LMFDB - Embedded newform 432.2.l.a.107.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(107,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("432.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.l (of order $4$, degree $2$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.6
Character	$\chi$	$=$	432.107
Dual form			432.2.l.a.323.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.715232 - 1.22002i) q^{2} +(-0.976886 + 1.74519i) q^{4} +(-2.47363 + 2.47363i) q^{5} -0.311286 q^{7} +(2.82786 - 0.0563981i) q^{8} +O(q^{10})$	\(q+(-0.715232 - 1.22002i) q^{2} +(-0.976886 + 1.74519i) q^{4} +(-2.47363 + 2.47363i) q^{5} -0.311286 q^{7} +(2.82786 - 0.0563981i) q^{8} +(4.78709 + 1.24865i) q^{10} +(-3.17339 - 3.17339i) q^{11} +(3.97250 - 3.97250i) q^{13} +(0.222642 + 0.379775i) q^{14} +(-2.09139 - 3.40971i) q^{16} -5.33481i q^{17} +(0.217738 + 0.217738i) q^{19} +(-1.90050 - 6.73341i) q^{20} +(-1.60188 + 6.14130i) q^{22} -5.06671i q^{23} -7.23768i q^{25} +(-7.68778 - 2.00526i) q^{26} +(0.304091 - 0.543254i) q^{28} +(5.16434 + 5.16434i) q^{29} -4.95910i q^{31} +(-2.66408 + 4.99026i) q^{32} +(-6.50856 + 3.81563i) q^{34} +(0.770007 - 0.770007i) q^{35} +(1.46773 + 1.46773i) q^{37} +(0.109911 - 0.421377i) q^{38} +(-6.85558 + 7.13460i) q^{40} +0.728609 q^{41} +(-2.55436 + 2.55436i) q^{43} +(8.63822 - 2.43813i) q^{44} +(-6.18147 + 3.62387i) q^{46} +7.10397 q^{47} -6.90310 q^{49} +(-8.83010 + 5.17662i) q^{50} +(3.05209 + 10.8135i) q^{52} +(-2.78744 + 2.78744i) q^{53} +15.6996 q^{55} +(-0.880275 + 0.0175560i) q^{56} +(2.60688 - 9.99429i) q^{58} +(-7.25672 - 7.25672i) q^{59} +(-8.33771 + 8.33771i) q^{61} +(-6.05018 + 3.54690i) q^{62} +(7.99364 - 0.318972i) q^{64} +19.6530i q^{65} +(-9.25935 - 9.25935i) q^{67} +(9.31026 + 5.21150i) q^{68} +(-1.49016 - 0.388688i) q^{70} -4.78284i q^{71} -9.78836i q^{73} +(0.740889 - 2.84042i) q^{74} +(-0.592700 + 0.167289i) q^{76} +(0.987833 + 0.987833i) q^{77} -15.2509i q^{79} +(13.6077 + 3.26104i) q^{80} +(-0.521124 - 0.888916i) q^{82} +(0.0624788 - 0.0624788i) q^{83} +(13.1963 + 13.1963i) q^{85} +(4.94332 + 1.28940i) q^{86} +(-9.15289 - 8.79495i) q^{88} +1.82987 q^{89} +(-1.23659 + 1.23659i) q^{91} +(8.84238 + 4.94960i) q^{92} +(-5.08099 - 8.66697i) q^{94} -1.07721 q^{95} +1.66456 q^{97} +(4.93732 + 8.42191i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 4 q^{10} - 20 q^{16} + 8 q^{19} + 4 q^{22} - 12 q^{28} - 36 q^{34} - 12 q^{40} + 32 q^{43} - 16 q^{46} + 32 q^{49} - 60 q^{52} + 64 q^{55} - 48 q^{58} - 16 q^{61} + 48 q^{64} - 32 q^{67} - 72 q^{70} - 96 q^{76} + 40 q^{82} - 16 q^{85} + 36 q^{88} + 24 q^{91} - 36 q^{94}+O(q^{100}) $ 32 * q - 4 * q^10 - 20 * q^16 + 8 * q^19 + 4 * q^22 - 12 * q^28 - 36 * q^34 - 12 * q^40 + 32 * q^43 - 16 * q^46 + 32 * q^49 - 60 * q^52 + 64 * q^55 - 48 * q^58 - 16 * q^61 + 48 * q^64 - 32 * q^67 - 72 * q^70 - 96 * q^76 + 40 * q^82 - 16 * q^85 + 36 * q^88 + 24 * q^91 - 36 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.715232	−	1.22002i	−0.505745	−	0.862683i
$2$	−0.715232	−	1.22002i	−0.505745	−	0.862683i
$3$		0			0
$3$		0			0
$4$	−0.976886	+	1.74519i	−0.488443	+	0.872596i
$5$	−2.47363	+	2.47363i	−1.10624	+	1.10624i	−0.112600	+	0.993640i	$0.535918\pi$
$5$	−2.47363	+	2.47363i	−1.10624	+	1.10624i	−0.993640	+	0.112600i	$0.964082\pi$
$6$		0			0
$7$	−0.311286			−0.117655			−0.0588276	−	0.998268i	$-0.518736\pi$
$7$	−0.311286			−0.117655			−0.0588276	+	0.998268i	$0.518736\pi$
$8$	2.82786	−	0.0563981i	0.999801	−	0.0199397i
$9$		0			0
$10$	4.78709	+	1.24865i	1.51381	+	0.394859i
$11$	−3.17339	−	3.17339i	−0.956813	−	0.956813i	0.0422921	−	0.999105i	$-0.486534\pi$
$11$	−3.17339	−	3.17339i	−0.956813	−	0.956813i	−0.999105	+	0.0422921i	$0.986534\pi$
$12$		0			0
$13$	3.97250	−	3.97250i	1.10177	−	1.10177i	0.107577	−	0.994197i	$-0.465691\pi$
$13$	3.97250	−	3.97250i	1.10177	−	1.10177i	0.994197	−	0.107577i	$-0.0343093\pi$
$14$	0.222642	+	0.379775i	0.0595036	+	0.101499i
$15$		0			0
$16$	−2.09139	−	3.40971i	−0.522847	−	0.852427i
$17$		−	5.33481i		−	1.29388i	−0.762540	−	0.646941i	$-0.776048\pi$
$17$		−	5.33481i		−	1.29388i	0.762540	−	0.646941i	$-0.223952\pi$
$18$		0			0
$19$	0.217738	+	0.217738i	0.0499525	+	0.0499525i	0.731642	−	0.681689i	$-0.238754\pi$
$19$	0.217738	+	0.217738i	0.0499525	+	0.0499525i	−0.681689	+	0.731642i	$0.738754\pi$
$20$	−1.90050	−	6.73341i	−0.424965	−	1.50564i
$21$		0			0
$22$	−1.60188	+	6.14130i	−0.341522	+	1.30933i
$23$		−	5.06671i		−	1.05648i	−0.849095	−	0.528241i	$-0.822852\pi$
$23$		−	5.06671i		−	1.05648i	0.849095	−	0.528241i	$-0.177148\pi$
$24$		0			0
$25$		−	7.23768i		−	1.44754i
$26$	−7.68778	−	2.00526i	−1.50770	−	0.393264i
$27$		0			0
$28$	0.304091	−	0.543254i	0.0574679	−	0.102665i
$29$	5.16434	+	5.16434i	0.958994	+	0.958994i	0.999192	−	0.0401979i	$-0.0127988\pi$
$29$	5.16434	+	5.16434i	0.958994	+	0.958994i	−0.0401979	+	0.999192i	$0.512799\pi$
$30$		0			0
$31$		−	4.95910i		−	0.890680i	−0.895362	−	0.445340i	$-0.853083\pi$
$31$		−	4.95910i		−	0.890680i	0.895362	−	0.445340i	$-0.146917\pi$
$32$	−2.66408	+	4.99026i	−0.470947	+	0.882162i
$33$		0			0
$34$	−6.50856	+	3.81563i	−1.11621	+	0.654374i
$35$	0.770007	−	0.770007i	0.130155	−	0.130155i
$36$		0			0
$37$	1.46773	+	1.46773i	0.241293	+	0.241293i	0.817385	−	0.576092i	$-0.195423\pi$
$37$	1.46773	+	1.46773i	0.241293	+	0.241293i	−0.576092	+	0.817385i	$0.695423\pi$
$38$	0.109911	−	0.421377i	0.0178299	−	0.0683564i
$39$		0			0
$40$	−6.85558	+	7.13460i	−1.08396	+	1.12808i
$41$	0.728609			0.113790			0.0568948	−	0.998380i	$-0.481880\pi$
$41$	0.728609			0.113790			0.0568948	+	0.998380i	$0.481880\pi$
$42$		0			0
$43$	−2.55436	+	2.55436i	−0.389536	+	0.389536i	−0.874522	−	0.484986i	$-0.838825\pi$
$43$	−2.55436	+	2.55436i	−0.389536	+	0.389536i	0.484986	+	0.874522i	$0.338825\pi$
$44$	8.63822	−	2.43813i	1.30226	−	0.367562i
$45$		0			0
$46$	−6.18147	+	3.62387i	−0.911409	+	0.534311i
$47$	7.10397			1.03622			0.518110	−	0.855314i	$-0.326636\pi$
$47$	7.10397			1.03622			0.518110	+	0.855314i	$0.326636\pi$
$48$		0			0
$49$	−6.90310			−0.986157
$50$	−8.83010	+	5.17662i	−1.24876	+	0.732085i
$51$		0			0
$52$	3.05209	+	10.8135i	0.423249	+	1.49956i
$53$	−2.78744	+	2.78744i	−0.382884	+	0.382884i	−0.872140	−	0.489256i	$-0.837268\pi$
$53$	−2.78744	+	2.78744i	−0.382884	+	0.382884i	0.489256	+	0.872140i	$0.337268\pi$
$54$		0			0
$55$	15.6996			2.11693
$56$	−0.880275	+	0.0175560i	−0.117632	+	0.00234601i
$57$		0			0
$58$	2.60688	−	9.99429i	0.342301	−	1.31231i
$59$	−7.25672	−	7.25672i	−0.944745	−	0.944745i	0.0538066	−	0.998551i	$-0.482865\pi$
$59$	−7.25672	−	7.25672i	−0.944745	−	0.944745i	−0.998551	+	0.0538066i	$0.982865\pi$
$60$		0			0
$61$	−8.33771	+	8.33771i	−1.06753	+	1.06753i	−0.0699866	+	0.997548i	$0.522296\pi$
$61$	−8.33771	+	8.33771i	−1.06753	+	1.06753i	−0.997548	+	0.0699866i	$0.977704\pi$
$62$	−6.05018	+	3.54690i	−0.768374	+	0.450457i
$63$		0			0
$64$	7.99364	−	0.318972i	0.999205	−	0.0398716i
$65$			19.6530i			2.43765i
$66$		0			0
$67$	−9.25935	−	9.25935i	−1.13121	−	1.13121i	−0.989976	−	0.141233i	$-0.954893\pi$
$67$	−9.25935	−	9.25935i	−1.13121	−	1.13121i	−0.141233	−	0.989976i	$-0.545107\pi$
$68$	9.31026	+	5.21150i	1.12904	+	0.631987i
$69$		0			0
$70$	−1.49016	−	0.388688i	−0.178108	−	0.0464571i
$71$		−	4.78284i		−	0.567619i	−0.958881	−	0.283809i	$-0.908402\pi$
$71$		−	4.78284i		−	0.567619i	0.958881	−	0.283809i	$-0.0915983\pi$
$72$		0			0
$73$		−	9.78836i		−	1.14564i	−0.819681	−	0.572820i	$-0.805849\pi$
$73$		−	9.78836i		−	1.14564i	0.819681	−	0.572820i	$-0.194151\pi$
$74$	0.740889	−	2.84042i	0.0861266	−	0.330192i
$75$		0			0
$76$	−0.592700	+	0.167289i	−0.0679873	+	0.0191894i
$77$	0.987833	+	0.987833i	0.112574	+	0.112574i
$78$		0			0
$79$		−	15.2509i		−	1.71586i	−0.513768	−	0.857929i	$-0.671751\pi$
$79$		−	15.2509i		−	1.71586i	0.513768	−	0.857929i	$-0.328249\pi$
$80$	13.6077	+	3.26104i	1.52138	+	0.364595i
$81$		0			0
$82$	−0.521124	−	0.888916i	−0.0575486	−	0.0981643i
$83$	0.0624788	−	0.0624788i	0.00685794	−	0.00685794i	−0.703669	−	0.710527i	$-0.748456\pi$
$83$	0.0624788	−	0.0624788i	0.00685794	−	0.00685794i	0.710527	+	0.703669i	$0.248456\pi$
$84$		0			0
$85$	13.1963	+	13.1963i	1.43134	+	1.43134i
$86$	4.94332	+	1.28940i	0.533051	+	0.139040i
$87$		0			0
$88$	−9.15289	−	8.79495i	−0.975702	−	0.937544i
$89$	1.82987			0.193966			0.0969829	−	0.995286i	$-0.469081\pi$
$89$	1.82987			0.193966			0.0969829	+	0.995286i	$0.469081\pi$
$90$		0			0
$91$	−1.23659	+	1.23659i	−0.129629	+	0.129629i
$92$	8.84238	+	4.94960i	0.921881	+	0.516031i
$93$		0			0
$94$	−5.08099	−	8.66697i	−0.524064	−	0.893929i
$95$	−1.07721			−0.110519
$96$		0			0
$97$	1.66456			0.169010			0.0845051	−	0.996423i	$-0.473069\pi$
$97$	1.66456			0.169010			0.0845051	+	0.996423i	$0.473069\pi$
$98$	4.93732	+	8.42191i	0.498745	+	0.850741i
$99$		0			0
$100$	12.6311	+	7.07039i	1.26311	+	0.707039i
$101$	−4.27402	+	4.27402i	−0.425281	+	0.425281i	−0.887017	−	0.461736i	$-0.847227\pi$
$101$	−4.27402	+	4.27402i	−0.425281	+	0.425281i	0.461736	+	0.887017i	$0.347227\pi$
$102$		0			0
$103$	1.38989			0.136949			0.0684747	−	0.997653i	$-0.478187\pi$
$103$	1.38989			0.136949			0.0684747	+	0.997653i	$0.478187\pi$
$104$	11.0097	−	11.4577i	1.07959	−	1.12352i
$105$		0			0
$106$	5.39438	+	1.40706i	0.523949	+	0.136666i
$107$	3.89903	+	3.89903i	0.376934	+	0.376934i	0.869995	−	0.493061i	$-0.164122\pi$
$107$	3.89903	+	3.89903i	0.376934	+	0.376934i	−0.493061	+	0.869995i	$0.664122\pi$
$108$		0			0
$109$	5.87085	−	5.87085i	0.562325	−	0.562325i	−0.367642	−	0.929967i	$-0.619835\pi$
$109$	5.87085	−	5.87085i	0.562325	−	0.562325i	0.929967	+	0.367642i	$0.119835\pi$
$110$	−11.2288	−	19.1538i	−1.07063	−	1.82624i
$111$		0			0
$112$	0.651020	+	1.06140i	0.0615156	+	0.100292i
$113$			7.06597i			0.664711i	0.943154	+	0.332355i	$0.107843\pi$
$113$			7.06597i			0.664711i	−0.943154	+	0.332355i	$0.892157\pi$
$114$		0			0
$115$	12.5332	+	12.5332i	1.16872	+	1.16872i
$116$	−14.0577	+	3.96779i	−1.30523	+	0.368400i
$117$		0			0
$118$	−3.66309	+	14.0436i	−0.337215	+	1.29282i
$119$			1.66065i			0.152232i
$120$		0			0
$121$			9.14081i			0.830983i
$122$	16.1356	+	4.20876i	1.46084	+	0.381043i
$123$		0			0
$124$	8.65457	+	4.84447i	0.777203	+	0.435047i
$125$	5.53519	+	5.53519i	0.495082	+	0.495082i
$126$		0			0
$127$			6.81912i			0.605099i	0.953134	+	0.302549i	$0.0978377\pi$
$127$			6.81912i			0.605099i	−0.953134	+	0.302549i	$0.902162\pi$
$128$	−6.10646	−	9.52424i	−0.539740	−	0.841832i
$129$		0			0
$130$	23.9770	−	14.0564i	2.10292	−	1.23283i
$131$	8.48147	−	8.48147i	0.741029	−	0.741029i	−0.231747	−	0.972776i	$-0.574444\pi$
$131$	8.48147	−	8.48147i	0.741029	−	0.741029i	0.972776	+	0.231747i	$0.0744441\pi$
$132$		0			0
$133$	−0.0677788	−	0.0677788i	−0.00587717	−	0.00587717i
$134$	−4.67399	+	17.9192i	−0.403771	+	1.54798i
$135$		0			0
$136$	−0.300873	−	15.0861i	−0.0257997	−	1.29362i
$137$	4.31404			0.368574			0.184287	−	0.982873i	$-0.441002\pi$
$137$	4.31404			0.368574			0.184287	+	0.982873i	$0.441002\pi$
$138$		0			0
$139$	−15.5855	+	15.5855i	−1.32194	+	1.32194i	−0.409738	+	0.912203i	$0.634380\pi$
$139$	−15.5855	+	15.5855i	−1.32194	+	1.32194i	−0.912203	+	0.409738i	$0.865620\pi$
$140$	0.591600	+	2.09602i	0.0499993	+	0.177146i
$141$		0			0
$142$	−5.83515	+	3.42084i	−0.489675	+	0.287071i
$143$	−25.2126			−2.10838
$144$		0			0
$145$	−25.5493			−2.12176
$146$	−11.9420	+	7.00095i	−0.988325	+	0.579403i
$147$		0			0
$148$	−3.99527	+	1.12766i	−0.328409	+	0.0926934i
$149$	13.7498	−	13.7498i	1.12643	−	1.12643i	0.135677	−	0.990753i	$-0.456679\pi$
$149$	13.7498	−	13.7498i	1.12643	−	1.12643i	0.990753	−	0.135677i	$-0.0433210\pi$
$150$		0			0
$151$	1.55741			0.126741			0.0633703	−	0.997990i	$-0.479815\pi$
$151$	1.55741			0.126741			0.0633703	+	0.997990i	$0.479815\pi$
$152$	0.628013	+	0.603453i	0.0509386	+	0.0489465i
$153$		0			0
$154$	0.498644	−	1.91170i	0.0401819	−	0.154049i
$155$	12.2670	+	12.2670i	0.985306	+	0.985306i
$156$		0			0
$157$	−4.01517	+	4.01517i	−0.320446	+	0.320446i	−0.848938	−	0.528492i	$-0.822757\pi$
$157$	−4.01517	+	4.01517i	−0.320446	+	0.320446i	0.528492	+	0.848938i	$0.322757\pi$
$158$	−18.6063	+	10.9079i	−1.48024	+	0.867787i
$159$		0			0
$160$	−5.75411	−	18.9340i	−0.454903	−	1.49686i
$161$			1.57720i			0.124301i
$162$		0			0
$163$	4.68161	+	4.68161i	0.366692	+	0.366692i	0.866269	−	0.499577i	$-0.166511\pi$
$163$	4.68161	+	4.68161i	0.366692	+	0.366692i	−0.499577	+	0.866269i	$0.666511\pi$
$164$	−0.711768	+	1.27156i	−0.0555797	+	0.0992923i
$165$		0			0
$166$	−0.120912	−	0.0315384i	−0.00938460	−	0.00244786i
$167$		−	8.65340i		−	0.669620i	−0.942286	−	0.334810i	$-0.891328\pi$
$167$		−	8.65340i		−	0.669620i	0.942286	−	0.334810i	$-0.108672\pi$
$168$		0			0
$169$		−	18.5615i		−	1.42781i
$170$	6.66132	−	25.5382i	0.510900	−	1.95869i
$171$		0			0
$172$	−1.96252	−	6.95315i	−0.149641	−	0.530173i
$173$	−3.44281	−	3.44281i	−0.261752	−	0.261752i	0.564014	−	0.825765i	$-0.309256\pi$
$173$	−3.44281	−	3.44281i	−0.261752	−	0.261752i	−0.825765	+	0.564014i	$0.809256\pi$
$174$		0			0
$175$			2.25299i			0.170310i
$176$	−4.18355	+	17.4571i	−0.315347	+	1.31588i
$177$		0			0
$178$	−1.30878	−	2.23247i	−0.0980973	−	0.167331i
$179$	16.5307	−	16.5307i	1.23556	−	1.23556i	0.273769	−	0.961796i	$-0.411730\pi$
$179$	16.5307	−	16.5307i	1.23556	−	1.23556i	0.961796	−	0.273769i	$-0.0882703\pi$
$180$		0			0
$181$	6.46762	+	6.46762i	0.480735	+	0.480735i	0.905366	−	0.424631i	$-0.139596\pi$
$181$	6.46762	+	6.46762i	0.480735	+	0.480735i	−0.424631	+	0.905366i	$0.639596\pi$
$182$	2.39310	+	0.624211i	0.177388	+	0.0462696i
$183$		0			0
$184$	−0.285753	−	14.3280i	−0.0210660	−	1.05627i
$185$	−7.26124			−0.533857
$186$		0			0
$187$	−16.9294	+	16.9294i	−1.23800	+	1.23800i
$188$	−6.93977	+	12.3978i	−0.506135	+	0.904201i
$189$		0			0
$190$	0.770452	+	1.31421i	0.0558945	+	0.0953428i
$191$	−4.14780			−0.300124			−0.150062	−	0.988677i	$-0.547947\pi$
$191$	−4.14780			−0.300124			−0.150062	+	0.988677i	$0.547947\pi$
$192$		0			0
$193$	17.9131			1.28942			0.644708	−	0.764429i	$-0.276979\pi$
$193$	17.9131			1.28942			0.644708	+	0.764429i	$0.276979\pi$
$194$	−1.19054	−	2.03079i	−0.0854761	−	0.145802i
$195$		0			0
$196$	6.74355	−	12.0472i	0.481682	−	0.860517i
$197$	−9.63300	+	9.63300i	−0.686323	+	0.686323i	−0.961417	−	0.275094i	$-0.911291\pi$
$197$	−9.63300	+	9.63300i	−0.686323	+	0.686323i	0.275094	+	0.961417i	$0.411291\pi$
$198$		0			0
$199$	−1.80346			−0.127844			−0.0639218	−	0.997955i	$-0.520361\pi$
$199$	−1.80346			−0.127844			−0.0639218	+	0.997955i	$0.520361\pi$
$200$	−0.408191	−	20.4672i	−0.0288635	−	1.44725i
$201$		0			0
$202$	8.27130	+	2.15747i	0.581967	+	0.151799i
$203$	−1.60759	−	1.60759i	−0.112831	−	0.112831i
$204$		0			0
$205$	−1.80231	+	1.80231i	−0.125879	+	0.125879i
$206$	−0.994090	−	1.69568i	−0.0692616	−	0.118144i
$207$		0			0
$208$	−21.8531	−	5.23703i	−1.51524	−	0.363123i
$209$		−	1.38193i		−	0.0955904i
$210$		0			0
$211$	−18.4184	−	18.4184i	−1.26798	−	1.26798i	−0.947132	−	0.320844i	$-0.896034\pi$
$211$	−18.4184	−	18.4184i	−1.26798	−	1.26798i	−0.320844	−	0.947132i	$-0.603966\pi$
$212$	−2.14160	−	7.58762i	−0.147086	−	0.521120i
$213$		0			0
$214$	1.96818	−	7.54561i	0.134542	−	0.515807i
$215$		−	12.6371i		−	0.861840i
$216$		0			0
$217$			1.54370i			0.104793i
$218$	−11.3616	−	2.96352i	−0.769502	−	0.200715i
$219$		0			0
$220$	−15.3367	+	27.3988i	−1.03400	+	1.84722i
$221$	−21.1925	−	21.1925i	−1.42556	−	1.42556i
$222$		0			0
$223$			12.6500i			0.847106i	0.905871	+	0.423553i	$0.139217\pi$
$223$			12.6500i			0.847106i	−0.905871	+	0.423553i	$0.860783\pi$
$224$	0.829291	−	1.55340i	0.0554093	−	0.103791i
$225$		0			0
$226$	8.62061	−	5.05381i	0.573435	−	0.336174i
$227$	−16.9804	+	16.9804i	−1.12703	+	1.12703i	−0.136368	+	0.990658i	$0.543543\pi$
$227$	−16.9804	+	16.9804i	−1.12703	+	1.12703i	−0.990658	+	0.136368i	$0.956457\pi$
$228$		0			0
$229$	14.2438	+	14.2438i	0.941256	+	0.941256i	0.998368	−	0.0571117i	$-0.0181891\pi$
$229$	14.2438	+	14.2438i	0.941256	+	0.941256i	−0.0571117	+	0.998368i	$0.518189\pi$
$230$	6.32656	−	24.2548i	0.417161	−	1.59931i
$231$		0			0
$232$	14.8953	+	14.3128i	0.977925	+	0.939681i
$233$	−10.7550			−0.704585			−0.352293	−	0.935890i	$-0.614598\pi$
$233$	−10.7550			−0.704585			−0.352293	+	0.935890i	$0.614598\pi$
$234$		0			0
$235$	−17.5726	+	17.5726i	−1.14631	+	1.14631i
$236$	19.7534	−	5.57538i	1.28583	−	0.362926i
$237$		0			0
$238$	2.02603	−	1.18775i	0.131328	−	0.0769905i
$239$	9.73910			0.629970			0.314985	−	0.949097i	$-0.398000\pi$
$239$	9.73910			0.629970			0.314985	+	0.949097i	$0.398000\pi$
$240$		0			0
$241$	−17.4407			−1.12345			−0.561727	−	0.827323i	$-0.689863\pi$
$241$	−17.4407			−1.12345			−0.561727	+	0.827323i	$0.689863\pi$
$242$	11.1520	−	6.53780i	0.716875	−	0.420266i
$243$		0			0
$244$	−6.40591	−	22.6959i	−0.410096	−	1.45296i
$245$	17.0757	−	17.0757i	1.09093	−	1.09093i
$246$		0			0
$247$	1.72993			0.110073
$248$	−0.279684	−	14.0237i	−0.0177599	−	0.890503i
$249$		0			0
$250$	2.79408	−	10.7120i	0.176713	−	0.677484i
$251$	−1.39153	−	1.39153i	−0.0878325	−	0.0878325i	0.661825	−	0.749658i	$-0.269782\pi$
$251$	−1.39153	−	1.39153i	−0.0878325	−	0.0878325i	−0.749658	+	0.661825i	$0.769782\pi$
$252$		0			0
$253$	−16.0786	+	16.0786i	−1.01086	+	1.01086i
$254$	8.31944	−	4.87725i	0.522008	−	0.306026i
$255$		0			0
$256$	−7.25221	+	14.2620i	−0.453263	+	0.891377i
$257$		−	8.60369i		−	0.536683i	−0.963324	−	0.268342i	$-0.913524\pi$
$257$		−	8.60369i		−	0.536683i	0.963324	−	0.268342i	$-0.0864756\pi$
$258$		0			0
$259$	−0.456884	−	0.456884i	−0.0283894	−	0.0283894i
$260$	−34.2982	−	19.1987i	−2.12709	−	1.19066i
$261$		0			0
$262$	−16.4138	−	4.28132i	−1.01405	−	0.264501i
$263$			20.8175i			1.28366i	0.766847	+	0.641830i	$0.221824\pi$
$263$			20.8175i			1.28366i	−0.766847	+	0.641830i	$0.778176\pi$
$264$		0			0
$265$		−	13.7902i		−	0.847123i
$266$	−0.0342138	+	0.131169i	−0.00209778	+	0.00804248i
$267$		0			0
$268$	25.2047	−	7.11400i	1.53962	−	0.434557i
$269$	10.6886	+	10.6886i	0.651695	+	0.651695i	0.953401	−	0.301706i	$-0.0975561\pi$
$269$	10.6886	+	10.6886i	0.651695	+	0.651695i	−0.301706	+	0.953401i	$0.597556\pi$
$270$		0			0
$271$		−	11.4439i		−	0.695168i	−0.937649	−	0.347584i	$-0.887002\pi$
$271$		−	11.4439i		−	0.695168i	0.937649	−	0.347584i	$-0.112998\pi$
$272$	−18.1901	+	11.1571i	−1.10294	+	0.676501i
$273$		0			0
$274$	−3.08554	−	5.26321i	−0.186404	−	0.317962i
$275$	−22.9680	+	22.9680i	−1.38502	+	1.38502i
$276$		0			0
$277$	15.6763	+	15.6763i	0.941897	+	0.941897i	0.998402	−	0.0565054i	$-0.0179958\pi$
$277$	15.6763	+	15.6763i	0.941897	+	0.941897i	−0.0565054	+	0.998402i	$0.517996\pi$
$278$	30.1617	+	7.86732i	1.80898	+	0.471850i
$279$		0			0
$280$	2.13405	−	2.22090i	0.127534	−	0.132724i
$281$	4.07777			0.243259			0.121630	−	0.992576i	$-0.461188\pi$
$281$	4.07777			0.243259			0.121630	+	0.992576i	$0.461188\pi$
$282$		0			0
$283$	11.4231	−	11.4231i	0.679030	−	0.679030i	−0.280750	−	0.959781i	$-0.590583\pi$
$283$	11.4231	−	11.4231i	0.679030	−	0.679030i	0.959781	+	0.280750i	$0.0905833\pi$
$284$	8.34697	+	4.67229i	0.495302	+	0.277250i
$285$		0			0
$286$	18.0329	+	30.7598i	1.06631	+	1.81887i
$287$	−0.226806			−0.0133879
$288$		0			0
$289$	−11.4602			−0.674129
$290$	18.2737	+	31.1706i	1.07307	+	1.83040i
$291$		0			0
$292$	17.0826	+	9.56211i	0.999681	+	0.559580i
$293$	−5.07475	+	5.07475i	−0.296470	+	0.296470i	−0.839630	−	0.543159i	$-0.817228\pi$
$293$	−5.07475	+	5.07475i	−0.296470	+	0.296470i	0.543159	+	0.839630i	$0.317228\pi$
$294$		0			0
$295$	35.9009			2.09023
$296$	4.23332	+	4.06776i	0.246057	+	0.236434i
$297$		0			0
$298$	−26.6094	−	6.94072i	−1.54144	−	0.402065i
$299$	−20.1275	−	20.1275i	−1.16400	−	1.16400i
$300$		0			0
$301$	0.795136	−	0.795136i	0.0458309	−	0.0458309i
$302$	−1.11391	−	1.90007i	−0.0640984	−	0.109337i
$303$		0			0
$304$	0.287049	−	1.19780i	0.0164634	−	0.0686984i
$305$		−	41.2488i		−	2.36190i
$306$		0			0
$307$	9.58448	+	9.58448i	0.547015	+	0.547015i	0.925576	−	0.378561i	$-0.123581\pi$
$307$	9.58448	+	9.58448i	0.547015	+	0.547015i	−0.378561	+	0.925576i	$0.623581\pi$
$308$	−2.68896	+	0.758957i	−0.153218	+	0.0432456i
$309$		0			0
$310$	6.19219	−	23.7396i	0.351693	−	1.34832i
$311$			33.4689i			1.89784i	0.315510	+	0.948922i	$0.397824\pi$
$311$			33.4689i			1.89784i	−0.315510	+	0.948922i	$0.602176\pi$
$312$		0			0
$313$			25.6632i			1.45057i	0.688449	+	0.725285i	$0.258292\pi$
$313$			25.6632i			1.45057i	−0.688449	+	0.725285i	$0.741708\pi$
$314$	7.77036	+	2.02680i	0.438507	+	0.114379i
$315$		0			0
$316$	26.6157	+	14.8984i	1.49725	+	0.838099i
$317$	−19.1284	−	19.1284i	−1.07436	−	1.07436i	−0.997004	−	0.0773548i	$-0.975353\pi$
$317$	−19.1284	−	19.1284i	−1.07436	−	1.07436i	−0.0773548	−	0.997004i	$-0.524647\pi$
$318$		0			0
$319$		−	32.7769i		−	1.83516i
$320$	−18.9843	+	20.5623i	−1.06125	+	1.14947i
$321$		0			0
$322$	1.92421	−	1.12806i	0.107232	−	0.0628644i
$323$	1.16159	−	1.16159i	0.0646326	−	0.0646326i
$324$		0			0
$325$	−28.7517	−	28.7517i	−1.59486	−	1.59486i
$326$	2.36321	−	9.06008i	0.130886	−	0.501791i
$327$		0			0
$328$	2.06041	−	0.0410922i	0.113767	−	0.00226894i
$329$	−2.21137			−0.121917
$330$		0			0
$331$	23.5444	−	23.5444i	1.29412	−	1.29412i	0.361900	−	0.932217i	$-0.382128\pi$
$331$	23.5444	−	23.5444i	1.29412	−	1.29412i	0.932217	−	0.361900i	$-0.117872\pi$
$332$	0.0480028	+	0.170072i	0.00263449	+	0.00933392i
$333$		0			0
$334$	−10.5573	+	6.18919i	−0.577670	+	0.338657i
$335$	45.8084			2.50278
$336$		0			0
$337$	9.50540			0.517792			0.258896	−	0.965905i	$-0.416641\pi$
$337$	9.50540			0.517792			0.258896	+	0.965905i	$0.416641\pi$
$338$	−22.6454	+	13.2758i	−1.23175	+	0.722109i
$339$		0			0
$340$	−35.9215	+	10.1388i	−1.94811	+	0.549854i
$341$	−15.7371	+	15.7371i	−0.852214	+	0.852214i
$342$		0			0
$343$	4.32784			0.233682
$344$	−7.07931	+	7.36743i	−0.381691	+	0.397225i
$345$		0			0
$346$	−1.73788	+	6.66269i	−0.0934289	+	0.358188i
$347$	2.52520	+	2.52520i	0.135560	+	0.135560i	0.771631	−	0.636071i	$-0.219441\pi$
$347$	2.52520	+	2.52520i	0.135560	+	0.135560i	−0.636071	+	0.771631i	$0.719441\pi$
$348$		0			0
$349$	17.4786	−	17.4786i	0.935608	−	0.935608i	−0.0624409	−	0.998049i	$-0.519888\pi$
$349$	17.4786	−	17.4786i	0.935608	−	0.935608i	0.998049	+	0.0624409i	$0.0198885\pi$
$350$	2.74869	−	1.61141i	0.146924	−	0.0861335i
$351$		0			0
$352$	24.2902	−	7.38189i	1.29467	−	0.393456i
$353$		−	3.01832i		−	0.160649i	−0.996769	−	0.0803246i	$-0.974404\pi$
$353$		−	3.01832i		−	0.160649i	0.996769	−	0.0803246i	$-0.0255957\pi$
$354$		0			0
$355$	11.8310	+	11.8310i	0.627923	+	0.627923i
$356$	−1.78758	+	3.19347i	−0.0947413	+	0.169254i
$357$		0			0
$358$	−31.9911	−	8.34447i	−1.69078	−	0.441019i
$359$			13.9366i			0.735547i	0.929915	+	0.367773i	$0.119880\pi$
$359$			13.9366i			0.735547i	−0.929915	+	0.367773i	$0.880120\pi$
$360$		0			0
$361$		−	18.9052i		−	0.995009i
$362$	3.26476	−	12.5165i	0.171592	−	0.657851i
$363$		0			0
$364$	−0.950075	−	3.36608i	−0.0497975	−	0.176431i
$365$	24.2128	+	24.2128i	1.26735	+	1.26735i
$366$		0			0
$367$			12.7809i			0.667156i	0.942723	+	0.333578i	$0.108256\pi$
$367$			12.7809i			0.667156i	−0.942723	+	0.333578i	$0.891744\pi$
$368$	−17.2760	+	10.5964i	−0.900573	+	0.552378i
$369$		0			0
$370$	5.19347	+	8.85884i	0.269996	+	0.460549i
$371$	0.867691	−	0.867691i	0.0450483	−	0.0450483i
$372$		0			0
$373$	9.46505	+	9.46505i	0.490082	+	0.490082i	0.908332	−	0.418250i	$-0.137356\pi$
$373$	9.46505	+	9.46505i	0.490082	+	0.490082i	−0.418250	+	0.908332i	$0.637356\pi$
$374$	32.7627	+	8.54573i	1.69412	+	0.441889i
$375$		0			0
$376$	20.0891	−	0.400650i	1.03601	−	0.0206620i
$377$	41.0307			2.11319
$378$		0			0
$379$	6.47456	−	6.47456i	0.332576	−	0.332576i	−0.520988	−	0.853564i	$-0.674436\pi$
$379$	6.47456	−	6.47456i	0.332576	−	0.332576i	0.853564	+	0.520988i	$0.174436\pi$
$380$	1.05231	−	1.87993i	0.0539822	−	0.0964384i
$381$		0			0
$382$	2.96664	+	5.06039i	0.151787	+	0.258912i
$383$	20.3558			1.04013			0.520066	−	0.854126i	$-0.325907\pi$
$383$	20.3558			1.04013			0.520066	+	0.854126i	$0.325907\pi$
$384$		0			0
$385$	−4.88706			−0.249068
$386$	−12.8120	−	21.8543i	−0.652116	−	1.11236i
$387$		0			0
$388$	−1.62608	+	2.90497i	−0.0825518	+	0.147477i
$389$	13.4195	−	13.4195i	0.680397	−	0.680397i	−0.279693	−	0.960090i	$-0.590233\pi$
$389$	13.4195	−	13.4195i	0.680397	−	0.680397i	0.960090	+	0.279693i	$0.0902326\pi$
$390$		0			0
$391$	−27.0299			−1.36696
$392$	−19.5210	+	0.389322i	−0.985961	+	0.0196637i
$393$		0			0
$394$	18.6423	+	4.86260i	0.939184	+	0.244974i
$395$	37.7250	+	37.7250i	1.89815	+	1.89815i
$396$		0			0
$397$	0.765194	−	0.765194i	0.0384040	−	0.0384040i	−0.687644	−	0.726048i	$-0.741355\pi$
$397$	0.765194	−	0.765194i	0.0384040	−	0.0384040i	0.726048	+	0.687644i	$0.241355\pi$
$398$	1.28989	+	2.20025i	0.0646563	+	0.110288i
$399$		0			0
$400$	−24.6784	+	15.1368i	−1.23392	+	0.756839i
$401$			0.608629i			0.0303935i	0.999885	+	0.0151968i	$0.00483746\pi$
$401$			0.608629i			0.0303935i	−0.999885	+	0.0151968i	$0.995163\pi$
$402$		0			0
$403$	−19.7000	−	19.7000i	−0.981328	−	0.981328i
$404$	−3.28375	−	11.6342i	−0.163373	−	0.578824i
$405$		0			0
$406$	−0.811487	+	3.11108i	−0.0402734	+	0.154401i
$407$		−	9.31536i		−	0.461745i
$408$		0			0
$409$			14.4626i			0.715128i	0.933889	+	0.357564i	$0.116393\pi$
$409$			14.4626i			0.715128i	−0.933889	+	0.357564i	$0.883607\pi$
$410$	3.48792	+	0.909779i	0.172256	+	0.0449308i
$411$		0			0
$412$	−1.35776	+	2.42562i	−0.0668920	+	0.119502i
$413$	2.25892	+	2.25892i	0.111154	+	0.111154i
$414$		0			0
$415$			0.309099i			0.0151731i
$416$	9.24077	+	30.4069i	0.453066	+	1.49082i
$417$		0			0
$418$	−1.68599	+	0.988404i	−0.0824642	+	0.0483444i
$419$	−4.44806	+	4.44806i	−0.217302	+	0.217302i	−0.807360	−	0.590059i	$-0.799105\pi$
$419$	−4.44806	+	4.44806i	−0.217302	+	0.217302i	0.590059	+	0.807360i	$0.299105\pi$
$420$		0			0
$421$	−17.3430	−	17.3430i	−0.845245	−	0.845245i	0.144291	−	0.989535i	$-0.453910\pi$
$421$	−17.3430	−	17.3430i	−0.845245	−	0.845245i	−0.989535	+	0.144291i	$0.953910\pi$
$422$	−9.29735	+	35.6442i	−0.452588	+	1.73513i
$423$		0			0
$424$	−7.72529	+	8.03970i	−0.375173	+	0.390442i
$425$	−38.6116			−1.87294
$426$		0			0
$427$	2.59542	−	2.59542i	0.125601	−	0.125601i
$428$	−10.6135	+	2.99565i	−0.513022	+	0.144800i
$429$		0			0
$430$	−15.4174	+	9.03843i	−0.743495	+	0.435872i
$431$	−21.3898			−1.03031			−0.515156	−	0.857097i	$-0.672266\pi$
$431$	−21.3898			−1.03031			−0.515156	+	0.857097i	$0.672266\pi$
$432$		0			0
$433$	27.4801			1.32061			0.660305	−	0.750998i	$-0.270427\pi$
$433$	27.4801			1.32061			0.660305	+	0.750998i	$0.270427\pi$
$434$	1.88334	−	1.10410i	0.0904032	−	0.0529986i
$435$		0			0
$436$	4.51060	+	15.9809i	0.216019	+	0.765346i
$437$	1.10321	−	1.10321i	0.0527739	−	0.0527739i
$438$		0			0
$439$	−20.9157			−0.998251			−0.499126	−	0.866530i	$-0.666345\pi$
$439$	−20.9157			−0.998251			−0.499126	+	0.866530i	$0.666345\pi$
$440$	44.3963	−	0.885427i	2.11651	−	0.0422111i
$441$		0			0
$442$	−10.6977	+	41.0129i	−0.508837	+	1.95078i
$443$	−12.0433	−	12.0433i	−0.572193	−	0.572193i	0.360548	−	0.932741i	$-0.382590\pi$
$443$	−12.0433	−	12.0433i	−0.572193	−	0.572193i	−0.932741	+	0.360548i	$0.882590\pi$
$444$		0			0
$445$	−4.52642	+	4.52642i	−0.214573	+	0.214573i
$446$	15.4332	−	9.04768i	0.730784	−	0.428420i
$447$		0			0
$448$	−2.48831	+	0.0992918i	−0.117562	+	0.00469109i
$449$		−	35.1219i		−	1.65751i	−0.559615	−	0.828753i	$-0.689051\pi$
$449$		−	35.1219i		−	1.65751i	0.559615	−	0.828753i	$-0.310949\pi$
$450$		0			0
$451$	−2.31216	−	2.31216i	−0.108875	−	0.108875i
$452$	−12.3315	−	6.90265i	−0.580024	−	0.324673i
$453$		0			0
$454$	32.8612	+	8.57145i	1.54225	+	0.402278i
$455$		−	6.11771i		−	0.286803i
$456$		0			0
$457$		−	3.76527i		−	0.176132i	−0.996115	−	0.0880658i	$-0.971931\pi$
$457$		−	3.76527i		−	0.176132i	0.996115	−	0.0880658i	$-0.0280686\pi$
$458$	7.19006	−	27.5653i	0.335970	−	1.28804i
$459$		0			0
$460$	−34.1162	+	9.62929i	−1.59068	+	0.448968i
$461$	−1.53673	−	1.53673i	−0.0715728	−	0.0715728i	0.670414	−	0.741987i	$-0.266116\pi$
$461$	−1.53673	−	1.53673i	−0.0715728	−	0.0715728i	−0.741987	+	0.670414i	$0.766116\pi$
$462$		0			0
$463$		−	3.83977i		−	0.178449i	−0.996012	−	0.0892245i	$-0.971561\pi$
$463$		−	3.83977i		−	0.178449i	0.996012	−	0.0892245i	$-0.0284389\pi$
$464$	6.80826	−	28.4095i	0.316065	−	1.31888i
$465$		0			0
$466$	7.69234	+	13.1213i	0.356341	+	0.607834i
$467$	−14.8059	+	14.8059i	−0.685134	+	0.685134i	−0.961152	−	0.276019i	$-0.910985\pi$
$467$	−14.8059	+	14.8059i	−0.685134	+	0.685134i	0.276019	+	0.961152i	$0.410985\pi$
$468$		0			0
$469$	2.88231	+	2.88231i	0.133093	+	0.133093i
$470$	34.0073	+	8.87039i	1.56864	+	0.409160i
$471$		0			0
$472$	−20.9303	−	20.1118i	−0.963395	−	0.925719i
$473$	16.2119			0.745426
$474$		0			0
$475$	1.57592	−	1.57592i	0.0723080	−	0.0723080i
$476$	−2.89816	−	1.62227i	−0.132837	−	0.0743566i
$477$		0			0
$478$	−6.96572	−	11.8819i	−0.318605	−	0.543464i
$479$	−3.43292			−0.156854			−0.0784272	−	0.996920i	$-0.524990\pi$
$479$	−3.43292			−0.156854			−0.0784272	+	0.996920i	$0.524990\pi$
$480$		0			0
$481$	11.6611			0.531701
$482$	12.4741	+	21.2779i	0.568181	+	0.969184i
$483$		0			0
$484$	−15.9525	−	8.92954i	−0.725112	−	0.405888i
$485$	−4.11749	+	4.11749i	−0.186966	+	0.186966i
$486$		0			0
$487$	−2.89639			−0.131248			−0.0656241	−	0.997844i	$-0.520904\pi$
$487$	−2.89639			−0.131248			−0.0656241	+	0.997844i	$0.520904\pi$
$488$	−23.1077	+	24.0482i	−1.04604	+	1.08861i
$489$		0			0
$490$	−33.0458	−	8.61957i	−1.49286	−	0.389393i
$491$	15.0942	+	15.0942i	0.681192	+	0.681192i	0.960269	−	0.279077i	$-0.0900285\pi$
$491$	15.0942	+	15.0942i	0.681192	+	0.681192i	−0.279077	+	0.960269i	$0.590028\pi$
$492$		0			0
$493$	27.5508	−	27.5508i	1.24082	−	1.24082i
$494$	−1.23730	−	2.11054i	−0.0556688	−	0.0949579i
$495$		0			0
$496$	−16.9091	+	10.3714i	−0.759239	+	0.465689i
$497$			1.48883i			0.0667833i
$498$		0			0
$499$	13.6146	+	13.6146i	0.609472	+	0.609472i	0.942808	−	0.333336i	$-0.108174\pi$
$499$	13.6146	+	13.6146i	0.609472	+	0.609472i	−0.333336	+	0.942808i	$0.608174\pi$
$500$	−15.0672	+	4.25271i	−0.673826	+	0.190187i
$501$		0			0
$502$	−0.702423	+	2.69295i	−0.0313507	+	0.120192i
$503$			27.8824i			1.24321i	0.783329	+	0.621607i	$0.213520\pi$
$503$			27.8824i			1.24321i	−0.783329	+	0.621607i	$0.786480\pi$
$504$		0			0
$505$		−	21.1447i		−	0.940927i
$506$	31.1162	+	8.11627i	1.38328	+	0.360812i
$507$		0			0
$508$	−11.9007	−	6.66150i	−0.528007	−	0.295556i
$509$	−14.5880	−	14.5880i	−0.646603	−	0.646603i	0.305568	−	0.952170i	$-0.401154\pi$
$509$	−14.5880	−	14.5880i	−0.646603	−	0.646603i	−0.952170	+	0.305568i	$0.901154\pi$
$510$		0			0
$511$			3.04698i			0.134791i
$512$	22.5869	−	1.35284i	0.998211	−	0.0597875i
$513$		0			0
$514$	−10.4967	+	6.15363i	−0.462987	+	0.271425i
$515$	−3.43806	+	3.43806i	−0.151499	+	0.151499i
$516$		0			0
$517$	−22.5437	−	22.5437i	−0.991469	−	0.991469i
$518$	−0.230629	+	0.884185i	−0.0101332	+	0.0388488i
$519$		0			0
$520$	1.10839	+	55.5760i	0.0486062	+	2.43717i
$521$	−33.2262			−1.45567			−0.727833	−	0.685754i	$-0.759473\pi$
$521$	−33.2262			−1.45567			−0.727833	+	0.685754i	$0.759473\pi$
$522$		0			0
$523$	24.6136	−	24.6136i	1.07628	−	1.07628i	0.0794362	−	0.996840i	$-0.474688\pi$
$523$	24.6136	−	24.6136i	1.07628	−	1.07628i	0.996840	−	0.0794362i	$-0.0253120\pi$
$524$	6.51635	+	23.0872i	0.284668	+	1.00857i
$525$		0			0
$526$	25.3977	−	14.8893i	1.10739	−	0.649205i
$527$	−26.4558			−1.15243
$528$		0			0
$529$	−2.67154			−0.116154
$530$	−16.8242	+	9.86317i	−0.730799	+	0.428429i
$531$		0			0
$532$	0.184499	−	0.0520748i	0.00799906	−	0.00225773i
$533$	2.89440	−	2.89440i	0.125370	−	0.125370i
$534$		0			0
$535$	−19.2895			−0.833959
$536$	−26.7064	−	25.6620i	−1.15354	−	1.10843i
$537$		0			0
$538$	5.39545	−	20.6851i	0.232614	−	0.891798i
$539$	21.9062	+	21.9062i	0.943568	+	0.943568i
$540$		0			0
$541$	10.3562	−	10.3562i	0.445249	−	0.445249i	−0.448523	−	0.893771i	$-0.648050\pi$
$541$	10.3562	−	10.3562i	0.445249	−	0.445249i	0.893771	+	0.448523i	$0.148050\pi$
$542$	−13.9618	+	8.18505i	−0.599709	+	0.351578i
$543$		0			0
$544$	26.6221	+	14.2123i	1.14141	+	0.609349i
$545$			29.0446i			1.24413i
$546$		0			0
$547$	−13.2717	−	13.2717i	−0.567457	−	0.567457i	0.363958	−	0.931415i	$-0.381425\pi$
$547$	−13.2717	−	13.2717i	−0.567457	−	0.567457i	−0.931415	+	0.363958i	$0.881425\pi$
$548$	−4.21433	+	7.52883i	−0.180027	+	0.321616i
$549$		0			0
$550$	44.4488	+	11.5939i	1.89530	+	0.494366i
$551$			2.24895i			0.0958083i
$552$		0			0
$553$			4.74739i			0.201880i
$554$	7.91317	−	30.3375i	0.336198	−	1.28892i
$555$		0			0
$556$	−11.9744	−	42.4248i	−0.507827	−	1.79921i
$557$	3.50868	+	3.50868i	0.148668	+	0.148668i	0.777523	−	0.628855i	$-0.216476\pi$
$557$	3.50868	+	3.50868i	0.148668	+	0.148668i	−0.628855	+	0.777523i	$0.716476\pi$
$558$		0			0
$559$			20.2944i			0.858360i
$560$	−4.23588	−	1.01512i	−0.178999	−	0.0428965i
$561$		0			0
$562$	−2.91655	−	4.97495i	−0.123027	−	0.209856i
$563$	7.00949	−	7.00949i	0.295415	−	0.295415i	−0.543800	−	0.839215i	$-0.683015\pi$
$563$	7.00949	−	7.00949i	0.295415	−	0.295415i	0.839215	+	0.543800i	$0.183015\pi$
$564$		0			0
$565$	−17.4786	−	17.4786i	−0.735330	−	0.735330i
$566$	−22.1065	−	5.76620i	−0.929204	−	0.242371i
$567$		0			0
$568$	−0.269743	−	13.5252i	−0.0113182	−	0.567506i
$569$	25.7645			1.08010			0.540052	−	0.841632i	$-0.318405\pi$
$569$	25.7645			1.08010			0.540052	+	0.841632i	$0.318405\pi$
$570$		0			0
$571$	−26.8405	+	26.8405i	−1.12324	+	1.12324i	−0.131988	+	0.991251i	$0.542136\pi$
$571$	−26.8405	+	26.8405i	−1.12324	+	1.12324i	−0.991251	+	0.131988i	$0.957864\pi$
$572$	24.6298	−	44.0008i	1.02983	−	1.83977i
$573$		0			0
$574$	0.162219	+	0.276707i	0.00677088	+	0.0115495i
$575$	−36.6712			−1.52930
$576$		0			0
$577$	23.3116			0.970475			0.485237	−	0.874382i	$-0.338733\pi$
$577$	23.3116			0.970475			0.485237	+	0.874382i	$0.338733\pi$
$578$	8.19669	+	13.9816i	0.340937	+	0.581559i
$579$		0			0
$580$	24.9588	−	44.5885i	1.03636	−	1.85143i
$581$	−0.0194488	+	0.0194488i	−0.000806872	+	0.000806872i
$582$		0			0
$583$	17.6912			0.732697
$584$	−0.552045	−	27.6802i	−0.0228438	−	1.14541i
$585$		0			0
$586$	9.82092	+	2.56166i	0.405698	+	0.105821i
$587$	−29.8792	−	29.8792i	−1.23325	−	1.23325i	−0.962709	−	0.270539i	$-0.912798\pi$
$587$	−29.8792	−	29.8792i	−1.23325	−	1.23325i	−0.270539	−	0.962709i	$-0.587202\pi$
$588$		0			0
$589$	1.07978	−	1.07978i	0.0444917	−	0.0444917i
$590$	−25.6775	−	43.7997i	−1.05712	−	1.80321i
$591$		0			0
$592$	1.93494	−	8.07412i	0.0795255	−	0.331844i
$593$		−	22.5833i		−	0.927386i	−0.885996	−	0.463693i	$-0.846524\pi$
$593$		−	22.5833i		−	0.927386i	0.885996	−	0.463693i	$-0.153476\pi$
$594$		0			0
$595$	−4.10784	−	4.10784i	−0.168405	−	0.168405i
$596$	10.5641	+	37.4281i	0.432721	+	1.53312i
$597$		0			0
$598$	−10.1601	+	38.9518i	−0.415477	+	1.59286i
$599$		−	2.48261i		−	0.101437i	−0.998713	−	0.0507184i	$-0.983849\pi$
$599$		−	2.48261i		−	0.101437i	0.998713	−	0.0507184i	$-0.0161511\pi$
$600$		0			0
$601$		−	7.17267i		−	0.292579i	−0.989242	−	0.146290i	$-0.953267\pi$
$601$		−	7.17267i		−	0.292579i	0.989242	−	0.146290i	$-0.0467331\pi$
$602$	−1.53879	−	0.401373i	−0.0627163	−	0.0163588i
$603$		0			0
$604$	−1.52142	+	2.71799i	−0.0619056	+	0.110593i
$605$	−22.6110	−	22.6110i	−0.919267	−	0.919267i
$606$		0			0
$607$			3.30808i			0.134271i	0.997744	+	0.0671354i	$0.0213859\pi$
$607$			3.30808i			0.134271i	−0.997744	+	0.0671354i	$0.978614\pi$
$608$	−1.66664	+	0.506498i	−0.0675912	+	0.0205412i
$609$		0			0
$610$	−50.3243	+	29.5025i	−2.03757	+	1.19452i
$611$	28.2205	−	28.2205i	1.14168	−	1.14168i
$612$		0			0
$613$	22.5156	+	22.5156i	0.909398	+	0.909398i	0.996224	−	0.0868254i	$-0.0276722\pi$
$613$	22.5156	+	22.5156i	0.909398	+	0.909398i	−0.0868254	+	0.996224i	$0.527672\pi$
$614$	4.83811	−	18.5484i	0.195250	−	0.748551i
$615$		0			0
$616$	2.84917	+	2.73775i	0.114796	+	0.110307i
$617$	2.16974			0.0873503			0.0436751	−	0.999046i	$-0.486093\pi$
$617$	2.16974			0.0873503			0.0436751	+	0.999046i	$0.486093\pi$
$618$		0			0
$619$	2.85968	−	2.85968i	0.114940	−	0.114940i	−0.647297	−	0.762238i	$-0.724101\pi$
$619$	2.85968	−	2.85968i	0.114940	−	0.114940i	0.762238	+	0.647297i	$0.224101\pi$
$620$	−33.3916	+	9.42477i	−1.34104	+	0.378508i
$621$		0			0
$622$	40.8326	−	23.9380i	1.63724	−	0.959826i
$623$	−0.569613			−0.0228211
$624$		0			0
$625$	8.80440			0.352176
$626$	31.3096	−	18.3551i	1.25138	−	0.733619i
$627$		0			0
$628$	−3.08488	−	10.9296i	−0.123100	−	0.436139i
$629$	7.83006	−	7.83006i	0.312205	−	0.312205i
$630$		0			0
$631$	−2.09867			−0.0835466			−0.0417733	−	0.999127i	$-0.513301\pi$
$631$	−2.09867			−0.0835466			−0.0417733	+	0.999127i	$0.513301\pi$
$632$	−0.860121	−	43.1274i	−0.0342138	−	1.71552i
$633$		0			0
$634$	−9.65575	+	37.0182i	−0.383479	+	1.47018i
$635$	−16.8680	−	16.8680i	−0.669385	−	0.669385i
$636$		0			0
$637$	−27.4226	+	27.4226i	−1.08652	+	1.08652i
$638$	−39.9884	+	23.4431i	−1.58316	+	0.928122i
$639$		0			0
$640$	38.6645	+	8.45433i	1.52835	+	0.334187i
$641$			41.9546i			1.65711i	0.559911	+	0.828553i	$0.310835\pi$
$641$			41.9546i			1.65711i	−0.559911	+	0.828553i	$0.689165\pi$
$642$		0			0
$643$	20.3606	+	20.3606i	0.802944	+	0.802944i	0.983555	−	0.180610i	$-0.0578073\pi$
$643$	20.3606	+	20.3606i	0.802944	+	0.802944i	−0.180610	+	0.983555i	$0.557807\pi$
$644$	−2.75251	−	1.54074i	−0.108464	−	0.0607137i
$645$		0			0
$646$	−2.24797	−	0.586354i	−0.0884451	−	0.0230698i
$647$		−	6.92134i		−	0.272106i	−0.990702	−	0.136053i	$-0.956558\pi$
$647$		−	6.92134i		−	0.272106i	0.990702	−	0.136053i	$-0.0434417\pi$
$648$		0			0
$649$			46.0568i			1.80789i
$650$	−14.5134	+	55.6417i	−0.569264	+	2.18245i
$651$		0			0
$652$	−12.7437	+	3.59690i	−0.499082	+	0.140866i
$653$	−4.21712	−	4.21712i	−0.165028	−	0.165028i	0.619762	−	0.784790i	$-0.287229\pi$
$653$	−4.21712	−	4.21712i	−0.165028	−	0.165028i	−0.784790	+	0.619762i	$0.787229\pi$
$654$		0			0
$655$			41.9600i			1.63951i
$656$	−1.52380	−	2.48434i	−0.0594945	−	0.0969973i
$657$		0			0
$658$	1.58164	+	2.69791i	0.0616588	+	0.105175i
$659$	21.2854	−	21.2854i	0.829160	−	0.829160i	−0.158241	−	0.987401i	$-0.550582\pi$
$659$	21.2854	−	21.2854i	0.829160	−	0.829160i	0.987401	+	0.158241i	$0.0505822\pi$
$660$		0			0
$661$	−25.2323	−	25.2323i	−0.981424	−	0.981424i	0.0184067	−	0.999831i	$-0.494141\pi$
$661$	−25.2323	−	25.2323i	−0.981424	−	0.981424i	−0.999831	+	0.0184067i	$0.994141\pi$
$662$	−45.5643	−	11.8849i	−1.77091	−	0.461919i
$663$		0			0
$664$	0.173158	−	0.180205i	0.00671983	−	0.00699332i
$665$	0.335319			0.0130031
$666$		0			0
$667$	26.1662	−	26.1662i	1.01316	−	1.01316i
$668$	15.1018	+	8.45339i	0.584308	+	0.327071i
$669$		0			0
$670$	−32.7636	−	55.8870i	−1.26577	−	2.15910i
$671$	52.9176			2.04286
$672$		0			0
$673$	13.5761			0.523319			0.261659	−	0.965160i	$-0.415730\pi$
$673$	13.5761			0.523319			0.261659	+	0.965160i	$0.415730\pi$
$674$	−6.79857	−	11.5968i	−0.261871	−	0.446691i
$675$		0			0
$676$	32.3935	+	18.1325i	1.24590	+	0.697405i
$677$	14.6444	−	14.6444i	0.562831	−	0.562831i	−0.367279	−	0.930111i	$-0.619711\pi$
$677$	14.6444	−	14.6444i	0.562831	−	0.562831i	0.930111	+	0.367279i	$0.119711\pi$
$678$		0			0
$679$	−0.518154			−0.0198849
$680$	38.0617	+	36.5732i	1.45960	+	1.40252i
$681$		0			0
$682$	30.4553	+	7.94389i	1.16619	+	0.304187i
$683$	−2.07220	−	2.07220i	−0.0792905	−	0.0792905i	0.666349	−	0.745640i	$-0.267856\pi$
$683$	−2.07220	−	2.07220i	−0.0792905	−	0.0792905i	−0.745640	+	0.666349i	$0.767856\pi$
$684$		0			0
$685$	−10.6713	+	10.6713i	−0.407731	+	0.407731i
$686$	−3.09541	−	5.28005i	−0.118183	−	0.201593i
$687$		0			0
$688$	14.0517	+	3.36746i	0.535718	+	0.128383i
$689$			22.1462i			0.843703i
$690$		0			0
$691$	3.62067	+	3.62067i	0.137737	+	0.137737i	0.772613	−	0.634877i	$-0.218949\pi$
$691$	3.62067	+	3.62067i	0.137737	+	0.137737i	−0.634877	+	0.772613i	$0.718949\pi$
$692$	9.37158	−	2.64512i	0.356254	−	0.100553i
$693$		0			0
$694$	1.27469	−	4.88690i	0.0483864	−	0.185504i
$695$		−	77.1053i		−	2.92477i
$696$		0			0
$697$		−	3.88699i		−	0.147230i
$698$	−33.8254	−	8.82295i	−1.28031	−	0.333953i
$699$		0			0
$700$	−3.93190	−	2.20092i	−0.148612	−	0.0831868i
$701$	−6.45188	−	6.45188i	−0.243684	−	0.243684i	0.574688	−	0.818372i	$-0.305123\pi$
$701$	−6.45188	−	6.45188i	−0.243684	−	0.243684i	−0.818372	+	0.574688i	$0.805123\pi$
$702$		0			0
$703$			0.639161i			0.0241064i
$704$	−26.3792	−	24.3547i	−0.994202	−	0.917903i
$705$		0			0
$706$	−3.68241	+	2.15880i	−0.138589	+	0.0812476i
$707$	1.33045	−	1.33045i	0.0500365	−	0.0500365i
$708$		0			0
$709$	3.86674	+	3.86674i	0.145219	+	0.145219i	0.775978	−	0.630760i	$-0.217257\pi$
$709$	3.86674	+	3.86674i	0.145219	+	0.145219i	−0.630760	+	0.775978i	$0.717257\pi$
$710$	5.97211	−	22.8959i	0.224129	−	0.859267i
$711$		0			0
$712$	5.17463	−	0.103201i	0.193927	−	0.00386763i
$713$	−25.1263			−0.940987
$714$		0			0
$715$	62.3666	−	62.3666i	2.33238	−	2.33238i
$716$	12.7006	+	44.9979i	0.474645	+	1.68165i
$717$		0			0
$718$	17.0029	−	9.96792i	0.634543	−	0.371999i
$719$	−0.392829			−0.0146501			−0.00732503	−	0.999973i	$-0.502332\pi$
$719$	−0.392829			−0.0146501			−0.00732503	+	0.999973i	$0.502332\pi$
$720$		0			0
$721$	−0.432652			−0.0161128
$722$	−23.0647	+	13.5216i	−0.858378	+	0.503221i
$723$		0			0
$724$	−17.6054	+	4.96911i	−0.654299	+	0.184675i
$725$	37.3778	−	37.3778i	1.38818	−	1.38818i
$726$		0			0
$727$	−33.4774			−1.24161			−0.620805	−	0.783965i	$-0.713194\pi$
$727$	−33.4774			−1.24161			−0.620805	+	0.783965i	$0.713194\pi$
$728$	−3.42716	+	3.56664i	−0.127019	+	0.132188i
$729$		0			0
$730$	12.2223	−	46.8578i	0.452366	−	1.73428i
$731$	13.6270	+	13.6270i	0.504013	+	0.504013i
$732$		0			0
$733$	4.94464	−	4.94464i	0.182634	−	0.182634i	−0.609868	−	0.792503i	$-0.708778\pi$
$733$	4.94464	−	4.94464i	0.182634	−	0.182634i	0.792503	+	0.609868i	$0.208778\pi$
$734$	15.5929	−	9.14129i	0.575544	−	0.337411i
$735$		0			0
$736$	25.2842	+	13.4981i	0.931988	+	0.497547i
$737$			58.7671i			2.16471i
$738$		0			0
$739$	2.53239	+	2.53239i	0.0931556	+	0.0931556i	0.752149	−	0.658993i	$-0.229017\pi$
$739$	2.53239	+	2.53239i	0.0931556	+	0.0931556i	−0.658993	+	0.752149i	$0.729017\pi$
$740$	7.09340	−	12.6722i	0.260759	−	0.465841i
$741$		0			0
$742$	−1.67920	−	0.437998i	−0.0616453	−	0.0160794i
$743$		−	12.0489i		−	0.442031i	−0.975270	−	0.221016i	$-0.929063\pi$
$743$		−	12.0489i		−	0.442031i	0.975270	−	0.221016i	$-0.0709372\pi$
$744$		0			0
$745$			68.0240i			2.49221i
$746$	4.77782	−	18.3172i	0.174929	−	0.670642i
$747$		0			0
$748$	−13.0070	−	46.0832i	−0.475582	−	1.68497i
$749$	−1.21372	−	1.21372i	−0.0443482	−	0.0443482i
$750$		0			0
$751$			19.8450i			0.724155i	0.932148	+	0.362077i	$0.117932\pi$
$751$			19.8450i			0.724155i	−0.932148	+	0.362077i	$0.882068\pi$
$752$	−14.8571	−	24.2225i	−0.541784	−	0.883302i
$753$		0			0
$754$	−29.3465	−	50.0582i	−1.06874	−	1.82301i
$755$	−3.85246	+	3.85246i	−0.140206	+	0.140206i
$756$		0			0
$757$	−29.3381	−	29.3381i	−1.06631	−	1.06631i	−0.997639	−	0.0686734i	$-0.978123\pi$
$757$	−29.3381	−	29.3381i	−1.06631	−	1.06631i	−0.0686734	−	0.997639i	$-0.521877\pi$
$758$	−12.5299	−	3.26826i	−0.455106	−	0.118709i
$759$		0			0
$760$	−3.04619	+	0.0607524i	−0.110497	+	0.00220372i
$761$	−9.69377			−0.351399			−0.175700	−	0.984444i	$-0.556219\pi$
$761$	−9.69377			−0.351399			−0.175700	+	0.984444i	$0.556219\pi$
$762$		0			0
$763$	−1.82751	+	1.82751i	−0.0661605	+	0.0661605i
$764$	4.05193	−	7.23871i	0.146594	−	0.261887i
$765$		0			0
$766$	−14.5591	−	24.8344i	−0.526042	−	0.897304i
$767$	−57.6547			−2.08179
$768$		0			0
$769$	−33.3038			−1.20097			−0.600483	−	0.799638i	$-0.705025\pi$
$769$	−33.3038			−1.20097			−0.600483	+	0.799638i	$0.705025\pi$
$770$	3.49538	+	5.96230i	0.125965	+	0.214867i
$771$		0			0
$772$	−17.4991	+	31.2619i	−0.629806	+	1.12514i
$773$	−27.8428	+	27.8428i	−1.00144	+	1.00144i	−0.00143855	+	0.999999i	$0.500458\pi$
$773$	−27.8428	+	27.8428i	−1.00144	+	1.00144i	−0.999999	+	0.00143855i	$0.999542\pi$
$774$		0			0
$775$	−35.8923			−1.28929
$776$	4.70714	−	0.0938778i	0.168977	−	0.00337002i
$777$		0			0
$778$	−25.9701	−	6.77398i	−0.931074	−	0.242859i
$779$	0.158646	+	0.158646i	0.00568407	+	0.00568407i
$780$		0			0
$781$	−15.1778	+	15.1778i	−0.543105	+	0.543105i
$782$	19.3327	+	32.9770i	0.691335	+	1.17925i
$783$		0			0
$784$	14.4370	+	23.5376i	0.515609	+	0.840627i
$785$		−	19.8641i		−	0.708980i
$786$		0			0
$787$	−26.1715	−	26.1715i	−0.932913	−	0.932913i	0.0649743	−	0.997887i	$-0.479303\pi$
$787$	−26.1715	−	26.1715i	−0.932913	−	0.932913i	−0.997887	+	0.0649743i	$0.979303\pi$
$788$	−7.40108	−	26.2218i	−0.263653	−	0.934112i
$789$		0			0
$790$	19.0430	−	73.0073i	0.677521	−	2.59748i
$791$		−	2.19954i		−	0.0782067i
$792$		0			0
$793$			66.2432i			2.35236i
$794$	−1.48084	−	0.386259i	−0.0525531	−	0.0137078i
$795$		0			0
$796$	1.76177	−	3.14737i	0.0624443	−	0.111556i
$797$	11.7487	+	11.7487i	0.416160	+	0.416160i	0.883878	−	0.467718i	$-0.154924\pi$
$797$	11.7487	+	11.7487i	0.416160	+	0.416160i	−0.467718	+	0.883878i	$0.654924\pi$
$798$		0			0
$799$		−	37.8983i		−	1.34075i
$800$	36.1179	+	19.2817i	1.27696	+	0.681712i
$801$		0			0
$802$	0.742539	−	0.435311i	0.0262200	−	0.0153714i
$803$	−31.0623	+	31.0623i	−1.09616	+	1.09616i
$804$		0			0
$805$	−3.90140	−	3.90140i	−0.137506	−	0.137506i
$806$	−9.94429	+	38.1245i	−0.350273	+	1.34288i
$807$		0			0
$808$	−11.8453	+	12.3274i	−0.416717	+	0.433677i
$809$	10.1204			0.355816			0.177908	−	0.984047i	$-0.443067\pi$
$809$	10.1204			0.355816			0.177908	+	0.984047i	$0.443067\pi$
$810$		0			0
$811$	−37.8122	+	37.8122i	−1.32777	+	1.32777i	−0.420452	+	0.907315i	$0.638128\pi$
$811$	−37.8122	+	37.8122i	−1.32777	+	1.32777i	−0.907315	+	0.420452i	$0.861872\pi$
$812$	4.37598	−	1.23512i	0.153567	−	0.0433441i
$813$		0			0
$814$	−11.3649	+	6.66264i	−0.398340	+	0.233525i
$815$	−23.1611			−0.811298
$816$		0			0
$817$	−1.11236			−0.0389166
$818$	17.6446	−	10.3441i	0.616929	−	0.361673i
$819$		0			0
$820$	−1.38472	−	4.90602i	−0.0483566	−	0.171326i
$821$	−2.94612	+	2.94612i	−0.102820	+	0.102820i	−0.756646	−	0.653825i	$-0.773163\pi$
$821$	−2.94612	+	2.94612i	−0.102820	+	0.102820i	0.653825	+	0.756646i	$0.273163\pi$
$822$		0			0
$823$	1.26037			0.0439338			0.0219669	−	0.999759i	$-0.493007\pi$
$823$	1.26037			0.0439338			0.0219669	+	0.999759i	$0.493007\pi$
$824$	3.93041	−	0.0783869i	0.136922	−	0.00273074i
$825$		0			0
$826$	1.14027	−	4.37157i	0.0396751	−	0.152106i
$827$	−7.27135	−	7.27135i	−0.252850	−	0.252850i	0.569288	−	0.822138i	$-0.307219\pi$
$827$	−7.27135	−	7.27135i	−0.252850	−	0.252850i	−0.822138	+	0.569288i	$0.807219\pi$
$828$		0			0
$829$	16.4009	−	16.4009i	0.569627	−	0.569627i	−0.362397	−	0.932024i	$-0.618042\pi$
$829$	16.4009	−	16.4009i	0.569627	−	0.569627i	0.932024	+	0.362397i	$0.118042\pi$
$830$	0.377106	−	0.221077i	0.0130895	−	0.00767371i
$831$		0			0
$832$	30.4876	−	33.0219i	1.05697	−	1.14483i
$833$			36.8267i			1.27597i
$834$		0			0
$835$	21.4053	+	21.4053i	0.740761	+	0.740761i
$836$	2.41174	+	1.34999i	0.0834118	+	0.0466905i
$837$		0			0
$838$	8.60810	+	2.24532i	0.297362	+	0.0775632i
$839$			25.5162i			0.880916i	0.897773	+	0.440458i	$0.145184\pi$
$839$			25.5162i			0.880916i	−0.897773	+	0.440458i	$0.854816\pi$
$840$		0			0
$841$			24.3408i			0.839338i
$842$	−8.75448	+	33.5630i	−0.301699	+	1.15666i
$843$		0			0
$844$	50.1364	−	14.1510i	1.72576	−	0.487096i
$845$	45.9144	+	45.9144i	1.57950	+	1.57950i
$846$		0			0
$847$		−	2.84541i		−	0.0977694i
$848$	15.3339	+	3.67474i	0.526570	+	0.126191i
$849$		0			0
$850$	27.6163	+	47.1069i	0.947231	+	1.61575i
$851$	7.43656	−	7.43656i	0.254922	−	0.254922i
$852$		0			0
$853$	−9.59179	−	9.59179i	−0.328417	−	0.328417i	0.523567	−	0.851984i	$-0.324601\pi$
$853$	−9.59179	−	9.59179i	−0.328417	−	0.328417i	−0.851984	+	0.523567i	$0.824601\pi$
$854$	−5.02278	−	1.31013i	−0.171876	−	0.0448317i
$855$		0			0
$856$	11.2458	+	10.8060i	0.384375	+	0.369343i
$857$	41.6495			1.42272			0.711359	−	0.702829i	$-0.248080\pi$
$857$	41.6495			1.42272			0.711359	+	0.702829i	$0.248080\pi$
$858$		0			0
$859$	6.71181	−	6.71181i	0.229004	−	0.229004i	−0.583272	−	0.812277i	$-0.698228\pi$
$859$	6.71181	−	6.71181i	0.229004	−	0.229004i	0.812277	+	0.583272i	$0.198228\pi$
$860$	22.0541	+	12.3450i	0.752038	+	0.420960i
$861$		0			0
$862$	15.2987	+	26.0960i	0.521075	+	0.888832i
$863$	1.30072			0.0442771			0.0221386	−	0.999755i	$-0.492952\pi$
$863$	1.30072			0.0442771			0.0221386	+	0.999755i	$0.492952\pi$
$864$		0			0
$865$	17.0324			0.579120
$866$	−19.6547	−	33.5262i	−0.667892	−	1.13927i
$867$		0			0
$868$	−2.69405	−	1.50802i	−0.0914420	−	0.0511855i
$869$	−48.3970	+	48.3970i	−1.64176	+	1.64176i
$870$		0			0
$871$	−73.5656			−2.49267
$872$	16.2709	−	16.9331i	0.551001	−	0.573426i
$873$		0			0
$874$	−2.13500	−	0.556887i	−0.0722173	−	0.0188370i
$875$	−1.72303	−	1.72303i	−0.0582490	−	0.0582490i
$876$		0			0
$877$	−27.6186	+	27.6186i	−0.932614	+	0.932614i	−0.997869	−	0.0652543i	$-0.979214\pi$
$877$	−27.6186	+	27.6186i	−0.932614	+	0.932614i	0.0652543	+	0.997869i	$0.479214\pi$
$878$	14.9596	+	25.5175i	0.504861	+	0.861174i
$879$		0			0
$880$	−32.8339	−	53.5310i	−1.10683	−	1.80453i
$881$		−	14.2556i		−	0.480285i	−0.970738	−	0.240142i	$-0.922806\pi$
$881$		−	14.2556i		−	0.480285i	0.970738	−	0.240142i	$-0.0771941\pi$
$882$		0			0
$883$	36.8230	+	36.8230i	1.23919	+	1.23919i	0.960332	+	0.278860i	$0.0899564\pi$
$883$	36.8230	+	36.8230i	1.23919	+	1.23919i	0.278860	+	0.960332i	$0.410044\pi$
$884$	57.6877	−	16.2823i	1.94025	−	0.547634i
$885$		0			0
$886$	−6.07927	+	23.3067i	−0.204237	+	0.783005i
$887$			42.5168i			1.42757i	0.700363	+	0.713787i	$0.253021\pi$
$887$			42.5168i			1.42757i	−0.700363	+	0.713787i	$0.746979\pi$
$888$		0			0
$889$		−	2.12270i		−	0.0711930i
$890$	8.75975	+	2.28487i	0.293628	+	0.0765891i
$891$		0			0
$892$	−22.0767	−	12.3576i	−0.739181	−	0.413763i
$893$	1.54680	+	1.54680i	0.0517618	+	0.0517618i
$894$		0			0
$895$			81.7818i			2.73366i
$896$	1.90086	+	2.96477i	0.0635032	+	0.0990459i
$897$		0			0
$898$	−42.8494	+	25.1203i	−1.42990	+	0.838276i
$899$	25.6105	−	25.6105i	0.854157	−	0.854157i
$900$		0			0
$901$	14.8704	+	14.8704i	0.495406	+	0.495406i
$902$	−1.16715	+	4.47461i	−0.0388617	+	0.148988i
$903$		0			0
$904$	0.398508	+	19.9816i	0.0132542	+	0.664579i
$905$	−31.9970			−1.06362
$906$		0			0
$907$	8.04360	−	8.04360i	0.267083	−	0.267083i	−0.560841	−	0.827924i	$-0.689522\pi$
$907$	8.04360	−	8.04360i	0.267083	−	0.267083i	0.827924	+	0.560841i	$0.189522\pi$
$908$	−13.0461	−	46.2219i	−0.432950	−	1.53393i
$909$		0			0
$910$	−7.46371	+	4.37558i	−0.247420	+	0.145049i
$911$	49.7237			1.64742			0.823709	−	0.567013i	$-0.191901\pi$
$911$	49.7237			1.64742			0.823709	+	0.567013i	$0.191901\pi$
$912$		0			0
$913$	−0.396539			−0.0131235
$914$	−4.59369	+	2.69304i	−0.151946	+	0.0890778i
$915$		0			0
$916$	−38.7727	+	10.9436i	−1.28109	+	0.361586i
$917$	−2.64016	+	2.64016i	−0.0871859	+	0.0871859i
$918$		0			0
$919$	−6.98274			−0.230339			−0.115170	−	0.993346i	$-0.536741\pi$
$919$	−6.98274			−0.230339			−0.115170	+	0.993346i	$0.536741\pi$
$920$	36.1489	+	34.7352i	1.19179	+	1.14519i
$921$		0			0
$922$	−0.775721	+	2.97396i	−0.0255470	+	0.0979423i
$923$	−18.9998	−	18.9998i	−0.625388	−	0.625388i
$924$		0			0
$925$	10.6230	−	10.6230i	0.349281	−	0.349281i
$926$	−4.68458	+	2.74632i	−0.153945	+	0.0902498i
$927$		0			0
$928$	−39.5296	+	12.0132i	−1.29762	+	0.394353i
$929$		−	14.7177i		−	0.482873i	−0.970417	−	0.241437i	$-0.922381\pi$
$929$		−	14.7177i		−	0.482873i	0.970417	−	0.241437i	$-0.0776186\pi$
$930$		0			0
$931$	−1.50307	−	1.50307i	−0.0492610	−	0.0492610i
$932$	10.5064	−	18.7696i	0.344150	−	0.614818i
$933$		0			0
$934$	28.6530	+	7.47379i	0.937556	+	0.244550i
$935$		−	83.7543i		−	2.73906i
$936$		0			0
$937$		−	6.77583i		−	0.221357i	−0.993856	−	0.110678i	$-0.964698\pi$
$937$		−	6.77583i		−	0.221357i	0.993856	−	0.110678i	$-0.0353024\pi$
$938$	1.45495	−	5.57799i	0.0475057	−	0.182128i
$939$		0			0
$940$	−13.5011	−	47.8339i	−0.440357	−	1.56017i
$941$	22.0746	+	22.0746i	0.719612	+	0.719612i	0.968526	−	0.248914i	$-0.0800737\pi$
$941$	22.0746	+	22.0746i	0.719612	+	0.719612i	−0.248914	+	0.968526i	$0.580074\pi$
$942$		0			0
$943$		−	3.69165i		−	0.120217i
$944$	−9.56669	+	39.9199i	−0.311369	+	1.29928i
$945$		0			0
$946$	−11.5953	−	19.7788i	−0.376996	−	0.643066i
$947$	20.2366	−	20.2366i	0.657600	−	0.657600i	−0.297212	−	0.954812i	$-0.596057\pi$
$947$	20.2366	−	20.2366i	0.657600	−	0.657600i	0.954812	+	0.297212i	$0.0960567\pi$
$948$		0			0
$949$	−38.8843	−	38.8843i	−1.26224	−	1.26224i
$950$	−3.04979	−	0.795500i	−0.0989484	−	0.0258094i
$951$		0			0
$952$	0.0936577	+	4.69610i	0.00303546	+	0.152202i
$953$	7.68400			0.248909			0.124455	−	0.992225i	$-0.460282\pi$
$953$	7.68400			0.248909			0.124455	+	0.992225i	$0.460282\pi$
$954$		0			0
$955$	10.2601	−	10.2601i	0.332010	−	0.332010i
$956$	−9.51400	+	16.9966i	−0.307705	+	0.549709i
$957$		0			0
$958$	2.45534	+	4.18823i	0.0793284	+	0.135316i
$959$	−1.34290			−0.0433646
$960$		0			0
$961$	6.40737			0.206689
$962$	−8.34040	−	14.2268i	−0.268905	−	0.458689i
$963$		0			0
$964$	17.0376	−	30.4373i	0.548743	−	0.980321i
$965$	−44.3105	+	44.3105i	−1.42640	+	1.42640i
$966$		0			0
$967$	61.6223			1.98164			0.990820	−	0.135191i	$-0.0431648\pi$
$967$	61.6223			1.98164			0.990820	+	0.135191i	$0.0431648\pi$
$968$	0.515525	+	25.8490i	0.0165696	+	0.830818i
$969$		0			0
$970$	7.96838	+	2.07845i	0.255849	+	0.0667351i
$971$	−17.5795	−	17.5795i	−0.564154	−	0.564154i	0.366331	−	0.930485i	$-0.380614\pi$
$971$	−17.5795	−	17.5795i	−0.564154	−	0.564154i	−0.930485	+	0.366331i	$0.880614\pi$
$972$		0			0
$973$	4.85154	−	4.85154i	0.155533	−	0.155533i
$974$	2.07159	+	3.53365i	0.0663782	+	0.113226i
$975$		0			0
$976$	45.8665	+	10.9918i	1.46815	+	0.351838i
$977$		−	42.1856i		−	1.34964i	−0.737983	−	0.674819i	$-0.764222\pi$
$977$		−	42.1856i		−	1.34964i	0.737983	−	0.674819i	$-0.235778\pi$
$978$		0			0
$979$	−5.80689	−	5.80689i	−0.185589	−	0.185589i
$980$	13.1194	+	46.4814i	0.419082	+	1.48479i
$981$		0			0
$982$	7.61934	−	29.2110i	0.243143	−	0.932162i
$983$			24.5788i			0.783942i	0.919978	+	0.391971i	$0.128207\pi$
$983$			24.5788i			0.783942i	−0.919978	+	0.391971i	$0.871793\pi$
$984$		0			0
$985$		−	47.6569i		−	1.51848i
$986$	−53.3176	−	13.9072i	−1.69798	−	0.442897i
$987$		0			0
$988$	−1.68994	+	3.01906i	−0.0537643	+	0.0960490i
$989$	12.9422	+	12.9422i	0.411537	+	0.411537i
$990$		0			0
$991$			33.6641i			1.06937i	0.845050	+	0.534687i	$0.179571\pi$
$991$			33.6641i			1.06937i	−0.845050	+	0.534687i	$0.820429\pi$
$992$	24.7472	+	13.2114i	0.785724	+	0.419463i
$993$		0			0
$994$	1.81640	−	1.06486i	0.0576128	−	0.0337753i
$995$	4.46108	−	4.46108i	0.141426	−	0.141426i
$996$		0			0
$997$	10.3111	+	10.3111i	0.326556	+	0.326556i	0.851275	−	0.524719i	$-0.175830\pi$
$997$	10.3111	+	10.3111i	0.326556	+	0.326556i	−0.524719	+	0.851275i	$0.675830\pi$
$998$	6.87244	−	26.3476i	0.217543	−	0.834018i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.l.a.107.6	✓	32
3.2	odd	2	inner	432.2.l.a.107.11	yes	32
4.3	odd	2		1728.2.l.a.1295.2		32
12.11	even	2		1728.2.l.a.1295.15		32
16.3	odd	4	inner	432.2.l.a.323.11	yes	32
16.13	even	4		1728.2.l.a.431.15		32
48.29	odd	4		1728.2.l.a.431.2		32
48.35	even	4	inner	432.2.l.a.323.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.l.a.107.6	✓	32	1.1	even	1	trivial
432.2.l.a.107.11	yes	32	3.2	odd	2	inner
432.2.l.a.323.6	yes	32	48.35	even	4	inner
432.2.l.a.323.11	yes	32	16.3	odd	4	inner
1728.2.l.a.431.2		32	48.29	odd	4
1728.2.l.a.431.15		32	16.13	even	4
1728.2.l.a.1295.2		32	4.3	odd	2
1728.2.l.a.1295.15		32	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.715232 - 1.22002i) q^{2} +(-0.976886 + 1.74519i) q^{4} +(-2.47363 + 2.47363i) q^{5} -0.311286 q^{7} +(2.82786 - 0.0563981i) q^{8} +O(q^{10})\)	\(q+(-0.715232 - 1.22002i) q^{2} +(-0.976886 + 1.74519i) q^{4} +(-2.47363 + 2.47363i) q^{5} -0.311286 q^{7} +(2.82786 - 0.0563981i) q^{8} +(4.78709 + 1.24865i) q^{10} +(-3.17339 - 3.17339i) q^{11} +(3.97250 - 3.97250i) q^{13} +(0.222642 + 0.379775i) q^{14} +(-2.09139 - 3.40971i) q^{16} -5.33481i q^{17} +(0.217738 + 0.217738i) q^{19} +(-1.90050 - 6.73341i) q^{20} +(-1.60188 + 6.14130i) q^{22} -5.06671i q^{23} -7.23768i q^{25} +(-7.68778 - 2.00526i) q^{26} +(0.304091 - 0.543254i) q^{28} +(5.16434 + 5.16434i) q^{29} -4.95910i q^{31} +(-2.66408 + 4.99026i) q^{32} +(-6.50856 + 3.81563i) q^{34} +(0.770007 - 0.770007i) q^{35} +(1.46773 + 1.46773i) q^{37} +(0.109911 - 0.421377i) q^{38} +(-6.85558 + 7.13460i) q^{40} +0.728609 q^{41} +(-2.55436 + 2.55436i) q^{43} +(8.63822 - 2.43813i) q^{44} +(-6.18147 + 3.62387i) q^{46} +7.10397 q^{47} -6.90310 q^{49} +(-8.83010 + 5.17662i) q^{50} +(3.05209 + 10.8135i) q^{52} +(-2.78744 + 2.78744i) q^{53} +15.6996 q^{55} +(-0.880275 + 0.0175560i) q^{56} +(2.60688 - 9.99429i) q^{58} +(-7.25672 - 7.25672i) q^{59} +(-8.33771 + 8.33771i) q^{61} +(-6.05018 + 3.54690i) q^{62} +(7.99364 - 0.318972i) q^{64} +19.6530i q^{65} +(-9.25935 - 9.25935i) q^{67} +(9.31026 + 5.21150i) q^{68} +(-1.49016 - 0.388688i) q^{70} -4.78284i q^{71} -9.78836i q^{73} +(0.740889 - 2.84042i) q^{74} +(-0.592700 + 0.167289i) q^{76} +(0.987833 + 0.987833i) q^{77} -15.2509i q^{79} +(13.6077 + 3.26104i) q^{80} +(-0.521124 - 0.888916i) q^{82} +(0.0624788 - 0.0624788i) q^{83} +(13.1963 + 13.1963i) q^{85} +(4.94332 + 1.28940i) q^{86} +(-9.15289 - 8.79495i) q^{88} +1.82987 q^{89} +(-1.23659 + 1.23659i) q^{91} +(8.84238 + 4.94960i) q^{92} +(-5.08099 - 8.66697i) q^{94} -1.07721 q^{95} +1.66456 q^{97} +(4.93732 + 8.42191i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 4 q^{10} - 20 q^{16} + 8 q^{19} + 4 q^{22} - 12 q^{28} - 36 q^{34} - 12 q^{40} + 32 q^{43} - 16 q^{46} + 32 q^{49} - 60 q^{52} + 64 q^{55} - 48 q^{58} - 16 q^{61} + 48 q^{64} - 32 q^{67} - 72 q^{70} - 96 q^{76} + 40 q^{82} - 16 q^{85} + 36 q^{88} + 24 q^{91} - 36 q^{94}+O(q^{100}) \) 32 * q - 4 * q^10 - 20 * q^16 + 8 * q^19 + 4 * q^22 - 12 * q^28 - 36 * q^34 - 12 * q^40 + 32 * q^43 - 16 * q^46 + 32 * q^49 - 60 * q^52 + 64 * q^55 - 48 * q^58 - 16 * q^61 + 48 * q^64 - 32 * q^67 - 72 * q^70 - 96 * q^76 + 40 * q^82 - 16 * q^85 + 36 * q^88 + 24 * q^91 - 36 * q^94

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