LMFDB - Embedded newform 756.2.n.b.19.9

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			19.9
Character	$\chi$	$=$	756.19
Dual form			756.2.n.b.199.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08144 + 0.911308i) q^{2} +(0.339034 - 1.97105i) q^{4} -0.815110i q^{5} +(0.448419 - 2.60747i) q^{7} +(1.42959 + 2.44055i) q^{8} +O(q^{10})$	\(q+(-1.08144 + 0.911308i) q^{2} +(0.339034 - 1.97105i) q^{4} -0.815110i q^{5} +(0.448419 - 2.60747i) q^{7} +(1.42959 + 2.44055i) q^{8} +(0.742817 + 0.881495i) q^{10} +4.82284i q^{11} +(2.20303 - 1.27192i) q^{13} +(1.89127 + 3.22848i) q^{14} +(-3.77011 - 1.33651i) q^{16} +(0.503257 - 0.290555i) q^{17} +(-2.24125 + 3.88195i) q^{19} +(-1.60663 - 0.276350i) q^{20} +(-4.39509 - 5.21562i) q^{22} -6.47618i q^{23} +4.33560 q^{25} +(-1.22334 + 3.38315i) q^{26} +(-4.98744 - 1.76788i) q^{28} +(3.16210 - 5.47692i) q^{29} +(4.81219 - 8.33495i) q^{31} +(5.29513 - 1.99038i) q^{32} +(-0.279458 + 0.772841i) q^{34} +(-2.12538 - 0.365511i) q^{35} +(1.62993 - 2.82313i) q^{37} +(-1.11388 - 6.24058i) q^{38} +(1.98931 - 1.16528i) q^{40} +(-3.04709 + 1.75924i) q^{41} +(4.72260 + 2.72659i) q^{43} +(9.50608 + 1.63511i) q^{44} +(5.90179 + 7.00361i) q^{46} +(-4.79019 - 8.29685i) q^{47} +(-6.59784 - 2.33848i) q^{49} +(-4.68870 + 3.95106i) q^{50} +(-1.76012 - 4.77352i) q^{52} +(1.09484 + 1.89632i) q^{53} +3.93115 q^{55} +(7.00472 - 2.63324i) q^{56} +(1.57153 + 8.80463i) q^{58} +(5.60288 - 9.70447i) q^{59} +(-6.27670 + 3.62386i) q^{61} +(2.39161 + 13.3992i) q^{62} +(-3.91253 + 6.97797i) q^{64} +(-1.03676 - 1.79571i) q^{65} +(4.34796 + 2.51030i) q^{67} +(-0.402079 - 1.09045i) q^{68} +(2.63157 - 1.54160i) q^{70} +3.64207i q^{71} +(2.26126 - 1.30554i) q^{73} +(0.810061 + 4.53842i) q^{74} +(6.89168 + 5.73374i) q^{76} +(12.5754 + 2.16265i) q^{77} +(8.78313 - 5.07094i) q^{79} +(-1.08940 + 3.07306i) q^{80} +(1.69204 - 4.67935i) q^{82} +(0.820993 - 1.42200i) q^{83} +(-0.236835 - 0.410210i) q^{85} +(-7.59199 + 1.35509i) q^{86} +(-11.7704 + 6.89469i) q^{88} +(1.90724 + 1.10115i) q^{89} +(-2.32862 - 6.31470i) q^{91} +(-12.7649 - 2.19565i) q^{92} +(12.7413 + 4.60722i) q^{94} +(3.16422 + 1.82686i) q^{95} +(6.14759 + 3.54931i) q^{97} +(9.26626 - 3.48373i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.08144	+	0.911308i	−0.764695	+	0.644392i
$2$	−1.08144	+	0.911308i	−0.764695	+	0.644392i
$3$		0			0
$3$		0			0
$4$	0.339034	−	1.97105i	0.169517	−	0.985527i
$5$		−	0.815110i		−	0.364528i	−0.983250	−	0.182264i	$-0.941657\pi$
$5$		−	0.815110i		−	0.364528i	0.983250	−	0.182264i	$-0.0583426\pi$
$6$		0			0
$7$	0.448419	−	2.60747i	0.169487	−	0.985532i
$7$	0.448419	−	2.60747i	0.169487	−	0.985532i
$8$	1.42959	+	2.44055i	0.505437	+	0.862863i
$9$		0			0
$10$	0.742817	+	0.881495i	0.234899	+	0.278753i
$11$			4.82284i			1.45414i	0.686563	+	0.727070i	$0.259119\pi$
$11$			4.82284i			1.45414i	−0.686563	+	0.727070i	$0.740881\pi$
$12$		0			0
$13$	2.20303	−	1.27192i	0.611011	−	0.352767i	−0.162350	−	0.986733i	$-0.551907\pi$
$13$	2.20303	−	1.27192i	0.611011	−	0.352767i	0.773361	+	0.633966i	$0.218574\pi$
$14$	1.89127	+	3.22848i	0.505464	+	0.862848i
$15$		0			0
$16$	−3.77011	−	1.33651i	−0.942528	−	0.334128i
$17$	0.503257	−	0.290555i	0.122058	−	0.0704700i	−0.437728	−	0.899107i	$-0.644217\pi$
$17$	0.503257	−	0.290555i	0.122058	−	0.0704700i	0.559786	+	0.828637i	$0.310883\pi$
$18$		0			0
$19$	−2.24125	+	3.88195i	−0.514177	+	0.890581i	0.485687	+	0.874133i	$0.338569\pi$
$19$	−2.24125	+	3.88195i	−0.514177	+	0.890581i	−0.999865	+	0.0164486i	$0.994764\pi$
$20$	−1.60663	−	0.276350i	−0.359253	−	0.0617938i
$21$		0			0
$22$	−4.39509	−	5.21562i	−0.937037	−	1.11197i
$23$		−	6.47618i		−	1.35038i	−0.737646	−	0.675188i	$-0.764063\pi$
$23$		−	6.47618i		−	1.35038i	0.737646	−	0.675188i	$-0.235937\pi$
$24$		0			0
$25$	4.33560			0.867119
$26$	−1.22334	+	3.38315i	−0.239917	+	0.663490i
$27$		0			0
$28$	−4.98744	−	1.76788i	−0.942538	−	0.334098i
$29$	3.16210	−	5.47692i	0.587188	−	1.01704i	−0.407411	−	0.913245i	$-0.633568\pi$
$29$	3.16210	−	5.47692i	0.587188	−	1.01704i	0.994599	−	0.103794i	$-0.0330983\pi$
$30$		0			0
$31$	4.81219	−	8.33495i	0.864294	−	1.49700i	−0.00345157	−	0.999994i	$-0.501099\pi$
$31$	4.81219	−	8.33495i	0.864294	−	1.49700i	0.867746	−	0.497008i	$-0.165568\pi$
$32$	5.29513	−	1.99038i	0.936056	−	0.351852i
$33$		0			0
$34$	−0.279458	+	0.772841i	−0.0479266	+	0.132541i
$35$	−2.12538	−	0.365511i	−0.359255	−	0.0617827i
$36$		0			0
$37$	1.62993	−	2.82313i	0.267959	−	0.464119i	−0.700375	−	0.713775i	$-0.746984\pi$
$37$	1.62993	−	2.82313i	0.267959	−	0.464119i	0.968335	+	0.249655i	$0.0803173\pi$
$38$	−1.11388	−	6.24058i	−0.180695	−	1.01235i
$39$		0			0
$40$	1.98931	−	1.16528i	0.314538	−	0.184246i
$41$	−3.04709	+	1.75924i	−0.475875	+	0.274747i	−0.718696	−	0.695325i	$-0.755261\pi$
$41$	−3.04709	+	1.75924i	−0.475875	+	0.274747i	0.242821	+	0.970071i	$0.421927\pi$
$42$		0			0
$43$	4.72260	+	2.72659i	0.720190	+	0.415802i	0.814823	−	0.579710i	$-0.196834\pi$
$43$	4.72260	+	2.72659i	0.720190	+	0.415802i	−0.0946327	+	0.995512i	$0.530168\pi$
$44$	9.50608	+	1.63511i	1.43310	+	0.246502i
$45$		0			0
$46$	5.90179	+	7.00361i	0.870172	+	1.03263i
$47$	−4.79019	−	8.29685i	−0.698721	−	1.21022i	−0.968910	−	0.247413i	$-0.920420\pi$
$47$	−4.79019	−	8.29685i	−0.698721	−	1.21022i	0.270190	−	0.962807i	$-0.412914\pi$
$48$		0			0
$49$	−6.59784	−	2.33848i	−0.942549	−	0.334069i
$50$	−4.68870	+	3.95106i	−0.663082	+	0.558765i
$51$		0			0
$52$	−1.76012	−	4.77352i	−0.244085	−	0.661968i
$53$	1.09484	+	1.89632i	0.150388	+	0.260480i	0.931370	−	0.364074i	$-0.118614\pi$
$53$	1.09484	+	1.89632i	0.150388	+	0.260480i	−0.780982	+	0.624553i	$0.785281\pi$
$54$		0			0
$55$	3.93115			0.530076
$56$	7.00472	−	2.63324i	0.936045	−	0.351881i
$57$		0			0
$58$	1.57153	+	8.80463i	0.206353	+	1.15610i
$59$	5.60288	−	9.70447i	0.729432	−	1.26341i	−0.227691	−	0.973733i	$-0.573118\pi$
$59$	5.60288	−	9.70447i	0.729432	−	1.26341i	0.957123	−	0.289680i	$-0.0935490\pi$
$60$		0			0
$61$	−6.27670	+	3.62386i	−0.803649	+	0.463987i	−0.844746	−	0.535168i	$-0.820248\pi$
$61$	−6.27670	+	3.62386i	−0.803649	+	0.463987i	0.0410962	+	0.999155i	$0.486915\pi$
$62$	2.39161	+	13.3992i	0.303735	+	1.70169i
$63$		0			0
$64$	−3.91253	+	6.97797i	−0.489066	+	0.872247i
$65$	−1.03676	−	1.79571i	−0.128594	−	0.222731i
$66$		0			0
$67$	4.34796	+	2.51030i	0.531188	+	0.306682i	0.741500	−	0.670953i	$-0.234115\pi$
$67$	4.34796	+	2.51030i	0.531188	+	0.306682i	−0.210312	+	0.977634i	$0.567448\pi$
$68$	−0.402079	−	1.09045i	−0.0487593	−	0.132237i
$69$		0			0
$70$	2.63157	−	1.54160i	0.314532	−	0.184256i
$71$			3.64207i			0.432234i	0.976367	+	0.216117i	$0.0693392\pi$
$71$			3.64207i			0.432234i	−0.976367	+	0.216117i	$0.930661\pi$
$72$		0			0
$73$	2.26126	−	1.30554i	0.264661	−	0.152802i	−0.361798	−	0.932257i	$-0.617837\pi$
$73$	2.26126	−	1.30554i	0.264661	−	0.152802i	0.626459	+	0.779454i	$0.284504\pi$
$74$	0.810061	+	4.53842i	0.0941677	+	0.527581i
$75$		0			0
$76$	6.89168	+	5.73374i	0.790530	+	0.657705i
$77$	12.5754	+	2.16265i	1.43310	+	0.246457i
$78$		0			0
$79$	8.78313	−	5.07094i	0.988179	−	0.570526i	0.0834497	−	0.996512i	$-0.473406\pi$
$79$	8.78313	−	5.07094i	0.988179	−	0.570526i	0.904730	+	0.425986i	$0.140073\pi$
$80$	−1.08940	+	3.07306i	−0.121799	+	0.343578i
$81$		0			0
$82$	1.69204	−	4.67935i	0.186855	−	0.516747i
$83$	0.820993	−	1.42200i	0.0901157	−	0.156085i	−0.817444	−	0.576008i	$-0.804610\pi$
$83$	0.820993	−	1.42200i	0.0901157	−	0.156085i	0.907560	+	0.419923i	$0.137943\pi$
$84$		0			0
$85$	−0.236835	−	0.410210i	−0.0256883	−	0.0444935i
$86$	−7.59199	+	1.35509i	−0.818665	+	0.146123i
$87$		0			0
$88$	−11.7704	+	6.89469i	−1.25472	+	0.734977i
$89$	1.90724	+	1.10115i	0.202167	+	0.116721i	0.597666	−	0.801745i	$-0.296095\pi$
$89$	1.90724	+	1.10115i	0.202167	+	0.116721i	−0.395499	+	0.918466i	$0.629428\pi$
$90$		0			0
$91$	−2.32862	−	6.31470i	−0.244106	−	0.661961i
$92$	−12.7649	−	2.19565i	−1.33083	−	0.228912i
$93$		0			0
$94$	12.7413	+	4.60722i	1.31416	+	0.475199i
$95$	3.16422	+	1.82686i	0.324642	+	0.187432i
$96$		0			0
$97$	6.14759	+	3.54931i	0.624193	+	0.360378i	0.778500	−	0.627645i	$-0.215981\pi$
$97$	6.14759	+	3.54931i	0.624193	+	0.360378i	−0.154307	+	0.988023i	$0.549314\pi$
$98$	9.26626	−	3.48373i	0.936034	−	0.351910i
$99$		0			0
$100$	1.46992	−	8.54569i	0.146992	−	0.854569i
$101$			9.41732i			0.937058i	0.883448	+	0.468529i	$0.155216\pi$
$101$			9.41732i			0.937058i	−0.883448	+	0.468529i	$0.844784\pi$
$102$		0			0
$103$	−5.15217			−0.507659			−0.253829	−	0.967249i	$-0.581690\pi$
$103$	−5.15217			−0.507659			−0.253829	+	0.967249i	$0.581690\pi$
$104$	6.25362	+	3.55827i	0.613218	+	0.348917i
$105$		0			0
$106$	−2.91214	−	1.05302i	−0.282852	−	0.102279i
$107$	−10.4663	−	6.04271i	−1.01181	−	0.584170i	−0.100091	−	0.994978i	$-0.531913\pi$
$107$	−10.4663	−	6.04271i	−1.01181	−	0.584170i	−0.911722	+	0.410808i	$0.865247\pi$
$108$		0			0
$109$	1.83950	+	3.18610i	0.176192	+	0.305173i	0.940573	−	0.339591i	$-0.110289\pi$
$109$	1.83950	+	3.18610i	0.176192	+	0.305173i	−0.764381	+	0.644764i	$0.776955\pi$
$110$	−4.25131	+	3.58249i	−0.405346	+	0.341577i
$111$		0			0
$112$	−5.17551	+	9.23115i	−0.489039	+	0.872262i
$113$	2.77892	+	4.81323i	0.261419	+	0.452790i	0.966619	−	0.256218i	$-0.0824764\pi$
$113$	2.77892	+	4.81323i	0.261419	+	0.452790i	−0.705201	+	0.709008i	$0.749143\pi$
$114$		0			0
$115$	−5.27880			−0.492250
$116$	−9.72325	−	8.08954i	−0.902781	−	0.751095i
$117$		0			0
$118$	2.78457	+	15.6008i	0.256341	+	1.43617i
$119$	−0.531946	−	1.44252i	−0.0487634	−	0.132236i
$120$		0			0
$121$	−12.2598			−1.11453
$122$	3.48544	−	9.63900i	0.315557	−	0.872674i
$123$		0			0
$124$	−14.7972	−	12.3109i	−1.32882	−	1.10555i
$125$		−	7.60954i		−	0.680618i
$126$		0			0
$127$			1.07938i			0.0957798i	0.998853	+	0.0478899i	$0.0152497\pi$
$127$			1.07938i			0.0957798i	−0.998853	+	0.0478899i	$0.984750\pi$
$128$	−2.12791	−	11.1118i	−0.188082	−	0.982153i
$129$		0			0
$130$	2.75764	+	0.997156i	0.241861	+	0.0874564i
$131$	8.74823			0.764336			0.382168	−	0.924093i	$-0.375178\pi$
$131$	8.74823			0.764336			0.382168	+	0.924093i	$0.375178\pi$
$132$		0			0
$133$	9.11707	+	7.58474i	0.790551	+	0.657680i
$134$	−6.98972	+	1.24759i	−0.603820	+	0.107776i
$135$		0			0
$136$	1.42857	+	0.812846i	0.122499	+	0.0697009i
$137$	8.62094			0.736537			0.368268	−	0.929720i	$-0.379951\pi$
$137$	8.62094			0.736537			0.368268	+	0.929720i	$0.379951\pi$
$138$		0			0
$139$	−4.64043	−	8.03745i	−0.393596	−	0.681728i	0.599325	−	0.800506i	$-0.295436\pi$
$139$	−4.64043	−	8.03745i	−0.393596	−	0.681728i	−0.992921	+	0.118778i	$0.962102\pi$
$140$	−1.44102	+	4.06532i	−0.121788	+	0.343582i
$141$		0			0
$142$	−3.31905	−	3.93869i	−0.278528	−	0.330527i
$143$	6.13427	+	10.6249i	0.512974	+	0.888496i
$144$		0			0
$145$	−4.46430	−	2.57746i	−0.370740	−	0.214047i
$146$	−1.25568	+	3.47258i	−0.103920	+	0.287393i
$147$		0			0
$148$	−5.01194	−	4.16983i	−0.411979	−	0.342758i
$149$	−10.9454			−0.896681			−0.448340	−	0.893863i	$-0.647985\pi$
$149$	−10.9454			−0.896681			−0.448340	+	0.893863i	$0.647985\pi$
$150$		0			0
$151$		−	0.380125i		−	0.0309341i	−0.999880	−	0.0154671i	$-0.995076\pi$
$151$		−	0.380125i		−	0.0309341i	0.999880	−	0.0154671i	$-0.00492351\pi$
$152$	−12.6782	+	0.0797446i	−1.02833	+	0.00646814i
$153$		0			0
$154$	−15.5704	+	9.12131i	−1.25470	+	0.735016i
$155$	−6.79391	−	3.92246i	−0.545700	−	0.315060i
$156$		0			0
$157$	4.29740	+	2.48111i	0.342970	+	0.198014i	0.661585	−	0.749871i	$-0.269884\pi$
$157$	4.29740	+	2.48111i	0.342970	+	0.198014i	−0.318615	+	0.947884i	$0.603218\pi$
$158$	−4.87725	+	13.4881i	−0.388014	+	1.07305i
$159$		0			0
$160$	−1.62238	−	4.31611i	−0.128260	−	0.341219i
$161$	−16.8865	−	2.90404i	−1.33084	−	0.228871i
$162$		0			0
$163$	17.9942	+	10.3890i	1.40942	+	0.813727i	0.995332	−	0.0965111i	$-0.0307683\pi$
$163$	17.9942	+	10.3890i	1.40942	+	0.813727i	0.414085	+	0.910238i	$0.364102\pi$
$164$	2.43448	+	6.60241i	0.190101	+	0.515562i
$165$		0			0
$166$	0.408026	+	2.28599i	0.0316689	+	0.177427i
$167$	1.02852	+	1.78145i	0.0795893	+	0.137853i	0.903073	−	0.429487i	$-0.141306\pi$
$167$	1.02852	+	1.78145i	0.0795893	+	0.137853i	−0.823483	+	0.567340i	$0.807972\pi$
$168$		0			0
$169$	−3.26443	+	5.65416i	−0.251110	+	0.434936i
$170$	0.629951	+	0.227789i	0.0483150	+	0.0174706i
$171$		0			0
$172$	6.97539	−	8.38409i	0.531869	−	0.639281i
$173$	−12.4933	+	7.21301i	−0.949848	+	0.548395i	−0.893034	−	0.449990i	$-0.851428\pi$
$173$	−12.4933	+	7.21301i	−0.949848	+	0.548395i	−0.0568140	+	0.998385i	$0.518094\pi$
$174$		0			0
$175$	1.94416	−	11.3050i	0.146965	−	0.854574i
$176$	6.44577	−	18.1826i	0.485868	−	1.37057i
$177$		0			0
$178$	−3.06605	+	0.547258i	−0.229810	+	0.0410188i
$179$	3.35237	−	1.93549i	0.250568	−	0.144666i	−0.369456	−	0.929248i	$-0.620456\pi$
$179$	3.35237	−	1.93549i	0.250568	−	0.144666i	0.620024	+	0.784583i	$0.287123\pi$
$180$		0			0
$181$		−	24.8665i		−	1.84831i	−0.382012	−	0.924157i	$-0.624769\pi$
$181$		−	24.8665i		−	1.84831i	0.382012	−	0.924157i	$-0.375231\pi$
$182$	8.27291	+	4.70690i	0.613229	+	0.348898i
$183$		0			0
$184$	15.8054	−	9.25829i	1.16519	−	0.682530i
$185$	−2.30116	−	1.32858i	−0.169185	−	0.0976788i
$186$		0			0
$187$	1.40130	+	2.42713i	0.102473	+	0.177489i
$188$	−17.9776	+	6.62880i	−1.31115	+	0.483455i
$189$		0			0
$190$	−5.08676	+	0.907933i	−0.369032	+	0.0658684i
$191$	−16.0508	+	9.26695i	−1.16140	+	0.670533i	−0.951639	−	0.307220i	$-0.900601\pi$
$191$	−16.0508	+	9.26695i	−1.16140	+	0.670533i	−0.209759	+	0.977753i	$0.567268\pi$
$192$		0			0
$193$	−13.1752	+	22.8201i	−0.948371	+	1.64263i	−0.199515	+	0.979895i	$0.563937\pi$
$193$	−13.1752	+	22.8201i	−0.948371	+	1.64263i	−0.748856	+	0.662732i	$0.769397\pi$
$194$	−9.88278	+	1.76397i	−0.709542	+	0.126646i
$195$		0			0
$196$	−6.84617	+	12.2119i	−0.489012	+	0.872277i
$197$	5.05586			0.360215			0.180107	−	0.983647i	$-0.442355\pi$
$197$	5.05586			0.360215			0.180107	+	0.983647i	$0.442355\pi$
$198$		0			0
$199$	−10.9222	−	18.9178i	−0.774255	−	1.34105i	−0.935212	−	0.354088i	$-0.884791\pi$
$199$	−10.9222	−	18.9178i	−0.774255	−	1.34105i	0.160957	−	0.986961i	$-0.448542\pi$
$200$	6.19813	+	10.5812i	0.438274	+	0.748205i
$201$		0			0
$202$	−8.58208	−	10.1843i	−0.603833	−	0.716564i
$203$	−12.8630	−	10.7011i	−0.902805	−	0.751067i
$204$		0			0
$205$	1.43397	+	2.48371i	0.100153	+	0.173470i
$206$	5.57178	−	4.69522i	0.388204	−	0.327131i
$207$		0			0
$208$	−10.0056	+	1.85091i	−0.693764	+	0.128338i
$209$	−18.7220	−	10.8092i	−1.29503	−	0.747686i
$210$		0			0
$211$	−22.2066	+	12.8210i	−1.52876	+	0.882632i	−0.529350	+	0.848403i	$0.677564\pi$
$211$	−22.2066	+	12.8210i	−1.52876	+	0.882632i	−0.999414	+	0.0342290i	$0.989102\pi$
$212$	4.10894	−	1.51507i	0.282203	−	0.104056i
$213$		0			0
$214$	16.8254	−	3.00317i	1.15016	−	0.205292i
$215$	2.22248	−	3.84944i	0.151572	−	0.262530i
$216$		0			0
$217$	−19.5753	−	16.2852i	−1.32886	−	1.10551i
$218$	−4.89283	−	1.76923i	−0.331384	−	0.119828i
$219$		0			0
$220$	1.33279	−	7.74850i	0.0898569	−	0.522404i
$221$	0.739127	−	1.28021i	0.0497191	−	0.0861160i
$222$		0			0
$223$	−12.3031	+	21.3096i	−0.823876	+	1.42699i	0.0789002	+	0.996883i	$0.474859\pi$
$223$	−12.3031	+	21.3096i	−0.823876	+	1.42699i	−0.902776	+	0.430112i	$0.858474\pi$
$224$	−2.81541	−	14.6994i	−0.188113	−	0.982147i
$225$		0			0
$226$	−7.39157	−	2.67278i	−0.491680	−	0.177790i
$227$	21.9553			1.45722			0.728611	−	0.684928i	$-0.240166\pi$
$227$	21.9553			1.45722			0.728611	+	0.684928i	$0.240166\pi$
$228$		0			0
$229$			10.7070i			0.707539i	0.935333	+	0.353769i	$0.115100\pi$
$229$			10.7070i			0.707539i	−0.935333	+	0.353769i	$0.884900\pi$
$230$	5.70871	−	4.81061i	0.376421	−	0.317202i
$231$		0			0
$232$	17.8872	−	0.112509i	1.17435	−	0.00738658i
$233$	−2.17122	+	3.76066i	−0.142241	+	0.246369i	−0.928340	−	0.371731i	$-0.878764\pi$
$233$	−2.17122	+	3.76066i	−0.142241	+	0.246369i	0.786099	+	0.618101i	$0.212098\pi$
$234$		0			0
$235$	−6.76285	+	3.90453i	−0.441159	+	0.254704i
$236$	−17.2285	−	14.3337i	−1.12148	−	0.933046i
$237$		0			0
$238$	1.88985	+	1.07524i	0.122501	+	0.0696971i
$239$	−9.17613	+	5.29784i	−0.593554	+	0.342689i	−0.766502	−	0.642242i	$-0.778004\pi$
$239$	−9.17613	+	5.29784i	−0.593554	+	0.342689i	0.172947	+	0.984931i	$0.444671\pi$
$240$		0			0
$241$			6.82353i			0.439542i	0.975551	+	0.219771i	$0.0705311\pi$
$241$			6.82353i			0.439542i	−0.975551	+	0.219771i	$0.929469\pi$
$242$	13.2582	−	11.1724i	0.852272	−	0.718192i
$243$		0			0
$244$	5.01480	+	13.6003i	0.321040	+	0.870672i
$245$	−1.90612	+	5.37797i	−0.121778	+	0.343586i
$246$		0			0
$247$			11.4028i			0.725540i
$248$	27.2213	−	0.171220i	1.72855	−	0.0108725i
$249$		0			0
$250$	6.93464	+	8.22928i	0.438585	+	0.520465i
$251$	9.85832			0.622252			0.311126	−	0.950369i	$-0.399294\pi$
$251$	9.85832			0.622252			0.311126	+	0.950369i	$0.399294\pi$
$252$		0			0
$253$	31.2336			1.96364
$254$	−0.983651	−	1.16729i	−0.0617198	−	0.0732423i
$255$		0			0
$256$	12.4275	+	10.0776i	0.776718	+	0.629849i
$257$		−	13.6871i		−	0.853777i	−0.904304	−	0.426888i	$-0.859610\pi$
$257$		−	13.6871i		−	0.853777i	0.904304	−	0.426888i	$-0.140390\pi$
$258$		0			0
$259$	−6.63034	−	5.51595i	−0.411989	−	0.342745i
$260$	−3.89095	+	1.43469i	−0.241306	+	0.0889759i
$261$		0			0
$262$	−9.46070	+	7.97233i	−0.584484	+	0.492532i
$263$			15.6014i			0.962025i	0.876714	+	0.481013i	$0.159731\pi$
$263$			15.6014i			0.962025i	−0.876714	+	0.481013i	$0.840269\pi$
$264$		0			0
$265$	1.54571	−	0.892417i	0.0949523	−	0.0548207i
$266$	−16.7716	+	0.106012i	−1.02833	+	0.00650003i
$267$		0			0
$268$	6.42204	−	7.71899i	0.392289	−	0.471513i
$269$	−18.5276	+	10.6969i	−1.12965	+	0.652202i	−0.943846	−	0.330386i	$-0.892821\pi$
$269$	−18.5276	+	10.6969i	−1.12965	+	0.652202i	−0.185801	+	0.982587i	$0.559488\pi$
$270$		0			0
$271$	−1.36221	+	2.35942i	−0.0827485	+	0.143325i	−0.904430	−	0.426623i	$-0.859703\pi$
$271$	−1.36221	+	2.35942i	−0.0827485	+	0.143325i	0.821681	+	0.569948i	$0.193036\pi$
$272$	−2.28566	+	0.422819i	−0.138589	+	0.0256371i
$273$		0			0
$274$	−9.32305	+	7.85633i	−0.563226	+	0.474619i
$275$			20.9099i			1.26091i
$276$		0			0
$277$	11.3909			0.684414			0.342207	−	0.939625i	$-0.388826\pi$
$277$	11.3909			0.684414			0.342207	+	0.939625i	$0.388826\pi$
$278$	12.3429	+	4.46318i	0.740281	+	0.267684i
$279$		0			0
$280$	−2.14638	−	5.70962i	−0.128271	−	0.341215i
$281$	15.5146	−	26.8721i	0.925524	−	1.60305i	0.134808	−	0.990872i	$-0.456958\pi$
$281$	15.5146	−	26.8721i	0.925524	−	1.60305i	0.790716	−	0.612183i	$-0.209708\pi$
$282$		0			0
$283$	−2.02780	+	3.51226i	−0.120540	+	0.208782i	−0.919981	−	0.391963i	$-0.871796\pi$
$283$	−2.02780	+	3.51226i	−0.120540	+	0.208782i	0.799441	+	0.600745i	$0.205129\pi$
$284$	7.17871	+	1.23479i	0.425978	+	0.0732711i
$285$		0			0
$286$	−16.3164	−	5.89997i	−0.964809	−	0.348873i
$287$	3.22079	+	8.73407i	0.190117	+	0.515556i
$288$		0			0
$289$	−8.33116	+	14.4300i	−0.490068	+	0.848823i
$290$	7.17674	−	1.28097i	0.421433	−	0.0752214i
$291$		0			0
$292$	−1.80665	−	4.89970i	−0.105726	−	0.286733i
$293$	18.5526	−	10.7113i	1.08385	−	0.625762i	0.151919	−	0.988393i	$-0.451455\pi$
$293$	18.5526	−	10.7113i	1.08385	−	0.625762i	0.931933	+	0.362631i	$0.118121\pi$
$294$		0			0
$295$	−7.91021	−	4.56696i	−0.460550	−	0.265899i
$296$	9.22011	−	0.0579938i	0.535908	−	0.00337082i
$297$		0			0
$298$	11.8368	−	9.97462i	0.685687	−	0.577814i
$299$	−8.23718	−	14.2672i	−0.476369	−	0.825095i
$300$		0			0
$301$	9.22723	−	11.0914i	0.531849	−	0.639298i
$302$	0.346411	+	0.411083i	0.0199337	+	0.0236552i
$303$		0			0
$304$	13.6380	−	11.6399i	0.782194	−	0.667597i
$305$	2.95384	+	5.11620i	0.169137	+	0.292953i
$306$		0			0
$307$	19.4087			1.10771			0.553856	−	0.832613i	$-0.313156\pi$
$307$	19.4087			1.10771			0.553856	+	0.832613i	$0.313156\pi$
$308$	8.52621	−	24.0536i	0.485826	−	1.37058i
$309$		0			0
$310$	10.9218	−	1.94943i	0.620316	−	0.110720i
$311$	−5.36479	+	9.29209i	−0.304209	+	0.526906i	−0.977085	−	0.212850i	$-0.931726\pi$
$311$	−5.36479	+	9.29209i	−0.304209	+	0.526906i	0.672876	+	0.739756i	$0.265059\pi$
$312$		0			0
$313$	21.1362	−	12.2030i	1.19469	−	0.689754i	0.235323	−	0.971917i	$-0.424385\pi$
$313$	21.1362	−	12.2030i	1.19469	−	0.689754i	0.959366	+	0.282163i	$0.0910520\pi$
$314$	−6.90844	+	1.23309i	−0.389866	+	0.0695870i
$315$		0			0
$316$	−7.01732	−	19.0312i	−0.394755	−	1.07059i
$317$	16.0620	+	27.8202i	0.902132	+	1.56254i	0.824721	+	0.565539i	$0.191332\pi$
$317$	16.0620	+	27.8202i	0.902132	+	1.56254i	0.0774105	+	0.996999i	$0.475335\pi$
$318$		0			0
$319$	26.4143	+	15.2503i	1.47892	+	0.853854i
$320$	5.68782	+	3.18914i	0.317959	+	0.178279i
$321$		0			0
$322$	20.9082	−	12.2482i	1.16517	−	0.682566i
$323$			2.60483i			0.144936i
$324$		0			0
$325$	9.55146	−	5.51454i	0.529819	−	0.305891i
$326$	−28.9273	+	5.16322i	−1.60213	+	0.285964i
$327$		0			0
$328$	−8.64959	−	4.92156i	−0.477594	−	0.271748i
$329$	−23.7818	+	8.76982i	−1.31113	+	0.483496i
$330$		0			0
$331$	−22.6433	+	13.0731i	−1.24459	+	0.718565i	−0.970025	−	0.243004i	$-0.921867\pi$
$331$	−22.6433	+	13.0731i	−1.24459	+	0.718565i	−0.274565	+	0.961569i	$0.588534\pi$
$332$	−2.52450	−	2.10033i	−0.138550	−	0.115271i
$333$		0			0
$334$	−2.73574	−	0.989236i	−0.149693	−	0.0541286i
$335$	2.04617	−	3.54407i	0.111794	−	0.193633i
$336$		0			0
$337$	2.89594	+	5.01591i	0.157752	+	0.273234i	0.934058	−	0.357122i	$-0.116242\pi$
$337$	2.89594	+	5.01591i	0.157752	+	0.273234i	−0.776306	+	0.630356i	$0.782909\pi$
$338$	−1.62239	−	9.08956i	−0.0882464	−	0.494407i
$339$		0			0
$340$	−0.888841	+	0.327739i	−0.0482042	+	0.0177741i
$341$	40.1981	+	23.2084i	2.17685	+	1.25681i
$342$		0			0
$343$	−9.05613	+	16.1551i	−0.488985	+	0.872292i
$344$	0.0970134	+	15.4236i	0.00523061	+	0.831587i
$345$		0			0
$346$	6.93750	−	19.1857i	0.372962	−	1.03143i
$347$	12.9078	+	7.45234i	0.692929	+	0.400063i	0.804708	−	0.593670i	$-0.202322\pi$
$347$	12.9078	+	7.45234i	0.692929	+	0.400063i	−0.111779	+	0.993733i	$0.535655\pi$
$348$		0			0
$349$	−2.24929	−	1.29863i	−0.120402	−	0.0695140i	0.438590	−	0.898687i	$-0.355478\pi$
$349$	−2.24929	−	1.29863i	−0.120402	−	0.0695140i	−0.558991	+	0.829173i	$0.688812\pi$
$350$	8.19979	+	13.9974i	0.438297	+	0.748192i
$351$		0			0
$352$	9.59926	+	25.5376i	0.511642	+	1.36116i
$353$		−	13.4676i		−	0.716810i	−0.933566	−	0.358405i	$-0.883321\pi$
$353$		−	13.4676i		−	0.716810i	0.933566	−	0.358405i	$-0.116679\pi$
$354$		0			0
$355$	2.96869			0.157562
$356$	2.81704	−	3.38595i	0.149303	−	0.179455i
$357$		0			0
$358$	−1.86157	+	5.14817i	−0.0983868	+	0.272089i
$359$	15.7293	+	9.08130i	0.830159	+	0.479293i	0.853907	−	0.520425i	$-0.174227\pi$
$359$	15.7293	+	9.08130i	0.830159	+	0.479293i	−0.0237479	+	0.999718i	$0.507560\pi$
$360$		0			0
$361$	−0.546375	−	0.946350i	−0.0287566	−	0.0498079i
$362$	22.6611	+	26.8917i	1.19104	+	1.41340i
$363$		0			0
$364$	−13.2361	+	2.44893i	−0.693760	+	0.128359i
$365$	−1.06416	−	1.84318i	−0.0557007	−	0.0964764i
$366$		0			0
$367$	11.1737			0.583260			0.291630	−	0.956531i	$-0.405802\pi$
$367$	11.1737			0.583260			0.291630	+	0.956531i	$0.405802\pi$
$368$	−8.65547	+	24.4159i	−0.451198	+	1.27277i
$369$		0			0
$370$	3.69931	−	0.660289i	0.192318	−	0.0343268i
$371$	5.43556	−	2.00442i	0.282200	−	0.104064i
$372$		0			0
$373$	−30.8024			−1.59489			−0.797445	−	0.603392i	$-0.793815\pi$
$373$	−30.8024			−1.59489			−0.797445	+	0.603392i	$0.793815\pi$
$374$	−3.72729	−	1.34778i	−0.192733	−	0.0696920i
$375$		0			0
$376$	13.4008	−	23.5518i	0.691095	−	1.21459i
$377$		−	16.0878i		−	0.828563i
$378$		0			0
$379$		−	5.54837i		−	0.285001i	−0.989795	−	0.142500i	$-0.954486\pi$
$379$		−	5.54837i		−	0.285001i	0.989795	−	0.142500i	$-0.0455142\pi$
$380$	4.67363	−	5.61748i	0.239752	−	0.288171i
$381$		0			0
$382$	8.91300	−	24.6489i	0.456029	−	1.26115i
$383$	−8.61343			−0.440126			−0.220063	−	0.975486i	$-0.570626\pi$
$383$	−8.61343			−0.440126			−0.220063	+	0.975486i	$0.570626\pi$
$384$		0			0
$385$	1.76280	−	10.2504i	0.0898407	−	0.522407i
$386$	−6.54794	−	36.6853i	−0.333281	−	1.86723i
$387$		0			0
$388$	9.08013	−	10.9139i	0.460974	−	0.554069i
$389$	−3.48137			−0.176513			−0.0882563	−	0.996098i	$-0.528129\pi$
$389$	−3.48137			−0.176513			−0.0882563	+	0.996098i	$0.528129\pi$
$390$		0			0
$391$	−1.88169	−	3.25918i	−0.0951611	−	0.164824i
$392$	−3.72505	−	19.4454i	−0.188143	−	0.982142i
$393$		0			0
$394$	−5.46762	+	4.60745i	−0.275455	+	0.232120i
$395$	−4.13338	−	7.15922i	−0.207973	−	0.360219i
$396$		0			0
$397$	−15.5989	−	9.00601i	−0.782885	−	0.451999i	0.0545667	−	0.998510i	$-0.482622\pi$
$397$	−15.5989	−	9.00601i	−0.782885	−	0.451999i	−0.837452	+	0.546511i	$0.815956\pi$
$398$	29.0517	+	10.5050i	1.45623	+	0.526570i
$399$		0			0
$400$	−16.3457	−	5.79457i	−0.817284	−	0.289728i
$401$	−14.3056			−0.714390			−0.357195	−	0.934030i	$-0.616267\pi$
$401$	−14.3056			−0.714390			−0.357195	+	0.934030i	$0.616267\pi$
$402$		0			0
$403$		−	24.4829i		−	1.21958i
$404$	18.5621	+	3.19279i	0.923497	+	0.158847i
$405$		0			0
$406$	23.6625	−	0.149569i	1.17435	−	0.00742300i
$407$	13.6155	+	7.86091i	0.674895	+	0.389651i
$408$		0			0
$409$	−33.9241	−	19.5861i	−1.67744	−	0.968469i	−0.963286	−	0.268479i	$-0.913479\pi$
$409$	−33.9241	−	19.5861i	−1.67744	−	0.968469i	−0.714152	−	0.699991i	$-0.753188\pi$
$410$	−3.81418	−	1.37920i	−0.188369	−	0.0681138i
$411$		0			0
$412$	−1.74676	+	10.1552i	−0.0860569	+	0.500312i
$413$	−22.7917	−	18.9610i	−1.12151	−	0.933011i
$414$		0			0
$415$	−1.15909	−	0.669200i	−0.0568974	−	0.0328497i
$416$	9.13374	−	11.1198i	0.447819	−	0.545195i
$417$		0			0
$418$	30.0973	−	5.37205i	1.47211	−	0.262756i
$419$	11.3503	+	19.6592i	0.554497	+	0.960417i	0.997942	+	0.0641156i	$0.0204226\pi$
$419$	11.3503	+	19.6592i	0.554497	+	0.960417i	−0.443446	+	0.896301i	$0.646244\pi$
$420$		0			0
$421$	−0.931761	+	1.61386i	−0.0454113	+	0.0786546i	−0.887838	−	0.460157i	$-0.847793\pi$
$421$	−0.931761	+	1.61386i	−0.0454113	+	0.0786546i	0.842426	+	0.538811i	$0.181126\pi$
$422$	12.3313	−	34.1022i	0.600277	−	1.66007i
$423$		0			0
$424$	−3.06288	+	5.38298i	−0.148747	+	0.261421i
$425$	2.18192	−	1.25973i	0.105839	−	0.0611059i
$426$		0			0
$427$	6.63452	+	17.9913i	0.321067	+	0.870662i
$428$	−15.4589	+	18.5809i	−0.747236	+	0.898142i
$429$		0			0
$430$	1.10455	+	6.18831i	0.0532660	+	0.298427i
$431$	3.78493	−	2.18523i	0.182314	−	0.105259i	−0.406065	−	0.913844i	$-0.633100\pi$
$431$	3.78493	−	2.18523i	0.182314	−	0.105259i	0.588379	+	0.808585i	$0.299766\pi$
$432$		0			0
$433$			9.78275i			0.470129i	0.971980	+	0.235065i	$0.0755302\pi$
$433$			9.78275i			0.470129i	−0.971980	+	0.235065i	$0.924470\pi$
$434$	36.0104	−	0.227619i	1.72855	−	0.0109261i
$435$		0			0
$436$	6.90363	−	2.54555i	0.330624	−	0.121910i
$437$	25.1402	+	14.5147i	1.20262	+	0.694333i
$438$		0			0
$439$	−0.192573	−	0.333547i	−0.00919103	−	0.0159193i	0.861393	−	0.507939i	$-0.169592\pi$
$439$	−0.192573	−	0.333547i	−0.00919103	−	0.0159193i	−0.870584	+	0.492019i	$0.836259\pi$
$440$	5.61994	+	9.59414i	0.267920	+	0.457383i
$441$		0			0
$442$	0.367339	+	2.05804i	0.0174725	+	0.0978911i
$443$	14.0237	−	8.09657i	0.666285	−	0.384680i	−0.128383	−	0.991725i	$-0.540979\pi$
$443$	14.0237	−	8.09657i	0.666285	−	0.384680i	0.794668	+	0.607045i	$0.207645\pi$
$444$		0			0
$445$	0.897555	−	1.55461i	0.0425482	−	0.0736956i
$446$	−6.11451	−	34.2570i	−0.289531	−	1.62211i
$447$		0			0
$448$	16.4404	+	13.3309i	0.776737	+	0.629825i
$449$	33.2361			1.56851			0.784253	−	0.620441i	$-0.213046\pi$
$449$	33.2361			1.56851			0.784253	+	0.620441i	$0.213046\pi$
$450$		0			0
$451$	−8.48451	−	14.6956i	−0.399520	−	0.691989i
$452$	10.4293	−	3.84555i	0.490552	−	0.180879i
$453$		0			0
$454$	−23.7433	+	20.0080i	−1.11433	+	0.939023i
$455$	−5.14718	+	1.89808i	−0.241303	+	0.0889834i
$456$		0			0
$457$	2.76931	+	4.79659i	0.129543	+	0.224375i	0.923500	−	0.383599i	$-0.125316\pi$
$457$	2.76931	+	4.79659i	0.129543	+	0.224375i	−0.793957	+	0.607974i	$0.791982\pi$
$458$	−9.75738	−	11.5790i	−0.455933	−	0.541051i
$459$		0			0
$460$	−1.78969	+	10.4048i	−0.0834449	+	0.485126i
$461$	−5.35007	−	3.08886i	−0.249178	−	0.143863i	0.370210	−	0.928948i	$-0.379286\pi$
$461$	−5.35007	−	3.08886i	−0.249178	−	0.143863i	−0.619388	+	0.785085i	$0.712619\pi$
$462$		0			0
$463$	−10.1830	+	5.87914i	−0.473243	+	0.273227i	−0.717596	−	0.696459i	$-0.754758\pi$
$463$	−10.1830	+	5.87914i	−0.473243	+	0.273227i	0.244353	+	0.969686i	$0.421424\pi$
$464$	−19.2414	+	16.4224i	−0.893262	+	0.762392i
$465$		0			0
$466$	−1.07907	−	6.04559i	−0.0499872	−	0.280056i
$467$	−13.8715	+	24.0262i	−0.641897	+	1.11180i	0.343112	+	0.939295i	$0.388519\pi$
$467$	−13.8715	+	24.0262i	−0.641897	+	1.11180i	−0.985009	+	0.172504i	$0.944814\pi$
$468$		0			0
$469$	8.49524	−	10.2115i	0.392274	−	0.471525i
$470$	3.75540	−	10.3856i	0.173223	−	0.479050i
$471$		0			0
$472$	31.6940	−	0.199353i	1.45884	−	0.00917596i
$473$	−13.1499	+	22.7763i	−0.604634	+	1.04726i
$474$		0			0
$475$	−9.71714	+	16.8306i	−0.445853	+	0.772240i
$476$	−3.02363	+	0.559430i	−0.138588	+	0.0256414i
$477$		0			0
$478$	5.09549	−	14.0916i	0.233062	−	0.644534i
$479$	−7.15041			−0.326710			−0.163355	−	0.986567i	$-0.552232\pi$
$479$	−7.15041			−0.326710			−0.163355	+	0.986567i	$0.552232\pi$
$480$		0			0
$481$		−	8.29259i		−	0.378109i
$482$	−6.21834	−	7.37926i	−0.283238	−	0.336116i
$483$		0			0
$484$	−4.15649	+	24.1647i	−0.188931	+	1.09840i
$485$	2.89308	−	5.01096i	0.131368	−	0.227536i
$486$		0			0
$487$	6.67495	−	3.85379i	0.302471	−	0.174632i	−0.341081	−	0.940034i	$-0.610793\pi$
$487$	6.67495	−	3.85379i	0.302471	−	0.174632i	0.643552	+	0.765402i	$0.277460\pi$
$488$	−17.8173	−	10.1379i	−0.806552	−	0.458923i
$489$		0			0
$490$	−2.83963	−	7.55302i	−0.128281	−	0.341211i
$491$	−22.3770	+	12.9194i	−1.00986	+	0.583043i	−0.911151	−	0.412073i	$-0.864805\pi$
$491$	−22.3770	+	12.9194i	−1.00986	+	0.583043i	−0.0987099	+	0.995116i	$0.531472\pi$
$492$		0			0
$493$		−	3.67507i		−	0.165517i
$494$	−10.3914	−	12.3314i	−0.467532	−	0.554817i
$495$		0			0
$496$	−29.2822	+	24.9922i	−1.31481	+	1.12218i
$497$	9.49660	+	1.63317i	0.425981	+	0.0732578i
$498$		0			0
$499$		−	37.2132i		−	1.66589i	−0.553353	−	0.832947i	$-0.686652\pi$
$499$		−	37.2132i		−	1.66589i	0.553353	−	0.832947i	$-0.313348\pi$
$500$	−14.9988	−	2.57989i	−0.670767	−	0.115376i
$501$		0			0
$502$	−10.6612	+	8.98397i	−0.475833	+	0.400974i
$503$	−11.8075			−0.526469			−0.263235	−	0.964732i	$-0.584789\pi$
$503$	−11.8075			−0.526469			−0.263235	+	0.964732i	$0.584789\pi$
$504$		0			0
$505$	7.67615			0.341584
$506$	−33.7773	+	28.4634i	−1.50158	+	1.26535i
$507$		0			0
$508$	2.12752	+	0.365948i	0.0943936	+	0.0162363i
$509$		−	3.68262i		−	0.163229i	−0.996664	−	0.0816146i	$-0.973992\pi$
$509$		−	3.68262i		−	0.163229i	0.996664	−	0.0816146i	$-0.0260077\pi$
$510$		0			0
$511$	−2.39017	−	6.48162i	−0.105735	−	0.286730i
$512$	−22.6234	+	0.426943i	−0.999822	+	0.0188684i
$513$		0			0
$514$	12.4732	+	14.8018i	0.550167	+	0.652879i
$515$			4.19959i			0.185056i
$516$		0			0
$517$	40.0144	−	23.1023i	1.75983	−	1.01604i
$518$	12.1971	−	0.0770968i	0.535908	−	0.00338744i
$519$		0			0
$520$	2.90038	−	5.09739i	0.127190	−	0.223535i
$521$	10.9116	−	6.29980i	0.478045	−	0.275999i	−0.241557	−	0.970387i	$-0.577658\pi$
$521$	10.9116	−	6.29980i	0.478045	−	0.275999i	0.719601	+	0.694387i	$0.244325\pi$
$522$		0			0
$523$	−9.32093	+	16.1443i	−0.407576	+	0.705942i	−0.994618	−	0.103615i	$-0.966959\pi$
$523$	−9.32093	+	16.1443i	−0.407576	+	0.705942i	0.587042	+	0.809557i	$0.300292\pi$
$524$	2.96595	−	17.2432i	0.129568	−	0.753274i
$525$		0			0
$526$	−14.2177	−	16.8720i	−0.619922	−	0.735656i
$527$		−	5.59283i		−	0.243627i
$528$		0			0
$529$	−18.9408			−0.823515
$530$	−0.858330	+	2.37372i	−0.0372835	+	0.103108i
$531$		0			0
$532$	18.0409	−	15.3988i	0.782173	−	0.667621i
$533$	−4.47522	+	7.75131i	−0.193843	+	0.335746i
$534$		0			0
$535$	−4.92547	+	8.53117i	−0.212947	+	0.368835i
$536$	0.0893175	+	14.2001i	0.00385793	+	0.613351i
$537$		0			0
$538$	10.2883	−	28.4524i	0.443561	−	1.22667i
$539$	11.2781	−	31.8203i	0.485783	−	1.37060i
$540$		0			0
$541$	−9.06775	+	15.7058i	−0.389853	+	0.675245i	−0.992429	−	0.122816i	$-0.960807\pi$
$541$	−9.06775	+	15.7058i	−0.389853	+	0.675245i	0.602577	+	0.798061i	$0.294141\pi$
$542$	−0.677006	−	3.79297i	−0.0290799	−	0.162922i
$543$		0			0
$544$	2.08650	−	2.54020i	0.0894578	−	0.108910i
$545$	2.59702	−	1.49939i	0.111244	−	0.0642269i
$546$		0			0
$547$	24.9748	+	14.4192i	1.06784	+	0.616520i	0.927592	−	0.373596i	$-0.121875\pi$
$547$	24.9748	+	14.4192i	1.06784	+	0.616520i	0.140252	+	0.990116i	$0.455209\pi$
$548$	2.92279	−	16.9923i	0.124856	−	0.725877i
$549$		0			0
$550$	−19.0553	−	22.6128i	−0.812523	−	0.964214i
$551$	14.1741	+	24.5503i	0.603837	+	1.04588i
$552$		0			0
$553$	−9.28382	−	25.1757i	−0.394788	−	1.07058i
$554$	−12.3186	+	10.3806i	−0.523368	+	0.441031i
$555$		0			0
$556$	−17.4155	+	6.42156i	−0.738583	+	0.272335i
$557$	6.31355	+	10.9354i	0.267514	+	0.463347i	0.968219	−	0.250103i	$-0.0804646\pi$
$557$	6.31355	+	10.9354i	0.267514	+	0.463347i	−0.700705	+	0.713451i	$0.747131\pi$
$558$		0			0
$559$	13.8721			0.586725
$560$	7.52440	+	4.21861i	0.317964	+	0.178269i
$561$		0			0
$562$	7.71061	+	43.1992i	0.325252	+	1.82225i
$563$	−4.68690	+	8.11795i	−0.197529	+	0.342131i	−0.947727	−	0.319083i	$-0.896625\pi$
$563$	−4.68690	+	8.11795i	−0.197529	+	0.342131i	0.750197	+	0.661214i	$0.229958\pi$
$564$		0			0
$565$	3.92331	−	2.26512i	0.165055	−	0.0952945i
$566$	−1.00780	−	5.64626i	−0.0423609	−	0.237330i
$567$		0			0
$568$	−8.88863	+	5.20667i	−0.372959	+	0.218467i
$569$	19.6969	+	34.1161i	0.825739	+	1.43022i	0.901353	+	0.433084i	$0.142575\pi$
$569$	19.6969	+	34.1161i	0.825739	+	1.43022i	−0.0756147	+	0.997137i	$0.524092\pi$
$570$		0			0
$571$	5.00184	+	2.88781i	0.209320	+	0.120851i	0.600995	−	0.799252i	$-0.294771\pi$
$571$	5.00184	+	2.88781i	0.209320	+	0.120851i	−0.391675	+	0.920104i	$0.628104\pi$
$572$	23.0219	−	8.48879i	0.962595	−	0.354934i
$573$		0			0
$574$	−11.4425	−	6.51026i	−0.477602	−	0.271733i
$575$		−	28.0781i		−	1.17094i
$576$		0			0
$577$	−25.4955	+	14.7198i	−1.06139	+	0.612794i	−0.925817	−	0.377973i	$-0.876621\pi$
$577$	−25.4955	+	14.7198i	−1.06139	+	0.612794i	−0.135574	+	0.990767i	$0.543288\pi$
$578$	−4.14050	−	23.1974i	−0.172222	−	0.964886i
$579$		0			0
$580$	−6.59387	+	7.92552i	−0.273795	+	0.329089i
$581$	−3.33968	−	2.77837i	−0.138553	−	0.115266i
$582$		0			0
$583$	−9.14565	+	5.28025i	−0.378774	+	0.218685i
$584$	6.41892	+	3.65233i	0.265617	+	0.151134i
$585$		0			0
$586$	−10.3022	+	28.4908i	−0.425580	+	1.17694i
$587$	2.66633	−	4.61821i	0.110051	−	0.190614i	−0.805740	−	0.592270i	$-0.798232\pi$
$587$	2.66633	−	4.61821i	0.110051	−	0.190614i	0.915791	+	0.401656i	$0.131565\pi$
$588$		0			0
$589$	21.5706	+	37.3614i	0.888801	+	1.53945i
$590$	12.7163	−	2.26973i	0.523524	−	0.0934435i
$591$		0			0
$592$	−9.91817	+	8.46508i	−0.407634	+	0.347913i
$593$	−37.9363	−	21.9025i	−1.55786	−	0.899429i	−0.997462	−	0.0712043i	$-0.977316\pi$
$593$	−37.9363	−	21.9025i	−1.55786	−	0.899429i	−0.560396	−	0.828225i	$-0.689351\pi$
$594$		0			0
$595$	−1.17581	+	0.433594i	−0.0482036	+	0.0177756i
$596$	−3.71086	+	21.5740i	−0.152003	+	0.883703i
$597$		0			0
$598$	21.9099	+	7.92256i	0.895961	+	0.323978i
$599$	−19.8313	−	11.4496i	−0.810283	−	0.467817i	0.0367710	−	0.999324i	$-0.488293\pi$
$599$	−19.8313	−	11.4496i	−0.810283	−	0.467817i	−0.847054	+	0.531506i	$0.821626\pi$
$600$		0			0
$601$	−23.6446	−	13.6512i	−0.964482	−	0.556844i	−0.0669322	−	0.997758i	$-0.521321\pi$
$601$	−23.6446	−	13.6512i	−0.964482	−	0.556844i	−0.897549	+	0.440914i	$0.854654\pi$
$602$	0.128969	+	20.4036i	0.00525640	+	0.831587i
$603$		0			0
$604$	−0.749247	−	0.128875i	−0.0304864	−	0.00524386i
$605$			9.99307i			0.406276i
$606$		0			0
$607$	−11.7323			−0.476198			−0.238099	−	0.971241i	$-0.576524\pi$
$607$	−11.7323			−0.476198			−0.238099	+	0.971241i	$0.576524\pi$
$608$	−4.14115	+	25.0164i	−0.167946	+	1.01455i
$609$		0			0
$610$	−7.85685	−	2.84102i	−0.318115	−	0.115029i
$611$	−21.1059	−	12.1855i	−0.853852	−	0.492972i
$612$		0			0
$613$	−1.66771	−	2.88856i	−0.0673582	−	0.116668i	0.830379	−	0.557198i	$-0.188124\pi$
$613$	−1.66771	−	2.88856i	−0.0673582	−	0.116668i	−0.897738	+	0.440531i	$0.854790\pi$
$614$	−20.9894	+	17.6873i	−0.847062	+	0.713801i
$615$		0			0
$616$	12.6997	+	33.7826i	0.511685	+	1.36114i
$617$	−14.7956	−	25.6267i	−0.595648	−	1.03169i	−0.993455	−	0.114224i	$-0.963562\pi$
$617$	−14.7956	−	25.6267i	−0.595648	−	1.03169i	0.397807	−	0.917469i	$-0.369771\pi$
$618$		0			0
$619$	31.6426			1.27182			0.635912	−	0.771762i	$-0.280624\pi$
$619$	31.6426			1.27182			0.635912	+	0.771762i	$0.280624\pi$
$620$	−10.0348	+	12.0613i	−0.403006	+	0.484394i
$621$		0			0
$622$	−2.66625	−	14.9378i	−0.106907	−	0.598952i
$623$	3.72645	−	4.47930i	0.149297	−	0.179459i
$624$		0			0
$625$	15.4754			0.619015
$626$	−11.7369	+	32.4584i	−0.469101	+	1.29730i
$627$		0			0
$628$	6.34736	−	7.62923i	0.253287	−	0.304440i
$629$		−	1.89434i		−	0.0755325i
$630$		0			0
$631$			6.61866i			0.263485i	0.991284	+	0.131742i	$0.0420572\pi$
$631$			6.61866i			0.263485i	−0.991284	+	0.131742i	$0.957943\pi$
$632$	24.9322	+	14.1863i	0.991748	+	0.564299i
$633$		0			0
$634$	−42.7229	−	15.4485i	−1.69674	−	0.613539i
$635$	0.879816			0.0349145
$636$		0			0
$637$	−17.5096	+	3.24018i	−0.693756	+	0.128381i
$638$	−42.4633	+	7.57926i	−1.68114	+	0.300066i
$639$		0			0
$640$	−9.05734	+	1.73448i	−0.358023	+	0.0685613i
$641$	−30.2812			−1.19604			−0.598018	−	0.801483i	$-0.704045\pi$
$641$	−30.2812			−1.19604			−0.598018	+	0.801483i	$0.704045\pi$
$642$		0			0
$643$	−8.34512	−	14.4542i	−0.329099	−	0.570017i	0.653234	−	0.757156i	$-0.273412\pi$
$643$	−8.34512	−	14.4542i	−0.329099	−	0.570017i	−0.982333	+	0.187139i	$0.940078\pi$
$644$	−11.4491	+	32.2996i	−0.451158	+	1.27278i
$645$		0			0
$646$	−2.37380	−	2.81697i	−0.0933959	−	0.110832i
$647$	−14.3660	−	24.8826i	−0.564786	−	0.978237i	−0.997070	−	0.0764997i	$-0.975626\pi$
$647$	−14.3660	−	24.8826i	−0.564786	−	0.978237i	0.432284	−	0.901737i	$-0.357708\pi$
$648$		0			0
$649$	46.8031	+	27.0218i	1.83718	+	1.06070i
$650$	−5.30390	+	14.6680i	−0.208036	+	0.575325i
$651$		0			0
$652$	26.5779	−	31.9454i	1.04087	−	1.25108i
$653$	9.26322			0.362498			0.181249	−	0.983437i	$-0.441986\pi$
$653$	9.26322			0.362498			0.181249	+	0.983437i	$0.441986\pi$
$654$		0			0
$655$		−	7.13077i		−	0.278622i
$656$	13.8391	−	2.56005i	0.540326	−	0.0999533i
$657$		0			0
$658$	17.7267	−	31.1566i	0.691057	−	1.21461i
$659$	0.465951	+	0.269017i	0.0181509	+	0.0104794i	0.509048	−	0.860738i	$-0.329998\pi$
$659$	0.465951	+	0.269017i	0.0181509	+	0.0104794i	−0.490897	+	0.871218i	$0.663331\pi$
$660$		0			0
$661$	20.0465	+	11.5739i	0.779719	+	0.450171i	0.836331	−	0.548225i	$-0.184696\pi$
$661$	20.0465	+	11.5739i	0.779719	+	0.450171i	−0.0566117	+	0.998396i	$0.518030\pi$
$662$	12.5738	−	34.7729i	0.488695	−	1.35149i
$663$		0			0
$664$	4.64415	−	0.0292113i	0.180228	−	0.00113362i
$665$	6.18240	−	7.43142i	0.239743	−	0.288178i
$666$		0			0
$667$	−35.4695	−	20.4783i	−1.37339	−	0.792924i
$668$	3.86004	−	1.42330i	0.149349	−	0.0550691i
$669$		0			0
$670$	1.01693	+	5.69739i	0.0392873	+	0.220110i
$671$	−17.4773	−	30.2715i	−0.674703	−	1.16862i
$672$		0			0
$673$	−11.9724	+	20.7368i	−0.461503	+	0.799346i	−0.999036	−	0.0438961i	$-0.986023\pi$
$673$	−11.9724	+	20.7368i	−0.461503	+	0.799346i	0.537533	+	0.843243i	$0.319356\pi$
$674$	−7.70283	−	2.78533i	−0.296702	−	0.107287i
$675$		0			0
$676$	10.0379	+	8.35133i	0.386073	+	0.321205i
$677$	30.3955	−	17.5489i	1.16819	−	0.674457i	0.214940	−	0.976627i	$-0.431044\pi$
$677$	30.3955	−	17.5489i	1.16819	−	0.674457i	0.953254	+	0.302170i	$0.0977109\pi$
$678$		0			0
$679$	12.0114	−	14.4381i	0.460957	−	0.554083i
$680$	0.662559	−	1.16444i	0.0254080	−	0.0446542i
$681$		0			0
$682$	−64.6220	+	11.5344i	−2.47450	+	0.441673i
$683$	−21.2103	+	12.2458i	−0.811591	+	0.468572i	−0.847508	−	0.530783i	$-0.821898\pi$
$683$	−21.2103	+	12.2458i	−0.811591	+	0.468572i	0.0359174	+	0.999355i	$0.488565\pi$
$684$		0			0
$685$		−	7.02702i		−	0.268488i
$686$	−4.92857	−	25.7237i	−0.188174	−	0.982136i
$687$		0			0
$688$	−14.1606	−	16.5914i	−0.539868	−	0.632540i
$689$	4.82394	+	2.78510i	0.183778	+	0.106104i
$690$		0			0
$691$	−8.60329	−	14.9013i	−0.327285	−	0.566874i	0.654687	−	0.755900i	$-0.272800\pi$
$691$	−8.60329	−	14.9013i	−0.327285	−	0.566874i	−0.981972	+	0.189026i	$0.939467\pi$
$692$	9.98157	+	27.0704i	0.379443	+	1.02906i
$693$		0			0
$694$	−20.7505	+	3.70374i	−0.787677	+	0.140592i
$695$	−6.55141	+	3.78246i	−0.248509	+	0.143477i
$696$		0			0
$697$	−1.02231	+	1.77069i	−0.0387228	+	0.0670699i
$698$	3.61593	−	0.645406i	0.136865	−	0.0244290i
$699$		0			0
$700$	−21.6235	−	7.66482i	−0.817293	−	0.289703i
$701$	−3.54331			−0.133829			−0.0669145	−	0.997759i	$-0.521315\pi$
$701$	−3.54331			−0.133829			−0.0669145	+	0.997759i	$0.521315\pi$
$702$		0			0
$703$	7.30617	+	12.6547i	0.275557	+	0.477279i
$704$	−33.6536	−	18.8695i	−1.26837	−	0.711171i
$705$		0			0
$706$	12.2732	+	14.5645i	0.461907	+	0.548141i
$707$	24.5554	+	4.22291i	0.923502	+	0.158819i
$708$		0			0
$709$	1.50550	+	2.60760i	0.0565401	+	0.0979304i	0.892910	−	0.450235i	$-0.148660\pi$
$709$	1.50550	+	2.60760i	0.0565401	+	0.0979304i	−0.836370	+	0.548165i	$0.815326\pi$
$710$	−3.21046	+	2.70539i	−0.120487	+	0.101531i
$711$		0			0
$712$	0.0391792	+	6.22890i	0.00146830	+	0.233438i
$713$	−53.9786	−	31.1646i	−2.02152	−	1.16712i
$714$		0			0
$715$	8.66044	−	5.00011i	0.323882	−	0.186993i
$716$	−2.67839	−	7.26391i	−0.100096	−	0.271465i
$717$		0			0
$718$	−25.2862	+	4.51332i	−0.943671	+	0.168436i
$719$	8.34116	−	14.4473i	0.311073	−	0.538794i	−0.667522	−	0.744590i	$-0.732645\pi$
$719$	8.34116	−	14.4473i	0.311073	−	0.538794i	0.978595	+	0.205796i	$0.0659784\pi$
$720$		0			0
$721$	−2.31033	+	13.4342i	−0.0860413	+	0.500314i
$722$	1.45329	+	0.525506i	0.0540858	+	0.0195573i
$723$		0			0
$724$	−49.0133	−	8.43061i	−1.82156	−	0.313321i
$725$	13.7096	−	23.7457i	0.509162	−	0.881894i
$726$		0			0
$727$	18.9577	−	32.8358i	0.703104	−	1.21781i	−0.264268	−	0.964449i	$-0.585130\pi$
$727$	18.9577	−	32.8358i	0.703104	−	1.21781i	0.967372	−	0.253362i	$-0.0815364\pi$
$728$	12.0823	−	14.7106i	0.447802	−	0.545209i
$729$		0			0
$730$	2.83053	+	1.02351i	0.104763	+	0.0378820i
$731$	3.16891			0.117206
$732$		0			0
$733$			23.5357i			0.869311i	0.900597	+	0.434655i	$0.143130\pi$
$733$			23.5357i			0.869311i	−0.900597	+	0.434655i	$0.856870\pi$
$734$	−12.0837	+	10.1826i	−0.446016	+	0.375848i
$735$		0			0
$736$	−12.8900	−	34.2922i	−0.475132	−	1.26403i
$737$	−12.1068	+	20.9695i	−0.445958	+	0.772422i
$738$		0			0
$739$	−24.3790	+	14.0752i	−0.896797	+	0.517766i	−0.876160	−	0.482021i	$-0.839903\pi$
$739$	−24.3790	+	14.0752i	−0.896797	+	0.517766i	−0.0206373	+	0.999787i	$0.506570\pi$
$740$	−3.39887	+	4.08528i	−0.124945	+	0.150178i
$741$		0			0
$742$	−4.05159	+	7.12114i	−0.148739	+	0.261425i
$743$	43.7349	−	25.2504i	1.60448	−	0.926347i	0.613904	−	0.789381i	$-0.289598\pi$
$743$	43.7349	−	25.2504i	1.60448	−	0.926347i	0.990576	−	0.136966i	$-0.0437350\pi$
$744$		0			0
$745$			8.92170i			0.326866i
$746$	33.3110	−	28.0705i	1.21960	−	1.02773i
$747$		0			0
$748$	5.25909	−	1.93916i	0.192291	−	0.0709029i
$749$	−20.4495	+	24.5809i	−0.747208	+	0.898165i
$750$		0			0
$751$		−	4.07788i		−	0.148804i	−0.997228	−	0.0744020i	$-0.976295\pi$
$751$		−	4.07788i		−	0.148804i	0.997228	−	0.0744020i	$-0.0237048\pi$
$752$	6.97072	+	37.6822i	0.254196	+	1.37413i
$753$		0			0
$754$	14.6609	+	17.3980i	0.533920	+	0.633598i
$755$	−0.309844			−0.0112764
$756$		0			0
$757$	−6.31380			−0.229479			−0.114739	−	0.993396i	$-0.536603\pi$
$757$	−6.31380			−0.229479			−0.114739	+	0.993396i	$0.536603\pi$
$758$	5.05628	+	6.00024i	0.183652	+	0.217939i
$759$		0			0
$760$	0.0650006	+	10.3341i	0.00235782	+	0.374857i
$761$		−	17.7730i		−	0.644272i	−0.946693	−	0.322136i	$-0.895599\pi$
$761$		−	17.7730i		−	0.644272i	0.946693	−	0.322136i	$-0.104401\pi$
$762$		0			0
$763$	9.13254	−	3.36773i	0.330620	−	0.121920i
$764$	12.8239	+	34.7789i	0.463952	+	1.25826i
$765$		0			0
$766$	9.31493	−	7.84949i	0.336562	−	0.283614i
$767$		−	28.5057i		−	1.02928i
$768$		0			0
$769$	21.8160	−	12.5955i	0.786706	−	0.454205i	−0.0520959	−	0.998642i	$-0.516590\pi$
$769$	21.8160	−	12.5955i	0.786706	−	0.454205i	0.838801	+	0.544437i	$0.183257\pi$
$770$	7.43487	+	12.6916i	0.267934	+	0.457374i
$771$		0			0
$772$	40.5128	+	33.7058i	1.45809	+	1.21310i
$773$	−35.8079	+	20.6737i	−1.28792	+	0.743582i	−0.978283	−	0.207272i	$-0.933541\pi$
$773$	−35.8079	+	20.6737i	−1.28792	+	0.743582i	−0.309639	+	0.950854i	$0.600208\pi$
$774$		0			0
$775$	20.8637	−	36.1370i	0.749446	−	1.29808i
$776$	0.126286	+	20.0775i	0.00453341	+	0.720742i
$777$		0			0
$778$	3.76490	−	3.17260i	0.134978	−	0.113743i
$779$		−	15.7715i		−	0.565074i
$780$		0			0
$781$	−17.5651			−0.628529
$782$	5.00505	+	1.80982i	0.178980	+	0.0647189i
$783$		0			0
$784$	21.7492	+	17.6344i	0.776757	+	0.629801i
$785$	2.02238	−	3.50286i	0.0721817	−	0.125022i
$786$		0			0
$787$	−9.74425	+	16.8775i	−0.347345	+	0.601619i	−0.985777	−	0.168059i	$-0.946250\pi$
$787$	−9.74425	+	16.8775i	−0.347345	+	0.601619i	0.638432	+	0.769678i	$0.279583\pi$
$788$	1.71411	−	9.96537i	0.0610626	−	0.355002i
$789$		0			0
$790$	10.9943	+	3.97550i	0.391158	+	0.141442i
$791$	13.7965	−	5.08761i	0.490547	−	0.180895i
$792$		0			0
$793$	−9.21852	+	15.9669i	−0.327359	+	0.567003i
$794$	25.0765	−	4.47590i	0.889933	−	0.158844i
$795$		0			0
$796$	−40.9911	+	15.1145i	−1.45289	+	0.535719i
$797$	−19.1331	+	11.0465i	−0.677729	+	0.391287i	−0.798999	−	0.601333i	$-0.794637\pi$
$797$	−19.1331	+	11.0465i	−0.677729	+	0.391287i	0.121270	+	0.992620i	$0.461303\pi$
$798$		0			0
$799$	−4.82139	−	2.78363i	−0.170568	−	0.0984778i
$800$	22.9575	−	8.62946i	0.811672	−	0.305098i
$801$		0			0
$802$	15.4707	−	13.0369i	0.546290	−	0.460347i
$803$	6.29642	+	10.9057i	0.222196	+	0.384854i
$804$		0			0
$805$	−2.36711	+	13.7643i	−0.0834298	+	0.485129i
$806$	22.3115	+	26.4768i	0.785888	+	0.932607i
$807$		0			0
$808$	−22.9834	+	13.4629i	−0.808553	+	0.473624i
$809$	3.36792	+	5.83340i	0.118410	+	0.205091i	0.919138	−	0.393937i	$-0.128887\pi$
$809$	3.36792	+	5.83340i	0.118410	+	0.205091i	−0.800728	+	0.599028i	$0.795554\pi$
$810$		0			0
$811$	52.9099			1.85792			0.928960	−	0.370181i	$-0.120704\pi$
$811$	52.9099			1.85792			0.928960	+	0.370181i	$0.120704\pi$
$812$	−25.4534	+	21.7256i	−0.893238	+	0.762420i
$813$		0			0
$814$	−21.8881	+	3.90679i	−0.767177	+	0.136933i
$815$	8.46816	−	14.6673i	0.296627	−	0.513772i
$816$		0			0
$817$	−21.1690	+	12.2219i	−0.740611	+	0.427592i
$818$	54.5359	−	9.73409i	1.90680	−	0.340344i
$819$		0			0
$820$	5.38170	−	1.98437i	0.187937	−	0.0692973i
$821$	5.94412	+	10.2955i	0.207451	+	0.359316i	0.950911	−	0.309465i	$-0.100150\pi$
$821$	5.94412	+	10.2955i	0.207451	+	0.359316i	−0.743460	+	0.668781i	$0.766816\pi$
$822$		0			0
$823$	−24.1063	−	13.9178i	−0.840293	−	0.485143i	0.0170709	−	0.999854i	$-0.494566\pi$
$823$	−24.1063	−	13.9178i	−0.840293	−	0.485143i	−0.857364	+	0.514711i	$0.827899\pi$
$824$	−7.36551	−	12.5741i	−0.256590	−	0.438040i
$825$		0			0
$826$	41.9272	−	0.265019i	1.45884	−	0.00922120i
$827$			30.7186i			1.06819i	0.845424	+	0.534095i	$0.179348\pi$
$827$			30.7186i			1.06819i	−0.845424	+	0.534095i	$0.820652\pi$
$828$		0			0
$829$	11.1106	−	6.41474i	0.385889	−	0.222793i	−0.294488	−	0.955655i	$-0.595149\pi$
$829$	11.1106	−	6.41474i	0.385889	−	0.222793i	0.680377	+	0.732862i	$0.261816\pi$
$830$	1.86333	−	0.332586i	0.0646773	−	0.0115442i
$831$		0			0
$832$	0.255999	+	20.3491i	0.00887516	+	0.705479i
$833$	−3.99987	+	0.740181i	−0.138587	+	0.0256457i
$834$		0			0
$835$	1.45208	−	0.838358i	0.0502513	−	0.0290126i
$836$	−27.6529	+	33.2375i	−0.956395	+	1.14954i
$837$		0			0
$838$	−30.1903	−	10.9167i	−1.04291	−	0.377113i
$839$	−1.26520	+	2.19139i	−0.0436795	+	0.0756551i	−0.887039	−	0.461695i	$-0.847241\pi$
$839$	−1.26520	+	2.19139i	−0.0436795	+	0.0756551i	0.843359	+	0.537350i	$0.180575\pi$
$840$		0			0
$841$	−5.49779	−	9.52246i	−0.189579	−	0.328361i
$842$	−0.463076	−	2.59442i	−0.0159587	−	0.0894094i
$843$		0			0
$844$	17.7420	+	48.1171i	0.610707	+	1.65626i
$845$	4.60877	+	2.66087i	0.158546	+	0.0915368i
$846$		0			0
$847$	−5.49752	+	31.9671i	−0.188897	+	1.09840i
$848$	−1.59322	−	8.61261i	−0.0547115	−	0.295758i
$849$		0			0
$850$	−1.21161	+	3.35073i	−0.0415580	+	0.114929i
$851$	−18.2831	−	10.5557i	−0.626736	−	0.361846i
$852$		0			0
$853$	15.4010	+	8.89177i	0.527320	+	0.304448i	0.739924	−	0.672690i	$-0.234861\pi$
$853$	15.4010	+	8.89177i	0.527320	+	0.304448i	−0.212605	+	0.977138i	$0.568195\pi$
$854$	−23.5705	−	13.4105i	−0.806566	−	0.458898i
$855$		0			0
$856$	−0.215002	−	34.1820i	−0.00734862	−	1.16832i
$857$		−	23.9404i		−	0.817787i	−0.912582	−	0.408894i	$-0.865915\pi$
$857$		−	23.9404i		−	0.817787i	0.912582	−	0.408894i	$-0.134085\pi$
$858$		0			0
$859$	46.6964			1.59326			0.796629	−	0.604468i	$-0.206614\pi$
$859$	46.6964			1.59326			0.796629	+	0.604468i	$0.206614\pi$
$860$	−6.83396	−	5.68571i	−0.233036	−	0.193881i
$861$		0			0
$862$	−2.10177	+	5.81244i	−0.0715865	+	0.197973i
$863$	34.3329	+	19.8221i	1.16870	+	0.674752i	0.953375	−	0.301789i	$-0.0975840\pi$
$863$	34.3329	+	19.8221i	1.16870	+	0.674752i	0.215330	+	0.976541i	$0.430917\pi$
$864$		0			0
$865$	5.87940	+	10.1834i	0.199905	+	0.346246i
$866$	−8.91511	−	10.5795i	−0.302948	−	0.359505i
$867$		0			0
$868$	−38.7357	+	33.0627i	−1.31478	+	1.12222i
$869$	24.4563	+	42.3596i	0.829624	+	1.43695i
$870$		0			0
$871$	12.7716			0.432749
$872$	−5.14609	+	9.04420i	−0.174269	+	0.306275i
$873$		0			0
$874$	−40.4151	+	7.21367i	−1.36706	+	0.244006i
$875$	−19.8417	−	3.41226i	−0.670771	−	0.115356i
$876$		0			0
$877$	30.1854			1.01929			0.509644	−	0.860385i	$-0.329777\pi$
$877$	30.1854			1.01929			0.509644	+	0.860385i	$0.329777\pi$
$878$	0.512221	+	0.185218i	0.0172866	+	0.00625081i
$879$		0			0
$880$	−14.8209	−	5.25402i	−0.499611	−	0.177113i
$881$			15.0652i			0.507560i	0.967262	+	0.253780i	$0.0816739\pi$
$881$			15.0652i			0.507560i	−0.967262	+	0.253780i	$0.918326\pi$
$882$		0			0
$883$		−	16.1352i		−	0.542993i	−0.962439	−	0.271497i	$-0.912481\pi$
$883$		−	16.1352i		−	0.542993i	0.962439	−	0.271497i	$-0.0875186\pi$
$884$	−2.27277	−	1.89089i	−0.0764414	−	0.0635976i
$885$		0			0
$886$	−7.78732	+	21.5359i	−0.261620	+	0.723512i
$887$	21.9524			0.737090			0.368545	−	0.929610i	$-0.379856\pi$
$887$	21.9524			0.737090			0.368545	+	0.929610i	$0.379856\pi$
$888$		0			0
$889$	2.81446	+	0.484016i	0.0943941	+	0.0162334i
$890$	0.446076	+	2.49917i	0.0149525	+	0.0837724i
$891$		0			0
$892$	37.8312	+	31.4747i	1.26668	+	1.05385i
$893$	42.9440			1.43707
$894$		0			0
$895$	−1.57764	−	2.73255i	−0.0527347	−	0.0913392i
$896$	−29.9279	+	0.565720i	−0.999821	+	0.0188994i
$897$		0			0
$898$	−35.9429	+	30.2883i	−1.19943	+	1.01073i
$899$	−30.4333	−	52.7120i	−1.01501	−	1.75804i
$900$		0			0
$901$	1.10197	+	0.636224i	0.0367120	+	0.0211957i
$902$	22.5677	+	8.16044i	0.751424	+	0.271713i
$903$		0			0
$904$	−7.77418	+	13.6630i	−0.258565	+	0.454426i
$905$	−20.2690			−0.673763
$906$		0			0
$907$		−	20.3672i		−	0.676280i	−0.941096	−	0.338140i	$-0.890202\pi$
$907$		−	20.3672i		−	0.676280i	0.941096	−	0.338140i	$-0.109798\pi$
$908$	7.44359	−	43.2750i	0.247024	−	1.43613i
$909$		0			0
$910$	3.83664	−	6.74333i	0.127183	−	0.223539i
$911$	−12.6090	−	7.27984i	−0.417756	−	0.241192i	0.276361	−	0.961054i	$-0.410872\pi$
$911$	−12.6090	−	7.27984i	−0.417756	−	0.241192i	−0.694117	+	0.719862i	$0.744205\pi$
$912$		0			0
$913$	6.85809	+	3.95952i	0.226970	+	0.131041i
$914$	−7.36602	−	2.66354i	−0.243646	−	0.0881019i
$915$		0			0
$916$	21.1041	+	3.63004i	0.697299	+	0.119940i
$917$	3.92287	−	22.8108i	0.129545	−	0.753278i
$918$		0			0
$919$	9.46004	+	5.46176i	0.312058	+	0.180167i	0.647847	−	0.761770i	$-0.275670\pi$
$919$	9.46004	+	5.46176i	0.312058	+	0.180167i	−0.335789	+	0.941937i	$0.609003\pi$
$920$	−7.54653	−	12.8831i	−0.248802	−	0.424745i
$921$		0			0
$922$	8.60070	−	1.53514i	0.283249	−	0.0505570i
$923$	4.63242	+	8.02359i	0.152478	+	0.264100i
$924$		0			0
$925$	7.06673	−	12.2399i	0.232353	−	0.402447i
$926$	5.65459	−	15.6378i	0.185821	−	0.513889i
$927$		0			0
$928$	5.84261	−	35.2948i	0.191793	−	1.15861i
$929$	−31.8073	+	18.3640i	−1.04357	+	0.602503i	−0.920841	−	0.389938i	$-0.872496\pi$
$929$	−31.8073	+	18.3640i	−1.04357	+	0.602503i	−0.122724	+	0.992441i	$0.539163\pi$
$930$		0			0
$931$	23.8653	−	20.3714i	0.782153	−	0.667645i
$932$	6.67635	+	5.55458i	0.218691	+	0.181946i
$933$		0			0
$934$	−6.89401	−	38.6241i	−0.225579	−	1.26382i
$935$	1.97838	−	1.14222i	0.0646998	−	0.0373544i
$936$		0			0
$937$		−	9.07200i		−	0.296369i	−0.988960	−	0.148185i	$-0.952657\pi$
$937$		−	9.07200i		−	0.296369i	0.988960	−	0.148185i	$-0.0473430\pi$
$938$	0.118738	+	18.7850i	0.00387695	+	0.613351i
$939$		0			0
$940$	5.40321	+	14.6537i	0.176233	+	0.477951i
$941$	8.03035	+	4.63632i	0.261782	+	0.151140i	0.625147	−	0.780507i	$-0.285039\pi$
$941$	8.03035	+	4.63632i	0.261782	+	0.151140i	−0.363365	+	0.931647i	$0.618372\pi$
$942$		0			0
$943$	11.3931	+	19.7335i	0.371011	+	0.642610i
$944$	−34.0936	+	29.0986i	−1.10965	+	0.947079i
$945$		0			0
$946$	−6.53538	−	36.6149i	−0.212484	−	1.19045i
$947$	2.85766	−	1.64987i	0.0928616	−	0.0536137i	−0.452850	−	0.891587i	$-0.649593\pi$
$947$	2.85766	−	1.64987i	0.0928616	−	0.0536137i	0.545712	+	0.837973i	$0.316259\pi$
$948$		0			0
$949$	3.32109	−	5.75230i	0.107807	−	0.186728i
$950$	−4.82932	−	27.0566i	−0.156684	−	0.877832i
$951$		0			0
$952$	2.76007	−	3.36045i	0.0894544	−	0.108913i
$953$	16.0636			0.520349			0.260175	−	0.965562i	$-0.416220\pi$
$953$	16.0636			0.520349			0.260175	+	0.965562i	$0.416220\pi$
$954$		0			0
$955$	7.55359	+	13.0832i	0.244428	+	0.423362i
$956$	7.33131	+	19.8828i	0.237111	+	0.643056i
$957$		0			0
$958$	7.73275	−	6.51622i	0.249834	−	0.210530i
$959$	3.86580	−	22.4789i	0.124833	−	0.725881i
$960$		0			0
$961$	−30.8143	−	53.3719i	−0.994010	−	1.72168i
$962$	7.55710	+	8.96795i	0.243651	+	0.289138i
$963$		0			0
$964$	13.4496	+	2.31341i	0.433181	+	0.0745100i
$965$	18.6009	+	10.7392i	0.598784	+	0.345708i
$966$		0			0
$967$	13.4318	−	7.75487i	0.431938	−	0.249380i	−0.268234	−	0.963354i	$-0.586440\pi$
$967$	13.4318	−	7.75487i	0.431938	−	0.249380i	0.700172	+	0.713974i	$0.253107\pi$
$968$	−17.5265	−	29.9206i	−0.563323	−	0.961683i
$969$		0			0
$970$	1.43783	+	8.05556i	0.0461660	+	0.258648i
$971$	−15.4979	+	26.8432i	−0.497352	+	0.861439i	−0.999995	−	0.00305480i	$-0.999028\pi$
$971$	−15.4979	+	26.8432i	−0.497352	+	0.861439i	0.502643	+	0.864494i	$0.332361\pi$
$972$		0			0
$973$	−23.0383	+	8.49564i	−0.738574	+	0.272358i
$974$	−3.70659	+	10.2506i	−0.118767	+	0.328450i
$975$		0			0
$976$	28.5072	−	5.27346i	0.912493	−	0.168799i
$977$	17.0004	−	29.4456i	0.543891	−	0.942048i	−0.454784	−	0.890602i	$-0.650284\pi$
$977$	17.0004	−	29.4456i	0.543891	−	0.942048i	0.998676	−	0.0514460i	$-0.0163830\pi$
$978$		0			0
$979$	−5.31065	+	9.19831i	−0.169729	+	0.293979i
$980$	9.95402	+	5.58038i	0.317970	+	0.178259i
$981$		0			0
$982$	12.4259	−	34.3639i	0.396527	−	1.09660i
$983$	−34.5769			−1.10283			−0.551416	−	0.834230i	$-0.685912\pi$
$983$	−34.5769			−1.10283			−0.551416	+	0.834230i	$0.685912\pi$
$984$		0			0
$985$		−	4.12108i		−	0.131309i
$986$	3.34912	+	3.97437i	0.106658	+	0.126570i
$987$		0			0
$988$	22.4755	+	3.86593i	0.715040	+	0.122991i
$989$	17.6579	−	30.5844i	0.561489	−	0.972527i
$990$		0			0
$991$	−46.4705	+	26.8297i	−1.47618	+	0.852275i	−0.999639	−	0.0268752i	$-0.991444\pi$
$991$	−46.4705	+	26.8297i	−1.47618	+	0.852275i	−0.476545	+	0.879150i	$0.658111\pi$
$992$	8.89147	−	53.7127i	0.282305	−	1.70538i
$993$		0			0
$994$	−11.7583	+	6.88814i	−0.372952	+	0.218479i
$995$	−15.4201	+	8.90281i	−0.488851	+	0.282238i
$996$		0			0
$997$		−	44.0629i		−	1.39548i	−0.716349	−	0.697742i	$-0.754188\pi$
$997$		−	44.0629i		−	1.39548i	0.716349	−	0.697742i	$-0.245812\pi$
$998$	33.9127	+	40.2440i	1.07349	+	1.27390i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.n.b.19.9		84
3.2	odd	2		252.2.n.b.187.34	yes	84
4.3	odd	2	inner	756.2.n.b.19.37		84
7.3	odd	6		756.2.bj.b.451.19		84
9.4	even	3		756.2.bj.b.523.19		84
9.5	odd	6		252.2.bj.b.103.24	yes	84
12.11	even	2		252.2.n.b.187.6	yes	84
21.17	even	6		252.2.bj.b.115.24	yes	84
28.3	even	6		756.2.bj.b.451.20		84
36.23	even	6		252.2.bj.b.103.23	yes	84
36.31	odd	6		756.2.bj.b.523.20		84
63.31	odd	6	inner	756.2.n.b.199.37		84
63.59	even	6		252.2.n.b.31.6	✓	84
84.59	odd	6		252.2.bj.b.115.23	yes	84
252.31	even	6	inner	756.2.n.b.199.9		84
252.59	odd	6		252.2.n.b.31.34	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.6	✓	84	63.59	even	6
252.2.n.b.31.34	yes	84	252.59	odd	6
252.2.n.b.187.6	yes	84	12.11	even	2
252.2.n.b.187.34	yes	84	3.2	odd	2
252.2.bj.b.103.23	yes	84	36.23	even	6
252.2.bj.b.103.24	yes	84	9.5	odd	6
252.2.bj.b.115.23	yes	84	84.59	odd	6
252.2.bj.b.115.24	yes	84	21.17	even	6
756.2.n.b.19.9		84	1.1	even	1	trivial
756.2.n.b.19.37		84	4.3	odd	2	inner
756.2.n.b.199.9		84	252.31	even	6	inner
756.2.n.b.199.37		84	63.31	odd	6	inner
756.2.bj.b.451.19		84	7.3	odd	6
756.2.bj.b.451.20		84	28.3	even	6
756.2.bj.b.523.19		84	9.4	even	3
756.2.bj.b.523.20		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)

\(f(q)\)	\(=\)	\(q+(-1.08144 + 0.911308i) q^{2} +(0.339034 - 1.97105i) q^{4} -0.815110i q^{5} +(0.448419 - 2.60747i) q^{7} +(1.42959 + 2.44055i) q^{8} +O(q^{10})\)	\(q+(-1.08144 + 0.911308i) q^{2} +(0.339034 - 1.97105i) q^{4} -0.815110i q^{5} +(0.448419 - 2.60747i) q^{7} +(1.42959 + 2.44055i) q^{8} +(0.742817 + 0.881495i) q^{10} +4.82284i q^{11} +(2.20303 - 1.27192i) q^{13} +(1.89127 + 3.22848i) q^{14} +(-3.77011 - 1.33651i) q^{16} +(0.503257 - 0.290555i) q^{17} +(-2.24125 + 3.88195i) q^{19} +(-1.60663 - 0.276350i) q^{20} +(-4.39509 - 5.21562i) q^{22} -6.47618i q^{23} +4.33560 q^{25} +(-1.22334 + 3.38315i) q^{26} +(-4.98744 - 1.76788i) q^{28} +(3.16210 - 5.47692i) q^{29} +(4.81219 - 8.33495i) q^{31} +(5.29513 - 1.99038i) q^{32} +(-0.279458 + 0.772841i) q^{34} +(-2.12538 - 0.365511i) q^{35} +(1.62993 - 2.82313i) q^{37} +(-1.11388 - 6.24058i) q^{38} +(1.98931 - 1.16528i) q^{40} +(-3.04709 + 1.75924i) q^{41} +(4.72260 + 2.72659i) q^{43} +(9.50608 + 1.63511i) q^{44} +(5.90179 + 7.00361i) q^{46} +(-4.79019 - 8.29685i) q^{47} +(-6.59784 - 2.33848i) q^{49} +(-4.68870 + 3.95106i) q^{50} +(-1.76012 - 4.77352i) q^{52} +(1.09484 + 1.89632i) q^{53} +3.93115 q^{55} +(7.00472 - 2.63324i) q^{56} +(1.57153 + 8.80463i) q^{58} +(5.60288 - 9.70447i) q^{59} +(-6.27670 + 3.62386i) q^{61} +(2.39161 + 13.3992i) q^{62} +(-3.91253 + 6.97797i) q^{64} +(-1.03676 - 1.79571i) q^{65} +(4.34796 + 2.51030i) q^{67} +(-0.402079 - 1.09045i) q^{68} +(2.63157 - 1.54160i) q^{70} +3.64207i q^{71} +(2.26126 - 1.30554i) q^{73} +(0.810061 + 4.53842i) q^{74} +(6.89168 + 5.73374i) q^{76} +(12.5754 + 2.16265i) q^{77} +(8.78313 - 5.07094i) q^{79} +(-1.08940 + 3.07306i) q^{80} +(1.69204 - 4.67935i) q^{82} +(0.820993 - 1.42200i) q^{83} +(-0.236835 - 0.410210i) q^{85} +(-7.59199 + 1.35509i) q^{86} +(-11.7704 + 6.89469i) q^{88} +(1.90724 + 1.10115i) q^{89} +(-2.32862 - 6.31470i) q^{91} +(-12.7649 - 2.19565i) q^{92} +(12.7413 + 4.60722i) q^{94} +(3.16422 + 1.82686i) q^{95} +(6.14759 + 3.54931i) q^{97} +(9.26626 - 3.48373i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + q^{2} + q^{4} + 16 q^{8}+O(q^{10}) \) 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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