LMFDB - Embedded newform 756.2.n.b.19.4

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			19.4
Character	$\chi$	$=$	756.19
Dual form			756.2.n.b.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34403 - 0.439974i) q^{2} +(1.61285 + 1.18268i) q^{4} +2.88398i q^{5} +(-2.24777 + 1.39554i) q^{7} +(-1.64737 - 2.29917i) q^{8} +O(q^{10})$	\(q+(-1.34403 - 0.439974i) q^{2} +(1.61285 + 1.18268i) q^{4} +2.88398i q^{5} +(-2.24777 + 1.39554i) q^{7} +(-1.64737 - 2.29917i) q^{8} +(1.26887 - 3.87616i) q^{10} -2.30073i q^{11} +(-4.22314 + 2.43823i) q^{13} +(3.63508 - 0.886694i) q^{14} +(1.20255 + 3.81496i) q^{16} +(-3.54408 + 2.04617i) q^{17} +(0.308511 - 0.534357i) q^{19} +(-3.41081 + 4.65141i) q^{20} +(-1.01226 + 3.09226i) q^{22} -8.41949i q^{23} -3.31732 q^{25} +(6.74880 - 1.41899i) q^{26} +(-5.27578 - 0.407592i) q^{28} +(0.811434 - 1.40545i) q^{29} +(0.821847 - 1.42348i) q^{31} +(0.0622189 - 5.65651i) q^{32} +(5.66362 - 1.19082i) q^{34} +(-4.02471 - 6.48251i) q^{35} +(4.02614 - 6.97347i) q^{37} +(-0.649752 + 0.582456i) q^{38} +(6.63074 - 4.75098i) q^{40} +(-0.216148 + 0.124793i) q^{41} +(-6.51826 - 3.76332i) q^{43} +(2.72103 - 3.71073i) q^{44} +(-3.70435 + 11.3161i) q^{46} +(-1.47573 - 2.55604i) q^{47} +(3.10493 - 6.27371i) q^{49} +(4.45858 + 1.45953i) q^{50} +(-9.69493 - 1.06212i) q^{52} +(4.57041 + 7.91618i) q^{53} +6.63526 q^{55} +(6.91149 + 2.86902i) q^{56} +(-1.70895 + 1.53195i) q^{58} +(-0.762534 + 1.32075i) q^{59} +(-8.38475 + 4.84094i) q^{61} +(-1.73088 + 1.55161i) q^{62} +(-2.57234 + 7.57516i) q^{64} +(-7.03181 - 12.1794i) q^{65} +(-7.07839 - 4.08671i) q^{67} +(-8.13602 - 0.891338i) q^{68} +(2.55721 + 10.4835i) q^{70} +11.6557i q^{71} +(-4.66559 + 2.69368i) q^{73} +(-8.47940 + 7.60118i) q^{74} +(1.12955 - 0.496966i) q^{76} +(3.21077 + 5.17152i) q^{77} +(2.05637 - 1.18725i) q^{79} +(-11.0022 + 3.46811i) q^{80} +(0.345415 - 0.0726264i) q^{82} +(-3.53143 + 6.11661i) q^{83} +(-5.90112 - 10.2210i) q^{85} +(7.10499 + 7.92589i) q^{86} +(-5.28977 + 3.79016i) q^{88} +(-12.0481 - 6.95597i) q^{89} +(6.08999 - 11.3742i) q^{91} +(9.95755 - 13.5793i) q^{92} +(0.858838 + 4.08468i) q^{94} +(1.54107 + 0.889738i) q^{95} +(-10.3880 - 5.99749i) q^{97} +(-6.93339 + 7.06598i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.34403	−	0.439974i	−0.950374	−	0.311108i
$2$	−1.34403	−	0.439974i	−0.950374	−	0.311108i
$3$		0			0
$3$		0			0
$4$	1.61285	+	1.18268i	0.806423	+	0.591339i
$5$			2.88398i			1.28975i	0.764287	+	0.644877i	$0.223091\pi$
$5$			2.88398i			1.28975i	−0.764287	+	0.644877i	$0.776909\pi$
$6$		0			0
$7$	−2.24777	+	1.39554i	−0.849577	+	0.527465i
$7$	−2.24777	+	1.39554i	−0.849577	+	0.527465i
$8$	−1.64737	−	2.29917i	−0.582433	−	0.812878i
$9$		0			0
$10$	1.26887	−	3.87616i	0.401253	−	1.22575i
$11$		−	2.30073i		−	0.693697i	−0.937921	−	0.346849i	$-0.887252\pi$
$11$		−	2.30073i		−	0.693697i	0.937921	−	0.346849i	$-0.112748\pi$
$12$		0			0
$13$	−4.22314	+	2.43823i	−1.17129	+	0.676244i	−0.953983	−	0.299859i	$-0.903060\pi$
$13$	−4.22314	+	2.43823i	−1.17129	+	0.676244i	−0.217306	+	0.976104i	$0.569727\pi$
$14$	3.63508	−	0.886694i	0.971515	−	0.236979i
$15$		0			0
$16$	1.20255	+	3.81496i	0.300637	+	0.953739i
$17$	−3.54408	+	2.04617i	−0.859565	+	0.496270i	−0.863867	−	0.503720i	$-0.831964\pi$
$17$	−3.54408	+	2.04617i	−0.859565	+	0.496270i	0.00430136	+	0.999991i	$0.498631\pi$
$18$		0			0
$19$	0.308511	−	0.534357i	0.0707773	−	0.122590i	−0.828465	−	0.560041i	$-0.810785\pi$
$19$	0.308511	−	0.534357i	0.0707773	−	0.122590i	0.899242	+	0.437451i	$0.144119\pi$
$20$	−3.41081	+	4.65141i	−0.762681	+	1.04009i
$21$		0			0
$22$	−1.01226	+	3.09226i	−0.215815	+	0.659272i
$23$		−	8.41949i		−	1.75559i	−0.479041	−	0.877793i	$-0.659015\pi$
$23$		−	8.41949i		−	1.75559i	0.479041	−	0.877793i	$-0.340985\pi$
$24$		0			0
$25$	−3.31732			−0.663464
$26$	6.74880	−	1.41899i	1.32355	−	0.278287i
$27$		0			0
$28$	−5.27578	−	0.407592i	−0.997029	−	0.0770276i
$29$	0.811434	−	1.40545i	0.150680	−	0.260985i	−0.780798	−	0.624784i	$-0.785187\pi$
$29$	0.811434	−	1.40545i	0.150680	−	0.260985i	0.931477	+	0.363799i	$0.118521\pi$
$30$		0			0
$31$	0.821847	−	1.42348i	0.147608	−	0.255665i	−0.782735	−	0.622355i	$-0.786176\pi$
$31$	0.821847	−	1.42348i	0.147608	−	0.255665i	0.930343	+	0.366691i	$0.119509\pi$
$32$	0.0622189	−	5.65651i	0.0109989	−	0.999940i
$33$		0			0
$34$	5.66362	−	1.19082i	0.971303	−	0.204225i
$35$	−4.02471	−	6.48251i	−0.680300	−	1.09574i
$36$		0			0
$37$	4.02614	−	6.97347i	0.661893	−	1.14643i	−0.318225	−	0.948015i	$-0.603087\pi$
$37$	4.02614	−	6.97347i	0.661893	−	1.14643i	0.980118	−	0.198416i	$-0.0635799\pi$
$38$	−0.649752	+	0.582456i	−0.105404	+	0.0944868i
$39$		0			0
$40$	6.63074	−	4.75098i	1.04841	−	0.751195i
$41$	−0.216148	+	0.124793i	−0.0337566	+	0.0194894i	−0.516783	−	0.856116i	$-0.672871\pi$
$41$	−0.216148	+	0.124793i	−0.0337566	+	0.0194894i	0.483027	+	0.875606i	$0.339537\pi$
$42$		0			0
$43$	−6.51826	−	3.76332i	−0.994026	−	0.573901i	−0.0875504	−	0.996160i	$-0.527904\pi$
$43$	−6.51826	−	3.76332i	−0.994026	−	0.573901i	−0.906475	+	0.422259i	$0.861237\pi$
$44$	2.72103	−	3.71073i	0.410210	−	0.559414i
$45$		0			0
$46$	−3.70435	+	11.3161i	−0.546177	+	1.66846i
$47$	−1.47573	−	2.55604i	−0.215257	−	0.372836i	0.738095	−	0.674697i	$-0.235726\pi$
$47$	−1.47573	−	2.55604i	−0.215257	−	0.372836i	−0.953352	+	0.301860i	$0.902392\pi$
$48$		0			0
$49$	3.10493	−	6.27371i	0.443561	−	0.896244i
$50$	4.45858	+	1.45953i	0.630539	+	0.206409i
$51$		0			0
$52$	−9.69493	−	1.06212i	−1.34444	−	0.147290i
$53$	4.57041	+	7.91618i	0.627794	+	1.08737i	0.987993	+	0.154496i	$0.0493753\pi$
$53$	4.57041	+	7.91618i	0.627794	+	1.08737i	−0.360199	+	0.932875i	$0.617291\pi$
$54$		0			0
$55$	6.63526			0.894698
$56$	6.91149	+	2.86902i	0.923587	+	0.383389i
$57$		0			0
$58$	−1.70895	+	1.53195i	−0.224396	+	0.201155i
$59$	−0.762534	+	1.32075i	−0.0992735	+	0.171947i	−0.911384	−	0.411557i	$-0.864985\pi$
$59$	−0.762534	+	1.32075i	−0.0992735	+	0.171947i	0.812111	+	0.583503i	$0.198319\pi$
$60$		0			0
$61$	−8.38475	+	4.84094i	−1.07356	+	0.619818i	−0.929151	−	0.369700i	$-0.879460\pi$
$61$	−8.38475	+	4.84094i	−1.07356	+	0.619818i	−0.144406	+	0.989519i	$0.546127\pi$
$62$	−1.73088	+	1.55161i	−0.219822	+	0.197055i
$63$		0			0
$64$	−2.57234	+	7.57516i	−0.321543	+	0.946895i
$65$	−7.03181	−	12.1794i	−0.872188	−	1.51067i
$66$		0			0
$67$	−7.07839	−	4.08671i	−0.864763	−	0.499271i	0.000841386	−	1.00000i	$-0.499732\pi$
$67$	−7.07839	−	4.08671i	−0.864763	−	0.499271i	−0.865604	+	0.500728i	$0.833066\pi$
$68$	−8.13602	−	0.891338i	−0.986637	−	0.108091i
$69$		0			0
$70$	2.55721	+	10.4835i	0.305644	+	1.25301i
$71$			11.6557i			1.38328i	0.722244	+	0.691638i	$0.243111\pi$
$71$			11.6557i			1.38328i	−0.722244	+	0.691638i	$0.756889\pi$
$72$		0			0
$73$	−4.66559	+	2.69368i	−0.546066	+	0.315272i	−0.747534	−	0.664224i	$-0.768762\pi$
$73$	−4.66559	+	2.69368i	−0.546066	+	0.315272i	0.201468	+	0.979495i	$0.435429\pi$
$74$	−8.47940	+	7.60118i	−0.985710	+	0.883619i
$75$		0			0
$76$	1.12955	−	0.496966i	0.129569	−	0.0570059i
$77$	3.21077	+	5.17152i	0.365901	+	0.589349i
$78$		0			0
$79$	2.05637	−	1.18725i	0.231360	−	0.133576i	−0.379839	−	0.925052i	$-0.624021\pi$
$79$	2.05637	−	1.18725i	0.231360	−	0.133576i	0.611199	+	0.791477i	$0.290687\pi$
$80$	−11.0022	+	3.46811i	−1.23009	+	0.387747i
$81$		0			0
$82$	0.345415	−	0.0726264i	0.0381447	−	0.00802024i
$83$	−3.53143	+	6.11661i	−0.387624	+	0.671385i	−0.992129	−	0.125216i	$-0.960038\pi$
$83$	−3.53143	+	6.11661i	−0.387624	+	0.671385i	0.604505	+	0.796601i	$0.293371\pi$
$84$		0			0
$85$	−5.90112	−	10.2210i	−0.640066	−	1.10863i
$86$	7.10499	+	7.92589i	0.766151	+	0.854670i
$87$		0			0
$88$	−5.28977	+	3.79016i	−0.563892	+	0.404033i
$89$	−12.0481	−	6.95597i	−1.27710	−	0.737332i	−0.300783	−	0.953693i	$-0.597248\pi$
$89$	−12.0481	−	6.95597i	−1.27710	−	0.737332i	−0.976313	+	0.216361i	$0.930581\pi$
$90$		0			0
$91$	6.08999	−	11.3742i	0.638405	−	1.19234i
$92$	9.95755	−	13.5793i	1.03815	−	1.41574i
$93$		0			0
$94$	0.858838	+	4.08468i	0.0885824	+	0.421303i
$95$	1.54107	+	0.889738i	0.158111	+	0.0912852i
$96$		0			0
$97$	−10.3880	−	5.99749i	−1.05474	−	0.608953i	−0.130766	−	0.991413i	$-0.541744\pi$
$97$	−10.3880	−	5.99749i	−1.05474	−	0.608953i	−0.923972	+	0.382460i	$0.875077\pi$
$98$	−6.93339	+	7.06598i	−0.700378	+	0.713772i
$99$		0			0
$100$	−5.35032	−	3.92332i	−0.535032	−	0.392332i
$101$			4.08359i			0.406333i	0.979144	+	0.203166i	$0.0651232\pi$
$101$			4.08359i			0.406333i	−0.979144	+	0.203166i	$0.934877\pi$
$102$		0			0
$103$	−6.39089			−0.629713			−0.314856	−	0.949139i	$-0.601956\pi$
$103$	−6.39089			−0.629713			−0.314856	+	0.949139i	$0.601956\pi$
$104$	12.5630	+	5.69304i	1.23190	+	0.558249i
$105$		0			0
$106$	−2.65987	−	12.6505i	−0.258349	−	1.22872i
$107$	−5.06327	−	2.92328i	−0.489485	−	0.282604i	0.234876	−	0.972025i	$-0.424532\pi$
$107$	−5.06327	−	2.92328i	−0.489485	−	0.282604i	−0.724361	+	0.689421i	$0.757865\pi$
$108$		0			0
$109$	7.02228	+	12.1629i	0.672612	+	1.16500i	0.977161	+	0.212502i	$0.0681611\pi$
$109$	7.02228	+	12.1629i	0.672612	+	1.16500i	−0.304549	+	0.952497i	$0.598506\pi$
$110$	−8.91801	−	2.91934i	−0.850299	−	0.278348i
$111$		0			0
$112$	−8.02697	−	6.89693i	−0.758478	−	0.651699i
$113$	−3.90522	−	6.76404i	−0.367372	−	0.636308i	0.621781	−	0.783191i	$-0.286409\pi$
$113$	−3.90522	−	6.76404i	−0.367372	−	0.636308i	−0.989154	+	0.146883i	$0.953076\pi$
$114$		0			0
$115$	24.2816			2.26427
$116$	2.97091	−	1.30710i	0.275842	−	0.121361i
$117$		0			0
$118$	1.60597	−	1.43963i	0.147841	−	0.132529i
$119$	5.11075	−	9.54524i	0.468501	−	0.875010i
$120$		0			0
$121$	5.70662			0.518784
$122$	13.3993	−	2.81731i	1.21311	−	0.255067i
$123$		0			0
$124$	3.00903	−	1.32388i	0.270219	−	0.118888i
$125$			4.85281i			0.434049i
$126$		0			0
$127$			14.7826i			1.31174i	0.754872	+	0.655872i	$0.227699\pi$
$127$			14.7826i			1.31174i	−0.754872	+	0.655872i	$0.772301\pi$
$128$	6.79018	−	9.04950i	0.600173	−	0.799870i
$129$		0			0
$130$	4.09234	+	19.4634i	0.358922	+	1.70705i
$131$	−9.15379			−0.799770			−0.399885	−	0.916565i	$-0.630950\pi$
$131$	−9.15379			−0.799770			−0.399885	+	0.916565i	$0.630950\pi$
$132$		0			0
$133$	0.0522558	+	1.63165i	0.00453115	+	0.141482i
$134$	7.71554	+	8.60698i	0.666521	+	0.743530i
$135$		0			0
$136$	10.5429	+	4.77762i	0.904047	+	0.409678i
$137$	−20.9553			−1.79033			−0.895164	−	0.445737i	$-0.852942\pi$
$137$	−20.9553			−1.79033			−0.895164	+	0.445737i	$0.852942\pi$
$138$		0			0
$139$	−3.12470	−	5.41214i	−0.265033	−	0.459051i	0.702539	−	0.711645i	$-0.252050\pi$
$139$	−3.12470	−	5.41214i	−0.265033	−	0.459051i	−0.967572	+	0.252594i	$0.918716\pi$
$140$	1.17548	−	15.2152i	0.0993466	−	1.28592i
$141$		0			0
$142$	5.12820	−	15.6656i	0.430349	−	1.31463i
$143$	5.60973	+	9.71633i	0.469109	+	0.812521i
$144$		0			0
$145$	4.05327	+	2.34016i	0.336606	+	0.194339i
$146$	7.45586	−	1.56766i	0.617051	−	0.129740i
$147$		0			0
$148$	14.7409	−	6.48552i	1.21170	−	0.533106i
$149$	−9.43320			−0.772798			−0.386399	−	0.922332i	$-0.626281\pi$
$149$	−9.43320			−0.772798			−0.386399	+	0.922332i	$0.626281\pi$
$150$		0			0
$151$		−	1.73869i		−	0.141493i	−0.997494	−	0.0707465i	$-0.977462\pi$
$151$		−	1.73869i		−	0.141493i	0.997494	−	0.0707465i	$-0.0225381\pi$
$152$	−1.73681	+	0.170965i	−0.140874	+	0.0138671i
$153$		0			0
$154$	−2.04005	−	8.36334i	−0.164392	−	0.673937i
$155$	4.10528	+	2.37019i	0.329744	+	0.190378i
$156$		0			0
$157$	19.3676	+	11.1819i	1.54570	+	0.892411i	0.998462	+	0.0554341i	$0.0176543\pi$
$157$	19.3676	+	11.1819i	1.54570	+	0.892411i	0.547239	+	0.836977i	$0.315679\pi$
$158$	−3.28618	+	0.690948i	−0.261435	+	0.0549689i
$159$		0			0
$160$	16.3132	+	0.179438i	1.28968	+	0.0141858i
$161$	11.7498	+	18.9251i	0.926010	+	1.49150i
$162$		0			0
$163$	7.26243	+	4.19297i	0.568838	+	0.328419i	0.756685	−	0.653780i	$-0.226818\pi$
$163$	7.26243	+	4.19297i	0.568838	+	0.328419i	−0.187847	+	0.982198i	$0.560151\pi$
$164$	−0.496203	−	0.0543613i	−0.0387469	−	0.00424490i
$165$		0			0
$166$	7.43750	−	6.66719i	0.577262	−	0.517474i
$167$	2.80662	+	4.86122i	0.217183	+	0.376172i	0.953946	−	0.299979i	$-0.0969798\pi$
$167$	2.80662	+	4.86122i	0.217183	+	0.376172i	−0.736763	+	0.676152i	$0.763646\pi$
$168$		0			0
$169$	5.38997	−	9.33570i	0.414613	−	0.718131i
$170$	3.43431	+	16.3337i	0.263399	+	1.25274i
$171$		0			0
$172$	−6.06216	−	13.7787i	−0.462235	−	1.05061i
$173$	9.80186	−	5.65911i	0.745222	−	0.430254i	−0.0787430	−	0.996895i	$-0.525091\pi$
$173$	9.80186	−	5.65911i	0.745222	−	0.430254i	0.823965	+	0.566641i	$0.191757\pi$
$174$		0			0
$175$	7.45656	−	4.62946i	0.563663	−	0.349954i
$176$	8.77720	−	2.76674i	0.661606	−	0.208551i
$177$		0			0
$178$	13.1326	+	14.6499i	0.984329	+	1.09806i
$179$	−1.87423	+	1.08209i	−0.140087	+	0.0808792i	−0.568405	−	0.822749i	$-0.692439\pi$
$179$	−1.87423	+	1.08209i	−0.140087	+	0.0808792i	0.428319	+	0.903628i	$0.359106\pi$
$180$		0			0
$181$			1.77875i			0.132213i	0.997813	+	0.0661066i	$0.0210577\pi$
$181$			1.77875i			0.132213i	−0.997813	+	0.0661066i	$0.978942\pi$
$182$	−13.1895	+	12.6078i	−0.977669	+	0.934552i
$183$		0			0
$184$	−19.3578	+	13.8700i	−1.42708	+	1.02251i
$185$	20.1113	+	11.6113i	1.47861	+	0.853678i
$186$		0			0
$187$	4.70770	+	8.15398i	0.344261	+	0.596278i
$188$	0.642845	−	5.86781i	0.0468843	−	0.427954i
$189$		0			0
$190$	−1.67979	−	1.87387i	−0.121865	−	0.135945i
$191$	4.42849	−	2.55679i	0.320435	−	0.185003i	−0.331152	−	0.943578i	$-0.607437\pi$
$191$	4.42849	−	2.55679i	0.320435	−	0.185003i	0.651586	+	0.758575i	$0.274104\pi$
$192$		0			0
$193$	−3.61302	+	6.25794i	−0.260071	+	0.450456i	−0.966261	−	0.257566i	$-0.917079\pi$
$193$	−3.61302	+	6.25794i	−0.260071	+	0.450456i	0.706189	+	0.708023i	$0.250413\pi$
$194$	11.3230	+	12.6313i	0.812946	+	0.906872i
$195$		0			0
$196$	12.4275	−	6.44640i	0.887682	−	0.460457i
$197$	4.34716			0.309722			0.154861	−	0.987936i	$-0.450507\pi$
$197$	4.34716			0.309722			0.154861	+	0.987936i	$0.450507\pi$
$198$		0			0
$199$	−10.2773	−	17.8008i	−0.728540	−	1.26187i	−0.957500	−	0.288432i	$-0.906866\pi$
$199$	−10.2773	−	17.8008i	−0.728540	−	1.26187i	0.228961	−	0.973436i	$-0.426467\pi$
$200$	5.46485	+	7.62707i	0.386423	+	0.539315i
$201$		0			0
$202$	1.79667	−	5.48848i	0.126414	−	0.386168i
$203$	0.137441	+	4.29151i	0.00964649	+	0.301205i
$204$		0			0
$205$	−0.359900	−	0.623365i	−0.0251365	−	0.0435377i
$206$	8.58956	+	2.81182i	0.598463	+	0.195909i
$207$		0			0
$208$	−14.3803	−	13.1790i	−0.997093	−	0.913801i
$209$	−1.22941	−	0.709802i	−0.0850403	−	0.0490980i
$210$		0			0
$211$	−4.36555	+	2.52045i	−0.300537	+	0.173515i	−0.642684	−	0.766131i	$-0.722179\pi$
$211$	−4.36555	+	2.52045i	−0.300537	+	0.173515i	0.342147	+	0.939646i	$0.388846\pi$
$212$	−1.99092	+	18.1729i	−0.136737	+	1.24812i
$213$		0			0
$214$	5.51903	+	6.15669i	0.377273	+	0.420862i
$215$	10.8533	−	18.7985i	0.740191	−	1.28205i
$216$		0			0
$217$	0.139205	+	4.34658i	0.00944985	+	0.295065i
$218$	−4.08679	−	19.4370i	−0.276793	−	1.31644i
$219$		0			0
$220$	10.7017	+	7.84738i	0.721506	+	0.529070i
$221$	9.97811	−	17.2826i	0.671200	−	1.16255i
$222$		0			0
$223$	−12.5132	+	21.6734i	−0.837943	+	1.45136i	0.0536683	+	0.998559i	$0.482909\pi$
$223$	−12.5132	+	21.6734i	−0.837943	+	1.45136i	−0.891611	+	0.452801i	$0.850425\pi$
$224$	7.75405	+	12.8014i	0.518089	+	0.855327i
$225$		0			0
$226$	2.27274	+	10.8093i	0.151181	+	0.719023i
$227$	−11.1012			−0.736810			−0.368405	−	0.929665i	$-0.620096\pi$
$227$	−11.1012			−0.736810			−0.368405	+	0.929665i	$0.620096\pi$
$228$		0			0
$229$		−	24.7571i		−	1.63599i	−0.575224	−	0.817996i	$-0.695085\pi$
$229$		−	24.7571i		−	1.63599i	0.575224	−	0.817996i	$-0.304915\pi$
$230$	−32.6353	−	10.6833i	−2.15191	−	0.704434i
$231$		0			0
$232$	−4.56809	+	0.449666i	−0.299910	+	0.0295220i
$233$	9.46392	−	16.3920i	0.620002	−	1.07387i	−0.369483	−	0.929238i	$-0.620465\pi$
$233$	9.46392	−	16.3920i	0.620002	−	1.07387i	0.989485	−	0.144637i	$-0.0462015\pi$
$234$		0			0
$235$	7.37155	−	4.25597i	0.480867	−	0.277629i
$236$	−2.79187	+	1.22833i	−0.181735	+	0.0799576i
$237$		0			0
$238$	−11.0687	+	10.5805i	−0.717475	+	0.685833i
$239$	−4.90588	+	2.83241i	−0.317335	+	0.183213i	−0.650204	−	0.759760i	$-0.725317\pi$
$239$	−4.90588	+	2.83241i	−0.317335	+	0.183213i	0.332869	+	0.942973i	$0.391983\pi$
$240$		0			0
$241$			6.47555i			0.417127i	0.978009	+	0.208563i	$0.0668788\pi$
$241$			6.47555i			0.417127i	−0.978009	+	0.208563i	$0.933121\pi$
$242$	−7.66989	−	2.51076i	−0.493039	−	0.161398i
$243$		0			0
$244$	−19.2486	−	2.10877i	−1.23226	−	0.135000i
$245$	18.0932	+	8.95453i	1.15593	+	0.572084i
$246$		0			0
$247$			3.00889i			0.191451i
$248$	−4.62671	+	0.455436i	−0.293796	+	0.0289202i
$249$		0			0
$250$	2.13511	−	6.52234i	0.135036	−	0.412509i
$251$	22.7077			1.43330			0.716650	−	0.697433i	$-0.245675\pi$
$251$	22.7077			1.43330			0.716650	+	0.697433i	$0.245675\pi$
$252$		0			0
$253$	−19.3710			−1.21784
$254$	6.50396	−	19.8683i	0.408095	−	1.24665i
$255$		0			0
$256$	−13.1078	+	9.17532i	−0.819235	+	0.573457i
$257$		−	9.24937i		−	0.576960i	−0.957486	−	0.288480i	$-0.906850\pi$
$257$		−	9.24937i		−	0.576960i	0.957486	−	0.288480i	$-0.0931499\pi$
$258$		0			0
$259$	0.681950	+	21.2934i	0.0423743	+	1.32311i
$260$	3.06314	−	27.9599i	0.189968	−	1.73400i
$261$		0			0
$262$	12.3030	+	4.02742i	0.760081	+	0.248815i
$263$			17.1809i			1.05942i	0.848179	+	0.529710i	$0.177699\pi$
$263$			17.1809i			1.05942i	−0.848179	+	0.529710i	$0.822301\pi$
$264$		0			0
$265$	−22.8301	+	13.1810i	−1.40244	+	0.809699i
$266$	0.647650	−	2.21598i	0.0397100	−	0.135871i
$267$		0			0
$268$	−6.58309	−	14.9627i	−0.402126	−	0.913992i
$269$	−6.56990	+	3.79313i	−0.400574	+	0.231271i	−0.686731	−	0.726911i	$-0.740955\pi$
$269$	−6.56990	+	3.79313i	−0.400574	+	0.231271i	0.286158	+	0.958182i	$0.407622\pi$
$270$		0			0
$271$	7.21584	−	12.4982i	0.438331	−	0.759212i	−0.559230	−	0.829013i	$-0.688903\pi$
$271$	7.21584	−	12.4982i	0.438331	−	0.759212i	0.997561	+	0.0698007i	$0.0222363\pi$
$272$	−12.0680	−	11.0599i	−0.731729	−	0.670604i
$273$		0			0
$274$	28.1645	+	9.21976i	1.70148	+	0.556986i
$275$			7.63227i			0.460243i
$276$		0			0
$277$	−7.47063			−0.448867			−0.224433	−	0.974489i	$-0.572053\pi$
$277$	−7.47063			−0.448867			−0.224433	+	0.974489i	$0.572053\pi$
$278$	1.81850	+	8.64887i	0.109066	+	0.518725i
$279$		0			0
$280$	−8.27419	+	19.9326i	−0.494477	+	1.19120i
$281$	1.25478	−	2.17335i	0.0748540	−	0.129651i	−0.826169	−	0.563423i	$-0.809484\pi$
$281$	1.25478	−	2.17335i	0.0748540	−	0.129651i	0.901023	+	0.433772i	$0.142818\pi$
$282$		0			0
$283$	−5.45325	+	9.44531i	−0.324162	+	0.561465i	−0.981342	−	0.192268i	$-0.938416\pi$
$283$	−5.45325	+	9.44531i	−0.324162	+	0.561465i	0.657180	+	0.753733i	$0.271749\pi$
$284$	−13.7849	+	18.7988i	−0.817985	+	1.11551i
$285$		0			0
$286$	−3.26472	−	15.5272i	−0.193047	−	0.918142i
$287$	0.311696	−	0.582148i	0.0183988	−	0.0343631i
$288$		0			0
$289$	−0.126337	+	0.218822i	−0.00743160	+	0.0128719i
$290$	−4.41812	−	4.92858i	−0.259441	−	0.289416i
$291$		0			0
$292$	−10.7106	−	1.17340i	−0.626793	−	0.0686680i
$293$	1.64025	−	0.947001i	0.0958246	−	0.0553244i	−0.451322	−	0.892361i	$-0.649047\pi$
$293$	1.64025	−	0.947001i	0.0958246	−	0.0553244i	0.547147	+	0.837037i	$0.315714\pi$
$294$		0			0
$295$	−3.80901	−	2.19913i	−0.221769	−	0.128038i
$296$	−22.6657	+	2.23113i	−1.31742	+	0.129682i
$297$		0			0
$298$	12.6785	+	4.15036i	0.734447	+	0.240424i
$299$	20.5287	+	35.5567i	1.18720	+	2.05630i
$300$		0			0
$301$	19.9034	−	0.637434i	1.14721	−	0.0367411i
$302$	−0.764980	+	2.33686i	−0.0440197	+	0.134471i
$303$		0			0
$304$	2.40955	+	0.534367i	0.138197	+	0.0306480i
$305$	−13.9611	−	24.1814i	−0.799413	−	1.38462i
$306$		0			0
$307$	−6.05907			−0.345809			−0.172905	−	0.984939i	$-0.555315\pi$
$307$	−6.05907			−0.345809			−0.172905	+	0.984939i	$0.555315\pi$
$308$	−0.937760	+	12.1382i	−0.0534338	+	0.691636i
$309$		0			0
$310$	−4.47481	−	4.99182i	−0.254152	−	0.283517i
$311$	8.17065	−	14.1520i	0.463315	−	0.802485i	−0.535809	−	0.844340i	$-0.679993\pi$
$311$	8.17065	−	14.1520i	0.463315	−	0.802485i	0.999124	+	0.0418540i	$0.0133264\pi$
$312$		0			0
$313$	7.76756	−	4.48460i	0.439049	−	0.253485i	−0.264145	−	0.964483i	$-0.585090\pi$
$313$	7.76756	−	4.48460i	0.439049	−	0.253485i	0.703194	+	0.710998i	$0.251757\pi$
$314$	−21.1109	−	23.5500i	−1.19136	−	1.32900i
$315$		0			0
$316$	4.72074	+	0.517178i	0.265562	+	0.0290936i
$317$	11.9737	+	20.7391i	0.672511	+	1.16482i	0.977190	+	0.212367i	$0.0681174\pi$
$317$	11.9737	+	20.7391i	0.672511	+	1.16482i	−0.304679	+	0.952455i	$0.598549\pi$
$318$		0			0
$319$	−3.23356	−	1.86689i	−0.181044	−	0.104526i
$320$	−21.8466	−	7.41857i	−1.22126	−	0.414711i
$321$		0			0
$322$	−7.46552	−	30.6055i	−0.416037	−	1.70558i
$323$			2.52507i			0.140499i
$324$		0			0
$325$	14.0095	−	8.08840i	0.777108	−	0.448664i
$326$	−7.91615	−	8.83076i	−0.438435	−	0.489091i
$327$		0			0
$328$	0.642995	+	0.291379i	0.0355035	+	0.0160887i
$329$	6.88416	+	3.68594i	0.379536	+	0.203212i
$330$		0			0
$331$	−1.77373	+	1.02407i	−0.0974932	+	0.0562877i	−0.547954	−	0.836509i	$-0.684593\pi$
$331$	−1.77373	+	1.02407i	−0.0974932	+	0.0562877i	0.450461	+	0.892796i	$0.351260\pi$
$332$	−12.9296	+	5.68861i	−0.709605	+	0.312203i
$333$		0			0
$334$	−1.63339	−	7.76847i	−0.0893749	−	0.425072i
$335$	11.7860	−	20.4139i	0.643937	−	1.11533i
$336$		0			0
$337$	−9.20885	−	15.9502i	−0.501638	−	0.868863i	−0.999998	−	0.00189247i	$-0.999398\pi$
$337$	−9.20885	−	15.9502i	−0.501638	−	0.868863i	0.498360	−	0.866970i	$-0.333936\pi$
$338$	−11.3518	+	10.1760i	−0.617454	+	0.553503i
$339$		0			0
$340$	2.57060	−	23.4641i	0.139410	−	1.27252i
$341$	−3.27505	−	1.89085i	−0.177354	−	0.102395i
$342$		0			0
$343$	1.77607	+	18.4349i	0.0958987	+	0.995391i
$344$	2.08549	+	21.1862i	0.112442	+	1.14228i
$345$		0			0
$346$	−15.6639	+	3.29346i	−0.842095	+	0.177058i
$347$	3.05104	+	1.76152i	0.163789	+	0.0945634i	0.579654	−	0.814863i	$-0.303188\pi$
$347$	3.05104	+	1.76152i	0.163789	+	0.0945634i	−0.415865	+	0.909426i	$0.636521\pi$
$348$		0			0
$349$	28.0774	+	16.2105i	1.50295	+	0.867727i	0.999994	+	0.00341285i	$0.00108635\pi$
$349$	28.0774	+	16.2105i	1.50295	+	0.867727i	0.502953	+	0.864314i	$0.332247\pi$
$350$	−12.0587	+	2.94145i	−0.644565	+	0.157227i
$351$		0			0
$352$	−13.0141	−	0.143149i	−0.693655	−	0.00762987i
$353$			10.2823i			0.547270i	0.961834	+	0.273635i	$0.0882261\pi$
$353$			10.2823i			0.547270i	−0.961834	+	0.273635i	$0.911774\pi$
$354$		0			0
$355$	−33.6147			−1.78409
$356$	−11.2051	−	25.4679i	−0.593867	−	1.34980i
$357$		0			0
$358$	2.99512	−	0.629750i	0.158297	−	0.0332833i
$359$	−28.6039	−	16.5145i	−1.50966	−	0.871600i	−0.999937	−	0.0112597i	$-0.996416\pi$
$359$	−28.6039	−	16.5145i	−1.50966	−	0.871600i	−0.509720	−	0.860341i	$-0.670251\pi$
$360$		0			0
$361$	9.30964	+	16.1248i	0.489981	+	0.848672i
$362$	0.782602	−	2.39069i	0.0411326	−	0.125652i
$363$		0			0
$364$	23.2742	−	11.1423i	1.21990	−	0.584014i
$365$	−7.76851	−	13.4555i	−0.406623	−	0.704291i
$366$		0			0
$367$	−32.2874			−1.68539			−0.842694	−	0.538393i	$-0.819032\pi$
$367$	−32.2874			−1.68539			−0.842694	+	0.538393i	$0.819032\pi$
$368$	32.1200	−	10.1248i	1.67437	−	0.527793i
$369$		0			0
$370$	−21.9216	−	24.4544i	−1.13965	−	1.27132i
$371$	−21.3206	−	11.4155i	−1.10691	−	0.592666i
$372$		0			0
$373$	18.9378			0.980562			0.490281	−	0.871564i	$-0.336894\pi$
$373$	18.9378			0.980562			0.490281	+	0.871564i	$0.336894\pi$
$374$	−2.73977	−	13.0305i	−0.141670	−	0.673790i
$375$		0			0
$376$	−3.44569	+	7.60369i	−0.177698	+	0.392130i
$377$			7.91386i			0.407585i
$378$		0			0
$379$		−	13.4461i		−	0.690679i	−0.938478	−	0.345340i	$-0.887764\pi$
$379$		−	13.4461i		−	0.690679i	0.938478	−	0.345340i	$-0.112236\pi$
$380$	1.43324	+	3.25760i	0.0735236	+	0.167112i
$381$		0			0
$382$	−7.07696	+	1.48799i	−0.362089	+	0.0761322i
$383$	−1.26005			−0.0643853			−0.0321927	−	0.999482i	$-0.510249\pi$
$383$	−1.26005			−0.0643853			−0.0321927	+	0.999482i	$0.510249\pi$
$384$		0			0
$385$	−14.9145	+	9.25978i	−0.760115	+	0.471922i
$386$	7.60935	−	6.82124i	0.387306	−	0.347192i
$387$		0			0
$388$	−9.66109	−	21.9587i	−0.490467	−	1.11478i
$389$	−7.89072			−0.400075			−0.200038	−	0.979788i	$-0.564106\pi$
$389$	−7.89072			−0.400075			−0.200038	+	0.979788i	$0.564106\pi$
$390$		0			0
$391$	17.2278	+	29.8393i	0.871245	+	1.50904i
$392$	−19.5393	+	3.19638i	−0.986882	+	0.161442i
$393$		0			0
$394$	−5.84273	−	1.91264i	−0.294352	−	0.0963573i
$395$	3.42399	+	5.93052i	0.172280	+	0.298397i
$396$		0			0
$397$	0.706070	+	0.407650i	0.0354366	+	0.0204593i	0.517614	−	0.855614i	$-0.326820\pi$
$397$	0.706070	+	0.407650i	0.0354366	+	0.0204593i	−0.482177	+	0.876074i	$0.660154\pi$
$398$	5.98115	+	28.4466i	0.299808	+	1.42590i
$399$		0			0
$400$	−3.98923	−	12.6554i	−0.199461	−	0.632771i
$401$	−9.69896			−0.484343			−0.242171	−	0.970233i	$-0.577860\pi$
$401$	−9.69896			−0.484343			−0.242171	+	0.970233i	$0.577860\pi$
$402$		0			0
$403$			8.01542i			0.399276i
$404$	−4.82958	+	6.58621i	−0.240280	+	0.327676i
$405$		0			0
$406$	1.70342	−	5.82839i	0.0845395	−	0.289258i
$407$	−16.0441	−	9.26307i	−0.795277	−	0.459153i
$408$		0			0
$409$	−7.14429	−	4.12476i	−0.353262	−	0.203956i	0.312859	−	0.949800i	$-0.398713\pi$
$409$	−7.14429	−	4.12476i	−0.353262	−	0.203956i	−0.666121	+	0.745844i	$0.732047\pi$
$410$	0.209453	+	0.996168i	0.0103441	+	0.0491973i
$411$		0			0
$412$	−10.3075	−	7.55836i	−0.507815	−	0.372374i
$413$	−0.129159	−	4.03289i	−0.00635548	−	0.198445i
$414$		0			0
$415$	−17.6402	−	10.1845i	−0.865921	−	0.499940i
$416$	13.5291	+	24.0400i	0.663321	+	1.17866i
$417$		0			0
$418$	1.34008	+	1.49491i	0.0655453	+	0.0731182i
$419$	3.43548	+	5.95043i	0.167834	+	0.290698i	0.937658	−	0.347559i	$-0.112989\pi$
$419$	3.43548	+	5.95043i	0.167834	+	0.290698i	−0.769824	+	0.638256i	$0.779656\pi$
$420$		0			0
$421$	12.0431	−	20.8593i	0.586947	−	1.01662i	−0.407683	−	0.913124i	$-0.633663\pi$
$421$	12.0431	−	20.8593i	0.586947	−	1.01662i	0.994630	−	0.103498i	$-0.0330036\pi$
$422$	6.97637	−	1.46684i	0.339604	−	0.0714047i
$423$		0			0
$424$	10.6715	−	23.5490i	0.518252	−	1.14364i
$425$	11.7568	−	6.78781i	0.570290	−	0.329257i
$426$		0			0
$427$	12.0912	−	22.5826i	0.585136	−	1.09285i
$428$	−4.70898	−	10.7030i	−0.227617	−	0.517350i
$429$		0			0
$430$	−22.8581	+	20.4906i	−1.10231	+	0.988146i
$431$	−30.1452	+	17.4043i	−1.45204	+	0.838337i	−0.998597	−	0.0529473i	$-0.983138\pi$
$431$	−30.1452	+	17.4043i	−1.45204	+	0.838337i	−0.453445	+	0.891284i	$0.649805\pi$
$432$		0			0
$433$			17.6046i			0.846022i	0.906125	+	0.423011i	$0.139027\pi$
$433$			17.6046i			0.846022i	−0.906125	+	0.423011i	$0.860973\pi$
$434$	1.72528	−	5.90319i	0.0828162	−	0.283362i
$435$		0			0
$436$	−3.05899	+	27.9220i	−0.146499	+	1.33722i
$437$	−4.49901	−	2.59751i	−0.215217	−	0.124256i
$438$		0			0
$439$	1.73743	+	3.00931i	0.0829228	+	0.143626i	0.904504	−	0.426465i	$-0.140241\pi$
$439$	1.73743	+	3.00931i	0.0829228	+	0.143626i	−0.821581	+	0.570091i	$0.806908\pi$
$440$	−10.9307	−	15.2556i	−0.521102	−	0.727281i
$441$		0			0
$442$	−21.0148	+	18.8383i	−0.999571	+	0.896044i
$443$	−11.6348	+	6.71735i	−0.552786	+	0.319151i	−0.750245	−	0.661160i	$-0.770064\pi$
$443$	−11.6348	+	6.71735i	−0.552786	+	0.319151i	0.197459	+	0.980311i	$0.436731\pi$
$444$		0			0
$445$	20.0609	−	34.7464i	0.950976	−	1.64714i
$446$	26.3538	−	23.6243i	1.24789	−	1.11864i
$447$		0			0
$448$	−4.78943	−	20.6170i	−0.226279	−	0.974062i
$449$	−13.7666			−0.649687			−0.324843	−	0.945768i	$-0.605312\pi$
$449$	−13.7666			−0.649687			−0.324843	+	0.945768i	$0.605312\pi$
$450$		0			0
$451$	0.287115	+	0.497298i	0.0135197	+	0.0234169i
$452$	1.70116	−	15.5280i	0.0800159	−	0.730375i
$453$		0			0
$454$	14.9203	+	4.88422i	0.700246	+	0.229228i
$455$	32.8028	+	17.5634i	1.53782	+	0.823385i
$456$		0			0
$457$	13.2983	+	23.0333i	0.622068	+	1.07745i	0.989100	+	0.147244i	$0.0470404\pi$
$457$	13.2983	+	23.0333i	0.622068	+	1.07745i	−0.367033	+	0.930208i	$0.619626\pi$
$458$	−10.8925	+	33.2743i	−0.508971	+	1.55481i
$459$		0			0
$460$	39.1625	+	28.7173i	1.82596	+	1.33895i
$461$	22.4719	+	12.9742i	1.04662	+	0.604268i	0.921702	−	0.387899i	$-0.126799\pi$
$461$	22.4719	+	12.9742i	1.04662	+	0.604268i	0.124921	+	0.992167i	$0.460132\pi$
$462$		0			0
$463$	−8.26087	+	4.76941i	−0.383915	+	0.221653i	−0.679520	−	0.733657i	$-0.737812\pi$
$463$	−8.26087	+	4.76941i	−0.383915	+	0.221653i	0.295605	+	0.955310i	$0.404479\pi$
$464$	6.33750	+	1.40547i	0.294211	+	0.0652474i
$465$		0			0
$466$	−19.9319	+	17.8675i	−0.923325	+	0.827695i
$467$	3.31730	−	5.74573i	0.153506	−	0.265880i	−0.779008	−	0.627014i	$-0.784277\pi$
$467$	3.31730	−	5.74573i	0.153506	−	0.265880i	0.932514	+	0.361134i	$0.117610\pi$
$468$		0			0
$469$	21.6138	−	0.692210i	0.998031	−	0.0319633i
$470$	−11.7801	+	2.47687i	−0.543376	+	0.114249i
$471$		0			0
$472$	4.29280	−	0.422568i	0.197592	−	0.0194503i
$473$	−8.65840	+	14.9968i	−0.398114	+	0.689553i
$474$		0			0
$475$	−1.02343	+	1.77263i	−0.0469582	+	0.0813339i
$476$	19.5318	−	9.35063i	0.895238	−	0.428586i
$477$		0			0
$478$	7.83984	−	1.64839i	0.358586	−	0.0753957i
$479$	−27.9090			−1.27520			−0.637598	−	0.770369i	$-0.720072\pi$
$479$	−27.9090			−1.27520			−0.637598	+	0.770369i	$0.720072\pi$
$480$		0			0
$481$			39.2666i			1.79040i
$482$	2.84907	−	8.70335i	0.129772	−	0.396427i
$483$		0			0
$484$	9.20391	+	6.74910i	0.418359	+	0.306777i
$485$	17.2966	−	29.9586i	0.785400	−	1.36035i
$486$		0			0
$487$	−32.6742	+	18.8645i	−1.48061	+	0.854831i	−0.999759	−	0.0219714i	$-0.993006\pi$
$487$	−32.6742	+	18.8645i	−1.48061	+	0.854831i	−0.480851	+	0.876802i	$0.659672\pi$
$488$	24.9429	+	11.3031i	1.12911	+	0.511668i
$489$		0			0
$490$	−20.3781	−	19.9957i	−0.920590	−	0.903315i
$491$	−2.27638	+	1.31427i	−0.102732	+	0.0593121i	−0.550486	−	0.834845i	$-0.685557\pi$
$491$	−2.27638	+	1.31427i	−0.102732	+	0.0593121i	0.447754	+	0.894157i	$0.352224\pi$
$492$		0			0
$493$			6.64134i			0.299111i
$494$	1.32383	−	4.04404i	0.0595620	−	0.181950i
$495$		0			0
$496$	6.41882	+	1.42351i	0.288214	+	0.0639174i
$497$	−16.2660	−	26.1993i	−0.729630	−	1.17520i
$498$		0			0
$499$		−	30.8820i		−	1.38247i	−0.722631	−	0.691234i	$-0.757067\pi$
$499$		−	30.8820i		−	1.38247i	0.722631	−	0.691234i	$-0.242933\pi$
$500$	−5.73932	+	7.82684i	−0.256670	+	0.350027i
$501$		0			0
$502$	−30.5199	−	9.99081i	−1.36217	−	0.445912i
$503$	19.7686			0.881436			0.440718	−	0.897646i	$-0.354724\pi$
$503$	19.7686			0.881436			0.440718	+	0.897646i	$0.354724\pi$
$504$		0			0
$505$	−11.7770			−0.524069
$506$	26.0353	+	8.52273i	1.15741	+	0.378882i
$507$		0			0
$508$	−17.4831	+	23.8421i	−0.775686	+	1.05782i
$509$			24.8342i			1.10076i	0.834915	+	0.550379i	$0.185517\pi$
$509$			24.8342i			1.10076i	−0.834915	+	0.550379i	$0.814483\pi$
$510$		0			0
$511$	6.72803	−	12.5658i	0.297630	−	0.555878i
$512$	21.6542	−	6.56485i	0.956988	−	0.290128i
$513$		0			0
$514$	−4.06948	+	12.4315i	−0.179497	+	0.548328i
$515$		−	18.4312i		−	0.812174i
$516$		0			0
$517$	−5.88076	+	3.39526i	−0.258636	+	0.149323i
$518$	8.45197	−	28.9190i	0.371358	−	1.27063i
$519$		0			0
$520$	−16.4186	+	36.2314i	−0.720003	+	1.58885i
$521$	28.0791	−	16.2115i	1.23017	−	0.710238i	0.263104	−	0.964768i	$-0.415254\pi$
$521$	28.0791	−	16.2115i	1.23017	−	0.710238i	0.967065	+	0.254529i	$0.0819205\pi$
$522$		0			0
$523$	3.72094	−	6.44486i	0.162705	−	0.281814i	−0.773133	−	0.634244i	$-0.781311\pi$
$523$	3.72094	−	6.44486i	0.162705	−	0.281814i	0.935838	+	0.352430i	$0.114645\pi$
$524$	−14.7636	−	10.8260i	−0.644953	−	0.472935i
$525$		0			0
$526$	7.55915	−	23.0917i	0.329595	−	1.00685i
$527$			6.72657i			0.293014i
$528$		0			0
$529$	−47.8878			−2.08208
$530$	36.4836	−	7.67099i	1.58475	−	0.333207i
$531$		0			0
$532$	−1.84544	+	2.69340i	−0.0800098	+	0.116774i
$533$	0.608548	−	1.05404i	0.0263592	−	0.0456554i
$534$		0			0
$535$	8.43067	−	14.6023i	0.364490	−	0.631314i
$536$	2.26470	+	23.0067i	0.0978201	+	0.993739i
$537$		0			0
$538$	10.4990	−	2.20751i	0.452645	−	0.0951725i
$539$	−14.4341	−	7.14361i	−0.621722	−	0.307697i
$540$		0			0
$541$	−14.4680	+	25.0594i	−0.622030	+	1.07739i	0.367078	+	0.930190i	$0.380358\pi$
$541$	−14.4680	+	25.0594i	−0.622030	+	1.07739i	−0.989107	+	0.147197i	$0.952975\pi$
$542$	−15.1972	+	13.6232i	−0.652776	+	0.585167i
$543$		0			0
$544$	11.3537	+	20.1744i	0.486786	+	0.864972i
$545$	−35.0776	+	20.2521i	−1.50256	+	0.867504i
$546$		0			0
$547$	−12.0358	−	6.94888i	−0.514614	−	0.297113i	0.220114	−	0.975474i	$-0.429357\pi$
$547$	−12.0358	−	6.94888i	−0.514614	−	0.297113i	−0.734728	+	0.678361i	$0.762690\pi$
$548$	−33.7976	−	24.7833i	−1.44376	−	1.05869i
$549$		0			0
$550$	3.35800	−	10.2580i	0.143185	−	0.437403i
$551$	−0.500673	−	0.867191i	−0.0213294	−	0.0369436i
$552$		0			0
$553$	−2.96539	+	5.53840i	−0.126101	+	0.235517i
$554$	10.0408	+	3.28688i	0.426592	+	0.139646i
$555$		0			0
$556$	1.36116	−	12.4245i	0.0577259	−	0.526914i
$557$	−3.43086	−	5.94243i	−0.145370	−	0.251789i	0.784141	−	0.620583i	$-0.213104\pi$
$557$	−3.43086	−	5.94243i	−0.145370	−	0.251789i	−0.929511	+	0.368794i	$0.879771\pi$
$558$		0			0
$559$	36.7034			1.55239
$560$	19.8906	−	23.1496i	0.840531	−	0.978249i
$561$		0			0
$562$	−2.64268	+	2.36898i	−0.111475	+	0.0999293i
$563$	19.8978	−	34.4640i	0.838593	−	1.45249i	−0.0524789	−	0.998622i	$-0.516712\pi$
$563$	19.8978	−	34.4640i	0.838593	−	1.45249i	0.891071	−	0.453863i	$-0.149954\pi$
$564$		0			0
$565$	19.5073	−	11.2626i	0.820680	−	0.473820i
$566$	11.4850	−	10.2955i	0.482752	−	0.432753i
$567$		0			0
$568$	26.7984	−	19.2012i	1.12444	−	0.805666i
$569$	−0.133857	−	0.231848i	−0.00561159	−	0.00971956i	0.863206	−	0.504852i	$-0.168453\pi$
$569$	−0.133857	−	0.231848i	−0.00561159	−	0.00971956i	−0.868818	+	0.495132i	$0.835120\pi$
$570$		0			0
$571$	28.5925	+	16.5079i	1.19656	+	0.690834i	0.959786	−	0.280732i	$-0.0905771\pi$
$571$	28.5925	+	16.5079i	1.19656	+	0.690834i	0.236772	+	0.971565i	$0.423910\pi$
$572$	−2.44366	+	22.3054i	−0.102175	+	0.932638i
$573$		0			0
$574$	−0.675060	+	0.645288i	−0.0281764	+	0.0269338i
$575$			27.9301i			1.16477i
$576$		0			0
$577$	2.15927	−	1.24665i	0.0898915	−	0.0518989i	−0.454380	−	0.890808i	$-0.650139\pi$
$577$	2.15927	−	1.24665i	0.0898915	−	0.0518989i	0.544272	+	0.838909i	$0.316806\pi$
$578$	0.266077	−	0.238519i	0.0110674	−	0.00992110i
$579$		0			0
$580$	3.76965	+	8.56803i	0.156526	+	0.355768i
$581$	−0.598155	−	18.6770i	−0.0248157	−	0.774851i
$582$		0			0
$583$	18.2130	−	10.5153i	0.754306	−	0.435499i
$584$	13.8792	+	6.28949i	0.574325	+	0.260261i
$585$		0			0
$586$	−2.62121	+	0.551131i	−0.108281	+	0.0227670i
$587$	2.07534	−	3.59459i	0.0856583	−	0.148365i	−0.820013	−	0.572345i	$-0.806034\pi$
$587$	2.07534	−	3.59459i	0.0856583	−	0.148365i	0.905672	+	0.423980i	$0.139367\pi$
$588$		0			0
$589$	−0.507098	−	0.878319i	−0.0208946	−	0.0361905i
$590$	4.15187	+	4.63157i	0.170930	+	0.190679i
$591$		0			0
$592$	31.4451	+	6.97361i	1.29239	+	0.286613i
$593$	10.8901	+	6.28739i	0.447202	+	0.258192i	0.706648	−	0.707565i	$-0.250207\pi$
$593$	10.8901	+	6.28739i	0.447202	+	0.258192i	−0.259446	+	0.965758i	$0.583540\pi$
$594$		0			0
$595$	27.5282	+	14.7393i	1.12855	+	0.604251i
$596$	−15.2143	−	11.1564i	−0.623202	−	0.456985i
$597$		0			0
$598$	−11.9472	−	56.8215i	−0.488557	−	2.32360i
$599$	−5.00849	−	2.89165i	−0.204641	−	0.118150i	0.394177	−	0.919034i	$-0.371030\pi$
$599$	−5.00849	−	2.89165i	−0.204641	−	0.118150i	−0.598819	+	0.800885i	$0.704363\pi$
$600$		0			0
$601$	−22.7080	−	13.1105i	−0.926280	−	0.534788i	−0.0406466	−	0.999174i	$-0.512942\pi$
$601$	−22.7080	−	13.1105i	−0.926280	−	0.534788i	−0.885633	+	0.464386i	$0.846275\pi$
$602$	−27.0313	−	7.90025i	−1.10171	−	0.321990i
$603$		0			0
$604$	2.05632	−	2.80425i	0.0836703	−	0.114103i
$605$			16.4578i			0.669103i
$606$		0			0
$607$	−1.67256			−0.0678871			−0.0339436	−	0.999424i	$-0.510807\pi$
$607$	−1.67256			−0.0678871			−0.0339436	+	0.999424i	$0.510807\pi$
$608$	−3.00340	−	1.77834i	−0.121804	−	0.0721213i
$609$		0			0
$610$	8.12505	+	38.6431i	0.328973	+	1.56461i
$611$	12.4644	+	7.19635i	0.504257	+	0.291133i
$612$		0			0
$613$	−20.0588	−	34.7428i	−0.810166	−	1.40325i	−0.912748	−	0.408524i	$-0.866044\pi$
$613$	−20.0588	−	34.7428i	−0.810166	−	1.40325i	0.102582	−	0.994725i	$-0.467290\pi$
$614$	8.14358	+	2.66583i	0.328648	+	0.107584i
$615$		0			0
$616$	6.60085	−	15.9015i	0.265956	−	0.640690i
$617$	1.39950	+	2.42400i	0.0563416	+	0.0975865i	0.892821	−	0.450413i	$-0.148723\pi$
$617$	1.39950	+	2.42400i	0.0563416	+	0.0975865i	−0.836479	+	0.547999i	$0.815390\pi$
$618$		0			0
$619$	24.9098			1.00121			0.500605	−	0.865676i	$-0.333111\pi$
$619$	24.9098			1.00121			0.500605	+	0.865676i	$0.333111\pi$
$620$	3.81802	+	8.67798i	0.153336	+	0.348516i
$621$		0			0
$622$	−17.2081	+	15.4259i	−0.689983	+	0.618520i
$623$	36.7887	−	1.17821i	1.47391	−	0.0472039i
$624$		0			0
$625$	−30.5820			−1.22328
$626$	−12.4130	+	2.60993i	−0.496122	+	0.104314i
$627$		0			0
$628$	18.0124	+	40.9403i	0.718772	+	1.63369i
$629$			32.9527i			1.31391i
$630$		0			0
$631$			24.4900i			0.974933i	0.873142	+	0.487466i	$0.162079\pi$
$631$			24.4900i			0.974933i	−0.873142	+	0.487466i	$0.837921\pi$
$632$	−6.11728	−	2.77211i	−0.243332	−	0.110268i
$633$		0			0
$634$	−6.96841	−	33.1421i	−0.276751	−	1.31624i
$635$	−42.6327			−1.69183
$636$		0			0
$637$	2.18422	+	34.0653i	0.0865418	+	1.34972i
$638$	3.52462	+	3.93185i	0.139541	+	0.155663i
$639$		0			0
$640$	26.0985	+	19.5827i	1.03164	+	0.774075i
$641$	7.93158			0.313279			0.156639	−	0.987656i	$-0.449934\pi$
$641$	7.93158			0.313279			0.156639	+	0.987656i	$0.449934\pi$
$642$		0			0
$643$	11.6480	+	20.1750i	0.459354	+	0.795625i	0.998927	−	0.0463143i	$-0.0147476\pi$
$643$	11.6480	+	20.1750i	0.459354	+	0.795625i	−0.539573	+	0.841939i	$0.681414\pi$
$644$	−3.43171	+	44.4194i	−0.135229	+	1.75037i
$645$		0			0
$646$	1.11096	−	3.39378i	0.0437103	−	0.133526i
$647$	−14.6952	−	25.4529i	−0.577729	−	1.00066i	−0.995739	−	0.0922139i	$-0.970606\pi$
$647$	−14.6952	−	25.4529i	−0.577729	−	1.00066i	0.418010	−	0.908442i	$-0.362728\pi$
$648$		0			0
$649$	3.03869	+	1.75439i	0.119279	+	0.0688658i
$650$	−22.3879	+	4.70725i	−0.878127	+	0.184634i
$651$		0			0
$652$	6.75426	+	15.3517i	0.264517	+	0.601220i
$653$	46.1517			1.80606			0.903028	−	0.429582i	$-0.141339\pi$
$653$	46.1517			1.80606			0.903028	+	0.429582i	$0.141339\pi$
$654$		0			0
$655$		−	26.3993i		−	1.03151i
$656$	−0.736007	−	0.674524i	−0.0287362	−	0.0263357i
$657$		0			0
$658$	−7.63081	−	7.98287i	−0.297480	−	0.311205i
$659$	13.7222	+	7.92254i	0.534543	+	0.308618i	0.742864	−	0.669442i	$-0.233467\pi$
$659$	13.7222	+	7.92254i	0.534543	+	0.308618i	−0.208322	+	0.978060i	$0.566800\pi$
$660$		0			0
$661$	11.5391	+	6.66210i	0.448819	+	0.259126i	0.707331	−	0.706882i	$-0.249899\pi$
$661$	11.5391	+	6.66210i	0.448819	+	0.259126i	−0.258512	+	0.966008i	$0.583232\pi$
$662$	2.83452	−	0.595981i	0.110167	−	0.0231635i
$663$		0			0
$664$	19.8807	−	1.95698i	0.771520	−	0.0759456i
$665$	−4.70564	+	0.150705i	−0.182477	+	0.00584407i
$666$		0			0
$667$	−11.8331	−	6.83186i	−0.458181	−	0.264531i
$668$	−1.22260	+	11.1597i	−0.0473038	+	0.431783i
$669$		0			0
$670$	−24.8223	+	22.2514i	−0.958970	+	0.859648i
$671$	11.1377	+	19.2911i	0.429966	+	0.744724i
$672$		0			0
$673$	6.69218	−	11.5912i	0.257965	−	0.446808i	−0.707732	−	0.706481i	$-0.750282\pi$
$673$	6.69218	−	11.5912i	0.257965	−	0.446808i	0.965697	+	0.259673i	$0.0836149\pi$
$674$	5.35933	+	25.4892i	0.206434	+	0.981809i
$675$		0			0
$676$	19.7343	−	8.68245i	0.759012	−	0.333940i
$677$	4.05452	−	2.34088i	0.155828	−	0.0899672i	−0.420059	−	0.907497i	$-0.637990\pi$
$677$	4.05452	−	2.34088i	0.155828	−	0.0899672i	0.575886	+	0.817530i	$0.304657\pi$
$678$		0			0
$679$	31.7195	−	1.01586i	1.21728	−	0.0389851i
$680$	−13.7785	+	30.4055i	−0.528383	+	1.16600i
$681$		0			0
$682$	3.56985	+	3.98230i	0.136697	+	0.152490i
$683$	31.2594	−	18.0476i	1.19611	−	0.690573i	0.236422	−	0.971650i	$-0.424025\pi$
$683$	31.2594	−	18.0476i	1.19611	−	0.690573i	0.959685	+	0.281078i	$0.0906918\pi$
$684$		0			0
$685$		−	60.4344i		−	2.30908i
$686$	5.72378	−	25.5585i	0.218535	−	0.975829i
$687$		0			0
$688$	6.51839	−	29.3924i	0.248511	−	1.12058i
$689$	−38.6030	−	22.2875i	−1.47066	−	0.849084i
$690$		0			0
$691$	4.37292	+	7.57411i	0.166354	+	0.288133i	0.937135	−	0.348967i	$-0.113467\pi$
$691$	4.37292	+	7.57411i	0.166354	+	0.288133i	−0.770782	+	0.637099i	$0.780134\pi$
$692$	22.5018	+	2.46517i	0.855390	+	0.0937119i
$693$		0			0
$694$	−3.32568	−	3.70992i	−0.126241	−	0.140827i
$695$	15.6085	−	9.01156i	0.592063	−	0.341828i
$696$		0			0
$697$	0.510696	−	0.884552i	0.0193440	−	0.0335048i
$698$	−30.6047	−	34.1407i	−1.15841	−	1.29224i
$699$		0			0
$700$	17.5014	+	1.35211i	0.661492	+	0.0511050i
$701$	−40.7123			−1.53768			−0.768841	−	0.639440i	$-0.779166\pi$
$701$	−40.7123			−1.53768			−0.768841	+	0.639440i	$0.779166\pi$
$702$		0			0
$703$	−2.48421	−	4.30279i	−0.0936939	−	0.162283i
$704$	17.4284	+	5.91827i	0.656859	+	0.223053i
$705$		0			0
$706$	4.52393	−	13.8197i	0.170260	−	0.520112i
$707$	−5.69883	−	9.17898i	−0.214326	−	0.345211i
$708$		0			0
$709$	−9.47395	−	16.4094i	−0.355802	−	0.616267i	0.631453	−	0.775414i	$-0.282459\pi$
$709$	−9.47395	−	16.4094i	−0.355802	−	0.616267i	−0.987255	+	0.159147i	$0.949125\pi$
$710$	45.1793	+	14.7896i	1.69555	+	0.555044i
$711$		0			0
$712$	3.85474	+	39.1597i	0.144462	+	1.46757i
$713$	−11.9850	−	6.91953i	−0.448841	−	0.259139i
$714$		0			0
$715$	−28.0217	+	16.1783i	−1.04795	+	0.605035i
$716$	−4.30262	−	0.471371i	−0.160796	−	0.0176160i
$717$		0			0
$718$	31.1786	+	34.7809i	1.16358	+	1.29801i
$719$	−9.16079	+	15.8669i	−0.341640	+	0.591737i	−0.984737	−	0.174047i	$-0.944316\pi$
$719$	−9.16079	+	15.8669i	−0.341640	+	0.591737i	0.643098	+	0.765784i	$0.277649\pi$
$720$		0			0
$721$	14.3652	−	8.91875i	0.534989	−	0.332151i
$722$	−5.41798	−	25.7682i	−0.201637	−	0.958994i
$723$		0			0
$724$	−2.10368	+	2.86884i	−0.0781828	+	0.106620i
$725$	−2.69179	+	4.66231i	−0.0999704	+	0.173154i
$726$		0			0
$727$	24.7364	−	42.8448i	0.917424	−	1.58902i	0.114110	−	0.993468i	$-0.463598\pi$
$727$	24.7364	−	42.8448i	0.917424	−	1.58902i	0.803314	−	0.595556i	$-0.203068\pi$
$728$	−36.1836	+	4.73554i	−1.34105	+	0.175511i
$729$		0			0
$730$	4.52109	+	21.5025i	0.167333	+	0.795844i
$731$	30.8016			1.13924
$732$		0			0
$733$		−	28.1521i		−	1.03982i	−0.854220	−	0.519911i	$-0.825965\pi$
$733$		−	28.1521i		−	1.03982i	0.854220	−	0.519911i	$-0.174035\pi$
$734$	43.3953	+	14.2056i	1.60175	+	0.524338i
$735$		0			0
$736$	−47.6250	−	0.523851i	−1.75548	−	0.0193094i
$737$	−9.40243	+	16.2855i	−0.346343	+	0.599884i
$738$		0			0
$739$	−0.274010	+	0.158200i	−0.0100796	+	0.00581948i	−0.505031	−	0.863101i	$-0.668519\pi$
$739$	−0.274010	+	0.158200i	−0.0100796	+	0.00581948i	0.494952	+	0.868920i	$0.335186\pi$
$740$	18.7041	+	42.5124i	0.687575	+	1.56279i
$741$		0			0
$742$	23.6330	+	24.7234i	0.867595	+	0.907623i
$743$	−13.3820	+	7.72609i	−0.490937	+	0.283443i	−0.724963	−	0.688788i	$-0.758143\pi$
$743$	−13.3820	+	7.72609i	−0.490937	+	0.283443i	0.234026	+	0.972230i	$0.424810\pi$
$744$		0			0
$745$		−	27.2051i		−	0.996719i
$746$	−25.4530	−	8.33214i	−0.931901	−	0.305061i
$747$		0			0
$748$	−2.05073	+	18.7188i	−0.0749822	+	0.684428i
$749$	15.4606	−	0.495147i	0.564918	−	0.0180923i
$750$		0			0
$751$		−	47.1347i		−	1.71997i	−0.510318	−	0.859986i	$-0.670472\pi$
$751$		−	47.1347i		−	1.71997i	0.510318	−	0.859986i	$-0.329528\pi$
$752$	7.97654	−	8.70359i	0.290874	−	0.317387i
$753$		0			0
$754$	3.48189	−	10.6365i	0.126803	−	0.387358i
$755$	5.01435			0.182491
$756$		0			0
$757$	12.2405			0.444888			0.222444	−	0.974945i	$-0.428596\pi$
$757$	12.2405			0.444888			0.222444	+	0.974945i	$0.428596\pi$
$758$	−5.91593	+	18.0720i	−0.214876	+	0.656404i
$759$		0			0
$760$	−0.493059	−	5.00891i	−0.0178851	−	0.181692i
$761$		−	4.78888i		−	0.173597i	−0.996226	−	0.0867985i	$-0.972336\pi$
$761$		−	4.78888i		−	0.173597i	0.996226	−	0.0867985i	$-0.0276636\pi$
$762$		0			0
$763$	−32.7583	−	17.5396i	−1.18593	−	0.634976i
$764$	10.1663	+	1.11377i	0.367805	+	0.0402948i
$765$		0			0
$766$	1.69354	+	0.554387i	0.0611902	+	0.0200308i
$767$		−	7.43695i		−	0.268533i
$768$		0			0
$769$	−23.0936	+	13.3331i	−0.832775	+	0.480803i	−0.854802	−	0.518954i	$-0.826321\pi$
$769$	−23.0936	+	13.3331i	−0.832775	+	0.480803i	0.0220266	+	0.999757i	$0.492988\pi$
$770$	24.1197	−	5.88345i	0.869213	−	0.212025i
$771$		0			0
$772$	−13.2284	+	5.82005i	−0.476100	+	0.209468i
$773$	11.8079	−	6.81730i	0.424701	−	0.245201i	−0.272386	−	0.962188i	$-0.587813\pi$
$773$	11.8079	−	6.81730i	0.424701	−	0.245201i	0.697087	+	0.716987i	$0.254479\pi$
$774$		0			0
$775$	−2.72633	+	4.72214i	−0.0979326	+	0.169624i
$776$	3.32358	+	33.7638i	0.119310	+	1.21205i
$777$		0			0
$778$	10.6054	+	3.47171i	0.380221	+	0.124467i
$779$			0.154000i			0.00551762i
$780$		0			0
$781$	26.8167			0.959575
$782$	−10.0261	−	47.6848i	−0.358534	−	1.70520i
$783$		0			0
$784$	27.6677	+	4.30073i	0.988134	+	0.153597i
$785$	−32.2483	+	55.8556i	−1.15099	+	1.99357i
$786$		0			0
$787$	−23.0646	+	39.9490i	−0.822163	+	1.42403i	0.0819047	+	0.996640i	$0.473900\pi$
$787$	−23.0646	+	39.9490i	−0.822163	+	1.42403i	−0.904068	+	0.427389i	$0.859434\pi$
$788$	7.01130	+	5.14129i	0.249767	+	0.183151i
$789$		0			0
$790$	−1.99268	−	9.47728i	−0.0708963	−	0.337186i
$791$	18.2175	+	9.75410i	0.647741	+	0.346816i
$792$		0			0
$793$	23.6067	−	40.8879i	0.838297	−	1.45197i
$794$	−0.769626	−	0.858546i	−0.0273130	−	0.0304687i
$795$		0			0
$796$	4.47692	−	40.8648i	0.158680	−	1.44841i
$797$	−10.2839	+	5.93744i	−0.364276	+	0.210315i	−0.670955	−	0.741498i	$-0.734116\pi$
$797$	−10.2839	+	5.93744i	−0.364276	+	0.210315i	0.306679	+	0.951813i	$0.400782\pi$
$798$		0			0
$799$	10.4602	+	6.03920i	0.370055	+	0.213652i
$800$	−0.206400	+	18.7645i	−0.00729734	+	0.663424i
$801$		0			0
$802$	13.0357	+	4.26729i	0.460307	+	0.150683i
$803$	6.19744	+	10.7343i	0.218703	+	0.378805i
$804$		0			0
$805$	−54.5794	+	33.8860i	−1.92367	+	1.19432i
$806$	3.52657	−	10.7730i	0.124218	−	0.379462i
$807$		0			0
$808$	9.38887	−	6.72719i	0.330299	−	0.236662i
$809$	0.118023	+	0.204421i	0.00414946	+	0.00718707i	0.868093	−	0.496402i	$-0.165346\pi$
$809$	0.118023	+	0.204421i	0.00414946	+	0.00718707i	−0.863943	+	0.503589i	$0.832013\pi$
$810$		0			0
$811$	−38.4776			−1.35113			−0.675565	−	0.737300i	$-0.736100\pi$
$811$	−38.4776			−1.35113			−0.675565	+	0.737300i	$0.736100\pi$
$812$	−4.85380	+	7.08409i	−0.170335	+	0.248603i
$813$		0			0
$814$	17.4883	+	19.5088i	0.612964	+	0.683785i
$815$	−12.0924	+	20.9447i	−0.423579	+	0.733660i
$816$		0			0
$817$	−4.02191	+	2.32205i	−0.140709	+	0.0812383i
$818$	7.78737	+	8.68711i	0.272279	+	0.303738i
$819$		0			0
$820$	0.156777	−	1.43104i	0.00547487	−	0.0499740i
$821$	−5.77846	−	10.0086i	−0.201670	−	0.349302i	0.747397	−	0.664378i	$-0.231303\pi$
$821$	−5.77846	−	10.0086i	−0.201670	−	0.349302i	−0.949067	+	0.315076i	$0.897970\pi$
$822$		0			0
$823$	−13.9739	−	8.06786i	−0.487101	−	0.281228i	0.236270	−	0.971687i	$-0.424075\pi$
$823$	−13.9739	−	8.06786i	−0.487101	−	0.281228i	−0.723371	+	0.690460i	$0.757408\pi$
$824$	10.5282	+	14.6937i	0.366766	+	0.511880i
$825$		0			0
$826$	−1.60077	+	5.47715i	−0.0556979	+	0.190575i
$827$			38.7636i			1.34794i	0.738758	+	0.673971i	$0.235413\pi$
$827$			38.7636i			1.34794i	−0.738758	+	0.673971i	$0.764587\pi$
$828$		0			0
$829$	−37.3363	+	21.5561i	−1.29674	+	0.748675i	−0.979840	−	0.199782i	$-0.935976\pi$
$829$	−37.3363	+	21.5561i	−1.29674	+	0.748675i	−0.316904	+	0.948458i	$0.602643\pi$
$830$	19.2280	+	21.4496i	0.667414	+	0.744525i
$831$		0			0
$832$	−7.60665	−	38.2630i	−0.263713	−	1.32653i
$833$	1.83300	+	28.5877i	0.0635098	+	0.990507i
$834$		0			0
$835$	−14.0196	+	8.09424i	−0.485169	+	0.280113i
$836$	−1.14339	−	2.59880i	−0.0395449	−	0.0898814i
$837$		0			0
$838$	−1.99937	−	9.50910i	−0.0690670	−	0.328486i
$839$	−7.11267	+	12.3195i	−0.245557	+	0.425316i	−0.962288	−	0.272033i	$-0.912304\pi$
$839$	−7.11267	+	12.3195i	−0.245557	+	0.425316i	0.716731	+	0.697349i	$0.245637\pi$
$840$		0			0
$841$	13.1831	+	22.8339i	0.454591	+	0.787375i
$842$	−25.3639	+	22.7370i	−0.874099	+	0.783567i
$843$		0			0
$844$	−10.0218	−	1.09794i	−0.344966	−	0.0377926i
$845$	26.9239	+	15.5445i	0.926211	+	0.534748i
$846$		0			0
$847$	−12.8272	+	7.96383i	−0.440747	+	0.273640i
$848$	−24.7037	+	26.9555i	−0.848330	+	0.925655i
$849$		0			0
$850$	−18.7880	+	3.95034i	−0.644424	+	0.135496i
$851$	−58.7131	−	33.8980i	−2.01266	−	1.16201i
$852$		0			0
$853$	0.104188	+	0.0601528i	0.00356732	+	0.00205959i	0.501783	−	0.864994i	$-0.332678\pi$
$853$	0.104188	+	0.0601528i	0.00356732	+	0.00205959i	−0.498215	+	0.867053i	$0.666011\pi$
$854$	−26.1868	+	25.0319i	−0.896092	+	0.856573i
$855$		0			0
$856$	1.61997	+	16.4570i	0.0553694	+	0.562489i
$857$		−	37.2946i		−	1.27396i	−0.770880	−	0.636980i	$-0.780183\pi$
$857$		−	37.2946i		−	1.27396i	0.770880	−	0.636980i	$-0.219817\pi$
$858$		0			0
$859$	47.6470			1.62569			0.812847	−	0.582477i	$-0.197917\pi$
$859$	47.6470			1.62569			0.812847	+	0.582477i	$0.197917\pi$
$860$	39.7373	−	17.4831i	1.35503	−	0.596169i
$861$		0			0
$862$	48.1735	−	10.1289i	1.64080	−	0.344992i
$863$	−22.9114	−	13.2279i	−0.779913	−	0.450283i	0.0564863	−	0.998403i	$-0.482010\pi$
$863$	−22.9114	−	13.2279i	−0.779913	−	0.450283i	−0.836400	+	0.548120i	$0.815344\pi$
$864$		0			0
$865$	16.3207	+	28.2683i	0.554922	+	0.961152i
$866$	7.74555	−	23.6611i	0.263205	−	0.804038i
$867$		0			0
$868$	−4.91608	+	7.17499i	−0.166863	+	0.243535i
$869$	−2.73154	−	4.73116i	−0.0926610	−	0.160494i
$870$		0			0
$871$	39.8574			1.35052
$872$	16.3963	−	36.1823i	0.555250	−	1.22529i
$873$		0			0
$874$	4.90398	+	5.47058i	0.165880	+	0.185045i
$875$	−6.77230	−	10.9080i	−0.228946	−	0.368758i
$876$		0			0
$877$	−1.14693			−0.0387290			−0.0193645	−	0.999812i	$-0.506164\pi$
$877$	−1.14693			−0.0387290			−0.0193645	+	0.999812i	$0.506164\pi$
$878$	−1.01114	−	4.80903i	−0.0341243	−	0.162297i
$879$		0			0
$880$	7.97921	+	25.3132i	0.268979	+	0.853309i
$881$		−	15.3416i		−	0.516872i	−0.966028	−	0.258436i	$-0.916793\pi$
$881$		−	15.3416i		−	0.516872i	0.966028	−	0.258436i	$-0.0832070\pi$
$882$		0			0
$883$		−	3.77848i		−	0.127156i	−0.997977	−	0.0635781i	$-0.979749\pi$
$883$		−	3.77848i		−	0.127156i	0.997977	−	0.0635781i	$-0.0202512\pi$
$884$	36.5329	−	16.0733i	1.22873	−	0.540603i
$885$		0			0
$886$	18.5930	−	3.90934i	0.624644	−	0.131337i
$887$	−34.0188			−1.14224			−0.571119	−	0.820867i	$-0.693491\pi$
$887$	−34.0188			−1.14224			−0.571119	+	0.820867i	$0.693491\pi$
$888$		0			0
$889$	−20.6298	−	33.2279i	−0.691900	−	1.11443i
$890$	−42.2500	+	37.8741i	−1.41622	+	1.26954i
$891$		0			0
$892$	−45.8145	+	20.1569i	−1.53398	+	0.674902i
$893$	−1.82111			−0.0609413
$894$		0			0
$895$	−3.12072	−	5.40525i	−0.104314	−	0.180677i
$896$	−2.63380	+	29.8172i	−0.0879891	+	0.996121i
$897$		0			0
$898$	18.5028	+	6.05695i	0.617446	+	0.202123i
$899$	−1.33375	−	2.31012i	−0.0444830	−	0.0770469i
$900$		0			0
$901$	−32.3958	−	18.7037i	−1.07926	−	0.623111i
$902$	−0.167094	−	0.794708i	−0.00556362	−	0.0264609i
$903$		0			0
$904$	−9.11832	+	20.1216i	−0.303271	+	0.669236i
$905$	−5.12986			−0.170522
$906$		0			0
$907$		−	54.8033i		−	1.81971i	−0.414921	−	0.909857i	$-0.636191\pi$
$907$		−	54.8033i		−	1.81971i	0.414921	−	0.909857i	$-0.363809\pi$
$908$	−17.9045	−	13.1291i	−0.594181	−	0.435705i
$909$		0			0
$910$	−36.3606	−	38.0382i	−1.20534	−	1.26095i
$911$	−10.6659	−	6.15799i	−0.353379	−	0.204023i	0.312794	−	0.949821i	$-0.398735\pi$
$911$	−10.6659	−	6.15799i	−0.353379	−	0.204023i	−0.666172	+	0.745798i	$0.732068\pi$
$912$		0			0
$913$	14.0727	+	8.12487i	0.465738	+	0.268894i
$914$	−7.73928	−	36.8084i	−0.255993	−	1.21751i
$915$		0			0
$916$	29.2796	−	39.9293i	0.967426	−	1.31930i
$917$	20.5756	−	12.7745i	0.679466	−	0.421851i
$918$		0			0
$919$	15.5914	+	9.00170i	0.514313	+	0.296939i	0.734605	−	0.678495i	$-0.237368\pi$
$919$	15.5914	+	9.00170i	0.514313	+	0.296939i	−0.220292	+	0.975434i	$0.570701\pi$
$920$	−40.0008	−	55.8275i	−1.31879	−	1.84058i
$921$		0			0
$922$	−24.4947	−	27.3248i	−0.806690	−	0.899894i
$923$	−28.4193	−	49.2237i	−0.935433	−	1.62022i
$924$		0			0
$925$	−13.3560	+	23.1332i	−0.439142	+	0.760616i
$926$	13.2013	−	2.77568i	0.433821	−	0.0912146i
$927$		0			0
$928$	−7.89943	−	4.67733i	−0.259312	−	0.153541i
$929$	−37.3308	+	21.5530i	−1.22479	+	0.707130i	−0.965934	−	0.258787i	$-0.916677\pi$
$929$	−37.3308	+	21.5530i	−1.22479	+	0.707130i	−0.258851	+	0.965917i	$0.583344\pi$
$930$		0			0
$931$	−2.39450	−	3.59465i	−0.0784764	−	0.117810i
$932$	34.6503	−	15.2450i	1.13501	−	0.499366i
$933$		0			0
$934$	−6.98652	+	6.26292i	−0.228606	+	0.204929i
$935$	−23.5159	+	13.5769i	−0.769052	+	0.444012i
$936$		0			0
$937$		−	9.29097i		−	0.303523i	−0.988417	−	0.151761i	$-0.951505\pi$
$937$		−	9.29097i		−	0.303523i	0.988417	−	0.151761i	$-0.0484945\pi$
$938$	−29.3541	−	8.57913i	−0.958447	−	0.280119i
$939$		0			0
$940$	16.9226	+	1.85395i	0.551955	+	0.0604692i
$941$	−25.8051	−	14.8986i	−0.841222	−	0.485680i	0.0164571	−	0.999865i	$-0.494761\pi$
$941$	−25.8051	−	14.8986i	−0.841222	−	0.485680i	−0.857680	+	0.514185i	$0.828095\pi$
$942$		0			0
$943$	1.05069	+	1.81985i	0.0342153	+	0.0592626i
$944$	−5.95558	−	1.32077i	−0.193838	−	0.0429875i
$945$		0			0
$946$	18.2354	−	16.3467i	0.592883	−	0.531477i
$947$	0.869750	−	0.502150i	0.0282631	−	0.0163177i	−0.485802	−	0.874069i	$-0.661472\pi$
$947$	0.869750	−	0.502150i	0.0282631	−	0.0163177i	0.514065	+	0.857751i	$0.328139\pi$
$948$		0			0
$949$	13.1357	−	22.7516i	0.426401	−	0.738549i
$950$	2.15543	−	1.93219i	0.0699315	−	0.0626886i
$951$		0			0
$952$	−30.3654	+	3.97408i	−0.984148	+	0.128801i
$953$	27.1024			0.877932			0.438966	−	0.898504i	$-0.355345\pi$
$953$	27.1024			0.877932			0.438966	+	0.898504i	$0.355345\pi$
$954$		0			0
$955$	7.37373	+	12.7717i	0.238608	+	0.413282i
$956$	−11.2623	−	1.23383i	−0.364247	−	0.0399049i
$957$		0			0
$958$	37.5107	+	12.2792i	1.21191	+	0.396724i
$959$	47.1026	−	29.2439i	1.52102	−	0.944336i
$960$		0			0
$961$	14.1491	+	24.5070i	0.456424	+	0.790549i
$962$	17.2763	−	52.7756i	0.557010	−	1.70155i
$963$		0			0
$964$	−7.65849	+	10.4441i	−0.246663	+	0.336381i
$965$	−18.0478	−	10.4199i	−0.580978	−	0.335428i
$966$		0			0
$967$	−28.1124	+	16.2307i	−0.904033	+	0.521944i	−0.878506	−	0.477730i	$-0.841460\pi$
$967$	−28.1124	+	16.2307i	−0.904033	+	0.521944i	−0.0255266	+	0.999674i	$0.508126\pi$
$968$	−9.40092	−	13.1205i	−0.302157	−	0.421708i
$969$		0			0
$970$	−36.4282	+	32.6553i	−1.16964	+	1.04850i
$971$	20.1407	−	34.8847i	0.646345	−	1.11950i	−0.337644	−	0.941274i	$-0.609630\pi$
$971$	20.1407	−	34.8847i	0.646345	−	1.11950i	0.983989	−	0.178228i	$-0.0570366\pi$
$972$		0			0
$973$	14.5765	+	7.80458i	0.467300	+	0.250203i
$974$	52.2151	−	10.9787i	1.67308	−	0.351779i
$975$		0			0
$976$	−28.5510	−	26.1660i	−0.913895	−	0.837553i
$977$	−4.87670	+	8.44669i	−0.156019	+	0.270234i	−0.933430	−	0.358760i	$-0.883200\pi$
$977$	−4.87670	+	8.44669i	−0.156019	+	0.270234i	0.777410	+	0.628994i	$0.216533\pi$
$978$		0			0
$979$	−16.0038	+	27.7195i	−0.511485	+	0.885918i
$980$	18.5913	+	35.8407i	0.593876	+	1.14489i
$981$		0			0
$982$	3.63777	−	0.764873i	0.116086	−	0.0244081i
$983$	−19.7170			−0.628876			−0.314438	−	0.949278i	$-0.601816\pi$
$983$	−19.7170			−0.628876			−0.314438	+	0.949278i	$0.601816\pi$
$984$		0			0
$985$			12.5371i			0.399466i
$986$	2.92202	−	8.92618i	0.0930560	−	0.284268i
$987$		0			0
$988$	−3.55855	+	4.85287i	−0.113212	+	0.154390i
$989$	−31.6852	+	54.8804i	−1.00753	+	1.74510i
$990$		0			0
$991$	9.26536	−	5.34936i	0.294324	−	0.169928i	−0.345566	−	0.938394i	$-0.612313\pi$
$991$	9.26536	−	5.34936i	0.294324	−	0.169928i	0.639890	+	0.768466i	$0.278980\pi$
$992$	−8.00080	−	4.73735i	−0.254026	−	0.150411i
$993$		0			0
$994$	10.3350	+	42.3693i	0.327808	+	1.34387i
$995$	51.3372	−	29.6395i	1.62750	−	0.939636i
$996$		0			0
$997$		−	33.7280i		−	1.06818i	−0.845429	−	0.534088i	$-0.820655\pi$
$997$		−	33.7280i		−	1.06818i	0.845429	−	0.534088i	$-0.179345\pi$
$998$	−13.5873	+	41.5064i	−0.430098	+	1.31386i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.n.b.19.4		84
3.2	odd	2		252.2.n.b.187.39	yes	84
4.3	odd	2	inner	756.2.n.b.19.25		84
7.3	odd	6		756.2.bj.b.451.31		84
9.4	even	3		756.2.bj.b.523.31		84
9.5	odd	6		252.2.bj.b.103.12	yes	84
12.11	even	2		252.2.n.b.187.18	yes	84
21.17	even	6		252.2.bj.b.115.12	yes	84
28.3	even	6		756.2.bj.b.451.32		84
36.23	even	6		252.2.bj.b.103.11	yes	84
36.31	odd	6		756.2.bj.b.523.32		84
63.31	odd	6	inner	756.2.n.b.199.25		84
63.59	even	6		252.2.n.b.31.18	✓	84
84.59	odd	6		252.2.bj.b.115.11	yes	84
252.31	even	6	inner	756.2.n.b.199.4		84
252.59	odd	6		252.2.n.b.31.39	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.18	✓	84	63.59	even	6
252.2.n.b.31.39	yes	84	252.59	odd	6
252.2.n.b.187.18	yes	84	12.11	even	2
252.2.n.b.187.39	yes	84	3.2	odd	2
252.2.bj.b.103.11	yes	84	36.23	even	6
252.2.bj.b.103.12	yes	84	9.5	odd	6
252.2.bj.b.115.11	yes	84	84.59	odd	6
252.2.bj.b.115.12	yes	84	21.17	even	6
756.2.n.b.19.4		84	1.1	even	1	trivial
756.2.n.b.19.25		84	4.3	odd	2	inner
756.2.n.b.199.4		84	252.31	even	6	inner
756.2.n.b.199.25		84	63.31	odd	6	inner
756.2.bj.b.451.31		84	7.3	odd	6
756.2.bj.b.451.32		84	28.3	even	6
756.2.bj.b.523.31		84	9.4	even	3
756.2.bj.b.523.32		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)

\(f(q)\)	\(=\)	\(q+(-1.34403 - 0.439974i) q^{2} +(1.61285 + 1.18268i) q^{4} +2.88398i q^{5} +(-2.24777 + 1.39554i) q^{7} +(-1.64737 - 2.29917i) q^{8} +O(q^{10})\)	\(q+(-1.34403 - 0.439974i) q^{2} +(1.61285 + 1.18268i) q^{4} +2.88398i q^{5} +(-2.24777 + 1.39554i) q^{7} +(-1.64737 - 2.29917i) q^{8} +(1.26887 - 3.87616i) q^{10} -2.30073i q^{11} +(-4.22314 + 2.43823i) q^{13} +(3.63508 - 0.886694i) q^{14} +(1.20255 + 3.81496i) q^{16} +(-3.54408 + 2.04617i) q^{17} +(0.308511 - 0.534357i) q^{19} +(-3.41081 + 4.65141i) q^{20} +(-1.01226 + 3.09226i) q^{22} -8.41949i q^{23} -3.31732 q^{25} +(6.74880 - 1.41899i) q^{26} +(-5.27578 - 0.407592i) q^{28} +(0.811434 - 1.40545i) q^{29} +(0.821847 - 1.42348i) q^{31} +(0.0622189 - 5.65651i) q^{32} +(5.66362 - 1.19082i) q^{34} +(-4.02471 - 6.48251i) q^{35} +(4.02614 - 6.97347i) q^{37} +(-0.649752 + 0.582456i) q^{38} +(6.63074 - 4.75098i) q^{40} +(-0.216148 + 0.124793i) q^{41} +(-6.51826 - 3.76332i) q^{43} +(2.72103 - 3.71073i) q^{44} +(-3.70435 + 11.3161i) q^{46} +(-1.47573 - 2.55604i) q^{47} +(3.10493 - 6.27371i) q^{49} +(4.45858 + 1.45953i) q^{50} +(-9.69493 - 1.06212i) q^{52} +(4.57041 + 7.91618i) q^{53} +6.63526 q^{55} +(6.91149 + 2.86902i) q^{56} +(-1.70895 + 1.53195i) q^{58} +(-0.762534 + 1.32075i) q^{59} +(-8.38475 + 4.84094i) q^{61} +(-1.73088 + 1.55161i) q^{62} +(-2.57234 + 7.57516i) q^{64} +(-7.03181 - 12.1794i) q^{65} +(-7.07839 - 4.08671i) q^{67} +(-8.13602 - 0.891338i) q^{68} +(2.55721 + 10.4835i) q^{70} +11.6557i q^{71} +(-4.66559 + 2.69368i) q^{73} +(-8.47940 + 7.60118i) q^{74} +(1.12955 - 0.496966i) q^{76} +(3.21077 + 5.17152i) q^{77} +(2.05637 - 1.18725i) q^{79} +(-11.0022 + 3.46811i) q^{80} +(0.345415 - 0.0726264i) q^{82} +(-3.53143 + 6.11661i) q^{83} +(-5.90112 - 10.2210i) q^{85} +(7.10499 + 7.92589i) q^{86} +(-5.28977 + 3.79016i) q^{88} +(-12.0481 - 6.95597i) q^{89} +(6.08999 - 11.3742i) q^{91} +(9.95755 - 13.5793i) q^{92} +(0.858838 + 4.08468i) q^{94} +(1.54107 + 0.889738i) q^{95} +(-10.3880 - 5.99749i) q^{97} +(-6.93339 + 7.06598i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + q^{2} + q^{4} + 16 q^{8}+O(q^{10}) \) 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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