LMFDB - Embedded newform 756.2.bj.b.451.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(451,756)]

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, 1]))

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

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

chi := DirichletCharacter("756.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bj (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			451.20
Character	$\chi$	$=$	756.451
Dual form			756.2.bj.b.523.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.248495 + 1.39221i) q^{2} +(-1.87650 - 0.691915i) q^{4} +(-0.705906 - 0.407555i) q^{5} +(2.03393 - 1.69208i) q^{7} +(1.42959 - 2.44055i) q^{8} +O(q^{10})$	\(q+(-0.248495 + 1.39221i) q^{2} +(-1.87650 - 0.691915i) q^{4} +(-0.705906 - 0.407555i) q^{5} +(2.03393 - 1.69208i) q^{7} +(1.42959 - 2.44055i) q^{8} +(0.742817 - 0.881495i) q^{10} +(-4.17670 + 2.41142i) q^{11} +(-2.20303 + 1.27192i) q^{13} +(1.85031 + 3.25213i) q^{14} +(3.04251 + 2.59676i) q^{16} +(0.503257 + 0.290555i) q^{17} +(-2.24125 - 3.88195i) q^{19} +(1.04264 + 1.25320i) q^{20} +(-2.31931 - 6.41407i) q^{22} +(-5.60853 - 3.23809i) q^{23} +(-2.16780 - 3.75474i) q^{25} +(-1.22334 - 3.38315i) q^{26} +(-4.98744 + 1.76788i) q^{28} +(3.16210 - 5.47692i) q^{29} -9.62438 q^{31} +(-4.37128 + 3.59053i) q^{32} +(-0.529571 + 0.628438i) q^{34} +(-2.12538 + 0.365511i) q^{35} +(1.62993 + 2.82313i) q^{37} +(5.96144 - 2.15564i) q^{38} +(-2.00382 + 1.14016i) q^{40} +(3.04709 - 1.75924i) q^{41} +(-4.72260 - 2.72659i) q^{43} +(9.50608 - 1.63511i) q^{44} +(5.90179 - 7.00361i) q^{46} +9.58038 q^{47} +(1.27373 - 6.88314i) q^{49} +(5.76607 - 2.08500i) q^{50} +(5.01405 - 0.862450i) q^{52} +(1.09484 - 1.89632i) q^{53} +3.93115 q^{55} +(-1.22191 - 7.38288i) q^{56} +(6.83926 + 5.76330i) q^{58} -11.2058 q^{59} +7.24771i q^{61} +(2.39161 - 13.3992i) q^{62} +(-3.91253 - 6.97797i) q^{64} +2.07351 q^{65} +5.02059i q^{67} +(-0.743322 - 0.893438i) q^{68} +(0.0192776 - 3.04980i) q^{70} -3.64207i q^{71} +(2.26126 + 1.30554i) q^{73} +(-4.33542 + 1.56768i) q^{74} +(1.51972 + 8.83524i) q^{76} +(-4.41480 + 11.9720i) q^{77} -10.1419i q^{79} +(-1.08940 - 3.07306i) q^{80} +(1.69204 + 4.67935i) q^{82} +(0.820993 - 1.42200i) q^{83} +(-0.236835 - 0.410210i) q^{85} +(4.96954 - 5.89731i) q^{86} +(-0.0857994 + 13.6408i) q^{88} +(1.90724 - 1.10115i) q^{89} +(-2.32862 + 6.31470i) q^{91} +(8.28393 + 9.95690i) q^{92} +(-2.38068 + 13.3379i) q^{94} +3.65373i q^{95} +(-6.14759 - 3.54931i) q^{97} +(9.26626 + 3.48373i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8}+O(q^{10}) $ 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8	$ 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8} - 18 q^{10} + 18 q^{13} - 14 q^{14} + 14 q^{16} - 6 q^{17} + 24 q^{20} + 6 q^{22} + 16 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} + 18 q^{32} - 24 q^{34} + 2 q^{37} - 33 q^{38} + 6 q^{40} - 6 q^{41} + 13 q^{44} + 10 q^{46} - 28 q^{49} + 17 q^{50} - 27 q^{52} + 2 q^{53} - 58 q^{56} - 13 q^{58} - 8 q^{64} + 100 q^{65} + 18 q^{68} - 19 q^{70} + 30 q^{73} + 23 q^{74} + 2 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} + 9 q^{86} + q^{88} + 102 q^{89} - 28 q^{92} + 6 q^{97} - 21 q^{98}+O(q^{100}) $ 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8 - 18 * q^10 + 18 * q^13 - 14 * q^14 + 14 * q^16 - 6 * q^17 + 24 * q^20 + 6 * q^22 + 16 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 + 18 * q^32 - 24 * q^34 + 2 * q^37 - 33 * q^38 + 6 * q^40 - 6 * q^41 + 13 * q^44 + 10 * q^46 - 28 * q^49 + 17 * q^50 - 27 * q^52 + 2 * q^53 - 58 * q^56 - 13 * q^58 - 8 * q^64 + 100 * q^65 + 18 * q^68 - 19 * q^70 + 30 * q^73 + 23 * q^74 + 2 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 + 9 * q^86 + q^88 + 102 * q^89 - 28 * q^92 + 6 * q^97 - 21 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.248495	+	1.39221i	−0.175713	+	0.984442i
$2$	−0.248495	+	1.39221i	−0.175713	+	0.984442i
$3$		0			0
$3$		0			0
$4$	−1.87650	−	0.691915i	−0.938250	−	0.345957i
$5$	−0.705906	−	0.407555i	−0.315691	−	0.182264i	0.333779	−	0.942651i	$-0.391676\pi$
$5$	−0.705906	−	0.407555i	−0.315691	−	0.182264i	−0.649470	+	0.760387i	$0.725009\pi$
$6$		0			0
$7$	2.03393	−	1.69208i	0.768753	−	0.639546i
$7$	2.03393	−	1.69208i	0.768753	−	0.639546i
$8$	1.42959	−	2.44055i	0.505437	−	0.862863i
$9$		0			0
$10$	0.742817	−	0.881495i	0.234899	−	0.278753i
$11$	−4.17670	+	2.41142i	−1.25932	+	0.727070i	−0.972943	−	0.231046i	$-0.925785\pi$
$11$	−4.17670	+	2.41142i	−1.25932	+	0.727070i	−0.286380	+	0.958116i	$0.592452\pi$
$12$		0			0
$13$	−2.20303	+	1.27192i	−0.611011	+	0.352767i	−0.773361	−	0.633966i	$-0.781426\pi$
$13$	−2.20303	+	1.27192i	−0.611011	+	0.352767i	0.162350	+	0.986733i	$0.448093\pi$
$14$	1.85031	+	3.25213i	0.494516	+	0.869169i
$15$		0			0
$16$	3.04251	+	2.59676i	0.760627	+	0.649189i
$17$	0.503257	+	0.290555i	0.122058	+	0.0704700i	0.559786	−	0.828637i	$-0.310883\pi$
$17$	0.503257	+	0.290555i	0.122058	+	0.0704700i	−0.437728	+	0.899107i	$0.644217\pi$
$18$		0			0
$19$	−2.24125	−	3.88195i	−0.514177	−	0.890581i	−0.999865	−	0.0164486i	$-0.994764\pi$
$19$	−2.24125	−	3.88195i	−0.514177	−	0.890581i	0.485687	−	0.874133i	$-0.338569\pi$
$20$	1.04264	+	1.25320i	0.233141	+	0.280225i
$21$		0			0
$22$	−2.31931	−	6.41407i	−0.494479	−	1.36749i
$23$	−5.60853	−	3.23809i	−1.16946	−	0.675188i	−0.215907	−	0.976414i	$-0.569271\pi$
$23$	−5.60853	−	3.23809i	−1.16946	−	0.675188i	−0.953553	+	0.301226i	$0.902604\pi$
$24$		0			0
$25$	−2.16780	−	3.75474i	−0.433560	−	0.750947i
$26$	−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
$31$	−9.62438			−1.72859			−0.864294	−	0.502986i	$-0.832235\pi$
$31$	−9.62438			−1.72859			−0.864294	+	0.502986i	$0.832235\pi$
$32$	−4.37128	+	3.59053i	−0.772741	+	0.634722i
$33$		0			0
$34$	−0.529571	+	0.628438i	−0.0908207	+	0.107776i
$35$	−2.12538	+	0.365511i	−0.359255	+	0.0617827i
$36$		0			0
$37$	1.62993	+	2.82313i	0.267959	+	0.464119i	0.968335	−	0.249655i	$-0.0803173\pi$
$37$	1.62993	+	2.82313i	0.267959	+	0.464119i	−0.700375	+	0.713775i	$0.746984\pi$
$38$	5.96144	−	2.15564i	0.967073	−	0.349691i
$39$		0			0
$40$	−2.00382	+	1.14016i	−0.316831	+	0.180275i
$41$	3.04709	−	1.75924i	0.475875	−	0.274747i	−0.242821	−	0.970071i	$-0.578073\pi$
$41$	3.04709	−	1.75924i	0.475875	−	0.274747i	0.718696	+	0.695325i	$0.244739\pi$
$42$		0			0
$43$	−4.72260	−	2.72659i	−0.720190	−	0.415802i	0.0946327	−	0.995512i	$-0.469832\pi$
$43$	−4.72260	−	2.72659i	−0.720190	−	0.415802i	−0.814823	+	0.579710i	$0.803166\pi$
$44$	9.50608	−	1.63511i	1.43310	−	0.246502i
$45$		0			0
$46$	5.90179	−	7.00361i	0.870172	−	1.03263i
$47$	9.58038			1.39744			0.698721	−	0.715395i	$-0.253753\pi$
$47$	9.58038			1.39744			0.698721	+	0.715395i	$0.253753\pi$
$48$		0			0
$49$	1.27373	−	6.88314i	0.181962	−	0.983306i
$50$	5.76607	−	2.08500i	0.815445	−	0.294863i
$51$		0			0
$52$	5.01405	−	0.862450i	0.695324	−	0.119600i
$53$	1.09484	−	1.89632i	0.150388	−	0.260480i	−0.780982	−	0.624553i	$-0.785281\pi$
$53$	1.09484	−	1.89632i	0.150388	−	0.260480i	0.931370	+	0.364074i	$0.118614\pi$
$54$		0			0
$55$	3.93115			0.530076
$56$	−1.22191	−	7.38288i	−0.163284	−	0.986579i
$57$		0			0
$58$	6.83926	+	5.76330i	0.898039	+	0.756759i
$59$	−11.2058			−1.45886			−0.729432	−	0.684053i	$-0.760216\pi$
$59$	−11.2058			−1.45886			−0.729432	+	0.684053i	$0.760216\pi$
$60$		0			0
$61$			7.24771i			0.927974i	0.885842	+	0.463987i	$0.153582\pi$
$61$			7.24771i			0.927974i	−0.885842	+	0.463987i	$0.846418\pi$
$62$	2.39161	−	13.3992i	0.303735	−	1.70169i
$63$		0			0
$64$	−3.91253	−	6.97797i	−0.489066	−	0.872247i
$65$	2.07351			0.257187
$66$		0			0
$67$			5.02059i			0.613363i	0.951812	+	0.306682i	$0.0992187\pi$
$67$			5.02059i			0.613363i	−0.951812	+	0.306682i	$0.900781\pi$
$68$	−0.743322	−	0.893438i	−0.0901410	−	0.108345i
$69$		0			0
$70$	0.0192776	−	3.04980i	0.00230411	−	0.364521i
$71$		−	3.64207i		−	0.432234i	−0.976367	−	0.216117i	$-0.930661\pi$
$71$		−	3.64207i		−	0.432234i	0.976367	−	0.216117i	$-0.0693392\pi$
$72$		0			0
$73$	2.26126	+	1.30554i	0.264661	+	0.152802i	0.626459	−	0.779454i	$-0.284504\pi$
$73$	2.26126	+	1.30554i	0.264661	+	0.152802i	−0.361798	+	0.932257i	$0.617837\pi$
$74$	−4.33542	+	1.56768i	−0.503982	+	0.182239i
$75$		0			0
$76$	1.51972	+	8.83524i	0.174324	+	1.01347i
$77$	−4.41480	+	11.9720i	−0.503113	+	1.36433i
$78$		0			0
$79$		−	10.1419i		−	1.14105i	−0.821280	−	0.570526i	$-0.806740\pi$
$79$		−	10.1419i		−	1.14105i	0.821280	−	0.570526i	$-0.193260\pi$
$80$	−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
$86$	4.96954	−	5.89731i	0.535879	−	0.635923i
$87$		0			0
$88$	−0.0857994	+	13.6408i	−0.00914624	+	1.45411i
$89$	1.90724	−	1.10115i	0.202167	−	0.116721i	−0.395499	−	0.918466i	$-0.629428\pi$
$89$	1.90724	−	1.10115i	0.202167	−	0.116721i	0.597666	+	0.801745i	$0.296095\pi$
$90$		0			0
$91$	−2.32862	+	6.31470i	−0.244106	+	0.661961i
$92$	8.28393	+	9.95690i	0.863660	+	1.03808i
$93$		0			0
$94$	−2.38068	+	13.3379i	−0.245548	+	1.37570i
$95$			3.65373i			0.374864i
$96$		0			0
$97$	−6.14759	−	3.54931i	−0.624193	−	0.360378i	0.154307	−	0.988023i	$-0.450686\pi$
$97$	−6.14759	−	3.54931i	−0.624193	−	0.360378i	−0.778500	+	0.627645i	$0.784019\pi$
$98$	9.26626	+	3.48373i	0.936034	+	0.351910i
$99$		0			0
$100$	1.46992	+	8.54569i	0.146992	+	0.854569i
$101$	−8.15564	+	4.70866i	−0.811516	+	0.468529i	−0.847482	−	0.530824i	$-0.821883\pi$
$101$	−8.15564	+	4.70866i	−0.811516	+	0.468529i	0.0359658	+	0.999353i	$0.488549\pi$
$102$		0			0
$103$	2.57609	−	4.46191i	0.253829	−	0.439645i	−0.710748	−	0.703447i	$-0.751643\pi$
$103$	2.57609	−	4.46191i	0.253829	−	0.439645i	0.964577	+	0.263802i	$0.0849765\pi$
$104$	−0.0452555	+	7.19493i	−0.00443767	+	0.705521i
$105$		0			0
$106$	2.36802	+	1.99548i	0.230002	+	0.193818i
$107$	−10.4663	+	6.04271i	−1.01181	+	0.584170i	−0.911722	−	0.410808i	$-0.865247\pi$
$107$	−10.4663	+	6.04271i	−1.01181	+	0.584170i	−0.100091	+	0.994978i	$0.531913\pi$
$108$		0			0
$109$	1.83950	−	3.18610i	0.176192	−	0.305173i	−0.764381	−	0.644764i	$-0.776955\pi$
$109$	1.83950	−	3.18610i	0.176192	−	0.305173i	0.940573	+	0.339591i	$0.110289\pi$
$110$	−0.976870	+	5.47298i	−0.0931409	+	0.521828i
$111$		0			0
$112$	10.5822	+	0.133455i	0.999920	+	0.0126103i
$113$	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
$115$	2.63940	+	4.57157i	0.246125	+	0.426301i
$116$	−9.72325	+	8.08954i	−0.902781	+	0.751095i
$117$		0			0
$118$	2.78457	−	15.6008i	0.256341	−	1.43617i
$119$	1.51523	−	0.260581i	0.138901	−	0.0238875i
$120$		0			0
$121$	6.12989	−	10.6173i	0.557263	−	0.965207i
$122$	−10.0903	−	1.80102i	−0.913537	−	0.163057i
$123$		0			0
$124$	18.0601	+	6.65925i	1.62185	+	0.598018i
$125$			7.60954i			0.680618i
$126$		0			0
$127$		−	1.07938i		−	0.0957798i	−0.998853	−	0.0478899i	$-0.984750\pi$
$127$		−	1.07938i		−	0.0957798i	0.998853	−	0.0478899i	$-0.0152497\pi$
$128$	10.6871	−	3.71308i	0.944611	−	0.328193i
$129$		0			0
$130$	−0.515257	+	2.88677i	−0.0451911	+	0.253186i
$131$	−4.37411	+	7.57619i	−0.382168	+	0.661935i	−0.991372	−	0.131079i	$-0.958156\pi$
$131$	−4.37411	+	7.57619i	−0.382168	+	0.661935i	0.609204	+	0.793014i	$0.291489\pi$
$132$		0			0
$133$	−11.1271	−	4.10325i	−0.964843	−	0.355797i
$134$	−6.98972	−	1.24759i	−0.603820	−	0.107776i
$135$		0			0
$136$	1.42857	−	0.812846i	0.122499	−	0.0697009i
$137$	−4.31047	−	7.46595i	−0.368268	−	0.637859i	0.621027	−	0.783789i	$-0.286716\pi$
$137$	−4.31047	−	7.46595i	−0.368268	−	0.637859i	−0.989295	+	0.145930i	$0.953383\pi$
$138$		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	$0.962102\pi$
$140$	4.24118	+	0.784699i	0.358445	+	0.0663192i
$141$		0			0
$142$	5.07053	+	0.905036i	0.425509	+	0.0759489i
$143$	6.13427	−	10.6249i	0.512974	−	0.888496i
$144$		0			0
$145$	−4.46430	+	2.57746i	−0.370740	+	0.214047i
$146$	−2.37950	+	2.82374i	−0.196929	+	0.233694i
$147$		0			0
$148$	−1.10521	−	6.42538i	−0.0908474	−	0.528163i
$149$	5.47269	−	9.47898i	0.448340	−	0.776548i	−0.549938	−	0.835206i	$-0.685349\pi$
$149$	5.47269	−	9.47898i	0.448340	−	0.776548i	0.998278	+	0.0586572i	$0.0186819\pi$
$150$		0			0
$151$	0.329198	−	0.190062i	0.0267897	−	0.0154671i	−0.486545	−	0.873655i	$-0.661743\pi$
$151$	0.329198	−	0.190062i	0.0267897	−	0.0154671i	0.513335	+	0.858188i	$0.328410\pi$
$152$	−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
$157$			4.96221i			0.396028i	0.980199	+	0.198014i	$0.0634491\pi$
$157$			4.96221i			0.396028i	−0.980199	+	0.198014i	$0.936551\pi$
$158$	14.1196	+	2.52021i	1.12330	+	0.200497i
$159$		0			0
$160$	4.54905	−	0.753039i	0.359634	−	0.0595330i
$161$	−16.8865	+	2.90404i	−1.33084	+	0.228871i
$162$		0			0
$163$	17.9942	−	10.3890i	1.40942	−	0.813727i	0.414085	−	0.910238i	$-0.364102\pi$
$163$	17.9942	−	10.3890i	1.40942	−	0.813727i	0.995332	+	0.0965111i	$0.0307683\pi$
$164$	−6.93510	+	1.19288i	−0.541540	+	0.0931485i
$165$		0			0
$166$	1.77571	+	1.49636i	0.137822	+	0.116140i
$167$	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
$173$			14.4260i			1.09679i	0.836220	+	0.548395i	$0.184761\pi$
$173$			14.4260i			1.09679i	−0.836220	+	0.548395i	$0.815239\pi$
$174$		0			0
$175$	−10.7625	−	3.96878i	−0.813565	−	0.300012i
$176$	−18.9695	−	3.50912i	−1.42988	−	0.264510i
$177$		0			0
$178$	1.05909	+	2.92891i	0.0793819	+	0.219531i
$179$	3.35237	+	1.93549i	0.250568	+	0.144666i	0.620024	−	0.784583i	$-0.287123\pi$
$179$	3.35237	+	1.93549i	0.250568	+	0.144666i	−0.369456	+	0.929248i	$0.620456\pi$
$180$		0			0
$181$			24.8665i			1.84831i	0.382012	+	0.924157i	$0.375231\pi$
$181$			24.8665i			1.84831i	−0.382012	+	0.924157i	$0.624769\pi$
$182$	−8.21275	−	4.81110i	−0.608769	−	0.356623i
$183$		0			0
$184$	−15.9206	+	9.05874i	−1.17368	+	0.667819i
$185$		−	2.65715i		−	0.195358i
$186$		0			0
$187$	−2.80260			−0.204947
$188$	−17.9776	−	6.62880i	−1.31115	−	0.483455i
$189$		0			0
$190$	−5.08676	−	0.907933i	−0.369032	−	0.0658684i
$191$			18.5339i			1.34107i	0.741880	+	0.670533i	$0.233935\pi$
$191$			18.5339i			1.34107i	−0.741880	+	0.670533i	$0.766065\pi$
$192$		0			0
$193$	26.3504			1.89674			0.948371	−	0.317163i	$-0.102730\pi$
$193$	26.3504			1.89674			0.948371	+	0.317163i	$0.102730\pi$
$194$	6.46904	−	7.67675i	0.464450	−	0.551159i
$195$		0			0
$196$	−7.15271	+	12.0349i	−0.510908	+	0.859636i
$197$	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	0.160957	+	0.986961i	$0.448542\pi$
$199$	−10.9222	+	18.9178i	−0.774255	+	1.34105i	−0.935212	+	0.354088i	$0.884791\pi$
$200$	−12.2627	−	0.0771312i	−0.867102	−	0.00545400i
$201$		0			0
$202$	−4.52881	−	12.5244i	−0.318646	−	0.881217i
$203$	−2.83590	−	16.4902i	−0.199041	−	1.15739i
$204$		0			0
$205$	−2.86794			−0.200306
$206$	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	$-0.322436\pi$
$211$	22.2066	−	12.8210i	1.52876	−	0.882632i	0.999414	−	0.0342290i	$-0.0108975\pi$
$212$	−3.36656	+	2.80091i	−0.231217	+	0.192367i
$213$		0			0
$214$	−5.81190	−	16.0728i	−0.397293	−	1.09872i
$215$	2.22248	+	3.84944i	0.151572	+	0.262530i
$216$		0			0
$217$	−19.5753	+	16.2852i	−1.32886	+	1.10551i
$218$	3.97862	+	3.35269i	0.269466	+	0.227073i
$219$		0			0
$220$	−7.37680	−	2.72002i	−0.497344	−	0.183384i
$221$	−1.47825			−0.0994382
$222$		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
$227$	−10.9776	−	19.0138i	−0.728611	−	1.26199i	−0.957470	−	0.288532i	$-0.906833\pi$
$227$	−10.9776	−	19.0138i	−0.728611	−	1.26199i	0.228859	−	0.973459i	$-0.426500\pi$
$228$		0			0
$229$	9.27254	+	5.35350i	0.612747	+	0.353769i	0.774040	−	0.633137i	$-0.218233\pi$
$229$	9.27254	+	5.35350i	0.612747	+	0.353769i	−0.161293	+	0.986907i	$0.551566\pi$
$230$	−7.02047	+	2.53858i	−0.462916	+	0.167389i
$231$		0			0
$232$	−8.84617	−	15.5470i	−0.580779	−	1.02071i
$233$	−2.17122	−	3.76066i	−0.142241	−	0.246369i	0.786099	−	0.618101i	$-0.212098\pi$
$233$	−2.17122	−	3.76066i	−0.142241	−	0.246369i	−0.928340	+	0.371731i	$0.878764\pi$
$234$		0			0
$235$	−6.76285	−	3.90453i	−0.441159	−	0.254704i
$236$	21.0276	+	7.75343i	1.36878	+	0.504705i
$237$		0			0
$238$	−0.0137434	+	2.17427i	−0.000890855	+	0.140937i
$239$	9.17613	−	5.29784i	0.593554	−	0.342689i	−0.172947	−	0.984931i	$-0.555329\pi$
$239$	9.17613	−	5.29784i	0.593554	−	0.342689i	0.766502	+	0.642242i	$0.221996\pi$
$240$		0			0
$241$	−5.90935	+	3.41177i	−0.380655	+	0.219771i	−0.678103	−	0.734967i	$-0.737198\pi$
$241$	−5.90935	+	3.41177i	−0.380655	+	0.219771i	0.297448	+	0.954738i	$0.403864\pi$
$242$	13.2582	+	11.1724i	0.852272	+	0.718192i
$243$		0			0
$244$	5.01480	−	13.6003i	0.321040	−	0.870672i
$245$	−3.70440	+	4.33973i	−0.236665	+	0.277255i
$246$		0			0
$247$	9.87508	+	5.70138i	0.628336	+	0.362770i
$248$	−13.7589	+	23.4887i	−0.873693	+	1.49154i
$249$		0			0
$250$	−10.5941	−	1.89093i	−0.670028	−	0.119593i
$251$	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
$254$	1.50273	+	0.268221i	0.0942896	+	0.0168297i
$255$		0			0
$256$	2.51370	+	15.8013i	0.157106	+	0.987582i
$257$	−11.8534	−	6.84354i	−0.739392	−	0.426888i	0.0824560	−	0.996595i	$-0.473724\pi$
$257$	−11.8534	−	6.84354i	−0.739392	−	0.426888i	−0.821848	+	0.569706i	$0.807057\pi$
$258$		0			0
$259$	8.09213	+	2.98406i	0.502820	+	0.185421i
$260$	−3.89095	−	1.43469i	−0.241306	−	0.0889759i
$261$		0			0
$262$	−9.46070	−	7.97233i	−0.584484	−	0.492532i
$263$	−13.5112	+	7.80071i	−0.833138	+	0.481013i	−0.854926	−	0.518750i	$-0.826398\pi$
$263$	−13.5112	+	7.80071i	−0.833138	+	0.481013i	0.0217878	+	0.999763i	$0.493064\pi$
$264$		0			0
$265$	−1.54571	+	0.892417i	−0.0949523	+	0.0548207i
$266$	8.47762	−	14.4716i	0.519796	−	0.887313i
$267$		0			0
$268$	3.47382	−	9.42115i	0.212198	−	0.575488i
$269$	−18.5276	−	10.6969i	−1.12965	−	0.652202i	−0.185801	−	0.982587i	$-0.559488\pi$
$269$	−18.5276	−	10.6969i	−1.12965	−	0.652202i	−0.943846	+	0.330386i	$0.892821\pi$
$270$		0			0
$271$	−1.36221	−	2.35942i	−0.0827485	−	0.143325i	0.821681	−	0.569948i	$-0.193036\pi$
$271$	−1.36221	−	2.35942i	−0.0827485	−	0.143325i	−0.904430	+	0.426623i	$0.859703\pi$
$272$	0.776661	+	2.19085i	0.0470920	+	0.132840i
$273$		0			0
$274$	11.4653	−	4.14583i	0.692645	−	0.250459i
$275$	18.1085	+	10.4549i	1.09198	+	0.630457i
$276$		0			0
$277$	−5.69546	−	9.86482i	−0.342207	−	0.592720i	0.642635	−	0.766172i	$-0.277841\pi$
$277$	−5.69546	−	9.86482i	−0.342207	−	0.592720i	−0.984842	+	0.173453i	$0.944508\pi$
$278$	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
$283$	4.05561			0.241081			0.120540	−	0.992708i	$-0.461537\pi$
$283$	4.05561			0.241081			0.120540	+	0.992708i	$0.461537\pi$
$284$	−2.52000	+	6.83434i	−0.149535	+	0.405544i
$285$		0			0
$286$	13.2677	+	11.1804i	0.784537	+	0.661112i
$287$	3.22079	−	8.73407i	0.190117	−	0.515556i
$288$		0			0
$289$	−8.33116	−	14.4300i	−0.490068	−	0.848823i
$290$	−2.47901	−	6.85573i	−0.145573	−	0.402582i
$291$		0			0
$292$	−3.33994	−	4.01445i	−0.195455	−	0.234928i
$293$	−18.5526	+	10.7113i	−1.08385	+	0.625762i	−0.931933	−	0.362631i	$-0.881879\pi$
$293$	−18.5526	+	10.7113i	−1.08385	+	0.625762i	−0.151919	+	0.988393i	$0.548545\pi$
$294$		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
$299$	16.4744			0.952737
$300$		0			0
$301$	−14.2190	+	2.44532i	−0.819572	+	0.140946i
$302$	0.182803	+	0.505542i	0.0105191	+	0.0290907i
$303$		0			0
$304$	3.26148	−	17.6308i	0.187059	−	1.01120i
$305$	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	$0.313156\pi$
$308$	16.5680	−	19.4107i	0.944047	−	1.10603i
$309$		0			0
$310$	−7.14915	+	8.48383i	−0.406044	+	0.481849i
$311$	10.7296			0.608419			0.304209	−	0.952605i	$-0.401608\pi$
$311$	10.7296			0.608419			0.304209	+	0.952605i	$0.401608\pi$
$312$		0			0
$313$		−	24.4060i		−	1.37951i	−0.724044	−	0.689754i	$-0.757719\pi$
$313$		−	24.4060i		−	1.37951i	0.724044	−	0.689754i	$-0.242281\pi$
$314$	−6.90844	−	1.23309i	−0.389866	−	0.0695870i
$315$		0			0
$316$	−7.01732	+	19.0312i	−0.394755	+	1.07059i
$317$	−32.1240			−1.80426			−0.902132	−	0.431460i	$-0.857999\pi$
$317$	−32.1240			−1.80426			−0.902132	+	0.431460i	$0.857999\pi$
$318$		0			0
$319$			30.5006i			1.70771i
$320$	−0.0820284	+	6.52037i	−0.00458553	+	0.364500i
$321$		0			0
$322$	0.153163	−	24.2311i	0.00853546	−	1.35035i
$323$		−	2.60483i		−	0.144936i
$324$		0			0
$325$	9.55146	+	5.51454i	0.529819	+	0.305891i
$326$	9.99216	+	27.6334i	0.553415	+	1.53047i
$327$		0			0
$328$	0.0625944	−	9.95154i	0.00345620	−	0.549482i
$329$	19.4858	−	16.2108i	1.07429	−	0.893728i
$330$		0			0
$331$			26.1463i			1.43713i	0.695460	+	0.718565i	$0.255201\pi$
$331$			26.1463i			1.43713i	−0.695460	+	0.718565i	$0.744799\pi$
$332$	−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	$0.782909\pi$
$338$	−7.06059	−	5.94981i	−0.384046	−	0.323627i
$339$		0			0
$340$	0.160590	+	0.933628i	0.00870923	+	0.0506331i
$341$	40.1981	−	23.2084i	2.17685	−	1.25681i
$342$		0			0
$343$	−9.05613	−	16.1551i	−0.488985	−	0.872292i
$344$	−13.4058	+	7.62781i	−0.722791	+	0.411264i
$345$		0			0
$346$	−20.0840	−	3.58479i	−1.07973	−	0.192720i
$347$			14.9047i			0.800126i	0.916488	+	0.400063i	$0.131012\pi$
$347$			14.9047i			0.800126i	−0.916488	+	0.400063i	$0.868988\pi$
$348$		0			0
$349$	2.24929	+	1.29863i	0.120402	+	0.0695140i	0.558991	−	0.829173i	$-0.311188\pi$
$349$	2.24929	+	1.29863i	0.120402	+	0.0695140i	−0.438590	+	0.898687i	$0.644522\pi$
$350$	8.19979	−	13.9974i	0.438297	−	0.748192i
$351$		0			0
$352$	9.59926	−	25.5376i	0.511642	−	1.36116i
$353$	11.6633	−	6.73382i	0.620775	−	0.358405i	−0.156395	−	0.987695i	$-0.549987\pi$
$353$	11.6633	−	6.73382i	0.620775	−	0.358405i	0.777171	+	0.629290i	$0.216654\pi$
$354$		0			0
$355$	−1.48434	+	2.57096i	−0.0787808	+	0.136452i
$356$	−4.34084	+	0.746652i	−0.230064	+	0.0395725i
$357$		0			0
$358$	−3.52766	+	4.18625i	−0.186443	+	0.221250i
$359$	15.7293	−	9.08130i	0.830159	−	0.479293i	−0.0237479	−	0.999718i	$-0.507560\pi$
$359$	15.7293	−	9.08130i	0.830159	−	0.479293i	0.853907	+	0.520425i	$0.174227\pi$
$360$		0			0
$361$	−0.546375	+	0.946350i	−0.0287566	+	0.0498079i
$362$	−34.6194	−	6.17921i	−1.81956	−	0.324772i
$363$		0			0
$364$	8.73889	−	10.2383i	0.458042	−	0.536635i
$365$	−1.06416	−	1.84318i	−0.0557007	−	0.0964764i
$366$		0			0
$367$	−5.58683	−	9.67667i	−0.291630	−	0.505118i	0.682565	−	0.730825i	$-0.260864\pi$
$367$	−5.58683	−	9.67667i	−0.291630	−	0.505118i	−0.974195	+	0.225707i	$0.927531\pi$
$368$	−8.65547	−	24.4159i	−0.451198	−	1.27277i
$369$		0			0
$370$	3.69931	+	0.660289i	0.192318	+	0.0343268i
$371$	−0.981896	−	5.70954i	−0.0509775	−	0.296425i
$372$		0			0
$373$	15.4012	−	26.6757i	0.797445	−	1.38121i	−0.123831	−	0.992303i	$-0.539518\pi$
$373$	15.4012	−	26.6757i	0.797445	−	1.38121i	0.921275	−	0.388911i	$-0.127149\pi$
$374$	0.696433	−	3.90182i	0.0360117	−	0.201758i
$375$		0			0
$376$	13.6960	−	23.3813i	0.706319	−	1.20580i
$377$			16.0878i			0.828563i
$378$		0			0
$379$			5.54837i			0.285001i	0.989795	+	0.142500i	$0.0455142\pi$
$379$			5.54837i			0.285001i	−0.989795	+	0.142500i	$0.954486\pi$
$380$	2.52807	−	6.85622i	0.129687	−	0.351717i
$381$		0			0
$382$	−25.8031	−	4.60558i	−1.32020	−	0.235642i
$383$	4.30672	−	7.45945i	0.220063	−	0.381160i	−0.734764	−	0.678323i	$-0.762707\pi$
$383$	4.30672	−	7.45945i	0.220063	−	0.381160i	0.954827	+	0.297163i	$0.0960404\pi$
$384$		0			0
$385$	7.99567	−	6.65181i	0.407497	−	0.339008i
$386$	−6.54794	+	36.6853i	−0.333281	+	1.86723i
$387$		0			0
$388$	9.08013	+	10.9139i	0.460974	+	0.554069i
$389$	1.74069	+	3.01496i	0.0882563	+	0.152864i	0.906774	−	0.421617i	$-0.138537\pi$
$389$	1.74069	+	3.01496i	0.0882563	+	0.152864i	−0.818518	+	0.574481i	$0.805204\pi$
$390$		0			0
$391$	−1.88169	−	3.25918i	−0.0951611	−	0.164824i
$392$	−14.9777	−	12.9487i	−0.756488	−	0.654008i
$393$		0			0
$394$	−1.25636	+	7.03882i	−0.0632943	+	0.354611i
$395$	−4.13338	+	7.15922i	−0.207973	+	0.360219i
$396$		0			0
$397$	−15.5989	+	9.00601i	−0.782885	+	0.451999i	−0.837452	−	0.546511i	$-0.815956\pi$
$397$	−15.5989	+	9.00601i	−0.782885	+	0.451999i	0.0545667	+	0.998510i	$0.482622\pi$
$398$	−23.6235	−	19.9070i	−1.18414	−	0.997848i
$399$		0			0
$400$	3.15460	−	17.0531i	0.157730	−	0.852653i
$401$	7.15282	−	12.3891i	0.357195	−	0.618680i	−0.630296	−	0.776355i	$-0.717067\pi$
$401$	7.15282	−	12.3891i	0.357195	−	0.618680i	0.987491	+	0.157675i	$0.0503999\pi$
$402$		0			0
$403$	21.2028	−	12.2414i	1.05619	−	0.609790i
$404$	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
$409$		−	39.1722i		−	1.93694i	−0.249133	−	0.968469i	$-0.580146\pi$
$409$		−	39.1722i		−	1.93694i	0.249133	−	0.968469i	$-0.419854\pi$
$410$	0.712670	−	3.99278i	0.0351962	−	0.197189i
$411$		0			0
$412$	−7.92129	+	6.59035i	−0.390254	+	0.324683i
$413$	−22.7917	+	18.9610i	−1.12151	+	0.933011i
$414$		0			0
$415$	−1.15909	+	0.669200i	−0.0568974	+	0.0328497i
$416$	5.06320	−	13.4700i	0.248244	−	0.660420i
$417$		0			0
$418$	−19.7010	+	23.3790i	−0.963606	+	1.14350i
$419$	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
$425$		−	2.51946i		−	0.122212i
$426$		0			0
$427$	12.2637	+	14.7413i	0.593482	+	0.713383i
$428$	23.8210	−	4.09737i	1.15143	−	0.198054i
$429$		0			0
$430$	−5.91150	+	2.13759i	−0.285078	+	0.103084i
$431$	3.78493	+	2.18523i	0.182314	+	0.105259i	0.588379	−	0.808585i	$-0.299766\pi$
$431$	3.78493	+	2.18523i	0.182314	+	0.105259i	−0.406065	+	0.913844i	$0.633100\pi$
$432$		0			0
$433$		−	9.78275i		−	0.470129i	−0.971980	−	0.235065i	$-0.924470\pi$
$433$		−	9.78275i		−	0.470129i	0.971980	−	0.235065i	$-0.0755302\pi$
$434$	−17.8081	−	31.2997i	−0.854815	−	1.50244i
$435$		0			0
$436$	−5.65632	+	4.70594i	−0.270889	+	0.225374i
$437$			29.0294i			1.38867i
$438$		0			0
$439$	0.385147			0.0183821			0.00919103	−	0.999958i	$-0.497074\pi$
$439$	0.385147			0.0183821			0.00919103	+	0.999958i	$0.497074\pi$
$440$	5.61994	−	9.59414i	0.267920	−	0.457383i
$441$		0			0
$442$	0.367339	−	2.05804i	0.0174725	−	0.0978911i
$443$		−	16.1931i		−	0.769360i	−0.923050	−	0.384680i	$-0.874312\pi$
$443$		−	16.1931i		−	0.769360i	0.923050	−	0.384680i	$-0.125688\pi$
$444$		0			0
$445$	−1.79511			−0.0850964
$446$	−26.6101	−	22.4238i	−1.26003	−	1.06180i
$447$		0			0
$448$	−19.7651	−	7.57239i	−0.933813	−	0.357762i
$449$	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
$452$	−1.88430	−	10.9548i	−0.0886299	−	0.515270i
$453$		0			0
$454$	29.1991	−	10.5583i	1.37038	−	0.495527i
$455$	4.21738	−	3.50855i	0.197714	−	0.164483i
$456$		0			0
$457$	−5.53862			−0.259086			−0.129543	−	0.991574i	$-0.541351\pi$
$457$	−5.53862			−0.259086			−0.129543	+	0.991574i	$0.541351\pi$
$458$	−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	0.619388	−	0.785085i	$-0.287381\pi$
$461$	5.35007	+	3.08886i	0.249178	+	0.143863i	−0.370210	+	0.928948i	$0.620714\pi$
$462$		0			0
$463$	10.1830	−	5.87914i	0.473243	−	0.273227i	−0.244353	−	0.969686i	$-0.578576\pi$
$463$	10.1830	−	5.87914i	0.473243	−	0.273227i	0.717596	+	0.696459i	$0.245242\pi$
$464$	23.8430	−	8.45237i	1.10688	−	0.392391i
$465$		0			0
$466$	5.77517	−	2.08829i	0.267530	−	0.0967381i
$467$	−13.8715	−	24.0262i	−0.641897	−	1.11180i	−0.985009	−	0.172504i	$-0.944814\pi$
$467$	−13.8715	−	24.0262i	−0.641897	−	1.11180i	0.343112	−	0.939295i	$-0.388519\pi$
$468$		0			0
$469$	8.49524	+	10.2115i	0.392274	+	0.471525i
$470$	7.11646	−	8.44505i	0.328258	−	0.389541i
$471$		0			0
$472$	−16.0197	+	27.3482i	−0.737365	+	1.25880i
$473$	26.2999			1.20927
$474$		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
$479$	3.57520	+	6.19243i	0.163355	+	0.282939i	0.936070	−	0.351814i	$-0.114435\pi$
$479$	3.57520	+	6.19243i	0.163355	+	0.282939i	−0.772715	+	0.634753i	$0.781102\pi$
$480$		0			0
$481$	−7.18159	−	4.14629i	−0.327452	−	0.189055i
$482$	−3.28145	−	9.07487i	−0.149466	−	0.413349i
$483$		0			0
$484$	−18.8490	+	15.6820i	−0.856773	+	0.712817i
$485$	2.89308	+	5.01096i	0.131368	+	0.227536i
$486$		0			0
$487$	6.67495	+	3.85379i	0.302471	+	0.174632i	0.643552	−	0.765402i	$-0.277460\pi$
$487$	6.67495	+	3.85379i	0.302471	+	0.174632i	−0.341081	+	0.940034i	$0.610793\pi$
$488$	17.6884	+	10.3613i	0.800715	+	0.469033i
$489$		0			0
$490$	−5.12130	−	6.23570i	−0.231357	−	0.281700i
$491$	22.3770	−	12.9194i	1.00986	−	0.583043i	0.0987099	−	0.995116i	$-0.468528\pi$
$491$	22.3770	−	12.9194i	1.00986	−	0.583043i	0.911151	+	0.412073i	$0.135195\pi$
$492$		0			0
$493$	3.18270	−	1.83753i	0.143342	−	0.0827583i
$494$	−10.3914	+	12.3314i	−0.467532	+	0.554817i
$495$		0			0
$496$	−29.2822	−	24.9922i	−1.31481	−	1.12218i
$497$	−6.16267	−	7.40771i	−0.276433	−	0.332281i
$498$		0			0
$499$	−32.2276	−	18.6066i	−1.44271	−	0.832947i	−0.444676	−	0.895691i	$-0.646681\pi$
$499$	−32.2276	−	18.6066i	−1.44271	−	0.832947i	−0.998030	+	0.0627448i	$0.980015\pi$
$500$	5.26515	−	14.2793i	0.235465	−	0.638590i
$501$		0			0
$502$	−2.44974	+	13.7249i	−0.109337	+	0.612571i
$503$	−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
$506$	−7.76138	+	43.4837i	−0.345036	+	1.93309i
$507$		0			0
$508$	−0.746842	+	2.02546i	−0.0331357	+	0.0898654i
$509$	−3.18924	−	1.84131i	−0.141361	−	0.0816146i	0.427652	−	0.903944i	$-0.359341\pi$
$509$	−3.18924	−	1.84131i	−0.141361	−	0.0816146i	−0.569012	+	0.822329i	$0.692674\pi$
$510$		0			0
$511$	6.80833	−	1.17086i	0.301183	−	0.0517958i
$512$	−22.6234	−	0.426943i	−0.999822	−	0.0188684i
$513$		0			0
$514$	12.4732	−	14.8018i	0.550167	−	0.652879i
$515$	−3.63695	+	2.09979i	−0.160263	+	0.0925280i
$516$		0			0
$517$	−40.0144	+	23.1023i	−1.75983	+	1.01604i
$518$	−6.16530	+	10.5244i	−0.270888	+	0.462416i
$519$		0			0
$520$	2.96428	−	5.06050i	0.129992	−	0.221918i
$521$	10.9116	+	6.29980i	0.478045	+	0.275999i	0.719601	−	0.694387i	$-0.244325\pi$
$521$	10.9116	+	6.29980i	0.478045	+	0.275999i	−0.241557	+	0.970387i	$0.577658\pi$
$522$		0			0
$523$	−9.32093	−	16.1443i	−0.407576	−	0.705942i	0.587042	−	0.809557i	$-0.300292\pi$
$523$	−9.32093	−	16.1443i	−0.407576	−	0.705942i	−0.994618	+	0.103615i	$0.966959\pi$
$524$	13.4501	−	11.1902i	0.587571	−	0.488846i
$525$		0			0
$526$	−7.50276	−	20.7489i	−0.327136	−	0.904696i
$527$	−4.84353	−	2.79641i	−0.210988	−	0.121814i
$528$		0			0
$529$	9.47042	+	16.4033i	0.411758	+	0.713185i
$530$	−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
$535$	9.85094			0.425893
$536$	12.2530	+	7.17740i	0.529249	+	0.310017i
$537$		0			0
$538$	19.4964	−	23.1362i	0.840548	−	0.997471i
$539$	11.2781	+	31.8203i	0.485783	+	1.37060i
$540$		0			0
$541$	−9.06775	−	15.7058i	−0.389853	−	0.675245i	0.602577	−	0.798061i	$-0.294141\pi$
$541$	−9.06775	−	15.7058i	−0.389853	−	0.675245i	−0.992429	+	0.122816i	$0.960807\pi$
$542$	3.62331	−	1.31018i	0.155635	−	0.0562771i
$543$		0			0
$544$	−3.24312	+	0.536859i	−0.139048	+	0.0230176i
$545$	−2.59702	+	1.49939i	−0.111244	+	0.0642269i
$546$		0			0
$547$	−24.9748	−	14.4192i	−1.06784	−	0.616520i	−0.140252	−	0.990116i	$-0.544791\pi$
$547$	−24.9748	−	14.4192i	−1.06784	−	0.616520i	−0.927592	+	0.373596i	$0.878125\pi$
$548$	2.92279	+	16.9923i	0.124856	+	0.725877i
$549$		0			0
$550$	−19.0553	+	22.6128i	−0.812523	+	0.964214i
$551$	−28.3482			−1.20767
$552$		0			0
$553$	−17.1609	−	20.6279i	−0.729755	−	0.877186i
$554$	15.1492	−	5.47792i	0.643628	−	0.232734i
$555$		0			0
$556$	3.14653	+	18.2931i	0.133442	+	0.775799i
$557$	6.31355	−	10.9354i	0.267514	−	0.463347i	−0.700705	−	0.713451i	$-0.747131\pi$
$557$	6.31355	−	10.9354i	0.267514	−	0.463347i	0.968219	+	0.250103i	$0.0804646\pi$
$558$		0			0
$559$	13.8721			0.586725
$560$	−7.41562	−	4.40702i	−0.313367	−	0.186231i
$561$		0			0
$562$	33.5563	+	28.2772i	1.41549	+	1.19280i
$563$	9.37380			0.395059			0.197529	−	0.980297i	$-0.436708\pi$
$563$	9.37380			0.395059			0.197529	+	0.980297i	$0.436708\pi$
$564$		0			0
$565$		−	4.53025i		−	0.190589i
$566$	−1.00780	+	5.64626i	−0.0423609	+	0.237330i
$567$		0			0
$568$	−8.88863	−	5.20667i	−0.372959	−	0.218467i
$569$	−39.3939			−1.65148			−0.825739	−	0.564053i	$-0.809241\pi$
$569$	−39.3939			−1.65148			−0.825739	+	0.564053i	$0.809241\pi$
$570$		0			0
$571$			5.77562i			0.241702i	0.992671	+	0.120851i	$0.0385624\pi$
$571$			5.77562i			0.241702i	−0.992671	+	0.120851i	$0.961438\pi$
$572$	−18.8625	+	15.6932i	−0.788679	+	0.656165i
$573$		0			0
$574$	11.3593	+	6.65439i	0.474129	+	0.277749i
$575$			28.0781i			1.17094i
$576$		0			0
$577$	−25.4955	−	14.7198i	−1.06139	−	0.612794i	−0.135574	−	0.990767i	$-0.543288\pi$
$577$	−25.4955	−	14.7198i	−1.06139	−	0.612794i	−0.925817	+	0.377973i	$0.876621\pi$
$578$	22.1598	−	8.01294i	0.921727	−	0.333294i
$579$		0			0
$580$	10.1606	−	1.74770i	0.421898	−	0.0725691i
$581$	−0.736299	−	4.28144i	−0.0305468	−	0.177624i
$582$		0			0
$583$			10.5605i			0.437371i
$584$	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
$590$	−8.32382	+	9.87781i	−0.342686	+	0.406663i
$591$		0			0
$592$	−2.37189	+	12.8219i	−0.0974842	+	0.526978i
$593$	−37.9363	+	21.9025i	−1.55786	+	0.899429i	−0.560396	+	0.828225i	$0.689351\pi$
$593$	−37.9363	+	21.9025i	−1.55786	+	0.899429i	−0.997462	+	0.0712043i	$0.977316\pi$
$594$		0			0
$595$	−1.17581	−	0.433594i	−0.0482036	−	0.0177756i
$596$	−16.8282	+	14.0007i	−0.689308	+	0.573490i
$597$		0			0
$598$	−4.09380	+	22.9358i	−0.167408	+	0.937914i
$599$		−	22.8992i		−	0.935635i	−0.883825	−	0.467817i	$-0.845041\pi$
$599$		−	22.8992i		−	0.935635i	0.883825	−	0.467817i	$-0.154959\pi$
$600$		0			0
$601$	23.6446	+	13.6512i	0.964482	+	0.556844i	0.897549	−	0.440914i	$-0.145346\pi$
$601$	23.6446	+	13.6512i	0.964482	+	0.556844i	0.0669322	+	0.997758i	$0.478679\pi$
$602$	0.128969	−	20.4036i	0.00525640	−	0.831587i
$603$		0			0
$604$	−0.749247	+	0.128875i	−0.0304864	+	0.00524386i
$605$	−8.65425	+	4.99654i	−0.351845	+	0.203138i
$606$		0			0
$607$	5.86613	−	10.1604i	0.238099	−	0.412399i	−0.722070	−	0.691820i	$-0.756809\pi$
$607$	5.86613	−	10.1604i	0.238099	−	0.412399i	0.960169	+	0.279421i	$0.0901424\pi$
$608$	23.7354	+	8.92185i	0.962597	+	0.361829i
$609$		0			0
$610$	6.38882	+	5.38372i	0.258676	+	0.217981i
$611$	−21.1059	+	12.1855i	−0.853852	+	0.492972i
$612$		0			0
$613$	−1.66771	+	2.88856i	−0.0673582	+	0.116668i	−0.897738	−	0.440531i	$-0.854790\pi$
$613$	−1.66771	+	2.88856i	−0.0673582	+	0.116668i	0.830379	+	0.557198i	$0.188124\pi$
$614$	−4.82296	+	27.0210i	−0.194639	+	1.09048i
$615$		0			0
$616$	22.9068	+	27.8896i	0.922940	+	1.12370i
$617$	−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
$619$	−15.8213	−	27.4033i	−0.635912	−	1.10143i	−0.986321	−	0.164835i	$-0.947291\pi$
$619$	−15.8213	−	27.4033i	−0.635912	−	1.10143i	0.350410	−	0.936597i	$-0.386042\pi$
$620$	−10.0348	−	12.0613i	−0.403006	−	0.484394i
$621$		0			0
$622$	−2.66625	+	14.9378i	−0.106907	+	0.598952i
$623$	2.01596	−	5.46685i	0.0807679	−	0.219025i
$624$		0			0
$625$	−7.73768	+	13.4021i	−0.309507	+	0.536082i
$626$	33.9783	+	6.06477i	1.35804	+	0.242397i
$627$		0			0
$628$	3.43343	−	9.31159i	0.137009	−	0.371573i
$629$			1.89434i			0.0755325i
$630$		0			0
$631$		−	6.61866i		−	0.263485i	−0.991284	−	0.131742i	$-0.957943\pi$
$631$		−	6.61866i		−	0.263485i	0.991284	−	0.131742i	$-0.0420572\pi$
$632$	−24.7517	−	14.4988i	−0.984571	−	0.576730i
$633$		0			0
$634$	7.98266	−	44.7234i	0.317032	−	1.77619i
$635$	−0.439908	+	0.761943i	−0.0174572	+	0.0302368i
$636$		0			0
$637$	5.94873	+	16.7839i	0.235697	+	0.665001i
$638$	−42.4633	−	7.57926i	−1.68114	−	0.300066i
$639$		0			0
$640$	−9.05734	−	1.73448i	−0.358023	−	0.0685613i
$641$	15.1406	+	26.2243i	0.598018	+	1.03580i	0.993113	+	0.117157i	$0.0373781\pi$
$641$	15.1406	+	26.2243i	0.598018	+	1.03580i	−0.395096	+	0.918640i	$0.629289\pi$
$642$		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	$0.940078\pi$
$644$	33.6968	+	6.23456i	1.32784	+	0.245676i
$645$		0			0
$646$	3.62647	+	0.647286i	0.142681	+	0.0254671i
$647$	−14.3660	+	24.8826i	−0.564786	+	0.978237i	0.432284	+	0.901737i	$0.357708\pi$
$647$	−14.3660	+	24.8826i	−0.564786	+	0.978237i	−0.997070	+	0.0764997i	$0.975626\pi$
$648$		0			0
$649$	46.8031	−	27.0218i	1.83718	−	1.06070i
$650$	−10.0509	+	11.9273i	−0.394228	+	0.467827i
$651$		0			0
$652$	−40.9545	+	7.04444i	−1.60390	+	0.275881i
$653$	−4.63161	+	8.02218i	−0.181249	+	0.313932i	−0.942306	−	0.334753i	$-0.891347\pi$
$653$	−4.63161	+	8.02218i	−0.181249	+	0.313932i	0.761057	+	0.648685i	$0.224681\pi$
$654$		0			0
$655$	6.17543	−	3.56538i	0.241294	−	0.139311i
$656$	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	0.490897	−	0.871218i	$-0.336669\pi$
$659$	−0.465951	−	0.269017i	−0.0181509	−	0.0104794i	−0.509048	+	0.860738i	$0.670002\pi$
$660$		0			0
$661$			23.1477i			0.900342i	0.892942	+	0.450171i	$0.148637\pi$
$661$			23.1477i			0.900342i	−0.892942	+	0.450171i	$0.851363\pi$
$662$	−36.4011	−	6.49722i	−1.41477	−	0.252522i
$663$		0			0
$664$	−2.29678	−	4.03656i	−0.0891322	−	0.156649i
$665$	6.18240	+	7.43142i	0.239743	+	0.288178i
$666$		0			0
$667$	−35.4695	+	20.4783i	−1.37339	+	0.792924i
$668$	−0.697408	−	4.05454i	−0.0269835	−	0.156875i
$669$		0			0
$670$	4.42563	+	3.72938i	0.170977	+	0.144079i
$671$	−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
$677$		−	35.0977i		−	1.34891i	−0.738314	−	0.674457i	$-0.764378\pi$
$677$		−	35.0977i		−	1.34891i	0.738314	−	0.674457i	$-0.235622\pi$
$678$		0			0
$679$	−18.5095	+	3.18316i	−0.710329	+	0.122159i
$680$	−1.33971	−	0.00842668i	−0.0513756	−	0.000323149i
$681$		0			0
$682$	22.3220	+	61.7315i	0.854752	+	2.36382i
$683$	−21.2103	−	12.2458i	−0.811591	−	0.468572i	0.0359174	−	0.999355i	$-0.488565\pi$
$683$	−21.2103	−	12.2458i	−0.811591	−	0.468572i	−0.847508	+	0.530783i	$0.821898\pi$
$684$		0			0
$685$			7.02702i			0.268488i
$686$	24.7417	−	8.59359i	0.944641	−	0.328105i
$687$		0			0
$688$	−7.28824	−	20.5591i	−0.277862	−	0.783810i
$689$			5.57021i			0.212208i
$690$		0			0
$691$	17.2066			0.654569			0.327285	−	0.944926i	$-0.393866\pi$
$691$	17.2066			0.654569			0.327285	+	0.944926i	$0.393866\pi$
$692$	9.98157	−	27.0704i	0.379443	−	1.02906i
$693$		0			0
$694$	−20.7505	−	3.70374i	−0.787677	−	0.140592i
$695$			7.56492i			0.286954i
$696$		0			0
$697$	2.04462			0.0774456
$698$	−2.36690	+	2.80878i	−0.0895886	+	0.106314i
$699$		0			0
$700$	17.4497	+	14.8941i	0.659537	+	0.562945i
$701$	−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
$704$	33.1683	+	19.7102i	1.25008	+	0.742854i
$705$		0			0
$706$	6.47661	+	17.9111i	0.243751	+	0.674093i
$707$	−8.62056	+	23.3771i	−0.324210	+	0.879185i
$708$		0			0
$709$	−3.01099			−0.113080			−0.0565401	−	0.998400i	$-0.518007\pi$
$709$	−3.01099			−0.113080			−0.0565401	+	0.998400i	$0.518007\pi$
$710$	−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
$716$	−4.95153	−	5.95151i	−0.185047	−	0.222418i
$717$		0			0
$718$	8.73444	+	24.1551i	0.325966	+	0.901461i
$719$	8.34116	+	14.4473i	0.311073	+	0.538794i	0.978595	−	0.205796i	$-0.0659784\pi$
$719$	8.34116	+	14.4473i	0.311073	+	0.538794i	−0.667522	+	0.744590i	$0.732645\pi$
$720$		0			0
$721$	−2.31033	−	13.4342i	−0.0860413	−	0.500314i
$722$	−1.18175	−	0.995833i	−0.0439800	−	0.0370611i
$723$		0			0
$724$	17.2055	−	46.6620i	0.639438	−	1.73418i
$725$	−27.4192			−1.01832
$726$		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
$731$	−1.58445	−	2.74435i	−0.0586031	−	0.101504i
$732$		0			0
$733$	20.3825	+	11.7678i	0.752845	+	0.434655i	0.826721	−	0.562612i	$-0.190204\pi$
$733$	20.3825	+	11.7678i	0.752845	+	0.434655i	−0.0738758	+	0.997267i	$0.523537\pi$
$734$	14.8603	−	5.37344i	0.548502	−	0.198337i
$735$		0			0
$736$	36.1429	−	5.98301i	1.33225	−	0.220537i
$737$	−12.1068	−	20.9695i	−0.445958	−	0.772422i
$738$		0			0
$739$	−24.3790	−	14.0752i	−0.896797	−	0.517766i	−0.0206373	−	0.999787i	$-0.506570\pi$
$739$	−24.3790	−	14.0752i	−0.896797	−	0.517766i	−0.876160	+	0.482021i	$0.839903\pi$
$740$	−1.83852	+	4.98614i	−0.0675854	+	0.183294i
$741$		0			0
$742$	8.19288	+	0.0517866i	0.300770	+	0.00190115i
$743$	−43.7349	+	25.2504i	−1.60448	+	0.926347i	−0.613904	+	0.789381i	$0.710402\pi$
$743$	−43.7349	+	25.2504i	−1.60448	+	0.926347i	−0.990576	+	0.136966i	$0.956265\pi$
$744$		0			0
$745$	−7.72641	+	4.46085i	−0.283074	+	0.163433i
$746$	33.3110	+	28.0705i	1.21960	+	1.02773i
$747$		0			0
$748$	5.25909	+	1.93916i	0.192291	+	0.0709029i
$749$	−11.0629	+	30.0002i	−0.404230	+	1.09618i
$750$		0			0
$751$	−3.53155	−	2.03894i	−0.128868	−	0.0744020i	0.434180	−	0.900826i	$-0.357038\pi$
$751$	−3.53155	−	2.03894i	−0.128868	−	0.0744020i	−0.563048	+	0.826424i	$0.690371\pi$
$752$	29.1484	+	24.8779i	1.06293	+	0.907204i
$753$		0			0
$754$	−22.3976	−	3.99774i	−0.815672	−	0.145589i
$755$	−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	$0.536603\pi$
$758$	−7.72450	−	1.37874i	−0.280566	−	0.0500782i
$759$		0			0
$760$	8.91709	+	5.22334i	0.323457	+	0.189470i
$761$	−15.3919	−	8.88652i	−0.557956	−	0.322136i	0.194368	−	0.980929i	$-0.437734\pi$
$761$	−15.3919	−	8.88652i	−0.557956	−	0.322136i	−0.752325	+	0.658792i	$0.771068\pi$
$762$		0			0
$763$	−1.64973	−	9.59287i	−0.0597243	−	0.347285i
$764$	12.8239	−	34.7789i	0.463952	−	1.25826i
$765$		0			0
$766$	9.31493	+	7.84949i	0.336562	+	0.283614i
$767$	24.6866	−	14.2528i	0.891383	−	0.514640i
$768$		0			0
$769$	−21.8160	+	12.5955i	−0.786706	+	0.454205i	−0.838801	−	0.544437i	$-0.816743\pi$
$769$	−21.8160	+	12.5955i	−0.786706	+	0.454205i	0.0520959	+	0.998642i	$0.483410\pi$
$770$	7.27384	+	12.7846i	0.262131	+	0.460725i
$771$		0			0
$772$	−49.4465	−	18.2322i	−1.77962	−	0.656192i
$773$	−35.8079	−	20.6737i	−1.28792	−	0.743582i	−0.309639	−	0.950854i	$-0.600208\pi$
$773$	−35.8079	−	20.6737i	−1.28792	−	0.743582i	−0.978283	+	0.207272i	$0.933541\pi$
$774$		0			0
$775$	20.8637	+	36.1370i	0.749446	+	1.29808i
$776$	−17.4508	+	9.92941i	−0.626448	+	0.356445i
$777$		0			0
$778$	−4.63001	+	1.67420i	−0.165994	+	0.0600230i
$779$	−13.6585	−	7.88576i	−0.489368	−	0.282537i
$780$		0			0
$781$	8.78255	+	15.2118i	0.314264	+	0.544322i
$782$	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
$787$	19.4885			0.694690			0.347345	−	0.937737i	$-0.387083\pi$
$787$	19.4885			0.694690			0.347345	+	0.937737i	$0.387083\pi$
$788$	−9.48732	−	3.49822i	−0.337972	−	0.124619i
$789$		0			0
$790$	−8.94002	−	7.53356i	−0.318071	−	0.268032i
$791$	13.7965	+	5.08761i	0.490547	+	0.180895i
$792$		0			0
$793$	−9.21852	−	15.9669i	−0.327359	−	0.567003i
$794$	−8.66202	−	23.9549i	−0.307404	−	0.850126i
$795$		0			0
$796$	33.5851	−	27.9421i	1.19039	−	0.990381i
$797$	19.1331	−	11.0465i	0.677729	−	0.391287i	−0.121270	−	0.992620i	$-0.538697\pi$
$797$	19.1331	−	11.0465i	0.677729	−	0.391287i	0.798999	+	0.601333i	$0.205363\pi$
$798$		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
$803$	−12.5928			−0.444392
$804$		0			0
$805$	13.1038	+	4.83218i	0.461849	+	0.170312i
$806$	11.7739	+	32.5607i	0.414717	+	1.14690i
$807$		0			0
$808$	−0.167536	+	26.6357i	−0.00589390	+	0.937040i
$809$	3.36792	−	5.83340i	0.118410	−	0.205091i	−0.800728	−	0.599028i	$-0.795554\pi$
$809$	3.36792	−	5.83340i	0.118410	−	0.205091i	0.919138	+	0.393937i	$0.128887\pi$
$810$		0			0
$811$	52.9099			1.85792			0.928960	−	0.370181i	$-0.120704\pi$
$811$	52.9099			1.85792			0.928960	+	0.370181i	$0.120704\pi$
$812$	−6.08826	+	32.9061i	−0.213656	+	1.15478i
$813$		0			0
$814$	14.3274	−	17.0022i	0.502176	−	0.595928i
$815$	−16.9363			−0.593253
$816$		0			0
$817$			24.4439i			0.855183i
$818$	54.5359	+	9.73409i	1.90680	+	0.340344i
$819$		0			0
$820$	5.38170	+	1.98437i	0.187937	+	0.0692973i
$821$	−11.8882			−0.414903			−0.207451	−	0.978245i	$-0.566517\pi$
$821$	−11.8882			−0.414903			−0.207451	+	0.978245i	$0.566517\pi$
$822$		0			0
$823$		−	27.8356i		−	0.970287i	−0.874435	−	0.485143i	$-0.838767\pi$
$823$		−	27.8356i		−	0.970287i	0.874435	−	0.485143i	$-0.161233\pi$
$824$	−7.20675	−	12.6658i	−0.251059	−	0.441233i
$825$		0			0
$826$	−20.7341	−	36.4426i	−0.721432	−	1.26800i
$827$		−	30.7186i		−	1.06819i	−0.845424	−	0.534095i	$-0.820652\pi$
$827$		−	30.7186i		−	1.06819i	0.845424	−	0.534095i	$-0.179348\pi$
$828$		0			0
$829$	11.1106	+	6.41474i	0.385889	+	0.222793i	0.680377	−	0.732862i	$-0.261816\pi$
$829$	11.1106	+	6.41474i	0.385889	+	0.222793i	−0.294488	+	0.955655i	$0.595149\pi$
$830$	−0.643640	−	1.77999i	−0.0223411	−	0.0617843i
$831$		0			0
$832$	17.4949	+	10.3963i	0.606525	+	0.360426i
$833$	2.64095	−	3.09390i	0.0915035	−	0.107197i
$834$		0			0
$835$		−	1.67672i		−	0.0580252i
$836$	−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
$842$	−2.01529	−	1.69824i	−0.0694515	−	0.0585253i
$843$		0			0
$844$	−50.5417	+	8.69350i	−1.73972	+	0.299243i
$845$	4.60877	−	2.66087i	0.158546	−	0.0915368i
$846$		0			0
$847$	−5.49752	−	31.9671i	−0.188897	−	1.09840i
$848$	8.25535	−	2.92653i	0.283490	−	0.100498i
$849$		0			0
$850$	3.50762	+	0.626074i	0.120310	+	0.0214742i
$851$		−	21.1115i		−	0.723692i
$852$		0			0
$853$	−15.4010	−	8.89177i	−0.527320	−	0.304448i	0.212605	−	0.977138i	$-0.431805\pi$
$853$	−15.4010	−	8.89177i	−0.527320	−	0.304448i	−0.739924	+	0.672690i	$0.765139\pi$
$854$	−23.5705	+	13.4105i	−0.806566	+	0.458898i
$855$		0			0
$856$	−0.215002	+	34.1820i	−0.00734862	+	1.16832i
$857$	20.7330	−	11.9702i	0.708224	−	0.408894i	−0.102179	−	0.994766i	$-0.532581\pi$
$857$	20.7330	−	11.9702i	0.708224	−	0.408894i	0.810403	+	0.585873i	$0.199248\pi$
$858$		0			0
$859$	−23.3482	+	40.4402i	−0.796629	+	1.37980i	0.125170	+	0.992135i	$0.460052\pi$
$859$	−23.3482	+	40.4402i	−0.796629	+	1.37980i	−0.921799	+	0.387667i	$0.873281\pi$
$860$	−1.50699	−	8.76124i	−0.0513880	−	0.298756i
$861$		0			0
$862$	−3.98284	+	4.72641i	−0.135656	+	0.160982i
$863$	34.3329	−	19.8221i	1.16870	−	0.674752i	0.215330	−	0.976541i	$-0.430917\pi$
$863$	34.3329	−	19.8221i	1.16870	−	0.674752i	0.953375	+	0.301789i	$0.0975840\pi$
$864$		0			0
$865$	5.87940	−	10.1834i	0.199905	−	0.346246i
$866$	13.6197	+	2.43097i	0.462815	+	0.0826076i
$867$		0			0
$868$	48.0010	−	17.0148i	1.62926	−	0.577519i
$869$	24.4563	+	42.3596i	0.829624	+	1.43695i
$870$		0			0
$871$	−6.38580	−	11.0605i	−0.216375	−	0.374772i
$872$	−5.14609	−	9.04420i	−0.174269	−	0.306275i
$873$		0			0
$874$	−40.4151	−	7.21367i	−1.36706	−	0.244006i
$875$	12.8759	+	15.4773i	0.435286	+	0.523227i
$876$		0			0
$877$	−15.0927	+	26.1413i	−0.509644	+	0.882730i	0.490293	+	0.871557i	$0.336890\pi$
$877$	−15.0927	+	26.1413i	−0.509644	+	0.882730i	−0.999938	+	0.0111721i	$0.996444\pi$
$878$	−0.0957071	+	0.536206i	−0.00322996	+	0.0180961i
$879$		0			0
$880$	11.9605	+	10.2082i	0.403190	+	0.344119i
$881$		−	15.0652i		−	0.507560i	−0.967262	−	0.253780i	$-0.918326\pi$
$881$		−	15.0652i		−	0.507560i	0.967262	−	0.253780i	$-0.0816739\pi$
$882$		0			0
$883$			16.1352i			0.542993i	0.962439	+	0.271497i	$0.0875186\pi$
$883$			16.1352i			0.542993i	−0.962439	+	0.271497i	$0.912481\pi$
$884$	2.77395	+	1.02283i	0.0932979	+	0.0344014i
$885$		0			0
$886$	22.5443	+	4.02392i	0.757390	+	0.135186i
$887$	−10.9762	+	19.0114i	−0.368545	+	0.638339i	−0.989338	−	0.145636i	$-0.953477\pi$
$887$	−10.9762	+	19.0114i	−0.368545	+	0.638339i	0.620793	+	0.783974i	$0.286811\pi$
$888$		0			0
$889$	−1.82640	−	2.19539i	−0.0612556	−	0.0736310i
$890$	0.446076	−	2.49917i	0.0149525	−	0.0837724i
$891$		0			0
$892$	37.8312	−	31.4747i	1.26668	−	1.05385i
$893$	−21.4720	−	37.1906i	−0.718533	−	1.24454i
$894$		0			0
$895$	−1.57764	−	2.73255i	−0.0527347	−	0.0913392i
$896$	15.4539	−	25.6355i	0.516278	−	0.856421i
$897$		0			0
$898$	−8.25900	+	46.2716i	−0.275606	+	1.54410i
$899$	−30.4333	+	52.7120i	−1.01501	+	1.75804i
$900$		0			0
$901$	1.10197	−	0.636224i	0.0367120	−	0.0211957i
$902$	−18.3510	−	15.4640i	−0.611022	−	0.514895i
$903$		0			0
$904$	15.7196	+	0.0988751i	0.522827	+	0.00328854i
$905$	10.1345	−	17.5534i	0.336882	−	0.583496i
$906$		0			0
$907$	17.6385	−	10.1836i	0.585676	−	0.338140i	−0.177710	−	0.984083i	$-0.556869\pi$
$907$	17.6385	−	10.1836i	0.585676	−	0.338140i	0.763386	+	0.645943i	$0.223536\pi$
$908$	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	0.694117	−	0.719862i	$-0.255795\pi$
$911$	12.6090	+	7.27984i	0.417756	+	0.241192i	−0.276361	+	0.961054i	$0.589128\pi$
$912$		0			0
$913$			7.91904i			0.262082i
$914$	1.37632	−	7.71093i	0.0455246	−	0.255055i
$915$		0			0
$916$	−13.6958	−	16.4617i	−0.452520	−	0.543909i
$917$	3.92287	+	22.8108i	0.129545	+	0.753278i
$918$		0			0
$919$	9.46004	−	5.46176i	0.312058	−	0.180167i	−0.335789	−	0.941937i	$-0.609003\pi$
$919$	9.46004	−	5.46176i	0.312058	−	0.180167i	0.647847	+	0.761770i	$0.275670\pi$
$920$	14.9304	+	0.0939110i	0.492241	+	0.00309615i
$921$		0			0
$922$	−5.62982	+	6.68086i	−0.185408	+	0.220022i
$923$	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
$929$			36.7280i			1.20501i	0.798117	+	0.602503i	$0.205830\pi$
$929$			36.7280i			1.20501i	−0.798117	+	0.602503i	$0.794170\pi$
$930$		0			0
$931$	−29.5748	+	10.4822i	−0.969274	+	0.343541i
$932$	1.47224	+	8.55918i	0.0482247	+	0.280365i
$933$		0			0
$934$	36.8965	−	13.3417i	1.20729	−	0.436553i
$935$	1.97838	+	1.14222i	0.0646998	+	0.0373544i
$936$		0			0
$937$			9.07200i			0.296369i	0.988960	+	0.148185i	$0.0473430\pi$
$937$			9.07200i			0.296369i	−0.988960	+	0.148185i	$0.952657\pi$
$938$	−16.3276	+	9.28965i	−0.533116	+	0.303318i
$939$		0			0
$940$	9.98888	+	12.0062i	0.325801	+	0.391598i
$941$			9.27264i			0.302280i	0.988512	+	0.151140i	$0.0482944\pi$
$941$			9.27264i			0.302280i	−0.988512	+	0.151140i	$0.951706\pi$
$942$		0			0
$943$	−22.7862			−0.742022
$944$	−34.0936	−	29.0986i	−1.10965	−	0.947079i
$945$		0			0
$946$	−6.53538	+	36.6149i	−0.212484	+	1.19045i
$947$		−	3.29975i		−	0.107227i	−0.998562	−	0.0536137i	$-0.982926\pi$
$947$		−	3.29975i		−	0.107227i	0.998562	−	0.0536137i	$-0.0170739\pi$
$948$		0			0
$949$	−6.64218			−0.215614
$950$	−21.0170	−	17.7106i	−0.681883	−	0.574608i
$951$		0			0
$952$	1.53020	−	4.07052i	0.0495941	−	0.131926i
$953$	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
$956$	−20.8847	+	3.59230i	−0.675458	+	0.116183i
$957$		0			0
$958$	−9.50959	+	3.43865i	−0.307241	+	0.111098i
$959$	−21.4002	−	7.89156i	−0.691048	−	0.254832i
$960$		0			0
$961$	61.6286			1.98802
$962$	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	−0.700172	−	0.713974i	$-0.746893\pi$
$967$	−13.4318	+	7.75487i	−0.431938	+	0.249380i	0.268234	+	0.963354i	$0.413560\pi$
$968$	−17.1487	−	30.1387i	−0.551181	−	0.968693i
$969$		0			0
$970$	−7.69523	+	2.78258i	−0.247079	+	0.0893432i
$971$	−15.4979	−	26.8432i	−0.497352	−	0.861439i	0.502643	−	0.864494i	$-0.332361\pi$
$971$	−15.4979	−	26.8432i	−0.497352	−	0.861439i	−0.999995	+	0.00305480i	$0.999028\pi$
$972$		0			0
$973$	−23.0383	−	8.49564i	−0.738574	−	0.272358i
$974$	−7.02397	+	8.33529i	−0.225063	+	0.267080i
$975$		0			0
$976$	−18.8205	+	22.0512i	−0.602431	+	0.705842i
$977$	−34.0008			−1.08778			−0.543891	−	0.839156i	$-0.683050\pi$
$977$	−34.0008			−1.08778			−0.543891	+	0.839156i	$0.683050\pi$
$978$		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
$983$	17.2885	+	29.9445i	0.551416	+	0.955081i	0.998173	+	0.0604255i	$0.0192458\pi$
$983$	17.2885	+	29.9445i	0.551416	+	0.955081i	−0.446756	+	0.894656i	$0.647421\pi$
$984$		0			0
$985$	−3.56896	−	2.06054i	−0.113717	−	0.0656543i
$986$	1.76735	+	4.88761i	0.0562838	+	0.155653i
$987$		0			0
$988$	−14.5857	−	17.5314i	−0.464034	−	0.557747i
$989$	17.6579	+	30.5844i	0.561489	+	0.972527i
$990$		0			0
$991$	−46.4705	−	26.8297i	−1.47618	−	0.852275i	−0.476545	−	0.879150i	$-0.658111\pi$
$991$	−46.4705	−	26.8297i	−1.47618	−	0.852275i	−0.999639	+	0.0268752i	$0.991444\pi$
$992$	42.0709	−	34.5566i	1.33575	−	1.09717i
$993$		0			0
$994$	11.8445	−	6.73895i	0.375684	−	0.213747i
$995$	15.4201	−	8.90281i	0.488851	−	0.282238i
$996$		0			0
$997$	38.1596	−	22.0314i	1.20853	−	0.697742i	0.246088	−	0.969247i	$-0.420855\pi$
$997$	38.1596	−	22.0314i	1.20853	−	0.697742i	0.962437	+	0.271505i	$0.0875214\pi$
$998$	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.bj.b.451.20		84
3.2	odd	2		252.2.bj.b.115.23	yes	84
4.3	odd	2	inner	756.2.bj.b.451.19		84
7.5	odd	6		756.2.n.b.19.37		84
9.4	even	3		756.2.n.b.199.9		84
9.5	odd	6		252.2.n.b.31.34	yes	84
12.11	even	2		252.2.bj.b.115.24	yes	84
21.5	even	6		252.2.n.b.187.6	yes	84
28.19	even	6		756.2.n.b.19.9		84
36.23	even	6		252.2.n.b.31.6	✓	84
36.31	odd	6		756.2.n.b.199.37		84
63.5	even	6		252.2.bj.b.103.23	yes	84
63.40	odd	6	inner	756.2.bj.b.523.20		84
84.47	odd	6		252.2.n.b.187.34	yes	84
252.103	even	6	inner	756.2.bj.b.523.19		84
252.131	odd	6		252.2.bj.b.103.24	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.6	✓	84	36.23	even	6
252.2.n.b.31.34	yes	84	9.5	odd	6
252.2.n.b.187.6	yes	84	21.5	even	6
252.2.n.b.187.34	yes	84	84.47	odd	6
252.2.bj.b.103.23	yes	84	63.5	even	6
252.2.bj.b.103.24	yes	84	252.131	odd	6
252.2.bj.b.115.23	yes	84	3.2	odd	2
252.2.bj.b.115.24	yes	84	12.11	even	2
756.2.n.b.19.9		84	28.19	even	6
756.2.n.b.19.37		84	7.5	odd	6
756.2.n.b.199.9		84	9.4	even	3
756.2.n.b.199.37		84	36.31	odd	6
756.2.bj.b.451.19		84	4.3	odd	2	inner
756.2.bj.b.451.20		84	1.1	even	1	trivial
756.2.bj.b.523.19		84	252.103	even	6	inner
756.2.bj.b.523.20		84	63.40	odd	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.bj (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.248495 + 1.39221i) q^{2} +(-1.87650 - 0.691915i) q^{4} +(-0.705906 - 0.407555i) q^{5} +(2.03393 - 1.69208i) q^{7} +(1.42959 - 2.44055i) q^{8} +O(q^{10})\)	\(q+(-0.248495 + 1.39221i) q^{2} +(-1.87650 - 0.691915i) q^{4} +(-0.705906 - 0.407555i) q^{5} +(2.03393 - 1.69208i) q^{7} +(1.42959 - 2.44055i) q^{8} +(0.742817 - 0.881495i) q^{10} +(-4.17670 + 2.41142i) q^{11} +(-2.20303 + 1.27192i) q^{13} +(1.85031 + 3.25213i) q^{14} +(3.04251 + 2.59676i) q^{16} +(0.503257 + 0.290555i) q^{17} +(-2.24125 - 3.88195i) q^{19} +(1.04264 + 1.25320i) q^{20} +(-2.31931 - 6.41407i) q^{22} +(-5.60853 - 3.23809i) q^{23} +(-2.16780 - 3.75474i) q^{25} +(-1.22334 - 3.38315i) q^{26} +(-4.98744 + 1.76788i) q^{28} +(3.16210 - 5.47692i) q^{29} -9.62438 q^{31} +(-4.37128 + 3.59053i) q^{32} +(-0.529571 + 0.628438i) q^{34} +(-2.12538 + 0.365511i) q^{35} +(1.62993 + 2.82313i) q^{37} +(5.96144 - 2.15564i) q^{38} +(-2.00382 + 1.14016i) q^{40} +(3.04709 - 1.75924i) q^{41} +(-4.72260 - 2.72659i) q^{43} +(9.50608 - 1.63511i) q^{44} +(5.90179 - 7.00361i) q^{46} +9.58038 q^{47} +(1.27373 - 6.88314i) q^{49} +(5.76607 - 2.08500i) q^{50} +(5.01405 - 0.862450i) q^{52} +(1.09484 - 1.89632i) q^{53} +3.93115 q^{55} +(-1.22191 - 7.38288i) q^{56} +(6.83926 + 5.76330i) q^{58} -11.2058 q^{59} +7.24771i q^{61} +(2.39161 - 13.3992i) q^{62} +(-3.91253 - 6.97797i) q^{64} +2.07351 q^{65} +5.02059i q^{67} +(-0.743322 - 0.893438i) q^{68} +(0.0192776 - 3.04980i) q^{70} -3.64207i q^{71} +(2.26126 + 1.30554i) q^{73} +(-4.33542 + 1.56768i) q^{74} +(1.51972 + 8.83524i) q^{76} +(-4.41480 + 11.9720i) q^{77} -10.1419i q^{79} +(-1.08940 - 3.07306i) q^{80} +(1.69204 + 4.67935i) q^{82} +(0.820993 - 1.42200i) q^{83} +(-0.236835 - 0.410210i) q^{85} +(4.96954 - 5.89731i) q^{86} +(-0.0857994 + 13.6408i) q^{88} +(1.90724 - 1.10115i) q^{89} +(-2.32862 + 6.31470i) q^{91} +(8.28393 + 9.95690i) q^{92} +(-2.38068 + 13.3379i) q^{94} +3.65373i q^{95} +(-6.14759 - 3.54931i) q^{97} +(9.26626 + 3.48373i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8}+O(q^{10}) \) 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8	\( 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8} - 18 q^{10} + 18 q^{13} - 14 q^{14} + 14 q^{16} - 6 q^{17} + 24 q^{20} + 6 q^{22} + 16 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} + 18 q^{32} - 24 q^{34} + 2 q^{37} - 33 q^{38} + 6 q^{40} - 6 q^{41} + 13 q^{44} + 10 q^{46} - 28 q^{49} + 17 q^{50} - 27 q^{52} + 2 q^{53} - 58 q^{56} - 13 q^{58} - 8 q^{64} + 100 q^{65} + 18 q^{68} - 19 q^{70} + 30 q^{73} + 23 q^{74} + 2 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} + 9 q^{86} + q^{88} + 102 q^{89} - 28 q^{92} + 6 q^{97} - 21 q^{98}+O(q^{100}) \) 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8 - 18 * q^10 + 18 * q^13 - 14 * q^14 + 14 * q^16 - 6 * q^17 + 24 * q^20 + 6 * q^22 + 16 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 + 18 * q^32 - 24 * q^34 + 2 * q^37 - 33 * q^38 + 6 * q^40 - 6 * q^41 + 13 * q^44 + 10 * q^46 - 28 * q^49 + 17 * q^50 - 27 * q^52 + 2 * q^53 - 58 * q^56 - 13 * q^58 - 8 * q^64 + 100 * q^65 + 18 * q^68 - 19 * q^70 + 30 * q^73 + 23 * q^74 + 2 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 + 9 * q^86 + q^88 + 102 * q^89 - 28 * q^92 + 6 * q^97 - 21 * q^98

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