LMFDB - Embedded newform 432.2.be.b.95.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(47,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 7]))

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

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

chi := DirichletCharacter("432.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.be (of order $18$, degree $6$, 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:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			95.5
Character	$\chi$	$=$	432.95
Dual form			432.2.be.b.191.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.63553 + 0.570126i) q^{3} +(2.34697 - 2.79701i) q^{5} +(0.550750 - 1.51317i) q^{7} +(2.34991 + 1.86492i) q^{9} +O(q^{10})$	\(q+(1.63553 + 0.570126i) q^{3} +(2.34697 - 2.79701i) q^{5} +(0.550750 - 1.51317i) q^{7} +(2.34991 + 1.86492i) q^{9} +(-2.21396 + 1.85773i) q^{11} +(0.121792 - 0.690719i) q^{13} +(5.43318 - 3.23652i) q^{15} +(-5.56131 - 3.21082i) q^{17} +(-1.62624 + 0.938910i) q^{19} +(1.76347 - 2.16084i) q^{21} +(-2.18387 + 0.794864i) q^{23} +(-1.44675 - 8.20494i) q^{25} +(2.78011 + 4.38987i) q^{27} +(5.54988 - 0.978594i) q^{29} +(3.63921 + 9.99865i) q^{31} +(-4.68013 + 1.77614i) q^{33} +(-2.93977 - 5.09183i) q^{35} +(-4.10464 + 7.10944i) q^{37} +(0.592992 - 1.06025i) q^{39} +(6.18442 + 1.09048i) q^{41} +(5.65989 + 6.74520i) q^{43} +(10.7314 - 2.19583i) q^{45} +(-1.67459 - 0.609501i) q^{47} +(3.37594 + 2.83275i) q^{49} +(-7.26511 - 8.42204i) q^{51} -0.849889i q^{53} +10.5525i q^{55} +(-3.19506 + 0.608453i) q^{57} +(-4.54459 - 3.81337i) q^{59} +(-9.95979 - 3.62507i) q^{61} +(4.11616 - 2.52872i) q^{63} +(-1.64610 - 1.96175i) q^{65} +(-14.5520 - 2.56590i) q^{67} +(-4.02496 + 0.0549417i) q^{69} +(5.80783 - 10.0595i) q^{71} +(3.12044 + 5.40475i) q^{73} +(2.31165 - 14.2443i) q^{75} +(1.59173 + 4.37325i) q^{77} +(4.47831 - 0.789647i) q^{79} +(2.04418 + 8.76478i) q^{81} +(-1.28300 - 7.27624i) q^{83} +(-22.0329 + 8.01933i) q^{85} +(9.63492 + 1.56361i) q^{87} +(-6.02277 + 3.47725i) q^{89} +(-0.978101 - 0.564707i) q^{91} +(0.251545 + 18.4279i) q^{93} +(-1.19060 + 6.75220i) q^{95} +(1.35281 - 1.13514i) q^{97} +(-8.66711 + 0.236660i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q + 3 * q^5 + 6 * q^9	$ 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) $ 36 * q + 3 * q^5 + 6 * q^9 - 18 * q^11 + 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 + 27 * q^31 + 27 * q^33 + 27 * q^35 - 45 * q^39 + 18 * q^41 + 27 * q^45 + 45 * q^47 - 63 * q^51 - 9 * q^57 + 54 * q^59 - 63 * q^63 - 57 * q^65 - 63 * q^69 + 36 * q^71 + 9 * q^73 - 45 * q^75 - 81 * q^77 - 54 * q^81 - 27 * q^83 - 36 * q^85 + 45 * q^87 - 63 * q^89 + 27 * q^91 - 63 * q^93 - 72 * q^95 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.63553	+	0.570126i	0.944273	+	0.329162i
$3$	1.63553	+	0.570126i	0.944273	+	0.329162i
$4$		0			0
$5$	2.34697	−	2.79701i	1.04960	−	1.25086i	0.0824620	−	0.996594i	$-0.473722\pi$
$5$	2.34697	−	2.79701i	1.04960	−	1.25086i	0.967134	−	0.254266i	$-0.0818339\pi$
$6$		0			0
$7$	0.550750	−	1.51317i	0.208164	−	0.571926i	−0.791042	−	0.611762i	$-0.790461\pi$
$7$	0.550750	−	1.51317i	0.208164	−	0.571926i	0.999206	+	0.0398355i	$0.0126834\pi$
$8$		0			0
$9$	2.34991	+	1.86492i	0.783304	+	0.621639i
$10$		0			0
$11$	−2.21396	+	1.85773i	−0.667533	+	0.560127i	−0.912334	−	0.409447i	$-0.865722\pi$
$11$	−2.21396	+	1.85773i	−0.667533	+	0.560127i	0.244801	+	0.969573i	$0.421277\pi$
$12$		0			0
$13$	0.121792	−	0.690719i	0.0337791	−	0.191571i	−0.963249	−	0.268610i	$-0.913436\pi$
$13$	0.121792	−	0.690719i	0.0337791	−	0.191571i	0.997028	+	0.0770394i	$0.0245467\pi$
$14$		0			0
$15$	5.43318	−	3.23652i	1.40284	−	0.835666i
$16$		0			0
$17$	−5.56131	−	3.21082i	−1.34882	−	0.778739i	−0.360734	−	0.932669i	$-0.617474\pi$
$17$	−5.56131	−	3.21082i	−1.34882	−	0.778739i	−0.988082	+	0.153930i	$0.950807\pi$
$18$		0			0
$19$	−1.62624	+	0.938910i	−0.373085	+	0.215401i	−0.674805	−	0.737996i	$-0.735772\pi$
$19$	−1.62624	+	0.938910i	−0.373085	+	0.215401i	0.301720	+	0.953396i	$0.402439\pi$
$20$		0			0
$21$	1.76347	−	2.16084i	0.384820	−	0.471535i
$22$		0			0
$23$	−2.18387	+	0.794864i	−0.455369	+	0.165741i	−0.559513	−	0.828822i	$-0.689012\pi$
$23$	−2.18387	+	0.794864i	−0.455369	+	0.165741i	0.104144	+	0.994562i	$0.466790\pi$
$24$		0			0
$25$	−1.44675	−	8.20494i	−0.289351	−	1.64099i
$26$		0			0
$27$	2.78011	+	4.38987i	0.535033	+	0.844831i
$28$		0			0
$29$	5.54988	−	0.978594i	1.03059	−	0.181720i	0.367313	−	0.930097i	$-0.380278\pi$
$29$	5.54988	−	0.978594i	1.03059	−	0.181720i	0.663274	+	0.748377i	$0.269167\pi$
$30$		0			0
$31$	3.63921	+	9.99865i	0.653622	+	1.79581i	0.603917	+	0.797047i	$0.293606\pi$
$31$	3.63921	+	9.99865i	0.653622	+	1.79581i	0.0497045	+	0.998764i	$0.484172\pi$
$32$		0			0
$33$	−4.68013	+	1.77614i	−0.814706	+	0.309186i
$34$		0			0
$35$	−2.93977	−	5.09183i	−0.496911	−	0.860676i
$36$		0			0
$37$	−4.10464	+	7.10944i	−0.674798	+	1.16878i	0.301730	+	0.953393i	$0.402436\pi$
$37$	−4.10464	+	7.10944i	−0.674798	+	1.16878i	−0.976528	+	0.215391i	$0.930897\pi$
$38$		0			0
$39$	0.592992	−	1.06025i	0.0949547	−	0.169777i
$40$		0			0
$41$	6.18442	+	1.09048i	0.965843	+	0.170304i	0.634258	−	0.773121i	$-0.281306\pi$
$41$	6.18442	+	1.09048i	0.965843	+	0.170304i	0.331585	+	0.943425i	$0.392417\pi$
$42$		0			0
$43$	5.65989	+	6.74520i	0.863125	+	1.02863i	0.999280	+	0.0379452i	$0.0120812\pi$
$43$	5.65989	+	6.74520i	0.863125	+	1.02863i	−0.136154	+	0.990688i	$0.543474\pi$
$44$		0			0
$45$	10.7314	−	2.19583i	1.59974	−	0.327334i
$46$		0			0
$47$	−1.67459	−	0.609501i	−0.244264	−	0.0889049i	0.216987	−	0.976174i	$-0.430377\pi$
$47$	−1.67459	−	0.609501i	−0.244264	−	0.0889049i	−0.461251	+	0.887270i	$0.652599\pi$
$48$		0			0
$49$	3.37594	+	2.83275i	0.482277	+	0.404679i
$50$		0			0
$51$	−7.26511	−	8.42204i	−1.01732	−	1.17932i
$52$		0			0
$53$		−	0.849889i		−	0.116741i	−0.998295	−	0.0583706i	$-0.981409\pi$
$53$		−	0.849889i		−	0.116741i	0.998295	−	0.0583706i	$-0.0185905\pi$
$54$		0			0
$55$			10.5525i			1.42290i
$56$		0			0
$57$	−3.19506	+	0.608453i	−0.423196	+	0.0805916i
$58$		0			0
$59$	−4.54459	−	3.81337i	−0.591656	−	0.496458i	0.297096	−	0.954848i	$-0.403982\pi$
$59$	−4.54459	−	3.81337i	−0.591656	−	0.496458i	−0.888751	+	0.458390i	$0.848426\pi$
$60$		0			0
$61$	−9.95979	−	3.62507i	−1.27522	−	0.464142i	−0.386372	−	0.922343i	$-0.626272\pi$
$61$	−9.95979	−	3.62507i	−1.27522	−	0.464142i	−0.888849	+	0.458201i	$0.848494\pi$
$62$		0			0
$63$	4.11616	−	2.52872i	0.518587	−	0.318589i
$64$		0			0
$65$	−1.64610	−	1.96175i	−0.204174	−	0.243325i
$66$		0			0
$67$	−14.5520	−	2.56590i	−1.77781	−	0.313475i	−0.814156	−	0.580646i	$-0.802800\pi$
$67$	−14.5520	−	2.56590i	−1.77781	−	0.313475i	−0.963649	+	0.267171i	$0.913911\pi$
$68$		0			0
$69$	−4.02496	+	0.0549417i	−0.484548	+	0.00661420i
$70$		0			0
$71$	5.80783	−	10.0595i	0.689263	−	1.19384i	−0.282814	−	0.959175i	$-0.591268\pi$
$71$	5.80783	−	10.0595i	0.689263	−	1.19384i	0.972077	−	0.234663i	$-0.0753988\pi$
$72$		0			0
$73$	3.12044	+	5.40475i	0.365219	+	0.632579i	0.988811	−	0.149171i	$-0.0476606\pi$
$73$	3.12044	+	5.40475i	0.365219	+	0.632579i	−0.623592	+	0.781750i	$0.714327\pi$
$74$		0			0
$75$	2.31165	−	14.2443i	0.266926	−	1.64479i
$76$		0			0
$77$	1.59173	+	4.37325i	0.181395	+	0.498378i
$78$		0			0
$79$	4.47831	−	0.789647i	0.503849	−	0.0888422i	0.0840543	−	0.996461i	$-0.473213\pi$
$79$	4.47831	−	0.789647i	0.503849	−	0.0888422i	0.419795	+	0.907619i	$0.362102\pi$
$80$		0			0
$81$	2.04418	+	8.76478i	0.227131	+	0.973864i
$82$		0			0
$83$	−1.28300	−	7.27624i	−0.140827	−	0.798671i	−0.970623	−	0.240604i	$-0.922654\pi$
$83$	−1.28300	−	7.27624i	−0.140827	−	0.798671i	0.829796	−	0.558067i	$-0.188457\pi$
$84$		0			0
$85$	−22.0329	+	8.01933i	−2.38981	+	0.869818i
$86$		0			0
$87$	9.63492	+	1.56361i	1.03297	+	0.167637i
$88$		0			0
$89$	−6.02277	+	3.47725i	−0.638412	+	0.368588i	−0.784003	−	0.620757i	$-0.786825\pi$
$89$	−6.02277	+	3.47725i	−0.638412	+	0.368588i	0.145590	+	0.989345i	$0.453492\pi$
$90$		0			0
$91$	−0.978101	−	0.564707i	−0.102533	−	0.0591974i
$92$		0			0
$93$	0.251545	+	18.4279i	0.0260840	+	1.91088i
$94$		0			0
$95$	−1.19060	+	6.75220i	−0.122152	+	0.692761i
$96$		0			0
$97$	1.35281	−	1.13514i	0.137357	−	0.115256i	−0.571521	−	0.820588i	$-0.693646\pi$
$97$	1.35281	−	1.13514i	0.137357	−	0.115256i	0.708878	+	0.705331i	$0.249202\pi$
$98$		0			0
$99$	−8.66711	+	0.236660i	−0.871078	+	0.0237853i
$100$		0			0
$101$	3.88953	−	10.6864i	0.387023	−	1.06334i	−0.581312	−	0.813681i	$-0.697460\pi$
$101$	3.88953	−	10.6864i	0.387023	−	1.06334i	0.968335	−	0.249656i	$-0.0803175\pi$
$102$		0			0
$103$	10.6329	−	12.6718i	1.04769	−	1.24859i	0.0799054	−	0.996802i	$-0.474538\pi$
$103$	10.6329	−	12.6718i	1.04769	−	1.24859i	0.967783	−	0.251784i	$-0.0810174\pi$
$104$		0			0
$105$	−1.90509	−	10.0039i	−0.185918	−	0.976278i
$106$		0			0
$107$	−16.6875			−1.61324			−0.806619	−	0.591071i	$-0.798705\pi$
$107$	−16.6875			−1.61324			−0.806619	+	0.591071i	$0.798705\pi$
$108$		0			0
$109$	10.2128			0.978212			0.489106	−	0.872224i	$-0.337323\pi$
$109$	10.2128			0.978212			0.489106	+	0.872224i	$0.337323\pi$
$110$		0			0
$111$	−10.7665	+	9.28753i	−1.02191	+	0.881534i
$112$		0			0
$113$	−9.06215	+	10.7998i	−0.852495	+	1.01596i	0.147144	+	0.989115i	$0.452992\pi$
$113$	−9.06215	+	10.7998i	−0.852495	+	1.01596i	−0.999639	+	0.0268492i	$0.991453\pi$
$114$		0			0
$115$	−2.90224	+	7.97383i	−0.270635	+	0.743564i
$116$		0			0
$117$	1.57433	−	1.39600i	0.145547	−	0.129060i
$118$		0			0
$119$	−7.92143	+	6.64687i	−0.726156	+	0.609317i
$120$		0			0
$121$	−0.459688	+	2.60702i	−0.0417898	+	0.237002i
$122$		0			0
$123$	9.49308	+	5.30941i	0.855962	+	0.478733i
$124$		0			0
$125$	−10.5345	−	6.08208i	−0.942232	−	0.543998i
$126$		0			0
$127$	−6.11030	+	3.52779i	−0.542202	+	0.313040i	−0.745971	−	0.665979i	$-0.768014\pi$
$127$	−6.11030	+	3.52779i	−0.542202	+	0.313040i	0.203769	+	0.979019i	$0.434681\pi$
$128$		0			0
$129$	5.41131	+	14.2588i	0.476439	+	1.25542i
$130$		0			0
$131$	−13.6909	+	4.98310i	−1.19618	+	0.435375i	−0.861891	−	0.507094i	$-0.830720\pi$
$131$	−13.6909	+	4.98310i	−1.19618	+	0.435375i	−0.334293	+	0.942469i	$0.608497\pi$
$132$		0			0
$133$	0.525082	+	2.97789i	0.0455304	+	0.258216i
$134$		0			0
$135$	18.8033	+	2.52689i	1.61833	+	0.217480i
$136$		0			0
$137$	14.3046	−	2.52229i	1.22212	−	0.215493i	0.474884	−	0.880048i	$-0.342490\pi$
$137$	14.3046	−	2.52229i	1.22212	−	0.215493i	0.747240	+	0.664555i	$0.231379\pi$
$138$		0			0
$139$	−3.14344	−	8.63654i	−0.266624	−	0.732542i	−0.998683	−	0.0513016i	$-0.983663\pi$
$139$	−3.14344	−	8.63654i	−0.266624	−	0.732542i	0.732060	−	0.681240i	$-0.238559\pi$
$140$		0			0
$141$	−2.39135	−	1.95158i	−0.201388	−	0.164353i
$142$		0			0
$143$	1.01353	+	1.75548i	0.0847553	+	0.146801i
$144$		0			0
$145$	10.2883	−	17.8198i	0.854394	−	1.47985i
$146$		0			0
$147$	3.90642	+	6.55776i	0.322196	+	0.540875i
$148$		0			0
$149$	−1.24126	−	0.218868i	−0.101688	−	0.0179304i	0.122573	−	0.992460i	$-0.460886\pi$
$149$	−1.24126	−	0.218868i	−0.101688	−	0.0179304i	−0.224261	+	0.974529i	$0.571997\pi$
$150$		0			0
$151$	−7.74987	−	9.23593i	−0.630675	−	0.751609i	0.352191	−	0.935928i	$-0.385437\pi$
$151$	−7.74987	−	9.23593i	−0.630675	−	0.751609i	−0.982867	+	0.184319i	$0.940992\pi$
$152$		0			0
$153$	−7.08067	−	17.9165i	−0.572439	−	1.44847i
$154$		0			0
$155$	36.5074	+	13.2876i	2.93235	+	1.06729i
$156$		0			0
$157$	−2.80380	−	2.35267i	−0.223767	−	0.187763i	0.524011	−	0.851711i	$-0.324435\pi$
$157$	−2.80380	−	2.35267i	−0.223767	−	0.187763i	−0.747779	+	0.663948i	$0.768879\pi$
$158$		0			0
$159$	0.484544	−	1.39002i	0.0384268	−	0.110236i
$160$		0			0
$161$			3.74235i			0.294939i
$162$		0			0
$163$			2.44194i			0.191267i	0.995417	+	0.0956336i	$0.0304877\pi$
$163$			2.44194i			0.191267i	−0.995417	+	0.0956336i	$0.969512\pi$
$164$		0			0
$165$	−6.01625	+	17.2589i	−0.468364	+	1.34360i
$166$		0			0
$167$	−4.06934	−	3.41458i	−0.314895	−	0.264229i	0.471617	−	0.881804i	$-0.343671\pi$
$167$	−4.06934	−	3.41458i	−0.314895	−	0.264229i	−0.786512	+	0.617575i	$0.788115\pi$
$168$		0			0
$169$	11.7537	+	4.27801i	0.904134	+	0.329078i
$170$		0			0
$171$	−5.57251	−	0.826444i	−0.426141	−	0.0631998i
$172$		0			0
$173$	−16.8612	−	20.0945i	−1.28194	−	1.52775i	−0.698560	−	0.715551i	$-0.746176\pi$
$173$	−16.8612	−	20.0945i	−1.28194	−	1.52775i	−0.583377	−	0.812202i	$-0.698269\pi$
$174$		0			0
$175$	−13.2123	−	2.32969i	−0.998757	−	0.176108i
$176$		0			0
$177$	−5.25872	−	8.82786i	−0.395269	−	0.663543i
$178$		0			0
$179$	−5.42787	+	9.40134i	−0.405698	+	0.702689i	−0.994402	−	0.105659i	$-0.966305\pi$
$179$	−5.42787	+	9.40134i	−0.405698	+	0.702689i	0.588705	+	0.808348i	$0.299638\pi$
$180$		0			0
$181$	2.12621	+	3.68270i	0.158040	+	0.273733i	0.934162	−	0.356850i	$-0.116149\pi$
$181$	2.12621	+	3.68270i	0.158040	+	0.273733i	−0.776122	+	0.630583i	$0.782816\pi$
$182$		0			0
$183$	−14.2228	−	11.6072i	−1.05138	−	0.858032i
$184$		0			0
$185$	10.2517	+	28.1663i	0.753720	+	2.07083i
$186$		0			0
$187$	18.2773	−	3.22279i	1.33657	−	0.235674i
$188$		0			0
$189$	8.17379	−	1.78907i	0.594556	−	0.130136i
$190$		0			0
$191$	−1.25388	−	7.11111i	−0.0907276	−	0.514542i	−0.995973	−	0.0896529i	$-0.971424\pi$
$191$	−1.25388	−	7.11111i	−0.0907276	−	0.514542i	0.905245	−	0.424889i	$-0.139687\pi$
$192$		0			0
$193$	−15.5914	+	5.67481i	−1.12229	+	0.408482i	−0.835489	−	0.549507i	$-0.814815\pi$
$193$	−15.5914	+	5.67481i	−1.12229	+	0.408482i	−0.286805	+	0.957989i	$0.592593\pi$
$194$		0			0
$195$	−1.57381	−	4.14699i	−0.112703	−	0.296972i
$196$		0			0
$197$	4.35620	−	2.51505i	0.310367	−	0.179190i	−0.336724	−	0.941603i	$-0.609319\pi$
$197$	4.35620	−	2.51505i	0.310367	−	0.179190i	0.647091	+	0.762413i	$0.275986\pi$
$198$		0			0
$199$	12.8199	+	7.40159i	0.908781	+	0.524685i	0.880039	−	0.474902i	$-0.157517\pi$
$199$	12.8199	+	7.40159i	0.908781	+	0.524685i	0.0287420	+	0.999587i	$0.490850\pi$
$200$		0			0
$201$	−22.3373	−	12.4931i	−1.57555	−	0.881193i
$202$		0			0
$203$	1.57582	−	8.93690i	0.110601	−	0.627247i
$204$		0			0
$205$	17.5647	−	14.7385i	1.22677	−	1.02938i
$206$		0			0
$207$	−6.61426	−	2.20488i	−0.459723	−	0.153249i
$208$		0			0
$209$	1.85618	−	5.09982i	0.128395	−	0.352762i
$210$		0			0
$211$	7.82727	−	9.32818i	0.538851	−	0.642178i	−0.426078	−	0.904686i	$-0.640105\pi$
$211$	7.82727	−	9.32818i	0.538851	−	0.642178i	0.964930	+	0.262508i	$0.0845497\pi$
$212$		0			0
$213$	15.2340	−	13.1413i	1.04382	−	0.900430i
$214$		0			0
$215$	32.1500			2.19261
$216$		0			0
$217$	17.1340			1.16313
$218$		0			0
$219$	2.02217	+	10.6187i	0.136646	+	0.717544i
$220$		0			0
$221$	−2.89510	+	3.45025i	−0.194746	+	0.232089i
$222$		0			0
$223$	3.42628	−	9.41364i	0.229441	−	0.630384i	−0.770535	−	0.637398i	$-0.780011\pi$
$223$	3.42628	−	9.41364i	0.229441	−	0.630384i	0.999975	+	0.00701461i	$0.00223284\pi$
$224$		0			0
$225$	11.9018	−	21.9790i	0.793453	−	1.46526i
$226$		0			0
$227$	7.69615	−	6.45783i	0.510811	−	0.428622i	−0.350603	−	0.936524i	$-0.614023\pi$
$227$	7.69615	−	6.45783i	0.510811	−	0.428622i	0.861415	+	0.507903i	$0.169579\pi$
$228$		0			0
$229$	−2.02551	+	11.4872i	−0.133849	+	0.759096i	0.841805	+	0.539782i	$0.181493\pi$
$229$	−2.02551	+	11.4872i	−0.133849	+	0.759096i	−0.975654	+	0.219315i	$0.929618\pi$
$230$		0			0
$231$	0.110022	+	8.06006i	0.00723890	+	0.530313i
$232$		0			0
$233$	11.1464	+	6.43535i	0.730222	+	0.421594i	0.818503	−	0.574502i	$-0.194804\pi$
$233$	11.1464	+	6.43535i	0.730222	+	0.421594i	−0.0882815	+	0.996096i	$0.528137\pi$
$234$		0			0
$235$	−5.63499	+	3.25336i	−0.367586	+	0.212226i
$236$		0			0
$237$	7.77461	+	1.26171i	0.505015	+	0.0819569i
$238$		0			0
$239$	3.79461	−	1.38112i	0.245453	−	0.0893375i	−0.216364	−	0.976313i	$-0.569420\pi$
$239$	3.79461	−	1.38112i	0.245453	−	0.0893375i	0.461817	+	0.886975i	$0.347198\pi$
$240$		0			0
$241$	−3.73127	−	21.1611i	−0.240352	−	1.36311i	−0.831043	−	0.556208i	$-0.812256\pi$
$241$	−3.73127	−	21.1611i	−0.240352	−	1.36311i	0.590691	−	0.806898i	$-0.298855\pi$
$242$		0			0
$243$	−1.65372	+	15.5005i	−0.106086	+	0.994357i
$244$		0			0
$245$	15.8465	−	2.79416i	1.01239	−	0.178512i
$246$		0			0
$247$	0.450459	+	1.23763i	0.0286620	+	0.0787483i
$248$		0			0
$249$	2.04999	−	12.6320i	0.129913	−	0.800519i
$250$		0			0
$251$	−2.12275	−	3.67671i	−0.133987	−	0.232072i	0.791223	−	0.611528i	$-0.209445\pi$
$251$	−2.12275	−	3.67671i	−0.133987	−	0.232072i	−0.925210	+	0.379455i	$0.876111\pi$
$252$		0			0
$253$	3.35835	−	5.81684i	0.211138	−	0.365702i
$254$		0			0
$255$	−40.6075	+	0.554302i	−2.54294	+	0.0347117i
$256$		0			0
$257$	5.12260	+	0.903252i	0.319539	+	0.0563433i	0.331117	−	0.943590i	$-0.392574\pi$
$257$	5.12260	+	0.903252i	0.319539	+	0.0563433i	−0.0115784	+	0.999933i	$0.503686\pi$
$258$		0			0
$259$	8.49719	+	10.1266i	0.527990	+	0.629233i
$260$		0			0
$261$	14.8667	+	8.05045i	0.920228	+	0.498310i
$262$		0			0
$263$	22.9602	+	8.35683i	1.41579	+	0.515304i	0.932823	−	0.360336i	$-0.117338\pi$
$263$	22.9602	+	8.35683i	1.41579	+	0.515304i	0.482964	+	0.875640i	$0.339560\pi$
$264$		0			0
$265$	−2.37715	−	1.99466i	−0.146027	−	0.122531i
$266$		0			0
$267$	−11.8329	+	2.25340i	−0.724161	+	0.137906i
$268$		0			0
$269$		−	0.485873i		−	0.0296242i	−0.999890	−	0.0148121i	$-0.995285\pi$
$269$		−	0.485873i		−	0.0296242i	0.999890	−	0.0148121i	$-0.00471501\pi$
$270$		0			0
$271$		−	15.4958i		−	0.941306i	−0.882318	−	0.470653i	$-0.844018\pi$
$271$		−	15.4958i		−	0.941306i	0.882318	−	0.470653i	$-0.155982\pi$
$272$		0			0
$273$	−1.27776	−	1.48124i	−0.0773335	−	0.0896485i
$274$		0			0
$275$	18.4456	+	15.4777i	1.11231	+	0.933341i
$276$		0			0
$277$	−13.7884	−	5.01856i	−0.828463	−	0.301536i	−0.107235	−	0.994234i	$-0.534200\pi$
$277$	−13.7884	−	5.01856i	−0.828463	−	0.301536i	−0.721228	+	0.692698i	$0.756422\pi$
$278$		0			0
$279$	−10.0948	+	30.2828i	−0.604361	+	1.81298i
$280$		0			0
$281$	0.732164	+	0.872559i	0.0436772	+	0.0520525i	0.787441	−	0.616390i	$-0.211406\pi$
$281$	0.732164	+	0.872559i	0.0436772	+	0.0520525i	−0.743764	+	0.668443i	$0.766961\pi$
$282$		0			0
$283$	4.21444	+	0.743119i	0.250522	+	0.0441739i	0.297499	−	0.954722i	$-0.403848\pi$
$283$	4.21444	+	0.743119i	0.250522	+	0.0441739i	−0.0469766	+	0.998896i	$0.514959\pi$
$284$		0			0
$285$	−5.79686	+	10.3646i	−0.343376	+	0.613948i
$286$		0			0
$287$	5.05615	−	8.75752i	0.298455	−	0.516940i
$288$		0			0
$289$	12.1188	+	20.9903i	0.712869	+	1.23472i
$290$		0			0
$291$	2.85974	−	1.08529i	0.167641	−	0.0636207i
$292$		0			0
$293$	−2.29569	−	6.30736i	−0.134116	−	0.368480i	0.854396	−	0.519622i	$-0.173927\pi$
$293$	−2.29569	−	6.30736i	−0.134116	−	0.368480i	−0.988512	+	0.151142i	$0.951705\pi$
$294$		0			0
$295$	−21.3320	+	3.76141i	−1.24200	+	0.218998i
$296$		0			0
$297$	−14.3102	−	4.55428i	−0.830365	−	0.264266i
$298$		0			0
$299$	0.283049	+	1.60525i	0.0163691	+	0.0928340i
$300$		0			0
$301$	13.3238	−	4.84948i	0.767974	−	0.279520i
$302$		0			0
$303$	12.4540	−	15.2604i	0.715466	−	0.876687i
$304$		0			0
$305$	−33.5147	+	19.3497i	−1.91904	+	1.10796i
$306$		0			0
$307$	−9.47236	−	5.46887i	−0.540616	−	0.312125i	0.204713	−	0.978822i	$-0.434374\pi$
$307$	−9.47236	−	5.46887i	−0.540616	−	0.312125i	−0.745329	+	0.666697i	$0.767707\pi$
$308$		0			0
$309$	24.6149	−	14.6630i	1.40029	−	0.834147i
$310$		0			0
$311$	−1.99845	+	11.3338i	−0.113322	+	0.642678i	0.874246	+	0.485483i	$0.161356\pi$
$311$	−1.99845	+	11.3338i	−0.113322	+	0.642678i	−0.987568	+	0.157195i	$0.949755\pi$
$312$		0			0
$313$	−5.50981	+	4.62328i	−0.311433	+	0.261323i	−0.785084	−	0.619389i	$-0.787380\pi$
$313$	−5.50981	+	4.62328i	−0.311433	+	0.261323i	0.473651	+	0.880713i	$0.342936\pi$
$314$		0			0
$315$	2.58763	−	17.4478i	0.145797	−	0.983070i
$316$		0			0
$317$	−5.58824	+	15.3536i	−0.313867	+	0.862342i	0.678000	+	0.735062i	$0.262847\pi$
$317$	−5.58824	+	15.3536i	−0.313867	+	0.862342i	−0.991867	+	0.127280i	$0.959375\pi$
$318$		0			0
$319$	−10.4692	+	12.4767i	−0.586164	+	0.698564i
$320$		0			0
$321$	−27.2928	−	9.51396i	−1.52334	−	0.531018i
$322$		0			0
$323$	12.0587			0.670964
$324$		0			0
$325$	−5.84351			−0.324140
$326$		0			0
$327$	16.7034	+	5.82260i	0.923700	+	0.321991i
$328$		0			0
$329$	−1.84456	+	2.19826i	−0.101694	+	0.121194i
$330$		0			0
$331$	8.42268	−	23.1411i	0.462952	−	1.27195i	−0.460302	−	0.887762i	$-0.652259\pi$
$331$	8.42268	−	23.1411i	0.462952	−	1.27195i	0.923255	−	0.384189i	$-0.125519\pi$
$332$		0			0
$333$	−22.9040	+	9.05175i	−1.25513	+	0.496033i
$334$		0			0
$335$	−41.3299	+	34.6799i	−2.25809	+	1.89476i
$336$		0			0
$337$	0.871464	−	4.94232i	0.0474717	−	0.269225i	−0.951829	−	0.306631i	$-0.900798\pi$
$337$	0.871464	−	4.94232i	0.0474717	−	0.269225i	0.999300	+	0.0374058i	$0.0119094\pi$
$338$		0			0
$339$	−20.9787	+	12.4969i	−1.13941	+	0.678738i
$340$		0			0
$341$	−26.6319	−	15.3759i	−1.44220	−	0.832652i
$342$		0			0
$343$	15.9076	−	9.18425i	0.858929	−	0.495903i
$344$		0			0
$345$	−9.29278	+	11.3868i	−0.500307	+	0.613044i
$346$		0			0
$347$	14.1651	−	5.15569i	0.760424	−	0.276772i	0.0674388	−	0.997723i	$-0.478517\pi$
$347$	14.1651	−	5.15569i	0.760424	−	0.276772i	0.692985	+	0.720952i	$0.256295\pi$
$348$		0			0
$349$	−0.0306727	−	0.173953i	−0.00164187	−	0.00931151i	0.983976	−	0.178302i	$-0.0570604\pi$
$349$	−0.0306727	−	0.173953i	−0.00164187	−	0.00931151i	−0.985618	+	0.168990i	$0.945949\pi$
$350$		0			0
$351$	3.37076	−	1.38562i	0.179918	−	0.0739591i
$352$		0			0
$353$	4.03523	−	0.711520i	0.214774	−	0.0378704i	−0.0652259	−	0.997871i	$-0.520777\pi$
$353$	4.03523	−	0.711520i	0.214774	−	0.0378704i	0.280000	+	0.960000i	$0.409666\pi$
$354$		0			0
$355$	−14.5056	−	39.8538i	−0.769877	−	2.11522i
$356$		0			0
$357$	−16.7453	+	6.35493i	−0.886254	+	0.336339i
$358$		0			0
$359$	0.130804	+	0.226558i	0.00690355	+	0.0119573i	0.869457	−	0.494009i	$-0.164469\pi$
$359$	0.130804	+	0.226558i	0.00690355	+	0.0119573i	−0.862553	+	0.505967i	$0.831136\pi$
$360$		0			0
$361$	−7.73689	+	13.4007i	−0.407205	+	0.705300i
$362$		0			0
$363$	−2.23816	+	4.00178i	−0.117473	+	0.210039i
$364$		0			0
$365$	22.4407	+	3.95690i	1.17460	+	0.207114i
$366$		0			0
$367$	−9.25704	−	11.0321i	−0.483214	−	0.575872i	0.468264	−	0.883588i	$-0.344880\pi$
$367$	−9.25704	−	11.0321i	−0.483214	−	0.575872i	−0.951478	+	0.307717i	$0.900435\pi$
$368$		0			0
$369$	12.4992	+	14.0959i	0.650681	+	0.733806i
$370$		0			0
$371$	−1.28603	−	0.468077i	−0.0667674	−	0.0243013i
$372$		0			0
$373$	0.506826	+	0.425278i	0.0262425	+	0.0220200i	0.655815	−	0.754922i	$-0.272325\pi$
$373$	0.506826	+	0.425278i	0.0262425	+	0.0220200i	−0.629572	+	0.776942i	$0.716770\pi$
$374$		0			0
$375$	−13.7619	−	15.9534i	−0.710661	−	0.823830i
$376$		0			0
$377$		−	3.95259i		−	0.203569i
$378$		0			0
$379$			1.73288i			0.0890121i	0.999009	+	0.0445061i	$0.0141714\pi$
$379$			1.73288i			0.0890121i	−0.999009	+	0.0445061i	$0.985829\pi$
$380$		0			0
$381$	−12.0049	+	2.28615i	−0.615028	+	0.117123i
$382$		0			0
$383$	−17.1332	−	14.3765i	−0.875466	−	0.734603i	0.0897757	−	0.995962i	$-0.471385\pi$
$383$	−17.1332	−	14.3765i	−0.875466	−	0.734603i	−0.965242	+	0.261359i	$0.915829\pi$
$384$		0			0
$385$	15.9678	+	5.81179i	0.813792	+	0.296196i
$386$		0			0
$387$	0.721026	+	26.4058i	0.0366518	+	1.34228i
$388$		0			0
$389$	2.05959	+	2.45453i	0.104426	+	0.124450i	0.815726	−	0.578439i	$-0.196338\pi$
$389$	2.05959	+	2.45453i	0.104426	+	0.124450i	−0.711300	+	0.702888i	$0.751893\pi$
$390$		0			0
$391$	14.6974	+	2.59154i	0.743277	+	0.131060i
$392$		0			0
$393$	−25.2329	+	0.344435i	−1.27283	+	0.0173745i
$394$		0			0
$395$	8.30181	−	14.3791i	0.417709	−	0.723494i
$396$		0			0
$397$	6.32972	+	10.9634i	0.317680	+	0.550237i	0.980003	−	0.198981i	$-0.0637630\pi$
$397$	6.32972	+	10.9634i	0.317680	+	0.550237i	−0.662324	+	0.749218i	$0.730430\pi$
$398$		0			0
$399$	−0.838985	+	5.16979i	−0.0420018	+	0.258813i
$400$		0			0
$401$	−4.72777	−	12.9894i	−0.236094	−	0.648662i	−0.999994	−	0.00332813i	$-0.998941\pi$
$401$	−4.72777	−	12.9894i	−0.236094	−	0.648662i	0.763901	−	0.645334i	$-0.223282\pi$
$402$		0			0
$403$	7.34949	−	1.29591i	0.366104	−	0.0645540i
$404$		0			0
$405$	29.3128	+	14.8531i	1.45656	+	0.738055i
$406$		0			0
$407$	−4.11993	−	23.3653i	−0.204217	−	1.15817i
$408$		0			0
$409$	35.2902	−	12.8446i	1.74499	−	0.635124i	0.745482	−	0.666526i	$-0.232219\pi$
$409$	35.2902	−	12.8446i	1.74499	−	0.635124i	0.999507	+	0.0314018i	$0.00999714\pi$
$410$		0			0
$411$	24.8336	+	4.03015i	1.22495	+	0.198793i
$412$		0			0
$413$	−8.27323	+	4.77655i	−0.407099	+	0.235039i
$414$		0			0
$415$	−23.3629	−	13.4885i	−1.14684	−	0.662127i
$416$		0			0
$417$	−0.217277	−	15.9175i	−0.0106401	−	0.779482i
$418$		0			0
$419$	−6.05967	+	34.3661i	−0.296034	+	1.67889i	0.366934	+	0.930247i	$0.380407\pi$
$419$	−6.05967	+	34.3661i	−0.296034	+	1.67889i	−0.662969	+	0.748647i	$0.730704\pi$
$420$		0			0
$421$	−3.66182	+	3.07264i	−0.178466	+	0.149751i	−0.727645	−	0.685954i	$-0.759385\pi$
$421$	−3.66182	+	3.07264i	−0.178466	+	0.149751i	0.549179	+	0.835705i	$0.314941\pi$
$422$		0			0
$423$	−2.79847	−	4.55524i	−0.136066	−	0.221484i
$424$		0			0
$425$	−18.2988	+	50.2755i	−0.887621	+	2.43872i
$426$		0			0
$427$	−10.9707	+	13.0744i	−0.530910	+	0.632714i
$428$		0			0
$429$	0.656808	+	3.44897i	0.0317110	+	0.166518i
$430$		0			0
$431$	−27.7539			−1.33686			−0.668430	−	0.743775i	$-0.733033\pi$
$431$	−27.7539			−1.33686			−0.668430	+	0.743775i	$0.733033\pi$
$432$		0			0
$433$	2.25395			0.108318			0.0541589	−	0.998532i	$-0.482752\pi$
$433$	2.25395			0.108318			0.0541589	+	0.998532i	$0.482752\pi$
$434$		0			0
$435$	26.9863	−	23.2792i	1.29389	−	1.11615i
$436$		0			0
$437$	2.80519	−	3.34310i	0.134191	−	0.159922i
$438$		0			0
$439$	5.90435	−	16.2221i	0.281799	−	0.774237i	−0.715349	−	0.698767i	$-0.753732\pi$
$439$	5.90435	−	16.2221i	0.281799	−	0.774237i	0.997148	−	0.0754693i	$-0.0240455\pi$
$440$		0			0
$441$	2.65032	+	12.9526i	0.126206	+	0.616789i
$442$		0			0
$443$	−5.44673	+	4.57035i	−0.258782	+	0.217144i	−0.762943	−	0.646466i	$-0.776246\pi$
$443$	−5.44673	+	4.57035i	−0.258782	+	0.217144i	0.504161	+	0.863610i	$0.331802\pi$
$444$		0			0
$445$	−4.40936	+	25.0067i	−0.209024	+	1.18543i
$446$		0			0
$447$	−1.90534	−	1.06564i	−0.0901194	−	0.0504031i
$448$		0			0
$449$	15.7138	+	9.07236i	0.741579	+	0.428151i	0.822643	−	0.568558i	$-0.192499\pi$
$449$	15.7138	+	9.07236i	0.741579	+	0.428151i	−0.0810641	+	0.996709i	$0.525832\pi$
$450$		0			0
$451$	−15.7178	+	9.07470i	−0.740124	+	0.427311i
$452$		0			0
$453$	−7.40949	−	19.5240i	−0.348128	−	0.917319i
$454$		0			0
$455$	−3.87506	+	1.41041i	−0.181666	+	0.0661209i
$456$		0			0
$457$	−4.70335	−	26.6740i	−0.220014	−	1.24776i	−0.871991	−	0.489521i	$-0.837172\pi$
$457$	−4.70335	−	26.6740i	−0.220014	−	1.24776i	0.651978	−	0.758238i	$-0.273939\pi$
$458$		0			0
$459$	−1.36597	−	33.3399i	−0.0637581	−	1.55617i
$460$		0			0
$461$	12.6352	−	2.22793i	0.588482	−	0.103765i	0.128525	−	0.991706i	$-0.458976\pi$
$461$	12.6352	−	2.22793i	0.588482	−	0.103765i	0.459957	+	0.887941i	$0.347865\pi$
$462$		0			0
$463$	0.136338	+	0.374586i	0.00633617	+	0.0174085i	0.942820	−	0.333301i	$-0.108163\pi$
$463$	0.136338	+	0.374586i	0.00633617	+	0.0174085i	−0.936484	+	0.350710i	$0.885940\pi$
$464$		0			0
$465$	52.1334	+	42.5461i	2.41763	+	1.97303i
$466$		0			0
$467$	−4.12333	−	7.14182i	−0.190805	−	0.330484i	0.754712	−	0.656056i	$-0.227777\pi$
$467$	−4.12333	−	7.14182i	−0.190805	−	0.330484i	−0.945517	+	0.325572i	$0.894443\pi$
$468$		0			0
$469$	−11.8972	+	20.6065i	−0.549360	+	0.951519i
$470$		0			0
$471$	−3.24438	−	5.44637i	−0.149493	−	0.250956i
$472$		0			0
$473$	−25.0615	−	4.41902i	−1.15233	−	0.203187i
$474$		0			0
$475$	10.0565	+	11.9848i	0.461423	+	0.549902i
$476$		0			0
$477$	1.58497	−	1.99717i	0.0725709	−	0.0914439i
$478$		0			0
$479$	23.0690	+	8.39642i	1.05405	+	0.383642i	0.810189	−	0.586169i	$-0.199364\pi$
$479$	23.0690	+	8.39642i	1.05405	+	0.383642i	0.243859	+	0.969811i	$0.421587\pi$
$480$		0			0
$481$	4.41071	+	3.70102i	0.201111	+	0.168752i
$482$		0			0
$483$	−2.13361	+	6.12073i	−0.0970827	+	0.278503i
$484$		0			0
$485$		−	6.44797i		−	0.292787i
$486$		0			0
$487$		−	5.60176i		−	0.253840i	−0.991913	−	0.126920i	$-0.959491\pi$
$487$		−	5.60176i		−	0.253840i	0.991913	−	0.126920i	$-0.0405092\pi$
$488$		0			0
$489$	−1.39221	+	3.99386i	−0.0629580	+	0.180609i
$490$		0			0
$491$	27.3869	+	22.9803i	1.23595	+	1.03709i	0.997829	+	0.0658512i	$0.0209763\pi$
$491$	27.3869	+	22.9803i	1.23595	+	1.03709i	0.238122	+	0.971235i	$0.423468\pi$
$492$		0			0
$493$	−34.0067	−	12.3774i	−1.53158	−	0.557451i
$494$		0			0
$495$	−19.6795	+	24.7974i	−0.884528	+	1.11456i
$496$		0			0
$497$	−12.0231	−	14.3285i	−0.539308	−	0.642722i
$498$		0			0
$499$	40.9591	+	7.22219i	1.83358	+	0.323310i	0.980205	−	0.197987i	$-0.0634404\pi$
$499$	40.9591	+	7.22219i	1.83358	+	0.323310i	0.853376	+	0.521297i	$0.174551\pi$
$500$		0			0
$501$	−4.70879	−	7.90469i	−0.210373	−	0.353156i
$502$		0			0
$503$	−10.1863	+	17.6431i	−0.454183	+	0.786668i	−0.998641	−	0.0521202i	$-0.983402\pi$
$503$	−10.1863	+	17.6431i	−0.454183	+	0.786668i	0.544458	+	0.838788i	$0.316735\pi$
$504$		0			0
$505$	−20.7614	−	35.9597i	−0.923868	−	1.60019i
$506$		0			0
$507$	16.7846	+	13.6979i	0.745430	+	0.608347i
$508$		0			0
$509$	2.66835	+	7.33124i	0.118273	+	0.324952i	0.984676	−	0.174393i	$-0.0557963\pi$
$509$	2.66835	+	7.33124i	0.118273	+	0.324952i	−0.866403	+	0.499345i	$0.833574\pi$
$510$		0			0
$511$	9.89692	−	1.74509i	0.437814	−	0.0771984i
$512$		0			0
$513$	−8.64283	−	4.52871i	−0.381590	−	0.199947i
$514$		0			0
$515$	−10.4880	−	59.4805i	−0.462157	−	2.62102i
$516$		0			0
$517$	4.83976	−	1.76153i	0.212852	−	0.0774719i
$518$		0			0
$519$	−16.1207	−	42.4781i	−0.707620	−	1.86458i
$520$		0			0
$521$	10.5688	−	6.10193i	0.463030	−	0.267330i	−0.250288	−	0.968172i	$-0.580525\pi$
$521$	10.5688	−	6.10193i	0.463030	−	0.267330i	0.713317	+	0.700841i	$0.247192\pi$
$522$		0			0
$523$	−1.11506	−	0.643783i	−0.0487584	−	0.0281507i	0.475423	−	0.879758i	$-0.342295\pi$
$523$	−1.11506	−	0.643783i	−0.0487584	−	0.0281507i	−0.524181	+	0.851607i	$0.675628\pi$
$524$		0			0
$525$	−20.2809	−	11.3430i	−0.885131	−	0.495047i
$526$		0			0
$527$	11.8651	−	67.2905i	0.516853	−	2.93122i
$528$		0			0
$529$	−13.4815	+	11.3124i	−0.586154	+	0.491841i
$530$		0			0
$531$	−3.56779	−	17.4364i	−0.154829	−	0.756674i
$532$		0			0
$533$	1.50643	−	4.13888i	0.0652507	−	0.179275i
$534$		0			0
$535$	−39.1650	+	46.6750i	−1.69325	+	2.01794i
$536$		0			0
$537$	−14.2374	+	12.2816i	−0.614389	+	0.529990i
$538$		0			0
$539$	−12.7367			−0.548607
$540$		0			0
$541$	−33.3756			−1.43493			−0.717465	−	0.696594i	$-0.754698\pi$
$541$	−33.3756			−1.43493			−0.717465	+	0.696594i	$0.754698\pi$
$542$		0			0
$543$	1.37787	+	7.23537i	0.0591302	+	0.310500i
$544$		0			0
$545$	23.9692	−	28.5654i	1.02673	−	1.22361i
$546$		0			0
$547$	−15.6515	+	43.0020i	−0.669208	+	1.83863i	−0.139980	+	0.990154i	$0.544704\pi$
$547$	−15.6515	+	43.0020i	−0.669208	+	1.83863i	−0.529228	+	0.848480i	$0.677518\pi$
$548$		0			0
$549$	−16.6442	−	27.0928i	−0.710357	−	1.15629i
$550$		0			0
$551$	−8.10663	+	6.80227i	−0.345354	+	0.289786i
$552$		0			0
$553$	1.27156	−	7.21136i	0.0540721	−	0.306658i
$554$		0			0
$555$	0.708606	+	51.9116i	0.0300786	+	2.20353i
$556$		0			0
$557$	18.3056	+	10.5687i	0.775631	+	0.447811i	0.834880	−	0.550432i	$-0.185537\pi$
$557$	18.3056	+	10.5687i	0.775631	+	0.447811i	−0.0592484	+	0.998243i	$0.518870\pi$
$558$		0			0
$559$	5.34837	−	3.08788i	0.226212	−	0.130603i
$560$		0			0
$561$	31.7305	+	5.14942i	1.33966	+	0.217409i
$562$		0			0
$563$	−14.9675	+	5.44771i	−0.630803	+	0.229594i	−0.637581	−	0.770383i	$-0.720065\pi$
$563$	−14.9675	+	5.44771i	−0.630803	+	0.229594i	0.00677752	+	0.999977i	$0.497843\pi$
$564$		0			0
$565$	8.93869	+	50.6938i	0.376053	+	2.13270i
$566$		0			0
$567$	14.3885	+	1.73401i	0.604259	+	0.0728215i
$568$		0			0
$569$	5.38391	−	0.949329i	0.225705	−	0.0397979i	−0.0596516	−	0.998219i	$-0.518999\pi$
$569$	5.38391	−	0.949329i	0.225705	−	0.0397979i	0.285357	+	0.958421i	$0.407888\pi$
$570$		0			0
$571$	5.95709	+	16.3670i	0.249297	+	0.684937i	0.999713	+	0.0239711i	$0.00763096\pi$
$571$	5.95709	+	16.3670i	0.249297	+	0.684937i	−0.750416	+	0.660966i	$0.770147\pi$
$572$		0			0
$573$	2.00347	−	12.3453i	0.0836962	−	0.515732i
$574$		0			0
$575$	9.68134	+	16.7686i	0.403740	+	0.699298i
$576$		0			0
$577$	−6.89556	+	11.9435i	−0.287066	+	0.497213i	−0.973108	−	0.230349i	$-0.926013\pi$
$577$	−6.89556	+	11.9435i	−0.287066	+	0.497213i	0.686042	+	0.727562i	$0.259347\pi$
$578$		0			0
$579$	−28.7356	+	0.392247i	−1.19421	+	0.0163012i
$580$		0			0
$581$	−11.7168	−	2.06599i	−0.486096	−	0.0857118i
$582$		0			0
$583$	1.57886	+	1.88162i	0.0653899	+	0.0779286i
$584$		0			0
$585$	−0.209701	−	7.67979i	−0.00867006	−	0.317520i
$586$		0			0
$587$	21.4195	+	7.79604i	0.884075	+	0.321777i	0.743853	−	0.668343i	$-0.232996\pi$
$587$	21.4195	+	7.79604i	0.884075	+	0.321777i	0.140222	+	0.990120i	$0.455218\pi$
$588$		0			0
$589$	−15.3061	−	12.8433i	−0.630676	−	0.529200i
$590$		0			0
$591$	8.55859	−	1.62986i	0.352054	−	0.0670435i
$592$		0			0
$593$		−	34.0284i		−	1.39738i	−0.715426	−	0.698689i	$-0.753767\pi$
$593$		−	34.0284i		−	1.39738i	0.715426	−	0.698689i	$-0.246233\pi$
$594$		0			0
$595$			37.7563i			1.54786i
$596$		0			0
$597$	16.7475	+	19.4145i	0.685431	+	0.794582i
$598$		0			0
$599$	−25.6710	−	21.5405i	−1.04889	−	0.880122i	−0.0559128	−	0.998436i	$-0.517807\pi$
$599$	−25.6710	−	21.5405i	−1.04889	−	0.880122i	−0.992976	+	0.118313i	$0.962251\pi$
$600$		0			0
$601$	33.9607	+	12.3607i	1.38529	+	0.504203i	0.923777	−	0.382931i	$-0.125085\pi$
$601$	33.9607	+	12.3607i	1.38529	+	0.504203i	0.461510	+	0.887135i	$0.347308\pi$
$602$		0			0
$603$	−29.4107	−	33.1678i	−1.19769	−	1.35070i
$604$		0			0
$605$	6.21298	+	7.40434i	0.252594	+	0.301029i
$606$		0			0
$607$	20.9011	+	3.68542i	0.848348	+	0.149587i	0.580889	−	0.813983i	$-0.302705\pi$
$607$	20.9011	+	3.68542i	0.848348	+	0.149587i	0.267459	+	0.963569i	$0.413816\pi$
$608$		0			0
$609$	7.67245	−	13.7181i	0.310904	−	0.555887i
$610$		0			0
$611$	−0.624946	+	1.08244i	−0.0252826	+	0.0437908i
$612$		0			0
$613$	−17.4558	−	30.2343i	−0.705032	−	1.22115i	−0.966680	−	0.255987i	$-0.917599\pi$
$613$	−17.4558	−	30.2343i	−0.705032	−	1.22115i	0.261648	−	0.965163i	$-0.415734\pi$
$614$		0			0
$615$	37.1304	−	14.0912i	1.49724	−	0.568213i
$616$		0			0
$617$	−4.96269	−	13.6349i	−0.199790	−	0.548920i	0.798823	−	0.601566i	$-0.205456\pi$
$617$	−4.96269	−	13.6349i	−0.199790	−	0.548920i	−0.998613	+	0.0526468i	$0.983234\pi$
$618$		0			0
$619$	2.94818	−	0.519843i	0.118497	−	0.0208943i	−0.114085	−	0.993471i	$-0.536394\pi$
$619$	2.94818	−	0.519843i	0.118497	−	0.0208943i	0.232582	+	0.972577i	$0.425283\pi$
$620$		0			0
$621$	−9.56076	−	7.37710i	−0.383660	−	0.296033i
$622$		0			0
$623$	1.94464	+	11.0286i	0.0779103	+	0.441851i
$624$		0			0
$625$	−2.59037	+	0.942816i	−0.103615	+	0.0377126i
$626$		0			0
$627$	5.94338	−	7.28265i	0.237356	−	0.290841i
$628$		0			0
$629$	45.6543	−	26.3585i	1.82036	−	1.05098i
$630$		0			0
$631$	42.0709	+	24.2896i	1.67481	+	0.966955i	0.964882	+	0.262685i	$0.0846080\pi$
$631$	42.0709	+	24.2896i	1.67481	+	0.966955i	0.709933	+	0.704269i	$0.248725\pi$
$632$		0			0
$633$	18.1200	−	10.7940i	0.720204	−	0.429022i
$634$		0			0
$635$	−4.47345	+	25.3702i	−0.177523	+	1.00678i
$636$		0			0
$637$	2.36780	−	1.98682i	0.0938156	−	0.0787206i
$638$		0			0
$639$	32.4079	−	12.8077i	1.28204	−	0.506666i
$640$		0			0
$641$	5.70164	−	15.6651i	0.225201	−	0.618735i	−0.774707	−	0.632321i	$-0.782102\pi$
$641$	5.70164	−	15.6651i	0.225201	−	0.618735i	0.999908	+	0.0135858i	$0.00432462\pi$
$642$		0			0
$643$	24.0202	−	28.6262i	0.947265	−	1.12891i	−0.0442639	−	0.999020i	$-0.514094\pi$
$643$	24.0202	−	28.6262i	0.947265	−	1.12891i	0.991529	−	0.129887i	$-0.0414613\pi$
$644$		0			0
$645$	52.5822	+	18.3295i	2.07042	+	0.721725i
$646$		0			0
$647$	30.1624			1.18580			0.592902	−	0.805274i	$-0.297982\pi$
$647$	30.1624			1.18580			0.592902	+	0.805274i	$0.297982\pi$
$648$		0			0
$649$	17.1457			0.673029
$650$		0			0
$651$	28.0232	+	9.76854i	1.09831	+	0.382859i
$652$		0			0
$653$	−1.61055	+	1.91938i	−0.0630256	+	0.0751110i	−0.796636	−	0.604459i	$-0.793389\pi$
$653$	−1.61055	+	1.91938i	−0.0630256	+	0.0751110i	0.733611	+	0.679570i	$0.237834\pi$
$654$		0			0
$655$	−18.1945	+	49.9888i	−0.710916	+	1.95323i
$656$		0			0
$657$	−2.74666	+	18.5200i	−0.107157	+	0.722536i
$658$		0			0
$659$	−26.7567	+	22.4515i	−1.04229	+	0.874587i	−0.992262	−	0.124161i	$-0.960376\pi$
$659$	−26.7567	+	22.4515i	−1.04229	+	0.874587i	−0.0500301	+	0.998748i	$0.515932\pi$
$660$		0			0
$661$	5.01298	−	28.4300i	0.194982	−	1.10580i	−0.717461	−	0.696598i	$-0.754696\pi$
$661$	5.01298	−	28.4300i	0.194982	−	1.10580i	0.912444	−	0.409202i	$-0.134193\pi$
$662$		0			0
$663$	−6.70210	+	3.99241i	−0.260288	+	0.155052i
$664$		0			0
$665$	9.56154	+	5.52036i	0.370781	+	0.214070i
$666$		0			0
$667$	−11.3424	+	6.54853i	−0.439179	+	0.253560i
$668$		0			0
$669$	10.9707	−	13.4429i	0.424154	−	0.519731i
$670$		0			0
$671$	28.7849	−	10.4769i	1.11123	−	0.404455i
$672$		0			0
$673$	5.70280	+	32.3422i	0.219827	+	1.24670i	0.872331	+	0.488915i	$0.162607\pi$
$673$	5.70280	+	32.3422i	0.219827	+	1.24670i	−0.652504	+	0.757785i	$0.726282\pi$
$674$		0			0
$675$	31.9965	−	29.1617i	1.23155	−	1.12244i
$676$		0			0
$677$	−4.92975	+	0.869249i	−0.189466	+	0.0334079i	−0.267576	−	0.963537i	$-0.586223\pi$
$677$	−4.92975	+	0.869249i	−0.189466	+	0.0334079i	0.0781100	+	0.996945i	$0.475111\pi$
$678$		0			0
$679$	−0.972608	−	2.67222i	−0.0373253	−	0.102550i
$680$		0			0
$681$	16.2691	−	6.17420i	0.623431	−	0.236596i
$682$		0			0
$683$	−15.9017	−	27.5426i	−0.608463	−	1.05389i	−0.991494	−	0.130153i	$-0.958453\pi$
$683$	−15.9017	−	27.5426i	−0.608463	−	1.05389i	0.383031	−	0.923735i	$-0.374880\pi$
$684$		0			0
$685$	26.5176	−	45.9298i	1.01318	−	1.75489i
$686$		0			0
$687$	−9.86193	+	17.6329i	−0.376256	+	0.672736i
$688$		0			0
$689$	−0.587035	−	0.103510i	−0.0223642	−	0.00394342i
$690$		0			0
$691$	−17.8704	−	21.2971i	−0.679822	−	0.810180i	0.310263	−	0.950651i	$-0.399583\pi$
$691$	−17.8704	−	21.2971i	−0.679822	−	0.810180i	−0.990085	+	0.140471i	$0.955138\pi$
$692$		0			0
$693$	−4.41531	+	13.2452i	−0.167724	+	0.503143i
$694$		0			0
$695$	−31.5341	−	11.4775i	−1.19615	−	0.435365i
$696$		0			0
$697$	−30.8921	−	25.9216i	−1.17012	−	0.981849i
$698$		0			0
$699$	14.5612	+	16.8800i	0.550756	+	0.638461i
$700$		0			0
$701$			50.2148i			1.89659i	0.317393	+	0.948294i	$0.397193\pi$
$701$			50.2148i			1.89659i	−0.317393	+	0.948294i	$0.602807\pi$
$702$		0			0
$703$		−	15.4155i		−	0.581408i
$704$		0			0
$705$	−11.0710	+	2.10832i	−0.416959	+	0.0794038i
$706$		0			0
$707$	−14.0282	−	11.7711i	−0.527586	−	0.442697i
$708$		0			0
$709$	1.61463	+	0.587679i	0.0606388	+	0.0220707i	0.372161	−	0.928168i	$-0.378617\pi$
$709$	1.61463	+	0.587679i	0.0606388	+	0.0220707i	−0.311523	+	0.950239i	$0.600839\pi$
$710$		0			0
$711$	11.9963	+	6.49607i	0.449895	+	0.243622i
$712$		0			0
$713$	−15.8951	−	18.9431i	−0.595278	−	0.709425i
$714$		0			0
$715$	7.28880	+	1.28521i	0.272586	+	0.0480642i
$716$		0			0
$717$	6.99361	−	0.0954644i	0.261181	−	0.00356518i
$718$		0			0
$719$	−24.3767	+	42.2217i	−0.909099	+	1.57461i	−0.0937803	+	0.995593i	$0.529895\pi$
$719$	−24.3767	+	42.2217i	−0.909099	+	1.57461i	−0.815319	+	0.579013i	$0.803438\pi$
$720$		0			0
$721$	−13.3185	−	23.0684i	−0.496008	−	0.859112i
$722$		0			0
$723$	5.96189	−	36.7369i	0.221725	−	1.36626i
$724$		0			0
$725$	−16.0586	−	44.1207i	−0.596402	−	1.63860i
$726$		0			0
$727$	−39.8914	+	7.03393i	−1.47949	+	0.260874i	−0.854374	−	0.519659i	$-0.826059\pi$
$727$	−39.8914	+	7.03393i	−1.47949	+	0.260874i	−0.625115	+	0.780532i	$0.714948\pi$
$728$		0			0
$729$	−11.5419	+	24.4087i	−0.427479	+	0.904025i
$730$		0			0
$731$	−9.81877	−	55.6850i	−0.363160	−	2.05959i
$732$		0			0
$733$	16.7735	−	6.10505i	0.619543	−	0.225495i	−0.0131304	−	0.999914i	$-0.504180\pi$
$733$	16.7735	−	6.10505i	0.619543	−	0.225495i	0.632674	+	0.774418i	$0.281957\pi$
$734$		0			0
$735$	27.5104	+	4.46455i	1.01473	+	0.164677i
$736$		0			0
$737$	36.9842	−	21.3528i	1.36233	−	0.786541i
$738$		0			0
$739$	−1.22996	−	0.710118i	−0.0452448	−	0.0261221i	0.477207	−	0.878791i	$-0.341649\pi$
$739$	−1.22996	−	0.710118i	−0.0452448	−	0.0261221i	−0.522452	+	0.852669i	$0.674983\pi$
$740$		0			0
$741$	0.0311361	+	2.28099i	0.00114381	+	0.0837944i
$742$		0			0
$743$	1.09307	−	6.19911i	0.0401009	−	0.227423i	−0.958170	−	0.286198i	$-0.907608\pi$
$743$	1.09307	−	6.19911i	0.0401009	−	0.227423i	0.998271	+	0.0587751i	$0.0187195\pi$
$744$		0			0
$745$	−3.52538	+	2.95814i	−0.129160	+	0.108378i
$746$		0			0
$747$	10.5546	−	19.4912i	0.386174	−	0.713146i
$748$		0			0
$749$	−9.19063	+	25.2511i	−0.335818	+	0.922653i
$750$		0			0
$751$	−11.8427	+	14.1136i	−0.432146	+	0.515012i	−0.937540	−	0.347877i	$-0.886903\pi$
$751$	−11.8427	+	14.1136i	−0.432146	+	0.515012i	0.505394	+	0.862889i	$0.331347\pi$
$752$		0			0
$753$	−1.37563	−	7.22361i	−0.0501308	−	0.263243i
$754$		0			0
$755$	−44.0217			−1.60211
$756$		0			0
$757$	10.3039			0.374500			0.187250	−	0.982312i	$-0.440043\pi$
$757$	10.3039			0.374500			0.187250	+	0.982312i	$0.440043\pi$
$758$		0			0
$759$	8.80902	−	7.59893i	0.319747	−	0.275824i
$760$		0			0
$761$	−12.5156	+	14.9156i	−0.453692	+	0.540689i	−0.943601	−	0.331085i	$-0.892585\pi$
$761$	−12.5156	+	14.9156i	−0.453692	+	0.540689i	0.489909	+	0.871773i	$0.337030\pi$
$762$		0			0
$763$	5.62472	−	15.4538i	0.203629	−	0.559465i
$764$		0			0
$765$	−66.7308	−	22.2448i	−2.41266	−	0.804263i
$766$		0			0
$767$	−3.18746	+	2.67460i	−0.115093	+	0.0965741i
$768$		0			0
$769$	−4.85410	+	27.5290i	−0.175043	+	0.992721i	0.763050	+	0.646339i	$0.223701\pi$
$769$	−4.85410	+	27.5290i	−0.175043	+	0.992721i	−0.938094	+	0.346382i	$0.887410\pi$
$770$		0			0
$771$	7.86319	+	4.39782i	0.283186	+	0.158384i
$772$		0			0
$773$	15.1159	+	8.72717i	0.543681	+	0.313894i	0.746569	−	0.665307i	$-0.231700\pi$
$773$	15.1159	+	8.72717i	0.543681	+	0.313894i	−0.202888	+	0.979202i	$0.565033\pi$
$774$		0			0
$775$	76.7733	−	44.3251i	2.75778	−	1.59220i
$776$		0			0
$777$	8.12399	+	21.4067i	0.291446	+	0.767963i
$778$		0			0
$779$	−11.0812	+	4.03323i	−0.397025	+	0.144505i
$780$		0			0
$781$	5.82947	+	33.0606i	0.208595	+	1.18300i
$782$		0			0
$783$	19.7252	+	21.6427i	0.704921	+	0.773446i
$784$		0			0
$785$	−13.1609	+	2.32061i	−0.469731	+	0.0828263i
$786$		0			0
$787$	−0.407887	−	1.12066i	−0.0145396	−	0.0399472i	0.932211	−	0.361916i	$-0.117877\pi$
$787$	−0.407887	−	1.12066i	−0.0145396	−	0.0399472i	−0.946750	+	0.321969i	$0.895655\pi$
$788$		0			0
$789$	32.7876	+	26.7581i	1.16727	+	0.952612i
$790$		0			0
$791$	11.3511	+	19.6606i	0.403598	+	0.699052i
$792$		0			0
$793$	−3.71693	+	6.43791i	−0.131992	+	0.228617i
$794$		0			0
$795$	−2.75068	−	4.61760i	−0.0975567	−	0.163770i
$796$		0			0
$797$	−32.9150	−	5.80381i	−1.16591	−	0.205581i	−0.442999	−	0.896522i	$-0.646085\pi$
$797$	−32.9150	−	5.80381i	−1.16591	−	0.205581i	−0.722911	+	0.690941i	$0.757196\pi$
$798$		0			0
$799$	7.35591	+	8.76644i	0.260234	+	0.310134i
$800$		0			0
$801$	−20.6378	−	3.06073i	−0.729199	−	0.108146i
$802$		0			0
$803$	−16.9491	−	6.16896i	−0.598120	−	0.217698i
$804$		0			0
$805$	10.4674	+	8.78318i	0.368927	+	0.309566i
$806$		0			0
$807$	0.277009	−	0.794660i	0.00975117	−	0.0279733i
$808$		0			0
$809$			8.30675i			0.292050i	0.989281	+	0.146025i	$0.0466480\pi$
$809$			8.30675i			0.292050i	−0.989281	+	0.146025i	$0.953352\pi$
$810$		0			0
$811$		−	12.7345i		−	0.447168i	−0.974685	−	0.223584i	$-0.928224\pi$
$811$		−	12.7345i		−	0.447168i	0.974685	−	0.223584i	$-0.0717757\pi$
$812$		0			0
$813$	8.83459	−	25.3439i	0.309843	−	0.888850i
$814$		0			0
$815$	6.83012	+	5.73115i	0.239249	+	0.200753i
$816$		0			0
$817$	−15.5375	−	5.65518i	−0.543588	−	0.197850i
$818$		0			0
$819$	−1.24532	−	3.15109i	−0.0435150	−	0.110108i
$820$		0			0
$821$	−36.4313	−	43.4172i	−1.27146	−	1.51527i	−0.748928	−	0.662652i	$-0.769431\pi$
$821$	−36.4313	−	43.4172i	−1.27146	−	1.51527i	−0.522535	−	0.852618i	$-0.675014\pi$
$822$		0			0
$823$	−26.7109	−	4.70985i	−0.931082	−	0.164175i	−0.312520	−	0.949911i	$-0.601173\pi$
$823$	−26.7109	−	4.70985i	−0.931082	−	0.164175i	−0.618562	+	0.785736i	$0.712284\pi$
$824$		0			0
$825$	21.3441	+	35.8306i	0.743106	+	1.24746i
$826$		0			0
$827$	−8.85977	+	15.3456i	−0.308084	+	0.533618i	−0.977943	−	0.208871i	$-0.933021\pi$
$827$	−8.85977	+	15.3456i	−0.308084	+	0.533618i	0.669859	+	0.742488i	$0.266355\pi$
$828$		0			0
$829$	12.5854	+	21.7986i	0.437110	+	0.757096i	0.997465	−	0.0711559i	$-0.0226688\pi$
$829$	12.5854	+	21.7986i	0.437110	+	0.757096i	−0.560355	+	0.828252i	$0.689335\pi$
$830$		0			0
$831$	−19.6901	−	16.0691i	−0.683042	−	0.557432i
$832$		0			0
$833$	−9.67919	−	26.5933i	−0.335364	−	0.921405i
$834$		0			0
$835$	−19.1012	+	3.36806i	−0.661026	+	0.116557i
$836$		0			0
$837$	−33.7754	+	43.7731i	−1.16745	+	1.51302i
$838$		0			0
$839$	2.05100	+	11.6318i	0.0708085	+	0.401575i	0.999526	+	0.0307868i	$0.00980130\pi$
$839$	2.05100	+	11.6318i	0.0708085	+	0.401575i	−0.928717	+	0.370788i	$0.879088\pi$
$840$		0			0
$841$	2.59245	−	0.943576i	0.0893949	−	0.0325371i
$842$		0			0
$843$	0.700007	+	1.84452i	0.0241095	+	0.0635287i
$844$		0			0
$845$	39.5513	−	22.8350i	1.36061	−	0.785547i
$846$		0			0
$847$	3.69170	+	2.13140i	0.126848	+	0.0732359i
$848$		0			0
$849$	6.46917	+	3.61815i	0.222021	+	0.124175i
$850$		0			0
$851$	3.31296	−	18.7887i	0.113567	−	0.644069i
$852$		0			0
$853$	3.75866	−	3.15389i	0.128694	−	0.107987i	−0.576169	−	0.817331i	$-0.695453\pi$
$853$	3.75866	−	3.15389i	0.128694	−	0.107987i	0.704863	+	0.709344i	$0.251008\pi$
$854$		0			0
$855$	−15.3901	+	13.6467i	−0.526330	+	0.466708i
$856$		0			0
$857$	−3.12251	+	8.57903i	−0.106663	+	0.293054i	−0.981530	−	0.191309i	$-0.938727\pi$
$857$	−3.12251	+	8.57903i	−0.106663	+	0.293054i	0.874867	+	0.484364i	$0.160949\pi$
$858$		0			0
$859$	−5.34842	+	6.37400i	−0.182486	+	0.217478i	−0.849530	−	0.527540i	$-0.823115\pi$
$859$	−5.34842	+	6.37400i	−0.182486	+	0.217478i	0.667045	+	0.745018i	$0.267559\pi$
$860$		0			0
$861$	13.2624	−	11.4405i	0.451981	−	0.389892i
$862$		0			0
$863$	2.59045			0.0881800			0.0440900	−	0.999028i	$-0.485961\pi$
$863$	2.59045			0.0881800			0.0440900	+	0.999028i	$0.485961\pi$
$864$		0			0
$865$	−95.7772			−3.25652
$866$		0			0
$867$	7.85347	+	41.2395i	0.266718	+	1.40057i
$868$		0			0
$869$	−8.44783	+	10.0677i	−0.286573	+	0.341525i
$870$		0			0
$871$	−3.54464	+	9.73881i	−0.120105	+	0.329987i
$872$		0			0
$873$	5.29593	−	0.144608i	0.179240	−	0.00489425i
$874$		0			0
$875$	−15.0051	+	12.5908i	−0.507265	+	0.425646i
$876$		0			0
$877$	5.82942	−	33.0603i	0.196846	−	1.11637i	−0.712920	−	0.701245i	$-0.752628\pi$
$877$	5.82942	−	33.0603i	0.196846	−	1.11637i	0.909766	−	0.415122i	$-0.136261\pi$
$878$		0			0
$879$	−0.158680	−	11.6247i	−0.00535214	−	0.392091i
$880$		0			0
$881$	23.6202	+	13.6372i	0.795786	+	0.459447i	0.841996	−	0.539484i	$-0.181381\pi$
$881$	23.6202	+	13.6372i	0.795786	+	0.459447i	−0.0462093	+	0.998932i	$0.514714\pi$
$882$		0			0
$883$	−46.2713	+	26.7147i	−1.55715	+	0.899022i	−0.559624	+	0.828746i	$0.689055\pi$
$883$	−46.2713	+	26.7147i	−1.55715	+	0.899022i	−0.997528	+	0.0702756i	$0.977612\pi$
$884$		0			0
$885$	−37.0337	−	6.01005i	−1.24487	−	0.202026i
$886$		0			0
$887$	−21.1663	+	7.70392i	−0.710696	+	0.258672i	−0.671971	−	0.740578i	$-0.734552\pi$
$887$	−21.1663	+	7.70392i	−0.710696	+	0.258672i	−0.0387255	+	0.999250i	$0.512330\pi$
$888$		0			0
$889$	1.97290	+	11.1889i	0.0661690	+	0.375263i
$890$		0			0
$891$	−20.8083	−	15.6073i	−0.697105	−	0.522864i
$892$		0			0
$893$	3.29555	−	0.581095i	0.110281	−	0.0194456i
$894$		0			0
$895$	13.5566	+	37.2464i	0.453147	+	1.24501i
$896$		0			0
$897$	−0.452260	+	2.78681i	−0.0151005	+	0.0930488i
$898$		0			0
$899$	29.9818	+	51.9300i	0.999949	+	1.73196i
$900$		0			0
$901$	−2.72884	+	4.72650i	−0.0909110	+	0.157462i
$902$		0			0
$903$	24.5564	−	0.335200i	0.817185	−	0.0111548i
$904$		0			0
$905$	15.2907	+	2.69616i	0.508280	+	0.0896234i
$906$		0			0
$907$	1.59486	+	1.90068i	0.0529566	+	0.0631112i	0.791873	−	0.610686i	$-0.209106\pi$
$907$	1.59486	+	1.90068i	0.0529566	+	0.0631112i	−0.738916	+	0.673798i	$0.764662\pi$
$908$		0			0
$909$	29.0693	−	17.8585i	0.964168	−	0.592328i
$910$		0			0
$911$	35.5999	+	12.9573i	1.17948	+	0.429294i	0.856017	−	0.516948i	$-0.172932\pi$
$911$	35.5999	+	12.9573i	1.17948	+	0.429294i	0.323459	+	0.946242i	$0.395154\pi$
$912$		0			0
$913$	16.3578	+	13.7258i	0.541364	+	0.454258i
$914$		0			0
$915$	−65.8460	+	12.5394i	−2.17680	+	0.414540i
$916$		0			0
$917$			23.4612i			0.774758i
$918$		0			0
$919$		−	20.6611i		−	0.681547i	−0.940145	−	0.340773i	$-0.889311\pi$
$919$		−	20.6611i		−	0.681547i	0.940145	−	0.340773i	$-0.110689\pi$
$920$		0			0
$921$	−12.3744	−	14.3449i	−0.407750	−	0.472682i
$922$		0			0
$923$	−6.24091	−	5.23674i	−0.205422	−	0.172370i
$924$		0			0
$925$	64.2709	+	23.3927i	2.11321	+	0.769147i
$926$		0			0
$927$	48.6181	−	9.94813i	1.59683	−	0.326739i
$928$		0			0
$929$	3.39557	+	4.04669i	0.111405	+	0.132768i	0.818865	−	0.573986i	$-0.194604\pi$
$929$	3.39557	+	4.04669i	0.111405	+	0.132768i	−0.707460	+	0.706753i	$0.750159\pi$
$930$		0			0
$931$	−8.14979	−	1.43703i	−0.267099	−	0.0470967i
$932$		0			0
$933$	−9.73019	+	17.3973i	−0.318552	+	0.569563i
$934$		0			0
$935$	33.8822	−	58.6856i	1.10807	−	1.91923i
$936$		0			0
$937$	−4.49555	−	7.78652i	−0.146863	−	0.254375i	0.783203	−	0.621766i	$-0.213584\pi$
$937$	−4.49555	−	7.78652i	−0.146863	−	0.254375i	−0.930067	+	0.367391i	$0.880251\pi$
$938$		0			0
$939$	−11.6473	+	4.42022i	−0.380095	+	0.144248i
$940$		0			0
$941$	11.3041	+	31.0577i	0.368502	+	1.01245i	0.975931	+	0.218078i	$0.0699786\pi$
$941$	11.3041	+	31.0577i	0.368502	+	1.01245i	−0.607429	+	0.794374i	$0.707799\pi$
$942$		0			0
$943$	−14.3728	+	2.53430i	−0.468041	+	0.0825283i
$944$		0			0
$945$	14.1796	−	27.0611i	0.461262	−	0.880296i
$946$		0			0
$947$	−3.46718	−	19.6634i	−0.112668	−	0.638973i	−0.987878	−	0.155230i	$-0.950388\pi$
$947$	−3.46718	−	19.6634i	−0.112668	−	0.638973i	0.875210	−	0.483743i	$-0.160723\pi$
$948$		0			0
$949$	4.11321	−	1.49709i	0.133520	−	0.0485975i
$950$		0			0
$951$	−17.8932	+	21.9252i	−0.580227	+	0.710973i
$952$		0			0
$953$	−30.9122	+	17.8471i	−1.00134	+	0.578126i	−0.908645	−	0.417569i	$-0.862882\pi$
$953$	−30.9122	+	17.8471i	−1.00134	+	0.578126i	−0.0926976	+	0.995694i	$0.529549\pi$
$954$		0			0
$955$	−22.8327	−	13.1824i	−0.738847	−	0.426574i
$956$		0			0
$957$	−24.2361	+	14.4373i	−0.783440	+	0.466692i
$958$		0			0
$959$	4.06160	−	23.0345i	0.131156	−	0.743823i
$960$		0			0
$961$	−62.9818	+	52.8480i	−2.03167	+	1.70477i
$962$		0			0
$963$	−39.2141	−	31.1207i	−1.26366	−	1.00285i
$964$		0			0
$965$	−20.7201	+	56.9279i	−0.667002	+	1.83257i
$966$		0			0
$967$	5.26542	−	6.27508i	0.169324	−	0.201793i	−0.674709	−	0.738084i	$-0.735731\pi$
$967$	5.26542	−	6.27508i	0.169324	−	0.201793i	0.844033	+	0.536291i	$0.180175\pi$
$968$		0			0
$969$	19.7224	+	6.87498i	0.633573	+	0.220856i
$970$		0			0
$971$	1.68822			0.0541777			0.0270888	−	0.999633i	$-0.491376\pi$
$971$	1.68822			0.0541777			0.0270888	+	0.999633i	$0.491376\pi$
$972$		0			0
$973$	−14.7999			−0.474461
$974$		0			0
$975$	−9.55724	−	3.33154i	−0.306077	−	0.106695i
$976$		0			0
$977$	−2.53912	+	3.02601i	−0.0812337	+	0.0968105i	−0.805130	−	0.593098i	$-0.797905\pi$
$977$	−2.53912	+	3.02601i	−0.0812337	+	0.0968105i	0.723897	+	0.689908i	$0.242349\pi$
$978$		0			0
$979$	6.87436	−	18.8872i	0.219706	−	0.603636i
$980$		0			0
$981$	23.9993	+	19.0461i	0.766238	+	0.608095i
$982$		0			0
$983$	−22.1836	+	18.6142i	−0.707545	+	0.593701i	−0.923909	−	0.382612i	$-0.875025\pi$
$983$	−22.1836	+	18.6142i	−0.707545	+	0.593701i	0.216364	+	0.976313i	$0.430580\pi$
$984$		0			0
$985$	3.18924	−	18.0871i	0.101618	−	0.576303i
$986$		0			0
$987$	−4.27012	+	2.54369i	−0.135920	+	0.0809666i
$988$		0			0
$989$	−17.7220	−	10.2318i	−0.563527	−	0.325352i
$990$		0			0
$991$	17.6233	−	10.1748i	0.559823	−	0.323214i	−0.193251	−	0.981149i	$-0.561903\pi$
$991$	17.6233	−	10.1748i	0.559823	−	0.323214i	0.753074	+	0.657935i	$0.228570\pi$
$992$		0			0
$993$	26.9689	−	33.0460i	0.855832	−	1.04868i
$994$		0			0
$995$	50.7903	−	18.4861i	1.61016	−	0.586050i
$996$		0			0
$997$	−5.71220	−	32.3955i	−0.180907	−	1.02597i	−0.931102	−	0.364758i	$-0.881152\pi$
$997$	−5.71220	−	32.3955i	−0.180907	−	1.02597i	0.750195	−	0.661217i	$-0.229960\pi$
$998$		0			0
$999$	−42.6209	+	1.74622i	−1.34846	+	0.0552480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.b.95.5	✓	36
4.3	odd	2		432.2.be.c.95.2	yes	36
27.2	odd	18		432.2.be.c.191.2	yes	36
108.83	even	18	inner	432.2.be.b.191.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.95.5	✓	36	1.1	even	1	trivial
432.2.be.b.191.5	yes	36	108.83	even	18	inner
432.2.be.c.95.2	yes	36	4.3	odd	2
432.2.be.c.191.2	yes	36	27.2	odd	18

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.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.63553 + 0.570126i) q^{3} +(2.34697 - 2.79701i) q^{5} +(0.550750 - 1.51317i) q^{7} +(2.34991 + 1.86492i) q^{9} +O(q^{10})\)	\(q+(1.63553 + 0.570126i) q^{3} +(2.34697 - 2.79701i) q^{5} +(0.550750 - 1.51317i) q^{7} +(2.34991 + 1.86492i) q^{9} +(-2.21396 + 1.85773i) q^{11} +(0.121792 - 0.690719i) q^{13} +(5.43318 - 3.23652i) q^{15} +(-5.56131 - 3.21082i) q^{17} +(-1.62624 + 0.938910i) q^{19} +(1.76347 - 2.16084i) q^{21} +(-2.18387 + 0.794864i) q^{23} +(-1.44675 - 8.20494i) q^{25} +(2.78011 + 4.38987i) q^{27} +(5.54988 - 0.978594i) q^{29} +(3.63921 + 9.99865i) q^{31} +(-4.68013 + 1.77614i) q^{33} +(-2.93977 - 5.09183i) q^{35} +(-4.10464 + 7.10944i) q^{37} +(0.592992 - 1.06025i) q^{39} +(6.18442 + 1.09048i) q^{41} +(5.65989 + 6.74520i) q^{43} +(10.7314 - 2.19583i) q^{45} +(-1.67459 - 0.609501i) q^{47} +(3.37594 + 2.83275i) q^{49} +(-7.26511 - 8.42204i) q^{51} -0.849889i q^{53} +10.5525i q^{55} +(-3.19506 + 0.608453i) q^{57} +(-4.54459 - 3.81337i) q^{59} +(-9.95979 - 3.62507i) q^{61} +(4.11616 - 2.52872i) q^{63} +(-1.64610 - 1.96175i) q^{65} +(-14.5520 - 2.56590i) q^{67} +(-4.02496 + 0.0549417i) q^{69} +(5.80783 - 10.0595i) q^{71} +(3.12044 + 5.40475i) q^{73} +(2.31165 - 14.2443i) q^{75} +(1.59173 + 4.37325i) q^{77} +(4.47831 - 0.789647i) q^{79} +(2.04418 + 8.76478i) q^{81} +(-1.28300 - 7.27624i) q^{83} +(-22.0329 + 8.01933i) q^{85} +(9.63492 + 1.56361i) q^{87} +(-6.02277 + 3.47725i) q^{89} +(-0.978101 - 0.564707i) q^{91} +(0.251545 + 18.4279i) q^{93} +(-1.19060 + 6.75220i) q^{95} +(1.35281 - 1.13514i) q^{97} +(-8.66711 + 0.236660i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q + 3 * q^5 + 6 * q^9	\( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) \) 36 * q + 3 * q^5 + 6 * q^9 - 18 * q^11 + 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 + 27 * q^31 + 27 * q^33 + 27 * q^35 - 45 * q^39 + 18 * q^41 + 27 * q^45 + 45 * q^47 - 63 * q^51 - 9 * q^57 + 54 * q^59 - 63 * q^63 - 57 * q^65 - 63 * q^69 + 36 * q^71 + 9 * q^73 - 45 * q^75 - 81 * q^77 - 54 * q^81 - 27 * q^83 - 36 * q^85 + 45 * q^87 - 63 * q^89 + 27 * q^91 - 63 * q^93 - 72 * q^95 + 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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