LMFDB - Embedded newform 288.3.u.a.163.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,3,Mod(19,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 0]))

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

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

chi := DirichletCharacter("288.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	288.u (of order $8$, degree $4$, 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:	$7.84743161358$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			163.6
Character	$\chi$	$=$	288.163
Dual form			288.3.u.a.235.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.46783 - 1.35848i) q^{2} +(0.309042 - 3.98804i) q^{4} +(-1.74699 - 4.21761i) q^{5} +(-0.392379 - 0.392379i) q^{7} +(-4.96407 - 6.27359i) q^{8} +O(q^{10})$	\(q+(1.46783 - 1.35848i) q^{2} +(0.309042 - 3.98804i) q^{4} +(-1.74699 - 4.21761i) q^{5} +(-0.392379 - 0.392379i) q^{7} +(-4.96407 - 6.27359i) q^{8} +(-8.29385 - 3.81747i) q^{10} +(-2.90924 - 7.02353i) q^{11} +(-4.50555 + 10.8774i) q^{13} +(-1.10898 - 0.0429045i) q^{14} +(-15.8090 - 2.46495i) q^{16} -10.5402i q^{17} +(-1.88707 - 0.781651i) q^{19} +(-17.3599 + 5.66366i) q^{20} +(-13.8116 - 6.35718i) q^{22} +(0.445453 - 0.445453i) q^{23} +(2.94139 - 2.94139i) q^{25} +(8.16334 + 22.0868i) q^{26} +(-1.68608 + 1.44356i) q^{28} +(-0.741814 - 0.307270i) q^{29} -47.6947i q^{31} +(-26.5535 + 17.8581i) q^{32} +(-14.3187 - 15.4712i) q^{34} +(-0.969419 + 2.34038i) q^{35} +(14.5080 + 35.0255i) q^{37} +(-3.83176 + 1.41623i) q^{38} +(-17.7874 + 31.8965i) q^{40} +(11.3365 + 11.3365i) q^{41} +(-14.6421 - 35.3493i) q^{43} +(-28.9092 + 9.43161i) q^{44} +(0.0487080 - 1.25899i) q^{46} +80.5164 q^{47} -48.6921i q^{49} +(0.321625 - 8.31328i) q^{50} +(41.9870 + 21.3299i) q^{52} +(66.6128 - 27.5919i) q^{53} +(-24.5401 + 24.5401i) q^{55} +(-0.513828 + 4.40942i) q^{56} +(-1.50628 + 0.556724i) q^{58} +(-65.0706 + 26.9531i) q^{59} +(87.4322 + 36.2156i) q^{61} +(-64.7925 - 70.0077i) q^{62} +(-14.7160 + 62.2852i) q^{64} +53.7476 q^{65} +(-7.12379 + 17.1984i) q^{67} +(-42.0348 - 3.25737i) q^{68} +(1.75643 + 4.75222i) q^{70} +(14.8103 + 14.8103i) q^{71} +(18.6720 + 18.6720i) q^{73} +(68.8769 + 31.7025i) q^{74} +(-3.70044 + 7.28417i) q^{76} +(-1.61436 + 3.89741i) q^{77} -36.2398 q^{79} +(17.2220 + 70.9824i) q^{80} +(32.0406 + 1.23959i) q^{82} +(-27.0868 - 11.2197i) q^{83} +(-44.4545 + 18.4137i) q^{85} +(-69.5135 - 31.9955i) q^{86} +(-29.6211 + 53.1167i) q^{88} +(56.4944 - 56.4944i) q^{89} +(6.03592 - 2.50016i) q^{91} +(-1.63882 - 1.91415i) q^{92} +(118.184 - 109.380i) q^{94} +9.32448i q^{95} +158.579 q^{97} +(-66.1474 - 71.4716i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8	$ 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 44 q^{10} + 4 q^{11} - 4 q^{13} + 20 q^{14} + 16 q^{16} - 4 q^{19} - 76 q^{20} + 144 q^{22} + 68 q^{23} - 4 q^{25} - 96 q^{26} + 56 q^{28} + 4 q^{29} + 24 q^{32} - 48 q^{34} - 92 q^{35} - 4 q^{37} + 396 q^{38} - 408 q^{40} + 4 q^{41} + 92 q^{43} + 188 q^{44} - 36 q^{46} + 8 q^{47} - 308 q^{50} + 420 q^{52} + 164 q^{53} + 252 q^{55} - 552 q^{56} + 528 q^{58} - 124 q^{59} - 68 q^{61} - 216 q^{62} - 232 q^{64} + 8 q^{65} - 164 q^{67} + 368 q^{68} - 664 q^{70} + 260 q^{71} - 4 q^{73} + 532 q^{74} - 516 q^{76} - 220 q^{77} - 520 q^{79} - 312 q^{80} + 636 q^{82} + 484 q^{83} + 96 q^{85} - 688 q^{86} + 672 q^{88} + 4 q^{89} - 196 q^{91} - 616 q^{92} + 40 q^{94} - 8 q^{97} + 328 q^{98}+O(q^{100}) $ 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 44 * q^10 + 4 * q^11 - 4 * q^13 + 20 * q^14 + 16 * q^16 - 4 * q^19 - 76 * q^20 + 144 * q^22 + 68 * q^23 - 4 * q^25 - 96 * q^26 + 56 * q^28 + 4 * q^29 + 24 * q^32 - 48 * q^34 - 92 * q^35 - 4 * q^37 + 396 * q^38 - 408 * q^40 + 4 * q^41 + 92 * q^43 + 188 * q^44 - 36 * q^46 + 8 * q^47 - 308 * q^50 + 420 * q^52 + 164 * q^53 + 252 * q^55 - 552 * q^56 + 528 * q^58 - 124 * q^59 - 68 * q^61 - 216 * q^62 - 232 * q^64 + 8 * q^65 - 164 * q^67 + 368 * q^68 - 664 * q^70 + 260 * q^71 - 4 * q^73 + 532 * q^74 - 516 * q^76 - 220 * q^77 - 520 * q^79 - 312 * q^80 + 636 * q^82 + 484 * q^83 + 96 * q^85 - 688 * q^86 + 672 * q^88 + 4 * q^89 - 196 * q^91 - 616 * q^92 + 40 * q^94 - 8 * q^97 + 328 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.46783	−	1.35848i	0.733914	−	0.679242i
$2$	1.46783	−	1.35848i	0.733914	−	0.679242i
$3$		0			0
$3$		0			0
$4$	0.309042	−	3.98804i	0.0772606	−	0.997011i
$5$	−1.74699	−	4.21761i	−0.349399	−	0.843523i	−0.996691	−	0.0812812i	$-0.974099\pi$
$5$	−1.74699	−	4.21761i	−0.349399	−	0.843523i	0.647293	−	0.762242i	$-0.275901\pi$
$6$		0			0
$7$	−0.392379	−	0.392379i	−0.0560541	−	0.0560541i	0.678524	−	0.734578i	$-0.262620\pi$
$7$	−0.392379	−	0.392379i	−0.0560541	−	0.0560541i	−0.734578	+	0.678524i	$0.762620\pi$
$8$	−4.96407	−	6.27359i	−0.620509	−	0.784199i
$9$		0			0
$10$	−8.29385	−	3.81747i	−0.829385	−	0.381747i
$11$	−2.90924	−	7.02353i	−0.264477	−	0.638503i	0.734729	−	0.678361i	$-0.237309\pi$
$11$	−2.90924	−	7.02353i	−0.264477	−	0.638503i	−0.999205	+	0.0398581i	$0.987309\pi$
$12$		0			0
$13$	−4.50555	+	10.8774i	−0.346581	+	0.836720i	0.650438	+	0.759559i	$0.274585\pi$
$13$	−4.50555	+	10.8774i	−0.346581	+	0.836720i	−0.997019	+	0.0771604i	$0.975415\pi$
$14$	−1.10898	−	0.0429045i	−0.0792132	−	0.00306461i
$15$		0			0
$16$	−15.8090	−	2.46495i	−0.988062	−	0.154059i
$17$		−	10.5402i		−	0.620012i	−0.950735	−	0.310006i	$-0.899669\pi$
$17$		−	10.5402i		−	0.620012i	0.950735	−	0.310006i	$-0.100331\pi$
$18$		0			0
$19$	−1.88707	−	0.781651i	−0.0993196	−	0.0411395i	0.332470	−	0.943114i	$-0.392118\pi$
$19$	−1.88707	−	0.781651i	−0.0993196	−	0.0411395i	−0.431790	+	0.901974i	$0.642118\pi$
$20$	−17.3599	+	5.66366i	−0.867996	+	0.283183i
$21$		0			0
$22$	−13.8116	−	6.35718i	−0.627801	−	0.288963i
$23$	0.445453	−	0.445453i	0.0193675	−	0.0193675i	−0.697357	−	0.716724i	$-0.745641\pi$
$23$	0.445453	−	0.445453i	0.0193675	−	0.0193675i	0.716724	+	0.697357i	$0.245641\pi$
$24$		0			0
$25$	2.94139	−	2.94139i	0.117656	−	0.117656i
$26$	8.16334	+	22.0868i	0.313975	+	0.849493i
$27$		0			0
$28$	−1.68608	+	1.44356i	−0.0602173	+	0.0515558i
$29$	−0.741814	−	0.307270i	−0.0255798	−	0.0105955i	0.369857	−	0.929089i	$-0.379407\pi$
$29$	−0.741814	−	0.307270i	−0.0255798	−	0.0105955i	−0.395437	+	0.918493i	$0.629407\pi$
$30$		0			0
$31$		−	47.6947i		−	1.53854i	−0.638924	−	0.769270i	$-0.720620\pi$
$31$		−	47.6947i		−	1.53854i	0.638924	−	0.769270i	$-0.279380\pi$
$32$	−26.5535	+	17.8581i	−0.829796	+	0.558067i
$33$		0			0
$34$	−14.3187	−	15.4712i	−0.421138	−	0.455036i
$35$	−0.969419	+	2.34038i	−0.0276977	+	0.0668681i
$36$		0			0
$37$	14.5080	+	35.0255i	0.392109	+	0.946635i	0.989480	+	0.144670i	$0.0462120\pi$
$37$	14.5080	+	35.0255i	0.392109	+	0.946635i	−0.597371	+	0.801965i	$0.703788\pi$
$38$	−3.83176	+	1.41623i	−0.100836	+	0.0372692i
$39$		0			0
$40$	−17.7874	+	31.8965i	−0.444685	+	0.797412i
$41$	11.3365	+	11.3365i	0.276501	+	0.276501i	0.831711	−	0.555209i	$-0.187362\pi$
$41$	11.3365	+	11.3365i	0.276501	+	0.276501i	−0.555209	+	0.831711i	$0.687362\pi$
$42$		0			0
$43$	−14.6421	−	35.3493i	−0.340515	−	0.822076i	−0.997664	−	0.0683149i	$-0.978238\pi$
$43$	−14.6421	−	35.3493i	−0.340515	−	0.822076i	0.657149	−	0.753761i	$-0.271762\pi$
$44$	−28.9092	+	9.43161i	−0.657028	+	0.214355i
$45$		0			0
$46$	0.0487080	−	1.25899i	0.00105887	−	0.0273694i
$47$	80.5164			1.71312			0.856558	−	0.516051i	$-0.172598\pi$
$47$	80.5164			1.71312			0.856558	+	0.516051i	$0.172598\pi$
$48$		0			0
$49$		−	48.6921i		−	0.993716i
$50$	0.321625	−	8.31328i	0.00643251	−	0.166266i
$51$		0			0
$52$	41.9870	+	21.3299i	0.807442	+	0.410190i
$53$	66.6128	−	27.5919i	1.25685	−	0.520602i	0.347905	−	0.937530i	$-0.386893\pi$
$53$	66.6128	−	27.5919i	1.25685	−	0.520602i	0.908940	+	0.416927i	$0.136893\pi$
$54$		0			0
$55$	−24.5401	+	24.5401i	−0.446184	+	0.446184i
$56$	−0.513828	+	4.40942i	−0.00917551	+	0.0787396i
$57$		0			0
$58$	−1.50628	+	0.556724i	−0.0259703	+	0.00959869i
$59$	−65.0706	+	26.9531i	−1.10289	+	0.456833i	−0.858484	−	0.512840i	$-0.828594\pi$
$59$	−65.0706	+	26.9531i	−1.10289	+	0.456833i	−0.244408	+	0.969673i	$0.578594\pi$
$60$		0			0
$61$	87.4322	+	36.2156i	1.43331	+	0.593698i	0.958168	−	0.286208i	$-0.0923948\pi$
$61$	87.4322	+	36.2156i	1.43331	+	0.593698i	0.475147	+	0.879906i	$0.342395\pi$
$62$	−64.7925	−	70.0077i	−1.04504	−	1.12916i
$63$		0			0
$64$	−14.7160	+	62.2852i	−0.229937	+	0.973205i
$65$	53.7476			0.826887
$66$		0			0
$67$	−7.12379	+	17.1984i	−0.106325	+	0.256692i	−0.968084	−	0.250627i	$-0.919363\pi$
$67$	−7.12379	+	17.1984i	−0.106325	+	0.256692i	0.861759	+	0.507319i	$0.169363\pi$
$68$	−42.0348	−	3.25737i	−0.618159	−	0.0479025i
$69$		0			0
$70$	1.75643	+	4.75222i	0.0250919	+	0.0678889i
$71$	14.8103	+	14.8103i	0.208596	+	0.208596i	0.803671	−	0.595074i	$-0.202877\pi$
$71$	14.8103	+	14.8103i	0.208596	+	0.208596i	−0.595074	+	0.803671i	$0.702877\pi$
$72$		0			0
$73$	18.6720	+	18.6720i	0.255781	+	0.255781i	0.823336	−	0.567555i	$-0.192110\pi$
$73$	18.6720	+	18.6720i	0.255781	+	0.255781i	−0.567555	+	0.823336i	$0.692110\pi$
$74$	68.8769	+	31.7025i	0.930769	+	0.428412i
$75$		0			0
$76$	−3.70044	+	7.28417i	−0.0486901	+	0.0958443i
$77$	−1.61436	+	3.89741i	−0.0209657	+	0.0506157i
$78$		0			0
$79$	−36.2398			−0.458732			−0.229366	−	0.973340i	$-0.573665\pi$
$79$	−36.2398			−0.458732			−0.229366	+	0.973340i	$0.573665\pi$
$80$	17.2220	+	70.9824i	0.215275	+	0.887281i
$81$		0			0
$82$	32.0406	+	1.23959i	0.390739	+	0.0151170i
$83$	−27.0868	−	11.2197i	−0.326347	−	0.135177i	0.213494	−	0.976944i	$-0.431516\pi$
$83$	−27.0868	−	11.2197i	−0.326347	−	0.135177i	−0.539841	+	0.841767i	$0.681516\pi$
$84$		0			0
$85$	−44.4545	+	18.4137i	−0.522994	+	0.216631i
$86$	−69.5135	−	31.9955i	−0.808297	−	0.372041i
$87$		0			0
$88$	−29.6211	+	53.1167i	−0.336603	+	0.603599i
$89$	56.4944	−	56.4944i	0.634769	−	0.634769i	−0.314491	−	0.949260i	$-0.601834\pi$
$89$	56.4944	−	56.4944i	0.634769	−	0.634769i	0.949260	+	0.314491i	$0.101834\pi$
$90$		0			0
$91$	6.03592	−	2.50016i	0.0663288	−	0.0274743i
$92$	−1.63882	−	1.91415i	−0.0178133	−	0.0208060i
$93$		0			0
$94$	118.184	−	109.380i	1.25728	−	1.16362i
$95$			9.32448i			0.0981525i
$96$		0			0
$97$	158.579			1.63484			0.817419	−	0.576043i	$-0.195404\pi$
$97$	158.579			1.63484			0.817419	+	0.576043i	$0.195404\pi$
$98$	−66.1474	−	71.4716i	−0.674974	−	0.729302i
$99$		0			0
$100$	−10.8214	−	12.6394i	−0.108214	−	0.126394i
$101$	53.8420	+	129.986i	0.533089	+	1.28699i	0.929468	+	0.368903i	$0.120267\pi$
$101$	53.8420	+	129.986i	0.533089	+	1.28699i	−0.396379	+	0.918087i	$0.629733\pi$
$102$		0			0
$103$	9.94607	+	9.94607i	0.0965638	+	0.0965638i	0.753738	−	0.657175i	$-0.228249\pi$
$103$	9.94607	+	9.94607i	0.0965638	+	0.0965638i	−0.657175	+	0.753738i	$0.728249\pi$
$104$	90.6060	−	25.7300i	0.871211	−	0.247404i
$105$		0			0
$106$	60.2930	−	130.993i	0.568802	−	1.23578i
$107$	−68.8129	−	166.129i	−0.643111	−	1.55261i	−0.822461	−	0.568822i	$-0.807399\pi$
$107$	−68.8129	−	166.129i	−0.643111	−	1.55261i	0.179350	−	0.983785i	$-0.442601\pi$
$108$		0			0
$109$	3.61301	−	8.72257i	0.0331469	−	0.0800236i	−0.906439	−	0.422336i	$-0.861210\pi$
$109$	3.61301	−	8.72257i	0.0331469	−	0.0800236i	0.939586	+	0.342313i	$0.111210\pi$
$110$	−2.68333	+	69.3580i	−0.0243939	+	0.630528i
$111$		0			0
$112$	5.23591	+	7.17030i	0.0467492	+	0.0640205i
$113$			85.8345i			0.759598i	0.925069	+	0.379799i	$0.124007\pi$
$113$			85.8345i			0.759598i	−0.925069	+	0.379799i	$0.875993\pi$
$114$		0			0
$115$	−2.65695	−	1.10055i	−0.0231039	−	0.00956997i
$116$	−1.45466	+	2.86343i	−0.0125401	+	0.0246847i
$117$		0			0
$118$	−58.8971	+	127.960i	−0.499128	+	1.08441i
$119$	−4.13575	+	4.13575i	−0.0347542	+	0.0347542i
$120$		0			0
$121$	44.6936	−	44.6936i	0.369369	−	0.369369i
$122$	177.534	−	65.6169i	1.45520	−	0.537844i
$123$		0			0
$124$	−190.209	−	14.7397i	−1.53394	−	0.118869i
$125$	−122.985	−	50.9419i	−0.983877	−	0.407535i
$126$		0			0
$127$		−	17.2873i		−	0.136120i	−0.997681	−	0.0680601i	$-0.978319\pi$
$127$		−	17.2873i		−	0.136120i	0.997681	−	0.0680601i	$-0.0216810\pi$
$128$	63.0128	+	111.415i	0.492288	+	0.870432i
$129$		0			0
$130$	78.8923	−	73.0153i	0.606864	−	0.561656i
$131$	40.2223	−	97.1053i	0.307041	−	0.741262i	−0.692758	−	0.721171i	$-0.743604\pi$
$131$	40.2223	−	97.1053i	0.307041	−	0.741262i	0.999798	−	0.0200911i	$-0.00639562\pi$
$132$		0			0
$133$	0.433744	+	1.04715i	0.00326123	+	0.00787331i
$134$	12.9072	+	34.9218i	0.0963223	+	0.260610i
$135$		0			0
$136$	−66.1250	+	52.3224i	−0.486213	+	0.384723i
$137$	−25.5351	−	25.5351i	−0.186387	−	0.186387i	0.607745	−	0.794132i	$-0.292074\pi$
$137$	−25.5351	−	25.5351i	−0.186387	−	0.186387i	−0.794132	+	0.607745i	$0.792074\pi$
$138$		0			0
$139$	−52.2202	−	126.071i	−0.375685	−	0.906984i	−0.992764	−	0.120083i	$-0.961684\pi$
$139$	−52.2202	−	126.071i	−0.375685	−	0.906984i	0.617079	−	0.786901i	$-0.288316\pi$
$140$	9.03396	+	4.58936i	0.0645283	+	0.0327812i
$141$		0			0
$142$	41.8587	+	1.61943i	0.294779	+	0.0114045i
$143$	89.5052			0.625910
$144$		0			0
$145$			3.66548i			0.0252792i
$146$	52.7730	+	2.04169i	0.361459	+	0.0139842i
$147$		0			0
$148$	144.167	−	47.0343i	0.974100	−	0.317799i
$149$	−151.298	+	62.6697i	−1.01542	+	0.420602i	−0.827430	−	0.561569i	$-0.810198\pi$
$149$	−151.298	+	62.6697i	−1.01542	+	0.420602i	−0.187993	+	0.982170i	$0.560198\pi$
$150$		0			0
$151$	−123.292	+	123.292i	−0.816505	+	0.816505i	−0.985600	−	0.169095i	$-0.945916\pi$
$151$	−123.292	+	123.292i	−0.816505	+	0.816505i	0.169095	+	0.985600i	$0.445916\pi$
$152$	4.46380	+	15.7189i	0.0293671	+	0.103414i
$153$		0			0
$154$	2.92496	+	7.91381i	0.0189933	+	0.0513883i
$155$	−201.158	+	83.3223i	−1.29779	+	0.537563i
$156$		0			0
$157$	107.069	+	44.3494i	0.681968	+	0.282480i	0.696649	−	0.717412i	$-0.254673\pi$
$157$	107.069	+	44.3494i	0.681968	+	0.282480i	−0.0146813	+	0.999892i	$0.504673\pi$
$158$	−53.1939	+	49.2312i	−0.336670	+	0.311590i
$159$		0			0
$160$	121.707	+	80.7943i	0.760671	+	0.504964i
$161$	−0.349573			−0.00217126
$162$		0			0
$163$	−48.6441	+	117.437i	−0.298430	+	0.720474i	0.701539	+	0.712631i	$0.252497\pi$
$163$	−48.6441	+	117.437i	−0.298430	+	0.720474i	−0.999969	+	0.00784306i	$0.997503\pi$
$164$	48.7141	−	41.7072i	0.297037	−	0.254312i
$165$		0			0
$166$	−55.0006	+	20.3284i	−0.331329	+	0.122460i
$167$	−88.6392	−	88.6392i	−0.530774	−	0.530774i	0.390029	−	0.920803i	$-0.372465\pi$
$167$	−88.6392	−	88.6392i	−0.530774	−	0.530774i	−0.920803	+	0.390029i	$0.872465\pi$
$168$		0			0
$169$	21.4841	+	21.4841i	0.127125	+	0.127125i
$170$	−40.2370	+	87.4189i	−0.236688	+	0.514229i
$171$		0			0
$172$	−145.499	+	47.4691i	−0.845927	+	0.275983i
$173$	−87.2836	+	210.721i	−0.504530	+	1.21804i	0.442463	+	0.896787i	$0.354105\pi$
$173$	−87.2836	+	210.721i	−0.504530	+	1.21804i	−0.946993	+	0.321255i	$0.895895\pi$
$174$		0			0
$175$	−2.30827			−0.0131901
$176$	28.6795	+	118.206i	0.162952	+	0.671625i
$177$		0			0
$178$	6.17737	−	159.671i	0.0347043	−	0.897028i
$179$	5.53118	+	2.29109i	0.0309005	+	0.0127994i	0.398080	−	0.917351i	$-0.369677\pi$
$179$	5.53118	+	2.29109i	0.0309005	+	0.0127994i	−0.367180	+	0.930150i	$0.619677\pi$
$180$		0			0
$181$	−273.836	+	113.427i	−1.51291	+	0.626666i	−0.976155	−	0.217075i	$-0.930348\pi$
$181$	−273.836	+	113.427i	−1.51291	+	0.626666i	−0.536751	+	0.843741i	$0.680348\pi$
$182$	5.46327	−	11.8695i	0.0300180	−	0.0652171i
$183$		0			0
$184$	−5.00586	−	0.583331i	−0.0272057	−	0.00317028i
$185$	122.379	−	122.379i	0.661506	−	0.661506i
$186$		0			0
$187$	−74.0295	+	30.6640i	−0.395880	+	0.163979i
$188$	24.8830	−	321.103i	0.132356	−	1.70800i
$189$		0			0
$190$	12.6672	+	13.6867i	0.0666693	+	0.0720355i
$191$			140.503i			0.735620i	0.929901	+	0.367810i	$0.119892\pi$
$191$			140.503i			0.735620i	−0.929901	+	0.367810i	$0.880108\pi$
$192$		0			0
$193$	−159.719			−0.827560			−0.413780	−	0.910377i	$-0.635792\pi$
$193$	−159.719			−0.827560			−0.413780	+	0.910377i	$0.635792\pi$
$194$	232.767	−	215.427i	1.19983	−	1.11045i
$195$		0			0
$196$	−194.186	−	15.0479i	−0.990746	−	0.0767751i
$197$	23.3511	+	56.3745i	0.118533	+	0.286165i	0.971999	−	0.234984i	$-0.0755037\pi$
$197$	23.3511	+	56.3745i	0.118533	+	0.286165i	−0.853466	+	0.521149i	$0.825504\pi$
$198$		0			0
$199$	138.741	+	138.741i	0.697191	+	0.697191i	0.963804	−	0.266613i	$-0.0859044\pi$
$199$	138.741	+	138.741i	0.697191	+	0.697191i	−0.266613	+	0.963804i	$0.585904\pi$
$200$	−33.0543	−	3.85181i	−0.165272	−	0.0192591i
$201$		0			0
$202$	255.615	+	117.654i	1.26542	+	0.582444i
$203$	0.170506	+	0.411638i	0.000839931	+	0.00202777i
$204$		0			0
$205$	28.0083	−	67.6180i	0.136626	−	0.329844i
$206$	28.1107	+	1.08755i	0.136460	+	0.00527937i
$207$		0			0
$208$	98.0403	−	160.854i	0.471348	−	0.773337i
$209$			15.5279i			0.0742963i
$210$		0			0
$211$	−194.276	−	80.4718i	−0.920740	−	0.381383i	−0.128582	−	0.991699i	$-0.541043\pi$
$211$	−194.276	−	80.4718i	−0.920740	−	0.381383i	−0.792158	+	0.610316i	$0.791043\pi$
$212$	−89.4516	−	274.182i	−0.421942	−	1.29331i
$213$		0			0
$214$	−326.689	−	150.368i	−1.52658	−	0.702653i
$215$	−123.510	+	123.510i	−0.574464	+	0.574464i
$216$		0			0
$217$	−18.7144	+	18.7144i	−0.0862414	+	0.0862414i
$218$	−6.54620	−	17.7115i	−0.0300284	−	0.0812452i
$219$		0			0
$220$	90.2831	+	105.451i	0.410378	+	0.479323i
$221$	114.650	+	47.4894i	0.518776	+	0.214884i
$222$		0			0
$223$		−	285.957i		−	1.28232i	−0.767408	−	0.641160i	$-0.778454\pi$
$223$		−	285.957i		−	1.28232i	0.767408	−	0.641160i	$-0.221546\pi$
$224$	17.4262	+	3.41187i	0.0777954	+	0.0152316i
$225$		0			0
$226$	116.605	+	125.990i	0.515951	+	0.557480i
$227$	−8.02885	+	19.3834i	−0.0353694	+	0.0853893i	−0.940577	−	0.339580i	$-0.889715\pi$
$227$	−8.02885	+	19.3834i	−0.0353694	+	0.0853893i	0.905208	+	0.424969i	$0.139715\pi$
$228$		0			0
$229$	−66.9028	−	161.518i	−0.292152	−	0.705317i	0.707848	−	0.706365i	$-0.249666\pi$
$229$	−66.9028	−	161.518i	−0.292152	−	0.705317i	−0.999999	+	0.00104819i	$0.999666\pi$
$230$	−5.39503	+	1.99402i	−0.0234566	+	0.00866963i
$231$		0			0
$232$	1.75474	+	6.17915i	0.00756352	+	0.0266343i
$233$	−282.286	−	282.286i	−1.21153	−	1.21153i	−0.970525	−	0.241001i	$-0.922524\pi$
$233$	−282.286	−	282.286i	−1.21153	−	1.21153i	−0.241001	−	0.970525i	$-0.577476\pi$
$234$		0			0
$235$	−140.662	−	339.587i	−0.598560	−	1.44505i
$236$	87.3807	+	267.834i	0.370257	+	1.13489i
$237$		0			0
$238$	−0.452223	+	11.6889i	−0.00190010	+	0.0491131i
$239$	−13.1618			−0.0550704			−0.0275352	−	0.999621i	$-0.508766\pi$
$239$	−13.1618			−0.0550704			−0.0275352	+	0.999621i	$0.508766\pi$
$240$		0			0
$241$			231.745i			0.961599i	0.876830	+	0.480800i	$0.159654\pi$
$241$			231.745i			0.961599i	−0.876830	+	0.480800i	$0.840346\pi$
$242$	4.88701	−	126.318i	0.0201943	−	0.521976i
$243$		0			0
$244$	171.450	−	337.491i	0.702663	−	1.38316i
$245$	−205.364	+	85.0647i	−0.838222	+	0.347203i
$246$		0			0
$247$	17.0046	−	17.0046i	0.0688445	−	0.0688445i
$248$	−299.217	+	236.760i	−1.20652	+	0.954678i
$249$		0			0
$250$	−249.724	+	92.2986i	−0.998896	+	0.369194i
$251$	−131.701	+	54.5521i	−0.524703	+	0.217339i	−0.629281	−	0.777177i	$-0.716651\pi$
$251$	−131.701	+	54.5521i	−0.524703	+	0.217339i	0.104578	+	0.994517i	$0.466651\pi$
$252$		0			0
$253$	−4.42459	−	1.83272i	−0.0174885	−	0.00724397i
$254$	−23.4845	−	25.3748i	−0.0924586	−	0.0999006i
$255$		0			0
$256$	243.848	+	77.9367i	0.952531	+	0.304440i
$257$	70.0955			0.272745			0.136373	−	0.990658i	$-0.456456\pi$
$257$	70.0955			0.272745			0.136373	+	0.990658i	$0.456456\pi$
$258$		0			0
$259$	8.05061	−	19.4359i	0.0310834	−	0.0750420i
$260$	16.6103	−	214.348i	0.0638858	−	0.824415i
$261$		0			0
$262$	−72.8765	−	197.175i	−0.278155	−	0.752577i
$263$	245.883	+	245.883i	0.934916	+	0.934916i	0.998008	−	0.0630921i	$-0.0200962\pi$
$263$	245.883	+	245.883i	0.934916	+	0.934916i	−0.0630921	+	0.998008i	$0.520096\pi$
$264$		0			0
$265$	−232.744	−	232.744i	−0.878280	−	0.878280i
$266$	2.05920	+	0.947803i	0.00774135	+	0.00356317i
$267$		0			0
$268$	66.3862	+	33.7250i	0.247710	+	0.125840i
$269$	−7.33716	+	17.7135i	−0.0272757	+	0.0658493i	−0.936931	−	0.349516i	$-0.886346\pi$
$269$	−7.33716	+	17.7135i	−0.0272757	+	0.0658493i	0.909655	+	0.415365i	$0.136346\pi$
$270$		0			0
$271$	327.600			1.20886			0.604429	−	0.796659i	$-0.293401\pi$
$271$	327.600			1.20886			0.604429	+	0.796659i	$0.293401\pi$
$272$	−25.9811	+	166.630i	−0.0955187	+	0.612610i
$273$		0			0
$274$	−72.1701	−	2.79213i	−0.263394	−	0.0101902i
$275$	−29.2161	−	12.1017i	−0.106240	−	0.0440063i
$276$		0			0
$277$	−31.9345	+	13.2277i	−0.115287	+	0.0477535i	−0.439581	−	0.898203i	$-0.644873\pi$
$277$	−31.9345	+	13.2277i	−0.115287	+	0.0477535i	0.324294	+	0.945956i	$0.394873\pi$
$278$	−247.916	−	114.110i	−0.891783	−	0.410468i
$279$		0			0
$280$	19.4949	−	5.53609i	0.0696246	−	0.0197718i
$281$	263.413	−	263.413i	0.937413	−	0.937413i	−0.0607409	−	0.998154i	$-0.519346\pi$
$281$	263.413	−	263.413i	0.937413	−	0.937413i	0.998154	+	0.0607409i	$0.0193463\pi$
$282$		0			0
$283$	−268.113	+	111.056i	−0.947397	+	0.392425i	−0.802252	−	0.596986i	$-0.796365\pi$
$283$	−268.113	+	111.056i	−0.947397	+	0.392425i	−0.145145	+	0.989410i	$0.546365\pi$
$284$	63.6413	−	54.4873i	0.224089	−	0.191857i
$285$		0			0
$286$	131.378	−	121.591i	0.459365	−	0.425145i
$287$		−	8.89644i		−	0.0309980i
$288$		0			0
$289$	177.904			0.615585
$290$	4.97950	+	5.38030i	0.0171707	+	0.0185528i
$291$		0			0
$292$	80.2353	−	68.6944i	0.274778	−	0.235255i
$293$	−44.7772	−	108.102i	−0.152823	−	0.368948i	0.828863	−	0.559451i	$-0.188988\pi$
$293$	−44.7772	−	108.102i	−0.152823	−	0.368948i	−0.981687	+	0.190503i	$0.938988\pi$
$294$		0			0
$295$	227.356	+	227.356i	0.770698	+	0.770698i
$296$	147.717	−	264.887i	0.499043	−	0.894887i
$297$		0			0
$298$	−136.944	+	297.524i	−0.459543	+	0.998404i
$299$	2.83834	+	6.85237i	0.00949279	+	0.0229176i
$300$		0			0
$301$	−8.12503	+	19.6155i	−0.0269934	+	0.0651679i
$302$	−13.4814	+	348.462i	−0.0446403	+	1.15385i
$303$		0			0
$304$	27.9060	+	17.0087i	0.0917960	+	0.0559495i
$305$		−	432.024i		−	1.41647i
$306$		0			0
$307$	430.497	+	178.318i	1.40227	+	0.580839i	0.950340	−	0.311215i	$-0.100736\pi$
$307$	430.497	+	178.318i	1.40227	+	0.580839i	0.451930	+	0.892054i	$0.350736\pi$
$308$	15.0441	+	7.64260i	0.0488446	+	0.0248136i
$309$		0			0
$310$	−182.073	+	395.573i	−0.587333	+	1.27604i
$311$	61.3250	−	61.3250i	0.197187	−	0.197187i	−0.601606	−	0.798793i	$-0.705472\pi$
$311$	61.3250	−	61.3250i	0.197187	−	0.197187i	0.798793	+	0.601606i	$0.205472\pi$
$312$		0			0
$313$	129.308	−	129.308i	0.413124	−	0.413124i	−0.469701	−	0.882826i	$-0.655638\pi$
$313$	129.308	−	129.308i	0.413124	−	0.413124i	0.882826	+	0.469701i	$0.155638\pi$
$314$	217.407	−	80.3541i	0.692379	−	0.255905i
$315$		0			0
$316$	−11.1996	+	144.526i	−0.0354419	+	0.457361i
$317$	286.711	+	118.760i	0.904452	+	0.374636i	0.785930	−	0.618315i	$-0.212184\pi$
$317$	286.711	+	118.760i	0.904452	+	0.374636i	0.118522	+	0.992951i	$0.462184\pi$
$318$		0			0
$319$			6.10408i			0.0191350i
$320$	288.403	−	46.7454i	0.901261	−	0.146079i
$321$		0			0
$322$	−0.513113	+	0.474889i	−0.00159352	+	0.00147481i
$323$	−8.23877	+	19.8901i	−0.0255070	+	0.0615794i
$324$		0			0
$325$	18.7420	+	45.2471i	0.0576676	+	0.139222i
$326$	88.1354	+	238.460i	0.270354	+	0.731472i
$327$		0			0
$328$	14.8455	−	127.396i	0.0452606	−	0.388403i
$329$	−31.5929	−	31.5929i	−0.0960271	−	0.0960271i
$330$		0			0
$331$	123.164	+	297.345i	0.372098	+	0.898324i	0.993395	+	0.114748i	$0.0366061\pi$
$331$	123.164	+	297.345i	0.372098	+	0.898324i	−0.621297	+	0.783575i	$0.713394\pi$
$332$	−53.1158	+	104.556i	−0.159987	+	0.314928i
$333$		0			0
$334$	−250.522	−	9.69223i	−0.750066	−	0.0290187i
$335$	84.9812			0.253675
$336$		0			0
$337$			263.653i			0.782354i	0.920315	+	0.391177i	$0.127932\pi$
$337$			263.653i			0.782354i	−0.920315	+	0.391177i	$0.872068\pi$
$338$	60.7209	+	2.34918i	0.179648	+	0.00695023i
$339$		0			0
$340$	59.6962	+	182.977i	0.175577	+	0.538168i
$341$	−334.985	+	138.755i	−0.982362	+	0.406908i
$342$		0			0
$343$	−38.3323	+	38.3323i	−0.111756	+	0.111756i
$344$	−149.082	+	267.335i	−0.433379	+	0.777137i
$345$		0			0
$346$	158.144	+	427.876i	0.457064	+	1.23664i
$347$	388.417	−	160.888i	1.11936	−	0.463653i	0.255208	−	0.966886i	$-0.417856\pi$
$347$	388.417	−	160.888i	1.11936	−	0.463653i	0.864151	+	0.503233i	$0.167856\pi$
$348$		0			0
$349$	448.277	+	185.683i	1.28446	+	0.532042i	0.917330	−	0.398127i	$-0.130340\pi$
$349$	448.277	+	185.683i	1.28446	+	0.532042i	0.367132	+	0.930169i	$0.380340\pi$
$350$	−3.38815	+	3.13575i	−0.00968044	+	0.00895930i
$351$		0			0
$352$	202.678	+	134.546i	0.575789	+	0.382232i
$353$	106.951			0.302976			0.151488	−	0.988459i	$-0.451593\pi$
$353$	106.951			0.302976			0.151488	+	0.988459i	$0.451593\pi$
$354$		0			0
$355$	36.5908	−	88.3379i	0.103073	−	0.248839i
$356$	−207.843	−	242.761i	−0.583829	−	0.681914i
$357$		0			0
$358$	11.2312	−	4.15109i	0.0313722	−	0.0115952i
$359$	208.761	+	208.761i	0.581508	+	0.581508i	0.935317	−	0.353810i	$-0.115114\pi$
$359$	208.761	+	208.761i	0.581508	+	0.581508i	−0.353810	+	0.935317i	$0.615114\pi$
$360$		0			0
$361$	−252.315	−	252.315i	−0.698935	−	0.698935i
$362$	−247.856	+	538.492i	−0.684685	+	1.48755i
$363$		0			0
$364$	−8.10539	−	24.8442i	−0.0222676	−	0.0682532i
$365$	46.1315	−	111.371i	0.126388	−	0.305127i
$366$		0			0
$367$	711.002			1.93734			0.968668	−	0.248361i	$-0.0798919\pi$
$367$	711.002			1.93734			0.968668	+	0.248361i	$0.0798919\pi$
$368$	−8.14019	+	5.94415i	−0.0221201	+	0.0161526i
$369$		0			0
$370$	13.3815	−	345.880i	0.0361661	−	0.934811i
$371$	−36.9639	−	15.3110i	−0.0996332	−	0.0412694i
$372$		0			0
$373$	−587.430	+	243.321i	−1.57488	+	0.652336i	−0.987592	−	0.157043i	$-0.949804\pi$
$373$	−587.430	+	243.321i	−1.57488	+	0.652336i	−0.587287	+	0.809379i	$0.699804\pi$
$374$	−67.0060	+	145.577i	−0.179160	+	0.389244i
$375$		0			0
$376$	−399.689	−	505.128i	−1.06300	−	1.34342i
$377$	6.68456	−	6.68456i	0.0177309	−	0.0177309i
$378$		0			0
$379$	−34.5203	+	14.2988i	−0.0910825	+	0.0377276i	−0.427759	−	0.903893i	$-0.640697\pi$
$379$	−34.5203	+	14.2988i	−0.0910825	+	0.0377276i	0.336677	+	0.941620i	$0.390697\pi$
$380$	37.1864	+	2.88166i	0.0978591	+	0.00758332i
$381$		0			0
$382$	190.872	+	206.235i	0.499664	+	0.539882i
$383$		−	347.623i		−	0.907631i	−0.891096	−	0.453815i	$-0.850063\pi$
$383$		−	347.623i		−	0.907631i	0.891096	−	0.453815i	$-0.149937\pi$
$384$		0			0
$385$	19.2580			0.0500209
$386$	−234.440	+	216.976i	−0.607359	+	0.562114i
$387$		0			0
$388$	49.0077	−	632.421i	0.126309	−	1.62995i
$389$	60.7529	+	146.670i	0.156177	+	0.377045i	0.982529	−	0.186109i	$-0.0595878\pi$
$389$	60.7529	+	146.670i	0.156177	+	0.377045i	−0.826352	+	0.563154i	$0.809588\pi$
$390$		0			0
$391$	−4.69517	−	4.69517i	−0.0120081	−	0.0120081i
$392$	−305.474	+	241.711i	−0.779271	+	0.616610i
$393$		0			0
$394$	110.859	+	51.0260i	0.281368	+	0.129508i
$395$	63.3107	+	152.846i	0.160280	+	0.386951i
$396$		0			0
$397$	179.460	−	433.255i	0.452041	−	1.09132i	−0.519505	−	0.854468i	$-0.673883\pi$
$397$	179.460	−	433.255i	0.452041	−	1.09132i	0.971545	−	0.236855i	$-0.0761165\pi$
$398$	392.126	+	15.1706i	0.985240	+	0.0381171i
$399$		0			0
$400$	−53.7507	+	39.2500i	−0.134377	+	0.0981250i
$401$			680.550i			1.69713i	0.529089	+	0.848566i	$0.322534\pi$
$401$			680.550i			1.69713i	−0.529089	+	0.848566i	$0.677466\pi$
$402$		0			0
$403$	518.792	+	214.891i	1.28733	+	0.533228i
$404$	535.029	−	174.553i	1.32433	−	0.432062i
$405$		0			0
$406$	0.809477	+	0.372584i	0.00199379	+	0.000917696i
$407$	203.795	−	203.795i	0.500725	−	0.500725i
$408$		0			0
$409$	239.915	−	239.915i	0.586589	−	0.586589i	−0.350117	−	0.936706i	$-0.613858\pi$
$409$	239.915	−	239.915i	0.586589	−	0.586589i	0.936706	+	0.350117i	$0.113858\pi$
$410$	−50.7466	−	137.301i	−0.123772	−	0.334879i
$411$		0			0
$412$	42.7391	−	36.5916i	0.103736	−	0.0888146i
$413$	36.1082	+	14.9565i	0.0874289	+	0.0362143i
$414$		0			0
$415$			133.843i			0.322512i
$416$	−74.6112	−	369.292i	−0.179354	−	0.887722i
$417$		0			0
$418$	21.0944	+	22.7923i	0.0504652	+	0.0545271i
$419$	−33.5102	+	80.9009i	−0.0799767	+	0.193081i	−0.958810	−	0.284048i	$-0.908322\pi$
$419$	−33.5102	+	80.9009i	−0.0799767	+	0.193081i	0.878833	+	0.477129i	$0.158322\pi$
$420$		0			0
$421$	37.2975	+	90.0441i	0.0885926	+	0.213882i	0.961966	−	0.273170i	$-0.0880723\pi$
$421$	37.2975	+	90.0441i	0.0885926	+	0.213882i	−0.873373	+	0.487052i	$0.838072\pi$
$422$	−394.484	+	145.802i	−0.934796	+	0.345503i
$423$		0			0
$424$	−503.771	−	280.933i	−1.18814	−	0.662579i
$425$	−31.0028	−	31.0028i	−0.0729479	−	0.0729479i
$426$		0			0
$427$	−20.0963	−	48.5167i	−0.0470639	−	0.113622i
$428$	−683.796	+	223.088i	−1.59765	+	0.521233i
$429$		0			0
$430$	−13.5051	+	349.077i	−0.0314073	+	0.811808i
$431$	509.094			1.18119			0.590596	−	0.806967i	$-0.298893\pi$
$431$	509.094			1.18119			0.590596	+	0.806967i	$0.298893\pi$
$432$		0			0
$433$			66.0083i			0.152444i	0.997091	+	0.0762220i	$0.0242858\pi$
$433$			66.0083i			0.152444i	−0.997091	+	0.0762220i	$0.975714\pi$
$434$	−2.04632	+	52.8927i	−0.00471502	+	0.121873i
$435$		0			0
$436$	−33.6694	−	17.1045i	−0.0772235	−	0.0392305i
$437$	−1.18879	+	0.492414i	−0.00272035	+	0.00112681i
$438$		0			0
$439$	−39.8501	+	39.8501i	−0.0907747	+	0.0907747i	−0.751036	−	0.660261i	$-0.770446\pi$
$439$	−39.8501	+	39.8501i	−0.0907747	+	0.0907747i	0.660261	+	0.751036i	$0.270446\pi$
$440$	275.774	+	32.1358i	0.626758	+	0.0730360i
$441$		0			0
$442$	232.800	−	86.0433i	0.526696	−	0.194668i
$443$	193.778	−	80.2656i	0.437423	−	0.181187i	−0.153094	−	0.988212i	$-0.548924\pi$
$443$	193.778	−	80.2656i	0.437423	−	0.181187i	0.590517	+	0.807025i	$0.298924\pi$
$444$		0			0
$445$	−336.967	−	139.576i	−0.757229	−	0.313655i
$446$	−388.468	−	419.736i	−0.871005	−	0.941113i
$447$		0			0
$448$	30.2136	−	18.6651i	0.0674410	−	0.0416632i
$449$	−124.217			−0.276652			−0.138326	−	0.990387i	$-0.544172\pi$
$449$	−124.217			−0.276652			−0.138326	+	0.990387i	$0.544172\pi$
$450$		0			0
$451$	46.6418	−	112.603i	0.103419	−	0.249675i
$452$	342.312	+	26.5265i	0.757327	+	0.0586870i
$453$		0			0
$454$	14.5470	+	39.3585i	0.0320419	+	0.0866928i
$455$	−21.0894	−	21.0894i	−0.0463504	−	0.0463504i
$456$		0			0
$457$	−573.100	−	573.100i	−1.25405	−	1.25405i	−0.953889	−	0.300159i	$-0.902960\pi$
$457$	−573.100	−	573.100i	−1.25405	−	1.25405i	−0.300159	−	0.953889i	$-0.597040\pi$
$458$	−317.621	−	146.194i	−0.693495	−	0.319200i
$459$		0			0
$460$	−5.21014	+	10.2559i	−0.0113264	+	0.0222955i
$461$	86.0707	−	207.793i	0.186704	−	0.450744i	−0.802617	−	0.596495i	$-0.796560\pi$
$461$	86.0707	−	207.793i	0.186704	−	0.450744i	0.989321	+	0.145750i	$0.0465596\pi$
$462$		0			0
$463$	−555.587			−1.19997			−0.599986	−	0.800010i	$-0.704827\pi$
$463$	−555.587			−1.19997			−0.599986	+	0.800010i	$0.704827\pi$
$464$	10.9699	+	6.68616i	0.0236421	+	0.0144098i
$465$		0			0
$466$	−797.827	−	30.8664i	−1.71208	−	0.0662370i
$467$	319.806	+	132.468i	0.684809	+	0.283657i	0.697835	−	0.716258i	$-0.254147\pi$
$467$	319.806	+	132.468i	0.684809	+	0.283657i	−0.0130269	+	0.999915i	$0.504147\pi$
$468$		0			0
$469$	9.54349	−	3.95304i	0.0203486	−	0.00842866i
$470$	−667.791	−	307.369i	−1.42083	−	0.653977i
$471$		0			0
$472$	492.108	+	274.429i	1.04260	+	0.581418i
$473$	−205.679	+	205.679i	−0.434839	+	0.434839i
$474$		0			0
$475$	−7.84975	+	3.25147i	−0.0165258	+	0.00684521i
$476$	15.2154	+	17.7717i	0.0319652	+	0.0373355i
$477$		0			0
$478$	−19.3193	+	17.8801i	−0.0404170	+	0.0374061i
$479$		−	239.576i		−	0.500159i	−0.968225	−	0.250079i	$-0.919543\pi$
$479$		−	239.576i		−	0.500159i	0.968225	−	0.250079i	$-0.0804567\pi$
$480$		0			0
$481$	−446.351			−0.927965
$482$	314.822	+	340.163i	0.653159	+	0.705732i
$483$		0			0
$484$	−164.428	−	192.052i	−0.339727	−	0.396802i
$485$	−277.037	−	668.826i	−0.571210	−	1.37902i
$486$		0			0
$487$	−269.525	−	269.525i	−0.553439	−	0.553439i	0.373992	−	0.927432i	$-0.377989\pi$
$487$	−269.525	−	269.525i	−0.553439	−	0.553439i	−0.927432	+	0.373992i	$0.877989\pi$
$488$	−206.818	−	728.291i	−0.423807	−	1.49240i
$489$		0			0
$490$	−185.881	+	403.845i	−0.379348	+	0.824173i
$491$	−285.394	−	689.002i	−0.581250	−	1.40326i	−0.891680	−	0.452666i	$-0.850473\pi$
$491$	−285.394	−	689.002i	−0.581250	−	1.40326i	0.310430	−	0.950596i	$-0.399527\pi$
$492$		0			0
$493$	−3.23869	+	7.81888i	−0.00656934	+	0.0158598i
$494$	1.85936	−	48.0603i	0.00376389	−	0.0972881i
$495$		0			0
$496$	−117.565	+	754.005i	−0.237026	+	1.52017i
$497$		−	11.6225i		−	0.0233854i
$498$		0			0
$499$	581.267	+	240.769i	1.16486	+	0.482503i	0.879492	−	0.475914i	$-0.157883\pi$
$499$	581.267	+	240.769i	1.16486	+	0.482503i	0.285373	+	0.958417i	$0.407883\pi$
$500$	−241.166	+	474.725i	−0.482332	+	0.949449i
$501$		0			0
$502$	−119.206	+	258.986i	−0.237461	+	0.515909i
$503$	−204.189	+	204.189i	−0.405942	+	0.405942i	−0.880321	−	0.474379i	$-0.842673\pi$
$503$	−204.189	+	204.189i	−0.405942	+	0.405942i	0.474379	+	0.880321i	$0.342673\pi$
$504$		0			0
$505$	454.169	−	454.169i	0.899345	−	0.899345i
$506$	−8.98426	+	3.32061i	−0.0177555	+	0.00656246i
$507$		0			0
$508$	−68.9424	−	5.34250i	−0.135713	−	0.0105167i
$509$	397.562	+	164.676i	0.781066	+	0.323528i	0.737345	−	0.675516i	$-0.236079\pi$
$509$	397.562	+	164.676i	0.781066	+	0.323528i	0.0437202	+	0.999044i	$0.486079\pi$
$510$		0			0
$511$		−	14.6530i		−	0.0286751i
$512$	463.803	−	216.866i	0.905865	−	0.423566i
$513$		0			0
$514$	102.888	−	95.2236i	0.200172	−	0.185260i
$515$	24.5730	−	59.3244i	0.0477145	−	0.115193i
$516$		0			0
$517$	−234.242	−	565.510i	−0.453079	−	1.09383i
$518$	−14.5864	−	39.4652i	−0.0281591	−	0.0761876i
$519$		0			0
$520$	−266.807	−	337.191i	−0.513091	−	0.648444i
$521$	333.835	+	333.835i	0.640759	+	0.640759i	0.950742	−	0.309983i	$-0.100324\pi$
$521$	333.835	+	333.835i	0.640759	+	0.640759i	−0.309983	+	0.950742i	$0.600324\pi$
$522$		0			0
$523$	−211.672	−	511.022i	−0.404727	−	0.977097i	−0.986502	−	0.163748i	$-0.947642\pi$
$523$	−211.672	−	511.022i	−0.404727	−	0.977097i	0.581775	−	0.813350i	$-0.302358\pi$
$524$	−374.830	−	190.418i	−0.715324	−	0.363393i
$525$		0			0
$526$	694.942	+	26.8860i	1.32118	+	0.0511141i
$527$	−502.712			−0.953913
$528$		0			0
$529$			528.603i			0.999250i
$530$	−657.808	−	25.4494i	−1.24115	−	0.0480177i
$531$		0			0
$532$	4.31013	−	1.40618i	0.00810174	−	0.00264319i
$533$	−174.389	+	72.2343i	−0.327184	+	0.135524i
$534$		0			0
$535$	−580.452	+	580.452i	−1.08496	+	1.08496i
$536$	143.259	−	40.6821i	0.267273	−	0.0758994i
$537$		0			0
$538$	13.2938	+	35.9677i	0.0247096	+	0.0668545i
$539$	−341.990	+	141.657i	−0.634490	+	0.262815i
$540$		0			0
$541$	−529.582	−	219.360i	−0.978896	−	0.405472i	−0.164879	−	0.986314i	$-0.552723\pi$
$541$	−529.582	−	219.360i	−0.978896	−	0.405472i	−0.814016	+	0.580842i	$0.802723\pi$
$542$	480.861	−	445.040i	0.887198	−	0.821107i
$543$		0			0
$544$	188.228	+	279.879i	0.346008	+	0.514484i
$545$	−43.1003			−0.0790832
$546$		0			0
$547$	−68.4960	+	165.364i	−0.125221	+	0.302311i	−0.974041	−	0.226371i	$-0.927314\pi$
$547$	−68.4960	+	165.364i	−0.125221	+	0.302311i	0.848820	+	0.528682i	$0.177314\pi$
$548$	−109.726	+	93.9435i	−0.200231	+	0.171430i
$549$		0			0
$550$	−59.3243	+	21.9264i	−0.107862	+	0.0398662i
$551$	1.15968	+	1.15968i	0.00210468	+	0.00210468i
$552$		0			0
$553$	14.2197	+	14.2197i	0.0257138	+	0.0257138i
$554$	−28.9048	+	62.7986i	−0.0521747	+	0.113355i
$555$		0			0
$556$	−518.914	+	169.295i	−0.933299	+	0.304488i
$557$	308.610	−	745.049i	0.554057	−	1.33761i	−0.360351	−	0.932817i	$-0.617343\pi$
$557$	308.610	−	745.049i	0.554057	−	1.33761i	0.914408	−	0.404794i	$-0.132657\pi$
$558$		0			0
$559$	450.477			0.805863
$560$	21.0945	−	34.6095i	0.0376687	−	0.0618027i
$561$		0			0
$562$	28.8028	−	744.487i	0.0512506	−	1.32471i
$563$	347.195	+	143.813i	0.616687	+	0.255440i	0.669085	−	0.743186i	$-0.266686\pi$
$563$	347.195	+	143.813i	0.616687	+	0.255440i	−0.0523978	+	0.998626i	$0.516686\pi$
$564$		0			0
$565$	362.017	−	149.952i	0.640738	−	0.265402i
$566$	−242.676	+	527.239i	−0.428757	+	0.931518i
$567$		0			0
$568$	19.3945	−	166.434i	0.0341452	−	0.293017i
$569$	−717.322	+	717.322i	−1.26067	+	1.26067i	−0.309903	+	0.950768i	$0.600297\pi$
$569$	−717.322	+	717.322i	−1.26067	+	1.26067i	−0.950768	+	0.309903i	$0.899703\pi$
$570$		0			0
$571$	−327.041	+	135.465i	−0.572751	+	0.237241i	−0.650210	−	0.759754i	$-0.725319\pi$
$571$	−327.041	+	135.465i	−0.572751	+	0.237241i	0.0774591	+	0.996996i	$0.475319\pi$
$572$	27.6609	−	356.951i	0.0483582	−	0.624039i
$573$		0			0
$574$	−12.0857	−	13.0584i	−0.0210552	−	0.0227499i
$575$		−	2.62050i		−	0.00455740i
$576$		0			0
$577$	531.710			0.921507			0.460754	−	0.887528i	$-0.347579\pi$
$577$	531.710			0.921507			0.460754	+	0.887528i	$0.347579\pi$
$578$	261.133	−	241.680i	0.451787	−	0.418131i
$579$		0			0
$580$	14.6181	+	1.13279i	0.0252036	+	0.00195309i
$581$	6.22591	+	15.0307i	0.0107158	+	0.0258703i
$582$		0			0
$583$	−387.585	−	387.585i	−0.664812	−	0.664812i
$584$	24.4514	−	209.830i	0.0418689	−	0.359298i
$585$		0			0
$586$	−212.580	−	97.8456i	−0.362764	−	0.166972i
$587$	−105.581	−	254.894i	−0.179865	−	0.434232i	0.808073	−	0.589082i	$-0.200510\pi$
$587$	−105.581	−	254.894i	−0.179865	−	0.434232i	−0.987938	+	0.154850i	$0.950510\pi$
$588$		0			0
$589$	−37.2806	+	90.0034i	−0.0632948	+	0.152807i
$590$	642.579	+	24.8602i	1.08912	+	0.0421359i
$591$		0			0
$592$	−143.021	−	589.479i	−0.241590	−	0.995742i
$593$		−	405.861i		−	0.684419i	−0.939624	−	0.342210i	$-0.888825\pi$
$593$		−	405.861i		−	0.684419i	0.939624	−	0.342210i	$-0.111175\pi$
$594$		0			0
$595$	24.6681	+	10.2179i	0.0414590	+	0.0171729i
$596$	203.172	+	622.751i	0.340892	+	1.04488i
$597$		0			0
$598$	13.4750	+	6.20226i	0.0225335	+	0.0103717i
$599$	−561.484	+	561.484i	−0.937370	+	0.937370i	−0.998151	−	0.0607815i	$-0.980641\pi$
$599$	−561.484	+	561.484i	−0.937370	+	0.937370i	0.0607815	+	0.998151i	$0.480641\pi$
$600$		0			0
$601$	−358.762	+	358.762i	−0.596941	+	0.596941i	−0.939497	−	0.342556i	$-0.888707\pi$
$601$	−358.762	+	358.762i	−0.596941	+	0.596941i	0.342556	+	0.939497i	$0.388707\pi$
$602$	14.7213	+	39.8300i	0.0244539	+	0.0661628i
$603$		0			0
$604$	453.592	+	529.797i	0.750981	+	0.877148i
$605$	−266.580	−	110.421i	−0.440628	−	0.182514i
$606$		0			0
$607$		−	571.923i		−	0.942213i	−0.882076	−	0.471107i	$-0.843855\pi$
$607$		−	571.923i		−	0.942213i	0.882076	−	0.471107i	$-0.156145\pi$
$608$	64.0672	−	12.9440i	0.105374	−	0.0212895i
$609$		0			0
$610$	−586.897	−	634.137i	−0.962126	−	1.03957i
$611$	−362.771	+	875.806i	−0.593733	+	1.43340i
$612$		0			0
$613$	401.254	+	968.712i	0.654574	+	1.58028i	0.806068	+	0.591823i	$0.201591\pi$
$613$	401.254	+	968.712i	0.654574	+	1.58028i	−0.151494	+	0.988458i	$0.548409\pi$
$614$	874.137	−	323.083i	1.42368	−	0.526194i
$615$		0			0
$616$	32.4645	−	9.21918i	0.0527022	−	0.0149662i
$617$	151.870	+	151.870i	0.246143	+	0.246143i	0.819386	−	0.573242i	$-0.194315\pi$
$617$	151.870	+	151.870i	0.246143	+	0.246143i	−0.573242	+	0.819386i	$0.694315\pi$
$618$		0			0
$619$	146.518	+	353.725i	0.236701	+	0.571446i	0.996938	−	0.0781999i	$-0.0249173\pi$
$619$	146.518	+	353.725i	0.236701	+	0.571446i	−0.760237	+	0.649646i	$0.774917\pi$
$620$	270.127	+	827.977i	0.435688	+	1.33545i
$621$		0			0
$622$	6.70557	−	173.324i	0.0107807	−	0.278656i
$623$	−44.3344			−0.0711628
$624$		0			0
$625$			503.703i			0.805924i
$626$	14.1391	−	365.465i	0.0225865	−	0.583809i
$627$		0			0
$628$	209.956	−	413.290i	0.334325	−	0.658105i
$629$	369.176	−	152.918i	0.586925	−	0.243112i
$630$		0			0
$631$	−682.535	+	682.535i	−1.08167	+	1.08167i	−0.0853189	+	0.996354i	$0.527191\pi$
$631$	−682.535	+	682.535i	−1.08167	+	1.08167i	−0.996354	+	0.0853189i	$0.972809\pi$
$632$	179.897	+	227.354i	0.284647	+	0.359737i
$633$		0			0
$634$	582.176	−	215.174i	0.918259	−	0.339391i
$635$	−72.9111	+	30.2007i	−0.114821	+	0.0475602i
$636$		0			0
$637$	529.641	+	219.385i	0.831462	+	0.344403i
$638$	8.29229	+	8.95974i	0.0129973	+	0.0140435i
$639$		0			0
$640$	359.824	−	460.406i	0.562225	−	0.719384i
$641$	−38.9310			−0.0607348			−0.0303674	−	0.999539i	$-0.509668\pi$
$641$	−38.9310			−0.0607348			−0.0303674	+	0.999539i	$0.509668\pi$
$642$		0			0
$643$	318.631	−	769.243i	0.495538	−	1.19633i	−0.456326	−	0.889813i	$-0.650835\pi$
$643$	318.631	−	769.243i	0.495538	−	1.19633i	0.951864	−	0.306522i	$-0.0991652\pi$
$644$	−0.108033	+	1.39411i	−0.000167753	+	0.00216477i
$645$		0			0
$646$	14.9273	+	40.3876i	0.0231073	+	0.0625194i
$647$	157.445	+	157.445i	0.243346	+	0.243346i	0.818233	−	0.574887i	$-0.194954\pi$
$647$	157.445	+	157.445i	0.243346	+	0.243346i	−0.574887	+	0.818233i	$0.694954\pi$
$648$		0			0
$649$	378.612	+	378.612i	0.583378	+	0.583378i
$650$	88.9774	+	40.9543i	0.136888	+	0.0630067i
$651$		0			0
$652$	453.312	+	230.288i	0.695264	+	0.353202i
$653$	15.6861	−	37.8696i	0.0240216	−	0.0579933i	−0.911414	−	0.411492i	$-0.865008\pi$
$653$	15.6861	−	37.8696i	0.0240216	−	0.0579933i	0.935435	+	0.353498i	$0.115008\pi$
$654$		0			0
$655$	−479.821			−0.732551
$656$	−151.275	−	207.163i	−0.230603	−	0.315798i
$657$		0			0
$658$	−89.2915	−	3.45452i	−0.135701	−	0.00525003i
$659$	−187.169	−	77.5281i	−0.284020	−	0.117645i	0.236125	−	0.971723i	$-0.424122\pi$
$659$	−187.169	−	77.5281i	−0.284020	−	0.117645i	−0.520146	+	0.854078i	$0.674122\pi$
$660$		0			0
$661$	30.1818	−	12.5017i	0.0456608	−	0.0189133i	−0.359736	−	0.933054i	$-0.617133\pi$
$661$	30.1818	−	12.5017i	0.0456608	−	0.0189133i	0.405397	+	0.914141i	$0.367133\pi$
$662$	584.723	+	269.135i	0.883267	+	0.406548i
$663$		0			0
$664$	64.0729	+	225.627i	0.0964954	+	0.339800i
$665$	3.65873	−	3.65873i	0.00550184	−	0.00550184i
$666$		0			0
$667$	−0.467318	+	0.193569i	−0.000700627	+	0.000290209i
$668$	−380.890	+	326.104i	−0.570195	+	0.488179i
$669$		0			0
$670$	124.738	−	115.446i	0.186176	−	0.172307i
$671$		−	719.443i		−	1.07219i
$672$		0			0
$673$	−327.878			−0.487189			−0.243595	−	0.969877i	$-0.578327\pi$
$673$	−327.878			−0.487189			−0.243595	+	0.969877i	$0.578327\pi$
$674$	358.169	+	386.998i	0.531408	+	0.574181i
$675$		0			0
$676$	92.3192	−	79.0402i	0.136567	−	0.116923i
$677$	−117.661	−	284.058i	−0.173797	−	0.419583i	0.812846	−	0.582478i	$-0.197917\pi$
$677$	−117.661	−	284.058i	−0.173797	−	0.419583i	−0.986643	+	0.162895i	$0.947917\pi$
$678$		0			0
$679$	−62.2231	−	62.2231i	−0.0916393	−	0.0916393i
$680$	336.195	+	187.483i	0.494405	+	0.275710i
$681$		0			0
$682$	−303.204	+	658.741i	−0.444581	+	0.965897i
$683$	324.811	+	784.162i	0.475564	+	1.14811i	0.961669	+	0.274213i	$0.0884175\pi$
$683$	324.811	+	784.162i	0.475564	+	1.14811i	−0.486104	+	0.873901i	$0.661583\pi$
$684$		0			0
$685$	−63.0875	+	152.307i	−0.0920985	+	0.222345i
$686$	−4.19143	+	108.339i	−0.00610996	+	0.157929i
$687$		0			0
$688$	144.343	+	594.928i	0.209801	+	0.864721i
$689$			848.888i			1.23206i
$690$		0			0
$691$	826.286	+	342.259i	1.19578	+	0.495309i	0.889634	−	0.456674i	$-0.150959\pi$
$691$	826.286	+	342.259i	1.19578	+	0.495309i	0.306149	+	0.951984i	$0.400959\pi$
$692$	813.391	+	413.213i	1.17542	+	0.597128i
$693$		0			0
$694$	351.567	−	763.815i	0.506580	−	1.10060i
$695$	−440.490	+	440.490i	−0.633798	+	0.633798i
$696$		0			0
$697$	119.490	−	119.490i	0.171434	−	0.171434i
$698$	910.241	−	336.427i	1.30407	−	0.481988i
$699$		0			0
$700$	−0.713355	+	9.20550i	−0.00101908	+	0.0131507i
$701$	−430.597	−	178.359i	−0.614260	−	0.254435i	0.0537885	−	0.998552i	$-0.482870\pi$
$701$	−430.597	−	178.359i	−0.614260	−	0.254435i	−0.668049	+	0.744117i	$0.732870\pi$
$702$		0			0
$703$		−	77.4359i		−	0.110151i
$704$	480.274	−	77.8444i	0.682207	−	0.110574i
$705$		0			0
$706$	156.985	−	145.291i	0.222359	−	0.205794i
$707$	29.8773	−	72.1301i	0.0422592	−	0.102023i
$708$		0			0
$709$	−77.1066	−	186.152i	−0.108754	−	0.262555i	0.860128	−	0.510078i	$-0.170384\pi$
$709$	−77.1066	−	186.152i	−0.108754	−	0.262555i	−0.968882	+	0.247523i	$0.920384\pi$
$710$	−66.2967	−	179.373i	−0.0933756	−	0.252638i
$711$		0			0
$712$	−634.866	−	73.9807i	−0.891665	−	0.103906i
$713$	−21.2458	−	21.2458i	−0.0297977	−	0.0297977i
$714$		0			0
$715$	−156.365	−	377.498i	−0.218692	−	0.527970i
$716$	10.8463	−	21.3506i	0.0151485	−	0.0298192i
$717$		0			0
$718$	590.025	+	22.8270i	0.821762	+	0.0317924i
$719$	−809.898			−1.12642			−0.563212	−	0.826313i	$-0.690434\pi$
$719$	−809.898			−1.12642			−0.563212	+	0.826313i	$0.690434\pi$
$720$		0			0
$721$		−	7.80525i		−	0.0108256i
$722$	−713.122	−	27.5894i	−0.987704	−	0.0382124i
$723$		0			0
$724$	367.723	+	1127.12i	0.507905	+	1.55680i
$725$	−3.08576	+	1.27817i	−0.00425623	+	0.00176299i
$726$		0			0
$727$	542.456	−	542.456i	0.746156	−	0.746156i	−0.227599	−	0.973755i	$-0.573087\pi$
$727$	542.456	−	542.456i	0.746156	−	0.746156i	0.973755	+	0.227599i	$0.0730875\pi$
$728$	−45.6477	−	25.4559i	−0.0627029	−	0.0349670i
$729$		0			0
$730$	−83.5830	−	226.143i	−0.114497	−	0.309785i
$731$	−372.588	+	154.331i	−0.509697	+	0.211123i
$732$		0			0
$733$	562.276	+	232.903i	0.767089	+	0.317739i	0.731693	−	0.681635i	$-0.238731\pi$
$733$	562.276	+	232.903i	0.767089	+	0.317739i	0.0353965	+	0.999373i	$0.488731\pi$
$734$	1043.63	−	965.885i	1.42184	−	1.31592i
$735$		0			0
$736$	−3.87337	+	19.7833i	−0.00526273	+	0.0268795i
$737$	141.518			0.192019
$738$		0			0
$739$	−305.819	+	738.312i	−0.413828	+	0.999070i	0.570272	+	0.821456i	$0.306838\pi$
$739$	−305.819	+	738.312i	−0.413828	+	0.999070i	−0.984100	+	0.177614i	$0.943162\pi$
$740$	−450.231	−	525.871i	−0.608420	−	0.710637i
$741$		0			0
$742$	−75.0564	+	27.7410i	−0.101154	+	0.0373868i
$743$	−581.334	−	581.334i	−0.782414	−	0.782414i	0.197823	−	0.980238i	$-0.436613\pi$
$743$	−581.334	−	581.334i	−0.782414	−	0.782414i	−0.980238	+	0.197823i	$0.936613\pi$
$744$		0			0
$745$	528.633	+	528.633i	0.709574	+	0.709574i
$746$	−531.698	+	1155.17i	−0.712732	+	1.54848i
$747$		0			0
$748$	99.4112	+	304.709i	0.132903	+	0.407365i
$749$	−38.1847	+	92.1861i	−0.0509810	+	0.123079i
$750$		0			0
$751$	−187.901			−0.250201			−0.125100	−	0.992144i	$-0.539925\pi$
$751$	−187.901			−0.250201			−0.125100	+	0.992144i	$0.539925\pi$
$752$	−1272.88	−	198.469i	−1.69266	−	0.263922i
$753$		0			0
$754$	0.730922	−	18.8927i	0.000969392	−	0.0250566i
$755$	735.390	+	304.608i	0.974026	+	0.403455i
$756$		0			0
$757$	−168.645	+	69.8549i	−0.222780	+	0.0922786i	−0.491282	−	0.871001i	$-0.663472\pi$
$757$	−168.645	+	69.8549i	−0.222780	+	0.0922786i	0.268502	+	0.963279i	$0.413472\pi$
$758$	−31.2452	+	67.8833i	−0.0412206	+	0.0895559i
$759$		0			0
$760$	58.4980	−	46.2874i	0.0769711	−	0.0609045i
$761$	−391.406	+	391.406i	−0.514331	+	0.514331i	−0.915850	−	0.401520i	$-0.868482\pi$
$761$	−391.406	+	391.406i	−0.514331	+	0.514331i	0.401520	+	0.915850i	$0.368482\pi$
$762$		0			0
$763$	−4.84022	+	2.00488i	−0.00634367	+	0.00262763i
$764$	560.334	+	43.4215i	0.733421	+	0.0568345i
$765$		0			0
$766$	−472.240	−	510.250i	−0.616501	−	0.666123i
$767$		−	829.235i		−	1.08114i
$768$		0			0
$769$	184.433			0.239835			0.119918	−	0.992784i	$-0.461737\pi$
$769$	184.433			0.239835			0.119918	+	0.992784i	$0.461737\pi$
$770$	28.2675	−	26.1617i	0.0367110	−	0.0339763i
$771$		0			0
$772$	−49.3600	+	636.967i	−0.0639378	+	0.825087i
$773$	140.532	+	339.275i	0.181801	+	0.438907i	0.988338	−	0.152277i	$-0.0486607\pi$
$773$	140.532	+	339.275i	0.181801	+	0.438907i	−0.806537	+	0.591184i	$0.798661\pi$
$774$		0			0
$775$	−140.289	−	140.289i	−0.181018	−	0.181018i
$776$	−787.199	−	994.862i	−1.01443	−	1.28204i
$777$		0			0
$778$	288.424	+	132.755i	0.370725	+	0.170637i
$779$	−12.5317	−	30.2541i	−0.0160869	−	0.0388371i
$780$		0			0
$781$	60.9340	−	147.108i	0.0780206	−	0.188358i
$782$	−13.2700	−	0.513392i	−0.0169693	−	0.000656512i
$783$		0			0
$784$	−120.024	+	769.772i	−0.153091	+	0.981852i
$785$		−	529.054i		−	0.673954i
$786$		0			0
$787$	−926.743	−	383.870i	−1.17756	−	0.487763i	−0.293878	−	0.955843i	$-0.594946\pi$
$787$	−926.743	−	383.870i	−1.17756	−	0.487763i	−0.883686	+	0.468080i	$0.844946\pi$
$788$	232.040	−	75.7030i	0.294467	−	0.0960697i
$789$		0			0
$790$	300.568	+	138.345i	0.380465	+	0.175120i
$791$	33.6796	−	33.6796i	0.0425785	−	0.0425785i
$792$		0			0
$793$	−787.860	+	787.860i	−0.993518	+	0.993518i
$794$	−325.153	−	879.738i	−0.409513	−	1.10798i
$795$		0			0
$796$	596.182	−	510.428i	0.748973	−	0.641242i
$797$	871.860	+	361.136i	1.09393	+	0.453119i	0.855374	−	0.518010i	$-0.173327\pi$
$797$	871.860	+	361.136i	1.09393	+	0.453119i	0.238553	+	0.971130i	$0.423327\pi$
$798$		0			0
$799$		−	848.660i		−	1.06215i
$800$	−25.5764	+	130.632i	−0.0319705	+	0.163290i
$801$		0			0
$802$	924.516	+	998.931i	1.15276	+	1.24555i
$803$	76.8221	−	185.465i	0.0956689	−	0.230965i
$804$		0			0
$805$	0.610701	+	1.47436i	0.000758635	+	0.00183151i
$806$	1053.42	−	389.348i	1.30698	−	0.483062i
$807$		0			0
$808$	548.204	−	983.042i	0.678470	−	1.21664i
$809$	−744.003	−	744.003i	−0.919658	−	0.919658i	0.0773465	−	0.997004i	$-0.475355\pi$
$809$	−744.003	−	744.003i	−0.919658	−	0.919658i	−0.997004	+	0.0773465i	$0.975355\pi$
$810$		0			0
$811$	−307.315	−	741.925i	−0.378934	−	0.914827i	−0.992166	−	0.124924i	$-0.960131\pi$
$811$	−307.315	−	741.925i	−0.378934	−	0.914827i	0.613233	−	0.789902i	$-0.289869\pi$
$812$	1.69432	−	0.552772i	0.00208661	−	0.000680754i
$813$		0			0
$814$	22.2839	−	575.989i	0.0273758	−	0.707603i
$815$	580.286			0.712007
$816$		0			0
$817$			78.1517i			0.0956569i
$818$	26.2335	−	678.075i	0.0320702	−	0.828943i
$819$		0			0
$820$	−261.008	−	132.595i	−0.318302	−	0.161701i
$821$	948.269	−	392.786i	1.15502	−	0.478424i	0.278804	−	0.960348i	$-0.410062\pi$
$821$	948.269	−	392.786i	1.15502	−	0.478424i	0.876213	+	0.481924i	$0.160062\pi$
$822$		0			0
$823$	492.275	−	492.275i	0.598147	−	0.598147i	−0.341672	−	0.939819i	$-0.610993\pi$
$823$	492.275	−	492.275i	0.598147	−	0.598147i	0.939819	+	0.341672i	$0.110993\pi$
$824$	13.0246	−	111.771i	0.0158066	−	0.135644i
$825$		0			0
$826$	73.3187	−	27.0988i	0.0887636	−	0.0328072i
$827$	1350.77	−	559.506i	1.63333	−	0.676549i	0.637734	−	0.770257i	$-0.279872\pi$
$827$	1350.77	−	559.506i	1.63333	−	0.676549i	0.995600	+	0.0937082i	$0.0298721\pi$
$828$		0			0
$829$	441.547	+	182.895i	0.532627	+	0.220621i	0.632753	−	0.774354i	$-0.281925\pi$
$829$	441.547	+	182.895i	0.532627	+	0.220621i	−0.100127	+	0.994975i	$0.531925\pi$
$830$	181.823	+	196.458i	0.219064	+	0.236696i
$831$		0			0
$832$	−611.194	−	440.700i	−0.734608	−	0.529687i
$833$	−513.225			−0.616116
$834$		0			0
$835$	−218.994	+	528.698i	−0.262268	+	0.633171i
$836$	61.9260	+	4.79879i	0.0740742	+	0.00574018i
$837$		0			0
$838$	60.7152	+	164.272i	0.0724526	+	0.196028i
$839$	−849.569	−	849.569i	−1.01260	−	1.01260i	−0.999920	−	0.0126775i	$-0.995965\pi$
$839$	−849.569	−	849.569i	−1.01260	−	1.01260i	−0.0126775	−	0.999920i	$-0.504035\pi$
$840$		0			0
$841$	−594.221	−	594.221i	−0.706565	−	0.706565i
$842$	177.070	+	81.5013i	0.210297	+	0.0967949i
$843$		0			0
$844$	−380.965	+	749.913i	−0.451380	+	0.888522i
$845$	53.0792	−	128.144i	0.0628156	−	0.151650i
$846$		0			0
$847$	−35.0736			−0.0414093
$848$	−1121.09	+	272.003i	−1.32204	+	0.320758i
$849$		0			0
$850$	−87.6237	−	3.39000i	−0.103087	−	0.00398823i
$851$	22.0649	+	9.13957i	0.0259282	+	0.0107398i
$852$		0			0
$853$	773.493	−	320.391i	0.906791	−	0.375605i	0.119964	−	0.992778i	$-0.461722\pi$
$853$	773.493	−	320.391i	0.906791	−	0.375605i	0.786827	+	0.617173i	$0.211722\pi$
$854$	−95.4071	−	43.9138i	−0.111718	−	0.0514213i
$855$		0			0
$856$	−700.634	+	1256.38i	−0.818497	+	1.46773i
$857$	259.040	−	259.040i	0.302264	−	0.302264i	−0.539635	−	0.841899i	$-0.681438\pi$
$857$	259.040	−	259.040i	0.302264	−	0.302264i	0.841899	+	0.539635i	$0.181438\pi$
$858$		0			0
$859$	−762.123	+	315.682i	−0.887221	+	0.367499i	−0.779293	−	0.626660i	$-0.784422\pi$
$859$	−762.123	+	315.682i	−0.887221	+	0.367499i	−0.107928	+	0.994159i	$0.534422\pi$
$860$	454.393	+	530.732i	0.528364	+	0.617130i
$861$		0			0
$862$	747.263	−	691.596i	0.866894	−	0.802316i
$863$			1078.25i			1.24942i	0.780855	+	0.624712i	$0.214784\pi$
$863$			1078.25i			1.24942i	−0.780855	+	0.624712i	$0.785216\pi$
$864$		0			0
$865$	1041.22			1.20373
$866$	89.6712	+	96.8888i	0.103546	+	0.111881i
$867$		0			0
$868$	68.8502	+	80.4173i	0.0793206	+	0.0926467i
$869$	105.430	+	254.532i	0.121324	+	0.292902i
$870$		0			0
$871$	−154.976	−	154.976i	−0.177929	−	0.177929i
$872$	−72.6571	+	20.6329i	−0.0833224	+	0.0236616i
$873$		0			0
$874$	−1.07601	+	2.33773i	−0.00123113	+	0.00267475i
$875$	28.2680	+	68.2450i	0.0323063	+	0.0779943i
$876$		0			0
$877$	387.984	−	936.676i	0.442399	−	1.06805i	−0.532706	−	0.846301i	$-0.678825\pi$
$877$	387.984	−	936.676i	0.442399	−	1.06805i	0.975105	−	0.221745i	$-0.0711753\pi$
$878$	−4.35740	+	112.629i	−0.00496287	+	0.128279i
$879$		0			0
$880$	448.444	−	327.464i	0.509596	−	0.372118i
$881$			1281.50i			1.45460i	0.686318	+	0.727301i	$0.259226\pi$
$881$			1281.50i			1.45460i	−0.686318	+	0.727301i	$0.740774\pi$
$882$		0			0
$883$	−1014.19	−	420.092i	−1.14857	−	0.475755i	−0.274519	−	0.961582i	$-0.588519\pi$
$883$	−1014.19	−	420.092i	−1.14857	−	0.475755i	−0.874055	+	0.485826i	$0.838519\pi$
$884$	224.821	−	442.551i	0.254323	−	0.500624i
$885$		0			0
$886$	175.394	−	381.061i	0.197961	−	0.430091i
$887$	57.0987	−	57.0987i	0.0643728	−	0.0643728i	−0.674187	−	0.738560i	$-0.735506\pi$
$887$	57.0987	−	57.0987i	0.0643728	−	0.0643728i	0.738560	+	0.674187i	$0.235506\pi$
$888$		0			0
$889$	−6.78316	+	6.78316i	−0.00763010	+	0.00763010i
$890$	−684.222	+	252.890i	−0.768789	+	0.284146i
$891$		0			0
$892$	−1140.41	−	88.3729i	−1.27849	−	0.0990728i
$893$	−151.940	−	62.9358i	−0.170146	−	0.0704768i
$894$		0			0
$895$		−	27.3309i		−	0.0305373i
$896$	18.9921	−	68.4419i	0.0211965	−	0.0763860i
$897$		0			0
$898$	−182.329	+	168.747i	−0.203039	+	0.187914i
$899$	−14.6551	+	35.3806i	−0.0163016	+	0.0393555i
$900$		0			0
$901$	−290.825	−	702.113i	−0.322780	−	0.779260i
$902$	−84.5076	−	228.645i	−0.0936892	−	0.253486i
$903$		0			0
$904$	538.491	−	426.089i	0.595676	−	0.471337i
$905$	956.779	+	956.779i	1.05721	+	1.05721i
$906$		0			0
$907$	312.323	+	754.015i	0.344348	+	0.831329i	0.997266	+	0.0739002i	$0.0235446\pi$
$907$	312.323	+	754.015i	0.344348	+	0.831329i	−0.652918	+	0.757429i	$0.726455\pi$
$908$	74.8204	+	38.0097i	0.0824014	+	0.0418609i
$909$		0			0
$910$	−59.6053	−	2.30602i	−0.0655003	−	0.00253409i
$911$	−1374.15			−1.50840			−0.754201	−	0.656644i	$-0.771976\pi$
$911$	−1374.15			−1.50840			−0.754201	+	0.656644i	$0.771976\pi$
$912$		0			0
$913$			222.886i			0.244125i
$914$	−1619.76	−	62.6655i	−1.77217	−	0.0685618i
$915$		0			0
$916$	−664.815	+	216.895i	−0.725781	+	0.236785i
$917$	−53.8844	+	22.3196i	−0.0587616	+	0.0243399i
$918$		0			0
$919$	−317.523	+	317.523i	−0.345510	+	0.345510i	−0.858434	−	0.512924i	$-0.828562\pi$
$919$	−317.523	+	317.523i	−0.345510	+	0.345510i	0.512924	+	0.858434i	$0.328562\pi$
$920$	6.28493	+	22.1318i	0.00683145	+	0.0240564i
$921$		0			0
$922$	−155.947	−	421.930i	−0.169139	−	0.457625i
$923$	−227.826	+	94.3687i	−0.246832	+	0.102241i
$924$		0			0
$925$	145.697	+	60.3498i	0.157511	+	0.0652430i
$926$	−815.507	+	754.756i	−0.880677	+	0.815071i
$927$		0			0
$928$	25.1850	−	5.08834i	0.0271390	−	0.00548313i
$929$	46.9926			0.0505841			0.0252920	−	0.999680i	$-0.491948\pi$
$929$	46.9926			0.0505841			0.0252920	+	0.999680i	$0.491948\pi$
$930$		0			0
$931$	−38.0602	+	91.8855i	−0.0408810	+	0.0986955i
$932$	−1213.01	+	1038.53i	−1.30151	+	1.11430i
$933$		0			0
$934$	649.375	−	240.011i	0.695263	−	0.256971i
$935$	258.658	+	258.658i	0.276640	+	0.276640i
$936$		0			0
$937$	381.311	+	381.311i	0.406949	+	0.406949i	0.880673	−	0.473724i	$-0.157091\pi$
$937$	381.311	+	381.311i	0.406949	+	0.406949i	−0.473724	+	0.880673i	$0.657091\pi$
$938$	8.63806	−	18.7671i	0.00920902	−	0.0200075i
$939$		0			0
$940$	−1397.76	+	456.018i	−1.48698	+	0.485125i
$941$	−319.284	+	770.819i	−0.339303	+	0.819149i	0.658480	+	0.752598i	$0.271200\pi$
$941$	−319.284	+	770.819i	−0.339303	+	0.819149i	−0.997783	+	0.0665513i	$0.978800\pi$
$942$		0			0
$943$	10.0998			0.0107103
$944$	1095.14	−	265.706i	1.16010	−	0.281468i
$945$		0			0
$946$	−22.4899	+	581.313i	−0.0237737	+	0.614496i
$947$	46.3711	+	19.2075i	0.0489663	+	0.0202825i	0.407032	−	0.913414i	$-0.366564\pi$
$947$	46.3711	+	19.2075i	0.0489663	+	0.0202825i	−0.358066	+	0.933696i	$0.616564\pi$
$948$		0			0
$949$	−287.230	+	118.975i	−0.302666	+	0.125368i
$950$	−7.10502	+	15.4364i	−0.00747897	+	0.0162488i
$951$		0			0
$952$	46.4762	+	5.41586i	0.0488195	+	0.00568893i
$953$	456.351	−	456.351i	0.478858	−	0.478858i	−0.425909	−	0.904766i	$-0.640045\pi$
$953$	456.351	−	456.351i	0.478858	−	0.478858i	0.904766	+	0.425909i	$0.140045\pi$
$954$		0			0
$955$	592.589	−	245.459i	0.620512	−	0.257025i
$956$	−4.06756	+	52.4899i	−0.00425477	+	0.0549058i
$957$		0			0
$958$	−325.460	−	351.657i	−0.339729	−	0.367074i
$959$			20.0388i			0.0208955i
$960$		0			0
$961$	−1313.79			−1.36710
$962$	−655.167	+	606.361i	−0.681047	+	0.630313i
$963$		0			0
$964$	924.211	+	71.6192i	0.958725	+	0.0742938i
$965$	279.028	+	673.634i	0.289148	+	0.698066i
$966$		0			0
$967$	476.069	+	476.069i	0.492316	+	0.492316i	0.909035	−	0.416719i	$-0.136820\pi$
$967$	476.069	+	476.069i	0.492316	+	0.492316i	−0.416719	+	0.909035i	$0.636820\pi$
$968$	−502.252	−	58.5273i	−0.518855	−	0.0604621i
$969$		0			0
$970$	−1315.23	−	605.372i	−1.35591	−	0.624095i
$971$	502.303	+	1212.67i	0.517305	+	1.24888i	0.939553	+	0.342404i	$0.111241\pi$
$971$	502.303	+	1212.67i	0.517305	+	1.24888i	−0.422248	+	0.906480i	$0.638759\pi$
$972$		0			0
$973$	−28.9774	+	69.9576i	−0.0297815	+	0.0718988i
$974$	−761.762	−	29.4711i	−0.782096	−	0.0302579i
$975$		0			0
$976$	−1292.94	−	788.048i	−1.32474	−	0.807426i
$977$		−	1.17535i		−	0.00120302i	−1.00000		0.000601512i	$-0.999809\pi$
$977$		−	1.17535i		−	0.00120302i	1.00000		0.000601512i	$-0.000191467\pi$
$978$		0			0
$979$	−561.146	−	232.434i	−0.573183	−	0.237420i
$980$	275.775	+	845.291i	0.281404	+	0.862542i
$981$		0			0
$982$	−1354.91	−	623.634i	−1.37974	−	0.635065i
$983$	1006.98	−	1006.98i	1.02439	−	1.02439i	0.0246998	−	0.999695i	$-0.492137\pi$
$983$	1006.98	−	1006.98i	1.02439	−	1.02439i	0.999695	−	0.0246998i	$-0.00786298\pi$
$984$		0			0
$985$	196.972	−	196.972i	0.199971	−	0.199971i
$986$	5.86799	+	15.8765i	0.00595130	+	0.0161019i
$987$		0			0
$988$	−62.5599	−	73.0702i	−0.0633198	−	0.0739577i
$989$	−22.2688	−	9.22405i	−0.0225165	−	0.00932665i
$990$		0			0
$991$			1294.48i			1.30624i	0.757256	+	0.653118i	$0.226539\pi$
$991$			1294.48i			1.30624i	−0.757256	+	0.653118i	$0.773461\pi$
$992$	851.739	+	1266.46i	0.858607	+	1.27667i
$993$		0			0
$994$	−15.7890	−	17.0599i	−0.0158843	−	0.0171629i
$995$	342.777	−	827.536i	0.344499	−	0.831694i
$996$		0			0
$997$	82.2498	+	198.568i	0.0824973	+	0.199166i	0.959746	−	0.280871i	$-0.0906233\pi$
$997$	82.2498	+	198.568i	0.0824973	+	0.199166i	−0.877248	+	0.480037i	$0.840623\pi$
$998$	1180.28	−	436.235i	1.18265	−	0.437109i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.u.a.163.6		28
3.2	odd	2		32.3.h.a.3.2	✓	28
12.11	even	2		128.3.h.a.47.1		28
24.5	odd	2		256.3.h.b.95.1		28
24.11	even	2		256.3.h.a.95.7		28
32.11	odd	8	inner	288.3.u.a.235.6		28
96.5	odd	8		256.3.h.a.159.7		28
96.11	even	8		32.3.h.a.11.2	yes	28
96.53	odd	8		128.3.h.a.79.1		28
96.59	even	8		256.3.h.b.159.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.2	✓	28	3.2	odd	2
32.3.h.a.11.2	yes	28	96.11	even	8
128.3.h.a.47.1		28	12.11	even	2
128.3.h.a.79.1		28	96.53	odd	8
256.3.h.a.95.7		28	24.11	even	2
256.3.h.a.159.7		28	96.5	odd	8
256.3.h.b.95.1		28	24.5	odd	2
256.3.h.b.159.1		28	96.59	even	8
288.3.u.a.163.6		28	1.1	even	1	trivial
288.3.u.a.235.6		28	32.11	odd	8	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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	288.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.46783 - 1.35848i) q^{2} +(0.309042 - 3.98804i) q^{4} +(-1.74699 - 4.21761i) q^{5} +(-0.392379 - 0.392379i) q^{7} +(-4.96407 - 6.27359i) q^{8} +O(q^{10})\)	\(q+(1.46783 - 1.35848i) q^{2} +(0.309042 - 3.98804i) q^{4} +(-1.74699 - 4.21761i) q^{5} +(-0.392379 - 0.392379i) q^{7} +(-4.96407 - 6.27359i) q^{8} +(-8.29385 - 3.81747i) q^{10} +(-2.90924 - 7.02353i) q^{11} +(-4.50555 + 10.8774i) q^{13} +(-1.10898 - 0.0429045i) q^{14} +(-15.8090 - 2.46495i) q^{16} -10.5402i q^{17} +(-1.88707 - 0.781651i) q^{19} +(-17.3599 + 5.66366i) q^{20} +(-13.8116 - 6.35718i) q^{22} +(0.445453 - 0.445453i) q^{23} +(2.94139 - 2.94139i) q^{25} +(8.16334 + 22.0868i) q^{26} +(-1.68608 + 1.44356i) q^{28} +(-0.741814 - 0.307270i) q^{29} -47.6947i q^{31} +(-26.5535 + 17.8581i) q^{32} +(-14.3187 - 15.4712i) q^{34} +(-0.969419 + 2.34038i) q^{35} +(14.5080 + 35.0255i) q^{37} +(-3.83176 + 1.41623i) q^{38} +(-17.7874 + 31.8965i) q^{40} +(11.3365 + 11.3365i) q^{41} +(-14.6421 - 35.3493i) q^{43} +(-28.9092 + 9.43161i) q^{44} +(0.0487080 - 1.25899i) q^{46} +80.5164 q^{47} -48.6921i q^{49} +(0.321625 - 8.31328i) q^{50} +(41.9870 + 21.3299i) q^{52} +(66.6128 - 27.5919i) q^{53} +(-24.5401 + 24.5401i) q^{55} +(-0.513828 + 4.40942i) q^{56} +(-1.50628 + 0.556724i) q^{58} +(-65.0706 + 26.9531i) q^{59} +(87.4322 + 36.2156i) q^{61} +(-64.7925 - 70.0077i) q^{62} +(-14.7160 + 62.2852i) q^{64} +53.7476 q^{65} +(-7.12379 + 17.1984i) q^{67} +(-42.0348 - 3.25737i) q^{68} +(1.75643 + 4.75222i) q^{70} +(14.8103 + 14.8103i) q^{71} +(18.6720 + 18.6720i) q^{73} +(68.8769 + 31.7025i) q^{74} +(-3.70044 + 7.28417i) q^{76} +(-1.61436 + 3.89741i) q^{77} -36.2398 q^{79} +(17.2220 + 70.9824i) q^{80} +(32.0406 + 1.23959i) q^{82} +(-27.0868 - 11.2197i) q^{83} +(-44.4545 + 18.4137i) q^{85} +(-69.5135 - 31.9955i) q^{86} +(-29.6211 + 53.1167i) q^{88} +(56.4944 - 56.4944i) q^{89} +(6.03592 - 2.50016i) q^{91} +(-1.63882 - 1.91415i) q^{92} +(118.184 - 109.380i) q^{94} +9.32448i q^{95} +158.579 q^{97} +(-66.1474 - 71.4716i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8	\( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 44 q^{10} + 4 q^{11} - 4 q^{13} + 20 q^{14} + 16 q^{16} - 4 q^{19} - 76 q^{20} + 144 q^{22} + 68 q^{23} - 4 q^{25} - 96 q^{26} + 56 q^{28} + 4 q^{29} + 24 q^{32} - 48 q^{34} - 92 q^{35} - 4 q^{37} + 396 q^{38} - 408 q^{40} + 4 q^{41} + 92 q^{43} + 188 q^{44} - 36 q^{46} + 8 q^{47} - 308 q^{50} + 420 q^{52} + 164 q^{53} + 252 q^{55} - 552 q^{56} + 528 q^{58} - 124 q^{59} - 68 q^{61} - 216 q^{62} - 232 q^{64} + 8 q^{65} - 164 q^{67} + 368 q^{68} - 664 q^{70} + 260 q^{71} - 4 q^{73} + 532 q^{74} - 516 q^{76} - 220 q^{77} - 520 q^{79} - 312 q^{80} + 636 q^{82} + 484 q^{83} + 96 q^{85} - 688 q^{86} + 672 q^{88} + 4 q^{89} - 196 q^{91} - 616 q^{92} + 40 q^{94} - 8 q^{97} + 328 q^{98}+O(q^{100}) \) 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 44 * q^10 + 4 * q^11 - 4 * q^13 + 20 * q^14 + 16 * q^16 - 4 * q^19 - 76 * q^20 + 144 * q^22 + 68 * q^23 - 4 * q^25 - 96 * q^26 + 56 * q^28 + 4 * q^29 + 24 * q^32 - 48 * q^34 - 92 * q^35 - 4 * q^37 + 396 * q^38 - 408 * q^40 + 4 * q^41 + 92 * q^43 + 188 * q^44 - 36 * q^46 + 8 * q^47 - 308 * q^50 + 420 * q^52 + 164 * q^53 + 252 * q^55 - 552 * q^56 + 528 * q^58 - 124 * q^59 - 68 * q^61 - 216 * q^62 - 232 * q^64 + 8 * q^65 - 164 * q^67 + 368 * q^68 - 664 * q^70 + 260 * q^71 - 4 * q^73 + 532 * q^74 - 516 * q^76 - 220 * q^77 - 520 * q^79 - 312 * q^80 + 636 * q^82 + 484 * q^83 + 96 * q^85 - 688 * q^86 + 672 * q^88 + 4 * q^89 - 196 * q^91 - 616 * q^92 + 40 * q^94 - 8 * q^97 + 328 * q^98

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