971i	0.916084	−	0.400985i	$-0.131332\pi$
$678$		0			0
$679$	−11.3554	−	31.0658i	−0.435782	−	1.19220i
$680$	−20.7971	−	12.0072i	−0.797532	−	0.460456i
$681$		0			0
$682$	−13.7354	+	3.68038i	−0.525954	+	0.140929i
$683$	31.6796	−	8.48852i	1.21219	−	0.324804i	0.404567	−	0.914509i	$-0.367422\pi$
$683$	31.6796	−	8.48852i	1.21219	−	0.324804i	0.807619	+	0.589704i	$0.200756\pi$
$684$		0			0
$685$	−18.7211	−	10.8087i	−0.715298	−	0.412977i
$686$	0.128050	+	31.0412i	0.00488897	+	1.18516i
$687$		0			0
$688$			4.29078i			0.163585i
$689$	10.1810	−	20.4042i	0.387864	−	0.777340i
$690$		0			0
$691$	−11.6421	+	43.4491i	−0.442888	+	1.65288i	0.278564	+	0.960418i	$0.410141\pi$
$691$	−11.6421	+	43.4491i	−0.442888	+	1.65288i	−0.721453	+	0.692464i	$0.756525\pi$
$692$	−6.67003	+	3.85094i	−0.253556	+	0.146391i
$693$		0			0
$694$	−5.60257	+	5.60257i	−0.212671	+	0.212671i
$695$	8.47670	+	31.6355i	0.321540	+	1.20000i
$696$		0			0
$697$	14.4897	+	14.4897i	0.548838	+	0.548838i
$698$	−33.7142	−	19.4649i	−1.27610	−	0.736758i
$699$		0			0
$700$	1.86199	+	0.865146i	0.0703766	+	0.0326994i
$701$		−	38.7293i		−	1.46279i	−0.681956	−	0.731393i	$-0.738871\pi$
$701$		−	38.7293i		−	1.46279i	0.681956	−	0.731393i	$-0.261129\pi$
$702$		0			0
$703$			13.4670i			0.507919i
$704$	−2.53525	−	0.679319i	−0.0955510	−	0.0256028i
$705$		0			0
$706$	11.0210	−	19.0889i	0.414780	−	0.718420i
$707$	17.3136	−	12.1586i	0.651144	−	0.457272i
$708$		0			0
$709$	−28.4986	+	7.63617i	−1.07029	+	0.286782i	−0.750611	−	0.660745i	$-0.770241\pi$
$709$	−28.4986	+	7.63617i	−1.07029	+	0.286782i	−0.319675	+	0.947527i	$0.603574\pi$
$710$	27.7187	−	27.7187i	1.04026	−	1.04026i
$711$		0			0
$712$	8.00915	+	13.8723i	0.300156	+	0.519885i
$713$	24.9490	+	6.68507i	0.934348	+	0.250358i
$714$		0			0
$715$	−0.432246	−	7.10276i	−0.0161651	−	0.265628i
$716$	4.86122			0.181672
$717$		0			0
$718$	7.87793	+	13.6450i	0.294002	+	0.509226i
$719$	4.23114	−	7.32855i	0.157795	−	0.273309i	−0.776278	−	0.630390i	$-0.782895\pi$
$719$	4.23114	−	7.32855i	0.157795	−	0.273309i	0.934073	+	0.357082i	$0.116228\pi$
$720$		0			0
$721$	2.42146	+	27.2459i	0.0901799	+	1.01469i
$722$	17.9981	−	4.82258i	0.669820	−	0.179478i
$723$		0			0
$724$	−4.24676	−	2.45187i	−0.157830	−	0.0911229i
$725$	−6.07418	+	3.50693i	−0.225589	+	0.130244i
$726$		0			0
$727$	−3.27056			−0.121299			−0.0606493	−	0.998159i	$-0.519317\pi$
$727$	−3.27056			−0.121299			−0.0606493	+	0.998159i	$0.519317\pi$
$728$	−7.61032	−	17.4515i	−0.282057	−	0.646794i
$729$		0			0
$730$	4.74076	+	1.27028i	0.175463	+	0.0470153i
$731$	4.48103	−	2.58712i	0.165737	−	0.0956882i
$732$		0			0
$733$	−9.76212	−	9.76212i	−0.360572	−	0.360572i	0.503451	−	0.864023i	$-0.332063\pi$
$733$	−9.76212	−	9.76212i	−0.360572	−	0.360572i	−0.864023	+	0.503451i	$0.832063\pi$
$734$	−11.8502	+	3.17526i	−0.437400	+	0.117201i
$735$		0			0
$736$	−9.14692	−	9.14692i	−0.337160	−	0.337160i
$737$	0.420703	−	0.728680i	0.0154968	−	0.0268413i
$738$		0			0
$739$	11.0030	−	41.0638i	0.404753	−	1.51056i	−0.399759	−	0.916620i	$-0.630906\pi$
$739$	11.0030	−	41.0638i	0.404753	−	1.51056i	0.804512	−	0.593937i	$-0.202427\pi$
$740$	−7.80292			−0.286841
$741$		0			0
$742$	−4.83212	+	27.6264i	−0.177393	+	1.01420i
$743$	47.1919	+	12.6450i	1.73130	+	0.463901i	0.980482	−	0.196606i	$-0.0629921\pi$
$743$	47.1919	+	12.6450i	1.73130	+	0.463901i	0.750820	+	0.660507i	$0.229659\pi$
$744$		0			0
$745$	18.8021	−	32.5663i	0.688857	−	1.19314i
$746$	−1.28606	+	1.28606i	−0.0470858	+	0.0470858i
$747$		0			0
$748$	−1.23083	−	4.59352i	−0.0450036	−	0.167956i
$749$	−28.2597	+	19.8456i	−1.03259	+	0.725142i
$750$		0			0
$751$	−9.96838	+	5.75525i	−0.363751	+	0.210012i	−0.670725	−	0.741706i	$-0.734017\pi$
$751$	−9.96838	+	5.75525i	−0.363751	+	0.210012i	0.306974	+	0.951718i	$0.400684\pi$
$752$	−14.7136	−	3.94250i	−0.536550	−	0.143768i
$753$		0			0
$754$	−43.3109	−	8.82548i	−1.57729	−	0.321405i
$755$		−	0.0732428i		−	0.00266558i
$756$		0			0
$757$	−8.97468	−	15.5446i	−0.326190	−	0.564978i	0.655562	−	0.755141i	$-0.272432\pi$
$757$	−8.97468	−	15.5446i	−0.326190	−	0.564978i	−0.981753	+	0.190163i	$0.939098\pi$
$758$	37.8230	+	21.8371i	1.37379	+	0.793160i
$759$		0			0
$760$	2.91545	+	10.8806i	0.105754	+	0.394681i
$761$	−2.86608	−	10.6964i	−0.103895	−	0.387743i	0.894322	−	0.447424i	$-0.147658\pi$
$761$	−2.86608	−	10.6964i	−0.103895	−	0.387743i	−0.998218	+	0.0596806i	$0.980992\pi$
$762$		0			0
$763$	−23.7605	−	19.8818i	−0.860188	−	0.719770i
$764$	15.1571	−	8.75096i	0.548365	−	0.316599i
$765$		0			0
$766$	8.93422			0.322806
$767$	−1.79763	−	0.366304i	−0.0649087	−	0.0132265i
$768$		0			0
$769$	2.87361	−	10.7245i	0.103625	−	0.386734i	−0.894561	−	0.446947i	$-0.852511\pi$
$769$	2.87361	−	10.7245i	0.103625	−	0.386734i	0.998186	+	0.0602130i	$0.0191780\pi$
$770$	3.00463	+	8.21997i	0.108279	+	0.296227i
$771$		0			0
$772$	5.54545	−	5.54545i	0.199585	−	0.199585i
$773$	2.67962	−	0.718001i	0.0963792	−	0.0258247i	−0.210307	−	0.977635i	$-0.567446\pi$
$773$	2.67962	−	0.718001i	0.0963792	−	0.0258247i	0.306686	+	0.951811i	$0.400780\pi$
$774$		0			0
$775$	−5.85959	+	5.85959i	−0.210483	+	0.210483i
$776$	−21.6079	−	12.4753i	−0.775678	−	0.447838i
$777$		0			0
$778$	−1.49192	+	5.56791i	−0.0534879	+	0.199619i
$779$		−	9.61197i		−	0.344385i
$780$		0			0
$781$	−11.4223			−0.408724
$782$	−7.76103	+	28.9646i	−0.277534	+	1.03577i
$783$		0			0
$784$	22.4070	+	26.5549i	0.800249	+	0.948390i
$785$	10.2183	−	10.2183i	0.364707	−	0.364707i
$786$		0			0
$787$	10.0968	+	37.6817i	0.359912	+	1.34321i	0.874189	+	0.485585i	$0.161393\pi$
$787$	10.0968	+	37.6817i	0.359912	+	1.34321i	−0.514278	+	0.857624i	$0.671940\pi$
$788$	2.64999	+	2.64999i	0.0944020	+	0.0944020i
$789$		0			0
$790$	19.5467	+	33.8559i	0.695441	+	1.20454i
$791$	−19.4710	−	9.04692i	−0.692311	−	0.321672i
$792$		0			0
$793$	−39.1793	+	25.9150i	−1.39130	+	0.920269i
$794$			1.00709i			0.0357403i
$795$		0			0
$796$	−15.1101	+	8.72381i	−0.535563	+	0.309207i
$797$	−16.0998	+	27.8857i	−0.570285	+	0.987763i	0.426251	+	0.904605i	$0.359834\pi$
$797$	−16.0998	+	27.8857i	−0.570285	+	0.987763i	−0.996536	+	0.0831583i	$0.973499\pi$
$798$		0			0
$799$	4.75426	+	17.7431i	0.168193	+	0.627707i
$800$	4.00873	−	1.07414i	0.141730	−	0.0379764i
$801$		0			0
$802$	10.0498	−	17.4068i	0.354871	−	0.614655i
$803$	−0.715059	−	1.23852i	−0.0252339	−	0.0437064i
$804$		0			0
$805$	2.73896	−	15.6593i	0.0965356	−	0.551917i
$806$	−52.1261	+	3.17219i	−1.83606	+	0.111736i
$807$		0			0
$808$	4.13051	−	15.4153i	0.145311	−	0.542308i
$809$	5.89662	+	10.2133i	0.207314	+	0.359079i	0.950868	−	0.309598i	$-0.100194\pi$
$809$	5.89662	+	10.2133i	0.207314	+	0.359079i	−0.743553	+	0.668677i	$0.766861\pi$
$810$		0			0
$811$	−14.4330	−	14.4330i	−0.506811	−	0.506811i	0.406735	−	0.913546i	$-0.366667\pi$
$811$	−14.4330	−	14.4330i	−0.506811	−	0.506811i	−0.913546	+	0.406735i	$0.866667\pi$
$812$	15.5987	−	1.38632i	0.547407	−	0.0486505i
$813$		0			0
$814$	5.58107	+	5.58107i	0.195616	+	0.195616i
$815$	28.6480	+	16.5399i	1.00350	+	0.579369i
$816$		0			0
$817$	−2.34438	−	0.628174i	−0.0820194	−	0.0219770i
$818$	19.4551			0.680232
$819$		0			0
$820$	5.56926			0.194487
$821$	−8.75856	−	2.34685i	−0.305676	−	0.0819056i	0.102721	−	0.994710i	$-0.467245\pi$
$821$	−8.75856	−	2.34685i	−0.305676	−	0.0819056i	−0.408396	+	0.912805i	$0.633912\pi$
$822$		0			0
$823$	−14.1019	−	8.14175i	−0.491562	−	0.283804i	0.233660	−	0.972318i	$-0.424930\pi$
$823$	−14.1019	−	8.14175i	−0.491562	−	0.283804i	−0.725222	+	0.688515i	$0.758263\pi$
$824$	14.5902	+	14.5902i	0.508273	+	0.508273i
$825$		0			0
$826$	2.24750	−	0.199745i	0.0782004	−	0.00695001i
$827$	27.1227	+	27.1227i	0.943148	+	0.943148i	0.998469	−	0.0553203i	$-0.0176180\pi$
$827$	27.1227	+	27.1227i	0.943148	+	0.943148i	−0.0553203	+	0.998469i	$0.517618\pi$
$828$		0			0
$829$	1.40529	+	2.43404i	0.0488079	+	0.0845377i	0.889397	−	0.457135i	$-0.151124\pi$
$829$	1.40529	+	2.43404i	0.0488079	+	0.0845377i	−0.840589	+	0.541673i	$0.817791\pi$
$830$	1.52651	−	5.69702i	0.0529860	−	0.197746i
$831$		0			0
$832$	−8.62510	−	4.30360i	−0.299021	−	0.149201i
$833$	14.2221	−	39.4117i	0.492766	−	1.36554i
$834$		0			0
$835$	6.75692	+	11.7033i	0.233833	+	0.405010i
$836$	−1.11534	+	1.93183i	−0.0385750	+	0.0668138i
$837$		0			0
$838$	57.9299	−	15.5223i	2.00116	−	0.536208i
$839$	−9.79321	−	36.5488i	−0.338099	−	1.26180i	−0.900470	−	0.434918i	$-0.856777\pi$
$839$	−9.79321	−	36.5488i	−0.338099	−	1.26180i	0.562371	−	0.826885i	$-0.309889\pi$
$840$		0			0
$841$	−12.2485	+	21.2150i	−0.422363	+	0.731553i
$842$	7.12836	−	4.11556i	0.245660	−	0.141832i
$843$		0			0
$844$			11.9689i			0.411986i
$845$	3.65283	−	25.8765i	0.125661	−	0.890180i
$846$		0			0
$847$	−11.1887	+	24.0807i	−0.384449	+	0.827422i
$848$	15.6961	+	27.1864i	0.539006	+	0.933586i
$849$		0			0
$850$	−6.80270	−	6.80270i	−0.233331	−	0.233331i
$851$	−3.71058	−	13.8481i	−0.127197	−	0.474706i
$852$		0			0
$853$	−7.88711	+	7.88711i	−0.270050	+	0.270050i	−0.829120	−	0.559070i	$-0.811158\pi$
$853$	−7.88711	+	7.88711i	−0.270050	+	0.270050i	0.559070	+	0.829120i	$0.311158\pi$
$854$	37.0757	−	44.3087i	1.26871	−	1.51621i
$855$		0			0
$856$	−6.74193	+	25.1612i	−0.230434	+	0.859993i
$857$	17.7293			0.605621			0.302811	−	0.953051i	$-0.402075\pi$
$857$	17.7293			0.605621			0.302811	+	0.953051i	$0.402075\pi$
$858$		0			0
$859$			3.70465i			0.126401i	0.998001	+	0.0632005i	$0.0201308\pi$
$859$			3.70465i			0.126401i	−0.998001	+	0.0632005i	$0.979869\pi$
$860$	0.363970	−	1.35835i	0.0124113	−	0.0463195i
$861$		0			0
$862$	−0.712607	−	0.411424i	−0.0242715	−	0.0140132i
$863$	−27.8842	+	27.8842i	−0.949191	+	0.949191i	−0.998770	−	0.0495793i	$-0.984212\pi$
$863$	−27.8842	+	27.8842i	−0.949191	+	0.949191i	0.0495793	+	0.998770i	$0.484212\pi$
$864$		0			0
$865$	−18.4801	+	4.95174i	−0.628344	+	0.168364i
$866$	21.0805	−	21.0805i	0.716345	−	0.716345i
$867$		0			0
$868$	17.3776	−	6.35201i	0.589835	−	0.215601i
$869$	2.94827	−	11.0031i	0.100013	−	0.373254i
$870$		0			0
$871$	2.04824	−	2.31369i	0.0694021	−	0.0783966i
$872$	−23.3705			−0.791425
$873$		0			0
$874$	12.1812	−	7.03283i	0.412036	−	0.237889i
$875$	24.3064	+	20.3386i	0.821705	+	0.687569i
$876$		0			0
$877$	−10.3037	−	38.4541i	−0.347933	−	1.29850i	−0.889148	−	0.457619i	$-0.848702\pi$
$877$	−10.3037	−	38.4541i	−0.347933	−	1.29850i	0.541215	−	0.840884i	$-0.317964\pi$
$878$	12.4078	+	46.3064i	0.418742	+	1.56277i
$879$		0			0
$880$	8.48373	+	4.89808i	0.285986	+	0.165114i
$881$	−1.49665	−	2.59227i	−0.0504233	−	0.0873357i	0.839712	−	0.543032i	$-0.182724\pi$
$881$	−1.49665	−	2.59227i	−0.0504233	−	0.0873357i	−0.890135	+	0.455696i	$0.849390\pi$
$882$		0			0
$883$			1.38623i			0.0466504i	0.999728	+	0.0233252i	$0.00742531\pi$
$883$			1.38623i			0.0466504i	−0.999728	+	0.0233252i	$0.992575\pi$
$884$	−1.06088	−	17.4325i	−0.0356811	−	0.586320i
$885$		0			0
$886$	−11.9342	−	3.19777i	−0.400939	−	0.107431i
$887$	−30.8094	+	17.7878i	−1.03448	+	0.597256i	−0.918264	−	0.395968i	$-0.870409\pi$
$887$	−30.8094	+	17.7878i	−1.03448	+	0.597256i	−0.116214	+	0.993224i	$0.537076\pi$
$888$		0			0
$889$	11.9716	+	17.0473i	0.401515	+	0.571747i
$890$	−6.99906	−	26.1209i	−0.234609	−	0.875573i
$891$		0			0
$892$	12.2168	−	12.2168i	0.409049	−	0.409049i
$893$	4.30817	−	7.46197i	0.144168	−	0.249705i
$894$		0			0
$895$	11.6642	+	3.12540i	0.389890	+	0.104471i
$896$	34.2363	+	5.98825i	1.14375	+	0.200053i
$897$		0			0
$898$	39.0804			1.30413
$899$	−16.3588	+	61.0519i	−0.545597	+	2.03620i
$900$		0			0
$901$	18.9279	−	32.7841i	0.630580	−	1.09220i
$902$	−3.98343	−	3.98343i	−0.132634	−	0.132634i
$903$		0			0
$904$	−15.6439	+	4.19178i	−0.520310	+	0.139417i
$905$	−8.61344	−	8.61344i	−0.286320	−	0.286320i
$906$		0			0
$907$	−43.1379	+	24.9057i	−1.43237	+	0.826979i	−0.997301	−	0.0734190i	$-0.976609\pi$
$907$	−43.1379	+	24.9057i	−1.43237	+	0.826979i	−0.435068	+	0.900398i	$0.643276\pi$
$908$	−10.5660	−	2.83116i	−0.350646	−	0.0939553i
$909$		0			0
$910$	4.78479	+	31.7832i	0.158614	+	1.05360i
$911$	55.7036			1.84554			0.922772	−	0.385347i	$-0.125918\pi$
$911$	55.7036			1.84554			0.922772	+	0.385347i	$0.125918\pi$
$912$		0			0
$913$	−1.48834	+	0.859293i	−0.0492568	+	0.0284385i
$914$	−6.54953	−	3.78137i	−0.216639	−	0.125077i
$915$		0			0
$916$	−5.62180	+	1.50636i	−0.185749	+	0.0497714i
$917$	−52.6012	+	4.67490i	−1.73704	+	0.154379i
$918$		0			0
$919$	10.0323	−	17.3764i	0.330934	−	0.573194i	−0.651762	−	0.758424i	$-0.725970\pi$
$919$	10.0323	−	17.3764i	0.330934	−	0.573194i	0.982695	+	0.185230i	$0.0593030\pi$
$920$	−5.99587	−	10.3852i	−0.197678	−	0.342388i
$921$		0			0
$922$	−55.8406			−1.83901
$923$	−41.1038	−	8.37574i	−1.35295	−	0.275691i
$924$		0			0
$925$	4.44286	+	1.19046i	0.146080	+	0.0391421i
$926$	−34.4873	−	59.7338i	−1.13332	−	1.96297i
$927$		0			0
$928$	22.3831	−	22.3831i	0.734762	−	0.734762i
$929$	30.5947	−	8.19783i	1.00378	−	0.268962i	0.280752	−	0.959780i	$-0.409416\pi$
$929$	30.5947	−	8.19783i	1.00378	−	0.268962i	0.723029	+	0.690818i	$0.242749\pi$
$930$		0			0
$931$	−17.7894	+	8.35495i	−0.583023	+	0.273823i
$932$	−9.38923	+	16.2626i	−0.307555	+	0.532700i
$933$		0			0
$934$	−9.25619	−	2.48019i	−0.302872	−	0.0811542i
$935$		−	11.8132i		−	0.386332i
$936$		0			0
$937$			43.3600i			1.41651i	0.705957	+	0.708255i	$0.250517\pi$
$937$			43.3600i			1.41651i	−0.705957	+	0.708255i	$0.749483\pi$
$938$	−1.60142	+	3.44662i	−0.0522882	+	0.112536i
$939$		0			0
$940$	4.32353	+	2.49619i	0.141018	+	0.0814168i
$941$	27.4469	+	27.4469i	0.894743	+	0.894743i	0.994965	−	0.100222i	$-0.0319553\pi$
$941$	27.4469	+	27.4469i	0.894743	+	0.894743i	−0.100222	+	0.994965i	$0.531955\pi$
$942$		0			0
$943$	2.64839	+	9.88393i	0.0862435	+	0.321865i
$944$	1.78586	−	1.78586i	0.0581246	−	0.0581246i
$945$		0			0
$946$	−1.23190	+	0.711236i	−0.0400524	+	0.0231243i
$947$	−10.6763	+	39.8444i	−0.346932	+	1.29477i	0.543406	+	0.839470i	$0.317134\pi$
$947$	−10.6763	+	39.8444i	−0.346932	+	1.29477i	−0.890339	+	0.455299i	$0.849532\pi$
$948$		0			0
$949$	−1.66499	−	4.98120i	−0.0540480	−	0.161697i
$950$			4.51266i			0.146410i
$951$		0			0
$952$	−10.8508	−	29.6853i	−0.351677	−	0.962106i
$953$	9.00364	+	5.19825i	0.291656	+	0.168388i	0.638689	−	0.769465i	$-0.279477\pi$
$953$	9.00364	+	5.19825i	0.291656	+	0.168388i	−0.347032	+	0.937853i	$0.612811\pi$
$954$		0			0
$955$	41.9947	−	11.2524i	1.35892	−	0.364120i
$956$	3.06546	−	0.821387i	0.0991439	−	0.0265655i
$957$		0			0
$958$	−48.3721	−	27.9277i	−1.56283	−	0.902301i
$959$	−9.76769	−	26.7221i	−0.315415	−	0.862903i
$960$		0			0
$961$			43.6760i			1.40890i
$962$	15.9913	+	24.1762i	0.515579	+	0.779472i
$963$		0			0
$964$	−0.667940	+	2.49279i	−0.0215129	+	0.0802873i
$965$	16.8713	−	9.74062i	0.543105	−	0.313562i
$966$		0			0
$967$	15.1251	−	15.1251i	0.486390	−	0.486390i	−0.420775	−	0.907165i	$-0.638242\pi$
$967$	15.1251	−	15.1251i	0.486390	−	0.486390i	0.907165	+	0.420775i	$0.138242\pi$
$968$	5.18415	+	19.3475i	0.166625	+	0.621853i
$969$		0			0
$970$	29.7847	+	29.7847i	0.956331	+	0.956331i
$971$	15.1229	+	8.73122i	0.485318	+	0.280198i	0.722630	−	0.691235i	$-0.242933\pi$
$971$	15.1229	+	8.73122i	0.485318	+	0.280198i	−0.237312	+	0.971433i	$0.576266\pi$
$972$		0			0
$973$	−18.1634	+	39.0918i	−0.582292	+	1.25323i
$974$			25.3407i			0.811968i
$975$		0			0
$976$		−	64.6679i		−	2.06997i
$977$	−11.5532	−	3.09568i	−0.369621	−	0.0990396i	0.0692272	−	0.997601i	$-0.477947\pi$
$977$	−11.5532	−	3.09568i	−0.369621	−	0.0990396i	−0.438848	+	0.898561i	$0.644613\pi$
$978$		0			0
$979$	−3.93986	+	6.82405i	−0.125919	+	0.218097i
$980$	−4.84093	−	10.3073i	−0.154638	−	0.329255i
$981$		0			0
$982$	−7.10215	+	1.90302i	−0.226639	+	0.0607277i
$983$	−8.69175	+	8.69175i	−0.277224	+	0.277224i	−0.832000	−	0.554776i	$-0.812804\pi$
$983$	−8.69175	+	8.69175i	−0.277224	+	0.277224i	0.554776	+	0.832000i	$0.312804\pi$
$984$		0			0
$985$	4.65472	+	8.06222i	0.148312	+	0.256884i
$986$	−70.8782	−	18.9918i	−2.25722	−	0.604821i
$987$		0			0
$988$	−5.43019	+	6.13393i	−0.172757	+	0.195146i
$989$	2.58379			0.0821598
$990$		0			0
$991$	19.1774	+	33.2162i	0.609189	+	1.05515i	0.991374	+	0.131060i	$0.0418382\pi$
$991$	19.1774	+	33.2162i	0.609189	+	1.05515i	−0.382186	+	0.924086i	$0.624829\pi$
$992$	18.6996	−	32.3886i	0.593712	−	1.02834i
$993$		0			0
$994$	51.3902	−	4.56728i	1.63000	−	0.144865i
$995$	−41.8644	+	11.2175i	−1.32719	+	0.355619i
$996$		0			0
$997$	−33.1334	−	19.1296i	−1.04935	−	0.605840i	−0.126879	−	0.991918i	$-0.540496\pi$
$997$	−33.1334	−	19.1296i	−1.04935	−	0.605840i	−0.922466	+	0.386078i	$0.873829\pi$
$998$	−29.0891	+	16.7946i	−0.920800	+	0.531624i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.g.496.2		32
3.2	odd	2		91.2.bc.a.41.8	yes	32
7.6	odd	2	inner	819.2.fm.g.496.1		32
13.7	odd	12	inner	819.2.fm.g.748.1		32
21.2	odd	6		637.2.x.b.80.2		32
21.5	even	6		637.2.x.b.80.1		32
21.11	odd	6		637.2.bb.b.509.1		32
21.17	even	6		637.2.bb.b.509.2		32
21.20	even	2		91.2.bc.a.41.7	yes	32
39.20	even	12		91.2.bc.a.20.7	✓	32
91.20	even	12	inner	819.2.fm.g.748.2		32
273.20	odd	12		91.2.bc.a.20.8	yes	32
273.59	odd	12		637.2.x.b.215.1		32
273.137	even	12		637.2.x.b.215.2		32
273.215	odd	12		637.2.bb.b.423.1		32
273.254	even	12		637.2.bb.b.423.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.20.7	✓	32	39.20	even	12
91.2.bc.a.20.8	yes	32	273.20	odd	12
91.2.bc.a.41.7	yes	32	21.20	even	2
91.2.bc.a.41.8	yes	32	3.2	odd	2
637.2.x.b.80.1		32	21.5	even	6
637.2.x.b.80.2		32	21.2	odd	6
637.2.x.b.215.1		32	273.59	odd	12
637.2.x.b.215.2		32	273.137	even	12
637.2.bb.b.423.1		32	273.215	odd	12
637.2.bb.b.423.2		32	273.254	even	12
637.2.bb.b.509.1		32	21.11	odd	6
637.2.bb.b.509.2		32	21.17	even	6
819.2.fm.g.496.1		32	7.6	odd	2	inner
819.2.fm.g.496.2		32	1.1	even	1	trivial
819.2.fm.g.748.1		32	13.7	odd	12	inner
819.2.fm.g.748.2		32	91.20	even	12	inner

Overview	Random
Universe	Knowledge

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fm (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61897 - 0.433802i) q^{2} +(0.700831 + 0.404625i) q^{4} +(1.42145 + 1.42145i) q^{5} +(0.234216 + 2.63536i) q^{7} +(1.41124 + 1.41124i) q^{8} +O(q^{10})\)	\(q+(-1.61897 - 0.433802i) q^{2} +(0.700831 + 0.404625i) q^{4} +(1.42145 + 1.42145i) q^{5} +(0.234216 + 2.63536i) q^{7} +(1.41124 + 1.41124i) q^{8} +(-1.68466 - 2.91792i) q^{10} +(-0.254101 + 0.948318i) q^{11} +(-1.60977 + 3.22624i) q^{13} +(0.764036 - 4.36818i) q^{14} +(-2.48181 - 4.29862i) q^{16} +(-2.99281 + 5.18370i) q^{17} +(2.71200 - 0.726678i) q^{19} +(0.421043 + 1.57135i) q^{20} +(0.822765 - 1.42507i) q^{22} +(-2.58851 + 1.49448i) q^{23} -0.958941i q^{25} +(4.00573 - 4.52487i) q^{26} +(-0.902188 + 1.94172i) q^{28} +(-3.65708 - 6.33425i) q^{29} +(-6.11048 - 6.11048i) q^{31} +(1.12013 + 4.18037i) q^{32} +(7.09397 - 7.09397i) q^{34} +(-3.41312 + 4.07897i) q^{35} +(-1.24143 + 4.63309i) q^{37} -4.70588 q^{38} +4.01202i q^{40} +(0.886060 - 3.30682i) q^{41} +(-0.748633 - 0.432224i) q^{43} +(-0.561795 + 0.561795i) q^{44} +(4.83903 - 1.29661i) q^{46} +(2.17001 - 2.17001i) q^{47} +(-6.89029 + 1.23449i) q^{49} +(-0.415990 + 1.55250i) q^{50} +(-2.43360 + 1.60970i) q^{52} -6.32446 q^{53} +(-1.70918 + 0.986797i) q^{55} +(-3.38859 + 4.04966i) q^{56} +(3.17290 + 11.8414i) q^{58} +(0.131692 + 0.491481i) q^{59} +(11.2829 + 6.51419i) q^{61} +(7.24196 + 12.5434i) q^{62} +2.67342i q^{64} +(-6.87417 + 2.29773i) q^{65} +(-0.827827 - 0.221815i) q^{67} +(-4.19491 + 2.42193i) q^{68} +(7.29521 - 5.12312i) q^{70} +(3.01121 + 11.2380i) q^{71} +(-1.03002 + 1.03002i) q^{73} +(4.01968 - 6.96230i) q^{74} +(2.19469 + 0.588064i) q^{76} +(-2.55868 - 0.447537i) q^{77} -11.6027 q^{79} +(2.58251 - 9.63806i) q^{80} +(-2.86901 + 4.96927i) q^{82} +(1.23779 + 1.23779i) q^{83} +(-11.6225 + 3.11424i) q^{85} +(1.02452 + 1.02452i) q^{86} +(-1.69690 + 0.979707i) q^{88} +(7.75255 + 2.07729i) q^{89} +(-8.87935 - 3.48670i) q^{91} -2.41881 q^{92} +(-4.45454 + 2.57183i) q^{94} +(4.88792 + 2.82204i) q^{95} +(-12.0756 + 3.23566i) q^{97} +(11.6907 + 0.990414i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8}+O(q^{10}) \) 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8	\( 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8} + 4 q^{11} + 32 q^{14} + 12 q^{16} + 4 q^{22} + 12 q^{23} + 24 q^{28} - 4 q^{29} - 4 q^{32} + 20 q^{35} + 4 q^{37} - 48 q^{43} - 24 q^{44} + 84 q^{46} + 24 q^{49} + 44 q^{50} - 72 q^{53} - 60 q^{56} - 16 q^{58} - 4 q^{65} - 56 q^{67} + 56 q^{70} - 84 q^{71} + 24 q^{74} - 80 q^{79} + 36 q^{85} + 48 q^{86} - 228 q^{88} - 48 q^{91} - 24 q^{92} + 84 q^{95} + 32 q^{98}+O(q^{100}) \) 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8 + 4 * q^11 + 32 * q^14 + 12 * q^16 + 4 * q^22 + 12 * q^23 + 24 * q^28 - 4 * q^29 - 4 * q^32 + 20 * q^35 + 4 * q^37 - 48 * q^43 - 24 * q^44 + 84 * q^46 + 24 * q^49 + 44 * q^50 - 72 * q^53 - 60 * q^56 - 16 * q^58 - 4 * q^65 - 56 * q^67 + 56 * q^70 - 84 * q^71 + 24 * q^74 - 80 * q^79 + 36 * q^85 + 48 * q^86 - 228 * q^88 - 48 * q^91 - 24 * q^92 + 84 * q^95 + 32 * q^98

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