LMFDB - Embedded newform 975.2.o.p.476.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(476,975)] 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("975.476"); 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, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.o (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,0,0,12,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == 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			476.6
Character	$\chi$	$=$	975.476
Dual form			975.2.o.p.551.6

$q$-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} +(-0.455401 - 1.67111i) q^{3} -0.503463i q^{4} +(2.37916 + 1.36015i) 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} +(-0.841342 + 0.229277i) q^{12} +(-2.19240 + 2.86241i) q^{13} -3.28107i q^{14} +4.75345 q^{16} +2.78074 q^{17} +(1.18948 - 4.59525i) q^{18} +(-1.21080 - 1.21080i) q^{19} +(3.11816 + 1.78263i) q^{21} +0.655464 q^{22} +5.66438 q^{23} +(-2.03551 + 3.56050i) q^{24} +(-0.749610 - 5.65536i) q^{26} +(3.72083 + 3.62704i) 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} +2.70931 q^{38} +(5.78182 + 2.36020i) q^{39} +(3.08783 - 3.08783i) q^{41} +(-5.48304 + 1.49420i) q^{42} +0.831012i q^{43} +(-0.147479 + 0.147479i) q^{44} +(-6.33735 + 6.33735i) q^{46} +(-8.76367 - 8.76367i) q^{47} +(-2.16473 - 7.94354i) q^{48} +2.69978i q^{49} +(-1.26635 - 4.64692i) q^{51} +(1.44112 + 1.10379i) q^{52} +0.258401i q^{53} +(-8.22086 + 0.104926i) 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} +4.43070 q^{62} +(1.55895 - 6.02260i) q^{63} +5.09987i q^{64} +(-0.298499 - 1.09535i) q^{66} +(-9.29391 - 9.29391i) q^{67} -1.40000i 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} +0.859060 q^{77} +(-9.10936 + 3.82814i) q^{78} +16.3100 q^{79} +(4.36672 - 7.86967i) q^{81} +6.90938i q^{82} +(10.1694 - 10.1694i) q^{83} +(0.897486 - 1.56988i) q^{84} +(-0.929743 - 0.929743i) q^{86} +(-12.2698 + 3.34370i) q^{87} +0.980926i q^{88} +(-4.97395 - 4.97395i) q^{89} +(-0.982449 - 7.41200i) q^{91} -2.85180i q^{92} +(-2.40722 + 4.21070i) q^{93} +19.6097 q^{94} +(4.18821 + 2.39437i) q^{96} +(8.41532 + 8.41532i) q^{97} +(-3.02053 - 3.02053i) q^{98} +(1.20314 + 0.311433i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 12 q^{6} + 16 q^{7} - 64 q^{16} - 4 q^{18} - 16 q^{19} - 12 q^{21} + 8 q^{24} + 24 q^{27} - 32 q^{28} + 32 q^{31} + 4 q^{33} - 16 q^{34} - 32 q^{37} - 8 q^{39} - 8 q^{42} - 40 q^{46} - 8 q^{48} - 32 q^{54}+ \cdots - 20 q^{99}+O(q^{100}) $ 40 * q + 12 * q^6 + 16 * q^7 - 64 * q^16 - 4 * q^18 - 16 * q^19 - 12 * q^21 + 8 * q^24 + 24 * q^27 - 32 * q^28 + 32 * q^31 + 4 * q^33 - 16 * q^34 - 32 * q^37 - 8 * q^39 - 8 * q^42 - 40 * q^46 - 8 * q^48 - 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 + 12 * q^78 + 40 * q^79 + 72 * q^81 + 124 * q^84 - 16 * q^87 + 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	$-0.938970\pi$
$2$	−1.11881	+	1.11881i	−0.791117	+	0.791117i	0.190559	+	0.981676i	$0.438970\pi$
$3$	−0.455401	−	1.67111i	−0.262926	−	0.964816i
$3$	−0.455401	−	1.67111i	−0.262926	−	0.964816i
$4$		−	0.503463i		−	0.251731i
$5$		0			0
$5$		0			0
$6$	2.37916	+	1.36015i	0.971287	+	0.555277i
$7$	−1.46633	+	1.46633i	−0.554219	+	0.554219i	−0.927656	−	0.373437i	$-0.878179\pi$
$7$	−1.46633	+	1.46633i	−0.554219	+	0.554219i	0.373437	+	0.927656i	$0.378179\pi$
$8$	−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	0.661566	−	0.749887i	$-0.269892\pi$
$11$	−0.292930	−	0.292930i	−0.0883216	−	0.0883216i	−0.749887	+	0.661566i	$0.769892\pi$
$12$	−0.841342	+	0.229277i	−0.242874	+	0.0661867i
$13$	−2.19240	+	2.86241i	−0.608063	+	0.793889i
$13$	−2.19240	+	2.86241i	−0.608063	+	0.793889i
$14$		−	3.28107i		−	0.876904i
$15$		0			0
$16$	4.75345			1.18836
$17$	2.78074			0.674427			0.337214	−	0.941428i	$-0.390516\pi$
$17$	2.78074			0.674427			0.337214	+	0.941428i	$0.390516\pi$
$18$	1.18948	−	4.59525i	0.280363	−	1.08311i
$19$	−1.21080	−	1.21080i	−0.277777	−	0.277777i	0.554444	−	0.832221i	$-0.312931\pi$
$19$	−1.21080	−	1.21080i	−0.277777	−	0.277777i	−0.832221	+	0.554444i	$0.812931\pi$
$20$		0			0
$21$	3.11816	+	1.78263i	0.680438	+	0.389001i
$22$	0.655464			0.139745
$23$	5.66438			1.18111			0.590553	−	0.806999i	$-0.298910\pi$
$23$	5.66438			1.18111			0.590553	+	0.806999i	$0.298910\pi$
$24$	−2.03551	+	3.56050i	−0.415496	+	0.726784i
$25$		0			0
$26$	−0.749610	−	5.65536i	−0.147011	−	1.10911i
$27$	3.72083	+	3.62704i	0.716074	+	0.698025i
$28$	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	−0.412899	−	0.910777i	$-0.635484\pi$
$37$	3.02847	−	3.02847i	0.497878	−	0.497878i	0.910777	+	0.412899i	$0.135484\pi$
$38$	2.70931			0.439508
$39$	5.78182	+	2.36020i	0.925832	+	0.377934i
$40$		0			0
$41$	3.08783	−	3.08783i	0.482238	−	0.482238i	−0.423608	−	0.905846i	$-0.639236\pi$
$41$	3.08783	−	3.08783i	0.482238	−	0.482238i	0.905846	+	0.423608i	$0.139236\pi$
$42$	−5.48304	+	1.49420i	−0.846051	+	0.230561i
$43$			0.831012i			0.126728i	0.997990	+	0.0633640i	$0.0201829\pi$
$43$			0.831012i			0.126728i	−0.997990	+	0.0633640i	$0.979817\pi$
$44$	−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	−0.941611	−	0.336702i	$-0.890688\pi$
$47$	−8.76367	−	8.76367i	−1.27831	−	1.27831i	−0.336702	−	0.941611i	$-0.609312\pi$
$48$	−2.16473	−	7.94354i	−0.312451	−	1.14655i
$49$			2.69978i			0.385682i
$50$		0			0
$51$	−1.26635	−	4.64692i	−0.177324	−	0.650698i
$52$	1.44112	+	1.10379i	0.199847	+	0.153068i
$53$			0.258401i			0.0354940i	0.999843	+	0.0177470i	$0.00564935\pi$
$53$			0.258401i			0.0354940i	−0.999843	+	0.0177470i	$0.994351\pi$
$54$	−8.22086	+	0.104926i	−1.11872	+	0.0142787i
$55$		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	$0.575303\pi$
$62$	4.43070			0.562699
$63$	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	−0.989259	−	0.146173i	$-0.953304\pi$
$67$	−9.29391	−	9.29391i	−1.13543	−	1.13543i	−0.146173	−	0.989259i	$-0.546696\pi$
$68$		−	1.40000i		−	0.169775i
$69$	−2.57957	−	9.46581i	−0.310543	−	1.13955i
$70$		0			0
$71$	7.88169	−	7.88169i	0.935385	−	0.935385i	−0.0626508	−	0.998036i	$-0.519955\pi$
$71$	7.88169	−	7.88169i	0.935385	−	0.935385i	0.998036	+	0.0626508i	$0.0199554\pi$
$72$	6.87696	+	1.78010i	0.810457	+	0.209787i
$73$	11.5212	−	11.5212i	1.34845	−	1.34845i	0.461107	−	0.887345i	$-0.347453\pi$
$73$	11.5212	−	11.5212i	1.34845	−	1.34845i	0.887345	−	0.461107i	$-0.152547\pi$
$74$			6.77656i			0.787759i
$75$		0			0
$76$	−0.609593	+	0.609593i	−0.0699252	+	0.0699252i
$77$	0.859060			0.0978990
$78$	−9.10936	+	3.82814i	−1.03143	+	0.433451i
$79$	16.3100			1.83502			0.917512	−	0.397708i	$-0.130194\pi$
$79$	16.3100			1.83502			0.917512	+	0.397708i	$0.130194\pi$
$80$		0			0
$81$	4.36672	−	7.86967i	0.485191	−	0.874408i
$82$			6.90938i			0.763013i
$83$	10.1694	−	10.1694i	1.11624	−	1.11624i	0.123950	−	0.992288i	$-0.460444\pi$
$83$	10.1694	−	10.1694i	1.11624	−	1.11624i	0.992288	−	0.123950i	$-0.0395564\pi$
$84$	0.897486	−	1.56988i	0.0979237	−	0.171288i
$85$		0			0
$86$	−0.929743	−	0.929743i	−0.100257	−	0.100257i
$87$	−12.2698	+	3.34370i	−1.31546	+	0.358483i
$88$			0.980926i			0.104567i
$89$	−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
$92$		−	2.85180i		−	0.297321i
$93$	−2.40722	+	4.21070i	−0.249617	+	0.436629i
$94$	19.6097			2.02259
$95$		0			0
$96$	4.18821	+	2.39437i	0.427458	+	0.244374i
$97$	8.41532	+	8.41532i	0.854447	+	0.854447i	0.990677	−	0.136231i	$-0.0434988\pi$
$97$	8.41532	+	8.41532i	0.854447	+	0.854447i	−0.136231	+	0.990677i	$0.543499\pi$
$98$	−3.02053	−	3.02053i	−0.305120	−	0.305120i
$99$	1.20314	+	0.311433i	0.120920	+	0.0313002i
$100$		0			0
$101$	−6.35267			−0.632114			−0.316057	−	0.948740i	$-0.602359\pi$
$101$	−6.35267			−0.632114			−0.316057	+	0.948740i	$0.602359\pi$
$102$	6.61581	+	3.78220i	0.655063	+	0.374494i
$103$			7.54935i			0.743860i	0.928261	+	0.371930i	$0.121304\pi$
$103$			7.54935i			0.743860i	−0.928261	+	0.371930i	$0.878696\pi$
$104$	8.46346	−	1.12182i	0.829910	−	0.110003i
$105$		0			0
$106$	−0.289101	−	0.289101i	−0.0280799	−	0.0280799i
$107$		−	3.69172i		−	0.356892i	−0.983950	−	0.178446i	$-0.942893\pi$
$107$		−	3.69172i		−	0.356892i	0.983950	−	0.178446i	$-0.0571070\pi$
$108$	1.82608	−	1.87330i	0.175715	−	0.180258i
$109$	10.1957	+	10.1957i	0.976570	+	0.976570i	0.999732	−	0.0231620i	$-0.00737335\pi$
$109$	10.1957	+	10.1957i	0.976570	+	0.976570i	−0.0231620	+	0.999732i	$0.507373\pi$
$110$		0			0
$111$	−6.44008	−	3.68174i	−0.611266	−	0.349456i
$112$	−6.97011	+	6.97011i	−0.658613	+	0.658613i
$113$			17.3519i			1.63233i	0.577820	+	0.816164i	$0.303903\pi$
$113$			17.3519i			1.63233i	−0.577820	+	0.816164i	$0.696097\pi$
$114$	−1.23382	−	4.52755i	−0.115558	−	0.424044i
$115$		0			0
$116$	−3.69659			−0.343219
$117$	1.31111	−	10.7369i	0.121212	−	0.992627i
$118$	5.33522			0.491147
$119$	−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
$127$		−	21.0990i		−	1.87224i	−0.351686	−	0.936118i	$-0.614392\pi$
$127$		−	21.0990i		−	1.87224i	0.351686	−	0.936118i	$-0.385608\pi$
$128$	−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	$0.141783\pi$
$131$			9.86242i			0.861684i	−0.902427	+	0.430842i	$0.858217\pi$
$132$	0.313616	+	0.179292i	0.0272968	+	0.0156053i
$133$	3.55086			0.307899
$134$	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	0.371961	−	0.928249i	$-0.378686\pi$
$137$	−6.51118	−	6.51118i	−0.556288	−	0.556288i	−0.928249	+	0.371961i	$0.878686\pi$
$138$	13.4765	+	7.70438i	1.14719	+	0.655840i
$139$	−4.65409			−0.394755			−0.197377	−	0.980328i	$-0.563242\pi$
$139$	−4.65409			−0.394755			−0.197377	+	0.980328i	$0.563242\pi$
$140$		0			0
$141$	−10.6541	+	18.6361i	−0.897235	+	1.56944i
$142$			17.6362i			1.48000i
$143$	1.48070	−	0.196265i	0.123823	−	0.0164125i
$144$	−12.2887	+	7.23500i	−1.02406	+	0.602916i
$145$		0			0
$146$			25.7800i			2.13356i
$147$	4.51163	−	1.22948i	0.372113	−	0.101406i
$148$	−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	$0.157743\pi$
$152$			4.05458i			0.328870i
$153$	−7.18881	+	4.23242i	−0.581181	+	0.342171i
$154$	−0.961124	+	0.961124i	−0.0774496	+	0.0774496i
$155$		0			0
$156$	1.18827	−	2.91093i	0.0951379	−	0.233061i
$157$	15.9533			1.27321			0.636606	−	0.771190i	$-0.280338\pi$
$157$	15.9533			1.27321			0.636606	+	0.771190i	$0.280338\pi$
$158$	−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	$-0.827943\pi$
$163$	−4.37713	+	4.37713i	−0.342843	+	0.342843i	0.514592	+	0.857435i	$0.327943\pi$
$164$	−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	0.537585	−	0.843209i	$-0.319337\pi$
$167$	−3.94953	−	3.94953i	−0.305624	−	0.305624i	−0.843209	+	0.537585i	$0.819337\pi$
$168$	−2.23613	−	8.20557i	−0.172521	−	0.633073i
$169$	−3.38676	−	12.5511i	−0.260520	−	0.965468i
$170$		0			0
$171$	4.97309	+	1.28729i	0.380302	+	0.0984412i
$172$	0.418383			0.0319014
$173$	9.74943			0.741235			0.370618	−	0.928786i	$-0.379146\pi$
$173$	9.74943			0.741235			0.370618	+	0.928786i	$0.379146\pi$
$174$	9.98663	−	17.4686i	0.757084	−	1.32429i
$175$		0			0
$176$	−1.39243	−	1.39243i	−0.104958	−	0.104958i
$177$	−2.89866	+	5.07031i	−0.217876	+	0.381108i
$178$	11.1298			0.834213
$179$	−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	$0.935794\pi$
$182$	9.39177	+	7.19343i	0.696165	+	0.533212i
$183$	1.66723	+	6.11794i	0.123245	+	0.452251i
$184$	−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
$189$	−10.7744	+	0.137518i	−0.783720	+	0.0100030i
$190$		0			0
$191$		−	8.13709i		−	0.588779i	−0.955686	−	0.294390i	$-0.904884\pi$
$191$		−	8.13709i		−	0.588779i	0.955686	−	0.294390i	$-0.0951163\pi$
$192$	8.52244	−	2.32248i	0.615054	−	0.167611i
$193$	−2.02917	+	2.02917i	−0.146063	+	0.146063i	−0.776357	−	0.630294i	$-0.782934\pi$
$193$	−2.02917	+	2.02917i	−0.146063	+	0.146063i	0.630294	+	0.776357i	$0.282934\pi$
$194$	−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	$-0.799955\pi$
$197$	−3.10238	+	3.10238i	−0.221036	+	0.221036i	0.587899	+	0.808934i	$0.299955\pi$
$198$	−1.69452	+	0.997650i	−0.120424	+	0.0708999i
$199$			3.79864i			0.269279i	0.990895	+	0.134639i	$0.0429876\pi$
$199$			3.79864i			0.269279i	−0.990895	+	0.134639i	$0.957012\pi$
$200$		0			0
$201$	−11.2987	+	19.7636i	−0.796949	+	1.39402i
$202$	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
$207$	−14.6437	+	8.62148i	−1.01781	+	0.599234i
$208$	−10.4215	+	13.6063i	−0.722599	+	0.943428i
$209$			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	$0.434105\pi$
$212$	0.130095			0.00893496
$213$	−16.7605	−	9.58185i	−1.14841	−	0.656537i
$214$	4.13032	+	4.13032i	0.282343	+	0.282343i
$215$		0			0
$216$	−0.157026	−	12.3028i	−0.0106843	−	0.837101i
$217$	5.80694			0.394201
$218$	−22.8140			−1.54516
$219$	−24.4999	−	14.0064i	−1.65555	−	0.946465i
$220$		0			0
$221$	−6.09649	+	7.95960i	−0.410094	+	0.535421i
$222$	11.3244	−	3.08605i	0.760042	−	0.207122i
$223$	−4.16343	−	4.16343i	−0.278804	−	0.278804i	0.553827	−	0.832631i	$-0.313167\pi$
$223$	−4.16343	−	4.16343i	−0.278804	−	0.278804i	−0.832631	+	0.553827i	$0.813167\pi$
$224$		−	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	$-0.627627\pi$
$227$	7.99122	−	7.99122i	0.530396	−	0.530396i	0.920690	+	0.390294i	$0.127627\pi$
$228$	1.29631	+	0.741088i	0.0858501	+	0.0490798i
$229$	−14.7738	+	14.7738i	−0.976279	+	0.976279i	−0.999725	−	0.0234464i	$-0.992536\pi$
$229$	−14.7738	+	14.7738i	−0.976279	+	0.976279i	0.0234464	+	0.999725i	$0.492536\pi$
$230$		0			0
$231$	−0.391217	−	1.43558i	−0.0257402	−	0.0944545i
$232$	−12.2935	+	12.2935i	−0.807110	+	0.807110i
$233$	−15.0434			−0.985527			−0.492764	−	0.870163i	$-0.664013\pi$
$233$	−15.0434			−0.985527			−0.492764	+	0.870163i	$0.664013\pi$
$234$	10.5457	+	13.4794i	0.689391	+	0.881176i
$235$		0			0
$236$	−1.20042	+	1.20042i	−0.0781409	+	0.0781409i
$237$	−7.42762	−	27.2559i	−0.482475	−	1.77046i
$238$		−	9.12380i		−	0.591408i
$239$	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
$243$	−15.1397	−	3.71341i	−0.971212	−	0.238216i
$244$			1.84318i			0.117997i
$245$		0			0
$246$	11.5463	−	3.14654i	0.736167	−	0.200616i
$247$	6.12037	−	0.811246i	0.389430	−	0.0516183i
$248$			6.63071i			0.421050i
$249$	−21.6254	−	12.3631i	−1.37045	−	0.783477i
$250$		0			0
$251$	5.50029			0.347175			0.173588	−	0.984818i	$-0.444464\pi$
$251$	5.50029			0.347175			0.173588	+	0.984818i	$0.444464\pi$
$252$	−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
$257$	−7.45007			−0.464723			−0.232361	−	0.972630i	$-0.574645\pi$
$257$	−7.45007			−0.464723			−0.232361	+	0.972630i	$0.574645\pi$
$258$	−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
$263$		−	23.1846i		−	1.42962i	−0.699317	−	0.714812i	$-0.746512\pi$
$263$		−	23.1846i		−	1.42962i	0.699317	−	0.714812i	$-0.253488\pi$
$264$	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	$0.288110\pi$
$272$	13.2181			0.801464
$273$	−11.9389	+	5.01721i	−0.722572	+	0.303656i
$274$	14.5695			0.880177
$275$		0			0
$276$	−4.76568	+	1.29872i	−0.286860	+	0.0781735i
$277$		−	28.6741i		−	1.72286i	−0.507874	−	0.861431i	$-0.669569\pi$
$277$		−	28.6741i		−	1.72286i	0.507874	−	0.861431i	$-0.330431\pi$
$278$	5.20703	−	5.20703i	0.312297	−	0.312297i
$279$	8.13280	+	2.10518i	0.486898	+	0.126034i
$280$		0			0
$281$	0.811843	+	0.811843i	0.0484305	+	0.0484305i	0.730907	−	0.682477i	$-0.239097\pi$
$281$	0.811843	+	0.811843i	0.0484305	+	0.0484305i	−0.682477	+	0.730907i	$0.739097\pi$
$282$	−8.93030	−	32.7700i	−0.531791	−	1.95143i
$283$			22.9639i			1.36506i	0.730857	+	0.682531i	$0.239121\pi$
$283$			22.9639i			1.36506i	−0.730857	+	0.682531i	$0.760879\pi$
$284$	−3.96814	−	3.96814i	−0.235466	−	0.235466i
$285$		0			0
$286$	−1.43704	+	1.87621i	−0.0849739	+	0.110942i
$287$			9.05553i			0.534531i
$288$	2.09393	−	8.08936i	0.123386	−	0.476670i
$289$	−9.26751			−0.545148
$290$		0			0
$291$	10.2306	−	17.8953i	0.599728	−	1.04904i
$292$	−5.80048	−	5.80048i	−0.339447	−	0.339447i
$293$	8.25860	+	8.25860i	0.482472	+	0.482472i	0.905920	−	0.423448i	$-0.139180\pi$
$293$	8.25860	+	8.25860i	0.482472	+	0.482472i	−0.423448	+	0.905920i	$0.639180\pi$
$294$	−3.67209	+	6.42320i	−0.214161	+	0.374608i
$295$		0			0
$296$	−10.1414			−0.589455
$297$	−0.0274721	−	2.15241i	−0.00159409	−	0.124895i
$298$		−	26.5802i		−	1.53975i
$299$	−12.4186	+	16.2138i	−0.718186	+	0.937666i
$300$		0			0
$301$	−1.21853	−	1.21853i	−0.0702351	−	0.0702351i
$302$			11.1133i			0.639496i
$303$	2.89301	+	10.6160i	0.166199	+	0.609874i
$304$	−5.75549	−	5.75549i	−0.330100	−	0.330100i
$305$		0			0
$306$	3.30763	−	12.7782i	0.189085	−	0.730479i
$307$	−22.4159	+	22.4159i	−1.27934	+	1.27934i	−0.338310	+	0.941035i	$0.609855\pi$
$307$	−22.4159	+	22.4159i	−1.27934	+	1.27934i	−0.941035	+	0.338310i	$0.890145\pi$
$308$		−	0.432505i		−	0.0246443i
$309$	12.6158	−	3.43798i	0.717688	−	0.195580i
$310$		0			0
$311$	21.6419			1.22720			0.613600	−	0.789617i	$-0.289721\pi$
$311$	21.6419			1.22720			0.613600	+	0.789617i	$0.289721\pi$
$312$	−5.72895	−	13.6325i	−0.324338	−	0.771788i
$313$	−7.12210			−0.402565			−0.201282	−	0.979533i	$-0.564511\pi$
$313$	−7.12210			−0.402565			−0.201282	+	0.979533i	$0.564511\pi$
$314$	−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	$-0.953029\pi$
$317$	−14.9932	+	14.9932i	−0.842104	+	0.842104i	0.147028	+	0.989132i	$0.453029\pi$
$318$	−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
$322$		−	18.5853i		−	1.03572i
$323$	−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
$328$	−10.3401			−0.570939
$329$	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
$336$	14.8220	+	8.47362i	0.808607	+	0.462274i
$337$			32.1622i			1.75199i	0.482323	+	0.875993i	$0.339793\pi$
$337$			32.1622i			1.75199i	−0.482323	+	0.875993i	$0.660207\pi$
$338$	17.8314	+	10.2531i	0.969900	+	0.557697i
$339$	28.9969	−	7.90207i	1.57490	−	0.429181i
$340$		0			0
$341$			1.16006i			0.0628207i
$342$	−7.00416	+	4.12371i	−0.378742	+	0.222985i
$343$	−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
$347$			11.3661i			0.610165i	0.952326	+	0.305082i	$0.0986840\pi$
$347$			11.3661i			0.610165i	−0.952326	+	0.305082i	$0.901316\pi$
$348$	1.68343	+	6.17740i	0.0902413	+	0.331144i
$349$	0.388646	−	0.388646i	0.0208038	−	0.0208038i	−0.696628	−	0.717432i	$-0.745317\pi$
$349$	0.388646	−	0.388646i	0.0208038	−	0.0208038i	0.717432	+	0.696628i	$0.245317\pi$
$350$		0			0
$351$	−18.5396	+	2.69859i	−0.989572	+	0.144040i
$352$	1.15386			0.0615011
$353$	−10.9517	+	10.9517i	−0.582900	+	0.582900i	−0.935699	−	0.352799i	$-0.885230\pi$
$353$	−10.9517	+	10.9517i	−0.582900	+	0.582900i	0.352799	+	0.935699i	$0.385230\pi$
$354$	−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
$363$	−18.0954	+	4.93126i	−0.949764	+	0.258824i
$364$	−3.73166	+	0.494626i	−0.195592	+	0.0259255i
$365$		0			0
$366$	−8.71011	−	4.97950i	−0.455285	−	0.260282i
$367$	23.2059			1.21134			0.605669	−	0.795717i	$-0.292906\pi$
$367$	23.2059			1.21134			0.605669	+	0.795717i	$0.292906\pi$
$368$	26.9254			1.40358
$369$	−3.28288	+	12.6826i	−0.170900	+	0.660227i
$370$		0			0
$371$	−0.378899	−	0.378899i	−0.0196715	−	0.0196715i
$372$	2.11993	+	1.21195i	0.109913	+	0.0628365i
$373$	20.3615			1.05428			0.527139	−	0.849779i	$-0.323265\pi$
$373$	20.3615			1.05428			0.527139	+	0.849779i	$0.323265\pi$
$374$	1.82267			0.0942481
$375$		0			0
$376$			29.3467i			1.51344i
$377$	21.0167	+	16.0973i	1.08242	+	0.829054i
$378$	11.9006	−	12.2083i	0.612101	−	0.627928i
$379$	−2.24383	−	2.24383i	−0.115258	−	0.115258i	0.647126	−	0.762383i	$-0.275971\pi$
$379$	−2.24383	−	2.24383i	−0.115258	−	0.115258i	−0.762383	+	0.647126i	$0.775971\pi$
$380$		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	−0.781776	−	0.623559i	$-0.785686\pi$
$383$	−3.09636	+	3.09636i	−0.158217	+	0.158217i	0.623559	+	0.781776i	$0.285686\pi$
$384$	−11.7253	+	20.5098i	−0.598354	+	1.04664i
$385$		0			0
$386$		−	4.54050i		−	0.231105i
$387$	−1.26484	−	2.14835i	−0.0642955	−	0.109207i
$388$	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
$393$	16.4812	−	4.49136i	0.831366	−	0.226559i
$394$		−	6.94194i		−	0.349730i
$395$		0			0
$396$	0.156795	−	0.605737i	0.00787925	−	0.0304394i
$397$	−13.4071	+	13.4071i	−0.672884	+	0.672884i	−0.958380	−	0.285496i	$-0.907842\pi$
$397$	−13.4071	+	13.4071i	−0.672884	+	0.672884i	0.285496	+	0.958380i	$0.407842\pi$
$398$	−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	0.817232	−	0.576309i	$-0.195507\pi$
$401$	4.82449	+	4.82449i	0.240923	+	0.240923i	−0.576309	+	0.817232i	$0.695507\pi$
$402$	−9.47062	−	34.7528i	−0.472351	−	1.73331i
$403$	10.0090	−	1.32668i	0.498585	−	0.0660867i
$404$			3.19833i			0.159123i
$405$		0			0
$406$	−24.0907			−1.19560
$407$	−1.77426			−0.0879467
$408$	−5.66021	+	9.90081i	−0.280222	+	0.490163i
$409$	−2.33925	−	2.33925i	−0.115669	−	0.115669i	0.646903	−	0.762572i	$-0.276064\pi$
$409$	−2.33925	−	2.33925i	−0.115669	−	0.115669i	−0.762572	+	0.646903i	$0.776064\pi$
$410$		0			0
$411$	−7.91571	+	13.8461i	−0.390453	+	0.682978i
$412$	3.80082			0.187253
$413$	6.99242			0.344074
$414$	6.73768	−	26.0292i	0.331139	−	1.27927i
$415$		0			0
$416$	−1.31959	−	9.95556i	−0.0646985	−	0.488112i
$417$	2.11948	+	7.77749i	0.103791	+	0.380866i
$418$	−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
$428$	−1.85864			−0.0898409
$429$	−1.00229	−	2.38504i	−0.0483912	−	0.115151i
$430$		0			0
$431$	25.6108	−	25.6108i	1.23363	−	1.23363i	0.271068	−	0.962560i	$-0.412623\pi$
$431$	25.6108	−	25.6108i	1.23363	−	1.23363i	0.962560	−	0.271068i	$-0.0873767\pi$
$432$	17.6868	+	17.2410i	0.850955	+	0.829507i
$433$			32.5410i			1.56382i	0.623392	+	0.781909i	$0.285754\pi$
$433$			32.5410i			1.56382i	−0.623392	+	0.781909i	$0.714246\pi$
$434$	−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
$438$	43.0812	−	11.7402i	2.05850	−	0.560970i
$439$		−	33.7542i		−	1.61100i	−0.592595	−	0.805501i	$-0.701896\pi$
$439$		−	33.7542i		−	1.61100i	0.592595	−	0.805501i	$-0.298104\pi$
$440$		0			0
$441$	−4.10920	−	6.97952i	−0.195676	−	0.332358i
$442$	−2.08447	−	15.7261i	−0.0991479	−	0.748012i
$443$		−	30.3054i		−	1.43985i	−0.694050	−	0.719927i	$-0.744175\pi$
$443$		−	30.3054i		−	1.43985i	0.694050	−	0.719927i	$-0.255825\pi$
$444$	−1.85362	+	3.24234i	−0.0879689	+	0.153875i
$445$		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
$452$	8.73603			0.410908
$453$	−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	$-0.113017\pi$
$457$	12.6125	+	12.6125i	0.589987	+	0.589987i	−0.347641	+	0.937628i	$0.613017\pi$
$458$		−	33.0580i		−	1.54470i
$459$	10.3466	+	10.0858i	0.482940	+	0.470767i
$460$		0			0
$461$	13.1232	−	13.1232i	0.611207	−	0.611207i	−0.332054	−	0.943260i	$-0.607742\pi$
$461$	13.1232	−	13.1232i	0.611207	−	0.611207i	0.943260	+	0.332054i	$0.107742\pi$
$462$	2.04384	+	1.16845i	0.0950881	+	0.0543611i
$463$	23.7400	−	23.7400i	1.10329	−	1.10329i	0.109278	−	0.994011i	$-0.465146\pi$
$463$	23.7400	−	23.7400i	1.10329	−	1.10329i	0.994011	−	0.109278i	$-0.0348540\pi$
$464$		−	34.9014i		−	1.62026i
$465$		0			0
$466$	16.8307	−	16.8307i	0.779667	−	0.779667i
$467$	−20.9138			−0.967776			−0.483888	−	0.875130i	$-0.660776\pi$
$467$	−20.9138			−0.967776			−0.483888	+	0.875130i	$0.660776\pi$
$468$	−5.40563	−	0.660093i	−0.249875	−	0.0305128i
$469$	27.2558			1.25856
$470$		0			0
$471$	−7.26515	−	26.6597i	−0.334760	−	1.22841i
$472$			7.98436i			0.367510i
$473$	0.243428	−	0.243428i	0.0111928	−	0.0111928i
$474$	38.8042	+	22.1840i	1.78234	+	1.01895i
$475$		0			0
$476$	2.05285	+	2.05285i	0.0940923	+	0.0940923i
$477$	−0.393299	−	0.668022i	−0.0180079	−	0.0305866i
$478$			11.4894i			0.525513i
$479$	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
$482$			9.20221i			0.419149i
$483$	17.6624	+	10.0975i	0.803669	+	0.459451i
$484$	−5.45169			−0.247804
$485$		0			0
$486$	21.0930	−	12.7838i	0.956799	−	0.579886i
$487$	−17.2586	−	17.2586i	−0.782061	−	0.782061i	0.198117	−	0.980178i	$-0.436517\pi$
$487$	−17.2586	−	17.2586i	−0.782061	−	0.782061i	−0.980178	+	0.198117i	$0.936517\pi$
$488$	6.12976	+	6.12976i	0.277481	+	0.277481i
$489$	9.30801	+	5.32131i	0.420923	+	0.240638i
$490$		0			0
$491$	−33.3522			−1.50516			−0.752582	−	0.658498i	$-0.771192\pi$
$491$	−33.3522			−1.50516			−0.752582	+	0.658498i	$0.771192\pi$
$492$	−1.88995	+	3.30589i	−0.0852055	+	0.149041i
$493$		−	20.4171i		−	0.919538i
$494$	−5.93989	+	7.75515i	−0.267248	+	0.348921i
$495$		0			0
$496$	−9.41230	−	9.41230i	−0.422625	−	0.422625i
$497$			23.1143i			1.03682i
$498$	38.0265	−	10.3628i	1.70401	−	0.464367i
$499$	−17.9656	−	17.9656i	−0.804252	−	0.804252i	0.179505	−	0.983757i	$-0.442550\pi$
$499$	−17.9656	−	17.9656i	−0.804252	−	0.804252i	−0.983757	+	0.179505i	$0.942550\pi$
$500$		0			0
$501$	−4.80148	+	8.39872i	−0.214514	+	0.375227i
$502$	−6.15377	+	6.15377i	−0.274656	+	0.274656i
$503$		−	38.5906i		−	1.72067i	−0.509731	−	0.860334i	$-0.670255\pi$
$503$		−	38.5906i		−	1.72067i	0.509731	−	0.860334i	$-0.329745\pi$
$504$	−12.6941	+	7.47365i	−0.565439	+	0.332903i
$505$		0			0
$506$	3.71280			0.165054
$507$	−19.4319	+	11.3754i	−0.863002	+	0.505201i
$508$	−10.6226			−0.471300
$509$	−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
$517$			5.13428i			0.225805i
$518$	−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	$-0.901713\pi$
$521$		−	13.8731i		−	0.607791i	0.952705	−	0.303896i	$-0.0982874\pi$
$522$	−33.7398	−	8.73356i	−1.47675	−	0.382257i
$523$	24.2698			1.06124			0.530622	−	0.847609i	$-0.321958\pi$
$523$	24.2698			1.06124			0.530622	+	0.847609i	$0.321958\pi$
$524$	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
$531$	9.79310	+	2.53495i	0.424984	+	0.110007i
$532$		−	1.78773i		−	0.0775077i
$533$	2.06887	+	15.6084i	0.0896127	+	0.676074i
$534$	−5.06852	−	18.5991i	−0.219336	−	0.804862i
$535$		0			0
$536$			31.1223i			1.34428i
$537$	0.585055	+	2.14688i	0.0252470	+	0.0926447i
$538$	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	$0.0141555\pi$
$542$		−	6.22205i		−	0.267260i
$543$	9.00852	−	2.45495i	0.386592	−	0.105352i
$544$	−5.47672	+	5.47672i	−0.234813	+	0.234813i
$545$		0			0
$546$	7.74399	−	18.9706i	0.331412	−	0.811866i
$547$	19.3984			0.829418			0.414709	−	0.909954i	$-0.363883\pi$
$547$	19.3984			0.829418			0.414709	+	0.909954i	$0.363883\pi$
$548$	−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	0.398873	−	0.917006i	$-0.369402\pi$
$557$	−12.2284	−	12.2284i	−0.518134	−	0.518134i	−0.917006	+	0.398873i	$0.869402\pi$
$558$	−11.4543	+	6.74375i	−0.484900	+	0.285486i
$559$	−2.37869	−	1.82191i	−0.100608	−	0.0770586i
$560$		0			0
$561$	−0.990268	+	1.73217i	−0.0418091	+	0.0731323i
$562$	−1.81659			−0.0766284
$563$	13.2701			0.559267			0.279633	−	0.960107i	$-0.409787\pi$
$563$	13.2701			0.559267			0.279633	+	0.960107i	$0.409787\pi$
$564$	9.38256	+	5.36393i	0.395077	+	0.225862i
$565$		0			0
$566$	−25.6922	−	25.6922i	−1.07992	−	1.07992i
$567$	5.13647	+	17.9425i	0.215711	+	0.753516i
$568$	−26.3932			−1.10744
$569$	−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	$-0.0542415\pi$
$572$	−0.0988121	−	0.745479i	−0.00413154	−	0.0311700i
$573$	−13.5980	+	3.70564i	−0.568063	+	0.154805i
$574$	−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	$-0.474280\pi$
$577$	−22.0036	−	22.0036i	−0.916023	−	0.916023i	−0.996737	+	0.0807147i	$0.974280\pi$
$578$	10.3686	−	10.3686i	0.431275	−	0.431275i
$579$	4.31505	+	2.46688i	0.179327	+	0.102520i
$580$		0			0
$581$			29.8234i			1.23728i
$582$	8.57532	+	31.4674i	0.355459	+	1.30437i
$583$	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	$-0.813822\pi$
$587$	−6.82405	+	6.82405i	−0.281659	+	0.281659i	0.552112	+	0.833770i	$0.313822\pi$
$588$	−0.618998	−	2.27144i	−0.0255271	−	0.0936724i
$589$			4.79501i			0.197575i
$590$		0			0
$591$	6.59725	+	3.77159i	0.271375	+	0.155143i
$592$	14.3957	−	14.3957i	0.591659	−	0.591659i
$593$	1.95435	+	1.95435i	0.0802556	+	0.0802556i	0.746095	−	0.665839i	$-0.231926\pi$
$593$	1.95435	+	1.95435i	0.0802556	+	0.0802556i	−0.665839	+	0.746095i	$0.731926\pi$
$594$	2.43887	+	2.37740i	0.100068	+	0.0975457i
$595$		0			0
$596$	5.98054	+	5.98054i	0.244972	+	0.244972i
$597$	6.34795	−	1.72991i	0.259804	−	0.0708004i
$598$	−4.24607	−	32.0341i	−0.173635	−	1.30997i
$599$			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	$0.451847\pi$
$602$	2.72661			0.111128
$603$	38.1726	+	9.88100i	1.55451	+	0.402385i
$604$	−2.50048	−	2.50048i	−0.101743	−	0.101743i
$605$		0			0
$606$	−15.1140	−	8.64055i	−0.613965	−	0.350998i
$607$	5.61074			0.227733			0.113867	−	0.993496i	$-0.463676\pi$
$607$	5.61074			0.227733			0.113867	+	0.993496i	$0.463676\pi$
$608$	4.76940			0.193425
$609$	13.0886	−	22.8945i	0.530378	−	0.927733i
$610$		0			0
$611$	44.2987	−	5.87173i	1.79213	−	0.237545i
$612$	2.13087	+	3.61930i	0.0861352	+	0.146301i
$613$	−16.7181	−	16.7181i	−0.675238	−	0.675238i	0.283680	−	0.958919i	$-0.408445\pi$
$613$	−16.7181	−	16.7181i	−0.675238	−	0.675238i	−0.958919	+	0.283680i	$0.908445\pi$
$614$		−	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	0.271854	−	0.962339i	$-0.412363\pi$
$617$	30.6567	−	30.6567i	1.23419	−	1.23419i	0.962339	−	0.271854i	$-0.0876366\pi$
$618$	−10.2682	+	17.9611i	−0.413048	+	0.722501i
$619$	−20.5920	+	20.5920i	−0.827663	+	0.827663i	−0.987193	−	0.159530i	$-0.949002\pi$
$619$	−20.5920	+	20.5920i	−0.827663	+	0.827663i	0.159530	+	0.987193i	$0.449002\pi$
$620$		0			0
$621$	21.0762	+	20.5450i	0.845758	+	0.824441i
$622$	−24.2131	+	24.2131i	−0.970859	+	0.970859i
$623$	14.5869			0.584410
$624$	27.4836	+	11.2191i	1.10022	+	0.449123i
$625$		0			0
$626$	7.96826	−	7.96826i	0.318476	−	0.318476i
$627$	1.18542	−	0.323043i	0.0473410	−	0.0129011i
$628$		−	8.03189i		−	0.320507i
$629$	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
$633$	−2.71933	−	9.97866i	−0.108084	−	0.396616i
$634$		−	33.5491i		−	1.33241i
$635$		0			0
$636$	−0.0592454	−	0.217403i	−0.00234923	−	0.00862060i
$637$	−7.72786	−	5.91899i	−0.306189	−	0.234519i
$638$		−	4.81263i		−	0.190534i
$639$	−8.37957	+	32.3722i	−0.331491	+	1.28063i
$640$		0			0
$641$	−27.5035			−1.08632			−0.543161	−	0.839629i	$-0.682773\pi$
$641$	−27.5035			−1.08632			−0.543161	+	0.839629i	$0.682773\pi$
$642$	5.02127	−	8.78318i	0.198174	−	0.346645i
$643$	−27.9426	−	27.9426i	−1.10195	−	1.10195i	−0.994176	−	0.107771i	$-0.965629\pi$
$643$	−27.9426	−	27.9426i	−1.10195	−	1.10195i	−0.107771	−	0.994176i	$-0.534371\pi$
$644$	4.18167	+	4.18167i	0.164781	+	0.164781i
$645$		0			0
$646$	7.53387			0.296416
$647$	−16.9805			−0.667572			−0.333786	−	0.942649i	$-0.608326\pi$
$647$	−16.9805			−0.667572			−0.333786	+	0.942649i	$0.608326\pi$
$648$	−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
$653$			42.0032i			1.64371i	0.569695	+	0.821856i	$0.307061\pi$
$653$			42.0032i			1.64371i	−0.569695	+	0.821856i	$0.692939\pi$
$654$	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	$0.342236\pi$
$662$	14.5018			0.563627
$663$	16.0777	+	6.56309i	0.624407	+	0.254889i
$664$	−34.0541			−1.32155
$665$		0			0
$666$	−10.3143	−	17.5189i	−0.399670	−	0.678843i
$667$		−	41.5897i		−	1.61036i
$668$	−1.98844	+	1.98844i	−0.0769351	+	0.0769351i
$669$	−5.06152	+	8.85359i	−0.195690	+	0.342299i
$670$		0			0
$671$	1.07242	+	1.07242i	0.0414002	+	0.0414002i
$672$	−9.65221	+	2.63036i	−0.372342	+	0.101468i
$673$		−	25.8635i		−	0.996966i	−0.866899	−	0.498483i	$-0.833891\pi$
$673$		−	25.8635i		−	0.996966i	0.866899	−	0.498483i	$-0.166109\pi$
$674$	−35.9833	−	35.9833i	−1.38603	−	1.38603i
$675$		0			0
$676$	−6.31901	+	1.70511i	−0.243039	+	0.0655810i
$677$		−	21.1738i		−	0.813775i	−0.913478	−	0.406887i	$-0.866614\pi$
$677$		−	21.1738i		−	0.813775i	0.913478	−	0.406887i	$-0.133386\pi$
$678$	−23.6011	+	41.2829i	−0.906394	+	1.58546i
$679$	−24.6792			−0.947101
$680$		0			0
$681$	−16.9934	−	9.71501i	−0.651190	−	0.372280i
$682$	−1.29788	−	1.29788i	−0.0496985	−	0.0496985i
$683$	−13.2249	−	13.2249i	−0.506038	−	0.506038i	0.407270	−	0.913308i	$-0.366481\pi$
$683$	−13.2249	−	13.2249i	−0.506038	−	0.506038i	−0.913308	+	0.407270i	$0.866481\pi$
$684$	0.648101	−	2.50377i	0.0247807	−	0.0957339i
$685$		0			0
$686$	31.8257			1.21511
$687$	31.4166	+	17.9606i	1.19862	+	0.685240i
$688$			3.95017i			0.150599i
$689$	−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	$0.614033\pi$
$692$		−	4.90847i		−	0.186592i
$693$	−2.22086	+	1.30753i	−0.0843635	+	0.0496691i
$694$	−12.7165	−	12.7165i	−0.482712	−	0.482712i
$695$		0			0
$696$	26.1423	+	14.9454i	0.990923	+	0.566502i
$697$	8.58644	−	8.58644i	0.325235	−	0.325235i
$698$			0.869642i			0.0329164i
$699$	6.85079	+	25.1392i	0.259121	+	0.950852i
$700$		0			0
$701$	−14.2724			−0.539063			−0.269531	−	0.962992i	$-0.586869\pi$
$701$	−14.2724			−0.539063			−0.269531	+	0.962992i	$0.586869\pi$
$702$	17.7231	−	23.7615i	0.668914	−	0.896819i
$703$	−7.33376			−0.276598
$704$	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	−0.740921	−	0.671592i	$-0.765611\pi$
$709$	−1.84603	+	1.84603i	−0.0693291	+	0.0693291i	0.671592	+	0.740921i	$0.265611\pi$
$710$		0			0
$711$	−42.1651	+	24.8247i	−1.58131	+	0.931000i
$712$			16.6561i			0.624216i
$713$	−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
$718$	−8.50571			−0.317430
$719$	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
$726$	14.7282	−	25.7624i	0.546614	−	0.956134i
$727$		−	5.12985i		−	0.190256i	−0.995465	−	0.0951279i	$-0.969674\pi$
$727$		−	5.12985i		−	0.190256i	0.995465	−	0.0951279i	$-0.0303260\pi$
$728$	−10.7652	+	14.0551i	−0.398986	+	0.520918i
$729$	0.689112	+	26.9912i	0.0255227	+	0.999674i
$730$		0			0
$731$			2.31082i			0.0854689i
$732$	3.08016	−	0.839386i	0.113846	−	0.0310246i
$733$	−6.65960	−	6.65960i	−0.245978	−	0.245978i	0.573340	−	0.819318i	$-0.305647\pi$
$733$	−6.65960	−	6.65960i	−0.245978	−	0.245978i	−0.819318	+	0.573340i	$0.805647\pi$
$734$	−25.9629	+	25.9629i	−0.958309	+	0.958309i
$735$		0			0
$736$	−11.1561	+	11.1561i	−0.411220	+	0.411220i
$737$			5.44492i			0.200566i
$738$	−10.5164	−	17.8623i	−0.387115	−	0.657519i
$739$	−15.3715	+	15.3715i	−0.565448	+	0.565448i	−0.930850	−	0.365402i	$-0.880932\pi$
$739$	−15.3715	+	15.3715i	−0.565448	+	0.565448i	0.365402	+	0.930850i	$0.380932\pi$
$740$		0			0
$741$	−4.14291	−	9.85837i	−0.152193	−	0.362156i
$742$	0.847831			0.0311249
$743$	−10.7883	+	10.7883i	−0.395784	+	0.395784i	−0.876743	−	0.480959i	$-0.840288\pi$
$743$	−10.7883	+	10.7883i	−0.395784	+	0.395784i	0.480959	+	0.876743i	$0.340288\pi$
$744$	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
$753$	−2.50484	−	9.19160i	−0.0912814	−	0.334960i
$754$	−41.5235	+	5.50388i	−1.51220	+	0.200439i
$755$		0			0
$756$	0.0692351	+	5.42449i	0.00251806	+	0.197287i
$757$	−6.53480			−0.237511			−0.118756	−	0.992924i	$-0.537891\pi$
$757$	−6.53480			−0.237511			−0.118756	+	0.992924i	$0.537891\pi$
$758$	5.02083			0.182365
$759$	−2.01718	+	3.52845i	−0.0732191	+	0.128074i
$760$		0			0
$761$	19.3550	+	19.3550i	0.701618	+	0.701618i	0.964758	−	0.263139i	$-0.0847579\pi$
$761$	19.3550	+	19.3550i	0.701618	+	0.701618i	−0.263139	+	0.964758i	$0.584758\pi$
$762$	28.6977	−	50.1979i	1.03961	−	1.81848i
$763$	−29.9004			−1.08247
$764$	−4.09672			−0.148214
$765$		0			0
$766$		−	6.92846i		−	0.250336i
$767$	12.0523	−	1.59752i	0.435185	−	0.0576831i
$768$	−5.18322	−	19.0200i	−0.187033	−	0.686326i
$769$	1.85581	+	1.85581i	0.0669221	+	0.0669221i	0.739776	−	0.672854i	$-0.234932\pi$
$769$	1.85581	+	1.85581i	0.0669221	+	0.0669221i	−0.672854	+	0.739776i	$0.734932\pi$
$770$		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	−0.793708	−	0.608299i	$-0.791852\pi$
$773$	−5.15489	+	5.15489i	−0.185408	+	0.185408i	0.608299	+	0.793708i	$0.291852\pi$
$774$	3.81870	+	0.988473i	0.137260	+	0.0355299i
$775$		0			0
$776$		−	28.1802i		−	1.01161i
$777$	14.8419	−	4.04463i	0.532450	−	0.145100i
$778$	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
$783$	26.6309	−	27.3195i	0.951712	−	0.976320i
$784$			12.8333i			0.458331i
$785$		0			0
$786$	−13.4143	+	23.4643i	−0.478473	+	0.836942i
$787$	10.3937	−	10.3937i	0.370494	−	0.370494i	−0.497163	−	0.867657i	$-0.665625\pi$
$787$	10.3937	−	10.3937i	0.370494	−	0.370494i	0.867657	+	0.497163i	$0.165625\pi$
$788$	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
$792$	−1.49302	−	2.53591i	−0.0530521	−	0.0901096i
$793$	8.02639	−	10.4793i	0.285025	−	0.372130i
$794$		−	30.0000i		−	1.06466i
$795$		0			0
$796$	1.91248			0.0677859
$797$	28.4028			1.00608			0.503039	−	0.864264i	$-0.332215\pi$
$797$	28.4028			1.00608			0.503039	+	0.864264i	$0.332215\pi$
$798$	8.44806	+	4.82968i	0.299058	+	0.170969i
$799$	−24.3695	−	24.3695i	−0.862130	−	0.862130i
$800$		0			0
$801$	20.4294	+	5.28815i	0.721836	+	0.186847i
$802$	−10.7954			−0.381197
$803$	−6.74979			−0.238195
$804$	9.95024	+	5.68847i	0.350918	+	0.200617i
$805$		0			0
$806$	−9.71387	+	12.6825i	−0.342156	+	0.446721i
$807$	−44.6933	+	12.1796i	−1.57328	+	0.428741i
$808$	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
$818$	5.23435			0.183015
$819$	13.8213	+	17.6663i	0.482955	+	0.617311i
$820$		0			0
$821$	8.79819	−	8.79819i	0.307059	−	0.307059i	−0.536709	−	0.843768i	$-0.680333\pi$
$821$	8.79819	−	8.79819i	0.307059	−	0.307059i	0.843768	+	0.536709i	$0.180333\pi$
$822$	−6.63498	−	24.3473i	−0.231421	−	0.849209i
$823$			6.05273i			0.210985i	0.994420	+	0.105493i	$0.0336419\pi$
$823$			6.05273i			0.210985i	−0.994420	+	0.105493i	$0.966358\pi$
$824$	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	0.991580	+	0.129495i	$0.0413355\pi$
$827$	32.2394	+	32.2394i	1.12107	+	1.12107i	0.129495	+	0.991580i	$0.458664\pi$
$828$	4.34059	+	7.37254i	0.150846	+	0.256214i
$829$		−	14.4284i		−	0.501119i	−0.968101	−	0.250559i	$-0.919385\pi$
$829$		−	14.4284i		−	0.501119i	0.968101	−	0.250559i	$-0.0806145\pi$
$830$		0			0
$831$	−47.9177	+	13.0582i	−1.66225	+	0.452985i
$832$	−14.5979	−	11.1809i	−0.506091	−	0.387630i
$833$			7.50737i			0.260115i
$834$	−11.0728	−	6.33024i	−0.383420	−	0.219198i
$835$		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
$842$	−34.8119			−1.19970
$843$	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
$848$			1.22829i			0.0421798i
$849$	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	$-0.913734\pi$
$853$	−20.3214	+	20.3214i	−0.695793	+	0.695793i	0.267707	+	0.963500i	$0.413734\pi$
$854$			12.0120i			0.411043i
$855$		0			0
$856$	−6.18118	+	6.18118i	−0.211269	+	0.211269i
$857$	23.5604			0.804807			0.402404	−	0.915462i	$-0.368175\pi$
$857$	23.5604			0.804807			0.402404	+	0.915462i	$0.368175\pi$
$858$	3.78978	+	1.54703i	0.129381	+	0.0528146i
$859$	−23.0208			−0.785460			−0.392730	−	0.919654i	$-0.628469\pi$
$859$	−23.0208			−0.785460			−0.392730	+	0.919654i	$0.628469\pi$
$860$		0			0
$861$	15.1328	−	4.12390i	0.515724	−	0.140542i
$862$			57.3071i			1.95189i
$863$	0.128867	−	0.128867i	0.00438669	−	0.00438669i	−0.704910	−	0.709297i	$-0.749013\pi$
$863$	0.128867	−	0.128867i	0.00438669	−	0.00438669i	0.709297	+	0.704910i	$0.249013\pi$
$864$	−14.4718	+	0.184710i	−0.492341	+	0.00628395i
$865$		0			0
$866$	−36.4071	−	36.4071i	−1.23716	−	1.23716i
$867$	4.22043	+	15.4870i	0.143333	+	0.525967i
$868$		−	2.92358i		−	0.0992327i
$869$	−4.77770	−	4.77770i	−0.162072	−	0.162072i
$870$		0			0
$871$	46.9790	−	6.22699i	1.59182	−	0.210994i
$872$		−	34.1421i		−	1.15620i
$873$	−34.5640	−	8.94691i	−1.16981	−	0.302807i
$874$	15.3466			0.519105
$875$		0			0
$876$	−7.05170	+	12.3348i	−0.238255	+	0.416754i
$877$	−23.8978	−	23.8978i	−0.806973	−	0.806973i	0.177202	−	0.984175i	$-0.443296\pi$
$877$	−23.8978	−	23.8978i	−0.806973	−	0.806973i	−0.984175	+	0.177202i	$0.943296\pi$
$878$	37.7645	+	37.7645i	1.27449	+	1.27449i
$879$	10.0401	−	17.5620i	0.338643	−	0.592352i
$880$		0			0
$881$	−23.2229			−0.782400			−0.391200	−	0.920306i	$-0.627940\pi$
$881$	−23.2229			−0.782400			−0.391200	+	0.920306i	$0.627940\pi$
$882$	12.4061	+	3.21133i	0.417737	+	0.108131i
$883$			11.7041i			0.393876i	0.980416	+	0.196938i	$0.0630998\pi$
$883$			11.7041i			0.393876i	−0.980416	+	0.196938i	$0.936900\pi$
$884$	4.00736	+	3.06935i	0.134782	+	0.103234i
$885$		0			0
$886$	33.9059	+	33.9059i	1.13909	+	1.13909i
$887$			6.56575i			0.220456i	0.993906	+	0.110228i	$0.0351582\pi$
$887$			6.56575i			0.220456i	−0.993906	+	0.110228i	$0.964842\pi$
$888$	4.61839	+	16.9474i	0.154983	+	0.568716i
$889$	30.9380	+	30.9380i	1.03763	+	1.03763i
$890$		0			0
$891$	−3.58440	+	1.02612i	−0.120082	+	0.0343763i
$892$	−2.09613	+	2.09613i	−0.0701837	+	0.0701837i
$893$			21.2221i			0.710172i
$894$	−44.4185	+	12.1047i	−1.48558	+	0.404840i
$895$		0			0
$896$	28.2849			0.944932
$897$	32.7504	+	13.3691i	1.09351	+	0.446380i
$898$	−42.3701			−1.41391
$899$	−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
$907$			21.6880i			0.720139i	0.932926	+	0.360069i	$0.117247\pi$
$907$			21.6880i			0.720139i	−0.932926	+	0.360069i	$0.882753\pi$
$908$	−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	$0.0340446\pi$
$911$			6.44406i			0.213501i	−0.994286	+	0.106751i	$0.965955\pi$
$912$	−6.99700	+	12.2391i	−0.231694	+	0.405277i
$913$	−5.95785			−0.197176
$914$	−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	$-0.324952\pi$
$919$	31.6869			1.04525			0.522626	+	0.852562i	$0.324952\pi$
$920$		0			0
$921$	47.6677	+	27.2513i	1.57071	+	0.897959i
$922$			29.3646i			0.967072i
$923$	5.28079	+	39.8404i	0.173819	+	1.31136i
$924$	−0.722763	+	0.196963i	−0.0237772	+	0.00647961i
$925$		0			0
$926$			53.1209i			1.74566i
$927$	−11.4905	−	19.5167i	−0.377397	−	0.641014i
$928$	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
$932$			7.57380i			0.248088i
$933$	−9.85575	−	36.1660i	−0.322663	−	1.18402i
$934$	23.3985	−	23.3985i	0.765624	−	0.765624i
$935$		0			0
$936$	−20.1724	+	15.7820i	−0.659357	+	0.515850i
$937$	0.784915			0.0256421			0.0128210	−	0.999918i	$-0.495919\pi$
$937$	0.784915			0.0256421			0.0128210	+	0.999918i	$0.495919\pi$
$938$	−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	$0.615041\pi$
$941$	−39.5408	+	39.5408i	−1.28899	+	1.28899i	−0.935399	+	0.353595i	$0.884959\pi$
$942$	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	0.951270	−	0.308360i	$-0.0997802\pi$
$947$	19.7845	+	19.7845i	0.642910	+	0.642910i	−0.308360	+	0.951270i	$0.599780\pi$
$948$	−13.7223	+	3.73953i	−0.445680	+	0.121454i
$949$	7.71927	+	58.2373i	0.250578	+	1.89046i
$950$		0			0
$951$	31.8833	+	18.2274i	1.03389	+	0.591065i
$952$	13.6541			0.442532
$953$	−52.5727			−1.70300			−0.851498	−	0.524357i	$-0.824306\pi$
$953$	−52.5727			−1.70300			−0.851498	+	0.524357i	$0.824306\pi$
$954$	1.18741	+	0.307363i	0.0384440	+	0.00995123i
$955$		0			0
$956$	−2.58511	−	2.58511i	−0.0836085	−	0.0836085i
$957$	4.57367	+	2.61473i	0.147846	+	0.0845222i
$958$	−27.9336			−0.902495
$959$	19.0950			0.616611
$960$		0			0
$961$		−	23.1584i		−	0.747046i
$962$	−19.3973	−	14.8569i	−0.625393	−	0.479007i
$963$	5.61898	+	9.54390i	0.181069	+	0.307548i
$964$	−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	$-0.134093\pi$
$967$	15.6621	+	15.6621i	0.503658	+	0.503658i	−0.408915	+	0.912573i	$0.634093\pi$
$968$	−18.1304	+	18.1304i	−0.582732	+	0.582732i
$969$	−4.09319	+	7.15979i	−0.131492	+	0.230006i
$970$		0			0
$971$			18.1426i			0.582225i	0.956689	+	0.291113i	$0.0940254\pi$
$971$			18.1426i			0.582225i	−0.956689	+	0.291113i	$0.905975\pi$
$972$	−1.86957	+	7.62227i	−0.0599663	+	0.244485i
$973$	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	$-0.588289\pi$
$977$	21.5034	−	21.5034i	0.687954	−	0.687954i	0.961779	+	0.273826i	$0.0882891\pi$
$978$	−16.3674	+	4.46035i	−0.523372	+	0.142626i
$979$			2.91403i			0.0931329i
$980$		0			0
$981$	−41.8764	−	10.8397i	−1.33701	−	0.346086i
$982$	37.3147	−	37.3147i	1.19076	−	1.19076i
$983$	31.4759	+	31.4759i	1.00392	+	1.00392i	0.999992	+	0.00393200i	$0.00125160\pi$
$983$	31.4759	+	31.4759i	1.00392	+	1.00392i	0.00393200	+	0.999992i	$0.498748\pi$
$984$	4.70891	+	17.2795i	0.150115	+	0.550851i
$985$		0			0
$986$	22.8428	+	22.8428i	0.727462	+	0.727462i
$987$	−11.7042	−	42.9489i	−0.372548	−	1.36708i
$988$	−0.408432	−	3.08138i	−0.0129940	−	0.0980317i
$989$			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	$0.746177\pi$
$992$	7.79970			0.247641
$993$	−7.87889	+	13.7817i	−0.250029	+	0.437349i
$994$	−25.8604	−	25.8604i	−0.820243	−	0.820243i
$995$		0			0
$996$	−6.22434	+	10.8876i	−0.197226	+	0.344986i
$997$	44.9600			1.42390			0.711949	−	0.702231i	$-0.247813\pi$
$997$	44.9600			1.42390			0.711949	+	0.702231i	$0.247813\pi$
$998$	40.2002			1.27251
$999$	22.2528	−	0.284022i	0.704048	−	0.00898606i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11881 + 1.11881i) q^{2} +(-0.455401 - 1.67111i) q^{3} -0.503463i q^{4} +(2.37916 + 1.36015i) 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} +(-0.841342 + 0.229277i) q^{12} +(-2.19240 + 2.86241i) q^{13} -3.28107i q^{14} +4.75345 q^{16} +2.78074 q^{17} +(1.18948 - 4.59525i) q^{18} +(-1.21080 - 1.21080i) q^{19} +(3.11816 + 1.78263i) q^{21} +0.655464 q^{22} +5.66438 q^{23} +(-2.03551 + 3.56050i) q^{24} +(-0.749610 - 5.65536i) q^{26} +(3.72083 + 3.62704i) 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} +2.70931 q^{38} +(5.78182 + 2.36020i) q^{39} +(3.08783 - 3.08783i) q^{41} +(-5.48304 + 1.49420i) q^{42} +0.831012i q^{43} +(-0.147479 + 0.147479i) q^{44} +(-6.33735 + 6.33735i) q^{46} +(-8.76367 - 8.76367i) q^{47} +(-2.16473 - 7.94354i) q^{48} +2.69978i q^{49} +(-1.26635 - 4.64692i) q^{51} +(1.44112 + 1.10379i) q^{52} +0.258401i q^{53} +(-8.22086 + 0.104926i) 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} +4.43070 q^{62} +(1.55895 - 6.02260i) q^{63} +5.09987i q^{64} +(-0.298499 - 1.09535i) q^{66} +(-9.29391 - 9.29391i) q^{67} -1.40000i 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} +0.859060 q^{77} +(-9.10936 + 3.82814i) q^{78} +16.3100 q^{79} +(4.36672 - 7.86967i) q^{81} +6.90938i q^{82} +(10.1694 - 10.1694i) q^{83} +(0.897486 - 1.56988i) q^{84} +(-0.929743 - 0.929743i) q^{86} +(-12.2698 + 3.34370i) q^{87} +0.980926i q^{88} +(-4.97395 - 4.97395i) q^{89} +(-0.982449 - 7.41200i) q^{91} -2.85180i q^{92} +(-2.40722 + 4.21070i) q^{93} +19.6097 q^{94} +(4.18821 + 2.39437i) q^{96} +(8.41532 + 8.41532i) q^{97} +(-3.02053 - 3.02053i) q^{98} +(1.20314 + 0.311433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{6} + 16 q^{7} - 64 q^{16} - 4 q^{18} - 16 q^{19} - 12 q^{21} + 8 q^{24} + 24 q^{27} - 32 q^{28} + 32 q^{31} + 4 q^{33} - 16 q^{34} - 32 q^{37} - 8 q^{39} - 8 q^{42} - 40 q^{46} - 8 q^{48} - 32 q^{54}+ \cdots - 20 q^{99}+O(q^{100}) \) 40 * q + 12 * q^6 + 16 * q^7 - 64 * q^16 - 4 * q^18 - 16 * q^19 - 12 * q^21 + 8 * q^24 + 24 * q^27 - 32 * q^28 + 32 * q^31 + 4 * q^33 - 16 * q^34 - 32 * q^37 - 8 * q^39 - 8 * q^42 - 40 * q^46 - 8 * q^48 - 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 + 12 * q^78 + 40 * q^79 + 72 * q^81 + 124 * q^84 - 16 * q^87 + 8 * q^91 + 108 * q^93 - 32 * q^94 - 76 * q^96 - 24 * q^97 - 20 * q^99

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