LMFDB - Embedded newform 450.2.l.c.379.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [450,2,Mod(19,450)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(450, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("450.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.l (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,4,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + \cdots + 11105 $ x^16 - 4x^15 - 24x^14 + 94x^13 + 262x^12 - 936x^11 - 1584x^10 + 4642x^9 + 6259x^8 - 11958x^7 - 15752x^6 + 14670x^5 + 18271x^4 - 10440x^3 + 1135x^2 + 21080*x + 11105
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			379.3
Root			$3.42137 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	450.379
Dual form			450.2.l.c.19.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.951057 + 0.309017i) q^{2} +(0.809017 + 0.587785i) q^{4} +(-2.23558 - 0.0466062i) q^{5} +3.52206i q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.11176 - 0.735158i) q^{10} +(-1.62388 + 4.99779i) q^{11} +(-0.588802 + 0.191313i) q^{13} +(-1.08838 + 3.34968i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-2.02525 - 2.78752i) q^{17} +(1.83995 - 1.33680i) q^{19} +(-1.78123 - 1.35175i) q^{20} +(-3.08880 + 4.25137i) q^{22} +(8.51557 + 2.76688i) q^{23} +(4.99566 + 0.208384i) q^{25} -0.619103 q^{26} +(-2.07022 + 2.84941i) q^{28} +(2.16949 + 1.57623i) q^{29} +(-7.90309 + 5.74193i) q^{31} +1.00000i q^{32} +(-1.06474 - 3.27693i) q^{34} +(0.164150 - 7.87386i) q^{35} +(-0.952702 + 0.309552i) q^{37} +(2.16299 - 0.702799i) q^{38} +(-1.27634 - 1.83602i) q^{40} +(-1.94584 - 5.98868i) q^{41} -1.51251i q^{43} +(-4.25137 + 3.08880i) q^{44} +(7.24378 + 5.26291i) q^{46} +(6.27522 - 8.63710i) q^{47} -5.40494 q^{49} +(4.68676 + 1.74193i) q^{50} +(-0.588802 - 0.191313i) q^{52} +(-0.325260 + 0.447681i) q^{53} +(3.86324 - 11.0973i) q^{55} +(-2.84941 + 2.07022i) q^{56} +(1.57623 + 2.16949i) q^{58} +(0.0861451 + 0.265127i) q^{59} +(1.13786 - 3.50196i) q^{61} +(-9.29064 + 3.01871i) q^{62} +(-0.309017 + 0.951057i) q^{64} +(1.32523 - 0.400255i) q^{65} +(-7.00176 - 9.63710i) q^{67} -3.44557i q^{68} +(2.58927 - 7.43777i) q^{70} +(3.84168 + 2.79115i) q^{71} +(9.35277 + 3.03890i) q^{73} -1.00173 q^{74} +2.27431 q^{76} +(-17.6025 - 5.71941i) q^{77} +(5.27525 + 3.83269i) q^{79} +(-0.646508 - 2.14057i) q^{80} -6.29687i q^{82} +(1.56335 + 2.15177i) q^{83} +(4.39770 + 6.32612i) q^{85} +(0.467392 - 1.43848i) q^{86} +(-4.99779 + 1.62388i) q^{88} +(-4.13649 + 12.7308i) q^{89} +(-0.673818 - 2.07380i) q^{91} +(5.26291 + 7.24378i) q^{92} +(8.63710 - 6.27522i) q^{94} +(-4.17567 + 2.90278i) q^{95} +(-2.56983 + 3.53706i) q^{97} +(-5.14040 - 1.67022i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 4 q^{5} + 2 q^{10} - 2 q^{11} + 20 q^{13} - 2 q^{14} - 4 q^{16} + 30 q^{17} + 4 q^{20} - 20 q^{22} + 10 q^{23} + 24 q^{25} - 4 q^{26} + 10 q^{29} - 18 q^{31} + 12 q^{34} + 34 q^{35} + 20 q^{37}+ \cdots - 60 q^{98}+O(q^{100}) $ 16 * q + 4 * q^4 - 4 * q^5 + 2 * q^10 - 2 * q^11 + 20 * q^13 - 2 * q^14 - 4 * q^16 + 30 * q^17 + 4 * q^20 - 20 * q^22 + 10 * q^23 + 24 * q^25 - 4 * q^26 + 10 * q^29 - 18 * q^31 + 12 * q^34 + 34 * q^35 + 20 * q^37 - 10 * q^38 - 2 * q^40 - 22 * q^41 - 8 * q^44 - 6 * q^46 + 50 * q^47 - 52 * q^49 - 12 * q^50 + 20 * q^52 - 30 * q^53 + 18 * q^55 + 2 * q^56 - 30 * q^58 - 20 * q^59 + 12 * q^61 - 50 * q^62 + 4 * q^64 + 8 * q^65 - 50 * q^67 - 12 * q^70 + 28 * q^71 + 20 * q^73 - 12 * q^74 + 20 * q^76 - 100 * q^77 - 20 * q^79 - 4 * q^80 + 30 * q^83 - 4 * q^85 + 6 * q^86 - 70 * q^89 + 12 * q^91 + 30 * q^92 + 2 * q^94 + 30 * q^95 - 10 * q^97 - 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$3$		0			0
$3$		0			0
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−2.23558	−	0.0466062i	−0.999783	−	0.0208429i
$5$	−2.23558	−	0.0466062i	−0.999783	−	0.0208429i
$6$		0			0
$7$			3.52206i			1.33122i	0.746302	+	0.665608i	$0.231828\pi$
$7$			3.52206i			1.33122i	−0.746302	+	0.665608i	$0.768172\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$		0			0
$10$	−2.11176	−	0.735158i	−0.667798	−	0.232477i
$11$	−1.62388	+	4.99779i	−0.489618	+	1.50689i	0.335561	+	0.942018i	$0.391074\pi$
$11$	−1.62388	+	4.99779i	−0.489618	+	1.50689i	−0.825179	+	0.564871i	$0.808926\pi$
$12$		0			0
$13$	−0.588802	+	0.191313i	−0.163304	+	0.0530608i	−0.389528	−	0.921015i	$-0.627362\pi$
$13$	−0.588802	+	0.191313i	−0.163304	+	0.0530608i	0.226224	+	0.974075i	$0.427362\pi$
$14$	−1.08838	+	3.34968i	−0.290881	+	0.895240i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−2.02525	−	2.78752i	−0.491196	−	0.676073i	0.489412	−	0.872053i	$-0.337211\pi$
$17$	−2.02525	−	2.78752i	−0.491196	−	0.676073i	−0.980608	+	0.195979i	$0.937211\pi$
$18$		0			0
$19$	1.83995	−	1.33680i	0.422114	−	0.306684i	−0.356374	−	0.934343i	$-0.615987\pi$
$19$	1.83995	−	1.33680i	0.422114	−	0.306684i	0.778488	+	0.627660i	$0.215987\pi$
$20$	−1.78123	−	1.35175i	−0.398295	−	0.302260i
$21$		0			0
$22$	−3.08880	+	4.25137i	−0.658535	+	0.906395i
$23$	8.51557	+	2.76688i	1.77562	+	0.576934i	0.998618	−	0.0525639i	$-0.0167393\pi$
$23$	8.51557	+	2.76688i	1.77562	+	0.576934i	0.777002	+	0.629498i	$0.216739\pi$
$24$		0			0
$25$	4.99566	+	0.208384i	0.999131	+	0.0416768i
$26$	−0.619103			−0.121416
$27$		0			0
$28$	−2.07022	+	2.84941i	−0.391234	+	0.538488i
$29$	2.16949	+	1.57623i	0.402864	+	0.292698i	0.770706	−	0.637190i	$-0.219904\pi$
$29$	2.16949	+	1.57623i	0.402864	+	0.292698i	−0.367843	+	0.929888i	$0.619904\pi$
$30$		0			0
$31$	−7.90309	+	5.74193i	−1.41944	+	1.03128i	−0.427572	+	0.903981i	$0.640631\pi$
$31$	−7.90309	+	5.74193i	−1.41944	+	1.03128i	−0.991864	+	0.127300i	$0.959369\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−1.06474	−	3.27693i	−0.182601	−	0.561989i
$35$	0.164150	−	7.87386i	0.0277464	−	1.33093i
$36$		0			0
$37$	−0.952702	+	0.309552i	−0.156623	+	0.0508900i	−0.386279	−	0.922382i	$-0.626240\pi$
$37$	−0.952702	+	0.309552i	−0.156623	+	0.0508900i	0.229656	+	0.973272i	$0.426240\pi$
$38$	2.16299	−	0.702799i	0.350884	−	0.114009i
$39$		0			0
$40$	−1.27634	−	1.83602i	−0.201807	−	0.290300i
$41$	−1.94584	−	5.98868i	−0.303889	−	0.935274i	−0.980089	−	0.198557i	$-0.936375\pi$
$41$	−1.94584	−	5.98868i	−0.303889	−	0.935274i	0.676200	−	0.736718i	$-0.263625\pi$
$42$		0			0
$43$		−	1.51251i		−	0.230656i	−0.993327	−	0.115328i	$-0.963208\pi$
$43$		−	1.51251i		−	0.230656i	0.993327	−	0.115328i	$-0.0367919\pi$
$44$	−4.25137	+	3.08880i	−0.640918	+	0.465654i
$45$		0			0
$46$	7.24378	+	5.26291i	1.06804	+	0.775974i
$47$	6.27522	−	8.63710i	0.915335	−	1.25985i	−0.0499772	−	0.998750i	$-0.515915\pi$
$47$	6.27522	−	8.63710i	0.915335	−	1.25985i	0.965312	−	0.261100i	$-0.0840851\pi$
$48$		0			0
$49$	−5.40494			−0.772134
$50$	4.68676	+	1.74193i	0.662808	+	0.246346i
$51$		0			0
$52$	−0.588802	−	0.191313i	−0.0816522	−	0.0265304i
$53$	−0.325260	+	0.447681i	−0.0446778	+	0.0614938i	−0.830771	−	0.556614i	$-0.812100\pi$
$53$	−0.325260	+	0.447681i	−0.0446778	+	0.0614938i	0.786094	+	0.618107i	$0.212100\pi$
$54$		0			0
$55$	3.86324	−	11.0973i	0.520920	−	1.49636i
$56$	−2.84941	+	2.07022i	−0.380768	+	0.276644i
$57$		0			0
$58$	1.57623	+	2.16949i	0.206968	+	0.284868i
$59$	0.0861451	+	0.265127i	0.0112151	+	0.0345166i	0.956507	−	0.291708i	$-0.0942235\pi$
$59$	0.0861451	+	0.265127i	0.0112151	+	0.0345166i	−0.945292	+	0.326224i	$0.894223\pi$
$60$		0			0
$61$	1.13786	−	3.50196i	0.145688	−	0.448380i	−0.851411	−	0.524499i	$-0.824253\pi$
$61$	1.13786	−	3.50196i	0.145688	−	0.448380i	0.997099	+	0.0761185i	$0.0242527\pi$
$62$	−9.29064	+	3.01871i	−1.17991	+	0.383377i
$63$		0			0
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	1.32523	−	0.400255i	0.164375	−	0.0496455i
$66$		0			0
$67$	−7.00176	−	9.63710i	−0.855401	−	1.17736i	−0.982647	−	0.185487i	$-0.940614\pi$
$67$	−7.00176	−	9.63710i	−0.855401	−	1.17736i	0.127245	−	0.991871i	$-0.459386\pi$
$68$		−	3.44557i		−	0.417836i
$69$		0			0
$70$	2.58927	−	7.43777i	0.309477	−	0.888983i
$71$	3.84168	+	2.79115i	0.455924	+	0.331248i	0.791930	−	0.610612i	$-0.209076\pi$
$71$	3.84168	+	2.79115i	0.455924	+	0.331248i	−0.336006	+	0.941860i	$0.609076\pi$
$72$		0			0
$73$	9.35277	+	3.03890i	1.09466	+	0.355676i	0.800045	−	0.599940i	$-0.204809\pi$
$73$	9.35277	+	3.03890i	1.09466	+	0.355676i	0.294614	+	0.955616i	$0.404809\pi$
$74$	−1.00173			−0.116449
$75$		0			0
$76$	2.27431			0.260881
$77$	−17.6025	−	5.71941i	−2.00599	−	0.651787i
$78$		0			0
$79$	5.27525	+	3.83269i	0.593512	+	0.431212i	0.843570	−	0.537019i	$-0.180450\pi$
$79$	5.27525	+	3.83269i	0.593512	+	0.431212i	−0.250058	+	0.968231i	$0.580450\pi$
$80$	−0.646508	−	2.14057i	−0.0722818	−	0.239323i
$81$		0			0
$82$		−	6.29687i		−	0.695373i
$83$	1.56335	+	2.15177i	0.171600	+	0.236187i	0.886151	−	0.463396i	$-0.153369\pi$
$83$	1.56335	+	2.15177i	0.171600	+	0.236187i	−0.714551	+	0.699583i	$0.753369\pi$
$84$		0			0
$85$	4.39770	+	6.32612i	0.476998	+	0.686164i
$86$	0.467392	−	1.43848i	0.0504002	−	0.155116i
$87$		0			0
$88$	−4.99779	+	1.62388i	−0.532766	+	0.173106i
$89$	−4.13649	+	12.7308i	−0.438467	+	1.34946i	0.451024	+	0.892512i	$0.351059\pi$
$89$	−4.13649	+	12.7308i	−0.438467	+	1.34946i	−0.889491	+	0.456952i	$0.848941\pi$
$90$		0			0
$91$	−0.673818	−	2.07380i	−0.0706353	−	0.217393i
$92$	5.26291	+	7.24378i	0.548697	+	0.755216i
$93$		0			0
$94$	8.63710	−	6.27522i	0.890848	−	0.647239i
$95$	−4.17567	+	2.90278i	−0.428414	+	0.297819i
$96$		0			0
$97$	−2.56983	+	3.53706i	−0.260926	+	0.359134i	−0.919300	−	0.393557i	$-0.871244\pi$
$97$	−2.56983	+	3.53706i	−0.260926	+	0.359134i	0.658374	+	0.752691i	$0.271244\pi$
$98$	−5.14040	−	1.67022i	−0.519259	−	0.168717i
$99$		0			0
$100$	3.91909	+	3.10496i	0.391909	+	0.310496i
$101$	14.2687			1.41979			0.709893	−	0.704309i	$-0.248743\pi$
$101$	14.2687			1.41979			0.709893	+	0.704309i	$0.248743\pi$
$102$		0			0
$103$	10.3852	−	14.2939i	1.02328	−	1.40842i	0.113401	−	0.993549i	$-0.463825\pi$
$103$	10.3852	−	14.2939i	1.02328	−	1.40842i	0.909879	−	0.414875i	$-0.136175\pi$
$104$	−0.500865	−	0.363900i	−0.0491138	−	0.0356833i
$105$		0			0
$106$	−0.447681	+	0.325260i	−0.0434827	+	0.0315920i
$107$			0.723713i			0.0699640i	0.999388	+	0.0349820i	$0.0111374\pi$
$107$			0.723713i			0.0699640i	−0.999388	+	0.0349820i	$0.988863\pi$
$108$		0			0
$109$	0.795198	+	2.44737i	0.0761661	+	0.234415i	0.981890	−	0.189454i	$-0.0606717\pi$
$109$	0.795198	+	2.44737i	0.0761661	+	0.234415i	−0.905724	+	0.423869i	$0.860672\pi$
$110$	7.10341	−	9.36033i	0.677284	−	0.892473i
$111$		0			0
$112$	−3.34968	+	1.08838i	−0.316515	+	0.102842i
$113$	14.4448	−	4.69339i	1.35885	−	0.441517i	0.463191	−	0.886258i	$-0.346704\pi$
$113$	14.4448	−	4.69339i	1.35885	−	0.441517i	0.895659	+	0.444741i	$0.146704\pi$
$114$		0			0
$115$	−18.9083	−	6.58246i	−1.76321	−	0.613818i
$116$	0.828671	+	2.55039i	0.0769401	+	0.236797i
$117$		0			0
$118$			0.278771i			0.0256630i
$119$	9.81783	−	7.13307i	0.899999	−	0.653888i
$120$		0			0
$121$	−13.4417	−	9.76597i	−1.22197	−	0.887815i
$122$	2.16433	−	2.97895i	0.195949	−	0.269701i
$123$		0			0
$124$	−9.76875			−0.877260
$125$	−11.1585	−	0.698687i	−0.998045	−	0.0624925i
$126$		0			0
$127$	4.15027	+	1.34850i	0.368277	+	0.119660i	0.487308	−	0.873230i	$-0.337979\pi$
$127$	4.15027	+	1.34850i	0.368277	+	0.119660i	−0.119031	+	0.992891i	$0.537979\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$		0			0
$130$	1.38406	+	0.0288540i	0.121390	+	0.00253066i
$131$	−0.499797	+	0.363124i	−0.0436675	+	0.0317263i	−0.609405	−	0.792859i	$-0.708592\pi$
$131$	−0.499797	+	0.363124i	−0.0436675	+	0.0317263i	0.565737	+	0.824585i	$0.308592\pi$
$132$		0			0
$133$	4.70831	+	6.48043i	0.408262	+	0.561925i
$134$	−3.68104	−	11.3291i	−0.317994	−	0.978684i
$135$		0			0
$136$	1.06474	−	3.27693i	0.0913006	−	0.280994i
$137$	−8.81784	+	2.86509i	−0.753359	+	0.244781i	−0.660426	−	0.750891i	$-0.729624\pi$
$137$	−8.81784	+	2.86509i	−0.753359	+	0.244781i	−0.0929329	+	0.995672i	$0.529624\pi$
$138$		0			0
$139$	−5.79774	+	17.8436i	−0.491757	+	1.51347i	0.330192	+	0.943914i	$0.392886\pi$
$139$	−5.79774	+	17.8436i	−0.491757	+	1.51347i	−0.821950	+	0.569560i	$0.807114\pi$
$140$	4.76094	−	6.27361i	0.402373	−	0.530216i
$141$		0			0
$142$	2.79115	+	3.84168i	0.234228	+	0.322387i
$143$		−	3.25338i		−	0.272061i
$144$		0			0
$145$	−4.77661	−	3.62489i	−0.396676	−	0.301031i
$146$	7.95594	+	5.78033i	0.658438	+	0.478383i
$147$		0			0
$148$	−0.952702	−	0.309552i	−0.0783116	−	0.0254450i
$149$	−16.8396			−1.37955			−0.689777	−	0.724022i	$-0.742291\pi$
$149$	−16.8396			−1.37955			−0.689777	+	0.724022i	$0.742291\pi$
$150$		0			0
$151$	16.7932			1.36661			0.683305	−	0.730133i	$-0.260542\pi$
$151$	16.7932			1.36661			0.683305	+	0.730133i	$0.260542\pi$
$152$	2.16299	+	0.702799i	0.175442	+	0.0570045i
$153$		0			0
$154$	−14.9736	−	10.8790i	−1.20661	−	0.876652i
$155$	17.9356	−	12.4682i	1.44062	−	1.00147i
$156$		0			0
$157$		−	4.55451i		−	0.363489i	−0.983346	−	0.181745i	$-0.941826\pi$
$157$		−	4.55451i		−	0.363489i	0.983346	−	0.181745i	$-0.0581744\pi$
$158$	3.83269	+	5.27525i	0.304913	+	0.419676i
$159$		0			0
$160$	0.0466062	−	2.23558i	0.00368454	−	0.176738i
$161$	−9.74512	+	29.9924i	−0.768023	+	2.36373i
$162$		0			0
$163$	19.2239	−	6.24624i	1.50574	−	0.489243i	0.564051	−	0.825740i	$-0.309242\pi$
$163$	19.2239	−	6.24624i	1.50574	−	0.489243i	0.941685	+	0.336497i	$0.109242\pi$
$164$	1.94584	−	5.98868i	0.151945	−	0.467637i
$165$		0			0
$166$	0.821902	+	2.52955i	0.0637920	+	0.196331i
$167$	4.22725	+	5.81831i	0.327114	+	0.450234i	0.940623	−	0.339454i	$-0.110242\pi$
$167$	4.22725	+	5.81831i	0.327114	+	0.450234i	−0.613508	+	0.789688i	$0.710242\pi$
$168$		0			0
$169$	−10.2071	+	7.41592i	−0.785164	+	0.570455i
$170$	2.22759	+	7.37547i	0.170848	+	0.565672i
$171$		0			0
$172$	0.889032	−	1.22365i	0.0677881	−	0.0933023i
$173$	−5.83145	−	1.89475i	−0.443357	−	0.144055i	0.0788271	−	0.996888i	$-0.474883\pi$
$173$	−5.83145	−	1.89475i	−0.443357	−	0.144055i	−0.522184	+	0.852833i	$0.674883\pi$
$174$		0			0
$175$	−0.733941	+	17.5950i	−0.0554807	+	1.33006i
$176$	−5.25498			−0.396109
$177$		0			0
$178$	−7.86808	+	10.8295i	−0.589737	+	0.811704i
$179$	−11.5930	−	8.42280i	−0.866501	−	0.629549i	0.0631451	−	0.998004i	$-0.479887\pi$
$179$	−11.5930	−	8.42280i	−0.866501	−	0.629549i	−0.929646	+	0.368455i	$0.879887\pi$
$180$		0			0
$181$	−12.7254	+	9.24554i	−0.945871	+	0.687215i	−0.949827	−	0.312777i	$-0.898741\pi$
$181$	−12.7254	+	9.24554i	−0.945871	+	0.687215i	0.00395575	+	0.999992i	$0.498741\pi$
$182$		−	2.18052i		−	0.161631i
$183$		0			0
$184$	2.76688	+	8.51557i	0.203977	+	0.627776i
$185$	2.14427	−	0.647626i	0.157650	−	0.0476144i
$186$		0			0
$187$	17.2202	−	5.59518i	1.25927	−	0.409160i
$188$	10.1535	−	3.29908i	0.740521	−	0.240610i
$189$		0			0
$190$	−4.86830	+	1.47036i	−0.353184	+	0.106671i
$191$	1.11938	+	3.44511i	0.0809958	+	0.249279i	0.983352	−	0.181712i	$-0.0581639\pi$
$191$	1.11938	+	3.44511i	0.0809958	+	0.249279i	−0.902356	+	0.430992i	$0.858164\pi$
$192$		0			0
$193$		−	9.72486i		−	0.700010i	−0.936748	−	0.350005i	$-0.886180\pi$
$193$		−	9.72486i		−	0.700010i	0.936748	−	0.350005i	$-0.113820\pi$
$194$	−3.53706	+	2.56983i	−0.253946	+	0.184503i
$195$		0			0
$196$	−4.37269	−	3.17694i	−0.312335	−	0.226925i
$197$	−4.15786	+	5.72280i	−0.296235	+	0.407732i	−0.931027	−	0.364951i	$-0.881086\pi$
$197$	−4.15786	+	5.72280i	−0.296235	+	0.407732i	0.634792	+	0.772683i	$0.281086\pi$
$198$		0			0
$199$	17.6745			1.25291			0.626455	−	0.779457i	$-0.284505\pi$
$199$	17.6745			1.25291			0.626455	+	0.779457i	$0.284505\pi$
$200$	2.76779	+	4.16406i	0.195712	+	0.294443i
$201$		0			0
$202$	13.5703	+	4.40926i	0.954804	+	0.310235i
$203$	−5.55157	+	7.64108i	−0.389644	+	0.536298i
$204$		0			0
$205$	4.07098	+	13.4789i	0.284329	+	0.941405i
$206$	14.2939	−	10.3852i	0.995906	−	0.723568i
$207$		0			0
$208$	−0.363900	−	0.500865i	−0.0252319	−	0.0347287i
$209$	3.69320	+	11.3665i	0.255464	+	0.786237i
$210$		0			0
$211$	−3.63522	+	11.1881i	−0.250259	+	0.770218i	0.744468	+	0.667658i	$0.232703\pi$
$211$	−3.63522	+	11.1881i	−0.250259	+	0.770218i	−0.994727	+	0.102559i	$0.967297\pi$
$212$	−0.526281	+	0.170999i	−0.0361451	+	0.0117443i
$213$		0			0
$214$	−0.223640	+	0.688292i	−0.0152877	+	0.0470507i
$215$	−0.0704924	+	3.38135i	−0.00480754	+	0.230606i
$216$		0			0
$217$	−20.2234	−	27.8352i	−1.37286	−	1.88958i
$218$			2.57331i			0.174287i
$219$		0			0
$220$	9.64825	−	6.70713i	0.650485	−	0.452195i
$221$	1.72576	+	1.25384i	0.116087	+	0.0843424i
$222$		0			0
$223$	−12.0789	−	3.92466i	−0.808860	−	0.262815i	−0.124745	−	0.992189i	$-0.539811\pi$
$223$	−12.0789	−	3.92466i	−0.808860	−	0.262815i	−0.684115	+	0.729374i	$0.739811\pi$
$224$	−3.52206			−0.235328
$225$		0			0
$226$	15.1881			1.01030
$227$	−13.5679	−	4.40848i	−0.900533	−	0.292601i	−0.178076	−	0.984017i	$-0.556987\pi$
$227$	−13.5679	−	4.40848i	−0.900533	−	0.292601i	−0.722457	+	0.691416i	$0.756987\pi$
$228$		0			0
$229$	7.12184	+	5.17432i	0.470625	+	0.341929i	0.797685	−	0.603075i	$-0.206058\pi$
$229$	7.12184	+	5.17432i	0.470625	+	0.341929i	−0.327060	+	0.945004i	$0.606058\pi$
$230$	−15.9488	−	12.1033i	−1.05163	−	0.798067i
$231$		0			0
$232$			2.68163i			0.176058i
$233$	−8.86158	−	12.1969i	−0.580542	−	0.799047i	0.413213	−	0.910634i	$-0.364406\pi$
$233$	−8.86158	−	12.1969i	−0.580542	−	0.799047i	−0.993755	+	0.111587i	$0.964406\pi$
$234$		0			0
$235$	−14.4313	+	19.0165i	−0.941395	+	1.24050i
$236$	−0.0861451	+	0.265127i	−0.00560757	+	0.0172583i
$237$		0			0
$238$	11.5416	−	3.75008i	0.748128	−	0.243081i
$239$	−1.93007	+	5.94013i	−0.124846	+	0.384235i	−0.993873	−	0.110529i	$-0.964746\pi$
$239$	−1.93007	+	5.94013i	−0.124846	+	0.384235i	0.869027	+	0.494764i	$0.164746\pi$
$240$		0			0
$241$	−4.57636	−	14.0846i	−0.294790	−	0.907269i	−0.983292	−	0.182035i	$-0.941732\pi$
$241$	−4.57636	−	14.0846i	−0.294790	−	0.907269i	0.688503	−	0.725234i	$-0.258268\pi$
$242$	−9.76597	−	13.4417i	−0.627780	−	0.864065i
$243$		0			0
$244$	2.97895	−	2.16433i	0.190708	−	0.138557i
$245$	12.0832	+	0.251903i	0.771966	+	0.0160935i
$246$		0			0
$247$	−0.827619	+	1.13912i	−0.0526601	+	0.0724805i
$248$	−9.29064	−	3.01871i	−0.589956	−	0.191688i
$249$		0			0
$250$	−10.3964	−	4.11265i	−0.657529	−	0.260107i
$251$	−18.2744			−1.15347			−0.576735	−	0.816931i	$-0.695673\pi$
$251$	−18.2744			−1.15347			−0.576735	+	0.816931i	$0.695673\pi$
$252$		0			0
$253$	−27.6565	+	38.0659i	−1.73875	+	2.39319i
$254$	3.53043	+	2.56501i	0.221519	+	0.160943i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$		−	1.80149i		−	0.112374i	−0.998420	−	0.0561868i	$-0.982106\pi$
$257$		−	1.80149i		−	0.112374i	0.998420	−	0.0561868i	$-0.0178942\pi$
$258$		0			0
$259$	−1.09026	−	3.35548i	−0.0677455	−	0.208499i
$260$	1.30740	+	0.455139i	0.0810814	+	0.0282265i
$261$		0			0
$262$	−0.587547	+	0.190905i	−0.0362987	+	0.0117942i
$263$	13.5087	−	4.38923i	0.832981	−	0.270652i	0.138680	−	0.990337i	$-0.455714\pi$
$263$	13.5087	−	4.38923i	0.832981	−	0.270652i	0.694300	+	0.719685i	$0.255714\pi$
$264$		0			0
$265$	0.748009	−	0.985670i	0.0459498	−	0.0605492i
$266$	2.47530	+	7.61820i	0.151771	+	0.467102i
$267$		0			0
$268$		−	11.9121i		−	0.727648i
$269$	5.05075	−	3.66959i	0.307950	−	0.223739i	−0.423066	−	0.906099i	$-0.639046\pi$
$269$	5.05075	−	3.66959i	0.307950	−	0.223739i	0.731016	+	0.682360i	$0.239046\pi$
$270$		0			0
$271$	19.2926	+	14.0169i	1.17194	+	0.851464i	0.991240	−	0.132074i	$-0.0421637\pi$
$271$	19.2926	+	14.0169i	1.17194	+	0.851464i	0.180700	+	0.983538i	$0.442164\pi$
$272$	2.02525	−	2.78752i	0.122799	−	0.169018i
$273$		0			0
$274$	−9.27162			−0.560119
$275$	−9.15380	+	24.6288i	−0.551995	+	1.48517i
$276$		0			0
$277$	6.63226	+	2.15495i	0.398494	+	0.129478i	0.501406	−	0.865212i	$-0.332816\pi$
$277$	6.63226	+	2.15495i	0.398494	+	0.129478i	−0.102913	+	0.994690i	$0.532816\pi$
$278$	−11.0279	+	15.1787i	−0.661412	+	0.910356i
$279$		0			0
$280$	6.46658	−	4.49534i	0.386452	−	0.268648i
$281$	9.41192	−	6.83816i	0.561468	−	0.407931i	−0.270528	−	0.962712i	$-0.587198\pi$
$281$	9.41192	−	6.83816i	0.561468	−	0.407931i	0.831996	+	0.554782i	$0.187198\pi$
$282$		0			0
$283$	−5.64568	−	7.77061i	−0.335601	−	0.461915i	0.607549	−	0.794282i	$-0.292153\pi$
$283$	−5.64568	−	7.77061i	−0.335601	−	0.461915i	−0.943150	+	0.332367i	$0.892153\pi$
$284$	1.46739	+	4.51617i	0.0870737	+	0.267985i
$285$		0			0
$286$	1.00535	−	3.09415i	0.0594475	−	0.182961i
$287$	21.0925	−	6.85337i	1.24505	−	0.404542i
$288$		0			0
$289$	1.58466	−	4.87709i	0.0932154	−	0.286888i
$290$	−3.42267	−	4.92353i	−0.200986	−	0.289120i
$291$		0			0
$292$	5.78033	+	7.95594i	0.338268	+	0.465586i
$293$			8.52716i			0.498162i	0.968483	+	0.249081i	$0.0801286\pi$
$293$			8.52716i			0.498162i	−0.968483	+	0.249081i	$0.919871\pi$
$294$		0			0
$295$	−0.180228	−	0.596729i	−0.0104933	−	0.0347429i
$296$	−0.810416	−	0.588802i	−0.0471045	−	0.0342234i
$297$		0			0
$298$	−16.0154	−	5.20372i	−0.927748	−	0.301444i
$299$	−5.54333			−0.320579
$300$		0			0
$301$	5.32717			0.307053
$302$	15.9713	+	5.18938i	0.919043	+	0.298615i
$303$		0			0
$304$	1.83995	+	1.33680i	0.105528	+	0.0766709i
$305$	−2.70698	+	7.77589i	−0.155001	+	0.445246i
$306$		0			0
$307$			2.85794i			0.163111i	0.996669	+	0.0815557i	$0.0259889\pi$
$307$			2.85794i			0.163111i	−0.996669	+	0.0815557i	$0.974011\pi$
$308$	−10.8790	−	14.9736i	−0.619886	−	0.853200i
$309$		0			0
$310$	20.9107	−	6.31558i	1.18765	−	0.358701i
$311$	3.14017	−	9.66444i	0.178063	−	0.548020i	−0.821697	−	0.569924i	$-0.806973\pi$
$311$	3.14017	−	9.66444i	0.178063	−	0.548020i	0.999760	+	0.0219035i	$0.00697267\pi$
$312$		0			0
$313$	17.3127	−	5.62523i	0.978570	−	0.317957i	0.224299	−	0.974520i	$-0.427991\pi$
$313$	17.3127	−	5.62523i	0.978570	−	0.317957i	0.754271	+	0.656564i	$0.227991\pi$
$314$	1.40742	−	4.33159i	0.0794253	−	0.244446i
$315$		0			0
$316$	2.01497	+	6.20143i	0.113351	+	0.348857i
$317$	18.3838	+	25.3031i	1.03254	+	1.42116i	0.903026	+	0.429586i	$0.141340\pi$
$317$	18.3838	+	25.3031i	1.03254	+	1.42116i	0.129510	+	0.991578i	$0.458660\pi$
$318$		0			0
$319$	−11.4006	+	8.28304i	−0.638312	+	0.463761i
$320$	0.735158	−	2.11176i	0.0410966	−	0.118051i
$321$		0			0
$322$	−18.5363	+	25.5131i	−1.03299	+	1.42179i
$323$	−7.45274	−	2.42154i	−0.414681	−	0.134738i
$324$		0			0
$325$	−2.98132	+	0.833039i	−0.165374	+	0.0462087i
$326$	20.2133			1.11951
$327$		0			0
$328$	3.70121	−	5.09427i	0.204365	−	0.281284i
$329$	30.4204	+	22.1017i	1.67713	+	1.21851i
$330$		0			0
$331$	−2.77650	+	2.01724i	−0.152610	+	0.110878i	−0.661470	−	0.749972i	$-0.730067\pi$
$331$	−2.77650	+	2.01724i	−0.152610	+	0.110878i	0.508860	+	0.860849i	$0.330067\pi$
$332$			2.65973i			0.145972i
$333$		0			0
$334$	2.22240	+	6.83983i	0.121604	+	0.374259i
$335$	15.2039	+	21.8708i	0.830676	+	1.19493i
$336$		0			0
$337$	−11.1497	+	3.62277i	−0.607365	+	0.197345i	−0.596523	−	0.802596i	$-0.703451\pi$
$337$	−11.1497	+	3.62277i	−0.607365	+	0.197345i	−0.0108427	+	0.999941i	$0.503451\pi$
$338$	−11.9992	+	3.89878i	−0.652671	+	0.212066i
$339$		0			0
$340$	−0.160585	+	7.70285i	−0.00870892	+	0.417746i
$341$	−15.8633	−	48.8221i	−0.859045	−	2.64387i
$342$		0			0
$343$			5.61791i			0.303339i
$344$	1.22365	−	0.889032i	0.0659747	−	0.0479334i
$345$		0			0
$346$	−4.96053	−	3.60403i	−0.266680	−	0.193754i
$347$	19.0502	−	26.2204i	1.02267	−	1.40758i	0.112355	−	0.993668i	$-0.464161\pi$
$347$	19.0502	−	26.2204i	1.02267	−	1.40758i	0.910315	−	0.413916i	$-0.135839\pi$
$348$		0			0
$349$	11.3708			0.608665			0.304333	−	0.952566i	$-0.401567\pi$
$349$	11.3708			0.608665			0.304333	+	0.952566i	$0.401567\pi$
$350$	−6.13518	+	16.5071i	−0.327939	+	0.882339i
$351$		0			0
$352$	−4.99779	−	1.62388i	−0.266383	−	0.0865531i
$353$	−1.22685	+	1.68861i	−0.0652984	+	0.0898756i	−0.840417	−	0.541940i	$-0.817690\pi$
$353$	−1.22685	+	1.68861i	−0.0652984	+	0.0898756i	0.775119	+	0.631816i	$0.217690\pi$
$354$		0			0
$355$	−8.45831	−	6.41888i	−0.448921	−	0.340679i
$356$	−10.8295	+	7.86808i	−0.573961	+	0.417007i
$357$		0			0
$358$	−8.42280	−	11.5930i	−0.445159	−	0.612708i
$359$	2.10507	+	6.47874i	0.111101	+	0.341935i	0.991114	−	0.133015i	$-0.0424660\pi$
$359$	2.10507	+	6.47874i	0.111101	+	0.341935i	−0.880013	+	0.474950i	$0.842466\pi$
$360$		0			0
$361$	−4.27294	+	13.1508i	−0.224892	+	0.692146i
$362$	−14.9596	+	4.86067i	−0.786259	+	0.255471i
$363$		0			0
$364$	0.673818	−	2.07380i	0.0353177	−	0.108697i
$365$	−20.7673	−	7.22961i	−1.08701	−	0.378415i
$366$		0			0
$367$	−0.0913045	−	0.125670i	−0.00476606	−	0.00655991i	0.806627	−	0.591060i	$-0.201291\pi$
$367$	−0.0913045	−	0.125670i	−0.00476606	−	0.00655991i	−0.811393	+	0.584500i	$0.801291\pi$
$368$			8.95380i			0.466749i
$369$		0			0
$370$	2.23945	+	0.0466868i	0.116423	+	0.00242713i
$371$	−1.57676	−	1.14559i	−0.0818615	−	0.0594758i
$372$		0			0
$373$	−28.2902	−	9.19203i	−1.46481	−	0.475945i	−0.535274	−	0.844679i	$-0.679792\pi$
$373$	−28.2902	−	9.19203i	−1.46481	−	0.475945i	−0.929535	+	0.368733i	$0.879792\pi$
$374$	18.1064			0.936259
$375$		0			0
$376$	10.6760			0.550575
$377$	−1.57895	−	0.513032i	−0.0813201	−	0.0264225i
$378$		0			0
$379$	−13.4962	−	9.80558i	−0.693254	−	0.503679i	0.184474	−	0.982837i	$-0.440942\pi$
$379$	−13.4962	−	9.80558i	−0.693254	−	0.503679i	−0.877728	+	0.479159i	$0.840942\pi$
$380$	−5.08440	−	0.105997i	−0.260824	−	0.00543751i
$381$		0			0
$382$			3.62240i			0.185338i
$383$	−6.62972	−	9.12503i	−0.338763	−	0.466267i	0.605317	−	0.795985i	$-0.293046\pi$
$383$	−6.62972	−	9.12503i	−0.338763	−	0.466267i	−0.944080	+	0.329718i	$0.893046\pi$
$384$		0			0
$385$	39.0853	+	13.6066i	1.99197	+	0.693456i
$386$	3.00515	−	9.24889i	0.152958	−	0.470756i
$387$		0			0
$388$	−4.15806	+	1.35104i	−0.211094	+	0.0685885i
$389$	2.05849	−	6.33537i	0.104369	−	0.321216i	−0.885213	−	0.465187i	$-0.845987\pi$
$389$	2.05849	−	6.33537i	0.104369	−	0.321216i	0.989582	+	0.143971i	$0.0459872\pi$
$390$		0			0
$391$	−9.53346	−	29.3410i	−0.482128	−	1.48384i
$392$	−3.17694	−	4.37269i	−0.160460	−	0.220854i
$393$		0			0
$394$	−5.72280	+	4.15786i	−0.288310	+	0.209470i
$395$	−11.6146	−	8.81416i	−0.584395	−	0.443488i
$396$		0			0
$397$	21.8794	−	30.1144i	1.09810	−	1.51140i	0.260213	−	0.965551i	$-0.416207\pi$
$397$	21.8794	−	30.1144i	1.09810	−	1.51140i	0.837884	−	0.545849i	$-0.183793\pi$
$398$	16.8094	+	5.46171i	0.842580	+	0.273771i
$399$		0			0
$400$	1.34556	+	4.81555i	0.0672779	+	0.240777i
$401$	−19.6891			−0.983228			−0.491614	−	0.870813i	$-0.663593\pi$
$401$	−19.6891			−0.983228			−0.491614	+	0.870813i	$0.663593\pi$
$402$		0			0
$403$	3.55485	−	4.89283i	0.177080	−	0.243729i
$404$	11.5436	+	8.38692i	0.574316	+	0.417265i
$405$		0			0
$406$	−7.64108	+	5.55157i	−0.379220	+	0.275520i
$407$		−	5.26407i		−	0.260930i
$408$		0			0
$409$	−9.13460	−	28.1134i	−0.451677	−	1.39012i	−0.874993	−	0.484136i	$-0.839134\pi$
$409$	−9.13460	−	28.1134i	−0.451677	−	1.39012i	0.423316	−	0.905982i	$-0.360866\pi$
$410$	−0.293473	+	14.0772i	−0.0144936	+	0.695222i
$411$		0			0
$412$	16.8035	−	5.45980i	0.827851	−	0.268985i
$413$	−0.933796	+	0.303409i	−0.0459491	+	0.0149298i
$414$		0			0
$415$	−3.39471	−	4.88331i	−0.166640	−	0.239712i
$416$	−0.191313	−	0.588802i	−0.00937991	−	0.0288684i
$417$		0			0
$418$			11.9514i			0.584564i
$419$	0.946768	−	0.687867i	0.0462526	−	0.0336045i	−0.564419	−	0.825489i	$-0.690900\pi$
$419$	0.946768	−	0.687867i	0.0462526	−	0.0336045i	0.610671	+	0.791884i	$0.290900\pi$
$420$		0			0
$421$	−6.73922	−	4.89633i	−0.328449	−	0.238632i	0.411323	−	0.911490i	$-0.365067\pi$
$421$	−6.73922	−	4.89633i	−0.328449	−	0.238632i	−0.739772	+	0.672857i	$0.765067\pi$
$422$	−6.91460	+	9.51713i	−0.336597	+	0.463287i
$423$		0			0
$424$	−0.553365			−0.0268738
$425$	−9.53659	−	14.3475i	−0.462593	−	0.695957i
$426$		0			0
$427$	12.3341	+	4.00760i	0.596891	+	0.193942i
$428$	−0.425388	+	0.585496i	−0.0205619	+	0.0283010i
$429$		0			0
$430$	−1.11194	+	3.19407i	−0.0536223	+	0.154032i
$431$	−15.1227	+	10.9873i	−0.728435	+	0.529239i	−0.889068	−	0.457775i	$-0.848646\pi$
$431$	−15.1227	+	10.9873i	−0.728435	+	0.529239i	0.160633	+	0.987014i	$0.448646\pi$
$432$		0			0
$433$	11.1140	+	15.2972i	0.534107	+	0.735135i	0.987749	−	0.156049i	$-0.0498758\pi$
$433$	11.1140	+	15.2972i	0.534107	+	0.735135i	−0.453643	+	0.891184i	$0.649876\pi$
$434$	−10.6321	−	32.7222i	−0.510357	−	1.57072i
$435$		0			0
$436$	−0.795198	+	2.44737i	−0.0380831	+	0.117208i
$437$	19.3670	−	6.29273i	0.926450	−	0.301022i
$438$		0			0
$439$	12.6264	−	38.8602i	0.602627	−	1.85469i	0.0902783	−	0.995917i	$-0.471224\pi$
$439$	12.6264	−	38.8602i	0.602627	−	1.85469i	0.512348	−	0.858778i	$-0.328776\pi$
$440$	11.2486	−	3.39739i	0.536258	−	0.161964i
$441$		0			0
$442$	1.25384	+	1.72576i	0.0596391	+	0.0820862i
$443$		−	5.99083i		−	0.284633i	−0.989821	−	0.142317i	$-0.954545\pi$
$443$		−	5.99083i		−	0.284633i	0.989821	−	0.142317i	$-0.0454551\pi$
$444$		0			0
$445$	9.84080	−	28.2680i	0.466499	−	1.34003i
$446$	−10.2749	−	7.46514i	−0.486530	−	0.353485i
$447$		0			0
$448$	−3.34968	−	1.08838i	−0.158258	−	0.0514210i
$449$	12.4505			0.587574			0.293787	−	0.955871i	$-0.405084\pi$
$449$	12.4505			0.587574			0.293787	+	0.955871i	$0.405084\pi$
$450$		0			0
$451$	33.0899			1.55814
$452$	14.4448	+	4.69339i	0.679425	+	0.220759i
$453$		0			0
$454$	−11.5415	−	8.38543i	−0.541672	−	0.393548i
$455$	1.40972	+	4.66755i	0.0660889	+	0.218818i
$456$		0			0
$457$		−	1.11807i		−	0.0523011i	−0.999658	−	0.0261506i	$-0.991675\pi$
$457$		−	1.11807i		−	0.0523011i	0.999658	−	0.0261506i	$-0.00832493\pi$
$458$	5.17432	+	7.12184i	0.241780	+	0.332782i
$459$		0			0
$460$	−11.4281	−	16.4393i	−0.532837	−	0.766489i
$461$	9.29974	−	28.6216i	0.433132	−	1.33304i	−0.461857	−	0.886954i	$-0.652817\pi$
$461$	9.29974	−	28.6216i	0.433132	−	1.33304i	0.894989	−	0.446089i	$-0.147183\pi$
$462$		0			0
$463$	20.0062	−	6.50042i	0.929768	−	0.302100i	0.195300	−	0.980743i	$-0.437432\pi$
$463$	20.0062	−	6.50042i	0.929768	−	0.302100i	0.734468	+	0.678644i	$0.237432\pi$
$464$	−0.828671	+	2.55039i	−0.0384701	+	0.118399i
$465$		0			0
$466$	−4.65881	−	14.3383i	−0.215815	−	0.664211i
$467$	2.07849	+	2.86080i	0.0961812	+	0.132382i	0.854395	−	0.519624i	$-0.173928\pi$
$467$	2.07849	+	2.86080i	0.0961812	+	0.132382i	−0.758214	+	0.652006i	$0.773928\pi$
$468$		0			0
$469$	33.9425	−	24.6607i	1.56732	−	1.13872i
$470$	−19.6014	+	13.6262i	−0.904145	+	0.628531i
$471$		0			0
$472$	−0.163858	+	0.225531i	−0.00754216	+	0.0103809i
$473$	7.55921	+	2.45614i	0.347573	+	0.112933i
$474$		0			0
$475$	9.47034	−	6.29479i	0.434529	−	0.288825i
$476$	12.1355			0.556230
$477$		0			0
$478$	−3.67120	+	5.05298i	−0.167917	+	0.231118i
$479$	−32.7132	−	23.7675i	−1.49470	−	1.08597i	−0.972432	−	0.233187i	$-0.925085\pi$
$479$	−32.7132	−	23.7675i	−1.49470	−	1.08597i	−0.522272	−	0.852779i	$-0.674915\pi$
$480$		0			0
$481$	0.501731	−	0.364529i	0.0228770	−	0.0166211i
$482$		−	14.8094i		−	0.674551i
$483$		0			0
$484$	−5.13427	−	15.8017i	−0.233376	−	0.718258i
$485$	5.90990	−	7.78762i	0.268355	−	0.353618i
$486$		0			0
$487$	−25.3973	+	8.25208i	−1.15086	+	0.373938i	−0.821468	−	0.570255i	$-0.806844\pi$
$487$	−25.3973	+	8.25208i	−1.15086	+	0.373938i	−0.329394	+	0.944193i	$0.606844\pi$
$488$	3.50196	−	1.13786i	0.158526	−	0.0515083i
$489$		0			0
$490$	11.4139	+	3.97348i	0.515630	+	0.179504i
$491$	−10.2314	−	31.4891i	−0.461738	−	1.42108i	−0.863040	−	0.505136i	$-0.831442\pi$
$491$	−10.2314	−	31.4891i	−0.461738	−	1.42108i	0.401302	−	0.915946i	$-0.368558\pi$
$492$		0			0
$493$		−	9.23975i		−	0.416137i
$494$	−1.13912	+	0.827619i	−0.0512514	+	0.0372363i
$495$		0			0
$496$	−7.90309	−	5.74193i	−0.354859	−	0.257820i
$497$	−9.83059	+	13.5307i	−0.440962	+	0.606933i
$498$		0			0
$499$	−6.01303			−0.269180			−0.134590	−	0.990901i	$-0.542972\pi$
$499$	−6.01303			−0.269180			−0.134590	+	0.990901i	$0.542972\pi$
$500$	−8.61673	−	7.12404i	−0.385352	−	0.318597i
$501$		0			0
$502$	−17.3800	−	5.64710i	−0.775707	−	0.252042i
$503$	−3.91890	+	5.39391i	−0.174735	+	0.240502i	−0.887398	−	0.461005i	$-0.847489\pi$
$503$	−3.91890	+	5.39391i	−0.174735	+	0.240502i	0.712662	+	0.701507i	$0.247489\pi$
$504$		0			0
$505$	−31.8988	−	0.665008i	−1.41948	−	0.0295925i
$506$	−38.0659	+	27.6565i	−1.69224	+	1.22948i
$507$		0			0
$508$	2.56501	+	3.53043i	0.113804	+	0.156638i
$509$	−5.43941	−	16.7408i	−0.241098	−	0.742022i	−0.996254	−	0.0864773i	$-0.972439\pi$
$509$	−5.43941	−	16.7408i	−0.241098	−	0.742022i	0.755156	−	0.655545i	$-0.227561\pi$
$510$		0			0
$511$	−10.7032	+	32.9411i	−0.473482	+	1.45723i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$		0			0
$514$	0.556690	−	1.71331i	0.0245545	−	0.0755711i
$515$	−23.8831	+	31.4713i	−1.05241	+	1.38679i
$516$		0			0
$517$	32.9762	+	45.3878i	1.45029	+	1.99615i
$518$		−	3.52816i		−	0.155018i
$519$		0			0
$520$	1.10276	+	0.836871i	0.0483594	+	0.0366992i
$521$	14.9188	+	10.8391i	0.653605	+	0.474872i	0.864497	−	0.502638i	$-0.167637\pi$
$521$	14.9188	+	10.8391i	0.653605	+	0.474872i	−0.210892	+	0.977509i	$0.567637\pi$
$522$		0			0
$523$	−9.81016	−	3.18752i	−0.428968	−	0.139380i	0.0865719	−	0.996246i	$-0.472409\pi$
$523$	−9.81016	−	3.18752i	−0.428968	−	0.139380i	−0.515540	+	0.856865i	$0.672409\pi$
$524$	−0.617783			−0.0269880
$525$		0			0
$526$	14.2039			0.619318
$527$	32.0115	+	10.4012i	1.39444	+	0.453082i
$528$		0			0
$529$	46.2520	+	33.6040i	2.01096	+	1.46105i
$530$	1.01599	−	0.706280i	0.0441317	−	0.0306788i
$531$		0			0
$532$			8.01025i			0.347288i
$533$	2.29143	+	3.15388i	0.0992528	+	0.136610i
$534$		0			0
$535$	0.0337295	−	1.61792i	0.00145825	−	0.0699488i
$536$	3.68104	−	11.3291i	0.158997	−	0.489342i
$537$		0			0
$538$	5.93752	−	1.92922i	0.255985	−	0.0831744i
$539$	8.77697	−	27.0127i	0.378051	−	1.16352i
$540$		0			0
$541$	−11.5756	−	35.6262i	−0.497676	−	1.53169i	−0.812745	−	0.582620i	$-0.802028\pi$
$541$	−11.5756	−	35.6262i	−0.497676	−	1.53169i	0.315069	−	0.949069i	$-0.397972\pi$
$542$	14.0169	+	19.2926i	0.602076	+	0.828687i
$543$		0			0
$544$	2.78752	−	2.02525i	0.119514	−	0.0868320i
$545$	−1.66367	−	5.50835i	−0.0712637	−	0.235952i
$546$		0			0
$547$	−6.49261	+	8.93631i	−0.277604	+	0.382089i	−0.924938	−	0.380117i	$-0.875884\pi$
$547$	−6.49261	+	8.93631i	−0.277604	+	0.382089i	0.647334	+	0.762206i	$0.275884\pi$
$548$	−8.81784	−	2.86509i	−0.376679	−	0.122391i
$549$		0			0
$550$	−16.3165	+	20.5947i	−0.695738	+	0.878162i
$551$	6.09886			0.259820
$552$		0			0
$553$	−13.4990	+	18.5798i	−0.574035	+	0.790092i
$554$	5.64173	+	4.09896i	0.239694	+	0.174148i
$555$		0			0
$556$	−15.1787	+	11.0279i	−0.643719	+	0.467689i
$557$			29.7087i			1.25880i	0.777082	+	0.629400i	$0.216699\pi$
$557$			29.7087i			1.25880i	−0.777082	+	0.629400i	$0.783301\pi$
$558$		0			0
$559$	0.289364	+	0.890570i	0.0122388	+	0.0376671i
$560$	7.53922	−	2.27704i	0.318590	−	0.0962226i
$561$		0			0
$562$	11.0644	−	3.59504i	0.466723	−	0.151647i
$563$	17.4332	−	5.66439i	0.734722	−	0.238726i	0.0823274	−	0.996605i	$-0.473765\pi$
$563$	17.4332	−	5.66439i	0.734722	−	0.238726i	0.652394	+	0.757880i	$0.273765\pi$
$564$		0			0
$565$	−32.5112	+	9.81925i	−1.36776	+	0.413099i
$566$	−2.96811	−	9.13490i	−0.124759	−	0.383969i
$567$		0			0
$568$			4.74858i			0.199246i
$569$	17.7915	−	12.9263i	0.745859	−	0.541898i	−0.148681	−	0.988885i	$-0.547503\pi$
$569$	17.7915	−	12.9263i	0.745859	−	0.541898i	0.894541	+	0.446987i	$0.147503\pi$
$570$		0			0
$571$	−20.2890	−	14.7408i	−0.849069	−	0.616885i	0.0758199	−	0.997122i	$-0.475843\pi$
$571$	−20.2890	−	14.7408i	−0.849069	−	0.616885i	−0.924889	+	0.380237i	$0.875843\pi$
$572$	1.91229	−	2.63204i	0.0799567	−	0.110051i
$573$		0			0
$574$	22.1780			0.925691
$575$	41.9643	+	15.5969i	1.75003	+	0.650435i
$576$		0			0
$577$	−33.2751	−	10.8117i	−1.38526	−	0.450099i	−0.480866	−	0.876794i	$-0.659678\pi$
$577$	−33.2751	−	10.8117i	−1.38526	−	0.450099i	−0.904395	+	0.426695i	$0.859678\pi$
$578$	3.01421	−	4.14870i	0.125374	−	0.172563i
$579$		0			0
$580$	−1.73370	−	5.74022i	−0.0719879	−	0.238350i
$581$	−7.57866	+	5.50622i	−0.314416	+	0.228437i
$582$		0			0
$583$	−1.70923	−	2.35256i	−0.0707892	−	0.0974330i
$584$	3.03890	+	9.35277i	0.125751	+	0.387020i
$585$		0			0
$586$	−2.63504	+	8.10981i	−0.108852	+	0.335013i
$587$	−9.87738	+	3.20936i	−0.407683	+	0.132464i	−0.505677	−	0.862723i	$-0.668757\pi$
$587$	−9.87738	+	3.20936i	−0.407683	+	0.132464i	0.0979941	+	0.995187i	$0.468757\pi$
$588$		0			0
$589$	−6.86547	+	21.1298i	−0.282887	+	0.870636i
$590$	0.0129925	−	0.623216i	0.000534891	−	0.0256574i
$591$		0			0
$592$	−0.588802	−	0.810416i	−0.0241996	−	0.0333079i
$593$			0.948200i			0.0389379i	0.999810	+	0.0194690i	$0.00619755\pi$
$593$			0.948200i			0.0389379i	−0.999810	+	0.0194690i	$0.993802\pi$
$594$		0			0
$595$	−22.2810	+	15.4890i	−0.913433	+	0.634987i
$596$	−13.6235	−	9.89807i	−0.558041	−	0.405441i
$597$		0			0
$598$	−5.27202	−	1.71298i	−0.215589	−	0.0700491i
$599$	25.4901			1.04150			0.520748	−	0.853710i	$-0.325653\pi$
$599$	25.4901			1.04150			0.520748	+	0.853710i	$0.325653\pi$
$600$		0			0
$601$	−16.6409			−0.678797			−0.339399	−	0.940643i	$-0.610224\pi$
$601$	−16.6409			−0.678797			−0.339399	+	0.940643i	$0.610224\pi$
$602$	5.06644	+	1.64618i	0.206492	+	0.0670935i
$603$		0			0
$604$	13.5860	+	9.87079i	0.552805	+	0.401637i
$605$	29.5949	+	22.4591i	1.20320	+	0.913092i
$606$		0			0
$607$			33.2662i			1.35023i	0.737712	+	0.675116i	$0.235906\pi$
$607$			33.2662i			1.35023i	−0.737712	+	0.675116i	$0.764094\pi$
$608$	1.33680	+	1.83995i	0.0542145	+	0.0746199i
$609$		0			0
$610$	−4.97738	+	6.55881i	−0.201528	+	0.265558i
$611$	−2.04247	+	6.28607i	−0.0826295	+	0.254307i
$612$		0			0
$613$	−15.4852	+	5.03144i	−0.625440	+	0.203218i	−0.604554	−	0.796564i	$-0.706649\pi$
$613$	−15.4852	+	5.03144i	−0.625440	+	0.203218i	−0.0208859	+	0.999782i	$0.506649\pi$
$614$	−0.883153	+	2.71807i	−0.0356412	+	0.109692i
$615$		0			0
$616$	−5.71941	−	17.6025i	−0.230442	−	0.709226i
$617$	−28.5243	−	39.2603i	−1.14834	−	1.58056i	−0.747280	−	0.664509i	$-0.768641\pi$
$617$	−28.5243	−	39.2603i	−1.14834	−	1.58056i	−0.401063	−	0.916050i	$-0.631359\pi$
$618$		0			0
$619$	−19.9552	+	14.4983i	−0.802066	+	0.582735i	−0.911519	−	0.411257i	$-0.865090\pi$
$619$	−19.9552	+	14.4983i	−0.802066	+	0.582735i	0.109454	+	0.993992i	$0.465090\pi$
$620$	21.8389	+	0.455284i	0.877069	+	0.0182847i
$621$		0			0
$622$	5.97296	−	8.22107i	0.239494	−	0.329635i
$623$	−44.8388	−	14.5690i	−1.79643	−	0.583694i
$624$		0			0
$625$	24.9132	+	2.08203i	0.996526	+	0.0832811i
$626$	18.2036			0.727563
$627$		0			0
$628$	2.67707	−	3.68467i	0.106827	−	0.147034i
$629$	2.79234	+	2.02876i	0.111338	+	0.0808918i
$630$		0			0
$631$	9.54099	−	6.93194i	0.379821	−	0.275956i	−0.381451	−	0.924389i	$-0.624575\pi$
$631$	9.54099	−	6.93194i	0.379821	−	0.275956i	0.761272	+	0.648433i	$0.224575\pi$
$632$			6.52057i			0.259374i
$633$		0			0
$634$	9.66493	+	29.7456i	0.383843	+	1.18135i
$635$	−9.21542	−	3.20812i	−0.365703	−	0.127310i
$636$		0			0
$637$	3.18244	−	1.03404i	0.126093	−	0.0409700i
$638$	−13.4022	+	4.35465i	−0.530600	+	0.172402i
$639$		0			0
$640$	1.35175	−	1.78123i	0.0534325	−	0.0704093i
$641$	4.20359	+	12.9373i	0.166032	+	0.510994i	0.999111	−	0.0421603i	$-0.0134240\pi$
$641$	4.20359	+	12.9373i	0.166032	+	0.510994i	−0.833079	+	0.553154i	$0.813424\pi$
$642$		0			0
$643$		−	20.9102i		−	0.824617i	−0.911044	−	0.412308i	$-0.864723\pi$
$643$		−	20.9102i		−	0.824617i	0.911044	−	0.412308i	$-0.135277\pi$
$644$	−25.5131	+	18.5363i	−1.00536	+	0.730433i
$645$		0			0
$646$	−6.33968	−	4.60604i	−0.249431	−	0.181222i
$647$	−26.9722	+	37.1240i	−1.06039	+	1.45950i	−0.180941	+	0.983494i	$0.557914\pi$
$647$	−26.9722	+	37.1240i	−1.06039	+	1.45950i	−0.879444	+	0.476002i	$0.842086\pi$
$648$		0			0
$649$	−1.46494			−0.0575039
$650$	−3.09283	−	0.129011i	−0.121311	−	0.00506023i
$651$		0			0
$652$	19.2239	+	6.24624i	0.752868	+	0.244622i
$653$	1.53183	−	2.10838i	0.0599450	−	0.0825072i	−0.777992	−	0.628274i	$-0.783762\pi$
$653$	1.53183	−	2.10838i	0.0599450	−	0.0825072i	0.837937	+	0.545767i	$0.183762\pi$
$654$		0			0
$655$	1.13426	−	0.788499i	0.0443192	−	0.0308092i
$656$	5.09427	−	3.70121i	0.198898	−	0.144508i
$657$		0			0
$658$	22.1017	+	30.4204i	0.861615	+	1.18591i
$659$	7.39977	+	22.7742i	0.288254	+	0.887155i	0.985404	+	0.170230i	$0.0544511\pi$
$659$	7.39977	+	22.7742i	0.288254	+	0.887155i	−0.697150	+	0.716925i	$0.745549\pi$
$660$		0			0
$661$	8.01908	−	24.6802i	0.311906	−	0.959948i	−0.665103	−	0.746751i	$-0.731613\pi$
$661$	8.01908	−	24.6802i	0.311906	−	0.959948i	0.977009	−	0.213196i	$-0.0683874\pi$
$662$	−3.26397	+	1.06053i	−0.126858	+	0.0412186i
$663$		0			0
$664$	−0.821902	+	2.52955i	−0.0318960	+	0.0981657i
$665$	−10.2238	−	14.7070i	−0.396461	−	0.570312i
$666$		0			0
$667$	14.1132	+	19.4252i	0.546466	+	0.752145i
$668$			7.19183i			0.278260i
$669$		0			0
$670$	7.70127	+	25.4987i	0.297526	+	0.985099i
$671$	15.6543	+	11.3735i	0.604328	+	0.439070i
$672$		0			0
$673$	14.0845	+	4.57632i	0.542916	+	0.176404i	0.567620	−	0.823291i	$-0.307864\pi$
$673$	14.0845	+	4.57632i	0.542916	+	0.176404i	−0.0247037	+	0.999695i	$0.507864\pi$
$674$	−11.7235			−0.451574
$675$		0			0
$676$	−12.6167			−0.485258
$677$	−33.2224	−	10.7946i	−1.27684	−	0.414870i	−0.409373	−	0.912367i	$-0.634253\pi$
$677$	−33.2224	−	10.7946i	−1.27684	−	0.414870i	−0.867466	+	0.497497i	$0.834253\pi$
$678$		0			0
$679$	−12.4578	−	9.05109i	−0.478085	−	0.347349i
$680$	−2.53304	+	7.27622i	−0.0971375	+	0.279030i
$681$		0			0
$682$		−	51.3346i		−	1.96571i
$683$	12.3485	+	16.9963i	0.472504	+	0.650346i	0.977043	−	0.213043i	$-0.0683375\pi$
$683$	12.3485	+	16.9963i	0.472504	+	0.650346i	−0.504539	+	0.863389i	$0.668338\pi$
$684$		0			0
$685$	19.8465	−	5.99418i	0.758297	−	0.229026i
$686$	−1.73603	+	5.34295i	−0.0662819	+	0.203995i
$687$		0			0
$688$	1.43848	−	0.467392i	0.0548417	−	0.0178192i
$689$	0.105866	−	0.325822i	0.00403318	−	0.0124128i
$690$		0			0
$691$	−7.23231	−	22.2588i	−0.275130	−	0.846763i	−0.989185	−	0.146673i	$-0.953143\pi$
$691$	−7.23231	−	22.2588i	−0.275130	−	0.846763i	0.714055	−	0.700090i	$-0.246857\pi$
$692$	−3.60403	−	4.96053i	−0.137005	−	0.188571i
$693$		0			0
$694$	26.2204	−	19.0502i	0.995312	−	0.723137i
$695$	13.7929	−	39.6206i	0.523196	−	1.50290i
$696$		0			0
$697$	−12.7528	+	17.5527i	−0.483045	+	0.664854i
$698$	10.8143	+	3.51377i	0.409326	+	0.132998i
$699$		0			0
$700$	−10.9359	+	13.8033i	−0.413337	+	0.521715i
$701$	43.2849			1.63485			0.817424	−	0.576037i	$-0.195402\pi$
$701$	43.2849			1.63485			0.817424	+	0.576037i	$0.195402\pi$
$702$		0			0
$703$	−1.33912	+	1.84314i	−0.0505057	+	0.0695152i
$704$	−4.25137	−	3.08880i	−0.160230	−	0.116414i
$705$		0			0
$706$	−1.68861	+	1.22685i	−0.0635516	+	0.0461730i
$707$			50.2552i			1.89004i
$708$		0			0
$709$	7.72993	+	23.7903i	0.290303	+	0.893462i	0.984759	+	0.173926i	$0.0556454\pi$
$709$	7.72993	+	23.7903i	0.290303	+	0.893462i	−0.694455	+	0.719536i	$0.744355\pi$
$710$	−6.06079	−	8.71848i	−0.227457	−	0.327199i
$711$		0			0
$712$	−12.7308	+	4.13649i	−0.477108	+	0.155022i
$713$	−83.1865	+	27.0289i	−3.11536	+	1.01224i
$714$		0			0
$715$	−0.151627	+	7.27319i	−0.00567054	+	0.272002i
$716$	−4.42813	−	13.6284i	−0.165487	−	0.509316i
$717$		0			0
$718$			6.81215i			0.254227i
$719$	24.9533	−	18.1296i	0.930601	−	0.676121i	−0.0155391	−	0.999879i	$-0.504946\pi$
$719$	24.9533	−	18.1296i	0.930601	−	0.676121i	0.946140	+	0.323758i	$0.104946\pi$
$720$		0			0
$721$	50.3442	+	36.5772i	1.87492	+	1.36221i
$722$	−8.12762	+	11.1867i	−0.302479	+	0.416326i
$723$		0			0
$724$	−15.7294			−0.584580
$725$	10.5096	+	8.32636i	0.390315	+	0.309233i
$726$		0			0
$727$	0.623458	+	0.202574i	0.0231228	+	0.00751304i	0.320556	−	0.947230i	$-0.396130\pi$
$727$	0.623458	+	0.202574i	0.0231228	+	0.00751304i	−0.297433	+	0.954743i	$0.596130\pi$
$728$	1.28168	−	1.76408i	0.0475022	−	0.0653811i
$729$		0			0
$730$	−17.5168	−	13.2932i	−0.648324	−	0.492003i
$731$	−4.21616	+	3.06322i	−0.155940	+	0.113297i
$732$		0			0
$733$	8.05975	+	11.0933i	0.297694	+	0.409740i	0.931494	−	0.363756i	$-0.118506\pi$
$733$	8.05975	+	11.0933i	0.297694	+	0.409740i	−0.633800	+	0.773497i	$0.718506\pi$
$734$	−0.0480016	−	0.147734i	−0.00177177	−	0.00545295i
$735$		0			0
$736$	−2.76688	+	8.51557i	−0.101988	+	0.313888i
$737$	59.5342	−	19.3438i	2.19297	−	0.712539i
$738$		0			0
$739$	3.38589	−	10.4207i	0.124552	−	0.383332i	−0.869267	−	0.494343i	$-0.835409\pi$
$739$	3.38589	−	10.4207i	0.124552	−	0.383332i	0.993819	+	0.111011i	$0.0354088\pi$
$740$	2.11542	+	0.736430i	0.0777642	+	0.0270717i
$741$		0			0
$742$	−1.14559	−	1.57676i	−0.0420558	−	0.0578848i
$743$			5.67053i			0.208032i	0.994576	+	0.104016i	$0.0331692\pi$
$743$			5.67053i			0.208032i	−0.994576	+	0.104016i	$0.966831\pi$
$744$		0			0
$745$	37.6463	+	0.784829i	1.37925	+	0.0287539i
$746$	−24.0650	−	17.4843i	−0.881084	−	0.640145i
$747$		0			0
$748$	17.2202	+	5.59518i	0.629633	+	0.204580i
$749$	−2.54896			−0.0931371
$750$		0			0
$751$	−22.2909			−0.813408			−0.406704	−	0.913560i	$-0.633322\pi$
$751$	−22.2909			−0.813408			−0.406704	+	0.913560i	$0.633322\pi$
$752$	10.1535	+	3.29908i	0.370261	+	0.120305i
$753$		0			0
$754$	−1.34314	−	0.975846i	−0.0489141	−	0.0355382i
$755$	−37.5426	−	0.782666i	−1.36631	−	0.0284841i
$756$		0			0
$757$		−	17.3894i		−	0.632030i	−0.948754	−	0.316015i	$-0.897655\pi$
$757$		−	17.3894i		−	0.632030i	0.948754	−	0.316015i	$-0.102345\pi$
$758$	−9.80558	−	13.4962i	−0.356155	−	0.490205i
$759$		0			0
$760$	−4.80279	−	1.67197i	−0.174216	−	0.0606489i
$761$	−4.78812	+	14.7363i	−0.173569	+	0.534191i	−0.999565	−	0.0294850i	$-0.990613\pi$
$761$	−4.78812	+	14.7363i	−0.173569	+	0.534191i	0.825996	+	0.563676i	$0.190613\pi$
$762$		0			0
$763$	−8.61978	+	2.80074i	−0.312057	+	0.101393i
$764$	−1.11938	+	3.44511i	−0.0404979	+	0.124640i
$765$		0			0
$766$	−3.48545	−	10.7271i	−0.125934	−	0.387586i
$767$	−0.101445	−	0.139627i	−0.00366296	−	0.00504163i
$768$		0			0
$769$	−39.5215	+	28.7140i	−1.42518	+	1.03545i	−0.434292	+	0.900772i	$0.643002\pi$
$769$	−39.5215	+	28.7140i	−1.42518	+	1.03545i	−0.990889	+	0.134683i	$0.956998\pi$
$770$	32.9677	+	25.0187i	1.18807	+	0.901610i
$771$		0			0
$772$	5.71613	−	7.86757i	0.205728	−	0.283160i
$773$	1.02281	+	0.332330i	0.0367878	+	0.0119531i	0.327353	−	0.944902i	$-0.393843\pi$
$773$	1.02281	+	0.332330i	0.0367878	+	0.0119531i	−0.290565	+	0.956855i	$0.593843\pi$
$774$		0			0
$775$	−40.6776	+	27.0378i	−1.46118	+	0.971227i
$776$	−4.37205			−0.156947
$777$		0			0
$778$	3.91547	−	5.38919i	0.140377	−	0.193212i
$779$	−11.5859	−	8.41768i	−0.415109	−	0.301595i
$780$		0			0
$781$	−20.1880	+	14.6674i	−0.722383	+	0.524842i
$782$		−	30.8509i		−	1.10323i
$783$		0			0
$784$	−1.67022	−	5.14040i	−0.0596506	−	0.183586i
$785$	−0.212268	+	10.1820i	−0.00757617	+	0.363410i
$786$		0			0
$787$	35.9953	−	11.6956i	1.28310	−	0.416903i	0.413426	−	0.910538i	$-0.364332\pi$
$787$	35.9953	−	11.6956i	1.28310	−	0.416903i	0.869669	+	0.493635i	$0.164332\pi$
$788$	−6.72755	+	2.18591i	−0.239659	+	0.0778700i
$789$		0			0
$790$	−8.32244	−	11.9719i	−0.296099	−	0.425940i
$791$	16.5304	+	50.8755i	0.587755	+	1.80892i
$792$		0			0
$793$			2.27965i			0.0809527i
$794$	30.1144	−	21.8794i	1.06872	−	0.776471i
$795$		0			0
$796$	14.2990	+	10.3888i	0.506813	+	0.368221i
$797$	−6.79344	+	9.35037i	−0.240636	+	0.331207i	−0.912204	−	0.409736i	$-0.865621\pi$
$797$	−6.79344	+	9.35037i	−0.240636	+	0.331207i	0.671568	+	0.740943i	$0.265621\pi$
$798$		0			0
$799$	−36.7850			−1.30136
$800$	−0.208384	+	4.99566i	−0.00736748	+	0.176623i
$801$		0			0
$802$	−18.7255	−	6.08427i	−0.661219	−	0.214843i
$803$	−30.3755	+	41.8083i	−1.07193	+	1.47538i
$804$		0			0
$805$	23.1839	−	66.5963i	0.817123	−	2.34721i
$806$	4.89283	−	3.55485i	0.172342	−	0.125214i
$807$		0			0
$808$	8.38692	+	11.5436i	0.295051	+	0.406103i
$809$	−6.24192	−	19.2106i	−0.219454	−	0.675410i	−0.998807	−	0.0488254i	$-0.984452\pi$
$809$	−6.24192	−	19.2106i	−0.219454	−	0.675410i	0.779353	−	0.626585i	$-0.215548\pi$
$810$		0			0
$811$	−12.8802	+	39.6412i	−0.452285	+	1.39199i	0.422008	+	0.906592i	$0.361326\pi$
$811$	−12.8802	+	39.6412i	−0.452285	+	1.39199i	−0.874293	+	0.485399i	$0.838674\pi$
$812$	−8.98262	+	2.91863i	−0.315228	+	0.102424i
$813$		0			0
$814$	1.62669	−	5.00643i	0.0570154	−	0.175475i
$815$	−43.2678	+	13.0680i	−1.51561	+	0.457753i
$816$		0			0
$817$	−2.02193	−	2.78295i	−0.0707384	−	0.0973631i
$818$		−	29.5602i		−	1.03355i
$819$		0			0
$820$	−4.62919	+	13.2975i	−0.161658	+	0.464369i
$821$	−26.4710	−	19.2323i	−0.923844	−	0.671212i	0.0206340	−	0.999787i	$-0.493432\pi$
$821$	−26.4710	−	19.2323i	−0.923844	−	0.671212i	−0.944478	+	0.328575i	$0.893432\pi$
$822$		0			0
$823$	31.8460	+	10.3474i	1.11008	+	0.360687i	0.805974	−	0.591950i	$-0.201642\pi$
$823$	31.8460	+	10.3474i	1.11008	+	0.360687i	0.304107	+	0.952638i	$0.401642\pi$
$824$	17.6683			0.615504
$825$		0			0
$826$	−0.981851			−0.0341630
$827$	−8.32052	−	2.70350i	−0.289333	−	0.0940100i	0.160755	−	0.986994i	$-0.448607\pi$
$827$	−8.32052	−	2.70350i	−0.289333	−	0.0940100i	−0.450088	+	0.892984i	$0.648607\pi$
$828$		0			0
$829$	15.3302	+	11.1381i	0.532441	+	0.386841i	0.821270	−	0.570539i	$-0.193266\pi$
$829$	15.3302	+	11.1381i	0.532441	+	0.386841i	−0.288829	+	0.957381i	$0.593266\pi$
$830$	−1.71954	−	5.69333i	−0.0596860	−	0.197618i
$831$		0			0
$832$		−	0.619103i		−	0.0214635i
$833$	10.9464	+	15.0664i	0.379269	+	0.522019i
$834$		0			0
$835$	−9.17919	−	13.2043i	−0.317659	−	0.456955i
$836$	−3.69320	+	11.3665i	−0.127732	+	0.393118i
$837$		0			0
$838$	1.11299	−	0.361633i	0.0384477	−	0.0124924i
$839$	−3.54657	+	10.9152i	−0.122441	+	0.376835i	−0.993426	−	0.114474i	$-0.963482\pi$
$839$	−3.54657	+	10.9152i	−0.122441	+	0.376835i	0.870985	+	0.491309i	$0.163482\pi$
$840$		0			0
$841$	−6.73930	−	20.7414i	−0.232390	−	0.715222i
$842$	−4.89633	−	6.73922i	−0.168739	−	0.232249i
$843$		0			0
$844$	−9.51713	+	6.91460i	−0.327593	+	0.238010i
$845$	23.1645	−	16.1032i	0.796884	−	0.553966i
$846$		0			0
$847$	34.3964	−	47.3425i	1.18187	−	1.62671i
$848$	−0.526281	−	0.170999i	−0.0180726	−	0.00587213i
$849$		0			0
$850$	−4.63621	−	16.5923i	−0.159021	−	0.569110i
$851$	−8.96929			−0.307463
$852$		0			0
$853$	−6.10223	+	8.39899i	−0.208936	+	0.287576i	−0.900605	−	0.434639i	$-0.856876\pi$
$853$	−6.10223	+	8.39899i	−0.208936	+	0.287576i	0.691668	+	0.722215i	$0.256876\pi$
$854$	10.4920	+	7.62292i	0.359030	+	0.260851i
$855$		0			0
$856$	−0.585496	+	0.425388i	−0.0200119	+	0.0145395i
$857$		−	32.7252i		−	1.11787i	−0.829211	−	0.558936i	$-0.811210\pi$
$857$		−	32.7252i		−	1.11787i	0.829211	−	0.558936i	$-0.188790\pi$
$858$		0			0
$859$	−6.38693	−	19.6569i	−0.217919	−	0.670686i	−0.998933	−	0.0461730i	$-0.985297\pi$
$859$	−6.38693	−	19.6569i	−0.217919	−	0.670686i	0.781014	−	0.624513i	$-0.214703\pi$
$860$	−2.04453	+	2.69413i	−0.0697180	+	0.0918691i
$861$		0			0
$862$	−17.7778	+	5.77636i	−0.605515	+	0.196744i
$863$	53.5643	−	17.4041i	1.82335	−	0.592443i	0.823673	−	0.567065i	$-0.191921\pi$
$863$	53.5643	−	17.4041i	1.82335	−	0.592443i	0.999678	−	0.0253777i	$-0.00807885\pi$
$864$		0			0
$865$	12.9484	+	4.50766i	0.440258	+	0.153265i
$866$	5.84299	+	17.9829i	0.198553	+	0.611083i
$867$		0			0
$868$		−	34.4062i		−	1.16782i
$869$	−27.7213	+	20.1407i	−0.940382	+	0.683228i
$870$		0			0
$871$	5.96636	+	4.33481i	0.202162	+	0.146879i
$872$	−1.51256	+	2.08185i	−0.0512216	+	0.0705005i
$873$		0			0
$874$	20.3637			0.688812
$875$	2.46082	−	39.3009i	0.0831910	−	1.32861i
$876$		0			0
$877$	−42.8777	−	13.9318i	−1.44788	−	0.470443i	−0.523533	−	0.852006i	$-0.675386\pi$
$877$	−42.8777	−	13.9318i	−1.44788	−	0.470443i	−0.924343	+	0.381562i	$0.875386\pi$
$878$	24.0169	−	33.0564i	0.810531	−	1.11560i
$879$		0			0
$880$	11.7479	+	0.244915i	0.396023	+	0.00825607i
$881$	25.2754	−	18.3636i	0.851550	−	0.618687i	−0.0740232	−	0.997257i	$-0.523584\pi$
$881$	25.2754	−	18.3636i	0.851550	−	0.618687i	0.925573	+	0.378569i	$0.123584\pi$
$882$		0			0
$883$	15.7843	+	21.7253i	0.531185	+	0.731113i	0.987310	−	0.158802i	$-0.0507633\pi$
$883$	15.7843	+	21.7253i	0.531185	+	0.731113i	−0.456126	+	0.889915i	$0.650763\pi$
$884$	0.659183	+	2.02876i	0.0221707	+	0.0682345i
$885$		0			0
$886$	1.85127	−	5.69762i	0.0621946	−	0.191415i
$887$	−13.8750	+	4.50825i	−0.465876	+	0.151372i	−0.532543	−	0.846403i	$-0.678763\pi$
$887$	−13.8750	+	4.50825i	−0.465876	+	0.151372i	0.0666671	+	0.997775i	$0.478763\pi$
$888$		0			0
$889$	−4.74952	+	14.6175i	−0.159294	+	0.490256i
$890$	18.0945	−	23.8435i	0.606527	−	0.799236i
$891$		0			0
$892$	−7.46514	−	10.2749i	−0.249952	−	0.344029i
$893$		−	24.2806i		−	0.812519i
$894$		0			0
$895$	25.5245	+	19.3702i	0.853191	+	0.647473i
$896$	−2.84941	−	2.07022i	−0.0951921	−	0.0691611i
$897$		0			0
$898$	11.8411	+	3.84740i	0.395142	+	0.128390i
$899$	−26.1962			−0.873693
$900$		0			0
$901$	1.90665			0.0635199
$902$	31.4704	+	10.2254i	1.04785	+	0.340467i
$903$		0			0
$904$	12.2875	+	8.92737i	0.408675	+	0.296920i
$905$	28.8796	−	20.0761i	0.959989	−	0.667351i
$906$		0			0
$907$			29.5506i			0.981211i	0.871382	+	0.490606i	$0.163224\pi$
$907$			29.5506i			0.981211i	−0.871382	+	0.490606i	$0.836776\pi$
$908$	−8.38543	−	11.5415i	−0.278280	−	0.383020i
$909$		0			0
$910$	−0.101626	+	4.87473i	−0.00336886	+	0.161596i
$911$	−1.30316	+	4.01073i	−0.0431757	+	0.132881i	−0.970321	−	0.241821i	$-0.922255\pi$
$911$	−1.30316	+	4.01073i	−0.0431757	+	0.132881i	0.927145	+	0.374703i	$0.122255\pi$
$912$		0			0
$913$	−13.2928	+	4.31908i	−0.439926	+	0.142941i
$914$	0.345503	−	1.06335i	0.0114282	−	0.0351724i
$915$		0			0
$916$	2.72030	+	8.37223i	0.0898813	+	0.276626i
$917$	−1.27895	−	1.76032i	−0.0422345	−	0.0581308i
$918$		0			0
$919$	23.0230	−	16.7272i	0.759459	−	0.551779i	−0.139286	−	0.990252i	$-0.544481\pi$
$919$	23.0230	−	16.7272i	0.759459	−	0.551779i	0.898744	+	0.438473i	$0.144481\pi$
$920$	−5.78870	−	19.1662i	−0.190848	−	0.631892i
$921$		0			0
$922$	17.6892	−	24.3470i	0.582561	−	0.801827i
$923$	−2.79597	−	0.908467i	−0.0920306	−	0.0299026i
$924$		0			0
$925$	−4.82388	+	1.34789i	−0.158608	+	0.0443182i
$926$	21.0358			0.691279
$927$		0			0
$928$	−1.57623	+	2.16949i	−0.0517421	+	0.0712169i
$929$	21.2379	+	15.4302i	0.696792	+	0.506249i	0.878886	−	0.477032i	$-0.158288\pi$
$929$	21.2379	+	15.4302i	0.696792	+	0.506249i	−0.182094	+	0.983281i	$0.558288\pi$
$930$		0			0
$931$	−9.94483	+	7.22534i	−0.325929	+	0.236801i
$932$		−	15.0762i		−	0.493838i
$933$		0			0
$934$	1.09273	+	3.36307i	0.0357552	+	0.110043i
$935$	−38.7580	+	11.7059i	−1.26752	+	0.382825i
$936$		0			0
$937$	5.07121	−	1.64774i	0.165669	−	0.0538292i	−0.225008	−	0.974357i	$-0.572241\pi$
$937$	5.07121	−	1.64774i	0.165669	−	0.0538292i	0.390677	+	0.920528i	$0.372241\pi$
$938$	39.9018	−	12.9649i	1.30284	−	0.423318i
$939$		0			0
$940$	−22.8528	+	6.90214i	−0.745375	+	0.225123i
$941$	2.62746	+	8.08650i	0.0856529	+	0.263612i	0.984705	−	0.174229i	$-0.0557432\pi$
$941$	2.62746	+	8.08650i	0.0856529	+	0.263612i	−0.899052	+	0.437841i	$0.855743\pi$
$942$		0			0
$943$		−	56.3809i		−	1.83602i
$944$	−0.225531	+	0.163858i	−0.00734040	+	0.00533311i
$945$		0			0
$946$	6.43025	+	4.67185i	0.209065	+	0.151895i
$947$	13.1250	−	18.0650i	0.426504	−	0.587033i	−0.540642	−	0.841253i	$-0.681819\pi$
$947$	13.1250	−	18.0650i	0.426504	−	0.587033i	0.967146	+	0.254220i	$0.0818187\pi$
$948$		0			0
$949$	−6.08831			−0.197635
$950$	10.9520	−	3.06021i	0.355331	−	0.0992863i
$951$		0			0
$952$	11.5416	+	3.75008i	0.374064	+	0.121541i
$953$	8.02894	−	11.0509i	0.260083	−	0.357973i	−0.658928	−	0.752206i	$-0.728990\pi$
$953$	8.02894	−	11.0509i	0.260083	−	0.357973i	0.919011	+	0.394233i	$0.128990\pi$
$954$		0			0
$955$	−2.34191	−	7.75400i	−0.0757825	−	0.250913i
$956$	−5.05298	+	3.67120i	−0.163425	+	0.118735i
$957$		0			0
$958$	−23.7675	−	32.7132i	−0.767894	−	1.05692i
$959$	−10.0910	−	31.0570i	−0.325856	−	1.00288i
$960$		0			0
$961$	19.9095	−	61.2752i	0.642243	−	1.97662i
$962$	0.589821	−	0.191644i	0.0190166	−	0.00617886i
$963$		0			0
$964$	4.57636	−	14.0846i	0.147395	−	0.453634i
$965$	−0.453238	+	21.7407i	−0.0145903	+	0.699858i
$966$		0			0
$967$	18.4843	+	25.4414i	0.594414	+	0.818141i	0.995183	−	0.0980386i	$-0.0312569\pi$
$967$	18.4843	+	25.4414i	0.594414	+	0.818141i	−0.400769	+	0.916179i	$0.631257\pi$
$968$		−	16.6149i		−	0.534022i
$969$		0			0
$970$	8.02716	−	5.58021i	0.257737	−	0.179170i
$971$	−3.40793	−	2.47601i	−0.109366	−	0.0794589i	0.531758	−	0.846896i	$-0.321532\pi$
$971$	−3.40793	−	2.47601i	−0.109366	−	0.0794589i	−0.641124	+	0.767437i	$0.721532\pi$
$972$		0			0
$973$	−62.8463	−	20.4200i	−2.01476	−	0.654635i
$974$	−26.7043			−0.855661
$975$		0			0
$976$	3.68218			0.117864
$977$	13.5077	+	4.38892i	0.432149	+	0.140414i	0.517011	−	0.855979i	$-0.327045\pi$
$977$	13.5077	+	4.38892i	0.432149	+	0.140414i	−0.0848613	+	0.996393i	$0.527045\pi$
$978$		0			0
$979$	−56.9087	−	41.3466i	−1.81881	−	1.32144i
$980$	9.62744	+	7.30611i	0.307537	+	0.233385i
$981$		0			0
$982$		−	33.1096i		−	1.05657i
$983$	18.9158	+	26.0353i	0.603319	+	0.830398i	0.996007	−	0.0892742i	$-0.0284547\pi$
$983$	18.9158	+	26.0353i	0.603319	+	0.830398i	−0.392688	+	0.919672i	$0.628455\pi$
$984$		0			0
$985$	9.56194	−	12.6000i	0.304669	−	0.401469i
$986$	2.85524	−	8.78752i	0.0909293	−	0.279852i
$987$		0			0
$988$	−1.33912	+	0.435105i	−0.0426030	+	0.0138425i
$989$	4.18494	−	12.8799i	0.133073	−	0.409557i
$990$		0			0
$991$	12.2198	+	37.6086i	0.388174	+	1.19468i	0.934152	+	0.356876i	$0.116158\pi$
$991$	12.2198	+	37.6086i	0.388174	+	1.19468i	−0.545978	+	0.837799i	$0.683842\pi$
$992$	−5.74193	−	7.90309i	−0.182306	−	0.250923i
$993$		0			0
$994$	−13.5307	+	9.83059i	−0.429166	+	0.311808i
$995$	−39.5127	−	0.823740i	−1.25264	−	0.0261143i
$996$		0			0
$997$	−1.66750	+	2.29512i	−0.0528104	+	0.0726873i	−0.834605	−	0.550848i	$-0.814304\pi$
$997$	−1.66750	+	2.29512i	−0.0528104	+	0.0726873i	0.781795	+	0.623535i	$0.214304\pi$
$998$	−5.71873	−	1.85813i	−0.181023	−	0.0588181i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.l.c.379.3		16
3.2	odd	2		150.2.h.b.79.2	yes	16
15.2	even	4		750.2.g.f.601.1		16
15.8	even	4		750.2.g.g.601.4		16
15.14	odd	2		750.2.h.d.649.3		16
25.19	even	10	inner	450.2.l.c.19.3		16
75.8	even	20		750.2.g.g.151.4		16
75.17	even	20		750.2.g.f.151.1		16
75.38	even	20		3750.2.a.u.1.7		8
75.41	odd	10		3750.2.c.k.1249.7		16
75.44	odd	10		150.2.h.b.19.2	✓	16
75.56	odd	10		750.2.h.d.349.4		16
75.59	odd	10		3750.2.c.k.1249.10		16
75.62	even	20		3750.2.a.v.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.19.2	✓	16	75.44	odd	10
150.2.h.b.79.2	yes	16	3.2	odd	2
450.2.l.c.19.3		16	25.19	even	10	inner
450.2.l.c.379.3		16	1.1	even	1	trivial
750.2.g.f.151.1		16	75.17	even	20
750.2.g.f.601.1		16	15.2	even	4
750.2.g.g.151.4		16	75.8	even	20
750.2.g.g.601.4		16	15.8	even	4
750.2.h.d.349.4		16	75.56	odd	10
750.2.h.d.649.3		16	15.14	odd	2
3750.2.a.u.1.7		8	75.38	even	20
3750.2.a.v.1.2		8	75.62	even	20
3750.2.c.k.1249.7		16	75.41	odd	10
3750.2.c.k.1249.10		16	75.59	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.809017 + 0.587785i) q^{4} +(-2.23558 - 0.0466062i) q^{5} +3.52206i q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.11176 - 0.735158i) q^{10} +(-1.62388 + 4.99779i) q^{11} +(-0.588802 + 0.191313i) q^{13} +(-1.08838 + 3.34968i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-2.02525 - 2.78752i) q^{17} +(1.83995 - 1.33680i) q^{19} +(-1.78123 - 1.35175i) q^{20} +(-3.08880 + 4.25137i) q^{22} +(8.51557 + 2.76688i) q^{23} +(4.99566 + 0.208384i) q^{25} -0.619103 q^{26} +(-2.07022 + 2.84941i) q^{28} +(2.16949 + 1.57623i) q^{29} +(-7.90309 + 5.74193i) q^{31} +1.00000i q^{32} +(-1.06474 - 3.27693i) q^{34} +(0.164150 - 7.87386i) q^{35} +(-0.952702 + 0.309552i) q^{37} +(2.16299 - 0.702799i) q^{38} +(-1.27634 - 1.83602i) q^{40} +(-1.94584 - 5.98868i) q^{41} -1.51251i q^{43} +(-4.25137 + 3.08880i) q^{44} +(7.24378 + 5.26291i) q^{46} +(6.27522 - 8.63710i) q^{47} -5.40494 q^{49} +(4.68676 + 1.74193i) q^{50} +(-0.588802 - 0.191313i) q^{52} +(-0.325260 + 0.447681i) q^{53} +(3.86324 - 11.0973i) q^{55} +(-2.84941 + 2.07022i) q^{56} +(1.57623 + 2.16949i) q^{58} +(0.0861451 + 0.265127i) q^{59} +(1.13786 - 3.50196i) q^{61} +(-9.29064 + 3.01871i) q^{62} +(-0.309017 + 0.951057i) q^{64} +(1.32523 - 0.400255i) q^{65} +(-7.00176 - 9.63710i) q^{67} -3.44557i q^{68} +(2.58927 - 7.43777i) q^{70} +(3.84168 + 2.79115i) q^{71} +(9.35277 + 3.03890i) q^{73} -1.00173 q^{74} +2.27431 q^{76} +(-17.6025 - 5.71941i) q^{77} +(5.27525 + 3.83269i) q^{79} +(-0.646508 - 2.14057i) q^{80} -6.29687i q^{82} +(1.56335 + 2.15177i) q^{83} +(4.39770 + 6.32612i) q^{85} +(0.467392 - 1.43848i) q^{86} +(-4.99779 + 1.62388i) q^{88} +(-4.13649 + 12.7308i) q^{89} +(-0.673818 - 2.07380i) q^{91} +(5.26291 + 7.24378i) q^{92} +(8.63710 - 6.27522i) q^{94} +(-4.17567 + 2.90278i) q^{95} +(-2.56983 + 3.53706i) q^{97} +(-5.14040 - 1.67022i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 4 q^{5} + 2 q^{10} - 2 q^{11} + 20 q^{13} - 2 q^{14} - 4 q^{16} + 30 q^{17} + 4 q^{20} - 20 q^{22} + 10 q^{23} + 24 q^{25} - 4 q^{26} + 10 q^{29} - 18 q^{31} + 12 q^{34} + 34 q^{35} + 20 q^{37}+ \cdots - 60 q^{98}+O(q^{100}) \) 16 * q + 4 * q^4 - 4 * q^5 + 2 * q^10 - 2 * q^11 + 20 * q^13 - 2 * q^14 - 4 * q^16 + 30 * q^17 + 4 * q^20 - 20 * q^22 + 10 * q^23 + 24 * q^25 - 4 * q^26 + 10 * q^29 - 18 * q^31 + 12 * q^34 + 34 * q^35 + 20 * q^37 - 10 * q^38 - 2 * q^40 - 22 * q^41 - 8 * q^44 - 6 * q^46 + 50 * q^47 - 52 * q^49 - 12 * q^50 + 20 * q^52 - 30 * q^53 + 18 * q^55 + 2 * q^56 - 30 * q^58 - 20 * q^59 + 12 * q^61 - 50 * q^62 + 4 * q^64 + 8 * q^65 - 50 * q^67 - 12 * q^70 + 28 * q^71 + 20 * q^73 - 12 * q^74 + 20 * q^76 - 100 * q^77 - 20 * q^79 - 4 * q^80 + 30 * q^83 - 4 * q^85 + 6 * q^86 - 70 * q^89 + 12 * q^91 + 30 * q^92 + 2 * q^94 + 30 * q^95 - 10 * q^97 - 60 * q^98

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