LMFDB - Embedded newform 432.2.be.c.47.6

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			47.6
Character	$\chi$	$=$	432.47
Dual form			432.2.be.c.239.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.65284 + 0.517813i) q^{3} +(-2.52917 + 0.445961i) q^{5} +(1.40789 - 1.67786i) q^{7} +(2.46374 + 1.71172i) q^{9} +O(q^{10})$	\(q+(1.65284 + 0.517813i) q^{3} +(-2.52917 + 0.445961i) q^{5} +(1.40789 - 1.67786i) q^{7} +(2.46374 + 1.71172i) q^{9} +(-0.751810 + 4.26373i) q^{11} +(5.33154 + 1.94052i) q^{13} +(-4.41123 - 0.572537i) q^{15} +(5.53709 - 3.19684i) q^{17} +(2.85493 + 1.64830i) q^{19} +(3.19584 - 2.04421i) q^{21} +(-3.31503 + 2.78164i) q^{23} +(1.49936 - 0.545724i) q^{25} +(3.18581 + 4.10495i) q^{27} +(0.131941 + 0.362506i) q^{29} +(-4.37197 - 5.21032i) q^{31} +(-3.45043 + 6.65795i) q^{33} +(-2.81254 + 4.87147i) q^{35} +(-3.81950 - 6.61557i) q^{37} +(7.80734 + 5.96811i) q^{39} +(-0.138464 + 0.380428i) q^{41} +(-9.35445 - 1.64944i) q^{43} +(-6.99458 - 3.23050i) q^{45} +(-6.74409 - 5.65897i) q^{47} +(0.382480 + 2.16915i) q^{49} +(10.8073 - 2.41668i) q^{51} -7.00741i q^{53} -11.1190i q^{55} +(3.86523 + 4.20269i) q^{57} +(-0.296830 - 1.68341i) q^{59} +(8.66165 + 7.26798i) q^{61} +(6.34071 - 1.72389i) q^{63} +(-14.3498 - 2.53025i) q^{65} +(0.683922 - 1.87906i) q^{67} +(-6.91957 + 2.88103i) q^{69} +(1.85419 + 3.21154i) q^{71} +(5.37828 - 9.31546i) q^{73} +(2.76079 - 0.125602i) q^{75} +(6.09548 + 7.26431i) q^{77} +(2.34025 + 6.42979i) q^{79} +(3.14002 + 8.43447i) q^{81} +(-1.31616 + 0.479045i) q^{83} +(-12.5786 + 10.5547i) q^{85} +(0.0303672 + 0.667485i) q^{87} +(-6.85289 - 3.95652i) q^{89} +(10.7622 - 6.21354i) q^{91} +(-4.52819 - 10.8757i) q^{93} +(-7.95569 - 2.89564i) q^{95} +(2.09088 - 11.8580i) q^{97} +(-9.15058 + 9.21782i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{18}\right)$

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
$3$	1.65284	+	0.517813i	0.954266	+	0.298960i
$3$	1.65284	+	0.517813i	0.954266	+	0.298960i
$4$		0			0
$5$	−2.52917	+	0.445961i	−1.13108	+	0.199440i	−0.707700	−	0.706513i	$-0.750267\pi$
$5$	−2.52917	+	0.445961i	−1.13108	+	0.199440i	−0.423379	+	0.905952i	$0.639156\pi$
$6$		0			0
$7$	1.40789	−	1.67786i	0.532134	−	0.634172i	−0.431271	−	0.902222i	$-0.641935\pi$
$7$	1.40789	−	1.67786i	0.532134	−	0.634172i	0.963405	+	0.268050i	$0.0863792\pi$
$8$		0			0
$9$	2.46374	+	1.71172i	0.821246	+	0.570574i
$10$		0			0
$11$	−0.751810	+	4.26373i	−0.226679	+	1.28556i	0.632769	+	0.774340i	$0.281918\pi$
$11$	−0.751810	+	4.26373i	−0.226679	+	1.28556i	−0.859449	+	0.511222i	$0.829193\pi$
$12$		0			0
$13$	5.33154	+	1.94052i	1.47870	+	0.538204i	0.950449	−	0.310882i	$-0.100624\pi$
$13$	5.33154	+	1.94052i	1.47870	+	0.538204i	0.528255	+	0.849086i	$0.322846\pi$
$14$		0			0
$15$	−4.41123	−	0.572537i	−1.13898	−	0.147828i
$16$		0			0
$17$	5.53709	−	3.19684i	1.34294	−	0.775347i	0.355703	−	0.934599i	$-0.384241\pi$
$17$	5.53709	−	3.19684i	1.34294	−	0.775347i	0.987238	+	0.159252i	$0.0509081\pi$
$18$		0			0
$19$	2.85493	+	1.64830i	0.654967	+	0.378145i	0.790357	−	0.612647i	$-0.209895\pi$
$19$	2.85493	+	1.64830i	0.654967	+	0.378145i	−0.135390	+	0.990792i	$0.543229\pi$
$20$		0			0
$21$	3.19584	−	2.04421i	0.697389	−	0.446082i
$22$		0			0
$23$	−3.31503	+	2.78164i	−0.691232	+	0.580012i	−0.919264	−	0.393641i	$-0.871215\pi$
$23$	−3.31503	+	2.78164i	−0.691232	+	0.580012i	0.228033	+	0.973654i	$0.426771\pi$
$24$		0			0
$25$	1.49936	−	0.545724i	0.299873	−	0.109145i
$26$		0			0
$27$	3.18581	+	4.10495i	0.613109	+	0.789998i
$28$		0			0
$29$	0.131941	+	0.362506i	0.0245009	+	0.0673157i	0.951340	−	0.308143i	$-0.0997075\pi$
$29$	0.131941	+	0.362506i	0.0245009	+	0.0673157i	−0.926839	+	0.375459i	$0.877485\pi$
$30$		0			0
$31$	−4.37197	−	5.21032i	−0.785230	−	0.935800i	0.213927	−	0.976850i	$-0.431374\pi$
$31$	−4.37197	−	5.21032i	−0.785230	−	0.935800i	−0.999157	+	0.0410491i	$0.986930\pi$
$32$		0			0
$33$	−3.45043	+	6.65795i	−0.600644	+	1.15900i
$34$		0			0
$35$	−2.81254	+	4.87147i	−0.475407	+	0.823428i
$36$		0			0
$37$	−3.81950	−	6.61557i	−0.627922	−	1.08759i	−0.987968	−	0.154658i	$-0.950572\pi$
$37$	−3.81950	−	6.61557i	−0.627922	−	1.08759i	0.360046	−	0.932934i	$-0.382761\pi$
$38$		0			0
$39$	7.80734	+	5.96811i	1.25018	+	0.955662i
$40$		0			0
$41$	−0.138464	+	0.380428i	−0.0216245	+	0.0594128i	−0.950035	−	0.312143i	$-0.898953\pi$
$41$	−0.138464	+	0.380428i	−0.0216245	+	0.0594128i	0.928411	+	0.371556i	$0.121175\pi$
$42$		0			0
$43$	−9.35445	−	1.64944i	−1.42654	−	0.251538i	−0.593538	−	0.804806i	$-0.702269\pi$
$43$	−9.35445	−	1.64944i	−1.42654	−	0.251538i	−0.833003	+	0.553269i	$0.813380\pi$
$44$		0			0
$45$	−6.99458	−	3.23050i	−1.04269	−	0.481575i
$46$		0			0
$47$	−6.74409	−	5.65897i	−0.983727	−	0.825445i	0.000920318	−	1.00000i	$-0.499707\pi$
$47$	−6.74409	−	5.65897i	−0.983727	−	0.825445i	−0.984648	+	0.174554i	$0.944151\pi$
$48$		0			0
$49$	0.382480	+	2.16915i	0.0546400	+	0.309879i
$50$		0			0
$51$	10.8073	−	2.41668i	1.51332	−	0.338402i
$52$		0			0
$53$		−	7.00741i		−	0.962542i	−0.876572	−	0.481271i	$-0.840175\pi$
$53$		−	7.00741i		−	0.962542i	0.876572	−	0.481271i	$-0.159825\pi$
$54$		0			0
$55$		−	11.1190i		−	1.49928i
$56$		0			0
$57$	3.86523	+	4.20269i	0.511962	+	0.556660i
$58$		0			0
$59$	−0.296830	−	1.68341i	−0.0386440	−	0.219161i	0.959370	−	0.282150i	$-0.0910477\pi$
$59$	−0.296830	−	1.68341i	−0.0386440	−	0.219161i	−0.998014	+	0.0629893i	$0.979937\pi$
$60$		0			0
$61$	8.66165	+	7.26798i	1.10901	+	0.930570i	0.997998	−	0.0632489i	$-0.0201462\pi$
$61$	8.66165	+	7.26798i	1.10901	+	0.930570i	0.111012	+	0.993819i	$0.464591\pi$
$62$		0			0
$63$	6.34071	−	1.72389i	0.798855	−	0.217190i
$64$		0			0
$65$	−14.3498	−	2.53025i	−1.77987	−	0.313839i
$66$		0			0
$67$	0.683922	−	1.87906i	0.0835543	−	0.229564i	−0.890879	−	0.454241i	$-0.849911\pi$
$67$	0.683922	−	1.87906i	0.0835543	−	0.229564i	0.974433	+	0.224677i	$0.0721328\pi$
$68$		0			0
$69$	−6.91957	+	2.88103i	−0.833019	+	0.346835i
$70$		0			0
$71$	1.85419	+	3.21154i	0.220051	+	0.381140i	0.954823	−	0.297174i	$-0.0960442\pi$
$71$	1.85419	+	3.21154i	0.220051	+	0.381140i	−0.734772	+	0.678314i	$0.762711\pi$
$72$		0			0
$73$	5.37828	−	9.31546i	0.629481	−	1.09029i	−0.358176	−	0.933654i	$-0.616601\pi$
$73$	5.37828	−	9.31546i	0.629481	−	1.09029i	0.987656	−	0.156638i	$-0.0500656\pi$
$74$		0			0
$75$	2.76079	−	0.125602i	0.318788	−	0.0145033i
$76$		0			0
$77$	6.09548	+	7.26431i	0.694644	+	0.827845i
$78$		0			0
$79$	2.34025	+	6.42979i	0.263299	+	0.723408i	0.998940	+	0.0460362i	$0.0146590\pi$
$79$	2.34025	+	6.42979i	0.263299	+	0.723408i	−0.735641	+	0.677372i	$0.763119\pi$
$80$		0			0
$81$	3.14002	+	8.43447i	0.348891	+	0.937163i
$82$		0			0
$83$	−1.31616	+	0.479045i	−0.144468	+	0.0525820i	−0.413242	−	0.910621i	$-0.635604\pi$
$83$	−1.31616	+	0.479045i	−0.144468	+	0.0525820i	0.268774	+	0.963203i	$0.413381\pi$
$84$		0			0
$85$	−12.5786	+	10.5547i	−1.36434	+	1.14482i
$86$		0			0
$87$	0.0303672	+	0.667485i	0.00325571	+	0.0715619i
$88$		0			0
$89$	−6.85289	−	3.95652i	−0.726404	−	0.419390i	0.0907009	−	0.995878i	$-0.471089\pi$
$89$	−6.85289	−	3.95652i	−0.726404	−	0.419390i	−0.817105	+	0.576488i	$0.804423\pi$
$90$		0			0
$91$	10.7622	−	6.21354i	1.12818	−	0.651356i
$92$		0			0
$93$	−4.52819	−	10.8757i	−0.469551	−	1.12775i
$94$		0			0
$95$	−7.95569	−	2.89564i	−0.816237	−	0.297086i
$96$		0			0
$97$	2.09088	−	11.8580i	0.212297	−	1.20399i	−0.673239	−	0.739424i	$-0.735098\pi$
$97$	2.09088	−	11.8580i	0.212297	−	1.20399i	0.885536	−	0.464570i	$-0.153791\pi$
$98$		0			0
$99$	−9.15058	+	9.21782i	−0.919668	+	0.926426i
$100$		0			0
$101$	−1.06468	+	1.26884i	−0.105940	+	0.126254i	−0.816409	−	0.577474i	$-0.804038\pi$
$101$	−1.06468	+	1.26884i	−0.105940	+	0.126254i	0.710469	+	0.703728i	$0.248483\pi$
$102$		0			0
$103$	−2.83638	+	0.500131i	−0.279477	+	0.0492793i	−0.311630	−	0.950204i	$-0.600875\pi$
$103$	−2.83638	+	0.500131i	−0.279477	+	0.0492793i	0.0321527	+	0.999483i	$0.489764\pi$
$104$		0			0
$105$	−7.17118	+	6.59537i	−0.699836	+	0.643642i
$106$		0			0
$107$	12.6955			1.22732			0.613659	−	0.789571i	$-0.289697\pi$
$107$	12.6955			1.22732			0.613659	+	0.789571i	$0.289697\pi$
$108$		0			0
$109$	−6.54537			−0.626933			−0.313466	−	0.949599i	$-0.601490\pi$
$109$	−6.54537			−0.626933			−0.313466	+	0.949599i	$0.601490\pi$
$110$		0			0
$111$	−2.88738	−	12.9122i	−0.274058	−	1.22558i
$112$		0			0
$113$	−10.2726	+	1.81134i	−0.966367	+	0.170397i	−0.634494	−	0.772928i	$-0.718791\pi$
$113$	−10.2726	+	1.81134i	−0.966367	+	0.170397i	−0.331873	+	0.943324i	$0.607680\pi$
$114$		0			0
$115$	7.14378	−	8.51362i	0.666160	−	0.793899i
$116$		0			0
$117$	9.81389	+	13.9071i	0.907295	+	1.28571i
$118$		0			0
$119$	2.43177	−	13.7913i	0.222920	−	1.26424i
$120$		0			0
$121$	−7.27754	−	2.64881i	−0.661595	−	0.240801i
$122$		0			0
$123$	−0.425850	+	0.557086i	−0.0383976	+	0.0502308i
$124$		0			0
$125$	7.57180	−	4.37158i	0.677243	−	0.391006i
$126$		0			0
$127$	−12.0771	−	6.97273i	−1.07167	−	0.618730i	−0.143034	−	0.989718i	$-0.545686\pi$
$127$	−12.0771	−	6.97273i	−1.07167	−	0.618730i	−0.928638	+	0.370988i	$0.879019\pi$
$128$		0			0
$129$	−14.6073	−	7.57012i	−1.28610	−	0.666512i
$130$		0			0
$131$	−12.8891	+	10.8153i	−1.12613	+	0.944933i	−0.998898	−	0.0469403i	$-0.985053\pi$
$131$	−12.8891	+	10.8153i	−1.12613	+	0.944933i	−0.127230	+	0.991873i	$0.540608\pi$
$132$		0			0
$133$	6.78506	−	2.46956i	0.588339	−	0.214138i
$134$		0			0
$135$	−9.88810	−	8.96138i	−0.851032	−	0.771273i
$136$		0			0
$137$	−7.20373	−	19.7921i	−0.615456	−	1.69095i	−0.717841	−	0.696207i	$-0.754869\pi$
$137$	−7.20373	−	19.7921i	−0.615456	−	1.69095i	0.102384	−	0.994745i	$-0.467353\pi$
$138$		0			0
$139$	−5.34649	−	6.37169i	−0.453483	−	0.540440i	0.490061	−	0.871688i	$-0.336975\pi$
$139$	−5.34649	−	6.37169i	−0.453483	−	0.540440i	−0.943544	+	0.331248i	$0.892530\pi$
$140$		0			0
$141$	−8.21660	−	12.8455i	−0.691962	−	1.08179i
$142$		0			0
$143$	−12.2822	+	21.2733i	−1.02709	+	1.77897i
$144$		0			0
$145$	−0.495366	−	0.858000i	−0.0411379	−	0.0712530i
$146$		0			0
$147$	−0.491038	+	3.78331i	−0.0405002	+	0.312042i
$148$		0			0
$149$	−2.34190	+	6.43432i	−0.191856	+	0.527120i	−0.997903	−	0.0647320i	$-0.979381\pi$
$149$	−2.34190	+	6.43432i	−0.191856	+	0.527120i	0.806047	+	0.591852i	$0.201603\pi$
$150$		0			0
$151$	9.29194	+	1.63842i	0.756167	+	0.133333i	0.538425	−	0.842674i	$-0.319020\pi$
$151$	9.29194	+	1.63842i	0.756167	+	0.133333i	0.217742	+	0.976006i	$0.430131\pi$
$152$		0			0
$153$	19.1140	+	1.60177i	1.54528	+	0.129496i
$154$		0			0
$155$	13.3811	+	11.2281i	1.07479	+	0.901859i
$156$		0			0
$157$	1.84720	+	10.4760i	0.147422	+	0.836074i	0.965390	+	0.260810i	$0.0839897\pi$
$157$	1.84720	+	10.4760i	0.147422	+	0.836074i	−0.817968	+	0.575264i	$0.804899\pi$
$158$		0			0
$159$	3.62853	−	11.5821i	0.287761	−	0.918521i
$160$		0			0
$161$			9.47842i			0.747004i
$162$		0			0
$163$			13.7337i			1.07570i	0.843039	+	0.537852i	$0.180764\pi$
$163$			13.7337i			1.07570i	−0.843039	+	0.537852i	$0.819236\pi$
$164$		0			0
$165$	5.75755	−	18.3779i	0.448225	−	1.43071i
$166$		0			0
$167$	0.294930	+	1.67263i	0.0228223	+	0.129432i	0.994090	−	0.108557i	$-0.0346230\pi$
$167$	0.294930	+	1.67263i	0.0228223	+	0.129432i	−0.971268	+	0.237989i	$0.923512\pi$
$168$		0			0
$169$	14.7011	+	12.3357i	1.13086	+	0.948901i
$170$		0			0
$171$	4.21239	+	8.94782i	0.322129	+	0.684257i
$172$		0			0
$173$	0.171533	+	0.0302458i	0.0130414	+	0.00229955i	0.180165	−	0.983636i	$-0.442337\pi$
$173$	0.171533	+	0.0302458i	0.0130414	+	0.00229955i	−0.167124	+	0.985936i	$0.553448\pi$
$174$		0			0
$175$	1.19530	−	3.28405i	0.0903558	−	0.248251i
$176$		0			0
$177$	0.381079	−	2.93610i	0.0286436	−	0.220691i
$178$		0			0
$179$	−11.3351	−	19.6329i	−0.847223	−	1.46743i	−0.883677	−	0.468097i	$-0.844940\pi$
$179$	−11.3351	−	19.6329i	−0.847223	−	1.46743i	0.0364543	−	0.999335i	$-0.488394\pi$
$180$		0			0
$181$	−5.78896	+	10.0268i	−0.430290	+	0.745284i	−0.996898	−	0.0787036i	$-0.974922\pi$
$181$	−5.78896	+	10.0268i	−0.430290	+	0.745284i	0.566608	+	0.823987i	$0.308255\pi$
$182$		0			0
$183$	10.5528	+	16.4979i	0.780088	+	1.21956i
$184$		0			0
$185$	12.6105	+	15.0286i	0.927139	+	1.10492i
$186$		0			0
$187$	9.46761	+	26.0121i	0.692340	+	1.90219i
$188$		0			0
$189$	11.3728	+	0.433992i	0.827251	+	0.0315682i
$190$		0			0
$191$	18.0496	−	6.56951i	1.30602	−	0.475353i	0.407069	−	0.913397i	$-0.366551\pi$
$191$	18.0496	−	6.56951i	1.30602	−	0.475353i	0.898953	+	0.438044i	$0.144329\pi$
$192$		0			0
$193$	6.28804	−	5.27629i	0.452623	−	0.379796i	−0.387785	−	0.921750i	$-0.626760\pi$
$193$	6.28804	−	5.27629i	0.452623	−	0.379796i	0.840408	+	0.541954i	$0.182315\pi$
$194$		0			0
$195$	−22.4076	−	11.6126i	−1.60465	−	0.831596i
$196$		0			0
$197$	13.9850	+	8.07425i	0.996391	+	0.575266i	0.907178	−	0.420746i	$-0.138232\pi$
$197$	13.9850	+	8.07425i	0.996391	+	0.575266i	0.0892122	+	0.996013i	$0.471565\pi$
$198$		0			0
$199$	−1.42031	+	0.820018i	−0.100683	+	0.0581295i	−0.549496	−	0.835496i	$-0.685180\pi$
$199$	−1.42031	+	0.820018i	−0.100683	+	0.0581295i	0.448813	+	0.893626i	$0.351847\pi$
$200$		0			0
$201$	2.10341	−	2.75163i	0.148363	−	0.194085i
$202$		0			0
$203$	0.793995	+	0.288991i	0.0557275	+	0.0202832i
$204$		0			0
$205$	0.180544	−	1.02392i	0.0126098	−	0.0715135i
$206$		0			0
$207$	−12.9288	+	1.17883i	−0.898611	+	0.0819343i
$208$		0			0
$209$	−9.17426	+	10.9335i	−0.634597	+	0.756283i
$210$		0			0
$211$	−14.5381	+	2.56346i	−1.00084	+	0.176476i	−0.649981	−	0.759951i	$-0.725223\pi$
$211$	−14.5381	+	2.56346i	−1.00084	+	0.176476i	−0.350864	+	0.936427i	$0.614112\pi$
$212$		0			0
$213$	1.40169	+	6.26828i	0.0960420	+	0.429495i
$214$		0			0
$215$	24.3946			1.66370
$216$		0			0
$217$	−14.8975			−1.01131
$218$		0			0
$219$	13.7131	−	12.6120i	0.926645	−	0.852239i
$220$		0			0
$221$	35.7248	−	6.29924i	2.40311	−	0.423733i
$222$		0			0
$223$	−13.6087	+	16.2182i	−0.911308	+	1.08605i	0.0846660	+	0.996409i	$0.473018\pi$
$223$	−13.6087	+	16.2182i	−0.911308	+	1.08605i	−0.995974	+	0.0896449i	$0.971427\pi$
$224$		0			0
$225$	4.62817	+	1.22197i	0.308545	+	0.0814648i
$226$		0			0
$227$	3.65627	−	20.7357i	0.242675	−	1.37628i	−0.583155	−	0.812361i	$-0.698182\pi$
$227$	3.65627	−	20.7357i	0.242675	−	1.37628i	0.825830	−	0.563919i	$-0.190707\pi$
$228$		0			0
$229$	−21.1473	−	7.69700i	−1.39746	−	0.508632i	−0.470033	−	0.882649i	$-0.655758\pi$
$229$	−21.1473	−	7.69700i	−1.39746	−	0.508632i	−0.927422	+	0.374017i	$0.877980\pi$
$230$		0			0
$231$	6.31328	+	15.1630i	0.415383	+	0.997655i
$232$		0			0
$233$	22.3267	−	12.8903i	1.46267	−	0.844472i	0.463534	−	0.886079i	$-0.346581\pi$
$233$	22.3267	−	12.8903i	1.46267	−	0.844472i	0.999134	+	0.0416070i	$0.0132478\pi$
$234$		0			0
$235$	19.5806	+	11.3049i	1.27730	+	0.737450i
$236$		0			0
$237$	0.538625	+	11.8392i	0.0349875	+	0.769039i
$238$		0			0
$239$	8.25623	−	6.92780i	0.534051	−	0.448122i	−0.335446	−	0.942059i	$-0.608887\pi$
$239$	8.25623	−	6.92780i	0.534051	−	0.448122i	0.869498	+	0.493937i	$0.164443\pi$
$240$		0			0
$241$	23.7530	−	8.64537i	1.53006	−	0.556897i	0.566426	−	0.824112i	$-0.308326\pi$
$241$	23.7530	−	8.64537i	1.53006	−	0.556897i	0.963637	+	0.267215i	$0.0861034\pi$
$242$		0			0
$243$	0.822462	+	15.5667i	0.0527609	+	0.998607i
$244$		0			0
$245$	−1.93471	−	5.31558i	−0.123604	−	0.339600i
$246$		0			0
$247$	12.0226	+	14.3280i	0.764982	+	0.911671i
$248$		0			0
$249$	−2.42346	+	0.110255i	−0.153581	+	0.00698715i
$250$		0			0
$251$	7.50990	−	13.0075i	0.474021	−	0.821028i	−0.525537	−	0.850771i	$-0.676135\pi$
$251$	7.50990	−	13.0075i	0.474021	−	0.821028i	0.999558	+	0.0297426i	$0.00946877\pi$
$252$		0			0
$253$	−9.36788	−	16.2257i	−0.588954	−	1.02010i
$254$		0			0
$255$	−26.2557	+	10.9318i	−1.64420	+	0.684577i
$256$		0			0
$257$	−6.91255	+	18.9921i	−0.431193	+	1.18469i	0.513888	+	0.857857i	$0.328205\pi$
$257$	−6.91255	+	18.9921i	−0.431193	+	1.18469i	−0.945081	+	0.326836i	$0.894018\pi$
$258$		0			0
$259$	−16.4775	−	2.90542i	−1.02386	−	0.180534i
$260$		0			0
$261$	−0.295440	+	1.11897i	−0.0182873	+	0.0692624i
$262$		0			0
$263$	−3.94316	−	3.30870i	−0.243146	−	0.204023i	0.513068	−	0.858348i	$-0.328509\pi$
$263$	−3.94316	−	3.30870i	−0.243146	−	0.204023i	−0.756214	+	0.654324i	$0.772953\pi$
$264$		0			0
$265$	3.12503	+	17.7229i	0.191969	+	1.08871i
$266$		0			0
$267$	−9.27797	−	10.0880i	−0.567802	−	0.617375i
$268$		0			0
$269$			5.82144i			0.354939i	0.984126	+	0.177470i	$0.0567912\pi$
$269$			5.82144i			0.354939i	−0.984126	+	0.177470i	$0.943209\pi$
$270$		0			0
$271$			4.39965i			0.267260i	0.991031	+	0.133630i	$0.0426634\pi$
$271$			4.39965i			0.267260i	−0.991031	+	0.133630i	$0.957337\pi$
$272$		0			0
$273$	21.0056	−	4.69718i	1.27131	−	0.284286i
$274$		0			0
$275$	1.19958	+	6.80316i	0.0723374	+	0.410246i
$276$		0			0
$277$	−7.99331	−	6.70718i	−0.480271	−	0.402995i	0.370253	−	0.928931i	$-0.379271\pi$
$277$	−7.99331	−	6.70718i	−0.480271	−	0.402995i	−0.850525	+	0.525935i	$0.823715\pi$
$278$		0			0
$279$	−1.85279	−	20.3205i	−0.110924	−	1.21655i
$280$		0			0
$281$	−4.88693	−	0.861697i	−0.291530	−	0.0514045i	0.0259707	−	0.999663i	$-0.491732\pi$
$281$	−4.88693	−	0.861697i	−0.291530	−	0.0514045i	−0.317500	+	0.948258i	$0.602843\pi$
$282$		0			0
$283$	0.925706	−	2.54336i	0.0550275	−	0.151187i	−0.909133	−	0.416505i	$-0.863255\pi$
$283$	0.925706	−	2.54336i	0.0550275	−	0.151187i	0.964161	+	0.265318i	$0.0854770\pi$
$284$		0			0
$285$	−11.6501	−	8.90558i	−0.690090	−	0.527521i
$286$		0			0
$287$	0.443362	+	0.767926i	0.0261709	+	0.0453292i
$288$		0			0
$289$	11.9396	−	20.6799i	0.702327	−	1.21647i
$290$		0			0
$291$	9.59610	−	18.5166i	0.562533	−	1.08546i
$292$		0			0
$293$	1.38940	+	1.65583i	0.0811699	+	0.0967345i	0.805101	−	0.593138i	$-0.202111\pi$
$293$	1.38940	+	1.65583i	0.0811699	+	0.0967345i	−0.723931	+	0.689872i	$0.757667\pi$
$294$		0			0
$295$	1.50147	+	4.12525i	0.0874189	+	0.240182i
$296$		0			0
$297$	−19.8975	+	10.4973i	−1.15457	+	0.609113i
$298$		0			0
$299$	−23.0721	+	8.39754i	−1.33429	+	0.485642i
$300$		0			0
$301$	−15.9376	+	13.3732i	−0.918629	+	0.770821i
$302$		0			0
$303$	−2.41677	+	1.54588i	−0.138840	+	0.0888083i
$304$		0			0
$305$	−25.1480	−	14.5192i	−1.43997	−	0.831368i
$306$		0			0
$307$	−2.33463	+	1.34790i	−0.133244	+	0.0769287i	−0.565140	−	0.824995i	$-0.691178\pi$
$307$	−2.33463	+	1.34790i	−0.133244	+	0.0769287i	0.431896	+	0.901923i	$0.357845\pi$
$308$		0			0
$309$	−4.94705	−	0.642082i	−0.281428	−	0.0365267i
$310$		0			0
$311$	0.211163	+	0.0768571i	0.0119740	+	0.00435817i	0.348000	−	0.937494i	$-0.386861\pi$
$311$	0.211163	+	0.0768571i	0.0119740	+	0.00435817i	−0.336026	+	0.941853i	$0.609083\pi$
$312$		0			0
$313$	−1.54162	+	8.74295i	−0.0871374	+	0.494181i	0.909737	+	0.415184i	$0.136283\pi$
$313$	−1.54162	+	8.74295i	−0.0871374	+	0.494181i	−0.996875	+	0.0789969i	$0.974828\pi$
$314$		0			0
$315$	−15.2680	+	7.18773i	−0.860252	+	0.404983i
$316$		0			0
$317$	2.12018	−	2.52673i	0.119081	−	0.141915i	−0.703210	−	0.710982i	$-0.748251\pi$
$317$	2.12018	−	2.52673i	0.119081	−	0.141915i	0.822292	+	0.569066i	$0.192695\pi$
$318$		0			0
$319$	−1.64482	+	0.290027i	−0.0920924	+	0.0162384i
$320$		0			0
$321$	20.9836	+	6.57389i	1.17119	+	0.366919i
$322$		0			0
$323$	21.0774			1.17278
$324$		0			0
$325$	9.05291			0.502165
$326$		0			0
$327$	−10.8184	−	3.38928i	−0.598261	−	0.187428i
$328$		0			0
$329$	−18.9899	+	3.34844i	−1.04695	+	0.184605i
$330$		0			0
$331$	−14.8545	+	17.7029i	−0.816478	+	0.973041i	−0.999950	−	0.00998434i	$-0.996822\pi$
$331$	−14.8545	+	17.7029i	−0.816478	+	0.973041i	0.183472	+	0.983025i	$0.441266\pi$
$332$		0			0
$333$	1.91376	−	22.8370i	0.104873	−	1.25146i
$334$		0			0
$335$	−0.891768	+	5.05746i	−0.0487225	+	0.276319i
$336$		0			0
$337$	9.67555	+	3.52161i	0.527061	+	0.191834i	0.591826	−	0.806066i	$-0.298407\pi$
$337$	9.67555	+	3.52161i	0.527061	+	0.191834i	−0.0647647	+	0.997901i	$0.520630\pi$
$338$		0			0
$339$	−17.9169	−	2.32545i	−0.973112	−	0.126301i
$340$		0			0
$341$	25.5023	−	14.7237i	1.38103	−	0.797335i
$342$		0			0
$343$	17.4560	+	10.0782i	0.942534	+	0.544172i
$344$		0			0
$345$	16.2160	−	10.3725i	0.873038	−	0.558436i
$346$		0			0
$347$	27.5760	−	23.1390i	1.48036	−	1.24217i	0.574560	−	0.818462i	$-0.305173\pi$
$347$	27.5760	−	23.1390i	1.48036	−	1.24217i	0.905799	−	0.423707i	$-0.139271\pi$
$348$		0			0
$349$	−21.1590	+	7.70125i	−1.13262	+	0.412238i	−0.839241	−	0.543759i	$-0.817000\pi$
$349$	−21.1590	+	7.70125i	−1.13262	+	0.412238i	−0.293374	+	0.955998i	$0.594778\pi$
$350$		0			0
$351$	9.01951	+	28.0679i	0.481426	+	1.49815i
$352$		0			0
$353$	9.62764	+	26.4517i	0.512428	+	1.40788i	0.878700	+	0.477375i	$0.158412\pi$
$353$	9.62764	+	26.4517i	0.512428	+	1.40788i	−0.366272	+	0.930508i	$0.619366\pi$
$354$		0			0
$355$	−6.12178	−	7.29565i	−0.324910	−	0.387213i
$356$		0			0
$357$	11.1606	−	21.5355i	0.590683	−	1.13978i
$358$		0			0
$359$	−13.4479	+	23.2924i	−0.709753	+	1.22933i	0.255196	+	0.966889i	$0.417860\pi$
$359$	−13.4479	+	23.2924i	−0.709753	+	1.22933i	−0.964949	+	0.262439i	$0.915473\pi$
$360$		0			0
$361$	−4.06623	−	7.04293i	−0.214012	−	0.370680i
$362$		0			0
$363$	−10.6570	−	8.14645i	−0.559347	−	0.427578i
$364$		0			0
$365$	−9.44827	+	25.9589i	−0.494545	+	1.35875i
$366$		0			0
$367$	27.9737	+	4.93252i	1.46022	+	0.257475i	0.846642	−	0.532162i	$-0.178620\pi$
$367$	27.9737	+	4.93252i	1.46022	+	0.257475i	0.613574	+	0.789638i	$0.289731\pi$
$368$		0			0
$369$	−0.992327	+	0.700262i	−0.0516585	+	0.0364542i
$370$		0			0
$371$	−11.7575	−	9.86569i	−0.610418	−	0.512201i
$372$		0			0
$373$	2.05586	+	11.6594i	0.106448	+	0.603699i	0.990632	+	0.136559i	$0.0436045\pi$
$373$	2.05586	+	11.6594i	0.106448	+	0.603699i	−0.884183	+	0.467140i	$0.845284\pi$
$374$		0			0
$375$	14.7786	−	3.30473i	0.763165	−	0.170656i
$376$		0			0
$377$			2.18875i			0.112726i
$378$		0			0
$379$		−	21.1690i		−	1.08738i	−0.839286	−	0.543690i	$-0.817027\pi$
$379$		−	21.1690i		−	1.08738i	0.839286	−	0.543690i	$-0.182973\pi$
$380$		0			0
$381$	−16.3509	−	17.7785i	−0.837684	−	0.910819i
$382$		0			0
$383$	−3.40920	−	19.3346i	−0.174202	−	0.987950i	−0.939061	−	0.343751i	$-0.888302\pi$
$383$	−3.40920	−	19.3346i	−0.174202	−	0.987950i	0.764859	−	0.644198i	$-0.222809\pi$
$384$		0			0
$385$	−18.6561	−	15.6543i	−0.950804	−	0.797819i
$386$		0			0
$387$	−20.2235	−	20.0760i	−1.02802	−	1.02052i
$388$		0			0
$389$	−8.24025	−	1.45298i	−0.417798	−	0.0736690i	−0.0392022	−	0.999231i	$-0.512482\pi$
$389$	−8.24025	−	1.45298i	−0.417798	−	0.0736690i	−0.378595	+	0.925562i	$0.623593\pi$
$390$		0			0
$391$	−9.46316	+	25.9998i	−0.478572	+	1.31487i
$392$		0			0
$393$	−26.9039	+	11.2017i	−1.35712	+	0.565051i
$394$		0			0
$395$	−8.78634	−	15.2184i	−0.442089	−	0.765720i
$396$		0			0
$397$	−13.4307	+	23.2627i	−0.674068	+	1.16752i	0.302672	+	0.953095i	$0.402121\pi$
$397$	−13.4307	+	23.2627i	−0.674068	+	1.16752i	−0.976740	+	0.214426i	$0.931212\pi$
$398$		0			0
$399$	12.4934	−	0.568386i	0.625451	−	0.0284549i
$400$		0			0
$401$	−12.5634	−	14.9724i	−0.627385	−	0.747688i	0.354937	−	0.934890i	$-0.384502\pi$
$401$	−12.5634	−	14.9724i	−0.627385	−	0.747688i	−0.982321	+	0.187203i	$0.940058\pi$
$402$		0			0
$403$	−13.1986	−	36.2629i	−0.657471	−	1.80639i
$404$		0			0
$405$	−11.7031	−	19.9319i	−0.581531	−	0.990424i
$406$		0			0
$407$	31.0785	−	11.3117i	1.54051	−	0.560698i
$408$		0			0
$409$	−2.96469	+	2.48767i	−0.146594	+	0.123007i	−0.713136	−	0.701026i	$-0.752726\pi$
$409$	−2.96469	+	2.48767i	−0.146594	+	0.123007i	0.566541	+	0.824033i	$0.308281\pi$
$410$		0			0
$411$	−1.65799	−	36.4433i	−0.0817825	−	1.79761i
$412$		0			0
$413$	−3.24243	−	1.87202i	−0.159550	−	0.0921161i
$414$		0			0
$415$	3.11517	−	1.79854i	0.152918	−	0.0882871i
$416$		0			0
$417$	−5.53752	−	13.2999i	−0.271174	−	0.651297i
$418$		0			0
$419$	5.55790	+	2.02291i	0.271521	+	0.0988256i	0.474192	−	0.880421i	$-0.342740\pi$
$419$	5.55790	+	2.02291i	0.271521	+	0.0988256i	−0.202671	+	0.979247i	$0.564962\pi$
$420$		0			0
$421$	−2.43514	+	13.8103i	−0.118681	+	0.673075i	0.866180	+	0.499732i	$0.166568\pi$
$421$	−2.43514	+	13.8103i	−0.118681	+	0.673075i	−0.984862	+	0.173343i	$0.944543\pi$
$422$		0			0
$423$	−6.92911	−	25.4862i	−0.336905	−	1.23918i
$424$		0			0
$425$	6.55752	−	7.81495i	0.318086	−	0.379081i
$426$		0			0
$427$	24.3894	−	4.30050i	1.18028	−	0.208116i
$428$		0			0
$429$	−31.3160	+	28.8015i	−1.51195	+	1.39055i
$430$		0			0
$431$	34.8272			1.67757			0.838784	−	0.544465i	$-0.183267\pi$
$431$	34.8272			1.67757			0.838784	+	0.544465i	$0.183267\pi$
$432$		0			0
$433$	−13.7584			−0.661187			−0.330593	−	0.943773i	$-0.607249\pi$
$433$	−13.7584			−0.661187			−0.330593	+	0.943773i	$0.607249\pi$
$434$		0			0
$435$	−0.374476	−	1.67464i	−0.0179548	−	0.0802929i
$436$		0			0
$437$	−14.0492	+	2.47725i	−0.672062	+	0.118503i
$438$		0			0
$439$	14.8296	−	17.6732i	0.707779	−	0.843498i	−0.285604	−	0.958348i	$-0.592194\pi$
$439$	14.8296	−	17.6732i	0.707779	−	0.843498i	0.993383	+	0.114850i	$0.0366387\pi$
$440$		0			0
$441$	−2.77065	+	5.99892i	−0.131936	+	0.285663i
$442$		0			0
$443$	−4.37334	+	24.8025i	−0.207784	+	1.17840i	0.685215	+	0.728341i	$0.259708\pi$
$443$	−4.37334	+	24.8025i	−0.207784	+	1.17840i	−0.892999	+	0.450059i	$0.851403\pi$
$444$		0			0
$445$	19.0966	+	6.95058i	0.905264	+	0.329489i
$446$		0			0
$447$	−7.20256	+	9.42221i	−0.340669	+	0.445655i
$448$		0			0
$449$	−11.0355	+	6.37137i	−0.520799	+	0.300683i	−0.737261	−	0.675608i	$-0.763881\pi$
$449$	−11.0355	+	6.37137i	−0.520799	+	0.300683i	0.216463	+	0.976291i	$0.430548\pi$
$450$		0			0
$451$	−1.51794	−	0.876384i	−0.0714771	−	0.0412673i
$452$		0			0
$453$	14.5097	+	7.51953i	0.681723	+	0.353298i
$454$		0			0
$455$	−24.4484	+	20.5146i	−1.14616	+	0.961741i
$456$		0			0
$457$	−17.7529	+	6.46151i	−0.830444	+	0.302257i	−0.722041	−	0.691850i	$-0.756796\pi$
$457$	−17.7529	+	6.46151i	−0.830444	+	0.302257i	−0.108403	+	0.994107i	$0.534574\pi$
$458$		0			0
$459$	30.7630	+	12.5450i	1.43589	+	0.585549i
$460$		0			0
$461$	2.34645	+	6.44682i	0.109285	+	0.300258i	0.982265	−	0.187498i	$-0.0600378\pi$
$461$	2.34645	+	6.44682i	0.109285	+	0.300258i	−0.872980	+	0.487756i	$0.837816\pi$
$462$		0			0
$463$	4.22001	+	5.02921i	0.196120	+	0.233727i	0.855138	−	0.518400i	$-0.173472\pi$
$463$	4.22001	+	5.02921i	0.196120	+	0.233727i	−0.659018	+	0.752127i	$0.729028\pi$
$464$		0			0
$465$	16.3027	+	25.4870i	0.756019	+	1.18193i
$466$		0			0
$467$	−19.4184	+	33.6337i	−0.898578	+	1.55638i	−0.0692651	+	0.997598i	$0.522065\pi$
$467$	−19.4184	+	33.6337i	−0.898578	+	1.55638i	−0.829313	+	0.558784i	$0.811268\pi$
$468$		0			0
$469$	−2.18991	−	3.79304i	−0.101121	−	0.175146i
$470$		0			0
$471$	−2.37148	+	18.2716i	−0.109272	+	0.841911i
$472$		0			0
$473$	14.0655	−	38.6448i	0.646735	−	1.77689i
$474$		0			0
$475$	5.18010	+	0.913391i	0.237679	+	0.0419093i
$476$		0			0
$477$	11.9947	−	17.2644i	0.549201	−	0.790484i
$478$		0			0
$479$	1.85078	+	1.55299i	0.0845645	+	0.0709580i	0.684090	−	0.729398i	$-0.260200\pi$
$479$	1.85078	+	1.55299i	0.0845645	+	0.0709580i	−0.599525	+	0.800356i	$0.704644\pi$
$480$		0			0
$481$	−7.52616	−	42.6830i	−0.343164	−	1.94618i
$482$		0			0
$483$	−4.90805	+	15.6663i	−0.223324	+	0.712840i
$484$		0			0
$485$			30.9233i			1.40415i
$486$		0			0
$487$		−	1.69185i		−	0.0766648i	−0.999265	−	0.0383324i	$-0.987795\pi$
$487$		−	1.69185i		−	0.0766648i	0.999265	−	0.0383324i	$-0.0122046\pi$
$488$		0			0
$489$	−7.11147	+	22.6995i	−0.321592	+	1.02651i
$490$		0			0
$491$	1.07391	+	6.09047i	0.0484650	+	0.274859i	0.999404	−	0.0345196i	$-0.0109901\pi$
$491$	1.07391	+	6.09047i	0.0484650	+	0.274859i	−0.950939	+	0.309378i	$0.899879\pi$
$492$		0			0
$493$	1.88945	+	1.58543i	0.0850964	+	0.0714043i
$494$		0			0
$495$	19.0326	−	27.3943i	0.855451	−	1.23128i
$496$		0			0
$497$	7.99902	+	1.41044i	0.358805	+	0.0632670i
$498$		0			0
$499$	7.06711	−	19.4167i	0.316367	−	0.869213i	−0.674967	−	0.737848i	$-0.735842\pi$
$499$	7.06711	−	19.4167i	0.316367	−	0.869213i	0.991334	−	0.131364i	$-0.0419358\pi$
$500$		0			0
$501$	−0.378639	+	2.91730i	−0.0169163	+	0.130335i
$502$		0			0
$503$	−15.4292	−	26.7241i	−0.687954	−	1.19157i	−0.972499	−	0.232908i	$-0.925176\pi$
$503$	−15.4292	−	26.7241i	−0.687954	−	1.19157i	0.284545	−	0.958663i	$-0.408157\pi$
$504$		0			0
$505$	2.12691	−	3.68392i	0.0946463	−	0.163932i
$506$		0			0
$507$	17.9110	+	28.0014i	0.795455	+	1.24358i
$508$		0			0
$509$	−25.1823	−	30.0112i	−1.11619	−	1.33022i	−0.938162	−	0.346195i	$-0.887473\pi$
$509$	−25.1823	−	30.0112i	−1.11619	−	1.33022i	−0.178026	−	0.984026i	$-0.556971\pi$
$510$		0			0
$511$	−8.05801	−	22.1392i	−0.356465	−	0.979380i
$512$		0			0
$513$	2.32909	+	16.9705i	0.102832	+	0.749267i
$514$		0			0
$515$	6.95066	−	2.52983i	0.306283	−	0.111478i
$516$		0			0
$517$	29.1986	−	24.5005i	1.28415	−	1.07753i
$518$		0			0
$519$	0.267854	+	0.138813i	0.0117575	+	0.00609322i
$520$		0			0
$521$	−0.354649	−	0.204757i	−0.0155375	−	0.00897056i	0.492211	−	0.870476i	$-0.336189\pi$
$521$	−0.354649	−	0.204757i	−0.0155375	−	0.00897056i	−0.507749	+	0.861505i	$0.669522\pi$
$522$		0			0
$523$	−11.5381	+	6.66155i	−0.504528	+	0.291289i	−0.730581	−	0.682826i	$-0.760751\pi$
$523$	−11.5381	+	6.66155i	−0.504528	+	0.291289i	0.226054	+	0.974115i	$0.427418\pi$
$524$		0			0
$525$	3.67615	−	4.80905i	0.160440	−	0.209884i
$526$		0			0
$527$	−40.8646	−	14.8735i	−1.78009	−	0.647899i
$528$		0			0
$529$	−0.742008	+	4.20814i	−0.0322612	+	0.182962i
$530$		0			0
$531$	2.15021	−	4.65557i	0.0933113	−	0.202035i
$532$		0			0
$533$	−1.47646	+	1.75957i	−0.0639525	+	0.0762156i
$534$		0			0
$535$	−32.1090	+	5.66169i	−1.38820	+	0.244776i
$536$		0			0
$537$	−8.56884	−	38.3194i	−0.369773	−	1.65361i
$538$		0			0
$539$	−9.53622			−0.410754
$540$		0			0
$541$	27.7454			1.19287			0.596434	−	0.802662i	$-0.296584\pi$
$541$	27.7454			1.19287			0.596434	+	0.802662i	$0.296584\pi$
$542$		0			0
$543$	−14.7602	+	13.5750i	−0.633420	+	0.582559i
$544$		0			0
$545$	16.5544	−	2.91898i	0.709111	−	0.125035i
$546$		0			0
$547$	−22.7506	+	27.1131i	−0.972744	+	1.15927i	0.0144745	+	0.999895i	$0.495392\pi$
$547$	−22.7506	+	27.1131i	−0.972744	+	1.15927i	−0.987218	+	0.159375i	$0.949052\pi$
$548$		0			0
$549$	8.89927	+	32.7327i	0.379812	+	1.39700i
$550$		0			0
$551$	−0.220834	+	1.25241i	−0.00940783	+	0.0533545i
$552$		0			0
$553$	14.0831	+	5.12584i	0.598876	+	0.217973i
$554$		0			0
$555$	13.0610	+	31.3696i	0.554410	+	1.33157i
$556$		0			0
$557$	4.22184	−	2.43748i	0.178885	−	0.103279i	−0.407884	−	0.913034i	$-0.633733\pi$
$557$	4.22184	−	2.43748i	0.178885	−	0.103279i	0.586769	+	0.809755i	$0.300400\pi$
$558$		0			0
$559$	−46.6729	−	26.9466i	−1.97405	−	1.13972i
$560$		0			0
$561$	2.17904	+	47.8961i	0.0919990	+	2.02218i
$562$		0			0
$563$	17.8937	−	15.0146i	0.754131	−	0.632791i	−0.182461	−	0.983213i	$-0.558406\pi$
$563$	17.8937	−	15.0146i	0.754131	−	0.632791i	0.936592	+	0.350422i	$0.113962\pi$
$564$		0			0
$565$	25.1734	−	9.16238i	1.05905	−	0.385464i
$566$		0			0
$567$	18.5727	+	6.60631i	0.779980	+	0.277439i
$568$		0			0
$569$	−1.89142	−	5.19662i	−0.0792923	−	0.217854i	0.893712	−	0.448641i	$-0.148092\pi$
$569$	−1.89142	−	5.19662i	−0.0792923	−	0.217854i	−0.973004	+	0.230788i	$0.925870\pi$
$570$		0			0
$571$	−5.47700	−	6.52724i	−0.229205	−	0.273156i	0.639168	−	0.769067i	$-0.279279\pi$
$571$	−5.47700	−	6.52724i	−0.229205	−	0.273156i	−0.868374	+	0.495911i	$0.834834\pi$
$572$		0			0
$573$	33.2348	−	1.51202i	1.38840	−	0.0631655i
$574$		0			0
$575$	−3.45243	+	5.97978i	−0.143976	+	0.249374i
$576$		0			0
$577$	11.9313	+	20.6656i	0.496706	+	0.860319i	0.999993	−	0.00379980i	$-0.00120952\pi$
$577$	11.9313	+	20.6656i	0.496706	+	0.860319i	−0.503287	+	0.864119i	$0.667876\pi$
$578$		0			0
$579$	13.1252	−	5.46482i	0.545466	−	0.227110i
$580$		0			0
$581$	−1.04925	+	2.88279i	−0.0435302	+	0.119598i
$582$		0			0
$583$	29.8777	+	5.26824i	1.23741	+	0.218188i
$584$		0			0
$585$	−31.0230	−	30.7967i	−1.28264	−	1.27329i
$586$		0			0
$587$	−15.5765	−	13.0702i	−0.642910	−	0.539466i	0.262000	−	0.965068i	$-0.415618\pi$
$587$	−15.5765	−	13.0702i	−0.642910	−	0.539466i	−0.904910	+	0.425602i	$0.860062\pi$
$588$		0			0
$589$	−3.89355	−	22.0814i	−0.160431	−	0.909849i
$590$		0			0
$591$	18.9340	+	20.5870i	0.778840	+	0.846838i
$592$		0			0
$593$		−	4.06230i		−	0.166819i	−0.996515	−	0.0834094i	$-0.973419\pi$
$593$		−	4.06230i		−	0.166819i	0.996515	−	0.0834094i	$-0.0265809\pi$
$594$		0			0
$595$			35.9650i			1.47442i
$596$		0			0
$597$	−2.77216	+	0.619899i	−0.113457	+	0.0253708i
$598$		0			0
$599$	4.78180	+	27.1190i	0.195379	+	1.10805i	0.911878	+	0.410462i	$0.134633\pi$
$599$	4.78180	+	27.1190i	0.195379	+	1.10805i	−0.716499	+	0.697589i	$0.754256\pi$
$600$		0			0
$601$	5.76201	+	4.83490i	0.235037	+	0.197220i	0.752697	−	0.658367i	$-0.228752\pi$
$601$	5.76201	+	4.83490i	0.235037	+	0.197220i	−0.517660	+	0.855586i	$0.673197\pi$
$602$		0			0
$603$	4.90143	−	3.45883i	0.199602	−	0.140854i
$604$		0			0
$605$	19.5874	+	3.45379i	0.796341	+	0.140416i
$606$		0			0
$607$	−12.5106	+	34.3727i	−0.507791	+	1.39514i	0.375719	+	0.926733i	$0.377396\pi$
$607$	−12.5106	+	34.3727i	−0.507791	+	1.39514i	−0.883511	+	0.468411i	$0.844827\pi$
$608$		0			0
$609$	1.16270	+	0.888795i	0.0471150	+	0.0360158i
$610$		0			0
$611$	−24.9751	−	43.2581i	−1.01038	−	1.75003i
$612$		0			0
$613$	13.0121	−	22.5376i	0.525552	−	0.910283i	−0.474005	−	0.880522i	$-0.657192\pi$
$613$	13.0121	−	22.5376i	0.525552	−	0.910283i	0.999557	−	0.0297610i	$-0.00947463\pi$
$614$		0			0
$615$	0.828608	−	1.59888i	0.0334127	−	0.0644730i
$616$		0			0
$617$	9.69439	+	11.5533i	0.390281	+	0.465119i	0.925031	−	0.379891i	$-0.124039\pi$
$617$	9.69439	+	11.5533i	0.390281	+	0.465119i	−0.534750	+	0.845010i	$0.679594\pi$
$618$		0			0
$619$	−5.42776	−	14.9126i	−0.218160	−	0.599390i	0.781541	−	0.623854i	$-0.214434\pi$
$619$	−5.42776	−	14.9126i	−0.218160	−	0.599390i	−0.999701	+	0.0244646i	$0.992212\pi$
$620$		0			0
$621$	−21.9795	−	4.74627i	−0.882009	−	0.190461i
$622$		0			0
$623$	−16.2866	+	5.92785i	−0.652510	+	0.237494i
$624$		0			0
$625$	−23.3123	+	19.5613i	−0.932492	+	0.782454i
$626$		0			0
$627$	−20.8250	+	13.3207i	−0.831672	+	0.531976i
$628$		0			0
$629$	−42.2978	−	24.4207i	−1.68652	−	0.973715i
$630$		0			0
$631$	6.79006	−	3.92024i	0.270308	−	0.156062i	−0.358720	−	0.933445i	$-0.616787\pi$
$631$	6.79006	−	3.92024i	0.270308	−	0.156062i	0.629028	+	0.777383i	$0.283453\pi$
$632$		0			0
$633$	−25.3565	−	3.29104i	−1.00783	−	0.130807i
$634$		0			0
$635$	33.6547	+	12.2493i	1.33555	+	0.486099i
$636$		0			0
$637$	−2.17008	+	12.3071i	−0.0859817	+	0.487626i
$638$		0			0
$639$	−0.929038	+	11.0863i	−0.0367522	+	0.438565i
$640$		0			0
$641$	2.91672	−	3.47601i	0.115204	−	0.137294i	−0.705361	−	0.708849i	$-0.749215\pi$
$641$	2.91672	−	3.47601i	0.115204	−	0.137294i	0.820564	+	0.571554i	$0.193659\pi$
$642$		0			0
$643$	34.2656	−	6.04196i	1.35131	−	0.238272i	0.549318	−	0.835613i	$-0.314887\pi$
$643$	34.2656	−	6.04196i	1.35131	−	0.238272i	0.801987	+	0.597342i	$0.203776\pi$
$644$		0			0
$645$	40.3203	+	12.6318i	1.58761	+	0.497378i
$646$		0			0
$647$	14.0701			0.553153			0.276576	−	0.960992i	$-0.410800\pi$
$647$	14.0701			0.553153			0.276576	+	0.960992i	$0.410800\pi$
$648$		0			0
$649$	7.40076			0.290505
$650$		0			0
$651$	−24.6231	−	7.71411i	−0.965055	−	0.302340i
$652$		0			0
$653$	20.1254	−	3.54865i	0.787567	−	0.138869i	0.234622	−	0.972087i	$-0.424615\pi$
$653$	20.1254	−	3.54865i	0.787567	−	0.138869i	0.552945	+	0.833217i	$0.313504\pi$
$654$		0			0
$655$	27.7756	−	33.1017i	1.08528	−	1.29339i
$656$		0			0
$657$	29.1962	−	13.7447i	1.13905	−	0.536233i
$658$		0			0
$659$	−6.56089	+	37.2087i	−0.255576	+	1.44944i	0.539014	+	0.842297i	$0.318797\pi$
$659$	−6.56089	+	37.2087i	−0.255576	+	1.44944i	−0.794590	+	0.607147i	$0.792314\pi$
$660$		0			0
$661$	−7.02492	−	2.55686i	−0.273238	−	0.0994505i	0.201767	−	0.979434i	$-0.435332\pi$
$661$	−7.02492	−	2.55686i	−0.273238	−	0.0994505i	−0.475005	+	0.879983i	$0.657554\pi$
$662$		0			0
$663$	62.3090	+	8.08714i	2.41988	+	0.314078i
$664$		0			0
$665$	−16.0592	+	9.27181i	−0.622751	+	0.359545i
$666$		0			0
$667$	−1.44575	−	0.834705i	−0.0559797	−	0.0323199i
$668$		0			0
$669$	−30.8910	+	19.7593i	−1.19432	+	0.763940i
$670$		0			0
$671$	−37.5006	+	31.4668i	−1.44770	+	1.21476i
$672$		0			0
$673$	17.8914	−	6.51195i	0.689664	−	0.251017i	0.0266725	−	0.999644i	$-0.491509\pi$
$673$	17.8914	−	6.51195i	0.689664	−	0.251017i	0.662991	+	0.748627i	$0.269287\pi$
$674$		0			0
$675$	7.01685	+	4.41625i	0.270079	+	0.169981i
$676$		0			0
$677$	4.20531	+	11.5540i	0.161623	+	0.444056i	0.993897	−	0.110308i	$-0.0351837\pi$
$677$	4.20531	+	11.5540i	0.161623	+	0.444056i	−0.832274	+	0.554364i	$0.812961\pi$
$678$		0			0
$679$	−16.9523	−	20.2030i	−0.650570	−	0.775319i
$680$		0			0
$681$	16.7805	−	32.3795i	0.643028	−	1.24079i
$682$		0			0
$683$	−14.1366	+	24.4853i	−0.540921	+	0.936903i	0.457931	+	0.888988i	$0.348591\pi$
$683$	−14.1366	+	24.4853i	−0.540921	+	0.936903i	−0.998851	+	0.0479145i	$0.984742\pi$
$684$		0			0
$685$	27.0460	+	46.8450i	1.03337	+	1.78986i
$686$		0			0
$687$	−30.9675	−	23.6723i	−1.18148	−	0.903153i
$688$		0			0
$689$	13.5980	−	37.3603i	0.518044	−	1.42331i
$690$		0			0
$691$	−9.74960	−	1.71912i	−0.370892	−	0.0653983i	−0.0149045	−	0.999889i	$-0.504744\pi$
$691$	−9.74960	−	1.71912i	−0.370892	−	0.0653983i	−0.355988	+	0.934491i	$0.615856\pi$
$692$		0			0
$693$	2.58320	+	28.3311i	0.0981275	+	1.07621i
$694$		0			0
$695$	16.3637	+	13.7308i	0.620711	+	0.520838i
$696$		0			0
$697$	0.449477	+	2.54911i	0.0170252	+	0.0965545i
$698$		0			0
$699$	43.5771	−	9.74453i	1.64824	−	0.368572i
$700$		0			0
$701$			9.95360i			0.375942i	0.982175	+	0.187971i	$0.0601911\pi$
$701$			9.95360i			0.375942i	−0.982175	+	0.187971i	$0.939809\pi$
$702$		0			0
$703$		−	25.1827i		−	0.949783i
$704$		0			0
$705$	26.5098	+	28.8243i	0.998417	+	1.08558i
$706$		0			0
$707$	0.629978	+	3.57278i	0.0236927	+	0.134368i
$708$		0			0
$709$	−17.3138	−	14.5280i	−0.650232	−	0.545610i	0.256909	−	0.966436i	$-0.417296\pi$
$709$	−17.3138	−	14.5280i	−0.650232	−	0.545610i	−0.907141	+	0.420826i	$0.861740\pi$
$710$		0			0
$711$	−5.24024	+	19.8472i	−0.196524	+	0.744328i
$712$		0			0
$713$	28.9865	+	5.11109i	1.08555	+	0.191412i
$714$		0			0
$715$	21.5766	−	59.2813i	0.806920	−	2.21699i
$716$		0			0
$717$	17.2335	−	7.17534i	0.643597	−	0.267968i
$718$		0			0
$719$	16.3460	+	28.3121i	0.609602	+	1.05586i	0.991306	+	0.131577i	$0.0420040\pi$
$719$	16.3460	+	28.3121i	0.609602	+	1.05586i	−0.381704	+	0.924285i	$0.624663\pi$
$720$		0			0
$721$	−3.15417	+	5.46319i	−0.117468	+	0.203460i
$722$		0			0
$723$	43.7365	−	1.98979i	1.62658	−	0.0740011i
$724$		0			0
$725$	0.395657	+	0.471525i	0.0146943	+	0.0175120i
$726$		0			0
$727$	−3.76774	−	10.3518i	−0.139738	−	0.383926i	0.850007	−	0.526771i	$-0.176597\pi$
$727$	−3.76774	−	10.3518i	−0.139738	−	0.383926i	−0.989745	+	0.142844i	$0.954375\pi$
$728$		0			0
$729$	−6.70127	+	26.1552i	−0.248195	+	0.968710i
$730$		0			0
$731$	−57.0694	+	20.7716i	−2.11079	+	0.768264i
$732$		0			0
$733$	24.1879	−	20.2961i	0.893402	−	0.749653i	−0.0754875	−	0.997147i	$-0.524051\pi$
$733$	24.1879	−	20.2961i	0.893402	−	0.749653i	0.968890	+	0.247493i	$0.0796068\pi$
$734$		0			0
$735$	−0.445288	−	9.78761i	−0.0164247	−	0.361022i
$736$		0			0
$737$	7.49762	+	4.32875i	0.276178	+	0.159452i
$738$		0			0
$739$	6.54458	−	3.77851i	0.240746	−	0.138995i	−0.374773	−	0.927116i	$-0.622280\pi$
$739$	6.54458	−	3.77851i	0.240746	−	0.138995i	0.615520	+	0.788122i	$0.288946\pi$
$740$		0			0
$741$	12.4522	+	29.9074i	0.457444	+	1.09867i
$742$		0			0
$743$	27.9075	+	10.1575i	1.02383	+	0.372643i	0.798728	−	0.601692i	$-0.205507\pi$
$743$	27.9075	+	10.1575i	1.02383	+	0.372643i	0.225101	+	0.974336i	$0.427729\pi$
$744$		0			0
$745$	3.05361	−	17.3179i	0.111876	−	0.634479i
$746$		0			0
$747$	−4.06268	−	1.07267i	−0.148646	−	0.0392468i
$748$		0			0
$749$	17.8739	−	21.3013i	0.653098	−	0.778331i
$750$		0			0
$751$	35.8098	−	6.31424i	1.30672	−	0.230410i	0.523430	−	0.852068i	$-0.324652\pi$
$751$	35.8098	−	6.31424i	1.30672	−	0.230410i	0.783288	+	0.621659i	$0.213541\pi$
$752$		0			0
$753$	19.1481	−	17.6106i	0.697796	−	0.641766i
$754$		0			0
$755$	−24.2316			−0.881877
$756$		0			0
$757$	20.1447			0.732170			0.366085	−	0.930581i	$-0.380698\pi$
$757$	20.1447			0.732170			0.366085	+	0.930581i	$0.380698\pi$
$758$		0			0
$759$	−7.08173	−	31.6692i	−0.257050	−	1.14952i
$760$		0			0
$761$	−17.1911	+	3.03125i	−0.623175	+	0.109883i	−0.476315	−	0.879275i	$-0.658028\pi$
$761$	−17.1911	+	3.03125i	−0.623175	+	0.109883i	−0.146860	+	0.989157i	$0.546917\pi$
$762$		0			0
$763$	−9.21519	+	10.9822i	−0.333612	+	0.397584i
$764$		0			0
$765$	−49.0570	+	4.47296i	−1.77366	+	0.161720i
$766$		0			0
$767$	1.68413	−	9.55117i	0.0608104	−	0.344873i
$768$		0			0
$769$	11.4962	+	4.18429i	0.414565	+	0.150889i	0.540878	−	0.841101i	$-0.318092\pi$
$769$	11.4962	+	4.18429i	0.414565	+	0.150889i	−0.126313	+	0.991990i	$0.540314\pi$
$770$		0			0
$771$	−21.2597	+	27.8114i	−0.765648	+	1.00160i
$772$		0			0
$773$	−28.3344	+	16.3589i	−1.01912	+	0.588389i	−0.913849	−	0.406055i	$-0.866904\pi$
$773$	−28.3344	+	16.3589i	−1.01912	+	0.588389i	−0.105270	+	0.994444i	$0.533571\pi$
$774$		0			0
$775$	−9.39857	−	5.42627i	−0.337607	−	0.194917i
$776$		0			0
$777$	−25.7301	−	13.3344i	−0.923062	−	0.478370i
$778$		0			0
$779$	−1.02236	+	0.857866i	−0.0366300	+	0.0307362i
$780$		0			0
$781$	−15.0871	+	5.49127i	−0.539860	+	0.196493i
$782$		0			0
$783$	−1.06773	+	1.69649i	−0.0381576	+	0.0606275i
$784$		0			0
$785$	−9.34376	−	25.6718i	−0.333493	−	0.916265i
$786$		0			0
$787$	12.3621	+	14.7326i	0.440662	+	0.525161i	0.939967	−	0.341266i	$-0.110856\pi$
$787$	12.3621	+	14.7326i	0.440662	+	0.525161i	−0.499305	+	0.866427i	$0.666411\pi$
$788$		0			0
$789$	−4.80411	−	7.51057i	−0.171031	−	0.267383i
$790$		0			0
$791$	−11.4236	+	19.7862i	−0.406176	+	0.703517i
$792$		0			0
$793$	32.0762	+	55.5577i	1.13906	+	1.97291i
$794$		0			0
$795$	−4.01200	+	30.9113i	−0.142291	+	1.09631i
$796$		0			0
$797$	8.63834	−	23.7336i	0.305986	−	0.840689i	−0.687443	−	0.726238i	$-0.741267\pi$
$797$	8.63834	−	23.7336i	0.305986	−	0.840689i	0.993429	−	0.114451i	$-0.0365108\pi$
$798$		0			0
$799$	−55.4335	−	9.77441i	−1.96109	−	0.345794i
$800$		0			0
$801$	−10.1113	−	21.4781i	−0.357264	−	0.758890i
$802$		0			0
$803$	35.6751	+	29.9350i	1.25895	+	1.05638i
$804$		0			0
$805$	−4.22701	−	23.9725i	−0.148982	−	0.844921i
$806$		0			0
$807$	−3.01442	+	9.62188i	−0.106112	+	0.338706i
$808$		0			0
$809$			49.8253i			1.75177i	0.482524	+	0.875883i	$0.339720\pi$
$809$			49.8253i			1.75177i	−0.482524	+	0.875883i	$0.660280\pi$
$810$		0			0
$811$			11.3567i			0.398788i	0.979919	+	0.199394i	$0.0638974\pi$
$811$			11.3567i			0.398788i	−0.979919	+	0.199394i	$0.936103\pi$
$812$		0			0
$813$	−2.27820	+	7.27191i	−0.0798999	+	0.255037i
$814$		0			0
$815$	−6.12468	−	34.7348i	−0.214538	−	1.21671i
$816$		0			0
$817$	−23.9876	−	20.1280i	−0.839219	−	0.704188i
$818$		0			0
$819$	37.1510	+	3.11329i	1.29816	+	0.108787i
$820$		0			0
$821$	−13.4593	−	2.37323i	−0.469732	−	0.0828264i	−0.0662282	−	0.997805i	$-0.521097\pi$
$821$	−13.4593	−	2.37323i	−0.469732	−	0.0828264i	−0.403503	+	0.914978i	$0.632208\pi$
$822$		0			0
$823$	1.04306	−	2.86579i	0.0363588	−	0.0998950i	−0.920185	−	0.391484i	$-0.871962\pi$
$823$	1.04306	−	2.86579i	0.0363588	−	0.0998950i	0.956544	+	0.291589i	$0.0941840\pi$
$824$		0			0
$825$	−1.54005	+	11.8657i	−0.0536178	+	0.413110i
$826$		0			0
$827$	−25.4306	−	44.0471i	−0.884308	−	1.53167i	−0.846505	−	0.532381i	$-0.821297\pi$
$827$	−25.4306	−	44.0471i	−0.884308	−	1.53167i	−0.0378029	−	0.999285i	$-0.512036\pi$
$828$		0			0
$829$	−27.1171	+	46.9683i	−0.941817	+	1.63128i	−0.179816	+	0.983700i	$0.557550\pi$
$829$	−27.1171	+	46.9683i	−0.941817	+	1.63128i	−0.762001	+	0.647575i	$0.775783\pi$
$830$		0			0
$831$	−9.73857	−	15.2249i	−0.337827	−	0.528146i
$832$		0			0
$833$	9.05225	+	10.7881i	0.313642	+	0.373784i
$834$		0			0
$835$	−1.49185	−	4.09884i	−0.0516278	−	0.141846i
$836$		0			0
$837$	7.45984	−	34.5458i	0.257850	−	1.19408i
$838$		0			0
$839$	−22.6300	+	8.23664i	−0.781274	+	0.284361i	−0.701704	−	0.712469i	$-0.747577\pi$
$839$	−22.6300	+	8.23664i	−0.781274	+	0.284361i	−0.0795703	+	0.996829i	$0.525355\pi$
$840$		0			0
$841$	22.1013	−	18.5452i	0.762113	−	0.639489i
$842$		0			0
$843$	−7.63109	−	3.95476i	−0.262829	−	0.136209i
$844$		0			0
$845$	−42.6829	−	24.6430i	−1.46834	−	0.847745i
$846$		0			0
$847$	−14.6903	+	8.48147i	−0.504766	+	0.291427i
$848$		0			0
$849$	2.84702	−	3.72441i	0.0977096	−	0.127821i
$850$		0			0
$851$	31.0639	+	11.3063i	1.06486	+	0.387576i
$852$		0			0
$853$	2.03654	−	11.5498i	0.0697299	−	0.395458i	−0.929889	−	0.367841i	$-0.880097\pi$
$853$	2.03654	−	11.5498i	0.0697299	−	0.395458i	0.999619	−	0.0276169i	$-0.00879184\pi$
$854$		0			0
$855$	−14.6442	−	20.7520i	−0.500822	−	0.709704i
$856$		0			0
$857$	2.68192	−	3.19618i	0.0916125	−	0.109179i	−0.718291	−	0.695743i	$-0.755075\pi$
$857$	2.68192	−	3.19618i	0.0916125	−	0.109179i	0.809903	+	0.586564i	$0.199520\pi$
$858$		0			0
$859$	12.3931	−	2.18524i	0.422848	−	0.0745596i	0.0418249	−	0.999125i	$-0.486683\pi$
$859$	12.3931	−	2.18524i	0.422848	−	0.0745596i	0.381023	+	0.924565i	$0.375572\pi$
$860$		0			0
$861$	0.335163	+	1.49884i	0.0114223	+	0.0510802i
$862$		0			0
$863$	−16.6241			−0.565891			−0.282946	−	0.959136i	$-0.591312\pi$
$863$	−16.6241			−0.565891			−0.282946	+	0.959136i	$0.591312\pi$
$864$		0			0
$865$	−0.447324			−0.0152095
$866$		0			0
$867$	30.4425	−	27.9981i	1.03388	−	0.950865i
$868$		0			0
$869$	−29.1743	+	5.14422i	−0.989671	+	0.174506i
$870$		0			0
$871$	7.29271	−	8.69112i	0.247104	−	0.294487i
$872$		0			0
$873$	25.4489	−	25.6359i	0.861316	−	0.867645i
$874$		0			0
$875$	3.32538	−	18.8592i	0.112418	−	0.637556i
$876$		0			0
$877$	−8.10635	−	2.95047i	−0.273732	−	0.0996303i	0.201507	−	0.979487i	$-0.435416\pi$
$877$	−8.10635	−	2.95047i	−0.273732	−	0.0996303i	−0.475239	+	0.879857i	$0.657638\pi$
$878$		0			0
$879$	1.43905	+	3.45627i	0.0485379	+	0.116577i
$880$		0			0
$881$	−23.4592	+	13.5442i	−0.790362	+	0.456316i	−0.840090	−	0.542447i	$-0.817498\pi$
$881$	−23.4592	+	13.5442i	−0.790362	+	0.456316i	0.0497279	+	0.998763i	$0.484165\pi$
$882$		0			0
$883$	2.25256	+	1.30052i	0.0758047	+	0.0437658i	0.537423	−	0.843313i	$-0.319398\pi$
$883$	2.25256	+	1.30052i	0.0758047	+	0.0437658i	−0.461619	+	0.887079i	$0.652731\pi$
$884$		0			0
$885$	0.345573	+	7.59585i	0.0116163	+	0.255332i
$886$		0			0
$887$	39.7742	−	33.3745i	1.33549	−	1.12061i	0.352726	−	0.935727i	$-0.385255\pi$
$887$	39.7742	−	33.3745i	1.33549	−	1.12061i	0.982761	−	0.184880i	$-0.0591895\pi$
$888$		0			0
$889$	−28.7026	+	10.4469i	−0.962654	+	0.350377i
$890$		0			0
$891$	−38.3230	+	7.04707i	−1.28387	+	0.236086i
$892$		0			0
$893$	−9.92629	−	27.2722i	−0.332170	−	0.912631i
$894$		0			0
$895$	37.4238	+	44.6000i	1.25094	+	1.49081i
$896$		0			0
$897$	−42.4827	+	1.93275i	−1.41846	+	0.0645327i
$898$		0			0
$899$	1.31193	−	2.27232i	0.0437552	−	0.0757863i
$900$		0			0
$901$	−22.4016	−	38.8007i	−0.746305	−	1.29264i
$902$		0			0
$903$	−33.2671	+	13.8511i	−1.10706	+	0.460935i
$904$		0			0
$905$	10.1697	−	27.9411i	0.338053	−	0.928792i
$906$		0			0
$907$	21.8982	+	3.86125i	0.727118	+	0.128211i	0.524941	−	0.851138i	$-0.324087\pi$
$907$	21.8982	+	3.86125i	0.727118	+	0.128211i	0.202177	+	0.979349i	$0.435198\pi$
$908$		0			0
$909$	−4.79500	+	1.30365i	−0.159040	+	0.0432393i
$910$		0			0
$911$	−3.79027	−	3.18041i	−0.125577	−	0.105372i	0.577836	−	0.816153i	$-0.303897\pi$
$911$	−3.79027	−	3.18041i	−0.125577	−	0.105372i	−0.703413	+	0.710781i	$0.748342\pi$
$912$		0			0
$913$	−1.05301	−	5.97192i	−0.0348496	−	0.197642i
$914$		0			0
$915$	−34.0473	−	37.0199i	−1.12557	−	1.22384i
$916$		0			0
$917$			36.8529i			1.21699i
$918$		0			0
$919$		−	38.3117i		−	1.26379i	−0.775055	−	0.631894i	$-0.782278\pi$
$919$		−	38.3117i		−	1.26379i	0.775055	−	0.631894i	$-0.217722\pi$
$920$		0			0
$921$	−4.55672	+	1.01896i	−0.150149	+	0.0335757i
$922$		0			0
$923$	3.65359	+	20.7206i	0.120260	+	0.682026i
$924$		0			0
$925$	−9.33709	−	7.83475i	−0.307002	−	0.257605i
$926$		0			0
$927$	−7.84419	−	3.62290i	−0.257637	−	0.118992i
$928$		0			0
$929$	−8.91232	−	1.57148i	−0.292404	−	0.0515587i	0.0255221	−	0.999674i	$-0.491875\pi$
$929$	−8.91232	−	1.57148i	−0.292404	−	0.0515587i	−0.317926	+	0.948116i	$0.602986\pi$
$930$		0			0
$931$	−2.48345	+	6.82322i	−0.0813918	+	0.223622i
$932$		0			0
$933$	0.309221	+	0.236375i	0.0101234	+	0.00773858i
$934$		0			0
$935$	−35.5456	−	61.5668i	−1.16246	−	2.01345i
$936$		0			0
$937$	−20.4465	+	35.4143i	−0.667957	+	1.15693i	0.310518	+	0.950568i	$0.399498\pi$
$937$	−20.4465	+	35.4143i	−0.667957	+	1.15693i	−0.978475	+	0.206367i	$0.933836\pi$
$938$		0			0
$939$	−7.07526	+	13.6524i	−0.230892	+	0.445529i
$940$		0			0
$941$	−36.5718	−	43.5846i	−1.19221	−	1.42082i	−0.882711	−	0.469917i	$-0.844284\pi$
$941$	−36.5718	−	43.5846i	−1.19221	−	1.42082i	−0.309497	−	0.950901i	$-0.600161\pi$
$942$		0			0
$943$	−0.599200	−	1.64629i	−0.0195126	−	0.0536105i
$944$		0			0
$945$	−28.9574	+	3.97420i	−0.941983	+	0.129281i
$946$		0			0
$947$	7.37132	−	2.68294i	0.239536	−	0.0871839i	−0.219463	−	0.975621i	$-0.570430\pi$
$947$	7.37132	−	2.68294i	0.239536	−	0.0871839i	0.458999	+	0.888437i	$0.348208\pi$
$948$		0			0
$949$	46.7514	−	39.2291i	1.51761	−	1.27343i
$950$		0			0
$951$	4.81268	−	3.07842i	0.156062	−	0.0998244i
$952$		0			0
$953$	21.6204	+	12.4825i	0.700353	+	0.404349i	0.807479	−	0.589896i	$-0.200831\pi$
$953$	21.6204	+	12.4825i	0.700353	+	0.404349i	−0.107126	+	0.994245i	$0.534165\pi$
$954$		0			0
$955$	−42.7208	+	24.6648i	−1.38241	+	0.798135i
$956$		0			0
$957$	−2.86880	−	0.372344i	−0.0927352	−	0.0120362i
$958$		0			0
$959$	−43.3505	−	15.7783i	−1.39986	−	0.509507i
$960$		0			0
$961$	−2.65014	+	15.0297i	−0.0854885	+	0.484829i
$962$		0			0
$963$	31.2783	+	21.7311i	1.00793	+	0.700276i
$964$		0			0
$965$	−13.5505	+	16.1489i	−0.436206	+	0.519850i
$966$		0			0
$967$	−52.9546	+	9.33733i	−1.70291	+	0.300268i	−0.938708	−	0.344714i	$-0.887976\pi$
$967$	−52.9546	+	9.33733i	−1.70291	+	0.300268i	−0.764198	+	0.644982i	$0.776865\pi$
$968$		0			0
$969$	34.8374	+	10.9141i	1.11914	+	0.350613i
$970$		0			0
$971$	45.9381			1.47422			0.737111	−	0.675771i	$-0.236189\pi$
$971$	45.9381			1.47422			0.737111	+	0.675771i	$0.236189\pi$
$972$		0			0
$973$	−18.2181			−0.584046
$974$		0			0
$975$	14.9630	+	4.68772i	0.479199	+	0.150127i
$976$		0			0
$977$	−35.0623	+	6.18243i	−1.12174	+	0.197794i	−0.703606	−	0.710590i	$-0.748428\pi$
$977$	−35.0623	+	6.18243i	−1.12174	+	0.197794i	−0.418137	+	0.908384i	$0.637317\pi$
$978$		0			0
$979$	22.0216	−	26.2443i	0.703813	−	0.838771i
$980$		0			0
$981$	−16.1261	−	11.2039i	−0.514866	−	0.357711i
$982$		0			0
$983$	0.786431	−	4.46007i	0.0250832	−	0.142254i	−0.969694	−	0.244322i	$-0.921435\pi$
$983$	0.786431	−	4.46007i	0.0250832	−	0.142254i	0.994777	+	0.102068i	$0.0325458\pi$
$984$		0			0
$985$	−38.9713	−	14.1844i	−1.24173	−	0.451952i
$986$		0			0
$987$	−33.1211	−	4.29882i	−1.05426	−	0.136833i
$988$		0			0
$989$	35.5984	−	20.5528i	1.13196	−	0.653540i
$990$		0			0
$991$	12.9902	+	7.49988i	0.412647	+	0.238242i	0.691926	−	0.721968i	$-0.256762\pi$
$991$	12.9902	+	7.49988i	0.412647	+	0.238242i	−0.279280	+	0.960210i	$0.590096\pi$
$992$		0			0
$993$	−33.7189	+	21.5682i	−1.07004	+	0.684445i
$994$		0			0
$995$	3.22652	−	2.70737i	0.102288	−	0.0858294i
$996$		0			0
$997$	−34.3123	+	12.4886i	−1.08668	+	0.395519i	−0.822390	−	0.568924i	$-0.807360\pi$
$997$	−34.3123	+	12.4886i	−1.08668	+	0.395519i	−0.264290	+	0.964443i	$0.585138\pi$
$998$		0			0
$999$	14.9884	−	36.7548i	0.474212	−	1.16287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.c.47.6	yes	36
4.3	odd	2		432.2.be.b.47.1	✓	36
27.23	odd	18		432.2.be.b.239.1	yes	36
108.23	even	18	inner	432.2.be.c.239.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.47.1	✓	36	4.3	odd	2
432.2.be.b.239.1	yes	36	27.23	odd	18
432.2.be.c.47.6	yes	36	1.1	even	1	trivial
432.2.be.c.239.6	yes	36	108.23	even	18	inner

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)

\(f(q)\)	\(=\)	\(q+(1.65284 + 0.517813i) q^{3} +(-2.52917 + 0.445961i) q^{5} +(1.40789 - 1.67786i) q^{7} +(2.46374 + 1.71172i) q^{9} +O(q^{10})\)	\(q+(1.65284 + 0.517813i) q^{3} +(-2.52917 + 0.445961i) q^{5} +(1.40789 - 1.67786i) q^{7} +(2.46374 + 1.71172i) q^{9} +(-0.751810 + 4.26373i) q^{11} +(5.33154 + 1.94052i) q^{13} +(-4.41123 - 0.572537i) q^{15} +(5.53709 - 3.19684i) q^{17} +(2.85493 + 1.64830i) q^{19} +(3.19584 - 2.04421i) q^{21} +(-3.31503 + 2.78164i) q^{23} +(1.49936 - 0.545724i) q^{25} +(3.18581 + 4.10495i) q^{27} +(0.131941 + 0.362506i) q^{29} +(-4.37197 - 5.21032i) q^{31} +(-3.45043 + 6.65795i) q^{33} +(-2.81254 + 4.87147i) q^{35} +(-3.81950 - 6.61557i) q^{37} +(7.80734 + 5.96811i) q^{39} +(-0.138464 + 0.380428i) q^{41} +(-9.35445 - 1.64944i) q^{43} +(-6.99458 - 3.23050i) q^{45} +(-6.74409 - 5.65897i) q^{47} +(0.382480 + 2.16915i) q^{49} +(10.8073 - 2.41668i) q^{51} -7.00741i q^{53} -11.1190i q^{55} +(3.86523 + 4.20269i) q^{57} +(-0.296830 - 1.68341i) q^{59} +(8.66165 + 7.26798i) q^{61} +(6.34071 - 1.72389i) q^{63} +(-14.3498 - 2.53025i) q^{65} +(0.683922 - 1.87906i) q^{67} +(-6.91957 + 2.88103i) q^{69} +(1.85419 + 3.21154i) q^{71} +(5.37828 - 9.31546i) q^{73} +(2.76079 - 0.125602i) q^{75} +(6.09548 + 7.26431i) q^{77} +(2.34025 + 6.42979i) q^{79} +(3.14002 + 8.43447i) q^{81} +(-1.31616 + 0.479045i) q^{83} +(-12.5786 + 10.5547i) q^{85} +(0.0303672 + 0.667485i) q^{87} +(-6.85289 - 3.95652i) q^{89} +(10.7622 - 6.21354i) q^{91} +(-4.52819 - 10.8757i) q^{93} +(-7.95569 - 2.89564i) q^{95} +(2.09088 - 11.8580i) q^{97} +(-9.15058 + 9.21782i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 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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