LMFDB - Embedded newform 135.3.g.b.82.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,3,Mod(28,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("135.28"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.g (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 286x^{12} + 16269x^{8} + 85684x^{4} + 62500 $ x^16 + 286x^12 + 16269x^8 + 85684*x^4 + 62500
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{8}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			82.7
Root			$2.04178 + 2.04178i$ of defining polynomial
Character	$\chi$	$=$	135.82
Dual form			135.3.g.b.28.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.04178 + 2.04178i) q^{2} +4.33774i q^{4} +(-4.12923 + 2.81948i) q^{5} +(8.42562 + 8.42562i) q^{7} +(-0.689596 + 0.689596i) q^{8} +(-14.1877 - 2.67423i) q^{10} -12.2996 q^{11} +(0.663508 - 0.663508i) q^{13} +34.4066i q^{14} +14.5350 q^{16} +(7.47753 + 7.47753i) q^{17} -25.0163i q^{19} +(-12.2302 - 17.9115i) q^{20} +(-25.1131 - 25.1131i) q^{22} +(18.1099 - 18.1099i) q^{23} +(9.10111 - 23.2845i) q^{25} +2.70947 q^{26} +(-36.5482 + 36.5482i) q^{28} -3.38342i q^{29} +28.8829 q^{31} +(32.4356 + 32.4356i) q^{32} +30.5350i q^{34} +(-58.5472 - 11.0355i) q^{35} +(-2.59583 - 2.59583i) q^{37} +(51.0778 - 51.0778i) q^{38} +(0.903202 - 4.79180i) q^{40} -23.3394 q^{41} +(-11.6343 + 11.6343i) q^{43} -53.3525i q^{44} +73.9528 q^{46} +(-49.0360 - 49.0360i) q^{47} +92.9823i q^{49} +(66.1244 - 28.9595i) q^{50} +(2.87812 + 2.87812i) q^{52} +(27.6894 - 27.6894i) q^{53} +(50.7879 - 34.6784i) q^{55} -11.6205 q^{56} +(6.90820 - 6.90820i) q^{58} +87.7539i q^{59} -79.0489 q^{61} +(58.9725 + 58.9725i) q^{62} +74.3129i q^{64} +(-0.869033 + 4.61052i) q^{65} +(-45.3085 - 45.3085i) q^{67} +(-32.4356 + 32.4356i) q^{68} +(-97.0085 - 142.073i) q^{70} +88.7641 q^{71} +(12.8174 - 12.8174i) q^{73} -10.6002i q^{74} +108.514 q^{76} +(-103.632 - 103.632i) q^{77} +30.3588i q^{79} +(-60.0182 + 40.9810i) q^{80} +(-47.6540 - 47.6540i) q^{82} +(-107.379 + 107.379i) q^{83} +(-51.9592 - 9.79374i) q^{85} -47.5092 q^{86} +(8.48175 - 8.48175i) q^{88} -117.891i q^{89} +11.1809 q^{91} +(78.5559 + 78.5559i) q^{92} -200.242i q^{94} +(70.5328 + 103.298i) q^{95} +(13.5295 + 13.5295i) q^{97} +(-189.850 + 189.850i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{7} + 40 q^{10} + 40 q^{13} - 152 q^{16} - 136 q^{22} - 32 q^{25} - 112 q^{28} + 200 q^{31} + 16 q^{37} - 48 q^{40} + 136 q^{43} + 152 q^{46} + 640 q^{52} + 248 q^{55} + 48 q^{58} - 280 q^{61}+ \cdots + 448 q^{97}+O(q^{100}) $ 16 * q + 16 * q^7 + 40 * q^10 + 40 * q^13 - 152 * q^16 - 136 * q^22 - 32 * q^25 - 112 * q^28 + 200 * q^31 + 16 * q^37 - 48 * q^40 + 136 * q^43 + 152 * q^46 + 640 * q^52 + 248 * q^55 + 48 * q^58 - 280 * q^61 - 344 * q^67 - 696 * q^70 - 776 * q^73 + 144 * q^76 - 880 * q^82 - 176 * q^85 + 1200 * q^88 + 152 * q^91 + 448 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	2.04178	+	2.04178i	1.02089	+	1.02089i	0.999777	+	0.0211136i	$0.00672116\pi$
$2$	2.04178	+	2.04178i	1.02089	+	1.02089i	0.0211136	+	0.999777i	$0.493279\pi$
$3$		0			0
$3$		0			0
$4$			4.33774i			1.08444i
$5$	−4.12923	+	2.81948i	−0.825846	+	0.563895i
$5$	−4.12923	+	2.81948i	−0.825846	+	0.563895i
$6$		0			0
$7$	8.42562	+	8.42562i	1.20366	+	1.20366i	0.973045	+	0.230616i	$0.0740740\pi$
$7$	8.42562	+	8.42562i	1.20366	+	1.20366i	0.230616	+	0.973045i	$0.425926\pi$
$8$	−0.689596	+	0.689596i	−0.0861995	+	0.0861995i
$9$		0			0
$10$	−14.1877	−	2.67423i	−1.41877	−	0.267423i
$11$	−12.2996			−1.11815			−0.559073	−	0.829119i	$-0.688843\pi$
$11$	−12.2996			−1.11815			−0.559073	+	0.829119i	$0.688843\pi$
$12$		0			0
$13$	0.663508	−	0.663508i	0.0510390	−	0.0510390i	−0.681127	−	0.732166i	$-0.738510\pi$
$13$	0.663508	−	0.663508i	0.0510390	−	0.0510390i	0.732166	+	0.681127i	$0.238510\pi$
$14$			34.4066i			2.45761i
$15$		0			0
$16$	14.5350			0.908435
$17$	7.47753	+	7.47753i	0.439855	+	0.439855i	0.891963	−	0.452108i	$-0.149328\pi$
$17$	7.47753	+	7.47753i	0.439855	+	0.439855i	−0.452108	+	0.891963i	$0.649328\pi$
$18$		0			0
$19$		−	25.0163i		−	1.31665i	−0.752735	−	0.658323i	$-0.771266\pi$
$19$		−	25.0163i		−	1.31665i	0.752735	−	0.658323i	$-0.228734\pi$
$20$	−12.2302	−	17.9115i	−0.611508	−	0.895577i
$21$		0			0
$22$	−25.1131	−	25.1131i	−1.14150	−	1.14150i
$23$	18.1099	−	18.1099i	0.787386	−	0.787386i	−0.193679	−	0.981065i	$-0.562042\pi$
$23$	18.1099	−	18.1099i	0.787386	−	0.787386i	0.981065	+	0.193679i	$0.0620421\pi$
$24$		0			0
$25$	9.10111	−	23.2845i	0.364044	−	0.931382i
$26$	2.70947			0.104211
$27$		0			0
$28$	−36.5482	+	36.5482i	−1.30529	+	1.30529i
$29$		−	3.38342i		−	0.116670i	−0.998297	−	0.0583348i	$-0.981421\pi$
$29$		−	3.38342i		−	0.116670i	0.998297	−	0.0583348i	$-0.0185791\pi$
$30$		0			0
$31$	28.8829			0.931705			0.465853	−	0.884862i	$-0.345748\pi$
$31$	28.8829			0.931705			0.465853	+	0.884862i	$0.345748\pi$
$32$	32.4356	+	32.4356i	1.01361	+	1.01361i
$33$		0			0
$34$			30.5350i			0.898087i
$35$	−58.5472	−	11.0355i	−1.67278	−	0.315300i
$36$		0			0
$37$	−2.59583	−	2.59583i	−0.0701575	−	0.0701575i	0.671157	−	0.741315i	$-0.265797\pi$
$37$	−2.59583	−	2.59583i	−0.0701575	−	0.0701575i	−0.741315	+	0.671157i	$0.765797\pi$
$38$	51.0778	−	51.0778i	1.34415	−	1.34415i
$39$		0			0
$40$	0.903202	−	4.79180i	0.0225800	−	0.119795i
$41$	−23.3394			−0.569255			−0.284627	−	0.958638i	$-0.591870\pi$
$41$	−23.3394			−0.569255			−0.284627	+	0.958638i	$0.591870\pi$
$42$		0			0
$43$	−11.6343	+	11.6343i	−0.270564	+	0.270564i	−0.829327	−	0.558763i	$-0.811276\pi$
$43$	−11.6343	+	11.6343i	−0.270564	+	0.270564i	0.558763	+	0.829327i	$0.311276\pi$
$44$		−	53.3525i		−	1.21256i
$45$		0			0
$46$	73.9528			1.60767
$47$	−49.0360	−	49.0360i	−1.04332	−	1.04332i	−0.999018	−	0.0443011i	$-0.985894\pi$
$47$	−49.0360	−	49.0360i	−1.04332	−	1.04332i	−0.0443011	−	0.999018i	$-0.514106\pi$
$48$		0			0
$49$			92.9823i			1.89760i
$50$	66.1244	−	28.9595i	1.32249	−	0.579189i
$51$		0			0
$52$	2.87812	+	2.87812i	0.0553486	+	0.0553486i
$53$	27.6894	−	27.6894i	0.522442	−	0.522442i	−0.395866	−	0.918308i	$-0.629556\pi$
$53$	27.6894	−	27.6894i	0.522442	−	0.522442i	0.918308	+	0.395866i	$0.129556\pi$
$54$		0			0
$55$	50.7879	−	34.6784i	0.923416	−	0.630517i
$56$	−11.6205			−0.207510
$57$		0			0
$58$	6.90820	−	6.90820i	0.119107	−	0.119107i
$59$			87.7539i			1.48735i	0.668539	+	0.743677i	$0.266920\pi$
$59$			87.7539i			1.48735i	−0.668539	+	0.743677i	$0.733080\pi$
$60$		0			0
$61$	−79.0489			−1.29588			−0.647942	−	0.761690i	$-0.724370\pi$
$61$	−79.0489			−1.29588			−0.647942	+	0.761690i	$0.724370\pi$
$62$	58.9725	+	58.9725i	0.951169	+	0.951169i
$63$		0			0
$64$			74.3129i			1.16114i
$65$	−0.869033	+	4.61052i	−0.0133697	+	0.0709311i
$66$		0			0
$67$	−45.3085	−	45.3085i	−0.676246	−	0.676246i	0.282902	−	0.959149i	$-0.408703\pi$
$67$	−45.3085	−	45.3085i	−0.676246	−	0.676246i	−0.959149	+	0.282902i	$0.908703\pi$
$68$	−32.4356	+	32.4356i	−0.476994	+	0.476994i
$69$		0			0
$70$	−97.0085	−	142.073i	−1.38584	−	2.02961i
$71$	88.7641			1.25020			0.625099	−	0.780546i	$-0.285059\pi$
$71$	88.7641			1.25020			0.625099	+	0.780546i	$0.285059\pi$
$72$		0			0
$73$	12.8174	−	12.8174i	0.175581	−	0.175581i	−0.613845	−	0.789426i	$-0.710378\pi$
$73$	12.8174	−	12.8174i	0.175581	−	0.175581i	0.789426	+	0.613845i	$0.210378\pi$
$74$		−	10.6002i		−	0.143246i
$75$		0			0
$76$	108.514			1.42782
$77$	−103.632	−	103.632i	−1.34587	−	1.34587i
$78$		0			0
$79$			30.3588i			0.384289i	0.981367	+	0.192144i	$0.0615442\pi$
$79$			30.3588i			0.384289i	−0.981367	+	0.192144i	$0.938456\pi$
$80$	−60.0182	+	40.9810i	−0.750228	+	0.512262i
$81$		0			0
$82$	−47.6540	−	47.6540i	−0.581147	−	0.581147i
$83$	−107.379	+	107.379i	−1.29373	+	1.29373i	−0.361260	+	0.932465i	$0.617653\pi$
$83$	−107.379	+	107.379i	−1.29373	+	1.29373i	−0.932465	+	0.361260i	$0.882347\pi$
$84$		0			0
$85$	−51.9592	−	9.79374i	−0.611284	−	0.115220i
$86$	−47.5092			−0.552433
$87$		0			0
$88$	8.48175	−	8.48175i	0.0963835	−	0.0963835i
$89$		−	117.891i		−	1.32462i	−0.749231	−	0.662309i	$-0.769577\pi$
$89$		−	117.891i		−	1.32462i	0.749231	−	0.662309i	$-0.230423\pi$
$90$		0			0
$91$	11.1809			0.122867
$92$	78.5559	+	78.5559i	0.853869	+	0.853869i
$93$		0			0
$94$		−	200.242i		−	2.13023i
$95$	70.5328	+	103.298i	0.742451	+	1.08735i
$96$		0			0
$97$	13.5295	+	13.5295i	0.139480	+	0.139480i	0.773399	−	0.633919i	$-0.218555\pi$
$97$	13.5295	+	13.5295i	0.139480	+	0.139480i	−0.633919	+	0.773399i	$0.718555\pi$
$98$	−189.850	+	189.850i	−1.93724	+	1.93724i
$99$		0			0
$100$	101.002	+	39.4783i	1.01002	+	0.394783i
$101$	19.6506			0.194561			0.0972804	−	0.995257i	$-0.468986\pi$
$101$	19.6506			0.194561			0.0972804	+	0.995257i	$0.468986\pi$
$102$		0			0
$103$	−121.219	+	121.219i	−1.17689	+	1.17689i	−0.196354	+	0.980533i	$0.562910\pi$
$103$	−121.219	+	121.219i	−1.17689	+	1.17689i	−0.980533	+	0.196354i	$0.937090\pi$
$104$			0.915104i			0.00879908i
$105$		0			0
$106$	113.072			1.06671
$107$	10.5840	+	10.5840i	0.0989155	+	0.0989155i	0.754833	−	0.655917i	$-0.227718\pi$
$107$	10.5840	+	10.5840i	0.0989155	+	0.0989155i	−0.655917	+	0.754833i	$0.727718\pi$
$108$		0			0
$109$		−	9.08051i		−	0.0833075i	−0.999132	−	0.0416537i	$-0.986737\pi$
$109$		−	9.08051i		−	0.0833075i	0.999132	−	0.0416537i	$-0.0132626\pi$
$110$	174.503	+	32.8920i	1.58640	+	0.299018i
$111$		0			0
$112$	122.466	+	122.466i	1.09345	+	1.09345i
$113$	108.813	−	108.813i	0.962949	−	0.962949i	−0.0363886	−	0.999338i	$-0.511585\pi$
$113$	108.813	−	108.813i	0.962949	−	0.962949i	0.999338	+	0.0363886i	$0.0115854\pi$
$114$		0			0
$115$	−23.7195	+	125.840i	−0.206257	+	1.09426i
$116$	14.6764			0.126521
$117$		0			0
$118$	−179.174	+	179.174i	−1.51843	+	1.51843i
$119$			126.006i			1.05887i
$120$		0			0
$121$	30.2801			0.250248
$122$	−161.400	−	161.400i	−1.32295	−	1.32295i
$123$		0			0
$124$			125.286i			1.01037i
$125$	28.0696	+	121.808i	0.224557	+	0.974461i
$126$		0			0
$127$	−115.169	−	115.169i	−0.906841	−	0.906841i	0.0891750	−	0.996016i	$-0.471577\pi$
$127$	−115.169	−	115.169i	−0.906841	−	0.906841i	−0.996016	+	0.0891750i	$0.971577\pi$
$128$	−21.9884	+	21.9884i	−0.171784	+	0.171784i
$129$		0			0
$130$	−11.1880	+	7.63930i	−0.0860619	+	0.0587638i
$131$	−18.8578			−0.143952			−0.0719762	−	0.997406i	$-0.522931\pi$
$131$	−18.8578			−0.143952			−0.0719762	+	0.997406i	$0.522931\pi$
$132$		0			0
$133$	210.778	−	210.778i	1.58480	−	1.58480i
$134$		−	185.020i		−	1.38075i
$135$		0			0
$136$	−10.3129			−0.0758305
$137$	−53.4836	−	53.4836i	−0.390391	−	0.390391i	0.484436	−	0.874827i	$-0.339025\pi$
$137$	−53.4836	−	53.4836i	−0.390391	−	0.390391i	−0.874827	+	0.484436i	$0.839025\pi$
$138$		0			0
$139$			44.9528i			0.323401i	0.986840	+	0.161701i	$0.0516979\pi$
$139$			44.9528i			0.323401i	−0.986840	+	0.161701i	$0.948302\pi$
$140$	47.8692	−	253.963i	0.341923	−	1.81402i
$141$		0			0
$142$	181.237	+	181.237i	1.27632	+	1.27632i
$143$	−8.16088	+	8.16088i	−0.0570691	+	0.0570691i
$144$		0			0
$145$	9.53947	+	13.9709i	0.0657894	+	0.0963512i
$146$	52.3406			0.358498
$147$		0			0
$148$	11.2600	−	11.2600i	0.0760813	−	0.0760813i
$149$		−	164.230i		−	1.10222i	−0.834434	−	0.551108i	$-0.814205\pi$
$149$		−	164.230i		−	1.10222i	0.834434	−	0.551108i	$-0.185795\pi$
$150$		0			0
$151$	38.4022			0.254319			0.127159	−	0.991882i	$-0.459414\pi$
$151$	38.4022			0.254319			0.127159	+	0.991882i	$0.459414\pi$
$152$	17.2511	+	17.2511i	0.113494	+	0.113494i
$153$		0			0
$154$		−	423.187i		−	2.74797i
$155$	−119.264	+	81.4346i	−0.769446	+	0.525384i
$156$		0			0
$157$	−46.0663	−	46.0663i	−0.293416	−	0.293416i	0.545012	−	0.838428i	$-0.316525\pi$
$157$	−46.0663	−	46.0663i	−0.293416	−	0.293416i	−0.838428	+	0.545012i	$0.816525\pi$
$158$	−61.9860	+	61.9860i	−0.392317	+	0.392317i
$159$		0			0
$160$	−225.385	−	42.4827i	−1.40866	−	0.265517i
$161$	305.174			1.89549
$162$		0			0
$163$	20.9849	−	20.9849i	0.128742	−	0.128742i	−0.639800	−	0.768542i	$-0.720983\pi$
$163$	20.9849	−	20.9849i	0.128742	−	0.128742i	0.768542	+	0.639800i	$0.220983\pi$
$164$		−	101.240i		−	0.617320i
$165$		0			0
$166$	−438.490			−2.64150
$167$	66.3800	+	66.3800i	0.397485	+	0.397485i	0.877345	−	0.479860i	$-0.159313\pi$
$167$	66.3800	+	66.3800i	0.397485	+	0.397485i	−0.479860	+	0.877345i	$0.659313\pi$
$168$		0			0
$169$			168.120i			0.994790i
$170$	−86.0926	−	126.086i	−0.506427	−	0.741682i
$171$		0			0
$172$	−50.4664	−	50.4664i	−0.293409	−	0.293409i
$173$	140.922	−	140.922i	0.814575	−	0.814575i	−0.170741	−	0.985316i	$-0.554616\pi$
$173$	140.922	−	140.922i	0.814575	−	0.814575i	0.985316	+	0.170741i	$0.0546160\pi$
$174$		0			0
$175$	272.869	−	119.504i	1.55925	−	0.682882i
$176$	−178.774			−1.01576
$177$		0			0
$178$	240.708	−	240.708i	1.35229	−	1.35229i
$179$			45.6130i			0.254821i	0.991850	+	0.127411i	$0.0406666\pi$
$179$			45.6130i			0.254821i	−0.991850	+	0.127411i	$0.959333\pi$
$180$		0			0
$181$	−104.793			−0.578968			−0.289484	−	0.957183i	$-0.593484\pi$
$181$	−104.793			−0.578968			−0.289484	+	0.957183i	$0.593484\pi$
$182$	22.8290	+	22.8290i	0.125434	+	0.125434i
$183$		0			0
$184$			24.9770i			0.135744i
$185$	18.0377	+	3.39990i	0.0975009	+	0.0183778i
$186$		0			0
$187$	−91.9706	−	91.9706i	−0.491821	−	0.491821i
$188$	212.706	−	212.706i	1.13141	−	1.13141i
$189$		0			0
$190$	−66.8994	+	354.925i	−0.352102	+	1.86802i
$191$	101.295			0.530338			0.265169	−	0.964202i	$-0.414572\pi$
$191$	101.295			0.530338			0.265169	+	0.964202i	$0.414572\pi$
$192$		0			0
$193$	200.041	−	200.041i	1.03648	−	1.03648i	0.0371741	−	0.999309i	$-0.488164\pi$
$193$	200.041	−	200.041i	1.03648	−	1.03648i	0.999309	−	0.0371741i	$-0.0118356\pi$
$194$			55.2487i			0.284787i
$195$		0			0
$196$	−403.333			−2.05782
$197$	5.26310	+	5.26310i	0.0267163	+	0.0267163i	0.720339	−	0.693622i	$-0.243986\pi$
$197$	5.26310	+	5.26310i	0.0267163	+	0.0267163i	−0.693622	+	0.720339i	$0.743986\pi$
$198$		0			0
$199$			141.070i			0.708895i	0.935076	+	0.354448i	$0.115331\pi$
$199$			141.070i			0.708895i	−0.935076	+	0.354448i	$0.884669\pi$
$200$	9.78083	+	22.3330i	0.0489042	+	0.111665i
$201$		0			0
$202$	40.1223	+	40.1223i	0.198625	+	0.198625i
$203$	28.5074	−	28.5074i	0.140431	−	0.140431i
$204$		0			0
$205$	96.3739	−	65.8050i	0.470117	−	0.321000i
$206$	−495.007			−2.40295
$207$		0			0
$208$	9.64406	−	9.64406i	0.0463657	−	0.0463657i
$209$			307.690i			1.47220i
$210$		0			0
$211$	−45.1068			−0.213777			−0.106888	−	0.994271i	$-0.534089\pi$
$211$	−45.1068			−0.213777			−0.106888	+	0.994271i	$0.534089\pi$
$212$	120.110	+	120.110i	0.566555	+	0.566555i
$213$		0			0
$214$			43.2203i			0.201964i
$215$	15.2380	−	80.8431i	0.0708746	−	0.376014i
$216$		0			0
$217$	243.356	+	243.356i	1.12146	+	1.12146i
$218$	18.5404	−	18.5404i	0.0850478	−	0.0850478i
$219$		0			0
$220$	150.426	+	220.305i	0.683755	+	1.00139i
$221$	9.92280			0.0448995
$222$		0			0
$223$	−3.96818	+	3.96818i	−0.0177945	+	0.0177945i	−0.715948	−	0.698154i	$-0.754005\pi$
$223$	−3.96818	+	3.96818i	−0.0177945	+	0.0177945i	0.698154	+	0.715948i	$0.254005\pi$
$224$			546.580i			2.44009i
$225$		0			0
$226$	444.346			1.96613
$227$	53.7498	+	53.7498i	0.236783	+	0.236783i	0.815517	−	0.578734i	$-0.196453\pi$
$227$	53.7498	+	53.7498i	0.236783	+	0.236783i	−0.578734	+	0.815517i	$0.696453\pi$
$228$		0			0
$229$		−	55.1897i		−	0.241003i	−0.992713	−	0.120502i	$-0.961550\pi$
$229$		−	55.1897i		−	0.241003i	0.992713	−	0.120502i	$-0.0384503\pi$
$230$	−305.368	+	208.508i	−1.32769	+	0.906557i
$231$		0			0
$232$	2.33319	+	2.33319i	0.0100569	+	0.0100569i
$233$	96.4842	−	96.4842i	0.414095	−	0.414095i	−0.469067	−	0.883162i	$-0.655410\pi$
$233$	96.4842	−	96.4842i	0.414095	−	0.414095i	0.883162	+	0.469067i	$0.155410\pi$
$234$		0			0
$235$	340.737	+	64.2252i	1.44994	+	0.273299i
$236$	−380.654			−1.61294
$237$		0			0
$238$	−257.276	+	257.276i	−1.08099	+	1.08099i
$239$			147.427i			0.616848i	0.951249	+	0.308424i	$0.0998015\pi$
$239$			147.427i			0.616848i	−0.951249	+	0.308424i	$0.900198\pi$
$240$		0			0
$241$	−358.998			−1.48962			−0.744809	−	0.667278i	$-0.767459\pi$
$241$	−358.998			−1.48962			−0.744809	+	0.667278i	$0.767459\pi$
$242$	61.8253	+	61.8253i	0.255476	+	0.255476i
$243$		0			0
$244$		−	342.894i		−	1.40530i
$245$	−262.161	−	383.945i	−1.07005	−	1.56712i
$246$		0			0
$247$	−16.5985	−	16.5985i	−0.0672004	−	0.0672004i
$248$	−19.9175	+	19.9175i	−0.0803125	+	0.0803125i
$249$		0			0
$250$	−191.393	+	306.017i	−0.765570	+	1.22407i
$251$	−154.041			−0.613710			−0.306855	−	0.951756i	$-0.599277\pi$
$251$	−154.041			−0.613710			−0.306855	+	0.951756i	$0.599277\pi$
$252$		0			0
$253$	−222.744	+	222.744i	−0.880411	+	0.880411i
$254$		−	470.299i		−	1.85157i
$255$		0			0
$256$	207.461			0.810394
$257$	244.160	+	244.160i	0.950040	+	0.950040i	0.998810	−	0.0487696i	$-0.0155300\pi$
$257$	244.160	+	244.160i	0.950040	+	0.950040i	−0.0487696	+	0.998810i	$0.515530\pi$
$258$		0			0
$259$		−	43.7430i		−	0.168892i
$260$	−19.9992	−	3.76964i	−0.0769202	−	0.0144986i
$261$		0			0
$262$	−38.5035	−	38.5035i	−0.146960	−	0.146960i
$263$	−184.303	+	184.303i	−0.700773	+	0.700773i	−0.964577	−	0.263803i	$-0.915023\pi$
$263$	−184.303	+	184.303i	−0.700773	+	0.700773i	0.263803	+	0.964577i	$0.415023\pi$
$264$		0			0
$265$	−36.2664	+	192.406i	−0.136854	+	0.726060i
$266$	860.725			3.23581
$267$		0			0
$268$	196.537	−	196.537i	0.733345	−	0.733345i
$269$			194.835i			0.724296i	0.932121	+	0.362148i	$0.117956\pi$
$269$			194.835i			0.724296i	−0.932121	+	0.362148i	$0.882044\pi$
$270$		0			0
$271$	−307.130			−1.13332			−0.566661	−	0.823951i	$-0.691765\pi$
$271$	−307.130			−1.13332			−0.566661	+	0.823951i	$0.691765\pi$
$272$	108.686	+	108.686i	0.399579	+	0.399579i
$273$		0			0
$274$		−	218.404i		−	0.797094i
$275$	−111.940	+	286.390i	−0.407054	+	1.04142i
$276$		0			0
$277$	−75.0856	−	75.0856i	−0.271067	−	0.271067i	0.558462	−	0.829530i	$-0.311391\pi$
$277$	−75.0856	−	75.0856i	−0.271067	−	0.271067i	−0.829530	+	0.558462i	$0.811391\pi$
$278$	−91.7838	+	91.7838i	−0.330157	+	0.330157i
$279$		0			0
$280$	47.9839	−	32.7639i	0.171371	−	0.117014i
$281$	−1.14960			−0.00409109			−0.00204554	−	0.999998i	$-0.500651\pi$
$281$	−1.14960			−0.00409109			−0.00204554	+	0.999998i	$0.500651\pi$
$282$		0			0
$283$	226.854	−	226.854i	0.801605	−	0.801605i	−0.181742	−	0.983346i	$-0.558173\pi$
$283$	226.854	−	226.854i	0.801605	−	0.801605i	0.983346	+	0.181742i	$0.0581734\pi$
$284$			385.036i			1.35576i
$285$		0			0
$286$	−33.3254			−0.116523
$287$	−196.649	−	196.649i	−0.685189	−	0.685189i
$288$		0			0
$289$		−	177.173i		−	0.613056i
$290$	−9.04805	+	48.0031i	−0.0312002	+	0.165528i
$291$		0			0
$292$	55.5986	+	55.5986i	0.190406	+	0.190406i
$293$	72.6950	−	72.6950i	0.248106	−	0.248106i	−0.572087	−	0.820193i	$-0.693866\pi$
$293$	72.6950	−	72.6950i	0.248106	−	0.248106i	0.820193	+	0.572087i	$0.193866\pi$
$294$		0			0
$295$	−247.420	−	362.356i	−0.838712	−	1.22833i
$296$	3.58015			0.0120951
$297$		0			0
$298$	335.322	−	335.322i	1.12524	−	1.12524i
$299$		−	24.0321i		−	0.0803748i
$300$		0			0
$301$	−196.052			−0.651335
$302$	78.4088	+	78.4088i	0.259632	+	0.259632i
$303$		0			0
$304$		−	363.611i		−	1.19609i
$305$	326.411	−	222.876i	1.07020	−	0.730742i
$306$		0			0
$307$	−74.6079	−	74.6079i	−0.243023	−	0.243023i	0.575077	−	0.818099i	$-0.304972\pi$
$307$	−74.6079	−	74.6079i	−0.243023	−	0.243023i	−0.818099	+	0.575077i	$0.804972\pi$
$308$	449.528	−	449.528i	1.45951	−	1.45951i
$309$		0			0
$310$	−409.783	−	77.2396i	−1.32188	−	0.249160i
$311$	−597.260			−1.92045			−0.960225	−	0.279227i	$-0.909922\pi$
$311$	−597.260			−1.92045			−0.960225	+	0.279227i	$0.909922\pi$
$312$		0			0
$313$	−119.926	+	119.926i	−0.383149	+	0.383149i	−0.872235	−	0.489086i	$-0.837330\pi$
$313$	−119.926	+	119.926i	−0.383149	+	0.383149i	0.489086	+	0.872235i	$0.337330\pi$
$314$		−	188.115i		−	0.599091i
$315$		0			0
$316$	−131.689			−0.416736
$317$	−288.991	−	288.991i	−0.911643	−	0.911643i	0.0847581	−	0.996402i	$-0.472988\pi$
$317$	−288.991	−	288.991i	−0.911643	−	0.911643i	−0.996402	+	0.0847581i	$0.972988\pi$
$318$		0			0
$319$			41.6147i			0.130454i
$320$	−209.524	−	306.855i	−0.654761	−	0.958923i
$321$		0			0
$322$	623.098	+	623.098i	1.93509	+	1.93509i
$323$	187.060	−	187.060i	0.579133	−	0.579133i
$324$		0			0
$325$	−9.41081	−	21.4881i	−0.0289564	−	0.0661173i
$326$	85.6933			0.262863
$327$		0			0
$328$	16.0948	−	16.0948i	0.0490694	−	0.0490694i
$329$		−	826.318i		−	2.51160i
$330$		0			0
$331$	420.290			1.26976			0.634879	−	0.772611i	$-0.281050\pi$
$331$	420.290			1.26976			0.634879	+	0.772611i	$0.281050\pi$
$332$	−465.783	−	465.783i	−1.40296	−	1.40296i
$333$		0			0
$334$			271.067i			0.811578i
$335$	314.835	+	59.3431i	0.939807	+	0.177143i
$336$		0			0
$337$	−205.557	−	205.557i	−0.609962	−	0.609962i	0.332974	−	0.942936i	$-0.391948\pi$
$337$	−205.557	−	205.557i	−0.609962	−	0.609962i	−0.942936	+	0.332974i	$0.891948\pi$
$338$	−343.263	+	343.263i	−1.01557	+	1.01557i
$339$		0			0
$340$	42.4827	−	225.385i	0.124949	−	0.662898i
$341$	−355.248			−1.04178
$342$		0			0
$343$	−370.578	+	370.578i	−1.08040	+	1.08040i
$344$		−	16.0459i		−	0.0466450i
$345$		0			0
$346$	575.462			1.66318
$347$	388.193	+	388.193i	1.11871	+	1.11871i	0.991931	+	0.126783i	$0.0404651\pi$
$347$	388.193	+	388.193i	1.11871	+	1.11871i	0.126783	+	0.991931i	$0.459535\pi$
$348$		0			0
$349$			435.439i			1.24768i	0.781554	+	0.623838i	$0.214428\pi$
$349$			435.439i			1.24768i	−0.781554	+	0.623838i	$0.785572\pi$
$350$	801.141	+	313.138i	2.28897	+	0.894680i
$351$		0			0
$352$	−398.945	−	398.945i	−1.13337	−	1.13337i
$353$	−235.342	+	235.342i	−0.666692	+	0.666692i	−0.956949	−	0.290257i	$-0.906259\pi$
$353$	−235.342	+	235.342i	−0.666692	+	0.666692i	0.290257	+	0.956949i	$0.406259\pi$
$354$		0			0
$355$	−366.527	+	250.268i	−1.03247	+	0.704981i
$356$	511.381			1.43646
$357$		0			0
$358$	−93.1318	+	93.1318i	−0.260145	+	0.260145i
$359$			114.922i			0.320116i	0.987108	+	0.160058i	$0.0511682\pi$
$359$			114.922i			0.320116i	−0.987108	+	0.160058i	$0.948832\pi$
$360$		0			0
$361$	−264.815			−0.733559
$362$	−213.965	−	213.965i	−0.591063	−	0.591063i
$363$		0			0
$364$			48.5000i			0.133242i
$365$	−16.7877	+	89.0643i	−0.0459936	+	0.244012i
$366$		0			0
$367$	369.732	+	369.732i	1.00744	+	1.00744i	0.999972	+	0.00747267i	$0.00237865\pi$
$367$	369.732	+	369.732i	1.00744	+	1.00744i	0.00747267	+	0.999972i	$0.497621\pi$
$368$	263.226	−	263.226i	0.715289	−	0.715289i
$369$		0			0
$370$	29.8871	+	43.7708i	0.0807759	+	0.118299i
$371$	466.602			1.25769
$372$		0			0
$373$	150.598	−	150.598i	0.403747	−	0.403747i	−0.475804	−	0.879551i	$-0.657843\pi$
$373$	150.598	−	150.598i	0.403747	−	0.403747i	0.879551	+	0.475804i	$0.157843\pi$
$374$		−	375.568i		−	1.00419i
$375$		0			0
$376$	67.6300			0.179867
$377$	−2.24492	−	2.24492i	−0.00595470	−	0.00595470i
$378$		0			0
$379$			672.519i			1.77446i	0.461331	+	0.887228i	$0.347372\pi$
$379$			672.519i			1.77446i	−0.461331	+	0.887228i	$0.652628\pi$
$380$	−448.080	+	305.953i	−1.17916	+	0.805140i
$381$		0			0
$382$	206.821	+	206.821i	0.541417	+	0.541417i
$383$	−215.302	+	215.302i	−0.562146	+	0.562146i	−0.929917	−	0.367771i	$-0.880121\pi$
$383$	−215.302	+	215.302i	−0.562146	+	0.562146i	0.367771	+	0.929917i	$0.380121\pi$
$384$		0			0
$385$	720.107	+	135.732i	1.87041	+	0.352551i
$386$	816.881			2.11627
$387$		0			0
$388$	−58.6876	+	58.6876i	−0.151257	+	0.151257i
$389$		−	711.699i		−	1.82956i	−0.403952	−	0.914780i	$-0.632364\pi$
$389$		−	711.699i		−	1.82956i	0.403952	−	0.914780i	$-0.367636\pi$
$390$		0			0
$391$	270.834			0.692671
$392$	−64.1202	−	64.1202i	−0.163572	−	0.163572i
$393$		0			0
$394$			21.4922i			0.0545488i
$395$	−85.5959	−	125.359i	−0.216699	−	0.317363i
$396$		0			0
$397$	−41.4605	−	41.4605i	−0.104435	−	0.104435i	0.652959	−	0.757393i	$-0.273527\pi$
$397$	−41.4605	−	41.4605i	−0.104435	−	0.104435i	−0.757393	+	0.652959i	$0.773527\pi$
$398$	−288.034	+	288.034i	−0.723705	+	0.723705i
$399$		0			0
$400$	132.284	−	338.440i	0.330711	−	0.846100i
$401$	−166.372			−0.414892			−0.207446	−	0.978246i	$-0.566515\pi$
$401$	−166.372			−0.414892			−0.207446	+	0.978246i	$0.566515\pi$
$402$		0			0
$403$	19.1640	−	19.1640i	0.0475534	−	0.0475534i
$404$			85.2394i			0.210989i
$405$		0			0
$406$	116.412			0.286729
$407$	31.9277	+	31.9277i	0.0784463	+	0.0784463i
$408$		0			0
$409$			23.7379i			0.0580390i	0.999579	+	0.0290195i	$0.00923848\pi$
$409$			23.7379i			0.0580390i	−0.999579	+	0.0290195i	$0.990762\pi$
$410$	331.134	+	62.4151i	0.807644	+	0.152232i
$411$		0			0
$412$	−525.818	−	525.818i	−1.27626	−	1.27626i
$413$	−739.382	+	739.382i	−1.79027	+	1.79027i
$414$		0			0
$415$	140.640	−	746.147i	0.338893	−	1.79794i
$416$	43.0425			0.103468
$417$		0			0
$418$	−628.236	+	628.236i	−1.50296	+	1.50296i
$419$		−	499.572i		−	1.19229i	−0.802875	−	0.596147i	$-0.796697\pi$
$419$		−	499.572i		−	1.19229i	0.802875	−	0.596147i	$-0.203303\pi$
$420$		0			0
$421$	−3.80963			−0.00904901			−0.00452450	−	0.999990i	$-0.501440\pi$
$421$	−3.80963			−0.00904901			−0.00452450	+	0.999990i	$0.501440\pi$
$422$	−92.0983	−	92.0983i	−0.218242	−	0.218242i
$423$		0			0
$424$			38.1890i			0.0900685i
$425$	242.165	−	106.057i	0.569799	−	0.249546i
$426$		0			0
$427$	−666.036	−	666.036i	−1.55980	−	1.55980i
$428$	−45.9105	+	45.9105i	−0.107267	+	0.107267i
$429$		0			0
$430$	196.177	−	133.951i	0.456225	−	0.311514i
$431$	−767.834			−1.78152			−0.890759	−	0.454477i	$-0.849826\pi$
$431$	−767.834			−1.78152			−0.890759	+	0.454477i	$0.849826\pi$
$432$		0			0
$433$	367.840	−	367.840i	0.849516	−	0.849516i	−0.140557	−	0.990073i	$-0.544889\pi$
$433$	367.840	−	367.840i	0.849516	−	0.849516i	0.990073	+	0.140557i	$0.0448893\pi$
$434$			993.760i			2.28977i
$435$		0			0
$436$	39.3889			0.0903416
$437$	−453.042	−	453.042i	−1.03671	−	1.03671i
$438$		0			0
$439$		−	137.458i		−	0.313116i	−0.987669	−	0.156558i	$-0.949960\pi$
$439$		−	137.458i		−	0.313116i	0.987669	−	0.156558i	$-0.0500398\pi$
$440$	−11.1090	+	58.9372i	−0.0252478	+	0.133948i
$441$		0			0
$442$	20.2602	+	20.2602i	0.0458375	+	0.0458375i
$443$	−312.553	+	312.553i	−0.705538	+	0.705538i	−0.965594	−	0.260055i	$-0.916259\pi$
$443$	−312.553	+	312.553i	−0.705538	+	0.705538i	0.260055	+	0.965594i	$0.416259\pi$
$444$		0			0
$445$	332.391	+	486.799i	0.746946	+	1.09393i
$446$	−16.2043			−0.0363326
$447$		0			0
$448$	−626.133	+	626.133i	−1.39762	+	1.39762i
$449$			827.291i			1.84252i	0.388949	+	0.921259i	$0.372838\pi$
$449$			827.291i			1.84252i	−0.388949	+	0.921259i	$0.627162\pi$
$450$		0			0
$451$	287.066			0.636509
$452$	472.004	+	472.004i	1.04426	+	1.04426i
$453$		0			0
$454$			219.491i			0.483459i
$455$	−46.1687	+	31.5244i	−0.101470	+	0.0692843i
$456$		0			0
$457$	−626.172	−	626.172i	−1.37018	−	1.37018i	−0.860167	−	0.510013i	$-0.829640\pi$
$457$	−626.172	−	626.172i	−1.37018	−	1.37018i	−0.510013	−	0.860167i	$-0.670360\pi$
$458$	112.685	−	112.685i	0.246038	−	0.246038i
$459$		0			0
$460$	−545.862	−	102.889i	−1.18666	−	0.223672i
$461$	261.839			0.567980			0.283990	−	0.958827i	$-0.408342\pi$
$461$	261.839			0.567980			0.283990	+	0.958827i	$0.408342\pi$
$462$		0			0
$463$	119.188	−	119.188i	0.257426	−	0.257426i	−0.566580	−	0.824007i	$-0.691734\pi$
$463$	119.188	−	119.188i	0.257426	−	0.257426i	0.824007	+	0.566580i	$0.191734\pi$
$464$		−	49.1779i		−	0.105987i
$465$		0			0
$466$	393.999			0.845492
$467$	−63.7603	−	63.7603i	−0.136532	−	0.136532i	0.635538	−	0.772070i	$-0.280778\pi$
$467$	−63.7603	−	63.7603i	−0.136532	−	0.136532i	−0.772070	+	0.635538i	$0.780778\pi$
$468$		0			0
$469$		−	763.505i		−	1.62794i
$470$	564.576	+	826.844i	1.20123	+	1.75924i
$471$		0			0
$472$	−60.5147	−	60.5147i	−0.128209	−	0.128209i
$473$	143.097	−	143.097i	0.302530	−	0.302530i
$474$		0			0
$475$	−582.493	−	227.676i	−1.22630	−	0.479318i
$476$	−546.580			−1.14828
$477$		0			0
$478$	−301.013	+	301.013i	−0.629734	+	0.629734i
$479$		−	38.8332i		−	0.0810714i	−0.999178	−	0.0405357i	$-0.987094\pi$
$479$		−	38.8332i		−	0.0810714i	0.999178	−	0.0405357i	$-0.0129064\pi$
$480$		0			0
$481$	−3.44470			−0.00716155
$482$	−732.995	−	732.995i	−1.52074	−	1.52074i
$483$		0			0
$484$			131.347i			0.271378i
$485$	−94.0127	−	17.7204i	−0.193841	−	0.0365369i
$486$		0			0
$487$	394.799	+	394.799i	0.810676	+	0.810676i	0.984735	−	0.174059i	$-0.0556883\pi$
$487$	394.799	+	394.799i	0.810676	+	0.810676i	−0.174059	+	0.984735i	$0.555688\pi$
$488$	54.5118	−	54.5118i	0.111704	−	0.111704i
$489$		0			0
$490$	248.657	−	1319.21i	0.507462	−	2.69226i
$491$	460.743			0.938377			0.469188	−	0.883098i	$-0.344547\pi$
$491$	460.743			0.938377			0.469188	+	0.883098i	$0.344547\pi$
$492$		0			0
$493$	25.2996	−	25.2996i	0.0513177	−	0.0513177i
$494$		−	67.7810i		−	0.137209i
$495$		0			0
$496$	419.811			0.846394
$497$	747.893	+	747.893i	1.50481	+	1.50481i
$498$		0			0
$499$			850.644i			1.70470i	0.522974	+	0.852349i	$0.324822\pi$
$499$			850.644i			1.70470i	−0.522974	+	0.852349i	$0.675178\pi$
$500$	−528.370	+	121.759i	−1.05674	+	0.243518i
$501$		0			0
$502$	−314.519	−	314.519i	−0.626531	−	0.626531i
$503$	196.093	−	196.093i	0.389847	−	0.389847i	−0.484786	−	0.874633i	$-0.661103\pi$
$503$	196.093	−	196.093i	0.389847	−	0.389847i	0.874633	+	0.484786i	$0.161103\pi$
$504$		0			0
$505$	−81.1420	+	55.4045i	−0.160677	+	0.109712i
$506$	−909.589			−1.79761
$507$		0			0
$508$	499.573	−	499.573i	0.983411	−	0.983411i
$509$			390.319i			0.766835i	0.923575	+	0.383417i	$0.125253\pi$
$509$			390.319i			0.766835i	−0.923575	+	0.383417i	$0.874747\pi$
$510$		0			0
$511$	215.989			0.422679
$512$	511.543	+	511.543i	0.999108	+	0.999108i
$513$		0			0
$514$			997.044i			1.93977i
$515$	158.768	−	842.318i	0.308287	−	1.63557i
$516$		0			0
$517$	603.123	+	603.123i	1.16658	+	1.16658i
$518$	89.3136	−	89.3136i	0.172420	−	0.172420i
$519$		0			0
$520$	−2.58011	−	3.77868i	−0.00496176	−	0.00726668i
$521$	679.963			1.30511			0.652556	−	0.757741i	$-0.273697\pi$
$521$	679.963			1.30511			0.652556	+	0.757741i	$0.273697\pi$
$522$		0			0
$523$	442.612	−	442.612i	0.846295	−	0.846295i	−0.143374	−	0.989669i	$-0.545795\pi$
$523$	442.612	−	442.612i	0.846295	−	0.846295i	0.989669	+	0.143374i	$0.0457951\pi$
$524$		−	81.8002i		−	0.156107i
$525$		0			0
$526$	−752.615			−1.43083
$527$	215.973	+	215.973i	0.409815	+	0.409815i
$528$		0			0
$529$		−	126.935i		−	0.239952i
$530$	−466.899	+	318.803i	−0.880941	+	0.601514i
$531$		0			0
$532$	914.300	+	914.300i	1.71861	+	1.71861i
$533$	−15.4859	+	15.4859i	−0.0290542	+	0.0290542i
$534$		0			0
$535$	−73.5448	−	13.8624i	−0.137467	−	0.0259110i
$536$	62.4891			0.116584
$537$		0			0
$538$	−397.811	+	397.811i	−0.739427	+	0.739427i
$539$		−	1143.64i		−	2.12179i
$540$		0			0
$541$	780.447			1.44260			0.721300	−	0.692623i	$-0.243545\pi$
$541$	780.447			1.44260			0.721300	+	0.692623i	$0.243545\pi$
$542$	−627.093	−	627.093i	−1.15700	−	1.15700i
$543$		0			0
$544$			485.076i			0.891684i
$545$	25.6023	+	37.4955i	0.0469767	+	0.0687992i
$546$		0			0
$547$	−245.581	−	245.581i	−0.448960	−	0.448960i	0.446048	−	0.895009i	$-0.352831\pi$
$547$	−245.581	−	245.581i	−0.448960	−	0.448960i	−0.895009	+	0.446048i	$0.852831\pi$
$548$	231.998	−	231.998i	0.423354	−	0.423354i
$549$		0			0
$550$	−813.304	+	356.190i	−1.47873	+	0.647618i
$551$	−84.6406			−0.153613
$552$		0			0
$553$	−255.792	+	255.792i	−0.462553	+	0.462553i
$554$		−	306.617i		−	0.553460i
$555$		0			0
$556$	−194.994			−0.350708
$557$	670.322	+	670.322i	1.20345	+	1.20345i	0.973110	+	0.230341i	$0.0739840\pi$
$557$	670.322	+	670.322i	1.20345	+	1.20345i	0.230341	+	0.973110i	$0.426016\pi$
$558$		0			0
$559$			15.4388i			0.0276187i
$560$	−850.981	−	160.401i	−1.51961	−	0.286430i
$561$		0			0
$562$	−2.34722	−	2.34722i	−0.00417655	−	0.00417655i
$563$	308.161	−	308.161i	0.547354	−	0.547354i	−0.378320	−	0.925675i	$-0.623498\pi$
$563$	308.161	−	308.161i	0.547354	−	0.547354i	0.925675	+	0.378320i	$0.123498\pi$
$564$		0			0
$565$	−142.519	+	756.111i	−0.252246	+	1.33825i
$566$	926.373			1.63670
$567$		0			0
$568$	−61.2113	+	61.2113i	−0.107766	+	0.107766i
$569$			773.974i			1.36024i	0.733103	+	0.680118i	$0.238072\pi$
$569$			773.974i			1.36024i	−0.733103	+	0.680118i	$0.761928\pi$
$570$		0			0
$571$	467.801			0.819267			0.409633	−	0.912250i	$-0.365657\pi$
$571$	467.801			0.819267			0.409633	+	0.912250i	$0.365657\pi$
$572$	−35.3998	−	35.3998i	−0.0618877	−	0.0618877i
$573$		0			0
$574$		−	803.030i		−	1.39901i
$575$	−256.860	−	586.500i	−0.446713	−	1.02000i
$576$		0			0
$577$	272.029	+	272.029i	0.471454	+	0.471454i	0.902385	−	0.430931i	$-0.141815\pi$
$577$	272.029	+	272.029i	0.471454	+	0.471454i	−0.430931	+	0.902385i	$0.641815\pi$
$578$	361.749	−	361.749i	0.625863	−	0.625863i
$579$		0			0
$580$	−60.6022	+	41.3798i	−0.104487	+	0.0713444i
$581$	−1809.47			−3.11441
$582$		0			0
$583$	−340.569	+	340.569i	−0.584166	+	0.584166i
$584$			17.6776i			0.0302699i
$585$		0			0
$586$	296.855			0.506578
$587$	−99.9169	−	99.9169i	−0.170216	−	0.170216i	0.616858	−	0.787074i	$-0.288405\pi$
$587$	−99.9169	−	99.9169i	−0.170216	−	0.170216i	−0.787074	+	0.616858i	$0.788405\pi$
$588$		0			0
$589$		−	722.542i		−	1.22673i
$590$	234.675	−	1245.03i	0.397754	−	2.11022i
$591$		0			0
$592$	−37.7303	−	37.7303i	−0.0637336	−	0.0637336i
$593$	94.3094	−	94.3094i	0.159038	−	0.159038i	−0.623102	−	0.782140i	$-0.714128\pi$
$593$	94.3094	−	94.3094i	0.159038	−	0.159038i	0.782140	+	0.623102i	$0.214128\pi$
$594$		0			0
$595$	−355.270	−	520.307i	−0.597093	−	0.874465i
$596$	712.388			1.19528
$597$		0			0
$598$	49.0682	−	49.0682i	0.0820539	−	0.0820539i
$599$			835.468i			1.39477i	0.716696	+	0.697386i	$0.245654\pi$
$599$			835.468i			1.39477i	−0.716696	+	0.697386i	$0.754346\pi$
$600$		0			0
$601$	359.618			0.598366			0.299183	−	0.954196i	$-0.403286\pi$
$601$	359.618			0.598366			0.299183	+	0.954196i	$0.403286\pi$
$602$	−400.295	−	400.295i	−0.664942	−	0.664942i
$603$		0			0
$604$			166.579i			0.275793i
$605$	−125.033	+	85.3739i	−0.206667	+	0.141114i
$606$		0			0
$607$	364.454	+	364.454i	0.600419	+	0.600419i	0.940424	−	0.340005i	$-0.110429\pi$
$607$	364.454	+	364.454i	0.600419	+	0.600419i	−0.340005	+	0.940424i	$0.610429\pi$
$608$	811.418	−	811.418i	1.33457	−	1.33457i
$609$		0			0
$610$	1121.52	+	211.395i	1.83857	+	0.346550i
$611$	−65.0715			−0.106500
$612$		0			0
$613$	−470.150	+	470.150i	−0.766965	+	0.766965i	−0.977571	−	0.210606i	$-0.932456\pi$
$613$	−470.150	+	470.150i	−0.766965	+	0.766965i	0.210606	+	0.977571i	$0.432456\pi$
$614$		−	304.666i		−	0.496199i
$615$		0			0
$616$	142.928			0.232026
$617$	179.232	+	179.232i	0.290490	+	0.290490i	0.837274	−	0.546784i	$-0.184148\pi$
$617$	179.232	+	179.232i	0.290490	+	0.290490i	−0.546784	+	0.837274i	$0.684148\pi$
$618$		0			0
$619$			102.707i			0.165924i	0.996553	+	0.0829618i	$0.0264380\pi$
$619$			102.707i			0.165924i	−0.996553	+	0.0829618i	$0.973562\pi$
$620$	−353.242	−	517.337i	−0.569745	−	0.834414i
$621$		0			0
$622$	−1219.47	−	1219.47i	−1.96057	−	1.96057i
$623$	993.305	−	993.305i	1.59439	−	1.59439i
$624$		0			0
$625$	−459.340	−	423.830i	−0.734943	−	0.678128i
$626$	−489.724			−0.782306
$627$		0			0
$628$	199.824	−	199.824i	0.318191	−	0.318191i
$629$		−	38.8208i		−	0.0617183i
$630$		0			0
$631$	−1201.04			−1.90339			−0.951696	−	0.307042i	$-0.900661\pi$
$631$	−1201.04			−1.90339			−0.951696	+	0.307042i	$0.900661\pi$
$632$	−20.9353	−	20.9353i	−0.0331255	−	0.0331255i
$633$		0			0
$634$		−	1180.11i		−	1.86138i
$635$	800.274	+	150.843i	1.26027	+	0.237548i
$636$		0			0
$637$	61.6945	+	61.6945i	0.0968516	+	0.0968516i
$638$	−84.9681	+	84.9681i	−0.133179	+	0.133179i
$639$		0			0
$640$	28.7994	−	152.791i	0.0449991	−	0.238736i
$641$	570.401			0.889862			0.444931	−	0.895565i	$-0.353228\pi$
$641$	570.401			0.889862			0.444931	+	0.895565i	$0.353228\pi$
$642$		0			0
$643$	−626.716	+	626.716i	−0.974676	+	0.974676i	−0.999687	−	0.0250116i	$-0.992038\pi$
$643$	−626.716	+	626.716i	−0.974676	+	0.974676i	0.0250116	+	0.999687i	$0.492038\pi$
$644$			1323.77i			2.05554i
$645$		0			0
$646$	763.871			1.18246
$647$	−254.010	−	254.010i	−0.392596	−	0.392596i	0.483016	−	0.875612i	$-0.339541\pi$
$647$	−254.010	−	254.010i	−0.392596	−	0.392596i	−0.875612	+	0.483016i	$0.839541\pi$
$648$		0			0
$649$		−	1079.34i		−	1.66308i
$650$	24.6592	−	63.0889i	0.0379373	−	0.0970598i
$651$		0			0
$652$	91.0272	+	91.0272i	0.139612	+	0.139612i
$653$	216.664	−	216.664i	0.331798	−	0.331798i	−0.521471	−	0.853269i	$-0.674617\pi$
$653$	216.664	−	216.664i	0.331798	−	0.331798i	0.853269	+	0.521471i	$0.174617\pi$
$654$		0			0
$655$	77.8681	−	53.1690i	0.118883	−	0.0811741i
$656$	−339.238			−0.517131
$657$		0			0
$658$	1687.16	−	1687.16i	2.56407	−	2.56407i
$659$			397.641i			0.603401i	0.953403	+	0.301701i	$0.0975543\pi$
$659$			397.641i			0.603401i	−0.953403	+	0.301701i	$0.902446\pi$
$660$		0			0
$661$	−694.578			−1.05080			−0.525399	−	0.850856i	$-0.676084\pi$
$661$	−694.578			−1.05080			−0.525399	+	0.850856i	$0.676084\pi$
$662$	858.141	+	858.141i	1.29628	+	1.29628i
$663$		0			0
$664$		−	148.096i		−	0.223037i
$665$	−276.067	+	1464.63i	−0.415139	+	2.20246i
$666$		0			0
$667$	−61.2733	−	61.2733i	−0.0918640	−	0.0918640i
$668$	−287.939	+	287.939i	−0.431047	+	0.431047i
$669$		0			0
$670$	521.660	+	763.991i	0.778597	+	1.14028i
$671$	972.269			1.44899
$672$		0			0
$673$	−119.442	+	119.442i	−0.177477	+	0.177477i	−0.790255	−	0.612778i	$-0.790052\pi$
$673$	−119.442	+	119.442i	−0.177477	+	0.177477i	0.612778	+	0.790255i	$0.290052\pi$
$674$		−	839.406i		−	1.24541i
$675$		0			0
$676$	−729.259			−1.07879
$677$	−184.870	−	184.870i	−0.273072	−	0.273072i	0.557264	−	0.830336i	$-0.311851\pi$
$677$	−184.870	−	184.870i	−0.273072	−	0.273072i	−0.830336	+	0.557264i	$0.811851\pi$
$678$		0			0
$679$			227.989i			0.335772i
$680$	42.5845	−	29.0771i	0.0626243	−	0.0427604i
$681$		0			0
$682$	−725.338	−	725.338i	−1.06355	−	1.06355i
$683$	−545.616	+	545.616i	−0.798852	+	0.798852i	−0.982915	−	0.184062i	$-0.941075\pi$
$683$	−545.616	+	545.616i	−0.798852	+	0.798852i	0.184062	+	0.982915i	$0.441075\pi$
$684$		0			0
$685$	371.642	+	70.0505i	0.542543	+	0.102263i
$686$	−1513.28			−2.20595
$687$		0			0
$688$	−169.104	+	169.104i	−0.245790	+	0.245790i
$689$		−	36.7443i		−	0.0533299i
$690$		0			0
$691$	356.160			0.515426			0.257713	−	0.966221i	$-0.417031\pi$
$691$	356.160			0.515426			0.257713	+	0.966221i	$0.417031\pi$
$692$	611.281	+	611.281i	0.883355	+	0.883355i
$693$		0			0
$694$			1585.21i			2.28417i
$695$	−126.743	−	185.620i	−0.182364	−	0.267080i
$696$		0			0
$697$	−174.521	−	174.521i	−0.250389	−	0.250389i
$698$	−889.071	+	889.071i	−1.27374	+	1.27374i
$699$		0			0
$700$	518.379	+	1183.64i	0.740541	+	1.69091i
$701$	−357.763			−0.510361			−0.255180	−	0.966893i	$-0.582135\pi$
$701$	−357.763			−0.510361			−0.255180	+	0.966893i	$0.582135\pi$
$702$		0			0
$703$	−64.9380	+	64.9380i	−0.0923727	+	0.0923727i
$704$		−	914.019i		−	1.29832i
$705$		0			0
$706$	−961.034			−1.36124
$707$	165.569	+	165.569i	0.234185	+	0.234185i
$708$		0			0
$709$		−	374.521i		−	0.528238i	−0.964490	−	0.264119i	$-0.914919\pi$
$709$		−	374.521i		−	0.528238i	0.964490	−	0.264119i	$-0.0850812\pi$
$710$	−1259.36	−	237.376i	−1.77375	−	0.334332i
$711$		0			0
$712$	81.2971	+	81.2971i	0.114181	+	0.114181i
$713$	523.065	−	523.065i	0.733612	−	0.733612i
$714$		0			0
$715$	10.6888	−	56.7075i	0.0149493	−	0.0793112i
$716$	−197.858			−0.276337
$717$		0			0
$718$	−234.645	+	234.645i	−0.326804	+	0.326804i
$719$		−	889.235i		−	1.23677i	−0.785877	−	0.618383i	$-0.787788\pi$
$719$		−	889.235i		−	1.23677i	0.785877	−	0.618383i	$-0.212212\pi$
$720$		0			0
$721$	−2042.70			−2.83314
$722$	−540.694	−	540.694i	−0.748883	−	0.748883i
$723$		0			0
$724$		−	454.566i		−	0.627854i
$725$	−78.7813	−	30.7929i	−0.108664	−	0.0424729i
$726$		0			0
$727$	317.430	+	317.430i	0.436630	+	0.436630i	0.890876	−	0.454246i	$-0.150091\pi$
$727$	317.430	+	317.430i	0.436630	+	0.436630i	−0.454246	+	0.890876i	$0.650091\pi$
$728$	−7.71032	+	7.71032i	−0.0105911	+	0.0105911i
$729$		0			0
$730$	−216.127	+	147.573i	−0.296064	+	0.202155i
$731$	−173.991			−0.238018
$732$		0			0
$733$	486.332	−	486.332i	0.663482	−	0.663482i	−0.292717	−	0.956199i	$-0.594559\pi$
$733$	486.332	−	486.332i	0.663482	−	0.663482i	0.956199	+	0.292717i	$0.0945594\pi$
$734$			1509.82i			2.05698i
$735$		0			0
$736$	1174.81			1.59621
$737$	557.276	+	557.276i	0.756141	+	0.756141i
$738$		0			0
$739$			337.793i			0.457095i	0.973533	+	0.228547i	$0.0733976\pi$
$739$			337.793i			0.457095i	−0.973533	+	0.228547i	$0.926602\pi$
$740$	−14.7479	+	78.2427i	−0.0199296	+	0.105733i
$741$		0			0
$742$	952.699	+	952.699i	1.28396	+	1.28396i
$743$	74.2798	−	74.2798i	0.0999729	−	0.0999729i	−0.655351	−	0.755324i	$-0.727479\pi$
$743$	74.2798	−	74.2798i	0.0999729	−	0.0999729i	0.755324	+	0.655351i	$0.227479\pi$
$744$		0			0
$745$	463.043	+	678.145i	0.621534	+	0.910261i
$746$	614.975			0.824364
$747$		0			0
$748$	398.945	−	398.945i	0.533349	−	0.533349i
$749$			178.353i			0.238121i
$750$		0			0
$751$	740.383			0.985863			0.492932	−	0.870068i	$-0.335925\pi$
$751$	740.383			0.985863			0.492932	+	0.870068i	$0.335925\pi$
$752$	−712.736	−	712.736i	−0.947788	−	0.947788i
$753$		0			0
$754$		−	9.16729i		−	0.0121582i
$755$	−158.571	+	108.274i	−0.210028	+	0.143409i
$756$		0			0
$757$	957.088	+	957.088i	1.26432	+	1.26432i	0.948980	+	0.315337i	$0.102118\pi$
$757$	957.088	+	957.088i	1.26432	+	1.26432i	0.315337	+	0.948980i	$0.397882\pi$
$758$	−1373.14	+	1373.14i	−1.81153	+	1.81153i
$759$		0			0
$760$	−119.873	−	22.5948i	−0.157728	−	0.0297299i
$761$	405.738			0.533165			0.266582	−	0.963812i	$-0.414106\pi$
$761$	405.738			0.533165			0.266582	+	0.963812i	$0.414106\pi$
$762$		0			0
$763$	76.5090	−	76.5090i	0.100274	−	0.100274i
$764$			439.390i			0.575118i
$765$		0			0
$766$	−879.199			−1.14778
$767$	58.2254	+	58.2254i	0.0759132	+	0.0759132i
$768$		0			0
$769$			844.782i			1.09855i	0.835643	+	0.549273i	$0.185095\pi$
$769$			844.782i			1.09855i	−0.835643	+	0.549273i	$0.814905\pi$
$770$	1193.17	+	1747.44i	1.54957	+	2.26940i
$771$		0			0
$772$	867.727	+	867.727i	1.12400	+	1.12400i
$773$	−501.313	+	501.313i	−0.648529	+	0.648529i	−0.952637	−	0.304108i	$-0.901642\pi$
$773$	−501.313	+	501.313i	−0.648529	+	0.648529i	0.304108	+	0.952637i	$0.401642\pi$
$774$		0			0
$775$	262.866	−	672.524i	0.339182	−	0.867773i
$776$	−18.6598			−0.0240461
$777$		0			0
$778$	1453.13	−	1453.13i	1.86778	−	1.86778i
$779$			583.866i			0.749507i
$780$		0			0
$781$	−1091.76			−1.39790
$782$	552.984	+	552.984i	0.707141	+	0.707141i
$783$		0			0
$784$			1351.49i			1.72384i
$785$	320.101	+	60.3356i	0.407772	+	0.0768606i
$786$		0			0
$787$	−719.703	−	719.703i	−0.914490	−	0.914490i	0.0821317	−	0.996621i	$-0.473827\pi$
$787$	−719.703	−	719.703i	−0.914490	−	0.914490i	−0.996621	+	0.0821317i	$0.973827\pi$
$788$	−22.8300	+	22.8300i	−0.0289721	+	0.0289721i
$789$		0			0
$790$	81.1866	−	430.723i	0.102768	−	0.545219i
$791$	1833.64			2.31813
$792$		0			0
$793$	−52.4495	+	52.4495i	−0.0661406	+	0.0661406i
$794$		−	169.307i		−	0.213233i
$795$		0			0
$796$	−611.926			−0.768751
$797$	−1009.06	−	1009.06i	−1.26608	−	1.26608i	−0.948097	−	0.317980i	$-0.896996\pi$
$797$	−1009.06	−	1009.06i	−1.26608	−	1.26608i	−0.317980	−	0.948097i	$-0.603004\pi$
$798$		0			0
$799$		−	733.336i		−	0.917818i
$800$	1050.45	−	460.048i	1.31306	−	0.575060i
$801$		0			0
$802$	−339.695	−	339.695i	−0.423559	−	0.423559i
$803$	−157.649	+	157.649i	−0.196325	+	0.196325i
$804$		0			0
$805$	−1260.13	+	860.431i	−1.56538	+	1.06886i
$806$	78.2574			0.0970936
$807$		0			0
$808$	−13.5510	+	13.5510i	−0.0167710	+	0.0167710i
$809$			549.873i			0.679694i	0.940481	+	0.339847i	$0.110375\pi$
$809$			549.873i			0.679694i	−0.940481	+	0.339847i	$0.889625\pi$
$810$		0			0
$811$	1542.32			1.90175			0.950876	−	0.309573i	$-0.100186\pi$
$811$	1542.32			1.90175			0.950876	+	0.309573i	$0.100186\pi$
$812$	123.658	+	123.658i	0.152288	+	0.152288i
$813$		0			0
$814$			130.379i			0.160170i
$815$	−27.4851	+	145.818i	−0.0337241	+	0.178918i
$816$		0			0
$817$	291.046	+	291.046i	0.356237	+	0.356237i
$818$	−48.4677	+	48.4677i	−0.0592514	+	0.0592514i
$819$		0			0
$820$	285.445	+	418.045i	0.348104	+	0.509811i
$821$	−810.024			−0.986631			−0.493316	−	0.869850i	$-0.664215\pi$
$821$	−810.024			−0.986631			−0.493316	+	0.869850i	$0.664215\pi$
$822$		0			0
$823$	−58.0577	+	58.0577i	−0.0705440	+	0.0705440i	−0.741499	−	0.670954i	$-0.765885\pi$
$823$	−58.0577	+	58.0577i	−0.0705440	+	0.0705440i	0.670954	+	0.741499i	$0.265885\pi$
$824$		−	167.185i		−	0.202894i
$825$		0			0
$826$	−3019.31			−3.65534
$827$	−924.549	−	924.549i	−1.11796	−	1.11796i	−0.992041	−	0.125915i	$-0.959813\pi$
$827$	−924.549	−	924.549i	−1.11796	−	1.11796i	−0.125915	−	0.992041i	$-0.540187\pi$
$828$		0			0
$829$		−	114.907i		−	0.138610i	−0.997596	−	0.0693048i	$-0.977922\pi$
$829$		−	114.907i		−	0.138610i	0.997596	−	0.0693048i	$-0.0220781\pi$
$830$	1810.63	−	1236.31i	2.18148	−	1.48953i
$831$		0			0
$832$	49.3072	+	49.3072i	0.0592635	+	0.0592635i
$833$	−695.278	+	695.278i	−0.834667	+	0.834667i
$834$		0			0
$835$	−461.255	−	86.9416i	−0.552402	−	0.104122i
$836$	−1334.68			−1.59651
$837$		0			0
$838$	1020.02	−	1020.02i	1.21720	−	1.21720i
$839$		−	764.160i		−	0.910798i	−0.890287	−	0.455399i	$-0.849497\pi$
$839$		−	764.160i		−	0.910798i	0.890287	−	0.455399i	$-0.150503\pi$
$840$		0			0
$841$	829.552			0.986388
$842$	−7.77844	−	7.77844i	−0.00923805	−	0.00923805i
$843$		0			0
$844$		−	195.662i		−	0.231827i
$845$	−474.009	−	694.204i	−0.560957	−	0.821544i
$846$		0			0
$847$	255.128	+	255.128i	0.301214	+	0.301214i
$848$	402.465	−	402.465i	0.474605	−	0.474605i
$849$		0			0
$850$	710.993	+	277.902i	0.836462	+	0.326944i
$851$	−94.0203			−0.110482
$852$		0			0
$853$	519.867	−	519.867i	0.609458	−	0.609458i	−0.333347	−	0.942804i	$-0.608178\pi$
$853$	519.867	−	519.867i	0.609458	−	0.609458i	0.942804	+	0.333347i	$0.108178\pi$
$854$		−	2719.80i		−	3.18478i
$855$		0			0
$856$	−14.5973			−0.0170529
$857$	−508.368	−	508.368i	−0.593194	−	0.593194i	0.345299	−	0.938493i	$-0.387778\pi$
$857$	−508.368	−	508.368i	−0.593194	−	0.593194i	−0.938493	+	0.345299i	$0.887778\pi$
$858$		0			0
$859$		−	1204.68i		−	1.40243i	−0.712952	−	0.701213i	$-0.752642\pi$
$859$		−	1204.68i		−	1.40243i	0.712952	−	0.701213i	$-0.247358\pi$
$860$	350.676	+	66.0987i	0.407763	+	0.0768589i
$861$		0			0
$862$	−1567.75	−	1567.75i	−1.81873	−	1.81873i
$863$	214.571	−	214.571i	0.248634	−	0.248634i	−0.571776	−	0.820410i	$-0.693745\pi$
$863$	214.571	−	214.571i	0.248634	−	0.248634i	0.820410	+	0.571776i	$0.193745\pi$
$864$		0			0
$865$	−184.573	+	979.223i	−0.213379	+	1.13205i
$866$	1502.10			1.73453
$867$		0			0
$868$	−1055.62	+	1055.62i	−1.21615	+	1.21615i
$869$		−	373.401i		−	0.429690i
$870$		0			0
$871$	−60.1251			−0.0690299
$872$	6.26188	+	6.26188i	0.00718106	+	0.00718106i
$873$		0			0
$874$		−	1850.02i		−	2.11673i
$875$	−789.801	+	1262.81i	−0.902630	+	1.44321i
$876$		0			0
$877$	−223.700	−	223.700i	−0.255075	−	0.255075i	0.567973	−	0.823047i	$-0.307728\pi$
$877$	−223.700	−	223.700i	−0.255075	−	0.255075i	−0.823047	+	0.567973i	$0.807728\pi$
$878$	280.659	−	280.659i	0.319657	−	0.319657i
$879$		0			0
$880$	738.200	−	504.049i	0.838864	−	0.572783i
$881$	435.585			0.494421			0.247211	−	0.968962i	$-0.420486\pi$
$881$	435.585			0.494421			0.247211	+	0.968962i	$0.420486\pi$
$882$		0			0
$883$	−434.695	+	434.695i	−0.492293	+	0.492293i	−0.909028	−	0.416735i	$-0.863174\pi$
$883$	−434.695	+	434.695i	−0.492293	+	0.492293i	0.416735	+	0.909028i	$0.363174\pi$
$884$			43.0425i			0.0486906i
$885$		0			0
$886$	−1276.33			−1.44055
$887$	−405.058	−	405.058i	−0.456660	−	0.456660i	0.440897	−	0.897558i	$-0.354660\pi$
$887$	−405.058	−	405.058i	−0.456660	−	0.456660i	−0.897558	+	0.440897i	$0.854660\pi$
$888$		0			0
$889$		−	1940.74i		−	2.18306i
$890$	−315.268	+	1672.61i	−0.354234	+	1.87933i
$891$		0			0
$892$	−17.2130	−	17.2130i	−0.0192970	−	0.0192970i
$893$	−1226.70	+	1226.70i	−1.37368	+	1.37368i
$894$		0			0
$895$	−128.605	−	188.347i	−0.143693	−	0.210443i
$896$	−370.532			−0.413540
$897$		0			0
$898$	−1689.15	+	1689.15i	−1.88101	+	1.88101i
$899$		−	97.7228i		−	0.108702i
$900$		0			0
$901$	414.097			0.459597
$902$	586.125	+	586.125i	0.649806	+	0.649806i
$903$		0			0
$904$			150.074i			0.166011i
$905$	432.716	−	295.462i	0.478139	−	0.326477i
$906$		0			0
$907$	559.934	+	559.934i	0.617347	+	0.617347i	0.944850	−	0.327503i	$-0.106207\pi$
$907$	559.934	+	559.934i	0.617347	+	0.617347i	−0.327503	+	0.944850i	$0.606207\pi$
$908$	−233.153	+	233.153i	−0.256776	+	0.256776i
$909$		0			0
$910$	−158.632	−	29.9004i	−0.174321	−	0.0328576i
$911$	945.486			1.03786			0.518928	−	0.854818i	$-0.326331\pi$
$911$	945.486			1.03786			0.518928	+	0.854818i	$0.326331\pi$
$912$		0			0
$913$	1320.72	−	1320.72i	1.44657	−	1.44657i
$914$		−	2557.01i		−	2.79761i
$915$		0			0
$916$	239.399			0.261352
$917$	−158.889	−	158.889i	−0.173270	−	0.173270i
$918$		0			0
$919$		−	825.147i		−	0.897875i	−0.893563	−	0.448937i	$-0.851803\pi$
$919$		−	825.147i		−	0.897875i	0.893563	−	0.448937i	$-0.148197\pi$
$920$	−70.4220	−	103.136i	−0.0765456	−	0.112104i
$921$		0			0
$922$	534.618	+	534.618i	0.579846	+	0.579846i
$923$	58.8956	−	58.8956i	0.0638089	−	0.0638089i
$924$		0			0
$925$	−84.0676	+	36.8178i	−0.0908839	+	0.0398030i
$926$	486.714			0.525609
$927$		0			0
$928$	109.743	−	109.743i	0.118258	−	0.118258i
$929$		−	923.085i		−	0.993633i	−0.867856	−	0.496817i	$-0.834502\pi$
$929$		−	923.085i		−	0.993633i	0.867856	−	0.496817i	$-0.165498\pi$
$930$		0			0
$931$	2326.07			2.49847
$932$	418.523	+	418.523i	0.449059	+	0.449059i
$933$		0			0
$934$		−	260.369i		−	0.278768i
$935$	639.077	+	120.459i	0.683505	+	0.128833i
$936$		0			0
$937$	967.522	+	967.522i	1.03257	+	1.03257i	0.999451	+	0.0331234i	$0.0105454\pi$
$937$	967.522	+	967.522i	1.03257	+	1.03257i	0.0331234	+	0.999451i	$0.489455\pi$
$938$	1558.91	−	1558.91i	1.66195	−	1.66195i
$939$		0			0
$940$	−278.592	+	1478.03i	−0.296375	+	1.57237i
$941$	811.885			0.862789			0.431395	−	0.902163i	$-0.358022\pi$
$941$	811.885			0.862789			0.431395	+	0.902163i	$0.358022\pi$
$942$		0			0
$943$	−422.674	+	422.674i	−0.448223	+	0.448223i
$944$			1275.50i			1.35117i
$945$		0			0
$946$	584.344			0.617700
$947$	−872.363	−	872.363i	−0.921186	−	0.921186i	0.0759275	−	0.997113i	$-0.475808\pi$
$947$	−872.363	−	872.363i	−0.921186	−	0.921186i	−0.997113	+	0.0759275i	$0.975808\pi$
$948$		0			0
$949$		−	17.0089i		−	0.0179229i
$950$	−724.458	−	1654.19i	−0.762588	−	1.74125i
$951$		0			0
$952$	−86.8930	−	86.8930i	−0.0912742	−	0.0912742i
$953$	719.749	−	719.749i	0.755245	−	0.755245i	−0.220208	−	0.975453i	$-0.570674\pi$
$953$	719.749	−	719.749i	0.755245	−	0.755245i	0.975453	+	0.220208i	$0.0706736\pi$
$954$		0			0
$955$	−418.269	+	285.598i	−0.437978	+	0.299055i
$956$	−639.499			−0.668932
$957$		0			0
$958$	79.2889	−	79.2889i	0.0827650	−	0.0827650i
$959$		−	901.266i		−	0.939797i
$960$		0			0
$961$	−126.780			−0.131925
$962$	−7.03333	−	7.03333i	−0.00731116	−	0.00731116i
$963$		0			0
$964$		−	1557.24i		−	1.61539i
$965$	−262.005	+	1390.03i	−0.271508	+	1.44044i
$966$		0			0
$967$	−1048.66	−	1048.66i	−1.08445	−	1.08445i	−0.996089	−	0.0883570i	$-0.971838\pi$
$967$	−1048.66	−	1048.66i	−1.08445	−	1.08445i	−0.0883570	−	0.996089i	$-0.528162\pi$
$968$	−20.8810	+	20.8810i	−0.0215713	+	0.0215713i
$969$		0			0
$970$	−155.772	−	228.135i	−0.160590	−	0.235190i
$971$	−798.883			−0.822742			−0.411371	−	0.911468i	$-0.634950\pi$
$971$	−798.883			−0.822742			−0.411371	+	0.911468i	$0.634950\pi$
$972$		0			0
$973$	−378.755	+	378.755i	−0.389266	+	0.389266i
$974$			1612.19i			1.65522i
$975$		0			0
$976$	−1148.97			−1.17723
$977$	302.515	+	302.515i	0.309637	+	0.309637i	0.844769	−	0.535132i	$-0.179738\pi$
$977$	302.515	+	302.515i	0.309637	+	0.309637i	−0.535132	+	0.844769i	$0.679738\pi$
$978$		0			0
$979$			1450.01i			1.48112i
$980$	1665.46	−	1137.19i	1.69945	−	1.16040i
$981$		0			0
$982$	940.736	+	940.736i	0.957980	+	0.957980i
$983$	304.386	−	304.386i	0.309650	−	0.309650i	−0.535124	−	0.844774i	$-0.679735\pi$
$983$	304.386	−	304.386i	0.309650	−	0.309650i	0.844774	+	0.535124i	$0.179735\pi$
$984$		0			0
$985$	−36.5718	−	6.89338i	−0.0371287	−	0.00699836i
$986$	103.313			0.104779
$987$		0			0
$988$	72.0000	−	72.0000i	0.0728745	−	0.0728745i
$989$			421.390i			0.426077i
$990$		0			0
$991$	575.226			0.580450			0.290225	−	0.956958i	$-0.406270\pi$
$991$	575.226			0.580450			0.290225	+	0.956958i	$0.406270\pi$
$992$	936.833	+	936.833i	0.944388	+	0.944388i
$993$		0			0
$994$			3054.07i			3.07250i
$995$	−397.744	−	582.511i	−0.399743	−	0.585439i
$996$		0			0
$997$	291.949	+	291.949i	0.292828	+	0.292828i	0.838196	−	0.545369i	$-0.183610\pi$
$997$	291.949	+	291.949i	0.292828	+	0.292828i	−0.545369	+	0.838196i	$0.683610\pi$
$998$	−1736.83	+	1736.83i	−1.74031	+	1.74031i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.g.b.82.7	yes	16
3.2	odd	2	inner	135.3.g.b.82.2	yes	16
5.2	odd	4		675.3.g.j.568.2		16
5.3	odd	4	inner	135.3.g.b.28.7	yes	16
5.4	even	2		675.3.g.j.82.2		16
9.2	odd	6		405.3.l.n.352.2		32
9.4	even	3		405.3.l.n.217.2		32
9.5	odd	6		405.3.l.n.217.7		32
9.7	even	3		405.3.l.n.352.7		32
15.2	even	4		675.3.g.j.568.7		16
15.8	even	4	inner	135.3.g.b.28.2	✓	16
15.14	odd	2		675.3.g.j.82.7		16
45.13	odd	12		405.3.l.n.298.7		32
45.23	even	12		405.3.l.n.298.2		32
45.38	even	12		405.3.l.n.28.7		32
45.43	odd	12		405.3.l.n.28.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.g.b.28.2	✓	16	15.8	even	4	inner
135.3.g.b.28.7	yes	16	5.3	odd	4	inner
135.3.g.b.82.2	yes	16	3.2	odd	2	inner
135.3.g.b.82.7	yes	16	1.1	even	1	trivial
405.3.l.n.28.2		32	45.43	odd	12
405.3.l.n.28.7		32	45.38	even	12
405.3.l.n.217.2		32	9.4	even	3
405.3.l.n.217.7		32	9.5	odd	6
405.3.l.n.298.2		32	45.23	even	12
405.3.l.n.298.7		32	45.13	odd	12
405.3.l.n.352.2		32	9.2	odd	6
405.3.l.n.352.7		32	9.7	even	3
675.3.g.j.82.2		16	5.4	even	2
675.3.g.j.82.7		16	15.14	odd	2
675.3.g.j.568.2		16	5.2	odd	4
675.3.g.j.568.7		16	15.2	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.04178 + 2.04178i) q^{2} +4.33774i q^{4} +(-4.12923 + 2.81948i) q^{5} +(8.42562 + 8.42562i) q^{7} +(-0.689596 + 0.689596i) q^{8} +(-14.1877 - 2.67423i) q^{10} -12.2996 q^{11} +(0.663508 - 0.663508i) q^{13} +34.4066i q^{14} +14.5350 q^{16} +(7.47753 + 7.47753i) q^{17} -25.0163i q^{19} +(-12.2302 - 17.9115i) q^{20} +(-25.1131 - 25.1131i) q^{22} +(18.1099 - 18.1099i) q^{23} +(9.10111 - 23.2845i) q^{25} +2.70947 q^{26} +(-36.5482 + 36.5482i) q^{28} -3.38342i q^{29} +28.8829 q^{31} +(32.4356 + 32.4356i) q^{32} +30.5350i q^{34} +(-58.5472 - 11.0355i) q^{35} +(-2.59583 - 2.59583i) q^{37} +(51.0778 - 51.0778i) q^{38} +(0.903202 - 4.79180i) q^{40} -23.3394 q^{41} +(-11.6343 + 11.6343i) q^{43} -53.3525i q^{44} +73.9528 q^{46} +(-49.0360 - 49.0360i) q^{47} +92.9823i q^{49} +(66.1244 - 28.9595i) q^{50} +(2.87812 + 2.87812i) q^{52} +(27.6894 - 27.6894i) q^{53} +(50.7879 - 34.6784i) q^{55} -11.6205 q^{56} +(6.90820 - 6.90820i) q^{58} +87.7539i q^{59} -79.0489 q^{61} +(58.9725 + 58.9725i) q^{62} +74.3129i q^{64} +(-0.869033 + 4.61052i) q^{65} +(-45.3085 - 45.3085i) q^{67} +(-32.4356 + 32.4356i) q^{68} +(-97.0085 - 142.073i) q^{70} +88.7641 q^{71} +(12.8174 - 12.8174i) q^{73} -10.6002i q^{74} +108.514 q^{76} +(-103.632 - 103.632i) q^{77} +30.3588i q^{79} +(-60.0182 + 40.9810i) q^{80} +(-47.6540 - 47.6540i) q^{82} +(-107.379 + 107.379i) q^{83} +(-51.9592 - 9.79374i) q^{85} -47.5092 q^{86} +(8.48175 - 8.48175i) q^{88} -117.891i q^{89} +11.1809 q^{91} +(78.5559 + 78.5559i) q^{92} -200.242i q^{94} +(70.5328 + 103.298i) q^{95} +(13.5295 + 13.5295i) q^{97} +(-189.850 + 189.850i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{7} + 40 q^{10} + 40 q^{13} - 152 q^{16} - 136 q^{22} - 32 q^{25} - 112 q^{28} + 200 q^{31} + 16 q^{37} - 48 q^{40} + 136 q^{43} + 152 q^{46} + 640 q^{52} + 248 q^{55} + 48 q^{58} - 280 q^{61}+ \cdots + 448 q^{97}+O(q^{100}) \) 16 * q + 16 * q^7 + 40 * q^10 + 40 * q^13 - 152 * q^16 - 136 * q^22 - 32 * q^25 - 112 * q^28 + 200 * q^31 + 16 * q^37 - 48 * q^40 + 136 * q^43 + 152 * q^46 + 640 * q^52 + 248 * q^55 + 48 * q^58 - 280 * q^61 - 344 * q^67 - 696 * q^70 - 776 * q^73 + 144 * q^76 - 880 * q^82 - 176 * q^85 + 1200 * q^88 + 152 * q^91 + 448 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more