LMFDB - Embedded newform 975.2.n.r.749.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(749,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.749"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.n (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,0,0,12,16,0,0,0,0,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			749.15
Character	$\chi$	$=$	975.749
Dual form			975.2.n.r.824.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.11881 + 1.11881i) q^{2} +(1.67111 + 0.455401i) q^{3} +0.503463i q^{4} +(1.36015 + 2.37916i) q^{6} +(-1.46633 - 1.46633i) q^{7} +(1.67434 - 1.67434i) q^{8} +(2.58522 + 1.52205i) q^{9} +(0.292930 + 0.292930i) q^{11} +(-0.229277 + 0.841342i) q^{12} +(2.86241 + 2.19240i) q^{13} -3.28107i q^{14} +4.75345 q^{16} -2.78074i q^{17} +(1.18948 + 4.59525i) q^{18} +(1.21080 + 1.21080i) q^{19} +(-1.78263 - 3.11816i) q^{21} +0.655464i q^{22} +5.66438i q^{23} +(3.56050 - 2.03551i) q^{24} +(0.749610 + 5.65536i) q^{26} +(3.62704 + 3.72083i) q^{27} +(0.738240 - 0.738240i) q^{28} -7.34233i q^{29} +(-1.98010 - 1.98010i) q^{31} +(1.96952 + 1.96952i) q^{32} +(0.356117 + 0.622918i) q^{33} +(3.11111 - 3.11111i) q^{34} +(-0.766296 + 1.30156i) q^{36} +(3.02847 + 3.02847i) q^{37} +2.70931i q^{38} +(3.78498 + 4.96729i) q^{39} +(-3.08783 + 3.08783i) q^{41} +(1.49420 - 5.48304i) q^{42} +0.831012 q^{43} +(-0.147479 + 0.147479i) q^{44} +(-6.33735 + 6.33735i) q^{46} +(-8.76367 + 8.76367i) q^{47} +(7.94354 + 2.16473i) q^{48} -2.69978i q^{49} +(1.26635 - 4.64692i) q^{51} +(-1.10379 + 1.44112i) q^{52} -0.258401 q^{53} +(-0.104926 + 8.22086i) q^{54} -4.91025 q^{56} +(1.47198 + 2.57478i) q^{57} +(8.21465 - 8.21465i) q^{58} +(-2.38433 - 2.38433i) q^{59} -3.66100 q^{61} -4.43070i q^{62} +(-1.55895 - 6.02260i) q^{63} -5.09987i q^{64} +(-0.298499 + 1.09535i) q^{66} +(9.29391 - 9.29391i) q^{67} +1.40000 q^{68} +(-2.57957 + 9.46581i) q^{69} +(-7.88169 + 7.88169i) q^{71} +(6.87696 - 1.78010i) q^{72} +(-11.5212 - 11.5212i) q^{73} +6.77656i q^{74} +(-0.609593 + 0.609593i) q^{76} -0.859060i q^{77} +(-1.32278 + 9.79210i) q^{78} -16.3100 q^{79} +(4.36672 + 7.86967i) q^{81} -6.90938 q^{82} +(10.1694 + 10.1694i) q^{83} +(1.56988 - 0.897486i) q^{84} +(0.929743 + 0.929743i) q^{86} +(3.34370 - 12.2698i) q^{87} +0.980926 q^{88} +(-4.97395 - 4.97395i) q^{89} +(-0.982449 - 7.41200i) q^{91} -2.85180 q^{92} +(-2.40722 - 4.21070i) q^{93} -19.6097 q^{94} +(2.39437 + 4.18821i) q^{96} +(-8.41532 + 8.41532i) q^{97} +(3.02053 - 3.02053i) q^{98} +(0.311433 + 1.20314i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 12 q^{6} + 16 q^{7} + 24 q^{12} - 24 q^{13} - 64 q^{16} - 4 q^{18} + 16 q^{19} - 12 q^{21} - 8 q^{24} - 32 q^{28} + 32 q^{31} - 4 q^{33} + 16 q^{34} - 32 q^{37} + 8 q^{39} + 32 q^{43} - 40 q^{46}+ \cdots + 20 q^{99}+O(q^{100}) $ 40 * q + 12 * q^6 + 16 * q^7 + 24 * q^12 - 24 * q^13 - 64 * q^16 - 4 * q^18 + 16 * q^19 - 12 * q^21 - 8 * q^24 - 32 * q^28 + 32 * q^31 - 4 * q^33 + 16 * q^34 - 32 * q^37 + 8 * q^39 + 32 * q^43 - 40 * q^46 + 8 * q^52 + 32 * q^54 - 36 * q^57 - 24 * q^58 + 8 * q^61 + 8 * q^63 - 48 * q^66 - 32 * q^67 - 132 * q^72 - 64 * q^73 + 16 * q^76 + 108 * q^78 - 40 * q^79 + 72 * q^81 + 128 * q^82 - 124 * q^84 + 80 * q^88 + 8 * q^91 + 108 * q^93 + 32 * q^94 - 76 * q^96 + 24 * q^97 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.11881	+	1.11881i	0.791117	+	0.791117i	0.981676	−	0.190559i	$-0.0610301\pi$
$2$	1.11881	+	1.11881i	0.791117	+	0.791117i	−0.190559	+	0.981676i	$0.561030\pi$
$3$	1.67111	+	0.455401i	0.964816	+	0.262926i
$3$	1.67111	+	0.455401i	0.964816	+	0.262926i
$4$			0.503463i			0.251731i
$5$		0			0
$5$		0			0
$6$	1.36015	+	2.37916i	0.555277	+	0.971287i
$7$	−1.46633	−	1.46633i	−0.554219	−	0.554219i	0.373437	−	0.927656i	$-0.378179\pi$
$7$	−1.46633	−	1.46633i	−0.554219	−	0.554219i	−0.927656	+	0.373437i	$0.878179\pi$
$8$	1.67434	−	1.67434i	0.591968	−	0.591968i
$9$	2.58522	+	1.52205i	0.861740	+	0.507350i
$10$		0			0
$11$	0.292930	+	0.292930i	0.0883216	+	0.0883216i	0.749887	−	0.661566i	$-0.230108\pi$
$11$	0.292930	+	0.292930i	0.0883216	+	0.0883216i	−0.661566	+	0.749887i	$0.730108\pi$
$12$	−0.229277	+	0.841342i	−0.0661867	+	0.242874i
$13$	2.86241	+	2.19240i	0.793889	+	0.608063i
$13$	2.86241	+	2.19240i	0.793889	+	0.608063i
$14$		−	3.28107i		−	0.876904i
$15$		0			0
$16$	4.75345			1.18836
$17$		−	2.78074i		−	0.674427i	−0.941428	−	0.337214i	$-0.890516\pi$
$17$		−	2.78074i		−	0.674427i	0.941428	−	0.337214i	$-0.109484\pi$
$18$	1.18948	+	4.59525i	0.280363	+	1.08311i
$19$	1.21080	+	1.21080i	0.277777	+	0.277777i	0.832221	−	0.554444i	$-0.187069\pi$
$19$	1.21080	+	1.21080i	0.277777	+	0.277777i	−0.554444	+	0.832221i	$0.687069\pi$
$20$		0			0
$21$	−1.78263	−	3.11816i	−0.389001	−	0.680438i
$22$			0.655464i			0.139745i
$23$			5.66438i			1.18111i	0.806999	+	0.590553i	$0.201090\pi$
$23$			5.66438i			1.18111i	−0.806999	+	0.590553i	$0.798910\pi$
$24$	3.56050	−	2.03551i	0.726784	−	0.415496i
$25$		0			0
$26$	0.749610	+	5.65536i	0.147011	+	1.10911i
$27$	3.62704	+	3.72083i	0.698025	+	0.716074i
$28$	0.738240	−	0.738240i	0.139514	−	0.139514i
$29$		−	7.34233i		−	1.36344i	−0.731615	−	0.681718i	$-0.761233\pi$
$29$		−	7.34233i		−	1.36344i	0.731615	−	0.681718i	$-0.238767\pi$
$30$		0			0
$31$	−1.98010	−	1.98010i	−0.355636	−	0.355636i	0.506565	−	0.862202i	$-0.330915\pi$
$31$	−1.98010	−	1.98010i	−0.355636	−	0.355636i	−0.862202	+	0.506565i	$0.830915\pi$
$32$	1.96952	+	1.96952i	0.348166	+	0.348166i
$33$	0.356117	+	0.622918i	0.0619920	+	0.108436i
$34$	3.11111	−	3.11111i	0.533551	−	0.533551i
$35$		0			0
$36$	−0.766296	+	1.30156i	−0.127716	+	0.216927i
$37$	3.02847	+	3.02847i	0.497878	+	0.497878i	0.910777	−	0.412899i	$-0.135484\pi$
$37$	3.02847	+	3.02847i	0.497878	+	0.497878i	−0.412899	+	0.910777i	$0.635484\pi$
$38$			2.70931i			0.439508i
$39$	3.78498	+	4.96729i	0.606082	+	0.795403i
$40$		0			0
$41$	−3.08783	+	3.08783i	−0.482238	+	0.482238i	−0.905846	−	0.423608i	$-0.860764\pi$
$41$	−3.08783	+	3.08783i	−0.482238	+	0.482238i	0.423608	+	0.905846i	$0.360764\pi$
$42$	1.49420	−	5.48304i	0.230561	−	0.846051i
$43$	0.831012			0.126728			0.0633640	−	0.997990i	$-0.479817\pi$
$43$	0.831012			0.126728			0.0633640	+	0.997990i	$0.479817\pi$
$44$	−0.147479	+	0.147479i	−0.0222333	+	0.0222333i
$45$		0			0
$46$	−6.33735	+	6.33735i	−0.934392	+	0.934392i
$47$	−8.76367	+	8.76367i	−1.27831	+	1.27831i	−0.336702	+	0.941611i	$0.609312\pi$
$47$	−8.76367	+	8.76367i	−1.27831	+	1.27831i	−0.941611	+	0.336702i	$0.890688\pi$
$48$	7.94354	+	2.16473i	1.14655	+	0.312451i
$49$		−	2.69978i		−	0.385682i
$50$		0			0
$51$	1.26635	−	4.64692i	0.177324	−	0.650698i
$52$	−1.10379	+	1.44112i	−0.153068	+	0.199847i
$53$	−0.258401			−0.0354940			−0.0177470	−	0.999843i	$-0.505649\pi$
$53$	−0.258401			−0.0354940			−0.0177470	+	0.999843i	$0.505649\pi$
$54$	−0.104926	+	8.22086i	−0.0142787	+	1.11872i
$55$		0			0
$56$	−4.91025			−0.656160
$57$	1.47198	+	2.57478i	0.194969	+	0.341038i
$58$	8.21465	−	8.21465i	1.07864	−	1.07864i
$59$	−2.38433	−	2.38433i	−0.310414	−	0.310414i	0.534656	−	0.845070i	$-0.320441\pi$
$59$	−2.38433	−	2.38433i	−0.310414	−	0.310414i	−0.845070	+	0.534656i	$0.820441\pi$
$60$		0			0
$61$	−3.66100			−0.468744			−0.234372	−	0.972147i	$-0.575303\pi$
$61$	−3.66100			−0.468744			−0.234372	+	0.972147i	$0.575303\pi$
$62$		−	4.43070i		−	0.562699i
$63$	−1.55895	−	6.02260i	−0.196409	−	0.758776i
$64$		−	5.09987i		−	0.637483i
$65$		0			0
$66$	−0.298499	+	1.09535i	−0.0367427	+	0.134829i
$67$	9.29391	−	9.29391i	1.13543	−	1.13543i	0.146173	−	0.989259i	$-0.453304\pi$
$67$	9.29391	−	9.29391i	1.13543	−	1.13543i	0.989259	−	0.146173i	$-0.0466957\pi$
$68$	1.40000			0.169775
$69$	−2.57957	+	9.46581i	−0.310543	+	1.13955i
$70$		0			0
$71$	−7.88169	+	7.88169i	−0.935385	+	0.935385i	−0.998036	−	0.0626508i	$-0.980045\pi$
$71$	−7.88169	+	7.88169i	−0.935385	+	0.935385i	0.0626508	+	0.998036i	$0.480045\pi$
$72$	6.87696	−	1.78010i	0.810457	−	0.209787i
$73$	−11.5212	−	11.5212i	−1.34845	−	1.34845i	−0.887345	−	0.461107i	$-0.847453\pi$
$73$	−11.5212	−	11.5212i	−1.34845	−	1.34845i	−0.461107	−	0.887345i	$-0.652547\pi$
$74$			6.77656i			0.787759i
$75$		0			0
$76$	−0.609593	+	0.609593i	−0.0699252	+	0.0699252i
$77$		−	0.859060i		−	0.0978990i
$78$	−1.32278	+	9.79210i	−0.149775	+	1.10874i
$79$	−16.3100			−1.83502			−0.917512	−	0.397708i	$-0.869806\pi$
$79$	−16.3100			−1.83502			−0.917512	+	0.397708i	$0.869806\pi$
$80$		0			0
$81$	4.36672	+	7.86967i	0.485191	+	0.874408i
$82$	−6.90938			−0.763013
$83$	10.1694	+	10.1694i	1.11624	+	1.11624i	0.992288	+	0.123950i	$0.0395564\pi$
$83$	10.1694	+	10.1694i	1.11624	+	1.11624i	0.123950	+	0.992288i	$0.460444\pi$
$84$	1.56988	−	0.897486i	0.171288	−	0.0979237i
$85$		0			0
$86$	0.929743	+	0.929743i	0.100257	+	0.100257i
$87$	3.34370	−	12.2698i	0.358483	−	1.31546i
$88$	0.980926			0.104567
$89$	−4.97395	−	4.97395i	−0.527238	−	0.527238i	0.392510	−	0.919748i	$-0.371607\pi$
$89$	−4.97395	−	4.97395i	−0.527238	−	0.527238i	−0.919748	+	0.392510i	$0.871607\pi$
$90$		0			0
$91$	−0.982449	−	7.41200i	−0.102989	−	0.776988i
$92$	−2.85180			−0.297321
$93$	−2.40722	−	4.21070i	−0.249617	−	0.436629i
$94$	−19.6097			−2.02259
$95$		0			0
$96$	2.39437	+	4.18821i	0.244374	+	0.427458i
$97$	−8.41532	+	8.41532i	−0.854447	+	0.854447i	−0.990677	−	0.136231i	$-0.956501\pi$
$97$	−8.41532	+	8.41532i	−0.854447	+	0.854447i	0.136231	+	0.990677i	$0.456501\pi$
$98$	3.02053	−	3.02053i	0.305120	−	0.305120i
$99$	0.311433	+	1.20314i	0.0313002	+	0.120920i
$100$		0			0
$101$	6.35267			0.632114			0.316057	−	0.948740i	$-0.397641\pi$
$101$	6.35267			0.632114			0.316057	+	0.948740i	$0.397641\pi$
$102$	6.61581	−	3.78220i	0.655063	−	0.374494i
$103$	7.54935			0.743860			0.371930	−	0.928261i	$-0.378696\pi$
$103$	7.54935			0.743860			0.371930	+	0.928261i	$0.378696\pi$
$104$	8.46346	−	1.12182i	0.829910	−	0.110003i
$105$		0			0
$106$	−0.289101	−	0.289101i	−0.0280799	−	0.0280799i
$107$	−3.69172			−0.356892			−0.178446	−	0.983950i	$-0.557107\pi$
$107$	−3.69172			−0.356892			−0.178446	+	0.983950i	$0.557107\pi$
$108$	−1.87330	+	1.82608i	−0.180258	+	0.175715i
$109$	−10.1957	−	10.1957i	−0.976570	−	0.976570i	0.0231620	−	0.999732i	$-0.492627\pi$
$109$	−10.1957	−	10.1957i	−0.976570	−	0.976570i	−0.999732	+	0.0231620i	$0.992627\pi$
$110$		0			0
$111$	3.68174	+	6.44008i	0.349456	+	0.611266i
$112$	−6.97011	−	6.97011i	−0.658613	−	0.658613i
$113$	−17.3519			−1.63233			−0.816164	−	0.577820i	$-0.803903\pi$
$113$	−17.3519			−1.63233			−0.816164	+	0.577820i	$0.803903\pi$
$114$	−1.23382	+	4.52755i	−0.115558	+	0.424044i
$115$		0			0
$116$	3.69659			0.343219
$117$	4.06301	+	10.0246i	0.375625	+	0.926772i
$118$		−	5.33522i		−	0.491147i
$119$	−4.07746	+	4.07746i	−0.373781	+	0.373781i
$120$		0			0
$121$		−	10.8284i		−	0.984399i
$122$	−4.09596	−	4.09596i	−0.370831	−	0.370831i
$123$	−6.56631	+	3.75390i	−0.592064	+	0.338478i
$124$	0.996906	−	0.996906i	0.0895248	−	0.0895248i
$125$		0			0
$126$	4.99396	−	8.48230i	0.444898	−	0.755663i
$127$	21.0990			1.87224			0.936118	−	0.351686i	$-0.114392\pi$
$127$	21.0990			1.87224			0.936118	+	0.351686i	$0.114392\pi$
$128$	9.64482	−	9.64482i	0.852489	−	0.852489i
$129$	1.38871	+	0.378444i	0.122269	+	0.0333201i
$130$		0			0
$131$		−	9.86242i		−	0.861684i	−0.902427	−	0.430842i	$-0.858217\pi$
$131$		−	9.86242i		−	0.861684i	0.902427	−	0.430842i	$-0.141783\pi$
$132$	−0.313616	+	0.179292i	−0.0272968	+	0.0156053i
$133$		−	3.55086i		−	0.307899i
$134$	20.7962			1.79652
$135$		0			0
$136$	−4.65589	−	4.65589i	−0.399239	−	0.399239i
$137$	−6.51118	+	6.51118i	−0.556288	+	0.556288i	−0.928249	−	0.371961i	$-0.878686\pi$
$137$	−6.51118	+	6.51118i	−0.556288	+	0.556288i	0.371961	+	0.928249i	$0.378686\pi$
$138$	−13.4765	+	7.70438i	−1.14719	+	0.655840i
$139$	4.65409			0.394755			0.197377	−	0.980328i	$-0.436758\pi$
$139$	4.65409			0.394755			0.197377	+	0.980328i	$0.436758\pi$
$140$		0			0
$141$	−18.6361	+	10.6541i	−1.56944	+	0.897235i
$142$	−17.6362			−1.48000
$143$	0.196265	+	1.48070i	0.0164125	+	0.123823i
$144$	12.2887	+	7.23500i	1.02406	+	0.602916i
$145$		0			0
$146$		−	25.7800i		−	2.13356i
$147$	1.22948	−	4.51163i	0.101406	−	0.372113i
$148$	−1.52472	+	1.52472i	−0.125331	+	0.125331i
$149$	−11.8788	+	11.8788i	−0.973150	+	0.973150i	−0.999649	−	0.0264986i	$-0.991564\pi$
$149$	−11.8788	+	11.8788i	−0.973150	+	0.973150i	0.0264986	+	0.999649i	$0.491564\pi$
$150$		0			0
$151$	4.96656	−	4.96656i	0.404173	−	0.404173i	−0.475528	−	0.879701i	$-0.657743\pi$
$151$	4.96656	−	4.96656i	0.404173	−	0.404173i	0.879701	+	0.475528i	$0.157743\pi$
$152$	4.05458			0.328870
$153$	4.23242	−	7.18881i	0.342171	−	0.581181i
$154$	0.961124	−	0.961124i	0.0774496	−	0.0774496i
$155$		0			0
$156$	−2.50084	+	1.90560i	−0.200228	+	0.152570i
$157$			15.9533i			1.27321i	0.771190	+	0.636606i	$0.219662\pi$
$157$			15.9533i			1.27321i	−0.771190	+	0.636606i	$0.780338\pi$
$158$	−18.2478	−	18.2478i	−1.45172	−	1.45172i
$159$	−0.431816	−	0.117676i	−0.0342452	−	0.00933231i
$160$		0			0
$161$	8.30583	−	8.30583i	0.654591	−	0.654591i
$162$	−3.91913	+	13.6902i	−0.307916	+	1.07560i
$163$	4.37713	+	4.37713i	0.342843	+	0.342843i	0.857435	−	0.514592i	$-0.172057\pi$
$163$	4.37713	+	4.37713i	0.342843	+	0.342843i	−0.514592	+	0.857435i	$0.672057\pi$
$164$	−1.55461	−	1.55461i	−0.121394	−	0.121394i
$165$		0			0
$166$			22.7553i			1.76615i
$167$	−3.94953	+	3.94953i	−0.305624	+	0.305624i	−0.843209	−	0.537585i	$-0.819337\pi$
$167$	−3.94953	+	3.94953i	−0.305624	+	0.305624i	0.537585	+	0.843209i	$0.319337\pi$
$168$	−8.20557	−	2.23613i	−0.633073	−	0.172521i
$169$	3.38676	+	12.5511i	0.260520	+	0.965468i
$170$		0			0
$171$	1.28729	+	4.97309i	0.0984412	+	0.380302i
$172$			0.418383i			0.0319014i
$173$			9.74943i			0.741235i	0.928786	+	0.370618i	$0.120854\pi$
$173$			9.74943i			0.741235i	−0.928786	+	0.370618i	$0.879146\pi$
$174$	17.4686	−	9.98663i	1.32429	−	0.757084i
$175$		0			0
$176$	1.39243	+	1.39243i	0.104958	+	0.104958i
$177$	−2.89866	−	5.07031i	−0.217876	−	0.381108i
$178$		−	11.1298i		−	0.834213i
$179$	−1.28470			−0.0960232			−0.0480116	−	0.998847i	$-0.515288\pi$
$179$	−1.28470			−0.0960232			−0.0480116	+	0.998847i	$0.515288\pi$
$180$		0			0
$181$			5.39074i			0.400690i	0.979725	+	0.200345i	$0.0642064\pi$
$181$			5.39074i			0.400690i	−0.979725	+	0.200345i	$0.935794\pi$
$182$	7.19343	−	9.39177i	0.533212	−	0.696165i
$183$	−6.11794	−	1.66723i	−0.452251	−	0.123245i
$184$	9.48409	+	9.48409i	0.699176	+	0.699176i
$185$		0			0
$186$	2.01775	−	7.40419i	0.147948	−	0.542901i
$187$	0.814560	−	0.814560i	0.0595665	−	0.0595665i
$188$	−4.41218	−	4.41218i	−0.321792	−	0.321792i
$189$	0.137518	−	10.7744i	0.0100030	−	0.783720i
$190$		0			0
$191$			8.13709i			0.588779i	0.955686	+	0.294390i	$0.0951163\pi$
$191$			8.13709i			0.588779i	−0.955686	+	0.294390i	$0.904884\pi$
$192$	2.32248	−	8.52244i	0.167611	−	0.615054i
$193$	2.02917	+	2.02917i	0.146063	+	0.146063i	0.776357	−	0.630294i	$-0.217066\pi$
$193$	2.02917	+	2.02917i	0.146063	+	0.146063i	−0.630294	+	0.776357i	$0.717066\pi$
$194$	−18.8303			−1.35193
$195$		0			0
$196$	1.35924			0.0970884
$197$	3.10238	+	3.10238i	0.221036	+	0.221036i	0.808934	−	0.587899i	$-0.200045\pi$
$197$	3.10238	+	3.10238i	0.221036	+	0.221036i	−0.587899	+	0.808934i	$0.700045\pi$
$198$	−0.997650	+	1.69452i	−0.0708999	+	0.120424i
$199$		−	3.79864i		−	0.269279i	−0.990895	−	0.134639i	$-0.957012\pi$
$199$		−	3.79864i		−	0.269279i	0.990895	−	0.134639i	$-0.0429876\pi$
$200$		0			0
$201$	19.7636	−	11.2987i	1.39402	−	0.796949i
$202$	7.10742	+	7.10742i	0.500076	+	0.500076i
$203$	−10.7662	+	10.7662i	−0.755642	+	0.755642i
$204$	2.33955	+	0.637560i	0.163801	+	0.0446381i
$205$		0			0
$206$	8.44627	+	8.44627i	0.588480	+	0.588480i
$207$	−8.62148	+	14.6437i	−0.599234	+	1.01781i
$208$	13.6063	+	10.4215i	0.943428	+	0.722599i
$209$			0.709359i			0.0490674i
$210$		0			0
$211$	5.97128			0.411080			0.205540	−	0.978649i	$-0.434105\pi$
$211$	5.97128			0.411080			0.205540	+	0.978649i	$0.434105\pi$
$212$		−	0.130095i		−	0.00893496i
$213$	−16.7605	+	9.58185i	−1.14841	+	0.656537i
$214$	−4.13032	−	4.13032i	−0.282343	−	0.282343i
$215$		0			0
$216$	12.3028	+	0.157026i	0.837101	+	0.0106843i
$217$			5.80694i			0.394201i
$218$		−	22.8140i		−	1.54516i
$219$	−14.0064	−	24.4999i	−0.946465	−	1.65555i
$220$		0			0
$221$	6.09649	−	7.95960i	0.410094	−	0.535421i
$222$	−3.08605	+	11.3244i	−0.207122	+	0.760042i
$223$	−4.16343	+	4.16343i	−0.278804	+	0.278804i	−0.832631	−	0.553827i	$-0.813167\pi$
$223$	−4.16343	+	4.16343i	−0.278804	+	0.278804i	0.553827	+	0.832631i	$0.313167\pi$
$224$		−	5.77592i		−	0.385920i
$225$		0			0
$226$	−19.4134	−	19.4134i	−1.29136	−	1.29136i
$227$	−7.99122	−	7.99122i	−0.530396	−	0.530396i	0.390294	−	0.920690i	$-0.372373\pi$
$227$	−7.99122	−	7.99122i	−0.530396	−	0.530396i	−0.920690	+	0.390294i	$0.872373\pi$
$228$	−1.29631	+	0.741088i	−0.0858501	+	0.0490798i
$229$	14.7738	−	14.7738i	0.976279	−	0.976279i	−0.0234464	−	0.999725i	$-0.507464\pi$
$229$	14.7738	−	14.7738i	0.976279	−	0.976279i	0.999725	+	0.0234464i	$0.00746389\pi$
$230$		0			0
$231$	0.391217	−	1.43558i	0.0257402	−	0.0944545i
$232$	−12.2935	−	12.2935i	−0.807110	−	0.807110i
$233$		−	15.0434i		−	0.985527i	−0.870163	−	0.492764i	$-0.835987\pi$
$233$		−	15.0434i		−	0.985527i	0.870163	−	0.492764i	$-0.164013\pi$
$234$	−6.66984	+	15.7613i	−0.436021	+	1.03035i
$235$		0			0
$236$	1.20042	−	1.20042i	0.0781409	−	0.0781409i
$237$	−27.2559	−	7.42762i	−1.77046	−	0.482475i
$238$	−9.12380			−0.591408
$239$	5.13466	−	5.13466i	0.332134	−	0.332134i	−0.521263	−	0.853396i	$-0.674539\pi$
$239$	5.13466	−	5.13466i	0.332134	−	0.332134i	0.853396	+	0.521263i	$0.174539\pi$
$240$		0			0
$241$	4.11251	−	4.11251i	0.264910	−	0.264910i	−0.562135	−	0.827045i	$-0.690020\pi$
$241$	4.11251	−	4.11251i	0.264910	−	0.264910i	0.827045	+	0.562135i	$0.190020\pi$
$242$	12.1149	−	12.1149i	0.778774	−	0.778774i
$243$	3.71341	+	15.1397i	0.238216	+	0.971212i
$244$		−	1.84318i		−	0.117997i
$245$		0			0
$246$	−11.5463	−	3.14654i	−0.736167	−	0.200616i
$247$	0.811246	+	6.12037i	0.0516183	+	0.389430i
$248$	−6.63071			−0.421050
$249$	12.3631	+	21.6254i	0.783477	+	1.37045i
$250$		0			0
$251$	−5.50029			−0.347175			−0.173588	−	0.984818i	$-0.555536\pi$
$251$	−5.50029			−0.347175			−0.173588	+	0.984818i	$0.555536\pi$
$252$	3.03215	−	0.784874i	0.191008	−	0.0494424i
$253$	−1.65926	+	1.65926i	−0.104317	+	0.104317i
$254$	23.6058	+	23.6058i	1.48116	+	1.48116i
$255$		0			0
$256$	11.3817			0.711354
$257$			7.45007i			0.464723i	0.972630	+	0.232361i	$0.0746452\pi$
$257$			7.45007i			0.464723i	−0.972630	+	0.232361i	$0.925355\pi$
$258$	1.13030	+	1.97711i	0.0703692	+	0.123089i
$259$		−	8.88146i		−	0.551867i
$260$		0			0
$261$	11.1754	−	18.9815i	0.691740	−	1.17493i
$262$	11.0342	−	11.0342i	0.681692	−	0.681692i
$263$	23.1846			1.42962			0.714812	−	0.699317i	$-0.246512\pi$
$263$	23.1846			1.42962			0.714812	+	0.699317i	$0.246512\pi$
$264$	1.63924	+	0.446715i	0.100888	+	0.0274934i
$265$		0			0
$266$	3.97273	−	3.97273i	0.243584	−	0.243584i
$267$	−6.04688	−	10.5772i	−0.370063	−	0.647312i
$268$	4.67914	+	4.67914i	0.285824	+	0.285824i
$269$		−	26.7447i		−	1.63065i	−0.579002	−	0.815326i	$-0.696558\pi$
$269$		−	26.7447i		−	1.63065i	0.579002	−	0.815326i	$-0.303442\pi$
$270$		0			0
$271$	−2.78066	+	2.78066i	−0.168913	+	0.168913i	−0.786501	−	0.617588i	$-0.788110\pi$
$271$	−2.78066	+	2.78066i	−0.168913	+	0.168913i	0.617588	+	0.786501i	$0.288110\pi$
$272$		−	13.2181i		−	0.801464i
$273$	1.73365	−	12.8337i	0.104925	−	0.776729i
$274$	−14.5695			−0.880177
$275$		0			0
$276$	−4.76568	−	1.29872i	−0.286860	−	0.0781735i
$277$	28.6741			1.72286			0.861431	−	0.507874i	$-0.169569\pi$
$277$	28.6741			1.72286			0.861431	+	0.507874i	$0.169569\pi$
$278$	5.20703	+	5.20703i	0.312297	+	0.312297i
$279$	−2.10518	−	8.13280i	−0.126034	−	0.486898i
$280$		0			0
$281$	−0.811843	−	0.811843i	−0.0484305	−	0.0484305i	0.682477	−	0.730907i	$-0.260903\pi$
$281$	−0.811843	−	0.811843i	−0.0484305	−	0.0484305i	−0.730907	+	0.682477i	$0.760903\pi$
$282$	−32.7700	−	8.93030i	−1.95143	−	0.531791i
$283$	22.9639			1.36506			0.682531	−	0.730857i	$-0.260879\pi$
$283$	22.9639			1.36506			0.682531	+	0.730857i	$0.260879\pi$
$284$	−3.96814	−	3.96814i	−0.235466	−	0.235466i
$285$		0			0
$286$	−1.43704	+	1.87621i	−0.0849739	+	0.110942i
$287$	9.05553			0.534531
$288$	2.09393	+	8.08936i	0.123386	+	0.476670i
$289$	9.26751			0.545148
$290$		0			0
$291$	−17.8953	+	10.2306i	−1.04904	+	0.599728i
$292$	5.80048	−	5.80048i	0.339447	−	0.339447i
$293$	−8.25860	+	8.25860i	−0.482472	+	0.482472i	−0.905920	−	0.423448i	$-0.860820\pi$
$293$	−8.25860	+	8.25860i	−0.482472	+	0.482472i	0.423448	+	0.905920i	$0.360820\pi$
$294$	6.42320	−	3.67209i	0.374608	−	0.214161i
$295$		0			0
$296$	10.1414			0.589455
$297$	−0.0274721	+	2.15241i	−0.00159409	+	0.124895i
$298$	−26.5802			−1.53975
$299$	−12.4186	+	16.2138i	−0.718186	+	0.937666i
$300$		0			0
$301$	−1.21853	−	1.21853i	−0.0702351	−	0.0702351i
$302$	11.1133			0.639496
$303$	10.6160	+	2.89301i	0.609874	+	0.166199i
$304$	5.75549	+	5.75549i	0.330100	+	0.330100i
$305$		0			0
$306$	12.7782	−	3.30763i	0.730479	−	0.189085i
$307$	−22.4159	−	22.4159i	−1.27934	−	1.27934i	−0.941035	−	0.338310i	$-0.890145\pi$
$307$	−22.4159	−	22.4159i	−1.27934	−	1.27934i	−0.338310	−	0.941035i	$-0.609855\pi$
$308$	0.432505			0.0246443
$309$	12.6158	+	3.43798i	0.717688	+	0.195580i
$310$		0			0
$311$	−21.6419			−1.22720			−0.613600	−	0.789617i	$-0.710279\pi$
$311$	−21.6419			−1.22720			−0.613600	+	0.789617i	$0.710279\pi$
$312$	14.6542	+	1.97959i	0.829633	+	0.112072i
$313$			7.12210i			0.402565i	0.979533	+	0.201282i	$0.0645109\pi$
$313$			7.12210i			0.402565i	−0.979533	+	0.201282i	$0.935489\pi$
$314$	−17.8487	+	17.8487i	−1.00726	+	1.00726i
$315$		0			0
$316$		−	8.21150i		−	0.461933i
$317$	14.9932	+	14.9932i	0.842104	+	0.842104i	0.989132	−	0.147028i	$-0.0469707\pi$
$317$	14.9932	+	14.9932i	0.842104	+	0.842104i	−0.147028	+	0.989132i	$0.546971\pi$
$318$	−0.351462	−	0.614776i	−0.0197090	−	0.0344749i
$319$	2.15078	−	2.15078i	0.120421	−	0.120421i
$320$		0			0
$321$	−6.16927	−	1.68121i	−0.344335	−	0.0938361i
$322$	18.5853			1.03572
$323$	3.36692	−	3.36692i	0.187340	−	0.187340i
$324$	−3.96209	+	2.19848i	−0.220116	+	0.122138i
$325$		0			0
$326$			9.79433i			0.542458i
$327$	−12.3950	−	21.6812i	−0.685445	−	1.19898i
$328$			10.3401i			0.570939i
$329$	25.7008			1.41693
$330$		0			0
$331$	−6.48090	−	6.48090i	−0.356223	−	0.356223i	0.506196	−	0.862418i	$-0.331051\pi$
$331$	−6.48090	−	6.48090i	−0.356223	−	0.356223i	−0.862418	+	0.506196i	$0.831051\pi$
$332$	−5.11992	+	5.11992i	−0.280992	+	0.280992i
$333$	3.21978	+	12.4388i	0.176443	+	0.681640i
$334$	−8.83753			−0.483568
$335$		0			0
$336$	−8.47362	−	14.8220i	−0.462274	−	0.808607i
$337$	−32.1622			−1.75199			−0.875993	−	0.482323i	$-0.839793\pi$
$337$	−32.1622			−1.75199			−0.875993	+	0.482323i	$0.839793\pi$
$338$	−10.2531	+	17.8314i	−0.557697	+	0.969900i
$339$	−28.9969	−	7.90207i	−1.57490	−	0.429181i
$340$		0			0
$341$		−	1.16006i		−	0.0628207i
$342$	−4.12371	+	7.00416i	−0.222985	+	0.378742i
$343$	−14.2230	+	14.2230i	−0.767972	+	0.767972i
$344$	1.39139	−	1.39139i	0.0750190	−	0.0750190i
$345$		0			0
$346$	−10.9077	+	10.9077i	−0.586404	+	0.586404i
$347$	11.3661			0.610165			0.305082	−	0.952326i	$-0.401316\pi$
$347$	11.3661			0.610165			0.305082	+	0.952326i	$0.401316\pi$
$348$	6.17740	+	1.68343i	0.331144	+	0.0902413i
$349$	−0.388646	+	0.388646i	−0.0208038	+	0.0208038i	−0.717432	−	0.696628i	$-0.754683\pi$
$349$	−0.388646	+	0.388646i	−0.0208038	+	0.0208038i	0.696628	+	0.717432i	$0.254683\pi$
$350$		0			0
$351$	2.22453	+	18.6025i	0.118737	+	0.992926i
$352$			1.15386i			0.0615011i
$353$	−10.9517	−	10.9517i	−0.582900	−	0.582900i	0.352799	−	0.935699i	$-0.385230\pi$
$353$	−10.9517	−	10.9517i	−0.582900	−	0.582900i	−0.935699	+	0.352799i	$0.885230\pi$
$354$	2.42967	−	8.91574i	0.129135	−	0.473866i
$355$		0			0
$356$	2.50420	−	2.50420i	0.132722	−	0.132722i
$357$	−8.67078	+	4.95701i	−0.458906	+	0.262353i
$358$	−1.43734	−	1.43734i	−0.0759655	−	0.0759655i
$359$	3.80124	+	3.80124i	0.200622	+	0.200622i	0.800266	−	0.599645i	$-0.204691\pi$
$359$	3.80124	+	3.80124i	0.200622	+	0.200622i	−0.599645	+	0.800266i	$0.704691\pi$
$360$		0			0
$361$		−	16.0679i		−	0.845680i
$362$	−6.03120	+	6.03120i	−0.316993	+	0.316993i
$363$	4.93126	−	18.0954i	0.258824	−	0.949764i
$364$	3.73166	−	0.494626i	0.195592	−	0.0259255i
$365$		0			0
$366$	−4.97950	−	8.71011i	−0.260282	−	0.455285i
$367$			23.2059i			1.21134i	0.795717	+	0.605669i	$0.207094\pi$
$367$			23.2059i			1.21134i	−0.795717	+	0.605669i	$0.792906\pi$
$368$			26.9254i			1.40358i
$369$	−12.6826	+	3.28288i	−0.660227	+	0.170900i
$370$		0			0
$371$	0.378899	+	0.378899i	0.0196715	+	0.0196715i
$372$	2.11993	−	1.21195i	0.109913	−	0.0628365i
$373$		−	20.3615i		−	1.05428i	−0.849779	−	0.527139i	$-0.823265\pi$
$373$		−	20.3615i		−	1.05428i	0.849779	−	0.527139i	$-0.176735\pi$
$374$	1.82267			0.0942481
$375$		0			0
$376$			29.3467i			1.51344i
$377$	16.0973	−	21.0167i	0.829054	−	1.08242i
$378$	12.2083	−	11.9006i	0.627928	−	0.612101i
$379$	2.24383	+	2.24383i	0.115258	+	0.115258i	0.762383	−	0.647126i	$-0.224029\pi$
$379$	2.24383	+	2.24383i	0.115258	+	0.115258i	−0.647126	+	0.762383i	$0.724029\pi$
$380$		0			0
$381$	35.2588	+	9.60852i	1.80636	+	0.492259i
$382$	−9.10384	+	9.10384i	−0.465793	+	0.465793i
$383$	−3.09636	−	3.09636i	−0.158217	−	0.158217i	0.623559	−	0.781776i	$-0.285686\pi$
$383$	−3.09636	−	3.09636i	−0.158217	−	0.158217i	−0.781776	+	0.623559i	$0.785686\pi$
$384$	20.5098	−	11.7253i	1.04664	−	0.598354i
$385$		0			0
$386$			4.54050i			0.231105i
$387$	2.14835	+	1.26484i	0.109207	+	0.0642955i
$388$	−4.23680	−	4.23680i	−0.215091	−	0.215091i
$389$	−19.3062			−0.978864			−0.489432	−	0.872041i	$-0.662796\pi$
$389$	−19.3062			−0.978864			−0.489432	+	0.872041i	$0.662796\pi$
$390$		0			0
$391$	15.7511			0.796570
$392$	−4.52034	−	4.52034i	−0.228312	−	0.228312i
$393$	4.49136	−	16.4812i	0.226559	−	0.831366i
$394$			6.94194i			0.349730i
$395$		0			0
$396$	−0.605737	+	0.156795i	−0.0304394	+	0.00787925i
$397$	−13.4071	−	13.4071i	−0.672884	−	0.672884i	0.285496	−	0.958380i	$-0.407842\pi$
$397$	−13.4071	−	13.4071i	−0.672884	−	0.672884i	−0.958380	+	0.285496i	$0.907842\pi$
$398$	4.24995	−	4.24995i	0.213031	−	0.213031i
$399$	1.61707	−	5.93388i	0.0809545	−	0.297065i
$400$		0			0
$401$	−4.82449	−	4.82449i	−0.240923	−	0.240923i	0.576309	−	0.817232i	$-0.304493\pi$
$401$	−4.82449	−	4.82449i	−0.240923	−	0.240923i	−0.817232	+	0.576309i	$0.804493\pi$
$402$	34.7528	+	9.47062i	1.73331	+	0.472351i
$403$	−1.32668	−	10.0090i	−0.0660867	−	0.498585i
$404$			3.19833i			0.159123i
$405$		0			0
$406$	−24.0907			−1.19560
$407$			1.77426i			0.0879467i
$408$	−5.66021	−	9.90081i	−0.280222	−	0.490163i
$409$	2.33925	+	2.33925i	0.115669	+	0.115669i	0.762572	−	0.646903i	$-0.223936\pi$
$409$	2.33925	+	2.33925i	0.115669	+	0.115669i	−0.646903	+	0.762572i	$0.723936\pi$
$410$		0			0
$411$	−13.8461	+	7.91571i	−0.682978	+	0.390453i
$412$			3.80082i			0.187253i
$413$			6.99242i			0.344074i
$414$	−26.0292	+	6.73768i	−1.27927	+	0.331139i
$415$		0			0
$416$	1.31959	+	9.95556i	0.0646985	+	0.488112i
$417$	7.77749	+	2.11948i	0.380866	+	0.103791i
$418$	−0.793637	+	0.793637i	−0.0388180	+	0.0388180i
$419$		−	11.3389i		−	0.553942i	−0.960878	−	0.276971i	$-0.910669\pi$
$419$		−	11.3389i		−	0.553942i	0.960878	−	0.276971i	$-0.0893306\pi$
$420$		0			0
$421$	15.5576	+	15.5576i	0.758230	+	0.758230i	0.976000	−	0.217770i	$-0.0698783\pi$
$421$	15.5576	+	15.5576i	0.758230	+	0.758230i	−0.217770	+	0.976000i	$0.569878\pi$
$422$	6.68071	+	6.68071i	0.325212	+	0.325212i
$423$	−35.9948	+	9.31726i	−1.75013	+	0.453021i
$424$	−0.432650	+	0.432650i	−0.0210113	+	0.0210113i
$425$		0			0
$426$	−29.4720	−	8.03155i	−1.42792	−	0.389130i
$427$	5.36823	+	5.36823i	0.259787	+	0.259787i
$428$		−	1.85864i		−	0.0898409i
$429$	−0.346333	+	2.56380i	−0.0167211	+	0.123781i
$430$		0			0
$431$	−25.6108	+	25.6108i	−1.23363	+	1.23363i	−0.271068	+	0.962560i	$0.587377\pi$
$431$	−25.6108	+	25.6108i	−1.23363	+	1.23363i	−0.962560	+	0.271068i	$0.912623\pi$
$432$	17.2410	+	17.6868i	0.829507	+	0.850955i
$433$	32.5410			1.56382			0.781909	−	0.623392i	$-0.214246\pi$
$433$	32.5410			1.56382			0.781909	+	0.623392i	$0.214246\pi$
$434$	−6.49685	+	6.49685i	−0.311859	+	0.311859i
$435$		0			0
$436$	5.13315	−	5.13315i	0.245833	−	0.245833i
$437$	−6.85844	+	6.85844i	−0.328084	+	0.328084i
$438$	11.7402	−	43.0812i	0.560970	−	2.05850i
$439$			33.7542i			1.61100i	0.592595	+	0.805501i	$0.298104\pi$
$439$			33.7542i			1.61100i	−0.592595	+	0.805501i	$0.701896\pi$
$440$		0			0
$441$	4.10920	−	6.97952i	0.195676	−	0.332358i
$442$	15.7261	−	2.08447i	0.748012	−	0.0991479i
$443$	30.3054			1.43985			0.719927	−	0.694050i	$-0.244175\pi$
$443$	30.3054			1.43985			0.719927	+	0.694050i	$0.244175\pi$
$444$	−3.24234	+	1.85362i	−0.153875	+	0.0879689i
$445$		0			0
$446$	−9.31616			−0.441133
$447$	−25.2604	+	14.4412i	−1.19478	+	0.683044i
$448$	−7.47806	+	7.47806i	−0.353305	+	0.353305i
$449$	18.9354	+	18.9354i	0.893616	+	0.893616i	0.994861	−	0.101246i	$-0.0322828\pi$
$449$	18.9354	+	18.9354i	0.893616	+	0.893616i	−0.101246	+	0.994861i	$0.532283\pi$
$450$		0			0
$451$	−1.80903			−0.0851841
$452$		−	8.73603i		−	0.410908i
$453$	10.5615	−	6.03790i	0.496220	−	0.283685i
$454$		−	17.8813i		−	0.839211i
$455$		0			0
$456$	6.77565	+	1.84646i	0.317299	+	0.0864685i
$457$	−12.6125	+	12.6125i	−0.589987	+	0.589987i	−0.937628	−	0.347641i	$-0.886983\pi$
$457$	−12.6125	+	12.6125i	−0.589987	+	0.589987i	0.347641	+	0.937628i	$0.386983\pi$
$458$	33.0580			1.54470
$459$	10.3466	−	10.0858i	0.482940	−	0.470767i
$460$		0			0
$461$	−13.1232	+	13.1232i	−0.611207	+	0.611207i	−0.943260	−	0.332054i	$-0.892258\pi$
$461$	−13.1232	+	13.1232i	−0.611207	+	0.611207i	0.332054	+	0.943260i	$0.392258\pi$
$462$	2.04384	−	1.16845i	0.0950881	−	0.0543611i
$463$	−23.7400	−	23.7400i	−1.10329	−	1.10329i	−0.994011	−	0.109278i	$-0.965146\pi$
$463$	−23.7400	−	23.7400i	−1.10329	−	1.10329i	−0.109278	−	0.994011i	$-0.534854\pi$
$464$		−	34.9014i		−	1.62026i
$465$		0			0
$466$	16.8307	−	16.8307i	0.779667	−	0.779667i
$467$			20.9138i			0.967776i	0.875130	+	0.483888i	$0.160776\pi$
$467$			20.9138i			0.967776i	−0.875130	+	0.483888i	$0.839224\pi$
$468$	−5.04700	+	2.04557i	−0.233297	+	0.0945566i
$469$	−27.2558			−1.25856
$470$		0			0
$471$	−7.26515	+	26.6597i	−0.334760	+	1.22841i
$472$	−7.98436			−0.367510
$473$	0.243428	+	0.243428i	0.0111928	+	0.0111928i
$474$	−22.1840	−	38.8042i	−1.01895	−	1.78234i
$475$		0			0
$476$	−2.05285	−	2.05285i	−0.0940923	−	0.0940923i
$477$	−0.668022	−	0.393299i	−0.0305866	−	0.0180079i
$478$	11.4894			0.525513
$479$	12.4837	+	12.4837i	0.570393	+	0.570393i	0.932238	−	0.361845i	$-0.117853\pi$
$479$	12.4837	+	12.4837i	0.570393	+	0.570393i	−0.361845	+	0.932238i	$0.617853\pi$
$480$		0			0
$481$	2.02910	+	15.3084i	0.0925190	+	0.698001i
$482$	9.20221			0.419149
$483$	17.6624	−	10.0975i	0.803669	−	0.459451i
$484$	5.45169			0.247804
$485$		0			0
$486$	−12.7838	+	21.0930i	−0.579886	+	0.956799i
$487$	17.2586	−	17.2586i	0.782061	−	0.782061i	−0.198117	−	0.980178i	$-0.563483\pi$
$487$	17.2586	−	17.2586i	0.782061	−	0.782061i	0.980178	+	0.198117i	$0.0634827\pi$
$488$	−6.12976	+	6.12976i	−0.277481	+	0.277481i
$489$	5.32131	+	9.30801i	0.240638	+	0.420923i
$490$		0			0
$491$	33.3522			1.50516			0.752582	−	0.658498i	$-0.228808\pi$
$491$	33.3522			1.50516			0.752582	+	0.658498i	$0.228808\pi$
$492$	−1.88995	−	3.30589i	−0.0852055	−	0.149041i
$493$	−20.4171			−0.919538
$494$	−5.93989	+	7.75515i	−0.267248	+	0.348921i
$495$		0			0
$496$	−9.41230	−	9.41230i	−0.422625	−	0.422625i
$497$	23.1143			1.03682
$498$	−10.3628	+	38.0265i	−0.464367	+	1.70401i
$499$	17.9656	+	17.9656i	0.804252	+	0.804252i	0.983757	−	0.179505i	$-0.0574497\pi$
$499$	17.9656	+	17.9656i	0.804252	+	0.804252i	−0.179505	+	0.983757i	$0.557450\pi$
$500$		0			0
$501$	−8.39872	+	4.80148i	−0.375227	+	0.214514i
$502$	−6.15377	−	6.15377i	−0.274656	−	0.274656i
$503$	38.5906			1.72067			0.860334	−	0.509731i	$-0.170255\pi$
$503$	38.5906			1.72067			0.860334	+	0.509731i	$0.170255\pi$
$504$	−12.6941	−	7.47365i	−0.565439	−	0.332903i
$505$		0			0
$506$	−3.71280			−0.165054
$507$	−0.0561329	+	22.5166i	−0.00249295	+	0.999997i
$508$			10.6226i			0.471300i
$509$	−5.99503	+	5.99503i	−0.265725	+	0.265725i	−0.827375	−	0.561650i	$-0.810167\pi$
$509$	−5.99503	+	5.99503i	−0.265725	+	0.265725i	0.561650	+	0.827375i	$0.310167\pi$
$510$		0			0
$511$			33.7876i			1.49467i
$512$	−6.55574	−	6.55574i	−0.289725	−	0.289725i
$513$	−0.113554	+	8.89681i	−0.00501352	+	0.392804i
$514$	−8.33520	+	8.33520i	−0.367650	+	0.367650i
$515$		0			0
$516$	−0.190532	+	0.699165i	−0.00838772	+	0.0307790i
$517$	−5.13428			−0.225805
$518$	9.93664	−	9.93664i	0.436591	−	0.436591i
$519$	−4.43990	+	16.2924i	−0.194890	+	0.715156i
$520$		0			0
$521$			13.8731i			0.607791i	0.952705	+	0.303896i	$0.0982874\pi$
$521$			13.8731i			0.607791i	−0.952705	+	0.303896i	$0.901713\pi$
$522$	33.7398	−	8.73356i	1.47675	−	0.382257i
$523$		−	24.2698i		−	1.06124i	−0.847609	−	0.530622i	$-0.821958\pi$
$523$		−	24.2698i		−	1.06124i	0.847609	−	0.530622i	$-0.178042\pi$
$524$	4.96536			0.216913
$525$		0			0
$526$	25.9391	+	25.9391i	1.13100	+	1.13100i
$527$	−5.50613	+	5.50613i	−0.239851	+	0.239851i
$528$	1.69279	+	2.96101i	0.0736690	+	0.128861i
$529$	−9.08521			−0.395009
$530$		0			0
$531$	−2.53495	−	9.79310i	−0.110007	−	0.424984i
$532$	1.78773			0.0775077
$533$	−15.6084	+	2.06887i	−0.676074	+	0.0896127i
$534$	5.06852	−	18.5991i	0.219336	−	0.804862i
$535$		0			0
$536$		−	31.1223i		−	1.34428i
$537$	−2.14688	−	0.585055i	−0.0926447	−	0.0252470i
$538$	29.9222	−	29.9222i	1.29004	−	1.29004i
$539$	0.790845	−	0.790845i	0.0340641	−	0.0340641i
$540$		0			0
$541$	22.2024	−	22.2024i	0.954555	−	0.954555i	−0.0444563	−	0.999011i	$-0.514156\pi$
$541$	22.2024	−	22.2024i	0.954555	−	0.954555i	0.999011	+	0.0444563i	$0.0141555\pi$
$542$	−6.22205			−0.267260
$543$	−2.45495	+	9.00852i	−0.105352	+	0.386592i
$544$	5.47672	−	5.47672i	0.234813	−	0.234813i
$545$		0			0
$546$	16.2980	−	12.4188i	0.697492	−	0.531475i
$547$			19.3984i			0.829418i	0.909954	+	0.414709i	$0.136117\pi$
$547$			19.3984i			0.829418i	−0.909954	+	0.414709i	$0.863883\pi$
$548$	−3.27814	−	3.27814i	−0.140035	−	0.140035i
$549$	−9.46450	−	5.57224i	−0.403935	−	0.237817i
$550$		0			0
$551$	8.89010	−	8.89010i	0.378731	−	0.378731i
$552$	11.5299	+	20.1680i	0.490745	+	0.858408i
$553$	23.9158	+	23.9158i	1.01701	+	1.01701i
$554$	32.0809	+	32.0809i	1.36299	+	1.36299i
$555$		0			0
$556$			2.34316i			0.0993721i
$557$	−12.2284	+	12.2284i	−0.518134	+	0.518134i	−0.917006	−	0.398873i	$-0.869402\pi$
$557$	−12.2284	+	12.2284i	−0.518134	+	0.518134i	0.398873	+	0.917006i	$0.369402\pi$
$558$	6.74375	−	11.4543i	0.285486	−	0.484900i
$559$	2.37869	+	1.82191i	0.100608	+	0.0770586i
$560$		0			0
$561$	1.73217	−	0.990268i	0.0731323	−	0.0418091i
$562$		−	1.81659i		−	0.0766284i
$563$			13.2701i			0.559267i	0.960107	+	0.279633i	$0.0902129\pi$
$563$			13.2701i			0.559267i	−0.960107	+	0.279633i	$0.909787\pi$
$564$	−5.36393	−	9.38256i	−0.225862	−	0.395077i
$565$		0			0
$566$	25.6922	+	25.6922i	1.07992	+	1.07992i
$567$	5.13647	−	17.9425i	0.215711	−	0.753516i
$568$			26.3932i			1.10744i
$569$	−1.99616			−0.0836833			−0.0418417	−	0.999124i	$-0.513323\pi$
$569$	−1.99616			−0.0836833			−0.0418417	+	0.999124i	$0.513323\pi$
$570$		0			0
$571$		−	8.10449i		−	0.339162i	−0.985516	−	0.169581i	$-0.945758\pi$
$571$		−	8.10449i		−	0.339162i	0.985516	−	0.169581i	$-0.0542415\pi$
$572$	−0.745479	+	0.0988121i	−0.0311700	+	0.00413154i
$573$	−3.70564	+	13.5980i	−0.154805	+	0.568063i
$574$	10.1314	+	10.1314i	0.422876	+	0.422876i
$575$		0			0
$576$	7.76226	−	13.1843i	0.323427	−	0.549345i
$577$	22.0036	−	22.0036i	0.916023	−	0.916023i	−0.0807147	−	0.996737i	$-0.525720\pi$
$577$	22.0036	−	22.0036i	0.916023	−	0.916023i	0.996737	+	0.0807147i	$0.0257203\pi$
$578$	10.3686	+	10.3686i	0.431275	+	0.431275i
$579$	2.46688	+	4.31505i	0.102520	+	0.179327i
$580$		0			0
$581$		−	29.8234i		−	1.23728i
$582$	−31.4674	−	8.57532i	−1.30437	−	0.355459i
$583$	−0.0756932	−	0.0756932i	−0.00313489	−	0.00313489i
$584$	−38.5807			−1.59648
$585$		0			0
$586$	−18.4796			−0.763384
$587$	6.82405	+	6.82405i	0.281659	+	0.281659i	0.833770	−	0.552112i	$-0.186178\pi$
$587$	6.82405	+	6.82405i	0.281659	+	0.281659i	−0.552112	+	0.833770i	$0.686178\pi$
$588$	2.27144	+	0.618998i	0.0936724	+	0.0255271i
$589$		−	4.79501i		−	0.197575i
$590$		0			0
$591$	3.77159	+	6.59725i	0.155143	+	0.271375i
$592$	14.3957	+	14.3957i	0.591659	+	0.591659i
$593$	−1.95435	+	1.95435i	−0.0802556	+	0.0802556i	−0.746095	−	0.665839i	$-0.768074\pi$
$593$	−1.95435	+	1.95435i	−0.0802556	+	0.0802556i	0.665839	+	0.746095i	$0.268074\pi$
$594$	−2.43887	+	2.37740i	−0.100068	+	0.0975457i
$595$		0			0
$596$	−5.98054	−	5.98054i	−0.244972	−	0.244972i
$597$	1.72991	−	6.34795i	0.0708004	−	0.259804i
$598$	−32.0341	+	4.24607i	−1.30997	+	0.173635i
$599$			4.69516i			0.191839i	0.995389	+	0.0959195i	$0.0305791\pi$
$599$			4.69516i			0.191839i	−0.995389	+	0.0959195i	$0.969421\pi$
$600$		0			0
$601$	7.38898			0.301403			0.150701	−	0.988579i	$-0.451847\pi$
$601$	7.38898			0.301403			0.150701	+	0.988579i	$0.451847\pi$
$602$		−	2.72661i		−	0.111128i
$603$	38.1726	−	9.88100i	1.55451	−	0.402385i
$604$	2.50048	+	2.50048i	0.101743	+	0.101743i
$605$		0			0
$606$	8.64055	+	15.1140i	0.350998	+	0.613965i
$607$			5.61074i			0.227733i	0.993496	+	0.113867i	$0.0363236\pi$
$607$			5.61074i			0.227733i	−0.993496	+	0.113867i	$0.963676\pi$
$608$			4.76940i			0.193425i
$609$	−22.8945	+	13.0886i	−0.927733	+	0.530378i
$610$		0			0
$611$	−44.2987	+	5.87173i	−1.79213	+	0.237545i
$612$	3.61930	+	2.13087i	0.146301	+	0.0861352i
$613$	−16.7181	+	16.7181i	−0.675238	+	0.675238i	−0.958919	−	0.283680i	$-0.908445\pi$
$613$	−16.7181	+	16.7181i	−0.675238	+	0.675238i	0.283680	+	0.958919i	$0.408445\pi$
$614$		−	50.1582i		−	2.02422i
$615$		0			0
$616$	−1.43836	−	1.43836i	−0.0579531	−	0.0579531i
$617$	−30.6567	−	30.6567i	−1.23419	−	1.23419i	−0.962339	−	0.271854i	$-0.912363\pi$
$617$	−30.6567	−	30.6567i	−1.23419	−	1.23419i	−0.271854	−	0.962339i	$-0.587637\pi$
$618$	10.2682	+	17.9611i	0.413048	+	0.722501i
$619$	20.5920	−	20.5920i	0.827663	−	0.827663i	−0.159530	−	0.987193i	$-0.550998\pi$
$619$	20.5920	−	20.5920i	0.827663	−	0.827663i	0.987193	+	0.159530i	$0.0509979\pi$
$620$		0			0
$621$	−21.0762	+	20.5450i	−0.845758	+	0.824441i
$622$	−24.2131	−	24.2131i	−0.970859	−	0.970859i
$623$			14.5869i			0.584410i
$624$	17.9917	+	23.6118i	0.720245	+	0.945227i
$625$		0			0
$626$	−7.96826	+	7.96826i	−0.318476	+	0.318476i
$627$	−0.323043	+	1.18542i	−0.0129011	+	0.0473410i
$628$	−8.03189			−0.320507
$629$	8.42138	−	8.42138i	0.335782	−	0.335782i
$630$		0			0
$631$	2.48933	−	2.48933i	0.0990986	−	0.0990986i	−0.655819	−	0.754918i	$-0.727677\pi$
$631$	2.48933	−	2.48933i	0.0990986	−	0.0990986i	0.754918	+	0.655819i	$0.227677\pi$
$632$	−27.3085	+	27.3085i	−1.08628	+	1.08628i
$633$	9.97866	+	2.71933i	0.396616	+	0.108084i
$634$			33.5491i			1.33241i
$635$		0			0
$636$	0.0592454	−	0.217403i	0.00234923	−	0.00862060i
$637$	5.91899	−	7.72786i	0.234519	−	0.306189i
$638$	4.81263			0.190534
$639$	−32.3722	+	8.37957i	−1.28063	+	0.331491i
$640$		0			0
$641$	27.5035			1.08632			0.543161	−	0.839629i	$-0.317227\pi$
$641$	27.5035			1.08632			0.543161	+	0.839629i	$0.317227\pi$
$642$	−5.02127	−	8.78318i	−0.198174	−	0.346645i
$643$	−27.9426	+	27.9426i	−1.10195	+	1.10195i	−0.107771	+	0.994176i	$0.534371\pi$
$643$	−27.9426	+	27.9426i	−1.10195	+	1.10195i	−0.994176	+	0.107771i	$0.965629\pi$
$644$	4.18167	+	4.18167i	0.164781	+	0.164781i
$645$		0			0
$646$	7.53387			0.296416
$647$			16.9805i			0.667572i	0.942649	+	0.333786i	$0.108326\pi$
$647$			16.9805i			0.667572i	−0.942649	+	0.333786i	$0.891674\pi$
$648$	20.4879	+	5.86513i	0.804839	+	0.230404i
$649$		−	1.39688i		−	0.0548325i
$650$		0			0
$651$	−2.64449	+	9.70403i	−0.103646	+	0.380331i
$652$	−2.20372	+	2.20372i	−0.0863044	+	0.0863044i
$653$	−42.0032			−1.64371			−0.821856	−	0.569695i	$-0.807061\pi$
$653$	−42.0032			−1.64371			−0.821856	+	0.569695i	$0.807061\pi$
$654$	10.3895	−	38.1248i	0.406263	−	1.49080i
$655$		0			0
$656$	−14.6778	+	14.6778i	−0.573074	+	0.573074i
$657$	−12.2489	−	47.3206i	−0.477877	−	1.84615i
$658$	28.7543	+	28.7543i	1.12096	+	1.12096i
$659$		−	7.23414i		−	0.281802i	−0.990024	−	0.140901i	$-0.955000\pi$
$659$		−	7.23414i		−	0.281802i	0.990024	−	0.140901i	$-0.0450000\pi$
$660$		0			0
$661$	−10.3889	+	10.3889i	−0.404082	+	0.404082i	−0.879669	−	0.475587i	$-0.842236\pi$
$661$	−10.3889	+	10.3889i	−0.404082	+	0.404082i	0.475587	+	0.879669i	$0.342236\pi$
$662$		−	14.5018i		−	0.563627i
$663$	13.8127	−	10.5250i	0.536441	−	0.408758i
$664$	34.0541			1.32155
$665$		0			0
$666$	−10.3143	+	17.5189i	−0.399670	+	0.678843i
$667$	41.5897			1.61036
$668$	−1.98844	−	1.98844i	−0.0769351	−	0.0769351i
$669$	−8.85359	+	5.06152i	−0.342299	+	0.195690i
$670$		0			0
$671$	−1.07242	−	1.07242i	−0.0414002	−	0.0414002i
$672$	2.63036	−	9.65221i	0.101468	−	0.372342i
$673$	−25.8635			−0.996966			−0.498483	−	0.866899i	$-0.666109\pi$
$673$	−25.8635			−0.996966			−0.498483	+	0.866899i	$0.666109\pi$
$674$	−35.9833	−	35.9833i	−1.38603	−	1.38603i
$675$		0			0
$676$	−6.31901	+	1.70511i	−0.243039	+	0.0655810i
$677$	−21.1738			−0.813775			−0.406887	−	0.913478i	$-0.633386\pi$
$677$	−21.1738			−0.813775			−0.406887	+	0.913478i	$0.633386\pi$
$678$	−23.6011	−	41.2829i	−0.906394	−	1.58546i
$679$	24.6792			0.947101
$680$		0			0
$681$	−9.71501	−	16.9934i	−0.372280	−	0.651190i
$682$	1.29788	−	1.29788i	0.0496985	−	0.0496985i
$683$	13.2249	−	13.2249i	0.506038	−	0.506038i	−0.407270	−	0.913308i	$-0.633519\pi$
$683$	13.2249	−	13.2249i	0.506038	−	0.506038i	0.913308	+	0.407270i	$0.133519\pi$
$684$	−2.50377	+	0.648101i	−0.0957339	+	0.0247807i
$685$		0			0
$686$	−31.8257			−1.21511
$687$	31.4166	−	17.9606i	1.19862	−	0.685240i
$688$	3.95017			0.150599
$689$	−0.739648	−	0.566518i	−0.0281783	−	0.0215826i
$690$		0			0
$691$	15.4010	+	15.4010i	0.585883	+	0.585883i	0.936514	−	0.350630i	$-0.114033\pi$
$691$	15.4010	+	15.4010i	0.585883	+	0.585883i	−0.350630	+	0.936514i	$0.614033\pi$
$692$	−4.90847			−0.186592
$693$	1.30753	−	2.22086i	0.0496691	−	0.0843635i
$694$	12.7165	+	12.7165i	0.482712	+	0.482712i
$695$		0			0
$696$	−14.9454	−	26.1423i	−0.566502	−	0.990923i
$697$	8.58644	+	8.58644i	0.325235	+	0.325235i
$698$	−0.869642			−0.0329164
$699$	6.85079	−	25.1392i	0.259121	−	0.950852i
$700$		0			0
$701$	14.2724			0.539063			0.269531	−	0.962992i	$-0.413131\pi$
$701$	14.2724			0.539063			0.269531	+	0.962992i	$0.413131\pi$
$702$	−18.3238	+	23.3014i	−0.691585	+	0.879455i
$703$			7.33376i			0.276598i
$704$	1.49390	−	1.49390i	0.0563035	−	0.0563035i
$705$		0			0
$706$		−	24.5057i		−	0.922284i
$707$	−9.31508	−	9.31508i	−0.350330	−	0.350330i
$708$	2.55271	−	1.45936i	0.0959368	−	0.0548463i
$709$	1.84603	−	1.84603i	0.0693291	−	0.0693291i	−0.671592	−	0.740921i	$-0.734389\pi$
$709$	1.84603	−	1.84603i	0.0693291	−	0.0693291i	0.740921	+	0.671592i	$0.234389\pi$
$710$		0			0
$711$	−42.1651	−	24.8247i	−1.58131	−	0.931000i
$712$	−16.6561			−0.624216
$713$	11.2160	−	11.2160i	0.420044	−	0.420044i
$714$	−15.2469	−	4.15499i	−0.570600	−	0.155497i
$715$		0			0
$716$		−	0.646800i		−	0.0241720i
$717$	10.9189	−	6.24226i	0.407775	−	0.233121i
$718$			8.50571i			0.317430i
$719$	45.7040			1.70447			0.852237	−	0.523156i	$-0.175246\pi$
$719$	45.7040			1.70447			0.852237	+	0.523156i	$0.175246\pi$
$720$		0			0
$721$	−11.0698	−	11.0698i	−0.412261	−	0.412261i
$722$	17.9769	−	17.9769i	0.669032	−	0.669032i
$723$	8.74530	−	4.99961i	0.325241	−	0.185938i
$724$	−2.71404			−0.100866
$725$		0			0
$726$	25.7624	−	14.7282i	0.956134	−	0.546614i
$727$	5.12985			0.190256			0.0951279	−	0.995465i	$-0.469674\pi$
$727$	5.12985			0.190256			0.0951279	+	0.995465i	$0.469674\pi$
$728$	−14.0551	−	10.7652i	−0.520918	−	0.398986i
$729$	−0.689112	+	26.9912i	−0.0255227	+	0.999674i
$730$		0			0
$731$		−	2.31082i		−	0.0854689i
$732$	0.839386	−	3.08016i	0.0310246	−	0.113846i
$733$	−6.65960	+	6.65960i	−0.245978	+	0.245978i	−0.819318	−	0.573340i	$-0.805647\pi$
$733$	−6.65960	+	6.65960i	−0.245978	+	0.245978i	0.573340	+	0.819318i	$0.305647\pi$
$734$	−25.9629	+	25.9629i	−0.958309	+	0.958309i
$735$		0			0
$736$	−11.1561	+	11.1561i	−0.411220	+	0.411220i
$737$	5.44492			0.200566
$738$	−17.8623	−	10.5164i	−0.657519	−	0.387115i
$739$	15.3715	−	15.3715i	0.565448	−	0.565448i	−0.365402	−	0.930850i	$-0.619068\pi$
$739$	15.3715	−	15.3715i	0.565448	−	0.565448i	0.930850	+	0.365402i	$0.119068\pi$
$740$		0			0
$741$	−1.43154	+	10.5973i	−0.0525890	+	0.389300i
$742$			0.847831i			0.0311249i
$743$	−10.7883	−	10.7883i	−0.395784	−	0.395784i	0.480959	−	0.876743i	$-0.340288\pi$
$743$	−10.7883	−	10.7883i	−0.395784	−	0.395784i	−0.876743	+	0.480959i	$0.840288\pi$
$744$	−11.0806	−	3.01963i	−0.406236	−	0.110705i
$745$		0			0
$746$	22.7806	−	22.7806i	0.834056	−	0.834056i
$747$	10.8118	+	41.7686i	0.395583	+	1.52823i
$748$	0.410100	+	0.410100i	0.0149948	+	0.0149948i
$749$	5.41326	+	5.41326i	0.197796	+	0.197796i
$750$		0			0
$751$		−	47.2418i		−	1.72388i	−0.507012	−	0.861939i	$-0.669250\pi$
$751$		−	47.2418i		−	1.72388i	0.507012	−	0.861939i	$-0.330750\pi$
$752$	−41.6577	+	41.6577i	−1.51910	+	1.51910i
$753$	−9.19160	−	2.50484i	−0.334960	−	0.0912814i
$754$	41.5235	−	5.50388i	1.51220	−	0.200439i
$755$		0			0
$756$	5.42449	+	0.0692351i	0.197287	+	0.00251806i
$757$		−	6.53480i		−	0.237511i	−0.992924	−	0.118756i	$-0.962109\pi$
$757$		−	6.53480i		−	0.237511i	0.992924	−	0.118756i	$-0.0378905\pi$
$758$			5.02083i			0.182365i
$759$	−3.52845	+	2.01718i	−0.128074	+	0.0732191i
$760$		0			0
$761$	−19.3550	−	19.3550i	−0.701618	−	0.701618i	0.263139	−	0.964758i	$-0.415242\pi$
$761$	−19.3550	−	19.3550i	−0.701618	−	0.701618i	−0.964758	+	0.263139i	$0.915242\pi$
$762$	28.6977	+	50.1979i	1.03961	+	1.81848i
$763$			29.9004i			1.08247i
$764$	−4.09672			−0.148214
$765$		0			0
$766$		−	6.92846i		−	0.250336i
$767$	−1.59752	−	12.0523i	−0.0576831	−	0.435185i
$768$	19.0200	+	5.18322i	0.686326	+	0.187033i
$769$	−1.85581	−	1.85581i	−0.0669221	−	0.0669221i	0.672854	−	0.739776i	$-0.265068\pi$
$769$	−1.85581	−	1.85581i	−0.0669221	−	0.0669221i	−0.739776	+	0.672854i	$0.765068\pi$
$770$		0			0
$771$	−3.39277	+	12.4499i	−0.122188	+	0.448372i
$772$	−1.02161	+	1.02161i	−0.0367686	+	0.0367686i
$773$	−5.15489	−	5.15489i	−0.185408	−	0.185408i	0.608299	−	0.793708i	$-0.291852\pi$
$773$	−5.15489	−	5.15489i	−0.185408	−	0.185408i	−0.793708	+	0.608299i	$0.791852\pi$
$774$	0.988473	+	3.81870i	0.0355299	+	0.137260i
$775$		0			0
$776$			28.1802i			1.01161i
$777$	4.04463	−	14.8419i	0.145100	−	0.532450i
$778$	−21.5999	−	21.5999i	−0.774396	−	0.774396i
$779$	−7.47750			−0.267909
$780$		0			0
$781$	−4.61756			−0.165229
$782$	17.6225	+	17.6225i	0.630180	+	0.630180i
$783$	27.3195	−	26.6309i	0.976320	−	0.951712i
$784$		−	12.8333i		−	0.458331i
$785$		0			0
$786$	23.4643	−	13.4143i	0.836942	−	0.478473i
$787$	10.3937	+	10.3937i	0.370494	+	0.370494i	0.867657	−	0.497163i	$-0.165625\pi$
$787$	10.3937	+	10.3937i	0.370494	+	0.370494i	−0.497163	+	0.867657i	$0.665625\pi$
$788$	−1.56193	+	1.56193i	−0.0556416	+	0.0556416i
$789$	38.7440	+	10.5583i	1.37932	+	0.375885i
$790$		0			0
$791$	25.4435	+	25.4435i	0.904667	+	0.904667i
$792$	2.53591	+	1.49302i	0.0901096	+	0.0530521i
$793$	−10.4793	−	8.02639i	−0.372130	−	0.285025i
$794$		−	30.0000i		−	1.06466i
$795$		0			0
$796$	1.91248			0.0677859
$797$		−	28.4028i		−	1.00608i	−0.864264	−	0.503039i	$-0.832215\pi$
$797$		−	28.4028i		−	1.00608i	0.864264	−	0.503039i	$-0.167785\pi$
$798$	8.44806	−	4.82968i	0.299058	−	0.170969i
$799$	24.3695	+	24.3695i	0.862130	+	0.862130i
$800$		0			0
$801$	−5.28815	−	20.4294i	−0.186847	−	0.721836i
$802$		−	10.7954i		−	0.381197i
$803$		−	6.74979i		−	0.238195i
$804$	5.68847	+	9.95024i	0.200617	+	0.350918i
$805$		0			0
$806$	9.71387	−	12.6825i	0.342156	−	0.446721i
$807$	12.1796	−	44.6933i	0.428741	−	1.57328i
$808$	10.6365	−	10.6365i	0.374191	−	0.374191i
$809$		−	23.7943i		−	0.836561i	−0.908318	−	0.418281i	$-0.862633\pi$
$809$		−	23.7943i		−	0.836561i	0.908318	−	0.418281i	$-0.137367\pi$
$810$		0			0
$811$	12.0402	+	12.0402i	0.422789	+	0.422789i	0.886163	−	0.463374i	$-0.153361\pi$
$811$	12.0402	+	12.0402i	0.422789	+	0.422789i	−0.463374	+	0.886163i	$0.653361\pi$
$812$	−5.42040	−	5.42040i	−0.190219	−	0.190219i
$813$	−5.91310	+	3.38047i	−0.207382	+	0.118558i
$814$	−1.98505	+	1.98505i	−0.0695761	+	0.0695761i
$815$		0			0
$816$	6.01953	−	22.0889i	0.210726	−	0.773266i
$817$	1.00619	+	1.00619i	0.0352021	+	0.0352021i
$818$			5.23435i			0.183015i
$819$	8.74159	−	20.6570i	0.305456	−	0.721813i
$820$		0			0
$821$	−8.79819	+	8.79819i	−0.307059	+	0.307059i	−0.843768	−	0.536709i	$-0.819667\pi$
$821$	−8.79819	+	8.79819i	−0.307059	+	0.307059i	0.536709	+	0.843768i	$0.319667\pi$
$822$	−24.3473	−	6.63498i	−0.849209	−	0.231421i
$823$	6.05273			0.210985			0.105493	−	0.994420i	$-0.466358\pi$
$823$	6.05273			0.210985			0.105493	+	0.994420i	$0.466358\pi$
$824$	12.6402	−	12.6402i	0.440341	−	0.440341i
$825$		0			0
$826$	−7.82317	+	7.82317i	−0.272203	+	0.272203i
$827$	32.2394	−	32.2394i	1.12107	−	1.12107i	0.129495	−	0.991580i	$-0.458664\pi$
$827$	32.2394	−	32.2394i	1.12107	−	1.12107i	0.991580	−	0.129495i	$-0.0413355\pi$
$828$	−7.37254	−	4.34059i	−0.256214	−	0.150846i
$829$			14.4284i			0.501119i	0.968101	+	0.250559i	$0.0806145\pi$
$829$			14.4284i			0.501119i	−0.968101	+	0.250559i	$0.919385\pi$
$830$		0			0
$831$	47.9177	+	13.0582i	1.66225	+	0.452985i
$832$	11.1809	−	14.5979i	0.387630	−	0.506091i
$833$	−7.50737			−0.260115
$834$	6.33024	+	11.0728i	0.219198	+	0.383420i
$835$		0			0
$836$	−0.357136			−0.0123518
$837$	0.185701	−	14.5495i	0.00641878	−	0.502904i
$838$	12.6861	−	12.6861i	0.438233	−	0.438233i
$839$	−16.5805	−	16.5805i	−0.572423	−	0.572423i	0.360382	−	0.932805i	$-0.382646\pi$
$839$	−16.5805	−	16.5805i	−0.572423	−	0.572423i	−0.932805	+	0.360382i	$0.882646\pi$
$840$		0			0
$841$	−24.9097			−0.858956
$842$			34.8119i			1.19970i
$843$	−0.986965	−	1.72639i	−0.0339929	−	0.0594602i
$844$			3.00632i			0.103482i
$845$		0			0
$846$	−50.6955	−	29.8470i	−1.74295	−	1.02616i
$847$	−15.8779	+	15.8779i	−0.545572	+	0.545572i
$848$	−1.22829			−0.0421798
$849$	38.3752	+	10.4578i	1.31703	+	0.358910i
$850$		0			0
$851$	−17.1544	+	17.1544i	−0.588046	+	0.588046i
$852$	−4.82410	−	8.43829i	−0.165271	−	0.289091i
$853$	20.3214	+	20.3214i	0.695793	+	0.695793i	0.963500	−	0.267707i	$-0.0862660\pi$
$853$	20.3214	+	20.3214i	0.695793	+	0.695793i	−0.267707	+	0.963500i	$0.586266\pi$
$854$			12.0120i			0.411043i
$855$		0			0
$856$	−6.18118	+	6.18118i	−0.211269	+	0.211269i
$857$		−	23.5604i		−	0.804807i	−0.915462	−	0.402404i	$-0.868175\pi$
$857$		−	23.5604i		−	0.804807i	0.915462	−	0.402404i	$-0.131825\pi$
$858$	−3.25588	+	2.48092i	−0.111154	+	0.0846971i
$859$	23.0208			0.785460			0.392730	−	0.919654i	$-0.371531\pi$
$859$	23.0208			0.785460			0.392730	+	0.919654i	$0.371531\pi$
$860$		0			0
$861$	15.1328	+	4.12390i	0.515724	+	0.140542i
$862$	−57.3071			−1.95189
$863$	0.128867	+	0.128867i	0.00438669	+	0.00438669i	0.709297	−	0.704910i	$-0.249013\pi$
$863$	0.128867	+	0.128867i	0.00438669	+	0.00438669i	−0.704910	+	0.709297i	$0.749013\pi$
$864$	−0.184710	+	14.4718i	−0.00628395	+	0.492341i
$865$		0			0
$866$	36.4071	+	36.4071i	1.23716	+	1.23716i
$867$	15.4870	+	4.22043i	0.525967	+	0.143333i
$868$	−2.92358			−0.0992327
$869$	−4.77770	−	4.77770i	−0.162072	−	0.162072i
$870$		0			0
$871$	46.9790	−	6.22699i	1.59182	−	0.210994i
$872$	−34.1421			−1.15620
$873$	−34.5640	+	8.94691i	−1.16981	+	0.302807i
$874$	−15.3466			−0.519105
$875$		0			0
$876$	12.3348	−	7.05170i	0.416754	−	0.238255i
$877$	23.8978	−	23.8978i	0.806973	−	0.806973i	−0.177202	−	0.984175i	$-0.556704\pi$
$877$	23.8978	−	23.8978i	0.806973	−	0.806973i	0.984175	+	0.177202i	$0.0567045\pi$
$878$	−37.7645	+	37.7645i	−1.27449	+	1.27449i
$879$	−17.5620	+	10.0401i	−0.592352	+	0.338643i
$880$		0			0
$881$	23.2229			0.782400			0.391200	−	0.920306i	$-0.372060\pi$
$881$	23.2229			0.782400			0.391200	+	0.920306i	$0.372060\pi$
$882$	12.4061	−	3.21133i	0.417737	−	0.108131i
$883$	11.7041			0.393876			0.196938	−	0.980416i	$-0.436900\pi$
$883$	11.7041			0.393876			0.196938	+	0.980416i	$0.436900\pi$
$884$	4.00736	+	3.06935i	0.134782	+	0.103234i
$885$		0			0
$886$	33.9059	+	33.9059i	1.13909	+	1.13909i
$887$	6.56575			0.220456			0.110228	−	0.993906i	$-0.464842\pi$
$887$	6.56575			0.220456			0.110228	+	0.993906i	$0.464842\pi$
$888$	16.9474	+	4.61839i	0.568716	+	0.154983i
$889$	−30.9380	−	30.9380i	−1.03763	−	1.03763i
$890$		0			0
$891$	−1.02612	+	3.58440i	−0.0343763	+	0.120082i
$892$	−2.09613	−	2.09613i	−0.0701837	−	0.0701837i
$893$	−21.2221			−0.710172
$894$	−44.4185	−	12.1047i	−1.48558	−	0.404840i
$895$		0			0
$896$	−28.2849			−0.944932
$897$	−28.1366	+	21.4396i	−0.939454	+	0.715846i
$898$			42.3701i			1.41391i
$899$	−14.5385	+	14.5385i	−0.484887	+	0.484887i
$900$		0			0
$901$			0.718544i			0.0239382i
$902$	−2.02396	−	2.02396i	−0.0673905	−	0.0673905i
$903$	−1.48138	−	2.59123i	−0.0492973	−	0.0862306i
$904$	−29.0529	+	29.0529i	−0.966286	+	0.966286i
$905$		0			0
$906$	18.5715	+	5.06099i	0.616996	+	0.168140i
$907$	−21.6880			−0.720139			−0.360069	−	0.932926i	$-0.617247\pi$
$907$	−21.6880			−0.720139			−0.360069	+	0.932926i	$0.617247\pi$
$908$	4.02328	−	4.02328i	0.133517	−	0.133517i
$909$	16.4230	+	9.66909i	0.544718	+	0.320703i
$910$		0			0
$911$		−	6.44406i		−	0.213501i	−0.994286	−	0.106751i	$-0.965955\pi$
$911$		−	6.44406i		−	0.213501i	0.994286	−	0.106751i	$-0.0340446\pi$
$912$	6.99700	+	12.2391i	0.231694	+	0.405277i
$913$			5.95785i			0.197176i
$914$	−28.2219			−0.933497
$915$		0			0
$916$	7.43805	+	7.43805i	0.245760	+	0.245760i
$917$	−14.4615	+	14.4615i	−0.477562	+	0.477562i
$918$	22.8600	+	0.291772i	0.754493	+	0.00962991i
$919$	−31.6869			−1.04525			−0.522626	−	0.852562i	$-0.675048\pi$
$919$	−31.6869			−1.04525			−0.522626	+	0.852562i	$0.675048\pi$
$920$		0			0
$921$	−27.2513	−	47.6677i	−0.897959	−	1.57071i
$922$	−29.3646			−0.967072
$923$	−39.8404	+	5.28079i	−1.31136	+	0.173819i
$924$	0.722763	+	0.196963i	0.0237772	+	0.00647961i
$925$		0			0
$926$		−	53.1209i		−	1.74566i
$927$	19.5167	+	11.4905i	0.641014	+	0.377397i
$928$	14.4609	−	14.4609i	0.474702	−	0.474702i
$929$	14.6798	−	14.6798i	0.481629	−	0.481629i	−0.424022	−	0.905652i	$-0.639382\pi$
$929$	14.6798	−	14.6798i	0.481629	−	0.481629i	0.905652	+	0.424022i	$0.139382\pi$
$930$		0			0
$931$	3.26889	−	3.26889i	0.107134	−	0.107134i
$932$	7.57380			0.248088
$933$	−36.1660	−	9.85575i	−1.18402	−	0.322663i
$934$	−23.3985	+	23.3985i	−0.765624	+	0.765624i
$935$		0			0
$936$	23.5874	+	9.98167i	0.770977	+	0.326261i
$937$			0.784915i			0.0256421i	0.999918	+	0.0128210i	$0.00408117\pi$
$937$			0.784915i			0.0256421i	−0.999918	+	0.0128210i	$0.995919\pi$
$938$	−30.4940	−	30.4940i	−0.995665	−	0.995665i
$939$	−3.24341	+	11.9018i	−0.105845	+	0.388401i
$940$		0			0
$941$	39.5408	−	39.5408i	1.28899	−	1.28899i	0.353595	−	0.935399i	$-0.384959\pi$
$941$	39.5408	−	39.5408i	1.28899	−	1.28899i	0.935399	−	0.353595i	$-0.115041\pi$
$942$	−37.9554	+	21.6988i	−1.23665	+	0.706985i
$943$	−17.4906	−	17.4906i	−0.569574	−	0.569574i
$944$	−11.3338	−	11.3338i	−0.368884	−	0.368884i
$945$		0			0
$946$			0.544698i			0.0177097i
$947$	19.7845	−	19.7845i	0.642910	−	0.642910i	−0.308360	−	0.951270i	$-0.599780\pi$
$947$	19.7845	−	19.7845i	0.642910	−	0.642910i	0.951270	+	0.308360i	$0.0997802\pi$
$948$	3.73953	−	13.7223i	0.121454	−	0.445680i
$949$	−7.71927	−	58.2373i	−0.250578	−	1.89046i
$950$		0			0
$951$	18.2274	+	31.8833i	0.591065	+	1.03389i
$952$			13.6541i			0.442532i
$953$		−	52.5727i		−	1.70300i	−0.524357	−	0.851498i	$-0.675694\pi$
$953$		−	52.5727i		−	1.70300i	0.524357	−	0.851498i	$-0.324306\pi$
$954$	−0.307363	−	1.18741i	−0.00995123	−	0.0384440i
$955$		0			0
$956$	2.58511	+	2.58511i	0.0836085	+	0.0836085i
$957$	4.57367	−	2.61473i	0.147846	−	0.0845222i
$958$			27.9336i			0.902495i
$959$	19.0950			0.616611
$960$		0			0
$961$		−	23.1584i		−	0.747046i
$962$	−14.8569	+	19.3973i	−0.479007	+	0.625393i
$963$	−9.54390	−	5.61898i	−0.307548	−	0.181069i
$964$	2.07049	+	2.07049i	0.0666861	+	0.0666861i
$965$		0			0
$966$	31.0580	+	8.46375i	0.999275	+	0.272317i
$967$	−15.6621	+	15.6621i	−0.503658	+	0.503658i	−0.912573	−	0.408915i	$-0.865907\pi$
$967$	−15.6621	+	15.6621i	−0.503658	+	0.503658i	0.408915	+	0.912573i	$0.365907\pi$
$968$	−18.1304	−	18.1304i	−0.582732	−	0.582732i
$969$	7.15979	−	4.09319i	0.230006	−	0.131492i
$970$		0			0
$971$		−	18.1426i		−	0.582225i	−0.956689	−	0.291113i	$-0.905975\pi$
$971$		−	18.1426i		−	0.582225i	0.956689	−	0.291113i	$-0.0940254\pi$
$972$	−7.62227	+	1.86957i	−0.244485	+	0.0599663i
$973$	−6.82441	−	6.82441i	−0.218781	−	0.218781i
$974$	38.6181			1.23740
$975$		0			0
$976$	−17.4024			−0.557037
$977$	−21.5034	−	21.5034i	−0.687954	−	0.687954i	0.273826	−	0.961779i	$-0.411711\pi$
$977$	−21.5034	−	21.5034i	−0.687954	−	0.687954i	−0.961779	+	0.273826i	$0.911711\pi$
$978$	−4.46035	+	16.3674i	−0.142626	+	0.523372i
$979$		−	2.91403i		−	0.0931329i
$980$		0			0
$981$	−10.8397	−	41.8764i	−0.346086	−	1.33701i
$982$	37.3147	+	37.3147i	1.19076	+	1.19076i
$983$	−31.4759	+	31.4759i	−1.00392	+	1.00392i	−0.00393200	+	0.999992i	$0.501252\pi$
$983$	−31.4759	+	31.4759i	−1.00392	+	1.00392i	−0.999992	+	0.00393200i	$0.998748\pi$
$984$	−4.70891	+	17.2795i	−0.150115	+	0.550851i
$985$		0			0
$986$	−22.8428	−	22.8428i	−0.727462	−	0.727462i
$987$	42.9489	+	11.7042i	1.36708	+	0.372548i
$988$	−3.08138	+	0.408432i	−0.0980317	+	0.0129940i
$989$			4.70717i			0.149679i
$990$		0			0
$991$	−43.9818			−1.39713			−0.698563	−	0.715548i	$-0.746177\pi$
$991$	−43.9818			−1.39713			−0.698563	+	0.715548i	$0.746177\pi$
$992$		−	7.79970i		−	0.247641i
$993$	−7.87889	−	13.7817i	−0.250029	−	0.437349i
$994$	25.8604	+	25.8604i	0.820243	+	0.820243i
$995$		0			0
$996$	−10.8876	+	6.22434i	−0.344986	+	0.197226i
$997$			44.9600i			1.42390i	0.702231	+	0.711949i	$0.252187\pi$
$997$			44.9600i			1.42390i	−0.702231	+	0.711949i	$0.747813\pi$
$998$			40.2002i			1.27251i
$999$	−0.284022	+	22.2528i	−0.00898606	+	0.704048i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.n.r.749.15		40
3.2	odd	2	inner	975.2.n.r.749.6		40
5.2	odd	4		195.2.o.a.86.6	✓	40
5.3	odd	4		975.2.o.p.476.15		40
5.4	even	2		975.2.n.q.749.6		40
13.5	odd	4		975.2.n.q.824.15		40
15.2	even	4		195.2.o.a.86.15	yes	40
15.8	even	4		975.2.o.p.476.6		40
15.14	odd	2		975.2.n.q.749.15		40
39.5	even	4		975.2.n.q.824.6		40
65.18	even	4		975.2.o.p.551.6		40
65.44	odd	4	inner	975.2.n.r.824.6		40
65.57	even	4		195.2.o.a.161.15	yes	40
195.44	even	4	inner	975.2.n.r.824.15		40
195.83	odd	4		975.2.o.p.551.15		40
195.122	odd	4		195.2.o.a.161.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.o.a.86.6	✓	40	5.2	odd	4
195.2.o.a.86.15	yes	40	15.2	even	4
195.2.o.a.161.6	yes	40	195.122	odd	4
195.2.o.a.161.15	yes	40	65.57	even	4
975.2.n.q.749.6		40	5.4	even	2
975.2.n.q.749.15		40	15.14	odd	2
975.2.n.q.824.6		40	39.5	even	4
975.2.n.q.824.15		40	13.5	odd	4
975.2.n.r.749.6		40	3.2	odd	2	inner
975.2.n.r.749.15		40	1.1	even	1	trivial
975.2.n.r.824.6		40	65.44	odd	4	inner
975.2.n.r.824.15		40	195.44	even	4	inner
975.2.o.p.476.6		40	15.8	even	4
975.2.o.p.476.15		40	5.3	odd	4
975.2.o.p.551.6		40	65.18	even	4
975.2.o.p.551.15		40	195.83	odd	4

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.n (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.11881 + 1.11881i) q^{2} +(1.67111 + 0.455401i) q^{3} +0.503463i q^{4} +(1.36015 + 2.37916i) q^{6} +(-1.46633 - 1.46633i) q^{7} +(1.67434 - 1.67434i) q^{8} +(2.58522 + 1.52205i) q^{9} +(0.292930 + 0.292930i) q^{11} +(-0.229277 + 0.841342i) q^{12} +(2.86241 + 2.19240i) q^{13} -3.28107i q^{14} +4.75345 q^{16} -2.78074i q^{17} +(1.18948 + 4.59525i) q^{18} +(1.21080 + 1.21080i) q^{19} +(-1.78263 - 3.11816i) q^{21} +0.655464i q^{22} +5.66438i q^{23} +(3.56050 - 2.03551i) q^{24} +(0.749610 + 5.65536i) q^{26} +(3.62704 + 3.72083i) q^{27} +(0.738240 - 0.738240i) q^{28} -7.34233i q^{29} +(-1.98010 - 1.98010i) q^{31} +(1.96952 + 1.96952i) q^{32} +(0.356117 + 0.622918i) q^{33} +(3.11111 - 3.11111i) q^{34} +(-0.766296 + 1.30156i) q^{36} +(3.02847 + 3.02847i) q^{37} +2.70931i q^{38} +(3.78498 + 4.96729i) q^{39} +(-3.08783 + 3.08783i) q^{41} +(1.49420 - 5.48304i) q^{42} +0.831012 q^{43} +(-0.147479 + 0.147479i) q^{44} +(-6.33735 + 6.33735i) q^{46} +(-8.76367 + 8.76367i) q^{47} +(7.94354 + 2.16473i) q^{48} -2.69978i q^{49} +(1.26635 - 4.64692i) q^{51} +(-1.10379 + 1.44112i) q^{52} -0.258401 q^{53} +(-0.104926 + 8.22086i) q^{54} -4.91025 q^{56} +(1.47198 + 2.57478i) q^{57} +(8.21465 - 8.21465i) q^{58} +(-2.38433 - 2.38433i) q^{59} -3.66100 q^{61} -4.43070i q^{62} +(-1.55895 - 6.02260i) q^{63} -5.09987i q^{64} +(-0.298499 + 1.09535i) q^{66} +(9.29391 - 9.29391i) q^{67} +1.40000 q^{68} +(-2.57957 + 9.46581i) q^{69} +(-7.88169 + 7.88169i) q^{71} +(6.87696 - 1.78010i) q^{72} +(-11.5212 - 11.5212i) q^{73} +6.77656i q^{74} +(-0.609593 + 0.609593i) q^{76} -0.859060i q^{77} +(-1.32278 + 9.79210i) q^{78} -16.3100 q^{79} +(4.36672 + 7.86967i) q^{81} -6.90938 q^{82} +(10.1694 + 10.1694i) q^{83} +(1.56988 - 0.897486i) q^{84} +(0.929743 + 0.929743i) q^{86} +(3.34370 - 12.2698i) q^{87} +0.980926 q^{88} +(-4.97395 - 4.97395i) q^{89} +(-0.982449 - 7.41200i) q^{91} -2.85180 q^{92} +(-2.40722 - 4.21070i) q^{93} -19.6097 q^{94} +(2.39437 + 4.18821i) q^{96} +(-8.41532 + 8.41532i) q^{97} +(3.02053 - 3.02053i) q^{98} +(0.311433 + 1.20314i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{6} + 16 q^{7} + 24 q^{12} - 24 q^{13} - 64 q^{16} - 4 q^{18} + 16 q^{19} - 12 q^{21} - 8 q^{24} - 32 q^{28} + 32 q^{31} - 4 q^{33} + 16 q^{34} - 32 q^{37} + 8 q^{39} + 32 q^{43} - 40 q^{46}+ \cdots + 20 q^{99}+O(q^{100}) \) 40 * q + 12 * q^6 + 16 * q^7 + 24 * q^12 - 24 * q^13 - 64 * q^16 - 4 * q^18 + 16 * q^19 - 12 * q^21 - 8 * q^24 - 32 * q^28 + 32 * q^31 - 4 * q^33 + 16 * q^34 - 32 * q^37 + 8 * q^39 + 32 * q^43 - 40 * q^46 + 8 * q^52 + 32 * q^54 - 36 * q^57 - 24 * q^58 + 8 * q^61 + 8 * q^63 - 48 * q^66 - 32 * q^67 - 132 * q^72 - 64 * q^73 + 16 * q^76 + 108 * q^78 - 40 * q^79 + 72 * q^81 + 128 * q^82 - 124 * q^84 + 80 * q^88 + 8 * q^91 + 108 * q^93 + 32 * q^94 - 76 * q^96 + 24 * q^97 + 20 * q^99

Introduction

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