LMFDB - Embedded newform 432.2.k.d.109.3

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			109.3
Character	$\chi$	$=$	432.109
Dual form			432.2.k.d.325.3

$q$-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	−0.807447	−	0.589940i	$-0.799151\pi$
$5$	−0.486359	+	0.486359i	−0.217506	+	0.217506i	0.589940	+	0.807447i	$0.299151\pi$
$6$		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	−0.780884	−	0.624677i	$-0.785231\pi$
$11$	−0.518080	+	0.518080i	−0.156207	+	0.156207i	0.624677	+	0.780884i	$0.285231\pi$
$12$		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	$-0.546957\pi$
$17$	−1.21206			−0.293969			−0.146984	+	0.989139i	$0.546957\pi$
$18$		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	$0.257165\pi$
$23$			6.93326i			1.44568i	−0.691013	+	0.722842i	$0.742835\pi$
$24$		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	0.913829	−	0.406098i	$-0.133111\pi$
$29$	2.73422	+	2.73422i	0.507731	+	0.507731i	−0.406098	+	0.913829i	$0.633111\pi$
$30$		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	$0.332409\pi$
$41$			11.0719i			1.72914i	−0.502513	+	0.864570i	$0.667591\pi$
$42$		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	$-0.217020\pi$
$47$	10.6461			1.55289			0.776446	+	0.630184i	$0.217020\pi$
$48$		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	−0.276290	−	0.961074i	$-0.589105\pi$
$53$	4.98531	−	4.98531i	0.684785	−	0.684785i	0.961074	+	0.276290i	$0.0891049\pi$
$54$		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	−0.939778	−	0.341785i	$-0.888968\pi$
$59$	−4.59327	+	4.59327i	−0.597993	+	0.597993i	0.341785	+	0.939778i	$0.388968\pi$
$60$		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	$0.121310\pi$
$71$			6.26816i			0.743894i	−0.928254	+	0.371947i	$0.878690\pi$
$72$		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	$-0.984543\pi$
$83$	−9.54191	−	9.54191i	−1.04736	−	1.04736i	−0.0485399	−	0.998821i	$-0.515457\pi$
$84$		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	$0.194623\pi$
$89$			10.8309i			1.14807i	−0.818831	+	0.574035i	$0.805377\pi$
$90$		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	−0.136467	−	0.990645i	$-0.543575\pi$
$101$	8.58437	−	8.58437i	0.854177	−	0.854177i	0.990645	+	0.136467i	$0.0435749\pi$
$102$		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	−0.364064	−	0.931374i	$-0.618611\pi$
$107$	5.86830	−	5.86830i	0.567310	−	0.567310i	0.931374	+	0.364064i	$0.118611\pi$
$108$		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	$-0.764007\pi$
$113$	−15.6801			−1.47506			−0.737528	+	0.675316i	$0.764007\pi$
$114$		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	0.229298	−	0.973356i	$-0.426357\pi$
$131$	−8.51613	−	8.51613i	−0.744058	−	0.744058i	−0.973356	+	0.229298i	$0.926357\pi$
$132$		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	$-0.816462\pi$
$137$		−	12.7623i		−	1.09036i	0.838319	−	0.545179i	$-0.183538\pi$
$138$		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	−0.409062	−	0.912507i	$-0.634144\pi$
$149$	6.14532	−	6.14532i	0.503444	−	0.503444i	0.912507	+	0.409062i	$0.134144\pi$
$150$		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	$0.0588519\pi$
$167$			4.75140i			0.367674i	−0.982957	+	0.183837i	$0.941148\pi$
$168$		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	0.659758	−	0.751478i	$-0.270659\pi$
$173$	−1.20639	−	1.20639i	−0.0917204	−	0.0917204i	−0.751478	+	0.659758i	$0.770659\pi$
$174$		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	0.573069	−	0.819507i	$-0.305753\pi$
$179$	−3.29712	−	3.29712i	−0.246438	−	0.246438i	−0.819507	+	0.573069i	$0.805753\pi$
$180$		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	$-0.101070\pi$
$191$	26.2589			1.90002			0.950012	+	0.312213i	$0.101070\pi$
$192$		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	$-0.379414\pi$
$197$	18.2314	−	18.2314i	1.29893	−	1.29893i	0.929097	−	0.369837i	$-0.120586\pi$
$198$		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	$-0.894404\pi$
$227$	−19.1520	−	19.1520i	−1.27117	−	1.27117i	−0.325689	−	0.945477i	$-0.605596\pi$
$228$		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	$0.240134\pi$
$233$			20.9077i			1.36971i	−0.728680	+	0.684855i	$0.759866\pi$
$234$		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	$-0.460974\pi$
$239$	3.78133			0.244594			0.122297	+	0.992494i	$0.460974\pi$
$240$		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	−0.371113	−	0.928588i	$-0.621024\pi$
$251$	8.83206	−	8.83206i	0.557475	−	0.557475i	0.928588	+	0.371113i	$0.121024\pi$
$252$		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	$-0.509642\pi$
$257$	−0.971040			−0.0605718			−0.0302859	+	0.999541i	$0.509642\pi$
$258$		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	$0.0512532\pi$
$263$			5.19996i			0.320644i	−0.987065	+	0.160322i	$0.948747\pi$
$264$		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	0.120481	−	0.992716i	$-0.461556\pi$
$269$	−14.3057	−	14.3057i	−0.872235	−	0.872235i	−0.992716	+	0.120481i	$0.961556\pi$
$270$		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	$-0.804486\pi$
$281$		−	19.3220i		−	1.15265i	0.817219	−	0.576327i	$-0.195514\pi$
$282$		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	−0.684023	−	0.729460i	$-0.739771\pi$
$293$	0.777756	−	0.777756i	0.0454370	−	0.0454370i	0.729460	+	0.684023i	$0.239771\pi$
$294$		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	$0.0291528\pi$
$311$			3.22577i			0.182917i	−0.995809	+	0.0914584i	$0.970847\pi$
$312$		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	$0.0161833\pi$
$317$	18.6863	+	18.6863i	1.04953	+	1.04953i	0.0508195	+	0.998708i	$0.483817\pi$
$318$		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	−0.356462	−	0.934310i	$-0.616017\pi$
$347$	10.7641	−	10.7641i	0.577847	−	0.577847i	0.934310	+	0.356462i	$0.116017\pi$
$348$		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	$-0.600838\pi$
$353$	−11.7058			−0.623038			−0.311519	+	0.950240i	$0.600838\pi$
$354$		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	$0.0154857\pi$
$359$			1.84284i			0.0972614i	−0.998817	+	0.0486307i	$0.984514\pi$
$360$		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	$-0.611674\pi$
$383$	−13.4520			−0.687365			−0.343683	+	0.939086i	$0.611674\pi$
$384$		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	$0.580180\pi$
$389$	−24.0164	+	24.0164i	−1.21768	+	1.21768i	−0.968443	+	0.249237i	$0.919820\pi$
$390$		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	$-0.328441\pi$
$401$	20.5557			1.02650			0.513250	+	0.858239i	$0.328441\pi$
$402$		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	$0.0757221\pi$
$419$	24.7167	+	24.7167i	1.20749	+	1.20749i	0.235651	+	0.971838i	$0.424278\pi$
$420$		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	$-0.686967\pi$
$431$	−23.0101			−1.10836			−0.554178	+	0.832398i	$0.686967\pi$
$432$		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	$0.586316\pi$
$443$	−25.9162	+	25.9162i	−1.23132	+	1.23132i	−0.963459	+	0.267857i	$0.913684\pi$
$444$		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	$-0.342715\pi$
$449$	20.0989			0.948526			0.474263	+	0.880383i	$0.342715\pi$
$450$		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	$0.0273684\pi$
$461$	23.2354	+	23.2354i	1.08218	+	1.08218i	0.0858743	+	0.996306i	$0.472632\pi$
$462$		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	$0.0757978\pi$
$467$	26.0978	+	26.0978i	1.20766	+	1.20766i	0.235882	+	0.971782i	$0.424202\pi$
$468$		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	$-0.350342\pi$
$479$	19.8302			0.906063			0.453032	+	0.891494i	$0.350342\pi$
$480$		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	−0.239721	−	0.970842i	$-0.577056\pi$
$491$	16.2005	−	16.2005i	0.731120	−	0.731120i	0.970842	+	0.239721i	$0.0770561\pi$
$492$		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	$0.113416\pi$
$503$			15.6462i			0.697630i	−0.937192	+	0.348815i	$0.886584\pi$
$504$		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	0.535192	−	0.844730i	$-0.320239\pi$
$509$	−6.98349	−	6.98349i	−0.309538	−	0.309538i	−0.844730	+	0.535192i	$0.820239\pi$
$510$		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	$0.129907\pi$
$521$			18.1179i			0.793757i	−0.917871	+	0.396879i	$0.870093\pi$
$522$		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	0.743819	−	0.668381i	$-0.233013\pi$
$557$	1.78039	+	1.78039i	0.0754376	+	0.0754376i	−0.668381	+	0.743819i	$0.733013\pi$
$558$		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	0.425357	−	0.905026i	$-0.360149\pi$
$563$	−11.3814	−	11.3814i	−0.479669	−	0.479669i	−0.905026	+	0.425357i	$0.860149\pi$
$564$		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	$-0.906168\pi$
$569$		−	13.8605i		−	0.581061i	0.956866	−	0.290531i	$-0.0938318\pi$
$570$		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	−0.863984	−	0.503519i	$-0.832038\pi$
$587$	−8.73339	+	8.73339i	−0.360465	+	0.360465i	0.503519	+	0.863984i	$0.332038\pi$
$588$		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	$-0.550089\pi$
$593$	−7.63224			−0.313418			−0.156709	+	0.987645i	$0.550089\pi$
$594$		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	$-0.769716\pi$
$599$		−	32.4033i		−	1.32396i	0.749521	−	0.661981i	$-0.230284\pi$
$600$		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	$-0.690973\pi$
$617$		−	41.0030i		−	1.65072i	0.564609	−	0.825359i	$-0.309027\pi$
$618$		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	$-0.338902\pi$
$641$	24.5469			0.969546			0.484773	+	0.874640i	$0.338902\pi$
$642$		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	$-0.848457\pi$
$647$		−	23.3150i		−	0.916607i	0.888796	−	0.458303i	$-0.151543\pi$
$648$		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	0.281199	−	0.959649i	$-0.409268\pi$
$653$	−17.3370	−	17.3370i	−0.678450	−	0.678450i	−0.959649	+	0.281199i	$0.909268\pi$
$654$		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	0.451960	−	0.892038i	$-0.350725\pi$
$659$	−11.2972	−	11.2972i	−0.440078	−	0.440078i	−0.892038	+	0.451960i	$0.850725\pi$
$660$		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	−0.985374	−	0.170407i	$-0.945492\pi$
$677$	−21.2048	+	21.2048i	−0.814967	+	0.814967i	0.170407	+	0.985374i	$0.445492\pi$
$678$		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	−0.575275	−	0.817960i	$-0.695105\pi$
$683$	6.34238	−	6.34238i	0.242685	−	0.242685i	0.817960	+	0.575275i	$0.195105\pi$
$684$		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	0.455436	−	0.890269i	$-0.349484\pi$
$701$	−11.5128	−	11.5128i	−0.434833	−	0.434833i	−0.890269	+	0.455436i	$0.849484\pi$
$702$		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	$-0.604660\pi$
$719$	−17.3169			−0.645813			−0.322907	+	0.946431i	$0.604660\pi$
$720$		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	$-0.717600\pi$
$743$		−	42.2662i		−	1.55060i	0.631595	−	0.775298i	$-0.282400\pi$
$744$		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	$-0.863831\pi$
$761$		−	22.8887i		−	0.829716i	0.909886	−	0.414858i	$-0.136169\pi$
$762$		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	−0.932563	−	0.361006i	$-0.882433\pi$
$773$	−15.8909	+	15.8909i	−0.571557	+	0.571557i	0.361006	+	0.932563i	$0.382433\pi$
$774$		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	0.999932	−	0.0116775i	$-0.00371715\pi$
$797$	27.8996	+	27.8996i	0.988254	+	0.988254i	−0.0116775	+	0.999932i	$0.503717\pi$
$798$		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	$-0.784586\pi$
$809$		−	35.6252i		−	1.25251i	0.779617	−	0.626257i	$-0.215414\pi$
$810$		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	−0.791634	−	0.610996i	$-0.790769\pi$
$821$	−5.17584	+	5.17584i	−0.180638	+	0.180638i	0.610996	+	0.791634i	$0.290769\pi$
$822$		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	$-0.448783\pi$
$827$	32.9934	−	32.9934i	1.14729	−	1.14729i	0.987083	−	0.160209i	$-0.0512167\pi$
$828$		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	$-0.887948\pi$
$839$		−	19.9744i		−	0.689593i	0.938678	−	0.344796i	$-0.112052\pi$
$840$		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	$-0.844281\pi$
$857$		−	27.5136i		−	0.939848i	0.882707	−	0.469924i	$-0.155719\pi$
$858$		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	$-0.644433\pi$
$863$	−25.7540			−0.876677			−0.438339	+	0.898810i	$0.644433\pi$
$864$		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	$-0.219114\pi$
$881$	45.8454			1.54457			0.772285	+	0.635276i	$0.219114\pi$
$882$		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	$0.0585605\pi$
$887$			10.8967i			0.365875i	−0.983125	+	0.182937i	$0.941439\pi$
$888$		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	$-0.415063\pi$
$911$	15.9173			0.527363			0.263682	+	0.964610i	$0.415063\pi$
$912$		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	$-0.387121\pi$
$929$	21.1670			0.694466			0.347233	+	0.937779i	$0.387121\pi$
$930$		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	0.306410	−	0.951899i	$-0.400872\pi$
$941$	−19.8008	−	19.8008i	−0.645489	−	0.645489i	−0.951899	+	0.306410i	$0.900872\pi$
$942$		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	0.957400	−	0.288766i	$-0.0932450\pi$
$947$	20.5761	+	20.5761i	0.668634	+	0.668634i	−0.288766	+	0.957400i	$0.593245\pi$
$948$		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	$-0.972917\pi$
$953$		−	5.24677i		−	0.169960i	0.996383	−	0.0849798i	$-0.0270826\pi$
$954$		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	−0.850363	−	0.526196i	$-0.823618\pi$
$971$	−10.1013	+	10.1013i	−0.324167	+	0.324167i	0.526196	+	0.850363i	$0.323618\pi$
$972$		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	$-0.551058\pi$
$977$	−9.98449			−0.319432			−0.159716	+	0.987163i	$0.551058\pi$
$978$		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	$-0.855888\pi$
$983$		−	27.4294i		−	0.874862i	0.899252	−	0.437431i	$-0.144112\pi$
$984$		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.109.3	✓	32
3.2	odd	2	inner	432.2.k.d.109.14	yes	32
4.3	odd	2		1728.2.k.d.1297.8		32
12.11	even	2		1728.2.k.d.1297.9		32
16.5	even	4	inner	432.2.k.d.325.3	yes	32
16.11	odd	4		1728.2.k.d.433.8		32
48.5	odd	4	inner	432.2.k.d.325.14	yes	32
48.11	even	4		1728.2.k.d.433.9		32

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