LMFDB - Embedded newform 975.2.o.p.551.15

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)

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")

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);

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			551.15
Character	$\chi$	$=$	975.551
Dual form			975.2.o.p.476.15

$q$-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} +(-0.455401 - 1.67111i) 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} +(0.841342 - 0.229277i) q^{12} +(-2.19240 - 2.86241i) q^{13} -3.28107i q^{14} +4.75345 q^{16} -2.78074 q^{17} +(-4.59525 - 1.18948i) q^{18} +(-1.21080 + 1.21080i) q^{19} +(-1.78263 + 3.11816i) q^{21} +0.655464 q^{22} -5.66438 q^{23} +(-3.56050 - 2.03551i) 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} +(-0.622918 - 0.356117i) q^{33} +(-3.11111 - 3.11111i) q^{34} +(-0.766296 - 1.30156i) q^{36} +(3.02847 + 3.02847i) q^{37} -2.70931 q^{38} +(-3.78498 + 4.96729i) 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} +(0.104926 + 8.22086i) q^{54} -4.91025 q^{56} +(2.57478 + 1.47198i) q^{57} +(8.21465 - 8.21465i) q^{58} +(2.38433 - 2.38433i) q^{59} -3.66100 q^{61} -4.43070 q^{62} +(6.02260 + 1.55895i) 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} +(-1.78010 + 6.87696i) q^{72} +(11.5212 + 11.5212i) q^{73} +6.77656i q^{74} +(-0.609593 - 0.609593i) q^{76} -0.859060 q^{77} +(-9.79210 + 1.32278i) q^{78} +16.3100 q^{79} +(4.36672 - 7.86967i) q^{81} -6.90938i q^{82} +(-10.1694 - 10.1694i) q^{83} +(-1.56988 - 0.897486i) 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} +(4.21070 + 2.40722i) 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} - 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 $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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	$0.561030\pi$
$3$	−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
$6$	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	−0.661566	−	0.749887i	$-0.730108\pi$
$11$	0.292930	−	0.292930i	0.0883216	−	0.0883216i	0.749887	+	0.661566i	$0.230108\pi$
$12$	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	$-0.609484\pi$
$17$	−2.78074			−0.674427			−0.337214	+	0.941428i	$0.609484\pi$
$18$	−4.59525	−	1.18948i	−1.08311	−	0.280363i
$19$	−1.21080	+	1.21080i	−0.277777	+	0.277777i	−0.832221	−	0.554444i	$-0.812931\pi$
$19$	−1.21080	+	1.21080i	−0.277777	+	0.277777i	0.554444	+	0.832221i	$0.312931\pi$
$20$		0			0
$21$	−1.78263	+	3.11816i	−0.389001	+	0.680438i
$22$	0.655464			0.139745
$23$	−5.66438			−1.18111			−0.590553	−	0.806999i	$-0.701090\pi$
$23$	−5.66438			−1.18111			−0.590553	+	0.806999i	$0.701090\pi$
$24$	−3.56050	−	2.03551i	−0.726784	−	0.415496i
$25$		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	−0.862202	−	0.506565i	$-0.830915\pi$
$31$	−1.98010	+	1.98010i	−0.355636	+	0.355636i	0.506565	+	0.862202i	$0.330915\pi$
$32$	1.96952	+	1.96952i	0.348166	+	0.348166i
$33$	−0.622918	−	0.356117i	−0.108436	−	0.0619920i
$34$	−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	$0.635484\pi$
$38$	−2.70931			−0.439508
$39$	−3.78498	+	4.96729i	−0.606082	+	0.795403i
$40$		0			0
$41$	−3.08783	−	3.08783i	−0.482238	−	0.482238i	0.423608	−	0.905846i	$-0.360764\pi$
$41$	−3.08783	−	3.08783i	−0.482238	−	0.482238i	−0.905846	+	0.423608i	$0.860764\pi$
$42$	−5.48304	+	1.49420i	−0.846051	+	0.230561i
$43$		−	0.831012i		−	0.126728i	−0.997990	−	0.0633640i	$-0.979817\pi$
$43$		−	0.831012i		−	0.126728i	0.997990	−	0.0633640i	$-0.0201829\pi$
$44$	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	$-0.390688\pi$
$47$	8.76367	−	8.76367i	1.27831	−	1.27831i	0.941611	−	0.336702i	$-0.109312\pi$
$48$	−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	$0.994351\pi$
$54$	0.104926	+	8.22086i	0.0142787	+	1.11872i
$55$		0			0
$56$	−4.91025			−0.656160
$57$	2.57478	+	1.47198i	0.341038	+	0.194969i
$58$	8.21465	−	8.21465i	1.07864	−	1.07864i
$59$	2.38433	−	2.38433i	0.310414	−	0.310414i	−0.534656	−	0.845070i	$-0.679559\pi$
$59$	2.38433	−	2.38433i	0.310414	−	0.310414i	0.845070	+	0.534656i	$0.179559\pi$
$60$		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
$63$	6.02260	+	1.55895i	0.758776	+	0.196409i
$64$		−	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	$0.546696\pi$
$67$	−9.29391	+	9.29391i	−1.13543	+	1.13543i	−0.989259	+	0.146173i	$0.953304\pi$
$68$		−	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	$-0.480045\pi$
$71$	−7.88169	−	7.88169i	−0.935385	−	0.935385i	−0.998036	+	0.0626508i	$0.980045\pi$
$72$	−1.78010	+	6.87696i	−0.209787	+	0.810457i
$73$	11.5212	+	11.5212i	1.34845	+	1.34845i	0.887345	+	0.461107i	$0.152547\pi$
$73$	11.5212	+	11.5212i	1.34845	+	1.34845i	0.461107	+	0.887345i	$0.347453\pi$
$74$			6.77656i			0.787759i
$75$		0			0
$76$	−0.609593	−	0.609593i	−0.0699252	−	0.0699252i
$77$	−0.859060			−0.0978990
$78$	−9.79210	+	1.32278i	−1.10874	+	0.149775i
$79$	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	−0.992288	−	0.123950i	$-0.960444\pi$
$83$	−10.1694	−	10.1694i	−1.11624	−	1.11624i	−0.123950	−	0.992288i	$-0.539556\pi$
$84$	−1.56988	−	0.897486i	−0.171288	−	0.0979237i
$85$		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	$-0.628393\pi$
$89$	4.97395	−	4.97395i	0.527238	−	0.527238i	0.919748	+	0.392510i	$0.128393\pi$
$90$		0			0
$91$	−0.982449	+	7.41200i	−0.102989	+	0.776988i
$92$		−	2.85180i		−	0.297321i
$93$	4.21070	+	2.40722i	0.436629	+	0.249617i
$94$	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	−0.136231	−	0.990677i	$-0.543499\pi$
$97$	8.41532	−	8.41532i	0.854447	−	0.854447i	0.990677	+	0.136231i	$0.0434988\pi$
$98$	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	$0.397641\pi$
$102$	−3.78220	+	6.61581i	−0.374494	+	0.655063i
$103$		−	7.54935i		−	0.743860i	−0.928261	−	0.371930i	$-0.878696\pi$
$103$		−	7.54935i		−	0.743860i	0.928261	−	0.371930i	$-0.121304\pi$
$104$	−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	−0.0231620	−	0.999732i	$-0.507373\pi$
$109$	10.1957	−	10.1957i	0.976570	−	0.976570i	0.999732	+	0.0231620i	$0.00737335\pi$
$110$		0			0
$111$	3.68174	−	6.44008i	0.349456	−	0.611266i
$112$	−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
$117$	10.0246	+	4.06301i	0.926772	+	0.375625i
$118$	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
$123$	−3.75390	+	6.56631i	−0.338478	+	0.592064i
$124$	−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	$0.385608\pi$
$127$			21.0990i			1.87224i	−0.351686	+	0.936118i	$0.614392\pi$
$128$	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	$0.858217\pi$
$132$	0.179292	−	0.313616i	0.0156053	−	0.0272968i
$133$	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	$-0.621314\pi$
$137$	6.51118	−	6.51118i	0.556288	−	0.556288i	0.928249	+	0.371961i	$0.121314\pi$
$138$	−7.70438	+	13.4765i	−0.655840	+	1.14719i
$139$	−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
$141$	−18.6361	−	10.6541i	−1.56944	−	0.897235i
$142$		−	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	$-0.00843576\pi$
$149$	11.8788	+	11.8788i	0.973150	+	0.973150i	−0.0264986	+	0.999649i	$0.508436\pi$
$150$		0			0
$151$	4.96656	+	4.96656i	0.404173	+	0.404173i	0.879701	−	0.475528i	$-0.157743\pi$
$151$	4.96656	+	4.96656i	0.404173	+	0.404173i	−0.475528	+	0.879701i	$0.657743\pi$
$152$			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
$156$	−2.50084	−	1.90560i	−0.200228	−	0.152570i
$157$	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
$162$	13.6902	−	3.91913i	1.07560	−	0.307916i
$163$	−4.37713	−	4.37713i	−0.342843	−	0.342843i	0.514592	−	0.857435i	$-0.327943\pi$
$163$	−4.37713	−	4.37713i	−0.342843	−	0.342843i	−0.857435	+	0.514592i	$0.827943\pi$
$164$	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	$-0.680663\pi$
$167$	3.94953	−	3.94953i	0.305624	−	0.305624i	0.843209	+	0.537585i	$0.180663\pi$
$168$	2.23613	+	8.20557i	0.172521	+	0.633073i
$169$	−3.38676	+	12.5511i	−0.260520	+	0.965468i
$170$		0			0
$171$	1.28729	−	4.97309i	0.0984412	−	0.380302i
$172$	0.418383			0.0319014
$173$	−9.74943			−0.741235			−0.370618	−	0.928786i	$-0.620854\pi$
$173$	−9.74943			−0.741235			−0.370618	+	0.928786i	$0.620854\pi$
$174$	−17.4686	−	9.98663i	−1.32429	−	0.757084i
$175$		0			0
$176$	1.39243	−	1.39243i	0.104958	−	0.104958i
$177$	−5.07031	−	2.89866i	−0.381108	−	0.217876i
$178$	11.1298			0.834213
$179$	1.28470			0.0960232			0.0480116	−	0.998847i	$-0.484712\pi$
$179$	1.28470			0.0960232			0.0480116	+	0.998847i	$0.484712\pi$
$180$		0			0
$181$		−	5.39074i		−	0.400690i	−0.979725	−	0.200345i	$-0.935794\pi$
$181$		−	5.39074i		−	0.400690i	0.979725	−	0.200345i	$-0.0642064\pi$
$182$	−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
$189$	−0.137518	−	10.7744i	−0.0100030	−	0.783720i
$190$		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	0.630294	−	0.776357i	$-0.282934\pi$
$193$	−2.02917	−	2.02917i	−0.146063	−	0.146063i	−0.776357	+	0.630294i	$0.782934\pi$
$194$	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	$0.700045\pi$
$198$	−1.69452	+	0.997650i	−0.120424	+	0.0708999i
$199$		−	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
$207$	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
$213$	−9.58185	+	16.7605i	−0.656537	+	1.14841i
$214$	4.13032	−	4.13032i	0.282343	−	0.282343i
$215$		0			0
$216$	12.3028	−	0.157026i	0.837101	−	0.0106843i
$217$	5.80694			0.394201
$218$	22.8140			1.54516
$219$	14.0064	−	24.4999i	0.946465	−	1.65555i
$220$		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	−0.832631	−	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	$0.872373\pi$
$228$	−0.741088	+	1.29631i	−0.0490798	+	0.0858501i
$229$	−14.7738	−	14.7738i	−0.976279	−	0.976279i	0.0234464	−	0.999725i	$-0.492536\pi$
$229$	−14.7738	−	14.7738i	−0.976279	−	0.976279i	−0.999725	+	0.0234464i	$0.992536\pi$
$230$		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	$-0.335987\pi$
$233$	15.0434			0.985527			0.492764	+	0.870163i	$0.335987\pi$
$234$	6.66984	+	15.7613i	0.436021	+	1.03035i
$235$		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	$-0.325461\pi$
$239$	−5.13466	−	5.13466i	−0.332134	−	0.332134i	−0.853396	+	0.521263i	$0.825461\pi$
$240$		0			0
$241$	4.11251	+	4.11251i	0.264910	+	0.264910i	0.827045	−	0.562135i	$-0.190020\pi$
$241$	4.11251	+	4.11251i	0.264910	+	0.264910i	−0.562135	+	0.827045i	$0.690020\pi$
$242$	−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
$249$	−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	$0.555536\pi$
$252$	−0.784874	+	3.03215i	−0.0494424	+	0.191008i
$253$	−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	$-0.425355\pi$
$257$	7.45007			0.464723			0.232361	+	0.972630i	$0.425355\pi$
$258$	−1.97711	−	1.13030i	−0.123089	−	0.0703692i
$259$		−	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
$267$	−10.5772	−	6.04688i	−0.647312	−	0.370063i
$268$	−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	0.617588	−	0.786501i	$-0.288110\pi$
$271$	−2.78066	−	2.78066i	−0.168913	−	0.168913i	−0.786501	+	0.617588i	$0.788110\pi$
$272$	−13.2181			−0.801464
$273$	12.8337	−	1.73365i	0.776729	−	0.104925i
$274$	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	$0.330431\pi$
$277$			28.6741i			1.72286i	−0.507874	+	0.861431i	$0.669569\pi$
$278$	−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	−0.730907	−	0.682477i	$-0.760903\pi$
$281$	−0.811843	+	0.811843i	−0.0484305	+	0.0484305i	0.682477	+	0.730907i	$0.260903\pi$
$282$	−8.93030	−	32.7700i	−0.531791	−	1.95143i
$283$		−	22.9639i		−	1.36506i	−0.730857	−	0.682531i	$-0.760879\pi$
$283$		−	22.9639i		−	1.36506i	0.730857	−	0.682531i	$-0.239121\pi$
$284$	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
$288$	−8.08936	−	2.09393i	−0.476670	−	0.123386i
$289$	−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
$297$	2.15241	−	0.0274721i	0.124895	−	0.00159409i
$298$			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
$306$	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	$-0.609855\pi$
$308$		−	0.432505i		−	0.0246443i
$309$	−12.6158	+	3.43798i	−0.717688	+	0.195580i
$310$		0			0
$311$	−21.6419			−1.22720			−0.613600	−	0.789617i	$-0.710279\pi$
$311$	−21.6419			−1.22720			−0.613600	+	0.789617i	$0.710279\pi$
$312$	1.97959	+	14.6542i	0.112072	+	0.829633i
$313$	−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	$-0.0469707\pi$
$317$	14.9932	+	14.9932i	0.842104	+	0.842104i	−0.147028	+	0.989132i	$0.546971\pi$
$318$	0.614776	+	0.351462i	0.0344749	+	0.0197090i
$319$	−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
$327$	−21.6812	−	12.3950i	−1.19898	−	0.685445i
$328$	−10.3401			−0.570939
$329$	−25.7008			−1.41693
$330$		0			0
$331$	−6.48090	+	6.48090i	−0.356223	+	0.356223i	−0.862418	−	0.506196i	$-0.831051\pi$
$331$	−6.48090	+	6.48090i	−0.356223	+	0.356223i	0.506196	+	0.862418i	$0.331051\pi$
$332$	5.11992	−	5.11992i	0.280992	−	0.280992i
$333$	−12.4388	−	3.21978i	−0.681640	−	0.176443i
$334$	8.83753			0.483568
$335$		0			0
$336$	−8.47362	+	14.8220i	−0.462274	+	0.808607i
$337$		−	32.1622i		−	1.75199i	−0.482323	−	0.875993i	$-0.660207\pi$
$337$		−	32.1622i		−	1.75199i	0.482323	−	0.875993i	$-0.339793\pi$
$338$	−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	0.717432	−	0.696628i	$-0.245317\pi$
$349$	0.388646	+	0.388646i	0.0208038	+	0.0208038i	−0.696628	+	0.717432i	$0.745317\pi$
$350$		0			0
$351$	2.22453	−	18.6025i	0.118737	−	0.992926i
$352$	1.15386			0.0615011
$353$	10.9517	+	10.9517i	0.582900	+	0.582900i	0.935699	−	0.352799i	$-0.114770\pi$
$353$	10.9517	+	10.9517i	0.582900	+	0.582900i	−0.352799	+	0.935699i	$0.614770\pi$
$354$	−2.42967	−	8.91574i	−0.129135	−	0.473866i
$355$		0			0
$356$	2.50420	+	2.50420i	0.132722	+	0.132722i
$357$	4.95701	−	8.67078i	0.262353	−	0.458906i
$358$	1.43734	+	1.43734i	0.0759655	+	0.0759655i
$359$	−3.80124	+	3.80124i	−0.200622	+	0.200622i	−0.800266	−	0.599645i	$-0.795309\pi$
$359$	−3.80124	+	3.80124i	−0.200622	+	0.200622i	0.599645	+	0.800266i	$0.295309\pi$
$360$		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
$366$	−4.97950	+	8.71011i	−0.260282	+	0.455285i
$367$	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
$369$	12.6826	+	3.28288i	0.660227	+	0.170900i
$370$		0			0
$371$	0.378899	−	0.378899i	0.0196715	−	0.0196715i
$372$	−1.21195	+	2.11993i	−0.0628365	+	0.109913i
$373$	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	−0.762383	−	0.647126i	$-0.775971\pi$
$379$	−2.24383	+	2.24383i	−0.115258	+	0.115258i	0.647126	+	0.762383i	$0.275971\pi$
$380$		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	$-0.214314\pi$
$383$	3.09636	+	3.09636i	0.158217	+	0.158217i	−0.623559	+	0.781776i	$0.714314\pi$
$384$	−20.5098	−	11.7253i	−1.04664	−	0.598354i
$385$		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	$-0.337204\pi$
$389$	19.3062			0.978864			0.489432	+	0.872041i	$0.337204\pi$
$390$		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
$396$	−0.605737	−	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	−0.817232	−	0.576309i	$-0.804493\pi$
$401$	−4.82449	+	4.82449i	−0.240923	+	0.240923i	0.576309	+	0.817232i	$0.304493\pi$
$402$	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
$408$	9.90081	+	5.66021i	0.490163	+	0.280222i
$409$	−2.33925	+	2.33925i	−0.115669	+	0.115669i	−0.762572	−	0.646903i	$-0.776064\pi$
$409$	−2.33925	+	2.33925i	−0.115669	+	0.115669i	0.646903	+	0.762572i	$0.276064\pi$
$410$		0			0
$411$	−13.8461	−	7.91571i	−0.682978	−	0.390453i
$412$	3.80082			0.187253
$413$	−6.99242			−0.344074
$414$	26.0292	+	6.73768i	1.27927	+	0.331139i
$415$		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	−0.217770	−	0.976000i	$-0.569878\pi$
$421$	15.5576	−	15.5576i	0.758230	−	0.758230i	0.976000	+	0.217770i	$0.0698783\pi$
$422$	6.68071	+	6.68071i	0.325212	+	0.325212i
$423$	−9.31726	+	35.9948i	−0.453021	+	1.75013i
$424$	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
$429$	0.346333	+	2.56380i	0.0167211	+	0.123781i
$430$		0			0
$431$	−25.6108	−	25.6108i	−1.23363	−	1.23363i	−0.962560	−	0.271068i	$-0.912623\pi$
$431$	−25.6108	−	25.6108i	−1.23363	−	1.23363i	−0.271068	−	0.962560i	$-0.587377\pi$
$432$	17.6868	+	17.2410i	0.850955	+	0.829507i
$433$		−	32.5410i		−	1.56382i	−0.623392	−	0.781909i	$-0.714246\pi$
$433$		−	32.5410i		−	1.56382i	0.623392	−	0.781909i	$-0.285754\pi$
$434$	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	$0.298104\pi$
$439$			33.7542i			1.61100i	−0.592595	+	0.805501i	$0.701896\pi$
$440$		0			0
$441$	4.10920	+	6.97952i	0.195676	+	0.332358i
$442$	−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	$-0.255825\pi$
$444$	3.24234	+	1.85362i	0.153875	+	0.0879689i
$445$		0			0
$446$	−9.31616			−0.441133
$447$	14.4412	−	25.2604i	0.683044	−	1.19478i
$448$	−7.47806	+	7.47806i	−0.353305	+	0.353305i
$449$	−18.9354	+	18.9354i	−0.893616	+	0.893616i	−0.994861	−	0.101246i	$-0.967717\pi$
$449$	−18.9354	+	18.9354i	−0.893616	+	0.893616i	0.101246	+	0.994861i	$0.467717\pi$
$450$		0			0
$451$	−1.80903			−0.0851841
$452$	−8.73603			−0.410908
$453$	6.03790	−	10.5615i	0.283685	−	0.496220i
$454$		−	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	−0.347641	−	0.937628i	$-0.613017\pi$
$457$	12.6125	−	12.6125i	0.589987	−	0.589987i	0.937628	+	0.347641i	$0.113017\pi$
$458$		−	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	$-0.392258\pi$
$461$	−13.1232	−	13.1232i	−0.611207	−	0.611207i	−0.943260	+	0.332054i	$0.892258\pi$
$462$	−1.16845	+	2.04384i	−0.0543611	+	0.0950881i
$463$	23.7400	+	23.7400i	1.10329	+	1.10329i	0.994011	+	0.109278i	$0.0348540\pi$
$463$	23.7400	+	23.7400i	1.10329	+	1.10329i	0.109278	+	0.994011i	$0.465146\pi$
$464$		−	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	$-0.339224\pi$
$467$	20.9138			0.967776			0.483888	+	0.875130i	$0.339224\pi$
$468$	−2.04557	+	5.04700i	−0.0945566	+	0.233297i
$469$	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
$474$	22.1840	−	38.8042i	1.01895	−	1.78234i
$475$		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	$-0.882147\pi$
$479$	−12.4837	+	12.4837i	−0.570393	+	0.570393i	0.361845	+	0.932238i	$0.382147\pi$
$480$		0			0
$481$	2.02910	−	15.3084i	0.0925190	−	0.698001i
$482$			9.20221i			0.419149i
$483$	10.0975	−	17.6624i	0.459451	−	0.803669i
$484$	−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	−0.980178	−	0.198117i	$-0.936517\pi$
$487$	−17.2586	+	17.2586i	−0.782061	+	0.782061i	0.198117	+	0.980178i	$0.436517\pi$
$488$	−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	$0.228808\pi$
$492$	−3.30589	−	1.88995i	−0.149041	−	0.0852055i
$493$			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	−0.983757	−	0.179505i	$-0.942550\pi$
$499$	−17.9656	+	17.9656i	−0.804252	+	0.804252i	0.179505	+	0.983757i	$0.442550\pi$
$500$		0			0
$501$	−8.39872	−	4.80148i	−0.375227	−	0.214514i
$502$	−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
$507$	22.5166	−	0.0561329i	0.999997	−	0.00249295i
$508$	−10.6226			−0.471300
$509$	5.99503	+	5.99503i	0.265725	+	0.265725i	0.827375	−	0.561650i	$-0.189833\pi$
$509$	5.99503	+	5.99503i	0.265725	+	0.265725i	−0.561650	+	0.827375i	$0.689833\pi$
$510$		0			0
$511$		−	33.7876i		−	1.49467i
$512$	−6.55574	−	6.55574i	−0.289725	−	0.289725i
$513$	−8.89681	+	0.113554i	−0.392804	+	0.00501352i
$514$	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	$-0.0982874\pi$
$522$	−8.73356	+	33.7398i	−0.382257	+	1.47675i
$523$	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
$528$	−2.96101	−	1.69279i	−0.128861	−	0.0736690i
$529$	9.08521			0.395009
$530$		0			0
$531$	−2.53495	+	9.79310i	−0.110007	+	0.424984i
$532$			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	0.999011	−	0.0444563i	$-0.0141555\pi$
$541$	22.2024	+	22.2024i	0.954555	+	0.954555i	−0.0444563	+	0.999011i	$0.514156\pi$
$542$		−	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
$546$	16.2980	+	12.4188i	0.697492	+	0.531475i
$547$	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
$552$	20.1680	+	11.5299i	0.858408	+	0.490745i
$553$	−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	$-0.630598\pi$
$557$	12.2284	−	12.2284i	0.518134	−	0.518134i	0.917006	+	0.398873i	$0.130598\pi$
$558$	11.4543	−	6.74375i	0.484900	−	0.285486i
$559$	−2.37869	+	1.82191i	−0.100608	+	0.0770586i
$560$		0			0
$561$	1.73217	+	0.990268i	0.0731323	+	0.0418091i
$562$	−1.81659			−0.0766284
$563$	−13.2701			−0.559267			−0.279633	−	0.960107i	$-0.590213\pi$
$563$	−13.2701			−0.559267			−0.279633	+	0.960107i	$0.590213\pi$
$564$	5.36393	−	9.38256i	0.225862	−	0.395077i
$565$		0			0
$566$	25.6922	−	25.6922i	1.07992	−	1.07992i
$567$	−17.9425	+	5.13647i	−0.753516	+	0.215711i
$568$	−26.3932			−1.10744
$569$	1.99616			0.0836833			0.0418417	−	0.999124i	$-0.486677\pi$
$569$	1.99616			0.0836833			0.0418417	+	0.999124i	$0.486677\pi$
$570$		0			0
$571$			8.10449i			0.339162i	0.985516	+	0.169581i	$0.0542415\pi$
$571$			8.10449i			0.339162i	−0.985516	+	0.169581i	$0.945758\pi$
$572$	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	−0.996737	−	0.0807147i	$-0.974280\pi$
$577$	−22.0036	+	22.0036i	−0.916023	+	0.916023i	0.0807147	+	0.996737i	$0.474280\pi$
$578$	−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
$582$	−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	$-0.186178\pi$
$587$	6.82405	+	6.82405i	0.281659	+	0.281659i	−0.552112	+	0.833770i	$0.686178\pi$
$588$	−0.618998	−	2.27144i	−0.0255271	−	0.0936724i
$589$		−	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
$597$	−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
$603$	9.88100	−	38.1726i	0.402385	−	1.55451i
$604$	−2.50048	+	2.50048i	−0.101743	+	0.101743i
$605$		0			0
$606$	8.64055	−	15.1140i	0.350998	−	0.613965i
$607$	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
$609$	22.8945	+	13.0886i	0.927733	+	0.530378i
$610$		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	−0.958919	−	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	$-0.587637\pi$
$618$	−17.9611	−	10.2682i	−0.722501	−	0.413048i
$619$	−20.5920	−	20.5920i	−0.827663	−	0.827663i	0.159530	−	0.987193i	$-0.449002\pi$
$619$	−20.5920	−	20.5920i	−0.827663	−	0.827663i	−0.987193	+	0.159530i	$0.949002\pi$
$620$		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
$624$	−17.9917	+	23.6118i	−0.720245	+	0.945227i
$625$		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	0.754918	−	0.655819i	$-0.227677\pi$
$631$	2.48933	+	2.48933i	0.0990986	+	0.0990986i	−0.655819	+	0.754918i	$0.727677\pi$
$632$	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
$639$	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	$0.317227\pi$
$642$	−8.78318	−	5.02127i	−0.346645	−	0.198174i
$643$	−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
$647$	16.9805			0.667572			0.333786	−	0.942649i	$-0.391674\pi$
$647$	16.9805			0.667572			0.333786	+	0.942649i	$0.391674\pi$
$648$	−5.86513	−	20.4879i	−0.230404	−	0.804839i
$649$		−	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
$657$	−47.3206	−	12.2489i	−1.84615	−	0.477877i
$658$	−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	0.475587	−	0.879669i	$-0.342236\pi$
$661$	−10.3889	−	10.3889i	−0.404082	−	0.404082i	−0.879669	+	0.475587i	$0.842236\pi$
$662$	−14.5018			−0.563627
$663$	10.5250	−	13.8127i	0.408758	−	0.536441i
$664$	−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
$669$	8.85359	+	5.06152i	0.342299	+	0.195690i
$670$		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	$0.166109\pi$
$673$			25.8635i			0.996966i	−0.866899	+	0.498483i	$0.833891\pi$
$674$	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	$-0.133386\pi$
$678$	41.2829	+	23.6011i	1.58546	+	0.906394i
$679$	−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
$687$	−17.9606	+	31.4166i	−0.685240	+	1.19862i
$688$		−	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	−0.350630	−	0.936514i	$-0.614033\pi$
$691$	15.4010	−	15.4010i	0.585883	−	0.585883i	0.936514	+	0.350630i	$0.114033\pi$
$692$		−	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
$696$	−14.9454	+	26.1423i	−0.566502	+	0.990923i
$697$	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	$-0.413131\pi$
$701$	14.2724			0.539063			0.269531	+	0.962992i	$0.413131\pi$
$702$	23.3014	−	18.3238i	0.879455	−	0.691585i
$703$	−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
$708$	1.45936	−	2.55271i	0.0548463	−	0.0959368i
$709$	−1.84603	−	1.84603i	−0.0693291	−	0.0693291i	0.671592	−	0.740921i	$-0.265611\pi$
$709$	−1.84603	−	1.84603i	−0.0693291	−	0.0693291i	−0.740921	+	0.671592i	$0.765611\pi$
$710$		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
$717$	−6.24226	+	10.9189i	−0.233121	+	0.407775i
$718$	−8.50571			−0.317430
$719$	−45.7040			−1.70447			−0.852237	−	0.523156i	$-0.824754\pi$
$719$	−45.7040			−1.70447			−0.852237	+	0.523156i	$0.824754\pi$
$720$		0			0
$721$	−11.0698	+	11.0698i	−0.412261	+	0.412261i
$722$	−17.9769	+	17.9769i	−0.669032	+	0.669032i
$723$	4.99961	−	8.74530i	0.185938	−	0.325241i
$724$	2.71404			0.100866
$725$		0			0
$726$	25.7624	+	14.7282i	0.956134	+	0.546614i
$727$			5.12985i			0.190256i	0.995465	+	0.0951279i	$0.0303260\pi$
$727$			5.12985i			0.190256i	−0.995465	+	0.0951279i	$0.969674\pi$
$728$	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	−0.819318	−	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
$737$			5.44492i			0.200566i
$738$	10.5164	+	17.8623i	0.387115	+	0.657519i
$739$	−15.3715	−	15.3715i	−0.565448	−	0.565448i	0.365402	−	0.930850i	$-0.380932\pi$
$739$	−15.3715	−	15.3715i	−0.565448	−	0.565448i	−0.930850	+	0.365402i	$0.880932\pi$
$740$		0			0
$741$	−1.43154	−	10.5973i	−0.0525890	−	0.389300i
$742$	0.847831			0.0311249
$743$	10.7883	+	10.7883i	0.395784	+	0.395784i	0.876743	−	0.480959i	$-0.159712\pi$
$743$	10.7883	+	10.7883i	0.395784	+	0.395784i	−0.480959	+	0.876743i	$0.659712\pi$
$744$	11.0806	−	3.01963i	0.406236	−	0.110705i
$745$		0			0
$746$	22.7806	+	22.7806i	0.834056	+	0.834056i
$747$	41.7686	+	10.8118i	1.52823	+	0.395583i
$748$	−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	$0.330750\pi$
$751$			47.2418i			1.72388i	−0.507012	+	0.861939i	$0.669250\pi$
$752$	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
$756$	5.42449	−	0.0692351i	0.197287	−	0.00251806i
$757$	−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
$759$	3.52845	+	2.01718i	0.128074	+	0.0732191i
$760$		0			0
$761$	−19.3550	+	19.3550i	−0.701618	+	0.701618i	−0.964758	−	0.263139i	$-0.915242\pi$
$761$	−19.3550	+	19.3550i	−0.701618	+	0.701618i	0.263139	+	0.964758i	$0.415242\pi$
$762$	50.1979	+	28.6977i	1.81848	+	1.03961i
$763$	−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	−0.672854	−	0.739776i	$-0.734932\pi$
$769$	1.85581	−	1.85581i	0.0669221	−	0.0669221i	0.739776	+	0.672854i	$0.234932\pi$
$770$		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	$-0.208148\pi$
$773$	5.15489	+	5.15489i	0.185408	+	0.185408i	−0.608299	+	0.793708i	$0.708148\pi$
$774$	−0.988473	+	3.81870i	−0.0355299	+	0.137260i
$775$		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
$786$	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
$792$	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	$-0.667785\pi$
$797$	−28.4028			−1.00608			−0.503039	+	0.864264i	$0.667785\pi$
$798$	4.82968	−	8.44806i	0.170969	−	0.299058i
$799$	−24.3695	+	24.3695i	−0.862130	+	0.862130i
$800$		0			0
$801$	−5.28815	+	20.4294i	−0.186847	+	0.721836i
$802$	−10.7954			−0.381197
$803$	6.74979			0.238195
$804$	−5.68847	+	9.95024i	−0.200617	+	0.350918i
$805$		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	−0.463374	−	0.886163i	$-0.653361\pi$
$811$	12.0402	−	12.0402i	0.422789	−	0.422789i	0.886163	+	0.463374i	$0.153361\pi$
$812$	−5.42040	−	5.42040i	−0.190219	−	0.190219i
$813$	−3.38047	+	5.91310i	−0.118558	+	0.207382i
$814$	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
$819$	−8.74159	−	20.6570i	−0.305456	−	0.721813i
$820$		0			0
$821$	−8.79819	−	8.79819i	−0.307059	−	0.307059i	0.536709	−	0.843768i	$-0.319667\pi$
$821$	−8.79819	−	8.79819i	−0.307059	−	0.307059i	−0.843768	+	0.536709i	$0.819667\pi$
$822$	−6.63498	−	24.3473i	−0.231421	−	0.849209i
$823$		−	6.05273i		−	0.210985i	−0.994420	−	0.105493i	$-0.966358\pi$
$823$		−	6.05273i		−	0.210985i	0.994420	−	0.105493i	$-0.0336419\pi$
$824$	−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	$0.541336\pi$
$827$	−32.2394	+	32.2394i	−1.12107	+	1.12107i	−0.991580	+	0.129495i	$0.958664\pi$
$828$	4.34059	+	7.37254i	0.150846	+	0.256214i
$829$			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
$832$	−14.5979	+	11.1809i	−0.506091	+	0.387630i
$833$			7.50737i			0.260115i
$834$	−6.33024	+	11.0728i	−0.219198	+	0.383420i
$835$		0			0
$836$	−0.357136			−0.0123518
$837$	−14.5495	+	0.185701i	−0.502904	+	0.00641878i
$838$	12.6861	−	12.6861i	0.438233	−	0.438233i
$839$	16.5805	−	16.5805i	0.572423	−	0.572423i	−0.360382	−	0.932805i	$-0.617354\pi$
$839$	16.5805	−	16.5805i	0.572423	−	0.572423i	0.932805	+	0.360382i	$0.117354\pi$
$840$		0			0
$841$	−24.9097			−0.858956
$842$	34.8119			1.19970
$843$	1.72639	+	0.986965i	0.0594602	+	0.0339929i
$844$			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
$852$	−8.43829	−	4.82410i	−0.289091	−	0.165271i
$853$	−20.3214	−	20.3214i	−0.695793	−	0.695793i	0.267707	−	0.963500i	$-0.413734\pi$
$853$	−20.3214	−	20.3214i	−0.695793	−	0.695793i	−0.963500	+	0.267707i	$0.913734\pi$
$854$			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	$-0.631825\pi$
$857$	−23.5604			−0.804807			−0.402404	+	0.915462i	$0.631825\pi$
$858$	−2.48092	+	3.25588i	−0.0846971	+	0.111154i
$859$	−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	$-0.250987\pi$
$863$	−0.128867	−	0.128867i	−0.00438669	−	0.00438669i	−0.709297	+	0.704910i	$0.750987\pi$
$864$	0.184710	+	14.4718i	0.00628395	+	0.492341i
$865$		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
$873$	−8.94691	+	34.5640i	−0.302807	+	1.16981i
$874$	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	−0.984175	−	0.177202i	$-0.943296\pi$
$877$	−23.8978	+	23.8978i	−0.806973	+	0.806973i	0.177202	+	0.984175i	$0.443296\pi$
$878$	−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	$0.372060\pi$
$882$	−3.21133	+	12.4061i	−0.108131	+	0.417737i
$883$		−	11.7041i		−	0.393876i	−0.980416	−	0.196938i	$-0.936900\pi$
$883$		−	11.7041i		−	0.393876i	0.980416	−	0.196938i	$-0.0630998\pi$
$884$	−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
$891$	−1.02612	−	3.58440i	−0.0343763	−	0.120082i
$892$	−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
$897$	21.4396	−	28.1366i	0.715846	−	0.939454i
$898$	−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
$903$	2.59123	+	1.48138i	0.0862306	+	0.0492973i
$904$	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	$-0.882753\pi$
$907$		−	21.6880i		−	0.720139i	0.932926	−	0.360069i	$-0.117247\pi$
$908$	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	$0.965955\pi$
$912$	12.2391	+	6.99700i	0.405277	+	0.231694i
$913$	−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
$918$	−0.291772	−	22.8600i	−0.00962991	−	0.754493i
$919$	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
$921$	−27.2513	+	47.6677i	−0.897959	+	1.57071i
$922$		−	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	$-0.360618\pi$
$929$	−14.6798	−	14.6798i	−0.481629	−	0.481629i	−0.905652	+	0.424022i	$0.860618\pi$
$930$		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
$936$	23.5874	−	9.98167i	0.770977	−	0.326261i
$937$	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	0.935399	+	0.353595i	$0.115041\pi$
$941$	39.5408	+	39.5408i	1.28899	+	1.28899i	0.353595	+	0.935399i	$0.384959\pi$
$942$	21.6988	−	37.9554i	0.706985	−	1.23665i
$943$	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	$-0.900220\pi$
$947$	−19.7845	+	19.7845i	−0.642910	+	0.642910i	0.308360	+	0.951270i	$0.400220\pi$
$948$	13.7223	−	3.73953i	0.445680	−	0.121454i
$949$	7.71927	−	58.2373i	0.250578	−	1.89046i
$950$		0			0
$951$	18.2274	−	31.8833i	0.591065	−	1.03389i
$952$	13.6541			0.442532
$953$	52.5727			1.70300			0.851498	−	0.524357i	$-0.175694\pi$
$953$	52.5727			1.70300			0.851498	+	0.524357i	$0.175694\pi$
$954$	0.307363	−	1.18741i	0.00995123	−	0.0384440i
$955$		0			0
$956$	2.58511	−	2.58511i	0.0836085	−	0.0836085i
$957$	−2.61473	+	4.57367i	−0.0845222	+	0.147846i
$958$	−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	−0.408915	−	0.912573i	$-0.634093\pi$
$967$	15.6621	−	15.6621i	0.503658	−	0.503658i	0.912573	+	0.408915i	$0.134093\pi$
$968$	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	$0.0940254\pi$
$971$			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	$-0.411711\pi$
$977$	−21.5034	−	21.5034i	−0.687954	−	0.687954i	−0.961779	+	0.273826i	$0.911711\pi$
$978$	−16.3674	+	4.46035i	−0.523372	+	0.142626i
$979$		−	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
$987$	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
$993$	13.7817	+	7.87889i	0.437349	+	0.250029i
$994$	−25.8604	+	25.8604i	−0.820243	+	0.820243i
$995$		0			0
$996$	−10.8876	−	6.22434i	−0.344986	−	0.197226i
$997$	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
$999$	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.o.p.551.15		40
3.2	odd	2	inner	975.2.o.p.551.6		40
5.2	odd	4		975.2.n.q.824.6		40
5.3	odd	4		975.2.n.r.824.15		40
5.4	even	2		195.2.o.a.161.6	yes	40
13.8	odd	4	inner	975.2.o.p.476.6		40
15.2	even	4		975.2.n.q.824.15		40
15.8	even	4		975.2.n.r.824.6		40
15.14	odd	2		195.2.o.a.161.15	yes	40
39.8	even	4	inner	975.2.o.p.476.15		40
65.8	even	4		975.2.n.q.749.15		40
65.34	odd	4		195.2.o.a.86.15	yes	40
65.47	even	4		975.2.n.r.749.6		40
195.8	odd	4		975.2.n.q.749.6		40
195.47	odd	4		975.2.n.r.749.15		40
195.164	even	4		195.2.o.a.86.6	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.o.a.86.6	✓	40	195.164	even	4
195.2.o.a.86.15	yes	40	65.34	odd	4
195.2.o.a.161.6	yes	40	5.4	even	2
195.2.o.a.161.15	yes	40	15.14	odd	2
975.2.n.q.749.6		40	195.8	odd	4
975.2.n.q.749.15		40	65.8	even	4
975.2.n.q.824.6		40	5.2	odd	4
975.2.n.q.824.15		40	15.2	even	4
975.2.n.r.749.6		40	65.47	even	4
975.2.n.r.749.15		40	195.47	odd	4
975.2.n.r.824.6		40	15.8	even	4
975.2.n.r.824.15		40	5.3	odd	4
975.2.o.p.476.6		40	13.8	odd	4	inner
975.2.o.p.476.15		40	39.8	even	4	inner
975.2.o.p.551.6		40	3.2	odd	2	inner
975.2.o.p.551.15		40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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} +(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} +(0.841342 - 0.229277i) q^{12} +(-2.19240 - 2.86241i) q^{13} -3.28107i q^{14} +4.75345 q^{16} -2.78074 q^{17} +(-4.59525 - 1.18948i) q^{18} +(-1.21080 + 1.21080i) q^{19} +(-1.78263 + 3.11816i) q^{21} +0.655464 q^{22} -5.66438 q^{23} +(-3.56050 - 2.03551i) 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} +(-0.622918 - 0.356117i) q^{33} +(-3.11111 - 3.11111i) q^{34} +(-0.766296 - 1.30156i) q^{36} +(3.02847 + 3.02847i) q^{37} -2.70931 q^{38} +(-3.78498 + 4.96729i) 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} +(0.104926 + 8.22086i) q^{54} -4.91025 q^{56} +(2.57478 + 1.47198i) q^{57} +(8.21465 - 8.21465i) q^{58} +(2.38433 - 2.38433i) q^{59} -3.66100 q^{61} -4.43070 q^{62} +(6.02260 + 1.55895i) 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} +(-1.78010 + 6.87696i) q^{72} +(11.5212 + 11.5212i) q^{73} +6.77656i q^{74} +(-0.609593 - 0.609593i) q^{76} -0.859060 q^{77} +(-9.79210 + 1.32278i) q^{78} +16.3100 q^{79} +(4.36672 - 7.86967i) q^{81} -6.90938i q^{82} +(-10.1694 - 10.1694i) q^{83} +(-1.56988 - 0.897486i) 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} +(4.21070 + 2.40722i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{6} + 16 q^{7} - 64 q^{16} - 4 q^{18} - 16 q^{19} - 12 q^{21} + 8 q^{24} + 24 q^{27} - 32 q^{28} + 32 q^{31} + 4 q^{33} - 16 q^{34} - 32 q^{37} - 8 q^{39} - 8 q^{42} - 40 q^{46} - 8 q^{48} - 32 q^{54}+ \cdots - 20 q^{99}+O(q^{100}) \) 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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