LMFDB - Embedded newform 288.3.u.a.235.6

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			235.6
Character	$\chi$	$=$	288.235
Dual form			288.3.u.a.163.6

$q$-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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$	$-1$

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	0.647293	+	0.762242i	$0.275901\pi$
$5$	−1.74699	+	4.21761i	−0.349399	+	0.843523i	−0.996691	+	0.0812812i	$0.974099\pi$
$6$		0			0
$7$	−0.392379	+	0.392379i	−0.0560541	+	0.0560541i	−0.734578	−	0.678524i	$-0.762620\pi$
$7$	−0.392379	+	0.392379i	−0.0560541	+	0.0560541i	0.678524	+	0.734578i	$0.262620\pi$
$8$	−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	−0.999205	−	0.0398581i	$-0.987309\pi$
$11$	−2.90924	+	7.02353i	−0.264477	+	0.638503i	0.734729	+	0.678361i	$0.237309\pi$
$12$		0			0
$13$	−4.50555	−	10.8774i	−0.346581	−	0.836720i	−0.997019	−	0.0771604i	$-0.975415\pi$
$13$	−4.50555	−	10.8774i	−0.346581	−	0.836720i	0.650438	−	0.759559i	$-0.274585\pi$
$14$	−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	$0.100331\pi$
$17$			10.5402i			0.620012i	−0.950735	+	0.310006i	$0.899669\pi$
$18$		0			0
$19$	−1.88707	+	0.781651i	−0.0993196	+	0.0411395i	−0.431790	−	0.901974i	$-0.642118\pi$
$19$	−1.88707	+	0.781651i	−0.0993196	+	0.0411395i	0.332470	+	0.943114i	$0.392118\pi$
$20$	−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	0.716724	−	0.697357i	$-0.245641\pi$
$23$	0.445453	+	0.445453i	0.0193675	+	0.0193675i	−0.697357	+	0.716724i	$0.745641\pi$
$24$		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	−0.395437	−	0.918493i	$-0.629407\pi$
$29$	−0.741814	+	0.307270i	−0.0255798	+	0.0105955i	0.369857	+	0.929089i	$0.379407\pi$
$30$		0			0
$31$			47.6947i			1.53854i	0.638924	+	0.769270i	$0.279380\pi$
$31$			47.6947i			1.53854i	−0.638924	+	0.769270i	$0.720620\pi$
$32$	−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	−0.597371	−	0.801965i	$-0.703788\pi$
$37$	14.5080	−	35.0255i	0.392109	−	0.946635i	0.989480	−	0.144670i	$-0.0462120\pi$
$38$	−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	−0.555209	−	0.831711i	$-0.687362\pi$
$41$	11.3365	−	11.3365i	0.276501	−	0.276501i	0.831711	+	0.555209i	$0.187362\pi$
$42$		0			0
$43$	−14.6421	+	35.3493i	−0.340515	+	0.822076i	0.657149	+	0.753761i	$0.271762\pi$
$43$	−14.6421	+	35.3493i	−0.340515	+	0.822076i	−0.997664	+	0.0683149i	$0.978238\pi$
$44$	−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	0.908940	−	0.416927i	$-0.136893\pi$
$53$	66.6128	+	27.5919i	1.25685	+	0.520602i	0.347905	+	0.937530i	$0.386893\pi$
$54$		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	−0.244408	−	0.969673i	$-0.578594\pi$
$59$	−65.0706	−	26.9531i	−1.10289	−	0.456833i	−0.858484	+	0.512840i	$0.828594\pi$
$60$		0			0
$61$	87.4322	−	36.2156i	1.43331	−	0.593698i	0.475147	−	0.879906i	$-0.342395\pi$
$61$	87.4322	−	36.2156i	1.43331	−	0.593698i	0.958168	+	0.286208i	$0.0923948\pi$
$62$	−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	0.861759	−	0.507319i	$-0.169363\pi$
$67$	−7.12379	−	17.1984i	−0.106325	−	0.256692i	−0.968084	+	0.250627i	$0.919363\pi$
$68$	−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	−0.595074	−	0.803671i	$-0.702877\pi$
$71$	14.8103	−	14.8103i	0.208596	−	0.208596i	0.803671	+	0.595074i	$0.202877\pi$
$72$		0			0
$73$	18.6720	−	18.6720i	0.255781	−	0.255781i	−0.567555	−	0.823336i	$-0.692110\pi$
$73$	18.6720	−	18.6720i	0.255781	−	0.255781i	0.823336	+	0.567555i	$0.192110\pi$
$74$	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	−0.539841	−	0.841767i	$-0.681516\pi$
$83$	−27.0868	+	11.2197i	−0.326347	+	0.135177i	0.213494	+	0.976944i	$0.431516\pi$
$84$		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	0.949260	−	0.314491i	$-0.101834\pi$
$89$	56.4944	+	56.4944i	0.634769	+	0.634769i	−0.314491	+	0.949260i	$0.601834\pi$
$90$		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	−0.396379	−	0.918087i	$-0.629733\pi$
$101$	53.8420	−	129.986i	0.533089	−	1.28699i	0.929468	−	0.368903i	$-0.120267\pi$
$102$		0			0
$103$	9.94607	−	9.94607i	0.0965638	−	0.0965638i	−0.657175	−	0.753738i	$-0.728249\pi$
$103$	9.94607	−	9.94607i	0.0965638	−	0.0965638i	0.753738	+	0.657175i	$0.228249\pi$
$104$	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	0.179350	+	0.983785i	$0.442601\pi$
$107$	−68.8129	+	166.129i	−0.643111	+	1.55261i	−0.822461	+	0.568822i	$0.807399\pi$
$108$		0			0
$109$	3.61301	+	8.72257i	0.0331469	+	0.0800236i	0.939586	−	0.342313i	$-0.111210\pi$
$109$	3.61301	+	8.72257i	0.0331469	+	0.0800236i	−0.906439	+	0.422336i	$0.861210\pi$
$110$	−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	$-0.875993\pi$
$113$		−	85.8345i		−	0.759598i	0.925069	−	0.379799i	$-0.124007\pi$
$114$		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	$0.0216810\pi$
$127$			17.2873i			0.136120i	−0.997681	+	0.0680601i	$0.978319\pi$
$128$	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	0.999798	+	0.0200911i	$0.00639562\pi$
$131$	40.2223	+	97.1053i	0.307041	+	0.741262i	−0.692758	+	0.721171i	$0.743604\pi$
$132$		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	−0.794132	−	0.607745i	$-0.792074\pi$
$137$	−25.5351	+	25.5351i	−0.186387	+	0.186387i	0.607745	+	0.794132i	$0.292074\pi$
$138$		0			0
$139$	−52.2202	+	126.071i	−0.375685	+	0.906984i	0.617079	+	0.786901i	$0.288316\pi$
$139$	−52.2202	+	126.071i	−0.375685	+	0.906984i	−0.992764	+	0.120083i	$0.961684\pi$
$140$	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	−0.187993	−	0.982170i	$-0.560198\pi$
$149$	−151.298	−	62.6697i	−1.01542	−	0.420602i	−0.827430	+	0.561569i	$0.810198\pi$
$150$		0			0
$151$	−123.292	−	123.292i	−0.816505	−	0.816505i	0.169095	−	0.985600i	$-0.445916\pi$
$151$	−123.292	−	123.292i	−0.816505	−	0.816505i	−0.985600	+	0.169095i	$0.945916\pi$
$152$	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	−0.0146813	−	0.999892i	$-0.504673\pi$
$157$	107.069	−	44.3494i	0.681968	−	0.282480i	0.696649	+	0.717412i	$0.254673\pi$
$158$	−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	−0.999969	−	0.00784306i	$-0.997503\pi$
$163$	−48.6441	−	117.437i	−0.298430	−	0.720474i	0.701539	−	0.712631i	$-0.252497\pi$
$164$	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	−0.920803	−	0.390029i	$-0.872465\pi$
$167$	−88.6392	+	88.6392i	−0.530774	+	0.530774i	0.390029	+	0.920803i	$0.372465\pi$
$168$		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	−0.946993	−	0.321255i	$-0.895895\pi$
$173$	−87.2836	−	210.721i	−0.504530	−	1.21804i	0.442463	−	0.896787i	$-0.354105\pi$
$174$		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	−0.367180	−	0.930150i	$-0.619677\pi$
$179$	5.53118	−	2.29109i	0.0309005	−	0.0127994i	0.398080	+	0.917351i	$0.369677\pi$
$180$		0			0
$181$	−273.836	−	113.427i	−1.51291	−	0.626666i	−0.536751	−	0.843741i	$-0.680348\pi$
$181$	−273.836	−	113.427i	−1.51291	−	0.626666i	−0.976155	+	0.217075i	$0.930348\pi$
$182$	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	$-0.880108\pi$
$191$		−	140.503i		−	0.735620i	0.929901	−	0.367810i	$-0.119892\pi$
$192$		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	−0.853466	−	0.521149i	$-0.825504\pi$
$197$	23.3511	−	56.3745i	0.118533	−	0.286165i	0.971999	+	0.234984i	$0.0755037\pi$
$198$		0			0
$199$	138.741	−	138.741i	0.697191	−	0.697191i	−0.266613	−	0.963804i	$-0.585904\pi$
$199$	138.741	−	138.741i	0.697191	−	0.697191i	0.963804	+	0.266613i	$0.0859044\pi$
$200$	−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	−0.792158	−	0.610316i	$-0.791043\pi$
$211$	−194.276	+	80.4718i	−0.920740	+	0.381383i	−0.128582	+	0.991699i	$0.541043\pi$
$212$	−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	$0.221546\pi$
$223$			285.957i			1.28232i	−0.767408	+	0.641160i	$0.778454\pi$
$224$	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	0.905208	−	0.424969i	$-0.139715\pi$
$227$	−8.02885	−	19.3834i	−0.0353694	−	0.0853893i	−0.940577	+	0.339580i	$0.889715\pi$
$228$		0			0
$229$	−66.9028	+	161.518i	−0.292152	+	0.705317i	−0.999999	−	0.00104819i	$-0.999666\pi$
$229$	−66.9028	+	161.518i	−0.292152	+	0.705317i	0.707848	+	0.706365i	$0.249666\pi$
$230$	−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	−0.241001	+	0.970525i	$0.577476\pi$
$233$	−282.286	+	282.286i	−1.21153	+	1.21153i	−0.970525	+	0.241001i	$0.922524\pi$
$234$		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	$-0.840346\pi$
$241$		−	231.745i		−	0.961599i	0.876830	−	0.480800i	$-0.159654\pi$
$242$	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	0.104578	−	0.994517i	$-0.466651\pi$
$251$	−131.701	−	54.5521i	−0.524703	−	0.217339i	−0.629281	+	0.777177i	$0.716651\pi$
$252$		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	−0.0630921	−	0.998008i	$-0.520096\pi$
$263$	245.883	−	245.883i	0.934916	−	0.934916i	0.998008	+	0.0630921i	$0.0200962\pi$
$264$		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	0.909655	−	0.415365i	$-0.136346\pi$
$269$	−7.33716	−	17.7135i	−0.0272757	−	0.0658493i	−0.936931	+	0.349516i	$0.886346\pi$
$270$		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	0.324294	−	0.945956i	$-0.394873\pi$
$277$	−31.9345	−	13.2277i	−0.115287	−	0.0477535i	−0.439581	+	0.898203i	$0.644873\pi$
$278$	−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	0.998154	−	0.0607409i	$-0.0193463\pi$
$281$	263.413	+	263.413i	0.937413	+	0.937413i	−0.0607409	+	0.998154i	$0.519346\pi$
$282$		0			0
$283$	−268.113	−	111.056i	−0.947397	−	0.392425i	−0.145145	−	0.989410i	$-0.546365\pi$
$283$	−268.113	−	111.056i	−0.947397	−	0.392425i	−0.802252	+	0.596986i	$0.796365\pi$
$284$	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	−0.981687	−	0.190503i	$-0.938988\pi$
$293$	−44.7772	+	108.102i	−0.152823	+	0.368948i	0.828863	+	0.559451i	$0.188988\pi$
$294$		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	0.451930	−	0.892054i	$-0.350736\pi$
$307$	430.497	−	178.318i	1.40227	−	0.580839i	0.950340	+	0.311215i	$0.100736\pi$
$308$	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	0.798793	−	0.601606i	$-0.205472\pi$
$311$	61.3250	+	61.3250i	0.197187	+	0.197187i	−0.601606	+	0.798793i	$0.705472\pi$
$312$		0			0
$313$	129.308	+	129.308i	0.413124	+	0.413124i	0.882826	−	0.469701i	$-0.155638\pi$
$313$	129.308	+	129.308i	0.413124	+	0.413124i	−0.469701	+	0.882826i	$0.655638\pi$
$314$	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	0.118522	−	0.992951i	$-0.462184\pi$
$317$	286.711	−	118.760i	0.904452	−	0.374636i	0.785930	+	0.618315i	$0.212184\pi$
$318$		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	−0.621297	−	0.783575i	$-0.713394\pi$
$331$	123.164	−	297.345i	0.372098	−	0.898324i	0.993395	−	0.114748i	$-0.0366061\pi$
$332$	−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	$-0.872068\pi$
$337$		−	263.653i		−	0.782354i	0.920315	−	0.391177i	$-0.127932\pi$
$338$	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	0.864151	−	0.503233i	$-0.167856\pi$
$347$	388.417	+	160.888i	1.11936	+	0.463653i	0.255208	+	0.966886i	$0.417856\pi$
$348$		0			0
$349$	448.277	−	185.683i	1.28446	−	0.532042i	0.367132	−	0.930169i	$-0.380340\pi$
$349$	448.277	−	185.683i	1.28446	−	0.532042i	0.917330	+	0.398127i	$0.130340\pi$
$350$	−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	−0.353810	−	0.935317i	$-0.615114\pi$
$359$	208.761	−	208.761i	0.581508	−	0.581508i	0.935317	+	0.353810i	$0.115114\pi$
$360$		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	−0.587287	−	0.809379i	$-0.699804\pi$
$373$	−587.430	−	243.321i	−1.57488	−	0.652336i	−0.987592	+	0.157043i	$0.949804\pi$
$374$	−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	0.336677	−	0.941620i	$-0.390697\pi$
$379$	−34.5203	−	14.2988i	−0.0910825	−	0.0377276i	−0.427759	+	0.903893i	$0.640697\pi$
$380$	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	$0.149937\pi$
$383$			347.623i			0.907631i	−0.891096	+	0.453815i	$0.850063\pi$
$384$		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	−0.826352	−	0.563154i	$-0.809588\pi$
$389$	60.7529	−	146.670i	0.156177	−	0.377045i	0.982529	+	0.186109i	$0.0595878\pi$
$390$		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	0.971545	+	0.236855i	$0.0761165\pi$
$397$	179.460	+	433.255i	0.452041	+	1.09132i	−0.519505	+	0.854468i	$0.673883\pi$
$398$	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	$-0.677466\pi$
$401$		−	680.550i		−	1.69713i	0.529089	−	0.848566i	$-0.322534\pi$
$402$		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	0.936706	−	0.350117i	$-0.113858\pi$
$409$	239.915	+	239.915i	0.586589	+	0.586589i	−0.350117	+	0.936706i	$0.613858\pi$
$410$	−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	0.878833	−	0.477129i	$-0.158322\pi$
$419$	−33.5102	−	80.9009i	−0.0799767	−	0.193081i	−0.958810	+	0.284048i	$0.908322\pi$
$420$		0			0
$421$	37.2975	−	90.0441i	0.0885926	−	0.213882i	−0.873373	−	0.487052i	$-0.838072\pi$
$421$	37.2975	−	90.0441i	0.0885926	−	0.213882i	0.961966	+	0.273170i	$0.0880723\pi$
$422$	−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	$-0.975714\pi$
$433$		−	66.0083i		−	0.152444i	0.997091	−	0.0762220i	$-0.0242858\pi$
$434$	−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	0.660261	−	0.751036i	$-0.270446\pi$
$439$	−39.8501	−	39.8501i	−0.0907747	−	0.0907747i	−0.751036	+	0.660261i	$0.770446\pi$
$440$	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	0.590517	−	0.807025i	$-0.298924\pi$
$443$	193.778	+	80.2656i	0.437423	+	0.181187i	−0.153094	+	0.988212i	$0.548924\pi$
$444$		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	−0.300159	+	0.953889i	$0.597040\pi$
$457$	−573.100	+	573.100i	−1.25405	+	1.25405i	−0.953889	+	0.300159i	$0.902960\pi$
$458$	−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	0.989321	−	0.145750i	$-0.0465596\pi$
$461$	86.0707	+	207.793i	0.186704	+	0.450744i	−0.802617	+	0.596495i	$0.796560\pi$
$462$		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	−0.0130269	−	0.999915i	$-0.504147\pi$
$467$	319.806	−	132.468i	0.684809	−	0.283657i	0.697835	+	0.716258i	$0.254147\pi$
$468$		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	$0.0804567\pi$
$479$			239.576i			0.500159i	−0.968225	+	0.250079i	$0.919543\pi$
$480$		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	−0.927432	−	0.373992i	$-0.877989\pi$
$487$	−269.525	+	269.525i	−0.553439	+	0.553439i	0.373992	+	0.927432i	$0.377989\pi$
$488$	−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	0.310430	+	0.950596i	$0.399527\pi$
$491$	−285.394	+	689.002i	−0.581250	+	1.40326i	−0.891680	+	0.452666i	$0.850473\pi$
$492$		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	0.285373	−	0.958417i	$-0.407883\pi$
$499$	581.267	−	240.769i	1.16486	−	0.482503i	0.879492	+	0.475914i	$0.157883\pi$
$500$	−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	0.474379	−	0.880321i	$-0.342673\pi$
$503$	−204.189	−	204.189i	−0.405942	−	0.405942i	−0.880321	+	0.474379i	$0.842673\pi$
$504$		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	0.0437202	−	0.999044i	$-0.486079\pi$
$509$	397.562	−	164.676i	0.781066	−	0.323528i	0.737345	+	0.675516i	$0.236079\pi$
$510$		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	−0.309983	−	0.950742i	$-0.600324\pi$
$521$	333.835	−	333.835i	0.640759	−	0.640759i	0.950742	+	0.309983i	$0.100324\pi$
$522$		0			0
$523$	−211.672	+	511.022i	−0.404727	+	0.977097i	0.581775	+	0.813350i	$0.302358\pi$
$523$	−211.672	+	511.022i	−0.404727	+	0.977097i	−0.986502	+	0.163748i	$0.947642\pi$
$524$	−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	−0.814016	−	0.580842i	$-0.802723\pi$
$541$	−529.582	+	219.360i	−0.978896	+	0.405472i	−0.164879	+	0.986314i	$0.552723\pi$
$542$	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	0.848820	−	0.528682i	$-0.177314\pi$
$547$	−68.4960	−	165.364i	−0.125221	−	0.302311i	−0.974041	+	0.226371i	$0.927314\pi$
$548$	−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	0.914408	+	0.404794i	$0.132657\pi$
$557$	308.610	+	745.049i	0.554057	+	1.33761i	−0.360351	+	0.932817i	$0.617343\pi$
$558$		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	−0.0523978	−	0.998626i	$-0.516686\pi$
$563$	347.195	−	143.813i	0.616687	−	0.255440i	0.669085	+	0.743186i	$0.266686\pi$
$564$		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	−0.950768	−	0.309903i	$-0.899703\pi$
$569$	−717.322	−	717.322i	−1.26067	−	1.26067i	−0.309903	−	0.950768i	$-0.600297\pi$
$570$		0			0
$571$	−327.041	−	135.465i	−0.572751	−	0.237241i	0.0774591	−	0.996996i	$-0.475319\pi$
$571$	−327.041	−	135.465i	−0.572751	−	0.237241i	−0.650210	+	0.759754i	$0.725319\pi$
$572$	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	−0.987938	−	0.154850i	$-0.950510\pi$
$587$	−105.581	+	254.894i	−0.179865	+	0.434232i	0.808073	+	0.589082i	$0.200510\pi$
$588$		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	$0.111175\pi$
$593$			405.861i			0.684419i	−0.939624	+	0.342210i	$0.888825\pi$
$594$		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	0.0607815	−	0.998151i	$-0.480641\pi$
$599$	−561.484	−	561.484i	−0.937370	−	0.937370i	−0.998151	+	0.0607815i	$0.980641\pi$
$600$		0			0
$601$	−358.762	−	358.762i	−0.596941	−	0.596941i	0.342556	−	0.939497i	$-0.388707\pi$
$601$	−358.762	−	358.762i	−0.596941	−	0.596941i	−0.939497	+	0.342556i	$0.888707\pi$
$602$	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	$0.156145\pi$
$607$			571.923i			0.942213i	−0.882076	+	0.471107i	$0.843855\pi$
$608$	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	−0.151494	−	0.988458i	$-0.548409\pi$
$613$	401.254	−	968.712i	0.654574	−	1.58028i	0.806068	−	0.591823i	$-0.201591\pi$
$614$	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	−0.573242	−	0.819386i	$-0.694315\pi$
$617$	151.870	−	151.870i	0.246143	−	0.246143i	0.819386	+	0.573242i	$0.194315\pi$
$618$		0			0
$619$	146.518	−	353.725i	0.236701	−	0.571446i	−0.760237	−	0.649646i	$-0.774917\pi$
$619$	146.518	−	353.725i	0.236701	−	0.571446i	0.996938	+	0.0781999i	$0.0249173\pi$
$620$	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	−0.996354	−	0.0853189i	$-0.972809\pi$
$631$	−682.535	−	682.535i	−1.08167	−	1.08167i	−0.0853189	−	0.996354i	$-0.527191\pi$
$632$	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	0.951864	+	0.306522i	$0.0991652\pi$
$643$	318.631	+	769.243i	0.495538	+	1.19633i	−0.456326	+	0.889813i	$0.650835\pi$
$644$	−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	−0.574887	−	0.818233i	$-0.694954\pi$
$647$	157.445	−	157.445i	0.243346	−	0.243346i	0.818233	+	0.574887i	$0.194954\pi$
$648$		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	0.935435	−	0.353498i	$-0.115008\pi$
$653$	15.6861	+	37.8696i	0.0240216	+	0.0579933i	−0.911414	+	0.411492i	$0.865008\pi$
$654$		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	−0.520146	−	0.854078i	$-0.674122\pi$
$659$	−187.169	+	77.5281i	−0.284020	+	0.117645i	0.236125	+	0.971723i	$0.424122\pi$
$660$		0			0
$661$	30.1818	+	12.5017i	0.0456608	+	0.0189133i	0.405397	−	0.914141i	$-0.367133\pi$
$661$	30.1818	+	12.5017i	0.0456608	+	0.0189133i	−0.359736	+	0.933054i	$0.617133\pi$
$662$	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	−0.986643	−	0.162895i	$-0.947917\pi$
$677$	−117.661	+	284.058i	−0.173797	+	0.419583i	0.812846	+	0.582478i	$0.197917\pi$
$678$		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	−0.486104	−	0.873901i	$-0.661583\pi$
$683$	324.811	−	784.162i	0.475564	−	1.14811i	0.961669	−	0.274213i	$-0.0884175\pi$
$684$		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	0.306149	−	0.951984i	$-0.400959\pi$
$691$	826.286	−	342.259i	1.19578	−	0.495309i	0.889634	+	0.456674i	$0.150959\pi$
$692$	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	−0.668049	−	0.744117i	$-0.732870\pi$
$701$	−430.597	+	178.359i	−0.614260	+	0.254435i	0.0537885	+	0.998552i	$0.482870\pi$
$702$		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	−0.968882	−	0.247523i	$-0.920384\pi$
$709$	−77.1066	+	186.152i	−0.108754	+	0.262555i	0.860128	+	0.510078i	$0.170384\pi$
$710$	−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	0.973755	−	0.227599i	$-0.0730875\pi$
$727$	542.456	+	542.456i	0.746156	+	0.746156i	−0.227599	+	0.973755i	$0.573087\pi$
$728$	−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	0.0353965	−	0.999373i	$-0.488731\pi$
$733$	562.276	−	232.903i	0.767089	−	0.317739i	0.731693	+	0.681635i	$0.238731\pi$
$734$	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	−0.984100	−	0.177614i	$-0.943162\pi$
$739$	−305.819	−	738.312i	−0.413828	−	0.999070i	0.570272	−	0.821456i	$-0.306838\pi$
$740$	−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	−0.980238	−	0.197823i	$-0.936613\pi$
$743$	−581.334	+	581.334i	−0.782414	+	0.782414i	0.197823	+	0.980238i	$0.436613\pi$
$744$		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	0.268502	−	0.963279i	$-0.413472\pi$
$757$	−168.645	−	69.8549i	−0.222780	−	0.0922786i	−0.491282	+	0.871001i	$0.663472\pi$
$758$	−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	0.401520	−	0.915850i	$-0.368482\pi$
$761$	−391.406	−	391.406i	−0.514331	−	0.514331i	−0.915850	+	0.401520i	$0.868482\pi$
$762$		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	−0.806537	−	0.591184i	$-0.798661\pi$
$773$	140.532	−	339.275i	0.181801	−	0.438907i	0.988338	+	0.152277i	$0.0486607\pi$
$774$		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	−0.883686	−	0.468080i	$-0.844946\pi$
$787$	−926.743	+	383.870i	−1.17756	+	0.487763i	−0.293878	+	0.955843i	$0.594946\pi$
$788$	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	0.238553	−	0.971130i	$-0.423327\pi$
$797$	871.860	−	361.136i	1.09393	−	0.453119i	0.855374	+	0.518010i	$0.173327\pi$
$798$		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	−0.997004	−	0.0773465i	$-0.975355\pi$
$809$	−744.003	+	744.003i	−0.919658	+	0.919658i	0.0773465	+	0.997004i	$0.475355\pi$
$810$		0			0
$811$	−307.315	+	741.925i	−0.378934	+	0.914827i	0.613233	+	0.789902i	$0.289869\pi$
$811$	−307.315	+	741.925i	−0.378934	+	0.914827i	−0.992166	+	0.124924i	$0.960131\pi$
$812$	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	0.876213	−	0.481924i	$-0.160062\pi$
$821$	948.269	+	392.786i	1.15502	+	0.478424i	0.278804	+	0.960348i	$0.410062\pi$
$822$		0			0
$823$	492.275	+	492.275i	0.598147	+	0.598147i	0.939819	−	0.341672i	$-0.110993\pi$
$823$	492.275	+	492.275i	0.598147	+	0.598147i	−0.341672	+	0.939819i	$0.610993\pi$
$824$	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	0.995600	−	0.0937082i	$-0.0298721\pi$
$827$	1350.77	+	559.506i	1.63333	+	0.676549i	0.637734	+	0.770257i	$0.279872\pi$
$828$		0			0
$829$	441.547	−	182.895i	0.532627	−	0.220621i	−0.100127	−	0.994975i	$-0.531925\pi$
$829$	441.547	−	182.895i	0.532627	−	0.220621i	0.632753	+	0.774354i	$0.281925\pi$
$830$	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	−0.0126775	+	0.999920i	$0.504035\pi$
$839$	−849.569	+	849.569i	−1.01260	+	1.01260i	−0.999920	+	0.0126775i	$0.995965\pi$
$840$		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	0.786827	−	0.617173i	$-0.211722\pi$
$853$	773.493	+	320.391i	0.906791	+	0.375605i	0.119964	+	0.992778i	$0.461722\pi$
$854$	−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	0.841899	−	0.539635i	$-0.181438\pi$
$857$	259.040	+	259.040i	0.302264	+	0.302264i	−0.539635	+	0.841899i	$0.681438\pi$
$858$		0			0
$859$	−762.123	−	315.682i	−0.887221	−	0.367499i	−0.107928	−	0.994159i	$-0.534422\pi$
$859$	−762.123	−	315.682i	−0.887221	−	0.367499i	−0.779293	+	0.626660i	$0.784422\pi$
$860$	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	$-0.785216\pi$
$863$		−	1078.25i		−	1.24942i	0.780855	−	0.624712i	$-0.214784\pi$
$864$		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	0.975105	+	0.221745i	$0.0711753\pi$
$877$	387.984	+	936.676i	0.442399	+	1.06805i	−0.532706	+	0.846301i	$0.678825\pi$
$878$	−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	$-0.740774\pi$
$881$		−	1281.50i		−	1.45460i	0.686318	−	0.727301i	$-0.259226\pi$
$882$		0			0
$883$	−1014.19	+	420.092i	−1.14857	+	0.475755i	−0.874055	−	0.485826i	$-0.838519\pi$
$883$	−1014.19	+	420.092i	−1.14857	+	0.475755i	−0.274519	+	0.961582i	$0.588519\pi$
$884$	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	0.738560	−	0.674187i	$-0.235506\pi$
$887$	57.0987	+	57.0987i	0.0643728	+	0.0643728i	−0.674187	+	0.738560i	$0.735506\pi$
$888$		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	−0.652918	−	0.757429i	$-0.726455\pi$
$907$	312.323	−	754.015i	0.344348	−	0.831329i	0.997266	−	0.0739002i	$-0.0235446\pi$
$908$	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	0.512924	−	0.858434i	$-0.328562\pi$
$919$	−317.523	−	317.523i	−0.345510	−	0.345510i	−0.858434	+	0.512924i	$0.828562\pi$
$920$	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	−0.473724	−	0.880673i	$-0.657091\pi$
$937$	381.311	−	381.311i	0.406949	−	0.406949i	0.880673	+	0.473724i	$0.157091\pi$
$938$	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	−0.997783	−	0.0665513i	$-0.978800\pi$
$941$	−319.284	−	770.819i	−0.339303	−	0.819149i	0.658480	−	0.752598i	$-0.271200\pi$
$942$		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	−0.358066	−	0.933696i	$-0.616564\pi$
$947$	46.3711	−	19.2075i	0.0489663	−	0.0202825i	0.407032	+	0.913414i	$0.366564\pi$
$948$		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	0.904766	−	0.425909i	$-0.140045\pi$
$953$	456.351	+	456.351i	0.478858	+	0.478858i	−0.425909	+	0.904766i	$0.640045\pi$
$954$		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	−0.416719	−	0.909035i	$-0.636820\pi$
$967$	476.069	−	476.069i	0.492316	−	0.492316i	0.909035	+	0.416719i	$0.136820\pi$
$968$	−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	−0.422248	−	0.906480i	$-0.638759\pi$
$971$	502.303	−	1212.67i	0.517305	−	1.24888i	0.939553	−	0.342404i	$-0.111241\pi$
$972$		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	$0.000191467\pi$
$977$			1.17535i			0.00120302i	−1.00000		0.000601512i	$0.999809\pi$
$978$		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	0.999695	+	0.0246998i	$0.00786298\pi$
$983$	1006.98	+	1006.98i	1.02439	+	1.02439i	0.0246998	+	0.999695i	$0.492137\pi$
$984$		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	$-0.773461\pi$
$991$		−	1294.48i		−	1.30624i	0.757256	−	0.653118i	$-0.226539\pi$
$992$	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	−0.877248	−	0.480037i	$-0.840623\pi$
$997$	82.2498	−	198.568i	0.0824973	−	0.199166i	0.959746	+	0.280871i	$0.0906233\pi$
$998$	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.235.6		28
3.2	odd	2		32.3.h.a.11.2	yes	28
12.11	even	2		128.3.h.a.79.1		28
24.5	odd	2		256.3.h.b.159.1		28
24.11	even	2		256.3.h.a.159.7		28
32.3	odd	8	inner	288.3.u.a.163.6		28
96.29	odd	8		128.3.h.a.47.1		28
96.35	even	8		32.3.h.a.3.2	✓	28
96.77	odd	8		256.3.h.a.95.7		28
96.83	even	8		256.3.h.b.95.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.2	✓	28	96.35	even	8
32.3.h.a.11.2	yes	28	3.2	odd	2
128.3.h.a.47.1		28	96.29	odd	8
128.3.h.a.79.1		28	12.11	even	2
256.3.h.a.95.7		28	96.77	odd	8
256.3.h.a.159.7		28	24.11	even	2
256.3.h.b.95.1		28	96.83	even	8
256.3.h.b.159.1		28	24.5	odd	2
288.3.u.a.163.6		28	32.3	odd	8	inner
288.3.u.a.235.6		28	1.1	even	1	trivial

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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