LMFDB - Embedded newform 819.2.bm.f.550.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(478,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.478");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.bm (of order $6$, degree $2$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			550.5
Root			$-1.38488 + 0.286553i$ of defining polynomial
Character	$\chi$	$=$	819.550
Dual form			819.2.bm.f.478.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.37905i q^{2} +0.0982074 q^{4} +(0.697972 - 0.402974i) q^{5} +(0.0699870 + 2.64483i) q^{7} +2.89354i q^{8} +O(q^{10})$	\(q+1.37905i q^{2} +0.0982074 q^{4} +(0.697972 - 0.402974i) q^{5} +(0.0699870 + 2.64483i) q^{7} +2.89354i q^{8} +(0.555723 + 0.962541i) q^{10} +(-4.56532 + 2.63579i) q^{11} +(-2.36581 - 2.72084i) q^{13} +(-3.64736 + 0.0965159i) q^{14} -3.79394 q^{16} -0.560102 q^{17} +(5.06165 + 2.92234i) q^{19} +(0.0685460 - 0.0395750i) q^{20} +(-3.63490 - 6.29583i) q^{22} -1.60488 q^{23} +(-2.17522 + 3.76760i) q^{25} +(3.75219 - 3.26258i) q^{26} +(0.00687324 + 0.259741i) q^{28} +(1.14008 - 1.97467i) q^{29} +(3.01022 + 1.73795i) q^{31} +0.555034i q^{32} -0.772411i q^{34} +(1.11465 + 1.81781i) q^{35} +1.24196i q^{37} +(-4.03007 + 6.98029i) q^{38} +(1.16602 + 2.01961i) q^{40} +(-0.803413 - 0.463851i) q^{41} +(2.22356 + 3.85131i) q^{43} +(-0.448348 + 0.258854i) q^{44} -2.21321i q^{46} +(3.32915 - 1.92209i) q^{47} +(-6.99020 + 0.370207i) q^{49} +(-5.19572 - 2.99975i) q^{50} +(-0.232340 - 0.267207i) q^{52} +(2.72727 - 4.72377i) q^{53} +(-2.12431 + 3.67941i) q^{55} +(-7.65292 + 0.202510i) q^{56} +(2.72318 + 1.57223i) q^{58} +10.9940i q^{59} +(-3.65107 + 6.32385i) q^{61} +(-2.39673 + 4.15126i) q^{62} -8.35330 q^{64} +(-2.74769 - 0.945710i) q^{65} +(6.36144 - 3.67278i) q^{67} -0.0550061 q^{68} +(-2.50686 + 1.53716i) q^{70} +(8.06668 - 4.65730i) q^{71} +(4.33139 + 2.50073i) q^{73} -1.71273 q^{74} +(0.497091 + 0.286996i) q^{76} +(-7.29072 - 11.8900i) q^{77} +(-5.68437 - 9.84562i) q^{79} +(-2.64806 + 1.52886i) q^{80} +(0.639676 - 1.10795i) q^{82} -5.81962i q^{83} +(-0.390935 + 0.225707i) q^{85} +(-5.31117 + 3.06641i) q^{86} +(-7.62677 - 13.2100i) q^{88} -5.00946i q^{89} +(7.03057 - 6.44756i) q^{91} -0.157611 q^{92} +(2.65067 + 4.59109i) q^{94} +4.71051 q^{95} +(9.22171 - 5.32416i) q^{97} +(-0.510535 - 9.63988i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7}+O(q^{10}) $ 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7	$ 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7} + 12 q^{10} - 12 q^{11} - 2 q^{13} - 4 q^{14} + 16 q^{16} + 34 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 6 q^{23} - 5 q^{25} + 6 q^{26} - 9 q^{28} + q^{29} + 18 q^{31} + 6 q^{35} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 15 q^{47} - 3 q^{49} - 18 q^{50} - 7 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{56} - 24 q^{58} + 5 q^{61} - 41 q^{62} + 2 q^{64} - 21 q^{65} + 15 q^{67} - 22 q^{68} + 3 q^{70} - 30 q^{71} + 42 q^{73} - 66 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} + 63 q^{80} + 5 q^{82} - 21 q^{85} + 57 q^{86} - 14 q^{88} - 7 q^{91} + 66 q^{92} + q^{94} + 4 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7 + 12 * q^10 - 12 * q^11 - 2 * q^13 - 4 * q^14 + 16 * q^16 + 34 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 + 6 * q^23 - 5 * q^25 + 6 * q^26 - 9 * q^28 + q^29 + 18 * q^31 + 6 * q^35 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 15 * q^47 - 3 * q^49 - 18 * q^50 - 7 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^56 - 24 * q^58 + 5 * q^61 - 41 * q^62 + 2 * q^64 - 21 * q^65 + 15 * q^67 - 22 * q^68 + 3 * q^70 - 30 * q^71 + 42 * q^73 - 66 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 + 63 * q^80 + 5 * q^82 - 21 * q^85 + 57 * q^86 - 14 * q^88 - 7 * q^91 + 66 * q^92 + q^94 + 4 * q^95 - 3 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$			1.37905i			0.975139i	0.873084	+	0.487570i	$0.162116\pi$
$2$			1.37905i			0.975139i	−0.873084	+	0.487570i	$0.837884\pi$
$3$		0			0
$3$		0			0
$4$	0.0982074			0.0491037
$5$	0.697972	−	0.402974i	0.312142	−	0.180216i	−0.335742	−	0.941954i	$-0.608987\pi$
$5$	0.697972	−	0.402974i	0.312142	−	0.180216i	0.647885	+	0.761738i	$0.275654\pi$
$6$		0			0
$7$	0.0699870	+	2.64483i	0.0264526	+	0.999650i
$7$	0.0699870	+	2.64483i	0.0264526	+	0.999650i
$8$			2.89354i			1.02302i
$9$		0			0
$10$	0.555723	+	0.962541i	0.175735	+	0.304382i
$11$	−4.56532	+	2.63579i	−1.37650	+	0.794720i	−0.991736	−	0.128296i	$-0.959049\pi$
$11$	−4.56532	+	2.63579i	−1.37650	+	0.794720i	−0.384760	+	0.923017i	$0.625716\pi$
$12$		0			0
$13$	−2.36581	−	2.72084i	−0.656156	−	0.754625i
$13$	−2.36581	−	2.72084i	−0.656156	−	0.754625i
$14$	−3.64736	+	0.0965159i	−0.974798	+	0.0257950i
$15$		0			0
$16$	−3.79394			−0.948485
$17$	−0.560102			−0.135845			−0.0679223	−	0.997691i	$-0.521637\pi$
$17$	−0.560102			−0.135845			−0.0679223	+	0.997691i	$0.521637\pi$
$18$		0			0
$19$	5.06165	+	2.92234i	1.16122	+	0.670431i	0.951596	−	0.307351i	$-0.0994424\pi$
$19$	5.06165	+	2.92234i	1.16122	+	0.670431i	0.209625	+	0.977782i	$0.432776\pi$
$20$	0.0685460	−	0.0395750i	0.0153273	−	0.00884925i
$21$		0			0
$22$	−3.63490	−	6.29583i	−0.774963	−	1.34228i
$23$	−1.60488			−0.334640			−0.167320	−	0.985903i	$-0.553511\pi$
$23$	−1.60488			−0.334640			−0.167320	+	0.985903i	$0.553511\pi$
$24$		0			0
$25$	−2.17522	+	3.76760i	−0.435045	+	0.753520i
$26$	3.75219	−	3.26258i	0.735864	−	0.639844i
$27$		0			0
$28$	0.00687324	+	0.259741i	0.00129892	+	0.0490865i
$29$	1.14008	−	1.97467i	0.211707	−	0.366687i	−0.740542	−	0.672010i	$-0.765431\pi$
$29$	1.14008	−	1.97467i	0.211707	−	0.366687i	0.952249	+	0.305323i	$0.0987644\pi$
$30$		0			0
$31$	3.01022	+	1.73795i	0.540651	+	0.312145i	0.745343	−	0.666681i	$-0.232286\pi$
$31$	3.01022	+	1.73795i	0.540651	+	0.312145i	−0.204692	+	0.978827i	$0.565619\pi$
$32$			0.555034i			0.0981171i
$33$		0			0
$34$		−	0.772411i		−	0.132467i
$35$	1.11465	+	1.81781i	0.188409	+	0.307266i
$36$		0			0
$37$			1.24196i			0.204177i	0.994775	+	0.102088i	$0.0325524\pi$
$37$			1.24196i			0.204177i	−0.994775	+	0.102088i	$0.967448\pi$
$38$	−4.03007	+	6.98029i	−0.653764	+	1.13235i
$39$		0			0
$40$	1.16602	+	2.01961i	0.184364	+	0.319329i
$41$	−0.803413	−	0.463851i	−0.125472	−	0.0724413i	0.435950	−	0.899971i	$-0.356412\pi$
$41$	−0.803413	−	0.463851i	−0.125472	−	0.0724413i	−0.561422	+	0.827529i	$0.689746\pi$
$42$		0			0
$43$	2.22356	+	3.85131i	0.339089	+	0.587320i	0.984262	−	0.176717i	$-0.0565478\pi$
$43$	2.22356	+	3.85131i	0.339089	+	0.587320i	−0.645172	+	0.764037i	$0.723214\pi$
$44$	−0.448348	+	0.258854i	−0.0675910	+	0.0390237i
$45$		0			0
$46$		−	2.21321i		−	0.326320i
$47$	3.32915	−	1.92209i	0.485607	−	0.280365i	−0.237143	−	0.971475i	$-0.576211\pi$
$47$	3.32915	−	1.92209i	0.485607	−	0.280365i	0.722750	+	0.691109i	$0.242878\pi$
$48$		0			0
$49$	−6.99020	+	0.370207i	−0.998601	+	0.0528867i
$50$	−5.19572	−	2.99975i	−0.734786	−	0.424229i
$51$		0			0
$52$	−0.232340	−	0.267207i	−0.0322197	−	0.0370549i
$53$	2.72727	−	4.72377i	0.374620	−	0.648860i	−0.615650	−	0.788019i	$-0.711107\pi$
$53$	2.72727	−	4.72377i	0.374620	−	0.648860i	0.990270	+	0.139159i	$0.0444400\pi$
$54$		0			0
$55$	−2.12431	+	3.67941i	−0.286442	+	0.496132i
$56$	−7.65292	+	0.202510i	−1.02266	+	0.0270616i
$57$		0			0
$58$	2.72318	+	1.57223i	0.357571	+	0.206444i
$59$			10.9940i			1.43129i	0.698463	+	0.715646i	$0.253868\pi$
$59$			10.9940i			1.43129i	−0.698463	+	0.715646i	$0.746132\pi$
$60$		0			0
$61$	−3.65107	+	6.32385i	−0.467472	+	0.809686i	−0.999309	−	0.0371610i	$-0.988169\pi$
$61$	−3.65107	+	6.32385i	−0.467472	+	0.809686i	0.531837	+	0.846847i	$0.321502\pi$
$62$	−2.39673	+	4.15126i	−0.304385	+	0.527210i
$63$		0			0
$64$	−8.35330			−1.04416
$65$	−2.74769	−	0.945710i	−0.340809	−	0.117301i
$66$		0			0
$67$	6.36144	−	3.67278i	0.777174	−	0.448701i	−0.0582541	−	0.998302i	$-0.518553\pi$
$67$	6.36144	−	3.67278i	0.777174	−	0.448701i	0.835428	+	0.549600i	$0.185220\pi$
$68$	−0.0550061			−0.00667047
$69$		0			0
$70$	−2.50686	+	1.53716i	−0.299627	+	0.183725i
$71$	8.06668	−	4.65730i	0.957339	−	0.552720i	0.0619857	−	0.998077i	$-0.480257\pi$
$71$	8.06668	−	4.65730i	0.957339	−	0.552720i	0.895353	+	0.445357i	$0.146923\pi$
$72$		0			0
$73$	4.33139	+	2.50073i	0.506951	+	0.292688i	0.731579	−	0.681756i	$-0.238784\pi$
$73$	4.33139	+	2.50073i	0.506951	+	0.292688i	−0.224629	+	0.974444i	$0.572117\pi$
$74$	−1.71273			−0.199101
$75$		0			0
$76$	0.497091	+	0.286996i	0.0570202	+	0.0329207i
$77$	−7.29072	−	11.8900i	−0.830854	−	1.35499i
$78$		0			0
$79$	−5.68437	−	9.84562i	−0.639542	−	1.10772i	−0.985533	−	0.169481i	$-0.945791\pi$
$79$	−5.68437	−	9.84562i	−0.639542	−	1.10772i	0.345992	−	0.938238i	$-0.387543\pi$
$80$	−2.64806	+	1.52886i	−0.296062	+	0.170932i
$81$		0			0
$82$	0.639676	−	1.10795i	0.0706404	−	0.122353i
$83$		−	5.81962i		−	0.638786i	−0.947622	−	0.319393i	$-0.896521\pi$
$83$		−	5.81962i		−	0.638786i	0.947622	−	0.319393i	$-0.103479\pi$
$84$		0			0
$85$	−0.390935	+	0.225707i	−0.0424029	+	0.0244813i
$86$	−5.31117	+	3.06641i	−0.572719	+	0.330659i
$87$		0			0
$88$	−7.62677	−	13.2100i	−0.813016	−	1.40819i
$89$		−	5.00946i		−	0.531001i	−0.964111	−	0.265501i	$-0.914463\pi$
$89$		−	5.00946i		−	0.531001i	0.964111	−	0.265501i	$-0.0855373\pi$
$90$		0			0
$91$	7.03057	−	6.44756i	0.737004	−	0.675888i
$92$	−0.157611			−0.0164320
$93$		0			0
$94$	2.65067	+	4.59109i	0.273395	+	0.473534i
$95$	4.71051			0.483289
$96$		0			0
$97$	9.22171	−	5.32416i	0.936323	−	0.540586i	0.0475172	−	0.998870i	$-0.484869\pi$
$97$	9.22171	−	5.32416i	0.936323	−	0.540586i	0.888806	+	0.458284i	$0.151536\pi$
$98$	−0.510535	−	9.63988i	−0.0515719	−	0.973774i
$99$		0			0
$100$	−0.213623	+	0.370006i	−0.0213623	+	0.0370006i
$101$	−1.95777	−	3.39096i	−0.194805	−	0.337413i	0.752031	−	0.659127i	$-0.229074\pi$
$101$	−1.95777	−	3.39096i	−0.194805	−	0.337413i	−0.946837	+	0.321715i	$0.895741\pi$
$102$		0			0
$103$	4.22690	+	7.32120i	0.416488	+	0.721379i	0.995583	−	0.0938810i	$-0.0299273\pi$
$103$	4.22690	+	7.32120i	0.416488	+	0.721379i	−0.579095	+	0.815260i	$0.696594\pi$
$104$	7.87287	−	6.84556i	0.771998	−	0.671262i
$105$		0			0
$106$	6.51434	+	3.76106i	0.632729	+	0.365306i
$107$	9.67522			0.935339			0.467670	−	0.883903i	$-0.345094\pi$
$107$	9.67522			0.935339			0.467670	+	0.883903i	$0.345094\pi$
$108$		0			0
$109$	−12.6126	−	7.28189i	−1.20807	−	0.697478i	−0.245731	−	0.969338i	$-0.579028\pi$
$109$	−12.6126	−	7.28189i	−1.20807	−	0.697478i	−0.962337	+	0.271860i	$0.912361\pi$
$110$	−5.07411	−	2.92954i	−0.483798	−	0.279321i
$111$		0			0
$112$	−0.265526	−	10.0343i	−0.0250899	−	0.948153i
$113$	9.75572	+	16.8974i	0.917741	+	1.58957i	0.802838	+	0.596197i	$0.203322\pi$
$113$	9.75572	+	16.8974i	0.917741	+	1.58957i	0.114903	+	0.993377i	$0.463344\pi$
$114$		0			0
$115$	−1.12016	+	0.646723i	−0.104455	+	0.0603073i
$116$	0.111964	−	0.193927i	0.0103956	−	0.0180057i
$117$		0			0
$118$	−15.1613			−1.39571
$119$	−0.0391998	−	1.48137i	−0.00359344	−	0.135797i
$120$		0			0
$121$	8.39477	−	14.5402i	0.763161	−	1.32183i
$122$	−8.72093	−	5.03503i	−0.789556	−	0.455850i
$123$		0			0
$124$	0.295626	+	0.170680i	0.0265480	+	0.0153275i
$125$			7.53598i			0.674038i
$126$		0			0
$127$	−0.958656	+	1.66044i	−0.0850670	+	0.147340i	−0.905420	−	0.424517i	$-0.860444\pi$
$127$	−0.958656	+	1.66044i	−0.0850670	+	0.147340i	0.820353	+	0.571858i	$0.193777\pi$
$128$		−	10.4096i		−	0.920087i
$129$		0			0
$130$	1.30419	−	3.78922i	0.114385	−	0.332337i
$131$	7.79078	+	13.4940i	0.680684	+	1.17898i	0.974772	+	0.223201i	$0.0716506\pi$
$131$	7.79078	+	13.4940i	0.680684	+	1.17898i	−0.294089	+	0.955778i	$0.595016\pi$
$132$		0			0
$133$	−7.37484	+	13.5917i	−0.639479	+	1.17855i
$134$	5.06496	+	8.77278i	0.437546	+	0.757852i
$135$		0			0
$136$		−	1.62068i		−	0.138972i
$137$			7.85105i			0.670761i	0.942083	+	0.335380i	$0.108865\pi$
$137$			7.85105i			0.670761i	−0.942083	+	0.335380i	$0.891135\pi$
$138$		0			0
$139$	−4.96241	−	8.59514i	−0.420906	−	0.729030i	0.575122	−	0.818067i	$-0.304954\pi$
$139$	−4.96241	−	8.59514i	−0.420906	−	0.729030i	−0.996028	+	0.0890370i	$0.971621\pi$
$140$	0.109466	+	0.178522i	0.00925160	+	0.0150879i
$141$		0			0
$142$	6.42267	+	11.1244i	0.538979	+	0.933538i
$143$	17.9722	+	6.18574i	1.50291	+	0.517278i
$144$		0			0
$145$		−	1.83769i		−	0.152612i
$146$	−3.44864	+	5.97322i	−0.285412	+	0.494347i
$147$		0			0
$148$			0.121969i			0.0100258i
$149$	−6.85827	−	3.95962i	−0.561851	−	0.324385i	0.192037	−	0.981388i	$-0.438491\pi$
$149$	−6.85827	−	3.95962i	−0.561851	−	0.324385i	−0.753888	+	0.657003i	$0.771824\pi$
$150$		0			0
$151$	1.30005	+	0.750582i	0.105796	+	0.0610815i	0.551965	−	0.833868i	$-0.313878\pi$
$151$	1.30005	+	0.750582i	0.105796	+	0.0610815i	−0.446168	+	0.894949i	$0.647212\pi$
$152$	−8.45592	+	14.6461i	−0.685866	+	1.18795i
$153$		0			0
$154$	16.3970	−	10.0543i	1.32131	−	0.810198i
$155$	2.80140			0.225014
$156$		0			0
$157$	−1.92846	+	3.34019i	−0.153908	+	0.266576i	−0.932661	−	0.360754i	$-0.882519\pi$
$157$	−1.92846	+	3.34019i	−0.153908	+	0.266576i	0.778753	+	0.627331i	$0.215853\pi$
$158$	13.5777	−	7.83906i	1.08018	−	0.623642i
$159$		0			0
$160$	0.223664	+	0.387398i	0.0176822	+	0.0306265i
$161$	−0.112320	−	4.24462i	−0.00885209	−	0.334523i
$162$		0			0
$163$	12.4369	+	7.18042i	0.974130	+	0.562414i	0.900493	−	0.434871i	$-0.143206\pi$
$163$	12.4369	+	7.18042i	0.974130	+	0.562414i	0.0736372	+	0.997285i	$0.476539\pi$
$164$	−0.0789011	−	0.0455536i	−0.00616114	−	0.00355714i
$165$		0			0
$166$	8.02557			0.622905
$167$	3.91563	+	2.26069i	0.303000	+	0.174937i	0.643790	−	0.765202i	$-0.277361\pi$
$167$	3.91563	+	2.26069i	0.303000	+	0.174937i	−0.340790	+	0.940140i	$0.610694\pi$
$168$		0			0
$169$	−1.80593	+	12.8740i	−0.138918	+	0.990304i
$170$	−0.311262	−	0.539121i	−0.0238727	−	0.0413487i
$171$		0			0
$172$	0.218370	+	0.378227i	0.0166505	+	0.0288396i
$173$	9.75896	−	16.9030i	0.741960	−	1.28511i	−0.209642	−	0.977778i	$-0.567230\pi$
$173$	9.75896	−	16.9030i	0.741960	−	1.28511i	0.951602	−	0.307334i	$-0.0994369\pi$
$174$		0			0
$175$	−10.1169	−	5.48940i	−0.764764	−	0.414960i
$176$	17.3206	−	10.0000i	1.30559	−	0.753780i
$177$		0			0
$178$	6.90832			0.517800
$179$	−10.4098	−	18.0303i	−0.778065	−	1.34765i	−0.933055	−	0.359733i	$-0.882868\pi$
$179$	−10.4098	−	18.0303i	−0.778065	−	1.34765i	0.154990	−	0.987916i	$-0.450465\pi$
$180$		0			0
$181$	16.5522			1.23031			0.615157	−	0.788405i	$-0.289093\pi$
$181$	16.5522			1.23031			0.615157	+	0.788405i	$0.289093\pi$
$182$	8.89155	+	9.69554i	0.659085	+	0.718681i
$183$		0			0
$184$		−	4.64378i		−	0.342344i
$185$	0.500477	+	0.866851i	0.0367958	+	0.0637322i
$186$		0			0
$187$	2.55704	−	1.47631i	0.186990	−	0.107958i
$188$	0.326948	−	0.188763i	0.0238451	−	0.0137670i
$189$		0			0
$190$			6.49606i			0.471274i
$191$	−2.12504	+	3.68068i	−0.153762	+	0.266324i	−0.932608	−	0.360892i	$-0.882472\pi$
$191$	−2.12504	+	3.68068i	−0.153762	+	0.266324i	0.778845	+	0.627216i	$0.215806\pi$
$192$		0			0
$193$	−10.0435	+	5.79861i	−0.722946	+	0.417393i	−0.815836	−	0.578283i	$-0.803723\pi$
$193$	−10.0435	+	5.79861i	−0.722946	+	0.417393i	0.0928898	+	0.995676i	$0.470390\pi$
$194$	7.34231	+	12.7172i	0.527147	+	0.913045i
$195$		0			0
$196$	−0.686490	+	0.0363570i	−0.0490350	+	0.00259693i
$197$	12.4892	+	7.21066i	0.889821	+	0.513738i	0.873884	−	0.486135i	$-0.161594\pi$
$197$	12.4892	+	7.21066i	0.889821	+	0.513738i	0.0159371	+	0.999873i	$0.494927\pi$
$198$		0			0
$199$	−7.05924			−0.500416			−0.250208	−	0.968192i	$-0.580499\pi$
$199$	−7.05924			−0.500416			−0.250208	+	0.968192i	$0.580499\pi$
$200$	−10.9017	−	6.29410i	−0.770867	−	0.445060i
$201$		0			0
$202$	4.67632	−	2.69987i	0.329024	−	0.189962i
$203$	5.30245	+	2.87710i	0.372159	+	0.201933i
$204$		0			0
$205$	−0.747680			−0.0522202
$206$	−10.0963	+	5.82912i	−0.703445	+	0.406134i
$207$		0			0
$208$	8.97572	+	10.3227i	0.622354	+	0.715751i
$209$	−30.8107			−2.13122
$210$		0			0
$211$	13.2113	−	22.8827i	0.909505	−	1.57531i	0.0947513	−	0.995501i	$-0.469794\pi$
$211$	13.2113	−	22.8827i	0.909505	−	1.57531i	0.814754	−	0.579807i	$-0.196872\pi$
$212$	0.267838	−	0.463909i	0.0183952	−	0.0318614i
$213$		0			0
$214$			13.3427i			0.912086i
$215$	3.10396	+	1.79207i	0.211688	+	0.122218i
$216$		0			0
$217$	−4.38590	+	8.08314i	−0.297734	+	0.548719i
$218$	10.0421	−	17.3935i	0.680138	−	1.17803i
$219$		0			0
$220$	−0.208623	+	0.361345i	−0.0140654	+	0.0243619i
$221$	1.32509	+	1.52395i	0.0891353	+	0.102512i
$222$		0			0
$223$	19.9191	+	11.5003i	1.33388	+	0.770115i	0.985892	−	0.167384i	$-0.0535321\pi$
$223$	19.9191	+	11.5003i	1.33388	+	0.770115i	0.347987	+	0.937499i	$0.386865\pi$
$224$	−1.46797	+	0.0388452i	−0.0980828	+	0.00259545i
$225$		0			0
$226$	−23.3024	+	13.4537i	−1.55006	+	0.894925i
$227$		−	0.453367i		−	0.0300911i	−0.999887	−	0.0150455i	$-0.995211\pi$
$227$		−	0.453367i		−	0.0300911i	0.999887	−	0.0150455i	$-0.00478932\pi$
$228$		0			0
$229$	15.0112	−	8.66674i	0.991970	−	0.572714i	0.0861077	−	0.996286i	$-0.472557\pi$
$229$	15.0112	−	8.66674i	0.991970	−	0.572714i	0.905863	+	0.423571i	$0.139224\pi$
$230$	−0.891867	−	1.54476i	−0.0588080	−	0.101858i
$231$		0			0
$232$	5.71380	+	3.29886i	0.375129	+	0.216581i
$233$	−3.90756	−	6.76809i	−0.255992	−	0.443392i	0.709172	−	0.705035i	$-0.249069\pi$
$233$	−3.90756	−	6.76809i	−0.255992	−	0.443392i	−0.965165	+	0.261643i	$0.915736\pi$
$234$		0			0
$235$	1.54910	−	2.68313i	0.101052	−	0.175028i
$236$			1.07969i			0.0702818i
$237$		0			0
$238$	2.04289	−	0.0540587i	0.132421	−	0.00350411i
$239$		−	13.5314i		−	0.875276i	−0.899151	−	0.437638i	$-0.855815\pi$
$239$		−	13.5314i		−	0.875276i	0.899151	−	0.437638i	$-0.144185\pi$
$240$		0			0
$241$			22.5592i			1.45317i	0.687078	+	0.726583i	$0.258893\pi$
$241$			22.5592i			1.45317i	−0.687078	+	0.726583i	$0.741107\pi$
$242$	20.0517	+	11.5768i	1.28897	+	0.744188i
$243$		0			0
$244$	−0.358563	+	0.621049i	−0.0229546	+	0.0397586i
$245$	−4.72978	+	3.07526i	−0.302175	+	0.196471i
$246$		0			0
$247$	−4.02364	−	20.6856i	−0.256018	−	1.31619i
$248$	−5.02884	+	8.71020i	−0.319331	+	0.553098i
$249$		0			0
$250$	−10.3925			−0.657281
$251$	3.36618	+	5.83039i	0.212471	+	0.368011i	0.952487	−	0.304578i	$-0.0985154\pi$
$251$	3.36618	+	5.83039i	0.212471	+	0.368011i	−0.740016	+	0.672589i	$0.765182\pi$
$252$		0			0
$253$	7.32677	−	4.23011i	0.460630	−	0.265945i
$254$	−2.28984	−	1.32204i	−0.143677	−	0.0829521i
$255$		0			0
$256$	−2.35120			−0.146950
$257$	16.5381			1.03162			0.515811	−	0.856703i	$-0.327491\pi$
$257$	16.5381			1.03162			0.515811	+	0.856703i	$0.327491\pi$
$258$		0			0
$259$	−3.28476	+	0.0869209i	−0.204105	+	0.00540100i
$260$	−0.269844	−	0.0928757i	−0.0167350	−	0.00575991i
$261$		0			0
$262$	−18.6090	+	10.7439i	−1.14967	+	0.663761i
$263$	−5.01137	−	8.67994i	−0.309014	−	0.535228i	0.669133	−	0.743143i	$-0.266666\pi$
$263$	−5.01137	−	8.67994i	−0.309014	−	0.535228i	−0.978147	+	0.207915i	$0.933332\pi$
$264$		0			0
$265$		−	4.39608i		−	0.270049i
$266$	−18.7437	−	10.1703i	−1.14925	−	0.623581i
$267$		0			0
$268$	0.624740	−	0.360694i	0.0381621	−	0.0220329i
$269$	15.7230			0.958647			0.479323	−	0.877638i	$-0.340882\pi$
$269$	15.7230			0.958647			0.479323	+	0.877638i	$0.340882\pi$
$270$		0			0
$271$		−	5.21618i		−	0.316860i	−0.987370	−	0.158430i	$-0.949357\pi$
$271$		−	5.21618i		−	0.316860i	0.987370	−	0.158430i	$-0.0506433\pi$
$272$	2.12499			0.128847
$273$		0			0
$274$	−10.8270			−0.654085
$275$		−	22.9337i		−	1.38296i
$276$		0			0
$277$	19.2724			1.15797			0.578983	−	0.815340i	$-0.303450\pi$
$277$	19.2724			1.15797			0.578983	+	0.815340i	$0.303450\pi$
$278$	11.8532	−	6.84343i	0.710906	−	0.410442i
$279$		0			0
$280$	−5.25991	+	3.22527i	−0.314340	+	0.192747i
$281$		−	2.14283i		−	0.127831i	−0.997955	−	0.0639153i	$-0.979641\pi$
$281$		−	2.14283i		−	0.127831i	0.997955	−	0.0639153i	$-0.0203588\pi$
$282$		0			0
$283$	−7.87512	−	13.6401i	−0.468127	−	0.810820i	0.531209	−	0.847241i	$-0.321738\pi$
$283$	−7.87512	−	13.6401i	−0.468127	−	0.810820i	−0.999337	+	0.0364203i	$0.988405\pi$
$284$	0.792207	−	0.457381i	0.0470089	−	0.0271406i
$285$		0			0
$286$	−8.53048	+	24.7847i	−0.504418	+	1.46555i
$287$	1.17058	−	2.15735i	0.0690969	−	0.127344i
$288$		0			0
$289$	−16.6863			−0.981546
$290$	2.53427			0.148817
$291$		0			0
$292$	0.425374	+	0.245590i	0.0248932	+	0.0143721i
$293$	20.0474	−	11.5744i	1.17118	−	0.676182i	0.217223	−	0.976122i	$-0.430300\pi$
$293$	20.0474	−	11.5744i	1.17118	−	0.676182i	0.953958	+	0.299940i	$0.0969668\pi$
$294$		0			0
$295$	4.43029	+	7.67348i	0.257941	+	0.446767i
$296$	−3.59366			−0.208877
$297$		0			0
$298$	5.46054	−	9.45793i	0.316320	−	0.547883i
$299$	3.79682	+	4.36661i	0.219576	+	0.252528i
$300$		0			0
$301$	−10.0304	+	6.15046i	−0.578145	+	0.354507i
$302$	−1.03509	+	1.79283i	−0.0595629	+	0.103166i
$303$		0			0
$304$	−19.2036	−	11.0872i	−1.10140	−	0.635894i
$305$			5.88515i			0.336983i
$306$		0			0
$307$		−	4.23590i		−	0.241756i	−0.992667	−	0.120878i	$-0.961429\pi$
$307$		−	4.23590i		−	0.241756i	0.992667	−	0.120878i	$-0.0385709\pi$
$308$	−0.716002	−	1.16769i	−0.0407980	−	0.0665351i
$309$		0			0
$310$			3.86328i			0.219420i
$311$	−13.6251	+	23.5993i	−0.772606	+	1.33819i	0.163524	+	0.986539i	$0.447714\pi$
$311$	−13.6251	+	23.5993i	−0.772606	+	1.33819i	−0.936130	+	0.351654i	$0.885619\pi$
$312$		0			0
$313$	−1.34849	−	2.33565i	−0.0762209	−	0.132018i	0.825396	−	0.564555i	$-0.190952\pi$
$313$	−1.34849	−	2.33565i	−0.0762209	−	0.132018i	−0.901617	+	0.432536i	$0.857619\pi$
$314$	−4.60631	−	2.65945i	−0.259949	−	0.150082i
$315$		0			0
$316$	−0.558247	−	0.966913i	−0.0314039	−	0.0543931i
$317$	−20.8456	+	12.0352i	−1.17081	+	0.675966i	−0.953870	−	0.300220i	$-0.902940\pi$
$317$	−20.8456	+	12.0352i	−1.17081	+	0.675966i	−0.216937	+	0.976186i	$0.569607\pi$
$318$		0			0
$319$			12.0200i			0.672991i
$320$	−5.83037	+	3.36617i	−0.325928	+	0.188174i
$321$		0			0
$322$	5.85356	−	0.154896i	0.326206	−	0.00863202i
$323$	−2.83504	−	1.63681i	−0.157746	−	0.0910745i
$324$		0			0
$325$	15.3972	−	2.99497i	0.854082	−	0.166131i
$326$	−9.90220	+	17.1511i	−0.548432	+	0.949912i
$327$		0			0
$328$	1.34217	−	2.32471i	0.0741091	−	0.128361i
$329$	5.31659	+	8.67051i	0.293113	+	0.478021i
$330$		0			0
$331$	0.536696	+	0.309862i	0.0294995	+	0.0170315i	0.514677	−	0.857384i	$-0.327912\pi$
$331$	0.536696	+	0.309862i	0.0294995	+	0.0170315i	−0.485178	+	0.874416i	$0.661245\pi$
$332$		−	0.571530i		−	0.0313668i
$333$		0			0
$334$	−3.11762	+	5.39987i	−0.170588	+	0.295468i
$335$	2.96007	−	5.12699i	0.161726	−	0.280117i
$336$		0			0
$337$	−5.72118			−0.311652			−0.155826	−	0.987784i	$-0.549804\pi$
$337$	−5.72118			−0.311652			−0.155826	+	0.987784i	$0.549804\pi$
$338$	−17.7539	−	2.49048i	−0.965684	−	0.135464i
$339$		0			0
$340$	−0.0383927	+	0.0221660i	−0.00208214	+	0.00120212i
$341$	−18.3235			−0.992272
$342$		0			0
$343$	−1.46836	−	18.4620i	−0.0792837	−	0.996852i
$344$	−11.1439	+	6.43396i	−0.600841	+	0.346896i
$345$		0			0
$346$	23.3102	+	13.4581i	1.25316	+	0.723514i
$347$	1.86486			0.100111			0.0500554	−	0.998746i	$-0.484060\pi$
$347$	1.86486			0.100111			0.0500554	+	0.998746i	$0.484060\pi$
$348$		0			0
$349$	−19.3273	−	11.1586i	−1.03457	−	0.597307i	−0.116277	−	0.993217i	$-0.537096\pi$
$349$	−19.3273	−	11.1586i	−1.03457	−	0.597307i	−0.918290	+	0.395909i	$0.870429\pi$
$350$	7.57019	−	13.9517i	0.404644	−	0.745751i
$351$		0			0
$352$	−1.46295	−	2.53391i	−0.0779756	−	0.135058i
$353$	−2.01956	+	1.16600i	−0.107491	+	0.0620597i	−0.552781	−	0.833326i	$-0.686434\pi$
$353$	−2.01956	+	1.16600i	−0.107491	+	0.0620597i	0.445291	+	0.895386i	$0.353100\pi$
$354$		0			0
$355$	3.75354	−	6.50133i	0.199217	−	0.345055i
$356$		−	0.491966i		−	0.0260741i
$357$		0			0
$358$	24.8648	−	14.3557i	1.31415	−	0.758722i
$359$	2.83281	−	1.63553i	0.149510	−	0.0863197i	−0.423379	−	0.905953i	$-0.639156\pi$
$359$	2.83281	−	1.63553i	0.149510	−	0.0863197i	0.572889	+	0.819633i	$0.305823\pi$
$360$		0			0
$361$	7.58017	+	13.1292i	0.398956	+	0.691013i
$362$			22.8264i			1.19973i
$363$		0			0
$364$	0.690454	−	0.633198i	0.0361896	−	0.0331886i
$365$	4.03092			0.210988
$366$		0			0
$367$	−2.07645	−	3.59652i	−0.108390	−	0.187737i	0.806728	−	0.590923i	$-0.201236\pi$
$367$	−2.07645	−	3.59652i	−0.108390	−	0.187737i	−0.915118	+	0.403186i	$0.867903\pi$
$368$	6.08880			0.317401
$369$		0			0
$370$	−1.19544	+	0.690185i	−0.0621477	+	0.0358810i
$371$	12.6844	+	6.88256i	0.658543	+	0.357325i
$372$		0			0
$373$	5.55446	−	9.62061i	0.287599	−	0.498136i	−0.685637	−	0.727944i	$-0.740476\pi$
$373$	5.55446	−	9.62061i	0.287599	−	0.498136i	0.973236	+	0.229807i	$0.0738096\pi$
$374$	2.03591	+	3.52630i	0.105275	+	0.182341i
$375$		0			0
$376$	5.56165	+	9.63305i	0.286820	+	0.496787i
$377$	−8.06996	+	1.56972i	−0.415624	+	0.0808447i
$378$		0			0
$379$	−4.01862	−	2.32015i	−0.206422	−	0.119178i	0.393225	−	0.919442i	$-0.371359\pi$
$379$	−4.01862	−	2.32015i	−0.206422	−	0.119178i	−0.599648	+	0.800264i	$0.704693\pi$
$380$	0.462607			0.0237312
$381$		0			0
$382$	−5.07586	−	2.93055i	−0.259703	−	0.149940i
$383$	3.17773	+	1.83466i	0.162374	+	0.0937469i	0.578985	−	0.815338i	$-0.303449\pi$
$383$	3.17773	+	1.83466i	0.162374	+	0.0937469i	−0.416611	+	0.909085i	$0.636782\pi$
$384$		0			0
$385$	−9.88008	−	5.36092i	−0.503535	−	0.273218i
$386$	−7.99661	−	13.8505i	−0.407017	−	0.704973i
$387$		0			0
$388$	0.905640	−	0.522872i	0.0459769	−	0.0265448i
$389$	−8.44156	+	14.6212i	−0.428004	+	0.741324i	−0.996696	−	0.0812262i	$-0.974116\pi$
$389$	−8.44156	+	14.6212i	−0.428004	+	0.741324i	0.568692	+	0.822551i	$0.307450\pi$
$390$		0			0
$391$	0.898894			0.0454590
$392$	−1.07121	−	20.2265i	−0.0541042	−	1.02159i
$393$		0			0
$394$	−9.94390	+	17.2233i	−0.500966	+	0.867699i
$395$	−7.93506	−	4.58131i	−0.399256	−	0.230511i
$396$		0			0
$397$	−14.4700	−	8.35428i	−0.726230	−	0.419289i	0.0908114	−	0.995868i	$-0.471054\pi$
$397$	−14.4700	−	8.35428i	−0.726230	−	0.419289i	−0.817041	+	0.576579i	$0.804387\pi$
$398$		−	9.73508i		−	0.487976i
$399$		0			0
$400$	8.25267	−	14.2940i	0.412633	−	0.714702i
$401$		−	25.3134i		−	1.26409i	−0.774931	−	0.632046i	$-0.782215\pi$
$401$		−	25.3134i		−	1.26409i	0.774931	−	0.632046i	$-0.217785\pi$
$402$		0			0
$403$	−2.39291	−	12.3020i	−0.119199	−	0.612805i
$404$	−0.192267	−	0.333017i	−0.00956566	−	0.0165682i
$405$		0			0
$406$	−3.96768	+	7.31237i	−0.196913	+	0.362907i
$407$	−3.27354	−	5.66994i	−0.162263	−	0.281048i
$408$		0			0
$409$		−	5.73343i		−	0.283500i	−0.989903	−	0.141750i	$-0.954727\pi$
$409$		−	5.73343i		−	0.283500i	0.989903	−	0.141750i	$-0.0452729\pi$
$410$		−	1.03109i		−	0.0509220i
$411$		0			0
$412$	0.415112	+	0.718996i	0.0204511	+	0.0354224i
$413$	−29.0771	+	0.769435i	−1.43079	+	0.0378614i
$414$		0			0
$415$	−2.34516	−	4.06193i	−0.115119	−	0.199392i
$416$	1.51016	−	1.31310i	0.0740416	−	0.0643801i
$417$		0			0
$418$		−	42.4897i		−	2.07824i
$419$	−17.1729	+	29.7443i	−0.838950	+	1.45310i	0.0518229	+	0.998656i	$0.483497\pi$
$419$	−17.1729	+	29.7443i	−0.838950	+	1.45310i	−0.890773	+	0.454448i	$0.849836\pi$
$420$		0			0
$421$			2.94167i			0.143368i	0.997427	+	0.0716842i	$0.0228374\pi$
$421$			2.94167i			0.143368i	−0.997427	+	0.0716842i	$0.977163\pi$
$422$	31.5565	+	18.2191i	1.53614	+	0.886894i
$423$		0			0
$424$	13.6684	+	7.89148i	0.663798	+	0.383244i
$425$	1.21835	−	2.11024i	0.0590985	−	0.102362i
$426$		0			0
$427$	−16.9810	−	9.21387i	−0.821768	−	0.445890i
$428$	0.950178			0.0459286
$429$		0			0
$430$	−2.47137	+	4.28053i	−0.119180	+	0.206426i
$431$	−34.3773	+	19.8478i	−1.65590	+	0.956033i	−0.681321	+	0.731985i	$0.738594\pi$
$431$	−34.3773	+	19.8478i	−1.65590	+	0.956033i	−0.974578	+	0.224048i	$0.928073\pi$
$432$		0			0
$433$	−4.91827	−	8.51869i	−0.236357	−	0.409382i	0.723309	−	0.690524i	$-0.242620\pi$
$433$	−4.91827	−	8.51869i	−0.236357	−	0.409382i	−0.959666	+	0.281142i	$0.909287\pi$
$434$	−11.1471	−	6.04840i	−0.535078	−	0.290332i
$435$		0			0
$436$	−1.23865	−	0.715135i	−0.0593206	−	0.0342488i
$437$	−8.12331	−	4.69000i	−0.388591	−	0.224353i
$438$		0			0
$439$	−28.5465			−1.36245			−0.681226	−	0.732073i	$-0.738553\pi$
$439$	−28.5465			−1.36245			−0.681226	+	0.732073i	$0.738553\pi$
$440$	−10.6465	−	6.14678i	−0.507554	−	0.293036i
$441$		0			0
$442$	−2.10161	+	1.82737i	−0.0999632	+	0.0869193i
$443$	1.66951	+	2.89167i	0.0793207	+	0.137387i	0.902957	−	0.429731i	$-0.141392\pi$
$443$	1.66951	+	2.89167i	0.0793207	+	0.137387i	−0.823636	+	0.567118i	$0.808058\pi$
$444$		0			0
$445$	−2.01868	−	3.49646i	−0.0956947	−	0.165748i
$446$	−15.8595	+	27.4695i	−0.750969	+	1.30072i
$447$		0			0
$448$	−0.584622	−	22.0930i	−0.0276208	−	1.04380i
$449$	−15.7487	+	9.09253i	−0.743228	+	0.429103i	−0.823242	−	0.567691i	$-0.807837\pi$
$449$	−15.7487	+	9.09253i	−0.743228	+	0.429103i	0.0800136	+	0.996794i	$0.474504\pi$
$450$		0			0
$451$	4.89045			0.230282
$452$	0.958084	+	1.65945i	0.0450645	+	0.0780539i
$453$		0			0
$454$	0.625219			0.0293430
$455$	2.30894	−	7.33336i	0.108245	−	0.343793i
$456$		0			0
$457$			8.72932i			0.408341i	0.978935	+	0.204170i	$0.0654496\pi$
$457$			8.72932i			0.408341i	−0.978935	+	0.204170i	$0.934550\pi$
$458$	11.9519	+	20.7013i	0.558476	+	0.967309i
$459$		0			0
$460$	−0.110008	+	0.0635130i	−0.00512914	+	0.00296131i
$461$	1.96695	−	1.13562i	0.0916099	−	0.0528910i	−0.453495	−	0.891259i	$-0.649823\pi$
$461$	1.96695	−	1.13562i	0.0916099	−	0.0528910i	0.545105	+	0.838368i	$0.316490\pi$
$462$		0			0
$463$			5.48326i			0.254829i	0.991850	+	0.127414i	$0.0406678\pi$
$463$			5.48326i			0.254829i	−0.991850	+	0.127414i	$0.959332\pi$
$464$	−4.32538	+	7.49178i	−0.200801	+	0.347797i
$465$		0			0
$466$	9.33356	−	5.38873i	0.432369	−	0.249628i
$467$	−9.44095	−	16.3522i	−0.436875	−	0.756690i	0.560572	−	0.828106i	$-0.310581\pi$
$467$	−9.44095	−	16.3522i	−0.436875	−	0.756690i	−0.997447	+	0.0714164i	$0.977248\pi$
$468$		0			0
$469$	10.1591	+	16.5679i	0.469103	+	0.765032i
$470$	3.70018	+	2.13630i	0.170677	+	0.0985401i
$471$		0			0
$472$	−31.8115			−1.46424
$473$	−20.3025	−	11.7217i	−0.933510	−	0.538962i
$474$		0			0
$475$	−22.0204	+	12.7135i	−1.01037	+	0.583335i
$476$	−0.00384971	−	0.145482i	−0.000176451	−	0.00666814i
$477$		0			0
$478$	18.6606			0.853516
$479$	28.6961	−	16.5677i	1.31116	−	0.756997i	0.328869	−	0.944375i	$-0.393332\pi$
$479$	28.6961	−	16.5677i	1.31116	−	0.756997i	0.982288	+	0.187378i	$0.0599991\pi$
$480$		0			0
$481$	3.37917	−	2.93823i	0.154077	−	0.133972i
$482$	−31.1104			−1.41704
$483$		0			0
$484$	0.824428	−	1.42795i	0.0374740	−	0.0649069i
$485$	4.29100	−	7.43222i	0.194844	−	0.337480i
$486$		0			0
$487$			15.9563i			0.723048i	0.932363	+	0.361524i	$0.117743\pi$
$487$			15.9563i			0.723048i	−0.932363	+	0.361524i	$0.882257\pi$
$488$	−18.2983	−	10.5645i	−0.828326	−	0.478234i
$489$		0			0
$490$	−4.24096	−	6.52263i	−0.191587	−	0.294662i
$491$	15.8464	−	27.4468i	0.715138	−	1.23866i	−0.247769	−	0.968819i	$-0.579697\pi$
$491$	15.8464	−	27.4468i	0.715138	−	1.23866i	0.962906	−	0.269836i	$-0.0869694\pi$
$492$		0			0
$493$	−0.638559	+	1.10602i	−0.0287593	+	0.0498125i
$494$	28.5266	−	5.54882i	1.28347	−	0.249653i
$495$		0			0
$496$	−11.4206	−	6.59368i	−0.512800	−	0.296065i
$497$	12.8823	+	21.0090i	0.577850	+	0.942383i
$498$		0			0
$499$	20.9738	−	12.1092i	0.938916	−	0.542083i	0.0492955	−	0.998784i	$-0.484302\pi$
$499$	20.9738	−	12.1092i	0.938916	−	0.542083i	0.889620	+	0.456701i	$0.150969\pi$
$500$			0.740089i			0.0330978i
$501$		0			0
$502$	−8.04043	+	4.64215i	−0.358862	+	0.207189i
$503$	0.427249	+	0.740017i	0.0190501	+	0.0329957i	0.875393	−	0.483411i	$-0.160602\pi$
$503$	0.427249	+	0.740017i	0.0190501	+	0.0329957i	−0.856343	+	0.516407i	$0.827269\pi$
$504$		0			0
$505$	−2.73294	−	1.57786i	−0.121614	−	0.0702139i
$506$	5.83356	+	10.1040i	0.259333	+	0.449179i
$507$		0			0
$508$	−0.0941471	+	0.163068i	−0.00417710	+	0.00723495i
$509$			1.30000i			0.0576215i	0.999585	+	0.0288108i	$0.00917202\pi$
$509$			1.30000i			0.0576215i	−0.999585	+	0.0288108i	$0.990828\pi$
$510$		0			0
$511$	−6.31085	+	11.6308i	−0.279176	+	0.514516i
$512$		−	24.0616i		−	1.06338i
$513$		0			0
$514$			22.8070i			1.00597i
$515$	5.90051	+	3.40666i	0.260007	+	0.150115i
$516$		0			0
$517$	−10.1324	+	17.5499i	−0.445624	+	0.771844i
$518$	−0.119869	−	4.52987i	−0.00526673	−	0.199031i
$519$		0			0
$520$	2.73645	−	7.95057i	0.120001	−	0.348655i
$521$	−12.5228	+	21.6901i	−0.548632	+	0.950259i	0.449736	+	0.893161i	$0.351518\pi$
$521$	−12.5228	+	21.6901i	−0.548632	+	0.950259i	−0.998369	+	0.0570974i	$0.981815\pi$
$522$		0			0
$523$	12.8239			0.560752			0.280376	−	0.959890i	$-0.409541\pi$
$523$	12.8239			0.560752			0.280376	+	0.959890i	$0.409541\pi$
$524$	0.765112	+	1.32521i	0.0334241	+	0.0578922i
$525$		0			0
$526$	11.9701	−	6.91095i	0.521922	−	0.301332i
$527$	−1.68603	−	0.973429i	−0.0734446	−	0.0424032i
$528$		0			0
$529$	−20.4244			−0.888016
$530$	6.06244			0.263335
$531$		0			0
$532$	−0.724263	+	1.33480i	−0.0314008	+	0.0578711i
$533$	0.638656	+	3.28334i	0.0276632	+	0.142217i
$534$		0			0
$535$	6.75303	−	3.89886i	0.291959	−	0.168563i
$536$	10.6273	+	18.4071i	0.459031	+	0.795066i
$537$		0			0
$538$			21.6828i			0.934814i
$539$	30.9367	−	20.1148i	1.33254	−	0.866406i
$540$		0			0
$541$	−24.8938	+	14.3725i	−1.07027	+	0.617920i	−0.928255	−	0.371944i	$-0.878691\pi$
$541$	−24.8938	+	14.3725i	−1.07027	+	0.617920i	−0.142014	+	0.989865i	$0.545358\pi$
$542$	7.19340			0.308983
$543$		0			0
$544$		−	0.310876i		−	0.0133287i
$545$	−11.7376			−0.502785
$546$		0			0
$547$	−8.88085			−0.379718			−0.189859	−	0.981811i	$-0.560803\pi$
$547$	−8.88085			−0.379718			−0.189859	+	0.981811i	$0.560803\pi$
$548$			0.771031i			0.0329368i
$549$		0			0
$550$	31.6269			1.34857
$551$	11.5413	−	6.66339i	0.491677	−	0.283870i
$552$		0			0
$553$	25.6421	−	15.7232i	1.09041	−	0.668620i
$554$			26.5777i			1.12918i
$555$		0			0
$556$	−0.487345	−	0.844106i	−0.0206680	−	0.0357981i
$557$	−33.5389	+	19.3637i	−1.42109	+	0.820465i	−0.996392	−	0.0848711i	$-0.972952\pi$
$557$	−33.5389	+	19.3637i	−1.42109	+	0.820465i	−0.424695	+	0.905336i	$0.639619\pi$
$558$		0			0
$559$	5.21830	−	15.1614i	0.220711	−	0.641259i
$560$	−4.22890	−	6.89666i	−0.178704	−	0.291437i
$561$		0			0
$562$	2.95508			0.124653
$563$	6.90882			0.291172			0.145586	−	0.989346i	$-0.453493\pi$
$563$	6.90882			0.291172			0.145586	+	0.989346i	$0.453493\pi$
$564$		0			0
$565$	13.6184	+	7.86260i	0.572932	+	0.330782i
$566$	18.8105	−	10.8602i	0.790663	−	0.456489i
$567$		0			0
$568$	13.4761	+	23.3413i	0.565444	+	0.979379i
$569$	−2.83745			−0.118952			−0.0594759	−	0.998230i	$-0.518943\pi$
$569$	−2.83745			−0.118952			−0.0594759	+	0.998230i	$0.518943\pi$
$570$		0			0
$571$	−23.3362	+	40.4195i	−0.976589	+	1.69150i	−0.302001	+	0.953307i	$0.597655\pi$
$571$	−23.3362	+	40.4195i	−0.976589	+	1.69150i	−0.674588	+	0.738195i	$0.735679\pi$
$572$	1.76500	+	0.607485i	0.0737985	+	0.0254002i
$573$		0			0
$574$	2.97511	+	1.61429i	0.124179	+	0.0673791i
$575$	3.49096	−	6.04653i	0.145583	−	0.252158i
$576$		0			0
$577$	−9.88033	−	5.70441i	−0.411323	−	0.237478i	0.280035	−	0.959990i	$-0.409654\pi$
$577$	−9.88033	−	5.70441i	−0.411323	−	0.237478i	−0.691358	+	0.722512i	$0.742987\pi$
$578$		−	23.0113i		−	0.957144i
$579$		0			0
$580$		−	0.180474i		−	0.00749379i
$581$	15.3919	−	0.407298i	0.638563	−	0.0168975i
$582$		0			0
$583$			28.7541i			1.19087i
$584$	−7.23597	+	12.5331i	−0.299426	+	0.518622i
$585$		0			0
$586$	15.9617	+	27.6465i	0.659371	+	1.14206i
$587$	40.2191	+	23.2205i	1.66002	+	0.958413i	0.972702	+	0.232057i	$0.0745456\pi$
$587$	40.2191	+	23.2205i	1.66002	+	0.958413i	0.687318	+	0.726356i	$0.258788\pi$
$588$		0			0
$589$	10.1578	+	17.5938i	0.418544	+	0.724939i
$590$	−10.5821	+	6.10961i	−0.435660	+	0.251529i
$591$		0			0
$592$		−	4.71191i		−	0.193658i
$593$	−17.5462	+	10.1303i	−0.720535	+	0.416001i	−0.814950	−	0.579532i	$-0.803235\pi$
$593$	−17.5462	+	10.1303i	−0.720535	+	0.416001i	0.0944146	+	0.995533i	$0.469902\pi$
$594$		0			0
$595$	−0.624315	−	1.01816i	−0.0255944	−	0.0417404i
$596$	−0.673533	−	0.388864i	−0.0275890	−	0.0159285i
$597$		0			0
$598$	−6.02179	+	5.23603i	−0.246249	+	0.214117i
$599$	−19.4938	+	33.7642i	−0.796494	+	1.37957i	0.125391	+	0.992107i	$0.459981\pi$
$599$	−19.4938	+	33.7642i	−0.796494	+	1.37957i	−0.921886	+	0.387462i	$0.873352\pi$
$600$		0			0
$601$	−9.56951	+	16.5749i	−0.390348	+	0.676103i	−0.992495	−	0.122282i	$-0.960979\pi$
$601$	−9.56951	+	16.5749i	−0.390348	+	0.676103i	0.602147	+	0.798385i	$0.294312\pi$
$602$	−8.48182	−	13.8325i	−0.345693	−	0.563771i
$603$		0			0
$604$	0.127674	+	0.0737127i	0.00519499	+	0.00299933i
$605$		−	13.5315i		−	0.550134i
$606$		0			0
$607$	−21.6668	+	37.5280i	−0.879428	+	1.52321i	−0.0274572	+	0.999623i	$0.508741\pi$
$607$	−21.6668	+	37.5280i	−0.879428	+	1.52321i	−0.851970	+	0.523590i	$0.824592\pi$
$608$	−1.62200	+	2.80939i	−0.0657808	+	0.113936i
$609$		0			0
$610$	−8.11595			−0.328605
$611$	−13.1058	−	4.51081i	−0.530205	−	0.182488i
$612$		0			0
$613$	8.92834	−	5.15478i	0.360612	−	0.208200i	−0.308737	−	0.951147i	$-0.599906\pi$
$613$	8.92834	−	5.15478i	0.360612	−	0.208200i	0.669349	+	0.742948i	$0.266573\pi$
$614$	5.84154			0.235745
$615$		0			0
$616$	34.4042	−	21.0960i	1.38619	−	0.849982i
$617$	9.58684	−	5.53497i	0.385952	−	0.222829i	−0.294453	−	0.955666i	$-0.595137\pi$
$617$	9.58684	−	5.53497i	0.385952	−	0.222829i	0.680405	+	0.732837i	$0.261804\pi$
$618$		0			0
$619$	29.2384	+	16.8808i	1.17519	+	0.678498i	0.954897	−	0.296936i	$-0.0959647\pi$
$619$	29.2384	+	16.8808i	1.17519	+	0.678498i	0.220295	+	0.975433i	$0.429298\pi$
$620$	0.275118			0.0110490
$621$		0			0
$622$	−32.5447	−	18.7897i	−1.30492	−	0.753399i
$623$	13.2491	−	0.350597i	0.530816	−	0.0140464i
$624$		0			0
$625$	−7.83931	−	13.5781i	−0.313573	−	0.543124i
$626$	3.22098	−	1.85964i	0.128736	−	0.0743260i
$627$		0			0
$628$	−0.189389	+	0.328031i	−0.00755745	+	0.0130899i
$629$		−	0.695623i		−	0.0277363i
$630$		0			0
$631$	33.4264	−	19.2987i	1.33068	−	0.768271i	0.345280	−	0.938500i	$-0.387784\pi$
$631$	33.4264	−	19.2987i	1.33068	−	0.768271i	0.985405	+	0.170229i	$0.0544507\pi$
$632$	28.4887	−	16.4480i	1.13322	−	0.654265i
$633$		0			0
$634$	−16.5972	−	28.7473i	−0.659161	−	1.14170i
$635$			1.54525i			0.0613215i
$636$		0			0
$637$	17.5447	+	18.1434i	0.695148	+	0.718867i
$638$	−16.5763			−0.656260
$639$		0			0
$640$	−4.19480	−	7.26560i	−0.165814	−	0.287198i
$641$	19.5228			0.771105			0.385553	−	0.922686i	$-0.374011\pi$
$641$	19.5228			0.771105			0.385553	+	0.922686i	$0.374011\pi$
$642$		0			0
$643$	10.8009	−	6.23589i	0.425945	−	0.245920i	−0.271673	−	0.962390i	$-0.587577\pi$
$643$	10.8009	−	6.23589i	0.425945	−	0.245920i	0.697618	+	0.716470i	$0.254243\pi$
$644$	−0.0110307	−	0.416853i	−0.000434670	−	0.0164263i
$645$		0			0
$646$	2.25725	−	3.90967i	0.0888103	−	0.153824i
$647$	−17.9695	−	31.1241i	−0.706455	−	1.22362i	−0.966164	−	0.257929i	$-0.916960\pi$
$647$	−17.9695	−	31.1241i	−0.706455	−	1.22362i	0.259709	−	0.965687i	$-0.416373\pi$
$648$		0			0
$649$	−28.9778	−	50.1910i	−1.13748	−	1.97017i
$650$	4.13023	+	21.2336i	0.162001	+	0.832849i
$651$		0			0
$652$	1.22139	+	0.705171i	0.0478334	+	0.0276166i
$653$	−4.85888			−0.190143			−0.0950713	−	0.995470i	$-0.530308\pi$
$653$	−4.85888			−0.190143			−0.0950713	+	0.995470i	$0.530308\pi$
$654$		0			0
$655$	10.8755	+	6.27897i	0.424941	+	0.245340i
$656$	3.04810	+	1.75982i	0.119008	+	0.0687095i
$657$		0			0
$658$	−11.9571	+	7.33186i	−0.466137	+	0.285826i
$659$	−11.8103	−	20.4560i	−0.460063	−	0.796853i	0.538900	−	0.842370i	$-0.318840\pi$
$659$	−11.8103	−	20.4560i	−0.460063	−	0.796853i	−0.998964	+	0.0455166i	$0.985507\pi$
$660$		0			0
$661$	14.1970	−	8.19662i	0.552198	−	0.318812i	−0.197810	−	0.980240i	$-0.563383\pi$
$661$	14.1970	−	8.19662i	0.552198	−	0.318812i	0.750008	+	0.661429i	$0.230050\pi$
$662$	−0.427316	+	0.740134i	−0.0166081	+	0.0287661i
$663$		0			0
$664$	16.8393			0.653492
$665$	0.329675	+	12.4585i	0.0127842	+	0.483119i
$666$		0			0
$667$	−1.82968	+	3.16910i	−0.0708456	+	0.122708i
$668$	0.384544	+	0.222016i	0.0148784	+	0.00859007i
$669$		0			0
$670$	7.07040	+	4.08210i	0.273154	+	0.157705i
$671$		−	38.4939i		−	1.48604i
$672$		0			0
$673$	−7.12678	+	12.3439i	−0.274717	+	0.475824i	−0.970064	−	0.242851i	$-0.921918\pi$
$673$	−7.12678	+	12.3439i	−0.274717	+	0.475824i	0.695347	+	0.718675i	$0.255251\pi$
$674$		−	7.88982i		−	0.303904i
$675$		0			0
$676$	−0.177356	+	1.26432i	−0.00682138	+	0.0486276i
$677$	−5.13574	−	8.89537i	−0.197383	−	0.341877i	0.750296	−	0.661102i	$-0.229911\pi$
$677$	−5.13574	−	8.89537i	−0.197383	−	0.341877i	−0.947679	+	0.319225i	$0.896577\pi$
$678$		0			0
$679$	14.7269	+	24.0172i	0.565165	+	0.921695i
$680$	−0.653092	−	1.13119i	−0.0250449	−	0.0433791i
$681$		0			0
$682$		−	25.2691i		−	0.967604i
$683$			2.22201i			0.0850230i	0.999096	+	0.0425115i	$0.0135359\pi$
$683$			2.22201i			0.0850230i	−0.999096	+	0.0425115i	$0.986464\pi$
$684$		0			0
$685$	3.16377	+	5.47981i	0.120881	+	0.209373i
$686$	25.4601	−	2.02494i	0.972069	−	0.0773127i
$687$		0			0
$688$	−8.43604	−	14.6117i	−0.321621	−	0.557064i
$689$	−19.3048	+	3.75506i	−0.735455	+	0.143056i
$690$		0			0
$691$			2.64015i			0.100436i	0.998738	+	0.0502179i	$0.0159916\pi$
$691$			2.64015i			0.100436i	−0.998738	+	0.0502179i	$0.984008\pi$
$692$	0.958402	−	1.66000i	0.0364330	−	0.0631038i
$693$		0			0
$694$			2.57174i			0.0976220i
$695$	−6.92724	−	3.99944i	−0.262765	−	0.151708i
$696$		0			0
$697$	0.449993	+	0.259804i	0.0170447	+	0.00984077i
$698$	15.3884	−	26.6534i	0.582458	−	1.00885i
$699$		0			0
$700$	−0.993552	−	0.539100i	−0.0375527	−	0.0203761i
$701$	8.89991			0.336145			0.168072	−	0.985775i	$-0.446246\pi$
$701$	8.89991			0.336145			0.168072	+	0.985775i	$0.446246\pi$
$702$		0			0
$703$	−3.62943	+	6.28635i	−0.136886	+	0.237094i
$704$	38.1355	−	22.0175i	1.43729	−	0.829818i
$705$		0			0
$706$	−1.60797	−	2.78509i	−0.0605168	−	0.104818i
$707$	8.83147	−	5.41528i	0.332142	−	0.203663i
$708$		0			0
$709$	−35.1558	−	20.2972i	−1.32030	−	0.762278i	−0.336527	−	0.941674i	$-0.609252\pi$
$709$	−35.1558	−	20.2972i	−1.32030	−	0.762278i	−0.983777	+	0.179396i	$0.942586\pi$
$710$	8.96569	+	5.17634i	0.336476	+	0.194265i
$711$		0			0
$712$	14.4951			0.543226
$713$	−4.83103	−	2.78920i	−0.180923	−	0.104456i
$714$		0			0
$715$	15.0368	−	2.92487i	0.562344	−	0.109384i
$716$	−1.02232	−	1.77071i	−0.0382059	−	0.0661745i
$717$		0			0
$718$	2.25548	+	3.90661i	0.0841738	+	0.145793i
$719$	−7.25674	+	12.5690i	−0.270631	+	0.468746i	−0.969024	−	0.246968i	$-0.920566\pi$
$719$	−7.25674	+	12.5690i	−0.270631	+	0.468746i	0.698393	+	0.715715i	$0.253899\pi$
$720$		0			0
$721$	−19.0675	+	11.6918i	−0.710109	+	0.435425i
$722$	−18.1059	+	10.4535i	−0.673834	+	0.389038i
$723$		0			0
$724$	1.62555			0.0604129
$725$	4.95984	+	8.59070i	0.184204	+	0.319051i
$726$		0			0
$727$	30.6942			1.13839			0.569193	−	0.822204i	$-0.307256\pi$
$727$	30.6942			1.13839			0.569193	+	0.822204i	$0.307256\pi$
$728$	18.6563	+	20.3433i	0.691449	+	0.753971i
$729$		0			0
$730$			5.55885i			0.205742i
$731$	−1.24542	−	2.15713i	−0.0460635	−	0.0797842i
$732$		0			0
$733$	−11.4873	+	6.63218i	−0.424292	+	0.244965i	−0.696912	−	0.717157i	$-0.745443\pi$
$733$	−11.4873	+	6.63218i	−0.424292	+	0.244965i	0.272620	+	0.962122i	$0.412110\pi$
$734$	4.95980	−	2.86354i	0.183069	−	0.105695i
$735$		0			0
$736$		−	0.890761i		−	0.0328339i
$737$	−19.3613	+	33.5348i	−0.713184	+	1.23527i
$738$		0			0
$739$	−6.28279	+	3.62737i	−0.231116	+	0.133435i	−0.611087	−	0.791564i	$-0.709267\pi$
$739$	−6.28279	+	3.62737i	−0.231116	+	0.133435i	0.379971	+	0.924999i	$0.375934\pi$
$740$	0.0491505	+	0.0851312i	0.00180681	+	0.00312948i
$741$		0			0
$742$	−9.49142	+	17.4925i	−0.348441	+	0.642171i
$743$	40.0705	+	23.1347i	1.47004	+	0.848730i	0.999435	−	0.0336128i	$-0.0107013\pi$
$743$	40.0705	+	23.1347i	1.47004	+	0.848730i	0.470608	+	0.882342i	$0.344035\pi$
$744$		0			0
$745$	−6.38250			−0.233837
$746$	13.2673	+	7.65991i	0.485752	+	0.280449i
$747$		0			0
$748$	0.251121	−	0.144985i	0.00918188	−	0.00530116i
$749$	0.677140	+	25.5893i	0.0247421	+	0.935012i
$750$		0			0
$751$	36.0260			1.31461			0.657305	−	0.753625i	$-0.271697\pi$
$751$	36.0260			1.31461			0.657305	+	0.753625i	$0.271697\pi$
$752$	−12.6306	+	7.29229i	−0.460591	+	0.265922i
$753$		0			0
$754$	−2.16473	−	11.1289i	−0.0788349	−	0.405291i
$755$	1.20986			0.0440313
$756$		0			0
$757$	5.28132	−	9.14751i	0.191953	−	0.332472i	−0.753945	−	0.656938i	$-0.771851\pi$
$757$	5.28132	−	9.14751i	0.191953	−	0.332472i	0.945897	+	0.324466i	$0.105185\pi$
$758$	3.19961	−	5.54189i	0.116215	−	0.201291i
$759$		0			0
$760$			13.6301i			0.494415i
$761$	−6.76541	−	3.90601i	−0.245246	−	0.141593i	0.372340	−	0.928097i	$-0.378556\pi$
$761$	−6.76541	−	3.90601i	−0.245246	−	0.141593i	−0.617585	+	0.786504i	$0.711889\pi$
$762$		0			0
$763$	18.3766	−	33.8678i	0.665278	−	1.22609i
$764$	−0.208695	+	0.361470i	−0.00755031	+	0.0130775i
$765$		0			0
$766$	−2.53010	+	4.38226i	−0.0914163	+	0.158338i
$767$	29.9128	−	26.0096i	1.08009	−	0.939152i
$768$		0			0
$769$	21.9030	+	12.6457i	0.789844	+	0.456017i	0.839908	−	0.542729i	$-0.182609\pi$
$769$	21.9030	+	12.6457i	0.789844	+	0.456017i	−0.0500637	+	0.998746i	$0.515942\pi$
$770$	7.39300	−	13.6252i	0.266425	−	0.491017i
$771$		0			0
$772$	−0.986345	+	0.569467i	−0.0354993	+	0.0204956i
$773$		−	46.6004i		−	1.67610i	−0.545592	−	0.838051i	$-0.683695\pi$
$773$		−	46.6004i		−	1.67610i	0.545592	−	0.838051i	$-0.316305\pi$
$774$		0			0
$775$	−13.0958	+	7.56086i	−0.470415	+	0.271594i
$776$	15.4057	+	26.6834i	0.553032	+	0.957879i
$777$		0			0
$778$	−20.1634	−	11.6414i	−0.722895	−	0.417363i
$779$	−2.71106	−	4.69570i	−0.0971339	−	0.168241i
$780$		0			0
$781$	−24.5513	+	42.5241i	−0.878515	+	1.52163i
$782$			1.23962i			0.0443289i
$783$		0			0
$784$	26.5204	−	1.40454i	0.947158	−	0.0501622i
$785$			3.10848i			0.110946i
$786$		0			0
$787$		−	39.7332i		−	1.41633i	−0.706045	−	0.708167i	$-0.749522\pi$
$787$		−	39.7332i		−	1.41633i	0.706045	−	0.708167i	$-0.250478\pi$
$788$	1.22653	+	0.708140i	0.0436935	+	0.0252265i
$789$		0			0
$790$	6.31788	−	10.9429i	0.224780	−	0.389330i
$791$	−44.0079	+	26.9848i	−1.56474	+	0.959468i
$792$		0			0
$793$	25.8439	−	5.02700i	0.917744	−	0.178514i
$794$	11.5210	−	19.9550i	0.408865	−	0.708175i
$795$		0			0
$796$	−0.693270			−0.0245723
$797$	1.39299	+	2.41273i	0.0493422	+	0.0854632i	0.889642	−	0.456659i	$-0.150954\pi$
$797$	1.39299	+	2.41273i	0.0493422	+	0.0854632i	−0.840299	+	0.542123i	$0.817621\pi$
$798$		0			0
$799$	−1.86467	+	1.07656i	−0.0659671	+	0.0380861i
$800$	−2.09115	−	1.20732i	−0.0739332	−	0.0426853i
$801$		0			0
$802$	34.9086			1.23267
$803$	−26.3656			−0.930421
$804$		0			0
$805$	−1.78887	−	2.91736i	−0.0630493	−	0.102823i
$806$	16.9651	−	3.29995i	0.597570	−	0.116236i
$807$		0			0
$808$	9.81188	−	5.66489i	0.345181	−	0.199290i
$809$	−20.7293	−	35.9042i	−0.728803	−	1.26232i	−0.957389	−	0.288801i	$-0.906744\pi$
$809$	−20.7293	−	35.9042i	−0.728803	−	1.26232i	0.228586	−	0.973524i	$-0.426590\pi$
$810$		0			0
$811$		−	27.8622i		−	0.978375i	−0.872179	−	0.489188i	$-0.837293\pi$
$811$		−	27.8622i		−	0.978375i	0.872179	−	0.489188i	$-0.162707\pi$
$812$	0.520740	+	0.282553i	0.0182744	+	0.00991566i
$813$		0			0
$814$	7.81915	−	4.51439i	0.274061	−	0.158229i
$815$	11.5741			0.405423
$816$		0			0
$817$			25.9920i			0.909344i
$818$	7.90671			0.276452
$819$		0			0
$820$	−0.0734276			−0.00256420
$821$			22.4202i			0.782469i	0.920291	+	0.391235i	$0.127952\pi$
$821$			22.4202i			0.782469i	−0.920291	+	0.391235i	$0.872048\pi$
$822$		0			0
$823$	2.36166			0.0823221			0.0411611	−	0.999153i	$-0.486894\pi$
$823$	2.36166			0.0823221			0.0411611	+	0.999153i	$0.486894\pi$
$824$	−21.1842	+	12.2307i	−0.737987	+	0.426077i
$825$		0			0
$826$	−1.06109	−	40.0990i	−0.0369201	−	1.39522i
$827$			43.3148i			1.50620i	0.657904	+	0.753102i	$0.271443\pi$
$827$			43.3148i			1.50620i	−0.657904	+	0.753102i	$0.728557\pi$
$828$		0			0
$829$	−27.4640	−	47.5690i	−0.953864	−	1.65214i	−0.736947	−	0.675951i	$-0.763733\pi$
$829$	−27.4640	−	47.5690i	−0.953864	−	1.65214i	−0.216917	−	0.976190i	$-0.569600\pi$
$830$	5.60162	−	3.23410i	0.194435	−	0.112257i
$831$		0			0
$832$	19.7623	+	22.7280i	0.685134	+	0.787951i
$833$	3.91523	−	0.207353i	0.135655	−	0.00718437i
$834$		0			0
$835$	3.64400			0.126106
$836$	−3.02584			−0.104651
$837$		0			0
$838$	−41.0190	−	23.6824i	−1.41698	−	0.818093i
$839$	12.7661	−	7.37052i	0.440735	−	0.254459i	−0.263174	−	0.964748i	$-0.584769\pi$
$839$	12.7661	−	7.37052i	0.440735	−	0.254459i	0.703910	+	0.710290i	$0.251436\pi$
$840$		0			0
$841$	11.9004	+	20.6122i	0.410360	+	0.710765i
$842$	−4.05673			−0.139804
$843$		0			0
$844$	1.29745	−	2.24725i	0.0446600	−	0.0773535i
$845$	3.92738	+	9.71340i	0.135106	+	0.334151i
$846$		0			0
$847$	39.0437	+	21.1851i	1.34156	+	0.727928i
$848$	−10.3471	+	17.9217i	−0.355321	+	0.615434i
$849$		0			0
$850$	2.91013	+	1.68017i	0.0998168	+	0.0576292i
$851$		−	1.99319i		−	0.0683256i
$852$		0			0
$853$		−	24.1038i		−	0.825297i	−0.910890	−	0.412649i	$-0.864604\pi$
$853$		−	24.1038i		−	0.825297i	0.910890	−	0.412649i	$-0.135396\pi$
$854$	12.7064	−	23.4177i	0.434805	−	0.801338i
$855$		0			0
$856$			27.9957i			0.956873i
$857$	9.29249	−	16.0951i	0.317425	−	0.549797i	−0.662525	−	0.749040i	$-0.730515\pi$
$857$	9.29249	−	16.0951i	0.317425	−	0.549797i	0.979950	+	0.199243i	$0.0638483\pi$
$858$		0			0
$859$	−14.7487	−	25.5456i	−0.503221	−	0.871604i	−0.999993	−	0.00372294i	$-0.998815\pi$
$859$	−14.7487	−	25.5456i	−0.503221	−	0.871604i	0.496772	−	0.867881i	$-0.334518\pi$
$860$	0.304832	+	0.175995i	0.0103947	+	0.00600137i
$861$		0			0
$862$	−27.3712	−	47.4083i	−0.932266	−	1.61473i
$863$	16.1457	−	9.32173i	0.549606	−	0.317315i	−0.199357	−	0.979927i	$-0.563885\pi$
$863$	16.1457	−	9.32173i	0.549606	−	0.317315i	0.748963	+	0.662612i	$0.230552\pi$
$864$		0			0
$865$		−	15.7304i		−	0.534851i
$866$	11.7477	−	6.78256i	0.399204	−	0.230481i
$867$		0			0
$868$	−0.430728	+	0.793824i	−0.0146199	+	0.0269441i
$869$	51.9020	+	29.9656i	1.76065	+	1.01651i
$870$		0			0
$871$	−25.0430	−	8.61938i	−0.848549	−	0.292056i
$872$	21.0705	−	36.4951i	0.713536	−	1.23588i
$873$		0			0
$874$	6.46776	−	11.2025i	0.218775	−	0.378930i
$875$	−19.9313	+	0.527420i	−0.673802	+	0.0178301i
$876$		0			0
$877$	−32.6941	−	18.8759i	−1.10400	−	0.637395i	−0.166731	−	0.986002i	$-0.553321\pi$
$877$	−32.6941	−	18.8759i	−1.10400	−	0.637395i	−0.937269	+	0.348608i	$0.886655\pi$
$878$		−	39.3673i		−	1.32858i
$879$		0			0
$880$	8.05950	−	13.9595i	0.271686	−	0.470574i
$881$	−14.9149	+	25.8334i	−0.502497	+	0.870350i	0.497499	+	0.867464i	$0.334252\pi$
$881$	−14.9149	+	25.8334i	−0.502497	+	0.870350i	−0.999996	+	0.00288515i	$0.999082\pi$
$882$		0			0
$883$	−32.3979			−1.09028			−0.545138	−	0.838346i	$-0.683523\pi$
$883$	−32.3979			−1.09028			−0.545138	+	0.838346i	$0.683523\pi$
$884$	0.130134	+	0.149663i	0.00437687	+	0.00503371i
$885$		0			0
$886$	−3.98777	+	2.30234i	−0.133972	+	0.0773487i
$887$	25.9198			0.870302			0.435151	−	0.900358i	$-0.356695\pi$
$887$	25.9198			0.870302			0.435151	+	0.900358i	$0.356695\pi$
$888$		0			0
$889$	−4.45867	−	2.41927i	−0.149539	−	0.0811397i
$890$	4.82181	−	2.78387i	0.161627	−	0.0933156i
$891$		0			0
$892$	1.95620	+	1.12941i	0.0654984	+	0.0378155i
$893$	22.4680			0.751863
$894$		0			0
$895$	−14.5315	−	8.38976i	−0.485734	−	0.280439i
$896$	27.5316	−	0.728536i	0.919765	−	0.0243387i
$897$		0			0
$898$	−12.5391	−	21.7184i	−0.418435	−	0.724751i
$899$	6.86376	−	3.96280i	0.228919	−	0.132167i
$900$		0			0
$901$	−1.52755	+	2.64579i	−0.0508901	+	0.0881442i
$902$			6.74420i			0.224557i
$903$		0			0
$904$	−48.8934	+	28.2286i	−1.62617	+	0.938869i
$905$	11.5529	−	6.67010i	0.384033	−	0.221722i
$906$		0			0
$907$	7.77113	+	13.4600i	0.258036	+	0.446931i	0.965716	−	0.259602i	$-0.0835914\pi$
$907$	7.77113	+	13.4600i	0.258036	+	0.446931i	−0.707680	+	0.706533i	$0.750258\pi$
$908$		−	0.0445240i		−	0.00147758i
$909$		0			0
$910$	10.1131	+	3.18415i	0.335246	+	0.105554i
$911$	−23.6358			−0.783090			−0.391545	−	0.920159i	$-0.628059\pi$
$911$	−23.6358			−0.783090			−0.391545	+	0.920159i	$0.628059\pi$
$912$		0			0
$913$	15.3393	+	26.5684i	0.507656	+	0.879287i
$914$	−12.0382			−0.398189
$915$		0			0
$916$	1.47421	−	0.851138i	0.0487094	−	0.0281224i
$917$	−35.1441	+	21.5497i	−1.16056	+	0.711633i
$918$		0			0
$919$	−22.2409	+	38.5223i	−0.733659	+	1.27073i	0.221651	+	0.975126i	$0.428856\pi$
$919$	−22.2409	+	38.5223i	−0.733659	+	1.27073i	−0.955309	+	0.295608i	$0.904478\pi$
$920$	−1.87132	−	3.24123i	−0.0616957	−	0.106860i
$921$		0			0
$922$	1.56608	+	2.71253i	0.0515761	+	0.0893324i
$923$	−31.7560	−	10.9299i	−1.04526	−	0.359761i
$924$		0			0
$925$	−4.67920	−	2.70154i	−0.153851	−	0.0888259i
$926$	−7.56171			−0.248493
$927$		0			0
$928$	1.09601	+	0.632782i	0.0359783	+	0.0207721i
$929$	2.54846	+	1.47135i	0.0836121	+	0.0482735i	0.541223	−	0.840879i	$-0.317961\pi$
$929$	2.54846	+	1.47135i	0.0836121	+	0.0482735i	−0.457611	+	0.889152i	$0.651295\pi$
$930$		0			0
$931$	−36.4638	−	18.5539i	−1.19505	−	0.608080i
$932$	−0.383751	−	0.664676i	−0.0125702	−	0.0217722i
$933$		0			0
$934$	22.5506	−	13.0196i	0.737878	−	0.426014i
$935$	1.18983	−	2.06085i	0.0389116	−	0.0673968i
$936$		0			0
$937$	−0.951020			−0.0310685			−0.0155342	−	0.999879i	$-0.504945\pi$
$937$	−0.951020			−0.0310685			−0.0155342	+	0.999879i	$0.504945\pi$
$938$	−22.8480	+	14.0099i	−0.746013	+	0.457440i
$939$		0			0
$940$	0.152133	−	0.263503i	0.00496205	−	0.00859451i
$941$	19.1125	+	11.0346i	0.623050	+	0.359718i	0.778056	−	0.628196i	$-0.216206\pi$
$941$	19.1125	+	11.0346i	0.623050	+	0.359718i	−0.155006	+	0.987914i	$0.549540\pi$
$942$		0			0
$943$	1.28938	+	0.744423i	0.0419879	+	0.0242417i
$944$		−	41.7105i		−	1.35756i
$945$		0			0
$946$	16.1648	−	27.9983i	0.525563	−	0.910302i
$947$			51.1717i			1.66286i	0.555631	+	0.831429i	$0.312477\pi$
$947$			51.1717i			1.66286i	−0.555631	+	0.831429i	$0.687523\pi$
$948$		0			0
$949$	−3.44314	−	17.7012i	−0.111769	−	0.574607i
$950$	−17.5326	−	30.3674i	−0.568833	−	0.985248i
$951$		0			0
$952$	4.28641	−	0.113426i	0.138923	−	0.00367617i
$953$	−22.9235	−	39.7047i	−0.742565	−	1.28616i	−0.951324	−	0.308194i	$-0.900275\pi$
$953$	−22.9235	−	39.7047i	−0.742565	−	1.28616i	0.208758	−	0.977967i	$-0.433058\pi$
$954$		0			0
$955$			3.42534i			0.110842i
$956$		−	1.32889i		−	0.0429793i
$957$		0			0
$958$	22.8478	+	39.5735i	0.738177	+	1.27856i
$959$	−20.7647	+	0.549471i	−0.670526	+	0.0177434i
$960$		0			0
$961$	−9.45905	−	16.3836i	−0.305131	−	0.528502i
$962$	4.05198	+	4.66006i	0.130641	+	0.150246i
$963$		0			0
$964$			2.21548i			0.0713559i
$965$	−4.67338	+	8.09453i	−0.150441	+	0.260572i
$966$		0			0
$967$		−	19.2609i		−	0.619387i	−0.950836	−	0.309694i	$-0.899773\pi$
$967$		−	19.2609i		−	0.619387i	0.950836	−	0.309694i	$-0.100227\pi$
$968$	42.0726	+	24.2906i	1.35226	+	0.780730i
$969$		0			0
$970$	10.2494	+	5.91752i	0.329090	+	0.190000i
$971$	23.6663	−	40.9912i	0.759487	−	1.31547i	−0.183625	−	0.982996i	$-0.558783\pi$
$971$	23.6663	−	40.9912i	0.759487	−	1.31547i	0.943112	−	0.332474i	$-0.107883\pi$
$972$		0			0
$973$	22.3853	−	13.7262i	0.717641	−	0.440043i
$974$	−22.0046			−0.705072
$975$		0			0
$976$	13.8520	−	23.9923i	0.443390	−	0.767975i
$977$	−41.4454	+	23.9285i	−1.32596	+	0.765541i	−0.984672	−	0.174418i	$-0.944195\pi$
$977$	−41.4454	+	23.9285i	−1.32596	+	0.765541i	−0.341285	+	0.939960i	$0.610862\pi$
$978$		0			0
$979$	13.2039	+	22.8698i	0.421998	+	0.730921i
$980$	−0.464499	+	0.302014i	−0.0148379	+	0.00964747i
$981$		0			0
$982$	37.8506	+	21.8531i	1.20786	+	0.697359i
$983$	−13.6560	−	7.88432i	−0.435560	−	0.251471i	0.266152	−	0.963931i	$-0.414248\pi$
$983$	−13.6560	−	7.88432i	−0.435560	−	0.251471i	−0.701712	+	0.712460i	$0.747581\pi$
$984$		0			0
$985$	11.6228			0.370335
$986$	−1.52526	−	0.880608i	−0.0485741	−	0.0280443i
$987$		0			0
$988$	−0.395151	−	2.03148i	−0.0125714	−	0.0646300i
$989$	−3.56853	−	6.18088i	−0.113473	−	0.196541i
$990$		0			0
$991$	6.06892	+	10.5117i	0.192786	+	0.333914i	0.946172	−	0.323663i	$-0.104914\pi$
$991$	6.06892	+	10.5117i	0.192786	+	0.333914i	−0.753387	+	0.657578i	$0.771581\pi$
$992$	−0.964622	+	1.67077i	−0.0306268	+	0.0530471i
$993$		0			0
$994$	−28.9726	+	17.7654i	−0.918954	+	0.563485i
$995$	−4.92715	+	2.84469i	−0.156201	+	0.0901828i
$996$		0			0
$997$	33.7876			1.07006			0.535032	−	0.844832i	$-0.320299\pi$
$997$	33.7876			1.07006			0.535032	+	0.844832i	$0.320299\pi$
$998$	16.6993	+	28.9240i	0.528607	+	0.915574i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.bm.f.550.5		12
3.2	odd	2		91.2.k.b.4.2	✓	12
7.2	even	3		819.2.do.e.667.5		12
13.10	even	6		819.2.do.e.361.5		12
21.2	odd	6		91.2.u.b.30.2	yes	12
21.5	even	6		637.2.u.g.30.2		12
21.11	odd	6		637.2.q.g.589.5		12
21.17	even	6		637.2.q.i.589.5		12
21.20	even	2		637.2.k.i.459.2		12
39.20	even	12		1183.2.e.j.508.3		24
39.23	odd	6		91.2.u.b.88.2	yes	12
39.32	even	12		1183.2.e.j.508.10		24
91.23	even	6	inner	819.2.bm.f.478.2		12
273.23	odd	6		91.2.k.b.23.5	yes	12
273.32	even	12		8281.2.a.cp.1.3		12
273.59	odd	12		8281.2.a.co.1.10		12
273.62	even	6		637.2.u.g.361.2		12
273.101	even	6		637.2.q.i.491.5		12
273.137	even	12		8281.2.a.cp.1.10		12
273.149	even	12		1183.2.e.j.170.10		24
273.179	odd	6		637.2.q.g.491.5		12
273.227	odd	12		8281.2.a.co.1.3		12
273.254	even	12		1183.2.e.j.170.3		24
273.257	even	6		637.2.k.i.569.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.2	✓	12	3.2	odd	2
91.2.k.b.23.5	yes	12	273.23	odd	6
91.2.u.b.30.2	yes	12	21.2	odd	6
91.2.u.b.88.2	yes	12	39.23	odd	6
637.2.k.i.459.2		12	21.20	even	2
637.2.k.i.569.5		12	273.257	even	6
637.2.q.g.491.5		12	273.179	odd	6
637.2.q.g.589.5		12	21.11	odd	6
637.2.q.i.491.5		12	273.101	even	6
637.2.q.i.589.5		12	21.17	even	6
637.2.u.g.30.2		12	21.5	even	6
637.2.u.g.361.2		12	273.62	even	6
819.2.bm.f.478.2		12	91.23	even	6	inner
819.2.bm.f.550.5		12	1.1	even	1	trivial
819.2.do.e.361.5		12	13.10	even	6
819.2.do.e.667.5		12	7.2	even	3
1183.2.e.j.170.3		24	273.254	even	12
1183.2.e.j.170.10		24	273.149	even	12
1183.2.e.j.508.3		24	39.20	even	12
1183.2.e.j.508.10		24	39.32	even	12
8281.2.a.co.1.3		12	273.227	odd	12
8281.2.a.co.1.10		12	273.59	odd	12
8281.2.a.cp.1.3		12	273.32	even	12
8281.2.a.cp.1.10		12	273.137	even	12

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.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.37905i q^{2} +0.0982074 q^{4} +(0.697972 - 0.402974i) q^{5} +(0.0699870 + 2.64483i) q^{7} +2.89354i q^{8} +O(q^{10})\)	\(q+1.37905i q^{2} +0.0982074 q^{4} +(0.697972 - 0.402974i) q^{5} +(0.0699870 + 2.64483i) q^{7} +2.89354i q^{8} +(0.555723 + 0.962541i) q^{10} +(-4.56532 + 2.63579i) q^{11} +(-2.36581 - 2.72084i) q^{13} +(-3.64736 + 0.0965159i) q^{14} -3.79394 q^{16} -0.560102 q^{17} +(5.06165 + 2.92234i) q^{19} +(0.0685460 - 0.0395750i) q^{20} +(-3.63490 - 6.29583i) q^{22} -1.60488 q^{23} +(-2.17522 + 3.76760i) q^{25} +(3.75219 - 3.26258i) q^{26} +(0.00687324 + 0.259741i) q^{28} +(1.14008 - 1.97467i) q^{29} +(3.01022 + 1.73795i) q^{31} +0.555034i q^{32} -0.772411i q^{34} +(1.11465 + 1.81781i) q^{35} +1.24196i q^{37} +(-4.03007 + 6.98029i) q^{38} +(1.16602 + 2.01961i) q^{40} +(-0.803413 - 0.463851i) q^{41} +(2.22356 + 3.85131i) q^{43} +(-0.448348 + 0.258854i) q^{44} -2.21321i q^{46} +(3.32915 - 1.92209i) q^{47} +(-6.99020 + 0.370207i) q^{49} +(-5.19572 - 2.99975i) q^{50} +(-0.232340 - 0.267207i) q^{52} +(2.72727 - 4.72377i) q^{53} +(-2.12431 + 3.67941i) q^{55} +(-7.65292 + 0.202510i) q^{56} +(2.72318 + 1.57223i) q^{58} +10.9940i q^{59} +(-3.65107 + 6.32385i) q^{61} +(-2.39673 + 4.15126i) q^{62} -8.35330 q^{64} +(-2.74769 - 0.945710i) q^{65} +(6.36144 - 3.67278i) q^{67} -0.0550061 q^{68} +(-2.50686 + 1.53716i) q^{70} +(8.06668 - 4.65730i) q^{71} +(4.33139 + 2.50073i) q^{73} -1.71273 q^{74} +(0.497091 + 0.286996i) q^{76} +(-7.29072 - 11.8900i) q^{77} +(-5.68437 - 9.84562i) q^{79} +(-2.64806 + 1.52886i) q^{80} +(0.639676 - 1.10795i) q^{82} -5.81962i q^{83} +(-0.390935 + 0.225707i) q^{85} +(-5.31117 + 3.06641i) q^{86} +(-7.62677 - 13.2100i) q^{88} -5.00946i q^{89} +(7.03057 - 6.44756i) q^{91} -0.157611 q^{92} +(2.65067 + 4.59109i) q^{94} +4.71051 q^{95} +(9.22171 - 5.32416i) q^{97} +(-0.510535 - 9.63988i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7}+O(q^{10}) \) 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7	\( 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7} + 12 q^{10} - 12 q^{11} - 2 q^{13} - 4 q^{14} + 16 q^{16} + 34 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 6 q^{23} - 5 q^{25} + 6 q^{26} - 9 q^{28} + q^{29} + 18 q^{31} + 6 q^{35} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 15 q^{47} - 3 q^{49} - 18 q^{50} - 7 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{56} - 24 q^{58} + 5 q^{61} - 41 q^{62} + 2 q^{64} - 21 q^{65} + 15 q^{67} - 22 q^{68} + 3 q^{70} - 30 q^{71} + 42 q^{73} - 66 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} + 63 q^{80} + 5 q^{82} - 21 q^{85} + 57 q^{86} - 14 q^{88} - 7 q^{91} + 66 q^{92} + q^{94} + 4 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7 + 12 * q^10 - 12 * q^11 - 2 * q^13 - 4 * q^14 + 16 * q^16 + 34 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 + 6 * q^23 - 5 * q^25 + 6 * q^26 - 9 * q^28 + q^29 + 18 * q^31 + 6 * q^35 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 15 * q^47 - 3 * q^49 - 18 * q^50 - 7 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^56 - 24 * q^58 + 5 * q^61 - 41 * q^62 + 2 * q^64 - 21 * q^65 + 15 * q^67 - 22 * q^68 + 3 * q^70 - 30 * q^71 + 42 * q^73 - 66 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 + 63 * q^80 + 5 * q^82 - 21 * q^85 + 57 * q^86 - 14 * q^88 - 7 * q^91 + 66 * q^92 + q^94 + 4 * q^95 - 3 * q^97 + 18 * q^98

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