LMFDB - Embedded newform 756.2.bb.a.611.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(611,756)]

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, 5, 2]))

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

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

chi := DirichletCharacter("756.611");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bb (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:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			611.36
Character	$\chi$	$=$	756.611
Dual form			756.2.bb.a.683.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12310 - 0.859445i) q^{2} +(0.522707 - 1.93049i) q^{4} +(-2.12868 + 1.22899i) q^{5} +(-2.32866 + 1.25593i) q^{7} +(-1.07210 - 2.61737i) q^{8} +O(q^{10})$	\(q+(1.12310 - 0.859445i) q^{2} +(0.522707 - 1.93049i) q^{4} +(-2.12868 + 1.22899i) q^{5} +(-2.32866 + 1.25593i) q^{7} +(-1.07210 - 2.61737i) q^{8} +(-1.33447 + 3.20977i) q^{10} +(-1.86626 + 3.23245i) q^{11} +(-0.708051 + 1.22638i) q^{13} +(-1.53591 + 3.41189i) q^{14} +(-3.45355 - 2.01816i) q^{16} +(-3.50791 + 2.02529i) q^{17} +(-1.98185 - 1.14422i) q^{19} +(1.25988 + 4.75179i) q^{20} +(0.682123 + 5.23432i) q^{22} +(-1.80849 - 3.13240i) q^{23} +(0.520855 - 0.902147i) q^{25} +(0.258795 + 1.98588i) q^{26} +(1.20735 + 5.15192i) q^{28} +(4.59226 - 2.65135i) q^{29} +6.22098i q^{31} +(-5.61318 + 0.701549i) q^{32} +(-2.19911 + 5.28947i) q^{34} +(3.41344 - 5.53538i) q^{35} +(2.37386 - 4.11165i) q^{37} +(-3.20921 + 0.418217i) q^{38} +(5.49888 + 4.25394i) q^{40} +(7.67307 + 4.43005i) q^{41} +(-10.5542 + 6.09346i) q^{43} +(5.26470 + 5.29241i) q^{44} +(-4.72324 - 1.96370i) q^{46} -8.67939 q^{47} +(3.84529 - 5.84925i) q^{49} +(-0.190374 - 1.46085i) q^{50} +(1.99741 + 2.00792i) q^{52} +(6.93030 - 4.00121i) q^{53} -9.17448i q^{55} +(5.78377 + 4.74848i) q^{56} +(2.87889 - 6.92453i) q^{58} +3.51395 q^{59} -10.4658 q^{61} +(5.34660 + 6.98679i) q^{62} +(-5.70122 + 5.61213i) q^{64} -3.48076i q^{65} -10.9623i q^{67} +(2.07619 + 7.83061i) q^{68} +(-0.923722 - 9.15045i) q^{70} -2.01888 q^{71} +(0.474356 + 0.821609i) q^{73} +(-0.867655 - 6.65800i) q^{74} +(-3.24483 + 3.22784i) q^{76} +(0.286144 - 9.87116i) q^{77} -4.03670i q^{79} +(9.83182 + 0.0516145i) q^{80} +(12.4250 - 1.61920i) q^{82} +(0.112352 + 0.194599i) q^{83} +(4.97815 - 8.62241i) q^{85} +(-6.61641 + 15.9143i) q^{86} +(10.4613 + 1.41918i) q^{88} +(8.55343 + 4.93832i) q^{89} +(0.108562 - 3.74508i) q^{91} +(-6.99236 + 1.85394i) q^{92} +(-9.74782 + 7.45946i) q^{94} +5.62497 q^{95} +(6.52412 + 11.3001i) q^{97} +(-0.708472 - 9.87411i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) $ 88 * q - 2 * q^4 + 6 * q^5	$ 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) $ 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.12310	−	0.859445i	0.794152	−	0.607720i
$2$	1.12310	−	0.859445i	0.794152	−	0.607720i
$3$		0			0
$3$		0			0
$4$	0.522707	−	1.93049i	0.261354	−	0.965243i
$5$	−2.12868	+	1.22899i	−0.951975	+	0.549623i	−0.893694	−	0.448677i	$-0.851895\pi$
$5$	−2.12868	+	1.22899i	−0.951975	+	0.549623i	−0.0582811	+	0.998300i	$0.518562\pi$
$6$		0			0
$7$	−2.32866	+	1.25593i	−0.880150	+	0.474696i
$7$	−2.32866	+	1.25593i	−0.880150	+	0.474696i
$8$	−1.07210	−	2.61737i	−0.379043	−	0.925379i
$9$		0			0
$10$	−1.33447	+	3.20977i	−0.421996	+	1.01502i
$11$	−1.86626	+	3.23245i	−0.562698	+	0.974621i	0.434562	+	0.900642i	$0.356903\pi$
$11$	−1.86626	+	3.23245i	−0.562698	+	0.974621i	−0.997260	+	0.0739794i	$0.976430\pi$
$12$		0			0
$13$	−0.708051	+	1.22638i	−0.196378	+	0.340137i	−0.947351	−	0.320196i	$-0.896251\pi$
$13$	−0.708051	+	1.22638i	−0.196378	+	0.340137i	0.750973	+	0.660332i	$0.229585\pi$
$14$	−1.53591	+	3.41189i	−0.410490	+	0.911865i
$15$		0			0
$16$	−3.45355	−	2.01816i	−0.863389	−	0.504539i
$17$	−3.50791	+	2.02529i	−0.850794	+	0.491206i	−0.860919	−	0.508743i	$-0.830110\pi$
$17$	−3.50791	+	2.02529i	−0.850794	+	0.491206i	0.0101248	+	0.999949i	$0.496777\pi$
$18$		0			0
$19$	−1.98185	−	1.14422i	−0.454668	−	0.262503i	0.255132	−	0.966906i	$-0.417881\pi$
$19$	−1.98185	−	1.14422i	−0.454668	−	0.262503i	−0.709800	+	0.704404i	$0.751215\pi$
$20$	1.25988	+	4.75179i	0.281718	+	1.06253i
$21$		0			0
$22$	0.682123	+	5.23432i	0.145429	+	1.11596i
$23$	−1.80849	−	3.13240i	−0.377096	−	0.653150i	0.613542	−	0.789662i	$-0.289744\pi$
$23$	−1.80849	−	3.13240i	−0.377096	−	0.653150i	−0.990638	+	0.136512i	$0.956411\pi$
$24$		0			0
$25$	0.520855	−	0.902147i	0.104171	−	0.180429i
$26$	0.258795	+	1.98588i	0.0507539	+	0.389463i
$27$		0			0
$28$	1.20735	+	5.15192i	0.228167	+	0.973622i
$29$	4.59226	−	2.65135i	0.852762	−	0.492342i	−0.00881973	−	0.999961i	$-0.502807\pi$
$29$	4.59226	−	2.65135i	0.852762	−	0.492342i	0.861582	+	0.507619i	$0.169474\pi$
$30$		0			0
$31$			6.22098i			1.11732i	0.829396	+	0.558661i	$0.188685\pi$
$31$			6.22098i			1.11732i	−0.829396	+	0.558661i	$0.811315\pi$
$32$	−5.61318	+	0.701549i	−0.992280	+	0.124017i
$33$		0			0
$34$	−2.19911	+	5.28947i	−0.377144	+	0.907136i
$35$	3.41344	−	5.53538i	0.576976	−	0.935650i
$36$		0			0
$37$	2.37386	−	4.11165i	0.390261	−	0.675952i	−0.602223	−	0.798328i	$-0.705718\pi$
$37$	2.37386	−	4.11165i	0.390261	−	0.675952i	0.992484	+	0.122376i	$0.0390515\pi$
$38$	−3.20921	+	0.418217i	−0.520603	+	0.0678438i
$39$		0			0
$40$	5.49888	+	4.25394i	0.869449	+	0.672607i
$41$	7.67307	+	4.43005i	1.19833	+	0.691857i	0.960183	−	0.279372i	$-0.0901261\pi$
$41$	7.67307	+	4.43005i	1.19833	+	0.691857i	0.238149	+	0.971229i	$0.423459\pi$
$42$		0			0
$43$	−10.5542	+	6.09346i	−1.60950	+	0.929244i	−0.620016	+	0.784590i	$0.712874\pi$
$43$	−10.5542	+	6.09346i	−1.60950	+	0.929244i	−0.989482	+	0.144654i	$0.953793\pi$
$44$	5.26470	+	5.29241i	0.793683	+	0.797861i
$45$		0			0
$46$	−4.72324	−	1.96370i	−0.696403	−	0.289531i
$47$	−8.67939			−1.26602			−0.633010	−	0.774144i	$-0.718181\pi$
$47$	−8.67939			−1.26602			−0.633010	+	0.774144i	$0.718181\pi$
$48$		0			0
$49$	3.84529	−	5.84925i	0.549327	−	0.835608i
$50$	−0.190374	−	1.46085i	−0.0269230	−	0.206595i
$51$		0			0
$52$	1.99741	+	2.00792i	0.276991	+	0.278448i
$53$	6.93030	−	4.00121i	0.951950	−	0.549609i	0.0582640	−	0.998301i	$-0.481443\pi$
$53$	6.93030	−	4.00121i	0.951950	−	0.549609i	0.893686	+	0.448693i	$0.148110\pi$
$54$		0			0
$55$		−	9.17448i		−	1.23709i
$56$	5.78377	+	4.74848i	0.772889	+	0.634542i
$57$		0			0
$58$	2.87889	−	6.92453i	0.378016	−	0.909235i
$59$	3.51395			0.457478			0.228739	−	0.973488i	$-0.426540\pi$
$59$	3.51395			0.457478			0.228739	+	0.973488i	$0.426540\pi$
$60$		0			0
$61$	−10.4658			−1.34001			−0.670003	−	0.742359i	$-0.733707\pi$
$61$	−10.4658			−1.34001			−0.670003	+	0.742359i	$0.733707\pi$
$62$	5.34660	+	6.98679i	0.679018	+	0.887323i
$63$		0			0
$64$	−5.70122	+	5.61213i	−0.712653	+	0.701517i
$65$		−	3.48076i		−	0.431736i
$66$		0			0
$67$		−	10.9623i		−	1.33926i	−0.742695	−	0.669630i	$-0.766453\pi$
$67$		−	10.9623i		−	1.33926i	0.742695	−	0.669630i	$-0.233547\pi$
$68$	2.07619	+	7.83061i	0.251775	+	0.949601i
$69$		0			0
$70$	−0.923722	−	9.15045i	−0.110406	−	1.09369i
$71$	−2.01888			−0.239597			−0.119799	−	0.992798i	$-0.538225\pi$
$71$	−2.01888			−0.239597			−0.119799	+	0.992798i	$0.538225\pi$
$72$		0			0
$73$	0.474356	+	0.821609i	0.0555192	+	0.0961621i	0.892449	−	0.451148i	$-0.148985\pi$
$73$	0.474356	+	0.821609i	0.0555192	+	0.0961621i	−0.836930	+	0.547310i	$0.815652\pi$
$74$	−0.867655	−	6.65800i	−0.100863	−	0.773977i
$75$		0			0
$76$	−3.24483	+	3.22784i	−0.372208	+	0.370259i
$77$	0.286144	−	9.87116i	0.0326092	−	1.12492i
$78$		0			0
$79$		−	4.03670i		−	0.454164i	−0.973876	−	0.227082i	$-0.927081\pi$
$79$		−	4.03670i		−	0.454164i	0.973876	−	0.227082i	$-0.0729185\pi$
$80$	9.83182	+	0.0516145i	1.09923	+	0.00577068i
$81$		0			0
$82$	12.4250	−	1.61920i	1.37211	−	0.178810i
$83$	0.112352	+	0.194599i	0.0123322	+	0.0213601i	0.872126	−	0.489282i	$-0.162741\pi$
$83$	0.112352	+	0.194599i	0.0123322	+	0.0213601i	−0.859793	+	0.510642i	$0.829408\pi$
$84$		0			0
$85$	4.97815	−	8.62241i	0.539956	−	0.935232i
$86$	−6.61641	+	15.9143i	−0.713465	+	1.71608i
$87$		0			0
$88$	10.4613	+	1.41918i	1.11518	+	0.151286i
$89$	8.55343	+	4.93832i	0.906662	+	0.523461i	0.879356	−	0.476166i	$-0.157974\pi$
$89$	8.55343	+	4.93832i	0.906662	+	0.523461i	0.0273061	+	0.999627i	$0.491307\pi$
$90$		0			0
$91$	0.108562	−	3.74508i	0.0113804	−	0.392591i
$92$	−6.99236	+	1.85394i	−0.729004	+	0.193286i
$93$		0			0
$94$	−9.74782	+	7.45946i	−1.00541	+	0.769385i
$95$	5.62497			0.577110
$96$		0			0
$97$	6.52412	+	11.3001i	0.662424	+	1.14735i	0.979977	+	0.199111i	$0.0638056\pi$
$97$	6.52412	+	11.3001i	0.662424	+	1.14735i	−0.317553	+	0.948241i	$0.602861\pi$
$98$	−0.708472	−	9.87411i	−0.0715665	−	0.997436i
$99$		0			0
$100$	−1.46933	−	1.47706i	−0.146933	−	0.147706i
$101$	−4.74693	−	2.74064i	−0.472337	−	0.272704i	0.244880	−	0.969553i	$-0.421251\pi$
$101$	−4.74693	−	2.74064i	−0.472337	−	0.272704i	−0.717218	+	0.696849i	$0.754585\pi$
$102$		0			0
$103$	−14.2427	+	8.22305i	−1.40338	+	0.810241i	−0.994738	−	0.102454i	$-0.967330\pi$
$103$	−14.2427	+	8.22305i	−1.40338	+	0.810241i	−0.408641	+	0.912695i	$0.633997\pi$
$104$	3.96899	+	0.538433i	0.389191	+	0.0527977i
$105$		0			0
$106$	4.34460	−	10.4500i	0.421985	−	1.01499i
$107$	−4.38000	+	7.58638i	−0.423431	+	0.733404i	−0.996272	−	0.0862625i	$-0.972508\pi$
$107$	−4.38000	+	7.58638i	−0.423431	+	0.733404i	0.572842	+	0.819666i	$0.305841\pi$
$108$		0			0
$109$	−5.83206	−	10.1014i	−0.558610	−	0.967541i	−0.997613	−	0.0690550i	$-0.978002\pi$
$109$	−5.83206	−	10.1014i	−0.558610	−	0.967541i	0.439003	−	0.898486i	$-0.355332\pi$
$110$	−7.88497	−	10.3039i	−0.751802	−	0.982435i
$111$		0			0
$112$	10.5768	+	0.362180i	0.999414	+	0.0342228i
$113$	8.35926	+	4.82622i	0.786373	+	0.454013i	0.838684	−	0.544618i	$-0.183325\pi$
$113$	8.35926	+	4.82622i	0.786373	+	0.454013i	−0.0523109	+	0.998631i	$0.516659\pi$
$114$		0			0
$115$	7.69939	+	4.44525i	0.717972	+	0.414521i
$116$	−2.71798	−	10.2512i	−0.252358	−	0.951798i
$117$		0			0
$118$	3.94652	−	3.02005i	0.363307	−	0.278018i
$119$	5.62510	−	9.12190i	0.515652	−	0.836203i
$120$		0			0
$121$	−1.46584	−	2.53890i	−0.133258	−	0.230809i
$122$	−11.7541	+	8.99476i	−1.06417	+	0.814348i
$123$		0			0
$124$	12.0095	+	3.25175i	1.07849	+	0.292016i
$125$		−	9.72943i		−	0.870227i
$126$		0			0
$127$			0.937979i			0.0832322i	0.999134	+	0.0416161i	$0.0132506\pi$
$127$			0.937979i			0.0832322i	−0.999134	+	0.0416161i	$0.986749\pi$
$128$	−1.57972	+	11.2029i	−0.139629	+	0.990204i
$129$		0			0
$130$	−2.99153	−	3.90924i	−0.262374	−	0.342863i
$131$	−3.48595	−	6.03784i	−0.304569	−	0.527529i	0.672596	−	0.740009i	$-0.265179\pi$
$131$	−3.48595	−	6.03784i	−0.304569	−	0.527529i	−0.977165	+	0.212481i	$0.931846\pi$
$132$		0			0
$133$	6.05211	+	0.175438i	0.524785	+	0.0152124i
$134$	−9.42152	−	12.3118i	−0.813895	−	1.06358i
$135$		0			0
$136$	9.06176	+	7.01019i	0.777039	+	0.601119i
$137$	−12.6158	−	7.28375i	−1.07784	−	0.622293i	−0.147529	−	0.989058i	$-0.547132\pi$
$137$	−12.6158	−	7.28375i	−1.07784	−	0.622293i	−0.930314	+	0.366765i	$0.880465\pi$
$138$		0			0
$139$	11.2990	+	6.52347i	0.958368	+	0.553314i	0.895670	−	0.444719i	$-0.146696\pi$
$139$	11.2990	+	6.52347i	0.958368	+	0.553314i	0.0626973	+	0.998033i	$0.480030\pi$
$140$	−8.90174	−	9.48298i	−0.752335	−	0.801458i
$141$		0			0
$142$	−2.26741	+	1.73512i	−0.190277	+	0.145608i
$143$	−2.64281	−	4.57748i	−0.221003	−	0.382788i
$144$		0			0
$145$	−6.51698	+	11.2877i	−0.541205	+	0.937395i
$146$	1.23888	+	0.515066i	0.102530	+	0.0426272i
$147$		0			0
$148$	−6.69665	−	6.73190i	−0.550462	−	0.553359i
$149$	−19.2464	+	11.1119i	−1.57672	+	0.910321i	−0.581410	+	0.813611i	$0.697499\pi$
$149$	−19.2464	+	11.1119i	−1.57672	+	0.910321i	−0.995313	+	0.0967108i	$0.969168\pi$
$150$		0			0
$151$	−1.95469	−	1.12854i	−0.159071	−	0.0918395i	0.418352	−	0.908285i	$-0.362608\pi$
$151$	−1.95469	−	1.12854i	−0.159071	−	0.0918395i	−0.577422	+	0.816446i	$0.695941\pi$
$152$	−0.870117	+	6.41395i	−0.0705758	+	0.520240i
$153$		0			0
$154$	−8.16236	−	11.3322i	−0.657741	−	0.913177i
$155$	−7.64556	−	13.2425i	−0.614106	−	1.06366i
$156$		0			0
$157$	−2.22361			−0.177463			−0.0887317	−	0.996056i	$-0.528281\pi$
$157$	−2.22361			−0.177463			−0.0887317	+	0.996056i	$0.528281\pi$
$158$	−3.46932	−	4.53362i	−0.276004	−	0.360675i
$159$		0			0
$160$	11.0865	−	8.39194i	0.876463	−	0.663441i
$161$	8.14542	+	5.02294i	0.641949	+	0.395863i
$162$		0			0
$163$	−0.479974	−	0.277113i	−0.0375945	−	0.0217052i	0.481085	−	0.876674i	$-0.340243\pi$
$163$	−0.479974	−	0.277113i	−0.0375945	−	0.0217052i	−0.518679	+	0.854969i	$0.673576\pi$
$164$	12.5629	−	12.4971i	0.980999	−	0.975862i
$165$		0			0
$166$	0.293430	+	0.121994i	0.0227746	+	0.00946859i
$167$	5.78903	−	10.0269i	0.447968	−	0.775904i	−0.550285	−	0.834977i	$-0.685481\pi$
$167$	5.78903	−	10.0269i	0.447968	−	0.775904i	0.998254	+	0.0590727i	$0.0188144\pi$
$168$		0			0
$169$	5.49733	+	9.52165i	0.422871	+	0.732435i
$170$	−1.81953	−	13.9623i	−0.139552	−	1.07086i
$171$		0			0
$172$	6.24659	+	23.5598i	0.476298	+	1.79642i
$173$		−	10.6600i		−	0.810468i	−0.914213	−	0.405234i	$-0.867190\pi$
$173$		−	10.6600i		−	0.810468i	0.914213	−	0.405234i	$-0.132810\pi$
$174$		0			0
$175$	−0.0798601	+	2.75495i	−0.00603686	+	0.208254i
$176$	12.9688	−	7.39705i	0.977562	−	0.557574i
$177$		0			0
$178$	13.8506	−	1.80497i	1.03814	−	0.135288i
$179$	10.5947	+	18.3506i	0.791886	+	1.37159i	0.924798	+	0.380459i	$0.124234\pi$
$179$	10.5947	+	18.3506i	0.791886	+	1.37159i	−0.132911	+	0.991128i	$0.542433\pi$
$180$		0			0
$181$	−16.5889			−1.23304			−0.616521	−	0.787338i	$-0.711459\pi$
$181$	−16.5889			−1.23304			−0.616521	+	0.787338i	$0.711459\pi$
$182$	−3.09677	−	4.29940i	−0.229548	−	0.318693i
$183$		0			0
$184$	−6.25976	+	8.09171i	−0.461475	+	0.596529i
$185$			11.6699i			0.857985i
$186$		0			0
$187$		−	15.1189i		−	1.10560i
$188$	−4.53678	+	16.7554i	−0.330879	+	1.22202i
$189$		0			0
$190$	6.31741	−	4.83436i	0.458313	−	0.350721i
$191$	16.4855			1.19285			0.596423	−	0.802670i	$-0.296588\pi$
$191$	16.4855			1.19285			0.596423	+	0.802670i	$0.296588\pi$
$192$		0			0
$193$	23.1708			1.66787			0.833936	−	0.551861i	$-0.186082\pi$
$193$	23.1708			1.66787			0.833936	+	0.551861i	$0.186082\pi$
$194$	17.0391	+	7.08402i	1.22333	+	0.508603i
$195$		0			0
$196$	−9.28194	−	10.4807i	−0.662996	−	0.748623i
$197$			14.4116i			1.02679i	0.858154	+	0.513393i	$0.171611\pi$
$197$			14.4116i			1.02679i	−0.858154	+	0.513393i	$0.828389\pi$
$198$		0			0
$199$	2.36477	−	1.36530i	0.167634	−	0.0967837i	−0.413836	−	0.910352i	$-0.635811\pi$
$199$	2.36477	−	1.36530i	0.167634	−	0.0967837i	0.581470	+	0.813568i	$0.302478\pi$
$200$	−2.91966	−	0.396081i	−0.206451	−	0.0280071i
$201$		0			0
$202$	−7.68671	+	1.00171i	−0.540835	+	0.0704803i
$203$	−7.36391	+	11.9416i	−0.516845	+	0.838138i
$204$		0			0
$205$	−21.7780			−1.52104
$206$	−8.92876	+	21.4762i	−0.622096	+	1.49632i
$207$		0			0
$208$	4.92032	−	2.80641i	0.341163	−	0.194590i
$209$	7.39729	−	4.27083i	0.511681	−	0.295419i
$210$		0			0
$211$	7.91848	+	4.57174i	0.545131	+	0.314731i	0.747156	−	0.664649i	$-0.231419\pi$
$211$	7.91848	+	4.57174i	0.545131	+	0.314731i	−0.202025	+	0.979380i	$0.564752\pi$
$212$	−4.10177	−	15.4703i	−0.281710	−	1.06251i
$213$		0			0
$214$	1.60090	+	12.2846i	0.109436	+	0.839761i
$215$	14.9777	−	25.9421i	1.02147	−	1.76923i
$216$		0			0
$217$	−7.81311	−	14.4865i	−0.530389	−	0.983410i
$218$	−15.2316	−	6.33257i	−1.03161	−	0.428896i
$219$		0			0
$220$	−17.7112	−	4.79557i	−1.19409	−	0.323317i
$221$		−	5.73605i		−	0.385848i
$222$		0			0
$223$	7.77997	−	4.49177i	0.520985	−	0.300791i	−0.216352	−	0.976315i	$-0.569416\pi$
$223$	7.77997	−	4.49177i	0.520985	−	0.300791i	0.737338	+	0.675524i	$0.236083\pi$
$224$	12.1901	−	8.68342i	0.814484	−	0.580186i
$225$		0			0
$226$	13.5362	−	1.76400i	0.900412	−	0.117340i
$227$	−5.18438	+	8.97960i	−0.344099	+	0.595997i	−0.985190	−	0.171468i	$-0.945149\pi$
$227$	−5.18438	+	8.97960i	−0.344099	+	0.595997i	0.641091	+	0.767465i	$0.278482\pi$
$228$		0			0
$229$	1.85500	+	3.21296i	0.122582	+	0.212318i	0.920785	−	0.390070i	$-0.127549\pi$
$229$	1.85500	+	3.21296i	0.122582	+	0.212318i	−0.798203	+	0.602388i	$0.794216\pi$
$230$	12.4676	−	1.62475i	0.822092	−	0.107133i
$231$		0			0
$232$	−11.8629	−	9.17715i	−0.778837	−	0.602509i
$233$	−12.9602	−	7.48260i	−0.849054	−	0.490201i	0.0112778	−	0.999936i	$-0.496410\pi$
$233$	−12.9602	−	7.48260i	−0.849054	−	0.490201i	−0.860331	+	0.509735i	$0.829743\pi$
$234$		0			0
$235$	18.4757	−	10.6669i	1.20522	−	0.695833i
$236$	1.83677	−	6.78364i	0.119563	−	0.441577i
$237$		0			0
$238$	−1.52223	−	15.0793i	−0.0986714	−	0.977444i
$239$	−6.84478	+	11.8555i	−0.442752	+	0.766869i	−0.997893	−	0.0648877i	$-0.979331\pi$
$239$	−6.84478	+	11.8555i	−0.442752	+	0.766869i	0.555141	+	0.831756i	$0.312664\pi$
$240$		0			0
$241$	−5.86918	+	10.1657i	−0.378067	+	0.654832i	−0.990781	−	0.135473i	$-0.956745\pi$
$241$	−5.86918	+	10.1657i	−0.378067	+	0.654832i	0.612714	+	0.790305i	$0.290078\pi$
$242$	−3.82833	−	1.59164i	−0.246094	−	0.102314i
$243$		0			0
$244$	−5.47054	+	20.2040i	−0.350215	+	1.29343i
$245$	−0.996689	+	17.1770i	−0.0636761	+	1.09740i
$246$		0			0
$247$	2.80650	−	1.62034i	0.178574	−	0.103100i
$248$	16.2826	−	6.66949i	1.03395	−	0.423513i
$249$		0			0
$250$	−8.36192	−	10.9271i	−0.528854	−	0.691092i
$251$	−17.6466			−1.11384			−0.556922	−	0.830565i	$-0.688018\pi$
$251$	−17.6466			−1.11384			−0.556922	+	0.830565i	$0.688018\pi$
$252$		0			0
$253$	13.5004			0.848765
$254$	0.806142	+	1.05344i	0.0505819	+	0.0660990i
$255$		0			0
$256$	7.85408	+	13.9396i	0.490880	+	0.871227i
$257$	−12.9216	+	7.46029i	−0.806027	+	0.465360i	−0.845574	−	0.533858i	$-0.820742\pi$
$257$	−12.9216	+	7.46029i	−0.806027	+	0.465360i	0.0395470	+	0.999218i	$0.487409\pi$
$258$		0			0
$259$	−0.363973	+	12.5560i	−0.0226162	+	0.780194i
$260$	−6.71956	−	1.81942i	−0.416730	−	0.112836i
$261$		0			0
$262$	−9.10426	−	3.78512i	−0.562463	−	0.233845i
$263$	−0.426605	+	0.738902i	−0.0263056	+	0.0455626i	−0.878879	−	0.477046i	$-0.841708\pi$
$263$	−0.426605	+	0.738902i	−0.0263056	+	0.0455626i	0.852573	+	0.522608i	$0.175041\pi$
$264$		0			0
$265$	−9.83493	+	17.0346i	−0.604155	+	1.04643i
$266$	6.94791	−	5.00443i	0.426004	−	0.306841i
$267$		0			0
$268$	−21.1626	−	5.73008i	−1.29271	−	0.350021i
$269$	−6.98964	+	4.03547i	−0.426166	+	0.246047i	−0.697712	−	0.716378i	$-0.745798\pi$
$269$	−6.98964	+	4.03547i	−0.426166	+	0.246047i	0.271546	+	0.962425i	$0.412465\pi$
$270$		0			0
$271$	13.5435	+	7.81935i	0.822710	+	0.474992i	0.851350	−	0.524598i	$-0.175784\pi$
$271$	13.5435	+	7.81935i	0.822710	+	0.474992i	−0.0286401	+	0.999590i	$0.509118\pi$
$272$	16.2021	+	0.0850570i	0.982398	+	0.00515734i
$273$		0			0
$274$	−20.4288	+	2.66223i	−1.23415	+	0.160831i
$275$	1.94410	+	3.36728i	0.117234	+	0.203054i
$276$		0			0
$277$	10.1234	−	17.5343i	0.608259	−	1.05353i	−0.383269	−	0.923637i	$-0.625202\pi$
$277$	10.1234	−	17.5343i	0.608259	−	1.05353i	0.991527	−	0.129898i	$-0.0414650\pi$
$278$	18.2965	−	2.38435i	1.09735	−	0.143004i
$279$		0			0
$280$	−18.1476	−	2.99977i	−1.08453	−	0.179271i
$281$	−5.50545	+	3.17857i	−0.328428	+	0.189618i	−0.655143	−	0.755505i	$-0.727392\pi$
$281$	−5.50545	+	3.17857i	−0.328428	+	0.189618i	0.326715	+	0.945123i	$0.394058\pi$
$282$		0			0
$283$		−	10.2267i		−	0.607915i	−0.952686	−	0.303958i	$-0.901692\pi$
$283$		−	10.2267i		−	0.607915i	0.952686	−	0.303958i	$-0.0983081\pi$
$284$	−1.05528	+	3.89743i	−0.0626196	+	0.231270i
$285$		0			0
$286$	−6.90224	−	2.86962i	−0.408138	−	0.169684i
$287$	−23.4318	−	0.679237i	−1.38313	−	0.0400941i
$288$		0			0
$289$	−0.296366	+	0.513321i	−0.0174333	+	0.0301954i
$290$	2.38198	+	18.2782i	0.139874	+	1.07334i
$291$		0			0
$292$	1.83406	−	0.486277i	0.107330	−	0.0284572i
$293$	−20.6599	−	11.9280i	−1.20696	−	0.696840i	−0.244868	−	0.969556i	$-0.578745\pi$
$293$	−20.6599	−	11.9280i	−1.20696	−	0.696840i	−0.962094	+	0.272716i	$0.912078\pi$
$294$		0			0
$295$	−7.48009	+	4.31863i	−0.435507	+	0.251440i
$296$	−13.3067	−	1.80519i	−0.773437	−	0.104925i
$297$		0			0
$298$	−12.0655	+	29.0210i	−0.698937	+	1.68114i
$299$	5.12201			0.296214
$300$		0			0
$301$	16.9241	−	27.4449i	0.975490	−	1.58190i
$302$	−3.16524	+	0.412486i	−0.182139	+	0.0237359i
$303$		0			0
$304$	4.53521	+	7.95133i	0.260112	+	0.456040i
$305$	22.2783	−	12.8624i	1.27565	−	0.736498i
$306$		0			0
$307$			6.44982i			0.368111i	0.982916	+	0.184055i	$0.0589226\pi$
$307$			6.44982i			0.368111i	−0.982916	+	0.184055i	$0.941077\pi$
$308$	−18.9066	−	5.71212i	−1.07730	−	0.325478i
$309$		0			0
$310$	−19.9679	−	8.30170i	−1.13410	−	0.471505i
$311$	−0.506148			−0.0287010			−0.0143505	−	0.999897i	$-0.504568\pi$
$311$	−0.506148			−0.0287010			−0.0143505	+	0.999897i	$0.504568\pi$
$312$		0			0
$313$	25.3829			1.43472			0.717362	−	0.696700i	$-0.245349\pi$
$313$	25.3829			1.43472			0.717362	+	0.696700i	$0.245349\pi$
$314$	−2.49734	+	1.91107i	−0.140933	+	0.107848i
$315$		0			0
$316$	−7.79279	−	2.11001i	−0.438379	−	0.118697i
$317$			24.0636i			1.35155i	0.737109	+	0.675774i	$0.236191\pi$
$317$			24.0636i			1.35155i	−0.737109	+	0.675774i	$0.763809\pi$
$318$		0			0
$319$			19.7924i			1.10816i
$320$	5.23880	−	18.9532i	0.292858	−	1.05952i
$321$		0			0
$322$	13.4651	−	1.35928i	0.750379	−	0.0757495i
$323$	9.26955			0.515772
$324$		0			0
$325$	0.737584	+	1.27753i	0.0409138	+	0.0708647i
$326$	−0.777222	+	0.101286i	−0.0430464	+	0.00560970i
$327$		0			0
$328$	3.36880	−	24.8327i	0.186011	−	1.37115i
$329$	20.2113	−	10.9007i	1.11429	−	0.600975i
$330$		0			0
$331$		−	6.70550i		−	0.368568i	−0.982873	−	0.184284i	$-0.941003\pi$
$331$		−	6.70550i		−	0.368568i	0.982873	−	0.184284i	$-0.0589965\pi$
$332$	0.434399	−	0.115176i	0.0238407	−	0.00632108i
$333$		0			0
$334$	−2.11591	−	16.2366i	−0.115777	−	0.888425i
$335$	13.4726	+	23.3353i	0.736089	+	1.27494i
$336$		0			0
$337$	−15.3334	+	26.5582i	−0.835263	+	1.44672i	0.0585525	+	0.998284i	$0.481351\pi$
$337$	−15.3334	+	26.5582i	−0.835263	+	1.44672i	−0.893816	+	0.448434i	$0.851982\pi$
$338$	14.3574	+	5.96911i	0.780939	+	0.324677i
$339$		0			0
$340$	−14.0433	−	14.1172i	−0.761606	−	0.765615i
$341$	−20.1090	−	11.6100i	−1.08897	−	0.628715i
$342$		0			0
$343$	−1.60811	+	18.4503i	−0.0868298	+	0.996223i
$344$	27.2639	+	21.0914i	1.46997	+	1.13717i
$345$		0			0
$346$	−9.16172	−	11.9723i	−0.492537	−	0.643634i
$347$	−9.03400			−0.484971			−0.242485	−	0.970155i	$-0.577963\pi$
$347$	−9.03400			−0.484971			−0.242485	+	0.970155i	$0.577963\pi$
$348$		0			0
$349$	10.9004	+	18.8800i	0.583485	+	1.01063i	0.995062	+	0.0992507i	$0.0316446\pi$
$349$	10.9004	+	18.8800i	0.583485	+	1.01063i	−0.411578	+	0.911375i	$0.635022\pi$
$350$	2.27804	+	3.16272i	0.121766	+	0.169054i
$351$		0			0
$352$	8.20792	−	19.4536i	0.437484	−	1.03688i
$353$	10.3246	+	5.96092i	0.549524	+	0.317268i	0.748930	−	0.662649i	$-0.230568\pi$
$353$	10.3246	+	5.96092i	0.549524	+	0.317268i	−0.199406	+	0.979917i	$0.563901\pi$
$354$		0			0
$355$	4.29756	−	2.48120i	0.228091	−	0.131688i
$356$	14.0043	−	13.9310i	0.742227	−	0.738340i
$357$		0			0
$358$	27.6703	+	11.5040i	1.46242	+	0.608003i
$359$	−5.13759	+	8.89857i	−0.271152	+	0.469649i	−0.969157	−	0.246444i	$-0.920738\pi$
$359$	−5.13759	+	8.89857i	−0.271152	+	0.469649i	0.698005	+	0.716093i	$0.254071\pi$
$360$		0			0
$361$	−6.88151	−	11.9191i	−0.362185	−	0.627322i
$362$	−18.6310	+	14.2572i	−0.979223	+	0.749344i
$363$		0			0
$364$	−7.17308	−	2.16716i	−0.375972	−	0.113590i
$365$	−2.01951	−	1.16596i	−0.105706	−	0.0610293i
$366$		0			0
$367$	−23.7626	−	13.7194i	−1.24040	−	0.716145i	−0.271224	−	0.962516i	$-0.587428\pi$
$367$	−23.7626	−	13.7194i	−1.24040	−	0.716145i	−0.969176	+	0.246371i	$0.920762\pi$
$368$	−0.0759517	+	14.4677i	−0.00395926	+	0.754182i
$369$		0			0
$370$	10.0296	+	13.1064i	0.521415	+	0.681371i
$371$	−11.1131	+	18.0214i	−0.576961	+	0.935625i
$372$		0			0
$373$	2.53260	+	4.38660i	0.131133	+	0.227129i	0.924114	−	0.382118i	$-0.124805\pi$
$373$	2.53260	+	4.38660i	0.131133	+	0.227129i	−0.792980	+	0.609247i	$0.791472\pi$
$374$	−12.9939	−	16.9800i	−0.671896	−	0.878016i
$375$		0			0
$376$	9.30513	+	22.7172i	0.479876	+	1.17155i
$377$			7.50915i			0.386741i
$378$		0			0
$379$		−	1.02589i		−	0.0526966i	−0.999653	−	0.0263483i	$-0.991612\pi$
$379$		−	1.02589i		−	0.0526966i	0.999653	−	0.0263483i	$-0.00838790\pi$
$380$	2.94021	−	10.8589i	0.150830	−	0.557052i
$381$		0			0
$382$	18.5148	−	14.1683i	0.947300	−	0.724916i
$383$	12.6343	+	21.8833i	0.645584	+	1.11818i	0.984166	+	0.177248i	$0.0567193\pi$
$383$	12.6343	+	21.8833i	0.645584	+	1.11818i	−0.338582	+	0.940937i	$0.609947\pi$
$384$		0			0
$385$	11.5225	+	21.3642i	0.587241	+	1.08882i
$386$	26.0232	−	19.9141i	1.32454	−	1.01360i
$387$		0			0
$388$	25.2249	−	6.68808i	1.28060	−	0.339536i
$389$	8.06115	+	4.65411i	0.408717	+	0.235973i	0.690238	−	0.723582i	$-0.257506\pi$
$389$	8.06115	+	4.65411i	0.408717	+	0.235973i	−0.281522	+	0.959555i	$0.590839\pi$
$390$		0			0
$391$	12.6880	+	7.32545i	0.641662	+	0.370464i
$392$	−19.4322	−	3.79357i	−0.981472	−	0.191604i
$393$		0			0
$394$	12.3860	+	16.1857i	0.623998	+	0.815423i
$395$	4.96108	+	8.59284i	0.249619	+	0.432353i
$396$		0			0
$397$	−7.25979	+	12.5743i	−0.364358	+	0.631087i	−0.988673	−	0.150086i	$-0.952045\pi$
$397$	−7.25979	+	12.5743i	−0.364358	+	0.631087i	0.624315	+	0.781173i	$0.285378\pi$
$398$	1.48247	−	3.56576i	0.0743096	−	0.178736i
$399$		0			0
$400$	−3.61948	+	2.06445i	−0.180974	+	0.103222i
$401$	15.5515	−	8.97868i	0.776607	−	0.448374i	−0.0586197	−	0.998280i	$-0.518670\pi$
$401$	15.5515	−	8.97868i	0.776607	−	0.448374i	0.835226	+	0.549906i	$0.185337\pi$
$402$		0			0
$403$	−7.62929	−	4.40477i	−0.380042	−	0.219417i
$404$	−7.77203	+	7.73133i	−0.386673	+	0.384648i
$405$		0			0
$406$	1.99277	+	19.7405i	0.0988996	+	0.979706i
$407$	8.86048	+	15.3468i	0.439198	+	0.760713i
$408$		0			0
$409$	−0.316834			−0.0156664			−0.00783322	−	0.999969i	$-0.502493\pi$
$409$	−0.316834			−0.0156664			−0.00783322	+	0.999969i	$0.502493\pi$
$410$	−24.4589	+	18.7170i	−1.20794	+	0.924367i
$411$		0			0
$412$	8.42970	+	31.7937i	0.415302	+	1.56636i
$413$	−8.18279	+	4.41327i	−0.402649	+	0.217163i
$414$		0			0
$415$	−0.478323	−	0.276160i	−0.0234800	−	0.0135562i
$416$	3.11405	−	7.38063i	0.152679	−	0.361865i
$417$		0			0
$418$	4.63735	−	11.1541i	0.226820	−	0.545567i
$419$	8.80022	−	15.2424i	0.429919	−	0.744641i	−0.566947	−	0.823754i	$-0.691876\pi$
$419$	8.80022	−	15.2424i	0.429919	−	0.744641i	0.996866	+	0.0791133i	$0.0252089\pi$
$420$		0			0
$421$	−11.4743	−	19.8741i	−0.559224	−	0.968605i	−0.997561	−	0.0697943i	$-0.977766\pi$
$421$	−11.4743	−	19.8741i	−0.559224	−	0.968605i	0.438337	−	0.898811i	$-0.355568\pi$
$422$	12.8224	−	1.67099i	0.624185	−	0.0813423i
$423$		0			0
$424$	−17.9026	−	13.8495i	−0.869426	−	0.672590i
$425$			4.21954i			0.204678i
$426$		0			0
$427$	24.3712	−	13.1443i	1.17941	−	0.636096i
$428$	12.3560	+	12.4210i	0.597248	+	0.600391i
$429$		0			0
$430$	−5.47438	−	42.0080i	−0.263998	−	2.02581i
$431$	11.3929	+	19.7331i	0.548778	+	0.950512i	0.998359	+	0.0572722i	$0.0182403\pi$
$431$	11.3929	+	19.7331i	0.548778	+	0.950512i	−0.449580	+	0.893240i	$0.648426\pi$
$432$		0			0
$433$	−25.9567			−1.24740			−0.623700	−	0.781664i	$-0.714371\pi$
$433$	−25.9567			−1.24740			−0.623700	+	0.781664i	$0.714371\pi$
$434$	−21.2253	−	9.55489i	−1.01885	−	0.458649i
$435$		0			0
$436$	−22.5491	+	5.97862i	−1.07991	+	0.286324i
$437$			8.27726i			0.395955i
$438$		0			0
$439$		−	3.92585i		−	0.187371i	−0.995602	−	0.0936854i	$-0.970135\pi$
$439$		−	3.92585i		−	0.187371i	0.995602	−	0.0936854i	$-0.0298648\pi$
$440$	−24.0130	+	9.83592i	−1.14477	+	0.468909i
$441$		0			0
$442$	−4.92982	−	6.44215i	−0.234488	−	0.306422i
$443$	11.3376			0.538667			0.269334	−	0.963047i	$-0.413197\pi$
$443$	11.3376			0.538667			0.269334	+	0.963047i	$0.413197\pi$
$444$		0			0
$445$	−24.2767			−1.15083
$446$	4.87725	−	11.7312i	0.230945	−	0.555487i
$447$		0			0
$448$	6.22776	−	20.2291i	0.294234	−	0.955733i
$449$			15.6718i			0.739600i	0.929111	+	0.369800i	$0.120574\pi$
$449$			15.6718i			0.739600i	−0.929111	+	0.369800i	$0.879426\pi$
$450$		0			0
$451$	−28.6398	+	16.5352i	−1.34860	+	0.778613i
$452$	13.6864	−	13.6147i	0.643754	−	0.640384i
$453$		0			0
$454$	1.89491	+	14.5407i	0.0889323	+	0.682428i
$455$	4.37159	+	8.10550i	0.204943	+	0.379992i
$456$		0			0
$457$	−17.4854			−0.817934			−0.408967	−	0.912549i	$-0.634111\pi$
$457$	−17.4854			−0.817934			−0.408967	+	0.912549i	$0.634111\pi$
$458$	4.84471	+	2.01420i	0.226379	+	0.0941174i
$459$		0			0
$460$	12.6060	−	12.5400i	0.587759	−	0.584681i
$461$	−2.17782	+	1.25736i	−0.101431	+	0.0585613i	−0.549857	−	0.835259i	$-0.685318\pi$
$461$	−2.17782	+	1.25736i	−0.101431	+	0.0585613i	0.448426	+	0.893820i	$0.351985\pi$
$462$		0			0
$463$	15.3322	+	8.85204i	0.712547	+	0.411389i	0.812003	−	0.583653i	$-0.198377\pi$
$463$	15.3322	+	8.85204i	0.712547	+	0.411389i	−0.0994566	+	0.995042i	$0.531710\pi$
$464$	−21.2105	−	0.111349i	−0.984671	−	0.00516927i
$465$		0			0
$466$	−20.9865	+	2.73491i	−0.972182	+	0.126692i
$467$	11.9222	−	20.6498i	0.551693	−	0.955560i	−0.446460	−	0.894804i	$-0.647315\pi$
$467$	11.9222	−	20.6498i	0.551693	−	0.955560i	0.998153	−	0.0607566i	$-0.0193514\pi$
$468$		0			0
$469$	13.7679	+	25.5275i	0.635742	+	1.17875i
$470$	11.5824	−	27.8588i	0.534255	−	1.28503i
$471$		0			0
$472$	−3.76729	−	9.19731i	−0.173404	−	0.423340i
$473$		−	45.4879i		−	2.09153i
$474$		0			0
$475$	−2.06451	+	1.19195i	−0.0947264	+	0.0546903i
$476$	−14.6694	−	15.6273i	−0.672372	−	0.716274i
$477$		0			0
$478$	2.50179	+	19.1976i	0.114429	+	0.878079i
$479$	−0.892404	+	1.54569i	−0.0407750	+	0.0706243i	−0.885693	−	0.464272i	$-0.846316\pi$
$479$	−0.892404	+	1.54569i	−0.0407750	+	0.0706243i	0.844918	+	0.534896i	$0.179649\pi$
$480$		0			0
$481$	3.36163	+	5.82252i	0.153277	+	0.265484i
$482$	2.14521	+	16.4614i	0.0977114	+	0.749795i
$483$		0			0
$484$	−5.66752	+	1.50267i	−0.257615	+	0.0683034i
$485$	−27.7755	−	16.0362i	−1.26122	−	0.728167i
$486$		0			0
$487$	14.2958	−	8.25366i	0.647803	−	0.374009i	−0.139811	−	0.990178i	$-0.544649\pi$
$487$	14.2958	−	8.25366i	0.647803	−	0.374009i	0.787614	+	0.616169i	$0.211316\pi$
$488$	11.2203	+	27.3928i	0.507919	+	1.24001i
$489$		0			0
$490$	13.6433	+	20.1481i	0.616343	+	0.910199i
$491$	−16.6450	+	28.8300i	−0.751179	+	1.30108i	0.196072	+	0.980589i	$0.437181\pi$
$491$	−16.6450	+	28.8300i	−0.751179	+	1.30108i	−0.947252	+	0.320491i	$0.896152\pi$
$492$		0			0
$493$	−10.7395	+	18.6014i	−0.483683	+	0.837764i
$494$	1.75939	−	4.23184i	0.0791589	−	0.190399i
$495$		0			0
$496$	12.5549	−	21.4845i	0.563733	−	0.964683i
$497$	4.70129	−	2.53557i	0.210882	−	0.113736i
$498$		0			0
$499$	−24.1980	+	13.9707i	−1.08325	+	0.625417i	−0.931772	−	0.363044i	$-0.881738\pi$
$499$	−24.1980	+	13.9707i	−1.08325	+	0.625417i	−0.151481	+	0.988460i	$0.548404\pi$
$500$	−18.7825	−	5.08564i	−0.839981	−	0.227437i
$501$		0			0
$502$	−19.8189	+	15.1663i	−0.884560	+	0.676905i
$503$	−1.00731			−0.0449138			−0.0224569	−	0.999748i	$-0.507149\pi$
$503$	−1.00731			−0.0449138			−0.0224569	+	0.999748i	$0.507149\pi$
$504$		0			0
$505$	13.4729			0.599538
$506$	15.1623	−	11.6029i	0.674048	−	0.515811i
$507$		0			0
$508$	1.81076	+	0.490288i	0.0803393	+	0.0217530i
$509$	4.63448	−	2.67572i	0.205420	−	0.118599i	−0.393761	−	0.919213i	$-0.628826\pi$
$509$	4.63448	−	2.67572i	0.205420	−	0.118599i	0.599181	+	0.800614i	$0.295493\pi$
$510$		0			0
$511$	−2.13650	−	1.31749i	−0.0945130	−	0.0582823i
$512$	20.8013	+	8.90545i	0.919295	+	0.393569i
$513$		0			0
$514$	−8.10054	+	19.4841i	−0.357299	+	0.859405i
$515$	20.2122	−	35.0085i	0.890654	−	1.54266i
$516$		0			0
$517$	16.1980	−	28.0557i	0.712386	−	1.23389i
$518$	10.3824	+	14.4145i	0.456179	+	0.633337i
$519$		0			0
$520$	−9.11044	+	3.73171i	−0.399519	+	0.163646i
$521$	−0.0326842	+	0.0188702i	−0.00143192	+	0.000826719i	−0.500716	−	0.865612i	$-0.666930\pi$
$521$	−0.0326842	+	0.0188702i	−0.00143192	+	0.000826719i	0.499284	+	0.866438i	$0.333596\pi$
$522$		0			0
$523$	−22.6882	−	13.0990i	−0.992086	−	0.572781i	−0.0861890	−	0.996279i	$-0.527469\pi$
$523$	−22.6882	−	13.0990i	−0.992086	−	0.572781i	−0.905897	+	0.423498i	$0.860802\pi$
$524$	−13.4781	+	3.57355i	−0.588794	+	0.156111i
$525$		0			0
$526$	0.155926	+	1.19650i	0.00679867	+	0.0521701i
$527$	−12.5993	−	21.8227i	−0.548835	−	0.950610i
$528$		0			0
$529$	4.95873	−	8.58878i	0.215597	−	0.373425i
$530$	3.59470	+	27.5842i	0.156144	+	1.19818i
$531$		0			0
$532$	3.50216	−	11.5918i	0.151838	−	0.502569i
$533$	−10.8658	+	6.27340i	−0.470652	+	0.271731i
$534$		0			0
$535$		−	21.5320i		−	0.930909i
$536$	−28.6924	+	11.7527i	−1.23932	+	0.507637i
$537$		0			0
$538$	−4.38180	+	10.5395i	−0.188913	+	0.454388i
$539$	11.7311	+	23.3459i	0.505296	+	1.00558i
$540$		0			0
$541$	3.71877	−	6.44110i	0.159882	−	0.276925i	−0.774944	−	0.632030i	$-0.782222\pi$
$541$	3.71877	−	6.44110i	0.159882	−	0.276925i	0.934826	+	0.355106i	$0.115555\pi$
$542$	21.9310	−	2.85800i	0.942018	−	0.122762i
$543$		0			0
$544$	18.2697	−	13.8293i	0.783308	−	0.592927i
$545$	24.8292	+	14.3351i	1.06357	+	0.614050i
$546$		0			0
$547$	1.62692	−	0.939303i	0.0695621	−	0.0401617i	−0.464816	−	0.885408i	$-0.653879\pi$
$547$	1.62692	−	0.939303i	0.0695621	−	0.0401617i	0.534378	+	0.845246i	$0.320546\pi$
$548$	−20.6556	+	20.5474i	−0.882362	+	0.877742i
$549$		0			0
$550$	5.07741	+	2.11094i	0.216501	+	0.0900109i
$551$	−12.1349			−0.516965
$552$		0			0
$553$	5.06980	+	9.40009i	0.215590	+	0.399732i
$554$	−3.70015	−	28.3933i	−0.157204	−	1.20632i
$555$		0			0
$556$	18.4995	−	18.4027i	0.784555	−	0.780447i
$557$	8.36838	−	4.83149i	0.354580	−	0.204717i	−0.312121	−	0.950042i	$-0.601039\pi$
$557$	8.36838	−	4.83149i	0.354580	−	0.204717i	0.666700	+	0.745326i	$0.267706\pi$
$558$		0			0
$559$		−	17.2579i		−	0.729932i
$560$	−22.9598	+	12.2279i	−0.970227	+	0.516722i
$561$		0			0
$562$	−3.45136	+	8.30149i	−0.145587	+	0.350177i
$563$	−14.8934			−0.627684			−0.313842	−	0.949475i	$-0.601616\pi$
$563$	−14.8934			−0.627684			−0.313842	+	0.949475i	$0.601616\pi$
$564$		0			0
$565$	−23.7256			−0.998144
$566$	−8.78930	−	11.4856i	−0.369442	−	0.482777i
$567$		0			0
$568$	2.16444	+	5.28416i	0.0908177	+	0.221718i
$569$			3.81856i			0.160082i	0.996792	+	0.0800412i	$0.0255052\pi$
$569$			3.81856i			0.160082i	−0.996792	+	0.0800412i	$0.974495\pi$
$570$		0			0
$571$		−	4.52811i		−	0.189496i	−0.995501	−	0.0947478i	$-0.969796\pi$
$571$		−	4.52811i		−	0.189496i	0.995501	−	0.0947478i	$-0.0302045\pi$
$572$	−10.2182	+	2.70923i	−0.427244	+	0.113279i
$573$		0			0
$574$	−26.9000	+	19.3755i	−1.12278	+	0.808717i
$575$	−3.76784			−0.157130
$576$		0			0
$577$	11.9152	+	20.6378i	0.496038	+	0.859162i	0.999990	−	0.00456937i	$-0.00145448\pi$
$577$	11.9152	+	20.6378i	0.496038	+	0.859162i	−0.503952	+	0.863732i	$0.668121\pi$
$578$	0.108323	+	0.831222i	0.00450563	+	0.0345743i
$579$		0			0
$580$	18.3843	+	18.4811i	0.763369	+	0.767387i
$581$	−0.506032	−	0.312049i	−0.0209938	−	0.0129460i
$582$		0			0
$583$			29.8692i			1.23705i
$584$	1.64190	−	2.12241i	0.0679422	−	0.0878259i
$585$		0			0
$586$	−33.4545	+	4.35971i	−1.38199	+	0.180098i
$587$	−8.04599	−	13.9361i	−0.332094	−	0.575203i	0.650829	−	0.759225i	$-0.274422\pi$
$587$	−8.04599	−	13.9361i	−0.332094	−	0.575203i	−0.982922	+	0.184022i	$0.941088\pi$
$588$		0			0
$589$	7.11819	−	12.3291i	0.293300	−	0.508010i
$590$	−4.68926	+	11.2790i	−0.193054	+	0.464348i
$591$		0			0
$592$	−16.4962	+	9.40899i	−0.677991	+	0.386707i
$593$	−21.5747	−	12.4561i	−0.885966	−	0.511513i	−0.0133450	−	0.999911i	$-0.504248\pi$
$593$	−21.5747	−	12.4561i	−0.885966	−	0.511513i	−0.872621	+	0.488398i	$0.837581\pi$
$594$		0			0
$595$	−0.763275	+	26.3308i	−0.0312912	+	1.07946i
$596$	11.3911	+	42.9631i	0.466599	+	1.75984i
$597$		0			0
$598$	5.75253	−	4.40209i	0.235238	−	0.180015i
$599$	10.4068			0.425210			0.212605	−	0.977138i	$-0.431805\pi$
$599$	10.4068			0.425210			0.212605	+	0.977138i	$0.431805\pi$
$600$		0			0
$601$	−19.7275	−	34.1690i	−0.804701	−	1.39378i	−0.916493	−	0.400052i	$-0.868992\pi$
$601$	−19.7275	−	34.1690i	−0.804701	−	1.39378i	0.111791	−	0.993732i	$-0.464341\pi$
$602$	−4.57989	−	45.3687i	−0.186663	−	1.84909i
$603$		0			0
$604$	−3.20037	+	3.18361i	−0.130221	+	0.129539i
$605$	6.24060	+	3.60301i	0.253716	+	0.146483i
$606$		0			0
$607$	−8.95952	+	5.17278i	−0.363656	+	0.209957i	−0.670683	−	0.741744i	$-0.733999\pi$
$607$	−8.95952	+	5.17278i	−0.363656	+	0.209957i	0.307027	+	0.951701i	$0.400666\pi$
$608$	11.9272	+	5.03237i	0.483713	+	0.204089i
$609$		0			0
$610$	13.9662	−	33.5927i	0.565477	−	1.36013i
$611$	6.14545	−	10.6442i	0.248618	−	0.430620i
$612$		0			0
$613$	−18.1531	−	31.4421i	−0.733196	−	1.26993i	−0.955510	−	0.294958i	$-0.904694\pi$
$613$	−18.1531	−	31.4421i	−0.733196	−	1.26993i	0.222314	−	0.974975i	$-0.428639\pi$
$614$	5.54327	+	7.24379i	0.223708	+	0.292336i
$615$		0			0
$616$	−26.1432	+	9.83388i	−1.05334	+	0.396218i
$617$	5.74103	+	3.31459i	0.231125	+	0.133440i	0.611091	−	0.791560i	$-0.290731\pi$
$617$	5.74103	+	3.31459i	0.231125	+	0.133440i	−0.379966	+	0.925001i	$0.624064\pi$
$618$		0			0
$619$	33.2288	+	19.1847i	1.33558	+	0.771097i	0.986148	−	0.165865i	$-0.0530416\pi$
$619$	33.2288	+	19.1847i	1.33558	+	0.771097i	0.349431	+	0.936962i	$0.386375\pi$
$620$	−29.5608	+	7.83770i	−1.18719	+	0.314769i
$621$		0			0
$622$	−0.568455	+	0.435007i	−0.0227930	+	0.0174422i
$623$	−26.1202	−	0.757169i	−1.04648	−	0.0303353i
$624$		0			0
$625$	14.5617	+	25.2216i	0.582468	+	1.00886i
$626$	28.5075	−	21.8152i	1.13939	−	0.871911i
$627$		0			0
$628$	−1.16230	+	4.29265i	−0.0463807	+	0.171295i
$629$			19.2311i			0.766794i
$630$		0			0
$631$		−	24.9683i		−	0.993973i	−0.867758	−	0.496986i	$-0.834440\pi$
$631$		−	24.9683i		−	0.993973i	0.867758	−	0.496986i	$-0.165560\pi$
$632$	−10.5655	+	4.32772i	−0.420274	+	0.172148i
$633$		0			0
$634$	20.6814	+	27.0259i	0.821363	+	1.07333i
$635$	−1.15277	−	1.99666i	−0.0457463	−	0.0792350i
$636$		0			0
$637$	4.45075	+	8.85735i	0.176345	+	0.350941i
$638$	17.0105	+	22.2288i	0.673451	+	0.880047i
$639$		0			0
$640$	−10.4056	−	25.7888i	−0.411316	−	1.01939i
$641$	6.56452	+	3.79003i	0.259283	+	0.149697i	0.624007	−	0.781418i	$-0.285503\pi$
$641$	6.56452	+	3.79003i	0.259283	+	0.149697i	−0.364724	+	0.931116i	$0.618837\pi$
$642$		0			0
$643$	−29.8134	−	17.2128i	−1.17573	−	0.678806i	−0.220705	−	0.975341i	$-0.570836\pi$
$643$	−29.8134	−	17.2128i	−1.17573	−	0.678806i	−0.955022	+	0.296535i	$0.904169\pi$
$644$	13.9544	−	13.0991i	0.549880	−	0.516176i
$645$		0			0
$646$	10.4106	−	7.96667i	0.409601	−	0.313445i
$647$	−18.3282	−	31.7454i	−0.720557	−	1.24804i	−0.960777	−	0.277323i	$-0.910553\pi$
$647$	−18.3282	−	31.7454i	−0.720557	−	1.24804i	0.240220	−	0.970719i	$-0.422780\pi$
$648$		0			0
$649$	−6.55794	+	11.3587i	−0.257422	+	0.445868i
$650$	1.92635	+	0.800884i	0.0755576	+	0.0314132i
$651$		0			0
$652$	−0.785849	+	0.781734i	−0.0307762	+	0.0306151i
$653$	−12.7716	+	7.37370i	−0.499792	+	0.288555i	−0.728628	−	0.684910i	$-0.759841\pi$
$653$	−12.7716	+	7.37370i	−0.499792	+	0.288555i	0.228836	+	0.973465i	$0.426508\pi$
$654$		0			0
$655$	14.8409	+	8.56842i	0.579884	+	0.334796i
$656$	−17.5588	−	30.7849i	−0.685557	−	1.20195i
$657$		0			0
$658$	13.3308	−	29.6131i	0.519688	−	1.15444i
$659$	−14.0724	−	24.3742i	−0.548184	−	0.949483i	−0.998399	−	0.0565626i	$-0.981986\pi$
$659$	−14.0724	−	24.3742i	−0.548184	−	0.949483i	0.450215	−	0.892920i	$-0.351347\pi$
$660$		0			0
$661$	1.04116			0.0404965			0.0202483	−	0.999795i	$-0.493554\pi$
$661$	1.04116			0.0404965			0.0202483	+	0.999795i	$0.493554\pi$
$662$	−5.76301	−	7.53094i	−0.223986	−	0.292698i
$663$		0			0
$664$	0.388886	−	0.502696i	0.0150917	−	0.0195084i
$665$	−13.0986	+	7.06456i	−0.507943	+	0.273952i
$666$		0			0
$667$	−16.6101	−	9.58986i	−0.643147	−	0.371321i
$668$	−16.3308	−	16.4168i	−0.631858	−	0.635184i
$669$		0			0
$670$	35.1865	+	14.6289i	1.35937	+	0.565162i
$671$	19.5318	−	33.8301i	0.754018	−	1.30600i
$672$		0			0
$673$	6.14987	+	10.6519i	0.237060	+	0.410600i	0.959869	−	0.280448i	$-0.0904829\pi$
$673$	6.14987	+	10.6519i	0.237060	+	0.410600i	−0.722809	+	0.691047i	$0.757150\pi$
$674$	5.60441	+	43.0058i	0.215874	+	1.65652i
$675$		0			0
$676$	21.2549	−	5.63548i	0.817496	−	0.216749i
$677$			9.34125i			0.359013i	0.983757	+	0.179507i	$0.0574502\pi$
$677$			9.34125i			0.359013i	−0.983757	+	0.179507i	$0.942550\pi$
$678$		0			0
$679$	−29.3846	−	18.1202i	−1.12768	−	0.695391i
$680$	−27.9051	−	3.78560i	−1.07011	−	0.145171i
$681$		0			0
$682$	−32.5626	+	4.24348i	−1.24689	+	0.162491i
$683$	−10.8870	−	18.8568i	−0.416578	−	0.721535i	0.579014	−	0.815317i	$-0.303437\pi$
$683$	−10.8870	−	18.8568i	−0.416578	−	0.721535i	−0.995593	+	0.0937826i	$0.970104\pi$
$684$		0			0
$685$	35.8068			1.36811
$686$	14.0510	+	22.1036i	0.536468	+	0.843920i
$687$		0			0
$688$	48.7470	+	0.255909i	1.85846	+	0.00975644i
$689$			11.3322i			0.431724i
$690$		0			0
$691$		−	24.4555i		−	0.930329i	−0.885224	−	0.465165i	$-0.845995\pi$
$691$		−	24.4555i		−	0.930329i	0.885224	−	0.465165i	$-0.154005\pi$
$692$	−20.5791	−	5.57208i	−0.782298	−	0.211819i
$693$		0			0
$694$	−10.1461	+	7.76423i	−0.385140	+	0.294726i
$695$	−32.0692			−1.21646
$696$		0			0
$697$	−35.8886			−1.35938
$698$	28.4686	+	11.8359i	1.07755	+	0.447995i
$699$		0			0
$700$	5.27664	+	1.59420i	0.199438	+	0.0602551i
$701$		−	10.4921i		−	0.396279i	−0.980174	−	0.198140i	$-0.936510\pi$
$701$		−	10.4921i		−	0.396279i	0.980174	−	0.198140i	$-0.0634900\pi$
$702$		0			0
$703$	−9.40929	+	5.43246i	−0.354878	+	0.204889i
$704$	−7.50101	−	28.9026i	−0.282705	−	1.08931i
$705$		0			0
$706$	16.7187	−	2.17874i	0.629215	−	0.0819978i
$707$	14.4960	+	0.420209i	0.545179	+	0.0158036i
$708$		0			0
$709$	6.69447			0.251416			0.125708	−	0.992067i	$-0.459880\pi$
$709$	6.69447			0.251416			0.125708	+	0.992067i	$0.459880\pi$
$710$	2.69413	−	6.48015i	0.101109	−	0.243196i
$711$		0			0
$712$	3.75532	−	27.6818i	0.140737	−	1.03742i
$713$	19.4866	−	11.2506i	0.729778	−	0.421338i
$714$		0			0
$715$	11.2514	+	6.49600i	0.420779	+	0.242937i
$716$	40.9635	−	10.8610i	1.53088	−	0.405894i
$717$		0			0
$718$	1.87781	+	14.4095i	0.0700791	+	0.537757i
$719$	−8.66863	+	15.0145i	−0.323285	+	0.559947i	−0.981164	−	0.193177i	$-0.938121\pi$
$719$	−8.66863	+	15.0145i	−0.323285	+	0.559947i	0.657879	+	0.753124i	$0.271454\pi$
$720$		0			0
$721$	22.8389	−	37.0365i	0.850565	−	1.37931i
$722$	−17.9725	−	7.47209i	−0.668866	−	0.278082i
$723$		0			0
$724$	−8.67113	+	32.0246i	−0.322260	+	1.19019i
$725$		−	5.52386i		−	0.205151i
$726$		0			0
$727$	−18.0236	+	10.4059i	−0.668458	+	0.385934i	−0.795492	−	0.605964i	$-0.792787\pi$
$727$	−18.0236	+	10.4059i	−0.668458	+	0.385934i	0.127034	+	0.991898i	$0.459454\pi$
$728$	−9.91864	+	3.73094i	−0.367609	+	0.138278i
$729$		0			0
$730$	−3.27019	+	0.426163i	−0.121035	+	0.0157730i
$731$	24.6821	−	42.7507i	0.912900	−	1.58119i
$732$		0			0
$733$	−0.847870	−	1.46855i	−0.0313168	−	0.0542423i	0.849942	−	0.526876i	$-0.176637\pi$
$733$	−0.847870	−	1.46855i	−0.0313168	−	0.0542423i	−0.881259	+	0.472634i	$0.843303\pi$
$734$	−38.4789	+	5.01447i	−1.42028	+	0.185088i
$735$		0			0
$736$	12.3489	+	16.3140i	0.455187	+	0.601341i
$737$	35.4352	+	20.4585i	1.30527	+	0.753599i
$738$		0			0
$739$	42.4863	−	24.5295i	1.56288	−	0.902331i	0.565920	−	0.824460i	$-0.308521\pi$
$739$	42.4863	−	24.5295i	1.56288	−	0.902331i	0.996963	−	0.0778716i	$-0.0248124\pi$
$740$	22.5285	+	6.09992i	0.828165	+	0.224238i
$741$		0			0
$742$	3.00734	+	29.7909i	0.110403	+	1.09366i
$743$	13.4749	−	23.3392i	0.494346	−	0.856232i	−0.505633	−	0.862749i	$-0.668741\pi$
$743$	13.4749	−	23.3392i	0.494346	−	0.856232i	0.999979	+	0.00651646i	$0.00207427\pi$
$744$		0			0
$745$	27.3129	−	47.3073i	1.00067	−	1.73321i
$746$	6.61441	+	2.74995i	0.242171	+	0.100683i
$747$		0			0
$748$	−29.1868	−	7.90275i	−1.06718	−	0.288953i
$749$	0.671564	−	23.1671i	0.0245384	−	0.846506i
$750$		0			0
$751$	29.1105	−	16.8069i	1.06226	−	0.613294i	0.136201	−	0.990681i	$-0.456511\pi$
$751$	29.1105	−	16.8069i	1.06226	−	0.613294i	0.926056	+	0.377387i	$0.123177\pi$
$752$	29.9747	+	17.5164i	1.09307	+	0.638757i
$753$		0			0
$754$	6.45370	+	8.43353i	0.235030	+	0.307131i
$755$	5.54789			0.201908
$756$		0			0
$757$	30.1721			1.09662			0.548312	−	0.836274i	$-0.315271\pi$
$757$	30.1721			1.09662			0.548312	+	0.836274i	$0.315271\pi$
$758$	−0.881700	−	1.15218i	−0.0320248	−	0.0418491i
$759$		0			0
$760$	−6.03051	−	14.7226i	−0.218749	−	0.534046i
$761$	13.7774	−	7.95440i	0.499432	−	0.288347i	−0.229047	−	0.973415i	$-0.573561\pi$
$761$	13.7774	−	7.95440i	0.499432	−	0.288347i	0.728479	+	0.685068i	$0.240228\pi$
$762$		0			0
$763$	26.2675	+	16.1981i	0.950948	+	0.586410i
$764$	8.61706	−	31.8249i	0.311754	−	1.15139i
$765$		0			0
$766$	32.9971	+	13.7186i	1.19223	+	0.495674i
$767$	−2.48806	+	4.30944i	−0.0898386	+	0.155605i
$768$		0			0
$769$	−2.11592	+	3.66489i	−0.0763022	+	0.132159i	−0.901652	−	0.432463i	$-0.857645\pi$
$769$	−2.11592	+	3.66489i	−0.0763022	+	0.132159i	0.825350	+	0.564622i	$0.190978\pi$
$770$	31.3023	+	14.0912i	1.12806	+	0.507812i
$771$		0			0
$772$	12.1116	−	44.7310i	0.435904	−	1.60990i
$773$	24.1708	−	13.9550i	0.869362	−	0.501927i	0.00222598	−	0.999998i	$-0.499291\pi$
$773$	24.1708	−	13.9550i	0.869362	−	0.501927i	0.867136	+	0.498071i	$0.165958\pi$
$774$		0			0
$775$	5.61224	+	3.24023i	0.201598	+	0.116392i
$776$	22.5821	−	29.1908i	0.810648	−	1.04789i
$777$		0			0
$778$	13.0534	−	1.70109i	0.467988	−	0.0609871i
$779$	−10.1379	−	17.5594i	−0.363229	−	0.629131i
$780$		0			0
$781$	3.76776	−	6.52595i	0.134821	−	0.233517i
$782$	20.5458	−	2.67747i	0.734715	−	0.0957463i
$783$		0			0
$784$	−25.0846	+	12.4403i	−0.895879	+	0.444297i
$785$	4.73336	−	2.73281i	0.168941	−	0.0975380i
$786$		0			0
$787$			6.45630i			0.230142i	0.993357	+	0.115071i	$0.0367096\pi$
$787$			6.45630i			0.230142i	−0.993357	+	0.115071i	$0.963290\pi$
$788$	27.8214	+	7.53305i	0.991097	+	0.268354i
$789$		0			0
$790$	12.9569	+	5.38684i	0.460985	+	0.191655i
$791$	−25.5272	−	0.739981i	−0.907644	−	0.0263107i
$792$		0			0
$793$	7.41030	−	12.8350i	0.263148	−	0.455785i
$794$	2.65348	+	20.3616i	0.0941683	+	0.722607i
$795$		0			0
$796$	−1.39961	−	5.27881i	−0.0496080	−	0.187103i
$797$	−29.3156	−	16.9254i	−1.03841	−	0.599528i	−0.119029	−	0.992891i	$-0.537978\pi$
$797$	−29.3156	−	16.9254i	−1.03841	−	0.599528i	−0.919383	+	0.393363i	$0.871312\pi$
$798$		0			0
$799$	30.4465	−	17.5783i	1.07712	−	0.621876i
$800$	−2.29075	+	5.42932i	−0.0809904	+	0.191956i
$801$		0			0
$802$	9.74924	−	23.4497i	0.344258	−	0.828036i
$803$	−3.54109			−0.124962
$804$		0			0
$805$	−23.5122	−	0.681568i	−0.828695	−	0.0240221i
$806$	−12.3541	+	1.60996i	−0.435155	+	0.0567084i
$807$		0			0
$808$	−2.08410	+	15.3627i	−0.0733185	+	0.540458i
$809$	−6.11435	+	3.53012i	−0.214969	+	0.124112i	−0.603619	−	0.797273i	$-0.706275\pi$
$809$	−6.11435	+	3.53012i	−0.214969	+	0.124112i	0.388650	+	0.921386i	$0.372942\pi$
$810$		0			0
$811$		−	40.7979i		−	1.43261i	−0.697789	−	0.716304i	$-0.745833\pi$
$811$		−	40.7979i		−	1.43261i	0.697789	−	0.716304i	$-0.254167\pi$
$812$	19.2040	+	20.4579i	0.673928	+	0.717932i
$813$		0			0
$814$	23.1410	+	9.62090i	0.811090	+	0.337212i
$815$	1.36228			0.0477187
$816$		0			0
$817$	27.8891			0.975716
$818$	−0.355836	+	0.272302i	−0.0124415	+	0.00952081i
$819$		0			0
$820$	−11.3835	+	42.0422i	−0.397530	+	1.46818i
$821$		−	37.0350i		−	1.29253i	−0.763113	−	0.646265i	$-0.776330\pi$
$821$		−	37.0350i		−	1.29253i	0.763113	−	0.646265i	$-0.223670\pi$
$822$		0			0
$823$			11.7953i			0.411158i	0.978641	+	0.205579i	$0.0659077\pi$
$823$			11.7953i			0.411158i	−0.978641	+	0.205579i	$0.934092\pi$
$824$	36.7923	+	28.4626i	1.28172	+	0.991541i
$825$		0			0
$826$	−5.39713	+	11.9892i	−0.187790	+	0.417158i
$827$	9.85297			0.342621			0.171311	−	0.985217i	$-0.445200\pi$
$827$	9.85297			0.342621			0.171311	+	0.985217i	$0.445200\pi$
$828$		0			0
$829$	−6.91019	−	11.9688i	−0.240001	−	0.415693i	0.720713	−	0.693233i	$-0.243814\pi$
$829$	−6.91019	−	11.9688i	−0.240001	−	0.415693i	−0.960714	+	0.277540i	$0.910481\pi$
$830$	−0.774549	+	0.100937i	−0.0268850	+	0.00350359i
$831$		0			0
$832$	−2.84585	−	10.9655i	−0.0986622	−	0.380162i
$833$	−1.64247	+	28.3065i	−0.0569083	+	0.980762i
$834$		0			0
$835$			28.4587i			0.984855i
$836$	−4.37816	−	16.5128i	−0.151422	−	0.571106i
$837$		0			0
$838$	−3.21651	−	24.6821i	−0.111112	−	0.852628i
$839$	21.5036	+	37.2454i	0.742388	+	1.28585i	0.951405	+	0.307942i	$0.0996402\pi$
$839$	21.5036	+	37.2454i	0.742388	+	1.28585i	−0.209017	+	0.977912i	$0.567026\pi$
$840$		0			0
$841$	−0.440737	+	0.763379i	−0.0151978	+	0.0263234i
$842$	−29.9675	−	12.4591i	−1.03275	−	0.429368i
$843$		0			0
$844$	12.9647	−	12.8968i	0.446264	−	0.443928i
$845$	−23.4041	−	13.5124i	−0.805126	−	0.464840i
$846$		0			0
$847$	6.60211	+	4.07125i	0.226851	+	0.139890i
$848$	−32.0093	−	0.168040i	−1.09920	−	0.00577053i
$849$		0			0
$850$	3.62646	+	4.73896i	0.124387	+	0.162545i
$851$	−17.1724			−0.588663
$852$		0			0
$853$	−27.0808	−	46.9054i	−0.927230	−	1.60601i	−0.787935	−	0.615759i	$-0.788849\pi$
$853$	−27.0808	−	46.9054i	−0.927230	−	1.60601i	−0.139296	−	0.990251i	$-0.544484\pi$
$854$	16.0745	−	35.7080i	0.550059	−	1.22190i
$855$		0			0
$856$	24.5521	+	3.33075i	0.839175	+	0.113843i
$857$	−30.3446	−	17.5194i	−1.03655	−	0.598453i	−0.117696	−	0.993050i	$-0.537551\pi$
$857$	−30.3446	−	17.5194i	−1.03655	−	0.598453i	−0.918854	+	0.394597i	$0.870884\pi$
$858$		0			0
$859$	−28.0725	+	16.2077i	−0.957822	+	0.552999i	−0.895502	−	0.445058i	$-0.853183\pi$
$859$	−28.0725	+	16.2077i	−0.957822	+	0.552999i	−0.0623198	+	0.998056i	$0.519850\pi$
$860$	−42.2519	−	42.4743i	−1.44078	−	1.44836i
$861$		0			0
$862$	29.7550	+	12.3707i	1.01346	+	0.421347i
$863$	0.619701	−	1.07335i	0.0210949	−	0.0365374i	−0.855285	−	0.518157i	$-0.826618\pi$
$863$	0.619701	−	1.07335i	0.0210949	−	0.0365374i	0.876380	+	0.481620i	$0.159951\pi$
$864$		0			0
$865$	13.1011	+	22.6918i	0.445452	+	0.771545i
$866$	−29.1520	+	22.3084i	−0.990624	+	0.758069i
$867$		0			0
$868$	−32.0500	+	7.51089i	−1.08785	+	0.254936i
$869$	13.0484	+	7.53352i	0.442638	+	0.255557i
$870$		0			0
$871$	13.4440	+	7.76188i	0.455532	+	0.263001i
$872$	−20.1866	+	26.0943i	−0.683605	+	0.883665i
$873$		0			0
$874$	7.11385	+	9.29619i	0.240630	+	0.314448i
$875$	12.2195	+	22.6565i	0.413094	+	0.765930i
$876$		0			0
$877$	−24.0478	−	41.6520i	−0.812037	−	1.40649i	−0.911436	−	0.411441i	$-0.865025\pi$
$877$	−24.0478	−	41.6520i	−0.812037	−	1.40649i	0.0993995	−	0.995048i	$-0.468308\pi$
$878$	−3.37406	−	4.40913i	−0.113869	−	0.148801i
$879$		0			0
$880$	−18.5156	+	31.6846i	−0.624159	+	1.06809i
$881$		−	5.79121i		−	0.195111i	−0.995230	−	0.0975554i	$-0.968898\pi$
$881$		−	5.79121i		−	0.195111i	0.995230	−	0.0975554i	$-0.0311023\pi$
$882$		0			0
$883$			52.6107i			1.77049i	0.465125	+	0.885245i	$0.346009\pi$
$883$			52.6107i			1.77049i	−0.465125	+	0.885245i	$0.653991\pi$
$884$	−11.0734	−	2.99827i	−0.372437	−	0.100843i
$885$		0			0
$886$	12.7333	−	9.74408i	0.427784	−	0.327359i
$887$	−23.8466	−	41.3034i	−0.800689	−	1.38683i	−0.919163	−	0.393877i	$-0.871134\pi$
$887$	−23.8466	−	41.3034i	−0.800689	−	1.38683i	0.118474	−	0.992957i	$-0.462200\pi$
$888$		0			0
$889$	−1.17803	−	2.18423i	−0.0395100	−	0.0732568i
$890$	−27.2652	+	20.8645i	−0.913930	+	0.699379i
$891$		0			0
$892$	−4.60465	−	17.3670i	−0.154175	−	0.581490i
$893$	17.2013	+	9.93116i	0.575618	+	0.332333i
$894$		0			0
$895$	−45.1055	−	26.0417i	−1.50771	−	0.870478i
$896$	−10.3914	−	28.0717i	−0.347152	−	0.937809i
$897$		0			0
$898$	13.4691	+	17.6010i	0.449469	+	0.587354i
$899$	16.4940	+	28.5684i	0.550105	+	0.952810i
$900$		0			0
$901$	−16.2073	+	28.0718i	−0.539942	+	0.935207i
$902$	−17.9543	+	43.1851i	−0.597812	+	1.43791i
$903$		0			0
$904$	3.67007	−	27.0534i	0.122065	−	0.899784i
$905$	35.3125	−	20.3877i	1.17383	−	0.677709i
$906$		0			0
$907$	−5.19604	−	2.99994i	−0.172532	−	0.0996113i	0.411247	−	0.911524i	$-0.365093\pi$
$907$	−5.19604	−	2.99994i	−0.172532	−	0.0996113i	−0.583779	+	0.811913i	$0.698427\pi$
$908$	14.6251	+	14.7021i	0.485351	+	0.487905i
$909$		0			0
$910$	11.8760	+	5.34615i	0.393685	+	0.177223i
$911$	−8.56559	−	14.8360i	−0.283791	−	0.491540i	0.688525	−	0.725213i	$-0.258259\pi$
$911$	−8.56559	−	14.8360i	−0.283791	−	0.491540i	−0.972315	+	0.233673i	$0.924925\pi$
$912$		0			0
$913$	−0.838712			−0.0277573
$914$	−19.6379	+	15.0278i	−0.649564	+	0.497075i
$915$		0			0
$916$	7.17219	−	1.90162i	0.236976	−	0.0628313i
$917$	15.7007	+	9.68196i	0.518482	+	0.319726i
$918$		0			0
$919$	−7.67873	−	4.43332i	−0.253298	−	0.146242i	0.367975	−	0.929836i	$-0.380051\pi$
$919$	−7.67873	−	4.43332i	−0.253298	−	0.146242i	−0.621273	+	0.783594i	$0.713384\pi$
$920$	3.38036	−	24.9179i	0.111447	−	0.821518i
$921$		0			0
$922$	−1.36527	+	3.28386i	−0.0449628	+	0.108148i
$923$	1.42947	−	2.47592i	0.0470517	−	0.0814959i
$924$		0			0
$925$	−2.47288	−	4.28315i	−0.0813077	−	0.140829i
$926$	24.8274	−	3.23545i	0.815879	−	0.106323i
$927$		0			0
$928$	−23.9172	+	18.1042i	−0.785120	+	0.594299i
$929$		−	10.7326i		−	0.352124i	−0.984379	−	0.176062i	$-0.943664\pi$
$929$		−	10.7326i		−	0.352124i	0.984379	−	0.176062i	$-0.0563360\pi$
$930$		0			0
$931$	−14.3136	+	7.19249i	−0.469111	+	0.235724i
$932$	−21.2195	+	21.1084i	−0.695067	+	0.691427i
$933$		0			0
$934$	−4.35760	−	33.4383i	−0.142585	−	1.09413i
$935$	18.5810	+	32.1833i	0.607665	+	1.05251i
$936$		0			0
$937$	−21.5535			−0.704121			−0.352061	−	0.935977i	$-0.614519\pi$
$937$	−21.5535			−0.704121			−0.352061	+	0.935977i	$0.614519\pi$
$938$	37.4022	+	16.8372i	1.22123	+	0.549753i
$939$		0			0
$940$	−10.9350	−	41.2427i	−0.356660	−	1.34519i
$941$			10.1707i			0.331554i	0.986163	+	0.165777i	$0.0530133\pi$
$941$			10.1707i			0.331554i	−0.986163	+	0.165777i	$0.946987\pi$
$942$		0			0
$943$		−	32.0468i		−	1.04359i
$944$	−12.1356	−	7.09171i	−0.394981	−	0.230816i
$945$		0			0
$946$	−39.0943	−	51.0874i	−1.27107	−	1.66100i
$947$	−6.23262			−0.202533			−0.101267	−	0.994859i	$-0.532289\pi$
$947$	−6.23262			−0.202533			−0.101267	+	0.994859i	$0.532289\pi$
$948$		0			0
$949$	−1.34347			−0.0436110
$950$	−1.29424	+	3.11301i	−0.0419907	+	0.101000i
$951$		0			0
$952$	−29.9060	−	4.94341i	−0.969260	−	0.160217i
$953$			24.0752i			0.779871i	0.920842	+	0.389936i	$0.127503\pi$
$953$			24.0752i			0.779871i	−0.920842	+	0.389936i	$0.872497\pi$
$954$		0			0
$955$	−35.0923	+	20.2605i	−1.13556	+	0.655615i
$956$	19.3091	+	19.4107i	0.624500	+	0.627787i
$957$		0			0
$958$	0.326176	+	2.50294i	0.0105383	+	0.0808662i
$959$	38.5258	+	1.11678i	1.24406	+	0.0360628i
$960$		0			0
$961$	−7.70065			−0.248408
$962$	8.77959	+	3.65013i	0.283065	+	0.117685i
$963$		0			0
$964$	16.5569	+	16.6441i	0.533263	+	0.536069i
$965$	−49.3233	+	28.4768i	−1.58777	+	0.916701i
$966$		0			0
$967$	1.08046	+	0.623806i	0.0347454	+	0.0200603i	0.517272	−	0.855821i	$-0.326948\pi$
$967$	1.08046	+	0.623806i	0.0347454	+	0.0200603i	−0.482527	+	0.875881i	$0.660281\pi$
$968$	−5.07373	+	6.55858i	−0.163076	+	0.210801i
$969$		0			0
$970$	−44.9770	+	5.86129i	−1.44412	+	0.188195i
$971$	−7.33316	+	12.7014i	−0.235332	+	0.407608i	−0.959369	−	0.282154i	$-0.908951\pi$
$971$	−7.33316	+	12.7014i	−0.235332	+	0.407608i	0.724037	+	0.689761i	$0.242285\pi$
$972$		0			0
$973$	−34.5045	−	1.00021i	−1.10616	−	0.0320653i
$974$	8.96200	−	21.5561i	0.287161	−	0.690703i
$975$		0			0
$976$	36.1441	+	21.1216i	1.15695	+	0.676085i
$977$			42.0613i			1.34566i	0.739797	+	0.672830i	$0.234921\pi$
$977$			42.0613i			1.34566i	−0.739797	+	0.672830i	$0.765079\pi$
$978$		0			0
$979$	−31.9258	+	18.4324i	−1.02035	+	0.589101i
$980$	32.6390	+	10.9027i	1.04262	+	0.348272i
$981$		0			0
$982$	6.08381	+	46.6845i	0.194142	+	1.48976i
$983$	−3.51155	+	6.08218i	−0.112001	+	0.193992i	−0.916577	−	0.399858i	$-0.869059\pi$
$983$	−3.51155	+	6.08218i	−0.112001	+	0.193992i	0.804576	+	0.593850i	$0.202393\pi$
$984$		0			0
$985$	−17.7118	−	30.6777i	−0.564345	−	0.977474i
$986$	3.92532	+	30.1212i	0.125008	+	0.959255i
$987$		0			0
$988$	−1.66106	−	6.26488i	−0.0528452	−	0.199312i
$989$	38.1743	+	22.0399i	1.21387	+	0.700829i
$990$		0			0
$991$	−34.0177	+	19.6402i	−1.08061	+	0.623890i	−0.931061	−	0.364864i	$-0.881115\pi$
$991$	−34.0177	+	19.6402i	−1.08061	+	0.623890i	−0.149548	+	0.988754i	$0.547782\pi$
$992$	−4.36432	−	34.9195i	−0.138567	−	1.10870i
$993$		0			0
$994$	3.10083	−	6.88820i	0.0983523	−	0.218481i
$995$	−3.35590	+	5.81258i	−0.106389	+	0.184271i
$996$		0			0
$997$	2.27039	−	3.93243i	0.0719039	−	0.124541i	−0.827832	−	0.560976i	$-0.810426\pi$
$997$	2.27039	−	3.93243i	0.0719039	−	0.124541i	0.899736	+	0.436435i	$0.143759\pi$
$998$	−15.1697	+	36.4874i	−0.480189	+	1.15499i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bb.a.611.36		88
3.2	odd	2		252.2.bb.a.23.9	yes	88
4.3	odd	2	inner	756.2.bb.a.611.9		88
7.4	even	3		756.2.o.a.179.24		88
9.2	odd	6		756.2.o.a.359.38		88
9.7	even	3		252.2.o.a.191.7	yes	88
12.11	even	2		252.2.bb.a.23.36	yes	88
21.11	odd	6		252.2.o.a.95.21	yes	88
28.11	odd	6		756.2.o.a.179.38		88
36.7	odd	6		252.2.o.a.191.21	yes	88
36.11	even	6		756.2.o.a.359.24		88
63.11	odd	6	inner	756.2.bb.a.683.9		88
63.25	even	3		252.2.bb.a.11.36	yes	88
84.11	even	6		252.2.o.a.95.7	✓	88
252.11	even	6	inner	756.2.bb.a.683.36		88
252.151	odd	6		252.2.bb.a.11.9	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.7	✓	88	84.11	even	6
252.2.o.a.95.21	yes	88	21.11	odd	6
252.2.o.a.191.7	yes	88	9.7	even	3
252.2.o.a.191.21	yes	88	36.7	odd	6
252.2.bb.a.11.9	yes	88	252.151	odd	6
252.2.bb.a.11.36	yes	88	63.25	even	3
252.2.bb.a.23.9	yes	88	3.2	odd	2
252.2.bb.a.23.36	yes	88	12.11	even	2
756.2.o.a.179.24		88	7.4	even	3
756.2.o.a.179.38		88	28.11	odd	6
756.2.o.a.359.24		88	36.11	even	6
756.2.o.a.359.38		88	9.2	odd	6
756.2.bb.a.611.9		88	4.3	odd	2	inner
756.2.bb.a.611.36		88	1.1	even	1	trivial
756.2.bb.a.683.9		88	63.11	odd	6	inner
756.2.bb.a.683.36		88	252.11	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.12310 - 0.859445i) q^{2} +(0.522707 - 1.93049i) q^{4} +(-2.12868 + 1.22899i) q^{5} +(-2.32866 + 1.25593i) q^{7} +(-1.07210 - 2.61737i) q^{8} +O(q^{10})\)	\(q+(1.12310 - 0.859445i) q^{2} +(0.522707 - 1.93049i) q^{4} +(-2.12868 + 1.22899i) q^{5} +(-2.32866 + 1.25593i) q^{7} +(-1.07210 - 2.61737i) q^{8} +(-1.33447 + 3.20977i) q^{10} +(-1.86626 + 3.23245i) q^{11} +(-0.708051 + 1.22638i) q^{13} +(-1.53591 + 3.41189i) q^{14} +(-3.45355 - 2.01816i) q^{16} +(-3.50791 + 2.02529i) q^{17} +(-1.98185 - 1.14422i) q^{19} +(1.25988 + 4.75179i) q^{20} +(0.682123 + 5.23432i) q^{22} +(-1.80849 - 3.13240i) q^{23} +(0.520855 - 0.902147i) q^{25} +(0.258795 + 1.98588i) q^{26} +(1.20735 + 5.15192i) q^{28} +(4.59226 - 2.65135i) q^{29} +6.22098i q^{31} +(-5.61318 + 0.701549i) q^{32} +(-2.19911 + 5.28947i) q^{34} +(3.41344 - 5.53538i) q^{35} +(2.37386 - 4.11165i) q^{37} +(-3.20921 + 0.418217i) q^{38} +(5.49888 + 4.25394i) q^{40} +(7.67307 + 4.43005i) q^{41} +(-10.5542 + 6.09346i) q^{43} +(5.26470 + 5.29241i) q^{44} +(-4.72324 - 1.96370i) q^{46} -8.67939 q^{47} +(3.84529 - 5.84925i) q^{49} +(-0.190374 - 1.46085i) q^{50} +(1.99741 + 2.00792i) q^{52} +(6.93030 - 4.00121i) q^{53} -9.17448i q^{55} +(5.78377 + 4.74848i) q^{56} +(2.87889 - 6.92453i) q^{58} +3.51395 q^{59} -10.4658 q^{61} +(5.34660 + 6.98679i) q^{62} +(-5.70122 + 5.61213i) q^{64} -3.48076i q^{65} -10.9623i q^{67} +(2.07619 + 7.83061i) q^{68} +(-0.923722 - 9.15045i) q^{70} -2.01888 q^{71} +(0.474356 + 0.821609i) q^{73} +(-0.867655 - 6.65800i) q^{74} +(-3.24483 + 3.22784i) q^{76} +(0.286144 - 9.87116i) q^{77} -4.03670i q^{79} +(9.83182 + 0.0516145i) q^{80} +(12.4250 - 1.61920i) q^{82} +(0.112352 + 0.194599i) q^{83} +(4.97815 - 8.62241i) q^{85} +(-6.61641 + 15.9143i) q^{86} +(10.4613 + 1.41918i) q^{88} +(8.55343 + 4.93832i) q^{89} +(0.108562 - 3.74508i) q^{91} +(-6.99236 + 1.85394i) q^{92} +(-9.74782 + 7.45946i) q^{94} +5.62497 q^{95} +(6.52412 + 11.3001i) q^{97} +(-0.708472 - 9.87411i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 88 * q - 2 * q^4 + 6 * q^5	\( 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) \) 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

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