LMFDB - Embedded newform 756.2.n.b.19.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(19,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 5]))

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

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

chi := DirichletCharacter("756.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.16
Character	$\chi$	$=$	756.19
Dual form			756.2.n.b.199.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.640648 + 1.26078i) q^{2} +(-1.17914 - 1.61543i) q^{4} +1.05993i q^{5} +(-0.349222 - 2.62260i) q^{7} +(2.79212 - 0.451713i) q^{8} +O(q^{10})$	\(q+(-0.640648 + 1.26078i) q^{2} +(-1.17914 - 1.61543i) q^{4} +1.05993i q^{5} +(-0.349222 - 2.62260i) q^{7} +(2.79212 - 0.451713i) q^{8} +(-1.33634 - 0.679041i) q^{10} -2.69962i q^{11} +(-2.33504 + 1.34814i) q^{13} +(3.53026 + 1.23987i) q^{14} +(-1.21926 + 3.80965i) q^{16} +(-7.01250 + 4.04867i) q^{17} +(-3.48409 + 6.03463i) q^{19} +(1.71224 - 1.24980i) q^{20} +(3.40363 + 1.72951i) q^{22} +3.26452i q^{23} +3.87655 q^{25} +(-0.203766 - 3.80766i) q^{26} +(-3.82486 + 3.65656i) q^{28} +(-0.511543 + 0.886019i) q^{29} +(-4.25476 + 7.36946i) q^{31} +(-4.02202 - 3.97786i) q^{32} +(-0.611942 - 11.4350i) q^{34} +(2.77977 - 0.370150i) q^{35} +(0.487561 - 0.844481i) q^{37} +(-5.37627 - 8.25875i) q^{38} +(0.478783 + 2.95945i) q^{40} +(3.77646 - 2.18034i) q^{41} +(-5.77718 - 3.33546i) q^{43} +(-4.36106 + 3.18323i) q^{44} +(-4.11585 - 2.09141i) q^{46} +(-2.37636 - 4.11598i) q^{47} +(-6.75609 + 1.83174i) q^{49} +(-2.48351 + 4.88749i) q^{50} +(4.93117 + 2.18247i) q^{52} +(-1.93958 - 3.35945i) q^{53} +2.86140 q^{55} +(-2.15973 - 7.16488i) q^{56} +(-0.789357 - 1.21257i) q^{58} +(-1.19560 + 2.07084i) q^{59} +(-3.20716 + 1.85166i) q^{61} +(-6.56548 - 10.0856i) q^{62} +(7.59191 - 2.52247i) q^{64} +(-1.42893 - 2.47498i) q^{65} +(-1.69381 - 0.977924i) q^{67} +(14.8091 + 6.55429i) q^{68} +(-1.31418 + 3.74182i) q^{70} +12.7952i q^{71} +(2.43771 - 1.40741i) q^{73} +(0.752350 + 1.15572i) q^{74} +(13.8568 - 1.48734i) q^{76} +(-7.08003 + 0.942767i) q^{77} +(-6.57420 + 3.79562i) q^{79} +(-4.03795 - 1.29233i) q^{80} +(0.329550 + 6.15812i) q^{82} +(1.06909 - 1.85171i) q^{83} +(-4.29130 - 7.43275i) q^{85} +(7.90642 - 5.14691i) q^{86} +(-1.21945 - 7.53767i) q^{88} +(-3.80947 - 2.19940i) q^{89} +(4.35108 + 5.65309i) q^{91} +(5.27362 - 3.84933i) q^{92} +(6.71176 - 0.359178i) q^{94} +(-6.39627 - 3.69289i) q^{95} +(-4.91146 - 2.83563i) q^{97} +(2.01885 - 9.69145i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + q^{2} + q^{4} + 16 q^{8}+O(q^{10}) $ 84 * q + q^2 + q^4 + 16 * q^8	$ 84 q + q^{2} + q^{4} + 16 q^{8} - 18 q^{10} - 18 q^{13} + 25 q^{14} - 7 q^{16} - 6 q^{17} - 24 q^{20} + 6 q^{22} - 32 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} - 9 q^{32} + 24 q^{34} + 2 q^{37} + 6 q^{41} + 13 q^{44} + 10 q^{46} + 2 q^{49} + 17 q^{50} + 2 q^{53} + 32 q^{56} + 26 q^{58} - 24 q^{61} - 8 q^{64} - 50 q^{65} - 4 q^{70} + 30 q^{73} - 46 q^{74} - 46 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} - 18 q^{86} - 2 q^{88} + 102 q^{89} - 28 q^{92} + 3 q^{94} - 6 q^{97} - 21 q^{98}+O(q^{100}) $ 84 * q + q^2 + q^4 + 16 * q^8 - 18 * q^10 - 18 * q^13 + 25 * q^14 - 7 * q^16 - 6 * q^17 - 24 * q^20 + 6 * q^22 - 32 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 - 9 * q^32 + 24 * q^34 + 2 * q^37 + 6 * q^41 + 13 * q^44 + 10 * q^46 + 2 * q^49 + 17 * q^50 + 2 * q^53 + 32 * q^56 + 26 * q^58 - 24 * q^61 - 8 * q^64 - 50 * q^65 - 4 * q^70 + 30 * q^73 - 46 * q^74 - 46 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 - 18 * q^86 - 2 * q^88 + 102 * q^89 - 28 * q^92 + 3 * q^94 - 6 * q^97 - 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.640648	+	1.26078i	−0.453007	+	0.891507i
$2$	−0.640648	+	1.26078i	−0.453007	+	0.891507i
$3$		0			0
$3$		0			0
$4$	−1.17914	−	1.61543i	−0.589570	−	0.807717i
$5$			1.05993i			0.474014i	0.971508	+	0.237007i	$0.0761665\pi$
$5$			1.05993i			0.474014i	−0.971508	+	0.237007i	$0.923834\pi$
$6$		0			0
$7$	−0.349222	−	2.62260i	−0.131994	−	0.991251i
$7$	−0.349222	−	2.62260i	−0.131994	−	0.991251i
$8$	2.79212	−	0.451713i	0.987165	−	0.159704i
$9$		0			0
$10$	−1.33634	−	0.679041i	−0.422587	−	0.214732i
$11$		−	2.69962i		−	0.813966i	−0.913436	−	0.406983i	$-0.866581\pi$
$11$		−	2.69962i		−	0.813966i	0.913436	−	0.406983i	$-0.133419\pi$
$12$		0			0
$13$	−2.33504	+	1.34814i	−0.647624	+	0.373906i	−0.787545	−	0.616257i	$-0.788648\pi$
$13$	−2.33504	+	1.34814i	−0.647624	+	0.373906i	0.139921	+	0.990163i	$0.455315\pi$
$14$	3.53026	+	1.23987i	0.943501	+	0.331370i
$15$		0			0
$16$	−1.21926	+	3.80965i	−0.304815	+	0.952412i
$17$	−7.01250	+	4.04867i	−1.70078	+	0.981947i	−0.755812	+	0.654789i	$0.772757\pi$
$17$	−7.01250	+	4.04867i	−1.70078	+	0.981947i	−0.944970	+	0.327158i	$0.893909\pi$
$18$		0			0
$19$	−3.48409	+	6.03463i	−0.799306	+	1.38444i	0.120763	+	0.992681i	$0.461466\pi$
$19$	−3.48409	+	6.03463i	−0.799306	+	1.38444i	−0.920069	+	0.391757i	$0.871867\pi$
$20$	1.71224	−	1.24980i	0.382869	−	0.279465i
$21$		0			0
$22$	3.40363	+	1.72951i	0.725656	+	0.368732i
$23$			3.26452i			0.680700i	0.940299	+	0.340350i	$0.110546\pi$
$23$			3.26452i			0.680700i	−0.940299	+	0.340350i	$0.889454\pi$
$24$		0			0
$25$	3.87655			0.775311
$26$	−0.203766	−	3.80766i	−0.0399618	−	0.746744i
$27$		0			0
$28$	−3.82486	+	3.65656i	−0.722831	+	0.691025i
$29$	−0.511543	+	0.886019i	−0.0949912	+	0.164530i	−0.909605	−	0.415474i	$-0.863616\pi$
$29$	−0.511543	+	0.886019i	−0.0949912	+	0.164530i	0.814614	+	0.580004i	$0.196949\pi$
$30$		0			0
$31$	−4.25476	+	7.36946i	−0.764178	+	1.32359i	0.176502	+	0.984300i	$0.443522\pi$
$31$	−4.25476	+	7.36946i	−0.764178	+	1.32359i	−0.940680	+	0.339295i	$0.889812\pi$
$32$	−4.02202	−	3.97786i	−0.710999	−	0.703193i
$33$		0			0
$34$	−0.611942	−	11.4350i	−0.104947	−	1.96109i
$35$	2.77977	−	0.370150i	0.469867	−	0.0625669i
$36$		0			0
$37$	0.487561	−	0.844481i	0.0801546	−	0.138832i	−0.823162	−	0.567807i	$-0.807792\pi$
$37$	0.487561	−	0.844481i	0.0801546	−	0.138832i	0.903316	+	0.428975i	$0.141125\pi$
$38$	−5.37627	−	8.25875i	−0.872146	−	1.33975i
$39$		0			0
$40$	0.478783	+	2.95945i	0.0757022	+	0.467930i
$41$	3.77646	−	2.18034i	0.589784	−	0.340512i	−0.175228	−	0.984528i	$-0.556066\pi$
$41$	3.77646	−	2.18034i	0.589784	−	0.340512i	0.765012	+	0.644016i	$0.222733\pi$
$42$		0			0
$43$	−5.77718	−	3.33546i	−0.881012	−	0.508652i	−0.0100199	−	0.999950i	$-0.503189\pi$
$43$	−5.77718	−	3.33546i	−0.881012	−	0.508652i	−0.870992	+	0.491297i	$0.836523\pi$
$44$	−4.36106	+	3.18323i	−0.657454	+	0.479890i
$45$		0			0
$46$	−4.11585	−	2.09141i	−0.606849	−	0.308362i
$47$	−2.37636	−	4.11598i	−0.346628	−	0.600377i	0.639020	−	0.769190i	$-0.279340\pi$
$47$	−2.37636	−	4.11598i	−0.346628	−	0.600377i	−0.985648	+	0.168813i	$0.946007\pi$
$48$		0			0
$49$	−6.75609	+	1.83174i	−0.965155	+	0.261678i
$50$	−2.48351	+	4.88749i	−0.351221	+	0.691195i
$51$		0			0
$52$	4.93117	+	2.18247i	0.683830	+	0.302654i
$53$	−1.93958	−	3.35945i	−0.266422	−	0.461456i	0.701513	−	0.712656i	$-0.252508\pi$
$53$	−1.93958	−	3.35945i	−0.266422	−	0.461456i	−0.967935	+	0.251200i	$0.919175\pi$
$54$		0			0
$55$	2.86140			0.385831
$56$	−2.15973	−	7.16488i	−0.288607	−	0.957448i
$57$		0			0
$58$	−0.789357	−	1.21257i	−0.103648	−	0.159218i
$59$	−1.19560	+	2.07084i	−0.155654	+	0.269601i	−0.933297	−	0.359105i	$-0.883082\pi$
$59$	−1.19560	+	2.07084i	−0.155654	+	0.269601i	0.777643	+	0.628706i	$0.216415\pi$
$60$		0			0
$61$	−3.20716	+	1.85166i	−0.410635	+	0.237080i	−0.691063	−	0.722795i	$-0.742857\pi$
$61$	−3.20716	+	1.85166i	−0.410635	+	0.237080i	0.280428	+	0.959875i	$0.409524\pi$
$62$	−6.56548	−	10.0856i	−0.833817	−	1.28087i
$63$		0			0
$64$	7.59191	−	2.52247i	0.948989	−	0.315309i
$65$	−1.42893	−	2.47498i	−0.177237	−	0.306983i
$66$		0			0
$67$	−1.69381	−	0.977924i	−0.206932	−	0.119472i	0.392953	−	0.919559i	$-0.371454\pi$
$67$	−1.69381	−	0.977924i	−0.206932	−	0.119472i	−0.599885	+	0.800086i	$0.704787\pi$
$68$	14.8091	+	6.55429i	1.79586	+	0.794824i
$69$		0			0
$70$	−1.31418	+	3.74182i	−0.157074	+	0.447233i
$71$			12.7952i			1.51851i	0.650793	+	0.759255i	$0.274436\pi$
$71$			12.7952i			1.51851i	−0.650793	+	0.759255i	$0.725564\pi$
$72$		0			0
$73$	2.43771	−	1.40741i	0.285312	−	0.164725i	−0.350514	−	0.936558i	$-0.613993\pi$
$73$	2.43771	−	1.40741i	0.285312	−	0.164725i	0.635826	+	0.771833i	$0.280660\pi$
$74$	0.752350	+	1.15572i	0.0874590	+	0.134350i
$75$		0			0
$76$	13.8568	−	1.48734i	1.58948	−	0.170610i
$77$	−7.08003	+	0.942767i	−0.806844	+	0.107438i
$78$		0			0
$79$	−6.57420	+	3.79562i	−0.739655	+	0.427040i	−0.821944	−	0.569568i	$-0.807110\pi$
$79$	−6.57420	+	3.79562i	−0.739655	+	0.427040i	0.0822886	+	0.996609i	$0.473777\pi$
$80$	−4.03795	−	1.29233i	−0.451457	−	0.144486i
$81$		0			0
$82$	0.329550	+	6.15812i	0.0363927	+	0.680050i
$83$	1.06909	−	1.85171i	0.117348	−	0.203252i	−0.801368	−	0.598171i	$-0.795894\pi$
$83$	1.06909	−	1.85171i	0.117348	−	0.203252i	0.918716	+	0.394919i	$0.129228\pi$
$84$		0			0
$85$	−4.29130	−	7.43275i	−0.465457	−	0.806195i
$86$	7.90642	−	5.14691i	0.852571	−	0.555005i
$87$		0			0
$88$	−1.21945	−	7.53767i	−0.129994	−	0.803518i
$89$	−3.80947	−	2.19940i	−0.403803	−	0.233136i	0.284321	−	0.958729i	$-0.408232\pi$
$89$	−3.80947	−	2.19940i	−0.403803	−	0.233136i	−0.688124	+	0.725593i	$0.741565\pi$
$90$		0			0
$91$	4.35108	+	5.65309i	0.456117	+	0.592605i
$92$	5.27362	−	3.84933i	0.549813	−	0.401320i
$93$		0			0
$94$	6.71176	−	0.359178i	0.692265	−	0.0370464i
$95$	−6.39627	−	3.69289i	−0.656243	−	0.378882i
$96$		0			0
$97$	−4.91146	−	2.83563i	−0.498683	−	0.287915i	0.229486	−	0.973312i	$-0.426295\pi$
$97$	−4.91146	−	2.83563i	−0.498683	−	0.287915i	−0.728170	+	0.685397i	$0.759629\pi$
$98$	2.01885	−	9.69145i	0.203934	−	0.978985i
$99$		0			0
$100$	−4.57100	−	6.26232i	−0.457100	−	0.626232i
$101$		−	8.43606i		−	0.839420i	−0.907658	−	0.419710i	$-0.862132\pi$
$101$		−	8.43606i		−	0.839420i	0.907658	−	0.419710i	$-0.137868\pi$
$102$		0			0
$103$	7.86520			0.774981			0.387490	−	0.921874i	$-0.373342\pi$
$103$	7.86520			0.774981			0.387490	+	0.921874i	$0.373342\pi$
$104$	−5.91076	+	4.81893i	−0.579597	+	0.472535i
$105$		0			0
$106$	5.47813	−	0.293161i	0.532083	−	0.0284743i
$107$	4.00395	+	2.31168i	0.387076	+	0.223479i	0.680893	−	0.732383i	$-0.261592\pi$
$107$	4.00395	+	2.31168i	0.387076	+	0.223479i	−0.293816	+	0.955862i	$0.594925\pi$
$108$		0			0
$109$	−8.80372	−	15.2485i	−0.843244	−	1.46054i	−0.887138	−	0.461505i	$-0.847310\pi$
$109$	−8.80372	−	15.2485i	−0.843244	−	1.46054i	0.0438939	−	0.999036i	$-0.486024\pi$
$110$	−1.83315	+	3.60760i	−0.174784	+	0.343971i
$111$		0			0
$112$	10.4170	+	1.86722i	0.984312	+	0.176435i
$113$	8.00328	+	13.8621i	0.752886	+	1.30404i	0.946419	+	0.322942i	$0.104672\pi$
$113$	8.00328	+	13.8621i	0.752886	+	1.30404i	−0.193533	+	0.981094i	$0.561995\pi$
$114$		0			0
$115$	−3.46016			−0.322661
$116$	2.03449	−	0.218376i	0.188897	−	0.0202757i
$117$		0			0
$118$	−1.84492	−	2.83408i	−0.169839	−	0.260898i
$119$	13.0670	+	16.9771i	1.19785	+	1.55629i
$120$		0			0
$121$	3.71206			0.337460
$122$	−0.279871	−	5.22979i	−0.0253383	−	0.473483i
$123$		0			0
$124$	16.9218	−	1.81634i	1.51963	−	0.163112i
$125$			9.40851i			0.841522i
$126$		0			0
$127$		−	14.4863i		−	1.28545i	−0.766098	−	0.642724i	$-0.777804\pi$
$127$		−	14.4863i		−	1.28545i	0.766098	−	0.642724i	$-0.222196\pi$
$128$	−1.68345	+	11.1878i	−0.148798	+	0.988868i
$129$		0			0
$130$	4.03584	−	0.215977i	0.353967	−	0.0189425i
$131$	10.8598			0.948824			0.474412	−	0.880303i	$-0.342661\pi$
$131$	10.8598			0.948824			0.474412	+	0.880303i	$0.342661\pi$
$132$		0			0
$133$	17.0432	+	7.02997i	1.47783	+	0.609575i
$134$	2.31809	−	1.50902i	0.200252	−	0.130360i
$135$		0			0
$136$	−17.7509	+	14.4720i	−1.52213	+	1.24097i
$137$	9.73636			0.831833			0.415917	−	0.909403i	$-0.363461\pi$
$137$	9.73636			0.831833			0.415917	+	0.909403i	$0.363461\pi$
$138$		0			0
$139$	−2.46836	−	4.27533i	−0.209364	−	0.362628i	0.742151	−	0.670233i	$-0.233806\pi$
$139$	−2.46836	−	4.27533i	−0.209364	−	0.362628i	−0.951514	+	0.307605i	$0.900473\pi$
$140$	−3.87569	−	4.05408i	−0.327556	−	0.342632i
$141$		0			0
$142$	−16.1319	−	8.19722i	−1.35376	−	0.687895i
$143$	3.63946	+	6.30372i	0.304347	+	0.527144i
$144$		0			0
$145$	−0.939116	−	0.542199i	−0.0779894	−	0.0450272i
$146$	0.212725	+	3.97507i	0.0176053	+	0.328979i
$147$		0			0
$148$	−1.93911	+	0.208138i	−0.159394	+	0.0171088i
$149$	−9.06574			−0.742694			−0.371347	−	0.928494i	$-0.621104\pi$
$149$	−9.06574			−0.742694			−0.371347	+	0.928494i	$0.621104\pi$
$150$		0			0
$151$			2.10052i			0.170938i	0.996341	+	0.0854689i	$0.0272388\pi$
$151$			2.10052i			0.170938i	−0.996341	+	0.0854689i	$0.972761\pi$
$152$	−7.00210	+	18.4232i	−0.567946	+	1.49432i
$153$		0			0
$154$	3.34718	−	9.53035i	0.269724	−	0.767977i
$155$	−7.81110	−	4.50974i	−0.627403	−	0.362231i
$156$		0			0
$157$	−15.9400	−	9.20296i	−1.27215	−	0.734476i	−0.296758	−	0.954953i	$-0.595905\pi$
$157$	−15.9400	−	9.20296i	−1.27215	−	0.734476i	−0.975392	+	0.220477i	$0.929239\pi$
$158$	−0.573693	−	10.7203i	−0.0456406	−	0.852860i
$159$		0			0
$160$	4.21625	−	4.26305i	0.333324	−	0.337024i
$161$	8.56154	−	1.14004i	0.674744	−	0.0898481i
$162$		0			0
$163$	13.8740	+	8.01017i	1.08670	+	0.627405i	0.932695	−	0.360665i	$-0.117450\pi$
$163$	13.8740	+	8.01017i	1.08670	+	0.627405i	0.154002	+	0.988070i	$0.450784\pi$
$164$	−7.97517	−	3.52970i	−0.622756	−	0.275623i
$165$		0			0
$166$	1.64970	+	2.53418i	0.128041	+	0.196691i
$167$	0.0138224	+	0.0239411i	0.00106961	+	0.00185262i	0.866560	−	0.499073i	$-0.166326\pi$
$167$	0.0138224	+	0.0239411i	0.00106961	+	0.00185262i	−0.865490	+	0.500926i	$0.832993\pi$
$168$		0			0
$169$	−2.86505	+	4.96241i	−0.220389	+	0.381724i
$170$	12.1203	−	0.648614i	0.929583	−	0.0497464i
$171$		0			0
$172$	1.42389	+	13.2656i	0.108571	+	1.01149i
$173$	4.11732	−	2.37714i	0.313034	−	0.180730i	−0.335249	−	0.942129i	$-0.608821\pi$
$173$	4.11732	−	2.37714i	0.313034	−	0.180730i	0.648283	+	0.761399i	$0.275487\pi$
$174$		0			0
$175$	−1.35378	−	10.1667i	−0.102336	−	0.768527i
$176$	10.2846	+	3.29153i	0.775230	+	0.248109i
$177$		0			0
$178$	5.21349	−	3.39387i	0.390768	−	0.254381i
$179$	−3.17006	+	1.83024i	−0.236941	+	0.136798i	−0.613770	−	0.789485i	$-0.710348\pi$
$179$	−3.17006	+	1.83024i	−0.236941	+	0.136798i	0.376829	+	0.926283i	$0.377015\pi$
$180$		0			0
$181$			12.2768i			0.912526i	0.889845	+	0.456263i	$0.150812\pi$
$181$			12.2768i			0.912526i	−0.889845	+	0.456263i	$0.849188\pi$
$182$	−9.91482	+	1.86412i	−0.734935	+	0.138178i
$183$		0			0
$184$	1.47463	+	9.11495i	0.108711	+	0.671963i
$185$	0.895089	+	0.516780i	0.0658082	+	0.0379944i
$186$		0			0
$187$	10.9299	+	18.9311i	0.799271	+	1.38438i
$188$	−3.84703	+	8.69216i	−0.280573	+	0.633941i
$189$		0			0
$190$	8.75368	−	5.69846i	0.635059	−	0.413409i
$191$	−15.0060	+	8.66370i	−1.08579	+	0.626883i	−0.932453	−	0.361290i	$-0.882336\pi$
$191$	−15.0060	+	8.66370i	−1.08579	+	0.626883i	−0.153340	+	0.988173i	$0.549003\pi$
$192$		0			0
$193$	1.07157	−	1.85602i	0.0771334	−	0.133599i	−0.824879	−	0.565310i	$-0.808757\pi$
$193$	1.07157	−	1.85602i	0.0771334	−	0.133599i	0.902012	+	0.431711i	$0.142090\pi$
$194$	6.72163	−	4.37564i	0.482585	−	0.314152i
$195$		0			0
$196$	10.9254	+	8.75414i	0.780388	+	0.625296i
$197$	−15.3799			−1.09577			−0.547886	−	0.836553i	$-0.684567\pi$
$197$	−15.3799			−1.09577			−0.547886	+	0.836553i	$0.684567\pi$
$198$		0			0
$199$	2.79870	+	4.84750i	0.198395	+	0.343630i	0.948008	−	0.318246i	$-0.103094\pi$
$199$	2.79870	+	4.84750i	0.198395	+	0.343630i	−0.749613	+	0.661876i	$0.769761\pi$
$200$	10.8238	−	1.75109i	0.765359	−	0.123821i
$201$		0			0
$202$	10.6360	+	5.40455i	0.748349	+	0.380263i
$203$	2.50232	+	1.03216i	0.175628	+	0.0724432i
$204$		0			0
$205$	2.31100	+	4.00277i	0.161407	+	0.279566i
$206$	−5.03882	+	9.91630i	−0.351072	+	0.690901i
$207$		0			0
$208$	−2.28891	−	10.5394i	−0.158707	−	0.730777i
$209$	16.2912	+	9.40572i	1.12689	+	0.650607i
$210$		0			0
$211$	5.47775	−	3.16258i	0.377104	−	0.217721i	−0.299454	−	0.954111i	$-0.596804\pi$
$211$	5.47775	−	3.16258i	0.377104	−	0.217721i	0.676557	+	0.736390i	$0.263471\pi$
$212$	−3.13994	+	7.09453i	−0.215652	+	0.487255i
$213$		0			0
$214$	−5.47965	+	3.56713i	−0.374581	+	0.243844i
$215$	3.53534	−	6.12339i	0.241108	−	0.417612i
$216$		0			0
$217$	20.8130	+	8.58497i	1.41288	+	0.582786i
$218$	24.8651	−	1.33065i	1.68408	−	0.0901230i
$219$		0			0
$220$	−3.37399	−	4.62241i	−0.227474	−	0.311643i
$221$	10.9163	−	18.9076i	0.734312	−	1.27186i
$222$		0			0
$223$	−6.11784	+	10.5964i	−0.409681	+	0.709588i	−0.994854	−	0.101320i	$-0.967693\pi$
$223$	−6.11784	+	10.5964i	−0.409681	+	0.709588i	0.585173	+	0.810909i	$0.301027\pi$
$224$	−9.02777	+	11.9373i	−0.603193	+	0.797595i
$225$		0			0
$226$	−22.6044	+	1.20967i	−1.50362	+	0.0804658i
$227$	9.05993			0.601328			0.300664	−	0.953730i	$-0.402792\pi$
$227$	9.05993			0.601328			0.300664	+	0.953730i	$0.402792\pi$
$228$		0			0
$229$			13.8428i			0.914756i	0.889272	+	0.457378i	$0.151211\pi$
$229$			13.8428i			0.914756i	−0.889272	+	0.457378i	$0.848789\pi$
$230$	2.21674	−	4.36250i	0.146168	−	0.287655i
$231$		0			0
$232$	−1.02807	+	2.70495i	−0.0674959	+	0.177588i
$233$	9.76646	−	16.9160i	0.639822	−	1.10820i	−0.345649	−	0.938364i	$-0.612341\pi$
$233$	9.76646	−	16.9160i	0.639822	−	1.10820i	0.985472	−	0.169841i	$-0.0543253\pi$
$234$		0			0
$235$	4.36264	−	2.51877i	0.284587	−	0.164306i
$236$	4.75510	−	0.510397i	0.309530	−	0.0332240i
$237$		0			0
$238$	−29.7758	+	5.59824i	−1.93008	+	0.362880i
$239$	7.53604	−	4.35094i	0.487466	−	0.281439i	−0.236057	−	0.971739i	$-0.575855\pi$
$239$	7.53604	−	4.35094i	0.487466	−	0.281439i	0.723523	+	0.690301i	$0.242522\pi$
$240$		0			0
$241$			14.6933i			0.946479i	0.880934	+	0.473240i	$0.156916\pi$
$241$			14.6933i			0.946479i	−0.880934	+	0.473240i	$0.843084\pi$
$242$	−2.37813	+	4.68010i	−0.152872	+	0.300848i
$243$		0			0
$244$	6.77292	+	2.99760i	0.433592	+	0.191902i
$245$	−1.94152	−	7.16097i	−0.124039	−	0.457497i
$246$		0			0
$247$		−	18.7881i		−	1.19546i
$248$	−8.55094	+	22.4984i	−0.542985	+	1.42865i
$249$		0			0
$250$	−11.8621	−	6.02754i	−0.750223	−	0.381215i
$251$	−24.9521			−1.57496			−0.787481	−	0.616339i	$-0.788615\pi$
$251$	−24.9521			−1.57496			−0.787481	+	0.616339i	$0.788615\pi$
$252$		0			0
$253$	8.81296			0.554066
$254$	18.2640	+	9.28060i	1.14599	+	0.582317i
$255$		0			0
$256$	−13.0268	−	9.28989i	−0.814176	−	0.580618i
$257$			8.35180i			0.520971i	0.965478	+	0.260485i	$0.0838826\pi$
$257$			8.35180i			0.520971i	−0.965478	+	0.260485i	$0.916117\pi$
$258$		0			0
$259$	−2.38500	−	0.983768i	−0.148197	−	0.0611283i
$260$	−2.31326	+	5.22668i	−0.143462	+	0.324145i
$261$		0			0
$262$	−6.95730	+	13.6918i	−0.429824	+	0.845884i
$263$		−	13.6382i		−	0.840970i	−0.907299	−	0.420485i	$-0.861860\pi$
$263$		−	13.6382i		−	0.840970i	0.907299	−	0.420485i	$-0.138140\pi$
$264$		0			0
$265$	3.56078	−	2.05582i	0.218737	−	0.126288i
$266$	−19.7819	+	16.9840i	−1.21291	+	1.04135i
$267$		0			0
$268$	0.417471	+	3.88935i	0.0255011	+	0.237580i
$269$	−1.96107	+	1.13222i	−0.119568	+	0.0690329i	−0.558591	−	0.829443i	$-0.688658\pi$
$269$	−1.96107	+	1.13222i	−0.119568	+	0.0690329i	0.439023	+	0.898476i	$0.355325\pi$
$270$		0			0
$271$	9.35385	−	16.2013i	0.568206	−	0.984162i	−0.428538	−	0.903524i	$-0.640971\pi$
$271$	9.35385	−	16.2013i	0.568206	−	0.984162i	0.996743	−	0.0806376i	$-0.0256956\pi$
$272$	−6.87395	−	31.6515i	−0.416795	−	1.91916i
$273$		0			0
$274$	−6.23758	+	12.2754i	−0.376826	+	0.741585i
$275$		−	10.4652i		−	0.631076i
$276$		0			0
$277$	−10.1500			−0.609854			−0.304927	−	0.952376i	$-0.598632\pi$
$277$	−10.1500			−0.609854			−0.304927	+	0.952376i	$0.598632\pi$
$278$	6.97160	−	0.373084i	0.418129	−	0.0223761i
$279$		0			0
$280$	7.59426	−	2.28916i	0.453844	−	0.136804i
$281$	−16.5394	+	28.6470i	−0.986656	+	1.70894i	−0.352321	+	0.935879i	$0.614607\pi$
$281$	−16.5394	+	28.6470i	−0.986656	+	1.70894i	−0.634335	+	0.773059i	$0.718726\pi$
$282$		0			0
$283$	1.66921	−	2.89115i	0.0992240	−	0.171861i	−0.812140	−	0.583463i	$-0.801697\pi$
$283$	1.66921	−	2.89115i	0.0992240	−	0.171861i	0.911364	+	0.411602i	$0.135031\pi$
$284$	20.6698	−	15.0873i	1.22653	−	0.895268i
$285$		0			0
$286$	−10.2792	+	0.550090i	−0.607823	+	0.0325275i
$287$	−7.03699	−	9.14273i	−0.415380	−	0.539678i
$288$		0			0
$289$	24.2835	−	42.0602i	1.42844	−	2.47413i
$290$	1.28524	−	0.836662i	0.0754717	−	0.0491305i
$291$		0			0
$292$	−5.14798	−	2.27842i	−0.301263	−	0.133335i
$293$	2.78361	−	1.60712i	0.162620	−	0.0938888i	−0.416481	−	0.909144i	$-0.636737\pi$
$293$	2.78361	−	1.60712i	0.162620	−	0.0938888i	0.579101	+	0.815256i	$0.303404\pi$
$294$		0			0
$295$	−2.19495	−	1.26725i	−0.127795	−	0.0737823i
$296$	0.979869	−	2.57813i	0.0569537	−	0.149851i
$297$		0			0
$298$	5.80795	−	11.4299i	0.336445	−	0.662117i
$299$	−4.40102	−	7.62280i	−0.254518	−	0.440838i
$300$		0			0
$301$	−6.73006	+	16.3161i	−0.387914	+	0.940442i
$302$	−2.64829	−	1.34569i	−0.152392	−	0.0774359i
$303$		0			0
$304$	−18.7418	−	20.6309i	−1.07492	−	1.18327i
$305$	−1.96262	−	3.39936i	−0.112379	−	0.194647i
$306$		0			0
$307$	−24.8754			−1.41971			−0.709857	−	0.704345i	$-0.751241\pi$
$307$	−24.8754			−1.41971			−0.709857	+	0.704345i	$0.751241\pi$
$308$	9.87132	+	10.3257i	0.562471	+	0.588359i
$309$		0			0
$310$	10.6900	−	6.95893i	0.607149	−	0.395241i
$311$	1.22570	−	2.12297i	0.0695028	−	0.120382i	−0.829180	−	0.558982i	$-0.811192\pi$
$311$	1.22570	−	2.12297i	0.0695028	−	0.120382i	0.898683	+	0.438600i	$0.144525\pi$
$312$		0			0
$313$	12.7905	−	7.38459i	0.722961	−	0.417402i	−0.0928807	−	0.995677i	$-0.529608\pi$
$313$	12.7905	−	7.38459i	0.722961	−	0.417402i	0.815841	+	0.578276i	$0.196274\pi$
$314$	21.8148	−	14.2010i	1.23108	−	0.801408i
$315$		0			0
$316$	13.8835	+	6.14463i	0.781006	+	0.345662i
$317$	−13.0215	−	22.5540i	−0.731362	−	1.26676i	−0.956301	−	0.292384i	$-0.905552\pi$
$317$	−13.0215	−	22.5540i	−0.731362	−	1.26676i	0.224939	−	0.974373i	$-0.427782\pi$
$318$		0			0
$319$	2.39191	+	1.38097i	0.133921	+	0.0773196i
$320$	2.67364	+	8.04688i	0.149461	+	0.449834i
$321$		0			0
$322$	−4.04759	+	11.5246i	−0.225563	+	0.642241i
$323$		−	56.4238i		−	3.13950i
$324$		0			0
$325$	−9.05192	+	5.22613i	−0.502110	+	0.289893i
$326$	−18.9875	+	12.3604i	−1.05162	+	0.684580i
$327$		0			0
$328$	9.55945	−	7.79365i	0.527832	−	0.430332i
$329$	−9.96469	+	7.66964i	−0.549371	+	0.422841i
$330$		0			0
$331$	16.5799	−	9.57238i	0.911311	−	0.526146i	0.0304583	−	0.999536i	$-0.490303\pi$
$331$	16.5799	−	9.57238i	0.911311	−	0.526146i	0.880853	+	0.473390i	$0.156970\pi$
$332$	−4.25193	+	0.456389i	−0.233355	+	0.0250476i
$333$		0			0
$334$	−0.0390398	+	0.00208921i	−0.00213616	+	0.000114316i
$335$	1.03653	−	1.79532i	0.0566316	−	0.0980888i
$336$		0			0
$337$	−0.842812	−	1.45979i	−0.0459109	−	0.0795200i	0.842157	−	0.539233i	$-0.181286\pi$
$337$	−0.842812	−	1.45979i	−0.0459109	−	0.0795200i	−0.888068	+	0.459713i	$0.847952\pi$
$338$	−4.42103	−	6.79137i	−0.240472	−	0.369402i
$339$		0			0
$340$	−6.94708	+	15.6966i	−0.376758	+	0.851265i
$341$	19.8947	+	11.4862i	1.07736	+	0.622014i
$342$		0			0
$343$	7.16331	+	17.0788i	0.386782	+	0.922171i
$344$	−17.6373	−	6.70338i	−0.950938	−	0.361422i
$345$		0			0
$346$	0.359296	+	6.71395i	0.0193159	+	0.360944i
$347$	−8.69149	−	5.01803i	−0.466584	−	0.269382i	0.248225	−	0.968702i	$-0.420153\pi$
$347$	−8.69149	−	5.01803i	−0.466584	−	0.269382i	−0.714808	+	0.699320i	$0.753486\pi$
$348$		0			0
$349$	14.3598	+	8.29062i	0.768661	+	0.443787i	0.832397	−	0.554180i	$-0.186968\pi$
$349$	14.3598	+	8.29062i	0.768661	+	0.443787i	−0.0637355	+	0.997967i	$0.520301\pi$
$350$	13.6852	+	4.80643i	0.731506	+	0.256915i
$351$		0			0
$352$	−10.7387	+	10.8579i	−0.572375	+	0.578729i
$353$		−	21.8233i		−	1.16154i	−0.814068	−	0.580770i	$-0.802752\pi$
$353$		−	21.8233i		−	1.16154i	0.814068	−	0.580770i	$-0.197248\pi$
$354$		0			0
$355$	−13.5620			−0.719795
$356$	0.938913	+	8.74735i	0.0497623	+	0.463609i
$357$		0			0
$358$	−0.276633	−	5.16929i	−0.0146205	−	0.273206i
$359$	16.2283	+	9.36941i	0.856497	+	0.494499i	0.862838	−	0.505481i	$-0.168685\pi$
$359$	16.2283	+	9.36941i	0.856497	+	0.494499i	−0.00634068	+	0.999980i	$0.502018\pi$
$360$		0			0
$361$	−14.7778	−	25.5959i	−0.777780	−	1.34715i
$362$	−15.4783	−	7.86510i	−0.813524	−	0.413380i
$363$		0			0
$364$	4.00167	−	13.6947i	0.209744	−	0.717795i
$365$	1.49176	+	2.58380i	0.0780820	+	0.135242i
$366$		0			0
$367$	7.84465			0.409488			0.204744	−	0.978816i	$-0.434364\pi$
$367$	7.84465			0.409488			0.204744	+	0.978816i	$0.434364\pi$
$368$	−12.4367	−	3.98030i	−0.648307	−	0.207487i
$369$		0			0
$370$	−1.22498	+	0.797437i	−0.0636838	+	0.0414568i
$371$	−8.13317	+	6.25995i	−0.422253	+	0.325000i
$372$		0			0
$373$	11.2419			0.582084			0.291042	−	0.956710i	$-0.405998\pi$
$373$	11.2419			0.582084			0.291042	+	0.956710i	$0.405998\pi$
$374$	−30.8701	+	1.65201i	−1.59626	+	0.0854233i
$375$		0			0
$376$	−8.49433	−	10.4189i	−0.438061	−	0.537313i
$377$		−	2.75852i		−	0.142071i
$378$		0			0
$379$			3.63286i			0.186608i	0.995638	+	0.0933039i	$0.0297428\pi$
$379$			3.63286i			0.186608i	−0.995638	+	0.0933039i	$0.970257\pi$
$380$	1.57648	+	14.6872i	0.0808716	+	0.753437i
$381$		0			0
$382$	−1.30949	−	24.4696i	−0.0669992	−	1.25198i
$383$	−15.3699			−0.785366			−0.392683	−	0.919674i	$-0.628453\pi$
$383$	−15.3699			−0.785366			−0.392683	+	0.919674i	$0.628453\pi$
$384$		0			0
$385$	−0.999265	−	7.50432i	−0.0509273	−	0.382455i
$386$	1.65353	+	2.54007i	0.0841624	+	0.129286i
$387$		0			0
$388$	1.21052	+	11.2778i	0.0614548	+	0.572541i
$389$	−27.1114			−1.37460			−0.687300	−	0.726373i	$-0.741204\pi$
$389$	−27.1114			−1.37460			−0.687300	+	0.726373i	$0.741204\pi$
$390$		0			0
$391$	−13.2170	−	22.8925i	−0.668411	−	1.15772i
$392$	−18.0364	+	8.16626i	−0.910976	+	0.412459i
$393$		0			0
$394$	9.85309	−	19.3907i	0.496392	−	0.976888i
$395$	−4.02308	−	6.96818i	−0.202423	−	0.350607i
$396$		0			0
$397$	−16.9366	−	9.77834i	−0.850023	−	0.490761i	0.0106358	−	0.999943i	$-0.496614\pi$
$397$	−16.9366	−	9.77834i	−0.850023	−	0.490761i	−0.860658	+	0.509183i	$0.829948\pi$
$398$	−7.90462	+	0.423014i	−0.396223	+	0.0212038i
$399$		0			0
$400$	−4.72652	+	14.7683i	−0.236326	+	0.738415i
$401$	24.9871			1.24779			0.623897	−	0.781506i	$-0.285548\pi$
$401$	24.9871			1.24779			0.623897	+	0.781506i	$0.285548\pi$
$402$		0			0
$403$		−	22.9440i		−	1.14292i
$404$	−13.6279	+	9.94730i	−0.678014	+	0.494897i
$405$		0			0
$406$	−2.90443	+	2.49363i	−0.144144	+	0.123757i
$407$	−2.27978	−	1.31623i	−0.113004	−	0.0652430i
$408$		0			0
$409$	10.7510	+	6.20707i	0.531601	+	0.306920i	0.741668	−	0.670767i	$-0.234035\pi$
$409$	10.7510	+	6.20707i	0.531601	+	0.306920i	−0.210067	+	0.977687i	$0.567368\pi$
$410$	−6.52716	+	0.349300i	−0.322354	+	0.0172507i
$411$		0			0
$412$	−9.27417	−	12.7057i	−0.456905	−	0.625966i
$413$	5.84853	+	2.41241i	0.287787	+	0.118707i
$414$		0			0
$415$	1.96268	+	1.13316i	0.0963443	+	0.0556244i
$416$	14.7543	+	3.86624i	0.723388	+	0.189558i
$417$		0			0
$418$	−22.2955	+	14.5139i	−1.09051	+	0.709897i
$419$	15.0148	+	26.0064i	0.733521	+	1.27050i	0.955369	+	0.295415i	$0.0954578\pi$
$419$	15.0148	+	26.0064i	0.733521	+	1.27050i	−0.221848	+	0.975081i	$0.571209\pi$
$420$		0			0
$421$	−17.0435	+	29.5202i	−0.830649	+	1.43873i	0.0668755	+	0.997761i	$0.478697\pi$
$421$	−17.0435	+	29.5202i	−0.830649	+	1.43873i	−0.897524	+	0.440965i	$0.854636\pi$
$422$	0.478012	+	8.93235i	0.0232693	+	0.434820i
$423$		0			0
$424$	−6.93306	−	8.50388i	−0.336699	−	0.412985i
$425$	−27.1843	+	15.6949i	−1.31863	+	0.761314i
$426$		0			0
$427$	5.97617	+	7.76447i	0.289207	+	0.375749i
$428$	−0.986846	−	9.19391i	−0.0477010	−	0.444405i
$429$		0			0
$430$	5.45535	+	8.38024i	0.263080	+	0.404131i
$431$	8.99967	−	5.19596i	0.433499	−	0.250281i	−0.267337	−	0.963603i	$-0.586144\pi$
$431$	8.99967	−	5.19596i	0.433499	−	0.250281i	0.700836	+	0.713322i	$0.252810\pi$
$432$		0			0
$433$			37.3442i			1.79465i	0.441371	+	0.897325i	$0.354492\pi$
$433$			37.3442i			1.79465i	−0.441371	+	0.897325i	$0.645508\pi$
$434$	−24.1576	+	20.7407i	−1.15960	+	0.995587i
$435$		0			0
$436$	−14.2521	+	32.2020i	−0.682553	+	1.54219i
$437$	−19.7002	−	11.3739i	−0.942387	−	0.544087i
$438$		0			0
$439$	−9.49100	−	16.4389i	−0.452981	−	0.784585i	0.545589	−	0.838053i	$-0.316306\pi$
$439$	−9.49100	−	16.4389i	−0.452981	−	0.784585i	−0.998570	+	0.0534676i	$0.982973\pi$
$440$	7.98939	−	1.29253i	0.380879	−	0.0616190i
$441$		0			0
$442$	16.8449	+	25.8762i	0.801229	+	1.23081i
$443$	14.1654	−	8.17837i	0.673017	−	0.388566i	−0.124202	−	0.992257i	$-0.539637\pi$
$443$	14.1654	−	8.17837i	0.673017	−	0.388566i	0.797219	+	0.603691i	$0.206304\pi$
$444$		0			0
$445$	2.33120	−	4.03776i	0.110510	−	0.191408i
$446$	−9.44038	−	14.5018i	−0.447015	−	0.686682i
$447$		0			0
$448$	−9.26671	−	19.0297i	−0.437811	−	0.899067i
$449$	16.7544			0.790690			0.395345	−	0.918533i	$-0.370625\pi$
$449$	16.7544			0.790690			0.395345	+	0.918533i	$0.370625\pi$
$450$		0			0
$451$	−5.88608	−	10.1950i	−0.277165	−	0.480064i
$452$	12.9563	−	29.2741i	0.609414	−	1.37694i
$453$		0			0
$454$	−5.80422	+	11.4226i	−0.272406	+	0.536089i
$455$	−5.99187	+	4.61183i	−0.280903	+	0.216206i
$456$		0			0
$457$	−2.18675	−	3.78755i	−0.102292	−	0.177174i	0.810337	−	0.585964i	$-0.199284\pi$
$457$	−2.18675	−	3.78755i	−0.102292	−	0.177174i	−0.912628	+	0.408790i	$0.865951\pi$
$458$	−17.4527	−	8.86834i	−0.815511	−	0.414390i
$459$		0			0
$460$	4.08001	+	5.58966i	0.190231	+	0.260619i
$461$	26.4257	+	15.2569i	1.23077	+	0.710584i	0.967190	−	0.254054i	$-0.0817642\pi$
$461$	26.4257	+	15.2569i	1.23077	+	0.710584i	0.263578	+	0.964638i	$0.415098\pi$
$462$		0			0
$463$	20.1336	−	11.6242i	0.935689	−	0.540221i	0.0470829	−	0.998891i	$-0.485007\pi$
$463$	20.1336	−	11.6242i	0.935689	−	0.540221i	0.888606	+	0.458670i	$0.151674\pi$
$464$	−2.75172	−	3.02909i	−0.127745	−	0.140622i
$465$		0			0
$466$	15.0705	+	23.1506i	0.698128	+	1.07243i
$467$	−9.93664	+	17.2108i	−0.459813	+	0.796419i	−0.998951	−	0.0457981i	$-0.985417\pi$
$467$	−9.93664	+	17.2108i	−0.459813	+	0.796419i	0.539138	+	0.842218i	$0.318750\pi$
$468$		0			0
$469$	−1.97319	+	4.78371i	−0.0911133	+	0.220891i
$470$	0.380703	+	7.11398i	0.0175605	+	0.328143i
$471$		0			0
$472$	−2.40284	+	6.32212i	−0.110600	+	0.290999i
$473$	−9.00446	+	15.5962i	−0.414025	+	0.717113i
$474$		0			0
$475$	−13.5063	+	23.3936i	−0.619710	+	1.07337i
$476$	12.0176	−	41.1272i	0.550827	−	1.88506i
$477$		0			0
$478$	0.657628	+	12.2887i	0.0300792	+	0.562073i
$479$	−4.67514			−0.213613			−0.106806	−	0.994280i	$-0.534062\pi$
$479$	−4.67514			−0.213613			−0.106806	+	0.994280i	$0.534062\pi$
$480$		0			0
$481$			2.62920i			0.119881i
$482$	−18.5251	−	9.41324i	−0.843793	−	0.428761i
$483$		0			0
$484$	−4.37704	−	5.99659i	−0.198956	−	0.272572i
$485$	3.00557	−	5.20580i	0.136476	−	0.236383i
$486$		0			0
$487$	−26.7465	+	15.4421i	−1.21200	+	0.699750i	−0.963195	−	0.268804i	$-0.913372\pi$
$487$	−26.7465	+	15.4421i	−1.21200	+	0.699750i	−0.248807	+	0.968553i	$0.580038\pi$
$488$	−8.11838	+	6.61877i	−0.367502	+	0.299618i
$489$		0			0
$490$	10.2722	+	2.13983i	0.464053	+	0.0966678i
$491$	−17.7038	+	10.2213i	−0.798962	+	0.461281i	−0.843108	−	0.537744i	$-0.819277\pi$
$491$	−17.7038	+	10.2213i	−0.798962	+	0.461281i	0.0441461	+	0.999025i	$0.485943\pi$
$492$		0			0
$493$		−	8.28428i		−	0.373105i
$494$	23.6877	+	12.0366i	1.06576	+	0.541552i
$495$		0			0
$496$	−22.8874	−	25.1944i	−1.02767	−	1.13126i
$497$	33.5567	−	4.46837i	1.50522	−	0.200434i
$498$		0			0
$499$			15.4758i			0.692790i	0.938089	+	0.346395i	$0.112594\pi$
$499$			15.4758i			0.692790i	−0.938089	+	0.346395i	$0.887406\pi$
$500$	15.1988	−	11.0939i	0.679712	−	0.496136i
$501$		0			0
$502$	15.9855	−	31.4591i	0.713468	−	1.40409i
$503$	2.70437			0.120582			0.0602909	−	0.998181i	$-0.480797\pi$
$503$	2.70437			0.120582			0.0602909	+	0.998181i	$0.480797\pi$
$504$		0			0
$505$	8.94162			0.397897
$506$	−5.64601	+	11.1112i	−0.250996	+	0.493954i
$507$		0			0
$508$	−23.4016	+	17.0813i	−1.03828	+	0.757862i
$509$		−	35.2806i		−	1.56379i	−0.623413	−	0.781893i	$-0.714254\pi$
$509$		−	35.2806i		−	1.56379i	0.623413	−	0.781893i	$-0.285746\pi$
$510$		0			0
$511$	−4.54238	−	5.90164i	−0.200943	−	0.261073i
$512$	20.0581	−	10.4724i	0.886452	−	0.462820i
$513$		0			0
$514$	−10.5298	−	5.35056i	−0.464449	−	0.236003i
$515$			8.33654i			0.367352i
$516$		0			0
$517$	−11.1116	+	6.41526i	−0.488686	+	0.282143i
$518$	2.76826	−	2.37672i	0.121631	−	0.104427i
$519$		0			0
$520$	−5.10772	−	6.26498i	−0.223988	−	0.274737i
$521$	23.4381	−	13.5320i	1.02684	−	0.592847i	0.110763	−	0.993847i	$-0.464671\pi$
$521$	23.4381	−	13.5320i	1.02684	−	0.592847i	0.916078	+	0.401000i	$0.131337\pi$
$522$		0			0
$523$	16.0435	−	27.7882i	0.701534	−	1.21509i	−0.266394	−	0.963864i	$-0.585832\pi$
$523$	16.0435	−	27.7882i	0.701534	−	1.21509i	0.967928	−	0.251228i	$-0.0808344\pi$
$524$	−12.8052	−	17.5433i	−0.559398	−	0.766382i
$525$		0			0
$526$	17.1948	+	8.73731i	0.749731	+	0.380965i
$527$		−	68.9045i		−	3.00153i
$528$		0			0
$529$	12.3429			0.536648
$530$	0.310729	+	5.80642i	0.0134972	+	0.252215i
$531$		0			0
$532$	−8.73981	−	35.8214i	−0.378919	−	1.55306i
$533$	−5.87879	+	10.1824i	−0.254639	+	0.441047i
$534$		0			0
$535$	−2.45022	+	4.24390i	−0.105932	+	0.183480i
$536$	−5.17108	−	1.96537i	−0.223357	−	0.0848909i
$537$		0			0
$538$	−0.171131	−	3.19783i	−0.00737800	−	0.137868i
$539$	4.94501	+	18.2389i	0.212996	+	0.785603i
$540$		0			0
$541$	−20.6581	+	35.7809i	−0.888161	+	1.53834i	−0.0461139	+	0.998936i	$0.514684\pi$
$541$	−20.6581	+	35.7809i	−0.888161	+	1.53834i	−0.842047	+	0.539404i	$0.818650\pi$
$542$	14.4338	+	22.1725i	0.619986	+	0.952391i
$543$		0			0
$544$	44.3094	+	11.6109i	1.89975	+	0.497815i
$545$	16.1623	−	9.33131i	0.692317	−	0.399710i
$546$		0			0
$547$	−2.51810	−	1.45383i	−0.107666	−	0.0621612i	0.445200	−	0.895431i	$-0.353133\pi$
$547$	−2.51810	−	1.45383i	−0.107666	−	0.0621612i	−0.552866	+	0.833270i	$0.686466\pi$
$548$	−11.4805	−	15.7285i	−0.490424	−	0.671886i
$549$		0			0
$550$	13.1943	+	6.70452i	0.562609	+	0.285882i
$551$	−3.56453	−	6.17395i	−0.151854	−	0.263019i
$552$		0			0
$553$	12.2503	+	15.9160i	0.520934	+	0.676817i
$554$	6.50257	−	12.7969i	0.276268	−	0.543689i
$555$		0			0
$556$	−3.99597	+	9.02868i	−0.169467	+	0.382901i
$557$	3.49428	+	6.05228i	0.148058	+	0.256443i	0.930510	−	0.366268i	$-0.119365\pi$
$557$	3.49428	+	6.05228i	0.148058	+	0.256443i	−0.782452	+	0.622711i	$0.786031\pi$
$558$		0			0
$559$	17.9866			0.760753
$560$	−1.97911	+	11.0412i	−0.0836328	+	0.466578i
$561$		0			0
$562$	−25.5217	−	39.2052i	−1.07657	−	1.65377i
$563$	−11.6828	+	20.2352i	−0.492372	+	0.852813i	−0.999961	−	0.00878586i	$-0.997203\pi$
$563$	−11.6828	+	20.2352i	−0.492372	+	0.852813i	0.507589	+	0.861599i	$0.330537\pi$
$564$		0			0
$565$	−14.6928	+	8.48290i	−0.618132	+	0.356878i
$566$	2.57573	+	3.95671i	0.108266	+	0.166313i
$567$		0			0
$568$	5.77975	+	35.7258i	0.242513	+	1.49902i
$569$	17.4511	+	30.2262i	0.731589	+	1.26715i	0.956204	+	0.292702i	$0.0945543\pi$
$569$	17.4511	+	30.2262i	0.731589	+	1.26715i	−0.224615	+	0.974448i	$0.572112\pi$
$570$		0			0
$571$	27.1650	+	15.6837i	1.13682	+	0.656343i	0.945641	−	0.325213i	$-0.105436\pi$
$571$	27.1650	+	15.6837i	1.13682	+	0.656343i	0.191178	+	0.981555i	$0.438769\pi$
$572$	5.89182	−	13.3123i	0.246350	−	0.556614i
$573$		0			0
$574$	16.0352	−	3.01483i	0.669297	−	0.125837i
$575$			12.6551i			0.527754i
$576$		0			0
$577$	22.7304	−	13.1234i	0.946278	−	0.546334i	0.0543554	−	0.998522i	$-0.482690\pi$
$577$	22.7304	−	13.1234i	0.946278	−	0.546334i	0.891923	+	0.452188i	$0.149356\pi$
$578$	37.4715	+	57.5619i	1.55861	+	2.39426i
$579$		0			0
$580$	0.231462	+	2.15641i	0.00961095	+	0.0895400i
$581$	−5.22966	−	2.15713i	−0.216963	−	0.0894929i
$582$		0			0
$583$	−9.06924	+	5.23613i	−0.375610	+	0.216858i
$584$	6.17064	−	5.03081i	0.255343	−	0.208176i
$585$		0			0
$586$	0.242910	+	4.53912i	0.0100345	+	0.187509i
$587$	−5.56925	+	9.64623i	−0.229868	+	0.398143i	−0.957769	−	0.287540i	$-0.907163\pi$
$587$	−5.56925	+	9.64623i	−0.229868	+	0.398143i	0.727901	+	0.685682i	$0.240496\pi$
$588$		0			0
$589$	−29.6480	−	51.3518i	−1.22162	−	2.11591i
$590$	3.00392	−	1.95548i	0.123669	−	0.0805060i
$591$		0			0
$592$	2.62271	+	2.88708i	0.107793	+	0.118658i
$593$	−2.12516	−	1.22696i	−0.0872700	−	0.0503854i	0.455730	−	0.890118i	$-0.349378\pi$
$593$	−2.12516	−	1.22696i	−0.0872700	−	0.0503854i	−0.543000	+	0.839733i	$0.682712\pi$
$594$		0			0
$595$	−17.9945	+	13.8500i	−0.737703	+	0.567797i
$596$	10.6898	+	14.6451i	0.437870	+	0.599887i
$597$		0			0
$598$	12.4302	−	0.665199i	0.508308	−	0.0272020i
$599$	31.8737	+	18.4023i	1.30232	+	0.751896i	0.980802	−	0.195006i	$-0.0624727\pi$
$599$	31.8737	+	18.4023i	1.30232	+	0.751896i	0.321521	+	0.946903i	$0.395806\pi$
$600$		0			0
$601$	−21.1705	−	12.2228i	−0.863561	−	0.498577i	0.00164203	−	0.999999i	$-0.499477\pi$
$601$	−21.1705	−	12.2228i	−0.863561	−	0.498577i	−0.865203	+	0.501421i	$0.832811\pi$
$602$	−16.2594	−	18.9380i	−0.662683	−	0.771855i
$603$		0			0
$604$	3.39325	−	2.47680i	0.138069	−	0.100780i
$605$			3.93452i			0.159961i
$606$		0			0
$607$	−12.3053			−0.499459			−0.249729	−	0.968316i	$-0.580342\pi$
$607$	−12.3053			−0.499459			−0.249729	+	0.968316i	$0.580342\pi$
$608$	38.0180	−	10.4121i	1.54183	−	0.422268i
$609$		0			0
$610$	5.54320	−	0.296643i	0.224438	−	0.0120107i
$611$	11.0978	+	6.40732i	0.448969	+	0.259212i
$612$		0			0
$613$	2.07499	+	3.59399i	0.0838080	+	0.145160i	0.904883	−	0.425661i	$-0.139958\pi$
$613$	2.07499	+	3.59399i	0.0838080	+	0.145160i	−0.821075	+	0.570821i	$0.806625\pi$
$614$	15.9364	−	31.3625i	0.643140	−	1.26569i
$615$		0			0
$616$	−19.3424	+	5.83046i	−0.779329	+	0.234916i
$617$	−2.21526	−	3.83693i	−0.0891828	−	0.154469i	0.817983	−	0.575242i	$-0.195092\pi$
$617$	−2.21526	−	3.83693i	−0.0891828	−	0.154469i	−0.907166	+	0.420773i	$0.861759\pi$
$618$		0			0
$619$	39.4764			1.58669			0.793345	−	0.608772i	$-0.208338\pi$
$619$	39.4764			1.58669			0.793345	+	0.608772i	$0.208338\pi$
$620$	1.92519	+	17.9359i	0.0773174	+	0.720325i
$621$		0			0
$622$	1.89136	+	2.90541i	0.0758366	+	0.116496i
$623$	−4.43780	+	10.7588i	−0.177797	+	0.431042i
$624$		0			0
$625$	9.41043			0.376417
$626$	1.11615	+	20.8569i	0.0446105	+	0.833610i
$627$		0			0
$628$	3.92870	+	36.6016i	0.156772	+	1.46056i
$629$			7.89590i			0.314830i
$630$		0			0
$631$		−	6.09451i		−	0.242618i	−0.992615	−	0.121309i	$-0.961291\pi$
$631$		−	6.09451i		−	0.242618i	0.992615	−	0.121309i	$-0.0387093\pi$
$632$	−16.6415	+	13.5675i	−0.661962	+	0.539685i
$633$		0			0
$634$	36.7778	−	1.96816i	1.46063	−	0.0781655i
$635$	15.3544			0.609321
$636$		0			0
$637$	13.3063	−	13.3853i	0.527215	−	0.530346i
$638$	−3.27348	+	2.13096i	−0.129598	+	0.0843656i
$639$		0			0
$640$	−11.8582	−	1.78434i	−0.468737	−	0.0705323i
$641$	−14.3839			−0.568129			−0.284064	−	0.958805i	$-0.591683\pi$
$641$	−14.3839			−0.568129			−0.284064	+	0.958805i	$0.591683\pi$
$642$		0			0
$643$	−2.34451	−	4.06080i	−0.0924583	−	0.160142i	0.816087	−	0.577930i	$-0.196139\pi$
$643$	−2.34451	−	4.06080i	−0.0924583	−	0.160142i	−0.908545	+	0.417787i	$0.862806\pi$
$644$	−11.9369	−	12.4863i	−0.470381	−	0.492031i
$645$		0			0
$646$	71.1381	+	36.1478i	2.79889	+	1.42222i
$647$	−12.5308	−	21.7040i	−0.492638	−	0.853274i	0.507326	−	0.861754i	$-0.330634\pi$
$647$	−12.5308	−	21.7040i	−0.492638	−	0.853274i	−0.999964	+	0.00848030i	$0.997301\pi$
$648$		0			0
$649$	5.59049	+	3.22767i	0.219446	+	0.126697i
$650$	−0.789910	−	14.7606i	−0.0309828	−	0.578958i
$651$		0			0
$652$	−3.41951	−	31.8577i	−0.133918	−	1.24764i
$653$	−48.2429			−1.88789			−0.943946	−	0.330100i	$-0.892918\pi$
$653$	−48.2429			−1.88789			−0.943946	+	0.330100i	$0.892918\pi$
$654$		0			0
$655$			11.5106i			0.449756i
$656$	3.70184	+	17.0454i	0.144533	+	0.665510i
$657$		0			0
$658$	−3.28588	−	17.4768i	−0.128097	−	0.681318i
$659$	20.2388	+	11.6849i	0.788392	+	0.455179i	0.839396	−	0.543520i	$-0.182909\pi$
$659$	20.2388	+	11.6849i	0.788392	+	0.455179i	−0.0510039	+	0.998698i	$0.516242\pi$
$660$		0			0
$661$	2.44769	+	1.41317i	0.0952039	+	0.0549660i	0.546846	−	0.837233i	$-0.315828\pi$
$661$	2.44769	+	1.41317i	0.0952039	+	0.0549660i	−0.451642	+	0.892199i	$0.649162\pi$
$662$	1.44683	+	27.0361i	0.0562327	+	1.05079i
$663$		0			0
$664$	2.14858	−	5.65313i	0.0833812	−	0.219384i
$665$	−7.45126	+	18.0645i	−0.288947	+	0.700512i
$666$		0			0
$667$	−2.89243	−	1.66994i	−0.111995	−	0.0646605i
$668$	0.0223767	−	0.0505591i	0.000865782	−	0.00195619i
$669$		0			0
$670$	1.59946	+	2.45700i	0.0617924	+	0.0949224i
$671$	4.99876	+	8.65811i	0.192975	+	0.334243i
$672$		0			0
$673$	3.06361	−	5.30633i	0.118094	−	0.204544i	−0.800919	−	0.598773i	$-0.795655\pi$
$673$	3.06361	−	5.30633i	0.118094	−	0.204544i	0.919012	+	0.394229i	$0.128988\pi$
$674$	2.38043	−	0.127388i	0.0916906	−	0.00490680i
$675$		0			0
$676$	11.3948	−	1.22308i	0.438260	−	0.0470415i
$677$	−3.19573	+	1.84506i	−0.122822	+	0.0709112i	−0.560152	−	0.828390i	$-0.689257\pi$
$677$	−3.19573	+	1.84506i	−0.122822	+	0.0709112i	0.437330	+	0.899301i	$0.355924\pi$
$678$		0			0
$679$	−5.72155	+	13.8711i	−0.219573	+	0.532323i
$680$	−15.3393	−	18.8147i	−0.588235	−	0.721511i
$681$		0			0
$682$	−27.2272	+	17.7243i	−1.04258	+	0.678698i
$683$	−2.48721	+	1.43599i	−0.0951704	+	0.0549466i	−0.546830	−	0.837244i	$-0.684166\pi$
$683$	−2.48721	+	1.43599i	−0.0951704	+	0.0549466i	0.451659	+	0.892190i	$0.350832\pi$
$684$		0			0
$685$			10.3198i			0.394301i
$686$	−26.1219	−	1.91016i	−0.997337	−	0.0729304i
$687$		0			0
$688$	19.7508	−	17.9422i	0.752992	−	0.684041i
$689$	9.05801	+	5.22964i	0.345083	+	0.199234i
$690$		0			0
$691$	−12.6905	−	21.9807i	−0.482771	−	0.836184i	0.517033	−	0.855965i	$-0.327036\pi$
$691$	−12.6905	−	21.9807i	−0.482771	−	0.836184i	−0.999804	+	0.0197814i	$0.993703\pi$
$692$	−8.69501	−	3.84829i	−0.330535	−	0.146290i
$693$		0			0
$694$	11.8948	−	7.74327i	0.451522	−	0.293931i
$695$	4.53154	−	2.61628i	0.171891	−	0.0992413i
$696$		0			0
$697$	−17.6549	+	30.5793i	−0.668729	+	1.15827i
$698$	−19.6522	+	12.7932i	−0.743848	+	0.484229i
$699$		0			0
$700$	−14.8273	+	14.1749i	−0.560418	+	0.535759i
$701$	−23.9938			−0.906233			−0.453117	−	0.891451i	$-0.649688\pi$
$701$	−23.9938			−0.906233			−0.453117	+	0.891451i	$0.649688\pi$
$702$		0			0
$703$	3.39742	+	5.88450i	0.128136	+	0.221938i
$704$	−6.80972	−	20.4953i	−0.256651	−	0.772444i
$705$		0			0
$706$	27.5145	+	13.9811i	1.03552	+	0.526185i
$707$	−22.1244	+	2.94606i	−0.832075	+	0.110798i
$708$		0			0
$709$	−17.5122	−	30.3320i	−0.657684	−	1.13914i	−0.981214	−	0.192924i	$-0.938203\pi$
$709$	−17.5122	−	30.3320i	−0.657684	−	1.13914i	0.323530	−	0.946218i	$-0.395130\pi$
$710$	8.68846	−	17.0987i	0.326072	−	0.641703i
$711$		0			0
$712$	−11.6300	−	4.42021i	−0.435853	−	0.165654i
$713$	−24.0578	−	13.8898i	−0.900971	−	0.520176i
$714$		0			0
$715$	−6.68149	+	3.85756i	−0.249874	+	0.144265i
$716$	6.69457	+	2.96292i	0.250188	+	0.110730i
$717$		0			0
$718$	−22.2094	+	14.4578i	−0.828848	+	0.539562i
$719$	−19.7380	+	34.1872i	−0.736102	+	1.27497i	0.218136	+	0.975918i	$0.430002\pi$
$719$	−19.7380	+	34.1872i	−0.736102	+	1.27497i	−0.954238	+	0.299048i	$0.903331\pi$
$720$		0			0
$721$	−2.74670	−	20.6273i	−0.102293	−	0.768200i
$722$	41.7383	−	2.23361i	1.55334	−	0.0831265i
$723$		0			0
$724$	19.8323	−	14.4760i	0.737063	−	0.537998i
$725$	−1.98302	+	3.43470i	−0.0736477	+	0.127562i
$726$		0			0
$727$	9.31052	−	16.1263i	0.345308	−	0.598091i	−0.640102	−	0.768290i	$-0.721108\pi$
$727$	9.31052	−	16.1263i	0.345308	−	0.598091i	0.985410	+	0.170199i	$0.0544411\pi$
$728$	14.7023	+	13.8187i	0.544904	+	0.512155i
$729$		0			0
$730$	−4.21329	+	0.225473i	−0.155941	+	0.00834514i
$731$	54.0166			1.99788
$732$		0			0
$733$		−	44.3030i		−	1.63637i	−0.574956	−	0.818184i	$-0.694981\pi$
$733$		−	44.3030i		−	1.63637i	0.574956	−	0.818184i	$-0.305019\pi$
$734$	−5.02566	+	9.89039i	−0.185501	+	0.365061i
$735$		0			0
$736$	12.9858	−	13.1300i	0.478664	−	0.483977i
$737$	−2.64002	+	4.57265i	−0.0972464	+	0.168436i
$738$		0			0
$739$	−7.61365	+	4.39574i	−0.280072	+	0.161700i	−0.633456	−	0.773779i	$-0.718364\pi$
$739$	−7.61365	+	4.39574i	−0.280072	+	0.161700i	0.353384	+	0.935478i	$0.385031\pi$
$740$	−0.220611	−	2.05531i	−0.00810982	−	0.0755548i
$741$		0			0
$742$	−2.68193	−	14.2646i	−0.0984567	−	0.523669i
$743$	−18.7141	+	10.8046i	−0.686553	+	0.396382i	−0.802319	−	0.596895i	$-0.796401\pi$
$743$	−18.7141	+	10.8046i	−0.686553	+	0.396382i	0.115766	+	0.993276i	$0.463068\pi$
$744$		0			0
$745$		−	9.60903i		−	0.352047i
$746$	−7.20211	+	14.1736i	−0.263688	+	0.518932i
$747$		0			0
$748$	17.6941	−	39.9789i	0.646960	−	1.46177i
$749$	4.66435	−	11.3081i	0.170432	−	0.413187i
$750$		0			0
$751$			49.4586i			1.80477i	0.430930	+	0.902385i	$0.358186\pi$
$751$			49.4586i			1.80477i	−0.430930	+	0.902385i	$0.641814\pi$
$752$	18.5778	−	4.03465i	0.677463	−	0.147129i
$753$		0			0
$754$	3.47789	+	1.76724i	0.126657	+	0.0643592i
$755$	−2.22640			−0.0810269
$756$		0			0
$757$	−48.1032			−1.74834			−0.874170	−	0.485620i	$-0.838594\pi$
$757$	−48.1032			−1.74834			−0.874170	+	0.485620i	$0.838594\pi$
$758$	−4.58025	−	2.32739i	−0.166362	−	0.0845345i
$759$		0			0
$760$	−19.5273	−	7.42173i	−0.708330	−	0.269214i
$761$			3.23146i			0.117140i	0.998283	+	0.0585702i	$0.0186541\pi$
$761$			3.23146i			0.117140i	−0.998283	+	0.0585702i	$0.981346\pi$
$762$		0			0
$763$	−36.9163	+	28.4138i	−1.33646	+	1.02865i
$764$	31.6898	+	14.0254i	1.14650	+	0.507423i
$765$		0			0
$766$	9.84670	−	19.3781i	0.355776	−	0.700159i
$767$		−	6.44735i		−	0.232800i
$768$		0			0
$769$	34.6628	−	20.0126i	1.24997	−	0.721672i	0.278869	−	0.960329i	$-0.410040\pi$
$769$	34.6628	−	20.0126i	1.24997	−	0.721672i	0.971104	+	0.238657i	$0.0767071\pi$
$770$	10.1015	+	3.54777i	0.364032	+	0.127853i
$771$		0			0
$772$	−4.26180	+	0.457449i	−0.153386	+	0.0164639i
$773$	−27.1598	+	15.6807i	−0.976869	+	0.563995i	−0.901323	−	0.433147i	$-0.857403\pi$
$773$	−27.1598	+	15.6807i	−0.976869	+	0.563995i	−0.0755453	+	0.997142i	$0.524070\pi$
$774$		0			0
$775$	−16.4938	+	28.5681i	−0.592475	+	1.02620i
$776$	−14.9943	−	5.69887i	−0.538264	−	0.204578i
$777$		0			0
$778$	17.3688	−	34.1815i	0.622703	−	1.22547i
$779$			30.3860i			1.08869i
$780$		0			0
$781$	34.5421			1.23601
$782$	37.3298	−	1.99770i	1.33491	−	0.0714375i
$783$		0			0
$784$	1.25912	−	27.9717i	0.0449687	−	0.998988i
$785$	9.75447	−	16.8952i	0.348152	−	0.603017i
$786$		0			0
$787$	−16.0992	+	27.8846i	−0.573875	+	0.993980i	0.422288	+	0.906462i	$0.361227\pi$
$787$	−16.0992	+	27.8846i	−0.573875	+	0.993980i	−0.996163	+	0.0875186i	$0.972106\pi$
$788$	18.1350	+	24.8452i	0.646034	+	0.885073i
$789$		0			0
$790$	11.3627	−	0.608074i	0.404268	−	0.0216343i
$791$	33.5598	−	25.8304i	1.19325	−	0.918423i
$792$		0			0
$793$	4.99257	−	8.64739i	0.177291	−	0.307078i
$794$	23.1787	−	15.0889i	0.822583	−	0.535483i
$795$		0			0
$796$	4.53075	−	10.2370i	0.160588	−	0.362841i
$797$	−16.7898	+	9.69358i	−0.594724	+	0.343364i	−0.766963	−	0.641691i	$-0.778233\pi$
$797$	−16.7898	+	9.69358i	−0.594724	+	0.343364i	0.172239	+	0.985055i	$0.444900\pi$
$798$		0			0
$799$	33.3284	+	19.2422i	1.17908	+	0.680740i
$800$	−15.5916	−	15.4204i	−0.551245	−	0.545193i
$801$		0			0
$802$	−16.0079	+	31.5032i	−0.565259	+	1.11242i
$803$	−3.79947	−	6.58088i	−0.134081	−	0.232234i
$804$		0			0
$805$	1.20836	+	9.07462i	0.0425893	+	0.319838i
$806$	28.9274	+	14.6990i	1.01892	+	0.517752i
$807$		0			0
$808$	−3.81068	−	23.5545i	−0.134059	−	0.828646i
$809$	−16.7748	−	29.0549i	−0.589772	−	1.02152i	−0.994262	−	0.106973i	$-0.965884\pi$
$809$	−16.7748	−	29.0549i	−0.589772	−	1.02152i	0.404490	−	0.914543i	$-0.367449\pi$
$810$		0			0
$811$	12.0196			0.422064			0.211032	−	0.977479i	$-0.432318\pi$
$811$	12.0196			0.422064			0.211032	+	0.977479i	$0.432318\pi$
$812$	−1.28320	−	5.25939i	−0.0450315	−	0.184568i
$813$		0			0
$814$	3.12001	−	2.03106i	0.109356	−	0.0711886i
$815$	−8.49021	+	14.7055i	−0.297399	+	0.515110i
$816$		0			0
$817$	40.2565	−	23.2421i	1.40840	−	0.813138i
$818$	−14.7133	+	9.57806i	−0.514440	+	0.334889i
$819$		0			0
$820$	3.74122	−	8.45310i	0.130649	−	0.295195i
$821$	−5.79127	−	10.0308i	−0.202117	−	0.350076i	0.747094	−	0.664719i	$-0.231449\pi$
$821$	−5.79127	−	10.0308i	−0.202117	−	0.350076i	−0.949210	+	0.314642i	$0.898115\pi$
$822$		0			0
$823$	36.5262	+	21.0884i	1.27322	+	0.735096i	0.975593	−	0.219586i	$-0.0704705\pi$
$823$	36.5262	+	21.0884i	1.27322	+	0.735096i	0.297630	+	0.954681i	$0.403804\pi$
$824$	21.9606	−	3.55281i	0.765034	−	0.123768i
$825$		0			0
$826$	−6.78837	+	5.82822i	−0.236198	+	0.202790i
$827$			27.0948i			0.942178i	0.882086	+	0.471089i	$0.156139\pi$
$827$			27.0948i			0.942178i	−0.882086	+	0.471089i	$0.843861\pi$
$828$		0			0
$829$	−3.83015	+	2.21134i	−0.133027	+	0.0768029i	−0.565036	−	0.825066i	$-0.691138\pi$
$829$	−3.83015	+	2.21134i	−0.133027	+	0.0768029i	0.432010	+	0.901869i	$0.357805\pi$
$830$	−2.68605	+	1.74856i	−0.0932342	+	0.0606934i
$831$		0			0
$832$	−14.3268	+	16.1250i	−0.496692	+	0.559035i
$833$	39.9610	−	40.1983i	1.38456	−	1.39279i
$834$		0			0
$835$	−0.0253758	+	0.0146508i	−0.000878167	+	0.000507010i
$836$	−4.01526	−	37.4080i	−0.138871	−	1.29378i
$837$		0			0
$838$	−42.4076	+	2.26943i	−1.46495	+	0.0783962i
$839$	−25.3280	+	43.8694i	−0.874420	+	1.51454i	−0.0170407	+	0.999855i	$0.505424\pi$
$839$	−25.3280	+	43.8694i	−0.874420	+	1.51454i	−0.857379	+	0.514685i	$0.827909\pi$
$840$		0			0
$841$	13.9766	+	24.2083i	0.481953	+	0.834768i
$842$	−26.2996	−	40.4002i	−0.906345	−	1.39228i
$843$		0			0
$844$	−11.5680	−	5.11982i	−0.398186	−	0.176232i
$845$	−5.25980	−	3.03675i	−0.180943	−	0.104467i
$846$		0			0
$847$	−1.29633	−	9.73526i	−0.0445426	−	0.334508i
$848$	15.1632	−	3.29308i	0.520706	−	0.113085i
$849$		0			0
$850$	−2.37222	−	44.3284i	−0.0813666	−	1.52045i
$851$	2.75683	+	1.59165i	0.0945028	+	0.0545612i
$852$		0			0
$853$	−23.5900	−	13.6197i	−0.807705	−	0.466329i	0.0384530	−	0.999260i	$-0.487757\pi$
$853$	−23.5900	−	13.6197i	−0.807705	−	0.466329i	−0.846158	+	0.532931i	$0.821090\pi$
$854$	−13.6179	+	2.56035i	−0.465996	+	0.0876134i
$855$		0			0
$856$	12.2237	+	4.64587i	0.417799	+	0.158792i
$857$			17.3398i			0.592317i	0.955139	+	0.296159i	$0.0957057\pi$
$857$			17.3398i			0.592317i	−0.955139	+	0.296159i	$0.904294\pi$
$858$		0			0
$859$	−4.32980			−0.147731			−0.0738654	−	0.997268i	$-0.523534\pi$
$859$	−4.32980			−0.147731			−0.0738654	+	0.997268i	$0.523534\pi$
$860$	−14.0606	+	1.50922i	−0.479463	+	0.0514641i
$861$		0			0
$862$	0.785350	+	14.6754i	0.0267491	+	0.499846i
$863$	33.6005	+	19.3992i	1.14377	+	0.660358i	0.947362	−	0.320164i	$-0.103738\pi$
$863$	33.6005	+	19.3992i	1.14377	+	0.660358i	0.196411	+	0.980522i	$0.437071\pi$
$864$		0			0
$865$	2.51959	+	4.36407i	0.0856688	+	0.148383i
$866$	−47.0829	−	23.9245i	−1.59994	−	0.812988i
$867$		0			0
$868$	−10.6730	−	43.7450i	−0.362266	−	1.48480i
$869$	10.2467	+	17.7478i	0.347596	+	0.602054i
$870$		0			0
$871$	5.27350			0.178686
$872$	−31.4690	−	38.5989i	−1.06568	−	1.30713i
$873$		0			0
$874$	26.9609	−	17.5509i	0.911966	−	0.593670i
$875$	24.6748	−	3.28566i	0.834160	−	0.111076i
$876$		0			0
$877$	28.3411			0.957012			0.478506	−	0.878084i	$-0.341178\pi$
$877$	28.3411			0.957012			0.478506	+	0.878084i	$0.341178\pi$
$878$	26.8062	−	1.43453i	0.904667	−	0.0484130i
$879$		0			0
$880$	−3.48879	+	10.9009i	−0.117607	+	0.367470i
$881$			47.2247i			1.59104i	0.605927	+	0.795520i	$0.292802\pi$
$881$			47.2247i			1.59104i	−0.605927	+	0.795520i	$0.707198\pi$
$882$		0			0
$883$		−	31.8848i		−	1.07301i	−0.843897	−	0.536505i	$-0.819744\pi$
$883$		−	31.8848i		−	1.07301i	0.843897	−	0.536505i	$-0.180256\pi$
$884$	−43.4159	+	4.66013i	−1.46024	+	0.156737i
$885$		0			0
$886$	1.23613	+	23.0989i	0.0415286	+	0.776022i
$887$	31.6593			1.06302			0.531508	−	0.847053i	$-0.321625\pi$
$887$	31.6593			1.06302			0.531508	+	0.847053i	$0.321625\pi$
$888$		0			0
$889$	−37.9917	+	5.05893i	−1.27420	+	0.169671i
$890$	3.59726	+	5.52592i	0.120580	+	0.185229i
$891$		0			0
$892$	24.3316	−	2.61168i	0.814682	−	0.0874455i
$893$	33.1178			1.10825
$894$		0			0
$895$	−1.93992	−	3.36004i	−0.0648443	−	0.112314i
$896$	29.9289	+	0.508017i	0.999856	+	0.0169717i
$897$		0			0
$898$	−10.7337	+	21.1237i	−0.358188	+	0.704906i
$899$	−4.35299	−	7.53960i	−0.145180	−	0.251460i
$900$		0			0
$901$	27.2026	+	15.7054i	0.906251	+	0.523224i
$902$	16.6246	−	0.889660i	0.553538	−	0.0296224i
$903$		0			0
$904$	28.6078	+	35.0895i	0.951483	+	1.16706i
$905$	−13.0125			−0.432550
$906$		0			0
$907$		−	50.0286i		−	1.66117i	−0.556891	−	0.830586i	$-0.688006\pi$
$907$		−	50.0286i		−	1.66117i	0.556891	−	0.830586i	$-0.311994\pi$
$908$	−10.6829	−	14.6357i	−0.354525	−	0.485703i
$909$		0			0
$910$	−1.97583	−	10.5090i	−0.0654981	−	0.348370i
$911$	−25.2297	−	14.5664i	−0.835897	−	0.482605i	0.0199707	−	0.999801i	$-0.493643\pi$
$911$	−25.2297	−	14.5664i	−0.835897	−	0.482605i	−0.855867	+	0.517195i	$0.826976\pi$
$912$		0			0
$913$	−4.99892	−	2.88613i	−0.165440	−	0.0955169i
$914$	6.17621	−	0.330519i	0.204291	−	0.0109326i
$915$		0			0
$916$	22.3621	−	16.3226i	0.738864	−	0.539313i
$917$	−3.79248	−	28.4809i	−0.125239	−	0.940522i
$918$		0			0
$919$	19.2593	+	11.1193i	0.635304	+	0.366793i	0.782803	−	0.622269i	$-0.213789\pi$
$919$	19.2593	+	11.1193i	0.635304	+	0.366793i	−0.147499	+	0.989062i	$0.547122\pi$
$920$	−9.66119	+	1.56300i	−0.318520	+	0.0515305i
$921$		0			0
$922$	−36.1652	+	23.5427i	−1.19104	+	0.775339i
$923$	−17.2497	−	29.8773i	−0.567780	−	0.983424i
$924$		0			0
$925$	1.89006	−	3.27367i	0.0621447	−	0.107638i
$926$	1.75695	+	32.8311i	0.0577369	+	1.07890i
$927$		0			0
$928$	5.58190	−	1.52873i	0.183235	−	0.0501832i
$929$	−36.0808	+	20.8312i	−1.18377	+	0.683451i	−0.956884	−	0.290470i	$-0.906188\pi$
$929$	−36.0808	+	20.8312i	−1.18377	+	0.683451i	−0.226888	+	0.973921i	$0.572855\pi$
$930$		0			0
$931$	12.4850	−	47.1524i	0.409178	−	1.54536i
$932$	−38.8427	+	4.16926i	−1.27234	+	0.136569i
$933$		0			0
$934$	−15.3331	−	23.5540i	−0.501715	−	0.770710i
$935$	−20.0656	+	11.5849i	−0.656215	+	0.378866i
$936$		0			0
$937$			38.4609i			1.25646i	0.778026	+	0.628232i	$0.216221\pi$
$937$			38.4609i			1.25646i	−0.778026	+	0.628232i	$0.783779\pi$
$938$	−4.76710	−	5.55244i	−0.155651	−	0.181293i
$939$		0			0
$940$	−9.21307	−	4.07757i	−0.300497	−	0.132996i
$941$	2.73114	+	1.57682i	0.0890326	+	0.0514030i	0.543855	−	0.839179i	$-0.316964\pi$
$941$	2.73114	+	1.57682i	0.0890326	+	0.0514030i	−0.454823	+	0.890582i	$0.650297\pi$
$942$		0			0
$943$	7.11777	+	12.3283i	0.231786	+	0.401466i
$944$	−6.43144	−	7.07972i	−0.209325	−	0.230425i
$945$		0			0
$946$	−13.8947	−	21.3443i	−0.451755	−	0.693964i
$947$	17.3803	−	10.0345i	0.564782	−	0.326077i	−0.190280	−	0.981730i	$-0.560940\pi$
$947$	17.3803	−	10.0345i	0.564782	−	0.326077i	0.755063	+	0.655653i	$0.227606\pi$
$948$		0			0
$949$	−3.79477	+	6.57273i	−0.123183	+	0.213360i
$950$	−20.8414	−	32.0155i	−0.676184	−	1.03872i
$951$		0			0
$952$	44.1534	+	41.4997i	1.43102	+	1.34501i
$953$	−29.2121			−0.946273			−0.473136	−	0.880989i	$-0.656878\pi$
$953$	−29.2121			−0.946273			−0.473136	+	0.880989i	$0.656878\pi$
$954$		0			0
$955$	−9.18290	−	15.9052i	−0.297152	−	0.514682i
$956$	−15.9147	−	7.04362i	−0.514718	−	0.227807i
$957$		0			0
$958$	2.99512	−	5.89433i	0.0967680	−	0.190437i
$959$	−3.40015	−	25.5346i	−0.109797	−	0.824555i
$960$		0			0
$961$	−20.7060	−	35.8638i	−0.667935	−	1.15690i
$962$	−3.31484	−	1.68439i	−0.106875	−	0.0543069i
$963$		0			0
$964$	23.7361	−	17.3255i	0.764488	−	0.558016i
$965$	1.96724	+	1.13579i	0.0633278	+	0.0365623i
$966$		0			0
$967$	−40.7844	+	23.5469i	−1.31154	+	0.757217i	−0.982351	−	0.187047i	$-0.940108\pi$
$967$	−40.7844	+	23.5469i	−1.31154	+	0.757217i	−0.329188	+	0.944265i	$0.606775\pi$
$968$	10.3645	−	1.67678i	0.333129	−	0.0538939i
$969$		0			0
$970$	4.63786	+	7.12445i	0.148913	+	0.228752i
$971$	1.53241	−	2.65421i	0.0491774	−	0.0851777i	−0.840389	−	0.541984i	$-0.817673\pi$
$971$	1.53241	−	2.65421i	0.0491774	−	0.0851777i	0.889566	+	0.456806i	$0.151007\pi$
$972$		0			0
$973$	−10.3505	+	7.96657i	−0.331821	+	0.255396i
$974$	−2.33402	−	43.6145i	−0.0747869	−	1.39750i
$975$		0			0
$976$	−3.14380	−	14.4758i	−0.100630	−	0.463359i
$977$	−12.4473	+	21.5594i	−0.398226	+	0.689747i	−0.993507	−	0.113770i	$-0.963707\pi$
$977$	−12.4473	+	21.5594i	−0.398226	+	0.689747i	0.595281	+	0.803517i	$0.297041\pi$
$978$		0			0
$979$	−5.93754	+	10.2841i	−0.189764	+	0.328682i
$980$	−9.27875	+	11.5802i	−0.296399	+	0.369915i
$981$		0			0
$982$	−1.54491	−	28.8689i	−0.0493001	−	0.921244i
$983$	−38.2016			−1.21844			−0.609222	−	0.793000i	$-0.708518\pi$
$983$	−38.2016			−1.21844			−0.609222	+	0.793000i	$0.708518\pi$
$984$		0			0
$985$		−	16.3016i		−	0.519411i
$986$	10.4447	+	5.30731i	0.332626	+	0.169019i
$987$		0			0
$988$	−30.3510	+	22.1539i	−0.965595	+	0.704808i
$989$	10.8887	−	18.8597i	0.346240	−	0.599705i
$990$		0			0
$991$	−16.6116	+	9.59071i	−0.527685	+	0.304659i	−0.740073	−	0.672526i	$-0.765209\pi$
$991$	−16.6116	+	9.59071i	−0.527685	+	0.304659i	0.212388	+	0.977185i	$0.431876\pi$
$992$	46.4274	−	12.7153i	1.47407	−	0.403710i
$993$		0			0
$994$	−15.8644	+	45.1703i	−0.503188	+	1.43272i
$995$	−5.13800	+	2.96642i	−0.162885	+	0.0940420i
$996$		0			0
$997$			16.7831i			0.531525i	0.964039	+	0.265762i	$0.0856237\pi$
$997$			16.7831i			0.531525i	−0.964039	+	0.265762i	$0.914376\pi$
$998$	−19.5116	−	9.91452i	−0.617628	−	0.313839i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.n.b.19.16		84
3.2	odd	2		252.2.n.b.187.27	yes	84
4.3	odd	2	inner	756.2.n.b.19.41		84
7.3	odd	6		756.2.bj.b.451.13		84
9.4	even	3		756.2.bj.b.523.13		84
9.5	odd	6		252.2.bj.b.103.30	yes	84
12.11	even	2		252.2.n.b.187.2	yes	84
21.17	even	6		252.2.bj.b.115.30	yes	84
28.3	even	6		756.2.bj.b.451.14		84
36.23	even	6		252.2.bj.b.103.29	yes	84
36.31	odd	6		756.2.bj.b.523.14		84
63.31	odd	6	inner	756.2.n.b.199.41		84
63.59	even	6		252.2.n.b.31.2	✓	84
84.59	odd	6		252.2.bj.b.115.29	yes	84
252.31	even	6	inner	756.2.n.b.199.16		84
252.59	odd	6		252.2.n.b.31.27	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.2	✓	84	63.59	even	6
252.2.n.b.31.27	yes	84	252.59	odd	6
252.2.n.b.187.2	yes	84	12.11	even	2
252.2.n.b.187.27	yes	84	3.2	odd	2
252.2.bj.b.103.29	yes	84	36.23	even	6
252.2.bj.b.103.30	yes	84	9.5	odd	6
252.2.bj.b.115.29	yes	84	84.59	odd	6
252.2.bj.b.115.30	yes	84	21.17	even	6
756.2.n.b.19.16		84	1.1	even	1	trivial
756.2.n.b.19.41		84	4.3	odd	2	inner
756.2.n.b.199.16		84	252.31	even	6	inner
756.2.n.b.199.41		84	63.31	odd	6	inner
756.2.bj.b.451.13		84	7.3	odd	6
756.2.bj.b.451.14		84	28.3	even	6
756.2.bj.b.523.13		84	9.4	even	3
756.2.bj.b.523.14		84	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.640648 + 1.26078i) q^{2} +(-1.17914 - 1.61543i) q^{4} +1.05993i q^{5} +(-0.349222 - 2.62260i) q^{7} +(2.79212 - 0.451713i) q^{8} +O(q^{10})\)	\(q+(-0.640648 + 1.26078i) q^{2} +(-1.17914 - 1.61543i) q^{4} +1.05993i q^{5} +(-0.349222 - 2.62260i) q^{7} +(2.79212 - 0.451713i) q^{8} +(-1.33634 - 0.679041i) q^{10} -2.69962i q^{11} +(-2.33504 + 1.34814i) q^{13} +(3.53026 + 1.23987i) q^{14} +(-1.21926 + 3.80965i) q^{16} +(-7.01250 + 4.04867i) q^{17} +(-3.48409 + 6.03463i) q^{19} +(1.71224 - 1.24980i) q^{20} +(3.40363 + 1.72951i) q^{22} +3.26452i q^{23} +3.87655 q^{25} +(-0.203766 - 3.80766i) q^{26} +(-3.82486 + 3.65656i) q^{28} +(-0.511543 + 0.886019i) q^{29} +(-4.25476 + 7.36946i) q^{31} +(-4.02202 - 3.97786i) q^{32} +(-0.611942 - 11.4350i) q^{34} +(2.77977 - 0.370150i) q^{35} +(0.487561 - 0.844481i) q^{37} +(-5.37627 - 8.25875i) q^{38} +(0.478783 + 2.95945i) q^{40} +(3.77646 - 2.18034i) q^{41} +(-5.77718 - 3.33546i) q^{43} +(-4.36106 + 3.18323i) q^{44} +(-4.11585 - 2.09141i) q^{46} +(-2.37636 - 4.11598i) q^{47} +(-6.75609 + 1.83174i) q^{49} +(-2.48351 + 4.88749i) q^{50} +(4.93117 + 2.18247i) q^{52} +(-1.93958 - 3.35945i) q^{53} +2.86140 q^{55} +(-2.15973 - 7.16488i) q^{56} +(-0.789357 - 1.21257i) q^{58} +(-1.19560 + 2.07084i) q^{59} +(-3.20716 + 1.85166i) q^{61} +(-6.56548 - 10.0856i) q^{62} +(7.59191 - 2.52247i) q^{64} +(-1.42893 - 2.47498i) q^{65} +(-1.69381 - 0.977924i) q^{67} +(14.8091 + 6.55429i) q^{68} +(-1.31418 + 3.74182i) q^{70} +12.7952i q^{71} +(2.43771 - 1.40741i) q^{73} +(0.752350 + 1.15572i) q^{74} +(13.8568 - 1.48734i) q^{76} +(-7.08003 + 0.942767i) q^{77} +(-6.57420 + 3.79562i) q^{79} +(-4.03795 - 1.29233i) q^{80} +(0.329550 + 6.15812i) q^{82} +(1.06909 - 1.85171i) q^{83} +(-4.29130 - 7.43275i) q^{85} +(7.90642 - 5.14691i) q^{86} +(-1.21945 - 7.53767i) q^{88} +(-3.80947 - 2.19940i) q^{89} +(4.35108 + 5.65309i) q^{91} +(5.27362 - 3.84933i) q^{92} +(6.71176 - 0.359178i) q^{94} +(-6.39627 - 3.69289i) q^{95} +(-4.91146 - 2.83563i) q^{97} +(2.01885 - 9.69145i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + q^{2} + q^{4} + 16 q^{8}+O(q^{10}) \) 84 * q + q^2 + q^4 + 16 * q^8	\( 84 q + q^{2} + q^{4} + 16 q^{8} - 18 q^{10} - 18 q^{13} + 25 q^{14} - 7 q^{16} - 6 q^{17} - 24 q^{20} + 6 q^{22} - 32 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} - 9 q^{32} + 24 q^{34} + 2 q^{37} + 6 q^{41} + 13 q^{44} + 10 q^{46} + 2 q^{49} + 17 q^{50} + 2 q^{53} + 32 q^{56} + 26 q^{58} - 24 q^{61} - 8 q^{64} - 50 q^{65} - 4 q^{70} + 30 q^{73} - 46 q^{74} - 46 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} - 18 q^{86} - 2 q^{88} + 102 q^{89} - 28 q^{92} + 3 q^{94} - 6 q^{97} - 21 q^{98}+O(q^{100}) \) 84 * q + q^2 + q^4 + 16 * q^8 - 18 * q^10 - 18 * q^13 + 25 * q^14 - 7 * q^16 - 6 * q^17 - 24 * q^20 + 6 * q^22 - 32 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 - 9 * q^32 + 24 * q^34 + 2 * q^37 + 6 * q^41 + 13 * q^44 + 10 * q^46 + 2 * q^49 + 17 * q^50 + 2 * q^53 + 32 * q^56 + 26 * q^58 - 24 * q^61 - 8 * q^64 - 50 * q^65 - 4 * q^70 + 30 * q^73 - 46 * q^74 - 46 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 - 18 * q^86 - 2 * q^88 + 102 * q^89 - 28 * q^92 + 3 * q^94 - 6 * q^97 - 21 * q^98

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