LMFDB - Embedded newform 432.3.x.a.125.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,3,Mod(125,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 10]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("432.125");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.x (of order $12$, degree $4$, 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:	$11.7711474204$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			125.14
Character	$\chi$	$=$	432.125
Dual form			432.3.x.a.197.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22012 - 1.58471i) q^{2} +(-1.02259 + 3.86708i) q^{4} +(0.432017 - 0.115759i) q^{5} +(-7.23679 + 4.17816i) q^{7} +(7.37588 - 3.09780i) q^{8} +O(q^{10})$	\(q+(-1.22012 - 1.58471i) q^{2} +(-1.02259 + 3.86708i) q^{4} +(0.432017 - 0.115759i) q^{5} +(-7.23679 + 4.17816i) q^{7} +(7.37588 - 3.09780i) q^{8} +(-0.710557 - 0.543380i) q^{10} +(5.42030 - 20.2288i) q^{11} +(4.82865 - 1.29383i) q^{13} +(15.4509 + 6.37032i) q^{14} +(-13.9086 - 7.90891i) q^{16} +25.9977i q^{17} +(1.80229 + 1.80229i) q^{19} +(0.00586937 + 1.78902i) q^{20} +(-38.6702 + 16.0921i) q^{22} +(-1.78994 + 3.10027i) q^{23} +(-21.4774 + 12.4000i) q^{25} +(-7.94191 - 6.07337i) q^{26} +(-8.75698 - 32.2578i) q^{28} +(-49.2839 - 13.2056i) q^{29} +(-14.2968 + 24.7628i) q^{31} +(4.43691 + 31.6909i) q^{32} +(41.1987 - 31.7204i) q^{34} +(-2.64276 + 2.64276i) q^{35} +(-22.5902 + 22.5902i) q^{37} +(0.657083 - 5.05511i) q^{38} +(2.82791 - 2.19212i) q^{40} +(-16.3853 + 28.3801i) q^{41} +(15.1638 + 4.06313i) q^{43} +(72.6837 + 41.6466i) q^{44} +(7.09697 - 0.946180i) q^{46} +(-33.7785 + 19.5020i) q^{47} +(10.4141 - 18.0377i) q^{49} +(45.8554 + 18.9059i) q^{50} +(0.0656020 + 19.9959i) q^{52} +(-57.3208 - 57.3208i) q^{53} -9.36664i q^{55} +(-40.4346 + 53.2358i) q^{56} +(39.2055 + 94.2131i) q^{58} +(43.2875 - 11.5988i) q^{59} +(-18.9861 + 70.8572i) q^{61} +(56.6857 - 7.55743i) q^{62} +(44.8072 - 45.6980i) q^{64} +(1.93629 - 1.11792i) q^{65} +(-45.8800 + 12.2935i) q^{67} +(-100.535 - 26.5851i) q^{68} +(7.41249 + 0.963505i) q^{70} -26.4797 q^{71} +38.6468i q^{73} +(63.3617 + 8.23601i) q^{74} +(-8.81259 + 5.12657i) q^{76} +(45.2938 + 169.039i) q^{77} +(-29.8313 - 51.6693i) q^{79} +(-6.92427 - 1.80674i) q^{80} +(64.9662 - 8.66140i) q^{82} +(46.7170 + 12.5178i) q^{83} +(3.00945 + 11.2314i) q^{85} +(-12.0629 - 28.9877i) q^{86} +(-22.6855 - 165.997i) q^{88} +79.3499 q^{89} +(-29.5381 + 29.5381i) q^{91} +(-10.1586 - 10.0922i) q^{92} +(72.1189 + 29.7341i) q^{94} +(0.987248 + 0.569988i) q^{95} +(-16.3804 - 28.3718i) q^{97} +(-41.2910 + 5.50499i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5}+O(q^{10}) $ 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5	$ 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} - 120 q^{20} - 2 q^{22} - 72 q^{28} + 6 q^{29} - 4 q^{31} + 6 q^{32} + 6 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 160 q^{46} + 12 q^{47} + 472 q^{49} - 228 q^{50} - 2 q^{52} + 300 q^{56} - 92 q^{58} + 438 q^{59} - 2 q^{61} + 244 q^{64} + 12 q^{65} - 2 q^{67} + 144 q^{68} + 96 q^{70} - 246 q^{74} - 158 q^{76} + 6 q^{77} - 4 q^{79} - 388 q^{82} + 726 q^{83} + 48 q^{85} - 894 q^{86} + 22 q^{88} - 204 q^{91} + 348 q^{92} - 18 q^{94} + 12 q^{95} - 4 q^{97}+O(q^{100}) $ 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 - 120 * q^20 - 2 * q^22 - 72 * q^28 + 6 * q^29 - 4 * q^31 + 6 * q^32 + 6 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 160 * q^46 + 12 * q^47 + 472 * q^49 - 228 * q^50 - 2 * q^52 + 300 * q^56 - 92 * q^58 + 438 * q^59 - 2 * q^61 + 244 * q^64 + 12 * q^65 - 2 * q^67 + 144 * q^68 + 96 * q^70 - 246 * q^74 - 158 * q^76 + 6 * q^77 - 4 * q^79 - 388 * q^82 + 726 * q^83 + 48 * q^85 - 894 * q^86 + 22 * q^88 - 204 * q^91 + 348 * q^92 - 18 * q^94 + 12 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.22012	−	1.58471i	−0.610062	−	0.792354i
$2$	−1.22012	−	1.58471i	−0.610062	−	0.792354i
$3$		0			0
$3$		0			0
$4$	−1.02259	+	3.86708i	−0.255649	+	0.966770i
$5$	0.432017	−	0.115759i	0.0864034	−	0.0231517i	−0.215358	−	0.976535i	$-0.569092\pi$
$5$	0.432017	−	0.115759i	0.0864034	−	0.0231517i	0.301762	+	0.953383i	$0.402425\pi$
$6$		0			0
$7$	−7.23679	+	4.17816i	−1.03383	+	0.596880i	−0.918079	−	0.396398i	$-0.870260\pi$
$7$	−7.23679	+	4.17816i	−1.03383	+	0.596880i	−0.115748	+	0.993279i	$0.536927\pi$
$8$	7.37588	−	3.09780i	0.921985	−	0.387225i
$9$		0			0
$10$	−0.710557	−	0.543380i	−0.0710557	−	0.0543380i
$11$	5.42030	−	20.2288i	0.492755	−	1.83899i	−0.0495046	−	0.998774i	$-0.515764\pi$
$11$	5.42030	−	20.2288i	0.492755	−	1.83899i	0.542259	−	0.840211i	$-0.317569\pi$
$12$		0			0
$13$	4.82865	−	1.29383i	0.371435	−	0.0995257i	−0.0682726	−	0.997667i	$-0.521749\pi$
$13$	4.82865	−	1.29383i	0.371435	−	0.0995257i	0.439708	+	0.898141i	$0.355082\pi$
$14$	15.4509	+	6.37032i	1.10364	+	0.455023i
$15$		0			0
$16$	−13.9086	−	7.90891i	−0.869288	−	0.494307i
$17$			25.9977i			1.52928i	0.644460	+	0.764638i	$0.277082\pi$
$17$			25.9977i			1.52928i	−0.644460	+	0.764638i	$0.722918\pi$
$18$		0			0
$19$	1.80229	+	1.80229i	0.0948571	+	0.0948571i	0.752943	−	0.658086i	$-0.228634\pi$
$19$	1.80229	+	1.80229i	0.0948571	+	0.0948571i	−0.658086	+	0.752943i	$0.728634\pi$
$20$	0.00586937	+	1.78902i	0.000293469	+	0.0894509i
$21$		0			0
$22$	−38.6702	+	16.0921i	−1.75774	+	0.731459i
$23$	−1.78994	+	3.10027i	−0.0778236	+	0.134794i	−0.902311	−	0.431086i	$-0.858130\pi$
$23$	−1.78994	+	3.10027i	−0.0778236	+	0.134794i	0.824487	+	0.565881i	$0.191464\pi$
$24$		0			0
$25$	−21.4774	+	12.4000i	−0.859096	+	0.495999i
$26$	−7.94191	−	6.07337i	−0.305458	−	0.233591i
$27$		0			0
$28$	−8.75698	−	32.2578i	−0.312749	−	1.15206i
$29$	−49.2839	−	13.2056i	−1.69945	−	0.455365i	−0.726646	−	0.687012i	$-0.758922\pi$
$29$	−49.2839	−	13.2056i	−1.69945	−	0.455365i	−0.972800	+	0.231647i	$0.925589\pi$
$30$		0			0
$31$	−14.2968	+	24.7628i	−0.461188	+	0.798800i	−0.999020	−	0.0442511i	$-0.985910\pi$
$31$	−14.2968	+	24.7628i	−0.461188	+	0.798800i	0.537833	+	0.843052i	$0.319243\pi$
$32$	4.43691	+	31.6909i	0.138653	+	0.990341i
$33$		0			0
$34$	41.1987	−	31.7204i	1.21173	−	0.932953i
$35$	−2.64276	+	2.64276i	−0.0755073	+	0.0755073i
$36$		0			0
$37$	−22.5902	+	22.5902i	−0.610546	+	0.610546i	−0.943088	−	0.332542i	$-0.892094\pi$
$37$	−22.5902	+	22.5902i	−0.610546	+	0.610546i	0.332542	+	0.943088i	$0.392094\pi$
$38$	0.657083	−	5.05511i	0.0172917	−	0.133029i
$39$		0			0
$40$	2.82791	−	2.19212i	0.0706977	−	0.0548031i
$41$	−16.3853	+	28.3801i	−0.399640	+	0.692197i	−0.993681	−	0.112237i	$-0.964198\pi$
$41$	−16.3853	+	28.3801i	−0.399640	+	0.692197i	0.594041	+	0.804435i	$0.297532\pi$
$42$		0			0
$43$	15.1638	+	4.06313i	0.352647	+	0.0944915i	0.430794	−	0.902450i	$-0.358234\pi$
$43$	15.1638	+	4.06313i	0.352647	+	0.0944915i	−0.0781468	+	0.996942i	$0.524900\pi$
$44$	72.6837	+	41.6466i	1.65190	+	0.946514i
$45$		0			0
$46$	7.09697	−	0.946180i	0.154282	−	0.0205691i
$47$	−33.7785	+	19.5020i	−0.718691	+	0.414937i	−0.814271	−	0.580485i	$-0.802863\pi$
$47$	−33.7785	+	19.5020i	−0.718691	+	0.414937i	0.0955796	+	0.995422i	$0.469530\pi$
$48$		0			0
$49$	10.4141	−	18.0377i	0.212532	−	0.368117i
$50$	45.8554	+	18.9059i	0.917109	+	0.378117i
$51$		0			0
$52$	0.0656020	+	19.9959i	0.00126158	+	0.384536i
$53$	−57.3208	−	57.3208i	−1.08152	−	1.08152i	−0.996368	−	0.0851571i	$-0.972861\pi$
$53$	−57.3208	−	57.3208i	−1.08152	−	1.08152i	−0.0851571	−	0.996368i	$-0.527139\pi$
$54$		0			0
$55$		−	9.36664i		−	0.170303i
$56$	−40.4346	+	53.2358i	−0.722046	+	0.950639i
$57$		0			0
$58$	39.2055	+	94.2131i	0.675957	+	1.62436i
$59$	43.2875	−	11.5988i	0.733686	−	0.196591i	0.127416	−	0.991849i	$-0.459332\pi$
$59$	43.2875	−	11.5988i	0.733686	−	0.196591i	0.606270	+	0.795259i	$0.292665\pi$
$60$		0			0
$61$	−18.9861	+	70.8572i	−0.311248	+	1.16159i	0.616184	+	0.787602i	$0.288678\pi$
$61$	−18.9861	+	70.8572i	−0.311248	+	1.16159i	−0.927432	+	0.373991i	$0.877989\pi$
$62$	56.6857	−	7.55743i	0.914286	−	0.121894i
$63$		0			0
$64$	44.8072	−	45.6980i	0.700113	−	0.714032i
$65$	1.93629	−	1.11792i	0.0297890	−	0.0171987i
$66$		0			0
$67$	−45.8800	+	12.2935i	−0.684775	+	0.183485i	−0.584401	−	0.811465i	$-0.698671\pi$
$67$	−45.8800	+	12.2935i	−0.684775	+	0.183485i	−0.100374	+	0.994950i	$0.532004\pi$
$68$	−100.535	−	26.5851i	−1.47846	−	0.390957i
$69$		0			0
$70$	7.41249	+	0.963505i	0.105893	+	0.0137644i
$71$	−26.4797			−0.372953			−0.186477	−	0.982459i	$-0.559707\pi$
$71$	−26.4797			−0.372953			−0.186477	+	0.982459i	$0.559707\pi$
$72$		0			0
$73$			38.6468i			0.529408i	0.964330	+	0.264704i	$0.0852742\pi$
$73$			38.6468i			0.529408i	−0.964330	+	0.264704i	$0.914726\pi$
$74$	63.3617	+	8.23601i	0.856239	+	0.111297i
$75$		0			0
$76$	−8.81259	+	5.12657i	−0.115955	+	0.0674549i
$77$	45.2938	+	169.039i	0.588231	+	2.19531i
$78$		0			0
$79$	−29.8313	−	51.6693i	−0.377611	−	0.654042i	0.613103	−	0.790003i	$-0.289921\pi$
$79$	−29.8313	−	51.6693i	−0.377611	−	0.654042i	−0.990714	+	0.135961i	$0.956588\pi$
$80$	−6.92427	−	1.80674i	−0.0865534	−	0.0225843i
$81$		0			0
$82$	64.9662	−	8.66140i	0.792271	−	0.105627i
$83$	46.7170	+	12.5178i	0.562855	+	0.150817i	0.529018	−	0.848611i	$-0.322561\pi$
$83$	46.7170	+	12.5178i	0.562855	+	0.150817i	0.0338373	+	0.999427i	$0.489227\pi$
$84$		0			0
$85$	3.00945	+	11.2314i	0.0354053	+	0.132135i
$86$	−12.0629	−	28.9877i	−0.140266	−	0.337067i
$87$		0			0
$88$	−22.6855	−	165.997i	−0.257789	−	1.88632i
$89$	79.3499			0.891572			0.445786	−	0.895140i	$-0.352924\pi$
$89$	79.3499			0.891572			0.445786	+	0.895140i	$0.352924\pi$
$90$		0			0
$91$	−29.5381	+	29.5381i	−0.324595	+	0.324595i
$92$	−10.1586	−	10.0922i	−0.110420	−	0.109697i
$93$		0			0
$94$	72.1189	+	29.7341i	0.767223	+	0.316321i
$95$	0.987248	+	0.569988i	0.0103921	+	0.00599987i
$96$		0			0
$97$	−16.3804	−	28.3718i	−0.168871	−	0.292492i	0.769152	−	0.639065i	$-0.220679\pi$
$97$	−16.3804	−	28.3718i	−0.168871	−	0.292492i	−0.938023	+	0.346573i	$0.887345\pi$
$98$	−41.2910	+	5.50499i	−0.421337	+	0.0561733i
$99$		0			0
$100$	−25.9890	−	95.7349i	−0.259890	−	0.957349i
$101$	1.83509	−	6.84865i	0.0181692	−	0.0678084i	−0.956246	−	0.292564i	$-0.905492\pi$
$101$	1.83509	−	6.84865i	0.0181692	−	0.0678084i	0.974415	+	0.224755i	$0.0721583\pi$
$102$		0			0
$103$	129.386	+	74.7010i	1.25617	+	0.725252i	0.972328	−	0.233618i	$-0.0750566\pi$
$103$	129.386	+	74.7010i	1.25617	+	0.725252i	0.283845	+	0.958870i	$0.408390\pi$
$104$	31.6075	−	24.5014i	0.303919	−	0.235590i
$105$		0			0
$106$	−20.8982	+	160.775i	−0.197153	+	1.51675i
$107$	−35.2400	−	35.2400i	−0.329346	−	0.329346i	0.522992	−	0.852338i	$-0.324816\pi$
$107$	−35.2400	−	35.2400i	−0.329346	−	0.329346i	−0.852338	+	0.522992i	$0.824816\pi$
$108$		0			0
$109$	81.1059	+	81.1059i	0.744091	+	0.744091i	0.973363	−	0.229271i	$-0.0736343\pi$
$109$	81.1059	+	81.1059i	0.744091	+	0.744091i	−0.229271	+	0.973363i	$0.573634\pi$
$110$	−14.8434	+	11.4285i	−0.134940	+	0.103895i
$111$		0			0
$112$	133.698	−	0.877279i	1.19374	−	0.00783285i
$113$	−53.3280	−	30.7889i	−0.471929	−	0.272468i	0.245118	−	0.969493i	$-0.421173\pi$
$113$	−53.3280	−	30.7889i	−0.471929	−	0.272468i	−0.717047	+	0.697025i	$0.754507\pi$
$114$		0			0
$115$	−0.414402	+	1.54657i	−0.00360350	+	0.0134484i
$116$	101.465	−	177.081i	0.874695	−	1.52656i
$117$		0			0
$118$	−71.1969	−	54.4460i	−0.603363	−	0.461406i
$119$	−108.623	−	188.140i	−0.912795	−	1.58101i
$120$		0			0
$121$	−275.037	−	158.793i	−2.27303	−	1.31234i
$122$	135.453	−	56.3671i	1.11027	−	0.462025i
$123$		0			0
$124$	−81.1399	−	80.6092i	−0.654354	−	0.650075i
$125$	−15.7496	+	15.7496i	−0.125997	+	0.125997i
$126$		0			0
$127$	−67.0975			−0.528327			−0.264163	−	0.964478i	$-0.585096\pi$
$127$	−67.0975			−0.528327			−0.264163	+	0.964478i	$0.585096\pi$
$128$	−127.088	−	15.2491i	−0.992878	−	0.119133i
$129$		0			0
$130$	−4.13408	−	1.70445i	−0.0318006	−	0.0131112i
$131$	−33.7541	−	125.972i	−0.257665	−	0.961619i	−0.966588	−	0.256333i	$-0.917486\pi$
$131$	−33.7541	−	125.972i	−0.257665	−	0.961619i	0.708923	−	0.705285i	$-0.249181\pi$
$132$		0			0
$133$	−20.5730	−	5.51252i	−0.154684	−	0.0414475i
$134$	75.4608	+	57.7067i	0.563141	+	0.430647i
$135$		0			0
$136$	80.5357	+	191.756i	0.592174	+	1.40997i
$137$	−22.0318	−	38.1602i	−0.160816	−	0.278542i	0.774345	−	0.632763i	$-0.218079\pi$
$137$	−22.0318	−	38.1602i	−0.160816	−	0.278542i	−0.935162	+	0.354221i	$0.884746\pi$
$138$		0			0
$139$	−55.4608	−	206.983i	−0.398999	−	1.48908i	−0.814861	−	0.579656i	$-0.803187\pi$
$139$	−55.4608	−	206.983i	−0.398999	−	1.48908i	0.415862	−	0.909428i	$-0.363480\pi$
$140$	−7.51728	−	12.9222i	−0.0536949	−	0.0923016i
$141$		0			0
$142$	32.3085	+	41.9626i	0.227525	+	0.295511i
$143$		−	104.691i		−	0.732105i
$144$		0			0
$145$	−22.8202			−0.157380
$146$	61.2438	−	47.1539i	0.419478	−	0.322972i
$147$		0			0
$148$	−64.2575	−	110.459i	−0.434172	−	0.746343i
$149$	−247.536	+	66.3271i	−1.66132	+	0.445148i	−0.962749	−	0.270397i	$-0.912845\pi$
$149$	−247.536	+	66.3271i	−1.66132	+	0.445148i	−0.698566	+	0.715545i	$0.746178\pi$
$150$		0			0
$151$	110.925	−	64.0428i	0.734605	−	0.424125i	−0.0854993	−	0.996338i	$-0.527249\pi$
$151$	110.925	−	64.0428i	0.734605	−	0.424125i	0.820105	+	0.572214i	$0.193915\pi$
$152$	18.8766	+	7.71032i	0.124188	+	0.0507258i
$153$		0			0
$154$	212.613	−	278.026i	1.38060	−	1.80536i
$155$	−3.30996	+	12.3529i	−0.0213546	+	0.0796963i
$156$		0			0
$157$	93.1741	−	24.9659i	0.593466	−	0.159019i	0.0504291	−	0.998728i	$-0.483941\pi$
$157$	93.1741	−	24.9659i	0.593466	−	0.159019i	0.543037	+	0.839709i	$0.317274\pi$
$158$	−45.4829	+	110.317i	−0.287866	+	0.698208i
$159$		0			0
$160$	5.58531	+	13.1774i	0.0349082	+	0.0823587i
$161$		−	29.9147i		−	0.185805i
$162$		0			0
$163$	84.5646	+	84.5646i	0.518801	+	0.518801i	0.917209	−	0.398407i	$-0.130437\pi$
$163$	84.5646	+	84.5646i	0.518801	+	0.518801i	−0.398407	+	0.917209i	$0.630437\pi$
$164$	−92.9926	−	92.3844i	−0.567028	−	0.563320i
$165$		0			0
$166$	−37.1635	−	89.3059i	−0.223876	−	0.537988i
$167$	19.4639	−	33.7125i	0.116551	−	0.201872i	−0.801848	−	0.597528i	$-0.796150\pi$
$167$	19.4639	−	33.7125i	0.116551	−	0.201872i	0.918399	+	0.395657i	$0.129483\pi$
$168$		0			0
$169$	−124.716	+	72.0050i	−0.737967	+	0.426065i
$170$	14.1266	−	18.4729i	0.0830978	−	0.108664i
$171$		0			0
$172$	−31.2189	+	54.4848i	−0.181505	+	0.316772i
$173$	206.725	+	55.3918i	1.19494	+	0.320184i	0.800838	−	0.598882i	$-0.204388\pi$
$173$	206.725	+	55.3918i	1.19494	+	0.320184i	0.394105	+	0.919065i	$0.371055\pi$
$174$		0			0
$175$	103.618	−	179.472i	0.592104	−	1.02555i
$176$	−235.377	+	238.486i	−1.33737	+	1.35503i
$177$		0			0
$178$	−96.8167	−	125.746i	−0.543914	−	0.706440i
$179$	29.8384	−	29.8384i	0.166695	−	0.166695i	−0.618830	−	0.785525i	$-0.712393\pi$
$179$	29.8384	−	29.8384i	0.166695	−	0.166695i	0.785525	+	0.618830i	$0.212393\pi$
$180$		0			0
$181$	−165.386	+	165.386i	−0.913733	+	0.913733i	−0.996564	−	0.0828310i	$-0.973604\pi$
$181$	−165.386	+	165.386i	−0.913733	+	0.913733i	0.0828310	+	0.996564i	$0.473604\pi$
$182$	82.8494	+	10.7691i	0.455217	+	0.0591709i
$183$		0			0
$184$	−3.59837	+	28.4121i	−0.0195564	+	0.154414i
$185$	−7.14434	+	12.3744i	−0.0386180	+	0.0668884i
$186$		0			0
$187$	525.903	+	140.915i	2.81232	+	0.753558i
$188$	−40.8741	−	150.567i	−0.217416	−	0.800887i
$189$		0			0
$190$	−0.301301	−	2.25995i	−0.00158579	−	0.0118945i
$191$	−174.438	+	100.712i	−0.913290	+	0.527288i	−0.881488	−	0.472206i	$-0.843458\pi$
$191$	−174.438	+	100.712i	−0.913290	+	0.527288i	−0.0318019	+	0.999494i	$0.510125\pi$
$192$		0			0
$193$	−39.0114	+	67.5697i	−0.202132	+	0.350102i	−0.949215	−	0.314628i	$-0.898120\pi$
$193$	−39.0114	+	67.5697i	−0.202132	+	0.350102i	0.747083	+	0.664730i	$0.231454\pi$
$194$	−24.9748	+	60.5753i	−0.128736	+	0.312244i
$195$		0			0
$196$	59.1039	+	58.7174i	0.301551	+	0.299578i
$197$	37.5571	+	37.5571i	0.190645	+	0.190645i	0.795975	−	0.605330i	$-0.206959\pi$
$197$	37.5571	+	37.5571i	0.190645	+	0.190645i	−0.605330	+	0.795975i	$0.706959\pi$
$198$		0			0
$199$			31.6063i			0.158826i	0.996842	+	0.0794129i	$0.0253045\pi$
$199$			31.6063i			0.158826i	−0.996842	+	0.0794129i	$0.974695\pi$
$200$	−120.002	+	157.994i	−0.600010	+	0.789968i
$201$		0			0
$202$	−13.0921	+	5.44812i	−0.0648126	+	0.0269709i
$203$	411.833	−	110.350i	2.02873	−	0.543597i
$204$		0			0
$205$	−3.79347	+	14.1574i	−0.0185047	+	0.0690605i
$206$	−39.4876	−	296.183i	−0.191688	−	1.43778i
$207$		0			0
$208$	−77.3926	−	20.1940i	−0.372080	−	0.0970864i
$209$	46.2271	−	26.6892i	0.221182	−	0.127700i
$210$		0			0
$211$	294.118	−	78.8088i	1.39393	−	0.373501i	0.517766	−	0.855522i	$-0.326764\pi$
$211$	294.118	−	78.8088i	1.39393	−	0.373501i	0.876160	+	0.482021i	$0.160097\pi$
$212$	280.280	−	163.048i	1.32208	−	0.769095i
$213$		0			0
$214$	−12.8479	+	98.8422i	−0.0600370	+	0.461880i
$215$	7.02137			0.0326575
$216$		0			0
$217$		−	238.938i		−	1.10110i
$218$	29.5699	−	227.488i	0.135642	−	1.04353i
$219$		0			0
$220$	36.2215	+	9.57828i	0.164643	+	0.0435376i
$221$	33.6367	+	125.534i	0.152202	+	0.568026i
$222$		0			0
$223$	−8.67499	−	15.0255i	−0.0389013	−	0.0673790i	0.845919	−	0.533311i	$-0.179052\pi$
$223$	−8.67499	−	15.0255i	−0.0389013	−	0.0673790i	−0.884821	+	0.465932i	$0.845719\pi$
$224$	−164.519	−	210.802i	−0.734459	−	0.941082i
$225$		0			0
$226$	16.2753	+	122.076i	0.0720147	+	0.540157i
$227$	−353.809	−	94.8028i	−1.55863	−	0.417633i	−0.626400	−	0.779502i	$-0.715472\pi$
$227$	−353.809	−	94.8028i	−1.55863	−	0.417633i	−0.932229	+	0.361868i	$0.882139\pi$
$228$		0			0
$229$	−19.0781	−	71.2003i	−0.0833103	−	0.310918i	0.911679	−	0.410904i	$-0.134787\pi$
$229$	−19.0781	−	71.2003i	−0.0833103	−	0.310918i	−0.994989	+	0.0999859i	$0.968120\pi$
$230$	2.95648	−	1.23030i	0.0128543	−	0.00534914i
$231$		0			0
$232$	−404.421	+	55.2691i	−1.74319	+	0.238229i
$233$	353.927			1.51900			0.759500	−	0.650507i	$-0.225444\pi$
$233$	353.927			1.51900			0.759500	+	0.650507i	$0.225444\pi$
$234$		0			0
$235$	−12.3353	+	12.3353i	−0.0524908	+	0.0524908i
$236$	0.588103	+	179.257i	0.00249196	+	0.759564i
$237$		0			0
$238$	−165.614	+	401.689i	−0.695855	+	1.68777i
$239$	−233.969	−	135.082i	−0.978949	−	0.565197i	−0.0769965	−	0.997031i	$-0.524533\pi$
$239$	−233.969	−	135.082i	−0.978949	−	0.565197i	−0.901953	+	0.431835i	$0.857866\pi$
$240$		0			0
$241$	132.967	+	230.305i	0.551729	+	0.955622i	0.998150	+	0.0607993i	$0.0193650\pi$
$241$	132.967	+	230.305i	0.551729	+	0.955622i	−0.446421	+	0.894823i	$0.647302\pi$
$242$	83.9394	+	629.600i	0.346857	+	2.60165i
$243$		0			0
$244$	−254.595	−	145.879i	−1.04342	−	0.597865i
$245$	2.41104	−	8.99812i	0.00984098	−	0.0367270i
$246$		0			0
$247$	11.0345	+	6.37076i	0.0446740	+	0.0257925i
$248$	−28.7413	+	226.936i	−0.115892	+	0.915066i
$249$		0			0
$250$	44.1751	+	5.74206i	0.176700	+	0.0229682i
$251$	174.607	+	174.607i	0.695647	+	0.695647i	0.963469	−	0.267821i	$-0.0863037\pi$
$251$	174.607	+	174.607i	0.695647	+	0.695647i	−0.267821	+	0.963469i	$0.586304\pi$
$252$		0			0
$253$	53.0128	+	53.0128i	0.209537	+	0.209537i
$254$	81.8673	+	106.330i	0.322312	+	0.418622i
$255$		0			0
$256$	130.898	+	220.004i	0.511322	+	0.859389i
$257$	73.8786	+	42.6539i	0.287466	+	0.165968i	0.636798	−	0.771030i	$-0.280258\pi$
$257$	73.8786	+	42.6539i	0.287466	+	0.165968i	−0.349333	+	0.936999i	$0.613592\pi$
$258$		0			0
$259$	69.0950	−	257.866i	0.266776	−	0.995622i
$260$	2.34303	+	8.63095i	0.00901166	+	0.0331960i
$261$		0			0
$262$	−158.445	+	207.192i	−0.604751	+	0.790809i
$263$	221.662	+	383.929i	0.842819	+	1.45981i	0.887501	+	0.460805i	$0.152439\pi$
$263$	221.662	+	383.929i	0.842819	+	1.45981i	−0.0446820	+	0.999001i	$0.514227\pi$
$264$		0			0
$265$	−31.3989	−	18.1282i	−0.118487	−	0.0684082i
$266$	16.3659	+	39.3282i	0.0615259	+	0.147850i
$267$		0			0
$268$	−0.623324	−	189.993i	−0.00232584	−	0.708928i
$269$	−131.331	+	131.331i	−0.488220	+	0.488220i	−0.907744	−	0.419524i	$-0.862197\pi$
$269$	−131.331	+	131.331i	−0.488220	+	0.488220i	0.419524	+	0.907744i	$0.362197\pi$
$270$		0			0
$271$	−417.793			−1.54167			−0.770835	−	0.637034i	$-0.780161\pi$
$271$	−417.793			−1.54167			−0.770835	+	0.637034i	$0.780161\pi$
$272$	205.613	−	361.591i	0.755931	−	1.32938i
$273$		0			0
$274$	−33.5913	+	81.4742i	−0.122596	+	0.297351i
$275$	134.423	+	501.674i	0.488812	+	1.82427i
$276$		0			0
$277$	288.602	+	77.3307i	1.04189	+	0.279172i	0.738895	−	0.673821i	$-0.235348\pi$
$277$	288.602	+	77.3307i	1.04189	+	0.279172i	0.302991	+	0.952993i	$0.402015\pi$
$278$	−260.338	+	340.434i	−0.936467	+	1.22458i
$279$		0			0
$280$	−11.3059	+	27.6794i	−0.0403783	+	0.0988550i
$281$	52.8235	+	91.4929i	0.187984	+	0.325598i	0.944578	−	0.328287i	$-0.106471\pi$
$281$	52.8235	+	91.4929i	0.187984	+	0.325598i	−0.756594	+	0.653885i	$0.773138\pi$
$282$		0			0
$283$	−59.0719	−	220.459i	−0.208735	−	0.779009i	−0.988279	−	0.152661i	$-0.951216\pi$
$283$	−59.0719	−	220.459i	−0.208735	−	0.779009i	0.779544	−	0.626348i	$-0.215451\pi$
$284$	27.0780	−	102.399i	0.0953450	−	0.360560i
$285$		0			0
$286$	−165.905	+	127.736i	−0.580086	+	0.446630i
$287$		−	273.841i		−	0.954150i
$288$		0			0
$289$	−386.880			−1.33868
$290$	27.8434	+	36.1633i	0.0960118	+	0.124701i
$291$		0			0
$292$	−149.450	−	39.5200i	−0.511816	−	0.135342i
$293$	−244.922	+	65.6267i	−0.835912	+	0.223982i	−0.651291	−	0.758828i	$-0.725772\pi$
$293$	−244.922	+	65.6267i	−0.835912	+	0.223982i	−0.184621	+	0.982810i	$0.559106\pi$
$294$		0			0
$295$	17.3583	−	10.0218i	0.0588415	−	0.0339722i
$296$	−96.6427	+	236.603i	−0.326495	+	0.799333i
$297$		0			0
$298$	407.134	+	311.345i	1.36622	+	1.04478i
$299$	−4.63178	+	17.2860i	−0.0154909	+	0.0578128i
$300$		0			0
$301$	−126.714	+	33.9529i	−0.420976	+	0.112800i
$302$	−236.832	−	97.6441i	−0.784211	−	0.323325i
$303$		0			0
$304$	−10.8132	−	39.3214i	−0.0355696	−	0.129347i
$305$			32.8093i			0.107571i
$306$		0			0
$307$	−99.3313	−	99.3313i	−0.323555	−	0.323555i	0.526574	−	0.850129i	$-0.323476\pi$
$307$	−99.3313	−	99.3313i	−0.323555	−	0.323555i	−0.850129	+	0.526574i	$0.823476\pi$
$308$	−700.003	+	2.29656i	−2.27274	+	0.00745635i
$309$		0			0
$310$	23.6143	−	9.82679i	0.0761753	−	0.0316993i
$311$	198.297	−	343.460i	0.637610	−	1.10437i	−0.348346	−	0.937366i	$-0.613256\pi$
$311$	198.297	−	343.460i	0.637610	−	1.10437i	0.985956	−	0.167007i	$-0.0534102\pi$
$312$		0			0
$313$	482.430	−	278.531i	1.54131	−	0.889875i	0.542552	−	0.840022i	$-0.317458\pi$
$313$	482.430	−	278.531i	1.54131	−	0.889875i	0.998757	−	0.0498529i	$-0.0158752\pi$
$314$	−153.248	−	117.192i	−0.488050	−	0.373223i
$315$		0			0
$316$	230.315	−	62.5232i	0.728844	−	0.197858i
$317$	252.884	+	67.7601i	0.797742	+	0.213754i	0.634592	−	0.772847i	$-0.281168\pi$
$317$	252.884	+	67.7601i	0.797742	+	0.213754i	0.163150	+	0.986601i	$0.447835\pi$
$318$		0			0
$319$	−534.268	+	925.379i	−1.67482	+	2.90087i
$320$	14.0675	−	24.9291i	0.0439611	−	0.0779036i
$321$		0			0
$322$	−47.4060	+	36.4996i	−0.147224	+	0.113353i
$323$	−46.8553	+	46.8553i	−0.145063	+	0.145063i
$324$		0			0
$325$	−87.6634	+	87.6634i	−0.269734	+	0.269734i
$326$	30.8308	−	237.189i	0.0945731	−	0.727575i
$327$		0			0
$328$	−32.9398	+	260.086i	−0.100426	+	0.792947i
$329$	162.965	−	282.264i	0.495335	−	0.857945i
$330$		0			0
$331$	−262.320	−	70.2883i	−0.792506	−	0.212351i	−0.160215	−	0.987082i	$-0.551219\pi$
$331$	−262.320	−	70.2883i	−0.792506	−	0.212351i	−0.632291	+	0.774731i	$0.717885\pi$
$332$	−96.1797	+	167.858i	−0.289698	+	0.505595i
$333$		0			0
$334$	−77.1729	+	10.2888i	−0.231057	+	0.0308049i
$335$	−18.3978	+	10.6220i	−0.0549189	+	0.0317074i
$336$		0			0
$337$	210.750	−	365.030i	0.625372	−	1.08318i	−0.363097	−	0.931751i	$-0.618281\pi$
$337$	210.750	−	365.030i	0.625372	−	1.08318i	0.988469	−	0.151425i	$-0.0483861\pi$
$338$	266.276	+	109.784i	0.787800	+	0.324804i
$339$		0			0
$340$	−46.5103	+	0.152590i	−0.136795	+	0.000448794i
$341$	423.430	+	423.430i	1.24173	+	1.24173i
$342$		0			0
$343$		−	235.413i		−	0.686335i
$344$	124.433	−	17.0053i	0.361725	−	0.0494341i
$345$		0			0
$346$	−164.450	−	395.184i	−0.475290	−	1.14215i
$347$	174.682	−	46.8058i	0.503406	−	0.134887i	0.00182548	−	0.999998i	$-0.499419\pi$
$347$	174.682	−	46.8058i	0.503406	−	0.134887i	0.501580	+	0.865111i	$0.332752\pi$
$348$		0			0
$349$	−15.4778	+	57.7638i	−0.0443489	+	0.165512i	−0.984549	−	0.175111i	$-0.943971\pi$
$349$	−15.4778	+	57.7638i	−0.0443489	+	0.165512i	0.940200	+	0.340624i	$0.110638\pi$
$350$	−410.838	+	54.7736i	−1.17382	+	0.156496i
$351$		0			0
$352$	665.120	+	82.0207i	1.88954	+	0.233013i
$353$	7.41642	−	4.28187i	0.0210097	−	0.0121299i	−0.489458	−	0.872027i	$-0.662805\pi$
$353$	7.41642	−	4.28187i	0.0210097	−	0.0121299i	0.510468	+	0.859897i	$0.329472\pi$
$354$		0			0
$355$	−11.4397	+	3.06525i	−0.0322244	+	0.00863451i
$356$	−81.1428	+	306.852i	−0.227929	+	0.861945i
$357$		0			0
$358$	−83.6917	−	10.8786i	−0.233776	−	0.0303871i
$359$	−242.593			−0.675746			−0.337873	−	0.941192i	$-0.609707\pi$
$359$	−242.593			−0.675746			−0.337873	+	0.941192i	$0.609707\pi$
$360$		0			0
$361$		−	354.504i		−	0.982004i
$362$	463.879	+	60.2968i	1.28143	+	0.166566i
$363$		0			0
$364$	−84.0207	−	144.432i	−0.230826	−	0.396790i
$365$	4.47370	+	16.6961i	0.0122567	+	0.0457426i
$366$		0			0
$367$	110.239	+	190.940i	0.300379	+	0.520272i	0.976222	−	0.216774i	$-0.0695534\pi$
$367$	110.239	+	190.940i	0.300379	+	0.520272i	−0.675843	+	0.737046i	$0.736220\pi$
$368$	49.4153	−	28.9639i	0.134281	−	0.0787063i
$369$		0			0
$370$	28.3267	−	3.77656i	0.0765587	−	0.0102069i
$371$	654.314	+	175.323i	1.76365	+	0.472569i
$372$		0			0
$373$	−54.2918	−	202.620i	−0.145554	−	0.543217i	−0.999730	−	0.0232321i	$-0.992604\pi$
$373$	−54.2918	−	202.620i	−0.145554	−	0.543217i	0.854176	−	0.519985i	$-0.174062\pi$
$374$	−418.357	−	1005.34i	−1.11860	−	2.68807i
$375$		0			0
$376$	−188.733	+	248.484i	−0.501949	+	0.660861i
$377$	−255.061			−0.676554
$378$		0			0
$379$	346.957	−	346.957i	0.915453	−	0.915453i	−0.0812412	−	0.996694i	$-0.525888\pi$
$379$	346.957	−	346.957i	0.915453	−	0.915453i	0.996694	+	0.0812412i	$0.0258884\pi$
$380$	−3.21374	+	3.23490i	−0.00845722	+	0.00851289i
$381$		0			0
$382$	372.436	+	153.553i	0.974962	+	0.401970i
$383$	44.9048	+	25.9258i	0.117245	+	0.0676914i	0.557476	−	0.830193i	$-0.311770\pi$
$383$	44.9048	+	25.9258i	0.117245	+	0.0676914i	−0.440231	+	0.897885i	$0.645103\pi$
$384$		0			0
$385$	39.1354	+	67.7844i	0.101650	+	0.176063i
$386$	154.677	−	20.6218i	0.400717	−	0.0534243i
$387$		0			0
$388$	126.466	−	34.3317i	0.325944	−	0.0884837i
$389$	80.6288	−	300.911i	0.207272	−	0.773549i	−0.781473	−	0.623939i	$-0.785531\pi$
$389$	80.6288	−	300.911i	0.207272	−	0.773549i	0.988745	−	0.149610i	$-0.0478020\pi$
$390$		0			0
$391$	−80.5999	−	46.5344i	−0.206138	−	0.119014i
$392$	20.9357	−	165.305i	0.0534075	−	0.421696i
$393$		0			0
$394$	13.6927	−	105.341i	0.0347530	−	0.267363i
$395$	−18.8688	−	18.8688i	−0.0477691	−	0.0477691i
$396$		0			0
$397$	470.741	+	470.741i	1.18574	+	1.18574i	0.978232	+	0.207512i	$0.0665367\pi$
$397$	470.741	+	470.741i	1.18574	+	1.18574i	0.207512	+	0.978232i	$0.433463\pi$
$398$	50.0868	−	38.5636i	0.125846	−	0.0968935i
$399$		0			0
$400$	396.791	−	2.60359i	0.991977	−	0.00650899i
$401$	−529.827	−	305.896i	−1.32126	−	0.762832i	−0.337333	−	0.941385i	$-0.609525\pi$
$401$	−529.827	−	305.896i	−1.32126	−	0.762832i	−0.983930	+	0.178553i	$0.942858\pi$
$402$		0			0
$403$	−36.9954	+	138.069i	−0.0918000	+	0.342602i
$404$	24.6077	+	14.0998i	0.0609102	+	0.0349006i
$405$		0			0
$406$	−677.360	−	517.993i	−1.66837	−	1.27585i
$407$	334.528	+	579.419i	0.821936	+	1.42363i
$408$		0			0
$409$	310.635	+	179.345i	0.759499	+	0.438497i	0.829116	−	0.559077i	$-0.188844\pi$
$409$	310.635	+	179.345i	0.759499	+	0.438497i	−0.0696165	+	0.997574i	$0.522178\pi$
$410$	27.0639	−	11.2623i	0.0660094	−	0.0274689i
$411$		0			0
$412$	−421.184	+	423.957i	−1.02229	+	1.02902i
$413$	−264.801	+	264.801i	−0.641164	+	0.641164i
$414$		0			0
$415$	21.6315			0.0521242
$416$	62.4271	+	147.284i	0.150065	+	0.354048i
$417$		0			0
$418$	−98.6974	−	40.6922i	−0.236118	−	0.0973498i
$419$	−60.2617	−	224.900i	−0.143823	−	0.536754i	−0.999805	−	0.0197486i	$-0.993713\pi$
$419$	−60.2617	−	224.900i	−0.143823	−	0.536754i	0.855982	−	0.517005i	$-0.172953\pi$
$420$		0			0
$421$	−631.122	−	169.109i	−1.49910	−	0.401683i	−0.586303	−	0.810092i	$-0.699417\pi$
$421$	−631.122	−	169.109i	−1.49910	−	0.401683i	−0.912799	+	0.408409i	$0.866084\pi$
$422$	−483.750	−	369.935i	−1.14633	−	0.876623i
$423$		0			0
$424$	−600.360	−	245.223i	−1.41594	−	0.578356i
$425$	−322.371	−	558.363i	−0.758520	−	1.31379i
$426$		0			0
$427$	−158.654	−	592.106i	−0.371556	−	1.38666i
$428$	172.312	−	100.240i	0.402598	−	0.234205i
$429$		0			0
$430$	−8.56694	−	11.1268i	−0.0199231	−	0.0258763i
$431$		−	480.071i		−	1.11385i	−0.830562	−	0.556927i	$-0.811980\pi$
$431$		−	480.071i		−	1.11385i	0.830562	−	0.556927i	$-0.188020\pi$
$432$		0			0
$433$	−317.055			−0.732228			−0.366114	−	0.930570i	$-0.619312\pi$
$433$	−317.055			−0.732228			−0.366114	+	0.930570i	$0.619312\pi$
$434$	−378.646	+	291.534i	−0.872457	+	0.671737i
$435$		0			0
$436$	−396.582	+	230.705i	−0.909591	+	0.529139i
$437$	−8.81356	+	2.36159i	−0.0201683	+	0.00540409i
$438$		0			0
$439$	−157.780	+	91.0945i	−0.359409	+	0.207505i	−0.668821	−	0.743423i	$-0.733201\pi$
$439$	−157.780	+	91.0945i	−0.359409	+	0.207505i	0.309413	+	0.950928i	$0.399868\pi$
$440$	−29.0160	−	69.0872i	−0.0659455	−	0.157016i
$441$		0			0
$442$	157.893	−	206.471i	0.357225	−	0.467129i
$443$	−49.2888	+	183.948i	−0.111261	+	0.415233i	−0.998980	−	0.0451531i	$-0.985622\pi$
$443$	−49.2888	+	183.948i	−0.111261	+	0.415233i	0.887719	+	0.460386i	$0.152289\pi$
$444$		0			0
$445$	34.2805	−	9.18543i	0.0770348	−	0.0206414i
$446$	−13.2265	+	32.0803i	−0.0296558	+	0.0719289i
$447$		0			0
$448$	−133.327	+	517.919i	−0.297604	+	1.15607i
$449$		−	22.5026i		−	0.0501172i	−0.999686	−	0.0250586i	$-0.992023\pi$
$449$		−	22.5026i		−	0.0501172i	0.999686	−	0.0250586i	$-0.00797724\pi$
$450$		0			0
$451$	485.283	+	485.283i	1.07602	+	1.07602i
$452$	173.596	−	174.739i	0.384062	−	0.386591i
$453$		0			0
$454$	281.456	+	676.355i	0.619947	+	1.48977i
$455$	−9.34167	+	16.1802i	−0.0205311	+	0.0355610i
$456$		0			0
$457$	8.03399	−	4.63842i	0.0175798	−	0.0101497i	−0.491184	−	0.871056i	$-0.663436\pi$
$457$	8.03399	−	4.63842i	0.0175798	−	0.0101497i	0.508764	+	0.860906i	$0.330103\pi$
$458$	−89.5540	+	117.106i	−0.195533	+	0.255691i
$459$		0			0
$460$	−5.55694	−	3.18404i	−0.0120803	−	0.00692183i
$461$	−610.429	−	163.564i	−1.32414	−	0.354803i	−0.473614	−	0.880733i	$-0.657051\pi$
$461$	−610.429	−	163.564i	−1.32414	−	0.354803i	−0.850528	+	0.525930i	$0.823717\pi$
$462$		0			0
$463$	119.643	−	207.227i	0.258407	−	0.447574i	−0.707408	−	0.706805i	$-0.750136\pi$
$463$	119.643	−	207.227i	0.258407	−	0.447574i	0.965815	+	0.259231i	$0.0834691\pi$
$464$	581.029	+	573.454i	1.25222	+	1.23589i
$465$		0			0
$466$	−431.835	−	560.871i	−0.926684	−	1.20359i
$467$	−465.534	+	465.534i	−0.996860	+	0.996860i	−0.999995	−	0.00313466i	$-0.999002\pi$
$467$	−465.534	+	465.534i	−0.996860	+	0.996860i	0.00313466	+	0.999995i	$0.499002\pi$
$468$		0			0
$469$	280.659	−	280.659i	0.598421	−	0.598421i
$470$	34.5986	+	4.49726i	0.0736140	+	0.00956864i
$471$		0			0
$472$	283.352	−	219.648i	0.600323	−	0.465355i
$473$	164.385	−	284.723i	0.347537	−	0.601952i
$474$		0			0
$475$	−61.0567	−	16.3601i	−0.128540	−	0.0344423i
$476$	838.628	−	227.661i	1.76182	−	0.478280i
$477$		0			0
$478$	71.4056	+	535.589i	0.149384	+	1.12048i
$479$	272.785	−	157.493i	0.569489	−	0.328794i	−0.187456	−	0.982273i	$-0.560024\pi$
$479$	272.785	−	157.493i	0.569489	−	0.328794i	0.756945	+	0.653478i	$0.226691\pi$
$480$		0			0
$481$	−79.8523	+	138.308i	−0.166013	+	0.287543i
$482$	202.730	−	491.714i	0.420602	−	1.02015i
$483$		0			0
$484$	895.316	−	901.210i	1.84983	−	1.86200i
$485$	−10.3609	−	10.3609i	−0.0213627	−	0.0213627i
$486$		0			0
$487$			473.337i			0.971945i	0.873974	+	0.485973i	$0.161535\pi$
$487$			473.337i			0.971945i	−0.873974	+	0.485973i	$0.838465\pi$
$488$	79.4622	+	581.450i	0.162832	+	1.19149i
$489$		0			0
$490$	−17.2012	+	7.15803i	−0.0351044	+	0.0146082i
$491$	184.476	−	49.4303i	0.375716	−	0.100673i	−0.0660193	−	0.997818i	$-0.521030\pi$
$491$	184.476	−	49.4303i	0.375716	−	0.100673i	0.441735	+	0.897146i	$0.354363\pi$
$492$		0			0
$493$	343.315	−	1281.27i	0.696379	−	2.59892i
$494$	−3.36764	−	25.2595i	−0.00681709	−	0.0511326i
$495$		0			0
$496$	394.696	−	231.344i	0.795757	−	0.466419i
$497$	191.628	−	110.636i	0.385569	−	0.222609i
$498$		0			0
$499$	−235.171	+	63.0138i	−0.471284	+	0.126280i	−0.486641	−	0.873602i	$-0.661778\pi$
$499$	−235.171	+	63.0138i	−0.471284	+	0.126280i	0.0153574	+	0.999882i	$0.495111\pi$
$500$	−44.7996	−	77.0106i	−0.0895993	−	0.154021i
$501$		0			0
$502$	63.6590	−	489.744i	0.126811	−	0.975586i
$503$	−653.388			−1.29898			−0.649491	−	0.760369i	$-0.725018\pi$
$503$	−653.388			−1.29898			−0.649491	+	0.760369i	$0.725018\pi$
$504$		0			0
$505$		−	3.17116i		−	0.00627952i
$506$	19.3276	−	148.692i	0.0381968	−	0.293858i
$507$		0			0
$508$	68.6135	−	259.471i	0.135066	−	0.510770i
$509$	2.19594	+	8.19536i	0.00431422	+	0.0161009i	0.968049	−	0.250760i	$-0.0806804\pi$
$509$	2.19594	+	8.19536i	0.00431422	+	0.0161009i	−0.963735	+	0.266861i	$0.914014\pi$
$510$		0			0
$511$	−161.473	−	279.679i	−0.315993	−	0.547316i
$512$	188.929	−	475.867i	0.369003	−	0.929428i
$513$		0			0
$514$	−22.5472	−	169.119i	−0.0438662	−	0.329025i
$515$	64.5441	+	17.2945i	0.125328	+	0.0335816i
$516$		0			0
$517$	211.414	+	789.006i	0.408924	+	1.52612i
$518$	−492.947	+	205.133i	−0.951635	+	0.396010i
$519$		0			0
$520$	10.8187	−	14.2439i	0.0208053	−	0.0273920i
$521$	513.662			0.985916			0.492958	−	0.870053i	$-0.335916\pi$
$521$	513.662			0.985916			0.492958	+	0.870053i	$0.335916\pi$
$522$		0			0
$523$	−531.117	+	531.117i	−1.01552	+	1.01552i	−0.0156428	+	0.999878i	$0.504979\pi$
$523$	−531.117	+	531.117i	−1.01552	+	1.01552i	−0.999878	+	0.0156428i	$0.995021\pi$
$524$	521.661	−	1.71145i	0.995536	−	0.00326613i
$525$		0			0
$526$	337.961	−	819.710i	0.642511	−	1.55838i
$527$	−643.776	−	371.684i	−1.22159	−	0.705283i
$528$		0			0
$529$	258.092	+	447.029i	0.487887	+	0.845045i
$530$	9.58273	+	71.8767i	0.0180806	+	0.135616i
$531$		0			0
$532$	42.3552	−	73.9204i	0.0796150	−	0.138948i
$533$	−42.3996	+	158.237i	−0.0795490	+	0.296881i
$534$		0			0
$535$	−19.3036	−	11.1449i	−0.0360815	−	0.0208317i
$536$	−300.322	+	232.802i	−0.560303	+	0.434333i
$537$		0			0
$538$	368.362	+	47.8812i	0.684688	+	0.0889985i
$539$	−308.435	−	308.435i	−0.572235	−	0.572235i
$540$		0			0
$541$	491.796	+	491.796i	0.909049	+	0.909049i	0.996196	−	0.0871462i	$-0.0277747\pi$
$541$	491.796	+	491.796i	0.909049	+	0.909049i	−0.0871462	+	0.996196i	$0.527775\pi$
$542$	509.759	+	662.079i	0.940515	+	1.22155i
$543$		0			0
$544$	−823.890	+	115.349i	−1.51450	+	0.212039i
$545$	44.4278	+	25.6504i	0.0815190	+	0.0470650i
$546$		0			0
$547$	−74.6837	+	278.723i	−0.136533	+	0.509549i	0.863454	+	0.504428i	$0.168297\pi$
$547$	−74.6837	+	278.723i	−0.136533	+	0.509549i	−0.999987	+	0.00512086i	$0.998370\pi$
$548$	170.098	−	46.1764i	0.310398	−	0.0842634i
$549$		0			0
$550$	630.994	−	825.126i	1.14726	−	1.50023i
$551$	−65.0235	−	112.624i	−0.118010	−	0.204399i
$552$		0			0
$553$	431.766	+	249.280i	0.780770	+	0.450778i
$554$	−229.584	−	551.703i	−0.414411	−	0.995854i
$555$		0			0
$556$	857.132	−	2.81206i	1.54160	−	0.00505767i
$557$	560.781	−	560.781i	1.00679	−	1.00679i	0.00681189	−	0.999977i	$-0.497832\pi$
$557$	560.781	−	560.781i	1.00679	−	1.00679i	0.999977	−	0.00681189i	$-0.00216831\pi$
$558$		0			0
$559$	78.4779			0.140390
$560$	57.6584	−	15.8557i	0.102961	−	0.0283138i
$561$		0			0
$562$	80.5383	−	195.342i	0.143307	−	0.347584i
$563$	16.8240	+	62.7879i	0.0298827	+	0.111524i	0.979256	−	0.202626i	$-0.0649474\pi$
$563$	16.8240	+	62.7879i	0.0298827	+	0.111524i	−0.949374	+	0.314149i	$0.898281\pi$
$564$		0			0
$565$	−26.6027	−	7.12816i	−0.0470844	−	0.0126162i
$566$	−277.289	+	362.600i	−0.489909	+	0.640635i
$567$		0			0
$568$	−195.311	+	82.0289i	−0.343857	+	0.144417i
$569$	−376.781	−	652.605i	−0.662182	−	1.14693i	−0.980041	−	0.198795i	$-0.936297\pi$
$569$	−376.781	−	652.605i	−0.662182	−	1.14693i	0.317859	−	0.948138i	$-0.397036\pi$
$570$		0			0
$571$	51.4330	+	191.951i	0.0900753	+	0.336166i	0.996227	−	0.0867876i	$-0.0276601\pi$
$571$	51.4330	+	191.951i	0.0900753	+	0.336166i	−0.906152	+	0.422953i	$0.860993\pi$
$572$	404.848	+	107.056i	0.707777	+	0.187162i
$573$		0			0
$574$	−433.958	+	334.120i	−0.756024	+	0.582091i
$575$		−	88.7810i		−	0.154402i
$576$		0			0
$577$	321.494			0.557181			0.278591	−	0.960410i	$-0.410133\pi$
$577$	321.494			0.557181			0.278591	+	0.960410i	$0.410133\pi$
$578$	472.041	+	613.091i	0.816680	+	1.06071i
$579$		0			0
$580$	23.3358	−	88.2473i	0.0402341	−	0.152151i
$581$	−390.382	+	104.603i	−0.671914	+	0.180039i
$582$		0			0
$583$	−1470.23	+	848.837i	−2.52183	+	1.45598i
$584$	119.720	+	285.054i	0.205000	+	0.488106i
$585$		0			0
$586$	402.835	+	308.057i	0.687431	+	0.525695i
$587$	−139.206	+	519.522i	−0.237147	+	0.885046i	0.740022	+	0.672583i	$0.234815\pi$
$587$	−139.206	+	519.522i	−0.237147	+	0.885046i	−0.977169	+	0.212463i	$0.931851\pi$
$588$		0			0
$589$	−70.3966	+	18.8627i	−0.119519	+	0.0320250i
$590$	−37.0608	−	15.2799i	−0.0628150	−	0.0258982i
$591$		0			0
$592$	492.862	−	135.534i	0.832537	−	0.228943i
$593$			150.500i			0.253795i	0.991916	+	0.126897i	$0.0405019\pi$
$593$			150.500i			0.253795i	−0.991916	+	0.126897i	$0.959498\pi$
$594$		0			0
$595$	−68.7056	−	68.7056i	−0.115472	−	0.115472i
$596$	−3.36302	−	1025.07i	−0.00564265	−	1.71991i
$597$		0			0
$598$	33.0446	−	13.7511i	0.0552586	−	0.0229951i
$599$	−447.647	+	775.348i	−0.747325	+	1.29440i	0.201776	+	0.979432i	$0.435329\pi$
$599$	−447.647	+	775.348i	−0.747325	+	1.29440i	−0.949101	+	0.314972i	$0.898005\pi$
$600$		0			0
$601$	−864.629	+	499.194i	−1.43865	+	0.830605i	−0.997756	−	0.0669538i	$-0.978672\pi$
$601$	−864.629	+	499.194i	−1.43865	+	0.830605i	−0.440894	+	0.897559i	$0.645339\pi$
$602$	208.412	+	159.378i	0.346199	+	0.264747i
$603$		0			0
$604$	134.227	+	494.447i	0.222230	+	0.818621i
$605$	−137.202	−	36.7632i	−0.226781	−	0.0607657i
$606$		0			0
$607$	378.819	−	656.133i	0.624084	−	1.08094i	−0.364634	−	0.931151i	$-0.618806\pi$
$607$	378.819	−	656.133i	0.624084	−	1.08094i	0.988717	−	0.149794i	$-0.0478609\pi$
$608$	−49.1195	+	65.1127i	−0.0807886	+	0.107093i
$609$		0			0
$610$	51.9931	−	40.0314i	0.0852347	−	0.0656253i
$611$	−137.872	+	137.872i	−0.225650	+	0.225650i
$612$		0			0
$613$	325.410	−	325.410i	0.530849	−	0.530849i	−0.389976	−	0.920825i	$-0.627517\pi$
$613$	325.410	−	325.410i	0.530849	−	0.530849i	0.920825	+	0.389976i	$0.127517\pi$
$614$	−36.2145	+	278.608i	−0.0589813	+	0.453758i
$615$		0			0
$616$	857.730	+	1106.50i	1.39242	+	1.79626i
$617$	−167.571	+	290.242i	−0.271590	+	0.470408i	−0.969269	−	0.246002i	$-0.920883\pi$
$617$	−167.571	+	290.242i	−0.271590	+	0.470408i	0.697679	+	0.716411i	$0.254216\pi$
$618$		0			0
$619$	476.135	+	127.580i	0.769201	+	0.206107i	0.622018	−	0.783003i	$-0.286313\pi$
$619$	476.135	+	127.580i	0.769201	+	0.206107i	0.147183	+	0.989109i	$0.452980\pi$
$620$	−44.3850	−	25.4319i	−0.0715887	−	0.0410192i
$621$		0			0
$622$	−786.230	+	104.822i	−1.26404	+	0.168523i
$623$	−574.239	+	331.537i	−0.921731	+	0.532162i
$624$		0			0
$625$	305.019	−	528.308i	0.488030	−	0.845292i
$626$	−1030.01	−	424.668i	−1.64539	−	0.678383i
$627$		0			0
$628$	1.26586	+	385.842i	0.00201570	+	0.614398i
$629$	−587.293	−	587.293i	−0.933693	−	0.933693i
$630$		0			0
$631$		−	298.987i		−	0.473830i	−0.971530	−	0.236915i	$-0.923864\pi$
$631$		−	298.987i		−	0.473830i	0.971530	−	0.236915i	$-0.0761362\pi$
$632$	−380.093	−	288.695i	−0.601414	−	0.456796i
$633$		0			0
$634$	−201.170	−	483.423i	−0.317303	−	0.762497i
$635$	−28.9872	+	7.76711i	−0.0456492	+	0.0122317i
$636$		0			0
$637$	26.9482	−	100.572i	0.0423049	−	0.157884i
$638$	2118.33	−	282.419i	3.32026	−	0.442663i
$639$		0			0
$640$	−56.6695	+	8.12372i	−0.0885462	+	0.0126933i
$641$	360.071	−	207.887i	0.561734	−	0.324317i	−0.192107	−	0.981374i	$-0.561532\pi$
$641$	360.071	−	207.887i	0.561734	−	0.324317i	0.753841	+	0.657057i	$0.228199\pi$
$642$		0			0
$643$	175.560	−	47.0412i	0.273033	−	0.0731589i	−0.119705	−	0.992810i	$-0.538195\pi$
$643$	175.560	−	47.0412i	0.273033	−	0.0731589i	0.392738	+	0.919651i	$0.371528\pi$
$644$	115.682	+	30.5906i	0.179631	+	0.0475009i
$645$		0			0
$646$	131.421	+	17.0826i	0.203438	+	0.0264437i
$647$	56.1947			0.0868543			0.0434272	−	0.999057i	$-0.486172\pi$
$647$	56.1947			0.0868543			0.0434272	+	0.999057i	$0.486172\pi$
$648$		0			0
$649$		−	938.525i		−	1.44611i
$650$	245.881	+	31.9606i	0.378279	+	0.0491702i
$651$		0			0
$652$	−413.493	+	240.543i	−0.634192	+	0.368930i
$653$	25.0200	+	93.3761i	0.0383155	+	0.142995i	0.982434	−	0.186611i	$-0.0597505\pi$
$653$	25.0200	+	93.3761i	0.0383155	+	0.142995i	−0.944118	+	0.329607i	$0.893084\pi$
$654$		0			0
$655$	−29.1647	−	50.5147i	−0.0445262	−	0.0771217i
$656$	452.352	−	265.138i	0.689560	−	0.404174i
$657$		0			0
$658$	−646.144	+	86.1449i	−0.981981	+	0.130919i
$659$	−287.688	−	77.0858i	−0.436552	−	0.116974i	0.0338479	−	0.999427i	$-0.489224\pi$
$659$	−287.688	−	77.0858i	−0.436552	−	0.116974i	−0.470400	+	0.882453i	$0.655890\pi$
$660$		0			0
$661$	116.742	+	435.687i	0.176614	+	0.659133i	0.996271	+	0.0862784i	$0.0274975\pi$
$661$	116.742	+	435.687i	0.176614	+	0.659133i	−0.819657	+	0.572855i	$0.805836\pi$
$662$	208.676	+	501.460i	0.315221	+	0.757493i
$663$		0			0
$664$	383.356	−	52.3903i	0.577344	−	0.0789011i
$665$	−9.52601			−0.0143248
$666$		0			0
$667$	129.156	−	129.156i	0.193638	−	0.193638i
$668$	110.465	+	109.743i	0.165367	+	0.164286i
$669$		0			0
$670$	39.2804	+	16.1950i	0.0586274	+	0.0241717i
$671$	1330.45	+	768.135i	1.98278	+	1.14476i
$672$		0			0
$673$	−64.0278	−	110.899i	−0.0951379	−	0.164784i	0.814528	−	0.580124i	$-0.196996\pi$
$673$	−64.0278	−	110.899i	−0.0951379	−	0.164784i	−0.909666	+	0.415340i	$0.863663\pi$
$674$	−835.608	+	111.405i	−1.23977	+	0.165289i
$675$		0			0
$676$	−150.915	−	555.920i	−0.223247	−	0.822367i
$677$	192.154	−	717.129i	0.283832	−	1.05927i	−0.665857	−	0.746079i	$-0.731934\pi$
$677$	192.154	−	717.129i	0.283832	−	1.05927i	0.949689	−	0.313195i	$-0.101399\pi$
$678$		0			0
$679$	237.084	+	136.880i	0.349166	+	0.201591i
$680$	56.9902	+	73.5190i	0.0838091	+	0.108116i
$681$		0			0
$682$	154.375	−	1187.65i	0.226357	−	1.74142i
$683$	−413.911	−	413.911i	−0.606019	−	0.606019i	0.335885	−	0.941903i	$-0.390965\pi$
$683$	−413.911	−	413.911i	−0.606019	−	0.606019i	−0.941903	+	0.335885i	$0.890965\pi$
$684$		0			0
$685$	−13.9355	−	13.9355i	−0.0203438	−	0.0203438i
$686$	−373.061	+	287.233i	−0.543820	+	0.418707i
$687$		0			0
$688$	−178.773	−	176.442i	−0.259844	−	0.256456i
$689$	−350.946	−	202.619i	−0.509356	−	0.294077i
$690$		0			0
$691$	−128.886	+	481.009i	−0.186521	+	0.696105i	0.807779	+	0.589485i	$0.200669\pi$
$691$	−128.886	+	481.009i	−0.186521	+	0.696105i	−0.994300	+	0.106620i	$0.965997\pi$
$692$	−425.600	+	742.779i	−0.615030	+	1.07338i
$693$		0			0
$694$	−287.307	−	219.711i	−0.413987	−	0.316586i
$695$	−47.9200	−	82.9999i	−0.0689497	−	0.119424i
$696$		0			0
$697$	−737.817	−	425.979i	−1.05856	−	0.611160i
$698$	110.423	−	45.9513i	0.158200	−	0.0658327i
$699$		0			0
$700$	588.073	+	584.227i	0.840105	+	0.834610i
$701$	−270.798	+	270.798i	−0.386303	+	0.386303i	−0.873367	−	0.487064i	$-0.838068\pi$
$701$	−270.798	+	270.798i	−0.386303	+	0.386303i	0.487064	+	0.873367i	$0.338068\pi$
$702$		0			0
$703$	−81.4280			−0.115829
$704$	−681.550	−	1154.10i	−0.968110	−	1.63934i
$705$		0			0
$706$	−15.8345	−	6.52844i	−0.0224284	−	0.00924708i
$707$	15.3346	+	57.2296i	0.0216897	+	0.0809470i
$708$		0			0
$709$	411.392	+	110.232i	0.580242	+	0.155475i	0.536990	−	0.843589i	$-0.319561\pi$
$709$	411.392	+	110.232i	0.580242	+	0.155475i	0.0432524	+	0.999064i	$0.486228\pi$
$710$	18.8153	+	14.3885i	0.0265005	+	0.0202656i
$711$		0			0
$712$	585.275	−	245.810i	0.822016	−	0.345239i
$713$	−51.1810	−	88.6480i	−0.0717825	−	0.124331i
$714$		0			0
$715$	−12.1189	−	45.2283i	−0.0169495	−	0.0632563i
$716$	84.8749	+	145.900i	0.118540	+	0.203771i
$717$		0			0
$718$	295.993	+	384.438i	0.412247	+	0.535429i
$719$			1018.72i			1.41685i	0.705784	+	0.708427i	$0.250595\pi$
$719$			1018.72i			1.41685i	−0.705784	+	0.708427i	$0.749405\pi$
$720$		0			0
$721$	−1248.45			−1.73155
$722$	−561.784	+	432.538i	−0.778095	+	0.599083i
$723$		0			0
$724$	−470.437	−	808.682i	−0.649775	−	1.11696i
$725$	1222.24	−	327.498i	1.68585	−	0.451722i
$726$		0			0
$727$	409.462	−	236.403i	0.563221	−	0.325176i	−0.191216	−	0.981548i	$-0.561243\pi$
$727$	409.462	−	236.403i	0.563221	−	0.325176i	0.754437	+	0.656372i	$0.227910\pi$
$728$	−126.366	+	309.373i	−0.173580	+	0.424963i
$729$		0			0
$730$	20.9999	−	27.4608i	0.0287670	−	0.0376175i
$731$	−105.632	+	394.224i	−0.144504	+	0.539295i
$732$		0			0
$733$	−848.684	+	227.404i	−1.15782	+	0.310238i	−0.786096	−	0.618104i	$-0.787901\pi$
$733$	−848.684	+	227.404i	−1.15782	+	0.310238i	−0.371727	+	0.928342i	$0.621234\pi$
$734$	168.078	−	407.667i	0.228990	−	0.555405i
$735$		0			0
$736$	−106.192	−	42.9693i	−0.144283	−	0.0583822i
$737$			994.733i			1.34971i
$738$		0			0
$739$	48.3289	+	48.3289i	0.0653977	+	0.0653977i	0.739049	−	0.673651i	$-0.235275\pi$
$739$	48.3289	+	48.3289i	0.0653977	+	0.0653977i	−0.673651	+	0.739049i	$0.735275\pi$
$740$	−40.5469	−	40.2817i	−0.0547930	−	0.0544347i
$741$		0			0
$742$	−520.509	−	1250.81i	−0.701495	−	1.68573i
$743$	171.049	−	296.266i	0.230214	−	0.398743i	−0.727657	−	0.685941i	$-0.759391\pi$
$743$	171.049	−	296.266i	0.230214	−	0.398743i	0.957871	+	0.287199i	$0.0927240\pi$
$744$		0			0
$745$	−99.2618	+	57.3088i	−0.133237	+	0.0769246i
$746$	−254.850	+	333.258i	−0.341622	+	0.446726i
$747$		0			0
$748$	−1082.72	+	1889.61i	−1.44748	+	2.52622i
$749$	402.263	+	107.786i	0.537067	+	0.143907i
$750$		0			0
$751$	−583.913	+	1011.37i	−0.777514	+	1.34669i	0.155857	+	0.987780i	$0.450186\pi$
$751$	−583.913	+	1011.37i	−0.777514	+	1.34669i	−0.933371	+	0.358914i	$0.883147\pi$
$752$	624.051	−	4.09479i	0.829855	−	0.00544520i
$753$		0			0
$754$	311.206	+	404.197i	0.412740	+	0.536070i
$755$	40.5081	−	40.5081i	0.0536532	−	0.0536532i
$756$		0			0
$757$	−885.032	+	885.032i	−1.16913	+	1.16913i	−0.186716	+	0.982414i	$0.559785\pi$
$757$	−885.032	+	885.032i	−1.16913	+	1.16913i	−0.982414	+	0.186716i	$0.940215\pi$
$758$	−973.155	−	126.495i	−1.28385	−	0.166879i
$759$		0			0
$760$	9.04753	+	1.14586i	0.0119046	+	0.00150771i
$761$	−222.498	+	385.378i	−0.292376	+	0.506410i	−0.974371	−	0.224947i	$-0.927779\pi$
$761$	−222.498	+	385.378i	−0.292376	+	0.506410i	0.681995	+	0.731357i	$0.261113\pi$
$762$		0			0
$763$	−925.820	−	248.073i	−1.21339	−	0.325128i
$764$	−211.082	−	777.555i	−0.276285	−	1.01774i
$765$		0			0
$766$	−13.7046	−	102.794i	−0.0178912	−	0.134195i
$767$	194.013	−	112.014i	0.252951	−	0.146041i
$768$		0			0
$769$	27.2858	−	47.2604i	0.0354822	−	0.0614569i	−0.847739	−	0.530414i	$-0.822037\pi$
$769$	27.2858	−	47.2604i	0.0354822	−	0.0614569i	0.883221	+	0.468957i	$0.155370\pi$
$770$	59.6685	−	144.724i	0.0774915	−	0.187953i
$771$		0			0
$772$	−221.405	−	219.957i	−0.286793	−	0.284918i
$773$	125.828	+	125.828i	0.162779	+	0.162779i	0.783796	−	0.621018i	$-0.213281\pi$
$773$	125.828	+	125.828i	0.162779	+	0.162779i	−0.621018	+	0.783796i	$0.713281\pi$
$774$		0			0
$775$		−	709.121i		−	0.914995i
$776$	−208.710	−	158.523i	−0.268957	−	0.204283i
$777$		0			0
$778$	−575.233	+	239.375i	−0.739374	+	0.307680i
$779$	−80.6799	+	21.6181i	−0.103569	+	0.0277511i
$780$		0			0
$781$	−143.528	+	535.653i	−0.183774	+	0.685856i
$782$	24.5985	+	184.505i	0.0314559	+	0.235940i
$783$		0			0
$784$	−287.504	+	168.515i	−0.366714	+	0.214943i
$785$	37.3628	−	21.5714i	0.0475959	−	0.0274795i
$786$		0			0
$787$	−1260.30	+	337.696i	−1.60140	+	0.429093i	−0.945464	−	0.325728i	$-0.894391\pi$
$787$	−1260.30	+	337.696i	−1.60140	+	0.429093i	−0.655932	+	0.754820i	$0.727724\pi$
$788$	−183.642	+	106.830i	−0.233048	+	0.135572i
$789$		0			0
$790$	−6.87924	+	52.9238i	−0.00870790	+	0.0669921i
$791$	514.565			0.650524
$792$		0			0
$793$			366.710i			0.462434i
$794$	171.624	−	1320.35i	0.216151	−	1.66291i
$795$		0			0
$796$	−122.224	−	32.3205i	−0.153548	−	0.0406036i
$797$	−94.6123	−	353.098i	−0.118711	−	0.443034i	0.880827	−	0.473438i	$-0.156987\pi$
$797$	−94.6123	−	353.098i	−0.118711	−	0.443034i	−0.999538	+	0.0304042i	$0.990321\pi$
$798$		0			0
$799$	−507.007	−	878.163i	−0.634552	−	1.09908i
$800$	−488.260	−	625.621i	−0.610325	−	0.782026i
$801$		0			0
$802$	161.699	+	1212.85i	0.201620	+	1.51228i
$803$	781.779	+	209.477i	0.973573	+	0.260868i
$804$		0			0
$805$	−3.46288	−	12.9236i	−0.00430171	−	0.0160542i
$806$	263.938	−	109.834i	0.327466	−	0.136271i
$807$		0			0
$808$	−7.68036	−	56.1996i	−0.00950540	−	0.0695539i
$809$	857.219			1.05960			0.529802	−	0.848121i	$-0.322266\pi$
$809$	857.219			1.05960			0.529802	+	0.848121i	$0.322266\pi$
$810$		0			0
$811$	−854.936	+	854.936i	−1.05417	+	1.05417i	−0.0557286	+	0.998446i	$0.517748\pi$
$811$	−854.936	+	854.936i	−1.05417	+	1.05417i	−0.998446	+	0.0557286i	$0.982252\pi$
$812$	5.59515	+	1705.43i	0.00689058	+	2.10029i
$813$		0			0
$814$	510.044	−	1237.09i	0.626590	−	1.51977i
$815$	46.3224	+	26.7442i	0.0568373	+	0.0328150i
$816$		0			0
$817$	20.0066	+	34.6525i	0.0244879	+	0.0424143i
$818$	−94.8037	−	711.090i	−0.115897	−	0.869303i
$819$		0			0
$820$	−50.8686	−	29.1469i	−0.0620349	−	0.0355450i
$821$	83.1824	−	310.441i	0.101318	−	0.378125i	−0.896583	−	0.442876i	$-0.853958\pi$
$821$	83.1824	−	310.441i	0.101318	−	0.378125i	0.997902	+	0.0647501i	$0.0206250\pi$
$822$		0			0
$823$	822.249	+	474.725i	0.999087	+	0.576823i	0.907978	−	0.419018i	$-0.137626\pi$
$823$	822.249	+	474.725i	0.999087	+	0.576823i	0.0911090	+	0.995841i	$0.470959\pi$
$824$	1185.74	+	150.174i	1.43901	+	0.182249i
$825$		0			0
$826$	742.721	+	96.5419i	0.899178	+	0.116879i
$827$	−630.068	−	630.068i	−0.761872	−	0.761872i	0.214789	−	0.976661i	$-0.431094\pi$
$827$	−630.068	−	630.068i	−0.761872	−	0.761872i	−0.976661	+	0.214789i	$0.931094\pi$
$828$		0			0
$829$	−1126.08	−	1126.08i	−1.35836	−	1.35836i	−0.875945	−	0.482410i	$-0.839761\pi$
$829$	−1126.08	−	1126.08i	−1.35836	−	1.35836i	−0.482410	−	0.875945i	$-0.660239\pi$
$830$	−26.3932	−	34.2797i	−0.0317990	−	0.0413008i
$831$		0			0
$832$	157.233	−	278.633i	0.188982	−	0.334896i
$833$	468.939	+	270.742i	0.562952	+	0.325021i
$834$		0			0
$835$	4.50624	−	16.8175i	0.00539669	−	0.0201407i
$836$	55.9377	+	206.056i	0.0669112	+	0.246478i
$837$		0			0
$838$	−282.874	+	369.903i	−0.337558	+	0.441412i
$839$	−811.916	−	1406.28i	−0.967719	−	1.67614i	−0.702126	−	0.712053i	$-0.747766\pi$
$839$	−811.916	−	1406.28i	−0.967719	−	1.67614i	−0.265593	−	0.964085i	$-0.585568\pi$
$840$		0			0
$841$	1526.19	+	881.147i	1.81473	+	1.04774i
$842$	502.059	+	1206.48i	0.596270	+	1.43287i
$843$		0			0
$844$	3.99588	+	1217.97i	0.00473446	+	1.44309i
$845$	−45.5444	+	45.5444i	−0.0538987	+	0.0538987i
$846$		0			0
$847$	2653.85			3.13323
$848$	343.907	+	1250.60i	0.405551	+	1.47476i
$849$		0			0
$850$	−491.509	+	1192.14i	−0.578246	+	1.40251i
$851$	−29.6006	−	110.471i	−0.0347833	−	0.129813i
$852$		0			0
$853$	484.839	+	129.912i	0.568393	+	0.152300i	0.531560	−	0.847021i	$-0.321606\pi$
$853$	484.839	+	129.912i	0.568393	+	0.152300i	0.0368336	+	0.999321i	$0.488273\pi$
$854$	−744.736	+	973.863i	−0.872057	+	1.14035i
$855$		0			0
$856$	−369.092	−	150.759i	−0.431183	−	0.176121i
$857$	570.829	+	988.705i	0.666078	+	1.15368i	0.978992	+	0.203899i	$0.0653615\pi$
$857$	570.829	+	988.705i	0.666078	+	1.15368i	−0.312914	+	0.949782i	$0.601305\pi$
$858$		0			0
$859$	−140.207	−	523.261i	−0.163222	−	0.609151i	−0.998260	−	0.0589600i	$-0.981222\pi$
$859$	−140.207	−	523.261i	−0.163222	−	0.609151i	0.835039	−	0.550191i	$-0.185445\pi$
$860$	−7.18001	+	27.1522i	−0.00834885	+	0.0315723i
$861$		0			0
$862$	−760.772	+	585.746i	−0.882566	+	0.679520i
$863$			28.7631i			0.0333292i	0.999861	+	0.0166646i	$0.00530475\pi$
$863$			28.7631i			0.0333292i	−0.999861	+	0.0166646i	$0.994695\pi$
$864$		0			0
$865$	95.7208			0.110660
$866$	386.846	+	502.439i	0.446704	+	0.580183i
$867$		0			0
$868$	923.991	+	244.336i	1.06451	+	0.281494i
$869$	−1206.90	+	323.389i	−1.38884	+	0.372139i
$870$		0			0
$871$	−205.633	+	118.722i	−0.236088	+	0.136306i
$872$	849.478	+	346.978i	0.974172	+	0.397910i
$873$		0			0
$874$	14.4961	+	11.0855i	0.0165859	+	0.0126836i
$875$	48.1723	−	179.781i	0.0550541	−	0.205465i
$876$		0			0
$877$	−973.836	+	260.939i	−1.11042	+	0.297535i	−0.767000	−	0.641647i	$-0.778251\pi$
$877$	−973.836	+	260.939i	−1.11042	+	0.297535i	−0.343417	+	0.939183i	$0.611585\pi$
$878$	336.870	+	138.889i	0.383679	+	0.158188i
$879$		0			0
$880$	−74.0799	+	130.277i	−0.0841817	+	0.148042i
$881$		−	442.006i		−	0.501710i	−0.968025	−	0.250855i	$-0.919288\pi$
$881$		−	442.006i		−	0.501710i	0.968025	−	0.250855i	$-0.0807117\pi$
$882$		0			0
$883$	−278.551	−	278.551i	−0.315459	−	0.315459i	0.531561	−	0.847020i	$-0.321606\pi$
$883$	−278.551	−	278.551i	−0.315459	−	0.315459i	−0.847020	+	0.531561i	$0.821606\pi$
$884$	−519.846	+	1.70550i	−0.588061	+	0.00192930i
$885$		0			0
$886$	351.643	−	146.331i	0.396888	−	0.165160i
$887$	−353.953	+	613.064i	−0.399045	+	0.691166i	−0.993608	−	0.112883i	$-0.963992\pi$
$887$	−353.953	+	613.064i	−0.399045	+	0.691166i	0.594563	+	0.804049i	$0.297325\pi$
$888$		0			0
$889$	485.570	−	280.344i	0.546198	−	0.315348i
$890$	−56.3827	−	43.1172i	−0.0633513	−	0.0484463i
$891$		0			0
$892$	66.9758	−	18.1818i	0.0750850	−	0.0203832i
$893$	−96.0267	−	25.7303i	−0.107533	−	0.0288133i
$894$		0			0
$895$	9.43665	−	16.3447i	0.0105437	−	0.0182623i
$896$	983.425	−	420.642i	1.09757	−	0.469466i
$897$		0			0
$898$	−35.6601	+	27.4560i	−0.0397106	+	0.0305746i
$899$	1031.61	−	1031.61i	1.14751	−	1.14751i
$900$		0			0
$901$	1490.21	−	1490.21i	1.65395	−	1.65395i
$902$	176.926	−	1361.14i	0.196149	−	1.50902i
$903$		0			0
$904$	−488.719	−	61.8959i	−0.540618	−	0.0684689i
$905$	−52.3046	+	90.5942i	−0.0577951	+	0.100104i
$906$		0			0
$907$	1006.46	+	269.681i	1.10966	+	0.297333i	0.766692	−	0.642015i	$-0.221901\pi$
$907$	1006.46	+	269.681i	1.10966	+	0.297333i	0.342968	+	0.939347i	$0.388568\pi$
$908$	728.413	−	1271.26i	0.802217	−	1.40007i
$909$		0			0
$910$	37.0390	−	4.93810i	0.0407021	−	0.00542648i
$911$	−867.790	+	501.019i	−0.952569	+	0.549966i	−0.893878	−	0.448310i	$-0.852026\pi$
$911$	−867.790	+	501.019i	−0.952569	+	0.549966i	−0.0586910	+	0.998276i	$0.518693\pi$
$912$		0			0
$913$	506.440	−	877.180i	0.554699	−	0.960766i
$914$	−17.1530	−	7.07206i	−0.0187670	−	0.00773749i
$915$		0			0
$916$	294.846	−	0.967325i	0.321884	−	0.00105603i
$917$	770.603	+	770.603i	0.840352	+	0.840352i
$918$		0			0
$919$		−	1047.84i		−	1.14020i	−0.821576	−	0.570100i	$-0.806905\pi$
$919$		−	1047.84i		−	1.14020i	0.821576	−	0.570100i	$-0.193095\pi$
$920$	1.73439	+	12.6911i	0.00188520	+	0.0137946i
$921$		0			0
$922$	485.598	+	1166.92i	0.526679	+	1.26564i
$923$	−127.861	+	34.2603i	−0.138528	+	0.0371184i
$924$		0			0
$925$	205.061	−	765.297i	0.221687	−	0.827348i
$926$	−474.373	+	63.2442i	−0.512282	+	0.0682982i
$927$		0			0
$928$	199.829	−	1620.45i	0.215333	−	1.74617i
$929$	−1368.64	+	790.183i	−1.47324	+	0.850573i	−0.999546	−	0.0301183i	$-0.990412\pi$
$929$	−1368.64	+	790.183i	−1.47324	+	0.850573i	−0.473690	+	0.880692i	$0.657078\pi$
$930$		0			0
$931$	51.2783	−	13.7400i	0.0550787	−	0.0147583i
$932$	−361.924	+	1368.66i	−0.388330	+	1.46852i
$933$		0			0
$934$	1305.74	+	169.726i	1.39801	+	0.181719i
$935$	243.511			0.260440
$936$		0			0
$937$			810.532i			0.865029i	0.901627	+	0.432514i	$0.142374\pi$
$937$			810.532i			0.865029i	−0.901627	+	0.432514i	$0.857626\pi$
$938$	−787.202	−	102.324i	−0.839235	−	0.109087i
$939$		0			0
$940$	−35.0877	−	60.3158i	−0.0373273	−	0.0641658i
$941$	−219.396	−	818.799i	−0.233152	−	0.870137i	−0.978973	−	0.203990i	$-0.934609\pi$
$941$	−219.396	−	818.799i	−0.233152	−	0.870137i	0.745821	−	0.666147i	$-0.232058\pi$
$942$		0			0
$943$	−58.6573	−	101.597i	−0.0622029	−	0.107739i
$944$	−693.802	−	181.033i	−0.734960	−	0.191772i
$945$		0			0
$946$	−651.773	+	86.8954i	−0.688978	+	0.0918556i
$947$	−150.555	−	40.3411i	−0.158981	−	0.0425988i	0.178451	−	0.983949i	$-0.442891\pi$
$947$	−150.555	−	40.3411i	−0.158981	−	0.0425988i	−0.337432	+	0.941350i	$0.609558\pi$
$948$		0			0
$949$	50.0025	+	186.612i	0.0526897	+	0.196641i
$950$	48.5708	+	116.718i	0.0511272	+	0.122861i
$951$		0			0
$952$	−1384.01	−	1051.21i	−1.45379	−	1.10421i
$953$	−488.369			−0.512455			−0.256227	−	0.966617i	$-0.582480\pi$
$953$	−488.369			−0.512455			−0.256227	+	0.966617i	$0.582480\pi$
$954$		0			0
$955$	−63.7020	+	63.7020i	−0.0667037	+	0.0667037i
$956$	761.628	−	766.642i	0.796682	−	0.801927i
$957$		0			0
$958$	−582.411	−	240.124i	−0.607945	−	0.250651i
$959$	318.879	+	184.105i	0.332512	+	0.191976i
$960$		0			0
$961$	71.7020	+	124.192i	0.0746119	+	0.129232i
$962$	316.608	−	42.2107i	0.329114	−	0.0438781i
$963$		0			0
$964$	−1026.58	+	278.684i	−1.06492	+	0.289091i
$965$	−9.03180	+	33.7071i	−0.00935938	+	0.0349297i
$966$		0			0
$967$	1242.23	+	717.199i	1.28462	+	0.741674i	0.977689	−	0.210058i	$-0.0673653\pi$
$967$	1242.23	+	717.199i	1.28462	+	0.741674i	0.306929	+	0.951732i	$0.400699\pi$
$968$	−2520.55	−	319.226i	−2.60387	−	0.329779i
$969$		0			0
$970$	−3.77741	+	29.0606i	−0.00389424	+	0.0299594i
$971$	889.980	+	889.980i	0.916560	+	0.916560i	0.996777	−	0.0802175i	$-0.0255615\pi$
$971$	889.980	+	889.980i	0.916560	+	0.916560i	−0.0802175	+	0.996777i	$0.525561\pi$
$972$		0			0
$973$	1266.17	+	1266.17i	1.30130	+	1.30130i
$974$	750.101	−	577.530i	0.770124	−	0.592947i
$975$		0			0
$976$	824.474	−	835.365i	0.844748	−	0.855907i
$977$	608.234	+	351.164i	0.622553	+	0.359431i	0.777862	−	0.628435i	$-0.216304\pi$
$977$	608.234	+	351.164i	0.622553	+	0.359431i	−0.155309	+	0.987866i	$0.549637\pi$
$978$		0			0
$979$	430.100	−	1605.16i	0.439326	−	1.63959i
$980$	32.3309	+	18.5251i	0.0329907	+	0.0189032i
$981$		0			0
$982$	−303.417	−	232.030i	−0.308978	−	0.236283i
$983$	902.729	+	1563.57i	0.918341	+	1.59061i	0.801935	+	0.597411i	$0.203804\pi$
$983$	902.729	+	1563.57i	0.918341	+	1.59061i	0.116406	+	0.993202i	$0.462863\pi$
$984$		0			0
$985$	20.5728	+	11.8777i	0.0208861	+	0.0120586i
$986$	−2449.32	+	1019.25i	−2.48410	+	1.03373i
$987$		0			0
$988$	−35.9200	+	36.1565i	−0.0363563	+	0.0365956i
$989$	−39.7392	+	39.7392i	−0.0401812	+	0.0401812i
$990$		0			0
$991$	94.2676			0.0951238			0.0475619	−	0.998868i	$-0.484855\pi$
$991$	94.2676			0.0951238			0.0475619	+	0.998868i	$0.484855\pi$
$992$	−848.190	−	343.209i	−0.855030	−	0.345977i
$993$		0			0
$994$	−409.136	−	168.684i	−0.411606	−	0.169702i
$995$	3.65870	+	13.6545i	0.00367709	+	0.0137231i
$996$		0			0
$997$	−1192.49	−	319.525i	−1.19607	−	0.320487i	−0.394790	−	0.918772i	$-0.629183\pi$
$997$	−1192.49	−	319.525i	−1.19607	−	0.320487i	−0.801284	+	0.598285i	$0.795849\pi$
$998$	386.796	+	295.792i	0.387571	+	0.296385i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.x.a.125.14		184
3.2	odd	2		144.3.w.a.77.33	yes	184
9.2	odd	6	inner	432.3.x.a.413.29		184
9.7	even	3		144.3.w.a.29.18	yes	184
16.5	even	4	inner	432.3.x.a.341.29		184
48.5	odd	4		144.3.w.a.5.18	✓	184
144.101	odd	12	inner	432.3.x.a.197.14		184
144.133	even	12		144.3.w.a.101.33	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.w.a.5.18	✓	184	48.5	odd	4
144.3.w.a.29.18	yes	184	9.7	even	3
144.3.w.a.77.33	yes	184	3.2	odd	2
144.3.w.a.101.33	yes	184	144.133	even	12
432.3.x.a.125.14		184	1.1	even	1	trivial
432.3.x.a.197.14		184	144.101	odd	12	inner
432.3.x.a.341.29		184	16.5	even	4	inner
432.3.x.a.413.29		184	9.2	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22012 - 1.58471i) q^{2} +(-1.02259 + 3.86708i) q^{4} +(0.432017 - 0.115759i) q^{5} +(-7.23679 + 4.17816i) q^{7} +(7.37588 - 3.09780i) q^{8} +O(q^{10})\)	\(q+(-1.22012 - 1.58471i) q^{2} +(-1.02259 + 3.86708i) q^{4} +(0.432017 - 0.115759i) q^{5} +(-7.23679 + 4.17816i) q^{7} +(7.37588 - 3.09780i) q^{8} +(-0.710557 - 0.543380i) q^{10} +(5.42030 - 20.2288i) q^{11} +(4.82865 - 1.29383i) q^{13} +(15.4509 + 6.37032i) q^{14} +(-13.9086 - 7.90891i) q^{16} +25.9977i q^{17} +(1.80229 + 1.80229i) q^{19} +(0.00586937 + 1.78902i) q^{20} +(-38.6702 + 16.0921i) q^{22} +(-1.78994 + 3.10027i) q^{23} +(-21.4774 + 12.4000i) q^{25} +(-7.94191 - 6.07337i) q^{26} +(-8.75698 - 32.2578i) q^{28} +(-49.2839 - 13.2056i) q^{29} +(-14.2968 + 24.7628i) q^{31} +(4.43691 + 31.6909i) q^{32} +(41.1987 - 31.7204i) q^{34} +(-2.64276 + 2.64276i) q^{35} +(-22.5902 + 22.5902i) q^{37} +(0.657083 - 5.05511i) q^{38} +(2.82791 - 2.19212i) q^{40} +(-16.3853 + 28.3801i) q^{41} +(15.1638 + 4.06313i) q^{43} +(72.6837 + 41.6466i) q^{44} +(7.09697 - 0.946180i) q^{46} +(-33.7785 + 19.5020i) q^{47} +(10.4141 - 18.0377i) q^{49} +(45.8554 + 18.9059i) q^{50} +(0.0656020 + 19.9959i) q^{52} +(-57.3208 - 57.3208i) q^{53} -9.36664i q^{55} +(-40.4346 + 53.2358i) q^{56} +(39.2055 + 94.2131i) q^{58} +(43.2875 - 11.5988i) q^{59} +(-18.9861 + 70.8572i) q^{61} +(56.6857 - 7.55743i) q^{62} +(44.8072 - 45.6980i) q^{64} +(1.93629 - 1.11792i) q^{65} +(-45.8800 + 12.2935i) q^{67} +(-100.535 - 26.5851i) q^{68} +(7.41249 + 0.963505i) q^{70} -26.4797 q^{71} +38.6468i q^{73} +(63.3617 + 8.23601i) q^{74} +(-8.81259 + 5.12657i) q^{76} +(45.2938 + 169.039i) q^{77} +(-29.8313 - 51.6693i) q^{79} +(-6.92427 - 1.80674i) q^{80} +(64.9662 - 8.66140i) q^{82} +(46.7170 + 12.5178i) q^{83} +(3.00945 + 11.2314i) q^{85} +(-12.0629 - 28.9877i) q^{86} +(-22.6855 - 165.997i) q^{88} +79.3499 q^{89} +(-29.5381 + 29.5381i) q^{91} +(-10.1586 - 10.0922i) q^{92} +(72.1189 + 29.7341i) q^{94} +(0.987248 + 0.569988i) q^{95} +(-16.3804 - 28.3718i) q^{97} +(-41.2910 + 5.50499i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5	\( 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} - 120 q^{20} - 2 q^{22} - 72 q^{28} + 6 q^{29} - 4 q^{31} + 6 q^{32} + 6 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 160 q^{46} + 12 q^{47} + 472 q^{49} - 228 q^{50} - 2 q^{52} + 300 q^{56} - 92 q^{58} + 438 q^{59} - 2 q^{61} + 244 q^{64} + 12 q^{65} - 2 q^{67} + 144 q^{68} + 96 q^{70} - 246 q^{74} - 158 q^{76} + 6 q^{77} - 4 q^{79} - 388 q^{82} + 726 q^{83} + 48 q^{85} - 894 q^{86} + 22 q^{88} - 204 q^{91} + 348 q^{92} - 18 q^{94} + 12 q^{95} - 4 q^{97}+O(q^{100}) \) 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 - 120 * q^20 - 2 * q^22 - 72 * q^28 + 6 * q^29 - 4 * q^31 + 6 * q^32 + 6 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 160 * q^46 + 12 * q^47 + 472 * q^49 - 228 * q^50 - 2 * q^52 + 300 * q^56 - 92 * q^58 + 438 * q^59 - 2 * q^61 + 244 * q^64 + 12 * q^65 - 2 * q^67 + 144 * q^68 + 96 * q^70 - 246 * q^74 - 158 * q^76 + 6 * q^77 - 4 * q^79 - 388 * q^82 + 726 * q^83 + 48 * q^85 - 894 * q^86 + 22 * q^88 - 204 * q^91 + 348 * q^92 - 18 * q^94 + 12 * q^95 - 4 * q^97

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