LMFDB - Embedded newform 432.2.k.d.109.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(109,432)]

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([0, 3, 0]))

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

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

chi := DirichletCharacter("432.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.k (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			109.14
Character	$\chi$	$=$	432.109
Dual form			432.2.k.d.325.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.27588 + 0.610024i) q^{2} +(1.25574 + 1.55664i) q^{4} +(0.486359 - 0.486359i) q^{5} +0.822162i q^{7} +(0.652590 + 2.75211i) q^{8} +O(q^{10})$	\(q+(1.27588 + 0.610024i) q^{2} +(1.25574 + 1.55664i) q^{4} +(0.486359 - 0.486359i) q^{5} +0.822162i q^{7} +(0.652590 + 2.75211i) q^{8} +(0.917226 - 0.323845i) q^{10} +(0.518080 - 0.518080i) q^{11} +(2.51433 + 2.51433i) q^{13} +(-0.501539 + 1.04898i) q^{14} +(-0.846229 + 3.90946i) q^{16} +1.21206 q^{17} +(-0.571137 - 0.571137i) q^{19} +(1.36782 + 0.146343i) q^{20} +(0.977049 - 0.344967i) q^{22} -6.93326i q^{23} +4.52691i q^{25} +(1.67419 + 4.74179i) q^{26} +(-1.27981 + 1.03242i) q^{28} +(-2.73422 - 2.73422i) q^{29} -3.84191 q^{31} +(-3.46455 + 4.47179i) q^{32} +(1.54645 + 0.739389i) q^{34} +(0.399866 + 0.399866i) q^{35} +(3.38240 - 3.38240i) q^{37} +(-0.380295 - 1.07711i) q^{38} +(1.65591 + 1.02112i) q^{40} -11.0719i q^{41} +(-2.46985 + 2.46985i) q^{43} +(1.45704 + 0.155887i) q^{44} +(4.22946 - 8.84601i) q^{46} -10.6461 q^{47} +6.32405 q^{49} +(-2.76152 + 5.77580i) q^{50} +(-0.756549 + 7.07126i) q^{52} +(-4.98531 + 4.98531i) q^{53} -0.503946i q^{55} +(-2.26268 + 0.536535i) q^{56} +(-1.82059 - 5.15647i) q^{58} +(4.59327 - 4.59327i) q^{59} +(5.85448 + 5.85448i) q^{61} +(-4.90181 - 2.34366i) q^{62} +(-7.14825 + 3.59200i) q^{64} +2.44574 q^{65} +(-9.63213 - 9.63213i) q^{67} +(1.52204 + 1.88674i) q^{68} +(0.266253 + 0.754109i) q^{70} -6.26816i q^{71} -8.86516i q^{73} +(6.37888 - 2.25219i) q^{74} +(0.171852 - 1.60625i) q^{76} +(0.425946 + 0.425946i) q^{77} -10.3330 q^{79} +(1.48983 + 2.31297i) q^{80} +(6.75412 - 14.1264i) q^{82} +(9.54191 + 9.54191i) q^{83} +(0.589499 - 0.589499i) q^{85} +(-4.65791 + 1.64457i) q^{86} +(1.76391 + 1.08772i) q^{88} -10.8309i q^{89} +(-2.06719 + 2.06719i) q^{91} +(10.7926 - 8.70638i) q^{92} +(-13.5831 - 6.49437i) q^{94} -0.555555 q^{95} +5.88667 q^{97} +(8.06873 + 3.85782i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} + 24 q^{16} + 16 q^{19} + 32 q^{22} + 24 q^{28} - 8 q^{34} + 56 q^{40} - 16 q^{43} - 32 q^{49} - 16 q^{52} - 32 q^{61} + 24 q^{64} + 32 q^{67} - 96 q^{70} - 48 q^{76} - 32 q^{79} + 32 q^{85} - 88 q^{88} - 48 q^{91} - 96 q^{94}+O(q^{100}) $ 32 * q - 8 * q^10 + 24 * q^16 + 16 * q^19 + 32 * q^22 + 24 * q^28 - 8 * q^34 + 56 * q^40 - 16 * q^43 - 32 * q^49 - 16 * q^52 - 32 * q^61 + 24 * q^64 + 32 * q^67 - 96 * q^70 - 48 * q^76 - 32 * q^79 + 32 * q^85 - 88 * q^88 - 48 * q^91 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.27588	+	0.610024i	0.902184	+	0.431352i
$2$	1.27588	+	0.610024i	0.902184	+	0.431352i
$3$		0			0
$3$		0			0
$4$	1.25574	+	1.55664i	0.627871	+	0.778318i
$5$	0.486359	−	0.486359i	0.217506	−	0.217506i	−0.589940	−	0.807447i	$-0.700849\pi$
$5$	0.486359	−	0.486359i	0.217506	−	0.217506i	0.807447	+	0.589940i	$0.200849\pi$
$6$		0			0
$7$			0.822162i			0.310748i	0.987856	+	0.155374i	$0.0496583\pi$
$7$			0.822162i			0.310748i	−0.987856	+	0.155374i	$0.950342\pi$
$8$	0.652590	+	2.75211i	0.230725	+	0.973019i
$9$		0			0
$10$	0.917226	−	0.323845i	0.290052	−	0.102409i
$11$	0.518080	−	0.518080i	0.156207	−	0.156207i	−0.624677	−	0.780884i	$-0.714769\pi$
$11$	0.518080	−	0.518080i	0.156207	−	0.156207i	0.780884	+	0.624677i	$0.214769\pi$
$12$		0			0
$13$	2.51433	+	2.51433i	0.697351	+	0.697351i	0.963838	−	0.266488i	$-0.0858631\pi$
$13$	2.51433	+	2.51433i	0.697351	+	0.697351i	−0.266488	+	0.963838i	$0.585863\pi$
$14$	−0.501539	+	1.04898i	−0.134042	+	0.280352i
$15$		0			0
$16$	−0.846229	+	3.90946i	−0.211557	+	0.977366i
$17$	1.21206			0.293969			0.146984	−	0.989139i	$-0.453043\pi$
$17$	1.21206			0.293969			0.146984	+	0.989139i	$0.453043\pi$
$18$		0			0
$19$	−0.571137	−	0.571137i	−0.131028	−	0.131028i	0.638551	−	0.769579i	$-0.279534\pi$
$19$	−0.571137	−	0.571137i	−0.131028	−	0.131028i	−0.769579	+	0.638551i	$0.779534\pi$
$20$	1.36782	+	0.146343i	0.305855	+	0.0327232i
$21$		0			0
$22$	0.977049	−	0.344967i	0.208308	−	0.0735472i
$23$		−	6.93326i		−	1.44568i	−0.691013	−	0.722842i	$-0.742835\pi$
$23$		−	6.93326i		−	1.44568i	0.691013	−	0.722842i	$-0.257165\pi$
$24$		0			0
$25$			4.52691i			0.905382i
$26$	1.67419	+	4.74179i	0.328335	+	0.929942i
$27$		0			0
$28$	−1.27981	+	1.03242i	−0.241861	+	0.195110i
$29$	−2.73422	−	2.73422i	−0.507731	−	0.507731i	0.406098	−	0.913829i	$-0.366889\pi$
$29$	−2.73422	−	2.73422i	−0.507731	−	0.507731i	−0.913829	+	0.406098i	$0.866889\pi$
$30$		0			0
$31$	−3.84191			−0.690027			−0.345013	−	0.938598i	$-0.612126\pi$
$31$	−3.84191			−0.690027			−0.345013	+	0.938598i	$0.612126\pi$
$32$	−3.46455	+	4.47179i	−0.612452	+	0.790508i
$33$		0			0
$34$	1.54645	+	0.739389i	0.265214	+	0.126804i
$35$	0.399866	+	0.399866i	0.0675897	+	0.0675897i
$36$		0			0
$37$	3.38240	−	3.38240i	0.556063	−	0.556063i	−0.372121	−	0.928184i	$-0.621369\pi$
$37$	3.38240	−	3.38240i	0.556063	−	0.556063i	0.928184	+	0.372121i	$0.121369\pi$
$38$	−0.380295	−	1.07711i	−0.0616920	−	0.174730i
$39$		0			0
$40$	1.65591	+	1.02112i	0.261822	+	0.161454i
$41$		−	11.0719i		−	1.72914i	−0.502513	−	0.864570i	$-0.667591\pi$
$41$		−	11.0719i		−	1.72914i	0.502513	−	0.864570i	$-0.332409\pi$
$42$		0			0
$43$	−2.46985	+	2.46985i	−0.376649	+	0.376649i	−0.869892	−	0.493243i	$-0.835811\pi$
$43$	−2.46985	+	2.46985i	−0.376649	+	0.376649i	0.493243	+	0.869892i	$0.335811\pi$
$44$	1.45704	+	0.155887i	0.219656	+	0.0235009i
$45$		0			0
$46$	4.22946	−	8.84601i	0.623599	−	1.30427i
$47$	−10.6461			−1.55289			−0.776446	−	0.630184i	$-0.782980\pi$
$47$	−10.6461			−1.55289			−0.776446	+	0.630184i	$0.782980\pi$
$48$		0			0
$49$	6.32405			0.903436
$50$	−2.76152	+	5.77580i	−0.390539	+	0.816821i
$51$		0			0
$52$	−0.756549	+	7.07126i	−0.104915	+	0.980607i
$53$	−4.98531	+	4.98531i	−0.684785	+	0.684785i	−0.961074	−	0.276290i	$-0.910895\pi$
$53$	−4.98531	+	4.98531i	−0.684785	+	0.684785i	0.276290	+	0.961074i	$0.410895\pi$
$54$		0			0
$55$		−	0.503946i		−	0.0679520i
$56$	−2.26268	+	0.536535i	−0.302364	+	0.0716975i
$57$		0			0
$58$	−1.82059	−	5.15647i	−0.239056	−	0.677078i
$59$	4.59327	−	4.59327i	0.597993	−	0.597993i	−0.341785	−	0.939778i	$-0.611032\pi$
$59$	4.59327	−	4.59327i	0.597993	−	0.597993i	0.939778	+	0.341785i	$0.111032\pi$
$60$		0			0
$61$	5.85448	+	5.85448i	0.749590	+	0.749590i	0.974402	−	0.224812i	$-0.0721770\pi$
$61$	5.85448	+	5.85448i	0.749590	+	0.749590i	−0.224812	+	0.974402i	$0.572177\pi$
$62$	−4.90181	−	2.34366i	−0.622531	−	0.297645i
$63$		0			0
$64$	−7.14825	+	3.59200i	−0.893532	+	0.449000i
$65$	2.44574			0.303356
$66$		0			0
$67$	−9.63213	−	9.63213i	−1.17675	−	1.17675i	−0.980567	−	0.196185i	$-0.937145\pi$
$67$	−9.63213	−	9.63213i	−1.17675	−	1.17675i	−0.196185	−	0.980567i	$-0.562855\pi$
$68$	1.52204	+	1.88674i	0.184574	+	0.228801i
$69$		0			0
$70$	0.266253	+	0.754109i	0.0318234	+	0.0901333i
$71$		−	6.26816i		−	0.743894i	−0.928254	−	0.371947i	$-0.878690\pi$
$71$		−	6.26816i		−	0.743894i	0.928254	−	0.371947i	$-0.121310\pi$
$72$		0			0
$73$		−	8.86516i		−	1.03759i	−0.854899	−	0.518794i	$-0.826381\pi$
$73$		−	8.86516i		−	1.03759i	0.854899	−	0.518794i	$-0.173619\pi$
$74$	6.37888	−	2.25219i	0.741530	−	0.261812i
$75$		0			0
$76$	0.171852	−	1.60625i	0.0197128	−	0.184250i
$77$	0.425946	+	0.425946i	0.0485410	+	0.0485410i
$78$		0			0
$79$	−10.3330			−1.16255			−0.581275	−	0.813707i	$-0.697446\pi$
$79$	−10.3330			−1.16255			−0.581275	+	0.813707i	$0.697446\pi$
$80$	1.48983	+	2.31297i	0.166568	+	0.258598i
$81$		0			0
$82$	6.75412	−	14.1264i	0.745868	−	1.56000i
$83$	9.54191	+	9.54191i	1.04736	+	1.04736i	0.998821	+	0.0485399i	$0.0154568\pi$
$83$	9.54191	+	9.54191i	1.04736	+	1.04736i	0.0485399	+	0.998821i	$0.484543\pi$
$84$		0			0
$85$	0.589499	−	0.589499i	0.0639401	−	0.0639401i
$86$	−4.65791	+	1.64457i	−0.502275	+	0.177338i
$87$		0			0
$88$	1.76391	+	1.08772i	0.188033	+	0.115951i
$89$		−	10.8309i		−	1.14807i	−0.818831	−	0.574035i	$-0.805377\pi$
$89$		−	10.8309i		−	1.14807i	0.818831	−	0.574035i	$-0.194623\pi$
$90$		0			0
$91$	−2.06719	+	2.06719i	−0.216701	+	0.216701i
$92$	10.7926	−	8.70638i	1.12520	−	0.907703i
$93$		0			0
$94$	−13.5831	−	6.49437i	−1.40099	−	0.669843i
$95$	−0.555555			−0.0569987
$96$		0			0
$97$	5.88667			0.597701			0.298851	−	0.954300i	$-0.403397\pi$
$97$	5.88667			0.597701			0.298851	+	0.954300i	$0.403397\pi$
$98$	8.06873	+	3.85782i	0.815065	+	0.389699i
$99$		0			0
$100$	−7.04675	+	5.68463i	−0.704675	+	0.568463i
$101$	−8.58437	+	8.58437i	−0.854177	+	0.854177i	−0.990645	−	0.136467i	$-0.956425\pi$
$101$	−8.58437	+	8.58437i	−0.854177	+	0.854177i	0.136467	+	0.990645i	$0.456425\pi$
$102$		0			0
$103$		−	10.2742i		−	1.01235i	−0.862431	−	0.506175i	$-0.831059\pi$
$103$		−	10.2742i		−	1.01235i	0.862431	−	0.506175i	$-0.168941\pi$
$104$	−5.27890	+	8.56056i	−0.517639	+	0.839432i
$105$		0			0
$106$	−9.40181	+	3.31950i	−0.913185	+	0.322418i
$107$	−5.86830	+	5.86830i	−0.567310	+	0.567310i	−0.931374	−	0.364064i	$-0.881389\pi$
$107$	−5.86830	+	5.86830i	−0.567310	+	0.567310i	0.364064	+	0.931374i	$0.381389\pi$
$108$		0			0
$109$	−6.99710	−	6.99710i	−0.670201	−	0.670201i	0.287562	−	0.957762i	$-0.407155\pi$
$109$	−6.99710	−	6.99710i	−0.670201	−	0.670201i	−0.957762	+	0.287562i	$0.907155\pi$
$110$	0.307419	−	0.642974i	0.0293113	−	0.0613052i
$111$		0			0
$112$	−3.21421	−	0.695737i	−0.303715	−	0.0657410i
$113$	15.6801			1.47506			0.737528	−	0.675316i	$-0.235993\pi$
$113$	15.6801			1.47506			0.737528	+	0.675316i	$0.235993\pi$
$114$		0			0
$115$	−3.37205	−	3.37205i	−0.314446	−	0.314446i
$116$	0.822710	−	7.68964i	0.0763867	−	0.713965i
$117$		0			0
$118$	8.66247	−	3.05846i	0.797445	−	0.281554i
$119$			0.996514i			0.0913503i
$120$		0			0
$121$			10.4632i			0.951199i
$122$	3.89824	+	11.0410i	0.352930	+	0.999605i
$123$		0			0
$124$	−4.82444	−	5.98045i	−0.433247	−	0.537060i
$125$	4.63350	+	4.63350i	0.414433	+	0.414433i
$126$		0			0
$127$	−1.93870			−0.172031			−0.0860157	−	0.996294i	$-0.527414\pi$
$127$	−1.93870			−0.172031			−0.0860157	+	0.996294i	$0.527414\pi$
$128$	−11.3115	+	0.222360i	−0.999807	+	0.0196540i
$129$		0			0
$130$	3.12047	+	1.49196i	0.273683	+	0.130853i
$131$	8.51613	+	8.51613i	0.744058	+	0.744058i	0.973356	−	0.229298i	$-0.0736431\pi$
$131$	8.51613	+	8.51613i	0.744058	+	0.744058i	−0.229298	+	0.973356i	$0.573643\pi$
$132$		0			0
$133$	0.469567	−	0.469567i	0.0407166	−	0.0407166i
$134$	−6.41361	−	18.1653i	−0.554052	−	1.56924i
$135$		0			0
$136$	0.790981	+	3.33574i	0.0678261	+	0.286037i
$137$			12.7623i			1.09036i	0.838319	+	0.545179i	$0.183538\pi$
$137$			12.7623i			1.09036i	−0.838319	+	0.545179i	$0.816462\pi$
$138$		0			0
$139$	−0.256730	+	0.256730i	−0.0217755	+	0.0217755i	−0.717911	−	0.696135i	$-0.754901\pi$
$139$	−0.256730	+	0.256730i	−0.0217755	+	0.0217755i	0.696135	+	0.717911i	$0.254901\pi$
$140$	−0.120317	+	1.12457i	−0.0101687	+	0.0950438i
$141$		0			0
$142$	3.82373	−	7.99743i	0.320880	−	0.671129i
$143$	2.60525			0.217862
$144$		0			0
$145$	−2.65962			−0.220869
$146$	5.40796	−	11.3109i	0.447566	−	0.936096i
$147$		0			0
$148$	9.51258	+	1.01774i	0.781929	+	0.0836581i
$149$	−6.14532	+	6.14532i	−0.503444	+	0.503444i	−0.912507	−	0.409062i	$-0.865856\pi$
$149$	−6.14532	+	6.14532i	−0.503444	+	0.503444i	0.409062	+	0.912507i	$0.365856\pi$
$150$		0			0
$151$		−	6.33297i		−	0.515370i	−0.966229	−	0.257685i	$-0.917040\pi$
$151$		−	6.33297i		−	0.515370i	0.966229	−	0.257685i	$-0.0829597\pi$
$152$	1.19911	−	1.94455i	0.0972611	−	0.157724i
$153$		0			0
$154$	0.283619	+	0.803293i	0.0228546	+	0.0647312i
$155$	−1.86855	+	1.86855i	−0.150085	+	0.150085i
$156$		0			0
$157$	10.8797	+	10.8797i	0.868293	+	0.868293i	0.992283	−	0.123990i	$-0.0395691\pi$
$157$	10.8797	+	10.8797i	0.868293	+	0.868293i	−0.123990	+	0.992283i	$0.539569\pi$
$158$	−13.1836	−	6.30336i	−1.04883	−	0.501469i
$159$		0			0
$160$	0.489877	+	3.85991i	0.0387282	+	0.305153i
$161$	5.70027			0.449244
$162$		0			0
$163$	9.82064	+	9.82064i	0.769212	+	0.769212i	0.977968	−	0.208756i	$-0.0669413\pi$
$163$	9.82064	+	9.82064i	0.769212	+	0.769212i	−0.208756	+	0.977968i	$0.566941\pi$
$164$	17.2349	−	13.9034i	1.34582	−	1.08568i
$165$		0			0
$166$	6.35354	+	17.9951i	0.493131	+	1.39669i
$167$		−	4.75140i		−	0.367674i	−0.982957	−	0.183837i	$-0.941148\pi$
$167$		−	4.75140i		−	0.367674i	0.982957	−	0.183837i	$-0.0588519\pi$
$168$		0			0
$169$		−	0.356246i		−	0.0274035i
$170$	1.11174	−	0.392521i	0.0852664	−	0.0301050i
$171$		0			0
$172$	−6.94616	−	0.743165i	−0.529639	−	0.0566658i
$173$	1.20639	+	1.20639i	0.0917204	+	0.0917204i	0.751478	−	0.659758i	$-0.229341\pi$
$173$	1.20639	+	1.20639i	0.0917204	+	0.0917204i	−0.659758	+	0.751478i	$0.729341\pi$
$174$		0			0
$175$	−3.72186			−0.281346
$176$	1.58700	+	2.46383i	0.119625	+	0.185718i
$177$		0			0
$178$	6.60709	−	13.8189i	0.495222	−	1.03577i
$179$	3.29712	+	3.29712i	0.246438	+	0.246438i	0.819507	−	0.573069i	$-0.194247\pi$
$179$	3.29712	+	3.29712i	0.246438	+	0.246438i	−0.573069	+	0.819507i	$0.694247\pi$
$180$		0			0
$181$	2.76680	−	2.76680i	0.205655	−	0.205655i	−0.596763	−	0.802418i	$-0.703547\pi$
$181$	2.76680	−	2.76680i	0.205655	−	0.205655i	0.802418	+	0.596763i	$0.203547\pi$
$182$	−3.89853	+	1.37645i	−0.288978	+	0.102029i
$183$		0			0
$184$	19.0811	−	4.52458i	1.40668	−	0.333556i
$185$		−	3.29012i		−	0.241894i
$186$		0			0
$187$	0.627947	−	0.627947i	0.0459200	−	0.0459200i
$188$	−13.3687	−	16.5721i	−0.975015	−	1.20864i
$189$		0			0
$190$	−0.708822	−	0.338902i	−0.0514233	−	0.0245865i
$191$	−26.2589			−1.90002			−0.950012	−	0.312213i	$-0.898930\pi$
$191$	−26.2589			−1.90002			−0.950012	+	0.312213i	$0.898930\pi$
$192$		0			0
$193$	10.4752			0.754020			0.377010	−	0.926209i	$-0.376952\pi$
$193$	10.4752			0.754020			0.377010	+	0.926209i	$0.376952\pi$
$194$	7.51069	+	3.59101i	0.539236	+	0.257820i
$195$		0			0
$196$	7.94137	+	9.84424i	0.567241	+	0.703160i
$197$	−18.2314	+	18.2314i	−1.29893	+	1.29893i	−0.369837	+	0.929097i	$0.620586\pi$
$197$	−18.2314	+	18.2314i	−1.29893	+	1.29893i	−0.929097	+	0.369837i	$0.879414\pi$
$198$		0			0
$199$			23.9832i			1.70013i	0.526682	+	0.850063i	$0.323436\pi$
$199$			23.9832i			1.70013i	−0.526682	+	0.850063i	$0.676564\pi$
$200$	−12.4586	+	2.95422i	−0.880954	+	0.208895i
$201$		0			0
$202$	−16.1893	+	5.71596i	−1.13908	+	0.402173i
$203$	2.24797	−	2.24797i	0.157777	−	0.157777i
$204$		0			0
$205$	−5.38491	−	5.38491i	−0.376099	−	0.376099i
$206$	6.26753	−	13.1087i	0.436680	−	0.913326i
$207$		0			0
$208$	−11.9574	+	7.70199i	−0.829096	+	0.534037i
$209$	−0.591789			−0.0409349
$210$		0			0
$211$	−0.442902	−	0.442902i	−0.0304907	−	0.0304907i	0.691697	−	0.722188i	$-0.256863\pi$
$211$	−0.442902	−	0.442902i	−0.0304907	−	0.0304907i	−0.722188	+	0.691697i	$0.756863\pi$
$212$	−14.0206	−	1.50005i	−0.962936	−	0.103024i
$213$		0			0
$214$	−11.0670	+	3.90744i	−0.756528	+	0.267107i
$215$			2.40247i			0.163847i
$216$		0			0
$217$		−	3.15867i		−	0.214425i
$218$	−4.65906	−	13.1959i	−0.315551	−	0.893736i
$219$		0			0
$220$	0.784460	−	0.632825i	0.0528883	−	0.0426651i
$221$	3.04754	+	3.04754i	0.204999	+	0.204999i
$222$		0			0
$223$	15.1551			1.01486			0.507432	−	0.861692i	$-0.330595\pi$
$223$	15.1551			1.01486			0.507432	+	0.861692i	$0.330595\pi$
$224$	−3.67653	−	2.84843i	−0.245649	−	0.190318i
$225$		0			0
$226$	20.0059	+	9.56522i	1.33077	+	0.636269i
$227$	19.1520	+	19.1520i	1.27117	+	1.27117i	0.945477	+	0.325689i	$0.105596\pi$
$227$	19.1520	+	19.1520i	1.27117	+	1.27117i	0.325689	+	0.945477i	$0.394404\pi$
$228$		0			0
$229$	−11.9099	+	11.9099i	−0.787030	+	0.787030i	−0.981006	−	0.193976i	$-0.937862\pi$
$229$	−11.9099	+	11.9099i	−0.787030	+	0.787030i	0.193976	+	0.981006i	$0.437862\pi$
$230$	−2.24530	−	6.35937i	−0.148051	−	0.419324i
$231$		0			0
$232$	5.74055	−	9.30919i	0.376885	−	0.611178i
$233$		−	20.9077i		−	1.36971i	−0.728680	−	0.684855i	$-0.759866\pi$
$233$		−	20.9077i		−	1.36971i	0.728680	−	0.684855i	$-0.240134\pi$
$234$		0			0
$235$	−5.17782	+	5.17782i	−0.337764	+	0.337764i
$236$	12.9180	+	1.38209i	0.840891	+	0.0899664i
$237$		0			0
$238$	−0.607898	+	1.27143i	−0.0394042	+	0.0824148i
$239$	−3.78133			−0.244594			−0.122297	−	0.992494i	$-0.539026\pi$
$239$	−3.78133			−0.244594			−0.122297	+	0.992494i	$0.539026\pi$
$240$		0			0
$241$	−6.24292			−0.402142			−0.201071	−	0.979577i	$-0.564442\pi$
$241$	−6.24292			−0.402142			−0.201071	+	0.979577i	$0.564442\pi$
$242$	−6.38280	+	13.3498i	−0.410302	+	0.858156i
$243$		0			0
$244$	−1.76158	+	16.4650i	−0.112774	+	1.05406i
$245$	3.07576	−	3.07576i	0.196503	−	0.196503i
$246$		0			0
$247$		−	2.87206i		−	0.182745i
$248$	−2.50719	−	10.5734i	−0.159207	−	0.671409i
$249$		0			0
$250$	3.08524	+	8.73833i	0.195128	+	0.552661i
$251$	−8.83206	+	8.83206i	−0.557475	+	0.557475i	−0.928588	−	0.371113i	$-0.878976\pi$
$251$	−8.83206	+	8.83206i	−0.557475	+	0.557475i	0.371113	+	0.928588i	$0.378976\pi$
$252$		0			0
$253$	−3.59198	−	3.59198i	−0.225826	−	0.225826i
$254$	−2.47354	−	1.18265i	−0.155204	−	0.0742061i
$255$		0			0
$256$	−14.5678	−	6.61660i	−0.910487	−	0.413537i
$257$	0.971040			0.0605718			0.0302859	−	0.999541i	$-0.490358\pi$
$257$	0.971040			0.0605718			0.0302859	+	0.999541i	$0.490358\pi$
$258$		0			0
$259$	2.78088	+	2.78088i	0.172796	+	0.172796i
$260$	3.07121	+	3.80712i	0.190469	+	0.236108i
$261$		0			0
$262$	5.67052	+	16.0606i	0.350326	+	0.992228i
$263$		−	5.19996i		−	0.320644i	−0.987065	−	0.160322i	$-0.948747\pi$
$263$		−	5.19996i		−	0.320644i	0.987065	−	0.160322i	$-0.0512532\pi$
$264$		0			0
$265$			4.84930i			0.297890i
$266$	0.885559	−	0.312664i	0.0542971	−	0.0191707i
$267$		0			0
$268$	2.89826	−	27.0892i	0.177039	−	1.65474i
$269$	14.3057	+	14.3057i	0.872235	+	0.872235i	0.992716	−	0.120481i	$-0.0384437\pi$
$269$	14.3057	+	14.3057i	0.872235	+	0.872235i	−0.120481	+	0.992716i	$0.538444\pi$
$270$		0			0
$271$	21.0158			1.27662			0.638311	−	0.769779i	$-0.279634\pi$
$271$	21.0158			1.27662			0.638311	+	0.769779i	$0.279634\pi$
$272$	−1.02568	+	4.73852i	−0.0621912	+	0.287315i
$273$		0			0
$274$	−7.78533	+	16.2832i	−0.470329	+	0.983704i
$275$	2.34530	+	2.34530i	0.141427	+	0.141427i
$276$		0			0
$277$	6.65942	−	6.65942i	0.400126	−	0.400126i	−0.478152	−	0.878277i	$-0.658693\pi$
$277$	6.65942	−	6.65942i	0.400126	−	0.400126i	0.878277	+	0.478152i	$0.158693\pi$
$278$	−0.484168	+	0.170945i	−0.0290385	+	0.0102526i
$279$		0			0
$280$	−0.839528	+	1.36143i	−0.0501714	+	0.0813607i
$281$			19.3220i			1.15265i	0.817219	+	0.576327i	$0.195514\pi$
$281$			19.3220i			1.15265i	−0.817219	+	0.576327i	$0.804486\pi$
$282$		0			0
$283$	8.18134	−	8.18134i	0.486330	−	0.486330i	−0.420816	−	0.907146i	$-0.638256\pi$
$283$	8.18134	−	8.18134i	0.486330	−	0.486330i	0.907146	+	0.420816i	$0.138256\pi$
$284$	9.75725	−	7.87119i	0.578986	−	0.467069i
$285$		0			0
$286$	3.32399	+	1.58927i	0.196552	+	0.0939753i
$287$	9.10290			0.537327
$288$		0			0
$289$	−15.5309			−0.913582
$290$	−3.39336	−	1.62243i	−0.199265	−	0.0952725i
$291$		0			0
$292$	13.7998	−	11.1323i	0.807574	−	0.651471i
$293$	−0.777756	+	0.777756i	−0.0454370	+	0.0454370i	−0.729460	−	0.684023i	$-0.760229\pi$
$293$	−0.777756	+	0.777756i	−0.0454370	+	0.0454370i	0.684023	+	0.729460i	$0.260229\pi$
$294$		0			0
$295$		−	4.46796i		−	0.260134i
$296$	11.5161	+	7.10142i	0.669357	+	0.412762i
$297$		0			0
$298$	−11.5895	+	4.09190i	−0.671361	+	0.237037i
$299$	17.4325	−	17.4325i	1.00815	−	1.00815i
$300$		0			0
$301$	−2.03062	−	2.03062i	−0.117043	−	0.117043i
$302$	3.86327	−	8.08012i	0.222306	−	0.464958i
$303$		0			0
$304$	2.71615	−	1.74953i	0.155782	−	0.100342i
$305$	5.69476			0.326081
$306$		0			0
$307$	20.0652	+	20.0652i	1.14518	+	1.14518i	0.987488	+	0.157694i	$0.0504060\pi$
$307$	20.0652	+	20.0652i	1.14518	+	1.14518i	0.157694	+	0.987488i	$0.449594\pi$
$308$	−0.128165	+	1.19792i	−0.00730287	+	0.0682578i
$309$		0			0
$310$	−3.52390	+	1.24418i	−0.200144	+	0.0706648i
$311$		−	3.22577i		−	0.182917i	−0.995809	−	0.0914584i	$-0.970847\pi$
$311$		−	3.22577i		−	0.182917i	0.995809	−	0.0914584i	$-0.0291528\pi$
$312$		0			0
$313$		−	4.55844i		−	0.257658i	−0.991667	−	0.128829i	$-0.958878\pi$
$313$		−	4.55844i		−	0.257658i	0.991667	−	0.128829i	$-0.0411218\pi$
$314$	7.24430	+	20.5180i	0.408820	+	1.15790i
$315$		0			0
$316$	−12.9755	−	16.0847i	−0.729931	−	0.904834i
$317$	−18.6863	−	18.6863i	−1.04953	−	1.04953i	−0.998708	−	0.0508195i	$-0.983817\pi$
$317$	−18.6863	−	18.6863i	−1.04953	−	1.04953i	−0.0508195	−	0.998708i	$-0.516183\pi$
$318$		0			0
$319$	−2.83308			−0.158622
$320$	−1.72961	+	5.22362i	−0.0966883	+	0.292009i
$321$		0			0
$322$	7.27286	+	3.47730i	0.405301	+	0.193782i
$323$	−0.692255	−	0.692255i	−0.0385181	−	0.0385181i
$324$		0			0
$325$	−11.3822	+	11.3822i	−0.631369	+	0.631369i
$326$	6.53914	+	18.5208i	0.362169	+	1.02577i
$327$		0			0
$328$	30.4711	−	7.22541i	1.68249	−	0.398956i
$329$		−	8.75282i		−	0.482558i
$330$		0			0
$331$	14.2265	−	14.2265i	0.781962	−	0.781962i	−0.198200	−	0.980162i	$-0.563510\pi$
$331$	14.2265	−	14.2265i	0.781962	−	0.781962i	0.980162	+	0.198200i	$0.0635096\pi$
$332$	−2.87111	+	26.8355i	−0.157573	+	1.47279i
$333$		0			0
$334$	2.89847	−	6.06221i	0.158597	−	0.331710i
$335$	−9.36935			−0.511902
$336$		0			0
$337$	−26.3610			−1.43598			−0.717988	−	0.696055i	$-0.754937\pi$
$337$	−26.3610			−1.43598			−0.717988	+	0.696055i	$0.754937\pi$
$338$	0.217319	−	0.454527i	0.0118206	−	0.0247230i
$339$		0			0
$340$	1.65789	+	0.177377i	0.0899118	+	0.00961961i
$341$	−1.99041	+	1.99041i	−0.107787	+	0.107787i
$342$		0			0
$343$			10.9545i			0.591489i
$344$	−8.40911	−	5.18551i	−0.453389	−	0.279584i
$345$		0			0
$346$	0.803285	+	2.27514i	0.0431849	+	0.122312i
$347$	−10.7641	+	10.7641i	−0.577847	+	0.577847i	−0.934310	−	0.356462i	$-0.883983\pi$
$347$	−10.7641	+	10.7641i	−0.577847	+	0.577847i	0.356462	+	0.934310i	$0.383983\pi$
$348$		0			0
$349$	−4.96775	−	4.96775i	−0.265918	−	0.265918i	0.561535	−	0.827453i	$-0.310211\pi$
$349$	−4.96775	−	4.96775i	−0.265918	−	0.265918i	−0.827453	+	0.561535i	$0.810211\pi$
$350$	−4.74864	−	2.27042i	−0.253826	−	0.121359i
$351$		0			0
$352$	0.521828	+	4.11166i	0.0278135	+	0.219152i
$353$	11.7058			0.623038			0.311519	−	0.950240i	$-0.399162\pi$
$353$	11.7058			0.623038			0.311519	+	0.950240i	$0.399162\pi$
$354$		0			0
$355$	−3.04858	−	3.04858i	−0.161802	−	0.161802i
$356$	16.8597	−	13.6008i	0.893563	−	0.720839i
$357$		0			0
$358$	2.19541	+	6.21805i	0.116031	+	0.328634i
$359$		−	1.84284i		−	0.0972614i	−0.998817	−	0.0486307i	$-0.984514\pi$
$359$		−	1.84284i		−	0.0972614i	0.998817	−	0.0486307i	$-0.0154857\pi$
$360$		0			0
$361$		−	18.3476i		−	0.965663i
$362$	5.21792	−	1.84229i	0.274248	−	0.0968286i
$363$		0			0
$364$	−5.81372	−	0.622006i	−0.304722	−	0.0326020i
$365$	−4.31165	−	4.31165i	−0.225682	−	0.225682i
$366$		0			0
$367$	−1.81786			−0.0948917			−0.0474459	−	0.998874i	$-0.515108\pi$
$367$	−1.81786			−0.0948917			−0.0474459	+	0.998874i	$0.515108\pi$
$368$	27.1053	+	5.86712i	1.41296	+	0.305845i
$369$		0			0
$370$	2.00705	−	4.19780i	0.104342	−	0.218233i
$371$	−4.09873	−	4.09873i	−0.212796	−	0.212796i
$372$		0			0
$373$	11.9430	−	11.9430i	0.618386	−	0.618386i	−0.326731	−	0.945117i	$-0.605947\pi$
$373$	11.9430	−	11.9430i	0.618386	−	0.618386i	0.945117	+	0.326731i	$0.105947\pi$
$374$	1.18425	−	0.418122i	0.0612360	−	0.0216206i
$375$		0			0
$376$	−6.94753	−	29.2992i	−0.358292	−	1.51099i
$377$		−	13.7495i		−	0.708133i
$378$		0			0
$379$	−0.259378	+	0.259378i	−0.0133234	+	0.0133234i	−0.713737	−	0.700414i	$-0.752999\pi$
$379$	−0.259378	+	0.259378i	−0.0133234	+	0.0133234i	0.700414	+	0.713737i	$0.252999\pi$
$380$	−0.697633	−	0.864797i	−0.0357878	−	0.0443631i
$381$		0			0
$382$	−33.5032	−	16.0185i	−1.71417	−	0.819580i
$383$	13.4520			0.687365			0.343683	−	0.939086i	$-0.388326\pi$
$383$	13.4520			0.687365			0.343683	+	0.939086i	$0.388326\pi$
$384$		0			0
$385$	0.414325			0.0211160
$386$	13.3651	+	6.39011i	0.680264	+	0.325248i
$387$		0			0
$388$	7.39214	+	9.16340i	0.375279	+	0.465201i
$389$	24.0164	−	24.0164i	1.21768	−	1.21768i	0.249237	−	0.968443i	$-0.419820\pi$
$389$	24.0164	−	24.0164i	1.21768	−	1.21768i	0.968443	−	0.249237i	$-0.0801797\pi$
$390$		0			0
$391$		−	8.40356i		−	0.424986i
$392$	4.12701	+	17.4045i	0.208446	+	0.879060i
$393$		0			0
$394$	−34.3827	+	12.1395i	−1.73217	+	0.611579i
$395$	−5.02553	+	5.02553i	−0.252862	+	0.252862i
$396$		0			0
$397$	−21.2299	−	21.2299i	−1.06550	−	1.06550i	−0.997699	−	0.0678000i	$-0.978402\pi$
$397$	−21.2299	−	21.2299i	−1.06550	−	1.06550i	−0.0678000	−	0.997699i	$-0.521598\pi$
$398$	−14.6303	+	30.5997i	−0.733353	+	1.53382i
$399$		0			0
$400$	−17.6978	−	3.83080i	−0.884889	−	0.191540i
$401$	−20.5557			−1.02650			−0.513250	−	0.858239i	$-0.671559\pi$
$401$	−20.5557			−1.02650			−0.513250	+	0.858239i	$0.671559\pi$
$402$		0			0
$403$	−9.65984	−	9.65984i	−0.481191	−	0.481191i
$404$	−24.1425	−	2.58299i	−1.20113	−	0.128509i
$405$		0			0
$406$	4.23946	−	1.49682i	0.210401	−	0.0742861i
$407$		−	3.50471i		−	0.173722i
$408$		0			0
$409$			11.3679i			0.562106i	0.959692	+	0.281053i	$0.0906836\pi$
$409$			11.3679i			0.562106i	−0.959692	+	0.281053i	$0.909316\pi$
$410$	−3.58558	−	10.1554i	−0.177079	−	0.501541i
$411$		0			0
$412$	15.9932	−	12.9018i	0.787931	−	0.635625i
$413$	3.77641	+	3.77641i	0.185825	+	0.185825i
$414$		0			0
$415$	9.28159			0.455615
$416$	−19.9546	+	2.53252i	−0.978355	+	0.124167i
$417$		0			0
$418$	−0.755052	−	0.361006i	−0.0369308	−	0.0176574i
$419$	−24.7167	−	24.7167i	−1.20749	−	1.20749i	−0.971838	−	0.235651i	$-0.924278\pi$
$419$	−24.7167	−	24.7167i	−1.20749	−	1.20749i	−0.235651	−	0.971838i	$-0.575722\pi$
$420$		0			0
$421$	−18.1917	+	18.1917i	−0.886611	+	0.886611i	−0.994196	−	0.107585i	$-0.965688\pi$
$421$	−18.1917	+	18.1917i	−0.886611	+	0.886611i	0.107585	+	0.994196i	$0.465688\pi$
$422$	−0.294909	−	0.835272i	−0.0143560	−	0.0406604i
$423$		0			0
$424$	−16.9735	−	10.4668i	−0.824306	−	0.508311i
$425$			5.48691i			0.266154i
$426$		0			0
$427$	−4.81333	+	4.81333i	−0.232934	+	0.232934i
$428$	−16.5039	−	1.76574i	−0.797744	−	0.0853502i
$429$		0			0
$430$	−1.46556	+	3.06526i	−0.0706758	+	0.147820i
$431$	23.0101			1.10836			0.554178	−	0.832398i	$-0.313033\pi$
$431$	23.0101			1.10836			0.554178	+	0.832398i	$0.313033\pi$
$432$		0			0
$433$	−26.4533			−1.27126			−0.635632	−	0.771992i	$-0.719260\pi$
$433$	−26.4533			−1.27126			−0.635632	+	0.771992i	$0.719260\pi$
$434$	1.92687	−	4.03009i	0.0924925	−	0.193450i
$435$		0			0
$436$	2.10539	−	19.6785i	0.100830	−	0.942428i
$437$	−3.95984	+	3.95984i	−0.189425	+	0.189425i
$438$		0			0
$439$			4.35311i			0.207762i	0.994590	+	0.103881i	$0.0331262\pi$
$439$			4.35311i			0.207762i	−0.994590	+	0.103881i	$0.966874\pi$
$440$	1.38692	−	0.328870i	0.0661186	−	0.0156783i
$441$		0			0
$442$	2.02922	+	5.74736i	0.0965202	+	0.273374i
$443$	25.9162	−	25.9162i	1.23132	−	1.23132i	0.267857	−	0.963459i	$-0.413684\pi$
$443$	25.9162	−	25.9162i	1.23132	−	1.23132i	0.963459	−	0.267857i	$-0.0863156\pi$
$444$		0			0
$445$	−5.26769	−	5.26769i	−0.249712	−	0.249712i
$446$	19.3361	+	9.24500i	0.915593	+	0.437763i
$447$		0			0
$448$	−2.95321	−	5.87702i	−0.139526	−	0.277663i
$449$	−20.0989			−0.948526			−0.474263	−	0.880383i	$-0.657285\pi$
$449$	−20.0989			−0.948526			−0.474263	+	0.880383i	$0.657285\pi$
$450$		0			0
$451$	−5.73613	−	5.73613i	−0.270104	−	0.270104i
$452$	19.6901	+	24.4082i	0.926145	+	1.14806i
$453$		0			0
$454$	12.7525	+	36.1189i	0.598505	+	1.69515i
$455$			2.01079i			0.0942675i
$456$		0			0
$457$		−	22.3334i		−	1.04471i	−0.852727	−	0.522356i	$-0.825053\pi$
$457$		−	22.3334i		−	1.04471i	0.852727	−	0.522356i	$-0.174947\pi$
$458$	−22.4610	+	7.93030i	−1.04953	+	0.370559i
$459$		0			0
$460$	1.01463	−	9.48348i	0.0473075	−	0.442170i
$461$	−23.2354	−	23.2354i	−1.08218	−	1.08218i	−0.996306	−	0.0858743i	$-0.972632\pi$
$461$	−23.2354	−	23.2354i	−1.08218	−	1.08218i	−0.0858743	−	0.996306i	$-0.527368\pi$
$462$		0			0
$463$	17.1493			0.796998			0.398499	−	0.917169i	$-0.369531\pi$
$463$	17.1493			0.796998			0.398499	+	0.917169i	$0.369531\pi$
$464$	13.0031	−	8.37554i	0.603653	−	0.388825i
$465$		0			0
$466$	12.7542	−	26.6757i	0.590827	−	1.23573i
$467$	−26.0978	−	26.0978i	−1.20766	−	1.20766i	−0.971782	−	0.235882i	$-0.924202\pi$
$467$	−26.0978	−	26.0978i	−1.20766	−	1.20766i	−0.235882	−	0.971782i	$-0.575798\pi$
$468$		0			0
$469$	7.91918	−	7.91918i	0.365674	−	0.365674i
$470$	−9.76488	+	3.44768i	−0.450420	+	0.159030i
$471$		0			0
$472$	15.6387	+	9.64368i	0.719831	+	0.443886i
$473$			2.55916i			0.117670i
$474$		0			0
$475$	2.58549	−	2.58549i	0.118630	−	0.118630i
$476$	−1.55121	+	1.25136i	−0.0710996	+	0.0573562i
$477$		0			0
$478$	−4.82452	−	2.30670i	−0.220668	−	0.105506i
$479$	−19.8302			−0.906063			−0.453032	−	0.891494i	$-0.649658\pi$
$479$	−19.8302			−0.906063			−0.453032	+	0.891494i	$0.649658\pi$
$480$		0			0
$481$	17.0090			0.775542
$482$	−7.96522	−	3.80833i	−0.362806	−	0.173465i
$483$		0			0
$484$	−16.2874	+	13.1391i	−0.740335	+	0.597230i
$485$	2.86304	−	2.86304i	0.130004	−	0.130004i
$486$		0			0
$487$			0.473158i			0.0214408i	0.999943	+	0.0107204i	$0.00341248\pi$
$487$			0.473158i			0.0214408i	−0.999943	+	0.0107204i	$0.996588\pi$
$488$	−12.2916	+	19.9328i	−0.556415	+	0.902314i
$489$		0			0
$490$	5.80058	−	2.04801i	0.262044	−	0.0925198i
$491$	−16.2005	+	16.2005i	−0.731120	+	0.731120i	−0.970842	−	0.239721i	$-0.922944\pi$
$491$	−16.2005	+	16.2005i	−0.731120	+	0.731120i	0.239721	+	0.970842i	$0.422944\pi$
$492$		0			0
$493$	−3.31405	−	3.31405i	−0.149257	−	0.149257i
$494$	1.75202	−	3.66440i	0.0788273	−	0.164869i
$495$		0			0
$496$	3.25113	−	15.0198i	0.145980	−	0.674408i
$497$	5.15345			0.231164
$498$		0			0
$499$	8.50481	+	8.50481i	0.380728	+	0.380728i	0.871364	−	0.490637i	$-0.163236\pi$
$499$	8.50481	+	8.50481i	0.380728	+	0.380728i	−0.490637	+	0.871364i	$0.663236\pi$
$500$	−1.39419	+	13.0311i	−0.0623502	+	0.582770i
$501$		0			0
$502$	−16.6564	+	5.88088i	−0.743413	+	0.262477i
$503$		−	15.6462i		−	0.697630i	−0.937192	−	0.348815i	$-0.886584\pi$
$503$		−	15.6462i		−	0.697630i	0.937192	−	0.348815i	$-0.113416\pi$
$504$		0			0
$505$			8.35017i			0.371578i
$506$	−2.39174	−	6.77414i	−0.106326	−	0.301147i
$507$		0			0
$508$	−2.43450	−	3.01784i	−0.108013	−	0.133895i
$509$	6.98349	+	6.98349i	0.309538	+	0.309538i	0.844730	−	0.535192i	$-0.179761\pi$
$509$	6.98349	+	6.98349i	0.309538	+	0.309538i	−0.535192	+	0.844730i	$0.679761\pi$
$510$		0			0
$511$	7.28860			0.322429
$512$	−14.5505	−	17.3287i	−0.643046	−	0.765827i
$513$		0			0
$514$	1.23893	+	0.592358i	0.0546469	+	0.0261278i
$515$	−4.99697	−	4.99697i	−0.220193	−	0.220193i
$516$		0			0
$517$	−5.51553	+	5.51553i	−0.242573	+	0.242573i
$518$	1.85167	+	5.24447i	0.0813576	+	0.230429i
$519$		0			0
$520$	1.59606	+	6.73095i	0.0699920	+	0.295172i
$521$		−	18.1179i		−	0.793757i	−0.917871	−	0.396879i	$-0.870093\pi$
$521$		−	18.1179i		−	0.793757i	0.917871	−	0.396879i	$-0.129907\pi$
$522$		0			0
$523$	13.5805	−	13.5805i	0.593833	−	0.593833i	−0.344832	−	0.938665i	$-0.612064\pi$
$523$	13.5805	−	13.5805i	0.593833	−	0.593833i	0.938665	+	0.344832i	$0.112064\pi$
$524$	−2.56246	+	23.9506i	−0.111941	+	1.04629i
$525$		0			0
$526$	3.17210	−	6.63453i	0.138310	−	0.289279i
$527$	−4.65664			−0.202846
$528$		0			0
$529$	−25.0701			−1.09000
$530$	−2.95819	+	6.18712i	−0.128495	+	0.268751i
$531$		0			0
$532$	1.32060	+	0.141290i	0.0572553	+	0.00612571i
$533$	27.8384	−	27.8384i	1.20582	−	1.20582i
$534$		0			0
$535$			5.70820i			0.246787i
$536$	20.2229	−	32.7945i	0.873495	−	1.41651i
$537$		0			0
$538$	9.52555	+	26.9792i	0.410676	+	1.16316i
$539$	3.27636	−	3.27636i	0.141123	−	0.141123i
$540$		0			0
$541$	6.34677	+	6.34677i	0.272869	+	0.272869i	0.830254	−	0.557385i	$-0.188195\pi$
$541$	6.34677	+	6.34677i	0.272869	+	0.272869i	−0.557385	+	0.830254i	$0.688195\pi$
$542$	26.8137	+	12.8202i	1.15175	+	0.550673i
$543$		0			0
$544$	−4.19926	+	5.42010i	−0.180042	+	0.232385i
$545$	−6.80620			−0.291546
$546$		0			0
$547$	22.8795	+	22.8795i	0.978257	+	0.978257i	0.999769	−	0.0215112i	$-0.00684777\pi$
$547$	22.8795	+	22.8795i	0.978257	+	0.978257i	−0.0215112	+	0.999769i	$0.506848\pi$
$548$	−19.8663	+	16.0262i	−0.848646	+	0.684604i
$549$		0			0
$550$	1.56163	+	4.42301i	0.0665883	+	0.188598i
$551$			3.12322i			0.133054i
$552$		0			0
$553$		−	8.49538i		−	0.361260i
$554$	12.5590	−	4.43421i	0.533582	−	0.188392i
$555$		0			0
$556$	−0.722021	−	0.0772486i	−0.0306205	−	0.00327607i
$557$	−1.78039	−	1.78039i	−0.0754376	−	0.0754376i	0.668381	−	0.743819i	$-0.266987\pi$
$557$	−1.78039	−	1.78039i	−0.0754376	−	0.0754376i	−0.743819	+	0.668381i	$0.766987\pi$
$558$		0			0
$559$	−12.4201			−0.525313
$560$	−1.90164	+	1.22488i	−0.0803589	+	0.0517608i
$561$		0			0
$562$	−11.7869	+	24.6526i	−0.497200	+	1.03991i
$563$	11.3814	+	11.3814i	0.479669	+	0.479669i	0.905026	−	0.425357i	$-0.139851\pi$
$563$	11.3814	+	11.3814i	0.479669	+	0.479669i	−0.425357	+	0.905026i	$0.639851\pi$
$564$		0			0
$565$	7.62614	−	7.62614i	0.320834	−	0.320834i
$566$	15.4292	−	5.44759i	0.648539	−	0.228979i
$567$		0			0
$568$	17.2507	−	4.09054i	0.723823	−	0.171635i
$569$			13.8605i			0.581061i	0.956866	+	0.290531i	$0.0938318\pi$
$569$			13.8605i			0.581061i	−0.956866	+	0.290531i	$0.906168\pi$
$570$		0			0
$571$	8.30455	−	8.30455i	0.347535	−	0.347535i	−0.511656	−	0.859191i	$-0.670968\pi$
$571$	8.30455	−	8.30455i	0.347535	−	0.347535i	0.859191	+	0.511656i	$0.170968\pi$
$572$	3.27152	+	4.05543i	0.136789	+	0.169566i
$573$		0			0
$574$	11.6142	+	5.55299i	0.484768	+	0.231777i
$575$	31.3863			1.30890
$576$		0			0
$577$	41.6898			1.73557			0.867784	−	0.496942i	$-0.165544\pi$
$577$	41.6898			1.73557			0.867784	+	0.496942i	$0.165544\pi$
$578$	−19.8156	−	9.47422i	−0.824219	−	0.394076i
$579$		0			0
$580$	−3.33979	−	4.14006i	−0.138677	−	0.171907i
$581$	−7.84500	+	7.84500i	−0.325466	+	0.325466i
$582$		0			0
$583$			5.16558i			0.213936i
$584$	24.3979	−	5.78532i	1.00959	−	0.239398i
$585$		0			0
$586$	−1.46677	+	0.517873i	−0.0605918	+	0.0213932i
$587$	8.73339	−	8.73339i	0.360465	−	0.360465i	−0.503519	−	0.863984i	$-0.667962\pi$
$587$	8.73339	−	8.73339i	0.360465	−	0.360465i	0.863984	+	0.503519i	$0.167962\pi$
$588$		0			0
$589$	2.19425	+	2.19425i	0.0904127	+	0.0904127i
$590$	2.72556	−	5.70058i	0.112210	−	0.234689i
$591$		0			0
$592$	10.3611	+	16.0856i	0.425838	+	0.661116i
$593$	7.63224			0.313418			0.156709	−	0.987645i	$-0.449911\pi$
$593$	7.63224			0.313418			0.156709	+	0.987645i	$0.449911\pi$
$594$		0			0
$595$	0.484664	+	0.484664i	0.0198693	+	0.0198693i
$596$	−17.2830	−	1.84909i	−0.707938	−	0.0757418i
$597$		0			0
$598$	32.8761	−	11.6076i	1.34440	−	0.474669i
$599$			32.4033i			1.32396i	0.749521	+	0.661981i	$0.230284\pi$
$599$			32.4033i			1.32396i	−0.749521	+	0.661981i	$0.769716\pi$
$600$		0			0
$601$			38.1611i			1.55662i	0.627878	+	0.778311i	$0.283924\pi$
$601$			38.1611i			1.55662i	−0.627878	+	0.778311i	$0.716076\pi$
$602$	−1.35210	−	3.82956i	−0.0551075	−	0.156081i
$603$		0			0
$604$	9.85813	−	7.95258i	0.401122	−	0.323586i
$605$	5.08886	+	5.08886i	0.206892	+	0.206892i
$606$		0			0
$607$	−15.7623			−0.639771			−0.319885	−	0.947456i	$-0.603644\pi$
$607$	−15.7623			−0.639771			−0.319885	+	0.947456i	$0.603644\pi$
$608$	4.53274	−	0.575268i	0.183827	−	0.0233302i
$609$		0			0
$610$	7.26583	+	3.47394i	0.294185	+	0.140656i
$611$	−26.7678	−	26.7678i	−1.08291	−	1.08291i
$612$		0			0
$613$	−1.59513	+	1.59513i	−0.0644266	+	0.0644266i	−0.738586	−	0.674159i	$-0.764506\pi$
$613$	−1.59513	+	1.59513i	−0.0644266	+	0.0644266i	0.674159	+	0.738586i	$0.264506\pi$
$614$	13.3605	+	37.8411i	0.539188	+	1.52714i
$615$		0			0
$616$	−0.894283	+	1.45022i	−0.0360317	+	0.0584310i
$617$			41.0030i			1.65072i	0.564609	+	0.825359i	$0.309027\pi$
$617$			41.0030i			1.65072i	−0.564609	+	0.825359i	$0.690973\pi$
$618$		0			0
$619$	−29.6437	+	29.6437i	−1.19148	+	1.19148i	−0.214827	+	0.976652i	$0.568919\pi$
$619$	−29.6437	+	29.6437i	−1.19148	+	1.19148i	−0.976652	+	0.214827i	$0.931081\pi$
$620$	−5.25505	−	0.562235i	−0.211048	−	0.0225799i
$621$		0			0
$622$	1.96780	−	4.11570i	0.0789016	−	0.165025i
$623$	8.90473			0.356761
$624$		0			0
$625$	−18.1275			−0.725099
$626$	2.78076	−	5.81602i	0.111141	−	0.232455i
$627$		0			0
$628$	−3.27364	+	30.5978i	−0.130632	+	1.22098i
$629$	4.09969	−	4.09969i	0.163465	−	0.163465i
$630$		0			0
$631$		−	28.7106i		−	1.14295i	−0.820620	−	0.571475i	$-0.806372\pi$
$631$		−	28.7106i		−	1.14295i	0.820620	−	0.571475i	$-0.193628\pi$
$632$	−6.74320	−	28.4375i	−0.268230	−	1.13118i
$633$		0			0
$634$	−12.4424	−	35.2406i	−0.494150	−	1.39958i
$635$	−0.942902	+	0.942902i	−0.0374179	+	0.0374179i
$636$		0			0
$637$	15.9008	+	15.9008i	0.630012	+	0.630012i
$638$	−3.61468	−	1.72825i	−0.143106	−	0.0684221i
$639$		0			0
$640$	−5.39331	+	5.60961i	−0.213189	+	0.221739i
$641$	−24.5469			−0.969546			−0.484773	−	0.874640i	$-0.661098\pi$
$641$	−24.5469			−0.969546			−0.484773	+	0.874640i	$0.661098\pi$
$642$		0			0
$643$	7.33561	+	7.33561i	0.289288	+	0.289288i	0.836799	−	0.547511i	$-0.184424\pi$
$643$	7.33561	+	7.33561i	0.289288	+	0.289288i	−0.547511	+	0.836799i	$0.684424\pi$
$644$	7.15806	+	8.87324i	0.282067	+	0.349655i
$645$		0			0
$646$	−0.460942	−	1.30553i	−0.0181355	−	0.0513653i
$647$			23.3150i			0.916607i	0.888796	+	0.458303i	$0.151543\pi$
$647$			23.3150i			0.916607i	−0.888796	+	0.458303i	$0.848457\pi$
$648$		0			0
$649$		−	4.75936i		−	0.186821i
$650$	−21.4657	+	7.57888i	−0.841953	+	0.297268i
$651$		0			0
$652$	−2.95498	+	27.6193i	−0.115726	+	1.08166i
$653$	17.3370	+	17.3370i	0.678450	+	0.678450i	0.959649	−	0.281199i	$-0.0907321\pi$
$653$	17.3370	+	17.3370i	0.678450	+	0.678450i	−0.281199	+	0.959649i	$0.590732\pi$
$654$		0			0
$655$	8.28379			0.323675
$656$	43.2852	+	9.36935i	1.69000	+	0.365812i
$657$		0			0
$658$	5.33943	−	11.1675i	0.208153	−	0.435356i
$659$	11.2972	+	11.2972i	0.440078	+	0.440078i	0.892038	−	0.451960i	$-0.149275\pi$
$659$	11.2972	+	11.2972i	0.440078	+	0.440078i	−0.451960	+	0.892038i	$0.649275\pi$
$660$		0			0
$661$	0.587609	−	0.587609i	0.0228554	−	0.0228554i	−0.695587	−	0.718442i	$-0.744856\pi$
$661$	0.587609	−	0.587609i	0.0228554	−	0.0228554i	0.718442	+	0.695587i	$0.244856\pi$
$662$	26.8299	−	9.47283i	1.04277	−	0.368172i
$663$		0			0
$664$	−20.0335	+	32.4874i	−0.777449	+	1.26076i
$665$		−	0.456756i		−	0.0177123i
$666$		0			0
$667$	−18.9570	+	18.9570i	−0.734019	+	0.734019i
$668$	7.39619	−	5.96653i	0.286167	−	0.230852i
$669$		0			0
$670$	−11.9542	−	5.71553i	−0.461830	−	0.220810i
$671$	6.06618			0.234182
$672$		0			0
$673$	40.7850			1.57215			0.786074	−	0.618133i	$-0.212111\pi$
$673$	40.7850			1.57215			0.786074	+	0.618133i	$0.212111\pi$
$674$	−33.6335	−	16.0809i	−1.29551	−	0.619411i
$675$		0			0
$676$	0.554545	−	0.447352i	0.0213286	−	0.0172059i
$677$	21.2048	−	21.2048i	0.814967	−	0.814967i	−0.170407	−	0.985374i	$-0.554508\pi$
$677$	21.2048	−	21.2048i	0.814967	−	0.814967i	0.985374	+	0.170407i	$0.0545083\pi$
$678$		0			0
$679$			4.83980i			0.185735i
$680$	2.00707	+	1.23767i	0.0769675	+	0.0474623i
$681$		0			0
$682$	−3.75373	+	1.32533i	−0.143738	+	0.0507495i
$683$	−6.34238	+	6.34238i	−0.242685	+	0.242685i	−0.817960	−	0.575275i	$-0.804895\pi$
$683$	−6.34238	+	6.34238i	−0.242685	+	0.242685i	0.575275	+	0.817960i	$0.304895\pi$
$684$		0			0
$685$	6.20707	+	6.20707i	0.237160	+	0.237160i
$686$	−6.68253	+	13.9767i	−0.255140	+	0.533632i
$687$		0			0
$688$	−7.56574	−	11.7459i	−0.288441	−	0.447807i
$689$	−25.0695			−0.955070
$690$		0			0
$691$	−13.6284	−	13.6284i	−0.518448	−	0.518448i	0.398654	−	0.917101i	$-0.369478\pi$
$691$	−13.6284	−	13.6284i	−0.518448	−	0.518448i	−0.917101	+	0.398654i	$0.869478\pi$
$692$	−0.362997	+	3.39283i	−0.0137991	+	0.128976i
$693$		0			0
$694$	−20.3001	+	7.16734i	−0.770580	+	0.272069i
$695$			0.249726i			0.00947264i
$696$		0			0
$697$		−	13.4199i		−	0.508313i
$698$	−3.30781	−	9.36871i	−0.125202	−	0.354611i
$699$		0			0
$700$	−4.67369	−	5.79357i	−0.176649	−	0.218976i
$701$	11.5128	+	11.5128i	0.434833	+	0.434833i	0.890269	−	0.455436i	$-0.150516\pi$
$701$	11.5128	+	11.5128i	0.434833	+	0.434833i	−0.455436	+	0.890269i	$0.650516\pi$
$702$		0			0
$703$	−3.86362			−0.145719
$704$	−1.84242	+	5.56431i	−0.0694389	+	0.209713i
$705$		0			0
$706$	14.9352	+	7.14083i	0.562095	+	0.268749i
$707$	−7.05775	−	7.05775i	−0.265434	−	0.265434i
$708$		0			0
$709$	−17.2265	+	17.2265i	−0.646953	+	0.646953i	−0.952255	−	0.305302i	$-0.901242\pi$
$709$	−17.2265	+	17.2265i	−0.646953	+	0.646953i	0.305302	+	0.952255i	$0.401242\pi$
$710$	−2.02991	−	5.74932i	−0.0761813	−	0.215768i
$711$		0			0
$712$	29.8078	−	7.06812i	1.11709	−	0.264889i
$713$			26.6369i			0.997561i
$714$		0			0
$715$	1.26709	−	1.26709i	0.0473864	−	0.0473864i
$716$	−0.992085	+	9.27274i	−0.0370760	+	0.346539i
$717$		0			0
$718$	1.12418	−	2.35124i	0.0419539	−	0.0877476i
$719$	17.3169			0.645813			0.322907	−	0.946431i	$-0.395340\pi$
$719$	17.3169			0.645813			0.322907	+	0.946431i	$0.395340\pi$
$720$		0			0
$721$	8.44709			0.314586
$722$	11.1925	−	23.4093i	0.416541	−	0.871206i
$723$		0			0
$724$	7.78128	+	0.832514i	0.289189	+	0.0309402i
$725$	12.3775	−	12.3775i	0.459691	−	0.459691i
$726$		0			0
$727$			41.3494i			1.53356i	0.641907	+	0.766782i	$0.278143\pi$
$727$			41.3494i			1.53356i	−0.641907	+	0.766782i	$0.721857\pi$
$728$	−7.03817	−	4.34012i	−0.260852	−	0.160855i
$729$		0			0
$730$	−2.87094	−	8.13136i	−0.106258	−	0.300955i
$731$	−2.99362	+	2.99362i	−0.110723	+	0.110723i
$732$		0			0
$733$	10.7557	+	10.7557i	0.397270	+	0.397270i	0.877269	−	0.479999i	$-0.159363\pi$
$733$	10.7557	+	10.7557i	0.397270	+	0.397270i	−0.479999	+	0.877269i	$0.659363\pi$
$734$	−2.31938	−	1.10894i	−0.0856098	−	0.0409318i
$735$		0			0
$736$	31.0041	+	24.0207i	1.14282	+	0.885413i
$737$	−9.98043			−0.367634
$738$		0			0
$739$	−26.7357	−	26.7357i	−0.983488	−	0.983488i	0.0163782	−	0.999866i	$-0.494786\pi$
$739$	−26.7357	−	26.7357i	−0.983488	−	0.983488i	−0.999866	+	0.0163782i	$0.994786\pi$
$740$	5.12152	−	4.13154i	0.188271	−	0.151878i
$741$		0			0
$742$	−2.72917	−	7.72982i	−0.100191	−	0.283771i
$743$			42.2662i			1.55060i	0.631595	+	0.775298i	$0.282400\pi$
$743$			42.2662i			1.55060i	−0.631595	+	0.775298i	$0.717600\pi$
$744$		0			0
$745$			5.97766i			0.219005i
$746$	22.5234	−	7.95234i	0.824640	−	0.291156i
$747$		0			0
$748$	1.76602	+	0.188946i	0.0645722	+	0.00690854i
$749$	−4.82469	−	4.82469i	−0.176290	−	0.176290i
$750$		0			0
$751$	−6.73000			−0.245581			−0.122791	−	0.992433i	$-0.539184\pi$
$751$	−6.73000			−0.245581			−0.122791	+	0.992433i	$0.539184\pi$
$752$	9.00903	−	41.6205i	0.328525	−	1.51774i
$753$		0			0
$754$	8.38750	−	17.5427i	0.305455	−	0.638866i
$755$	−3.08010	−	3.08010i	−0.112096	−	0.112096i
$756$		0			0
$757$	12.2938	−	12.2938i	0.446827	−	0.446827i	−0.447471	−	0.894298i	$-0.647675\pi$
$757$	12.2938	−	12.2938i	0.446827	−	0.446827i	0.894298	+	0.447471i	$0.147675\pi$
$758$	−0.489163	+	0.172709i	−0.0177672	+	0.00627306i
$759$		0			0
$760$	−0.362550	−	1.52895i	−0.0131511	−	0.0554609i
$761$			22.8887i			0.829716i	0.909886	+	0.414858i	$0.136169\pi$
$761$			22.8887i			0.829716i	−0.909886	+	0.414858i	$0.863831\pi$
$762$		0			0
$763$	5.75275	−	5.75275i	0.208264	−	0.208264i
$764$	−32.9743	−	40.8755i	−1.19297	−	1.47882i
$765$		0			0
$766$	17.1632	+	8.20605i	0.620130	+	0.296497i
$767$	23.0980			0.834022
$768$		0			0
$769$	15.7818			0.569107			0.284554	−	0.958660i	$-0.408155\pi$
$769$	15.7818			0.569107			0.284554	+	0.958660i	$0.408155\pi$
$770$	0.528629	+	0.252748i	0.0190505	+	0.00910842i
$771$		0			0
$772$	13.1541	+	16.3060i	0.473427	+	0.586867i
$773$	15.8909	−	15.8909i	0.571557	−	0.571557i	−0.361006	−	0.932563i	$-0.617567\pi$
$773$	15.8909	−	15.8909i	0.571557	−	0.571557i	0.932563	+	0.361006i	$0.117567\pi$
$774$		0			0
$775$		−	17.3920i		−	0.624738i
$776$	3.84158	+	16.2008i	0.137905	+	0.581574i
$777$		0			0
$778$	45.2926	−	15.9915i	1.62382	−	0.573322i
$779$	−6.32357	+	6.32357i	−0.226565	+	0.226565i
$780$		0			0
$781$	−3.24741	−	3.24741i	−0.116201	−	0.116201i
$782$	5.12638	−	10.7219i	0.183319	−	0.383416i
$783$		0			0
$784$	−5.35159	+	24.7236i	−0.191128	+	0.882987i
$785$	10.5829			0.377719
$786$		0			0
$787$	−4.24194	−	4.24194i	−0.151209	−	0.151209i	0.627449	−	0.778658i	$-0.284099\pi$
$787$	−4.24194	−	4.24194i	−0.151209	−	0.151209i	−0.778658	+	0.627449i	$0.784099\pi$
$788$	−51.2736	−	5.48573i	−1.82655	−	0.195421i
$789$		0			0
$790$	−9.47768	+	3.34628i	−0.337201	+	0.119055i
$791$			12.8916i			0.458371i
$792$		0			0
$793$			29.4402i			1.04545i
$794$	−14.1361	−	40.0376i	−0.501670	−	1.42088i
$795$		0			0
$796$	−37.3331	+	30.1167i	−1.32324	+	1.06746i
$797$	−27.8996	−	27.8996i	−0.988254	−	0.988254i	0.0116775	−	0.999932i	$-0.496283\pi$
$797$	−27.8996	−	27.8996i	−0.988254	−	0.988254i	−0.999932	+	0.0116775i	$0.996283\pi$
$798$		0			0
$799$	−12.9038			−0.456502
$800$	−20.2434	−	15.6837i	−0.715711	−	0.554503i
$801$		0			0
$802$	−26.2266	−	12.5395i	−0.926092	−	0.442783i
$803$	−4.59286	−	4.59286i	−0.162079	−	0.162079i
$804$		0			0
$805$	2.77238	−	2.77238i	0.0977134	−	0.0977134i
$806$	−6.43206	−	18.2175i	−0.226560	−	0.641685i
$807$		0			0
$808$	−29.2272	−	18.0231i	−1.02821	−	0.634050i
$809$			35.6252i			1.25251i	0.779617	+	0.626257i	$0.215414\pi$
$809$			35.6252i			1.25251i	−0.779617	+	0.626257i	$0.784586\pi$
$810$		0			0
$811$	29.8335	−	29.8335i	1.04759	−	1.04759i	0.0487857	−	0.998809i	$-0.484465\pi$
$811$	29.8335	−	29.8335i	1.04759	−	1.04759i	0.998809	−	0.0487857i	$-0.0155351\pi$
$812$	6.32214	+	0.676402i	0.221863	+	0.0237370i
$813$		0			0
$814$	2.13795	−	4.47158i	0.0749353	−	0.156729i
$815$	9.55271			0.334617
$816$		0			0
$817$	2.82125			0.0987030
$818$	−6.93468	+	14.5041i	−0.242465	+	0.507122i
$819$		0			0
$820$	1.62029	−	15.1444i	0.0565830	−	0.528866i
$821$	5.17584	−	5.17584i	0.180638	−	0.180638i	−0.610996	−	0.791634i	$-0.709231\pi$
$821$	5.17584	−	5.17584i	0.180638	−	0.180638i	0.791634	+	0.610996i	$0.209231\pi$
$822$		0			0
$823$		−	14.1810i		−	0.494320i	−0.968975	−	0.247160i	$-0.920503\pi$
$823$		−	14.1810i		−	0.494320i	0.968975	−	0.247160i	$-0.0794973\pi$
$824$	28.2759	−	6.70487i	0.985036	−	0.233575i
$825$		0			0
$826$	2.51455	+	7.12196i	0.0874923	+	0.247805i
$827$	−32.9934	+	32.9934i	−1.14729	+	1.14729i	−0.160209	+	0.987083i	$0.551217\pi$
$827$	−32.9934	+	32.9934i	−1.14729	+	1.14729i	−0.987083	+	0.160209i	$0.948783\pi$
$828$		0			0
$829$	36.9151	+	36.9151i	1.28211	+	1.28211i	0.939462	+	0.342653i	$0.111325\pi$
$829$	36.9151	+	36.9151i	1.28211	+	1.28211i	0.342653	+	0.939462i	$0.388675\pi$
$830$	11.8422	+	5.66199i	0.411049	+	0.196531i
$831$		0			0
$832$	−27.0046	−	8.94160i	−0.936216	−	0.309994i
$833$	7.66516			0.265582
$834$		0			0
$835$	−2.31088	−	2.31088i	−0.0799715	−	0.0799715i
$836$	−0.743134	−	0.921200i	−0.0257018	−	0.0318604i
$837$		0			0
$838$	−16.4577	−	46.6133i	−0.568524	−	1.61023i
$839$			19.9744i			0.689593i	0.938678	+	0.344796i	$0.112052\pi$
$839$			19.9744i			0.689593i	−0.938678	+	0.344796i	$0.887948\pi$
$840$		0			0
$841$		−	14.0481i		−	0.484418i
$842$	−34.3079	+	12.1131i	−1.18233	+	0.417444i
$843$		0			0
$844$	0.133267	−	1.24561i	0.00458724	−	0.0428756i
$845$	−0.173263	−	0.173263i	−0.00596044	−	0.00596044i
$846$		0			0
$847$	−8.60244			−0.295583
$848$	−15.2712	−	23.7086i	−0.524414	−	0.814156i
$849$		0			0
$850$	−3.34715	+	7.00064i	−0.114806	+	0.240120i
$851$	−23.4510	−	23.4510i	−0.803892	−	0.803892i
$852$		0			0
$853$	21.4072	−	21.4072i	0.732969	−	0.732969i	−0.238238	−	0.971207i	$-0.576570\pi$
$853$	21.4072	−	21.4072i	0.732969	−	0.732969i	0.971207	+	0.238238i	$0.0765697\pi$
$854$	−9.07749	+	3.20499i	−0.310625	+	0.109672i
$855$		0			0
$856$	−19.9798	−	12.3206i	−0.682896	−	0.421110i
$857$			27.5136i			0.939848i	0.882707	+	0.469924i	$0.155719\pi$
$857$			27.5136i			0.939848i	−0.882707	+	0.469924i	$0.844281\pi$
$858$		0			0
$859$	−28.1279	+	28.1279i	−0.959711	+	0.959711i	−0.999219	−	0.0395084i	$-0.987421\pi$
$859$	−28.1279	+	28.1279i	−0.959711	+	0.959711i	0.0395084	+	0.999219i	$0.487421\pi$
$860$	−3.73977	+	3.01688i	−0.127525	+	0.102875i
$861$		0			0
$862$	29.3581	+	14.0367i	0.999940	+	0.478092i
$863$	25.7540			0.876677			0.438339	−	0.898810i	$-0.355567\pi$
$863$	25.7540			0.876677			0.438339	+	0.898810i	$0.355567\pi$
$864$		0			0
$865$	1.17348			0.0398996
$866$	−33.7512	−	16.1371i	−1.14691	−	0.548362i
$867$		0			0
$868$	4.91690	−	3.96647i	0.166890	−	0.134631i
$869$	−5.35331	+	5.35331i	−0.181599	+	0.181599i
$870$		0			0
$871$		−	48.4368i		−	1.64122i
$872$	14.6906	−	23.8230i	0.497485	−	0.806750i
$873$		0			0
$874$	−7.46788	+	2.63668i	−0.252605	+	0.0891872i
$875$	−3.80949	+	3.80949i	−0.128784	+	0.128784i
$876$		0			0
$877$	−39.9079	−	39.9079i	−1.34759	−	1.34759i	−0.888267	−	0.459327i	$-0.848091\pi$
$877$	−39.9079	−	39.9079i	−1.34759	−	1.34759i	−0.459327	−	0.888267i	$-0.651909\pi$
$878$	−2.65550	+	5.55404i	−0.0896188	+	0.187440i
$879$		0			0
$880$	1.97016	+	0.426453i	0.0664140	+	0.0143757i
$881$	−45.8454			−1.54457			−0.772285	−	0.635276i	$-0.780886\pi$
$881$	−45.8454			−1.54457			−0.772285	+	0.635276i	$0.780886\pi$
$882$		0			0
$883$	−17.4056	−	17.4056i	−0.585746	−	0.585746i	0.350731	−	0.936476i	$-0.385933\pi$
$883$	−17.4056	−	17.4056i	−0.585746	−	0.585746i	−0.936476	+	0.350731i	$0.885933\pi$
$884$	−0.916987	+	8.57082i	−0.0308416	+	0.288268i
$885$		0			0
$886$	48.8755	−	17.2565i	1.64200	−	0.579742i
$887$		−	10.8967i		−	0.365875i	−0.983125	−	0.182937i	$-0.941439\pi$
$887$		−	10.8967i		−	0.365875i	0.983125	−	0.182937i	$-0.0585605\pi$
$888$		0			0
$889$		−	1.59392i		−	0.0534585i
$890$	−3.50752	−	9.93436i	−0.117572	−	0.333000i
$891$		0			0
$892$	19.0309	+	23.5910i	0.637203	+	0.789886i
$893$	6.08037	+	6.08037i	0.203472	+	0.203472i
$894$		0			0
$895$	3.20717			0.107204
$896$	−0.182816	−	9.29991i	−0.00610744	−	0.310688i
$897$		0			0
$898$	−25.6438	−	12.2608i	−0.855745	−	0.409149i
$899$	10.5046	+	10.5046i	0.350348	+	0.350348i
$900$		0			0
$901$	−6.04252	+	6.04252i	−0.201305	+	0.201305i
$902$	−3.81944	−	10.8178i	−0.127173	−	0.360193i
$903$		0			0
$904$	10.2327	+	43.1533i	0.340333	+	1.43526i
$905$		−	2.69131i		−	0.0894623i
$906$		0			0
$907$	−10.9736	+	10.9736i	−0.364371	+	0.364371i	−0.865419	−	0.501048i	$-0.832948\pi$
$907$	−10.9736	+	10.9736i	−0.364371	+	0.364371i	0.501048	+	0.865419i	$0.332948\pi$
$908$	−5.76275	+	53.8628i	−0.191243	+	1.78750i
$909$		0			0
$910$	−1.22663	+	2.56553i	−0.0406625	+	0.0850466i
$911$	−15.9173			−0.527363			−0.263682	−	0.964610i	$-0.584937\pi$
$911$	−15.9173			−0.527363			−0.263682	+	0.964610i	$0.584937\pi$
$912$		0			0
$913$	9.88695			0.327210
$914$	13.6239	−	28.4947i	0.450639	−	0.942522i
$915$		0			0
$916$	−33.4952	−	3.58363i	−1.10671	−	0.118407i
$917$	−7.00164	+	7.00164i	−0.231215	+	0.231215i
$918$		0			0
$919$		−	20.2824i		−	0.669056i	−0.942386	−	0.334528i	$-0.891423\pi$
$919$		−	20.2824i		−	0.669056i	0.942386	−	0.334528i	$-0.108577\pi$
$920$	7.07970	−	11.4808i	0.233411	−	0.378512i
$921$		0			0
$922$	−15.4714	−	43.8197i	−0.509524	−	1.44313i
$923$	15.7603	−	15.7603i	0.518755	−	0.518755i
$924$		0			0
$925$	15.3118	+	15.3118i	0.503449	+	0.503449i
$926$	21.8805	+	10.4615i	0.719038	+	0.343787i
$927$		0			0
$928$	21.6997	−	2.75399i	0.712326	−	0.0904043i
$929$	−21.1670			−0.694466			−0.347233	−	0.937779i	$-0.612879\pi$
$929$	−21.1670			−0.694466			−0.347233	+	0.937779i	$0.612879\pi$
$930$		0			0
$931$	−3.61190	−	3.61190i	−0.118375	−	0.118375i
$932$	32.5457	−	26.2547i	1.06607	−	0.860000i
$933$		0			0
$934$	−17.3774	−	49.2180i	−0.568606	−	1.61046i
$935$		−	0.610815i		−	0.0199758i
$936$		0			0
$937$		−	21.6225i		−	0.706377i	−0.935552	−	0.353189i	$-0.885097\pi$
$937$		−	21.6225i		−	0.706377i	0.935552	−	0.353189i	$-0.114903\pi$
$938$	14.9348	−	5.27303i	0.487639	−	0.172171i
$939$		0			0
$940$	−14.5620	−	1.55798i	−0.474960	−	0.0508156i
$941$	19.8008	+	19.8008i	0.645489	+	0.645489i	0.951899	−	0.306410i	$-0.0991280\pi$
$941$	19.8008	+	19.8008i	0.645489	+	0.645489i	−0.306410	+	0.951899i	$0.599128\pi$
$942$		0			0
$943$	−76.7643			−2.49979
$944$	14.0703	+	21.8442i	0.457948	+	0.710967i
$945$		0			0
$946$	−1.56115	+	3.26519i	−0.0507574	+	0.106160i
$947$	−20.5761	−	20.5761i	−0.668634	−	0.668634i	0.288766	−	0.957400i	$-0.406755\pi$
$947$	−20.5761	−	20.5761i	−0.668634	−	0.668634i	−0.957400	+	0.288766i	$0.906755\pi$
$948$		0			0
$949$	22.2900	−	22.2900i	0.723563	−	0.723563i
$950$	4.87598	−	1.72156i	0.158198	−	0.0558548i
$951$		0			0
$952$	−2.74252	+	0.650315i	−0.0888856	+	0.0210768i
$953$			5.24677i			0.169960i	0.996383	+	0.0849798i	$0.0270826\pi$
$953$			5.24677i			0.169960i	−0.996383	+	0.0849798i	$0.972917\pi$
$954$		0			0
$955$	−12.7712	+	12.7712i	−0.413267	+	0.413267i
$956$	−4.74837	−	5.88615i	−0.153573	−	0.190372i
$957$		0			0
$958$	−25.3009	−	12.0969i	−0.817436	−	0.390832i
$959$	−10.4927			−0.338827
$960$		0			0
$961$	−16.2398			−0.523863
$962$	21.7014	+	10.3759i	0.699681	+	0.334532i
$963$		0			0
$964$	−7.83949	−	9.71795i	−0.252493	−	0.312994i
$965$	5.09470	−	5.09470i	0.164004	−	0.164004i
$966$		0			0
$967$			52.3469i			1.68336i	0.539974	+	0.841682i	$0.318434\pi$
$967$			52.3469i			1.68336i	−0.539974	+	0.841682i	$0.681566\pi$
$968$	−28.7959	+	6.82817i	−0.925534	+	0.219466i
$969$		0			0
$970$	5.39941	−	1.90637i	0.173365	−	0.0612099i
$971$	10.1013	−	10.1013i	0.324167	−	0.324167i	−0.526196	−	0.850363i	$-0.676382\pi$
$971$	10.1013	−	10.1013i	0.324167	−	0.324167i	0.850363	+	0.526196i	$0.176382\pi$
$972$		0			0
$973$	−0.211074	−	0.211074i	−0.00676671	−	0.00676671i
$974$	−0.288638	+	0.603693i	−0.00924855	+	0.0193436i
$975$		0			0
$976$	−27.8421	+	17.9336i	−0.891204	+	0.574042i
$977$	9.98449			0.319432			0.159716	−	0.987163i	$-0.448942\pi$
$977$	9.98449			0.319432			0.159716	+	0.987163i	$0.448942\pi$
$978$		0			0
$979$	−5.61126	−	5.61126i	−0.179337	−	0.179337i
$980$	8.65019	+	0.925478i	0.276320	+	0.0295633i
$981$		0			0
$982$	−30.5527	+	10.7872i	−0.974975	+	0.344234i
$983$			27.4294i			0.874862i	0.899252	+	0.437431i	$0.144112\pi$
$983$			27.4294i			0.874862i	−0.899252	+	0.437431i	$0.855888\pi$
$984$		0			0
$985$			17.7340i			0.565052i
$986$	−2.20668	−	6.24998i	−0.0702750	−	0.199040i
$987$		0			0
$988$	4.47075	−	3.60656i	0.142233	−	0.114740i
$989$	17.1241	+	17.1241i	0.544516	+	0.544516i
$990$		0			0
$991$	−61.2255			−1.94489			−0.972447	−	0.233126i	$-0.925105\pi$
$991$	−61.2255			−1.94489			−0.972447	+	0.233126i	$0.925105\pi$
$992$	13.3105	−	17.1802i	0.422608	−	0.545471i
$993$		0			0
$994$	6.57518	+	3.14373i	0.208552	+	0.0997130i
$995$	11.6645	+	11.6645i	0.369788	+	0.369788i
$996$		0			0
$997$	18.8495	−	18.8495i	0.596970	−	0.596970i	−0.342535	−	0.939505i	$-0.611286\pi$
$997$	18.8495	−	18.8495i	0.596970	−	0.596970i	0.939505	+	0.342535i	$0.111286\pi$
$998$	5.66298	+	16.0393i	0.179259	+	0.507714i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.k.d.109.14	yes	32
3.2	odd	2	inner	432.2.k.d.109.3	✓	32
4.3	odd	2		1728.2.k.d.1297.9		32
12.11	even	2		1728.2.k.d.1297.8		32
16.5	even	4	inner	432.2.k.d.325.14	yes	32
16.11	odd	4		1728.2.k.d.433.9		32
48.5	odd	4	inner	432.2.k.d.325.3	yes	32
48.11	even	4		1728.2.k.d.433.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.k.d.109.3	✓	32	3.2	odd	2	inner
432.2.k.d.109.14	yes	32	1.1	even	1	trivial
432.2.k.d.325.3	yes	32	48.5	odd	4	inner
432.2.k.d.325.14	yes	32	16.5	even	4	inner
1728.2.k.d.433.8		32	48.11	even	4
1728.2.k.d.433.9		32	16.11	odd	4
1728.2.k.d.1297.8		32	12.11	even	2
1728.2.k.d.1297.9		32	4.3	odd	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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.27588 + 0.610024i) q^{2} +(1.25574 + 1.55664i) q^{4} +(0.486359 - 0.486359i) q^{5} +0.822162i q^{7} +(0.652590 + 2.75211i) q^{8} +O(q^{10})\)	\(q+(1.27588 + 0.610024i) q^{2} +(1.25574 + 1.55664i) q^{4} +(0.486359 - 0.486359i) q^{5} +0.822162i q^{7} +(0.652590 + 2.75211i) q^{8} +(0.917226 - 0.323845i) q^{10} +(0.518080 - 0.518080i) q^{11} +(2.51433 + 2.51433i) q^{13} +(-0.501539 + 1.04898i) q^{14} +(-0.846229 + 3.90946i) q^{16} +1.21206 q^{17} +(-0.571137 - 0.571137i) q^{19} +(1.36782 + 0.146343i) q^{20} +(0.977049 - 0.344967i) q^{22} -6.93326i q^{23} +4.52691i q^{25} +(1.67419 + 4.74179i) q^{26} +(-1.27981 + 1.03242i) q^{28} +(-2.73422 - 2.73422i) q^{29} -3.84191 q^{31} +(-3.46455 + 4.47179i) q^{32} +(1.54645 + 0.739389i) q^{34} +(0.399866 + 0.399866i) q^{35} +(3.38240 - 3.38240i) q^{37} +(-0.380295 - 1.07711i) q^{38} +(1.65591 + 1.02112i) q^{40} -11.0719i q^{41} +(-2.46985 + 2.46985i) q^{43} +(1.45704 + 0.155887i) q^{44} +(4.22946 - 8.84601i) q^{46} -10.6461 q^{47} +6.32405 q^{49} +(-2.76152 + 5.77580i) q^{50} +(-0.756549 + 7.07126i) q^{52} +(-4.98531 + 4.98531i) q^{53} -0.503946i q^{55} +(-2.26268 + 0.536535i) q^{56} +(-1.82059 - 5.15647i) q^{58} +(4.59327 - 4.59327i) q^{59} +(5.85448 + 5.85448i) q^{61} +(-4.90181 - 2.34366i) q^{62} +(-7.14825 + 3.59200i) q^{64} +2.44574 q^{65} +(-9.63213 - 9.63213i) q^{67} +(1.52204 + 1.88674i) q^{68} +(0.266253 + 0.754109i) q^{70} -6.26816i q^{71} -8.86516i q^{73} +(6.37888 - 2.25219i) q^{74} +(0.171852 - 1.60625i) q^{76} +(0.425946 + 0.425946i) q^{77} -10.3330 q^{79} +(1.48983 + 2.31297i) q^{80} +(6.75412 - 14.1264i) q^{82} +(9.54191 + 9.54191i) q^{83} +(0.589499 - 0.589499i) q^{85} +(-4.65791 + 1.64457i) q^{86} +(1.76391 + 1.08772i) q^{88} -10.8309i q^{89} +(-2.06719 + 2.06719i) q^{91} +(10.7926 - 8.70638i) q^{92} +(-13.5831 - 6.49437i) q^{94} -0.555555 q^{95} +5.88667 q^{97} +(8.06873 + 3.85782i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} + 24 q^{16} + 16 q^{19} + 32 q^{22} + 24 q^{28} - 8 q^{34} + 56 q^{40} - 16 q^{43} - 32 q^{49} - 16 q^{52} - 32 q^{61} + 24 q^{64} + 32 q^{67} - 96 q^{70} - 48 q^{76} - 32 q^{79} + 32 q^{85} - 88 q^{88} - 48 q^{91} - 96 q^{94}+O(q^{100}) \) 32 * q - 8 * q^10 + 24 * q^16 + 16 * q^19 + 32 * q^22 + 24 * q^28 - 8 * q^34 + 56 * q^40 - 16 * q^43 - 32 * q^49 - 16 * q^52 - 32 * q^61 + 24 * q^64 + 32 * q^67 - 96 * q^70 - 48 * q^76 - 32 * q^79 + 32 * q^85 - 88 * q^88 - 48 * q^91 - 96 * q^94

Introduction

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