LMFDB - Embedded newform 819.2.fm.g.748.4

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			748.4
Character	$\chi$	$=$	819.748
Dual form			819.2.fm.g.496.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.112775 - 0.0302180i) q^{2} +(-1.72025 + 0.993184i) q^{4} +(1.24841 - 1.24841i) q^{5} +(-2.18126 - 1.49736i) q^{7} +(-0.329103 + 0.329103i) q^{8} +(0.103066 - 0.178515i) q^{10} +(0.506699 + 1.89103i) q^{11} +(-1.85749 + 3.09026i) q^{13} +(-0.291240 - 0.102952i) q^{14} +(1.95920 - 3.39343i) q^{16} +(2.13907 + 3.70498i) q^{17} +(4.12248 + 1.10462i) q^{19} +(-0.907674 + 3.38749i) q^{20} +(0.114286 + 0.197949i) q^{22} +(5.53927 + 3.19810i) q^{23} +1.88292i q^{25} +(-0.116097 + 0.404635i) q^{26} +(5.23946 + 0.409435i) q^{28} +(3.57954 - 6.19995i) q^{29} +(-3.02628 + 3.02628i) q^{31} +(0.359327 - 1.34103i) q^{32} +(0.353191 + 0.353191i) q^{34} +(-4.59245 + 0.853791i) q^{35} +(-0.732202 - 2.73261i) q^{37} +0.498293 q^{38} +0.821715i q^{40} +(2.94901 + 11.0059i) q^{41} +(-1.55234 + 0.896243i) q^{43} +(-2.74978 - 2.74978i) q^{44} +(0.721333 + 0.193281i) q^{46} +(4.68665 + 4.68665i) q^{47} +(2.51581 + 6.53228i) q^{49} +(0.0568982 + 0.212347i) q^{50} +(0.126138 - 7.16084i) q^{52} -4.27793 q^{53} +(2.99335 + 1.72821i) q^{55} +(1.21065 - 0.225074i) q^{56} +(0.216333 - 0.807367i) q^{58} +(0.436704 - 1.62980i) q^{59} +(2.66960 - 1.54129i) q^{61} +(-0.249841 + 0.432737i) q^{62} +7.67470i q^{64} +(1.53901 + 6.17685i) q^{65} +(-0.0190380 + 0.00510122i) q^{67} +(-7.35945 - 4.24898i) q^{68} +(-0.492115 + 0.235061i) q^{70} +(-1.23109 + 4.59449i) q^{71} +(0.698492 + 0.698492i) q^{73} +(-0.165148 - 0.286046i) q^{74} +(-8.18877 + 2.19417i) q^{76} +(1.72631 - 4.88353i) q^{77} -5.93719 q^{79} +(-1.79052 - 6.68230i) q^{80} +(0.665151 + 1.15208i) q^{82} +(-9.87683 + 9.87683i) q^{83} +(7.29580 + 1.95490i) q^{85} +(-0.147983 + 0.147983i) q^{86} +(-0.789099 - 0.455587i) q^{88} +(7.76240 - 2.07993i) q^{89} +(8.67892 - 3.95934i) q^{91} -12.7052 q^{92} +(0.670159 + 0.386917i) q^{94} +(6.52558 - 3.76755i) q^{95} +(14.2676 + 3.82300i) q^{97} +(0.481114 + 0.660657i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$-1$

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 $

$2$	0.112775	−	0.0302180i	0.0797441	−	0.0213674i	−0.218726	−	0.975786i	$-0.570190\pi$
$2$	0.112775	−	0.0302180i	0.0797441	−	0.0213674i	0.298471	+	0.954419i	$0.403524\pi$
$3$		0			0
$3$		0			0
$4$	−1.72025	+	0.993184i	−0.860123	+	0.496592i
$5$	1.24841	−	1.24841i	0.558308	−	0.558308i	−0.370518	−	0.928825i	$-0.620820\pi$
$5$	1.24841	−	1.24841i	0.558308	−	0.558308i	0.928825	+	0.370518i	$0.120820\pi$
$6$		0			0
$7$	−2.18126	−	1.49736i	−0.824440	−	0.565950i
$7$	−2.18126	−	1.49736i	−0.824440	−	0.565950i
$8$	−0.329103	+	0.329103i	−0.116356	+	0.116356i
$9$		0			0
$10$	0.103066	−	0.178515i	0.0325922	−	0.0564514i
$11$	0.506699	+	1.89103i	0.152775	+	0.570166i	0.999286	+	0.0377930i	$0.0120328\pi$
$11$	0.506699	+	1.89103i	0.152775	+	0.570166i	−0.846510	+	0.532373i	$0.821301\pi$
$12$		0			0
$13$	−1.85749	+	3.09026i	−0.515175	+	0.857085i
$13$	−1.85749	+	3.09026i	−0.515175	+	0.857085i
$14$	−0.291240	−	0.102952i	−0.0778371	−	0.0275151i
$15$		0			0
$16$	1.95920	−	3.39343i	0.489800	−	0.848358i
$17$	2.13907	+	3.70498i	0.518801	+	0.898589i	0.999761	+	0.0218471i	$0.00695471\pi$
$17$	2.13907	+	3.70498i	0.518801	+	0.898589i	−0.480960	+	0.876742i	$0.659712\pi$
$18$		0			0
$19$	4.12248	+	1.10462i	0.945762	+	0.253416i	0.698563	−	0.715549i	$-0.253823\pi$
$19$	4.12248	+	1.10462i	0.945762	+	0.253416i	0.247199	+	0.968965i	$0.420490\pi$
$20$	−0.907674	+	3.38749i	−0.202962	+	0.757465i
$21$		0			0
$22$	0.114286	+	0.197949i	0.0243659	+	0.0422030i
$23$	5.53927	+	3.19810i	1.15502	+	0.666850i	0.950105	−	0.311930i	$-0.100976\pi$
$23$	5.53927	+	3.19810i	1.15502	+	0.666850i	0.204913	+	0.978780i	$0.434309\pi$
$24$		0			0
$25$			1.88292i			0.376585i
$26$	−0.116097	+	0.404635i	−0.0227685	+	0.0793554i
$27$		0			0
$28$	5.23946	+	0.409435i	0.990166	+	0.0773760i
$29$	3.57954	−	6.19995i	0.664704	−	1.15130i	−0.314661	−	0.949204i	$-0.601891\pi$
$29$	3.57954	−	6.19995i	0.664704	−	1.15130i	0.979365	−	0.202097i	$-0.0647758\pi$
$30$		0			0
$31$	−3.02628	+	3.02628i	−0.543535	+	0.543535i	−0.924563	−	0.381028i	$-0.875570\pi$
$31$	−3.02628	+	3.02628i	−0.543535	+	0.543535i	0.381028	+	0.924563i	$0.375570\pi$
$32$	0.359327	−	1.34103i	0.0635206	−	0.237062i
$33$		0			0
$34$	0.353191	+	0.353191i	0.0605718	+	0.0605718i
$35$	−4.59245	+	0.853791i	−0.776265	+	0.144317i
$36$		0			0
$37$	−0.732202	−	2.73261i	−0.120373	−	0.449239i	0.879259	−	0.476343i	$-0.158038\pi$
$37$	−0.732202	−	2.73261i	−0.120373	−	0.449239i	−0.999633	+	0.0271042i	$0.991371\pi$
$38$	0.498293			0.0808338
$39$		0			0
$40$			0.821715i			0.129925i
$41$	2.94901	+	11.0059i	0.460558	+	1.71883i	0.671212	+	0.741266i	$0.265774\pi$
$41$	2.94901	+	11.0059i	0.460558	+	1.71883i	−0.210654	+	0.977561i	$0.567559\pi$
$42$		0			0
$43$	−1.55234	+	0.896243i	−0.236730	+	0.136676i	−0.613673	−	0.789561i	$-0.710309\pi$
$43$	−1.55234	+	0.896243i	−0.236730	+	0.136676i	0.376943	+	0.926236i	$0.376975\pi$
$44$	−2.74978	−	2.74978i	−0.414545	−	0.414545i
$45$		0			0
$46$	0.721333	+	0.193281i	0.106355	+	0.0284977i
$47$	4.68665	+	4.68665i	0.683618	+	0.683618i	0.960814	−	0.277196i	$-0.0894050\pi$
$47$	4.68665	+	4.68665i	0.683618	+	0.683618i	−0.277196	+	0.960814i	$0.589405\pi$
$48$		0			0
$49$	2.51581	+	6.53228i	0.359402	+	0.933183i
$50$	0.0568982	+	0.212347i	0.00804663	+	0.0300304i
$51$		0			0
$52$	0.126138	−	7.16084i	0.0174922	−	0.993030i
$53$	−4.27793			−0.587619			−0.293809	−	0.955864i	$-0.594923\pi$
$53$	−4.27793			−0.587619			−0.293809	+	0.955864i	$0.594923\pi$
$54$		0			0
$55$	2.99335	+	1.72821i	0.403624	+	0.233032i
$56$	1.21065	−	0.225074i	0.161780	−	0.0300768i
$57$		0			0
$58$	0.216333	−	0.807367i	0.0284060	−	0.106013i
$59$	0.436704	−	1.62980i	0.0568541	−	0.212182i	−0.931655	−	0.363344i	$-0.881635\pi$
$59$	0.436704	−	1.62980i	0.0568541	−	0.212182i	0.988509	+	0.151162i	$0.0483015\pi$
$60$		0			0
$61$	2.66960	−	1.54129i	0.341807	−	0.197342i	−0.319264	−	0.947666i	$-0.603436\pi$
$61$	2.66960	−	1.54129i	0.341807	−	0.197342i	0.661071	+	0.750323i	$0.270102\pi$
$62$	−0.249841	+	0.432737i	−0.0317298	+	0.0549577i
$63$		0			0
$64$			7.67470i			0.959338i
$65$	1.53901	+	6.17685i	0.190891	+	0.766144i
$66$		0			0
$67$	−0.0190380	+	0.00510122i	−0.00232586	+	0.000623213i	−0.259982	−	0.965614i	$-0.583717\pi$
$67$	−0.0190380	+	0.00510122i	−0.00232586	+	0.000623213i	0.257656	+	0.966237i	$0.417050\pi$
$68$	−7.35945	−	4.24898i	−0.892465	−	0.515265i
$69$		0			0
$70$	−0.492115	+	0.235061i	−0.0588189	+	0.0280952i
$71$	−1.23109	+	4.59449i	−0.146104	+	0.545266i	0.853600	+	0.520929i	$0.174414\pi$
$71$	−1.23109	+	4.59449i	−0.146104	+	0.545266i	−0.999704	+	0.0243373i	$0.992252\pi$
$72$		0			0
$73$	0.698492	+	0.698492i	0.0817523	+	0.0817523i	0.746800	−	0.665048i	$-0.231589\pi$
$73$	0.698492	+	0.698492i	0.0817523	+	0.0817523i	−0.665048	+	0.746800i	$0.731589\pi$
$74$	−0.165148	−	0.286046i	−0.0191981	−	0.0332521i
$75$		0			0
$76$	−8.18877	+	2.19417i	−0.939316	+	0.251689i
$77$	1.72631	−	4.88353i	0.196731	−	0.556530i
$78$		0			0
$79$	−5.93719			−0.667987			−0.333993	−	0.942575i	$-0.608396\pi$
$79$	−5.93719			−0.667987			−0.333993	+	0.942575i	$0.608396\pi$
$80$	−1.79052	−	6.68230i	−0.200186	−	0.747104i
$81$		0			0
$82$	0.665151	+	1.15208i	0.0734536	+	0.127225i
$83$	−9.87683	+	9.87683i	−1.08412	+	1.08412i	−0.0880033	+	0.996120i	$0.528049\pi$
$83$	−9.87683	+	9.87683i	−1.08412	+	1.08412i	−0.996120	+	0.0880033i	$0.971951\pi$
$84$		0			0
$85$	7.29580	+	1.95490i	0.791340	+	0.212039i
$86$	−0.147983	+	0.147983i	−0.0159574	+	0.0159574i
$87$		0			0
$88$	−0.789099	−	0.455587i	−0.0841183	−	0.0485657i
$89$	7.76240	−	2.07993i	0.822813	−	0.220472i	0.177237	−	0.984168i	$-0.443284\pi$
$89$	7.76240	−	2.07993i	0.822813	−	0.220472i	0.645576	+	0.763696i	$0.276617\pi$
$90$		0			0
$91$	8.67892	−	3.95934i	0.909798	−	0.415052i
$92$	−12.7052			−1.32461
$93$		0			0
$94$	0.670159	+	0.386917i	0.0691216	+	0.0399074i
$95$	6.52558	−	3.76755i	0.669511	−	0.386542i
$96$		0			0
$97$	14.2676	+	3.82300i	1.44866	+	0.388167i	0.895557	−	0.444946i	$-0.146777\pi$
$97$	14.2676	+	3.82300i	1.44866	+	0.388167i	0.553102	+	0.833113i	$0.313444\pi$
$98$	0.481114	+	0.660657i	0.0485999	+	0.0667364i
$99$		0			0
$100$	−1.87009	−	3.23909i	−0.187009	−	0.323909i
$101$	8.00479	−	13.8647i	0.796506	−	1.37959i	−0.125372	−	0.992110i	$-0.540012\pi$
$101$	8.00479	−	13.8647i	0.796506	−	1.37959i	0.921878	−	0.387480i	$-0.126654\pi$
$102$		0			0
$103$	−11.8151			−1.16418			−0.582088	−	0.813126i	$-0.697764\pi$
$103$	−11.8151			−1.16418			−0.582088	+	0.813126i	$0.697764\pi$
$104$	−0.405710	−	1.62832i	−0.0397831	−	0.159670i
$105$		0			0
$106$	−0.482444	+	0.129271i	−0.0468591	+	0.0125559i
$107$	3.99556	−	6.92051i	0.386265	−	0.669031i	−0.605679	−	0.795709i	$-0.707098\pi$
$107$	3.99556	−	6.92051i	0.386265	−	0.669031i	0.991944	+	0.126678i	$0.0404316\pi$
$108$		0			0
$109$	−8.75647	−	8.75647i	−0.838718	−	0.838718i	0.149972	−	0.988690i	$-0.452082\pi$
$109$	−8.75647	−	8.75647i	−0.838718	−	0.838718i	−0.988690	+	0.149972i	$0.952082\pi$
$110$	0.389799	+	0.104446i	0.0371659	+	0.00995857i
$111$		0			0
$112$	−9.35472	+	4.46833i	−0.883938	+	0.422218i
$113$	−4.27217	−	7.39961i	−0.401892	−	0.696097i	0.592063	−	0.805892i	$-0.298314\pi$
$113$	−4.27217	−	7.39961i	−0.401892	−	0.696097i	−0.993954	+	0.109795i	$0.964981\pi$
$114$		0			0
$115$	10.9079	−	2.92275i	1.01716	−	0.272548i
$116$			14.2206i			1.32035i
$117$		0			0
$118$		−	0.196998i		−	0.0181351i
$119$	0.881822	−	11.2845i	0.0808365	−	1.03445i
$120$		0			0
$121$	6.20705	−	3.58364i	0.564277	−	0.325785i
$122$	0.254490	−	0.254490i	0.0230404	−	0.0230404i
$123$		0			0
$124$	2.20029	−	8.21159i	0.197592	−	0.737422i
$125$	8.59274	+	8.59274i	0.768558	+	0.768558i
$126$		0			0
$127$	−5.29483	−	3.05697i	−0.469840	−	0.271262i	0.246333	−	0.969185i	$-0.420774\pi$
$127$	−5.29483	−	3.05697i	−0.469840	−	0.271262i	−0.716173	+	0.697923i	$0.754108\pi$
$128$	0.950568	+	3.54757i	0.0840191	+	0.313564i
$129$		0			0
$130$	0.360215	+	0.650090i	0.0315929	+	0.0570166i
$131$		−	5.76435i		−	0.503634i	−0.967775	−	0.251817i	$-0.918972\pi$
$131$		−	5.76435i		−	0.503634i	0.967775	−	0.251817i	$-0.0810280\pi$
$132$		0			0
$133$	−7.33820	−	8.58230i	−0.636303	−	0.744180i
$134$	−0.00199287	+	0.00115058i	−0.000172157	+	9.93951e-5i
$135$		0			0
$136$	−1.92330	−	0.515346i	−0.164921	−	0.0441905i
$137$	6.06188	+	1.62427i	0.517901	+	0.138771i	0.508296	−	0.861183i	$-0.330276\pi$
$137$	6.06188	+	1.62427i	0.517901	+	0.138771i	0.00960548	+	0.999954i	$0.496942\pi$
$138$		0			0
$139$	−18.1314	+	10.4682i	−1.53789	+	0.887900i	−0.538927	+	0.842353i	$0.681170\pi$
$139$	−18.1314	+	10.4682i	−1.53789	+	0.887900i	−0.998962	+	0.0455477i	$0.985497\pi$
$140$	7.05217	−	6.02988i	0.596017	−	0.509618i
$141$		0			0
$142$			0.555346i			0.0466036i
$143$	−6.78495	−	1.94673i	−0.567386	−	0.162794i
$144$		0			0
$145$	−3.27135	−	12.2089i	−0.271671	−	1.01389i
$146$	0.0998797	+	0.0576656i	0.00826610	+	0.00477244i
$147$		0			0
$148$	3.97356	+	3.97356i	0.326624	+	0.326624i
$149$	−4.00070	+	14.9308i	−0.327750	+	1.22318i	0.583768	+	0.811921i	$0.301578\pi$
$149$	−4.00070	+	14.9308i	−0.327750	+	1.22318i	−0.911518	+	0.411260i	$0.865089\pi$
$150$		0			0
$151$	3.12599	−	3.12599i	0.254390	−	0.254390i	−0.568378	−	0.822768i	$-0.692429\pi$
$151$	3.12599	−	3.12599i	0.254390	−	0.254390i	0.822768	+	0.568378i	$0.192429\pi$
$152$	−1.72026	+	0.993190i	−0.139531	+	0.0805583i
$153$		0			0
$154$	0.0471139	−	0.602907i	0.00379655	−	0.0485837i
$155$			7.55609i			0.606920i
$156$		0			0
$157$			6.93064i			0.553125i	0.960996	+	0.276563i	$0.0891953\pi$
$157$			6.93064i			0.553125i	−0.960996	+	0.276563i	$0.910805\pi$
$158$	−0.669569	+	0.179410i	−0.0532680	+	0.0142731i
$159$		0			0
$160$	−1.22557	−	2.12274i	−0.0968896	−	0.167818i
$161$	−7.29389	−	15.2702i	−0.574839	−	1.20346i
$162$		0			0
$163$	−12.4944	−	3.34785i	−0.978634	−	0.262224i	−0.266165	−	0.963928i	$-0.585757\pi$
$163$	−12.4944	−	3.34785i	−0.978634	−	0.262224i	−0.712469	+	0.701703i	$0.752423\pi$
$164$	−16.0039	−	16.0039i	−1.24969	−	1.24969i
$165$		0			0
$166$	−0.815404	+	1.41232i	−0.0632876	+	0.109617i
$167$	0.900490	−	0.241286i	0.0696820	−	0.0186712i	−0.223810	−	0.974633i	$-0.571849\pi$
$167$	0.900490	−	0.241286i	0.0696820	−	0.0186712i	0.293492	+	0.955962i	$0.405183\pi$
$168$		0			0
$169$	−6.09946	−	11.4803i	−0.469189	−	0.883098i
$170$	0.881858			0.0676355
$171$		0			0
$172$	1.78027	−	3.08352i	0.135744	−	0.235116i
$173$	0.263780	+	0.456880i	0.0200548	+	0.0347360i	0.875879	−	0.482531i	$-0.160283\pi$
$173$	0.263780	+	0.456880i	0.0200548	+	0.0347360i	−0.855824	+	0.517267i	$0.826949\pi$
$174$		0			0
$175$	2.81942	−	4.10715i	0.213128	−	0.310471i
$176$	7.40979	+	1.98545i	0.558534	+	0.149659i
$177$		0			0
$178$	0.812555	−	0.469129i	0.0609036	−	0.0351627i
$179$	−7.16206	−	4.13502i	−0.535317	−	0.309066i	0.207862	−	0.978158i	$-0.433350\pi$
$179$	−7.16206	−	4.13502i	−0.535317	−	0.309066i	−0.743179	+	0.669093i	$0.766683\pi$
$180$		0			0
$181$	14.9785			1.11334			0.556672	−	0.830732i	$-0.312078\pi$
$181$	14.9785			1.11334			0.556672	+	0.830732i	$0.312078\pi$
$182$	0.859124	−	0.708775i	0.0636825	−	0.0525379i
$183$		0			0
$184$	−2.87550	+	0.770488i	−0.211985	+	0.0568011i
$185$	−4.32553	−	2.49734i	−0.318019	−	0.183608i
$186$		0			0
$187$	−5.92234	+	5.92234i	−0.433085	+	0.433085i
$188$	−12.7169	−	3.40748i	−0.927475	−	0.248516i
$189$		0			0
$190$	0.622076	−	0.622076i	0.0451301	−	0.0451301i
$191$	−7.26461	−	12.5827i	−0.525649	−	0.910450i	−0.999554	−	0.0298741i	$-0.990489\pi$
$191$	−7.26461	−	12.5827i	−0.525649	−	0.910450i	0.473905	−	0.880576i	$-0.342844\pi$
$192$		0			0
$193$	5.06711	+	18.9107i	0.364738	+	1.36122i	0.867775	+	0.496957i	$0.165549\pi$
$193$	5.06711	+	18.9107i	0.364738	+	1.36122i	−0.503037	+	0.864265i	$0.667784\pi$
$194$	1.72456			0.123816
$195$		0			0
$196$	−10.8156	−	8.73846i	−0.772541	−	0.624176i
$197$	21.0175	−	5.63163i	1.49744	−	0.401237i	0.585196	−	0.810892i	$-0.301018\pi$
$197$	21.0175	−	5.63163i	1.49744	−	0.401237i	0.912240	+	0.409655i	$0.134351\pi$
$198$		0			0
$199$	−9.64065	−	16.6981i	−0.683408	−	1.18370i	−0.973934	−	0.226830i	$-0.927164\pi$
$199$	−9.64065	−	16.6981i	−0.683408	−	1.18370i	0.290527	−	0.956867i	$-0.406170\pi$
$200$	−0.619676	−	0.619676i	−0.0438177	−	0.0438177i
$201$		0			0
$202$	0.483778	−	1.80548i	0.0340385	−	0.127033i
$203$	−17.0915	+	8.16384i	−1.19959	+	0.572989i
$204$		0			0
$205$	17.4215	+	10.0583i	1.21677	+	0.702501i
$206$	−1.33245	+	0.357029i	−0.0928363	+	0.0248754i
$207$		0			0
$208$	6.84741	+	12.3577i	0.474782	+	0.856853i
$209$			8.35542i			0.577957i
$210$		0			0
$211$	1.51130	−	2.61764i	0.104042	−	0.180206i	−0.809304	−	0.587389i	$-0.800156\pi$
$211$	1.51130	−	2.61764i	0.104042	−	0.180206i	0.913346	+	0.407184i	$0.133489\pi$
$212$	7.35909	−	4.24877i	0.505424	−	0.291807i
$213$		0			0
$214$	0.241476	−	0.901200i	0.0165070	−	0.0616048i
$215$	−0.819079	+	3.05685i	−0.0558607	+	0.208475i
$216$		0			0
$217$	11.1325	−	2.06967i	0.755726	−	0.140498i
$218$	−1.25212	−	0.722910i	−0.0848040	−	0.0489616i
$219$		0			0
$220$	−6.86574			−0.462888
$221$	−15.4227	−	0.271670i	−1.03744	−	0.0182745i
$222$		0			0
$223$	1.13865	+	4.24949i	0.0762495	+	0.284567i	0.993514	−	0.113712i	$-0.0362742\pi$
$223$	1.13865	+	4.24949i	0.0762495	+	0.284567i	−0.917264	+	0.398279i	$0.869608\pi$
$224$	−2.79179	+	2.38709i	−0.186534	+	0.159494i
$225$		0			0
$226$	−0.705396	−	0.705396i	−0.0469223	−	0.0469223i
$227$	3.95917	+	1.06086i	0.262780	+	0.0704116i	0.387803	−	0.921742i	$-0.373234\pi$
$227$	3.95917	+	1.06086i	0.262780	+	0.0704116i	−0.125024	+	0.992154i	$0.539901\pi$
$228$		0			0
$229$	9.60039	+	9.60039i	0.634412	+	0.634412i	0.949171	−	0.314760i	$-0.101924\pi$
$229$	9.60039	+	9.60039i	0.634412	+	0.634412i	−0.314760	+	0.949171i	$0.601924\pi$
$230$	1.14182	−	0.659228i	0.0752892	−	0.0434682i
$231$		0			0
$232$	0.862385	+	3.21846i	0.0566183	+	0.211303i
$233$			16.3500i			1.07113i	0.844495	+	0.535563i	$0.179900\pi$
$233$			16.3500i			1.07113i	−0.844495	+	0.535563i	$0.820100\pi$
$234$		0			0
$235$	11.7018			0.763339
$236$	0.867456	+	3.23739i	0.0564666	+	0.210736i
$237$		0			0
$238$	−0.241548	−	1.29926i	−0.0156572	−	0.0842184i
$239$	−6.11495	−	6.11495i	−0.395543	−	0.395543i	0.481115	−	0.876658i	$-0.340232\pi$
$239$	−6.11495	−	6.11495i	−0.395543	−	0.395543i	−0.876658	+	0.481115i	$0.840232\pi$
$240$		0			0
$241$	3.47625	−	12.9736i	0.223925	−	0.835700i	−0.758907	−	0.651199i	$-0.774266\pi$
$241$	3.47625	−	12.9736i	0.223925	−	0.835700i	0.982832	−	0.184501i	$-0.0590670\pi$
$242$	0.591711	−	0.591711i	0.0380366	−	0.0380366i
$243$		0			0
$244$	−3.06158	+	5.30281i	−0.195997	+	0.339478i
$245$	11.2958	+	5.01422i	0.721660	+	0.320347i
$246$		0			0
$247$	−11.0710	+	10.6877i	−0.704432	+	0.680045i
$248$		−	1.99192i		−	0.126487i
$249$		0			0
$250$	1.22870	+	0.709393i	0.0777101	+	0.0448659i
$251$	1.74301	+	3.01899i	0.110018	+	0.190557i	0.915777	−	0.401686i	$-0.131576\pi$
$251$	1.74301	+	3.01899i	0.110018	+	0.190557i	−0.805759	+	0.592243i	$0.798242\pi$
$252$		0			0
$253$	−3.24095	+	12.0954i	−0.203756	+	0.760430i
$254$	−0.689501	−	0.184751i	−0.0432631	−	0.0115923i
$255$		0			0
$256$	−7.46030	−	12.9216i	−0.466269	−	0.807601i
$257$	−6.72396	+	11.6462i	−0.419429	+	0.726472i	−0.995882	−	0.0906578i	$-0.971103\pi$
$257$	−6.72396	+	11.6462i	−0.419429	+	0.726472i	0.576453	+	0.817130i	$0.304436\pi$
$258$		0			0
$259$	−2.49459	+	7.05692i	−0.155006	+	0.438496i
$260$	−8.78223	−	9.09717i	−0.544651	−	0.564183i
$261$		0			0
$262$	−0.174187	−	0.650076i	−0.0107613	−	0.0401618i
$263$	10.2679	−	17.7846i	0.633147	−	1.09664i	−0.353757	−	0.935337i	$-0.615096\pi$
$263$	10.2679	−	17.7846i	0.633147	−	1.09664i	0.986904	−	0.161306i	$-0.0515705\pi$
$264$		0			0
$265$	−5.34063	+	5.34063i	−0.328072	+	0.328072i
$266$	−1.08691	−	0.746125i	−0.0666426	−	0.0457479i
$267$		0			0
$268$	0.0276836	−	0.0276836i	0.00169104	−	0.00169104i
$269$	9.29875	−	5.36864i	0.566955	−	0.327332i	−0.188977	−	0.981981i	$-0.560517\pi$
$269$	9.29875	−	5.36864i	0.566955	−	0.327332i	0.755932	+	0.654650i	$0.227184\pi$
$270$		0			0
$271$	−1.44767	+	0.387901i	−0.0879396	+	0.0235633i	−0.302521	−	0.953143i	$-0.597828\pi$
$271$	−1.44767	+	0.387901i	−0.0879396	+	0.0235633i	0.214581	+	0.976706i	$0.431161\pi$
$272$	16.7635			1.01643
$273$		0			0
$274$	0.732712			0.0442647
$275$	−3.56065	+	0.954075i	−0.214716	+	0.0575329i
$276$		0			0
$277$	4.07919	−	2.35512i	0.245095	−	0.141506i	−0.372421	−	0.928064i	$-0.621472\pi$
$277$	4.07919	−	2.35512i	0.245095	−	0.141506i	0.617516	+	0.786558i	$0.288139\pi$
$278$	−1.72845	+	1.72845i	−0.103666	+	0.103666i
$279$		0			0
$280$	1.23041	−	1.79238i	0.0735308	−	0.107115i
$281$	−8.01227	+	8.01227i	−0.477972	+	0.477972i	−0.904483	−	0.426511i	$-0.859743\pi$
$281$	−8.01227	+	8.01227i	−0.477972	+	0.477972i	0.426511	+	0.904483i	$0.359743\pi$
$282$		0			0
$283$	−3.93934	+	6.82313i	−0.234169	+	0.405593i	−0.959031	−	0.283301i	$-0.908570\pi$
$283$	−3.93934	+	6.82313i	−0.234169	+	0.405593i	0.724862	+	0.688894i	$0.241904\pi$
$284$	−2.44540	−	9.12636i	−0.145108	−	0.541550i
$285$		0			0
$286$	−0.824001	−	0.0145147i	−0.0487242	−	0.000858275i
$287$	10.0472	−	28.4224i	0.593067	−	1.67772i
$288$		0			0
$289$	−0.651246	+	1.12799i	−0.0383086	+	0.0663525i
$290$	−0.737855	−	1.27800i	−0.0433284	−	0.0750469i
$291$		0			0
$292$	−1.89531	−	0.507847i	−0.110915	−	0.0297195i
$293$	−3.16216	+	11.8013i	−0.184735	+	0.689442i	0.809952	+	0.586497i	$0.199493\pi$
$293$	−3.16216	+	11.8013i	−0.184735	+	0.689442i	−0.994687	+	0.102945i	$0.967173\pi$
$294$		0			0
$295$	−1.48948	−	2.57986i	−0.0867210	−	0.150205i
$296$	1.14028	+	0.658343i	0.0662776	+	0.0382654i
$297$		0			0
$298$			1.80472i			0.104545i
$299$	−20.1721	+	11.1774i	−1.16658	+	0.646404i
$300$		0			0
$301$	4.72806	+	0.369472i	0.272521	+	0.0212960i
$302$	0.258073	−	0.446996i	0.0148504	−	0.0257217i
$303$		0			0
$304$	11.8252	−	11.8252i	0.678221	−	0.678221i
$305$	1.40859	−	5.25694i	0.0806558	−	0.301011i
$306$		0			0
$307$	−7.97207	−	7.97207i	−0.454990	−	0.454990i	0.442017	−	0.897007i	$-0.354263\pi$
$307$	−7.97207	−	7.97207i	−0.454990	−	0.454990i	−0.897007	+	0.442017i	$0.854263\pi$
$308$	1.88058	+	10.1154i	0.107156	+	0.576380i
$309$		0			0
$310$	0.228330	+	0.852140i	0.0129683	+	0.0483983i
$311$	13.0428			0.739588			0.369794	−	0.929114i	$-0.379428\pi$
$311$	13.0428			0.739588			0.369794	+	0.929114i	$0.379428\pi$
$312$		0			0
$313$		−	3.57391i		−	0.202009i	−0.994886	−	0.101005i	$-0.967794\pi$
$313$		−	3.57391i		−	0.202009i	0.994886	−	0.101005i	$-0.0322057\pi$
$314$	0.209430	+	0.781604i	0.0118188	+	0.0441085i
$315$		0			0
$316$	10.2134	−	5.89673i	0.574551	−	0.331717i
$317$	−23.4565	−	23.4565i	−1.31745	−	1.31745i	−0.915788	−	0.401662i	$-0.868433\pi$
$317$	−23.4565	−	23.4565i	−1.31745	−	1.31745i	−0.401662	−	0.915788i	$-0.631567\pi$
$318$		0			0
$319$	13.5380	+	3.62750i	0.757983	+	0.203101i
$320$	9.58121	+	9.58121i	0.535606	+	0.535606i
$321$		0			0
$322$	−1.28401	−	1.50169i	−0.0715548	−	0.0836860i
$323$	4.72570	+	17.6366i	0.262945	+	0.981324i
$324$		0			0
$325$	−5.81873	−	3.49751i	−0.322765	−	0.194007i
$326$	−1.51022			−0.0836434
$327$		0			0
$328$	−4.59260	−	2.65154i	−0.253584	−	0.146407i
$329$	−3.20520	−	17.2404i	−0.176708	−	0.950495i
$330$		0			0
$331$	−0.245395	+	0.915826i	−0.0134881	+	0.0503383i	−0.972342	−	0.233562i	$-0.924962\pi$
$331$	−0.245395	+	0.915826i	−0.0134881	+	0.0503383i	0.958854	+	0.283900i	$0.0916285\pi$
$332$	7.18106	−	26.8001i	0.394112	−	1.47085i
$333$		0			0
$334$	0.0942618	−	0.0544221i	0.00515778	−	0.00297784i
$335$	−0.0173989	+	0.0301357i	−0.000950602	+	0.00164649i
$336$		0			0
$337$		−	14.1901i		−	0.772982i	−0.922293	−	0.386491i	$-0.873687\pi$
$337$		−	14.1901i		−	0.772982i	0.922293	−	0.386491i	$-0.126313\pi$
$338$	−1.03478	−	1.11038i	−0.0562846	−	0.0603965i
$339$		0			0
$340$	−14.4921	+	3.88316i	−0.785947	+	0.210594i
$341$	−7.25617	−	4.18935i	−0.392944	−	0.226866i
$342$		0			0
$343$	4.29355	−	18.0157i	0.231830	−	0.972756i
$344$	0.215923	−	0.805837i	0.0116418	−	0.0434478i
$345$		0			0
$346$	0.0435539	+	0.0435539i	0.00234147	+	0.00234147i
$347$	6.92103	+	11.9876i	0.371540	+	0.643527i	0.989803	−	0.142445i	$-0.0454965\pi$
$347$	6.92103	+	11.9876i	0.371540	+	0.643527i	−0.618262	+	0.785972i	$0.712163\pi$
$348$		0			0
$349$	14.7875	−	3.96231i	0.791559	−	0.212098i	0.159684	−	0.987168i	$-0.448952\pi$
$349$	14.7875	−	3.96231i	0.791559	−	0.212098i	0.631875	+	0.775071i	$0.282286\pi$
$350$	0.193851	−	0.548382i	0.0103617	−	0.0293123i
$351$		0			0
$352$	2.71798			0.144869
$353$	4.07649	+	15.2137i	0.216970	+	0.809742i	0.985464	+	0.169885i	$0.0543398\pi$
$353$	4.07649	+	15.2137i	0.216970	+	0.809742i	−0.768494	+	0.639857i	$0.778994\pi$
$354$		0			0
$355$	4.19892	+	7.27274i	0.222856	+	0.385997i
$356$	−11.2875	+	11.2875i	−0.598235	+	0.598235i
$357$		0			0
$358$	−0.932655	−	0.249904i	−0.0492924	−	0.0132078i
$359$	4.68787	−	4.68787i	0.247416	−	0.247416i	−0.572493	−	0.819910i	$-0.694024\pi$
$359$	4.68787	−	4.68787i	0.247416	−	0.247416i	0.819910	+	0.572493i	$0.194024\pi$
$360$		0			0
$361$	−0.679814	−	0.392491i	−0.0357797	−	0.0206574i
$362$	1.68920	−	0.452621i	0.0887826	−	0.0237892i
$363$		0			0
$364$	−10.9975	+	15.4308i	−0.576427	+	0.808794i
$365$	1.74402			0.0912859
$366$		0			0
$367$	28.4547	+	16.4284i	1.48533	+	0.857553i	0.999860	−	0.0167033i	$-0.00531706\pi$
$367$	28.4547	+	16.4284i	1.48533	+	0.857553i	0.485465	+	0.874256i	$0.338650\pi$
$368$	21.7051	−	12.5314i	1.13145	−	0.653246i
$369$		0			0
$370$	−0.563277	−	0.150930i	−0.0292834	−	0.00784646i
$371$	9.33128	+	6.40561i	0.484456	+	0.332563i
$372$		0			0
$373$	−3.93986	−	6.82405i	−0.203998	−	0.353336i	0.745815	−	0.666153i	$-0.232060\pi$
$373$	−3.93986	−	6.82405i	−0.203998	−	0.353336i	−0.949813	+	0.312818i	$0.898727\pi$
$374$	−0.488932	+	0.846855i	−0.0252821	+	0.0437899i
$375$		0			0
$376$	−3.08478			−0.159086
$377$	12.5105	+	22.5781i	0.644324	+	1.16283i
$378$		0			0
$379$	10.8095	−	2.89639i	0.555245	−	0.148778i	0.0297243	−	0.999558i	$-0.490537\pi$
$379$	10.8095	−	2.89639i	0.555245	−	0.148778i	0.525521	+	0.850781i	$0.323870\pi$
$380$	−7.48374	+	12.9622i	−0.383908	+	0.664947i
$381$		0			0
$382$	−1.19949	−	1.19949i	−0.0613713	−	0.0613713i
$383$	−2.32841	−	0.623897i	−0.118976	−	0.0318796i	0.198840	−	0.980032i	$-0.436283\pi$
$383$	−2.32841	−	0.623897i	−0.118976	−	0.0318796i	−0.317816	+	0.948152i	$0.602949\pi$
$384$		0			0
$385$	−3.94153	−	8.25182i	−0.200879	−	0.420552i
$386$	1.14289	+	1.97954i	0.0581715	+	0.100756i
$387$		0			0
$388$	−28.3408	+	7.59389i	−1.43879	+	0.385522i
$389$			16.8210i			0.852858i	0.904521	+	0.426429i	$0.140229\pi$
$389$			16.8210i			0.852858i	−0.904521	+	0.426429i	$0.859771\pi$
$390$		0			0
$391$			27.3638i			1.38385i
$392$	−2.97776	−	1.32183i	−0.150400	−	0.0667627i
$393$		0			0
$394$	2.20008	−	1.27022i	0.110838	−	0.0639926i
$395$	−7.41208	+	7.41208i	−0.372942	+	0.372942i
$396$		0			0
$397$	−6.08873	+	22.7234i	−0.305585	+	1.14046i	0.626856	+	0.779135i	$0.284341\pi$
$397$	−6.08873	+	22.7234i	−0.305585	+	1.14046i	−0.932441	+	0.361322i	$0.882325\pi$
$398$	−1.59181	−	1.59181i	−0.0797903	−	0.0797903i
$399$		0			0
$400$	6.38957	+	3.68902i	0.319479	+	0.184451i
$401$	−2.23318	−	8.33434i	−0.111520	−	0.416197i	0.887483	−	0.460840i	$-0.152452\pi$
$401$	−2.23318	−	8.33434i	−0.111520	−	0.416197i	−0.999003	+	0.0446427i	$0.985785\pi$
$402$		0			0
$403$	−3.73071	−	14.9733i	−0.185840	−	0.745872i
$404$			31.8009i			1.58216i
$405$		0			0
$406$	−1.68080	+	1.43715i	−0.0834168	+	0.0713246i
$407$	4.79644	−	2.76922i	0.237751	−	0.137265i
$408$		0			0
$409$	−12.9780	−	3.47744i	−0.641720	−	0.171948i	−0.0767375	−	0.997051i	$-0.524450\pi$
$409$	−12.9780	−	3.47744i	−0.641720	−	0.171948i	−0.564982	+	0.825103i	$0.691117\pi$
$410$	2.26865	+	0.607883i	0.112041	+	0.0300212i
$411$		0			0
$412$	20.3249	−	11.7346i	1.00133	−	0.578121i
$413$	−3.39297	+	2.90112i	−0.166957	+	0.142755i
$414$		0			0
$415$			24.6608i			1.21055i
$416$	3.47668	+	3.60136i	0.170458	+	0.176571i
$417$		0			0
$418$	0.252484	+	0.942285i	0.0123494	+	0.0460886i
$419$	15.0514	+	8.68991i	0.735308	+	0.424530i	0.820361	−	0.571846i	$-0.193773\pi$
$419$	15.0514	+	8.68991i	0.735308	+	0.424530i	−0.0850532	+	0.996376i	$0.527106\pi$
$420$		0			0
$421$	−21.2490	−	21.2490i	−1.03561	−	1.03561i	−0.999342	−	0.0362722i	$-0.988452\pi$
$421$	−21.2490	−	21.2490i	−1.03561	−	1.03561i	−0.0362722	−	0.999342i	$-0.511548\pi$
$422$	0.0913368	−	0.340874i	0.00444621	−	0.0165935i
$423$		0			0
$424$	1.40788	−	1.40788i	0.0683727	−	0.0683727i
$425$	−6.97619	+	4.02771i	−0.338395	+	0.195372i
$426$		0			0
$427$	−8.13097	−	0.635391i	−0.393485	−	0.0307487i
$428$			15.8733i			0.767265i
$429$		0			0
$430$			0.369487i			0.0178183i
$431$	−23.3087	+	6.24554i	−1.12274	+	0.300837i	−0.771991	−	0.635633i	$-0.780739\pi$
$431$	−23.3087	+	6.24554i	−1.12274	+	0.300837i	−0.350748	+	0.936470i	$0.614073\pi$
$432$		0			0
$433$	−2.27124	−	3.93391i	−0.109149	−	0.189051i	0.806277	−	0.591538i	$-0.201479\pi$
$433$	−2.27124	−	3.93391i	−0.109149	−	0.189051i	−0.915426	+	0.402487i	$0.868146\pi$
$434$	1.19293	−	0.569811i	0.0572626	−	0.0273518i
$435$		0			0
$436$	23.7601	+	6.36649i	1.13790	+	0.304900i
$437$	19.3029	+	19.3029i	0.923381	+	0.923381i
$438$		0			0
$439$	8.50036	−	14.7231i	0.405700	−	0.702693i	−0.588703	−	0.808350i	$-0.700361\pi$
$439$	8.50036	−	14.7231i	0.405700	−	0.702693i	0.994403	+	0.105657i	$0.0336944\pi$
$440$	−1.55388	+	0.416362i	−0.0740785	+	0.0198493i
$441$		0			0
$442$	−1.74750	+	0.435405i	−0.0831203	+	0.0207101i
$443$	36.6165			1.73970			0.869851	−	0.493315i	$-0.164215\pi$
$443$	36.6165			1.73970			0.869851	+	0.493315i	$0.164215\pi$
$444$		0			0
$445$	7.09408	−	12.2873i	0.336292	−	0.582474i
$446$	0.256823	+	0.444830i	0.0121609	+	0.0210633i
$447$		0			0
$448$	11.4918	−	16.7405i	0.542937	−	0.790916i
$449$	32.7480	+	8.77481i	1.54547	+	0.414109i	0.928030	−	0.372505i	$-0.121501\pi$
$449$	32.7480	+	8.77481i	1.54547	+	0.414109i	0.617445	+	0.786614i	$0.288168\pi$
$450$		0			0
$451$	−19.3181	+	11.1533i	−0.909654	+	0.525189i
$452$	14.6984	+	8.48610i	0.691353	+	0.399153i
$453$		0			0
$454$	0.478554			0.0224596
$455$	5.89199	−	15.7778i	0.276221	−	0.739674i
$456$		0			0
$457$	−2.18565	+	0.585644i	−0.102241	+	0.0273953i	−0.309577	−	0.950874i	$-0.600187\pi$
$457$	−2.18565	+	0.585644i	−0.102241	+	0.0273953i	0.207336	+	0.978270i	$0.433521\pi$
$458$	1.37279	+	0.792582i	0.0641463	+	0.0370349i
$459$		0			0
$460$	−15.8614	+	15.8614i	−0.739540	+	0.739540i
$461$	24.5455	+	6.57694i	1.14320	+	0.306319i	0.780235	−	0.625486i	$-0.215099\pi$
$461$	24.5455	+	6.57694i	1.14320	+	0.306319i	0.362961	+	0.931804i	$0.381766\pi$
$462$		0			0
$463$	−22.6265	+	22.6265i	−1.05154	+	1.05154i	−0.0529442	+	0.998597i	$0.516861\pi$
$463$	−22.6265	+	22.6265i	−1.05154	+	1.05154i	−0.998597	+	0.0529442i	$0.983139\pi$
$464$	−14.0261	−	24.2939i	−0.651144	−	1.12781i
$465$		0			0
$466$	0.494066	+	1.84388i	0.0228871	+	0.0854160i
$467$	11.2941			0.522627			0.261314	−	0.965254i	$-0.415844\pi$
$467$	11.2941			0.522627			0.261314	+	0.965254i	$0.415844\pi$
$468$		0			0
$469$	0.0491652	+	0.0173797i	0.00227024	+	0.000802520i
$470$	1.31967	−	0.353604i	0.0608718	−	0.0163105i
$471$		0			0
$472$	0.392653	+	0.680095i	0.0180733	+	0.0313039i
$473$	−2.48139	−	2.48139i	−0.114094	−	0.114094i
$474$		0			0
$475$	−2.07991	+	7.76231i	−0.0954326	+	0.356159i
$476$	9.69063	+	20.2879i	0.444169	+	0.929895i
$477$		0			0
$478$	−0.874396	−	0.504833i	−0.0399939	−	0.0230905i
$479$	−19.3716	+	5.19059i	−0.885109	+	0.237164i	−0.672610	−	0.739997i	$-0.734827\pi$
$479$	−19.3716	+	5.19059i	−0.885109	+	0.237164i	−0.212499	+	0.977161i	$0.568160\pi$
$480$		0			0
$481$	9.80456	+	2.81311i	0.447049	+	0.128267i
$482$		−	1.56814i		−	0.0714269i
$483$		0			0
$484$	−7.11843	+	12.3295i	−0.323565	+	0.560431i
$485$	22.5846	−	13.0392i	1.02551	−	0.592081i
$486$		0			0
$487$	−8.13109	+	30.3456i	−0.368455	+	1.37509i	0.494221	+	0.869336i	$0.335453\pi$
$487$	−8.13109	+	30.3456i	−0.368455	+	1.37509i	−0.862676	+	0.505756i	$0.831213\pi$
$488$	−0.371329	+	1.38582i	−0.0168093	+	0.0627331i
$489$		0			0
$490$	1.42540	+	0.224144i	0.0643931	+	0.0101258i
$491$	16.8341	+	9.71919i	0.759714	+	0.438621i	0.829193	−	0.558962i	$-0.188800\pi$
$491$	16.8341	+	9.71919i	0.759714	+	0.438621i	−0.0694792	+	0.997583i	$0.522134\pi$
$492$		0			0
$493$	30.6276			1.37940
$494$	−0.925574	+	1.53986i	−0.0416436	+	0.0692814i
$495$		0			0
$496$	4.34038	+	16.1985i	0.194889	+	0.727336i
$497$	9.56495	−	8.17841i	0.429047	−	0.366852i
$498$		0			0
$499$	11.8051	+	11.8051i	0.528471	+	0.528471i	0.920116	−	0.391645i	$-0.128094\pi$
$499$	11.8051	+	11.8051i	0.528471	+	0.528471i	−0.391645	+	0.920116i	$0.628094\pi$
$500$	−23.3158	−	6.24745i	−1.04271	−	0.279394i
$501$		0			0
$502$	0.287797	+	0.287797i	0.0128450	+	0.0128450i
$503$	−25.9585	+	14.9871i	−1.15743	+	0.668243i	−0.950687	−	0.310153i	$-0.899620\pi$
$503$	−25.9585	+	14.9871i	−1.15743	+	0.668243i	−0.206743	+	0.978395i	$0.566287\pi$
$504$		0			0
$505$	−7.31560	−	27.3022i	−0.325540	−	1.21493i
$506$			1.46199i			0.0649935i
$507$		0			0
$508$	12.1445			0.538827
$509$	3.62928	+	13.5446i	0.160865	+	0.600356i	0.998532	+	0.0541739i	$0.0172525\pi$
$509$	3.62928	+	13.5446i	0.160865	+	0.600356i	−0.837667	+	0.546182i	$0.816081\pi$
$510$		0			0
$511$	−0.477699	−	2.56949i	−0.0211322	−	0.113668i
$512$	−6.42580	−	6.42580i	−0.283983	−	0.283983i
$513$		0			0
$514$	−0.406370	+	1.51659i	−0.0179242	+	0.0668940i
$515$	−14.7501	+	14.7501i	−0.649969	+	0.649969i
$516$		0			0
$517$	−6.48785	+	11.2373i	−0.285335	+	0.494215i
$518$	−0.0680817	+	0.871228i	−0.00299134	+	0.0382795i
$519$		0			0
$520$	−2.53932	−	1.52633i	−0.111356	−	0.0669339i
$521$		−	0.875247i		−	0.0383452i	−0.999816	−	0.0191726i	$-0.993897\pi$
$521$		−	0.875247i		−	0.0383452i	0.999816	−	0.0191726i	$-0.00610321\pi$
$522$		0			0
$523$	−11.7198	−	6.76640i	−0.512469	−	0.295874i	0.221379	−	0.975188i	$-0.428944\pi$
$523$	−11.7198	−	6.76640i	−0.512469	−	0.295874i	−0.733848	+	0.679314i	$0.762278\pi$
$524$	5.72506	+	9.91610i	0.250100	+	0.433187i
$525$		0			0
$526$	0.620553	−	2.31593i	0.0270574	−	0.100980i
$527$	−17.6857	−	4.73887i	−0.770401	−	0.206428i
$528$		0			0
$529$	8.95568	+	15.5117i	0.389377	+	0.674421i
$530$	−0.440907	+	0.763674i	−0.0191518	+	0.0331719i
$531$		0			0
$532$	21.1473	+	7.47548i	0.916853	+	0.324103i
$533$	−39.4888	−	11.3301i	−1.71045	−	0.490759i
$534$		0			0
$535$	−3.65155	−	13.6278i	−0.157870	−	0.589180i
$536$	0.00458664	−	0.00794430i	0.000198113	−	0.000343141i
$537$		0			0
$538$	0.886440	−	0.886440i	0.0382171	−	0.0382171i
$539$	−11.0779	+	8.06736i	−0.477161	+	0.347486i
$540$		0			0
$541$	8.68791	−	8.68791i	0.373522	−	0.373522i	−0.495236	−	0.868758i	$-0.664918\pi$
$541$	8.68791	−	8.68791i	0.373522	−	0.373522i	0.868758	+	0.495236i	$0.164918\pi$
$542$	−0.151539	+	0.0874914i	−0.00650918	+	0.00375808i
$543$		0			0
$544$	5.73710	−	1.53725i	0.245976	−	0.0659091i
$545$	−21.8634			−0.936526
$546$		0			0
$547$	16.2786			0.696022			0.348011	−	0.937490i	$-0.386857\pi$
$547$	16.2786			0.696022			0.348011	+	0.937490i	$0.386857\pi$
$548$	−12.0411	+	3.22641i	−0.514371	+	0.137825i
$549$		0			0
$550$	−0.372723	+	0.215192i	−0.0158930	+	0.00917582i
$551$	21.6051	−	21.6051i	0.920410	−	0.920410i
$552$		0			0
$553$	12.9506	+	8.89013i	0.550715	+	0.378047i
$554$	0.388865	−	0.388865i	0.0165213	−	0.0165213i
$555$		0			0
$556$	20.7937	−	36.0157i	0.881849	−	1.52741i
$557$	−2.13873	−	7.98185i	−0.0906210	−	0.338202i	0.905698	−	0.423923i	$-0.139347\pi$
$557$	−2.13873	−	7.98185i	−0.0906210	−	0.338202i	−0.996319	+	0.0857210i	$0.972681\pi$
$558$		0			0
$559$	0.113826	−	6.46190i	0.00481433	−	0.273309i
$560$	−6.10024	+	17.2569i	−0.257782	+	0.729237i
$561$		0			0
$562$	−0.661470	+	1.14570i	−0.0279024	+	0.0483285i
$563$	−14.0767	−	24.3815i	−0.593261	−	1.02756i	−0.993790	−	0.111274i	$-0.964507\pi$
$563$	−14.0767	−	24.3815i	−0.593261	−	1.02756i	0.400528	−	0.916284i	$-0.368827\pi$
$564$		0			0
$565$	−14.5712	−	3.90435i	−0.613016	−	0.164257i
$566$	−0.238078	+	0.888519i	−0.0100072	+	0.0373472i
$567$		0			0
$568$	−1.10691	−	1.91722i	−0.0464448	−	0.0804447i
$569$	8.62645	+	4.98048i	0.361640	+	0.208793i	0.669800	−	0.742542i	$-0.266380\pi$
$569$	8.62645	+	4.98048i	0.361640	+	0.208793i	−0.308160	+	0.951335i	$0.599713\pi$
$570$		0			0
$571$		−	5.15214i		−	0.215610i	−0.994172	−	0.107805i	$-0.965618\pi$
$571$		−	5.15214i		−	0.215610i	0.994172	−	0.107805i	$-0.0343823\pi$
$572$	13.6052	−	3.38986i	0.568864	−	0.141737i
$573$		0			0
$574$	0.274205	−	3.50895i	0.0114451	−	0.146461i
$575$	−6.02177	+	10.4300i	−0.251125	+	0.434962i
$576$		0			0
$577$	−9.50342	+	9.50342i	−0.395633	+	0.395633i	−0.876689	−	0.481057i	$-0.840253\pi$
$577$	−9.50342	+	9.50342i	−0.395633	+	0.395633i	0.481057	+	0.876689i	$0.340253\pi$
$578$	−0.0393588	+	0.146889i	−0.00163711	+	0.00610978i
$579$		0			0
$580$	17.7532	+	17.7532i	0.737161	+	0.737161i
$581$	36.3332	−	6.75477i	1.50735	−	0.280235i
$582$		0			0
$583$	−2.16762	−	8.08967i	−0.0897737	−	0.335040i
$584$	−0.459752			−0.0190247
$585$		0			0
$586$			1.42645i			0.0589263i
$587$	−9.73498	−	36.3314i	−0.401806	−	1.49956i	−0.809872	−	0.586607i	$-0.800463\pi$
$587$	−9.73498	−	36.3314i	−0.401806	−	1.49956i	0.408066	−	0.912952i	$-0.366203\pi$
$588$		0			0
$589$	−15.8186	+	9.13289i	−0.651795	+	0.376314i
$590$	−0.245935	−	0.245935i	−0.0101250	−	0.0101250i
$591$		0			0
$592$	−10.7075	−	2.86906i	−0.440074	−	0.117918i
$593$	−25.8396	−	25.8396i	−1.06110	−	1.06110i	−0.998007	−	0.0630974i	$-0.979902\pi$
$593$	−25.8396	−	25.8396i	−1.06110	−	1.06110i	−0.0630974	−	0.998007i	$-0.520098\pi$
$594$		0			0
$595$	−12.9868	−	15.1886i	−0.532409	−	0.622672i
$596$	−7.94687	−	29.6581i	−0.325517	−	1.21484i
$597$		0			0
$598$	−1.93716	+	1.87009i	−0.0792162	+	0.0764738i
$599$	−5.32027			−0.217381			−0.108690	−	0.994076i	$-0.534666\pi$
$599$	−5.32027			−0.217381			−0.108690	+	0.994076i	$0.534666\pi$
$600$		0			0
$601$	−21.4564	−	12.3879i	−0.875225	−	0.505312i	−0.00614424	−	0.999981i	$-0.501956\pi$
$601$	−21.4564	−	12.3879i	−0.875225	−	0.505312i	−0.869081	+	0.494669i	$0.835289\pi$
$602$	0.544373	−	0.101205i	0.0221870	−	0.00412482i
$603$		0			0
$604$	−2.27279	+	8.48216i	−0.0924785	+	0.345134i
$605$	3.27510	−	12.2228i	0.133152	−	0.496929i
$606$		0			0
$607$	19.5367	−	11.2795i	0.792971	−	0.457822i	−0.0480365	−	0.998846i	$-0.515296\pi$
$607$	19.5367	−	11.2795i	0.792971	−	0.457822i	0.841007	+	0.541024i	$0.181963\pi$
$608$	2.96263	−	5.13143i	0.120151	−	0.208107i
$609$		0			0
$610$		−	0.635418i		−	0.0257273i
$611$	−23.1884	+	5.77758i	−0.938102	+	0.233736i
$612$		0			0
$613$	−22.2201	+	5.95385i	−0.897459	+	0.240474i	−0.677925	−	0.735131i	$-0.737121\pi$
$613$	−22.2201	+	5.95385i	−0.897459	+	0.240474i	−0.219535	+	0.975605i	$0.570454\pi$
$614$	−1.13995	−	0.658151i	−0.0460047	−	0.0265608i
$615$		0			0
$616$	1.03905	+	2.17532i	0.0418647	+	0.0876462i
$617$	−7.79350	+	29.0858i	−0.313755	+	1.17095i	0.611389	+	0.791330i	$0.290611\pi$
$617$	−7.79350	+	29.0858i	−0.313755	+	1.17095i	−0.925143	+	0.379618i	$0.876055\pi$
$618$		0			0
$619$	7.55579	+	7.55579i	0.303693	+	0.303693i	0.842457	−	0.538764i	$-0.181109\pi$
$619$	7.55579	+	7.55579i	0.303693	+	0.303693i	−0.538764	+	0.842457i	$0.681109\pi$
$620$	−7.50459	−	12.9983i	−0.301392	−	0.522026i
$621$		0			0
$622$	1.47090	−	0.394127i	0.0589778	−	0.0158031i
$623$	−20.0462	−	7.08625i	−0.803135	−	0.283905i
$624$		0			0
$625$	12.0400			0.481599
$626$	−0.107997	−	0.403049i	−0.00431641	−	0.0161091i
$627$		0			0
$628$	−6.88340	−	11.9224i	−0.274678	−	0.475755i
$629$	8.55805	−	8.55805i	0.341232	−	0.341232i
$630$		0			0
$631$	13.6759	+	3.66444i	0.544428	+	0.145879i	0.520543	−	0.853836i	$-0.325730\pi$
$631$	13.6759	+	3.66444i	0.544428	+	0.145879i	0.0238855	+	0.999715i	$0.492396\pi$
$632$	1.95395	−	1.95395i	0.0777240	−	0.0777240i
$633$		0			0
$634$	−3.35413	−	1.93651i	−0.133209	−	0.0769085i
$635$	−10.4265	+	2.79377i	−0.413763	+	0.110867i
$636$		0			0
$637$	−24.8596	−	4.35912i	−0.984972	−	0.172715i
$638$	1.63637			0.0647844
$639$		0			0
$640$	5.61554	+	3.24213i	0.221974	+	0.128157i
$641$	32.0667	−	18.5137i	1.26656	−	0.731248i	0.292224	−	0.956350i	$-0.405605\pi$
$641$	32.0667	−	18.5137i	1.26656	−	0.731248i	0.974335	+	0.225102i	$0.0722714\pi$
$642$		0			0
$643$	−33.2886	−	8.91965i	−1.31277	−	0.351757i	−0.466507	−	0.884517i	$-0.654488\pi$
$643$	−33.2886	−	8.91965i	−1.31277	−	0.351757i	−0.846266	+	0.532761i	$0.821155\pi$
$644$	27.7134	+	19.0243i	1.09206	+	0.749662i
$645$		0			0
$646$	1.06588	+	1.84617i	0.0419366	+	0.0726364i
$647$	−3.03363	+	5.25440i	−0.119264	+	0.206572i	−0.919476	−	0.393145i	$-0.871387\pi$
$647$	−3.03363	+	5.25440i	−0.119264	+	0.206572i	0.800212	+	0.599717i	$0.204720\pi$
$648$		0			0
$649$	3.30328			0.129665
$650$	−0.761896	−	0.218602i	−0.0298840	−	0.00857428i
$651$		0			0
$652$	24.8184	−	6.65007i	0.971964	−	0.260437i
$653$	15.1009	−	26.1555i	0.590943	−	1.02354i	−0.403162	−	0.915129i	$-0.632089\pi$
$653$	15.1009	−	26.1555i	0.590943	−	1.02354i	0.994106	−	0.108416i	$-0.0345777\pi$
$654$		0			0
$655$	−7.19630	−	7.19630i	−0.281183	−	0.281183i
$656$	43.1253	+	11.5554i	1.68376	+	0.451162i
$657$		0			0
$658$	−0.882439	−	1.84744i	−0.0344010	−	0.0720206i
$659$	−4.37179	−	7.57216i	−0.170301	−	0.294969i	0.768224	−	0.640181i	$-0.221141\pi$
$659$	−4.37179	−	7.57216i	−0.170301	−	0.294969i	−0.938525	+	0.345211i	$0.887807\pi$
$660$		0			0
$661$	17.3494	−	4.64874i	0.674812	−	0.180815i	0.0948903	−	0.995488i	$-0.469750\pi$
$661$	17.3494	−	4.64874i	0.674812	−	0.180815i	0.579921	+	0.814673i	$0.303083\pi$
$662$			0.110698i			0.00430239i
$663$		0			0
$664$		−	6.50100i		−	0.252288i
$665$	−19.8754	−	1.55315i	−0.770734	−	0.0602287i
$666$		0			0
$667$	39.6561	−	22.8955i	1.53549	−	0.886516i
$668$	−1.30942	+	1.30942i	−0.0506631	+	0.0506631i
$669$		0			0
$670$	−0.00105152	+	0.00392433i	−4.06238e−5	+	0.000151610i
$671$	4.26731	+	4.26731i	0.164738	+	0.164738i
$672$		0			0
$673$	22.0524	+	12.7319i	0.850057	+	0.490780i	0.860670	−	0.509163i	$-0.170045\pi$
$673$	22.0524	+	12.7319i	0.850057	+	0.490780i	−0.0106133	+	0.999944i	$0.503378\pi$
$674$	−0.428796	−	1.60029i	−0.0165166	−	0.0616408i
$675$		0			0
$676$	21.8946	+	13.6910i	0.842100	+	0.526577i
$677$		−	21.8547i		−	0.839946i	−0.907537	−	0.419973i	$-0.862039\pi$
$677$		−	21.8547i		−	0.839946i	0.907537	−	0.419973i	$-0.137961\pi$
$678$		0			0
$679$	−25.3970	−	29.7028i	−0.974649	−	1.13989i
$680$	−3.04444	+	1.75771i	−0.116749	+	0.0674050i
$681$		0			0
$682$	−0.944911	−	0.253188i	−0.0361825	−	0.00969507i
$683$	−30.9579	−	8.29515i	−1.18457	−	0.317405i	−0.387833	−	0.921729i	$-0.626776\pi$
$683$	−30.9579	−	8.29515i	−1.18457	−	0.317405i	−0.796738	+	0.604324i	$0.793443\pi$
$684$		0			0
$685$	9.59550	−	5.53997i	0.366625	−	0.211671i
$686$	−0.0601935	−	2.16147i	−0.00229820	−	0.0825252i
$687$		0			0
$688$			7.02368i			0.267775i
$689$	7.94621	−	13.2199i	0.302726	−	0.503639i
$690$		0			0
$691$	−7.27863	−	27.1642i	−0.276892	−	1.03337i	−0.954563	−	0.298010i	$-0.903677\pi$
$691$	−7.27863	−	27.1642i	−0.276892	−	1.03337i	0.677671	−	0.735365i	$-0.262989\pi$
$692$	−0.907533	−	0.523964i	−0.0344992	−	0.0199181i
$693$		0			0
$694$	1.14276	+	1.14276i	0.0433786	+	0.0433786i
$695$	−9.56691	+	35.7042i	−0.362894	+	1.35434i
$696$		0			0
$697$	−34.4683	+	34.4683i	−1.30558	+	1.30558i
$698$	1.54794	−	0.893701i	0.0585902	−	0.0338271i
$699$		0			0
$700$	−0.770936	+	9.86551i	−0.0291386	+	0.372881i
$701$		−	41.8411i		−	1.58032i	−0.612904	−	0.790158i	$-0.709999\pi$
$701$		−	41.8411i		−	1.58032i	0.612904	−	0.790158i	$-0.290001\pi$
$702$		0			0
$703$		−	12.0740i		−	0.455378i
$704$	−14.5131	+	3.88876i	−0.546981	+	0.146563i
$705$		0			0
$706$	0.919455	+	1.59254i	0.0346041	+	0.0599361i
$707$	−38.2210	+	18.2565i	−1.43745	+	0.686606i
$708$		0			0
$709$	−36.1012	−	9.67328i	−1.35581	−	0.363288i	−0.493532	−	0.869727i	$-0.664295\pi$
$709$	−36.1012	−	9.67328i	−1.35581	−	0.363288i	−0.862275	+	0.506440i	$0.830961\pi$
$710$	0.693302	+	0.693302i	0.0260192	+	0.0260192i
$711$		0			0
$712$	−1.87012	+	3.23914i	−0.0700857	+	0.121392i
$713$	−26.4417	+	7.08503i	−0.990249	+	0.265336i
$714$		0			0
$715$	−10.9008	+	6.04011i	−0.407665	+	0.225887i
$716$	16.4273			0.613918
$717$		0			0
$718$	0.387018	−	0.670334i	0.0144434	−	0.0250166i
$719$	−14.7469	−	25.5425i	−0.549968	−	0.952573i	−0.998276	−	0.0586936i	$-0.981307\pi$
$719$	−14.7469	−	25.5425i	−0.549968	−	0.952573i	0.448308	−	0.893879i	$-0.352027\pi$
$720$		0			0
$721$	25.7718	+	17.6915i	0.959794	+	0.658866i
$722$	−0.0885265	−	0.0237206i	−0.00329461	−	0.000882789i
$723$		0			0
$724$	−25.7667	+	14.8764i	−0.957612	+	0.552878i
$725$	11.6740	+	6.74000i	0.433562	+	0.250317i
$726$		0			0
$727$	−3.04387			−0.112891			−0.0564455	−	0.998406i	$-0.517977\pi$
$727$	−3.04387			−0.112891			−0.0564455	+	0.998406i	$0.517977\pi$
$728$	−1.55323	+	4.15929i	−0.0575665	+	0.154154i
$729$		0			0
$730$	0.196682	−	0.0527007i	0.00727952	−	0.00195054i
$731$	−6.64113	−	3.83426i	−0.245631	−	0.141815i
$732$		0			0
$733$	0.928339	−	0.928339i	0.0342890	−	0.0342890i	−0.689754	−	0.724043i	$-0.742282\pi$
$733$	0.928339	−	0.928339i	0.0342890	−	0.0342890i	0.724043	+	0.689754i	$0.242282\pi$
$734$	3.70542	+	0.992865i	0.136770	+	0.0366473i
$735$		0			0
$736$	6.27914	−	6.27914i	0.231452	−	0.231452i
$737$	−0.0192931	−	0.0334166i	−0.000710669	−	0.00123091i
$738$		0			0
$739$	−7.76649	−	28.9849i	−0.285695	−	1.06623i	−0.948330	−	0.317285i	$-0.897229\pi$
$739$	−7.76649	−	28.9849i	−0.285695	−	1.06623i	0.662635	−	0.748942i	$-0.269438\pi$
$740$	9.92129			0.364714
$741$		0			0
$742$	1.24590	+	0.440421i	0.0457385	+	0.0161684i
$743$	39.4397	−	10.5678i	1.44690	−	0.387697i	0.551958	−	0.833872i	$-0.313881\pi$
$743$	39.4397	−	10.5678i	1.44690	−	0.387697i	0.894946	+	0.446175i	$0.147214\pi$
$744$		0			0
$745$	13.6453	+	23.6344i	0.499926	+	0.865897i
$746$	−0.650528	−	0.650528i	−0.0238175	−	0.0238175i
$747$		0			0
$748$	4.30591	−	16.0699i	0.157440	−	0.587573i
$749$	−19.0779	+	9.11265i	−0.697090	+	0.332969i
$750$		0			0
$751$	−31.0690	−	17.9377i	−1.13372	−	0.654556i	−0.188856	−	0.982005i	$-0.560478\pi$
$751$	−31.0690	−	17.9377i	−1.13372	−	0.654556i	−0.944869	+	0.327448i	$0.893811\pi$
$752$	25.0859	−	6.72175i	0.914789	−	0.245117i
$753$		0			0
$754$	2.09314	+	2.16820i	0.0762277	+	0.0789614i
$755$		−	7.80507i		−	0.284056i
$756$		0			0
$757$	−0.439138	+	0.760610i	−0.0159607	+	0.0276448i	−0.873895	−	0.486114i	$-0.838414\pi$
$757$	−0.439138	+	0.760610i	−0.0159607	+	0.0276448i	0.857935	+	0.513759i	$0.171747\pi$
$758$	1.13152	−	0.653282i	0.0410986	−	0.0237283i
$759$		0			0
$760$	−0.907679	+	3.38750i	−0.0329250	+	0.122878i
$761$	9.46773	−	35.3341i	0.343205	−	1.28086i	−0.551490	−	0.834181i	$-0.685941\pi$
$761$	9.46773	−	35.3341i	0.343205	−	1.28086i	0.894695	−	0.446677i	$-0.147393\pi$
$762$		0			0
$763$	5.98855	+	32.2118i	0.216800	+	1.16614i
$764$	24.9938	+	14.4302i	0.904245	+	0.522066i
$765$		0			0
$766$	−0.281440			−0.0101689
$767$	4.22535	+	4.37687i	0.152568	+	0.158040i
$768$		0			0
$769$	7.85943	+	29.3318i	0.283418	+	1.05773i	0.949987	+	0.312288i	$0.101096\pi$
$769$	7.85943	+	29.3318i	0.283418	+	1.05773i	−0.666569	+	0.745443i	$0.732238\pi$
$770$	−0.693860	−	0.811496i	−0.0250050	−	0.0292443i
$771$		0			0
$772$	−27.4985	−	27.4985i	−0.989692	−	0.989692i
$773$	19.1599	+	5.13389i	0.689134	+	0.184653i	0.586359	−	0.810052i	$-0.300561\pi$
$773$	19.1599	+	5.13389i	0.689134	+	0.184653i	0.102776	+	0.994705i	$0.467228\pi$
$774$		0			0
$775$	−5.69824	−	5.69824i	−0.204687	−	0.204687i
$776$	−5.95369	+	3.43737i	−0.213725	+	0.123394i
$777$		0			0
$778$	0.508297	+	1.89699i	0.0182233	+	0.0680104i
$779$			48.6290i			1.74231i
$780$		0			0
$781$	−9.31209			−0.333213
$782$	0.826882	+	3.08596i	0.0295692	+	0.110354i
$783$		0			0
$784$	27.0958	+	4.26080i	0.967708	+	0.152171i
$785$	8.65231	+	8.65231i	0.308814	+	0.308814i
$786$		0			0
$787$	2.27486	−	8.48989i	0.0810900	−	0.302632i	−0.913455	−	0.406940i	$-0.866596\pi$
$787$	2.27486	−	8.48989i	0.0810900	−	0.302632i	0.994545	+	0.104308i	$0.0332626\pi$
$788$	−30.5620	+	30.5620i	−1.08873	+	1.08873i
$789$		0			0
$790$	−0.611921	+	1.05988i	−0.0217712	+	0.0377087i
$791$	−1.76118	+	22.5375i	−0.0626204	+	0.801340i
$792$		0			0
$793$	−0.195750	+	11.1127i	−0.00695128	+	0.394624i
$794$			2.74663i			0.0974743i
$795$		0			0
$796$	33.1686	+	19.1499i	1.17563	+	0.678750i
$797$	−12.3887	−	21.4579i	−0.438832	−	0.760079i	0.558768	−	0.829324i	$-0.311274\pi$
$797$	−12.3887	−	21.4579i	−0.438832	−	0.760079i	−0.997600	+	0.0692450i	$0.977941\pi$
$798$		0			0
$799$	−7.33886	+	27.3890i	−0.259630	+	0.968953i
$800$	2.52505	+	0.676585i	0.0892739	+	0.0239209i
$801$		0			0
$802$	−0.503695	−	0.872425i	−0.0177861	−	0.0308064i
$803$	−0.966941	+	1.67479i	−0.0341226	+	0.0591021i
$804$		0			0
$805$	−28.1693	−	9.95773i	−0.992838	−	0.350964i
$806$	−0.873195	−	1.57588i	−0.0307570	−	0.0555080i
$807$		0			0
$808$	1.92852	+	7.19733i	0.0678450	+	0.253201i
$809$	3.75373	−	6.50166i	0.131974	−	0.228586i	−0.792463	−	0.609920i	$-0.791202\pi$
$809$	3.75373	−	6.50166i	0.131974	−	0.228586i	0.924438	+	0.381334i	$0.124535\pi$
$810$		0			0
$811$	32.4572	−	32.4572i	1.13973	−	1.13973i	0.151229	−	0.988499i	$-0.451677\pi$
$811$	32.4572	−	32.4572i	1.13973	−	1.13973i	0.988499	−	0.151229i	$-0.0483229\pi$
$812$	21.2934	−	31.0188i	0.747250	−	1.08855i
$813$		0			0
$814$	0.457239	−	0.457239i	0.0160262	−	0.0160262i
$815$	−19.7777	+	11.4186i	−0.692781	+	0.399977i
$816$		0			0
$817$	−7.38949	+	1.98001i	−0.258526	+	0.0692717i
$818$	−1.56868			−0.0548475
$819$		0			0
$820$	−39.9589			−1.39543
$821$	−30.4367	+	8.15549i	−1.06225	+	0.284629i	−0.747305	−	0.664482i	$-0.768652\pi$
$821$	−30.4367	+	8.15549i	−1.06225	+	0.284629i	−0.314944	+	0.949110i	$0.601986\pi$
$822$		0			0
$823$	27.4139	−	15.8274i	0.955590	−	0.551710i	0.0607767	−	0.998151i	$-0.480642\pi$
$823$	27.4139	−	15.8274i	0.955590	−	0.551710i	0.894813	+	0.446442i	$0.147309\pi$
$824$	3.88839	−	3.88839i	0.135459	−	0.135459i
$825$		0			0
$826$	−0.294977	+	0.429704i	−0.0102636	+	0.0149513i
$827$	−25.1824	+	25.1824i	−0.875678	+	0.875678i	−0.993084	−	0.117406i	$-0.962542\pi$
$827$	−25.1824	+	25.1824i	−0.875678	+	0.875678i	0.117406	+	0.993084i	$0.462542\pi$
$828$		0			0
$829$	1.05432	−	1.82614i	0.0366182	−	0.0634246i	−0.847135	−	0.531377i	$-0.821675\pi$
$829$	1.05432	−	1.82614i	0.0366182	−	0.0634246i	0.883754	+	0.467952i	$0.155008\pi$
$830$	0.745200	+	2.78112i	0.0258663	+	0.0965342i
$831$		0			0
$832$	−23.7169	−	14.2557i	−0.822234	−	0.494227i
$833$	−18.8205	+	23.2940i	−0.652090	+	0.807091i
$834$		0			0
$835$	0.822960	−	1.42541i	0.0284797	−	0.0493283i
$836$	−8.29847	−	14.3734i	−0.287009	−	0.497114i
$837$		0			0
$838$	1.96001	+	0.525184i	0.0677076	+	0.0181422i
$839$	6.14897	−	22.9483i	0.212286	−	0.792262i	−0.774818	−	0.632184i	$-0.782159\pi$
$839$	6.14897	−	22.9483i	0.212286	−	0.792262i	0.987104	−	0.160078i	$-0.0511746\pi$
$840$		0			0
$841$	−11.1262	−	19.2712i	−0.383663	−	0.664525i
$842$	−3.03847	−	1.75426i	−0.104713	−	0.0604558i
$843$		0			0
$844$			6.00398i			0.206666i
$845$	−21.9468	−	6.71748i	−0.754992	−	0.231088i
$846$		0			0
$847$	−18.9052	−	1.47734i	−0.649591	−	0.0507620i
$848$	−8.38131	+	14.5169i	−0.287815	+	0.498511i
$849$		0			0
$850$	−0.665032	+	0.665032i	−0.0228104	+	0.0228104i
$851$	4.68331	−	17.4783i	0.160542	−	0.599150i
$852$		0			0
$853$	−4.73993	−	4.73993i	−0.162292	−	0.162292i	0.621289	−	0.783581i	$-0.286609\pi$
$853$	−4.73993	−	4.73993i	−0.162292	−	0.162292i	−0.783581	+	0.621289i	$0.786609\pi$
$854$	−0.936173	+	0.174046i	−0.0320352	+	0.00595572i
$855$		0			0
$856$	0.962612	+	3.59252i	0.0329014	+	0.122790i
$857$	11.3220			0.386751			0.193376	−	0.981125i	$-0.438056\pi$
$857$	11.3220			0.386751			0.193376	+	0.981125i	$0.438056\pi$
$858$		0			0
$859$		−	48.4452i		−	1.65293i	−0.562988	−	0.826465i	$-0.690348\pi$
$859$		−	48.4452i		−	1.65293i	0.562988	−	0.826465i	$-0.309652\pi$
$860$	−1.62699	−	6.07202i	−0.0554800	−	0.207054i
$861$		0			0
$862$	−2.43991	+	1.40868i	−0.0831038	+	0.0479800i
$863$	13.2582	+	13.2582i	0.451313	+	0.451313i	0.895790	−	0.444477i	$-0.146610\pi$
$863$	13.2582	+	13.2582i	0.451313	+	0.451313i	−0.444477	+	0.895790i	$0.646610\pi$
$864$		0			0
$865$	0.899682	+	0.241069i	0.0305901	+	0.00819660i
$866$	−0.375015	−	0.375015i	−0.0127435	−	0.0127435i
$867$		0			0
$868$	−17.0951	+	14.6170i	−0.580246	+	0.496133i
$869$	−3.00837	−	11.2274i	−0.102052	−	0.380863i
$870$		0			0
$871$	0.0195988	−	0.0683079i	0.000664080	−	0.00231452i
$872$	5.76357			0.195179
$873$		0			0
$874$	2.76018	+	1.59359i	0.0933645	+	0.0539040i
$875$	−5.87658	−	31.6095i	−0.198665	−	1.06860i
$876$		0			0
$877$	1.83431	−	6.84575i	0.0619403	−	0.231164i	−0.928015	−	0.372542i	$-0.878486\pi$
$877$	1.83431	−	6.84575i	0.0619403	−	0.231164i	0.989956	+	0.141377i	$0.0451530\pi$
$878$	0.513728	−	1.91726i	0.0173375	−	0.0647044i
$879$		0			0
$880$	11.7291	−	6.77183i	0.395389	−	0.228278i
$881$	12.1808	−	21.0977i	0.410380	−	0.710800i	−0.584551	−	0.811357i	$-0.698729\pi$
$881$	12.1808	−	21.0977i	0.410380	−	0.710800i	0.994931	+	0.100557i	$0.0320626\pi$
$882$		0			0
$883$			4.51673i			0.152000i	0.997108	+	0.0760000i	$0.0242149\pi$
$883$			4.51673i			0.152000i	−0.997108	+	0.0760000i	$0.975785\pi$
$884$	26.8006	−	14.8502i	0.901401	−	0.499467i
$885$		0			0
$886$	4.12943	−	1.10648i	0.138731	−	0.0371729i
$887$	−38.3035	−	22.1145i	−1.28611	−	0.742533i	−0.308148	−	0.951338i	$-0.599709\pi$
$887$	−38.3035	−	22.1145i	−1.28611	−	0.742533i	−0.977957	+	0.208805i	$0.933042\pi$
$888$		0			0
$889$	6.97202	+	14.5963i	0.233834	+	0.489545i
$890$	0.428738	−	1.60007i	0.0143713	−	0.0536346i
$891$		0			0
$892$	−6.17928	−	6.17928i	−0.206898	−	0.206898i
$893$	14.1437	+	24.4976i	0.473300	+	0.819780i
$894$		0			0
$895$	−14.1034	+	3.77900i	−0.471426	+	0.126318i
$896$	3.23856	−	9.16152i	0.108193	−	0.306065i
$897$		0			0
$898$	3.95832			0.132091
$899$	7.93007	+	29.5954i	0.264483	+	0.987063i
$900$		0			0
$901$	−9.15079	−	15.8496i	−0.304857	−	0.528028i
$902$	−1.84157	+	1.84157i	−0.0613176	+	0.0613176i
$903$		0			0
$904$	3.84122	+	1.02925i	0.127757	+	0.0342324i
$905$	18.6994	−	18.6994i	0.621589	−	0.621589i
$906$		0			0
$907$	29.3466	+	16.9433i	0.974439	+	0.562593i	0.900587	−	0.434676i	$-0.143137\pi$
$907$	29.3466	+	16.9433i	0.974439	+	0.562593i	0.0738526	+	0.997269i	$0.476471\pi$
$908$	−7.86438	+	2.10725i	−0.260989	+	0.0699317i
$909$		0			0
$910$	0.187697	−	1.95739i	0.00622209	−	0.0648868i
$911$	−4.66390			−0.154522			−0.0772610	−	0.997011i	$-0.524617\pi$
$911$	−4.66390			−0.154522			−0.0772610	+	0.997011i	$0.524617\pi$
$912$		0			0
$913$	−23.6819	−	13.6728i	−0.783757	−	0.452502i
$914$	−0.228791	+	0.132092i	−0.00756772	+	0.00436923i
$915$		0			0
$916$	−26.0500	−	6.98007i	−0.860716	−	0.230628i
$917$	−8.63132	+	12.5736i	−0.285031	+	0.415216i
$918$		0			0
$919$	−12.0900	−	20.9405i	−0.398812	−	0.690763i	0.594767	−	0.803898i	$-0.297244\pi$
$919$	−12.0900	−	20.9405i	−0.398812	−	0.690763i	−0.993580	+	0.113135i	$0.963911\pi$
$920$	−2.62793	+	4.55170i	−0.0866402	+	0.150065i
$921$		0			0
$922$	2.96686			0.0977084
$923$	−11.9115	−	12.3386i	−0.392070	−	0.406131i
$924$		0			0
$925$	5.14530	−	1.37868i	0.169177	−	0.0453307i
$926$	−1.86798	+	3.23543i	−0.0613856	+	0.106323i
$927$		0			0
$928$	−7.02806	−	7.02806i	−0.230708	−	0.230708i
$929$	15.0006	+	4.01941i	0.492155	+	0.131872i	0.496357	−	0.868119i	$-0.334671\pi$
$929$	15.0006	+	4.01941i	0.492155	+	0.131872i	−0.00420200	+	0.999991i	$0.501338\pi$
$930$		0			0
$931$	3.15573	+	29.7082i	0.103425	+	0.973647i
$932$	−16.2386	−	28.1261i	−0.531913	−	0.921300i
$933$		0			0
$934$	1.27369	−	0.341285i	0.0416765	−	0.0111672i
$935$			14.7871i			0.483589i
$936$		0			0
$937$		−	25.4720i		−	0.832134i	−0.909334	−	0.416067i	$-0.863408\pi$
$937$		−	25.4720i		−	0.832134i	0.909334	−	0.416067i	$-0.136592\pi$
$938$	0.00606980		0.000474322i	0.000198186		1.54872e-5i
$939$		0			0
$940$	−20.1299	+	11.6220i	−0.656565	+	0.379068i
$941$	12.6726	−	12.6726i	0.413116	−	0.413116i	−0.469706	−	0.882823i	$-0.655640\pi$
$941$	12.6726	−	12.6726i	0.413116	−	0.413116i	0.882823	+	0.469706i	$0.155640\pi$
$942$		0			0
$943$	−18.8625	+	70.3957i	−0.614246	+	2.29240i
$944$	−4.67503	−	4.67503i	−0.152159	−	0.152159i
$945$		0			0
$946$	−0.354822	−	0.204856i	−0.0115362	−	0.00666046i
$947$	−3.21690	−	12.0056i	−0.104535	−	0.390130i	0.893757	−	0.448552i	$-0.148060\pi$
$947$	−3.21690	−	12.0056i	−0.104535	−	0.390130i	−0.998292	+	0.0584214i	$0.981393\pi$
$948$		0			0
$949$	−3.45597	+	0.861083i	−0.112185	+	0.0279519i
$950$			0.938247i			0.0304408i
$951$		0			0
$952$	3.42356	+	4.00398i	0.110958	+	0.129770i
$953$	−25.0716	+	14.4751i	−0.812147	+	0.468893i	−0.847701	−	0.530474i	$-0.822014\pi$
$953$	−25.0716	+	14.4751i	−0.812147	+	0.468893i	0.0355538	+	0.999368i	$0.488680\pi$
$954$		0			0
$955$	−24.7776	−	6.63914i	−0.801785	−	0.214838i
$956$	16.5925	+	4.44594i	0.536639	+	0.143792i
$957$		0			0
$958$	−2.02778	+	1.17074i	−0.0655147	+	0.0378249i
$959$	−10.7904	−	12.6198i	−0.348441	−	0.407514i
$960$		0			0
$961$			12.6833i			0.409139i
$962$	1.19072	+	0.0209745i	0.0383903	+	0.000676243i
$963$		0			0
$964$	6.90512	+	25.7703i	0.222399	+	0.830004i
$965$	29.9342	+	17.2825i	0.963617	+	0.556344i
$966$		0			0
$967$	20.8937	+	20.8937i	0.671895	+	0.671895i	0.958153	−	0.286258i	$-0.0924113\pi$
$967$	20.8937	+	20.8937i	0.671895	+	0.671895i	−0.286258	+	0.958153i	$0.592411\pi$
$968$	−0.863372	+	3.22215i	−0.0277498	+	0.103564i
$969$		0			0
$970$	2.15297	−	2.15297i	0.0691276	−	0.0691276i
$971$	35.5507	−	20.5252i	1.14088	−	0.658685i	0.194229	−	0.980956i	$-0.437780\pi$
$971$	35.5507	−	20.5252i	1.14088	−	0.658685i	0.946647	+	0.322271i	$0.104446\pi$
$972$		0			0
$973$	55.2241	+	4.31546i	1.77040	+	0.138347i
$974$			3.66794i			0.117528i
$975$		0			0
$976$		−	12.0788i		−	0.386633i
$977$	22.0546	−	5.90951i	0.705589	−	0.189062i	0.111856	−	0.993724i	$-0.464320\pi$
$977$	22.0546	−	5.90951i	0.705589	−	0.189062i	0.593733	+	0.804662i	$0.297654\pi$
$978$		0			0
$979$	7.86639	+	13.6250i	0.251411	+	0.435457i
$980$	−24.4115	+	2.59309i	−0.779798	+	0.0828334i
$981$		0			0
$982$	2.19217	+	0.587390i	0.0699549	+	0.0187444i
$983$	21.0430	+	21.0430i	0.671167	+	0.671167i	0.957985	−	0.286818i	$-0.0925976\pi$
$983$	21.0430	+	21.0430i	0.671167	+	0.671167i	−0.286818	+	0.957985i	$0.592598\pi$
$984$		0			0
$985$	19.2080	−	33.2692i	0.612017	−	1.06004i
$986$	3.45403	−	0.925505i	0.109999	−	0.0294741i
$987$		0			0
$988$	8.42998	−	29.3811i	0.268193	−	0.934737i
$989$	−11.4651			−0.364569
$990$		0			0
$991$	1.24883	−	2.16303i	0.0396703	−	0.0687110i	−0.845509	−	0.533962i	$-0.820703\pi$
$991$	1.24883	−	2.16303i	0.0396703	−	0.0687110i	0.885179	+	0.465251i	$0.154036\pi$
$992$	2.97089	+	5.14574i	0.0943259	+	0.163377i
$993$		0			0
$994$	0.831554	−	1.21136i	0.0263753	−	0.0384219i
$995$	−32.8817	−	8.81062i	−1.04242	−	0.279315i
$996$		0			0
$997$	−5.16724	+	2.98331i	−0.163648	+	0.0944823i	−0.579587	−	0.814910i	$-0.696786\pi$
$997$	−5.16724	+	2.98331i	−0.163648	+	0.0944823i	0.415939	+	0.909392i	$0.363453\pi$
$998$	1.68806	+	0.974599i	0.0534345	+	0.0308504i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.g.748.4		32
3.2	odd	2		91.2.bc.a.20.5	✓	32
7.6	odd	2	inner	819.2.fm.g.748.3		32
13.2	odd	12	inner	819.2.fm.g.496.3		32
21.2	odd	6		637.2.bb.b.423.4		32
21.5	even	6		637.2.bb.b.423.3		32
21.11	odd	6		637.2.x.b.215.4		32
21.17	even	6		637.2.x.b.215.3		32
21.20	even	2		91.2.bc.a.20.6	yes	32
39.2	even	12		91.2.bc.a.41.6	yes	32
91.41	even	12	inner	819.2.fm.g.496.4		32
273.2	even	12		637.2.x.b.80.4		32
273.41	odd	12		91.2.bc.a.41.5	yes	32
273.80	odd	12		637.2.bb.b.509.4		32
273.158	even	12		637.2.bb.b.509.3		32
273.236	odd	12		637.2.x.b.80.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.20.5	✓	32	3.2	odd	2
91.2.bc.a.20.6	yes	32	21.20	even	2
91.2.bc.a.41.5	yes	32	273.41	odd	12
91.2.bc.a.41.6	yes	32	39.2	even	12
637.2.x.b.80.3		32	273.236	odd	12
637.2.x.b.80.4		32	273.2	even	12
637.2.x.b.215.3		32	21.17	even	6
637.2.x.b.215.4		32	21.11	odd	6
637.2.bb.b.423.3		32	21.5	even	6
637.2.bb.b.423.4		32	21.2	odd	6
637.2.bb.b.509.3		32	273.158	even	12
637.2.bb.b.509.4		32	273.80	odd	12
819.2.fm.g.496.3		32	13.2	odd	12	inner
819.2.fm.g.496.4		32	91.41	even	12	inner
819.2.fm.g.748.3		32	7.6	odd	2	inner
819.2.fm.g.748.4		32	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.112775 - 0.0302180i) q^{2} +(-1.72025 + 0.993184i) q^{4} +(1.24841 - 1.24841i) q^{5} +(-2.18126 - 1.49736i) q^{7} +(-0.329103 + 0.329103i) q^{8} +(0.103066 - 0.178515i) q^{10} +(0.506699 + 1.89103i) q^{11} +(-1.85749 + 3.09026i) q^{13} +(-0.291240 - 0.102952i) q^{14} +(1.95920 - 3.39343i) q^{16} +(2.13907 + 3.70498i) q^{17} +(4.12248 + 1.10462i) q^{19} +(-0.907674 + 3.38749i) q^{20} +(0.114286 + 0.197949i) q^{22} +(5.53927 + 3.19810i) q^{23} +1.88292i q^{25} +(-0.116097 + 0.404635i) q^{26} +(5.23946 + 0.409435i) q^{28} +(3.57954 - 6.19995i) q^{29} +(-3.02628 + 3.02628i) q^{31} +(0.359327 - 1.34103i) q^{32} +(0.353191 + 0.353191i) q^{34} +(-4.59245 + 0.853791i) q^{35} +(-0.732202 - 2.73261i) q^{37} +0.498293 q^{38} +0.821715i q^{40} +(2.94901 + 11.0059i) q^{41} +(-1.55234 + 0.896243i) q^{43} +(-2.74978 - 2.74978i) q^{44} +(0.721333 + 0.193281i) q^{46} +(4.68665 + 4.68665i) q^{47} +(2.51581 + 6.53228i) q^{49} +(0.0568982 + 0.212347i) q^{50} +(0.126138 - 7.16084i) q^{52} -4.27793 q^{53} +(2.99335 + 1.72821i) q^{55} +(1.21065 - 0.225074i) q^{56} +(0.216333 - 0.807367i) q^{58} +(0.436704 - 1.62980i) q^{59} +(2.66960 - 1.54129i) q^{61} +(-0.249841 + 0.432737i) q^{62} +7.67470i q^{64} +(1.53901 + 6.17685i) q^{65} +(-0.0190380 + 0.00510122i) q^{67} +(-7.35945 - 4.24898i) q^{68} +(-0.492115 + 0.235061i) q^{70} +(-1.23109 + 4.59449i) q^{71} +(0.698492 + 0.698492i) q^{73} +(-0.165148 - 0.286046i) q^{74} +(-8.18877 + 2.19417i) q^{76} +(1.72631 - 4.88353i) q^{77} -5.93719 q^{79} +(-1.79052 - 6.68230i) q^{80} +(0.665151 + 1.15208i) q^{82} +(-9.87683 + 9.87683i) q^{83} +(7.29580 + 1.95490i) q^{85} +(-0.147983 + 0.147983i) q^{86} +(-0.789099 - 0.455587i) q^{88} +(7.76240 - 2.07993i) q^{89} +(8.67892 - 3.95934i) q^{91} -12.7052 q^{92} +(0.670159 + 0.386917i) q^{94} +(6.52558 - 3.76755i) q^{95} +(14.2676 + 3.82300i) q^{97} +(0.481114 + 0.660657i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8} + 4 q^{11} + 32 q^{14} + 12 q^{16} + 4 q^{22} + 12 q^{23} + 24 q^{28} - 4 q^{29} - 4 q^{32} + 20 q^{35} + 4 q^{37} - 48 q^{43} - 24 q^{44} + 84 q^{46} + 24 q^{49} + 44 q^{50}+ \cdots + 32 q^{98}+O(q^{100}) \) 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

Introduction

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